Finite Group Databasebeta

← C149×#18707 #49197656

Subgroups — C149×#18707 #49197656

Order 38144.

874 conjugacy classes of subgroups.

The subgroup lattice has 736 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3547×C149C211yesmaximal, characteristic
2#3252×C149C211yesmaximal, characteristic, complemented
3#3235×C149C211yesmaximal, characteristic, complemented
4#3170×C149C211yesmaximal, characteristic, complemented
5#1649×C149C211yesmaximal, characteristic, complemented
6#1647×C149C211yesmaximal, characteristic, complemented
7#1646×C149C211yesmaximal, characteristic, complemented
8#1644×C149C211yesmaximal, characteristic, complemented
9#1637×C149C211yesmaximal, characteristic, complemented
10#1635×C149C211yesmaximal, characteristic, complemented
11#1634×C149C211yesmaximal, characteristic, complemented
12#1632×C149C211yesmaximal, characteristic, complemented
13#1559×C149C211yesmaximal, characteristic, complemented
14#1494×C149C211yesmaximal, characteristic, complemented
15#1492×C149C211yesmaximal, characteristic, complemented
16#562×C149—22no—
17#555×C149—21no—
18#555×C149C2211yescharacteristic
19#554×C149C2211yescharacteristic
20#553×C149—21no—
21#552×C149—21no—
22D4×Q8×C149C2211yescharacteristic
23#548×C149—21no—
24#547×C149C2211yescharacteristic
25#544×C149—21no—
26#542×C149—22no—
27#540×C149—21no—
28#537×C149—21no—
29#536×C149—21no—
30#533×C149C2211yescharacteristic
31#533×C149C2211yescharacteristic
32#532×C149C2211yescharacteristic
33#529×C149C2211yescharacteristic
34#501×C149—21no—
35#500×C149C2211yescharacteristic
36#494×C149C2211yescharacteristic
37#490×C149—21no—
38#487×C149C2211yescharacteristic
39#487×C149C2211yescharacteristic
40#482×C149—21no—
41#482×C149—21no—
42#479×C149—21no—
43#477×C149C2211yescharacteristic
44#476×C149C2211yescharacteristic
45#476×C149C2211yescharacteristic
46#476×C149C2211yescharacteristic
47#474×C149C2211yescharacteristic
48#474×C149C2211yescharacteristic
49#470×C149—21no—
50#468×C149—21no—
51#467×C149—22no—
52#464×C149—21no—
53#462×C149C2211yescharacteristic
54#461×C149C2211yescharacteristic
55C4×Q16×C149—22no—
56#432×C149C2211yescharacteristic
57#423×C149C2211yescharacteristic
58C2×C4×C8×C149C2211yescharacteristic
59#333×C149C2211yescharacteristic
60#333×C149C2211yescharacteristic
61#332×C149C2211yescharacteristic
62#332×C149C2211yescharacteristic
63Q8⋊C8×C149C2211yescharacteristic
64Q8⋊C8×C149C2211yescharacteristic
65D4⋊C8×C149C2211yescharacteristic
66D4⋊C8×C149C2211yescharacteristic
67D4⋊C8×C149C2211yescharacteristic
68D4⋊C8×C149C2211yescharacteristic
69D4⋊C8×C149C2211yescharacteristic
70D4⋊C8×C149C2211yescharacteristic
71C2×#41×C149—21no—
72C2×#41×C149—21no—
73C22×Q8×C149—21no—
74C2×Q16×C149—22no—
75C2×Q16×C149—21no—
76C2×SD16×C149—21no—
77C2×M16×C149—21no—
78C22×C8×C149—21no—
79C4⋊Q8×C149—22no—
80C4⋊Q8×C149—21no—
81C4⋊Q8×C149D411yescharacteristic
82C4⋊Q8×C149C2311yescharacteristic
83C4⋊Q8×C149C2311yescharacteristic
84C4⋊Q8×C149C2311yescharacteristic
85C4⋊Q8×C149C2311yescharacteristic
86#127×C149D411yescharacteristic
87#126×C149—22no—
88#126×C149—21no—
89#125×C149—22no—
90#125×C149—21no—
91#125×C149—21no—
92#125×C149—21no—
93#125×C149D411yescharacteristic
94#124×C149—22no—
95#124×C149—22no—
96#124×C149—22no—
97#124×C149—21no—
98#124×C149D411yescharacteristic
99#123×C149—22no—
100#123×C149—22no—
101#123×C149—22no—
102#123×C149—21no—
103#123×C149—22no—
104C22⋊Q8×C149—22no—
105C22⋊Q8×C149—22no—
106C22⋊Q8×C149—21no—
107C22⋊Q8×C149—22no—
108C22⋊Q8×C149—21no—
109C22⋊Q8×C149—21no—
110C22⋊Q8×C149—21no—
111C22⋊Q8×C149—22no—
112C22⋊Q8×C149—21no—
113C22⋊Q8×C149—21no—
114C22⋊Q8×C149D412yes—
115C22⋊Q8×C149D411yescharacteristic
116#121×C149—22no—
117#121×C149—22no—
118#121×C149—22no—
119#121×C149—22no—
120#121×C149—21no—
121#121×C149—21no—
122#121×C149—21no—
123#121×C149—21no—
124#121×C149D411yescharacteristic
125#121×C149D411yescharacteristic
126#121×C149D411yescharacteristic
127C4×Q8×C149—21no—
128C4×Q8×C149—21no—
129C4×Q8×C149—21no—
130C4×Q8×C149D412yes—
131C4×Q8×C149C2311yescharacteristic
132C4×D4×C149—22no—
133C4×D4×C149—21no—
134C4×D4×C149—21no—
135C4×D4×C149—21no—
136C4×D4×C149—21no—
137C4×D4×C149C2311yescharacteristic
138C4×D4×C149C2311yescharacteristic
139C4×D4×C149C2311yescharacteristic
140#117×C149—22no—
141#117×C149—21no—
142#117×C149—21no—
143#117×C149—21no—
144#117×C149—21no—
145#117×C149—21no—
146C2×C4⋊C4×C149—21no—
147C2×C4⋊C4×C149—21no—
148C2×C42×C149C2311yescharacteristic
149#107×C149—22no—
150#107×C149—21no—
151#107×C149—21no—
152#107×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—22no—
162#103×C149—21no—
163#103×C149—22no—
164#103×C149—21no—
165#103×C149—21no—
166#102×C149—21no—
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
176#41×C149—81no—
177#41×C149—81no—
178#41×C149—81no—
179#41×C149—81no—
180C2×Q8×C149—22no—
181C2×Q8×C149—21no—
182C2×Q8×C149—21no—
183C2×Q8×C149—21no—
184C2×Q8×C149—21no—
185C2×Q8×C149—81no—
186C2×Q8×C149—81no—
187C2×Q8×C149C2×D411yescharacteristic
188C2×Q8×C149C2×D412yes—
189C2×D4×C149—22no—
190C2×D4×C149—22no—
191C2×D4×C149—21no—
192C2×D4×C149—21no—
193C2×D4×C149—21no—
194C2×D4×C149—21no—
195C2×D4×C149—21no—
196C2×D4×C149C2×D411yescharacteristic
197C2×D4×C149C2×D411yescharacteristic
198C2×D4×C149C2×D411yescharacteristic
199C22×C4×C149—22no—
200C22×C4×C149—22no—
201C22×C4×C149—22no—
202C22×C4×C149—21no—
203C22×C4×C149—21no—
204C22×C4×C149—21no—
205C22×C4×C149C2×D411yescharacteristic
206C22×C4×C149C2×D411yescharacteristic
207C22×C4×C149C2×D411yescharacteristic
208Q16×C149—44no—
209Q16×C149—81no—
210SD16×C149—81no—
211M16×C149—81no—
212C2×C8×C149—21no—
213C2×C8×C149—21no—
214C2×C8×C149—21no—
215C2×C8×C149—21no—
216C2×C8×C149—21no—
217C2×C8×C149—21no—
218C2×C8×C149—42no—
219C4⋊C4×C149—22no—
220C4⋊C4×C149—22no—
221C4⋊C4×C149—22no—
222C4⋊C4×C149—22no—
223C4⋊C4×C149—21no—
224C4⋊C4×C149—21no—
225C4⋊C4×C149—21no—
226C4⋊C4×C149—21no—
227C4⋊C4×C149—22no—
228C4⋊C4×C149—22no—
229C4⋊C4×C149—21no—
230C4⋊C4×C149—21no—
231C4⋊C4×C149—21no—
232C4⋊C4×C149—21no—
233C4⋊C4×C149—21no—
234C4⋊C4×C149—21no—
235C4⋊C4×C149—21no—
236C4⋊C4×C149—21no—
237C4⋊C4×C149—41no—
238C4⋊C4×C149—41no—
239C4⋊C4×C149C2×D411yescharacteristic
240C4⋊C4×C149C2×D411yescharacteristic
241C4⋊C4×C149C2×D412yes—
242C4⋊C4×C149C2×D411yescharacteristic
243C4⋊C4×C149C2×D411yescharacteristic
244C22⋊C4×C149—22no—
245C22⋊C4×C149—22no—
246C22⋊C4×C149—22no—
247C22⋊C4×C149—22no—
248C22⋊C4×C149—22no—
249C22⋊C4×C149—22no—
250C22⋊C4×C149—21no—
251C22⋊C4×C149—21no—
252C22⋊C4×C149—21no—
253C22⋊C4×C149—21no—
254C22⋊C4×C149—21no—
255C22⋊C4×C149—21no—
256C22⋊C4×C149—21no—
257C22⋊C4×C149—21no—
258C22⋊C4×C149—21no—
259C22⋊C4×C149—41no—
260C42×C149—22no—
261C42×C149—22no—
262C42×C149—21no—
263C42×C149—41no—
264C42×C149C2×D411yescharacteristic
265C42×C149C2×D411yescharacteristic
266C42×C149C2×D411yescharacteristic
267C42×C149C2411yescharacteristic
268C23×C149—21no—
269C23×C149—21no—
270C23×C149—21no—
271C23×C149#12011yescharacteristic
272Q8×C149—21no—
273Q8×C149—21no—
274Q8×C149—42no—
275Q8×C149—42no—
276Q8×C149—41no—
277Q8×C149—41no—
278Q8×C149—41no—
279Q8×C149—41no—
280Q8×C149—81no—
281Q8×C149—82no—
282D4×C149—21no—
283D4×C149—21no—
284D4×C149—21no—
285D4×C149—21no—
286D4×C149—21no—
287D4×C149—21no—
288D4×C149—81no—
289D4×C149—81no—
290D4×C149—81no—
291D4×C149—81no—
292D4×C149—81no—
293D4×C149—82no—
294D4×C149—82no—
295C2×C4×C149—21no—
296C2×C4×C149—21no—
297C2×C4×C149—21no—
298C2×C4×C149—21no—
299C2×C4×C149—21no—
300C2×C4×C149—22no—
301C2×C4×C149—21no—
302C2×C4×C149—21no—
303C2×C4×C149—21no—
304C2×C4×C149—22no—
305C2×C4×C149—21no—
306C2×C4×C149—41no—
307C2×C4×C149—41no—
308C2×C4×C149—41no—
309C2×C4×C149—41no—
310C2×C4×C149—41no—
311C2×C4×C149—41no—
312C2×C4×C149—41no—
313C2×C4×C149—41no—
314C2×C4×C149—41no—
315C2×C4×C149—82no—
316C2×C4×C149—82no—
317C2×C4×C149—82no—
318C2×C4×C149#12011yescharacteristic
319C2×C4×C149#12011yescharacteristic
320C2×C4×C149#12011yescharacteristic
321C2×C4×C149C22×D411yescharacteristic
322C2×C4×C149C22×D411yescharacteristic
323C2×C4×C149C22×D411yescharacteristic
324C8×C149—22no—
325C8×C149—41no—
326C8×C149—41no—
327C8×C149—41no—
328C8×C149—41no—
329C8×C149—41no—
330C22×C149—21no—
331C22×C149—21no—
332C22×C149—21no—
333C22×C149—41no—
334C22×C149—41no—
335C22×C149—41no—
336C22×C149—41no—
337C22×C149—41no—
338C22×C149—41no—
339C22×C149—41no—
340C22×C149—41no—
341C22×C149—41no—
342C22×C149C2×#12011yescharacteristic
343C4×C149—21no—
344C4×C149—21no—
345C4×C149—21no—
346C4×C149—21no—
347C4×C149—41no—
348C4×C149—41no—
349C4×C149—41no—
350C4×C149—42no—
351C4×C149—41no—
352C4×C149—41no—
353C4×C149—42no—
354C4×C149—81no—
355C4×C149—81no—
356C4×C149#57611yescharacteristic
357C4×C149#57711yescharacteristic
358C4×C149#57811yescharacteristic
359C4×C149#57811yescharacteristic
360C2×C149—41no—
361C2×C149—81no—
362C2×C149—81no—
363C2×C149—81no—
364C2×C149#301111yescharacteristic
365C2×C149#301211yescharacteristic
366C2×C149#301811yescharacteristic
367#18707C14911yesmaximal, characteristic, direct product factor, Sylow
368C149#1870711yescharacteristic, direct product factor, Sylow
369#3547C2×C14911yescharacteristic
370#3252C2×C14911yescharacteristic, complemented
371#3235C2×C14911yescharacteristic, complemented
372#3170C2×C14911yescharacteristic, complemented
373#1649C2×C14911yescharacteristic, complemented
374#1647C2×C14911yescharacteristic, complemented
375#1646C2×C14911yescharacteristic, complemented
376#1644C2×C14911yescharacteristic, complemented
377#1637C2×C14911yescharacteristic, complemented
378#1635C2×C14911yescharacteristic, complemented
379#1634C2×C14911yescharacteristic, complemented
380#1632C2×C14911yescharacteristic, complemented
381#1559C2×C14911yescharacteristic, complemented
382#1494C2×C14911yescharacteristic, complemented
383#1492C2×C14911yescharacteristic, complemented
384#562—22no—
385#555—21no—
386#555C22×C14911yescharacteristic
387#554C22×C14911yescharacteristic
388#553—21no—
389#552—21no—
390D4×Q8C22×C14911yescharacteristic
391#548—21no—
392#547C22×C14911yescharacteristic
393#544—21no—
394#542—22no—
395#540—21no—
396#537—21no—
397#536—21no—
398#533C22×C14911yescharacteristic
399#533C22×C14911yescharacteristic
400#532C22×C14911yescharacteristic
401#529C22×C14911yescharacteristic
402#501—21no—
403#500C22×C14911yescharacteristic
404#494C22×C14911yescharacteristic
405#490—21no—
406#487C22×C14911yescharacteristic
407#487C22×C14911yescharacteristic
408#482—21no—
409#482—21no—
410#479—21no—
411#477C22×C14911yescharacteristic
412#476C22×C14911yescharacteristic
413#476C22×C14911yescharacteristic
414#476C22×C14911yescharacteristic
415#474C22×C14911yescharacteristic
416#474C22×C14911yescharacteristic
417#470—21no—
418#468—21no—
419#467—22no—
420#464—21no—
421#462C22×C14911yescharacteristic
422#461C22×C14911yescharacteristic
423C4×Q16—22no—
424#432C22×C14911yescharacteristic
425#423C22×C14911yescharacteristic
426C2×C4×C8C22×C14911yescharacteristic
427#333C22×C14911yescharacteristic
428#333C22×C14911yescharacteristic
429#332C22×C14911yescharacteristic
430#332C22×C14911yescharacteristic
431Q8⋊C8C22×C14911yescharacteristic
432Q8⋊C8C22×C14911yescharacteristic
433D4⋊C8C22×C14911yescharacteristic
434D4⋊C8C22×C14911yescharacteristic
435D4⋊C8C22×C14911yescharacteristic
436D4⋊C8C22×C14911yescharacteristic
437D4⋊C8C22×C14911yescharacteristic
438D4⋊C8C22×C14911yescharacteristic
439C2×#41—21no—
440C2×#41—21no—
441C22×Q8—21no—
442C2×Q16—22no—
443C2×Q16—21no—
444C2×SD16—21no—
445C2×M16—21no—
446C22×C8—21no—
447C4⋊Q8—22no—
448C4⋊Q8—21no—
449C4⋊Q8D4×C14911yescharacteristic
450C4⋊Q8C23×C14911yescharacteristic
451C4⋊Q8C23×C14911yescharacteristic
452C4⋊Q8C23×C14911yescharacteristic
453C4⋊Q8C23×C14911yescharacteristic
454#127D4×C14911yescharacteristic
455#126—22no—
456#126—21no—
457#125—22no—
458#125—21no—
459#125—21no—
460#125—21no—
461#125D4×C14911yescharacteristic
462#124—22no—
463#124—22no—
464#124—22no—
465#124—21no—
466#124D4×C14911yescharacteristic
467#123—22no—
468#123—22no—
469#123—22no—
470#123—21no—
471#123—22no—
472C22⋊Q8—22no—
473C22⋊Q8—22no—
474C22⋊Q8—21no—
475C22⋊Q8—22no—
476C22⋊Q8—21no—
477C22⋊Q8—21no—
478C22⋊Q8—21no—
479C22⋊Q8—22no—
480C22⋊Q8—21no—
481C22⋊Q8—21no—
482C22⋊Q8D4×C14911yescharacteristic
483C22⋊Q8D4×C14912yes—
484#121—22no—
485#121—22no—
486#121—22no—
487#121—22no—
488#121—21no—
489#121—21no—
490#121—21no—
491#121—21no—
492#121D4×C14911yescharacteristic
493#121D4×C14911yescharacteristic
494#121D4×C14911yescharacteristic
495C4×Q8—21no—
496C4×Q8—21no—
497C4×Q8—21no—
498C4×Q8D4×C14912yes—
499C4×Q8C23×C14911yescharacteristic
500C4×D4—22no—
501C4×D4—21no—
502C4×D4—21no—
503C4×D4—21no—
504C4×D4—21no—
505C4×D4C23×C14911yescharacteristic
506C4×D4C23×C14911yescharacteristic
507C4×D4C23×C14911yescharacteristic
508#117—22no—
509#117—21no—
510#117—21no—
511#117—21no—
512#117—21no—
513#117—21no—
514C2×C4⋊C4—21no—
515C2×C4⋊C4—21no—
516C2×C42C23×C14911yescharacteristic
517#107—22no—
518#107—21no—
519#107—21no—
520#107—21no—
521#106—21no—
522#106—21no—
523#106—21no—
524C4⋊C8—21no—
525C4⋊C8C23×C14911yescharacteristic
526C4⋊C8C23×C14911yescharacteristic
527C4⋊C8C23×C14911yescharacteristic
528C4⋊C8C23×C14911yescharacteristic
529#103—22no—
530#103—21no—
531#103—22no—
532#103—21no—
533#103—21no—
534#102—21no—
535#102—21no—
536#102—21no—
537#102—21no—
538#102—21no—
539C22⋊C8—21no—
540#97—21no—
541C4×C8—21no—
542C4×C8C23×C14911yescharacteristic
543C4×C8C23×C14911yescharacteristic
544#41—81no—
545#41—81no—
546#41—81no—
547#41—81no—
548C2×Q8—22no—
549C2×Q8—21no—
550C2×Q8—21no—
551C2×Q8—21no—
552C2×Q8—21no—
553C2×Q8—81no—
554C2×Q8—81no—
555C2×Q8C2×D4×C14911yescharacteristic
556C2×Q8C2×D4×C14912yes—
557C2×D4—22no—
558C2×D4—22no—
559C2×D4—21no—
560C2×D4—21no—
561C2×D4—21no—
562C2×D4—21no—
563C2×D4—21no—
564C2×D4C2×D4×C14911yescharacteristic
565C2×D4C2×D4×C14911yescharacteristic
566C2×D4C2×D4×C14911yescharacteristic
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4C2×D4×C14911yescharacteristic
574C22×C4C2×D4×C14911yescharacteristic
575C22×C4C2×D4×C14911yescharacteristic
576Q16—44no—
577Q16—81no—
578SD16—81no—
579M16—81no—
580C2×C8—21no—
581C2×C8—21no—
582C2×C8—21no—
583C2×C8—21no—
584C2×C8—21no—
585C2×C8—21no—
586C2×C8—42no—
587C4⋊C4—22no—
588C4⋊C4—22no—
589C4⋊C4—22no—
590C4⋊C4—22no—
591C4⋊C4—21no—
592C4⋊C4—21no—
593C4⋊C4—21no—
594C4⋊C4—21no—
595C4⋊C4—22no—
596C4⋊C4—22no—
597C4⋊C4—21no—
598C4⋊C4—21no—
599C4⋊C4—21no—
600C4⋊C4—21no—
601C4⋊C4—21no—
602C4⋊C4—21no—
603C4⋊C4—21no—
604C4⋊C4—21no—
605C4⋊C4—41no—
606C4⋊C4—41no—
607C4⋊C4C2×D4×C14911yescharacteristic
608C4⋊C4C2×D4×C14911yescharacteristic
609C4⋊C4C2×D4×C14912yes—
610C4⋊C4C2×D4×C14911yescharacteristic
611C4⋊C4C2×D4×C14911yescharacteristic
612C22⋊C4—22no—
613C22⋊C4—22no—
614C22⋊C4—22no—
615C22⋊C4—22no—
616C22⋊C4—22no—
617C22⋊C4—22no—
618C22⋊C4—21no—
619C22⋊C4—21no—
620C22⋊C4—21no—
621C22⋊C4—21no—
622C22⋊C4—21no—
623C22⋊C4—21no—
624C22⋊C4—21no—
625C22⋊C4—21no—
626C22⋊C4—21no—
627C22⋊C4—41no—
628C42—22no—
629C42—22no—
630C42—21no—
631C42—41no—
632C42C2×D4×C14911yescharacteristic
633C42C2×D4×C14911yescharacteristic
634C42C2×D4×C14911yescharacteristic
635C42C24×C14911yescharacteristic
636C23—21no—
637C23—21no—
638C23—21no—
639C23#120×C14911yescharacteristic
640Q8—21no—
641Q8—21no—
642Q8—42no—
643Q8—42no—
644Q8—41no—
645Q8—41no—
646Q8—41no—
647Q8—41no—
648Q8—81no—
649Q8—82no—
650D4—21no—
651D4—21no—
652D4—21no—
653D4—21no—
654D4—21no—
655D4—21no—
656D4—81no—
657D4—81no—
658D4—81no—
659D4—81no—
660D4—81no—
661D4—82no—
662D4—82no—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—21no—
666C2×C4—21no—
667C2×C4—21no—
668C2×C4—22no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—22no—
673C2×C4—21no—
674C2×C4—41no—
675C2×C4—41no—
676C2×C4—41no—
677C2×C4—41no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—82no—
684C2×C4—82no—
685C2×C4—82no—
686C2×C4#120×C14911yescharacteristic
687C2×C4#120×C14911yescharacteristic
688C2×C4#120×C14911yescharacteristic
689C2×C4C22×D4×C14911yescharacteristic
690C2×C4C22×D4×C14911yescharacteristic
691C2×C4C22×D4×C14911yescharacteristic
692C8—22no—
693C8—41no—
694C8—41no—
695C8—41no—
696C8—41no—
697C8—41no—
698C22—21no—
699C22—21no—
700C22—21no—
701C22—41no—
702C22—41no—
703C22—41no—
704C22—41no—
705C22—41no—
706C22—41no—
707C22—41no—
708C22—41no—
709C22—41no—
710C22C2×#120×C14911yescharacteristic
711C4—21no—
712C4—21no—
713C4—21no—
714C4—21no—
715C4—41no—
716C4—41no—
717C4—41no—
718C4—42no—
719C4—41no—
720C4—41no—
721C4—42no—
722C4—81no—
723C4—81no—
724C4#576×C14911yescharacteristic
725C4#577×C14911yescharacteristic
726C4#578×C14911yescharacteristic
727C4#578×C14911yescharacteristic
728C2—41no—
729C2—81no—
730C2—81no—
731C2—81no—
732C2#3011×C14911yescharacteristic
733C2#3012×C14911yescharacteristic
734C2#3018×C14911yescharacteristic
subgroupG/H
center, socleC22×C149C2×#120
commutator, Frattini, cosocleC42C24×C149
prime radical#3547×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. #3252×C149C2semidirect
3. #3235×C149C2semidirect
4. #3170×C149C2semidirect
5. #1649×C149C2semidirect
6. #1647×C149C2semidirect
7. #1646×C149C2semidirect
8. #1644×C149C2semidirect
9. #1637×C149C2semidirect
10. #1635×C149C2semidirect
11. #1634×C149C2semidirect
12. #1632×C149C2semidirect
13. #1559×C149C2semidirect
14. #1494×C149C2semidirect
15. #1492×C149C2semidirect
367. #18707C149direct (N × H)
368. C149#18707direct (N × H)
370. #3252C2×C149semidirect
371. #3235C2×C149semidirect
372. #3170C2×C149semidirect
373. #1649C2×C149semidirect
374. #1647C2×C149semidirect
375. #1646C2×C149semidirect
376. #1644C2×C149semidirect
377. #1637C2×C149semidirect
378. #1635C2×C149semidirect
379. #1634C2×C149semidirect
380. #1632C2×C149semidirect
381. #1559C2×C149semidirect
382. #1494C2×C149semidirect
383. #1492C2×C149semidirect

Maximal subgroups

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

subgroupindex
#3547×C1492
#3252×C1492
#3235×C1492
#3170×C1492
#1649×C1492
#1647×C1492
#1646×C1492
#1644×C1492
#1637×C1492
#1635×C1492
#1634×C1492
#1632×C1492
#1559×C1492
#1494×C1492
#1492×C1492
#18707149