Finite Group Databasebeta

← C73×#18974 #32928378

Subgroups — C73×#18974 #32928378

Order 18688.

930 conjugacy classes of subgroups.

The subgroup lattice has 780 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C73×#3546C211yesmaximal, characteristic
2C73×#3254C211yesmaximal, characteristic, complemented
3C73×#3248C211yesmaximal, characteristic, complemented
4C73×#3228C211yesmaximal, characteristic, complemented
5C73×#1654C211yesmaximal, characteristic, complemented
6C73×#1652C211yesmaximal, characteristic, complemented
7C73×#1650C211yesmaximal, characteristic, complemented
8C73×#1647C211yesmaximal, characteristic, complemented
9C73×#1642C211yesmaximal, characteristic, complemented
10C73×#1641C211yesmaximal, characteristic, complemented
11C73×#1639C211yesmaximal, characteristic, complemented
12C73×#1639C211yesmaximal, characteristic, complemented
13C73×#1547C211yesmaximal, characteristic, complemented
14C73×#1495C211yesmaximal, characteristic, complemented
15C73×#1480C211yesmaximal, 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#498×C73C2211yescharacteristic, complemented
36#486×C73C2211yescharacteristic
37#486×C73C2211yescharacteristic
38#482×C73—22no—
39#479×C73—21no—
40#478×C73—22no—
41#477×C73—21no—
42#475×C73C2211yescharacteristic, complemented
43#474×C73C2211yescharacteristic
44#474×C73C2211yescharacteristic
45#474×C73C2211yescharacteristic, complemented
46#468×C73—21no—
47#468×C73—21no—
48#467×C73—21no—
49#465×C73—21no—
50#464×C73—21no—
51#462×C73C2211yescharacteristic, complemented
52#461×C73C2211yescharacteristic
53#461×C73C2211yescharacteristic
54#461×C73C2211yescharacteristic, complemented
55#460×C73—21no—
56#431×C73C2211yescharacteristic, complemented
57#423×C73C2211yescharacteristic, complemented
58C2×C4⋊C8×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×Q16×C73—21no—
78C2×SD16×C73—21no—
79C2×SD16×C73—21no—
80C2×SD16×C73—21no—
81C2×M16×C73—21no—
82C22×C8×C73—21no—
83C4⋊Q8×C73D411yescharacteristic
84C4⋊Q8×C73C2311yescharacteristic
85C4⋊Q8×C73C2311yescharacteristic
86C4⋊Q8×C73C2311yescharacteristic
87#127×C73—22no—
88#127×C73—21no—
89#127×C73D411yescharacteristic
90#127×C73C2311yescharacteristic
91#126×C73—22no—
92#126×C73—22no—
93#126×C73—21no—
94#125×C73—21no—
95#125×C73D411yescharacteristic
96#124×C73—22no—
97#124×C73—21no—
98#124×C73—21no—
99#124×C73—21no—
100#124×C73D411yescharacteristic
101#123×C73—22no—
102#123×C73—22no—
103#123×C73—21no—
104#123×C73—22no—
105C22⋊Q8×C73—22no—
106C22⋊Q8×C73—21no—
107C22⋊Q8×C73—21no—
108C22⋊Q8×C73—21no—
109C22⋊Q8×C73—21no—
110C22⋊Q8×C73D411yescharacteristic
111#121×C73—22no—
112#121×C73—22no—
113#121×C73—22no—
114#121×C73—22no—
115#121×C73—22no—
116#121×C73—21no—
117#121×C73—22no—
118#121×C73—21no—
119#121×C73—21no—
120#121×C73—21no—
121#121×C73—21no—
122#121×C73—21no—
123#121×C73D411yescharacteristic
124#121×C73D411yescharacteristic
125#121×C73D411yescharacteristic
126#121×C73D412yes—
127#120×C73—22no—
128#120×C73—22no—
129#120×C73—22no—
130#120×C73—22no—
131C4×Q8×C73—21no—
132C4×Q8×C73—21no—
133C4×Q8×C73—21no—
134C4×Q8×C73C2311yescharacteristic
135C4×D4×C73—22no—
136C4×D4×C73—21no—
137C4×D4×C73—21no—
138C4×D4×C73—21no—
139C4×D4×C73—21no—
140C4×D4×C73D412yes—
141C4×D4×C73C2311yescharacteristic
142C4×D4×C73C2311yescharacteristic
143C4×D4×C73C2311yescharacteristic
144#117×C73—21no—
145#117×C73—21no—
146#117×C73—21no—
147C2×C4⋊C4×C73—21no—
148C2×C22⋊C4×C73—22no—
149C2×C42×C73C2311yescharacteristic
150#107×C73—21no—
151#107×C73—21no—
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×C73—21no—
159C4⋊C8×C73C2311yescharacteristic
160C4⋊C8×C73C2311yescharacteristic
161C4⋊C8×C73C2311yescharacteristic
162C4⋊C8×C73C2311yescharacteristic
163#103×C73—21no—
164#103×C73—21no—
165#103×C73—21no—
166#103×C73—21no—
167#103×C73—21no—
168#102×C73—21no—
169#102×C73—21no—
170#102×C73—21no—
171#102×C73—22no—
172#102×C73—22no—
173C22⋊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
220Q16×C73—81no—
221SD16×C73—81no—
222SD16×C73—81no—
223SD16×C73—81no—
224M16×C73—81no—
225C2×C8×C73—21no—
226C2×C8×C73—21no—
227C2×C8×C73—21no—
228C2×C8×C73—21no—
229C2×C8×C73—21no—
230C2×C8×C73—21no—
231C2×C8×C73—81no—
232C4⋊C4×C73—22no—
233C4⋊C4×C73—22no—
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—21no—
244C4⋊C4×C73—41no—
245C4⋊C4×C73—41no—
246C4⋊C4×C73C2×D411yescharacteristic
247C4⋊C4×C73C2×D411yescharacteristic
248C4⋊C4×C73C2×D411yescharacteristic
249C4⋊C4×C73C2×D411yescharacteristic
250C4⋊C4×C73C2×D412yes—
251C22⋊C4×C73—22no—
252C22⋊C4×C73—22no—
253C22⋊C4×C73—22no—
254C22⋊C4×C73—22no—
255C22⋊C4×C73—22no—
256C22⋊C4×C73—21no—
257C22⋊C4×C73—21no—
258C22⋊C4×C73—21no—
259C22⋊C4×C73—21no—
260C22⋊C4×C73—21no—
261C22⋊C4×C73—21no—
262C22⋊C4×C73—22no—
263C22⋊C4×C73—22no—
264C22⋊C4×C73—21no—
265C22⋊C4×C73—21no—
266C22⋊C4×C73—21no—
267C22⋊C4×C73—41no—
268C42×C73—22no—
269C42×C73—21no—
270C42×C73—41no—
271C42×C73C2×D411yescharacteristic
272C42×C73C2×D411yescharacteristic
273C42×C73C2×D411yescharacteristic
274C42×C73C2411yescharacteristic
275C23×C73—21no—
276C23×C73—21no—
277C23×C73—22no—
278C23×C73—21no—
279C23×C73—82no—
280C23×C73—82no—
281C23×C73—82no—
282C23×C73#12011yescharacteristic
283Q8×C73—21no—
284Q8×C73—21no—
285Q8×C73—41no—
286Q8×C73—41no—
287Q8×C73—41no—
288Q8×C73—41no—
289Q8×C73—41no—
290Q8×C73—41no—
291Q8×C73—81no—
292D4×C73—21no—
293D4×C73—21no—
294D4×C73—21no—
295D4×C73—21no—
296D4×C73—21no—
297D4×C73—21no—
298D4×C73—42no—
299D4×C73—41no—
300D4×C73—41no—
301D4×C73—41no—
302D4×C73—41no—
303D4×C73—81no—
304D4×C73—81no—
305D4×C73—81no—
306D4×C73—81no—
307D4×C73—81no—
308D4×C73—82no—
309D4×C73—82no—
310D4×C73—82no—
311D4×C73—82no—
312D4×C73—82no—
313D4×C73—82no—
314C2×C4×C73—21no—
315C2×C4×C73—21no—
316C2×C4×C73—21no—
317C2×C4×C73—21no—
318C2×C4×C73—21no—
319C2×C4×C73—21no—
320C2×C4×C73—21no—
321C2×C4×C73—22no—
322C2×C4×C73—21no—
323C2×C4×C73—21no—
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—41no—
332C2×C4×C73—41no—
333C2×C4×C73—82no—
334C2×C4×C73—82no—
335C2×C4×C73—82no—
336C2×C4×C73#12011yescharacteristic
337C2×C4×C73#12011yescharacteristic
338C2×C4×C73#12011yescharacteristic
339C2×C4×C73C22×D411yescharacteristic
340C2×C4×C73C22×D411yescharacteristic
341C2×C4×C73C22×D411yescharacteristic
342C8×C73—41no—
343C8×C73—41no—
344C8×C73—41no—
345C8×C73—41no—
346C8×C73—41no—
347C8×C73—41no—
348C22×C73—21no—
349C22×C73—21no—
350C22×C73—21no—
351C22×C73—41no—
352C22×C73—41no—
353C22×C73—41no—
354C22×C73—41no—
355C22×C73—42no—
356C22×C73—42no—
357C22×C73—41no—
358C22×C73—41no—
359C22×C73—42no—
360C22×C73—41no—
361C22×C73—41no—
362C22×C73—41no—
363C22×C73—164no—
364C22×C73C2×#12011yescharacteristic
365C4×C73—21no—
366C4×C73—21no—
367C4×C73—21no—
368C4×C73—21no—
369C4×C73—41no—
370C4×C73—41no—
371C4×C73—41no—
372C4×C73—41no—
373C4×C73—42no—
374C4×C73—41no—
375C4×C73—81no—
376C4×C73—81no—
377C4×C73#57611yescharacteristic
378C4×C73#57611yescharacteristic
379C4×C73#57711yescharacteristic
380C4×C73#57711yescharacteristic
381#18974C7311yesmaximal, characteristic, direct product factor, Sylow
382C2×C73—41no—
383C2×C73—81no—
384C2×C73—82no—
385C2×C73—81no—
386C2×C73—81no—
387C2×C73#301211yescharacteristic
388C2×C73#301211yescharacteristic
389C2×C73#302211yescharacteristic
390#3546C2×C7311yescharacteristic
391#3254C2×C7311yescharacteristic, complemented
392#3248C2×C7311yescharacteristic, complemented
393#3228C2×C7311yescharacteristic, complemented
394#1654C2×C7311yescharacteristic, complemented
395#1652C2×C7311yescharacteristic, complemented
396#1650C2×C7311yescharacteristic, complemented
397#1647C2×C7311yescharacteristic, complemented
398#1642C2×C7311yescharacteristic, complemented
399#1641C2×C7311yescharacteristic, complemented
400#1639C2×C7311yescharacteristic, complemented
401#1639C2×C7311yescharacteristic, complemented
402#1547C2×C7311yescharacteristic, complemented
403#1495C2×C7311yescharacteristic, complemented
404#1480C2×C7311yescharacteristic, complemented
405C73#1897411yescharacteristic, direct product factor, Sylow
406#560—22no—
407#556C22×C7311yescharacteristic
408#553—21no—
409#550—21no—
410#550C22×C7311yescharacteristic
411#547C22×C7311yescharacteristic
412#546—21no—
413#546—21no—
414D42C22×C7311yescharacteristic
415#542—21no—
416#538—22no—
417#537—21no—
418#535—21no—
419#535—21no—
420#533C22×C7311yescharacteristic, complemented
421#532C22×C7311yescharacteristic
422#532C22×C7311yescharacteristic
423#529C22×C7311yescharacteristic
424#500C22×C7311yescharacteristic, complemented
425#498C22×C7311yescharacteristic, complemented
426#486C22×C7311yescharacteristic
427#486C22×C7311yescharacteristic
428#482—22no—
429#479—21no—
430#478—22no—
431#477—21no—
432#475C22×C7311yescharacteristic, complemented
433#474C22×C7311yescharacteristic
434#474C22×C7311yescharacteristic
435#474C22×C7311yescharacteristic, complemented
436#468—21no—
437#468—21no—
438#467—21no—
439#465—21no—
440#464—21no—
441#462C22×C7311yescharacteristic, complemented
442#461C22×C7311yescharacteristic
443#461C22×C7311yescharacteristic
444#461C22×C7311yescharacteristic, complemented
445#460—21no—
446#431C22×C7311yescharacteristic, complemented
447#423C22×C7311yescharacteristic, complemented
448C2×C4⋊C8C22×C7311yescharacteristic, complemented
449#332C22×C7311yescharacteristic, complemented
450#332C22×C7311yescharacteristic, complemented
451#331C22×C7311yescharacteristic
452#331C22×C7311yescharacteristic
453Q8⋊C8C22×C7311yescharacteristic, complemented
454Q8⋊C8C22×C7311yescharacteristic, complemented
455D4⋊C8C22×C7311yescharacteristic
456D4⋊C8C22×C7311yescharacteristic
457D4⋊C8C22×C7311yescharacteristic
458D4⋊C8C22×C7311yescharacteristic
459D4⋊C8C22×C7311yescharacteristic, complemented
460D4⋊C8C22×C7311yescharacteristic, complemented
461C2×#41—21no—
462C2×#41—21no—
463C2×#41—21no—
464C2×#41—21no—
465C22×D4—21no—
466C22×D4—21no—
467C2×Q16—21no—
468C2×SD16—21no—
469C2×SD16—21no—
470C2×SD16—21no—
471C2×M16—21no—
472C22×C8—21no—
473C4⋊Q8D4×C7311yescharacteristic
474C4⋊Q8C23×C7311yescharacteristic
475C4⋊Q8C23×C7311yescharacteristic
476C4⋊Q8C23×C7311yescharacteristic
477#127—22no—
478#127—21no—
479#127D4×C7311yescharacteristic
480#127C23×C7311yescharacteristic
481#126—22no—
482#126—22no—
483#126—21no—
484#125—21no—
485#125D4×C7311yescharacteristic
486#124—22no—
487#124—21no—
488#124—21no—
489#124—21no—
490#124D4×C7311yescharacteristic
491#123—22no—
492#123—22no—
493#123—21no—
494#123—22no—
495C22⋊Q8—22no—
496C22⋊Q8—21no—
497C22⋊Q8—21no—
498C22⋊Q8—21no—
499C22⋊Q8—21no—
500C22⋊Q8D4×C7311yescharacteristic
501#121—22no—
502#121—22no—
503#121—22no—
504#121—22no—
505#121—22no—
506#121—21no—
507#121—22no—
508#121—21no—
509#121—21no—
510#121—21no—
511#121—21no—
512#121—21no—
513#121D4×C7311yescharacteristic
514#121D4×C7311yescharacteristic
515#121D4×C7311yescharacteristic
516#121D4×C7312yes—
517#120—22no—
518#120—22no—
519#120—22no—
520#120—22no—
521C4×Q8—21no—
522C4×Q8—21no—
523C4×Q8—21no—
524C4×Q8C23×C7311yescharacteristic
525C4×D4—22no—
526C4×D4—21no—
527C4×D4—21no—
528C4×D4—21no—
529C4×D4—21no—
530C4×D4D4×C7312yes—
531C4×D4C23×C7311yescharacteristic
532C4×D4C23×C7311yescharacteristic
533C4×D4C23×C7311yescharacteristic
534#117—21no—
535#117—21no—
536#117—21no—
537C2×C4⋊C4—21no—
538C2×C22⋊C4—22no—
539C2×C42C23×C7311yescharacteristic
540#107—21no—
541#107—21no—
542#107—21no—
543#107—22no—
544#106—21no—
545#106—22no—
546C4⋊C8—21no—
547C4⋊C8—21no—
548C4⋊C8—21no—
549C4⋊C8C23×C7311yescharacteristic
550C4⋊C8C23×C7311yescharacteristic
551C4⋊C8C23×C7311yescharacteristic
552C4⋊C8C23×C7311yescharacteristic
553#103—21no—
554#103—21no—
555#103—21no—
556#103—21no—
557#103—21no—
558#102—21no—
559#102—21no—
560#102—21no—
561#102—22no—
562#102—22no—
563C22⋊C8—21no—
564C4×C8C23×C7311yescharacteristic
565C4×C8C23×C7311yescharacteristic
566C24—22no—
567#41—81no—
568#41—81no—
569#41—81no—
570#41—81no—
571#41—81no—
572#41—81no—
573#41—81no—
574#41—81no—
575C2×Q8—21no—
576C2×Q8—21no—
577C2×Q8—21no—
578C2×Q8—21no—
579C2×Q8C2×D4×C7311yescharacteristic
580C2×D4—22no—
581C2×D4—22no—
582C2×D4—22no—
583C2×D4—22no—
584C2×D4—22no—
585C2×D4—21no—
586C2×D4—21no—
587C2×D4—22no—
588C2×D4—21no—
589C2×D4—21no—
590C2×D4—21no—
591C2×D4—21no—
592C2×D4—21no—
593C2×D4—81no—
594C2×D4—81no—
595C2×D4—81no—
596C2×D4—81no—
597C2×D4C2×D4×C7311yescharacteristic
598C2×D4C2×D4×C7311yescharacteristic
599C2×D4C2×D4×C7311yescharacteristic
600C2×D4C2×D4×C7312yes—
601C22×C4—22no—
602C22×C4—22no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—22no—
607C22×C4C2×D4×C7311yescharacteristic
608C22×C4C2×D4×C7311yescharacteristic
609C22×C4C2×D4×C7311yescharacteristic
610Q16—81no—
611SD16—81no—
612SD16—81no—
613SD16—81no—
614M16—81no—
615C2×C8—21no—
616C2×C8—21no—
617C2×C8—21no—
618C2×C8—21no—
619C2×C8—21no—
620C2×C8—21no—
621C2×C8—81no—
622C4⋊C4—22no—
623C4⋊C4—22no—
624C4⋊C4—21no—
625C4⋊C4—21no—
626C4⋊C4—21no—
627C4⋊C4—21no—
628C4⋊C4—21no—
629C4⋊C4—21no—
630C4⋊C4—21no—
631C4⋊C4—21no—
632C4⋊C4—21no—
633C4⋊C4—21no—
634C4⋊C4—41no—
635C4⋊C4—41no—
636C4⋊C4C2×D4×C7311yescharacteristic
637C4⋊C4C2×D4×C7311yescharacteristic
638C4⋊C4C2×D4×C7311yescharacteristic
639C4⋊C4C2×D4×C7311yescharacteristic
640C4⋊C4C2×D4×C7312yes—
641C22⋊C4—22no—
642C22⋊C4—22no—
643C22⋊C4—22no—
644C22⋊C4—22no—
645C22⋊C4—22no—
646C22⋊C4—21no—
647C22⋊C4—21no—
648C22⋊C4—21no—
649C22⋊C4—21no—
650C22⋊C4—21no—
651C22⋊C4—21no—
652C22⋊C4—22no—
653C22⋊C4—22no—
654C22⋊C4—21no—
655C22⋊C4—21no—
656C22⋊C4—21no—
657C22⋊C4—41no—
658C42—22no—
659C42—21no—
660C42—41no—
661C42C2×D4×C7311yescharacteristic
662C42C2×D4×C7311yescharacteristic
663C42C2×D4×C7311yescharacteristic
664C42C24×C7311yescharacteristic
665C23—21no—
666C23—21no—
667C23—22no—
668C23—21no—
669C23—82no—
670C23—82no—
671C23—82no—
672C23#120×C7311yescharacteristic
673Q8—21no—
674Q8—21no—
675Q8—41no—
676Q8—41no—
677Q8—41no—
678Q8—41no—
679Q8—41no—
680Q8—41no—
681Q8—81no—
682D4—21no—
683D4—21no—
684D4—21no—
685D4—21no—
686D4—21no—
687D4—21no—
688D4—42no—
689D4—41no—
690D4—41no—
691D4—41no—
692D4—41no—
693D4—81no—
694D4—81no—
695D4—81no—
696D4—81no—
697D4—82no—
698D4—81no—
699D4—82no—
700D4—82no—
701D4—82no—
702D4—82no—
703D4—82no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—22no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—82no—
724C2×C4—82no—
725C2×C4—82no—
726C2×C4#120×C7311yescharacteristic
727C2×C4#120×C7311yescharacteristic
728C2×C4#120×C7311yescharacteristic
729C2×C4C22×D4×C7311yescharacteristic
730C2×C4C22×D4×C7311yescharacteristic
731C2×C4C22×D4×C7311yescharacteristic
732C8—41no—
733C8—41no—
734C8—41no—
735C8—41no—
736C8—41no—
737C8—41no—
738C22—21no—
739C22—21no—
740C22—21no—
741C22—41no—
742C22—41no—
743C22—41no—
744C22—41no—
745C22—42no—
746C22—42no—
747C22—41no—
748C22—41no—
749C22—42no—
750C22—41no—
751C22—41no—
752C22—41no—
753C22—164no—
754C22C2×#120×C7311yescharacteristic
755C4—21no—
756C4—21no—
757C4—21no—
758C4—21no—
759C4—41no—
760C4—41no—
761C4—41no—
762C4—41no—
763C4—42no—
764C4—41no—
765C4—81no—
766C4—81no—
767C4#576×C7311yescharacteristic
768C4#576×C7311yescharacteristic
769C4#577×C7311yescharacteristic
770C4#577×C7311yescharacteristic
771C2—41no—
772C2—81no—
773C2—81no—
774C2—82no—
775C2—81no—
776C2C73×#301211yescharacteristic
777C2C73×#301211yescharacteristic
778C2C73×#302211yescharacteristic
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×#3254C2semidirect
3. C73×#3248C2semidirect
4. C73×#3228C2semidirect
5. C73×#1654C2semidirect
6. C73×#1652C2semidirect
7. C73×#1650C2semidirect
8. C73×#1647C2semidirect
9. C73×#1642C2semidirect
10. C73×#1641C2semidirect
11. C73×#1639C2semidirect
12. C73×#1639C2semidirect
13. C73×#1547C2semidirect
14. C73×#1495C2semidirect
15. C73×#1480C2semidirect
30. #533×C73C22semidirect
34. #500×C73C22semidirect
35. #498×C73C22semidirect
42. #475×C73C22semidirect
45. #474×C73C22semidirect
51. #462×C73C22semidirect
54. #461×C73C22semidirect
56. #431×C73C22semidirect
57. #423×C73C22semidirect
58. C2×C4⋊C8×C73C22semidirect
59. #332×C73C22semidirect
60. #332×C73C22semidirect
63. Q8⋊C8×C73C22semidirect
64. Q8⋊C8×C73C22semidirect
69. D4⋊C8×C73C22semidirect
70. D4⋊C8×C73C22semidirect
381. #18974C73direct (N × H)
391. #3254C2×C73semidirect
392. #3248C2×C73semidirect
393. #3228C2×C73semidirect
394. #1654C2×C73semidirect
395. #1652C2×C73semidirect
396. #1650C2×C73semidirect
397. #1647C2×C73semidirect
398. #1642C2×C73semidirect
399. #1641C2×C73semidirect
400. #1639C2×C73semidirect
401. #1639C2×C73semidirect
402. #1547C2×C73semidirect
403. #1495C2×C73semidirect
404. #1480C2×C73semidirect
405. C73#18974direct (N × H)
420. #533C22×C73semidirect
424. #500C22×C73semidirect
425. #498C22×C73semidirect
432. #475C22×C73semidirect
435. #474C22×C73semidirect
441. #462C22×C73semidirect
444. #461C22×C73semidirect
446. #431C22×C73semidirect
447. #423C22×C73semidirect
448. C2×C4⋊C8C22×C73semidirect
449. #332C22×C73semidirect
450. #332C22×C73semidirect
453. Q8⋊C8C22×C73semidirect
454. Q8⋊C8C22×C73semidirect
459. D4⋊C8C22×C73semidirect
460. 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×#32542
C73×#32482
C73×#32282
C73×#16542
C73×#16522
C73×#16502
C73×#16472
C73×#16422
C73×#16412
C73×#16392
C73×#15472
C73×#14952
C73×#14802
#1897473