Finite Group Databasebeta

← C151×#24106 #50329031

Subgroups — C151×#24106 #50329031

Order 38656.

1046 conjugacy classes of subgroups.

The subgroup lattice has 706 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#552×C151C211yesmaximal, characteristic
2C2×#485×C151C211yesmaximal, characteristic, complemented
3C2×#428×C151C211yesmaximal, characteristic, complemented
4#2485×C151C211yesmaximal, characteristic
5#2059×C151C211yesmaximal, characteristic, complemented
6#2059×C151C211yesmaximal, characteristic, complemented
7#2036×C151C211yesmaximal, characteristic, complemented
8#2035×C151C211yesmaximal, characteristic, complemented
9#1894×C151C211yesmaximal, characteristic, complemented
10#1870×C151C211yesmaximal, characteristic
11#1865×C151C211yesmaximal, characteristic, complemented
12#1863×C151C211yesmaximal, characteristic, complemented
13#1854×C151C211yesmaximal, characteristic, complemented
14#1854×C151C211yesmaximal, characteristic, complemented
15#1824×C151C211yesmaximal, characteristic, complemented
16C22×M16×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×C4×Q8×C151C2211yescharacteristic
26C2×C4×D4×C151C2211yescharacteristic
27C2×#117×C151—21no—
28C2×#117×C151C2211yescharacteristic
29C2×#117×C151C2211yescharacteristic
30C22×C4⋊C4×C151C2211yescharacteristic
31#485×C151—24no—
32#428×C151—24no—
33C2×#107×C151C2211yescharacteristic
34C2×#107×C151C2211yescharacteristic
35C2×#107×C151C2211yescharacteristic
36C2×#106×C151C2211yescharacteristic
37C2×#106×C151C2211yescharacteristic
38C2×#106×C151C2211yescharacteristic
39C2×#103×C151C2211yescharacteristic
40C2×#103×C151C2211yescharacteristic
41C2×#103×C151C2211yescharacteristic
42C2×#103×C151C2211yescharacteristic
43C2×C22⋊C8×C151C2211yescharacteristic
44C2×C22⋊C8×C151C2211yescharacteristic
45C2×C22⋊C8×C151C2211yescharacteristic
46#397×C151—21no—
47#394×C151—21no—
48#389×C151C2211yescharacteristic
49#389×C151C2211yescharacteristic
50#388×C151—21no—
51#387×C151—21no—
52#380×C151C2211yescharacteristic
53#380×C151C2211yescharacteristic
54#380×C151C2211yescharacteristic
55#340×C151C2211yescharacteristic
56#340×C151C2211yescharacteristic
57#340×C151C2211yescharacteristic
58#340×C151C2211yescharacteristic
59#340×C151C2211yescharacteristic
60#340×C151C2211yescharacteristic
61#336×C151C2211yescharacteristic
62#336×C151C2211yescharacteristic
63C22×Q8×C151C2311yescharacteristic
64C22×D4×C151D411yescharacteristic
65C23×C4×C151—21no—
66C23×C4×C151C2311yescharacteristic
67C23×C4×C151C2311yescharacteristic
68C2×M16×C151—22no—
69C2×M16×C151—22no—
70C2×M16×C151—22no—
71C22×C8×C151C2311yescharacteristic
72C22×C8×C151C2311yescharacteristic
73C22×C8×C151C2311yescharacteristic
74C22×C8×C151C2311yescharacteristic
75#126×C151—28no—
76#125×C151—28no—
77#125×C151—22no—
78#125×C151—22no—
79#123×C151—28no—
80C22⋊Q8×C151—22no—
81C22⋊Q8×C151—22no—
82C22⋊Q8×C151—22no—
83C22⋊Q8×C151D414yes—
84C4×Q8×C151—22no—
85C4×Q8×C151—22no—
86C4×D4×C151—22no—
87C4×D4×C151—22no—
88#117×C151—28no—
89#117×C151—22no—
90#117×C151—22no—
91#117×C151—22no—
92#117×C151—22no—
93C2×C4⋊C4×C151—21no—
94C2×C4⋊C4×C151—22no—
95C2×C4⋊C4×C151—21no—
96C2×C4⋊C4×C151—21no—
97C2×C4⋊C4×C151—21no—
98C2×C4⋊C4×C151—21no—
99C2×C4⋊C4×C151—21no—
100C2×C4⋊C4×C151—21no—
101C2×C4⋊C4×C151—21no—
102C2×C4⋊C4×C151D411yescharacteristic
103C2×C4⋊C4×C151D414yes—
104C2×C4⋊C4×C151C2311yescharacteristic
105C2×C4⋊C4×C151C2311yescharacteristic
106C2×C4⋊C4×C151C2311yescharacteristic
107C2×C4⋊C4×C151C2311yescharacteristic
108C2×C4⋊C4×C151C2311yescharacteristic
109C2×C4⋊C4×C151C2311yescharacteristic
110C2×C4⋊C4×C151C2311yescharacteristic
111C2×C22⋊C4×C151—21no—
112C2×C22⋊C4×C151—21no—
113C2×C22⋊C4×C151—21no—
114C2×C22⋊C4×C151—21no—
115C2×C22⋊C4×C151—21no—
116C2×C22⋊C4×C151—21no—
117C2×C22⋊C4×C151—21no—
118C2×C22⋊C4×C151D411yescharacteristic
119C2×C22⋊C4×C151D411yescharacteristic
120C2×C42×C151—21no—
121C2×C42×C151—21no—
122C2×C42×C151—21no—
123C2×C42×C151C2311yescharacteristic
124#107×C151—22no—
125#107×C151—22no—
126#107×C151—22no—
127#106×C151—22no—
128#106×C151—22no—
129#106×C151—22no—
130#103×C151—22no—
131#103×C151—22no—
132#103×C151—22no—
133#103×C151—22no—
134C22⋊C8×C151—22no—
135C22⋊C8×C151—22no—
136C22⋊C8×C151—22no—
137#95×C151—21no—
138#95×C151—21no—
139#95×C151—21no—
140#95×C151—21no—
141#95×C151—21no—
142C24×C151C2×D411yescharacteristic
143C24×C151C2×D411yescharacteristic
144C2×Q8×C151—21no—
145C2×Q8×C151—21no—
146C2×Q8×C151—21no—
147C2×Q8×C151—21no—
148C2×Q8×C151—21no—
149C2×Q8×C151C2×D412yes—
150C2×D4×C151—22no—
151C2×D4×C151—41no—
152C2×D4×C151—41no—
153C22×C4×C151—21no—
154C22×C4×C151—21no—
155C22×C4×C151—21no—
156C22×C4×C151—21no—
157C22×C4×C151—24no—
158C22×C4×C151—21no—
159C22×C4×C151—21no—
160C22×C4×C151—21no—
161C22×C4×C151—21no—
162C22×C4×C151—21no—
163C22×C4×C151—21no—
164C22×C4×C151—21no—
165C22×C4×C151—21no—
166C22×C4×C151—21no—
167C22×C4×C151—21no—
168C22×C4×C151—21no—
169C22×C4×C151—21no—
170C22×C4×C151—21no—
171C22×C4×C151—21no—
172C22×C4×C151—42no—
173C22×C4×C151—42no—
174C22×C4×C151C2×D411yescharacteristic
175C22×C4×C151C2×D411yescharacteristic
176C22×C4×C151C2×D411yescharacteristic
177C22×C4×C151C2×D411yescharacteristic
178C22×C4×C151C2×D412yes—
179C22×C4×C151C2×D412yes—
180C22×C4×C151C2411yescharacteristic
181M16×C151—28no—
182C2×C8×C151—21no—
183C2×C8×C151—21no—
184C2×C8×C151—21no—
185C2×C8×C151—21no—
186C2×C8×C151—21no—
187C2×C8×C151—21no—
188C2×C8×C151—21no—
189C2×C8×C151—21no—
190C2×C8×C151—21no—
191C2×C8×C151—21no—
192C2×C8×C151#4112yes—
193C2×C8×C151#4112yes—
194C4⋊C4×C151—24no—
195C4⋊C4×C151—24no—
196C4⋊C4×C151—24no—
197C4⋊C4×C151—24no—
198C4⋊C4×C151—24no—
199C4⋊C4×C151—24no—
200C4⋊C4×C151—22no—
201C4⋊C4×C151—21no—
202C4⋊C4×C151—21no—
203C4⋊C4×C151—21no—
204C4⋊C4×C151—21no—
205C4⋊C4×C151—21no—
206C4⋊C4×C151—21no—
207C4⋊C4×C151—21no—
208C4⋊C4×C151—21no—
209C4⋊C4×C151—21no—
210C4⋊C4×C151—21no—
211C4⋊C4×C151—21no—
212C4⋊C4×C151—42no—
213C4⋊C4×C151—81no—
214C4⋊C4×C151C2×D412yes—
215C4⋊C4×C151C2×D412yes—
216C4⋊C4×C151C2×D412yes—
217C22⋊C4×C151—24no—
218C22⋊C4×C151—24no—
219C22⋊C4×C151—24no—
220C22⋊C4×C151—22no—
221C22⋊C4×C151—22no—
222C22⋊C4×C151—42no—
223C22⋊C4×C151—42no—
224C22⋊C4×C151—81no—
225C22⋊C4×C151—81no—
226C42×C151—24no—
227C42×C151—24no—
228C42×C151—21no—
229C42×C151—21no—
230C42×C151—42no—
231C23×C151—21no—
232C23×C151—21no—
233C23×C151—21no—
234C23×C151—21no—
235C23×C151—21no—
236C23×C151—21no—
237C23×C151—21no—
238C23×C151—21no—
239C23×C151—21no—
240C23×C151—21no—
241C23×C151—21no—
242C23×C151—21no—
243C23×C151—21no—
244C23×C151#12012yes—
245C23×C151C22×D411yescharacteristic
246Q8×C151—22no—
247Q8×C151—22no—
248Q8×C151—41no—
249Q8×C151—41no—
250D4×C151—44no—
251C2×C4×C151—21no—
252C2×C4×C151—21no—
253C2×C4×C151—22no—
254C2×C4×C151—22no—
255C2×C4×C151—22no—
256C2×C4×C151—22no—
257C2×C4×C151—22no—
258C2×C4×C151—21no—
259C2×C4×C151—21no—
260C2×C4×C151—22no—
261C2×C4×C151—22no—
262C2×C4×C151—21no—
263C2×C4×C151—22no—
264C2×C4×C151—21no—
265C2×C4×C151—21no—
266C2×C4×C151—21no—
267C2×C4×C151—21no—
268C2×C4×C151—21no—
269C2×C4×C151—21no—
270C2×C4×C151—48no—
271C2×C4×C151—41no—
272C2×C4×C151—41no—
273C2×C4×C151—41no—
274C2×C4×C151—41no—
275C2×C4×C151—41no—
276C2×C4×C151—41no—
277C2×C4×C151—41no—
278C2×C4×C151—41no—
279C2×C4×C151—41no—
280C2×C4×C151—41no—
281C2×C4×C151—41no—
282C2×C4×C151—41no—
283C2×C4×C151—41no—
284C2×C4×C151—41no—
285C2×C4×C151—41no—
286C2×C4×C151—41no—
287C2×C4×C151—41no—
288C2×C4×C151—41no—
289C2×C4×C151—41no—
290C2×C4×C151—41no—
291C2×C4×C151—41no—
292C2×C4×C151—41no—
293C2×C4×C151—41no—
294C2×C4×C151—41no—
295C2×C4×C151#12012yes—
296C2×C4×C151C22×D411yescharacteristic
297C2×C4×C151C22×D411yescharacteristic
298C2×C4×C151C2×#4111yescharacteristic
299C2×C4×C151C2×#4111yescharacteristic
300C2×C4×C1512−1+411yescharacteristic
301C2×C4×C1512−1+411yescharacteristic
302C8×C151—22no—
303C8×C151—22no—
304C8×C151—41no—
305C8×C151—41no—
306C22×C151—22no—
307C22×C151—22no—
308C22×C151—22no—
309C22×C151—41no—
310C22×C151—41no—
311C22×C151—41no—
312C22×C151—41no—
313C22×C151—41no—
314C22×C151—41no—
315C22×C151—41no—
316C22×C151—41no—
317C22×C151—41no—
318C22×C151—41no—
319C22×C151—41no—
320C22×C151C2×#12011yescharacteristic
321C22×C151#54711yescharacteristic
322C22×C151#54711yescharacteristic
323C22×C151#57511yescharacteristic
324C22×C151#57511yescharacteristic
325C22×C151#57711yescharacteristic
326C22×C151#57811yescharacteristic
327C4×C151—22no—
328C4×C151—41no—
329C4×C151—42no—
330C4×C151—41no—
331C4×C151—42no—
332C4×C151—42no—
333C4×C151—41no—
334C4×C151—42no—
335C4×C151—81no—
336C4×C151—81no—
337C4×C151—81no—
338C4×C151—81no—
339C4×C151#52511yescharacteristic
340C4×C151#53611yescharacteristic
341C4×C151#54711yescharacteristic
342C4×C151#54711yescharacteristic
343C2×C151—42no—
344C2×C151—81no—
345C2×C151#240611yescharacteristic
346C2×C151#300511yescharacteristic
347C2×C151#301311yescharacteristic
348C2×C151#334811yescharacteristic
349C2×C151#334911yescharacteristic
350C2×C151#335111yescharacteristic
351C2×C151#335211yescharacteristic
352#24106C15111yesmaximal, characteristic, direct product factor, Sylow
353C151#2410611yescharacteristic, direct product factor, Sylow
354C2×#552C2×C15111yescharacteristic
355C2×#485C2×C15111yescharacteristic, complemented
356C2×#428C2×C15111yescharacteristic, complemented
357#2485C2×C15111yescharacteristic
358#2059C2×C15111yescharacteristic, complemented
359#2059C2×C15111yescharacteristic, complemented
360#2036C2×C15111yescharacteristic, complemented
361#2035C2×C15111yescharacteristic, complemented
362#1894C2×C15111yescharacteristic, complemented
363#1870C2×C15111yescharacteristic
364#1865C2×C15111yescharacteristic, complemented
365#1863C2×C15111yescharacteristic, complemented
366#1854C2×C15111yescharacteristic, complemented
367#1854C2×C15111yescharacteristic, complemented
368#1824C2×C15111yescharacteristic, complemented
369C22×M16C22×C15111yescharacteristic
370#552—24no—
371#552—24no—
372C2×#126—21no—
373C2×#125—21no—
374C2×#125C22×C15111yescharacteristic
375C2×#123—21no—
376C2×C22⋊Q8C22×C15111yescharacteristic
377C2×C22⋊Q8C22×C15111yescharacteristic
378C2×C4×Q8C22×C15111yescharacteristic
379C2×C4×D4C22×C15111yescharacteristic
380C2×#117—21no—
381C2×#117C22×C15111yescharacteristic
382C2×#117C22×C15111yescharacteristic
383C22×C4⋊C4C22×C15111yescharacteristic
384#485—24no—
385#428—24no—
386C2×#107C22×C15111yescharacteristic
387C2×#107C22×C15111yescharacteristic
388C2×#107C22×C15111yescharacteristic
389C2×#106C22×C15111yescharacteristic
390C2×#106C22×C15111yescharacteristic
391C2×#106C22×C15111yescharacteristic
392C2×#103C22×C15111yescharacteristic
393C2×#103C22×C15111yescharacteristic
394C2×#103C22×C15111yescharacteristic
395C2×#103C22×C15111yescharacteristic
396C2×C22⋊C8C22×C15111yescharacteristic
397C2×C22⋊C8C22×C15111yescharacteristic
398C2×C22⋊C8C22×C15111yescharacteristic
399#397—21no—
400#394—21no—
401#389C22×C15111yescharacteristic
402#389C22×C15111yescharacteristic
403#388—21no—
404#387—21no—
405#380C22×C15111yescharacteristic
406#380C22×C15111yescharacteristic
407#380C22×C15111yescharacteristic
408#340C22×C15111yescharacteristic
409#340C22×C15111yescharacteristic
410#340C22×C15111yescharacteristic
411#340C22×C15111yescharacteristic
412#340C22×C15111yescharacteristic
413#340C22×C15111yescharacteristic
414#336C22×C15111yescharacteristic
415#336C22×C15111yescharacteristic
416C22×Q8C23×C15111yescharacteristic
417C22×D4D4×C15111yescharacteristic
418C23×C4—21no—
419C23×C4C23×C15111yescharacteristic
420C23×C4C23×C15111yescharacteristic
421C2×M16—22no—
422C2×M16—22no—
423C2×M16—22no—
424C22×C8C23×C15111yescharacteristic
425C22×C8C23×C15111yescharacteristic
426C22×C8C23×C15111yescharacteristic
427C22×C8C23×C15111yescharacteristic
428#126—28no—
429#125—28no—
430#125—22no—
431#125—22no—
432#123—28no—
433C22⋊Q8—22no—
434C22⋊Q8—22no—
435C22⋊Q8—22no—
436C22⋊Q8D4×C15114yes—
437C4×Q8—22no—
438C4×Q8—22no—
439C4×D4—22no—
440C4×D4—22no—
441#117—28no—
442#117—22no—
443#117—22no—
444#117—22no—
445#117—22no—
446C2×C4⋊C4—21no—
447C2×C4⋊C4—22no—
448C2×C4⋊C4—21no—
449C2×C4⋊C4—21no—
450C2×C4⋊C4—21no—
451C2×C4⋊C4—21no—
452C2×C4⋊C4—21no—
453C2×C4⋊C4—21no—
454C2×C4⋊C4—21no—
455C2×C4⋊C4D4×C15111yescharacteristic
456C2×C4⋊C4D4×C15114yes—
457C2×C4⋊C4C23×C15111yescharacteristic
458C2×C4⋊C4C23×C15111yescharacteristic
459C2×C4⋊C4C23×C15111yescharacteristic
460C2×C4⋊C4C23×C15111yescharacteristic
461C2×C4⋊C4C23×C15111yescharacteristic
462C2×C4⋊C4C23×C15111yescharacteristic
463C2×C4⋊C4C23×C15111yescharacteristic
464C2×C22⋊C4—21no—
465C2×C22⋊C4—21no—
466C2×C22⋊C4—21no—
467C2×C22⋊C4—21no—
468C2×C22⋊C4—21no—
469C2×C22⋊C4—21no—
470C2×C22⋊C4—21no—
471C2×C22⋊C4D4×C15111yescharacteristic
472C2×C22⋊C4D4×C15111yescharacteristic
473C2×C42—21no—
474C2×C42—21no—
475C2×C42—21no—
476C2×C42C23×C15111yescharacteristic
477#107—22no—
478#107—22no—
479#107—22no—
480#106—22no—
481#106—22no—
482#106—22no—
483#103—22no—
484#103—22no—
485#103—22no—
486#103—22no—
487C22⋊C8—22no—
488C22⋊C8—22no—
489C22⋊C8—22no—
490#95—21no—
491#95—21no—
492#95—21no—
493#95—21no—
494#95—21no—
495C24C2×D4×C15111yescharacteristic
496C24C2×D4×C15111yescharacteristic
497C2×Q8—21no—
498C2×Q8—21no—
499C2×Q8—21no—
500C2×Q8—21no—
501C2×Q8—21no—
502C2×Q8C2×D4×C15112yes—
503C2×D4—22no—
504C2×D4—41no—
505C2×D4—41no—
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—24no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—42no—
526C22×C4—42no—
527C22×C4C2×D4×C15111yescharacteristic
528C22×C4C2×D4×C15111yescharacteristic
529C22×C4C2×D4×C15111yescharacteristic
530C22×C4C2×D4×C15111yescharacteristic
531C22×C4C2×D4×C15112yes—
532C22×C4C2×D4×C15112yes—
533C22×C4C24×C15111yescharacteristic
534M16—28no—
535C2×C8—21no—
536C2×C8—21no—
537C2×C8—21no—
538C2×C8—21no—
539C2×C8—21no—
540C2×C8—21no—
541C2×C8—21no—
542C2×C8—21no—
543C2×C8—21no—
544C2×C8—21no—
545C2×C8#41×C15112yes—
546C2×C8#41×C15112yes—
547C4⋊C4—24no—
548C4⋊C4—24no—
549C4⋊C4—24no—
550C4⋊C4—24no—
551C4⋊C4—24no—
552C4⋊C4—24no—
553C4⋊C4—22no—
554C4⋊C4—21no—
555C4⋊C4—21no—
556C4⋊C4—21no—
557C4⋊C4—21no—
558C4⋊C4—21no—
559C4⋊C4—21no—
560C4⋊C4—21no—
561C4⋊C4—21no—
562C4⋊C4—21no—
563C4⋊C4—21no—
564C4⋊C4—21no—
565C4⋊C4—42no—
566C4⋊C4—81no—
567C4⋊C4C2×D4×C15112yes—
568C4⋊C4C2×D4×C15112yes—
569C4⋊C4C2×D4×C15112yes—
570C22⋊C4—24no—
571C22⋊C4—24no—
572C22⋊C4—24no—
573C22⋊C4—22no—
574C22⋊C4—22no—
575C22⋊C4—42no—
576C22⋊C4—42no—
577C22⋊C4—81no—
578C22⋊C4—81no—
579C42—24no—
580C42—24no—
581C42—21no—
582C42—21no—
583C42—42no—
584C23—21no—
585C23—21no—
586C23—21no—
587C23—21no—
588C23—21no—
589C23—21no—
590C23—21no—
591C23—21no—
592C23—21no—
593C23—21no—
594C23—21no—
595C23—21no—
596C23—21no—
597C23#120×C15112yes—
598C23C22×D4×C15111yescharacteristic
599Q8—22no—
600Q8—22no—
601Q8—41no—
602Q8—41no—
603D4—44no—
604C2×C4—21no—
605C2×C4—21no—
606C2×C4—22no—
607C2×C4—22no—
608C2×C4—22no—
609C2×C4—22no—
610C2×C4—21no—
611C2×C4—21no—
612C2×C4—22no—
613C2×C4—22no—
614C2×C4—22no—
615C2×C4—21no—
616C2×C4—22no—
617C2×C4—21no—
618C2×C4—21no—
619C2×C4—21no—
620C2×C4—21no—
621C2×C4—21no—
622C2×C4—21no—
623C2×C4—48no—
624C2×C4—41no—
625C2×C4—41no—
626C2×C4—41no—
627C2×C4—41no—
628C2×C4—41no—
629C2×C4—41no—
630C2×C4—41no—
631C2×C4—41no—
632C2×C4—41no—
633C2×C4—41no—
634C2×C4—41no—
635C2×C4—41no—
636C2×C4—41no—
637C2×C4—41no—
638C2×C4—41no—
639C2×C4—41no—
640C2×C4—41no—
641C2×C4—41no—
642C2×C4—41no—
643C2×C4—41no—
644C2×C4—41no—
645C2×C4—41no—
646C2×C4—41no—
647C2×C4—41no—
648C2×C4#120×C15112yes—
649C2×C4C22×D4×C15111yescharacteristic
650C2×C4C22×D4×C15111yescharacteristic
651C2×C4C2×#41×C15111yescharacteristic
652C2×C4C2×#41×C15111yescharacteristic
653C2×C42−1+4×C15111yescharacteristic
654C2×C42−1+4×C15111yescharacteristic
655C8—22no—
656C8—22no—
657C8—41no—
658C8—41no—
659C22—22no—
660C22—22no—
661C22—22no—
662C22—41no—
663C22—41no—
664C22—41no—
665C22—41no—
666C22—41no—
667C22—41no—
668C22—41no—
669C22—41no—
670C22—41no—
671C22—41no—
672C22—41no—
673C22C2×#120×C15111yescharacteristic
674C22#547×C15111yescharacteristic
675C22#547×C15111yescharacteristic
676C22#575×C15111yescharacteristic
677C22#575×C15111yescharacteristic
678C22#577×C15111yescharacteristic
679C22#578×C15111yescharacteristic
680C4—22no—
681C4—41no—
682C4—42no—
683C4—41no—
684C4—42no—
685C4—42no—
686C4—41no—
687C4—42no—
688C4—81no—
689C4—81no—
690C4—81no—
691C4—81no—
692C4#525×C15111yescharacteristic
693C4#536×C15111yescharacteristic
694C4#547×C15111yescharacteristic
695C4#547×C15111yescharacteristic
696C2—42no—
697C2—81no—
698C2#2406×C15111yescharacteristic
699C2#3005×C15111yescharacteristic
700C2#3013×C15111yescharacteristic
701C2#3348×C15111yescharacteristic
702C2#3349×C15111yescharacteristic
703C2#3351×C15111yescharacteristic
704C2#3352×C15111yescharacteristic
subgroupG/H
center, socleC23×C151C22×D4
commutator, Frattini, cosocleC22×C4C24×C151
prime radicalC22×D4×C151D4
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
2. C2×#485×C151C2semidirect
3. C2×#428×C151C2semidirect
5. #2059×C151C2semidirect
6. #2059×C151C2semidirect
7. #2036×C151C2semidirect
8. #2035×C151C2semidirect
9. #1894×C151C2semidirect
11. #1865×C151C2semidirect
12. #1863×C151C2semidirect
13. #1854×C151C2semidirect
14. #1854×C151C2semidirect
15. #1824×C151C2semidirect
352. #24106C151direct (N × H)
353. C151#24106direct (N × H)
355. C2×#485C2×C151semidirect
356. C2×#428C2×C151semidirect
358. #2059C2×C151semidirect
359. #2059C2×C151semidirect
360. #2036C2×C151semidirect
361. #2035C2×C151semidirect
362. #1894C2×C151semidirect
364. #1865C2×C151semidirect
365. #1863C2×C151semidirect
366. #1854C2×C151semidirect
367. #1854C2×C151semidirect
368. #1824C2×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×#485×C1512
C2×#428×C1512
#2485×C1512
#2059×C1512
#2036×C1512
#2035×C1512
#1894×C1512
#1870×C1512
#1865×C1512
#1863×C1512
#1854×C1512
#1824×C1512
#24106151