Finite Group Databasebeta

← C2×#1660×C151 #50323908

Subgroups — C2×#1660×C151 #50323908

Order 38656.

958 conjugacy classes of subgroups.

The subgroup lattice has 338 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#563×C151C211yesmaximal, characteristic
2C2×#501×C151C212yesmaximal, complemented
3C2×#497×C151C211yesmaximal, characteristic
4#1660×C151C218yesmaximal, direct product factor
5C2×#330×C151C212yesmaximal, complemented
6C2×#329×C151C211yesmaximal, characteristic
7C22×Q16×C151—21no—
8C22×SD16×C151—21no—
9#563×C151—24no—
10#563×C151—22no—
11#563×C151C2214yes—
12C2×C4⋊Q8×C151—21no—
13C2×C4⋊Q8×C151C2211yescharacteristic
14C2×#126×C151—22no—
15C2×#125×C151C2212yes—
16C2×#124×C151C2211yescharacteristic
17C2×#123×C151—21no—
18C2×C22⋊Q8×C151—22no—
19#501×C151—24no—
20#501×C151C2218yescomplemented
21#497×C151—22no—
22#497×C151C2214yes—
23C2×#107×C151—22no—
24C2×#106×C151—22no—
25C2×#97×C151C2211yescharacteristic
26C2×#97×C151C2212yes—
27#330×C151C2218yescomplemented
28#329×C151C2214yes—
29C22×Q8×C151—21no—
30C22×Q8×C151—21no—
31C22×Q8×C151D411yescharacteristic
32C22×D4×C151D411yescharacteristic
33C23×C4×C151—21no—
34C2×Q16×C151—24no—
35C2×Q16×C151—44no—
36C2×SD16×C151—24no—
37C2×SD16×C151—44no—
38C22×C8×C151—22no—
39C22×C8×C151—21no—
40C4⋊Q8×C151—24no—
41C4⋊Q8×C151—21no—
42C4⋊Q8×C151—24no—
43C4⋊Q8×C151—22no—
44C4⋊Q8×C151C2312yes—
45#126×C151—28no—
46#126×C151—28no—
47#125×C151—22no—
48#125×C151—22no—
49#125×C151D414yes—
50#125×C151C2314yes—
51#124×C151—22no—
52#124×C151D412yes—
53#124×C151C2312yes—
54#123×C151—24no—
55#123×C151—24no—
56C22⋊Q8×C151—28no—
57C22⋊Q8×C151—28no—
58C2×C4⋊C4×C151—22no—
59C2×C4⋊C4×C151—22no—
60C2×C4⋊C4×C151—22no—
61C2×C4⋊C4×C151—22no—
62C2×C4⋊C4×C151D412yes—
63C2×C4⋊C4×C151D412yes—
64C2×C22⋊C4×C151—22no—
65C2×C22⋊C4×C151—21no—
66C2×C22⋊C4×C151—22no—
67C2×C42×C151—21no—
68C2×C42×C151C2311yescharacteristic
69#107×C151—28no—
70#106×C151—28no—
71#97×C151—21no—
72#97×C151—22no—
73#97×C151C2312yes—
74#97×C151C2314yes—
75C24×C151—21no—
76C2×Q8×C151—24no—
77C2×Q8×C151—21no—
78C2×Q8×C151—22no—
79C2×Q8×C151—42no—
80C2×Q8×C151—42no—
81C2×Q8×C151—42no—
82C2×Q8×C151—41no—
83C2×Q8×C151—82no—
84C2×Q8×C151C2×D412yes—
85C2×D4×C151—21no—
86C2×D4×C151—42no—
87C2×D4×C151C2×D412yes—
88C22×C4×C151—22no—
89C22×C4×C151—21no—
90C22×C4×C151—22no—
91C22×C4×C151—24no—
92C22×C4×C151—41no—
93C22×C4×C151—82no—
94C22×C4×C151C2×D412yes—
95C22×C4×C151C2×D411yescharacteristic
96Q16×C151—48no—
97SD16×C151—48no—
98C2×C8×C151—28no—
99C2×C8×C151—24no—
100C2×C8×C151—24no—
101C2×C8×C151—22no—
102C4⋊C4×C151—28no—
103C4⋊C4×C151—24no—
104C4⋊C4×C151—24no—
105C4⋊C4×C151—22no—
106C4⋊C4×C151—22no—
107C4⋊C4×C151—24no—
108C4⋊C4×C151—24no—
109C4⋊C4×C151—24no—
110C4⋊C4×C151—42no—
111C4⋊C4×C151C2×D414yes—
112C4⋊C4×C151C2×D414yes—
113C22⋊C4×C151—28no—
114C22⋊C4×C151—24no—
115C22⋊C4×C151—24no—
116C22⋊C4×C151—24no—
117C42×C151—24no—
118C42×C151C2×D412yes—
119C42×C151C2×D411yescharacteristic
120C42×C151C2411yescharacteristic
121C23×C151—22no—
122C23×C151—42no—
123C23×C151—44no—
124C23×C151#12011yescharacteristic
125Q8×C151—42no—
126Q8×C151—42no—
127Q8×C151—42no—
128Q8×C151—81no—
129Q8×C151—82no—
130Q8×C151—84no—
131D4×C151—42no—
132D4×C151—81no—
133C2×C4×C151—22no—
134C2×C4×C151—24no—
135C2×C4×C151—22no—
136C2×C4×C151—24no—
137C2×C4×C151—24no—
138C2×C4×C151—42no—
139C2×C4×C151—44no—
140C2×C4×C151—44no—
141C2×C4×C151—42no—
142C2×C4×C151—84no—
143C2×C4×C151—82no—
144C2×C4×C151#12011yescharacteristic
145C2×C4×C151#12012yes—
146C2×C4×C151C22×D411yescharacteristic
147C2×C4×C151C22×D412yes—
148C8×C151—28no—
149C8×C151—24no—
150C22×C151—42no—
151C22×C151—44no—
152C22×C151—84no—
153C22×C151#45312yes—
154C22×C151#45614yes—
155C22×C151C2×#12011yescharacteristic
156C4×C151—21no—
157C4×C151—21no—
158C4×C151—22no—
159C4×C151—22no—
160C4×C151—44no—
161C4×C151—42no—
162C4×C151—44no—
163C4×C151—82no—
164C2×C151—82no—
165C2×C151#166014yesdirect product factor
166C2×C151C2×#45311yescharacteristic
167C2×C151C2×#45612yes—
168C2×#1660C15111yesmaximal, characteristic, direct product factor, Sylow
169C151C2×#166011yescharacteristic, direct product factor, Sylow
170C2×#563C2×C15111yescharacteristic
171C2×#501C2×C15112yescomplemented
172C2×#497C2×C15111yescharacteristic
173#1660C2×C15118yesdirect product factor
174C2×#330C2×C15112yescomplemented
175C2×#329C2×C15111yescharacteristic
176C22×Q16—21no—
177C22×SD16—21no—
178#563—24no—
179#563—22no—
180#563C22×C15114yes—
181C2×C4⋊Q8—21no—
182C2×C4⋊Q8C22×C15111yescharacteristic
183C2×#126—22no—
184C2×#125C22×C15112yes—
185C2×#124C22×C15111yescharacteristic
186C2×#123—21no—
187C2×C22⋊Q8—22no—
188#501—24no—
189#501C22×C15118yescomplemented
190#497—22no—
191#497C22×C15114yes—
192C2×#107—22no—
193C2×#106—22no—
194C2×#97C22×C15111yescharacteristic
195C2×#97C22×C15112yes—
196#330C22×C15118yescomplemented
197#329C22×C15114yes—
198C22×Q8—21no—
199C22×Q8—21no—
200C22×Q8D4×C15111yescharacteristic
201C22×D4D4×C15111yescharacteristic
202C23×C4—21no—
203C2×Q16—24no—
204C2×Q16—44no—
205C2×SD16—24no—
206C2×SD16—44no—
207C22×C8—21no—
208C22×C8—22no—
209C4⋊Q8—24no—
210C4⋊Q8—24no—
211C4⋊Q8—22no—
212C4⋊Q8—21no—
213C4⋊Q8C23×C15112yes—
214#126—28no—
215#126—28no—
216#125—22no—
217#125—22no—
218#125D4×C15114yes—
219#125C23×C15114yes—
220#124—22no—
221#124D4×C15112yes—
222#124C23×C15112yes—
223#123—24no—
224#123—24no—
225C22⋊Q8—28no—
226C22⋊Q8—28no—
227C2×C4⋊C4—22no—
228C2×C4⋊C4—22no—
229C2×C4⋊C4—22no—
230C2×C4⋊C4—22no—
231C2×C4⋊C4D4×C15112yes—
232C2×C4⋊C4D4×C15112yes—
233C2×C22⋊C4—22no—
234C2×C22⋊C4—21no—
235C2×C22⋊C4—22no—
236C2×C42—21no—
237C2×C42C23×C15111yescharacteristic
238#107—28no—
239#106—28no—
240#97—21no—
241#97—22no—
242#97C23×C15114yes—
243#97C23×C15112yes—
244C24—21no—
245C2×Q8—24no—
246C2×Q8—21no—
247C2×Q8—22no—
248C2×Q8—42no—
249C2×Q8—42no—
250C2×Q8—42no—
251C2×Q8—41no—
252C2×Q8—82no—
253C2×Q8C2×D4×C15112yes—
254C2×D4—21no—
255C2×D4—42no—
256C2×D4C2×D4×C15112yes—
257C22×C4—22no—
258C22×C4—21no—
259C22×C4—22no—
260C22×C4—24no—
261C22×C4—41no—
262C22×C4—82no—
263C22×C4C2×D4×C15112yes—
264C22×C4C2×D4×C15111yescharacteristic
265Q16—48no—
266SD16—48no—
267C2×C8—24no—
268C2×C8—28no—
269C2×C8—24no—
270C2×C8—22no—
271C4⋊C4—28no—
272C4⋊C4—24no—
273C4⋊C4—24no—
274C4⋊C4—22no—
275C4⋊C4—22no—
276C4⋊C4—24no—
277C4⋊C4—24no—
278C4⋊C4—24no—
279C4⋊C4—42no—
280C4⋊C4C2×D4×C15114yes—
281C4⋊C4C2×D4×C15114yes—
282C22⋊C4—28no—
283C22⋊C4—24no—
284C22⋊C4—24no—
285C22⋊C4—24no—
286C42—24no—
287C42C2×D4×C15112yes—
288C42C2×D4×C15111yescharacteristic
289C42C24×C15111yescharacteristic
290C23—22no—
291C23—42no—
292C23—44no—
293C23#120×C15111yescharacteristic
294Q8—42no—
295Q8—42no—
296Q8—42no—
297Q8—81no—
298Q8—82no—
299Q8—84no—
300D4—42no—
301D4—81no—
302C2×C4—22no—
303C2×C4—24no—
304C2×C4—24no—
305C2×C4—22no—
306C2×C4—24no—
307C2×C4—44no—
308C2×C4—42no—
309C2×C4—44no—
310C2×C4—42no—
311C2×C4—84no—
312C2×C4—82no—
313C2×C4#120×C15112yes—
314C2×C4#120×C15111yescharacteristic
315C2×C4C22×D4×C15112yes—
316C2×C4C22×D4×C15111yescharacteristic
317C8—24no—
318C8—28no—
319C22—42no—
320C22—44no—
321C22—84no—
322C22#453×C15112yes—
323C22#456×C15114yes—
324C22C2×#120×C15111yescharacteristic
325C4—21no—
326C4—21no—
327C4—22no—
328C4—22no—
329C4—44no—
330C4—42no—
331C4—44no—
332C4—82no—
333C2—82no—
334C2#1660×C15114yesdirect product factor
335C2C2×#453×C15111yescharacteristic
336C2C2×#456×C15112yes—
subgroupG/H
center, socleC23×C151#120
commutator, Frattini, cosocleC42C24×C151
prime radicalC22×D4×C151D4
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C23×C151 ◁ C2×C42×C151 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#501×C151C2semidirect
4. #1660×C151C2direct (N × H)
5. C2×#330×C151C2semidirect
20. #501×C151C22semidirect
27. #330×C151C22semidirect
165. C2×C151#1660direct (N × H)
168. C2×#1660C151direct (N × H)
169. C151C2×#1660direct (N × H)
171. C2×#501C2×C151semidirect
173. #1660C2×C151direct (N × H)
174. C2×#330C2×C151semidirect
189. #501C22×C151semidirect
196. #330C22×C151semidirect
334. C2#1660×C151direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#563×C1512
C2×#501×C1512
C2×#497×C1512
#1660×C1512
C2×#330×C1512
C2×#329×C1512
C2×#1660151