Finite Group Databasebeta

← C151×#11003 #50315928

Subgroups — C151×#11003 #50315928

Order 38656.

1292 conjugacy classes of subgroups.

The subgroup lattice has 802 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3449×C151C211yesmaximal, characteristic
2C2×#421×C151C211yesmaximal, characteristic, complemented
3C2×#421×C151C211yesmaximal, characteristic, complemented
4C2×#421×C151C211yesmaximal, characteristic, complemented
5#2896×C151C211yesmaximal, characteristic, complemented
6C2×#344×C151C211yesmaximal, characteristic, complemented
7#1740×C151C211yesmaximal, characteristic, complemented
8C22×#41×C151C2211yescharacteristic
9C22×#41×C151C2211yescharacteristic
10C22×M16×C151C2211yescharacteristic
11C22×M16×C151C2211yescharacteristic
12#537×C151—22no—
13#536×C151—21no—
14#536×C151C412yescomplemented
15#535×C151—21no—
16#535×C151C412yescomplemented
17#534×C151—22no—
18#532×C151—22no—
19#525×C151—22no—
20#525×C151—22no—
21C2×#117×C151C2211yescharacteristic
22C2×#117×C151C2211yescharacteristic
23C2×#117×C151C2211yescharacteristic
24#421×C151—22no—
25#421×C151—22no—
26#421×C151—22no—
27#421×C151—22no—
28#421×C151—22no—
29#421×C151—22no—
30C2×#104×C151—22no—
31C2×#104×C151—22no—
32C2×#104×C151—22no—
33#419×C151—21no—
34#418×C151—21no—
35#417×C151—22no—
36#416×C151—22no—
37#344×C151—22no—
38#342×C151—22no—
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×C151—21no—
49C2×#41×C151—21no—
50C2×#41×C151—21no—
51C2×#41×C151—21no—
52C2×#41×C151—21no—
53C2×#41×C151—21no—
54C2×#41×C151—21no—
55C2×#41×C151—21no—
56C2×#41×C151—21no—
57C2×#41×C151—21no—
58C2×#41×C151—21no—
59C2×#41×C151C2×C412yes—
60C2×#41×C151D412yes—
61C2×#41×C151D412yes—
62C2×#41×C151D412yes—
63C22×Q8×C151C2×C411yescharacteristic
64C22×Q8×C151D411yescharacteristic
65C22×D4×C151—21no—
66C22×D4×C151—21no—
67C22×D4×C151C2×C411yescharacteristic
68C22×D4×C151D411yescharacteristic
69C23×C4×C151—21no—
70C23×C4×C151—21no—
71C23×C4×C151C2311yescharacteristic
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×C151—21no—
82C2×M16×C151D412yescomplemented
83C2×M16×C151D412yescomplemented
84C22×C8×C151—21no—
85C22×C8×C151—21no—
86C4⋊Q8×C151—22no—
87#127×C151—22no—
88#124×C151—22no—
89#124×C151—22no—
90#123×C151—24no—
91#123×C151—24no—
92C22⋊Q8×C151—24no—
93C22⋊Q8×C151—24no—
94#121×C151—24no—
95#121×C151—28no—
96#121×C151—24no—
97#120×C151—24no—
98#120×C151—24no—
99C4×D4×C151—28no—
100#117×C151—21no—
101#117×C151—21no—
102#117×C151—21no—
103#117×C151—21no—
104#117×C151—21no—
105#117×C151—21no—
106#117×C151—21no—
107#117×C151—21no—
108#117×C151—21no—
109#117×C151C2×C412yes—
110#117×C151D412yes—
111#117×C151D412yescomplemented
112C2×C4⋊C4×C151—21no—
113C2×C4⋊C4×C151—21no—
114C2×C4⋊C4×C151—21no—
115C2×C22⋊C4×C151—21no—
116C2×C22⋊C4×C151—21no—
117C2×C22⋊C4×C151D412yes—
118C2×C42×C151—21no—
119C2×C42×C151—21no—
120C2×C42×C151D412yescomplemented
121#104×C151—28no—
122#104×C151—28no—
123#104×C151—28no—
124#103×C151—24no—
125#102×C151—24no—
126C24×C151—21no—
127C24×C151—21no—
128C24×C151C2×D411yescharacteristic
129#41×C151—22no—
130#41×C151—22no—
131#41×C151—22no—
132#41×C151—22no—
133#41×C151—22no—
134#41×C151—22no—
135#41×C151—22no—
136#41×C151—22no—
137#41×C151—22no—
138#41×C151—22no—
139#41×C151—22no—
140#41×C151—22no—
141#41×C151—22no—
142#41×C151—22no—
143#41×C151—22no—
144#41×C151—22no—
145#41×C151—41no—
146#41×C151—41no—
147#41×C151—41no—
148#41×C151—41no—
149#41×C151—41no—
150#41×C151—41no—
151#41×C151—41no—
152#41×C151—41no—
153#41×C151—41no—
154#41×C151—41no—
155#41×C151—41no—
156#41×C151—41no—
157#41×C151—41no—
158#41×C151—41no—
159#41×C151—41no—
160#41×C151—41no—
161C2×Q8×C151—21no—
162C2×Q8×C151—21no—
163C2×Q8×C151—21no—
164C2×Q8×C151—21no—
165C2×Q8×C151—21no—
166C2×Q8×C151—21no—
167C2×Q8×C151—21no—
168C2×Q8×C151—21no—
169C2×Q8×C151—21no—
170C2×Q8×C151—21no—
171C2×Q8×C151C22⋊C412yes—
172C2×Q8×C151C22⋊C412yes—
173C2×D4×C151—22no—
174C2×D4×C151—22no—
175C2×D4×C151—22no—
176C2×D4×C151—22no—
177C2×D4×C151—28no—
178C2×D4×C151—21no—
179C2×D4×C151—21no—
180C2×D4×C151—21no—
181C2×D4×C151—21no—
182C2×D4×C151—21no—
183C2×D4×C151—21no—
184C2×D4×C151—21no—
185C2×D4×C151—21no—
186C2×D4×C151—21no—
187C2×D4×C151—21no—
188C2×D4×C151—41no—
189C2×D4×C151—41no—
190C2×D4×C151—41no—
191C2×D4×C151—41no—
192C2×D4×C151—41no—
193C2×D4×C151—41no—
194C2×D4×C151—41no—
195C2×D4×C151—41no—
196C2×D4×C151C22⋊C412yes—
197C2×D4×C151C22⋊C412yes—
198C22×C4×C151—21no—
199C22×C4×C151—21no—
200C22×C4×C151—22no—
201C22×C4×C151—22no—
202C22×C4×C151—22no—
203C22×C4×C151—22no—
204C22×C4×C151—22no—
205C22×C4×C151—22no—
206C22×C4×C151—41no—
207C22×C4×C151—41no—
208C22×C4×C151—41no—
209C22×C4×C151—41no—
210C22×C4×C151—41no—
211C22×C4×C151—41no—
212C22×C4×C151—41no—
213C22×C4×C151—41no—
214C22×C4×C151—41no—
215C22×C4×C151C22×C411yescharacteristic
216C22×C4×C151C2×D411yescharacteristic
217C22×C4×C151C2×D411yescharacteristic
218C22×C4×C151C2×D411yescharacteristic
219C22×C4×C151C2×D411yescharacteristic
220C22×C4×C151C2×D411yescharacteristic
221C22×C4×C151C2×D411yescharacteristic
222C22×C4×C151C2×D411yescharacteristic
223C22×C4×C151C2×D411yescharacteristic
224C22×C4×C151C2×D411yescharacteristic
225C22×C4×C151#4111yescharacteristic
226C22×C4×C151#4111yescharacteristic
227C22×C4×C151#4111yescharacteristic
228C22×C4×C151#4111yescharacteristic
229M16×C151—22no—
230M16×C151—22no—
231M16×C151—22no—
232M16×C151—22no—
233M16×C151—41no—
234M16×C151—41no—
235M16×C151—41no—
236M16×C151—41no—
237C2×C8×C151—22no—
238C2×C8×C151—22no—
239C2×C8×C151—41no—
240C2×C8×C151—41no—
241C2×C8×C151—41no—
242C2×C8×C151—41no—
243C4⋊C4×C151—28no—
244C4⋊C4×C151—22no—
245C4⋊C4×C151—22no—
246C4⋊C4×C151—22no—
247C4⋊C4×C151—41no—
248C4⋊C4×C151—41no—
249C4⋊C4×C151—41no—
250C22⋊C4×C151—28no—
251C22⋊C4×C151—28no—
252C22⋊C4×C151—22no—
253C22⋊C4×C151—22no—
254C22⋊C4×C151—41no—
255C22⋊C4×C151—41no—
256C22⋊C4×C151—41no—
257C22⋊C4×C151C22⋊C414yes—
258C42×C151—22no—
259C42×C151—22no—
260C42×C151—22no—
261C42×C151—22no—
262C42×C151—22no—
263C42×C151—41no—
264C23×C151—22no—
265C23×C151—22no—
266C23×C151—41no—
267C23×C151—41no—
268C23×C151—41no—
269C23×C151—41no—
270C23×C151—81no—
271C23×C151—82no—
272C23×C151—82no—
273C23×C151C2×C22⋊C411yescharacteristic
274C23×C151#12011yescharacteristic
275C23×C151#12011yescharacteristic
276C23×C151#12111yescharacteristic
277C23×C151#12111yescharacteristic
278C23×C151#12411yescharacteristic
279C23×C151#12711yescharacteristic
280Q8×C151—22no—
281Q8×C151—22no—
282Q8×C151—22no—
283Q8×C151—22no—
284Q8×C151—41no—
285Q8×C151—41no—
286Q8×C151—41no—
287Q8×C151—41no—
288D4×C151—22no—
289D4×C151—22no—
290D4×C151—22no—
291D4×C151—22no—
292D4×C151—42no—
293D4×C151—42no—
294D4×C151—42no—
295D4×C151—42no—
296D4×C151—42no—
297D4×C151—42no—
298D4×C151—42no—
299D4×C151—42no—
300D4×C151—41no—
301D4×C151—41no—
302D4×C151—41no—
303D4×C151—41no—
304D4×C151—88no—
305C2×C4×C151—22no—
306C2×C4×C151—22no—
307C2×C4×C151—24no—
308C2×C4×C151—41no—
309C2×C4×C151—41no—
310C2×C4×C151—41no—
311C2×C4×C151—41no—
312C2×C4×C151—42no—
313C2×C4×C151—42no—
314C2×C4×C151—42no—
315C2×C4×C151—42no—
316C2×C4×C151—42no—
317C2×C4×C151—42no—
318C2×C4×C151—42no—
319C2×C4×C151—42no—
320C2×C4×C151—42no—
321C2×C4×C151—42no—
322C2×C4×C151—82no—
323C2×C4×C151—82no—
324C2×C4×C151—82no—
325C2×C4×C151C2×C22⋊C411yescharacteristic
326C2×C4×C151C2×C22⋊C411yescharacteristic
327C2×C4×C151C4×D411yescharacteristic
328C2×C4×C151C4×D411yescharacteristic
329C2×C4×C151C4×D411yescharacteristic
330C2×C4×C151C4×D411yescharacteristic
331C2×C4×C151#12011yescharacteristic
332C2×C4×C151#12011yescharacteristic
333C2×C4×C151#12011yescharacteristic
334C2×C4×C151#12011yescharacteristic
335C2×C4×C151#12011yescharacteristic
336C2×C4×C151#12011yescharacteristic
337C2×C4×C151#12111yescharacteristic
338C2×C4×C151#12111yescharacteristic
339C2×C4×C151#12111yescharacteristic
340C2×C4×C151#12111yescharacteristic
341C2×C4×C151#12111yescharacteristic
342C2×C4×C151#12111yescharacteristic
343C2×C4×C151#12111yescharacteristic
344C2×C4×C151#12111yescharacteristic
345C2×C4×C151#12111yescharacteristic
346C2×C4×C151#12111yescharacteristic
347C2×C4×C151#12311yescharacteristic
348C2×C4×C151#12311yescharacteristic
349C2×C4×C151#12311yescharacteristic
350C2×C4×C151#12311yescharacteristic
351C2×C4×C151#12411yescharacteristic
352C2×C4×C151#12711yescharacteristic
353C8×C151—42no—
354C8×C151—42no—
355C22×C151—41no—
356C22×C151—41no—
357C22×C151—41no—
358C22×C151—41no—
359C22×C151—41no—
360C22×C151—41no—
361C22×C151—41no—
362C22×C151—44no—
363C22×C151—44no—
364C22×C151—42no—
365C22×C151—42no—
366C22×C151—82no—
367C22×C151—82no—
368C22×C151—82no—
369C22×C151—82no—
370C22×C151#37911yescharacteristic
371C22×C151#39011yescharacteristic
372C22×C151#39011yescharacteristic
373C22×C151#39211yescharacteristic
374C22×C151#39211yescharacteristic
375C22×C151#39411yescharacteristic
376C22×C151#39411yescharacteristic
377C4×C151—44no—
378C4×C151—42no—
379C4×C151—42no—
380C4×C151—82no—
381C4×C151—82no—
382C4×C151#38611yescharacteristic
383C4×C151#38611yescharacteristic
384C4×C151#38611yescharacteristic
385C4×C151#38611yescharacteristic
386C4×C151#39211yescharacteristic
387C4×C151#39211yescharacteristic
388C4×C151#39411yescharacteristic
389C4×C151#39411yescharacteristic
390C2×C151—21no—
391C2×C151—21no—
392C2×C151—21no—
393C2×C151—21no—
394C2×C151—21no—
395C2×C151—21no—
396C2×C151—21no—
397C2×C151—82no—
398C2×C151—82no—
399C2×C151#143811yescharacteristic
400#11003C15111yesmaximal, characteristic, direct product factor, Sylow
401C151#1100311yescharacteristic, direct product factor, Sylow
402#3449C2×C15111yescharacteristic
403C2×#421C2×C15111yescharacteristic, complemented
404C2×#421C2×C15111yescharacteristic, complemented
405C2×#421C2×C15111yescharacteristic, complemented
406#2896C2×C15111yescharacteristic, complemented
407C2×#344C2×C15111yescharacteristic, complemented
408#1740C2×C15111yescharacteristic, complemented
409C22×#41C22×C15111yescharacteristic
410C22×#41C22×C15111yescharacteristic
411C22×M16C22×C15111yescharacteristic
412C22×M16C22×C15111yescharacteristic
413#537—22no—
414#536—21no—
415#536C4×C15112yescomplemented
416#535—21no—
417#535C4×C15112yescomplemented
418#534—22no—
419#532—22no—
420#525—22no—
421#525—22no—
422C2×#117C22×C15111yescharacteristic
423C2×#117C22×C15111yescharacteristic
424C2×#117C22×C15111yescharacteristic
425#421—22no—
426#421—22no—
427#421—22no—
428#421—22no—
429#421—22no—
430#421—22no—
431C2×#104—22no—
432C2×#104—22no—
433C2×#104—22no—
434#419—21no—
435#418—21no—
436#417—22no—
437#416—22no—
438#344—22no—
439#342—22no—
440C2×#41—21no—
441C2×#41—21no—
442C2×#41—21no—
443C2×#41—21no—
444C2×#41—21no—
445C2×#41—21no—
446C2×#41—21no—
447C2×#41—21no—
448C2×#41—21no—
449C2×#41—21no—
450C2×#41—21no—
451C2×#41—21no—
452C2×#41—21no—
453C2×#41—21no—
454C2×#41—21no—
455C2×#41—21no—
456C2×#41—21no—
457C2×#41—21no—
458C2×#41—21no—
459C2×#41—21no—
460C2×#41C2×C4×C15112yes—
461C2×#41D4×C15112yes—
462C2×#41D4×C15112yes—
463C2×#41D4×C15112yes—
464C22×Q8C2×C4×C15111yescharacteristic
465C22×Q8D4×C15111yescharacteristic
466C22×D4—21no—
467C22×D4—21no—
468C22×D4C2×C4×C15111yescharacteristic
469C22×D4D4×C15111yescharacteristic
470C23×C4—21no—
471C23×C4—21no—
472C23×C4C23×C15111yescharacteristic
473C2×M16—21no—
474C2×M16—21no—
475C2×M16—21no—
476C2×M16—21no—
477C2×M16—21no—
478C2×M16—21no—
479C2×M16—21no—
480C2×M16—21no—
481C2×M16—21no—
482C2×M16—21no—
483C2×M16D4×C15112yescomplemented
484C2×M16D4×C15112yescomplemented
485C22×C8—21no—
486C22×C8—21no—
487C4⋊Q8—22no—
488#127—22no—
489#124—22no—
490#124—22no—
491#123—24no—
492#123—24no—
493C22⋊Q8—24no—
494C22⋊Q8—24no—
495#121—24no—
496#121—28no—
497#121—24no—
498#120—24no—
499#120—24no—
500C4×D4—28no—
501#117—21no—
502#117—21no—
503#117—21no—
504#117—21no—
505#117—21no—
506#117—21no—
507#117—21no—
508#117—21no—
509#117—21no—
510#117C2×C4×C15112yes—
511#117D4×C15112yes—
512#117D4×C15112yescomplemented
513C2×C4⋊C4—21no—
514C2×C4⋊C4—21no—
515C2×C4⋊C4—21no—
516C2×C22⋊C4—21no—
517C2×C22⋊C4—21no—
518C2×C22⋊C4D4×C15112yes—
519C2×C42—21no—
520C2×C42—21no—
521C2×C42D4×C15112yescomplemented
522#104—28no—
523#104—28no—
524#104—28no—
525#103—24no—
526#102—24no—
527C24—21no—
528C24—21no—
529C24C2×D4×C15111yescharacteristic
530#41—22no—
531#41—22no—
532#41—22no—
533#41—22no—
534#41—22no—
535#41—22no—
536#41—22no—
537#41—22no—
538#41—22no—
539#41—22no—
540#41—22no—
541#41—22no—
542#41—22no—
543#41—22no—
544#41—22no—
545#41—22no—
546#41—41no—
547#41—41no—
548#41—41no—
549#41—41no—
550#41—41no—
551#41—41no—
552#41—41no—
553#41—41no—
554#41—41no—
555#41—41no—
556#41—41no—
557#41—41no—
558#41—41no—
559#41—41no—
560#41—41no—
561#41—41no—
562C2×Q8—21no—
563C2×Q8—21no—
564C2×Q8—21no—
565C2×Q8—21no—
566C2×Q8—21no—
567C2×Q8—21no—
568C2×Q8—21no—
569C2×Q8—21no—
570C2×Q8—21no—
571C2×Q8—21no—
572C2×Q8C22⋊C4×C15112yes—
573C2×Q8C22⋊C4×C15112yes—
574C2×D4—22no—
575C2×D4—22no—
576C2×D4—22no—
577C2×D4—22no—
578C2×D4—28no—
579C2×D4—21no—
580C2×D4—21no—
581C2×D4—21no—
582C2×D4—21no—
583C2×D4—21no—
584C2×D4—21no—
585C2×D4—21no—
586C2×D4—21no—
587C2×D4—21no—
588C2×D4—21no—
589C2×D4—41no—
590C2×D4—41no—
591C2×D4—41no—
592C2×D4—41no—
593C2×D4—41no—
594C2×D4—41no—
595C2×D4—41no—
596C2×D4—41no—
597C2×D4C22⋊C4×C15112yes—
598C2×D4C22⋊C4×C15112yes—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—22no—
602C22×C4—22no—
603C22×C4—22no—
604C22×C4—22no—
605C22×C4—22no—
606C22×C4—22no—
607C22×C4—41no—
608C22×C4—41no—
609C22×C4—41no—
610C22×C4—41no—
611C22×C4—41no—
612C22×C4—41no—
613C22×C4—41no—
614C22×C4—41no—
615C22×C4—41no—
616C22×C4C22×C4×C15111yescharacteristic
617C22×C4C2×D4×C15111yescharacteristic
618C22×C4C2×D4×C15111yescharacteristic
619C22×C4C2×D4×C15111yescharacteristic
620C22×C4C2×D4×C15111yescharacteristic
621C22×C4C2×D4×C15111yescharacteristic
622C22×C4C2×D4×C15111yescharacteristic
623C22×C4C2×D4×C15111yescharacteristic
624C22×C4C2×D4×C15111yescharacteristic
625C22×C4C2×D4×C15111yescharacteristic
626C22×C4#41×C15111yescharacteristic
627C22×C4#41×C15111yescharacteristic
628C22×C4#41×C15111yescharacteristic
629C22×C4#41×C15111yescharacteristic
630M16—22no—
631M16—22no—
632M16—22no—
633M16—22no—
634M16—41no—
635M16—41no—
636M16—41no—
637M16—41no—
638C2×C8—22no—
639C2×C8—22no—
640C2×C8—41no—
641C2×C8—41no—
642C2×C8—41no—
643C2×C8—41no—
644C4⋊C4—28no—
645C4⋊C4—22no—
646C4⋊C4—22no—
647C4⋊C4—22no—
648C4⋊C4—41no—
649C4⋊C4—41no—
650C4⋊C4—41no—
651C22⋊C4—28no—
652C22⋊C4—28no—
653C22⋊C4—22no—
654C22⋊C4—22no—
655C22⋊C4—41no—
656C22⋊C4—41no—
657C22⋊C4—41no—
658C22⋊C4C22⋊C4×C15114yes—
659C42—22no—
660C42—22no—
661C42—22no—
662C42—22no—
663C42—22no—
664C42—41no—
665C23—22no—
666C23—22no—
667C23—41no—
668C23—41no—
669C23—41no—
670C23—41no—
671C23—81no—
672C23—82no—
673C23—82no—
674C23C2×C22⋊C4×C15111yescharacteristic
675C23#120×C15111yescharacteristic
676C23#120×C15111yescharacteristic
677C23#121×C15111yescharacteristic
678C23#121×C15111yescharacteristic
679C23#124×C15111yescharacteristic
680C23#127×C15111yescharacteristic
681Q8—22no—
682Q8—22no—
683Q8—22no—
684Q8—22no—
685Q8—41no—
686Q8—41no—
687Q8—41no—
688Q8—41no—
689D4—22no—
690D4—22no—
691D4—22no—
692D4—22no—
693D4—42no—
694D4—42no—
695D4—42no—
696D4—42no—
697D4—42no—
698D4—42no—
699D4—42no—
700D4—42no—
701D4—41no—
702D4—41no—
703D4—41no—
704D4—41no—
705D4—88no—
706C2×C4—24no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—41no—
710C2×C4—41no—
711C2×C4—41no—
712C2×C4—41no—
713C2×C4—42no—
714C2×C4—42no—
715C2×C4—42no—
716C2×C4—42no—
717C2×C4—42no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—82no—
724C2×C4—82no—
725C2×C4—82no—
726C2×C4C2×C22⋊C4×C15111yescharacteristic
727C2×C4C2×C22⋊C4×C15111yescharacteristic
728C2×C4C4×D4×C15111yescharacteristic
729C2×C4C4×D4×C15111yescharacteristic
730C2×C4C4×D4×C15111yescharacteristic
731C2×C4C4×D4×C15111yescharacteristic
732C2×C4#120×C15111yescharacteristic
733C2×C4#120×C15111yescharacteristic
734C2×C4#120×C15111yescharacteristic
735C2×C4#120×C15111yescharacteristic
736C2×C4#120×C15111yescharacteristic
737C2×C4#120×C15111yescharacteristic
738C2×C4#121×C15111yescharacteristic
739C2×C4#121×C15111yescharacteristic
740C2×C4#121×C15111yescharacteristic
741C2×C4#121×C15111yescharacteristic
742C2×C4#121×C15111yescharacteristic
743C2×C4#121×C15111yescharacteristic
744C2×C4#121×C15111yescharacteristic
745C2×C4#121×C15111yescharacteristic
746C2×C4#121×C15111yescharacteristic
747C2×C4#121×C15111yescharacteristic
748C2×C4#123×C15111yescharacteristic
749C2×C4#123×C15111yescharacteristic
750C2×C4#123×C15111yescharacteristic
751C2×C4#123×C15111yescharacteristic
752C2×C4#124×C15111yescharacteristic
753C2×C4#127×C15111yescharacteristic
754C8—42no—
755C8—42no—
756C22—41no—
757C22—41no—
758C22—41no—
759C22—41no—
760C22—41no—
761C22—41no—
762C22—41no—
763C22—44no—
764C22—44no—
765C22—42no—
766C22—42no—
767C22—82no—
768C22—82no—
769C22—82no—
770C22—82no—
771C22#379×C15111yescharacteristic
772C22#390×C15111yescharacteristic
773C22#390×C15111yescharacteristic
774C22#392×C15111yescharacteristic
775C22#392×C15111yescharacteristic
776C22#394×C15111yescharacteristic
777C22#394×C15111yescharacteristic
778C4—44no—
779C4—42no—
780C4—42no—
781C4—82no—
782C4—82no—
783C4#386×C15111yescharacteristic
784C4#386×C15111yescharacteristic
785C4#386×C15111yescharacteristic
786C4#386×C15111yescharacteristic
787C4#392×C15111yescharacteristic
788C4#392×C15111yescharacteristic
789C4#394×C15111yescharacteristic
790C4#394×C15111yescharacteristic
791C2—21no—
792C2—21no—
793C2—21no—
794C2—21no—
795C2—21no—
796C2—21no—
797C2—21no—
798C2—82no—
799C2—82no—
800C2#1438×C15111yescharacteristic
subgroupG/H
centerC4×C151#392
commutatorC22×C4C22×C4×C151
Frattini, cosocleC23×C4C23×C151
socleC2×C151#1438
prime radical#3449×C151C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C4×C151 ◁ C23×C4×C151 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#421×C151C2semidirect
3. C2×#421×C151C2semidirect
4. C2×#421×C151C2semidirect
5. #2896×C151C2semidirect
6. C2×#344×C151C2semidirect
7. #1740×C151C2semidirect
14. #536×C151C4semidirect
16. #535×C151C4semidirect
82. C2×M16×C151D4semidirect
83. C2×M16×C151D4semidirect
111. #117×C151D4semidirect
120. C2×C42×C151D4semidirect
400. #11003C151direct (N × H)
401. C151#11003direct (N × H)
403. C2×#421C2×C151semidirect
404. C2×#421C2×C151semidirect
405. C2×#421C2×C151semidirect
406. #2896C2×C151semidirect
407. C2×#344C2×C151semidirect
408. #1740C2×C151semidirect
415. #536C4×C151semidirect
417. #535C4×C151semidirect
483. C2×M16D4×C151semidirect
484. C2×M16D4×C151semidirect
512. #117D4×C151semidirect
521. C2×C42D4×C151semidirect

Maximal subgroups

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

subgroupindex
#3449×C1512
C2×#421×C1512
#2896×C1512
C2×#344×C1512
#1740×C1512
#11003151