Finite Group Databasebeta

← #33249539

Subgroups — #33249539

Order 18688.

2522 conjugacy classes of subgroups.

The subgroup lattice has 1608 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17989171C211yesmaximal, characteristic
2#22613119C211yesmaximal, characteristic, complemented
3#22613089C211yesmaximal, characteristic, complemented
4#22613080C211yesmaximal, characteristic, complemented
5#22613048C211yesmaximal, characteristic, complemented
6#22613010C211yesmaximal, characteristic, complemented
7#22613006C211yesmaximal, characteristic, complemented
8#22612975C211yesmaximal, characteristic, complemented
9#22612950C211yesmaximal, characteristic, complemented
10#22612942C211yesmaximal, characteristic, complemented
11#22612941C211yesmaximal, characteristic, complemented
12#22612922C211yesmaximal, characteristic, complemented
13#22612866C211yesmaximal, characteristic, complemented
14#22612857C211yesmaximal, characteristic, complemented
15#22612839C211yesmaximal, characteristic, complemented
16#22612829C211yesmaximal, characteristic, complemented
17#22612743C211yesmaximal, characteristic, complemented
18#22612726C211yesmaximal, characteristic, complemented
19#22612702C211yesmaximal, characteristic, complemented
20#22612702C211yesmaximal, characteristic, complemented
21#22612645C211yesmaximal, characteristic, complemented
22#22612628C211yesmaximal, characteristic, complemented
23#22612619C211yesmaximal, characteristic, complemented
24#22612599C211yesmaximal, characteristic, complemented
25#22612587C211yesmaximal, characteristic, complemented
26#22612584C211yesmaximal, characteristic, complemented
27#22612525C211yesmaximal, characteristic, complemented
28#22612436C211yesmaximal, characteristic, complemented
29#22612432C211yesmaximal, characteristic, complemented
30#385×D73C211yesmaximal, characteristic, complemented
31C73×#2379C211yesmaximal, characteristic, complemented
32C23×C4×D73C2211yescharacteristic
33#17989171C4116yescomplemented
34C2×#14556585C2211yescharacteristic
35C2×#14556584C2211yescharacteristic
36C2×#14556580C2211yescharacteristic
37C2×#14556575C2211yescharacteristic
38C2×#14556573C2211yescharacteristic
39C2×#14556567C2211yescharacteristic
40C2×#14556564C2211yescharacteristic
41C2×#14556564C2211yescharacteristic
42C2×#14556563C2211yescharacteristic
43C2×#14556561C2211yescharacteristic
44C2×#14556559C2211yescharacteristic
45C2×Q8×Dic73C2211yescharacteristic, complemented
46C2×C4×D292C2211yescharacteristic
47C2×D4×Dic73C2211yescharacteristic
48C2×#14556553C2211yescharacteristic
49C2×#14556553C2211yescharacteristic
50C2×#14556553C2211yescharacteristic
51C2×C4×C22⋊D73C2211yescharacteristic
52C2×C4×C22⋊D73C2211yescharacteristic, complemented
53C2×#14556551C2211yescharacteristic
54C2×#14556551C2211yescharacteristic
55C2×#14556551C2211yescharacteristic
56C2×#14556551C2211yescharacteristic
57C2×#14556549C2211yescharacteristic, complemented
58C22×#11924007C2211yescharacteristic, complemented
59C2×C4⋊C4×D73C2211yescharacteristic
60C2×C4⋊C4×D73C2211yescharacteristic
61C2×C22⋊C4×D73C2211yescharacteristic
62C2×C22⋊C4×D73C2211yescharacteristic
63#17988494C2211yescharacteristic, complemented
64#17988490C2211yescharacteristic
65#17988489C2211yescharacteristic
66#17988487C2211yescharacteristic
67#17988487C2211yescharacteristic
68#17988487C2211yescharacteristic, complemented
69#17988484C2211yescharacteristic, complemented
70#17988484C2211yescharacteristic, complemented
71#17988484C2211yescharacteristic, complemented
72#17988483C2211yescharacteristic, complemented
73#17988483C2211yescharacteristic, complemented
74#17988483C2211yescharacteristic, complemented
75#17988482C2211yescharacteristic, complemented
76#17988482C2211yescharacteristic, complemented
77#17988481C2211yescharacteristic
78#17988480C2211yescharacteristic
79#17988480C2211yescharacteristic
80#17988480C2211yescharacteristic, complemented
81#17988480C2211yescharacteristic, complemented
82#17988479C2211yescharacteristic
83#17988479C2211yescharacteristic
84#17988478C2211yescharacteristic
85#17988477C2211yescharacteristic
86#17988477C2211yescharacteristic
87#17988477C2211yescharacteristic, complemented
88#17988476C2211yescharacteristic
89#17988476C2211yescharacteristic
90#17988476C2211yescharacteristic
91#17988476C2211yescharacteristic, complemented
92#17988476C2211yescharacteristic, complemented
93#17988476C2211yescharacteristic, complemented
94#17988475C2211yescharacteristic
95#17988475C2211yescharacteristic
96#17988475C2211yescharacteristic
97#17988474C2211yescharacteristic, complemented
98#17988474C2211yescharacteristic, complemented
99#17988472C2211yescharacteristic, complemented
100#17988470C2211yescharacteristic, complemented
101#17988470C2211yescharacteristic, complemented
102#17988470C2211yescharacteristic, complemented
103#17988469C2211yescharacteristic, complemented
104#17988469C2211yescharacteristic, complemented
105#17988469C2211yescharacteristic, complemented
106#17988468C2211yescharacteristic, complemented
107#17988468C2211yescharacteristic, complemented
108#17988468C2211yescharacteristic, complemented
109#17988466C2211yescharacteristic
110#17988466C2211yescharacteristic
111#17988465C2211yescharacteristic
112#17988465C2211yescharacteristic
113#17988465C2211yescharacteristic
114#17988465C2211yescharacteristic
115#17988464C2211yescharacteristic, complemented
116#17988463C2211yescharacteristic
117#17988463C2211yescharacteristic
118#17988463C2211yescharacteristic
119#17988463C2211yescharacteristic
120#17988463C2211yescharacteristic, complemented
121#17988462C2211yescharacteristic
122#17988462C2211yescharacteristic, complemented
123#17988461C2211yescharacteristic
124#17988461C2211yescharacteristic
125#17988461C2211yescharacteristic
126#17988461C2211yescharacteristic
127#17988461C2211yescharacteristic
128#17988461C2211yescharacteristic
129#17988461C2211yescharacteristic, complemented
130#17988461C2211yescharacteristic, complemented
131#17988461C2211yescharacteristic, complemented
132#17988460C2211yescharacteristic
133#17988460C2211yescharacteristic
134#17988459C2211yescharacteristic
135#17988458C2211yescharacteristic
136#17988458C2211yescharacteristic
137#17988458C2211yescharacteristic
138#17988458C2211yescharacteristic
139#17988456C2211yescharacteristic, complemented
140#17988454C2211yescharacteristic, complemented
141#17988448C2211yescharacteristic, complemented
142#17988446C2211yescharacteristic
143#17988446C2211yescharacteristic, complemented
144#17988445C2211yescharacteristic, complemented
145#17988444C2211yescharacteristic
146#17988444C2211yescharacteristic, complemented
147#17988442C2211yescharacteristic
148#17988442C2211yescharacteristic
149C4×#11924007C2211yescharacteristic, complemented
150C4×C4⋊Dic73C2211yescharacteristic, complemented
151C4×C4⋊Dic73C2211yescharacteristic, complemented
152C4×C4⋊Dic73C2211yescharacteristic, complemented
153#17988438C2211yescharacteristic, complemented
154#17988438C2211yescharacteristic, complemented
155#17988438C2211yescharacteristic, complemented
156C22⋊C4×Dic73C2211yescharacteristic
157C22⋊C4×Dic73C2211yescharacteristic
158C22⋊C4×Dic73C2211yescharacteristic, complemented
159C22⋊C4×Dic73C2211yescharacteristic, complemented
160C4×#11924005C2211yescharacteristic
161C4×#11924005C2211yescharacteristic
162C4×#11924005C2211yescharacteristic, complemented
163#17988434C2211yescharacteristic
164#17988434C2211yescharacteristic
165#17988434C2211yescharacteristic
166#17988434C2211yescharacteristic
167#17988434C2211yescharacteristic
168#17988434C2211yescharacteristic
169#17988433C2211yescharacteristic, complemented
170#95×D73C2211yescharacteristic
171#95×D73C2211yescharacteristic
172#95×D73C2211yescharacteristic, complemented
173C2×#124×C73C2211yescharacteristic
174#391×C73C2211yescharacteristic, complemented
175#391×C73C2211yescharacteristic, complemented
176#388×C73C2211yescharacteristic
177#388×C73C2211yescharacteristic
178#388×C73C2211yescharacteristic, complemented
179#388×C73C2211yescharacteristic, complemented
180#386×C73C2211yescharacteristic
181#386×C73C2211yescharacteristic
182#385×C73C2211yescharacteristic
183#385×C73C2211yescharacteristic
184#385×C73C2211yescharacteristic, complemented
185#385×C73C2211yescharacteristic, complemented
186#382×C73C2211yescharacteristic, complemented
187#382×C73C2211yescharacteristic, complemented
188C24×D73C2311yescharacteristic
189C22×D292C2311yescharacteristic
190C22×D292C2311yescharacteristic
191C22×C22⋊D73C2311yescharacteristic
192C22×C22⋊D73C2311yescharacteristic
193C22×C22⋊D73C2311yescharacteristic
194C22×C22⋊D73C2311yescharacteristic
195C23×Dic73C2311yescharacteristic
196C23×Dic73C2311yescharacteristic
197C23×Dic73C2311yescharacteristic
198C22×C4×D73—42no—
199C22×C4×D73—42no—
200C22×C4×D73—42no—
201C22×C4×D73C2311yescharacteristic
202C22×C4×D73C2311yescharacteristic
203C22×C4×D73C2311yescharacteristic
204C22×C4×D73C2311yescharacteristic
205C22×C4×D73C2311yescharacteristic
206C22×C4×D73C2311yescharacteristic
207C22×C4×D73C2311yescharacteristic
208C22×C4×D73C2311yescharacteristic
209C22×C4×D73C2311yescharacteristic
210C22×C4×D73C2311yescharacteristic
211C22×C4×D73C2311yescharacteristic
212#14556585C2×C418yescomplemented
213#14556584C2×C418yescomplemented
214#14556580C2×C418yescomplemented
215#14556575C2×C418yescomplemented
216#14556573C2×C418yescomplemented
217#14556567C2×C418yescomplemented
218#14556564C2×C418yescomplemented
219#14556564C2×C418yescomplemented
220#14556563C2×C418yescomplemented
221#14556561C2×C418yescomplemented
222#14556559C2×C418yescomplemented
223Q8×Dic73—42no—
224C4×D292C2×C418yescomplemented
225D4×Dic73—42no—
226#14556553—42no—
227#14556553—42no—
228#14556553—42no—
229C4×C22⋊D73—42no—
230C4×C22⋊D73—42no—
231#14556551—42no—
232#14556551—42no—
233#14556551—42no—
234#14556551C2×C418yescomplemented
235#14556549—42no—
236C2×C4⋊Dic73C2311yescharacteristic
237C2×C4⋊Dic73C2311yescharacteristic
238C2×C4⋊Dic73C2311yescharacteristic
239C2×C4⋊Dic73C2311yescharacteristic
240C2×C4⋊Dic73C2311yescharacteristic
241C2×C4⋊Dic73C2311yescharacteristic
242C2×C4⋊Dic73C2311yescharacteristic
243C2×C4⋊Dic73C2311yescharacteristic
244C2×#11924007—42no—
245C2×#11924007C2311yescharacteristic
246C2×#11924007C2311yescharacteristic
247C2×#11924007C2311yescharacteristic
248C2×#11924007C2311yescharacteristic
249C2×#11924007C2311yescharacteristic
250C2×#11924007C2311yescharacteristic
251C2×#11924007C2311yescharacteristic
252C2×#11924007C2311yescharacteristic
253C2×#11924007C2311yescharacteristic
254C2×#11924007C2311yescharacteristic
255C2×#11924007C2311yescharacteristic
256C2×#11924007C2311yescharacteristic
257C2×#11924007C2311yescharacteristic
258C2×#11924007C2311yescharacteristic
259C2×#11924007C2311yescharacteristic
260C2×#11924007C2311yescharacteristic
261C4⋊C4×D73—42no—
262C4⋊C4×D73—42no—
263C2×C22⋊Dic73C2311yescharacteristic
264C2×C22⋊Dic73C2311yescharacteristic
265C2×C22⋊Dic73C2311yescharacteristic
266C2×C22⋊Dic73C2311yescharacteristic
267C2×C22⋊Dic73C2311yescharacteristic
268C2×C22⋊Dic73C2311yescharacteristic
269C2×C22⋊Dic73C2311yescharacteristic
270C2×C22⋊Dic73C2311yescharacteristic
271C2×#11924005C2311yescharacteristic
272C2×#11924005C2311yescharacteristic
273C2×#11924005C2311yescharacteristic
274C2×#11924005C2311yescharacteristic
275C2×#11924005C2311yescharacteristic
276C2×#11924005C2311yescharacteristic
277C2×#11924005C2311yescharacteristic
278C2×#11924005C2311yescharacteristic
279C2×#11924005C2311yescharacteristic
280C2×#11924005C2311yescharacteristic
281C2×#11924005C2311yescharacteristic
282C2×#11924005C2311yescharacteristic
283C2×#11924005C2311yescharacteristic
284C2×#11924005C2311yescharacteristic
285C2×#11924005C2311yescharacteristic
286C2×#11924005C2311yescharacteristic
287C2×#11924005C2311yescharacteristic
288C2×#11924005C2311yescharacteristic
289C2×#11924005C2311yescharacteristic
290C2×#11924005C2311yescharacteristic
291C2×#11924005C2311yescharacteristic
292C2×#11924005C2311yescharacteristic
293C2×#11924005C2311yescharacteristic
294C2×#11924005C2311yescharacteristic
295C22⋊C4×D73—42no—
296C22⋊C4×D73C2×C418yescomplemented
297C2×C4×Dic73C2311yescharacteristic
298C2×C4×Dic73C2311yescharacteristic
299C2×C4×Dic73C2311yescharacteristic
300C2×C4×Dic73C2311yescharacteristic
301C2×C4×Dic73C2311yescharacteristic
302C2×C4×Dic73C2311yescharacteristic
303C2×C4×Dic73C2311yescharacteristic
304C2×C4×Dic73C2311yescharacteristic
305C2×C4×Dic73C2311yescharacteristic
306C2×C4×Dic73C2311yescharacteristic
307C2×C4×Dic73C2311yescharacteristic
308C2×C4×Dic73C2311yescharacteristic
309C2×C4×Dic73C2311yescharacteristic
310C2×C4×Dic73C2311yescharacteristic
311C2×C4×Dic73C2311yescharacteristic
312#14556498C2311yescharacteristic
313#14556498C2311yescharacteristic
314#14556498C2311yescharacteristic
315#14556498C2311yescharacteristic
316#14556498C2311yescharacteristic
317#14556498C2311yescharacteristic
318#14556498C2311yescharacteristic
319#14556498C2311yescharacteristic
320#14556498C2311yescharacteristic
321#14556498C2311yescharacteristic
322#14556498C2311yescharacteristic
323#14556498C2311yescharacteristic
324#14556498C2311yescharacteristic
325#14556498C2311yescharacteristic
326#14556498C2311yescharacteristic
327#14556498C2311yescharacteristic
328#14556498C2311yescharacteristic
329#14556498C2311yescharacteristic
330#14556498C2311yescharacteristic
331#14556498C2311yescharacteristic
332#14556498C2311yescharacteristic
333#14556498C2311yescharacteristic
334#14556498C2311yescharacteristic
335#14556498C2311yescharacteristic
336#14556498C2311yescharacteristic
337#14556498C2311yescharacteristic
338#14556498C2311yescharacteristic
339#14556498C2311yescharacteristic
340C22×Q8×C73C2311yescharacteristic
341C22×D4×C73C2311yescharacteristic
342C23×C4×C73C2311yescharacteristic
343C23×C4×C73C2311yescharacteristic
344#124×C73C2×C418yescomplemented
345C2×C4⋊C4×C73C2311yescharacteristic
346C2×C4⋊C4×C73C2311yescharacteristic
347C2×C4⋊C4×C73C2311yescharacteristic
348C2×C4⋊C4×C73C2311yescharacteristic
349C2×C4⋊C4×C73C2311yescharacteristic
350C2×C4⋊C4×C73C2311yescharacteristic
351C2×C22⋊C4×C73C2311yescharacteristic
352C2×C22⋊C4×C73C2311yescharacteristic
353C2×C22⋊C4×C73C2311yescharacteristic
354C2×C22⋊C4×C73C2311yescharacteristic
355C2×C22⋊C4×C73C2311yescharacteristic
356C2×C22⋊C4×C73C2311yescharacteristic
357C2×C22⋊C4×C73C2311yescharacteristic
358C2×C22⋊C4×C73C2311yescharacteristic
359C2×C22⋊C4×C73C2311yescharacteristic
360C2×C22⋊C4×C73C2311yescharacteristic
361C2×C42×C73C2311yescharacteristic
362C2×C42×C73C2311yescharacteristic
363C2×C42×C73C2311yescharacteristic
364#95×C73C2311yescharacteristic
365#95×C73C2311yescharacteristic
366#95×C73C2311yescharacteristic
367#95×C73C2311yescharacteristic
368#95×C73C2311yescharacteristic
369#95×C73C2311yescharacteristic
370#95×C73C2311yescharacteristic
371#95×C73C2311yescharacteristic
372#95×C73C2311yescharacteristic
373#95×C73C2311yescharacteristic
374#95×C73C2311yescharacteristic
375#95×C73C2311yescharacteristic
376C23×D73—22no—
377C23×D73—22no—
378C23×D73—41no—
379C23×D73—41no—
380C23×D73—41no—
381C23×D73—41no—
382C23×D73C22×C414yes—
383C23×D73C2411yescharacteristic
384C23×D73C2411yescharacteristic
385C23×D73C2411yescharacteristic
386C2×D292—22no—
387C2×D292—22no—
388C2×D292—41no—
389C2×D292—41no—
390C2×D292C22×C414yes—
391C2×D292C22×C414yes—
392C2×C22⋊D73—22no—
393C2×C22⋊D73—22no—
394C2×C22⋊D73—41no—
395C2×C22⋊D73—41no—
396C2×C22⋊D73—41no—
397C2×C22⋊D73—41no—
398C2×C22⋊D73—41no—
399C2×C22⋊D73—41no—
400C2×C22⋊D73C22×C414yes—
401C2×C22⋊D73C22×C414yes—
402C2×C22⋊D73C22×C414yes—
403C2×C22⋊D73C22×C414yescomplemented
404C22×Dic73—22no—
405C22×Dic73—22no—
406C22×Dic73—22no—
407C22×Dic73—41no—
408C22×Dic73—41no—
409C22×Dic73—41no—
410C22×Dic73—41no—
411C22×Dic73—41no—
412C22×Dic73C22×C414yescomplemented
413C22×Dic73C2411yescharacteristic
414C22×Dic73C2411yescharacteristic
415C22×Dic73C2411yescharacteristic
416C22×Dic73C2411yescharacteristic
417C22×Dic73C2411yescharacteristic
418C22×Dic73C2411yescharacteristic
419C22×Dic73C2411yescharacteristic
420C22×Dic73C2411yescharacteristic
421C22×Dic73C2411yescharacteristic
422C22×Dic73C2411yescharacteristic
423C22×Dic73C2411yescharacteristic
424C22×Dic73C2411yescharacteristic
425C22×Dic73C2411yescharacteristic
426C2×C4×D73—22no—
427C2×C4×D73—22no—
428C2×C4×D73—22no—
429C2×C4×D73—22no—
430C2×C4×D73—22no—
431C2×C4×D73—22no—
432C2×C4×D73—22no—
433C2×C4×D73—22no—
434C2×C4×D73—22no—
435C2×C4×D73—41no—
436C2×C4×D73—41no—
437C2×C4×D73—41no—
438C2×C4×D73—41no—
439C2×C4×D73—41no—
440C2×C4×D73—41no—
441C2×C4×D73—41no—
442C2×C4×D73—41no—
443C2×C4×D73—41no—
444C2×C4×D73—41no—
445C2×C4×D73—41no—
446C2×C4×D73—41no—
447C2×C4×D73—416no—
448C2×C4×D73—41no—
449C2×C4×D73—41no—
450C2×C4×D73—41no—
451C2×C4×D73—41no—
452C2×C4×D73—41no—
453C2×C4×D73—41no—
454C2×C4×D73—41no—
455C2×C4×D73—41no—
456C2×C4×D73—41no—
457C2×C4×D73C22×C414yes—
458C2×C4×D73C22×C414yes—
459C2×C4×D73C22×C414yescomplemented
460C4⋊Dic73—22no—
461C4⋊Dic73—22no—
462C4⋊Dic73—22no—
463C4⋊Dic73—41no—
464C4⋊Dic73—41no—
465C4⋊Dic73—41no—
466C4⋊Dic73C22×C414yescomplemented
467C4⋊Dic73C22×C414yescomplemented
468#11924007—22no—
469#11924007—22no—
470#11924007—22no—
471#11924007—41no—
472#11924007—41no—
473#11924007—41no—
474#11924007—41no—
475#11924007—41no—
476#11924007—41no—
477#11924007—41no—
478#11924007—41no—
479#11924007—41no—
480#11924007C22×C414yescomplemented
481#11924007C22×C414yescomplemented
482#11924007C22×C414yescomplemented
483#11924007C22×C414yescomplemented
484C22⋊Dic73—22no—
485C22⋊Dic73—41no—
486C22⋊Dic73—41no—
487C22⋊Dic73—41no—
488C22⋊Dic73—41no—
489C22⋊Dic73—41no—
490C22⋊Dic73C22×C414yes—
491C22⋊Dic73C22×C414yes—
492#11924005—22no—
493#11924005—22no—
494#11924005—22no—
495#11924005—22no—
496#11924005—22no—
497#11924005—41no—
498#11924005—41no—
499#11924005—41no—
500#11924005—41no—
501#11924005—41no—
502#11924005—41no—
503#11924005—41no—
504#11924005—41no—
505#11924005—41no—
506#11924005—41no—
507#11924005—41no—
508#11924005C22×C414yes—
509#11924005C22×C414yes—
510#11924005C22×C414yes—
511#11924005C22×C414yes—
512#11924005C22×C414yes—
513#11924005C22×C414yes—
514#11924005C22×C414yescomplemented
515#11924005C22×C414yescomplemented
516C4×Dic73—22no—
517C4×Dic73—22no—
518C4×Dic73—41no—
519C4×Dic73—41no—
520C4×Dic73—41no—
521C4×Dic73—41no—
522C4×Dic73—41no—
523C4×Dic73—41no—
524C4×Dic73—41no—
525C4×Dic73—41no—
526C4×Dic73—41no—
527C4×Dic73—41no—
528C4×Dic73—41no—
529C4×Dic73—41no—
530C4×Dic73C22×C414yescomplemented
531C24×C73C2411yescharacteristic
532C24×C73C2411yescharacteristic
533C2×Q8×C73—41no—
534C2×Q8×C73—41no—
535C2×Q8×C73C22×C414yescomplemented
536C2×D4×C73—41no—
537C2×D4×C73—41no—
538C2×D4×C73C22×C414yes—
539C22×C4×C73—41no—
540C22×C4×C73—41no—
541C22×C4×C73—41no—
542C22×C4×C73—41no—
543C22×C4×C73—41no—
544C22×C4×C73—41no—
545C22×C4×C73C2411yescharacteristic
546C22×C4×C73C2411yescharacteristic
547C22×C4×C73C2411yescharacteristic
548C22×C4×C73C2411yescharacteristic
549C22×C4×C73C2411yescharacteristic
550C22×C4×C73C2411yescharacteristic
551C22×C4×C73C2411yescharacteristic
552C22×C4×C73C2411yescharacteristic
553C22×C4×C73C2411yescharacteristic
554C22×C4×C73C2411yescharacteristic
555C22×C4×C73C2411yescharacteristic
556C22×C4×C73C2411yescharacteristic
557C22×C4×C73C2411yescharacteristic
558C4⋊C4×C73—41no—
559C4⋊C4×C73—41no—
560C4⋊C4×C73—41no—
561C4⋊C4×C73—41no—
562C4⋊C4×C73—41no—
563C4⋊C4×C73—41no—
564C22⋊C4×C73—41no—
565C22⋊C4×C73—41no—
566C22⋊C4×C73—41no—
567C22⋊C4×C73—41no—
568C22⋊C4×C73—41no—
569C22⋊C4×C73—41no—
570C22⋊C4×C73C22×C414yes—
571C22⋊C4×C73C22×C414yes—
572C22⋊C4×C73C22×C414yescomplemented
573C22⋊C4×C73C22×C414yescomplemented
574C42×C73—41no—
575C42×C73—41no—
576C42×C73C22×C414yescomplemented
577C23×C73—21no—
578C23×C73—21no—
579C23×C73—21no—
580C23×C73—21no—
581C23×C73—21no—
582C23×C73—21no—
583C23×C73—21no—
584C23×C73—21no—
585C23×C73—21no—
586C23×C73—21no—
587C23×C73—21no—
588C23×C73—21no—
589C23×C73C23×C412yes—
590C23×C73C23×C412yes—
591C23×C73C2511yescharacteristic
592C22×D73—21no—
593C22×D73—21no—
594C22×D73—21no—
595C22×D73—21no—
596C22×D73—21no—
597C22×D73—21no—
598C22×D73—21no—
599C22×D73—21no—
600C22×D73—21no—
601C22×D73—21no—
602C22×D73—21no—
603C22×D73—21no—
604C22×D73—21no—
605C22×D73—21no—
606C22×D73—21no—
607C22×D73—21no—
608C22×D73—28no—
609C22×D73—44no—
610C22×D73—44no—
611C22×D73—44no—
612C22×D73—44no—
613C22×D73—44no—
614C22×D73—44no—
615C22×D73C23×C412yes—
616C22×D73C23×C412yes—
617C22×D73C23×C412yes—
618C22×D73H(5,𝔽2)12yes—
619C22×D732−1+412yes—
620Q8×C73—44no—
621D4×C73—44no—
622C2×C4×C73—21no—
623C2×C4×C73—21no—
624C2×C4×C73—21no—
625C2×C4×C73—21no—
626C2×C4×C73—21no—
627C2×C4×C73—21no—
628C2×C4×C73—21no—
629C2×C4×C73—21no—
630C2×C4×C73—21no—
631C2×C4×C73—21no—
632C2×C4×C73—21no—
633C2×C4×C73—21no—
634C2×C4×C73—21no—
635C2×C4×C73—21no—
636C2×C4×C73—21no—
637C2×C4×C73—21no—
638C2×C4×C73—21no—
639C2×C4×C73—21no—
640C2×C4×C73—21no—
641C2×C4×C73—21no—
642C2×C4×C73—21no—
643C2×C4×C73—21no—
644C2×C4×C73—21no—
645C2×C4×C73—21no—
646C2×C4×C73—21no—
647C2×C4×C73—21no—
648C2×C4×C73—21no—
649C2×C4×C73—21no—
650C2×C4×C73—21no—
651C2×C4×C73—21no—
652C2×C4×C73—21no—
653C2×C4×C73—21no—
654C2×C4×C73—21no—
655C2×C4×C73—21no—
656C2×C4×C73—44no—
657C2×C4×C73—82no—
658C2×C4×C73C23×C412yes—
659C2×C4×C73C23×C412yes—
660C2×C4×C73C23×C412yes—
661C2×C4×C73C23×C412yes—
662C2×C4×C73C23×C412yes—
663C22⋊D73—28no—
664C22⋊D73—44no—
665C22⋊D73—44no—
666C22⋊D73—44no—
667C2×Dic73—21no—
668C2×Dic73—21no—
669C2×Dic73—21no—
670C2×Dic73—21no—
671C2×Dic73—21no—
672C2×Dic73—21no—
673C2×Dic73—21no—
674C2×Dic73—21no—
675C2×Dic73—21no—
676C2×Dic73—21no—
677C2×Dic73—21no—
678C2×Dic73—21no—
679C2×Dic73—21no—
680C2×Dic73—21no—
681C2×Dic73—21no—
682C2×Dic73—21no—
683C2×Dic73—21no—
684C2×Dic73—21no—
685C2×Dic73—21no—
686C2×Dic73—21no—
687C2×Dic73—21no—
688C2×Dic73—21no—
689C2×Dic73—21no—
690C2×Dic73—21no—
691C2×Dic73—21no—
692C2×Dic73—21no—
693C2×Dic73—21no—
694C2×Dic73—21no—
695C2×Dic73—21no—
696C2×Dic73—21no—
697C2×Dic73—21no—
698C2×Dic73—21no—
699C2×Dic73—44no—
700C2×Dic73—44no—
701C2×Dic73—82no—
702C2×Dic73C23×C412yes—
703C2×Dic73C23×C412yes—
704C2×Dic73C23×C412yes—
705C2×Dic73C23×C412yes—
706C2×Dic73C23×C412yes—
707C2×Dic73H(5,𝔽2)12yes—
708C2×Dic73H(5,𝔽2)12yes—
709D292—28no—
710D292—44no—
711C4×D73—44no—
712C4×D73—44no—
713C4×D73—44no—
714C4×D73—44no—
715C4×D73—44no—
716C4×D73—44no—
717C4×D73—44no—
718C4×D73—82no—
719C4×D73—82no—
720C4×D73—82no—
721C4×D73—82no—
722C22×C73—22no—
723C22×C73—22no—
724C22×C73—22no—
725C22×C73—22no—
726C22×C73—22no—
727C22×C73—22no—
728C22×C73—41no—
729C22×C73—41no—
730C22×C73—41no—
731C22×C73—41no—
732C22×C73—41no—
733C22×C73—41no—
734C22×C73—41no—
735C22×C73—41no—
736C22×C73C24×C411yescharacteristic
737C22×C73C2×H(5,𝔽2)11yescharacteristic
738C22×C73C2×H(5,𝔽2)11yescharacteristic
739C22×C73C2×H(5,𝔽2)11yescharacteristic
740C22×C73C2×2−1+411yescharacteristic
741C22×C73#58511yescharacteristic
742C22×C73#58511yescharacteristic
743C2×D73—22no—
744C2×D73—22no—
745C2×D73—22no—
746C2×D73—22no—
747C2×D73—22no—
748C2×D73—22no—
749C2×D73—22no—
750C2×D73—22no—
751C2×D73—22no—
752C2×D73—22no—
753C2×D73—22no—
754C2×D73—22no—
755C2×D73—416no—
756C2×D73—41no—
757C2×D73—41no—
758C2×D73—41no—
759C2×D73—41no—
760C2×D73—41no—
761C2×D73—41no—
762C2×D73—41no—
763C2×D73—41no—
764C2×D73#52014yes—
765C4×C73—22no—
766C4×C73—22no—
767C4×C73—22no—
768C4×C73—22no—
769C4×C73—22no—
770C4×C73—41no—
771C4×C73—41no—
772C4×C73—41no—
773C4×C73—41no—
774C4×C73—41no—
775C4×C73—41no—
776C4×C73—41no—
777C4×C73—41no—
778Dic73—22no—
779Dic73—22no—
780Dic73—22no—
781Dic73—22no—
782Dic73—22no—
783Dic73—22no—
784Dic73—22no—
785Dic73—41no—
786Dic73—41no—
787Dic73—41no—
788Dic73—41no—
789Dic73—41no—
790Dic73—41no—
791#34416—731nomaximal, Sylow
792C2×C73—42no—
793C2×C73—42no—
794C2×C73C2×#52011yescharacteristic
795C2×C73C4×H(5,𝔽2)11yescharacteristic
796C2×C73C4×H(5,𝔽2)11yescharacteristic
797C2×C73#353211yescharacteristic
798C2×C73#353311yescharacteristic
799C2×C73#354111yescharacteristic
800C2×C73#354111yescharacteristic
801D73—24no—
802D73—42no—
803D73—42no—
804C2×#538—731no—
805#2383—731no—
806#2379D7311yescharacteristic, complemented
807#2377—731no—
808#2376—731no—
809#2373—731no—
810#2368—731no—
811#2367—731no—
812#2364—731no—
813#2361—731no—
814#2361—731no—
815#2360—731no—
816#2359—731no—
817#2353—731no—
818#2352—731no—
819#2349—731no—
820D4×C4⋊C4—731no—
821#2337—731no—
822#2335—731no—
823#2334—731no—
824#2334—731no—
825#2326—731no—
826#2325—731no—
827#2324—731no—
828#2322—731no—
829#2321—731no—
830#2321—731no—
831#2312—731no—
832C4×#120—731no—
833C4×#120—731no—
834C2×#385—731no—
835C73#3441611yescharacteristic, complemented, Sylow
836C24×C4—731no—
837#538—7316no—
838C2×#126—731no—
839C2×#126—731no—
840C2×#124—731no—
841C2×#124C2×D7311yescharacteristic
842C2×#123—731no—
843C2×#123—731no—
844C2×C22⋊Q8—731no—
845C2×#121—731no—
846C2×#121—731no—
847C2×#121—731no—
848C2×#120—731no—
849C2×#120—731no—
850C2×C4×Q8—731no—
851C2×C4×D4—731no—
852C2×C4×D4—731no—
853C2×C4×D4—731no—
854C2×C4×D4—731no—
855C2×C4×D4—731no—
856C2×C4×D4—731no—
857C2×C4×D4—731no—
858C2×C4×D4—731no—
859C2×C4×D4—731no—
860C2×C4×D4—731no—
861C2×C4×D4—731no—
862C2×#117—731no—
863C22×C4⋊C4—731no—
864C22×C4⋊C4—731no—
865C22×C4⋊C4—731no—
866C22×C22⋊C4—731no—
867C22×C22⋊C4—731no—
868#391—731no—
869#391C2×D7311yescharacteristic, complemented
870#391C2×D7311yescharacteristic, complemented
871#390—731no—
872#390—731no—
873#390—731no—
874#390—731no—
875#390—731no—
876#389—731no—
877#389—731no—
878#389—731no—
879#389—731no—
880#389—731no—
881#389—731no—
882#389—731no—
883#389—731no—
884#388—731no—
885#388—731no—
886#388—731no—
887#388—731no—
888#388—731no—
889#388—731no—
890#388—731no—
891#388—731no—
892#388—731no—
893#388—731no—
894#388—731no—
895#388—731no—
896#388—731no—
897#388—731no—
898#388—731no—
899#388—731no—
900#388—731no—
901#388—731no—
902#388—731no—
903#388—731no—
904#388C2×D7311yescharacteristic
905#388C2×D7311yescharacteristic
906#388C2×D7311yescharacteristic, complemented
907#388C2×D7311yescharacteristic, complemented
908#387—731no—
909#387—731no—
910#387—731no—
911#387—731no—
912#387—731no—
913#387—731no—
914#387—731no—
915#387—731no—
916#387—731no—
917#387—731no—
918#387—731no—
919#387—731no—
920#386—731no—
921#386—731no—
922#386—731no—
923#386—731no—
924#386—731no—
925#386—731no—
926#386—731no—
927#386—731no—
928#386—731no—
929#386—731no—
930#386—731no—
931#386—731no—
932#386C2×D7311yescharacteristic
933#386C2×D7311yescharacteristic
934#385—731no—
935#385—731no—
936#385—731no—
937#385—731no—
938#385—731no—
939#385—731no—
940#385—731no—
941#385—731no—
942#385—731no—
943#385—731no—
944#385—731no—
945#385—731no—
946#385—731no—
947#385—731no—
948#385—731no—
949#385—731no—
950#385—731no—
951#385—731no—
952#385C2×D7311yescharacteristic
953#385C2×D7311yescharacteristic
954#385C2×D7311yescharacteristic, complemented
955#385C2×D7311yescharacteristic, complemented
956#384—731no—
957#383—731no—
958#382C2×D7311yescharacteristic, complemented
959#382C2×D7311yescharacteristic, complemented
960#381—731no—
961#380—731no—
962#380—731no—
963#380—731no—
964#380—731no—
965#380—731no—
966#379—731no—
967#379—731no—
968C4×C4⋊C4—731no—
969C4×C4⋊C4—731no—
970C4×C4⋊C4—731no—
971C4×C4⋊C4—731no—
972C4×C4⋊C4—731no—
973C4×C4⋊C4—731no—
974C4×C4⋊C4—731no—
975C4×C22⋊C4—731no—
976C4×C22⋊C4—731no—
977C4×C22⋊C4—731no—
978C4×C22⋊C4—731no—
979C4×C22⋊C4—731no—
980C4×C22⋊C4—731no—
981C4×C22⋊C4—731no—
982C4×C22⋊C4—731no—
983C4×C22⋊C4—731no—
984C4×C22⋊C4—731no—
985C4×C22⋊C4—731no—
986C4×C22⋊C4—731no—
987C4×C22⋊C4—731no—
988#376—731no—
989C2×#95—731no—
990C2×#95—731no—
991C2×#95—731no—
992C25—731no—
993C22×Q8C22×D7311yescharacteristic
994C22×D4—731no—
995C22×D4—731no—
996C22×D4—731no—
997C22×D4—731no—
998C22×D4—731no—
999C22×D4—731no—
1000C22×D4C22×D7311yescharacteristic
1001C23×C4—2922no—
1002C23×C4—2922no—
1003C23×C4—2922no—
1004C23×C4—731no—
1005C23×C4—731no—
1006C23×C4—731no—
1007C23×C4—731no—
1008C23×C4—731no—
1009C23×C4—731no—
1010C23×C4—731no—
1011C23×C4—731no—
1012C23×C4—731no—
1013C23×C4—731no—
1014C23×C4—731no—
1015C23×C4—731no—
1016C23×C4—731no—
1017C23×C4—731no—
1018C23×C4C22×D7311yescharacteristic
1019C23×C4C22×D7311yescharacteristic
1020#126—738no—
1021#126—738no—
1022#124—738no—
1023#124C4×D7318yescomplemented
1024#123—738no—
1025#123—738no—
1026C22⋊Q8—738no—
1027#121—738no—
1028#121—738no—
1029#121—738no—
1030#120—738no—
1031#120—738no—
1032C4×Q8—2922no—
1033C4×D4—2922no—
1034C4×D4—2922no—
1035C4×D4—2922no—
1036C4×D4—2922no—
1037C4×D4—2922no—
1038C4×D4—2922no—
1039C4×D4—2922no—
1040C4×D4—2922no—
1041C4×D4—2922no—
1042C4×D4—738no—
1043C4×D4—738no—
1044#117—2922no—
1045C2×C4⋊C4—2922no—
1046C2×C4⋊C4—2922no—
1047C2×C4⋊C4—2922no—
1048C2×C4⋊C4—731no—
1049C2×C4⋊C4—731no—
1050C2×C4⋊C4—731no—
1051C2×C4⋊C4—731no—
1052C2×C4⋊C4—731no—
1053C2×C4⋊C4—731no—
1054C2×C4⋊C4—731no—
1055C2×C4⋊C4—731no—
1056C2×C4⋊C4—731no—
1057C2×C4⋊C4—731no—
1058C2×C4⋊C4—731no—
1059C2×C4⋊C4—731no—
1060C2×C4⋊C4—731no—
1061C2×C4⋊C4—731no—
1062C2×C4⋊C4—731no—
1063C2×C4⋊C4—731no—
1064C2×C4⋊C4—731no—
1065C2×C4⋊C4—731no—
1066C2×C4⋊C4—731no—
1067C2×C4⋊C4—731no—
1068C2×C4⋊C4—731no—
1069C2×C4⋊C4—731no—
1070C2×C4⋊C4—731no—
1071C2×C4⋊C4—731no—
1072C2×C4⋊C4C22×D7311yescharacteristic
1073C2×C4⋊C4C22×D7311yescharacteristic
1074C2×C4⋊C4C22×D7311yescharacteristic
1075C2×C4⋊C4C22×D7311yescharacteristic
1076C2×C4⋊C4C22×D7311yescharacteristic
1077C2×C4⋊C4C22×D7311yescharacteristic
1078C2×C22⋊C4—2922no—
1079C2×C22⋊C4—731no—
1080C2×C22⋊C4—731no—
1081C2×C22⋊C4—731no—
1082C2×C22⋊C4—731no—
1083C2×C22⋊C4—731no—
1084C2×C22⋊C4—731no—
1085C2×C22⋊C4—731no—
1086C2×C22⋊C4—731no—
1087C2×C22⋊C4—731no—
1088C2×C22⋊C4—731no—
1089C2×C22⋊C4—731no—
1090C2×C22⋊C4—731no—
1091C2×C22⋊C4—731no—
1092C2×C22⋊C4—731no—
1093C2×C22⋊C4—731no—
1094C2×C22⋊C4—731no—
1095C2×C22⋊C4—731no—
1096C2×C22⋊C4—731no—
1097C2×C22⋊C4—731no—
1098C2×C22⋊C4—731no—
1099C2×C22⋊C4—731no—
1100C2×C22⋊C4—731no—
1101C2×C22⋊C4—731no—
1102C2×C22⋊C4—731no—
1103C2×C22⋊C4—731no—
1104C2×C22⋊C4—731no—
1105C2×C22⋊C4—738no—
1106C2×C22⋊C4—731no—
1107C2×C22⋊C4—731no—
1108C2×C22⋊C4—731no—
1109C2×C22⋊C4—731no—
1110C2×C22⋊C4—731no—
1111C2×C22⋊C4—731no—
1112C2×C22⋊C4C22×D7311yescharacteristic
1113C2×C22⋊C4C22×D7311yescharacteristic
1114C2×C22⋊C4C22×D7311yescharacteristic
1115C2×C22⋊C4C22×D7311yescharacteristic
1116C2×C22⋊C4C22×D7311yescharacteristic
1117C2×C22⋊C4C22×D7311yescharacteristic
1118C2×C22⋊C4C22×D7311yescharacteristic
1119C2×C22⋊C4C22×D7311yescharacteristic
1120C2×C22⋊C4C22×D7311yescharacteristic
1121C2×C22⋊C4C22×D7311yescharacteristic
1122C2×C42—731no—
1123C2×C42—731no—
1124C2×C42—731no—
1125C2×C42—731no—
1126C2×C42—731no—
1127C2×C42—731no—
1128C2×C42—731no—
1129C2×C42—731no—
1130C2×C42—731no—
1131C2×C42—731no—
1132C2×C42—731no—
1133C2×C42—731no—
1134C2×C42—731no—
1135C2×C42—731no—
1136C2×C42—731no—
1137C2×C42C22×D7311yescharacteristic
1138C2×C42C22×D7311yescharacteristic
1139C2×C42C22×D7311yescharacteristic
1140#95—731no—
1141#95—731no—
1142#95—731no—
1143#95—731no—
1144#95—731no—
1145#95—731no—
1146#95—731no—
1147#95—731no—
1148#95—731no—
1149#95—731no—
1150#95—731no—
1151#95—731no—
1152#95—731no—
1153#95—731no—
1154#95—731no—
1155#95—731no—
1156#95—731no—
1157#95—731no—
1158#95—731no—
1159#95—731no—
1160#95—731no—
1161#95—731no—
1162#95—731no—
1163#95—731no—
1164#95—731no—
1165#95—731no—
1166#95—731no—
1167#95—731no—
1168#95C22×D7311yescharacteristic
1169#95C22×D7311yescharacteristic
1170#95C22×D7311yescharacteristic
1171#95C22×D7311yescharacteristic
1172#95C22×D7311yescharacteristic
1173#95C22×D7311yescharacteristic
1174#95C22×D7311yescharacteristic
1175#95C22×D7311yescharacteristic
1176#95C22×D7311yescharacteristic
1177#95C22×D7311yescharacteristic
1178#95C22×D7311yescharacteristic
1179#95C22×D7311yescharacteristic
1180C24—2921no—
1181C24—2921no—
1182C24—2921no—
1183C24—2921no—
1184C24—734no—
1185C24—731no—
1186C24—731no—
1187C24—731no—
1188C24—1462no—
1189C24—1462no—
1190C24C23×D7311yescharacteristic
1191C24C23×D7311yescharacteristic
1192C2×Q8—41no—
1193C2×Q8—41no—
1194C2×Q8C2×C4×D7314yescomplemented
1195C2×D4—41no—
1196C2×D4—41no—
1197C2×D4—2921no—
1198C2×D4—2921no—
1199C2×D4—2921no—
1200C2×D4—2921no—
1201C2×D4—2921no—
1202C2×D4—2921no—
1203C2×D4—2921no—
1204C2×D4—2921no—
1205C2×D4—734no—
1206C2×D4—734no—
1207C2×D4—734no—
1208C2×D4—734no—
1209C2×D4—734no—
1210C2×D4—734no—
1211C2×D4—1462no—
1212C2×D4—1462no—
1213C2×D4—1462no—
1214C2×D4—1462no—
1215C2×D4C2×C4×D7314yes—
1216C22×C4—41no—
1217C22×C4—41no—
1218C22×C4—41no—
1219C22×C4—41no—
1220C22×C4—41no—
1221C22×C4—41no—
1222C22×C4—2921no—
1223C22×C4—2921no—
1224C22×C4—2921no—
1225C22×C4—2921no—
1226C22×C4—2921no—
1227C22×C4—2921no—
1228C22×C4—2921no—
1229C22×C4—2921no—
1230C22×C4—2921no—
1231C22×C4—2921no—
1232C22×C4—2921no—
1233C22×C4—2921no—
1234C22×C4—2921no—
1235C22×C4—2921no—
1236C22×C4—2921no—
1237C22×C4—2921no—
1238C22×C4—2921no—
1239C22×C4—2921no—
1240C22×C4—2921no—
1241C22×C4—2921no—
1242C22×C4—2921no—
1243C22×C4—29216no—
1244C22×C4—2921no—
1245C22×C4—2921no—
1246C22×C4—2921no—
1247C22×C4—2921no—
1248C22×C4—2921no—
1249C22×C4—734no—
1250C22×C4—734no—
1251C22×C4—734no—
1252C22×C4—734no—
1253C22×C4—731no—
1254C22×C4—731no—
1255C22×C4—731no—
1256C22×C4—731no—
1257C22×C4—731no—
1258C22×C4—731no—
1259C22×C4—731no—
1260C22×C4—731no—
1261C22×C4—731no—
1262C22×C4—731no—
1263C22×C4—731no—
1264C22×C4—731no—
1265C22×C4—731no—
1266C22×C4—1462no—
1267C22×C4—1462no—
1268C22×C4—1462no—
1269C22×C4—1462no—
1270C22×C4—1462no—
1271C22×C4—1462no—
1272C22×C4—1462no—
1273C22×C4—1462no—
1274C22×C4—1462no—
1275C22×C4—1462no—
1276C22×C4—1462no—
1277C22×C4—1462no—
1278C22×C4C23×D7311yescharacteristic
1279C22×C4C23×D7311yescharacteristic
1280C22×C4C23×D7311yescharacteristic
1281C22×C4C23×D7311yescharacteristic
1282C22×C4C23×D7311yescharacteristic
1283C22×C4C23×D7311yescharacteristic
1284C22×C4C23×D7311yescharacteristic
1285C22×C4C23×D7311yescharacteristic
1286C22×C4C23×D7311yescharacteristic
1287C22×C4C23×D7311yescharacteristic
1288C22×C4C23×D7311yescharacteristic
1289C22×C4C23×D7311yescharacteristic
1290C22×C4C23×D7311yescharacteristic
1291C4⋊C4—41no—
1292C4⋊C4—41no—
1293C4⋊C4—41no—
1294C4⋊C4—41no—
1295C4⋊C4—41no—
1296C4⋊C4—41no—
1297C4⋊C4—2921no—
1298C4⋊C4—2921no—
1299C4⋊C4—2921no—
1300C4⋊C4—2921no—
1301C4⋊C4—2921no—
1302C4⋊C4—2921no—
1303C4⋊C4—2921no—
1304C4⋊C4—2921no—
1305C4⋊C4—2921no—
1306C4⋊C4—2921no—
1307C4⋊C4—2921no—
1308C4⋊C4—2921no—
1309C4⋊C4—734no—
1310C4⋊C4—734no—
1311C4⋊C4—734no—
1312C4⋊C4—734no—
1313C4⋊C4—734no—
1314C4⋊C4—734no—
1315C4⋊C4—1462no—
1316C4⋊C4—1462no—
1317C4⋊C4—1462no—
1318C4⋊C4—1462no—
1319C4⋊C4—1462no—
1320C4⋊C4—1462no—
1321C22⋊C4—41no—
1322C22⋊C4—41no—
1323C22⋊C4—41no—
1324C22⋊C4—41no—
1325C22⋊C4—41no—
1326C22⋊C4—41no—
1327C22⋊C4—2921no—
1328C22⋊C4—2921no—
1329C22⋊C4—2921no—
1330C22⋊C4—2921no—
1331C22⋊C4—2921no—
1332C22⋊C4—2921no—
1333C22⋊C4—2921no—
1334C22⋊C4—2921no—
1335C22⋊C4—2921no—
1336C22⋊C4—2921no—
1337C22⋊C4—2921no—
1338C22⋊C4—2921no—
1339C22⋊C4—2921no—
1340C22⋊C4—2921no—
1341C22⋊C4—2921no—
1342C22⋊C4—2921no—
1343C22⋊C4—734no—
1344C22⋊C4—734no—
1345C22⋊C4—734no—
1346C22⋊C4—734no—
1347C22⋊C4—734no—
1348C22⋊C4—734no—
1349C22⋊C4—734no—
1350C22⋊C4—734no—
1351C22⋊C4—734no—
1352C22⋊C4—734no—
1353C22⋊C4—1462no—
1354C22⋊C4—1462no—
1355C22⋊C4—1462no—
1356C22⋊C4—1462no—
1357C22⋊C4—1462no—
1358C22⋊C4—1462no—
1359C22⋊C4C2×C4×D7314yes—
1360C22⋊C4C2×C4×D7314yes—
1361C22⋊C4C2×C4×D7314yescomplemented
1362C22⋊C4C2×C4×D7314yescomplemented
1363C42—41no—
1364C42—41no—
1365C42—2921no—
1366C42—2921no—
1367C42—2921no—
1368C42—2921no—
1369C42—2921no—
1370C42—2921no—
1371C42—2921no—
1372C42—2921no—
1373C42—2921no—
1374C42—2921no—
1375C42—2921no—
1376C42—2921no—
1377C42—734no—
1378C42—1462no—
1379C42—1462no—
1380C42C2×C4×D7314yescomplemented
1381C23—21no—
1382C23—21no—
1383C23—21no—
1384C23—21no—
1385C23—21no—
1386C23—21no—
1387C23—21no—
1388C23—21no—
1389C23—21no—
1390C23—21no—
1391C23—21no—
1392C23—21no—
1393C23—2924no—
1394C23—2924no—
1395C23—2924no—
1396C23—2924no—
1397C23—2924no—
1398C23—2924no—
1399C23—732no—
1400C23—732no—
1401C23—732no—
1402C23—732no—
1403C23—732no—
1404C23—1468no—
1405C23—1461no—
1406C23—1461no—
1407C23—1461no—
1408C23—1461no—
1409C23—1461no—
1410C23—1461no—
1411C23—1461no—
1412C23—1461no—
1413C23—1461no—
1414C23—1461no—
1415C23—1461no—
1416C23—1461no—
1417C23—1461no—
1418C23—1461no—
1419C23—1461no—
1420C23—1461no—
1421C23C22×C4×D7312yes—
1422C23C22×C4×D7312yes—
1423C23C24×D7311yescharacteristic
1424Q8—44no—
1425D4—44no—
1426D4—2924no—
1427D4—2924no—
1428D4—2924no—
1429D4—2924no—
1430D4—1468no—
1431D4—1468no—
1432C2×C4—21no—
1433C2×C4—21no—
1434C2×C4—21no—
1435C2×C4—21no—
1436C2×C4—21no—
1437C2×C4—21no—
1438C2×C4—21no—
1439C2×C4—21no—
1440C2×C4—21no—
1441C2×C4—21no—
1442C2×C4—21no—
1443C2×C4—21no—
1444C2×C4—21no—
1445C2×C4—21no—
1446C2×C4—21no—
1447C2×C4—21no—
1448C2×C4—21no—
1449C2×C4—21no—
1450C2×C4—21no—
1451C2×C4—21no—
1452C2×C4—21no—
1453C2×C4—21no—
1454C2×C4—21no—
1455C2×C4—21no—
1456C2×C4—21no—
1457C2×C4—21no—
1458C2×C4—21no—
1459C2×C4—21no—
1460C2×C4—21no—
1461C2×C4—21no—
1462C2×C4—21no—
1463C2×C4—21no—
1464C2×C4—21no—
1465C2×C4—21no—
1466C2×C4—44no—
1467C2×C4—82no—
1468C2×C4—2924no—
1469C2×C4—2924no—
1470C2×C4—2924no—
1471C2×C4—2924no—
1472C2×C4—2924no—
1473C2×C4—2924no—
1474C2×C4—2924no—
1475C2×C4—2924no—
1476C2×C4—2924no—
1477C2×C4—5842no—
1478C2×C4—5842no—
1479C2×C4—5842no—
1480C2×C4—5842no—
1481C2×C4—5842no—
1482C2×C4—732no—
1483C2×C4—732no—
1484C2×C4—732no—
1485C2×C4—732no—
1486C2×C4—732no—
1487C2×C4—732no—
1488C2×C4—732no—
1489C2×C4—1461no—
1490C2×C4—1461no—
1491C2×C4—1461no—
1492C2×C4—1461no—
1493C2×C4—1461no—
1494C2×C4—1461no—
1495C2×C4—1461no—
1496C2×C4—1461no—
1497C2×C4—1461no—
1498C2×C4—1461no—
1499C2×C4—1461no—
1500C2×C4—1461no—
1501C2×C4—1461no—
1502C2×C4—1461no—
1503C2×C4—1461no—
1504C2×C4—1461no—
1505C2×C4—1461no—
1506C2×C4—1461no—
1507C2×C4—1461no—
1508C2×C4—1461no—
1509C2×C4—1461no—
1510C2×C4—1461no—
1511C2×C4—1461no—
1512C2×C4—1461no—
1513C2×C4—1461no—
1514C2×C4—1461no—
1515C2×C4—1461no—
1516C2×C4—1461no—
1517C2×C4—1461no—
1518C2×C4—1461no—
1519C2×C4—1461no—
1520C2×C4—1461no—
1521C2×C4C22×C4×D7312yes—
1522C2×C4C22×C4×D7312yes—
1523C2×C4C22×C4×D7312yes—
1524C2×C4C22×C4×D7312yes—
1525C2×C4C22×C4×D7312yes—
1526C22—22no—
1527C22—22no—
1528C22—22no—
1529C22—22no—
1530C22—22no—
1531C22—22no—
1532C22—41no—
1533C22—41no—
1534C22—41no—
1535C22—41no—
1536C22—41no—
1537C22—41no—
1538C22—41no—
1539C22—41no—
1540C22—29216no—
1541C22—2921no—
1542C22—2921no—
1543C22—2921no—
1544C22—2921no—
1545C22—2921no—
1546C22—2921no—
1547C22—2921no—
1548C22—2921no—
1549C22—734no—
1550C22—1462no—
1551C22—1462no—
1552C22—1462no—
1553C22—1462no—
1554C22—1462no—
1555C22—1462no—
1556C22—1462no—
1557C22—1462no—
1558C22—1462no—
1559C22—1462no—
1560C22—1462no—
1561C22—1462no—
1562C22C23×C4×D7311yescharacteristic
1563C22H(5,𝔽2)×D7311yescharacteristic
1564C22H(5,𝔽2)×D7311yescharacteristic
1565C22H(5,𝔽2)×D7311yescharacteristic
1566C222−1+4×D7311yescharacteristic
1567C22#1798942211yescharacteristic
1568C22#1798942411yescharacteristic
1569C4—22no—
1570C4—22no—
1571C4—22no—
1572C4—22no—
1573C4—22no—
1574C4—41no—
1575C4—41no—
1576C4—41no—
1577C4—41no—
1578C4—41no—
1579C4—41no—
1580C4—41no—
1581C4—41no—
1582C4—2921no—
1583C4—2921no—
1584C4—2921no—
1585C4—2921no—
1586C4—2921no—
1587C4—2921no—
1588C4—1462no—
1589C4—1462no—
1590C4—1462no—
1591C4—1462no—
1592C4—1462no—
1593C4—1462no—
1594C4—1462no—
1595C2—42no—
1596C2—42no—
1597C2—2922no—
1598C2—2922no—
1599C2—1464no—
1600C2#520×D7311yescharacteristic
1601C2#2262313511yescharacteristic
1602C2#2262313711yescharacteristic
1603C2#2262408811yescharacteristic
1604C2#2262409311yescharacteristic
1605C2#2262421311yescharacteristic
1606C2#2262422111yescharacteristic
subgroupG/H
center, FrattiniC23C24×D73
commutatorC22×C73C24×C4
FittingC73×#2379C2
socle, cosocleC23×C73C25
prime radicalC2×#17989171C2
hypercenter#2379D73
hypocenterC73#34416
LCSG ▷ C22×C73 ▷ C73
UCSC1 ◁ C23 ◁ #2379

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. #22613119C2semidirect
3. #22613089C2semidirect
4. #22613080C2semidirect
5. #22613048C2semidirect
6. #22613010C2semidirect
7. #22613006C2semidirect
8. #22612975C2semidirect
9. #22612950C2semidirect
10. #22612942C2semidirect
11. #22612941C2semidirect
12. #22612922C2semidirect
13. #22612866C2semidirect
14. #22612857C2semidirect
15. #22612839C2semidirect
16. #22612829C2semidirect
17. #22612743C2semidirect
18. #22612726C2semidirect
19. #22612702C2semidirect
20. #22612702C2semidirect
21. #22612645C2semidirect
22. #22612628C2semidirect
23. #22612619C2semidirect
24. #22612599C2semidirect
25. #22612587C2semidirect
26. #22612584C2semidirect
27. #22612525C2semidirect
28. #22612436C2semidirect
29. #22612432C2semidirect
30. #385×D73C2semidirect
31. C73×#2379C2semidirect
33. #17989171C4semidirect
45. C2×Q8×Dic73C22semidirect
52. C2×C4×C22⋊D73C22semidirect
57. C2×#14556549C22semidirect
58. C22×#11924007C22semidirect
63. #17988494C22semidirect
68. #17988487C22semidirect
69. #17988484C22semidirect
70. #17988484C22semidirect
71. #17988484C22semidirect
72. #17988483C22semidirect
73. #17988483C22semidirect
74. #17988483C22semidirect
75. #17988482C22semidirect
76. #17988482C22semidirect
80. #17988480C22semidirect
81. #17988480C22semidirect
87. #17988477C22semidirect
91. #17988476C22semidirect
92. #17988476C22semidirect
93. #17988476C22semidirect
97. #17988474C22semidirect
98. #17988474C22semidirect
99. #17988472C22semidirect
100. #17988470C22semidirect
101. #17988470C22semidirect
102. #17988470C22semidirect
103. #17988469C22semidirect
104. #17988469C22semidirect
105. #17988469C22semidirect
106. #17988468C22semidirect
107. #17988468C22semidirect
108. #17988468C22semidirect
115. #17988464C22semidirect
120. #17988463C22semidirect
122. #17988462C22semidirect
129. #17988461C22semidirect
130. #17988461C22semidirect
131. #17988461C22semidirect
139. #17988456C22semidirect
140. #17988454C22semidirect
141. #17988448C22semidirect
143. #17988446C22semidirect
144. #17988445C22semidirect
146. #17988444C22semidirect
149. C4×#11924007C22semidirect
150. C4×C4⋊Dic73C22semidirect
151. C4×C4⋊Dic73C22semidirect
152. C4×C4⋊Dic73C22semidirect
153. #17988438C22semidirect
154. #17988438C22semidirect
155. #17988438C22semidirect
158. C22⋊C4×Dic73C22semidirect
159. C22⋊C4×Dic73C22semidirect
162. C4×#11924005C22semidirect
169. #17988433C22semidirect
172. #95×D73C22semidirect
174. #391×C73C22semidirect
175. #391×C73C22semidirect
178. #388×C73C22semidirect
179. #388×C73C22semidirect
184. #385×C73C22semidirect
185. #385×C73C22semidirect
186. #382×C73C22semidirect
187. #382×C73C22semidirect
212. #14556585C2×C4semidirect
213. #14556584C2×C4semidirect
214. #14556580C2×C4semidirect
215. #14556575C2×C4semidirect
216. #14556573C2×C4semidirect
217. #14556567C2×C4semidirect
218. #14556564C2×C4semidirect
219. #14556564C2×C4semidirect
220. #14556563C2×C4semidirect
221. #14556561C2×C4semidirect
222. #14556559C2×C4semidirect
224. C4×D292C2×C4semidirect
234. #14556551C2×C4semidirect
296. C22⋊C4×D73C2×C4semidirect
344. #124×C73C2×C4semidirect
403. C2×C22⋊D73C22×C4semidirect
412. C22×Dic73C22×C4semidirect
459. C2×C4×D73C22×C4semidirect
466. C4⋊Dic73C22×C4semidirect
467. C4⋊Dic73C22×C4semidirect
480. #11924007C22×C4semidirect
481. #11924007C22×C4semidirect
482. #11924007C22×C4semidirect
483. #11924007C22×C4semidirect
514. #11924005C22×C4semidirect
515. #11924005C22×C4semidirect
530. C4×Dic73C22×C4semidirect
535. C2×Q8×C73C22×C4semidirect
572. C22⋊C4×C73C22×C4semidirect
573. C22⋊C4×C73C22×C4semidirect
576. C42×C73C22×C4semidirect
806. #2379D73semidirect
835. C73#34416semidirect
869. #391C2×D73semidirect
870. #391C2×D73semidirect
906. #388C2×D73semidirect
907. #388C2×D73semidirect
954. #385C2×D73semidirect
955. #385C2×D73semidirect
958. #382C2×D73semidirect
959. #382C2×D73semidirect
1023. #124C4×D73semidirect
1194. C2×Q8C2×C4×D73semidirect
1361. C22⋊C4C2×C4×D73semidirect
1362. C22⋊C4C2×C4×D73semidirect
1380. C42C2×C4×D73semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#179891712
#226131192
#226130892
#226130802
#226130482
#226130102
#226130062
#226129752
#226129502
#226129422
#226129412
#226129222
#226128662
#226128572
#226128392
#226128292
#226127432
#226127262
#226127022
#226126452
#226126282
#226126192
#226125992
#226125872
#226125842
#226125252
#226124362
#226124322
#385×D732
C73×#23792
#3441673