Finite Group Databasebeta

← C151×#19314 #50324239

Subgroups — C151×#19314 #50324239

Order 38656.

630 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3165×C151C211yesmaximal, characteristic, complemented
2#3116×C151C211yesmaximal, characteristic
3#3039×C151C211yesmaximal, characteristic
4#2970×C151C211yesmaximal, characteristic
5#1694×C151C212yesmaximal, complemented
6#1692×C151C212yesmaximal, complemented
7#1673×C151C212yesmaximal, complemented
8#1671×C151C212yesmaximal, complemented
9#1569×C151C211yesmaximal, characteristic, complemented
10#1559×C151C211yesmaximal, characteristic, complemented
11#1556×C151C211yesmaximal, characteristic, complemented
12C2×#137×C151—21no—
13#533×C151C2211yescharacteristic
14C2×C4⋊Q8×C151C2211yescharacteristic
15C4×#41×C151C2211yescharacteristic
16#501×C151—21no—
17#501×C151—21no—
18#500×C151C2212yes—
19#498×C151C2212yes—
20#485×C151—21no—
21#477×C151C2211yescharacteristic
22#476×C151C2211yescharacteristic
23#462×C151—21no—
24#462×C151C2211yescharacteristic
25#462×C151C2212yes—
26#461×C151—21no—
27#461×C151C2211yescharacteristic
28#461×C151C2212yes—
29#452×C151—21no—
30#446×C151C2212yes—
31#441×C151—21no—
32#440×C151—21no—
33#435×C151—22no—
34C8×D4×C151C2212yes—
35#432×C151—21no—
36#432×C151C2211yescharacteristic
37#432×C151C2211yescharacteristic
38#428×C151—22no—
39#423×C151C2211yescharacteristic
40#419×C151—21no—
41C4×M16×C151C2211yescharacteristic
42C2×#97×C151—21no—
43#335×C151C2212yes—
44#334×C151C2212yes—
45#333×C151C2212yes—
46#332×C151C2212yes—
47#332×C151C2212yes—
48#332×C151C2212yes—
49C2×#41×C151D411yescharacteristic
50C22×Q8×C151—21no—
51#137×C151—44no—
52C2×Q16×C151—21no—
53C2×Q16×C151—22no—
54C2×SD16×C151—21no—
55C2×SD16×C151—22no—
56C2×M16×C151—21no—
57C2×M16×C151D412yes—
58C22×C8×C151—22no—
59C4⋊Q8×C151—21no—
60C4⋊Q8×C151—21no—
61C4⋊Q8×C151—21no—
62C4⋊Q8×C151C2312yes—
63C4⋊Q8×C151C2311yescharacteristic
64C4⋊Q8×C151C2311yescharacteristic
65#125×C151—21no—
66C22⋊Q8×C151—21no—
67C22⋊Q8×C151—21no—
68C4×Q8×C151—21no—
69C4×Q8×C151—21no—
70C4×Q8×C151D411yescharacteristic
71C4×Q8×C151C2311yescharacteristic
72C4×D4×C151—21no—
73C4×D4×C151—21no—
74C4×D4×C151D411yescharacteristic
75C4×D4×C151C2311yescharacteristic
76#117×C151—21no—
77#117×C151—21no—
78#117×C151D411yescharacteristic
79C2×C4⋊C4×C151—21no—
80C2×C4⋊C4×C151—21no—
81C2×C42×C151—21no—
82C2×C42×C151C2311yescharacteristic
83#107×C151—22no—
84#107×C151—22no—
85#107×C151—21no—
86#106×C151—22no—
87#106×C151—22no—
88#106×C151—21no—
89C4⋊C8×C151—22no—
90C4⋊C8×C151—21no—
91C4⋊C8×C151C2312yes—
92C4⋊C8×C151C2312yes—
93C4⋊C8×C151C2311yescharacteristic
94C4⋊C8×C151C2311yescharacteristic
95#103×C151—22no—
96#103×C151—22no—
97#103×C151—21no—
98#103×C151—21no—
99#103×C151—21no—
100#102×C151—21no—
101C22⋊C8×C151—21no—
102C22⋊C8×C151—21no—
103C22⋊C8×C151—22no—
104#97×C151—22no—
105#97×C151—21no—
106#97×C151—21no—
107#97×C151D411yescharacteristic
108#97×C151D411yescharacteristic
109C4×C8×C151C2312yes—
110#41×C151—22no—
111#41×C151—41no—
112C2×Q8×C151—21no—
113C2×Q8×C151—22no—
114C2×Q8×C151—21no—
115C2×Q8×C151—42no—
116C2×Q8×C151—42no—
117C2×Q8×C151—41no—
118C2×Q8×C151C2×D411yescharacteristic
119C2×D4×C151—21no—
120C2×D4×C151C2×D411yescharacteristic
121C22×C4×C151—21no—
122C22×C4×C151—21no—
123C22×C4×C151—21no—
124C22×C4×C151—41no—
125C22×C4×C151C2×D411yescharacteristic
126C22×C4×C151C2×D411yescharacteristic
127C22×C4×C151#4111yescharacteristic
128Q16×C151—42no—
129Q16×C151—44no—
130SD16×C151—42no—
131SD16×C151—44no—
132M16×C151—24no—
133M16×C151—42no—
134C2×C8×C151—22no—
135C2×C8×C151—21no—
136C2×C8×C151—21no—
137C2×C8×C151—22no—
138C2×C8×C151—44no—
139C2×C8×C151C2×D412yes—
140C2×C8×C151C2×D412yes—
141C4⋊C4×C151—21no—
142C4⋊C4×C151—21no—
143C4⋊C4×C151—21no—
144C4⋊C4×C151—21no—
145C4⋊C4×C151—22no—
146C4⋊C4×C151—21no—
147C4⋊C4×C151—22no—
148C4⋊C4×C151—21no—
149C4⋊C4×C151—41no—
150C4⋊C4×C151—41no—
151C4⋊C4×C151—41no—
152C4⋊C4×C151—41no—
153C4⋊C4×C151C2×D411yescharacteristic
154C4⋊C4×C151C2×D411yescharacteristic
155C22⋊C4×C151—21no—
156C22⋊C4×C151—21no—
157C22⋊C4×C151—21no—
158C22⋊C4×C151—41no—
159C42×C151—21no—
160C42×C151—21no—
161C42×C151—21no—
162C42×C151—41no—
163C42×C151C2×D411yescharacteristic
164C42×C151C2×D411yescharacteristic
165C42×C151#4111yescharacteristic
166C42×C151C2411yescharacteristic
167C23×C151—21no—
168C23×C151#12111yescharacteristic
169Q8×C151—21no—
170Q8×C151—21no—
171Q8×C151—42no—
172Q8×C151—41no—
173Q8×C151—42no—
174Q8×C151—41no—
175Q8×C151—81no—
176Q8×C151—82no—
177D4×C151—21no—
178D4×C151—42no—
179D4×C151AGL(1,ℤ/8)12yes—
180C2×C4×C151—21no—
181C2×C4×C151—22no—
182C2×C4×C151—21no—
183C2×C4×C151—21no—
184C2×C4×C151—21no—
185C2×C4×C151—21no—
186C2×C4×C151—41no—
187C2×C4×C151—42no—
188C2×C4×C151—42no—
189C2×C4×C151—42no—
190C2×C4×C151—41no—
191C2×C4×C151—41no—
192C2×C4×C151—81no—
193C2×C4×C151—82no—
194C2×C4×C151#12111yescharacteristic
195C2×C4×C151#12111yescharacteristic
196C2×C4×C151#12111yescharacteristic
197C2×C4×C151C22×D411yescharacteristic
198C2×C4×C151C22×D411yescharacteristic
199C2×C4×C151C2×#4111yescharacteristic
200C8×C151—22no—
201C8×C151—42no—
202C8×C151—41no—
203C8×C151—42no—
204C8×C151—41no—
205C8×C151#13714yescomplemented
206C22×C151—21no—
207C22×C151—21no—
208C22×C151—22no—
209C22×C151—21no—
210C22×C151—41no—
211C22×C151—41no—
212C22×C151C2×#12111yescharacteristic
213C4×C151—21no—
214C4×C151—21no—
215C4×C151—21no—
216C4×C151—21no—
217C4×C151—41no—
218C4×C151—41no—
219C4×C151—41no—
220C4×C151—82no—
221C4×C151—81no—
222C4×C151—81no—
223C4×C151C2×AGL(1,ℤ/8)11yescharacteristic
224C4×C151C2×#13712yes—
225C4×C151#57511yescharacteristic
226C2×C151—41no—
227C2×C151—42no—
228C2×C151#303911yescharacteristic
229C2×C151#305511yescharacteristic
230C2×C151#306911yescharacteristic
231#19314C15111yesmaximal, characteristic, direct product factor, Sylow
232C151#1931411yescharacteristic, direct product factor, Sylow
233#3165C2×C15111yescharacteristic, complemented
234#3116C2×C15111yescharacteristic
235#3039C2×C15111yescharacteristic
236#2970C2×C15111yescharacteristic
237#1694C2×C15112yescomplemented
238#1692C2×C15112yescomplemented
239#1673C2×C15112yescomplemented
240#1671C2×C15112yescomplemented
241#1569C2×C15111yescharacteristic, complemented
242#1559C2×C15111yescharacteristic, complemented
243#1556C2×C15111yescharacteristic, complemented
244C2×#137—21no—
245#533C22×C15111yescharacteristic
246C2×C4⋊Q8C22×C15111yescharacteristic
247C4×#41C22×C15111yescharacteristic
248#501—21no—
249#501—21no—
250#500C22×C15112yes—
251#498C22×C15112yes—
252#485—21no—
253#477C22×C15111yescharacteristic
254#476C22×C15111yescharacteristic
255#462—21no—
256#462C22×C15111yescharacteristic
257#462C22×C15112yes—
258#461—21no—
259#461C22×C15111yescharacteristic
260#461C22×C15112yes—
261#452—21no—
262#446C22×C15112yes—
263#441—21no—
264#440—21no—
265#435—22no—
266C8×D4C22×C15112yes—
267#432—21no—
268#432C22×C15111yescharacteristic
269#432C22×C15111yescharacteristic
270#428—22no—
271#423C22×C15111yescharacteristic
272#419—21no—
273C4×M16C22×C15111yescharacteristic
274C2×#97—21no—
275#335C22×C15112yes—
276#334C22×C15112yes—
277#333C22×C15112yes—
278#332C22×C15112yes—
279#332C22×C15112yes—
280#332C22×C15112yes—
281C2×#41D4×C15111yescharacteristic
282C22×Q8—21no—
283#137—44no—
284C2×Q16—22no—
285C2×Q16—21no—
286C2×SD16—22no—
287C2×SD16—21no—
288C2×M16—21no—
289C2×M16D4×C15112yes—
290C22×C8—22no—
291C4⋊Q8—21no—
292C4⋊Q8—21no—
293C4⋊Q8—21no—
294C4⋊Q8C23×C15112yes—
295C4⋊Q8C23×C15111yescharacteristic
296C4⋊Q8C23×C15111yescharacteristic
297#125—21no—
298C22⋊Q8—21no—
299C22⋊Q8—21no—
300C4×Q8—21no—
301C4×Q8—21no—
302C4×Q8D4×C15111yescharacteristic
303C4×Q8C23×C15111yescharacteristic
304C4×D4—21no—
305C4×D4—21no—
306C4×D4D4×C15111yescharacteristic
307C4×D4C23×C15111yescharacteristic
308#117—21no—
309#117—21no—
310#117D4×C15111yescharacteristic
311C2×C4⋊C4—21no—
312C2×C4⋊C4—21no—
313C2×C42—21no—
314C2×C42C23×C15111yescharacteristic
315#107—22no—
316#107—22no—
317#107—21no—
318#106—22no—
319#106—22no—
320#106—21no—
321C4⋊C8—22no—
322C4⋊C8—21no—
323C4⋊C8C23×C15112yes—
324C4⋊C8C23×C15111yescharacteristic
325C4⋊C8C23×C15111yescharacteristic
326C4⋊C8C23×C15112yes—
327#103—21no—
328#103—22no—
329#103—22no—
330#103—21no—
331#103—21no—
332#102—21no—
333C22⋊C8—21no—
334C22⋊C8—21no—
335C22⋊C8—22no—
336#97—22no—
337#97—21no—
338#97—21no—
339#97D4×C15111yescharacteristic
340#97D4×C15111yescharacteristic
341C4×C8C23×C15112yes—
342#41—22no—
343#41—41no—
344C2×Q8—21no—
345C2×Q8—22no—
346C2×Q8—21no—
347C2×Q8—42no—
348C2×Q8—42no—
349C2×Q8—41no—
350C2×Q8C2×D4×C15111yescharacteristic
351C2×D4—21no—
352C2×D4C2×D4×C15111yescharacteristic
353C22×C4—21no—
354C22×C4—21no—
355C22×C4—21no—
356C22×C4—41no—
357C22×C4C2×D4×C15111yescharacteristic
358C22×C4C2×D4×C15111yescharacteristic
359C22×C4#41×C15111yescharacteristic
360Q16—44no—
361Q16—42no—
362SD16—44no—
363SD16—42no—
364M16—24no—
365M16—42no—
366C2×C8—22no—
367C2×C8—21no—
368C2×C8—21no—
369C2×C8—22no—
370C2×C8—44no—
371C2×C8C2×D4×C15112yes—
372C2×C8C2×D4×C15112yes—
373C4⋊C4—21no—
374C4⋊C4—21no—
375C4⋊C4—21no—
376C4⋊C4—21no—
377C4⋊C4—22no—
378C4⋊C4—21no—
379C4⋊C4—22no—
380C4⋊C4—21no—
381C4⋊C4—41no—
382C4⋊C4—41no—
383C4⋊C4—41no—
384C4⋊C4—41no—
385C4⋊C4C2×D4×C15111yescharacteristic
386C4⋊C4C2×D4×C15111yescharacteristic
387C22⋊C4—21no—
388C22⋊C4—21no—
389C22⋊C4—21no—
390C22⋊C4—41no—
391C42—21no—
392C42—21no—
393C42—21no—
394C42—41no—
395C42C2×D4×C15111yescharacteristic
396C42C2×D4×C15111yescharacteristic
397C42#41×C15111yescharacteristic
398C42C24×C15111yescharacteristic
399C23—21no—
400C23#121×C15111yescharacteristic
401Q8—21no—
402Q8—21no—
403Q8—42no—
404Q8—41no—
405Q8—41no—
406Q8—42no—
407Q8—81no—
408Q8—82no—
409D4—21no—
410D4—42no—
411D4AGL(1,ℤ/8)×C15112yes—
412C2×C4—21no—
413C2×C4—22no—
414C2×C4—21no—
415C2×C4—21no—
416C2×C4—21no—
417C2×C4—21no—
418C2×C4—41no—
419C2×C4—42no—
420C2×C4—42no—
421C2×C4—41no—
422C2×C4—41no—
423C2×C4—42no—
424C2×C4—81no—
425C2×C4—82no—
426C2×C4#121×C15111yescharacteristic
427C2×C4#121×C15111yescharacteristic
428C2×C4#121×C15111yescharacteristic
429C2×C4C22×D4×C15111yescharacteristic
430C2×C4C22×D4×C15111yescharacteristic
431C2×C4C2×#41×C15111yescharacteristic
432C8—22no—
433C8—42no—
434C8—41no—
435C8—42no—
436C8—41no—
437C8#137×C15114yescomplemented
438C22—21no—
439C22—21no—
440C22—22no—
441C22—21no—
442C22—41no—
443C22—41no—
444C22C2×#121×C15111yescharacteristic
445C4—21no—
446C4—21no—
447C4—21no—
448C4—21no—
449C4—41no—
450C4—41no—
451C4—41no—
452C4—82no—
453C4—81no—
454C4—81no—
455C4C2×AGL(1,ℤ/8)×C15111yescharacteristic
456C4C2×#137×C15112yes—
457C4#575×C15111yescharacteristic
458C2—41no—
459C2—42no—
460C2#3039×C15111yescharacteristic
461C2#3055×C15111yescharacteristic
462C2#3069×C15111yescharacteristic
subgroupG/H
center, socleC22×C151C2×#121
commutator, Frattini, cosocleC42C24×C151
prime radicalC2×#41×C151D4
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C151 ◁ C2×C42×C151 ◁ G

Complements

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

NH ≅ G/Ntype
1. #3165×C151C2semidirect
5. #1694×C151C2semidirect
6. #1692×C151C2semidirect
7. #1673×C151C2semidirect
8. #1671×C151C2semidirect
9. #1569×C151C2semidirect
10. #1559×C151C2semidirect
11. #1556×C151C2semidirect
205. C8×C151#137semidirect
231. #19314C151direct (N × H)
232. C151#19314direct (N × H)
233. #3165C2×C151semidirect
237. #1694C2×C151semidirect
238. #1692C2×C151semidirect
239. #1673C2×C151semidirect
240. #1671C2×C151semidirect
241. #1569C2×C151semidirect
242. #1559C2×C151semidirect
243. #1556C2×C151semidirect
437. C8#137×C151semidirect

Maximal subgroups

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

subgroupindex
#3165×C1512
#3116×C1512
#3039×C1512
#2970×C1512
#1694×C1512
#1692×C1512
#1673×C1512
#1671×C1512
#1569×C1512
#1559×C1512
#1556×C1512
#19314151