Finite Group Databasebeta

← C151×#24346 #50329271

Subgroups — C151×#24346 #50329271

Order 38656.

1064 conjugacy classes of subgroups.

The subgroup lattice has 678 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#557×C151C211yesmaximal, characteristic, complemented
2C2×#478×C151C211yesmaximal, characteristic
3C2×#440×C151C211yesmaximal, characteristic
4#2538×C151C211yesmaximal, characteristic
5#2059×C151C211yesmaximal, characteristic, complemented
6#2057×C151C211yesmaximal, characteristic, complemented
7#2025×C151C211yesmaximal, characteristic
8#2023×C151C211yesmaximal, characteristic
9#1992×C151C211yesmaximal, characteristic, complemented
10#1985×C151C211yesmaximal, characteristic, complemented
11#1880×C151C211yesmaximal, characteristic
12#1880×C151C211yesmaximal, characteristic
13#1865×C151C211yesmaximal, characteristic, complemented
14#1863×C151C211yesmaximal, characteristic, complemented
15#1803×C151C211yesmaximal, characteristic, complemented
16C22×SD16×C151C2211yescharacteristic
17#557×C151—24no—
18#557×C151—24no—
19C2×C4⋊Q8×C151—21no—
20C2×C4⋊Q8×C151C2211yescharacteristic
21C2×#125×C151—21no—
22C2×#125×C151—21no—
23C2×#125×C151C2211yescharacteristic
24C2×#125×C151C2211yescharacteristic
25C2×C22⋊Q8×C151—21no—
26C2×C4×Q8×C151—21no—
27C2×C4×Q8×C151C2211yescharacteristic
28C2×C4×Q8×C151C2211yescharacteristic
29C2×C4×Q8×C151C2211yescharacteristic
30C2×C4×Q8×C151C2211yescharacteristic
31C2×C4×D4×C151C2211yescharacteristic
32#478×C151—24no—
33#440×C151—24no—
34C2×#107×C151C2211yescharacteristic
35C2×#107×C151C2211yescharacteristic
36C2×#106×C151C2211yescharacteristic
37C2×C4⋊C8×C151C2211yescharacteristic
38C2×#103×C151C2211yescharacteristic
39C2×#103×C151C2211yescharacteristic
40C2×#103×C151C2211yescharacteristic
41C2×#102×C151C2211yescharacteristic
42C2×#102×C151C2211yescharacteristic
43C2×#102×C151C2211yescharacteristic
44C2×#97×C151C2211yescharacteristic
45#396×C151—21no—
46#396×C151—21no—
47#390×C151C2211yescharacteristic
48#390×C151C2211yescharacteristic
49#389×C151C2211yescharacteristic
50#389×C151C2211yescharacteristic
51#384×C151C2211yescharacteristic
52#380×C151—21no—
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—
68C2×SD16×C151—22no—
69C2×SD16×C151—22no—
70C2×SD16×C151Q814yescomplemented
71C22×C8×C151C2311yescharacteristic
72C22×C8×C151C2311yescharacteristic
73C22×C8×C151C2311yescharacteristic
74C22×C8×C151C2311yescharacteristic
75C4⋊Q8×C151—28no—
76C4⋊Q8×C151—22no—
77C4⋊Q8×C151—22no—
78#125×C151—28no—
79#125×C151—28no—
80#125×C151—22no—
81#125×C151—22no—
82#125×C151—22no—
83#125×C151D414yes—
84C22⋊Q8×C151—44no—
85C4×Q8×C151—28no—
86C4×Q8×C151—22no—
87C4×Q8×C151—22no—
88C4×Q8×C151—22no—
89C4×Q8×C151—22no—
90C4×Q8×C151—22no—
91C4×Q8×C151—22no—
92C4×Q8×C151—22no—
93C4×Q8×C151D414yes—
94C4×D4×C151—22no—
95C4×D4×C151—22no—
96C2×C4⋊C4×C151—21no—
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×C151—21no—
106C2×C4⋊C4×C151—21no—
107C2×C4⋊C4×C151—21no—
108C2×C4⋊C4×C151D411yescharacteristic
109C2×C4⋊C4×C151D411yescharacteristic
110C2×C4⋊C4×C151D411yescharacteristic
111C2×C4⋊C4×C151C2311yescharacteristic
112C2×C4⋊C4×C151C2311yescharacteristic
113C2×C4⋊C4×C151C2311yescharacteristic
114C2×C4⋊C4×C151C2311yescharacteristic
115C2×C4⋊C4×C151C2311yescharacteristic
116C2×C4⋊C4×C151C2311yescharacteristic
117C2×C22⋊C4×C151—21no—
118C2×C22⋊C4×C151—21no—
119C2×C22⋊C4×C151—21no—
120C2×C22⋊C4×C151—21no—
121C2×C22⋊C4×C151—21no—
122C2×C42×C151—21no—
123C2×C42×C151—21no—
124C2×C42×C151—21no—
125C2×C42×C151C2311yescharacteristic
126C2×C42×C151C2311yescharacteristic
127C2×C42×C151C2311yescharacteristic
128#107×C151—22no—
129#107×C151—22no—
130#106×C151—22no—
131C4⋊C8×C151—22no—
132#103×C151—22no—
133#103×C151—22no—
134#103×C151—22no—
135#102×C151—22no—
136#102×C151—22no—
137#102×C151—22no—
138#97×C151—22no—
139#95×C151—21no—
140#95×C151—21no—
141C24×C151—21no—
142C2×Q8×C151—24no—
143C2×Q8×C151—22no—
144C2×Q8×C151—22no—
145C2×Q8×C151—21no—
146C2×Q8×C151—21no—
147C2×Q8×C151—21no—
148C2×Q8×C151—41no—
149C2×Q8×C151—42no—
150C2×Q8×C151—42no—
151C2×Q8×C151C2×D412yes—
152C2×Q8×C151C2×Q812yes—
153C2×Q8×C151#4112yes—
154C2×D4×C151—21no—
155C2×D4×C151—21no—
156C2×D4×C151—21no—
157C2×D4×C151—21no—
158C2×D4×C151—21no—
159C2×D4×C151C2×Q812yes—
160C22×C4×C151—21no—
161C22×C4×C151—21no—
162C22×C4×C151—21no—
163C22×C4×C151—21no—
164C22×C4×C151—21no—
165C22×C4×C151—21no—
166C22×C4×C151—21no—
167C22×C4×C151—42no—
168C22×C4×C151—42no—
169C22×C4×C151—42no—
170C22×C4×C151C2×D411yescharacteristic
171C22×C4×C151C2×D411yescharacteristic
172C22×C4×C151C2×D411yescharacteristic
173C22×C4×C151C2×D411yescharacteristic
174C22×C4×C151C2×D411yescharacteristic
175C22×C4×C151C2×D411yescharacteristic
176C22×C4×C151C2411yescharacteristic
177SD16×C151—28no—
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—
188C2×C8×C151—21no—
189C2×C8×C151C2×Q812yes—
190C4⋊C4×C151—24no—
191C4⋊C4×C151—24no—
192C4⋊C4×C151—24no—
193C4⋊C4×C151—24no—
194C4⋊C4×C151—24no—
195C4⋊C4×C151—24no—
196C4⋊C4×C151—24no—
197C4⋊C4×C151—24no—
198C4⋊C4×C151—22no—
199C4⋊C4×C151—22no—
200C4⋊C4×C151—22no—
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—21no—
208C4⋊C4×C151—21no—
209C4⋊C4×C151—21no—
210C4⋊C4×C151—42no—
211C4⋊C4×C151—42no—
212C4⋊C4×C151—42no—
213C4⋊C4×C151—81no—
214C4⋊C4×C151C2×D412yes—
215C4⋊C4×C151C2×D412yes—
216C4⋊C4×C151C2×D412yes—
217C22⋊C4×C151—42no—
218C22⋊C4×C151—42no—
219C22⋊C4×C151—42no—
220C22⋊C4×C151—81no—
221C22⋊C4×C151—81no—
222C42×C151—24no—
223C42×C151—24no—
224C42×C151—24no—
225C42×C151—21no—
226C42×C151—21no—
227C42×C151—21no—
228C42×C151—21no—
229C42×C151C2×D412yes—
230C42×C151C2×D412yes—
231C23×C151—22no—
232C23×C151—41no—
233C23×C151—41no—
234C23×C151—41no—
235C23×C151—41no—
236C23×C151—41no—
237C23×C151—41no—
238C23×C151C22×D411yescharacteristic
239Q8×C151—22no—
240Q8×C151—22no—
241Q8×C151—22no—
242Q8×C151—44no—
243Q8×C151—48no—
244Q8×C151C22⋊Q814yescomplemented
245D4×C151—22no—
246D4×C151—22no—
247D4×C151—41no—
248D4×C151—41no—
249C2×C4×C151—21no—
250C2×C4×C151—22no—
251C2×C4×C151—22no—
252C2×C4×C151—22no—
253C2×C4×C151—21no—
254C2×C4×C151—21no—
255C2×C4×C151—21no—
256C2×C4×C151—21no—
257C2×C4×C151—21no—
258C2×C4×C151—21no—
259C2×C4×C151—22no—
260C2×C4×C151—22no—
261C2×C4×C151—21no—
262C2×C4×C151—21no—
263C2×C4×C151—22no—
264C2×C4×C151—21no—
265C2×C4×C151—21no—
266C2×C4×C151—21no—
267C2×C4×C151—21no—
268C2×C4×C151—21no—
269C2×C4×C151—21no—
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—41no—
284C2×C4×C151—41no—
285C2×C4×C151—84no—
286C2×C4×C151#12012yes—
287C2×C4×C151#12012yes—
288C2×C4×C151AGL(1,ℤ/8)12yes—
289C2×C4×C151C22×D411yescharacteristic
290C2×C4×C151C22×D411yescharacteristic
291C2×C4×C151C22×Q811yescharacteristic
292C2×C4×C151C2×#4111yescharacteristic
293C2×C4×C1512−1+411yescharacteristic
294C2×C4×C1512−1+411yescharacteristic
295C8×C151—22no—
296C8×C151—41no—
297C8×C151—41no—
298C8×C151—41no—
299C22×C151—42no—
300C22×C151—42no—
301C22×C151—42no—
302C22×C151—81no—
303C22×C151—81no—
304C22×C151—81no—
305C22×C151—81no—
306C22×C151C2×#12011yescharacteristic
307C22×C151#54811yescharacteristic
308C22×C151D4×Q811yescharacteristic
309C22×C151C2×AGL(1,ℤ/8)11yescharacteristic
310C22×C151#57511yescharacteristic
311C22×C151#57711yescharacteristic
312C22×C151#57811yescharacteristic
313C4×C151—24no—
314C4×C151—22no—
315C4×C151—22no—
316C4×C151—22no—
317C4×C151—41no—
318C4×C151—42no—
319C4×C151—42no—
320C4×C151—41no—
321C4×C151—41no—
322C4×C151—42no—
323C4×C151—81no—
324C4×C151—81no—
325C4×C151—81no—
326C4×C151C2×C22⋊Q811yescharacteristic
327C4×C151#53611yescharacteristic
328C4×C151#54811yescharacteristic
329C4×C151D4×Q811yescharacteristic
330C2×C151—82no—
331C2×C151#240911yescharacteristic
332C2×C151#300611yescharacteristic
333C2×C151#301311yescharacteristic
334C2×C151#336811yescharacteristic
335C2×C151#337711yescharacteristic
336C2×C151#338611yescharacteristic
337C2×C151#338811yescharacteristic
338#24346C15111yesmaximal, characteristic, direct product factor, Sylow
339C151#2434611yescharacteristic, direct product factor, Sylow
340C2×#557C2×C15111yescharacteristic, complemented
341C2×#478C2×C15111yescharacteristic
342C2×#440C2×C15111yescharacteristic
343#2538C2×C15111yescharacteristic
344#2059C2×C15111yescharacteristic, complemented
345#2057C2×C15111yescharacteristic, complemented
346#2025C2×C15111yescharacteristic
347#2023C2×C15111yescharacteristic
348#1992C2×C15111yescharacteristic, complemented
349#1985C2×C15111yescharacteristic, complemented
350#1880C2×C15111yescharacteristic
351#1880C2×C15111yescharacteristic
352#1865C2×C15111yescharacteristic, complemented
353#1863C2×C15111yescharacteristic, complemented
354#1803C2×C15111yescharacteristic, complemented
355C22×SD16C22×C15111yescharacteristic
356#557—24no—
357#557—24no—
358C2×C4⋊Q8—21no—
359C2×C4⋊Q8C22×C15111yescharacteristic
360C2×#125—21no—
361C2×#125—21no—
362C2×#125C22×C15111yescharacteristic
363C2×#125C22×C15111yescharacteristic
364C2×C22⋊Q8—21no—
365C2×C4×Q8—21no—
366C2×C4×Q8C22×C15111yescharacteristic
367C2×C4×Q8C22×C15111yescharacteristic
368C2×C4×Q8C22×C15111yescharacteristic
369C2×C4×Q8C22×C15111yescharacteristic
370C2×C4×D4C22×C15111yescharacteristic
371#478—24no—
372#440—24no—
373C2×#107C22×C15111yescharacteristic
374C2×#107C22×C15111yescharacteristic
375C2×#106C22×C15111yescharacteristic
376C2×C4⋊C8C22×C15111yescharacteristic
377C2×#103C22×C15111yescharacteristic
378C2×#103C22×C15111yescharacteristic
379C2×#103C22×C15111yescharacteristic
380C2×#102C22×C15111yescharacteristic
381C2×#102C22×C15111yescharacteristic
382C2×#102C22×C15111yescharacteristic
383C2×#97C22×C15111yescharacteristic
384#396—21no—
385#396—21no—
386#390C22×C15111yescharacteristic
387#390C22×C15111yescharacteristic
388#389C22×C15111yescharacteristic
389#389C22×C15111yescharacteristic
390#384C22×C15111yescharacteristic
391#380—21no—
392#340C22×C15111yescharacteristic
393#340C22×C15111yescharacteristic
394#340C22×C15111yescharacteristic
395#340C22×C15111yescharacteristic
396#340C22×C15111yescharacteristic
397#340C22×C15111yescharacteristic
398#336C22×C15111yescharacteristic
399#336C22×C15111yescharacteristic
400#336C22×C15111yescharacteristic
401#336C22×C15111yescharacteristic
402C22×Q8—21no—
403C22×Q8D4×C15111yescharacteristic
404C22×Q8C23×C15111yescharacteristic
405C22×D4C23×C15111yescharacteristic
406C23×C4—21no—
407C2×SD16—22no—
408C2×SD16—22no—
409C2×SD16Q8×C15114yescomplemented
410C22×C8C23×C15111yescharacteristic
411C22×C8C23×C15111yescharacteristic
412C22×C8C23×C15111yescharacteristic
413C22×C8C23×C15111yescharacteristic
414C4⋊Q8—28no—
415C4⋊Q8—22no—
416C4⋊Q8—22no—
417#125—28no—
418#125—28no—
419#125—22no—
420#125—22no—
421#125—22no—
422#125D4×C15114yes—
423C22⋊Q8—44no—
424C4×Q8—28no—
425C4×Q8—22no—
426C4×Q8—22no—
427C4×Q8—22no—
428C4×Q8—22no—
429C4×Q8—22no—
430C4×Q8—22no—
431C4×Q8—22no—
432C4×Q8D4×C15114yes—
433C4×D4—22no—
434C4×D4—22no—
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⋊C4—21no—
444C2×C4⋊C4—21no—
445C2×C4⋊C4—21no—
446C2×C4⋊C4—21no—
447C2×C4⋊C4D4×C15111yescharacteristic
448C2×C4⋊C4D4×C15111yescharacteristic
449C2×C4⋊C4D4×C15111yescharacteristic
450C2×C4⋊C4C23×C15111yescharacteristic
451C2×C4⋊C4C23×C15111yescharacteristic
452C2×C4⋊C4C23×C15111yescharacteristic
453C2×C4⋊C4C23×C15111yescharacteristic
454C2×C4⋊C4C23×C15111yescharacteristic
455C2×C4⋊C4C23×C15111yescharacteristic
456C2×C22⋊C4—21no—
457C2×C22⋊C4—21no—
458C2×C22⋊C4—21no—
459C2×C22⋊C4—21no—
460C2×C22⋊C4—21no—
461C2×C42—21no—
462C2×C42—21no—
463C2×C42—21no—
464C2×C42C23×C15111yescharacteristic
465C2×C42C23×C15111yescharacteristic
466C2×C42C23×C15111yescharacteristic
467#107—22no—
468#107—22no—
469#106—22no—
470C4⋊C8—22no—
471#103—22no—
472#103—22no—
473#103—22no—
474#102—22no—
475#102—22no—
476#102—22no—
477#97—22no—
478#95—21no—
479#95—21no—
480C24—21no—
481C2×Q8—24no—
482C2×Q8—22no—
483C2×Q8—22no—
484C2×Q8—21no—
485C2×Q8—21no—
486C2×Q8—21no—
487C2×Q8—41no—
488C2×Q8—42no—
489C2×Q8—42no—
490C2×Q8C2×D4×C15112yes—
491C2×Q8C2×Q8×C15112yes—
492C2×Q8#41×C15112yes—
493C2×D4—21no—
494C2×D4—21no—
495C2×D4—21no—
496C2×D4—21no—
497C2×D4—21no—
498C2×D4C2×Q8×C15112yes—
499C22×C4—21no—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—21no—
506C22×C4—42no—
507C22×C4—42no—
508C22×C4—42no—
509C22×C4C2×D4×C15111yescharacteristic
510C22×C4C2×D4×C15111yescharacteristic
511C22×C4C2×D4×C15111yescharacteristic
512C22×C4C2×D4×C15111yescharacteristic
513C22×C4C2×D4×C15111yescharacteristic
514C22×C4C2×D4×C15111yescharacteristic
515C22×C4C24×C15111yescharacteristic
516SD16—28no—
517C2×C8—21no—
518C2×C8—21no—
519C2×C8—21no—
520C2×C8—21no—
521C2×C8—21no—
522C2×C8—21no—
523C2×C8—21no—
524C2×C8—21no—
525C2×C8—21no—
526C2×C8—21no—
527C2×C8—21no—
528C2×C8C2×Q8×C15112yes—
529C4⋊C4—24no—
530C4⋊C4—24no—
531C4⋊C4—24no—
532C4⋊C4—24no—
533C4⋊C4—24no—
534C4⋊C4—24no—
535C4⋊C4—24no—
536C4⋊C4—24no—
537C4⋊C4—22no—
538C4⋊C4—22no—
539C4⋊C4—22no—
540C4⋊C4—21no—
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—42no—
550C4⋊C4—42no—
551C4⋊C4—42no—
552C4⋊C4—81no—
553C4⋊C4C2×D4×C15112yes—
554C4⋊C4C2×D4×C15112yes—
555C4⋊C4C2×D4×C15112yes—
556C22⋊C4—42no—
557C22⋊C4—42no—
558C22⋊C4—42no—
559C22⋊C4—81no—
560C22⋊C4—81no—
561C42—24no—
562C42—24no—
563C42—24no—
564C42—21no—
565C42—21no—
566C42—21no—
567C42—21no—
568C42C2×D4×C15112yes—
569C42C2×D4×C15112yes—
570C23—22no—
571C23—41no—
572C23—41no—
573C23—41no—
574C23—41no—
575C23—41no—
576C23—41no—
577C23C22×D4×C15111yescharacteristic
578Q8—22no—
579Q8—22no—
580Q8—22no—
581Q8—44no—
582Q8—48no—
583Q8C22⋊Q8×C15114yescomplemented
584D4—22no—
585D4—22no—
586D4—41no—
587D4—41no—
588C2×C4—22no—
589C2×C4—21no—
590C2×C4—22no—
591C2×C4—22no—
592C2×C4—21no—
593C2×C4—21no—
594C2×C4—21no—
595C2×C4—21no—
596C2×C4—21no—
597C2×C4—21no—
598C2×C4—21no—
599C2×C4—22no—
600C2×C4—21no—
601C2×C4—22no—
602C2×C4—22no—
603C2×C4—21no—
604C2×C4—21no—
605C2×C4—21no—
606C2×C4—21no—
607C2×C4—21no—
608C2×C4—21no—
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—41no—
622C2×C4—41no—
623C2×C4—41no—
624C2×C4—84no—
625C2×C4#120×C15112yes—
626C2×C4#120×C15112yes—
627C2×C4AGL(1,ℤ/8)×C15112yes—
628C2×C4C22×D4×C15111yescharacteristic
629C2×C4C22×D4×C15111yescharacteristic
630C2×C4C22×Q8×C15111yescharacteristic
631C2×C4C2×#41×C15111yescharacteristic
632C2×C42−1+4×C15111yescharacteristic
633C2×C42−1+4×C15111yescharacteristic
634C8—22no—
635C8—41no—
636C8—41no—
637C8—41no—
638C22—42no—
639C22—42no—
640C22—42no—
641C22—81no—
642C22—81no—
643C22—81no—
644C22—81no—
645C22C2×#120×C15111yescharacteristic
646C22#548×C15111yescharacteristic
647C22D4×Q8×C15111yescharacteristic
648C22C2×AGL(1,ℤ/8)×C15111yescharacteristic
649C22#575×C15111yescharacteristic
650C22#577×C15111yescharacteristic
651C22#578×C15111yescharacteristic
652C4—24no—
653C4—22no—
654C4—22no—
655C4—22no—
656C4—41no—
657C4—42no—
658C4—42no—
659C4—41no—
660C4—41no—
661C4—42no—
662C4—81no—
663C4—81no—
664C4—81no—
665C4C2×C22⋊Q8×C15111yescharacteristic
666C4#536×C15111yescharacteristic
667C4#548×C15111yescharacteristic
668C4D4×Q8×C15111yescharacteristic
669C2—82no—
670C2#2409×C15111yescharacteristic
671C2#3006×C15111yescharacteristic
672C2#3013×C15111yescharacteristic
673C2#3368×C15111yescharacteristic
674C2#3377×C15111yescharacteristic
675C2#3386×C15111yescharacteristic
676C2#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
1. C2×#557×C151C2semidirect
5. #2059×C151C2semidirect
6. #2057×C151C2semidirect
9. #1992×C151C2semidirect
10. #1985×C151C2semidirect
13. #1865×C151C2semidirect
14. #1863×C151C2semidirect
15. #1803×C151C2semidirect
70. C2×SD16×C151Q8semidirect
244. Q8×C151C22⋊Q8semidirect
338. #24346C151direct (N × H)
339. C151#24346direct (N × H)
340. C2×#557C2×C151semidirect
344. #2059C2×C151semidirect
345. #2057C2×C151semidirect
348. #1992C2×C151semidirect
349. #1985C2×C151semidirect
352. #1865C2×C151semidirect
353. #1863C2×C151semidirect
354. #1803C2×C151semidirect
409. C2×SD16Q8×C151semidirect
583. Q8C22⋊Q8×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#557×C1512
C2×#478×C1512
C2×#440×C1512
#2538×C1512
#2059×C1512
#2057×C1512
#2025×C1512
#2023×C1512
#1992×C1512
#1985×C1512
#1880×C1512
#1865×C1512
#1863×C1512
#1803×C1512
#24346151