Finite Group Databasebeta

← C151×#21420 #50326345

Subgroups — C151×#21420 #50326345

Order 38656.

1678 conjugacy classes of subgroups.

The subgroup lattice has 798 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×C4×C22⋊C4×C151C211yesmaximal, characteristic, complemented
4#1996×C151C212yesmaximal, complemented
5#1964×C151C212yesmaximal, complemented
6#1898×C151C214yesmaximal, complemented
7C4×#99×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×C22⋊C4×C151C2212yes—
29C22×C42×C151—21no—
30C2×#99×C151C2218yes—
31#381×C151—21no—
32#380×C151—21no—
33#380×C151C2212yes—
34#379×C151C2212yes—
35C4×C22⋊C4×C151—21no—
36C4×C22⋊C4×C151—21no—
37C4×C22⋊C4×C151—21no—
38C4×C22⋊C4×C151C2212yes—
39C4×C22⋊C4×C151C2212yes—
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×C151C2×C411yescharacteristic, complemented
110C2×C4⋊C4×C151C2×C411yescharacteristic, complemented
111C2×C4⋊C4×C151C2×C412yescomplemented
112C2×C4⋊C4×C151C2×C412yescomplemented
113C2×C22⋊C4×C151—28no—
114C2×C22⋊C4×C151—22no—
115C2×C22⋊C4×C151—22no—
116C2×C22⋊C4×C151—22no—
117C2×C22⋊C4×C151C2×C412yes—
118C2×C22⋊C4×C151C2×C412yes—
119C2×C22⋊C4×C151C2×C412yescomplemented
120C2×C22⋊C4×C151C2×C412yescomplemented
121C2×C22⋊C4×C151C2314yes—
122C2×C22⋊C4×C151C2312yes—
123C2×C22⋊C4×C151C2314yes—
124C2×C42×C151—22no—
125C2×C42×C151—22no—
126C2×C42×C151—22no—
127C2×C42×C151—44no—
128C2×C42×C151C2×C412yescomplemented
129#99×C151—216no—
130#95×C151—22no—
131#95×C151—22no—
132#95×C151—22no—
133#95×C151—22no—
134C24×C151—24no—
135C24×C151—42no—
136C24×C151—42no—
137C24×C151C22×C411yescharacteristic
138C24×C151C22×C411yescharacteristic
139C24×C151C22×C412yes—
140C24×C151C2×D411yescharacteristic
141C24×C151C2×D411yescharacteristic
142C24×C151C2×D411yescharacteristic
143C24×C151C2×D411yescharacteristic
144C24×C151C2411yescharacteristic
145#41×C151—44no—
146#41×C151—44no—
147#41×C151—44no—
148#41×C151—44no—
149C2×Q8×C151—21no—
150C2×Q8×C151—21no—
151C2×Q8×C151—42no—
152C2×D4×C151—22no—
153C2×D4×C151—22no—
154C2×D4×C151—22no—
155C2×D4×C151—22no—
156C2×D4×C151—22no—
157C2×D4×C151—22no—
158C2×D4×C151—28no—
159C2×D4×C151—21no—
160C2×D4×C151—21no—
161C2×D4×C151—42no—
162C2×D4×C151—44no—
163C2×D4×C151—44no—
164C22×C4×C151—24no—
165C22×C4×C151—24no—
166C22×C4×C151—24no—
167C22×C4×C151—28no—
168C22×C4×C151—24no—
169C22×C4×C151—22no—
170C22×C4×C151—22no—
171C22×C4×C151—24no—
172C22×C4×C151—42no—
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—44no—
184C22×C4×C151—44no—
185C22×C4×C151—44no—
186C22×C4×C151C22⋊C411yescharacteristic
187C22×C4×C151C22⋊C411yescharacteristic
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×C412yes—
203C22×C4×C151C22×C411yescharacteristic
204C22×C4×C151C22×C411yescharacteristic
205C22×C4×C151C22×C412yes—
206C22×C4×C151C22×C412yes—
207C22×C4×C151C22×C411yescharacteristic
208C22×C4×C151C22×C411yescharacteristic
209C22×C4×C151C2×D411yescharacteristic
210C22×C4×C151C2×D411yescharacteristic
211C22×C4×C151C2×D411yescharacteristic
212C22×C4×C151C2×D411yescharacteristic
213C22×C4×C151C2×D411yescharacteristic
214C22×C4×C151C2×D411yescharacteristic
215C22×C4×C151C2×D411yescharacteristic
216C22×C4×C151C2×D411yescharacteristic
217C4⋊C4×C151—21no—
218C4⋊C4×C151—21no—
219C4⋊C4×C151—21no—
220C4⋊C4×C151—21no—
221C4⋊C4×C151—22no—
222C4⋊C4×C151—22no—
223C4⋊C4×C151—22no—
224C4⋊C4×C151—22no—
225C4⋊C4×C151—44no—
226C22⋊C4×C151—28no—
227C22⋊C4×C151—22no—
228C22⋊C4×C151—22no—
229C22⋊C4×C151—22no—
230C22⋊C4×C151—22no—
231C22⋊C4×C151—22no—
232C22⋊C4×C151—22no—
233C22⋊C4×C151—24no—
234C22⋊C4×C151—22no—
235C22⋊C4×C151—22no—
236C22⋊C4×C151—22no—
237C22⋊C4×C151—22no—
238C22⋊C4×C151—28no—
239C22⋊C4×C151—44no—
240C22⋊C4×C151—44no—
241C22⋊C4×C151#4118yescomplemented
242C42×C151—22no—
243C42×C151—22no—
244C42×C151—44no—
245C42×C151—44no—
246C42×C151—44no—
247C23×C151—22no—
248C23×C151—22no—
249C23×C151—22no—
250C23×C151—22no—
251C23×C151—22no—
252C23×C151—22no—
253C23×C151—22no—
254C23×C151—22no—
255C23×C151—22no—
256C23×C151—22no—
257C23×C151—22no—
258C23×C151—22no—
259C23×C151—22no—
260C23×C151—24no—
261C23×C151—41no—
262C23×C151—41no—
263C23×C151—41no—
264C23×C151—41no—
265C23×C151—41no—
266C23×C151—41no—
267C23×C151—41no—
268C23×C151—41no—
269C23×C151—416no—
270C23×C151—42no—
271C23×C151—42no—
272C23×C151C2×C22⋊C411yescharacteristic
273C23×C151C2×C22⋊C411yescharacteristic
274C23×C151C2×C22⋊C411yescharacteristic
275C23×C151C2×C22⋊C411yescharacteristic
276C23×C151C23×C411yescharacteristic
277C23×C151C22×D411yescharacteristic
278C23×C151C22×D411yescharacteristic
279C23×C151C2×#4114yes—
280Q8×C151—42no—
281Q8×C151—42no—
282D4×C151—42no—
283D4×C151—44no—
284D4×C151—44no—
285D4×C151—44no—
286D4×C151—44no—
287D4×C151—44no—
288D4×C151—44no—
289D4×C151—42no—
290C2×C4×C151—22no—
291C2×C4×C151—22no—
292C2×C4×C151—22no—
293C2×C4×C151—22no—
294C2×C4×C151—22no—
295C2×C4×C151—22no—
296C2×C4×C151—22no—
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—24no—
309C2×C4×C151—28no—
310C2×C4×C151—41no—
311C2×C4×C151—41no—
312C2×C4×C151—41no—
313C2×C4×C151—41no—
314C2×C4×C151—41no—
315C2×C4×C151—41no—
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—44no—
323C2×C4×C151—44no—
324C2×C4×C151—416no—
325C2×C4×C151—44no—
326C2×C4×C151—44no—
327C2×C4×C151—42no—
328C2×C4×C151—42no—
329C2×C4×C151—44no—
330C2×C4×C151—44no—
331C2×C4×C151—44no—
332C2×C4×C151#9914yescomplemented
333C2×C4×C151C2×C22⋊C411yescharacteristic
334C2×C4×C151C2×C22⋊C411yescharacteristic
335C2×C4×C151C2×C22⋊C411yescharacteristic
336C2×C4×C151C2×C22⋊C411yescharacteristic
337C2×C4×C151C2×C22⋊C411yescharacteristic
338C2×C4×C151C2×C22⋊C411yescharacteristic
339C2×C4×C151C2×C22⋊C411yescharacteristic
340C2×C4×C151C2×C22⋊C411yescharacteristic
341C22×C151—28no—
342C22×C151—21no—
343C22×C151—21no—
344C22×C151—21no—
345C22×C151—21no—
346C22×C151—21no—
347C22×C151—21no—
348C22×C151—21no—
349C22×C151—21no—
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—44no—
359C22×C151—44no—
360C22×C151—44no—
361C22×C151—44no—
362C22×C151—44no—
363C22×C151—44no—
364C22×C151—42no—
365C22×C151—42no—
366C22×C151—42no—
367C22×C151—84no—
368C22×C151C2×#9912yes—
369C22×C151#41012yes—
370C22×C151C22×C22⋊C411yescharacteristic
371C22×C151C4×#4112yes—
372C22×C151#52512yes—
373C22×C151#53212yes—
374C4×C151—21no—
375C4×C151—21no—
376C4×C151—21no—
377C4×C151—21no—
378C4×C151—21no—
379C4×C151—21no—
380C4×C151—48no—
381C4×C151—42no—
382C4×C151—42no—
383C4×C151—42no—
384C4×C151—84no—
385C4×C151C2×#9912yes—
386C4×C151C2×#9912yes—
387C2×C151—22no—
388C2×C151—22no—
389C2×C151—22no—
390C2×C151—22no—
391C2×C151—22no—
392C2×C151—41no—
393C2×C151—41no—
394C2×C151—82no—
395C2×C151#229711yescharacteristic
396C2×C151C22×#9911yescharacteristic
397C2×C151C2×#41011yescharacteristic
398#21420C15111yesmaximal, characteristic, direct product factor, Sylow
399C151#2142011yescharacteristic, direct product factor, Sylow
400C2×#525C2×C15111yescharacteristic
401#2280C2×C15111yescharacteristic, complemented
402C2×C4×C22⋊C4C2×C15111yescharacteristic, complemented
403#1996C2×C15112yescomplemented
404#1964C2×C15112yescomplemented
405#1898C2×C15114yescomplemented
406C4×#99C2×C15114yescomplemented
407C22×#41C4×C15111yescharacteristic, complemented
408C24×C4C22×C15111yescharacteristic
409#525—21no—
410#525—21no—
411#525—21no—
412#525—21no—
413#525—21no—
414#525—21no—
415#525—21no—
416#525—21no—
417C2×#123C4×C15112yescomplemented
418C2×C22⋊Q8C4×C15111yescharacteristic, complemented
419C2×C22⋊Q8C22×C15111yescharacteristic
420C2×#121C4×C15111yescharacteristic, complemented
421C2×#121C22×C15111yescharacteristic
422C2×#120C22×C15112yes—
423C2×C4×D4C4×C15112yescomplemented
424C2×C4×D4C22×C15112yes—
425C2×#117—21no—
426C2×#117C4×C15111yescharacteristic, complemented
427C22×C22⋊C4C22×C15112yes—
428C22×C42—21no—
429C2×#99C22×C15118yes—
430#381—21no—
431#380—21no—
432#380C22×C15112yes—
433#379C22×C15112yes—
434C4×C22⋊C4—21no—
435C4×C22⋊C4—21no—
436C4×C22⋊C4—21no—
437C4×C22⋊C4C22×C15112yes—
438C4×C22⋊C4C22×C15112yes—
439C4×C22⋊C4C22×C15112yes—
440C2×#95—21no—
441#342C22×C15118yes—
442C25C23×C15111yescharacteristic
443C2×#41—21no—
444C2×#41—21no—
445C2×#41—21no—
446C2×#41—21no—
447C2×#41—44no—
448C22×Q8C2×C4×C15111yescharacteristic, complemented
449C22×D4C2×C4×C15112yes—
450C22×D4C2×C4×C15112yes—
451C22×D4C2×C4×C15111yescharacteristic, complemented
452C22×D4C23×C15112yes—
453C23×C4—22no—
454C23×C4—44no—
455C23×C4C2×C4×C15111yescharacteristic
456C23×C4C2×C4×C15111yescharacteristic
457C23×C4C2×C4×C15111yescharacteristic
458C23×C4C2×C4×C15111yescharacteristic
459C23×C4C2×C4×C15112yescomplemented
460C23×C4D4×C15111yescharacteristic
461C23×C4D4×C15111yescharacteristic
462C23×C4D4×C15111yescharacteristic
463C23×C4D4×C15111yescharacteristic
464C23×C4D4×C15111yescharacteristic
465C23×C4D4×C15111yescharacteristic
466C23×C4D4×C15111yescharacteristic
467C23×C4D4×C15111yescharacteristic
468C23×C4C23×C15111yescharacteristic
469C23×C4C23×C15111yescharacteristic
470#123—22no—
471#123—22no—
472#123—22no—
473#123—22no—
474C22⋊Q8—21no—
475C22⋊Q8—21no—
476C22⋊Q8—21no—
477C22⋊Q8—21no—
478C22⋊Q8—21no—
479C22⋊Q8—21no—
480C22⋊Q8—21no—
481C22⋊Q8—21no—
482#121—21no—
483#121—21no—
484#121—21no—
485#121—21no—
486#121—21no—
487#121—21no—
488#121—21no—
489#121—21no—
490#120—22no—
491#120—22no—
492#120—22no—
493#120—22no—
494C4×D4—22no—
495C4×D4—22no—
496C4×D4—22no—
497C4×D4—22no—
498C4×D4—22no—
499C4×D4—22no—
500C4×D4—22no—
501C4×D4—22no—
502#117—21no—
503#117—21no—
504#117—21no—
505#117—21no—
506#117—44no—
507C2×C4⋊C4—22no—
508C2×C4⋊C4C2×C4×C15111yescharacteristic, complemented
509C2×C4⋊C4C2×C4×C15111yescharacteristic, complemented
510C2×C4⋊C4C2×C4×C15112yescomplemented
511C2×C4⋊C4C2×C4×C15112yescomplemented
512C2×C22⋊C4—22no—
513C2×C22⋊C4—28no—
514C2×C22⋊C4—22no—
515C2×C22⋊C4—22no—
516C2×C22⋊C4C2×C4×C15112yes—
517C2×C22⋊C4C2×C4×C15112yes—
518C2×C22⋊C4C2×C4×C15112yescomplemented
519C2×C22⋊C4C2×C4×C15112yescomplemented
520C2×C22⋊C4C23×C15114yes—
521C2×C22⋊C4C23×C15112yes—
522C2×C22⋊C4C23×C15114yes—
523C2×C42—22no—
524C2×C42—22no—
525C2×C42—22no—
526C2×C42—44no—
527C2×C42C2×C4×C15112yescomplemented
528#99—216no—
529#95—22no—
530#95—22no—
531#95—22no—
532#95—22no—
533C24—24no—
534C24—42no—
535C24—42no—
536C24C22×C4×C15111yescharacteristic
537C24C22×C4×C15111yescharacteristic
538C24C22×C4×C15112yes—
539C24C2×D4×C15111yescharacteristic
540C24C2×D4×C15111yescharacteristic
541C24C2×D4×C15111yescharacteristic
542C24C2×D4×C15111yescharacteristic
543C24C24×C15111yescharacteristic
544#41—44no—
545#41—44no—
546#41—44no—
547#41—44no—
548C2×Q8—21no—
549C2×Q8—21no—
550C2×Q8—42no—
551C2×D4—22no—
552C2×D4—22no—
553C2×D4—22no—
554C2×D4—22no—
555C2×D4—22no—
556C2×D4—22no—
557C2×D4—28no—
558C2×D4—21no—
559C2×D4—21no—
560C2×D4—42no—
561C2×D4—44no—
562C2×D4—44no—
563C22×C4—24no—
564C22×C4—24no—
565C22×C4—24no—
566C22×C4—28no—
567C22×C4—24no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—24no—
571C22×C4—42no—
572C22×C4—42no—
573C22×C4—42no—
574C22×C4—42no—
575C22×C4—42no—
576C22×C4—42no—
577C22×C4—42no—
578C22×C4—42no—
579C22×C4—42no—
580C22×C4—42no—
581C22×C4—42no—
582C22×C4—44no—
583C22×C4—44no—
584C22×C4—44no—
585C22×C4C22⋊C4×C15111yescharacteristic
586C22×C4C22⋊C4×C15111yescharacteristic
587C22×C4C22⋊C4×C15111yescharacteristic
588C22×C4C22⋊C4×C15111yescharacteristic
589C22×C4C22⋊C4×C15111yescharacteristic
590C22×C4C22⋊C4×C15111yescharacteristic
591C22×C4C22⋊C4×C15111yescharacteristic
592C22×C4C22⋊C4×C15111yescharacteristic
593C22×C4C22⋊C4×C15111yescharacteristic
594C22×C4C22⋊C4×C15111yescharacteristic
595C22×C4C22⋊C4×C15111yescharacteristic
596C22×C4C22⋊C4×C15111yescharacteristic
597C22×C4C22⋊C4×C15111yescharacteristic
598C22×C4C22⋊C4×C15111yescharacteristic
599C22×C4C22⋊C4×C15111yescharacteristic
600C22×C4C22⋊C4×C15111yescharacteristic
601C22×C4C22×C4×C15112yes—
602C22×C4C22×C4×C15111yescharacteristic
603C22×C4C22×C4×C15111yescharacteristic
604C22×C4C22×C4×C15112yes—
605C22×C4C22×C4×C15112yes—
606C22×C4C22×C4×C15111yescharacteristic
607C22×C4C22×C4×C15111yescharacteristic
608C22×C4C2×D4×C15111yescharacteristic
609C22×C4C2×D4×C15111yescharacteristic
610C22×C4C2×D4×C15111yescharacteristic
611C22×C4C2×D4×C15111yescharacteristic
612C22×C4C2×D4×C15111yescharacteristic
613C22×C4C2×D4×C15111yescharacteristic
614C22×C4C2×D4×C15111yescharacteristic
615C22×C4C2×D4×C15111yescharacteristic
616C4⋊C4—21no—
617C4⋊C4—21no—
618C4⋊C4—21no—
619C4⋊C4—21no—
620C4⋊C4—22no—
621C4⋊C4—22no—
622C4⋊C4—22no—
623C4⋊C4—22no—
624C4⋊C4—44no—
625C22⋊C4—28no—
626C22⋊C4—22no—
627C22⋊C4—22no—
628C22⋊C4—22no—
629C22⋊C4—22no—
630C22⋊C4—22no—
631C22⋊C4—22no—
632C22⋊C4—24no—
633C22⋊C4—22no—
634C22⋊C4—22no—
635C22⋊C4—22no—
636C22⋊C4—22no—
637C22⋊C4—28no—
638C22⋊C4—44no—
639C22⋊C4—44no—
640C22⋊C4#41×C15118yescomplemented
641C42—22no—
642C42—22no—
643C42—44no—
644C42—44no—
645C42—44no—
646C23—22no—
647C23—22no—
648C23—22no—
649C23—22no—
650C23—22no—
651C23—22no—
652C23—22no—
653C23—22no—
654C23—22no—
655C23—22no—
656C23—22no—
657C23—22no—
658C23—22no—
659C23—24no—
660C23—41no—
661C23—41no—
662C23—41no—
663C23—41no—
664C23—41no—
665C23—41no—
666C23—41no—
667C23—41no—
668C23—416no—
669C23—42no—
670C23—42no—
671C23C2×C22⋊C4×C15111yescharacteristic
672C23C2×C22⋊C4×C15111yescharacteristic
673C23C2×C22⋊C4×C15111yescharacteristic
674C23C2×C22⋊C4×C15111yescharacteristic
675C23C23×C4×C15111yescharacteristic
676C23C22×D4×C15111yescharacteristic
677C23C22×D4×C15111yescharacteristic
678C23C2×#41×C15114yes—
679Q8—42no—
680Q8—42no—
681D4—42no—
682D4—44no—
683D4—44no—
684D4—44no—
685D4—44no—
686D4—44no—
687D4—44no—
688D4—42no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—24no—
708C2×C4—28no—
709C2×C4—41no—
710C2×C4—41no—
711C2×C4—41no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—44no—
722C2×C4—44no—
723C2×C4—416no—
724C2×C4—44no—
725C2×C4—44no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—44no—
729C2×C4—44no—
730C2×C4—44no—
731C2×C4#99×C15114yescomplemented
732C2×C4C2×C22⋊C4×C15111yescharacteristic
733C2×C4C2×C22⋊C4×C15111yescharacteristic
734C2×C4C2×C22⋊C4×C15111yescharacteristic
735C2×C4C2×C22⋊C4×C15111yescharacteristic
736C2×C4C2×C22⋊C4×C15111yescharacteristic
737C2×C4C2×C22⋊C4×C15111yescharacteristic
738C2×C4C2×C22⋊C4×C15111yescharacteristic
739C2×C4C2×C22⋊C4×C15111yescharacteristic
740C22—28no—
741C22—21no—
742C22—21no—
743C22—21no—
744C22—21no—
745C22—21no—
746C22—21no—
747C22—21no—
748C22—21no—
749C22—21no—
750C22—21no—
751C22—21no—
752C22—21no—
753C22—21no—
754C22—21no—
755C22—21no—
756C22—21no—
757C22—44no—
758C22—44no—
759C22—44no—
760C22—44no—
761C22—44no—
762C22—44no—
763C22—42no—
764C22—42no—
765C22—42no—
766C22—84no—
767C22C2×#99×C15112yes—
768C22#410×C15112yes—
769C22C22×C22⋊C4×C15111yescharacteristic
770C22C4×#41×C15112yes—
771C22#525×C15112yes—
772C22#532×C15112yes—
773C4—21no—
774C4—21no—
775C4—21no—
776C4—21no—
777C4—21no—
778C4—21no—
779C4—48no—
780C4—42no—
781C4—42no—
782C4—42no—
783C4—84no—
784C4C2×#99×C15112yes—
785C4C2×#99×C15112yes—
786C2—22no—
787C2—22no—
788C2—22no—
789C2—22no—
790C2—22no—
791C2—41no—
792C2—41no—
793C2—82no—
794C2#2297×C15111yescharacteristic
795C2C22×#99×C15111yescharacteristic
796C2C2×#410×C15111yescharacteristic
subgroupG/H
centerC2×C4×C151C2×C22⋊C4
commutatorC23C23×C4×C151
Frattini, cosocleC24C24×C151
socleC22×C151C22×C22⋊C4
prime radicalC2×#525×C151C2
LCSG ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C151 ◁ C24×C4×C151 ◁ G

Complements

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

NH ≅ G/Ntype
2. #2280×C151C2semidirect
3. C2×C4×C22⋊C4×C151C2semidirect
4. #1996×C151C2semidirect
5. #1964×C151C2semidirect
6. #1898×C151C2semidirect
7. C4×#99×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
109. C2×C4⋊C4×C151C2×C4semidirect
110. C2×C4⋊C4×C151C2×C4semidirect
111. C2×C4⋊C4×C151C2×C4semidirect
112. C2×C4⋊C4×C151C2×C4semidirect
119. C2×C22⋊C4×C151C2×C4semidirect
120. C2×C22⋊C4×C151C2×C4semidirect
128. C2×C42×C151C2×C4semidirect
241. C22⋊C4×C151#41semidirect
332. C2×C4×C151#99semidirect
398. #21420C151direct (N × H)
399. C151#21420direct (N × H)
401. #2280C2×C151semidirect
402. C2×C4×C22⋊C4C2×C151semidirect
403. #1996C2×C151semidirect
404. #1964C2×C151semidirect
405. #1898C2×C151semidirect
406. C4×#99C2×C151semidirect
407. C22×#41C4×C151semidirect
417. C2×#123C4×C151semidirect
418. C2×C22⋊Q8C4×C151semidirect
420. C2×#121C4×C151semidirect
423. C2×C4×D4C4×C151semidirect
426. C2×#117C4×C151semidirect
448. C22×Q8C2×C4×C151semidirect
451. C22×D4C2×C4×C151semidirect
459. C23×C4C2×C4×C151semidirect
508. C2×C4⋊C4C2×C4×C151semidirect
509. C2×C4⋊C4C2×C4×C151semidirect
510. C2×C4⋊C4C2×C4×C151semidirect
511. C2×C4⋊C4C2×C4×C151semidirect
518. C2×C22⋊C4C2×C4×C151semidirect
519. C2×C22⋊C4C2×C4×C151semidirect
527. C2×C42C2×C4×C151semidirect
640. C22⋊C4#41×C151semidirect
731. 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×C4×C22⋊C4×C1512
#1996×C1512
#1964×C1512
#1898×C1512
C4×#99×C1512
#21420151