Finite Group Databasebeta

← C151×#23778 #50328703

Subgroups — C151×#23778 #50328703

Order 38656.

768 conjugacy classes of subgroups.

The subgroup lattice has 590 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#125×C151C211yesmaximal, characteristic, complemented
2#2293×C151C211yesmaximal, characteristic
3#2101×C151C211yesmaximal, characteristic, complemented
4#2092×C151C211yesmaximal, characteristic
5#2088×C151C211yesmaximal, characteristic, complemented
6#2087×C151C211yesmaximal, characteristic, complemented
7#2067×C151C211yesmaximal, characteristic
8#2065×C151C211yesmaximal, characteristic
9#2059×C151C211yesmaximal, characteristic, complemented
10#2025×C151C211yesmaximal, characteristic
11C4×#107×C151C211yesmaximal, characteristic, complemented
12C4×#106×C151C211yesmaximal, characteristic, complemented
13C4×C4⋊C8×C151C211yesmaximal, characteristic, complemented
14C4×#102×C151C211yesmaximal, characteristic
15C4×#102×C151C211yesmaximal, characteristic
16C2×#125×C151C2211yescharacteristic
17C2×C4×D4×C151C2211yescharacteristic
18C2×#117×C151—21no—
19C2×#107×C151C2211yescharacteristic
20C2×#107×C151C2211yescharacteristic
21C2×#106×C151C2211yescharacteristic
22C2×#106×C151C2211yescharacteristic
23C2×C4⋊C8×C151C2211yescharacteristic
24C2×C4⋊C8×C151C2211yescharacteristic
25C2×#102×C151C2211yescharacteristic
26C2×#102×C151C2211yescharacteristic
27C2×#102×C151C2211yescharacteristic
28C2×#102×C151C2211yescharacteristic
29C2×C4×C8×C151C2211yescharacteristic
30C2×C4×C8×C151C2211yescharacteristic
31#390×C151C2211yescharacteristic
32#390×C151C2211yescharacteristic
33#389×C151C2211yescharacteristic
34#389×C151C2211yescharacteristic
35#389×C151C2211yescharacteristic
36#389×C151C2211yescharacteristic
37#388×C151—21no—
38#388×C151—21no—
39#387×C151—21no—
40#387×C151—21no—
41#382×C151C2211yescharacteristic
42C4×C4⋊C4×C151—21no—
43C4×C4⋊C4×C151—21no—
44C4×C4⋊C4×C151C2211yescharacteristic
45C4×C4⋊C4×C151C2211yescharacteristic
46C4×C4⋊C4×C151C2211yescharacteristic
47C4×C22⋊C4×C151—21no—
48C43×C151C2211yescharacteristic
49#340×C151C2211yescharacteristic
50#340×C151C2211yescharacteristic
51#340×C151C2211yescharacteristic
52#340×C151C2211yescharacteristic
53#340×C151C2211yescharacteristic
54#340×C151C2211yescharacteristic
55#340×C151C2211yescharacteristic
56#340×C151C2211yescharacteristic
57#336×C151C2211yescharacteristic
58#336×C151C2211yescharacteristic
59C22×D4×C151C2311yescharacteristic
60C23×C4×C151—21no—
61C22×C8×C151C2311yescharacteristic
62C22×C8×C151C2311yescharacteristic
63C22×C8×C151C2311yescharacteristic
64C22×C8×C151C2311yescharacteristic
65#125×C151—22no—
66#125×C151—22no—
67C4×D4×C151—22no—
68C4×D4×C151Q814yes—
69#117×C151—44no—
70C2×C4⋊C4×C151—21no—
71C2×C4⋊C4×C151—21no—
72C2×C4⋊C4×C151—21no—
73C2×C4⋊C4×C151—21no—
74C2×C4⋊C4×C151—21no—
75C2×C4⋊C4×C151—21no—
76C2×C4⋊C4×C151C2311yescharacteristic
77C2×C4⋊C4×C151C2311yescharacteristic
78C2×C4⋊C4×C151C2311yescharacteristic
79C2×C4⋊C4×C151C2311yescharacteristic
80C2×C4⋊C4×C151C2311yescharacteristic
81C2×C4⋊C4×C151C2311yescharacteristic
82C2×C4⋊C4×C151C2311yescharacteristic
83C2×C22⋊C4×C151—21no—
84C2×C22⋊C4×C151—21no—
85C2×C22⋊C4×C151—21no—
86C2×C22⋊C4×C151—21no—
87C2×C22⋊C4×C151—21no—
88C2×C42×C151—21no—
89C2×C42×C151—21no—
90C2×C42×C151—21no—
91C2×C42×C151D411yescharacteristic
92C2×C42×C151D411yescharacteristic
93C2×C42×C151D411yescharacteristic
94C2×C42×C151D411yescharacteristic
95C2×C42×C151C2311yescharacteristic
96C2×C42×C151C2311yescharacteristic
97C2×C42×C151C2311yescharacteristic
98#107×C151—22no—
99#107×C151—22no—
100#106×C151—22no—
101#106×C151—22no—
102C4⋊C8×C151—22no—
103C4⋊C8×C151—22no—
104#102×C151—22no—
105#102×C151—22no—
106#102×C151—22no—
107#102×C151—22no—
108C4×C8×C151—22no—
109C4×C8×C151—22no—
110#95×C151—21no—
111#95×C151—21no—
112#95×C151—21no—
113#95×C151—21no—
114#95×C151—21no—
115#95×C151—21no—
116#95×C151—21no—
117#95×C151—21no—
118#95×C151—21no—
119C24×C151—21no—
120C2×D4×C151—21no—
121C2×D4×C151—21no—
122C2×D4×C151—21no—
123C2×D4×C151—21no—
124C2×D4×C151—21no—
125C2×D4×C151C2×Q812yes—
126C22×C4×C151—21no—
127C22×C4×C151—21no—
128C22×C4×C151—21no—
129C22×C4×C151—24no—
130C22×C4×C151—21no—
131C22×C4×C151—21no—
132C22×C4×C151—21no—
133C22×C4×C151—21no—
134C22×C4×C151—42no—
135C22×C4×C151—42no—
136C22×C4×C151C2×D411yescharacteristic
137C22×C4×C151C2×D411yescharacteristic
138C22×C4×C151C2×D411yescharacteristic
139C22×C4×C151C2×D411yescharacteristic
140C22×C4×C151C2×D411yescharacteristic
141C22×C4×C151C2×D411yescharacteristic
142C22×C4×C151C2411yescharacteristic
143C2×C8×C151—21no—
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×C151#4112yes—
154C2×C8×C151#4112yes—
155C4⋊C4×C151—24no—
156C4⋊C4×C151—24no—
157C4⋊C4×C151—21no—
158C4⋊C4×C151—21no—
159C4⋊C4×C151—21no—
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—42no—
169C4⋊C4×C151—42no—
170C4⋊C4×C151—42no—
171C4⋊C4×C151—42no—
172C4⋊C4×C151C2×Q812yes—
173C4⋊C4×C151#4112yes—
174C4⋊C4×C151#4112yes—
175C22⋊C4×C151—24no—
176C22⋊C4×C151—42no—
177C22⋊C4×C151—42no—
178C22⋊C4×C151—42no—
179C22⋊C4×C151—42no—
180C42×C151—22no—
181C42×C151—22no—
182C42×C151—22no—
183C42×C151—21no—
184C42×C151—21no—
185C42×C151—21no—
186C42×C151—21no—
187C42×C151—41no—
188C42×C151—42no—
189C42×C151—42no—
190C42×C151—42no—
191C42×C151C2×Q812yes—
192C42×C151#4112yes—
193C23×C151—22no—
194C23×C151—41no—
195C23×C151—41no—
196C23×C151—41no—
197C23×C151—41no—
198C23×C151—41no—
199C23×C151—41no—
200C23×C151C22×D411yescharacteristic
201D4×C151—22no—
202D4×C151—22no—
203D4×C151—41no—
204D4×C151—41no—
205C2×C4×C151—21no—
206C2×C4×C151—21no—
207C2×C4×C151—21no—
208C2×C4×C151—21no—
209C2×C4×C151—22no—
210C2×C4×C151—21no—
211C2×C4×C151—21no—
212C2×C4×C151—22no—
213C2×C4×C151—22no—
214C2×C4×C151—21no—
215C2×C4×C151—21no—
216C2×C4×C151—21no—
217C2×C4×C151—21no—
218C2×C4×C151—21no—
219C2×C4×C151—21no—
220C2×C4×C151—21no—
221C2×C4×C151—41no—
222C2×C4×C151—41no—
223C2×C4×C151—41no—
224C2×C4×C151—41no—
225C2×C4×C151—41no—
226C2×C4×C151—41no—
227C2×C4×C151—48no—
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×C151—41no—
240C2×C4×C151C22⋊Q812yes—
241C2×C4×C151C22⋊Q812yes—
242C2×C4×C151#13512yes—
243C2×C4×C151#13512yes—
244C2×C4×C151AGL(1,ℤ/8)12yes—
245C2×C4×C151C22×Q811yescharacteristic
246C2×C4×C151C2×#4111yescharacteristic
247C2×C4×C151C2×#4111yescharacteristic
248C2×C4×C151C2×#4111yescharacteristic
249C2×C4×C151C2×#4111yescharacteristic
250C2×C4×C151C2×#4111yescharacteristic
251C8×C151—22no—
252C8×C151—22no—
253C8×C151—41no—
254C8×C151—41no—
255C22×C151—42no—
256C22×C151—42no—
257C22×C151—42no—
258C22×C151—81no—
259C22×C151—81no—
260C22×C151—81no—
261C22×C151—81no—
262C22×C151C2×C22⋊Q811yescharacteristic
263C22×C151#52511yescharacteristic
264C22×C151#53211yescharacteristic
265C22×C151C2×#13511yescharacteristic
266C22×C151C2×#13511yescharacteristic
267C22×C151C2×AGL(1,ℤ/8)11yescharacteristic
268C22×C151#57511yescharacteristic
269C4×C151—22no—
270C4×C151—22no—
271C4×C151—42no—
272C4×C151—41no—
273C4×C151—42no—
274C4×C151—41no—
275C4×C151—42no—
276C4×C151—41no—
277C4×C151—81no—
278C4×C151—81no—
279C4×C151—81no—
280C4×C151—81no—
281C4×C151#47814yes—
282C4×C151#52911yescharacteristic
283C4×C151#52911yescharacteristic
284C4×C151#53311yescharacteristic
285C4×C151#53311yescharacteristic
286C2×C151—82no—
287C2×C151#239611yescharacteristic
288C2×C151C2×#47811yescharacteristic
289C2×C151#307611yescharacteristic
290C2×C151#310211yescharacteristic
291C2×C151#310611yescharacteristic
292C2×C151#316811yescharacteristic
293C2×C151#317111yescharacteristic
294#23778C15111yesmaximal, characteristic, direct product factor, Sylow
295C151#2377811yescharacteristic, direct product factor, Sylow
296C4×#125C2×C15111yescharacteristic, complemented
297#2293C2×C15111yescharacteristic
298#2101C2×C15111yescharacteristic, complemented
299#2092C2×C15111yescharacteristic
300#2088C2×C15111yescharacteristic, complemented
301#2087C2×C15111yescharacteristic, complemented
302#2067C2×C15111yescharacteristic
303#2065C2×C15111yescharacteristic
304#2059C2×C15111yescharacteristic, complemented
305#2025C2×C15111yescharacteristic
306C4×#107C2×C15111yescharacteristic, complemented
307C4×#106C2×C15111yescharacteristic, complemented
308C4×C4⋊C8C2×C15111yescharacteristic, complemented
309C4×#102C2×C15111yescharacteristic
310C4×#102C2×C15111yescharacteristic
311C2×#125C22×C15111yescharacteristic
312C2×C4×D4C22×C15111yescharacteristic
313C2×#117—21no—
314C2×#107C22×C15111yescharacteristic
315C2×#107C22×C15111yescharacteristic
316C2×#106C22×C15111yescharacteristic
317C2×#106C22×C15111yescharacteristic
318C2×C4⋊C8C22×C15111yescharacteristic
319C2×C4⋊C8C22×C15111yescharacteristic
320C2×#102C22×C15111yescharacteristic
321C2×#102C22×C15111yescharacteristic
322C2×#102C22×C15111yescharacteristic
323C2×#102C22×C15111yescharacteristic
324C2×C4×C8C22×C15111yescharacteristic
325C2×C4×C8C22×C15111yescharacteristic
326#390C22×C15111yescharacteristic
327#390C22×C15111yescharacteristic
328#389C22×C15111yescharacteristic
329#389C22×C15111yescharacteristic
330#389C22×C15111yescharacteristic
331#389C22×C15111yescharacteristic
332#388—21no—
333#388—21no—
334#387—21no—
335#387—21no—
336#382C22×C15111yescharacteristic
337C4×C4⋊C4—21no—
338C4×C4⋊C4—21no—
339C4×C4⋊C4C22×C15111yescharacteristic
340C4×C4⋊C4C22×C15111yescharacteristic
341C4×C4⋊C4C22×C15111yescharacteristic
342C4×C22⋊C4—21no—
343C43C22×C15111yescharacteristic
344#340C22×C15111yescharacteristic
345#340C22×C15111yescharacteristic
346#340C22×C15111yescharacteristic
347#340C22×C15111yescharacteristic
348#340C22×C15111yescharacteristic
349#340C22×C15111yescharacteristic
350#340C22×C15111yescharacteristic
351#340C22×C15111yescharacteristic
352#336C22×C15111yescharacteristic
353#336C22×C15111yescharacteristic
354C22×D4C23×C15111yescharacteristic
355C23×C4—21no—
356C22×C8C23×C15111yescharacteristic
357C22×C8C23×C15111yescharacteristic
358C22×C8C23×C15111yescharacteristic
359C22×C8C23×C15111yescharacteristic
360#125—22no—
361#125—22no—
362C4×D4—22no—
363C4×D4Q8×C15114yes—
364#117—44no—
365C2×C4⋊C4—21no—
366C2×C4⋊C4—21no—
367C2×C4⋊C4—21no—
368C2×C4⋊C4—21no—
369C2×C4⋊C4—21no—
370C2×C4⋊C4—21no—
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×C22⋊C4—21no—
379C2×C22⋊C4—21no—
380C2×C22⋊C4—21no—
381C2×C22⋊C4—21no—
382C2×C22⋊C4—21no—
383C2×C42—21no—
384C2×C42—21no—
385C2×C42—21no—
386C2×C42D4×C15111yescharacteristic
387C2×C42D4×C15111yescharacteristic
388C2×C42D4×C15111yescharacteristic
389C2×C42D4×C15111yescharacteristic
390C2×C42C23×C15111yescharacteristic
391C2×C42C23×C15111yescharacteristic
392C2×C42C23×C15111yescharacteristic
393#107—22no—
394#107—22no—
395#106—22no—
396#106—22no—
397C4⋊C8—22no—
398C4⋊C8—22no—
399#102—22no—
400#102—22no—
401#102—22no—
402#102—22no—
403C4×C8—22no—
404C4×C8—22no—
405#95—21no—
406#95—21no—
407#95—21no—
408#95—21no—
409#95—21no—
410#95—21no—
411#95—21no—
412#95—21no—
413#95—21no—
414C24—21no—
415C2×D4—21no—
416C2×D4—21no—
417C2×D4—21no—
418C2×D4—21no—
419C2×D4—21no—
420C2×D4C2×Q8×C15112yes—
421C22×C4—21no—
422C22×C4—21no—
423C22×C4—21no—
424C22×C4—24no—
425C22×C4—21no—
426C22×C4—21no—
427C22×C4—21no—
428C22×C4—21no—
429C22×C4—42no—
430C22×C4—42no—
431C22×C4C2×D4×C15111yescharacteristic
432C22×C4C2×D4×C15111yescharacteristic
433C22×C4C2×D4×C15111yescharacteristic
434C22×C4C2×D4×C15111yescharacteristic
435C22×C4C2×D4×C15111yescharacteristic
436C22×C4C2×D4×C15111yescharacteristic
437C22×C4C24×C15111yescharacteristic
438C2×C8—21no—
439C2×C8—21no—
440C2×C8—21no—
441C2×C8—21no—
442C2×C8—21no—
443C2×C8—21no—
444C2×C8—21no—
445C2×C8—21no—
446C2×C8—21no—
447C2×C8—21no—
448C2×C8#41×C15112yes—
449C2×C8#41×C15112yes—
450C4⋊C4—24no—
451C4⋊C4—24no—
452C4⋊C4—21no—
453C4⋊C4—21no—
454C4⋊C4—21no—
455C4⋊C4—21no—
456C4⋊C4—21no—
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—42no—
464C4⋊C4—42no—
465C4⋊C4—42no—
466C4⋊C4—42no—
467C4⋊C4C2×Q8×C15112yes—
468C4⋊C4#41×C15112yes—
469C4⋊C4#41×C15112yes—
470C22⋊C4—24no—
471C22⋊C4—42no—
472C22⋊C4—42no—
473C22⋊C4—42no—
474C22⋊C4—42no—
475C42—22no—
476C42—22no—
477C42—22no—
478C42—21no—
479C42—21no—
480C42—21no—
481C42—21no—
482C42—41no—
483C42—42no—
484C42—42no—
485C42—42no—
486C42C2×Q8×C15112yes—
487C42#41×C15112yes—
488C23—22no—
489C23—41no—
490C23—41no—
491C23—41no—
492C23—41no—
493C23—41no—
494C23—41no—
495C23C22×D4×C15111yescharacteristic
496D4—22no—
497D4—22no—
498D4—41no—
499D4—41no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—22no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—22no—
508C2×C4—22no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—48no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4C22⋊Q8×C15112yes—
536C2×C4C22⋊Q8×C15112yes—
537C2×C4#135×C15112yes—
538C2×C4#135×C15112yes—
539C2×C4AGL(1,ℤ/8)×C15112yes—
540C2×C4C22×Q8×C15111yescharacteristic
541C2×C4C2×#41×C15111yescharacteristic
542C2×C4C2×#41×C15111yescharacteristic
543C2×C4C2×#41×C15111yescharacteristic
544C2×C4C2×#41×C15111yescharacteristic
545C2×C4C2×#41×C15111yescharacteristic
546C8—22no—
547C8—22no—
548C8—41no—
549C8—41no—
550C22—42no—
551C22—42no—
552C22—42no—
553C22—81no—
554C22—81no—
555C22—81no—
556C22—81no—
557C22C2×C22⋊Q8×C15111yescharacteristic
558C22#525×C15111yescharacteristic
559C22#532×C15111yescharacteristic
560C22C2×#135×C15111yescharacteristic
561C22C2×#135×C15111yescharacteristic
562C22C2×AGL(1,ℤ/8)×C15111yescharacteristic
563C22#575×C15111yescharacteristic
564C4—22no—
565C4—22no—
566C4—41no—
567C4—42no—
568C4—41no—
569C4—42no—
570C4—41no—
571C4—42no—
572C4—81no—
573C4—81no—
574C4—81no—
575C4—81no—
576C4#478×C15114yes—
577C4#529×C15111yescharacteristic
578C4#529×C15111yescharacteristic
579C4#533×C15111yescharacteristic
580C4#533×C15111yescharacteristic
581C2—82no—
582C2#2396×C15111yescharacteristic
583C2C2×#478×C15111yescharacteristic
584C2#3076×C15111yescharacteristic
585C2#3102×C15111yescharacteristic
586C2#3106×C15111yescharacteristic
587C2#3168×C15111yescharacteristic
588C2#3171×C15111yescharacteristic
subgroupG/H
centerC22×C4×C151C2×D4
commutator, Frattini, cosocleC22×C4C24×C151
socleC23×C151C22×D4
prime radicalC22×D4×C151C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C4×C151 ◁ C43×C151 ◁ G

Complements

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

NH ≅ G/Ntype
1. C4×#125×C151C2semidirect
3. #2101×C151C2semidirect
5. #2088×C151C2semidirect
6. #2087×C151C2semidirect
9. #2059×C151C2semidirect
11. C4×#107×C151C2semidirect
12. C4×#106×C151C2semidirect
13. C4×C4⋊C8×C151C2semidirect
294. #23778C151direct (N × H)
295. C151#23778direct (N × H)
296. C4×#125C2×C151semidirect
298. #2101C2×C151semidirect
300. #2088C2×C151semidirect
301. #2087C2×C151semidirect
304. #2059C2×C151semidirect
306. C4×#107C2×C151semidirect
307. C4×#106C2×C151semidirect
308. C4×C4⋊C8C2×C151semidirect

Maximal subgroups

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

subgroupindex
C4×#125×C1512
#2293×C1512
#2101×C1512
#2092×C1512
#2088×C1512
#2087×C1512
#2067×C1512
#2065×C1512
#2059×C1512
#2025×C1512
C4×#107×C1512
C4×#106×C1512
C4×C4⋊C8×C1512
C4×#102×C1512
#23778151