Finite Group Databasebeta

← C149×#18418 #49197367

Subgroups — C149×#18418 #49197367

Order 38144.

1176 conjugacy classes of subgroups.

The subgroup lattice has 766 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3537×C149C211yesmaximal, characteristic, complemented
2#3192×C149C211yesmaximal, characteristic, complemented
3#3188×C149C211yesmaximal, characteristic, complemented
4#2656×C149C211yesmaximal, characteristic, complemented
5#1618×C149C212yesmaximal, complemented
6#1613×C149C212yesmaximal, complemented
7#1600×C149C212yesmaximal, complemented
8#1595×C149C212yesmaximal, complemented
9#1504×C149C211yesmaximal, characteristic, complemented
10C2×#327×C149C211yesmaximal, characteristic, complemented
11#1471×C149C211yesmaximal, characteristic, complemented
12#560×C149—22no—
13#553×C149—21no—
14#553×C149—21no—
15D42×C149—22no—
16D42×C149—21no—
17D42×C149—21no—
18#540×C149—21no—
19#538×C149—21no—
20#538×C149C2212yes—
21#535×C149—21no—
22#534×C149—21no—
23#534×C149C2212yes—
24#525×C149C2211yescharacteristic
25C2×#121×C149—22no—
26C2×#121×C149C2211yescharacteristic
27C2×#121×C149C2211yescharacteristic
28C2×#121×C149C2211yescharacteristic, complemented
29#484×C149C2211yescharacteristic, complemented
30#482×C149—21no—
31#481×C149—21no—
32#481×C149C2211yescharacteristic, complemented
33#481×C149C2212yescomplemented
34#469×C149—22no—
35#466×C149—21no—
36#465×C149—21no—
37#450×C149C2211yescharacteristic, complemented
38#449×C149—21no—
39#447×C149—21no—
40#447×C149C2211yescharacteristic, complemented
41#447×C149C2212yescomplemented
42#407×C149C2211yescharacteristic, complemented
43C2×C22⋊C8×C149C2211yescharacteristic, complemented
44#399×C149—21no—
45#399×C149C2212yescomplemented
46#392×C149—21no—
47#392×C149C2212yescomplemented
48C2×#95×C149C2211yescharacteristic, complemented
49#328×C149C2212yescomplemented
50#327×C149C2212yescomplemented
51#327×C149C2212yescomplemented
52#327×C149C2212yescomplemented
53#323×C149C2212yescomplemented
54#323×C149C2212yescomplemented
55C2×#41×C149D411yescharacteristic, complemented
56C22×D4×C149—22no—
57C22×D4×C149—21no—
58C22×D4×C149—21no—
59C22×D4×C149—22no—
60C22×D4×C149—21no—
61C22×D4×C149—22no—
62C22×D4×C149D412yes—
63C22×D4×C149D411yescharacteristic
64C22×D4×C149D411yescharacteristic, complemented
65C22×D4×C149C2311yescharacteristic
66C23×C4×C149—21no—
67C23×C4×C149C2311yescharacteristic
68C2×SD16×C149—21no—
69C2×D8×C149—22no—
70C2×D8×C149—21no—
71C2×M16×C149—21no—
72C22×C8×C149—21no—
73#127×C149—22no—
74#127×C149—21no—
75#126×C149—22no—
76#126×C149—22no—
77#125×C149—21no—
78#124×C149—22no—
79#123×C149—22no—
80#123×C149—21no—
81#123×C149—22no—
82#123×C149—22no—
83#123×C149—22no—
84C22⋊Q8×C149D411yescharacteristic, complemented
85C22⋊Q8×C149C2311yescharacteristic
86#121×C149—22no—
87#121×C149—21no—
88#121×C149—21no—
89#121×C149—22no—
90#121×C149—22no—
91#121×C149—22no—
92#121×C149—22no—
93#121×C149—21no—
94#121×C149—21no—
95#121×C149—21no—
96#121×C149—21no—
97#121×C149—21no—
98#121×C149—21no—
99#121×C149—22no—
100#121×C149—21no—
101#121×C149—21no—
102#121×C149—21no—
103#121×C149—21no—
104#121×C149—48no—
105#121×C149D411yescharacteristic, complemented
106#121×C149D412yescomplemented
107#121×C149C2312yes—
108#121×C149C2311yescharacteristic
109#120×C149—22no—
110#120×C149—22no—
111#120×C149—22no—
112#120×C149—21no—
113#120×C149—22no—
114#120×C149—22no—
115#120×C149—22no—
116C4×D4×C149—22no—
117C4×D4×C149—21no—
118C4×D4×C149—21no—
119C4×D4×C149—21no—
120C4×D4×C149—21no—
121C4×D4×C149—22no—
122#117×C149—21no—
123#117×C149D411yescharacteristic, complemented
124C2×C4⋊C4×C149—22no—
125C2×C4⋊C4×C149D411yescharacteristic
126C2×C4⋊C4×C149D411yescharacteristic, complemented
127C2×C4⋊C4×C149C2311yescharacteristic
128C2×C22⋊C4×C149—21no—
129C2×C22⋊C4×C149—22no—
130C2×C22⋊C4×C149—21no—
131C2×C22⋊C4×C149—22no—
132C2×C22⋊C4×C149C2312yes—
133#107×C149—21no—
134#106×C149—21no—
135#106×C149—22no—
136#103×C149—21no—
137#102×C149—22no—
138#102×C149—21no—
139#102×C149—21no—
140#102×C149—22no—
141#102×C149—21no—
142C22⋊C8×C149—21no—
143C22⋊C8×C149—21no—
144C22⋊C8×C149C2311yescharacteristic
145C22⋊C8×C149C2311yescharacteristic
146C22⋊C8×C149C2312yes—
147#95×C149—21no—
148#95×C149C2312yes—
149C24×C149—22no—
150C24×C149—21no—
151C24×C149—21no—
152C24×C149C2×D411yescharacteristic
153C24×C149C2×D412yes—
154#41×C149—81no—
155C2×Q8×C149C2×D411yescharacteristic
156C2×D4×C149—22no—
157C2×D4×C149—21no—
158C2×D4×C149—21no—
159C2×D4×C149—22no—
160C2×D4×C149—22no—
161C2×D4×C149—22no—
162C2×D4×C149—22no—
163C2×D4×C149—22no—
164C2×D4×C149—22no—
165C2×D4×C149—21no—
166C2×D4×C149—22no—
167C2×D4×C149—22no—
168C2×D4×C149—21no—
169C2×D4×C149—21no—
170C2×D4×C149—21no—
171C2×D4×C149—21no—
172C2×D4×C149—21no—
173C2×D4×C149—44no—
174C2×D4×C149—44no—
175C2×D4×C149—44no—
176C2×D4×C149—41no—
177C2×D4×C149—41no—
178C2×D4×C149—81no—
179C2×D4×C149—81no—
180C2×D4×C149—82no—
181C2×D4×C149—81no—
182C2×D4×C149—82no—
183C2×D4×C149—82no—
184C2×D4×C149—81no—
185C2×D4×C149—81no—
186C2×D4×C149—82no—
187C2×D4×C149—82no—
188C2×D4×C149—84no—
189C2×D4×C149C2×D411yescharacteristic
190C2×D4×C149C2×D412yes—
191C22×C4×C149—22no—
192C22×C4×C149—22no—
193C22×C4×C149—22no—
194C22×C4×C149—24no—
195C22×C4×C149—21no—
196C22×C4×C149—21no—
197C22×C4×C149—21no—
198C22×C4×C149—81no—
199C22×C4×C149—81no—
200C22×C4×C149—81no—
201C22×C4×C149C2×D412yes—
202C22×C4×C149C2×D411yescharacteristic
203C22×C4×C149C2×D411yescharacteristic
204C22×C4×C149C2×D411yescharacteristic
205C22×C4×C149C2×D411yescharacteristic
206C22×C4×C149C2×D411yescharacteristic
207C22×C4×C149C2411yescharacteristic
208SD16×C149—81no—
209D8×C149—81no—
210D8×C149—82no—
211M16×C149—81no—
212C2×C8×C149—21no—
213C2×C8×C149—22no—
214C2×C8×C149—21no—
215C2×C8×C149—81no—
216C4⋊C4×C149—22no—
217C4⋊C4×C149—22no—
218C4⋊C4×C149—21no—
219C4⋊C4×C149—21no—
220C4⋊C4×C149—21no—
221C4⋊C4×C149—21no—
222C4⋊C4×C149—21no—
223C4⋊C4×C149—21no—
224C4⋊C4×C149—21no—
225C4⋊C4×C149—44no—
226C4⋊C4×C149C2×D412yes—
227C4⋊C4×C149C2×D411yescharacteristic
228C4⋊C4×C149C2×D411yescharacteristic
229C22⋊C4×C149—22no—
230C22⋊C4×C149—22no—
231C22⋊C4×C149—22no—
232C22⋊C4×C149—22no—
233C22⋊C4×C149—22no—
234C22⋊C4×C149—21no—
235C22⋊C4×C149—21no—
236C22⋊C4×C149—21no—
237C22⋊C4×C149—22no—
238C22⋊C4×C149—21no—
239C22⋊C4×C149—22no—
240C22⋊C4×C149—22no—
241C22⋊C4×C149—22no—
242C22⋊C4×C149—21no—
243C22⋊C4×C149—44no—
244C22⋊C4×C149—44no—
245C22⋊C4×C149—41no—
246C22⋊C4×C149—41no—
247C42×C149—22no—
248C42×C149—21no—
249C23×C149—21no—
250C23×C149—21no—
251C23×C149—22no—
252C23×C149—22no—
253C23×C149—22no—
254C23×C149—21no—
255C23×C149—22no—
256C23×C149—22no—
257C23×C149—41no—
258C23×C149—42no—
259C23×C149—42no—
260C23×C149—42no—
261C23×C149—42no—
262C23×C149—42no—
263C23×C149—41no—
264C23×C149—41no—
265C23×C149—41no—
266C23×C149—81no—
267C23×C149—81no—
268C23×C149—82no—
269C23×C149—82no—
270C23×C149—82no—
271C23×C149#12011yescharacteristic
272C23×C149#12011yescharacteristic
273C23×C149C22×D411yescharacteristic
274Q8×C149—41no—
275D4×C149—42no—
276D4×C149—41no—
277D4×C149—42no—
278D4×C149—42no—
279D4×C149—42no—
280D4×C149—41no—
281D4×C149—41no—
282D4×C149—42no—
283D4×C149—41no—
284D4×C149—42no—
285D4×C149—41no—
286D4×C149—44no—
287D4×C149—42no—
288D4×C149—81no—
289D4×C149—82no—
290D4×C149—82no—
291D4×C149—81no—
292D4×C149—82no—
293D4×C149—82no—
294D4×C149—82no—
295D4×C149—82no—
296D4×C149—82no—
297D4×C149—88no—
298D4×C149—82no—
299D4×C149—82no—
300C2×C4×C149—24no—
301C2×C4×C149—21no—
302C2×C4×C149—22no—
303C2×C4×C149—22no—
304C2×C4×C149—21no—
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—42no—
313C2×C4×C149—42no—
314C2×C4×C149—42no—
315C2×C4×C149—42no—
316C2×C4×C149—42no—
317C2×C4×C149—41no—
318C2×C4×C149—81no—
319C2×C4×C149—84no—
320C2×C4×C149—82no—
321C2×C4×C149—82no—
322C2×C4×C149#12011yescharacteristic
323C2×C4×C149#12011yescharacteristic
324C2×C4×C149C22×D411yescharacteristic
325C2×C4×C149C22×D411yescharacteristic
326C8×C149—41no—
327C8×C149—41no—
328C8×C149—42no—
329C22×C149—21no—
330C22×C149—21no—
331C22×C149—21no—
332C22×C149—21no—
333C22×C149—21no—
334C22×C149—21no—
335C22×C149—21no—
336C22×C149—42no—
337C22×C149—42no—
338C22×C149—42no—
339C22×C149—42no—
340C22×C149—41no—
341C22×C149—42no—
342C22×C149—42no—
343C22×C149—41no—
344C22×C149—41no—
345C22×C149—42no—
346C22×C149—42no—
347C22×C149—82no—
348C22×C149—82no—
349C22×C149—82no—
350C22×C149—82no—
351C22×C149—81no—
352C22×C149—81no—
353C22×C149—81no—
354C22×C149—162no—
355C22×C149—164no—
356C22×C149#45312yes—
357C22×C149C2×#12011yescharacteristic
358C22×C149#57611yescharacteristic
359C22×C149#57711yescharacteristic
360C4×C149—21no—
361C4×C149—21no—
362C4×C149—21no—
363C4×C149—21no—
364C4×C149—44no—
365C4×C149—42no—
366C4×C149—41no—
367C4×C149—42no—
368C4×C149—41no—
369C4×C149—41no—
370C4×C149—81no—
371C2×C149—21no—
372C2×C149—21no—
373C2×C149—22no—
374C2×C149—41no—
375C2×C149—82no—
376C2×C149—82no—
377C2×C149—81no—
378C2×C149—161no—
379C2×C149#301211yescharacteristic
380C2×C149C2×#45311yescharacteristic
381C2×C149#302611yescharacteristic
382#18418C14911yesmaximal, characteristic, direct product factor, Sylow
383C149#1841811yescharacteristic, direct product factor, Sylow
384#3537C2×C14911yescharacteristic, complemented
385#3192C2×C14911yescharacteristic, complemented
386#3188C2×C14911yescharacteristic, complemented
387#2656C2×C14911yescharacteristic, complemented
388#1618C2×C14912yescomplemented
389#1613C2×C14912yescomplemented
390#1600C2×C14912yescomplemented
391#1595C2×C14912yescomplemented
392#1504C2×C14911yescharacteristic, complemented
393C2×#327C2×C14911yescharacteristic, complemented
394#1471C2×C14911yescharacteristic, complemented
395#560—22no—
396#553—21no—
397#553—21no—
398D42—22no—
399D42—21no—
400D42—21no—
401#540—21no—
402#538—21no—
403#538C22×C14912yes—
404#535—21no—
405#534—21no—
406#534C22×C14912yes—
407#525C22×C14911yescharacteristic
408C2×#121—22no—
409C2×#121C22×C14911yescharacteristic
410C2×#121C22×C14911yescharacteristic
411C2×#121C22×C14911yescharacteristic, complemented
412#484C22×C14911yescharacteristic, complemented
413#482—21no—
414#481—21no—
415#481C22×C14911yescharacteristic, complemented
416#481C22×C14912yescomplemented
417#469—22no—
418#466—21no—
419#465—21no—
420#450C22×C14911yescharacteristic, complemented
421#449—21no—
422#447—21no—
423#447C22×C14911yescharacteristic, complemented
424#447C22×C14912yescomplemented
425#407C22×C14911yescharacteristic, complemented
426C2×C22⋊C8C22×C14911yescharacteristic, complemented
427#399—21no—
428#399C22×C14912yescomplemented
429#392—21no—
430#392C22×C14912yescomplemented
431C2×#95C22×C14911yescharacteristic, complemented
432#328C22×C14912yescomplemented
433#327C22×C14912yescomplemented
434#327C22×C14912yescomplemented
435#327C22×C14912yescomplemented
436#323C22×C14912yescomplemented
437#323C22×C14912yescomplemented
438C2×#41D4×C14911yescharacteristic, complemented
439C22×D4—22no—
440C22×D4—21no—
441C22×D4—21no—
442C22×D4—22no—
443C22×D4—21no—
444C22×D4—22no—
445C22×D4D4×C14912yes—
446C22×D4D4×C14911yescharacteristic
447C22×D4D4×C14911yescharacteristic, complemented
448C22×D4C23×C14911yescharacteristic
449C23×C4—21no—
450C23×C4C23×C14911yescharacteristic
451C2×SD16—21no—
452C2×D8—22no—
453C2×D8—21no—
454C2×M16—21no—
455C22×C8—21no—
456#127—22no—
457#127—21no—
458#126—22no—
459#126—22no—
460#125—21no—
461#124—22no—
462#123—22no—
463#123—21no—
464#123—22no—
465#123—22no—
466#123—22no—
467C22⋊Q8D4×C14911yescharacteristic, complemented
468C22⋊Q8C23×C14911yescharacteristic
469#121—22no—
470#121—21no—
471#121—21no—
472#121—22no—
473#121—22no—
474#121—22no—
475#121—22no—
476#121—21no—
477#121—21no—
478#121—21no—
479#121—21no—
480#121—21no—
481#121—21no—
482#121—22no—
483#121—21no—
484#121—21no—
485#121—21no—
486#121—21no—
487#121—48no—
488#121D4×C14912yescomplemented
489#121D4×C14911yescharacteristic, complemented
490#121C23×C14912yes—
491#121C23×C14911yescharacteristic
492#120—22no—
493#120—22no—
494#120—22no—
495#120—21no—
496#120—22no—
497#120—22no—
498#120—22no—
499C4×D4—22no—
500C4×D4—21no—
501C4×D4—21no—
502C4×D4—21no—
503C4×D4—21no—
504C4×D4—22no—
505#117—21no—
506#117D4×C14911yescharacteristic, complemented
507C2×C4⋊C4—22no—
508C2×C4⋊C4D4×C14911yescharacteristic
509C2×C4⋊C4D4×C14911yescharacteristic, complemented
510C2×C4⋊C4C23×C14911yescharacteristic
511C2×C22⋊C4—21no—
512C2×C22⋊C4—22no—
513C2×C22⋊C4—22no—
514C2×C22⋊C4—21no—
515C2×C22⋊C4C23×C14912yes—
516#107—21no—
517#106—21no—
518#106—22no—
519#103—21no—
520#102—22no—
521#102—21no—
522#102—21no—
523#102—22no—
524#102—21no—
525C22⋊C8—21no—
526C22⋊C8—21no—
527C22⋊C8C23×C14911yescharacteristic
528C22⋊C8C23×C14911yescharacteristic
529C22⋊C8C23×C14912yes—
530#95—21no—
531#95C23×C14912yes—
532C24—22no—
533C24—21no—
534C24—21no—
535C24C2×D4×C14911yescharacteristic
536C24C2×D4×C14912yes—
537#41—81no—
538C2×Q8C2×D4×C14911yescharacteristic
539C2×D4—22no—
540C2×D4—21no—
541C2×D4—21no—
542C2×D4—22no—
543C2×D4—22no—
544C2×D4—22no—
545C2×D4—22no—
546C2×D4—22no—
547C2×D4—22no—
548C2×D4—21no—
549C2×D4—22no—
550C2×D4—22no—
551C2×D4—21no—
552C2×D4—21no—
553C2×D4—21no—
554C2×D4—21no—
555C2×D4—21no—
556C2×D4—44no—
557C2×D4—44no—
558C2×D4—44no—
559C2×D4—41no—
560C2×D4—41no—
561C2×D4—81no—
562C2×D4—81no—
563C2×D4—82no—
564C2×D4—81no—
565C2×D4—82no—
566C2×D4—82no—
567C2×D4—81no—
568C2×D4—81no—
569C2×D4—82no—
570C2×D4—82no—
571C2×D4—84no—
572C2×D4C2×D4×C14911yescharacteristic
573C2×D4C2×D4×C14912yes—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—24no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—81no—
582C22×C4—81no—
583C22×C4—81no—
584C22×C4C2×D4×C14912yes—
585C22×C4C2×D4×C14911yescharacteristic
586C22×C4C2×D4×C14911yescharacteristic
587C22×C4C2×D4×C14911yescharacteristic
588C22×C4C2×D4×C14911yescharacteristic
589C22×C4C2×D4×C14911yescharacteristic
590C22×C4C24×C14911yescharacteristic
591SD16—81no—
592D8—81no—
593D8—82no—
594M16—81no—
595C2×C8—21no—
596C2×C8—22no—
597C2×C8—21no—
598C2×C8—81no—
599C4⋊C4—22no—
600C4⋊C4—22no—
601C4⋊C4—21no—
602C4⋊C4—21no—
603C4⋊C4—21no—
604C4⋊C4—21no—
605C4⋊C4—21no—
606C4⋊C4—21no—
607C4⋊C4—21no—
608C4⋊C4—44no—
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—21no—
618C22⋊C4—21no—
619C22⋊C4—21no—
620C22⋊C4—22no—
621C22⋊C4—21no—
622C22⋊C4—22no—
623C22⋊C4—22no—
624C22⋊C4—22no—
625C22⋊C4—21no—
626C22⋊C4—44no—
627C22⋊C4—44no—
628C22⋊C4—41no—
629C22⋊C4—41no—
630C42—22no—
631C42—21no—
632C23—22no—
633C23—21no—
634C23—21no—
635C23—22no—
636C23—22no—
637C23—21no—
638C23—22no—
639C23—22no—
640C23—41no—
641C23—42no—
642C23—42no—
643C23—42no—
644C23—42no—
645C23—42no—
646C23—41no—
647C23—41no—
648C23—41no—
649C23—81no—
650C23—81no—
651C23—82no—
652C23—82no—
653C23—82no—
654C23#120×C14911yescharacteristic
655C23#120×C14911yescharacteristic
656C23C22×D4×C14911yescharacteristic
657Q8—41no—
658D4—42no—
659D4—41no—
660D4—42no—
661D4—42no—
662D4—42no—
663D4—41no—
664D4—41no—
665D4—44no—
666D4—42no—
667D4—42no—
668D4—41no—
669D4—42no—
670D4—41no—
671D4—81no—
672D4—82no—
673D4—82no—
674D4—81no—
675D4—82no—
676D4—82no—
677D4—82no—
678D4—82no—
679D4—82no—
680D4—88no—
681D4—82no—
682D4—82no—
683C2×C4—24no—
684C2×C4—21no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—21no—
688C2×C4—21no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—42no—
696C2×C4—42no—
697C2×C4—42no—
698C2×C4—42no—
699C2×C4—42no—
700C2×C4—41no—
701C2×C4—81no—
702C2×C4—84no—
703C2×C4—82no—
704C2×C4—82no—
705C2×C4#120×C14911yescharacteristic
706C2×C4#120×C14911yescharacteristic
707C2×C4C22×D4×C14911yescharacteristic
708C2×C4C22×D4×C14911yescharacteristic
709C8—41no—
710C8—41no—
711C8—42no—
712C22—21no—
713C22—21no—
714C22—21no—
715C22—21no—
716C22—21no—
717C22—21no—
718C22—21no—
719C22—42no—
720C22—42no—
721C22—42no—
722C22—42no—
723C22—41no—
724C22—42no—
725C22—42no—
726C22—41no—
727C22—41no—
728C22—42no—
729C22—42no—
730C22—82no—
731C22—82no—
732C22—82no—
733C22—82no—
734C22—81no—
735C22—81no—
736C22—81no—
737C22—162no—
738C22—164no—
739C22#453×C14912yes—
740C22C2×#120×C14911yescharacteristic
741C22#576×C14911yescharacteristic
742C22#577×C14911yescharacteristic
743C4—21no—
744C4—21no—
745C4—21no—
746C4—21no—
747C4—44no—
748C4—42no—
749C4—41no—
750C4—42no—
751C4—41no—
752C4—41no—
753C4—81no—
754C2—21no—
755C2—21no—
756C2—22no—
757C2—41no—
758C2—82no—
759C2—82no—
760C2—81no—
761C2—161no—
762C2#3012×C14911yescharacteristic
763C2C2×#453×C14911yescharacteristic
764C2#3026×C14911yescharacteristic
subgroupG/H
center, socleC22×C149C2×#120
commutator, Frattini, cosocleC22×C4C24×C149
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C149 ◁ C23×C4×C149 ◁ G

Complements

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

NH ≅ G/Ntype
1. #3537×C149C2semidirect
2. #3192×C149C2semidirect
3. #3188×C149C2semidirect
4. #2656×C149C2semidirect
5. #1618×C149C2semidirect
6. #1613×C149C2semidirect
7. #1600×C149C2semidirect
8. #1595×C149C2semidirect
9. #1504×C149C2semidirect
10. C2×#327×C149C2semidirect
11. #1471×C149C2semidirect
28. C2×#121×C149C22semidirect
29. #484×C149C22semidirect
32. #481×C149C22semidirect
33. #481×C149C22semidirect
37. #450×C149C22semidirect
40. #447×C149C22semidirect
41. #447×C149C22semidirect
42. #407×C149C22semidirect
43. C2×C22⋊C8×C149C22semidirect
45. #399×C149C22semidirect
47. #392×C149C22semidirect
48. C2×#95×C149C22semidirect
49. #328×C149C22semidirect
50. #327×C149C22semidirect
51. #327×C149C22semidirect
52. #327×C149C22semidirect
53. #323×C149C22semidirect
54. #323×C149C22semidirect
55. C2×#41×C149D4semidirect
64. C22×D4×C149D4semidirect
84. C22⋊Q8×C149D4semidirect
105. #121×C149D4semidirect
106. #121×C149D4semidirect
123. #117×C149D4semidirect
126. C2×C4⋊C4×C149D4semidirect
382. #18418C149direct (N × H)
383. C149#18418direct (N × H)
384. #3537C2×C149semidirect
385. #3192C2×C149semidirect
386. #3188C2×C149semidirect
387. #2656C2×C149semidirect
388. #1618C2×C149semidirect
389. #1613C2×C149semidirect
390. #1600C2×C149semidirect
391. #1595C2×C149semidirect
392. #1504C2×C149semidirect
393. C2×#327C2×C149semidirect
394. #1471C2×C149semidirect
411. C2×#121C22×C149semidirect
412. #484C22×C149semidirect
415. #481C22×C149semidirect
416. #481C22×C149semidirect
420. #450C22×C149semidirect
423. #447C22×C149semidirect
424. #447C22×C149semidirect
425. #407C22×C149semidirect
426. C2×C22⋊C8C22×C149semidirect
428. #399C22×C149semidirect
430. #392C22×C149semidirect
431. C2×#95C22×C149semidirect
432. #328C22×C149semidirect
433. #327C22×C149semidirect
434. #327C22×C149semidirect
435. #327C22×C149semidirect
436. #323C22×C149semidirect
437. #323C22×C149semidirect
438. C2×#41D4×C149semidirect
447. C22×D4D4×C149semidirect
467. C22⋊Q8D4×C149semidirect
488. #121D4×C149semidirect
489. #121D4×C149semidirect
506. #117D4×C149semidirect
509. C2×C4⋊C4D4×C149semidirect

Maximal subgroups

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

subgroupindex
#3537×C1492
#3192×C1492
#3188×C1492
#2656×C1492
#1618×C1492
#1613×C1492
#1600×C1492
#1595×C1492
#1504×C1492
C2×#327×C1492
#1471×C1492
#18418149