Finite Group Databasebeta

← C151×#12415 #50317340

Subgroups — C151×#12415 #50317340

Order 38656.

272 conjugacy classes of subgroups; only the 82 normal subgroups are shown.

normal subgroups only

This group has 272 conjugacy classes of subgroups — too many to draw. Only its 82 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3390×C151C211yesmaximal, characteristic
2#2255×C151C211yesmaximal, characteristic
3#2227×C151C211yesmaximal, characteristic
4#1694×C151C211yesmaximal, characteristic
5#1363×C151C211yesmaximal, characteristic
6#1338×C151C211yesmaximal, characteristic
7#1334×C151C211yesmaximal, characteristic
8#557×C151—21no—
9#501×C151—21no—
10#500×C151C2211yescharacteristic
11#499×C151C2211yescharacteristic
12#479×C151—21no—
13#479×C151—21no—
14#477×C151—21no—
15#462×C151—21no—
16#446×C151C2211yescharacteristic
17#441×C151—21no—
18C4×Q16×C151C2211yescharacteristic
19#367×C151—21no—
20#366×C151—21no—
21#366×C151—21no—
22C4⋊C16×C151C2211yescharacteristic
23#358×C151—21no—
24#346×C151C2211yescharacteristic
25#334×C151C2211yescharacteristic
26#332×C151—21no—
27C2×Q16×C151—41no—
28C2×Q16×C151D411yescharacteristic
29C4⋊Q8×C151—21no—
30C4⋊Q8×C151—21no—
31C4⋊Q8×C151—41no—
32#125×C151—21no—
33#125×C151—21no—
34#125×C151—41no—
35#125×C151—41no—
36C4×Q8×C151—21no—
37C4×Q8×C151—21no—
38C4×Q8×C151—21no—
39C4×Q8×C151—41no—
40C4×Q8×C151D411yescharacteristic
41C2×C16×C151—21no—
42C2×C16×C151—21no—
43#107×C151—21no—
44#107×C151—21no—
45#107×C151—21no—
46#107×C151D411yescharacteristic
47#107×C151D411yescharacteristic
48#107×C151D411yescharacteristic
49#106×C151—21no—
50#106×C151—21no—
51C4⋊C8×C151—21no—
52C4⋊C8×C151—21no—
53C4⋊C8×C151D411yescharacteristic
54#103×C151—21no—
55#103×C151—21no—
56#103×C151—21no—
57#103×C151—41no—
58#97×C151—21no—
59C4×C8×C151C2311yescharacteristic
60C2×Q8×C151—21no—
61C2×Q8×C151—41no—
62C2×Q8×C151—41no—
63C2×Q8×C151D811yescharacteristic
64Q16×C151—21no—
65Q16×C151—82no—
66Q16×C151Q1612yescomplemented
67C2×C8×C151—21no—
68C2×C8×C151—41no—
69C2×C8×C151C2×D411yescharacteristic
70C2×C8×C151C2×D411yescharacteristic
71C4⋊C4×C151—21no—
72C4⋊C4×C151—21no—
73C4⋊C4×C151—21no—
74C4⋊C4×C151—21no—
75C4⋊C4×C151—41no—
76C4⋊C4×C151—41no—
77C4⋊C4×C151—41no—
78C4⋊C4×C151—41no—
79C4⋊C4×C151—41no—
80C4⋊C4×C151—41no—
81C4⋊C4×C151—41no—
82C4⋊C4×C151—41no—
83C4⋊C4×C151—41no—
84C4⋊C4×C151—41no—
85C4⋊C4×C151D811yescharacteristic
86C42×C151—21no—
87C42×C151—41no—
88C42×C151—41no—
89C42×C151—41no—
90C42×C151C2×D411yescharacteristic
91C16×C151—22no—
92C16×C151—41no—
93Q8×C151—22no—
94Q8×C151—41no—
95Q8×C151—41no—
96Q8×C151—81no—
97Q8×C151—81no—
98Q8×C151—82no—
99C2×C4×C151—21no—
100C2×C4×C151—21no—
101C2×C4×C151—41no—
102C2×C4×C151—41no—
103C2×C4×C151—41no—
104C2×C4×C151—41no—
105C2×C4×C151—81no—
106C2×C4×C151#12011yescharacteristic
107C2×C4×C151C2×D811yescharacteristic
108C2×C4×C151AGL(1,ℤ/8)11yescharacteristic
109C8×C151—21no—
110C8×C151—41no—
111C8×C151—81no—
112C8×C151C2×Q1611yescharacteristic
113C8×C151#13711yescharacteristic
114C22×C151#44711yescharacteristic
115C4×C151—21no—
116C4×C151—21no—
117C4×C151—42no—
118C4×C151—41no—
119C4×C151—41no—
120C4×C151—81no—
121C4×C151—81no—
122C4×C151—81no—
123C4×C151—161no—
124C4×C151#45111yescharacteristic
125C4×C151#45611yescharacteristic
126C2×C151#164911yescharacteristic
127C2×C151#219011yescharacteristic
128C2×C151#219511yescharacteristic
129#12415C15111yesmaximal, characteristic, direct product factor, Sylow
130C151#1241511yescharacteristic, direct product factor, Sylow
131#3390C2×C15111yescharacteristic
132#2255C2×C15111yescharacteristic
133#2227C2×C15111yescharacteristic
134#1694C2×C15111yescharacteristic
135#1363C2×C15111yescharacteristic
136#1338C2×C15111yescharacteristic
137#1334C2×C15111yescharacteristic
138#557—21no—
139#501—21no—
140#500C22×C15111yescharacteristic
141#499C22×C15111yescharacteristic
142#479—21no—
143#479—21no—
144#477—21no—
145#462—21no—
146#446C22×C15111yescharacteristic
147#441—21no—
148C4×Q16C22×C15111yescharacteristic
149#367—21no—
150#366—21no—
151#366—21no—
152C4⋊C16C22×C15111yescharacteristic
153#358—21no—
154#346C22×C15111yescharacteristic
155#334C22×C15111yescharacteristic
156#332—21no—
157C2×Q16—41no—
158C2×Q16D4×C15111yescharacteristic
159C4⋊Q8—21no—
160C4⋊Q8—21no—
161C4⋊Q8—41no—
162#125—21no—
163#125—21no—
164#125—41no—
165#125—41no—
166C4×Q8—21no—
167C4×Q8—21no—
168C4×Q8—21no—
169C4×Q8—41no—
170C4×Q8D4×C15111yescharacteristic
171C2×C16—21no—
172C2×C16—21no—
173#107—21no—
174#107—21no—
175#107—21no—
176#107D4×C15111yescharacteristic
177#107D4×C15111yescharacteristic
178#107D4×C15111yescharacteristic
179#106—21no—
180#106—21no—
181C4⋊C8—21no—
182C4⋊C8—21no—
183C4⋊C8D4×C15111yescharacteristic
184#103—21no—
185#103—21no—
186#103—21no—
187#103—41no—
188#97—21no—
189C4×C8C23×C15111yescharacteristic
190C2×Q8—21no—
191C2×Q8—41no—
192C2×Q8—41no—
193C2×Q8D8×C15111yescharacteristic
194Q16—21no—
195Q16—82no—
196Q16Q16×C15112yescomplemented
197C2×C8—21no—
198C2×C8—41no—
199C2×C8C2×D4×C15111yescharacteristic
200C2×C8C2×D4×C15111yescharacteristic
201C4⋊C4—21no—
202C4⋊C4—21no—
203C4⋊C4—21no—
204C4⋊C4—21no—
205C4⋊C4—41no—
206C4⋊C4—41no—
207C4⋊C4—41no—
208C4⋊C4—41no—
209C4⋊C4—41no—
210C4⋊C4—41no—
211C4⋊C4—41no—
212C4⋊C4—41no—
213C4⋊C4—41no—
214C4⋊C4—41no—
215C4⋊C4D8×C15111yescharacteristic
216C42—21no—
217C42—41no—
218C42—41no—
219C42—41no—
220C42C2×D4×C15111yescharacteristic
221C16—22no—
222C16—41no—
223Q8—22no—
224Q8—41no—
225Q8—41no—
226Q8—81no—
227Q8—81no—
228Q8—82no—
229C2×C4—21no—
230C2×C4—21no—
231C2×C4—41no—
232C2×C4—41no—
233C2×C4—41no—
234C2×C4—41no—
235C2×C4—81no—
236C2×C4#120×C15111yescharacteristic
237C2×C4C2×D8×C15111yescharacteristic
238C2×C4AGL(1,ℤ/8)×C15111yescharacteristic
239C8—21no—
240C8—41no—
241C8—81no—
242C8C2×Q16×C15111yescharacteristic
243C8#137×C15111yescharacteristic
244C22#447×C15111yescharacteristic
245C4—21no—
246C4—21no—
247C4—42no—
248C4—41no—
249C4—41no—
250C4—81no—
251C4—81no—
252C4—81no—
253C4—161no—
254C4#451×C15111yescharacteristic
255C4#456×C15111yescharacteristic
256C2#1649×C15111yescharacteristic
257C2#2190×C15111yescharacteristic
258C2#2195×C15111yescharacteristic
subgroupG/H
center, socle, prime radicalC22×C151#447
commutator, Frattini, cosocleC4×C8C23×C151
LCSG ▷ C4×C8 ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C151 ◁ C42×C151 ◁ #446×C151 ◁ G

Complements

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

NH ≅ G/Ntype
66. Q16×C151Q16semidirect
129. #12415C151direct (N × H)
130. C151#12415direct (N × H)
196. Q16Q16×C151semidirect

Maximal subgroups

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

subgroupindex
#3390×C1512
#2255×C1512
#2227×C1512
#1694×C1512
#1363×C1512
#1338×C1512
#1334×C1512
#12415151