Finite Group Databasebeta

← C151×#24309 #50329234

Subgroups — C151×#24309 #50329234

Order 38656.

1068 conjugacy classes of subgroups.

The subgroup lattice has 706 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#544×C151C211yesmaximal, characteristic, complemented
2C2×#478×C151C211yesmaximal, characteristic, complemented
3C2×#476×C151C211yesmaximal, characteristic, complemented
4#2324×C151C211yesmaximal, characteristic
5#2059×C151C211yesmaximal, characteristic, complemented
6#2058×C151C211yesmaximal, characteristic, complemented
7#2025×C151C211yesmaximal, characteristic, complemented
8#2023×C151C211yesmaximal, characteristic, complemented
9#1989×C151C211yesmaximal, characteristic, complemented
10#1988×C151C211yesmaximal, characteristic, complemented
11#1875×C151C211yesmaximal, characteristic
12#1874×C151C211yesmaximal, characteristic
13#1854×C151C211yesmaximal, characteristic, complemented
14#1853×C151C211yesmaximal, characteristic, complemented
15#1798×C151C211yesmaximal, characteristic, complemented
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×#121×C151C2211yescharacteristic
27C2×C4×D4×C151C2211yescharacteristic
28C2×#117×C151C2211yescharacteristic
29C2×#117×C151C2211yescharacteristic
30C22×C4⋊C4×C151C2211yescharacteristic
31#478×C151—24no—
32#476×C151—24no—
33C2×#107×C151C2211yescharacteristic
34C2×#106×C151C2211yescharacteristic
35C2×#106×C151C2211yescharacteristic
36C2×#106×C151C2211yescharacteristic
37C2×C4⋊C8×C151C2211yescharacteristic
38C2×C4⋊C8×C151C2211yescharacteristic
39C2×#102×C151C2211yescharacteristic
40C2×#102×C151C2211yescharacteristic
41C2×#102×C151C2211yescharacteristic
42C2×#102×C151C2211yescharacteristic
43C2×C22⋊C8×C151C2211yescharacteristic
44C2×C22⋊C8×C151C2211yescharacteristic
45#390×C151—21no—
46#390×C151C2211yescharacteristic
47#389×C151C2211yescharacteristic
48#388×C151—21no—
49#386×C151—21no—
50#385×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×D4×C151—21no—
66C22×D4×C151C2311yescharacteristic
67C23×C4×C151—21no—
68C23×C4×C151—21no—
69C23×C4×C151C2311yescharacteristic
70C22×C8×C151C2311yescharacteristic
71C22×C8×C151C2311yescharacteristic
72C22×C8×C151C2311yescharacteristic
73C22×C8×C151C2311yescharacteristic
74C4⋊Q8×C151—28no—
75C4⋊Q8×C151—22no—
76C4⋊Q8×C151—22no—
77C4⋊Q8×C151—22no—
78C4⋊Q8×C151D414yescomplemented
79#125×C151—28no—
80#125×C151—22no—
81#125×C151—22no—
82#125×C151—22no—
83#125×C151D414yescomplemented
84C22⋊Q8×C151—28no—
85C22⋊Q8×C151—28no—
86#121×C151—22no—
87#121×C151Q814yescomplemented
88C4×D4×C151—22no—
89C4×D4×C151—22no—
90#117×C151—22no—
91#117×C151—22no—
92#117×C151—22no—
93#117×C151—22no—
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—21no—
101C2×C4⋊C4×C151—22no—
102C2×C4⋊C4×C151—22no—
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×C151—21no—
117C2×C22⋊C4×C151—21no—
118C2×C22⋊C4×C151—21no—
119C2×C22⋊C4×C151D411yescharacteristic
120C2×C22⋊C4×C151D411yescharacteristic
121C2×C42×C151—21no—
122C2×C42×C151—21no—
123C2×C42×C151C2311yescharacteristic
124C2×C42×C151C2311yescharacteristic
125#107×C151—22no—
126#106×C151—22no—
127#106×C151—22no—
128#106×C151—22no—
129C4⋊C8×C151—22no—
130C4⋊C8×C151—22no—
131#102×C151—22no—
132#102×C151—22no—
133#102×C151—22no—
134#102×C151—22no—
135C22⋊C8×C151—22no—
136C22⋊C8×C151—22no—
137#95×C151—21no—
138#95×C151—21no—
139#95×C151—21no—
140C24×C151—21no—
141C24×C151C2×D411yescharacteristic
142C2×Q8×C151—24no—
143C2×Q8×C151—24no—
144C2×Q8×C151—81no—
145C2×Q8×C151—81no—
146C2×Q8×C151—81no—
147C2×Q8×C151—81no—
148C2×D4×C151—24no—
149C2×D4×C151—21no—
150C2×D4×C151—21no—
151C2×D4×C151—21no—
152C2×D4×C151—21no—
153C2×D4×C151—21no—
154C2×D4×C151—81no—
155C2×D4×C151—81no—
156C2×D4×C151C2×Q812yes—
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—21no—
164C22×C4×C151—21no—
165C22×C4×C151—21no—
166C22×C4×C151—24no—
167C22×C4×C151—21no—
168C22×C4×C151—21no—
169C22×C4×C151—42no—
170C22×C4×C151—81no—
171C22×C4×C151—81no—
172C22×C4×C151—81no—
173C22×C4×C151—81no—
174C22×C4×C151C2×D411yescharacteristic
175C22×C4×C151C2×D411yescharacteristic
176C22×C4×C151C2×D411yescharacteristic
177C22×C4×C151C2×D411yescharacteristic
178C22×C4×C151C2×D411yescharacteristic
179C22×C4×C151C2×Q812yes—
180C22×C4×C151#4112yes—
181C22×C4×C151C2411yescharacteristic
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×C151—21no—
190C2×C8×C151—21no—
191C2×C8×C151—21no—
192C2×C8×C151—21no—
193C2×C8×C151—21no—
194C4⋊C4×C151—24no—
195C4⋊C4×C151—24no—
196C4⋊C4×C151—24no—
197C4⋊C4×C151—24no—
198C4⋊C4×C151—24no—
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—81no—
213C4⋊C4×C151C2×D412yes—
214C4⋊C4×C151C2×D412yes—
215C4⋊C4×C151C2×D412yes—
216C4⋊C4×C151C2×D412yes—
217C4⋊C4×C151C2×Q812yes—
218C22⋊C4×C151—24no—
219C22⋊C4×C151—22no—
220C22⋊C4×C151—22no—
221C22⋊C4×C151—24no—
222C22⋊C4×C151—42no—
223C22⋊C4×C151—81no—
224C22⋊C4×C151—81no—
225C22⋊C4×C151—81no—
226C42×C151—24no—
227C42×C151—21no—
228C42×C151—21no—
229C42×C151—81no—
230C42×C151C2×D412yes—
231C42×C151C2×D412yes—
232C23×C151—21no—
233C23×C151—21no—
234C23×C151—21no—
235C23×C151—21no—
236C23×C151—21no—
237C23×C151—21no—
238C23×C151—22no—
239C23×C151—41no—
240C23×C151—41no—
241C23×C151—41no—
242C23×C151—41no—
243C23×C151—41no—
244C23×C151—41no—
245C23×C151C22⋊Q812yes—
246C23×C151C22×D411yescharacteristic
247Q8×C151—84no—
248Q8×C151—84no—
249D4×C151—22no—
250D4×C151—22no—
251D4×C151—41no—
252D4×C151—41no—
253D4×C151—84no—
254C2×C4×C151—21no—
255C2×C4×C151—21no—
256C2×C4×C151—21no—
257C2×C4×C151—21no—
258C2×C4×C151—21no—
259C2×C4×C151—21no—
260C2×C4×C151—22no—
261C2×C4×C151—22no—
262C2×C4×C151—22no—
263C2×C4×C151—22no—
264C2×C4×C151—21no—
265C2×C4×C151—22no—
266C2×C4×C151—22no—
267C2×C4×C151—22no—
268C2×C4×C151—21no—
269C2×C4×C151—22no—
270C2×C4×C151—22no—
271C2×C4×C151—21no—
272C2×C4×C151—21no—
273C2×C4×C151—21no—
274C2×C4×C151—21no—
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—41no—
286C2×C4×C151—41no—
287C2×C4×C151—41no—
288C2×C4×C151—41no—
289C2×C4×C151—41no—
290C2×C4×C151—41no—
291C2×C4×C151—84no—
292C2×C4×C151—84no—
293C2×C4×C151#12012yes—
294C2×C4×C151#12012yes—
295C2×C4×C151C22⋊Q812yes—
296C2×C4×C151C22×D411yescharacteristic
297C2×C4×C151C22×D411yescharacteristic
298C2×C4×C151C22×Q811yescharacteristic
299C2×C4×C151C2×#4111yescharacteristic
300C2×C4×C1512−1+411yescharacteristic
301C2×C4×C1512−1+411yescharacteristic
302C8×C151—41no—
303C8×C151—41no—
304C8×C151—41no—
305C8×C151—41no—
306C22×C151—22no—
307C22×C151—22no—
308C22×C151—22no—
309C22×C151—41no—
310C22×C151—41no—
311C22×C151—41no—
312C22×C151—41no—
313C22×C151—42no—
314C22×C151—42no—
315C22×C151—42no—
316C22×C151—81no—
317C22×C151—81no—
318C22×C151—81no—
319C22×C151—81no—
320C22×C151C2×#12011yescharacteristic
321C22×C151C2×C22⋊Q811yescharacteristic
322C22×C151#53611yescharacteristic
323C22×C151#57611yescharacteristic
324C22×C151#57711yescharacteristic
325C22×C151#57711yescharacteristic
326C22×C151#57711yescharacteristic
327C4×C151—22no—
328C4×C151—22no—
329C4×C151—22no—
330C4×C151—42no—
331C4×C151—41no—
332C4×C151—42no—
333C4×C151—41no—
334C4×C151—42no—
335C4×C151—42no—
336C4×C151—42no—
337C4×C151—81no—
338C4×C151—81no—
339C4×C151#54811yescharacteristic
340C4×C151#54811yescharacteristic
341C4×C151D4×Q811yescharacteristic
342C4×C151D4×Q811yescharacteristic
343C2×C151—42no—
344C2×C151—82no—
345C2×C151#240911yescharacteristic
346C2×C151#301011yescharacteristic
347C2×C151#301211yescharacteristic
348C2×C151#308111yescharacteristic
349C2×C151#308411yescharacteristic
350C2×C151#324111yescharacteristic
351C2×C151#324411yescharacteristic
352#24309C15111yesmaximal, characteristic, direct product factor, Sylow
353C151#2430911yescharacteristic, direct product factor, Sylow
354C2×#544C2×C15111yescharacteristic, complemented
355C2×#478C2×C15111yescharacteristic, complemented
356C2×#476C2×C15111yescharacteristic, complemented
357#2324C2×C15111yescharacteristic
358#2059C2×C15111yescharacteristic, complemented
359#2058C2×C15111yescharacteristic, complemented
360#2025C2×C15111yescharacteristic, complemented
361#2023C2×C15111yescharacteristic, complemented
362#1989C2×C15111yescharacteristic, complemented
363#1988C2×C15111yescharacteristic, complemented
364#1875C2×C15111yescharacteristic
365#1874C2×C15111yescharacteristic
366#1854C2×C15111yescharacteristic, complemented
367#1853C2×C15111yescharacteristic, complemented
368#1798C2×C15111yescharacteristic, complemented
369#544—24no—
370#544—24no—
371C2×C4⋊Q8—21no—
372C2×C4⋊Q8C22×C15111yescharacteristic
373C2×C4⋊Q8C22×C15111yescharacteristic
374C2×#125—21no—
375C2×#125C22×C15111yescharacteristic
376C2×#125C22×C15111yescharacteristic
377C2×C22⋊Q8—21no—
378C2×C22⋊Q8—21no—
379C2×#121C22×C15111yescharacteristic
380C2×C4×D4C22×C15111yescharacteristic
381C2×#117C22×C15111yescharacteristic
382C2×#117C22×C15111yescharacteristic
383C22×C4⋊C4C22×C15111yescharacteristic
384#478—24no—
385#476—24no—
386C2×#107C22×C15111yescharacteristic
387C2×#106C22×C15111yescharacteristic
388C2×#106C22×C15111yescharacteristic
389C2×#106C22×C15111yescharacteristic
390C2×C4⋊C8C22×C15111yescharacteristic
391C2×C4⋊C8C22×C15111yescharacteristic
392C2×#102C22×C15111yescharacteristic
393C2×#102C22×C15111yescharacteristic
394C2×#102C22×C15111yescharacteristic
395C2×#102C22×C15111yescharacteristic
396C2×C22⋊C8C22×C15111yescharacteristic
397C2×C22⋊C8C22×C15111yescharacteristic
398#390—21no—
399#390C22×C15111yescharacteristic
400#389C22×C15111yescharacteristic
401#388—21no—
402#386—21no—
403#385—21no—
404#380C22×C15111yescharacteristic
405C4×C4⋊C4C22×C15111yescharacteristic
406#340C22×C15111yescharacteristic
407#340C22×C15111yescharacteristic
408#340C22×C15111yescharacteristic
409#340C22×C15111yescharacteristic
410#340C22×C15111yescharacteristic
411#340C22×C15111yescharacteristic
412#340C22×C15111yescharacteristic
413#340C22×C15111yescharacteristic
414#336C22×C15111yescharacteristic
415#336C22×C15111yescharacteristic
416C22×Q8—21no—
417C22×Q8—21no—
418C22×D4—21no—
419C22×D4C23×C15111yescharacteristic
420C23×C4—21no—
421C23×C4—21no—
422C23×C4C23×C15111yescharacteristic
423C22×C8C23×C15111yescharacteristic
424C22×C8C23×C15111yescharacteristic
425C22×C8C23×C15111yescharacteristic
426C22×C8C23×C15111yescharacteristic
427C4⋊Q8—28no—
428C4⋊Q8—22no—
429C4⋊Q8—22no—
430C4⋊Q8—22no—
431C4⋊Q8D4×C15114yescomplemented
432#125—28no—
433#125—22no—
434#125—22no—
435#125—22no—
436#125D4×C15114yescomplemented
437C22⋊Q8—28no—
438C22⋊Q8—28no—
439#121—22no—
440#121Q8×C15114yescomplemented
441C4×D4—22no—
442C4×D4—22no—
443#117—22no—
444#117—22no—
445#117—22no—
446#117—22no—
447C2×C4⋊C4—21no—
448C2×C4⋊C4—21no—
449C2×C4⋊C4—21no—
450C2×C4⋊C4—21no—
451C2×C4⋊C4—21no—
452C2×C4⋊C4—21no—
453C2×C4⋊C4—21no—
454C2×C4⋊C4—22no—
455C2×C4⋊C4—22no—
456C2×C4⋊C4—21no—
457C2×C4⋊C4D4×C15111yescharacteristic
458C2×C4⋊C4D4×C15111yescharacteristic
459C2×C4⋊C4C23×C15111yescharacteristic
460C2×C4⋊C4C23×C15111yescharacteristic
461C2×C4⋊C4C23×C15111yescharacteristic
462C2×C4⋊C4C23×C15111yescharacteristic
463C2×C4⋊C4C23×C15111yescharacteristic
464C2×C4⋊C4C23×C15111yescharacteristic
465C2×C4⋊C4C23×C15111yescharacteristic
466C2×C22⋊C4—21no—
467C2×C22⋊C4—21no—
468C2×C22⋊C4—21no—
469C2×C22⋊C4—21no—
470C2×C22⋊C4—21no—
471C2×C22⋊C4—21no—
472C2×C22⋊C4D4×C15111yescharacteristic
473C2×C22⋊C4D4×C15111yescharacteristic
474C2×C42—21no—
475C2×C42—21no—
476C2×C42C23×C15111yescharacteristic
477C2×C42C23×C15111yescharacteristic
478#107—22no—
479#106—22no—
480#106—22no—
481#106—22no—
482C4⋊C8—22no—
483C4⋊C8—22no—
484#102—22no—
485#102—22no—
486#102—22no—
487#102—22no—
488C22⋊C8—22no—
489C22⋊C8—22no—
490#95—21no—
491#95—21no—
492#95—21no—
493C24—21no—
494C24C2×D4×C15111yescharacteristic
495C2×Q8—24no—
496C2×Q8—24no—
497C2×Q8—81no—
498C2×Q8—81no—
499C2×Q8—81no—
500C2×Q8—81no—
501C2×D4—24no—
502C2×D4—21no—
503C2×D4—21no—
504C2×D4—21no—
505C2×D4—21no—
506C2×D4—21no—
507C2×D4—81no—
508C2×D4—81no—
509C2×D4C2×Q8×C15112yes—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—24no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—42no—
523C22×C4—81no—
524C22×C4—81no—
525C22×C4—81no—
526C22×C4—81no—
527C22×C4C2×D4×C15111yescharacteristic
528C22×C4C2×D4×C15111yescharacteristic
529C22×C4C2×D4×C15111yescharacteristic
530C22×C4C2×D4×C15111yescharacteristic
531C22×C4C2×D4×C15111yescharacteristic
532C22×C4C2×Q8×C15112yes—
533C22×C4#41×C15112yes—
534C22×C4C24×C15111yescharacteristic
535C2×C8—21no—
536C2×C8—21no—
537C2×C8—21no—
538C2×C8—21no—
539C2×C8—21no—
540C2×C8—21no—
541C2×C8—21no—
542C2×C8—21no—
543C2×C8—21no—
544C2×C8—21no—
545C2×C8—21no—
546C2×C8—21no—
547C4⋊C4—24no—
548C4⋊C4—24no—
549C4⋊C4—24no—
550C4⋊C4—24no—
551C4⋊C4—24no—
552C4⋊C4—24no—
553C4⋊C4—24no—
554C4⋊C4—22no—
555C4⋊C4—22no—
556C4⋊C4—21no—
557C4⋊C4—21no—
558C4⋊C4—21no—
559C4⋊C4—21no—
560C4⋊C4—21no—
561C4⋊C4—21no—
562C4⋊C4—21no—
563C4⋊C4—21no—
564C4⋊C4—21no—
565C4⋊C4—81no—
566C4⋊C4C2×D4×C15112yes—
567C4⋊C4C2×D4×C15112yes—
568C4⋊C4C2×D4×C15112yes—
569C4⋊C4C2×D4×C15112yes—
570C4⋊C4C2×Q8×C15112yes—
571C22⋊C4—24no—
572C22⋊C4—22no—
573C22⋊C4—22no—
574C22⋊C4—24no—
575C22⋊C4—42no—
576C22⋊C4—81no—
577C22⋊C4—81no—
578C22⋊C4—81no—
579C42—24no—
580C42—21no—
581C42—21no—
582C42—81no—
583C42C2×D4×C15112yes—
584C42C2×D4×C15112yes—
585C23—21no—
586C23—21no—
587C23—21no—
588C23—21no—
589C23—21no—
590C23—21no—
591C23—22no—
592C23—41no—
593C23—41no—
594C23—41no—
595C23—41no—
596C23—41no—
597C23—41no—
598C23C22⋊Q8×C15112yes—
599C23C22×D4×C15111yescharacteristic
600Q8—84no—
601Q8—84no—
602D4—22no—
603D4—22no—
604D4—41no—
605D4—41no—
606D4—84no—
607C2×C4—21no—
608C2×C4—21no—
609C2×C4—21no—
610C2×C4—21no—
611C2×C4—21no—
612C2×C4—21no—
613C2×C4—22no—
614C2×C4—22no—
615C2×C4—22no—
616C2×C4—22no—
617C2×C4—21no—
618C2×C4—22no—
619C2×C4—21no—
620C2×C4—22no—
621C2×C4—22no—
622C2×C4—22no—
623C2×C4—22no—
624C2×C4—21no—
625C2×C4—21no—
626C2×C4—21no—
627C2×C4—21no—
628C2×C4—41no—
629C2×C4—41no—
630C2×C4—41no—
631C2×C4—41no—
632C2×C4—41no—
633C2×C4—41no—
634C2×C4—41no—
635C2×C4—41no—
636C2×C4—41no—
637C2×C4—41no—
638C2×C4—41no—
639C2×C4—41no—
640C2×C4—41no—
641C2×C4—41no—
642C2×C4—41no—
643C2×C4—41no—
644C2×C4—84no—
645C2×C4—84no—
646C2×C4#120×C15112yes—
647C2×C4#120×C15112yes—
648C2×C4C22⋊Q8×C15112yes—
649C2×C4C22×D4×C15111yescharacteristic
650C2×C4C22×D4×C15111yescharacteristic
651C2×C4C22×Q8×C15111yescharacteristic
652C2×C4C2×#41×C15111yescharacteristic
653C2×C42−1+4×C15111yescharacteristic
654C2×C42−1+4×C15111yescharacteristic
655C8—41no—
656C8—41no—
657C8—41no—
658C8—41no—
659C22—22no—
660C22—22no—
661C22—22no—
662C22—41no—
663C22—41no—
664C22—41no—
665C22—41no—
666C22—42no—
667C22—42no—
668C22—42no—
669C22—81no—
670C22—81no—
671C22—81no—
672C22—81no—
673C22C2×#120×C15111yescharacteristic
674C22C2×C22⋊Q8×C15111yescharacteristic
675C22#536×C15111yescharacteristic
676C22#576×C15111yescharacteristic
677C22#577×C15111yescharacteristic
678C22#577×C15111yescharacteristic
679C22#577×C15111yescharacteristic
680C4—22no—
681C4—22no—
682C4—22no—
683C4—41no—
684C4—42no—
685C4—41no—
686C4—42no—
687C4—42no—
688C4—42no—
689C4—42no—
690C4—81no—
691C4—81no—
692C4#548×C15111yescharacteristic
693C4#548×C15111yescharacteristic
694C4D4×Q8×C15111yescharacteristic
695C4D4×Q8×C15111yescharacteristic
696C2—42no—
697C2—82no—
698C2#2409×C15111yescharacteristic
699C2#3010×C15111yescharacteristic
700C2#3012×C15111yescharacteristic
701C2#3081×C15111yescharacteristic
702C2#3084×C15111yescharacteristic
703C2#3241×C15111yescharacteristic
704C2#3244×C15111yescharacteristic
subgroupG/H
center, socleC23×C151C22×D4
commutator, Frattini, cosocleC22×C4C24×C151
prime radicalC2×#121×C151C22
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
1. C2×#544×C151C2semidirect
2. C2×#478×C151C2semidirect
3. C2×#476×C151C2semidirect
5. #2059×C151C2semidirect
6. #2058×C151C2semidirect
7. #2025×C151C2semidirect
8. #2023×C151C2semidirect
9. #1989×C151C2semidirect
10. #1988×C151C2semidirect
13. #1854×C151C2semidirect
14. #1853×C151C2semidirect
15. #1798×C151C2semidirect
78. C4⋊Q8×C151D4semidirect
83. #125×C151D4semidirect
87. #121×C151Q8semidirect
352. #24309C151direct (N × H)
353. C151#24309direct (N × H)
354. C2×#544C2×C151semidirect
355. C2×#478C2×C151semidirect
356. C2×#476C2×C151semidirect
358. #2059C2×C151semidirect
359. #2058C2×C151semidirect
360. #2025C2×C151semidirect
361. #2023C2×C151semidirect
362. #1989C2×C151semidirect
363. #1988C2×C151semidirect
366. #1854C2×C151semidirect
367. #1853C2×C151semidirect
368. #1798C2×C151semidirect
431. C4⋊Q8D4×C151semidirect
436. #125D4×C151semidirect
440. #121Q8×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×#478×C1512
C2×#476×C1512
#2324×C1512
#2059×C1512
#2058×C1512
#2025×C1512
#2023×C1512
#1989×C1512
#1988×C1512
#1875×C1512
#1874×C1512
#1854×C1512
#1853×C1512
#1798×C1512
#24309151