Finite Group Databasebeta

← C73×#18822 #32928226

Subgroups — C73×#18822 #32928226

Order 18688.

966 conjugacy classes of subgroups.

The subgroup lattice has 782 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C73×#3520C211yesmaximal, characteristic, complemented
2C73×#3251C211yesmaximal, characteristic, complemented
3C73×#3228C211yesmaximal, characteristic, complemented
4C73×#3036C211yesmaximal, characteristic, complemented
5C73×#1654C211yesmaximal, characteristic, complemented
6C73×#1651C211yesmaximal, characteristic, complemented
7C73×#1650C211yesmaximal, characteristic, complemented
8C73×#1647C211yesmaximal, characteristic, complemented
9C73×#1628C211yesmaximal, characteristic, complemented
10C73×#1627C211yesmaximal, characteristic, complemented
11C73×#1625C211yesmaximal, characteristic, complemented
12C73×#1625C211yesmaximal, characteristic, complemented
13C73×#1561C211yesmaximal, characteristic, complemented
14C73×#1495C211yesmaximal, characteristic, complemented
15C73×#1486C211yesmaximal, characteristic, complemented
16C2×AGL(1,ℤ/8)×C73—21no—
17#556×C73C2211yescharacteristic
18#554×C73—21no—
19#552×C73—21no—
20#551×C73—22no—
21D4×Q8×C73C2211yescharacteristic
22#548×C73—21no—
23#547×C73C2211yescharacteristic
24#547×C73C2211yescharacteristic
25#546×C73—21no—
26#542×C73—21no—
27#539×C73—22no—
28#533×C73C2211yescharacteristic
29#532×C73C2211yescharacteristic
30#529×C73C2211yescharacteristic
31#525×C73—21no—
32C2×C22⋊Q8×C73—21no—
33#520×C73—21no—
34C2×C4×D4×C73C2211yescharacteristic
35#500×C73C2211yescharacteristic, complemented
36#498×C73C2211yescharacteristic, complemented
37#486×C73C2211yescharacteristic, complemented
38#486×C73C2211yescharacteristic, complemented
39#482×C73—22no—
40#478×C73—22no—
41#478×C73—21no—
42#475×C73C2211yescharacteristic, complemented
43#474×C73C2211yescharacteristic, complemented
44#469×C73—21no—
45#468×C73—21no—
46#463×C73—21no—
47#463×C73—21no—
48#463×C73—21no—
49#461×C73C2211yescharacteristic
50#461×C73C2211yescharacteristic
51#460×C73C2211yescharacteristic, complemented
52#459×C73C2211yescharacteristic
53#459×C73C2211yescharacteristic
54#459×C73C2211yescharacteristic, complemented
55#431×C73C2211yescharacteristic
56#423×C73C2211yescharacteristic
57#423×C73C2211yescharacteristic
58#417×C73—21no—
59#332×C73C2211yescharacteristic, complemented
60#332×C73C2211yescharacteristic, complemented
61#332×C73C2211yescharacteristic, complemented
62#332×C73C2211yescharacteristic, complemented
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—
74C22×Q8×C73—21no—
75C22×D4×C73D411yescharacteristic
76C23×C4×C73—21no—
77AGL(1,ℤ/8)×C73—44no—
78C2×SD16×C73—21no—
79C2×SD16×C73—21no—
80C2×SD16×C73—21no—
81C2×D8×C73—21no—
82C2×D8×C73—21no—
83C2×D8×C73—21no—
84C2×M16×C73—21no—
85C2×M16×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—21no—
94#125×C73—22no—
95#125×C73D411yescharacteristic
96#125×C73D412yes—
97#124×C73—22no—
98#124×C73—21no—
99#124×C73—21no—
100#124×C73D411yescharacteristic
101#123×C73—22no—
102#123×C73—22no—
103#123×C73—21no—
104#123×C73—22no—
105#123×C73—22no—
106C22⋊Q8×C73—22no—
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—21no—
114C22⋊Q8×C73—22no—
115C22⋊Q8×C73—21no—
116C22⋊Q8×C73D411yescharacteristic
117#121×C73—22no—
118#121×C73—21no—
119#121×C73—21no—
120#121×C73—21no—
121#121×C73—21no—
122#121×C73D411yescharacteristic
123#120×C73—22no—
124C4×Q8×C73—21no—
125C4×Q8×C73—21no—
126C4×Q8×C73—21no—
127C4×Q8×C73C2311yescharacteristic
128C4×D4×C73—22no—
129C4×D4×C73—22no—
130C4×D4×C73—22no—
131C4×D4×C73—21no—
132C4×D4×C73—21no—
133C4×D4×C73—21no—
134C4×D4×C73—21no—
135C4×D4×C73—21no—
136C4×D4×C73—21no—
137C4×D4×C73D411yescharacteristic
138C4×D4×C73D411yescharacteristic
139C4×D4×C73C2311yescharacteristic
140C4×D4×C73C2311yescharacteristic
141C4×D4×C73C2311yescharacteristic
142#117×C73—22no—
143#117×C73—21no—
144#117×C73—21no—
145#117×C73D412yes—
146C2×C4⋊C4×C73—22no—
147C2×C4⋊C4×C73—21no—
148C2×C4⋊C4×C73—21no—
149C2×C4⋊C4×C73D411yescharacteristic
150C2×C22⋊C4×C73—22no—
151C2×C22⋊C4×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
177C24×C73—21no—
178#41×C73—42no—
179#41×C73—42no—
180#41×C73—42no—
181#41×C73—42no—
182#41×C73—81no—
183#41×C73—81no—
184C2×Q8×C73—22no—
185C2×Q8×C73—21no—
186C2×Q8×C73—21no—
187C2×Q8×C73—21no—
188C2×Q8×C73—81no—
189C2×Q8×C73—81no—
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—41no—
200C2×D4×C73—41no—
201C2×D4×C73C2×D411yescharacteristic
202C2×D4×C73C2×D411yescharacteristic
203C2×D4×C73C2×D411yescharacteristic
204C22×C4×C73—22no—
205C22×C4×C73—22no—
206C22×C4×C73—22no—
207C22×C4×C73—21no—
208C22×C4×C73—21no—
209C22×C4×C73—21no—
210C22×C4×C73—21no—
211C22×C4×C73—21no—
212C22×C4×C73—21no—
213C22×C4×C73—41no—
214C22×C4×C73—81no—
215C22×C4×C73—81no—
216C22×C4×C73C2×D411yescharacteristic
217C22×C4×C73C2×D411yescharacteristic
218C22×C4×C73C2×D411yescharacteristic
219SD16×C73—42no—
220SD16×C73—42no—
221SD16×C73—81no—
222D8×C73—42no—
223D8×C73—42no—
224D8×C73—81no—
225M16×C73—42no—
226M16×C73—81no—
227C2×C8×C73—21no—
228C2×C8×C73—21no—
229C2×C8×C73—21no—
230C2×C8×C73—21no—
231C2×C8×C73—21no—
232C2×C8×C73—21no—
233C4⋊C4×C73—22no—
234C4⋊C4×C73—22no—
235C4⋊C4×C73—22no—
236C4⋊C4×C73—22no—
237C4⋊C4×C73—21no—
238C4⋊C4×C73—22no—
239C4⋊C4×C73—21no—
240C4⋊C4×C73—21no—
241C4⋊C4×C73—21no—
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×C73C2×D411yescharacteristic
249C4⋊C4×C73C2×D411yescharacteristic
250C4⋊C4×C73C2×D411yescharacteristic
251C4⋊C4×C73C2×D412yes—
252C4⋊C4×C73C2×D411yescharacteristic
253C4⋊C4×C73C2×D412yes—
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—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—21no—
268C22⋊C4×C73—21no—
269C22⋊C4×C73—41no—
270C22⋊C4×C73—41no—
271C42×C73—22no—
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—21no—
281C23×C73—42no—
282C23×C73—42no—
283C23×C73—41no—
284C23×C73—81no—
285C23×C73#12011yescharacteristic
286Q8×C73—21no—
287Q8×C73—21no—
288Q8×C73—41no—
289Q8×C73—41no—
290Q8×C73—41no—
291Q8×C73—41no—
292Q8×C73—41no—
293Q8×C73—41no—
294Q8×C73—82no—
295D4×C73—21no—
296D4×C73—21no—
297D4×C73—21no—
298D4×C73—21no—
299D4×C73—21no—
300D4×C73—42no—
301D4×C73—42no—
302D4×C73—42no—
303D4×C73—44no—
304D4×C73—41no—
305D4×C73—41no—
306D4×C73—41no—
307D4×C73—41no—
308D4×C73—82no—
309D4×C73—82no—
310D4×C73AGL(1,ℤ/8)12yes—
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—22no—
320C2×C4×C73—21no—
321C2×C4×C73—21no—
322C2×C4×C73—41no—
323C2×C4×C73—44no—
324C2×C4×C73—41no—
325C2×C4×C73—41no—
326C2×C4×C73—41no—
327C2×C4×C73—41no—
328C2×C4×C73—41no—
329C2×C4×C73—41no—
330C2×C4×C73—41no—
331C2×C4×C73—81no—
332C2×C4×C73—81no—
333C2×C4×C73—82no—
334C2×C4×C73—81no—
335C2×C4×C73—82no—
336C2×C4×C73—82no—
337C2×C4×C73#12011yescharacteristic
338C2×C4×C73#12011yescharacteristic
339C2×C4×C73#12011yescharacteristic
340C2×C4×C73C22×D411yescharacteristic
341C2×C4×C73C22×D411yescharacteristic
342C2×C4×C73C22×D411yescharacteristic
343C8×C73—41no—
344C8×C73—41no—
345C8×C73—41no—
346C8×C73—41no—
347C8×C73—41no—
348C8×C73—41no—
349C22×C73—21no—
350C22×C73—22no—
351C22×C73—21no—
352C22×C73—21no—
353C22×C73—41no—
354C22×C73—41no—
355C22×C73—41no—
356C22×C73—41no—
357C22×C73—41no—
358C22×C73—41no—
359C22×C73—41no—
360C22×C73—41no—
361C22×C73—84no—
362C22×C73—81no—
363C22×C73—81no—
364C22×C73—81no—
365C22×C73C2×#12011yescharacteristic
366C4×C73—21no—
367C4×C73—21no—
368C4×C73—21no—
369C4×C73—21no—
370C4×C73—41no—
371C4×C73—42no—
372C4×C73—41no—
373C4×C73—41no—
374C4×C73—42no—
375C4×C73—41no—
376C4×C73—41no—
377C4×C73—81no—
378C4×C73C2×AGL(1,ℤ/8)11yescharacteristic
379C4×C73#57511yescharacteristic
380C4×C73#57611yescharacteristic
381C4×C73#57711yescharacteristic
382#18822C7311yesmaximal, characteristic, direct product factor, Sylow
383C2×C73—41no—
384C2×C73—42no—
385C2×C73—81no—
386C2×C73—81no—
387C2×C73—161no—
388C2×C73#300611yescharacteristic
389C2×C73#301211yescharacteristic
390C2×C73#302011yescharacteristic
391#3520C2×C7311yescharacteristic, complemented
392#3251C2×C7311yescharacteristic, complemented
393#3228C2×C7311yescharacteristic, complemented
394#3036C2×C7311yescharacteristic, complemented
395#1654C2×C7311yescharacteristic, complemented
396#1651C2×C7311yescharacteristic, complemented
397#1650C2×C7311yescharacteristic, complemented
398#1647C2×C7311yescharacteristic, complemented
399#1628C2×C7311yescharacteristic, complemented
400#1627C2×C7311yescharacteristic, complemented
401#1625C2×C7311yescharacteristic, complemented
402#1625C2×C7311yescharacteristic, complemented
403#1561C2×C7311yescharacteristic, complemented
404#1495C2×C7311yescharacteristic, complemented
405#1486C2×C7311yescharacteristic, complemented
406C73#1882211yescharacteristic, direct product factor, Sylow
407C2×AGL(1,ℤ/8)—21no—
408#556C22×C7311yescharacteristic
409#554—21no—
410#552—21no—
411#551—22no—
412D4×Q8C22×C7311yescharacteristic
413#548—21no—
414#547C22×C7311yescharacteristic
415#547C22×C7311yescharacteristic
416#546—21no—
417#542—21no—
418#539—22no—
419#533C22×C7311yescharacteristic
420#532C22×C7311yescharacteristic
421#529C22×C7311yescharacteristic
422#525—21no—
423C2×C22⋊Q8—21no—
424#520—21no—
425C2×C4×D4C22×C7311yescharacteristic
426#500C22×C7311yescharacteristic, complemented
427#498C22×C7311yescharacteristic, complemented
428#486C22×C7311yescharacteristic, complemented
429#486C22×C7311yescharacteristic, complemented
430#482—22no—
431#478—22no—
432#478—21no—
433#475C22×C7311yescharacteristic, complemented
434#474C22×C7311yescharacteristic, complemented
435#469—21no—
436#468—21no—
437#463—21no—
438#463—21no—
439#463—21no—
440#461C22×C7311yescharacteristic
441#461C22×C7311yescharacteristic
442#460C22×C7311yescharacteristic, complemented
443#459C22×C7311yescharacteristic
444#459C22×C7311yescharacteristic
445#459C22×C7311yescharacteristic, complemented
446#431C22×C7311yescharacteristic
447#423C22×C7311yescharacteristic
448#423C22×C7311yescharacteristic
449#417—21no—
450#332C22×C7311yescharacteristic, complemented
451#332C22×C7311yescharacteristic, complemented
452#332C22×C7311yescharacteristic, complemented
453#332C22×C7311yescharacteristic, complemented
454Q8⋊C8C22×C7311yescharacteristic, complemented
455Q8⋊C8C22×C7311yescharacteristic, complemented
456D4⋊C8C22×C7311yescharacteristic
457D4⋊C8C22×C7311yescharacteristic
458D4⋊C8C22×C7311yescharacteristic
459D4⋊C8C22×C7311yescharacteristic
460D4⋊C8C22×C7311yescharacteristic, complemented
461D4⋊C8C22×C7311yescharacteristic, complemented
462C2×#41—21no—
463C2×#41—21no—
464C2×#41—21no—
465C22×Q8—21no—
466C22×D4D4×C7311yescharacteristic
467C23×C4—21no—
468AGL(1,ℤ/8)—44no—
469C2×SD16—21no—
470C2×SD16—21no—
471C2×SD16—21no—
472C2×D8—21no—
473C2×D8—21no—
474C2×D8—21no—
475C2×M16—21no—
476C2×M16—21no—
477C4⋊Q8—21no—
478C4⋊Q8C23×C7311yescharacteristic
479C4⋊Q8C23×C7311yescharacteristic
480C4⋊Q8C23×C7311yescharacteristic
481#127C23×C7311yescharacteristic
482#126—22no—
483#126—22no—
484#126—21no—
485#125—22no—
486#125D4×C7311yescharacteristic
487#125D4×C7312yes—
488#124—22no—
489#124—21no—
490#124—21no—
491#124D4×C7311yescharacteristic
492#123—22no—
493#123—22no—
494#123—21no—
495#123—22no—
496#123—22no—
497C22⋊Q8—22no—
498C22⋊Q8—22no—
499C22⋊Q8—22no—
500C22⋊Q8—21no—
501C22⋊Q8—21no—
502C22⋊Q8—21no—
503C22⋊Q8—21no—
504C22⋊Q8—21no—
505C22⋊Q8—22no—
506C22⋊Q8—21no—
507C22⋊Q8D4×C7311yescharacteristic
508#121—22no—
509#121—21no—
510#121—21no—
511#121—21no—
512#121—21no—
513#121D4×C7311yescharacteristic
514#120—22no—
515C4×Q8—21no—
516C4×Q8—21no—
517C4×Q8—21no—
518C4×Q8C23×C7311yescharacteristic
519C4×D4—22no—
520C4×D4—22no—
521C4×D4—22no—
522C4×D4—21no—
523C4×D4—21no—
524C4×D4—21no—
525C4×D4—21no—
526C4×D4—21no—
527C4×D4—21no—
528C4×D4D4×C7311yescharacteristic
529C4×D4D4×C7311yescharacteristic
530C4×D4C23×C7311yescharacteristic
531C4×D4C23×C7311yescharacteristic
532C4×D4C23×C7311yescharacteristic
533#117—22no—
534#117—21no—
535#117—21no—
536#117D4×C7312yes—
537C2×C4⋊C4—22no—
538C2×C4⋊C4—21no—
539C2×C4⋊C4—21no—
540C2×C4⋊C4D4×C7311yescharacteristic
541C2×C22⋊C4—22no—
542C2×C22⋊C4—21no—
543C2×C42C23×C7311yescharacteristic
544#107—21no—
545#107—22no—
546#106—21no—
547#106—22no—
548C4⋊C8—21no—
549C4⋊C8—21no—
550C4⋊C8—21no—
551C4⋊C8C23×C7311yescharacteristic
552C4⋊C8C23×C7311yescharacteristic
553C4⋊C8C23×C7311yescharacteristic
554C4⋊C8C23×C7311yescharacteristic
555#103—21no—
556#103—21no—
557#103—21no—
558#102—21no—
559#102—21no—
560#102—21no—
561#102—21no—
562#102—21no—
563#102—22no—
564#102—22no—
565C22⋊C8—21no—
566C4×C8C23×C7311yescharacteristic
567C4×C8C23×C7311yescharacteristic
568C24—21no—
569#41—42no—
570#41—42no—
571#41—42no—
572#41—42no—
573#41—81no—
574#41—81no—
575C2×Q8—22no—
576C2×Q8—21no—
577C2×Q8—21no—
578C2×Q8—21no—
579C2×Q8—81no—
580C2×Q8—81no—
581C2×Q8C2×D4×C7311yescharacteristic
582C2×D4—22no—
583C2×D4—22no—
584C2×D4—21no—
585C2×D4—22no—
586C2×D4—21no—
587C2×D4—21no—
588C2×D4—21no—
589C2×D4—21no—
590C2×D4—41no—
591C2×D4—41no—
592C2×D4C2×D4×C7311yescharacteristic
593C2×D4C2×D4×C7311yescharacteristic
594C2×D4C2×D4×C7311yescharacteristic
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—22no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—41no—
605C22×C4—81no—
606C22×C4—81no—
607C22×C4C2×D4×C7311yescharacteristic
608C22×C4C2×D4×C7311yescharacteristic
609C22×C4C2×D4×C7311yescharacteristic
610SD16—42no—
611SD16—42no—
612SD16—81no—
613D8—42no—
614D8—42no—
615D8—81no—
616M16—42no—
617M16—81no—
618C2×C8—21no—
619C2×C8—21no—
620C2×C8—21no—
621C2×C8—21no—
622C2×C8—21no—
623C2×C8—21no—
624C4⋊C4—22no—
625C4⋊C4—22no—
626C4⋊C4—22no—
627C4⋊C4—22no—
628C4⋊C4—21no—
629C4⋊C4—22no—
630C4⋊C4—21no—
631C4⋊C4—21no—
632C4⋊C4—21no—
633C4⋊C4—22no—
634C4⋊C4—21no—
635C4⋊C4—21no—
636C4⋊C4—21no—
637C4⋊C4—21no—
638C4⋊C4—21no—
639C4⋊C4C2×D4×C7311yescharacteristic
640C4⋊C4C2×D4×C7311yescharacteristic
641C4⋊C4C2×D4×C7311yescharacteristic
642C4⋊C4C2×D4×C7312yes—
643C4⋊C4C2×D4×C7311yescharacteristic
644C4⋊C4C2×D4×C7312yes—
645C22⋊C4—22no—
646C22⋊C4—22no—
647C22⋊C4—22no—
648C22⋊C4—22no—
649C22⋊C4—22no—
650C22⋊C4—21no—
651C22⋊C4—22no—
652C22⋊C4—21no—
653C22⋊C4—21no—
654C22⋊C4—21no—
655C22⋊C4—21no—
656C22⋊C4—21no—
657C22⋊C4—21no—
658C22⋊C4—21no—
659C22⋊C4—21no—
660C22⋊C4—41no—
661C22⋊C4—41no—
662C42—22no—
663C42—22no—
664C42—21no—
665C42C2×D4×C7311yescharacteristic
666C42C2×D4×C7311yescharacteristic
667C42C2×D4×C7311yescharacteristic
668C42C24×C7311yescharacteristic
669C23—21no—
670C23—21no—
671C23—21no—
672C23—42no—
673C23—42no—
674C23—41no—
675C23—81no—
676C23#120×C7311yescharacteristic
677Q8—21no—
678Q8—21no—
679Q8—41no—
680Q8—41no—
681Q8—41no—
682Q8—41no—
683Q8—41no—
684Q8—41no—
685Q8—82no—
686D4—21no—
687D4—21no—
688D4—21no—
689D4—21no—
690D4—21no—
691D4—42no—
692D4—42no—
693D4—44no—
694D4—42no—
695D4—41no—
696D4—41no—
697D4—41no—
698D4—41no—
699D4—82no—
700D4—82no—
701D4AGL(1,ℤ/8)×C7312yes—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—22no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—22no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—41no—
714C2×C4—44no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—81no—
723C2×C4—81no—
724C2×C4—82no—
725C2×C4—81no—
726C2×C4—82no—
727C2×C4—82no—
728C2×C4#120×C7311yescharacteristic
729C2×C4#120×C7311yescharacteristic
730C2×C4#120×C7311yescharacteristic
731C2×C4C22×D4×C7311yescharacteristic
732C2×C4C22×D4×C7311yescharacteristic
733C2×C4C22×D4×C7311yescharacteristic
734C8—41no—
735C8—41no—
736C8—41no—
737C8—41no—
738C8—41no—
739C8—41no—
740C22—21no—
741C22—22no—
742C22—21no—
743C22—21no—
744C22—41no—
745C22—41no—
746C22—41no—
747C22—41no—
748C22—41no—
749C22—41no—
750C22—41no—
751C22—41no—
752C22—84no—
753C22—81no—
754C22—81no—
755C22—81no—
756C22C2×#120×C7311yescharacteristic
757C4—21no—
758C4—21no—
759C4—21no—
760C4—21no—
761C4—41no—
762C4—42no—
763C4—41no—
764C4—41no—
765C4—42no—
766C4—41no—
767C4—41no—
768C4—81no—
769C4C2×AGL(1,ℤ/8)×C7311yescharacteristic
770C4#575×C7311yescharacteristic
771C4#576×C7311yescharacteristic
772C4#577×C7311yescharacteristic
773C2—41no—
774C2—42no—
775C2—81no—
776C2—81no—
777C2—161no—
778C2C73×#300611yescharacteristic
779C2C73×#301211yescharacteristic
780C2C73×#302011yescharacteristic
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×#3520C2semidirect
2. C73×#3251C2semidirect
3. C73×#3228C2semidirect
4. C73×#3036C2semidirect
5. C73×#1654C2semidirect
6. C73×#1651C2semidirect
7. C73×#1650C2semidirect
8. C73×#1647C2semidirect
9. C73×#1628C2semidirect
10. C73×#1627C2semidirect
11. C73×#1625C2semidirect
12. C73×#1625C2semidirect
13. C73×#1561C2semidirect
14. C73×#1495C2semidirect
15. C73×#1486C2semidirect
35. #500×C73C22semidirect
36. #498×C73C22semidirect
37. #486×C73C22semidirect
38. #486×C73C22semidirect
42. #475×C73C22semidirect
43. #474×C73C22semidirect
51. #460×C73C22semidirect
54. #459×C73C22semidirect
59. #332×C73C22semidirect
60. #332×C73C22semidirect
61. #332×C73C22semidirect
62. #332×C73C22semidirect
63. Q8⋊C8×C73C22semidirect
64. Q8⋊C8×C73C22semidirect
69. D4⋊C8×C73C22semidirect
70. D4⋊C8×C73C22semidirect
382. #18822C73direct (N × H)
391. #3520C2×C73semidirect
392. #3251C2×C73semidirect
393. #3228C2×C73semidirect
394. #3036C2×C73semidirect
395. #1654C2×C73semidirect
396. #1651C2×C73semidirect
397. #1650C2×C73semidirect
398. #1647C2×C73semidirect
399. #1628C2×C73semidirect
400. #1627C2×C73semidirect
401. #1625C2×C73semidirect
402. #1625C2×C73semidirect
403. #1561C2×C73semidirect
404. #1495C2×C73semidirect
405. #1486C2×C73semidirect
406. C73#18822direct (N × H)
426. #500C22×C73semidirect
427. #498C22×C73semidirect
428. #486C22×C73semidirect
429. #486C22×C73semidirect
433. #475C22×C73semidirect
434. #474C22×C73semidirect
442. #460C22×C73semidirect
445. #459C22×C73semidirect
450. #332C22×C73semidirect
451. #332C22×C73semidirect
452. #332C22×C73semidirect
453. #332C22×C73semidirect
454. Q8⋊C8C22×C73semidirect
455. Q8⋊C8C22×C73semidirect
460. D4⋊C8C22×C73semidirect
461. D4⋊C8C22×C73semidirect

Maximal subgroups

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

subgroupindex
C73×#35202
C73×#32512
C73×#32282
C73×#30362
C73×#16542
C73×#16512
C73×#16502
C73×#16472
C73×#16282
C73×#16272
C73×#16252
C73×#15612
C73×#14952
C73×#14862
#1882273