Finite Group Databasebeta

← C151×#22661 #50327586

Subgroups — C151×#22661 #50327586

Order 38656.

1042 conjugacy classes of subgroups.

The subgroup lattice has 686 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#435×C151C211yesmaximal, characteristic
2C2×#428×C151C211yesmaximal, characteristic, complemented
3C22×#107×C151C211yesmaximal, characteristic, complemented
4#2352×C151C211yesmaximal, characteristic
5D4×C4⋊C4×C151C211yesmaximal, characteristic
6#1949×C151C211yesmaximal, characteristic, complemented
7#1947×C151C211yesmaximal, characteristic, complemented
8#1854×C151C211yesmaximal, characteristic, complemented
9#1853×C151C211yesmaximal, characteristic, complemented
10#1852×C151C211yesmaximal, characteristic, complemented
11#1852×C151C211yesmaximal, characteristic, complemented
12#1847×C151C211yesmaximal, characteristic, complemented
13#1809×C151C211yesmaximal, characteristic, complemented
14#1807×C151C211yesmaximal, characteristic, complemented
15#1776×C151C211yesmaximal, characteristic, complemented
16C22×M16×C151C2211yescharacteristic
17C23×C8×C151C2211yescharacteristic
18C2×C4×D4×C151—21no—
19C2×C4×D4×C151C2211yescharacteristic
20C2×#117×C151C2211yescharacteristic
21C22×C4⋊C4×C151C2211yescharacteristic
22C22×C4⋊C4×C151C2211yescharacteristic
23C22×C4⋊C4×C151C2211yescharacteristic
24#435×C151C418yescomplemented
25#428×C151—24no—
26C2×#107×C151—24no—
27C2×#107×C151C2211yescharacteristic
28C2×#107×C151C2211yescharacteristic
29C2×#107×C151C2211yescharacteristic
30C2×#107×C151C2211yescharacteristic
31C2×#107×C151C2211yescharacteristic
32C2×#107×C151C2211yescharacteristic
33C2×#106×C151C2211yescharacteristic
34C2×#106×C151C2211yescharacteristic
35C2×#106×C151C2211yescharacteristic
36C2×#106×C151C2211yescharacteristic
37C2×C4⋊C8×C151C2211yescharacteristic
38C2×C22⋊C8×C151C2211yescharacteristic
39C2×C22⋊C8×C151C2211yescharacteristic
40C2×#97×C151C2211yescharacteristic
41#389×C151—21no—
42#388×C151—21no—
43#387×C151—21no—
44#386×C151—21no—
45#385×C151—21no—
46#385×C151—21no—
47#384×C151C2211yescharacteristic
48#382×C151C2211yescharacteristic
49#380×C151C2211yescharacteristic
50#380×C151C2211yescharacteristic
51#380×C151C2211yescharacteristic
52#380×C151C2211yescharacteristic
53C4×C4⋊C4×C151C2211yescharacteristic
54C4×C4⋊C4×C151C2211yescharacteristic
55C4×C22⋊C4×C151—21no—
56#340×C151C2211yescharacteristic
57#340×C151C2211yescharacteristic
58#340×C151C2211yescharacteristic
59#340×C151C2211yescharacteristic
60#340×C151C2211yescharacteristic
61#340×C151C2211yescharacteristic
62C22×D4×C151D411yescharacteristic
63C23×C4×C151—21no—
64C23×C4×C151—21no—
65C23×C4×C151—21no—
66C23×C4×C151C2311yescharacteristic
67C23×C4×C151C2311yescharacteristic
68C2×M16×C151—22no—
69C2×M16×C151—22no—
70C2×M16×C151C2×C414yescomplemented
71C22×C8×C151—22no—
72C22×C8×C151—22no—
73C22×C8×C151C2×C414yescomplemented
74C22×C8×C151C2311yescharacteristic
75C22×C8×C151C2311yescharacteristic
76C22×C8×C151C2311yescharacteristic
77C22×C8×C151C2311yescharacteristic
78C4×D4×C151—44no—
79C4×D4×C151C2×C414yes—
80C4×D4×C151Q814yes—
81#117×C151—22no—
82#117×C151—41no—
83C2×C4⋊C4×C151—22no—
84C2×C4⋊C4×C151—22no—
85C2×C4⋊C4×C151—22no—
86C2×C4⋊C4×C151—21no—
87C2×C4⋊C4×C151—21no—
88C2×C4⋊C4×C151—21no—
89C2×C4⋊C4×C151—21no—
90C2×C4⋊C4×C151—21no—
91C2×C4⋊C4×C151—41no—
92C2×C4⋊C4×C151—41no—
93C2×C4⋊C4×C151—41no—
94C2×C4⋊C4×C151D411yescharacteristic
95C2×C4⋊C4×C151C2311yescharacteristic
96C2×C4⋊C4×C151C2311yescharacteristic
97C2×C4⋊C4×C151C2311yescharacteristic
98C2×C4⋊C4×C151C2311yescharacteristic
99C2×C4⋊C4×C151C2311yescharacteristic
100C2×C4⋊C4×C151C2311yescharacteristic
101C2×C4⋊C4×C151C2311yescharacteristic
102C2×C4⋊C4×C151C2311yescharacteristic
103C2×C22⋊C4×C151—21no—
104C2×C22⋊C4×C151—21no—
105C2×C22⋊C4×C151—21no—
106C2×C22⋊C4×C151—21no—
107C2×C22⋊C4×C151—21no—
108C2×C22⋊C4×C151D411yescharacteristic
109C2×C22⋊C4×C151D411yescharacteristic
110C2×C42×C151—21no—
111C2×C42×C151—21no—
112C2×C42×C151—21no—
113C2×C42×C151C2311yescharacteristic
114#107×C151—22no—
115#107×C151—22no—
116#107×C151—22no—
117#107×C151—22no—
118#107×C151—41no—
119#107×C151D414yescomplemented
120#106×C151—22no—
121#106×C151—22no—
122#106×C151—22no—
123#106×C151—41no—
124C4⋊C8×C151C2×C414yescomplemented
125C22⋊C8×C151C2×C414yescomplemented
126C22⋊C8×C151C2×C414yescomplemented
127#97×C151C2×C414yescomplemented
128#95×C151—21no—
129#95×C151—21no—
130#95×C151—21no—
131#95×C151—21no—
132#95×C151—21no—
133#95×C151—21no—
134#95×C151—21no—
135#95×C151—21no—
136C24×C151C2×D411yescharacteristic
137C24×C151C2×D411yescharacteristic
138C2×D4×C151—22no—
139C2×D4×C151—22no—
140C2×D4×C151C4⋊C414yes—
141C22×C4×C151—21no—
142C22×C4×C151—21no—
143C22×C4×C151—21no—
144C22×C4×C151—21no—
145C22×C4×C151—21no—
146C22×C4×C151—21no—
147C22×C4×C151—21no—
148C22×C4×C151—21no—
149C22×C4×C151—21no—
150C22×C4×C151—21no—
151C22×C4×C151—21no—
152C22×C4×C151—21no—
153C22×C4×C151—21no—
154C22×C4×C151—21no—
155C22×C4×C151—21no—
156C22×C4×C151—21no—
157C22×C4×C151—42no—
158C22×C4×C151—42no—
159C22×C4×C151—42no—
160C22×C4×C151—42no—
161C22×C4×C151—42no—
162C22×C4×C151—42no—
163C22×C4×C151—81no—
164C22×C4×C151—81no—
165C22×C4×C151—81no—
166C22×C4×C151C22×C412yes—
167C22×C4×C151C22×C412yes—
168C22×C4×C151C2×D411yescharacteristic
169C22×C4×C151C2×D411yescharacteristic
170C22×C4×C151C2×D411yescharacteristic
171C22×C4×C151C2×D411yescharacteristic
172C22×C4×C151C2×Q812yes—
173C22×C4×C151C2×Q812yes—
174C22×C4×C151C2411yescharacteristic
175M16×C151—28no—
176C2×C8×C151—21no—
177C2×C8×C151—21no—
178C2×C8×C151—21no—
179C2×C8×C151—21no—
180C2×C8×C151—21no—
181C2×C8×C151—21no—
182C2×C8×C151—28no—
183C2×C8×C151C22×C412yes—
184C2×C8×C151C22×C412yes—
185C2×C8×C151C22×C412yes—
186C2×C8×C151C22×C412yes—
187C2×C8×C151C2×D412yes—
188C2×C8×C151#4112yes—
189C4⋊C4×C151—21no—
190C4⋊C4×C151—21no—
191C4⋊C4×C151—21no—
192C4⋊C4×C151—21no—
193C4⋊C4×C151—21no—
194C4⋊C4×C151—21no—
195C4⋊C4×C151—21no—
196C4⋊C4×C151—21no—
197C4⋊C4×C151—21no—
198C4⋊C4×C151—21no—
199C4⋊C4×C151—21no—
200C4⋊C4×C151—21no—
201C4⋊C4×C151—21no—
202C4⋊C4×C151—21no—
203C4⋊C4×C151—42no—
204C4⋊C4×C151—42no—
205C4⋊C4×C151—42no—
206C4⋊C4×C151—42no—
207C4⋊C4×C151—81no—
208C4⋊C4×C151C4⋊C414yes—
209C4⋊C4×C151C2×D412yes—
210C4⋊C4×C151C2×D412yes—
211C22⋊C4×C151—42no—
212C22⋊C4×C151—42no—
213C22⋊C4×C151—42no—
214C22⋊C4×C151—42no—
215C22⋊C4×C151—81no—
216C22⋊C4×C151C4⋊C414yes—
217C22⋊C4×C151C4⋊C414yes—
218C42×C151—42no—
219C42×C151—42no—
220C42×C151—81no—
221C42×C151C22×C412yes—
222C42×C151C2×Q812yes—
223C23×C151—21no—
224C23×C151—21no—
225C23×C151—21no—
226C23×C151—21no—
227C23×C151—21no—
228C23×C151—21no—
229C23×C151—21no—
230C23×C151—21no—
231C23×C151—21no—
232C23×C151—21no—
233C23×C151C2×C4⋊C412yes—
234C23×C151C2×C4⋊C412yes—
235C23×C151AGL(1,ℤ/8)12yes—
236C23×C151#13712yes—
237C23×C151C22×D411yescharacteristic
238D4×C151—28no—
239C2×C4×C151—21no—
240C2×C4×C151—21no—
241C2×C4×C151—21no—
242C2×C4×C151—21no—
243C2×C4×C151—21no—
244C2×C4×C151—21no—
245C2×C4×C151—21no—
246C2×C4×C151—21no—
247C2×C4×C151—22no—
248C2×C4×C151—22no—
249C2×C4×C151—22no—
250C2×C4×C151—22no—
251C2×C4×C151—22no—
252C2×C4×C151—22no—
253C2×C4×C151—22no—
254C2×C4×C151—22no—
255C2×C4×C151—22no—
256C2×C4×C151—22no—
257C2×C4×C151—41no—
258C2×C4×C151—41no—
259C2×C4×C151—41no—
260C2×C4×C151—41no—
261C2×C4×C151—41no—
262C2×C4×C151—41no—
263C2×C4×C151—41no—
264C2×C4×C151—41no—
265C2×C4×C151—41no—
266C2×C4×C151—41no—
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—84no—
280C2×C4×C151—84no—
281C2×C4×C151—84no—
282C2×C4×C151C2×C4⋊C412yes—
283C2×C4×C151C2×C4⋊C412yes—
284C2×C4×C151C2×C4⋊C412yes—
285C2×C4×C151C2×C4⋊C412yes—
286C2×C4×C151C23×C411yescharacteristic
287C2×C4×C151C22×D411yescharacteristic
288C2×C4×C151C22×Q811yescharacteristic
289C2×C4×C151C2×#4111yescharacteristic
290C2×C4×C151H(5,𝔽2)11yescharacteristic
291C2×C4×C1512−1+411yescharacteristic
292C8×C151—22no—
293C8×C151—22no—
294C8×C151—22no—
295C8×C151C4×D414yescomplemented
296C22×C151—22no—
297C22×C151—22no—
298C22×C151—22no—
299C22×C151—22no—
300C22×C151—22no—
301C22×C151—22no—
302C22×C151—22no—
303C22×C151—22no—
304C22×C151—22no—
305C22×C151—41no—
306C22×C151—41no—
307C22×C151—41no—
308C22×C151—41no—
309C22×C151#42814yescomplemented
310C22×C151C22×C4⋊C411yescharacteristic
311C22×C151D4211yescharacteristic
312C22×C151#54711yescharacteristic
313C22×C151C2×AGL(1,ℤ/8)11yescharacteristic
314C22×C151C2×#13711yescharacteristic
315C22×C151#57611yescharacteristic
316C22×C151#57811yescharacteristic
317C4×C151—22no—
318C4×C151—22no—
319C4×C151—22no—
320C4×C151—22no—
321C4×C151—42no—
322C4×C151—42no—
323C4×C151—81no—
324C4×C151—81no—
325C4×C151—81no—
326C4×C151—81no—
327C4×C151—81no—
328C4×C151—81no—
329C4×C151C2×C4×D411yescharacteristic
330C4×C151#52011yescharacteristic
331C4×C151D4×Q811yescharacteristic
332C4×C151#55411yescharacteristic
333C2×C151—24no—
334C2×C151—42no—
335C2×C151D4×C4⋊C411yescharacteristic
336C2×C151C2×#42811yescharacteristic
337C2×C151#291311yescharacteristic
338C2×C151#326411yescharacteristic
339C2×C151#327011yescharacteristic
340C2×C151#334311yescharacteristic
341C2×C151#334611yescharacteristic
342#22661C15111yesmaximal, characteristic, direct product factor, Sylow
343C151#2266111yescharacteristic, direct product factor, Sylow
344C2×#435C2×C15111yescharacteristic
345C2×#428C2×C15111yescharacteristic, complemented
346C22×#107C2×C15111yescharacteristic, complemented
347#2352C2×C15111yescharacteristic
348D4×C4⋊C4C2×C15111yescharacteristic
349#1949C2×C15111yescharacteristic, complemented
350#1947C2×C15111yescharacteristic, complemented
351#1854C2×C15111yescharacteristic, complemented
352#1853C2×C15111yescharacteristic, complemented
353#1852C2×C15111yescharacteristic, complemented
354#1852C2×C15111yescharacteristic, complemented
355#1847C2×C15111yescharacteristic, complemented
356#1809C2×C15111yescharacteristic, complemented
357#1807C2×C15111yescharacteristic, complemented
358#1776C2×C15111yescharacteristic, complemented
359C22×M16C22×C15111yescharacteristic
360C23×C8C22×C15111yescharacteristic
361C2×C4×D4—21no—
362C2×C4×D4C22×C15111yescharacteristic
363C2×#117C22×C15111yescharacteristic
364C22×C4⋊C4C22×C15111yescharacteristic
365C22×C4⋊C4C22×C15111yescharacteristic
366C22×C4⋊C4C22×C15111yescharacteristic
367#435C4×C15118yescomplemented
368#428—24no—
369C2×#107—24no—
370C2×#107C22×C15111yescharacteristic
371C2×#107C22×C15111yescharacteristic
372C2×#107C22×C15111yescharacteristic
373C2×#107C22×C15111yescharacteristic
374C2×#107C22×C15111yescharacteristic
375C2×#107C22×C15111yescharacteristic
376C2×#106C22×C15111yescharacteristic
377C2×#106C22×C15111yescharacteristic
378C2×#106C22×C15111yescharacteristic
379C2×#106C22×C15111yescharacteristic
380C2×C4⋊C8C22×C15111yescharacteristic
381C2×C22⋊C8C22×C15111yescharacteristic
382C2×C22⋊C8C22×C15111yescharacteristic
383C2×#97C22×C15111yescharacteristic
384#389—21no—
385#388—21no—
386#387—21no—
387#386—21no—
388#385—21no—
389#385—21no—
390#384C22×C15111yescharacteristic
391#382C22×C15111yescharacteristic
392#380C22×C15111yescharacteristic
393#380C22×C15111yescharacteristic
394#380C22×C15111yescharacteristic
395#380C22×C15111yescharacteristic
396C4×C4⋊C4C22×C15111yescharacteristic
397C4×C4⋊C4C22×C15111yescharacteristic
398C4×C22⋊C4—21no—
399#340C22×C15111yescharacteristic
400#340C22×C15111yescharacteristic
401#340C22×C15111yescharacteristic
402#340C22×C15111yescharacteristic
403#340C22×C15111yescharacteristic
404#340C22×C15111yescharacteristic
405C22×D4D4×C15111yescharacteristic
406C23×C4—21no—
407C23×C4—21no—
408C23×C4—21no—
409C23×C4C23×C15111yescharacteristic
410C23×C4C23×C15111yescharacteristic
411C2×M16—22no—
412C2×M16—22no—
413C2×M16C2×C4×C15114yescomplemented
414C22×C8—22no—
415C22×C8—22no—
416C22×C8C2×C4×C15114yescomplemented
417C22×C8C23×C15111yescharacteristic
418C22×C8C23×C15111yescharacteristic
419C22×C8C23×C15111yescharacteristic
420C22×C8C23×C15111yescharacteristic
421C4×D4—44no—
422C4×D4C2×C4×C15114yes—
423C4×D4Q8×C15114yes—
424#117—22no—
425#117—41no—
426C2×C4⋊C4—22no—
427C2×C4⋊C4—22no—
428C2×C4⋊C4—22no—
429C2×C4⋊C4—21no—
430C2×C4⋊C4—21no—
431C2×C4⋊C4—21no—
432C2×C4⋊C4—21no—
433C2×C4⋊C4—21no—
434C2×C4⋊C4—41no—
435C2×C4⋊C4—41no—
436C2×C4⋊C4—41no—
437C2×C4⋊C4D4×C15111yescharacteristic
438C2×C4⋊C4C23×C15111yescharacteristic
439C2×C4⋊C4C23×C15111yescharacteristic
440C2×C4⋊C4C23×C15111yescharacteristic
441C2×C4⋊C4C23×C15111yescharacteristic
442C2×C4⋊C4C23×C15111yescharacteristic
443C2×C4⋊C4C23×C15111yescharacteristic
444C2×C4⋊C4C23×C15111yescharacteristic
445C2×C4⋊C4C23×C15111yescharacteristic
446C2×C22⋊C4—21no—
447C2×C22⋊C4—21no—
448C2×C22⋊C4—21no—
449C2×C22⋊C4—21no—
450C2×C22⋊C4—21no—
451C2×C22⋊C4D4×C15111yescharacteristic
452C2×C22⋊C4D4×C15111yescharacteristic
453C2×C42—21no—
454C2×C42—21no—
455C2×C42—21no—
456C2×C42C23×C15111yescharacteristic
457#107—22no—
458#107—22no—
459#107—22no—
460#107—22no—
461#107—41no—
462#107D4×C15114yescomplemented
463#106—22no—
464#106—22no—
465#106—22no—
466#106—41no—
467C4⋊C8C2×C4×C15114yescomplemented
468C22⋊C8C2×C4×C15114yescomplemented
469C22⋊C8C2×C4×C15114yescomplemented
470#97C2×C4×C15114yescomplemented
471#95—21no—
472#95—21no—
473#95—21no—
474#95—21no—
475#95—21no—
476#95—21no—
477#95—21no—
478#95—21no—
479C24C2×D4×C15111yescharacteristic
480C24C2×D4×C15111yescharacteristic
481C2×D4—22no—
482C2×D4—22no—
483C2×D4C4⋊C4×C15114yes—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—21no—
497C22×C4—21no—
498C22×C4—21no—
499C22×C4—21no—
500C22×C4—42no—
501C22×C4—42no—
502C22×C4—42no—
503C22×C4—42no—
504C22×C4—42no—
505C22×C4—42no—
506C22×C4—81no—
507C22×C4—81no—
508C22×C4—81no—
509C22×C4C22×C4×C15112yes—
510C22×C4C22×C4×C15112yes—
511C22×C4C2×D4×C15111yescharacteristic
512C22×C4C2×D4×C15111yescharacteristic
513C22×C4C2×D4×C15111yescharacteristic
514C22×C4C2×D4×C15111yescharacteristic
515C22×C4C2×Q8×C15112yes—
516C22×C4C2×Q8×C15112yes—
517C22×C4C24×C15111yescharacteristic
518M16—28no—
519C2×C8—21no—
520C2×C8—21no—
521C2×C8—21no—
522C2×C8—21no—
523C2×C8—21no—
524C2×C8—21no—
525C2×C8—28no—
526C2×C8C22×C4×C15112yes—
527C2×C8C22×C4×C15112yes—
528C2×C8C22×C4×C15112yes—
529C2×C8C22×C4×C15112yes—
530C2×C8C2×D4×C15112yes—
531C2×C8#41×C15112yes—
532C4⋊C4—21no—
533C4⋊C4—21no—
534C4⋊C4—21no—
535C4⋊C4—21no—
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—21no—
546C4⋊C4—42no—
547C4⋊C4—42no—
548C4⋊C4—42no—
549C4⋊C4—42no—
550C4⋊C4—81no—
551C4⋊C4C4⋊C4×C15114yes—
552C4⋊C4C2×D4×C15112yes—
553C4⋊C4C2×D4×C15112yes—
554C22⋊C4—42no—
555C22⋊C4—42no—
556C22⋊C4—42no—
557C22⋊C4—42no—
558C22⋊C4—81no—
559C22⋊C4C4⋊C4×C15114yes—
560C22⋊C4C4⋊C4×C15114yes—
561C42—42no—
562C42—42no—
563C42—81no—
564C42C22×C4×C15112yes—
565C42C2×Q8×C15112yes—
566C23—21no—
567C23—21no—
568C23—21no—
569C23—21no—
570C23—21no—
571C23—21no—
572C23—21no—
573C23—21no—
574C23—21no—
575C23—21no—
576C23C2×C4⋊C4×C15112yes—
577C23C2×C4⋊C4×C15112yes—
578C23AGL(1,ℤ/8)×C15112yes—
579C23#137×C15112yes—
580C23C22×D4×C15111yescharacteristic
581D4—28no—
582C2×C4—21no—
583C2×C4—21no—
584C2×C4—21no—
585C2×C4—21no—
586C2×C4—21no—
587C2×C4—21no—
588C2×C4—21no—
589C2×C4—21no—
590C2×C4—22no—
591C2×C4—22no—
592C2×C4—22no—
593C2×C4—22no—
594C2×C4—22no—
595C2×C4—22no—
596C2×C4—22no—
597C2×C4—22no—
598C2×C4—22no—
599C2×C4—22no—
600C2×C4—41no—
601C2×C4—41no—
602C2×C4—41no—
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—41no—
619C2×C4—41no—
620C2×C4—41no—
621C2×C4—41no—
622C2×C4—84no—
623C2×C4—84no—
624C2×C4—84no—
625C2×C4C2×C4⋊C4×C15112yes—
626C2×C4C2×C4⋊C4×C15112yes—
627C2×C4C2×C4⋊C4×C15112yes—
628C2×C4C2×C4⋊C4×C15112yes—
629C2×C4C23×C4×C15111yescharacteristic
630C2×C4C22×D4×C15111yescharacteristic
631C2×C4C22×Q8×C15111yescharacteristic
632C2×C4C2×#41×C15111yescharacteristic
633C2×C4H(5,𝔽2)×C15111yescharacteristic
634C2×C42−1+4×C15111yescharacteristic
635C8—22no—
636C8—22no—
637C8—22no—
638C8C4×D4×C15114yescomplemented
639C22—22no—
640C22—22no—
641C22—22no—
642C22—22no—
643C22—22no—
644C22—22no—
645C22—22no—
646C22—22no—
647C22—22no—
648C22—41no—
649C22—41no—
650C22—41no—
651C22—41no—
652C22#428×C15114yescomplemented
653C22C22×C4⋊C4×C15111yescharacteristic
654C22D42×C15111yescharacteristic
655C22#547×C15111yescharacteristic
656C22C2×AGL(1,ℤ/8)×C15111yescharacteristic
657C22C2×#137×C15111yescharacteristic
658C22#576×C15111yescharacteristic
659C22#578×C15111yescharacteristic
660C4—22no—
661C4—22no—
662C4—22no—
663C4—22no—
664C4—42no—
665C4—42no—
666C4—81no—
667C4—81no—
668C4—81no—
669C4—81no—
670C4—81no—
671C4—81no—
672C4C2×C4×D4×C15111yescharacteristic
673C4#520×C15111yescharacteristic
674C4D4×Q8×C15111yescharacteristic
675C4#554×C15111yescharacteristic
676C2—24no—
677C2—42no—
678C2D4×C4⋊C4×C15111yescharacteristic
679C2C2×#428×C15111yescharacteristic
680C2#2913×C15111yescharacteristic
681C2#3264×C15111yescharacteristic
682C2#3270×C15111yescharacteristic
683C2#3343×C15111yescharacteristic
684C2#3346×C15111yescharacteristic
subgroupG/H
center, socleC23×C151C22×D4
commutatorC2×C4C23×C4×C151
Frattini, cosocleC22×C4C24×C151
prime radicalC22×D4×C151D4
LCSG ▷ C2×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×#428×C151C2semidirect
3. C22×#107×C151C2semidirect
6. #1949×C151C2semidirect
7. #1947×C151C2semidirect
8. #1854×C151C2semidirect
9. #1853×C151C2semidirect
10. #1852×C151C2semidirect
11. #1852×C151C2semidirect
12. #1847×C151C2semidirect
13. #1809×C151C2semidirect
14. #1807×C151C2semidirect
15. #1776×C151C2semidirect
24. #435×C151C4semidirect
70. C2×M16×C151C2×C4semidirect
73. C22×C8×C151C2×C4semidirect
119. #107×C151D4semidirect
124. C4⋊C8×C151C2×C4semidirect
125. C22⋊C8×C151C2×C4semidirect
126. C22⋊C8×C151C2×C4semidirect
127. #97×C151C2×C4semidirect
295. C8×C151C4×D4semidirect
309. C22×C151#428semidirect
342. #22661C151direct (N × H)
343. C151#22661direct (N × H)
345. C2×#428C2×C151semidirect
346. C22×#107C2×C151semidirect
349. #1949C2×C151semidirect
350. #1947C2×C151semidirect
351. #1854C2×C151semidirect
352. #1853C2×C151semidirect
353. #1852C2×C151semidirect
354. #1852C2×C151semidirect
355. #1847C2×C151semidirect
356. #1809C2×C151semidirect
357. #1807C2×C151semidirect
358. #1776C2×C151semidirect
367. #435C4×C151semidirect
413. C2×M16C2×C4×C151semidirect
416. C22×C8C2×C4×C151semidirect
462. #107D4×C151semidirect
467. C4⋊C8C2×C4×C151semidirect
468. C22⋊C8C2×C4×C151semidirect
469. C22⋊C8C2×C4×C151semidirect
470. #97C2×C4×C151semidirect
638. C8C4×D4×C151semidirect
652. C22#428×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#435×C1512
C2×#428×C1512
C22×#107×C1512
#2352×C1512
D4×C4⋊C4×C1512
#1949×C1512
#1947×C1512
#1854×C1512
#1853×C1512
#1852×C1512
#1847×C1512
#1809×C1512
#1807×C1512
#1776×C1512
#22661151