Finite Group Databasebeta

← C151×#24311 #50329236

Subgroups — C151×#24311 #50329236

Order 38656.

1012 conjugacy classes of subgroups.

The subgroup lattice has 668 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#544×C151C211yesmaximal, characteristic
2C2×#479×C151C211yesmaximal, characteristic, complemented
3C2×#477×C151C211yesmaximal, characteristic, complemented
4#2323×C151C211yesmaximal, characteristic
5#2059×C151C211yesmaximal, characteristic, complemented
6#2057×C151C211yesmaximal, characteristic, complemented
7#2026×C151C211yesmaximal, characteristic, complemented
8#2024×C151C211yesmaximal, characteristic, complemented
9#1989×C151C211yesmaximal, characteristic, complemented
10#1988×C151C211yesmaximal, characteristic, complemented
11#1873×C151C211yesmaximal, characteristic
12#1872×C151C211yesmaximal, characteristic
13#1854×C151C211yesmaximal, characteristic
14#1852×C151C211yesmaximal, characteristic
15#1798×C151C211yesmaximal, characteristic
16#544×C151—24no—
17#544×C151—24no—
18C2×C4⋊Q8×C151—21no—
19C2×C4⋊Q8×C151C2211yescharacteristic
20C2×C4⋊Q8×C151C2211yescharacteristic
21C2×#125×C151—21no—
22C2×#125×C151C2211yescharacteristic
23C2×#125×C151C2211yescharacteristic
24C2×C22⋊Q8×C151—21no—
25C2×C22⋊Q8×C151—21no—
26C2×C22⋊Q8×C151C2211yescharacteristic
27C2×C4×Q8×C151C2211yescharacteristic
28C2×#117×C151C2211yescharacteristic
29C2×#117×C151C2211yescharacteristic
30C22×C4⋊C4×C151C2211yescharacteristic
31#479×C151—24no—
32#477×C151—24no—
33C2×#107×C151C2211yescharacteristic
34C2×#107×C151C2211yescharacteristic
35C2×#107×C151C2211yescharacteristic
36C2×#106×C151C2211yescharacteristic
37C2×C4⋊C8×C151C2211yescharacteristic
38C2×C4⋊C8×C151C2211yescharacteristic
39C2×#103×C151C2211yescharacteristic
40C2×#103×C151C2211yescharacteristic
41C2×#103×C151C2211yescharacteristic
42C2×#103×C151C2211yescharacteristic
43C2×C22⋊C8×C151C2211yescharacteristic
44C2×C22⋊C8×C151C2211yescharacteristic
45#391×C151C2211yescharacteristic
46#389×C151—21no—
47#389×C151C2211yescharacteristic
48#388×C151—21no—
49#388×C151—21no—
50#387×C151—21no—
51#380×C151C2211yescharacteristic
52C4×C4⋊C4×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#336×C151C2211yescharacteristic
62#336×C151C2211yescharacteristic
63C22×Q8×C151—21no—
64C22×Q8×C151—21no—
65C22×Q8×C151C2311yescharacteristic
66C23×C4×C151—21no—
67C23×C4×C151C2311yescharacteristic
68C22×C8×C151C2311yescharacteristic
69C22×C8×C151C2311yescharacteristic
70C22×C8×C151C2311yescharacteristic
71C22×C8×C151C2311yescharacteristic
72C4⋊Q8×C151—28no—
73C4⋊Q8×C151—22no—
74C4⋊Q8×C151—22no—
75C4⋊Q8×C151—22no—
76C4⋊Q8×C151D414yes—
77#125×C151—28no—
78#125×C151—22no—
79#125×C151—22no—
80#125×C151—22no—
81#125×C151D414yes—
82C22⋊Q8×C151—28no—
83C22⋊Q8×C151—28no—
84C22⋊Q8×C151—22no—
85C22⋊Q8×C151Q814yescomplemented
86C4×Q8×C151—22no—
87C4×Q8×C151—22no—
88#117×C151—22no—
89#117×C151—22no—
90#117×C151—22no—
91#117×C151—22no—
92C2×C4⋊C4×C151—21no—
93C2×C4⋊C4×C151—21no—
94C2×C4⋊C4×C151—21no—
95C2×C4⋊C4×C151—21no—
96C2×C4⋊C4×C151—21no—
97C2×C4⋊C4×C151—21no—
98C2×C4⋊C4×C151—21no—
99C2×C4⋊C4×C151—21no—
100C2×C4⋊C4×C151—22no—
101C2×C4⋊C4×C151—22no—
102C2×C4⋊C4×C151—21no—
103C2×C4⋊C4×C151—21no—
104C2×C4⋊C4×C151D411yescharacteristic
105C2×C4⋊C4×C151D411yescharacteristic
106C2×C4⋊C4×C151C2311yescharacteristic
107C2×C4⋊C4×C151C2311yescharacteristic
108C2×C4⋊C4×C151C2311yescharacteristic
109C2×C4⋊C4×C151C2311yescharacteristic
110C2×C4⋊C4×C151C2311yescharacteristic
111C2×C4⋊C4×C151C2311yescharacteristic
112C2×C4⋊C4×C151C2311yescharacteristic
113C2×C22⋊C4×C151—21no—
114C2×C22⋊C4×C151—21no—
115C2×C22⋊C4×C151—21no—
116C2×C22⋊C4×C151D411yescharacteristic
117C2×C22⋊C4×C151D411yescharacteristic
118C2×C42×C151—21no—
119C2×C42×C151—21no—
120C2×C42×C151—21no—
121C2×C42×C151C2311yescharacteristic
122C2×C42×C151C2311yescharacteristic
123#107×C151—22no—
124#107×C151—22no—
125#107×C151—22no—
126#106×C151—22no—
127C4⋊C8×C151—22no—
128C4⋊C8×C151—22no—
129#103×C151—22no—
130#103×C151—22no—
131#103×C151—22no—
132#103×C151—22no—
133C22⋊C8×C151—22no—
134C22⋊C8×C151—22no—
135#95×C151—21no—
136#95×C151—21no—
137#95×C151—21no—
138#95×C151—21no—
139#95×C151—21no—
140C24×C151C2×D411yescharacteristic
141C2×Q8×C151—24no—
142C2×Q8×C151—24no—
143C2×Q8×C151—21no—
144C2×Q8×C151—21no—
145C2×Q8×C151—21no—
146C2×Q8×C151—21no—
147C2×Q8×C151—21no—
148C2×Q8×C151—81no—
149C2×Q8×C151—81no—
150C2×Q8×C151—81no—
151C2×Q8×C151—81no—
152C2×Q8×C151C2×Q812yes—
153C22×C4×C151—21no—
154C22×C4×C151—21no—
155C22×C4×C151—21no—
156C22×C4×C151—21no—
157C22×C4×C151—21no—
158C22×C4×C151—21no—
159C22×C4×C151—21no—
160C22×C4×C151—21no—
161C22×C4×C151—21no—
162C22×C4×C151—21no—
163C22×C4×C151—24no—
164C22×C4×C151—21no—
165C22×C4×C151—21no—
166C22×C4×C151—81no—
167C22×C4×C151—81no—
168C22×C4×C151C2×D411yescharacteristic
169C22×C4×C151C2×D411yescharacteristic
170C22×C4×C151C2×D411yescharacteristic
171C22×C4×C151C2×D411yescharacteristic
172C22×C4×C151C2×D411yescharacteristic
173C22×C4×C151C2×Q812yes—
174C22×C4×C151#4112yes—
175C22×C4×C151C2411yescharacteristic
176C2×C8×C151—21no—
177C2×C8×C151—21no—
178C2×C8×C151—21no—
179C2×C8×C151—21no—
180C2×C8×C151—21no—
181C2×C8×C151—21no—
182C2×C8×C151—21no—
183C2×C8×C151—21no—
184C2×C8×C151—21no—
185C2×C8×C151—21no—
186C2×C8×C151—21no—
187C2×C8×C151—21no—
188C4⋊C4×C151—24no—
189C4⋊C4×C151—24no—
190C4⋊C4×C151—24no—
191C4⋊C4×C151—24no—
192C4⋊C4×C151—24no—
193C4⋊C4×C151—24no—
194C4⋊C4×C151—24no—
195C4⋊C4×C151—22no—
196C4⋊C4×C151—22no—
197C4⋊C4×C151—24no—
198C4⋊C4×C151—21no—
199C4⋊C4×C151—21no—
200C4⋊C4×C151—21no—
201C4⋊C4×C151—21no—
202C4⋊C4×C151—21no—
203C4⋊C4×C151—21no—
204C4⋊C4×C151—21no—
205C4⋊C4×C151—21no—
206C4⋊C4×C151—21no—
207C4⋊C4×C151—42no—
208C4⋊C4×C151—81no—
209C4⋊C4×C151C2×D412yes—
210C4⋊C4×C151C2×D412yes—
211C4⋊C4×C151C2×D412yes—
212C4⋊C4×C151C2×D412yes—
213C4⋊C4×C151C2×Q812yes—
214C22⋊C4×C151—24no—
215C22⋊C4×C151—24no—
216C22⋊C4×C151—22no—
217C22⋊C4×C151—22no—
218C22⋊C4×C151—81no—
219C42×C151—24no—
220C42×C151—21no—
221C42×C151—21no—
222C42×C151—42no—
223C42×C151—81no—
224C42×C151C2×D412yes—
225C42×C151C2×D412yes—
226C23×C151—21no—
227C23×C151—21no—
228C23×C151—21no—
229C23×C151—21no—
230C23×C151—21no—
231C23×C151—21no—
232C23×C151C22⋊Q812yes—
233C23×C151C22×D411yescharacteristic
234Q8×C151—22no—
235Q8×C151—22no—
236Q8×C151—41no—
237Q8×C151—41no—
238Q8×C151—84no—
239Q8×C151—84no—
240C2×C4×C151—21no—
241C2×C4×C151—21no—
242C2×C4×C151—21no—
243C2×C4×C151—21no—
244C2×C4×C151—21no—
245C2×C4×C151—21no—
246C2×C4×C151—22no—
247C2×C4×C151—22no—
248C2×C4×C151—22no—
249C2×C4×C151—22no—
250C2×C4×C151—21no—
251C2×C4×C151—22no—
252C2×C4×C151—22no—
253C2×C4×C151—22no—
254C2×C4×C151—21no—
255C2×C4×C151—22no—
256C2×C4×C151—22no—
257C2×C4×C151—22no—
258C2×C4×C151—21no—
259C2×C4×C151—21no—
260C2×C4×C151—21no—
261C2×C4×C151—21no—
262C2×C4×C151—41no—
263C2×C4×C151—41no—
264C2×C4×C151—41no—
265C2×C4×C151—41no—
266C2×C4×C151—41no—
267C2×C4×C151—41no—
268C2×C4×C151—41no—
269C2×C4×C151—41no—
270C2×C4×C151—41no—
271C2×C4×C151—41no—
272C2×C4×C151—41no—
273C2×C4×C151—41no—
274C2×C4×C151—41no—
275C2×C4×C151—41no—
276C2×C4×C151—41no—
277C2×C4×C151—41no—
278C2×C4×C151—41no—
279C2×C4×C151—41no—
280C2×C4×C151—84no—
281C2×C4×C151#12012yes—
282C2×C4×C151#12012yes—
283C2×C4×C151C22⋊Q812yes—
284C2×C4×C151C22×D411yescharacteristic
285C2×C4×C151C22×D411yescharacteristic
286C2×C4×C151C22×Q811yescharacteristic
287C2×C4×C151C2×#4111yescharacteristic
288C2×C4×C1512−1+411yescharacteristic
289C2×C4×C1512−1+411yescharacteristic
290C8×C151—41no—
291C8×C151—41no—
292C8×C151—41no—
293C8×C151—41no—
294C22×C151—22no—
295C22×C151—22no—
296C22×C151—22no—
297C22×C151—41no—
298C22×C151—41no—
299C22×C151—41no—
300C22×C151—41no—
301C22×C151C2×#12011yescharacteristic
302C22×C151C2×C22⋊Q811yescharacteristic
303C22×C151#53611yescharacteristic
304C22×C151#57611yescharacteristic
305C22×C151#57711yescharacteristic
306C22×C151#57811yescharacteristic
307C22×C151#57811yescharacteristic
308C4×C151—22no—
309C4×C151—22no—
310C4×C151—22no—
311C4×C151—42no—
312C4×C151—42no—
313C4×C151—41no—
314C4×C151—42no—
315C4×C151—41no—
316C4×C151—42no—
317C4×C151—42no—
318C4×C151—42no—
319C4×C151—81no—
320C4×C151—81no—
321C4×C151#54811yescharacteristic
322C4×C151#54811yescharacteristic
323C4×C151D4×Q811yescharacteristic
324C4×C151D4×Q811yescharacteristic
325C2×C151—42no—
326C2×C151#240911yescharacteristic
327C2×C151#301111yescharacteristic
328C2×C151#301211yescharacteristic
329C2×C151#308211yescharacteristic
330C2×C151#308311yescharacteristic
331C2×C151#324211yescharacteristic
332C2×C151#324311yescharacteristic
333#24311C15111yesmaximal, characteristic, direct product factor, Sylow
334C151#2431111yescharacteristic, direct product factor, Sylow
335C2×#544C2×C15111yescharacteristic
336C2×#479C2×C15111yescharacteristic, complemented
337C2×#477C2×C15111yescharacteristic, complemented
338#2323C2×C15111yescharacteristic
339#2059C2×C15111yescharacteristic, complemented
340#2057C2×C15111yescharacteristic, complemented
341#2026C2×C15111yescharacteristic, complemented
342#2024C2×C15111yescharacteristic, complemented
343#1989C2×C15111yescharacteristic, complemented
344#1988C2×C15111yescharacteristic, complemented
345#1873C2×C15111yescharacteristic
346#1872C2×C15111yescharacteristic
347#1854C2×C15111yescharacteristic
348#1852C2×C15111yescharacteristic
349#1798C2×C15111yescharacteristic
350#544—24no—
351#544—24no—
352C2×C4⋊Q8—21no—
353C2×C4⋊Q8C22×C15111yescharacteristic
354C2×C4⋊Q8C22×C15111yescharacteristic
355C2×#125—21no—
356C2×#125C22×C15111yescharacteristic
357C2×#125C22×C15111yescharacteristic
358C2×C22⋊Q8—21no—
359C2×C22⋊Q8—21no—
360C2×C22⋊Q8C22×C15111yescharacteristic
361C2×C4×Q8C22×C15111yescharacteristic
362C2×#117C22×C15111yescharacteristic
363C2×#117C22×C15111yescharacteristic
364C22×C4⋊C4C22×C15111yescharacteristic
365#479—24no—
366#477—24no—
367C2×#107C22×C15111yescharacteristic
368C2×#107C22×C15111yescharacteristic
369C2×#107C22×C15111yescharacteristic
370C2×#106C22×C15111yescharacteristic
371C2×C4⋊C8C22×C15111yescharacteristic
372C2×C4⋊C8C22×C15111yescharacteristic
373C2×#103C22×C15111yescharacteristic
374C2×#103C22×C15111yescharacteristic
375C2×#103C22×C15111yescharacteristic
376C2×#103C22×C15111yescharacteristic
377C2×C22⋊C8C22×C15111yescharacteristic
378C2×C22⋊C8C22×C15111yescharacteristic
379#391C22×C15111yescharacteristic
380#389—21no—
381#389C22×C15111yescharacteristic
382#388—21no—
383#388—21no—
384#387—21no—
385#380C22×C15111yescharacteristic
386C4×C4⋊C4C22×C15111yescharacteristic
387#340C22×C15111yescharacteristic
388#340C22×C15111yescharacteristic
389#340C22×C15111yescharacteristic
390#340C22×C15111yescharacteristic
391#340C22×C15111yescharacteristic
392#340C22×C15111yescharacteristic
393#340C22×C15111yescharacteristic
394#340C22×C15111yescharacteristic
395#336C22×C15111yescharacteristic
396#336C22×C15111yescharacteristic
397C22×Q8—21no—
398C22×Q8—21no—
399C22×Q8C23×C15111yescharacteristic
400C23×C4—21no—
401C23×C4C23×C15111yescharacteristic
402C22×C8C23×C15111yescharacteristic
403C22×C8C23×C15111yescharacteristic
404C22×C8C23×C15111yescharacteristic
405C22×C8C23×C15111yescharacteristic
406C4⋊Q8—28no—
407C4⋊Q8—22no—
408C4⋊Q8—22no—
409C4⋊Q8—22no—
410C4⋊Q8D4×C15114yes—
411#125—28no—
412#125—22no—
413#125—22no—
414#125—22no—
415#125D4×C15114yes—
416C22⋊Q8—28no—
417C22⋊Q8—28no—
418C22⋊Q8—22no—
419C22⋊Q8Q8×C15114yescomplemented
420C4×Q8—22no—
421C4×Q8—22no—
422#117—22no—
423#117—22no—
424#117—22no—
425#117—22no—
426C2×C4⋊C4—21no—
427C2×C4⋊C4—21no—
428C2×C4⋊C4—21no—
429C2×C4⋊C4—21no—
430C2×C4⋊C4—21no—
431C2×C4⋊C4—21no—
432C2×C4⋊C4—21no—
433C2×C4⋊C4—21no—
434C2×C4⋊C4—22no—
435C2×C4⋊C4—22no—
436C2×C4⋊C4—21no—
437C2×C4⋊C4—21no—
438C2×C4⋊C4D4×C15111yescharacteristic
439C2×C4⋊C4D4×C15111yescharacteristic
440C2×C4⋊C4C23×C15111yescharacteristic
441C2×C4⋊C4C23×C15111yescharacteristic
442C2×C4⋊C4C23×C15111yescharacteristic
443C2×C4⋊C4C23×C15111yescharacteristic
444C2×C4⋊C4C23×C15111yescharacteristic
445C2×C4⋊C4C23×C15111yescharacteristic
446C2×C4⋊C4C23×C15111yescharacteristic
447C2×C22⋊C4—21no—
448C2×C22⋊C4—21no—
449C2×C22⋊C4—21no—
450C2×C22⋊C4D4×C15111yescharacteristic
451C2×C22⋊C4D4×C15111yescharacteristic
452C2×C42—21no—
453C2×C42—21no—
454C2×C42—21no—
455C2×C42C23×C15111yescharacteristic
456C2×C42C23×C15111yescharacteristic
457#107—22no—
458#107—22no—
459#107—22no—
460#106—22no—
461C4⋊C8—22no—
462C4⋊C8—22no—
463#103—22no—
464#103—22no—
465#103—22no—
466#103—22no—
467C22⋊C8—22no—
468C22⋊C8—22no—
469#95—21no—
470#95—21no—
471#95—21no—
472#95—21no—
473#95—21no—
474C24C2×D4×C15111yescharacteristic
475C2×Q8—24no—
476C2×Q8—24no—
477C2×Q8—21no—
478C2×Q8—21no—
479C2×Q8—21no—
480C2×Q8—21no—
481C2×Q8—21no—
482C2×Q8—81no—
483C2×Q8—81no—
484C2×Q8—81no—
485C2×Q8—81no—
486C2×Q8C2×Q8×C15112yes—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—21no—
497C22×C4—24no—
498C22×C4—21no—
499C22×C4—21no—
500C22×C4—81no—
501C22×C4—81no—
502C22×C4C2×D4×C15111yescharacteristic
503C22×C4C2×D4×C15111yescharacteristic
504C22×C4C2×D4×C15111yescharacteristic
505C22×C4C2×D4×C15111yescharacteristic
506C22×C4C2×D4×C15111yescharacteristic
507C22×C4C2×Q8×C15112yes—
508C22×C4#41×C15112yes—
509C22×C4C24×C15111yescharacteristic
510C2×C8—21no—
511C2×C8—21no—
512C2×C8—21no—
513C2×C8—21no—
514C2×C8—21no—
515C2×C8—21no—
516C2×C8—21no—
517C2×C8—21no—
518C2×C8—21no—
519C2×C8—21no—
520C2×C8—21no—
521C2×C8—21no—
522C4⋊C4—24no—
523C4⋊C4—24no—
524C4⋊C4—24no—
525C4⋊C4—24no—
526C4⋊C4—24no—
527C4⋊C4—24no—
528C4⋊C4—24no—
529C4⋊C4—22no—
530C4⋊C4—22no—
531C4⋊C4—24no—
532C4⋊C4—21no—
533C4⋊C4—21no—
534C4⋊C4—21no—
535C4⋊C4—21no—
536C4⋊C4—21no—
537C4⋊C4—21no—
538C4⋊C4—21no—
539C4⋊C4—21no—
540C4⋊C4—21no—
541C4⋊C4—42no—
542C4⋊C4—81no—
543C4⋊C4C2×D4×C15112yes—
544C4⋊C4C2×D4×C15112yes—
545C4⋊C4C2×D4×C15112yes—
546C4⋊C4C2×D4×C15112yes—
547C4⋊C4C2×Q8×C15112yes—
548C22⋊C4—24no—
549C22⋊C4—24no—
550C22⋊C4—22no—
551C22⋊C4—22no—
552C22⋊C4—81no—
553C42—24no—
554C42—21no—
555C42—21no—
556C42—42no—
557C42—81no—
558C42C2×D4×C15112yes—
559C42C2×D4×C15112yes—
560C23—21no—
561C23—21no—
562C23—21no—
563C23—21no—
564C23—21no—
565C23—21no—
566C23C22⋊Q8×C15112yes—
567C23C22×D4×C15111yescharacteristic
568Q8—22no—
569Q8—22no—
570Q8—41no—
571Q8—41no—
572Q8—84no—
573Q8—84no—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—21no—
578C2×C4—21no—
579C2×C4—21no—
580C2×C4—22no—
581C2×C4—22no—
582C2×C4—22no—
583C2×C4—22no—
584C2×C4—21no—
585C2×C4—22no—
586C2×C4—21no—
587C2×C4—22no—
588C2×C4—22no—
589C2×C4—22no—
590C2×C4—22no—
591C2×C4—22no—
592C2×C4—21no—
593C2×C4—21no—
594C2×C4—21no—
595C2×C4—21no—
596C2×C4—41no—
597C2×C4—41no—
598C2×C4—41no—
599C2×C4—41no—
600C2×C4—41no—
601C2×C4—41no—
602C2×C4—41no—
603C2×C4—41no—
604C2×C4—41no—
605C2×C4—41no—
606C2×C4—41no—
607C2×C4—41no—
608C2×C4—41no—
609C2×C4—41no—
610C2×C4—41no—
611C2×C4—41no—
612C2×C4—41no—
613C2×C4—41no—
614C2×C4—84no—
615C2×C4#120×C15112yes—
616C2×C4#120×C15112yes—
617C2×C4C22⋊Q8×C15112yes—
618C2×C4C22×D4×C15111yescharacteristic
619C2×C4C22×D4×C15111yescharacteristic
620C2×C4C22×Q8×C15111yescharacteristic
621C2×C4C2×#41×C15111yescharacteristic
622C2×C42−1+4×C15111yescharacteristic
623C2×C42−1+4×C15111yescharacteristic
624C8—41no—
625C8—41no—
626C8—41no—
627C8—41no—
628C22—22no—
629C22—22no—
630C22—22no—
631C22—41no—
632C22—41no—
633C22—41no—
634C22—41no—
635C22C2×#120×C15111yescharacteristic
636C22C2×C22⋊Q8×C15111yescharacteristic
637C22#536×C15111yescharacteristic
638C22#576×C15111yescharacteristic
639C22#577×C15111yescharacteristic
640C22#578×C15111yescharacteristic
641C22#578×C15111yescharacteristic
642C4—22no—
643C4—22no—
644C4—22no—
645C4—42no—
646C4—41no—
647C4—42no—
648C4—41no—
649C4—42no—
650C4—42no—
651C4—42no—
652C4—42no—
653C4—81no—
654C4—81no—
655C4#548×C15111yescharacteristic
656C4#548×C15111yescharacteristic
657C4D4×Q8×C15111yescharacteristic
658C4D4×Q8×C15111yescharacteristic
659C2—42no—
660C2#2409×C15111yescharacteristic
661C2#3011×C15111yescharacteristic
662C2#3012×C15111yescharacteristic
663C2#3082×C15111yescharacteristic
664C2#3083×C15111yescharacteristic
665C2#3242×C15111yescharacteristic
666C2#3243×C15111yescharacteristic
subgroupG/H
center, socleC23×C151C22×D4
commutator, Frattini, cosocleC22×C4C24×C151
prime radicalC24×C151C2×D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C151 ◁ C2×#117×C151 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#479×C151C2semidirect
3. C2×#477×C151C2semidirect
5. #2059×C151C2semidirect
6. #2057×C151C2semidirect
7. #2026×C151C2semidirect
8. #2024×C151C2semidirect
9. #1989×C151C2semidirect
10. #1988×C151C2semidirect
85. C22⋊Q8×C151Q8semidirect
333. #24311C151direct (N × H)
334. C151#24311direct (N × H)
336. C2×#479C2×C151semidirect
337. C2×#477C2×C151semidirect
339. #2059C2×C151semidirect
340. #2057C2×C151semidirect
341. #2026C2×C151semidirect
342. #2024C2×C151semidirect
343. #1989C2×C151semidirect
344. #1988C2×C151semidirect
419. C22⋊Q8Q8×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#544×C1512
C2×#479×C1512
C2×#477×C1512
#2323×C1512
#2059×C1512
#2057×C1512
#2026×C1512
#2024×C1512
#1989×C1512
#1988×C1512
#1873×C1512
#1872×C1512
#1854×C1512
#1852×C1512
#1798×C1512
#24311151