Finite Group Databasebeta

← C149×#19068 #49198017

Subgroups — C149×#19068 #49198017

Order 38144.

920 conjugacy classes of subgroups.

The subgroup lattice has 892 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3545×C149C211yesmaximal, characteristic, complemented
2#3219×C149C211yesmaximal, characteristic, complemented
3#3213×C149C211yesmaximal, characteristic, complemented
4#3171×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#1529×C149C211yesmaximal, characteristic, complemented
15#1527×C149C211yesmaximal, characteristic, complemented
16#563×C149C2211yescharacteristic
17#562×C149C2211yescharacteristic
18#562×C149C2211yescharacteristic
19H(3,𝔽4)×C149C2211yescharacteristic
20#555×C149—21no—
21#551×C149—21no—
22#551×C149—21no—
23#551×C149—21no—
24#546×C149—21no—
25#546×C149—21no—
26#542×C149—21no—
27#542×C149—21no—
28#538×C149—21no—
29#538×C149—21no—
30#536×C149—21no—
31#534×C149—21no—
32#532×C149C2211yescharacteristic, complemented
33#529×C149C2211yescharacteristic
34#529×C149C2211yescharacteristic
35C2×#124×C149C2211yescharacteristic
36#501×C149C2211yescharacteristic, complemented
37#497×C149C2211yescharacteristic, complemented
38#496×C149C2211yescharacteristic
39#496×C149C2211yescharacteristic, complemented
40#496×C149C2211yescharacteristic, complemented
41#496×C149C2211yescharacteristic, complemented
42#491×C149C2211yescharacteristic, complemented
43#490×C149C2211yescharacteristic, complemented
44#490×C149C2211yescharacteristic, complemented
45#489×C149C2211yescharacteristic
46#489×C149C2211yescharacteristic, complemented
47#489×C149C2211yescharacteristic, complemented
48#469×C149—21no—
49#468×C149—21no—
50#464×C149—21no—
51#463×C149—21no—
52#463×C149—21no—
53#463×C149—21no—
54#452×C149—21no—
55#449×C149—21no—
56#448×C149—21no—
57#447×C149—21no—
58C4×SD16×C149—21no—
59C4×D8×C149—21no—
60#432×C149C2211yescharacteristic, complemented
61#432×C149C2211yescharacteristic, complemented
62C4×M16×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, complemented
70#329×C149C2211yescharacteristic, complemented
71#329×C149C2211yescharacteristic, complemented
72#329×C149C2211yescharacteristic, complemented
73#329×C149C2211yescharacteristic, complemented
74#329×C149C2211yescharacteristic, complemented
75C2×#41×C149—21no—
76C2×#41×C149—21no—
77C22×Q8×C149D411yescharacteristic
78C22×D4×C149—21no—
79C22×D4×C149D411yescharacteristic
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—
90C2×M16×C149—21no—
91C4⋊Q8×C149—21no—
92C4⋊Q8×C149—21no—
93C4⋊Q8×C149C2311yescharacteristic
94#127×C149C2311yescharacteristic
95#126×C149—21no—
96#126×C149—21no—
97#126×C149—21no—
98#126×C149—21no—
99#126×C149—21no—
100#126×C149—21no—
101#125×C149C2311yescharacteristic
102#125×C149C2311yescharacteristic
103#124×C149—21no—
104#124×C149—21no—
105#124×C149—21no—
106#124×C149—21no—
107#124×C149—21no—
108#124×C149—21no—
109#124×C149—21no—
110#124×C149—21no—
111#124×C149—21no—
112#124×C149D411yescharacteristic
113#124×C149D411yescharacteristic
114#124×C149C2311yescharacteristic
115#124×C149C2311yescharacteristic
116#124×C149C2311yescharacteristic
117#124×C149C2311yescharacteristic
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—
128#123×C149—21no—
129#123×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×C149—21no—
137C22⋊Q8×C149—21no—
138C22⋊Q8×C149D411yescharacteristic
139C22⋊Q8×C149D411yescharacteristic
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×C149D411yescharacteristic
151#121×C149D411yescharacteristic
152#120×C149—21no—
153#120×C149—21no—
154#120×C149—21no—
155#120×C149—21no—
156#120×C149—21no—
157#120×C149—21no—
158C4×Q8×C149D411yescharacteristic
159C4×Q8×C149D411yescharacteristic
160C4×D4×C149—21no—
161C4×D4×C149—21no—
162C4×D4×C149—21no—
163C4×D4×C149—21no—
164C4×D4×C149—21no—
165C4×D4×C149—21no—
166C4×D4×C149—21no—
167C4×D4×C149—21no—
168C4×D4×C149D411yescharacteristic
169C4×D4×C149D411yescharacteristic
170#117×C149—21no—
171#117×C149—21no—
172#117×C149—21no—
173#117×C149—21no—
174#117×C149—21no—
175C2×C22⋊C4×C149—21no—
176C2×C22⋊C4×C149—21no—
177C2×C22⋊C4×C149—21no—
178C2×C22⋊C4×C149—21no—
179C2×C22⋊C4×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×C149C2311yescharacteristic
200#97×C149C2311yescharacteristic
201#97×C149C2311yescharacteristic
202#97×C149C2311yescharacteristic
203#97×C149C2311yescharacteristic
204#97×C149C2311yescharacteristic
205C4×C8×C149—21no—
206C24×C149—21no—
207C24×C149—21no—
208#41×C149—82no—
209#41×C149—81no—
210#41×C149—81no—
211C2×Q8×C149—21no—
212C2×Q8×C149—21no—
213C2×Q8×C149—21no—
214C2×Q8×C149—81no—
215C2×Q8×C149C2×D411yescharacteristic
216C2×Q8×C149C2×D411yescharacteristic
217C2×Q8×C149C2×D411yescharacteristic
218C2×Q8×C149C2×D411yescharacteristic
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—41no—
233C2×D4×C149—81no—
234C2×D4×C149—82no—
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—41no—
248C22×C4×C149C2×D411yescharacteristic
249C22×C4×C149C2×D411yescharacteristic
250C22×C4×C149C2×D411yescharacteristic
251Q16×C149—81no—
252SD16×C149—42no—
253SD16×C149—81no—
254SD16×C149—81no—
255SD16×C149—81no—
256SD16×C149—81no—
257D8×C149—42no—
258D8×C149—81no—
259D8×C149—81no—
260D8×C149—81no—
261M16×C149—42no—
262C2×C8×C149—21no—
263C2×C8×C149—21no—
264C2×C8×C149—21no—
265C2×C8×C149—21no—
266C2×C8×C149—21no—
267C2×C8×C149—21no—
268C4⋊C4×C149—21no—
269C4⋊C4×C149—21no—
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×C149C2×D411yescharacteristic
285C4⋊C4×C149C2×D411yescharacteristic
286C4⋊C4×C149C2×D411yescharacteristic
287C4⋊C4×C149C2×D411yescharacteristic
288C22⋊C4×C149—21no—
289C22⋊C4×C149—21no—
290C22⋊C4×C149—21no—
291C22⋊C4×C149—21no—
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—42no—
331C23×C149—41no—
332C23×C149—81no—
333C23×C149—81no—
334C23×C149—81no—
335C23×C149—81no—
336C23×C149—81no—
337C23×C149#12011yescharacteristic
338Q8×C149—41no—
339Q8×C149—41no—
340Q8×C149—41no—
341Q8×C149—41no—
342Q8×C149—41no—
343Q8×C149—41no—
344Q8×C149—81no—
345Q8×C149—81no—
346D4×C149—41no—
347D4×C149—41no—
348D4×C149—41no—
349D4×C149—41no—
350D4×C149—41no—
351D4×C149—41no—
352D4×C149—41no—
353D4×C149—41no—
354D4×C149—41no—
355D4×C149—41no—
356D4×C149—42no—
357D4×C149—42no—
358D4×C149—81no—
359D4×C149—81no—
360D4×C149—81no—
361D4×C149—81no—
362D4×C149—81no—
363D4×C149—81no—
364D4×C149—81no—
365D4×C149—81no—
366D4×C149—82no—
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—21no—
375C2×C4×C149—41no—
376C2×C4×C149—41no—
377C2×C4×C149—41no—
378C2×C4×C149—42no—
379C2×C4×C149—41no—
380C2×C4×C149—81no—
381C2×C4×C149—81no—
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—81no—
416C22×C149—81no—
417C22×C149—81no—
418C22×C149—162no—
419C22×C149—162no—
420C22×C149C2×#12011yescharacteristic
421C4×C149—21no—
422C4×C149—21no—
423C4×C149—21no—
424C4×C149—21no—
425C4×C149—21no—
426C4×C149—21no—
427C4×C149—41no—
428C4×C149—41no—
429C4×C149—41no—
430C4×C149—41no—
431C4×C149—41no—
432C4×C149—41no—
433C4×C149—41no—
434C4×C149—41no—
435C4×C149—81no—
436C2×C149—41no—
437C2×C149—81no—
438C2×C149—81no—
439C2×C149—81no—
440C2×C149—81no—
441C2×C149—161no—
442C2×C149#301811yescharacteristic
443C2×C149#301911yescharacteristic
444C2×C149#302111yescharacteristic
445#19068C14911yesmaximal, characteristic, direct product factor, Sylow
446C149#1906811yescharacteristic, direct product factor, Sylow
447#3545C2×C14911yescharacteristic, complemented
448#3219C2×C14911yescharacteristic, complemented
449#3213C2×C14911yescharacteristic, complemented
450#3171C2×C14911yescharacteristic, complemented
451#1664C2×C14911yescharacteristic, complemented
452#1662C2×C14911yescharacteristic, complemented
453#1661C2×C14911yescharacteristic, complemented
454#1659C2×C14911yescharacteristic, complemented
455#1657C2×C14911yescharacteristic, complemented
456#1656C2×C14911yescharacteristic, complemented
457#1656C2×C14911yescharacteristic, complemented
458#1655C2×C14911yescharacteristic, complemented
459#1535C2×C14911yescharacteristic, complemented
460#1529C2×C14911yescharacteristic, complemented
461#1527C2×C14911yescharacteristic, complemented
462#563C22×C14911yescharacteristic
463#562C22×C14911yescharacteristic
464#562C22×C14911yescharacteristic
465H(3,𝔽4)C22×C14911yescharacteristic
466#555—21no—
467#551—21no—
468#551—21no—
469#551—21no—
470#546—21no—
471#546—21no—
472#542—21no—
473#542—21no—
474#538—21no—
475#538—21no—
476#536—21no—
477#534—21no—
478#532C22×C14911yescharacteristic, complemented
479#529C22×C14911yescharacteristic
480#529C22×C14911yescharacteristic
481C2×#124C22×C14911yescharacteristic
482#501C22×C14911yescharacteristic, complemented
483#497C22×C14911yescharacteristic, complemented
484#496C22×C14911yescharacteristic
485#496C22×C14911yescharacteristic, complemented
486#496C22×C14911yescharacteristic, complemented
487#496C22×C14911yescharacteristic, complemented
488#491C22×C14911yescharacteristic, complemented
489#490C22×C14911yescharacteristic, complemented
490#490C22×C14911yescharacteristic, complemented
491#489C22×C14911yescharacteristic
492#489C22×C14911yescharacteristic, complemented
493#489C22×C14911yescharacteristic, complemented
494#469—21no—
495#468—21no—
496#464—21no—
497#463—21no—
498#463—21no—
499#463—21no—
500#452—21no—
501#449—21no—
502#448—21no—
503#447—21no—
504C4×SD16—21no—
505C4×D8—21no—
506#432C22×C14911yescharacteristic, complemented
507#432C22×C14911yescharacteristic, complemented
508C4×M16C22×C14911yescharacteristic, complemented
509#330C22×C14911yescharacteristic, complemented
510#330C22×C14911yescharacteristic, complemented
511#330C22×C14911yescharacteristic, complemented
512#330C22×C14911yescharacteristic, complemented
513#329C22×C14911yescharacteristic
514#329C22×C14911yescharacteristic
515#329C22×C14911yescharacteristic, complemented
516#329C22×C14911yescharacteristic, complemented
517#329C22×C14911yescharacteristic, complemented
518#329C22×C14911yescharacteristic, complemented
519#329C22×C14911yescharacteristic, complemented
520#329C22×C14911yescharacteristic, complemented
521C2×#41—21no—
522C2×#41—21no—
523C22×Q8D4×C14911yescharacteristic
524C22×D4—21no—
525C22×D4D4×C14911yescharacteristic
526C2×Q16—21no—
527C2×SD16—21no—
528C2×SD16—21no—
529C2×SD16—21no—
530C2×SD16—21no—
531C2×SD16—21no—
532C2×D8—21no—
533C2×D8—21no—
534C2×D8—21no—
535C2×D8—21no—
536C2×M16—21no—
537C4⋊Q8—21no—
538C4⋊Q8—21no—
539C4⋊Q8C23×C14911yescharacteristic
540#127C23×C14911yescharacteristic
541#126—21no—
542#126—21no—
543#126—21no—
544#126—21no—
545#126—21no—
546#126—21no—
547#125C23×C14911yescharacteristic
548#125C23×C14911yescharacteristic
549#124—21no—
550#124—21no—
551#124—21no—
552#124—21no—
553#124—21no—
554#124—21no—
555#124—21no—
556#124—21no—
557#124—21no—
558#124D4×C14911yescharacteristic
559#124D4×C14911yescharacteristic
560#124C23×C14911yescharacteristic
561#124C23×C14911yescharacteristic
562#124C23×C14911yescharacteristic
563#124C23×C14911yescharacteristic
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—
573#123—21no—
574#123—21no—
575#123—21no—
576C22⋊Q8—21no—
577C22⋊Q8—21no—
578C22⋊Q8—21no—
579C22⋊Q8—21no—
580C22⋊Q8—21no—
581C22⋊Q8—21no—
582C22⋊Q8—21no—
583C22⋊Q8—21no—
584C22⋊Q8D4×C14911yescharacteristic
585C22⋊Q8D4×C14911yescharacteristic
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#121D4×C14911yescharacteristic
597#121D4×C14911yescharacteristic
598#120—21no—
599#120—21no—
600#120—21no—
601#120—21no—
602#120—21no—
603#120—21no—
604C4×Q8D4×C14911yescharacteristic
605C4×Q8D4×C14911yescharacteristic
606C4×D4—21no—
607C4×D4—21no—
608C4×D4—21no—
609C4×D4—21no—
610C4×D4—21no—
611C4×D4—21no—
612C4×D4—21no—
613C4×D4—21no—
614C4×D4D4×C14911yescharacteristic
615C4×D4D4×C14911yescharacteristic
616#117—21no—
617#117—21no—
618#117—21no—
619#117—21no—
620#117—21no—
621C2×C22⋊C4—21no—
622C2×C22⋊C4—21no—
623C2×C22⋊C4—21no—
624C2×C22⋊C4—21no—
625C2×C22⋊C4—21no—
626C2×C42C23×C14911yescharacteristic
627#107—21no—
628#106—21no—
629C4⋊C8—21no—
630C4⋊C8—21no—
631#103—21no—
632#103—21no—
633#103—21no—
634#103—21no—
635#103—21no—
636#102—21no—
637#102—21no—
638#102—21no—
639#102—21no—
640#102—21no—
641#102—21no—
642#102—21no—
643C22⋊C8—21no—
644C22⋊C8—21no—
645#97C23×C14911yescharacteristic
646#97C23×C14911yescharacteristic
647#97C23×C14911yescharacteristic
648#97C23×C14911yescharacteristic
649#97C23×C14911yescharacteristic
650#97C23×C14911yescharacteristic
651C4×C8—21no—
652C24—21no—
653C24—21no—
654#41—82no—
655#41—81no—
656#41—81no—
657C2×Q8—21no—
658C2×Q8—21no—
659C2×Q8—21no—
660C2×Q8—81no—
661C2×Q8C2×D4×C14911yescharacteristic
662C2×Q8C2×D4×C14911yescharacteristic
663C2×Q8C2×D4×C14911yescharacteristic
664C2×Q8C2×D4×C14911yescharacteristic
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—41no—
679C2×D4—81no—
680C2×D4—82no—
681C2×D4C2×D4×C14911yescharacteristic
682C2×D4C2×D4×C14911yescharacteristic
683C2×D4C2×D4×C14911yescharacteristic
684C2×D4C2×D4×C14911yescharacteristic
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×C4C2×D4×C14911yescharacteristic
695C22×C4C2×D4×C14911yescharacteristic
696C22×C4C2×D4×C14911yescharacteristic
697Q16—81no—
698SD16—42no—
699SD16—81no—
700SD16—81no—
701SD16—81no—
702SD16—81no—
703D8—42no—
704D8—81no—
705D8—81no—
706D8—81no—
707M16—42no—
708C2×C8—21no—
709C2×C8—21no—
710C2×C8—21no—
711C2×C8—21no—
712C2×C8—21no—
713C2×C8—21no—
714C4⋊C4—21no—
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⋊C4C2×D4×C14911yescharacteristic
731C4⋊C4C2×D4×C14911yescharacteristic
732C4⋊C4C2×D4×C14911yescharacteristic
733C4⋊C4C2×D4×C14911yescharacteristic
734C22⋊C4—21no—
735C22⋊C4—21no—
736C22⋊C4—21no—
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—21no—
762C22⋊C4—41no—
763C22⋊C4—41no—
764C42—21no—
765C42—21no—
766C42—21no—
767C42—21no—
768C42C2×D4×C14911yescharacteristic
769C42C2×D4×C14911yescharacteristic
770C42C2×D4×C14911yescharacteristic
771C42C24×C14911yescharacteristic
772C23—21no—
773C23—21no—
774C23—21no—
775C23—21no—
776C23—42no—
777C23—41no—
778C23—81no—
779C23—81no—
780C23—81no—
781C23—81no—
782C23—81no—
783C23#120×C14911yescharacteristic
784Q8—41no—
785Q8—41no—
786Q8—41no—
787Q8—41no—
788Q8—41no—
789Q8—41no—
790Q8—81no—
791Q8—81no—
792D4—41no—
793D4—41no—
794D4—41no—
795D4—41no—
796D4—41no—
797D4—41no—
798D4—41no—
799D4—41no—
800D4—41no—
801D4—41no—
802D4—42no—
803D4—42no—
804D4—81no—
805D4—81no—
806D4—81no—
807D4—81no—
808D4—81no—
809D4—81no—
810D4—81no—
811D4—81no—
812D4—82no—
813C2×C4—21no—
814C2×C4—21no—
815C2×C4—21no—
816C2×C4—21no—
817C2×C4—21no—
818C2×C4—21no—
819C2×C4—21no—
820C2×C4—21no—
821C2×C4—41no—
822C2×C4—41no—
823C2×C4—41no—
824C2×C4—42no—
825C2×C4—41no—
826C2×C4—81no—
827C2×C4—81no—
828C2×C4—82no—
829C2×C4—81no—
830C2×C4—81no—
831C2×C4—81no—
832C2×C4—81no—
833C2×C4—81no—
834C2×C4#120×C14911yescharacteristic
835C2×C4#120×C14911yescharacteristic
836C2×C4#120×C14911yescharacteristic
837C2×C4C22×D4×C14911yescharacteristic
838C2×C4C22×D4×C14911yescharacteristic
839C2×C4C22×D4×C14911yescharacteristic
840C8—22no—
841C8—41no—
842C8—41no—
843C8—41no—
844C8—41no—
845C8—41no—
846C22—21no—
847C22—21no—
848C22—21no—
849C22—41no—
850C22—41no—
851C22—41no—
852C22—41no—
853C22—41no—
854C22—41no—
855C22—41no—
856C22—41no—
857C22—41no—
858C22—41no—
859C22—41no—
860C22—41no—
861C22—81no—
862C22—81no—
863C22—81no—
864C22—162no—
865C22—162no—
866C22C2×#120×C14911yescharacteristic
867C4—21no—
868C4—21no—
869C4—21no—
870C4—21no—
871C4—21no—
872C4—21no—
873C4—41no—
874C4—41no—
875C4—41no—
876C4—41no—
877C4—41no—
878C4—41no—
879C4—41no—
880C4—41no—
881C4—81no—
882C2—41no—
883C2—81no—
884C2—81no—
885C2—81no—
886C2—81no—
887C2—161no—
888C2#3018×C14911yescharacteristic
889C2#3019×C14911yescharacteristic
890C2#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. #3545×C149C2semidirect
2. #3219×C149C2semidirect
3. #3213×C149C2semidirect
4. #3171×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. #1529×C149C2semidirect
15. #1527×C149C2semidirect
32. #532×C149C22semidirect
36. #501×C149C22semidirect
37. #497×C149C22semidirect
39. #496×C149C22semidirect
40. #496×C149C22semidirect
41. #496×C149C22semidirect
42. #491×C149C22semidirect
43. #490×C149C22semidirect
44. #490×C149C22semidirect
46. #489×C149C22semidirect
47. #489×C149C22semidirect
60. #432×C149C22semidirect
61. #432×C149C22semidirect
62. C4×M16×C149C22semidirect
63. #330×C149C22semidirect
64. #330×C149C22semidirect
65. #330×C149C22semidirect
66. #330×C149C22semidirect
69. #329×C149C22semidirect
70. #329×C149C22semidirect
71. #329×C149C22semidirect
72. #329×C149C22semidirect
73. #329×C149C22semidirect
74. #329×C149C22semidirect
445. #19068C149direct (N × H)
446. C149#19068direct (N × H)
447. #3545C2×C149semidirect
448. #3219C2×C149semidirect
449. #3213C2×C149semidirect
450. #3171C2×C149semidirect
451. #1664C2×C149semidirect
452. #1662C2×C149semidirect
453. #1661C2×C149semidirect
454. #1659C2×C149semidirect
455. #1657C2×C149semidirect
456. #1656C2×C149semidirect
457. #1656C2×C149semidirect
458. #1655C2×C149semidirect
459. #1535C2×C149semidirect
460. #1529C2×C149semidirect
461. #1527C2×C149semidirect
478. #532C22×C149semidirect
482. #501C22×C149semidirect
483. #497C22×C149semidirect
485. #496C22×C149semidirect
486. #496C22×C149semidirect
487. #496C22×C149semidirect
488. #491C22×C149semidirect
489. #490C22×C149semidirect
490. #490C22×C149semidirect
492. #489C22×C149semidirect
493. #489C22×C149semidirect
506. #432C22×C149semidirect
507. #432C22×C149semidirect
508. C4×M16C22×C149semidirect
509. #330C22×C149semidirect
510. #330C22×C149semidirect
511. #330C22×C149semidirect
512. #330C22×C149semidirect
515. #329C22×C149semidirect
516. #329C22×C149semidirect
517. #329C22×C149semidirect
518. #329C22×C149semidirect
519. #329C22×C149semidirect
520. #329C22×C149semidirect

Maximal subgroups

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

subgroupindex
#3545×C1492
#3219×C1492
#3213×C1492
#3171×C1492
#1664×C1492
#1662×C1492
#1661×C1492
#1659×C1492
#1657×C1492
#1656×C1492
#1655×C1492
#1535×C1492
#1529×C1492
#1527×C1492
#19068149