Finite Group Databasebeta

← #33250365

Subgroups — #33250365

Order 18688.

2314 conjugacy classes of subgroups.

The subgroup lattice has 1570 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17989171C211yesmaximal, characteristic
2#22613118C211yesmaximal, characteristic, complemented
3#22613092C211yesmaximal, characteristic, complemented
4#22613077C211yesmaximal, characteristic, complemented
5#22613069C211yesmaximal, characteristic, complemented
6#22613052C211yesmaximal, characteristic, complemented
7#22613051C211yesmaximal, characteristic, complemented
8#22613051C211yesmaximal, characteristic, complemented
9#22613006C211yesmaximal, characteristic, complemented
10#22612963C211yesmaximal, characteristic, complemented
11#22612925C211yesmaximal, characteristic, complemented
12#22612911C211yesmaximal, characteristic, complemented
13#22612877C211yesmaximal, characteristic, complemented
14#22612865C211yesmaximal, characteristic, complemented
15#22612779C211yesmaximal, characteristic, complemented
16#22612774C211yesmaximal, characteristic, complemented
17#22612743C211yesmaximal, characteristic, complemented
18#22612719C211yesmaximal, characteristic, complemented
19#22612691C211yesmaximal, characteristic, complemented
20#22612691C211yesmaximal, characteristic, complemented
21#22612645C211yesmaximal, characteristic, complemented
22#22612632C211yesmaximal, characteristic, complemented
23#22612621C211yesmaximal, characteristic, complemented
24#22612619C211yesmaximal, characteristic, complemented
25#22612591C211yesmaximal, characteristic, complemented
26#22612584C211yesmaximal, characteristic, complemented
27#22612575C211yesmaximal, characteristic, complemented
28C4×#14556573C211yesmaximal, characteristic, complemented
29#22612443C211yesmaximal, characteristic, complemented
30#22612375C211yesmaximal, characteristic, complemented
31C73×#2372C211yesmaximal, characteristic, complemented
32#17989171C4116yescomplemented
33C2×#14556585C2211yescharacteristic
34C2×#14556584C2211yescharacteristic
35C2×#14556580C2211yescharacteristic
36C2×#14556575C2211yescharacteristic
37C2×#14556573C2211yescharacteristic
38C2×#14556567C2211yescharacteristic
39C2×#14556564C2211yescharacteristic
40C2×#14556564C2211yescharacteristic
41C2×#14556563C2211yescharacteristic
42C2×#14556561C2211yescharacteristic
43C2×#14556559C2211yescharacteristic
44C2×Q8×Dic73C2211yescharacteristic, complemented
45C2×C4×D292C2211yescharacteristic
46C2×D4×Dic73C2211yescharacteristic
47C2×#14556553C2211yescharacteristic
48C2×C4×C22⋊D73C2211yescharacteristic
49C2×#14556551C2211yescharacteristic
50C2×#14556551C2211yescharacteristic
51C2×#14556551C2211yescharacteristic, complemented
52C2×#14556549C2211yescharacteristic
53C2×#14556548C2211yescharacteristic
54C2×#14556547C2211yescharacteristic, complemented
55C22×#11924005C2211yescharacteristic
56C2×C22⋊C4×D73C2211yescharacteristic
57C2×C22⋊C4×D73C2211yescharacteristic
58C2×C42×D73C2211yescharacteristic, complemented
59#17988494C2211yescharacteristic, complemented
60#17988490C2211yescharacteristic
61#17988489C2211yescharacteristic
62#17988489C2211yescharacteristic
63#17988489C2211yescharacteristic
64#17988487C2211yescharacteristic
65#17988487C2211yescharacteristic
66#17988487C2211yescharacteristic
67#17988487C2211yescharacteristic
68#17988487C2211yescharacteristic, complemented
69#17988485C2211yescharacteristic, complemented
70#17988485C2211yescharacteristic, complemented
71#17988484C2211yescharacteristic, complemented
72#17988484C2211yescharacteristic, complemented
73#17988483C2211yescharacteristic, complemented
74#17988482C2211yescharacteristic, complemented
75#17988481C2211yescharacteristic
76#17988481C2211yescharacteristic
77#17988481C2211yescharacteristic
78#17988480C2211yescharacteristic
79#17988480C2211yescharacteristic
80#17988480C2211yescharacteristic, complemented
81#17988480C2211yescharacteristic, complemented
82#17988479C2211yescharacteristic
83#17988479C2211yescharacteristic
84#17988479C2211yescharacteristic
85#17988479C2211yescharacteristic
86#17988479C2211yescharacteristic
87#17988478C2211yescharacteristic
88#17988478C2211yescharacteristic
89#17988478C2211yescharacteristic
90#17988478C2211yescharacteristic
91#17988477C2211yescharacteristic
92#17988477C2211yescharacteristic, complemented
93#17988476C2211yescharacteristic
94#17988476C2211yescharacteristic
95#17988476C2211yescharacteristic
96#17988476C2211yescharacteristic
97#17988476C2211yescharacteristic
98#17988476C2211yescharacteristic
99#17988476C2211yescharacteristic, complemented
100#17988476C2211yescharacteristic, complemented
101#17988476C2211yescharacteristic, complemented
102#17988475C2211yescharacteristic
103#17988474C2211yescharacteristic, complemented
104#17988474C2211yescharacteristic, complemented
105#17988474C2211yescharacteristic, complemented
106#17988472C2211yescharacteristic, complemented
107#17988472C2211yescharacteristic, complemented
108#17988472C2211yescharacteristic, complemented
109#17988471C2211yescharacteristic, complemented
110#17988471C2211yescharacteristic, complemented
111#17988471C2211yescharacteristic, complemented
112#17988470C2211yescharacteristic, complemented
113#17988469C2211yescharacteristic, complemented
114#17988469C2211yescharacteristic, complemented
115#17988466C2211yescharacteristic
116#17988466C2211yescharacteristic
117#17988466C2211yescharacteristic, complemented
118#17988465C2211yescharacteristic
119#17988465C2211yescharacteristic
120#17988465C2211yescharacteristic
121#17988465C2211yescharacteristic
122#17988464C2211yescharacteristic
123#17988464C2211yescharacteristic
124#17988463C2211yescharacteristic
125#17988463C2211yescharacteristic
126#17988463C2211yescharacteristic, complemented
127#17988462C2211yescharacteristic
128#17988462C2211yescharacteristic, complemented
129#17988461C2211yescharacteristic
130#17988461C2211yescharacteristic
131#17988461C2211yescharacteristic
132#17988461C2211yescharacteristic, complemented
133#17988461C2211yescharacteristic, complemented
134#17988461C2211yescharacteristic, complemented
135#17988460C2211yescharacteristic
136#17988459C2211yescharacteristic
137#17988459C2211yescharacteristic
138#17988458C2211yescharacteristic
139#17988456C2211yescharacteristic, complemented
140#17988454C2211yescharacteristic, complemented
141#17988449C2211yescharacteristic
142#17988449C2211yescharacteristic
143#17988449C2211yescharacteristic, complemented
144#17988446C2211yescharacteristic
145#17988446C2211yescharacteristic
146#17988446C2211yescharacteristic, complemented
147#17988445C2211yescharacteristic, complemented
148#17988445C2211yescharacteristic, complemented
149#17988442C2211yescharacteristic
150#17988442C2211yescharacteristic
151C4×#11924007C2211yescharacteristic, complemented
152C4×#11924007C2211yescharacteristic, complemented
153C4×C4⋊Dic73C2211yescharacteristic, complemented
154C4×C4⋊Dic73C2211yescharacteristic, complemented
155C4×C4⋊Dic73C2211yescharacteristic, complemented
156#17988438C2211yescharacteristic, complemented
157#17988438C2211yescharacteristic, complemented
158#17988438C2211yescharacteristic, complemented
159#17988438C2211yescharacteristic, complemented
160C22⋊C4×Dic73C2211yescharacteristic
161C22⋊C4×Dic73C2211yescharacteristic, complemented
162C4×#11924005C2211yescharacteristic
163C4×#11924005C2211yescharacteristic
164C4×#11924005C2211yescharacteristic
165C4×#11924005C2211yescharacteristic
166C4×#11924005C2211yescharacteristic, complemented
167C4×#11924005C2211yescharacteristic, complemented
168C4×C22⋊Dic73C2211yescharacteristic
169#17988434C2211yescharacteristic
170#17988434C2211yescharacteristic
171#17988433C2211yescharacteristic, complemented
172C2×#14556498C2211yescharacteristic, 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
182C4×C22⋊C4×C73C2211yescharacteristic
183C4×C22⋊C4×C73C2211yescharacteristic
184C4×C22⋊C4×C73C2211yescharacteristic, complemented
185C4×C22⋊C4×C73C2211yescharacteristic, complemented
186#376×C73C2211yescharacteristic, complemented
187#376×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×D73C2311yescharacteristic
199C22×C4×D73C2311yescharacteristic
200C22×C4×D73C2311yescharacteristic
201C22×C4×D73C2311yescharacteristic
202C22×C4×D73C2311yescharacteristic
203C22×C4×D73C2311yescharacteristic
204C22×C4×D73C2311yescharacteristic
205#14556585C2×C418yescomplemented
206#14556584C2×C418yescomplemented
207#14556580C2×C418yescomplemented
208#14556575C2×C418yescomplemented
209#14556573C2×C418yescomplemented
210#14556567C2×C418yescomplemented
211#14556564C2×C418yescomplemented
212#14556564C2×C418yescomplemented
213#14556563C2×C418yescomplemented
214#14556561C2×C418yescomplemented
215#14556559C2×C418yescomplemented
216Q8×Dic73—42no—
217C4×D292C2×C418yescomplemented
218D4×Dic73—42no—
219#14556553—42no—
220C4×C22⋊D73—42no—
221#14556551—42no—
222#14556551—42no—
223#14556551C2×C418yescomplemented
224#14556549—42no—
225#14556548—42no—
226#14556547—42no—
227C2×C4⋊Dic73C2311yescharacteristic
228C2×C4⋊Dic73C2311yescharacteristic
229C2×C4⋊Dic73C2311yescharacteristic
230C2×C4⋊Dic73C2311yescharacteristic
231C2×C4⋊Dic73C2311yescharacteristic
232C2×C4⋊Dic73C2311yescharacteristic
233C2×C4⋊Dic73C2311yescharacteristic
234C2×C4⋊Dic73C2311yescharacteristic
235C2×#11924007C2311yescharacteristic
236C2×#11924007C2311yescharacteristic
237C2×#11924007C2311yescharacteristic
238C2×#11924007C2311yescharacteristic
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×C22⋊Dic73C2311yescharacteristic
252C2×C22⋊Dic73C2311yescharacteristic
253C2×C22⋊Dic73C2311yescharacteristic
254C2×C22⋊Dic73C2311yescharacteristic
255C2×C22⋊Dic73C2311yescharacteristic
256C2×C22⋊Dic73C2311yescharacteristic
257C2×C22⋊Dic73C2311yescharacteristic
258C2×C22⋊Dic73C2311yescharacteristic
259C2×#11924005—42no—
260C2×#11924005C2311yescharacteristic
261C2×#11924005C2311yescharacteristic
262C2×#11924005C2311yescharacteristic
263C2×#11924005C2311yescharacteristic
264C2×#11924005C2311yescharacteristic
265C2×#11924005C2311yescharacteristic
266C2×#11924005C2311yescharacteristic
267C2×#11924005C2311yescharacteristic
268C2×#11924005C2311yescharacteristic
269C2×#11924005C2311yescharacteristic
270C2×#11924005C2311yescharacteristic
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
288C22⋊C4×D73—42no—
289C22⋊C4×D73C2×C418yescomplemented
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
304C2×C4×Dic73C2311yescharacteristic
305C42×D73—42no—
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
334C22×Q8×C73C2311yescharacteristic
335C22×D4×C73C2311yescharacteristic
336C23×C4×C73C2311yescharacteristic
337C23×C4×C73C2311yescharacteristic
338#124×C73C2×C418yescomplemented
339C2×C4⋊C4×C73C2311yescharacteristic
340C2×C4⋊C4×C73C2311yescharacteristic
341C2×C22⋊C4×C73C2311yescharacteristic
342C2×C22⋊C4×C73C2311yescharacteristic
343C2×C22⋊C4×C73C2311yescharacteristic
344C2×C22⋊C4×C73C2311yescharacteristic
345C2×C22⋊C4×C73C2311yescharacteristic
346C2×C22⋊C4×C73C2311yescharacteristic
347C2×C22⋊C4×C73C2311yescharacteristic
348C2×C22⋊C4×C73C2311yescharacteristic
349C2×C22⋊C4×C73C2311yescharacteristic
350C2×C22⋊C4×C73C2311yescharacteristic
351C2×C42×C73C2311yescharacteristic
352C2×C42×C73C2311yescharacteristic
353C2×C42×C73C2311yescharacteristic
354C2×C42×C73C2311yescharacteristic
355C2×C42×C73C2311yescharacteristic
356C2×C42×C73C2311yescharacteristic
357C2×C42×C73C2311yescharacteristic
358#95×C73C2311yescharacteristic
359#95×C73C2311yescharacteristic
360#95×C73C2311yescharacteristic
361#95×C73C2311yescharacteristic
362#95×C73C2311yescharacteristic
363#95×C73C2311yescharacteristic
364#95×C73C2311yescharacteristic
365#95×C73C2311yescharacteristic
366#95×C73C2311yescharacteristic
367#95×C73C2311yescharacteristic
368#95×C73C2311yescharacteristic
369#95×C73C2311yescharacteristic
370C23×D73—41no—
371C23×D73—41no—
372C23×D73—41no—
373C23×D73—41no—
374C23×D73—41no—
375C23×D73—41no—
376C23×D73C22×C414yes—
377C23×D73C2411yescharacteristic
378C23×D73C2411yescharacteristic
379C23×D73C2411yescharacteristic
380C2×D292—41no—
381C2×D292—41no—
382C2×D292—41no—
383C2×D292—41no—
384C2×D292C22×C414yes—
385C2×D292C22×C414yes—
386C2×C22⋊D73—41no—
387C2×C22⋊D73—41no—
388C2×C22⋊D73—41no—
389C2×C22⋊D73—41no—
390C2×C22⋊D73—41no—
391C2×C22⋊D73—41no—
392C2×C22⋊D73—41no—
393C2×C22⋊D73—41no—
394C2×C22⋊D73C22×C414yes—
395C2×C22⋊D73C22×C414yes—
396C2×C22⋊D73C22×C414yes—
397C2×C22⋊D73C22×C414yes—
398C22×Dic73—22no—
399C22×Dic73—41no—
400C22×Dic73—41no—
401C22×Dic73—41no—
402C22×Dic73—41no—
403C22×Dic73—41no—
404C22×Dic73—41no—
405C22×Dic73—41no—
406C22×Dic73C22×C414yes—
407C22×Dic73C2411yescharacteristic
408C22×Dic73C2411yescharacteristic
409C22×Dic73C2411yescharacteristic
410C22×Dic73C2411yescharacteristic
411C22×Dic73C2411yescharacteristic
412C22×Dic73C2411yescharacteristic
413C22×Dic73C2411yescharacteristic
414C22×Dic73C2411yescharacteristic
415C22×Dic73C2411yescharacteristic
416C22×Dic73C2411yescharacteristic
417C22×Dic73C2411yescharacteristic
418C22×Dic73C2411yescharacteristic
419C22×Dic73C2411yescharacteristic
420C2×C4×D73—22no—
421C2×C4×D73—22no—
422C2×C4×D73—22no—
423C2×C4×D73—41no—
424C2×C4×D73—41no—
425C2×C4×D73—41no—
426C2×C4×D73—41no—
427C2×C4×D73—41no—
428C2×C4×D73—41no—
429C2×C4×D73—41no—
430C2×C4×D73—41no—
431C2×C4×D73—41no—
432C2×C4×D73—41no—
433C2×C4×D73—41no—
434C2×C4×D73—41no—
435C2×C4×D73—41no—
436C2×C4×D73—41no—
437C2×C4×D73—41no—
438C2×C4×D73C22×C414yes—
439C2×C4×D73C22×C414yes—
440C2×C4×D73C22×C414yes—
441C4⋊Dic73—22no—
442C4⋊Dic73—22no—
443C4⋊Dic73—41no—
444C4⋊Dic73—41no—
445C4⋊Dic73—41no—
446C4⋊Dic73—41no—
447C4⋊Dic73C22×C414yes—
448C4⋊Dic73C22×C414yes—
449#11924007—22no—
450#11924007—41no—
451#11924007—41no—
452#11924007—41no—
453#11924007—41no—
454#11924007—41no—
455#11924007—41no—
456#11924007—41no—
457#11924007—41no—
458#11924007—41no—
459#11924007—41no—
460#11924007—41no—
461#11924007C22×C414yes—
462#11924007C22×C414yes—
463#11924007C22×C414yes—
464#11924007C22×C414yes—
465C22⋊Dic73—22no—
466C22⋊Dic73—41no—
467C22⋊Dic73—41no—
468C22⋊Dic73—41no—
469C22⋊Dic73—41no—
470C22⋊Dic73—41no—
471C22⋊Dic73C22×C414yes—
472C22⋊Dic73C22×C414yes—
473#11924005—22no—
474#11924005—22no—
475#11924005—22no—
476#11924005—41no—
477#11924005—41no—
478#11924005—41no—
479#11924005—41no—
480#11924005—41no—
481#11924005—41no—
482#11924005—41no—
483#11924005—41no—
484#11924005—41no—
485#11924005—41no—
486#11924005—41no—
487#11924005—41no—
488#11924005—41no—
489#11924005—41no—
490#11924005—41no—
491#11924005—41no—
492#11924005—41no—
493#11924005C22×C414yes—
494#11924005C22×C414yes—
495#11924005C22×C414yes—
496#11924005C22×C414yes—
497#11924005C22×C414yes—
498#11924005C22×C414yes—
499#11924005C22×C414yes—
500#11924005C22×C414yes—
501C4×Dic73—22no—
502C4×Dic73—22no—
503C4×Dic73—22no—
504C4×Dic73—22no—
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×Dic73—41no—
514C4×Dic73—41no—
515C4×Dic73C22×C414yes—
516C24×C73C2411yescharacteristic
517C24×C73C2411yescharacteristic
518C2×Q8×C73—41no—
519C2×Q8×C73—41no—
520C2×Q8×C73C22×C414yes—
521C2×D4×C73—41no—
522C2×D4×C73—41no—
523C2×D4×C73C22×C414yes—
524C22×C4×C73—22no—
525C22×C4×C73—41no—
526C22×C4×C73—41no—
527C22×C4×C73—41no—
528C22×C4×C73—41no—
529C22×C4×C73—41no—
530C22×C4×C73C2411yescharacteristic
531C22×C4×C73C2411yescharacteristic
532C22×C4×C73C2411yescharacteristic
533C22×C4×C73C2411yescharacteristic
534C22×C4×C73C2411yescharacteristic
535C22×C4×C73C2411yescharacteristic
536C22×C4×C73C2411yescharacteristic
537C22×C4×C73C2411yescharacteristic
538C22×C4×C73C2411yescharacteristic
539C22×C4×C73C2411yescharacteristic
540C22×C4×C73C2411yescharacteristic
541C22×C4×C73C2411yescharacteristic
542C22×C4×C73C2411yescharacteristic
543C4⋊C4×C73—41no—
544C4⋊C4×C73—41no—
545C22⋊C4×C73—22no—
546C22⋊C4×C73—41no—
547C22⋊C4×C73—41no—
548C22⋊C4×C73—41no—
549C22⋊C4×C73—41no—
550C22⋊C4×C73—41no—
551C22⋊C4×C73C22×C414yes—
552C22⋊C4×C73C22×C414yes—
553C22⋊C4×C73C22×C414yes—
554C22⋊C4×C73C22×C414yes—
555C42×C73—22no—
556C42×C73—41no—
557C42×C73—41no—
558C42×C73—41no—
559C42×C73—41no—
560C42×C73—41no—
561C42×C73C22×C414yes—
562C23×C73—21no—
563C23×C73—21no—
564C23×C73—21no—
565C23×C73—21no—
566C23×C73—21no—
567C23×C73—21no—
568C23×C73—21no—
569C23×C73—21no—
570C23×C73—21no—
571C23×C73—21no—
572C23×C73—21no—
573C23×C73—21no—
574C23×C73C23×C412yes—
575C23×C73C23×C412yes—
576C23×C73C2511yescharacteristic
577C22×D73—21no—
578C22×D73—21no—
579C22×D73—21no—
580C22×D73—21no—
581C22×D73—21no—
582C22×D73—21no—
583C22×D73—21no—
584C22×D73—21no—
585C22×D73—21no—
586C22×D73—21no—
587C22×D73—21no—
588C22×D73—21no—
589C22×D73—21no—
590C22×D73—21no—
591C22×D73—21no—
592C22×D73—21no—
593C22×D73—21no—
594C22×D73—21no—
595C22×D73—44no—
596C22×D73—44no—
597C22×D73—44no—
598C22×D73—82no—
599C22×D73—82no—
600C22×D73—82no—
601C22×D73—82no—
602C22×D73C23×C412yes—
603C22×D73C23×C412yes—
604C22×D73C23×C412yes—
605Q8×C73—44no—
606D4×C73—44no—
607C2×C4×C73—21no—
608C2×C4×C73—21no—
609C2×C4×C73—21no—
610C2×C4×C73—21no—
611C2×C4×C73—21no—
612C2×C4×C73—21no—
613C2×C4×C73—21no—
614C2×C4×C73—21no—
615C2×C4×C73—21no—
616C2×C4×C73—21no—
617C2×C4×C73—21no—
618C2×C4×C73—21no—
619C2×C4×C73—21no—
620C2×C4×C73—21no—
621C2×C4×C73—21no—
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—82no—
641C2×C4×C73—82no—
642C2×C4×C73C23×C412yes—
643C2×C4×C73C23×C412yes—
644C2×C4×C73C23×C412yes—
645C2×C4×C73C23×C412yes—
646C2×C4×C73C23×C412yes—
647C2×C4×C73H(5,𝔽2)12yes—
648C22⋊D73—44no—
649C22⋊D73—44no—
650C22⋊D73—44no—
651C22⋊D73—44no—
652C2×Dic73—21no—
653C2×Dic73—21no—
654C2×Dic73—21no—
655C2×Dic73—21no—
656C2×Dic73—21no—
657C2×Dic73—21no—
658C2×Dic73—21no—
659C2×Dic73—21no—
660C2×Dic73—21no—
661C2×Dic73—21no—
662C2×Dic73—21no—
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—44no—
686C2×Dic73—82no—
687C2×Dic73—82no—
688C2×Dic73C23×C412yes—
689C2×Dic73C23×C412yes—
690C2×Dic73C23×C412yes—
691C2×Dic73C23×C412yes—
692C2×Dic73C23×C412yes—
693C2×Dic73H(5,𝔽2)12yes—
694D292—44no—
695D292—44no—
696C4×D73—44no—
697C4×D73—44no—
698C4×D73—44no—
699C4×D73—44no—
700C4×D73—44no—
701C4×D73—82no—
702C4×D73—82no—
703C22×C73—22no—
704C22×C73—22no—
705C22×C73—22no—
706C22×C73—22no—
707C22×C73—22no—
708C22×C73—22no—
709C22×C73—41no—
710C22×C73—41no—
711C22×C73—41no—
712C22×C73—41no—
713C22×C73—41no—
714C22×C73—41no—
715C22×C73—41no—
716C22×C73—41no—
717C22×C73C24×C411yescharacteristic
718C22×C73C2×H(5,𝔽2)11yescharacteristic
719C22×C73C2×H(5,𝔽2)11yescharacteristic
720C22×C73#58511yescharacteristic
721C22×C73#58511yescharacteristic
722C22×C73#58511yescharacteristic
723C22×C73#58511yescharacteristic
724C2×D73—22no—
725C2×D73—22no—
726C2×D73—22no—
727C2×D73—22no—
728C2×D73—22no—
729C2×D73—22no—
730C2×D73—22no—
731C2×D73—22no—
732C2×D73—22no—
733C2×D73—41no—
734C2×D73—41no—
735C2×D73—41no—
736C2×D73—41no—
737C2×D73—41no—
738C2×D73—41no—
739C2×D73—41no—
740C2×D73—41no—
741C2×D73—41no—
742C2×D73—41no—
743C2×D73—41no—
744C2×D73—41no—
745C2×D73—88no—
746C4×C73—22no—
747C4×C73—22no—
748C4×C73—22no—
749C4×C73—22no—
750C4×C73—22no—
751C4×C73—22no—
752C4×C73—41no—
753C4×C73—41no—
754C4×C73—41no—
755C4×C73—41no—
756C4×C73—41no—
757C4×C73—41no—
758C4×C73—41no—
759Dic73—22no—
760Dic73—22no—
761Dic73—22no—
762Dic73—22no—
763Dic73—22no—
764Dic73—22no—
765Dic73—41no—
766Dic73—41no—
767Dic73—41no—
768Dic73—41no—
769Dic73—41no—
770Dic73—41no—
771Dic73—41no—
772#34451—731nomaximal, Sylow
773C2×C73—42no—
774C2×C73—42no—
775C2×C73#342811yescharacteristic
776C2×C73C4×H(5,𝔽2)11yescharacteristic
777C2×C73C4×H(5,𝔽2)11yescharacteristic
778C2×C73#353311yescharacteristic
779C2×C73#354211yescharacteristic
780C2×C73#355111yescharacteristic
781C2×C73#356811yescharacteristic
782D73—42no—
783D73—42no—
784D73—42no—
785C2×#538—731no—
786#2383—731no—
787#2378—731no—
788#2376—731no—
789#2375—731no—
790#2373—731no—
791#2373—731no—
792#2373—731no—
793#2372D7311yescharacteristic, complemented
794#2367—731no—
795#2362—731no—
796#2359—731no—
797#2358—731no—
798#2354—731no—
799#2353—731no—
800#2342—731no—
801#2342—731no—
802#2337—731no—
803#2335—731no—
804#2333—731no—
805#2333—731no—
806#2326—731no—
807#2325—731no—
808#2324—731no—
809#2324—731no—
810#2321—731no—
811#2321—731no—
812#2319—731no—
813C4×#123—731no—
814C4×#121—731no—
815#2290—731no—
816C73#3445111yescharacteristic, complemented, Sylow
817#538—7316no—
818C2×#126—731no—
819C2×#126—731no—
820C2×#124—731no—
821C2×#124C2×D7311yescharacteristic
822C2×#123—731no—
823C2×#123—731no—
824C2×C22⋊Q8—731no—
825C2×#121—731no—
826C2×#121—731no—
827C2×#121—731no—
828C2×#120—731no—
829C2×#120—731no—
830C2×C4×Q8—731no—
831C2×C4×D4—731no—
832C2×C4×D4—731no—
833C2×C4×D4—731no—
834C2×C4×D4—731no—
835C2×C4×D4—731no—
836C2×C4×D4—731no—
837C2×C4×D4—731no—
838C2×#117—731no—
839C2×#117—731no—
840C2×#117—731no—
841C22×C22⋊C4—731no—
842C22×C22⋊C4—731no—
843C22×C22⋊C4—731no—
844C22×C42—731no—
845#391—731no—
846#391C2×D7311yescharacteristic, complemented
847#391C2×D7311yescharacteristic, complemented
848#390—731no—
849#390—731no—
850#390—731no—
851#390—731no—
852#390—731no—
853#390—731no—
854#390—731no—
855#390—731no—
856#390—731no—
857#389—731no—
858#389—731no—
859#389—731no—
860#389—731no—
861#389—731no—
862#389—731no—
863#388—731no—
864#388—731no—
865#388—731no—
866#388—731no—
867#388—731no—
868#388—731no—
869#388—731no—
870#388—731no—
871#388—731no—
872#388—731no—
873#388—731no—
874#388—731no—
875#388—731no—
876#388—731no—
877#388—731no—
878#388—731no—
879#388—731no—
880#388—731no—
881#388—731no—
882#388—731no—
883#388—731no—
884#388—731no—
885#388—731no—
886#388—731no—
887#388—731no—
888#388—731no—
889#388—731no—
890#388—731no—
891#388C2×D7311yescharacteristic
892#388C2×D7311yescharacteristic
893#388C2×D7311yescharacteristic, complemented
894#388C2×D7311yescharacteristic, complemented
895#387—731no—
896#387—731no—
897#387—731no—
898#387—731no—
899#387—731no—
900#387—731no—
901#387—731no—
902#387—731no—
903#387—731no—
904#387—731no—
905#387—731no—
906#387—731no—
907#386—731no—
908#386—731no—
909#386—731no—
910#386—731no—
911#386—731no—
912#386—731no—
913#386—731no—
914#386—731no—
915#386—731no—
916#386—731no—
917#386—731no—
918#386—731no—
919#386C2×D7311yescharacteristic
920#386C2×D7311yescharacteristic
921#385—731no—
922#385—731no—
923#385—731no—
924#385—731no—
925#385—731no—
926#385—731no—
927#385—731no—
928#385—731no—
929#385—731no—
930#385—731no—
931#385—731no—
932#385—731no—
933#384—731no—
934#383—731no—
935#381—731no—
936#381—731no—
937#381—731no—
938#380—731no—
939#380—731no—
940#380—731no—
941#380—731no—
942#380—731no—
943#379—731no—
944#379—731no—
945C4×C4⋊C4—731no—
946C4×C4⋊C4—731no—
947C4×C4⋊C4—731no—
948C4×C4⋊C4—731no—
949C4×C4⋊C4—731no—
950C4×C4⋊C4—731no—
951C4×C4⋊C4—731no—
952C4×C4⋊C4—731no—
953C4×C4⋊C4—731no—
954C4×C22⋊C4—731no—
955C4×C22⋊C4—731no—
956C4×C22⋊C4—731no—
957C4×C22⋊C4—731no—
958C4×C22⋊C4—731no—
959C4×C22⋊C4—731no—
960C4×C22⋊C4—731no—
961C4×C22⋊C4—731no—
962C4×C22⋊C4—731no—
963C4×C22⋊C4—731no—
964C4×C22⋊C4—731no—
965C4×C22⋊C4C2×D7311yescharacteristic
966C4×C22⋊C4C2×D7311yescharacteristic
967C4×C22⋊C4C2×D7311yescharacteristic, complemented
968C4×C22⋊C4C2×D7311yescharacteristic, complemented
969#376—731no—
970#376C2×D7311yescharacteristic, complemented
971#376C2×D7311yescharacteristic, complemented
972C2×#95—731no—
973C25—731no—
974C22×Q8C22×D7311yescharacteristic
975C22×D4—731no—
976C22×D4—731no—
977C22×D4—731no—
978C22×D4—731no—
979C22×D4—731no—
980C22×D4—731no—
981C22×D4C22×D7311yescharacteristic
982C23×C4—731no—
983C23×C4—731no—
984C23×C4—731no—
985C23×C4—731no—
986C23×C4—731no—
987C23×C4—731no—
988C23×C4—731no—
989C23×C4—731no—
990C23×C4—731no—
991C23×C4—731no—
992C23×C4C22×D7311yescharacteristic
993C23×C4C22×D7311yescharacteristic
994#126—738no—
995#126—738no—
996#124—738no—
997#124C4×D7318yescomplemented
998#123—738no—
999#123—738no—
1000C22⋊Q8—738no—
1001#121—738no—
1002#121—738no—
1003#121—738no—
1004#120—738no—
1005#120—738no—
1006C4×Q8—2922no—
1007C4×D4—2922no—
1008C4×D4—2922no—
1009C4×D4—2922no—
1010C4×D4—2922no—
1011C4×D4—2922no—
1012C4×D4—738no—
1013C4×D4—738no—
1014#117—2922no—
1015#117—2922no—
1016#117—2922no—
1017C2×C4⋊C4—731no—
1018C2×C4⋊C4—731no—
1019C2×C4⋊C4—731no—
1020C2×C4⋊C4—731no—
1021C2×C4⋊C4—731no—
1022C2×C4⋊C4—731no—
1023C2×C4⋊C4—731no—
1024C2×C4⋊C4—731no—
1025C2×C4⋊C4—731no—
1026C2×C4⋊C4—731no—
1027C2×C4⋊C4—731no—
1028C2×C4⋊C4—731no—
1029C2×C4⋊C4—731no—
1030C2×C4⋊C4—731no—
1031C2×C4⋊C4—731no—
1032C2×C4⋊C4—731no—
1033C2×C4⋊C4—731no—
1034C2×C4⋊C4—731no—
1035C2×C4⋊C4—731no—
1036C2×C4⋊C4—731no—
1037C2×C4⋊C4—731no—
1038C2×C4⋊C4—731no—
1039C2×C4⋊C4—731no—
1040C2×C4⋊C4—731no—
1041C2×C4⋊C4C22×D7311yescharacteristic
1042C2×C4⋊C4C22×D7311yescharacteristic
1043C2×C22⋊C4—2922no—
1044C2×C22⋊C4—2922no—
1045C2×C22⋊C4—731no—
1046C2×C22⋊C4—731no—
1047C2×C22⋊C4—731no—
1048C2×C22⋊C4—731no—
1049C2×C22⋊C4—731no—
1050C2×C22⋊C4—731no—
1051C2×C22⋊C4—731no—
1052C2×C22⋊C4—731no—
1053C2×C22⋊C4—731no—
1054C2×C22⋊C4—731no—
1055C2×C22⋊C4—731no—
1056C2×C22⋊C4—731no—
1057C2×C22⋊C4—731no—
1058C2×C22⋊C4—731no—
1059C2×C22⋊C4—731no—
1060C2×C22⋊C4—731no—
1061C2×C22⋊C4—731no—
1062C2×C22⋊C4—731no—
1063C2×C22⋊C4—731no—
1064C2×C22⋊C4—731no—
1065C2×C22⋊C4—731no—
1066C2×C22⋊C4—731no—
1067C2×C22⋊C4—731no—
1068C2×C22⋊C4—731no—
1069C2×C22⋊C4—731no—
1070C2×C22⋊C4—731no—
1071C2×C22⋊C4—731no—
1072C2×C22⋊C4—731no—
1073C2×C22⋊C4—731no—
1074C2×C22⋊C4—731no—
1075C2×C22⋊C4—731no—
1076C2×C22⋊C4—731no—
1077C2×C22⋊C4—738no—
1078C2×C22⋊C4—731no—
1079C2×C22⋊C4—731no—
1080C2×C22⋊C4—731no—
1081C2×C22⋊C4—731no—
1082C2×C22⋊C4C22×D7311yescharacteristic
1083C2×C22⋊C4C22×D7311yescharacteristic
1084C2×C22⋊C4C22×D7311yescharacteristic
1085C2×C22⋊C4C22×D7311yescharacteristic
1086C2×C22⋊C4C22×D7311yescharacteristic
1087C2×C22⋊C4C22×D7311yescharacteristic
1088C2×C22⋊C4C22×D7311yescharacteristic
1089C2×C22⋊C4C22×D7311yescharacteristic
1090C2×C22⋊C4C22×D7311yescharacteristic
1091C2×C22⋊C4C22×D7311yescharacteristic
1092C2×C42—2922no—
1093C2×C42—731no—
1094C2×C42—731no—
1095C2×C42—731no—
1096C2×C42—731no—
1097C2×C42—731no—
1098C2×C42—731no—
1099C2×C42—731no—
1100C2×C42—731no—
1101C2×C42—731no—
1102C2×C42—731no—
1103C2×C42—731no—
1104C2×C42—731no—
1105C2×C42—731no—
1106C2×C42—731no—
1107C2×C42—731no—
1108C2×C42C22×D7311yescharacteristic
1109C2×C42C22×D7311yescharacteristic
1110C2×C42C22×D7311yescharacteristic
1111C2×C42C22×D7311yescharacteristic
1112C2×C42C22×D7311yescharacteristic
1113C2×C42C22×D7311yescharacteristic
1114C2×C42C22×D7311yescharacteristic
1115#95—731no—
1116#95—731no—
1117#95—731no—
1118#95—731no—
1119#95—731no—
1120#95—731no—
1121#95—731no—
1122#95—731no—
1123#95—731no—
1124#95—731no—
1125#95—731no—
1126#95—731no—
1127#95—731no—
1128#95—731no—
1129#95—731no—
1130#95—731no—
1131#95—731no—
1132#95—731no—
1133#95—731no—
1134#95—731no—
1135#95—731no—
1136#95—731no—
1137#95—731no—
1138#95—731no—
1139#95—731no—
1140#95—731no—
1141#95—731no—
1142#95—731no—
1143#95C22×D7311yescharacteristic
1144#95C22×D7311yescharacteristic
1145#95C22×D7311yescharacteristic
1146#95C22×D7311yescharacteristic
1147#95C22×D7311yescharacteristic
1148#95C22×D7311yescharacteristic
1149#95C22×D7311yescharacteristic
1150#95C22×D7311yescharacteristic
1151#95C22×D7311yescharacteristic
1152#95C22×D7311yescharacteristic
1153#95C22×D7311yescharacteristic
1154#95C22×D7311yescharacteristic
1155C24—2921no—
1156C24—2921no—
1157C24—2921no—
1158C24—2921no—
1159C24—2921no—
1160C24—2921no—
1161C24—734no—
1162C24—731no—
1163C24—731no—
1164C24—731no—
1165C24C23×D7311yescharacteristic
1166C24C23×D7311yescharacteristic
1167C2×Q8—41no—
1168C2×Q8—41no—
1169C2×Q8C2×C4×D7314yes—
1170C2×D4—41no—
1171C2×D4—41no—
1172C2×D4—2921no—
1173C2×D4—2921no—
1174C2×D4—2921no—
1175C2×D4—2921no—
1176C2×D4—2921no—
1177C2×D4—2921no—
1178C2×D4—2921no—
1179C2×D4—2921no—
1180C2×D4—2921no—
1181C2×D4—2921no—
1182C2×D4—2921no—
1183C2×D4—2921no—
1184C2×D4—734no—
1185C2×D4—734no—
1186C2×D4—734no—
1187C2×D4—734no—
1188C2×D4—734no—
1189C2×D4—734no—
1190C2×D4C2×C4×D7314yes—
1191C22×C4—22no—
1192C22×C4—41no—
1193C22×C4—41no—
1194C22×C4—41no—
1195C22×C4—41no—
1196C22×C4—41no—
1197C22×C4—2921no—
1198C22×C4—2921no—
1199C22×C4—2921no—
1200C22×C4—2921no—
1201C22×C4—2921no—
1202C22×C4—2921no—
1203C22×C4—2921no—
1204C22×C4—2921no—
1205C22×C4—2921no—
1206C22×C4—2921no—
1207C22×C4—2921no—
1208C22×C4—2921no—
1209C22×C4—2921no—
1210C22×C4—2921no—
1211C22×C4—2921no—
1212C22×C4—2921no—
1213C22×C4—2921no—
1214C22×C4—2921no—
1215C22×C4—2921no—
1216C22×C4—2921no—
1217C22×C4—2921no—
1218C22×C4—2921no—
1219C22×C4—734no—
1220C22×C4—734no—
1221C22×C4—734no—
1222C22×C4—734no—
1223C22×C4—731no—
1224C22×C4—731no—
1225C22×C4—731no—
1226C22×C4—731no—
1227C22×C4—731no—
1228C22×C4—731no—
1229C22×C4—731no—
1230C22×C4—731no—
1231C22×C4—731no—
1232C22×C4—731no—
1233C22×C4—731no—
1234C22×C4—731no—
1235C22×C4—731no—
1236C22×C4—1462no—
1237C22×C4—1462no—
1238C22×C4—1462no—
1239C22×C4—1462no—
1240C22×C4C23×D7311yescharacteristic
1241C22×C4C23×D7311yescharacteristic
1242C22×C4C23×D7311yescharacteristic
1243C22×C4C23×D7311yescharacteristic
1244C22×C4C23×D7311yescharacteristic
1245C22×C4C23×D7311yescharacteristic
1246C22×C4C23×D7311yescharacteristic
1247C22×C4C23×D7311yescharacteristic
1248C22×C4C23×D7311yescharacteristic
1249C22×C4C23×D7311yescharacteristic
1250C22×C4C23×D7311yescharacteristic
1251C22×C4C23×D7311yescharacteristic
1252C22×C4C23×D7311yescharacteristic
1253C4⋊C4—41no—
1254C4⋊C4—41no—
1255C4⋊C4—2921no—
1256C4⋊C4—2921no—
1257C4⋊C4—2921no—
1258C4⋊C4—2921no—
1259C4⋊C4—2921no—
1260C4⋊C4—2921no—
1261C4⋊C4—2921no—
1262C4⋊C4—2921no—
1263C4⋊C4—2921no—
1264C4⋊C4—2921no—
1265C4⋊C4—2921no—
1266C4⋊C4—2921no—
1267C4⋊C4—2921no—
1268C4⋊C4—2921no—
1269C4⋊C4—2921no—
1270C4⋊C4—734no—
1271C4⋊C4—734no—
1272C4⋊C4—734no—
1273C4⋊C4—734no—
1274C4⋊C4—734no—
1275C4⋊C4—734no—
1276C4⋊C4—1462no—
1277C4⋊C4—1462no—
1278C4⋊C4—1462no—
1279C22⋊C4—22no—
1280C22⋊C4—41no—
1281C22⋊C4—41no—
1282C22⋊C4—41no—
1283C22⋊C4—41no—
1284C22⋊C4—41no—
1285C22⋊C4—2921no—
1286C22⋊C4—2921no—
1287C22⋊C4—2921no—
1288C22⋊C4—2921no—
1289C22⋊C4—2921no—
1290C22⋊C4—2921no—
1291C22⋊C4—2921no—
1292C22⋊C4—2921no—
1293C22⋊C4—2921no—
1294C22⋊C4—2921no—
1295C22⋊C4—2921no—
1296C22⋊C4—2921no—
1297C22⋊C4—2921no—
1298C22⋊C4—2921no—
1299C22⋊C4—2921no—
1300C22⋊C4—2921no—
1301C22⋊C4—2921no—
1302C22⋊C4—2921no—
1303C22⋊C4—2921no—
1304C22⋊C4—2921no—
1305C22⋊C4—2921no—
1306C22⋊C4—2921no—
1307C22⋊C4—734no—
1308C22⋊C4—734no—
1309C22⋊C4—734no—
1310C22⋊C4—734no—
1311C22⋊C4—734no—
1312C22⋊C4—734no—
1313C22⋊C4—734no—
1314C22⋊C4—734no—
1315C22⋊C4—734no—
1316C22⋊C4—734no—
1317C22⋊C4—1462no—
1318C22⋊C4—1462no—
1319C22⋊C4—1462no—
1320C22⋊C4—1462no—
1321C22⋊C4C2×C4×D7314yes—
1322C22⋊C4C2×C4×D7314yes—
1323C22⋊C4C2×C4×D7314yes—
1324C22⋊C4C2×C4×D7314yes—
1325C42—22no—
1326C42—41no—
1327C42—41no—
1328C42—41no—
1329C42—41no—
1330C42—41no—
1331C42—2921no—
1332C42—2921no—
1333C42—2921no—
1334C42—2921no—
1335C42—2921no—
1336C42—2921no—
1337C42—2921no—
1338C42—2921no—
1339C42—2921no—
1340C42—2921no—
1341C42—734no—
1342C42—1462no—
1343C42—1462no—
1344C42—1462no—
1345C42—1462no—
1346C42C2×C4×D7314yes—
1347C23—21no—
1348C23—21no—
1349C23—21no—
1350C23—21no—
1351C23—21no—
1352C23—21no—
1353C23—21no—
1354C23—21no—
1355C23—21no—
1356C23—21no—
1357C23—21no—
1358C23—21no—
1359C23—2924no—
1360C23—2924no—
1361C23—2924no—
1362C23—5842no—
1363C23—5842no—
1364C23—5842no—
1365C23—5842no—
1366C23—732no—
1367C23—732no—
1368C23—732no—
1369C23—1461no—
1370C23—1461no—
1371C23—1461no—
1372C23—1461no—
1373C23—1461no—
1374C23—1461no—
1375C23—1461no—
1376C23—1461no—
1377C23—1461no—
1378C23—1461no—
1379C23—1461no—
1380C23—1461no—
1381C23—1461no—
1382C23—1461no—
1383C23—1461no—
1384C23—1461no—
1385C23—1461no—
1386C23—1461no—
1387C23C22×C4×D7312yes—
1388C23C22×C4×D7312yes—
1389C23C24×D7311yescharacteristic
1390Q8—44no—
1391D4—44no—
1392D4—2924no—
1393D4—2924no—
1394D4—2924no—
1395D4—2924no—
1396D4—2924no—
1397D4—2924no—
1398C2×C4—21no—
1399C2×C4—21no—
1400C2×C4—21no—
1401C2×C4—21no—
1402C2×C4—21no—
1403C2×C4—21no—
1404C2×C4—21no—
1405C2×C4—21no—
1406C2×C4—21no—
1407C2×C4—21no—
1408C2×C4—21no—
1409C2×C4—21no—
1410C2×C4—21no—
1411C2×C4—21no—
1412C2×C4—21no—
1413C2×C4—21no—
1414C2×C4—21no—
1415C2×C4—21no—
1416C2×C4—21no—
1417C2×C4—21no—
1418C2×C4—21no—
1419C2×C4—21no—
1420C2×C4—21no—
1421C2×C4—21no—
1422C2×C4—21no—
1423C2×C4—21no—
1424C2×C4—21no—
1425C2×C4—21no—
1426C2×C4—21no—
1427C2×C4—21no—
1428C2×C4—21no—
1429C2×C4—21no—
1430C2×C4—21no—
1431C2×C4—82no—
1432C2×C4—82no—
1433C2×C4—2924no—
1434C2×C4—2924no—
1435C2×C4—2924no—
1436C2×C4—2924no—
1437C2×C4—2924no—
1438C2×C4—2924no—
1439C2×C4—5842no—
1440C2×C4—5842no—
1441C2×C4—5842no—
1442C2×C4—5842no—
1443C2×C4—732no—
1444C2×C4—732no—
1445C2×C4—732no—
1446C2×C4—732no—
1447C2×C4—732no—
1448C2×C4—732no—
1449C2×C4—1461no—
1450C2×C4—1461no—
1451C2×C4—1461no—
1452C2×C4—1461no—
1453C2×C4—1461no—
1454C2×C4—1461no—
1455C2×C4—1461no—
1456C2×C4—1461no—
1457C2×C4—1461no—
1458C2×C4—1461no—
1459C2×C4—1461no—
1460C2×C4—1461no—
1461C2×C4—1461no—
1462C2×C4—1461no—
1463C2×C4—1461no—
1464C2×C4—1461no—
1465C2×C4—1461no—
1466C2×C4—1461no—
1467C2×C4—1461no—
1468C2×C4—1461no—
1469C2×C4—1461no—
1470C2×C4—1461no—
1471C2×C4—1461no—
1472C2×C4—1461no—
1473C2×C4—1461no—
1474C2×C4—1461no—
1475C2×C4—1461no—
1476C2×C4—1461no—
1477C2×C4—1461no—
1478C2×C4—1461no—
1479C2×C4—1461no—
1480C2×C4—1461no—
1481C2×C4—1461no—
1482C2×C4C22×C4×D7312yes—
1483C2×C4C22×C4×D7312yes—
1484C2×C4C22×C4×D7312yes—
1485C2×C4C22×C4×D7312yes—
1486C2×C4C22×C4×D7312yes—
1487C2×C4#1455663712yes—
1488C22—22no—
1489C22—22no—
1490C22—22no—
1491C22—22no—
1492C22—22no—
1493C22—22no—
1494C22—41no—
1495C22—41no—
1496C22—41no—
1497C22—41no—
1498C22—41no—
1499C22—41no—
1500C22—41no—
1501C22—41no—
1502C22—2921no—
1503C22—2921no—
1504C22—2921no—
1505C22—2921no—
1506C22—2921no—
1507C22—2921no—
1508C22—2921no—
1509C22—2921no—
1510C22—2921no—
1511C22—2921no—
1512C22—2921no—
1513C22—2921no—
1514C22—5848no—
1515C22—1462no—
1516C22—1462no—
1517C22—1462no—
1518C22—1462no—
1519C22—1462no—
1520C22—1462no—
1521C22—1462no—
1522C22—1462no—
1523C22—1462no—
1524C22C23×C4×D7311yescharacteristic
1525C22H(5,𝔽2)×D7311yescharacteristic
1526C22C2×#1455663711yescharacteristic
1527C22#1798942211yescharacteristic
1528C22#1798942311yescharacteristic
1529C22#1798942311yescharacteristic
1530C22#1798942311yescharacteristic
1531C4—22no—
1532C4—22no—
1533C4—22no—
1534C4—22no—
1535C4—22no—
1536C4—22no—
1537C4—41no—
1538C4—41no—
1539C4—41no—
1540C4—41no—
1541C4—41no—
1542C4—41no—
1543C4—41no—
1544C4—2921no—
1545C4—2921no—
1546C4—2921no—
1547C4—2921no—
1548C4—2921no—
1549C4—2921no—
1550C4—2921no—
1551C4—1462no—
1552C4—1462no—
1553C4—1462no—
1554C4—1462no—
1555C4—1462no—
1556C4—1462no—
1557C2—42no—
1558C2—42no—
1559C2—2922no—
1560C2—2922no—
1561C2—2922no—
1562C2#2262313011yescharacteristic
1563C2#2262313511yescharacteristic
1564C2C4×#1455663711yescharacteristic
1565C2#2262410311yescharacteristic
1566C2#2262425411yescharacteristic
1567C2#2262434611yescharacteristic
1568C2#2262462211yescharacteristic
subgroupG/H
center, FrattiniC23C24×D73
commutatorC22×C73C24×C4
FittingC73×#2372C2
socle, cosocleC23×C73C25
prime radicalC2×#17989171C2
hypercenter#2372D73
hypocenterC73#34451
LCSG ▷ C22×C73 ▷ C73
UCSC1 ◁ C23 ◁ #2372

Complements

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

NH ≅ G/Ntype
2. #22613118C2semidirect
3. #22613092C2semidirect
4. #22613077C2semidirect
5. #22613069C2semidirect
6. #22613052C2semidirect
7. #22613051C2semidirect
8. #22613051C2semidirect
9. #22613006C2semidirect
10. #22612963C2semidirect
11. #22612925C2semidirect
12. #22612911C2semidirect
13. #22612877C2semidirect
14. #22612865C2semidirect
15. #22612779C2semidirect
16. #22612774C2semidirect
17. #22612743C2semidirect
18. #22612719C2semidirect
19. #22612691C2semidirect
20. #22612691C2semidirect
21. #22612645C2semidirect
22. #22612632C2semidirect
23. #22612621C2semidirect
24. #22612619C2semidirect
25. #22612591C2semidirect
26. #22612584C2semidirect
27. #22612575C2semidirect
28. C4×#14556573C2semidirect
29. #22612443C2semidirect
30. #22612375C2semidirect
31. C73×#2372C2semidirect
32. #17989171C4semidirect
44. C2×Q8×Dic73C22semidirect
51. C2×#14556551C22semidirect
54. C2×#14556547C22semidirect
58. C2×C42×D73C22semidirect
59. #17988494C22semidirect
68. #17988487C22semidirect
69. #17988485C22semidirect
70. #17988485C22semidirect
71. #17988484C22semidirect
72. #17988484C22semidirect
73. #17988483C22semidirect
74. #17988482C22semidirect
80. #17988480C22semidirect
81. #17988480C22semidirect
92. #17988477C22semidirect
99. #17988476C22semidirect
100. #17988476C22semidirect
101. #17988476C22semidirect
103. #17988474C22semidirect
104. #17988474C22semidirect
105. #17988474C22semidirect
106. #17988472C22semidirect
107. #17988472C22semidirect
108. #17988472C22semidirect
109. #17988471C22semidirect
110. #17988471C22semidirect
111. #17988471C22semidirect
112. #17988470C22semidirect
113. #17988469C22semidirect
114. #17988469C22semidirect
117. #17988466C22semidirect
126. #17988463C22semidirect
128. #17988462C22semidirect
132. #17988461C22semidirect
133. #17988461C22semidirect
134. #17988461C22semidirect
139. #17988456C22semidirect
140. #17988454C22semidirect
143. #17988449C22semidirect
146. #17988446C22semidirect
147. #17988445C22semidirect
148. #17988445C22semidirect
151. C4×#11924007C22semidirect
152. C4×#11924007C22semidirect
153. C4×C4⋊Dic73C22semidirect
154. C4×C4⋊Dic73C22semidirect
155. C4×C4⋊Dic73C22semidirect
156. #17988438C22semidirect
157. #17988438C22semidirect
158. #17988438C22semidirect
159. #17988438C22semidirect
161. C22⋊C4×Dic73C22semidirect
166. C4×#11924005C22semidirect
167. C4×#11924005C22semidirect
171. #17988433C22semidirect
172. C2×#14556498C22semidirect
174. #391×C73C22semidirect
175. #391×C73C22semidirect
178. #388×C73C22semidirect
179. #388×C73C22semidirect
184. C4×C22⋊C4×C73C22semidirect
185. C4×C22⋊C4×C73C22semidirect
186. #376×C73C22semidirect
187. #376×C73C22semidirect
205. #14556585C2×C4semidirect
206. #14556584C2×C4semidirect
207. #14556580C2×C4semidirect
208. #14556575C2×C4semidirect
209. #14556573C2×C4semidirect
210. #14556567C2×C4semidirect
211. #14556564C2×C4semidirect
212. #14556564C2×C4semidirect
213. #14556563C2×C4semidirect
214. #14556561C2×C4semidirect
215. #14556559C2×C4semidirect
217. C4×D292C2×C4semidirect
223. #14556551C2×C4semidirect
289. C22⋊C4×D73C2×C4semidirect
338. #124×C73C2×C4semidirect
793. #2372D73semidirect
816. C73#34451semidirect
846. #391C2×D73semidirect
847. #391C2×D73semidirect
893. #388C2×D73semidirect
894. #388C2×D73semidirect
967. C4×C22⋊C4C2×D73semidirect
968. C4×C22⋊C4C2×D73semidirect
970. #376C2×D73semidirect
971. #376C2×D73semidirect
997. #124C4×D73semidirect

Maximal subgroups

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

subgroupindex
C2×#179891712
#226131182
#226130922
#226130772
#226130692
#226130522
#226130512
#226130062
#226129632
#226129252
#226129112
#226128772
#226128652
#226127792
#226127742
#226127432
#226127192
#226126912
#226126452
#226126322
#226126212
#226126192
#226125912
#226125842
#226125752
C4×#145565732
#226124432
#226123752
C73×#23722
#3445173