Finite Group Databasebeta

← C137×#18638 #46868024

Subgroups — C137×#18638 #46868024

Order 35072.

956 conjugacy classes of subgroups.

The subgroup lattice has 772 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3520×C137C211yesmaximal, characteristic, complemented
2#3247×C137C211yesmaximal, characteristic, complemented
3#3131×C137C211yesmaximal, characteristic, complemented
4#3109×C137C211yesmaximal, characteristic, complemented
5#1638×C137C211yesmaximal, characteristic, complemented
6#1637×C137C211yesmaximal, characteristic, complemented
7#1635×C137C211yesmaximal, characteristic, complemented
8#1635×C137C211yesmaximal, characteristic, complemented
9#1628×C137C211yesmaximal, characteristic, complemented
10#1627×C137C211yesmaximal, characteristic, complemented
11#1625×C137C211yesmaximal, characteristic, complemented
12#1625×C137C211yesmaximal, characteristic, complemented
13#1552×C137C211yesmaximal, characteristic, complemented
14#1494×C137C211yesmaximal, characteristic, complemented
15C2×D4⋊C8×C137C211yesmaximal, characteristic, complemented
16#556×C137C2211yescharacteristic
17#554×C137—21no—
18#552×C137—21no—
19#551×C137—22no—
20D4×Q8×C137C2211yescharacteristic
21#548×C137—21no—
22#547×C137C2211yescharacteristic
23#547×C137C2211yescharacteristic
24#546×C137—21no—
25#542×C137—21no—
26#539×C137—22no—
27#533×C137C2211yescharacteristic
28#532×C137C2211yescharacteristic
29#529×C137C2211yescharacteristic
30#525×C137—21no—
31C2×C22⋊Q8×C137—21no—
32#520×C137—21no—
33C2×C4×D4×C137C2211yescharacteristic
34#488×C137—22no—
35#487×C137C2211yescharacteristic, complemented
36#487×C137C2211yescharacteristic, complemented
37#486×C137C2211yescharacteristic, complemented
38#486×C137C2211yescharacteristic, complemented
39#481×C137—21no—
40#478×C137—21no—
41#477×C137C2211yescharacteristic, complemented
42#476×C137C2211yescharacteristic
43#476×C137C2211yescharacteristic
44#476×C137C2211yescharacteristic, complemented
45#466×C137—21no—
46#465×C137—21no—
47#463×C137—21no—
48#460×C137C2211yescharacteristic, complemented
49#459×C137C2211yescharacteristic
50#459×C137C2211yescharacteristic
51#459×C137C2211yescharacteristic, complemented
52#447×C137—21no—
53#442×C137—21no—
54#442×C137—21no—
55#432×C137C2211yescharacteristic
56C2×C4⋊C8×C137C2211yescharacteristic
57#416×C137—22no—
58C2×C4×C8×C137C2211yescharacteristic
59#332×C137C2211yescharacteristic, complemented
60#332×C137C2211yescharacteristic, complemented
61#332×C137C2211yescharacteristic, complemented
62#332×C137C2211yescharacteristic, complemented
63Q8⋊C8×C137C2211yescharacteristic, complemented
64Q8⋊C8×C137C2211yescharacteristic, complemented
65D4⋊C8×C137C2211yescharacteristic
66D4⋊C8×C137C2211yescharacteristic
67D4⋊C8×C137C2211yescharacteristic
68D4⋊C8×C137C2211yescharacteristic
69D4⋊C8×C137C2211yescharacteristic, complemented
70D4⋊C8×C137C2211yescharacteristic, complemented
71C2×#41×C137—21no—
72C2×#41×C137—21no—
73C2×#41×C137—21no—
74C22×Q8×C137—21no—
75C22×D4×C137D411yescharacteristic
76C23×C4×C137—21no—
77C2×SD16×C137—21no—
78C2×D8×C137—21no—
79C2×D8×C137—21no—
80C2×D8×C137—21no—
81C22×C8×C137—21no—
82C22×C8×C137—21no—
83C4⋊Q8×C137—21no—
84C4⋊Q8×C137C2311yescharacteristic
85C4⋊Q8×C137C2311yescharacteristic
86C4⋊Q8×C137C2311yescharacteristic
87#127×C137C2311yescharacteristic
88#126×C137—22no—
89#126×C137—22no—
90#126×C137—21no—
91#125×C137—22no—
92#125×C137D411yescharacteristic
93#125×C137D412yes—
94#124×C137—22no—
95#124×C137—21no—
96#124×C137—21no—
97#124×C137D411yescharacteristic
98#123×C137—22no—
99#123×C137—22no—
100#123×C137—21no—
101#123×C137—22no—
102#123×C137—22no—
103C22⋊Q8×C137—22no—
104C22⋊Q8×C137—22no—
105C22⋊Q8×C137—22no—
106C22⋊Q8×C137—21no—
107C22⋊Q8×C137—21no—
108C22⋊Q8×C137—21no—
109C22⋊Q8×C137—21no—
110C22⋊Q8×C137—21no—
111C22⋊Q8×C137—22no—
112C22⋊Q8×C137—21no—
113C22⋊Q8×C137D411yescharacteristic
114#121×C137—22no—
115#121×C137—21no—
116#121×C137—21no—
117#121×C137—21no—
118#121×C137—21no—
119#121×C137D411yescharacteristic
120#120×C137—22no—
121C4×Q8×C137—21no—
122C4×Q8×C137—21no—
123C4×Q8×C137—21no—
124C4×Q8×C137C2311yescharacteristic
125C4×D4×C137—22no—
126C4×D4×C137—22no—
127C4×D4×C137—22no—
128C4×D4×C137—21no—
129C4×D4×C137—21no—
130C4×D4×C137—21no—
131C4×D4×C137—21no—
132C4×D4×C137—21no—
133C4×D4×C137—21no—
134C4×D4×C137D411yescharacteristic
135C4×D4×C137D411yescharacteristic
136C4×D4×C137C2311yescharacteristic
137C4×D4×C137C2311yescharacteristic
138C4×D4×C137C2311yescharacteristic
139#117×C137—22no—
140#117×C137—21no—
141#117×C137—21no—
142#117×C137D412yes—
143C2×C4⋊C4×C137—22no—
144C2×C4⋊C4×C137—21no—
145C2×C4⋊C4×C137—21no—
146C2×C4⋊C4×C137D411yescharacteristic
147C2×C22⋊C4×C137—22no—
148C2×C22⋊C4×C137—21no—
149C2×C42×C137C2311yescharacteristic
150#107×C137—21no—
151#106×C137—21no—
152#106×C137—21no—
153#106×C137—21no—
154C4⋊C8×C137—21no—
155C4⋊C8×C137C2311yescharacteristic
156C4⋊C8×C137C2311yescharacteristic
157C4⋊C8×C137C2311yescharacteristic
158C4⋊C8×C137C2311yescharacteristic
159#103×C137—21no—
160#103×C137—22no—
161#103×C137—22no—
162#102×C137—21no—
163#102×C137—21no—
164#102×C137—21no—
165#102×C137—22no—
166#102×C137—22no—
167#102×C137—21no—
168#102×C137—21no—
169#102×C137—21no—
170#102×C137—21no—
171C22⋊C8×C137—21no—
172#97×C137—21no—
173C4×C8×C137—21no—
174C4×C8×C137C2311yescharacteristic
175C4×C8×C137C2311yescharacteristic
176C24×C137—21no—
177#41×C137—44no—
178#41×C137—42no—
179#41×C137—42no—
180#41×C137—81no—
181#41×C137—81no—
182C2×Q8×C137—22no—
183C2×Q8×C137—21no—
184C2×Q8×C137—21no—
185C2×Q8×C137—21no—
186C2×Q8×C137—81no—
187C2×Q8×C137—81no—
188C2×Q8×C137C2×D411yescharacteristic
189C2×D4×C137—22no—
190C2×D4×C137—22no—
191C2×D4×C137—21no—
192C2×D4×C137—22no—
193C2×D4×C137—21no—
194C2×D4×C137—21no—
195C2×D4×C137—21no—
196C2×D4×C137—21no—
197C2×D4×C137—41no—
198C2×D4×C137—41no—
199C2×D4×C137C2×D411yescharacteristic
200C2×D4×C137C2×D411yescharacteristic
201C2×D4×C137C2×D411yescharacteristic
202C22×C4×C137—22no—
203C22×C4×C137—22no—
204C22×C4×C137—22no—
205C22×C4×C137—21no—
206C22×C4×C137—21no—
207C22×C4×C137—21no—
208C22×C4×C137—21no—
209C22×C4×C137—21no—
210C22×C4×C137—21no—
211C22×C4×C137—41no—
212C22×C4×C137—81no—
213C22×C4×C137—81no—
214C22×C4×C137C2×D411yescharacteristic
215C22×C4×C137C2×D411yescharacteristic
216C22×C4×C137C2×D411yescharacteristic
217SD16×C137—81no—
218D8×C137—42no—
219D8×C137—42no—
220D8×C137—81no—
221C2×C8×C137—21no—
222C2×C8×C137—21no—
223C2×C8×C137—21no—
224C2×C8×C137—21no—
225C2×C8×C137—21no—
226C2×C8×C137—21no—
227C2×C8×C137—42no—
228C2×C8×C137—81no—
229C4⋊C4×C137—22no—
230C4⋊C4×C137—22no—
231C4⋊C4×C137—22no—
232C4⋊C4×C137—22no—
233C4⋊C4×C137—21no—
234C4⋊C4×C137—22no—
235C4⋊C4×C137—21no—
236C4⋊C4×C137—21no—
237C4⋊C4×C137—21no—
238C4⋊C4×C137—22no—
239C4⋊C4×C137—21no—
240C4⋊C4×C137—21no—
241C4⋊C4×C137—21no—
242C4⋊C4×C137—21no—
243C4⋊C4×C137—21no—
244C4⋊C4×C137C2×D412yes—
245C4⋊C4×C137C2×D412yes—
246C4⋊C4×C137C2×D411yescharacteristic
247C4⋊C4×C137C2×D411yescharacteristic
248C4⋊C4×C137C2×D411yescharacteristic
249C4⋊C4×C137C2×D411yescharacteristic
250C22⋊C4×C137—22no—
251C22⋊C4×C137—22no—
252C22⋊C4×C137—22no—
253C22⋊C4×C137—22no—
254C22⋊C4×C137—22no—
255C22⋊C4×C137—21no—
256C22⋊C4×C137—22no—
257C22⋊C4×C137—21no—
258C22⋊C4×C137—21no—
259C22⋊C4×C137—21no—
260C22⋊C4×C137—21no—
261C22⋊C4×C137—21no—
262C22⋊C4×C137—21no—
263C22⋊C4×C137—21no—
264C22⋊C4×C137—21no—
265C22⋊C4×C137—41no—
266C22⋊C4×C137—41no—
267C42×C137—22no—
268C42×C137—22no—
269C42×C137—21no—
270C42×C137C2×D411yescharacteristic
271C42×C137C2×D411yescharacteristic
272C42×C137C2×D411yescharacteristic
273C42×C137C2411yescharacteristic
274C23×C137—21no—
275C23×C137—21no—
276C23×C137—21no—
277C23×C137—42no—
278C23×C137—42no—
279C23×C137—41no—
280C23×C137—81no—
281C23×C137#12011yescharacteristic
282Q8×C137—21no—
283Q8×C137—21no—
284Q8×C137—42no—
285Q8×C137—41no—
286Q8×C137—41no—
287Q8×C137—41no—
288Q8×C137—41no—
289Q8×C137—82no—
290D4×C137—21no—
291D4×C137—21no—
292D4×C137—21no—
293D4×C137—21no—
294D4×C137—21no—
295D4×C137—42no—
296D4×C137—42no—
297D4×C137—44no—
298D4×C137—42no—
299D4×C137—41no—
300D4×C137—41no—
301D4×C137—41no—
302D4×C137—41no—
303D4×C137—82no—
304D4×C137—82no—
305D4×C137#13512yes—
306C2×C4×C137—22no—
307C2×C4×C137—21no—
308C2×C4×C137—21no—
309C2×C4×C137—21no—
310C2×C4×C137—21no—
311C2×C4×C137—21no—
312C2×C4×C137—22no—
313C2×C4×C137—21no—
314C2×C4×C137—21no—
315C2×C4×C137—22no—
316C2×C4×C137—21no—
317C2×C4×C137—21no—
318C2×C4×C137—44no—
319C2×C4×C137—41no—
320C2×C4×C137—41no—
321C2×C4×C137—41no—
322C2×C4×C137—41no—
323C2×C4×C137—41no—
324C2×C4×C137—41no—
325C2×C4×C137—41no—
326C2×C4×C137—81no—
327C2×C4×C137—81no—
328C2×C4×C137—82no—
329C2×C4×C137—81no—
330C2×C4×C137—82no—
331C2×C4×C137—82no—
332C2×C4×C137#12011yescharacteristic
333C2×C4×C137#12011yescharacteristic
334C2×C4×C137#12011yescharacteristic
335C2×C4×C137C22×D411yescharacteristic
336C2×C4×C137C22×D411yescharacteristic
337C2×C4×C137C22×D411yescharacteristic
338C8×C137—41no—
339C8×C137—41no—
340C8×C137—41no—
341C8×C137—41no—
342C8×C137—41no—
343C8×C137—41no—
344C22×C137—21no—
345C22×C137—21no—
346C22×C137—22no—
347C22×C137—41no—
348C22×C137—41no—
349C22×C137—41no—
350C22×C137—41no—
351C22×C137—41no—
352C22×C137—41no—
353C22×C137—41no—
354C22×C137—41no—
355C22×C137—84no—
356C22×C137—81no—
357C22×C137—81no—
358C22×C137—81no—
359C22×C137#45412yes—
360C22×C137C2×#12011yescharacteristic
361C4×C137—21no—
362C4×C137—21no—
363C4×C137—21no—
364C4×C137—21no—
365C4×C137—41no—
366C4×C137—42no—
367C4×C137—41no—
368C4×C137—41no—
369C4×C137—42no—
370C4×C137—41no—
371C4×C137—41no—
372C4×C137—81no—
373C4×C137C2×#13511yescharacteristic
374C4×C137#57511yescharacteristic
375C4×C137#57611yescharacteristic
376C4×C137#57711yescharacteristic
377C2×C137—22no—
378C2×C137—42no—
379C2×C137—81no—
380C2×C137—81no—
381C2×C137—161no—
382C2×C137#300211yescharacteristic
383C2×C137#301211yescharacteristic
384C2×C137C2×#45411yescharacteristic
385#18638C13711yesmaximal, characteristic, direct product factor, Sylow
386C137#1863811yescharacteristic, direct product factor, Sylow
387#3520C2×C13711yescharacteristic, complemented
388#3247C2×C13711yescharacteristic, complemented
389#3131C2×C13711yescharacteristic, complemented
390#3109C2×C13711yescharacteristic, complemented
391#1638C2×C13711yescharacteristic, complemented
392#1637C2×C13711yescharacteristic, complemented
393#1635C2×C13711yescharacteristic, complemented
394#1635C2×C13711yescharacteristic, complemented
395#1628C2×C13711yescharacteristic, complemented
396#1627C2×C13711yescharacteristic, complemented
397#1625C2×C13711yescharacteristic, complemented
398#1625C2×C13711yescharacteristic, complemented
399#1552C2×C13711yescharacteristic, complemented
400#1494C2×C13711yescharacteristic, complemented
401C2×D4⋊C8C2×C13711yescharacteristic, complemented
402#556C22×C13711yescharacteristic
403#554—21no—
404#552—21no—
405#551—22no—
406D4×Q8C22×C13711yescharacteristic
407#548—21no—
408#547C22×C13711yescharacteristic
409#547C22×C13711yescharacteristic
410#546—21no—
411#542—21no—
412#539—22no—
413#533C22×C13711yescharacteristic
414#532C22×C13711yescharacteristic
415#529C22×C13711yescharacteristic
416#525—21no—
417C2×C22⋊Q8—21no—
418#520—21no—
419C2×C4×D4C22×C13711yescharacteristic
420#488—22no—
421#487C22×C13711yescharacteristic, complemented
422#487C22×C13711yescharacteristic, complemented
423#486C22×C13711yescharacteristic, complemented
424#486C22×C13711yescharacteristic, complemented
425#481—21no—
426#478—21no—
427#477C22×C13711yescharacteristic, complemented
428#476C22×C13711yescharacteristic
429#476C22×C13711yescharacteristic
430#476C22×C13711yescharacteristic, complemented
431#466—21no—
432#465—21no—
433#463—21no—
434#460C22×C13711yescharacteristic, complemented
435#459C22×C13711yescharacteristic
436#459C22×C13711yescharacteristic
437#459C22×C13711yescharacteristic, complemented
438#447—21no—
439#442—21no—
440#442—21no—
441#432C22×C13711yescharacteristic
442C2×C4⋊C8C22×C13711yescharacteristic
443#416—22no—
444C2×C4×C8C22×C13711yescharacteristic
445#332C22×C13711yescharacteristic, complemented
446#332C22×C13711yescharacteristic, complemented
447#332C22×C13711yescharacteristic, complemented
448#332C22×C13711yescharacteristic, complemented
449Q8⋊C8C22×C13711yescharacteristic, complemented
450Q8⋊C8C22×C13711yescharacteristic, complemented
451D4⋊C8C22×C13711yescharacteristic
452D4⋊C8C22×C13711yescharacteristic
453D4⋊C8C22×C13711yescharacteristic
454D4⋊C8C22×C13711yescharacteristic
455D4⋊C8C22×C13711yescharacteristic, complemented
456D4⋊C8C22×C13711yescharacteristic, complemented
457C2×#41—21no—
458C2×#41—21no—
459C2×#41—21no—
460C22×Q8—21no—
461C22×D4D4×C13711yescharacteristic
462C23×C4—21no—
463C2×SD16—21no—
464C2×D8—21no—
465C2×D8—21no—
466C2×D8—21no—
467C22×C8—21no—
468C22×C8—21no—
469C4⋊Q8—21no—
470C4⋊Q8C23×C13711yescharacteristic
471C4⋊Q8C23×C13711yescharacteristic
472C4⋊Q8C23×C13711yescharacteristic
473#127C23×C13711yescharacteristic
474#126—22no—
475#126—22no—
476#126—21no—
477#125—22no—
478#125D4×C13711yescharacteristic
479#125D4×C13712yes—
480#124—22no—
481#124—21no—
482#124—21no—
483#124D4×C13711yescharacteristic
484#123—22no—
485#123—22no—
486#123—21no—
487#123—22no—
488#123—22no—
489C22⋊Q8—22no—
490C22⋊Q8—22no—
491C22⋊Q8—22no—
492C22⋊Q8—21no—
493C22⋊Q8—21no—
494C22⋊Q8—21no—
495C22⋊Q8—21no—
496C22⋊Q8—21no—
497C22⋊Q8—22no—
498C22⋊Q8—21no—
499C22⋊Q8D4×C13711yescharacteristic
500#121—22no—
501#121—21no—
502#121—21no—
503#121—21no—
504#121—21no—
505#121D4×C13711yescharacteristic
506#120—22no—
507C4×Q8—21no—
508C4×Q8—21no—
509C4×Q8—21no—
510C4×Q8C23×C13711yescharacteristic
511C4×D4—22no—
512C4×D4—22no—
513C4×D4—22no—
514C4×D4—21no—
515C4×D4—21no—
516C4×D4—21no—
517C4×D4—21no—
518C4×D4—21no—
519C4×D4—21no—
520C4×D4D4×C13711yescharacteristic
521C4×D4D4×C13711yescharacteristic
522C4×D4C23×C13711yescharacteristic
523C4×D4C23×C13711yescharacteristic
524C4×D4C23×C13711yescharacteristic
525#117—22no—
526#117—21no—
527#117—21no—
528#117D4×C13712yes—
529C2×C4⋊C4—22no—
530C2×C4⋊C4—21no—
531C2×C4⋊C4—21no—
532C2×C4⋊C4D4×C13711yescharacteristic
533C2×C22⋊C4—22no—
534C2×C22⋊C4—21no—
535C2×C42C23×C13711yescharacteristic
536#107—21no—
537#106—21no—
538#106—21no—
539#106—21no—
540C4⋊C8—21no—
541C4⋊C8C23×C13711yescharacteristic
542C4⋊C8C23×C13711yescharacteristic
543C4⋊C8C23×C13711yescharacteristic
544C4⋊C8C23×C13711yescharacteristic
545#103—21no—
546#103—22no—
547#103—22no—
548#102—21no—
549#102—21no—
550#102—21no—
551#102—22no—
552#102—22no—
553#102—21no—
554#102—21no—
555#102—21no—
556#102—21no—
557C22⋊C8—21no—
558#97—21no—
559C4×C8—21no—
560C4×C8C23×C13711yescharacteristic
561C4×C8C23×C13711yescharacteristic
562C24—21no—
563#41—44no—
564#41—42no—
565#41—42no—
566#41—81no—
567#41—81no—
568C2×Q8—22no—
569C2×Q8—21no—
570C2×Q8—21no—
571C2×Q8—21no—
572C2×Q8—81no—
573C2×Q8—81no—
574C2×Q8C2×D4×C13711yescharacteristic
575C2×D4—22no—
576C2×D4—22no—
577C2×D4—21no—
578C2×D4—22no—
579C2×D4—21no—
580C2×D4—21no—
581C2×D4—21no—
582C2×D4—21no—
583C2×D4—41no—
584C2×D4—41no—
585C2×D4C2×D4×C13711yescharacteristic
586C2×D4C2×D4×C13711yescharacteristic
587C2×D4C2×D4×C13711yescharacteristic
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—22no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—41no—
598C22×C4—81no—
599C22×C4—81no—
600C22×C4C2×D4×C13711yescharacteristic
601C22×C4C2×D4×C13711yescharacteristic
602C22×C4C2×D4×C13711yescharacteristic
603SD16—81no—
604D8—42no—
605D8—42no—
606D8—81no—
607C2×C8—21no—
608C2×C8—21no—
609C2×C8—21no—
610C2×C8—21no—
611C2×C8—21no—
612C2×C8—21no—
613C2×C8—42no—
614C2×C8—81no—
615C4⋊C4—22no—
616C4⋊C4—22no—
617C4⋊C4—22no—
618C4⋊C4—22no—
619C4⋊C4—21no—
620C4⋊C4—22no—
621C4⋊C4—21no—
622C4⋊C4—21no—
623C4⋊C4—21no—
624C4⋊C4—22no—
625C4⋊C4—21no—
626C4⋊C4—21no—
627C4⋊C4—21no—
628C4⋊C4—21no—
629C4⋊C4—21no—
630C4⋊C4C2×D4×C13712yes—
631C4⋊C4C2×D4×C13712yes—
632C4⋊C4C2×D4×C13711yescharacteristic
633C4⋊C4C2×D4×C13711yescharacteristic
634C4⋊C4C2×D4×C13711yescharacteristic
635C4⋊C4C2×D4×C13711yescharacteristic
636C22⋊C4—22no—
637C22⋊C4—22no—
638C22⋊C4—22no—
639C22⋊C4—22no—
640C22⋊C4—22no—
641C22⋊C4—21no—
642C22⋊C4—22no—
643C22⋊C4—21no—
644C22⋊C4—21no—
645C22⋊C4—21no—
646C22⋊C4—21no—
647C22⋊C4—21no—
648C22⋊C4—21no—
649C22⋊C4—21no—
650C22⋊C4—21no—
651C22⋊C4—41no—
652C22⋊C4—41no—
653C42—22no—
654C42—22no—
655C42—21no—
656C42C2×D4×C13711yescharacteristic
657C42C2×D4×C13711yescharacteristic
658C42C2×D4×C13711yescharacteristic
659C42C24×C13711yescharacteristic
660C23—21no—
661C23—21no—
662C23—21no—
663C23—42no—
664C23—42no—
665C23—41no—
666C23—81no—
667C23#120×C13711yescharacteristic
668Q8—21no—
669Q8—21no—
670Q8—42no—
671Q8—41no—
672Q8—41no—
673Q8—41no—
674Q8—41no—
675Q8—82no—
676D4—21no—
677D4—21no—
678D4—21no—
679D4—21no—
680D4—21no—
681D4—42no—
682D4—42no—
683D4—44no—
684D4—42no—
685D4—41no—
686D4—41no—
687D4—41no—
688D4—41no—
689D4—82no—
690D4—82no—
691D4#135×C13712yes—
692C2×C4—22no—
693C2×C4—21no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—21no—
698C2×C4—22no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—22no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—44no—
705C2×C4—41no—
706C2×C4—41no—
707C2×C4—41no—
708C2×C4—41no—
709C2×C4—41no—
710C2×C4—41no—
711C2×C4—41no—
712C2×C4—81no—
713C2×C4—81no—
714C2×C4—82no—
715C2×C4—81no—
716C2×C4—82no—
717C2×C4—82no—
718C2×C4#120×C13711yescharacteristic
719C2×C4#120×C13711yescharacteristic
720C2×C4#120×C13711yescharacteristic
721C2×C4C22×D4×C13711yescharacteristic
722C2×C4C22×D4×C13711yescharacteristic
723C2×C4C22×D4×C13711yescharacteristic
724C8—41no—
725C8—41no—
726C8—41no—
727C8—41no—
728C8—41no—
729C8—41no—
730C22—21no—
731C22—21no—
732C22—22no—
733C22—41no—
734C22—41no—
735C22—41no—
736C22—41no—
737C22—41no—
738C22—41no—
739C22—41no—
740C22—41no—
741C22—84no—
742C22—81no—
743C22—81no—
744C22—81no—
745C22#454×C13712yes—
746C22C2×#120×C13711yescharacteristic
747C4—21no—
748C4—21no—
749C4—21no—
750C4—21no—
751C4—41no—
752C4—42no—
753C4—41no—
754C4—41no—
755C4—42no—
756C4—41no—
757C4—41no—
758C4—81no—
759C4C2×#135×C13711yescharacteristic
760C4#575×C13711yescharacteristic
761C4#576×C13711yescharacteristic
762C4#577×C13711yescharacteristic
763C2—22no—
764C2—42no—
765C2—81no—
766C2—81no—
767C2—161no—
768C2#3002×C13711yescharacteristic
769C2#3012×C13711yescharacteristic
770C2C2×#454×C13711yescharacteristic
subgroupG/H
center, socleC22×C137C2×#120
commutator, Frattini, cosocleC42C24×C137
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C137 ◁ C2×C42×C137 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #3520×C137C2semidirect
2. #3247×C137C2semidirect
3. #3131×C137C2semidirect
4. #3109×C137C2semidirect
5. #1638×C137C2semidirect
6. #1637×C137C2semidirect
7. #1635×C137C2semidirect
8. #1635×C137C2semidirect
9. #1628×C137C2semidirect
10. #1627×C137C2semidirect
11. #1625×C137C2semidirect
12. #1625×C137C2semidirect
13. #1552×C137C2semidirect
14. #1494×C137C2semidirect
15. C2×D4⋊C8×C137C2semidirect
35. #487×C137C22semidirect
36. #487×C137C22semidirect
37. #486×C137C22semidirect
38. #486×C137C22semidirect
41. #477×C137C22semidirect
44. #476×C137C22semidirect
48. #460×C137C22semidirect
51. #459×C137C22semidirect
59. #332×C137C22semidirect
60. #332×C137C22semidirect
61. #332×C137C22semidirect
62. #332×C137C22semidirect
63. Q8⋊C8×C137C22semidirect
64. Q8⋊C8×C137C22semidirect
69. D4⋊C8×C137C22semidirect
70. D4⋊C8×C137C22semidirect
385. #18638C137direct (N × H)
386. C137#18638direct (N × H)
387. #3520C2×C137semidirect
388. #3247C2×C137semidirect
389. #3131C2×C137semidirect
390. #3109C2×C137semidirect
391. #1638C2×C137semidirect
392. #1637C2×C137semidirect
393. #1635C2×C137semidirect
394. #1635C2×C137semidirect
395. #1628C2×C137semidirect
396. #1627C2×C137semidirect
397. #1625C2×C137semidirect
398. #1625C2×C137semidirect
399. #1552C2×C137semidirect
400. #1494C2×C137semidirect
401. C2×D4⋊C8C2×C137semidirect
421. #487C22×C137semidirect
422. #487C22×C137semidirect
423. #486C22×C137semidirect
424. #486C22×C137semidirect
427. #477C22×C137semidirect
430. #476C22×C137semidirect
434. #460C22×C137semidirect
437. #459C22×C137semidirect
445. #332C22×C137semidirect
446. #332C22×C137semidirect
447. #332C22×C137semidirect
448. #332C22×C137semidirect
449. Q8⋊C8C22×C137semidirect
450. Q8⋊C8C22×C137semidirect
455. D4⋊C8C22×C137semidirect
456. D4⋊C8C22×C137semidirect

Maximal subgroups

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

subgroupindex
#3520×C1372
#3247×C1372
#3131×C1372
#3109×C1372
#1638×C1372
#1637×C1372
#1635×C1372
#1628×C1372
#1627×C1372
#1625×C1372
#1552×C1372
#1494×C1372
C2×D4⋊C8×C1372
#18638137