Finite Group Databasebeta

← C73×#18824 #32928228

Subgroups — C73×#18824 #32928228

Order 18688.

900 conjugacy classes of subgroups.

The subgroup lattice has 732 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C73×#3523C211yesmaximal, characteristic, complemented
2C73×#3251C211yesmaximal, characteristic
3C73×#3228C211yesmaximal, characteristic, complemented
4C73×#3037C211yesmaximal, characteristic, complemented
5C73×#1653C211yesmaximal, characteristic, complemented
6C73×#1652C211yesmaximal, characteristic, complemented
7C73×#1649C211yesmaximal, characteristic, complemented
8C73×#1648C211yesmaximal, characteristic, complemented
9C73×#1628C211yesmaximal, characteristic, complemented
10C73×#1627C211yesmaximal, characteristic, complemented
11C73×#1626C211yesmaximal, characteristic, complemented
12C73×#1626C211yesmaximal, characteristic, complemented
13C73×#1561C211yesmaximal, characteristic, complemented
14C73×#1495C211yesmaximal, characteristic, complemented
15C73×#1487C211yesmaximal, characteristic, complemented
16C2×#137×C73—21no—
17#557×C73—21no—
18#557×C73C2211yescharacteristic
19#557×C73C2211yescharacteristic
20#556×C73—21no—
21#556×C73C2211yescharacteristic
22#552×C73—22no—
23#552×C73—21no—
24D4×Q8×C73—21no—
25D4×Q8×C73C2211yescharacteristic
26#541×C73—22no—
27#541×C73—21no—
28#533×C73—21no—
29#533×C73C2211yescharacteristic
30#532×C73C2211yescharacteristic
31#529×C73—21no—
32#529×C73C2211yescharacteristic
33#519×C73—21no—
34C2×C4×Q8×C73C2211yescharacteristic
35#500×C73C2211yescharacteristic
36#498×C73C2211yescharacteristic
37#486×C73C2211yescharacteristic
38#486×C73C2211yescharacteristic
39#482×C73—22no—
40#478×C73—22no—
41#478×C73—21no—
42#475×C73C2211yescharacteristic
43#474×C73C2211yescharacteristic
44#469×C73—21no—
45#468×C73—21no—
46#464×C73—21no—
47#464×C73—21no—
48#463×C73—21no—
49#462×C73C2211yescharacteristic
50#462×C73C2211yescharacteristic
51#460×C73C2211yescharacteristic
52#460×C73C2211yescharacteristic
53#460×C73C2211yescharacteristic
54#459×C73C2211yescharacteristic
55#431×C73C2211yescharacteristic
56#423×C73C2211yescharacteristic
57#423×C73C2211yescharacteristic
58#417×C73—21no—
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
74#137×C73—44no—
75C2×Q16×C73—21no—
76C2×Q16×C73—21no—
77C2×SD16×C73—21no—
78C2×SD16×C73—21no—
79C2×SD16×C73—21no—
80C2×D8×C73—21no—
81C2×M16×C73—21no—
82C2×M16×C73—21no—
83C4⋊Q8×C73—22no—
84C4⋊Q8×C73—21no—
85C4⋊Q8×C73—21no—
86C4⋊Q8×C73—21no—
87C4⋊Q8×C73C2311yescharacteristic
88C4⋊Q8×C73C2311yescharacteristic
89C4⋊Q8×C73C2311yescharacteristic
90#127×C73C2311yescharacteristic
91#126×C73—22no—
92#126×C73—22no—
93#126×C73—22no—
94#126×C73—22no—
95#126×C73—21no—
96#125×C73—22no—
97#125×C73—22no—
98#125×C73—22no—
99#125×C73—21no—
100#125×C73—22no—
101#125×C73—22no—
102#125×C73—21no—
103#125×C73D411yescharacteristic
104#125×C73D412yes—
105#124×C73—21no—
106#124×C73—21no—
107#124×C73D411yescharacteristic
108#123×C73—22no—
109#123×C73—21no—
110C22⋊Q8×C73—22no—
111C22⋊Q8×C73—22no—
112C22⋊Q8×C73—21no—
113C22⋊Q8×C73—21no—
114C22⋊Q8×C73—21no—
115C22⋊Q8×C73—21no—
116C22⋊Q8×C73—22no—
117C22⋊Q8×C73D411yescharacteristic
118#121×C73—21no—
119#121×C73—21no—
120#121×C73D411yescharacteristic
121C4×Q8×C73—22no—
122C4×Q8×C73—22no—
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×C73—21no—
130C4×Q8×C73—21no—
131C4×Q8×C73—21no—
132C4×Q8×C73D411yescharacteristic
133C4×Q8×C73D411yescharacteristic
134C4×Q8×C73C2311yescharacteristic
135C4×Q8×C73C2311yescharacteristic
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×C73C2311yescharacteristic
143#117×C73—22no—
144#117×C73—22no—
145#117×C73—22no—
146#117×C73—21no—
147#117×C73—21no—
148#117×C73D412yes—
149C2×C4⋊C4×C73—21no—
150C2×C4⋊C4×C73D411yescharacteristic
151C2×C42×C73—21no—
152C2×C42×C73C2311yescharacteristic
153#107×C73—21no—
154#107×C73—22no—
155#106×C73—21no—
156#106×C73—22no—
157C4⋊C8×C73—21no—
158C4⋊C8×C73—21no—
159C4⋊C8×C73—21no—
160C4⋊C8×C73C2311yescharacteristic
161C4⋊C8×C73C2311yescharacteristic
162C4⋊C8×C73C2311yescharacteristic
163C4⋊C8×C73C2311yescharacteristic
164#103×C73—21no—
165#103×C73—21no—
166#103×C73—21no—
167#102×C73—21no—
168#102×C73—21no—
169#102×C73—21no—
170#102×C73—21no—
171#102×C73—21no—
172#102×C73—22no—
173#102×C73—22no—
174C22⋊C8×C73—21no—
175C4×C8×C73C2311yescharacteristic
176C4×C8×C73C2311yescharacteristic
177#41×C73—42no—
178#41×C73—42no—
179C2×Q8×C73—22no—
180C2×Q8×C73—21no—
181C2×Q8×C73—21no—
182C2×Q8×C73—21no—
183C2×Q8×C73—22no—
184C2×Q8×C73—21no—
185C2×Q8×C73—41no—
186C2×Q8×C73—42no—
187C2×Q8×C73—42no—
188C2×Q8×C73C2×D411yescharacteristic
189C2×Q8×C73C2×D411yescharacteristic
190C2×Q8×C73C2×D411yescharacteristic
191C2×D4×C73—21no—
192C2×D4×C73—21no—
193C2×D4×C73—21no—
194C2×D4×C73—21no—
195C2×D4×C73—41no—
196C2×D4×C73C2×D411yescharacteristic
197C22×C4×C73—22no—
198C22×C4×C73—21no—
199C22×C4×C73—21no—
200C22×C4×C73—21no—
201C22×C4×C73—41no—
202C22×C4×C73C2×D411yescharacteristic
203C22×C4×C73C2×D411yescharacteristic
204C22×C4×C73C2×D411yescharacteristic
205Q16×C73—42no—
206Q16×C73—42no—
207SD16×C73—42no—
208SD16×C73—42no—
209SD16×C73—81no—
210D8×C73—81no—
211M16×C73—42no—
212M16×C73—81no—
213C2×C8×C73—21no—
214C2×C8×C73—21no—
215C2×C8×C73—21no—
216C2×C8×C73—21no—
217C2×C8×C73—21no—
218C2×C8×C73—21no—
219C4⋊C4×C73—22no—
220C4⋊C4×C73—22no—
221C4⋊C4×C73—22no—
222C4⋊C4×C73—22no—
223C4⋊C4×C73—22no—
224C4⋊C4×C73—22no—
225C4⋊C4×C73—22no—
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—22no—
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×C73C2×D411yescharacteristic
243C4⋊C4×C73C2×D411yescharacteristic
244C4⋊C4×C73C2×D412yes—
245C4⋊C4×C73C2×D411yescharacteristic
246C4⋊C4×C73C2×D412yes—
247C4⋊C4×C73C2×D411yescharacteristic
248C22⋊C4×C73—22no—
249C22⋊C4×C73—22no—
250C22⋊C4×C73—22no—
251C22⋊C4×C73—21no—
252C22⋊C4×C73—22no—
253C22⋊C4×C73—21no—
254C22⋊C4×C73—21no—
255C22⋊C4×C73—21no—
256C22⋊C4×C73—21no—
257C22⋊C4×C73—41no—
258C22⋊C4×C73—41no—
259C42×C73—22no—
260C42×C73—22no—
261C42×C73—22no—
262C42×C73—21no—
263C42×C73—21no—
264C42×C73—22no—
265C42×C73—21no—
266C42×C73—21no—
267C42×C73—21no—
268C42×C73C2×D411yescharacteristic
269C42×C73C2×D411yescharacteristic
270C42×C73C2×D411yescharacteristic
271C42×C73C2411yescharacteristic
272C23×C73—21no—
273C23×C73—41no—
274C23×C73#12011yescharacteristic
275Q8×C73—21no—
276Q8×C73—21no—
277Q8×C73—21no—
278Q8×C73—21no—
279Q8×C73—21no—
280Q8×C73—42no—
281Q8×C73—44no—
282Q8×C73—41no—
283Q8×C73—41no—
284Q8×C73—41no—
285Q8×C73—41no—
286Q8×C73—41no—
287Q8×C73—41no—
288Q8×C73AGL(1,ℤ/8)12yes—
289D4×C73—21no—
290D4×C73—21no—
291D4×C73—42no—
292D4×C73—42no—
293D4×C73—41no—
294D4×C73—41no—
295D4×C73—41no—
296D4×C73—41no—
297D4×C73—82no—
298C2×C4×C73—21no—
299C2×C4×C73—21no—
300C2×C4×C73—21no—
301C2×C4×C73—21no—
302C2×C4×C73—21no—
303C2×C4×C73—21no—
304C2×C4×C73—21no—
305C2×C4×C73—22no—
306C2×C4×C73—21no—
307C2×C4×C73—21no—
308C2×C4×C73—21no—
309C2×C4×C73—21no—
310C2×C4×C73—22no—
311C2×C4×C73—41no—
312C2×C4×C73—42no—
313C2×C4×C73—44no—
314C2×C4×C73—42no—
315C2×C4×C73—41no—
316C2×C4×C73—41no—
317C2×C4×C73—41no—
318C2×C4×C73—82no—
319C2×C4×C73#12011yescharacteristic
320C2×C4×C73#12011yescharacteristic
321C2×C4×C73#12011yescharacteristic
322C2×C4×C73C22×D411yescharacteristic
323C2×C4×C73C22×D411yescharacteristic
324C2×C4×C73C22×D411yescharacteristic
325C8×C73—41no—
326C8×C73—41no—
327C8×C73—41no—
328C8×C73—41no—
329C8×C73—41no—
330C8×C73—41no—
331C22×C73—21no—
332C22×C73—21no—
333C22×C73—21no—
334C22×C73—41no—
335C22×C73—41no—
336C22×C73—41no—
337C22×C73—81no—
338C22×C73—81no—
339C22×C73—81no—
340C22×C73C2×#12011yescharacteristic
341C4×C73—21no—
342C4×C73—22no—
343C4×C73—21no—
344C4×C73—21no—
345C4×C73—21no—
346C4×C73—41no—
347C4×C73—42no—
348C4×C73—41no—
349C4×C73—41no—
350C4×C73—42no—
351C4×C73—41no—
352C4×C73—41no—
353C4×C73—41no—
354C4×C73—81no—
355C4×C73C2×AGL(1,ℤ/8)11yescharacteristic
356C4×C73#57511yescharacteristic
357C4×C73#57711yescharacteristic
358C4×C73#57811yescharacteristic
359#18824C7311yesmaximal, characteristic, direct product factor, Sylow
360C2×C73—41no—
361C2×C73—81no—
362C2×C73—161no—
363C2×C73#300611yescharacteristic
364C2×C73#301311yescharacteristic
365C2×C73#302011yescharacteristic
366#3523C2×C7311yescharacteristic, complemented
367#3251C2×C7311yescharacteristic
368#3228C2×C7311yescharacteristic, complemented
369#3037C2×C7311yescharacteristic, complemented
370#1653C2×C7311yescharacteristic, complemented
371#1652C2×C7311yescharacteristic, complemented
372#1649C2×C7311yescharacteristic, complemented
373#1648C2×C7311yescharacteristic, complemented
374#1628C2×C7311yescharacteristic, complemented
375#1627C2×C7311yescharacteristic, complemented
376#1626C2×C7311yescharacteristic, complemented
377#1626C2×C7311yescharacteristic, complemented
378#1561C2×C7311yescharacteristic, complemented
379#1495C2×C7311yescharacteristic, complemented
380#1487C2×C7311yescharacteristic, complemented
381C73#1882411yescharacteristic, direct product factor, Sylow
382C2×#137—21no—
383#557—21no—
384#557C22×C7311yescharacteristic
385#557C22×C7311yescharacteristic
386#556—21no—
387#556C22×C7311yescharacteristic
388#552—22no—
389#552—21no—
390D4×Q8—21no—
391D4×Q8C22×C7311yescharacteristic
392#541—22no—
393#541—21no—
394#533—21no—
395#533C22×C7311yescharacteristic
396#532C22×C7311yescharacteristic
397#529—21no—
398#529C22×C7311yescharacteristic
399#519—21no—
400C2×C4×Q8C22×C7311yescharacteristic
401#500C22×C7311yescharacteristic
402#498C22×C7311yescharacteristic
403#486C22×C7311yescharacteristic
404#486C22×C7311yescharacteristic
405#482—22no—
406#478—22no—
407#478—21no—
408#475C22×C7311yescharacteristic
409#474C22×C7311yescharacteristic
410#469—21no—
411#468—21no—
412#464—21no—
413#464—21no—
414#463—21no—
415#462C22×C7311yescharacteristic
416#462C22×C7311yescharacteristic
417#460C22×C7311yescharacteristic
418#460C22×C7311yescharacteristic
419#460C22×C7311yescharacteristic
420#459C22×C7311yescharacteristic
421#431C22×C7311yescharacteristic
422#423C22×C7311yescharacteristic
423#423C22×C7311yescharacteristic
424#417—21no—
425#332C22×C7311yescharacteristic
426#332C22×C7311yescharacteristic
427#332C22×C7311yescharacteristic
428#332C22×C7311yescharacteristic
429Q8⋊C8C22×C7311yescharacteristic
430Q8⋊C8C22×C7311yescharacteristic
431Q8⋊C8C22×C7311yescharacteristic
432Q8⋊C8C22×C7311yescharacteristic
433Q8⋊C8C22×C7311yescharacteristic
434Q8⋊C8C22×C7311yescharacteristic
435D4⋊C8C22×C7311yescharacteristic
436D4⋊C8C22×C7311yescharacteristic
437C2×#41—21no—
438C22×Q8—21no—
439C22×Q8D4×C7311yescharacteristic
440#137—44no—
441C2×Q16—21no—
442C2×Q16—21no—
443C2×SD16—21no—
444C2×SD16—21no—
445C2×SD16—21no—
446C2×D8—21no—
447C2×M16—21no—
448C2×M16—21no—
449C4⋊Q8—22no—
450C4⋊Q8—21no—
451C4⋊Q8—21no—
452C4⋊Q8—21no—
453C4⋊Q8C23×C7311yescharacteristic
454C4⋊Q8C23×C7311yescharacteristic
455C4⋊Q8C23×C7311yescharacteristic
456#127C23×C7311yescharacteristic
457#126—22no—
458#126—22no—
459#126—22no—
460#126—22no—
461#126—21no—
462#125—22no—
463#125—22no—
464#125—22no—
465#125—21no—
466#125—22no—
467#125—22no—
468#125—21no—
469#125D4×C7311yescharacteristic
470#125D4×C7312yes—
471#124—21no—
472#124—21no—
473#124D4×C7311yescharacteristic
474#123—22no—
475#123—21no—
476C22⋊Q8—22no—
477C22⋊Q8—22no—
478C22⋊Q8—21no—
479C22⋊Q8—21no—
480C22⋊Q8—21no—
481C22⋊Q8—21no—
482C22⋊Q8—22no—
483C22⋊Q8D4×C7311yescharacteristic
484#121—21no—
485#121—21no—
486#121D4×C7311yescharacteristic
487C4×Q8—22no—
488C4×Q8—22no—
489C4×Q8—21no—
490C4×Q8—21no—
491C4×Q8—21no—
492C4×Q8—21no—
493C4×Q8—21no—
494C4×Q8—21no—
495C4×Q8—21no—
496C4×Q8—21no—
497C4×Q8—21no—
498C4×Q8D4×C7311yescharacteristic
499C4×Q8D4×C7311yescharacteristic
500C4×Q8C23×C7311yescharacteristic
501C4×Q8C23×C7311yescharacteristic
502C4×Q8C23×C7311yescharacteristic
503C4×D4—22no—
504C4×D4—21no—
505C4×D4—21no—
506C4×D4—21no—
507C4×D4—21no—
508C4×D4C23×C7311yescharacteristic
509#117—22no—
510#117—22no—
511#117—22no—
512#117—21no—
513#117—21no—
514#117D4×C7312yes—
515C2×C4⋊C4—21no—
516C2×C4⋊C4D4×C7311yescharacteristic
517C2×C42—21no—
518C2×C42C23×C7311yescharacteristic
519#107—21no—
520#107—22no—
521#106—21no—
522#106—22no—
523C4⋊C8—21no—
524C4⋊C8—21no—
525C4⋊C8—21no—
526C4⋊C8C23×C7311yescharacteristic
527C4⋊C8C23×C7311yescharacteristic
528C4⋊C8C23×C7311yescharacteristic
529C4⋊C8C23×C7311yescharacteristic
530#103—21no—
531#103—21no—
532#103—21no—
533#102—21no—
534#102—21no—
535#102—21no—
536#102—21no—
537#102—21no—
538#102—22no—
539#102—22no—
540C22⋊C8—21no—
541C4×C8C23×C7311yescharacteristic
542C4×C8C23×C7311yescharacteristic
543#41—42no—
544#41—42no—
545C2×Q8—22no—
546C2×Q8—21no—
547C2×Q8—21no—
548C2×Q8—21no—
549C2×Q8—22no—
550C2×Q8—21no—
551C2×Q8—41no—
552C2×Q8—42no—
553C2×Q8—42no—
554C2×Q8C2×D4×C7311yescharacteristic
555C2×Q8C2×D4×C7311yescharacteristic
556C2×Q8C2×D4×C7311yescharacteristic
557C2×D4—21no—
558C2×D4—21no—
559C2×D4—21no—
560C2×D4—21no—
561C2×D4—41no—
562C2×D4C2×D4×C7311yescharacteristic
563C22×C4—22no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—41no—
568C22×C4C2×D4×C7311yescharacteristic
569C22×C4C2×D4×C7311yescharacteristic
570C22×C4C2×D4×C7311yescharacteristic
571Q16—42no—
572Q16—42no—
573SD16—42no—
574SD16—42no—
575SD16—81no—
576D8—81no—
577M16—42no—
578M16—81no—
579C2×C8—21no—
580C2×C8—21no—
581C2×C8—21no—
582C2×C8—21no—
583C2×C8—21no—
584C2×C8—21no—
585C4⋊C4—22no—
586C4⋊C4—22no—
587C4⋊C4—22no—
588C4⋊C4—22no—
589C4⋊C4—22no—
590C4⋊C4—22no—
591C4⋊C4—22no—
592C4⋊C4—22no—
593C4⋊C4—21no—
594C4⋊C4—21no—
595C4⋊C4—21no—
596C4⋊C4—22no—
597C4⋊C4—21no—
598C4⋊C4—21no—
599C4⋊C4—21no—
600C4⋊C4—22no—
601C4⋊C4—21no—
602C4⋊C4—21no—
603C4⋊C4—21no—
604C4⋊C4—21no—
605C4⋊C4—21no—
606C4⋊C4—21no—
607C4⋊C4—21no—
608C4⋊C4C2×D4×C7311yescharacteristic
609C4⋊C4C2×D4×C7311yescharacteristic
610C4⋊C4C2×D4×C7312yes—
611C4⋊C4C2×D4×C7311yescharacteristic
612C4⋊C4C2×D4×C7312yes—
613C4⋊C4C2×D4×C7311yescharacteristic
614C22⋊C4—22no—
615C22⋊C4—22no—
616C22⋊C4—22no—
617C22⋊C4—21no—
618C22⋊C4—22no—
619C22⋊C4—21no—
620C22⋊C4—21no—
621C22⋊C4—21no—
622C22⋊C4—21no—
623C22⋊C4—41no—
624C22⋊C4—41no—
625C42—22no—
626C42—22no—
627C42—22no—
628C42—21no—
629C42—21no—
630C42—22no—
631C42—21no—
632C42—21no—
633C42—21no—
634C42C2×D4×C7311yescharacteristic
635C42C2×D4×C7311yescharacteristic
636C42C2×D4×C7311yescharacteristic
637C42C24×C7311yescharacteristic
638C23—21no—
639C23—41no—
640C23#120×C7311yescharacteristic
641Q8—21no—
642Q8—21no—
643Q8—21no—
644Q8—21no—
645Q8—21no—
646Q8—42no—
647Q8—44no—
648Q8—41no—
649Q8—41no—
650Q8—41no—
651Q8—41no—
652Q8—41no—
653Q8—41no—
654Q8AGL(1,ℤ/8)×C7312yes—
655D4—21no—
656D4—21no—
657D4—42no—
658D4—42no—
659D4—41no—
660D4—41no—
661D4—41no—
662D4—41no—
663D4—82no—
664C2×C4—21no—
665C2×C4—21no—
666C2×C4—21no—
667C2×C4—21no—
668C2×C4—21no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—22no—
672C2×C4—21no—
673C2×C4—21no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—22no—
677C2×C4—41no—
678C2×C4—42no—
679C2×C4—44no—
680C2×C4—42no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—82no—
685C2×C4#120×C7311yescharacteristic
686C2×C4#120×C7311yescharacteristic
687C2×C4#120×C7311yescharacteristic
688C2×C4C22×D4×C7311yescharacteristic
689C2×C4C22×D4×C7311yescharacteristic
690C2×C4C22×D4×C7311yescharacteristic
691C8—41no—
692C8—41no—
693C8—41no—
694C8—41no—
695C8—41no—
696C8—41no—
697C22—21no—
698C22—21no—
699C22—21no—
700C22—41no—
701C22—41no—
702C22—41no—
703C22—81no—
704C22—81no—
705C22—81no—
706C22C2×#120×C7311yescharacteristic
707C4—21no—
708C4—22no—
709C4—21no—
710C4—21no—
711C4—21no—
712C4—41no—
713C4—42no—
714C4—41no—
715C4—41no—
716C4—42no—
717C4—41no—
718C4—41no—
719C4—41no—
720C4—81no—
721C4C2×AGL(1,ℤ/8)×C7311yescharacteristic
722C4#575×C7311yescharacteristic
723C4#577×C7311yescharacteristic
724C4#578×C7311yescharacteristic
725C2—41no—
726C2—81no—
727C2—161no—
728C2C73×#300611yescharacteristic
729C2C73×#301311yescharacteristic
730C2C73×#302011yescharacteristic
subgroupG/H
center, socleC22×C73C2×#120
commutator, Frattini, cosocleC42C24×C73
prime radicalC73×#3251C2
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×#3228C2semidirect
4. C73×#3037C2semidirect
5. C73×#1653C2semidirect
6. C73×#1652C2semidirect
7. C73×#1649C2semidirect
8. C73×#1648C2semidirect
9. C73×#1628C2semidirect
10. C73×#1627C2semidirect
11. C73×#1626C2semidirect
12. C73×#1626C2semidirect
13. C73×#1561C2semidirect
14. C73×#1495C2semidirect
15. C73×#1487C2semidirect
359. #18824C73direct (N × H)
366. #3523C2×C73semidirect
368. #3228C2×C73semidirect
369. #3037C2×C73semidirect
370. #1653C2×C73semidirect
371. #1652C2×C73semidirect
372. #1649C2×C73semidirect
373. #1648C2×C73semidirect
374. #1628C2×C73semidirect
375. #1627C2×C73semidirect
376. #1626C2×C73semidirect
377. #1626C2×C73semidirect
378. #1561C2×C73semidirect
379. #1495C2×C73semidirect
380. #1487C2×C73semidirect
381. C73#18824direct (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×#32512
C73×#32282
C73×#30372
C73×#16532
C73×#16522
C73×#16492
C73×#16482
C73×#16282
C73×#16272
C73×#16262
C73×#15612
C73×#14952
C73×#14872
#1882473