Finite Group Databasebeta

← C151×#22976 #50327901

Subgroups — C151×#22976 #50327901

Order 38656.

766 conjugacy classes of subgroups.

The subgroup lattice has 570 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#479×C151C211yesmaximal, characteristic
2#2370×C151C211yesmaximal, characteristic
3Q8×C4⋊C4×C151C211yesmaximal, characteristic
4#1992×C151C211yesmaximal, characteristic
5#1948×C151C211yesmaximal, characteristic
6#1943×C151C211yesmaximal, characteristic
7#1941×C151C211yesmaximal, characteristic
8#1921×C151C211yesmaximal, characteristic
9#1919×C151C211yesmaximal, characteristic
10#1865×C151C211yesmaximal, characteristic
11#1865×C151C211yesmaximal, characteristic
12#1771×C151C211yesmaximal, characteristic
13#1763×C151C211yesmaximal, characteristic
14#1763×C151C211yesmaximal, characteristic
15C4×#103×C151C211yesmaximal, characteristic
16C2×#125×C151C2211yescharacteristic
17C2×C4×Q8×C151C2211yescharacteristic
18C2×C4×Q8×C151C2211yescharacteristic
19C2×C4×Q8×C151C2211yescharacteristic
20#479×C151C418yescomplemented
21C2×#107×C151C2211yescharacteristic
22C2×#106×C151C2211yescharacteristic
23C2×#106×C151C2211yescharacteristic
24C2×#106×C151C2211yescharacteristic
25C2×C4⋊C8×C151C2211yescharacteristic
26C2×#103×C151C2211yescharacteristic
27C2×#103×C151C2211yescharacteristic
28C2×#103×C151C2211yescharacteristic
29C2×#103×C151C2211yescharacteristic
30C2×#97×C151C2211yescharacteristic
31C2×#97×C151C2211yescharacteristic
32C2×C4×C8×C151C2211yescharacteristic
33#389×C151—21no—
34#389×C151—21no—
35#389×C151—21no—
36#389×C151C2211yescharacteristic
37#389×C151C2211yescharacteristic
38#389×C151C2211yescharacteristic
39#389×C151C2211yescharacteristic
40#387×C151—21no—
41#387×C151—21no—
42#384×C151—21no—
43#384×C151C2211yescharacteristic
44C4×C4⋊C4×C151—21no—
45C4×C4⋊C4×C151—21no—
46C4×C4⋊C4×C151C2211yescharacteristic
47C4×C4⋊C4×C151C2211yescharacteristic
48C4×C4⋊C4×C151C2211yescharacteristic
49C4×C4⋊C4×C151C2211yescharacteristic
50#340×C151C2211yescharacteristic
51#340×C151C2211yescharacteristic
52#340×C151C2211yescharacteristic
53#340×C151C2211yescharacteristic
54#340×C151C2211yescharacteristic
55#340×C151C2211yescharacteristic
56#340×C151C2211yescharacteristic
57#340×C151C2211yescharacteristic
58#336×C151C2211yescharacteristic
59#336×C151C2211yescharacteristic
60C22×Q8×C151C2311yescharacteristic
61C22×C8×C151C2311yescharacteristic
62C22×C8×C151C2311yescharacteristic
63C22×C8×C151C2311yescharacteristic
64C22×C8×C151C2311yescharacteristic
65#125×C151—22no—
66#125×C151C2×C414yes—
67C4×Q8×C151—22no—
68C4×Q8×C151—22no—
69C4×Q8×C151—22no—
70C4×Q8×C151—41no—
71C4×Q8×C151—41no—
72C4×Q8×C151C2×C414yes—
73C2×C4⋊C4×C151—21no—
74C2×C4⋊C4×C151—21no—
75C2×C4⋊C4×C151—21no—
76C2×C4⋊C4×C151—21no—
77C2×C4⋊C4×C151—21no—
78C2×C4⋊C4×C151—21no—
79C2×C4⋊C4×C151—21no—
80C2×C4⋊C4×C151—21no—
81C2×C4⋊C4×C151—21no—
82C2×C4⋊C4×C151—21no—
83C2×C4⋊C4×C151—21no—
84C2×C4⋊C4×C151D411yescharacteristic
85C2×C4⋊C4×C151D411yescharacteristic
86C2×C4⋊C4×C151C2311yescharacteristic
87C2×C4⋊C4×C151C2311yescharacteristic
88C2×C4⋊C4×C151C2311yescharacteristic
89C2×C4⋊C4×C151C2311yescharacteristic
90C2×C4⋊C4×C151C2311yescharacteristic
91C2×C4⋊C4×C151C2311yescharacteristic
92C2×C4⋊C4×C151C2311yescharacteristic
93C2×C42×C151—21no—
94C2×C42×C151—21no—
95C2×C42×C151—21no—
96C2×C42×C151—21no—
97C2×C42×C151—21no—
98C2×C42×C151—21no—
99C2×C42×C151C2311yescharacteristic
100C2×C42×C151C2311yescharacteristic
101C2×C42×C151C2311yescharacteristic
102#107×C151C2×C414yes—
103#106×C151—41no—
104#106×C151—41no—
105#106×C151C2×C414yes—
106C4⋊C8×C151C2×C414yes—
107#103×C151—22no—
108#103×C151C2×C414yes—
109#103×C151C2×C414yes—
110#103×C151Q814yes—
111#97×C151—22no—
112#97×C151—41no—
113C4×C8×C151—41no—
114#95×C151—21no—
115#95×C151—21no—
116#95×C151—21no—
117#95×C151—21no—
118#95×C151—21no—
119#95×C151—21no—
120#95×C151—21no—
121#95×C151D411yescharacteristic
122#95×C151D411yescharacteristic
123C2×Q8×C151—21no—
124C2×Q8×C151—21no—
125C2×Q8×C151—21no—
126C2×Q8×C151C22×C412yes—
127C2×Q8×C151C2×Q812yes—
128C2×Q8×C151#4112yes—
129C22×C4×C151—21no—
130C22×C4×C151—21no—
131C22×C4×C151—21no—
132C22×C4×C151—21no—
133C22×C4×C151—21no—
134C22×C4×C151—21no—
135C22×C4×C151—21no—
136C22×C4×C151—21no—
137C22×C4×C151C2×D411yescharacteristic
138C22×C4×C151C2×D411yescharacteristic
139C22×C4×C151C2×D411yescharacteristic
140C22×C4×C151C2×D411yescharacteristic
141C22×C4×C151C2×D411yescharacteristic
142C22×C4×C151C2×D411yescharacteristic
143C22×C4×C151C2411yescharacteristic
144C2×C8×C151—21no—
145C2×C8×C151—21no—
146C2×C8×C151—21no—
147C2×C8×C151—21no—
148C2×C8×C151—21no—
149C2×C8×C151—21no—
150C2×C8×C151—21no—
151C2×C8×C151—21no—
152C2×C8×C151—21no—
153C2×C8×C151C22×C412yes—
154C2×C8×C151C22×C412yes—
155C2×C8×C151C2×Q812yes—
156C4⋊C4×C151—24no—
157C4⋊C4×C151—24no—
158C4⋊C4×C151—24no—
159C4⋊C4×C151—22no—
160C4⋊C4×C151—21no—
161C4⋊C4×C151—21no—
162C4⋊C4×C151—21no—
163C4⋊C4×C151—21no—
164C4⋊C4×C151—21no—
165C4⋊C4×C151—21no—
166C4⋊C4×C151—21no—
167C4⋊C4×C151—21no—
168C4⋊C4×C151—21no—
169C4⋊C4×C151—21no—
170C4⋊C4×C151—41no—
171C4⋊C4×C151—42no—
172C4⋊C4×C151—42no—
173C4⋊C4×C151—42no—
174C4⋊C4×C151—42no—
175C4⋊C4×C151—81no—
176C4⋊C4×C151—81no—
177C4⋊C4×C151—81no—
178C4⋊C4×C151—81no—
179C4⋊C4×C151C22×C412yes—
180C4⋊C4×C151C22×C412yes—
181C4⋊C4×C151C22×C412yes—
182C4⋊C4×C151C2×Q812yes—
183C42×C151—24no—
184C42×C151—21no—
185C42×C151—21no—
186C42×C151—21no—
187C42×C151—21no—
188C42×C151—42no—
189C42×C151—42no—
190C42×C151—42no—
191C42×C151—81no—
192C42×C151—81no—
193C42×C151C22×C412yes—
194C42×C151#4112yes—
195C23×C151C22×D411yescharacteristic
196Q8×C151—22no—
197Q8×C151—22no—
198Q8×C151—22no—
199Q8×C151C4×Q814yes—
200C2×C4×C151—22no—
201C2×C4×C151—22no—
202C2×C4×C151—21no—
203C2×C4×C151—22no—
204C2×C4×C151—21no—
205C2×C4×C151—21no—
206C2×C4×C151—21no—
207C2×C4×C151—21no—
208C2×C4×C151—21no—
209C2×C4×C151—22no—
210C2×C4×C151—22no—
211C2×C4×C151—22no—
212C2×C4×C151—21no—
213C2×C4×C151—21no—
214C2×C4×C151—21no—
215C2×C4×C151—22no—
216C2×C4×C151—21no—
217C2×C4×C151—21no—
218C2×C4×C151—21no—
219C2×C4×C151—21no—
220C2×C4×C151—21no—
221C2×C4×C151—21no—
222C2×C4×C151—41no—
223C2×C4×C151—41no—
224C2×C4×C151—41no—
225C2×C4×C151—41no—
226C2×C4×C151—41no—
227C2×C4×C151—41no—
228C2×C4×C151—41no—
229C2×C4×C151—41no—
230C2×C4×C151—41no—
231C2×C4×C151—41no—
232C2×C4×C151—41no—
233C2×C4×C151—41no—
234C2×C4×C151—41no—
235C2×C4×C151—41no—
236C2×C4×C151—41no—
237C2×C4×C151—41no—
238C2×C4×C151—41no—
239C2×C4×C151C4×D412yes—
240C2×C4×C151C4×D412yes—
241C2×C4×C151#13712yes—
242C2×C4×C151C23×C411yescharacteristic
243C2×C4×C151C22×Q811yescharacteristic
244C2×C4×C151C2×#4111yescharacteristic
245C2×C4×C151C2×#4111yescharacteristic
246C2×C4×C151H(5,𝔽2)11yescharacteristic
247C2×C4×C1512−1+411yescharacteristic
248C8×C151—22no—
249C8×C151—22no—
250C8×C151—22no—
251C8×C151—41no—
252C22×C151C2×C4×D411yescharacteristic
253C22×C151#54611yescharacteristic
254C22×C151D4×Q811yescharacteristic
255C22×C151C2×#13711yescharacteristic
256C22×C151#57511yescharacteristic
257C22×C151#57711yescharacteristic
258C22×C151#57711yescharacteristic
259C4×C151—24no—
260C4×C151—22no—
261C4×C151—22no—
262C4×C151—22no—
263C4×C151—42no—
264C4×C151—42no—
265C4×C151—42no—
266C4×C151—42no—
267C4×C151—41no—
268C4×C151—41no—
269C4×C151—41no—
270C4×C151—81no—
271C4×C151—81no—
272C4×C151—81no—
273C4×C151C2×C4×Q811yescharacteristic
274C4×C151#52011yescharacteristic
275C4×C151#55211yescharacteristic
276C4×C151#55411yescharacteristic
277C2×C151#236011yescharacteristic
278C2×C151C4×#13711yescharacteristic
279C2×C151#295211yescharacteristic
280C2×C151#331711yescharacteristic
281C2×C151#332011yescharacteristic
282C2×C151#338711yescharacteristic
283C2×C151#338811yescharacteristic
284#22976C15111yesmaximal, characteristic, direct product factor, Sylow
285C151#2297611yescharacteristic, direct product factor, Sylow
286C2×#479C2×C15111yescharacteristic
287#2370C2×C15111yescharacteristic
288Q8×C4⋊C4C2×C15111yescharacteristic
289#1992C2×C15111yescharacteristic
290#1948C2×C15111yescharacteristic
291#1943C2×C15111yescharacteristic
292#1941C2×C15111yescharacteristic
293#1921C2×C15111yescharacteristic
294#1919C2×C15111yescharacteristic
295#1865C2×C15111yescharacteristic
296#1865C2×C15111yescharacteristic
297#1771C2×C15111yescharacteristic
298#1763C2×C15111yescharacteristic
299#1763C2×C15111yescharacteristic
300C4×#103C2×C15111yescharacteristic
301C2×#125C22×C15111yescharacteristic
302C2×C4×Q8C22×C15111yescharacteristic
303C2×C4×Q8C22×C15111yescharacteristic
304C2×C4×Q8C22×C15111yescharacteristic
305#479C4×C15118yescomplemented
306C2×#107C22×C15111yescharacteristic
307C2×#106C22×C15111yescharacteristic
308C2×#106C22×C15111yescharacteristic
309C2×#106C22×C15111yescharacteristic
310C2×C4⋊C8C22×C15111yescharacteristic
311C2×#103C22×C15111yescharacteristic
312C2×#103C22×C15111yescharacteristic
313C2×#103C22×C15111yescharacteristic
314C2×#103C22×C15111yescharacteristic
315C2×#97C22×C15111yescharacteristic
316C2×#97C22×C15111yescharacteristic
317C2×C4×C8C22×C15111yescharacteristic
318#389—21no—
319#389—21no—
320#389—21no—
321#389C22×C15111yescharacteristic
322#389C22×C15111yescharacteristic
323#389C22×C15111yescharacteristic
324#389C22×C15111yescharacteristic
325#387—21no—
326#387—21no—
327#384—21no—
328#384C22×C15111yescharacteristic
329C4×C4⋊C4—21no—
330C4×C4⋊C4—21no—
331C4×C4⋊C4C22×C15111yescharacteristic
332C4×C4⋊C4C22×C15111yescharacteristic
333C4×C4⋊C4C22×C15111yescharacteristic
334C4×C4⋊C4C22×C15111yescharacteristic
335#340C22×C15111yescharacteristic
336#340C22×C15111yescharacteristic
337#340C22×C15111yescharacteristic
338#340C22×C15111yescharacteristic
339#340C22×C15111yescharacteristic
340#340C22×C15111yescharacteristic
341#340C22×C15111yescharacteristic
342#340C22×C15111yescharacteristic
343#336C22×C15111yescharacteristic
344#336C22×C15111yescharacteristic
345C22×Q8C23×C15111yescharacteristic
346C22×C8C23×C15111yescharacteristic
347C22×C8C23×C15111yescharacteristic
348C22×C8C23×C15111yescharacteristic
349C22×C8C23×C15111yescharacteristic
350#125—22no—
351#125C2×C4×C15114yes—
352C4×Q8—22no—
353C4×Q8—22no—
354C4×Q8—22no—
355C4×Q8—41no—
356C4×Q8—41no—
357C4×Q8C2×C4×C15114yes—
358C2×C4⋊C4—21no—
359C2×C4⋊C4—21no—
360C2×C4⋊C4—21no—
361C2×C4⋊C4—21no—
362C2×C4⋊C4—21no—
363C2×C4⋊C4—21no—
364C2×C4⋊C4—21no—
365C2×C4⋊C4—21no—
366C2×C4⋊C4—21no—
367C2×C4⋊C4—21no—
368C2×C4⋊C4—21no—
369C2×C4⋊C4D4×C15111yescharacteristic
370C2×C4⋊C4D4×C15111yescharacteristic
371C2×C4⋊C4C23×C15111yescharacteristic
372C2×C4⋊C4C23×C15111yescharacteristic
373C2×C4⋊C4C23×C15111yescharacteristic
374C2×C4⋊C4C23×C15111yescharacteristic
375C2×C4⋊C4C23×C15111yescharacteristic
376C2×C4⋊C4C23×C15111yescharacteristic
377C2×C4⋊C4C23×C15111yescharacteristic
378C2×C42—21no—
379C2×C42—21no—
380C2×C42—21no—
381C2×C42—21no—
382C2×C42—21no—
383C2×C42—21no—
384C2×C42C23×C15111yescharacteristic
385C2×C42C23×C15111yescharacteristic
386C2×C42C23×C15111yescharacteristic
387#107C2×C4×C15114yes—
388#106—41no—
389#106—41no—
390#106C2×C4×C15114yes—
391C4⋊C8C2×C4×C15114yes—
392#103—22no—
393#103C2×C4×C15114yes—
394#103C2×C4×C15114yes—
395#103Q8×C15114yes—
396#97—22no—
397#97—41no—
398C4×C8—41no—
399#95—21no—
400#95—21no—
401#95—21no—
402#95—21no—
403#95—21no—
404#95—21no—
405#95—21no—
406#95D4×C15111yescharacteristic
407#95D4×C15111yescharacteristic
408C2×Q8—21no—
409C2×Q8—21no—
410C2×Q8—21no—
411C2×Q8C22×C4×C15112yes—
412C2×Q8C2×Q8×C15112yes—
413C2×Q8#41×C15112yes—
414C22×C4—21no—
415C22×C4—21no—
416C22×C4—21no—
417C22×C4—21no—
418C22×C4—21no—
419C22×C4—21no—
420C22×C4—21no—
421C22×C4—21no—
422C22×C4C2×D4×C15111yescharacteristic
423C22×C4C2×D4×C15111yescharacteristic
424C22×C4C2×D4×C15111yescharacteristic
425C22×C4C2×D4×C15111yescharacteristic
426C22×C4C2×D4×C15111yescharacteristic
427C22×C4C2×D4×C15111yescharacteristic
428C22×C4C24×C15111yescharacteristic
429C2×C8—21no—
430C2×C8—21no—
431C2×C8—21no—
432C2×C8—21no—
433C2×C8—21no—
434C2×C8—21no—
435C2×C8—21no—
436C2×C8—21no—
437C2×C8—21no—
438C2×C8C22×C4×C15112yes—
439C2×C8C22×C4×C15112yes—
440C2×C8C2×Q8×C15112yes—
441C4⋊C4—24no—
442C4⋊C4—24no—
443C4⋊C4—24no—
444C4⋊C4—22no—
445C4⋊C4—21no—
446C4⋊C4—21no—
447C4⋊C4—21no—
448C4⋊C4—21no—
449C4⋊C4—21no—
450C4⋊C4—21no—
451C4⋊C4—21no—
452C4⋊C4—21no—
453C4⋊C4—21no—
454C4⋊C4—21no—
455C4⋊C4—41no—
456C4⋊C4—42no—
457C4⋊C4—42no—
458C4⋊C4—42no—
459C4⋊C4—42no—
460C4⋊C4—81no—
461C4⋊C4—81no—
462C4⋊C4—81no—
463C4⋊C4—81no—
464C4⋊C4C22×C4×C15112yes—
465C4⋊C4C22×C4×C15112yes—
466C4⋊C4C22×C4×C15112yes—
467C4⋊C4C2×Q8×C15112yes—
468C42—24no—
469C42—21no—
470C42—21no—
471C42—21no—
472C42—21no—
473C42—42no—
474C42—42no—
475C42—42no—
476C42—81no—
477C42—81no—
478C42C22×C4×C15112yes—
479C42#41×C15112yes—
480C23C22×D4×C15111yescharacteristic
481Q8—22no—
482Q8—22no—
483Q8—22no—
484Q8C4×Q8×C15114yes—
485C2×C4—22no—
486C2×C4—21no—
487C2×C4—22no—
488C2×C4—22no—
489C2×C4—21no—
490C2×C4—21no—
491C2×C4—21no—
492C2×C4—21no—
493C2×C4—21no—
494C2×C4—22no—
495C2×C4—22no—
496C2×C4—22no—
497C2×C4—21no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—22no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—41no—
508C2×C4—41no—
509C2×C4—41no—
510C2×C4—41no—
511C2×C4—41no—
512C2×C4—41no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4C4×D4×C15112yes—
525C2×C4C4×D4×C15112yes—
526C2×C4#137×C15112yes—
527C2×C4C23×C4×C15111yescharacteristic
528C2×C4C22×Q8×C15111yescharacteristic
529C2×C4C2×#41×C15111yescharacteristic
530C2×C4C2×#41×C15111yescharacteristic
531C2×C4H(5,𝔽2)×C15111yescharacteristic
532C2×C42−1+4×C15111yescharacteristic
533C8—22no—
534C8—22no—
535C8—22no—
536C8—41no—
537C22C2×C4×D4×C15111yescharacteristic
538C22#546×C15111yescharacteristic
539C22D4×Q8×C15111yescharacteristic
540C22C2×#137×C15111yescharacteristic
541C22#575×C15111yescharacteristic
542C22#577×C15111yescharacteristic
543C22#577×C15111yescharacteristic
544C4—24no—
545C4—22no—
546C4—22no—
547C4—22no—
548C4—42no—
549C4—42no—
550C4—42no—
551C4—42no—
552C4—41no—
553C4—41no—
554C4—41no—
555C4—81no—
556C4—81no—
557C4—81no—
558C4C2×C4×Q8×C15111yescharacteristic
559C4#520×C15111yescharacteristic
560C4#552×C15111yescharacteristic
561C4#554×C15111yescharacteristic
562C2#2360×C15111yescharacteristic
563C2C4×#137×C15111yescharacteristic
564C2#2952×C15111yescharacteristic
565C2#3317×C15111yescharacteristic
566C2#3320×C15111yescharacteristic
567C2#3387×C15111yescharacteristic
568C2#3388×C15111yescharacteristic
subgroupG/H
center, socle, prime radicalC23×C151C22×D4
commutatorC2×C4C23×C4×C151
Frattini, cosocleC22×C4C24×C151
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C151 ◁ C4×C4⋊C4×C151 ◁ G

Complements

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

NH ≅ G/Ntype
20. #479×C151C4semidirect
284. #22976C151direct (N × H)
285. C151#22976direct (N × H)
305. #479C4×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#479×C1512
#2370×C1512
Q8×C4⋊C4×C1512
#1992×C1512
#1948×C1512
#1943×C1512
#1941×C1512
#1921×C1512
#1919×C1512
#1865×C1512
#1771×C1512
#1763×C1512
C4×#103×C1512
#22976151