Finite Group Databasebeta

← C151×#19385 #50324310

Subgroups — C151×#19385 #50324310

Order 38656.

708 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3206×C151C211yesmaximal, characteristic, complemented
2C2×#474×C151C211yesmaximal, characteristic, complemented
3#3036×C151C211yesmaximal, characteristic
4#2972×C151C211yesmaximal, characteristic, complemented
5#1679×C151C214yesmaximal, complemented
6#1665×C151C214yesmaximal, complemented
7#1570×C151C211yesmaximal, characteristic, complemented
8#1549×C151C211yesmaximal, characteristic, complemented
9#1540×C151C211yesmaximal, characteristic, complemented
10C2×AGL(1,ℤ/8)×C151—21no—
11#532×C151C2211yescharacteristic
12C2×C4⋊Q8×C151C2211yescharacteristic
13C2×C4×D4×C151C2211yescharacteristic
14#492×C151C2212yescomplemented
15#487×C151C2212yescomplemented
16#474×C151—22no—
17#474×C151C2214yes—
18#463×C151—22no—
19#461×C151—22no—
20#461×C151C2212yes—
21#459×C151C2212yes—
22#448×C151—22no—
23C8×D4×C151—22no—
24C8×D4×C151C2214yes—
25#431×C151C2211yescharacteristic
26#431×C151C2211yescharacteristic
27C2×#107×C151—21no—
28#423×C151C2211yescharacteristic
29C2×C4⋊C8×C151C2211yescharacteristic
30#417×C151—21no—
31C2×#102×C151—21no—
32C2×C22⋊C8×C151—22no—
33#334×C151C2214yescomplemented
34#332×C151C2214yescomplemented
35#332×C151C2212yescomplemented
36#331×C151C2212yescomplemented
37C2×#41×C151—21no—
38C22×Q8×C151—21no—
39C22×D4×C151D411yescharacteristic
40C23×C4×C151—21no—
41AGL(1,ℤ/8)×C151—44no—
42C2×SD16×C151—22no—
43C2×SD16×C151—24no—
44C2×D8×C151—22no—
45C2×M16×C151—21no—
46C22×C8×C151—21no—
47C22×C8×C151—24no—
48C4⋊Q8×C151—21no—
49C4⋊Q8×C151—21no—
50C4⋊Q8×C151—21no—
51C4⋊Q8×C151C2311yescharacteristic
52C4⋊Q8×C151C2312yes—
53#127×C151C2311yescharacteristic
54#124×C151—21no—
55#121×C151—21no—
56#121×C151—21no—
57C4×D4×C151—21no—
58C4×D4×C151—21no—
59C4×D4×C151—21no—
60C4×D4×C151—21no—
61C4×D4×C151D412yes—
62C4×D4×C151C2312yes—
63C2×C4⋊C4×C151—21no—
64C2×C4⋊C4×C151—21no—
65C2×C4⋊C4×C151D411yescharacteristic
66C2×C22⋊C4×C151—21no—
67C2×C42×C151C2311yescharacteristic
68#107×C151—24no—
69C4⋊C8×C151—21no—
70C4⋊C8×C151—21no—
71C4⋊C8×C151D412yes—
72C4⋊C8×C151C2312yes—
73C4⋊C8×C151C2312yes—
74C4⋊C8×C151C2312yes—
75#103×C151—24no—
76#103×C151—22no—
77#102×C151—24no—
78#102×C151—22no—
79C22⋊C8×C151—21no—
80C22⋊C8×C151—24no—
81C22⋊C8×C151D412yes—
82C4×C8×C151—21no—
83C4×C8×C151C2312yes—
84C24×C151—21no—
85#41×C151—42no—
86#41×C151—42no—
87C2×Q8×C151—21no—
88C2×Q8×C151—22no—
89C2×Q8×C151—41no—
90C2×Q8×C151—82no—
91C2×D4×C151—21no—
92C2×D4×C151—22no—
93C2×D4×C151—21no—
94C2×D4×C151—21no—
95C2×D4×C151—21no—
96C2×D4×C151—41no—
97C2×D4×C151SD1614yescomplemented
98C2×D4×C151C2×D412yes—
99C22×C4×C151—21no—
100C22×C4×C151—22no—
101C22×C4×C151—22no—
102C22×C4×C151—41no—
103C22×C4×C151—41no—
104C22×C4×C151—82no—
105C22×C4×C151C2×D411yescharacteristic
106C22×C4×C151C2×D411yescharacteristic
107C22×C4×C151#4111yescharacteristic
108SD16×C151—44no—
109SD16×C151—84no—
110D8×C151—44no—
111M16×C151—42no—
112C2×C8×C151—22no—
113C2×C8×C151—22no—
114C2×C8×C151—22no—
115C2×C8×C151—42no—
116C2×C8×C151—84no—
117C2×C8×C151C2×D414yes—
118C4⋊C4×C151—21no—
119C4⋊C4×C151—22no—
120C4⋊C4×C151—21no—
121C4⋊C4×C151—22no—
122C4⋊C4×C151—21no—
123C4⋊C4×C151—41no—
124C4⋊C4×C151—41no—
125C4⋊C4×C151C2×D412yes—
126C22⋊C4×C151—22no—
127C22⋊C4×C151—22no—
128C22⋊C4×C151—41no—
129C22⋊C4×C151—41no—
130C42×C151C2×D411yescharacteristic
131C42×C151C2×D411yescharacteristic
132C42×C151#4111yescharacteristic
133C42×C151C2411yescharacteristic
134C23×C151—22no—
135C23×C151—24no—
136C23×C151—41no—
137C23×C151—81no—
138C23×C151—81no—
139C23×C151#12111yescharacteristic
140Q8×C151—41no—
141Q8×C151—41no—
142Q8×C151—44no—
143Q8×C151—82no—
144D4×C151—22no—
145D4×C151—24no—
146D4×C151—41no—
147D4×C151—41no—
148D4×C151—42no—
149D4×C151—81no—
150D4×C151—82no—
151D4×C151C2×SD1614yes—
152C2×C4×C151—22no—
153C2×C4×C151—22no—
154C2×C4×C151—41no—
155C2×C4×C151—44no—
156C2×C4×C151—42no—
157C2×C4×C151—41no—
158C2×C4×C151—82no—
159C2×C4×C151—81no—
160C2×C4×C151—82no—
161C2×C4×C151—82no—
162C2×C4×C151#12111yescharacteristic
163C2×C4×C151#12111yescharacteristic
164C2×C4×C151#12111yescharacteristic
165C2×C4×C151C2×SD1612yes—
166C2×C4×C151#13512yes—
167C2×C4×C151C22×D411yescharacteristic
168C2×C4×C151C22×D411yescharacteristic
169C2×C4×C151C2×#4111yescharacteristic
170C8×C151—24no—
171C8×C151—42no—
172C8×C151—42no—
173C8×C151—42no—
174C22×C151—21no—
175C22×C151—21no—
176C22×C151—24no—
177C22×C151—42no—
178C22×C151—42no—
179C22×C151—84no—
180C22×C151—81no—
181C22×C151—81no—
182C22×C151—81no—
183C22×C151#46512yes—
184C22×C151C2×#12111yescharacteristic
185C4×C151—21no—
186C4×C151—21no—
187C4×C151—21no—
188C4×C151—42no—
189C4×C151—82no—
190C4×C151—81no—
191C4×C151#46512yes—
192C4×C151C22×SD1611yescharacteristic
193C4×C151C2×#13511yescharacteristic
194C4×C151#57612yes—
195C2×C151—22no—
196C2×C151—44no—
197C2×C151—161no—
198C2×C151#304111yescharacteristic
199C2×C151C2×#46511yescharacteristic
200C2×C151#306911yescharacteristic
201#19385C15111yesmaximal, characteristic, direct product factor, Sylow
202C151#1938511yescharacteristic, direct product factor, Sylow
203#3206C2×C15111yescharacteristic, complemented
204C2×#474C2×C15111yescharacteristic, complemented
205#3036C2×C15111yescharacteristic
206#2972C2×C15111yescharacteristic, complemented
207#1679C2×C15114yescomplemented
208#1665C2×C15114yescomplemented
209#1570C2×C15111yescharacteristic, complemented
210#1549C2×C15111yescharacteristic, complemented
211#1540C2×C15111yescharacteristic, complemented
212C2×AGL(1,ℤ/8)—21no—
213#532C22×C15111yescharacteristic
214C2×C4⋊Q8C22×C15111yescharacteristic
215C2×C4×D4C22×C15111yescharacteristic
216#492C22×C15112yescomplemented
217#487C22×C15112yescomplemented
218#474—22no—
219#474C22×C15114yes—
220#463—22no—
221#461—22no—
222#461C22×C15112yes—
223#459C22×C15112yes—
224#448—22no—
225C8×D4—22no—
226C8×D4C22×C15114yes—
227#431C22×C15111yescharacteristic
228#431C22×C15111yescharacteristic
229C2×#107—21no—
230#423C22×C15111yescharacteristic
231C2×C4⋊C8C22×C15111yescharacteristic
232#417—21no—
233C2×#102—21no—
234C2×C22⋊C8—22no—
235#334C22×C15114yescomplemented
236#332C22×C15112yescomplemented
237#332C22×C15114yescomplemented
238#331C22×C15112yescomplemented
239C2×#41—21no—
240C22×Q8—21no—
241C22×D4D4×C15111yescharacteristic
242C23×C4—21no—
243AGL(1,ℤ/8)—44no—
244C2×SD16—22no—
245C2×SD16—24no—
246C2×D8—22no—
247C2×M16—21no—
248C22×C8—21no—
249C22×C8—24no—
250C4⋊Q8—21no—
251C4⋊Q8—21no—
252C4⋊Q8—21no—
253C4⋊Q8C23×C15112yes—
254C4⋊Q8C23×C15111yescharacteristic
255#127C23×C15111yescharacteristic
256#124—21no—
257#121—21no—
258#121—21no—
259C4×D4—21no—
260C4×D4—21no—
261C4×D4—21no—
262C4×D4—21no—
263C4×D4D4×C15112yes—
264C4×D4C23×C15112yes—
265C2×C4⋊C4—21no—
266C2×C4⋊C4—21no—
267C2×C4⋊C4D4×C15111yescharacteristic
268C2×C22⋊C4—21no—
269C2×C42C23×C15111yescharacteristic
270#107—24no—
271C4⋊C8—21no—
272C4⋊C8—21no—
273C4⋊C8D4×C15112yes—
274C4⋊C8C23×C15112yes—
275C4⋊C8C23×C15112yes—
276C4⋊C8C23×C15112yes—
277#103—24no—
278#103—22no—
279#102—24no—
280#102—22no—
281C22⋊C8—21no—
282C22⋊C8—24no—
283C22⋊C8D4×C15112yes—
284C4×C8—21no—
285C4×C8C23×C15112yes—
286C24—21no—
287#41—42no—
288#41—42no—
289C2×Q8—21no—
290C2×Q8—22no—
291C2×Q8—41no—
292C2×Q8—82no—
293C2×D4—21no—
294C2×D4—22no—
295C2×D4—21no—
296C2×D4—21no—
297C2×D4—21no—
298C2×D4—41no—
299C2×D4SD16×C15114yescomplemented
300C2×D4C2×D4×C15112yes—
301C22×C4—21no—
302C22×C4—22no—
303C22×C4—22no—
304C22×C4—41no—
305C22×C4—41no—
306C22×C4—82no—
307C22×C4C2×D4×C15111yescharacteristic
308C22×C4C2×D4×C15111yescharacteristic
309C22×C4#41×C15111yescharacteristic
310SD16—44no—
311SD16—84no—
312D8—44no—
313M16—42no—
314C2×C8—22no—
315C2×C8—22no—
316C2×C8—22no—
317C2×C8—42no—
318C2×C8—84no—
319C2×C8C2×D4×C15114yes—
320C4⋊C4—21no—
321C4⋊C4—22no—
322C4⋊C4—21no—
323C4⋊C4—22no—
324C4⋊C4—21no—
325C4⋊C4—41no—
326C4⋊C4—41no—
327C4⋊C4C2×D4×C15112yes—
328C22⋊C4—22no—
329C22⋊C4—22no—
330C22⋊C4—41no—
331C22⋊C4—41no—
332C42C2×D4×C15111yescharacteristic
333C42C2×D4×C15111yescharacteristic
334C42#41×C15111yescharacteristic
335C42C24×C15111yescharacteristic
336C23—22no—
337C23—24no—
338C23—41no—
339C23—81no—
340C23—81no—
341C23#121×C15111yescharacteristic
342Q8—41no—
343Q8—41no—
344Q8—44no—
345Q8—82no—
346D4—24no—
347D4—22no—
348D4—41no—
349D4—41no—
350D4—42no—
351D4—81no—
352D4—82no—
353D4C2×SD16×C15114yes—
354C2×C4—22no—
355C2×C4—22no—
356C2×C4—41no—
357C2×C4—44no—
358C2×C4—41no—
359C2×C4—42no—
360C2×C4—82no—
361C2×C4—81no—
362C2×C4—82no—
363C2×C4—82no—
364C2×C4#121×C15111yescharacteristic
365C2×C4#121×C15111yescharacteristic
366C2×C4#121×C15111yescharacteristic
367C2×C4C2×SD16×C15112yes—
368C2×C4#135×C15112yes—
369C2×C4C22×D4×C15111yescharacteristic
370C2×C4C22×D4×C15111yescharacteristic
371C2×C4C2×#41×C15111yescharacteristic
372C8—24no—
373C8—42no—
374C8—42no—
375C8—42no—
376C22—21no—
377C22—21no—
378C22—24no—
379C22—42no—
380C22—42no—
381C22—84no—
382C22—81no—
383C22—81no—
384C22—81no—
385C22#465×C15112yes—
386C22C2×#121×C15111yescharacteristic
387C4—21no—
388C4—21no—
389C4—21no—
390C4—42no—
391C4—82no—
392C4—81no—
393C4#465×C15112yes—
394C4C22×SD16×C15111yescharacteristic
395C4C2×#135×C15111yescharacteristic
396C4#576×C15112yes—
397C2—22no—
398C2—44no—
399C2—161no—
400C2#3041×C15111yescharacteristic
401C2C2×#465×C15111yescharacteristic
402C2#3069×C15111yescharacteristic
subgroupG/H
center, socleC22×C151C2×#121
commutator, Frattini, cosocleC42C24×C151
prime radical#3036×C151C2
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. #3206×C151C2semidirect
2. C2×#474×C151C2semidirect
4. #2972×C151C2semidirect
5. #1679×C151C2semidirect
6. #1665×C151C2semidirect
7. #1570×C151C2semidirect
8. #1549×C151C2semidirect
9. #1540×C151C2semidirect
14. #492×C151C22semidirect
15. #487×C151C22semidirect
33. #334×C151C22semidirect
34. #332×C151C22semidirect
35. #332×C151C22semidirect
36. #331×C151C22semidirect
97. C2×D4×C151SD16semidirect
201. #19385C151direct (N × H)
202. C151#19385direct (N × H)
203. #3206C2×C151semidirect
204. C2×#474C2×C151semidirect
206. #2972C2×C151semidirect
207. #1679C2×C151semidirect
208. #1665C2×C151semidirect
209. #1570C2×C151semidirect
210. #1549C2×C151semidirect
211. #1540C2×C151semidirect
216. #492C22×C151semidirect
217. #487C22×C151semidirect
235. #334C22×C151semidirect
236. #332C22×C151semidirect
237. #332C22×C151semidirect
238. #331C22×C151semidirect
299. C2×D4SD16×C151semidirect

Maximal subgroups

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

subgroupindex
#3206×C1512
C2×#474×C1512
#3036×C1512
#2972×C1512
#1679×C1512
#1665×C1512
#1570×C1512
#1549×C1512
#1540×C1512
#19385151