Finite Group Databasebeta

← C149×#18739 #49197688

Subgroups — C149×#18739 #49197688

Order 38144.

938 conjugacy classes of subgroups.

The subgroup lattice has 776 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3546×C149C211yesmaximal, characteristic
2#3246×C149C211yesmaximal, characteristic, complemented
3#3233×C149C211yesmaximal, characteristic, complemented
4#3182×C149C211yesmaximal, characteristic, complemented
5#1650×C149C211yesmaximal, characteristic, complemented
6#1647×C149C211yesmaximal, characteristic, complemented
7#1642×C149C211yesmaximal, characteristic, complemented
8#1639×C149C211yesmaximal, characteristic, complemented
9#1638×C149C211yesmaximal, characteristic, complemented
10#1635×C149C211yesmaximal, characteristic, complemented
11#1631×C149C211yesmaximal, characteristic, complemented
12#1629×C149C211yesmaximal, characteristic, complemented
13#1540×C149C211yesmaximal, characteristic, complemented
14#1484×C149C211yesmaximal, characteristic, complemented
15#1483×C149C211yesmaximal, characteristic, complemented
16#560×C149—22no—
17#556×C149C2211yescharacteristic
18#553×C149—21no—
19#550×C149—21no—
20#550×C149C2211yescharacteristic
21#547×C149C2211yescharacteristic
22#546×C149—21no—
23#546×C149—21no—
24D42×C149C2211yescharacteristic
25#542×C149—21no—
26#538×C149—22no—
27#537×C149—21no—
28#535×C149—21no—
29#535×C149—21no—
30#533×C149C2211yescharacteristic, complemented
31#532×C149C2211yescharacteristic
32#532×C149C2211yescharacteristic
33#529×C149C2211yescharacteristic
34#500×C149C2211yescharacteristic, complemented
35#499×C149—21no—
36#492×C149C2211yescharacteristic
37#488×C149—21no—
38#487×C149C2211yescharacteristic, complemented
39#486×C149C2211yescharacteristic
40#485×C149—21no—
41#482×C149—21no—
42#477×C149C2211yescharacteristic, complemented
43#476×C149C2211yescharacteristic
44#476×C149C2211yescharacteristic
45#476×C149C2211yescharacteristic, complemented
46#475×C149—21no—
47#475×C149C2211yescharacteristic, complemented
48#474×C149C2211yescharacteristic
49#468×C149—22no—
50#465×C149—21no—
51#465×C149—21no—
52#461×C149C2211yescharacteristic
53#461×C149C2211yescharacteristic, complemented
54#460×C149—21no—
55#440×C149—22no—
56#431×C149C2211yescharacteristic, complemented
57C2×C4⋊C8×C149C2211yescharacteristic, complemented
58C4×M16×C149C2211yescharacteristic, complemented
59#332×C149C2211yescharacteristic, complemented
60#332×C149C2211yescharacteristic, complemented
61#331×C149C2211yescharacteristic
62#331×C149C2211yescharacteristic
63Q8⋊C8×C149C2211yescharacteristic, complemented
64Q8⋊C8×C149C2211yescharacteristic, complemented
65D4⋊C8×C149C2211yescharacteristic
66D4⋊C8×C149C2211yescharacteristic
67D4⋊C8×C149C2211yescharacteristic
68D4⋊C8×C149C2211yescharacteristic
69D4⋊C8×C149C2211yescharacteristic, complemented
70D4⋊C8×C149C2211yescharacteristic, complemented
71C2×#41×C149—21no—
72C2×#41×C149—21no—
73C2×#41×C149—21no—
74C2×#41×C149—21no—
75C22×D4×C149—21no—
76C22×D4×C149—21no—
77C2×SD16×C149—22no—
78C2×SD16×C149—21no—
79C2×SD16×C149—21no—
80C2×M16×C149—21no—
81C22×C8×C149—21no—
82C4⋊Q8×C149D411yescharacteristic
83C4⋊Q8×C149C2311yescharacteristic
84C4⋊Q8×C149C2311yescharacteristic
85C4⋊Q8×C149C2311yescharacteristic
86#127×C149—22no—
87#127×C149—21no—
88#127×C149D411yescharacteristic
89#127×C149C2311yescharacteristic
90#126×C149—22no—
91#126×C149—22no—
92#126×C149—21no—
93#125×C149—21no—
94#125×C149D411yescharacteristic
95#124×C149—22no—
96#124×C149—21no—
97#124×C149—21no—
98#124×C149—21no—
99#124×C149D411yescharacteristic
100#123×C149—22no—
101#123×C149—22no—
102#123×C149—21no—
103#123×C149—22no—
104C22⋊Q8×C149—22no—
105C22⋊Q8×C149—21no—
106C22⋊Q8×C149—21no—
107C22⋊Q8×C149—21no—
108C22⋊Q8×C149—21no—
109C22⋊Q8×C149D411yescharacteristic
110#121×C149—22no—
111#121×C149—22no—
112#121×C149—22no—
113#121×C149—22no—
114#121×C149—22no—
115#121×C149—21no—
116#121×C149—22no—
117#121×C149—21no—
118#121×C149—21no—
119#121×C149—21no—
120#121×C149—21no—
121#121×C149—21no—
122#121×C149D411yescharacteristic
123#121×C149D411yescharacteristic
124#121×C149D412yes—
125#121×C149D411yescharacteristic
126#120×C149—22no—
127#120×C149—22no—
128#120×C149—22no—
129#120×C149—22no—
130C4×Q8×C149—21no—
131C4×Q8×C149—21no—
132C4×Q8×C149—21no—
133C4×Q8×C149C2311yescharacteristic
134C4×D4×C149—22no—
135C4×D4×C149—21no—
136C4×D4×C149—21no—
137C4×D4×C149—21no—
138C4×D4×C149—21no—
139C4×D4×C149D412yes—
140C4×D4×C149C2311yescharacteristic
141C4×D4×C149C2311yescharacteristic
142C4×D4×C149C2311yescharacteristic
143#117×C149—21no—
144#117×C149—21no—
145#117×C149—21no—
146C2×C4⋊C4×C149—21no—
147C2×C22⋊C4×C149—22no—
148C2×C42×C149C2311yescharacteristic
149#107×C149—22no—
150#107×C149—21no—
151#107×C149—21no—
152#106×C149—21no—
153#106×C149—21no—
154#106×C149—21no—
155#106×C149—21no—
156C4⋊C8×C149—21no—
157C4⋊C8×C149C2311yescharacteristic
158C4⋊C8×C149C2311yescharacteristic
159C4⋊C8×C149C2311yescharacteristic
160C4⋊C8×C149C2311yescharacteristic
161#103×C149—21no—
162#103×C149—21no—
163#103×C149—22no—
164#103×C149—21no—
165#103×C149—21no—
166#102×C149—22no—
167#102×C149—21no—
168#102×C149—21no—
169#102×C149—21no—
170#102×C149—21no—
171C22⋊C8×C149—21no—
172#97×C149—21no—
173C4×C8×C149—21no—
174C4×C8×C149C2311yescharacteristic
175C4×C8×C149C2311yescharacteristic
176C24×C149—22no—
177#41×C149—81no—
178#41×C149—81no—
179#41×C149—81no—
180#41×C149—81no—
181#41×C149—81no—
182#41×C149—81no—
183#41×C149—81no—
184#41×C149—81no—
185C2×Q8×C149—21no—
186C2×Q8×C149—21no—
187C2×Q8×C149—21no—
188C2×Q8×C149—21no—
189C2×Q8×C149C2×D411yescharacteristic
190C2×D4×C149—22no—
191C2×D4×C149—22no—
192C2×D4×C149—22no—
193C2×D4×C149—22no—
194C2×D4×C149—22no—
195C2×D4×C149—21no—
196C2×D4×C149—21no—
197C2×D4×C149—22no—
198C2×D4×C149—21no—
199C2×D4×C149—21no—
200C2×D4×C149—21no—
201C2×D4×C149—21no—
202C2×D4×C149—21no—
203C2×D4×C149—81no—
204C2×D4×C149—81no—
205C2×D4×C149—81no—
206C2×D4×C149—81no—
207C2×D4×C149C2×D411yescharacteristic
208C2×D4×C149C2×D411yescharacteristic
209C2×D4×C149C2×D411yescharacteristic
210C2×D4×C149C2×D412yes—
211C22×C4×C149—22no—
212C22×C4×C149—22no—
213C22×C4×C149—21no—
214C22×C4×C149—21no—
215C22×C4×C149—21no—
216C22×C4×C149—22no—
217C22×C4×C149C2×D411yescharacteristic
218C22×C4×C149C2×D411yescharacteristic
219C22×C4×C149C2×D411yescharacteristic
220SD16×C149—44no—
221SD16×C149—81no—
222SD16×C149—81no—
223M16×C149—42no—
224C2×C8×C149—21no—
225C2×C8×C149—21no—
226C2×C8×C149—21no—
227C2×C8×C149—21no—
228C2×C8×C149—21no—
229C2×C8×C149—21no—
230C2×C8×C149—81no—
231C4⋊C4×C149—22no—
232C4⋊C4×C149—22no—
233C4⋊C4×C149—21no—
234C4⋊C4×C149—21no—
235C4⋊C4×C149—21no—
236C4⋊C4×C149—21no—
237C4⋊C4×C149—21no—
238C4⋊C4×C149—21no—
239C4⋊C4×C149—21no—
240C4⋊C4×C149—21no—
241C4⋊C4×C149—21no—
242C4⋊C4×C149—21no—
243C4⋊C4×C149—41no—
244C4⋊C4×C149—41no—
245C4⋊C4×C149C2×D411yescharacteristic
246C4⋊C4×C149C2×D411yescharacteristic
247C4⋊C4×C149C2×D412yes—
248C4⋊C4×C149C2×D411yescharacteristic
249C4⋊C4×C149C2×D411yescharacteristic
250C22⋊C4×C149—22no—
251C22⋊C4×C149—22no—
252C22⋊C4×C149—22no—
253C22⋊C4×C149—22no—
254C22⋊C4×C149—22no—
255C22⋊C4×C149—21no—
256C22⋊C4×C149—21no—
257C22⋊C4×C149—21no—
258C22⋊C4×C149—21no—
259C22⋊C4×C149—21no—
260C22⋊C4×C149—21no—
261C22⋊C4×C149—22no—
262C22⋊C4×C149—22no—
263C22⋊C4×C149—21no—
264C22⋊C4×C149—21no—
265C22⋊C4×C149—21no—
266C22⋊C4×C149—41no—
267C42×C149—22no—
268C42×C149—21no—
269C42×C149—41no—
270C42×C149C2×D411yescharacteristic
271C42×C149C2×D411yescharacteristic
272C42×C149C2×D411yescharacteristic
273C42×C149C2411yescharacteristic
274C23×C149—21no—
275C23×C149—21no—
276C23×C149—22no—
277C23×C149—21no—
278C23×C149—82no—
279C23×C149—82no—
280C23×C149—82no—
281C23×C149#12011yescharacteristic
282Q8×C149—21no—
283Q8×C149—21no—
284Q8×C149—42no—
285Q8×C149—41no—
286Q8×C149—41no—
287Q8×C149—41no—
288Q8×C149—41no—
289Q8×C149—81no—
290D4×C149—21no—
291D4×C149—21no—
292D4×C149—21no—
293D4×C149—21no—
294D4×C149—21no—
295D4×C149—21no—
296D4×C149—42no—
297D4×C149—41no—
298D4×C149—41no—
299D4×C149—41no—
300D4×C149—41no—
301D4×C149—81no—
302D4×C149—81no—
303D4×C149—81no—
304D4×C149—81no—
305D4×C149—81no—
306D4×C149—82no—
307D4×C149—82no—
308D4×C149—82no—
309D4×C149—82no—
310D4×C149—82no—
311D4×C149—82no—
312C2×C4×C149—21no—
313C2×C4×C149—21no—
314C2×C4×C149—21no—
315C2×C4×C149—21no—
316C2×C4×C149—21no—
317C2×C4×C149—21no—
318C2×C4×C149—21no—
319C2×C4×C149—22no—
320C2×C4×C149—21no—
321C2×C4×C149—21no—
322C2×C4×C149—41no—
323C2×C4×C149—41no—
324C2×C4×C149—41no—
325C2×C4×C149—41no—
326C2×C4×C149—41no—
327C2×C4×C149—41no—
328C2×C4×C149—41no—
329C2×C4×C149—41no—
330C2×C4×C149—41no—
331C2×C4×C149—82no—
332C2×C4×C149—82no—
333C2×C4×C149—82no—
334C2×C4×C149#12011yescharacteristic
335C2×C4×C149#12011yescharacteristic
336C2×C4×C149#12011yescharacteristic
337C2×C4×C149C22×D411yescharacteristic
338C2×C4×C149C22×D411yescharacteristic
339C2×C4×C149C22×D411yescharacteristic
340C8×C149—22no—
341C8×C149—41no—
342C8×C149—41no—
343C8×C149—41no—
344C8×C149—41no—
345C8×C149—41no—
346C22×C149—21no—
347C22×C149—21no—
348C22×C149—21no—
349C22×C149—41no—
350C22×C149—41no—
351C22×C149—42no—
352C22×C149—41no—
353C22×C149—41no—
354C22×C149—41no—
355C22×C149—42no—
356C22×C149—41no—
357C22×C149—42no—
358C22×C149—41no—
359C22×C149—41no—
360C22×C149—41no—
361C22×C149—164no—
362C22×C149C2×#12011yescharacteristic
363C4×C149—21no—
364C4×C149—21no—
365C4×C149—21no—
366C4×C149—21no—
367C4×C149—41no—
368C4×C149—41no—
369C4×C149—41no—
370C4×C149—41no—
371C4×C149—42no—
372C4×C149—41no—
373C4×C149—81no—
374C4×C149—81no—
375C4×C149#57611yescharacteristic
376C4×C149#57711yescharacteristic
377C4×C149#57711yescharacteristic
378C4×C149#57711yescharacteristic
379C2×C149—41no—
380C2×C149—81no—
381C2×C149—82no—
382C2×C149—81no—
383C2×C149—81no—
384C2×C149#300911yescharacteristic
385C2×C149#301211yescharacteristic
386C2×C149#301811yescharacteristic
387#18739C14911yesmaximal, characteristic, direct product factor, Sylow
388C149#1873911yescharacteristic, direct product factor, Sylow
389#3546C2×C14911yescharacteristic
390#3246C2×C14911yescharacteristic, complemented
391#3233C2×C14911yescharacteristic, complemented
392#3182C2×C14911yescharacteristic, complemented
393#1650C2×C14911yescharacteristic, complemented
394#1647C2×C14911yescharacteristic, complemented
395#1642C2×C14911yescharacteristic, complemented
396#1639C2×C14911yescharacteristic, complemented
397#1638C2×C14911yescharacteristic, complemented
398#1635C2×C14911yescharacteristic, complemented
399#1631C2×C14911yescharacteristic, complemented
400#1629C2×C14911yescharacteristic, complemented
401#1540C2×C14911yescharacteristic, complemented
402#1484C2×C14911yescharacteristic, complemented
403#1483C2×C14911yescharacteristic, complemented
404#560—22no—
405#556C22×C14911yescharacteristic
406#553—21no—
407#550—21no—
408#550C22×C14911yescharacteristic
409#547C22×C14911yescharacteristic
410#546—21no—
411#546—21no—
412D42C22×C14911yescharacteristic
413#542—21no—
414#538—22no—
415#537—21no—
416#535—21no—
417#535—21no—
418#533C22×C14911yescharacteristic, complemented
419#532C22×C14911yescharacteristic
420#532C22×C14911yescharacteristic
421#529C22×C14911yescharacteristic
422#500C22×C14911yescharacteristic, complemented
423#499—21no—
424#492C22×C14911yescharacteristic
425#488—21no—
426#487C22×C14911yescharacteristic, complemented
427#486C22×C14911yescharacteristic
428#485—21no—
429#482—21no—
430#477C22×C14911yescharacteristic, complemented
431#476C22×C14911yescharacteristic
432#476C22×C14911yescharacteristic
433#476C22×C14911yescharacteristic, complemented
434#475—21no—
435#475C22×C14911yescharacteristic, complemented
436#474C22×C14911yescharacteristic
437#468—22no—
438#465—21no—
439#465—21no—
440#461C22×C14911yescharacteristic
441#461C22×C14911yescharacteristic, complemented
442#460—21no—
443#440—22no—
444#431C22×C14911yescharacteristic, complemented
445C2×C4⋊C8C22×C14911yescharacteristic, complemented
446C4×M16C22×C14911yescharacteristic, complemented
447#332C22×C14911yescharacteristic, complemented
448#332C22×C14911yescharacteristic, complemented
449#331C22×C14911yescharacteristic
450#331C22×C14911yescharacteristic
451Q8⋊C8C22×C14911yescharacteristic, complemented
452Q8⋊C8C22×C14911yescharacteristic, complemented
453D4⋊C8C22×C14911yescharacteristic
454D4⋊C8C22×C14911yescharacteristic
455D4⋊C8C22×C14911yescharacteristic
456D4⋊C8C22×C14911yescharacteristic
457D4⋊C8C22×C14911yescharacteristic, complemented
458D4⋊C8C22×C14911yescharacteristic, complemented
459C2×#41—21no—
460C2×#41—21no—
461C2×#41—21no—
462C2×#41—21no—
463C22×D4—21no—
464C22×D4—21no—
465C2×SD16—22no—
466C2×SD16—21no—
467C2×SD16—21no—
468C2×M16—21no—
469C22×C8—21no—
470C4⋊Q8D4×C14911yescharacteristic
471C4⋊Q8C23×C14911yescharacteristic
472C4⋊Q8C23×C14911yescharacteristic
473C4⋊Q8C23×C14911yescharacteristic
474#127—22no—
475#127—21no—
476#127D4×C14911yescharacteristic
477#127C23×C14911yescharacteristic
478#126—22no—
479#126—22no—
480#126—21no—
481#125—21no—
482#125D4×C14911yescharacteristic
483#124—22no—
484#124—21no—
485#124—21no—
486#124—21no—
487#124D4×C14911yescharacteristic
488#123—22no—
489#123—22no—
490#123—21no—
491#123—22no—
492C22⋊Q8—22no—
493C22⋊Q8—21no—
494C22⋊Q8—21no—
495C22⋊Q8—21no—
496C22⋊Q8—21no—
497C22⋊Q8D4×C14911yescharacteristic
498#121—22no—
499#121—22no—
500#121—22no—
501#121—22no—
502#121—22no—
503#121—21no—
504#121—22no—
505#121—21no—
506#121—21no—
507#121—21no—
508#121—21no—
509#121—21no—
510#121D4×C14911yescharacteristic
511#121D4×C14911yescharacteristic
512#121D4×C14911yescharacteristic
513#121D4×C14912yes—
514#120—22no—
515#120—22no—
516#120—22no—
517#120—22no—
518C4×Q8—21no—
519C4×Q8—21no—
520C4×Q8—21no—
521C4×Q8C23×C14911yescharacteristic
522C4×D4—22no—
523C4×D4—21no—
524C4×D4—21no—
525C4×D4—21no—
526C4×D4—21no—
527C4×D4D4×C14912yes—
528C4×D4C23×C14911yescharacteristic
529C4×D4C23×C14911yescharacteristic
530C4×D4C23×C14911yescharacteristic
531#117—21no—
532#117—21no—
533#117—21no—
534C2×C4⋊C4—21no—
535C2×C22⋊C4—22no—
536C2×C42C23×C14911yescharacteristic
537#107—22no—
538#107—21no—
539#107—21no—
540#106—21no—
541#106—21no—
542#106—21no—
543#106—21no—
544C4⋊C8—21no—
545C4⋊C8C23×C14911yescharacteristic
546C4⋊C8C23×C14911yescharacteristic
547C4⋊C8C23×C14911yescharacteristic
548C4⋊C8C23×C14911yescharacteristic
549#103—21no—
550#103—21no—
551#103—22no—
552#103—21no—
553#103—21no—
554#102—22no—
555#102—21no—
556#102—21no—
557#102—21no—
558#102—21no—
559C22⋊C8—21no—
560#97—21no—
561C4×C8—21no—
562C4×C8C23×C14911yescharacteristic
563C4×C8C23×C14911yescharacteristic
564C24—22no—
565#41—81no—
566#41—81no—
567#41—81no—
568#41—81no—
569#41—81no—
570#41—81no—
571#41—81no—
572#41—81no—
573C2×Q8—21no—
574C2×Q8—21no—
575C2×Q8—21no—
576C2×Q8—21no—
577C2×Q8C2×D4×C14911yescharacteristic
578C2×D4—22no—
579C2×D4—22no—
580C2×D4—22no—
581C2×D4—22no—
582C2×D4—22no—
583C2×D4—21no—
584C2×D4—21no—
585C2×D4—22no—
586C2×D4—21no—
587C2×D4—21no—
588C2×D4—21no—
589C2×D4—21no—
590C2×D4—21no—
591C2×D4—81no—
592C2×D4—81no—
593C2×D4—81no—
594C2×D4—81no—
595C2×D4C2×D4×C14911yescharacteristic
596C2×D4C2×D4×C14911yescharacteristic
597C2×D4C2×D4×C14911yescharacteristic
598C2×D4C2×D4×C14912yes—
599C22×C4—22no—
600C22×C4—22no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—22no—
605C22×C4C2×D4×C14911yescharacteristic
606C22×C4C2×D4×C14911yescharacteristic
607C22×C4C2×D4×C14911yescharacteristic
608SD16—44no—
609SD16—81no—
610SD16—81no—
611M16—42no—
612C2×C8—21no—
613C2×C8—21no—
614C2×C8—21no—
615C2×C8—21no—
616C2×C8—21no—
617C2×C8—21no—
618C2×C8—81no—
619C4⋊C4—22no—
620C4⋊C4—22no—
621C4⋊C4—21no—
622C4⋊C4—21no—
623C4⋊C4—21no—
624C4⋊C4—21no—
625C4⋊C4—21no—
626C4⋊C4—21no—
627C4⋊C4—21no—
628C4⋊C4—21no—
629C4⋊C4—21no—
630C4⋊C4—21no—
631C4⋊C4—41no—
632C4⋊C4—41no—
633C4⋊C4C2×D4×C14911yescharacteristic
634C4⋊C4C2×D4×C14911yescharacteristic
635C4⋊C4C2×D4×C14912yes—
636C4⋊C4C2×D4×C14911yescharacteristic
637C4⋊C4C2×D4×C14911yescharacteristic
638C22⋊C4—22no—
639C22⋊C4—22no—
640C22⋊C4—22no—
641C22⋊C4—22no—
642C22⋊C4—22no—
643C22⋊C4—21no—
644C22⋊C4—21no—
645C22⋊C4—21no—
646C22⋊C4—21no—
647C22⋊C4—21no—
648C22⋊C4—21no—
649C22⋊C4—22no—
650C22⋊C4—22no—
651C22⋊C4—21no—
652C22⋊C4—21no—
653C22⋊C4—21no—
654C22⋊C4—41no—
655C42—22no—
656C42—21no—
657C42—41no—
658C42C2×D4×C14911yescharacteristic
659C42C2×D4×C14911yescharacteristic
660C42C2×D4×C14911yescharacteristic
661C42C24×C14911yescharacteristic
662C23—21no—
663C23—21no—
664C23—22no—
665C23—21no—
666C23—82no—
667C23—82no—
668C23—82no—
669C23#120×C14911yescharacteristic
670Q8—21no—
671Q8—21no—
672Q8—42no—
673Q8—41no—
674Q8—41no—
675Q8—41no—
676Q8—41no—
677Q8—81no—
678D4—21no—
679D4—21no—
680D4—21no—
681D4—21no—
682D4—21no—
683D4—21no—
684D4—42no—
685D4—41no—
686D4—41no—
687D4—41no—
688D4—41no—
689D4—81no—
690D4—81no—
691D4—81no—
692D4—81no—
693D4—81no—
694D4—82no—
695D4—82no—
696D4—82no—
697D4—82no—
698D4—82no—
699D4—82no—
700C2×C4—21no—
701C2×C4—21no—
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—41no—
711C2×C4—41no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—82no—
720C2×C4—82no—
721C2×C4—82no—
722C2×C4#120×C14911yescharacteristic
723C2×C4#120×C14911yescharacteristic
724C2×C4#120×C14911yescharacteristic
725C2×C4C22×D4×C14911yescharacteristic
726C2×C4C22×D4×C14911yescharacteristic
727C2×C4C22×D4×C14911yescharacteristic
728C8—22no—
729C8—41no—
730C8—41no—
731C8—41no—
732C8—41no—
733C8—41no—
734C22—21no—
735C22—21no—
736C22—21no—
737C22—41no—
738C22—41no—
739C22—42no—
740C22—41no—
741C22—41no—
742C22—41no—
743C22—42no—
744C22—41no—
745C22—42no—
746C22—41no—
747C22—41no—
748C22—41no—
749C22—164no—
750C22C2×#120×C14911yescharacteristic
751C4—21no—
752C4—21no—
753C4—21no—
754C4—21no—
755C4—41no—
756C4—41no—
757C4—41no—
758C4—41no—
759C4—42no—
760C4—41no—
761C4—81no—
762C4—81no—
763C4#576×C14911yescharacteristic
764C4#577×C14911yescharacteristic
765C4#577×C14911yescharacteristic
766C4#577×C14911yescharacteristic
767C2—41no—
768C2—81no—
769C2—81no—
770C2—82no—
771C2—81no—
772C2#3009×C14911yescharacteristic
773C2#3012×C14911yescharacteristic
774C2#3018×C14911yescharacteristic
subgroupG/H
center, socleC22×C149C2×#120
commutator, Frattini, cosocleC42C24×C149
prime radical#3546×C149C2
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C149 ◁ C2×C42×C149 ◁ G

Complements

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

NH ≅ G/Ntype
2. #3246×C149C2semidirect
3. #3233×C149C2semidirect
4. #3182×C149C2semidirect
5. #1650×C149C2semidirect
6. #1647×C149C2semidirect
7. #1642×C149C2semidirect
8. #1639×C149C2semidirect
9. #1638×C149C2semidirect
10. #1635×C149C2semidirect
11. #1631×C149C2semidirect
12. #1629×C149C2semidirect
13. #1540×C149C2semidirect
14. #1484×C149C2semidirect
15. #1483×C149C2semidirect
30. #533×C149C22semidirect
34. #500×C149C22semidirect
38. #487×C149C22semidirect
42. #477×C149C22semidirect
45. #476×C149C22semidirect
47. #475×C149C22semidirect
53. #461×C149C22semidirect
56. #431×C149C22semidirect
57. C2×C4⋊C8×C149C22semidirect
58. C4×M16×C149C22semidirect
59. #332×C149C22semidirect
60. #332×C149C22semidirect
63. Q8⋊C8×C149C22semidirect
64. Q8⋊C8×C149C22semidirect
69. D4⋊C8×C149C22semidirect
70. D4⋊C8×C149C22semidirect
387. #18739C149direct (N × H)
388. C149#18739direct (N × H)
390. #3246C2×C149semidirect
391. #3233C2×C149semidirect
392. #3182C2×C149semidirect
393. #1650C2×C149semidirect
394. #1647C2×C149semidirect
395. #1642C2×C149semidirect
396. #1639C2×C149semidirect
397. #1638C2×C149semidirect
398. #1635C2×C149semidirect
399. #1631C2×C149semidirect
400. #1629C2×C149semidirect
401. #1540C2×C149semidirect
402. #1484C2×C149semidirect
403. #1483C2×C149semidirect
418. #533C22×C149semidirect
422. #500C22×C149semidirect
426. #487C22×C149semidirect
430. #477C22×C149semidirect
433. #476C22×C149semidirect
435. #475C22×C149semidirect
441. #461C22×C149semidirect
444. #431C22×C149semidirect
445. C2×C4⋊C8C22×C149semidirect
446. C4×M16C22×C149semidirect
447. #332C22×C149semidirect
448. #332C22×C149semidirect
451. Q8⋊C8C22×C149semidirect
452. Q8⋊C8C22×C149semidirect
457. D4⋊C8C22×C149semidirect
458. D4⋊C8C22×C149semidirect

Maximal subgroups

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

subgroupindex
#3546×C1492
#3246×C1492
#3233×C1492
#3182×C1492
#1650×C1492
#1647×C1492
#1642×C1492
#1639×C1492
#1638×C1492
#1635×C1492
#1631×C1492
#1629×C1492
#1540×C1492
#1484×C1492
#1483×C1492
#18739149