Finite Group Databasebeta

← C151×#24484 #50329409

Subgroups — C151×#24484 #50329409

Order 38656.

1012 conjugacy classes of subgroups.

The subgroup lattice has 754 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#482×C151C211yesmaximal, characteristic, complemented
2C2×#416×C151C211yesmaximal, characteristic, complemented
3#2431×C151C211yesmaximal, characteristic
4#2347×C151C211yesmaximal, characteristic, complemented
5#2066×C151C211yesmaximal, characteristic, complemented
6#2065×C151C211yesmaximal, characteristic, complemented
7#2042×C151C211yesmaximal, characteristic, complemented
8#2041×C151C211yesmaximal, characteristic, complemented
9#1983×C151C211yesmaximal, characteristic, complemented
10#1982×C151C211yesmaximal, characteristic, complemented
11#1928×C151C211yesmaximal, characteristic, complemented
12#1925×C151C211yesmaximal, characteristic, complemented
13#1893×C151C211yesmaximal, characteristic, complemented
14#1850×C151C211yesmaximal, characteristic, complemented
15#1788×C151C211yesmaximal, characteristic, complemented
16C22×#41×C151C2211yescharacteristic
17C23×C8×C151C2211yescharacteristic
18C2×#127×C151C2211yescharacteristic
19C2×#124×C151C2211yescharacteristic
20C2×#121×C151C2211yescharacteristic
21C2×#117×C151C2211yescharacteristic
22#482×C151—24no—
23C2×#107×C151C2211yescharacteristic
24C2×#106×C151C2211yescharacteristic
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×#102×C151C2211yescharacteristic
33C2×#102×C151C2211yescharacteristic
34C2×#102×C151C2211yescharacteristic
35C2×#102×C151C2211yescharacteristic
36C2×#102×C151C2211yescharacteristic
37C2×#102×C151C2211yescharacteristic
38C2×#102×C151C2211yescharacteristic
39C2×#102×C151C2211yescharacteristic
40C2×C22⋊C8×C151C2211yescharacteristic
41#392×C151—21no—
42#392×C151—21no—
43#391×C151C2211yescharacteristic
44#390×C151C2211yescharacteristic
45#389×C151C2211yescharacteristic
46#389×C151C2211yescharacteristic
47#388×C151—21no—
48#388×C151—21no—
49#386×C151—21no—
50#386×C151—21no—
51#383×C151—21no—
52#380×C151C2211yescharacteristic
53C4×C4⋊C4×C151—21no—
54C4×C4⋊C4×C151C2211yescharacteristic
55C4×C4⋊C4×C151C2211yescharacteristic
56C4×C22⋊C4×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—22no—
65C2×#41×C151—41no—
66C2×#41×C151—41no—
67C22×Q8×C151C2311yescharacteristic
68C22×D4×C151—21no—
69C22×D4×C151—21no—
70C22×D4×C151—21no—
71C22×D4×C151—21no—
72C22×D4×C151C2311yescharacteristic
73C22×D4×C151C2311yescharacteristic
74C23×C4×C151—21no—
75C23×C4×C151C2311yescharacteristic
76C22×C8×C151—22no—
77C22×C8×C151—41no—
78C22×C8×C151—41no—
79C22×C8×C151C2311yescharacteristic
80C22×C8×C151C2311yescharacteristic
81C22×C8×C151C2311yescharacteristic
82C22×C8×C151C2311yescharacteristic
83#127×C151—22no—
84#127×C151—41no—
85#124×C151—22no—
86#124×C151—41no—
87#121×C151—22no—
88#121×C151—22no—
89#117×C151—22no—
90#117×C151D414yescomplemented
91C2×C4⋊C4×C151—21no—
92C2×C4⋊C4×C151—21no—
93C2×C4⋊C4×C151C2311yescharacteristic
94C2×C4⋊C4×C151C2311yescharacteristic
95C2×C4⋊C4×C151C2311yescharacteristic
96C2×C4⋊C4×C151C2311yescharacteristic
97C2×C4⋊C4×C151C2311yescharacteristic
98C2×C22⋊C4×C151—21no—
99C2×C22⋊C4×C151—21no—
100C2×C22⋊C4×C151—21no—
101C2×C22⋊C4×C151—21no—
102C2×C22⋊C4×C151—21no—
103C2×C22⋊C4×C151—21no—
104C2×C22⋊C4×C151—21no—
105C2×C22⋊C4×C151D411yescharacteristic
106C2×C22⋊C4×C151D411yescharacteristic
107C2×C42×C151—21no—
108C2×C42×C151—21no—
109C2×C42×C151—21no—
110C2×C42×C151C2311yescharacteristic
111C2×C42×C151C2311yescharacteristic
112#107×C151—22no—
113#106×C151—22no—
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#102×C151—22no—
121#102×C151—22no—
122#102×C151—22no—
123#102×C151—22no—
124#102×C151—22no—
125#102×C151—41no—
126#102×C151—41no—
127#102×C151—41no—
128C22⋊C8×C151—22no—
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×C151—21no—
140C24×C151C2×D411yescharacteristic
141#41×C151—28no—
142#41×C151—44no—
143#41×C151—44no—
144#41×C151—44no—
145C2×Q8×C151—21no—
146C2×Q8×C151—21no—
147C2×Q8×C151—21no—
148C2×Q8×C151—21no—
149C2×Q8×C151—21no—
150C2×Q8×C151#4112yes—
151C2×D4×C151—21no—
152C2×D4×C151—21no—
153C2×D4×C151—21no—
154C2×D4×C151—21no—
155C2×D4×C151—21no—
156C2×D4×C151—21no—
157C2×D4×C151—21no—
158C2×D4×C151—21no—
159C2×D4×C151—21no—
160C2×D4×C151—21no—
161C2×D4×C151—21no—
162C2×D4×C151—42no—
163C2×D4×C151—42no—
164C2×D4×C151—42no—
165C2×D4×C151—42no—
166C2×D4×C151—42no—
167C2×D4×C151—42no—
168C2×D4×C151—42no—
169C2×D4×C151—42no—
170C2×D4×C151—81no—
171C2×D4×C151—81no—
172C2×D4×C151—81no—
173C2×D4×C151—81no—
174C2×D4×C151#4112yes—
175C22×C4×C151—21no—
176C22×C4×C151—21no—
177C22×C4×C151—21no—
178C22×C4×C151—21no—
179C22×C4×C151—21no—
180C22×C4×C151—21no—
181C22×C4×C151—21no—
182C22×C4×C151—21no—
183C22×C4×C151—21no—
184C22×C4×C151—21no—
185C22×C4×C151—42no—
186C22×C4×C151—42no—
187C22×C4×C151—42no—
188C22×C4×C151C2×D411yescharacteristic
189C22×C4×C151C2×D411yescharacteristic
190C22×C4×C151C2×D411yescharacteristic
191C22×C4×C151C2×D411yescharacteristic
192C22×C4×C151C2×D412yes—
193C22×C4×C151C2×D411yescharacteristic
194C22×C4×C151#4112yes—
195C22×C4×C151C2411yescharacteristic
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—21no—
208C2×C8×C151—44no—
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—42no—
218C4⋊C4×C151—42no—
219C4⋊C4×C151C2×D412yes—
220C4⋊C4×C151C2×D412yes—
221C22⋊C4×C151—24no—
222C22⋊C4×C151—22no—
223C22⋊C4×C151—41no—
224C22⋊C4×C151—42no—
225C22⋊C4×C151—42no—
226C22⋊C4×C151—42no—
227C22⋊C4×C151—81no—
228C22⋊C4×C151—81no—
229C22⋊C4×C151—81no—
230C42×C151—24no—
231C42×C151—21no—
232C42×C151—21no—
233C42×C151—21no—
234C42×C151—21no—
235C42×C151—81no—
236C42×C151—81no—
237C23×C151—21no—
238C23×C151—21no—
239C23×C151—21no—
240C23×C151—21no—
241C23×C151—21no—
242C23×C151—21no—
243C23×C151—22no—
244C23×C151—41no—
245C23×C151—41no—
246C23×C151—41no—
247C23×C151—41no—
248C23×C151—41no—
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#12112yes—
258C23×C151C22×D411yescharacteristic
259Q8×C151—22no—
260Q8×C151—22no—
261Q8×C151—41no—
262Q8×C151—41no—
263D4×C151—22no—
264D4×C151—22no—
265D4×C151—48no—
266D4×C151—41no—
267D4×C151—41no—
268D4×C151—41no—
269D4×C151—41no—
270D4×C151—41no—
271D4×C151—41no—
272D4×C151—84no—
273D4×C151—84no—
274D4×C151—84no—
275C2×C4×C151—21no—
276C2×C4×C151—21no—
277C2×C4×C151—21no—
278C2×C4×C151—21no—
279C2×C4×C151—22no—
280C2×C4×C151—22no—
281C2×C4×C151—22no—
282C2×C4×C151—22no—
283C2×C4×C151—22no—
284C2×C4×C151—22no—
285C2×C4×C151—22no—
286C2×C4×C151—21no—
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—48no—
296C2×C4×C151—41no—
297C2×C4×C151—41no—
298C2×C4×C151—41no—
299C2×C4×C151—41no—
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#12112yes—
312C2×C4×C151#13512yes—
313C2×C4×C151C22×D411yescharacteristic
314C2×C4×C151C2×#4111yescharacteristic
315C2×C4×C151C2×#4111yescharacteristic
316C2×C4×C151C2×#4111yescharacteristic
317C2×C4×C151H(5,𝔽2)11yescharacteristic
318C2×C4×C151H(5,𝔽2)11yescharacteristic
319C8×C151—41no—
320C8×C151—41no—
321C8×C151—41no—
322C8×C151—41no—
323C22×C151—22no—
324C22×C151—22no—
325C22×C151—22no—
326C22×C151—41no—
327C22×C151—41no—
328C22×C151—41no—
329C22×C151—41no—
330C22×C151—42no—
331C22×C151—42no—
332C22×C151—42no—
333C22×C151—81no—
334C22×C151—81no—
335C22×C151—81no—
336C22×C151—81no—
337C22×C151—81no—
338C22×C151—81no—
339C22×C151—81no—
340C22×C151—81no—
341C22×C151—81no—
342C22×C151—81no—
343C22×C151—81no—
344C22×C151C2×#12111yescharacteristic
345C22×C151#54611yescharacteristic
346C22×C151#54611yescharacteristic
347C22×C151C2×#13511yescharacteristic
348C22×C151#57511yescharacteristic
349C22×C151#57611yescharacteristic
350C22×C151#57711yescharacteristic
351C4×C151—22no—
352C4×C151—22no—
353C4×C151—42no—
354C4×C151—42no—
355C4×C151—42no—
356C4×C151—41no—
357C4×C151—41no—
358C4×C151—41no—
359C4×C151—81no—
360C4×C151—81no—
361C4×C151—81no—
362C4×C151#52511yescharacteristic
363C4×C151#53511yescharacteristic
364C4×C151#55111yescharacteristic
365C4×C151#55111yescharacteristic
366C2×C151—42no—
367C2×C151—82no—
368C2×C151—161no—
369C2×C151#241111yescharacteristic
370C2×C151#303511yescharacteristic
371C2×C151#304511yescharacteristic
372C2×C151#329711yescharacteristic
373C2×C151#330411yescharacteristic
374C2×C151#330911yescharacteristic
375C2×C151#331111yescharacteristic
376#24484C15111yesmaximal, characteristic, direct product factor, Sylow
377C151#2448411yescharacteristic, direct product factor, Sylow
378C2×#482C2×C15111yescharacteristic, complemented
379C2×#416C2×C15111yescharacteristic, complemented
380#2431C2×C15111yescharacteristic
381#2347C2×C15111yescharacteristic, complemented
382#2066C2×C15111yescharacteristic, complemented
383#2065C2×C15111yescharacteristic, complemented
384#2042C2×C15111yescharacteristic, complemented
385#2041C2×C15111yescharacteristic, complemented
386#1983C2×C15111yescharacteristic, complemented
387#1982C2×C15111yescharacteristic, complemented
388#1928C2×C15111yescharacteristic, complemented
389#1925C2×C15111yescharacteristic, complemented
390#1893C2×C15111yescharacteristic, complemented
391#1850C2×C15111yescharacteristic, complemented
392#1788C2×C15111yescharacteristic, complemented
393C22×#41C22×C15111yescharacteristic
394C23×C8C22×C15111yescharacteristic
395C2×#127C22×C15111yescharacteristic
396C2×#124C22×C15111yescharacteristic
397C2×#121C22×C15111yescharacteristic
398C2×#117C22×C15111yescharacteristic
399#482—24no—
400C2×#107C22×C15111yescharacteristic
401C2×#106C22×C15111yescharacteristic
402C2×C4⋊C8C22×C15111yescharacteristic
403C2×C4⋊C8C22×C15111yescharacteristic
404#416—24no—
405C2×#103C22×C15111yescharacteristic
406C2×#103C22×C15111yescharacteristic
407C2×#103C22×C15111yescharacteristic
408C2×#103C22×C15111yescharacteristic
409C2×#102C22×C15111yescharacteristic
410C2×#102C22×C15111yescharacteristic
411C2×#102C22×C15111yescharacteristic
412C2×#102C22×C15111yescharacteristic
413C2×#102C22×C15111yescharacteristic
414C2×#102C22×C15111yescharacteristic
415C2×#102C22×C15111yescharacteristic
416C2×#102C22×C15111yescharacteristic
417C2×C22⋊C8C22×C15111yescharacteristic
418#392—21no—
419#392—21no—
420#391C22×C15111yescharacteristic
421#390C22×C15111yescharacteristic
422#389C22×C15111yescharacteristic
423#389C22×C15111yescharacteristic
424#388—21no—
425#388—21no—
426#386—21no—
427#386—21no—
428#383—21no—
429#380C22×C15111yescharacteristic
430C4×C4⋊C4—21no—
431C4×C4⋊C4C22×C15111yescharacteristic
432C4×C4⋊C4C22×C15111yescharacteristic
433C4×C22⋊C4C22×C15111yescharacteristic
434#340C22×C15111yescharacteristic
435#340C22×C15111yescharacteristic
436#336C22×C15111yescharacteristic
437#336C22×C15111yescharacteristic
438C2×#41—22no—
439C2×#41—22no—
440C2×#41—22no—
441C2×#41—22no—
442C2×#41—41no—
443C2×#41—41no—
444C22×Q8C23×C15111yescharacteristic
445C22×D4—21no—
446C22×D4—21no—
447C22×D4—21no—
448C22×D4—21no—
449C22×D4C23×C15111yescharacteristic
450C22×D4C23×C15111yescharacteristic
451C23×C4—21no—
452C23×C4C23×C15111yescharacteristic
453C22×C8—22no—
454C22×C8—41no—
455C22×C8—41no—
456C22×C8C23×C15111yescharacteristic
457C22×C8C23×C15111yescharacteristic
458C22×C8C23×C15111yescharacteristic
459C22×C8C23×C15111yescharacteristic
460#127—22no—
461#127—41no—
462#124—22no—
463#124—41no—
464#121—22no—
465#121—22no—
466#117—22no—
467#117D4×C15114yescomplemented
468C2×C4⋊C4—21no—
469C2×C4⋊C4—21no—
470C2×C4⋊C4C23×C15111yescharacteristic
471C2×C4⋊C4C23×C15111yescharacteristic
472C2×C4⋊C4C23×C15111yescharacteristic
473C2×C4⋊C4C23×C15111yescharacteristic
474C2×C4⋊C4C23×C15111yescharacteristic
475C2×C22⋊C4—21no—
476C2×C22⋊C4—21no—
477C2×C22⋊C4—21no—
478C2×C22⋊C4—21no—
479C2×C22⋊C4—21no—
480C2×C22⋊C4—21no—
481C2×C22⋊C4—21no—
482C2×C22⋊C4D4×C15111yescharacteristic
483C2×C22⋊C4D4×C15111yescharacteristic
484C2×C42—21no—
485C2×C42—21no—
486C2×C42—21no—
487C2×C42C23×C15111yescharacteristic
488C2×C42C23×C15111yescharacteristic
489#107—22no—
490#106—22no—
491C4⋊C8—41no—
492C4⋊C8—41no—
493#103—22no—
494#103—22no—
495#103—22no—
496#103—41no—
497#102—22no—
498#102—22no—
499#102—22no—
500#102—22no—
501#102—22no—
502#102—41no—
503#102—41no—
504#102—41no—
505C22⋊C8—22no—
506#95—21no—
507#95—21no—
508#95—21no—
509#95—21no—
510#95—21no—
511#95—21no—
512#95—21no—
513#95D4×C15111yescharacteristic
514#95D4×C15111yescharacteristic
515C24—21no—
516C24—21no—
517C24C2×D4×C15111yescharacteristic
518#41—28no—
519#41—44no—
520#41—44no—
521#41—44no—
522C2×Q8—21no—
523C2×Q8—21no—
524C2×Q8—21no—
525C2×Q8—21no—
526C2×Q8—21no—
527C2×Q8#41×C15112yes—
528C2×D4—21no—
529C2×D4—21no—
530C2×D4—21no—
531C2×D4—21no—
532C2×D4—21no—
533C2×D4—21no—
534C2×D4—21no—
535C2×D4—21no—
536C2×D4—21no—
537C2×D4—21no—
538C2×D4—21no—
539C2×D4—42no—
540C2×D4—42no—
541C2×D4—42no—
542C2×D4—42no—
543C2×D4—42no—
544C2×D4—42no—
545C2×D4—42no—
546C2×D4—42no—
547C2×D4—81no—
548C2×D4—81no—
549C2×D4—81no—
550C2×D4—81no—
551C2×D4#41×C15112yes—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—42no—
563C22×C4—42no—
564C22×C4—42no—
565C22×C4C2×D4×C15111yescharacteristic
566C22×C4C2×D4×C15111yescharacteristic
567C22×C4C2×D4×C15111yescharacteristic
568C22×C4C2×D4×C15111yescharacteristic
569C22×C4C2×D4×C15112yes—
570C22×C4C2×D4×C15111yescharacteristic
571C22×C4#41×C15112yes—
572C22×C4C24×C15111yescharacteristic
573C2×C8—21no—
574C2×C8—21no—
575C2×C8—21no—
576C2×C8—21no—
577C2×C8—21no—
578C2×C8—21no—
579C2×C8—21no—
580C2×C8—21no—
581C2×C8—21no—
582C2×C8—21no—
583C2×C8—21no—
584C2×C8—21no—
585C2×C8—44no—
586C4⋊C4—21no—
587C4⋊C4—21no—
588C4⋊C4—21no—
589C4⋊C4—21no—
590C4⋊C4—21no—
591C4⋊C4—21no—
592C4⋊C4—21no—
593C4⋊C4—21no—
594C4⋊C4—42no—
595C4⋊C4—42no—
596C4⋊C4C2×D4×C15112yes—
597C4⋊C4C2×D4×C15112yes—
598C22⋊C4—24no—
599C22⋊C4—22no—
600C22⋊C4—41no—
601C22⋊C4—42no—
602C22⋊C4—42no—
603C22⋊C4—42no—
604C22⋊C4—81no—
605C22⋊C4—81no—
606C22⋊C4—81no—
607C42—24no—
608C42—21no—
609C42—21no—
610C42—21no—
611C42—21no—
612C42—81no—
613C42—81no—
614C23—21no—
615C23—21no—
616C23—21no—
617C23—21no—
618C23—21no—
619C23—21no—
620C23—22no—
621C23—41no—
622C23—41no—
623C23—41no—
624C23—41no—
625C23—41no—
626C23—41no—
627C23—41no—
628C23—41no—
629C23—41no—
630C23—41no—
631C23—41no—
632C23—41no—
633C23—41no—
634C23#121×C15112yes—
635C23C22×D4×C15111yescharacteristic
636Q8—22no—
637Q8—22no—
638Q8—41no—
639Q8—41no—
640D4—22no—
641D4—22no—
642D4—48no—
643D4—41no—
644D4—41no—
645D4—41no—
646D4—41no—
647D4—41no—
648D4—41no—
649D4—84no—
650D4—84no—
651D4—84no—
652C2×C4—21no—
653C2×C4—21no—
654C2×C4—21no—
655C2×C4—21no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—22no—
666C2×C4—21no—
667C2×C4—21no—
668C2×C4—21no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—48no—
673C2×C4—41no—
674C2×C4—41no—
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—41no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4#121×C15112yes—
689C2×C4#135×C15112yes—
690C2×C4C22×D4×C15111yescharacteristic
691C2×C4C2×#41×C15111yescharacteristic
692C2×C4C2×#41×C15111yescharacteristic
693C2×C4C2×#41×C15111yescharacteristic
694C2×C4H(5,𝔽2)×C15111yescharacteristic
695C2×C4H(5,𝔽2)×C15111yescharacteristic
696C8—41no—
697C8—41no—
698C8—41no—
699C8—41no—
700C22—22no—
701C22—22no—
702C22—22no—
703C22—41no—
704C22—41no—
705C22—41no—
706C22—41no—
707C22—42no—
708C22—42no—
709C22—42no—
710C22—81no—
711C22—81no—
712C22—81no—
713C22—81no—
714C22—81no—
715C22—81no—
716C22—81no—
717C22—81no—
718C22—81no—
719C22—81no—
720C22—81no—
721C22C2×#121×C15111yescharacteristic
722C22#546×C15111yescharacteristic
723C22#546×C15111yescharacteristic
724C22C2×#135×C15111yescharacteristic
725C22#575×C15111yescharacteristic
726C22#576×C15111yescharacteristic
727C22#577×C15111yescharacteristic
728C4—22no—
729C4—22no—
730C4—42no—
731C4—42no—
732C4—42no—
733C4—41no—
734C4—41no—
735C4—41no—
736C4—81no—
737C4—81no—
738C4—81no—
739C4#525×C15111yescharacteristic
740C4#535×C15111yescharacteristic
741C4#551×C15111yescharacteristic
742C4#551×C15111yescharacteristic
743C2—42no—
744C2—82no—
745C2—161no—
746C2#2411×C15111yescharacteristic
747C2#3035×C15111yescharacteristic
748C2#3045×C15111yescharacteristic
749C2#3297×C15111yescharacteristic
750C2#3304×C15111yescharacteristic
751C2#3309×C15111yescharacteristic
752C2#3311×C15111yescharacteristic
subgroupG/H
center, socleC23×C151C22×D4
commutator, Frattini, cosocleC22×C4C24×C151
prime radical#2431×C151C2
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
1. C2×#482×C151C2semidirect
2. C2×#416×C151C2semidirect
4. #2347×C151C2semidirect
5. #2066×C151C2semidirect
6. #2065×C151C2semidirect
7. #2042×C151C2semidirect
8. #2041×C151C2semidirect
9. #1983×C151C2semidirect
10. #1982×C151C2semidirect
11. #1928×C151C2semidirect
12. #1925×C151C2semidirect
13. #1893×C151C2semidirect
14. #1850×C151C2semidirect
15. #1788×C151C2semidirect
90. #117×C151D4semidirect
376. #24484C151direct (N × H)
377. C151#24484direct (N × H)
378. C2×#482C2×C151semidirect
379. C2×#416C2×C151semidirect
381. #2347C2×C151semidirect
382. #2066C2×C151semidirect
383. #2065C2×C151semidirect
384. #2042C2×C151semidirect
385. #2041C2×C151semidirect
386. #1983C2×C151semidirect
387. #1982C2×C151semidirect
388. #1928C2×C151semidirect
389. #1925C2×C151semidirect
390. #1893C2×C151semidirect
391. #1850C2×C151semidirect
392. #1788C2×C151semidirect
467. #117D4×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#482×C1512
C2×#416×C1512
#2431×C1512
#2347×C1512
#2066×C1512
#2065×C1512
#2042×C1512
#2041×C1512
#1983×C1512
#1982×C1512
#1928×C1512
#1925×C1512
#1893×C1512
#1850×C1512
#1788×C1512
#24484151