Finite Group Databasebeta

← #34099364

Subgroups — #34099364

Order 20096.

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

normal subgroups only

This group has 212 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#23757623C211yesmaximal, characteristic, complemented
2#23757553C211yesmaximal, characteristic, complemented
3#23757478C211yesmaximal, characteristic, complemented
4#23757022C211yesmaximal, characteristic, complemented
5D4⋊#11929434C211yesmaximal, characteristic, complemented
6D4⋊#11929434C211yesmaximal, characteristic, complemented
7#555×C157C211yesmaximal, characteristic
8C2×#14578942—21no—
9#19097771C2211yescharacteristic
10#19097704—21no—
11C4⋊#11929434C2211yescharacteristic
12C4⋊#11929434C2211yescharacteristic
13#19097695—22no—
14#19097694—21no—
15#19097692—21no—
16C4×#11929434C2211yescharacteristic
17C4⋊Q8×C157C2211yescharacteristic
18#124×C157—22no—
19#121×C157—21no—
20#121×C157—21no—
21C4×D4×C157C2211yescharacteristic
22C4×D4×C157C2211yescharacteristic
23#117×C157—21no—
24#117×C157—21no—
25C2×Dic314—21no—
26#14578942—42no—
27C2×#11929434—21no—
28C2×#11929434—21no—
29C2×#11929434—21no—
30C4⋊Dic157—21no—
31C4⋊Dic157—21no—
32C2×Q8×C157D412yes—
33C2×D4×C157—22no—
34C2×D4×C157D411yescharacteristic
35C2×D4×C157D411yescharacteristic
36C22×C4×C157—21no—
37C22×C4×C157—21no—
38C4⋊C4×C157—21no—
39C4⋊C4×C157—21no—
40C4⋊C4×C157D411yescharacteristic
41C4⋊C4×C157D411yescharacteristic
42C22⋊C4×C157—22no—
43C22⋊C4×C157—22no—
44C22⋊C4×C157—21no—
45C22⋊C4×C157—21no—
46C42×C157—22no—
47C42×C157C2311yescharacteristic
48Dic314—41no—
49Dic314—41no—
50C2×Dic157—41no—
51#11929434—41no—
52#11929434—41no—
53#11929434—41no—
54C23×C157—21no—
55C23×C157—21no—
56Q8×C157—42no—
57D4×C157—21no—
58D4×C157—21no—
59D4×C157—21no—
60D4×C157—21no—
61D4×C157—82no—
62C2×C4×C157—21no—
63C2×C4×C157—21no—
64C2×C4×C157—22no—
65C2×C4×C157—41no—
66C2×C4×C157—41no—
67C2×C4×C157—41no—
68C2×C4×C157—41no—
69C2×C4×C157C2×D411yescharacteristic
70C2×C4×C157C2×D411yescharacteristic
71C2×C4×C157C2×D411yescharacteristic
72C22×C157—41no—
73C22×C157—41no—
74C22×C157—41no—
75C22×C157—41no—
76C22×C157—41no—
77C22×C157—41no—
78C22×C157#12011yescharacteristic
79C4×C157—21no—
80C4×C157—41no—
81C4×C157—41no—
82C4×C157—42no—
83C4×C157#13511yescharacteristic
84C4×C157#13511yescharacteristic
85C4×C157AGL(1,ℤ/8)11yescharacteristic
86C4×C157#13711yescharacteristic
87Dic157—81no—
88C2×C157—81no—
89C2×C157—81no—
90C2×C157#44911yescharacteristic
91C2×C157#45211yescharacteristic
92C2×C157#45511yescharacteristic
93C157#164611yescharacteristic, complemented, Sylow
94#1646—1571nomaximal, Sylow
95#555D15711yescharacteristic
96#487—1571no—
97#474—1571no—
98#461—1571no—
99#333—1571no—
100D4⋊C8—1571no—
101D4⋊C8—1571no—
102C2×SD16—3141no—
103C4⋊Q8—1571no—
104C4⋊Q8C2×D15711yescharacteristic
105#124—22no—
106#121—21no—
107#121—21no—
108C4×D4C2×D15711yescharacteristic
109C4×D4C2×D15711yescharacteristic
110#117—21no—
111#117—21no—
112#107—3141no—
113C4⋊C8—1571no—
114C4⋊C8—1571no—
115#103—3142no—
116#103—3141no—
117#102—3141no—
118C4×C8—1571no—
119C2×Q8—3141no—
120C2×Q8C22⋊D15712yes—
121C2×D4—22no—
122C2×D4C22⋊D15711yescharacteristic
123C2×D4C22⋊D15711yescharacteristic
124C22×C4—21no—
125C22×C4—21no—
126SD16—6282no—
127C2×C8—3141no—
128C2×C8—3141no—
129C2×C8—3141no—
130C4⋊C4—21no—
131C4⋊C4—21no—
132C4⋊C4—3141no—
133C4⋊C4—3141no—
134C4⋊C4C22⋊D15711yescharacteristic
135C4⋊C4C22⋊D15711yescharacteristic
136C22⋊C4—22no—
137C22⋊C4—22no—
138C22⋊C4—21no—
139C22⋊C4—21no—
140C42—22no—
141C42C22×D15711yescharacteristic
142C23—21no—
143C23—21no—
144Q8—42no—
145Q8—6281no—
146Q8—6281no—
147D4—21no—
148D4—21no—
149D4—21no—
150D4—21no—
151D4—82no—
152C2×C4—21no—
153C2×C4—21no—
154C2×C4—22no—
155C2×C4—41no—
156C2×C4—41no—
157C2×C4—41no—
158C2×C4—41no—
159C2×C4—6281no—
160C2×C4C2×C22⋊D15711yescharacteristic
161C2×C4C2×C22⋊D15711yescharacteristic
162C2×C4C2×C22⋊D15711yescharacteristic
163C8—6281no—
164C8—6281no—
165C8—6281no—
166C22—41no—
167C22—41no—
168C22—41no—
169C22—41no—
170C22—41no—
171C22—41no—
172C22#1909774011yescharacteristic
173C4—21no—
174C4—41no—
175C4—41no—
176C4—42no—
177C4—12561no—
178C4#1909779111yescharacteristic
179C4#1909779111yescharacteristic
180C4#1909779611yescharacteristic
181C4#1909780111yescharacteristic
182C2—81no—
183C2—81no—
184C2#2375741811yescharacteristic
185C2#2375743511yescharacteristic
186C2#2375745111yescharacteristic
subgroupG/H
centerC22#19097740
commutator, cosocleC42×C157C23
FrattiniC42C22×D157
Fitting, prime radical#555×C157C2
socleC22×C157#120
hypercenter#555D157
hypocenterC157#1646
LCSG ▷ C42×C157 ▷ C22×C157 ▷ C157
UCSC1 ◁ C22 ◁ C42 ◁ #555

Complements

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

NH ≅ G/Ntype
1. #23757623C2semidirect
2. #23757553C2semidirect
3. #23757478C2semidirect
4. #23757022C2semidirect
5. D4⋊#11929434C2semidirect
6. D4⋊#11929434C2semidirect
93. C157#1646semidirect

Maximal subgroups

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

subgroupindex
#237576232
#237575532
#237574782
#237570222
D4⋊#119294342
#555×C1572
#1646157