Finite Group Databasebeta

← C151×#23786 #50328711

Subgroups — C151×#23786 #50328711

Order 38656.

712 conjugacy classes of subgroups.

The subgroup lattice has 586 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#2331×C151C211yesmaximal, characteristic, complemented
2#2319×C151C211yesmaximal, characteristic
3#2101×C151C211yesmaximal, characteristic, complemented
4#2092×C151C211yesmaximal, characteristic
5#2088×C151C211yesmaximal, characteristic, complemented
6#2086×C151C211yesmaximal, characteristic, complemented
7#2065×C151C211yesmaximal, characteristic
8#2065×C151C211yesmaximal, characteristic
9#2058×C151C211yesmaximal, characteristic, complemented
10#2023×C151C211yesmaximal, characteristic
11#1776×C151C211yesmaximal, characteristic, complemented
12C4×#106×C151C211yesmaximal, characteristic, complemented
13#1768×C151C211yesmaximal, characteristic, complemented
14#1762×C151C211yesmaximal, characteristic
15C4×#102×C151C211yesmaximal, characteristic
16C2×C4⋊Q8×C151C2211yescharacteristic
17C2×C4×D4×C151C2211yescharacteristic
18C2×#107×C151C2211yescharacteristic
19C2×#106×C151C2211yescharacteristic
20C2×#106×C151C2211yescharacteristic
21C2×#106×C151C2211yescharacteristic
22C2×C4⋊C8×C151C2211yescharacteristic
23C2×C4⋊C8×C151C2211yescharacteristic
24C2×#102×C151C2211yescharacteristic
25C2×#102×C151C2211yescharacteristic
26C2×#102×C151C2211yescharacteristic
27C2×#102×C151C2211yescharacteristic
28C2×#97×C151C2211yescharacteristic
29C2×C4×C8×C151C2211yescharacteristic
30#391×C151—21no—
31#391×C151—21no—
32#390×C151C2211yescharacteristic
33#390×C151C2211yescharacteristic
34#389×C151C2211yescharacteristic
35#389×C151C2211yescharacteristic
36#389×C151C2211yescharacteristic
37#389×C151C2211yescharacteristic
38#388×C151—21no—
39#388×C151—21no—
40#387×C151—21no—
41#387×C151—21no—
42#382×C151C2211yescharacteristic
43#381×C151—21no—
44#380×C151—21no—
45C4×C4⋊C4×C151C2211yescharacteristic
46C4×C4⋊C4×C151C2211yescharacteristic
47C4×C4⋊C4×C151C2211yescharacteristic
48#376×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×Q8×C151—21no—
60C22×D4×C151C2311yescharacteristic
61C23×C4×C151—21no—
62C22×C8×C151C2311yescharacteristic
63C22×C8×C151C2311yescharacteristic
64C22×C8×C151C2311yescharacteristic
65C22×C8×C151C2311yescharacteristic
66C4⋊Q8×C151—22no—
67C4⋊Q8×C151—22no—
68C4×D4×C151—22no—
69C4×D4×C151Q814yescomplemented
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×C151C2311yescharacteristic
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×C22⋊C4×C151—21no—
83C2×C22⋊C4×C151—21no—
84C2×C22⋊C4×C151—21no—
85C2×C22⋊C4×C151—21no—
86C2×C22⋊C4×C151—21no—
87C2×C42×C151—21no—
88C2×C42×C151—21no—
89C2×C42×C151—21no—
90C2×C42×C151C2311yescharacteristic
91C2×C42×C151C2311yescharacteristic
92C2×C42×C151C2311yescharacteristic
93#107×C151—22no—
94#106×C151—22no—
95#106×C151—22no—
96#106×C151—22no—
97C4⋊C8×C151—22no—
98C4⋊C8×C151—22no—
99#102×C151—22no—
100#102×C151—22no—
101#102×C151—22no—
102#102×C151—22no—
103#97×C151—22no—
104C4×C8×C151—22no—
105#95×C151—21no—
106#95×C151—21no—
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×C151D411yescharacteristic
115#95×C151D411yescharacteristic
116#95×C151D411yescharacteristic
117#95×C151D411yescharacteristic
118C24×C151—21no—
119C2×Q8×C151—24no—
120C2×Q8×C151—81no—
121C2×Q8×C151—81no—
122C2×D4×C151—21no—
123C2×D4×C151—21no—
124C2×D4×C151—21no—
125C2×D4×C151—21no—
126C2×D4×C151—21no—
127C2×D4×C151C2×Q812yes—
128C22×C4×C151—21no—
129C22×C4×C151—21no—
130C22×C4×C151—21no—
131C22×C4×C151—24no—
132C22×C4×C151—21no—
133C22×C4×C151—21no—
134C22×C4×C151—21no—
135C22×C4×C151—21no—
136C22×C4×C151—81no—
137C22×C4×C151—81no—
138C22×C4×C151C2×D411yescharacteristic
139C22×C4×C151C2×D411yescharacteristic
140C22×C4×C151C2×D411yescharacteristic
141C22×C4×C151C2×D411yescharacteristic
142C22×C4×C151C2×D411yescharacteristic
143C22×C4×C151C2×D411yescharacteristic
144C22×C4×C151C2411yescharacteristic
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—21no—
154C2×C8×C151—21no—
155C2×C8×C151#4112yes—
156C2×C8×C151#4112yes—
157C4⋊C4×C151—24no—
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—21no—
169C4⋊C4×C151—81no—
170C4⋊C4×C151—81no—
171C4⋊C4×C151—81no—
172C4⋊C4×C151—81no—
173C4⋊C4×C151C2×Q812yes—
174C4⋊C4×C151#4112yes—
175C4⋊C4×C151#4112yes—
176C22⋊C4×C151—24no—
177C22⋊C4×C151—81no—
178C22⋊C4×C151—81no—
179C22⋊C4×C151—81no—
180C22⋊C4×C151—81no—
181C42×C151—21no—
182C42×C151—21no—
183C42×C151—21no—
184C42×C151—21no—
185C42×C151—81no—
186C42×C151—81no—
187C42×C151—81no—
188C42×C151C2×Q812yes—
189C42×C151#4112yes—
190C23×C151—22no—
191C23×C151—41no—
192C23×C151—41no—
193C23×C151—41no—
194C23×C151—41no—
195C23×C151—41no—
196C23×C151—41no—
197C23×C151C22×D411yescharacteristic
198Q8×C151—84no—
199D4×C151—22no—
200D4×C151—22no—
201D4×C151—41no—
202D4×C151—41no—
203C2×C4×C151—21no—
204C2×C4×C151—21no—
205C2×C4×C151—21no—
206C2×C4×C151—21no—
207C2×C4×C151—22no—
208C2×C4×C151—21no—
209C2×C4×C151—22no—
210C2×C4×C151—22no—
211C2×C4×C151—21no—
212C2×C4×C151—21no—
213C2×C4×C151—21no—
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—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×C151—41no—
240C2×C4×C151—84no—
241C2×C4×C151C22⋊Q812yes—
242C2×C4×C151C22⋊Q812yes—
243C2×C4×C151C22×Q811yescharacteristic
244C2×C4×C151C2×#4111yescharacteristic
245C2×C4×C151C2×#4111yescharacteristic
246C2×C4×C151C2×#4111yescharacteristic
247C2×C4×C151C2×#4111yescharacteristic
248C2×C4×C151C2×#4111yescharacteristic
249C8×C151—22no—
250C8×C151—22no—
251C8×C151—41no—
252C8×C151—41no—
253C22×C151—42no—
254C22×C151—42no—
255C22×C151—42no—
256C22×C151—81no—
257C22×C151—81no—
258C22×C151—81no—
259C22×C151—81no—
260C22×C151C2×C22⋊Q811yescharacteristic
261C22×C151#52511yescharacteristic
262C22×C151#53211yescharacteristic
263C22×C151#57611yescharacteristic
264C22×C151#57711yescharacteristic
265C22×C151#57711yescharacteristic
266C22×C151#57711yescharacteristic
267C4×C151—22no—
268C4×C151—22no—
269C4×C151—42no—
270C4×C151—41no—
271C4×C151—42no—
272C4×C151—42no—
273C4×C151—41no—
274C4×C151—41no—
275C4×C151—41no—
276C4×C151—81no—
277C4×C151—81no—
278C4×C151—81no—
279C4×C151—81no—
280C4×C151#52911yescharacteristic
281C4×C151#52911yescharacteristic
282C4×C151#53311yescharacteristic
283C4×C151#53311yescharacteristic
284C2×C151—82no—
285C2×C151#239611yescharacteristic
286C2×C151#308111yescharacteristic
287C2×C151#308411yescharacteristic
288C2×C151#311811yescharacteristic
289C2×C151#312611yescharacteristic
290C2×C151#317311yescharacteristic
291C2×C151#317911yescharacteristic
292#23786C15111yesmaximal, characteristic, direct product factor, Sylow
293C151#2378611yescharacteristic, direct product factor, Sylow
294#2331C2×C15111yescharacteristic, complemented
295#2319C2×C15111yescharacteristic
296#2101C2×C15111yescharacteristic, complemented
297#2092C2×C15111yescharacteristic
298#2088C2×C15111yescharacteristic, complemented
299#2086C2×C15111yescharacteristic, complemented
300#2065C2×C15111yescharacteristic
301#2065C2×C15111yescharacteristic
302#2058C2×C15111yescharacteristic, complemented
303#2023C2×C15111yescharacteristic
304#1776C2×C15111yescharacteristic, complemented
305C4×#106C2×C15111yescharacteristic, complemented
306#1768C2×C15111yescharacteristic, complemented
307#1762C2×C15111yescharacteristic
308C4×#102C2×C15111yescharacteristic
309C2×C4⋊Q8C22×C15111yescharacteristic
310C2×C4×D4C22×C15111yescharacteristic
311C2×#107C22×C15111yescharacteristic
312C2×#106C22×C15111yescharacteristic
313C2×#106C22×C15111yescharacteristic
314C2×#106C22×C15111yescharacteristic
315C2×C4⋊C8C22×C15111yescharacteristic
316C2×C4⋊C8C22×C15111yescharacteristic
317C2×#102C22×C15111yescharacteristic
318C2×#102C22×C15111yescharacteristic
319C2×#102C22×C15111yescharacteristic
320C2×#102C22×C15111yescharacteristic
321C2×#97C22×C15111yescharacteristic
322C2×C4×C8C22×C15111yescharacteristic
323#391—21no—
324#391—21no—
325#390C22×C15111yescharacteristic
326#390C22×C15111yescharacteristic
327#389C22×C15111yescharacteristic
328#389C22×C15111yescharacteristic
329#389C22×C15111yescharacteristic
330#389C22×C15111yescharacteristic
331#388—21no—
332#388—21no—
333#387—21no—
334#387—21no—
335#382C22×C15111yescharacteristic
336#381—21no—
337#380—21no—
338C4×C4⋊C4C22×C15111yescharacteristic
339C4×C4⋊C4C22×C15111yescharacteristic
340C4×C4⋊C4C22×C15111yescharacteristic
341#376C22×C15111yescharacteristic
342#340C22×C15111yescharacteristic
343#340C22×C15111yescharacteristic
344#340C22×C15111yescharacteristic
345#340C22×C15111yescharacteristic
346#340C22×C15111yescharacteristic
347#340C22×C15111yescharacteristic
348#340C22×C15111yescharacteristic
349#340C22×C15111yescharacteristic
350#336C22×C15111yescharacteristic
351#336C22×C15111yescharacteristic
352C22×Q8—21no—
353C22×D4C23×C15111yescharacteristic
354C23×C4—21no—
355C22×C8C23×C15111yescharacteristic
356C22×C8C23×C15111yescharacteristic
357C22×C8C23×C15111yescharacteristic
358C22×C8C23×C15111yescharacteristic
359C4⋊Q8—22no—
360C4⋊Q8—22no—
361C4×D4—22no—
362C4×D4Q8×C15114yescomplemented
363C2×C4⋊C4—21no—
364C2×C4⋊C4—21no—
365C2×C4⋊C4—21no—
366C2×C4⋊C4—21no—
367C2×C4⋊C4—21no—
368C2×C4⋊C4C23×C15111yescharacteristic
369C2×C4⋊C4C23×C15111yescharacteristic
370C2×C4⋊C4C23×C15111yescharacteristic
371C2×C4⋊C4C23×C15111yescharacteristic
372C2×C4⋊C4C23×C15111yescharacteristic
373C2×C4⋊C4C23×C15111yescharacteristic
374C2×C4⋊C4C23×C15111yescharacteristic
375C2×C22⋊C4—21no—
376C2×C22⋊C4—21no—
377C2×C22⋊C4—21no—
378C2×C22⋊C4—21no—
379C2×C22⋊C4—21no—
380C2×C42—21no—
381C2×C42—21no—
382C2×C42—21no—
383C2×C42C23×C15111yescharacteristic
384C2×C42C23×C15111yescharacteristic
385C2×C42C23×C15111yescharacteristic
386#107—22no—
387#106—22no—
388#106—22no—
389#106—22no—
390C4⋊C8—22no—
391C4⋊C8—22no—
392#102—22no—
393#102—22no—
394#102—22no—
395#102—22no—
396#97—22no—
397C4×C8—22no—
398#95—21no—
399#95—21no—
400#95—21no—
401#95—21no—
402#95—21no—
403#95—21no—
404#95—21no—
405#95—21no—
406#95—21no—
407#95D4×C15111yescharacteristic
408#95D4×C15111yescharacteristic
409#95D4×C15111yescharacteristic
410#95D4×C15111yescharacteristic
411C24—21no—
412C2×Q8—24no—
413C2×Q8—81no—
414C2×Q8—81no—
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—81no—
430C22×C4—81no—
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—21no—
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—81no—
463C4⋊C4—81no—
464C4⋊C4—81no—
465C4⋊C4—81no—
466C4⋊C4C2×Q8×C15112yes—
467C4⋊C4#41×C15112yes—
468C4⋊C4#41×C15112yes—
469C22⋊C4—24no—
470C22⋊C4—81no—
471C22⋊C4—81no—
472C22⋊C4—81no—
473C22⋊C4—81no—
474C42—21no—
475C42—21no—
476C42—21no—
477C42—21no—
478C42—81no—
479C42—81no—
480C42—81no—
481C42C2×Q8×C15112yes—
482C42#41×C15112yes—
483C23—22no—
484C23—41no—
485C23—41no—
486C23—41no—
487C23—41no—
488C23—41no—
489C23—41no—
490C23C22×D4×C15111yescharacteristic
491Q8—84no—
492D4—22no—
493D4—22no—
494D4—41no—
495D4—41no—
496C2×C4—21no—
497C2×C4—21no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—22no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—22no—
504C2×C4—22no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
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×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—84no—
534C2×C4C22⋊Q8×C15112yes—
535C2×C4C22⋊Q8×C15112yes—
536C2×C4C22×Q8×C15111yescharacteristic
537C2×C4C2×#41×C15111yescharacteristic
538C2×C4C2×#41×C15111yescharacteristic
539C2×C4C2×#41×C15111yescharacteristic
540C2×C4C2×#41×C15111yescharacteristic
541C2×C4C2×#41×C15111yescharacteristic
542C8—22no—
543C8—22no—
544C8—41no—
545C8—41no—
546C22—42no—
547C22—42no—
548C22—42no—
549C22—81no—
550C22—81no—
551C22—81no—
552C22—81no—
553C22C2×C22⋊Q8×C15111yescharacteristic
554C22#525×C15111yescharacteristic
555C22#532×C15111yescharacteristic
556C22#576×C15111yescharacteristic
557C22#577×C15111yescharacteristic
558C22#577×C15111yescharacteristic
559C22#577×C15111yescharacteristic
560C4—22no—
561C4—22no—
562C4—41no—
563C4—42no—
564C4—42no—
565C4—41no—
566C4—41no—
567C4—41no—
568C4—42no—
569C4—81no—
570C4—81no—
571C4—81no—
572C4—81no—
573C4#529×C15111yescharacteristic
574C4#529×C15111yescharacteristic
575C4#533×C15111yescharacteristic
576C4#533×C15111yescharacteristic
577C2—82no—
578C2#2396×C15111yescharacteristic
579C2#3081×C15111yescharacteristic
580C2#3084×C15111yescharacteristic
581C2#3118×C15111yescharacteristic
582C2#3126×C15111yescharacteristic
583C2#3173×C15111yescharacteristic
584C2#3179×C15111yescharacteristic
subgroupG/H
center, socleC23×C151C22×D4
commutator, Frattini, cosocleC22×C4C24×C151
prime radicalC22×D4×C151C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C151 ◁ #376×C151 ◁ G

Complements

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

NH ≅ G/Ntype
1. #2331×C151C2semidirect
3. #2101×C151C2semidirect
5. #2088×C151C2semidirect
6. #2086×C151C2semidirect
9. #2058×C151C2semidirect
11. #1776×C151C2semidirect
12. C4×#106×C151C2semidirect
13. #1768×C151C2semidirect
69. C4×D4×C151Q8semidirect
292. #23786C151direct (N × H)
293. C151#23786direct (N × H)
294. #2331C2×C151semidirect
296. #2101C2×C151semidirect
298. #2088C2×C151semidirect
299. #2086C2×C151semidirect
302. #2058C2×C151semidirect
304. #1776C2×C151semidirect
305. C4×#106C2×C151semidirect
306. #1768C2×C151semidirect
362. C4×D4Q8×C151semidirect

Maximal subgroups

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

subgroupindex
#2331×C1512
#2319×C1512
#2101×C1512
#2092×C1512
#2088×C1512
#2086×C1512
#2065×C1512
#2058×C1512
#2023×C1512
#1776×C1512
C4×#106×C1512
#1768×C1512
#1762×C1512
C4×#102×C1512
#23786151