Finite Group Databasebeta

← C151×#23565 #50328490

Subgroups — C151×#23565 #50328490

Order 38656.

1334 conjugacy classes of subgroups; only the 366 normal subgroups are shown.

normal subgroups only

This group has 1334 conjugacy classes of subgroups — too many to draw. Only its 366 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×#543×C151C211yesmaximal, characteristic
2#2315×C151C213yesmaximal
3#2062×C151C218yesmaximal, complemented
4C2×#342×C151C213yesmaximal
5#543×C151—26no—
6#543×C151C2214yes—
7C2×C22⋊Q8×C151—26no—
8C22×C22⋊C4×C151C2211yescharacteristic
9C22×C22⋊C4×C151C2213yes—
10C22×C22⋊C4×C151C2213yes—
11#385×C151—26no—
12#385×C151C22112yes—
13#380×C151—26no—
14#342×C151C22112yes—
15C25×C151C2311yescharacteristic
16C22×Q8×C151—22no—
17C23×C4×C151—23no—
18C23×C4×C151D416yes—
19C23×C4×C151C2312yes—
20C22⋊Q8×C151—224no—
21C22⋊Q8×C151—224no—
22C2×C4⋊C4×C151—26no—
23C2×C4⋊C4×C151—212no—
24C2×C22⋊C4×C151—23no—
25C2×C22⋊C4×C151—26no—
26C2×C22⋊C4×C151—26no—
27C2×C22⋊C4×C151—23no—
28C2×C22⋊C4×C151—23no—
29C2×C22⋊C4×C151—26no—
30C2×C22⋊C4×C151D416yes—
31C2×C22⋊C4×C151Q8112yescomplemented
32C2×C22⋊C4×C151C2316yes—
33C2×C22⋊C4×C151C2316yes—
34#95×C151—212no—
35C24×C151—82no—
36C24×C151C2×D413yes—
37C24×C151C2×D413yes—
38C24×C151C2×Q816yes—
39C24×C151#4112yes—
40C24×C151C2411yescharacteristic
41C2×Q8×C151—28no—
42C2×Q8×C151—84no—
43C22×C4×C151—26no—
44C22×C4×C151—26no—
45C22×C4×C151—26no—
46C22×C4×C151—212no—
47C22×C4×C151—26no—
48C22×C4×C151—82no—
49C22×C4×C151—86no—
50C22×C4×C151—86no—
51C22×C4×C151C2×D4112yes—
52C4⋊C4×C151—224no—
53C4⋊C4×C151—812no—
54C22⋊C4×C151—212no—
55C22⋊C4×C151—212no—
56C22⋊C4×C151—212no—
57C22⋊C4×C151—26no—
58C22⋊C4×C151—43no—
59C22⋊C4×C151—41no—
60C22⋊C4×C151C2×Q8112yescomplemented
61C23×C151—46no—
62C23×C151—46no—
63C23×C151—42no—
64C23×C151—86no—
65C23×C151—82no—
66C23×C151#12013yes—
67C23×C151#12011yescharacteristic
68C23×C151C22⋊Q816yes—
69C23×C151C22⋊Q816yes—
70C23×C151C4⋊Q816yes—
71C23×C151C4⋊Q816yes—
72C23×C151C22×D413yes—
73C23×C151C22×Q813yes—
74C23×C151C2×#4111yescharacteristic
75Q8×C151—88no—
76C2×C4×C151—212no—
77C2×C4×C151—212no—
78C2×C4×C151—412no—
79C2×C4×C151—412no—
80C2×C4×C151—412no—
81C2×C4×C151—412no—
82C2×C4×C151—42no—
83C2×C4×C151—86no—
84C2×C4×C151—812no—
85C22×C151—22no—
86C22×C151—26no—
87C22×C151—26no—
88C22×C151—46no—
89C22×C151—46no—
90C22×C151—46no—
91C22×C151—46no—
92C22×C151—43no—
93C22×C151—41no—
94C22×C151#39516yes—
95C22×C151#39512yes—
96C22×C151C2×#12011yescharacteristic
97C22×C151C2×C22⋊Q813yes—
98C22×C151C2×C4⋊Q813yes—
99C4×C151—412no—
100C4×C151—412no—
101C4×C151—82no—
102C2×C151—23no—
103C2×C151—23no—
104C2×C151—22no—
105C2×C151—26no—
106C2×C151C2×#39511yescharacteristic
107C2×C151#302612yes—
108#23565C15111yesmaximal, characteristic, direct product factor, Sylow
109C151#2356511yescharacteristic, direct product factor, Sylow
110C2×#543C2×C15111yescharacteristic
111#2315C2×C15113yes—
112#2062C2×C15118yescomplemented
113C2×#342C2×C15113yes—
114#543—26no—
115#543C22×C15114yes—
116C2×C22⋊Q8—26no—
117C22×C22⋊C4C22×C15111yescharacteristic
118C22×C22⋊C4C22×C15113yes—
119C22×C22⋊C4C22×C15113yes—
120#385—26no—
121#385C22×C151112yes—
122#380—26no—
123#342C22×C151112yes—
124C25C23×C15111yescharacteristic
125C22×Q8—22no—
126C23×C4—23no—
127C23×C4D4×C15116yes—
128C23×C4C23×C15112yes—
129C22⋊Q8—224no—
130C22⋊Q8—224no—
131C2×C4⋊C4—26no—
132C2×C4⋊C4—212no—
133C2×C22⋊C4—26no—
134C2×C22⋊C4—26no—
135C2×C22⋊C4—26no—
136C2×C22⋊C4—23no—
137C2×C22⋊C4—23no—
138C2×C22⋊C4—23no—
139C2×C22⋊C4D4×C15116yes—
140C2×C22⋊C4Q8×C151112yescomplemented
141C2×C22⋊C4C23×C15116yes—
142C2×C22⋊C4C23×C15116yes—
143#95—212no—
144C24—82no—
145C24C2×D4×C15113yes—
146C24C2×D4×C15113yes—
147C24C2×Q8×C15116yes—
148C24#41×C15112yes—
149C24C24×C15111yescharacteristic
150C2×Q8—28no—
151C2×Q8—84no—
152C22×C4—26no—
153C22×C4—26no—
154C22×C4—26no—
155C22×C4—212no—
156C22×C4—26no—
157C22×C4—82no—
158C22×C4—86no—
159C22×C4—86no—
160C22×C4C2×D4×C151112yes—
161C4⋊C4—224no—
162C4⋊C4—812no—
163C22⋊C4—212no—
164C22⋊C4—212no—
165C22⋊C4—212no—
166C22⋊C4—26no—
167C22⋊C4—43no—
168C22⋊C4—41no—
169C22⋊C4C2×Q8×C151112yescomplemented
170C23—42no—
171C23—46no—
172C23—46no—
173C23—86no—
174C23—82no—
175C23#120×C15113yes—
176C23#120×C15111yescharacteristic
177C23C22⋊Q8×C15116yes—
178C23C22⋊Q8×C15116yes—
179C23C4⋊Q8×C15116yes—
180C23C4⋊Q8×C15116yes—
181C23C22×D4×C15113yes—
182C23C22×Q8×C15113yes—
183C23C2×#41×C15111yescharacteristic
184Q8—88no—
185C2×C4—212no—
186C2×C4—212no—
187C2×C4—412no—
188C2×C4—412no—
189C2×C4—412no—
190C2×C4—412no—
191C2×C4—42no—
192C2×C4—86no—
193C2×C4—812no—
194C22—22no—
195C22—26no—
196C22—26no—
197C22—46no—
198C22—46no—
199C22—46no—
200C22—46no—
201C22—43no—
202C22—41no—
203C22#395×C15116yes—
204C22#395×C15112yes—
205C22C2×#120×C15111yescharacteristic
206C22C2×C22⋊Q8×C15113yes—
207C22C2×C4⋊Q8×C15113yes—
208C4—412no—
209C4—412no—
210C4—82no—
211C2—23no—
212C2—22no—
213C2—26no—
214C2—23no—
215C2C2×#395×C15111yescharacteristic
216C2#3026×C15112yes—
subgroupG/H
center, socleC22×C151C2×#120
commutator, Frattini, cosocleC24C24×C151
prime radicalC25×C151C23
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C22×C151 ◁ C25×C151 ◁ G

Complements

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

NH ≅ G/Ntype
3. #2062×C151C2semidirect
31. C2×C22⋊C4×C151Q8semidirect
60. C22⋊C4×C151C2×Q8semidirect
108. #23565C151direct (N × H)
109. C151#23565direct (N × H)
112. #2062C2×C151semidirect
140. C2×C22⋊C4Q8×C151semidirect
169. C22⋊C4C2×Q8×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#543×C1512
#2315×C1512
#2062×C1512
C2×#342×C1512
#23565151