Finite Group Databasebeta

← C151×#23584 #50328509

Subgroups — C151×#23584 #50328509

Order 38656.

1114 conjugacy classes of subgroups.

The subgroup lattice has 740 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#541×C151C211yesmaximal, characteristic, complemented
2C2×#440×C151C211yesmaximal, characteristic, complemented
3C2×C4×SD16×C151C211yesmaximal, characteristic, complemented
4#2324×C151C211yesmaximal, characteristic
5#2059×C151C211yesmaximal, characteristic, complemented
6#2043×C151C211yesmaximal, characteristic, complemented
7#2036×C151C211yesmaximal, characteristic, complemented
8#2035×C151C211yesmaximal, characteristic, complemented
9#2025×C151C211yesmaximal, characteristic, complemented
10#2013×C151C211yesmaximal, characteristic, complemented
11#2000×C151C211yesmaximal, characteristic
12#2000×C151C211yesmaximal, characteristic
13#1763×C151C211yesmaximal, characteristic, complemented
14C4×#103×C151C211yesmaximal, characteristic, complemented
15#1750×C151C211yesmaximal, characteristic, complemented
16C22×SD16×C151C2211yescharacteristic
17C22×SD16×C151C2211yescharacteristic
18#541×C151—24no—
19#541×C151—24no—
20C2×C4⋊Q8×C151C2211yescharacteristic
21C2×#126×C151—21no—
22C2×#126×C151—21no—
23C2×#125×C151—21no—
24C2×#125×C151—21no—
25C2×#125×C151C2211yescharacteristic
26C2×C22⋊Q8×C151C2211yescharacteristic
27C2×C22⋊Q8×C151C2211yescharacteristic
28C2×#121×C151C2211yescharacteristic
29C2×C4×Q8×C151C2211yescharacteristic
30C2×C4×Q8×C151C2211yescharacteristic
31C2×C4×D4×C151C2211yescharacteristic
32C2×#117×C151C2211yescharacteristic
33#440×C151—24no—
34C4×SD16×C151—24no—
35C2×#107×C151C2211yescharacteristic
36C2×#106×C151C2211yescharacteristic
37C2×#103×C151C2211yescharacteristic
38C2×#103×C151C2211yescharacteristic
39C2×#103×C151C2211yescharacteristic
40C2×#103×C151C2211yescharacteristic
41C2×#103×C151C2211yescharacteristic
42C2×#103×C151C2211yescharacteristic
43C2×#102×C151C2211yescharacteristic
44C2×#102×C151C2211yescharacteristic
45C2×C22⋊C8×C151C2211yescharacteristic
46C2×C22⋊C8×C151C2211yescharacteristic
47C2×#97×C151C2211yescharacteristic
48C2×C4×C8×C151C2211yescharacteristic
49#390×C151—21no—
50#390×C151C2211yescharacteristic
51#389×C151C2211yescharacteristic
52#388×C151—21no—
53#386×C151—21no—
54#385×C151—21no—
55#380×C151C2211yescharacteristic
56C4×C4⋊C4×C151C2211yescharacteristic
57#340×C151C2211yescharacteristic
58#340×C151C2211yescharacteristic
59#340×C151C2211yescharacteristic
60#340×C151C2211yescharacteristic
61#336×C151C2211yescharacteristic
62#336×C151C2211yescharacteristic
63C22×Q8×C151C2311yescharacteristic
64C22×Q8×C151C2311yescharacteristic
65C22×D4×C151—21no—
66C22×D4×C151C2311yescharacteristic
67C23×C4×C151—21no—
68C23×C4×C151C2311yescharacteristic
69C2×SD16×C151—22no—
70C2×SD16×C151—22no—
71C2×SD16×C151—22no—
72C2×SD16×C151—22no—
73C2×SD16×C151—22no—
74C2×SD16×C151—22no—
75C22×C8×C151C2311yescharacteristic
76C22×C8×C151C2311yescharacteristic
77C22×C8×C151C2311yescharacteristic
78C22×C8×C151C2311yescharacteristic
79C4⋊Q8×C151—22no—
80C4⋊Q8×C151—22no—
81#126×C151—28no—
82#126×C151—28no—
83#125×C151—28no—
84#125×C151—28no—
85#125×C151—22no—
86#125×C151—22no—
87C22⋊Q8×C151—22no—
88C22⋊Q8×C151—22no—
89C22⋊Q8×C151—22no—
90C22⋊Q8×C151—22no—
91#121×C151—22no—
92#121×C151—22no—
93C4×Q8×C151—22no—
94C4×Q8×C151—22no—
95C4×Q8×C151D414yescomplemented
96C4×Q8×C151D414yescomplemented
97C4×D4×C151—22no—
98C4×D4×C151—22no—
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—21no—
108C2×C4⋊C4×C151—21no—
109C2×C4⋊C4×C151—21no—
110C2×C4⋊C4×C151D411yescharacteristic
111C2×C4⋊C4×C151D411yescharacteristic
112C2×C4⋊C4×C151C2311yescharacteristic
113C2×C4⋊C4×C151C2311yescharacteristic
114C2×C4⋊C4×C151C2311yescharacteristic
115C2×C4⋊C4×C151C2311yescharacteristic
116C2×C4⋊C4×C151C2311yescharacteristic
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×C151—21no—
129C2×C42×C151C2311yescharacteristic
130C2×C42×C151C2311yescharacteristic
131#107×C151—22no—
132#106×C151—22no—
133#103×C151—22no—
134#103×C151—22no—
135#103×C151—22no—
136#103×C151—22no—
137#103×C151—22no—
138#103×C151—22no—
139#102×C151—22no—
140#102×C151—22no—
141C22⋊C8×C151—22no—
142C22⋊C8×C151—22no—
143#97×C151—22no—
144C4×C8×C151—22no—
145#95×C151—21no—
146#95×C151—21no—
147#95×C151—21no—
148C24×C151—21no—
149C24×C151C2×D411yescharacteristic
150C2×Q8×C151—21no—
151C2×Q8×C151—21no—
152C2×Q8×C151—21no—
153C2×Q8×C151—21no—
154C2×Q8×C151—21no—
155C2×Q8×C151—21no—
156C2×Q8×C151—21no—
157C2×Q8×C151—21no—
158C2×Q8×C151—21no—
159C2×Q8×C151—21no—
160C2×Q8×C151C2×D412yes—
161C2×Q8×C151C2×D412yes—
162C2×D4×C151—24no—
163C2×D4×C151—21no—
164C2×D4×C151—21no—
165C2×D4×C151—21no—
166C2×D4×C151—21no—
167C2×D4×C151—21no—
168C2×D4×C151—81no—
169C2×D4×C151—81no—
170C2×D4×C151#4112yes—
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—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—42no—
185C22×C4×C151—81no—
186C22×C4×C151—81no—
187C22×C4×C151C2×D411yescharacteristic
188C22×C4×C151C2×D411yescharacteristic
189C22×C4×C151C2×D411yescharacteristic
190C22×C4×C151C2×D411yescharacteristic
191C22×C4×C151C2×D411yescharacteristic
192C22×C4×C151C2411yescharacteristic
193SD16×C151—28no—
194SD16×C151—28no—
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#4112yes—
206C2×C8×C151#4112yes—
207C4⋊C4×C151—24no—
208C4⋊C4×C151—24no—
209C4⋊C4×C151—24no—
210C4⋊C4×C151—24no—
211C4⋊C4×C151—24no—
212C4⋊C4×C151—24no—
213C4⋊C4×C151—24no—
214C4⋊C4×C151—24no—
215C4⋊C4×C151—22no—
216C4⋊C4×C151—22no—
217C4⋊C4×C151—21no—
218C4⋊C4×C151—21no—
219C4⋊C4×C151—21no—
220C4⋊C4×C151—21no—
221C4⋊C4×C151—21no—
222C4⋊C4×C151—21no—
223C4⋊C4×C151—21no—
224C4⋊C4×C151—81no—
225C4⋊C4×C151C2×D412yes—
226C4⋊C4×C151C2×D412yes—
227C4⋊C4×C151#4112yes—
228C22⋊C4×C151—24no—
229C22⋊C4×C151—24no—
230C22⋊C4×C151—24no—
231C22⋊C4×C151—22no—
232C22⋊C4×C151—22no—
233C22⋊C4×C151—42no—
234C22⋊C4×C151—81no—
235C22⋊C4×C151—81no—
236C22⋊C4×C151—81no—
237C42×C151—24no—
238C42×C151—24no—
239C42×C151—21no—
240C42×C151—21no—
241C42×C151—81no—
242C42×C151C2×D412yes—
243C42×C151C2×D412yes—
244C23×C151—21no—
245C23×C151—22no—
246C23×C151—21no—
247C23×C151—21no—
248C23×C151—21no—
249C23×C151—21no—
250C23×C151—21no—
251C23×C151—21no—
252C23×C151—41no—
253C23×C151—41no—
254C23×C151—41no—
255C23×C151—41no—
256C23×C151—41no—
257C23×C151—41no—
258C23×C151C22×D411yescharacteristic
259Q8×C151—22no—
260Q8×C151—22no—
261Q8×C151—22no—
262Q8×C151—22no—
263Q8×C151—41no—
264Q8×C151—41no—
265Q8×C151—41no—
266Q8×C151—41no—
267D4×C151—22no—
268D4×C151—22no—
269D4×C151—41no—
270D4×C151—41no—
271D4×C151—84no—
272C2×C4×C151—21no—
273C2×C4×C151—21no—
274C2×C4×C151—21no—
275C2×C4×C151—21no—
276C2×C4×C151—22no—
277C2×C4×C151—22no—
278C2×C4×C151—21no—
279C2×C4×C151—21no—
280C2×C4×C151—22no—
281C2×C4×C151—22no—
282C2×C4×C151—21no—
283C2×C4×C151—21no—
284C2×C4×C151—22no—
285C2×C4×C151—21no—
286C2×C4×C151—21no—
287C2×C4×C151—21no—
288C2×C4×C151—21no—
289C2×C4×C151—21no—
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—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—84no—
311C2×C4×C151#12012yes—
312C2×C4×C151#12012yes—
313C2×C4×C151C22×D411yescharacteristic
314C2×C4×C151C22×D411yescharacteristic
315C2×C4×C151C2×#4111yescharacteristic
316C2×C4×C151C2×#4111yescharacteristic
317C2×C4×C151C2×#4111yescharacteristic
318C2×C4×C151C2×#4111yescharacteristic
319C8×C151—22no—
320C8×C151—22no—
321C8×C151—41no—
322C8×C151—41no—
323C22×C151—41no—
324C22×C151—42no—
325C22×C151—41no—
326C22×C151—42no—
327C22×C151—41no—
328C22×C151—42no—
329C22×C151—41no—
330C22×C151—41no—
331C22×C151—41no—
332C22×C151—41no—
333C22×C151—81no—
334C22×C151—81no—
335C22×C151—81no—
336C22×C151—81no—
337C22×C151C2×#12011yescharacteristic
338C22×C151#52511yescharacteristic
339C22×C151#53211yescharacteristic
340C22×C151#57711yescharacteristic
341C22×C151#57711yescharacteristic
342C22×C151#57711yescharacteristic
343C22×C151#57811yescharacteristic
344C4×C151—22no—
345C4×C151—22no—
346C4×C151—42no—
347C4×C151—41no—
348C4×C151—42no—
349C4×C151—42no—
350C4×C151—41no—
351C4×C151—42no—
352C4×C151—41no—
353C4×C151—42no—
354C4×C151—81no—
355C4×C151—81no—
356C4×C151#52511yescharacteristic
357C4×C151#52511yescharacteristic
358C4×C151#53211yescharacteristic
359C4×C151#53211yescharacteristic
360C2×C151—81no—
361C2×C151—82no—
362C2×C151#238811yescharacteristic
363C2×C151#301011yescharacteristic
364C2×C151#301311yescharacteristic
365C2×C151#312011yescharacteristic
366C2×C151#312311yescharacteristic
367C2×C151#317411yescharacteristic
368C2×C151#317811yescharacteristic
369#23584C15111yesmaximal, characteristic, direct product factor, Sylow
370C151#2358411yescharacteristic, direct product factor, Sylow
371C2×#541C2×C15111yescharacteristic, complemented
372C2×#440C2×C15111yescharacteristic, complemented
373C2×C4×SD16C2×C15111yescharacteristic, complemented
374#2324C2×C15111yescharacteristic
375#2059C2×C15111yescharacteristic, complemented
376#2043C2×C15111yescharacteristic, complemented
377#2036C2×C15111yescharacteristic, complemented
378#2035C2×C15111yescharacteristic, complemented
379#2025C2×C15111yescharacteristic, complemented
380#2013C2×C15111yescharacteristic, complemented
381#2000C2×C15111yescharacteristic
382#2000C2×C15111yescharacteristic
383#1763C2×C15111yescharacteristic, complemented
384C4×#103C2×C15111yescharacteristic, complemented
385#1750C2×C15111yescharacteristic, complemented
386C22×SD16C22×C15111yescharacteristic
387C22×SD16C22×C15111yescharacteristic
388#541—24no—
389#541—24no—
390C2×C4⋊Q8C22×C15111yescharacteristic
391C2×#126—21no—
392C2×#126—21no—
393C2×#125—21no—
394C2×#125—21no—
395C2×#125C22×C15111yescharacteristic
396C2×C22⋊Q8C22×C15111yescharacteristic
397C2×C22⋊Q8C22×C15111yescharacteristic
398C2×#121C22×C15111yescharacteristic
399C2×C4×Q8C22×C15111yescharacteristic
400C2×C4×Q8C22×C15111yescharacteristic
401C2×C4×D4C22×C15111yescharacteristic
402C2×#117C22×C15111yescharacteristic
403#440—24no—
404C4×SD16—24no—
405C2×#107C22×C15111yescharacteristic
406C2×#106C22×C15111yescharacteristic
407C2×#103C22×C15111yescharacteristic
408C2×#103C22×C15111yescharacteristic
409C2×#103C22×C15111yescharacteristic
410C2×#103C22×C15111yescharacteristic
411C2×#103C22×C15111yescharacteristic
412C2×#103C22×C15111yescharacteristic
413C2×#102C22×C15111yescharacteristic
414C2×#102C22×C15111yescharacteristic
415C2×C22⋊C8C22×C15111yescharacteristic
416C2×C22⋊C8C22×C15111yescharacteristic
417C2×#97C22×C15111yescharacteristic
418C2×C4×C8C22×C15111yescharacteristic
419#390—21no—
420#390C22×C15111yescharacteristic
421#389C22×C15111yescharacteristic
422#388—21no—
423#386—21no—
424#385—21no—
425#380C22×C15111yescharacteristic
426C4×C4⋊C4C22×C15111yescharacteristic
427#340C22×C15111yescharacteristic
428#340C22×C15111yescharacteristic
429#340C22×C15111yescharacteristic
430#340C22×C15111yescharacteristic
431#336C22×C15111yescharacteristic
432#336C22×C15111yescharacteristic
433C22×Q8C23×C15111yescharacteristic
434C22×Q8C23×C15111yescharacteristic
435C22×D4—21no—
436C22×D4C23×C15111yescharacteristic
437C23×C4—21no—
438C23×C4C23×C15111yescharacteristic
439C2×SD16—22no—
440C2×SD16—22no—
441C2×SD16—22no—
442C2×SD16—22no—
443C2×SD16—22no—
444C2×SD16—22no—
445C22×C8C23×C15111yescharacteristic
446C22×C8C23×C15111yescharacteristic
447C22×C8C23×C15111yescharacteristic
448C22×C8C23×C15111yescharacteristic
449C4⋊Q8—22no—
450C4⋊Q8—22no—
451#126—28no—
452#126—28no—
453#125—28no—
454#125—28no—
455#125—22no—
456#125—22no—
457C22⋊Q8—22no—
458C22⋊Q8—22no—
459C22⋊Q8—22no—
460C22⋊Q8—22no—
461#121—22no—
462#121—22no—
463C4×Q8—22no—
464C4×Q8—22no—
465C4×Q8D4×C15114yescomplemented
466C4×Q8D4×C15114yescomplemented
467C4×D4—22no—
468C4×D4—22no—
469#117—22no—
470#117—22no—
471C2×C4⋊C4—21no—
472C2×C4⋊C4—21no—
473C2×C4⋊C4—21no—
474C2×C4⋊C4—21no—
475C2×C4⋊C4—21no—
476C2×C4⋊C4—21no—
477C2×C4⋊C4—21no—
478C2×C4⋊C4—21no—
479C2×C4⋊C4—21no—
480C2×C4⋊C4D4×C15111yescharacteristic
481C2×C4⋊C4D4×C15111yescharacteristic
482C2×C4⋊C4C23×C15111yescharacteristic
483C2×C4⋊C4C23×C15111yescharacteristic
484C2×C4⋊C4C23×C15111yescharacteristic
485C2×C4⋊C4C23×C15111yescharacteristic
486C2×C4⋊C4C23×C15111yescharacteristic
487C2×C22⋊C4—21no—
488C2×C22⋊C4—21no—
489C2×C22⋊C4—21no—
490C2×C22⋊C4—21no—
491C2×C22⋊C4—21no—
492C2×C22⋊C4—21no—
493C2×C22⋊C4—21no—
494C2×C22⋊C4D4×C15111yescharacteristic
495C2×C22⋊C4D4×C15111yescharacteristic
496C2×C42—21no—
497C2×C42—21no—
498C2×C42—21no—
499C2×C42C23×C15111yescharacteristic
500C2×C42C23×C15111yescharacteristic
501#107—22no—
502#106—22no—
503#103—22no—
504#103—22no—
505#103—22no—
506#103—22no—
507#103—22no—
508#103—22no—
509#102—22no—
510#102—22no—
511C22⋊C8—22no—
512C22⋊C8—22no—
513#97—22no—
514C4×C8—22no—
515#95—21no—
516#95—21no—
517#95—21no—
518C24—21no—
519C24C2×D4×C15111yescharacteristic
520C2×Q8—21no—
521C2×Q8—21no—
522C2×Q8—21no—
523C2×Q8—21no—
524C2×Q8—21no—
525C2×Q8—21no—
526C2×Q8—21no—
527C2×Q8—21no—
528C2×Q8—21no—
529C2×Q8—21no—
530C2×Q8C2×D4×C15112yes—
531C2×Q8C2×D4×C15112yes—
532C2×D4—24no—
533C2×D4—21no—
534C2×D4—21no—
535C2×D4—21no—
536C2×D4—21no—
537C2×D4—21no—
538C2×D4—81no—
539C2×D4—81no—
540C2×D4#41×C15112yes—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—42no—
555C22×C4—81no—
556C22×C4—81no—
557C22×C4C2×D4×C15111yescharacteristic
558C22×C4C2×D4×C15111yescharacteristic
559C22×C4C2×D4×C15111yescharacteristic
560C22×C4C2×D4×C15111yescharacteristic
561C22×C4C2×D4×C15111yescharacteristic
562C22×C4C24×C15111yescharacteristic
563SD16—28no—
564SD16—28no—
565C2×C8—21no—
566C2×C8—21no—
567C2×C8—21no—
568C2×C8—21no—
569C2×C8—21no—
570C2×C8—21no—
571C2×C8—21no—
572C2×C8—21no—
573C2×C8—21no—
574C2×C8—21no—
575C2×C8#41×C15112yes—
576C2×C8#41×C15112yes—
577C4⋊C4—24no—
578C4⋊C4—24no—
579C4⋊C4—24no—
580C4⋊C4—24no—
581C4⋊C4—24no—
582C4⋊C4—24no—
583C4⋊C4—24no—
584C4⋊C4—24no—
585C4⋊C4—22no—
586C4⋊C4—22no—
587C4⋊C4—21no—
588C4⋊C4—21no—
589C4⋊C4—21no—
590C4⋊C4—21no—
591C4⋊C4—21no—
592C4⋊C4—21no—
593C4⋊C4—21no—
594C4⋊C4—81no—
595C4⋊C4C2×D4×C15112yes—
596C4⋊C4C2×D4×C15112yes—
597C4⋊C4#41×C15112yes—
598C22⋊C4—24no—
599C22⋊C4—24no—
600C22⋊C4—24no—
601C22⋊C4—22no—
602C22⋊C4—22no—
603C22⋊C4—42no—
604C22⋊C4—81no—
605C22⋊C4—81no—
606C22⋊C4—81no—
607C42—24no—
608C42—24no—
609C42—21no—
610C42—21no—
611C42—81no—
612C42C2×D4×C15112yes—
613C42C2×D4×C15112yes—
614C23—21no—
615C23—22no—
616C23—21no—
617C23—21no—
618C23—21no—
619C23—21no—
620C23—21no—
621C23—21no—
622C23—41no—
623C23—41no—
624C23—41no—
625C23—41no—
626C23—41no—
627C23—41no—
628C23C22×D4×C15111yescharacteristic
629Q8—22no—
630Q8—22no—
631Q8—22no—
632Q8—22no—
633Q8—41no—
634Q8—41no—
635Q8—41no—
636Q8—41no—
637D4—22no—
638D4—22no—
639D4—41no—
640D4—41no—
641D4—84no—
642C2×C4—21no—
643C2×C4—21no—
644C2×C4—21no—
645C2×C4—21no—
646C2×C4—21no—
647C2×C4—21no—
648C2×C4—22no—
649C2×C4—22no—
650C2×C4—22no—
651C2×C4—22no—
652C2×C4—21no—
653C2×C4—21no—
654C2×C4—22no—
655C2×C4—21no—
656C2×C4—21no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—41no—
661C2×C4—41no—
662C2×C4—41no—
663C2×C4—41no—
664C2×C4—41no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—41no—
668C2×C4—41no—
669C2×C4—41no—
670C2×C4—41no—
671C2×C4—41no—
672C2×C4—41no—
673C2×C4—41no—
674C2×C4—41no—
675C2×C4—41no—
676C2×C4—41no—
677C2×C4—41no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—84no—
681C2×C4#120×C15112yes—
682C2×C4#120×C15112yes—
683C2×C4C22×D4×C15111yescharacteristic
684C2×C4C22×D4×C15111yescharacteristic
685C2×C4C2×#41×C15111yescharacteristic
686C2×C4C2×#41×C15111yescharacteristic
687C2×C4C2×#41×C15111yescharacteristic
688C2×C4C2×#41×C15111yescharacteristic
689C8—22no—
690C8—22no—
691C8—41no—
692C8—41no—
693C22—41no—
694C22—42no—
695C22—41no—
696C22—42no—
697C22—41no—
698C22—42no—
699C22—41no—
700C22—41no—
701C22—41no—
702C22—41no—
703C22—81no—
704C22—81no—
705C22—81no—
706C22—81no—
707C22C2×#120×C15111yescharacteristic
708C22#525×C15111yescharacteristic
709C22#532×C15111yescharacteristic
710C22#577×C15111yescharacteristic
711C22#577×C15111yescharacteristic
712C22#577×C15111yescharacteristic
713C22#578×C15111yescharacteristic
714C4—22no—
715C4—22no—
716C4—42no—
717C4—41no—
718C4—42no—
719C4—42no—
720C4—41no—
721C4—42no—
722C4—41no—
723C4—42no—
724C4—81no—
725C4—81no—
726C4#525×C15111yescharacteristic
727C4#525×C15111yescharacteristic
728C4#532×C15111yescharacteristic
729C4#532×C15111yescharacteristic
730C2—81no—
731C2—82no—
732C2#2388×C15111yescharacteristic
733C2#3010×C15111yescharacteristic
734C2#3013×C15111yescharacteristic
735C2#3120×C15111yescharacteristic
736C2#3123×C15111yescharacteristic
737C2#3174×C15111yescharacteristic
738C2#3178×C15111yescharacteristic
subgroupG/H
center, socleC23×C151C22×D4
commutator, Frattini, cosocleC22×C4C24×C151
prime radicalC2×#121×C151C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C151 ◁ C2×#117×C151 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#541×C151C2semidirect
2. C2×#440×C151C2semidirect
3. C2×C4×SD16×C151C2semidirect
5. #2059×C151C2semidirect
6. #2043×C151C2semidirect
7. #2036×C151C2semidirect
8. #2035×C151C2semidirect
9. #2025×C151C2semidirect
10. #2013×C151C2semidirect
13. #1763×C151C2semidirect
14. C4×#103×C151C2semidirect
15. #1750×C151C2semidirect
95. C4×Q8×C151D4semidirect
96. C4×Q8×C151D4semidirect
369. #23584C151direct (N × H)
370. C151#23584direct (N × H)
371. C2×#541C2×C151semidirect
372. C2×#440C2×C151semidirect
373. C2×C4×SD16C2×C151semidirect
375. #2059C2×C151semidirect
376. #2043C2×C151semidirect
377. #2036C2×C151semidirect
378. #2035C2×C151semidirect
379. #2025C2×C151semidirect
380. #2013C2×C151semidirect
383. #1763C2×C151semidirect
384. C4×#103C2×C151semidirect
385. #1750C2×C151semidirect
465. C4×Q8D4×C151semidirect
466. C4×Q8D4×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#541×C1512
C2×#440×C1512
C2×C4×SD16×C1512
#2324×C1512
#2059×C1512
#2043×C1512
#2036×C1512
#2035×C1512
#2025×C1512
#2013×C1512
#2000×C1512
#1763×C1512
C4×#103×C1512
#1750×C1512
#23584151