Finite Group Databasebeta

← C73×#18810 #32928214

Subgroups — C73×#18810 #32928214

Order 18688.

1042 conjugacy classes of subgroups.

The subgroup lattice has 814 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C73×#3519C211yesmaximal, characteristic, complemented
2C73×#3251C211yesmaximal, characteristic, complemented
3C73×#3207C211yesmaximal, characteristic, complemented
4C73×#3036C211yesmaximal, characteristic, complemented
5C73×#1646C211yesmaximal, characteristic, complemented
6C73×#1643C211yesmaximal, characteristic, complemented
7C73×#1642C211yesmaximal, characteristic, complemented
8C73×#1639C211yesmaximal, characteristic, complemented
9C73×#1624C211yesmaximal, characteristic, complemented
10C73×#1622C211yesmaximal, characteristic, complemented
11C73×#1621C211yesmaximal, characteristic, complemented
12C73×#1619C211yesmaximal, characteristic, complemented
13C73×#1560C211yesmaximal, characteristic, complemented
14C73×#1495C211yesmaximal, characteristic, complemented
15C73×#1486C211yesmaximal, characteristic, complemented
16C2×AGL(1,ℤ/8)×C73—21no—
17#555×C73C2211yescharacteristic
18#554×C73C2211yescharacteristic
19#553×C73—21no—
20#553×C73—21no—
21#550×C73C2211yescharacteristic
22#546×C73—22no—
23#546×C73—21no—
24D42×C73—21no—
25D42×C73C2211yescharacteristic
26#540×C73—21no—
27#538×C73—22no—
28#532×C73C2211yescharacteristic
29#532×C73C2211yescharacteristic, complemented
30#529×C73C2211yescharacteristic
31#525×C73—21no—
32C2×#121×C73—21no—
33#518×C73—21no—
34C2×C4×D4×C73C2211yescharacteristic
35#493×C73C2211yescharacteristic, complemented
36#492×C73C2211yescharacteristic, complemented
37#487×C73C2211yescharacteristic, complemented
38#486×C73C2211yescharacteristic, complemented
39#478×C73—21no—
40#475×C73C2211yescharacteristic, complemented
41#474×C73C2211yescharacteristic, complemented
42#469×C73—21no—
43#468×C73—21no—
44#463×C73—22no—
45#463×C73—21no—
46#463×C73—21no—
47#463×C73—21no—
48#461×C73C2211yescharacteristic
49#461×C73C2211yescharacteristic, complemented
50#460×C73C2211yescharacteristic, complemented
51#459×C73C2211yescharacteristic
52#459×C73C2211yescharacteristic, complemented
53#459×C73C2211yescharacteristic, complemented
54#449×C73—22no—
55#431×C73C2211yescharacteristic, complemented
56#423×C73C2211yescharacteristic, complemented
57#423×C73C2211yescharacteristic, complemented
58#417×C73—21no—
59#333×C73C2211yescharacteristic, complemented
60#333×C73C2211yescharacteristic, complemented
61#331×C73C2211yescharacteristic, complemented
62#331×C73C2211yescharacteristic, complemented
63Q8⋊C8×C73C2211yescharacteristic, complemented
64Q8⋊C8×C73C2211yescharacteristic, complemented
65D4⋊C8×C73C2211yescharacteristic
66D4⋊C8×C73C2211yescharacteristic
67D4⋊C8×C73C2211yescharacteristic, complemented
68D4⋊C8×C73C2211yescharacteristic, complemented
69D4⋊C8×C73C2211yescharacteristic, complemented
70D4⋊C8×C73C2211yescharacteristic, complemented
71C2×#41×C73—21no—
72C2×#41×C73—21no—
73C2×#41×C73D412yes—
74C22×D4×C73—22no—
75C22×D4×C73—21no—
76C22×D4×C73—21no—
77C22×D4×C73D411yescharacteristic
78C23×C4×C73—21no—
79AGL(1,ℤ/8)×C73—44no—
80C2×SD16×C73—21no—
81C2×SD16×C73—21no—
82C2×SD16×C73—22no—
83C2×SD16×C73—21no—
84C2×D8×C73—21no—
85C2×D8×C73—21no—
86C2×D8×C73—22no—
87C2×D8×C73—21no—
88C2×M16×C73—21no—
89C2×M16×C73—21no—
90C4⋊Q8×C73C2311yescharacteristic
91C4⋊Q8×C73C2311yescharacteristic
92#127×C73—21no—
93#127×C73C2311yescharacteristic
94#127×C73C2311yescharacteristic
95#126×C73—22no—
96#126×C73—21no—
97#125×C73—21no—
98#125×C73D411yescharacteristic
99#124×C73—22no—
100#124×C73—21no—
101#124×C73D411yescharacteristic
102#124×C73D412yes—
103#123×C73—22no—
104#123×C73—22no—
105#123×C73—22no—
106#123×C73—21no—
107C22⋊Q8×C73—21no—
108C22⋊Q8×C73—22no—
109C22⋊Q8×C73D411yescharacteristic
110#121×C73—22no—
111#121×C73—22no—
112#121×C73—22no—
113#121×C73—22no—
114#121×C73—21no—
115#121×C73—22no—
116#121×C73—21no—
117#121×C73—21no—
118#121×C73—21no—
119#121×C73—21no—
120#121×C73—21no—
121#121×C73—21no—
122#121×C73—21no—
123#121×C73—21no—
124#121×C73D411yescharacteristic
125#120×C73—22no—
126#120×C73—22no—
127#120×C73—22no—
128C4×Q8×C73C2311yescharacteristic
129C4×D4×C73—22no—
130C4×D4×C73—22no—
131C4×D4×C73—22no—
132C4×D4×C73—21no—
133C4×D4×C73—21no—
134C4×D4×C73—21no—
135C4×D4×C73—21no—
136C4×D4×C73—21no—
137C4×D4×C73—21no—
138C4×D4×C73—21no—
139C4×D4×C73—21no—
140C4×D4×C73—21no—
141C4×D4×C73D411yescharacteristic
142C4×D4×C73D411yescharacteristic
143C4×D4×C73C2311yescharacteristic
144C4×D4×C73C2311yescharacteristic
145C4×D4×C73C2311yescharacteristic
146#117×C73—21no—
147#117×C73—21no—
148#117×C73—21no—
149C2×C4⋊C4×C73—21no—
150C2×C4⋊C4×C73D411yescharacteristic
151C2×C22⋊C4×C73—22no—
152C2×C22⋊C4×C73—22no—
153C2×C22⋊C4×C73—21no—
154C2×C42×C73C2311yescharacteristic
155#107×C73—21no—
156#106×C73—21no—
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—22no—
165#103×C73—21no—
166#103×C73—21no—
167#103×C73—21no—
168#102×C73—22no—
169#102×C73—21no—
170#102×C73—21no—
171#102×C73—21no—
172#102×C73—21no—
173#102×C73—21no—
174C22⋊C8×C73—21no—
175C4×C8×C73C2311yescharacteristic
176C4×C8×C73C2311yescharacteristic
177C24×C73—22no—
178C24×C73—21no—
179#41×C73—42no—
180#41×C73—42no—
181#41×C73—81no—
182#41×C73—81no—
183#41×C73—82no—
184C2×Q8×C73—21no—
185C2×Q8×C73C2×D411yescharacteristic
186C2×Q8×C73C2×D412yes—
187C2×D4×C73—22no—
188C2×D4×C73—22no—
189C2×D4×C73—22no—
190C2×D4×C73—21no—
191C2×D4×C73—22no—
192C2×D4×C73—22no—
193C2×D4×C73—22no—
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—21no—
201C2×D4×C73—41no—
202C2×D4×C73—42no—
203C2×D4×C73—42no—
204C2×D4×C73—41no—
205C2×D4×C73—81no—
206C2×D4×C73—81no—
207C2×D4×C73—84no—
208C2×D4×C73C2×D411yescharacteristic
209C2×D4×C73C2×D411yescharacteristic
210C2×D4×C73C2×D411yescharacteristic
211C2×D4×C73C2×D412yes—
212C22×C4×C73—22no—
213C22×C4×C73—22no—
214C22×C4×C73—21no—
215C22×C4×C73—21no—
216C22×C4×C73—21no—
217C22×C4×C73—21no—
218C22×C4×C73—21no—
219C22×C4×C73—22no—
220C22×C4×C73—21no—
221C22×C4×C73—41no—
222C22×C4×C73—81no—
223C22×C4×C73—81no—
224C22×C4×C73C2×D411yescharacteristic
225C22×C4×C73C2×D411yescharacteristic
226C22×C4×C73C2×D411yescharacteristic
227SD16×C73—42no—
228SD16×C73—42no—
229SD16×C73—81no—
230SD16×C73—82no—
231D8×C73—42no—
232D8×C73—42no—
233D8×C73—81no—
234D8×C73—82no—
235M16×C73—42no—
236M16×C73—81no—
237C2×C8×C73—21no—
238C2×C8×C73—21no—
239C2×C8×C73—21no—
240C2×C8×C73—21no—
241C2×C8×C73—21no—
242C2×C8×C73—21no—
243C4⋊C4×C73—22no—
244C4⋊C4×C73—22no—
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×C73—21no—
252C4⋊C4×C73—21no—
253C4⋊C4×C73—21no—
254C4⋊C4×C73C2×D411yescharacteristic
255C4⋊C4×C73C2×D411yescharacteristic
256C4⋊C4×C73C2×D411yescharacteristic
257C4⋊C4×C73C2×D411yescharacteristic
258C22⋊C4×C73—22no—
259C22⋊C4×C73—22no—
260C22⋊C4×C73—22no—
261C22⋊C4×C73—22no—
262C22⋊C4×C73—22no—
263C22⋊C4×C73—21no—
264C22⋊C4×C73—21no—
265C22⋊C4×C73—21no—
266C22⋊C4×C73—21no—
267C22⋊C4×C73—22no—
268C22⋊C4×C73—21no—
269C22⋊C4×C73—21no—
270C22⋊C4×C73—22no—
271C22⋊C4×C73—21no—
272C22⋊C4×C73—21no—
273C22⋊C4×C73—21no—
274C22⋊C4×C73—41no—
275C22⋊C4×C73—41no—
276C42×C73—22no—
277C42×C73—21no—
278C42×C73C2×D411yescharacteristic
279C42×C73C2×D411yescharacteristic
280C42×C73C2×D411yescharacteristic
281C42×C73C2411yescharacteristic
282C23×C73—21no—
283C23×C73—21no—
284C23×C73—21no—
285C23×C73—22no—
286C23×C73—42no—
287C23×C73—42no—
288C23×C73—44no—
289C23×C73—41no—
290C23×C73—81no—
291C23×C73—82no—
292C23×C73—82no—
293C23×C73#12011yescharacteristic
294Q8×C73—21no—
295Q8×C73—21no—
296Q8×C73—42no—
297Q8×C73—41no—
298Q8×C73—41no—
299D4×C73—21no—
300D4×C73—21no—
301D4×C73—21no—
302D4×C73—21no—
303D4×C73—21no—
304D4×C73—42no—
305D4×C73—42no—
306D4×C73—42no—
307D4×C73—44no—
308D4×C73—42no—
309D4×C73—44no—
310D4×C73—41no—
311D4×C73—41no—
312D4×C73—41no—
313D4×C73—41no—
314D4×C73—41no—
315D4×C73—41no—
316D4×C73—41no—
317D4×C73—41no—
318D4×C73—82no—
319D4×C73—82no—
320D4×C73—82no—
321D4×C73—82no—
322D4×C73—82no—
323D4×C73AGL(1,ℤ/8)12yes—
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—81no—
343C2×C4×C73—81no—
344C2×C4×C73—82no—
345C2×C4×C73—82no—
346C2×C4×C73—81no—
347C2×C4×C73—82no—
348C2×C4×C73—82no—
349C2×C4×C73#12011yescharacteristic
350C2×C4×C73#12011yescharacteristic
351C2×C4×C73#12011yescharacteristic
352C2×C4×C73C22×D411yescharacteristic
353C2×C4×C73C22×D411yescharacteristic
354C2×C4×C73C22×D411yescharacteristic
355C8×C73—41no—
356C8×C73—41no—
357C8×C73—41no—
358C8×C73—41no—
359C8×C73—41no—
360C8×C73—41no—
361C22×C73—21no—
362C22×C73—22no—
363C22×C73—21no—
364C22×C73—21no—
365C22×C73—41no—
366C22×C73—41no—
367C22×C73—41no—
368C22×C73—41no—
369C22×C73—42no—
370C22×C73—41no—
371C22×C73—42no—
372C22×C73—41no—
373C22×C73—42no—
374C22×C73—41no—
375C22×C73—41no—
376C22×C73—84no—
377C22×C73—81no—
378C22×C73—81no—
379C22×C73—81no—
380C22×C73—164no—
381C22×C73C2×#12011yescharacteristic
382C4×C73—21no—
383C4×C73—21no—
384C4×C73—21no—
385C4×C73—21no—
386C4×C73—41no—
387C4×C73—41no—
388C4×C73—41no—
389C4×C73—41no—
390C4×C73—41no—
391C4×C73—42no—
392C4×C73—81no—
393C4×C73C2×AGL(1,ℤ/8)11yescharacteristic
394C4×C73#57511yescharacteristic
395C4×C73#57611yescharacteristic
396C4×C73#57711yescharacteristic
397#18810C7311yesmaximal, characteristic, direct product factor, Sylow
398C2×C73—41no—
399C2×C73—42no—
400C2×C73—81no—
401C2×C73—82no—
402C2×C73—81no—
403C2×C73—161no—
404C2×C73#300611yescharacteristic
405C2×C73#301211yescharacteristic
406C2×C73#301911yescharacteristic
407#3519C2×C7311yescharacteristic, complemented
408#3251C2×C7311yescharacteristic, complemented
409#3207C2×C7311yescharacteristic, complemented
410#3036C2×C7311yescharacteristic, complemented
411#1646C2×C7311yescharacteristic, complemented
412#1643C2×C7311yescharacteristic, complemented
413#1642C2×C7311yescharacteristic, complemented
414#1639C2×C7311yescharacteristic, complemented
415#1624C2×C7311yescharacteristic, complemented
416#1622C2×C7311yescharacteristic, complemented
417#1621C2×C7311yescharacteristic, complemented
418#1619C2×C7311yescharacteristic, complemented
419#1560C2×C7311yescharacteristic, complemented
420#1495C2×C7311yescharacteristic, complemented
421#1486C2×C7311yescharacteristic, complemented
422C73#1881011yescharacteristic, direct product factor, Sylow
423C2×AGL(1,ℤ/8)—21no—
424#555C22×C7311yescharacteristic
425#554C22×C7311yescharacteristic
426#553—21no—
427#553—21no—
428#550C22×C7311yescharacteristic
429#546—22no—
430#546—21no—
431D42—21no—
432D42C22×C7311yescharacteristic
433#540—21no—
434#538—22no—
435#532C22×C7311yescharacteristic
436#532C22×C7311yescharacteristic, complemented
437#529C22×C7311yescharacteristic
438#525—21no—
439C2×#121—21no—
440#518—21no—
441C2×C4×D4C22×C7311yescharacteristic
442#493C22×C7311yescharacteristic, complemented
443#492C22×C7311yescharacteristic, complemented
444#487C22×C7311yescharacteristic, complemented
445#486C22×C7311yescharacteristic, complemented
446#478—21no—
447#475C22×C7311yescharacteristic, complemented
448#474C22×C7311yescharacteristic, complemented
449#469—21no—
450#468—21no—
451#463—22no—
452#463—21no—
453#463—21no—
454#463—21no—
455#461C22×C7311yescharacteristic
456#461C22×C7311yescharacteristic, complemented
457#460C22×C7311yescharacteristic, complemented
458#459C22×C7311yescharacteristic
459#459C22×C7311yescharacteristic, complemented
460#459C22×C7311yescharacteristic, complemented
461#449—22no—
462#431C22×C7311yescharacteristic, complemented
463#423C22×C7311yescharacteristic, complemented
464#423C22×C7311yescharacteristic, complemented
465#417—21no—
466#333C22×C7311yescharacteristic, complemented
467#333C22×C7311yescharacteristic, complemented
468#331C22×C7311yescharacteristic, complemented
469#331C22×C7311yescharacteristic, complemented
470Q8⋊C8C22×C7311yescharacteristic, complemented
471Q8⋊C8C22×C7311yescharacteristic, complemented
472D4⋊C8C22×C7311yescharacteristic
473D4⋊C8C22×C7311yescharacteristic
474D4⋊C8C22×C7311yescharacteristic, complemented
475D4⋊C8C22×C7311yescharacteristic, complemented
476D4⋊C8C22×C7311yescharacteristic, complemented
477D4⋊C8C22×C7311yescharacteristic, complemented
478C2×#41—21no—
479C2×#41—21no—
480C2×#41D4×C7312yes—
481C22×D4—22no—
482C22×D4—21no—
483C22×D4—21no—
484C22×D4D4×C7311yescharacteristic
485C23×C4—21no—
486AGL(1,ℤ/8)—44no—
487C2×SD16—21no—
488C2×SD16—21no—
489C2×SD16—22no—
490C2×SD16—21no—
491C2×D8—21no—
492C2×D8—21no—
493C2×D8—22no—
494C2×D8—21no—
495C2×M16—21no—
496C2×M16—21no—
497C4⋊Q8C23×C7311yescharacteristic
498C4⋊Q8C23×C7311yescharacteristic
499#127—21no—
500#127C23×C7311yescharacteristic
501#127C23×C7311yescharacteristic
502#126—22no—
503#126—21no—
504#125—21no—
505#125D4×C7311yescharacteristic
506#124—22no—
507#124—21no—
508#124D4×C7311yescharacteristic
509#124D4×C7312yes—
510#123—22no—
511#123—22no—
512#123—22no—
513#123—21no—
514C22⋊Q8—21no—
515C22⋊Q8—22no—
516C22⋊Q8D4×C7311yescharacteristic
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#121—21no—
531#121D4×C7311yescharacteristic
532#120—22no—
533#120—22no—
534#120—22no—
535C4×Q8C23×C7311yescharacteristic
536C4×D4—22no—
537C4×D4—22no—
538C4×D4—22no—
539C4×D4—21no—
540C4×D4—21no—
541C4×D4—21no—
542C4×D4—21no—
543C4×D4—21no—
544C4×D4—21no—
545C4×D4—21no—
546C4×D4—21no—
547C4×D4—21no—
548C4×D4D4×C7311yescharacteristic
549C4×D4D4×C7311yescharacteristic
550C4×D4C23×C7311yescharacteristic
551C4×D4C23×C7311yescharacteristic
552C4×D4C23×C7311yescharacteristic
553#117—21no—
554#117—21no—
555#117—21no—
556C2×C4⋊C4—21no—
557C2×C4⋊C4D4×C7311yescharacteristic
558C2×C22⋊C4—22no—
559C2×C22⋊C4—22no—
560C2×C22⋊C4—21no—
561C2×C42C23×C7311yescharacteristic
562#107—21no—
563#106—21no—
564C4⋊C8—21no—
565C4⋊C8—21no—
566C4⋊C8—21no—
567C4⋊C8C23×C7311yescharacteristic
568C4⋊C8C23×C7311yescharacteristic
569C4⋊C8C23×C7311yescharacteristic
570C4⋊C8C23×C7311yescharacteristic
571#103—22no—
572#103—21no—
573#103—21no—
574#103—21no—
575#102—22no—
576#102—21no—
577#102—21no—
578#102—21no—
579#102—21no—
580#102—21no—
581C22⋊C8—21no—
582C4×C8C23×C7311yescharacteristic
583C4×C8C23×C7311yescharacteristic
584C24—22no—
585C24—21no—
586#41—42no—
587#41—42no—
588#41—81no—
589#41—81no—
590#41—82no—
591C2×Q8—21no—
592C2×Q8C2×D4×C7311yescharacteristic
593C2×Q8C2×D4×C7312yes—
594C2×D4—22no—
595C2×D4—22no—
596C2×D4—22no—
597C2×D4—21no—
598C2×D4—22no—
599C2×D4—22no—
600C2×D4—22no—
601C2×D4—22no—
602C2×D4—21no—
603C2×D4—21no—
604C2×D4—21no—
605C2×D4—21no—
606C2×D4—21no—
607C2×D4—21no—
608C2×D4—41no—
609C2×D4—42no—
610C2×D4—42no—
611C2×D4—41no—
612C2×D4—81no—
613C2×D4—81no—
614C2×D4—84no—
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—21no—
625C22×C4—21no—
626C22×C4—22no—
627C22×C4—21no—
628C22×C4—41no—
629C22×C4—81no—
630C22×C4—81no—
631C22×C4C2×D4×C7311yescharacteristic
632C22×C4C2×D4×C7311yescharacteristic
633C22×C4C2×D4×C7311yescharacteristic
634SD16—42no—
635SD16—42no—
636SD16—81no—
637SD16—82no—
638D8—42no—
639D8—42no—
640D8—81no—
641D8—82no—
642M16—42no—
643M16—81no—
644C2×C8—21no—
645C2×C8—21no—
646C2×C8—21no—
647C2×C8—21no—
648C2×C8—21no—
649C2×C8—21no—
650C4⋊C4—22no—
651C4⋊C4—22no—
652C4⋊C4—21no—
653C4⋊C4—21no—
654C4⋊C4—21no—
655C4⋊C4—21no—
656C4⋊C4—21no—
657C4⋊C4—21no—
658C4⋊C4—21no—
659C4⋊C4—21no—
660C4⋊C4—21no—
661C4⋊C4C2×D4×C7311yescharacteristic
662C4⋊C4C2×D4×C7311yescharacteristic
663C4⋊C4C2×D4×C7311yescharacteristic
664C4⋊C4C2×D4×C7311yescharacteristic
665C22⋊C4—22no—
666C22⋊C4—22no—
667C22⋊C4—22no—
668C22⋊C4—22no—
669C22⋊C4—22no—
670C22⋊C4—21no—
671C22⋊C4—21no—
672C22⋊C4—21no—
673C22⋊C4—21no—
674C22⋊C4—22no—
675C22⋊C4—21no—
676C22⋊C4—21no—
677C22⋊C4—22no—
678C22⋊C4—21no—
679C22⋊C4—21no—
680C22⋊C4—21no—
681C22⋊C4—41no—
682C22⋊C4—41no—
683C42—22no—
684C42—21no—
685C42C2×D4×C7311yescharacteristic
686C42C2×D4×C7311yescharacteristic
687C42C2×D4×C7311yescharacteristic
688C42C24×C7311yescharacteristic
689C23—21no—
690C23—21no—
691C23—21no—
692C23—22no—
693C23—42no—
694C23—42no—
695C23—44no—
696C23—41no—
697C23—81no—
698C23—82no—
699C23—82no—
700C23#120×C7311yescharacteristic
701Q8—21no—
702Q8—21no—
703Q8—42no—
704Q8—41no—
705Q8—41no—
706D4—21no—
707D4—21no—
708D4—21no—
709D4—21no—
710D4—21no—
711D4—42no—
712D4—42no—
713D4—42no—
714D4—44no—
715D4—42no—
716D4—44no—
717D4—41no—
718D4—41no—
719D4—41no—
720D4—41no—
721D4—41no—
722D4—41no—
723D4—41no—
724D4—41no—
725D4—82no—
726D4—82no—
727D4—82no—
728D4—82no—
729D4—82no—
730D4AGL(1,ℤ/8)×C7312yes—
731C2×C4—21no—
732C2×C4—21no—
733C2×C4—21no—
734C2×C4—21no—
735C2×C4—21no—
736C2×C4—21no—
737C2×C4—21no—
738C2×C4—22no—
739C2×C4—21no—
740C2×C4—21no—
741C2×C4—41no—
742C2×C4—41no—
743C2×C4—41no—
744C2×C4—41no—
745C2×C4—41no—
746C2×C4—41no—
747C2×C4—41no—
748C2×C4—41no—
749C2×C4—81no—
750C2×C4—81no—
751C2×C4—82no—
752C2×C4—82no—
753C2×C4—81no—
754C2×C4—82no—
755C2×C4—82no—
756C2×C4#120×C7311yescharacteristic
757C2×C4#120×C7311yescharacteristic
758C2×C4#120×C7311yescharacteristic
759C2×C4C22×D4×C7311yescharacteristic
760C2×C4C22×D4×C7311yescharacteristic
761C2×C4C22×D4×C7311yescharacteristic
762C8—41no—
763C8—41no—
764C8—41no—
765C8—41no—
766C8—41no—
767C8—41no—
768C22—21no—
769C22—22no—
770C22—21no—
771C22—21no—
772C22—41no—
773C22—41no—
774C22—41no—
775C22—41no—
776C22—42no—
777C22—41no—
778C22—42no—
779C22—41no—
780C22—42no—
781C22—41no—
782C22—41no—
783C22—84no—
784C22—81no—
785C22—81no—
786C22—81no—
787C22—164no—
788C22C2×#120×C7311yescharacteristic
789C4—21no—
790C4—21no—
791C4—21no—
792C4—21no—
793C4—41no—
794C4—41no—
795C4—41no—
796C4—41no—
797C4—41no—
798C4—42no—
799C4—81no—
800C4C2×AGL(1,ℤ/8)×C7311yescharacteristic
801C4#575×C7311yescharacteristic
802C4#576×C7311yescharacteristic
803C4#577×C7311yescharacteristic
804C2—41no—
805C2—42no—
806C2—81no—
807C2—81no—
808C2—82no—
809C2—161no—
810C2C73×#300611yescharacteristic
811C2C73×#301211yescharacteristic
812C2C73×#301911yescharacteristic
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×#3519C2semidirect
2. C73×#3251C2semidirect
3. C73×#3207C2semidirect
4. C73×#3036C2semidirect
5. C73×#1646C2semidirect
6. C73×#1643C2semidirect
7. C73×#1642C2semidirect
8. C73×#1639C2semidirect
9. C73×#1624C2semidirect
10. C73×#1622C2semidirect
11. C73×#1621C2semidirect
12. C73×#1619C2semidirect
13. C73×#1560C2semidirect
14. C73×#1495C2semidirect
15. C73×#1486C2semidirect
29. #532×C73C22semidirect
35. #493×C73C22semidirect
36. #492×C73C22semidirect
37. #487×C73C22semidirect
38. #486×C73C22semidirect
40. #475×C73C22semidirect
41. #474×C73C22semidirect
49. #461×C73C22semidirect
50. #460×C73C22semidirect
52. #459×C73C22semidirect
53. #459×C73C22semidirect
55. #431×C73C22semidirect
56. #423×C73C22semidirect
57. #423×C73C22semidirect
59. #333×C73C22semidirect
60. #333×C73C22semidirect
61. #331×C73C22semidirect
62. #331×C73C22semidirect
63. Q8⋊C8×C73C22semidirect
64. Q8⋊C8×C73C22semidirect
67. D4⋊C8×C73C22semidirect
68. D4⋊C8×C73C22semidirect
69. D4⋊C8×C73C22semidirect
70. D4⋊C8×C73C22semidirect
397. #18810C73direct (N × H)
407. #3519C2×C73semidirect
408. #3251C2×C73semidirect
409. #3207C2×C73semidirect
410. #3036C2×C73semidirect
411. #1646C2×C73semidirect
412. #1643C2×C73semidirect
413. #1642C2×C73semidirect
414. #1639C2×C73semidirect
415. #1624C2×C73semidirect
416. #1622C2×C73semidirect
417. #1621C2×C73semidirect
418. #1619C2×C73semidirect
419. #1560C2×C73semidirect
420. #1495C2×C73semidirect
421. #1486C2×C73semidirect
422. C73#18810direct (N × H)
436. #532C22×C73semidirect
442. #493C22×C73semidirect
443. #492C22×C73semidirect
444. #487C22×C73semidirect
445. #486C22×C73semidirect
447. #475C22×C73semidirect
448. #474C22×C73semidirect
456. #461C22×C73semidirect
457. #460C22×C73semidirect
459. #459C22×C73semidirect
460. #459C22×C73semidirect
462. #431C22×C73semidirect
463. #423C22×C73semidirect
464. #423C22×C73semidirect
466. #333C22×C73semidirect
467. #333C22×C73semidirect
468. #331C22×C73semidirect
469. #331C22×C73semidirect
470. Q8⋊C8C22×C73semidirect
471. Q8⋊C8C22×C73semidirect
474. D4⋊C8C22×C73semidirect
475. D4⋊C8C22×C73semidirect
476. D4⋊C8C22×C73semidirect
477. D4⋊C8C22×C73semidirect

Maximal subgroups

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

subgroupindex
C73×#35192
C73×#32512
C73×#32072
C73×#30362
C73×#16462
C73×#16432
C73×#16422
C73×#16392
C73×#16242
C73×#16222
C73×#16212
C73×#16192
C73×#15602
C73×#14952
C73×#14862
#1881073