Finite Group Databasebeta

← #34077063

Subgroups — #34077063

Order 19328.

368 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 368 conjugacy classes of subgroups — too many to draw. Only its 141 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#23752151C212yesmaximal
2#23752151C212yesmaximal
3#23752133C212yesmaximal
4#23752118C211yesmaximal, characteristic
5#23752111C212yesmaximal
6#23752110C211yesmaximal, characteristic
7#23752099C212yesmaximal
8#23752098C212yesmaximal
9#389×C151C211yesmaximal, characteristic
10C22×Dic302C2211yescharacteristic
11C2×C4⋊Dic151C2211yescharacteristic
12C2×C4⋊Dic151C2212yes—
13C2×C4⋊Dic151C2211yescharacteristic
14C2×C4⋊Dic151C2211yescharacteristic
15C2×C4⋊Dic151C2212yes—
16C2×Dic151⋊C4C2212yes—
17C2×C4×Dic151C2212yes—
18C151⋊#95C2212yes—
19C151⋊#95C2212yes—
20C151⋊#95C2212yes—
21C151⋊#95C2212yes—
22C151⋊#95C2212yes—
23C151⋊#95C2212yes—
24C151⋊#95C2212yes—
25C151⋊#95C2212yes—
26C2×C4⋊C4×C151C2212yes—
27C2×C4⋊C4×C151C2211yescharacteristic
28C2×C4⋊C4×C151C2211yescharacteristic
29C2×C42×C151C2211yescharacteristic
30#95×C151C2212yes—
31C2×Dic302—22no—
32C2×Dic302—41no—
33C2×Dic302—41no—
34C22×Dic151C2312yes—
35C22×Dic151C2312yes—
36C22×Dic151C2312yes—
37C22×Dic151C2312yes—
38C4⋊Dic151—22no—
39C4⋊Dic151—42no—
40C4⋊Dic151—41no—
41C4⋊Dic151—41no—
42C4⋊Dic151—42no—
43Dic151⋊C4—24no—
44C4×Dic151—42no—
45C22×C4×C151C2312yes—
46C22×C4×C151C2312yes—
47C22×C4×C151C2311yescharacteristic
48C22×C4×C151C2311yescharacteristic
49C22×C4×C151C2311yescharacteristic
50C4⋊C4×C151—24no—
51C4⋊C4×C151—41no—
52C4⋊C4×C151Q814yescomplemented
53C42×C151—41no—
54Dic302—44no—
55C2×Dic151—22no—
56C2×Dic151—22no—
57C2×Dic151—22no—
58C2×Dic151—22no—
59C2×Dic151—22no—
60C2×Dic151—22no—
61C2×Dic151—22no—
62C2×Dic151—22no—
63C2×Dic151—22no—
64C2×Dic151—22no—
65C2×Dic151—22no—
66C2×Dic151—22no—
67C23×C151C2411yescharacteristic
68C2×C4×C151—22no—
69C2×C4×C151—22no—
70C2×C4×C151—21no—
71C2×C4×C151—21no—
72C2×C4×C151—21no—
73C2×C4×C151—21no—
74C2×C4×C151—21no—
75C2×C4×C151—21no—
76C2×C4×C151—22no—
77C2×C4×C151—22no—
78C2×C4×C151—22no—
79C2×C4×C151C2×Q812yes—
80C2×C4×C151C2×Q814yes—
81C2×C4×C151#4112yes—
82C2×C4×C151#4112yes—
83C22×C151C22×Q811yescharacteristic
84C22×C151C2×#4111yescharacteristic
85C22×C151C2×#4111yescharacteristic
86C22×C151H(5,𝔽2)11yescharacteristic
87C22×C151H(5,𝔽2)11yescharacteristic
88C22×C1512−1+411yescharacteristic
89C22×C1512−1+411yescharacteristic
90C4×C151—22no—
91C4×C151—22no—
92C4×C151—22no—
93C4×C151—24no—
94C4×C151—42no—
95Dic151—42no—
96Dic151—42no—
97Dic151—42no—
98Dic151—42no—
99C2×C151#53811yescharacteristic
100C2×C151#53911yescharacteristic
101C2×C151#54411yescharacteristic
102C2×C151#55411yescharacteristic
103C2×C151#55611yescharacteristic
104C2×C151#55711yescharacteristic
105C2×C151#56311yescharacteristic
106C151#280511yescharacteristic, complemented, Sylow
107#2805—1511nomaximal, Sylow
108#400—1512no—
109#400—1512no—
110#395—1512no—
111#391—1511no—
112#389—1512no—
113#389—1511no—
114#389D15111yescharacteristic
115#387—1512no—
116#387—1512no—
117C22×Q8—1511no—
118C2×C4⋊C4—1512no—
119C2×C4⋊C4—1511no—
120C2×C4⋊C4—1511no—
121C2×C4⋊C4—1512no—
122C2×C4⋊C4—1511no—
123C2×C4⋊C4—1512no—
124C2×C4⋊C4C2×D15112yes—
125C2×C4⋊C4C2×D15111yescharacteristic
126C2×C4⋊C4C2×D15111yescharacteristic
127C2×C42—1512no—
128C2×C42C2×D15111yescharacteristic
129#95—1512no—
130#95—1512no—
131#95—1512no—
132#95—1512no—
133#95—1512no—
134#95—1512no—
135#95—1512no—
136#95—1512no—
137#95C2×D15112yes—
138C2×Q8—3022no—
139C2×Q8—6041no—
140C2×Q8—6041no—
141C22×C4—1512no—
142C22×C4—1512no—
143C22×C4—1512no—
144C22×C4—1512no—
145C22×C4C22×D15112yes—
146C22×C4C22×D15111yescharacteristic
147C22×C4C22×D15112yes—
148C22×C4C22×D15111yescharacteristic
149C22×C4C22×D15111yescharacteristic
150C4⋊C4—24no—
151C4⋊C4—41no—
152C4⋊C4—3022no—
153C4⋊C4—3024no—
154C4⋊C4—6041no—
155C4⋊C4—6042no—
156C4⋊C4—6041no—
157C4⋊C4—6042no—
158C4⋊C4Dic30214yescomplemented
159C42—41no—
160C42—6042no—
161C23C23×D15111yescharacteristic
162Q8—6044no—
163C2×C4—22no—
164C2×C4—21no—
165C2×C4—21no—
166C2×C4—21no—
167C2×C4—22no—
168C2×C4—21no—
169C2×C4—21no—
170C2×C4—21no—
171C2×C4—22no—
172C2×C4—22no—
173C2×C4—22no—
174C2×C4—3022no—
175C2×C4—3022no—
176C2×C4—3022no—
177C2×C4—3022no—
178C2×C4—3022no—
179C2×C4—3022no—
180C2×C4—3022no—
181C2×C4—3022no—
182C2×C4—3022no—
183C2×C4—3022no—
184C2×C4—3022no—
185C2×C4—3022no—
186C2×C4C2×Dic30212yes—
187C2×C4C2×Dic30214yes—
188C2×C4#1455900312yes—
189C2×C4#1455900512yes—
190C22C22×Dic30211yescharacteristic
191C22C2×#1455900311yescharacteristic
192C22C2×#1455900511yescharacteristic
193C22#1801278411yescharacteristic
194C22#1801278511yescharacteristic
195C22#1801278611yescharacteristic
196C22#1801278711yescharacteristic
197C4—22no—
198C4—22no—
199C4—22no—
200C4—24no—
201C4—42no—
202C4—6042no—
203C4—6042no—
204C4—6042no—
205C4—6042no—
206C2#2375280211yescharacteristic
207C2#2375280711yescharacteristic
208C2#2375284311yescharacteristic
209C2#2375291911yescharacteristic
210C2#2375293611yescharacteristic
211C2#2375294111yescharacteristic
212C2#2375296611yescharacteristic
subgroupG/H
center, FrattiniC23C23×D151
commutator, socle, prime radical, cosocleC23×C151C24
Fitting#389×C151C2
hypercenter#389D151
hypocenterC151#2805
LCSG ▷ C23×C151 ▷ C151
UCSC1 ◁ C23 ◁ #389

Complements

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

NH ≅ G/Ntype
52. C4⋊C4×C151Q8semidirect
106. C151#2805semidirect
158. C4⋊C4Dic302semidirect

Maximal subgroups

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

subgroupindex
#237521512
#237521332
#237521182
#237521112
#237521102
#237520992
#237520982
#389×C1512
#2805151