Finite Group Databasebeta

← #34079041

Subgroups — #34079041

Order 19328.

414 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 414 conjugacy classes of subgroups — too many to draw. Only its 133 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#23752723C211yesmaximal, characteristic
2#23752553C214yesmaximal, complemented
3#23752536C214yesmaximal, complemented
4#23752252C212yesmaximal, complemented
5#23752211C212yesmaximal, complemented
6#23752176C211yesmaximal, characteristic, complemented
7C2×#117×C151C211yesmaximal, characteristic, complemented
8C2×#14559004C2211yescharacteristic
9C2×#14558988C2212yes—
10#18012722—21no—
11#18012718C2212yes—
12#18012713C2212yes—
13#18012708—21no—
14C4×C22⋊D151—22no—
15#18012698C2211yescharacteristic
16#18012672C2214yescomplemented
17#18012670C2214yescomplemented
18#18012662C2214yescomplemented
19#18012659C2214yescomplemented
20C22⋊(C151⋊C8)C2214yes—
21C23×C4×C151C2211yescharacteristic
22#117×C151—22no—
23#117×C151C2214yes—
24C2×C4⋊C4×C151C2212yes—
25C2×C22⋊C4×C151—21no—
26C2×C42×C151—21no—
27#14559004—24no—
28C2×Dic302C2311yescharacteristic
29C2×D604C2311yescharacteristic
30C2×C22⋊D151—22no—
31C2×C22⋊D151—21no—
32C2×C4×D151—21no—
33#14558988—24no—
34C2×C151⋊C8C2314yes—
35C4⋊Dic151C2312yes—
36Dic151⋊C4—22no—
37C22⋊Dic151—21no—
38C22⋊Dic151—22no—
39(C2×D151)⋊C4—22no—
40C4×Dic151—21no—
41C24×C151D411yescharacteristic
42C22×C4×C151—24no—
43C22×C4×C151—22no—
44C22×C4×C151D412yes—
45C22×C4×C151D411yescharacteristic
46C22×C4×C151C2312yes—
47C22×C4×C151C2311yescharacteristic
48C4⋊C4×C151—22no—
49C4⋊C4×C151C2314yes—
50C22⋊C4×C151—24no—
51C42×C151—24no—
52C22×D151—21no—
53Dic302—22no—
54D604—22no—
55C22⋊D151—44no—
56C22⋊D151—42no—
57C2×Dic151—22no—
58C2×Dic151—21no—
59C4×D151—42no—
60C151⋊C8—24no—
61C23×C151—22no—
62C23×C151—42no—
63C23×C151C2×D412yes—
64C23×C151C2×D411yescharacteristic
65C2×C4×C151—22no—
66C2×C4×C151—24no—
67C2×C4×C151—24no—
68C2×C4×C151—24no—
69C2×C4×C151—44no—
70C2×C4×C151C2×D412yes—
71C2×C4×C151C2×D411yescharacteristic
72C2×C4×C151#4114yes—
73C2×C4×C151C2411yescharacteristic
74C22×C151—22no—
75C22×C151—22no—
76C22×C151—22no—
77C22×C151—22no—
78C22×C151—44no—
79C22×C151#12312yes—
80C22×C151C22×D411yescharacteristic
81C2×D151—41no—
82C2×D151—42no—
83C4×C151—22no—
84C4×C151—44no—
85C4×C151#12312yes—
86C4×C151C2×#4112yes—
87Dic151—41no—
88Dic151—42no—
89C2×C151—22no—
90C2×C151—42no—
91C2×C151C2×#12311yescharacteristic
92C2×C151#57512yes—
93D151—81no—
94C151#309311yescharacteristic, complemented, Sylow
95#3093—1511nomaximal, Sylow
96#525—1511no—
97C2×#117D15111yescharacteristic, complemented
98#485—1514no—
99#482—1514no—
100#428—1512no—
101#417—1512no—
102#407—1511no—
103C2×#41—1511no—
104C23×C4C2×D15111yescharacteristic
105C2×M16—1512no—
106#123—3021no—
107C22⋊Q8—1512no—
108#121—1512no—
109#120—3021no—
110C4×D4—3022no—
111#117—22no—
112#117—1511no—
113#117C2×D15114yes—
114C2×C4⋊C4C2×D15112yes—
115C2×C22⋊C4—21no—
116C2×C42—21no—
117#107—1514no—
118#106—1514no—
119#103—1514no—
120#102—1514no—
121C22⋊C8—1514no—
122C24C22⋊D15111yescharacteristic
123#41—3024no—
124C2×Q8—1511no—
125C2×D4—3022no—
126C2×D4—3021no—
127C2×D4—1511no—
128C22×C4—24no—
129C22×C4—22no—
130C22×C4—3021no—
131C22×C4C22⋊D15111yescharacteristic
132C22×C4C22⋊D15112yes—
133C22×C4C22×D15112yes—
134C22×C4C22×D15111yescharacteristic
135M16—3024no—
136C2×C8—1514no—
137C4⋊C4—22no—
138C4⋊C4—3022no—
139C4⋊C4—1512no—
140C4⋊C4C22×D15114yes—
141C22⋊C4—24no—
142C22⋊C4—3021no—
143C22⋊C4—3022no—
144C22⋊C4—3022no—
145C42—24no—
146C42—3021no—
147C23—22no—
148C23—42no—
149C23—3021no—
150C23C2×C22⋊D15112yes—
151C23C2×C22⋊D15111yescharacteristic
152Q8—3022no—
153D4—3022no—
154D4—6044no—
155D4—6042no—
156C2×C4—22no—
157C2×C4—24no—
158C2×C4—24no—
159C2×C4—24no—
160C2×C4—44no—
161C2×C4—3022no—
162C2×C4—3021no—
163C2×C4—6042no—
164C2×C4C2×C22⋊D15112yes—
165C2×C4C2×C22⋊D15111yescharacteristic
166C2×C4#1455900414yes—
167C2×C4C23×D15111yescharacteristic
168C8—3024no—
169C22—22no—
170C22—22no—
171C22—22no—
172C22—22no—
173C22—44no—
174C22—6041no—
175C22—6042no—
176C22#1801272212yes—
177C22C22×C22⋊D15111yescharacteristic
178C4—22no—
179C4—44no—
180C4—6041no—
181C4—6042no—
182C4#1801272212yes—
183C4C2×#1455900412yes—
184C2—22no—
185C2—42no—
186C2—12081no—
187C2C2×#1801272211yescharacteristic
188C2#2375301012yes—
subgroupG/H
centerC22C22×C22⋊D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
FittingC2×#117×C151C2
socleC22×C151C22×D4
prime radical#23752723C2
hypercenterC2×#117D151
hypocenterC151#3093
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#117

Complements

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

NH ≅ G/Ntype
2. #23752553C2semidirect
3. #23752536C2semidirect
4. #23752252C2semidirect
5. #23752211C2semidirect
6. #23752176C2semidirect
7. C2×#117×C151C2semidirect
16. #18012672C22semidirect
17. #18012670C22semidirect
18. #18012662C22semidirect
19. #18012659C22semidirect
94. C151#3093semidirect
97. C2×#117D151semidirect

Maximal subgroups

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

subgroupindex
#237527232
#237525532
#237525362
#237522522
#237522112
#237521762
C2×#117×C1512
#3093151