Finite Group Databasebeta

← C151×#23759 #50328684

Subgroups — C151×#23759 #50328684

Order 38656.

752 conjugacy classes of subgroups.

The subgroup lattice has 606 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×C22⋊Q8×C151C211yesmaximal, characteristic
2#2283×C151C211yesmaximal, characteristic
3#2101×C151C211yesmaximal, characteristic, complemented
4#2097×C151C211yesmaximal, characteristic, complemented
5#2085×C151C211yesmaximal, characteristic, complemented
6#2077×C151C211yesmaximal, characteristic
7#2075×C151C211yesmaximal, characteristic
8#2074×C151C211yesmaximal, characteristic, complemented
9#2036×C151C211yesmaximal, characteristic
10#2035×C151C211yesmaximal, characteristic
11C4×#107×C151C211yesmaximal, characteristic, complemented
12C4×#106×C151C211yesmaximal, characteristic, complemented
13C4×#103×C151C211yesmaximal, characteristic, complemented
14C4×#103×C151C211yesmaximal, characteristic, complemented
15C4×C22⋊C8×C151C211yesmaximal, characteristic
16C2×C22⋊Q8×C151C2211yescharacteristic
17C2×C4×Q8×C151C2211yescharacteristic
18C22×C42×C151C2211yescharacteristic
19C2×#107×C151C2211yescharacteristic
20C2×#107×C151C2211yescharacteristic
21C2×#106×C151C2211yescharacteristic
22C2×#106×C151C2211yescharacteristic
23C2×#103×C151C2211yescharacteristic
24C2×#103×C151C2211yescharacteristic
25C2×#103×C151C2211yescharacteristic
26C2×#103×C151C2211yescharacteristic
27C2×C22⋊C8×C151C2211yescharacteristic
28C2×C22⋊C8×C151C2211yescharacteristic
29C2×C4×C8×C151C2211yescharacteristic
30C2×C4×C8×C151C2211yescharacteristic
31#391×C151C2211yescharacteristic
32#389×C151C2211yescharacteristic
33#387×C151—21no—
34#385×C151—21no—
35#383×C151—21no—
36#382×C151C2211yescharacteristic
37#382×C151C2211yescharacteristic
38#381×C151—21no—
39#380×C151C2211yescharacteristic
40#380×C151C2211yescharacteristic
41#380×C151C2211yescharacteristic
42C4×C4⋊C4×C151—21no—
43C4×C4⋊C4×C151C2211yescharacteristic
44C4×C4⋊C4×C151C2211yescharacteristic
45C4×C4⋊C4×C151C2211yescharacteristic
46C4×C22⋊C4×C151—21no—
47C4×C22⋊C4×C151—21no—
48#376×C151—21no—
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×Q8×C151C2311yescharacteristic
60C23×C4×C151D411yescharacteristic
61C23×C4×C151D411yescharacteristic
62C23×C4×C151C2311yescharacteristic
63C22×C8×C151C2311yescharacteristic
64C22×C8×C151C2311yescharacteristic
65C22×C8×C151C2311yescharacteristic
66C22×C8×C151C2311yescharacteristic
67C22⋊Q8×C151—22no—
68C22⋊Q8×C151—22no—
69C4×Q8×C151—22no—
70C4×Q8×C151—22no—
71C2×C4⋊C4×C151—21no—
72C2×C4⋊C4×C151—21no—
73C2×C4⋊C4×C151—21no—
74C2×C4⋊C4×C151C2311yescharacteristic
75C2×C4⋊C4×C151C2311yescharacteristic
76C2×C4⋊C4×C151C2311yescharacteristic
77C2×C4⋊C4×C151C2311yescharacteristic
78C2×C4⋊C4×C151C2311yescharacteristic
79C2×C4⋊C4×C151C2311yescharacteristic
80C2×C4⋊C4×C151C2311yescharacteristic
81C2×C22⋊C4×C151—21no—
82C2×C22⋊C4×C151—21no—
83C2×C22⋊C4×C151—21no—
84C2×C22⋊C4×C151—21no—
85C2×C42×C151—22no—
86C2×C42×C151—22no—
87C2×C42×C151—21no—
88C2×C42×C151—21no—
89C2×C42×C151—21no—
90C2×C42×C151—21no—
91C2×C42×C151D411yescharacteristic
92C2×C42×C151D411yescharacteristic
93C2×C42×C151C2311yescharacteristic
94C2×C42×C151C2311yescharacteristic
95#107×C151—22no—
96#107×C151—22no—
97#106×C151—22no—
98#106×C151—22no—
99#103×C151—22no—
100#103×C151—22no—
101#103×C151—22no—
102#103×C151—22no—
103C22⋊C8×C151—22no—
104C22⋊C8×C151—22no—
105C4×C8×C151—22no—
106C4×C8×C151—22no—
107#95×C151—21no—
108#95×C151—21no—
109#95×C151—21no—
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—
119#95×C151—21no—
120C24×C151C2×D411yescharacteristic
121C2×Q8×C151—21no—
122C2×Q8×C151—21no—
123C2×Q8×C151—21no—
124C2×Q8×C151—21no—
125C2×Q8×C151—21no—
126C2×Q8×C151#4112yes—
127C22×C4×C151—22no—
128C22×C4×C151—21no—
129C22×C4×C151—21no—
130C22×C4×C151—22no—
131C22×C4×C151—22no—
132C22×C4×C151—22no—
133C22×C4×C151—22no—
134C22×C4×C151—21no—
135C22×C4×C151—21no—
136C22×C4×C151—21no—
137C22×C4×C151—21no—
138C22×C4×C151—21no—
139C22×C4×C151—21no—
140C22×C4×C151—21no—
141C22×C4×C151—21no—
142C22×C4×C151—21no—
143C22×C4×C151—21no—
144C22×C4×C151—21no—
145C22×C4×C151—21no—
146C22×C4×C151—41no—
147C22×C4×C151C2×D411yescharacteristic
148C22×C4×C151C2×D411yescharacteristic
149C22×C4×C151C2×D411yescharacteristic
150C22×C4×C151C2×D411yescharacteristic
151C22×C4×C151C2×D411yescharacteristic
152C22×C4×C151C2411yescharacteristic
153C2×C8×C151—21no—
154C2×C8×C151—21no—
155C2×C8×C151—21no—
156C2×C8×C151—21no—
157C2×C8×C151—21no—
158C2×C8×C151—21no—
159C2×C8×C151—21no—
160C2×C8×C151—21no—
161C2×C8×C151—21no—
162C2×C8×C151—21no—
163C2×C8×C151#4112yes—
164C2×C8×C151#4112yes—
165C4⋊C4×C151—24no—
166C4⋊C4×C151—21no—
167C4⋊C4×C151—21no—
168C4⋊C4×C151—21no—
169C4⋊C4×C151—21no—
170C4⋊C4×C151—21no—
171C4⋊C4×C151—21no—
172C4⋊C4×C151—21no—
173C4⋊C4×C151—21no—
174C4⋊C4×C151—21no—
175C4⋊C4×C151—21no—
176C4⋊C4×C151—21no—
177C4⋊C4×C151—21no—
178C4⋊C4×C151—21no—
179C4⋊C4×C151—42no—
180C4⋊C4×C151—42no—
181C4⋊C4×C151#4112yes—
182C22⋊C4×C151—24no—
183C22⋊C4×C151—42no—
184C22⋊C4×C151—42no—
185C22⋊C4×C151—42no—
186C42×C151—22no—
187C42×C151—22no—
188C42×C151—21no—
189C42×C151—21no—
190C42×C151—42no—
191C42×C151—42no—
192C42×C151—42no—
193C42×C151—42no—
194C42×C151#4112yes—
195C42×C151#4112yes—
196C23×C151—21no—
197C23×C151—21no—
198C23×C151—21no—
199C23×C151—21no—
200C23×C151—21no—
201C23×C151—21no—
202C23×C151#13512yes—
203C23×C151C22×D411yescharacteristic
204Q8×C151—22no—
205Q8×C151—22no—
206Q8×C151—41no—
207Q8×C151—41no—
208C2×C4×C151—21no—
209C2×C4×C151—21no—
210C2×C4×C151—21no—
211C2×C4×C151—21no—
212C2×C4×C151—21no—
213C2×C4×C151—22no—
214C2×C4×C151—22no—
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—44no—
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—44no—
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×C151—41no—
241C2×C4×C151—41no—
242C2×C4×C151—41no—
243C2×C4×C151—41no—
244C2×C4×C151—41no—
245C2×C4×C151—41no—
246C2×C4×C151—41no—
247C2×C4×C151—41no—
248C2×C4×C151—41no—
249C2×C4×C151#12312yes—
250C2×C4×C151#12312yes—
251C2×C4×C151#13512yes—
252C2×C4×C151#13712yes—
253C2×C4×C151C2×#4111yescharacteristic
254C2×C4×C151C2×#4111yescharacteristic
255C2×C4×C151C2×#4111yescharacteristic
256C2×C4×C151C2×#4111yescharacteristic
257C2×C4×C151C2×#4111yescharacteristic
258C2×C4×C151C2×#4111yescharacteristic
259C8×C151—22no—
260C8×C151—22no—
261C8×C151—41no—
262C8×C151—41no—
263C22×C151—22no—
264C22×C151—22no—
265C22×C151—22no—
266C22×C151—41no—
267C22×C151—41no—
268C22×C151—41no—
269C22×C151—41no—
270C22×C151C2×#12311yescharacteristic
271C22×C151#52511yescharacteristic
272C22×C151#53211yescharacteristic
273C22×C151C2×#13511yescharacteristic
274C22×C151C2×#13511yescharacteristic
275C22×C151C2×#13711yescharacteristic
276C22×C151#57511yescharacteristic
277C4×C151—22no—
278C4×C151—41no—
279C4×C151—41no—
280C4×C151—42no—
281C4×C151—41no—
282C4×C151—42no—
283C4×C151—81no—
284C4×C151—81no—
285C4×C151—81no—
286C4×C151—81no—
287C4×C151—81no—
288C4×C151—81no—
289C4×C151#48514yes—
290C4×C151#52911yescharacteristic
291C4×C151#52911yescharacteristic
292C4×C151#52911yescharacteristic
293C4×C151#52911yescharacteristic
294C2×C151—42no—
295C2×C151#239511yescharacteristic
296C2×C151C2×#48511yescharacteristic
297C2×C151#309111yescharacteristic
298C2×C151#310211yescharacteristic
299C2×C151#310811yescharacteristic
300C2×C151#316811yescharacteristic
301C2×C151#317211yescharacteristic
302#23759C15111yesmaximal, characteristic, direct product factor, Sylow
303C151#2375911yescharacteristic, direct product factor, Sylow
304C4×C22⋊Q8C2×C15111yescharacteristic
305#2283C2×C15111yescharacteristic
306#2101C2×C15111yescharacteristic, complemented
307#2097C2×C15111yescharacteristic, complemented
308#2085C2×C15111yescharacteristic, complemented
309#2077C2×C15111yescharacteristic
310#2075C2×C15111yescharacteristic
311#2074C2×C15111yescharacteristic, complemented
312#2036C2×C15111yescharacteristic
313#2035C2×C15111yescharacteristic
314C4×#107C2×C15111yescharacteristic, complemented
315C4×#106C2×C15111yescharacteristic, complemented
316C4×#103C2×C15111yescharacteristic, complemented
317C4×#103C2×C15111yescharacteristic, complemented
318C4×C22⋊C8C2×C15111yescharacteristic
319C2×C22⋊Q8C22×C15111yescharacteristic
320C2×C4×Q8C22×C15111yescharacteristic
321C22×C42C22×C15111yescharacteristic
322C2×#107C22×C15111yescharacteristic
323C2×#107C22×C15111yescharacteristic
324C2×#106C22×C15111yescharacteristic
325C2×#106C22×C15111yescharacteristic
326C2×#103C22×C15111yescharacteristic
327C2×#103C22×C15111yescharacteristic
328C2×#103C22×C15111yescharacteristic
329C2×#103C22×C15111yescharacteristic
330C2×C22⋊C8C22×C15111yescharacteristic
331C2×C22⋊C8C22×C15111yescharacteristic
332C2×C4×C8C22×C15111yescharacteristic
333C2×C4×C8C22×C15111yescharacteristic
334#391C22×C15111yescharacteristic
335#389C22×C15111yescharacteristic
336#387—21no—
337#385—21no—
338#383—21no—
339#382C22×C15111yescharacteristic
340#382C22×C15111yescharacteristic
341#381—21no—
342#380C22×C15111yescharacteristic
343#380C22×C15111yescharacteristic
344#380C22×C15111yescharacteristic
345C4×C4⋊C4—21no—
346C4×C4⋊C4C22×C15111yescharacteristic
347C4×C4⋊C4C22×C15111yescharacteristic
348C4×C4⋊C4C22×C15111yescharacteristic
349C4×C22⋊C4—21no—
350C4×C22⋊C4—21no—
351#376—21no—
352#340C22×C15111yescharacteristic
353#340C22×C15111yescharacteristic
354#340C22×C15111yescharacteristic
355#340C22×C15111yescharacteristic
356#340C22×C15111yescharacteristic
357#340C22×C15111yescharacteristic
358#340C22×C15111yescharacteristic
359#340C22×C15111yescharacteristic
360#336C22×C15111yescharacteristic
361#336C22×C15111yescharacteristic
362C22×Q8C23×C15111yescharacteristic
363C23×C4D4×C15111yescharacteristic
364C23×C4D4×C15111yescharacteristic
365C23×C4C23×C15111yescharacteristic
366C22×C8C23×C15111yescharacteristic
367C22×C8C23×C15111yescharacteristic
368C22×C8C23×C15111yescharacteristic
369C22×C8C23×C15111yescharacteristic
370C22⋊Q8—22no—
371C22⋊Q8—22no—
372C4×Q8—22no—
373C4×Q8—22no—
374C2×C4⋊C4—21no—
375C2×C4⋊C4—21no—
376C2×C4⋊C4—21no—
377C2×C4⋊C4C23×C15111yescharacteristic
378C2×C4⋊C4C23×C15111yescharacteristic
379C2×C4⋊C4C23×C15111yescharacteristic
380C2×C4⋊C4C23×C15111yescharacteristic
381C2×C4⋊C4C23×C15111yescharacteristic
382C2×C4⋊C4C23×C15111yescharacteristic
383C2×C4⋊C4C23×C15111yescharacteristic
384C2×C22⋊C4—21no—
385C2×C22⋊C4—21no—
386C2×C22⋊C4—21no—
387C2×C22⋊C4—21no—
388C2×C42—22no—
389C2×C42—22no—
390C2×C42—21no—
391C2×C42—21no—
392C2×C42—21no—
393C2×C42—21no—
394C2×C42D4×C15111yescharacteristic
395C2×C42D4×C15111yescharacteristic
396C2×C42C23×C15111yescharacteristic
397C2×C42C23×C15111yescharacteristic
398#107—22no—
399#107—22no—
400#106—22no—
401#106—22no—
402#103—22no—
403#103—22no—
404#103—22no—
405#103—22no—
406C22⋊C8—22no—
407C22⋊C8—22no—
408C4×C8—22no—
409C4×C8—22no—
410#95—21no—
411#95—21no—
412#95—21no—
413#95—21no—
414#95—21no—
415#95—21no—
416#95—21no—
417#95—21no—
418#95—21no—
419#95—21no—
420#95—21no—
421#95—21no—
422#95—21no—
423C24C2×D4×C15111yescharacteristic
424C2×Q8—21no—
425C2×Q8—21no—
426C2×Q8—21no—
427C2×Q8—21no—
428C2×Q8—21no—
429C2×Q8#41×C15112yes—
430C22×C4—22no—
431C22×C4—21no—
432C22×C4—21no—
433C22×C4—22no—
434C22×C4—22no—
435C22×C4—22no—
436C22×C4—22no—
437C22×C4—21no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—41no—
450C22×C4C2×D4×C15111yescharacteristic
451C22×C4C2×D4×C15111yescharacteristic
452C22×C4C2×D4×C15111yescharacteristic
453C22×C4C2×D4×C15111yescharacteristic
454C22×C4C2×D4×C15111yescharacteristic
455C22×C4C24×C15111yescharacteristic
456C2×C8—21no—
457C2×C8—21no—
458C2×C8—21no—
459C2×C8—21no—
460C2×C8—21no—
461C2×C8—21no—
462C2×C8—21no—
463C2×C8—21no—
464C2×C8—21no—
465C2×C8—21no—
466C2×C8#41×C15112yes—
467C2×C8#41×C15112yes—
468C4⋊C4—24no—
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4—21no—
473C4⋊C4—21no—
474C4⋊C4—21no—
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4—21no—
480C4⋊C4—21no—
481C4⋊C4—21no—
482C4⋊C4—42no—
483C4⋊C4—42no—
484C4⋊C4#41×C15112yes—
485C22⋊C4—24no—
486C22⋊C4—42no—
487C22⋊C4—42no—
488C22⋊C4—42no—
489C42—22no—
490C42—22no—
491C42—21no—
492C42—21no—
493C42—42no—
494C42—42no—
495C42—42no—
496C42—42no—
497C42#41×C15112yes—
498C42#41×C15112yes—
499C23—21no—
500C23—21no—
501C23—21no—
502C23—21no—
503C23—21no—
504C23—21no—
505C23#135×C15112yes—
506C23C22×D4×C15111yescharacteristic
507Q8—22no—
508Q8—22no—
509Q8—41no—
510Q8—41no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—22no—
517C2×C4—22no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—44no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—44no—
530C2×C4—41no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4#123×C15112yes—
553C2×C4#123×C15112yes—
554C2×C4#135×C15112yes—
555C2×C4#137×C15112yes—
556C2×C4C2×#41×C15111yescharacteristic
557C2×C4C2×#41×C15111yescharacteristic
558C2×C4C2×#41×C15111yescharacteristic
559C2×C4C2×#41×C15111yescharacteristic
560C2×C4C2×#41×C15111yescharacteristic
561C2×C4C2×#41×C15111yescharacteristic
562C8—22no—
563C8—22no—
564C8—41no—
565C8—41no—
566C22—22no—
567C22—22no—
568C22—22no—
569C22—41no—
570C22—41no—
571C22—41no—
572C22—41no—
573C22C2×#123×C15111yescharacteristic
574C22#525×C15111yescharacteristic
575C22#532×C15111yescharacteristic
576C22C2×#135×C15111yescharacteristic
577C22C2×#135×C15111yescharacteristic
578C22C2×#137×C15111yescharacteristic
579C22#575×C15111yescharacteristic
580C4—22no—
581C4—42no—
582C4—41no—
583C4—42no—
584C4—41no—
585C4—41no—
586C4—81no—
587C4—81no—
588C4—81no—
589C4—81no—
590C4—81no—
591C4—81no—
592C4#485×C15114yes—
593C4#529×C15111yescharacteristic
594C4#529×C15111yescharacteristic
595C4#529×C15111yescharacteristic
596C4#529×C15111yescharacteristic
597C2—42no—
598C2#2395×C15111yescharacteristic
599C2C2×#485×C15111yescharacteristic
600C2#3091×C15111yescharacteristic
601C2#3102×C15111yescharacteristic
602C2#3108×C15111yescharacteristic
603C2#3168×C15111yescharacteristic
604C2#3172×C15111yescharacteristic
subgroupG/H
centerC22×C4×C151C2×D4
commutator, Frattini, cosocleC22×C4C24×C151
socleC23×C151C22×D4
prime radicalC24×C151C2×D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C4×C151 ◁ C22×C42×C151 ◁ G

Complements

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

NH ≅ G/Ntype
3. #2101×C151C2semidirect
4. #2097×C151C2semidirect
5. #2085×C151C2semidirect
8. #2074×C151C2semidirect
11. C4×#107×C151C2semidirect
12. C4×#106×C151C2semidirect
13. C4×#103×C151C2semidirect
14. C4×#103×C151C2semidirect
302. #23759C151direct (N × H)
303. C151#23759direct (N × H)
306. #2101C2×C151semidirect
307. #2097C2×C151semidirect
308. #2085C2×C151semidirect
311. #2074C2×C151semidirect
314. C4×#107C2×C151semidirect
315. C4×#106C2×C151semidirect
316. C4×#103C2×C151semidirect
317. C4×#103C2×C151semidirect

Maximal subgroups

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

subgroupindex
C4×C22⋊Q8×C1512
#2283×C1512
#2101×C1512
#2097×C1512
#2085×C1512
#2077×C1512
#2075×C1512
#2074×C1512
#2036×C1512
#2035×C1512
C4×#107×C1512
C4×#106×C1512
C4×#103×C1512
C4×C22⋊C8×C1512
#23759151