Finite Group Databasebeta

← #34076998

Subgroups — #34076998

Order 19328.

376 conjugacy classes of subgroups; only the 129 normal subgroups are shown.

normal subgroups only

This group has 376 conjugacy classes of subgroups — too many to draw. Only its 129 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#23752152C212yesmaximal
2#23752146C212yesmaximal
3#23752132C211yesmaximal, characteristic
4#23752117C211yesmaximal, characteristic
5#23752116C212yesmaximal
6#23752116C212yesmaximal
7#23752099C212yesmaximal
8#23752093C212yesmaximal
9#400×C151C211yesmaximal, characteristic
10C22×Dic302C2211yescharacteristic
11C22×Dic302C2211yescharacteristic
12C2×C4⋊Dic151C2212yes—
13C2×Dic151⋊C4C2212yes—
14C2×Dic151⋊C4C2212yes—
15C2×Dic151⋊C4C2212yes—
16C2×C4×Dic151C2212yes—
17C2×C4×Dic151C2211yescharacteristic
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—24no—
32C2×Dic302—41no—
33C2×Dic302—41no—
34C2×Dic302—41no—
35C2×Dic302Q814yescomplemented
36C22×Dic151C2312yes—
37C22×Dic151C2312yes—
38C22×Dic151C2312yes—
39C22×Dic151C2312yes—
40C4⋊Dic151—42no—
41Dic151⋊C4—24no—
42Dic151⋊C4—24no—
43Dic151⋊C4—42no—
44C4×Dic151—41no—
45C4×Dic151—42no—
46C22×C4×C151C2312yes—
47C22×C4×C151C2312yes—
48C22×C4×C151C2311yescharacteristic
49C22×C4×C151C2311yescharacteristic
50C22×C4×C151C2311yescharacteristic
51C4⋊C4×C151—41no—
52C4⋊C4×C151—41no—
53Dic302—44no—
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×Dic151C2×Q814yes—
66C2×Dic151#4114yes—
67C23×C151C2411yescharacteristic
68C2×C4×C151—21no—
69C2×C4×C151—21no—
70C2×C4×C151—22no—
71C2×C4×C151—22no—
72C2×C4×C151—22no—
73C2×C4×C151—22no—
74C2×C4×C151—22no—
75C2×C4×C151—21no—
76C2×C4×C151—21no—
77C2×C4×C151—22no—
78C2×C4×C151—24no—
79C2×C4×C151C2×Q812yes—
80C22×C151C22×Q811yescharacteristic
81C22×C151C2×#4112yes—
82C22×C151H(5,𝔽2)11yescharacteristic
83C22×C151H(5,𝔽2)11yescharacteristic
84C22×C1512−1+412yes—
85C4×C151—22no—
86C4×C151—42no—
87C4×C151—41no—
88C4×C151—41no—
89C4×C151—42no—
90Dic151—24no—
91Dic151—24no—
92Dic151—42no—
93Dic151—42no—
94C2×C151#54212yes—
95C2×C151#54311yescharacteristic
96C2×C151#55111yescharacteristic
97C2×C151#55712yes—
98C2×C151#56311yescharacteristic
99C151#279911yescharacteristic, complemented, Sylow
100#2799—1511nomaximal, Sylow
101#400—1512no—
102#400D15111yescharacteristic
103#398—1512no—
104#395—1511no—
105#391—1511no—
106#391—1512no—
107#391—1512no—
108#387—1512no—
109#387—1512no—
110C22×Q8—1511no—
111C22×Q8—1511no—
112C2×C4⋊C4—1512no—
113C2×C4⋊C4—1512no—
114C2×C4⋊C4—1512no—
115C2×C4⋊C4—1512no—
116C2×C4⋊C4C2×D15111yescharacteristic
117C2×C4⋊C4C2×D15111yescharacteristic
118C2×C42—1511no—
119C2×C42—1512no—
120#95—1512no—
121#95—1512no—
122#95—1512no—
123#95—1512no—
124#95—1512no—
125#95—1512no—
126#95—1512no—
127#95—1511no—
128#95C2×D15112yes—
129#95C2×D15112yes—
130#95C2×D15111yescharacteristic
131C2×Q8—3024no—
132C2×Q8—6041no—
133C2×Q8—6041no—
134C2×Q8—6041no—
135C2×Q8—1514no—
136C22×C4—1512no—
137C22×C4—1512no—
138C22×C4—1512no—
139C22×C4—1512no—
140C22×C4C22×D15112yes—
141C22×C4C22×D15111yescharacteristic
142C22×C4C22×D15111yescharacteristic
143C22×C4C22×D15112yes—
144C22×C4C22×D15111yescharacteristic
145C4⋊C4—41no—
146C4⋊C4—41no—
147C4⋊C4—3024no—
148C4⋊C4—3024no—
149C4⋊C4—6042no—
150C4⋊C4—6042no—
151C42—6041no—
152C42—6042no—
153C23C23×D15111yescharacteristic
154Q8—6044no—
155Q8—6044no—
156C2×C4—21no—
157C2×C4—21no—
158C2×C4—22no—
159C2×C4—22no—
160C2×C4—22no—
161C2×C4—22no—
162C2×C4—21no—
163C2×C4—21no—
164C2×C4—22no—
165C2×C4—24no—
166C2×C4—22no—
167C2×C4—3022no—
168C2×C4—3022no—
169C2×C4—3022no—
170C2×C4—3022no—
171C2×C4—3022no—
172C2×C4—3022no—
173C2×C4—3022no—
174C2×C4—3022no—
175C2×C4—3022no—
176C2×C4—3022no—
177C2×C4—1514no—
178C2×C4—1514no—
179C2×C4Q8×D15112yes—
180C22C2×Q8×D15111yescharacteristic
181C22#41×D15112yes—
182C22#1801278411yescharacteristic
183C22#1801278511yescharacteristic
184C22#1801278612yes—
185C4—22no—
186C4—42no—
187C4—42no—
188C4—41no—
189C4—41no—
190C4—3024no—
191C4—3024no—
192C4—6042no—
193C4—6042no—
194C2#2375282812yes—
195C2#2375283711yescharacteristic
196C2#2375289011yescharacteristic
197C2#2375293912yes—
198C2#2375296211yescharacteristic
subgroupG/H
center, FrattiniC23C23×D151
commutator, socle, prime radical, cosocleC23×C151C24
Fitting#400×C151C2
hypercenter#400D151
hypocenterC151#2799
LCSG ▷ C23×C151 ▷ C151
UCSC1 ◁ C23 ◁ #400

Complements

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

NH ≅ G/Ntype
35. C2×Dic302Q8semidirect
99. C151#2799semidirect

Maximal subgroups

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

subgroupindex
#237521522
#237521462
#237521322
#237521172
#237521162
#237520992
#237520932
#400×C1512
#2799151