Finite Group Databasebeta

← C73×#18784 #32928188

Subgroups — C73×#18784 #32928188

Order 18688.

956 conjugacy classes of subgroups.

The subgroup lattice has 756 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C73×#3482C211yesmaximal, characteristic, complemented
2C73×#3228C211yesmaximal, characteristic, complemented
3C73×#3115C211yesmaximal, characteristic, complemented
4C73×#3035C211yesmaximal, characteristic, complemented
5C73×#1652C211yesmaximal, characteristic, complemented
6C73×#1651C211yesmaximal, characteristic, complemented
7C73×#1648C211yesmaximal, characteristic, complemented
8C73×#1647C211yesmaximal, characteristic, complemented
9C73×#1628C211yesmaximal, characteristic, complemented
10C73×#1627C211yesmaximal, characteristic, complemented
11C73×#1626C211yesmaximal, characteristic, complemented
12C73×#1625C211yesmaximal, characteristic, complemented
13C73×#1552C211yesmaximal, characteristic, complemented
14C73×#1488C211yesmaximal, characteristic, complemented
15C73×#1477C211yesmaximal, characteristic, complemented
16C2×#135×C73—21no—
17#557×C73C2211yescharacteristic
18#556×C73—21no—
19#556×C73C2211yescharacteristic
20#552×C73—22no—
21#552×C73—21no—
22D4×Q8×C73C2211yescharacteristic
23#548×C73—21no—
24#547×C73—21no—
25#547×C73C2211yescharacteristic
26#533×C73—21no—
27#533×C73C2211yescharacteristic
28#532×C73C2211yescharacteristic
29#529×C73—21no—
30#529×C73—22no—
31C4×#41×C73—21no—
32C4×#41×C73C2211yescharacteristic
33C4×#41×C73C2211yescharacteristic
34C2×C4×Q8×C73—21no—
35#500×C73C2211yescharacteristic
36#498×C73C2211yescharacteristic
37#486×C73C2211yescharacteristic
38#486×C73C2211yescharacteristic
39#482×C73—22no—
40#482×C73—21no—
41#478×C73—22no—
42#475×C73C2211yescharacteristic
43#474×C73C2211yescharacteristic
44#464×C73—21no—
45#463×C73—21no—
46#462×C73C2211yescharacteristic
47#461×C73C2211yescharacteristic
48#460×C73C2211yescharacteristic
49#460×C73C2211yescharacteristic
50#459×C73C2211yescharacteristic
51#459×C73C2211yescharacteristic
52#449×C73—21no—
53#442×C73—21no—
54#440×C73—21no—
55#432×C73C2211yescharacteristic
56#431×C73C2211yescharacteristic
57C2×C4⋊C8×C73C2211yescharacteristic
58#416×C73—21no—
59#332×C73C2211yescharacteristic
60#332×C73C2211yescharacteristic
61#332×C73C2211yescharacteristic
62#332×C73C2211yescharacteristic
63Q8⋊C8×C73C2211yescharacteristic
64Q8⋊C8×C73C2211yescharacteristic
65Q8⋊C8×C73C2211yescharacteristic
66Q8⋊C8×C73C2211yescharacteristic
67D4⋊C8×C73C2211yescharacteristic
68D4⋊C8×C73C2211yescharacteristic
69D4⋊C8×C73C2211yescharacteristic
70D4⋊C8×C73C2211yescharacteristic
71C2×#41×C73—21no—
72C2×#41×C73—21no—
73C2×#41×C73D411yescharacteristic
74C2×#41×C73D411yescharacteristic
75C22×Q8×C73—21no—
76#135×C73—44no—
77C2×Q16×C73—21no—
78C2×SD16×C73—21no—
79C2×SD16×C73—21no—
80C2×SD16×C73—21no—
81C2×D8×C73—21no—
82C2×D8×C73—21no—
83C22×C8×C73—21no—
84C4⋊Q8×C73—21no—
85C4⋊Q8×C73—21no—
86C4⋊Q8×C73C2311yescharacteristic
87C4⋊Q8×C73C2311yescharacteristic
88C4⋊Q8×C73C2311yescharacteristic
89#127×C73C2311yescharacteristic
90#126×C73—22no—
91#126×C73—22no—
92#126×C73—22no—
93#125×C73—22no—
94#125×C73—22no—
95#125×C73—21no—
96#125×C73D412yes—
97#124×C73—22no—
98#124×C73—21no—
99#124×C73—21no—
100#123×C73—22no—
101#123×C73—22no—
102#123×C73—22no—
103C22⋊Q8×C73—22no—
104C22⋊Q8×C73—21no—
105C22⋊Q8×C73—21no—
106C22⋊Q8×C73—21no—
107C22⋊Q8×C73—21no—
108C22⋊Q8×C73—22no—
109C22⋊Q8×C73—21no—
110#121×C73—22no—
111#121×C73—21no—
112#121×C73—21no—
113#121×C73—21no—
114C4×Q8×C73—22no—
115C4×Q8×C73—22no—
116C4×Q8×C73—21no—
117C4×Q8×C73—21no—
118C4×Q8×C73—21no—
119C4×Q8×C73—21no—
120C4×Q8×C73—21no—
121C4×Q8×C73D411yescharacteristic
122C4×Q8×C73D411yescharacteristic
123C4×Q8×C73C2311yescharacteristic
124C4×Q8×C73C2311yescharacteristic
125C4×D4×C73—22no—
126C4×D4×C73—22no—
127C4×D4×C73—21no—
128C4×D4×C73—21no—
129C4×D4×C73—21no—
130C4×D4×C73—21no—
131C4×D4×C73—21no—
132C4×D4×C73—21no—
133C4×D4×C73—21no—
134C4×D4×C73D411yescharacteristic
135C4×D4×C73D411yescharacteristic
136C4×D4×C73C2311yescharacteristic
137C4×D4×C73C2311yescharacteristic
138#117×C73—22no—
139#117×C73—22no—
140#117×C73—21no—
141#117×C73—21no—
142#117×C73—21no—
143#117×C73D411yescharacteristic
144#117×C73D411yescharacteristic
145#117×C73D412yes—
146C2×C4⋊C4×C73—22no—
147C2×C4⋊C4×C73—21no—
148C2×C42×C73—22no—
149C2×C42×C73—21no—
150C2×C42×C73—21no—
151C2×C42×C73C2311yescharacteristic
152#107×C73—21no—
153#107×C73—22no—
154#106×C73—21no—
155#106×C73—22no—
156C4⋊C8×C73—21no—
157C4⋊C8×C73—21no—
158C4⋊C8×C73C2311yescharacteristic
159C4⋊C8×C73C2311yescharacteristic
160C4⋊C8×C73C2311yescharacteristic
161C4⋊C8×C73C2311yescharacteristic
162#103×C73—21no—
163#103×C73—21no—
164#103×C73—21no—
165#102×C73—21no—
166#102×C73—21no—
167#102×C73—21no—
168#102×C73—21no—
169#102×C73—21no—
170#102×C73—22no—
171#102×C73—22no—
172C22⋊C8×C73—21no—
173C22⋊C8×C73—21no—
174#97×C73—21no—
175C4×C8×C73C2311yescharacteristic
176C4×C8×C73C2311yescharacteristic
177#41×C73—22no—
178#41×C73—22no—
179#41×C73—41no—
180#41×C73—41no—
181#41×C73—42no—
182#41×C73—42no—
183#41×C73—42no—
184#41×C73—42no—
185C2×Q8×C73—22no—
186C2×Q8×C73—21no—
187C2×Q8×C73—21no—
188C2×Q8×C73—21no—
189C2×Q8×C73—42no—
190C2×Q8×C73—42no—
191C2×Q8×C73C2×D411yescharacteristic
192C2×Q8×C73C2×D411yescharacteristic
193C2×D4×C73—22no—
194C2×D4×C73—21no—
195C2×D4×C73—21no—
196C2×D4×C73—21no—
197C2×D4×C73—21no—
198C2×D4×C73—21no—
199C2×D4×C73—41no—
200C2×D4×C73C2×D411yescharacteristic
201C2×D4×C73C2×D411yescharacteristic
202C22×C4×C73—22no—
203C22×C4×C73—22no—
204C22×C4×C73—21no—
205C22×C4×C73—21no—
206C22×C4×C73—21no—
207C22×C4×C73—21no—
208C22×C4×C73—21no—
209C22×C4×C73—21no—
210C22×C4×C73—41no—
211C22×C4×C73C2×D411yescharacteristic
212C22×C4×C73C2×D411yescharacteristic
213C22×C4×C73C2×D411yescharacteristic
214Q16×C73—42no—
215SD16×C73—42no—
216SD16×C73—42no—
217SD16×C73—42no—
218D8×C73—42no—
219D8×C73—42no—
220C2×C8×C73—21no—
221C2×C8×C73—21no—
222C2×C8×C73—21no—
223C2×C8×C73—21no—
224C2×C8×C73—21no—
225C2×C8×C73—21no—
226C2×C8×C73—42no—
227C4⋊C4×C73—22no—
228C4⋊C4×C73—22no—
229C4⋊C4×C73—22no—
230C4⋊C4×C73—22no—
231C4⋊C4×C73—22no—
232C4⋊C4×C73—22no—
233C4⋊C4×C73—21no—
234C4⋊C4×C73—22no—
235C4⋊C4×C73—22no—
236C4⋊C4×C73—21no—
237C4⋊C4×C73—21no—
238C4⋊C4×C73—21no—
239C4⋊C4×C73—21no—
240C4⋊C4×C73—21no—
241C4⋊C4×C73—21no—
242C4⋊C4×C73—21no—
243C4⋊C4×C73C2×D411yescharacteristic
244C4⋊C4×C73C2×D411yescharacteristic
245C4⋊C4×C73C2×D411yescharacteristic
246C4⋊C4×C73C2×D412yes—
247C4⋊C4×C73C2×D411yescharacteristic
248C4⋊C4×C73C2×D412yes—
249C22⋊C4×C73—22no—
250C22⋊C4×C73—22no—
251C22⋊C4×C73—22no—
252C22⋊C4×C73—22no—
253C22⋊C4×C73—21no—
254C22⋊C4×C73—21no—
255C22⋊C4×C73—22no—
256C22⋊C4×C73—21no—
257C22⋊C4×C73—21no—
258C22⋊C4×C73—21no—
259C22⋊C4×C73—21no—
260C22⋊C4×C73—41no—
261C22⋊C4×C73—41no—
262C42×C73—22no—
263C42×C73—22no—
264C42×C73—21no—
265C42×C73—21no—
266C42×C73—21no—
267C42×C73—22no—
268C42×C73—21no—
269C42×C73—21no—
270C42×C73—21no—
271C42×C73C2×D411yescharacteristic
272C42×C73C2×D411yescharacteristic
273C42×C73C2×D411yescharacteristic
274C42×C73C2411yescharacteristic
275C23×C73—21no—
276C23×C73—21no—
277C23×C73—41no—
278C23×C73#12011yescharacteristic
279Q8×C73—21no—
280Q8×C73—21no—
281Q8×C73—21no—
282Q8×C73—44no—
283Q8×C73—41no—
284Q8×C73—41no—
285Q8×C73—41no—
286Q8×C73—41no—
287Q8×C73—41no—
288Q8×C73—41no—
289Q8×C73#13512yescomplemented
290D4×C73—21no—
291D4×C73—21no—
292D4×C73—21no—
293D4×C73—42no—
294D4×C73—42no—
295D4×C73—42no—
296D4×C73—44no—
297D4×C73—41no—
298D4×C73—41no—
299D4×C73—41no—
300D4×C73—41no—
301D4×C73—82no—
302D4×C73AGL(1,ℤ/8)12yes—
303C2×C4×C73—21no—
304C2×C4×C73—21no—
305C2×C4×C73—21no—
306C2×C4×C73—21no—
307C2×C4×C73—21no—
308C2×C4×C73—21no—
309C2×C4×C73—21no—
310C2×C4×C73—21no—
311C2×C4×C73—22no—
312C2×C4×C73—21no—
313C2×C4×C73—21no—
314C2×C4×C73—22no—
315C2×C4×C73—41no—
316C2×C4×C73—42no—
317C2×C4×C73—42no—
318C2×C4×C73—42no—
319C2×C4×C73—42no—
320C2×C4×C73—44no—
321C2×C4×C73—44no—
322C2×C4×C73—41no—
323C2×C4×C73—41no—
324C2×C4×C73—41no—
325C2×C4×C73—41no—
326C2×C4×C73—41no—
327C2×C4×C73—82no—
328C2×C4×C73#12011yescharacteristic
329C2×C4×C73#12011yescharacteristic
330C2×C4×C73#12011yescharacteristic
331C2×C4×C73C22×D411yescharacteristic
332C2×C4×C73C22×D411yescharacteristic
333C2×C4×C73C22×D411yescharacteristic
334C8×C73—41no—
335C8×C73—41no—
336C8×C73—41no—
337C8×C73—41no—
338C8×C73—41no—
339C8×C73—41no—
340C22×C73—21no—
341C22×C73—21no—
342C22×C73—22no—
343C22×C73—21no—
344C22×C73—41no—
345C22×C73—41no—
346C22×C73—41no—
347C22×C73—41no—
348C22×C73—41no—
349C22×C73—81no—
350C22×C73—81no—
351C22×C73—81no—
352C22×C73C2×#12011yescharacteristic
353C4×C73—21no—
354C4×C73—22no—
355C4×C73—21no—
356C4×C73—21no—
357C4×C73—21no—
358C4×C73—42no—
359C4×C73—41no—
360C4×C73—41no—
361C4×C73—41no—
362C4×C73—42no—
363C4×C73—41no—
364C4×C73—41no—
365C4×C73—81no—
366C4×C73C2×#13511yescharacteristic
367C4×C73C2×AGL(1,ℤ/8)11yescharacteristic
368C4×C73#57511yescharacteristic
369C4×C73#57511yescharacteristic
370#18784C7311yesmaximal, characteristic, direct product factor, Sylow
371C2×C73—41no—
372C2×C73—42no—
373C2×C73—81no—
374C2×C73—161no—
375C2×C73#300211yescharacteristic
376C2×C73#300611yescharacteristic
377C2×C73#302011yescharacteristic
378#3482C2×C7311yescharacteristic, complemented
379#3228C2×C7311yescharacteristic, complemented
380#3115C2×C7311yescharacteristic, complemented
381#3035C2×C7311yescharacteristic, complemented
382#1652C2×C7311yescharacteristic, complemented
383#1651C2×C7311yescharacteristic, complemented
384#1648C2×C7311yescharacteristic, complemented
385#1647C2×C7311yescharacteristic, complemented
386#1628C2×C7311yescharacteristic, complemented
387#1627C2×C7311yescharacteristic, complemented
388#1626C2×C7311yescharacteristic, complemented
389#1625C2×C7311yescharacteristic, complemented
390#1552C2×C7311yescharacteristic, complemented
391#1488C2×C7311yescharacteristic, complemented
392#1477C2×C7311yescharacteristic, complemented
393C73#1878411yescharacteristic, direct product factor, Sylow
394C2×#135—21no—
395#557C22×C7311yescharacteristic
396#556—21no—
397#556C22×C7311yescharacteristic
398#552—22no—
399#552—21no—
400D4×Q8C22×C7311yescharacteristic
401#548—21no—
402#547—21no—
403#547C22×C7311yescharacteristic
404#533—21no—
405#533C22×C7311yescharacteristic
406#532C22×C7311yescharacteristic
407#529—21no—
408#529—22no—
409C4×#41—21no—
410C4×#41C22×C7311yescharacteristic
411C4×#41C22×C7311yescharacteristic
412C2×C4×Q8—21no—
413#500C22×C7311yescharacteristic
414#498C22×C7311yescharacteristic
415#486C22×C7311yescharacteristic
416#486C22×C7311yescharacteristic
417#482—21no—
418#482—22no—
419#478—22no—
420#475C22×C7311yescharacteristic
421#474C22×C7311yescharacteristic
422#464—21no—
423#463—21no—
424#462C22×C7311yescharacteristic
425#461C22×C7311yescharacteristic
426#460C22×C7311yescharacteristic
427#460C22×C7311yescharacteristic
428#459C22×C7311yescharacteristic
429#459C22×C7311yescharacteristic
430#449—21no—
431#442—21no—
432#440—21no—
433#432C22×C7311yescharacteristic
434#431C22×C7311yescharacteristic
435C2×C4⋊C8C22×C7311yescharacteristic
436#416—21no—
437#332C22×C7311yescharacteristic
438#332C22×C7311yescharacteristic
439#332C22×C7311yescharacteristic
440#332C22×C7311yescharacteristic
441Q8⋊C8C22×C7311yescharacteristic
442Q8⋊C8C22×C7311yescharacteristic
443Q8⋊C8C22×C7311yescharacteristic
444Q8⋊C8C22×C7311yescharacteristic
445D4⋊C8C22×C7311yescharacteristic
446D4⋊C8C22×C7311yescharacteristic
447D4⋊C8C22×C7311yescharacteristic
448D4⋊C8C22×C7311yescharacteristic
449C2×#41—21no—
450C2×#41—21no—
451C2×#41D4×C7311yescharacteristic
452C2×#41D4×C7311yescharacteristic
453C22×Q8—21no—
454#135—44no—
455C2×Q16—21no—
456C2×SD16—21no—
457C2×SD16—21no—
458C2×SD16—21no—
459C2×D8—21no—
460C2×D8—21no—
461C22×C8—21no—
462C4⋊Q8—21no—
463C4⋊Q8—21no—
464C4⋊Q8C23×C7311yescharacteristic
465C4⋊Q8C23×C7311yescharacteristic
466C4⋊Q8C23×C7311yescharacteristic
467#127C23×C7311yescharacteristic
468#126—22no—
469#126—22no—
470#126—22no—
471#125—22no—
472#125—22no—
473#125—21no—
474#125D4×C7312yes—
475#124—22no—
476#124—21no—
477#124—21no—
478#123—22no—
479#123—22no—
480#123—22no—
481C22⋊Q8—22no—
482C22⋊Q8—21no—
483C22⋊Q8—21no—
484C22⋊Q8—21no—
485C22⋊Q8—21no—
486C22⋊Q8—22no—
487C22⋊Q8—21no—
488#121—22no—
489#121—21no—
490#121—21no—
491#121—21no—
492C4×Q8—22no—
493C4×Q8—22no—
494C4×Q8—21no—
495C4×Q8—21no—
496C4×Q8—21no—
497C4×Q8—21no—
498C4×Q8—21no—
499C4×Q8D4×C7311yescharacteristic
500C4×Q8D4×C7311yescharacteristic
501C4×Q8C23×C7311yescharacteristic
502C4×Q8C23×C7311yescharacteristic
503C4×D4—22no—
504C4×D4—22no—
505C4×D4—21no—
506C4×D4—21no—
507C4×D4—21no—
508C4×D4—21no—
509C4×D4—21no—
510C4×D4—21no—
511C4×D4—21no—
512C4×D4D4×C7311yescharacteristic
513C4×D4D4×C7311yescharacteristic
514C4×D4C23×C7311yescharacteristic
515C4×D4C23×C7311yescharacteristic
516#117—22no—
517#117—22no—
518#117—21no—
519#117—21no—
520#117—21no—
521#117D4×C7311yescharacteristic
522#117D4×C7311yescharacteristic
523#117D4×C7312yes—
524C2×C4⋊C4—22no—
525C2×C4⋊C4—21no—
526C2×C42—22no—
527C2×C42—21no—
528C2×C42—21no—
529C2×C42C23×C7311yescharacteristic
530#107—21no—
531#107—22no—
532#106—21no—
533#106—22no—
534C4⋊C8—21no—
535C4⋊C8—21no—
536C4⋊C8C23×C7311yescharacteristic
537C4⋊C8C23×C7311yescharacteristic
538C4⋊C8C23×C7311yescharacteristic
539C4⋊C8C23×C7311yescharacteristic
540#103—21no—
541#103—21no—
542#103—21no—
543#102—21no—
544#102—21no—
545#102—21no—
546#102—21no—
547#102—21no—
548#102—22no—
549#102—22no—
550C22⋊C8—21no—
551C22⋊C8—21no—
552#97—21no—
553C4×C8C23×C7311yescharacteristic
554C4×C8C23×C7311yescharacteristic
555#41—22no—
556#41—22no—
557#41—41no—
558#41—41no—
559#41—42no—
560#41—42no—
561#41—42no—
562#41—42no—
563C2×Q8—22no—
564C2×Q8—21no—
565C2×Q8—21no—
566C2×Q8—21no—
567C2×Q8—42no—
568C2×Q8—42no—
569C2×Q8C2×D4×C7311yescharacteristic
570C2×Q8C2×D4×C7311yescharacteristic
571C2×D4—22no—
572C2×D4—21no—
573C2×D4—21no—
574C2×D4—21no—
575C2×D4—21no—
576C2×D4—21no—
577C2×D4—41no—
578C2×D4C2×D4×C7311yescharacteristic
579C2×D4C2×D4×C7311yescharacteristic
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—41no—
589C22×C4C2×D4×C7311yescharacteristic
590C22×C4C2×D4×C7311yescharacteristic
591C22×C4C2×D4×C7311yescharacteristic
592Q16—42no—
593SD16—42no—
594SD16—42no—
595SD16—42no—
596D8—42no—
597D8—42no—
598C2×C8—21no—
599C2×C8—21no—
600C2×C8—21no—
601C2×C8—21no—
602C2×C8—21no—
603C2×C8—21no—
604C2×C8—42no—
605C4⋊C4—22no—
606C4⋊C4—22no—
607C4⋊C4—22no—
608C4⋊C4—22no—
609C4⋊C4—22no—
610C4⋊C4—22no—
611C4⋊C4—21no—
612C4⋊C4—22no—
613C4⋊C4—22no—
614C4⋊C4—21no—
615C4⋊C4—21no—
616C4⋊C4—21no—
617C4⋊C4—21no—
618C4⋊C4—21no—
619C4⋊C4—21no—
620C4⋊C4—21no—
621C4⋊C4C2×D4×C7311yescharacteristic
622C4⋊C4C2×D4×C7311yescharacteristic
623C4⋊C4C2×D4×C7311yescharacteristic
624C4⋊C4C2×D4×C7312yes—
625C4⋊C4C2×D4×C7311yescharacteristic
626C4⋊C4C2×D4×C7312yes—
627C22⋊C4—22no—
628C22⋊C4—22no—
629C22⋊C4—22no—
630C22⋊C4—22no—
631C22⋊C4—21no—
632C22⋊C4—21no—
633C22⋊C4—22no—
634C22⋊C4—21no—
635C22⋊C4—21no—
636C22⋊C4—21no—
637C22⋊C4—21no—
638C22⋊C4—41no—
639C22⋊C4—41no—
640C42—22no—
641C42—22no—
642C42—21no—
643C42—21no—
644C42—21no—
645C42—22no—
646C42—21no—
647C42—21no—
648C42—21no—
649C42C2×D4×C7311yescharacteristic
650C42C2×D4×C7311yescharacteristic
651C42C2×D4×C7311yescharacteristic
652C42C24×C7311yescharacteristic
653C23—21no—
654C23—21no—
655C23—41no—
656C23#120×C7311yescharacteristic
657Q8—21no—
658Q8—21no—
659Q8—21no—
660Q8—44no—
661Q8—41no—
662Q8—41no—
663Q8—41no—
664Q8—41no—
665Q8—41no—
666Q8—41no—
667Q8#135×C7312yescomplemented
668D4—21no—
669D4—21no—
670D4—21no—
671D4—42no—
672D4—42no—
673D4—42no—
674D4—44no—
675D4—41no—
676D4—41no—
677D4—41no—
678D4—41no—
679D4—82no—
680D4AGL(1,ℤ/8)×C7312yes—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—21no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—21no—
689C2×C4—22no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—22no—
693C2×C4—41no—
694C2×C4—42no—
695C2×C4—42no—
696C2×C4—44no—
697C2×C4—42no—
698C2×C4—42no—
699C2×C4—44no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—82no—
706C2×C4#120×C7311yescharacteristic
707C2×C4#120×C7311yescharacteristic
708C2×C4#120×C7311yescharacteristic
709C2×C4C22×D4×C7311yescharacteristic
710C2×C4C22×D4×C7311yescharacteristic
711C2×C4C22×D4×C7311yescharacteristic
712C8—41no—
713C8—41no—
714C8—41no—
715C8—41no—
716C8—41no—
717C8—41no—
718C22—21no—
719C22—21no—
720C22—22no—
721C22—21no—
722C22—41no—
723C22—41no—
724C22—41no—
725C22—41no—
726C22—41no—
727C22—81no—
728C22—81no—
729C22—81no—
730C22C2×#120×C7311yescharacteristic
731C4—21no—
732C4—22no—
733C4—21no—
734C4—21no—
735C4—21no—
736C4—42no—
737C4—41no—
738C4—41no—
739C4—41no—
740C4—42no—
741C4—41no—
742C4—41no—
743C4—81no—
744C4C2×#135×C7311yescharacteristic
745C4C2×AGL(1,ℤ/8)×C7311yescharacteristic
746C4#575×C7311yescharacteristic
747C4#575×C7311yescharacteristic
748C2—41no—
749C2—42no—
750C2—81no—
751C2—161no—
752C2C73×#300211yescharacteristic
753C2C73×#300611yescharacteristic
754C2C73×#302011yescharacteristic
subgroupG/H
center, socleC22×C73C2×#120
commutator, Frattini, cosocleC42C24×C73
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C73 ◁ C2×C42×C73 ◁ G

Complements

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

NH ≅ G/Ntype
1. C73×#3482C2semidirect
2. C73×#3228C2semidirect
3. C73×#3115C2semidirect
4. C73×#3035C2semidirect
5. C73×#1652C2semidirect
6. C73×#1651C2semidirect
7. C73×#1648C2semidirect
8. C73×#1647C2semidirect
9. C73×#1628C2semidirect
10. C73×#1627C2semidirect
11. C73×#1626C2semidirect
12. C73×#1625C2semidirect
13. C73×#1552C2semidirect
14. C73×#1488C2semidirect
15. C73×#1477C2semidirect
289. Q8×C73#135semidirect
370. #18784C73direct (N × H)
378. #3482C2×C73semidirect
379. #3228C2×C73semidirect
380. #3115C2×C73semidirect
381. #3035C2×C73semidirect
382. #1652C2×C73semidirect
383. #1651C2×C73semidirect
384. #1648C2×C73semidirect
385. #1647C2×C73semidirect
386. #1628C2×C73semidirect
387. #1627C2×C73semidirect
388. #1626C2×C73semidirect
389. #1625C2×C73semidirect
390. #1552C2×C73semidirect
391. #1488C2×C73semidirect
392. #1477C2×C73semidirect
393. C73#18784direct (N × H)
667. Q8#135×C73semidirect

Maximal subgroups

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

subgroupindex
C73×#34822
C73×#32282
C73×#31152
C73×#30352
C73×#16522
C73×#16512
C73×#16482
C73×#16472
C73×#16282
C73×#16272
C73×#16262
C73×#16252
C73×#15522
C73×#14882
C73×#14772
#1878473