Finite Group Databasebeta

← #34070778

Subgroups — #34070778

Order 19328.

286 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 286 conjugacy classes of subgroups — too many to draw. Only its 55 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#23752780C211yesmaximal, characteristic
2#99×D151C212yesmaximal, complemented
3#23752007C211yesmaximal, characteristic, complemented
4#23752004C212yesmaximal, complemented
5#354×C151C211yesmaximal, characteristic, complemented
6C2×#14559005C411yescharacteristic, complemented
7C2×D4×D151C2211yescharacteristic
8#18012736C411yescharacteristic, complemented
9#18012735C2211yescharacteristic
10#18012728C411yescharacteristic, complemented
11#18012712—22no—
12#18012709—22no—
13#18012696C411yescharacteristic, complemented
14C22⋊C4×D151—22no—
15#18012654C2212yes—
16#18012653—22no—
17#124×C151C2211yescharacteristic
18#99×C151C2212yes—
19C23×D151D412yes—
20#14559005—42no—
21C2×D604—21no—
22C2×D604—22no—
23C2×D604C2×C411yescharacteristic
24C2×D604C2×C411yescharacteristic, complemented
25C2×C22⋊D151—22no—
26C2×C22⋊D151D412yes—
27D4×D151—42no—
28C2×C4×D151—21no—
29C2×C4×D151—42no—
30C2×C4×D151C2×C411yescharacteristic
31Dic151⋊C4—21no—
32C22⋊Dic151—22no—
33(C2×D151)⋊C4—21no—
34(C2×D151)⋊C4—22no—
35(C2×D151)⋊C4—42no—
36C4×Dic151C2×C411yescharacteristic, complemented
37C2×Q8×C151C2×C411yescharacteristic, complemented
38C2×D4×C151C2311yescharacteristic
39C22⋊C4×C151—22no—
40C22⋊C4×C151—22no—
41C42×C151C2×C411yescharacteristic, complemented
42C22×D151—22no—
43C22×D151—22no—
44C22×D151—21no—
45C22×D151—82no—
46C22×D151C22⋊C412yes—
47C22×D151C22⋊C411yescharacteristic
48D604—41no—
49D604—41no—
50D604—42no—
51D604—82no—
52C22⋊D151—42no—
53C22⋊D151—82no—
54C2×Dic151—21no—
55C2×Dic151—42no—
56C2×Dic151C22⋊C411yescharacteristic
57C4×D151—22no—
58C4×D151—42no—
59C4×D151—84no—
60C23×C151C2×D412yes—
61Q8×C151—41no—
62D4×C151—41no—
63C2×C4×C151—21no—
64C2×C4×C151—21no—
65C2×C4×C151—42no—
66C2×C4×C151C22×C411yescharacteristic
67C22×C151—22no—
68C22×C151—42no—
69C22×C151C2×C22⋊C411yescharacteristic
70C2×D151—22no—
71C2×D151—41no—
72C2×D151—44no—
73C2×D151—42no—
74C2×D151—42no—
75C2×D151—41no—
76C2×D151—82no—
77C2×D151#9912yes—
78C4×C151—21no—
79C4×C151—41no—
80C4×C151—41no—
81C4×C151—82no—
82Dic151—21no—
83Dic151—41no—
84Dic151—82no—
85C2×C151—21no—
86C2×C151—42no—
87C2×C151C2×#9911yescharacteristic
88D151—22no—
89D151—42no—
90D151—81no—
91C151#212711yescharacteristic, complemented, Sylow
92#2127—1511nomaximal, Sylow
93#535—1511no—
94C2×#99—1512no—
95#354—1511no—
96#354D15111yescharacteristic, complemented
97#353—1512no—
98C2×#41—1511no—
99C22×D4—1511no—
100#127—1511no—
101#127—1511no—
102#124—1511no—
103#124C2×D15111yescharacteristic
104#121—3022no—
105#120—3022no—
106#117—1511no—
107C2×C22⋊C4—3022no—
108#99—3022no—
109#99—1512no—
110#99C2×D15112yes—
111C24—1512no—
112#41—6042no—
113C2×Q8C4×D15111yescharacteristic, complemented
114C2×D4—3021no—
115C2×D4—3022no—
116C2×D4—3022no—
117C2×D4—6042no—
118C2×D4—1512no—
119C2×D4—1511no—
120C2×D4—1511no—
121C2×D4C22×D15111yescharacteristic
122C22×C4—3021no—
123C22×C4—6042no—
124C22×C4—1511no—
125C4⋊C4—3021no—
126C22⋊C4—22no—
127C22⋊C4—22no—
128C22⋊C4—3021no—
129C22⋊C4—3022no—
130C22⋊C4—3022no—
131C22⋊C4—6042no—
132C42—1511no—
133C42C4×D15111yescharacteristic, complemented
134C23—3022no—
135C23—3022no—
136C23—3021no—
137C23—1512no—
138C23—1511no—
139C23—12082no—
140C23D4×D15112yes—
141Q8—41no—
142D4—41no—
143D4—6041no—
144D4—6041no—
145D4—6042no—
146D4—6042no—
147D4—12082no—
148D4—12082no—
149C2×C4—21no—
150C2×C4—21no—
151C2×C4—42no—
152C2×C4—3022no—
153C2×C4—3021no—
154C2×C4—6042no—
155C2×C4—6042no—
156C2×C4—1511no—
157C2×C4—12084no—
158C2×C4C2×C4×D15111yescharacteristic
159C22—22no—
160C22—42no—
161C22—3022no—
162C22—6041no—
163C22—6042no—
164C22—6042no—
165C22—6044no—
166C22—6041no—
167C22—1512no—
168C22—12082no—
169C22C22⋊C4×D15111yescharacteristic
170C4—21no—
171C4—41no—
172C4—41no—
173C4—82no—
174C4—3021no—
175C4—6041no—
176C4—12082no—
177C2—21no—
178C2—42no—
179C2—3022no—
180C2—6042no—
181C2—12081no—
182C2#99×D15111yescharacteristic
subgroupG/H
centerC2#99×D151
commutatorC2×C4×C151C22×C4
FrattiniC2×D4C22×D151
Fitting#354×C151C2
socleC2×C151C2×#99
prime radical#23752780C2
cosocleC2×D4×C151C23
hypercenter#354D151
hypocenterC151#2127
LCSG ▷ C2×C4×C151 ▷ C22×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #354

Complements

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

NH ≅ G/Ntype
2. #99×D151C2semidirect
3. #23752007C2semidirect
4. #23752004C2semidirect
5. #354×C151C2semidirect
6. C2×#14559005C4semidirect
8. #18012736C4semidirect
10. #18012728C4semidirect
13. #18012696C4semidirect
24. C2×D604C2×C4semidirect
36. C4×Dic151C2×C4semidirect
37. C2×Q8×C151C2×C4semidirect
41. C42×C151C2×C4semidirect
91. C151#2127semidirect
96. #354D151semidirect
113. C2×Q8C4×D151semidirect
133. C42C4×D151semidirect

Maximal subgroups

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

subgroupindex
#237527802
#99×D1512
#237520072
#237520042
#354×C1512
#2127151