Finite Group Databasebeta

← C151×#17769 #50322694

Subgroups — C151×#17769 #50322694

Order 38656.

918 conjugacy classes of subgroups.

The subgroup lattice has 742 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3511×C151C211yesmaximal, characteristic
2#2989×C151C211yesmaximal, characteristic, complemented
3#2925×C151C211yesmaximal, characteristic, complemented
4#1561×C151C211yesmaximal, characteristic, complemented
5#1557×C151C211yesmaximal, characteristic, complemented
6#1557×C151C211yesmaximal, characteristic, complemented
7#1556×C151C211yesmaximal, characteristic, complemented
8#1553×C151C211yesmaximal, characteristic, complemented
9#1553×C151C211yesmaximal, characteristic, complemented
10#1552×C151C211yesmaximal, characteristic, complemented
11#1552×C151C211yesmaximal, characteristic, complemented
12#1547×C151C211yesmaximal, characteristic, complemented
13#1546×C151C211yesmaximal, characteristic, complemented
14#1544×C151C211yesmaximal, characteristic, complemented
15#1540×C151C211yesmaximal, characteristic, complemented
16#556×C151—21no—
17#555×C151C412yes—
18#554×C151C412yes—
19#553×C151C412yes—
20#553×C151C412yes—
21#548×C151—21no—
22#548×C151—21no—
23#547×C151—21no—
24#542×C151—21no—
25#542×C151—21no—
26#537×C151—21no—
27#533×C151C2211yescharacteristic
28#533×C151C2211yescharacteristic
29#532×C151C2211yescharacteristic
30#532×C151C2211yescharacteristic
31#532×C151C2211yescharacteristic
32C2×C4⋊Q8×C151C2211yescharacteristic
33#520×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#332×C151C2211yescharacteristic
56#332×C151C2211yescharacteristic
57#332×C151C2211yescharacteristic
58#332×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#331×C151C2211yescharacteristic
68#331×C151C2211yescharacteristic
69#331×C151C2211yescharacteristic
70#331×C151C2211yescharacteristic
71C2×#41×C151—21no—
72C2×#41×C151—21no—
73C2×#41×C151—21no—
74C2×#41×C151D411yescharacteristic
75C22×Q8×C151—21no—
76C2×M16×C151—21no—
77C2×M16×C151—21no—
78C2×M16×C151—21no—
79C22×C8×C151—21no—
80C22×C8×C151—21no—
81C4⋊Q8×C151—21no—
82C4⋊Q8×C151—21no—
83C4⋊Q8×C151C2×C412yes—
84C4⋊Q8×C151C2311yescharacteristic
85C4⋊Q8×C151C2311yescharacteristic
86C4⋊Q8×C151C2311yescharacteristic
87#127×C151C2311yescharacteristic
88#126×C151—22no—
89#126×C151—22no—
90#125×C151C2×C412yes—
91#125×C151C2×C412yes—
92#124×C151—22no—
93#124×C151—22no—
94#124×C151—21no—
95#124×C151—21no—
96#124×C151—21no—
97#123×C151—22no—
98#123×C151—22no—
99C22⋊Q8×C151—21no—
100C22⋊Q8×C151—21no—
101C22⋊Q8×C151—21no—
102C22⋊Q8×C151—21no—
103C22⋊Q8×C151—22no—
104C22⋊Q8×C151—22no—
105C22⋊Q8×C151—22no—
106#121×C151—22no—
107#121×C151—22no—
108#121×C151—22no—
109#121×C151—21no—
110#121×C151—21no—
111#121×C151—21no—
112#121×C151C2×C412yes—
113#121×C151C2×C412yes—
114#121×C151C2×C412yes—
115C4×Q8×C151—21no—
116C4×Q8×C151—21no—
117C4×Q8×C151—21no—
118C4×Q8×C151—21no—
119C4×Q8×C151C2×C411yescharacteristic
120C4×Q8×C151D411yescharacteristic
121C4×D4×C151—22no—
122C4×D4×C151—22no—
123C4×D4×C151—21no—
124C4×D4×C151—21no—
125C4×D4×C151—21no—
126C4×D4×C151C2×C412yes—
127C4×D4×C151C2×C412yes—
128C4×D4×C151C2×C412yes—
129C4×D4×C151C2×C411yescharacteristic
130C4×D4×C151C2×C411yescharacteristic
131C4×D4×C151C2×C411yescharacteristic
132C4×D4×C151D411yescharacteristic
133C4×D4×C151D411yescharacteristic
134C4×D4×C151D411yescharacteristic
135#117×C151—22no—
136#117×C151C2×C412yes—
137#117×C151C2×C412yes—
138#117×C151D411yescharacteristic
139#117×C151D411yescharacteristic
140#117×C151D411yescharacteristic
141C2×C4⋊C4×C151—21no—
142C2×C4⋊C4×C151—22no—
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—
176#41×C151—42no—
177#41×C151—42no—
178#41×C151—81no—
179#41×C151—81no—
180#41×C151—81no—
181#41×C151—81no—
182C2×Q8×C151—22no—
183C2×Q8×C151—21no—
184C2×Q8×C151—21no—
185C2×Q8×C151—21no—
186C2×Q8×C151—81no—
187C2×Q8×C151—81no—
188C2×Q8×C151C22⋊C411yescharacteristic
189C2×D4×C151—22no—
190C2×D4×C151—22no—
191C2×D4×C151—22no—
192C2×D4×C151—21no—
193C2×D4×C151—21no—
194C2×D4×C151C22⋊C411yescharacteristic
195C2×D4×C151C22⋊C411yescharacteristic
196C2×D4×C151C22⋊C411yescharacteristic
197C2×D4×C151C22×C412yes—
198C22×C4×C151—22no—
199C22×C4×C151—22no—
200C22×C4×C151—22no—
201C22×C4×C151—22no—
202C22×C4×C151C22×C411yescharacteristic
203C22×C4×C151C22×C411yescharacteristic
204C22×C4×C151C22×C411yescharacteristic
205C22×C4×C151C2×D411yescharacteristic
206C22×C4×C151C2×D411yescharacteristic
207C22×C4×C151C2×D411yescharacteristic
208C22×C4×C151C2×D411yescharacteristic
209C22×C4×C151C2×D411yescharacteristic
210C22×C4×C151C2×D411yescharacteristic
211M16×C151—42no—
212M16×C151—81no—
213M16×C151—81no—
214C2×C8×C151—21no—
215C2×C8×C151—21no—
216C2×C8×C151—21no—
217C2×C8×C151—21no—
218C2×C8×C151—21no—
219C2×C8×C151—21no—
220C2×C8×C151—21no—
221C2×C8×C151—21no—
222C2×C8×C151—42no—
223C2×C8×C151—81no—
224C4⋊C4×C151—22no—
225C4⋊C4×C151—22no—
226C4⋊C4×C151—22no—
227C4⋊C4×C151—22no—
228C4⋊C4×C151—22no—
229C4⋊C4×C151—22no—
230C4⋊C4×C151—21no—
231C4⋊C4×C151—21no—
232C4⋊C4×C151—21no—
233C4⋊C4×C151C22⋊C411yescharacteristic
234C4⋊C4×C151C22⋊C411yescharacteristic
235C4⋊C4×C151C22⋊C411yescharacteristic
236C4⋊C4×C151C22⋊C411yescharacteristic
237C4⋊C4×C151C22⋊C411yescharacteristic
238C4⋊C4×C151C22⋊C411yescharacteristic
239C4⋊C4×C151C22×C412yes—
240C4⋊C4×C151C22×C412yes—
241C4⋊C4×C151C22×C412yes—
242C22⋊C4×C151—22no—
243C22⋊C4×C151—22no—
244C22⋊C4×C151—22no—
245C22⋊C4×C151—22no—
246C22⋊C4×C151—22no—
247C22⋊C4×C151—22no—
248C22⋊C4×C151—22no—
249C22⋊C4×C151—22no—
250C22⋊C4×C151C22⋊C411yescharacteristic
251C22⋊C4×C151C22⋊C411yescharacteristic
252C22⋊C4×C151C22⋊C411yescharacteristic
253C22⋊C4×C151C22⋊C411yescharacteristic
254C22⋊C4×C151C22⋊C411yescharacteristic
255C22⋊C4×C151C22⋊C411yescharacteristic
256C42×C151—22no—
257C42×C151—22no—
258C42×C151C22×C411yescharacteristic
259C42×C151C22×C411yescharacteristic
260C42×C151C22×C411yescharacteristic
261C42×C151C2×D411yescharacteristic
262C42×C151C2×D411yescharacteristic
263C42×C151C2×D411yescharacteristic
264C42×C151C2×D411yescharacteristic
265C42×C151C2×D411yescharacteristic
266C42×C151C2×D411yescharacteristic
267C42×C151C2411yescharacteristic
268C23×C151—22no—
269C23×C151C2×C22⋊C411yescharacteristic
270C23×C151C2×C22⋊C411yescharacteristic
271C23×C151C2×C22⋊C411yescharacteristic
272Q8×C151—41no—
273Q8×C151—41no—
274Q8×C151—41no—
275Q8×C151—41no—
276Q8×C151—41no—
277Q8×C151—41no—
278Q8×C151—41no—
279Q8×C151—82no—
280D4×C151—41no—
281D4×C151—41no—
282D4×C151—41no—
283D4×C151—42no—
284D4×C151—44no—
285D4×C151—41no—
286D4×C151—41no—
287D4×C151—41no—
288D4×C151—41no—
289D4×C151—82no—
290D4×C151—82no—
291C2×C4×C151—21no—
292C2×C4×C151—21no—
293C2×C4×C151—21no—
294C2×C4×C151—21no—
295C2×C4×C151—21no—
296C2×C4×C151—21no—
297C2×C4×C151—21no—
298C2×C4×C151—21no—
299C2×C4×C151—21no—
300C2×C4×C151—21no—
301C2×C4×C151—21no—
302C2×C4×C151—21no—
303C2×C4×C151—22no—
304C2×C4×C151—22no—
305C2×C4×C151—22no—
306C2×C4×C151—41no—
307C2×C4×C151—41no—
308C2×C4×C151—41no—
309C2×C4×C151—44no—
310C2×C4×C151—82no—
311C2×C4×C151—82no—
312C2×C4×C151—82no—
313C2×C4×C151C2×C22⋊C411yescharacteristic
314C2×C4×C151C2×C22⋊C411yescharacteristic
315C2×C4×C151C2×C22⋊C411yescharacteristic
316C2×C4×C151C2×C22⋊C411yescharacteristic
317C2×C4×C151C2×C22⋊C411yescharacteristic
318C2×C4×C151C2×C22⋊C411yescharacteristic
319C2×C4×C151C2×C22⋊C411yescharacteristic
320C2×C4×C151C2×C22⋊C411yescharacteristic
321C2×C4×C151C2×C22⋊C411yescharacteristic
322C2×C4×C151C23×C411yescharacteristic
323C2×C4×C151C22×D411yescharacteristic
324C2×C4×C151C22×D411yescharacteristic
325C8×C151—41no—
326C8×C151—41no—
327C8×C151—41no—
328C8×C151—41no—
329C8×C151—41no—
330C8×C151—41no—
331C8×C151—41no—
332C8×C151—41no—
333C22×C151—21no—
334C22×C151—21no—
335C22×C151—21no—
336C22×C151—21no—
337C22×C151—21no—
338C22×C151—21no—
339C22×C151—21no—
340C22×C151—21no—
341C22×C151—21no—
342C22×C151—42no—
343C22×C151—42no—
344C22×C151—42no—
345C22×C151C22×C22⋊C411yescharacteristic
346C4×C151—21no—
347C4×C151—21no—
348C4×C151—21no—
349C4×C151—21no—
350C4×C151—21no—
351C4×C151—21no—
352C4×C151—21no—
353C4×C151—21no—
354C4×C151—21no—
355C4×C151—21no—
356C4×C151—42no—
357C4×C151—42no—
358C4×C151—42no—
359C4×C151#57511yescharacteristic
360C4×C151#57511yescharacteristic
361C4×C151#57611yescharacteristic
362C4×C151#57711yescharacteristic
363C2×C151—41no—
364C2×C151—41no—
365C2×C151—41no—
366C2×C151—82no—
367C2×C151#288911yescharacteristic
368C2×C151#289611yescharacteristic
369C2×C151#289711yescharacteristic
370#17769C15111yesmaximal, characteristic, direct product factor, Sylow
371C151#1776911yescharacteristic, direct product factor, Sylow
372#3511C2×C15111yescharacteristic
373#2989C2×C15111yescharacteristic, complemented
374#2925C2×C15111yescharacteristic, complemented
375#1561C2×C15111yescharacteristic, complemented
376#1557C2×C15111yescharacteristic, complemented
377#1557C2×C15111yescharacteristic, complemented
378#1556C2×C15111yescharacteristic, complemented
379#1553C2×C15111yescharacteristic, complemented
380#1553C2×C15111yescharacteristic, complemented
381#1552C2×C15111yescharacteristic, complemented
382#1552C2×C15111yescharacteristic, complemented
383#1547C2×C15111yescharacteristic, complemented
384#1546C2×C15111yescharacteristic, complemented
385#1544C2×C15111yescharacteristic, complemented
386#1540C2×C15111yescharacteristic, complemented
387#556—21no—
388#555C4×C15112yes—
389#554C4×C15112yes—
390#553C4×C15112yes—
391#553C4×C15112yes—
392#548—21no—
393#548—21no—
394#547—21no—
395#542—21no—
396#542—21no—
397#537—21no—
398#533C22×C15111yescharacteristic
399#533C22×C15111yescharacteristic
400#532C22×C15111yescharacteristic
401#532C22×C15111yescharacteristic
402#532C22×C15111yescharacteristic
403C2×C4⋊Q8C22×C15111yescharacteristic
404#520—21no—
405C4×#41C22×C15111yescharacteristic
406#446—21no—
407#436—21no—
408#435—21no—
409#435—21no—
410#433—21no—
411#433—21no—
412#432C22×C15111yescharacteristic
413#432C22×C15111yescharacteristic
414#432C22×C15111yescharacteristic
415#432C22×C15111yescharacteristic
416#431C22×C15111yescharacteristic
417#431C22×C15111yescharacteristic
418#431C22×C15111yescharacteristic
419#423C22×C15111yescharacteristic
420#423C22×C15111yescharacteristic
421#423C22×C15111yescharacteristic
422C2×C4⋊C8C22×C15111yescharacteristic
423C2×C4⋊C8C22×C15111yescharacteristic
424#408—21no—
425#405—21no—
426#332C22×C15111yescharacteristic
427#332C22×C15111yescharacteristic
428#332C22×C15111yescharacteristic
429#332C22×C15111yescharacteristic
430#332C22×C15111yescharacteristic
431#332C22×C15111yescharacteristic
432#332C22×C15111yescharacteristic
433#332C22×C15111yescharacteristic
434#332C22×C15111yescharacteristic
435#332C22×C15111yescharacteristic
436#332C22×C15111yescharacteristic
437#332C22×C15111yescharacteristic
438#331C22×C15111yescharacteristic
439#331C22×C15111yescharacteristic
440#331C22×C15111yescharacteristic
441#331C22×C15111yescharacteristic
442C2×#41—21no—
443C2×#41—21no—
444C2×#41—21no—
445C2×#41D4×C15111yescharacteristic
446C22×Q8—21no—
447C2×M16—21no—
448C2×M16—21no—
449C2×M16—21no—
450C22×C8—21no—
451C22×C8—21no—
452C4⋊Q8—21no—
453C4⋊Q8—21no—
454C4⋊Q8C2×C4×C15112yes—
455C4⋊Q8C23×C15111yescharacteristic
456C4⋊Q8C23×C15111yescharacteristic
457C4⋊Q8C23×C15111yescharacteristic
458#127C23×C15111yescharacteristic
459#126—22no—
460#126—22no—
461#125C2×C4×C15112yes—
462#125C2×C4×C15112yes—
463#124—22no—
464#124—22no—
465#124—21no—
466#124—21no—
467#124—21no—
468#123—22no—
469#123—22no—
470C22⋊Q8—22no—
471C22⋊Q8—21no—
472C22⋊Q8—21no—
473C22⋊Q8—21no—
474C22⋊Q8—21no—
475C22⋊Q8—22no—
476C22⋊Q8—22no—
477#121—22no—
478#121—22no—
479#121—22no—
480#121—21no—
481#121—21no—
482#121—21no—
483#121C2×C4×C15112yes—
484#121C2×C4×C15112yes—
485#121C2×C4×C15112yes—
486C4×Q8—21no—
487C4×Q8—21no—
488C4×Q8—21no—
489C4×Q8—21no—
490C4×Q8C2×C4×C15111yescharacteristic
491C4×Q8D4×C15111yescharacteristic
492C4×D4—22no—
493C4×D4—22no—
494C4×D4—21no—
495C4×D4—21no—
496C4×D4—21no—
497C4×D4C2×C4×C15112yes—
498C4×D4C2×C4×C15112yes—
499C4×D4C2×C4×C15112yes—
500C4×D4C2×C4×C15111yescharacteristic
501C4×D4C2×C4×C15111yescharacteristic
502C4×D4C2×C4×C15111yescharacteristic
503C4×D4D4×C15111yescharacteristic
504C4×D4D4×C15111yescharacteristic
505C4×D4D4×C15111yescharacteristic
506#117—22no—
507#117C2×C4×C15112yes—
508#117C2×C4×C15112yes—
509#117D4×C15111yescharacteristic
510#117D4×C15111yescharacteristic
511#117D4×C15111yescharacteristic
512C2×C4⋊C4—21no—
513C2×C4⋊C4—22no—
514C2×C4⋊C4C2×C4×C15112yes—
515C2×C42C23×C15111yescharacteristic
516C2×C42C23×C15111yescharacteristic
517C2×C42C23×C15111yescharacteristic
518C4⋊C8—21no—
519C4⋊C8—21no—
520C4⋊C8—21no—
521C4⋊C8—21no—
522C4⋊C8—21no—
523C4⋊C8C23×C15111yescharacteristic
524C4⋊C8C23×C15111yescharacteristic
525C4⋊C8C23×C15111yescharacteristic
526C4⋊C8C23×C15111yescharacteristic
527C4⋊C8C23×C15111yescharacteristic
528C4⋊C8C23×C15111yescharacteristic
529C4⋊C8C23×C15111yescharacteristic
530C4⋊C8C23×C15111yescharacteristic
531C22⋊C8—21no—
532C22⋊C8—21no—
533C22⋊C8—21no—
534C22⋊C8—21no—
535C22⋊C8—21no—
536C22⋊C8—21no—
537C22⋊C8—21no—
538#97—21no—
539#97—21no—
540#97—21no—
541#97—21no—
542C4×C8—21no—
543C4×C8—21no—
544C4×C8—21no—
545#41—41no—
546#41—41no—
547#41—42no—
548#41—42no—
549#41—81no—
550#41—81no—
551#41—81no—
552#41—81no—
553C2×Q8—22no—
554C2×Q8—21no—
555C2×Q8—21no—
556C2×Q8—21no—
557C2×Q8—81no—
558C2×Q8—81no—
559C2×Q8C22⋊C4×C15111yescharacteristic
560C2×D4—22no—
561C2×D4—22no—
562C2×D4—22no—
563C2×D4—21no—
564C2×D4—21no—
565C2×D4C22⋊C4×C15111yescharacteristic
566C2×D4C22⋊C4×C15111yescharacteristic
567C2×D4C22⋊C4×C15111yescharacteristic
568C2×D4C22×C4×C15112yes—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4C22×C4×C15111yescharacteristic
574C22×C4C22×C4×C15111yescharacteristic
575C22×C4C22×C4×C15111yescharacteristic
576C22×C4C2×D4×C15111yescharacteristic
577C22×C4C2×D4×C15111yescharacteristic
578C22×C4C2×D4×C15111yescharacteristic
579C22×C4C2×D4×C15111yescharacteristic
580C22×C4C2×D4×C15111yescharacteristic
581C22×C4C2×D4×C15111yescharacteristic
582M16—42no—
583M16—81no—
584M16—81no—
585C2×C8—21no—
586C2×C8—21no—
587C2×C8—21no—
588C2×C8—21no—
589C2×C8—21no—
590C2×C8—21no—
591C2×C8—21no—
592C2×C8—21no—
593C2×C8—42no—
594C2×C8—81no—
595C4⋊C4—22no—
596C4⋊C4—22no—
597C4⋊C4—22no—
598C4⋊C4—22no—
599C4⋊C4—22no—
600C4⋊C4—22no—
601C4⋊C4—21no—
602C4⋊C4—21no—
603C4⋊C4—21no—
604C4⋊C4C22⋊C4×C15111yescharacteristic
605C4⋊C4C22⋊C4×C15111yescharacteristic
606C4⋊C4C22⋊C4×C15111yescharacteristic
607C4⋊C4C22⋊C4×C15111yescharacteristic
608C4⋊C4C22⋊C4×C15111yescharacteristic
609C4⋊C4C22⋊C4×C15111yescharacteristic
610C4⋊C4C22×C4×C15112yes—
611C4⋊C4C22×C4×C15112yes—
612C4⋊C4C22×C4×C15112yes—
613C22⋊C4—22no—
614C22⋊C4—22no—
615C22⋊C4—22no—
616C22⋊C4—22no—
617C22⋊C4—22no—
618C22⋊C4—22no—
619C22⋊C4—22no—
620C22⋊C4—22no—
621C22⋊C4C22⋊C4×C15111yescharacteristic
622C22⋊C4C22⋊C4×C15111yescharacteristic
623C22⋊C4C22⋊C4×C15111yescharacteristic
624C22⋊C4C22⋊C4×C15111yescharacteristic
625C22⋊C4C22⋊C4×C15111yescharacteristic
626C22⋊C4C22⋊C4×C15111yescharacteristic
627C42—22no—
628C42—22no—
629C42C22×C4×C15111yescharacteristic
630C42C22×C4×C15111yescharacteristic
631C42C22×C4×C15111yescharacteristic
632C42C2×D4×C15111yescharacteristic
633C42C2×D4×C15111yescharacteristic
634C42C2×D4×C15111yescharacteristic
635C42C2×D4×C15111yescharacteristic
636C42C2×D4×C15111yescharacteristic
637C42C2×D4×C15111yescharacteristic
638C42C24×C15111yescharacteristic
639C23—22no—
640C23C2×C22⋊C4×C15111yescharacteristic
641C23C2×C22⋊C4×C15111yescharacteristic
642C23C2×C22⋊C4×C15111yescharacteristic
643Q8—41no—
644Q8—41no—
645Q8—41no—
646Q8—41no—
647Q8—41no—
648Q8—41no—
649Q8—41no—
650Q8—82no—
651D4—41no—
652D4—41no—
653D4—41no—
654D4—42no—
655D4—44no—
656D4—41no—
657D4—41no—
658D4—41no—
659D4—41no—
660D4—82no—
661D4—82no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—21no—
666C2×C4—21no—
667C2×C4—21no—
668C2×C4—21no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—21no—
673C2×C4—21no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—41no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—44no—
681C2×C4—82no—
682C2×C4—82no—
683C2×C4—82no—
684C2×C4C2×C22⋊C4×C15111yescharacteristic
685C2×C4C2×C22⋊C4×C15111yescharacteristic
686C2×C4C2×C22⋊C4×C15111yescharacteristic
687C2×C4C2×C22⋊C4×C15111yescharacteristic
688C2×C4C2×C22⋊C4×C15111yescharacteristic
689C2×C4C2×C22⋊C4×C15111yescharacteristic
690C2×C4C2×C22⋊C4×C15111yescharacteristic
691C2×C4C2×C22⋊C4×C15111yescharacteristic
692C2×C4C2×C22⋊C4×C15111yescharacteristic
693C2×C4C23×C4×C15111yescharacteristic
694C2×C4C22×D4×C15111yescharacteristic
695C2×C4C22×D4×C15111yescharacteristic
696C8—41no—
697C8—41no—
698C8—41no—
699C8—41no—
700C8—41no—
701C8—41no—
702C8—41no—
703C8—41no—
704C22—21no—
705C22—21no—
706C22—21no—
707C22—21no—
708C22—21no—
709C22—21no—
710C22—21no—
711C22—21no—
712C22—21no—
713C22—42no—
714C22—42no—
715C22—42no—
716C22C22×C22⋊C4×C15111yescharacteristic
717C4—21no—
718C4—21no—
719C4—21no—
720C4—21no—
721C4—21no—
722C4—21no—
723C4—21no—
724C4—21no—
725C4—21no—
726C4—21no—
727C4—42no—
728C4—42no—
729C4—42no—
730C4#575×C15111yescharacteristic
731C4#575×C15111yescharacteristic
732C4#576×C15111yescharacteristic
733C4#577×C15111yescharacteristic
734C2—41no—
735C2—41no—
736C2—41no—
737C2—82no—
738C2#2889×C15111yescharacteristic
739C2#2896×C15111yescharacteristic
740C2#2897×C15111yescharacteristic
subgroupG/H
center, socleC22×C151C22×C22⋊C4
commutatorC2×C4C23×C4×C151
Frattini, cosocleC42C24×C151
prime radical#3511×C151C2
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
2. #2989×C151C2semidirect
3. #2925×C151C2semidirect
4. #1561×C151C2semidirect
5. #1557×C151C2semidirect
6. #1557×C151C2semidirect
7. #1556×C151C2semidirect
8. #1553×C151C2semidirect
9. #1553×C151C2semidirect
10. #1552×C151C2semidirect
11. #1552×C151C2semidirect
12. #1547×C151C2semidirect
13. #1546×C151C2semidirect
14. #1544×C151C2semidirect
15. #1540×C151C2semidirect
370. #17769C151direct (N × H)
371. C151#17769direct (N × H)
373. #2989C2×C151semidirect
374. #2925C2×C151semidirect
375. #1561C2×C151semidirect
376. #1557C2×C151semidirect
377. #1557C2×C151semidirect
378. #1556C2×C151semidirect
379. #1553C2×C151semidirect
380. #1553C2×C151semidirect
381. #1552C2×C151semidirect
382. #1552C2×C151semidirect
383. #1547C2×C151semidirect
384. #1546C2×C151semidirect
385. #1544C2×C151semidirect
386. #1540C2×C151semidirect

Maximal subgroups

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

subgroupindex
#3511×C1512
#2989×C1512
#2925×C1512
#1561×C1512
#1557×C1512
#1556×C1512
#1553×C1512
#1552×C1512
#1547×C1512
#1546×C1512
#1544×C1512
#1540×C1512
#17769151