Finite Group Databasebeta

← C2×#23758175 #34116384

Subgroups — C2×#23758175 #34116384

Order 20096.

278 conjugacy classes of subgroups; only the 58 normal subgroups are shown.

normal subgroups only

This group has 278 conjugacy classes of subgroups — too many to draw. Only its 58 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×#19097831C211yesmaximal, characteristic
2C2×#19097829C211yesmaximal, characteristic
3#23758175C214yesmaximal, direct product factor
4C2×#19097754C211yesmaximal, characteristic
5C2×#14578963—21no—
6C2×C22⋊#10597845—21no—
7#19097831—21no—
8#19097831C2212yes—
9#19097829—21no—
10#19097829C2212yes—
11C22×C22⋊D157C2211yescharacteristic
12#19097754—21no—
13#19097754—21no—
14#19097754C412yescomplemented
15#19097754C2212yes—
16C2×#14578933—21no—
17C2×C22⋊Dic157C411yescharacteristic, complemented
18C2×#14578931—21no—
19C23×C4×C157C411yescharacteristic, complemented
20C22×#10597845—41no—
21#14578963—22no—
22#14578963—41no—
23C2×#11929441—41no—
24C22⋊#10597845—22no—
25C22⋊#10597845—41no—
26C23×D157D411yescharacteristic
27C2×C22⋊D157—41no—
28C2×C22⋊D157—41no—
29C2×C22⋊D157C2×C411yescharacteristic
30C2×C22⋊D157D411yescharacteristic
31C2×C22⋊D157D411yescharacteristic
32C2×C22⋊D157C2311yescharacteristic
33C22×Dic157—21no—
34C22×Dic157D411yescharacteristic
35#14578933—22no—
36#14578933—22no—
37C22⋊Dic157—21no—
38C22⋊Dic157C2×C412yescomplemented
39#14578931—22no—
40#14578931—22no—
41C24×C157C2×C411yescharacteristic
42C22×C4×C157—21no—
43C22×C4×C157—21no—
44C22×C4×C157—41no—
45C22×C4×C157—41no—
46C22×C4×C157C2×C412yescomplemented
47C2×#10597845—42no—
48C2×#10597845—82no—
49#11929441—42no—
50C22×D157—21no—
51C22×D157—21no—
52C22×D157—42no—
53C22×D157C22⋊C411yescharacteristic
54C22×D157C2×D411yescharacteristic
55C22⋊D157—41no—
56C22⋊D157—41no—
57C22⋊D157—41no—
58C22⋊D157—41no—
59C2×Dic157—21no—
60C2×Dic157—21no—
61C2×Dic157—22no—
62C2×Dic157—42no—
63C2×Dic157C22⋊C411yescharacteristic
64C2×Dic157C2×D411yescharacteristic
65C23×C157—21no—
66C23×C157—21no—
67C23×C157—42no—
68C23×C157C22⋊C411yescharacteristic
69C23×C157C22⋊C411yescharacteristic
70C23×C157C22×C411yescharacteristic
71C2×C4×C157—22no—
72C2×C4×C157—42no—
73C2×C4×C157—41no—
74C2×C4×C157—41no—
75C2×C4×C157—42no—
76C22×C157—22no—
77C22×C157—21no—
78C22×C157—21no—
79C22×C157—41no—
80C22×C157—41no—
81C22×C157—42no—
82C22×C157—42no—
83C22×C157#9911yescharacteristic
84C22×C157#9911yescharacteristic
85C22×C157C2×C22⋊C411yescharacteristic
86C2×D157—21no—
87C2×D157—21no—
88C2×D157—42no—
89C2×D157—41no—
90C2×D157—41no—
91C2×D157—81no—
92#10597845—82no—
93C4×C157—42no—
94Dic157—21no—
95Dic157—21no—
96Dic157—42no—
97C2×C157—21no—
98C2×C157—21no—
99C2×C157—41no—
100C2×C157—41no—
101C2×C157#35212yescomplemented
102C2×C157C2×#9911yescharacteristic
103D157—41no—
104D157—41no—
105C157C2×#35211yescharacteristic, complemented, Sylow
106C2×#352—1571nomaximal, Sylow
107C2×#123—1571no—
108C2×#100—1571no—
109C2×#99—1571no—
110#352—1574no—
111C22×D4—1571no—
112C23×C4#1059784511yescharacteristic, complemented
113C2×M16—3141no—
114#123—3141no—
115#123—3141no—
116#123—1572no—
117#123—1572no—
118C2×C4⋊C4—3141no—
119C2×C22⋊C4—3141no—
120C2×C22⋊C4—3141no—
121C2×C22⋊C4—1571no—
122#100—3141no—
123#100—1572no—
124#99—3141no—
125#99—1572no—
126C24—1571no—
127C24C2×#1059784511yescharacteristic
128C2×D4—6281no—
129C2×D4—6281no—
130C2×D4—1571no—
131C2×D4—1571no—
132C2×D4—1571no—
133C2×D4—1571no—
134C22×C4—21no—
135C22×C4—21no—
136C22×C4—41no—
137C22×C4—41no—
138C22×C4—3141no—
139C22×C4—6281no—
140C22×C4—1571no—
141C22×C4C2×#1059784512yescomplemented
142M16—3142no—
143M16—6281no—
144C2×C8—6281no—
145C4⋊C4—3142no—
146C4⋊C4—3142no—
147C22⋊C4—3142no—
148C22⋊C4—3142no—
149C22⋊C4—3141no—
150C22⋊C4—3142no—
151C22⋊C4—6281no—
152C22⋊C4—1572no—
153C23—21no—
154C23—21no—
155C23—42no—
156C23—3141no—
157C23—3141no—
158C23—6282no—
159C23—1571no—
160C23—1571no—
161C23C22⋊#1059784511yescharacteristic
162C23C22⋊#1059784511yescharacteristic
163C23C22×#1059784511yescharacteristic
164D4—6281no—
165D4—6281no—
166D4—6281no—
167D4—6281no—
168C2×C4—22no—
169C2×C4—42no—
170C2×C4—41no—
171C2×C4—41no—
172C2×C4—42no—
173C2×C4—3141no—
174C2×C4—3141no—
175C2×C4—3142no—
176C2×C4—6282no—
177C2×C4—6282no—
178C2×C4—1571no—
179C2×C4—1571no—
180C2×C4—12562no—
181C8—6282no—
182C22—22no—
183C22—21no—
184C22—21no—
185C22—41no—
186C22—41no—
187C22—42no—
188C22—42no—
189C22—3141no—
190C22—3141no—
191C22—6281no—
192C22—6281no—
193C22—6282no—
194C22—12561no—
195C22#1909782911yescharacteristic
196C22#1909782911yescharacteristic
197C22C2×C22⋊#1059784511yescharacteristic
198C4—42no—
199C4—3141no—
200C4—3141no—
201C4—6282no—
202C4—12562no—
203C2—21no—
204C2—21no—
205C2—41no—
206C2—41no—
207C2—6281no—
208C2—6281no—
209C2#2375817512yesdirect product factor
210C2C2×#1909782911yescharacteristic
subgroupG/H
centerC22#19097829
commutatorC23×C157C22×C4
FrattiniC23C22×#10597845
FittingC23×C4×C157C4
socleC22×C157#99
prime radicalC22×C22⋊D157C22
cosocleC2×C22⋊D157C23
hypercenterC23×C4#10597845
hypocenterC157C2×#352
LCSG ▷ C23×C157 ▷ C22×C157 ▷ C2×C157 ▷ C157
UCSC1 ◁ C22 ◁ C23 ◁ C24 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
3. #23758175C2direct (N × H)
14. #19097754C4semidirect
17. C2×C22⋊Dic157C4semidirect
19. C23×C4×C157C4semidirect
38. C22⋊Dic157C2×C4semidirect
46. C22×C4×C157C2×C4semidirect
101. C2×C157#352semidirect
105. C157C2×#352semidirect
112. C23×C4#10597845semidirect
141. C22×C4C2×#10597845semidirect
209. C2#23758175direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#190978312
C2×#190978292
#237581752
C2×#190977542
C2×#352157