Finite Group Databasebeta

← C151×#24334 #50329259

Subgroups — C151×#24334 #50329259

Order 38656.

1042 conjugacy classes of subgroups.

The subgroup lattice has 672 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#557×C151C211yesmaximal, characteristic, complemented
2C2×#478×C151C211yesmaximal, characteristic
3C2×C4×SD16×C151C211yesmaximal, characteristic
4#2580×C151C211yesmaximal, characteristic
5#2059×C151C211yesmaximal, characteristic, complemented
6#2058×C151C211yesmaximal, characteristic, complemented
7#2025×C151C211yesmaximal, characteristic
8#2023×C151C211yesmaximal, characteristic
9#1991×C151C211yesmaximal, characteristic, complemented
10#1984×C151C211yesmaximal, characteristic, complemented
11#1880×C151C211yesmaximal, characteristic
12#1880×C151C211yesmaximal, characteristic
13#1865×C151C211yesmaximal, characteristic, complemented
14#1863×C151C211yesmaximal, characteristic, complemented
15#1805×C151C211yesmaximal, characteristic, complemented
16C22×SD16×C151C2211yescharacteristic
17#557×C151—24no—
18#557×C151—24no—
19C2×C4⋊Q8×C151—21no—
20C2×C4⋊Q8×C151C2211yescharacteristic
21C2×#125×C151—21no—
22C2×#125×C151—21no—
23C2×#125×C151C2211yescharacteristic
24C2×#125×C151C2211yescharacteristic
25C2×C4×Q8×C151—21no—
26C2×C4×Q8×C151C2211yescharacteristic
27C2×C4×Q8×C151C2211yescharacteristic
28C2×C4×Q8×C151C2211yescharacteristic
29C2×C4×Q8×C151C2211yescharacteristic
30C2×C4×D4×C151C2211yescharacteristic
31#478×C151—24no—
32C4×SD16×C151—24no—
33C2×#107×C151C2211yescharacteristic
34C2×#106×C151C2211yescharacteristic
35C2×#106×C151C2211yescharacteristic
36C2×C4⋊C8×C151C2211yescharacteristic
37C2×#103×C151C2211yescharacteristic
38C2×#103×C151C2211yescharacteristic
39C2×#103×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×Q8×C151C2311yescharacteristic
66C22×D4×C151C2311yescharacteristic
67C23×C4×C151—21no—
68C2×SD16×C151—22no—
69C2×SD16×C151—22no—
70C2×SD16×C151Q814yescomplemented
71C22×C8×C151C2311yescharacteristic
72C22×C8×C151C2311yescharacteristic
73C22×C8×C151C2311yescharacteristic
74C22×C8×C151C2311yescharacteristic
75C4⋊Q8×C151—28no—
76C4⋊Q8×C151—22no—
77C4⋊Q8×C151—22no—
78#125×C151—28no—
79#125×C151—28no—
80#125×C151—22no—
81#125×C151—22no—
82#125×C151—22no—
83#125×C151D414yes—
84C4×Q8×C151—28no—
85C4×Q8×C151—22no—
86C4×Q8×C151—22no—
87C4×Q8×C151—22no—
88C4×Q8×C151—22no—
89C4×Q8×C151—22no—
90C4×Q8×C151—22no—
91C4×Q8×C151—22no—
92C4×Q8×C151D414yes—
93C4×D4×C151—22no—
94C4×D4×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×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×C42×C151—21no—
120C2×C42×C151—21no—
121C2×C42×C151—21no—
122C2×C42×C151C2311yescharacteristic
123C2×C42×C151C2311yescharacteristic
124C2×C42×C151C2311yescharacteristic
125#107×C151—22no—
126#106×C151—22no—
127#106×C151—22no—
128C4⋊C8×C151—22no—
129#103×C151—22no—
130#103×C151—22no—
131#103×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—
141C2×Q8×C151—24no—
142C2×Q8×C151—22no—
143C2×Q8×C151—22no—
144C2×Q8×C151—21no—
145C2×Q8×C151—21no—
146C2×Q8×C151—21no—
147C2×Q8×C151—41no—
148C2×Q8×C151—42no—
149C2×Q8×C151—42no—
150C2×Q8×C151C2×D412yes—
151C2×Q8×C151C2×Q812yes—
152C2×Q8×C151#4112yes—
153C2×D4×C151—21no—
154C2×D4×C151—21no—
155C2×D4×C151—21no—
156C2×D4×C151—21no—
157C2×D4×C151—21no—
158C2×D4×C151C2×Q812yes—
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—42no—
167C22×C4×C151—81no—
168C22×C4×C151—81no—
169C22×C4×C151C2×D411yescharacteristic
170C22×C4×C151C2×D411yescharacteristic
171C22×C4×C151C2×D411yescharacteristic
172C22×C4×C151C2×D411yescharacteristic
173C22×C4×C151C2×D411yescharacteristic
174C22×C4×C151C2×D411yescharacteristic
175C22×C4×C151C2411yescharacteristic
176SD16×C151—28no—
177C2×C8×C151—21no—
178C2×C8×C151—21no—
179C2×C8×C151—21no—
180C2×C8×C151—21no—
181C2×C8×C151—21no—
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×C151C2×Q812yes—
189C4⋊C4×C151—24no—
190C4⋊C4×C151—24no—
191C4⋊C4×C151—24no—
192C4⋊C4×C151—24no—
193C4⋊C4×C151—24no—
194C4⋊C4×C151—24no—
195C4⋊C4×C151—24no—
196C4⋊C4×C151—24no—
197C4⋊C4×C151—22no—
198C4⋊C4×C151—22no—
199C4⋊C4×C151—22no—
200C4⋊C4×C151—21no—
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—81no—
210C4⋊C4×C151—81no—
211C4⋊C4×C151C2×D412yes—
212C4⋊C4×C151C2×D412yes—
213C4⋊C4×C151C2×D412yes—
214C22⋊C4×C151—42no—
215C22⋊C4×C151—42no—
216C22⋊C4×C151—42no—
217C22⋊C4×C151—81no—
218C22⋊C4×C151—81no—
219C42×C151—24no—
220C42×C151—24no—
221C42×C151—24no—
222C42×C151—21no—
223C42×C151—21no—
224C42×C151—21no—
225C42×C151—21no—
226C42×C151C2×D412yes—
227C42×C151C2×D412yes—
228C23×C151—22no—
229C23×C151—41no—
230C23×C151—41no—
231C23×C151—41no—
232C23×C151—41no—
233C23×C151—41no—
234C23×C151—41no—
235C23×C151C22×D411yescharacteristic
236Q8×C151—22no—
237Q8×C151—22no—
238Q8×C151—22no—
239Q8×C151—44no—
240Q8×C151—48no—
241Q8×C151C22⋊Q814yes—
242D4×C151—22no—
243D4×C151—22no—
244D4×C151—41no—
245D4×C151—41no—
246C2×C4×C151—21no—
247C2×C4×C151—22no—
248C2×C4×C151—22no—
249C2×C4×C151—22no—
250C2×C4×C151—21no—
251C2×C4×C151—21no—
252C2×C4×C151—21no—
253C2×C4×C151—21no—
254C2×C4×C151—21no—
255C2×C4×C151—21no—
256C2×C4×C151—22no—
257C2×C4×C151—22no—
258C2×C4×C151—21no—
259C2×C4×C151—21no—
260C2×C4×C151—22no—
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—41no—
268C2×C4×C151—41no—
269C2×C4×C151—41no—
270C2×C4×C151—41no—
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—84no—
283C2×C4×C151#12012yes—
284C2×C4×C151#12012yes—
285C2×C4×C151#13512yes—
286C2×C4×C151C22×D411yescharacteristic
287C2×C4×C151C22×D411yescharacteristic
288C2×C4×C151C22×Q811yescharacteristic
289C2×C4×C151C2×#4111yescharacteristic
290C2×C4×C1512−1+411yescharacteristic
291C2×C4×C1512−1+411yescharacteristic
292C8×C151—22no—
293C8×C151—41no—
294C8×C151—41no—
295C8×C151—41no—
296C22×C151—42no—
297C22×C151—42no—
298C22×C151—42no—
299C22×C151—81no—
300C22×C151—81no—
301C22×C151—81no—
302C22×C151—81no—
303C22×C151C2×#12011yescharacteristic
304C22×C151#54811yescharacteristic
305C22×C151D4×Q811yescharacteristic
306C22×C151C2×#13511yescharacteristic
307C22×C151#57511yescharacteristic
308C22×C151#57711yescharacteristic
309C22×C151#57711yescharacteristic
310C4×C151—24no—
311C4×C151—22no—
312C4×C151—22no—
313C4×C151—22no—
314C4×C151—41no—
315C4×C151—42no—
316C4×C151—42no—
317C4×C151—41no—
318C4×C151—41no—
319C4×C151—42no—
320C4×C151—81no—
321C4×C151—81no—
322C4×C151—81no—
323C4×C151C2×C22⋊Q811yescharacteristic
324C4×C151#53611yescharacteristic
325C4×C151#54811yescharacteristic
326C4×C151D4×Q811yescharacteristic
327C2×C151—82no—
328C2×C151#240911yescharacteristic
329C2×C151#300211yescharacteristic
330C2×C151#301011yescharacteristic
331C2×C151#336511yescharacteristic
332C2×C151#337111yescharacteristic
333C2×C151#338111yescharacteristic
334C2×C151#338811yescharacteristic
335#24334C15111yesmaximal, characteristic, direct product factor, Sylow
336C151#2433411yescharacteristic, direct product factor, Sylow
337C2×#557C2×C15111yescharacteristic, complemented
338C2×#478C2×C15111yescharacteristic
339C2×C4×SD16C2×C15111yescharacteristic
340#2580C2×C15111yescharacteristic
341#2059C2×C15111yescharacteristic, complemented
342#2058C2×C15111yescharacteristic, complemented
343#2025C2×C15111yescharacteristic
344#2023C2×C15111yescharacteristic
345#1991C2×C15111yescharacteristic, complemented
346#1984C2×C15111yescharacteristic, complemented
347#1880C2×C15111yescharacteristic
348#1880C2×C15111yescharacteristic
349#1865C2×C15111yescharacteristic, complemented
350#1863C2×C15111yescharacteristic, complemented
351#1805C2×C15111yescharacteristic, complemented
352C22×SD16C22×C15111yescharacteristic
353#557—24no—
354#557—24no—
355C2×C4⋊Q8—21no—
356C2×C4⋊Q8C22×C15111yescharacteristic
357C2×#125—21no—
358C2×#125—21no—
359C2×#125C22×C15111yescharacteristic
360C2×#125C22×C15111yescharacteristic
361C2×C4×Q8—21no—
362C2×C4×Q8C22×C15111yescharacteristic
363C2×C4×Q8C22×C15111yescharacteristic
364C2×C4×Q8C22×C15111yescharacteristic
365C2×C4×Q8C22×C15111yescharacteristic
366C2×C4×D4C22×C15111yescharacteristic
367#478—24no—
368C4×SD16—24no—
369C2×#107C22×C15111yescharacteristic
370C2×#106C22×C15111yescharacteristic
371C2×#106C22×C15111yescharacteristic
372C2×C4⋊C8C22×C15111yescharacteristic
373C2×#103C22×C15111yescharacteristic
374C2×#103C22×C15111yescharacteristic
375C2×#103C22×C15111yescharacteristic
376C2×#102C22×C15111yescharacteristic
377C2×#102C22×C15111yescharacteristic
378C2×#102C22×C15111yescharacteristic
379C2×C4×C8C22×C15111yescharacteristic
380#399—21no—
381#393—21no—
382#390C22×C15111yescharacteristic
383#390C22×C15111yescharacteristic
384#389C22×C15111yescharacteristic
385#389C22×C15111yescharacteristic
386#385—21no—
387#385—21no—
388#382C22×C15111yescharacteristic
389#340C22×C15111yescharacteristic
390#340C22×C15111yescharacteristic
391#340C22×C15111yescharacteristic
392#340C22×C15111yescharacteristic
393#340C22×C15111yescharacteristic
394#340C22×C15111yescharacteristic
395#336C22×C15111yescharacteristic
396#336C22×C15111yescharacteristic
397#336C22×C15111yescharacteristic
398#336C22×C15111yescharacteristic
399C22×Q8—21no—
400C22×Q8D4×C15111yescharacteristic
401C22×Q8C23×C15111yescharacteristic
402C22×D4C23×C15111yescharacteristic
403C23×C4—21no—
404C2×SD16—22no—
405C2×SD16—22no—
406C2×SD16Q8×C15114yescomplemented
407C22×C8C23×C15111yescharacteristic
408C22×C8C23×C15111yescharacteristic
409C22×C8C23×C15111yescharacteristic
410C22×C8C23×C15111yescharacteristic
411C4⋊Q8—28no—
412C4⋊Q8—22no—
413C4⋊Q8—22no—
414#125—28no—
415#125—28no—
416#125—22no—
417#125—22no—
418#125—22no—
419#125D4×C15114yes—
420C4×Q8—28no—
421C4×Q8—22no—
422C4×Q8—22no—
423C4×Q8—22no—
424C4×Q8—22no—
425C4×Q8—22no—
426C4×Q8—22no—
427C4×Q8—22no—
428C4×Q8D4×C15114yes—
429C4×D4—22no—
430C4×D4—22no—
431C2×C4⋊C4—21no—
432C2×C4⋊C4—21no—
433C2×C4⋊C4—21no—
434C2×C4⋊C4—21no—
435C2×C4⋊C4—21no—
436C2×C4⋊C4—21no—
437C2×C4⋊C4—21no—
438C2×C4⋊C4—21no—
439C2×C4⋊C4—21no—
440C2×C4⋊C4—21no—
441C2×C4⋊C4D4×C15111yescharacteristic
442C2×C4⋊C4D4×C15111yescharacteristic
443C2×C4⋊C4D4×C15111yescharacteristic
444C2×C4⋊C4C23×C15111yescharacteristic
445C2×C4⋊C4C23×C15111yescharacteristic
446C2×C4⋊C4C23×C15111yescharacteristic
447C2×C4⋊C4C23×C15111yescharacteristic
448C2×C4⋊C4C23×C15111yescharacteristic
449C2×C4⋊C4C23×C15111yescharacteristic
450C2×C22⋊C4—21no—
451C2×C22⋊C4—21no—
452C2×C22⋊C4—21no—
453C2×C22⋊C4—21no—
454C2×C22⋊C4—21no—
455C2×C42—21no—
456C2×C42—21no—
457C2×C42—21no—
458C2×C42C23×C15111yescharacteristic
459C2×C42C23×C15111yescharacteristic
460C2×C42C23×C15111yescharacteristic
461#107—22no—
462#106—22no—
463#106—22no—
464C4⋊C8—22no—
465#103—22no—
466#103—22no—
467#103—22no—
468#102—22no—
469#102—22no—
470#102—22no—
471C4×C8—22no—
472#95—21no—
473#95—21no—
474#95—21no—
475#95—21no—
476C24—21no—
477C2×Q8—24no—
478C2×Q8—22no—
479C2×Q8—22no—
480C2×Q8—21no—
481C2×Q8—21no—
482C2×Q8—21no—
483C2×Q8—41no—
484C2×Q8—42no—
485C2×Q8—42no—
486C2×Q8C2×D4×C15112yes—
487C2×Q8C2×Q8×C15112yes—
488C2×Q8#41×C15112yes—
489C2×D4—21no—
490C2×D4—21no—
491C2×D4—21no—
492C2×D4—21no—
493C2×D4—21no—
494C2×D4C2×Q8×C15112yes—
495C22×C4—21no—
496C22×C4—21no—
497C22×C4—21no—
498C22×C4—21no—
499C22×C4—21no—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—42no—
503C22×C4—81no—
504C22×C4—81no—
505C22×C4C2×D4×C15111yescharacteristic
506C22×C4C2×D4×C15111yescharacteristic
507C22×C4C2×D4×C15111yescharacteristic
508C22×C4C2×D4×C15111yescharacteristic
509C22×C4C2×D4×C15111yescharacteristic
510C22×C4C2×D4×C15111yescharacteristic
511C22×C4C24×C15111yescharacteristic
512SD16—28no—
513C2×C8—21no—
514C2×C8—21no—
515C2×C8—21no—
516C2×C8—21no—
517C2×C8—21no—
518C2×C8—21no—
519C2×C8—21no—
520C2×C8—21no—
521C2×C8—21no—
522C2×C8—21no—
523C2×C8—21no—
524C2×C8C2×Q8×C15112yes—
525C4⋊C4—24no—
526C4⋊C4—24no—
527C4⋊C4—24no—
528C4⋊C4—24no—
529C4⋊C4—24no—
530C4⋊C4—24no—
531C4⋊C4—24no—
532C4⋊C4—24no—
533C4⋊C4—22no—
534C4⋊C4—22no—
535C4⋊C4—22no—
536C4⋊C4—21no—
537C4⋊C4—21no—
538C4⋊C4—21no—
539C4⋊C4—21no—
540C4⋊C4—21no—
541C4⋊C4—21no—
542C4⋊C4—21no—
543C4⋊C4—21no—
544C4⋊C4—21no—
545C4⋊C4—81no—
546C4⋊C4—81no—
547C4⋊C4C2×D4×C15112yes—
548C4⋊C4C2×D4×C15112yes—
549C4⋊C4C2×D4×C15112yes—
550C22⋊C4—42no—
551C22⋊C4—42no—
552C22⋊C4—42no—
553C22⋊C4—81no—
554C22⋊C4—81no—
555C42—24no—
556C42—24no—
557C42—24no—
558C42—21no—
559C42—21no—
560C42—21no—
561C42—21no—
562C42C2×D4×C15112yes—
563C42C2×D4×C15112yes—
564C23—22no—
565C23—41no—
566C23—41no—
567C23—41no—
568C23—41no—
569C23—41no—
570C23—41no—
571C23C22×D4×C15111yescharacteristic
572Q8—22no—
573Q8—22no—
574Q8—22no—
575Q8—44no—
576Q8—48no—
577Q8C22⋊Q8×C15114yes—
578D4—22no—
579D4—22no—
580D4—41no—
581D4—41no—
582C2×C4—22no—
583C2×C4—21no—
584C2×C4—22no—
585C2×C4—22no—
586C2×C4—21no—
587C2×C4—21no—
588C2×C4—21no—
589C2×C4—21no—
590C2×C4—21no—
591C2×C4—21no—
592C2×C4—21no—
593C2×C4—22no—
594C2×C4—21no—
595C2×C4—22no—
596C2×C4—22no—
597C2×C4—21no—
598C2×C4—21no—
599C2×C4—21no—
600C2×C4—21no—
601C2×C4—21no—
602C2×C4—21no—
603C2×C4—41no—
604C2×C4—41no—
605C2×C4—41no—
606C2×C4—41no—
607C2×C4—41no—
608C2×C4—41no—
609C2×C4—41no—
610C2×C4—41no—
611C2×C4—41no—
612C2×C4—41no—
613C2×C4—41no—
614C2×C4—41no—
615C2×C4—41no—
616C2×C4—41no—
617C2×C4—41no—
618C2×C4—84no—
619C2×C4#120×C15112yes—
620C2×C4#120×C15112yes—
621C2×C4#135×C15112yes—
622C2×C4C22×D4×C15111yescharacteristic
623C2×C4C22×D4×C15111yescharacteristic
624C2×C4C22×Q8×C15111yescharacteristic
625C2×C4C2×#41×C15111yescharacteristic
626C2×C42−1+4×C15111yescharacteristic
627C2×C42−1+4×C15111yescharacteristic
628C8—22no—
629C8—41no—
630C8—41no—
631C8—41no—
632C22—42no—
633C22—42no—
634C22—42no—
635C22—81no—
636C22—81no—
637C22—81no—
638C22—81no—
639C22C2×#120×C15111yescharacteristic
640C22#548×C15111yescharacteristic
641C22D4×Q8×C15111yescharacteristic
642C22C2×#135×C15111yescharacteristic
643C22#575×C15111yescharacteristic
644C22#577×C15111yescharacteristic
645C22#577×C15111yescharacteristic
646C4—24no—
647C4—22no—
648C4—22no—
649C4—22no—
650C4—41no—
651C4—42no—
652C4—42no—
653C4—41no—
654C4—41no—
655C4—42no—
656C4—81no—
657C4—81no—
658C4—81no—
659C4C2×C22⋊Q8×C15111yescharacteristic
660C4#536×C15111yescharacteristic
661C4#548×C15111yescharacteristic
662C4D4×Q8×C15111yescharacteristic
663C2—82no—
664C2#2409×C15111yescharacteristic
665C2#3002×C15111yescharacteristic
666C2#3010×C15111yescharacteristic
667C2#3365×C15111yescharacteristic
668C2#3371×C15111yescharacteristic
669C2#3381×C15111yescharacteristic
670C2#3388×C15111yescharacteristic
subgroupG/H
center, socleC23×C151C22×D4
commutator, Frattini, cosocleC22×C4C24×C151
prime radicalC22×D4×C151C23
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×#557×C151C2semidirect
5. #2059×C151C2semidirect
6. #2058×C151C2semidirect
9. #1991×C151C2semidirect
10. #1984×C151C2semidirect
13. #1865×C151C2semidirect
14. #1863×C151C2semidirect
15. #1805×C151C2semidirect
70. C2×SD16×C151Q8semidirect
335. #24334C151direct (N × H)
336. C151#24334direct (N × H)
337. C2×#557C2×C151semidirect
341. #2059C2×C151semidirect
342. #2058C2×C151semidirect
345. #1991C2×C151semidirect
346. #1984C2×C151semidirect
349. #1865C2×C151semidirect
350. #1863C2×C151semidirect
351. #1805C2×C151semidirect
406. C2×SD16Q8×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#557×C1512
C2×#478×C1512
C2×C4×SD16×C1512
#2580×C1512
#2059×C1512
#2058×C1512
#2025×C1512
#2023×C1512
#1991×C1512
#1984×C1512
#1880×C1512
#1865×C1512
#1863×C1512
#1805×C1512
#24334151