Finite Group Databasebeta

← #354×D157 #34101795

Subgroups — #354×D157 #34101795

Order 20096.

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

normal subgroups only

This group has 284 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#124×D157C211yesmaximal, characteristic
2#99×D157C212yesmaximal
3#23757068C211yesmaximal, characteristic, complemented
4#23757067C212yesmaximal, complemented
5#354×C157C211yesmaximal, characteristic, complemented
6C2×Q8×D157C411yescharacteristic, complemented
7C2×D4×D157C2211yescharacteristic
8#19097760C411yescharacteristic, complemented
9#19097759C411yescharacteristic, complemented
10#19097758C2211yescharacteristic
11#19097757—22no—
12C22⋊C4×D157—22no—
13C22⋊C4×D157—22no—
14C42×D157C411yescharacteristic, complemented
15#19097686C2212yes—
16#19097685—22no—
17#124×C157C2211yescharacteristic
18#99×C157C2212yes—
19C23×D157D412yes—
20C2×Dic314—21no—
21C2×Dic314C2×C411yescharacteristic, complemented
22Q8×D157—41no—
23Q8×D157—41no—
24C2×D628C2×C411yescharacteristic
25C2×C22⋊D157D412yes—
26D4×D157—41no—
27D4×D157—41no—
28C2×C4×D157—21no—
29C2×C4×D157—21no—
30C2×C4×D157—42no—
31C2×C4×D157C2×C411yescharacteristic
32C22⋊Dic157—22no—
33C22⋊Dic157—22no—
34#14578931—22no—
35#14578931—22no—
36#14578931—42no—
37C4×Dic157—21no—
38C4×Dic157C2×C411yescharacteristic, complemented
39C2×Q8×C157C2×C411yescharacteristic, complemented
40C2×D4×C157C2311yescharacteristic
41C22⋊C4×C157—22no—
42C22⋊C4×C157—22no—
43C42×C157C2×C411yescharacteristic, complemented
44C22×D157—22no—
45C22×D157—22no—
46C22×D157—44no—
47C22×D157C22⋊C411yescharacteristic
48C22×D157C22⋊C412yes—
49Dic314—42no—
50Dic314—41no—
51D628—41no—
52C22⋊D157—42no—
53C2×Dic157—21no—
54C2×Dic157—21no—
55C2×Dic157—42no—
56C2×Dic157C22⋊C411yescharacteristic
57C4×D157—21no—
58C4×D157—21no—
59C4×D157—42no—
60C4×D157—41no—
61C4×D157—41no—
62C4×D157—84no—
63C23×C157C2×D412yes—
64Q8×C157—41no—
65D4×C157—41no—
66C2×C4×C157—21no—
67C2×C4×C157—21no—
68C2×C4×C157—42no—
69C2×C4×C157C22×C411yescharacteristic
70C22×C157—22no—
71C22×C157—42no—
72C22×C157C2×C22⋊C411yescharacteristic
73C2×D157—22no—
74C2×D157—22no—
75C2×D157—44no—
76C2×D157—42no—
77C2×D157—82no—
78C2×D157#9911yescharacteristic
79C2×D157#9911yescharacteristic
80C4×C157—21no—
81C4×C157—41no—
82C4×C157—41no—
83C4×C157—82no—
84Dic157—21no—
85Dic157—41no—
86Dic157—41no—
87Dic157—82no—
88C2×C157—21no—
89C2×C157—42no—
90C2×C157C2×#9911yescharacteristic
91D157—21no—
92D157—42no—
93D157#35412yesdirect product factor
94C157C2×#35411yescharacteristic, complemented, Sylow
95C2×#354—1571nomaximal, Sylow
96C2×#124—1571no—
97C2×#99—1572no—
98#354—1571no—
99#354—1572no—
100#354D15711yescharacteristic, direct product factor
101C22×Q8—1571no—
102C22×D4—1571no—
103#124—3142no—
104#124—1571no—
105#124—1571no—
106#124—1571no—
107#124C2×D15711yescharacteristic
108C2×C22⋊C4—3142no—
109C2×C22⋊C4—3142no—
110C2×C42—1571no—
111#99—3142no—
112#99—1572no—
113#99C2×D15712yes—
114C24—1572no—
115C2×Q8—3141no—
116C2×Q8—6281no—
117C2×Q8—6281no—
118C2×Q8—1571no—
119C2×Q8C4×D15711yescharacteristic, complemented
120C2×D4—6281no—
121C2×D4—6281no—
122C2×D4—1572no—
123C2×D4—1571no—
124C2×D4C22×D15711yescharacteristic
125C22×C4—3141no—
126C22×C4—3141no—
127C22×C4—6282no—
128C22×C4—1571no—
129C22⋊C4—22no—
130C22⋊C4—22no—
131C22⋊C4—3142no—
132C22⋊C4—3142no—
133C22⋊C4—3142no—
134C22⋊C4—3142no—
135C22⋊C4—6282no—
136C42—3141no—
137C42—1571no—
138C42C4×D15711yescharacteristic, complemented
139C23—3142no—
140C23—3142no—
141C23—6284no—
142C23—1571no—
143C23—1572no—
144C23D4×D15712yes—
145Q8—41no—
146Q8—6281no—
147Q8—6282no—
148D4—41no—
149D4—6281no—
150D4—6282no—
151C2×C4—21no—
152C2×C4—21no—
153C2×C4—42no—
154C2×C4—3141no—
155C2×C4—3141no—
156C2×C4—3141no—
157C2×C4—3141no—
158C2×C4—6282no—
159C2×C4—6281no—
160C2×C4—6281no—
161C2×C4—6282no—
162C2×C4—1571no—
163C2×C4—12564no—
164C2×C4C2×C4×D15711yescharacteristic
165C22—22no—
166C22—42no—
167C22—3142no—
168C22—3142no—
169C22—6282no—
170C22—6284no—
171C22—1571no—
172C22—1571no—
173C22—12562no—
174C22C22⋊C4×D15711yescharacteristic
175C4—21no—
176C4—41no—
177C4—41no—
178C4—82no—
179C4—3141no—
180C4—6281no—
181C4—6281no—
182C4—12562no—
183C2—21no—
184C2—42no—
185C2—3141no—
186C2—6282no—
187C2—1572no—
188C2#99×D15711yescharacteristic
subgroupG/H
centerC2#99×D157
commutatorC2×C4×C157C22×C4
FrattiniC2×D4C22×D157
Fitting#354×C157C2
socleC2×C157C2×#99
prime radicalC2×D4×D157C22
cosocleC2×D4×C157C23
hypercenter#354D157
hypocenterC157C2×#354
LCSG ▷ C2×C4×C157 ▷ C22×C157 ▷ C2×C157 ▷ C157
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #354

Complements

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

NH ≅ G/Ntype
3. #23757068C2semidirect
4. #23757067C2semidirect
5. #354×C157C2semidirect
6. C2×Q8×D157C4semidirect
8. #19097760C4semidirect
9. #19097759C4semidirect
14. C42×D157C4semidirect
21. C2×Dic314C2×C4semidirect
38. C4×Dic157C2×C4semidirect
39. C2×Q8×C157C2×C4semidirect
43. C42×C157C2×C4semidirect
93. D157#354direct (N × H)
94. C157C2×#354semidirect
100. #354D157direct (N × H)
119. C2×Q8C4×D157semidirect
138. C42C4×D157semidirect

Maximal subgroups

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

subgroupindex
#124×D1572
#99×D1572
#237570682
#237570672
#354×C1572
C2×#354157