Finite Group Databasebeta

← C151×#12704 #50317629

Subgroups — C151×#12704 #50317629

Order 38656.

962 conjugacy classes of subgroups; only the 150 normal subgroups are shown.

normal subgroups only

This group has 962 conjugacy classes of subgroups — too many to draw. Only its 150 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
1C2×#536×C151C211yesmaximal, characteristic
2C2×#356×C151C214yesmaximal, complemented
3#1785×C151C212yesmaximal
4C22×#41×C151C2211yescharacteristic
5C23×Q8×C151C411yescharacteristic
6#536×C151—28no—
7C2×C4⋊Q8×C151C2212yes—
8C2×#124×C151C412yes—
9C2×#123×C151—22no—
10C2×C22⋊Q8×C151—22no—
11C2×#117×C151C411yescharacteristic
12C2×#101×C151C2214yes—
13C2×#100×C151—22no—
14#407×C151—22no—
15#356×C151—28no—
16C2×#41×C151—24no—
17C2×#41×C151—42no—
18C2×#41×C151—42no—
19C22×Q8×C151—21no—
20C22×Q8×C151—24no—
21C22×Q8×C151—42no—
22C22×Q8×C151—42no—
23C22×Q8×C151C2×C412yes—
24C22×Q8×C151C2311yescharacteristic
25C22×D4×C151C2×C411yescharacteristic
26C22×D4×C151D412yes—
27C23×C4×C151—21no—
28C23×C4×C151C2×C411yescharacteristic
29C23×C4×C151D412yes—
30C2×M16×C151—24no—
31C4⋊Q8×C151—24no—
32C4⋊Q8×C151D418yes—
33#124×C151—24no—
34#124×C151—24no—
35#123×C151—216no—
36C22⋊Q8×C151—216no—
37#117×C151—24no—
38C2×C4⋊C4×C151—21no—
39C2×C4⋊C4×C151—24no—
40C2×C22⋊C4×C151—21no—
41C2×C22⋊C4×C151—24no—
42C2×C42×C151C2×C412yes—
43#101×C151—28no—
44#100×C151—44no—
45C22⋊C8×C151—44no—
46C24×C151C22⋊C412yes—
47C24×C151C22⋊C411yescharacteristic
48#41×C151—416no—
49C2×Q8×C151—24no—
50C2×Q8×C151—22no—
51C2×Q8×C151—41no—
52C2×Q8×C151—41no—
53C2×Q8×C151—416no—
54C2×Q8×C151—42no—
55C2×Q8×C151—42no—
56C2×Q8×C151—42no—
57C2×Q8×C151—42no—
58C2×Q8×C151C22⋊C414yes—
59C2×Q8×C151C2×D414yes—
60C2×D4×C151—24no—
61C2×D4×C151—22no—
62C2×D4×C151—24no—
63C2×D4×C151—41no—
64C2×D4×C151—41no—
65C2×D4×C151—42no—
66C22×C4×C151—22no—
67C22×C4×C151—22no—
68C22×C4×C151—22no—
69C22×C4×C151—24no—
70C22×C4×C151—22no—
71C22×C4×C151—22no—
72C22×C4×C151—24no—
73C22×C4×C151—24no—
74C22×C4×C151—42no—
75C22×C4×C151—42no—
76C22×C4×C151—42no—
77C22×C4×C151C22⋊C411yescharacteristic
78C22×C4×C151C22×C411yescharacteristic
79C22×C4×C151C2×D412yes—
80M16×C151—44no—
81M16×C151—44no—
82C2×C8×C151—44no—
83C4⋊C4×C151—24no—
84C4⋊C4×C151—216no—
85C22⋊C4×C151—24no—
86C22⋊C4×C151—216no—
87C42×C151—22no—
88C42×C151C22⋊C414yes—
89C23×C151—21no—
90C23×C151—21no—
91C23×C151—22no—
92C23×C151—22no—
93C23×C151—22no—
94C23×C151—42no—
95C23×C151—44no—
96C23×C151#9912yes—
97C23×C151C2×C22⋊C411yescharacteristic
98Q8×C151—44no—
99Q8×C151—44no—
100Q8×C151—48no—
101Q8×C151—44no—
102D4×C151—48no—
103D4×C151—44no—
104C2×C4×C151—28no—
105C2×C4×C151—21no—
106C2×C4×C151—21no—
107C2×C4×C151—21no—
108C2×C4×C151—22no—
109C2×C4×C151—21no—
110C2×C4×C151—22no—
111C2×C4×C151—24no—
112C2×C4×C151—24no—
113C2×C4×C151—48no—
114C2×C4×C151—48no—
115C2×C4×C151—44no—
116C2×C4×C151—42no—
117C2×C4×C151—42no—
118C2×C4×C151#9912yes—
119C2×C4×C151C2×C22⋊C412yes—
120C2×C4×C151#12014yes—
121C8×C151—84no—
122C22×C151—22no—
123C22×C151—22no—
124C22×C151—42no—
125C22×C151—42no—
126C22×C151—44no—
127C22×C151—42no—
128C22×C151—44no—
129C22×C151—42no—
130C22×C151—82no—
131C22×C151#37911yescharacteristic
132C22×C151C2×#9911yescharacteristic
133C22×C151C2×#9911yescharacteristic
134C4×C151—24no—
135C4×C151—22no—
136C4×C151—22no—
137C4×C151—44no—
138C4×C151—44no—
139C2×C151—21no—
140C2×C151—21no—
141C2×C151—42no—
142C2×C151—82no—
143C2×C151#178111yescharacteristic
144C2×C151#213512yes—
145#12704C15111yesmaximal, characteristic, direct product factor, Sylow
146C151#1270411yescharacteristic, direct product factor, Sylow
147C2×#536C2×C15111yescharacteristic
148C2×#356C2×C15114yescomplemented
149#1785C2×C15112yes—
150C22×#41C22×C15111yescharacteristic
151C23×Q8C4×C15111yescharacteristic
152#536—28no—
153C2×C4⋊Q8C22×C15112yes—
154C2×#124C4×C15112yes—
155C2×#123—22no—
156C2×C22⋊Q8—22no—
157C2×#117C4×C15111yescharacteristic
158C2×#101C22×C15114yes—
159C2×#100—22no—
160#407—22no—
161#356—28no—
162C2×#41—24no—
163C2×#41—42no—
164C2×#41—42no—
165C22×Q8—24no—
166C22×Q8—21no—
167C22×Q8—42no—
168C22×Q8—42no—
169C22×Q8C2×C4×C15112yes—
170C22×Q8C23×C15111yescharacteristic
171C22×D4C2×C4×C15111yescharacteristic
172C22×D4D4×C15112yes—
173C23×C4—21no—
174C23×C4C2×C4×C15111yescharacteristic
175C23×C4D4×C15112yes—
176C2×M16—24no—
177C4⋊Q8—24no—
178C4⋊Q8D4×C15118yes—
179#124—24no—
180#124—24no—
181#123—216no—
182C22⋊Q8—216no—
183#117—24no—
184C2×C4⋊C4—21no—
185C2×C4⋊C4—24no—
186C2×C22⋊C4—21no—
187C2×C22⋊C4—24no—
188C2×C42C2×C4×C15112yes—
189#101—28no—
190#100—44no—
191C22⋊C8—44no—
192C24C22⋊C4×C15112yes—
193C24C22⋊C4×C15111yescharacteristic
194#41—416no—
195C2×Q8—24no—
196C2×Q8—22no—
197C2×Q8—41no—
198C2×Q8—41no—
199C2×Q8—416no—
200C2×Q8—42no—
201C2×Q8—42no—
202C2×Q8—42no—
203C2×Q8—42no—
204C2×Q8C22⋊C4×C15114yes—
205C2×Q8C2×D4×C15114yes—
206C2×D4—24no—
207C2×D4—22no—
208C2×D4—24no—
209C2×D4—41no—
210C2×D4—41no—
211C2×D4—42no—
212C22×C4—22no—
213C22×C4—22no—
214C22×C4—22no—
215C22×C4—24no—
216C22×C4—22no—
217C22×C4—22no—
218C22×C4—24no—
219C22×C4—24no—
220C22×C4—42no—
221C22×C4—42no—
222C22×C4—42no—
223C22×C4C22⋊C4×C15111yescharacteristic
224C22×C4C22×C4×C15111yescharacteristic
225C22×C4C2×D4×C15112yes—
226M16—44no—
227M16—44no—
228C2×C8—44no—
229C4⋊C4—24no—
230C4⋊C4—216no—
231C22⋊C4—24no—
232C22⋊C4—216no—
233C42—22no—
234C42C22⋊C4×C15114yes—
235C23—21no—
236C23—21no—
237C23—22no—
238C23—22no—
239C23—22no—
240C23—42no—
241C23—44no—
242C23#99×C15112yes—
243C23C2×C22⋊C4×C15111yescharacteristic
244Q8—44no—
245Q8—44no—
246Q8—48no—
247Q8—44no—
248D4—48no—
249D4—44no—
250C2×C4—28no—
251C2×C4—21no—
252C2×C4—22no—
253C2×C4—22no—
254C2×C4—21no—
255C2×C4—21no—
256C2×C4—21no—
257C2×C4—24no—
258C2×C4—24no—
259C2×C4—48no—
260C2×C4—48no—
261C2×C4—44no—
262C2×C4—42no—
263C2×C4—42no—
264C2×C4#99×C15112yes—
265C2×C4C2×C22⋊C4×C15112yes—
266C2×C4#120×C15114yes—
267C8—84no—
268C22—22no—
269C22—22no—
270C22—42no—
271C22—42no—
272C22—44no—
273C22—42no—
274C22—44no—
275C22—42no—
276C22—82no—
277C22#379×C15111yescharacteristic
278C22C2×#99×C15111yescharacteristic
279C22C2×#99×C15111yescharacteristic
280C4—24no—
281C4—22no—
282C4—22no—
283C4—44no—
284C4—44no—
285C2—21no—
286C2—21no—
287C2—42no—
288C2—82no—
289C2#1781×C15111yescharacteristic
290C2#2135×C15112yes—
subgroupG/H
center, socleC22×C151C2×#99
commutatorC22×C4C22×C4×C151
Frattini, cosocleC22×Q8C23×C151
prime radicalC22×#41×C151C22
LCSG ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C151 ◁ C22×C4×C151 ◁ C22×#41×C151 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#356×C151C2semidirect
145. #12704C151direct (N × H)
146. C151#12704direct (N × H)
148. C2×#356C2×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#536×C1512
C2×#356×C1512
#1785×C1512
#12704151