Finite Group Databasebeta

← #33101409

Subgroups — #33101409

Order 18688.

1530 conjugacy classes of subgroups.

The subgroup lattice has 826 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×Q8×C22⋊D73C211yesmaximal, characteristic
2C2×#17988650C211yesmaximal, characteristic
3C22×#14556515C211yesmaximal, characteristic, complemented
4C2×#103×D73C211yesmaximal, characteristic, complemented
5#22612827C211yesmaximal, characteristic
6#22610852C211yesmaximal, characteristic, complemented
7#22610731C211yesmaximal, characteristic, complemented
8#22610352C211yesmaximal, characteristic, complemented
9#22610351C211yesmaximal, characteristic, complemented
10#22610236C211yesmaximal, characteristic, complemented
11#22610235C211yesmaximal, characteristic, complemented
12#22609934C211yesmaximal, characteristic, complemented
13#22609864C211yesmaximal, characteristic, complemented
14#103×Dic73C211yesmaximal, characteristic, complemented
15C73×#1787C211yesmaximal, characteristic, complemented
16C22×Q8×D73C2211yescharacteristic
17C23×#10596831C2211yescharacteristic
18C22×C8×D73C2211yescharacteristic
19Q8×C22⋊D73—24no—
20Q8×C22⋊D73C418yescomplemented
21C2×#14556589—21no—
22C2×#14556589C2211yescharacteristic
23C2×#14556570—21no—
24C2×#14556570C2211yescharacteristic
25C2×#14556567—21no—
26C2×#14556567C2211yescharacteristic
27C2×Q8×Dic73C2211yescharacteristic
28C2×C4×C22⋊D73—21no—
29C2×C4×C22⋊D73C2211yescharacteristic
30C2×#14556551—21no—
31C22×C4⋊Dic73C2211yescharacteristic
32C2×C4⋊C4×D73C2211yescharacteristic
33#17988650—24no—
34C2×#14556520C2211yescharacteristic
35C2×#14556516C2211yescharacteristic
36C2×#14556516C2211yescharacteristic
37C2×#14556515—24no—
38C2×#14556515C2211yescharacteristic
39C2×#14556515C2211yescharacteristic
40C2×#14556515C2211yescharacteristic
41C2×#14556515C2211yescharacteristic
42C2×#14556514C2211yescharacteristic
43C2×#14556514C2211yescharacteristic
44#103×D73—24no—
45C2×#14556503C2211yescharacteristic
46C2×C8×Dic73C2211yescharacteristic
47#17988484—21no—
48#17988461—21no—
49#17988459—21no—
50#17988456C2211yescharacteristic
51#17988444C2211yescharacteristic
52C4⋊C4×Dic73C2211yescharacteristic
53#17988350C2211yescharacteristic
54#17988350C2211yescharacteristic
55#17988349C2211yescharacteristic
56#17988349C2211yescharacteristic
57C23×Q8×C73C2211yescharacteristic
58C2×#103×C73C2211yescharacteristic
59C2×#103×C73C2211yescharacteristic
60C2×#103×C73C2211yescharacteristic
61C2×#103×C73C2211yescharacteristic
62C2×C22⋊C8×C73C2211yescharacteristic
63#380×C73C2211yescharacteristic
64C22×Dic146—21no—
65C22×Dic146C2311yescharacteristic
66C2×Q8×D73—22no—
67C2×Q8×D73—22no—
68C2×Q8×D73—22no—
69C2×Q8×D73—41no—
70C2×Q8×D73—41no—
71C2×Q8×D73C2×C414yescomplemented
72C22×C22⋊D73D411yescharacteristic
73C23×Dic73—21no—
74C22×C4×D73—21no—
75C22×C4×D73—21no—
76C22×C4×D73C2311yescharacteristic
77C22×#10596831—22no—
78C22×#10596831—22no—
79C22×#10596831—41no—
80C22×#10596831C2311yescharacteristic
81C22×#10596831C2311yescharacteristic
82C2×C8×D73—22no—
83C2×C8×D73—22no—
84C2×C8×D73—41no—
85#14556589—28no—
86#14556589—22no—
87#14556589C2×C414yescomplemented
88#14556570—28no—
89#14556570—22no—
90#14556570C2×C414yescomplemented
91#14556567—22no—
92#14556567—28no—
93#14556567C2×C414yescomplemented
94Q8×Dic73—22no—
95Q8×Dic73C2×C414yescomplemented
96C4×C22⋊D73—28no—
97C4×C22⋊D73C2×C414yes—
98C4×C22⋊D73D414yes—
99#14556551—44no—
100C2×C4⋊Dic73—21no—
101C2×C4⋊Dic73—22no—
102C2×C4⋊Dic73—21no—
103C2×C4⋊Dic73—41no—
104C2×C4⋊Dic73C2311yescharacteristic
105C2×C4⋊Dic73C2311yescharacteristic
106C2×C4⋊Dic73C2311yescharacteristic
107C2×#11924007—21no—
108C2×#11924007—21no—
109C2×#11924007—21no—
110C2×#11924007—21no—
111C2×#11924007—21no—
112C2×#11924007—21no—
113C2×#11924007—21no—
114C2×#11924007D411yescharacteristic
115C4⋊C4×D73—22no—
116C4⋊C4×D73—41no—
117C2×C22⋊Dic73—21no—
118C2×C22⋊Dic73D411yescharacteristic
119C2×#11924005—21no—
120C2×#11924005—21no—
121C2×#11924005D411yescharacteristic
122C2×C4×Dic73—21no—
123C2×C4×Dic73—21no—
124C2×C4×Dic73C2311yescharacteristic
125#14556520—22no—
126#14556516—22no—
127#14556516—41no—
128#14556515—22no—
129#14556515—22no—
130#14556515—22no—
131#14556515D414yescomplemented
132#14556514—22no—
133#14556514—41no—
134#14556503—22no—
135C8×Dic73—22no—
136#14556498—21no—
137#14556498—21no—
138C22×Q8×C73—21no—
139C22×Q8×C73—22no—
140C22×Q8×C73—22no—
141C22×Q8×C73—22no—
142C22×Q8×C73—41no—
143C22×Q8×C73—41no—
144C22×Q8×C73C2×C414yescomplemented
145C22×Q8×C73C2311yescharacteristic
146C22×Q8×C73C2311yescharacteristic
147C23×C4×C73—21no—
148C23×C4×C73C2311yescharacteristic
149C22×C8×C73C2311yescharacteristic
150C22×C8×C73C2311yescharacteristic
151C2×C4⋊C4×C73C2311yescharacteristic
152C2×C4⋊C4×C73C2311yescharacteristic
153C2×C22⋊C4×C73—21no—
154#103×C73—22no—
155#103×C73—22no—
156#103×C73—41no—
157#103×C73—41no—
158C22⋊C8×C73—22no—
159#95×C73—21no—
160C23×D73C2×D411yescharacteristic
161C2×Dic146—21no—
162C2×Dic146—21no—
163C2×Dic146—21no—
164C2×Dic146—21no—
165C2×Dic146—21no—
166C2×Dic146—24no—
167C2×Dic146—42no—
168C2×Dic146—42no—
169C2×Dic146C22×C412yes—
170Q8×D73—28no—
171Q8×D73—44no—
172Q8×D73—44no—
173Q8×D73—44no—
174C2×C22⋊D73C22⋊C414yes—
175C2×C22⋊D73SD1614yes—
176C2×C22⋊D73Q1614yes—
177C22×Dic73—21no—
178C22×Dic73—21no—
179C22×Dic73—21no—
180C22×Dic73—21no—
181C22×Dic73—42no—
182C22×Dic73—42no—
183C22×Dic73—81no—
184C22×Dic73C2×D411yescharacteristic
185C22×Dic73C2×D411yescharacteristic
186C22×Dic73C2×D411yescharacteristic
187C2×C4×D73—21no—
188C2×C4×D73—21no—
189C2×C4×D73—21no—
190C2×C4×D73—21no—
191C2×C4×D73—24no—
192C2×C4×D73—42no—
193C2×C4×D73—42no—
194C2×C4×D73—42no—
195C2×C4×D73—42no—
196C2×C4×D73—81no—
197C2×C4×D73C22×C412yes—
198C2×C4×D73C2×D412yes—
199C2×#10596831—21no—
200C2×#10596831—21no—
201C2×#10596831—21no—
202C2×#10596831—21no—
203C2×#10596831—21no—
204C2×#10596831—44no—
205C2×#10596831C2×D412yes—
206C8×D73—44no—
207C4⋊Dic73—21no—
208C4⋊Dic73—21no—
209C4⋊Dic73—24no—
210C4⋊Dic73—21no—
211C4⋊Dic73—21no—
212C4⋊Dic73—42no—
213C4⋊Dic73C22×C412yes—
214C4⋊Dic73C2×D412yes—
215#11924007—24no—
216#11924007—24no—
217#11924007—24no—
218#11924007—24no—
219#11924007—42no—
220#11924007—42no—
221#11924007—81no—
222#11924007C22⋊C414yes—
223C22⋊Dic73—24no—
224C22⋊Dic73C22⋊C414yes—
225#11924005—24no—
226#11924005—42no—
227#11924005C22⋊C414yes—
228C4×Dic73—24no—
229C4×Dic73—42no—
230C4×Dic73C22×C412yes—
231C4×Dic73C2×D412yes—
232C24×C73C2×D411yescharacteristic
233C2×Q8×C73—24no—
234C2×Q8×C73—21no—
235C2×Q8×C73—21no—
236C2×Q8×C73—21no—
237C2×Q8×C73—21no—
238C2×Q8×C73—28no—
239C2×Q8×C73—21no—
240C2×Q8×C73—21no—
241C2×Q8×C73—21no—
242C2×Q8×C73—21no—
243C2×Q8×C73—42no—
244C2×Q8×C73—42no—
245C2×Q8×C73—44no—
246C2×Q8×C73—44no—
247C2×Q8×C73—44no—
248C2×Q8×C73C22×C412yes—
249C2×Q8×C73C22×C412yes—
250C2×Q8×C73C2×D412yes—
251C2×Q8×C73#4112yes—
252C22×C4×C73—21no—
253C22×C4×C73—21no—
254C22×C4×C73—21no—
255C22×C4×C73—21no—
256C22×C4×C73—21no—
257C22×C4×C73—24no—
258C22×C4×C73—21no—
259C22×C4×C73—21no—
260C22×C4×C73—21no—
261C22×C4×C73—42no—
262C22×C4×C73—42no—
263C22×C4×C73C22×C412yes—
264C22×C4×C73C2×D411yescharacteristic
265C22×C4×C73C2×D412yes—
266C22×C4×C73C2411yescharacteristic
267C2×C8×C73—21no—
268C2×C8×C73—21no—
269C2×C8×C73—21no—
270C2×C8×C73—21no—
271C2×C8×C73—21no—
272C2×C8×C73—21no—
273C4⋊C4×C73—21no—
274C4⋊C4×C73—21no—
275C4⋊C4×C73—21no—
276C4⋊C4×C73—21no—
277C22⋊C4×C73—42no—
278C23×C73—21no—
279C23×C73—21no—
280C23×C73—21no—
281C23×C73—21no—
282C23×C73C2×C22⋊C412yes—
283C23×C73C2×SD1612yes—
284C23×C73C2×Q1612yes—
285C23×C73C22×D411yescharacteristic
286C22×D73—21no—
287C22×D73—21no—
288C22×D73—21no—
289C22×D73—21no—
290C22×D73C2×C22⋊C412yes—
291C22×D73C2×SD1612yes—
292C22×D73C2×Q1612yes—
293Q8×C73—22no—
294Q8×C73—22no—
295Q8×C73—22no—
296Q8×C73—22no—
297Q8×C73—22no—
298Q8×C73—48no—
299Q8×C73—41no—
300Q8×C73—41no—
301Q8×C73C4×D414yescomplemented
302C2×C4×C73—22no—
303C2×C4×C73—21no—
304C2×C4×C73—22no—
305C2×C4×C73—21no—
306C2×C4×C73—22no—
307C2×C4×C73—22no—
308C2×C4×C73—22no—
309C2×C4×C73—22no—
310C2×C4×C73—22no—
311C2×C4×C73—22no—
312C2×C4×C73—48no—
313C2×C4×C73—41no—
314C2×C4×C73—41no—
315C2×C4×C73—41no—
316C2×C4×C73—41no—
317C2×C4×C73—41no—
318C2×C4×C73—41no—
319C2×C4×C73—41no—
320C2×C4×C73—41no—
321C2×C4×C73C2×C22⋊C412yes—
322C2×C4×C73C23×C411yescharacteristic
323C2×C4×C73C22×D411yescharacteristic
324C2×C4×C73C22×D411yescharacteristic
325C2×C4×C73C2×#4111yescharacteristic
326C2×C4×C73H(5,𝔽2)11yescharacteristic
327C2×C4×C73H(5,𝔽2)11yescharacteristic
328C22⋊D73#103116yescomplemented
329C2×Dic73—21no—
330C2×Dic73—21no—
331C2×Dic73—21no—
332C2×Dic73—21no—
333C2×Dic73—22no—
334C2×Dic73—22no—
335C2×Dic73—22no—
336C2×Dic73—41no—
337C2×Dic73—41no—
338C2×Dic73—41no—
339C2×Dic73—41no—
340C2×Dic73—41no—
341C2×Dic73—41no—
342C2×Dic73—41no—
343C2×Dic73—41no—
344C2×Dic73—41no—
345C2×Dic73—84no—
346C2×Dic73C2×C22⋊C412yes—
347C2×Dic73C2×C22⋊C412yes—
348C2×Dic73C2×C22⋊C412yes—
349C2×Dic73C2×SD1612yes—
350C2×Dic73C2×Q1612yes—
351C4×D73—22no—
352C4×D73—22no—
353C4×D73—22no—
354C4×D73—22no—
355C4×D73—48no—
356C4×D73—84no—
357Dic146—22no—
358Dic146—22no—
359Dic146—48no—
360Dic146—41no—
361Dic146—41no—
362C8×C73—41no—
363C8×C73—41no—
364#10596831—22no—
365#10596831—41no—
366C22×C73—22no—
367C22×C73—22no—
368C22×C73—22no—
369C22×C73—22no—
370C22×C73—22no—
371C22×C73—22no—
372C22×C73C2×#10314yescomplemented
373C22×C73C22×C22⋊C411yescharacteristic
374C22×C73D4211yescharacteristic
375C22×C73#54611yescharacteristic
376C22×C73C22×SD1611yescharacteristic
377C22×C73C22×Q1611yescharacteristic
378C22×C73#57711yescharacteristic
379C22×C73#57811yescharacteristic
380C2×D73—22no—
381C2×D73—22no—
382C2×D73—22no—
383C2×D73—22no—
384C2×D73—22no—
385C2×D73—22no—
386C2×D73C2×#10314yescomplemented
387C4×C73—24no—
388C4×C73—22no—
389C4×C73—42no—
390C4×C73—81no—
391C4×C73—81no—
392C4×C73C2×C4×D411yescharacteristic
393C4×C73#51811yescharacteristic
394C4×C73D4211yescharacteristic
395C4×C73#54611yescharacteristic
396Dic73—22no—
397Dic73—22no—
398Dic73—42no—
399Dic73—42no—
400Dic73—42no—
401Dic73—81no—
402Dic73C2×#10314yescomplemented
403D4×#103—731nomaximal, Sylow
404C2×C73—24no—
405C2×C73D4×C22⋊C411yescharacteristic
406C2×C73C22×#10311yescharacteristic
407C2×C73#289811yescharacteristic
408C2×C73D4×SD1611yescharacteristic
409C2×C73D4×Q1611yescharacteristic
410C2×C73#329811yescharacteristic
411C2×C73#329911yescharacteristic
412D73—24no—
413C2×D4×Q8—731no—
414C2×C8×D4—731no—
415C22×#103—731no—
416C22×#103—731no—
417D4×C4⋊C4—731no—
418#1981—731no—
419#1956—731no—
420#1892—731no—
421#1892—731no—
422#1872—731no—
423#1872—731no—
424#1803—731no—
425#1787—731no—
426#1787D7311yescharacteristic, complemented
427C4×#103—731no—
428C73D4×#10311yescharacteristic, complemented, Sylow
429C23×Q8—731no—
430C23×Q8C2×D7311yescharacteristic
431C23×C8—731no—
432C23×C8—731no—
433D4×Q8—738no—
434D4×Q8—1464no—
435C2×C4⋊Q8—731no—
436C2×C4⋊Q8—1461no—
437C2×C22⋊Q8—731no—
438C2×C22⋊Q8—731no—
439C2×C22⋊Q8—1461no—
440C2×C22⋊Q8—1461no—
441C2×C4×Q8—731no—
442C2×C4×D4—731no—
443C2×C4×D4—1461no—
444C2×C4×D4—1461no—
445C22×C4⋊C4—731no—
446C22×C4⋊C4—731no—
447C8×D4—1464no—
448C2×C4⋊C8—731no—
449C2×#103—731no—
450C2×#103—731no—
451C2×#103—731no—
452C2×#103—731no—
453C2×#103—731no—
454C2×#103—731no—
455C2×#103—731no—
456C2×#103—731no—
457C2×#103—1464no—
458C2×#103—1464no—
459C2×#103C2×D7311yescharacteristic
460C2×#103C2×D7311yescharacteristic
461C2×#103C2×D7311yescharacteristic
462C2×#103C2×D7311yescharacteristic
463C2×C22⋊C8—731no—
464C2×C22⋊C8C2×D7311yescharacteristic
465C2×C4×C8—731no—
466#389—1461no—
467#385—1461no—
468#385—1461no—
469#384—731no—
470#380—731no—
471#380C2×D7311yescharacteristic
472C4×C4⋊C4—731no—
473#340—731no—
474#340—731no—
475#340—731no—
476#340—731no—
477C22×Q8—21no—
478C22×Q8—22no—
479C22×Q8—22no—
480C22×Q8—22no—
481C22×Q8—41no—
482C22×Q8—41no—
483C22×Q8—2921no—
484C22×Q8—2921no—
485C22×Q8—734no—
486C22×Q8—731no—
487C22×Q8—1461no—
488C22×Q8—1462no—
489C22×Q8—1462no—
490C22×Q8—1462no—
491C22×Q8C4×D7314yescomplemented
492C22×Q8C22×D7311yescharacteristic
493C22×Q8C22×D7311yescharacteristic
494C22×D4—731no—
495C23×C4—21no—
496C23×C4—731no—
497C23×C4—1461no—
498C23×C4—1461no—
499C23×C4—1461no—
500C23×C4C22×D7311yescharacteristic
501C22×C8—2921no—
502C22×C8—2921no—
503C22×C8—731no—
504C22×C8—731no—
505C22×C8—1462no—
506C22×C8—1462no—
507C22×C8—1462no—
508C22×C8—1462no—
509C22×C8C22×D7311yescharacteristic
510C22×C8C22×D7311yescharacteristic
511C4⋊Q8—734no—
512C4⋊Q8—1462no—
513C4⋊Q8—1468no—
514C22⋊Q8—734no—
515C22⋊Q8—734no—
516C22⋊Q8—1468no—
517C22⋊Q8—1468no—
518C22⋊Q8—1462no—
519C22⋊Q8—1462no—
520C4×Q8—734no—
521C4×Q8—1462no—
522C4×D4—2924no—
523C4×D4—734no—
524C4×D4—734no—
525C4×D4—1468no—
526C2×C4⋊C4—2921no—
527C2×C4⋊C4—2921no—
528C2×C4⋊C4—731no—
529C2×C4⋊C4—731no—
530C2×C4⋊C4—731no—
531C2×C4⋊C4—731no—
532C2×C4⋊C4—1462no—
533C2×C4⋊C4—1461no—
534C2×C4⋊C4—1461no—
535C2×C4⋊C4—1461no—
536C2×C4⋊C4—1462no—
537C2×C4⋊C4—1461no—
538C2×C4⋊C4—1461no—
539C2×C4⋊C4—1461no—
540C2×C4⋊C4—1461no—
541C2×C4⋊C4—1461no—
542C2×C4⋊C4—1461no—
543C2×C4⋊C4C22×D7311yescharacteristic
544C2×C4⋊C4C22×D7311yescharacteristic
545C2×C22⋊C4—21no—
546C2×C22⋊C4—731no—
547C2×C22⋊C4—731no—
548C2×C22⋊C4—1461no—
549C2×C22⋊C4—1461no—
550C2×C22⋊C4—1461no—
551C2×C42—731no—
552C2×C42—1461no—
553C2×C42—1461no—
554C4⋊C8—1462no—
555#103—22no—
556#103—22no—
557#103—41no—
558#103—41no—
559#103—2921no—
560#103—2921no—
561#103—734no—
562#103—1462no—
563#103—1462no—
564#103—1462no—
565#103—1462no—
566#103—1462no—
567C22⋊C8—22no—
568C22⋊C8—1462no—
569C4×C8—1462no—
570#95—21no—
571#95—1461no—
572#95—1461no—
573C24—731no—
574C24D4×D7311yescharacteristic
575C2×Q8—24no—
576C2×Q8—21no—
577C2×Q8—21no—
578C2×Q8—21no—
579C2×Q8—21no—
580C2×Q8—28no—
581C2×Q8—21no—
582C2×Q8—21no—
583C2×Q8—21no—
584C2×Q8—21no—
585C2×Q8—42no—
586C2×Q8—42no—
587C2×Q8—44no—
588C2×Q8—44no—
589C2×Q8—44no—
590C2×Q8—2922no—
591C2×Q8—2922no—
592C2×Q8—2924no—
593C2×Q8—2924no—
594C2×Q8—2924no—
595C2×Q8—732no—
596C2×Q8—1464no—
597C2×Q8—1468no—
598C2×Q8—1461no—
599C2×Q8—1461no—
600C2×Q8—1461no—
601C2×Q8—1461no—
602C2×Q8—1461no—
603C2×Q8C2×C4×D7312yes—
604C2×Q8C2×C4×D7312yes—
605C2×Q8D4×D7312yes—
606C2×Q8#1192402712yes—
607C2×D4—734no—
608C2×D4—734no—
609C2×D4—734no—
610C22×C4—21no—
611C22×C4—21no—
612C22×C4—21no—
613C22×C4—21no—
614C22×C4—21no—
615C22×C4—24no—
616C22×C4—21no—
617C22×C4—21no—
618C22×C4—21no—
619C22×C4—42no—
620C22×C4—42no—
621C22×C4—2922no—
622C22×C4—2922no—
623C22×C4—2922no—
624C22×C4—2922no—
625C22×C4—2922no—
626C22×C4—2922no—
627C22×C4—5841no—
628C22×C4—5841no—
629C22×C4—731no—
630C22×C4—731no—
631C22×C4—731no—
632C22×C4—732no—
633C22×C4—732no—
634C22×C4—1464no—
635C22×C4—1461no—
636C22×C4—1461no—
637C22×C4—1461no—
638C22×C4—1461no—
639C22×C4—1461no—
640C22×C4—1461no—
641C22×C4—1461no—
642C22×C4—1461no—
643C22×C4C2×C4×D7312yes—
644C22×C4D4×D7311yescharacteristic
645C22×C4D4×D7312yes—
646C22×C4C23×D7311yescharacteristic
647C2×C8—21no—
648C2×C8—21no—
649C2×C8—21no—
650C2×C8—21no—
651C2×C8—21no—
652C2×C8—21no—
653C2×C8—2924no—
654C2×C8—2924no—
655C2×C8—732no—
656C2×C8—1461no—
657C2×C8—1461no—
658C2×C8—1461no—
659C2×C8—1461no—
660C2×C8—1461no—
661C4⋊C4—21no—
662C4⋊C4—21no—
663C4⋊C4—21no—
664C4⋊C4—21no—
665C4⋊C4—2922no—
666C4⋊C4—2922no—
667C4⋊C4—2922no—
668C4⋊C4—5841no—
669C4⋊C4—734no—
670C4⋊C4—732no—
671C4⋊C4—732no—
672C4⋊C4—1464no—
673C4⋊C4—1464no—
674C4⋊C4—1464no—
675C4⋊C4—1464no—
676C4⋊C4—1461no—
677C4⋊C4—1461no—
678C4⋊C4—1464no—
679C4⋊C4—1461no—
680C4⋊C4—1461no—
681C22⋊C4—42no—
682C22⋊C4—2922no—
683C22⋊C4—734no—
684C22⋊C4—734no—
685C22⋊C4—1464no—
686C22⋊C4—1464no—
687C42—2922no—
688C42—732no—
689C42—732no—
690C42—1464no—
691C23—21no—
692C23—21no—
693C23—21no—
694C23—21no—
695C23—732no—
696C23—732no—
697C23—732no—
698C23—1461no—
699C23—1461no—
700C23—1461no—
701C23—1461no—
702C23C22⋊C4×D7312yes—
703C23SD16×D7312yes—
704C23Q16×D7312yes—
705C23C2×D4×D7311yescharacteristic
706Q8—22no—
707Q8—22no—
708Q8—22no—
709Q8—22no—
710Q8—22no—
711Q8—48no—
712Q8—41no—
713Q8—41no—
714Q8—2928no—
715Q8—2921no—
716Q8—2921no—
717Q8—1462no—
718Q8—1462no—
719Q8#1455655114yescomplemented
720D4—7316no—
721C2×C4—21no—
722C2×C4—22no—
723C2×C4—21no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—48no—
732C2×C4—41no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—41no—
739C2×C4—41no—
740C2×C4—2928no—
741C2×C4—2921no—
742C2×C4—2921no—
743C2×C4—2921no—
744C2×C4—2921no—
745C2×C4—2921no—
746C2×C4—2921no—
747C2×C4—2921no—
748C2×C4—2921no—
749C2×C4—2921no—
750C2×C4—5844no—
751C2×C4—5844no—
752C2×C4—732no—
753C2×C4—732no—
754C2×C4—732no—
755C2×C4—732no—
756C2×C4—732no—
757C2×C4—1462no—
758C2×C4—1462no—
759C2×C4—1462no—
760C2×C4—1461no—
761C2×C4—1461no—
762C2×C4—1461no—
763C2×C4—1461no—
764C2×C4—1462no—
765C2×C4—1462no—
766C2×C4—1462no—
767C2×C4—1462no—
768C2×C4C22⋊C4×D7312yes—
769C2×C4C22×C4×D7311yescharacteristic
770C2×C4C2×D4×D7311yescharacteristic
771C2×C4C2×D4×D7311yescharacteristic
772C2×C4C2×#1192402711yescharacteristic
773C2×C4#1455663611yescharacteristic
774C2×C4#1455663611yescharacteristic
775C8—41no—
776C8—41no—
777C8—2921no—
778C8—1462no—
779C22—22no—
780C22—22no—
781C22—22no—
782C22—22no—
783C22—22no—
784C22—22no—
785C22—734no—
786C22—1462no—
787C22—1462no—
788C22—1462no—
789C22—1462no—
790C22—1462no—
791C22—1462no—
792C22#103×D7314yescomplemented
793C22C2×C22⋊C4×D7311yescharacteristic
794C22#1798921911yescharacteristic
795C22#1798922411yescharacteristic
796C22C2×SD16×D7311yescharacteristic
797C22C2×Q16×D7311yescharacteristic
798C22#1798939611yescharacteristic
799C22#1798940311yescharacteristic
800C4—22no—
801C4—24no—
802C4—42no—
803C4—81no—
804C4—81no—
805C4—2922no—
806C4—2922no—
807C4—2922no—
808C4—5841no—
809C4—734no—
810C4—1462no—
811C4—1462no—
812C4C2×#1455655111yescharacteristic
813C4#1798906011yescharacteristic
814C4#1798921911yescharacteristic
815C4#1798922411yescharacteristic
816C2—24no—
817C2—1464no—
818C2#2261274711yescharacteristic
819C2C2×#103×D7311yescharacteristic
820C2#2261846311yescharacteristic
821C2#2262162011yescharacteristic
822C2#2262167611yescharacteristic
823C2#2262178911yescharacteristic
824C2#2262180011yescharacteristic
subgroupG/H
centerC23C2×D4×D73
commutatorC2×C4×C73C23×C4
FrattiniC22×C4C23×D73
FittingC73×#1787C2
socleC23×C73C22×D4
prime radicalC22×C22⋊D73D4
cosocleC22×C4×C73C24
hypercenter#1787D73
hypocenterC73D4×#103
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1787

Complements

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

NH ≅ G/Ntype
3. C22×#14556515C2semidirect
4. C2×#103×D73C2semidirect
6. #22610852C2semidirect
7. #22610731C2semidirect
8. #22610352C2semidirect
9. #22610351C2semidirect
10. #22610236C2semidirect
11. #22610235C2semidirect
12. #22609934C2semidirect
13. #22609864C2semidirect
14. #103×Dic73C2semidirect
15. C73×#1787C2semidirect
20. Q8×C22⋊D73C4semidirect
71. C2×Q8×D73C2×C4semidirect
87. #14556589C2×C4semidirect
90. #14556570C2×C4semidirect
93. #14556567C2×C4semidirect
95. Q8×Dic73C2×C4semidirect
131. #14556515D4semidirect
144. C22×Q8×C73C2×C4semidirect
301. Q8×C73C4×D4semidirect
328. C22⋊D73#103semidirect
372. C22×C73C2×#103semidirect
386. C2×D73C2×#103semidirect
402. Dic73C2×#103semidirect
426. #1787D73semidirect
428. C73D4×#103semidirect
491. C22×Q8C4×D73semidirect
719. Q8#14556551semidirect
792. C22#103×D73semidirect

Maximal subgroups

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

subgroupindex
C2×Q8×C22⋊D732
C2×#179886502
C22×#145565152
C2×#103×D732
#226128272
#226108522
#226107312
#226103522
#226103512
#226102362
#226102352
#226099342
#226098642
#103×Dic732
C73×#17872
D4×#10373