Finite Group Databasebeta

← #353×D157 #34101792

Subgroups — #353×D157 #34101792

Order 20096.

368 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 368 conjugacy classes of subgroups — too many to draw. Only its 57 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#127×D157C211yesmaximal, characteristic
2#99×D157C212yesmaximal, complemented
3#23757066C211yesmaximal, characteristic, complemented
4#23757065C212yesmaximal, complemented
5#353×C157C211yesmaximal, characteristic, complemented
6C2×D4×D157—22no—
7C2×D4×D157C411yescharacteristic, complemented
8C2×D4×D157C2211yescharacteristic
9#19097768C411yescharacteristic, complemented
10#19097767—22no—
11#19097767C411yescharacteristic, complemented
12#19097767C2211yescharacteristic
13C22⋊C4×D157—22no—
14C42×D157C411yescharacteristic, complemented
15#19097686C2212yescomplemented
16#19097685—22no—
17#127×C157C2211yescharacteristic
18#99×C157C2212yescomplemented
19C23×D157—21no—
20C23×D157D412yes—
21C2×D628—22no—
22C2×D628C2×C411yescharacteristic
23C2×D628C2×C411yescharacteristic, complemented
24C2×C22⋊D157—22no—
25C2×C22⋊D157—21no—
26C2×C22⋊D157—22no—
27C2×C22⋊D157D412yes—
28D4×D157—41no—
29D4×D157—41no—
30D4×D157—41no—
31D4×D157—41no—
32D4×D157—48no—
33C2×C4×D157—21no—
34C2×C4×D157—42no—
35C2×C4×D157C2×C411yescharacteristic
36C22⋊Dic157—22no—
37#14578931—42no—
38C4×Dic157—21no—
39C4×Dic157C2×C411yescharacteristic, complemented
40C2×D4×C157—22no—
41C2×D4×C157C2×C411yescharacteristic, complemented
42C2×D4×C157C2311yescharacteristic
43C22⋊C4×C157—22no—
44C42×C157C2×C411yescharacteristic, complemented
45C22×D157—22no—
46C22×D157—22no—
47C22×D157—21no—
48C22×D157—44no—
49C22×D157—44no—
50C22×D157—41no—
51C22×D157—41no—
52C22×D157C22⋊C411yescharacteristic
53C22×D157C22⋊C412yes—
54D628—41no—
55D628—41no—
56D628—44no—
57C22⋊D157—42no—
58C22⋊D157—44no—
59C22⋊D157—44no—
60C22⋊D157—42no—
61C2×Dic157—21no—
62C2×Dic157—42no—
63C2×Dic157C22⋊C411yescharacteristic
64C4×D157—24no—
65C4×D157—21no—
66C4×D157—21no—
67C4×D157—84no—
68C23×C157—21no—
69C23×C157C2×D412yes—
70D4×C157—41no—
71D4×C157—41no—
72D4×C157—44no—
73C2×C4×C157—21no—
74C2×C4×C157—42no—
75C2×C4×C157C22×C411yescharacteristic
76C22×C157—22no—
77C22×C157—42no—
78C22×C157—42no—
79C22×C157—41no—
80C22×C157C2×C22⋊C411yescharacteristic
81C2×D157—22no—
82C2×D157—22no—
83C2×D157—44no—
84C2×D157—42no—
85C2×D157—42no—
86C2×D157—41no—
87C2×D157—82no—
88C2×D157—82no—
89C2×D157—82no—
90C2×D157#9911yescharacteristic
91C2×D157#9911yescharacteristic
92C4×C157—22no—
93C4×C157—21no—
94C4×C157—82no—
95Dic157—22no—
96Dic157—21no—
97Dic157—82no—
98C2×C157—21no—
99C2×C157—42no—
100C2×C157—81no—
101C2×C157C2×#9911yescharacteristic
102D157—21no—
103D157—42no—
104D157—81no—
105D157#35312yesdirect product factor
106C157C2×#35311yescharacteristic, complemented, Sylow
107C2×#353—1571nomaximal, Sylow
108C2×#127—1571no—
109C2×#99—1572no—
110#353—1571no—
111#353—1572no—
112#353D15711yescharacteristic, direct product factor
113C22×D4—3142no—
114C22×D4—1571no—
115C22×D4—1571no—
116#127—3142no—
117#127—1571no—
118#127—1571no—
119#127—1571no—
120#127C2×D15711yescharacteristic
121C2×C22⋊C4—3142no—
122C2×C42—1571no—
123#99—3142no—
124#99—1572no—
125#99C2×D15712yescomplemented
126C24—3141no—
127C24—1572no—
128C2×D4—22no—
129C2×D4—3142no—
130C2×D4—3142no—
131C2×D4—3142no—
132C2×D4—3141no—
133C2×D4—6281no—
134C2×D4—6281no—
135C2×D4—6281no—
136C2×D4—6281no—
137C2×D4—6288no—
138C2×D4—1572no—
139C2×D4—1571no—
140C2×D4—1571no—
141C2×D4C4×D15711yescharacteristic, complemented
142C2×D4C22×D15711yescharacteristic
143C22×C4—3141no—
144C22×C4—6282no—
145C22×C4—1571no—
146C22⋊C4—22no—
147C22⋊C4—3142no—
148C22⋊C4—6282no—
149C42—3141no—
150C42—1571no—
151C42C4×D15711yescharacteristic, complemented
152C23—21no—
153C23—3142no—
154C23—3142no—
155C23—3141no—
156C23—6284no—
157C23—6284no—
158C23—6281no—
159C23—6281no—
160C23—1571no—
161C23—1572no—
162C23D4×D15712yes—
163D4—41no—
164D4—41no—
165D4—44no—
166D4—6281no—
167D4—6281no—
168D4—6284no—
169D4—6282no—
170D4—6284no—
171D4—6284no—
172D4—6282no—
173C2×C4—21no—
174C2×C4—42no—
175C2×C4—3144no—
176C2×C4—3141no—
177C2×C4—3141no—
178C2×C4—3141no—
179C2×C4—6282no—
180C2×C4—1571no—
181C2×C4—12564no—
182C2×C4C2×C4×D15711yescharacteristic
183C22—22no—
184C22—42no—
185C22—42no—
186C22—41no—
187C22—3142no—
188C22—3142no—
189C22—6282no—
190C22—6282no—
191C22—6284no—
192C22—6281no—
193C22—1571no—
194C22—1571no—
195C22—12562no—
196C22—12562no—
197C22—12562no—
198C22C22⋊C4×D15711yescharacteristic
199C4—22no—
200C4—21no—
201C4—82no—
202C4—3142no—
203C4—3141no—
204C4—12562no—
205C2—21no—
206C2—42no—
207C2—81no—
208C2—3141no—
209C2—6282no—
210C2—1572no—
211C2—12561no—
212C2#99×D15711yescharacteristic
subgroupG/H
centerC2#99×D157
commutatorC2×C4×C157C22×C4
FrattiniC2×D4C22×D157
Fitting#353×C157C2
socleC2×C157C2×#99
prime radical#127×D157C2
cosocleC2×D4×C157C23
hypercenter#353D157
hypocenterC157C2×#353
LCSG ▷ C2×C4×C157 ▷ C22×C157 ▷ C2×C157 ▷ C157
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #353

Complements

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

NH ≅ G/Ntype
2. #99×D157C2semidirect
3. #23757066C2semidirect
4. #23757065C2semidirect
5. #353×C157C2semidirect
7. C2×D4×D157C4semidirect
9. #19097768C4semidirect
11. #19097767C4semidirect
14. C42×D157C4semidirect
15. #19097686C22semidirect
18. #99×C157C22semidirect
23. C2×D628C2×C4semidirect
39. C4×Dic157C2×C4semidirect
41. C2×D4×C157C2×C4semidirect
44. C42×C157C2×C4semidirect
105. D157#353direct (N × H)
106. C157C2×#353semidirect
112. #353D157direct (N × H)
125. #99C2×D157semidirect
141. C2×D4C4×D157semidirect
151. C42C4×D157semidirect

Maximal subgroups

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

subgroupindex
#127×D1572
#99×D1572
#237570662
#237570652
#353×C1572
C2×#353157