Finite Group Databasebeta

← C151×#24335 #50329260

Subgroups — C151×#24335 #50329260

Order 38656.

1118 conjugacy classes of subgroups.

The subgroup lattice has 712 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#554×C151C211yesmaximal, characteristic, complemented
2C2×#478×C151C211yesmaximal, characteristic, complemented
3C2×C4×D8×C151C211yesmaximal, characteristic
4#2580×C151C211yesmaximal, characteristic, complemented
5#2059×C151C211yesmaximal, characteristic, complemented
6#2057×C151C211yesmaximal, characteristic, complemented
7#2025×C151C211yesmaximal, characteristic, complemented
8#2023×C151C211yesmaximal, characteristic, complemented
9#1991×C151C211yesmaximal, characteristic, complemented
10#1984×C151C211yesmaximal, characteristic, complemented
11#1879×C151C211yesmaximal, characteristic
12#1879×C151C211yesmaximal, characteristic
13#1864×C151C211yesmaximal, characteristic, complemented
14#1862×C151C211yesmaximal, characteristic, complemented
15#1804×C151C211yesmaximal, characteristic, complemented
16C22×D8×C151C2211yescharacteristic
17#554×C151—24no—
18#554×C151—24no—
19C2×C4⋊Q8×C151C2211yescharacteristic
20C2×#125×C151C2211yescharacteristic
21C2×#125×C151C2211yescharacteristic
22C2×C22⋊Q8×C151—21no—
23C2×C22⋊Q8×C151—21no—
24C2×C22⋊Q8×C151—21no—
25C2×C4×Q8×C151C2211yescharacteristic
26C2×C4×D4×C151C2211yescharacteristic
27C2×C4×D4×C151C2211yescharacteristic
28C2×C4×D4×C151C2211yescharacteristic
29C2×C4×D4×C151C2211yescharacteristic
30C22×C4⋊C4×C151—21no—
31#478×C151—24no—
32C4×D8×C151—24no—
33C2×#107×C151C2211yescharacteristic
34C2×#107×C151C2211yescharacteristic
35C2×#106×C151C2211yescharacteristic
36C2×C4⋊C8×C151C2211yescharacteristic
37C2×#102×C151C2211yescharacteristic
38C2×#102×C151C2211yescharacteristic
39C2×#102×C151C2211yescharacteristic
40C2×#102×C151C2211yescharacteristic
41C2×#102×C151C2211yescharacteristic
42C2×#102×C151C2211yescharacteristic
43C2×C4×C8×C151C2211yescharacteristic
44#399×C151—21no—
45#393×C151—21no—
46#390×C151C2211yescharacteristic
47#390×C151C2211yescharacteristic
48#389×C151C2211yescharacteristic
49#389×C151C2211yescharacteristic
50#385×C151—21no—
51#385×C151—21no—
52#382×C151C2211yescharacteristic
53#340×C151C2211yescharacteristic
54#340×C151C2211yescharacteristic
55#340×C151C2211yescharacteristic
56#340×C151C2211yescharacteristic
57#340×C151C2211yescharacteristic
58#340×C151C2211yescharacteristic
59#336×C151C2211yescharacteristic
60#336×C151C2211yescharacteristic
61#336×C151C2211yescharacteristic
62#336×C151C2211yescharacteristic
63C22×Q8×C151—21no—
64C22×Q8×C151D411yescharacteristic
65C22×D4×C151C2311yescharacteristic
66C22×D4×C151C2311yescharacteristic
67C23×C4×C151—21no—
68C23×C4×C151—21no—
69C23×C4×C151—21no—
70C23×C4×C151—21no—
71C2×D8×C151—22no—
72C2×D8×C151—22no—
73C2×D8×C151Q814yescomplemented
74C22×C8×C151C2311yescharacteristic
75C22×C8×C151C2311yescharacteristic
76C22×C8×C151C2311yescharacteristic
77C22×C8×C151C2311yescharacteristic
78C4⋊Q8×C151—22no—
79C4⋊Q8×C151—22no—
80#125×C151—22no—
81#125×C151—22no—
82#125×C151—22no—
83#125×C151D414yes—
84C22⋊Q8×C151—28no—
85C22⋊Q8×C151—28no—
86C22⋊Q8×C151—28no—
87C4×Q8×C151—22no—
88C4×Q8×C151—22no—
89C4×D4×C151—22no—
90C4×D4×C151—22no—
91C4×D4×C151—22no—
92C4×D4×C151—22no—
93C4×D4×C151—22no—
94C4×D4×C151—22no—
95C4×D4×C151—22no—
96C4×D4×C151D414yes—
97C2×C4⋊C4×C151—28no—
98C2×C4⋊C4×C151—21no—
99C2×C4⋊C4×C151—21no—
100C2×C4⋊C4×C151—21no—
101C2×C4⋊C4×C151—21no—
102C2×C4⋊C4×C151—21no—
103C2×C4⋊C4×C151—21no—
104C2×C4⋊C4×C151—21no—
105C2×C4⋊C4×C151D411yescharacteristic
106C2×C4⋊C4×C151D411yescharacteristic
107C2×C4⋊C4×C151D411yescharacteristic
108C2×C4⋊C4×C151C2311yescharacteristic
109C2×C4⋊C4×C151C2311yescharacteristic
110C2×C4⋊C4×C151C2311yescharacteristic
111C2×C4⋊C4×C151C2311yescharacteristic
112C2×C4⋊C4×C151C2311yescharacteristic
113C2×C4⋊C4×C151C2311yescharacteristic
114C2×C22⋊C4×C151—21no—
115C2×C22⋊C4×C151—21no—
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×C42×C151C2311yescharacteristic
123C2×C42×C151C2311yescharacteristic
124C2×C42×C151C2311yescharacteristic
125#107×C151—22no—
126#107×C151—22no—
127#106×C151—22no—
128C4⋊C8×C151—22no—
129#102×C151—22no—
130#102×C151—22no—
131#102×C151—22no—
132#102×C151—22no—
133#102×C151—22no—
134#102×C151—22no—
135C4×C8×C151—22no—
136#95×C151—21no—
137#95×C151—21no—
138#95×C151—21no—
139#95×C151—21no—
140C24×C151—21no—
141C24×C151—21no—
142C2×Q8×C151—24no—
143C2×Q8×C151—22no—
144C2×Q8×C151—22no—
145C2×Q8×C151—41no—
146C2×Q8×C151—81no—
147C2×Q8×C151—81no—
148C2×D4×C151—21no—
149C2×D4×C151—21no—
150C2×D4×C151—21no—
151C2×D4×C151—21no—
152C2×D4×C151—21no—
153C2×D4×C151—21no—
154C2×D4×C151—21no—
155C2×D4×C151—21no—
156C2×D4×C151C2×D412yes—
157C2×D4×C151C2×Q812yes—
158C2×D4×C151C2×Q812yes—
159C2×D4×C151#4112yes—
160C22×C4×C151—24no—
161C22×C4×C151—21no—
162C22×C4×C151—21no—
163C22×C4×C151—21no—
164C22×C4×C151—24no—
165C22×C4×C151—24no—
166C22×C4×C151—21no—
167C22×C4×C151—21no—
168C22×C4×C151—21no—
169C22×C4×C151—42no—
170C22×C4×C151—42no—
171C22×C4×C151—42no—
172C22×C4×C151—81no—
173C22×C4×C151—81no—
174C22×C4×C151—81no—
175C22×C4×C151—81no—
176C22×C4×C151—81no—
177C22×C4×C151—81no—
178C22×C4×C151C2×D411yescharacteristic
179C22×C4×C151C2×D411yescharacteristic
180C22×C4×C151C2×D411yescharacteristic
181C22×C4×C151C2×D411yescharacteristic
182C22×C4×C151C2×D411yescharacteristic
183C22×C4×C151C2×D411yescharacteristic
184C22×C4×C151C2411yescharacteristic
185D8×C151—28no—
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—21no—
193C2×C8×C151—21no—
194C2×C8×C151—21no—
195C2×C8×C151—21no—
196C2×C8×C151—21no—
197C2×C8×C151C2×Q812yes—
198C4⋊C4×C151—24no—
199C4⋊C4×C151—24no—
200C4⋊C4×C151—24no—
201C4⋊C4×C151—22no—
202C4⋊C4×C151—24no—
203C4⋊C4×C151—24no—
204C4⋊C4×C151—22no—
205C4⋊C4×C151—22no—
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—21no—
213C4⋊C4×C151—21no—
214C4⋊C4×C151—21no—
215C4⋊C4×C151—81no—
216C4⋊C4×C151—81no—
217C4⋊C4×C151C2×D412yes—
218C4⋊C4×C151C2×D412yes—
219C4⋊C4×C151C2×D412yes—
220C22⋊C4×C151—24no—
221C22⋊C4×C151—24no—
222C22⋊C4×C151—24no—
223C22⋊C4×C151—42no—
224C22⋊C4×C151—42no—
225C22⋊C4×C151—42no—
226C22⋊C4×C151—81no—
227C22⋊C4×C151—81no—
228C42×C151—21no—
229C42×C151—21no—
230C42×C151—21no—
231C42×C151—21no—
232C42×C151C2×D412yes—
233C42×C151C2×D412yes—
234C23×C151—22no—
235C23×C151—22no—
236C23×C151—22no—
237C23×C151—22no—
238C23×C151—41no—
239C23×C151—41no—
240C23×C151—41no—
241C23×C151—41no—
242C23×C151—41no—
243C23×C151—41no—
244C23×C151—41no—
245C23×C151—41no—
246C23×C151—41no—
247C23×C151—41no—
248C23×C151C22×D411yescharacteristic
249Q8×C151—44no—
250Q8×C151—84no—
251D4×C151—22no—
252D4×C151—22no—
253D4×C151—22no—
254D4×C151—22no—
255D4×C151—22no—
256D4×C151—41no—
257D4×C151—41no—
258D4×C151C22⋊Q814yes—
259C2×C4×C151—21no—
260C2×C4×C151—21no—
261C2×C4×C151—21no—
262C2×C4×C151—21no—
263C2×C4×C151—21no—
264C2×C4×C151—21no—
265C2×C4×C151—21no—
266C2×C4×C151—21no—
267C2×C4×C151—22no—
268C2×C4×C151—22no—
269C2×C4×C151—21no—
270C2×C4×C151—22no—
271C2×C4×C151—21no—
272C2×C4×C151—21no—
273C2×C4×C151—21no—
274C2×C4×C151—21no—
275C2×C4×C151—21no—
276C2×C4×C151—21no—
277C2×C4×C151—48no—
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—84no—
294C2×C4×C151—84no—
295C2×C4×C151—84no—
296C2×C4×C151#12012yes—
297C2×C4×C151#12012yes—
298C2×C4×C151#13512yes—
299C2×C4×C151C22×D411yescharacteristic
300C2×C4×C151C22×D411yescharacteristic
301C2×C4×C151C22×Q811yescharacteristic
302C2×C4×C151C2×#4111yescharacteristic
303C2×C4×C1512−1+411yescharacteristic
304C2×C4×C1512−1+411yescharacteristic
305C8×C151—22no—
306C8×C151—41no—
307C8×C151—41no—
308C8×C151—41no—
309C22×C151—24no—
310C22×C151—42no—
311C22×C151—42no—
312C22×C151—42no—
313C22×C151—42no—
314C22×C151—42no—
315C22×C151—42no—
316C22×C151—42no—
317C22×C151—42no—
318C22×C151—42no—
319C22×C151—81no—
320C22×C151—81no—
321C22×C151—81no—
322C22×C151—81no—
323C22×C151C2×#12011yescharacteristic
324C22×C151#54811yescharacteristic
325C22×C151D4×Q811yescharacteristic
326C22×C151C2×#13511yescharacteristic
327C22×C151#57511yescharacteristic
328C22×C151#57611yescharacteristic
329C22×C151#57611yescharacteristic
330C4×C151—22no—
331C4×C151—22no—
332C4×C151—22no—
333C4×C151—41no—
334C4×C151—42no—
335C4×C151—41no—
336C4×C151—41no—
337C4×C151—42no—
338C4×C151—42no—
339C4×C151—81no—
340C4×C151—81no—
341C4×C151—81no—
342C4×C151C2×C22⋊Q811yescharacteristic
343C4×C151#53611yescharacteristic
344C4×C151#54811yescharacteristic
345C4×C151D4×Q811yescharacteristic
346C2×C151—44no—
347C2×C151—82no—
348C2×C151#240911yescharacteristic
349C2×C151#300211yescharacteristic
350C2×C151#300811yescharacteristic
351C2×C151#336111yescharacteristic
352C2×C151#337011yescharacteristic
353C2×C151#338011yescharacteristic
354C2×C151#338911yescharacteristic
355#24335C15111yesmaximal, characteristic, direct product factor, Sylow
356C151#2433511yescharacteristic, direct product factor, Sylow
357C2×#554C2×C15111yescharacteristic, complemented
358C2×#478C2×C15111yescharacteristic, complemented
359C2×C4×D8C2×C15111yescharacteristic
360#2580C2×C15111yescharacteristic, complemented
361#2059C2×C15111yescharacteristic, complemented
362#2057C2×C15111yescharacteristic, complemented
363#2025C2×C15111yescharacteristic, complemented
364#2023C2×C15111yescharacteristic, complemented
365#1991C2×C15111yescharacteristic, complemented
366#1984C2×C15111yescharacteristic, complemented
367#1879C2×C15111yescharacteristic
368#1879C2×C15111yescharacteristic
369#1864C2×C15111yescharacteristic, complemented
370#1862C2×C15111yescharacteristic, complemented
371#1804C2×C15111yescharacteristic, complemented
372C22×D8C22×C15111yescharacteristic
373#554—24no—
374#554—24no—
375C2×C4⋊Q8C22×C15111yescharacteristic
376C2×#125C22×C15111yescharacteristic
377C2×#125C22×C15111yescharacteristic
378C2×C22⋊Q8—21no—
379C2×C22⋊Q8—21no—
380C2×C22⋊Q8—21no—
381C2×C4×Q8C22×C15111yescharacteristic
382C2×C4×D4C22×C15111yescharacteristic
383C2×C4×D4C22×C15111yescharacteristic
384C2×C4×D4C22×C15111yescharacteristic
385C2×C4×D4C22×C15111yescharacteristic
386C22×C4⋊C4—21no—
387#478—24no—
388C4×D8—24no—
389C2×#107C22×C15111yescharacteristic
390C2×#107C22×C15111yescharacteristic
391C2×#106C22×C15111yescharacteristic
392C2×C4⋊C8C22×C15111yescharacteristic
393C2×#102C22×C15111yescharacteristic
394C2×#102C22×C15111yescharacteristic
395C2×#102C22×C15111yescharacteristic
396C2×#102C22×C15111yescharacteristic
397C2×#102C22×C15111yescharacteristic
398C2×#102C22×C15111yescharacteristic
399C2×C4×C8C22×C15111yescharacteristic
400#399—21no—
401#393—21no—
402#390C22×C15111yescharacteristic
403#390C22×C15111yescharacteristic
404#389C22×C15111yescharacteristic
405#389C22×C15111yescharacteristic
406#385—21no—
407#385—21no—
408#382C22×C15111yescharacteristic
409#340C22×C15111yescharacteristic
410#340C22×C15111yescharacteristic
411#340C22×C15111yescharacteristic
412#340C22×C15111yescharacteristic
413#340C22×C15111yescharacteristic
414#340C22×C15111yescharacteristic
415#336C22×C15111yescharacteristic
416#336C22×C15111yescharacteristic
417#336C22×C15111yescharacteristic
418#336C22×C15111yescharacteristic
419C22×Q8—21no—
420C22×Q8D4×C15111yescharacteristic
421C22×D4C23×C15111yescharacteristic
422C22×D4C23×C15111yescharacteristic
423C23×C4—21no—
424C23×C4—21no—
425C23×C4—21no—
426C23×C4—21no—
427C2×D8—22no—
428C2×D8—22no—
429C2×D8Q8×C15114yescomplemented
430C22×C8C23×C15111yescharacteristic
431C22×C8C23×C15111yescharacteristic
432C22×C8C23×C15111yescharacteristic
433C22×C8C23×C15111yescharacteristic
434C4⋊Q8—22no—
435C4⋊Q8—22no—
436#125—22no—
437#125—22no—
438#125—22no—
439#125D4×C15114yes—
440C22⋊Q8—28no—
441C22⋊Q8—28no—
442C22⋊Q8—28no—
443C4×Q8—22no—
444C4×Q8—22no—
445C4×D4—22no—
446C4×D4—22no—
447C4×D4—22no—
448C4×D4—22no—
449C4×D4—22no—
450C4×D4—22no—
451C4×D4—22no—
452C4×D4D4×C15114yes—
453C2×C4⋊C4—28no—
454C2×C4⋊C4—21no—
455C2×C4⋊C4—21no—
456C2×C4⋊C4—21no—
457C2×C4⋊C4—21no—
458C2×C4⋊C4—21no—
459C2×C4⋊C4—21no—
460C2×C4⋊C4—21no—
461C2×C4⋊C4D4×C15111yescharacteristic
462C2×C4⋊C4D4×C15111yescharacteristic
463C2×C4⋊C4D4×C15111yescharacteristic
464C2×C4⋊C4C23×C15111yescharacteristic
465C2×C4⋊C4C23×C15111yescharacteristic
466C2×C4⋊C4C23×C15111yescharacteristic
467C2×C4⋊C4C23×C15111yescharacteristic
468C2×C4⋊C4C23×C15111yescharacteristic
469C2×C4⋊C4C23×C15111yescharacteristic
470C2×C22⋊C4—21no—
471C2×C22⋊C4—21no—
472C2×C22⋊C4—21no—
473C2×C22⋊C4—21no—
474C2×C22⋊C4—21no—
475C2×C22⋊C4—21no—
476C2×C22⋊C4—21no—
477C2×C22⋊C4—21no—
478C2×C42C23×C15111yescharacteristic
479C2×C42C23×C15111yescharacteristic
480C2×C42C23×C15111yescharacteristic
481#107—22no—
482#107—22no—
483#106—22no—
484C4⋊C8—22no—
485#102—22no—
486#102—22no—
487#102—22no—
488#102—22no—
489#102—22no—
490#102—22no—
491C4×C8—22no—
492#95—21no—
493#95—21no—
494#95—21no—
495#95—21no—
496C24—21no—
497C24—21no—
498C2×Q8—24no—
499C2×Q8—22no—
500C2×Q8—22no—
501C2×Q8—41no—
502C2×Q8—81no—
503C2×Q8—81no—
504C2×D4—21no—
505C2×D4—21no—
506C2×D4—21no—
507C2×D4—21no—
508C2×D4—21no—
509C2×D4—21no—
510C2×D4—21no—
511C2×D4—21no—
512C2×D4C2×D4×C15112yes—
513C2×D4C2×Q8×C15112yes—
514C2×D4C2×Q8×C15112yes—
515C2×D4#41×C15112yes—
516C22×C4—24no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—24no—
521C22×C4—24no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—42no—
526C22×C4—42no—
527C22×C4—42no—
528C22×C4—81no—
529C22×C4—81no—
530C22×C4—81no—
531C22×C4—81no—
532C22×C4—81no—
533C22×C4—81no—
534C22×C4C2×D4×C15111yescharacteristic
535C22×C4C2×D4×C15111yescharacteristic
536C22×C4C2×D4×C15111yescharacteristic
537C22×C4C2×D4×C15111yescharacteristic
538C22×C4C2×D4×C15111yescharacteristic
539C22×C4C2×D4×C15111yescharacteristic
540C22×C4C24×C15111yescharacteristic
541D8—28no—
542C2×C8—21no—
543C2×C8—21no—
544C2×C8—21no—
545C2×C8—21no—
546C2×C8—21no—
547C2×C8—21no—
548C2×C8—21no—
549C2×C8—21no—
550C2×C8—21no—
551C2×C8—21no—
552C2×C8—21no—
553C2×C8C2×Q8×C15112yes—
554C4⋊C4—24no—
555C4⋊C4—24no—
556C4⋊C4—24no—
557C4⋊C4—22no—
558C4⋊C4—24no—
559C4⋊C4—24no—
560C4⋊C4—22no—
561C4⋊C4—22no—
562C4⋊C4—21no—
563C4⋊C4—21no—
564C4⋊C4—21no—
565C4⋊C4—21no—
566C4⋊C4—21no—
567C4⋊C4—21no—
568C4⋊C4—21no—
569C4⋊C4—21no—
570C4⋊C4—21no—
571C4⋊C4—81no—
572C4⋊C4—81no—
573C4⋊C4C2×D4×C15112yes—
574C4⋊C4C2×D4×C15112yes—
575C4⋊C4C2×D4×C15112yes—
576C22⋊C4—24no—
577C22⋊C4—24no—
578C22⋊C4—24no—
579C22⋊C4—42no—
580C22⋊C4—42no—
581C22⋊C4—42no—
582C22⋊C4—81no—
583C22⋊C4—81no—
584C42—21no—
585C42—21no—
586C42—21no—
587C42—21no—
588C42C2×D4×C15112yes—
589C42C2×D4×C15112yes—
590C23—22no—
591C23—22no—
592C23—22no—
593C23—22no—
594C23—41no—
595C23—41no—
596C23—41no—
597C23—41no—
598C23—41no—
599C23—41no—
600C23—41no—
601C23—41no—
602C23—41no—
603C23—41no—
604C23C22×D4×C15111yescharacteristic
605Q8—44no—
606Q8—84no—
607D4—22no—
608D4—22no—
609D4—22no—
610D4—22no—
611D4—22no—
612D4—41no—
613D4—41no—
614D4C22⋊Q8×C15114yes—
615C2×C4—21no—
616C2×C4—21no—
617C2×C4—21no—
618C2×C4—21no—
619C2×C4—21no—
620C2×C4—21no—
621C2×C4—21no—
622C2×C4—21no—
623C2×C4—21no—
624C2×C4—22no—
625C2×C4—22no—
626C2×C4—22no—
627C2×C4—21no—
628C2×C4—21no—
629C2×C4—21no—
630C2×C4—21no—
631C2×C4—21no—
632C2×C4—21no—
633C2×C4—48no—
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—41no—
649C2×C4—84no—
650C2×C4—84no—
651C2×C4—84no—
652C2×C4#120×C15112yes—
653C2×C4#120×C15112yes—
654C2×C4#135×C15112yes—
655C2×C4C22×D4×C15111yescharacteristic
656C2×C4C22×D4×C15111yescharacteristic
657C2×C4C22×Q8×C15111yescharacteristic
658C2×C4C2×#41×C15111yescharacteristic
659C2×C42−1+4×C15111yescharacteristic
660C2×C42−1+4×C15111yescharacteristic
661C8—22no—
662C8—41no—
663C8—41no—
664C8—41no—
665C22—24no—
666C22—42no—
667C22—42no—
668C22—42no—
669C22—42no—
670C22—42no—
671C22—42no—
672C22—42no—
673C22—42no—
674C22—42no—
675C22—81no—
676C22—81no—
677C22—81no—
678C22—81no—
679C22C2×#120×C15111yescharacteristic
680C22#548×C15111yescharacteristic
681C22D4×Q8×C15111yescharacteristic
682C22C2×#135×C15111yescharacteristic
683C22#575×C15111yescharacteristic
684C22#576×C15111yescharacteristic
685C22#576×C15111yescharacteristic
686C4—22no—
687C4—22no—
688C4—22no—
689C4—41no—
690C4—42no—
691C4—41no—
692C4—41no—
693C4—42no—
694C4—42no—
695C4—81no—
696C4—81no—
697C4—81no—
698C4C2×C22⋊Q8×C15111yescharacteristic
699C4#536×C15111yescharacteristic
700C4#548×C15111yescharacteristic
701C4D4×Q8×C15111yescharacteristic
702C2—44no—
703C2—82no—
704C2#2409×C15111yescharacteristic
705C2#3002×C15111yescharacteristic
706C2#3008×C15111yescharacteristic
707C2#3361×C15111yescharacteristic
708C2#3370×C15111yescharacteristic
709C2#3380×C15111yescharacteristic
710C2#3389×C15111yescharacteristic
subgroupG/H
center, socleC23×C151C22×D4
commutator, Frattini, cosocleC22×C4C24×C151
prime radicalC22×D8×C151C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C151 ◁ C2×C4×Q8×C151 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#554×C151C2semidirect
2. C2×#478×C151C2semidirect
4. #2580×C151C2semidirect
5. #2059×C151C2semidirect
6. #2057×C151C2semidirect
7. #2025×C151C2semidirect
8. #2023×C151C2semidirect
9. #1991×C151C2semidirect
10. #1984×C151C2semidirect
13. #1864×C151C2semidirect
14. #1862×C151C2semidirect
15. #1804×C151C2semidirect
73. C2×D8×C151Q8semidirect
355. #24335C151direct (N × H)
356. C151#24335direct (N × H)
357. C2×#554C2×C151semidirect
358. C2×#478C2×C151semidirect
360. #2580C2×C151semidirect
361. #2059C2×C151semidirect
362. #2057C2×C151semidirect
363. #2025C2×C151semidirect
364. #2023C2×C151semidirect
365. #1991C2×C151semidirect
366. #1984C2×C151semidirect
369. #1864C2×C151semidirect
370. #1862C2×C151semidirect
371. #1804C2×C151semidirect
429. C2×D8Q8×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#554×C1512
C2×#478×C1512
C2×C4×D8×C1512
#2580×C1512
#2059×C1512
#2057×C1512
#2025×C1512
#2023×C1512
#1991×C1512
#1984×C1512
#1879×C1512
#1864×C1512
#1862×C1512
#1804×C1512
#24335151