Finite Group Databasebeta

← #34079975

Subgroups — #34079975

Order 19328.

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

normal subgroups only

This group has 442 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#23752776C212yesmaximal, complemented
2#23752537C214yesmaximal, complemented
3#23752465C212yesmaximal, complemented
4#23752448C212yesmaximal, complemented
5#23752348C214yesmaximal, complemented
6#408×C151C211yesmaximal, characteristic, complemented
7C22×D604C2212yescomplemented
8C2×D1208C2212yes—
9C2×D1208C2212yes—
10#18012735—22no—
11#18012728—22no—
12#18012713C2214yes—
13#18012713C2214yescomplemented
14#18012707—22no—
15#18012707—22no—
16#18012698C2212yescomplemented
17#18012673C2212yescomplemented
18#18012671C2212yescomplemented
19#18012661C2214yescomplemented
20#18012661C2214yescomplemented
21C2×#41×C151C2211yescharacteristic
22C2×M16×C151C2211yescharacteristic, complemented
23C22×C8×C151C2211yescharacteristic, complemented
24C22⋊C8×C151C2214yescomplemented
25C23×D151—22no—
26C2×D604—22no—
27C2×D604—42no—
28C2×D604—42no—
29C2×D604C2314yes—
30C2×C22⋊D151—24no—
31C2×C22⋊D151—24no—
32D1208—42no—
33D1208—42no—
34C4⋊Dic151C2314yes—
35C22⋊Dic151—22no—
36(C2×D151)⋊C4—24no—
37(C2×D151)⋊C4—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—
50C22×D151—24no—
51C22×D151—44no—
52C22×D151—84no—
53D604—24no—
54D604—24no—
55D604—44no—
56C22⋊D151—84no—
57C22⋊D151—84no—
58C2×Dic151—24no—
59C23×C151C2×D412yes—
60C23×C151C2×D411yescharacteristic
61Q8×C151—41no—
62D4×C151—41no—
63D4×C151—42no—
64C2×C4×C151—22no—
65C2×C4×C151—22no—
66C2×C4×C151—21no—
67C2×C4×C151—21no—
68C2×C4×C151C2×D412yes—
69C2×C4×C151C2×D411yescharacteristic
70C2×C4×C151C2411yescharacteristic
71C8×C151—22no—
72C8×C151—22no—
73C22×C151—21no—
74C22×C151—22no—
75C22×C151—22no—
76C22×C151—24no—
77C22×C151C22×D411yescharacteristic
78C2×D151—44no—
79C2×D151—44no—
80C2×D151—44no—
81C2×D151—88no—
82C4×C151—21no—
83C4×C151—22no—
84C4×C151H(5,𝔽2)11yescharacteristic
85C4×C151H(5,𝔽2)11yescharacteristic
86Dic151—44no—
87C2×C151—42no—
88C2×C151—41no—
89C2×C151#53411yescharacteristic
90C2×C151#57612yes—
91D151—84no—
92C151#319911yescharacteristic, complemented, Sylow
93#3199—1511nomaximal, Sylow
94#535—1512no—
95#482—1514no—
96#469—1512no—
97#466—1512no—
98#447—1514no—
99#408D15111yescharacteristic, complemented
100C2×#41C2×D15111yescharacteristic
101C22×D4—1512no—
102C2×D8—1512no—
103C2×D8—1512no—
104C2×M16C2×D15111yescharacteristic, complemented
105C22×C8C2×D15111yescharacteristic, complemented
106#127—3022no—
107#124—3022no—
108#121—1514no—
109#121—1514no—
110#120—3022no—
111#120—3022no—
112#117—1512no—
113#107—1512no—
114#106—1512no—
115#102—1514no—
116#102—1514no—
117C22⋊C8C2×D15114yescomplemented
118C24—3022no—
119#41—41no—
120#41—41no—
121C2×Q8D60411yescharacteristic
122C2×D4—3024no—
123C2×D4—3024no—
124C2×D4—3022no—
125C2×D4—6042no—
126C2×D4—6042no—
127C2×D4—1514no—
128C2×D4D60411yescharacteristic
129C2×D4D60412yes—
130C22×C4C22×D15112yes—
131C22×C4C22×D15111yescharacteristic
132D8—6042no—
133D8—6042no—
134M16—41no—
135C2×C8—41no—
136C2×C8C22×D15112yes—
137C2×C8C22×D15112yes—
138C4⋊C4—1514no—
139C22⋊C4—3022no—
140C22⋊C4—3024no—
141C22⋊C4—3024no—
142C42—3022no—
143C23—3024no—
144C23—6044no—
145C23—12084no—
146C23C2×D60412yes—
147C23C2×D60411yescharacteristic
148Q8—41no—
149D4—42no—
150D4—41no—
151D4—3024no—
152D4—3024no—
153D4—6044no—
154D4—12084no—
155D4—12084no—
156C2×C4—21no—
157C2×C4—21no—
158C2×C4—22no—
159C2×C4—22no—
160C2×C4—3024no—
161C2×C4C2×D60412yes—
162C2×C4C2×D60411yescharacteristic
163C2×C4C23×D15111yescharacteristic
164C8—22no—
165C8—22no—
166C22—22no—
167C22—24no—
168C22—22no—
169C22—21no—
170C22—6044no—
171C22—6044no—
172C22—6044no—
173C22—12088no—
174C22C22×D60411yescharacteristic
175C4—22no—
176C4—21no—
177C4—6044no—
178C4#1801278411yescharacteristic
179C4#1801278411yescharacteristic
180C2—42no—
181C2—41no—
182C2—12084no—
183C2#2375277411yescharacteristic
184C2#2375301712yes—
subgroupG/H
centerC22C22×D604
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#408×C151C2
socleC22×C151C22×D4
hypercenter#408D151
hypocenterC151#3199
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
1. #23752776C2semidirect
2. #23752537C2semidirect
3. #23752465C2semidirect
4. #23752448C2semidirect
5. #23752348C2semidirect
6. #408×C151C2semidirect
7. C22×D604C22semidirect
13. #18012713C22semidirect
16. #18012698C22semidirect
17. #18012673C22semidirect
18. #18012671C22semidirect
19. #18012661C22semidirect
20. #18012661C22semidirect
22. C2×M16×C151C22semidirect
23. C22×C8×C151C22semidirect
24. C22⋊C8×C151C22semidirect
92. C151#3199semidirect
99. #408D151semidirect
104. C2×M16C2×D151semidirect
105. C22×C8C2×D151semidirect
117. C22⋊C8C2×D151semidirect

Maximal subgroups

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

subgroupindex
#237527762
#237525372
#237524652
#237524482
#237523482
#408×C1512
#3199151