Finite Group Databasebeta

← #34115908

Subgroups — #34115908

Order 20096.

324 conjugacy classes of subgroups; only the 100 normal subgroups are shown.

normal subgroups only

This group has 324 conjugacy classes of subgroups — too many to draw. Only its 100 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×#19097834C212yesmaximal
2#23758232C211yesmaximal, characteristic
3C4×C4⋊#10597845C211yesmaximal, characteristic
4#23758146C212yesmaximal
5C4×Q8×D157C211yesmaximal, characteristic
6C2×D157⋊C8C2212yes—
7C2×C4⋊#10597845C2212yes—
8C2×C4×#10597845—21no—
9#19097834C418yescomplemented
10#19097826—21no—
11#19097826—21no—
12(C2×#10597845)⋊C4—21no—
13C2×Q8×D157C2211yescharacteristic
14Q8×Dic157C411yescharacteristic, complemented
15C4×Dic314—21no—
16C4×Dic314C411yescharacteristic, complemented
17#19097736—21no—
18#19097736C411yescharacteristic, complemented
19C4⋊C4×D157—21no—
20C4⋊C4×D157C2211yescharacteristic
21C42×D157—21no—
22C42×D157C2211yescharacteristic
23C4×Q8×C157C411yescharacteristic, complemented
24C22×#10597845—22no—
25D157⋊C8—22no—
26D157⋊C8C2×C414yes—
27C2×#11929441—22no—
28C4⋊#10597845—22no—
29C4⋊#10597845C2×C414yes—
30C4×#10597845—42no—
31C2×Dic314—21no—
32C2×Dic314C2×C411yescharacteristic
33Q8×D157—22no—
34Q8×D157C2×C414yes—
35C2×C4×D157—21no—
36C2×C4×D157—21no—
37C2×C4×D157D411yescharacteristic
38C2×C4×D157D411yescharacteristic
39C2×C4×D157C2311yescharacteristic
40C4⋊Dic157—21no—
41C4⋊Dic157C2×C411yescharacteristic
42#14578933—21no—
43#14578933—21no—
44#14578933—21no—
45C4×Dic157—21no—
46C4×Dic157—21no—
47C4×Dic157—21no—
48C4×Dic157C2×C411yescharacteristic
49C4×Dic157D411yescharacteristic
50C4×Dic157D411yescharacteristic
51C2×Q8×C157C2×C411yescharacteristic
52C4⋊C4×C157—21no—
53C4⋊C4×C157C2×C411yescharacteristic
54C42×C157—21no—
55C42×C157C2×C411yescharacteristic
56C2×#10597845—24no—
57C2×#10597845—42no—
58C2×#10597845—42no—
59#11929441—24no—
60C22×D157C2×D411yescharacteristic
61Dic314—21no—
62Dic314—24no—
63Dic314C4212yescomplemented
64C2×Dic157—21no—
65C2×Dic157—21no—
66C2×Dic157C22⋊C411yescharacteristic
67C2×Dic157C22⋊C411yescharacteristic
68C2×Dic157C2×D411yescharacteristic
69C4×D157—24no—
70C4×D157—21no—
71C4×D157—21no—
72C4×D157—22no—
73C4×D157—41no—
74C4×D157—41no—
75C4×D157C22×C412yes—
76C4×D157#4112yes—
77Q8×C157—21no—
78Q8×C157C4212yescomplemented
79C2×C4×C157—21no—
80C2×C4×C157—21no—
81C2×C4×C157C22⋊C411yescharacteristic
82C2×C4×C157C22⋊C411yescharacteristic
83C2×C4×C157C22×C411yescharacteristic
84C22×C157C2×C22⋊C411yescharacteristic
85C2×D157C4×D412yes—
86C2×D157AGL(1,ℤ/8)11yescharacteristic
87C2×D157#13712yes—
88C2×D157#13711yescharacteristic
89#10597845—44no—
90C4×C157—22no—
91C4×C157—21no—
92C4×C157—21no—
93C4×C157—41no—
94C4×C157C2×C4211yescharacteristic
95C4×C157#11711yescharacteristic
96Dic157—22no—
97Dic157—21no—
98Dic157—21no—
99Dic157—41no—
100Dic157C4×D412yes—
101C2×C157C4×C22⋊C411yescharacteristic
102C2×C157#41711yescharacteristic
103C2×C157#41911yescharacteristic
104D157#44012yes—
105D157#44112yes—
106C157#176311yescharacteristic, complemented, Sylow
107#1763—1571nomaximal, Sylow
108C2×C4×Q8—1571no—
109C2×#103—1572no—
110C2×#97—1571no—
111C4×C4⋊C4—1571no—
112#340—1572no—
113C22×Q8—1571no—
114C22×C8—1572no—
115C4×Q8—3141no—
116C4×Q8—3141no—
117C4×Q8—1571no—
118C4×Q8—1571no—
119C4×Q8—1571no—
120C4×Q8#1059784511yescharacteristic, complemented
121C2×C4⋊C4—3141no—
122C2×C4⋊C4—1572no—
123C2×C4⋊C4—1571no—
124C2×C42—3141no—
125C2×C42—3141no—
126C2×C42—1571no—
127#103—1578no—
128#97—3141no—
129#97—3141no—
130#95—3141no—
131C2×Q8—3141no—
132C2×Q8—3142no—
133C2×Q8—1574no—
134C2×Q8—1571no—
135C2×Q8C2×#1059784511yescharacteristic
136C22×C4—3141no—
137C22×C4—3141no—
138C22×C4—3142no—
139C22×C4—1571no—
140C22×C4—1571no—
141C22×C4—1571no—
142C2×C8—3142no—
143C2×C8—3142no—
144C2×C8—1574no—
145C4⋊C4—21no—
146C4⋊C4—3141no—
147C4⋊C4—3141no—
148C4⋊C4—3141no—
149C4⋊C4—3142no—
150C4⋊C4—3141no—
151C4⋊C4—1574no—
152C4⋊C4—1571no—
153C4⋊C4C2×#1059784511yescharacteristic
154C42—21no—
155C42—3141no—
156C42—3141no—
157C42—3141no—
158C42—6282no—
159C42—1571no—
160C42—1571no—
161C42—1571no—
162C42C2×#1059784511yescharacteristic
163C23—1571no—
164Q8—21no—
165Q8—3144no—
166Q8—3141no—
167Q8—1572no—
168Q8C4×#1059784512yescomplemented
169C2×C4—21no—
170C2×C4—21no—
171C2×C4—3141no—
172C2×C4—3144no—
173C2×C4—3141no—
174C2×C4—3142no—
175C2×C4—3141no—
176C2×C4—3144no—
177C2×C4—3141no—
178C2×C4—6281no—
179C2×C4—6281no—
180C2×C4—6282no—
181C2×C4—6282no—
182C2×C4—1571no—
183C2×C4—1571no—
184C2×C4—1571no—
185C2×C4—1572no—
186C2×C4—1572no—
187C2×C4C22⋊#1059784511yescharacteristic
188C2×C4C22⋊#1059784511yescharacteristic
189C2×C4C22×#1059784511yescharacteristic
190C8—3144no—
191C22—1572no—
192C22—1571no—
193C22—1571no—
194C22—1572no—
195C22C2×C22⋊#1059784511yescharacteristic
196C4—22no—
197C4—21no—
198C4—21no—
199C4—41no—
200C4—3142no—
201C4—3141no—
202C4—3141no—
203C4—6284no—
204C4—6281no—
205C4—1572no—
206C4C2×C4×#1059784511yescharacteristic
207C4#1909785011yescharacteristic
208C2—1572no—
209C2—1572no—
210C2C4×C22⋊#1059784511yescharacteristic
211C2#2375826411yescharacteristic
212C2#2375826611yescharacteristic
subgroupG/H
centerC22C2×C22⋊#10597845
commutatorC4×C157C2×C42
FrattiniC2×C4C22×#10597845
FittingC4×Q8×C157C4
socleC22×C157C2×C22⋊C4
prime radicalC22×D157C2×D4
cosocleC2×C4×D157C23
hypercenterC4×Q8#10597845
hypocenterC157#1763
LCSG ▷ C4×C157 ▷ C2×C157 ▷ C157
UCSC1 ◁ C22 ◁ C42 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
9. #19097834C4semidirect
14. Q8×Dic157C4semidirect
16. C4×Dic314C4semidirect
18. #19097736C4semidirect
23. C4×Q8×C157C4semidirect
63. Dic314C42semidirect
78. Q8×C157C42semidirect
106. C157#1763semidirect
120. C4×Q8#10597845semidirect
168. Q8C4×#10597845semidirect

Maximal subgroups

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

subgroupindex
C2×#190978342
#237582322
C4×C4⋊#105978452
#237581462
C4×Q8×D1572
#1763157