Finite Group Databasebeta

← C151×#24125 #50329050

Subgroups — C151×#24125 #50329050

Order 38656.

1152 conjugacy classes of subgroups.

The subgroup lattice has 776 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#552×C151C211yesmaximal, characteristic, complemented
2C2×#478×C151C211yesmaximal, characteristic, complemented
3C2×C4×SD16×C151C211yesmaximal, characteristic, complemented
4#2535×C151C211yesmaximal, characteristic
5#2036×C151C211yesmaximal, characteristic, complemented
6#2035×C151C211yesmaximal, characteristic, complemented
7#2000×C151C211yesmaximal, characteristic, complemented
8#2000×C151C211yesmaximal, characteristic, complemented
9#1991×C151C211yesmaximal, characteristic, complemented
10#1954×C151C211yesmaximal, characteristic, complemented
11#1875×C151C211yesmaximal, characteristic, complemented
12#1874×C151C211yesmaximal, characteristic, complemented
13#1854×C151C211yesmaximal, characteristic, complemented
14#1853×C151C211yesmaximal, characteristic, complemented
15#1805×C151C211yesmaximal, characteristic, complemented
16C22×SD16×C151C2211yescharacteristic
17#552×C151—24no—
18#552×C151—24no—
19C2×#126×C151—21no—
20C2×#125×C151—21no—
21C2×#125×C151C2211yescharacteristic
22C2×#123×C151—21no—
23C2×C22⋊Q8×C151C2211yescharacteristic
24C2×C22⋊Q8×C151C2211yescharacteristic
25C2×#121×C151C2211yescharacteristic
26C2×#121×C151C2211yescharacteristic
27C2×C4×Q8×C151C2211yescharacteristic
28C2×C4×D4×C151C2211yescharacteristic
29C2×C4×D4×C151C2211yescharacteristic
30C2×#117×C151—21no—
31C2×#117×C151C2211yescharacteristic
32C22×C4⋊C4×C151C2211yescharacteristic
33#478×C151—24no—
34C4×SD16×C151—24no—
35C2×#107×C151C2211yescharacteristic
36C2×#106×C151C2211yescharacteristic
37C2×#106×C151C2211yescharacteristic
38C2×C4⋊C8×C151C2211yescharacteristic
39C2×#103×C151C2211yescharacteristic
40C2×#103×C151C2211yescharacteristic
41C2×#103×C151C2211yescharacteristic
42C2×#102×C151C2211yescharacteristic
43C2×#102×C151C2211yescharacteristic
44C2×#102×C151C2211yescharacteristic
45C2×C22⋊C8×C151C2211yescharacteristic
46C2×C22⋊C8×C151C2211yescharacteristic
47C2×C22⋊C8×C151C2211yescharacteristic
48C2×C22⋊C8×C151C2211yescharacteristic
49C2×C4×C8×C151C2211yescharacteristic
50#397×C151—21no—
51#392×C151—21no—
52#386×C151—21no—
53#386×C151—21no—
54#382×C151C2211yescharacteristic
55#380×C151C2211yescharacteristic
56#380×C151C2211yescharacteristic
57#340×C151C2211yescharacteristic
58#340×C151C2211yescharacteristic
59#340×C151C2211yescharacteristic
60#340×C151C2211yescharacteristic
61#340×C151C2211yescharacteristic
62#340×C151C2211yescharacteristic
63C22×Q8×C151C2311yescharacteristic
64C22×D4×C151—21no—
65C22×D4×C151—21no—
66C22×D4×C151D411yescharacteristic
67C22×D4×C151C2311yescharacteristic
68C23×C4×C151—21no—
69C23×C4×C151—21no—
70C23×C4×C151C2311yescharacteristic
71C23×C4×C151C2311yescharacteristic
72C2×SD16×C151—22no—
73C2×SD16×C151—22no—
74C2×SD16×C151—22no—
75C22×C8×C151C2311yescharacteristic
76C22×C8×C151C2311yescharacteristic
77C22×C8×C151C2311yescharacteristic
78C22×C8×C151C2311yescharacteristic
79#126×C151—28no—
80#125×C151—28no—
81#125×C151—22no—
82#125×C151D414yescomplemented
83#123×C151—28no—
84C22⋊Q8×C151—22no—
85C22⋊Q8×C151—22no—
86C22⋊Q8×C151—22no—
87C22⋊Q8×C151—22no—
88#121×C151—22no—
89#121×C151—22no—
90#121×C151—41no—
91#121×C151—41no—
92C4×Q8×C151—22no—
93C4×Q8×C151D414yescomplemented
94C4×D4×C151—22no—
95C4×D4×C151—22no—
96C4×D4×C151—22no—
97C4×D4×C151—22no—
98#117×C151—28no—
99#117×C151—22no—
100#117×C151—22no—
101C2×C4⋊C4×C151—21no—
102C2×C4⋊C4×C151—21no—
103C2×C4⋊C4×C151—21no—
104C2×C4⋊C4×C151—21no—
105C2×C4⋊C4×C151—21no—
106C2×C4⋊C4×C151—21no—
107C2×C4⋊C4×C151—22no—
108C2×C4⋊C4×C151—22no—
109C2×C4⋊C4×C151D411yescharacteristic
110C2×C4⋊C4×C151C2311yescharacteristic
111C2×C4⋊C4×C151C2311yescharacteristic
112C2×C4⋊C4×C151C2311yescharacteristic
113C2×C4⋊C4×C151C2311yescharacteristic
114C2×C4⋊C4×C151C2311yescharacteristic
115C2×C4⋊C4×C151C2311yescharacteristic
116C2×C22⋊C4×C151—21no—
117C2×C22⋊C4×C151—21no—
118C2×C22⋊C4×C151—21no—
119C2×C22⋊C4×C151—21no—
120C2×C22⋊C4×C151—21no—
121C2×C22⋊C4×C151—21no—
122C2×C22⋊C4×C151—21no—
123C2×C22⋊C4×C151—21no—
124C2×C22⋊C4×C151D411yescharacteristic
125C2×C22⋊C4×C151D411yescharacteristic
126C2×C42×C151—21no—
127C2×C42×C151—21no—
128C2×C42×C151C2311yescharacteristic
129#107×C151—22no—
130#106×C151—22no—
131#106×C151—22no—
132C4⋊C8×C151—22no—
133#103×C151—22no—
134#103×C151—41no—
135#103×C151—41no—
136#102×C151—22no—
137#102×C151—22no—
138#102×C151—22no—
139C22⋊C8×C151—22no—
140C22⋊C8×C151—22no—
141C22⋊C8×C151—41no—
142C22⋊C8×C151—41no—
143C4×C8×C151—22no—
144#95×C151—21no—
145#95×C151—21no—
146#95×C151—21no—
147#95×C151—21no—
148C24×C151—21no—
149C24×C151C2×D411yescharacteristic
150C24×C151C2×D411yescharacteristic
151C2×Q8×C151—21no—
152C2×Q8×C151—21no—
153C2×Q8×C151—21no—
154C2×Q8×C151—21no—
155C2×Q8×C151—21no—
156C2×Q8×C151C2×D412yes—
157C2×D4×C151—22no—
158C2×D4×C151—22no—
159C2×D4×C151—21no—
160C2×D4×C151—21no—
161C2×D4×C151—21no—
162C2×D4×C151—21no—
163C2×D4×C151—21no—
164C2×D4×C151—41no—
165C2×D4×C151—42no—
166C2×D4×C151—42no—
167C2×D4×C151—42no—
168C2×D4×C151—42no—
169C2×D4×C151—81no—
170C2×D4×C151—81no—
171C2×D4×C151#4112yes—
172C22×C4×C151—24no—
173C22×C4×C151—21no—
174C22×C4×C151—21no—
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—21no—
186C22×C4×C151—21no—
187C22×C4×C151—21no—
188C22×C4×C151—21no—
189C22×C4×C151—21no—
190C22×C4×C151—21no—
191C22×C4×C151—21no—
192C22×C4×C151—42no—
193C22×C4×C151—42no—
194C22×C4×C151—42no—
195C22×C4×C151—81no—
196C22×C4×C151—81no—
197C22×C4×C151C2×D411yescharacteristic
198C22×C4×C151C2×D411yescharacteristic
199C22×C4×C151C2×D411yescharacteristic
200C22×C4×C151C2×D411yescharacteristic
201C22×C4×C151C2411yescharacteristic
202SD16×C151—28no—
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—21no—
211C2×C8×C151—21no—
212C2×C8×C151—21no—
213C2×C8×C151—21no—
214C2×C8×C151#4112yes—
215C4⋊C4×C151—24no—
216C4⋊C4×C151—24no—
217C4⋊C4×C151—24no—
218C4⋊C4×C151—24no—
219C4⋊C4×C151—24no—
220C4⋊C4×C151—24no—
221C4⋊C4×C151—22no—
222C4⋊C4×C151—21no—
223C4⋊C4×C151—21no—
224C4⋊C4×C151—21no—
225C4⋊C4×C151—21no—
226C4⋊C4×C151—21no—
227C4⋊C4×C151—21no—
228C4⋊C4×C151—21no—
229C4⋊C4×C151—21no—
230C4⋊C4×C151—21no—
231C4⋊C4×C151C2×D412yes—
232C4⋊C4×C151C2×D412yes—
233C4⋊C4×C151C2×D412yes—
234C22⋊C4×C151—24no—
235C22⋊C4×C151—24no—
236C22⋊C4×C151—24no—
237C22⋊C4×C151—22no—
238C22⋊C4×C151—22no—
239C22⋊C4×C151—42no—
240C22⋊C4×C151—42no—
241C22⋊C4×C151—42no—
242C22⋊C4×C151—81no—
243C22⋊C4×C151—81no—
244C42×C151—24no—
245C42×C151—24no—
246C42×C151C2×D412yes—
247C42×C151C2×D412yes—
248C23×C151—21no—
249C23×C151—21no—
250C23×C151—21no—
251C23×C151—21no—
252C23×C151—21no—
253C23×C151—21no—
254C23×C151—21no—
255C23×C151—22no—
256C23×C151—21no—
257C23×C151—21no—
258C23×C151—21no—
259C23×C151—21no—
260C23×C151—21no—
261C23×C151—21no—
262C23×C151—41no—
263C23×C151—41no—
264C23×C151—41no—
265C23×C151—41no—
266C23×C151—41no—
267C23×C151—41no—
268C23×C151#13512yes—
269C23×C151C22×D411yescharacteristic
270Q8×C151—22no—
271Q8×C151—22no—
272Q8×C151—41no—
273Q8×C151—41no—
274D4×C151—22no—
275D4×C151—22no—
276D4×C151—44no—
277D4×C151—41no—
278D4×C151—41no—
279D4×C151—84no—
280D4×C151—84no—
281C2×C4×C151—21no—
282C2×C4×C151—21no—
283C2×C4×C151—21no—
284C2×C4×C151—21no—
285C2×C4×C151—22no—
286C2×C4×C151—21no—
287C2×C4×C151—22no—
288C2×C4×C151—22no—
289C2×C4×C151—21no—
290C2×C4×C151—22no—
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—41no—
312C2×C4×C151—41no—
313C2×C4×C151—41no—
314C2×C4×C151—41no—
315C2×C4×C151—41no—
316C2×C4×C151—41no—
317C2×C4×C151—41no—
318C2×C4×C151—41no—
319C2×C4×C151—41no—
320C2×C4×C151—41no—
321C2×C4×C151—84no—
322C2×C4×C151#12012yes—
323C2×C4×C151#12012yes—
324C2×C4×C151C22×D411yescharacteristic
325C2×C4×C151C22×D411yescharacteristic
326C2×C4×C151C2×#4111yescharacteristic
327C2×C4×C151C2×#4111yescharacteristic
328C2×C4×C151H(5,𝔽2)11yescharacteristic
329C2×C4×C1512−1+411yescharacteristic
330C8×C151—22no—
331C8×C151—41no—
332C8×C151—41no—
333C8×C151—41no—
334C22×C151—22no—
335C22×C151—22no—
336C22×C151—22no—
337C22×C151—41no—
338C22×C151—41no—
339C22×C151—41no—
340C22×C151—41no—
341C22×C151—41no—
342C22×C151—41no—
343C22×C151—41no—
344C22×C151—42no—
345C22×C151—41no—
346C22×C151—41no—
347C22×C151—42no—
348C22×C151—41no—
349C22×C151—41no—
350C22×C151—42no—
351C22×C151—81no—
352C22×C151—81no—
353C22×C151—81no—
354C22×C151—81no—
355C22×C151C2×#12011yescharacteristic
356C22×C151#54611yescharacteristic
357C22×C151#54711yescharacteristic
358C22×C151C2×#13511yescharacteristic
359C22×C151#57511yescharacteristic
360C22×C151#57711yescharacteristic
361C22×C151#57711yescharacteristic
362C4×C151—22no—
363C4×C151—22no—
364C4×C151—41no—
365C4×C151—41no—
366C4×C151—42no—
367C4×C151—42no—
368C4×C151—42no—
369C4×C151—42no—
370C4×C151—81no—
371C4×C151—81no—
372C4×C151—81no—
373C4×C151#52511yescharacteristic
374C4×C151#53711yescharacteristic
375C4×C151#54811yescharacteristic
376C4×C151#55011yescharacteristic
377C2×C151—42no—
378C2×C151—81no—
379C2×C151—82no—
380C2×C151#240711yescharacteristic
381C2×C151#300211yescharacteristic
382C2×C151#301011yescharacteristic
383C2×C151#329611yescharacteristic
384C2×C151#332311yescharacteristic
385C2×C151#333711yescharacteristic
386C2×C151#335111yescharacteristic
387#24125C15111yesmaximal, characteristic, direct product factor, Sylow
388C151#2412511yescharacteristic, direct product factor, Sylow
389C2×#552C2×C15111yescharacteristic, complemented
390C2×#478C2×C15111yescharacteristic, complemented
391C2×C4×SD16C2×C15111yescharacteristic, complemented
392#2535C2×C15111yescharacteristic
393#2036C2×C15111yescharacteristic, complemented
394#2035C2×C15111yescharacteristic, complemented
395#2000C2×C15111yescharacteristic, complemented
396#2000C2×C15111yescharacteristic, complemented
397#1991C2×C15111yescharacteristic, complemented
398#1954C2×C15111yescharacteristic, complemented
399#1875C2×C15111yescharacteristic, complemented
400#1874C2×C15111yescharacteristic, complemented
401#1854C2×C15111yescharacteristic, complemented
402#1853C2×C15111yescharacteristic, complemented
403#1805C2×C15111yescharacteristic, complemented
404C22×SD16C22×C15111yescharacteristic
405#552—24no—
406#552—24no—
407C2×#126—21no—
408C2×#125—21no—
409C2×#125C22×C15111yescharacteristic
410C2×#123—21no—
411C2×C22⋊Q8C22×C15111yescharacteristic
412C2×C22⋊Q8C22×C15111yescharacteristic
413C2×#121C22×C15111yescharacteristic
414C2×#121C22×C15111yescharacteristic
415C2×C4×Q8C22×C15111yescharacteristic
416C2×C4×D4C22×C15111yescharacteristic
417C2×C4×D4C22×C15111yescharacteristic
418C2×#117—21no—
419C2×#117C22×C15111yescharacteristic
420C22×C4⋊C4C22×C15111yescharacteristic
421#478—24no—
422C4×SD16—24no—
423C2×#107C22×C15111yescharacteristic
424C2×#106C22×C15111yescharacteristic
425C2×#106C22×C15111yescharacteristic
426C2×C4⋊C8C22×C15111yescharacteristic
427C2×#103C22×C15111yescharacteristic
428C2×#103C22×C15111yescharacteristic
429C2×#103C22×C15111yescharacteristic
430C2×#102C22×C15111yescharacteristic
431C2×#102C22×C15111yescharacteristic
432C2×#102C22×C15111yescharacteristic
433C2×C22⋊C8C22×C15111yescharacteristic
434C2×C22⋊C8C22×C15111yescharacteristic
435C2×C22⋊C8C22×C15111yescharacteristic
436C2×C22⋊C8C22×C15111yescharacteristic
437C2×C4×C8C22×C15111yescharacteristic
438#397—21no—
439#392—21no—
440#386—21no—
441#386—21no—
442#382C22×C15111yescharacteristic
443#380C22×C15111yescharacteristic
444#380C22×C15111yescharacteristic
445#340C22×C15111yescharacteristic
446#340C22×C15111yescharacteristic
447#340C22×C15111yescharacteristic
448#340C22×C15111yescharacteristic
449#340C22×C15111yescharacteristic
450#340C22×C15111yescharacteristic
451C22×Q8C23×C15111yescharacteristic
452C22×D4—21no—
453C22×D4—21no—
454C22×D4D4×C15111yescharacteristic
455C22×D4C23×C15111yescharacteristic
456C23×C4—21no—
457C23×C4—21no—
458C23×C4C23×C15111yescharacteristic
459C23×C4C23×C15111yescharacteristic
460C2×SD16—22no—
461C2×SD16—22no—
462C2×SD16—22no—
463C22×C8C23×C15111yescharacteristic
464C22×C8C23×C15111yescharacteristic
465C22×C8C23×C15111yescharacteristic
466C22×C8C23×C15111yescharacteristic
467#126—28no—
468#125—28no—
469#125—22no—
470#125D4×C15114yescomplemented
471#123—28no—
472C22⋊Q8—22no—
473C22⋊Q8—22no—
474C22⋊Q8—22no—
475C22⋊Q8—22no—
476#121—22no—
477#121—22no—
478#121—41no—
479#121—41no—
480C4×Q8—22no—
481C4×Q8D4×C15114yescomplemented
482C4×D4—22no—
483C4×D4—22no—
484C4×D4—22no—
485C4×D4—22no—
486#117—28no—
487#117—22no—
488#117—22no—
489C2×C4⋊C4—21no—
490C2×C4⋊C4—21no—
491C2×C4⋊C4—21no—
492C2×C4⋊C4—21no—
493C2×C4⋊C4—21no—
494C2×C4⋊C4—21no—
495C2×C4⋊C4—22no—
496C2×C4⋊C4—22no—
497C2×C4⋊C4D4×C15111yescharacteristic
498C2×C4⋊C4C23×C15111yescharacteristic
499C2×C4⋊C4C23×C15111yescharacteristic
500C2×C4⋊C4C23×C15111yescharacteristic
501C2×C4⋊C4C23×C15111yescharacteristic
502C2×C4⋊C4C23×C15111yescharacteristic
503C2×C4⋊C4C23×C15111yescharacteristic
504C2×C22⋊C4—21no—
505C2×C22⋊C4—21no—
506C2×C22⋊C4—21no—
507C2×C22⋊C4—21no—
508C2×C22⋊C4—21no—
509C2×C22⋊C4—21no—
510C2×C22⋊C4—21no—
511C2×C22⋊C4—21no—
512C2×C22⋊C4D4×C15111yescharacteristic
513C2×C22⋊C4D4×C15111yescharacteristic
514C2×C42—21no—
515C2×C42—21no—
516C2×C42C23×C15111yescharacteristic
517#107—22no—
518#106—22no—
519#106—22no—
520C4⋊C8—22no—
521#103—22no—
522#103—41no—
523#103—41no—
524#102—22no—
525#102—22no—
526#102—22no—
527C22⋊C8—22no—
528C22⋊C8—22no—
529C22⋊C8—41no—
530C22⋊C8—41no—
531C4×C8—22no—
532#95—21no—
533#95—21no—
534#95—21no—
535#95—21no—
536C24—21no—
537C24C2×D4×C15111yescharacteristic
538C24C2×D4×C15111yescharacteristic
539C2×Q8—21no—
540C2×Q8—21no—
541C2×Q8—21no—
542C2×Q8—21no—
543C2×Q8—21no—
544C2×Q8C2×D4×C15112yes—
545C2×D4—22no—
546C2×D4—22no—
547C2×D4—21no—
548C2×D4—21no—
549C2×D4—21no—
550C2×D4—21no—
551C2×D4—21no—
552C2×D4—41no—
553C2×D4—42no—
554C2×D4—42no—
555C2×D4—42no—
556C2×D4—42no—
557C2×D4—81no—
558C2×D4—81no—
559C2×D4#41×C15112yes—
560C22×C4—24no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—42no—
581C22×C4—42no—
582C22×C4—42no—
583C22×C4—81no—
584C22×C4—81no—
585C22×C4C2×D4×C15111yescharacteristic
586C22×C4C2×D4×C15111yescharacteristic
587C22×C4C2×D4×C15111yescharacteristic
588C22×C4C2×D4×C15111yescharacteristic
589C22×C4C24×C15111yescharacteristic
590SD16—28no—
591C2×C8—21no—
592C2×C8—21no—
593C2×C8—21no—
594C2×C8—21no—
595C2×C8—21no—
596C2×C8—21no—
597C2×C8—21no—
598C2×C8—21no—
599C2×C8—21no—
600C2×C8—21no—
601C2×C8—21no—
602C2×C8#41×C15112yes—
603C4⋊C4—24no—
604C4⋊C4—24no—
605C4⋊C4—24no—
606C4⋊C4—24no—
607C4⋊C4—24no—
608C4⋊C4—24no—
609C4⋊C4—22no—
610C4⋊C4—21no—
611C4⋊C4—21no—
612C4⋊C4—21no—
613C4⋊C4—21no—
614C4⋊C4—21no—
615C4⋊C4—21no—
616C4⋊C4—21no—
617C4⋊C4—21no—
618C4⋊C4—21no—
619C4⋊C4C2×D4×C15112yes—
620C4⋊C4C2×D4×C15112yes—
621C4⋊C4C2×D4×C15112yes—
622C22⋊C4—24no—
623C22⋊C4—24no—
624C22⋊C4—24no—
625C22⋊C4—22no—
626C22⋊C4—22no—
627C22⋊C4—42no—
628C22⋊C4—42no—
629C22⋊C4—42no—
630C22⋊C4—81no—
631C22⋊C4—81no—
632C42—24no—
633C42—24no—
634C42C2×D4×C15112yes—
635C42C2×D4×C15112yes—
636C23—21no—
637C23—21no—
638C23—21no—
639C23—21no—
640C23—21no—
641C23—21no—
642C23—21no—
643C23—22no—
644C23—21no—
645C23—21no—
646C23—21no—
647C23—21no—
648C23—21no—
649C23—21no—
650C23—41no—
651C23—41no—
652C23—41no—
653C23—41no—
654C23—41no—
655C23—41no—
656C23#135×C15112yes—
657C23C22×D4×C15111yescharacteristic
658Q8—22no—
659Q8—22no—
660Q8—41no—
661Q8—41no—
662D4—22no—
663D4—22no—
664D4—44no—
665D4—41no—
666D4—41no—
667D4—84no—
668D4—84no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—21no—
673C2×C4—21no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—21no—
678C2×C4—22no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—48no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—41no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—41no—
706C2×C4—41no—
707C2×C4—41no—
708C2×C4—41no—
709C2×C4—84no—
710C2×C4#120×C15112yes—
711C2×C4#120×C15112yes—
712C2×C4C22×D4×C15111yescharacteristic
713C2×C4C22×D4×C15111yescharacteristic
714C2×C4C2×#41×C15111yescharacteristic
715C2×C4C2×#41×C15111yescharacteristic
716C2×C4H(5,𝔽2)×C15111yescharacteristic
717C2×C42−1+4×C15111yescharacteristic
718C8—22no—
719C8—41no—
720C8—41no—
721C8—41no—
722C22—22no—
723C22—22no—
724C22—22no—
725C22—41no—
726C22—41no—
727C22—41no—
728C22—41no—
729C22—41no—
730C22—42no—
731C22—41no—
732C22—41no—
733C22—42no—
734C22—41no—
735C22—41no—
736C22—42no—
737C22—41no—
738C22—41no—
739C22—81no—
740C22—81no—
741C22—81no—
742C22—81no—
743C22C2×#120×C15111yescharacteristic
744C22#546×C15111yescharacteristic
745C22#547×C15111yescharacteristic
746C22C2×#135×C15111yescharacteristic
747C22#575×C15111yescharacteristic
748C22#577×C15111yescharacteristic
749C22#577×C15111yescharacteristic
750C4—22no—
751C4—22no—
752C4—41no—
753C4—41no—
754C4—42no—
755C4—42no—
756C4—42no—
757C4—42no—
758C4—81no—
759C4—81no—
760C4—81no—
761C4#525×C15111yescharacteristic
762C4#537×C15111yescharacteristic
763C4#548×C15111yescharacteristic
764C4#550×C15111yescharacteristic
765C2—42no—
766C2—81no—
767C2—82no—
768C2#2407×C15111yescharacteristic
769C2#3002×C15111yescharacteristic
770C2#3010×C15111yescharacteristic
771C2#3296×C15111yescharacteristic
772C2#3323×C15111yescharacteristic
773C2#3337×C15111yescharacteristic
774C2#3351×C15111yescharacteristic
subgroupG/H
center, socleC23×C151C22×D4
commutator, Frattini, cosocleC22×C4C24×C151
prime radical#2535×C151C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C151 ◁ C2×C4×D4×C151 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#552×C151C2semidirect
2. C2×#478×C151C2semidirect
3. C2×C4×SD16×C151C2semidirect
5. #2036×C151C2semidirect
6. #2035×C151C2semidirect
7. #2000×C151C2semidirect
8. #2000×C151C2semidirect
9. #1991×C151C2semidirect
10. #1954×C151C2semidirect
11. #1875×C151C2semidirect
12. #1874×C151C2semidirect
13. #1854×C151C2semidirect
14. #1853×C151C2semidirect
15. #1805×C151C2semidirect
82. #125×C151D4semidirect
93. C4×Q8×C151D4semidirect
387. #24125C151direct (N × H)
388. C151#24125direct (N × H)
389. C2×#552C2×C151semidirect
390. C2×#478C2×C151semidirect
391. C2×C4×SD16C2×C151semidirect
393. #2036C2×C151semidirect
394. #2035C2×C151semidirect
395. #2000C2×C151semidirect
396. #2000C2×C151semidirect
397. #1991C2×C151semidirect
398. #1954C2×C151semidirect
399. #1875C2×C151semidirect
400. #1874C2×C151semidirect
401. #1854C2×C151semidirect
402. #1853C2×C151semidirect
403. #1805C2×C151semidirect
470. #125D4×C151semidirect
481. C4×Q8D4×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#552×C1512
C2×#478×C1512
C2×C4×SD16×C1512
#2535×C1512
#2036×C1512
#2035×C1512
#2000×C1512
#1991×C1512
#1954×C1512
#1875×C1512
#1874×C1512
#1854×C1512
#1853×C1512
#1805×C1512
#24125151