Finite Group Databasebeta

← C151×#23922 #50328847

Subgroups — C151×#23922 #50328847

Order 38656.

1928 conjugacy classes of subgroups.

The subgroup lattice has 780 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#525×C151C211yesmaximal, characteristic
2C22×C22⋊Q8×C151C211yesmaximal, characteristic, complemented
3C2×#452×C151C212yesmaximal, complemented
4C2×#451×C151C211yesmaximal, characteristic, complemented
5C2×#448×C151C211yesmaximal, characteristic, complemented
6#2001×C151C212yesmaximal, complemented
7#2000×C151C212yesmaximal, complemented
8#1874×C151C211yesmaximal, characteristic, complemented
9#1873×C151C212yesmaximal, complemented
10#1872×C151C211yesmaximal, characteristic, complemented
11#1779×C151C211yesmaximal, characteristic, complemented
12C22×#41×C151C2211yescharacteristic
13C23×Q8×C151C2211yescharacteristic
14C24×C4×C151C2211yescharacteristic
15C22×Q16×C151C2212yescomplemented
16C22×SD16×C151C2212yescomplemented
17#525×C151—24no—
18#525×C151—24no—
19C2×#123×C151—21no—
20C2×C22⋊Q8×C151—21no—
21C2×C22⋊Q8×C151—21no—
22C2×C22⋊Q8×C151—28no—
23C2×C22⋊Q8×C151C2212yes—
24C2×C22⋊Q8×C151C2211yescharacteristic
25C2×C22⋊Q8×C151C2211yescharacteristic
26C2×C22⋊Q8×C151C2212yes—
27C2×#121×C151C2211yescharacteristic
28C2×#121×C151C2211yescharacteristic
29C2×#120×C151—21no—
30C2×C4×D4×C151—21no—
31C2×C4×D4×C151—21no—
32C2×#117×C151C2211yescharacteristic
33C22×C4⋊C4×C151—21no—
34C22×C4⋊C4×C151C2211yescharacteristic
35C22×C22⋊C4×C151—21no—
36#452×C151—28no—
37#451×C151—24no—
38#448×C151—24no—
39C2×#103×C151C2212yescomplemented
40C2×#103×C151C2212yescomplemented
41C2×#103×C151C2212yescomplemented
42C2×#102×C151C2212yescomplemented
43C2×C22⋊C8×C151C2211yescharacteristic
44C2×C22⋊C8×C151C2212yes—
45C2×C22⋊C8×C151C2211yescharacteristic
46C2×C22⋊C8×C151C2212yes—
47#340×C151C2212yescomplemented
48#340×C151C2212yescomplemented
49C25×C151D411yescharacteristic
50C2×#41×C151—22no—
51C2×#41×C151—24no—
52C2×#41×C151—22no—
53C2×#41×C151—42no—
54C22×Q8×C151—21no—
55C22×Q8×C151—24no—
56C22×Q8×C151—22no—
57C22×Q8×C151—22no—
58C22×Q8×C151—42no—
59C22×Q8×C151C2312yes—
60C22×Q8×C151C2311yescharacteristic
61C22×D4×C151—21no—
62C22×D4×C151—21no—
63C22×D4×C151—21no—
64C22×D4×C151C2311yescharacteristic
65C23×C4×C151—21no—
66C23×C4×C151—24no—
67C23×C4×C151—22no—
68C23×C4×C151—22no—
69C23×C4×C151—21no—
70C23×C4×C151—21no—
71C23×C4×C151—42no—
72C23×C4×C151D411yescharacteristic
73C23×C4×C151D411yescharacteristic
74C23×C4×C151D411yescharacteristic
75C23×C4×C151C2311yescharacteristic
76C23×C4×C151C2311yescharacteristic
77C23×C4×C151C2311yescharacteristic
78C2×Q16×C151—24no—
79C2×Q16×C151—24no—
80C2×Q16×C151—42no—
81C2×SD16×C151—24no—
82C2×SD16×C151—24no—
83C2×SD16×C151—42no—
84C22×C8×C151C2312yes—
85C22×C8×C151C2312yes—
86#123×C151—28no—
87C22⋊Q8×C151—28no—
88C22⋊Q8×C151—28no—
89C22⋊Q8×C151—24no—
90C22⋊Q8×C151—22no—
91C22⋊Q8×C151—24no—
92C22⋊Q8×C151—22no—
93C22⋊Q8×C151—24no—
94C22⋊Q8×C151—22no—
95C22⋊Q8×C151D414yes—
96C22⋊Q8×C151D418yescomplemented
97#121×C151—22no—
98#121×C151—22no—
99#121×C151—22no—
100#121×C151D414yes—
101#120×C151—28no—
102C4×D4×C151—28no—
103C4×D4×C151—28no—
104#117×C151—22no—
105#117×C151—22no—
106C2×C4⋊C4×C151—28no—
107C2×C4⋊C4×C151—22no—
108C2×C4⋊C4×C151—22no—
109C2×C4⋊C4×C151—21no—
110C2×C4⋊C4×C151—21no—
111C2×C4⋊C4×C151—21no—
112C2×C4⋊C4×C151—24no—
113C2×C4⋊C4×C151C2312yes—
114C2×C4⋊C4×C151C2311yescharacteristic
115C2×C4⋊C4×C151C2311yescharacteristic
116C2×C22⋊C4×C151—28no—
117C2×C22⋊C4×C151—21no—
118C2×C22⋊C4×C151—21no—
119C2×C22⋊C4×C151—22no—
120C2×C22⋊C4×C151—22no—
121C2×C22⋊C4×C151—21no—
122C2×C22⋊C4×C151—21no—
123C2×C22⋊C4×C151—21no—
124C2×C42×C151—21no—
125#103×C151—24no—
126#103×C151—24no—
127#103×C151—24no—
128#102×C151—24no—
129C22⋊C8×C151—22no—
130C22⋊C8×C151—22no—
131C22⋊C8×C151—24no—
132C22⋊C8×C151—42no—
133C24×C151—22no—
134C24×C151—22no—
135C24×C151—22no—
136C24×C151—22no—
137C24×C151—22no—
138C24×C151—21no—
139C24×C151—41no—
140C24×C151—41no—
141C24×C151C2×D411yescharacteristic
142C24×C151C2×D411yescharacteristic
143C24×C151C2×D411yescharacteristic
144#41×C151—48no—
145#41×C151—48no—
146C2×Q8×C151—24no—
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—22no—
154C2×Q8×C151—22no—
155C2×Q8×C151—48no—
156C2×Q8×C151—48no—
157C2×Q8×C151—42no—
158C2×Q8×C151—42no—
159C2×Q8×C151C2×D412yes—
160C2×Q8×C151C2×D414yes—
161C2×D4×C151—24no—
162C2×D4×C151—24no—
163C2×D4×C151—24no—
164C2×D4×C151—22no—
165C2×D4×C151—21no—
166C2×D4×C151—22no—
167C2×D4×C151—42no—
168C2×D4×C151—42no—
169C2×D4×C151—42no—
170C2×D4×C151—42no—
171C2×D4×C151—42no—
172C2×D4×C151—42no—
173C2×D4×C151C2×D412yes—
174C22×C4×C151—22no—
175C22×C4×C151—21no—
176C22×C4×C151—21no—
177C22×C4×C151—22no—
178C22×C4×C151—22no—
179C22×C4×C151—24no—
180C22×C4×C151—24no—
181C22×C4×C151—24no—
182C22×C4×C151—22no—
183C22×C4×C151—22no—
184C22×C4×C151—21no—
185C22×C4×C151—21no—
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—22no—
193C22×C4×C151—21no—
194C22×C4×C151—21no—
195C22×C4×C151—22no—
196C22×C4×C151—22no—
197C22×C4×C151—41no—
198C22×C4×C151—41no—
199C22×C4×C151—41no—
200C22×C4×C151—48no—
201C22×C4×C151—48no—
202C22×C4×C151—42no—
203C22×C4×C151—42no—
204C22×C4×C151—42no—
205C22×C4×C151—42no—
206C22×C4×C151—42no—
207C22×C4×C151—42no—
208C22×C4×C151C2×D411yescharacteristic
209C22×C4×C151C2×D411yescharacteristic
210C22×C4×C151C2×D411yescharacteristic
211C22×C4×C151C2×D412yes—
212C22×C4×C151C2×D412yes—
213C22×C4×C151C2×D414yes—
214C22×C4×C151C2411yescharacteristic
215Q16×C151—48no—
216SD16×C151—48no—
217C2×C8×C151—22no—
218C2×C8×C151—22no—
219C2×C8×C151—22no—
220C2×C8×C151—22no—
221C2×C8×C151—22no—
222C2×C8×C151—22no—
223C4⋊C4×C151—24no—
224C4⋊C4×C151—28no—
225C4⋊C4×C151—24no—
226C4⋊C4×C151—28no—
227C4⋊C4×C151—24no—
228C4⋊C4×C151—22no—
229C4⋊C4×C151—21no—
230C4⋊C4×C151—21no—
231C4⋊C4×C151C2×D414yes—
232C4⋊C4×C151C2×D412yes—
233C4⋊C4×C151C2×D412yes—
234C22⋊C4×C151—28no—
235C22⋊C4×C151—24no—
236C22⋊C4×C151—24no—
237C22⋊C4×C151—24no—
238C22⋊C4×C151—28no—
239C22⋊C4×C151—24no—
240C22⋊C4×C151—24no—
241C42×C151—24no—
242C23×C151—21no—
243C23×C151—21no—
244C23×C151—21no—
245C23×C151—21no—
246C23×C151—28no—
247C23×C151—21no—
248C23×C151—21no—
249C23×C151—21no—
250C23×C151—21no—
251C23×C151—21no—
252C23×C151—21no—
253C23×C151—21no—
254C23×C151—21no—
255C23×C151—21no—
256C23×C151—21no—
257C23×C151—21no—
258C23×C151—21no—
259C23×C151—22no—
260C23×C151—44no—
261C23×C151—44no—
262C23×C151—44no—
263C23×C151—44no—
264C23×C151—44no—
265C23×C151—44no—
266C23×C151—41no—
267C23×C151—41no—
268C23×C151—41no—
269C23×C151—41no—
270C23×C151—41no—
271C23×C151—41no—
272C23×C151#12012yes—
273C23×C151#12012yes—
274C23×C151#13512yes—
275C23×C151#13712yes—
276C23×C151#13712yes—
277C23×C151C22×D411yescharacteristic
278Q8×C151—24no—
279Q8×C151—24no—
280Q8×C151—24no—
281Q8×C151—48no—
282Q8×C151—42no—
283Q8×C151—42no—
284Q8×C151—42no—
285D4×C151—24no—
286D4×C151—48no—
287D4×C151—48no—
288D4×C151—48no—
289D4×C151—42no—
290C2×C4×C151—21no—
291C2×C4×C151—21no—
292C2×C4×C151—21no—
293C2×C4×C151—21no—
294C2×C4×C151—24no—
295C2×C4×C151—24no—
296C2×C4×C151—24no—
297C2×C4×C151—24no—
298C2×C4×C151—24no—
299C2×C4×C151—22no—
300C2×C4×C151—22no—
301C2×C4×C151—22no—
302C2×C4×C151—24no—
303C2×C4×C151—21no—
304C2×C4×C151—21no—
305C2×C4×C151—21no—
306C2×C4×C151—44no—
307C2×C4×C151—44no—
308C2×C4×C151—44no—
309C2×C4×C151—48no—
310C2×C4×C151—48no—
311C2×C4×C151—48no—
312C2×C4×C151—42no—
313C2×C4×C151—41no—
314C2×C4×C151—42no—
315C2×C4×C151—41no—
316C2×C4×C151—42no—
317C2×C4×C151—41no—
318C2×C4×C151—41no—
319C2×C4×C151—41no—
320C2×C4×C151—42no—
321C2×C4×C151—41no—
322C2×C4×C151—42no—
323C2×C4×C151—42no—
324C2×C4×C151#12012yes—
325C2×C4×C151#12012yes—
326C2×C4×C151C22×D411yescharacteristic
327C2×C4×C151C22×D412yes—
328C2×C4×C151C22×D411yescharacteristic
329C2×C4×C151H(5,𝔽2)12yes—
330C8×C151—42no—
331C8×C151—42no—
332C22×C151—22no—
333C22×C151—22no—
334C22×C151—22no—
335C22×C151—22no—
336C22×C151—22no—
337C22×C151—22no—
338C22×C151—22no—
339C22×C151—22no—
340C22×C151—22no—
341C22×C151—22no—
342C22×C151—22no—
343C22×C151—22no—
344C22×C151—416no—
345C22×C151—41no—
346C22×C151—41no—
347C22×C151—41no—
348C22×C151—41no—
349C22×C151—41no—
350C22×C151—41no—
351C22×C151—41no—
352C22×C151—41no—
353C22×C151—42no—
354C22×C151—42no—
355C22×C151—42no—
356C22×C151—81no—
357C22×C151—81no—
358C22×C151—81no—
359C22×C151—81no—
360C22×C151#45214yescomplemented
361C22×C151C2×#12011yescharacteristic
362C22×C151C2×#12011yescharacteristic
363C22×C151#53411yescharacteristic
364C22×C151C2×#13511yescharacteristic
365C22×C151C2×#13711yescharacteristic
366C22×C151C2×#13711yescharacteristic
367C22×C151#57511yescharacteristic
368C4×C151—22no—
369C4×C151—22no—
370C4×C151—41no—
371C4×C151—42no—
372C4×C151—44no—
373C4×C151—42no—
374C4×C151—44no—
375C4×C151—42no—
376C4×C151D4212yes—
377C4×C151D4212yes—
378C2×C151—24no—
379C2×C151—42no—
380C2×C151—42no—
381C2×C151—82no—
382C2×C151#240311yescharacteristic
383C2×C151C2×#45211yescharacteristic
384C2×C151#300211yescharacteristic
385C2×C151#300411yescharacteristic
386C2×C151#300711yescharacteristic
387C2×C151#319011yescharacteristic
388C2×C151#319611yescharacteristic
389#23922C15111yesmaximal, characteristic, direct product factor, Sylow
390C151#2392211yescharacteristic, direct product factor, Sylow
391C2×#525C2×C15111yescharacteristic
392C22×C22⋊Q8C2×C15111yescharacteristic, complemented
393C2×#452C2×C15112yescomplemented
394C2×#451C2×C15111yescharacteristic, complemented
395C2×#448C2×C15111yescharacteristic, complemented
396#2001C2×C15112yescomplemented
397#2000C2×C15112yescomplemented
398#1874C2×C15111yescharacteristic, complemented
399#1873C2×C15112yescomplemented
400#1872C2×C15111yescharacteristic, complemented
401#1779C2×C15111yescharacteristic, complemented
402C22×#41C22×C15111yescharacteristic
403C23×Q8C22×C15111yescharacteristic
404C24×C4C22×C15111yescharacteristic
405C22×Q16C22×C15112yescomplemented
406C22×SD16C22×C15112yescomplemented
407#525—24no—
408#525—24no—
409C2×#123—21no—
410C2×C22⋊Q8—21no—
411C2×C22⋊Q8—21no—
412C2×C22⋊Q8—28no—
413C2×C22⋊Q8C22×C15112yes—
414C2×C22⋊Q8C22×C15111yescharacteristic
415C2×C22⋊Q8C22×C15111yescharacteristic
416C2×C22⋊Q8C22×C15112yes—
417C2×#121C22×C15111yescharacteristic
418C2×#121C22×C15111yescharacteristic
419C2×#120—21no—
420C2×C4×D4—21no—
421C2×C4×D4—21no—
422C2×#117C22×C15111yescharacteristic
423C22×C4⋊C4—21no—
424C22×C4⋊C4C22×C15111yescharacteristic
425C22×C22⋊C4—21no—
426#452—28no—
427#451—24no—
428#448—24no—
429C2×#103C22×C15112yescomplemented
430C2×#103C22×C15112yescomplemented
431C2×#103C22×C15112yescomplemented
432C2×#102C22×C15112yescomplemented
433C2×C22⋊C8C22×C15111yescharacteristic
434C2×C22⋊C8C22×C15112yes—
435C2×C22⋊C8C22×C15111yescharacteristic
436C2×C22⋊C8C22×C15112yes—
437#340C22×C15112yescomplemented
438#340C22×C15112yescomplemented
439C25D4×C15111yescharacteristic
440C2×#41—22no—
441C2×#41—22no—
442C2×#41—24no—
443C2×#41—42no—
444C22×Q8—24no—
445C22×Q8—21no—
446C22×Q8—22no—
447C22×Q8—22no—
448C22×Q8—42no—
449C22×Q8C23×C15112yes—
450C22×Q8C23×C15111yescharacteristic
451C22×D4—21no—
452C22×D4—21no—
453C22×D4—21no—
454C22×D4C23×C15111yescharacteristic
455C23×C4—21no—
456C23×C4—21no—
457C23×C4—21no—
458C23×C4—24no—
459C23×C4—22no—
460C23×C4—22no—
461C23×C4—42no—
462C23×C4D4×C15111yescharacteristic
463C23×C4D4×C15111yescharacteristic
464C23×C4D4×C15111yescharacteristic
465C23×C4C23×C15111yescharacteristic
466C23×C4C23×C15111yescharacteristic
467C23×C4C23×C15111yescharacteristic
468C2×Q16—24no—
469C2×Q16—24no—
470C2×Q16—42no—
471C2×SD16—24no—
472C2×SD16—24no—
473C2×SD16—42no—
474C22×C8C23×C15112yes—
475C22×C8C23×C15112yes—
476#123—28no—
477C22⋊Q8—28no—
478C22⋊Q8—28no—
479C22⋊Q8—24no—
480C22⋊Q8—22no—
481C22⋊Q8—24no—
482C22⋊Q8—22no—
483C22⋊Q8—24no—
484C22⋊Q8—22no—
485C22⋊Q8D4×C15114yes—
486C22⋊Q8D4×C15118yescomplemented
487#121—22no—
488#121—22no—
489#121—22no—
490#121D4×C15114yes—
491#120—28no—
492C4×D4—28no—
493C4×D4—28no—
494#117—22no—
495#117—22no—
496C2×C4⋊C4—28no—
497C2×C4⋊C4—22no—
498C2×C4⋊C4—22no—
499C2×C4⋊C4—21no—
500C2×C4⋊C4—21no—
501C2×C4⋊C4—21no—
502C2×C4⋊C4—24no—
503C2×C4⋊C4C23×C15112yes—
504C2×C4⋊C4C23×C15111yescharacteristic
505C2×C4⋊C4C23×C15111yescharacteristic
506C2×C22⋊C4—28no—
507C2×C22⋊C4—22no—
508C2×C22⋊C4—22no—
509C2×C22⋊C4—21no—
510C2×C22⋊C4—21no—
511C2×C22⋊C4—21no—
512C2×C22⋊C4—21no—
513C2×C22⋊C4—21no—
514C2×C42—21no—
515#103—24no—
516#103—24no—
517#103—24no—
518#102—24no—
519C22⋊C8—22no—
520C22⋊C8—22no—
521C22⋊C8—24no—
522C22⋊C8—42no—
523C24—22no—
524C24—22no—
525C24—22no—
526C24—22no—
527C24—22no—
528C24—21no—
529C24—41no—
530C24—41no—
531C24C2×D4×C15111yescharacteristic
532C24C2×D4×C15111yescharacteristic
533C24C2×D4×C15111yescharacteristic
534#41—48no—
535#41—48no—
536C2×Q8—24no—
537C2×Q8—22no—
538C2×Q8—21no—
539C2×Q8—22no—
540C2×Q8—22no—
541C2×Q8—22no—
542C2×Q8—22no—
543C2×Q8—22no—
544C2×Q8—22no—
545C2×Q8—48no—
546C2×Q8—48no—
547C2×Q8—42no—
548C2×Q8—42no—
549C2×Q8C2×D4×C15112yes—
550C2×Q8C2×D4×C15114yes—
551C2×D4—24no—
552C2×D4—24no—
553C2×D4—24no—
554C2×D4—22no—
555C2×D4—21no—
556C2×D4—22no—
557C2×D4—42no—
558C2×D4—42no—
559C2×D4—42no—
560C2×D4—42no—
561C2×D4—42no—
562C2×D4—42no—
563C2×D4C2×D4×C15112yes—
564C22×C4—22no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—24no—
570C22×C4—24no—
571C22×C4—24no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—22no—
577C22×C4—21no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—41no—
588C22×C4—41no—
589C22×C4—41no—
590C22×C4—48no—
591C22×C4—48no—
592C22×C4—42no—
593C22×C4—42no—
594C22×C4—42no—
595C22×C4—42no—
596C22×C4—42no—
597C22×C4—42no—
598C22×C4C2×D4×C15111yescharacteristic
599C22×C4C2×D4×C15111yescharacteristic
600C22×C4C2×D4×C15111yescharacteristic
601C22×C4C2×D4×C15112yes—
602C22×C4C2×D4×C15112yes—
603C22×C4C2×D4×C15114yes—
604C22×C4C24×C15111yescharacteristic
605Q16—48no—
606SD16—48no—
607C2×C8—22no—
608C2×C8—22no—
609C2×C8—22no—
610C2×C8—22no—
611C2×C8—22no—
612C2×C8—22no—
613C4⋊C4—24no—
614C4⋊C4—28no—
615C4⋊C4—24no—
616C4⋊C4—28no—
617C4⋊C4—24no—
618C4⋊C4—22no—
619C4⋊C4—21no—
620C4⋊C4—21no—
621C4⋊C4C2×D4×C15114yes—
622C4⋊C4C2×D4×C15112yes—
623C4⋊C4C2×D4×C15112yes—
624C22⋊C4—28no—
625C22⋊C4—24no—
626C22⋊C4—24no—
627C22⋊C4—24no—
628C22⋊C4—28no—
629C22⋊C4—24no—
630C22⋊C4—24no—
631C42—24no—
632C23—21no—
633C23—21no—
634C23—21no—
635C23—21no—
636C23—28no—
637C23—21no—
638C23—21no—
639C23—21no—
640C23—21no—
641C23—21no—
642C23—21no—
643C23—21no—
644C23—21no—
645C23—21no—
646C23—21no—
647C23—21no—
648C23—21no—
649C23—22no—
650C23—44no—
651C23—44no—
652C23—44no—
653C23—44no—
654C23—44no—
655C23—44no—
656C23—41no—
657C23—41no—
658C23—41no—
659C23—41no—
660C23—41no—
661C23—41no—
662C23#120×C15112yes—
663C23#120×C15112yes—
664C23#135×C15112yes—
665C23#137×C15112yes—
666C23#137×C15112yes—
667C23C22×D4×C15111yescharacteristic
668Q8—24no—
669Q8—24no—
670Q8—24no—
671Q8—48no—
672Q8—42no—
673Q8—42no—
674Q8—42no—
675D4—24no—
676D4—48no—
677D4—48no—
678D4—48no—
679D4—42no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—24no—
685C2×C4—24no—
686C2×C4—24no—
687C2×C4—24no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—24no—
691C2×C4—21no—
692C2×C4—22no—
693C2×C4—24no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—44no—
697C2×C4—44no—
698C2×C4—44no—
699C2×C4—48no—
700C2×C4—48no—
701C2×C4—48no—
702C2×C4—41no—
703C2×C4—42no—
704C2×C4—41no—
705C2×C4—42no—
706C2×C4—42no—
707C2×C4—41no—
708C2×C4—41no—
709C2×C4—41no—
710C2×C4—42no—
711C2×C4—41no—
712C2×C4—42no—
713C2×C4—42no—
714C2×C4#120×C15112yes—
715C2×C4#120×C15112yes—
716C2×C4C22×D4×C15112yes—
717C2×C4C22×D4×C15111yescharacteristic
718C2×C4C22×D4×C15111yescharacteristic
719C2×C4H(5,𝔽2)×C15112yes—
720C8—42no—
721C8—42no—
722C22—22no—
723C22—22no—
724C22—22no—
725C22—22no—
726C22—22no—
727C22—22no—
728C22—22no—
729C22—22no—
730C22—22no—
731C22—22no—
732C22—22no—
733C22—22no—
734C22—416no—
735C22—41no—
736C22—41no—
737C22—41no—
738C22—41no—
739C22—41no—
740C22—41no—
741C22—41no—
742C22—41no—
743C22—42no—
744C22—42no—
745C22—42no—
746C22—81no—
747C22—81no—
748C22—81no—
749C22—81no—
750C22#452×C15114yescomplemented
751C22C2×#120×C15111yescharacteristic
752C22C2×#120×C15111yescharacteristic
753C22#534×C15111yescharacteristic
754C22C2×#135×C15111yescharacteristic
755C22C2×#137×C15111yescharacteristic
756C22C2×#137×C15111yescharacteristic
757C22#575×C15111yescharacteristic
758C4—22no—
759C4—22no—
760C4—41no—
761C4—42no—
762C4—44no—
763C4—42no—
764C4—44no—
765C4—42no—
766C4D42×C15112yes—
767C4D42×C15112yes—
768C2—24no—
769C2—42no—
770C2—42no—
771C2—82no—
772C2#2403×C15111yescharacteristic
773C2C2×#452×C15111yescharacteristic
774C2#3002×C15111yescharacteristic
775C2#3004×C15111yescharacteristic
776C2#3007×C15111yescharacteristic
777C2#3190×C15111yescharacteristic
778C2#3196×C15111yescharacteristic
subgroupG/H
center, socleC23×C151C22×D4
commutator, Frattini, cosocleC22×C4C24×C151
prime radicalC2×#525×C151C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C151 ◁ C24×C4×C151 ◁ G

Complements

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

NH ≅ G/Ntype
2. C22×C22⋊Q8×C151C2semidirect
3. C2×#452×C151C2semidirect
4. C2×#451×C151C2semidirect
5. C2×#448×C151C2semidirect
6. #2001×C151C2semidirect
7. #2000×C151C2semidirect
8. #1874×C151C2semidirect
9. #1873×C151C2semidirect
10. #1872×C151C2semidirect
11. #1779×C151C2semidirect
15. C22×Q16×C151C22semidirect
16. C22×SD16×C151C22semidirect
39. C2×#103×C151C22semidirect
40. C2×#103×C151C22semidirect
41. C2×#103×C151C22semidirect
42. C2×#102×C151C22semidirect
47. #340×C151C22semidirect
48. #340×C151C22semidirect
96. C22⋊Q8×C151D4semidirect
360. C22×C151#452semidirect
389. #23922C151direct (N × H)
390. C151#23922direct (N × H)
392. C22×C22⋊Q8C2×C151semidirect
393. C2×#452C2×C151semidirect
394. C2×#451C2×C151semidirect
395. C2×#448C2×C151semidirect
396. #2001C2×C151semidirect
397. #2000C2×C151semidirect
398. #1874C2×C151semidirect
399. #1873C2×C151semidirect
400. #1872C2×C151semidirect
401. #1779C2×C151semidirect
405. C22×Q16C22×C151semidirect
406. C22×SD16C22×C151semidirect
429. C2×#103C22×C151semidirect
430. C2×#103C22×C151semidirect
431. C2×#103C22×C151semidirect
432. C2×#102C22×C151semidirect
437. #340C22×C151semidirect
438. #340C22×C151semidirect
486. C22⋊Q8D4×C151semidirect
750. C22#452×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#525×C1512
C22×C22⋊Q8×C1512
C2×#452×C1512
C2×#451×C1512
C2×#448×C1512
#2001×C1512
#2000×C1512
#1874×C1512
#1873×C1512
#1872×C1512
#1779×C1512
#23922151