Finite Group Databasebeta

← #34067685

Subgroups — #34067685

Order 19328.

218 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 218 conjugacy classes of subgroups — too many to draw. Only its 69 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#23752746C211yesmaximal, characteristic
2#23752265C211yesmaximal, characteristic, complemented
3#23751948C212yesmaximal, complemented
4#23751945C212yesmaximal
5#383×C151C211yesmaximal, characteristic, complemented
6#18012733—21no—
7#18012731C411yescharacteristic, complemented
8#18012727C411yescharacteristic, complemented
9#18012722—21no—
10#18012718C2211yescharacteristic
11#18012713C2211yescharacteristic
12C4×Dic302C411yescharacteristic, complemented
13C4×D604C411yescharacteristic, complemented
14C4×C22⋊D151—21no—
15#18012696—21no—
16C4⋊(C151⋊C8)—21no—
17C22⋊(C151⋊C8)C2212yes—
18C4×C151⋊C8—21no—
19C2×C42×C151C2211yescharacteristic
20#95×C151—21no—
21#95×C151—21no—
22#95×C151C2212yes—
23C2×Dic302C2×C411yescharacteristic
24C2×D604C2×C411yescharacteristic
25C2×C22⋊D151—21no—
26C2×C4×D151—21no—
27C2×C151⋊C8—22no—
28C4⋊Dic151C2×C411yescharacteristic
29C4⋊Dic151C2×C411yescharacteristic
30Dic151⋊C4—21no—
31Dic151⋊C4—21no—
32Dic151⋊C4—21no—
33Dic151⋊C4—21no—
34C22⋊Dic151—21no—
35(C2×D151)⋊C4—21no—
36(C2×D151)⋊C4—21no—
37(C2×D151)⋊C4—21no—
38(C2×D151)⋊C4—21no—
39C4×Dic151—21no—
40C22×C4×C151—22no—
41C22×C4×C151D411yescharacteristic
42C22×C4×C151D411yescharacteristic
43C22×C4×C151C2311yescharacteristic
44C42×C151C2×C411yescharacteristic
45C42×C151C2×C411yescharacteristic
46C42×C151D411yescharacteristic
47C42×C151D411yescharacteristic
48C22×D151—21no—
49Dic302—41no—
50D604—41no—
51C22⋊D151—42no—
52C2×Dic151—21no—
53C2×Dic151—21no—
54C2×Dic151—21no—
55C4×D151—42no—
56C151⋊C8—42no—
57C23×C151C2×D411yescharacteristic
58C2×C4×C151—22no—
59C2×C4×C151—41no—
60C2×C4×C151—41no—
61C2×C4×C151—42no—
62C2×C4×C151—42no—
63C2×C4×C151—42no—
64C2×C4×C151C22⋊C411yescharacteristic
65C2×C4×C151C22⋊C411yescharacteristic
66C2×C4×C151C22⋊C411yescharacteristic
67C2×C4×C151C22⋊C411yescharacteristic
68C2×C4×C151C22×C411yescharacteristic
69C2×C4×C151C2×D411yescharacteristic
70C22×C151—21no—
71C22×C151—21no—
72C22×C151C2×C22⋊C411yescharacteristic
73C22×C151#13512yes—
74C2×D151—41no—
75C2×D151—41no—
76C2×D151—41no—
77C4×C151—21no—
78C4×C151—21no—
79C4×C151—21no—
80C4×C151—21no—
81C4×C151—21no—
82C4×C151—21no—
83C4×C151—82no—
84Dic151—41no—
85Dic151—41no—
86Dic151—41no—
87C2×C151—22no—
88C2×C151#41011yescharacteristic
89C2×C151#41611yescharacteristic
90C2×C151#42111yescharacteristic
91D151—81no—
92C151#152111yescharacteristic, complemented, Sylow
93#1521—1511nomaximal, Sylow
94#529—1511no—
95#431—1511no—
96#383D15111yescharacteristic, complemented
97#328—1512no—
98#327—1512no—
99#126—3021no—
100#125—1511no—
101#124—1511no—
102#123—3021no—
103C22⋊Q8—1511no—
104#121—1511no—
105C4×Q8—1511no—
106C4×D4—3021no—
107C4×D4—1511no—
108#117—3021no—
109C2×C42C2×D15111yescharacteristic
110C4⋊C8—3021no—
111C22⋊C8—1512no—
112C4×C8—3021no—
113#95—21no—
114#95—21no—
115#95C2×D15112yes—
116C2×Q8—1511no—
117C2×D4—3021no—
118C2×D4—1511no—
119C22×C4—22no—
120C22×C4—3021no—
121C22×C4C22⋊D15111yescharacteristic
122C22×C4C22⋊D15111yescharacteristic
123C22×C4C22×D15111yescharacteristic
124C2×C8—3022no—
125C4⋊C4—3021no—
126C4⋊C4—3021no—
127C4⋊C4—3021no—
128C4⋊C4—3021no—
129C4⋊C4—1511no—
130C4⋊C4—1511no—
131C22⋊C4—3021no—
132C22⋊C4—3021no—
133C22⋊C4—3021no—
134C22⋊C4—3021no—
135C22⋊C4—3021no—
136C42—3021no—
137C42C4×D15111yescharacteristic
138C42C4×D15111yescharacteristic
139C42D60411yescharacteristic
140C42D60411yescharacteristic
141C23—3021no—
142C23C2×C22⋊D15111yescharacteristic
143Q8—6041no—
144D4—6041no—
145D4—6042no—
146C2×C4—22no—
147C2×C4—41no—
148C2×C4—41no—
149C2×C4—42no—
150C2×C4—42no—
151C2×C4—42no—
152C2×C4—3021no—
153C2×C4—3021no—
154C2×C4—3021no—
155C2×C4—6042no—
156C2×C4(C2×D151)⋊C411yescharacteristic
157C2×C4(C2×D151)⋊C411yescharacteristic
158C2×C4(C2×D151)⋊C411yescharacteristic
159C2×C4(C2×D151)⋊C411yescharacteristic
160C2×C4C2×C4×D15111yescharacteristic
161C2×C4C2×D60411yescharacteristic
162C8—6042no—
163C22—21no—
164C22—21no—
165C22—6041no—
166C22—6041no—
167C22—6041no—
168C22C2×(C2×D151)⋊C411yescharacteristic
169C22#1801275912yes—
170C4—21no—
171C4—21no—
172C4—21no—
173C4—21no—
174C4—21no—
175C4—21no—
176C4—82no—
177C4—6041no—
178C4—6041no—
179C4—6041no—
180C2—22no—
181C2—12081no—
182C2#2375218511yescharacteristic
183C2#2375220611yescharacteristic
184C2#2375223011yescharacteristic
subgroupG/H
centerC22C2×(C2×D151)⋊C4
commutatorC2×C4×C151C22×C4
FrattiniC22×C4C22×D151
Fitting#383×C151C2
socleC22×C151C2×C22⋊C4
prime radical#18012713C22
cosocleC22×C4×C151C23
hypercenter#383D151
hypocenterC151#1521
LCSG ▷ C2×C4×C151 ▷ C22×C151 ▷ C151
UCSC1 ◁ C22 ◁ C2×C42 ◁ #383

Complements

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

NH ≅ G/Ntype
2. #23752265C2semidirect
3. #23751948C2semidirect
5. #383×C151C2semidirect
7. #18012731C4semidirect
8. #18012727C4semidirect
12. C4×Dic302C4semidirect
13. C4×D604C4semidirect
92. C151#1521semidirect
96. #383D151semidirect

Maximal subgroups

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

subgroupindex
#237527462
#237522652
#237519482
#237519452
#383×C1512
#1521151