Finite Group Databasebeta

← C151×#24537 #50329462

Subgroups — C151×#24537 #50329462

Order 38656.

1048 conjugacy classes of subgroups.

The subgroup lattice has 758 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#449×C151C211yesmaximal, characteristic
2C2×#416×C151C211yesmaximal, characteristic, complemented
3#2500×C151C211yesmaximal, characteristic, complemented
4#2339×C151C211yesmaximal, characteristic, complemented
5#2074×C151C211yesmaximal, characteristic, complemented
6#2072×C151C211yesmaximal, characteristic, complemented
7#2055×C151C211yesmaximal, characteristic, complemented
8#2055×C151C211yesmaximal, characteristic, complemented
9#1893×C151C211yesmaximal, characteristic, complemented
10#1879×C151C211yesmaximal, characteristic, complemented
11#1879×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×SD16×C151C2211yescharacteristic
18C22×D8×C151C2211yescharacteristic
19C23×C8×C151C2211yescharacteristic
20C2×#121×C151C2211yescharacteristic
21C2×C4×D4×C151C2211yescharacteristic
22C2×C4×D4×C151C2211yescharacteristic
23C2×#117×C151C2211yescharacteristic
24#449×C151—24no—
25C2×C4⋊C8×C151C2211yescharacteristic
26C2×C4⋊C8×C151C2211yescharacteristic
27#416×C151—24no—
28C2×#103×C151C2211yescharacteristic
29C2×#103×C151C2211yescharacteristic
30C2×#103×C151C2211yescharacteristic
31C2×#102×C151C2211yescharacteristic
32C2×#102×C151C2211yescharacteristic
33C2×#102×C151C2211yescharacteristic
34C2×#102×C151C2211yescharacteristic
35C2×#102×C151C2211yescharacteristic
36C2×C22⋊C8×C151C2211yescharacteristic
37#394×C151—21no—
38#394×C151—21no—
39#391×C151C2211yescharacteristic
40#391×C151C2211yescharacteristic
41#390×C151C2211yescharacteristic
42#390×C151C2211yescharacteristic
43#388×C151—21no—
44#388×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×D4×C151—21no—
69C22×D4×C151—21no—
70C22×D4×C151C2311yescharacteristic
71C22×D4×C151C2311yescharacteristic
72C23×C4×C151—21no—
73C23×C4×C151—21no—
74C23×C4×C151—21no—
75C23×C4×C151C2311yescharacteristic
76C2×SD16×C151—22no—
77C2×SD16×C151—41no—
78C2×SD16×C151—41no—
79C2×D8×C151—22no—
80C2×D8×C151—22no—
81C2×D8×C151—22no—
82C22×C8×C151—22no—
83C22×C8×C151—41no—
84C22×C8×C151—41no—
85C22×C8×C151C2311yescharacteristic
86C22×C8×C151C2311yescharacteristic
87C22×C8×C151C2311yescharacteristic
88C22×C8×C151C2311yescharacteristic
89#121×C151—22no—
90#121×C151—22no—
91C4×D4×C151—22no—
92C4×D4×C151—22no—
93C4×D4×C151—41no—
94C4×D4×C151—41no—
95#117×C151—22no—
96#117×C151—22no—
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×C151—21no—
110C2×C22⋊C4×C151—21no—
111C2×C22⋊C4×C151—21no—
112C2×C22⋊C4×C151—21no—
113C2×C22⋊C4×C151D411yescharacteristic
114C2×C22⋊C4×C151D411yescharacteristic
115C2×C42×C151—21no—
116C2×C42×C151C2311yescharacteristic
117C2×C42×C151C2311yescharacteristic
118C4⋊C8×C151—41no—
119C4⋊C8×C151—41no—
120#103×C151—22no—
121#103×C151—22no—
122#103×C151—22no—
123#102×C151—22no—
124#102×C151—22no—
125#102×C151—22no—
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×C151C2×D412yes—
151C2×D4×C151—24no—
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—42no—
162C2×D4×C151—42no—
163C2×D4×C151—42no—
164C2×D4×C151—81no—
165C2×D4×C151—81no—
166C2×D4×C151C2×D412yes—
167C2×D4×C151#4112yes—
168C2×D4×C151#4112yes—
169C22×C4×C151—21no—
170C22×C4×C151—21no—
171C22×C4×C151—21no—
172C22×C4×C151—21no—
173C22×C4×C151—21no—
174C22×C4×C151—24no—
175C22×C4×C151—21no—
176C22×C4×C151—21no—
177C22×C4×C151—21no—
178C22×C4×C151—21no—
179C22×C4×C151—21no—
180C22×C4×C151—42no—
181C22×C4×C151—42no—
182C22×C4×C151—42no—
183C22×C4×C151—42no—
184C22×C4×C151—42no—
185C22×C4×C151—42no—
186C22×C4×C151—81no—
187C22×C4×C151—81no—
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
196SD16×C151—44no—
197D8×C151—44no—
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—21no—
209C2×C8×C151—21no—
210C2×C8×C151—44no—
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—21no—
220C4⋊C4×C151—21no—
221C4⋊C4×C151—81no—
222C4⋊C4×C151—81no—
223C22⋊C4×C151—22no—
224C22⋊C4×C151—41no—
225C22⋊C4×C151—42no—
226C22⋊C4×C151—42no—
227C22⋊C4×C151—42no—
228C22⋊C4×C151—42no—
229C22⋊C4×C151—42no—
230C22⋊C4×C151—42no—
231C22⋊C4×C151—81no—
232C22⋊C4×C151—81no—
233C22⋊C4×C151—81no—
234C42×C151—21no—
235C42×C151—21no—
236C42×C151—21no—
237C42×C151—21no—
238C42×C151—42no—
239C23×C151—22no—
240C23×C151—22no—
241C23×C151—22no—
242C23×C151—21no—
243C23×C151—21no—
244C23×C151—21no—
245C23×C151—21no—
246C23×C151—21no—
247C23×C151—21no—
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—41no—
258C23×C151—41no—
259C23×C151#12112yes—
260C23×C151C22×D411yescharacteristic
261Q8×C151—22no—
262Q8×C151—22no—
263Q8×C151—41no—
264Q8×C151—41no—
265D4×C151—22no—
266D4×C151—22no—
267D4×C151—22no—
268D4×C151—48no—
269D4×C151—41no—
270D4×C151—41no—
271D4×C151—41no—
272D4×C151—41no—
273D4×C151—84no—
274D4×C151#12314yes—
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—21no—
285C2×C4×C151—21no—
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—48no—
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—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—84no—
312C2×C4×C151—84no—
313C2×C4×C151#12112yes—
314C2×C4×C151#13512yes—
315C2×C4×C151C22×D411yescharacteristic
316C2×C4×C151C2×#4111yescharacteristic
317C2×C4×C151C2×#4111yescharacteristic
318C2×C4×C151C2×#4111yescharacteristic
319C2×C4×C151H(5,𝔽2)11yescharacteristic
320C2×C4×C151H(5,𝔽2)11yescharacteristic
321C8×C151—41no—
322C8×C151—41no—
323C8×C151—41no—
324C8×C151—41no—
325C22×C151—22no—
326C22×C151—24no—
327C22×C151—22no—
328C22×C151—22no—
329C22×C151—42no—
330C22×C151—42no—
331C22×C151—41no—
332C22×C151—42no—
333C22×C151—41no—
334C22×C151—42no—
335C22×C151—41no—
336C22×C151—42no—
337C22×C151—42no—
338C22×C151—41no—
339C22×C151—81no—
340C22×C151—81no—
341C22×C151—81no—
342C22×C151—81no—
343C22×C151—81no—
344C22×C151—81no—
345C22×C151—81no—
346C22×C151C2×#12111yescharacteristic
347C22×C151#54611yescharacteristic
348C22×C151#54611yescharacteristic
349C22×C151C2×#13511yescharacteristic
350C22×C151#57511yescharacteristic
351C22×C151#57611yescharacteristic
352C22×C151#57711yescharacteristic
353C4×C151—22no—
354C4×C151—22no—
355C4×C151—42no—
356C4×C151—41no—
357C4×C151—41no—
358C4×C151—41no—
359C4×C151—81no—
360C4×C151—81no—
361C4×C151—81no—
362C4×C151—81no—
363C4×C151—81no—
364C4×C151C2×#12311yescharacteristic
365C4×C151#53411yescharacteristic
366C4×C151#55111yescharacteristic
367C4×C151#55111yescharacteristic
368C2×C151—42no—
369C2×C151—44no—
370C2×C151—161no—
371C2×C151#241211yescharacteristic
372C2×C151#303511yescharacteristic
373C2×C151#304511yescharacteristic
374C2×C151#329711yescharacteristic
375C2×C151#330311yescharacteristic
376C2×C151#330711yescharacteristic
377C2×C151#331911yescharacteristic
378#24537C15111yesmaximal, characteristic, direct product factor, Sylow
379C151#2453711yescharacteristic, direct product factor, Sylow
380C2×#449C2×C15111yescharacteristic
381C2×#416C2×C15111yescharacteristic, complemented
382#2500C2×C15111yescharacteristic, complemented
383#2339C2×C15111yescharacteristic, complemented
384#2074C2×C15111yescharacteristic, complemented
385#2072C2×C15111yescharacteristic, complemented
386#2055C2×C15111yescharacteristic, complemented
387#2055C2×C15111yescharacteristic, complemented
388#1893C2×C15111yescharacteristic, complemented
389#1879C2×C15111yescharacteristic, complemented
390#1879C2×C15111yescharacteristic, complemented
391#1850C2×C15111yescharacteristic, complemented
392#1825C2×C15111yescharacteristic, complemented
393#1804C2×C15111yescharacteristic, complemented
394#1802C2×C15111yescharacteristic, complemented
395C22×#41C22×C15111yescharacteristic
396C22×SD16C22×C15111yescharacteristic
397C22×D8C22×C15111yescharacteristic
398C23×C8C22×C15111yescharacteristic
399C2×#121C22×C15111yescharacteristic
400C2×C4×D4C22×C15111yescharacteristic
401C2×C4×D4C22×C15111yescharacteristic
402C2×#117C22×C15111yescharacteristic
403#449—24no—
404C2×C4⋊C8C22×C15111yescharacteristic
405C2×C4⋊C8C22×C15111yescharacteristic
406#416—24no—
407C2×#103C22×C15111yescharacteristic
408C2×#103C22×C15111yescharacteristic
409C2×#103C22×C15111yescharacteristic
410C2×#102C22×C15111yescharacteristic
411C2×#102C22×C15111yescharacteristic
412C2×#102C22×C15111yescharacteristic
413C2×#102C22×C15111yescharacteristic
414C2×#102C22×C15111yescharacteristic
415C2×C22⋊C8C22×C15111yescharacteristic
416#394—21no—
417#394—21no—
418#391C22×C15111yescharacteristic
419#391C22×C15111yescharacteristic
420#390C22×C15111yescharacteristic
421#390C22×C15111yescharacteristic
422#388—21no—
423#388—21no—
424#386—21no—
425#386—21no—
426#384C22×C15111yescharacteristic
427#382C22×C15111yescharacteristic
428#381—21no—
429#380C22×C15111yescharacteristic
430C4×C22⋊C4C22×C15111yescharacteristic
431C2×#95—21no—
432#340C22×C15111yescharacteristic
433#340C22×C15111yescharacteristic
434#340C22×C15111yescharacteristic
435#340C22×C15111yescharacteristic
436#340C22×C15111yescharacteristic
437#340C22×C15111yescharacteristic
438#336C22×C15111yescharacteristic
439#336C22×C15111yescharacteristic
440C2×#41—22no—
441C2×#41—22no—
442C2×#41—22no—
443C2×#41—41no—
444C2×#41—41no—
445C2×#41D4×C15114yes—
446C22×Q8C23×C15111yescharacteristic
447C22×D4—21no—
448C22×D4—21no—
449C22×D4C23×C15111yescharacteristic
450C22×D4C23×C15111yescharacteristic
451C23×C4—21no—
452C23×C4—21no—
453C23×C4—21no—
454C23×C4C23×C15111yescharacteristic
455C2×SD16—22no—
456C2×SD16—41no—
457C2×SD16—41no—
458C2×D8—22no—
459C2×D8—22no—
460C2×D8—22no—
461C22×C8—22no—
462C22×C8—41no—
463C22×C8—41no—
464C22×C8C23×C15111yescharacteristic
465C22×C8C23×C15111yescharacteristic
466C22×C8C23×C15111yescharacteristic
467C22×C8C23×C15111yescharacteristic
468#121—22no—
469#121—22no—
470C4×D4—22no—
471C4×D4—22no—
472C4×D4—41no—
473C4×D4—41no—
474#117—22no—
475#117—22no—
476C2×C4⋊C4—21no—
477C2×C4⋊C4—21no—
478C2×C4⋊C4C23×C15111yescharacteristic
479C2×C4⋊C4C23×C15111yescharacteristic
480C2×C4⋊C4C23×C15111yescharacteristic
481C2×C4⋊C4C23×C15111yescharacteristic
482C2×C4⋊C4C23×C15111yescharacteristic
483C2×C22⋊C4—21no—
484C2×C22⋊C4—21no—
485C2×C22⋊C4—21no—
486C2×C22⋊C4—21no—
487C2×C22⋊C4—21no—
488C2×C22⋊C4—21no—
489C2×C22⋊C4—21no—
490C2×C22⋊C4—21no—
491C2×C22⋊C4—21no—
492C2×C22⋊C4D4×C15111yescharacteristic
493C2×C22⋊C4D4×C15111yescharacteristic
494C2×C42—21no—
495C2×C42C23×C15111yescharacteristic
496C2×C42C23×C15111yescharacteristic
497C4⋊C8—41no—
498C4⋊C8—41no—
499#103—22no—
500#103—22no—
501#103—22no—
502#102—22no—
503#102—22no—
504#102—22no—
505#102—41no—
506#102—41no—
507C22⋊C8—22no—
508#95—21no—
509#95—21no—
510#95—21no—
511#95—21no—
512#95—21no—
513#95—21no—
514#95—21no—
515#95D4×C15111yescharacteristic
516#95D4×C15111yescharacteristic
517C24—21no—
518C24—21no—
519C24C2×D4×C15111yescharacteristic
520#41—28no—
521#41—44no—
522#41—44no—
523#41—44no—
524C2×Q8—21no—
525C2×Q8—21no—
526C2×Q8—21no—
527C2×Q8—21no—
528C2×Q8—21no—
529C2×Q8C2×D4×C15112yes—
530C2×D4—24no—
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—21no—
540C2×D4—42no—
541C2×D4—42no—
542C2×D4—42no—
543C2×D4—81no—
544C2×D4—81no—
545C2×D4C2×D4×C15112yes—
546C2×D4#41×C15112yes—
547C2×D4#41×C15112yes—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—24no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—42no—
560C22×C4—42no—
561C22×C4—42no—
562C22×C4—42no—
563C22×C4—42no—
564C22×C4—42no—
565C22×C4—81no—
566C22×C4—81no—
567C22×C4C2×D4×C15111yescharacteristic
568C22×C4C2×D4×C15111yescharacteristic
569C22×C4C2×D4×C15111yescharacteristic
570C22×C4C2×D4×C15111yescharacteristic
571C22×C4C2×D4×C15112yes—
572C22×C4C2×D4×C15111yescharacteristic
573C22×C4#41×C15112yes—
574C22×C4C24×C15111yescharacteristic
575SD16—44no—
576D8—44no—
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—21no—
586C2×C8—21no—
587C2×C8—21no—
588C2×C8—21no—
589C2×C8—44no—
590C4⋊C4—21no—
591C4⋊C4—21no—
592C4⋊C4—21no—
593C4⋊C4—21no—
594C4⋊C4—21no—
595C4⋊C4—21no—
596C4⋊C4—21no—
597C4⋊C4—21no—
598C4⋊C4—21no—
599C4⋊C4—21no—
600C4⋊C4—81no—
601C4⋊C4—81no—
602C22⋊C4—22no—
603C22⋊C4—41no—
604C22⋊C4—42no—
605C22⋊C4—42no—
606C22⋊C4—42no—
607C22⋊C4—42no—
608C22⋊C4—42no—
609C22⋊C4—42no—
610C22⋊C4—81no—
611C22⋊C4—81no—
612C22⋊C4—81no—
613C42—21no—
614C42—21no—
615C42—21no—
616C42—21no—
617C42—42no—
618C23—22no—
619C23—22no—
620C23—22no—
621C23—21no—
622C23—21no—
623C23—21no—
624C23—21no—
625C23—21no—
626C23—21no—
627C23—41no—
628C23—41no—
629C23—41no—
630C23—41no—
631C23—41no—
632C23—41no—
633C23—41no—
634C23—41no—
635C23—41no—
636C23—41no—
637C23—41no—
638C23#121×C15112yes—
639C23C22×D4×C15111yescharacteristic
640Q8—22no—
641Q8—22no—
642Q8—41no—
643Q8—41no—
644D4—22no—
645D4—22no—
646D4—22no—
647D4—48no—
648D4—41no—
649D4—41no—
650D4—41no—
651D4—41no—
652D4—84no—
653D4#123×C15114yes—
654C2×C4—21no—
655C2×C4—21no—
656C2×C4—21no—
657C2×C4—21no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—22no—
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—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—41no—
689C2×C4—41no—
690C2×C4—84no—
691C2×C4—84no—
692C2×C4#121×C15112yes—
693C2×C4#135×C15112yes—
694C2×C4C22×D4×C15111yescharacteristic
695C2×C4C2×#41×C15111yescharacteristic
696C2×C4C2×#41×C15111yescharacteristic
697C2×C4C2×#41×C15111yescharacteristic
698C2×C4H(5,𝔽2)×C15111yescharacteristic
699C2×C4H(5,𝔽2)×C15111yescharacteristic
700C8—41no—
701C8—41no—
702C8—41no—
703C8—41no—
704C22—22no—
705C22—24no—
706C22—22no—
707C22—22no—
708C22—42no—
709C22—42no—
710C22—41no—
711C22—42no—
712C22—41no—
713C22—42no—
714C22—41no—
715C22—42no—
716C22—42no—
717C22—41no—
718C22—81no—
719C22—81no—
720C22—81no—
721C22—81no—
722C22—81no—
723C22—81no—
724C22—81no—
725C22C2×#121×C15111yescharacteristic
726C22#546×C15111yescharacteristic
727C22#546×C15111yescharacteristic
728C22C2×#135×C15111yescharacteristic
729C22#575×C15111yescharacteristic
730C22#576×C15111yescharacteristic
731C22#577×C15111yescharacteristic
732C4—22no—
733C4—22no—
734C4—42no—
735C4—41no—
736C4—41no—
737C4—41no—
738C4—81no—
739C4—81no—
740C4—81no—
741C4—81no—
742C4—81no—
743C4C2×#123×C15111yescharacteristic
744C4#534×C15111yescharacteristic
745C4#551×C15111yescharacteristic
746C4#551×C15111yescharacteristic
747C2—42no—
748C2—44no—
749C2—161no—
750C2#2412×C15111yescharacteristic
751C2#3035×C15111yescharacteristic
752C2#3045×C15111yescharacteristic
753C2#3297×C15111yescharacteristic
754C2#3303×C15111yescharacteristic
755C2#3307×C15111yescharacteristic
756C2#3319×C15111yescharacteristic
subgroupG/H
center, socleC23×C151C22×D4
commutator, Frattini, cosocleC22×C4C24×C151
prime radicalC2×#449×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
2. C2×#416×C151C2semidirect
3. #2500×C151C2semidirect
4. #2339×C151C2semidirect
5. #2074×C151C2semidirect
6. #2072×C151C2semidirect
7. #2055×C151C2semidirect
8. #2055×C151C2semidirect
9. #1893×C151C2semidirect
10. #1879×C151C2semidirect
11. #1879×C151C2semidirect
12. #1850×C151C2semidirect
13. #1825×C151C2semidirect
14. #1804×C151C2semidirect
15. #1802×C151C2semidirect
378. #24537C151direct (N × H)
379. C151#24537direct (N × H)
381. C2×#416C2×C151semidirect
382. #2500C2×C151semidirect
383. #2339C2×C151semidirect
384. #2074C2×C151semidirect
385. #2072C2×C151semidirect
386. #2055C2×C151semidirect
387. #2055C2×C151semidirect
388. #1893C2×C151semidirect
389. #1879C2×C151semidirect
390. #1879C2×C151semidirect
391. #1850C2×C151semidirect
392. #1825C2×C151semidirect
393. #1804C2×C151semidirect
394. #1802C2×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#449×C1512
C2×#416×C1512
#2500×C1512
#2339×C1512
#2074×C1512
#2072×C1512
#2055×C1512
#1893×C1512
#1879×C1512
#1850×C1512
#1825×C1512
#1804×C1512
#1802×C1512
#24537151