Finite Group Databasebeta

← C73×#18931 #32928335

Subgroups — C73×#18931 #32928335

Order 18688.

986 conjugacy classes of subgroups.

The subgroup lattice has 788 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C73×#3543C211yesmaximal, characteristic
2C73×#3252C211yesmaximal, characteristic, complemented
3C73×#3233C211yesmaximal, characteristic, complemented
4C73×#3208C211yesmaximal, characteristic, complemented
5C73×#1642C211yesmaximal, characteristic, complemented
6C73×#1641C211yesmaximal, characteristic, complemented
7C73×#1640C211yesmaximal, characteristic, complemented
8C73×#1639C211yesmaximal, characteristic, complemented
9C73×#1631C211yesmaximal, characteristic, complemented
10C73×#1631C211yesmaximal, characteristic, complemented
11C73×#1630C211yesmaximal, characteristic, complemented
12C73×#1629C211yesmaximal, characteristic, complemented
13C73×#1545C211yesmaximal, characteristic, complemented
14C73×#1495C211yesmaximal, characteristic, complemented
15C73×#1482C211yesmaximal, characteristic, complemented
16#560×C73—22no—
17#559×C73C2211yescharacteristic
18#550×C73C2211yescharacteristic
19#550×C73C2211yescharacteristic
20#546×C73—21no—
21#546×C73—21no—
22D42×C73—21no—
23D42×C73—21no—
24D42×C73C2211yescharacteristic
25#540×C73—21no—
26#540×C73—21no—
27#535×C73—21no—
28#535×C73—21no—
29#534×C73—22no—
30#533×C73C2211yescharacteristic, complemented
31C2×#127×C73C2211yescharacteristic
32#529×C73C2211yescharacteristic
33#529×C73C2211yescharacteristic
34#499×C73—21no—
35#492×C73C2211yescharacteristic
36#492×C73C2211yescharacteristic, complemented
37#488×C73—21no—
38#486×C73C2211yescharacteristic
39#486×C73C2211yescharacteristic, complemented
40#485×C73—21no—
41#482×C73—21no—
42#479×C73—21no—
43#477×C73C2211yescharacteristic, complemented
44#477×C73C2211yescharacteristic, complemented
45#476×C73C2211yescharacteristic, complemented
46#476×C73C2211yescharacteristic, complemented
47#475×C73C2211yescharacteristic, complemented
48#474×C73C2211yescharacteristic, complemented
49#470×C73—21no—
50#468×C73—21no—
51#464×C73—21no—
52#462×C73C2211yescharacteristic, complemented
53#461×C73C2211yescharacteristic, complemented
54#460×C73—22no—
55#450×C73—22no—
56#431×C73C2211yescharacteristic, complemented
57#431×C73C2211yescharacteristic, complemented
58#423×C73C2211yescharacteristic, complemented
59#331×C73C2211yescharacteristic
60#331×C73C2211yescharacteristic
61#331×C73C2211yescharacteristic, complemented
62#331×C73C2211yescharacteristic, complemented
63Q8⋊C8×C73C2211yescharacteristic, complemented
64Q8⋊C8×C73C2211yescharacteristic, complemented
65Q8⋊C8×C73C2211yescharacteristic, complemented
66Q8⋊C8×C73C2211yescharacteristic, complemented
67D4⋊C8×C73C2211yescharacteristic, complemented
68D4⋊C8×C73C2211yescharacteristic, complemented
69D4⋊C8×C73C2211yescharacteristic, complemented
70D4⋊C8×C73C2211yescharacteristic, complemented
71C2×#41×C73—21no—
72C2×#41×C73—21no—
73C22×D4×C73—22no—
74C22×D4×C73—21no—
75C22×D4×C73—21no—
76C22×D4×C73—21no—
77C22×D4×C73—21no—
78C22×D4×C73D412yes—
79C2×Q16×C73—21no—
80C2×SD16×C73—22no—
81C2×SD16×C73—22no—
82C2×SD16×C73—21no—
83C2×M16×C73—21no—
84C4⋊Q8×C73C2311yescharacteristic
85C4⋊Q8×C73C2311yescharacteristic
86#127×C73—21no—
87#127×C73—21no—
88#127×C73—21no—
89#127×C73—21no—
90#127×C73D412yes—
91#127×C73C2311yescharacteristic
92#127×C73C2311yescharacteristic
93#126×C73—21no—
94#126×C73—21no—
95#125×C73—21no—
96#125×C73D411yescharacteristic
97#125×C73D411yescharacteristic
98#124×C73—21no—
99#124×C73—21no—
100#124×C73D411yescharacteristic
101#124×C73D411yescharacteristic
102#123×C73—22no—
103#123×C73—22no—
104#123×C73—22no—
105#123×C73—22no—
106#123×C73—21no—
107#123×C73—21no—
108C22⋊Q8×C73—21no—
109C22⋊Q8×C73—21no—
110C22⋊Q8×C73D411yescharacteristic
111C22⋊Q8×C73D411yescharacteristic
112#121×C73—22no—
113#121×C73—22no—
114#121×C73—22no—
115#121×C73—22no—
116#121×C73—22no—
117#121×C73—22no—
118#121×C73—22no—
119#121×C73—22no—
120#121×C73—21no—
121#121×C73—21no—
122#121×C73—21no—
123#121×C73—21no—
124#121×C73D411yescharacteristic
125#121×C73D411yescharacteristic
126#120×C73—22no—
127#120×C73—22no—
128#120×C73—22no—
129#120×C73—22no—
130#120×C73—22no—
131#120×C73—22no—
132C4×Q8×C73—21no—
133C4×Q8×C73—21no—
134C4×Q8×C73C2311yescharacteristic
135C4×Q8×C73C2311yescharacteristic
136C4×D4×C73—21no—
137C4×D4×C73—21no—
138C4×D4×C73—21no—
139C4×D4×C73—21no—
140C4×D4×C73—21no—
141C4×D4×C73—21no—
142C4×D4×C73C2311yescharacteristic
143C4×D4×C73C2311yescharacteristic
144#117×C73—21no—
145#117×C73—21no—
146#117×C73—21no—
147C2×C22⋊C4×C73—22no—
148C2×C42×C73C2311yescharacteristic
149#107×C73—21no—
150#107×C73—21no—
151#107×C73—21no—
152#106×C73—21no—
153#106×C73—21no—
154#106×C73—21no—
155C4⋊C8×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—21no—
164#103×C73—21no—
165#103×C73—21no—
166#102×C73—22no—
167#102×C73—22no—
168#102×C73—21no—
169#102×C73—21no—
170#102×C73—21no—
171C22⋊C8×C73—21no—
172C22⋊C8×C73—21no—
173C4×C8×C73—21no—
174C4×C8×C73C2311yescharacteristic
175C4×C8×C73C2311yescharacteristic
176C24×C73—22no—
177C24×C73—22no—
178#41×C73—81no—
179#41×C73—81no—
180#41×C73—81no—
181#41×C73—81no—
182C2×Q8×C73—21no—
183C2×Q8×C73—21no—
184C2×Q8×C73C2×D411yescharacteristic
185C2×Q8×C73C2×D411yescharacteristic
186C2×D4×C73—21no—
187C2×D4×C73—21no—
188C2×D4×C73—22no—
189C2×D4×C73—22no—
190C2×D4×C73—22no—
191C2×D4×C73—22no—
192C2×D4×C73—22no—
193C2×D4×C73—22no—
194C2×D4×C73—22no—
195C2×D4×C73—22no—
196C2×D4×C73—22no—
197C2×D4×C73—21no—
198C2×D4×C73—21no—
199C2×D4×C73—21no—
200C2×D4×C73—21no—
201C2×D4×C73—81no—
202C2×D4×C73—81no—
203C2×D4×C73—81no—
204C2×D4×C73—81no—
205C2×D4×C73—81no—
206C2×D4×C73—81no—
207C2×D4×C73—81no—
208C2×D4×C73—81no—
209C2×D4×C73—82no—
210C2×D4×C73—84no—
211C2×D4×C73C2×D411yescharacteristic
212C2×D4×C73C2×D411yescharacteristic
213C2×D4×C73C2×D412yes—
214C2×D4×C73C2×D412yes—
215C22×C4×C73—22no—
216C22×C4×C73—22no—
217C22×C4×C73—22no—
218C22×C4×C73—21no—
219C22×C4×C73—21no—
220C22×C4×C73C2×D411yescharacteristic
221C22×C4×C73C2×D411yescharacteristic
222C22×C4×C73C2×D411yescharacteristic
223Q16×C73—81no—
224SD16×C73—81no—
225SD16×C73—82no—
226SD16×C73—82no—
227M16×C73—81no—
228C2×C8×C73—21no—
229C2×C8×C73—21no—
230C2×C8×C73—21no—
231C2×C8×C73—21no—
232C2×C8×C73—21no—
233C2×C8×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—21no—
244C4⋊C4×C73—21no—
245C4⋊C4×C73—21no—
246C4⋊C4×C73—41no—
247C4⋊C4×C73—41no—
248C4⋊C4×C73C2×D411yescharacteristic
249C4⋊C4×C73C2×D411yescharacteristic
250C4⋊C4×C73C2×D411yescharacteristic
251C4⋊C4×C73C2×D411yescharacteristic
252C22⋊C4×C73—22no—
253C22⋊C4×C73—22no—
254C22⋊C4×C73—22no—
255C22⋊C4×C73—22no—
256C22⋊C4×C73—22no—
257C22⋊C4×C73—22no—
258C22⋊C4×C73—21no—
259C22⋊C4×C73—21no—
260C22⋊C4×C73—21no—
261C22⋊C4×C73—21no—
262C22⋊C4×C73—21no—
263C22⋊C4×C73—21no—
264C22⋊C4×C73—21no—
265C22⋊C4×C73—21no—
266C22⋊C4×C73—21no—
267C22⋊C4×C73—21no—
268C22⋊C4×C73—41no—
269C42×C73—21no—
270C42×C73—21no—
271C42×C73—41no—
272C42×C73C2×D411yescharacteristic
273C42×C73C2×D411yescharacteristic
274C42×C73C2×D411yescharacteristic
275C42×C73C2411yescharacteristic
276C23×C73—21no—
277C23×C73—21no—
278C23×C73—22no—
279C23×C73—22no—
280C23×C73—44no—
281C23×C73—82no—
282C23×C73—82no—
283C23×C73—82no—
284C23×C73—82no—
285C23×C73—82no—
286C23×C73#12011yescharacteristic
287Q8×C73—21no—
288Q8×C73—21no—
289Q8×C73—21no—
290Q8×C73—21no—
291Q8×C73—42no—
292Q8×C73—41no—
293Q8×C73—41no—
294D4×C73—21no—
295D4×C73—21no—
296D4×C73—21no—
297D4×C73—21no—
298D4×C73—42no—
299D4×C73—42no—
300D4×C73—42no—
301D4×C73—42no—
302D4×C73—41no—
303D4×C73—41no—
304D4×C73—41no—
305D4×C73—41no—
306D4×C73—41no—
307D4×C73—41no—
308D4×C73—41no—
309D4×C73—41no—
310D4×C73—82no—
311D4×C73—82no—
312D4×C73—82no—
313D4×C73—82no—
314D4×C73—82no—
315D4×C73—82no—
316D4×C73—82no—
317D4×C73—82no—
318D4×C73—82no—
319C2×C4×C73—21no—
320C2×C4×C73—21no—
321C2×C4×C73—21no—
322C2×C4×C73—21no—
323C2×C4×C73—21no—
324C2×C4×C73—21no—
325C2×C4×C73—21no—
326C2×C4×C73—21no—
327C2×C4×C73—21no—
328C2×C4×C73—21no—
329C2×C4×C73—41no—
330C2×C4×C73—41no—
331C2×C4×C73—41no—
332C2×C4×C73—41no—
333C2×C4×C73—41no—
334C2×C4×C73—41no—
335C2×C4×C73—41no—
336C2×C4×C73—82no—
337C2×C4×C73—82no—
338C2×C4×C73—82no—
339C2×C4×C73#12011yescharacteristic
340C2×C4×C73#12011yescharacteristic
341C2×C4×C73#12011yescharacteristic
342C2×C4×C73C22×D411yescharacteristic
343C2×C4×C73C22×D411yescharacteristic
344C2×C4×C73C22×D411yescharacteristic
345C8×C73—41no—
346C8×C73—41no—
347C8×C73—41no—
348C8×C73—41no—
349C8×C73—41no—
350C8×C73—41no—
351C22×C73—21no—
352C22×C73—21no—
353C22×C73—21no—
354C22×C73—41no—
355C22×C73—42no—
356C22×C73—41no—
357C22×C73—42no—
358C22×C73—41no—
359C22×C73—42no—
360C22×C73—41no—
361C22×C73—42no—
362C22×C73—42no—
363C22×C73—41no—
364C22×C73—41no—
365C22×C73—42no—
366C22×C73—164no—
367C22×C73—164no—
368C22×C73C2×#12011yescharacteristic
369C4×C73—21no—
370C4×C73—21no—
371C4×C73—21no—
372C4×C73—21no—
373C4×C73—41no—
374C4×C73—41no—
375C4×C73—41no—
376C4×C73—41no—
377C4×C73—41no—
378C4×C73—41no—
379C4×C73—81no—
380C4×C73—81no—
381C4×C73#57611yescharacteristic
382C4×C73#57711yescharacteristic
383C4×C73#57711yescharacteristic
384C4×C73#57711yescharacteristic
385#18931C7311yesmaximal, characteristic, direct product factor, Sylow
386C2×C73—41no—
387C2×C73—82no—
388C2×C73—81no—
389C2×C73—81no—
390C2×C73—82no—
391C2×C73#300911yescharacteristic
392C2×C73#301211yescharacteristic
393C2×C73#301911yescharacteristic
394#3543C2×C7311yescharacteristic
395#3252C2×C7311yescharacteristic, complemented
396#3233C2×C7311yescharacteristic, complemented
397#3208C2×C7311yescharacteristic, complemented
398#1642C2×C7311yescharacteristic, complemented
399#1641C2×C7311yescharacteristic, complemented
400#1640C2×C7311yescharacteristic, complemented
401#1639C2×C7311yescharacteristic, complemented
402#1631C2×C7311yescharacteristic, complemented
403#1631C2×C7311yescharacteristic, complemented
404#1630C2×C7311yescharacteristic, complemented
405#1629C2×C7311yescharacteristic, complemented
406#1545C2×C7311yescharacteristic, complemented
407#1495C2×C7311yescharacteristic, complemented
408#1482C2×C7311yescharacteristic, complemented
409C73#1893111yescharacteristic, direct product factor, Sylow
410#560—22no—
411#559C22×C7311yescharacteristic
412#550C22×C7311yescharacteristic
413#550C22×C7311yescharacteristic
414#546—21no—
415#546—21no—
416D42—21no—
417D42—21no—
418D42C22×C7311yescharacteristic
419#540—21no—
420#540—21no—
421#535—21no—
422#535—21no—
423#534—22no—
424#533C22×C7311yescharacteristic, complemented
425C2×#127C22×C7311yescharacteristic
426#529C22×C7311yescharacteristic
427#529C22×C7311yescharacteristic
428#499—21no—
429#492C22×C7311yescharacteristic
430#492C22×C7311yescharacteristic, complemented
431#488—21no—
432#486C22×C7311yescharacteristic
433#486C22×C7311yescharacteristic, complemented
434#485—21no—
435#482—21no—
436#479—21no—
437#477C22×C7311yescharacteristic, complemented
438#477C22×C7311yescharacteristic, complemented
439#476C22×C7311yescharacteristic, complemented
440#476C22×C7311yescharacteristic, complemented
441#475C22×C7311yescharacteristic, complemented
442#474C22×C7311yescharacteristic, complemented
443#470—21no—
444#468—21no—
445#464—21no—
446#462C22×C7311yescharacteristic, complemented
447#461C22×C7311yescharacteristic, complemented
448#460—22no—
449#450—22no—
450#431C22×C7311yescharacteristic, complemented
451#431C22×C7311yescharacteristic, complemented
452#423C22×C7311yescharacteristic, complemented
453#331C22×C7311yescharacteristic
454#331C22×C7311yescharacteristic
455#331C22×C7311yescharacteristic, complemented
456#331C22×C7311yescharacteristic, complemented
457Q8⋊C8C22×C7311yescharacteristic, complemented
458Q8⋊C8C22×C7311yescharacteristic, complemented
459Q8⋊C8C22×C7311yescharacteristic, complemented
460Q8⋊C8C22×C7311yescharacteristic, complemented
461D4⋊C8C22×C7311yescharacteristic, complemented
462D4⋊C8C22×C7311yescharacteristic, complemented
463D4⋊C8C22×C7311yescharacteristic, complemented
464D4⋊C8C22×C7311yescharacteristic, complemented
465C2×#41—21no—
466C2×#41—21no—
467C22×D4—22no—
468C22×D4—21no—
469C22×D4—21no—
470C22×D4—21no—
471C22×D4—21no—
472C22×D4D4×C7312yes—
473C2×Q16—21no—
474C2×SD16—22no—
475C2×SD16—22no—
476C2×SD16—21no—
477C2×M16—21no—
478C4⋊Q8C23×C7311yescharacteristic
479C4⋊Q8C23×C7311yescharacteristic
480#127—21no—
481#127—21no—
482#127—21no—
483#127—21no—
484#127D4×C7312yes—
485#127C23×C7311yescharacteristic
486#127C23×C7311yescharacteristic
487#126—21no—
488#126—21no—
489#125—21no—
490#125D4×C7311yescharacteristic
491#125D4×C7311yescharacteristic
492#124—21no—
493#124—21no—
494#124D4×C7311yescharacteristic
495#124D4×C7311yescharacteristic
496#123—22no—
497#123—22no—
498#123—22no—
499#123—22no—
500#123—21no—
501#123—21no—
502C22⋊Q8—21no—
503C22⋊Q8—21no—
504C22⋊Q8D4×C7311yescharacteristic
505C22⋊Q8D4×C7311yescharacteristic
506#121—22no—
507#121—22no—
508#121—22no—
509#121—22no—
510#121—22no—
511#121—22no—
512#121—22no—
513#121—22no—
514#121—21no—
515#121—21no—
516#121—21no—
517#121—21no—
518#121D4×C7311yescharacteristic
519#121D4×C7311yescharacteristic
520#120—22no—
521#120—22no—
522#120—22no—
523#120—22no—
524#120—22no—
525#120—22no—
526C4×Q8—21no—
527C4×Q8—21no—
528C4×Q8C23×C7311yescharacteristic
529C4×Q8C23×C7311yescharacteristic
530C4×D4—21no—
531C4×D4—21no—
532C4×D4—21no—
533C4×D4—21no—
534C4×D4—21no—
535C4×D4—21no—
536C4×D4C23×C7311yescharacteristic
537C4×D4C23×C7311yescharacteristic
538#117—21no—
539#117—21no—
540#117—21no—
541C2×C22⋊C4—22no—
542C2×C42C23×C7311yescharacteristic
543#107—21no—
544#107—21no—
545#107—21no—
546#106—21no—
547#106—21no—
548#106—21no—
549C4⋊C8—21no—
550C4⋊C8—21no—
551C4⋊C8C23×C7311yescharacteristic
552C4⋊C8C23×C7311yescharacteristic
553C4⋊C8C23×C7311yescharacteristic
554C4⋊C8C23×C7311yescharacteristic
555#103—21no—
556#103—21no—
557#103—21no—
558#103—21no—
559#103—21no—
560#102—22no—
561#102—22no—
562#102—21no—
563#102—21no—
564#102—21no—
565C22⋊C8—21no—
566C22⋊C8—21no—
567C4×C8—21no—
568C4×C8C23×C7311yescharacteristic
569C4×C8C23×C7311yescharacteristic
570C24—22no—
571C24—22no—
572#41—81no—
573#41—81no—
574#41—81no—
575#41—81no—
576C2×Q8—21no—
577C2×Q8—21no—
578C2×Q8C2×D4×C7311yescharacteristic
579C2×Q8C2×D4×C7311yescharacteristic
580C2×D4—21no—
581C2×D4—21no—
582C2×D4—22no—
583C2×D4—22no—
584C2×D4—22no—
585C2×D4—22no—
586C2×D4—22no—
587C2×D4—22no—
588C2×D4—22no—
589C2×D4—22no—
590C2×D4—22no—
591C2×D4—21no—
592C2×D4—21no—
593C2×D4—21no—
594C2×D4—21no—
595C2×D4—81no—
596C2×D4—81no—
597C2×D4—81no—
598C2×D4—81no—
599C2×D4—81no—
600C2×D4—81no—
601C2×D4—81no—
602C2×D4—81no—
603C2×D4—82no—
604C2×D4—84no—
605C2×D4C2×D4×C7311yescharacteristic
606C2×D4C2×D4×C7311yescharacteristic
607C2×D4C2×D4×C7312yes—
608C2×D4C2×D4×C7312yes—
609C22×C4—22no—
610C22×C4—22no—
611C22×C4—22no—
612C22×C4—21no—
613C22×C4—21no—
614C22×C4C2×D4×C7311yescharacteristic
615C22×C4C2×D4×C7311yescharacteristic
616C22×C4C2×D4×C7311yescharacteristic
617Q16—81no—
618SD16—81no—
619SD16—82no—
620SD16—82no—
621M16—81no—
622C2×C8—21no—
623C2×C8—21no—
624C2×C8—21no—
625C2×C8—21no—
626C2×C8—21no—
627C2×C8—21no—
628C4⋊C4—21no—
629C4⋊C4—21no—
630C4⋊C4—21no—
631C4⋊C4—21no—
632C4⋊C4—21no—
633C4⋊C4—21no—
634C4⋊C4—21no—
635C4⋊C4—21no—
636C4⋊C4—21no—
637C4⋊C4—21no—
638C4⋊C4—21no—
639C4⋊C4—21no—
640C4⋊C4—41no—
641C4⋊C4—41no—
642C4⋊C4C2×D4×C7311yescharacteristic
643C4⋊C4C2×D4×C7311yescharacteristic
644C4⋊C4C2×D4×C7311yescharacteristic
645C4⋊C4C2×D4×C7311yescharacteristic
646C22⋊C4—22no—
647C22⋊C4—22no—
648C22⋊C4—22no—
649C22⋊C4—22no—
650C22⋊C4—22no—
651C22⋊C4—22no—
652C22⋊C4—21no—
653C22⋊C4—21no—
654C22⋊C4—21no—
655C22⋊C4—21no—
656C22⋊C4—21no—
657C22⋊C4—21no—
658C22⋊C4—21no—
659C22⋊C4—21no—
660C22⋊C4—21no—
661C22⋊C4—21no—
662C22⋊C4—41no—
663C42—21no—
664C42—21no—
665C42—41no—
666C42C2×D4×C7311yescharacteristic
667C42C2×D4×C7311yescharacteristic
668C42C2×D4×C7311yescharacteristic
669C42C24×C7311yescharacteristic
670C23—21no—
671C23—21no—
672C23—22no—
673C23—22no—
674C23—44no—
675C23—82no—
676C23—82no—
677C23—82no—
678C23—82no—
679C23—82no—
680C23#120×C7311yescharacteristic
681Q8—21no—
682Q8—21no—
683Q8—21no—
684Q8—21no—
685Q8—42no—
686Q8—41no—
687Q8—41no—
688D4—21no—
689D4—21no—
690D4—21no—
691D4—21no—
692D4—42no—
693D4—42no—
694D4—42no—
695D4—42no—
696D4—41no—
697D4—41no—
698D4—41no—
699D4—41no—
700D4—41no—
701D4—41no—
702D4—41no—
703D4—41no—
704D4—82no—
705D4—82no—
706D4—82no—
707D4—82no—
708D4—82no—
709D4—82no—
710D4—82no—
711D4—82no—
712D4—82no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—21no—
716C2×C4—21no—
717C2×C4—21no—
718C2×C4—21no—
719C2×C4—21no—
720C2×C4—21no—
721C2×C4—21no—
722C2×C4—21no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—82no—
731C2×C4—82no—
732C2×C4—82no—
733C2×C4#120×C7311yescharacteristic
734C2×C4#120×C7311yescharacteristic
735C2×C4#120×C7311yescharacteristic
736C2×C4C22×D4×C7311yescharacteristic
737C2×C4C22×D4×C7311yescharacteristic
738C2×C4C22×D4×C7311yescharacteristic
739C8—41no—
740C8—41no—
741C8—41no—
742C8—41no—
743C8—41no—
744C8—41no—
745C22—21no—
746C22—21no—
747C22—21no—
748C22—41no—
749C22—42no—
750C22—41no—
751C22—42no—
752C22—41no—
753C22—42no—
754C22—41no—
755C22—42no—
756C22—42no—
757C22—41no—
758C22—41no—
759C22—42no—
760C22—164no—
761C22—164no—
762C22C2×#120×C7311yescharacteristic
763C4—21no—
764C4—21no—
765C4—21no—
766C4—21no—
767C4—41no—
768C4—41no—
769C4—41no—
770C4—41no—
771C4—41no—
772C4—41no—
773C4—81no—
774C4—81no—
775C4#576×C7311yescharacteristic
776C4#577×C7311yescharacteristic
777C4#577×C7311yescharacteristic
778C4#577×C7311yescharacteristic
779C2—41no—
780C2—81no—
781C2—81no—
782C2—82no—
783C2—82no—
784C2C73×#300911yescharacteristic
785C2C73×#301211yescharacteristic
786C2C73×#301911yescharacteristic
subgroupG/H
center, socleC22×C73C2×#120
commutator, Frattini, cosocleC42C24×C73
prime radicalC73×#3543C2
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×#3252C2semidirect
3. C73×#3233C2semidirect
4. C73×#3208C2semidirect
5. C73×#1642C2semidirect
6. C73×#1641C2semidirect
7. C73×#1640C2semidirect
8. C73×#1639C2semidirect
9. C73×#1631C2semidirect
10. C73×#1631C2semidirect
11. C73×#1630C2semidirect
12. C73×#1629C2semidirect
13. C73×#1545C2semidirect
14. C73×#1495C2semidirect
15. C73×#1482C2semidirect
30. #533×C73C22semidirect
36. #492×C73C22semidirect
39. #486×C73C22semidirect
43. #477×C73C22semidirect
44. #477×C73C22semidirect
45. #476×C73C22semidirect
46. #476×C73C22semidirect
47. #475×C73C22semidirect
48. #474×C73C22semidirect
52. #462×C73C22semidirect
53. #461×C73C22semidirect
56. #431×C73C22semidirect
57. #431×C73C22semidirect
58. #423×C73C22semidirect
61. #331×C73C22semidirect
62. #331×C73C22semidirect
63. Q8⋊C8×C73C22semidirect
64. Q8⋊C8×C73C22semidirect
65. Q8⋊C8×C73C22semidirect
66. Q8⋊C8×C73C22semidirect
67. D4⋊C8×C73C22semidirect
68. D4⋊C8×C73C22semidirect
69. D4⋊C8×C73C22semidirect
70. D4⋊C8×C73C22semidirect
385. #18931C73direct (N × H)
395. #3252C2×C73semidirect
396. #3233C2×C73semidirect
397. #3208C2×C73semidirect
398. #1642C2×C73semidirect
399. #1641C2×C73semidirect
400. #1640C2×C73semidirect
401. #1639C2×C73semidirect
402. #1631C2×C73semidirect
403. #1631C2×C73semidirect
404. #1630C2×C73semidirect
405. #1629C2×C73semidirect
406. #1545C2×C73semidirect
407. #1495C2×C73semidirect
408. #1482C2×C73semidirect
409. C73#18931direct (N × H)
424. #533C22×C73semidirect
430. #492C22×C73semidirect
433. #486C22×C73semidirect
437. #477C22×C73semidirect
438. #477C22×C73semidirect
439. #476C22×C73semidirect
440. #476C22×C73semidirect
441. #475C22×C73semidirect
442. #474C22×C73semidirect
446. #462C22×C73semidirect
447. #461C22×C73semidirect
450. #431C22×C73semidirect
451. #431C22×C73semidirect
452. #423C22×C73semidirect
455. #331C22×C73semidirect
456. #331C22×C73semidirect
457. Q8⋊C8C22×C73semidirect
458. Q8⋊C8C22×C73semidirect
459. Q8⋊C8C22×C73semidirect
460. Q8⋊C8C22×C73semidirect
461. D4⋊C8C22×C73semidirect
462. D4⋊C8C22×C73semidirect
463. D4⋊C8C22×C73semidirect
464. D4⋊C8C22×C73semidirect

Maximal subgroups

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

subgroupindex
C73×#35432
C73×#32522
C73×#32332
C73×#32082
C73×#16422
C73×#16412
C73×#16402
C73×#16392
C73×#16312
C73×#16302
C73×#16292
C73×#15452
C73×#14952
C73×#14822
#1893173