Finite Group Databasebeta

← #34068246

Subgroups — #34068246

Order 19328.

214 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 214 conjugacy classes of subgroups — too many to draw. Only its 57 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#23752919C211yesmaximal, characteristic
2#23752592C211yesmaximal, characteristic, complemented
3#23752508C211yesmaximal, characteristic, complemented
4#23752502C211yesmaximal, characteristic
5#23751960C211yesmaximal, characteristic, complemented
6#23751944C211yesmaximal, characteristic, complemented
7D4⋊C8×C151C211yesmaximal, characteristic
8C2×Dic604—22no—
9#18012739C2211yescharacteristic
10#18012739C2211yescharacteristic
11#18012730—21no—
12#18012718—21no—
13#18012716—22no—
14C4×Dic302C2211yescharacteristic
15D4×Dic151—21no—
16C2×C4⋊Dic151—21no—
17#18012673—21no—
18#18012670—21no—
19C4⋊(C151⋊C8)C2211yescharacteristic
20#18012664—21no—
21#18012660—21no—
22C4×D4×C151C2211yescharacteristic
23C4⋊C8×C151C2211yescharacteristic
24C4×C8×C151C2211yescharacteristic
25C2×Dic302—21no—
26C2×Dic302D411yescharacteristic
27C2×Dic302D412yes—
28C22×Dic151—22no—
29Dic604—44no—
30C2×C151⋊C8—21no—
31C4⋊Dic151—22no—
32C4⋊Dic151—21no—
33C4⋊Dic151—21no—
34C4⋊Dic151—21no—
35C4⋊Dic151—21no—
36C4⋊Dic151D411yescharacteristic
37Dic151⋊C4—22no—
38Dic151⋊C4—21no—
39C22⋊Dic151—22no—
40C4×Dic151—21no—
41C2×D4×C151D411yescharacteristic
42C22×C4×C151—21no—
43C2×C8×C151—21no—
44C2×C8×C151—21no—
45C4⋊C4×C151D411yescharacteristic
46C22⋊C4×C151—21no—
47C42×C151C2311yescharacteristic
48Dic302—21no—
49Dic302—21no—
50Dic302—42no—
51Dic302—42no—
52C2×Dic151—21no—
53C2×Dic151—21no—
54C2×Dic151—22no—
55C2×Dic151—41no—
56C2×Dic151—82no—
57C151⋊C8—41no—
58C23×C151—21no—
59D4×C151—21no—
60D4×C151Q1612yescomplemented
61C2×C4×C151—21no—
62C2×C4×C151—41no—
63C2×C4×C151—41no—
64C2×C4×C151C2×D411yescharacteristic
65C2×C4×C151C2×D411yescharacteristic
66C2×C4×C151C2×D411yescharacteristic
67C8×C151—22no—
68C8×C151—41no—
69C22×C151—22no—
70C22×C151—41no—
71C22×C151—41no—
72C22×C151#12011yescharacteristic
73C4×C151—21no—
74C4×C151—41no—
75C4×C151C2×Q1611yescharacteristic
76C4×C151#13511yescharacteristic
77C4×C151#13711yescharacteristic
78C4×C151#13711yescharacteristic
79Dic151—41no—
80Dic151—41no—
81Dic151—42no—
82Dic151—81no—
83C2×C151—42no—
84C2×C151#45111yescharacteristic
85C2×C151#45211yescharacteristic
86C2×C151#45311yescharacteristic
87C151#163211yescharacteristic, complemented, Sylow
88#1632—1511nomaximal, Sylow
89#554—1511no—
90#494—1511no—
91#477—1511no—
92#476—1511no—
93#333—1511no—
94Q8⋊C8—1511no—
95D4⋊C8D15111yescharacteristic
96C2×Q16—3022no—
97C4⋊Q8—1511no—
98C4⋊Q8—1511no—
99#125—3021no—
100C22⋊Q8—3022no—
101C22⋊Q8—3021no—
102C4×Q8—1511no—
103C4×D4—3021no—
104C4×D4C2×D15111yescharacteristic
105C2×C4⋊C4—3021no—
106#107—3021no—
107#106—3021no—
108C4⋊C8—1511no—
109C4⋊C8C2×D15111yescharacteristic
110#103—3021no—
111#102—3021no—
112C4×C8C2×D15111yescharacteristic
113C2×Q8—3021no—
114C2×Q8—1511no—
115C2×Q8—1512no—
116C2×D4D60411yescharacteristic
117C22×C4—21no—
118C22×C4—3022no—
119Q16—6044no—
120C2×C8—21no—
121C2×C8—21no—
122C2×C8—3021no—
123C4⋊C4—3022no—
124C4⋊C4—3022no—
125C4⋊C4—3021no—
126C4⋊C4—3021no—
127C4⋊C4—3021no—
128C4⋊C4—3021no—
129C4⋊C4—3021no—
130C4⋊C4—1511no—
131C4⋊C4D60411yescharacteristic
132C22⋊C4—21no—
133C22⋊C4—3022no—
134C42—3021no—
135C42C22×D15111yescharacteristic
136C23—21no—
137Q8—3021no—
138Q8—3021no—
139Q8—6042no—
140Q8—6042no—
141D4—21no—
142D4Dic60412yescomplemented
143C2×C4—21no—
144C2×C4—41no—
145C2×C4—41no—
146C2×C4—3021no—
147C2×C4—3021no—
148C2×C4—3022no—
149C2×C4—6041no—
150C2×C4—12082no—
151C2×C4D4×D15111yescharacteristic
152C2×C4D4×D15111yescharacteristic
153C2×C4C2×D60411yescharacteristic
154C8—22no—
155C8—41no—
156C8—6041no—
157C22—22no—
158C22—41no—
159C22—41no—
160C22#1801270911yescharacteristic
161C4—21no—
162C4—41no—
163C4—6041no—
164C4—6041no—
165C4—6042no—
166C4—12081no—
167C4C2×Dic60411yescharacteristic
168C4#1801275811yescharacteristic
169C4#1801276811yescharacteristic
170C4#1801277211yescharacteristic
171C2—42no—
172C2#2375237011yescharacteristic
173C2#2375237511yescharacteristic
174C2#2375238111yescharacteristic
subgroupG/H
centerC22#18012709
commutator, cosocleC42×C151C23
FrattiniC42C22×D151
FittingD4⋊C8×C151C2
socleC22×C151#120
prime radicalC2×D4×C151D4
hypercenterD4⋊C8D151
hypocenterC151#1632
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. #23752592C2semidirect
3. #23752508C2semidirect
5. #23751960C2semidirect
6. #23751944C2semidirect
60. D4×C151Q16semidirect
87. C151#1632semidirect
142. D4Dic604semidirect

Maximal subgroups

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

subgroupindex
#237529192
#237525922
#237525082
#237525022
#237519602
#237519442
D4⋊C8×C1512
#1632151