Finite Group Databasebeta

← #34068132

Subgroups — #34068132

Order 19328.

288 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 288 conjugacy classes of subgroups — too many to draw. Only its 53 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#23752774C211yesmaximal, characteristic
2#23752531C212yesmaximal, complemented
3#23752148C211yesmaximal, characteristic, complemented
4#23751947C212yesmaximal, complemented
5#323×C151C211yesmaximal, characteristic, complemented
6C22×C22⋊D151—21no—
7#18012723—22no—
8#18012713—21no—
9#18012713C2212yes—
10#18012709—22no—
11C2×C4⋊Dic151C2211yescharacteristic, complemented
12C2×Dic151⋊C4—21no—
13C2×C22⋊Dic151—21no—
14#18012671—22no—
15#18012661—22no—
16C151⋊#95C2211yescharacteristic, complemented
17C2×C22⋊C4×C151C2211yescharacteristic
18C22⋊C8×C151C2212yescomplemented
19C23×D151—21no—
20C2×D604—21no—
21C2×D604D412yes—
22C2×C22⋊D151—22no—
23C2×C22⋊D151—22no—
24C2×C22⋊D151—42no—
25C2×C22⋊D151—42no—
26C22×Dic151—21no—
27C22×Dic151—21no—
28C22×Dic151—21no—
29C4⋊Dic151—21no—
30C4⋊Dic151—22no—
31C4⋊Dic151D412yes—
32Dic151⋊C4—42no—
33C22⋊Dic151—42no—
34(C2×D151)⋊C4—22no—
35(C2×D151)⋊C4—22no—
36C24×C151D411yescharacteristic
37C22×C4×C151D411yescharacteristic
38C22×C4×C151C2311yescharacteristic
39C2×C8×C151—22no—
40C22⋊C4×C151—22no—
41C22×D151—22no—
42C22×D151—42no—
43C22×D151—81no—
44C22×D151—81no—
45D604—42no—
46D604—81no—
47C22⋊D151—44no—
48C22⋊D151—42no—
49C22⋊D151—42no—
50C2×Dic151—22no—
51C2×Dic151—22no—
52C2×Dic151—41no—
53C2×Dic151—42no—
54C2×Dic151—41no—
55C2×Dic151—41no—
56C2×Dic151—41no—
57C2×Dic151—41no—
58C23×C151—21no—
59C23×C151—21no—
60C23×C151—41no—
61C23×C151—41no—
62C23×C151SD1612yes—
63C23×C151C2×D411yescharacteristic
64C2×C4×C151—21no—
65C2×C4×C151—41no—
66C2×C4×C151—41no—
67C2×C4×C151C2×D412yes—
68C8×C151—42no—
69C22×C151—21no—
70C22×C151—21no—
71C22×C151—22no—
72C22×C151—42no—
73C22×C151—41no—
74C22×C151—41no—
75C22×C151—81no—
76C22×C151#12011yescharacteristic
77C22×C151C2×SD1611yescharacteristic
78C22×C151AGL(1,ℤ/8)11yescharacteristic
79C2×D151—42no—
80C2×D151—42no—
81C2×D151—42no—
82C2×D151—84no—
83C4×C151—22no—
84C4×C151—41no—
85Dic151—42no—
86Dic151—42no—
87Dic151—81no—
88C2×C151—21no—
89C2×C151—21no—
90C2×C151—42no—
91C2×C151#45011yescharacteristic
92C2×C151#45311yescharacteristic
93C2×C151#45811yescharacteristic
94D151—82no—
95C151#161311yescharacteristic, complemented, Sylow
96#1613—1511nomaximal, Sylow
97#534—1511no—
98#481—1512no—
99#399—1511no—
100#327—1512no—
101#323D15111yescharacteristic, complemented
102C22×D4—3021no—
103#123—3022no—
104#121—3021no—
105#121—1512no—
106#120—3022no—
107C2×C4⋊C4—3021no—
108C2×C4⋊C4—1511no—
109C2×C22⋊C4—3021no—
110C2×C22⋊C4C2×D15111yescharacteristic
111#106—3022no—
112#102—3022no—
113C22⋊C8C2×D15112yescomplemented
114#95—1511no—
115C24—3021no—
116C24D60411yescharacteristic
117C2×D4—3021no—
118C2×D4—3022no—
119C2×D4—3022no—
120C2×D4—6042no—
121C2×D4—6042no—
122C2×D4—1512no—
123C22×C4—3021no—
124C22×C4—3021no—
125C22×C4—3021no—
126C22×C4D60411yescharacteristic
127C22×C4C22×D15111yescharacteristic
128C2×C8—22no—
129C4⋊C4—3021no—
130C4⋊C4—3022no—
131C4⋊C4—6042no—
132C4⋊C4—1512no—
133C22⋊C4—22no—
134C22⋊C4—3022no—
135C22⋊C4—3022no—
136C22⋊C4—6042no—
137C23—21no—
138C23—21no—
139C23—41no—
140C23—41no—
141C23—3022no—
142C23—6042no—
143C23—12081no—
144C23—12081no—
145C23#1455899312yes—
146C23C2×D60411yescharacteristic
147D4—6042no—
148D4—6044no—
149D4—6042no—
150D4—6042no—
151D4—12081no—
152C2×C4—21no—
153C2×C4—41no—
154C2×C4—41no—
155C2×C4—3022no—
156C2×C4—3022no—
157C2×C4—6042no—
158C2×C4—6041no—
159C2×C4—6041no—
160C2×C4—6041no—
161C2×C4—6041no—
162C2×C4—6041no—
163C2×C4D4×D15112yes—
164C8—42no—
165C22—21no—
166C22—21no—
167C22—22no—
168C22—42no—
169C22—41no—
170C22—41no—
171C22—81no—
172C22—6042no—
173C22—6042no—
174C22—6042no—
175C22—12084no—
176C22#1801270911yescharacteristic
177C22C2×#1455899311yescharacteristic
178C22#1801276711yescharacteristic
179C4—22no—
180C4—41no—
181C4—6042no—
182C4—6042no—
183C4—12081no—
184C2—21no—
185C2—21no—
186C2—42no—
187C2—12082no—
188C2#2375236511yescharacteristic
189C2#2375238211yescharacteristic
190C2#2375240311yescharacteristic
subgroupG/H
centerC22#18012709
commutator, cosocleC22×C4×C151C23
FrattiniC22×C4C22×D151
Fitting#323×C151C2
socleC22×C151#120
prime radical#23752774C2
hypercenter#323D151
hypocenterC151#1613
LCSG ▷ C22×C4×C151 ▷ C22×C151 ▷ C151
UCSC1 ◁ C22 ◁ C22×C4 ◁ #323

Complements

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

NH ≅ G/Ntype
2. #23752531C2semidirect
3. #23752148C2semidirect
4. #23751947C2semidirect
5. #323×C151C2semidirect
11. C2×C4⋊Dic151C22semidirect
16. C151⋊#95C22semidirect
18. C22⋊C8×C151C22semidirect
95. C151#1613semidirect
101. #323D151semidirect
113. C22⋊C8C2×D151semidirect

Maximal subgroups

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

subgroupindex
#237527742
#237525312
#237521482
#237519472
#323×C1512
#1613151