Finite Group Databasebeta

← #34080005

Subgroups — #34080005

Order 19328.

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

normal subgroups only

This group has 378 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
1#23752783C212yesmaximal
2#23752554C214yesmaximal, complemented
3#23752470C212yesmaximal, complemented
4#23752453C212yesmaximal, complemented
5#23752370C214yesmaximal, complemented
6#408×C151C211yesmaximal, characteristic
7C22×Dic302C2212yes—
8C2×Dic604C2212yes—
9C2×Dic604C2212yes—
10#18012737—22no—
11#18012726—22no—
12#18012720—22no—
13#18012720—22no—
14#18012718C2214yes—
15#18012718C2214yes—
16#18012698C2212yes—
17#18012673C2212yes—
18#18012671C2212yes—
19#18012664C2214yes—
20#18012664C2214yes—
21C2×#41×C151C2211yescharacteristic
22C2×M16×C151C2211yescharacteristic
23C22×C8×C151C2211yescharacteristic
24C22⋊C8×C151C2214yes—
25C2×Dic302—22no—
26C2×Dic302—42no—
27C2×Dic302—42no—
28C2×Dic302C2314yes—
29C22×Dic151—22no—
30Dic604—42no—
31Dic604—42no—
32C4⋊Dic151C2314yes—
33Dic151⋊C4—24no—
34Dic151⋊C4—24no—
35C22⋊Dic151—22no—
36C22⋊Dic151—24no—
37C22⋊Dic151—24no—
38C4×Dic151—22no—
39#41×C151—41no—
40#41×C151—41no—
41C2×Q8×C151D411yescharacteristic
42C2×D4×C151D411yescharacteristic
43C2×D4×C151D412yes—
44C22×C4×C151C2312yes—
45C22×C4×C151C2311yescharacteristic
46M16×C151—41no—
47C2×C8×C151—41no—
48C2×C8×C151C2312yes—
49C2×C8×C151C2312yes—
50Dic302—24no—
51Dic302—24no—
52Dic302—44no—
53C2×Dic151—24no—
54C2×Dic151—24no—
55C2×Dic151—44no—
56C23×C151C2×D411yescharacteristic
57C23×C151C2×D412yes—
58Q8×C151—41no—
59D4×C151—41no—
60D4×C151—42no—
61C2×C4×C151—22no—
62C2×C4×C151—22no—
63C2×C4×C151—21no—
64C2×C4×C151—21no—
65C2×C4×C151C2×D412yes—
66C2×C4×C151C2×D411yescharacteristic
67C2×C4×C151C2411yescharacteristic
68C8×C151—22no—
69C8×C151—22no—
70C22×C151—21no—
71C22×C151—22no—
72C22×C151—22no—
73C22×C151—24no—
74C22×C151C22×D411yescharacteristic
75C4×C151—21no—
76C4×C151—22no—
77C4×C151H(5,𝔽2)11yescharacteristic
78C4×C151H(5,𝔽2)11yescharacteristic
79Dic151—44no—
80Dic151—44no—
81C2×C151—41no—
82C2×C151—42no—
83C2×C151#53411yescharacteristic
84C2×C151#57812yes—
85C151#320211yescharacteristic, complemented, Sylow
86#3202—1511nomaximal, Sylow
87#536—1512no—
88#485—1514no—
89#470—1512no—
90#467—1512no—
91#451—1514no—
92#408D15111yescharacteristic
93C2×#41C2×D15111yescharacteristic
94C22×Q8—1512no—
95C2×Q16—1512no—
96C2×Q16—1512no—
97C2×M16C2×D15111yescharacteristic
98C22×C8C2×D15111yescharacteristic
99C4⋊Q8—3022no—
100#124—3022no—
101#123—3022no—
102#123—3022no—
103C22⋊Q8—1514no—
104C22⋊Q8—1514no—
105#117—1512no—
106#107—1512no—
107#106—1512no—
108#103—1514no—
109#103—1514no—
110C22⋊C8C2×D15114yes—
111#41—41no—
112#41—41no—
113C2×Q8—3022no—
114C2×Q8—6042no—
115C2×Q8—6042no—
116C2×Q8—1514no—
117C2×Q8D60411yescharacteristic
118C2×D4D60411yescharacteristic
119C2×D4D60412yes—
120C22×C4—3022no—
121C22×C4C22×D15112yes—
122C22×C4C22×D15111yescharacteristic
123Q16—6042no—
124Q16—6042no—
125M16—41no—
126C2×C8—41no—
127C2×C8C22×D15112yes—
128C2×C8C22×D15112yes—
129C4⋊C4—3024no—
130C4⋊C4—3024no—
131C4⋊C4—1514no—
132C22⋊C4—3022no—
133C22⋊C4—3024no—
134C22⋊C4—3024no—
135C42—3022no—
136C23C2×D60411yescharacteristic
137C23C2×D60412yes—
138Q8—41no—
139Q8—3024no—
140Q8—3024no—
141Q8—6044no—
142D4—42no—
143D4—41no—
144C2×C4—21no—
145C2×C4—21no—
146C2×C4—22no—
147C2×C4—22no—
148C2×C4—3024no—
149C2×C4—3024no—
150C2×C4—6044no—
151C2×C4C2×D60412yes—
152C2×C4C2×D60411yescharacteristic
153C2×C4C23×D15111yescharacteristic
154C8—22no—
155C8—22no—
156C22—22no—
157C22—24no—
158C22—22no—
159C22—21no—
160C22C22×D60411yescharacteristic
161C4—22no—
162C4—21no—
163C4—6044no—
164C4—6044no—
165C4#1801278411yescharacteristic
166C4#1801278411yescharacteristic
167C2—42no—
168C2—41no—
169C2#2375277411yescharacteristic
170C2#2375302912yes—
subgroupG/H
centerC22C22×D604
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#408×C151C2
socleC22×C151C22×D4
prime radicalC2×#41×C151C22
hypercenter#408D151
hypocenterC151#3202
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C2×#41 ◁ #408

Complements

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

NH ≅ G/Ntype
2. #23752554C2semidirect
3. #23752470C2semidirect
4. #23752453C2semidirect
5. #23752370C2semidirect
85. C151#3202semidirect

Maximal subgroups

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

subgroupindex
#237527832
#237525542
#237524702
#237524532
#237523702
#408×C1512
#3202151