Finite Group Databasebeta

← #34098732

Subgroups — #34098732

Order 20096.

264 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 264 conjugacy classes of subgroups — too many to draw. Only its 61 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#124×D157C211yesmaximal, characteristic
2#23757328C211yesmaximal, characteristic, complemented
3#23757225C211yesmaximal, characteristic, complemented
4#23757013C211yesmaximal, characteristic, complemented
5#23757012C211yesmaximal, characteristic, complemented
6#23757012C211yesmaximal, characteristic, complemented
7#329×C157C211yesmaximal, characteristic, complemented
8C2×Q8×D157C411yescharacteristic
9C2×D4×D157C411yescharacteristic
10C2×#14578937—21no—
11#19097760C411yescharacteristic
12#19097759C2211yescharacteristic
13#19097758C411yescharacteristic
14#19097757—21no—
15#19097757—21no—
16C22⋊C4×D157—21no—
17C22⋊C4×D157—21no—
18C42×D157C2211yescharacteristic
19#19097700—21no—
20#19097683—21no—
21#19097682C2211yescharacteristic, complemented
22#19097682C2211yescharacteristic, complemented
23C8×Dic157—21no—
24#124×C157C2211yescharacteristic
25#97×C157C2211yescharacteristic, complemented
26#97×C157C2211yescharacteristic, complemented
27C23×D157—21no—
28C2×Dic314—21no—
29C2×Dic314C2×C411yescharacteristic
30Q8×D157—42no—
31C2×D628C2×C411yescharacteristic
32C2×C22⋊D157—21no—
33D4×D157—42no—
34C2×C4×D157—21no—
35C2×C4×D157C2×C411yescharacteristic
36C2×C4×D157D411yescharacteristic
37C2×C4×D157D411yescharacteristic
38#14578937—24no—
39C2×#11929434—21no—
40C2×#11929434—21no—
41C22⋊Dic157—21no—
42C22⋊Dic157—21no—
43#14578931—21no—
44#14578931—21no—
45#14578931—21no—
46#14578931—21no—
47C4×Dic157C2×C411yescharacteristic
48C4×Dic157D411yescharacteristic
49C4×Dic157D411yescharacteristic
50C2×Q8×C157C2×C411yescharacteristic
51C2×D4×C157C2×C411yescharacteristic
52C2×C8×C157—21no—
53C2×C8×C157—21no—
54C22⋊C4×C157—21no—
55C22⋊C4×C157—21no—
56C42×C157C2311yescharacteristic
57C22×D157—21no—
58C22×D157—42no—
59C22×D157—42no—
60C22×D157—42no—
61C22×D157C22⋊C411yescharacteristic
62Dic314—42no—
63Dic314—41no—
64D628—41no—
65C22⋊D157—42no—
66C2×Dic157—21no—
67C2×Dic157C22⋊C411yescharacteristic
68C2×Dic157C22⋊C411yescharacteristic
69C2×Dic157C22⋊C411yescharacteristic
70C4×D157—22no—
71C4×D157—22no—
72C4×D157—41no—
73C4×D157—42no—
74#11929434—22no—
75#11929434—41no—
76C23×C157—21no—
77Q8×C157—41no—
78D4×C157—41no—
79C2×C4×C157—21no—
80C2×C4×C157C22×C411yescharacteristic
81C2×C4×C157C2×D411yescharacteristic
82C2×C4×C157C2×D411yescharacteristic
83C8×C157—22no—
84C8×C157—41no—
85C22×C157—41no—
86C22×C157—41no—
87C22×C157—41no—
88C22×C157C2×C22⋊C411yescharacteristic
89C2×D157—21no—
90C2×D157—21no—
91C2×D157—41no—
92C2×D157—41no—
93C2×D157—41no—
94C2×D157—84no—
95C2×D157#10412yes—
96C4×C157—21no—
97C4×C157—21no—
98C4×C157—21no—
99C4×C157—41no—
100Dic157—21no—
101Dic157—21no—
102Dic157—41no—
103Dic157#10012yes—
104C2×C157—81no—
105C2×C157C2×#10011yescharacteristic
106C2×C157C2×#10411yescharacteristic
107C2×C157#42111yescharacteristic
108D157—22no—
109D157—81no—
110C157#152711yescharacteristic, complemented, Sylow
111#1527—1571nomaximal, Sylow
112C2×#124—1571no—
113#432—1571no—
114C4×M16—1571no—
115#329—1571no—
116#329—1571no—
117#329—1571no—
118#329D15711yescharacteristic, complemented
119C22×Q8—1571no—
120C22×D4—1571no—
121C2×M16—3141no—
122#124—3141no—
123#124—3141no—
124#124—1571no—
125#124—1571no—
126#124—1571no—
127#124C2×D15711yescharacteristic
128C2×C22⋊C4—3141no—
129C2×C22⋊C4—3141no—
130C2×C42—1571no—
131C4⋊C8—3141no—
132C22⋊C8—3141no—
133#97—1571no—
134#97—1571no—
135#97C2×D15711yescharacteristic, complemented
136#97C2×D15711yescharacteristic, complemented
137C4×C8—3141no—
138C24—3141no—
139C2×Q8—3141no—
140C2×Q8—6282no—
141C2×Q8—1571no—
142C2×Q8C4×D15711yescharacteristic
143C2×D4—3141no—
144C2×D4—6282no—
145C2×D4—1571no—
146C2×D4C4×D15711yescharacteristic
147C22×C4—3141no—
148C22×C4—1571no—
149C22×C4—1571no—
150C22×C4—1571no—
151M16—3144no—
152C2×C8—21no—
153C2×C8—21no—
154C2×C8—3141no—
155C2×C8—3141no—
156C22⋊C4—21no—
157C22⋊C4—21no—
158C22⋊C4—3141no—
159C22⋊C4—3141no—
160C22⋊C4—3141no—
161C22⋊C4—3141no—
162C22⋊C4—3141no—
163C22⋊C4—3141no—
164C42—1571no—
165C42—1571no—
166C42—1571no—
167C42C22×D15711yescharacteristic
168C23—21no—
169C23—3141no—
170C23—6282no—
171C23—6282no—
172C23—6282no—
173C23—1571no—
174Q8—41no—
175Q8—6281no—
176Q8—6282no—
177D4—41no—
178D4—6281no—
179D4—6282no—
180C2×C4—21no—
181C2×C4—3142no—
182C2×C4—3142no—
183C2×C4—3141no—
184C2×C4—6281no—
185C2×C4—6282no—
186C2×C4—1571no—
187C2×C4—1571no—
188C2×C4—1571no—
189C2×C4C2×C4×D15711yescharacteristic
190C2×C4D4×D15711yescharacteristic
191C2×C4D4×D15711yescharacteristic
192C8—22no—
193C8—41no—
194C8—3142no—
195C8—6281no—
196C22—41no—
197C22—41no—
198C22—41no—
199C22—3141no—
200C22—3141no—
201C22—6281no—
202C22—6281no—
203C22—6281no—
204C22—1572no—
205C22—12564no—
206C22C22⋊C4×D15711yescharacteristic
207C4—21no—
208C4—21no—
209C4—21no—
210C4—41no—
211C4—3141no—
212C4—3141no—
213C4—6281no—
214C4—1572no—
215C2—81no—
216C2—3142no—
217C2—12561no—
218C2#100×D15711yescharacteristic
219C2#104×D15711yescharacteristic
220C2#2375728811yescharacteristic
subgroupG/H
centerC22C22⋊C4×D157
commutatorC2×C4×C157C22×C4
FrattiniC42C22×D157
Fitting#329×C157C2
socleC22×C157C2×C22⋊C4
prime radicalC2×D4×D157C4
cosocleC42×C157C23
hypercenter#329D157
hypocenterC157#1527
LCSG ▷ C2×C4×C157 ▷ C22×C157 ▷ C157
UCSC1 ◁ C22 ◁ C42 ◁ #329

Complements

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

NH ≅ G/Ntype
2. #23757328C2semidirect
3. #23757225C2semidirect
4. #23757013C2semidirect
5. #23757012C2semidirect
6. #23757012C2semidirect
7. #329×C157C2semidirect
21. #19097682C22semidirect
22. #19097682C22semidirect
25. #97×C157C22semidirect
26. #97×C157C22semidirect
110. C157#1527semidirect
118. #329D157semidirect
135. #97C2×D157semidirect
136. #97C2×D157semidirect

Maximal subgroups

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

subgroupindex
#124×D1572
#237573282
#237572252
#237570132
#237570122
#329×C1572
#1527157