Finite Group Databasebeta

← #34100215

Subgroups — #34100215

Order 20096.

316 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 316 conjugacy classes of subgroups — too many to draw. Only its 81 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
1C2×C4⋊C4×D157C211yesmaximal, characteristic
2#23757236C212yesmaximal
3#23757042C211yesmaximal, characteristic, complemented
4#23757041C212yesmaximal, complemented
5#343×C157C211yesmaximal, characteristic, complemented
6C22×C4×D157C412yes—
7C22×C4×D157C2211yescharacteristic
8C2×#14578938C2212yes—
9C2×C4⋊Dic157C2211yescharacteristic
10C2×#14578933C412yes—
11C4⋊C4×D157—22no—
12C4⋊C4×D157—22no—
13#19097683—22no—
14#19097683—22no—
15C2×M16×C157C2212yes—
16C2×C4⋊C4×C157C2211yescharacteristic
17C23×D157C2×C411yescharacteristic
18C22×Dic157C2×C411yescharacteristic
19C22×Dic157C2×C412yes—
20C2×C4×D157—22no—
21C2×C4×D157—22no—
22C2×C4×D157—21no—
23C2×C4×D157—22no—
24C2×C4×D157—21no—
25C2×C4×D157—44no—
26C2×C4×D157D412yes—
27C2×C4×D157D412yes—
28#14578938—22no—
29#14578938—22no—
30C2×#11929434—22no—
31C4⋊Dic157—22no—
32#14578933—24no—
33C22×C4×C157C2×C412yes—
34C22×C4×C157C2311yescharacteristic
35M16×C157—22no—
36M16×C157—22no—
37C2×C8×C157—22no—
38C4⋊C4×C157—22no—
39C22×D157—21no—
40C22×D157—21no—
41C22×D157—22no—
42C22×D157—22no—
43C22×D157C22⋊C411yescharacteristic
44C22×D157C22⋊C411yescharacteristic
45C2×Dic157—21no—
46C2×Dic157—21no—
47C2×Dic157—22no—
48C2×Dic157—42no—
49C2×Dic157C22⋊C412yes—
50C4×D157—22no—
51C4×D157—22no—
52C4×D157—22no—
53C4×D157—22no—
54C4×D157—44no—
55C4×D157—44no—
56#11929434—42no—
57C23×C157C22×C411yescharacteristic
58C2×C4×C157—22no—
59C2×C4×C157—42no—
60C2×C4×C157C2×D412yes—
61C2×C4×C157#4111yescharacteristic
62C2×C4×C157#4112yes—
63C2×C4×C157#4111yescharacteristic
64C8×C157—42no—
65C22×C157—21no—
66C22×C157—21no—
67C22×C157C2×C22⋊C411yescharacteristic
68C22×C157#11711yescharacteristic
69C22×C157#11711yescharacteristic
70C2×D157—24no—
71C2×D157—24no—
72C2×D157—21no—
73C2×D157—21no—
74C2×D157—21no—
75C2×D157—21no—
76C2×D157#10012yes—
77C2×D157#10112yes—
78C4×C157—42no—
79C4×C157#12312yes—
80C4×C157#12312yes—
81Dic157—22no—
82Dic157—42no—
83C2×C157—21no—
84C2×C157—21no—
85C2×C157#38111yescharacteristic
86C2×C157C2×#10011yescharacteristic
87C2×C157C2×#10111yescharacteristic
88D157—22no—
89D157—22no—
90C157#182111yescharacteristic, complemented, Sylow
91#1821—1571nomaximal, Sylow
92C22×C4⋊C4—1571no—
93#407—1572no—
94#343—1572no—
95#343—1571no—
96#343D15711yescharacteristic, complemented
97C23×C4—1571no—
98C23×C4—1572no—
99C2×M16—1572no—
100C2×M16C2×D15712yes—
101C2×C4⋊C4—3142no—
102C2×C4⋊C4—3142no—
103C2×C4⋊C4—1572no—
104C2×C4⋊C4—1571no—
105C2×C4⋊C4C2×D15711yescharacteristic
106C22⋊C8—3142no—
107C22⋊C8—3142no—
108C24—1571no—
109C22×C4—3142no—
110C22×C4—3142no—
111C22×C4—3141no—
112C22×C4—3142no—
113C22×C4—3141no—
114C22×C4—6284no—
115C22×C4—1571no—
116C22×C4—1572no—
117C22×C4—1572no—
118C22×C4—1572no—
119C22×C4C4×D15712yes—
120C22×C4C22×D15711yescharacteristic
121M16—22no—
122M16—22no—
123M16—3142no—
124M16—3142no—
125C2×C8—22no—
126C2×C8—3142no—
127C4⋊C4—22no—
128C4⋊C4—3144no—
129C4⋊C4—3142no—
130C23—3142no—
131C23—3142no—
132C23—3141no—
133C23—3141no—
134C23—1571no—
135C23—1571no—
136C23C2×C4×D15711yescharacteristic
137C2×C4—22no—
138C2×C4—42no—
139C2×C4—3141no—
140C2×C4—3141no—
141C2×C4—3142no—
142C2×C4—3142no—
143C2×C4—3142no—
144C2×C4—3142no—
145C2×C4—3142no—
146C2×C4—6284no—
147C2×C4—6284no—
148C2×C4—6282no—
149C2×C4—1572no—
150C2×C4D4×D15712yes—
151C2×C4#1457895311yescharacteristic
152C2×C4#1457895412yes—
153C2×C4#1457895511yescharacteristic
154C8—42no—
155C8—6282no—
156C22—21no—
157C22—21no—
158C22—3144no—
159C22—3144no—
160C22—3141no—
161C22—3141no—
162C22—3141no—
163C22—3141no—
164C22—1572no—
165C22—1572no—
166C22C22⋊C4×D15711yescharacteristic
167C22#1909772811yescharacteristic
168C22#1909772911yescharacteristic
169C4—42no—
170C4—3142no—
171C4—6282no—
172C4#1909775312yes—
173C4#1909775612yes—
174C2—21no—
175C2—21no—
176C2—3142no—
177C2—3142no—
178C2#2375713511yescharacteristic
179C2#100×D15711yescharacteristic
180C2#101×D15711yescharacteristic
subgroupG/H
centerC22C22⋊C4×D157
commutatorC23×C157C22×C4
FrattiniC22×C4C22×D157
Fitting#343×C157C2
socleC22×C157C2×C22⋊C4
prime radicalC23×D157C2×C4
cosocleC22×C4×C157C23
hypercenter#343D157
hypocenterC157#1821
LCSG ▷ C23×C157 ▷ C2×C157 ▷ C157
UCSC1 ◁ C22 ◁ C22×C4 ◁ #343

Complements

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

NH ≅ G/Ntype
3. #23757042C2semidirect
4. #23757041C2semidirect
5. #343×C157C2semidirect
90. C157#1821semidirect
96. #343D157semidirect

Maximal subgroups

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

subgroupindex
C2×C4⋊C4×D1572
#237572362
#237570422
#237570412
#343×C1572
#1821157