Finite Group Databasebeta

← #34067646

Subgroups — #34067646

Order 19328.

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

normal subgroups only

This group has 222 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#23752269C211yesmaximal, characteristic, complemented
3#23751948C212yesmaximal, complemented
4#23751945C212yesmaximal
5#382×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—
18#18012650—21no—
19C2×C4⋊C4×C151—21no—
20C2×C42×C151C2211yescharacteristic
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
44C4⋊C4×C151—42no—
45C42×C151C2×C411yescharacteristic
46C42×C151C2×C411yescharacteristic
47C42×C151D411yescharacteristic
48C42×C151D411yescharacteristic
49C22×D151—21no—
50Dic302—41no—
51D604—41no—
52C22⋊D151—41no—
53C22⋊D151—41no—
54C2×Dic151—21no—
55C2×Dic151—21no—
56C2×Dic151—21no—
57C4×D151—42no—
58C151⋊C8—42no—
59C23×C151C2×D411yescharacteristic
60C2×C4×C151—21no—
61C2×C4×C151—21no—
62C2×C4×C151—41no—
63C2×C4×C151—41no—
64C2×C4×C151—42no—
65C2×C4×C151—42no—
66C2×C4×C151—42no—
67C2×C4×C151C22⋊C411yescharacteristic
68C2×C4×C151C22⋊C411yescharacteristic
69C2×C4×C151C22⋊C411yescharacteristic
70C2×C4×C151C22⋊C411yescharacteristic
71C2×C4×C151C22×C411yescharacteristic
72C2×C4×C151C2×D411yescharacteristic
73C22×C151—21no—
74C22×C151—21no—
75C22×C151C2×C22⋊C411yescharacteristic
76C22×C151AGL(1,ℤ/8)11yescharacteristic
77C22×C151#13711yescharacteristic
78C2×D151—41no—
79C2×D151—41no—
80C2×D151—41no—
81C4×C151—21no—
82C4×C151—21no—
83C4×C151—21no—
84C4×C151—21no—
85C4×C151—21no—
86C4×C151—21no—
87C4×C151—82no—
88Dic151—41no—
89Dic151—41no—
90Dic151—41no—
91C2×C151—21no—
92C2×C151—21no—
93C2×C151#41011yescharacteristic
94C2×C151#41711yescharacteristic
95C2×C151#42111yescharacteristic
96D151—81no—
97C151#151211yescharacteristic, complemented, Sylow
98#1512—1511nomaximal, Sylow
99#529—1511no—
100#432—1511no—
101#382D15111yescharacteristic, complemented
102#328—1512no—
103#327—1512no—
104#126—3021no—
105#125—1511no—
106#124—1511no—
107#123—3021no—
108C22⋊Q8—1511no—
109#121—1511no—
110C4×Q8—1511no—
111C4×D4—3021no—
112C4×D4—1511no—
113#117—3021no—
114C2×C4⋊C4—21no—
115C2×C42C2×D15111yescharacteristic
116C4⋊C8—3021no—
117C22⋊C8—1512no—
118#97—3021no—
119#95—21no—
120#95C2×D15112yes—
121C2×Q8—1511no—
122C2×D4—3021no—
123C2×D4—1511no—
124C22×C4—22no—
125C22×C4—3021no—
126C22×C4C22⋊D15111yescharacteristic
127C22×C4C22⋊D15111yescharacteristic
128C22×C4C22×D15111yescharacteristic
129C2×C8—3022no—
130C4⋊C4—42no—
131C4⋊C4—3021no—
132C4⋊C4—3021no—
133C4⋊C4—3021no—
134C4⋊C4—3021no—
135C4⋊C4—1511no—
136C4⋊C4—1511no—
137C22⋊C4—3021no—
138C22⋊C4—3021no—
139C22⋊C4—3021no—
140C22⋊C4—3021no—
141C22⋊C4—3021no—
142C42—3021no—
143C42C4×D15111yescharacteristic
144C42C4×D15111yescharacteristic
145C42D60411yescharacteristic
146C42D60411yescharacteristic
147C23—3021no—
148C23C2×C22⋊D15111yescharacteristic
149Q8—6041no—
150D4—6041no—
151D4—6041no—
152D4—6041no—
153C2×C4—21no—
154C2×C4—21no—
155C2×C4—41no—
156C2×C4—41no—
157C2×C4—42no—
158C2×C4—42no—
159C2×C4—42no—
160C2×C4—3021no—
161C2×C4—3021no—
162C2×C4—3021no—
163C2×C4—6042no—
164C2×C4(C2×D151)⋊C411yescharacteristic
165C2×C4(C2×D151)⋊C411yescharacteristic
166C2×C4(C2×D151)⋊C411yescharacteristic
167C2×C4(C2×D151)⋊C411yescharacteristic
168C2×C4C2×C4×D15111yescharacteristic
169C2×C4C2×D60411yescharacteristic
170C8—6042no—
171C22—21no—
172C22—21no—
173C22—6041no—
174C22—6041no—
175C22—6041no—
176C22C2×(C2×D151)⋊C411yescharacteristic
177C22#1801276511yescharacteristic
178C22#1801277011yescharacteristic
179C4—21no—
180C4—21no—
181C4—21no—
182C4—21no—
183C4—21no—
184C4—21no—
185C4—82no—
186C4—6041no—
187C4—6041no—
188C4—6041no—
189C2—21no—
190C2—21no—
191C2—12081no—
192C2#2375218511yescharacteristic
193C2#2375221111yescharacteristic
194C2#2375223011yescharacteristic
subgroupG/H
centerC22C2×(C2×D151)⋊C4
commutatorC2×C4×C151C22×C4
FrattiniC22×C4C22×D151
Fitting#382×C151C2
socleC22×C151C2×C22⋊C4
prime radical#18012713C22
cosocleC22×C4×C151C23
hypercenter#382D151
hypocenterC151#1512
LCSG ▷ C2×C4×C151 ▷ C22×C151 ▷ C151
UCSC1 ◁ C22 ◁ C2×C42 ◁ #382

Complements

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

NH ≅ G/Ntype
2. #23752269C2semidirect
3. #23751948C2semidirect
5. #382×C151C2semidirect
7. #18012731C4semidirect
8. #18012727C4semidirect
12. C4×Dic302C4semidirect
13. C4×D604C4semidirect
97. C151#1512semidirect
101. #382D151semidirect

Maximal subgroups

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

subgroupindex
#237527462
#237522692
#237519482
#237519452
#382×C1512
#1512151