Finite Group Databasebeta

← #33249522

Subgroups — #33249522

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×#17989172C211yesmaximal, characteristic
2#22613118C211yesmaximal, characteristic, complemented
3#22613100C211yesmaximal, characteristic, complemented
4#22613083C211yesmaximal, characteristic, complemented
5#22613081C211yesmaximal, characteristic, complemented
6#22613048C211yesmaximal, characteristic, complemented
7#22613009C211yesmaximal, characteristic, complemented
8#22612997C211yesmaximal, characteristic, complemented
9#22612976C211yesmaximal, characteristic, complemented
10#22612952C211yesmaximal, characteristic, complemented
11#22612942C211yesmaximal, characteristic, complemented
12#22612931C211yesmaximal, characteristic, complemented
13#22612929C211yesmaximal, characteristic, complemented
14#22612865C211yesmaximal, characteristic, complemented
15#22612858C211yesmaximal, characteristic, complemented
16#22612836C211yesmaximal, characteristic, complemented
17#22612829C211yesmaximal, characteristic, complemented
18#22612740C211yesmaximal, characteristic, complemented
19#22612719C211yesmaximal, characteristic, complemented
20#22612713C211yesmaximal, characteristic, complemented
21#22612704C211yesmaximal, characteristic, complemented
22#22612641C211yesmaximal, characteristic, complemented
23#22612632C211yesmaximal, characteristic, complemented
24#22612617C211yesmaximal, characteristic, complemented
25#22612601C211yesmaximal, characteristic, complemented
26#22612589C211yesmaximal, characteristic, complemented
27#22612527C211yesmaximal, characteristic, complemented
28#120×Dic73C211yesmaximal, characteristic, complemented
29#22612430C211yesmaximal, characteristic, complemented
30C2×#17988459C211yesmaximal, characteristic, complemented
31C73×#2321C211yesmaximal, characteristic, complemented
32C24×Dic73C2211yescharacteristic
33#17989172C4116yescomplemented
34C2×#14556584C2211yescharacteristic
35C2×#14556584C2211yescharacteristic
36C2×#14556578C2211yescharacteristic
37C2×#14556577C2211yescharacteristic
38C2×#14556573C2211yescharacteristic
39C2×#14556572C2211yescharacteristic
40C2×#14556568C2211yescharacteristic
41C2×#14556563C2211yescharacteristic
42C2×#14556563C2211yescharacteristic
43C2×#14556562C2211yescharacteristic
44C2×#14556560C2211yescharacteristic
45C2×#14556556C2211yescharacteristic, complemented
46C2×D4×Dic73C2211yescharacteristic
47C2×D4×Dic73C2211yescharacteristic
48C2×D4×Dic73C2211yescharacteristic
49C2×D4×Dic73C2211yescharacteristic
50C2×C4×C22⋊D73C2211yescharacteristic
51C2×#14556551C2211yescharacteristic
52C2×#14556551C2211yescharacteristic
53C2×#14556551C2211yescharacteristic
54C2×#14556551C2211yescharacteristic
55C2×#14556551C2211yescharacteristic, complemented
56C2×#14556547C2211yescharacteristic, complemented
57C22×#11924007C2211yescharacteristic
58C22×#11924007C2211yescharacteristic
59C2×C4⋊C4×D73C2211yescharacteristic, complemented
60C22×C22⋊Dic73C2211yescharacteristic
61#17988493C2211yescharacteristic, complemented
62#17988491C2211yescharacteristic, complemented
63#17988491C2211yescharacteristic, complemented
64#17988487C2211yescharacteristic
65#17988487C2211yescharacteristic
66#17988487C2211yescharacteristic, complemented
67#17988485C2211yescharacteristic, complemented
68#17988484C2211yescharacteristic, complemented
69#17988484C2211yescharacteristic, complemented
70#17988483C2211yescharacteristic, complemented
71#17988483C2211yescharacteristic, complemented
72#17988482C2211yescharacteristic, complemented
73#17988482C2211yescharacteristic, complemented
74#17988482C2211yescharacteristic, complemented
75#17988481C2211yescharacteristic
76#17988481C2211yescharacteristic
77#17988481C2211yescharacteristic
78#17988481C2211yescharacteristic
79#17988481C2211yescharacteristic
80#17988481C2211yescharacteristic
81#17988481C2211yescharacteristic, complemented
82#17988481C2211yescharacteristic, complemented
83#17988481C2211yescharacteristic, complemented
84#17988478C2211yescharacteristic, complemented
85#17988477C2211yescharacteristic, complemented
86#17988476C2211yescharacteristic, complemented
87#17988476C2211yescharacteristic, complemented
88#17988475C2211yescharacteristic
89#17988475C2211yescharacteristic
90#17988475C2211yescharacteristic
91#17988475C2211yescharacteristic
92#17988475C2211yescharacteristic
93#17988475C2211yescharacteristic
94#17988475C2211yescharacteristic, complemented
95#17988474C2211yescharacteristic, complemented
96#17988474C2211yescharacteristic, complemented
97#17988472C2211yescharacteristic, complemented
98#17988472C2211yescharacteristic, complemented
99#17988471C2211yescharacteristic, complemented
100#17988471C2211yescharacteristic, complemented
101#17988471C2211yescharacteristic, complemented
102#17988470C2211yescharacteristic, complemented
103#17988470C2211yescharacteristic, complemented
104#17988469C2211yescharacteristic, complemented
105#17988469C2211yescharacteristic, complemented
106#17988468C2211yescharacteristic, complemented
107#17988467C2211yescharacteristic
108#17988467C2211yescharacteristic
109#17988467C2211yescharacteristic
110#17988466C2211yescharacteristic
111#17988466C2211yescharacteristic, complemented
112#17988464C2211yescharacteristic
113#17988464C2211yescharacteristic
114#17988464C2211yescharacteristic
115#17988463C2211yescharacteristic
116#17988463C2211yescharacteristic
117#17988463C2211yescharacteristic, complemented
118#17988462C2211yescharacteristic
119#17988462C2211yescharacteristic
120#17988462C2211yescharacteristic
121#17988461C2211yescharacteristic, complemented
122#17988461C2211yescharacteristic, complemented
123#17988460C2211yescharacteristic
124#17988460C2211yescharacteristic, complemented
125#17988459C2211yescharacteristic
126#17988459C2211yescharacteristic
127#17988459C2211yescharacteristic
128#17988459C2211yescharacteristic
129#17988459C2211yescharacteristic
130#17988459C2211yescharacteristic
131#17988459C2211yescharacteristic
132#17988459C2211yescharacteristic
133#17988459C2211yescharacteristic
134#17988459C2211yescharacteristic
135#17988459C2211yescharacteristic
136#17988459C2211yescharacteristic, complemented
137#17988459C2211yescharacteristic, complemented
138#17988458C2211yescharacteristic, complemented
139#17988456C2211yescharacteristic, complemented
140#17988454C2211yescharacteristic, complemented
141#17988452C2211yescharacteristic, complemented
142#17988451C2211yescharacteristic, complemented
143#17988449C2211yescharacteristic, complemented
144#17988446C2211yescharacteristic, complemented
145#17988445C2211yescharacteristic
146#17988445C2211yescharacteristic
147#17988445C2211yescharacteristic, complemented
148#17988445C2211yescharacteristic, complemented
149#17988443C2211yescharacteristic
150C4×#11924007C2211yescharacteristic, complemented
151C4×#11924007C2211yescharacteristic, complemented
152C4×C4⋊Dic73C2211yescharacteristic, complemented
153#17988438C2211yescharacteristic, complemented
154#17988438C2211yescharacteristic, complemented
155#17988438C2211yescharacteristic, complemented
156#17988438C2211yescharacteristic, complemented
157C22⋊C4×Dic73C2211yescharacteristic
158C22⋊C4×Dic73C2211yescharacteristic
159C22⋊C4×Dic73C2211yescharacteristic
160C22⋊C4×Dic73C2211yescharacteristic
161C22⋊C4×Dic73C2211yescharacteristic
162C22⋊C4×Dic73C2211yescharacteristic
163C22⋊C4×Dic73C2211yescharacteristic
164C22⋊C4×Dic73C2211yescharacteristic
165C4×#11924005C2211yescharacteristic, complemented
166C4×#11924005C2211yescharacteristic, complemented
167C4×C22⋊Dic73C2211yescharacteristic
168C4×C22⋊Dic73C2211yescharacteristic, complemented
169#17988433C2211yescharacteristic, complemented
170C2×#14556498C2211yescharacteristic
171C2×#14556498C2211yescharacteristic
172C2×#14556498C2211yescharacteristic, complemented
173C2×#120×C73C2211yescharacteristic
174C2×C4×D4×C73C2211yescharacteristic
175C22×C22⋊C4×C73C2211yescharacteristic
176#390×C73C2211yescharacteristic
177#390×C73C2211yescharacteristic
178#388×C73C2211yescharacteristic
179#388×C73C2211yescharacteristic
180#388×C73C2211yescharacteristic
181#388×C73C2211yescharacteristic
182#386×C73C2211yescharacteristic
183#386×C73C2211yescharacteristic
184#386×C73C2211yescharacteristic
185#385×C73C2211yescharacteristic
186#379×C73C2211yescharacteristic
187C4×C22⋊C4×C73C2211yescharacteristic
188C22×Dic146C2311yescharacteristic
189C22×C22⋊D73C2311yescharacteristic
190C22×C22⋊D73C2311yescharacteristic
191C22×C22⋊D73C2311yescharacteristic
192C22×C22⋊D73C2311yescharacteristic
193C23×Dic73—42no—
194C23×Dic73—42no—
195C23×Dic73—42no—
196C23×Dic73C2311yescharacteristic
197C23×Dic73C2311yescharacteristic
198C23×Dic73C2311yescharacteristic
199C23×Dic73C2311yescharacteristic
200C23×Dic73C2311yescharacteristic
201C23×Dic73C2311yescharacteristic
202C23×Dic73C2311yescharacteristic
203C23×Dic73C2311yescharacteristic
204C23×Dic73C2311yescharacteristic
205C23×Dic73C2311yescharacteristic
206C22×C4×D73C2311yescharacteristic
207C22×C4×D73C2311yescharacteristic
208C22×C4×D73C2311yescharacteristic
209#14556584C2×C418yescomplemented
210#14556584C2×C418yescomplemented
211#14556578C2×C418yescomplemented
212#14556577C2×C418yescomplemented
213#14556573C2×C418yescomplemented
214#14556572C2×C418yescomplemented
215#14556568C2×C418yescomplemented
216#14556563C2×C418yescomplemented
217#14556563C2×C418yescomplemented
218#14556562C2×C418yescomplemented
219#14556560C2×C418yescomplemented
220#14556556—42no—
221D4×Dic73—42no—
222D4×Dic73—42no—
223D4×Dic73—42no—
224D4×Dic73C2×C418yescomplemented
225C4×C22⋊D73—42no—
226#14556551—42no—
227#14556551—42no—
228#14556551—42no—
229#14556551—42no—
230#14556551C2×C418yescomplemented
231#14556547—42no—
232C2×C4⋊Dic73C2311yescharacteristic
233C2×C4⋊Dic73C2311yescharacteristic
234C2×C4⋊Dic73C2311yescharacteristic
235C2×C4⋊Dic73C2311yescharacteristic
236C2×C4⋊Dic73C2311yescharacteristic
237C2×#11924007—42no—
238C2×#11924007—42no—
239C2×#11924007C2311yescharacteristic
240C2×#11924007C2311yescharacteristic
241C2×#11924007C2311yescharacteristic
242C2×#11924007C2311yescharacteristic
243C2×#11924007C2311yescharacteristic
244C2×#11924007C2311yescharacteristic
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—
262C2×C22⋊Dic73C2×C418yescomplemented
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×C22⋊Dic73C2311yescharacteristic
272C2×C22⋊Dic73C2311yescharacteristic
273C2×C22⋊Dic73C2311yescharacteristic
274C2×C22⋊Dic73C2311yescharacteristic
275C2×C22⋊Dic73C2311yescharacteristic
276C2×C22⋊Dic73C2311yescharacteristic
277C2×C22⋊Dic73C2311yescharacteristic
278C2×C22⋊Dic73C2311yescharacteristic
279C2×C22⋊Dic73C2311yescharacteristic
280C2×C22⋊Dic73C2311yescharacteristic
281C2×#11924005C2311yescharacteristic
282C2×#11924005C2311yescharacteristic
283C2×#11924005C2311yescharacteristic
284C2×#11924005C2311yescharacteristic
285C2×#11924005C2311yescharacteristic
286C2×#11924005C2311yescharacteristic
287C2×#11924005C2311yescharacteristic
288C2×#11924005C2311yescharacteristic
289C2×C4×Dic73C2311yescharacteristic
290C2×C4×Dic73C2311yescharacteristic
291C2×C4×Dic73C2311yescharacteristic
292C2×C4×Dic73C2311yescharacteristic
293C2×C4×Dic73C2311yescharacteristic
294C2×C4×Dic73C2311yescharacteristic
295C2×C4×Dic73C2311yescharacteristic
296C2×C4×Dic73C2311yescharacteristic
297C2×C4×Dic73C2311yescharacteristic
298C2×C4×Dic73C2311yescharacteristic
299C2×C4×Dic73C2311yescharacteristic
300C2×C4×Dic73C2311yescharacteristic
301C2×C4×Dic73C2311yescharacteristic
302C2×C4×Dic73C2311yescharacteristic
303C2×C4×Dic73C2311yescharacteristic
304#14556498C2311yescharacteristic
305#14556498C2311yescharacteristic
306#14556498C2311yescharacteristic
307#14556498C2311yescharacteristic
308#14556498C2311yescharacteristic
309#14556498C2311yescharacteristic
310#14556498C2311yescharacteristic
311#14556498C2311yescharacteristic
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
338C25×C73C2311yescharacteristic
339C22×D4×C73C2311yescharacteristic
340C22×D4×C73C2311yescharacteristic
341C22×D4×C73C2311yescharacteristic
342C23×C4×C73C2311yescharacteristic
343C23×C4×C73C2311yescharacteristic
344C23×C4×C73C2311yescharacteristic
345#120×C73C2×C418yescomplemented
346C4×D4×C73—42no—
347C2×C4⋊C4×C73C2311yescharacteristic
348C2×C4⋊C4×C73C2311yescharacteristic
349C2×C4⋊C4×C73C2311yescharacteristic
350C2×C22⋊C4×C73—42no—
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×C22⋊C4×C73C2311yescharacteristic
362C2×C22⋊C4×C73C2311yescharacteristic
363C2×C22⋊C4×C73C2311yescharacteristic
364C2×C22⋊C4×C73C2311yescharacteristic
365C2×C22⋊C4×C73C2311yescharacteristic
366C2×C22⋊C4×C73C2311yescharacteristic
367C2×C42×C73C2311yescharacteristic
368C2×C42×C73C2311yescharacteristic
369C2×C42×C73C2311yescharacteristic
370#95×C73C2311yescharacteristic
371#95×C73C2311yescharacteristic
372#95×C73C2311yescharacteristic
373#95×C73C2311yescharacteristic
374#95×C73C2311yescharacteristic
375#95×C73C2311yescharacteristic
376C23×D73C2411yescharacteristic
377C2×Dic146—41no—
378C2×Dic146—41no—
379C2×Dic146C22×C414yescomplemented
380C2×C22⋊D73—22no—
381C2×C22⋊D73—22no—
382C2×C22⋊D73—41no—
383C2×C22⋊D73—41no—
384C2×C22⋊D73—41no—
385C2×C22⋊D73—41no—
386C2×C22⋊D73—41no—
387C2×C22⋊D73—41no—
388C2×C22⋊D73C22×C414yes—
389C2×C22⋊D73C22×C414yes—
390C2×C22⋊D73C22×C414yes—
391C2×C22⋊D73C22×C414yescomplemented
392C22×Dic73—22no—
393C22×Dic73—22no—
394C22×Dic73—22no—
395C22×Dic73—22no—
396C22×Dic73—22no—
397C22×Dic73—22no—
398C22×Dic73—22no—
399C22×Dic73—22no—
400C22×Dic73—22no—
401C22×Dic73—41no—
402C22×Dic73—41no—
403C22×Dic73—41no—
404C22×Dic73—41no—
405C22×Dic73—41no—
406C22×Dic73—41no—
407C22×Dic73—41no—
408C22×Dic73—41no—
409C22×Dic73—41no—
410C22×Dic73—41no—
411C22×Dic73—41no—
412C22×Dic73—41no—
413C22×Dic73—41no—
414C22×Dic73—41no—
415C22×Dic73—41no—
416C22×Dic73—41no—
417C22×Dic73—41no—
418C22×Dic73—41no—
419C22×Dic73—416no—
420C22×Dic73C22×C414yes—
421C22×Dic73C22×C414yes—
422C22×Dic73C22×C414yescomplemented
423C22×Dic73C2411yescharacteristic
424C22×Dic73C2411yescharacteristic
425C22×Dic73C2411yescharacteristic
426C22×Dic73C2411yescharacteristic
427C22×Dic73C2411yescharacteristic
428C22×Dic73C2411yescharacteristic
429C22×Dic73C2411yescharacteristic
430C22×Dic73C2411yescharacteristic
431C22×Dic73C2411yescharacteristic
432C22×Dic73C2411yescharacteristic
433C22×Dic73C2411yescharacteristic
434C22×Dic73C2411yescharacteristic
435C22×Dic73C2411yescharacteristic
436C22×Dic73C2411yescharacteristic
437C22×Dic73C2411yescharacteristic
438C2×C4×D73—22no—
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×D73C22×C414yescomplemented
447C4⋊Dic73—22no—
448C4⋊Dic73—41no—
449C4⋊Dic73—41no—
450C4⋊Dic73C22×C414yescomplemented
451C4⋊Dic73C22×C414yescomplemented
452#11924007—22no—
453#11924007—22no—
454#11924007—22no—
455#11924007—22no—
456#11924007—22no—
457#11924007—41no—
458#11924007—41no—
459#11924007—41no—
460#11924007—41no—
461#11924007—41no—
462#11924007—41no—
463#11924007—41no—
464#11924007—41no—
465#11924007—41no—
466#11924007—41no—
467#11924007—41no—
468#11924007—41no—
469#11924007—41no—
470#11924007C22×C414yescomplemented
471#11924007C22×C414yescomplemented
472#11924007C22×C414yescomplemented
473#11924007C22×C414yescomplemented
474C22⋊Dic73—22no—
475C22⋊Dic73—22no—
476C22⋊Dic73—22no—
477C22⋊Dic73—41no—
478C22⋊Dic73—41no—
479C22⋊Dic73—41no—
480C22⋊Dic73—41no—
481C22⋊Dic73—41no—
482C22⋊Dic73—41no—
483C22⋊Dic73C22×C414yes—
484C22⋊Dic73C22×C414yes—
485C22⋊Dic73C22×C414yes—
486C22⋊Dic73C22×C414yes—
487C22⋊Dic73C22×C414yes—
488C22⋊Dic73C22×C414yes—
489C22⋊Dic73C22×C414yes—
490C22⋊Dic73C22×C414yescomplemented
491C22⋊Dic73C22×C414yescomplemented
492#11924005—22no—
493#11924005—41no—
494#11924005—41no—
495#11924005—41no—
496#11924005—41no—
497#11924005—41no—
498#11924005C22×C414yescomplemented
499#11924005C22×C414yescomplemented
500C4×Dic73—22no—
501C4×Dic73—22no—
502C4×Dic73—41no—
503C4×Dic73—41no—
504C4×Dic73—41no—
505C4×Dic73—41no—
506C4×Dic73—41no—
507C4×Dic73—41no—
508C4×Dic73—41no—
509C4×Dic73—41no—
510C4×Dic73—41no—
511C4×Dic73—41no—
512C4×Dic73—41no—
513C4×Dic73C22×C414yescomplemented
514C4×Dic73C22×C414yescomplemented
515C24×C73—22no—
516C24×C73—22no—
517C24×C73—41no—
518C24×C73—41no—
519C24×C73—41no—
520C24×C73—41no—
521C24×C73C22×C414yes—
522C24×C73C2411yescharacteristic
523C24×C73C2411yescharacteristic
524C24×C73C2411yescharacteristic
525C24×C73C2411yescharacteristic
526C2×D4×C73—22no—
527C2×D4×C73—22no—
528C2×D4×C73—41no—
529C2×D4×C73—41no—
530C2×D4×C73—41no—
531C2×D4×C73—41no—
532C2×D4×C73C22×C414yes—
533C2×D4×C73C22×C414yes—
534C2×D4×C73C22×C414yes—
535C22×C4×C73—22no—
536C22×C4×C73—22no—
537C22×C4×C73—41no—
538C22×C4×C73—41no—
539C22×C4×C73—41no—
540C22×C4×C73—41no—
541C22×C4×C73—41no—
542C22×C4×C73—41no—
543C22×C4×C73—41no—
544C22×C4×C73C2411yescharacteristic
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
555C4⋊C4×C73—41no—
556C4⋊C4×C73—41no—
557C4⋊C4×C73—41no—
558C22⋊C4×C73—22no—
559C22⋊C4×C73—22no—
560C22⋊C4×C73—41no—
561C22⋊C4×C73—41no—
562C22⋊C4×C73—41no—
563C22⋊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×C73—41no—
571C22⋊C4×C73C22×C414yes—
572C22⋊C4×C73C22×C414yes—
573C22⋊C4×C73C22×C414yes—
574C42×C73—41no—
575C42×C73—41no—
576C42×C73—41no—
577C23×C73—21no—
578C23×C73—21no—
579C23×C73—21no—
580C23×C73—21no—
581C23×C73—28no—
582C23×C73—21no—
583C23×C73—21no—
584C23×C73—21no—
585C23×C73—21no—
586C23×C73—21no—
587C23×C73—21no—
588C23×C73—21no—
589C23×C73—21no—
590C23×C73—21no—
591C23×C73—21no—
592C23×C73—21no—
593C23×C73—21no—
594C23×C73—21no—
595C23×C73—21no—
596C23×C73—21no—
597C23×C73—21no—
598C23×C73—21no—
599C23×C73—21no—
600C23×C73—44no—
601C23×C73—44no—
602C23×C73—44no—
603C23×C73—44no—
604C23×C73—44no—
605C23×C73—44no—
606C23×C73C23×C412yes—
607C23×C73C23×C412yes—
608C23×C73C23×C412yes—
609C23×C73C23×C412yes—
610C23×C73H(5,𝔽2)12yes—
611C23×C732−1+412yes—
612C23×C73C2511yescharacteristic
613C22×D73—21no—
614C22×D73—21no—
615C22×D73—21no—
616C22×D73—21no—
617C22×D73—21no—
618C22×D73—21no—
619C22×D73C23×C412yes—
620D4×C73—28no—
621D4×C73—44no—
622D4×C73—44no—
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—82no—
654C2×C4×C73—82no—
655C2×C4×C73—82no—
656C2×C4×C73C23×C412yes—
657C2×C4×C73C23×C412yes—
658C2×C4×C73C23×C412yes—
659C22⋊D73—28no—
660C22⋊D73—44no—
661C22⋊D73—44no—
662C22⋊D73—44no—
663C2×Dic73—21no—
664C2×Dic73—21no—
665C2×Dic73—21no—
666C2×Dic73—21no—
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—44no—
702C2×Dic73—44no—
703C2×Dic73—44no—
704C2×Dic73—44no—
705C2×Dic73—44no—
706C2×Dic73—44no—
707C2×Dic73—44no—
708C2×Dic73—82no—
709C2×Dic73C23×C412yes—
710C2×Dic73C23×C412yes—
711C2×Dic73C23×C412yes—
712C2×Dic73C23×C412yes—
713C2×Dic73C23×C412yes—
714C2×Dic73C23×C412yes—
715C2×Dic73C23×C412yes—
716C2×Dic73H(5,𝔽2)12yes—
717C2×Dic73H(5,𝔽2)12yes—
718C4×D73—44no—
719C4×D73—82no—
720C4×D73—82no—
721Dic146—44no—
722C22×C73—22no—
723C22×C73—22no—
724C22×C73—22no—
725C22×C73—22no—
726C22×C73—22no—
727C22×C73—22no—
728C22×C73—22no—
729C22×C73—22no—
730C22×C73—22no—
731C22×C73—22no—
732C22×C73—22no—
733C22×C73—22no—
734C22×C73—22no—
735C22×C73—22no—
736C22×C73—22no—
737C22×C73—416no—
738C22×C73—41no—
739C22×C73—41no—
740C22×C73—41no—
741C22×C73—41no—
742C22×C73—41no—
743C22×C73—41no—
744C22×C73—41no—
745C22×C73—41no—
746C22×C73—41no—
747C22×C73—41no—
748C22×C73—41no—
749C22×C73—41no—
750C22×C73#52014yes—
751C22×C73C24×C411yescharacteristic
752C22×C73C2×H(5,𝔽2)11yescharacteristic
753C22×C73C2×H(5,𝔽2)11yescharacteristic
754C22×C73C2×H(5,𝔽2)11yescharacteristic
755C22×C73C2×2−1+411yescharacteristic
756C22×C73#58511yescharacteristic
757C22×C73#58511yescharacteristic
758C2×D73—22no—
759C2×D73—22no—
760C2×D73—22no—
761C2×D73—41no—
762C2×D73—41no—
763C2×D73—41no—
764C2×D73—41no—
765C4×C73—22no—
766C4×C73—22no—
767C4×C73—22no—
768C4×C73—41no—
769C4×C73—41no—
770C4×C73—41no—
771C4×C73—41no—
772C4×C73—41no—
773C4×C73—41no—
774C4×C73—41no—
775C4×C73—41no—
776Dic73—22no—
777Dic73—22no—
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—24no—
793C2×C73—42no—
794C2×C73—42no—
795C2×C73—42no—
796C2×C73C2×#52011yescharacteristic
797C2×C73C4×H(5,𝔽2)11yescharacteristic
798C2×C73C4×H(5,𝔽2)11yescharacteristic
799C2×C73#353211yescharacteristic
800C2×C73#353311yescharacteristic
801C2×C73#354111yescharacteristic
802C2×C73#354111yescharacteristic
803D73—42no—
804C2×#538—731no—
805#2383—731no—
806#2379—731no—
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#2321D7311yescharacteristic, complemented
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×#124—731no—
842C2×#123—731no—
843C2×#123—731no—
844C2×C22⋊Q8—731no—
845C2×#121—731no—
846C2×#121—731no—
847C2×#121—731no—
848C2×#120—731no—
849C2×#120C2×D7311yescharacteristic
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×D4C2×D7311yescharacteristic
862C2×#117—731no—
863C22×C4⋊C4—731no—
864C22×C4⋊C4—731no—
865C22×C4⋊C4—731no—
866C22×C22⋊C4—731no—
867C22×C22⋊C4C2×D7311yescharacteristic
868#391—731no—
869#391—731no—
870#391—731no—
871#390—731no—
872#390—731no—
873#390—731no—
874#390C2×D7311yescharacteristic
875#390C2×D7311yescharacteristic
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
907#388C2×D7311yescharacteristic
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#386C2×D7311yescharacteristic
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#385—731no—
953#385—731no—
954#385—731no—
955#385C2×D7311yescharacteristic
956#384—731no—
957#383—731no—
958#382—731no—
959#382—731no—
960#381—731no—
961#380—731no—
962#380—731no—
963#380—731no—
964#380—731no—
965#380—731no—
966#379—731no—
967#379C2×D7311yescharacteristic
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⋊C4C2×D7311yescharacteristic
988#376—731no—
989C2×#95—731no—
990C2×#95—731no—
991C2×#95—731no—
992C25C22×D7311yescharacteristic
993C22×Q8—731no—
994C22×D4—731no—
995C22×D4—731no—
996C22×D4—731no—
997C22×D4—731no—
998C22×D4C22×D7311yescharacteristic
999C22×D4C22×D7311yescharacteristic
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×C4C22×D7311yescharacteristic
1018C23×C4C22×D7311yescharacteristic
1019C23×C4C22×D7311yescharacteristic
1020#126—738no—
1021#126—738no—
1022#124—738no—
1023#124—738no—
1024#123—738no—
1025#123—738no—
1026C22⋊Q8—738no—
1027#121—738no—
1028#121—738no—
1029#121—738no—
1030#120—738no—
1031#120C4×D7318yescomplemented
1032C4×Q8—2922no—
1033C4×D4—42no—
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⋊C4—731no—
1073C2×C4⋊C4—731no—
1074C2×C4⋊C4—731no—
1075C2×C4⋊C4C22×D7311yescharacteristic
1076C2×C4⋊C4C22×D7311yescharacteristic
1077C2×C4⋊C4C22×D7311yescharacteristic
1078C2×C22⋊C4—42no—
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—738no—
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—731no—
1106C2×C22⋊C4C22×D7311yescharacteristic
1107C2×C22⋊C4C22×D7311yescharacteristic
1108C2×C22⋊C4C22×D7311yescharacteristic
1109C2×C22⋊C4C22×D7311yescharacteristic
1110C2×C22⋊C4C22×D7311yescharacteristic
1111C2×C22⋊C4C22×D7311yescharacteristic
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#95—731no—
1169#95—731no—
1170#95—731no—
1171#95—731no—
1172#95—731no—
1173#95—731no—
1174#95C22×D7311yescharacteristic
1175#95C22×D7311yescharacteristic
1176#95C22×D7311yescharacteristic
1177#95C22×D7311yescharacteristic
1178#95C22×D7311yescharacteristic
1179#95C22×D7311yescharacteristic
1180C24—22no—
1181C24—22no—
1182C24—41no—
1183C24—41no—
1184C24—41no—
1185C24—41no—
1186C24—731no—
1187C24C2×C4×D7314yes—
1188C24C23×D7311yescharacteristic
1189C24C23×D7311yescharacteristic
1190C24C23×D7311yescharacteristic
1191C24C23×D7311yescharacteristic
1192C2×Q8—2921no—
1193C2×Q8—2921no—
1194C2×Q8—734no—
1195C2×D4—22no—
1196C2×D4—22no—
1197C2×D4—41no—
1198C2×D4—41no—
1199C2×D4—41no—
1200C2×D4—41no—
1201C2×D4—2921no—
1202C2×D4—2921no—
1203C2×D4—2921no—
1204C2×D4—2921no—
1205C2×D4—2921no—
1206C2×D4—2921no—
1207C2×D4—734no—
1208C2×D4—734no—
1209C2×D4—734no—
1210C2×D4—734no—
1211C2×D4—1462no—
1212C2×D4—1462no—
1213C2×D4C2×C4×D7314yes—
1214C2×D4C2×C4×D7314yes—
1215C2×D4C2×C4×D7314yes—
1216C22×C4—22no—
1217C22×C4—22no—
1218C22×C4—41no—
1219C22×C4—41no—
1220C22×C4—41no—
1221C22×C4—41no—
1222C22×C4—41no—
1223C22×C4—41no—
1224C22×C4—41no—
1225C22×C4—2921no—
1226C22×C4—2921no—
1227C22×C4—2921no—
1228C22×C4—2921no—
1229C22×C4—2921no—
1230C22×C4—2921no—
1231C22×C4—2921no—
1232C22×C4—29216no—
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—2921no—
1244C22×C4—2921no—
1245C22×C4—2921no—
1246C22×C4—2921no—
1247C22×C4—2921no—
1248C22×C4—2921no—
1249C22×C4—2921no—
1250C22×C4—2921no—
1251C22×C4—734no—
1252C22×C4—734no—
1253C22×C4—734no—
1254C22×C4—734no—
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—731no—
1267C22×C4—731no—
1268C22×C4—731no—
1269C22×C4—731no—
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×C4—1462no—
1279C22×C4—1462no—
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—2921no—
1295C4⋊C4—2921no—
1296C4⋊C4—2921no—
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—22no—
1322C22⋊C4—22no—
1323C22⋊C4—41no—
1324C22⋊C4—41no—
1325C22⋊C4—41no—
1326C22⋊C4—41no—
1327C22⋊C4—41no—
1328C22⋊C4—41no—
1329C22⋊C4—41no—
1330C22⋊C4—41no—
1331C22⋊C4—41no—
1332C22⋊C4—41no—
1333C22⋊C4—41no—
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—2921no—
1344C22⋊C4—2921no—
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—734no—
1354C22⋊C4—734no—
1355C22⋊C4—734no—
1356C22⋊C4—1462no—
1357C22⋊C4—1462no—
1358C22⋊C4—1462no—
1359C22⋊C4—1462no—
1360C22⋊C4C2×C4×D7314yes—
1361C22⋊C4C2×C4×D7314yes—
1362C22⋊C4C2×C4×D7314yes—
1363C42—41no—
1364C42—41no—
1365C42—41no—
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—734no—
1379C42—1462no—
1380C42—1462no—
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—21no—
1394C23—21no—
1395C23—21no—
1396C23—21no—
1397C23—21no—
1398C23—21no—
1399C23—21no—
1400C23—21no—
1401C23—21no—
1402C23—21no—
1403C23—28no—
1404C23—44no—
1405C23—44no—
1406C23—44no—
1407C23—44no—
1408C23—44no—
1409C23—44no—
1410C23—732no—
1411C23—1461no—
1412C23—1461no—
1413C23—1461no—
1414C23—1461no—
1415C23—1461no—
1416C23—1461no—
1417C23C22×C4×D7312yes—
1418C23C22×C4×D7312yes—
1419C23C22×C4×D7312yes—
1420C23C22×C4×D7312yes—
1421C23#1455663612yes—
1422C23#1455663812yes—
1423C23C24×D7311yescharacteristic
1424Q8—2924no—
1425D4—28no—
1426D4—44no—
1427D4—44no—
1428D4—2924no—
1429D4—2924no—
1430D4—2924no—
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—82no—
1463C2×C4—82no—
1464C2×C4—82no—
1465C2×C4—2924no—
1466C2×C4—2924no—
1467C2×C4—2924no—
1468C2×C4—2924no—
1469C2×C4—2924no—
1470C2×C4—2924no—
1471C2×C4—2924no—
1472C2×C4—2924no—
1473C2×C4—2924no—
1474C2×C4—2924no—
1475C2×C4—5842no—
1476C2×C4—5842no—
1477C2×C4—5842no—
1478C2×C4—732no—
1479C2×C4—732no—
1480C2×C4—732no—
1481C2×C4—732no—
1482C2×C4—732no—
1483C2×C4—732no—
1484C2×C4—732no—
1485C2×C4—732no—
1486C2×C4—732no—
1487C2×C4—1461no—
1488C2×C4—1461no—
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×C4—1461no—
1522C2×C4—1461no—
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—22no—
1533C22—22no—
1534C22—22no—
1535C22—22no—
1536C22—22no—
1537C22—22no—
1538C22—22no—
1539C22—22no—
1540C22—22no—
1541C22—416no—
1542C22—41no—
1543C22—41no—
1544C22—41no—
1545C22—41no—
1546C22—41no—
1547C22—41no—
1548C22—41no—
1549C22—41no—
1550C22—41no—
1551C22—41no—
1552C22—41no—
1553C22—41no—
1554C22—2921no—
1555C22—2921no—
1556C22—2921no—
1557C22—2921no—
1558C22—1462no—
1559C22—1462no—
1560C22—1462no—
1561C22#1798906614yes—
1562C22C23×C4×D7311yescharacteristic
1563C22H(5,𝔽2)×D7311yescharacteristic
1564C22H(5,𝔽2)×D7311yescharacteristic
1565C22C2×#1455663611yescharacteristic
1566C22C2×#1455663811yescharacteristic
1567C22#1798942211yescharacteristic
1568C22#1798942211yescharacteristic
1569C4—22no—
1570C4—22no—
1571C4—22no—
1572C4—41no—
1573C4—41no—
1574C4—41no—
1575C4—41no—
1576C4—41no—
1577C4—41no—
1578C4—41no—
1579C4—41no—
1580C4—2921no—
1581C4—2921no—
1582C4—2921no—
1583C4—2921no—
1584C4—2921no—
1585C4—2921no—
1586C4—1462no—
1587C4—1462no—
1588C4—1462no—
1589C4—1462no—
1590C4—1462no—
1591C4—1462no—
1592C4—1462no—
1593C4—1462no—
1594C4—1462no—
1595C2—24no—
1596C2—42no—
1597C2—42no—
1598C2—42no—
1599C2—2922no—
1600C2C2×#1798906611yescharacteristic
1601C2#2262313511yescharacteristic
1602C2#2262313511yescharacteristic
1603C2#2262408511yescharacteristic
1604C2#2262409211yescharacteristic
1605C2#2262421111yescharacteristic
1606C2#2262421111yescharacteristic
subgroupG/H
center, FrattiniC23C24×D73
commutatorC22×C73C24×C4
FittingC73×#2321C2
socle, cosocleC23×C73C25
prime radicalC2×#17989172C2
hypercenter#2321D73
hypocenterC73#34416
LCSG ▷ C22×C73 ▷ C73
UCSC1 ◁ C23 ◁ #2321

Complements

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

NH ≅ G/Ntype
2. #22613118C2semidirect
3. #22613100C2semidirect
4. #22613083C2semidirect
5. #22613081C2semidirect
6. #22613048C2semidirect
7. #22613009C2semidirect
8. #22612997C2semidirect
9. #22612976C2semidirect
10. #22612952C2semidirect
11. #22612942C2semidirect
12. #22612931C2semidirect
13. #22612929C2semidirect
14. #22612865C2semidirect
15. #22612858C2semidirect
16. #22612836C2semidirect
17. #22612829C2semidirect
18. #22612740C2semidirect
19. #22612719C2semidirect
20. #22612713C2semidirect
21. #22612704C2semidirect
22. #22612641C2semidirect
23. #22612632C2semidirect
24. #22612617C2semidirect
25. #22612601C2semidirect
26. #22612589C2semidirect
27. #22612527C2semidirect
28. #120×Dic73C2semidirect
29. #22612430C2semidirect
30. C2×#17988459C2semidirect
31. C73×#2321C2semidirect
33. #17989172C4semidirect
45. C2×#14556556C22semidirect
55. C2×#14556551C22semidirect
56. C2×#14556547C22semidirect
59. C2×C4⋊C4×D73C22semidirect
61. #17988493C22semidirect
62. #17988491C22semidirect
63. #17988491C22semidirect
66. #17988487C22semidirect
67. #17988485C22semidirect
68. #17988484C22semidirect
69. #17988484C22semidirect
70. #17988483C22semidirect
71. #17988483C22semidirect
72. #17988482C22semidirect
73. #17988482C22semidirect
74. #17988482C22semidirect
81. #17988481C22semidirect
82. #17988481C22semidirect
83. #17988481C22semidirect
84. #17988478C22semidirect
85. #17988477C22semidirect
86. #17988476C22semidirect
87. #17988476C22semidirect
94. #17988475C22semidirect
95. #17988474C22semidirect
96. #17988474C22semidirect
97. #17988472C22semidirect
98. #17988472C22semidirect
99. #17988471C22semidirect
100. #17988471C22semidirect
101. #17988471C22semidirect
102. #17988470C22semidirect
103. #17988470C22semidirect
104. #17988469C22semidirect
105. #17988469C22semidirect
106. #17988468C22semidirect
111. #17988466C22semidirect
117. #17988463C22semidirect
121. #17988461C22semidirect
122. #17988461C22semidirect
124. #17988460C22semidirect
136. #17988459C22semidirect
137. #17988459C22semidirect
138. #17988458C22semidirect
139. #17988456C22semidirect
140. #17988454C22semidirect
141. #17988452C22semidirect
142. #17988451C22semidirect
143. #17988449C22semidirect
144. #17988446C22semidirect
147. #17988445C22semidirect
148. #17988445C22semidirect
150. C4×#11924007C22semidirect
151. C4×#11924007C22semidirect
152. C4×C4⋊Dic73C22semidirect
153. #17988438C22semidirect
154. #17988438C22semidirect
155. #17988438C22semidirect
156. #17988438C22semidirect
165. C4×#11924005C22semidirect
166. C4×#11924005C22semidirect
168. C4×C22⋊Dic73C22semidirect
169. #17988433C22semidirect
172. C2×#14556498C22semidirect
209. #14556584C2×C4semidirect
210. #14556584C2×C4semidirect
211. #14556578C2×C4semidirect
212. #14556577C2×C4semidirect
213. #14556573C2×C4semidirect
214. #14556572C2×C4semidirect
215. #14556568C2×C4semidirect
216. #14556563C2×C4semidirect
217. #14556563C2×C4semidirect
218. #14556562C2×C4semidirect
219. #14556560C2×C4semidirect
224. D4×Dic73C2×C4semidirect
230. #14556551C2×C4semidirect
262. C2×C22⋊Dic73C2×C4semidirect
345. #120×C73C2×C4semidirect
379. C2×Dic146C22×C4semidirect
391. C2×C22⋊D73C22×C4semidirect
422. C22×Dic73C22×C4semidirect
446. C2×C4×D73C22×C4semidirect
450. C4⋊Dic73C22×C4semidirect
451. C4⋊Dic73C22×C4semidirect
470. #11924007C22×C4semidirect
471. #11924007C22×C4semidirect
472. #11924007C22×C4semidirect
473. #11924007C22×C4semidirect
490. C22⋊Dic73C22×C4semidirect
491. C22⋊Dic73C22×C4semidirect
498. #11924005C22×C4semidirect
499. #11924005C22×C4semidirect
513. C4×Dic73C22×C4semidirect
514. C4×Dic73C22×C4semidirect
830. #2321D73semidirect
835. C73#34416semidirect
1031. #120C4×D73semidirect

Maximal subgroups

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

subgroupindex
C2×#179891722
#226131182
#226131002
#226130832
#226130812
#226130482
#226130092
#226129972
#226129762
#226129522
#226129422
#226129312
#226129292
#226128652
#226128582
#226128362
#226128292
#226127402
#226127192
#226127132
#226127042
#226126412
#226126322
#226126172
#226126012
#226125892
#226125272
#120×Dic732
#226124302
C2×#179884592
C73×#23212
#3441673