Finite Group Databasebeta

← C151×#11807 #50316732

Subgroups — C151×#11807 #50316732

Order 38656.

388 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 388 conjugacy classes of subgroups — too many to draw. Only its 98 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#2621×C151C211yesmaximal, characteristic
2#1822×C151C211yesmaximal, characteristic
3#1464×C151C211yesmaximal, characteristic
4#1346×C151C214yesmaximal, complemented
5C2×C4⋊Q8×C151C411yescharacteristic
6C2×C22⋊Q8×C151—21no—
7C2×#117×C151C2211yescharacteristic
8#432×C151—21no—
9#407×C151—21no—
10#398×C151—21no—
11#398×C151C2212yes—
12#397×C151—21no—
13#397×C151C412yes—
14#391×C151—21no—
15#382×C151C411yescharacteristic
16#343×C151—21no—
17#343×C151C2212yes—
18#324×C151C2212yes—
19#323×C151—21no—
20C22×Q8×C151—21no—
21C23×C4×C151D411yescharacteristic
22C2×M16×C151—22no—
23C4⋊Q8×C151—41no—
24C4⋊Q8×C151—41no—
25C22⋊Q8×C151—44no—
26#117×C151—41no—
27#117×C151—41no—
28C2×C4⋊C4×C151—21no—
29C2×C4⋊C4×C151—21no—
30C2×C4⋊C4×C151—22no—
31C2×C4⋊C4×C151C2×C412yes—
32C2×C4⋊C4×C151D411yescharacteristic
33C2×C4⋊C4×C151C2311yescharacteristic
34C2×C22⋊C4×C151—22no—
35C2×C22⋊C4×C151C2×C411yescharacteristic
36C2×C22⋊C4×C151D411yescharacteristic
37C2×C42×C151C2×C411yescharacteristic
38C2×C42×C151D411yescharacteristic
39C4⋊C8×C151—41no—
40C22⋊C8×C151—22no—
41C22⋊C8×C151—41no—
42C22⋊C8×C151—41no—
43#97×C151—41no—
44#95×C151—21no—
45#95×C151—22no—
46#95×C151—22no—
47#95×C151C2×C412yes—
48C24×C151C22⋊C411yescharacteristic
49C2×Q8×C151—42no—
50C2×Q8×C151—42no—
51C2×Q8×C151—41no—
52C2×Q8×C151—41no—
53C22×C4×C151—21no—
54C22×C4×C151—21no—
55C22×C4×C151—22no—
56C22×C4×C151—22no—
57C22×C4×C151—22no—
58C22×C4×C151—41no—
59C22×C4×C151C22⋊C411yescharacteristic
60C22×C4×C151C22⋊C411yescharacteristic
61C22×C4×C151C22⋊C411yescharacteristic
62C22×C4×C151C22×C411yescharacteristic
63C22×C4×C151C2×D411yescharacteristic
64C22×C4×C151C2×D411yescharacteristic
65M16×C151—42no—
66M16×C151—42no—
67C2×C8×C151—42no—
68C2×C8×C151—42no—
69C4⋊C4×C151—41no—
70C4⋊C4×C151—41no—
71C4⋊C4×C151—42no—
72C4⋊C4×C151—42no—
73C4⋊C4×C151—42no—
74C4⋊C4×C151—44no—
75C22⋊C4×C151—41no—
76C22⋊C4×C151—41no—
77C22⋊C4×C151—44no—
78C42×C151—21no—
79C42×C151—21no—
80C42×C151—21no—
81C42×C151—21no—
82C23×C151—21no—
83C23×C151—21no—
84C23×C151—21no—
85C23×C151—41no—
86C23×C151—41no—
87C23×C151C2×C22⋊C411yescharacteristic
88Q8×C151—82no—
89Q8×C151—82no—
90C2×C4×C151—21no—
91C2×C4×C151—21no—
92C2×C4×C151—21no—
93C2×C4×C151—21no—
94C2×C4×C151—21no—
95C2×C4×C151—21no—
96C2×C4×C151—21no—
97C2×C4×C151—21no—
98C2×C4×C151—42no—
99C2×C4×C151—42no—
100C2×C4×C151—41no—
101C2×C4×C151—41no—
102C2×C4×C151—41no—
103C2×C4×C151—41no—
104C2×C4×C151—42no—
105C2×C4×C151—42no—
106C2×C4×C151—42no—
107C2×C4×C151—42no—
108C2×C4×C151—42no—
109C2×C4×C151—42no—
110C2×C4×C151#9911yescharacteristic
111C2×C4×C151#9911yescharacteristic
112C2×C4×C151AGL(1,ℤ/8)12yes—
113C8×C151—82no—
114C8×C151—82no—
115C22×C151—21no—
116C22×C151—21no—
117C22×C151—42no—
118C22×C151—41no—
119C22×C151—41no—
120C22×C151—41no—
121C22×C151—81no—
122C22×C151C2×#9911yescharacteristic
123C22×C151#41811yescharacteristic
124C22×C151#42111yescharacteristic
125C4×C151—22no—
126C4×C151—21no—
127C4×C151—21no—
128C4×C151—41no—
129C4×C151—41no—
130C4×C151—41no—
131C4×C151—41no—
132C4×C151—82no—
133C4×C151—82no—
134C2×C151—21no—
135C2×C151—21no—
136C2×C151—81no—
137C2×C151#151011yescharacteristic
138C2×C151#212311yescharacteristic
139C2×C151#213511yescharacteristic
140#11807C15111yesmaximal, characteristic, direct product factor, Sylow
141C151#1180711yescharacteristic, direct product factor, Sylow
142#2621C2×C15111yescharacteristic
143#1822C2×C15111yescharacteristic
144#1464C2×C15111yescharacteristic
145#1346C2×C15114yescomplemented
146C2×C4⋊Q8C4×C15111yescharacteristic
147C2×C22⋊Q8—21no—
148C2×#117C22×C15111yescharacteristic
149#432—21no—
150#407—21no—
151#398—21no—
152#398C22×C15112yes—
153#397—21no—
154#397C4×C15112yes—
155#391—21no—
156#382C4×C15111yescharacteristic
157#343—21no—
158#343C22×C15112yes—
159#324C22×C15112yes—
160#323—21no—
161C22×Q8—21no—
162C23×C4D4×C15111yescharacteristic
163C2×M16—22no—
164C4⋊Q8—41no—
165C4⋊Q8—41no—
166C22⋊Q8—44no—
167#117—41no—
168#117—41no—
169C2×C4⋊C4—21no—
170C2×C4⋊C4—21no—
171C2×C4⋊C4—22no—
172C2×C4⋊C4C2×C4×C15112yes—
173C2×C4⋊C4D4×C15111yescharacteristic
174C2×C4⋊C4C23×C15111yescharacteristic
175C2×C22⋊C4—22no—
176C2×C22⋊C4C2×C4×C15111yescharacteristic
177C2×C22⋊C4D4×C15111yescharacteristic
178C2×C42C2×C4×C15111yescharacteristic
179C2×C42D4×C15111yescharacteristic
180C4⋊C8—41no—
181C22⋊C8—22no—
182C22⋊C8—41no—
183C22⋊C8—41no—
184#97—41no—
185#95—21no—
186#95—22no—
187#95—22no—
188#95C2×C4×C15112yes—
189C24C22⋊C4×C15111yescharacteristic
190C2×Q8—42no—
191C2×Q8—42no—
192C2×Q8—41no—
193C2×Q8—41no—
194C22×C4—21no—
195C22×C4—21no—
196C22×C4—22no—
197C22×C4—22no—
198C22×C4—22no—
199C22×C4—41no—
200C22×C4C22⋊C4×C15111yescharacteristic
201C22×C4C22⋊C4×C15111yescharacteristic
202C22×C4C22⋊C4×C15111yescharacteristic
203C22×C4C22×C4×C15111yescharacteristic
204C22×C4C2×D4×C15111yescharacteristic
205C22×C4C2×D4×C15111yescharacteristic
206M16—42no—
207M16—42no—
208C2×C8—42no—
209C2×C8—42no—
210C4⋊C4—41no—
211C4⋊C4—41no—
212C4⋊C4—42no—
213C4⋊C4—42no—
214C4⋊C4—42no—
215C4⋊C4—44no—
216C22⋊C4—41no—
217C22⋊C4—41no—
218C22⋊C4—44no—
219C42—21no—
220C42—21no—
221C42—21no—
222C42—21no—
223C23—21no—
224C23—21no—
225C23—21no—
226C23—41no—
227C23—41no—
228C23C2×C22⋊C4×C15111yescharacteristic
229Q8—82no—
230Q8—82no—
231C2×C4—21no—
232C2×C4—21no—
233C2×C4—21no—
234C2×C4—21no—
235C2×C4—21no—
236C2×C4—21no—
237C2×C4—21no—
238C2×C4—21no—
239C2×C4—42no—
240C2×C4—42no—
241C2×C4—41no—
242C2×C4—41no—
243C2×C4—41no—
244C2×C4—41no—
245C2×C4—42no—
246C2×C4—42no—
247C2×C4—42no—
248C2×C4—42no—
249C2×C4—42no—
250C2×C4—42no—
251C2×C4#99×C15111yescharacteristic
252C2×C4#99×C15111yescharacteristic
253C2×C4AGL(1,ℤ/8)×C15112yes—
254C8—82no—
255C8—82no—
256C22—21no—
257C22—21no—
258C22—42no—
259C22—41no—
260C22—41no—
261C22—41no—
262C22—81no—
263C22C2×#99×C15111yescharacteristic
264C22#418×C15111yescharacteristic
265C22#421×C15111yescharacteristic
266C4—22no—
267C4—21no—
268C4—21no—
269C4—41no—
270C4—41no—
271C4—41no—
272C4—41no—
273C4—82no—
274C4—82no—
275C2—21no—
276C2—21no—
277C2—81no—
278C2#1510×C15111yescharacteristic
279C2#2123×C15111yescharacteristic
280C2#2135×C15111yescharacteristic
subgroupG/H
center, socleC22×C151C2×#99
commutatorC22×C4C22×C4×C151
Frattini, cosocleC2×C4⋊C4C23×C151
prime radicalC24×C151C22⋊C4
LCSG ▷ C22×C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C151 ◁ C22×C4×C151 ◁ C2×#117×C151 ◁ G

Complements

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

NH ≅ G/Ntype
4. #1346×C151C2semidirect
140. #11807C151direct (N × H)
141. C151#11807direct (N × H)
145. #1346C2×C151semidirect

Maximal subgroups

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

subgroupindex
#2621×C1512
#1822×C1512
#1464×C1512
#1346×C1512
#11807151