Finite Group Databasebeta

← #1964×C151 #34065296

Subgroups — #1964×C151 #34065296

Order 19328.

408 conjugacy classes of subgroups; only the 116 normal subgroups are shown.

normal subgroups only

This group has 408 conjugacy classes of subgroups — too many to draw. Only its 116 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×#121×C151C211yesmaximal, characteristic
2C2×#99×C151C214yesmaximal, complemented
3#380×C151C211yesmaximal, characteristic, complemented
4C4×C22⋊C4×C151C211yesmaximal, characteristic, complemented
5C22×D4×C151C411yescharacteristic, complemented
6C22×D4×C151C2212yes—
7C23×C4×C151C2211yescharacteristic
8#121×C151—21no—
9#121×C151—21no—
10#121×C151—21no—
11#121×C151—21no—
12C2×C4⋊C4×C151—21no—
13C2×C4⋊C4×C151C411yescharacteristic, complemented
14C2×C22⋊C4×C151C412yescomplemented
15C2×C22⋊C4×C151C2212yes—
16C2×C22⋊C4×C151C2212yes—
17C2×C42×C151—21no—
18#99×C151—28no—
19#95×C151—21no—
20#95×C151—21no—
21C24×C151C2×C412yes—
22C24×C151C2311yescharacteristic
23C2×D4×C151—24no—
24C2×D4×C151—22no—
25C2×D4×C151—22no—
26C2×D4×C151—24no—
27C2×D4×C151—21no—
28C2×D4×C151—21no—
29C2×D4×C151—42no—
30C22×C4×C151—22no—
31C22×C4×C151—22no—
32C22×C4×C151—42no—
33C22×C4×C151C2×C412yes—
34C22×C4×C151C2×C411yescharacteristic
35C22×C4×C151C2×C411yescharacteristic
36C22×C4×C151D411yescharacteristic
37C22×C4×C151D411yescharacteristic
38C22×C4×C151D411yescharacteristic
39C22×C4×C151D411yescharacteristic
40C4⋊C4×C151—21no—
41C4⋊C4×C151—21no—
42C4⋊C4×C151—42no—
43C22⋊C4×C151—22no—
44C22⋊C4×C151—22no—
45C22⋊C4×C151—22no—
46C22⋊C4×C151—24no—
47C22⋊C4×C151D414yescomplemented
48C42×C151—42no—
49C23×C151—22no—
50C23×C151—24no—
51C23×C151—41no—
52C23×C151—41no—
53C23×C151—42no—
54C23×C151—42no—
55C23×C151C22×C411yescharacteristic
56C23×C151C2×D411yescharacteristic
57C23×C151C2×D411yescharacteristic
58C23×C151C2×D412yes—
59C23×C151#4112yes—
60D4×C151—42no—
61D4×C151—44no—
62D4×C151—42no—
63D4×C151—42no—
64D4×C151—42no—
65C2×C4×C151—22no—
66C2×C4×C151—22no—
67C2×C4×C151—22no—
68C2×C4×C151—22no—
69C2×C4×C151—24no—
70C2×C4×C151—24no—
71C2×C4×C151—41no—
72C2×C4×C151—41no—
73C2×C4×C151—41no—
74C2×C4×C151—42no—
75C2×C4×C151—42no—
76C2×C4×C151—42no—
77C2×C4×C151—42no—
78C2×C4×C151—42no—
79C2×C4×C151C22⋊C411yescharacteristic
80C2×C4×C151C22⋊C411yescharacteristic
81C2×C4×C151C22⋊C411yescharacteristic
82C2×C4×C151C22⋊C411yescharacteristic
83C22×C151—21no—
84C22×C151—21no—
85C22×C151—21no—
86C22×C151—21no—
87C22×C151—21no—
88C22×C151—21no—
89C22×C151—42no—
90C22×C151—42no—
91C22×C151—42no—
92C22×C151—42no—
93C22×C151—42no—
94C22×C151—84no—
95C22×C151C2×C22⋊C411yescharacteristic
96C22×C151C4×D412yes—
97C22×C151#12112yes—
98C22×C151#12411yescharacteristic
99C22×C151#12711yescharacteristic
100C4×C151—21no—
101C4×C151—21no—
102C4×C151—21no—
103C4×C151—44no—
104C4×C151—42no—
105C4×C151—82no—
106C4×C151#9912yescomplemented
107C2×C151—22no—
108C2×C151—21no—
109C2×C151—22no—
110C2×C151—21no—
111C2×C151—82no—
112C2×C151#39011yescharacteristic
113C2×C151C2×#9911yescharacteristic
114C2×C151#41011yescharacteristic
115C151#196411yescharacteristic, direct product factor, Sylow
116#1964C15111yesmaximal, characteristic, direct product factor, Sylow
117C2×#121C2×C15111yescharacteristic
118C2×#99C2×C15114yescomplemented
119#380C2×C15111yescharacteristic, complemented
120C4×C22⋊C4C2×C15111yescharacteristic, complemented
121C22×D4C4×C15111yescharacteristic, complemented
122C22×D4C22×C15112yes—
123C23×C4C22×C15111yescharacteristic
124#121—21no—
125#121—21no—
126#121—21no—
127#121—21no—
128C2×C4⋊C4—21no—
129C2×C4⋊C4C4×C15111yescharacteristic, complemented
130C2×C22⋊C4C4×C15112yescomplemented
131C2×C22⋊C4C22×C15112yes—
132C2×C22⋊C4C22×C15112yes—
133C2×C42—21no—
134#99—28no—
135#95—21no—
136#95—21no—
137C24C2×C4×C15112yes—
138C24C23×C15111yescharacteristic
139C2×D4—24no—
140C2×D4—24no—
141C2×D4—22no—
142C2×D4—22no—
143C2×D4—21no—
144C2×D4—21no—
145C2×D4—42no—
146C22×C4—22no—
147C22×C4—22no—
148C22×C4—42no—
149C22×C4C2×C4×C15112yes—
150C22×C4C2×C4×C15111yescharacteristic
151C22×C4C2×C4×C15111yescharacteristic
152C22×C4D4×C15111yescharacteristic
153C22×C4D4×C15111yescharacteristic
154C22×C4D4×C15111yescharacteristic
155C22×C4D4×C15111yescharacteristic
156C4⋊C4—21no—
157C4⋊C4—21no—
158C4⋊C4—42no—
159C22⋊C4—22no—
160C22⋊C4—22no—
161C22⋊C4—22no—
162C22⋊C4—24no—
163C22⋊C4D4×C15114yescomplemented
164C42—42no—
165C23—22no—
166C23—24no—
167C23—41no—
168C23—41no—
169C23—42no—
170C23—42no—
171C23C22×C4×C15111yescharacteristic
172C23C2×D4×C15111yescharacteristic
173C23C2×D4×C15111yescharacteristic
174C23C2×D4×C15112yes—
175C23#41×C15112yes—
176D4—42no—
177D4—44no—
178D4—42no—
179D4—42no—
180D4—42no—
181C2×C4—22no—
182C2×C4—22no—
183C2×C4—22no—
184C2×C4—22no—
185C2×C4—24no—
186C2×C4—24no—
187C2×C4—41no—
188C2×C4—41no—
189C2×C4—41no—
190C2×C4—42no—
191C2×C4—42no—
192C2×C4—42no—
193C2×C4—42no—
194C2×C4—42no—
195C2×C4C22⋊C4×C15111yescharacteristic
196C2×C4C22⋊C4×C15111yescharacteristic
197C2×C4C22⋊C4×C15111yescharacteristic
198C2×C4C22⋊C4×C15111yescharacteristic
199C22—21no—
200C22—21no—
201C22—21no—
202C22—21no—
203C22—21no—
204C22—21no—
205C22—42no—
206C22—42no—
207C22—42no—
208C22—42no—
209C22—42no—
210C22—84no—
211C22C2×C22⋊C4×C15111yescharacteristic
212C22C4×D4×C15112yes—
213C22#121×C15112yes—
214C22#124×C15111yescharacteristic
215C22#127×C15111yescharacteristic
216C4—21no—
217C4—21no—
218C4—21no—
219C4—44no—
220C4—42no—
221C4—82no—
222C4#99×C15112yescomplemented
223C2—22no—
224C2—21no—
225C2—22no—
226C2—21no—
227C2—82no—
228C2#390×C15111yescharacteristic
229C2C2×#99×C15111yescharacteristic
230C2#410×C15111yescharacteristic
subgroupG/H
center, socleC22×C151C2×C22⋊C4
commutatorC23C22×C4×C151
Frattini, cosocleC24C23×C151
prime radicalC2×#121×C151C2
LCSG ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C151 ◁ C23×C4×C151 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#99×C151C2semidirect
3. #380×C151C2semidirect
4. C4×C22⋊C4×C151C2semidirect
5. C22×D4×C151C4semidirect
13. C2×C4⋊C4×C151C4semidirect
14. C2×C22⋊C4×C151C4semidirect
47. C22⋊C4×C151D4semidirect
106. C4×C151#99semidirect
115. C151#1964direct (N × H)
116. #1964C151direct (N × H)
118. C2×#99C2×C151semidirect
119. #380C2×C151semidirect
120. C4×C22⋊C4C2×C151semidirect
121. C22×D4C4×C151semidirect
129. C2×C4⋊C4C4×C151semidirect
130. C2×C22⋊C4C4×C151semidirect
163. C22⋊C4D4×C151semidirect
222. C4#99×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#121×C1512
C2×#99×C1512
#380×C1512
C4×C22⋊C4×C1512
#1964151