Finite Group Databasebeta

← #34068052

Subgroups — #34068052

Order 19328.

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

normal subgroups only

This group has 266 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#23752843C211yesmaximal, characteristic, complemented
2#23752365C212yesmaximal
3#23752129C211yesmaximal, characteristic
4#23751950C212yesmaximal, complemented
5#324×C151C211yesmaximal, characteristic, complemented
6C22×D604C2211yescharacteristic
7C2×#14558993—22no—
8#18012738—22no—
9#18012730—22no—
10#18012718—21no—
11#18012718C2212yes—
12#18012698—21no—
13C2×(C2×D151)⋊C4—21no—
14C2×(C2×D151)⋊C4—21no—
15#18012661—22no—
16C151⋊#95C2211yescharacteristic
17C2×C4⋊C4×C151C2211yescharacteristic
18C22⋊C8×C151C2212yes—
19C23×D151—21no—
20C2×Dic302—21no—
21C2×Dic302D412yes—
22C2×D604—22no—
23C2×D604—42no—
24C22×Dic151—21no—
25#14558993—44no—
26C4⋊Dic151—21no—
27C4⋊Dic151—21no—
28C4⋊Dic151—21no—
29C4⋊Dic151D412yes—
30Dic151⋊C4—22no—
31Dic151⋊C4—22no—
32C22⋊Dic151—22no—
33(C2×D151)⋊C4—42no—
34(C2×D151)⋊C4—42no—
35C4×Dic151—22no—
36C22×C4×C151D411yescharacteristic
37C22×C4×C151D411yescharacteristic
38C22×C4×C151C2311yescharacteristic
39C2×C8×C151—22no—
40C4⋊C4×C151—22no—
41C22×D151—22no—
42C22×D151—41no—
43C22×D151—41no—
44C22×D151—41no—
45C22×D151—41no—
46C22×D151—41no—
47C22×D151—41no—
48Dic302—42no—
49Dic302—81no—
50D604—24no—
51D604—42no—
52C2×Dic151—22no—
53C2×Dic151—22no—
54C2×Dic151—41no—
55C2×Dic151—41no—
56C2×Dic151—41no—
57C23×C151C2×D411yescharacteristic
58C2×C4×C151—21no—
59C2×C4×C151—21no—
60C2×C4×C151—21no—
61C2×C4×C151—41no—
62C2×C4×C151—41no—
63C2×C4×C151SD1612yescomplemented
64C2×C4×C151C2×D412yes—
65C8×C151—42no—
66C22×C151—21no—
67C22×C151—21no—
68C22×C151#12011yescharacteristic
69C22×C151C2×SD1611yescharacteristic
70C22×C151#13711yescharacteristic
71C2×D151—42no—
72C2×D151—42no—
73C2×D151—42no—
74C2×D151—81no—
75C2×D151—81no—
76C2×D151—81no—
77C2×D151—81no—
78C4×C151—22no—
79C4×C151—22no—
80C4×C151—41no—
81Dic151—42no—
82Dic151—42no—
83Dic151—81no—
84C2×C151—21no—
85C2×C151—21no—
86C2×C151#44811yescharacteristic
87C2×C151#45411yescharacteristic
88C2×C151B(4,𝔽2)11yescharacteristic
89D151—82no—
90C151#159911yescharacteristic, complemented, Sylow
91#1599—1511nomaximal, Sylow
92#544—1511no—
93#450—1512no—
94#394—1511no—
95#328—1512no—
96#324D15111yescharacteristic, complemented
97C22×D4—1511no—
98C2×SD16—3022no—
99C4⋊Q8—3022no—
100#125—3022no—
101C22⋊Q8—3021no—
102C22⋊Q8—1512no—
103#117—3021no—
104C2×C4⋊C4C2×D15111yescharacteristic
105C2×C22⋊C4—3021no—
106C2×C22⋊C4—3021no—
107#102—3022no—
108C22⋊C8C2×D15112yes—
109#95—1511no—
110C24—3021no—
111C2×Q8—3021no—
112C2×Q8—1512no—
113C2×D4—3022no—
114C2×D4—6042no—
115C22×C4—3021no—
116C22×C4D60411yescharacteristic
117C22×C4D60411yescharacteristic
118C22×C4C22×D15111yescharacteristic
119SD16—6044no—
120C2×C8—22no—
121C4⋊C4—22no—
122C4⋊C4—3022no—
123C4⋊C4—3021no—
124C4⋊C4—3021no—
125C4⋊C4—3021no—
126C4⋊C4—3022no—
127C4⋊C4—1512no—
128C22⋊C4—3022no—
129C22⋊C4—6042no—
130C22⋊C4—6042no—
131C42—3022no—
132C23—3022no—
133C23—6041no—
134C23—6041no—
135C23—6041no—
136C23—6041no—
137C23—6041no—
138C23—6041no—
139C23C2×D60411yescharacteristic
140Q8—6042no—
141Q8—12081no—
142D4—3024no—
143D4—6042no—
144C2×C4—21no—
145C2×C4—21no—
146C2×C4—21no—
147C2×C4—41no—
148C2×C4—41no—
149C2×C4—3022no—
150C2×C4—3022no—
151C2×C4—6041no—
152C2×C4—6041no—
153C2×C4—6041no—
154C2×C4#1455899312yescomplemented
155C2×C4D4×D15112yes—
156C8—42no—
157C22—21no—
158C22—21no—
159C22—6042no—
160C22—6042no—
161C22—6042no—
162C22—12081no—
163C22—12081no—
164C22—12081no—
165C22—12081no—
166C22#1801270911yescharacteristic
167C22C2×#1455899311yescharacteristic
168C22#1801277211yescharacteristic
169C4—22no—
170C4—22no—
171C4—41no—
172C4—6042no—
173C4—6042no—
174C4—12081no—
175C2—21no—
176C2—21no—
177C2—12082no—
178C2#2375235311yescharacteristic
179C2#2375238711yescharacteristic
180C2#2375240011yescharacteristic
subgroupG/H
centerC22#18012709
commutator, cosocleC22×C4×C151C23
FrattiniC22×C4C22×D151
Fitting#324×C151C2
socleC22×C151#120
prime radicalC22×D604C22
hypercenter#324D151
hypocenterC151#1599
LCSG ▷ C22×C4×C151 ▷ C22×C151 ▷ C151
UCSC1 ◁ C22 ◁ C22×C4 ◁ #324

Complements

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

NH ≅ G/Ntype
1. #23752843C2semidirect
4. #23751950C2semidirect
5. #324×C151C2semidirect
63. C2×C4×C151SD16semidirect
90. C151#1599semidirect
96. #324D151semidirect
154. C2×C4#14558993semidirect

Maximal subgroups

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

subgroupindex
#237528432
#237523652
#237521292
#237519502
#324×C1512
#1599151