Finite Group Databasebeta

← C73×#18866 #32928270

Subgroups — C73×#18866 #32928270

Order 18688.

1020 conjugacy classes of subgroups.

The subgroup lattice has 808 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C73×#3519C211yesmaximal, characteristic, complemented
2C73×#3212C211yesmaximal, characteristic, complemented
3C73×#3207C211yesmaximal, characteristic, complemented
4C73×#3100C211yesmaximal, characteristic, complemented
5C73×#1646C211yesmaximal, characteristic, complemented
6C73×#1644C211yesmaximal, characteristic, complemented
7C73×#1641C211yesmaximal, characteristic, complemented
8C73×#1639C211yesmaximal, characteristic, complemented
9C73×#1624C211yesmaximal, characteristic, complemented
10C73×#1622C211yesmaximal, characteristic, complemented
11C73×#1621C211yesmaximal, characteristic, complemented
12C73×#1619C211yesmaximal, characteristic, complemented
13C73×#1543C211yesmaximal, characteristic, complemented
14C73×#1482C211yesmaximal, characteristic, complemented
15C73×#1478C211yesmaximal, characteristic, complemented
16#555×C73C2211yescharacteristic
17#554×C73C2211yescharacteristic
18#553×C73—21no—
19#553×C73—21no—
20#550×C73C2211yescharacteristic
21#546×C73—22no—
22#546×C73—21no—
23D42×C73—21no—
24D42×C73C2211yescharacteristic
25#540×C73—21no—
26#538×C73—22no—
27#532×C73C2211yescharacteristic
28#532×C73C2211yescharacteristic, complemented
29#529×C73C2211yescharacteristic
30#525×C73—21no—
31C2×#121×C73—21no—
32#518×C73—21no—
33C2×C4×D4×C73C2211yescharacteristic
34#495×C73—21no—
35#493×C73C2211yescharacteristic, complemented
36#492×C73C2211yescharacteristic, complemented
37#488×C73—21no—
38#487×C73C2211yescharacteristic, complemented
39#486×C73C2211yescharacteristic, complemented
40#480×C73—21no—
41#474×C73C2211yescharacteristic
42#474×C73C2211yescharacteristic, complemented
43#463×C73—22no—
44#462×C73C2211yescharacteristic, complemented
45#461×C73C2211yescharacteristic, complemented
46#460×C73C2211yescharacteristic, complemented
47#459×C73C2211yescharacteristic
48#459×C73C2211yescharacteristic, complemented
49#459×C73C2211yescharacteristic, complemented
50#452×C73—21no—
51#449×C73—22no—
52#449×C73—21no—
53#447×C73—21no—
54C4×D8×C73—21no—
55C4×D8×C73—21no—
56#431×C73C2211yescharacteristic, complemented
57#431×C73C2211yescharacteristic, complemented
58#431×C73C2211yescharacteristic, complemented
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—
79C2×Q16×C73—21no—
80C2×SD16×C73—22no—
81C2×SD16×C73—21no—
82C2×SD16×C73—21no—
83C2×D8×C73—21no—
84C2×D8×C73—21no—
85C2×D8×C73—21no—
86C2×D8×C73—22no—
87C4⋊Q8×C73C2311yescharacteristic
88C4⋊Q8×C73C2311yescharacteristic
89#127×C73—21no—
90#127×C73C2311yescharacteristic
91#127×C73C2311yescharacteristic
92#126×C73—22no—
93#126×C73—21no—
94#125×C73—21no—
95#125×C73D411yescharacteristic
96#124×C73—22no—
97#124×C73—21no—
98#124×C73D412yes—
99#124×C73D411yescharacteristic
100#123×C73—22no—
101#123×C73—22no—
102#123×C73—22no—
103#123×C73—21no—
104C22⋊Q8×C73—21no—
105C22⋊Q8×C73—22no—
106C22⋊Q8×C73D411yescharacteristic
107#121×C73—22no—
108#121×C73—22no—
109#121×C73—22no—
110#121×C73—22no—
111#121×C73—21no—
112#121×C73—22no—
113#121×C73—21no—
114#121×C73—21no—
115#121×C73—21no—
116#121×C73—21no—
117#121×C73—21no—
118#121×C73—21no—
119#121×C73—21no—
120#121×C73—21no—
121#121×C73D411yescharacteristic
122#120×C73—22no—
123#120×C73—22no—
124#120×C73—22no—
125C4×Q8×C73C2311yescharacteristic
126C4×D4×C73—22no—
127C4×D4×C73—22no—
128C4×D4×C73—22no—
129C4×D4×C73—21no—
130C4×D4×C73—21no—
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×C73—21no—
138C4×D4×C73D411yescharacteristic
139C4×D4×C73D411yescharacteristic
140C4×D4×C73C2311yescharacteristic
141C4×D4×C73C2311yescharacteristic
142C4×D4×C73C2311yescharacteristic
143#117×C73—21no—
144#117×C73—21no—
145#117×C73—21no—
146C2×C4⋊C4×C73—21no—
147C2×C4⋊C4×C73D411yescharacteristic
148C2×C22⋊C4×C73—22no—
149C2×C22⋊C4×C73—22no—
150C2×C22⋊C4×C73—21no—
151C2×C42×C73C2311yescharacteristic
152#107×C73—21no—
153#107×C73—21no—
154C4⋊C8×C73—21no—
155C4⋊C8×C73C2311yescharacteristic
156C4⋊C8×C73C2311yescharacteristic
157C4⋊C8×C73C2311yescharacteristic
158C4⋊C8×C73C2311yescharacteristic
159#103×C73—22no—
160#103×C73—21no—
161#103×C73—21no—
162#102×C73—21no—
163#102×C73—21no—
164#102×C73—22no—
165#102×C73—21no—
166#102×C73—21no—
167#102×C73—21no—
168#102×C73—21no—
169C22⋊C8×C73—21no—
170C22⋊C8×C73—21no—
171C22⋊C8×C73—21no—
172C4×C8×C73—21no—
173C4×C8×C73—21no—
174C4×C8×C73C2311yescharacteristic
175C4×C8×C73C2311yescharacteristic
176C24×C73—22no—
177C24×C73—21no—
178#41×C73—81no—
179#41×C73—81no—
180#41×C73—81no—
181#41×C73—81no—
182#41×C73—82no—
183C2×Q8×C73—21no—
184C2×Q8×C73C2×D411yescharacteristic
185C2×Q8×C73C2×D412yes—
186C2×D4×C73—22no—
187C2×D4×C73—22no—
188C2×D4×C73—22no—
189C2×D4×C73—21no—
190C2×D4×C73—22no—
191C2×D4×C73—22no—
192C2×D4×C73—22no—
193C2×D4×C73—22no—
194C2×D4×C73—21no—
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×C73—42no—
202C2×D4×C73—42no—
203C2×D4×C73—41no—
204C2×D4×C73—81no—
205C2×D4×C73—81no—
206C2×D4×C73—84no—
207C2×D4×C73C2×D411yescharacteristic
208C2×D4×C73C2×D411yescharacteristic
209C2×D4×C73C2×D411yescharacteristic
210C2×D4×C73C2×D412yes—
211C22×C4×C73—22no—
212C22×C4×C73—22no—
213C22×C4×C73—21no—
214C22×C4×C73—21no—
215C22×C4×C73—21no—
216C22×C4×C73—21no—
217C22×C4×C73—21no—
218C22×C4×C73—22no—
219C22×C4×C73—21no—
220C22×C4×C73—41no—
221C22×C4×C73—81no—
222C22×C4×C73—81no—
223C22×C4×C73C2×D411yescharacteristic
224C22×C4×C73C2×D411yescharacteristic
225C22×C4×C73C2×D411yescharacteristic
226Q16×C73—81no—
227SD16×C73—81no—
228SD16×C73—81no—
229SD16×C73—82no—
230D8×C73—42no—
231D8×C73—42no—
232D8×C73—81no—
233D8×C73—82no—
234C2×C8×C73—21no—
235C2×C8×C73—21no—
236C2×C8×C73—21no—
237C2×C8×C73—21no—
238C2×C8×C73—21no—
239C2×C8×C73—21no—
240C4⋊C4×C73—22no—
241C4⋊C4×C73—22no—
242C4⋊C4×C73—21no—
243C4⋊C4×C73—21no—
244C4⋊C4×C73—21no—
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×C73C2×D411yescharacteristic
252C4⋊C4×C73C2×D411yescharacteristic
253C4⋊C4×C73C2×D411yescharacteristic
254C4⋊C4×C73C2×D411yescharacteristic
255C22⋊C4×C73—22no—
256C22⋊C4×C73—22no—
257C22⋊C4×C73—22no—
258C22⋊C4×C73—22no—
259C22⋊C4×C73—22no—
260C22⋊C4×C73—21no—
261C22⋊C4×C73—21no—
262C22⋊C4×C73—21no—
263C22⋊C4×C73—21no—
264C22⋊C4×C73—22no—
265C22⋊C4×C73—21no—
266C22⋊C4×C73—21no—
267C22⋊C4×C73—22no—
268C22⋊C4×C73—21no—
269C22⋊C4×C73—21no—
270C22⋊C4×C73—21no—
271C22⋊C4×C73—41no—
272C22⋊C4×C73—41no—
273C42×C73—22no—
274C42×C73—21no—
275C42×C73C2×D411yescharacteristic
276C42×C73C2×D411yescharacteristic
277C42×C73C2×D411yescharacteristic
278C42×C73C2411yescharacteristic
279C23×C73—21no—
280C23×C73—21no—
281C23×C73—21no—
282C23×C73—22no—
283C23×C73—42no—
284C23×C73—42no—
285C23×C73—44no—
286C23×C73—41no—
287C23×C73—81no—
288C23×C73—82no—
289C23×C73—82no—
290C23×C73#12011yescharacteristic
291Q8×C73—21no—
292Q8×C73—21no—
293Q8×C73—42no—
294Q8×C73—41no—
295Q8×C73—41no—
296D4×C73—21no—
297D4×C73—21no—
298D4×C73—21no—
299D4×C73—21no—
300D4×C73—21no—
301D4×C73—42no—
302D4×C73—42no—
303D4×C73—42no—
304D4×C73—44no—
305D4×C73—42no—
306D4×C73—44no—
307D4×C73—41no—
308D4×C73—41no—
309D4×C73—41no—
310D4×C73—41no—
311D4×C73—41no—
312D4×C73—41no—
313D4×C73—41no—
314D4×C73—41no—
315D4×C73—82no—
316D4×C73—82no—
317D4×C73—82no—
318D4×C73—82no—
319D4×C73—82no—
320D4×C73#13512yes—
321C2×C4×C73—21no—
322C2×C4×C73—21no—
323C2×C4×C73—21no—
324C2×C4×C73—21no—
325C2×C4×C73—21no—
326C2×C4×C73—21no—
327C2×C4×C73—21no—
328C2×C4×C73—22no—
329C2×C4×C73—21no—
330C2×C4×C73—21no—
331C2×C4×C73—41no—
332C2×C4×C73—41no—
333C2×C4×C73—41no—
334C2×C4×C73—41no—
335C2×C4×C73—41no—
336C2×C4×C73—41no—
337C2×C4×C73—41no—
338C2×C4×C73—41no—
339C2×C4×C73—81no—
340C2×C4×C73—81no—
341C2×C4×C73—82no—
342C2×C4×C73—82no—
343C2×C4×C73—81no—
344C2×C4×C73—82no—
345C2×C4×C73—82no—
346C2×C4×C73#12011yescharacteristic
347C2×C4×C73#12011yescharacteristic
348C2×C4×C73#12011yescharacteristic
349C2×C4×C73C22×D411yescharacteristic
350C2×C4×C73C22×D411yescharacteristic
351C2×C4×C73C22×D411yescharacteristic
352C8×C73—41no—
353C8×C73—41no—
354C8×C73—41no—
355C8×C73—41no—
356C8×C73—41no—
357C8×C73—41no—
358C22×C73—21no—
359C22×C73—22no—
360C22×C73—21no—
361C22×C73—21no—
362C22×C73—41no—
363C22×C73—41no—
364C22×C73—41no—
365C22×C73—41no—
366C22×C73—42no—
367C22×C73—41no—
368C22×C73—42no—
369C22×C73—41no—
370C22×C73—42no—
371C22×C73—41no—
372C22×C73—41no—
373C22×C73—84no—
374C22×C73—81no—
375C22×C73—81no—
376C22×C73—81no—
377C22×C73—164no—
378C22×C73C2×#12011yescharacteristic
379C4×C73—21no—
380C4×C73—21no—
381C4×C73—21no—
382C4×C73—21no—
383C4×C73—41no—
384C4×C73—41no—
385C4×C73—41no—
386C4×C73—41no—
387C4×C73—41no—
388C4×C73—42no—
389C4×C73—81no—
390C4×C73C2×#13511yescharacteristic
391C4×C73#57511yescharacteristic
392C4×C73#57611yescharacteristic
393C4×C73#57611yescharacteristic
394#18866C7311yesmaximal, characteristic, direct product factor, Sylow
395C2×C73—41no—
396C2×C73—42no—
397C2×C73—81no—
398C2×C73—82no—
399C2×C73—81no—
400C2×C73—161no—
401C2×C73#300211yescharacteristic
402C2×C73#300811yescharacteristic
403C2×C73#301911yescharacteristic
404#3519C2×C7311yescharacteristic, complemented
405#3212C2×C7311yescharacteristic, complemented
406#3207C2×C7311yescharacteristic, complemented
407#3100C2×C7311yescharacteristic, complemented
408#1646C2×C7311yescharacteristic, complemented
409#1644C2×C7311yescharacteristic, complemented
410#1641C2×C7311yescharacteristic, complemented
411#1639C2×C7311yescharacteristic, complemented
412#1624C2×C7311yescharacteristic, complemented
413#1622C2×C7311yescharacteristic, complemented
414#1621C2×C7311yescharacteristic, complemented
415#1619C2×C7311yescharacteristic, complemented
416#1543C2×C7311yescharacteristic, complemented
417#1482C2×C7311yescharacteristic, complemented
418#1478C2×C7311yescharacteristic, complemented
419C73#1886611yescharacteristic, direct product factor, Sylow
420#555C22×C7311yescharacteristic
421#554C22×C7311yescharacteristic
422#553—21no—
423#553—21no—
424#550C22×C7311yescharacteristic
425#546—22no—
426#546—21no—
427D42—21no—
428D42C22×C7311yescharacteristic
429#540—21no—
430#538—22no—
431#532C22×C7311yescharacteristic
432#532C22×C7311yescharacteristic, complemented
433#529C22×C7311yescharacteristic
434#525—21no—
435C2×#121—21no—
436#518—21no—
437C2×C4×D4C22×C7311yescharacteristic
438#495—21no—
439#493C22×C7311yescharacteristic, complemented
440#492C22×C7311yescharacteristic, complemented
441#488—21no—
442#487C22×C7311yescharacteristic, complemented
443#486C22×C7311yescharacteristic, complemented
444#480—21no—
445#474C22×C7311yescharacteristic
446#474C22×C7311yescharacteristic, complemented
447#463—22no—
448#462C22×C7311yescharacteristic, complemented
449#461C22×C7311yescharacteristic, complemented
450#460C22×C7311yescharacteristic, complemented
451#459C22×C7311yescharacteristic
452#459C22×C7311yescharacteristic, complemented
453#459C22×C7311yescharacteristic, complemented
454#452—21no—
455#449—22no—
456#449—21no—
457#447—21no—
458C4×D8—21no—
459C4×D8—21no—
460#431C22×C7311yescharacteristic, complemented
461#431C22×C7311yescharacteristic, complemented
462#431C22×C7311yescharacteristic, complemented
463#333C22×C7311yescharacteristic, complemented
464#333C22×C7311yescharacteristic, complemented
465#331C22×C7311yescharacteristic, complemented
466#331C22×C7311yescharacteristic, complemented
467Q8⋊C8C22×C7311yescharacteristic, complemented
468Q8⋊C8C22×C7311yescharacteristic, complemented
469D4⋊C8C22×C7311yescharacteristic
470D4⋊C8C22×C7311yescharacteristic
471D4⋊C8C22×C7311yescharacteristic, complemented
472D4⋊C8C22×C7311yescharacteristic, complemented
473D4⋊C8C22×C7311yescharacteristic, complemented
474D4⋊C8C22×C7311yescharacteristic, complemented
475C2×#41—21no—
476C2×#41—21no—
477C2×#41D4×C7312yes—
478C22×D4—22no—
479C22×D4—21no—
480C22×D4—21no—
481C22×D4D4×C7311yescharacteristic
482C23×C4—21no—
483C2×Q16—21no—
484C2×SD16—22no—
485C2×SD16—21no—
486C2×SD16—21no—
487C2×D8—21no—
488C2×D8—21no—
489C2×D8—21no—
490C2×D8—22no—
491C4⋊Q8C23×C7311yescharacteristic
492C4⋊Q8C23×C7311yescharacteristic
493#127—21no—
494#127C23×C7311yescharacteristic
495#127C23×C7311yescharacteristic
496#126—22no—
497#126—21no—
498#125—21no—
499#125D4×C7311yescharacteristic
500#124—22no—
501#124—21no—
502#124D4×C7311yescharacteristic
503#124D4×C7312yes—
504#123—22no—
505#123—22no—
506#123—22no—
507#123—21no—
508C22⋊Q8—21no—
509C22⋊Q8—22no—
510C22⋊Q8D4×C7311yescharacteristic
511#121—22no—
512#121—22no—
513#121—22no—
514#121—22no—
515#121—21no—
516#121—22no—
517#121—21no—
518#121—21no—
519#121—21no—
520#121—21no—
521#121—21no—
522#121—21no—
523#121—21no—
524#121—21no—
525#121D4×C7311yescharacteristic
526#120—22no—
527#120—22no—
528#120—22no—
529C4×Q8C23×C7311yescharacteristic
530C4×D4—22no—
531C4×D4—22no—
532C4×D4—22no—
533C4×D4—21no—
534C4×D4—21no—
535C4×D4—21no—
536C4×D4—21no—
537C4×D4—21no—
538C4×D4—21no—
539C4×D4—21no—
540C4×D4—21no—
541C4×D4—21no—
542C4×D4D4×C7311yescharacteristic
543C4×D4D4×C7311yescharacteristic
544C4×D4C23×C7311yescharacteristic
545C4×D4C23×C7311yescharacteristic
546C4×D4C23×C7311yescharacteristic
547#117—21no—
548#117—21no—
549#117—21no—
550C2×C4⋊C4—21no—
551C2×C4⋊C4D4×C7311yescharacteristic
552C2×C22⋊C4—22no—
553C2×C22⋊C4—22no—
554C2×C22⋊C4—21no—
555C2×C42C23×C7311yescharacteristic
556#107—21no—
557#107—21no—
558C4⋊C8—21no—
559C4⋊C8C23×C7311yescharacteristic
560C4⋊C8C23×C7311yescharacteristic
561C4⋊C8C23×C7311yescharacteristic
562C4⋊C8C23×C7311yescharacteristic
563#103—22no—
564#103—21no—
565#103—21no—
566#102—21no—
567#102—21no—
568#102—22no—
569#102—21no—
570#102—21no—
571#102—21no—
572#102—21no—
573C22⋊C8—21no—
574C22⋊C8—21no—
575C22⋊C8—21no—
576C4×C8—21no—
577C4×C8—21no—
578C4×C8C23×C7311yescharacteristic
579C4×C8C23×C7311yescharacteristic
580C24—22no—
581C24—21no—
582#41—81no—
583#41—81no—
584#41—81no—
585#41—81no—
586#41—82no—
587C2×Q8—21no—
588C2×Q8C2×D4×C7311yescharacteristic
589C2×Q8C2×D4×C7312yes—
590C2×D4—22no—
591C2×D4—22no—
592C2×D4—22no—
593C2×D4—21no—
594C2×D4—22no—
595C2×D4—22no—
596C2×D4—22no—
597C2×D4—22no—
598C2×D4—21no—
599C2×D4—21no—
600C2×D4—21no—
601C2×D4—21no—
602C2×D4—21no—
603C2×D4—21no—
604C2×D4—41no—
605C2×D4—42no—
606C2×D4—42no—
607C2×D4—41no—
608C2×D4—81no—
609C2×D4—81no—
610C2×D4—84no—
611C2×D4C2×D4×C7311yescharacteristic
612C2×D4C2×D4×C7311yescharacteristic
613C2×D4C2×D4×C7311yescharacteristic
614C2×D4C2×D4×C7312yes—
615C22×C4—22no—
616C22×C4—22no—
617C22×C4—21no—
618C22×C4—21no—
619C22×C4—21no—
620C22×C4—21no—
621C22×C4—21no—
622C22×C4—22no—
623C22×C4—21no—
624C22×C4—41no—
625C22×C4—81no—
626C22×C4—81no—
627C22×C4C2×D4×C7311yescharacteristic
628C22×C4C2×D4×C7311yescharacteristic
629C22×C4C2×D4×C7311yescharacteristic
630Q16—81no—
631SD16—81no—
632SD16—81no—
633SD16—82no—
634D8—42no—
635D8—42no—
636D8—81no—
637D8—82no—
638C2×C8—21no—
639C2×C8—21no—
640C2×C8—21no—
641C2×C8—21no—
642C2×C8—21no—
643C2×C8—21no—
644C4⋊C4—22no—
645C4⋊C4—22no—
646C4⋊C4—21no—
647C4⋊C4—21no—
648C4⋊C4—21no—
649C4⋊C4—21no—
650C4⋊C4—21no—
651C4⋊C4—21no—
652C4⋊C4—21no—
653C4⋊C4—21no—
654C4⋊C4—21no—
655C4⋊C4C2×D4×C7311yescharacteristic
656C4⋊C4C2×D4×C7311yescharacteristic
657C4⋊C4C2×D4×C7311yescharacteristic
658C4⋊C4C2×D4×C7311yescharacteristic
659C22⋊C4—22no—
660C22⋊C4—22no—
661C22⋊C4—22no—
662C22⋊C4—22no—
663C22⋊C4—22no—
664C22⋊C4—21no—
665C22⋊C4—21no—
666C22⋊C4—21no—
667C22⋊C4—21no—
668C22⋊C4—22no—
669C22⋊C4—21no—
670C22⋊C4—21no—
671C22⋊C4—22no—
672C22⋊C4—21no—
673C22⋊C4—21no—
674C22⋊C4—21no—
675C22⋊C4—41no—
676C22⋊C4—41no—
677C42—22no—
678C42—21no—
679C42C2×D4×C7311yescharacteristic
680C42C2×D4×C7311yescharacteristic
681C42C2×D4×C7311yescharacteristic
682C42C24×C7311yescharacteristic
683C23—21no—
684C23—21no—
685C23—21no—
686C23—22no—
687C23—42no—
688C23—42no—
689C23—44no—
690C23—41no—
691C23—81no—
692C23—82no—
693C23—82no—
694C23#120×C7311yescharacteristic
695Q8—21no—
696Q8—21no—
697Q8—42no—
698Q8—41no—
699Q8—41no—
700D4—21no—
701D4—21no—
702D4—21no—
703D4—21no—
704D4—21no—
705D4—42no—
706D4—42no—
707D4—42no—
708D4—44no—
709D4—42no—
710D4—44no—
711D4—41no—
712D4—41no—
713D4—41no—
714D4—41no—
715D4—41no—
716D4—41no—
717D4—41no—
718D4—41no—
719D4—82no—
720D4—82no—
721D4—82no—
722D4—82no—
723D4—82no—
724D4#135×C7312yes—
725C2×C4—21no—
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—21no—
729C2×C4—21no—
730C2×C4—21no—
731C2×C4—21no—
732C2×C4—22no—
733C2×C4—21no—
734C2×C4—21no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—41no—
739C2×C4—41no—
740C2×C4—41no—
741C2×C4—41no—
742C2×C4—41no—
743C2×C4—81no—
744C2×C4—81no—
745C2×C4—82no—
746C2×C4—82no—
747C2×C4—81no—
748C2×C4—82no—
749C2×C4—82no—
750C2×C4#120×C7311yescharacteristic
751C2×C4#120×C7311yescharacteristic
752C2×C4#120×C7311yescharacteristic
753C2×C4C22×D4×C7311yescharacteristic
754C2×C4C22×D4×C7311yescharacteristic
755C2×C4C22×D4×C7311yescharacteristic
756C8—41no—
757C8—41no—
758C8—41no—
759C8—41no—
760C8—41no—
761C8—41no—
762C22—21no—
763C22—22no—
764C22—21no—
765C22—21no—
766C22—41no—
767C22—41no—
768C22—41no—
769C22—41no—
770C22—42no—
771C22—41no—
772C22—42no—
773C22—41no—
774C22—42no—
775C22—41no—
776C22—41no—
777C22—84no—
778C22—81no—
779C22—81no—
780C22—81no—
781C22—164no—
782C22C2×#120×C7311yescharacteristic
783C4—21no—
784C4—21no—
785C4—21no—
786C4—21no—
787C4—41no—
788C4—41no—
789C4—41no—
790C4—41no—
791C4—41no—
792C4—42no—
793C4—81no—
794C4C2×#135×C7311yescharacteristic
795C4#575×C7311yescharacteristic
796C4#576×C7311yescharacteristic
797C4#576×C7311yescharacteristic
798C2—41no—
799C2—42no—
800C2—81no—
801C2—81no—
802C2—82no—
803C2—161no—
804C2C73×#300211yescharacteristic
805C2C73×#300811yescharacteristic
806C2C73×#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×#3212C2semidirect
3. C73×#3207C2semidirect
4. C73×#3100C2semidirect
5. C73×#1646C2semidirect
6. C73×#1644C2semidirect
7. C73×#1641C2semidirect
8. C73×#1639C2semidirect
9. C73×#1624C2semidirect
10. C73×#1622C2semidirect
11. C73×#1621C2semidirect
12. C73×#1619C2semidirect
13. C73×#1543C2semidirect
14. C73×#1482C2semidirect
15. C73×#1478C2semidirect
28. #532×C73C22semidirect
35. #493×C73C22semidirect
36. #492×C73C22semidirect
38. #487×C73C22semidirect
39. #486×C73C22semidirect
42. #474×C73C22semidirect
44. #462×C73C22semidirect
45. #461×C73C22semidirect
46. #460×C73C22semidirect
48. #459×C73C22semidirect
49. #459×C73C22semidirect
56. #431×C73C22semidirect
57. #431×C73C22semidirect
58. #431×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
394. #18866C73direct (N × H)
404. #3519C2×C73semidirect
405. #3212C2×C73semidirect
406. #3207C2×C73semidirect
407. #3100C2×C73semidirect
408. #1646C2×C73semidirect
409. #1644C2×C73semidirect
410. #1641C2×C73semidirect
411. #1639C2×C73semidirect
412. #1624C2×C73semidirect
413. #1622C2×C73semidirect
414. #1621C2×C73semidirect
415. #1619C2×C73semidirect
416. #1543C2×C73semidirect
417. #1482C2×C73semidirect
418. #1478C2×C73semidirect
419. C73#18866direct (N × H)
432. #532C22×C73semidirect
439. #493C22×C73semidirect
440. #492C22×C73semidirect
442. #487C22×C73semidirect
443. #486C22×C73semidirect
446. #474C22×C73semidirect
448. #462C22×C73semidirect
449. #461C22×C73semidirect
450. #460C22×C73semidirect
452. #459C22×C73semidirect
453. #459C22×C73semidirect
460. #431C22×C73semidirect
461. #431C22×C73semidirect
462. #431C22×C73semidirect
463. #333C22×C73semidirect
464. #333C22×C73semidirect
465. #331C22×C73semidirect
466. #331C22×C73semidirect
467. Q8⋊C8C22×C73semidirect
468. Q8⋊C8C22×C73semidirect
471. D4⋊C8C22×C73semidirect
472. D4⋊C8C22×C73semidirect
473. D4⋊C8C22×C73semidirect
474. 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×#32122
C73×#32072
C73×#31002
C73×#16462
C73×#16442
C73×#16412
C73×#16392
C73×#16242
C73×#16222
C73×#16212
C73×#16192
C73×#15432
C73×#14822
C73×#14782
#1886673