Finite Group Databasebeta

← #34077291

Subgroups — #34077291

Order 19328.

332 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 332 conjugacy classes of subgroups — too many to draw. Only its 117 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
1C151⋊#401C212yesmaximal
2#23752154C212yesmaximal
3#23752151C212yesmaximal
4#23752144C212yesmaximal
5#23752142C211yesmaximal, characteristic
6#23752133C212yesmaximal
7#23752117C211yesmaximal, characteristic
8#23752094C212yesmaximal
9#400×C151C211yesmaximal, characteristic
10C22×Dic302C2211yescharacteristic
11C2×C4⋊Dic151C2212yes—
12C2×C4⋊Dic151C2212yes—
13C2×C4⋊Dic151C2211yescharacteristic
14C2×Dic151⋊C4C2212yes—
15C2×Dic151⋊C4C2212yes—
16C2×C4×Dic151C2211yescharacteristic
17C151⋊#95C2212yes—
18C151⋊#95C2212yes—
19C151⋊#95C2212yes—
20C151⋊#95C2212yes—
21C151⋊#95C2212yes—
22C151⋊#95C2212yes—
23C151⋊#95C2212yes—
24C151⋊#95C2212yes—
25C151⋊#95C2211yescharacteristic
26C2×C4⋊C4×C151C2211yescharacteristic
27C2×C4⋊C4×C151C2211yescharacteristic
28#95×C151C2212yes—
29#95×C151C2212yes—
30#95×C151C2211yescharacteristic
31C2×Dic302—22no—
32C2×Dic302—41no—
33C2×Dic302—41no—
34C22×Dic151C2312yes—
35C22×Dic151C2312yes—
36C22×Dic151C2312yes—
37C22×Dic151C2312yes—
38C4⋊Dic151—42no—
39C4⋊Dic151—41no—
40C4⋊Dic151—42no—
41Dic151⋊C4—24no—
42Dic151⋊C4—42no—
43C4×Dic151—41no—
44C22×C4×C151C2312yes—
45C22×C4×C151C2312yes—
46C22×C4×C151C2311yescharacteristic
47C22×C4×C151C2311yescharacteristic
48C22×C4×C151C2311yescharacteristic
49C4⋊C4×C151—41no—
50C4⋊C4×C151—41no—
51Dic302—44no—
52C2×Dic151—22no—
53C2×Dic151—22no—
54C2×Dic151—22no—
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—
64C23×C151C2411yescharacteristic
65C2×C4×C151—21no—
66C2×C4×C151—21no—
67C2×C4×C151—22no—
68C2×C4×C151—22no—
69C2×C4×C151—21no—
70C2×C4×C151—21no—
71C2×C4×C151—22no—
72C2×C4×C151—22no—
73C2×C4×C151—24no—
74C2×C4×C151—22no—
75C2×C4×C151—22no—
76C2×C4×C151#4112yes—
77C22×C151C2×#4111yescharacteristic
78C22×C151H(5,𝔽2)11yescharacteristic
79C22×C151H(5,𝔽2)11yescharacteristic
80C22×C1512−1+412yes—
81C22×C1512−1+412yes—
82C4×C151—22no—
83C4×C151—42no—
84C4×C151—42no—
85C4×C151—41no—
86C4×C151—41no—
87Dic151—42no—
88Dic151—42no—
89Dic151—42no—
90Dic151—42no—
91C2×C151#53811yescharacteristic
92C2×C151#54112yes—
93C2×C151#56311yescharacteristic
94C2×C151#56312yes—
95C2×C151#56311yescharacteristic
96C151#283311yescharacteristic, complemented, Sylow
97#2833—1511nomaximal, Sylow
98#401—1512no—
99#400—1512no—
100#400—1512no—
101#400D15111yescharacteristic
102#398—1511no—
103#398—1512no—
104#395—1512no—
105#391—1511no—
106#387—1512no—
107C22×Q8—1511no—
108C2×C4⋊C4—1512no—
109C2×C4⋊C4—1512no—
110C2×C4⋊C4—1512no—
111C2×C4⋊C4—1512no—
112C2×C4⋊C4—1511no—
113C2×C4⋊C4C2×D15111yescharacteristic
114C2×C4⋊C4C2×D15111yescharacteristic
115C2×C42—1511no—
116#95—1512no—
117#95—1512no—
118#95—1512no—
119#95—1512no—
120#95—1512no—
121#95—1512no—
122#95—1512no—
123#95—1512no—
124#95—1511no—
125#95C2×D15112yes—
126#95C2×D15112yes—
127#95C2×D15111yescharacteristic
128C2×Q8—3022no—
129C2×Q8—6041no—
130C2×Q8—6041no—
131C22×C4—1512no—
132C22×C4—1512no—
133C22×C4—1512no—
134C22×C4—1512no—
135C22×C4C22×D15111yescharacteristic
136C22×C4C22×D15112yes—
137C22×C4C22×D15111yescharacteristic
138C22×C4C22×D15112yes—
139C22×C4C22×D15111yescharacteristic
140C4⋊C4—41no—
141C4⋊C4—41no—
142C4⋊C4—3024no—
143C4⋊C4—6042no—
144C4⋊C4—6041no—
145C4⋊C4—6042no—
146C4⋊C4—6042no—
147C42—6041no—
148C23C23×D15111yescharacteristic
149Q8—6044no—
150C2×C4—21no—
151C2×C4—21no—
152C2×C4—21no—
153C2×C4—22no—
154C2×C4—21no—
155C2×C4—22no—
156C2×C4—24no—
157C2×C4—22no—
158C2×C4—22no—
159C2×C4—22no—
160C2×C4—22no—
161C2×C4—3022no—
162C2×C4—3022no—
163C2×C4—3022no—
164C2×C4—3022no—
165C2×C4—3022no—
166C2×C4—3022no—
167C2×C4—3022no—
168C2×C4—3022no—
169C2×C4—3022no—
170C2×C4—3022no—
171C2×C4—3022no—
172C2×C4—3022no—
173C2×C4#1455900512yes—
174C22C2×#1455900511yescharacteristic
175C22#1801278411yescharacteristic
176C22#1801278511yescharacteristic
177C22#1801278612yes—
178C22#1801278612yes—
179C4—22no—
180C4—42no—
181C4—42no—
182C4—41no—
183C4—41no—
184C4—6042no—
185C4—6042no—
186C4—6042no—
187C4—6042no—
188C2#2375280211yescharacteristic
189C2#2375282512yes—
190C2#2375296211yescharacteristic
191C2#2375296412yes—
192C2#2375296511yescharacteristic
subgroupG/H
center, FrattiniC23C23×D151
commutator, socle, prime radical, cosocleC23×C151C24
Fitting#400×C151C2
hypercenter#400D151
hypocenterC151#2833
LCSG ▷ C23×C151 ▷ C151
UCSC1 ◁ C23 ◁ #400

Complements

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

NH ≅ G/Ntype
96. C151#2833semidirect

Maximal subgroups

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

subgroupindex
C151⋊#4012
#237521542
#237521512
#237521442
#237521422
#237521332
#237521172
#237520942
#400×C1512
#2833151