Finite Group Databasebeta

← C73×#18639 #32928043

Subgroups — C73×#18639 #32928043

Order 18688.

890 conjugacy classes of subgroups.

The subgroup lattice has 722 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C73×#3523C211yesmaximal, characteristic, complemented
2C73×#3247C211yesmaximal, characteristic
3C73×#3131C211yesmaximal, characteristic, complemented
4C73×#3112C211yesmaximal, characteristic, complemented
5C73×#1638C211yesmaximal, characteristic, complemented
6C73×#1637C211yesmaximal, characteristic, complemented
7C73×#1636C211yesmaximal, characteristic, complemented
8C73×#1636C211yesmaximal, characteristic, complemented
9C73×#1628C211yesmaximal, characteristic, complemented
10C73×#1627C211yesmaximal, characteristic, complemented
11C73×#1626C211yesmaximal, characteristic, complemented
12C73×#1626C211yesmaximal, characteristic, complemented
13C73×#1552C211yesmaximal, characteristic, complemented
14C73×#1494C211yesmaximal, characteristic, complemented
15C2×Q8⋊C8×C73C211yesmaximal, characteristic, complemented
16#557×C73—21no—
17#557×C73C2211yescharacteristic
18#557×C73C2211yescharacteristic
19#556×C73—21no—
20#556×C73C2211yescharacteristic
21#552×C73—22no—
22#552×C73—21no—
23D4×Q8×C73—21no—
24D4×Q8×C73C2211yescharacteristic
25#541×C73—22no—
26#541×C73—21no—
27#533×C73—21no—
28#533×C73C2211yescharacteristic
29#532×C73C2211yescharacteristic
30#529×C73—21no—
31#529×C73C2211yescharacteristic
32#519×C73—21no—
33C2×C4×Q8×C73C2211yescharacteristic
34#488×C73—22no—
35#487×C73C2211yescharacteristic
36#487×C73C2211yescharacteristic
37#486×C73C2211yescharacteristic
38#486×C73C2211yescharacteristic
39#480×C73—21no—
40#478×C73—21no—
41#477×C73C2211yescharacteristic
42#477×C73C2211yescharacteristic
43#477×C73C2211yescharacteristic
44#476×C73C2211yescharacteristic
45#466×C73—21no—
46#465×C73—21no—
47#463×C73—21no—
48#460×C73C2211yescharacteristic
49#460×C73C2211yescharacteristic
50#460×C73C2211yescharacteristic
51#459×C73C2211yescharacteristic
52#448×C73—21no—
53#440×C73—21no—
54#440×C73—21no—
55#432×C73C2211yescharacteristic
56C2×C4⋊C8×C73C2211yescharacteristic
57#416×C73—22no—
58C2×C4×C8×C73C2211yescharacteristic
59#332×C73C2211yescharacteristic
60#332×C73C2211yescharacteristic
61#332×C73C2211yescharacteristic
62#332×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—
72C22×Q8×C73—21no—
73C22×Q8×C73D411yescharacteristic
74C2×SD16×C73—21no—
75C2×SD16×C73—21no—
76C2×SD16×C73—21no—
77C2×D8×C73—21no—
78C22×C8×C73—21no—
79C22×C8×C73—21no—
80C4⋊Q8×C73—22no—
81C4⋊Q8×C73—21no—
82C4⋊Q8×C73—21no—
83C4⋊Q8×C73—21no—
84C4⋊Q8×C73C2311yescharacteristic
85C4⋊Q8×C73C2311yescharacteristic
86C4⋊Q8×C73C2311yescharacteristic
87#127×C73C2311yescharacteristic
88#126×C73—22no—
89#126×C73—22no—
90#126×C73—22no—
91#126×C73—22no—
92#126×C73—21no—
93#125×C73—22no—
94#125×C73—22no—
95#125×C73—22no—
96#125×C73—21no—
97#125×C73—22no—
98#125×C73—22no—
99#125×C73—21no—
100#125×C73D411yescharacteristic
101#125×C73D412yes—
102#124×C73—21no—
103#124×C73—21no—
104#124×C73D411yescharacteristic
105#123×C73—22no—
106#123×C73—21no—
107C22⋊Q8×C73—22no—
108C22⋊Q8×C73—22no—
109C22⋊Q8×C73—21no—
110C22⋊Q8×C73—21no—
111C22⋊Q8×C73—21no—
112C22⋊Q8×C73—21no—
113C22⋊Q8×C73—22no—
114C22⋊Q8×C73D411yescharacteristic
115#121×C73—21no—
116#121×C73—21no—
117#121×C73D411yescharacteristic
118C4×Q8×C73—22no—
119C4×Q8×C73—22no—
120C4×Q8×C73—21no—
121C4×Q8×C73—21no—
122C4×Q8×C73—21no—
123C4×Q8×C73—21no—
124C4×Q8×C73—21no—
125C4×Q8×C73—21no—
126C4×Q8×C73—21no—
127C4×Q8×C73—21no—
128C4×Q8×C73—21no—
129C4×Q8×C73D411yescharacteristic
130C4×Q8×C73D411yescharacteristic
131C4×Q8×C73C2311yescharacteristic
132C4×Q8×C73C2311yescharacteristic
133C4×Q8×C73C2311yescharacteristic
134C4×D4×C73—22no—
135C4×D4×C73—21no—
136C4×D4×C73—21no—
137C4×D4×C73—21no—
138C4×D4×C73—21no—
139C4×D4×C73C2311yescharacteristic
140#117×C73—22no—
141#117×C73—22no—
142#117×C73—22no—
143#117×C73—21no—
144#117×C73—21no—
145#117×C73D412yes—
146C2×C4⋊C4×C73—21no—
147C2×C4⋊C4×C73D411yescharacteristic
148C2×C42×C73—21no—
149C2×C42×C73C2311yescharacteristic
150#107×C73—21no—
151#107×C73—21no—
152#107×C73—21no—
153#106×C73—21no—
154C4⋊C8×C73—21no—
155C4⋊C8×C73C2311yescharacteristic
156C4⋊C8×C73C2311yescharacteristic
157C4⋊C8×C73C2311yescharacteristic
158C4⋊C8×C73C2311yescharacteristic
159#103×C73—21no—
160#103×C73—21no—
161#103×C73—21no—
162#103×C73—22no—
163#103×C73—22no—
164#102×C73—21no—
165#102×C73—22no—
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—44no—
177C2×Q8×C73—22no—
178C2×Q8×C73—21no—
179C2×Q8×C73—21no—
180C2×Q8×C73—21no—
181C2×Q8×C73—22no—
182C2×Q8×C73—21no—
183C2×Q8×C73—41no—
184C2×Q8×C73—42no—
185C2×Q8×C73—42no—
186C2×Q8×C73C2×D411yescharacteristic
187C2×Q8×C73C2×D411yescharacteristic
188C2×Q8×C73C2×D411yescharacteristic
189C2×D4×C73—21no—
190C2×D4×C73—21no—
191C2×D4×C73—21no—
192C2×D4×C73—21no—
193C2×D4×C73—41no—
194C2×D4×C73C2×D411yescharacteristic
195C22×C4×C73—22no—
196C22×C4×C73—21no—
197C22×C4×C73—21no—
198C22×C4×C73—21no—
199C22×C4×C73—41no—
200C22×C4×C73C2×D411yescharacteristic
201C22×C4×C73C2×D411yescharacteristic
202C22×C4×C73C2×D411yescharacteristic
203SD16×C73—42no—
204SD16×C73—42no—
205SD16×C73—81no—
206D8×C73—81no—
207C2×C8×C73—21no—
208C2×C8×C73—21no—
209C2×C8×C73—21no—
210C2×C8×C73—21no—
211C2×C8×C73—21no—
212C2×C8×C73—21no—
213C2×C8×C73—42no—
214C2×C8×C73—81no—
215C4⋊C4×C73—22no—
216C4⋊C4×C73—22no—
217C4⋊C4×C73—22no—
218C4⋊C4×C73—22no—
219C4⋊C4×C73—22no—
220C4⋊C4×C73—22no—
221C4⋊C4×C73—22no—
222C4⋊C4×C73—22no—
223C4⋊C4×C73—21no—
224C4⋊C4×C73—21no—
225C4⋊C4×C73—21no—
226C4⋊C4×C73—22no—
227C4⋊C4×C73—21no—
228C4⋊C4×C73—21no—
229C4⋊C4×C73—21no—
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×C73C2×D412yes—
239C4⋊C4×C73C2×D412yes—
240C4⋊C4×C73C2×D411yescharacteristic
241C4⋊C4×C73C2×D411yescharacteristic
242C4⋊C4×C73C2×D411yescharacteristic
243C4⋊C4×C73C2×D411yescharacteristic
244C22⋊C4×C73—22no—
245C22⋊C4×C73—22no—
246C22⋊C4×C73—22no—
247C22⋊C4×C73—21no—
248C22⋊C4×C73—22no—
249C22⋊C4×C73—21no—
250C22⋊C4×C73—21no—
251C22⋊C4×C73—21no—
252C22⋊C4×C73—21no—
253C22⋊C4×C73—41no—
254C22⋊C4×C73—41no—
255C42×C73—22no—
256C42×C73—22no—
257C42×C73—22no—
258C42×C73—21no—
259C42×C73—21no—
260C42×C73—22no—
261C42×C73—21no—
262C42×C73—21no—
263C42×C73—21no—
264C42×C73C2×D411yescharacteristic
265C42×C73C2×D411yescharacteristic
266C42×C73C2×D411yescharacteristic
267C42×C73C2411yescharacteristic
268C23×C73—21no—
269C23×C73—41no—
270C23×C73#12011yescharacteristic
271Q8×C73—21no—
272Q8×C73—21no—
273Q8×C73—21no—
274Q8×C73—21no—
275Q8×C73—21no—
276Q8×C73—42no—
277Q8×C73—44no—
278Q8×C73—42no—
279Q8×C73—41no—
280Q8×C73—41no—
281Q8×C73—41no—
282Q8×C73—41no—
283Q8×C73#13512yes—
284D4×C73—21no—
285D4×C73—21no—
286D4×C73—42no—
287D4×C73—42no—
288D4×C73—41no—
289D4×C73—41no—
290D4×C73—41no—
291D4×C73—41no—
292D4×C73—82no—
293C2×C4×C73—21no—
294C2×C4×C73—22no—
295C2×C4×C73—21no—
296C2×C4×C73—21no—
297C2×C4×C73—21no—
298C2×C4×C73—21no—
299C2×C4×C73—21no—
300C2×C4×C73—21no—
301C2×C4×C73—22no—
302C2×C4×C73—21no—
303C2×C4×C73—21no—
304C2×C4×C73—21no—
305C2×C4×C73—21no—
306C2×C4×C73—22no—
307C2×C4×C73—42no—
308C2×C4×C73—44no—
309C2×C4×C73—42no—
310C2×C4×C73—41no—
311C2×C4×C73—41no—
312C2×C4×C73—41no—
313C2×C4×C73—82no—
314C2×C4×C73#12011yescharacteristic
315C2×C4×C73#12011yescharacteristic
316C2×C4×C73#12011yescharacteristic
317C2×C4×C73C22×D411yescharacteristic
318C2×C4×C73C22×D411yescharacteristic
319C2×C4×C73C22×D411yescharacteristic
320C8×C73—41no—
321C8×C73—41no—
322C8×C73—41no—
323C8×C73—41no—
324C8×C73—41no—
325C8×C73—41no—
326C22×C73—21no—
327C22×C73—21no—
328C22×C73—41no—
329C22×C73—41no—
330C22×C73—41no—
331C22×C73—81no—
332C22×C73—81no—
333C22×C73—81no—
334C22×C73#45412yes—
335C22×C73C2×#12011yescharacteristic
336C4×C73—21no—
337C4×C73—22no—
338C4×C73—21no—
339C4×C73—21no—
340C4×C73—21no—
341C4×C73—41no—
342C4×C73—42no—
343C4×C73—41no—
344C4×C73—41no—
345C4×C73—42no—
346C4×C73—41no—
347C4×C73—41no—
348C4×C73—41no—
349C4×C73—81no—
350C4×C73C2×#13511yescharacteristic
351C4×C73#57511yescharacteristic
352C4×C73#57711yescharacteristic
353C4×C73#57811yescharacteristic
354#18639C7311yesmaximal, characteristic, direct product factor, Sylow
355C2×C73—22no—
356C2×C73—81no—
357C2×C73—161no—
358C2×C73#300211yescharacteristic
359C2×C73#301311yescharacteristic
360C2×C73C2×#45411yescharacteristic
361#3523C2×C7311yescharacteristic, complemented
362#3247C2×C7311yescharacteristic
363#3131C2×C7311yescharacteristic, complemented
364#3112C2×C7311yescharacteristic, complemented
365#1638C2×C7311yescharacteristic, complemented
366#1637C2×C7311yescharacteristic, complemented
367#1636C2×C7311yescharacteristic, complemented
368#1636C2×C7311yescharacteristic, complemented
369#1628C2×C7311yescharacteristic, complemented
370#1627C2×C7311yescharacteristic, complemented
371#1626C2×C7311yescharacteristic, complemented
372#1626C2×C7311yescharacteristic, complemented
373#1552C2×C7311yescharacteristic, complemented
374#1494C2×C7311yescharacteristic, complemented
375C2×Q8⋊C8C2×C7311yescharacteristic, complemented
376C73#1863911yescharacteristic, direct product factor, Sylow
377#557—21no—
378#557C22×C7311yescharacteristic
379#557C22×C7311yescharacteristic
380#556—21no—
381#556C22×C7311yescharacteristic
382#552—22no—
383#552—21no—
384D4×Q8—21no—
385D4×Q8C22×C7311yescharacteristic
386#541—22no—
387#541—21no—
388#533—21no—
389#533C22×C7311yescharacteristic
390#532C22×C7311yescharacteristic
391#529—21no—
392#529C22×C7311yescharacteristic
393#519—21no—
394C2×C4×Q8C22×C7311yescharacteristic
395#488—22no—
396#487C22×C7311yescharacteristic
397#487C22×C7311yescharacteristic
398#486C22×C7311yescharacteristic
399#486C22×C7311yescharacteristic
400#480—21no—
401#478—21no—
402#477C22×C7311yescharacteristic
403#477C22×C7311yescharacteristic
404#477C22×C7311yescharacteristic
405#476C22×C7311yescharacteristic
406#466—21no—
407#465—21no—
408#463—21no—
409#460C22×C7311yescharacteristic
410#460C22×C7311yescharacteristic
411#460C22×C7311yescharacteristic
412#459C22×C7311yescharacteristic
413#448—21no—
414#440—21no—
415#440—21no—
416#432C22×C7311yescharacteristic
417C2×C4⋊C8C22×C7311yescharacteristic
418#416—22no—
419C2×C4×C8C22×C7311yescharacteristic
420#332C22×C7311yescharacteristic
421#332C22×C7311yescharacteristic
422#332C22×C7311yescharacteristic
423#332C22×C7311yescharacteristic
424Q8⋊C8C22×C7311yescharacteristic
425Q8⋊C8C22×C7311yescharacteristic
426Q8⋊C8C22×C7311yescharacteristic
427Q8⋊C8C22×C7311yescharacteristic
428Q8⋊C8C22×C7311yescharacteristic
429Q8⋊C8C22×C7311yescharacteristic
430D4⋊C8C22×C7311yescharacteristic
431D4⋊C8C22×C7311yescharacteristic
432C2×#41—21no—
433C22×Q8—21no—
434C22×Q8D4×C7311yescharacteristic
435C2×SD16—21no—
436C2×SD16—21no—
437C2×SD16—21no—
438C2×D8—21no—
439C22×C8—21no—
440C22×C8—21no—
441C4⋊Q8—22no—
442C4⋊Q8—21no—
443C4⋊Q8—21no—
444C4⋊Q8—21no—
445C4⋊Q8C23×C7311yescharacteristic
446C4⋊Q8C23×C7311yescharacteristic
447C4⋊Q8C23×C7311yescharacteristic
448#127C23×C7311yescharacteristic
449#126—22no—
450#126—22no—
451#126—22no—
452#126—22no—
453#126—21no—
454#125—22no—
455#125—22no—
456#125—22no—
457#125—21no—
458#125—22no—
459#125—22no—
460#125—21no—
461#125D4×C7311yescharacteristic
462#125D4×C7312yes—
463#124—21no—
464#124—21no—
465#124D4×C7311yescharacteristic
466#123—22no—
467#123—21no—
468C22⋊Q8—22no—
469C22⋊Q8—22no—
470C22⋊Q8—21no—
471C22⋊Q8—21no—
472C22⋊Q8—21no—
473C22⋊Q8—21no—
474C22⋊Q8—22no—
475C22⋊Q8D4×C7311yescharacteristic
476#121—21no—
477#121—21no—
478#121D4×C7311yescharacteristic
479C4×Q8—22no—
480C4×Q8—22no—
481C4×Q8—21no—
482C4×Q8—21no—
483C4×Q8—21no—
484C4×Q8—21no—
485C4×Q8—21no—
486C4×Q8—21no—
487C4×Q8—21no—
488C4×Q8—21no—
489C4×Q8—21no—
490C4×Q8D4×C7311yescharacteristic
491C4×Q8D4×C7311yescharacteristic
492C4×Q8C23×C7311yescharacteristic
493C4×Q8C23×C7311yescharacteristic
494C4×Q8C23×C7311yescharacteristic
495C4×D4—22no—
496C4×D4—21no—
497C4×D4—21no—
498C4×D4—21no—
499C4×D4—21no—
500C4×D4C23×C7311yescharacteristic
501#117—22no—
502#117—22no—
503#117—22no—
504#117—21no—
505#117—21no—
506#117D4×C7312yes—
507C2×C4⋊C4—21no—
508C2×C4⋊C4D4×C7311yescharacteristic
509C2×C42—21no—
510C2×C42C23×C7311yescharacteristic
511#107—21no—
512#107—21no—
513#107—21no—
514#106—21no—
515C4⋊C8—21no—
516C4⋊C8C23×C7311yescharacteristic
517C4⋊C8C23×C7311yescharacteristic
518C4⋊C8C23×C7311yescharacteristic
519C4⋊C8C23×C7311yescharacteristic
520#103—21no—
521#103—21no—
522#103—21no—
523#103—22no—
524#103—22no—
525#102—21no—
526#102—22no—
527#102—22no—
528#102—21no—
529#102—21no—
530#102—21no—
531#102—21no—
532C22⋊C8—21no—
533#97—21no—
534C4×C8—21no—
535C4×C8C23×C7311yescharacteristic
536C4×C8C23×C7311yescharacteristic
537#41—44no—
538C2×Q8—22no—
539C2×Q8—21no—
540C2×Q8—21no—
541C2×Q8—21no—
542C2×Q8—22no—
543C2×Q8—21no—
544C2×Q8—41no—
545C2×Q8—42no—
546C2×Q8—42no—
547C2×Q8C2×D4×C7311yescharacteristic
548C2×Q8C2×D4×C7311yescharacteristic
549C2×Q8C2×D4×C7311yescharacteristic
550C2×D4—21no—
551C2×D4—21no—
552C2×D4—21no—
553C2×D4—21no—
554C2×D4—41no—
555C2×D4C2×D4×C7311yescharacteristic
556C22×C4—22no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—41no—
561C22×C4C2×D4×C7311yescharacteristic
562C22×C4C2×D4×C7311yescharacteristic
563C22×C4C2×D4×C7311yescharacteristic
564SD16—42no—
565SD16—42no—
566SD16—81no—
567D8—81no—
568C2×C8—21no—
569C2×C8—21no—
570C2×C8—21no—
571C2×C8—21no—
572C2×C8—21no—
573C2×C8—21no—
574C2×C8—42no—
575C2×C8—81no—
576C4⋊C4—22no—
577C4⋊C4—22no—
578C4⋊C4—22no—
579C4⋊C4—22no—
580C4⋊C4—22no—
581C4⋊C4—22no—
582C4⋊C4—22no—
583C4⋊C4—22no—
584C4⋊C4—21no—
585C4⋊C4—21no—
586C4⋊C4—21no—
587C4⋊C4—22no—
588C4⋊C4—21no—
589C4⋊C4—21no—
590C4⋊C4—21no—
591C4⋊C4—22no—
592C4⋊C4—21no—
593C4⋊C4—21no—
594C4⋊C4—21no—
595C4⋊C4—21no—
596C4⋊C4—21no—
597C4⋊C4—21no—
598C4⋊C4—21no—
599C4⋊C4C2×D4×C7312yes—
600C4⋊C4C2×D4×C7312yes—
601C4⋊C4C2×D4×C7311yescharacteristic
602C4⋊C4C2×D4×C7311yescharacteristic
603C4⋊C4C2×D4×C7311yescharacteristic
604C4⋊C4C2×D4×C7311yescharacteristic
605C22⋊C4—22no—
606C22⋊C4—22no—
607C22⋊C4—22no—
608C22⋊C4—21no—
609C22⋊C4—22no—
610C22⋊C4—21no—
611C22⋊C4—21no—
612C22⋊C4—21no—
613C22⋊C4—21no—
614C22⋊C4—41no—
615C22⋊C4—41no—
616C42—22no—
617C42—22no—
618C42—22no—
619C42—21no—
620C42—21no—
621C42—22no—
622C42—21no—
623C42—21no—
624C42—21no—
625C42C2×D4×C7311yescharacteristic
626C42C2×D4×C7311yescharacteristic
627C42C2×D4×C7311yescharacteristic
628C42C24×C7311yescharacteristic
629C23—21no—
630C23—41no—
631C23#120×C7311yescharacteristic
632Q8—21no—
633Q8—21no—
634Q8—21no—
635Q8—21no—
636Q8—21no—
637Q8—42no—
638Q8—44no—
639Q8—42no—
640Q8—41no—
641Q8—41no—
642Q8—41no—
643Q8—41no—
644Q8#135×C7312yes—
645D4—21no—
646D4—21no—
647D4—42no—
648D4—42no—
649D4—41no—
650D4—41no—
651D4—41no—
652D4—41no—
653D4—82no—
654C2×C4—22no—
655C2×C4—21no—
656C2×C4—21no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—21no—
662C2×C4—22no—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—21no—
666C2×C4—21no—
667C2×C4—22no—
668C2×C4—42no—
669C2×C4—44no—
670C2×C4—42no—
671C2×C4—41no—
672C2×C4—41no—
673C2×C4—41no—
674C2×C4—82no—
675C2×C4#120×C7311yescharacteristic
676C2×C4#120×C7311yescharacteristic
677C2×C4#120×C7311yescharacteristic
678C2×C4C22×D4×C7311yescharacteristic
679C2×C4C22×D4×C7311yescharacteristic
680C2×C4C22×D4×C7311yescharacteristic
681C8—41no—
682C8—41no—
683C8—41no—
684C8—41no—
685C8—41no—
686C8—41no—
687C22—21no—
688C22—21no—
689C22—41no—
690C22—41no—
691C22—41no—
692C22—81no—
693C22—81no—
694C22—81no—
695C22#454×C7312yes—
696C22C2×#120×C7311yescharacteristic
697C4—21no—
698C4—22no—
699C4—21no—
700C4—21no—
701C4—21no—
702C4—41no—
703C4—42no—
704C4—41no—
705C4—41no—
706C4—42no—
707C4—41no—
708C4—41no—
709C4—41no—
710C4—81no—
711C4C2×#135×C7311yescharacteristic
712C4#575×C7311yescharacteristic
713C4#577×C7311yescharacteristic
714C4#578×C7311yescharacteristic
715C2—22no—
716C2—81no—
717C2—161no—
718C2C73×#300211yescharacteristic
719C2C73×#301311yescharacteristic
720C2C2×#454×C7311yescharacteristic
subgroupG/H
center, socleC22×C73C2×#120
commutator, Frattini, cosocleC42C24×C73
prime radicalC73×#3247C2
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×#3523C2semidirect
3. C73×#3131C2semidirect
4. C73×#3112C2semidirect
5. C73×#1638C2semidirect
6. C73×#1637C2semidirect
7. C73×#1636C2semidirect
8. C73×#1636C2semidirect
9. C73×#1628C2semidirect
10. C73×#1627C2semidirect
11. C73×#1626C2semidirect
12. C73×#1626C2semidirect
13. C73×#1552C2semidirect
14. C73×#1494C2semidirect
15. C2×Q8⋊C8×C73C2semidirect
354. #18639C73direct (N × H)
361. #3523C2×C73semidirect
363. #3131C2×C73semidirect
364. #3112C2×C73semidirect
365. #1638C2×C73semidirect
366. #1637C2×C73semidirect
367. #1636C2×C73semidirect
368. #1636C2×C73semidirect
369. #1628C2×C73semidirect
370. #1627C2×C73semidirect
371. #1626C2×C73semidirect
372. #1626C2×C73semidirect
373. #1552C2×C73semidirect
374. #1494C2×C73semidirect
375. C2×Q8⋊C8C2×C73semidirect
376. C73#18639direct (N × H)

Maximal subgroups

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

subgroupindex
C73×#35232
C73×#32472
C73×#31312
C73×#31122
C73×#16382
C73×#16372
C73×#16362
C73×#16282
C73×#16272
C73×#16262
C73×#15522
C73×#14942
C2×Q8⋊C8×C732
#1863973