Finite Group Databasebeta

← C151×#8488 #50313413

Subgroups — C151×#8488 #50313413

Order 38656.

768 conjugacy classes of subgroups.

The subgroup lattice has 748 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3535×C151C211yesmaximal, characteristic
2#1899×C151C211yesmaximal, characteristic, complemented
3#1897×C151C211yesmaximal, characteristic, complemented
4#1873×C151C211yesmaximal, characteristic, complemented
5#1516×C151C211yesmaximal, characteristic, complemented
6#1511×C151C211yesmaximal, characteristic, complemented
7#1468×C151C211yesmaximal, characteristic, complemented
8#563×C151—21no—
9#562×C151—21no—
10#554×C151—21no—
11#552×C151—21no—
12#551×C151—21no—
13#551×C151—21no—
14#547×C151—21no—
15#546×C151—21no—
16#544×C151C411yescharacteristic, complemented
17#543×C151C411yescharacteristic, complemented
18#542×C151—21no—
19#539×C151—21no—
20#539×C151—21no—
21#539×C151C411yescharacteristic, complemented
22#538×C151C411yescharacteristic, complemented
23#536×C151—21no—
24#525×C151C2211yescharacteristic
25C2×#123×C151C2211yescharacteristic
26C2×C22⋊Q8×C151C2211yescharacteristic
27C2×#117×C151C2211yescharacteristic
28C2×#104×C151—21no—
29C2×#103×C151—21no—
30C2×#99×C151—21no—
31#407×C151C2211yescharacteristic
32C2×C22⋊C8×C151C2211yescharacteristic
33#381×C151C2211yescharacteristic
34#342×C151—21no—
35#340×C151—21no—
36#339×C151—21no—
37#328×C151—21no—
38#328×C151—21no—
39#328×C151—21no—
40#327×C151—21no—
41#324×C151—21no—
42#323×C151—21no—
43C2×#41×C151—21no—
44C2×#41×C151D411yescharacteristic
45C22×Q8×C151D411yescharacteristic
46C22×D4×C151D411yescharacteristic
47C23×C4×C151C2311yescharacteristic
48C2×M16×C151—21no—
49C22×C8×C151—21no—
50C4⋊Q8×C151—21no—
51C4⋊Q8×C151—21no—
52C4⋊Q8×C151—21no—
53#126×C151—21no—
54#126×C151—21no—
55#126×C151—21no—
56#126×C151—21no—
57#126×C151—21no—
58#126×C151—21no—
59#125×C151—21no—
60#125×C151—21no—
61#125×C151—21no—
62#125×C151—21no—
63#125×C151—21no—
64#124×C151—21no—
65#124×C151—21no—
66#124×C151—21no—
67#124×C151—21no—
68#123×C151—21no—
69#123×C151—21no—
70#123×C151—21no—
71#123×C151—21no—
72#123×C151—21no—
73#123×C151—21no—
74#123×C151—21no—
75#123×C151—21no—
76#123×C151—21no—
77#123×C151—21no—
78#123×C151—21no—
79#123×C151—21no—
80#123×C151—21no—
81#123×C151—21no—
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—
90C22⋊Q8×C151—21no—
91C22⋊Q8×C151—21no—
92C22⋊Q8×C151—21no—
93C22⋊Q8×C151—21no—
94C22⋊Q8×C151—21no—
95C22⋊Q8×C151—21no—
96C22⋊Q8×C151C2×C411yescharacteristic
97C22⋊Q8×C151C2×C411yescharacteristic
98C22⋊Q8×C151C2×C411yescharacteristic
99C22⋊Q8×C151D411yescharacteristic
100C22⋊Q8×C151D411yescharacteristic
101C22⋊Q8×C151D411yescharacteristic
102#121×C151—21no—
103#121×C151—21no—
104#121×C151—21no—
105#121×C151—21no—
106#121×C151C2×C411yescharacteristic
107#121×C151D411yescharacteristic
108#120×C151—21no—
109#120×C151—21no—
110C4×Q8×C151—21no—
111C4×D4×C151—21no—
112C4×D4×C151—21no—
113C4×D4×C151—21no—
114C4×D4×C151—21no—
115C4×D4×C151—21no—
116C4×D4×C151—21no—
117C4×D4×C151—21no—
118#117×C151—21no—
119#117×C151—21no—
120#117×C151—21no—
121#117×C151—42no—
122#117×C151D411yescharacteristic
123C2×C4⋊C4×C151—21no—
124C2×C4⋊C4×C151—21no—
125C2×C4⋊C4×C151—21no—
126C2×C4⋊C4×C151C2×C411yescharacteristic
127C2×C4⋊C4×C151D411yescharacteristic
128C2×C4⋊C4×C151D411yescharacteristic
129C2×C22⋊C4×C151—21no—
130C2×C22⋊C4×C151—21no—
131C2×C22⋊C4×C151—21no—
132C2×C22⋊C4×C151—21no—
133C2×C22⋊C4×C151C2×C411yescharacteristic
134C2×C22⋊C4×C151D411yescharacteristic
135C2×C22⋊C4×C151D411yescharacteristic
136C2×C42×C151—21no—
137#104×C151—42no—
138#103×C151—42no—
139#99×C151—42no—
140C22⋊C8×C151—21no—
141C22⋊C8×C151—21no—
142C22⋊C8×C151—21no—
143C22⋊C8×C151—21no—
144#95×C151—21no—
145#95×C151—21no—
146C24×C151C22⋊C411yescharacteristic
147C24×C151C2×D411yescharacteristic
148#41×C151—41no—
149#41×C151—41no—
150#41×C151—81no—
151#41×C151—81no—
152C2×Q8×C151—21no—
153C2×Q8×C151—21no—
154C2×Q8×C151—21no—
155C2×Q8×C151—41no—
156C2×Q8×C151—41no—
157C2×Q8×C151C22⋊C411yescharacteristic
158C2×Q8×C151C22⋊C411yescharacteristic
159C2×Q8×C151C22⋊C411yescharacteristic
160C2×D4×C151—21no—
161C2×D4×C151—21no—
162C2×D4×C151—21no—
163C2×D4×C151—21no—
164C2×D4×C151—21no—
165C2×D4×C151—21no—
166C2×D4×C151—21no—
167C2×D4×C151—41no—
168C2×D4×C151—41no—
169C2×D4×C151C22⋊C411yescharacteristic
170C22×C4×C151—21no—
171C22×C4×C151—21no—
172C22×C4×C151—21no—
173C22×C4×C151—21no—
174C22×C4×C151—21no—
175C22×C4×C151—21no—
176C22×C4×C151—21no—
177C22×C4×C151—41no—
178C22×C4×C151—41no—
179C22×C4×C151—41no—
180C22×C4×C151—41no—
181C22×C4×C151C22⋊C411yescharacteristic
182C22×C4×C151C22⋊C411yescharacteristic
183C22×C4×C151C22⋊C411yescharacteristic
184C22×C4×C151C22×C411yescharacteristic
185C22×C4×C151C2×D411yescharacteristic
186C22×C4×C151C2×D411yescharacteristic
187C22×C4×C151C2×D411yescharacteristic
188C22×C4×C151C2×D411yescharacteristic
189C22×C4×C151C2×D411yescharacteristic
190M16×C151—41no—
191M16×C151—41no—
192C2×C8×C151—41no—
193C2×C8×C151—41no—
194C2×C8×C151—41no—
195C2×C8×C151—41no—
196C4⋊C4×C151—21no—
197C4⋊C4×C151—21no—
198C4⋊C4×C151—21no—
199C4⋊C4×C151—21no—
200C4⋊C4×C151—21no—
201C4⋊C4×C151—21no—
202C4⋊C4×C151—21no—
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—21no—
213C4⋊C4×C151—21no—
214C4⋊C4×C151—21no—
215C4⋊C4×C151—21no—
216C4⋊C4×C151—21no—
217C4⋊C4×C151—21no—
218C4⋊C4×C151—21no—
219C4⋊C4×C151—22no—
220C4⋊C4×C151—41no—
221C4⋊C4×C151C22⋊C411yescharacteristic
222C4⋊C4×C151C22⋊C411yescharacteristic
223C4⋊C4×C151C22⋊C411yescharacteristic
224C4⋊C4×C151C22⋊C411yescharacteristic
225C22⋊C4×C151—21no—
226C22⋊C4×C151—21no—
227C22⋊C4×C151—21no—
228C22⋊C4×C151—21no—
229C22⋊C4×C151—21no—
230C22⋊C4×C151—21no—
231C22⋊C4×C151—21no—
232C22⋊C4×C151—21no—
233C22⋊C4×C151—21no—
234C22⋊C4×C151—21no—
235C22⋊C4×C151—21no—
236C22⋊C4×C151—21no—
237C22⋊C4×C151—21no—
238C22⋊C4×C151—21no—
239C22⋊C4×C151—21no—
240C22⋊C4×C151—21no—
241C22⋊C4×C151—21no—
242C22⋊C4×C151—21no—
243C22⋊C4×C151—21no—
244C22⋊C4×C151—21no—
245C22⋊C4×C151—21no—
246C22⋊C4×C151—21no—
247C22⋊C4×C151—21no—
248C22⋊C4×C151—22no—
249C22⋊C4×C151—41no—
250C22⋊C4×C151—41no—
251C22⋊C4×C151—41no—
252C42×C151—21no—
253C42×C151—21no—
254C42×C151—21no—
255C42×C151—21no—
256C42×C151—21no—
257C42×C151—22no—
258C42×C151—41no—
259C23×C151—21no—
260C23×C151—21no—
261C23×C151—21no—
262C23×C151—21no—
263C23×C151—41no—
264C23×C151—41no—
265C23×C151—41no—
266C23×C151—41no—
267C23×C151—41no—
268C23×C151C2×C22⋊C411yescharacteristic
269C23×C151#12011yescharacteristic
270C23×C151#12011yescharacteristic
271Q8×C151—41no—
272Q8×C151—41no—
273Q8×C151—41no—
274Q8×C151—81no—
275Q8×C151—81no—
276Q8×C151—81no—
277D4×C151—41no—
278D4×C151—42no—
279D4×C151—41no—
280D4×C151—41no—
281D4×C151—41no—
282D4×C151—41no—
283D4×C151—81no—
284D4×C151—81no—
285D4×C151—81no—
286D4×C151—81no—
287C2×C4×C151—21no—
288C2×C4×C151—21no—
289C2×C4×C151—21no—
290C2×C4×C151—21no—
291C2×C4×C151—21no—
292C2×C4×C151—21no—
293C2×C4×C151—21no—
294C2×C4×C151—21no—
295C2×C4×C151—21no—
296C2×C4×C151—21no—
297C2×C4×C151—21no—
298C2×C4×C151—21no—
299C2×C4×C151—21no—
300C2×C4×C151—21no—
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—42no—
311C2×C4×C151—81no—
312C2×C4×C151—81no—
313C2×C4×C151—81no—
314C2×C4×C151—81no—
315C2×C4×C151—81no—
316C2×C4×C151—81no—
317C2×C4×C151—81no—
318C2×C4×C151—81no—
319C2×C4×C151—81no—
320C2×C4×C151—81no—
321C2×C4×C151—81no—
322C2×C4×C151C2×C22⋊C411yescharacteristic
323C2×C4×C151C2×C22⋊C411yescharacteristic
324C2×C4×C151#12011yescharacteristic
325C2×C4×C151#12011yescharacteristic
326C8×C151—81no—
327C8×C151—81no—
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—41no—
337C22×C151—41no—
338C22×C151—41no—
339C22×C151—41no—
340C22×C151—41no—
341C22×C151—41no—
342C22×C151—81no—
343C22×C151—81no—
344C22×C151—161no—
345C22×C151#37911yescharacteristic
346C22×C151B(4,𝔽2)11yescharacteristic
347C22×C151#45811yescharacteristic
348C4×C151—21no—
349C4×C151—21no—
350C4×C151—21no—
351C4×C151—21no—
352C4×C151—41no—
353C4×C151—41no—
354C4×C151—41no—
355C4×C151—41no—
356C4×C151—41no—
357C4×C151—41no—
358C4×C151—41no—
359C4×C151—41no—
360C4×C151—41no—
361C4×C151—41no—
362C4×C151—82no—
363C4×C151—161no—
364C2×C151—21no—
365C2×C151—21no—
366C2×C151—41no—
367C2×C151—41no—
368C2×C151—81no—
369C2×C151—81no—
370C2×C151#179011yescharacteristic
371C2×C151#179411yescharacteristic
372C2×C151#179611yescharacteristic
373#8488C15111yesmaximal, characteristic, direct product factor, Sylow
374C151#848811yescharacteristic, direct product factor, Sylow
375#3535C2×C15111yescharacteristic
376#1899C2×C15111yescharacteristic, complemented
377#1897C2×C15111yescharacteristic, complemented
378#1873C2×C15111yescharacteristic, complemented
379#1516C2×C15111yescharacteristic, complemented
380#1511C2×C15111yescharacteristic, complemented
381#1468C2×C15111yescharacteristic, complemented
382#563—21no—
383#562—21no—
384#554—21no—
385#552—21no—
386#551—21no—
387#551—21no—
388#547—21no—
389#546—21no—
390#544C4×C15111yescharacteristic, complemented
391#543C4×C15111yescharacteristic, complemented
392#542—21no—
393#539—21no—
394#539—21no—
395#539C4×C15111yescharacteristic, complemented
396#538C4×C15111yescharacteristic, complemented
397#536—21no—
398#525C22×C15111yescharacteristic
399C2×#123C22×C15111yescharacteristic
400C2×C22⋊Q8C22×C15111yescharacteristic
401C2×#117C22×C15111yescharacteristic
402C2×#104—21no—
403C2×#103—21no—
404C2×#99—21no—
405#407C22×C15111yescharacteristic
406C2×C22⋊C8C22×C15111yescharacteristic
407#381C22×C15111yescharacteristic
408#342—21no—
409#340—21no—
410#339—21no—
411#328—21no—
412#328—21no—
413#328—21no—
414#327—21no—
415#324—21no—
416#323—21no—
417C2×#41—21no—
418C2×#41D4×C15111yescharacteristic
419C22×Q8D4×C15111yescharacteristic
420C22×D4D4×C15111yescharacteristic
421C23×C4C23×C15111yescharacteristic
422C2×M16—21no—
423C22×C8—21no—
424C4⋊Q8—21no—
425C4⋊Q8—21no—
426C4⋊Q8—21no—
427#126—21no—
428#126—21no—
429#126—21no—
430#126—21no—
431#126—21no—
432#126—21no—
433#125—21no—
434#125—21no—
435#125—21no—
436#125—21no—
437#125—21no—
438#124—21no—
439#124—21no—
440#124—21no—
441#124—21no—
442#123—21no—
443#123—21no—
444#123—21no—
445#123—21no—
446#123—21no—
447#123—21no—
448#123—21no—
449#123—21no—
450#123—21no—
451#123—21no—
452#123—21no—
453#123—21no—
454#123—21no—
455#123—21no—
456C22⋊Q8—21no—
457C22⋊Q8—21no—
458C22⋊Q8—21no—
459C22⋊Q8—21no—
460C22⋊Q8—21no—
461C22⋊Q8—21no—
462C22⋊Q8—21no—
463C22⋊Q8—21no—
464C22⋊Q8—21no—
465C22⋊Q8—21no—
466C22⋊Q8—21no—
467C22⋊Q8—21no—
468C22⋊Q8—21no—
469C22⋊Q8—21no—
470C22⋊Q8C2×C4×C15111yescharacteristic
471C22⋊Q8C2×C4×C15111yescharacteristic
472C22⋊Q8C2×C4×C15111yescharacteristic
473C22⋊Q8D4×C15111yescharacteristic
474C22⋊Q8D4×C15111yescharacteristic
475C22⋊Q8D4×C15111yescharacteristic
476#121—21no—
477#121—21no—
478#121—21no—
479#121—21no—
480#121C2×C4×C15111yescharacteristic
481#121D4×C15111yescharacteristic
482#120—21no—
483#120—21no—
484C4×Q8—21no—
485C4×D4—21no—
486C4×D4—21no—
487C4×D4—21no—
488C4×D4—21no—
489C4×D4—21no—
490C4×D4—21no—
491C4×D4—21no—
492#117—21no—
493#117—21no—
494#117—21no—
495#117—42no—
496#117D4×C15111yescharacteristic
497C2×C4⋊C4—21no—
498C2×C4⋊C4—21no—
499C2×C4⋊C4—21no—
500C2×C4⋊C4C2×C4×C15111yescharacteristic
501C2×C4⋊C4D4×C15111yescharacteristic
502C2×C4⋊C4D4×C15111yescharacteristic
503C2×C22⋊C4—21no—
504C2×C22⋊C4—21no—
505C2×C22⋊C4—21no—
506C2×C22⋊C4—21no—
507C2×C22⋊C4C2×C4×C15111yescharacteristic
508C2×C22⋊C4D4×C15111yescharacteristic
509C2×C22⋊C4D4×C15111yescharacteristic
510C2×C42—21no—
511#104—42no—
512#103—42no—
513#99—42no—
514C22⋊C8—21no—
515C22⋊C8—21no—
516C22⋊C8—21no—
517C22⋊C8—21no—
518#95—21no—
519#95—21no—
520C24C22⋊C4×C15111yescharacteristic
521C24C2×D4×C15111yescharacteristic
522#41—41no—
523#41—41no—
524#41—81no—
525#41—81no—
526C2×Q8—21no—
527C2×Q8—21no—
528C2×Q8—21no—
529C2×Q8—41no—
530C2×Q8—41no—
531C2×Q8C22⋊C4×C15111yescharacteristic
532C2×Q8C22⋊C4×C15111yescharacteristic
533C2×Q8C22⋊C4×C15111yescharacteristic
534C2×D4—21no—
535C2×D4—21no—
536C2×D4—21no—
537C2×D4—21no—
538C2×D4—21no—
539C2×D4—21no—
540C2×D4—21no—
541C2×D4—41no—
542C2×D4—41no—
543C2×D4C22⋊C4×C15111yescharacteristic
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—41no—
552C22×C4—41no—
553C22×C4—41no—
554C22×C4—41no—
555C22×C4C22⋊C4×C15111yescharacteristic
556C22×C4C22⋊C4×C15111yescharacteristic
557C22×C4C22⋊C4×C15111yescharacteristic
558C22×C4C22×C4×C15111yescharacteristic
559C22×C4C2×D4×C15111yescharacteristic
560C22×C4C2×D4×C15111yescharacteristic
561C22×C4C2×D4×C15111yescharacteristic
562C22×C4C2×D4×C15111yescharacteristic
563C22×C4C2×D4×C15111yescharacteristic
564M16—41no—
565M16—41no—
566C2×C8—41no—
567C2×C8—41no—
568C2×C8—41no—
569C2×C8—41no—
570C4⋊C4—21no—
571C4⋊C4—21no—
572C4⋊C4—21no—
573C4⋊C4—21no—
574C4⋊C4—21no—
575C4⋊C4—21no—
576C4⋊C4—21no—
577C4⋊C4—21no—
578C4⋊C4—21no—
579C4⋊C4—21no—
580C4⋊C4—21no—
581C4⋊C4—21no—
582C4⋊C4—21no—
583C4⋊C4—21no—
584C4⋊C4—21no—
585C4⋊C4—21no—
586C4⋊C4—21no—
587C4⋊C4—21no—
588C4⋊C4—21no—
589C4⋊C4—21no—
590C4⋊C4—21no—
591C4⋊C4—21no—
592C4⋊C4—21no—
593C4⋊C4—22no—
594C4⋊C4—41no—
595C4⋊C4C22⋊C4×C15111yescharacteristic
596C4⋊C4C22⋊C4×C15111yescharacteristic
597C4⋊C4C22⋊C4×C15111yescharacteristic
598C4⋊C4C22⋊C4×C15111yescharacteristic
599C22⋊C4—21no—
600C22⋊C4—21no—
601C22⋊C4—21no—
602C22⋊C4—21no—
603C22⋊C4—21no—
604C22⋊C4—21no—
605C22⋊C4—21no—
606C22⋊C4—21no—
607C22⋊C4—21no—
608C22⋊C4—21no—
609C22⋊C4—21no—
610C22⋊C4—21no—
611C22⋊C4—21no—
612C22⋊C4—21no—
613C22⋊C4—21no—
614C22⋊C4—21no—
615C22⋊C4—21no—
616C22⋊C4—21no—
617C22⋊C4—21no—
618C22⋊C4—21no—
619C22⋊C4—21no—
620C22⋊C4—21no—
621C22⋊C4—21no—
622C22⋊C4—22no—
623C22⋊C4—41no—
624C22⋊C4—41no—
625C22⋊C4—41no—
626C42—21no—
627C42—21no—
628C42—21no—
629C42—21no—
630C42—21no—
631C42—22no—
632C42—41no—
633C23—21no—
634C23—21no—
635C23—21no—
636C23—21no—
637C23—41no—
638C23—41no—
639C23—41no—
640C23—41no—
641C23—41no—
642C23C2×C22⋊C4×C15111yescharacteristic
643C23#120×C15111yescharacteristic
644C23#120×C15111yescharacteristic
645Q8—41no—
646Q8—41no—
647Q8—41no—
648Q8—81no—
649Q8—81no—
650Q8—81no—
651D4—41no—
652D4—42no—
653D4—41no—
654D4—41no—
655D4—41no—
656D4—41no—
657D4—81no—
658D4—81no—
659D4—81no—
660D4—81no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—21no—
666C2×C4—21no—
667C2×C4—21no—
668C2×C4—21no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—21no—
673C2×C4—21no—
674C2×C4—21no—
675C2×C4—41no—
676C2×C4—41no—
677C2×C4—41no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—42no—
685C2×C4—81no—
686C2×C4—81no—
687C2×C4—81no—
688C2×C4—81no—
689C2×C4—81no—
690C2×C4—81no—
691C2×C4—81no—
692C2×C4—81no—
693C2×C4—81no—
694C2×C4—81no—
695C2×C4—81no—
696C2×C4C2×C22⋊C4×C15111yescharacteristic
697C2×C4C2×C22⋊C4×C15111yescharacteristic
698C2×C4#120×C15111yescharacteristic
699C2×C4#120×C15111yescharacteristic
700C8—81no—
701C8—81no—
702C22—21no—
703C22—21no—
704C22—21no—
705C22—21no—
706C22—21no—
707C22—21no—
708C22—21no—
709C22—21no—
710C22—41no—
711C22—41no—
712C22—41no—
713C22—41no—
714C22—41no—
715C22—41no—
716C22—81no—
717C22—81no—
718C22—161no—
719C22#379×C15111yescharacteristic
720C22B(4,𝔽2)×C15111yescharacteristic
721C22#458×C15111yescharacteristic
722C4—21no—
723C4—21no—
724C4—21no—
725C4—21no—
726C4—41no—
727C4—41no—
728C4—41no—
729C4—41no—
730C4—41no—
731C4—41no—
732C4—41no—
733C4—41no—
734C4—41no—
735C4—41no—
736C4—82no—
737C4—161no—
738C2—21no—
739C2—21no—
740C2—41no—
741C2—41no—
742C2—81no—
743C2—81no—
744C2#1790×C15111yescharacteristic
745C2#1794×C15111yescharacteristic
746C2#1796×C15111yescharacteristic
subgroupG/H
center, socleC22×C151#379
commutatorC22×C4C22×C4×C151
Frattini, cosocleC23×C4C23×C151
prime radical#3535×C151C2
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C151 ◁ C23×C4×C151 ◁ G

Complements

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

NH ≅ G/Ntype
2. #1899×C151C2semidirect
3. #1897×C151C2semidirect
4. #1873×C151C2semidirect
5. #1516×C151C2semidirect
6. #1511×C151C2semidirect
7. #1468×C151C2semidirect
16. #544×C151C4semidirect
17. #543×C151C4semidirect
21. #539×C151C4semidirect
22. #538×C151C4semidirect
373. #8488C151direct (N × H)
374. C151#8488direct (N × H)
376. #1899C2×C151semidirect
377. #1897C2×C151semidirect
378. #1873C2×C151semidirect
379. #1516C2×C151semidirect
380. #1511C2×C151semidirect
381. #1468C2×C151semidirect
390. #544C4×C151semidirect
391. #543C4×C151semidirect
395. #539C4×C151semidirect
396. #538C4×C151semidirect

Maximal subgroups

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

subgroupindex
#3535×C1512
#1899×C1512
#1897×C1512
#1873×C1512
#1516×C1512
#1511×C1512
#1468×C1512
#8488151