Finite Group Databasebeta

← #34068375

Subgroups — #34068375

Order 19328.

234 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 234 conjugacy classes of subgroups — too many to draw. Only its 59 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
1D4×Dic302C211yesmaximal, characteristic
2#23752610C211yesmaximal, characteristic, complemented
3#23752498C211yesmaximal, characteristic, complemented
4#23752417C211yesmaximal, characteristic
5#23751959C211yesmaximal, characteristic, complemented
6#23751944C211yesmaximal, characteristic, complemented
7D4⋊C8×C151C211yesmaximal, characteristic
8C22×Dic302—21no—
9C2×#14558992—21no—
10#18012739C2211yescharacteristic
11#18012739C2211yescharacteristic
12#18012738—21no—
13#18012718—21no—
14#18012716—22no—
15C4×Dic302C2211yescharacteristic
16D4×Dic151—21no—
17#18012671—21no—
18#18012671—22no—
19C4⋊(C151⋊C8)C2211yescharacteristic
20#18012664—21no—
21#18012662—21no—
22C4×D4×C151C2211yescharacteristic
23C4⋊C8×C151C2211yescharacteristic
24C4×C8×C151C2211yescharacteristic
25C2×Dic302—22no—
26C2×Dic302—21no—
27C2×Dic302—21no—
28C2×Dic302—42no—
29C2×Dic302—42no—
30C2×Dic302D411yescharacteristic
31C22×Dic151—22no—
32#14558992—42no—
33C2×C151⋊C8—21no—
34C4⋊Dic151—21no—
35C4⋊Dic151—21no—
36C4⋊Dic151—21no—
37C4⋊Dic151D411yescharacteristic
38C4⋊Dic151D412yes—
39Dic151⋊C4—22no—
40Dic151⋊C4—21no—
41C22⋊Dic151—22no—
42C4×Dic151—21no—
43C2×D4×C151D411yescharacteristic
44C22×C4×C151—21no—
45C2×C8×C151—21no—
46C2×C8×C151—21no—
47C4⋊C4×C151D411yescharacteristic
48C22⋊C4×C151—21no—
49C42×C151C2311yescharacteristic
50Dic302—21no—
51Dic302—44no—
52Dic302—41no—
53Dic302—41no—
54Dic302—41no—
55Dic302—41no—
56Dic302SD1612yescomplemented
57C2×Dic151—21no—
58C2×Dic151—21no—
59C2×Dic151—22no—
60C2×Dic151—44no—
61C2×Dic151—41no—
62C151⋊C8—41no—
63C23×C151—21no—
64D4×C151—21no—
65D4×C151SD1612yes—
66C2×C4×C151—21no—
67C2×C4×C151—41no—
68C2×C4×C151—41no—
69C2×C4×C151C2×D411yescharacteristic
70C2×C4×C151C2×D411yescharacteristic
71C2×C4×C151C2×D411yescharacteristic
72C8×C151—22no—
73C8×C151—41no—
74C22×C151—22no—
75C22×C151—41no—
76C22×C151—41no—
77C22×C151#12011yescharacteristic
78C4×C151—21no—
79C4×C151—41no—
80C4×C151C2×SD1611yescharacteristic
81C4×C151C2×SD1611yescharacteristic
82C4×C151AGL(1,ℤ/8)11yescharacteristic
83C4×C151#13711yescharacteristic
84Dic151—22no—
85Dic151—42no—
86Dic151—41no—
87Dic151—81no—
88C2×C151—42no—
89C2×C151#44811yescharacteristic
90C2×C151#45011yescharacteristic
91C2×C151#45611yescharacteristic
92C151#165111yescharacteristic, complemented, Sylow
93#1651—1511nomaximal, Sylow
94D4×Q8—1511no—
95#498—1511no—
96#475—1511no—
97#461—1511no—
98#332—1511no—
99Q8⋊C8—1511no—
100D4⋊C8D15111yescharacteristic
101C22×Q8—3021no—
102C2×SD16—3021no—
103C4⋊Q8—3021no—
104C4⋊Q8—1511no—
105C4⋊Q8—1511no—
106C22⋊Q8—3022no—
107C22⋊Q8—3021no—
108C4×Q8—1511no—
109C4×D4—3021no—
110C4×D4C2×D15111yescharacteristic
111#106—3021no—
112#106—3022no—
113C4⋊C8—1511no—
114C4⋊C8C2×D15111yescharacteristic
115#103—3021no—
116#103—3021no—
117C4×C8C2×D15111yescharacteristic
118C2×Q8—3022no—
119C2×Q8—3021no—
120C2×Q8—3021no—
121C2×Q8—6042no—
122C2×Q8—6042no—
123C2×Q8—1511no—
124C2×D4D60411yescharacteristic
125C22×C4—21no—
126C22×C4—3022no—
127SD16—6042no—
128C2×C8—21no—
129C2×C8—21no—
130C2×C8—3021no—
131C4⋊C4—3022no—
132C4⋊C4—3021no—
133C4⋊C4—3021no—
134C4⋊C4—3021no—
135C4⋊C4—3021no—
136C4⋊C4—1511no—
137C4⋊C4—1512no—
138C4⋊C4D60411yescharacteristic
139C22⋊C4—21no—
140C22⋊C4—3022no—
141C42—3021no—
142C42C22×D15111yescharacteristic
143C23—21no—
144Q8—3021no—
145Q8—6044no—
146Q8—6041no—
147Q8—6041no—
148Q8—6041no—
149Q8—6041no—
150Q8—1512no—
151D4—21no—
152D4#1455899312yes—
153C2×C4—21no—
154C2×C4—41no—
155C2×C4—41no—
156C2×C4—3021no—
157C2×C4—3021no—
158C2×C4—3022no—
159C2×C4—6044no—
160C2×C4—6041no—
161C2×C4D4×D15111yescharacteristic
162C2×C4D4×D15111yescharacteristic
163C2×C4C2×D60411yescharacteristic
164C8—22no—
165C8—41no—
166C8—6041no—
167C22—22no—
168C22—41no—
169C22—41no—
170C22#1801270911yescharacteristic
171C4—21no—
172C4—41no—
173C4—3022no—
174C4—6042no—
175C4—6041no—
176C4—12081no—
177C4SD16×D15111yescharacteristic
178C4C2×#1455899311yescharacteristic
179C4#1801276311yescharacteristic
180C4#1801277211yescharacteristic
181C2—42no—
182C2#2375235311yescharacteristic
183C2#2375236411yescharacteristic
184C2#2375239611yescharacteristic
subgroupG/H
centerC22#18012709
commutator, cosocleC42×C151C23
FrattiniC42C22×D151
FittingD4⋊C8×C151C2
socleC22×C151#120
prime radicalC2×D4×C151D4
hypercenterD4⋊C8D151
hypocenterC151#1651
LCSG ▷ C42×C151 ▷ C22×C151 ▷ C151
UCSC1 ◁ C22 ◁ C42 ◁ D4⋊C8

Complements

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

NH ≅ G/Ntype
2. #23752610C2semidirect
3. #23752498C2semidirect
5. #23751959C2semidirect
6. #23751944C2semidirect
56. Dic302SD16semidirect
92. C151#1651semidirect

Maximal subgroups

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

subgroupindex
D4×Dic3022
#237526102
#237524982
#237524172
#237519592
#237519442
D4⋊C8×C1512
#1651151