Finite Group Databasebeta

← C151×#24337 #50329262

Subgroups — C151×#24337 #50329262

Order 38656.

1070 conjugacy classes of subgroups.

The subgroup lattice has 676 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#554×C151C211yesmaximal, characteristic
2C2×#479×C151C211yesmaximal, characteristic, complemented
3C2×C4×SD16×C151C211yesmaximal, characteristic
4#2581×C151C211yesmaximal, characteristic, complemented
5#2059×C151C211yesmaximal, characteristic, complemented
6#2058×C151C211yesmaximal, characteristic, complemented
7#2026×C151C211yesmaximal, characteristic, complemented
8#2024×C151C211yesmaximal, characteristic, complemented
9#1991×C151C211yesmaximal, characteristic, complemented
10#1984×C151C211yesmaximal, characteristic, complemented
11#1877×C151C211yesmaximal, characteristic
12#1877×C151C211yesmaximal, characteristic
13#1864×C151C211yesmaximal, characteristic
14#1862×C151C211yesmaximal, characteristic
15#1804×C151C211yesmaximal, characteristic
16C22×SD16×C151C2211yescharacteristic
17#554×C151—24no—
18#554×C151—24no—
19C2×C4⋊Q8×C151C2211yescharacteristic
20C2×#125×C151C2211yescharacteristic
21C2×#125×C151C2211yescharacteristic
22C2×C22⋊Q8×C151—21no—
23C2×C22⋊Q8×C151—21no—
24C2×C22⋊Q8×C151—21no—
25C2×C4×Q8×C151C2211yescharacteristic
26C2×C4×Q8×C151C2211yescharacteristic
27C2×C4×D4×C151C2211yescharacteristic
28C2×C4×D4×C151C2211yescharacteristic
29C2×C4×D4×C151C2211yescharacteristic
30C22×C4⋊C4×C151—21no—
31#479×C151—24no—
32C4×SD16×C151—24no—
33C2×#107×C151C2211yescharacteristic
34C2×#106×C151C2211yescharacteristic
35C2×#106×C151C2211yescharacteristic
36C2×C4⋊C8×C151C2211yescharacteristic
37C2×#103×C151C2211yescharacteristic
38C2×#103×C151C2211yescharacteristic
39C2×#103×C151C2211yescharacteristic
40C2×#102×C151C2211yescharacteristic
41C2×#102×C151C2211yescharacteristic
42C2×#102×C151C2211yescharacteristic
43C2×C4×C8×C151C2211yescharacteristic
44#400×C151—21no—
45#395×C151—21no—
46#391×C151C2211yescharacteristic
47#391×C151C2211yescharacteristic
48#389×C151C2211yescharacteristic
49#389×C151C2211yescharacteristic
50#387×C151—21no—
51#387×C151—21no—
52#382×C151C2211yescharacteristic
53#340×C151C2211yescharacteristic
54#340×C151C2211yescharacteristic
55#340×C151C2211yescharacteristic
56#340×C151C2211yescharacteristic
57#340×C151C2211yescharacteristic
58#340×C151C2211yescharacteristic
59#336×C151C2211yescharacteristic
60#336×C151C2211yescharacteristic
61#336×C151C2211yescharacteristic
62#336×C151C2211yescharacteristic
63C22×Q8×C151—21no—
64C22×Q8×C151D411yescharacteristic
65C22×Q8×C151C2311yescharacteristic
66C22×D4×C151C2311yescharacteristic
67C23×C4×C151—21no—
68C23×C4×C151—21no—
69C23×C4×C151—21no—
70C2×SD16×C151—22no—
71C2×SD16×C151—22no—
72C2×SD16×C151Q814yescomplemented
73C22×C8×C151C2311yescharacteristic
74C22×C8×C151C2311yescharacteristic
75C22×C8×C151C2311yescharacteristic
76C22×C8×C151C2311yescharacteristic
77C4⋊Q8×C151—22no—
78C4⋊Q8×C151—22no—
79#125×C151—22no—
80#125×C151—22no—
81#125×C151—22no—
82#125×C151D414yes—
83C22⋊Q8×C151—28no—
84C22⋊Q8×C151—28no—
85C22⋊Q8×C151—28no—
86C4×Q8×C151—22no—
87C4×Q8×C151—22no—
88C4×Q8×C151—22no—
89C4×Q8×C151—22no—
90C4×D4×C151—22no—
91C4×D4×C151—22no—
92C4×D4×C151—22no—
93C4×D4×C151—22no—
94C4×D4×C151—22no—
95C4×D4×C151D414yes—
96C2×C4⋊C4×C151—28no—
97C2×C4⋊C4×C151—21no—
98C2×C4⋊C4×C151—21no—
99C2×C4⋊C4×C151—21no—
100C2×C4⋊C4×C151—21no—
101C2×C4⋊C4×C151—21no—
102C2×C4⋊C4×C151—21no—
103C2×C4⋊C4×C151—21no—
104C2×C4⋊C4×C151—21no—
105C2×C4⋊C4×C151D411yescharacteristic
106C2×C4⋊C4×C151D411yescharacteristic
107C2×C4⋊C4×C151D411yescharacteristic
108C2×C4⋊C4×C151C2311yescharacteristic
109C2×C4⋊C4×C151C2311yescharacteristic
110C2×C4⋊C4×C151C2311yescharacteristic
111C2×C4⋊C4×C151C2311yescharacteristic
112C2×C4⋊C4×C151C2311yescharacteristic
113C2×C4⋊C4×C151C2311yescharacteristic
114C2×C22⋊C4×C151—21no—
115C2×C22⋊C4×C151—21no—
116C2×C22⋊C4×C151—21no—
117C2×C42×C151—21no—
118C2×C42×C151C2311yescharacteristic
119C2×C42×C151C2311yescharacteristic
120C2×C42×C151C2311yescharacteristic
121#107×C151—22no—
122#106×C151—22no—
123#106×C151—22no—
124C4⋊C8×C151—22no—
125#103×C151—22no—
126#103×C151—22no—
127#103×C151—22no—
128#102×C151—22no—
129#102×C151—22no—
130#102×C151—22no—
131C4×C8×C151—22no—
132#95×C151—21no—
133#95×C151—21no—
134#95×C151—21no—
135#95×C151—21no—
136#95×C151—21no—
137#95×C151—21no—
138#95×C151—21no—
139#95×C151—21no—
140C24×C151—21no—
141C2×Q8×C151—24no—
142C2×Q8×C151—22no—
143C2×Q8×C151—22no—
144C2×Q8×C151—21no—
145C2×Q8×C151—21no—
146C2×Q8×C151—21no—
147C2×Q8×C151—21no—
148C2×Q8×C151—21no—
149C2×Q8×C151—41no—
150C2×Q8×C151—81no—
151C2×Q8×C151—81no—
152C2×Q8×C151C2×Q812yes—
153C2×D4×C151—21no—
154C2×D4×C151—21no—
155C2×D4×C151—21no—
156C2×D4×C151C2×D412yes—
157C2×D4×C151C2×Q812yes—
158C2×D4×C151#4112yes—
159C22×C4×C151—24no—
160C22×C4×C151—21no—
161C22×C4×C151—21no—
162C22×C4×C151—21no—
163C22×C4×C151—21no—
164C22×C4×C151—24no—
165C22×C4×C151—24no—
166C22×C4×C151—21no—
167C22×C4×C151—21no—
168C22×C4×C151—21no—
169C22×C4×C151—42no—
170C22×C4×C151—42no—
171C22×C4×C151—81no—
172C22×C4×C151—81no—
173C22×C4×C151—81no—
174C22×C4×C151—81no—
175C22×C4×C151C2×D411yescharacteristic
176C22×C4×C151C2×D411yescharacteristic
177C22×C4×C151C2×D411yescharacteristic
178C22×C4×C151C2×D411yescharacteristic
179C22×C4×C151C2×D411yescharacteristic
180C22×C4×C151C2×D411yescharacteristic
181C22×C4×C151C2411yescharacteristic
182SD16×C151—28no—
183C2×C8×C151—21no—
184C2×C8×C151—21no—
185C2×C8×C151—21no—
186C2×C8×C151—21no—
187C2×C8×C151—21no—
188C2×C8×C151—21no—
189C2×C8×C151—21no—
190C2×C8×C151—21no—
191C2×C8×C151—21no—
192C2×C8×C151—21no—
193C2×C8×C151—21no—
194C2×C8×C151C2×Q812yes—
195C4⋊C4×C151—24no—
196C4⋊C4×C151—24no—
197C4⋊C4×C151—24no—
198C4⋊C4×C151—22no—
199C4⋊C4×C151—24no—
200C4⋊C4×C151—24no—
201C4⋊C4×C151—22no—
202C4⋊C4×C151—22no—
203C4⋊C4×C151—21no—
204C4⋊C4×C151—21no—
205C4⋊C4×C151—21no—
206C4⋊C4×C151—21no—
207C4⋊C4×C151—21no—
208C4⋊C4×C151—21no—
209C4⋊C4×C151—21no—
210C4⋊C4×C151—21no—
211C4⋊C4×C151—21no—
212C4⋊C4×C151—42no—
213C4⋊C4×C151—42no—
214C4⋊C4×C151—42no—
215C4⋊C4×C151C2×D412yes—
216C4⋊C4×C151C2×D412yes—
217C4⋊C4×C151C2×D412yes—
218C22⋊C4×C151—24no—
219C22⋊C4×C151—24no—
220C22⋊C4×C151—24no—
221C42×C151—21no—
222C42×C151—21no—
223C42×C151—21no—
224C42×C151—21no—
225C42×C151—42no—
226C42×C151C2×D412yes—
227C42×C151C2×D412yes—
228C23×C151—22no—
229C23×C151—22no—
230C23×C151—22no—
231C23×C151—41no—
232C23×C151—41no—
233C23×C151—41no—
234C23×C151—41no—
235C23×C151C22×D411yescharacteristic
236Q8×C151—22no—
237Q8×C151—22no—
238Q8×C151—44no—
239Q8×C151—41no—
240Q8×C151—41no—
241Q8×C151—84no—
242D4×C151—22no—
243D4×C151—22no—
244D4×C151—22no—
245D4×C151C22⋊Q814yes—
246C2×C4×C151—21no—
247C2×C4×C151—21no—
248C2×C4×C151—21no—
249C2×C4×C151—21no—
250C2×C4×C151—21no—
251C2×C4×C151—21no—
252C2×C4×C151—21no—
253C2×C4×C151—21no—
254C2×C4×C151—22no—
255C2×C4×C151—22no—
256C2×C4×C151—21no—
257C2×C4×C151—22no—
258C2×C4×C151—22no—
259C2×C4×C151—21no—
260C2×C4×C151—21no—
261C2×C4×C151—21no—
262C2×C4×C151—21no—
263C2×C4×C151—21no—
264C2×C4×C151—21no—
265C2×C4×C151—48no—
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—41no—
281C2×C4×C151—41no—
282C2×C4×C151—41no—
283C2×C4×C151—84no—
284C2×C4×C151—84no—
285C2×C4×C151#12012yes—
286C2×C4×C151#12012yes—
287C2×C4×C151#13512yes—
288C2×C4×C151C22×D411yescharacteristic
289C2×C4×C151C22×D411yescharacteristic
290C2×C4×C151C22×Q811yescharacteristic
291C2×C4×C151C2×#4111yescharacteristic
292C2×C4×C1512−1+411yescharacteristic
293C2×C4×C1512−1+411yescharacteristic
294C8×C151—22no—
295C8×C151—41no—
296C8×C151—41no—
297C8×C151—41no—
298C22×C151—24no—
299C22×C151—42no—
300C22×C151—42no—
301C22×C151—42no—
302C22×C151—42no—
303C22×C151—42no—
304C22×C151—42no—
305C22×C151C2×#12011yescharacteristic
306C22×C151#54811yescharacteristic
307C22×C151D4×Q811yescharacteristic
308C22×C151C2×#13511yescharacteristic
309C22×C151#57511yescharacteristic
310C22×C151#57711yescharacteristic
311C22×C151#57711yescharacteristic
312C4×C151—22no—
313C4×C151—22no—
314C4×C151—22no—
315C4×C151—42no—
316C4×C151—41no—
317C4×C151—42no—
318C4×C151—41no—
319C4×C151—41no—
320C4×C151—42no—
321C4×C151—42no—
322C4×C151—81no—
323C4×C151—81no—
324C4×C151—81no—
325C4×C151C2×C22⋊Q811yescharacteristic
326C4×C151#53611yescharacteristic
327C4×C151#54811yescharacteristic
328C4×C151D4×Q811yescharacteristic
329C2×C151—44no—
330C2×C151#240911yescharacteristic
331C2×C151#300211yescharacteristic
332C2×C151#300911yescharacteristic
333C2×C151#336011yescharacteristic
334C2×C151#337611yescharacteristic
335C2×C151#338111yescharacteristic
336C2×C151#338811yescharacteristic
337#24337C15111yesmaximal, characteristic, direct product factor, Sylow
338C151#2433711yescharacteristic, direct product factor, Sylow
339C2×#554C2×C15111yescharacteristic
340C2×#479C2×C15111yescharacteristic, complemented
341C2×C4×SD16C2×C15111yescharacteristic
342#2581C2×C15111yescharacteristic, complemented
343#2059C2×C15111yescharacteristic, complemented
344#2058C2×C15111yescharacteristic, complemented
345#2026C2×C15111yescharacteristic, complemented
346#2024C2×C15111yescharacteristic, complemented
347#1991C2×C15111yescharacteristic, complemented
348#1984C2×C15111yescharacteristic, complemented
349#1877C2×C15111yescharacteristic
350#1877C2×C15111yescharacteristic
351#1864C2×C15111yescharacteristic
352#1862C2×C15111yescharacteristic
353#1804C2×C15111yescharacteristic
354C22×SD16C22×C15111yescharacteristic
355#554—24no—
356#554—24no—
357C2×C4⋊Q8C22×C15111yescharacteristic
358C2×#125C22×C15111yescharacteristic
359C2×#125C22×C15111yescharacteristic
360C2×C22⋊Q8—21no—
361C2×C22⋊Q8—21no—
362C2×C22⋊Q8—21no—
363C2×C4×Q8C22×C15111yescharacteristic
364C2×C4×Q8C22×C15111yescharacteristic
365C2×C4×D4C22×C15111yescharacteristic
366C2×C4×D4C22×C15111yescharacteristic
367C2×C4×D4C22×C15111yescharacteristic
368C22×C4⋊C4—21no—
369#479—24no—
370C4×SD16—24no—
371C2×#107C22×C15111yescharacteristic
372C2×#106C22×C15111yescharacteristic
373C2×#106C22×C15111yescharacteristic
374C2×C4⋊C8C22×C15111yescharacteristic
375C2×#103C22×C15111yescharacteristic
376C2×#103C22×C15111yescharacteristic
377C2×#103C22×C15111yescharacteristic
378C2×#102C22×C15111yescharacteristic
379C2×#102C22×C15111yescharacteristic
380C2×#102C22×C15111yescharacteristic
381C2×C4×C8C22×C15111yescharacteristic
382#400—21no—
383#395—21no—
384#391C22×C15111yescharacteristic
385#391C22×C15111yescharacteristic
386#389C22×C15111yescharacteristic
387#389C22×C15111yescharacteristic
388#387—21no—
389#387—21no—
390#382C22×C15111yescharacteristic
391#340C22×C15111yescharacteristic
392#340C22×C15111yescharacteristic
393#340C22×C15111yescharacteristic
394#340C22×C15111yescharacteristic
395#340C22×C15111yescharacteristic
396#340C22×C15111yescharacteristic
397#336C22×C15111yescharacteristic
398#336C22×C15111yescharacteristic
399#336C22×C15111yescharacteristic
400#336C22×C15111yescharacteristic
401C22×Q8—21no—
402C22×Q8D4×C15111yescharacteristic
403C22×Q8C23×C15111yescharacteristic
404C22×D4C23×C15111yescharacteristic
405C23×C4—21no—
406C23×C4—21no—
407C23×C4—21no—
408C2×SD16—22no—
409C2×SD16—22no—
410C2×SD16Q8×C15114yescomplemented
411C22×C8C23×C15111yescharacteristic
412C22×C8C23×C15111yescharacteristic
413C22×C8C23×C15111yescharacteristic
414C22×C8C23×C15111yescharacteristic
415C4⋊Q8—22no—
416C4⋊Q8—22no—
417#125—22no—
418#125—22no—
419#125—22no—
420#125D4×C15114yes—
421C22⋊Q8—28no—
422C22⋊Q8—28no—
423C22⋊Q8—28no—
424C4×Q8—22no—
425C4×Q8—22no—
426C4×Q8—22no—
427C4×Q8—22no—
428C4×D4—22no—
429C4×D4—22no—
430C4×D4—22no—
431C4×D4—22no—
432C4×D4—22no—
433C4×D4D4×C15114yes—
434C2×C4⋊C4—28no—
435C2×C4⋊C4—21no—
436C2×C4⋊C4—21no—
437C2×C4⋊C4—21no—
438C2×C4⋊C4—21no—
439C2×C4⋊C4—21no—
440C2×C4⋊C4—21no—
441C2×C4⋊C4—21no—
442C2×C4⋊C4—21no—
443C2×C4⋊C4D4×C15111yescharacteristic
444C2×C4⋊C4D4×C15111yescharacteristic
445C2×C4⋊C4D4×C15111yescharacteristic
446C2×C4⋊C4C23×C15111yescharacteristic
447C2×C4⋊C4C23×C15111yescharacteristic
448C2×C4⋊C4C23×C15111yescharacteristic
449C2×C4⋊C4C23×C15111yescharacteristic
450C2×C4⋊C4C23×C15111yescharacteristic
451C2×C4⋊C4C23×C15111yescharacteristic
452C2×C22⋊C4—21no—
453C2×C22⋊C4—21no—
454C2×C22⋊C4—21no—
455C2×C42—21no—
456C2×C42C23×C15111yescharacteristic
457C2×C42C23×C15111yescharacteristic
458C2×C42C23×C15111yescharacteristic
459#107—22no—
460#106—22no—
461#106—22no—
462C4⋊C8—22no—
463#103—22no—
464#103—22no—
465#103—22no—
466#102—22no—
467#102—22no—
468#102—22no—
469C4×C8—22no—
470#95—21no—
471#95—21no—
472#95—21no—
473#95—21no—
474#95—21no—
475#95—21no—
476#95—21no—
477#95—21no—
478C24—21no—
479C2×Q8—24no—
480C2×Q8—22no—
481C2×Q8—22no—
482C2×Q8—21no—
483C2×Q8—21no—
484C2×Q8—21no—
485C2×Q8—21no—
486C2×Q8—21no—
487C2×Q8—41no—
488C2×Q8—81no—
489C2×Q8—81no—
490C2×Q8C2×Q8×C15112yes—
491C2×D4—21no—
492C2×D4—21no—
493C2×D4—21no—
494C2×D4C2×D4×C15112yes—
495C2×D4C2×Q8×C15112yes—
496C2×D4#41×C15112yes—
497C22×C4—24no—
498C22×C4—21no—
499C22×C4—21no—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—24no—
503C22×C4—24no—
504C22×C4—21no—
505C22×C4—21no—
506C22×C4—21no—
507C22×C4—42no—
508C22×C4—42no—
509C22×C4—81no—
510C22×C4—81no—
511C22×C4—81no—
512C22×C4—81no—
513C22×C4C2×D4×C15111yescharacteristic
514C22×C4C2×D4×C15111yescharacteristic
515C22×C4C2×D4×C15111yescharacteristic
516C22×C4C2×D4×C15111yescharacteristic
517C22×C4C2×D4×C15111yescharacteristic
518C22×C4C2×D4×C15111yescharacteristic
519C22×C4C24×C15111yescharacteristic
520SD16—28no—
521C2×C8—21no—
522C2×C8—21no—
523C2×C8—21no—
524C2×C8—21no—
525C2×C8—21no—
526C2×C8—21no—
527C2×C8—21no—
528C2×C8—21no—
529C2×C8—21no—
530C2×C8—21no—
531C2×C8—21no—
532C2×C8C2×Q8×C15112yes—
533C4⋊C4—24no—
534C4⋊C4—24no—
535C4⋊C4—24no—
536C4⋊C4—22no—
537C4⋊C4—24no—
538C4⋊C4—24no—
539C4⋊C4—22no—
540C4⋊C4—22no—
541C4⋊C4—21no—
542C4⋊C4—21no—
543C4⋊C4—21no—
544C4⋊C4—21no—
545C4⋊C4—21no—
546C4⋊C4—21no—
547C4⋊C4—21no—
548C4⋊C4—21no—
549C4⋊C4—21no—
550C4⋊C4—42no—
551C4⋊C4—42no—
552C4⋊C4—42no—
553C4⋊C4C2×D4×C15112yes—
554C4⋊C4C2×D4×C15112yes—
555C4⋊C4C2×D4×C15112yes—
556C22⋊C4—24no—
557C22⋊C4—24no—
558C22⋊C4—24no—
559C42—21no—
560C42—21no—
561C42—21no—
562C42—21no—
563C42—42no—
564C42C2×D4×C15112yes—
565C42C2×D4×C15112yes—
566C23—22no—
567C23—22no—
568C23—22no—
569C23—41no—
570C23—41no—
571C23—41no—
572C23—41no—
573C23C22×D4×C15111yescharacteristic
574Q8—22no—
575Q8—22no—
576Q8—44no—
577Q8—41no—
578Q8—41no—
579Q8—84no—
580D4—22no—
581D4—22no—
582D4—22no—
583D4C22⋊Q8×C15114yes—
584C2×C4—21no—
585C2×C4—21no—
586C2×C4—21no—
587C2×C4—21no—
588C2×C4—21no—
589C2×C4—21no—
590C2×C4—21no—
591C2×C4—21no—
592C2×C4—21no—
593C2×C4—22no—
594C2×C4—22no—
595C2×C4—22no—
596C2×C4—22no—
597C2×C4—21no—
598C2×C4—21no—
599C2×C4—21no—
600C2×C4—21no—
601C2×C4—21no—
602C2×C4—21no—
603C2×C4—48no—
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—41no—
615C2×C4—41no—
616C2×C4—41no—
617C2×C4—41no—
618C2×C4—41no—
619C2×C4—41no—
620C2×C4—41no—
621C2×C4—84no—
622C2×C4—84no—
623C2×C4#120×C15112yes—
624C2×C4#120×C15112yes—
625C2×C4#135×C15112yes—
626C2×C4C22×D4×C15111yescharacteristic
627C2×C4C22×D4×C15111yescharacteristic
628C2×C4C22×Q8×C15111yescharacteristic
629C2×C4C2×#41×C15111yescharacteristic
630C2×C42−1+4×C15111yescharacteristic
631C2×C42−1+4×C15111yescharacteristic
632C8—22no—
633C8—41no—
634C8—41no—
635C8—41no—
636C22—24no—
637C22—42no—
638C22—42no—
639C22—42no—
640C22—42no—
641C22—42no—
642C22—42no—
643C22C2×#120×C15111yescharacteristic
644C22#548×C15111yescharacteristic
645C22D4×Q8×C15111yescharacteristic
646C22C2×#135×C15111yescharacteristic
647C22#575×C15111yescharacteristic
648C22#577×C15111yescharacteristic
649C22#577×C15111yescharacteristic
650C4—22no—
651C4—22no—
652C4—22no—
653C4—42no—
654C4—41no—
655C4—42no—
656C4—41no—
657C4—41no—
658C4—42no—
659C4—42no—
660C4—81no—
661C4—81no—
662C4—81no—
663C4C2×C22⋊Q8×C15111yescharacteristic
664C4#536×C15111yescharacteristic
665C4#548×C15111yescharacteristic
666C4D4×Q8×C15111yescharacteristic
667C2—44no—
668C2#2409×C15111yescharacteristic
669C2#3002×C15111yescharacteristic
670C2#3009×C15111yescharacteristic
671C2#3360×C15111yescharacteristic
672C2#3376×C15111yescharacteristic
673C2#3381×C15111yescharacteristic
674C2#3388×C15111yescharacteristic
subgroupG/H
center, socleC23×C151C22×D4
commutator, Frattini, cosocleC22×C4C24×C151
prime radicalC22×D4×C151C23
LCSG ▷ C22×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×#479×C151C2semidirect
4. #2581×C151C2semidirect
5. #2059×C151C2semidirect
6. #2058×C151C2semidirect
7. #2026×C151C2semidirect
8. #2024×C151C2semidirect
9. #1991×C151C2semidirect
10. #1984×C151C2semidirect
72. C2×SD16×C151Q8semidirect
337. #24337C151direct (N × H)
338. C151#24337direct (N × H)
340. C2×#479C2×C151semidirect
342. #2581C2×C151semidirect
343. #2059C2×C151semidirect
344. #2058C2×C151semidirect
345. #2026C2×C151semidirect
346. #2024C2×C151semidirect
347. #1991C2×C151semidirect
348. #1984C2×C151semidirect
410. C2×SD16Q8×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×#479×C1512
C2×C4×SD16×C1512
#2581×C1512
#2059×C1512
#2058×C1512
#2026×C1512
#2024×C1512
#1991×C1512
#1984×C1512
#1877×C1512
#1864×C1512
#1862×C1512
#1804×C1512
#24337151