Finite Group Databasebeta

← C151×#22526 #50327451

Subgroups — C151×#22526 #50327451

Order 38656.

1066 conjugacy classes of subgroups.

The subgroup lattice has 646 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#554×C151C211yesmaximal, characteristic
2C2×#446×C151C211yesmaximal, characteristic, complemented
3#2355×C151C211yesmaximal, characteristic, complemented
4#1993×C151C211yesmaximal, characteristic, complemented
5#1992×C151C211yesmaximal, characteristic, complemented
6#1991×C151C211yesmaximal, characteristic, complemented
7#1989×C151C211yesmaximal, characteristic, complemented
8#1989×C151C211yesmaximal, characteristic, complemented
9#1988×C151C211yesmaximal, characteristic, complemented
10#1804×C151C211yesmaximal, characteristic
11#1804×C151C211yesmaximal, characteristic
12#1802×C151C211yesmaximal, characteristic
13#1762×C151C211yesmaximal, characteristic
14#1762×C151C211yesmaximal, characteristic
15C4×#102×C151C211yesmaximal, characteristic
16#554×C151—24no—
17#554×C151C418yescomplemented
18C2×C4⋊Q8×C151C2211yescharacteristic
19C2×#125×C151C2211yescharacteristic
20C2×#125×C151C2211yescharacteristic
21C2×C22⋊Q8×C151—21no—
22C2×C22⋊Q8×C151—21no—
23C2×C22⋊Q8×C151—21no—
24C2×C4×Q8×C151C2211yescharacteristic
25C2×C4×D4×C151C2211yescharacteristic
26C2×C4×D4×C151C2211yescharacteristic
27C2×C4×D4×C151C2211yescharacteristic
28C22×C4⋊C4×C151—21no—
29#446×C151—24no—
30C2×C4⋊C8×C151C2211yescharacteristic
31C2×C4⋊C8×C151C2211yescharacteristic
32C2×C4⋊C8×C151C2211yescharacteristic
33C2×#102×C151C2211yescharacteristic
34C2×#102×C151C2211yescharacteristic
35C2×#102×C151C2211yescharacteristic
36C2×#102×C151C2211yescharacteristic
37C2×#97×C151C2211yescharacteristic
38C2×#97×C151C2211yescharacteristic
39C2×C4×C8×C151C2211yescharacteristic
40#391×C151—21no—
41#387×C151—21no—
42#387×C151—21no—
43#384×C151C2211yescharacteristic
44#382×C151C2211yescharacteristic
45#382×C151C2211yescharacteristic
46C4×C4⋊C4×C151—21no—
47C4×C4⋊C4×C151C2211yescharacteristic
48C4×C4⋊C4×C151C2211yescharacteristic
49C4×C4⋊C4×C151C2211yescharacteristic
50#340×C151C2211yescharacteristic
51#340×C151C2211yescharacteristic
52#340×C151C2211yescharacteristic
53#340×C151C2211yescharacteristic
54#340×C151C2211yescharacteristic
55#340×C151C2211yescharacteristic
56#340×C151C2211yescharacteristic
57#340×C151C2211yescharacteristic
58#340×C151C2211yescharacteristic
59#340×C151C2211yescharacteristic
60#340×C151C2211yescharacteristic
61#340×C151C2211yescharacteristic
62C22×Q8×C151—21no—
63C22×Q8×C151D411yescharacteristic
64C22×D4×C151C2311yescharacteristic
65C23×C4×C151—21no—
66C23×C4×C151—21no—
67C23×C4×C151—21no—
68C22×C8×C151C2311yescharacteristic
69C22×C8×C151C2311yescharacteristic
70C22×C8×C151C2311yescharacteristic
71C22×C8×C151C2311yescharacteristic
72C4⋊Q8×C151—22no—
73C4⋊Q8×C151C2×C414yes—
74#125×C151—22no—
75#125×C151—22no—
76#125×C151C2×C414yes—
77#125×C151C2×C414yes—
78C22⋊Q8×C151—28no—
79C22⋊Q8×C151—28no—
80C22⋊Q8×C151—28no—
81C4×Q8×C151C2×C414yes—
82C4×Q8×C151D414yes—
83C4×D4×C151—22no—
84C4×D4×C151—22no—
85C4×D4×C151—22no—
86C4×D4×C151C2×C414yes—
87C4×D4×C151C2×C414yes—
88C4×D4×C151C2×C414yes—
89C2×C4⋊C4×C151—21no—
90C2×C4⋊C4×C151—21no—
91C2×C4⋊C4×C151—21no—
92C2×C4⋊C4×C151—21no—
93C2×C4⋊C4×C151—21no—
94C2×C4⋊C4×C151—28no—
95C2×C4⋊C4×C151—21no—
96C2×C4⋊C4×C151—21no—
97C2×C4⋊C4×C151D411yescharacteristic
98C2×C4⋊C4×C151D411yescharacteristic
99C2×C4⋊C4×C151D411yescharacteristic
100C2×C4⋊C4×C151C2311yescharacteristic
101C2×C4⋊C4×C151C2311yescharacteristic
102C2×C4⋊C4×C151C2311yescharacteristic
103C2×C4⋊C4×C151C2311yescharacteristic
104C2×C4⋊C4×C151C2311yescharacteristic
105C2×C4⋊C4×C151C2311yescharacteristic
106C2×C4⋊C4×C151C2311yescharacteristic
107C2×C22⋊C4×C151—21no—
108C2×C22⋊C4×C151—21no—
109C2×C22⋊C4×C151—21no—
110C2×C42×C151—21no—
111C2×C42×C151—21no—
112C2×C42×C151—21no—
113C2×C42×C151C2311yescharacteristic
114C2×C42×C151C2311yescharacteristic
115C2×C42×C151C2311yescharacteristic
116C4⋊C8×C151—22no—
117C4⋊C8×C151—22no—
118C4⋊C8×C151—22no—
119#102×C151—22no—
120#102×C151—22no—
121#102×C151—22no—
122#102×C151Q814yescomplemented
123#97×C151—22no—
124#97×C151—22no—
125C4×C8×C151—22no—
126#95×C151—21no—
127#95×C151—21no—
128#95×C151—21no—
129#95×C151—21no—
130#95×C151—21no—
131#95×C151—21no—
132#95×C151—21no—
133C24×C151—21no—
134C2×Q8×C151—24no—
135C2×Q8×C151—41no—
136C2×Q8×C151—41no—
137C2×Q8×C151—81no—
138C2×Q8×C151—81no—
139C2×Q8×C151C22⋊C414yes—
140C2×D4×C151—21no—
141C2×D4×C151—21no—
142C2×D4×C151—21no—
143C2×D4×C151C22×C412yes—
144C2×D4×C151C2×Q812yes—
145C2×D4×C151#4112yes—
146C22×C4×C151—21no—
147C22×C4×C151—21no—
148C22×C4×C151—21no—
149C22×C4×C151—21no—
150C22×C4×C151—24no—
151C22×C4×C151—24no—
152C22×C4×C151—24no—
153C22×C4×C151—21no—
154C22×C4×C151—21no—
155C22×C4×C151—21no—
156C22×C4×C151—42no—
157C22×C4×C151—42no—
158C22×C4×C151—81no—
159C22×C4×C151—81no—
160C22×C4×C151—81no—
161C22×C4×C151—81no—
162C22×C4×C151C2×D411yescharacteristic
163C22×C4×C151C2×D411yescharacteristic
164C22×C4×C151C2×D411yescharacteristic
165C22×C4×C151C2×D411yescharacteristic
166C22×C4×C151C2×D411yescharacteristic
167C22×C4×C151C2×D411yescharacteristic
168C22×C4×C151C2411yescharacteristic
169C2×C8×C151—21no—
170C2×C8×C151—21no—
171C2×C8×C151—21no—
172C2×C8×C151—21no—
173C2×C8×C151—21no—
174C2×C8×C151—21no—
175C2×C8×C151—21no—
176C2×C8×C151—21no—
177C2×C8×C151—21no—
178C2×C8×C151—21no—
179C2×C8×C151—21no—
180C2×C8×C151C2×Q812yes—
181C4⋊C4×C151—24no—
182C4⋊C4×C151—24no—
183C4⋊C4×C151—24no—
184C4⋊C4×C151—24no—
185C4⋊C4×C151—24no—
186C4⋊C4×C151—21no—
187C4⋊C4×C151—21no—
188C4⋊C4×C151—21no—
189C4⋊C4×C151—21no—
190C4⋊C4×C151—21no—
191C4⋊C4×C151—21no—
192C4⋊C4×C151—21no—
193C4⋊C4×C151—21no—
194C4⋊C4×C151—21no—
195C4⋊C4×C151—21no—
196C4⋊C4×C151—42no—
197C4⋊C4×C151—81no—
198C4⋊C4×C151C22⋊C414yes—
199C4⋊C4×C151C22⋊C414yes—
200C4⋊C4×C151C22⋊C414yes—
201C4⋊C4×C151C22×C412yes—
202C4⋊C4×C151C22×C412yes—
203C4⋊C4×C151C22×C412yes—
204C4⋊C4×C151C2×Q812yes—
205C22⋊C4×C151—24no—
206C22⋊C4×C151—24no—
207C22⋊C4×C151—24no—
208C42×C151—42no—
209C42×C151—81no—
210C42×C151—81no—
211C42×C151C22×C412yes—
212C42×C151C22×C412yes—
213C42×C151C22×C412yes—
214C42×C151C2×D412yes—
215C42×C151C2×D412yes—
216C42×C151C2×D412yes—
217C23×C151—22no—
218C23×C151—22no—
219C23×C151—22no—
220C23×C151—41no—
221C23×C151—41no—
222C23×C151—41no—
223C23×C151—41no—
224C23×C151C22×D411yescharacteristic
225Q8×C151—44no—
226Q8×C151—84no—
227D4×C151—22no—
228D4×C151—22no—
229D4×C151—22no—
230D4×C151C4×Q814yes—
231C2×C4×C151—21no—
232C2×C4×C151—21no—
233C2×C4×C151—21no—
234C2×C4×C151—21no—
235C2×C4×C151—21no—
236C2×C4×C151—21no—
237C2×C4×C151—21no—
238C2×C4×C151—21no—
239C2×C4×C151—21no—
240C2×C4×C151—21no—
241C2×C4×C151—21no—
242C2×C4×C151—21no—
243C2×C4×C151—22no—
244C2×C4×C151—22no—
245C2×C4×C151—22no—
246C2×C4×C151—22no—
247C2×C4×C151—48no—
248C2×C4×C151—41no—
249C2×C4×C151—41no—
250C2×C4×C151—41no—
251C2×C4×C151—41no—
252C2×C4×C151—41no—
253C2×C4×C151—41no—
254C2×C4×C151—41no—
255C2×C4×C151—41no—
256C2×C4×C151—41no—
257C2×C4×C151—41no—
258C2×C4×C151—41no—
259C2×C4×C151—41no—
260C2×C4×C151—41no—
261C2×C4×C151—41no—
262C2×C4×C151—41no—
263C2×C4×C151—41no—
264C2×C4×C151—41no—
265C2×C4×C151—84no—
266C2×C4×C151—84no—
267C2×C4×C151C2×C22⋊C412yes—
268C2×C4×C151C2×C22⋊C412yes—
269C2×C4×C151C2×C22⋊C412yes—
270C2×C4×C151C2×C22⋊C412yes—
271C2×C4×C151C2×C22⋊C412yes—
272C2×C4×C151C2×C22⋊C412yes—
273C2×C4×C151C23×C411yescharacteristic
274C2×C4×C151C22×D411yescharacteristic
275C2×C4×C151C22×Q811yescharacteristic
276C2×C4×C151C2×#4111yescharacteristic
277C2×C4×C1512−1+411yescharacteristic
278C2×C4×C1512−1+411yescharacteristic
279C8×C151—22no—
280C8×C151—41no—
281C8×C151—41no—
282C8×C151—41no—
283C22×C151—24no—
284C22×C151—42no—
285C22×C151—42no—
286C22×C151—42no—
287C22×C151—42no—
288C22×C151—42no—
289C22×C151—42no—
290C22×C151C22×C22⋊C411yescharacteristic
291C22×C151#54811yescharacteristic
292C22×C151D4×Q811yescharacteristic
293C22×C151#57511yescharacteristic
294C22×C151#57511yescharacteristic
295C22×C151#57611yescharacteristic
296C22×C151#57711yescharacteristic
297C4×C151—22no—
298C4×C151—22no—
299C4×C151—22no—
300C4×C151—22no—
301C4×C151—22no—
302C4×C151—22no—
303C4×C151—42no—
304C4×C151—42no—
305C4×C151—42no—
306C4×C151—42no—
307C4×C151—81no—
308C4×C151—81no—
309C4×C151—81no—
310C4×C151C2×C4×Q811yescharacteristic
311C4×C151#51911yescharacteristic
312C4×C151#54811yescharacteristic
313C4×C151D4×Q811yescharacteristic
314C2×C151—44no—
315C2×C151Q8×C22⋊C411yescharacteristic
316C2×C151#289611yescharacteristic
317C2×C151#289711yescharacteristic
318C2×C151#337011yescharacteristic
319C2×C151#337611yescharacteristic
320C2×C151#338811yescharacteristic
321C2×C151#338911yescharacteristic
322#22526C15111yesmaximal, characteristic, direct product factor, Sylow
323C151#2252611yescharacteristic, direct product factor, Sylow
324C2×#554C2×C15111yescharacteristic
325C2×#446C2×C15111yescharacteristic, complemented
326#2355C2×C15111yescharacteristic, complemented
327#1993C2×C15111yescharacteristic, complemented
328#1992C2×C15111yescharacteristic, complemented
329#1991C2×C15111yescharacteristic, complemented
330#1989C2×C15111yescharacteristic, complemented
331#1989C2×C15111yescharacteristic, complemented
332#1988C2×C15111yescharacteristic, complemented
333#1804C2×C15111yescharacteristic
334#1804C2×C15111yescharacteristic
335#1802C2×C15111yescharacteristic
336#1762C2×C15111yescharacteristic
337#1762C2×C15111yescharacteristic
338C4×#102C2×C15111yescharacteristic
339#554—24no—
340#554C4×C15118yescomplemented
341C2×C4⋊Q8C22×C15111yescharacteristic
342C2×#125C22×C15111yescharacteristic
343C2×#125C22×C15111yescharacteristic
344C2×C22⋊Q8—21no—
345C2×C22⋊Q8—21no—
346C2×C22⋊Q8—21no—
347C2×C4×Q8C22×C15111yescharacteristic
348C2×C4×D4C22×C15111yescharacteristic
349C2×C4×D4C22×C15111yescharacteristic
350C2×C4×D4C22×C15111yescharacteristic
351C22×C4⋊C4—21no—
352#446—24no—
353C2×C4⋊C8C22×C15111yescharacteristic
354C2×C4⋊C8C22×C15111yescharacteristic
355C2×C4⋊C8C22×C15111yescharacteristic
356C2×#102C22×C15111yescharacteristic
357C2×#102C22×C15111yescharacteristic
358C2×#102C22×C15111yescharacteristic
359C2×#102C22×C15111yescharacteristic
360C2×#97C22×C15111yescharacteristic
361C2×#97C22×C15111yescharacteristic
362C2×C4×C8C22×C15111yescharacteristic
363#391—21no—
364#387—21no—
365#387—21no—
366#384C22×C15111yescharacteristic
367#382C22×C15111yescharacteristic
368#382C22×C15111yescharacteristic
369C4×C4⋊C4—21no—
370C4×C4⋊C4C22×C15111yescharacteristic
371C4×C4⋊C4C22×C15111yescharacteristic
372C4×C4⋊C4C22×C15111yescharacteristic
373#340C22×C15111yescharacteristic
374#340C22×C15111yescharacteristic
375#340C22×C15111yescharacteristic
376#340C22×C15111yescharacteristic
377#340C22×C15111yescharacteristic
378#340C22×C15111yescharacteristic
379#340C22×C15111yescharacteristic
380#340C22×C15111yescharacteristic
381#340C22×C15111yescharacteristic
382#340C22×C15111yescharacteristic
383#340C22×C15111yescharacteristic
384#340C22×C15111yescharacteristic
385C22×Q8—21no—
386C22×Q8D4×C15111yescharacteristic
387C22×D4C23×C15111yescharacteristic
388C23×C4—21no—
389C23×C4—21no—
390C23×C4—21no—
391C22×C8C23×C15111yescharacteristic
392C22×C8C23×C15111yescharacteristic
393C22×C8C23×C15111yescharacteristic
394C22×C8C23×C15111yescharacteristic
395C4⋊Q8—22no—
396C4⋊Q8C2×C4×C15114yes—
397#125—22no—
398#125—22no—
399#125C2×C4×C15114yes—
400#125C2×C4×C15114yes—
401C22⋊Q8—28no—
402C22⋊Q8—28no—
403C22⋊Q8—28no—
404C4×Q8C2×C4×C15114yes—
405C4×Q8D4×C15114yes—
406C4×D4—22no—
407C4×D4—22no—
408C4×D4—22no—
409C4×D4C2×C4×C15114yes—
410C4×D4C2×C4×C15114yes—
411C4×D4C2×C4×C15114yes—
412C2×C4⋊C4—21no—
413C2×C4⋊C4—21no—
414C2×C4⋊C4—21no—
415C2×C4⋊C4—21no—
416C2×C4⋊C4—21no—
417C2×C4⋊C4—28no—
418C2×C4⋊C4—21no—
419C2×C4⋊C4—21no—
420C2×C4⋊C4D4×C15111yescharacteristic
421C2×C4⋊C4D4×C15111yescharacteristic
422C2×C4⋊C4D4×C15111yescharacteristic
423C2×C4⋊C4C23×C15111yescharacteristic
424C2×C4⋊C4C23×C15111yescharacteristic
425C2×C4⋊C4C23×C15111yescharacteristic
426C2×C4⋊C4C23×C15111yescharacteristic
427C2×C4⋊C4C23×C15111yescharacteristic
428C2×C4⋊C4C23×C15111yescharacteristic
429C2×C4⋊C4C23×C15111yescharacteristic
430C2×C22⋊C4—21no—
431C2×C22⋊C4—21no—
432C2×C22⋊C4—21no—
433C2×C42—21no—
434C2×C42—21no—
435C2×C42—21no—
436C2×C42C23×C15111yescharacteristic
437C2×C42C23×C15111yescharacteristic
438C2×C42C23×C15111yescharacteristic
439C4⋊C8—22no—
440C4⋊C8—22no—
441C4⋊C8—22no—
442#102—22no—
443#102—22no—
444#102—22no—
445#102Q8×C15114yescomplemented
446#97—22no—
447#97—22no—
448C4×C8—22no—
449#95—21no—
450#95—21no—
451#95—21no—
452#95—21no—
453#95—21no—
454#95—21no—
455#95—21no—
456C24—21no—
457C2×Q8—24no—
458C2×Q8—41no—
459C2×Q8—41no—
460C2×Q8—81no—
461C2×Q8—81no—
462C2×Q8C22⋊C4×C15114yes—
463C2×D4—21no—
464C2×D4—21no—
465C2×D4—21no—
466C2×D4C22×C4×C15112yes—
467C2×D4C2×Q8×C15112yes—
468C2×D4#41×C15112yes—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—21no—
473C22×C4—24no—
474C22×C4—24no—
475C22×C4—24no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—42no—
480C22×C4—42no—
481C22×C4—81no—
482C22×C4—81no—
483C22×C4—81no—
484C22×C4—81no—
485C22×C4C2×D4×C15111yescharacteristic
486C22×C4C2×D4×C15111yescharacteristic
487C22×C4C2×D4×C15111yescharacteristic
488C22×C4C2×D4×C15111yescharacteristic
489C22×C4C2×D4×C15111yescharacteristic
490C22×C4C2×D4×C15111yescharacteristic
491C22×C4C24×C15111yescharacteristic
492C2×C8—21no—
493C2×C8—21no—
494C2×C8—21no—
495C2×C8—21no—
496C2×C8—21no—
497C2×C8—21no—
498C2×C8—21no—
499C2×C8—21no—
500C2×C8—21no—
501C2×C8—21no—
502C2×C8—21no—
503C2×C8C2×Q8×C15112yes—
504C4⋊C4—24no—
505C4⋊C4—24no—
506C4⋊C4—24no—
507C4⋊C4—24no—
508C4⋊C4—24no—
509C4⋊C4—21no—
510C4⋊C4—21no—
511C4⋊C4—21no—
512C4⋊C4—21no—
513C4⋊C4—21no—
514C4⋊C4—21no—
515C4⋊C4—21no—
516C4⋊C4—21no—
517C4⋊C4—21no—
518C4⋊C4—21no—
519C4⋊C4—42no—
520C4⋊C4—81no—
521C4⋊C4C22⋊C4×C15114yes—
522C4⋊C4C22⋊C4×C15114yes—
523C4⋊C4C22⋊C4×C15114yes—
524C4⋊C4C22×C4×C15112yes—
525C4⋊C4C22×C4×C15112yes—
526C4⋊C4C22×C4×C15112yes—
527C4⋊C4C2×Q8×C15112yes—
528C22⋊C4—24no—
529C22⋊C4—24no—
530C22⋊C4—24no—
531C42—42no—
532C42—81no—
533C42—81no—
534C42C22×C4×C15112yes—
535C42C22×C4×C15112yes—
536C42C22×C4×C15112yes—
537C42C2×D4×C15112yes—
538C42C2×D4×C15112yes—
539C42C2×D4×C15112yes—
540C23—22no—
541C23—22no—
542C23—22no—
543C23—41no—
544C23—41no—
545C23—41no—
546C23—41no—
547C23C22×D4×C15111yescharacteristic
548Q8—44no—
549Q8—84no—
550D4—22no—
551D4—22no—
552D4—22no—
553D4C4×Q8×C15114yes—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—21no—
557C2×C4—21no—
558C2×C4—21no—
559C2×C4—21no—
560C2×C4—21no—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—22no—
567C2×C4—22no—
568C2×C4—22no—
569C2×C4—22no—
570C2×C4—48no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—41no—
577C2×C4—41no—
578C2×C4—41no—
579C2×C4—41no—
580C2×C4—41no—
581C2×C4—41no—
582C2×C4—41no—
583C2×C4—41no—
584C2×C4—41no—
585C2×C4—41no—
586C2×C4—41no—
587C2×C4—41no—
588C2×C4—84no—
589C2×C4—84no—
590C2×C4C2×C22⋊C4×C15112yes—
591C2×C4C2×C22⋊C4×C15112yes—
592C2×C4C2×C22⋊C4×C15112yes—
593C2×C4C2×C22⋊C4×C15112yes—
594C2×C4C2×C22⋊C4×C15112yes—
595C2×C4C2×C22⋊C4×C15112yes—
596C2×C4C23×C4×C15111yescharacteristic
597C2×C4C22×D4×C15111yescharacteristic
598C2×C4C22×Q8×C15111yescharacteristic
599C2×C4C2×#41×C15111yescharacteristic
600C2×C42−1+4×C15111yescharacteristic
601C2×C42−1+4×C15111yescharacteristic
602C8—22no—
603C8—41no—
604C8—41no—
605C8—41no—
606C22—24no—
607C22—42no—
608C22—42no—
609C22—42no—
610C22—42no—
611C22—42no—
612C22—42no—
613C22C22×C22⋊C4×C15111yescharacteristic
614C22#548×C15111yescharacteristic
615C22D4×Q8×C15111yescharacteristic
616C22#575×C15111yescharacteristic
617C22#575×C15111yescharacteristic
618C22#576×C15111yescharacteristic
619C22#577×C15111yescharacteristic
620C4—22no—
621C4—22no—
622C4—22no—
623C4—22no—
624C4—22no—
625C4—22no—
626C4—42no—
627C4—42no—
628C4—42no—
629C4—42no—
630C4—81no—
631C4—81no—
632C4—81no—
633C4C2×C4×Q8×C15111yescharacteristic
634C4#519×C15111yescharacteristic
635C4#548×C15111yescharacteristic
636C4D4×Q8×C15111yescharacteristic
637C2—44no—
638C2Q8×C22⋊C4×C15111yescharacteristic
639C2#2896×C15111yescharacteristic
640C2#2897×C15111yescharacteristic
641C2#3370×C15111yescharacteristic
642C2#3376×C15111yescharacteristic
643C2#3388×C15111yescharacteristic
644C2#3389×C15111yescharacteristic
subgroupG/H
center, socleC23×C151C22×D4
commutatorC2×C4C23×C4×C151
Frattini, cosocleC22×C4C24×C151
prime radicalC22×D4×C151C23
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C151 ◁ C2×C4×Q8×C151 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#446×C151C2semidirect
3. #2355×C151C2semidirect
4. #1993×C151C2semidirect
5. #1992×C151C2semidirect
6. #1991×C151C2semidirect
7. #1989×C151C2semidirect
8. #1989×C151C2semidirect
9. #1988×C151C2semidirect
17. #554×C151C4semidirect
122. #102×C151Q8semidirect
322. #22526C151direct (N × H)
323. C151#22526direct (N × H)
325. C2×#446C2×C151semidirect
326. #2355C2×C151semidirect
327. #1993C2×C151semidirect
328. #1992C2×C151semidirect
329. #1991C2×C151semidirect
330. #1989C2×C151semidirect
331. #1989C2×C151semidirect
332. #1988C2×C151semidirect
340. #554C4×C151semidirect
445. #102Q8×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#554×C1512
C2×#446×C1512
#2355×C1512
#1993×C1512
#1992×C1512
#1991×C1512
#1989×C1512
#1988×C1512
#1804×C1512
#1802×C1512
#1762×C1512
C4×#102×C1512
#22526151