Finite Group Databasebeta

← #34070780

Subgroups — #34070780

Order 19328.

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

normal subgroups only

This group has 270 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#23752775C211yesmaximal, characteristic
2#23752184C212yesmaximal, complemented
3#23752005C211yesmaximal, characteristic, complemented
4#23752004C212yesmaximal, complemented
5#353×C151C211yesmaximal, characteristic, complemented
6C2×#14559003C2211yescharacteristic
7C2×D4×D151C411yescharacteristic, complemented
8#18012735C2211yescharacteristic
9#18012727C411yescharacteristic, complemented
10#18012726C411yescharacteristic, complemented
11#18012711—22no—
12#18012707—22no—
13#18012696C411yescharacteristic, complemented
14#18012695—22no—
15#18012654C2212yescomplemented
16#18012653—22no—
17#127×C151C2211yescharacteristic
18#99×C151C2212yescomplemented
19C23×D151—21no—
20#14559003—42no—
21C2×Dic302C2×C411yescharacteristic
22C2×D604C2×C411yescharacteristic
23C2×C22⋊D151—21no—
24C2×C22⋊D151—22no—
25C2×C22⋊D151D412yes—
26D4×D151—42no—
27C22×Dic151D412yes—
28C2×C4×D151C2×C411yescharacteristic
29Dic151⋊C4—21no—
30Dic151⋊C4—42no—
31C22⋊Dic151—22no—
32C22⋊Dic151—22no—
33(C2×D151)⋊C4—21no—
34(C2×D151)⋊C4—22no—
35C4×Dic151—42no—
36C4×Dic151C2×C411yescharacteristic
37C2×D4×C151—22no—
38C2×D4×C151C2×C411yescharacteristic
39C2×D4×C151C2311yescharacteristic
40C22⋊C4×C151—22no—
41C42×C151C2×C411yescharacteristic
42C22×D151—21no—
43C22×D151—42no—
44C22×D151—82no—
45C22×D151C22⋊C411yescharacteristic
46Dic302—41no—
47D604—41no—
48C22⋊D151—42no—
49C22⋊D151—42no—
50C22⋊D151—82no—
51C2×Dic151—22no—
52C2×Dic151—22no—
53C2×Dic151—21no—
54C2×Dic151—42no—
55C2×Dic151C22⋊C412yes—
56C2×Dic151C22⋊C411yescharacteristic
57C4×D151—22no—
58C23×C151—21no—
59C23×C151C2×D412yes—
60D4×C151—41no—
61D4×C151—41no—
62D4×C151—82no—
63C2×C4×C151—21no—
64C2×C4×C151—42no—
65C2×C4×C151C22×C411yescharacteristic
66C22×C151—22no—
67C22×C151—42no—
68C22×C151—42no—
69C22×C151—41no—
70C22×C151C2×C22⋊C411yescharacteristic
71C2×D151—21no—
72C2×D151—41no—
73C2×D151—42no—
74C2×D151—41no—
75C2×D151—84no—
76C4×C151—21no—
77C4×C151—41no—
78C4×C151—82no—
79Dic151—22no—
80Dic151—41no—
81Dic151—82no—
82Dic151#9912yes—
83C2×C151—21no—
84C2×C151—42no—
85C2×C151—81no—
86C2×C151C2×#9911yescharacteristic
87D151—41no—
88D151—81no—
89C151#212811yescharacteristic, complemented, Sylow
90#2128—1511nomaximal, Sylow
91#535—1511no—
92#410—1512no—
93#353—1511no—
94#353—1512no—
95#353D15111yescharacteristic, complemented
96C2×#41—1511no—
97C22×D4—1511no—
98#127—1511no—
99#127C2×D15111yescharacteristic
100#124—1511no—
101#124—1511no—
102#121—3022no—
103#120—3022no—
104#117—3022no—
105#117—1511no—
106#99—3022no—
107#99—1512no—
108#99C2×D15112yescomplemented
109C24—3021no—
110#41—6042no—
111C2×Q8—1511no—
112C2×D4—22no—
113C2×D4—3022no—
114C2×D4—3021no—
115C2×D4—6042no—
116C2×D4—1512no—
117C2×D4—1511no—
118C2×D4C4×D15111yescharacteristic
119C2×D4C22×D15111yescharacteristic
120C22×C4—1512no—
121C22×C4—1511no—
122C4⋊C4—3021no—
123C4⋊C4—6042no—
124C22⋊C4—22no—
125C22⋊C4—3021no—
126C22⋊C4—3022no—
127C22⋊C4—3022no—
128C22⋊C4—3022no—
129C42—6042no—
130C42—1511no—
131C42C4×D15111yescharacteristic
132C23—21no—
133C23—3021no—
134C23—6042no—
135C23—1511no—
136C23—12082no—
137C23D4×D15112yes—
138Q8—6041no—
139D4—41no—
140D4—41no—
141D4—82no—
142D4—6041no—
143D4—6042no—
144D4—6042no—
145D4—12082no—
146C2×C4—21no—
147C2×C4—42no—
148C2×C4—3022no—
149C2×C4—3022no—
150C2×C4—3022no—
151C2×C4—3021no—
152C2×C4—6042no—
153C2×C4—1512no—
154C2×C4—1511no—
155C2×C4C2×C4×D15111yescharacteristic
156C22—22no—
157C22—42no—
158C22—42no—
159C22—41no—
160C22—3021no—
161C22—6041no—
162C22—6042no—
163C22—6041no—
164C22—12084no—
165C22C22⋊C4×D15111yescharacteristic
166C4—21no—
167C4—41no—
168C4—82no—
169C4—3022no—
170C4—6041no—
171C4—1512no—
172C4—12082no—
173C2—21no—
174C2—42no—
175C2—81no—
176C2—6041no—
177C2—12081no—
178C2#99×D15111yescharacteristic
subgroupG/H
centerC2#99×D151
commutatorC2×C4×C151C22×C4
FrattiniC2×D4C22×D151
Fitting#353×C151C2
socleC2×C151C2×#99
prime radical#23752775C2
cosocleC2×D4×C151C23
hypercenter#353D151
hypocenterC151#2128
LCSG ▷ C2×C4×C151 ▷ C22×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #353

Complements

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

NH ≅ G/Ntype
2. #23752184C2semidirect
3. #23752005C2semidirect
4. #23752004C2semidirect
5. #353×C151C2semidirect
7. C2×D4×D151C4semidirect
9. #18012727C4semidirect
10. #18012726C4semidirect
13. #18012696C4semidirect
15. #18012654C22semidirect
18. #99×C151C22semidirect
89. C151#2128semidirect
95. #353D151semidirect
108. #99C2×D151semidirect

Maximal subgroups

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

subgroupindex
#237527752
#237521842
#237520052
#237520042
#353×C1512
#2128151