Finite Group Databasebeta

← C73×#18962 #32928366

Subgroups — C73×#18962 #32928366

Order 18688.

964 conjugacy classes of subgroups.

The subgroup lattice has 800 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C73×#3546C211yesmaximal, characteristic, complemented
2C73×#3253C211yesmaximal, characteristic, complemented
3C73×#3247C211yesmaximal, characteristic, complemented
4C73×#3207C211yesmaximal, characteristic, complemented
5C73×#1638C211yesmaximal, characteristic, complemented
6C73×#1635C211yesmaximal, characteristic, complemented
7C73×#1631C211yesmaximal, characteristic, complemented
8C73×#1629C211yesmaximal, characteristic, complemented
9C73×#1628C211yesmaximal, characteristic, complemented
10C73×#1625C211yesmaximal, characteristic, complemented
11C73×#1621C211yesmaximal, characteristic, complemented
12C73×#1619C211yesmaximal, 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#532×C73C2211yescharacteristic
31#532×C73C2211yescharacteristic
32#532×C73C2211yescharacteristic, complemented
33#529×C73C2211yescharacteristic
34#493×C73C2211yescharacteristic
35#492×C73C2211yescharacteristic
36#487×C73C2211yescharacteristic, complemented
37#486×C73C2211yescharacteristic, complemented
38#478×C73—21no—
39#477×C73C2211yescharacteristic, complemented
40#476×C73—21no—
41#476×C73C2211yescharacteristic
42#476×C73C2211yescharacteristic
43#476×C73C2211yescharacteristic, complemented
44#469×C73—21no—
45#469×C73—21no—
46#466×C73—21no—
47#465×C73—21no—
48#463×C73—21no—
49#463×C73—22no—
50#460×C73C2211yescharacteristic, complemented
51#459×C73—21no—
52#459×C73C2211yescharacteristic
53#459×C73C2211yescharacteristic
54#459×C73C2211yescharacteristic, complemented
55#449×C73—22no—
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—
75C2×#41×C73—21no—
76C22×D4×C73—21no—
77C22×D4×C73—21no—
78C2×SD16×C73—21no—
79C2×SD16×C73—22no—
80C2×D8×C73—22no—
81C2×D8×C73—21no—
82C2×D8×C73—21no—
83C2×D8×C73—21no—
84C2×M16×C73—21no—
85C22×C8×C73—21no—
86C4⋊Q8×C73D411yescharacteristic
87C4⋊Q8×C73C2311yescharacteristic
88C4⋊Q8×C73C2311yescharacteristic
89#127×C73—22no—
90#127×C73—21no—
91#127×C73D411yescharacteristic
92#127×C73C2311yescharacteristic
93#127×C73C2311yescharacteristic
94#126×C73—22no—
95#126×C73—22no—
96#126×C73—21no—
97#125×C73D411yescharacteristic
98#124×C73—22no—
99#124×C73—21no—
100#124×C73—21no—
101#124×C73—21no—
102#124×C73—21no—
103#124×C73D411yescharacteristic
104#123×C73—22no—
105#123×C73—22no—
106#123×C73—21no—
107#123×C73—22no—
108C22⋊Q8×C73—22no—
109C22⋊Q8×C73—21no—
110C22⋊Q8×C73—21no—
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—21no—
118#121×C73—22no—
119#121×C73—21no—
120#121×C73—21no—
121#121×C73—21no—
122#121×C73—21no—
123#121×C73—21no—
124#121×C73—21no—
125#121×C73—21no—
126#121×C73D412yes—
127#121×C73D411yescharacteristic
128#121×C73D411yescharacteristic
129#121×C73D411yescharacteristic
130#120×C73—22no—
131#120×C73—22no—
132#120×C73—22no—
133#120×C73—22no—
134C4×Q8×C73—21no—
135C4×Q8×C73C2311yescharacteristic
136C4×D4×C73—22no—
137C4×D4×C73—21no—
138C4×D4×C73—21no—
139C4×D4×C73—21no—
140C4×D4×C73—21no—
141C4×D4×C73—21no—
142C4×D4×C73—21no—
143C4×D4×C73D412yes—
144C4×D4×C73C2311yescharacteristic
145C4×D4×C73C2311yescharacteristic
146C4×D4×C73C2311yescharacteristic
147#117×C73—21no—
148#117×C73—21no—
149C2×C4⋊C4×C73—21no—
150C2×C22⋊C4×C73—22no—
151C2×C42×C73C2311yescharacteristic
152#107×C73—21no—
153#106×C73—21no—
154#106×C73—21no—
155#106×C73—21no—
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—22no—
165#102×C73—21no—
166#102×C73—21no—
167#102×C73—21no—
168#102×C73—22no—
169#102×C73—21no—
170#102×C73—21no—
171#102×C73—21no—
172#102×C73—21no—
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—
185#41×C73—82no—
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—21no—
204C2×D4×C73—21no—
205C2×D4×C73—21no—
206C2×D4×C73—41no—
207C2×D4×C73—81no—
208C2×D4×C73—81no—
209C2×D4×C73—81no—
210C2×D4×C73—81no—
211C2×D4×C73C2×D411yescharacteristic
212C2×D4×C73C2×D411yescharacteristic
213C2×D4×C73C2×D411yescharacteristic
214C2×D4×C73C2×D412yes—
215C22×C4×C73—22no—
216C22×C4×C73—22no—
217C22×C4×C73—21no—
218C22×C4×C73—21no—
219C22×C4×C73—21no—
220C22×C4×C73—22no—
221C22×C4×C73—41no—
222C22×C4×C73C2×D411yescharacteristic
223C22×C4×C73C2×D411yescharacteristic
224C22×C4×C73C2×D411yescharacteristic
225SD16×C73—81no—
226SD16×C73—82no—
227D8×C73—81no—
228D8×C73—81no—
229D8×C73—81no—
230D8×C73—82no—
231M16×C73—81no—
232C2×C8×C73—21no—
233C2×C8×C73—21no—
234C2×C8×C73—21no—
235C2×C8×C73—21no—
236C2×C8×C73—21no—
237C2×C8×C73—21no—
238C2×C8×C73—81no—
239C4⋊C4×C73—22no—
240C4⋊C4×C73—22no—
241C4⋊C4×C73—21no—
242C4⋊C4×C73—21no—
243C4⋊C4×C73—21no—
244C4⋊C4×C73—21no—
245C4⋊C4×C73—21no—
246C4⋊C4×C73—21no—
247C4⋊C4×C73—21no—
248C4⋊C4×C73—21no—
249C4⋊C4×C73C2×D412yes—
250C4⋊C4×C73C2×D411yescharacteristic
251C4⋊C4×C73C2×D411yescharacteristic
252C4⋊C4×C73C2×D411yescharacteristic
253C4⋊C4×C73C2×D411yescharacteristic
254C22⋊C4×C73—22no—
255C22⋊C4×C73—22no—
256C22⋊C4×C73—22no—
257C22⋊C4×C73—22no—
258C22⋊C4×C73—22no—
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—22no—
266C22⋊C4×C73—22no—
267C22⋊C4×C73—21no—
268C22⋊C4×C73—21no—
269C22⋊C4×C73—21no—
270C22⋊C4×C73—41no—
271C22⋊C4×C73—41no—
272C42×C73—22no—
273C42×C73—21no—
274C42×C73C2×D411yescharacteristic
275C42×C73C2×D411yescharacteristic
276C42×C73C2×D411yescharacteristic
277C42×C73C2411yescharacteristic
278C23×C73—21no—
279C23×C73—21no—
280C23×C73—22no—
281C23×C73—21no—
282C23×C73—41no—
283C23×C73—82no—
284C23×C73—82no—
285C23×C73—82no—
286C23×C73#12011yescharacteristic
287Q8×C73—21no—
288Q8×C73—21no—
289Q8×C73—42no—
290Q8×C73—41no—
291Q8×C73—41no—
292Q8×C73—81no—
293D4×C73—21no—
294D4×C73—21no—
295D4×C73—21no—
296D4×C73—21no—
297D4×C73—21no—
298D4×C73—21no—
299D4×C73—42no—
300D4×C73—42no—
301D4×C73—41no—
302D4×C73—41no—
303D4×C73—41no—
304D4×C73—41no—
305D4×C73—41no—
306D4×C73—41no—
307D4×C73—41no—
308D4×C73—41no—
309D4×C73—81no—
310D4×C73—81no—
311D4×C73—81no—
312D4×C73—81no—
313D4×C73—81no—
314D4×C73—82no—
315D4×C73—82no—
316D4×C73—82no—
317D4×C73—82no—
318D4×C73—82no—
319D4×C73—82no—
320D4×C73—82no—
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—22no—
329C2×C4×C73—21no—
330C2×C4×C73—21no—
331C2×C4×C73—41no—
332C2×C4×C73—41no—
333C2×C4×C73—41no—
334C2×C4×C73—41no—
335C2×C4×C73—41no—
336C2×C4×C73—41no—
337C2×C4×C73—41no—
338C2×C4×C73—41no—
339C2×C4×C73—82no—
340C2×C4×C73—82no—
341C2×C4×C73—82no—
342C2×C4×C73—82no—
343C2×C4×C73#12011yescharacteristic
344C2×C4×C73#12011yescharacteristic
345C2×C4×C73#12011yescharacteristic
346C2×C4×C73C22×D411yescharacteristic
347C2×C4×C73C22×D411yescharacteristic
348C2×C4×C73C22×D411yescharacteristic
349C8×C73—41no—
350C8×C73—41no—
351C8×C73—41no—
352C8×C73—41no—
353C8×C73—41no—
354C8×C73—41no—
355C22×C73—21no—
356C22×C73—21no—
357C22×C73—21no—
358C22×C73—41no—
359C22×C73—41no—
360C22×C73—41no—
361C22×C73—41no—
362C22×C73—42no—
363C22×C73—42no—
364C22×C73—41no—
365C22×C73—41no—
366C22×C73—42no—
367C22×C73—41no—
368C22×C73—41no—
369C22×C73—41no—
370C22×C73—81no—
371C22×C73—81no—
372C22×C73—81no—
373C22×C73—164no—
374C22×C73C2×#12011yescharacteristic
375C4×C73—21no—
376C4×C73—21no—
377C4×C73—21no—
378C4×C73—21no—
379C4×C73—41no—
380C4×C73—41no—
381C4×C73—41no—
382C4×C73—41no—
383C4×C73—42no—
384C4×C73—41no—
385C4×C73—81no—
386C4×C73#57611yescharacteristic
387C4×C73#57611yescharacteristic
388C4×C73#57711yescharacteristic
389C4×C73#57711yescharacteristic
390#18962C7311yesmaximal, characteristic, direct product factor, Sylow
391C2×C73—41no—
392C2×C73—81no—
393C2×C73—82no—
394C2×C73—81no—
395C2×C73—81no—
396C2×C73—161no—
397C2×C73#301211yescharacteristic
398C2×C73#301211yescharacteristic
399C2×C73#302111yescharacteristic
400#3546C2×C7311yescharacteristic, complemented
401#3253C2×C7311yescharacteristic, complemented
402#3247C2×C7311yescharacteristic, complemented
403#3207C2×C7311yescharacteristic, complemented
404#1638C2×C7311yescharacteristic, complemented
405#1635C2×C7311yescharacteristic, complemented
406#1631C2×C7311yescharacteristic, complemented
407#1629C2×C7311yescharacteristic, complemented
408#1628C2×C7311yescharacteristic, complemented
409#1625C2×C7311yescharacteristic, complemented
410#1621C2×C7311yescharacteristic, complemented
411#1619C2×C7311yescharacteristic, complemented
412#1547C2×C7311yescharacteristic, complemented
413#1495C2×C7311yescharacteristic, complemented
414#1480C2×C7311yescharacteristic, complemented
415C73#1896211yescharacteristic, direct product factor, Sylow
416#560—22no—
417#556C22×C7311yescharacteristic
418#553—21no—
419#550—21no—
420#550C22×C7311yescharacteristic
421#547C22×C7311yescharacteristic
422#546—21no—
423#546—21no—
424D42C22×C7311yescharacteristic
425#542—21no—
426#538—22no—
427#537—21no—
428#535—21no—
429#535—21no—
430#532C22×C7311yescharacteristic
431#532C22×C7311yescharacteristic
432#532C22×C7311yescharacteristic, complemented
433#529C22×C7311yescharacteristic
434#493C22×C7311yescharacteristic
435#492C22×C7311yescharacteristic
436#487C22×C7311yescharacteristic, complemented
437#486C22×C7311yescharacteristic, complemented
438#478—21no—
439#477C22×C7311yescharacteristic, complemented
440#476—21no—
441#476C22×C7311yescharacteristic
442#476C22×C7311yescharacteristic
443#476C22×C7311yescharacteristic, complemented
444#469—21no—
445#469—21no—
446#466—21no—
447#465—21no—
448#463—21no—
449#463—22no—
450#460C22×C7311yescharacteristic, complemented
451#459—21no—
452#459C22×C7311yescharacteristic
453#459C22×C7311yescharacteristic
454#459C22×C7311yescharacteristic, complemented
455#449—22no—
456#431C22×C7311yescharacteristic, complemented
457#423C22×C7311yescharacteristic, complemented
458C2×C4⋊C8C22×C7311yescharacteristic, complemented
459#332C22×C7311yescharacteristic, complemented
460#332C22×C7311yescharacteristic, complemented
461#331C22×C7311yescharacteristic
462#331C22×C7311yescharacteristic
463Q8⋊C8C22×C7311yescharacteristic, complemented
464Q8⋊C8C22×C7311yescharacteristic, complemented
465D4⋊C8C22×C7311yescharacteristic
466D4⋊C8C22×C7311yescharacteristic
467D4⋊C8C22×C7311yescharacteristic
468D4⋊C8C22×C7311yescharacteristic
469D4⋊C8C22×C7311yescharacteristic, complemented
470D4⋊C8C22×C7311yescharacteristic, complemented
471C2×#41—21no—
472C2×#41—21no—
473C2×#41—21no—
474C2×#41—21no—
475C2×#41—21no—
476C22×D4—21no—
477C22×D4—21no—
478C2×SD16—21no—
479C2×SD16—22no—
480C2×D8—22no—
481C2×D8—21no—
482C2×D8—21no—
483C2×D8—21no—
484C2×M16—21no—
485C22×C8—21no—
486C4⋊Q8D4×C7311yescharacteristic
487C4⋊Q8C23×C7311yescharacteristic
488C4⋊Q8C23×C7311yescharacteristic
489#127—22no—
490#127—21no—
491#127D4×C7311yescharacteristic
492#127C23×C7311yescharacteristic
493#127C23×C7311yescharacteristic
494#126—22no—
495#126—22no—
496#126—21no—
497#125D4×C7311yescharacteristic
498#124—22no—
499#124—21no—
500#124—21no—
501#124—21no—
502#124—21no—
503#124D4×C7311yescharacteristic
504#123—22no—
505#123—22no—
506#123—21no—
507#123—22no—
508C22⋊Q8—22no—
509C22⋊Q8—21no—
510C22⋊Q8—21no—
511C22⋊Q8D4×C7311yescharacteristic
512#121—22no—
513#121—22no—
514#121—22no—
515#121—22no—
516#121—22no—
517#121—21no—
518#121—22no—
519#121—21no—
520#121—21no—
521#121—21no—
522#121—21no—
523#121—21no—
524#121—21no—
525#121—21no—
526#121D4×C7311yescharacteristic
527#121D4×C7311yescharacteristic
528#121D4×C7311yescharacteristic
529#121D4×C7312yes—
530#120—22no—
531#120—22no—
532#120—22no—
533#120—22no—
534C4×Q8—21no—
535C4×Q8C23×C7311yescharacteristic
536C4×D4—22no—
537C4×D4—21no—
538C4×D4—21no—
539C4×D4—21no—
540C4×D4—21no—
541C4×D4—21no—
542C4×D4—21no—
543C4×D4D4×C7312yes—
544C4×D4C23×C7311yescharacteristic
545C4×D4C23×C7311yescharacteristic
546C4×D4C23×C7311yescharacteristic
547#117—21no—
548#117—21no—
549C2×C4⋊C4—21no—
550C2×C22⋊C4—22no—
551C2×C42C23×C7311yescharacteristic
552#107—21no—
553#106—21no—
554#106—21no—
555#106—21no—
556C4⋊C8—21no—
557C4⋊C8—21no—
558C4⋊C8—21no—
559C4⋊C8C23×C7311yescharacteristic
560C4⋊C8C23×C7311yescharacteristic
561C4⋊C8C23×C7311yescharacteristic
562C4⋊C8C23×C7311yescharacteristic
563#103—21no—
564#103—22no—
565#102—21no—
566#102—21no—
567#102—21no—
568#102—22no—
569#102—21no—
570#102—21no—
571#102—21no—
572#102—21no—
573C22⋊C8—21no—
574C4×C8C23×C7311yescharacteristic
575C4×C8C23×C7311yescharacteristic
576C24—22no—
577#41—81no—
578#41—81no—
579#41—81no—
580#41—81no—
581#41—81no—
582#41—81no—
583#41—81no—
584#41—81no—
585#41—82no—
586C2×Q8—21no—
587C2×Q8—21no—
588C2×Q8—21no—
589C2×Q8C2×D4×C7311yescharacteristic
590C2×D4—22no—
591C2×D4—22no—
592C2×D4—22no—
593C2×D4—22no—
594C2×D4—22no—
595C2×D4—21no—
596C2×D4—21no—
597C2×D4—22no—
598C2×D4—21no—
599C2×D4—21no—
600C2×D4—21no—
601C2×D4—21no—
602C2×D4—21no—
603C2×D4—21no—
604C2×D4—21no—
605C2×D4—21no—
606C2×D4—41no—
607C2×D4—81no—
608C2×D4—81no—
609C2×D4—81no—
610C2×D4—81no—
611C2×D4C2×D4×C7311yescharacteristic
612C2×D4C2×D4×C7311yescharacteristic
613C2×D4C2×D4×C7311yescharacteristic
614C2×D4C2×D4×C7312yes—
615C22×C4—22no—
616C22×C4—22no—
617C22×C4—21no—
618C22×C4—21no—
619C22×C4—21no—
620C22×C4—22no—
621C22×C4—41no—
622C22×C4C2×D4×C7311yescharacteristic
623C22×C4C2×D4×C7311yescharacteristic
624C22×C4C2×D4×C7311yescharacteristic
625SD16—81no—
626SD16—82no—
627D8—81no—
628D8—81no—
629D8—81no—
630D8—82no—
631M16—81no—
632C2×C8—21no—
633C2×C8—21no—
634C2×C8—21no—
635C2×C8—21no—
636C2×C8—21no—
637C2×C8—21no—
638C2×C8—81no—
639C4⋊C4—22no—
640C4⋊C4—22no—
641C4⋊C4—21no—
642C4⋊C4—21no—
643C4⋊C4—21no—
644C4⋊C4—21no—
645C4⋊C4—21no—
646C4⋊C4—21no—
647C4⋊C4—21no—
648C4⋊C4—21no—
649C4⋊C4C2×D4×C7312yes—
650C4⋊C4C2×D4×C7311yescharacteristic
651C4⋊C4C2×D4×C7311yescharacteristic
652C4⋊C4C2×D4×C7311yescharacteristic
653C4⋊C4C2×D4×C7311yescharacteristic
654C22⋊C4—22no—
655C22⋊C4—22no—
656C22⋊C4—22no—
657C22⋊C4—22no—
658C22⋊C4—22no—
659C22⋊C4—21no—
660C22⋊C4—21no—
661C22⋊C4—21no—
662C22⋊C4—21no—
663C22⋊C4—21no—
664C22⋊C4—21no—
665C22⋊C4—22no—
666C22⋊C4—22no—
667C22⋊C4—21no—
668C22⋊C4—21no—
669C22⋊C4—21no—
670C22⋊C4—41no—
671C22⋊C4—41no—
672C42—22no—
673C42—21no—
674C42C2×D4×C7311yescharacteristic
675C42C2×D4×C7311yescharacteristic
676C42C2×D4×C7311yescharacteristic
677C42C24×C7311yescharacteristic
678C23—21no—
679C23—21no—
680C23—22no—
681C23—21no—
682C23—41no—
683C23—82no—
684C23—82no—
685C23—82no—
686C23#120×C7311yescharacteristic
687Q8—21no—
688Q8—21no—
689Q8—42no—
690Q8—41no—
691Q8—41no—
692Q8—81no—
693D4—21no—
694D4—21no—
695D4—21no—
696D4—21no—
697D4—21no—
698D4—21no—
699D4—42no—
700D4—42no—
701D4—41no—
702D4—41no—
703D4—41no—
704D4—41no—
705D4—41no—
706D4—41no—
707D4—41no—
708D4—41no—
709D4—81no—
710D4—81no—
711D4—81no—
712D4—81no—
713D4—82no—
714D4—81no—
715D4—82no—
716D4—82no—
717D4—82no—
718D4—82no—
719D4—82no—
720D4—82no—
721C2×C4—21no—
722C2×C4—21no—
723C2×C4—21no—
724C2×C4—21no—
725C2×C4—21no—
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—22no—
729C2×C4—21no—
730C2×C4—21no—
731C2×C4—41no—
732C2×C4—41no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—41no—
739C2×C4—82no—
740C2×C4—82no—
741C2×C4—82no—
742C2×C4—82no—
743C2×C4#120×C7311yescharacteristic
744C2×C4#120×C7311yescharacteristic
745C2×C4#120×C7311yescharacteristic
746C2×C4C22×D4×C7311yescharacteristic
747C2×C4C22×D4×C7311yescharacteristic
748C2×C4C22×D4×C7311yescharacteristic
749C8—41no—
750C8—41no—
751C8—41no—
752C8—41no—
753C8—41no—
754C8—41no—
755C22—21no—
756C22—21no—
757C22—21no—
758C22—41no—
759C22—41no—
760C22—41no—
761C22—41no—
762C22—42no—
763C22—42no—
764C22—41no—
765C22—41no—
766C22—42no—
767C22—41no—
768C22—41no—
769C22—41no—
770C22—81no—
771C22—81no—
772C22—81no—
773C22—164no—
774C22C2×#120×C7311yescharacteristic
775C4—21no—
776C4—21no—
777C4—21no—
778C4—21no—
779C4—41no—
780C4—41no—
781C4—41no—
782C4—41no—
783C4—42no—
784C4—41no—
785C4—81no—
786C4#576×C7311yescharacteristic
787C4#576×C7311yescharacteristic
788C4#577×C7311yescharacteristic
789C4#577×C7311yescharacteristic
790C2—41no—
791C2—81no—
792C2—81no—
793C2—82no—
794C2—81no—
795C2—161no—
796C2C73×#301211yescharacteristic
797C2C73×#301211yescharacteristic
798C2C73×#302111yescharacteristic
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×#3546C2semidirect
2. C73×#3253C2semidirect
3. C73×#3247C2semidirect
4. C73×#3207C2semidirect
5. C73×#1638C2semidirect
6. C73×#1635C2semidirect
7. C73×#1631C2semidirect
8. C73×#1629C2semidirect
9. C73×#1628C2semidirect
10. C73×#1625C2semidirect
11. C73×#1621C2semidirect
12. C73×#1619C2semidirect
13. C73×#1547C2semidirect
14. C73×#1495C2semidirect
15. C73×#1480C2semidirect
32. #532×C73C22semidirect
36. #487×C73C22semidirect
37. #486×C73C22semidirect
39. #477×C73C22semidirect
43. #476×C73C22semidirect
50. #460×C73C22semidirect
54. #459×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
390. #18962C73direct (N × H)
400. #3546C2×C73semidirect
401. #3253C2×C73semidirect
402. #3247C2×C73semidirect
403. #3207C2×C73semidirect
404. #1638C2×C73semidirect
405. #1635C2×C73semidirect
406. #1631C2×C73semidirect
407. #1629C2×C73semidirect
408. #1628C2×C73semidirect
409. #1625C2×C73semidirect
410. #1621C2×C73semidirect
411. #1619C2×C73semidirect
412. #1547C2×C73semidirect
413. #1495C2×C73semidirect
414. #1480C2×C73semidirect
415. C73#18962direct (N × H)
432. #532C22×C73semidirect
436. #487C22×C73semidirect
437. #486C22×C73semidirect
439. #477C22×C73semidirect
443. #476C22×C73semidirect
450. #460C22×C73semidirect
454. #459C22×C73semidirect
456. #431C22×C73semidirect
457. #423C22×C73semidirect
458. C2×C4⋊C8C22×C73semidirect
459. #332C22×C73semidirect
460. #332C22×C73semidirect
463. Q8⋊C8C22×C73semidirect
464. Q8⋊C8C22×C73semidirect
469. D4⋊C8C22×C73semidirect
470. 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×#32532
C73×#32472
C73×#32072
C73×#16382
C73×#16352
C73×#16312
C73×#16292
C73×#16282
C73×#16252
C73×#16212
C73×#16192
C73×#15472
C73×#14952
C73×#14802
#1896273