Finite Group Databasebeta

← C151×#17412 #50322337

Subgroups — C151×#17412 #50322337

Order 38656.

1046 conjugacy classes of subgroups.

The subgroup lattice has 720 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#551×C151C211yesmaximal, characteristic
2#2924×C151C212yesmaximal, complemented
3#1473×C151C212yesmaximal, complemented
4#1469×C151C212yesmaximal, complemented
5#1468×C151C212yesmaximal, complemented
6#1466×C151C211yesmaximal, characteristic, complemented
7#1464×C151C211yesmaximal, characteristic, complemented
8#1462×C151C211yesmaximal, characteristic, complemented
9#1460×C151C211yesmaximal, characteristic, complemented
10#1458×C151C211yesmaximal, characteristic, complemented
11C2×#323×C151C211yesmaximal, characteristic, complemented
12#551×C151—22no—
13#551×C151—22no—
14#551×C151—22no—
15#551×C151—22no—
16C2×#126×C151C411yescharacteristic
17C2×#126×C151C2211yescharacteristic
18C2×#124×C151C2211yescharacteristic
19C2×#123×C151C411yescharacteristic
20C2×#123×C151C411yescharacteristic
21C2×#123×C151C2211yescharacteristic
22C2×C22⋊Q8×C151C411yescharacteristic
23C2×C22⋊Q8×C151C411yescharacteristic
24C2×#120×C151C411yescharacteristic
25C2×C4×D4×C151C411yescharacteristic
26C2×C4×D4×C151C2211yescharacteristic
27C2×#117×C151C2211yescharacteristic
28C2×#117×C151C2211yescharacteristic
29C22×C22⋊C4×C151C411yescharacteristic
30C22×C22⋊C4×C151C2211yescharacteristic
31#433×C151—22no—
32#433×C151—22no—
33#432×C151C2212yescomplemented
34#432×C151C2212yescomplemented
35#431×C151C2212yescomplemented
36#431×C151C2212yescomplemented
37#424×C151—22no—
38#407×C151C2212yes—
39C2×C22⋊C8×C151C2212yes—
40#405×C151—22no—
41#324×C151C2212yescomplemented
42#324×C151C2212yescomplemented
43#323×C151C2211yescharacteristic
44#323×C151C2211yescharacteristic
45#323×C151C2212yes—
46#323×C151C2211yescharacteristic
47#323×C151C2211yescharacteristic
48#323×C151C2212yes—
49#323×C151C2212yescomplemented
50#323×C151C2212yescomplemented
51C25×C151C2×C411yescharacteristic
52C22×Q8×C151C2×C411yescharacteristic
53C22×D4×C151C2×C411yescharacteristic
54C22×D4×C151C2×C411yescharacteristic
55C22×D4×C151C2×C411yescharacteristic
56C23×C4×C151C2×C411yescharacteristic
57C23×C4×C151C2×C411yescharacteristic
58C23×C4×C151C2×C411yescharacteristic
59C23×C4×C151C2×C411yescharacteristic
60C23×C4×C151C2311yescharacteristic
61C2×M16×C151—22no—
62C22×C8×C151—22no—
63#126×C151—22no—
64#126×C151—22no—
65#126×C151—22no—
66#126×C151—22no—
67#124×C151—22no—
68#124×C151—22no—
69#123×C151—22no—
70#123×C151—22no—
71#123×C151—22no—
72#123×C151—22no—
73#123×C151—22no—
74#123×C151—22no—
75C22⋊Q8×C151—22no—
76C22⋊Q8×C151—22no—
77C22⋊Q8×C151—22no—
78C22⋊Q8×C151—22no—
79#120×C151—22no—
80#120×C151—22no—
81C4×D4×C151—21no—
82C4×D4×C151—21no—
83C4×D4×C151—21no—
84C4×D4×C151—21no—
85C4×D4×C151—22no—
86C4×D4×C151—22no—
87#117×C151—22no—
88#117×C151—22no—
89#117×C151D412yes—
90#117×C151D412yes—
91#117×C151D412yes—
92#117×C151D412yes—
93C2×C4⋊C4×C151C2×C411yescharacteristic
94C2×C4⋊C4×C151C2×C411yescharacteristic
95C2×C4⋊C4×C151C2×C411yescharacteristic
96C2×C4⋊C4×C151C2×C411yescharacteristic
97C2×C4⋊C4×C151C2×C411yescharacteristic
98C2×C4⋊C4×C151C2×C411yescharacteristic
99C2×C4⋊C4×C151C2×C411yescharacteristic
100C2×C4⋊C4×C151C2311yescharacteristic
101C2×C22⋊C4×C151—22no—
102C2×C22⋊C4×C151—22no—
103C2×C22⋊C4×C151—21no—
104C2×C22⋊C4×C151—21no—
105C2×C22⋊C4×C151—21no—
106C2×C22⋊C4×C151—21no—
107C2×C22⋊C4×C151C2×C411yescharacteristic
108C2×C22⋊C4×C151C2×C411yescharacteristic
109C2×C22⋊C4×C151C2×C411yescharacteristic
110C2×C22⋊C4×C151C2×C411yescharacteristic
111C2×C22⋊C4×C151C2×C411yescharacteristic
112C2×C22⋊C4×C151C2×C411yescharacteristic
113C2×C22⋊C4×C151C2×C411yescharacteristic
114C2×C22⋊C4×C151C2×C411yescharacteristic
115C2×C22⋊C4×C151C2×C411yescharacteristic
116C2×C22⋊C4×C151C2×C411yescharacteristic
117C2×C22⋊C4×C151C2×C411yescharacteristic
118C2×C22⋊C4×C151C2311yescharacteristic
119C2×C22⋊C4×C151C2311yescharacteristic
120C2×C22⋊C4×C151C2311yescharacteristic
121C2×C42×C151C2×C411yescharacteristic
122C2×C42×C151C2311yescharacteristic
123C2×C42×C151C2311yescharacteristic
124C4⋊C8×C151—22no—
125C4⋊C8×C151—22no—
126C4⋊C8×C151—22no—
127C4⋊C8×C151—22no—
128C22⋊C8×C151—22no—
129C22⋊C8×C151—22no—
130C22⋊C8×C151C2312yes—
131C22⋊C8×C151C2312yes—
132C22⋊C8×C151C2312yes—
133C22⋊C8×C151C2312yes—
134#97×C151—22no—
135#97×C151—22no—
136C4×C8×C151—22no—
137C4×C8×C151—22no—
138C24×C151—21no—
139C24×C151—21no—
140C24×C151—22no—
141C24×C151—41no—
142C24×C151—42no—
143C24×C151—81no—
144C24×C151C22×C411yescharacteristic
145C24×C151C22×C411yescharacteristic
146C24×C151C22×C411yescharacteristic
147C24×C151C22×C411yescharacteristic
148C2×Q8×C151—22no—
149C2×Q8×C151—81no—
150C2×D4×C151—21no—
151C2×D4×C151—21no—
152C2×D4×C151—22no—
153C2×D4×C151—22no—
154C2×D4×C151—22no—
155C2×D4×C151—41no—
156C2×D4×C151—42no—
157C2×D4×C151—81no—
158C22×C4×C151—22no—
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—21no—
167C22×C4×C151—41no—
168C22×C4×C151—42no—
169C22×C4×C151—81no—
170C22×C4×C151—81no—
171C22×C4×C151—81no—
172C22×C4×C151C22×C411yescharacteristic
173C22×C4×C151C22×C411yescharacteristic
174C22×C4×C151C22×C411yescharacteristic
175C22×C4×C151C22×C411yescharacteristic
176C22×C4×C151C22×C411yescharacteristic
177C22×C4×C151C22×C411yescharacteristic
178C22×C4×C151C22×C411yescharacteristic
179C22×C4×C151C22×C411yescharacteristic
180C22×C4×C151C22×C411yescharacteristic
181C22×C4×C151C22×C411yescharacteristic
182C22×C4×C151C2×D412yes—
183C22×C4×C151C2×D412yes—
184C22×C4×C151C2411yescharacteristic
185M16×C151—44no—
186C2×C8×C151—22no—
187C2×C8×C151—22no—
188C2×C8×C151—22no—
189C2×C8×C151—22no—
190C2×C8×C151—44no—
191C4⋊C4×C151—22no—
192C4⋊C4×C151—21no—
193C4⋊C4×C151—21no—
194C4⋊C4×C151—22no—
195C4⋊C4×C151—22no—
196C4⋊C4×C151—22no—
197C4⋊C4×C151—22no—
198C4⋊C4×C151C22⋊C412yes—
199C4⋊C4×C151C22⋊C412yes—
200C4⋊C4×C151C22⋊C412yes—
201C4⋊C4×C151C22⋊C412yes—
202C22⋊C4×C151—21no—
203C22⋊C4×C151—21no—
204C22⋊C4×C151—22no—
205C22⋊C4×C151—22no—
206C22⋊C4×C151—21no—
207C22⋊C4×C151—21no—
208C22⋊C4×C151—21no—
209C22⋊C4×C151—21no—
210C22⋊C4×C151—22no—
211C22⋊C4×C151—21no—
212C22⋊C4×C151—21no—
213C22⋊C4×C151—22no—
214C22⋊C4×C151—22no—
215C22⋊C4×C151—22no—
216C22⋊C4×C151—22no—
217C22⋊C4×C151—22no—
218C22⋊C4×C151C22⋊C411yescharacteristic
219C22⋊C4×C151C22⋊C411yescharacteristic
220C22⋊C4×C151C22⋊C411yescharacteristic
221C22⋊C4×C151C22⋊C411yescharacteristic
222C22⋊C4×C151C22⋊C412yes—
223C22⋊C4×C151C22⋊C412yes—
224C42×C151—21no—
225C42×C151—21no—
226C42×C151C2×D412yes—
227C42×C151C2×D412yes—
228C42×C151C2×D412yes—
229C42×C151C2×D412yes—
230C23×C151—21no—
231C23×C151—21no—
232C23×C151—21no—
233C23×C151—21no—
234C23×C151—22no—
235C23×C151—21no—
236C23×C151—21no—
237C23×C151—21no—
238C23×C151—21no—
239C23×C151—21no—
240C23×C151—21no—
241C23×C151—41no—
242C23×C151—42no—
243C23×C151—42no—
244C23×C151—41no—
245C23×C151—41no—
246C23×C151—42no—
247C23×C151—41no—
248C23×C151—41no—
249C23×C151—41no—
250C23×C151—41no—
251C23×C151—42no—
252C23×C151—81no—
253C23×C151—81no—
254C23×C151—84no—
255C23×C151—84no—
256C23×C151C2×C22⋊C411yescharacteristic
257C23×C151C2×C22⋊C411yescharacteristic
258C23×C151#13112yes—
259C23×C151C23×C411yescharacteristic
260Q8×C151—82no—
261D4×C151—44no—
262D4×C151—42no—
263D4×C151—42no—
264D4×C151—82no—
265C2×C4×C151—21no—
266C2×C4×C151—21no—
267C2×C4×C151—21no—
268C2×C4×C151—21no—
269C2×C4×C151—24no—
270C2×C4×C151—21no—
271C2×C4×C151—21no—
272C2×C4×C151—21no—
273C2×C4×C151—21no—
274C2×C4×C151—21no—
275C2×C4×C151—21no—
276C2×C4×C151—21no—
277C2×C4×C151—41no—
278C2×C4×C151—41no—
279C2×C4×C151—42no—
280C2×C4×C151—41no—
281C2×C4×C151—41no—
282C2×C4×C151—42no—
283C2×C4×C151—42no—
284C2×C4×C151—41no—
285C2×C4×C151—41no—
286C2×C4×C151—41no—
287C2×C4×C151—41no—
288C2×C4×C151—81no—
289C2×C4×C151—81no—
290C2×C4×C151—81no—
291C2×C4×C151—81no—
292C2×C4×C151—81no—
293C2×C4×C151—81no—
294C2×C4×C151C2×C22⋊C412yes—
295C2×C4×C151C2×C22⋊C411yescharacteristic
296C2×C4×C151C2×C22⋊C411yescharacteristic
297C2×C4×C151C2×C22⋊C412yes—
298C2×C4×C151C2×C22⋊C411yescharacteristic
299C2×C4×C151C2×C22⋊C411yescharacteristic
300C2×C4×C151C2×C22⋊C412yes—
301C2×C4×C151C22×D412yes—
302C8×C151—42no—
303C8×C151—42no—
304C8×C151—42no—
305C8×C151—42no—
306C22×C151—21no—
307C22×C151—21no—
308C22×C151—21no—
309C22×C151—21no—
310C22×C151—22no—
311C22×C151—21no—
312C22×C151—21no—
313C22×C151—21no—
314C22×C151—42no—
315C22×C151—42no—
316C22×C151—42no—
317C22×C151—42no—
318C22×C151—41no—
319C22×C151—41no—
320C22×C151—41no—
321C22×C151—41no—
322C22×C151—41no—
323C22×C151—41no—
324C22×C151—41no—
325C22×C151—41no—
326C22×C151—84no—
327C22×C151—81no—
328C22×C151—81no—
329C22×C151—81no—
330C22×C151—81no—
331C22×C151—84no—
332C22×C151#41012yes—
333C22×C151C22×C22⋊C411yescharacteristic
334C22×C151C2×#13111yescharacteristic
335C22×C151#56811yescharacteristic
336C4×C151—21no—
337C4×C151—21no—
338C4×C151—22no—
339C4×C151—22no—
340C4×C151—22no—
341C4×C151—21no—
342C4×C151—21no—
343C4×C151—22no—
344C4×C151—41no—
345C4×C151—41no—
346C4×C151—41no—
347C4×C151—41no—
348C4×C151—41no—
349C2×C151—21no—
350C2×C151—21no—
351C2×C151—22no—
352C2×C151—41no—
353C2×C151—42no—
354C2×C151—81no—
355C2×C151—81no—
356C2×C151#288011yescharacteristic
357C2×C151C2×#41011yescharacteristic
358C2×C151#288811yescharacteristic
359#17412C15111yesmaximal, characteristic, direct product factor, Sylow
360C151#1741211yescharacteristic, direct product factor, Sylow
361C2×#551C2×C15111yescharacteristic
362#2924C2×C15112yescomplemented
363#1473C2×C15112yescomplemented
364#1469C2×C15112yescomplemented
365#1468C2×C15112yescomplemented
366#1466C2×C15111yescharacteristic, complemented
367#1464C2×C15111yescharacteristic, complemented
368#1462C2×C15111yescharacteristic, complemented
369#1460C2×C15111yescharacteristic, complemented
370#1458C2×C15111yescharacteristic, complemented
371C2×#323C2×C15111yescharacteristic, complemented
372#551—22no—
373#551—22no—
374#551—22no—
375#551—22no—
376C2×#126C4×C15111yescharacteristic
377C2×#126C22×C15111yescharacteristic
378C2×#124C22×C15111yescharacteristic
379C2×#123C4×C15111yescharacteristic
380C2×#123C4×C15111yescharacteristic
381C2×#123C22×C15111yescharacteristic
382C2×C22⋊Q8C4×C15111yescharacteristic
383C2×C22⋊Q8C4×C15111yescharacteristic
384C2×#120C4×C15111yescharacteristic
385C2×C4×D4C4×C15111yescharacteristic
386C2×C4×D4C22×C15111yescharacteristic
387C2×#117C22×C15111yescharacteristic
388C2×#117C22×C15111yescharacteristic
389C22×C22⋊C4C4×C15111yescharacteristic
390C22×C22⋊C4C22×C15111yescharacteristic
391#433—22no—
392#433—22no—
393#432C22×C15112yescomplemented
394#432C22×C15112yescomplemented
395#431C22×C15112yescomplemented
396#431C22×C15112yescomplemented
397#424—22no—
398#407C22×C15112yes—
399C2×C22⋊C8C22×C15112yes—
400#405—22no—
401#324C22×C15112yescomplemented
402#324C22×C15112yescomplemented
403#323C22×C15111yescharacteristic
404#323C22×C15111yescharacteristic
405#323C22×C15112yes—
406#323C22×C15111yescharacteristic
407#323C22×C15111yescharacteristic
408#323C22×C15112yes—
409#323C22×C15112yescomplemented
410#323C22×C15112yescomplemented
411C25C2×C4×C15111yescharacteristic
412C22×Q8C2×C4×C15111yescharacteristic
413C22×D4C2×C4×C15111yescharacteristic
414C22×D4C2×C4×C15111yescharacteristic
415C22×D4C2×C4×C15111yescharacteristic
416C23×C4C2×C4×C15111yescharacteristic
417C23×C4C2×C4×C15111yescharacteristic
418C23×C4C2×C4×C15111yescharacteristic
419C23×C4C2×C4×C15111yescharacteristic
420C23×C4C23×C15111yescharacteristic
421C2×M16—22no—
422C22×C8—22no—
423#126—22no—
424#126—22no—
425#126—22no—
426#126—22no—
427#124—22no—
428#124—22no—
429#123—22no—
430#123—22no—
431#123—22no—
432#123—22no—
433#123—22no—
434#123—22no—
435C22⋊Q8—22no—
436C22⋊Q8—22no—
437C22⋊Q8—22no—
438C22⋊Q8—22no—
439#120—22no—
440#120—22no—
441C4×D4—21no—
442C4×D4—21no—
443C4×D4—21no—
444C4×D4—21no—
445C4×D4—22no—
446C4×D4—22no—
447#117—22no—
448#117—22no—
449#117D4×C15112yes—
450#117D4×C15112yes—
451#117D4×C15112yes—
452#117D4×C15112yes—
453C2×C4⋊C4C2×C4×C15111yescharacteristic
454C2×C4⋊C4C2×C4×C15111yescharacteristic
455C2×C4⋊C4C2×C4×C15111yescharacteristic
456C2×C4⋊C4C2×C4×C15111yescharacteristic
457C2×C4⋊C4C2×C4×C15111yescharacteristic
458C2×C4⋊C4C2×C4×C15111yescharacteristic
459C2×C4⋊C4C2×C4×C15111yescharacteristic
460C2×C4⋊C4C23×C15111yescharacteristic
461C2×C22⋊C4—22no—
462C2×C22⋊C4—22no—
463C2×C22⋊C4—21no—
464C2×C22⋊C4—21no—
465C2×C22⋊C4—21no—
466C2×C22⋊C4—21no—
467C2×C22⋊C4C2×C4×C15111yescharacteristic
468C2×C22⋊C4C2×C4×C15111yescharacteristic
469C2×C22⋊C4C2×C4×C15111yescharacteristic
470C2×C22⋊C4C2×C4×C15111yescharacteristic
471C2×C22⋊C4C2×C4×C15111yescharacteristic
472C2×C22⋊C4C2×C4×C15111yescharacteristic
473C2×C22⋊C4C2×C4×C15111yescharacteristic
474C2×C22⋊C4C2×C4×C15111yescharacteristic
475C2×C22⋊C4C2×C4×C15111yescharacteristic
476C2×C22⋊C4C2×C4×C15111yescharacteristic
477C2×C22⋊C4C2×C4×C15111yescharacteristic
478C2×C22⋊C4C23×C15111yescharacteristic
479C2×C22⋊C4C23×C15111yescharacteristic
480C2×C22⋊C4C23×C15111yescharacteristic
481C2×C42C2×C4×C15111yescharacteristic
482C2×C42C23×C15111yescharacteristic
483C2×C42C23×C15111yescharacteristic
484C4⋊C8—22no—
485C4⋊C8—22no—
486C4⋊C8—22no—
487C4⋊C8—22no—
488C22⋊C8—22no—
489C22⋊C8—22no—
490C22⋊C8C23×C15112yes—
491C22⋊C8C23×C15112yes—
492C22⋊C8C23×C15112yes—
493C22⋊C8C23×C15112yes—
494#97—22no—
495#97—22no—
496C4×C8—22no—
497C4×C8—22no—
498C24—21no—
499C24—21no—
500C24—22no—
501C24—41no—
502C24—42no—
503C24—81no—
504C24C22×C4×C15111yescharacteristic
505C24C22×C4×C15111yescharacteristic
506C24C22×C4×C15111yescharacteristic
507C24C22×C4×C15111yescharacteristic
508C2×Q8—22no—
509C2×Q8—81no—
510C2×D4—21no—
511C2×D4—21no—
512C2×D4—22no—
513C2×D4—22no—
514C2×D4—22no—
515C2×D4—41no—
516C2×D4—42no—
517C2×D4—81no—
518C22×C4—22no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—41no—
528C22×C4—42no—
529C22×C4—81no—
530C22×C4—81no—
531C22×C4—81no—
532C22×C4C22×C4×C15111yescharacteristic
533C22×C4C22×C4×C15111yescharacteristic
534C22×C4C22×C4×C15111yescharacteristic
535C22×C4C22×C4×C15111yescharacteristic
536C22×C4C22×C4×C15111yescharacteristic
537C22×C4C22×C4×C15111yescharacteristic
538C22×C4C22×C4×C15111yescharacteristic
539C22×C4C22×C4×C15111yescharacteristic
540C22×C4C22×C4×C15111yescharacteristic
541C22×C4C22×C4×C15111yescharacteristic
542C22×C4C2×D4×C15112yes—
543C22×C4C2×D4×C15112yes—
544C22×C4C24×C15111yescharacteristic
545M16—44no—
546C2×C8—22no—
547C2×C8—22no—
548C2×C8—22no—
549C2×C8—22no—
550C2×C8—44no—
551C4⋊C4—22no—
552C4⋊C4—21no—
553C4⋊C4—21no—
554C4⋊C4—22no—
555C4⋊C4—22no—
556C4⋊C4—22no—
557C4⋊C4—22no—
558C4⋊C4C22⋊C4×C15112yes—
559C4⋊C4C22⋊C4×C15112yes—
560C4⋊C4C22⋊C4×C15112yes—
561C4⋊C4C22⋊C4×C15112yes—
562C22⋊C4—21no—
563C22⋊C4—21no—
564C22⋊C4—22no—
565C22⋊C4—22no—
566C22⋊C4—21no—
567C22⋊C4—21no—
568C22⋊C4—21no—
569C22⋊C4—21no—
570C22⋊C4—22no—
571C22⋊C4—21no—
572C22⋊C4—21no—
573C22⋊C4—22no—
574C22⋊C4—22no—
575C22⋊C4—22no—
576C22⋊C4—22no—
577C22⋊C4—22no—
578C22⋊C4C22⋊C4×C15111yescharacteristic
579C22⋊C4C22⋊C4×C15111yescharacteristic
580C22⋊C4C22⋊C4×C15111yescharacteristic
581C22⋊C4C22⋊C4×C15111yescharacteristic
582C22⋊C4C22⋊C4×C15112yes—
583C22⋊C4C22⋊C4×C15112yes—
584C42—21no—
585C42—21no—
586C42C2×D4×C15112yes—
587C42C2×D4×C15112yes—
588C42C2×D4×C15112yes—
589C42C2×D4×C15112yes—
590C23—22no—
591C23—21no—
592C23—21no—
593C23—21no—
594C23—21no—
595C23—21no—
596C23—21no—
597C23—21no—
598C23—21no—
599C23—21no—
600C23—21no—
601C23—41no—
602C23—42no—
603C23—42no—
604C23—41no—
605C23—41no—
606C23—42no—
607C23—41no—
608C23—41no—
609C23—41no—
610C23—41no—
611C23—42no—
612C23—81no—
613C23—81no—
614C23—84no—
615C23—84no—
616C23C2×C22⋊C4×C15111yescharacteristic
617C23C2×C22⋊C4×C15111yescharacteristic
618C23#131×C15112yes—
619C23C23×C4×C15111yescharacteristic
620Q8—82no—
621D4—44no—
622D4—42no—
623D4—42no—
624D4—82no—
625C2×C4—24no—
626C2×C4—21no—
627C2×C4—21no—
628C2×C4—21no—
629C2×C4—21no—
630C2×C4—21no—
631C2×C4—21no—
632C2×C4—21no—
633C2×C4—21no—
634C2×C4—21no—
635C2×C4—21no—
636C2×C4—21no—
637C2×C4—41no—
638C2×C4—41no—
639C2×C4—42no—
640C2×C4—41no—
641C2×C4—41no—
642C2×C4—42no—
643C2×C4—42no—
644C2×C4—41no—
645C2×C4—41no—
646C2×C4—41no—
647C2×C4—41no—
648C2×C4—81no—
649C2×C4—81no—
650C2×C4—81no—
651C2×C4—81no—
652C2×C4—81no—
653C2×C4—81no—
654C2×C4C2×C22⋊C4×C15111yescharacteristic
655C2×C4C2×C22⋊C4×C15111yescharacteristic
656C2×C4C2×C22⋊C4×C15112yes—
657C2×C4C2×C22⋊C4×C15111yescharacteristic
658C2×C4C2×C22⋊C4×C15111yescharacteristic
659C2×C4C2×C22⋊C4×C15112yes—
660C2×C4C2×C22⋊C4×C15112yes—
661C2×C4C22×D4×C15112yes—
662C8—42no—
663C8—42no—
664C8—42no—
665C8—42no—
666C22—21no—
667C22—21no—
668C22—21no—
669C22—21no—
670C22—22no—
671C22—21no—
672C22—21no—
673C22—21no—
674C22—42no—
675C22—42no—
676C22—42no—
677C22—42no—
678C22—41no—
679C22—41no—
680C22—41no—
681C22—41no—
682C22—41no—
683C22—41no—
684C22—41no—
685C22—41no—
686C22—84no—
687C22—81no—
688C22—81no—
689C22—81no—
690C22—81no—
691C22—84no—
692C22#410×C15112yes—
693C22C22×C22⋊C4×C15111yescharacteristic
694C22C2×#131×C15111yescharacteristic
695C22#568×C15111yescharacteristic
696C4—21no—
697C4—21no—
698C4—22no—
699C4—22no—
700C4—22no—
701C4—21no—
702C4—21no—
703C4—22no—
704C4—41no—
705C4—41no—
706C4—41no—
707C4—41no—
708C4—41no—
709C2—21no—
710C2—21no—
711C2—22no—
712C2—41no—
713C2—42no—
714C2—81no—
715C2—81no—
716C2#2880×C15111yescharacteristic
717C2C2×#410×C15111yescharacteristic
718C2#2888×C15111yescharacteristic
subgroupG/H
center, socleC22×C151C22×C22⋊C4
commutatorC23C23×C4×C151
Frattini, cosocleC22×C4C24×C151
prime radicalC2×#120×C151C4
LCSG ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C151 ◁ C2×#117×C151 ◁ G

Complements

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

NH ≅ G/Ntype
2. #2924×C151C2semidirect
3. #1473×C151C2semidirect
4. #1469×C151C2semidirect
5. #1468×C151C2semidirect
6. #1466×C151C2semidirect
7. #1464×C151C2semidirect
8. #1462×C151C2semidirect
9. #1460×C151C2semidirect
10. #1458×C151C2semidirect
11. C2×#323×C151C2semidirect
33. #432×C151C22semidirect
34. #432×C151C22semidirect
35. #431×C151C22semidirect
36. #431×C151C22semidirect
41. #324×C151C22semidirect
42. #324×C151C22semidirect
49. #323×C151C22semidirect
50. #323×C151C22semidirect
359. #17412C151direct (N × H)
360. C151#17412direct (N × H)
362. #2924C2×C151semidirect
363. #1473C2×C151semidirect
364. #1469C2×C151semidirect
365. #1468C2×C151semidirect
366. #1466C2×C151semidirect
367. #1464C2×C151semidirect
368. #1462C2×C151semidirect
369. #1460C2×C151semidirect
370. #1458C2×C151semidirect
371. C2×#323C2×C151semidirect
393. #432C22×C151semidirect
394. #432C22×C151semidirect
395. #431C22×C151semidirect
396. #431C22×C151semidirect
401. #324C22×C151semidirect
402. #324C22×C151semidirect
409. #323C22×C151semidirect
410. #323C22×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#551×C1512
#2924×C1512
#1473×C1512
#1469×C1512
#1468×C1512
#1466×C1512
#1464×C1512
#1462×C1512
#1460×C1512
#1458×C1512
C2×#323×C1512
#17412151