Finite Group Databasebeta

← C151×#17767 #50322692

Subgroups — C151×#17767 #50322692

Order 38656.

862 conjugacy classes of subgroups.

The subgroup lattice has 704 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3509×C151C211yesmaximal, characteristic
2#2989×C151C211yesmaximal, characteristic
3#2925×C151C211yesmaximal, characteristic
4#1561×C151C211yesmaximal, characteristic, complemented
5#1559×C151C211yesmaximal, characteristic, complemented
6#1559×C151C211yesmaximal, characteristic, complemented
7#1556×C151C211yesmaximal, characteristic, complemented
8#1554×C151C211yesmaximal, characteristic, complemented
9#1554×C151C211yesmaximal, characteristic, complemented
10#1552×C151C211yesmaximal, characteristic, complemented
11#1552×C151C211yesmaximal, characteristic, complemented
12#1550×C151C211yesmaximal, characteristic, complemented
13#1549×C151C211yesmaximal, characteristic, complemented
14#1544×C151C211yesmaximal, characteristic, complemented
15#1542×C151C211yesmaximal, characteristic, complemented
16#557×C151—21no—
17#557×C151C412yes—
18#556×C151—21no—
19#556×C151C412yes—
20#552×C151—21no—
21#552×C151—21no—
22#552×C151C412yes—
23#552×C151C412yes—
24#541×C151—21no—
25#541×C151—21no—
26#536×C151—21no—
27#533×C151C2211yescharacteristic
28#533×C151C2211yescharacteristic
29#533×C151C2211yescharacteristic
30#533×C151C2211yescharacteristic
31#533×C151C2211yescharacteristic
32C2×C4⋊Q8×C151C2211yescharacteristic
33#519×C151—21no—
34C4×#41×C151C2211yescharacteristic
35#446×C151—21no—
36#436×C151—21no—
37#435×C151—21no—
38#435×C151—21no—
39#433×C151—21no—
40#433×C151—21no—
41#432×C151C2211yescharacteristic
42#432×C151C2211yescharacteristic
43#432×C151C2211yescharacteristic
44#432×C151C2211yescharacteristic
45#431×C151C2211yescharacteristic
46#431×C151C2211yescharacteristic
47#431×C151C2211yescharacteristic
48#423×C151C2211yescharacteristic
49#423×C151C2211yescharacteristic
50#423×C151C2211yescharacteristic
51C2×C4⋊C8×C151C2211yescharacteristic
52C2×C4⋊C8×C151C2211yescharacteristic
53#408×C151—21no—
54#405×C151—21no—
55#333×C151C2211yescharacteristic
56#333×C151C2211yescharacteristic
57#333×C151C2211yescharacteristic
58#333×C151C2211yescharacteristic
59#332×C151C2211yescharacteristic
60#332×C151C2211yescharacteristic
61#332×C151C2211yescharacteristic
62#332×C151C2211yescharacteristic
63#332×C151C2211yescharacteristic
64#332×C151C2211yescharacteristic
65#332×C151C2211yescharacteristic
66#332×C151C2211yescharacteristic
67#332×C151C2211yescharacteristic
68#332×C151C2211yescharacteristic
69#332×C151C2211yescharacteristic
70#332×C151C2211yescharacteristic
71C2×#41×C151D411yescharacteristic
72C22×Q8×C151—21no—
73C2×M16×C151—21no—
74C2×M16×C151—21no—
75C2×M16×C151—21no—
76C22×C8×C151—21no—
77C22×C8×C151—21no—
78C4⋊Q8×C151—21no—
79C4⋊Q8×C151—21no—
80C4⋊Q8×C151—22no—
81C4⋊Q8×C151C2×C412yes—
82C4⋊Q8×C151C2311yescharacteristic
83C4⋊Q8×C151C2311yescharacteristic
84C4⋊Q8×C151C2311yescharacteristic
85C4⋊Q8×C151C2311yescharacteristic
86#126×C151—22no—
87#126×C151—22no—
88#126×C151—22no—
89#126×C151—22no—
90#125×C151—22no—
91#125×C151—22no—
92#125×C151—22no—
93#125×C151—22no—
94#125×C151—21no—
95#125×C151—21no—
96#125×C151—21no—
97#125×C151C2×C412yes—
98#125×C151C2×C412yes—
99#124×C151—22no—
100#123×C151—22no—
101#123×C151—22no—
102C22⋊Q8×C151—21no—
103C22⋊Q8×C151—21no—
104C22⋊Q8×C151—21no—
105C22⋊Q8×C151—21no—
106C22⋊Q8×C151—21no—
107C22⋊Q8×C151—21no—
108C22⋊Q8×C151—21no—
109C22⋊Q8×C151C2×C412yes—
110C22⋊Q8×C151C2×C412yes—
111C22⋊Q8×C151C2×C412yes—
112C4×Q8×C151—22no—
113C4×Q8×C151—22no—
114C4×Q8×C151—21no—
115C4×Q8×C151—21no—
116C4×Q8×C151—21no—
117C4×Q8×C151—21no—
118C4×Q8×C151—21no—
119C4×Q8×C151—21no—
120C4×Q8×C151—21no—
121C4×Q8×C151C2×C411yescharacteristic
122C4×Q8×C151C2×C412yes—
123C4×Q8×C151C2×C412yes—
124C4×Q8×C151C2×C412yes—
125C4×Q8×C151D411yescharacteristic
126C4×D4×C151C2×C411yescharacteristic
127C4×D4×C151C2×C411yescharacteristic
128C4×D4×C151C2×C411yescharacteristic
129C4×D4×C151D411yescharacteristic
130C4×D4×C151D411yescharacteristic
131C4×D4×C151D411yescharacteristic
132#117×C151—21no—
133#117×C151—21no—
134#117×C151—21no—
135#117×C151—22no—
136#117×C151—22no—
137#117×C151C2×C412yes—
138#117×C151C2×C412yes—
139#117×C151D411yescharacteristic
140#117×C151D411yescharacteristic
141#117×C151D411yescharacteristic
142C2×C4⋊C4×C151—21no—
143C2×C4⋊C4×C151C2×C412yes—
144C2×C42×C151C2311yescharacteristic
145C2×C42×C151C2311yescharacteristic
146C2×C42×C151C2311yescharacteristic
147C4⋊C8×C151—21no—
148C4⋊C8×C151—21no—
149C4⋊C8×C151—21no—
150C4⋊C8×C151—21no—
151C4⋊C8×C151—21no—
152C4⋊C8×C151C2311yescharacteristic
153C4⋊C8×C151C2311yescharacteristic
154C4⋊C8×C151C2311yescharacteristic
155C4⋊C8×C151C2311yescharacteristic
156C4⋊C8×C151C2311yescharacteristic
157C4⋊C8×C151C2311yescharacteristic
158C4⋊C8×C151C2311yescharacteristic
159C4⋊C8×C151C2311yescharacteristic
160C22⋊C8×C151—21no—
161C22⋊C8×C151—21no—
162C22⋊C8×C151—21no—
163C22⋊C8×C151—21no—
164C22⋊C8×C151—21no—
165C22⋊C8×C151—21no—
166C22⋊C8×C151—21no—
167#97×C151—21no—
168#97×C151—21no—
169#97×C151—21no—
170#97×C151—21no—
171C4×C8×C151—21no—
172C4×C8×C151—21no—
173C4×C8×C151—21no—
174#41×C151—41no—
175#41×C151—41no—
176C2×Q8×C151—22no—
177C2×Q8×C151—21no—
178C2×Q8×C151—21no—
179C2×Q8×C151—21no—
180C2×Q8×C151—42no—
181C2×Q8×C151—42no—
182C2×Q8×C151C22⋊C411yescharacteristic
183C2×Q8×C151C22×C412yes—
184C2×D4×C151C22⋊C411yescharacteristic
185C2×D4×C151C22⋊C411yescharacteristic
186C2×D4×C151C22⋊C411yescharacteristic
187C22×C4×C151—22no—
188C22×C4×C151C22×C411yescharacteristic
189C22×C4×C151C22×C411yescharacteristic
190C22×C4×C151C22×C411yescharacteristic
191C22×C4×C151C2×D411yescharacteristic
192C22×C4×C151C2×D411yescharacteristic
193C22×C4×C151C2×D411yescharacteristic
194C22×C4×C151C2×D411yescharacteristic
195C22×C4×C151C2×D411yescharacteristic
196C22×C4×C151C2×D411yescharacteristic
197M16×C151—42no—
198M16×C151—81no—
199M16×C151—81no—
200C2×C8×C151—21no—
201C2×C8×C151—21no—
202C2×C8×C151—21no—
203C2×C8×C151—21no—
204C2×C8×C151—21no—
205C2×C8×C151—21no—
206C2×C8×C151—21no—
207C2×C8×C151—21no—
208C2×C8×C151—42no—
209C2×C8×C151—81no—
210C4⋊C4×C151—22no—
211C4⋊C4×C151—22no—
212C4⋊C4×C151—22no—
213C4⋊C4×C151—22no—
214C4⋊C4×C151—22no—
215C4⋊C4×C151—22no—
216C4⋊C4×C151—22no—
217C4⋊C4×C151—22no—
218C4⋊C4×C151—22no—
219C4⋊C4×C151—22no—
220C4⋊C4×C151—22no—
221C4⋊C4×C151—22no—
222C4⋊C4×C151—21no—
223C4⋊C4×C151—21no—
224C4⋊C4×C151—21no—
225C4⋊C4×C151—21no—
226C4⋊C4×C151—21no—
227C4⋊C4×C151C22⋊C411yescharacteristic
228C4⋊C4×C151C22⋊C411yescharacteristic
229C4⋊C4×C151C22⋊C411yescharacteristic
230C4⋊C4×C151C22⋊C411yescharacteristic
231C4⋊C4×C151C22⋊C411yescharacteristic
232C4⋊C4×C151C22⋊C411yescharacteristic
233C4⋊C4×C151C22×C412yes—
234C4⋊C4×C151C22×C412yes—
235C4⋊C4×C151C22×C412yes—
236C22⋊C4×C151—22no—
237C22⋊C4×C151—22no—
238C22⋊C4×C151—22no—
239C22⋊C4×C151—22no—
240C22⋊C4×C151—22no—
241C22⋊C4×C151C22⋊C411yescharacteristic
242C22⋊C4×C151C22⋊C411yescharacteristic
243C22⋊C4×C151C22⋊C411yescharacteristic
244C22⋊C4×C151C22⋊C411yescharacteristic
245C22⋊C4×C151C22⋊C411yescharacteristic
246C22⋊C4×C151C22⋊C411yescharacteristic
247C42×C151—22no—
248C42×C151—22no—
249C42×C151—22no—
250C42×C151—22no—
251C42×C151—22no—
252C42×C151C22×C411yescharacteristic
253C42×C151C22×C411yescharacteristic
254C42×C151C22×C411yescharacteristic
255C42×C151C2×D411yescharacteristic
256C42×C151C2×D411yescharacteristic
257C42×C151C2×D411yescharacteristic
258C42×C151C2×D411yescharacteristic
259C42×C151C2×D411yescharacteristic
260C42×C151C2×D411yescharacteristic
261C42×C151C2411yescharacteristic
262C23×C151C2×C22⋊C411yescharacteristic
263C23×C151C2×C22⋊C411yescharacteristic
264C23×C151C2×C22⋊C411yescharacteristic
265Q8×C151—41no—
266Q8×C151—42no—
267Q8×C151—44no—
268Q8×C151—41no—
269Q8×C151—41no—
270Q8×C151—41no—
271Q8×C151—41no—
272Q8×C151—41no—
273Q8×C151—41no—
274D4×C151—41no—
275D4×C151—41no—
276D4×C151—41no—
277C2×C4×C151—21no—
278C2×C4×C151—21no—
279C2×C4×C151—21no—
280C2×C4×C151—21no—
281C2×C4×C151—21no—
282C2×C4×C151—21no—
283C2×C4×C151—21no—
284C2×C4×C151—21no—
285C2×C4×C151—21no—
286C2×C4×C151—21no—
287C2×C4×C151—21no—
288C2×C4×C151—21no—
289C2×C4×C151—22no—
290C2×C4×C151—22no—
291C2×C4×C151—22no—
292C2×C4×C151—22no—
293C2×C4×C151—41no—
294C2×C4×C151—41no—
295C2×C4×C151—41no—
296C2×C4×C151—44no—
297C2×C4×C151C2×C22⋊C411yescharacteristic
298C2×C4×C151C2×C22⋊C411yescharacteristic
299C2×C4×C151C2×C22⋊C411yescharacteristic
300C2×C4×C151C2×C22⋊C411yescharacteristic
301C2×C4×C151C2×C22⋊C411yescharacteristic
302C2×C4×C151C2×C22⋊C411yescharacteristic
303C2×C4×C151C2×C22⋊C411yescharacteristic
304C2×C4×C151C2×C22⋊C411yescharacteristic
305C2×C4×C151C2×C22⋊C411yescharacteristic
306C2×C4×C151C23×C411yescharacteristic
307C2×C4×C151C22×D411yescharacteristic
308C2×C4×C151C22×D411yescharacteristic
309C8×C151—41no—
310C8×C151—41no—
311C8×C151—41no—
312C8×C151—41no—
313C8×C151—41no—
314C8×C151—41no—
315C8×C151—41no—
316C8×C151—41no—
317C22×C151—21no—
318C22×C151—21no—
319C22×C151—21no—
320C22×C151—21no—
321C22×C151—21no—
322C22×C151—21no—
323C22×C151—21no—
324C22×C151—21no—
325C22×C151—21no—
326C22×C151C22×C22⋊C411yescharacteristic
327C4×C151—21no—
328C4×C151—21no—
329C4×C151—21no—
330C4×C151—21no—
331C4×C151—21no—
332C4×C151—21no—
333C4×C151—21no—
334C4×C151—21no—
335C4×C151—21no—
336C4×C151—21no—
337C4×C151—42no—
338C4×C151—42no—
339C4×C151—42no—
340C4×C151—42no—
341C4×C151#57511yescharacteristic
342C4×C151#57511yescharacteristic
343C4×C151#57711yescharacteristic
344C4×C151#57811yescharacteristic
345C2×C151—41no—
346C2×C151—41no—
347C2×C151—41no—
348C2×C151#288911yescharacteristic
349C2×C151#289611yescharacteristic
350C2×C151#289811yescharacteristic
351#17767C15111yesmaximal, characteristic, direct product factor, Sylow
352C151#1776711yescharacteristic, direct product factor, Sylow
353#3509C2×C15111yescharacteristic
354#2989C2×C15111yescharacteristic
355#2925C2×C15111yescharacteristic
356#1561C2×C15111yescharacteristic, complemented
357#1559C2×C15111yescharacteristic, complemented
358#1559C2×C15111yescharacteristic, complemented
359#1556C2×C15111yescharacteristic, complemented
360#1554C2×C15111yescharacteristic, complemented
361#1554C2×C15111yescharacteristic, complemented
362#1552C2×C15111yescharacteristic, complemented
363#1552C2×C15111yescharacteristic, complemented
364#1550C2×C15111yescharacteristic, complemented
365#1549C2×C15111yescharacteristic, complemented
366#1544C2×C15111yescharacteristic, complemented
367#1542C2×C15111yescharacteristic, complemented
368#557—21no—
369#557C4×C15112yes—
370#556—21no—
371#556C4×C15112yes—
372#552—21no—
373#552—21no—
374#552C4×C15112yes—
375#552C4×C15112yes—
376#541—21no—
377#541—21no—
378#536—21no—
379#533C22×C15111yescharacteristic
380#533C22×C15111yescharacteristic
381#533C22×C15111yescharacteristic
382#533C22×C15111yescharacteristic
383#533C22×C15111yescharacteristic
384C2×C4⋊Q8C22×C15111yescharacteristic
385#519—21no—
386C4×#41C22×C15111yescharacteristic
387#446—21no—
388#436—21no—
389#435—21no—
390#435—21no—
391#433—21no—
392#433—21no—
393#432C22×C15111yescharacteristic
394#432C22×C15111yescharacteristic
395#432C22×C15111yescharacteristic
396#432C22×C15111yescharacteristic
397#431C22×C15111yescharacteristic
398#431C22×C15111yescharacteristic
399#431C22×C15111yescharacteristic
400#423C22×C15111yescharacteristic
401#423C22×C15111yescharacteristic
402#423C22×C15111yescharacteristic
403C2×C4⋊C8C22×C15111yescharacteristic
404C2×C4⋊C8C22×C15111yescharacteristic
405#408—21no—
406#405—21no—
407#333C22×C15111yescharacteristic
408#333C22×C15111yescharacteristic
409#333C22×C15111yescharacteristic
410#333C22×C15111yescharacteristic
411#332C22×C15111yescharacteristic
412#332C22×C15111yescharacteristic
413#332C22×C15111yescharacteristic
414#332C22×C15111yescharacteristic
415#332C22×C15111yescharacteristic
416#332C22×C15111yescharacteristic
417#332C22×C15111yescharacteristic
418#332C22×C15111yescharacteristic
419#332C22×C15111yescharacteristic
420#332C22×C15111yescharacteristic
421#332C22×C15111yescharacteristic
422#332C22×C15111yescharacteristic
423C2×#41D4×C15111yescharacteristic
424C22×Q8—21no—
425C2×M16—21no—
426C2×M16—21no—
427C2×M16—21no—
428C22×C8—21no—
429C22×C8—21no—
430C4⋊Q8—22no—
431C4⋊Q8—21no—
432C4⋊Q8—21no—
433C4⋊Q8C2×C4×C15112yes—
434C4⋊Q8C23×C15111yescharacteristic
435C4⋊Q8C23×C15111yescharacteristic
436C4⋊Q8C23×C15111yescharacteristic
437C4⋊Q8C23×C15111yescharacteristic
438#126—22no—
439#126—22no—
440#126—22no—
441#126—22no—
442#125—22no—
443#125—22no—
444#125—22no—
445#125—22no—
446#125—21no—
447#125—21no—
448#125—21no—
449#125C2×C4×C15112yes—
450#125C2×C4×C15112yes—
451#124—22no—
452#123—22no—
453#123—22no—
454C22⋊Q8—21no—
455C22⋊Q8—21no—
456C22⋊Q8—21no—
457C22⋊Q8—21no—
458C22⋊Q8—21no—
459C22⋊Q8—21no—
460C22⋊Q8—21no—
461C22⋊Q8C2×C4×C15112yes—
462C22⋊Q8C2×C4×C15112yes—
463C22⋊Q8C2×C4×C15112yes—
464C4×Q8—22no—
465C4×Q8—22no—
466C4×Q8—21no—
467C4×Q8—21no—
468C4×Q8—21no—
469C4×Q8—21no—
470C4×Q8—21no—
471C4×Q8—21no—
472C4×Q8—21no—
473C4×Q8C2×C4×C15112yes—
474C4×Q8C2×C4×C15112yes—
475C4×Q8C2×C4×C15112yes—
476C4×Q8C2×C4×C15111yescharacteristic
477C4×Q8D4×C15111yescharacteristic
478C4×D4C2×C4×C15111yescharacteristic
479C4×D4C2×C4×C15111yescharacteristic
480C4×D4C2×C4×C15111yescharacteristic
481C4×D4D4×C15111yescharacteristic
482C4×D4D4×C15111yescharacteristic
483C4×D4D4×C15111yescharacteristic
484#117—21no—
485#117—21no—
486#117—21no—
487#117—22no—
488#117—22no—
489#117C2×C4×C15112yes—
490#117C2×C4×C15112yes—
491#117D4×C15111yescharacteristic
492#117D4×C15111yescharacteristic
493#117D4×C15111yescharacteristic
494C2×C4⋊C4—21no—
495C2×C4⋊C4C2×C4×C15112yes—
496C2×C42C23×C15111yescharacteristic
497C2×C42C23×C15111yescharacteristic
498C2×C42C23×C15111yescharacteristic
499C4⋊C8—21no—
500C4⋊C8—21no—
501C4⋊C8—21no—
502C4⋊C8—21no—
503C4⋊C8—21no—
504C4⋊C8C23×C15111yescharacteristic
505C4⋊C8C23×C15111yescharacteristic
506C4⋊C8C23×C15111yescharacteristic
507C4⋊C8C23×C15111yescharacteristic
508C4⋊C8C23×C15111yescharacteristic
509C4⋊C8C23×C15111yescharacteristic
510C4⋊C8C23×C15111yescharacteristic
511C4⋊C8C23×C15111yescharacteristic
512C22⋊C8—21no—
513C22⋊C8—21no—
514C22⋊C8—21no—
515C22⋊C8—21no—
516C22⋊C8—21no—
517C22⋊C8—21no—
518C22⋊C8—21no—
519#97—21no—
520#97—21no—
521#97—21no—
522#97—21no—
523C4×C8—21no—
524C4×C8—21no—
525C4×C8—21no—
526#41—41no—
527#41—41no—
528C2×Q8—22no—
529C2×Q8—21no—
530C2×Q8—21no—
531C2×Q8—21no—
532C2×Q8—42no—
533C2×Q8—42no—
534C2×Q8C22⋊C4×C15111yescharacteristic
535C2×Q8C22×C4×C15112yes—
536C2×D4C22⋊C4×C15111yescharacteristic
537C2×D4C22⋊C4×C15111yescharacteristic
538C2×D4C22⋊C4×C15111yescharacteristic
539C22×C4—22no—
540C22×C4C22×C4×C15111yescharacteristic
541C22×C4C22×C4×C15111yescharacteristic
542C22×C4C22×C4×C15111yescharacteristic
543C22×C4C2×D4×C15111yescharacteristic
544C22×C4C2×D4×C15111yescharacteristic
545C22×C4C2×D4×C15111yescharacteristic
546C22×C4C2×D4×C15111yescharacteristic
547C22×C4C2×D4×C15111yescharacteristic
548C22×C4C2×D4×C15111yescharacteristic
549M16—42no—
550M16—81no—
551M16—81no—
552C2×C8—21no—
553C2×C8—21no—
554C2×C8—21no—
555C2×C8—21no—
556C2×C8—21no—
557C2×C8—21no—
558C2×C8—21no—
559C2×C8—21no—
560C2×C8—42no—
561C2×C8—81no—
562C4⋊C4—22no—
563C4⋊C4—22no—
564C4⋊C4—22no—
565C4⋊C4—22no—
566C4⋊C4—22no—
567C4⋊C4—22no—
568C4⋊C4—22no—
569C4⋊C4—22no—
570C4⋊C4—22no—
571C4⋊C4—22no—
572C4⋊C4—22no—
573C4⋊C4—22no—
574C4⋊C4—21no—
575C4⋊C4—21no—
576C4⋊C4—21no—
577C4⋊C4—21no—
578C4⋊C4—21no—
579C4⋊C4C22⋊C4×C15111yescharacteristic
580C4⋊C4C22⋊C4×C15111yescharacteristic
581C4⋊C4C22⋊C4×C15111yescharacteristic
582C4⋊C4C22⋊C4×C15111yescharacteristic
583C4⋊C4C22⋊C4×C15111yescharacteristic
584C4⋊C4C22⋊C4×C15111yescharacteristic
585C4⋊C4C22×C4×C15112yes—
586C4⋊C4C22×C4×C15112yes—
587C4⋊C4C22×C4×C15112yes—
588C22⋊C4—22no—
589C22⋊C4—22no—
590C22⋊C4—22no—
591C22⋊C4—22no—
592C22⋊C4—22no—
593C22⋊C4C22⋊C4×C15111yescharacteristic
594C22⋊C4C22⋊C4×C15111yescharacteristic
595C22⋊C4C22⋊C4×C15111yescharacteristic
596C22⋊C4C22⋊C4×C15111yescharacteristic
597C22⋊C4C22⋊C4×C15111yescharacteristic
598C22⋊C4C22⋊C4×C15111yescharacteristic
599C42—22no—
600C42—22no—
601C42—22no—
602C42—22no—
603C42—22no—
604C42C22×C4×C15111yescharacteristic
605C42C22×C4×C15111yescharacteristic
606C42C22×C4×C15111yescharacteristic
607C42C2×D4×C15111yescharacteristic
608C42C2×D4×C15111yescharacteristic
609C42C2×D4×C15111yescharacteristic
610C42C2×D4×C15111yescharacteristic
611C42C2×D4×C15111yescharacteristic
612C42C2×D4×C15111yescharacteristic
613C42C24×C15111yescharacteristic
614C23C2×C22⋊C4×C15111yescharacteristic
615C23C2×C22⋊C4×C15111yescharacteristic
616C23C2×C22⋊C4×C15111yescharacteristic
617Q8—41no—
618Q8—42no—
619Q8—44no—
620Q8—41no—
621Q8—41no—
622Q8—41no—
623Q8—41no—
624Q8—41no—
625Q8—41no—
626D4—41no—
627D4—41no—
628D4—41no—
629C2×C4—21no—
630C2×C4—21no—
631C2×C4—21no—
632C2×C4—21no—
633C2×C4—21no—
634C2×C4—21no—
635C2×C4—21no—
636C2×C4—21no—
637C2×C4—21no—
638C2×C4—21no—
639C2×C4—21no—
640C2×C4—21no—
641C2×C4—22no—
642C2×C4—22no—
643C2×C4—22no—
644C2×C4—22no—
645C2×C4—41no—
646C2×C4—41no—
647C2×C4—41no—
648C2×C4—44no—
649C2×C4C2×C22⋊C4×C15111yescharacteristic
650C2×C4C2×C22⋊C4×C15111yescharacteristic
651C2×C4C2×C22⋊C4×C15111yescharacteristic
652C2×C4C2×C22⋊C4×C15111yescharacteristic
653C2×C4C2×C22⋊C4×C15111yescharacteristic
654C2×C4C2×C22⋊C4×C15111yescharacteristic
655C2×C4C2×C22⋊C4×C15111yescharacteristic
656C2×C4C2×C22⋊C4×C15111yescharacteristic
657C2×C4C2×C22⋊C4×C15111yescharacteristic
658C2×C4C23×C4×C15111yescharacteristic
659C2×C4C22×D4×C15111yescharacteristic
660C2×C4C22×D4×C15111yescharacteristic
661C8—41no—
662C8—41no—
663C8—41no—
664C8—41no—
665C8—41no—
666C8—41no—
667C8—41no—
668C8—41no—
669C22—21no—
670C22—21no—
671C22—21no—
672C22—21no—
673C22—21no—
674C22—21no—
675C22—21no—
676C22—21no—
677C22—21no—
678C22C22×C22⋊C4×C15111yescharacteristic
679C4—21no—
680C4—21no—
681C4—21no—
682C4—21no—
683C4—21no—
684C4—21no—
685C4—21no—
686C4—21no—
687C4—21no—
688C4—21no—
689C4—42no—
690C4—42no—
691C4—42no—
692C4—42no—
693C4#575×C15111yescharacteristic
694C4#575×C15111yescharacteristic
695C4#577×C15111yescharacteristic
696C4#578×C15111yescharacteristic
697C2—41no—
698C2—41no—
699C2—41no—
700C2#2889×C15111yescharacteristic
701C2#2896×C15111yescharacteristic
702C2#2898×C15111yescharacteristic
subgroupG/H
center, socleC22×C151C22×C22⋊C4
commutatorC2×C4C23×C4×C151
Frattini, cosocleC42C24×C151
prime radicalC2×#41×C151D4
LCSG ▷ C2×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C151 ◁ C4×#41×C151 ◁ G

Complements

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

NH ≅ G/Ntype
4. #1561×C151C2semidirect
5. #1559×C151C2semidirect
6. #1559×C151C2semidirect
7. #1556×C151C2semidirect
8. #1554×C151C2semidirect
9. #1554×C151C2semidirect
10. #1552×C151C2semidirect
11. #1552×C151C2semidirect
12. #1550×C151C2semidirect
13. #1549×C151C2semidirect
14. #1544×C151C2semidirect
15. #1542×C151C2semidirect
351. #17767C151direct (N × H)
352. C151#17767direct (N × H)
356. #1561C2×C151semidirect
357. #1559C2×C151semidirect
358. #1559C2×C151semidirect
359. #1556C2×C151semidirect
360. #1554C2×C151semidirect
361. #1554C2×C151semidirect
362. #1552C2×C151semidirect
363. #1552C2×C151semidirect
364. #1550C2×C151semidirect
365. #1549C2×C151semidirect
366. #1544C2×C151semidirect
367. #1542C2×C151semidirect

Maximal subgroups

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

subgroupindex
#3509×C1512
#2989×C1512
#2925×C1512
#1561×C1512
#1559×C1512
#1556×C1512
#1554×C1512
#1552×C1512
#1550×C1512
#1549×C1512
#1544×C1512
#1542×C1512
#17767151