Finite Group Databasebeta

← #34101830

Subgroups — #34101830

Order 20096.

230 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 230 conjugacy classes of subgroups — too many to draw. Only its 65 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#23757844C211yesmaximal, characteristic
2#23757257C211yesmaximal, characteristic
3#23757071C214yesmaximal, complemented
4#413×C157C211yesmaximal, characteristic
5C22×Dic314C411yescharacteristic
6C2×#14578938—21no—
7#19097769C2212yes—
8#19097758C412yes—
9#19097752—21no—
10#19097752—21no—
11#19097750—21no—
12#19097750—21no—
13#19097730C411yescharacteristic
14#19097690C2212yes—
15#19097688—21no—
16C2×#41×C157C2211yescharacteristic
17C2×M16×C157—21no—
18#101×C157C2212yes—
19#100×C157—21no—
20C2×Dic314—21no—
21C2×Dic314—41no—
22C2×Dic314—41no—
23C2×Dic314C2×C412yes—
24C22×Dic157—21no—
25#14578938—22no—
26#14578938—41no—
27C2×#11929434—41no—
28C4⋊Dic157—21no—
29#14578933—22no—
30#14578933—22no—
31C22⋊Dic157—21no—
32C22⋊Dic157—22no—
33C22⋊Dic157—22no—
34C4×Dic157C2×C412yes—
35#41×C157—41no—
36#41×C157—41no—
37C2×Q8×C157C2311yescharacteristic
38C2×D4×C157C2×C411yescharacteristic
39C2×D4×C157D411yescharacteristic
40C2×D4×C157D411yescharacteristic
41C22×C4×C157C2×C411yescharacteristic
42C22×C4×C157D411yescharacteristic
43C22×C4×C157D411yescharacteristic
44M16×C157—22no—
45M16×C157—41no—
46C2×C8×C157—41no—
47Dic314—41no—
48Dic314—41no—
49Dic314—42no—
50C2×Dic157—22no—
51C2×Dic157—22no—
52C2×Dic157—42no—
53#11929434—42no—
54C23×C157C22⋊C411yescharacteristic
55C23×C157C22⋊C411yescharacteristic
56C23×C157C22⋊C411yescharacteristic
57Q8×C157—41no—
58D4×C157—41no—
59D4×C157—41no—
60D4×C157—41no—
61C2×C4×C157—21no—
62C2×C4×C157—21no—
63C2×C4×C157—21no—
64C2×C4×C157—21no—
65C2×C4×C157—21no—
66C2×C4×C157—21no—
67C2×C4×C157C22⋊C411yescharacteristic
68C2×C4×C157C22×C411yescharacteristic
69C2×C4×C157C2×D411yescharacteristic
70C2×C4×C157C2×D411yescharacteristic
71C8×C157—42no—
72C22×C157—21no—
73C22×C157—21no—
74C22×C157—21no—
75C22×C157—41no—
76C22×C157—41no—
77C22×C157—41no—
78C22×C157C2×C22⋊C411yescharacteristic
79C4×C157—21no—
80C4×C157—21no—
81C4×C157—21no—
82C4×C157#9911yescharacteristic
83C4×C157#9911yescharacteristic
84Dic157—42no—
85Dic157—42no—
86C2×C157—21no—
87C2×C157—41no—
88C2×C157—41no—
89C2×C157—41no—
90C2×C157C2×#9911yescharacteristic
91C157#213511yescharacteristic, complemented, Sylow
92#2135—1571nomaximal, Sylow
93#536—1571no—
94#413—1571no—
95#413D15711yescharacteristic
96#356—1574no—
97C2×#41C2×D15711yescharacteristic
98C22×Q8—1571no—
99C2×M16—21no—
100C2×M16—3141no—
101C4⋊Q8—1572no—
102#124—1572no—
103#123—3141no—
104#123—3141no—
105C22⋊Q8—3141no—
106C22⋊Q8—3141no—
107#117—1571no—
108#101—1572no—
109#101C2×D15712yes—
110#100—21no—
111#100—3141no—
112#41—41no—
113#41—41no—
114C2×Q8—3141no—
115C2×Q8—6281no—
116C2×Q8—6281no—
117C2×Q8—1572no—
118C2×Q8C22×D15711yescharacteristic
119C2×D4C4×D15711yescharacteristic
120C2×D4C22⋊D15711yescharacteristic
121C2×D4D62811yescharacteristic
122C22×C4—3141no—
123C22×C4C4×D15711yescharacteristic
124C22×C4C22⋊D15711yescharacteristic
125C22×C4D62811yescharacteristic
126M16—22no—
127M16—41no—
128M16—3142no—
129M16—6281no—
130C2×C8—41no—
131C2×C8—6281no—
132C4⋊C4—3142no—
133C4⋊C4—3142no—
134C4⋊C4—3141no—
135C22⋊C4—3141no—
136C22⋊C4—3142no—
137C22⋊C4—3142no—
138C42—1572no—
139C23#1457893111yescharacteristic
140C23#1457893111yescharacteristic
141C23#1457893111yescharacteristic
142Q8—41no—
143Q8—6282no—
144Q8—6281no—
145Q8—6281no—
146D4—41no—
147D4—41no—
148D4—41no—
149C2×C4—21no—
150C2×C4—21no—
151C2×C4—21no—
152C2×C4—21no—
153C2×C4—21no—
154C2×C4—21no—
155C2×C4—3142no—
156C2×C4—3142no—
157C2×C4—6282no—
158C2×C4#1457893111yescharacteristic
159C2×C4C2×C4×D15711yescharacteristic
160C2×C4C2×C22⋊D15711yescharacteristic
161C2×C4C2×D62811yescharacteristic
162C8—42no—
163C8—6282no—
164C22—21no—
165C22—21no—
166C22—21no—
167C22—41no—
168C22—41no—
169C22—41no—
170C22C2×#1457893111yescharacteristic
171C4—21no—
172C4—21no—
173C4—21no—
174C4—6282no—
175C4—6282no—
176C4#1909768511yescharacteristic
177C4#1909768511yescharacteristic
178C2—21no—
179C2—41no—
180C2—41no—
181C2—41no—
182C2C2×#1909768511yescharacteristic
subgroupG/H
centerC2C2×#19097685
commutatorC2×C4×C157C22×C4
FrattiniC2×Q8C22×D157
Fitting#413×C157C2
socleC2×C157C2×#99
prime radicalC2×#41×C157C22
cosocleC2×Q8×C157C23
hypercenter#413D157
hypocenterC157#2135
LCSG ▷ C2×C4×C157 ▷ C22×C157 ▷ C2×C157 ▷ C157
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×#41 ◁ #413

Complements

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

NH ≅ G/Ntype
3. #23757071C2semidirect
91. C157#2135semidirect

Maximal subgroups

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

subgroupindex
#237578442
#237572572
#237570712
#413×C1572
#2135157