Finite Group Databasebeta

← C149×#19010 #49197959

Subgroups — C149×#19010 #49197959

Order 38144.

920 conjugacy classes of subgroups.

The subgroup lattice has 890 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3529×C149C211yesmaximal, characteristic, complemented
2#3219×C149C211yesmaximal, characteristic, complemented
3#3214×C149C211yesmaximal, characteristic, complemented
4#3180×C149C211yesmaximal, characteristic, complemented
5#1664×C149C211yesmaximal, characteristic, complemented
6#1662×C149C211yesmaximal, characteristic, complemented
7#1661×C149C211yesmaximal, characteristic, complemented
8#1659×C149C211yesmaximal, characteristic, complemented
9#1657×C149C211yesmaximal, characteristic, complemented
10#1656×C149C211yesmaximal, characteristic, complemented
11#1656×C149C211yesmaximal, characteristic, complemented
12#1655×C149C211yesmaximal, characteristic, complemented
13#1535×C149C211yesmaximal, characteristic, complemented
14#1532×C149C211yesmaximal, characteristic, complemented
15#1530×C149C211yesmaximal, characteristic, complemented
16#563×C149—21no—
17#563×C149C2211yescharacteristic
18#562×C149—21no—
19#562×C149—21no—
20#562×C149C2211yescharacteristic
21#562×C149C2211yescharacteristic
22H(3,𝔽4)×C149C2211yescharacteristic
23#560×C149—21no—
24#560×C149—21no—
25#560×C149—21no—
26#532×C149—21no—
27#532×C149C2211yescharacteristic
28#532×C149C2211yescharacteristic, complemented
29#529×C149—21no—
30#529×C149—21no—
31#529×C149C2211yescharacteristic
32#529×C149C2211yescharacteristic
33#525×C149—21no—
34#525×C149—21no—
35#525×C149—21no—
36#501×C149C2211yescharacteristic, complemented
37#497×C149C2211yescharacteristic
38#496×C149C2211yescharacteristic
39#496×C149C2211yescharacteristic
40#496×C149C2211yescharacteristic
41#496×C149C2211yescharacteristic, complemented
42#491×C149C2211yescharacteristic, complemented
43#490×C149C2211yescharacteristic, complemented
44#490×C149C2211yescharacteristic, complemented
45#489×C149C2211yescharacteristic
46#489×C149C2211yescharacteristic
47#489×C149C2211yescharacteristic, complemented
48#466×C149—21no—
49#465×C149—21no—
50#464×C149—21no—
51#463×C149—21no—
52#461×C149—21no—
53#459×C149—21no—
54#452×C149—21no—
55#449×C149—21no—
56#449×C149—21no—
57#449×C149—21no—
58#442×C149—21no—
59#440×C149—21no—
60#432×C149C2211yescharacteristic, complemented
61#432×C149C2211yescharacteristic, complemented
62C2×#97×C149C2211yescharacteristic, complemented
63#330×C149C2211yescharacteristic, complemented
64#330×C149C2211yescharacteristic, complemented
65#330×C149C2211yescharacteristic, complemented
66#330×C149C2211yescharacteristic, complemented
67#329×C149C2211yescharacteristic
68#329×C149C2211yescharacteristic
69#329×C149C2211yescharacteristic
70#329×C149C2211yescharacteristic
71#329×C149C2211yescharacteristic
72#329×C149C2211yescharacteristic
73#329×C149C2211yescharacteristic, complemented
74#329×C149C2211yescharacteristic, complemented
75C2×#41×C149—21no—
76C2×#41×C149—21no—
77C2×#41×C149D411yescharacteristic
78C2×#41×C149D411yescharacteristic
79C23×C4×C149—21no—
80C2×Q16×C149—21no—
81C2×SD16×C149—21no—
82C2×SD16×C149—21no—
83C2×SD16×C149—21no—
84C2×SD16×C149—21no—
85C2×SD16×C149—21no—
86C2×D8×C149—21no—
87C2×D8×C149—21no—
88C2×D8×C149—21no—
89C2×D8×C149—21no—
90C22×C8×C149—21no—
91C4⋊Q8×C149—21no—
92C4⋊Q8×C149D411yescharacteristic
93C4⋊Q8×C149C2311yescharacteristic
94#127×C149—21no—
95#127×C149D411yescharacteristic
96#127×C149C2311yescharacteristic
97#126×C149—21no—
98#126×C149—21no—
99#126×C149—21no—
100#126×C149—21no—
101#126×C149—21no—
102#126×C149—21no—
103#125×C149—21no—
104#125×C149—21no—
105#125×C149C2311yescharacteristic
106#125×C149C2311yescharacteristic
107#124×C149—21no—
108#124×C149—21no—
109#124×C149—21no—
110#124×C149—21no—
111#124×C149—21no—
112#124×C149C2311yescharacteristic
113#124×C149C2311yescharacteristic
114#124×C149C2311yescharacteristic
115#124×C149C2311yescharacteristic
116#123×C149—21no—
117#123×C149—21no—
118#123×C149—21no—
119#123×C149—21no—
120#123×C149—21no—
121#123×C149—21no—
122#123×C149—21no—
123#123×C149—21no—
124#123×C149—21no—
125#123×C149—21no—
126#123×C149—21no—
127#123×C149—21no—
128C22⋊Q8×C149—21no—
129C22⋊Q8×C149—21no—
130C22⋊Q8×C149—21no—
131C22⋊Q8×C149—21no—
132C22⋊Q8×C149—21no—
133C22⋊Q8×C149—21no—
134C22⋊Q8×C149—21no—
135C22⋊Q8×C149—21no—
136C22⋊Q8×C149D411yescharacteristic
137C22⋊Q8×C149D411yescharacteristic
138#121×C149—21no—
139#121×C149—21no—
140#121×C149—21no—
141#121×C149—21no—
142#121×C149—21no—
143#121×C149—21no—
144#121×C149—21no—
145#121×C149—21no—
146#121×C149—21no—
147#121×C149—21no—
148#121×C149—21no—
149#121×C149—21no—
150#121×C149—21no—
151#121×C149—21no—
152#121×C149—21no—
153#121×C149—21no—
154#121×C149D411yescharacteristic
155#121×C149D411yescharacteristic
156#120×C149—21no—
157#120×C149—21no—
158#120×C149—21no—
159#120×C149—21no—
160#120×C149—21no—
161#120×C149—21no—
162C4×Q8×C149D411yescharacteristic
163C4×Q8×C149D411yescharacteristic
164C4×D4×C149—21no—
165C4×D4×C149—21no—
166C4×D4×C149—21no—
167C4×D4×C149—21no—
168C4×D4×C149—21no—
169C4×D4×C149—21no—
170C4×D4×C149—21no—
171C4×D4×C149—21no—
172C4×D4×C149—21no—
173C4×D4×C149—21no—
174C4×D4×C149D411yescharacteristic
175C4×D4×C149D411yescharacteristic
176#117×C149—21no—
177#117×C149—21no—
178#117×C149—21no—
179C2×C42×C149—21no—
180C2×C42×C149C2311yescharacteristic
181#107×C149—21no—
182#106×C149—21no—
183C4⋊C8×C149—21no—
184C4⋊C8×C149—21no—
185#103×C149—21no—
186#103×C149—21no—
187#103×C149—21no—
188#103×C149—21no—
189#103×C149—21no—
190#102×C149—21no—
191#102×C149—21no—
192#102×C149—21no—
193#102×C149—21no—
194#102×C149—21no—
195#102×C149—21no—
196#102×C149—21no—
197C22⋊C8×C149—21no—
198C22⋊C8×C149—21no—
199#97×C149—21no—
200#97×C149C2311yescharacteristic
201#97×C149C2311yescharacteristic
202#97×C149C2311yescharacteristic
203#97×C149C2311yescharacteristic
204#97×C149C2311yescharacteristic
205#97×C149C2311yescharacteristic
206C24×C149—21no—
207#41×C149—81no—
208#41×C149—81no—
209#41×C149—82no—
210#41×C149—81no—
211#41×C149—81no—
212C2×Q8×C149—21no—
213C2×Q8×C149—21no—
214C2×Q8×C149C2×D411yescharacteristic
215C2×Q8×C149C2×D411yescharacteristic
216C2×Q8×C149C2×D411yescharacteristic
217C2×Q8×C149C2×D411yescharacteristic
218C2×D4×C149—21no—
219C2×D4×C149—21no—
220C2×D4×C149—21no—
221C2×D4×C149—21no—
222C2×D4×C149—21no—
223C2×D4×C149—21no—
224C2×D4×C149—21no—
225C2×D4×C149—21no—
226C2×D4×C149—21no—
227C2×D4×C149—21no—
228C2×D4×C149—21no—
229C2×D4×C149—21no—
230C2×D4×C149—21no—
231C2×D4×C149—21no—
232C2×D4×C149—21no—
233C2×D4×C149—21no—
234C2×D4×C149—41no—
235C2×D4×C149C2×D411yescharacteristic
236C2×D4×C149C2×D411yescharacteristic
237C2×D4×C149C2×D411yescharacteristic
238C2×D4×C149C2×D411yescharacteristic
239C22×C4×C149—21no—
240C22×C4×C149—21no—
241C22×C4×C149—21no—
242C22×C4×C149—21no—
243C22×C4×C149—21no—
244C22×C4×C149—21no—
245C22×C4×C149—21no—
246C22×C4×C149—21no—
247C22×C4×C149—21no—
248C22×C4×C149—41no—
249C22×C4×C149—82no—
250C22×C4×C149C2×D411yescharacteristic
251C22×C4×C149C2×D411yescharacteristic
252C22×C4×C149C2×D411yescharacteristic
253Q16×C149—81no—
254SD16×C149—42no—
255SD16×C149—81no—
256SD16×C149—81no—
257SD16×C149—81no—
258SD16×C149—81no—
259D8×C149—42no—
260D8×C149—81no—
261D8×C149—81no—
262D8×C149—81no—
263C2×C8×C149—21no—
264C2×C8×C149—21no—
265C2×C8×C149—21no—
266C2×C8×C149—21no—
267C2×C8×C149—21no—
268C2×C8×C149—21no—
269C2×C8×C149—42no—
270C4⋊C4×C149—21no—
271C4⋊C4×C149—21no—
272C4⋊C4×C149—21no—
273C4⋊C4×C149—21no—
274C4⋊C4×C149—21no—
275C4⋊C4×C149—21no—
276C4⋊C4×C149—21no—
277C4⋊C4×C149—21no—
278C4⋊C4×C149—21no—
279C4⋊C4×C149—21no—
280C4⋊C4×C149—21no—
281C4⋊C4×C149—21no—
282C4⋊C4×C149—21no—
283C4⋊C4×C149—21no—
284C4⋊C4×C149—21no—
285C4⋊C4×C149—21no—
286C4⋊C4×C149—21no—
287C4⋊C4×C149—21no—
288C4⋊C4×C149C2×D411yescharacteristic
289C4⋊C4×C149C2×D411yescharacteristic
290C4⋊C4×C149C2×D411yescharacteristic
291C4⋊C4×C149C2×D411yescharacteristic
292C22⋊C4×C149—21no—
293C22⋊C4×C149—21no—
294C22⋊C4×C149—21no—
295C22⋊C4×C149—21no—
296C22⋊C4×C149—21no—
297C22⋊C4×C149—21no—
298C22⋊C4×C149—21no—
299C22⋊C4×C149—21no—
300C22⋊C4×C149—21no—
301C22⋊C4×C149—21no—
302C22⋊C4×C149—21no—
303C22⋊C4×C149—21no—
304C22⋊C4×C149—21no—
305C22⋊C4×C149—21no—
306C22⋊C4×C149—21no—
307C22⋊C4×C149—21no—
308C22⋊C4×C149—21no—
309C22⋊C4×C149—21no—
310C22⋊C4×C149—21no—
311C22⋊C4×C149—21no—
312C22⋊C4×C149—21no—
313C22⋊C4×C149—21no—
314C22⋊C4×C149—21no—
315C22⋊C4×C149—21no—
316C22⋊C4×C149—41no—
317C22⋊C4×C149—41no—
318C42×C149—21no—
319C42×C149—21no—
320C42×C149—21no—
321C42×C149—21no—
322C42×C149C2×D411yescharacteristic
323C42×C149C2×D411yescharacteristic
324C42×C149C2×D411yescharacteristic
325C42×C149C2411yescharacteristic
326C23×C149—21no—
327C23×C149—21no—
328C23×C149—21no—
329C23×C149—21no—
330C23×C149—41no—
331C23×C149—81no—
332C23×C149—81no—
333C23×C149—81no—
334C23×C149#12011yescharacteristic
335Q8×C149—41no—
336Q8×C149—41no—
337Q8×C149—41no—
338Q8×C149—41no—
339Q8×C149—41no—
340Q8×C149—41no—
341Q8×C149—81no—
342D4×C149—41no—
343D4×C149—41no—
344D4×C149—41no—
345D4×C149—41no—
346D4×C149—41no—
347D4×C149—41no—
348D4×C149—41no—
349D4×C149—41no—
350D4×C149—41no—
351D4×C149—41no—
352D4×C149—81no—
353D4×C149—81no—
354D4×C149—81no—
355D4×C149—81no—
356D4×C149—81no—
357D4×C149—81no—
358D4×C149—81no—
359D4×C149—81no—
360D4×C149—81no—
361D4×C149—81no—
362D4×C149—81no—
363D4×C149—81no—
364D4×C149—81no—
365D4×C149—82no—
366C2×C4×C149—21no—
367C2×C4×C149—21no—
368C2×C4×C149—21no—
369C2×C4×C149—21no—
370C2×C4×C149—21no—
371C2×C4×C149—21no—
372C2×C4×C149—21no—
373C2×C4×C149—21no—
374C2×C4×C149—41no—
375C2×C4×C149—41no—
376C2×C4×C149—41no—
377C2×C4×C149—42no—
378C2×C4×C149—42no—
379C2×C4×C149—42no—
380C2×C4×C149—42no—
381C2×C4×C149—41no—
382C2×C4×C149—82no—
383C2×C4×C149—81no—
384C2×C4×C149—81no—
385C2×C4×C149—81no—
386C2×C4×C149—81no—
387C2×C4×C149—81no—
388C2×C4×C149#12011yescharacteristic
389C2×C4×C149#12011yescharacteristic
390C2×C4×C149#12011yescharacteristic
391C2×C4×C149C22×D411yescharacteristic
392C2×C4×C149C22×D411yescharacteristic
393C2×C4×C149C22×D411yescharacteristic
394C8×C149—22no—
395C8×C149—41no—
396C8×C149—41no—
397C8×C149—41no—
398C8×C149—41no—
399C8×C149—41no—
400C22×C149—21no—
401C22×C149—21no—
402C22×C149—21no—
403C22×C149—41no—
404C22×C149—41no—
405C22×C149—41no—
406C22×C149—41no—
407C22×C149—41no—
408C22×C149—41no—
409C22×C149—41no—
410C22×C149—41no—
411C22×C149—41no—
412C22×C149—41no—
413C22×C149—41no—
414C22×C149—41no—
415C22×C149—84no—
416C22×C149—81no—
417C22×C149—81no—
418C22×C149—81no—
419C22×C149C2×#12011yescharacteristic
420C4×C149—21no—
421C4×C149—21no—
422C4×C149—21no—
423C4×C149—21no—
424C4×C149—21no—
425C4×C149—21no—
426C4×C149—41no—
427C4×C149—41no—
428C4×C149—41no—
429C4×C149—41no—
430C4×C149—41no—
431C4×C149—41no—
432C4×C149—41no—
433C4×C149—41no—
434C4×C149—81no—
435C2×C149—41no—
436C2×C149—81no—
437C2×C149—81no—
438C2×C149—81no—
439C2×C149—81no—
440C2×C149—161no—
441C2×C149#301811yescharacteristic
442C2×C149#301911yescharacteristic
443C2×C149#302111yescharacteristic
444#19010C14911yesmaximal, characteristic, direct product factor, Sylow
445C149#1901011yescharacteristic, direct product factor, Sylow
446#3529C2×C14911yescharacteristic, complemented
447#3219C2×C14911yescharacteristic, complemented
448#3214C2×C14911yescharacteristic, complemented
449#3180C2×C14911yescharacteristic, complemented
450#1664C2×C14911yescharacteristic, complemented
451#1662C2×C14911yescharacteristic, complemented
452#1661C2×C14911yescharacteristic, complemented
453#1659C2×C14911yescharacteristic, complemented
454#1657C2×C14911yescharacteristic, complemented
455#1656C2×C14911yescharacteristic, complemented
456#1656C2×C14911yescharacteristic, complemented
457#1655C2×C14911yescharacteristic, complemented
458#1535C2×C14911yescharacteristic, complemented
459#1532C2×C14911yescharacteristic, complemented
460#1530C2×C14911yescharacteristic, complemented
461#563—21no—
462#563C22×C14911yescharacteristic
463#562—21no—
464#562—21no—
465#562C22×C14911yescharacteristic
466#562C22×C14911yescharacteristic
467H(3,𝔽4)C22×C14911yescharacteristic
468#560—21no—
469#560—21no—
470#560—21no—
471#532—21no—
472#532C22×C14911yescharacteristic
473#532C22×C14911yescharacteristic, complemented
474#529—21no—
475#529—21no—
476#529C22×C14911yescharacteristic
477#529C22×C14911yescharacteristic
478#525—21no—
479#525—21no—
480#525—21no—
481#501C22×C14911yescharacteristic, complemented
482#497C22×C14911yescharacteristic
483#496C22×C14911yescharacteristic
484#496C22×C14911yescharacteristic
485#496C22×C14911yescharacteristic
486#496C22×C14911yescharacteristic, complemented
487#491C22×C14911yescharacteristic, complemented
488#490C22×C14911yescharacteristic, complemented
489#490C22×C14911yescharacteristic, complemented
490#489C22×C14911yescharacteristic
491#489C22×C14911yescharacteristic
492#489C22×C14911yescharacteristic, complemented
493#466—21no—
494#465—21no—
495#464—21no—
496#463—21no—
497#461—21no—
498#459—21no—
499#452—21no—
500#449—21no—
501#449—21no—
502#449—21no—
503#442—21no—
504#440—21no—
505#432C22×C14911yescharacteristic, complemented
506#432C22×C14911yescharacteristic, complemented
507C2×#97C22×C14911yescharacteristic, complemented
508#330C22×C14911yescharacteristic, complemented
509#330C22×C14911yescharacteristic, complemented
510#330C22×C14911yescharacteristic, complemented
511#330C22×C14911yescharacteristic, complemented
512#329C22×C14911yescharacteristic
513#329C22×C14911yescharacteristic
514#329C22×C14911yescharacteristic
515#329C22×C14911yescharacteristic
516#329C22×C14911yescharacteristic
517#329C22×C14911yescharacteristic
518#329C22×C14911yescharacteristic, complemented
519#329C22×C14911yescharacteristic, complemented
520C2×#41—21no—
521C2×#41—21no—
522C2×#41D4×C14911yescharacteristic
523C2×#41D4×C14911yescharacteristic
524C23×C4—21no—
525C2×Q16—21no—
526C2×SD16—21no—
527C2×SD16—21no—
528C2×SD16—21no—
529C2×SD16—21no—
530C2×SD16—21no—
531C2×D8—21no—
532C2×D8—21no—
533C2×D8—21no—
534C2×D8—21no—
535C22×C8—21no—
536C4⋊Q8—21no—
537C4⋊Q8D4×C14911yescharacteristic
538C4⋊Q8C23×C14911yescharacteristic
539#127—21no—
540#127D4×C14911yescharacteristic
541#127C23×C14911yescharacteristic
542#126—21no—
543#126—21no—
544#126—21no—
545#126—21no—
546#126—21no—
547#126—21no—
548#125—21no—
549#125—21no—
550#125C23×C14911yescharacteristic
551#125C23×C14911yescharacteristic
552#124—21no—
553#124—21no—
554#124—21no—
555#124—21no—
556#124—21no—
557#124C23×C14911yescharacteristic
558#124C23×C14911yescharacteristic
559#124C23×C14911yescharacteristic
560#124C23×C14911yescharacteristic
561#123—21no—
562#123—21no—
563#123—21no—
564#123—21no—
565#123—21no—
566#123—21no—
567#123—21no—
568#123—21no—
569#123—21no—
570#123—21no—
571#123—21no—
572#123—21no—
573C22⋊Q8—21no—
574C22⋊Q8—21no—
575C22⋊Q8—21no—
576C22⋊Q8—21no—
577C22⋊Q8—21no—
578C22⋊Q8—21no—
579C22⋊Q8—21no—
580C22⋊Q8—21no—
581C22⋊Q8D4×C14911yescharacteristic
582C22⋊Q8D4×C14911yescharacteristic
583#121—21no—
584#121—21no—
585#121—21no—
586#121—21no—
587#121—21no—
588#121—21no—
589#121—21no—
590#121—21no—
591#121—21no—
592#121—21no—
593#121—21no—
594#121—21no—
595#121—21no—
596#121—21no—
597#121—21no—
598#121—21no—
599#121D4×C14911yescharacteristic
600#121D4×C14911yescharacteristic
601#120—21no—
602#120—21no—
603#120—21no—
604#120—21no—
605#120—21no—
606#120—21no—
607C4×Q8D4×C14911yescharacteristic
608C4×Q8D4×C14911yescharacteristic
609C4×D4—21no—
610C4×D4—21no—
611C4×D4—21no—
612C4×D4—21no—
613C4×D4—21no—
614C4×D4—21no—
615C4×D4—21no—
616C4×D4—21no—
617C4×D4—21no—
618C4×D4—21no—
619C4×D4D4×C14911yescharacteristic
620C4×D4D4×C14911yescharacteristic
621#117—21no—
622#117—21no—
623#117—21no—
624C2×C42—21no—
625C2×C42C23×C14911yescharacteristic
626#107—21no—
627#106—21no—
628C4⋊C8—21no—
629C4⋊C8—21no—
630#103—21no—
631#103—21no—
632#103—21no—
633#103—21no—
634#103—21no—
635#102—21no—
636#102—21no—
637#102—21no—
638#102—21no—
639#102—21no—
640#102—21no—
641#102—21no—
642C22⋊C8—21no—
643C22⋊C8—21no—
644#97—21no—
645#97C23×C14911yescharacteristic
646#97C23×C14911yescharacteristic
647#97C23×C14911yescharacteristic
648#97C23×C14911yescharacteristic
649#97C23×C14911yescharacteristic
650#97C23×C14911yescharacteristic
651C24—21no—
652#41—81no—
653#41—81no—
654#41—82no—
655#41—81no—
656#41—81no—
657C2×Q8—21no—
658C2×Q8—21no—
659C2×Q8C2×D4×C14911yescharacteristic
660C2×Q8C2×D4×C14911yescharacteristic
661C2×Q8C2×D4×C14911yescharacteristic
662C2×Q8C2×D4×C14911yescharacteristic
663C2×D4—21no—
664C2×D4—21no—
665C2×D4—21no—
666C2×D4—21no—
667C2×D4—21no—
668C2×D4—21no—
669C2×D4—21no—
670C2×D4—21no—
671C2×D4—21no—
672C2×D4—21no—
673C2×D4—21no—
674C2×D4—21no—
675C2×D4—21no—
676C2×D4—21no—
677C2×D4—21no—
678C2×D4—21no—
679C2×D4—41no—
680C2×D4C2×D4×C14911yescharacteristic
681C2×D4C2×D4×C14911yescharacteristic
682C2×D4C2×D4×C14911yescharacteristic
683C2×D4C2×D4×C14911yescharacteristic
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—41no—
694C22×C4—82no—
695C22×C4C2×D4×C14911yescharacteristic
696C22×C4C2×D4×C14911yescharacteristic
697C22×C4C2×D4×C14911yescharacteristic
698Q16—81no—
699SD16—42no—
700SD16—81no—
701SD16—81no—
702SD16—81no—
703SD16—81no—
704D8—42no—
705D8—81no—
706D8—81no—
707D8—81no—
708C2×C8—21no—
709C2×C8—21no—
710C2×C8—21no—
711C2×C8—21no—
712C2×C8—21no—
713C2×C8—21no—
714C2×C8—42no—
715C4⋊C4—21no—
716C4⋊C4—21no—
717C4⋊C4—21no—
718C4⋊C4—21no—
719C4⋊C4—21no—
720C4⋊C4—21no—
721C4⋊C4—21no—
722C4⋊C4—21no—
723C4⋊C4—21no—
724C4⋊C4—21no—
725C4⋊C4—21no—
726C4⋊C4—21no—
727C4⋊C4—21no—
728C4⋊C4—21no—
729C4⋊C4—21no—
730C4⋊C4—21no—
731C4⋊C4—21no—
732C4⋊C4—21no—
733C4⋊C4C2×D4×C14911yescharacteristic
734C4⋊C4C2×D4×C14911yescharacteristic
735C4⋊C4C2×D4×C14911yescharacteristic
736C4⋊C4C2×D4×C14911yescharacteristic
737C22⋊C4—21no—
738C22⋊C4—21no—
739C22⋊C4—21no—
740C22⋊C4—21no—
741C22⋊C4—21no—
742C22⋊C4—21no—
743C22⋊C4—21no—
744C22⋊C4—21no—
745C22⋊C4—21no—
746C22⋊C4—21no—
747C22⋊C4—21no—
748C22⋊C4—21no—
749C22⋊C4—21no—
750C22⋊C4—21no—
751C22⋊C4—21no—
752C22⋊C4—21no—
753C22⋊C4—21no—
754C22⋊C4—21no—
755C22⋊C4—21no—
756C22⋊C4—21no—
757C22⋊C4—21no—
758C22⋊C4—21no—
759C22⋊C4—21no—
760C22⋊C4—21no—
761C22⋊C4—41no—
762C22⋊C4—41no—
763C42—21no—
764C42—21no—
765C42—21no—
766C42—21no—
767C42C2×D4×C14911yescharacteristic
768C42C2×D4×C14911yescharacteristic
769C42C2×D4×C14911yescharacteristic
770C42C24×C14911yescharacteristic
771C23—21no—
772C23—21no—
773C23—21no—
774C23—21no—
775C23—41no—
776C23—81no—
777C23—81no—
778C23—81no—
779C23#120×C14911yescharacteristic
780Q8—41no—
781Q8—41no—
782Q8—41no—
783Q8—41no—
784Q8—41no—
785Q8—41no—
786Q8—81no—
787D4—41no—
788D4—41no—
789D4—41no—
790D4—41no—
791D4—41no—
792D4—41no—
793D4—41no—
794D4—41no—
795D4—41no—
796D4—41no—
797D4—81no—
798D4—81no—
799D4—81no—
800D4—81no—
801D4—81no—
802D4—81no—
803D4—81no—
804D4—81no—
805D4—81no—
806D4—81no—
807D4—81no—
808D4—81no—
809D4—81no—
810D4—82no—
811C2×C4—21no—
812C2×C4—21no—
813C2×C4—21no—
814C2×C4—21no—
815C2×C4—21no—
816C2×C4—21no—
817C2×C4—21no—
818C2×C4—21no—
819C2×C4—41no—
820C2×C4—41no—
821C2×C4—41no—
822C2×C4—42no—
823C2×C4—42no—
824C2×C4—42no—
825C2×C4—42no—
826C2×C4—41no—
827C2×C4—82no—
828C2×C4—81no—
829C2×C4—81no—
830C2×C4—81no—
831C2×C4—81no—
832C2×C4—81no—
833C2×C4#120×C14911yescharacteristic
834C2×C4#120×C14911yescharacteristic
835C2×C4#120×C14911yescharacteristic
836C2×C4C22×D4×C14911yescharacteristic
837C2×C4C22×D4×C14911yescharacteristic
838C2×C4C22×D4×C14911yescharacteristic
839C8—22no—
840C8—41no—
841C8—41no—
842C8—41no—
843C8—41no—
844C8—41no—
845C22—21no—
846C22—21no—
847C22—21no—
848C22—41no—
849C22—41no—
850C22—41no—
851C22—41no—
852C22—41no—
853C22—41no—
854C22—41no—
855C22—41no—
856C22—41no—
857C22—41no—
858C22—41no—
859C22—41no—
860C22—84no—
861C22—81no—
862C22—81no—
863C22—81no—
864C22C2×#120×C14911yescharacteristic
865C4—21no—
866C4—21no—
867C4—21no—
868C4—21no—
869C4—21no—
870C4—21no—
871C4—41no—
872C4—41no—
873C4—41no—
874C4—41no—
875C4—41no—
876C4—41no—
877C4—41no—
878C4—41no—
879C4—81no—
880C2—41no—
881C2—81no—
882C2—81no—
883C2—81no—
884C2—81no—
885C2—161no—
886C2#3018×C14911yescharacteristic
887C2#3019×C14911yescharacteristic
888C2#3021×C14911yescharacteristic
subgroupG/H
center, socleC22×C149C2×#120
commutator, Frattini, cosocleC42C24×C149
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
1. #3529×C149C2semidirect
2. #3219×C149C2semidirect
3. #3214×C149C2semidirect
4. #3180×C149C2semidirect
5. #1664×C149C2semidirect
6. #1662×C149C2semidirect
7. #1661×C149C2semidirect
8. #1659×C149C2semidirect
9. #1657×C149C2semidirect
10. #1656×C149C2semidirect
11. #1656×C149C2semidirect
12. #1655×C149C2semidirect
13. #1535×C149C2semidirect
14. #1532×C149C2semidirect
15. #1530×C149C2semidirect
28. #532×C149C22semidirect
36. #501×C149C22semidirect
41. #496×C149C22semidirect
42. #491×C149C22semidirect
43. #490×C149C22semidirect
44. #490×C149C22semidirect
47. #489×C149C22semidirect
60. #432×C149C22semidirect
61. #432×C149C22semidirect
62. C2×#97×C149C22semidirect
63. #330×C149C22semidirect
64. #330×C149C22semidirect
65. #330×C149C22semidirect
66. #330×C149C22semidirect
73. #329×C149C22semidirect
74. #329×C149C22semidirect
444. #19010C149direct (N × H)
445. C149#19010direct (N × H)
446. #3529C2×C149semidirect
447. #3219C2×C149semidirect
448. #3214C2×C149semidirect
449. #3180C2×C149semidirect
450. #1664C2×C149semidirect
451. #1662C2×C149semidirect
452. #1661C2×C149semidirect
453. #1659C2×C149semidirect
454. #1657C2×C149semidirect
455. #1656C2×C149semidirect
456. #1656C2×C149semidirect
457. #1655C2×C149semidirect
458. #1535C2×C149semidirect
459. #1532C2×C149semidirect
460. #1530C2×C149semidirect
473. #532C22×C149semidirect
481. #501C22×C149semidirect
486. #496C22×C149semidirect
487. #491C22×C149semidirect
488. #490C22×C149semidirect
489. #490C22×C149semidirect
492. #489C22×C149semidirect
505. #432C22×C149semidirect
506. #432C22×C149semidirect
507. C2×#97C22×C149semidirect
508. #330C22×C149semidirect
509. #330C22×C149semidirect
510. #330C22×C149semidirect
511. #330C22×C149semidirect
518. #329C22×C149semidirect
519. #329C22×C149semidirect

Maximal subgroups

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

subgroupindex
#3529×C1492
#3219×C1492
#3214×C1492
#3180×C1492
#1664×C1492
#1662×C1492
#1661×C1492
#1659×C1492
#1657×C1492
#1656×C1492
#1655×C1492
#1535×C1492
#1532×C1492
#1530×C1492
#19010149