Finite Group Databasebeta

← C151×#17400 #50322325

Subgroups — C151×#17400 #50322325

Order 38656.

1406 conjugacy classes of subgroups.

The subgroup lattice has 766 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#525×C151C211yesmaximal, characteristic
2C2×#407×C151C211yesmaximal, characteristic, complemented
3C2×#407×C151C211yesmaximal, characteristic, complemented
4#1472×C151C212yesmaximal, complemented
5#1471×C151C212yesmaximal, complemented
6#1468×C151C214yesmaximal, complemented
7#1465×C151C214yesmaximal, complemented
8C22×#41×C151C411yescharacteristic
9C24×C4×C151C2211yescharacteristic
10C22×M16×C151—21no—
11C22×M16×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—
18#525×C151—21no—
19#525×C151—21no—
20C2×#123×C151C2212yes—
21C2×C22⋊Q8×C151C411yescharacteristic
22C2×C22⋊Q8×C151C2211yescharacteristic
23C2×#121×C151C411yescharacteristic
24C2×#121×C151C2211yescharacteristic
25C2×#120×C151C412yes—
26C2×C4×D4×C151C412yes—
27C2×C4×D4×C151C2212yes—
28C2×#117×C151C411yescharacteristic
29#407×C151—21no—
30#407×C151—21no—
31#407×C151—21no—
32#407×C151—21no—
33#407×C151C2212yes—
34#407×C151C2212yes—
35#407×C151C2212yes—
36#407×C151C2212yes—
37C2×C22⋊C8×C151—21no—
38C2×C22⋊C8×C151—21no—
39C2×C22⋊C8×C151C2212yes—
40C2×C22⋊C8×C151C2212yes—
41#324×C151C2218yescomplemented
42#323×C151C2218yescomplemented
43C25×C151C2×C411yescharacteristic
44C2×#41×C151—21no—
45C2×#41×C151—21no—
46C2×#41×C151—21no—
47C2×#41×C151—21no—
48C2×#41×C151—44no—
49C22×Q8×C151C2×C411yescharacteristic
50C22×D4×C151C2×C412yes—
51C22×D4×C151C2×C412yes—
52C22×D4×C151C2×C412yes—
53C22×D4×C151C2×C411yescharacteristic
54C23×C4×C151—44no—
55C23×C4×C151C2×C411yescharacteristic
56C23×C4×C151C2×C412yes—
57C23×C4×C151C2×C411yescharacteristic
58C23×C4×C151C2×C411yescharacteristic
59C23×C4×C151D411yescharacteristic
60C23×C4×C151D411yescharacteristic
61C23×C4×C151D411yescharacteristic
62C23×C4×C151D411yescharacteristic
63C23×C4×C151D411yescharacteristic
64C23×C4×C151D411yescharacteristic
65C23×C4×C151D411yescharacteristic
66C23×C4×C151D411yescharacteristic
67C23×C4×C151C2311yescharacteristic
68C23×C4×C151C2311yescharacteristic
69C23×C4×C151C2311yescharacteristic
70C2×M16×C151—22no—
71C2×M16×C151—22no—
72C2×M16×C151—22no—
73C2×M16×C151—22no—
74C2×M16×C151—44no—
75C2×M16×C151—44no—
76C22×C8×C151—22no—
77C22×C8×C151—22no—
78#123×C151—22no—
79#123×C151—22no—
80#123×C151—22no—
81#123×C151—22no—
82C22⋊Q8×C151—21no—
83C22⋊Q8×C151—21no—
84C22⋊Q8×C151—21no—
85C22⋊Q8×C151—21no—
86C22⋊Q8×C151—21no—
87C22⋊Q8×C151—21no—
88C22⋊Q8×C151—21no—
89C22⋊Q8×C151—21no—
90#121×C151—21no—
91#121×C151—21no—
92#121×C151—21no—
93#121×C151—21no—
94#121×C151—21no—
95#121×C151—21no—
96#121×C151—21no—
97#121×C151—21no—
98#120×C151—22no—
99#120×C151—22no—
100#120×C151—22no—
101#120×C151—22no—
102C4×D4×C151—22no—
103C4×D4×C151—22no—
104C4×D4×C151—22no—
105C4×D4×C151—22no—
106C4×D4×C151—22no—
107C4×D4×C151—22no—
108C4×D4×C151—22no—
109C4×D4×C151—22no—
110#117×C151—21no—
111#117×C151—21no—
112#117×C151—21no—
113#117×C151—21no—
114C2×C4⋊C4×C151C2×C411yescharacteristic
115C2×C4⋊C4×C151C2×C411yescharacteristic
116C2×C4⋊C4×C151C2×C412yes—
117C2×C4⋊C4×C151C2312yes—
118C2×C22⋊C4×C151C2×C412yes—
119C2×C22⋊C4×C151C2×C412yes—
120C2×C22⋊C4×C151C2×C412yes—
121C2×C22⋊C4×C151C2×C412yes—
122C2×C22⋊C4×C151C2312yes—
123C2×C42×C151C2×C412yes—
124C22⋊C8×C151—22no—
125C22⋊C8×C151—22no—
126C22⋊C8×C151—22no—
127C22⋊C8×C151—22no—
128C22⋊C8×C151—22no—
129C22⋊C8×C151—22no—
130C22⋊C8×C151C2314yes—
131C22⋊C8×C151C2314yes—
132C24×C151—42no—
133C24×C151—42no—
134C24×C151—42no—
135C24×C151C22⋊C411yescharacteristic
136C24×C151C22⋊C411yescharacteristic
137C24×C151C22⋊C411yescharacteristic
138C24×C151C22⋊C411yescharacteristic
139C24×C151C22×C411yescharacteristic
140C24×C151C22×C411yescharacteristic
141C24×C151C22×C412yes—
142C24×C151C22×C411yescharacteristic
143#41×C151—44no—
144#41×C151—44no—
145#41×C151—44no—
146#41×C151—44no—
147C2×Q8×C151—21no—
148C2×Q8×C151—21no—
149C2×Q8×C151—42no—
150C2×D4×C151—22no—
151C2×D4×C151—22no—
152C2×D4×C151—22no—
153C2×D4×C151—22no—
154C2×D4×C151—22no—
155C2×D4×C151—22no—
156C2×D4×C151—21no—
157C2×D4×C151—21no—
158C2×D4×C151—44no—
159C2×D4×C151—42no—
160C2×D4×C151—44no—
161C2×D4×C151—44no—
162C22×C4×C151—24no—
163C22×C4×C151—24no—
164C22×C4×C151—24no—
165C22×C4×C151—22no—
166C22×C4×C151—22no—
167C22×C4×C151—42no—
168C22×C4×C151—42no—
169C22×C4×C151—42no—
170C22×C4×C151—42no—
171C22×C4×C151—42no—
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—44no—
179C22×C4×C151C22⋊C411yescharacteristic
180C22×C4×C151C22⋊C411yescharacteristic
181C22×C4×C151C22⋊C411yescharacteristic
182C22×C4×C151C22⋊C411yescharacteristic
183C22×C4×C151C22⋊C411yescharacteristic
184C22×C4×C151C22⋊C411yescharacteristic
185C22×C4×C151C22⋊C411yescharacteristic
186C22×C4×C151C22⋊C411yescharacteristic
187C22×C4×C151C22⋊C411yescharacteristic
188C22×C4×C151C22⋊C411yescharacteristic
189C22×C4×C151C22⋊C411yescharacteristic
190C22×C4×C151C22⋊C411yescharacteristic
191C22×C4×C151C22×C412yes—
192C22×C4×C151C22×C411yescharacteristic
193C22×C4×C151C22×C411yescharacteristic
194C22×C4×C151C22×C412yes—
195C22×C4×C151C22×C412yes—
196C22×C4×C151C22×C411yescharacteristic
197C22×C4×C151C2×D411yescharacteristic
198C22×C4×C151C2×D411yescharacteristic
199C22×C4×C151C2×D411yescharacteristic
200C22×C4×C151C2×D411yescharacteristic
201C22×C4×C151C2×D411yescharacteristic
202C22×C4×C151C2×D411yescharacteristic
203C22×C4×C151C2×D411yescharacteristic
204C22×C4×C151C2×D411yescharacteristic
205C22×C4×C151C2×D411yescharacteristic
206C22×C4×C151C2×D411yescharacteristic
207C22×C4×C151C2×D411yescharacteristic
208C22×C4×C151C2×D411yescharacteristic
209C22×C4×C151C2411yescharacteristic
210M16×C151—44no—
211M16×C151—44no—
212M16×C151—44no—
213M16×C151—44no—
214C2×C8×C151—24no—
215C2×C8×C151—24no—
216C2×C8×C151—44no—
217C2×C8×C151—44no—
218C4⋊C4×C151—21no—
219C4⋊C4×C151—21no—
220C4⋊C4×C151—21no—
221C4⋊C4×C151—21no—
222C4⋊C4×C151—22no—
223C4⋊C4×C151—22no—
224C4⋊C4×C151—22no—
225C4⋊C4×C151—22no—
226C22⋊C4×C151—22no—
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—22no—
234C22⋊C4×C151—22no—
235C22⋊C4×C151—22no—
236C42×C151—22no—
237C42×C151—22no—
238C23×C151—22no—
239C23×C151—22no—
240C23×C151—22no—
241C23×C151—22no—
242C23×C151—22no—
243C23×C151—22no—
244C23×C151—22no—
245C23×C151—22no—
246C23×C151—22no—
247C23×C151—22no—
248C23×C151—24no—
249C23×C151—41no—
250C23×C151—41no—
251C23×C151—41no—
252C23×C151—41no—
253C23×C151—41no—
254C23×C151—41no—
255C23×C151—41no—
256C23×C151—41no—
257C23×C151—41no—
258C23×C151—41no—
259C23×C151—41no—
260C23×C151—41no—
261C23×C151—42no—
262C23×C151—42no—
263C23×C151—416no—
264C23×C151C2×C22⋊C411yescharacteristic
265C23×C151C2×C22⋊C411yescharacteristic
266C23×C151C2×C22⋊C411yescharacteristic
267C23×C151C2×C22⋊C411yescharacteristic
268C23×C151C2×C22⋊C411yescharacteristic
269C23×C151C2×C22⋊C411yescharacteristic
270C23×C151C23×C411yescharacteristic
271Q8×C151—42no—
272Q8×C151—42no—
273D4×C151—42no—
274D4×C151—44no—
275D4×C151—44no—
276D4×C151—44no—
277D4×C151—44no—
278D4×C151—44no—
279D4×C151—44no—
280D4×C151—42no—
281C2×C4×C151—22no—
282C2×C4×C151—22no—
283C2×C4×C151—22no—
284C2×C4×C151—22no—
285C2×C4×C151—22no—
286C2×C4×C151—22no—
287C2×C4×C151—22no—
288C2×C4×C151—22no—
289C2×C4×C151—22no—
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—24no—
300C2×C4×C151—41no—
301C2×C4×C151—41no—
302C2×C4×C151—41no—
303C2×C4×C151—41no—
304C2×C4×C151—41no—
305C2×C4×C151—41no—
306C2×C4×C151—41no—
307C2×C4×C151—41no—
308C2×C4×C151—41no—
309C2×C4×C151—41no—
310C2×C4×C151—41no—
311C2×C4×C151—41no—
312C2×C4×C151—44no—
313C2×C4×C151—44no—
314C2×C4×C151—42no—
315C2×C4×C151—42no—
316C2×C4×C151#9914yes—
317C2×C4×C151C2×C22⋊C411yescharacteristic
318C2×C4×C151C2×C22⋊C411yescharacteristic
319C2×C4×C151C2×C22⋊C411yescharacteristic
320C2×C4×C151C2×C22⋊C411yescharacteristic
321C2×C4×C151C2×C22⋊C411yescharacteristic
322C2×C4×C151C2×C22⋊C411yescharacteristic
323C2×C4×C151C22×D411yescharacteristic
324C2×C4×C151C22×D411yescharacteristic
325C8×C151—44no—
326C8×C151—44no—
327C22×C151—21no—
328C22×C151—21no—
329C22×C151—21no—
330C22×C151—21no—
331C22×C151—21no—
332C22×C151—21no—
333C22×C151—21no—
334C22×C151—21no—
335C22×C151—21no—
336C22×C151—21no—
337C22×C151—21no—
338C22×C151—21no—
339C22×C151—21no—
340C22×C151—21no—
341C22×C151—21no—
342C22×C151—21no—
343C22×C151—21no—
344C22×C151—21no—
345C22×C151—44no—
346C22×C151—44no—
347C22×C151—44no—
348C22×C151—44no—
349C22×C151—44no—
350C22×C151—44no—
351C22×C151—44no—
352C22×C151—42no—
353C22×C151—42no—
354C22×C151—42no—
355C22×C151—84no—
356C22×C151C2×#9912yes—
357C22×C151#41312yes—
358C22×C151C22×C22⋊C411yescharacteristic
359C22×C151#56812yes—
360C4×C151—21no—
361C4×C151—21no—
362C4×C151—21no—
363C4×C151—21no—
364C4×C151—21no—
365C4×C151—21no—
366C4×C151—42no—
367C4×C151—42no—
368C4×C151—42no—
369C4×C151C2×#9912yes—
370C4×C151C2×#9912yes—
371C2×C151—22no—
372C2×C151—22no—
373C2×C151—22no—
374C2×C151—41no—
375C2×C151—41no—
376C2×C151—41no—
377C2×C151—41no—
378C2×C151—82no—
379C2×C151#287911yescharacteristic
380C2×C151C22×#9911yescharacteristic
381C2×C151C2×#41311yescharacteristic
382#17400C15111yesmaximal, characteristic, direct product factor, Sylow
383C151#1740011yescharacteristic, direct product factor, Sylow
384C2×#525C2×C15111yescharacteristic
385C2×#407C2×C15111yescharacteristic, complemented
386C2×#407C2×C15111yescharacteristic, complemented
387#1472C2×C15112yescomplemented
388#1471C2×C15112yescomplemented
389#1468C2×C15114yescomplemented
390#1465C2×C15114yescomplemented
391C22×#41C4×C15111yescharacteristic
392C24×C4C22×C15111yescharacteristic
393C22×M16—21no—
394C22×M16—21no—
395#525—21no—
396#525—21no—
397#525—21no—
398#525—21no—
399#525—21no—
400#525—21no—
401#525—21no—
402#525—21no—
403C2×#123C22×C15112yes—
404C2×C22⋊Q8C4×C15111yescharacteristic
405C2×C22⋊Q8C22×C15111yescharacteristic
406C2×#121C4×C15111yescharacteristic
407C2×#121C22×C15111yescharacteristic
408C2×#120C4×C15112yes—
409C2×C4×D4C4×C15112yes—
410C2×C4×D4C22×C15112yes—
411C2×#117C4×C15111yescharacteristic
412#407—21no—
413#407—21no—
414#407—21no—
415#407—21no—
416#407C22×C15112yes—
417#407C22×C15112yes—
418#407C22×C15112yes—
419#407C22×C15112yes—
420C2×C22⋊C8—21no—
421C2×C22⋊C8—21no—
422C2×C22⋊C8C22×C15112yes—
423C2×C22⋊C8C22×C15112yes—
424#324C22×C15118yescomplemented
425#323C22×C15118yescomplemented
426C25C2×C4×C15111yescharacteristic
427C2×#41—21no—
428C2×#41—21no—
429C2×#41—21no—
430C2×#41—21no—
431C2×#41—44no—
432C22×Q8C2×C4×C15111yescharacteristic
433C22×D4C2×C4×C15112yes—
434C22×D4C2×C4×C15112yes—
435C22×D4C2×C4×C15112yes—
436C22×D4C2×C4×C15111yescharacteristic
437C23×C4—44no—
438C23×C4C2×C4×C15111yescharacteristic
439C23×C4C2×C4×C15112yes—
440C23×C4C2×C4×C15111yescharacteristic
441C23×C4C2×C4×C15111yescharacteristic
442C23×C4D4×C15111yescharacteristic
443C23×C4D4×C15111yescharacteristic
444C23×C4D4×C15111yescharacteristic
445C23×C4D4×C15111yescharacteristic
446C23×C4D4×C15111yescharacteristic
447C23×C4D4×C15111yescharacteristic
448C23×C4D4×C15111yescharacteristic
449C23×C4D4×C15111yescharacteristic
450C23×C4C23×C15111yescharacteristic
451C23×C4C23×C15111yescharacteristic
452C23×C4C23×C15111yescharacteristic
453C2×M16—22no—
454C2×M16—22no—
455C2×M16—22no—
456C2×M16—22no—
457C2×M16—44no—
458C2×M16—44no—
459C22×C8—22no—
460C22×C8—22no—
461#123—22no—
462#123—22no—
463#123—22no—
464#123—22no—
465C22⋊Q8—21no—
466C22⋊Q8—21no—
467C22⋊Q8—21no—
468C22⋊Q8—21no—
469C22⋊Q8—21no—
470C22⋊Q8—21no—
471C22⋊Q8—21no—
472C22⋊Q8—21no—
473#121—21no—
474#121—21no—
475#121—21no—
476#121—21no—
477#121—21no—
478#121—21no—
479#121—21no—
480#121—21no—
481#120—22no—
482#120—22no—
483#120—22no—
484#120—22no—
485C4×D4—22no—
486C4×D4—22no—
487C4×D4—22no—
488C4×D4—22no—
489C4×D4—22no—
490C4×D4—22no—
491C4×D4—22no—
492C4×D4—22no—
493#117—21no—
494#117—21no—
495#117—21no—
496#117—21no—
497C2×C4⋊C4C2×C4×C15111yescharacteristic
498C2×C4⋊C4C2×C4×C15111yescharacteristic
499C2×C4⋊C4C2×C4×C15112yes—
500C2×C4⋊C4C23×C15112yes—
501C2×C22⋊C4C2×C4×C15112yes—
502C2×C22⋊C4C2×C4×C15112yes—
503C2×C22⋊C4C2×C4×C15112yes—
504C2×C22⋊C4C2×C4×C15112yes—
505C2×C22⋊C4C23×C15112yes—
506C2×C42C2×C4×C15112yes—
507C22⋊C8—22no—
508C22⋊C8—22no—
509C22⋊C8—22no—
510C22⋊C8—22no—
511C22⋊C8—22no—
512C22⋊C8—22no—
513C22⋊C8C23×C15114yes—
514C22⋊C8C23×C15114yes—
515C24—42no—
516C24—42no—
517C24—42no—
518C24C22⋊C4×C15111yescharacteristic
519C24C22⋊C4×C15111yescharacteristic
520C24C22⋊C4×C15111yescharacteristic
521C24C22⋊C4×C15111yescharacteristic
522C24C22×C4×C15111yescharacteristic
523C24C22×C4×C15111yescharacteristic
524C24C22×C4×C15112yes—
525C24C22×C4×C15111yescharacteristic
526#41—44no—
527#41—44no—
528#41—44no—
529#41—44no—
530C2×Q8—21no—
531C2×Q8—21no—
532C2×Q8—42no—
533C2×D4—22no—
534C2×D4—22no—
535C2×D4—22no—
536C2×D4—22no—
537C2×D4—22no—
538C2×D4—22no—
539C2×D4—21no—
540C2×D4—21no—
541C2×D4—44no—
542C2×D4—42no—
543C2×D4—44no—
544C2×D4—44no—
545C22×C4—24no—
546C22×C4—24no—
547C22×C4—24no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—42no—
551C22×C4—42no—
552C22×C4—42no—
553C22×C4—42no—
554C22×C4—42no—
555C22×C4—42no—
556C22×C4—42no—
557C22×C4—42no—
558C22×C4—42no—
559C22×C4—42no—
560C22×C4—42no—
561C22×C4—44no—
562C22×C4C22⋊C4×C15111yescharacteristic
563C22×C4C22⋊C4×C15111yescharacteristic
564C22×C4C22⋊C4×C15111yescharacteristic
565C22×C4C22⋊C4×C15111yescharacteristic
566C22×C4C22⋊C4×C15111yescharacteristic
567C22×C4C22⋊C4×C15111yescharacteristic
568C22×C4C22⋊C4×C15111yescharacteristic
569C22×C4C22⋊C4×C15111yescharacteristic
570C22×C4C22⋊C4×C15111yescharacteristic
571C22×C4C22⋊C4×C15111yescharacteristic
572C22×C4C22⋊C4×C15111yescharacteristic
573C22×C4C22⋊C4×C15111yescharacteristic
574C22×C4C22×C4×C15112yes—
575C22×C4C22×C4×C15111yescharacteristic
576C22×C4C22×C4×C15111yescharacteristic
577C22×C4C22×C4×C15112yes—
578C22×C4C22×C4×C15112yes—
579C22×C4C22×C4×C15111yescharacteristic
580C22×C4C2×D4×C15111yescharacteristic
581C22×C4C2×D4×C15111yescharacteristic
582C22×C4C2×D4×C15111yescharacteristic
583C22×C4C2×D4×C15111yescharacteristic
584C22×C4C2×D4×C15111yescharacteristic
585C22×C4C2×D4×C15111yescharacteristic
586C22×C4C2×D4×C15111yescharacteristic
587C22×C4C2×D4×C15111yescharacteristic
588C22×C4C2×D4×C15111yescharacteristic
589C22×C4C2×D4×C15111yescharacteristic
590C22×C4C2×D4×C15111yescharacteristic
591C22×C4C2×D4×C15111yescharacteristic
592C22×C4C24×C15111yescharacteristic
593M16—44no—
594M16—44no—
595M16—44no—
596M16—44no—
597C2×C8—24no—
598C2×C8—24no—
599C2×C8—44no—
600C2×C8—44no—
601C4⋊C4—21no—
602C4⋊C4—21no—
603C4⋊C4—21no—
604C4⋊C4—21no—
605C4⋊C4—22no—
606C4⋊C4—22no—
607C4⋊C4—22no—
608C4⋊C4—22no—
609C22⋊C4—22no—
610C22⋊C4—22no—
611C22⋊C4—22no—
612C22⋊C4—22no—
613C22⋊C4—22no—
614C22⋊C4—22no—
615C22⋊C4—22no—
616C22⋊C4—22no—
617C22⋊C4—22no—
618C22⋊C4—22no—
619C42—22no—
620C42—22no—
621C23—22no—
622C23—22no—
623C23—22no—
624C23—22no—
625C23—22no—
626C23—22no—
627C23—22no—
628C23—22no—
629C23—22no—
630C23—22no—
631C23—24no—
632C23—41no—
633C23—41no—
634C23—41no—
635C23—41no—
636C23—41no—
637C23—41no—
638C23—41no—
639C23—41no—
640C23—41no—
641C23—41no—
642C23—41no—
643C23—41no—
644C23—42no—
645C23—42no—
646C23—416no—
647C23C2×C22⋊C4×C15111yescharacteristic
648C23C2×C22⋊C4×C15111yescharacteristic
649C23C2×C22⋊C4×C15111yescharacteristic
650C23C2×C22⋊C4×C15111yescharacteristic
651C23C2×C22⋊C4×C15111yescharacteristic
652C23C2×C22⋊C4×C15111yescharacteristic
653C23C23×C4×C15111yescharacteristic
654Q8—42no—
655Q8—42no—
656D4—42no—
657D4—44no—
658D4—44no—
659D4—44no—
660D4—44no—
661D4—44no—
662D4—44no—
663D4—42no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—24no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—41no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—44no—
696C2×C4—44no—
697C2×C4—42no—
698C2×C4—42no—
699C2×C4#99×C15114yes—
700C2×C4C2×C22⋊C4×C15111yescharacteristic
701C2×C4C2×C22⋊C4×C15111yescharacteristic
702C2×C4C2×C22⋊C4×C15111yescharacteristic
703C2×C4C2×C22⋊C4×C15111yescharacteristic
704C2×C4C2×C22⋊C4×C15111yescharacteristic
705C2×C4C2×C22⋊C4×C15111yescharacteristic
706C2×C4C22×D4×C15111yescharacteristic
707C2×C4C22×D4×C15111yescharacteristic
708C8—44no—
709C8—44no—
710C22—21no—
711C22—21no—
712C22—21no—
713C22—21no—
714C22—21no—
715C22—21no—
716C22—21no—
717C22—21no—
718C22—21no—
719C22—21no—
720C22—21no—
721C22—21no—
722C22—21no—
723C22—21no—
724C22—21no—
725C22—21no—
726C22—21no—
727C22—21no—
728C22—44no—
729C22—44no—
730C22—44no—
731C22—44no—
732C22—44no—
733C22—44no—
734C22—44no—
735C22—42no—
736C22—42no—
737C22—42no—
738C22—84no—
739C22C2×#99×C15112yes—
740C22#413×C15112yes—
741C22C22×C22⋊C4×C15111yescharacteristic
742C22#568×C15112yes—
743C4—21no—
744C4—21no—
745C4—21no—
746C4—21no—
747C4—21no—
748C4—21no—
749C4—42no—
750C4—42no—
751C4—42no—
752C4C2×#99×C15112yes—
753C4C2×#99×C15112yes—
754C2—22no—
755C2—22no—
756C2—22no—
757C2—41no—
758C2—41no—
759C2—41no—
760C2—41no—
761C2—82no—
762C2#2879×C15111yescharacteristic
763C2C22×#99×C15111yescharacteristic
764C2C2×#413×C15111yescharacteristic
subgroupG/H
center, socleC22×C151C22×C22⋊C4
commutatorC23C23×C4×C151
Frattini, cosocleC22×C4C24×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. C2×#407×C151C2semidirect
3. C2×#407×C151C2semidirect
4. #1472×C151C2semidirect
5. #1471×C151C2semidirect
6. #1468×C151C2semidirect
7. #1465×C151C2semidirect
41. #324×C151C22semidirect
42. #323×C151C22semidirect
382. #17400C151direct (N × H)
383. C151#17400direct (N × H)
385. C2×#407C2×C151semidirect
386. C2×#407C2×C151semidirect
387. #1472C2×C151semidirect
388. #1471C2×C151semidirect
389. #1468C2×C151semidirect
390. #1465C2×C151semidirect
424. #324C22×C151semidirect
425. #323C22×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#525×C1512
C2×#407×C1512
#1472×C1512
#1471×C1512
#1468×C1512
#1465×C1512
#17400151