Finite Group Databasebeta

← #34116182

Subgroups — #34116182

Order 20096.

362 conjugacy classes of subgroups; only the 66 normal subgroups are shown.

normal subgroups only

This group has 362 conjugacy classes of subgroups — too many to draw. Only its 66 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#23758340C211yesmaximal, characteristic, complemented
2#23758271C212yesmaximal, complemented
3D157⋊#100C211yesmaximal, characteristic, complemented
4#23758140C212yesmaximal, complemented
5#23757836C211yesmaximal, characteristic
6D157⋊M16C2212yes—
7D4×#10597845—24no—
8#19097850C2212yes—
9C2×C22⋊#10597845—22no—
10#19097835—24no—
11#19097831—22no—
12C2×#14578953C2211yescharacteristic
13C2×D4×D157C2211yescharacteristic
14#19097767C411yescharacteristic, complemented
15#19097759C411yescharacteristic, complemented
16#19097758C411yescharacteristic, complemented
17#19097743—22no—
18#19097739—22no—
19#19097728C2211yescharacteristic
20#127×C157C411yescharacteristic, complemented
21C22×#10597845—24no—
22#14578964—22no—
23#14578963—22no—
24D157⋊C8—22no—
25C4⋊#10597845—22no—
26C22⋊#10597845—24no—
27C22⋊#10597845—22no—
28C4×#10597845D414yescomplemented
29C23×D157D412yes—
30#14578953—22no—
31#14578953—22no—
32C2×Dic314C2×C411yescharacteristic, complemented
33C2×D628C2×C411yescharacteristic
34C2×C22⋊D157—21no—
35C2×C22⋊D157—22no—
36C2×C22⋊D157D412yes—
37D4×D157—22no—
38D4×D157—22no—
39C22×Dic157—21no—
40C2×C4×D157C2311yescharacteristic
41#14578933—21no—
42C22⋊Dic157—22no—
43#14578931—22no—
44#14578931—21no—
45C4×Dic157C2×C411yescharacteristic, complemented
46C2×D4×C157—22no—
47C2×D4×C157C2×C411yescharacteristic
48C2×D4×C157C2×C411yescharacteristic, complemented
49C42×C157C2×C411yescharacteristic, complemented
50C2×#10597845—24no—
51C2×#10597845—84no—
52#11929441—42no—
53C22×D157—22no—
54C22×D157—22no—
55C22×D157—82no—
56C22×D157C22⋊C412yes—
57C22×D157C2×D411yescharacteristic
58Dic314—22no—
59D628—22no—
60C22⋊D157—24no—
61C22⋊D157—41no—
62C22⋊D157—41no—
63C22⋊D157—82no—
64C2×Dic157—21no—
65C2×Dic157—21no—
66C2×Dic157—42no—
67C2×Dic157C2×D411yescharacteristic
68C4×D157C2×D412yes—
69C4×D157#4112yes—
70C23×C157—21no—
71C23×C157C22⋊C412yes—
72D4×C157—22no—
73D4×C157—22no—
74D4×C157—82no—
75C2×C4×C157—21no—
76C2×C4×C157C22×C411yescharacteristic
77C22×C157—22no—
78C22×C157—42no—
79C22×C157—42no—
80C22×C157—41no—
81C22×C157C2×C22⋊C411yescharacteristic
82C2×D157—22no—
83C2×D157—41no—
84C2×D157—44no—
85C2×D157—42no—
86C2×D157—82no—
87C2×D157#12011yescharacteristic
88C2×D157#12311yescharacteristic
89#10597845—44no—
90C4×C157—41no—
91C4×C157C4×D412yes—
92Dic157—41no—
93Dic157—41no—
94Dic157#12112yes—
95C2×C157—21no—
96C2×C157—42no—
97C2×C157—81no—
98C2×C157#38611yescharacteristic
99D157—21no—
100D157—21no—
101D157—42no—
102C157#191111yescharacteristic, complemented, Sylow
103#1911—1571nomaximal, Sylow
104#535—1571no—
105#518—1571no—
106#421—1572no—
107C2×#100—1571no—
108H(3,ℤ/4)—1572no—
109C2×#41—1571no—
110C22×D4—1571no—
111C2×M16—1572no—
112#127—1571no—
113#127#1059784511yescharacteristic, complemented
114#124—1571no—
115#124—1571no—
116#121—3142no—
117#120—3142no—
118C4×D4—3144no—
119#117—1572no—
120#117—1571no—
121C2×C22⋊C4—3142no—
122#104—3144no—
123#100—3142no—
124C24—1572no—
125#41—3142no—
126#41—3142no—
127C2×Q8—1571no—
128C2×D4—22no—
129C2×D4—3141no—
130C2×D4—3142no—
131C2×D4—3142no—
132C2×D4—3142no—
133C2×D4—1572no—
134C2×D4—1571no—
135C2×D4C2×#1059784511yescharacteristic
136C2×D4C2×#1059784511yescharacteristic, complemented
137C22×C4—3144no—
138C22×C4—3141no—
139C22×C4—1571no—
140M16—3142no—
141M16—3142no—
142C2×C8—3142no—
143C4⋊C4—3141no—
144C4⋊C4—3142no—
145C22⋊C4—3141no—
146C22⋊C4—3142no—
147C22⋊C4—3144no—
148C22⋊C4—3142no—
149C22⋊C4—3142no—
150C42—1574no—
151C42—1571no—
152C42C2×#1059784511yescharacteristic, complemented
153C23—21no—
154C23—3142no—
155C23—3142no—
156C23—1572no—
157C23—1571no—
158C23—12562no—
159C23C22⋊#1059784512yes—
160Q8—3142no—
161D4—22no—
162D4—22no—
163D4—82no—
164D4—3144no—
165D4—3142no—
166D4—6281no—
167D4—6281no—
168D4—12562no—
169C2×C4—21no—
170C2×C4—3144no—
171C2×C4—3141no—
172C2×C4—3141no—
173C2×C4—6282no—
174C2×C4—1571no—
175C2×C4—1572no—
176C2×C4—1572no—
177C2×C4—12564no—
178C2×C4C22×#1059784511yescharacteristic
179C8—6282no—
180C22—22no—
181C22—42no—
182C22—42no—
183C22—41no—
184C22—3142no—
185C22—6281no—
186C22—6282no—
187C22—6284no—
188C22—1571no—
189C22—1571no—
190C22—12562no—
191C22C2×C22⋊#1059784511yescharacteristic
192C4—41no—
193C4—6281no—
194C4—6284no—
195C4—6281no—
196C4—1572no—
197C4D4×#1059784512yes—
198C2—21no—
199C2—42no—
200C2—81no—
201C2—3141no—
202C2—3141no—
203C2—6282no—
204C2#2375822111yescharacteristic
subgroupG/H
centerC2#23758221
commutatorC2×C4×C157C22×C4
FrattiniC2×C4C22×#10597845
Fitting#127×C157C4
socleC2×C157#386
prime radical#23757836C2
cosocleC2×C4×D157C23
hypercenter#127#10597845
hypocenterC157#1911
LCSG ▷ C2×C4×C157 ▷ C2×C157 ▷ C157
UCSC1 ◁ C2 ◁ C2×C4 ◁ #127

Complements

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

NH ≅ G/Ntype
1. #23758340C2semidirect
2. #23758271C2semidirect
3. D157⋊#100C2semidirect
4. #23758140C2semidirect
14. #19097767C4semidirect
15. #19097759C4semidirect
16. #19097758C4semidirect
20. #127×C157C4semidirect
28. C4×#10597845D4semidirect
32. C2×Dic314C2×C4semidirect
45. C4×Dic157C2×C4semidirect
48. C2×D4×C157C2×C4semidirect
49. C42×C157C2×C4semidirect
102. C157#1911semidirect
113. #127#10597845semidirect
136. C2×D4C2×#10597845semidirect
152. C42C2×#10597845semidirect

Maximal subgroups

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

subgroupindex
#237583402
#237582712
D157⋊#1002
#237581402
#237578362
#1911157