Finite Group Databasebeta

← C73×#18739 #32928143

Subgroups — C73×#18739 #32928143

Order 18688.

938 conjugacy classes of subgroups.

The subgroup lattice has 776 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C73×#3546C211yesmaximal, characteristic
2C73×#3246C211yesmaximal, characteristic, complemented
3C73×#3233C211yesmaximal, characteristic, complemented
4C73×#3182C211yesmaximal, characteristic, complemented
5C73×#1650C211yesmaximal, characteristic, complemented
6C73×#1647C211yesmaximal, characteristic, complemented
7C73×#1642C211yesmaximal, characteristic, complemented
8C73×#1639C211yesmaximal, characteristic, complemented
9C73×#1638C211yesmaximal, characteristic, complemented
10C73×#1635C211yesmaximal, characteristic, complemented
11C73×#1631C211yesmaximal, characteristic, complemented
12C73×#1629C211yesmaximal, characteristic, complemented
13C73×#1540C211yesmaximal, characteristic, complemented
14C73×#1484C211yesmaximal, characteristic, complemented
15C73×#1483C211yesmaximal, characteristic, complemented
16#560×C73—22no—
17#556×C73C2211yescharacteristic
18#553×C73—21no—
19#550×C73—21no—
20#550×C73C2211yescharacteristic
21#547×C73C2211yescharacteristic
22#546×C73—21no—
23#546×C73—21no—
24D42×C73C2211yescharacteristic
25#542×C73—21no—
26#538×C73—22no—
27#537×C73—21no—
28#535×C73—21no—
29#535×C73—21no—
30#533×C73C2211yescharacteristic, complemented
31#532×C73C2211yescharacteristic
32#532×C73C2211yescharacteristic
33#529×C73C2211yescharacteristic
34#500×C73C2211yescharacteristic, complemented
35#499×C73—21no—
36#492×C73C2211yescharacteristic
37#488×C73—21no—
38#487×C73C2211yescharacteristic, complemented
39#486×C73C2211yescharacteristic
40#485×C73—21no—
41#482×C73—21no—
42#477×C73C2211yescharacteristic, complemented
43#476×C73C2211yescharacteristic
44#476×C73C2211yescharacteristic
45#476×C73C2211yescharacteristic, complemented
46#475×C73—21no—
47#475×C73C2211yescharacteristic, complemented
48#474×C73C2211yescharacteristic
49#468×C73—22no—
50#465×C73—21no—
51#465×C73—21no—
52#461×C73C2211yescharacteristic
53#461×C73C2211yescharacteristic, complemented
54#460×C73—21no—
55#440×C73—22no—
56#431×C73C2211yescharacteristic, complemented
57C2×C4⋊C8×C73C2211yescharacteristic, complemented
58C4×M16×C73C2211yescharacteristic, complemented
59#332×C73C2211yescharacteristic, complemented
60#332×C73C2211yescharacteristic, complemented
61#331×C73C2211yescharacteristic
62#331×C73C2211yescharacteristic
63Q8⋊C8×C73C2211yescharacteristic, complemented
64Q8⋊C8×C73C2211yescharacteristic, complemented
65D4⋊C8×C73C2211yescharacteristic
66D4⋊C8×C73C2211yescharacteristic
67D4⋊C8×C73C2211yescharacteristic
68D4⋊C8×C73C2211yescharacteristic
69D4⋊C8×C73C2211yescharacteristic, complemented
70D4⋊C8×C73C2211yescharacteristic, complemented
71C2×#41×C73—21no—
72C2×#41×C73—21no—
73C2×#41×C73—21no—
74C2×#41×C73—21no—
75C22×D4×C73—21no—
76C22×D4×C73—21no—
77C2×SD16×C73—22no—
78C2×SD16×C73—21no—
79C2×SD16×C73—21no—
80C2×M16×C73—21no—
81C22×C8×C73—21no—
82C4⋊Q8×C73D411yescharacteristic
83C4⋊Q8×C73C2311yescharacteristic
84C4⋊Q8×C73C2311yescharacteristic
85C4⋊Q8×C73C2311yescharacteristic
86#127×C73—22no—
87#127×C73—21no—
88#127×C73D411yescharacteristic
89#127×C73C2311yescharacteristic
90#126×C73—22no—
91#126×C73—22no—
92#126×C73—21no—
93#125×C73—21no—
94#125×C73D411yescharacteristic
95#124×C73—22no—
96#124×C73—21no—
97#124×C73—21no—
98#124×C73—21no—
99#124×C73D411yescharacteristic
100#123×C73—22no—
101#123×C73—22no—
102#123×C73—21no—
103#123×C73—22no—
104C22⋊Q8×C73—22no—
105C22⋊Q8×C73—21no—
106C22⋊Q8×C73—21no—
107C22⋊Q8×C73—21no—
108C22⋊Q8×C73—21no—
109C22⋊Q8×C73D411yescharacteristic
110#121×C73—22no—
111#121×C73—22no—
112#121×C73—22no—
113#121×C73—22no—
114#121×C73—22no—
115#121×C73—21no—
116#121×C73—22no—
117#121×C73—21no—
118#121×C73—21no—
119#121×C73—21no—
120#121×C73—21no—
121#121×C73—21no—
122#121×C73D411yescharacteristic
123#121×C73D411yescharacteristic
124#121×C73D412yes—
125#121×C73D411yescharacteristic
126#120×C73—22no—
127#120×C73—22no—
128#120×C73—22no—
129#120×C73—22no—
130C4×Q8×C73—21no—
131C4×Q8×C73—21no—
132C4×Q8×C73—21no—
133C4×Q8×C73C2311yescharacteristic
134C4×D4×C73—22no—
135C4×D4×C73—21no—
136C4×D4×C73—21no—
137C4×D4×C73—21no—
138C4×D4×C73—21no—
139C4×D4×C73D412yes—
140C4×D4×C73C2311yescharacteristic
141C4×D4×C73C2311yescharacteristic
142C4×D4×C73C2311yescharacteristic
143#117×C73—21no—
144#117×C73—21no—
145#117×C73—21no—
146C2×C4⋊C4×C73—21no—
147C2×C22⋊C4×C73—22no—
148C2×C42×C73C2311yescharacteristic
149#107×C73—22no—
150#107×C73—21no—
151#107×C73—21no—
152#106×C73—21no—
153#106×C73—21no—
154#106×C73—21no—
155#106×C73—21no—
156C4⋊C8×C73—21no—
157C4⋊C8×C73C2311yescharacteristic
158C4⋊C8×C73C2311yescharacteristic
159C4⋊C8×C73C2311yescharacteristic
160C4⋊C8×C73C2311yescharacteristic
161#103×C73—21no—
162#103×C73—21no—
163#103×C73—22no—
164#103×C73—21no—
165#103×C73—21no—
166#102×C73—22no—
167#102×C73—21no—
168#102×C73—21no—
169#102×C73—21no—
170#102×C73—21no—
171C22⋊C8×C73—21no—
172#97×C73—21no—
173C4×C8×C73—21no—
174C4×C8×C73C2311yescharacteristic
175C4×C8×C73C2311yescharacteristic
176C24×C73—22no—
177#41×C73—81no—
178#41×C73—81no—
179#41×C73—81no—
180#41×C73—81no—
181#41×C73—81no—
182#41×C73—81no—
183#41×C73—81no—
184#41×C73—81no—
185C2×Q8×C73—21no—
186C2×Q8×C73—21no—
187C2×Q8×C73—21no—
188C2×Q8×C73—21no—
189C2×Q8×C73C2×D411yescharacteristic
190C2×D4×C73—22no—
191C2×D4×C73—22no—
192C2×D4×C73—22no—
193C2×D4×C73—22no—
194C2×D4×C73—22no—
195C2×D4×C73—21no—
196C2×D4×C73—21no—
197C2×D4×C73—22no—
198C2×D4×C73—21no—
199C2×D4×C73—21no—
200C2×D4×C73—21no—
201C2×D4×C73—21no—
202C2×D4×C73—21no—
203C2×D4×C73—81no—
204C2×D4×C73—81no—
205C2×D4×C73—81no—
206C2×D4×C73—81no—
207C2×D4×C73C2×D411yescharacteristic
208C2×D4×C73C2×D411yescharacteristic
209C2×D4×C73C2×D411yescharacteristic
210C2×D4×C73C2×D412yes—
211C22×C4×C73—22no—
212C22×C4×C73—22no—
213C22×C4×C73—21no—
214C22×C4×C73—21no—
215C22×C4×C73—21no—
216C22×C4×C73—22no—
217C22×C4×C73C2×D411yescharacteristic
218C22×C4×C73C2×D411yescharacteristic
219C22×C4×C73C2×D411yescharacteristic
220SD16×C73—44no—
221SD16×C73—81no—
222SD16×C73—81no—
223M16×C73—42no—
224C2×C8×C73—21no—
225C2×C8×C73—21no—
226C2×C8×C73—21no—
227C2×C8×C73—21no—
228C2×C8×C73—21no—
229C2×C8×C73—21no—
230C2×C8×C73—81no—
231C4⋊C4×C73—22no—
232C4⋊C4×C73—22no—
233C4⋊C4×C73—21no—
234C4⋊C4×C73—21no—
235C4⋊C4×C73—21no—
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×C73—41no—
244C4⋊C4×C73—41no—
245C4⋊C4×C73C2×D411yescharacteristic
246C4⋊C4×C73C2×D411yescharacteristic
247C4⋊C4×C73C2×D412yes—
248C4⋊C4×C73C2×D411yescharacteristic
249C4⋊C4×C73C2×D411yescharacteristic
250C22⋊C4×C73—22no—
251C22⋊C4×C73—22no—
252C22⋊C4×C73—22no—
253C22⋊C4×C73—22no—
254C22⋊C4×C73—22no—
255C22⋊C4×C73—21no—
256C22⋊C4×C73—21no—
257C22⋊C4×C73—21no—
258C22⋊C4×C73—21no—
259C22⋊C4×C73—21no—
260C22⋊C4×C73—21no—
261C22⋊C4×C73—22no—
262C22⋊C4×C73—22no—
263C22⋊C4×C73—21no—
264C22⋊C4×C73—21no—
265C22⋊C4×C73—21no—
266C22⋊C4×C73—41no—
267C42×C73—22no—
268C42×C73—21no—
269C42×C73—41no—
270C42×C73C2×D411yescharacteristic
271C42×C73C2×D411yescharacteristic
272C42×C73C2×D411yescharacteristic
273C42×C73C2411yescharacteristic
274C23×C73—21no—
275C23×C73—21no—
276C23×C73—22no—
277C23×C73—21no—
278C23×C73—82no—
279C23×C73—82no—
280C23×C73—82no—
281C23×C73#12011yescharacteristic
282Q8×C73—21no—
283Q8×C73—21no—
284Q8×C73—42no—
285Q8×C73—41no—
286Q8×C73—41no—
287Q8×C73—41no—
288Q8×C73—41no—
289Q8×C73—81no—
290D4×C73—21no—
291D4×C73—21no—
292D4×C73—21no—
293D4×C73—21no—
294D4×C73—21no—
295D4×C73—21no—
296D4×C73—42no—
297D4×C73—41no—
298D4×C73—41no—
299D4×C73—41no—
300D4×C73—41no—
301D4×C73—81no—
302D4×C73—81no—
303D4×C73—81no—
304D4×C73—81no—
305D4×C73—81no—
306D4×C73—82no—
307D4×C73—82no—
308D4×C73—82no—
309D4×C73—82no—
310D4×C73—82no—
311D4×C73—82no—
312C2×C4×C73—21no—
313C2×C4×C73—21no—
314C2×C4×C73—21no—
315C2×C4×C73—21no—
316C2×C4×C73—21no—
317C2×C4×C73—21no—
318C2×C4×C73—21no—
319C2×C4×C73—22no—
320C2×C4×C73—21no—
321C2×C4×C73—21no—
322C2×C4×C73—41no—
323C2×C4×C73—41no—
324C2×C4×C73—41no—
325C2×C4×C73—41no—
326C2×C4×C73—41no—
327C2×C4×C73—41no—
328C2×C4×C73—41no—
329C2×C4×C73—41no—
330C2×C4×C73—41no—
331C2×C4×C73—82no—
332C2×C4×C73—82no—
333C2×C4×C73—82no—
334C2×C4×C73#12011yescharacteristic
335C2×C4×C73#12011yescharacteristic
336C2×C4×C73#12011yescharacteristic
337C2×C4×C73C22×D411yescharacteristic
338C2×C4×C73C22×D411yescharacteristic
339C2×C4×C73C22×D411yescharacteristic
340C8×C73—22no—
341C8×C73—41no—
342C8×C73—41no—
343C8×C73—41no—
344C8×C73—41no—
345C8×C73—41no—
346C22×C73—21no—
347C22×C73—21no—
348C22×C73—21no—
349C22×C73—41no—
350C22×C73—41no—
351C22×C73—42no—
352C22×C73—41no—
353C22×C73—41no—
354C22×C73—41no—
355C22×C73—42no—
356C22×C73—41no—
357C22×C73—42no—
358C22×C73—41no—
359C22×C73—41no—
360C22×C73—41no—
361C22×C73—164no—
362C22×C73C2×#12011yescharacteristic
363C4×C73—21no—
364C4×C73—21no—
365C4×C73—21no—
366C4×C73—21no—
367C4×C73—41no—
368C4×C73—41no—
369C4×C73—41no—
370C4×C73—41no—
371C4×C73—42no—
372C4×C73—41no—
373C4×C73—81no—
374C4×C73—81no—
375C4×C73#57611yescharacteristic
376C4×C73#57711yescharacteristic
377C4×C73#57711yescharacteristic
378C4×C73#57711yescharacteristic
379#18739C7311yesmaximal, characteristic, direct product factor, Sylow
380C2×C73—41no—
381C2×C73—81no—
382C2×C73—82no—
383C2×C73—81no—
384C2×C73—81no—
385C2×C73#300911yescharacteristic
386C2×C73#301211yescharacteristic
387C2×C73#301811yescharacteristic
388#3546C2×C7311yescharacteristic
389#3246C2×C7311yescharacteristic, complemented
390#3233C2×C7311yescharacteristic, complemented
391#3182C2×C7311yescharacteristic, complemented
392#1650C2×C7311yescharacteristic, complemented
393#1647C2×C7311yescharacteristic, complemented
394#1642C2×C7311yescharacteristic, complemented
395#1639C2×C7311yescharacteristic, complemented
396#1638C2×C7311yescharacteristic, complemented
397#1635C2×C7311yescharacteristic, complemented
398#1631C2×C7311yescharacteristic, complemented
399#1629C2×C7311yescharacteristic, complemented
400#1540C2×C7311yescharacteristic, complemented
401#1484C2×C7311yescharacteristic, complemented
402#1483C2×C7311yescharacteristic, complemented
403C73#1873911yescharacteristic, direct product factor, Sylow
404#560—22no—
405#556C22×C7311yescharacteristic
406#553—21no—
407#550—21no—
408#550C22×C7311yescharacteristic
409#547C22×C7311yescharacteristic
410#546—21no—
411#546—21no—
412D42C22×C7311yescharacteristic
413#542—21no—
414#538—22no—
415#537—21no—
416#535—21no—
417#535—21no—
418#533C22×C7311yescharacteristic, complemented
419#532C22×C7311yescharacteristic
420#532C22×C7311yescharacteristic
421#529C22×C7311yescharacteristic
422#500C22×C7311yescharacteristic, complemented
423#499—21no—
424#492C22×C7311yescharacteristic
425#488—21no—
426#487C22×C7311yescharacteristic, complemented
427#486C22×C7311yescharacteristic
428#485—21no—
429#482—21no—
430#477C22×C7311yescharacteristic, complemented
431#476C22×C7311yescharacteristic
432#476C22×C7311yescharacteristic
433#476C22×C7311yescharacteristic, complemented
434#475—21no—
435#475C22×C7311yescharacteristic, complemented
436#474C22×C7311yescharacteristic
437#468—22no—
438#465—21no—
439#465—21no—
440#461C22×C7311yescharacteristic
441#461C22×C7311yescharacteristic, complemented
442#460—21no—
443#440—22no—
444#431C22×C7311yescharacteristic, complemented
445C2×C4⋊C8C22×C7311yescharacteristic, complemented
446C4×M16C22×C7311yescharacteristic, complemented
447#332C22×C7311yescharacteristic, complemented
448#332C22×C7311yescharacteristic, complemented
449#331C22×C7311yescharacteristic
450#331C22×C7311yescharacteristic
451Q8⋊C8C22×C7311yescharacteristic, complemented
452Q8⋊C8C22×C7311yescharacteristic, complemented
453D4⋊C8C22×C7311yescharacteristic
454D4⋊C8C22×C7311yescharacteristic
455D4⋊C8C22×C7311yescharacteristic
456D4⋊C8C22×C7311yescharacteristic
457D4⋊C8C22×C7311yescharacteristic, complemented
458D4⋊C8C22×C7311yescharacteristic, complemented
459C2×#41—21no—
460C2×#41—21no—
461C2×#41—21no—
462C2×#41—21no—
463C22×D4—21no—
464C22×D4—21no—
465C2×SD16—22no—
466C2×SD16—21no—
467C2×SD16—21no—
468C2×M16—21no—
469C22×C8—21no—
470C4⋊Q8D4×C7311yescharacteristic
471C4⋊Q8C23×C7311yescharacteristic
472C4⋊Q8C23×C7311yescharacteristic
473C4⋊Q8C23×C7311yescharacteristic
474#127—22no—
475#127—21no—
476#127D4×C7311yescharacteristic
477#127C23×C7311yescharacteristic
478#126—22no—
479#126—22no—
480#126—21no—
481#125—21no—
482#125D4×C7311yescharacteristic
483#124—22no—
484#124—21no—
485#124—21no—
486#124—21no—
487#124D4×C7311yescharacteristic
488#123—22no—
489#123—22no—
490#123—21no—
491#123—22no—
492C22⋊Q8—22no—
493C22⋊Q8—21no—
494C22⋊Q8—21no—
495C22⋊Q8—21no—
496C22⋊Q8—21no—
497C22⋊Q8D4×C7311yescharacteristic
498#121—22no—
499#121—22no—
500#121—22no—
501#121—22no—
502#121—22no—
503#121—21no—
504#121—22no—
505#121—21no—
506#121—21no—
507#121—21no—
508#121—21no—
509#121—21no—
510#121D4×C7311yescharacteristic
511#121D4×C7311yescharacteristic
512#121D4×C7311yescharacteristic
513#121D4×C7312yes—
514#120—22no—
515#120—22no—
516#120—22no—
517#120—22no—
518C4×Q8—21no—
519C4×Q8—21no—
520C4×Q8—21no—
521C4×Q8C23×C7311yescharacteristic
522C4×D4—22no—
523C4×D4—21no—
524C4×D4—21no—
525C4×D4—21no—
526C4×D4—21no—
527C4×D4D4×C7312yes—
528C4×D4C23×C7311yescharacteristic
529C4×D4C23×C7311yescharacteristic
530C4×D4C23×C7311yescharacteristic
531#117—21no—
532#117—21no—
533#117—21no—
534C2×C4⋊C4—21no—
535C2×C22⋊C4—22no—
536C2×C42C23×C7311yescharacteristic
537#107—22no—
538#107—21no—
539#107—21no—
540#106—21no—
541#106—21no—
542#106—21no—
543#106—21no—
544C4⋊C8—21no—
545C4⋊C8C23×C7311yescharacteristic
546C4⋊C8C23×C7311yescharacteristic
547C4⋊C8C23×C7311yescharacteristic
548C4⋊C8C23×C7311yescharacteristic
549#103—21no—
550#103—21no—
551#103—22no—
552#103—21no—
553#103—21no—
554#102—22no—
555#102—21no—
556#102—21no—
557#102—21no—
558#102—21no—
559C22⋊C8—21no—
560#97—21no—
561C4×C8—21no—
562C4×C8C23×C7311yescharacteristic
563C4×C8C23×C7311yescharacteristic
564C24—22no—
565#41—81no—
566#41—81no—
567#41—81no—
568#41—81no—
569#41—81no—
570#41—81no—
571#41—81no—
572#41—81no—
573C2×Q8—21no—
574C2×Q8—21no—
575C2×Q8—21no—
576C2×Q8—21no—
577C2×Q8C2×D4×C7311yescharacteristic
578C2×D4—22no—
579C2×D4—22no—
580C2×D4—22no—
581C2×D4—22no—
582C2×D4—22no—
583C2×D4—21no—
584C2×D4—21no—
585C2×D4—22no—
586C2×D4—21no—
587C2×D4—21no—
588C2×D4—21no—
589C2×D4—21no—
590C2×D4—21no—
591C2×D4—81no—
592C2×D4—81no—
593C2×D4—81no—
594C2×D4—81no—
595C2×D4C2×D4×C7311yescharacteristic
596C2×D4C2×D4×C7311yescharacteristic
597C2×D4C2×D4×C7311yescharacteristic
598C2×D4C2×D4×C7312yes—
599C22×C4—22no—
600C22×C4—22no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—22no—
605C22×C4C2×D4×C7311yescharacteristic
606C22×C4C2×D4×C7311yescharacteristic
607C22×C4C2×D4×C7311yescharacteristic
608SD16—44no—
609SD16—81no—
610SD16—81no—
611M16—42no—
612C2×C8—21no—
613C2×C8—21no—
614C2×C8—21no—
615C2×C8—21no—
616C2×C8—21no—
617C2×C8—21no—
618C2×C8—81no—
619C4⋊C4—22no—
620C4⋊C4—22no—
621C4⋊C4—21no—
622C4⋊C4—21no—
623C4⋊C4—21no—
624C4⋊C4—21no—
625C4⋊C4—21no—
626C4⋊C4—21no—
627C4⋊C4—21no—
628C4⋊C4—21no—
629C4⋊C4—21no—
630C4⋊C4—21no—
631C4⋊C4—41no—
632C4⋊C4—41no—
633C4⋊C4C2×D4×C7311yescharacteristic
634C4⋊C4C2×D4×C7311yescharacteristic
635C4⋊C4C2×D4×C7312yes—
636C4⋊C4C2×D4×C7311yescharacteristic
637C4⋊C4C2×D4×C7311yescharacteristic
638C22⋊C4—22no—
639C22⋊C4—22no—
640C22⋊C4—22no—
641C22⋊C4—22no—
642C22⋊C4—22no—
643C22⋊C4—21no—
644C22⋊C4—21no—
645C22⋊C4—21no—
646C22⋊C4—21no—
647C22⋊C4—21no—
648C22⋊C4—21no—
649C22⋊C4—22no—
650C22⋊C4—22no—
651C22⋊C4—21no—
652C22⋊C4—21no—
653C22⋊C4—21no—
654C22⋊C4—41no—
655C42—22no—
656C42—21no—
657C42—41no—
658C42C2×D4×C7311yescharacteristic
659C42C2×D4×C7311yescharacteristic
660C42C2×D4×C7311yescharacteristic
661C42C24×C7311yescharacteristic
662C23—21no—
663C23—21no—
664C23—22no—
665C23—21no—
666C23—82no—
667C23—82no—
668C23—82no—
669C23#120×C7311yescharacteristic
670Q8—21no—
671Q8—21no—
672Q8—42no—
673Q8—41no—
674Q8—41no—
675Q8—41no—
676Q8—41no—
677Q8—81no—
678D4—21no—
679D4—21no—
680D4—21no—
681D4—21no—
682D4—21no—
683D4—21no—
684D4—42no—
685D4—41no—
686D4—41no—
687D4—41no—
688D4—41no—
689D4—81no—
690D4—81no—
691D4—81no—
692D4—81no—
693D4—82no—
694D4—81no—
695D4—82no—
696D4—82no—
697D4—82no—
698D4—82no—
699D4—82no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—22no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—41no—
711C2×C4—41no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—82no—
720C2×C4—82no—
721C2×C4—82no—
722C2×C4#120×C7311yescharacteristic
723C2×C4#120×C7311yescharacteristic
724C2×C4#120×C7311yescharacteristic
725C2×C4C22×D4×C7311yescharacteristic
726C2×C4C22×D4×C7311yescharacteristic
727C2×C4C22×D4×C7311yescharacteristic
728C8—22no—
729C8—41no—
730C8—41no—
731C8—41no—
732C8—41no—
733C8—41no—
734C22—21no—
735C22—21no—
736C22—21no—
737C22—41no—
738C22—41no—
739C22—42no—
740C22—41no—
741C22—41no—
742C22—41no—
743C22—42no—
744C22—41no—
745C22—42no—
746C22—41no—
747C22—41no—
748C22—41no—
749C22—164no—
750C22C2×#120×C7311yescharacteristic
751C4—21no—
752C4—21no—
753C4—21no—
754C4—21no—
755C4—41no—
756C4—41no—
757C4—41no—
758C4—41no—
759C4—42no—
760C4—41no—
761C4—81no—
762C4—81no—
763C4#576×C7311yescharacteristic
764C4#577×C7311yescharacteristic
765C4#577×C7311yescharacteristic
766C4#577×C7311yescharacteristic
767C2—41no—
768C2—81no—
769C2—81no—
770C2—82no—
771C2—81no—
772C2C73×#300911yescharacteristic
773C2C73×#301211yescharacteristic
774C2C73×#301811yescharacteristic
subgroupG/H
center, socleC22×C73C2×#120
commutator, Frattini, cosocleC42C24×C73
prime radicalC73×#3546C2
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
2. C73×#3246C2semidirect
3. C73×#3233C2semidirect
4. C73×#3182C2semidirect
5. C73×#1650C2semidirect
6. C73×#1647C2semidirect
7. C73×#1642C2semidirect
8. C73×#1639C2semidirect
9. C73×#1638C2semidirect
10. C73×#1635C2semidirect
11. C73×#1631C2semidirect
12. C73×#1629C2semidirect
13. C73×#1540C2semidirect
14. C73×#1484C2semidirect
15. C73×#1483C2semidirect
30. #533×C73C22semidirect
34. #500×C73C22semidirect
38. #487×C73C22semidirect
42. #477×C73C22semidirect
45. #476×C73C22semidirect
47. #475×C73C22semidirect
53. #461×C73C22semidirect
56. #431×C73C22semidirect
57. C2×C4⋊C8×C73C22semidirect
58. C4×M16×C73C22semidirect
59. #332×C73C22semidirect
60. #332×C73C22semidirect
63. Q8⋊C8×C73C22semidirect
64. Q8⋊C8×C73C22semidirect
69. D4⋊C8×C73C22semidirect
70. D4⋊C8×C73C22semidirect
379. #18739C73direct (N × H)
389. #3246C2×C73semidirect
390. #3233C2×C73semidirect
391. #3182C2×C73semidirect
392. #1650C2×C73semidirect
393. #1647C2×C73semidirect
394. #1642C2×C73semidirect
395. #1639C2×C73semidirect
396. #1638C2×C73semidirect
397. #1635C2×C73semidirect
398. #1631C2×C73semidirect
399. #1629C2×C73semidirect
400. #1540C2×C73semidirect
401. #1484C2×C73semidirect
402. #1483C2×C73semidirect
403. C73#18739direct (N × H)
418. #533C22×C73semidirect
422. #500C22×C73semidirect
426. #487C22×C73semidirect
430. #477C22×C73semidirect
433. #476C22×C73semidirect
435. #475C22×C73semidirect
441. #461C22×C73semidirect
444. #431C22×C73semidirect
445. C2×C4⋊C8C22×C73semidirect
446. C4×M16C22×C73semidirect
447. #332C22×C73semidirect
448. #332C22×C73semidirect
451. Q8⋊C8C22×C73semidirect
452. Q8⋊C8C22×C73semidirect
457. D4⋊C8C22×C73semidirect
458. D4⋊C8C22×C73semidirect

Maximal subgroups

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

subgroupindex
C73×#35462
C73×#32462
C73×#32332
C73×#31822
C73×#16502
C73×#16472
C73×#16422
C73×#16392
C73×#16382
C73×#16352
C73×#16312
C73×#16292
C73×#15402
C73×#14842
C73×#14832
#1873973