Finite Group Databasebeta

← C73×#18738 #32928142

Subgroups — C73×#18738 #32928142

Order 18688.

972 conjugacy classes of subgroups.

The subgroup lattice has 806 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C73×#3546C211yesmaximal, characteristic, complemented
2C73×#3245C211yesmaximal, characteristic, complemented
3C73×#3212C211yesmaximal, characteristic, complemented
4C73×#3184C211yesmaximal, characteristic, complemented
5C73×#1654C211yesmaximal, characteristic, complemented
6C73×#1652C211yesmaximal, characteristic, complemented
7C73×#1641C211yesmaximal, characteristic, complemented
8C73×#1639C211yesmaximal, characteristic, complemented
9C73×#1628C211yesmaximal, characteristic, complemented
10C73×#1625C211yesmaximal, characteristic, complemented
11C73×#1621C211yesmaximal, characteristic, complemented
12C73×#1619C211yesmaximal, 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#532×C73C2211yescharacteristic
31#532×C73C2211yescharacteristic
32#532×C73C2211yescharacteristic, complemented
33#529×C73C2211yescharacteristic
34#498×C73C2211yescharacteristic, complemented
35#495×C73—21no—
36#493×C73C2211yescharacteristic
37#488×C73—21no—
38#486×C73C2211yescharacteristic
39#486×C73C2211yescharacteristic, complemented
40#474×C73—21no—
41#474×C73C2211yescharacteristic
42#474×C73C2211yescharacteristic, complemented
43#469×C73—22no—
44#466×C73—21no—
45#466×C73—21no—
46#462×C73C2211yescharacteristic, complemented
47#461×C73C2211yescharacteristic
48#460×C73C2211yescharacteristic, complemented
49#459×C73—21no—
50#459×C73C2211yescharacteristic
51#459×C73C2211yescharacteristic
52#459×C73C2211yescharacteristic, complemented
53#452×C73—21no—
54#449×C73—21no—
55#442×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—
75C2×#41×C73—21no—
76C22×D4×C73—21no—
77C22×D4×C73—21no—
78C2×Q16×C73—21no—
79C2×SD16×C73—21no—
80C2×SD16×C73—21no—
81C2×D8×C73—22no—
82C2×D8×C73—21no—
83C2×D8×C73—21no—
84C2×D8×C73—21no—
85C2×M16×C73—21no—
86C22×C8×C73—21no—
87C4⋊Q8×C73D411yescharacteristic
88C4⋊Q8×C73C2311yescharacteristic
89C4⋊Q8×C73C2311yescharacteristic
90#127×C73—22no—
91#127×C73—21no—
92#127×C73D411yescharacteristic
93#127×C73C2311yescharacteristic
94#127×C73C2311yescharacteristic
95#126×C73—22no—
96#126×C73—22no—
97#126×C73—21no—
98#125×C73D411yescharacteristic
99#124×C73—22no—
100#124×C73—21no—
101#124×C73—21no—
102#124×C73—21no—
103#124×C73—21no—
104#124×C73D411yescharacteristic
105#123×C73—22no—
106#123×C73—22no—
107#123×C73—21no—
108#123×C73—22no—
109C22⋊Q8×C73—22no—
110C22⋊Q8×C73—21no—
111C22⋊Q8×C73—21no—
112C22⋊Q8×C73D411yescharacteristic
113#121×C73—22no—
114#121×C73—22no—
115#121×C73—22no—
116#121×C73—22no—
117#121×C73—22no—
118#121×C73—21no—
119#121×C73—22no—
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×C73—21no—
127#121×C73D411yescharacteristic
128#121×C73D411yescharacteristic
129#121×C73D411yescharacteristic
130#121×C73D412yes—
131#120×C73—22no—
132#120×C73—22no—
133#120×C73—22no—
134#120×C73—22no—
135C4×Q8×C73—21no—
136C4×Q8×C73C2311yescharacteristic
137C4×D4×C73—22no—
138C4×D4×C73—21no—
139C4×D4×C73—21no—
140C4×D4×C73—21no—
141C4×D4×C73—21no—
142C4×D4×C73—21no—
143C4×D4×C73—21no—
144C4×D4×C73D412yes—
145C4×D4×C73C2311yescharacteristic
146C4×D4×C73C2311yescharacteristic
147C4×D4×C73C2311yescharacteristic
148#117×C73—21no—
149#117×C73—21no—
150C2×C4⋊C4×C73—21no—
151C2×C22⋊C4×C73—22no—
152C2×C42×C73C2311yescharacteristic
153#107×C73—21no—
154#107×C73—21no—
155#106×C73—22no—
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#102×C73—22no—
164#102×C73—21no—
165#102×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—
185#41×C73—81no—
186#41×C73—81no—
187C2×Q8×C73—21no—
188C2×Q8×C73—21no—
189C2×Q8×C73—21no—
190C2×Q8×C73C2×D411yescharacteristic
191C2×D4×C73—22no—
192C2×D4×C73—22no—
193C2×D4×C73—22no—
194C2×D4×C73—22no—
195C2×D4×C73—22no—
196C2×D4×C73—21no—
197C2×D4×C73—21no—
198C2×D4×C73—22no—
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—21no—
207C2×D4×C73—41no—
208C2×D4×C73—81no—
209C2×D4×C73—81no—
210C2×D4×C73—81no—
211C2×D4×C73—81no—
212C2×D4×C73C2×D411yescharacteristic
213C2×D4×C73C2×D411yescharacteristic
214C2×D4×C73C2×D411yescharacteristic
215C2×D4×C73C2×D412yes—
216C22×C4×C73—22no—
217C22×C4×C73—22no—
218C22×C4×C73—21no—
219C22×C4×C73—21no—
220C22×C4×C73—21no—
221C22×C4×C73—22no—
222C22×C4×C73—41no—
223C22×C4×C73C2×D411yescharacteristic
224C22×C4×C73C2×D411yescharacteristic
225C22×C4×C73C2×D411yescharacteristic
226Q16×C73—81no—
227SD16×C73—81no—
228SD16×C73—81no—
229D8×C73—44no—
230D8×C73—81no—
231D8×C73—81no—
232D8×C73—81no—
233M16×C73—42no—
234C2×C8×C73—21no—
235C2×C8×C73—21no—
236C2×C8×C73—21no—
237C2×C8×C73—21no—
238C2×C8×C73—21no—
239C2×C8×C73—21no—
240C2×C8×C73—81no—
241C4⋊C4×C73—22no—
242C4⋊C4×C73—22no—
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×C73—21no—
250C4⋊C4×C73—21no—
251C4⋊C4×C73C2×D411yescharacteristic
252C4⋊C4×C73C2×D411yescharacteristic
253C4⋊C4×C73C2×D412yes—
254C4⋊C4×C73C2×D411yescharacteristic
255C4⋊C4×C73C2×D411yescharacteristic
256C22⋊C4×C73—22no—
257C22⋊C4×C73—22no—
258C22⋊C4×C73—22no—
259C22⋊C4×C73—22no—
260C22⋊C4×C73—22no—
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—22no—
268C22⋊C4×C73—22no—
269C22⋊C4×C73—21no—
270C22⋊C4×C73—21no—
271C22⋊C4×C73—21no—
272C22⋊C4×C73—41no—
273C22⋊C4×C73—41no—
274C42×C73—22no—
275C42×C73—21no—
276C42×C73C2×D411yescharacteristic
277C42×C73C2×D411yescharacteristic
278C42×C73C2×D411yescharacteristic
279C42×C73C2411yescharacteristic
280C23×C73—21no—
281C23×C73—21no—
282C23×C73—22no—
283C23×C73—21no—
284C23×C73—41no—
285C23×C73—82no—
286C23×C73—82no—
287C23×C73—82no—
288C23×C73#12011yescharacteristic
289Q8×C73—21no—
290Q8×C73—21no—
291Q8×C73—41no—
292Q8×C73—41no—
293Q8×C73—41no—
294Q8×C73—41no—
295Q8×C73—81no—
296D4×C73—21no—
297D4×C73—21no—
298D4×C73—21no—
299D4×C73—21no—
300D4×C73—21no—
301D4×C73—21no—
302D4×C73—42no—
303D4×C73—42no—
304D4×C73—41no—
305D4×C73—41no—
306D4×C73—41no—
307D4×C73—41no—
308D4×C73—41no—
309D4×C73—41no—
310D4×C73—41no—
311D4×C73—41no—
312D4×C73—81no—
313D4×C73—81no—
314D4×C73—81no—
315D4×C73—81no—
316D4×C73—81no—
317D4×C73—82no—
318D4×C73—82no—
319D4×C73—82no—
320D4×C73—82no—
321D4×C73—82no—
322D4×C73—82no—
323D4×C73—82no—
324C2×C4×C73—21no—
325C2×C4×C73—21no—
326C2×C4×C73—21no—
327C2×C4×C73—21no—
328C2×C4×C73—21no—
329C2×C4×C73—21no—
330C2×C4×C73—21no—
331C2×C4×C73—22no—
332C2×C4×C73—21no—
333C2×C4×C73—21no—
334C2×C4×C73—41no—
335C2×C4×C73—41no—
336C2×C4×C73—41no—
337C2×C4×C73—41no—
338C2×C4×C73—41no—
339C2×C4×C73—41no—
340C2×C4×C73—41no—
341C2×C4×C73—41no—
342C2×C4×C73—82no—
343C2×C4×C73—82no—
344C2×C4×C73—82no—
345C2×C4×C73—82no—
346C2×C4×C73#12011yescharacteristic
347C2×C4×C73#12011yescharacteristic
348C2×C4×C73#12011yescharacteristic
349C2×C4×C73C22×D411yescharacteristic
350C2×C4×C73C22×D411yescharacteristic
351C2×C4×C73C22×D411yescharacteristic
352C8×C73—22no—
353C8×C73—41no—
354C8×C73—41no—
355C8×C73—41no—
356C8×C73—41no—
357C8×C73—41no—
358C22×C73—21no—
359C22×C73—21no—
360C22×C73—21no—
361C22×C73—41no—
362C22×C73—41no—
363C22×C73—42no—
364C22×C73—41no—
365C22×C73—41no—
366C22×C73—41no—
367C22×C73—42no—
368C22×C73—41no—
369C22×C73—42no—
370C22×C73—41no—
371C22×C73—41no—
372C22×C73—41no—
373C22×C73—81no—
374C22×C73—81no—
375C22×C73—81no—
376C22×C73—164no—
377C22×C73C2×#12011yescharacteristic
378C4×C73—21no—
379C4×C73—21no—
380C4×C73—21no—
381C4×C73—21no—
382C4×C73—41no—
383C4×C73—41no—
384C4×C73—41no—
385C4×C73—41no—
386C4×C73—42no—
387C4×C73—41no—
388C4×C73—81no—
389C4×C73#57611yescharacteristic
390C4×C73#57611yescharacteristic
391C4×C73#57611yescharacteristic
392C4×C73#57711yescharacteristic
393#18738C7311yesmaximal, characteristic, direct product factor, Sylow
394C2×C73—41no—
395C2×C73—81no—
396C2×C73—82no—
397C2×C73—81no—
398C2×C73—81no—
399C2×C73—161no—
400C2×C73#300811yescharacteristic
401C2×C73#301211yescharacteristic
402C2×C73#301811yescharacteristic
403#3546C2×C7311yescharacteristic, complemented
404#3245C2×C7311yescharacteristic, complemented
405#3212C2×C7311yescharacteristic, complemented
406#3184C2×C7311yescharacteristic, complemented
407#1654C2×C7311yescharacteristic, complemented
408#1652C2×C7311yescharacteristic, complemented
409#1641C2×C7311yescharacteristic, complemented
410#1639C2×C7311yescharacteristic, complemented
411#1628C2×C7311yescharacteristic, complemented
412#1625C2×C7311yescharacteristic, complemented
413#1621C2×C7311yescharacteristic, complemented
414#1619C2×C7311yescharacteristic, complemented
415#1540C2×C7311yescharacteristic, complemented
416#1484C2×C7311yescharacteristic, complemented
417#1483C2×C7311yescharacteristic, complemented
418C73#1873811yescharacteristic, direct product factor, Sylow
419#560—22no—
420#556C22×C7311yescharacteristic
421#553—21no—
422#550—21no—
423#550C22×C7311yescharacteristic
424#547C22×C7311yescharacteristic
425#546—21no—
426#546—21no—
427D42C22×C7311yescharacteristic
428#542—21no—
429#538—22no—
430#537—21no—
431#535—21no—
432#535—21no—
433#532C22×C7311yescharacteristic
434#532C22×C7311yescharacteristic
435#532C22×C7311yescharacteristic, complemented
436#529C22×C7311yescharacteristic
437#498C22×C7311yescharacteristic, complemented
438#495—21no—
439#493C22×C7311yescharacteristic
440#488—21no—
441#486C22×C7311yescharacteristic
442#486C22×C7311yescharacteristic, complemented
443#474—21no—
444#474C22×C7311yescharacteristic
445#474C22×C7311yescharacteristic, complemented
446#469—22no—
447#466—21no—
448#466—21no—
449#462C22×C7311yescharacteristic, complemented
450#461C22×C7311yescharacteristic
451#460C22×C7311yescharacteristic, complemented
452#459—21no—
453#459C22×C7311yescharacteristic
454#459C22×C7311yescharacteristic
455#459C22×C7311yescharacteristic, complemented
456#452—21no—
457#449—21no—
458#442—22no—
459#431C22×C7311yescharacteristic, complemented
460C2×C4⋊C8C22×C7311yescharacteristic, complemented
461C4×M16C22×C7311yescharacteristic, complemented
462#332C22×C7311yescharacteristic, complemented
463#332C22×C7311yescharacteristic, complemented
464#331C22×C7311yescharacteristic
465#331C22×C7311yescharacteristic
466Q8⋊C8C22×C7311yescharacteristic, complemented
467Q8⋊C8C22×C7311yescharacteristic, complemented
468D4⋊C8C22×C7311yescharacteristic
469D4⋊C8C22×C7311yescharacteristic
470D4⋊C8C22×C7311yescharacteristic
471D4⋊C8C22×C7311yescharacteristic
472D4⋊C8C22×C7311yescharacteristic, complemented
473D4⋊C8C22×C7311yescharacteristic, complemented
474C2×#41—21no—
475C2×#41—21no—
476C2×#41—21no—
477C2×#41—21no—
478C2×#41—21no—
479C22×D4—21no—
480C22×D4—21no—
481C2×Q16—21no—
482C2×SD16—21no—
483C2×SD16—21no—
484C2×D8—22no—
485C2×D8—21no—
486C2×D8—21no—
487C2×D8—21no—
488C2×M16—21no—
489C22×C8—21no—
490C4⋊Q8D4×C7311yescharacteristic
491C4⋊Q8C23×C7311yescharacteristic
492C4⋊Q8C23×C7311yescharacteristic
493#127—22no—
494#127—21no—
495#127D4×C7311yescharacteristic
496#127C23×C7311yescharacteristic
497#127C23×C7311yescharacteristic
498#126—22no—
499#126—22no—
500#126—21no—
501#125D4×C7311yescharacteristic
502#124—22no—
503#124—21no—
504#124—21no—
505#124—21no—
506#124—21no—
507#124D4×C7311yescharacteristic
508#123—22no—
509#123—22no—
510#123—21no—
511#123—22no—
512C22⋊Q8—22no—
513C22⋊Q8—21no—
514C22⋊Q8—21no—
515C22⋊Q8D4×C7311yescharacteristic
516#121—22no—
517#121—22no—
518#121—22no—
519#121—22no—
520#121—22no—
521#121—21no—
522#121—22no—
523#121—21no—
524#121—21no—
525#121—21no—
526#121—21no—
527#121—21no—
528#121—21no—
529#121—21no—
530#121D4×C7311yescharacteristic
531#121D4×C7311yescharacteristic
532#121D4×C7311yescharacteristic
533#121D4×C7312yes—
534#120—22no—
535#120—22no—
536#120—22no—
537#120—22no—
538C4×Q8—21no—
539C4×Q8C23×C7311yescharacteristic
540C4×D4—22no—
541C4×D4—21no—
542C4×D4—21no—
543C4×D4—21no—
544C4×D4—21no—
545C4×D4—21no—
546C4×D4—21no—
547C4×D4D4×C7312yes—
548C4×D4C23×C7311yescharacteristic
549C4×D4C23×C7311yescharacteristic
550C4×D4C23×C7311yescharacteristic
551#117—21no—
552#117—21no—
553C2×C4⋊C4—21no—
554C2×C22⋊C4—22no—
555C2×C42C23×C7311yescharacteristic
556#107—21no—
557#107—21no—
558#106—22no—
559C4⋊C8—21no—
560C4⋊C8C23×C7311yescharacteristic
561C4⋊C8C23×C7311yescharacteristic
562C4⋊C8C23×C7311yescharacteristic
563C4⋊C8C23×C7311yescharacteristic
564#103—21no—
565#103—21no—
566#102—22no—
567#102—21no—
568#102—21no—
569#102—22no—
570#102—21no—
571#102—21no—
572#102—21no—
573#102—21no—
574C22⋊C8—21no—
575#97—21no—
576C4×C8—21no—
577C4×C8C23×C7311yescharacteristic
578C4×C8C23×C7311yescharacteristic
579C24—22no—
580#41—81no—
581#41—81no—
582#41—81no—
583#41—81no—
584#41—81no—
585#41—81no—
586#41—81no—
587#41—81no—
588#41—81no—
589#41—81no—
590C2×Q8—21no—
591C2×Q8—21no—
592C2×Q8—21no—
593C2×Q8C2×D4×C7311yescharacteristic
594C2×D4—22no—
595C2×D4—22no—
596C2×D4—22no—
597C2×D4—22no—
598C2×D4—22no—
599C2×D4—21no—
600C2×D4—21no—
601C2×D4—22no—
602C2×D4—21no—
603C2×D4—21no—
604C2×D4—21no—
605C2×D4—21no—
606C2×D4—21no—
607C2×D4—21no—
608C2×D4—21no—
609C2×D4—21no—
610C2×D4—41no—
611C2×D4—81no—
612C2×D4—81no—
613C2×D4—81no—
614C2×D4—81no—
615C2×D4C2×D4×C7311yescharacteristic
616C2×D4C2×D4×C7311yescharacteristic
617C2×D4C2×D4×C7311yescharacteristic
618C2×D4C2×D4×C7312yes—
619C22×C4—22no—
620C22×C4—22no—
621C22×C4—21no—
622C22×C4—21no—
623C22×C4—21no—
624C22×C4—22no—
625C22×C4—41no—
626C22×C4C2×D4×C7311yescharacteristic
627C22×C4C2×D4×C7311yescharacteristic
628C22×C4C2×D4×C7311yescharacteristic
629Q16—81no—
630SD16—81no—
631SD16—81no—
632D8—44no—
633D8—81no—
634D8—81no—
635D8—81no—
636M16—42no—
637C2×C8—21no—
638C2×C8—21no—
639C2×C8—21no—
640C2×C8—21no—
641C2×C8—21no—
642C2×C8—21no—
643C2×C8—81no—
644C4⋊C4—22no—
645C4⋊C4—22no—
646C4⋊C4—21no—
647C4⋊C4—21no—
648C4⋊C4—21no—
649C4⋊C4—21no—
650C4⋊C4—21no—
651C4⋊C4—21no—
652C4⋊C4—21no—
653C4⋊C4—21no—
654C4⋊C4C2×D4×C7311yescharacteristic
655C4⋊C4C2×D4×C7311yescharacteristic
656C4⋊C4C2×D4×C7312yes—
657C4⋊C4C2×D4×C7311yescharacteristic
658C4⋊C4C2×D4×C7311yescharacteristic
659C22⋊C4—22no—
660C22⋊C4—22no—
661C22⋊C4—22no—
662C22⋊C4—22no—
663C22⋊C4—22no—
664C22⋊C4—21no—
665C22⋊C4—21no—
666C22⋊C4—21no—
667C22⋊C4—21no—
668C22⋊C4—21no—
669C22⋊C4—21no—
670C22⋊C4—22no—
671C22⋊C4—22no—
672C22⋊C4—21no—
673C22⋊C4—21no—
674C22⋊C4—21no—
675C22⋊C4—41no—
676C22⋊C4—41no—
677C42—22no—
678C42—21no—
679C42C2×D4×C7311yescharacteristic
680C42C2×D4×C7311yescharacteristic
681C42C2×D4×C7311yescharacteristic
682C42C24×C7311yescharacteristic
683C23—21no—
684C23—21no—
685C23—22no—
686C23—21no—
687C23—41no—
688C23—82no—
689C23—82no—
690C23—82no—
691C23#120×C7311yescharacteristic
692Q8—21no—
693Q8—21no—
694Q8—41no—
695Q8—41no—
696Q8—41no—
697Q8—41no—
698Q8—81no—
699D4—21no—
700D4—21no—
701D4—21no—
702D4—21no—
703D4—21no—
704D4—21no—
705D4—42no—
706D4—42no—
707D4—41no—
708D4—41no—
709D4—41no—
710D4—41no—
711D4—41no—
712D4—41no—
713D4—41no—
714D4—41no—
715D4—81no—
716D4—81no—
717D4—81no—
718D4—81no—
719D4—82no—
720D4—81no—
721D4—82no—
722D4—82no—
723D4—82no—
724D4—82no—
725D4—82no—
726D4—82no—
727C2×C4—21no—
728C2×C4—21no—
729C2×C4—21no—
730C2×C4—21no—
731C2×C4—21no—
732C2×C4—21no—
733C2×C4—21no—
734C2×C4—22no—
735C2×C4—21no—
736C2×C4—21no—
737C2×C4—41no—
738C2×C4—41no—
739C2×C4—41no—
740C2×C4—41no—
741C2×C4—41no—
742C2×C4—41no—
743C2×C4—41no—
744C2×C4—41no—
745C2×C4—82no—
746C2×C4—82no—
747C2×C4—82no—
748C2×C4—82no—
749C2×C4#120×C7311yescharacteristic
750C2×C4#120×C7311yescharacteristic
751C2×C4#120×C7311yescharacteristic
752C2×C4C22×D4×C7311yescharacteristic
753C2×C4C22×D4×C7311yescharacteristic
754C2×C4C22×D4×C7311yescharacteristic
755C8—22no—
756C8—41no—
757C8—41no—
758C8—41no—
759C8—41no—
760C8—41no—
761C22—21no—
762C22—21no—
763C22—21no—
764C22—41no—
765C22—41no—
766C22—42no—
767C22—41no—
768C22—41no—
769C22—41no—
770C22—42no—
771C22—41no—
772C22—42no—
773C22—41no—
774C22—41no—
775C22—41no—
776C22—81no—
777C22—81no—
778C22—81no—
779C22—164no—
780C22C2×#120×C7311yescharacteristic
781C4—21no—
782C4—21no—
783C4—21no—
784C4—21no—
785C4—41no—
786C4—41no—
787C4—41no—
788C4—41no—
789C4—42no—
790C4—41no—
791C4—81no—
792C4#576×C7311yescharacteristic
793C4#576×C7311yescharacteristic
794C4#576×C7311yescharacteristic
795C4#577×C7311yescharacteristic
796C2—41no—
797C2—81no—
798C2—81no—
799C2—82no—
800C2—81no—
801C2—161no—
802C2C73×#300811yescharacteristic
803C2C73×#301211yescharacteristic
804C2C73×#301811yescharacteristic
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×#3245C2semidirect
3. C73×#3212C2semidirect
4. C73×#3184C2semidirect
5. C73×#1654C2semidirect
6. C73×#1652C2semidirect
7. C73×#1641C2semidirect
8. C73×#1639C2semidirect
9. C73×#1628C2semidirect
10. C73×#1625C2semidirect
11. C73×#1621C2semidirect
12. C73×#1619C2semidirect
13. C73×#1540C2semidirect
14. C73×#1484C2semidirect
15. C73×#1483C2semidirect
32. #532×C73C22semidirect
34. #498×C73C22semidirect
39. #486×C73C22semidirect
42. #474×C73C22semidirect
46. #462×C73C22semidirect
48. #460×C73C22semidirect
52. #459×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
393. #18738C73direct (N × H)
403. #3546C2×C73semidirect
404. #3245C2×C73semidirect
405. #3212C2×C73semidirect
406. #3184C2×C73semidirect
407. #1654C2×C73semidirect
408. #1652C2×C73semidirect
409. #1641C2×C73semidirect
410. #1639C2×C73semidirect
411. #1628C2×C73semidirect
412. #1625C2×C73semidirect
413. #1621C2×C73semidirect
414. #1619C2×C73semidirect
415. #1540C2×C73semidirect
416. #1484C2×C73semidirect
417. #1483C2×C73semidirect
418. C73#18738direct (N × H)
435. #532C22×C73semidirect
437. #498C22×C73semidirect
442. #486C22×C73semidirect
445. #474C22×C73semidirect
449. #462C22×C73semidirect
451. #460C22×C73semidirect
455. #459C22×C73semidirect
459. #431C22×C73semidirect
460. C2×C4⋊C8C22×C73semidirect
461. C4×M16C22×C73semidirect
462. #332C22×C73semidirect
463. #332C22×C73semidirect
466. Q8⋊C8C22×C73semidirect
467. Q8⋊C8C22×C73semidirect
472. D4⋊C8C22×C73semidirect
473. 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×#32452
C73×#32122
C73×#31842
C73×#16542
C73×#16522
C73×#16412
C73×#16392
C73×#16282
C73×#16252
C73×#16212
C73×#16192
C73×#15402
C73×#14842
C73×#14832
#1873873