Finite Group Databasebeta

← #34101823

Subgroups — #34101823

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#23757847C211yesmaximal, characteristic
2C2×#19097690C211yesmaximal, characteristic, complemented
3#23757071C212yesmaximal, complemented
4#23757069C212yesmaximal, complemented
5C2×#101×C157C211yesmaximal, characteristic, complemented
6C2×#14578954C411yescharacteristic
7C2×#14578938—21no—
8#19097769C411yescharacteristic
9#19097769C2211yescharacteristic
10#19097760C411yescharacteristic
11#19097760C2211yescharacteristic
12#19097754—21no—
13#19097754—21no—
14#19097747—21no—
15#19097747—21no—
16#19097730C411yescharacteristic
17#19097690—21no—
18#19097690C2212yes—
19C22×Q8×C157C2211yescharacteristic
20C2×M16×C157—21no—
21#101×C157—21no—
22#101×C157C2212yes—
23#14578954—41no—
24#14578954—41no—
25C2×Dic314C2×C411yescharacteristic
26C2×D628C2×C411yescharacteristic
27C2×C22⋊D157—21no—
28C2×C4×D157—21no—
29#14578938—22no—
30#14578938—41no—
31C2×#11929434—41no—
32C4⋊Dic157—21no—
33#14578933—21no—
34#14578933—21no—
35#14578933—21no—
36#14578933—21no—
37C22⋊Dic157—21no—
38#14578931—21no—
39#14578931—21no—
40#14578931—21no—
41#14578931—21no—
42C4×Dic157C2×C411yescharacteristic
43C4×Dic157C2×C411yescharacteristic
44C2×Q8×C157—41no—
45C2×Q8×C157—41no—
46C2×Q8×C157C2×C411yescharacteristic
47C2×Q8×C157D411yescharacteristic
48C2×Q8×C157D411yescharacteristic
49C2×Q8×C157C2311yescharacteristic
50C22×C4×C157C2×C411yescharacteristic
51C22×C4×C157D411yescharacteristic
52C22×C4×C157D411yescharacteristic
53M16×C157—22no—
54M16×C157—41no—
55C2×C8×C157—41no—
56C22×D157—21no—
57Dic314—41no—
58D628—41no—
59C22⋊D157—41no—
60C22⋊D157—41no—
61C2×Dic157—21no—
62C2×Dic157—21no—
63C2×Dic157—21no—
64C4×D157—42no—
65#11929434—42no—
66C23×C157C22⋊C411yescharacteristic
67Q8×C157—41no—
68Q8×C157—41no—
69Q8×C157—41no—
70Q8×C157—41no—
71C2×C4×C157—21no—
72C2×C4×C157—21no—
73C2×C4×C157—21no—
74C2×C4×C157—21no—
75C2×C4×C157—21no—
76C2×C4×C157—21no—
77C2×C4×C157C22⋊C411yescharacteristic
78C2×C4×C157C22⋊C411yescharacteristic
79C2×C4×C157C22⋊C411yescharacteristic
80C2×C4×C157C22×C411yescharacteristic
81C2×C4×C157C2×D411yescharacteristic
82C2×C4×C157C2×D411yescharacteristic
83C8×C157—42no—
84C22×C157—41no—
85C22×C157#9911yescharacteristic
86C22×C157#9911yescharacteristic
87C22×C157C2×C22⋊C411yescharacteristic
88C2×D157—42no—
89C2×D157—41no—
90C4×C157—21no—
91C4×C157—21no—
92C4×C157—21no—
93C4×C157—21no—
94C4×C157—21no—
95C4×C157—21no—
96Dic157—41no—
97Dic157—41no—
98Dic157—41no—
99C2×C157—21no—
100C2×C157—21no—
101C2×C157—21no—
102C2×C157C2×#9911yescharacteristic
103D157—81no—
104C157#213311yescharacteristic, complemented, Sylow
105#2133—1571nomaximal, Sylow
106#536—1571no—
107C2×#101—1571no—
108C2×#101D15711yescharacteristic, complemented
109#356—1572no—
110#355—1572no—
111C2×#41—1571no—
112C22×Q8C2×D15711yescharacteristic
113C2×M16—21no—
114C2×M16—3141no—
115C4⋊Q8—1571no—
116C4⋊Q8—1571no—
117#124—1571no—
118#124—1571no—
119#123—3141no—
120#123—3141no—
121C22⋊Q8—3141no—
122C22⋊Q8—3141no—
123#117—1571no—
124#101—21no—
125#101—3141no—
126#101—1572no—
127#101C2×D15712yes—
128#41—6281no—
129#41—6281no—
130C2×Q8—41no—
131C2×Q8—41no—
132C2×Q8—1571no—
133C2×Q8C4×D15711yescharacteristic
134C2×Q8C22⋊D15711yescharacteristic
135C2×Q8D62811yescharacteristic
136C2×Q8C22×D15711yescharacteristic
137C2×D4—3141no—
138C2×D4—1571no—
139C22×C4—3141no—
140C22×C4C4×D15711yescharacteristic
141C22×C4C22⋊D15711yescharacteristic
142C22×C4D62811yescharacteristic
143M16—22no—
144M16—41no—
145M16—3142no—
146M16—6281no—
147C2×C8—41no—
148C2×C8—6281no—
149C4⋊C4—3141no—
150C4⋊C4—3141no—
151C4⋊C4—3141no—
152C4⋊C4—3141no—
153C4⋊C4—3141no—
154C22⋊C4—3141no—
155C22⋊C4—3141no—
156C22⋊C4—3141no—
157C22⋊C4—3141no—
158C22⋊C4—3141no—
159C42—1571no—
160C42—1571no—
161C23—3141no—
162C23#1457893111yescharacteristic
163Q8—41no—
164Q8—41no—
165Q8—41no—
166Q8—41no—
167Q8—6281no—
168D4—6281no—
169D4—6281no—
170D4—6281no—
171C2×C4—21no—
172C2×C4—21no—
173C2×C4—21no—
174C2×C4—21no—
175C2×C4—21no—
176C2×C4—21no—
177C2×C4—3141no—
178C2×C4—3141no—
179C2×C4—3141no—
180C2×C4—6282no—
181C2×C4#1457893111yescharacteristic
182C2×C4#1457893111yescharacteristic
183C2×C4#1457893111yescharacteristic
184C2×C4C2×C4×D15711yescharacteristic
185C2×C4C2×C22⋊D15711yescharacteristic
186C2×C4C2×D62811yescharacteristic
187C8—42no—
188C8—6282no—
189C22—41no—
190C22—6282no—
191C22—6281no—
192C22#1909768511yescharacteristic
193C22#1909768511yescharacteristic
194C22C2×#1457893111yescharacteristic
195C4—21no—
196C4—21no—
197C4—21no—
198C4—21no—
199C4—21no—
200C4—21no—
201C4—6281no—
202C4—6281no—
203C4—6281no—
204C2—21no—
205C2—21no—
206C2—21no—
207C2—12561no—
208C2C2×#1909768511yescharacteristic
subgroupG/H
centerC2C2×#19097685
commutatorC2×C4×C157C22×C4
FrattiniC2×Q8C22×D157
FittingC2×#101×C157C2
socleC2×C157C2×#99
prime radicalC2×#14578954C4
cosocleC2×Q8×C157C23
hypercenterC2×#101D157
hypocenterC157#2133
LCSG ▷ C2×C4×C157 ▷ C22×C157 ▷ C2×C157 ▷ C157
UCSC1 ◁ C2 ◁ C23 ◁ C22×Q8 ◁ C2×#101

Complements

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

NH ≅ G/Ntype
2. C2×#19097690C2semidirect
3. #23757071C2semidirect
4. #23757069C2semidirect
5. C2×#101×C157C2semidirect
104. C157#2133semidirect
108. C2×#101D157semidirect

Maximal subgroups

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

subgroupindex
#237578472
C2×#190976902
#237570712
#237570692
C2×#101×C1572
#2133157