Finite Group Databasebeta

← C151×#21874 #50326799

Subgroups — C151×#21874 #50326799

Order 38656.

1598 conjugacy classes of subgroups.

The subgroup lattice has 822 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#525×C151C211yesmaximal, characteristic
2#2280×C151C211yesmaximal, characteristic, complemented
3C2×#380×C151C211yesmaximal, characteristic, complemented
4#1996×C151C212yesmaximal, complemented
5#1964×C151C212yesmaximal, complemented
6#1898×C151C214yesmaximal, complemented
7#1799×C151C214yesmaximal, complemented
8C22×#41×C151C411yescharacteristic, complemented
9C24×C4×C151C2211yescharacteristic
10#525×C151—21no—
11#525×C151—21no—
12#525×C151—21no—
13#525×C151—21no—
14#525×C151—21no—
15#525×C151—21no—
16#525×C151—21no—
17#525×C151—21no—
18C2×#123×C151C412yescomplemented
19C2×C22⋊Q8×C151C411yescharacteristic, complemented
20C2×C22⋊Q8×C151C2211yescharacteristic
21C2×#121×C151C411yescharacteristic, complemented
22C2×#121×C151C2211yescharacteristic
23C2×#120×C151C2212yes—
24C2×C4×D4×C151C412yescomplemented
25C2×C4×D4×C151C2212yes—
26C2×#117×C151—21no—
27C2×#117×C151C411yescharacteristic, complemented
28C22×C4⋊C4×C151—21no—
29C22×C22⋊C4×C151C2212yes—
30C2×#99×C151C2218yes—
31#381×C151—21no—
32#380×C151—21no—
33#380×C151—21no—
34#380×C151—21no—
35#380×C151C2212yes—
36#380×C151C2212yes—
37#380×C151C2212yes—
38#379×C151C2212yes—
39C4×C22⋊C4×C151—21no—
40C4×C22⋊C4×C151C2212yes—
41C2×#95×C151—21no—
42#342×C151C2218yes—
43C25×C151C2311yescharacteristic
44C2×#41×C151—21no—
45C2×#41×C151—21no—
46C2×#41×C151—21no—
47C2×#41×C151—21no—
48C2×#41×C151—44no—
49C22×Q8×C151C2×C411yescharacteristic, complemented
50C22×D4×C151C2×C412yes—
51C22×D4×C151C2×C412yes—
52C22×D4×C151C2×C411yescharacteristic, complemented
53C22×D4×C151C2312yes—
54C23×C4×C151—22no—
55C23×C4×C151—44no—
56C23×C4×C151C2×C411yescharacteristic
57C23×C4×C151C2×C411yescharacteristic
58C23×C4×C151C2×C411yescharacteristic
59C23×C4×C151C2×C411yescharacteristic
60C23×C4×C151C2×C412yescomplemented
61C23×C4×C151D411yescharacteristic
62C23×C4×C151D411yescharacteristic
63C23×C4×C151D411yescharacteristic
64C23×C4×C151D411yescharacteristic
65C23×C4×C151D411yescharacteristic
66C23×C4×C151D411yescharacteristic
67C23×C4×C151D411yescharacteristic
68C23×C4×C151D411yescharacteristic
69C23×C4×C151C2311yescharacteristic
70C23×C4×C151C2311yescharacteristic
71#123×C151—22no—
72#123×C151—22no—
73#123×C151—22no—
74#123×C151—22no—
75C22⋊Q8×C151—21no—
76C22⋊Q8×C151—21no—
77C22⋊Q8×C151—21no—
78C22⋊Q8×C151—21no—
79C22⋊Q8×C151—21no—
80C22⋊Q8×C151—21no—
81C22⋊Q8×C151—21no—
82C22⋊Q8×C151—21no—
83#121×C151—21no—
84#121×C151—21no—
85#121×C151—21no—
86#121×C151—21no—
87#121×C151—21no—
88#121×C151—21no—
89#121×C151—21no—
90#121×C151—21no—
91#120×C151—22no—
92#120×C151—22no—
93#120×C151—22no—
94#120×C151—22no—
95C4×D4×C151—22no—
96C4×D4×C151—22no—
97C4×D4×C151—22no—
98C4×D4×C151—22no—
99C4×D4×C151—22no—
100C4×D4×C151—22no—
101C4×D4×C151—22no—
102C4×D4×C151—22no—
103#117×C151—21no—
104#117×C151—21no—
105#117×C151—21no—
106#117×C151—21no—
107#117×C151—44no—
108C2×C4⋊C4×C151—22no—
109C2×C4⋊C4×C151—22no—
110C2×C4⋊C4×C151—22no—
111C2×C4⋊C4×C151—44no—
112C2×C4⋊C4×C151C2×C411yescharacteristic, complemented
113C2×C4⋊C4×C151C2×C411yescharacteristic, complemented
114C2×C4⋊C4×C151C2×C412yescomplemented
115C2×C4⋊C4×C151C2×C412yescomplemented
116C2×C22⋊C4×C151—22no—
117C2×C22⋊C4×C151—22no—
118C2×C22⋊C4×C151—22no—
119C2×C22⋊C4×C151—44no—
120C2×C22⋊C4×C151C2×C412yes—
121C2×C22⋊C4×C151C2×C412yes—
122C2×C22⋊C4×C151C2×C412yescomplemented
123C2×C22⋊C4×C151C2×C412yescomplemented
124C2×C22⋊C4×C151C2314yes—
125C2×C22⋊C4×C151C2314yes—
126C2×C22⋊C4×C151C2312yes—
127C2×C42×C151—22no—
128C2×C42×C151C2×C412yescomplemented
129#99×C151—48no—
130#95×C151—22no—
131#95×C151—22no—
132#95×C151—22no—
133#95×C151—22no—
134C24×C151—22no—
135C24×C151—22no—
136C24×C151—42no—
137C24×C151—42no—
138C24×C151C22×C411yescharacteristic
139C24×C151C22×C411yescharacteristic
140C24×C151C22×C412yes—
141C24×C151C2×D411yescharacteristic
142C24×C151C2×D411yescharacteristic
143C24×C151C2×D411yescharacteristic
144C24×C151C2×D411yescharacteristic
145C24×C151C2411yescharacteristic
146#41×C151—44no—
147#41×C151—44no—
148#41×C151—44no—
149#41×C151—44no—
150C2×Q8×C151—21no—
151C2×Q8×C151—21no—
152C2×Q8×C151—42no—
153C2×D4×C151—22no—
154C2×D4×C151—22no—
155C2×D4×C151—22no—
156C2×D4×C151—22no—
157C2×D4×C151—22no—
158C2×D4×C151—22no—
159C2×D4×C151—24no—
160C2×D4×C151—24no—
161C2×D4×C151—21no—
162C2×D4×C151—21no—
163C2×D4×C151—42no—
164C2×D4×C151—44no—
165C2×D4×C151—44no—
166C22×C4×C151—24no—
167C22×C4×C151—24no—
168C22×C4×C151—24no—
169C22×C4×C151—22no—
170C22×C4×C151—22no—
171C22×C4×C151—24no—
172C22×C4×C151—24no—
173C22×C4×C151—42no—
174C22×C4×C151—42no—
175C22×C4×C151—42no—
176C22×C4×C151—42no—
177C22×C4×C151—42no—
178C22×C4×C151—42no—
179C22×C4×C151—42no—
180C22×C4×C151—42no—
181C22×C4×C151—42no—
182C22×C4×C151—42no—
183C22×C4×C151—42no—
184C22×C4×C151—44no—
185C22×C4×C151—44no—
186C22×C4×C151—44no—
187C22×C4×C151—44no—
188C22×C4×C151C22⋊C411yescharacteristic
189C22×C4×C151C22⋊C411yescharacteristic
190C22×C4×C151C22⋊C411yescharacteristic
191C22×C4×C151C22⋊C411yescharacteristic
192C22×C4×C151C22⋊C411yescharacteristic
193C22×C4×C151C22⋊C411yescharacteristic
194C22×C4×C151C22⋊C411yescharacteristic
195C22×C4×C151C22⋊C411yescharacteristic
196C22×C4×C151C22⋊C411yescharacteristic
197C22×C4×C151C22⋊C411yescharacteristic
198C22×C4×C151C22⋊C411yescharacteristic
199C22×C4×C151C22⋊C411yescharacteristic
200C22×C4×C151C22⋊C411yescharacteristic
201C22×C4×C151C22⋊C411yescharacteristic
202C22×C4×C151C22⋊C411yescharacteristic
203C22×C4×C151C22⋊C411yescharacteristic
204C22×C4×C151C22×C412yes—
205C22×C4×C151C22×C411yescharacteristic
206C22×C4×C151C22×C411yescharacteristic
207C22×C4×C151C22×C412yes—
208C22×C4×C151C22×C412yes—
209C22×C4×C151C22×C411yescharacteristic
210C22×C4×C151C22×C411yescharacteristic
211C22×C4×C151C2×D411yescharacteristic
212C22×C4×C151C2×D411yescharacteristic
213C22×C4×C151C2×D411yescharacteristic
214C22×C4×C151C2×D411yescharacteristic
215C22×C4×C151C2×D411yescharacteristic
216C22×C4×C151C2×D411yescharacteristic
217C22×C4×C151C2×D411yescharacteristic
218C22×C4×C151C2×D411yescharacteristic
219C4⋊C4×C151—21no—
220C4⋊C4×C151—21no—
221C4⋊C4×C151—21no—
222C4⋊C4×C151—21no—
223C4⋊C4×C151—22no—
224C4⋊C4×C151—22no—
225C4⋊C4×C151—22no—
226C4⋊C4×C151—22no—
227C4⋊C4×C151—44no—
228C4⋊C4×C151—44no—
229C4⋊C4×C151—44no—
230C22⋊C4×C151—22no—
231C22⋊C4×C151—22no—
232C22⋊C4×C151—22no—
233C22⋊C4×C151—22no—
234C22⋊C4×C151—22no—
235C22⋊C4×C151—22no—
236C22⋊C4×C151—22no—
237C22⋊C4×C151—22no—
238C22⋊C4×C151—22no—
239C22⋊C4×C151—22no—
240C22⋊C4×C151—24no—
241C22⋊C4×C151—28no—
242C22⋊C4×C151—24no—
243C22⋊C4×C151—44no—
244C22⋊C4×C151—44no—
245C22⋊C4×C151—44no—
246C42×C151—22no—
247C42×C151—22no—
248C42×C151—44no—
249C23×C151—21no—
250C23×C151—21no—
251C23×C151—22no—
252C23×C151—22no—
253C23×C151—22no—
254C23×C151—22no—
255C23×C151—21no—
256C23×C151—21no—
257C23×C151—22no—
258C23×C151—22no—
259C23×C151—22no—
260C23×C151—22no—
261C23×C151—22no—
262C23×C151—22no—
263C23×C151—22no—
264C23×C151—24no—
265C23×C151—41no—
266C23×C151—41no—
267C23×C151—41no—
268C23×C151—41no—
269C23×C151—41no—
270C23×C151—41no—
271C23×C151—41no—
272C23×C151—41no—
273C23×C151—48no—
274C23×C151—48no—
275C23×C151—42no—
276C23×C151—42no—
277C23×C151C2×C22⋊C411yescharacteristic
278C23×C151C2×C22⋊C411yescharacteristic
279C23×C151C2×C22⋊C411yescharacteristic
280C23×C151C2×C22⋊C411yescharacteristic
281C23×C151C23×C411yescharacteristic
282C23×C151C22×D411yescharacteristic
283C23×C151C22×D411yescharacteristic
284C23×C151H(5,𝔽2)12yes—
285C23×C1512−1+412yes—
286Q8×C151—42no—
287Q8×C151—42no—
288D4×C151—42no—
289D4×C151—44no—
290D4×C151—44no—
291D4×C151—42no—
292D4×C151—42no—
293D4×C151—44no—
294D4×C151—44no—
295D4×C151—44no—
296D4×C151—42no—
297C2×C4×C151—22no—
298C2×C4×C151—22no—
299C2×C4×C151—22no—
300C2×C4×C151—22no—
301C2×C4×C151—22no—
302C2×C4×C151—22no—
303C2×C4×C151—22no—
304C2×C4×C151—22no—
305C2×C4×C151—22no—
306C2×C4×C151—22no—
307C2×C4×C151—22no—
308C2×C4×C151—22no—
309C2×C4×C151—22no—
310C2×C4×C151—22no—
311C2×C4×C151—22no—
312C2×C4×C151—22no—
313C2×C4×C151—22no—
314C2×C4×C151—22no—
315C2×C4×C151—24no—
316C2×C4×C151—41no—
317C2×C4×C151—41no—
318C2×C4×C151—41no—
319C2×C4×C151—41no—
320C2×C4×C151—41no—
321C2×C4×C151—41no—
322C2×C4×C151—41no—
323C2×C4×C151—41no—
324C2×C4×C151—41no—
325C2×C4×C151—41no—
326C2×C4×C151—41no—
327C2×C4×C151—41no—
328C2×C4×C151—44no—
329C2×C4×C151—44no—
330C2×C4×C151—42no—
331C2×C4×C151—42no—
332C2×C4×C151—44no—
333C2×C4×C151—44no—
334C2×C4×C151—44no—
335C2×C4×C151—44no—
336C2×C4×C151—44no—
337C2×C4×C151—44no—
338C2×C4×C151—88no—
339C2×C4×C151#9914yescomplemented
340C2×C4×C151C2×C22⋊C411yescharacteristic
341C2×C4×C151C2×C22⋊C411yescharacteristic
342C2×C4×C151C2×C22⋊C411yescharacteristic
343C2×C4×C151C2×C22⋊C411yescharacteristic
344C2×C4×C151C2×C22⋊C411yescharacteristic
345C2×C4×C151C2×C22⋊C411yescharacteristic
346C2×C4×C151C2×C22⋊C411yescharacteristic
347C2×C4×C151C2×C22⋊C411yescharacteristic
348C22×C151—24no—
349C22×C151—24no—
350C22×C151—21no—
351C22×C151—21no—
352C22×C151—21no—
353C22×C151—21no—
354C22×C151—21no—
355C22×C151—21no—
356C22×C151—21no—
357C22×C151—21no—
358C22×C151—21no—
359C22×C151—21no—
360C22×C151—21no—
361C22×C151—21no—
362C22×C151—21no—
363C22×C151—21no—
364C22×C151—21no—
365C22×C151—21no—
366C22×C151—42no—
367C22×C151—42no—
368C22×C151—44no—
369C22×C151—44no—
370C22×C151—44no—
371C22×C151—44no—
372C22×C151—42no—
373C22×C151—42no—
374C22×C151—42no—
375C22×C151—42no—
376C22×C151—42no—
377C22×C151—84no—
378C22×C151C2×#9912yes—
379C22×C151#41012yes—
380C22×C151C22×C22⋊C411yescharacteristic
381C22×C151#52012yes—
382C22×C151#53511yescharacteristic
383C22×C151#53611yescharacteristic
384C22×C151#53712yes—
385C4×C151—21no—
386C4×C151—21no—
387C4×C151—21no—
388C4×C151—21no—
389C4×C151—21no—
390C4×C151—21no—
391C4×C151—42no—
392C4×C151—42no—
393C4×C151—42no—
394C4×C151—84no—
395C4×C151—84no—
396C4×C151C2×#9912yes—
397C4×C151C2×#9912yes—
398C2×C151—21no—
399C2×C151—22no—
400C2×C151—21no—
401C2×C151—22no—
402C2×C151—22no—
403C2×C151—22no—
404C2×C151—41no—
405C2×C151—41no—
406C2×C151—82no—
407C2×C151#231111yescharacteristic
408C2×C151C22×#9911yescharacteristic
409C2×C151C2×#41011yescharacteristic
410#21874C15111yesmaximal, characteristic, direct product factor, Sylow
411C151#2187411yescharacteristic, direct product factor, Sylow
412C2×#525C2×C15111yescharacteristic
413#2280C2×C15111yescharacteristic, complemented
414C2×#380C2×C15111yescharacteristic, complemented
415#1996C2×C15112yescomplemented
416#1964C2×C15112yescomplemented
417#1898C2×C15114yescomplemented
418#1799C2×C15114yescomplemented
419C22×#41C4×C15111yescharacteristic, complemented
420C24×C4C22×C15111yescharacteristic
421#525—21no—
422#525—21no—
423#525—21no—
424#525—21no—
425#525—21no—
426#525—21no—
427#525—21no—
428#525—21no—
429C2×#123C4×C15112yescomplemented
430C2×C22⋊Q8C4×C15111yescharacteristic, complemented
431C2×C22⋊Q8C22×C15111yescharacteristic
432C2×#121C4×C15111yescharacteristic, complemented
433C2×#121C22×C15111yescharacteristic
434C2×#120C22×C15112yes—
435C2×C4×D4C4×C15112yescomplemented
436C2×C4×D4C22×C15112yes—
437C2×#117—21no—
438C2×#117C4×C15111yescharacteristic, complemented
439C22×C4⋊C4—21no—
440C22×C22⋊C4C22×C15112yes—
441C2×#99C22×C15118yes—
442#381—21no—
443#380—21no—
444#380—21no—
445#380—21no—
446#380C22×C15112yes—
447#380C22×C15112yes—
448#380C22×C15112yes—
449#379C22×C15112yes—
450C4×C22⋊C4—21no—
451C4×C22⋊C4C22×C15112yes—
452C2×#95—21no—
453#342C22×C15118yes—
454C25C23×C15111yescharacteristic
455C2×#41—21no—
456C2×#41—21no—
457C2×#41—21no—
458C2×#41—21no—
459C2×#41—44no—
460C22×Q8C2×C4×C15111yescharacteristic, complemented
461C22×D4C2×C4×C15112yes—
462C22×D4C2×C4×C15112yes—
463C22×D4C2×C4×C15111yescharacteristic, complemented
464C22×D4C23×C15112yes—
465C23×C4—22no—
466C23×C4—44no—
467C23×C4C2×C4×C15111yescharacteristic
468C23×C4C2×C4×C15111yescharacteristic
469C23×C4C2×C4×C15111yescharacteristic
470C23×C4C2×C4×C15111yescharacteristic
471C23×C4C2×C4×C15112yescomplemented
472C23×C4D4×C15111yescharacteristic
473C23×C4D4×C15111yescharacteristic
474C23×C4D4×C15111yescharacteristic
475C23×C4D4×C15111yescharacteristic
476C23×C4D4×C15111yescharacteristic
477C23×C4D4×C15111yescharacteristic
478C23×C4D4×C15111yescharacteristic
479C23×C4D4×C15111yescharacteristic
480C23×C4C23×C15111yescharacteristic
481C23×C4C23×C15111yescharacteristic
482#123—22no—
483#123—22no—
484#123—22no—
485#123—22no—
486C22⋊Q8—21no—
487C22⋊Q8—21no—
488C22⋊Q8—21no—
489C22⋊Q8—21no—
490C22⋊Q8—21no—
491C22⋊Q8—21no—
492C22⋊Q8—21no—
493C22⋊Q8—21no—
494#121—21no—
495#121—21no—
496#121—21no—
497#121—21no—
498#121—21no—
499#121—21no—
500#121—21no—
501#121—21no—
502#120—22no—
503#120—22no—
504#120—22no—
505#120—22no—
506C4×D4—22no—
507C4×D4—22no—
508C4×D4—22no—
509C4×D4—22no—
510C4×D4—22no—
511C4×D4—22no—
512C4×D4—22no—
513C4×D4—22no—
514#117—21no—
515#117—21no—
516#117—21no—
517#117—21no—
518#117—44no—
519C2×C4⋊C4—22no—
520C2×C4⋊C4—22no—
521C2×C4⋊C4—22no—
522C2×C4⋊C4—44no—
523C2×C4⋊C4C2×C4×C15111yescharacteristic, complemented
524C2×C4⋊C4C2×C4×C15111yescharacteristic, complemented
525C2×C4⋊C4C2×C4×C15112yescomplemented
526C2×C4⋊C4C2×C4×C15112yescomplemented
527C2×C22⋊C4—22no—
528C2×C22⋊C4—22no—
529C2×C22⋊C4—22no—
530C2×C22⋊C4—44no—
531C2×C22⋊C4C2×C4×C15112yes—
532C2×C22⋊C4C2×C4×C15112yes—
533C2×C22⋊C4C2×C4×C15112yescomplemented
534C2×C22⋊C4C2×C4×C15112yescomplemented
535C2×C22⋊C4C23×C15114yes—
536C2×C22⋊C4C23×C15114yes—
537C2×C22⋊C4C23×C15112yes—
538C2×C42—22no—
539C2×C42C2×C4×C15112yescomplemented
540#99—48no—
541#95—22no—
542#95—22no—
543#95—22no—
544#95—22no—
545C24—22no—
546C24—22no—
547C24—42no—
548C24—42no—
549C24C22×C4×C15111yescharacteristic
550C24C22×C4×C15111yescharacteristic
551C24C22×C4×C15112yes—
552C24C2×D4×C15111yescharacteristic
553C24C2×D4×C15111yescharacteristic
554C24C2×D4×C15111yescharacteristic
555C24C2×D4×C15111yescharacteristic
556C24C24×C15111yescharacteristic
557#41—44no—
558#41—44no—
559#41—44no—
560#41—44no—
561C2×Q8—21no—
562C2×Q8—21no—
563C2×Q8—42no—
564C2×D4—22no—
565C2×D4—22no—
566C2×D4—22no—
567C2×D4—22no—
568C2×D4—22no—
569C2×D4—22no—
570C2×D4—24no—
571C2×D4—24no—
572C2×D4—21no—
573C2×D4—21no—
574C2×D4—42no—
575C2×D4—44no—
576C2×D4—44no—
577C22×C4—24no—
578C22×C4—24no—
579C22×C4—24no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—24no—
583C22×C4—24no—
584C22×C4—42no—
585C22×C4—42no—
586C22×C4—42no—
587C22×C4—42no—
588C22×C4—42no—
589C22×C4—42no—
590C22×C4—42no—
591C22×C4—42no—
592C22×C4—42no—
593C22×C4—42no—
594C22×C4—42no—
595C22×C4—44no—
596C22×C4—44no—
597C22×C4—44no—
598C22×C4—44no—
599C22×C4C22⋊C4×C15111yescharacteristic
600C22×C4C22⋊C4×C15111yescharacteristic
601C22×C4C22⋊C4×C15111yescharacteristic
602C22×C4C22⋊C4×C15111yescharacteristic
603C22×C4C22⋊C4×C15111yescharacteristic
604C22×C4C22⋊C4×C15111yescharacteristic
605C22×C4C22⋊C4×C15111yescharacteristic
606C22×C4C22⋊C4×C15111yescharacteristic
607C22×C4C22⋊C4×C15111yescharacteristic
608C22×C4C22⋊C4×C15111yescharacteristic
609C22×C4C22⋊C4×C15111yescharacteristic
610C22×C4C22⋊C4×C15111yescharacteristic
611C22×C4C22⋊C4×C15111yescharacteristic
612C22×C4C22⋊C4×C15111yescharacteristic
613C22×C4C22⋊C4×C15111yescharacteristic
614C22×C4C22⋊C4×C15111yescharacteristic
615C22×C4C22×C4×C15112yes—
616C22×C4C22×C4×C15111yescharacteristic
617C22×C4C22×C4×C15111yescharacteristic
618C22×C4C22×C4×C15112yes—
619C22×C4C22×C4×C15112yes—
620C22×C4C22×C4×C15111yescharacteristic
621C22×C4C22×C4×C15111yescharacteristic
622C22×C4C2×D4×C15111yescharacteristic
623C22×C4C2×D4×C15111yescharacteristic
624C22×C4C2×D4×C15111yescharacteristic
625C22×C4C2×D4×C15111yescharacteristic
626C22×C4C2×D4×C15111yescharacteristic
627C22×C4C2×D4×C15111yescharacteristic
628C22×C4C2×D4×C15111yescharacteristic
629C22×C4C2×D4×C15111yescharacteristic
630C4⋊C4—21no—
631C4⋊C4—21no—
632C4⋊C4—21no—
633C4⋊C4—21no—
634C4⋊C4—22no—
635C4⋊C4—22no—
636C4⋊C4—22no—
637C4⋊C4—22no—
638C4⋊C4—44no—
639C4⋊C4—44no—
640C4⋊C4—44no—
641C22⋊C4—22no—
642C22⋊C4—22no—
643C22⋊C4—22no—
644C22⋊C4—22no—
645C22⋊C4—22no—
646C22⋊C4—22no—
647C22⋊C4—22no—
648C22⋊C4—22no—
649C22⋊C4—22no—
650C22⋊C4—22no—
651C22⋊C4—24no—
652C22⋊C4—28no—
653C22⋊C4—24no—
654C22⋊C4—44no—
655C22⋊C4—44no—
656C22⋊C4—44no—
657C42—22no—
658C42—22no—
659C42—44no—
660C23—22no—
661C23—22no—
662C23—21no—
663C23—21no—
664C23—22no—
665C23—22no—
666C23—22no—
667C23—22no—
668C23—22no—
669C23—22no—
670C23—21no—
671C23—21no—
672C23—22no—
673C23—22no—
674C23—22no—
675C23—24no—
676C23—41no—
677C23—41no—
678C23—41no—
679C23—41no—
680C23—41no—
681C23—41no—
682C23—41no—
683C23—41no—
684C23—48no—
685C23—48no—
686C23—42no—
687C23—42no—
688C23C2×C22⋊C4×C15111yescharacteristic
689C23C2×C22⋊C4×C15111yescharacteristic
690C23C2×C22⋊C4×C15111yescharacteristic
691C23C2×C22⋊C4×C15111yescharacteristic
692C23C23×C4×C15111yescharacteristic
693C23C22×D4×C15111yescharacteristic
694C23C22×D4×C15111yescharacteristic
695C23H(5,𝔽2)×C15112yes—
696C232−1+4×C15112yes—
697Q8—42no—
698Q8—42no—
699D4—42no—
700D4—44no—
701D4—44no—
702D4—44no—
703D4—44no—
704D4—42no—
705D4—42no—
706D4—44no—
707D4—42no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—24no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—41no—
731C2×C4—41no—
732C2×C4—41no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—41no—
739C2×C4—44no—
740C2×C4—44no—
741C2×C4—42no—
742C2×C4—42no—
743C2×C4—44no—
744C2×C4—44no—
745C2×C4—44no—
746C2×C4—44no—
747C2×C4—44no—
748C2×C4—44no—
749C2×C4—88no—
750C2×C4#99×C15114yescomplemented
751C2×C4C2×C22⋊C4×C15111yescharacteristic
752C2×C4C2×C22⋊C4×C15111yescharacteristic
753C2×C4C2×C22⋊C4×C15111yescharacteristic
754C2×C4C2×C22⋊C4×C15111yescharacteristic
755C2×C4C2×C22⋊C4×C15111yescharacteristic
756C2×C4C2×C22⋊C4×C15111yescharacteristic
757C2×C4C2×C22⋊C4×C15111yescharacteristic
758C2×C4C2×C22⋊C4×C15111yescharacteristic
759C22—24no—
760C22—24no—
761C22—21no—
762C22—21no—
763C22—21no—
764C22—21no—
765C22—21no—
766C22—21no—
767C22—21no—
768C22—21no—
769C22—21no—
770C22—21no—
771C22—21no—
772C22—21no—
773C22—21no—
774C22—21no—
775C22—21no—
776C22—21no—
777C22—42no—
778C22—42no—
779C22—44no—
780C22—44no—
781C22—44no—
782C22—44no—
783C22—42no—
784C22—42no—
785C22—42no—
786C22—42no—
787C22—42no—
788C22—84no—
789C22C2×#99×C15112yes—
790C22#410×C15112yes—
791C22C22×C22⋊C4×C15111yescharacteristic
792C22#520×C15112yes—
793C22#535×C15111yescharacteristic
794C22#536×C15111yescharacteristic
795C22#537×C15112yes—
796C4—21no—
797C4—21no—
798C4—21no—
799C4—21no—
800C4—21no—
801C4—21no—
802C4—42no—
803C4—42no—
804C4—42no—
805C4—84no—
806C4—84no—
807C4C2×#99×C15112yes—
808C4C2×#99×C15112yes—
809C2—21no—
810C2—22no—
811C2—22no—
812C2—22no—
813C2—21no—
814C2—22no—
815C2—41no—
816C2—41no—
817C2—82no—
818C2#2311×C15111yescharacteristic
819C2C22×#99×C15111yescharacteristic
820C2C2×#410×C15111yescharacteristic
subgroupG/H
center, socleC22×C151C22×C22⋊C4
commutatorC23C23×C4×C151
Frattini, cosocleC24C24×C151
prime radicalC2×#525×C151C2
LCSG ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C151 ◁ C24×C4×C151 ◁ G

Complements

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

NH ≅ G/Ntype
2. #2280×C151C2semidirect
3. C2×#380×C151C2semidirect
4. #1996×C151C2semidirect
5. #1964×C151C2semidirect
6. #1898×C151C2semidirect
7. #1799×C151C2semidirect
8. C22×#41×C151C4semidirect
18. C2×#123×C151C4semidirect
19. C2×C22⋊Q8×C151C4semidirect
21. C2×#121×C151C4semidirect
24. C2×C4×D4×C151C4semidirect
27. C2×#117×C151C4semidirect
49. C22×Q8×C151C2×C4semidirect
52. C22×D4×C151C2×C4semidirect
60. C23×C4×C151C2×C4semidirect
112. C2×C4⋊C4×C151C2×C4semidirect
113. C2×C4⋊C4×C151C2×C4semidirect
114. C2×C4⋊C4×C151C2×C4semidirect
115. C2×C4⋊C4×C151C2×C4semidirect
122. C2×C22⋊C4×C151C2×C4semidirect
123. C2×C22⋊C4×C151C2×C4semidirect
128. C2×C42×C151C2×C4semidirect
339. C2×C4×C151#99semidirect
410. #21874C151direct (N × H)
411. C151#21874direct (N × H)
413. #2280C2×C151semidirect
414. C2×#380C2×C151semidirect
415. #1996C2×C151semidirect
416. #1964C2×C151semidirect
417. #1898C2×C151semidirect
418. #1799C2×C151semidirect
419. C22×#41C4×C151semidirect
429. C2×#123C4×C151semidirect
430. C2×C22⋊Q8C4×C151semidirect
432. C2×#121C4×C151semidirect
435. C2×C4×D4C4×C151semidirect
438. C2×#117C4×C151semidirect
460. C22×Q8C2×C4×C151semidirect
463. C22×D4C2×C4×C151semidirect
471. C23×C4C2×C4×C151semidirect
523. C2×C4⋊C4C2×C4×C151semidirect
524. C2×C4⋊C4C2×C4×C151semidirect
525. C2×C4⋊C4C2×C4×C151semidirect
526. C2×C4⋊C4C2×C4×C151semidirect
533. C2×C22⋊C4C2×C4×C151semidirect
534. C2×C22⋊C4C2×C4×C151semidirect
539. C2×C42C2×C4×C151semidirect
750. C2×C4#99×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#525×C1512
#2280×C1512
C2×#380×C1512
#1996×C1512
#1964×C1512
#1898×C1512
#1799×C1512
#21874151