Finite Group Databasebeta

← C73×#18708 #32928112

Subgroups — C73×#18708 #32928112

Order 18688.

908 conjugacy classes of subgroups.

The subgroup lattice has 756 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C73×#3554C211yesmaximal, characteristic, complemented
2C73×#3251C211yesmaximal, characteristic, complemented
3C73×#3216C211yesmaximal, characteristic, complemented
4C73×#3169C211yesmaximal, characteristic, complemented
5C73×#1649C211yesmaximal, characteristic, complemented
6C73×#1648C211yesmaximal, characteristic, complemented
7C73×#1641C211yesmaximal, characteristic, complemented
8C73×#1640C211yesmaximal, characteristic, complemented
9C73×#1627C211yesmaximal, characteristic, complemented
10C73×#1626C211yesmaximal, characteristic, complemented
11C73×#1621C211yesmaximal, characteristic, complemented
12C73×#1620C211yesmaximal, characteristic, complemented
13C73×#1557C211yesmaximal, characteristic, complemented
14C73×#1494C211yesmaximal, characteristic, complemented
15C73×#1493C211yesmaximal, characteristic, complemented
16#562×C73—22no—
17#559×C73—21no—
18#559×C73C2211yescharacteristic
19#557×C73C2211yescharacteristic
20#554×C73—21no—
21#550×C73C2211yescharacteristic
22D4×Q8×C73C2211yescharacteristic
23#548×C73—21no—
24#547×C73—21no—
25#542×C73—21no—
26#542×C73—21no—
27#540×C73—21no—
28#539×C73—22no—
29#536×C73—21no—
30#533×C73C2211yescharacteristic
31#532×C73C2211yescharacteristic
32#532×C73C2211yescharacteristic
33#529×C73C2211yescharacteristic
34#500×C73C2211yescharacteristic
35#497×C73—21no—
36#493×C73C2211yescharacteristic
37#489×C73—21no—
38#486×C73C2211yescharacteristic
39#486×C73C2211yescharacteristic
40#478×C73—21no—
41#475×C73C2211yescharacteristic
42#474×C73C2211yescharacteristic
43#469×C73—21no—
44#468×C73—21no—
45#466×C73—22no—
46#463×C73—21no—
47#462×C73C2211yescharacteristic
48#462×C73C2211yescharacteristic
49#460×C73C2211yescharacteristic
50#460×C73C2211yescharacteristic
51#460×C73C2211yescharacteristic
52#459×C73C2211yescharacteristic
53#452×C73—21no—
54#452×C73—21no—
55C4×D8×C73—22no—
56#432×C73C2211yescharacteristic
57#423×C73C2211yescharacteristic
58C2×C4×C8×C73C2211yescharacteristic
59#332×C73C2211yescharacteristic
60#332×C73C2211yescharacteristic
61#331×C73C2211yescharacteristic
62#331×C73C2211yescharacteristic
63Q8⋊C8×C73C2211yescharacteristic
64Q8⋊C8×C73C2211yescharacteristic
65Q8⋊C8×C73C2211yescharacteristic
66Q8⋊C8×C73C2211yescharacteristic
67Q8⋊C8×C73C2211yescharacteristic
68Q8⋊C8×C73C2211yescharacteristic
69D4⋊C8×C73C2211yescharacteristic
70D4⋊C8×C73C2211yescharacteristic
71C2×#41×C73—21no—
72C2×#41×C73—21no—
73C2×#41×C73—21no—
74C22×Q8×C73—21no—
75C2×Q16×C73—21no—
76C2×Q16×C73—21no—
77C2×SD16×C73—21no—
78C2×SD16×C73—21no—
79C2×SD16×C73—21no—
80C2×D8×C73—22no—
81C2×D8×C73—21no—
82C2×M16×C73—21no—
83C22×C8×C73—21no—
84C4⋊Q8×C73—21no—
85C4⋊Q8×C73—21no—
86C4⋊Q8×C73D411yescharacteristic
87C4⋊Q8×C73D411yescharacteristic
88C4⋊Q8×C73C2311yescharacteristic
89C4⋊Q8×C73C2311yescharacteristic
90#127×C73—21no—
91#127×C73C2311yescharacteristic
92#127×C73C2311yescharacteristic
93#126×C73—22no—
94#126×C73—21no—
95#125×C73—22no—
96#125×C73—21no—
97#125×C73—21no—
98#125×C73D411yescharacteristic
99#124×C73—22no—
100#124×C73—22no—
101#124×C73—21no—
102#124×C73—21no—
103#124×C73—21no—
104#124×C73—21no—
105#124×C73D411yescharacteristic
106#123×C73—22no—
107#123×C73—22no—
108#123×C73—22no—
109#123×C73—22no—
110#123×C73—22no—
111#123×C73—22no—
112#123×C73—21no—
113C22⋊Q8×C73—22no—
114C22⋊Q8×C73—22no—
115C22⋊Q8×C73—22no—
116C22⋊Q8×C73—22no—
117C22⋊Q8×C73—21no—
118C22⋊Q8×C73—22no—
119C22⋊Q8×C73—21no—
120C22⋊Q8×C73D411yescharacteristic
121C22⋊Q8×C73D411yescharacteristic
122C22⋊Q8×C73D411yescharacteristic
123#121×C73—22no—
124#121×C73—22no—
125#121×C73—22no—
126#121×C73—21no—
127#121×C73—21no—
128#121×C73—21no—
129#121×C73—21no—
130#121×C73D412yes—
131#121×C73D411yescharacteristic
132C4×Q8×C73—21no—
133C4×Q8×C73—21no—
134C4×Q8×C73—21no—
135C4×Q8×C73C2311yescharacteristic
136C4×Q8×C73C2311yescharacteristic
137C4×Q8×C73C2311yescharacteristic
138C4×D4×C73—22no—
139C4×D4×C73—21no—
140C4×D4×C73—21no—
141C4×D4×C73—21no—
142C4×D4×C73—21no—
143C4×D4×C73—21no—
144C4×D4×C73—21no—
145C4×D4×C73—21no—
146C4×D4×C73—21no—
147C4×D4×C73D412yes—
148C4×D4×C73C2311yescharacteristic
149#117×C73—21no—
150#117×C73—21no—
151C2×C4⋊C4×C73—22no—
152C2×C42×C73C2311yescharacteristic
153#107×C73—22no—
154#107×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—21no—
164#102×C73—22no—
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
176#41×C73—81no—
177#41×C73—81no—
178#41×C73—81no—
179#41×C73—81no—
180#41×C73—81no—
181#41×C73—81no—
182C2×Q8×C73—22no—
183C2×Q8×C73—21no—
184C2×Q8×C73—21no—
185C2×Q8×C73—21no—
186C2×Q8×C73—81no—
187C2×Q8×C73—81no—
188C2×Q8×C73C2×D411yescharacteristic
189C2×Q8×C73C2×D411yescharacteristic
190C2×Q8×C73C2×D411yescharacteristic
191C2×D4×C73—22no—
192C2×D4×C73—22no—
193C2×D4×C73—21no—
194C2×D4×C73—22no—
195C2×D4×C73—21no—
196C2×D4×C73—21no—
197C2×D4×C73—21no—
198C2×D4×C73—21no—
199C2×D4×C73—21no—
200C2×D4×C73—41no—
201C2×D4×C73C2×D411yescharacteristic
202C2×D4×C73C2×D412yes—
203C22×C4×C73—22no—
204C22×C4×C73—22no—
205C22×C4×C73—22no—
206C22×C4×C73—21no—
207C22×C4×C73—22no—
208C22×C4×C73—41no—
209C22×C4×C73C2×D411yescharacteristic
210C22×C4×C73C2×D411yescharacteristic
211C22×C4×C73C2×D411yescharacteristic
212Q16×C73—81no—
213Q16×C73—81no—
214SD16×C73—81no—
215SD16×C73—81no—
216SD16×C73—81no—
217D8×C73—44no—
218D8×C73—81no—
219M16×C73—81no—
220C2×C8×C73—21no—
221C2×C8×C73—21no—
222C2×C8×C73—21no—
223C2×C8×C73—21no—
224C2×C8×C73—21no—
225C2×C8×C73—21no—
226C2×C8×C73—42no—
227C4⋊C4×C73—22no—
228C4⋊C4×C73—22no—
229C4⋊C4×C73—22no—
230C4⋊C4×C73—22no—
231C4⋊C4×C73—21no—
232C4⋊C4×C73—21no—
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—21no—
244C4⋊C4×C73—21no—
245C4⋊C4×C73C2×D411yescharacteristic
246C4⋊C4×C73C2×D411yescharacteristic
247C4⋊C4×C73C2×D411yescharacteristic
248C4⋊C4×C73C2×D411yescharacteristic
249C4⋊C4×C73C2×D412yes—
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—41no—
265C22⋊C4×C73—41no—
266C42×C73—22no—
267C42×C73—21no—
268C42×C73—21no—
269C42×C73—21no—
270C42×C73C2×D411yescharacteristic
271C42×C73C2×D411yescharacteristic
272C42×C73C2×D411yescharacteristic
273C42×C73C2411yescharacteristic
274C23×C73—21no—
275C23×C73—22no—
276C23×C73—41no—
277C23×C73#12011yescharacteristic
278Q8×C73—21no—
279Q8×C73—21no—
280Q8×C73—21no—
281Q8×C73—21no—
282Q8×C73—21no—
283Q8×C73—21no—
284Q8×C73—41no—
285Q8×C73—41no—
286Q8×C73—41no—
287Q8×C73—41no—
288Q8×C73—81no—
289Q8×C73—82no—
290D4×C73—21no—
291D4×C73—21no—
292D4×C73—42no—
293D4×C73—42no—
294D4×C73—41no—
295D4×C73—41no—
296D4×C73—41no—
297D4×C73—41no—
298D4×C73—41no—
299D4×C73—41no—
300D4×C73—41no—
301D4×C73—41no—
302D4×C73—81no—
303D4×C73—82no—
304D4×C73—82no—
305D4×C73—82no—
306D4×C73—82no—
307C2×C4×C73—21no—
308C2×C4×C73—21no—
309C2×C4×C73—21no—
310C2×C4×C73—21no—
311C2×C4×C73—21no—
312C2×C4×C73—21no—
313C2×C4×C73—21no—
314C2×C4×C73—21no—
315C2×C4×C73—21no—
316C2×C4×C73—22no—
317C2×C4×C73—21no—
318C2×C4×C73—21no—
319C2×C4×C73—41no—
320C2×C4×C73—41no—
321C2×C4×C73—41no—
322C2×C4×C73—41no—
323C2×C4×C73—82no—
324C2×C4×C73—82no—
325C2×C4×C73—82no—
326C2×C4×C73—82no—
327C2×C4×C73—82no—
328C2×C4×C73#12011yescharacteristic
329C2×C4×C73#12011yescharacteristic
330C2×C4×C73#12011yescharacteristic
331C2×C4×C73C22×D411yescharacteristic
332C2×C4×C73C22×D411yescharacteristic
333C2×C4×C73C22×D411yescharacteristic
334C8×C73—22no—
335C8×C73—41no—
336C8×C73—41no—
337C8×C73—41no—
338C8×C73—41no—
339C8×C73—41no—
340C22×C73—21no—
341C22×C73—21no—
342C22×C73—21no—
343C22×C73—41no—
344C22×C73—42no—
345C22×C73—41no—
346C22×C73—42no—
347C22×C73—42no—
348C22×C73—41no—
349C22×C73—81no—
350C22×C73—81no—
351C22×C73—81no—
352C22×C73C2×#12011yescharacteristic
353C4×C73—21no—
354C4×C73—21no—
355C4×C73—21no—
356C4×C73—21no—
357C4×C73—41no—
358C4×C73—41no—
359C4×C73—42no—
360C4×C73—41no—
361C4×C73—41no—
362C4×C73—41no—
363C4×C73—41no—
364C4×C73—41no—
365C4×C73—81no—
366C4×C73#57611yescharacteristic
367C4×C73#57611yescharacteristic
368C4×C73#57711yescharacteristic
369C4×C73#57811yescharacteristic
370#18708C7311yesmaximal, characteristic, direct product factor, Sylow
371C2×C73—41no—
372C2×C73—81no—
373C2×C73—82no—
374C2×C73—161no—
375C2×C73#300811yescharacteristic
376C2×C73#301311yescharacteristic
377C2×C73#301811yescharacteristic
378#3554C2×C7311yescharacteristic, complemented
379#3251C2×C7311yescharacteristic, complemented
380#3216C2×C7311yescharacteristic, complemented
381#3169C2×C7311yescharacteristic, complemented
382#1649C2×C7311yescharacteristic, complemented
383#1648C2×C7311yescharacteristic, complemented
384#1641C2×C7311yescharacteristic, complemented
385#1640C2×C7311yescharacteristic, complemented
386#1627C2×C7311yescharacteristic, complemented
387#1626C2×C7311yescharacteristic, complemented
388#1621C2×C7311yescharacteristic, complemented
389#1620C2×C7311yescharacteristic, complemented
390#1557C2×C7311yescharacteristic, complemented
391#1494C2×C7311yescharacteristic, complemented
392#1493C2×C7311yescharacteristic, complemented
393C73#1870811yescharacteristic, direct product factor, Sylow
394#562—22no—
395#559—21no—
396#559C22×C7311yescharacteristic
397#557C22×C7311yescharacteristic
398#554—21no—
399#550C22×C7311yescharacteristic
400D4×Q8C22×C7311yescharacteristic
401#548—21no—
402#547—21no—
403#542—21no—
404#542—21no—
405#540—21no—
406#539—22no—
407#536—21no—
408#533C22×C7311yescharacteristic
409#532C22×C7311yescharacteristic
410#532C22×C7311yescharacteristic
411#529C22×C7311yescharacteristic
412#500C22×C7311yescharacteristic
413#497—21no—
414#493C22×C7311yescharacteristic
415#489—21no—
416#486C22×C7311yescharacteristic
417#486C22×C7311yescharacteristic
418#478—21no—
419#475C22×C7311yescharacteristic
420#474C22×C7311yescharacteristic
421#469—21no—
422#468—21no—
423#466—22no—
424#463—21no—
425#462C22×C7311yescharacteristic
426#462C22×C7311yescharacteristic
427#460C22×C7311yescharacteristic
428#460C22×C7311yescharacteristic
429#460C22×C7311yescharacteristic
430#459C22×C7311yescharacteristic
431#452—21no—
432#452—21no—
433C4×D8—22no—
434#432C22×C7311yescharacteristic
435#423C22×C7311yescharacteristic
436C2×C4×C8C22×C7311yescharacteristic
437#332C22×C7311yescharacteristic
438#332C22×C7311yescharacteristic
439#331C22×C7311yescharacteristic
440#331C22×C7311yescharacteristic
441Q8⋊C8C22×C7311yescharacteristic
442Q8⋊C8C22×C7311yescharacteristic
443Q8⋊C8C22×C7311yescharacteristic
444Q8⋊C8C22×C7311yescharacteristic
445Q8⋊C8C22×C7311yescharacteristic
446Q8⋊C8C22×C7311yescharacteristic
447D4⋊C8C22×C7311yescharacteristic
448D4⋊C8C22×C7311yescharacteristic
449C2×#41—21no—
450C2×#41—21no—
451C2×#41—21no—
452C22×Q8—21no—
453C2×Q16—21no—
454C2×Q16—21no—
455C2×SD16—21no—
456C2×SD16—21no—
457C2×SD16—21no—
458C2×D8—22no—
459C2×D8—21no—
460C2×M16—21no—
461C22×C8—21no—
462C4⋊Q8—21no—
463C4⋊Q8—21no—
464C4⋊Q8D4×C7311yescharacteristic
465C4⋊Q8D4×C7311yescharacteristic
466C4⋊Q8C23×C7311yescharacteristic
467C4⋊Q8C23×C7311yescharacteristic
468#127—21no—
469#127C23×C7311yescharacteristic
470#127C23×C7311yescharacteristic
471#126—22no—
472#126—21no—
473#125—22no—
474#125—21no—
475#125—21no—
476#125D4×C7311yescharacteristic
477#124—22no—
478#124—22no—
479#124—21no—
480#124—21no—
481#124—21no—
482#124—21no—
483#124D4×C7311yescharacteristic
484#123—22no—
485#123—22no—
486#123—22no—
487#123—22no—
488#123—22no—
489#123—22no—
490#123—21no—
491C22⋊Q8—22no—
492C22⋊Q8—22no—
493C22⋊Q8—22no—
494C22⋊Q8—22no—
495C22⋊Q8—21no—
496C22⋊Q8—22no—
497C22⋊Q8—21no—
498C22⋊Q8D4×C7311yescharacteristic
499C22⋊Q8D4×C7311yescharacteristic
500C22⋊Q8D4×C7311yescharacteristic
501#121—22no—
502#121—22no—
503#121—22no—
504#121—21no—
505#121—21no—
506#121—21no—
507#121—21no—
508#121D4×C7311yescharacteristic
509#121D4×C7312yes—
510C4×Q8—21no—
511C4×Q8—21no—
512C4×Q8—21no—
513C4×Q8C23×C7311yescharacteristic
514C4×Q8C23×C7311yescharacteristic
515C4×Q8C23×C7311yescharacteristic
516C4×D4—22no—
517C4×D4—21no—
518C4×D4—21no—
519C4×D4—21no—
520C4×D4—21no—
521C4×D4—21no—
522C4×D4—21no—
523C4×D4—21no—
524C4×D4—21no—
525C4×D4D4×C7312yes—
526C4×D4C23×C7311yescharacteristic
527#117—21no—
528#117—21no—
529C2×C4⋊C4—22no—
530C2×C42C23×C7311yescharacteristic
531#107—22no—
532#107—21no—
533#106—21no—
534C4⋊C8—21no—
535C4⋊C8C23×C7311yescharacteristic
536C4⋊C8C23×C7311yescharacteristic
537C4⋊C8C23×C7311yescharacteristic
538C4⋊C8C23×C7311yescharacteristic
539#103—21no—
540#103—21no—
541#103—21no—
542#102—22no—
543#102—21no—
544#102—22no—
545#102—21no—
546#102—21no—
547#102—21no—
548#102—21no—
549C22⋊C8—21no—
550#97—21no—
551C4×C8—21no—
552C4×C8C23×C7311yescharacteristic
553C4×C8C23×C7311yescharacteristic
554#41—81no—
555#41—81no—
556#41—81no—
557#41—81no—
558#41—81no—
559#41—81no—
560C2×Q8—22no—
561C2×Q8—21no—
562C2×Q8—21no—
563C2×Q8—21no—
564C2×Q8—81no—
565C2×Q8—81no—
566C2×Q8C2×D4×C7311yescharacteristic
567C2×Q8C2×D4×C7311yescharacteristic
568C2×Q8C2×D4×C7311yescharacteristic
569C2×D4—22no—
570C2×D4—22no—
571C2×D4—21no—
572C2×D4—22no—
573C2×D4—21no—
574C2×D4—21no—
575C2×D4—21no—
576C2×D4—21no—
577C2×D4—21no—
578C2×D4—41no—
579C2×D4C2×D4×C7311yescharacteristic
580C2×D4C2×D4×C7312yes—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—21no—
585C22×C4—22no—
586C22×C4—41no—
587C22×C4C2×D4×C7311yescharacteristic
588C22×C4C2×D4×C7311yescharacteristic
589C22×C4C2×D4×C7311yescharacteristic
590Q16—81no—
591Q16—81no—
592SD16—81no—
593SD16—81no—
594SD16—81no—
595D8—44no—
596D8—81no—
597M16—81no—
598C2×C8—21no—
599C2×C8—21no—
600C2×C8—21no—
601C2×C8—21no—
602C2×C8—21no—
603C2×C8—21no—
604C2×C8—42no—
605C4⋊C4—22no—
606C4⋊C4—22no—
607C4⋊C4—22no—
608C4⋊C4—22no—
609C4⋊C4—21no—
610C4⋊C4—21no—
611C4⋊C4—21no—
612C4⋊C4—21no—
613C4⋊C4—21no—
614C4⋊C4—21no—
615C4⋊C4—21no—
616C4⋊C4—21no—
617C4⋊C4—21no—
618C4⋊C4—21no—
619C4⋊C4—21no—
620C4⋊C4—21no—
621C4⋊C4—21no—
622C4⋊C4—21no—
623C4⋊C4C2×D4×C7311yescharacteristic
624C4⋊C4C2×D4×C7311yescharacteristic
625C4⋊C4C2×D4×C7311yescharacteristic
626C4⋊C4C2×D4×C7311yescharacteristic
627C4⋊C4C2×D4×C7312yes—
628C22⋊C4—22no—
629C22⋊C4—22no—
630C22⋊C4—22no—
631C22⋊C4—22no—
632C22⋊C4—22no—
633C22⋊C4—21no—
634C22⋊C4—21no—
635C22⋊C4—21no—
636C22⋊C4—21no—
637C22⋊C4—21no—
638C22⋊C4—21no—
639C22⋊C4—22no—
640C22⋊C4—22no—
641C22⋊C4—21no—
642C22⋊C4—41no—
643C22⋊C4—41no—
644C42—22no—
645C42—21no—
646C42—21no—
647C42—21no—
648C42C2×D4×C7311yescharacteristic
649C42C2×D4×C7311yescharacteristic
650C42C2×D4×C7311yescharacteristic
651C42C24×C7311yescharacteristic
652C23—21no—
653C23—22no—
654C23—41no—
655C23#120×C7311yescharacteristic
656Q8—21no—
657Q8—21no—
658Q8—21no—
659Q8—21no—
660Q8—21no—
661Q8—21no—
662Q8—41no—
663Q8—41no—
664Q8—41no—
665Q8—41no—
666Q8—81no—
667Q8—82no—
668D4—21no—
669D4—21no—
670D4—42no—
671D4—42no—
672D4—41no—
673D4—41no—
674D4—41no—
675D4—41no—
676D4—41no—
677D4—41no—
678D4—41no—
679D4—41no—
680D4—82no—
681D4—81no—
682D4—82no—
683D4—82no—
684D4—82no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—21no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—21no—
694C2×C4—22no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—82no—
702C2×C4—82no—
703C2×C4—82no—
704C2×C4—82no—
705C2×C4—82no—
706C2×C4#120×C7311yescharacteristic
707C2×C4#120×C7311yescharacteristic
708C2×C4#120×C7311yescharacteristic
709C2×C4C22×D4×C7311yescharacteristic
710C2×C4C22×D4×C7311yescharacteristic
711C2×C4C22×D4×C7311yescharacteristic
712C8—22no—
713C8—41no—
714C8—41no—
715C8—41no—
716C8—41no—
717C8—41no—
718C22—21no—
719C22—21no—
720C22—21no—
721C22—41no—
722C22—42no—
723C22—41no—
724C22—42no—
725C22—42no—
726C22—41no—
727C22—81no—
728C22—81no—
729C22—81no—
730C22C2×#120×C7311yescharacteristic
731C4—21no—
732C4—21no—
733C4—21no—
734C4—21no—
735C4—41no—
736C4—41no—
737C4—42no—
738C4—41no—
739C4—41no—
740C4—41no—
741C4—41no—
742C4—41no—
743C4—81no—
744C4#576×C7311yescharacteristic
745C4#576×C7311yescharacteristic
746C4#577×C7311yescharacteristic
747C4#578×C7311yescharacteristic
748C2—41no—
749C2—81no—
750C2—82no—
751C2—161no—
752C2C73×#300811yescharacteristic
753C2C73×#301311yescharacteristic
754C2C73×#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×#3554C2semidirect
2. C73×#3251C2semidirect
3. C73×#3216C2semidirect
4. C73×#3169C2semidirect
5. C73×#1649C2semidirect
6. C73×#1648C2semidirect
7. C73×#1641C2semidirect
8. C73×#1640C2semidirect
9. C73×#1627C2semidirect
10. C73×#1626C2semidirect
11. C73×#1621C2semidirect
12. C73×#1620C2semidirect
13. C73×#1557C2semidirect
14. C73×#1494C2semidirect
15. C73×#1493C2semidirect
370. #18708C73direct (N × H)
378. #3554C2×C73semidirect
379. #3251C2×C73semidirect
380. #3216C2×C73semidirect
381. #3169C2×C73semidirect
382. #1649C2×C73semidirect
383. #1648C2×C73semidirect
384. #1641C2×C73semidirect
385. #1640C2×C73semidirect
386. #1627C2×C73semidirect
387. #1626C2×C73semidirect
388. #1621C2×C73semidirect
389. #1620C2×C73semidirect
390. #1557C2×C73semidirect
391. #1494C2×C73semidirect
392. #1493C2×C73semidirect
393. C73#18708direct (N × H)

Maximal subgroups

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

subgroupindex
C73×#35542
C73×#32512
C73×#32162
C73×#31692
C73×#16492
C73×#16482
C73×#16412
C73×#16402
C73×#16272
C73×#16262
C73×#16212
C73×#16202
C73×#15572
C73×#14942
C73×#14932
#1870873