Finite Group Databasebeta

← C151×#11005 #50315930

Subgroups — C151×#11005 #50315930

Order 38656.

1270 conjugacy classes of subgroups.

The subgroup lattice has 744 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#536×C151C211yesmaximal, characteristic
2C2×#421×C151C211yesmaximal, characteristic
3#2896×C151C211yesmaximal, characteristic
4C2×#419×C151C211yesmaximal, characteristic, complemented
5C2×#419×C151C211yesmaximal, characteristic, complemented
6C2×#344×C151C211yesmaximal, characteristic, complemented
7#1740×C151C211yesmaximal, characteristic, complemented
8C22×#41×C151C2211yescharacteristic
9C23×Q8×C151C2211yescharacteristic
10C22×M16×C151C2211yescharacteristic
11C22×M16×C151C2211yescharacteristic
12#536×C151—22no—
13#536×C151—22no—
14#536×C151—22no—
15#536×C151C414yescomplemented
16C2×C4⋊Q8×C151—21no—
17C2×#124×C151—21no—
18C2×#123×C151—22no—
19C2×C22⋊Q8×C151—22no—
20C2×#117×C151C2211yescharacteristic
21C2×#117×C151C2211yescharacteristic
22C2×#117×C151C2211yescharacteristic
23#421×C151—22no—
24#421×C151—22no—
25C2×#104×C151—22no—
26#419×C151—22no—
27#419×C151—22no—
28#419×C151—21no—
29#419×C151—22no—
30#419×C151—22no—
31#418×C151—21no—
32#417×C151—22no—
33#416×C151—22no—
34C2×#103×C151—22no—
35C2×#103×C151—22no—
36#344×C151—22no—
37#342×C151—22no—
38C2×#41×C151—21no—
39C2×#41×C151—21no—
40C2×#41×C151—21no—
41C2×#41×C151—21no—
42C2×#41×C151—21no—
43C2×#41×C151—21no—
44C2×#41×C151—21no—
45C2×#41×C151—21no—
46C2×#41×C151—21no—
47C2×#41×C151—21no—
48C2×#41×C151C2×C412yes—
49C2×#41×C151D412yes—
50C22×Q8×C151—21no—
51C22×Q8×C151—21no—
52C22×Q8×C151—21no—
53C22×Q8×C151—21no—
54C22×Q8×C151—21no—
55C22×Q8×C151—21no—
56C22×Q8×C151—21no—
57C22×Q8×C151—21no—
58C22×Q8×C151—21no—
59C22×Q8×C151—21no—
60C22×Q8×C151—21no—
61C22×Q8×C151C2×C412yes—
62C22×Q8×C151D412yes—
63C22×Q8×C151D411yescharacteristic
64C22×Q8×C151D412yes—
65C22×D4×C151—21no—
66C22×D4×C151D411yescharacteristic
67C23×C4×C151—21no—
68C23×C4×C151—21no—
69C23×C4×C151C2311yescharacteristic
70C2×M16×C151—21no—
71C2×M16×C151—21no—
72C2×M16×C151—21no—
73C2×M16×C151—21no—
74C2×M16×C151—21no—
75C2×M16×C151—21no—
76C2×M16×C151—21no—
77C2×M16×C151—21no—
78C2×M16×C151—21no—
79C2×M16×C151—21no—
80C2×M16×C151—21no—
81C2×M16×C151D412yes—
82C22×C8×C151—21no—
83C22×C8×C151D412yes—
84C4⋊Q8×C151—24no—
85C4⋊Q8×C151—24no—
86#124×C151—24no—
87#124×C151—24no—
88#123×C151—28no—
89#123×C151—28no—
90C22⋊Q8×C151—28no—
91C22⋊Q8×C151—28no—
92#117×C151—21no—
93#117×C151—21no—
94#117×C151—21no—
95#117×C151—21no—
96#117×C151—21no—
97#117×C151—21no—
98#117×C151—21no—
99#117×C151—21no—
100#117×C151—21no—
101#117×C151C2×C412yes—
102#117×C151D412yes—
103#117×C151D412yes—
104C2×C4⋊C4×C151—24no—
105C2×C4⋊C4×C151—21no—
106C2×C4⋊C4×C151—21no—
107C2×C4⋊C4×C151D412yes—
108C2×C22⋊C4×C151—24no—
109C2×C22⋊C4×C151—21no—
110C2×C22⋊C4×C151—21no—
111C2×C22⋊C4×C151D412yes—
112C2×C42×C151—21no—
113C2×C42×C151—21no—
114C2×C42×C151—21no—
115#104×C151—28no—
116#103×C151—28no—
117#103×C151—28no—
118#103×C151—24no—
119#102×C151—24no—
120C24×C151—21no—
121C24×C151C2×D411yescharacteristic
122#41×C151—22no—
123#41×C151—22no—
124#41×C151—22no—
125#41×C151—22no—
126#41×C151—22no—
127#41×C151—22no—
128#41×C151—22no—
129#41×C151—22no—
130#41×C151—41no—
131#41×C151—41no—
132#41×C151—41no—
133#41×C151—41no—
134#41×C151—41no—
135#41×C151—41no—
136#41×C151—41no—
137#41×C151—41no—
138C2×Q8×C151—22no—
139C2×Q8×C151—22no—
140C2×Q8×C151—22no—
141C2×Q8×C151—21no—
142C2×Q8×C151—22no—
143C2×Q8×C151—22no—
144C2×Q8×C151—22no—
145C2×Q8×C151—22no—
146C2×Q8×C151—22no—
147C2×Q8×C151—22no—
148C2×Q8×C151—21no—
149C2×Q8×C151—22no—
150C2×Q8×C151—22no—
151C2×Q8×C151—22no—
152C2×Q8×C151—22no—
153C2×Q8×C151—21no—
154C2×Q8×C151—21no—
155C2×Q8×C151—22no—
156C2×Q8×C151—22no—
157C2×Q8×C151—21no—
158C2×Q8×C151—41no—
159C2×Q8×C151—41no—
160C2×Q8×C151—41no—
161C2×Q8×C151—41no—
162C2×Q8×C151—41no—
163C2×Q8×C151—41no—
164C2×Q8×C151—41no—
165C2×Q8×C151—41no—
166C2×Q8×C151—41no—
167C2×Q8×C151—41no—
168C2×Q8×C151—41no—
169C2×Q8×C151—41no—
170C2×Q8×C151C22⋊C414yes—
171C2×Q8×C151C22⋊C412yes—
172C2×D4×C151—22no—
173C2×D4×C151—22no—
174C2×D4×C151—21no—
175C2×D4×C151—21no—
176C2×D4×C151—21no—
177C2×D4×C151—21no—
178C2×D4×C151—21no—
179C2×D4×C151—41no—
180C2×D4×C151—41no—
181C2×D4×C151—41no—
182C2×D4×C151—41no—
183C2×D4×C151C22⋊C412yes—
184C22×C4×C151—22no—
185C22×C4×C151—22no—
186C22×C4×C151—22no—
187C22×C4×C151—21no—
188C22×C4×C151—22no—
189C22×C4×C151—22no—
190C22×C4×C151—22no—
191C22×C4×C151—22no—
192C22×C4×C151—41no—
193C22×C4×C151—41no—
194C22×C4×C151—41no—
195C22×C4×C151—41no—
196C22×C4×C151—41no—
197C22×C4×C151—41no—
198C22×C4×C151—41no—
199C22×C4×C151—41no—
200C22×C4×C151—41no—
201C22×C4×C151C22×C411yescharacteristic
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×C151C2×D411yescharacteristic
210C22×C4×C151C2×D411yescharacteristic
211C22×C4×C151#4111yescharacteristic
212C22×C4×C151#4111yescharacteristic
213C22×C4×C151#4111yescharacteristic
214C22×C4×C151#4111yescharacteristic
215M16×C151—22no—
216M16×C151—22no—
217M16×C151—41no—
218M16×C151—41no—
219M16×C151—41no—
220M16×C151—41no—
221M16×C151—41no—
222M16×C151—41no—
223C2×C8×C151—22no—
224C2×C8×C151—22no—
225C2×C8×C151—22no—
226C2×C8×C151—22no—
227C2×C8×C151—41no—
228C2×C8×C151—41no—
229C4⋊C4×C151—216no—
230C4⋊C4×C151—22no—
231C4⋊C4×C151—22no—
232C4⋊C4×C151—22no—
233C4⋊C4×C151—22no—
234C4⋊C4×C151—22no—
235C4⋊C4×C151—41no—
236C22⋊C4×C151—216no—
237C22⋊C4×C151—22no—
238C22⋊C4×C151—22no—
239C22⋊C4×C151—41no—
240C22⋊C4×C151—41no—
241C22⋊C4×C151—41no—
242C22⋊C4×C151C22⋊C414yes—
243C42×C151—22no—
244C42×C151—22no—
245C42×C151—22no—
246C42×C151—41no—
247C42×C151—41no—
248C42×C151—41no—
249C23×C151—22no—
250C23×C151—42no—
251C23×C151—44no—
252C23×C151—41no—
253C23×C151—41no—
254C23×C151C2×C22⋊C411yescharacteristic
255C23×C151#12011yescharacteristic
256C23×C151#12011yescharacteristic
257C23×C151#12111yescharacteristic
258C23×C151#12111yescharacteristic
259C23×C151#12411yescharacteristic
260C23×C151#12711yescharacteristic
261Q8×C151—24no—
262Q8×C151—24no—
263Q8×C151—22no—
264Q8×C151—22no—
265Q8×C151—42no—
266Q8×C151—42no—
267Q8×C151—42no—
268Q8×C151—42no—
269Q8×C151—41no—
270Q8×C151—42no—
271Q8×C151—42no—
272Q8×C151—41no—
273D4×C151—22no—
274D4×C151—22no—
275D4×C151—42no—
276D4×C151—42no—
277D4×C151—42no—
278D4×C151—42no—
279D4×C151—41no—
280D4×C151—41no—
281C2×C4×C151—24no—
282C2×C4×C151—22no—
283C2×C4×C151—24no—
284C2×C4×C151—44no—
285C2×C4×C151—42no—
286C2×C4×C151—42no—
287C2×C4×C151—42no—
288C2×C4×C151—42no—
289C2×C4×C151—41no—
290C2×C4×C151—42no—
291C2×C4×C151—42no—
292C2×C4×C151—41no—
293C2×C4×C151—42no—
294C2×C4×C151—42no—
295C2×C4×C151—42no—
296C2×C4×C151—42no—
297C2×C4×C151—42no—
298C2×C4×C151—42no—
299C2×C4×C151—82no—
300C2×C4×C151—82no—
301C2×C4×C151C2×C22⋊C411yescharacteristic
302C2×C4×C151C2×C22⋊C411yescharacteristic
303C2×C4×C151C4×D411yescharacteristic
304C2×C4×C151C4×D411yescharacteristic
305C2×C4×C151C4×D411yescharacteristic
306C2×C4×C151C4×D411yescharacteristic
307C2×C4×C151#12011yescharacteristic
308C2×C4×C151#12011yescharacteristic
309C2×C4×C151#12011yescharacteristic
310C2×C4×C151#12011yescharacteristic
311C2×C4×C151#12011yescharacteristic
312C2×C4×C151#12011yescharacteristic
313C2×C4×C151#12111yescharacteristic
314C2×C4×C151#12111yescharacteristic
315C2×C4×C151#12111yescharacteristic
316C2×C4×C151#12111yescharacteristic
317C2×C4×C151#12111yescharacteristic
318C2×C4×C151#12111yescharacteristic
319C2×C4×C151#12111yescharacteristic
320C2×C4×C151#12111yescharacteristic
321C2×C4×C151#12111yescharacteristic
322C2×C4×C151#12111yescharacteristic
323C2×C4×C151#12311yescharacteristic
324C2×C4×C151#12311yescharacteristic
325C2×C4×C151#12311yescharacteristic
326C2×C4×C151#12311yescharacteristic
327C2×C4×C151#12411yescharacteristic
328C2×C4×C151#12711yescharacteristic
329C8×C151—42no—
330C8×C151—42no—
331C22×C151—22no—
332C22×C151—22no—
333C22×C151—22no—
334C22×C151—41no—
335C22×C151—41no—
336C22×C151—41no—
337C22×C151—41no—
338C22×C151—44no—
339C22×C151—42no—
340C22×C151—82no—
341C22×C151—82no—
342C22×C151#37911yescharacteristic
343C22×C151#39011yescharacteristic
344C22×C151#39011yescharacteristic
345C22×C151#39211yescharacteristic
346C22×C151#39211yescharacteristic
347C22×C151#39411yescharacteristic
348C22×C151#39411yescharacteristic
349C4×C151—44no—
350C4×C151—42no—
351C4×C151—44no—
352C4×C151—82no—
353C4×C151—82no—
354C4×C151#38611yescharacteristic
355C4×C151#38611yescharacteristic
356C4×C151#38611yescharacteristic
357C4×C151#38611yescharacteristic
358C4×C151#39211yescharacteristic
359C4×C151#39211yescharacteristic
360C4×C151#39411yescharacteristic
361C4×C151#39411yescharacteristic
362C2×C151—21no—
363C2×C151—21no—
364C2×C151—21no—
365C2×C151—21no—
366C2×C151—21no—
367C2×C151—21no—
368C2×C151—82no—
369C2×C151#143811yescharacteristic
370C2×C151#200912yes—
371#11005C15111yesmaximal, characteristic, direct product factor, Sylow
372C151#1100511yescharacteristic, direct product factor, Sylow
373C2×#536C2×C15111yescharacteristic
374C2×#421C2×C15111yescharacteristic
375#2896C2×C15111yescharacteristic
376C2×#419C2×C15111yescharacteristic, complemented
377C2×#419C2×C15111yescharacteristic, complemented
378C2×#344C2×C15111yescharacteristic, complemented
379#1740C2×C15111yescharacteristic, complemented
380C22×#41C22×C15111yescharacteristic
381C23×Q8C22×C15111yescharacteristic
382C22×M16C22×C15111yescharacteristic
383C22×M16C22×C15111yescharacteristic
384#536—22no—
385#536—22no—
386#536—22no—
387#536C4×C15114yescomplemented
388C2×C4⋊Q8—21no—
389C2×#124—21no—
390C2×#123—22no—
391C2×C22⋊Q8—22no—
392C2×#117C22×C15111yescharacteristic
393C2×#117C22×C15111yescharacteristic
394C2×#117C22×C15111yescharacteristic
395#421—22no—
396#421—22no—
397C2×#104—22no—
398#419—22no—
399#419—22no—
400#419—21no—
401#419—22no—
402#419—22no—
403#418—21no—
404#417—22no—
405#416—22no—
406C2×#103—22no—
407C2×#103—22no—
408#344—22no—
409#342—22no—
410C2×#41—21no—
411C2×#41—21no—
412C2×#41—21no—
413C2×#41—21no—
414C2×#41—21no—
415C2×#41—21no—
416C2×#41—21no—
417C2×#41—21no—
418C2×#41—21no—
419C2×#41—21no—
420C2×#41C2×C4×C15112yes—
421C2×#41D4×C15112yes—
422C22×Q8—21no—
423C22×Q8—21no—
424C22×Q8—21no—
425C22×Q8—21no—
426C22×Q8—21no—
427C22×Q8—21no—
428C22×Q8—21no—
429C22×Q8—21no—
430C22×Q8—21no—
431C22×Q8—21no—
432C22×Q8—21no—
433C22×Q8C2×C4×C15112yes—
434C22×Q8D4×C15112yes—
435C22×Q8D4×C15111yescharacteristic
436C22×Q8D4×C15112yes—
437C22×D4—21no—
438C22×D4D4×C15111yescharacteristic
439C23×C4—21no—
440C23×C4—21no—
441C23×C4C23×C15111yescharacteristic
442C2×M16—21no—
443C2×M16—21no—
444C2×M16—21no—
445C2×M16—21no—
446C2×M16—21no—
447C2×M16—21no—
448C2×M16—21no—
449C2×M16—21no—
450C2×M16—21no—
451C2×M16—21no—
452C2×M16—21no—
453C2×M16D4×C15112yes—
454C22×C8—21no—
455C22×C8D4×C15112yes—
456C4⋊Q8—24no—
457C4⋊Q8—24no—
458#124—24no—
459#124—24no—
460#123—28no—
461#123—28no—
462C22⋊Q8—28no—
463C22⋊Q8—28no—
464#117—21no—
465#117—21no—
466#117—21no—
467#117—21no—
468#117—21no—
469#117—21no—
470#117—21no—
471#117—21no—
472#117—21no—
473#117C2×C4×C15112yes—
474#117D4×C15112yes—
475#117D4×C15112yes—
476C2×C4⋊C4—24no—
477C2×C4⋊C4—21no—
478C2×C4⋊C4—21no—
479C2×C4⋊C4D4×C15112yes—
480C2×C22⋊C4—24no—
481C2×C22⋊C4—21no—
482C2×C22⋊C4—21no—
483C2×C22⋊C4D4×C15112yes—
484C2×C42—21no—
485C2×C42—21no—
486C2×C42—21no—
487#104—28no—
488#103—28no—
489#103—28no—
490#103—24no—
491#102—24no—
492C24—21no—
493C24C2×D4×C15111yescharacteristic
494#41—22no—
495#41—22no—
496#41—22no—
497#41—22no—
498#41—22no—
499#41—22no—
500#41—22no—
501#41—22no—
502#41—41no—
503#41—41no—
504#41—41no—
505#41—41no—
506#41—41no—
507#41—41no—
508#41—41no—
509#41—41no—
510C2×Q8—22no—
511C2×Q8—22no—
512C2×Q8—22no—
513C2×Q8—21no—
514C2×Q8—22no—
515C2×Q8—22no—
516C2×Q8—22no—
517C2×Q8—22no—
518C2×Q8—22no—
519C2×Q8—22no—
520C2×Q8—21no—
521C2×Q8—22no—
522C2×Q8—22no—
523C2×Q8—22no—
524C2×Q8—22no—
525C2×Q8—21no—
526C2×Q8—21no—
527C2×Q8—22no—
528C2×Q8—22no—
529C2×Q8—21no—
530C2×Q8—41no—
531C2×Q8—41no—
532C2×Q8—41no—
533C2×Q8—41no—
534C2×Q8—41no—
535C2×Q8—41no—
536C2×Q8—41no—
537C2×Q8—41no—
538C2×Q8—41no—
539C2×Q8—41no—
540C2×Q8—41no—
541C2×Q8—41no—
542C2×Q8C22⋊C4×C15114yes—
543C2×Q8C22⋊C4×C15112yes—
544C2×D4—22no—
545C2×D4—22no—
546C2×D4—21no—
547C2×D4—21no—
548C2×D4—21no—
549C2×D4—21no—
550C2×D4—21no—
551C2×D4—41no—
552C2×D4—41no—
553C2×D4—41no—
554C2×D4—41no—
555C2×D4C22⋊C4×C15112yes—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—21no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—41no—
565C22×C4—41no—
566C22×C4—41no—
567C22×C4—41no—
568C22×C4—41no—
569C22×C4—41no—
570C22×C4—41no—
571C22×C4—41no—
572C22×C4—41no—
573C22×C4C22×C4×C15111yescharacteristic
574C22×C4C2×D4×C15111yescharacteristic
575C22×C4C2×D4×C15111yescharacteristic
576C22×C4C2×D4×C15111yescharacteristic
577C22×C4C2×D4×C15111yescharacteristic
578C22×C4C2×D4×C15111yescharacteristic
579C22×C4C2×D4×C15111yescharacteristic
580C22×C4C2×D4×C15111yescharacteristic
581C22×C4C2×D4×C15111yescharacteristic
582C22×C4C2×D4×C15111yescharacteristic
583C22×C4#41×C15111yescharacteristic
584C22×C4#41×C15111yescharacteristic
585C22×C4#41×C15111yescharacteristic
586C22×C4#41×C15111yescharacteristic
587M16—22no—
588M16—22no—
589M16—41no—
590M16—41no—
591M16—41no—
592M16—41no—
593M16—41no—
594M16—41no—
595C2×C8—22no—
596C2×C8—22no—
597C2×C8—22no—
598C2×C8—22no—
599C2×C8—41no—
600C2×C8—41no—
601C4⋊C4—216no—
602C4⋊C4—22no—
603C4⋊C4—22no—
604C4⋊C4—22no—
605C4⋊C4—22no—
606C4⋊C4—22no—
607C4⋊C4—41no—
608C22⋊C4—216no—
609C22⋊C4—22no—
610C22⋊C4—22no—
611C22⋊C4—41no—
612C22⋊C4—41no—
613C22⋊C4—41no—
614C22⋊C4C22⋊C4×C15114yes—
615C42—22no—
616C42—22no—
617C42—22no—
618C42—41no—
619C42—41no—
620C42—41no—
621C23—22no—
622C23—42no—
623C23—44no—
624C23—41no—
625C23—41no—
626C23C2×C22⋊C4×C15111yescharacteristic
627C23#120×C15111yescharacteristic
628C23#120×C15111yescharacteristic
629C23#121×C15111yescharacteristic
630C23#121×C15111yescharacteristic
631C23#124×C15111yescharacteristic
632C23#127×C15111yescharacteristic
633Q8—24no—
634Q8—24no—
635Q8—22no—
636Q8—22no—
637Q8—42no—
638Q8—42no—
639Q8—42no—
640Q8—42no—
641Q8—41no—
642Q8—42no—
643Q8—42no—
644Q8—41no—
645D4—22no—
646D4—22no—
647D4—42no—
648D4—42no—
649D4—42no—
650D4—42no—
651D4—41no—
652D4—41no—
653C2×C4—24no—
654C2×C4—24no—
655C2×C4—22no—
656C2×C4—44no—
657C2×C4—42no—
658C2×C4—42no—
659C2×C4—41no—
660C2×C4—42no—
661C2×C4—42no—
662C2×C4—41no—
663C2×C4—42no—
664C2×C4—42no—
665C2×C4—42no—
666C2×C4—42no—
667C2×C4—42no—
668C2×C4—42no—
669C2×C4—42no—
670C2×C4—42no—
671C2×C4—82no—
672C2×C4—82no—
673C2×C4C2×C22⋊C4×C15111yescharacteristic
674C2×C4C2×C22⋊C4×C15111yescharacteristic
675C2×C4C4×D4×C15111yescharacteristic
676C2×C4C4×D4×C15111yescharacteristic
677C2×C4C4×D4×C15111yescharacteristic
678C2×C4C4×D4×C15111yescharacteristic
679C2×C4#120×C15111yescharacteristic
680C2×C4#120×C15111yescharacteristic
681C2×C4#120×C15111yescharacteristic
682C2×C4#120×C15111yescharacteristic
683C2×C4#120×C15111yescharacteristic
684C2×C4#120×C15111yescharacteristic
685C2×C4#121×C15111yescharacteristic
686C2×C4#121×C15111yescharacteristic
687C2×C4#121×C15111yescharacteristic
688C2×C4#121×C15111yescharacteristic
689C2×C4#121×C15111yescharacteristic
690C2×C4#121×C15111yescharacteristic
691C2×C4#121×C15111yescharacteristic
692C2×C4#121×C15111yescharacteristic
693C2×C4#121×C15111yescharacteristic
694C2×C4#121×C15111yescharacteristic
695C2×C4#123×C15111yescharacteristic
696C2×C4#123×C15111yescharacteristic
697C2×C4#123×C15111yescharacteristic
698C2×C4#123×C15111yescharacteristic
699C2×C4#124×C15111yescharacteristic
700C2×C4#127×C15111yescharacteristic
701C8—42no—
702C8—42no—
703C22—22no—
704C22—22no—
705C22—22no—
706C22—41no—
707C22—41no—
708C22—41no—
709C22—41no—
710C22—44no—
711C22—42no—
712C22—82no—
713C22—82no—
714C22#379×C15111yescharacteristic
715C22#390×C15111yescharacteristic
716C22#390×C15111yescharacteristic
717C22#392×C15111yescharacteristic
718C22#392×C15111yescharacteristic
719C22#394×C15111yescharacteristic
720C22#394×C15111yescharacteristic
721C4—44no—
722C4—42no—
723C4—44no—
724C4—82no—
725C4—82no—
726C4#386×C15111yescharacteristic
727C4#386×C15111yescharacteristic
728C4#386×C15111yescharacteristic
729C4#386×C15111yescharacteristic
730C4#392×C15111yescharacteristic
731C4#392×C15111yescharacteristic
732C4#394×C15111yescharacteristic
733C4#394×C15111yescharacteristic
734C2—21no—
735C2—21no—
736C2—21no—
737C2—21no—
738C2—21no—
739C2—21no—
740C2—82no—
741C2#1438×C15111yescharacteristic
742C2#2009×C15112yes—
subgroupG/H
center, socleC22×C151#392
commutatorC22×C4C22×C4×C151
Frattini, cosocleC23×C4C23×C151
prime radicalC22×#41×C151C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C151 ◁ C23×C4×C151 ◁ G

Complements

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

NH ≅ G/Ntype
4. C2×#419×C151C2semidirect
5. C2×#419×C151C2semidirect
6. C2×#344×C151C2semidirect
7. #1740×C151C2semidirect
15. #536×C151C4semidirect
371. #11005C151direct (N × H)
372. C151#11005direct (N × H)
376. C2×#419C2×C151semidirect
377. C2×#419C2×C151semidirect
378. C2×#344C2×C151semidirect
379. #1740C2×C151semidirect
387. #536C4×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#536×C1512
C2×#421×C1512
#2896×C1512
C2×#419×C1512
C2×#344×C1512
#1740×C1512
#11005151