Finite Group Databasebeta

← C151×#24207 #50329132

Subgroups — C151×#24207 #50329132

Order 38656.

1076 conjugacy classes of subgroups.

The subgroup lattice has 714 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#556×C151C211yesmaximal, characteristic
2C2×#464×C151C211yesmaximal, characteristic
3C2×#441×C151C211yesmaximal, characteristic, complemented
4#2582×C151C211yesmaximal, characteristic, complemented
5#2043×C151C211yesmaximal, characteristic, complemented
6#2042×C151C211yesmaximal, characteristic
7#2016×C151C211yesmaximal, characteristic, complemented
8#2015×C151C211yesmaximal, characteristic
9#1985×C151C211yesmaximal, characteristic, complemented
10#1959×C151C211yesmaximal, characteristic
11#1878×C151C211yesmaximal, characteristic, complemented
12#1877×C151C211yesmaximal, characteristic
13#1865×C151C211yesmaximal, characteristic, complemented
14#1864×C151C211yesmaximal, characteristic
15#1803×C151C211yesmaximal, characteristic, complemented
16C22×Q16×C151C2211yescharacteristic
17C22×Q16×C151C2211yescharacteristic
18C22×SD16×C151C2211yescharacteristic
19#556×C151—24no—
20#556×C151—24no—
21C2×C4⋊Q8×C151C2211yescharacteristic
22C2×#126×C151—21no—
23C2×#126×C151—21no—
24C2×#124×C151C2211yescharacteristic
25C2×#124×C151C2211yescharacteristic
26C2×C22⋊Q8×C151—21no—
27C2×C4×Q8×C151C2211yescharacteristic
28C2×C4×Q8×C151C2211yescharacteristic
29C2×C4×Q8×C151C2211yescharacteristic
30C2×C4×Q8×C151C2211yescharacteristic
31C2×C4×D4×C151C2211yescharacteristic
32C2×#117×C151—21no—
33#464×C151—24no—
34#441×C151—24no—
35C2×#106×C151C2211yescharacteristic
36C2×C4⋊C8×C151C2211yescharacteristic
37C2×#103×C151C2211yescharacteristic
38C2×#103×C151C2211yescharacteristic
39C2×#103×C151C2211yescharacteristic
40C2×#103×C151C2211yescharacteristic
41C2×#103×C151C2211yescharacteristic
42C2×#103×C151C2211yescharacteristic
43C2×#103×C151C2211yescharacteristic
44C2×#102×C151C2211yescharacteristic
45C2×#102×C151C2211yescharacteristic
46C2×#102×C151C2211yescharacteristic
47C2×#97×C151C2211yescharacteristic
48#398×C151—21no—
49#398×C151—21no—
50#391×C151—21no—
51#391×C151C2211yescharacteristic
52#391×C151C2211yescharacteristic
53#389×C151—21no—
54#389×C151C2211yescharacteristic
55#389×C151C2211yescharacteristic
56#384×C151C2211yescharacteristic
57#340×C151C2211yescharacteristic
58#340×C151C2211yescharacteristic
59#336×C151C2211yescharacteristic
60#336×C151C2211yescharacteristic
61#336×C151C2211yescharacteristic
62#336×C151C2211yescharacteristic
63C22×Q8×C151D411yescharacteristic
64C22×Q8×C151C2311yescharacteristic
65C22×Q8×C151C2311yescharacteristic
66C22×Q8×C151C2311yescharacteristic
67C22×D4×C151C2311yescharacteristic
68C23×C4×C151—21no—
69C2×Q16×C151—22no—
70C2×Q16×C151—22no—
71C2×Q16×C151—22no—
72C2×Q16×C151—22no—
73C2×Q16×C151—22no—
74C2×Q16×C151—41no—
75C2×SD16×C151—22no—
76C2×SD16×C151—22no—
77C2×SD16×C151—41no—
78C22×C8×C151C2311yescharacteristic
79C22×C8×C151C2311yescharacteristic
80C22×C8×C151C2311yescharacteristic
81C22×C8×C151C2311yescharacteristic
82C4⋊Q8×C151—22no—
83C4⋊Q8×C151—22no—
84#126×C151—28no—
85#126×C151—28no—
86#124×C151—22no—
87#124×C151—22no—
88#124×C151—22no—
89#124×C151D414yes—
90C22⋊Q8×C151—28no—
91C4×Q8×C151—22no—
92C4×Q8×C151—22no—
93C4×Q8×C151—22no—
94C4×Q8×C151—22no—
95C4×Q8×C151—22no—
96C4×Q8×C151—22no—
97C4×Q8×C151—22no—
98C4×Q8×C151D414yes—
99C4×D4×C151—22no—
100C4×D4×C151—22no—
101#117×C151—28no—
102C2×C4⋊C4×C151—21no—
103C2×C4⋊C4×C151—21no—
104C2×C4⋊C4×C151—21no—
105C2×C4⋊C4×C151—21no—
106C2×C4⋊C4×C151—21no—
107C2×C4⋊C4×C151—21no—
108C2×C4⋊C4×C151—21no—
109C2×C4⋊C4×C151—21no—
110C2×C4⋊C4×C151—21no—
111C2×C4⋊C4×C151D411yescharacteristic
112C2×C4⋊C4×C151D411yescharacteristic
113C2×C4⋊C4×C151D411yescharacteristic
114C2×C4⋊C4×C151C2311yescharacteristic
115C2×C4⋊C4×C151C2311yescharacteristic
116C2×C4⋊C4×C151C2311yescharacteristic
117C2×C4⋊C4×C151C2311yescharacteristic
118C2×C22⋊C4×C151—21no—
119C2×C22⋊C4×C151—21no—
120C2×C22⋊C4×C151—21no—
121C2×C22⋊C4×C151—21no—
122C2×C22⋊C4×C151—21no—
123C2×C42×C151—21no—
124C2×C42×C151—21no—
125C2×C42×C151—21no—
126C2×C42×C151C2311yescharacteristic
127C2×C42×C151C2311yescharacteristic
128C2×C42×C151C2311yescharacteristic
129#106×C151—22no—
130C4⋊C8×C151—22no—
131#103×C151—22no—
132#103×C151—22no—
133#103×C151—22no—
134#103×C151—22no—
135#103×C151—41no—
136#103×C151—41no—
137#103×C151—41no—
138#102×C151—22no—
139#102×C151—22no—
140#102×C151—41no—
141#97×C151—22no—
142#95×C151—21no—
143#95×C151—21no—
144#95×C151—21no—
145#95×C151—21no—
146#95×C151—21no—
147#95×C151—21no—
148C24×C151—21no—
149C2×Q8×C151—22no—
150C2×Q8×C151—22no—
151C2×Q8×C151—21no—
152C2×Q8×C151—21no—
153C2×Q8×C151—21no—
154C2×Q8×C151—21no—
155C2×Q8×C151—21no—
156C2×Q8×C151—21no—
157C2×Q8×C151—21no—
158C2×Q8×C151—21no—
159C2×Q8×C151—21no—
160C2×Q8×C151—21no—
161C2×Q8×C151—21no—
162C2×Q8×C151—21no—
163C2×Q8×C151—21no—
164C2×Q8×C151—21no—
165C2×Q8×C151—21no—
166C2×Q8×C151—41no—
167C2×Q8×C151C2×D412yes—
168C2×Q8×C151C2×D412yes—
169C2×Q8×C151#4112yes—
170C2×D4×C151—21no—
171C2×D4×C151—21no—
172C2×D4×C151—21no—
173C2×D4×C151—21no—
174C2×D4×C151—21no—
175C2×D4×C151C2×D412yes—
176C22×C4×C151—24no—
177C22×C4×C151—21no—
178C22×C4×C151—21no—
179C22×C4×C151—21no—
180C22×C4×C151—21no—
181C22×C4×C151—21no—
182C22×C4×C151—21no—
183C22×C4×C151—21no—
184C22×C4×C151—42no—
185C22×C4×C151—42no—
186C22×C4×C151C2×D411yescharacteristic
187C22×C4×C151C2×D411yescharacteristic
188C22×C4×C151C2×D411yescharacteristic
189C22×C4×C151C2×D411yescharacteristic
190C22×C4×C151C2×D411yescharacteristic
191C22×C4×C151C2×D411yescharacteristic
192C22×C4×C151C2411yescharacteristic
193Q16×C151—28no—
194Q16×C151—44no—
195SD16×C151—44no—
196C2×C8×C151—21no—
197C2×C8×C151—21no—
198C2×C8×C151—21no—
199C2×C8×C151—21no—
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#4112yes—
208C4⋊C4×C151—24no—
209C4⋊C4×C151—24no—
210C4⋊C4×C151—24no—
211C4⋊C4×C151—24no—
212C4⋊C4×C151—22no—
213C4⋊C4×C151—22no—
214C4⋊C4×C151—22no—
215C4⋊C4×C151—21no—
216C4⋊C4×C151—21no—
217C4⋊C4×C151—21no—
218C4⋊C4×C151—21no—
219C4⋊C4×C151—21no—
220C4⋊C4×C151—21no—
221C4⋊C4×C151—21no—
222C4⋊C4×C151—42no—
223C4⋊C4×C151—42no—
224C4⋊C4×C151—81no—
225C4⋊C4×C151—81no—
226C4⋊C4×C151—81no—
227C4⋊C4×C151C2×D412yes—
228C22⋊C4×C151—24no—
229C22⋊C4×C151—24no—
230C22⋊C4×C151—24no—
231C22⋊C4×C151—24no—
232C22⋊C4×C151—24no—
233C42×C151—24no—
234C42×C151—24no—
235C42×C151—21no—
236C42×C151—21no—
237C42×C151—21no—
238C42×C151—21no—
239C42×C151—42no—
240C42×C151C2×D412yes—
241C42×C151C2×D412yes—
242C23×C151—22no—
243C23×C151—41no—
244C23×C151—41no—
245C23×C151—41no—
246C23×C151—41no—
247C23×C151—41no—
248C23×C151—41no—
249C23×C151C22×D411yescharacteristic
250Q8×C151—22no—
251Q8×C151—22no—
252Q8×C151—22no—
253Q8×C151—22no—
254Q8×C151—22no—
255Q8×C151—22no—
256Q8×C151—44no—
257Q8×C151—41no—
258Q8×C151—41no—
259Q8×C151—41no—
260Q8×C151—41no—
261Q8×C151—41no—
262Q8×C151—41no—
263D4×C151—22no—
264D4×C151—22no—
265D4×C151—41no—
266D4×C151—41no—
267C2×C4×C151—21no—
268C2×C4×C151—21no—
269C2×C4×C151—21no—
270C2×C4×C151—21no—
271C2×C4×C151—21no—
272C2×C4×C151—21no—
273C2×C4×C151—21no—
274C2×C4×C151—22no—
275C2×C4×C151—22no—
276C2×C4×C151—21no—
277C2×C4×C151—22no—
278C2×C4×C151—21no—
279C2×C4×C151—22no—
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—48no—
287C2×C4×C151—41no—
288C2×C4×C151—41no—
289C2×C4×C151—41no—
290C2×C4×C151—41no—
291C2×C4×C151—41no—
292C2×C4×C151—41no—
293C2×C4×C151—41no—
294C2×C4×C151—41no—
295C2×C4×C151—41no—
296C2×C4×C151—41no—
297C2×C4×C151—41no—
298C2×C4×C151—41no—
299C2×C4×C151—41no—
300C2×C4×C151—41no—
301C2×C4×C151—41no—
302C2×C4×C151—41no—
303C2×C4×C151—41no—
304C2×C4×C151#12012yes—
305C2×C4×C151#12012yes—
306C2×C4×C151#13712yes—
307C2×C4×C151C22×D411yescharacteristic
308C2×C4×C151C22×D411yescharacteristic
309C2×C4×C151C2×#4111yescharacteristic
310C2×C4×C151C2×#4111yescharacteristic
311C2×C4×C151H(5,𝔽2)11yescharacteristic
312C2×C4×C1512−1+411yescharacteristic
313C8×C151—22no—
314C8×C151—41no—
315C8×C151—41no—
316C8×C151—41no—
317C22×C151—42no—
318C22×C151—42no—
319C22×C151—42no—
320C22×C151—81no—
321C22×C151—81no—
322C22×C151—81no—
323C22×C151—81no—
324C22×C151C2×#12011yescharacteristic
325C22×C151#54811yescharacteristic
326C22×C151#55011yescharacteristic
327C22×C151C2×#13711yescharacteristic
328C22×C151#57511yescharacteristic
329C22×C151#57711yescharacteristic
330C22×C151#57811yescharacteristic
331C4×C151—22no—
332C4×C151—22no—
333C4×C151—22no—
334C4×C151—42no—
335C4×C151—42no—
336C4×C151—42no—
337C4×C151—41no—
338C4×C151—42no—
339C4×C151—41no—
340C4×C151—41no—
341C4×C151—81no—
342C4×C151—81no—
343C4×C151—81no—
344C4×C151#52511yescharacteristic
345C4×C151#53711yescharacteristic
346C4×C151#54611yescharacteristic
347C4×C151#54711yescharacteristic
348C2×C151—82no—
349C2×C151#240711yescharacteristic
350C2×C151#300711yescharacteristic
351C2×C151#301311yescharacteristic
352C2×C151#336911yescharacteristic
353C2×C151#337711yescharacteristic
354C2×C151#339811yescharacteristic
355C2×C151#340111yescharacteristic
356#24207C15111yesmaximal, characteristic, direct product factor, Sylow
357C151#2420711yescharacteristic, direct product factor, Sylow
358C2×#556C2×C15111yescharacteristic
359C2×#464C2×C15111yescharacteristic
360C2×#441C2×C15111yescharacteristic, complemented
361#2582C2×C15111yescharacteristic, complemented
362#2043C2×C15111yescharacteristic, complemented
363#2042C2×C15111yescharacteristic
364#2016C2×C15111yescharacteristic, complemented
365#2015C2×C15111yescharacteristic
366#1985C2×C15111yescharacteristic, complemented
367#1959C2×C15111yescharacteristic
368#1878C2×C15111yescharacteristic, complemented
369#1877C2×C15111yescharacteristic
370#1865C2×C15111yescharacteristic, complemented
371#1864C2×C15111yescharacteristic
372#1803C2×C15111yescharacteristic, complemented
373C22×Q16C22×C15111yescharacteristic
374C22×Q16C22×C15111yescharacteristic
375C22×SD16C22×C15111yescharacteristic
376#556—24no—
377#556—24no—
378C2×C4⋊Q8C22×C15111yescharacteristic
379C2×#126—21no—
380C2×#126—21no—
381C2×#124C22×C15111yescharacteristic
382C2×#124C22×C15111yescharacteristic
383C2×C22⋊Q8—21no—
384C2×C4×Q8C22×C15111yescharacteristic
385C2×C4×Q8C22×C15111yescharacteristic
386C2×C4×Q8C22×C15111yescharacteristic
387C2×C4×Q8C22×C15111yescharacteristic
388C2×C4×D4C22×C15111yescharacteristic
389C2×#117—21no—
390#464—24no—
391#441—24no—
392C2×#106C22×C15111yescharacteristic
393C2×C4⋊C8C22×C15111yescharacteristic
394C2×#103C22×C15111yescharacteristic
395C2×#103C22×C15111yescharacteristic
396C2×#103C22×C15111yescharacteristic
397C2×#103C22×C15111yescharacteristic
398C2×#103C22×C15111yescharacteristic
399C2×#103C22×C15111yescharacteristic
400C2×#103C22×C15111yescharacteristic
401C2×#102C22×C15111yescharacteristic
402C2×#102C22×C15111yescharacteristic
403C2×#102C22×C15111yescharacteristic
404C2×#97C22×C15111yescharacteristic
405#398—21no—
406#398—21no—
407#391—21no—
408#391C22×C15111yescharacteristic
409#391C22×C15111yescharacteristic
410#389—21no—
411#389C22×C15111yescharacteristic
412#389C22×C15111yescharacteristic
413#384C22×C15111yescharacteristic
414#340C22×C15111yescharacteristic
415#340C22×C15111yescharacteristic
416#336C22×C15111yescharacteristic
417#336C22×C15111yescharacteristic
418#336C22×C15111yescharacteristic
419#336C22×C15111yescharacteristic
420C22×Q8D4×C15111yescharacteristic
421C22×Q8C23×C15111yescharacteristic
422C22×Q8C23×C15111yescharacteristic
423C22×Q8C23×C15111yescharacteristic
424C22×D4C23×C15111yescharacteristic
425C23×C4—21no—
426C2×Q16—22no—
427C2×Q16—22no—
428C2×Q16—22no—
429C2×Q16—22no—
430C2×Q16—22no—
431C2×Q16—41no—
432C2×SD16—22no—
433C2×SD16—22no—
434C2×SD16—41no—
435C22×C8C23×C15111yescharacteristic
436C22×C8C23×C15111yescharacteristic
437C22×C8C23×C15111yescharacteristic
438C22×C8C23×C15111yescharacteristic
439C4⋊Q8—22no—
440C4⋊Q8—22no—
441#126—28no—
442#126—28no—
443#124—22no—
444#124—22no—
445#124—22no—
446#124D4×C15114yes—
447C22⋊Q8—28no—
448C4×Q8—22no—
449C4×Q8—22no—
450C4×Q8—22no—
451C4×Q8—22no—
452C4×Q8—22no—
453C4×Q8—22no—
454C4×Q8—22no—
455C4×Q8D4×C15114yes—
456C4×D4—22no—
457C4×D4—22no—
458#117—28no—
459C2×C4⋊C4—21no—
460C2×C4⋊C4—21no—
461C2×C4⋊C4—21no—
462C2×C4⋊C4—21no—
463C2×C4⋊C4—21no—
464C2×C4⋊C4—21no—
465C2×C4⋊C4—21no—
466C2×C4⋊C4—21no—
467C2×C4⋊C4—21no—
468C2×C4⋊C4D4×C15111yescharacteristic
469C2×C4⋊C4D4×C15111yescharacteristic
470C2×C4⋊C4D4×C15111yescharacteristic
471C2×C4⋊C4C23×C15111yescharacteristic
472C2×C4⋊C4C23×C15111yescharacteristic
473C2×C4⋊C4C23×C15111yescharacteristic
474C2×C4⋊C4C23×C15111yescharacteristic
475C2×C22⋊C4—21no—
476C2×C22⋊C4—21no—
477C2×C22⋊C4—21no—
478C2×C22⋊C4—21no—
479C2×C22⋊C4—21no—
480C2×C42—21no—
481C2×C42—21no—
482C2×C42—21no—
483C2×C42C23×C15111yescharacteristic
484C2×C42C23×C15111yescharacteristic
485C2×C42C23×C15111yescharacteristic
486#106—22no—
487C4⋊C8—22no—
488#103—22no—
489#103—22no—
490#103—22no—
491#103—22no—
492#103—41no—
493#103—41no—
494#103—41no—
495#102—22no—
496#102—22no—
497#102—41no—
498#97—22no—
499#95—21no—
500#95—21no—
501#95—21no—
502#95—21no—
503#95—21no—
504#95—21no—
505C24—21no—
506C2×Q8—22no—
507C2×Q8—22no—
508C2×Q8—21no—
509C2×Q8—21no—
510C2×Q8—21no—
511C2×Q8—21no—
512C2×Q8—21no—
513C2×Q8—21no—
514C2×Q8—21no—
515C2×Q8—21no—
516C2×Q8—21no—
517C2×Q8—21no—
518C2×Q8—21no—
519C2×Q8—21no—
520C2×Q8—21no—
521C2×Q8—21no—
522C2×Q8—21no—
523C2×Q8—41no—
524C2×Q8C2×D4×C15112yes—
525C2×Q8C2×D4×C15112yes—
526C2×Q8#41×C15112yes—
527C2×D4—21no—
528C2×D4—21no—
529C2×D4—21no—
530C2×D4—21no—
531C2×D4—21no—
532C2×D4C2×D4×C15112yes—
533C22×C4—24no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—42no—
542C22×C4—42no—
543C22×C4C2×D4×C15111yescharacteristic
544C22×C4C2×D4×C15111yescharacteristic
545C22×C4C2×D4×C15111yescharacteristic
546C22×C4C2×D4×C15111yescharacteristic
547C22×C4C2×D4×C15111yescharacteristic
548C22×C4C2×D4×C15111yescharacteristic
549C22×C4C24×C15111yescharacteristic
550Q16—28no—
551Q16—44no—
552SD16—44no—
553C2×C8—21no—
554C2×C8—21no—
555C2×C8—21no—
556C2×C8—21no—
557C2×C8—21no—
558C2×C8—21no—
559C2×C8—21no—
560C2×C8—21no—
561C2×C8—21no—
562C2×C8—21no—
563C2×C8—21no—
564C2×C8#41×C15112yes—
565C4⋊C4—24no—
566C4⋊C4—24no—
567C4⋊C4—24no—
568C4⋊C4—24no—
569C4⋊C4—22no—
570C4⋊C4—22no—
571C4⋊C4—22no—
572C4⋊C4—21no—
573C4⋊C4—21no—
574C4⋊C4—21no—
575C4⋊C4—21no—
576C4⋊C4—21no—
577C4⋊C4—21no—
578C4⋊C4—21no—
579C4⋊C4—42no—
580C4⋊C4—42no—
581C4⋊C4—81no—
582C4⋊C4—81no—
583C4⋊C4—81no—
584C4⋊C4C2×D4×C15112yes—
585C22⋊C4—24no—
586C22⋊C4—24no—
587C22⋊C4—24no—
588C22⋊C4—24no—
589C22⋊C4—24no—
590C42—24no—
591C42—24no—
592C42—21no—
593C42—21no—
594C42—21no—
595C42—21no—
596C42—42no—
597C42C2×D4×C15112yes—
598C42C2×D4×C15112yes—
599C23—22no—
600C23—41no—
601C23—41no—
602C23—41no—
603C23—41no—
604C23—41no—
605C23—41no—
606C23C22×D4×C15111yescharacteristic
607Q8—22no—
608Q8—22no—
609Q8—22no—
610Q8—22no—
611Q8—22no—
612Q8—22no—
613Q8—44no—
614Q8—41no—
615Q8—41no—
616Q8—41no—
617Q8—41no—
618Q8—41no—
619Q8—41no—
620D4—22no—
621D4—22no—
622D4—41no—
623D4—41no—
624C2×C4—21no—
625C2×C4—21no—
626C2×C4—21no—
627C2×C4—21no—
628C2×C4—21no—
629C2×C4—21no—
630C2×C4—21no—
631C2×C4—22no—
632C2×C4—21no—
633C2×C4—22no—
634C2×C4—22no—
635C2×C4—21no—
636C2×C4—22no—
637C2×C4—21no—
638C2×C4—21no—
639C2×C4—21no—
640C2×C4—21no—
641C2×C4—21no—
642C2×C4—21no—
643C2×C4—48no—
644C2×C4—41no—
645C2×C4—41no—
646C2×C4—41no—
647C2×C4—41no—
648C2×C4—41no—
649C2×C4—41no—
650C2×C4—41no—
651C2×C4—41no—
652C2×C4—41no—
653C2×C4—41no—
654C2×C4—41no—
655C2×C4—41no—
656C2×C4—41no—
657C2×C4—41no—
658C2×C4—41no—
659C2×C4—41no—
660C2×C4—41no—
661C2×C4#120×C15112yes—
662C2×C4#120×C15112yes—
663C2×C4#137×C15112yes—
664C2×C4C22×D4×C15111yescharacteristic
665C2×C4C22×D4×C15111yescharacteristic
666C2×C4C2×#41×C15111yescharacteristic
667C2×C4C2×#41×C15111yescharacteristic
668C2×C4H(5,𝔽2)×C15111yescharacteristic
669C2×C42−1+4×C15111yescharacteristic
670C8—22no—
671C8—41no—
672C8—41no—
673C8—41no—
674C22—42no—
675C22—42no—
676C22—42no—
677C22—81no—
678C22—81no—
679C22—81no—
680C22—81no—
681C22C2×#120×C15111yescharacteristic
682C22#548×C15111yescharacteristic
683C22#550×C15111yescharacteristic
684C22C2×#137×C15111yescharacteristic
685C22#575×C15111yescharacteristic
686C22#577×C15111yescharacteristic
687C22#578×C15111yescharacteristic
688C4—22no—
689C4—22no—
690C4—22no—
691C4—42no—
692C4—42no—
693C4—42no—
694C4—41no—
695C4—42no—
696C4—41no—
697C4—41no—
698C4—81no—
699C4—81no—
700C4—81no—
701C4#525×C15111yescharacteristic
702C4#537×C15111yescharacteristic
703C4#546×C15111yescharacteristic
704C4#547×C15111yescharacteristic
705C2—82no—
706C2#2407×C15111yescharacteristic
707C2#3007×C15111yescharacteristic
708C2#3013×C15111yescharacteristic
709C2#3369×C15111yescharacteristic
710C2#3377×C15111yescharacteristic
711C2#3398×C15111yescharacteristic
712C2#3401×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
3. C2×#441×C151C2semidirect
4. #2582×C151C2semidirect
5. #2043×C151C2semidirect
7. #2016×C151C2semidirect
9. #1985×C151C2semidirect
11. #1878×C151C2semidirect
13. #1865×C151C2semidirect
15. #1803×C151C2semidirect
356. #24207C151direct (N × H)
357. C151#24207direct (N × H)
360. C2×#441C2×C151semidirect
361. #2582C2×C151semidirect
362. #2043C2×C151semidirect
364. #2016C2×C151semidirect
366. #1985C2×C151semidirect
368. #1878C2×C151semidirect
370. #1865C2×C151semidirect
372. #1803C2×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#556×C1512
C2×#464×C1512
C2×#441×C1512
#2582×C1512
#2043×C1512
#2042×C1512
#2016×C1512
#2015×C1512
#1985×C1512
#1959×C1512
#1878×C1512
#1877×C1512
#1865×C1512
#1864×C1512
#1803×C1512
#24207151