Finite Group Databasebeta

← C151×#24536 #50329461

Subgroups — C151×#24536 #50329461

Order 38656.

1006 conjugacy classes of subgroups.

The subgroup lattice has 722 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#452×C151C211yesmaximal, characteristic
2C2×#416×C151C211yesmaximal, characteristic
3#2499×C151C211yesmaximal, characteristic, complemented
4#2339×C151C211yesmaximal, characteristic
5#2074×C151C211yesmaximal, characteristic, complemented
6#2072×C151C211yesmaximal, characteristic, complemented
7#2056×C151C211yesmaximal, characteristic, complemented
8#2056×C151C211yesmaximal, characteristic, complemented
9#1892×C151C211yesmaximal, characteristic, complemented
10#1877×C151C211yesmaximal, characteristic, complemented
11#1877×C151C211yesmaximal, characteristic, complemented
12#1850×C151C211yesmaximal, characteristic, complemented
13#1825×C151C211yesmaximal, characteristic, complemented
14#1804×C151C211yesmaximal, characteristic, complemented
15#1802×C151C211yesmaximal, characteristic, complemented
16C22×#41×C151C2211yescharacteristic
17C22×Q16×C151C2211yescharacteristic
18C22×SD16×C151C2211yescharacteristic
19C23×C8×C151C2211yescharacteristic
20C2×C22⋊Q8×C151C2211yescharacteristic
21C2×C4×D4×C151C2211yescharacteristic
22C2×C4×D4×C151C2211yescharacteristic
23C2×#117×C151C2211yescharacteristic
24#452×C151—24no—
25C2×C4⋊C8×C151C2211yescharacteristic
26C2×C4⋊C8×C151C2211yescharacteristic
27#416×C151—24no—
28C2×#103×C151C2211yescharacteristic
29C2×#103×C151C2211yescharacteristic
30C2×#103×C151C2211yescharacteristic
31C2×#103×C151C2211yescharacteristic
32C2×#103×C151C2211yescharacteristic
33C2×#102×C151C2211yescharacteristic
34C2×#102×C151C2211yescharacteristic
35C2×#102×C151C2211yescharacteristic
36C2×C22⋊C8×C151C2211yescharacteristic
37#397×C151—21no—
38#397×C151—21no—
39#391×C151C2211yescharacteristic
40#391×C151C2211yescharacteristic
41#391×C151C2211yescharacteristic
42#391×C151C2211yescharacteristic
43#387×C151—21no—
44#387×C151—21no—
45#386×C151—21no—
46#386×C151—21no—
47#384×C151C2211yescharacteristic
48#382×C151C2211yescharacteristic
49#381×C151—21no—
50#380×C151C2211yescharacteristic
51C4×C22⋊C4×C151C2211yescharacteristic
52C2×#95×C151—21no—
53#340×C151C2211yescharacteristic
54#340×C151C2211yescharacteristic
55#340×C151C2211yescharacteristic
56#340×C151C2211yescharacteristic
57#340×C151C2211yescharacteristic
58#340×C151C2211yescharacteristic
59#336×C151C2211yescharacteristic
60#336×C151C2211yescharacteristic
61C2×#41×C151—22no—
62C2×#41×C151—22no—
63C2×#41×C151—22no—
64C2×#41×C151—41no—
65C2×#41×C151—41no—
66C2×#41×C151D414yes—
67C22×Q8×C151C2311yescharacteristic
68C22×Q8×C151C2311yescharacteristic
69C22×D4×C151—21no—
70C22×D4×C151C2311yescharacteristic
71C23×C4×C151—21no—
72C23×C4×C151—21no—
73C23×C4×C151—21no—
74C23×C4×C151C2311yescharacteristic
75C2×Q16×C151—22no—
76C2×Q16×C151—41no—
77C2×Q16×C151—41no—
78C2×SD16×C151—22no—
79C2×SD16×C151—22no—
80C2×SD16×C151—22no—
81C22×C8×C151—22no—
82C22×C8×C151—41no—
83C22×C8×C151—41no—
84C22×C8×C151C2311yescharacteristic
85C22×C8×C151C2311yescharacteristic
86C22×C8×C151C2311yescharacteristic
87C22×C8×C151C2311yescharacteristic
88C22⋊Q8×C151—22no—
89C22⋊Q8×C151—22no—
90C4×D4×C151—22no—
91C4×D4×C151—22no—
92C4×D4×C151—41no—
93C4×D4×C151—41no—
94#117×C151—22no—
95#117×C151—22no—
96C2×C4⋊C4×C151—21no—
97C2×C4⋊C4×C151—21no—
98C2×C4⋊C4×C151—21no—
99C2×C4⋊C4×C151C2311yescharacteristic
100C2×C4⋊C4×C151C2311yescharacteristic
101C2×C4⋊C4×C151C2311yescharacteristic
102C2×C4⋊C4×C151C2311yescharacteristic
103C2×C4⋊C4×C151C2311yescharacteristic
104C2×C22⋊C4×C151—21no—
105C2×C22⋊C4×C151—21no—
106C2×C22⋊C4×C151—21no—
107C2×C22⋊C4×C151—21no—
108C2×C22⋊C4×C151—21no—
109C2×C22⋊C4×C151D411yescharacteristic
110C2×C22⋊C4×C151D411yescharacteristic
111C2×C42×C151—21no—
112C2×C42×C151C2311yescharacteristic
113C2×C42×C151C2311yescharacteristic
114C4⋊C8×C151—41no—
115C4⋊C8×C151—41no—
116#103×C151—22no—
117#103×C151—22no—
118#103×C151—22no—
119#103×C151—41no—
120#103×C151—41no—
121#102×C151—22no—
122#102×C151—22no—
123#102×C151—22no—
124C22⋊C8×C151—22no—
125#95×C151—21no—
126#95×C151—21no—
127#95×C151—21no—
128#95×C151—21no—
129#95×C151—21no—
130#95×C151—21no—
131#95×C151—21no—
132#95×C151—21no—
133#95×C151—21no—
134#95×C151—21no—
135#95×C151—21no—
136#95×C151D411yescharacteristic
137#95×C151D411yescharacteristic
138C24×C151—21no—
139C24×C151C2×D411yescharacteristic
140#41×C151—28no—
141#41×C151—44no—
142#41×C151—44no—
143#41×C151—44no—
144C2×Q8×C151—21no—
145C2×Q8×C151—21no—
146C2×Q8×C151—21no—
147C2×Q8×C151—21no—
148C2×Q8×C151—21no—
149C2×Q8×C151—21no—
150C2×Q8×C151—21no—
151C2×Q8×C151—21no—
152C2×Q8×C151—21no—
153C2×Q8×C151—21no—
154C2×Q8×C151—21no—
155C2×Q8×C151C2×D412yes—
156C2×D4×C151—24no—
157C2×D4×C151—21no—
158C2×D4×C151—21no—
159C2×D4×C151—21no—
160C2×D4×C151—42no—
161C2×D4×C151—42no—
162C2×D4×C151C2×D412yes—
163C2×D4×C151#4112yes—
164C2×D4×C151#4112yes—
165C22×C4×C151—21no—
166C22×C4×C151—21no—
167C22×C4×C151—21no—
168C22×C4×C151—21no—
169C22×C4×C151—21no—
170C22×C4×C151—24no—
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—42no—
178C22×C4×C151—42no—
179C22×C4×C151—42no—
180C22×C4×C151—42no—
181C22×C4×C151—42no—
182C22×C4×C151—42no—
183C22×C4×C151—81no—
184C22×C4×C151—81no—
185C22×C4×C151C2×D411yescharacteristic
186C22×C4×C151C2×D411yescharacteristic
187C22×C4×C151C2×D411yescharacteristic
188C22×C4×C151C2×D411yescharacteristic
189C22×C4×C151C2×D412yes—
190C22×C4×C151C2×D411yescharacteristic
191C22×C4×C151#4112yes—
192C22×C4×C151C2411yescharacteristic
193Q16×C151—44no—
194SD16×C151—44no—
195C2×C8×C151—21no—
196C2×C8×C151—21no—
197C2×C8×C151—21no—
198C2×C8×C151—21no—
199C2×C8×C151—21no—
200C2×C8×C151—21no—
201C2×C8×C151—21no—
202C2×C8×C151—21no—
203C2×C8×C151—21no—
204C2×C8×C151—21no—
205C2×C8×C151—21no—
206C2×C8×C151—21no—
207C2×C8×C151—44no—
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—42no—
219C4⋊C4×C151—42no—
220C4⋊C4×C151—42no—
221C22⋊C4×C151—22no—
222C22⋊C4×C151—41no—
223C22⋊C4×C151—42no—
224C22⋊C4×C151—42no—
225C22⋊C4×C151—42no—
226C22⋊C4×C151—42no—
227C22⋊C4×C151—81no—
228C42×C151—21no—
229C42×C151—21no—
230C42×C151—21no—
231C42×C151—21no—
232C42×C151—42no—
233C23×C151—22no—
234C23×C151—22no—
235C23×C151—22no—
236C23×C151—21no—
237C23×C151—21no—
238C23×C151—21no—
239C23×C151—21no—
240C23×C151—21no—
241C23×C151—21no—
242C23×C151—41no—
243C23×C151—41no—
244C23×C151—41no—
245C23×C151—41no—
246C23×C151#12112yes—
247C23×C151C22×D411yescharacteristic
248Q8×C151—22no—
249Q8×C151—22no—
250Q8×C151—41no—
251Q8×C151—41no—
252Q8×C151—41no—
253Q8×C151—41no—
254Q8×C151—41no—
255Q8×C151—41no—
256D4×C151—22no—
257D4×C151—22no—
258D4×C151—22no—
259D4×C151—48no—
260D4×C151#12314yes—
261C2×C4×C151—21no—
262C2×C4×C151—21no—
263C2×C4×C151—21no—
264C2×C4×C151—21no—
265C2×C4×C151—22no—
266C2×C4×C151—22no—
267C2×C4×C151—22no—
268C2×C4×C151—22no—
269C2×C4×C151—22no—
270C2×C4×C151—21no—
271C2×C4×C151—21no—
272C2×C4×C151—21no—
273C2×C4×C151—21no—
274C2×C4×C151—21no—
275C2×C4×C151—21no—
276C2×C4×C151—21no—
277C2×C4×C151—21no—
278C2×C4×C151—21no—
279C2×C4×C151—48no—
280C2×C4×C151—41no—
281C2×C4×C151—41no—
282C2×C4×C151—41no—
283C2×C4×C151—41no—
284C2×C4×C151—41no—
285C2×C4×C151—41no—
286C2×C4×C151—41no—
287C2×C4×C151—41no—
288C2×C4×C151—41no—
289C2×C4×C151—41no—
290C2×C4×C151—41no—
291C2×C4×C151—41no—
292C2×C4×C151—41no—
293C2×C4×C151—41no—
294C2×C4×C151—41no—
295C2×C4×C151—41no—
296C2×C4×C151—41no—
297C2×C4×C151—41no—
298C2×C4×C151—41no—
299C2×C4×C151—41no—
300C2×C4×C151—84no—
301C2×C4×C151—84no—
302C2×C4×C151#12112yes—
303C2×C4×C151#13512yes—
304C2×C4×C151C22×D411yescharacteristic
305C2×C4×C151C2×#4111yescharacteristic
306C2×C4×C151C2×#4111yescharacteristic
307C2×C4×C151C2×#4111yescharacteristic
308C2×C4×C151H(5,𝔽2)11yescharacteristic
309C2×C4×C151H(5,𝔽2)11yescharacteristic
310C8×C151—41no—
311C8×C151—41no—
312C8×C151—41no—
313C8×C151—41no—
314C22×C151—22no—
315C22×C151—24no—
316C22×C151—22no—
317C22×C151—22no—
318C22×C151—42no—
319C22×C151—42no—
320C22×C151—41no—
321C22×C151—42no—
322C22×C151—41no—
323C22×C151—42no—
324C22×C151—42no—
325C22×C151—41no—
326C22×C151—41no—
327C22×C151—42no—
328C22×C151C2×#12111yescharacteristic
329C22×C151#54611yescharacteristic
330C22×C151#54611yescharacteristic
331C22×C151C2×#13511yescharacteristic
332C22×C151#57511yescharacteristic
333C22×C151#57711yescharacteristic
334C22×C151#57811yescharacteristic
335C4×C151—22no—
336C4×C151—22no—
337C4×C151—42no—
338C4×C151—41no—
339C4×C151—41no—
340C4×C151—41no—
341C4×C151—81no—
342C4×C151—81no—
343C4×C151—81no—
344C4×C151—81no—
345C4×C151—81no—
346C4×C151—81no—
347C4×C151C2×#12311yescharacteristic
348C4×C151#53411yescharacteristic
349C4×C151#55111yescharacteristic
350C4×C151#55111yescharacteristic
351C2×C151—42no—
352C2×C151—44no—
353C2×C151#241211yescharacteristic
354C2×C151#303511yescharacteristic
355C2×C151#304611yescharacteristic
356C2×C151#329611yescharacteristic
357C2×C151#330211yescharacteristic
358C2×C151#331111yescharacteristic
359C2×C151#331511yescharacteristic
360#24536C15111yesmaximal, characteristic, direct product factor, Sylow
361C151#2453611yescharacteristic, direct product factor, Sylow
362C2×#452C2×C15111yescharacteristic
363C2×#416C2×C15111yescharacteristic
364#2499C2×C15111yescharacteristic, complemented
365#2339C2×C15111yescharacteristic
366#2074C2×C15111yescharacteristic, complemented
367#2072C2×C15111yescharacteristic, complemented
368#2056C2×C15111yescharacteristic, complemented
369#2056C2×C15111yescharacteristic, complemented
370#1892C2×C15111yescharacteristic, complemented
371#1877C2×C15111yescharacteristic, complemented
372#1877C2×C15111yescharacteristic, complemented
373#1850C2×C15111yescharacteristic, complemented
374#1825C2×C15111yescharacteristic, complemented
375#1804C2×C15111yescharacteristic, complemented
376#1802C2×C15111yescharacteristic, complemented
377C22×#41C22×C15111yescharacteristic
378C22×Q16C22×C15111yescharacteristic
379C22×SD16C22×C15111yescharacteristic
380C23×C8C22×C15111yescharacteristic
381C2×C22⋊Q8C22×C15111yescharacteristic
382C2×C4×D4C22×C15111yescharacteristic
383C2×C4×D4C22×C15111yescharacteristic
384C2×#117C22×C15111yescharacteristic
385#452—24no—
386C2×C4⋊C8C22×C15111yescharacteristic
387C2×C4⋊C8C22×C15111yescharacteristic
388#416—24no—
389C2×#103C22×C15111yescharacteristic
390C2×#103C22×C15111yescharacteristic
391C2×#103C22×C15111yescharacteristic
392C2×#103C22×C15111yescharacteristic
393C2×#103C22×C15111yescharacteristic
394C2×#102C22×C15111yescharacteristic
395C2×#102C22×C15111yescharacteristic
396C2×#102C22×C15111yescharacteristic
397C2×C22⋊C8C22×C15111yescharacteristic
398#397—21no—
399#397—21no—
400#391C22×C15111yescharacteristic
401#391C22×C15111yescharacteristic
402#391C22×C15111yescharacteristic
403#391C22×C15111yescharacteristic
404#387—21no—
405#387—21no—
406#386—21no—
407#386—21no—
408#384C22×C15111yescharacteristic
409#382C22×C15111yescharacteristic
410#381—21no—
411#380C22×C15111yescharacteristic
412C4×C22⋊C4C22×C15111yescharacteristic
413C2×#95—21no—
414#340C22×C15111yescharacteristic
415#340C22×C15111yescharacteristic
416#340C22×C15111yescharacteristic
417#340C22×C15111yescharacteristic
418#340C22×C15111yescharacteristic
419#340C22×C15111yescharacteristic
420#336C22×C15111yescharacteristic
421#336C22×C15111yescharacteristic
422C2×#41—22no—
423C2×#41—22no—
424C2×#41—22no—
425C2×#41—41no—
426C2×#41—41no—
427C2×#41D4×C15114yes—
428C22×Q8C23×C15111yescharacteristic
429C22×Q8C23×C15111yescharacteristic
430C22×D4—21no—
431C22×D4C23×C15111yescharacteristic
432C23×C4—21no—
433C23×C4—21no—
434C23×C4—21no—
435C23×C4C23×C15111yescharacteristic
436C2×Q16—22no—
437C2×Q16—41no—
438C2×Q16—41no—
439C2×SD16—22no—
440C2×SD16—22no—
441C2×SD16—22no—
442C22×C8—22no—
443C22×C8—41no—
444C22×C8—41no—
445C22×C8C23×C15111yescharacteristic
446C22×C8C23×C15111yescharacteristic
447C22×C8C23×C15111yescharacteristic
448C22×C8C23×C15111yescharacteristic
449C22⋊Q8—22no—
450C22⋊Q8—22no—
451C4×D4—22no—
452C4×D4—22no—
453C4×D4—41no—
454C4×D4—41no—
455#117—22no—
456#117—22no—
457C2×C4⋊C4—21no—
458C2×C4⋊C4—21no—
459C2×C4⋊C4—21no—
460C2×C4⋊C4C23×C15111yescharacteristic
461C2×C4⋊C4C23×C15111yescharacteristic
462C2×C4⋊C4C23×C15111yescharacteristic
463C2×C4⋊C4C23×C15111yescharacteristic
464C2×C4⋊C4C23×C15111yescharacteristic
465C2×C22⋊C4—21no—
466C2×C22⋊C4—21no—
467C2×C22⋊C4—21no—
468C2×C22⋊C4—21no—
469C2×C22⋊C4—21no—
470C2×C22⋊C4D4×C15111yescharacteristic
471C2×C22⋊C4D4×C15111yescharacteristic
472C2×C42—21no—
473C2×C42C23×C15111yescharacteristic
474C2×C42C23×C15111yescharacteristic
475C4⋊C8—41no—
476C4⋊C8—41no—
477#103—22no—
478#103—22no—
479#103—22no—
480#103—41no—
481#103—41no—
482#102—22no—
483#102—22no—
484#102—22no—
485C22⋊C8—22no—
486#95—21no—
487#95—21no—
488#95—21no—
489#95—21no—
490#95—21no—
491#95—21no—
492#95—21no—
493#95—21no—
494#95—21no—
495#95—21no—
496#95—21no—
497#95D4×C15111yescharacteristic
498#95D4×C15111yescharacteristic
499C24—21no—
500C24C2×D4×C15111yescharacteristic
501#41—28no—
502#41—44no—
503#41—44no—
504#41—44no—
505C2×Q8—21no—
506C2×Q8—21no—
507C2×Q8—21no—
508C2×Q8—21no—
509C2×Q8—21no—
510C2×Q8—21no—
511C2×Q8—21no—
512C2×Q8—21no—
513C2×Q8—21no—
514C2×Q8—21no—
515C2×Q8—21no—
516C2×Q8C2×D4×C15112yes—
517C2×D4—24no—
518C2×D4—21no—
519C2×D4—21no—
520C2×D4—21no—
521C2×D4—42no—
522C2×D4—42no—
523C2×D4C2×D4×C15112yes—
524C2×D4#41×C15112yes—
525C2×D4#41×C15112yes—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—24no—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—42no—
539C22×C4—42no—
540C22×C4—42no—
541C22×C4—42no—
542C22×C4—42no—
543C22×C4—42no—
544C22×C4—81no—
545C22×C4—81no—
546C22×C4C2×D4×C15111yescharacteristic
547C22×C4C2×D4×C15111yescharacteristic
548C22×C4C2×D4×C15111yescharacteristic
549C22×C4C2×D4×C15111yescharacteristic
550C22×C4C2×D4×C15112yes—
551C22×C4C2×D4×C15111yescharacteristic
552C22×C4#41×C15112yes—
553C22×C4C24×C15111yescharacteristic
554Q16—44no—
555SD16—44no—
556C2×C8—21no—
557C2×C8—21no—
558C2×C8—21no—
559C2×C8—21no—
560C2×C8—21no—
561C2×C8—21no—
562C2×C8—21no—
563C2×C8—21no—
564C2×C8—21no—
565C2×C8—21no—
566C2×C8—21no—
567C2×C8—21no—
568C2×C8—44no—
569C4⋊C4—21no—
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—42no—
580C4⋊C4—42no—
581C4⋊C4—42no—
582C22⋊C4—22no—
583C22⋊C4—41no—
584C22⋊C4—42no—
585C22⋊C4—42no—
586C22⋊C4—42no—
587C22⋊C4—42no—
588C22⋊C4—81no—
589C42—21no—
590C42—21no—
591C42—21no—
592C42—21no—
593C42—42no—
594C23—22no—
595C23—22no—
596C23—22no—
597C23—21no—
598C23—21no—
599C23—21no—
600C23—21no—
601C23—21no—
602C23—21no—
603C23—41no—
604C23—41no—
605C23—41no—
606C23—41no—
607C23#121×C15112yes—
608C23C22×D4×C15111yescharacteristic
609Q8—22no—
610Q8—22no—
611Q8—41no—
612Q8—41no—
613Q8—41no—
614Q8—41no—
615Q8—41no—
616Q8—41no—
617D4—22no—
618D4—22no—
619D4—22no—
620D4—48no—
621D4#123×C15114yes—
622C2×C4—21no—
623C2×C4—21no—
624C2×C4—21no—
625C2×C4—21no—
626C2×C4—22no—
627C2×C4—22no—
628C2×C4—22no—
629C2×C4—22no—
630C2×C4—22no—
631C2×C4—21no—
632C2×C4—21no—
633C2×C4—21no—
634C2×C4—21no—
635C2×C4—21no—
636C2×C4—21no—
637C2×C4—21no—
638C2×C4—21no—
639C2×C4—21no—
640C2×C4—48no—
641C2×C4—41no—
642C2×C4—41no—
643C2×C4—41no—
644C2×C4—41no—
645C2×C4—41no—
646C2×C4—41no—
647C2×C4—41no—
648C2×C4—41no—
649C2×C4—41no—
650C2×C4—41no—
651C2×C4—41no—
652C2×C4—41no—
653C2×C4—41no—
654C2×C4—41no—
655C2×C4—41no—
656C2×C4—41no—
657C2×C4—41no—
658C2×C4—41no—
659C2×C4—41no—
660C2×C4—41no—
661C2×C4—84no—
662C2×C4—84no—
663C2×C4#121×C15112yes—
664C2×C4#135×C15112yes—
665C2×C4C22×D4×C15111yescharacteristic
666C2×C4C2×#41×C15111yescharacteristic
667C2×C4C2×#41×C15111yescharacteristic
668C2×C4C2×#41×C15111yescharacteristic
669C2×C4H(5,𝔽2)×C15111yescharacteristic
670C2×C4H(5,𝔽2)×C15111yescharacteristic
671C8—41no—
672C8—41no—
673C8—41no—
674C8—41no—
675C22—22no—
676C22—24no—
677C22—22no—
678C22—22no—
679C22—42no—
680C22—42no—
681C22—41no—
682C22—42no—
683C22—41no—
684C22—42no—
685C22—42no—
686C22—41no—
687C22—41no—
688C22—42no—
689C22C2×#121×C15111yescharacteristic
690C22#546×C15111yescharacteristic
691C22#546×C15111yescharacteristic
692C22C2×#135×C15111yescharacteristic
693C22#575×C15111yescharacteristic
694C22#577×C15111yescharacteristic
695C22#578×C15111yescharacteristic
696C4—22no—
697C4—22no—
698C4—42no—
699C4—41no—
700C4—41no—
701C4—41no—
702C4—81no—
703C4—81no—
704C4—81no—
705C4—81no—
706C4—81no—
707C4—81no—
708C4C2×#123×C15111yescharacteristic
709C4#534×C15111yescharacteristic
710C4#551×C15111yescharacteristic
711C4#551×C15111yescharacteristic
712C2—42no—
713C2—44no—
714C2#2412×C15111yescharacteristic
715C2#3035×C15111yescharacteristic
716C2#3046×C15111yescharacteristic
717C2#3296×C15111yescharacteristic
718C2#3302×C15111yescharacteristic
719C2#3311×C15111yescharacteristic
720C2#3315×C15111yescharacteristic
subgroupG/H
center, socleC23×C151C22×D4
commutator, Frattini, cosocleC22×C4C24×C151
prime radicalC22×#41×C151C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C151 ◁ C4×C22⋊C4×C151 ◁ G

Complements

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

NH ≅ G/Ntype
3. #2499×C151C2semidirect
5. #2074×C151C2semidirect
6. #2072×C151C2semidirect
7. #2056×C151C2semidirect
8. #2056×C151C2semidirect
9. #1892×C151C2semidirect
10. #1877×C151C2semidirect
11. #1877×C151C2semidirect
12. #1850×C151C2semidirect
13. #1825×C151C2semidirect
14. #1804×C151C2semidirect
15. #1802×C151C2semidirect
360. #24536C151direct (N × H)
361. C151#24536direct (N × H)
364. #2499C2×C151semidirect
366. #2074C2×C151semidirect
367. #2072C2×C151semidirect
368. #2056C2×C151semidirect
369. #2056C2×C151semidirect
370. #1892C2×C151semidirect
371. #1877C2×C151semidirect
372. #1877C2×C151semidirect
373. #1850C2×C151semidirect
374. #1825C2×C151semidirect
375. #1804C2×C151semidirect
376. #1802C2×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#452×C1512
C2×#416×C1512
#2499×C1512
#2339×C1512
#2074×C1512
#2072×C1512
#2056×C1512
#1892×C1512
#1877×C1512
#1850×C1512
#1825×C1512
#1804×C1512
#1802×C1512
#24536151