Finite Group Databasebeta

← #34110428

Subgroups — #34110428

Order 20096.

382 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 382 conjugacy classes of subgroups — too many to draw. Only its 121 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#23757878C211yesmaximal, characteristic
2#23757750C211yesmaximal, characteristic, complemented
3#23757598C212yesmaximal, complemented
4#23757581C212yesmaximal, complemented
5#23757474C212yesmaximal, complemented
6#23757414C212yesmaximal, complemented
7#23757375C212yesmaximal, complemented
8C4×#14578943C212yesmaximal, complemented
9#433×C157C211yesmaximal, characteristic, complemented
10C22×Dic314C2211yescharacteristic
11C2×#14578943C2212yes—
12C2×#14578943C2212yes—
13#19097768C2211yescharacteristic
14#19097763C2211yescharacteristic
15#19097756—22no—
16#19097745C2212yes—
17#19097744—22no—
18C4×Dic314C2212yes—
19C4×Dic314C2212yes—
20#19097736—22no—
21C4×D628C2212yes—
22#19097730C2211yescharacteristic
23#19097727—22no—
24#19097705C2212yes—
25#19097703C2212yes—
26#19097696C2212yes—
27#19097696C2212yes—
28#19097693C2212yes—
29#19097693C2212yes—
30#117×C157C2211yescharacteristic
31C4⋊C8×C157C2212yes—
32C22⋊C8×C157C2212yes—
33#97×C157C2211yescharacteristic
34C4×C8×C157C2211yescharacteristic
35C2×Dic314—24no—
36C2×Dic314—21no—
37C2×Dic314C2312yes—
38C2×D628—22no—
39C2×D628C2312yes—
40C2×C22⋊D157—22no—
41C22×Dic157—21no—
42C2×C4×D157—22no—
43#14578943—24no—
44#14578943—24no—
45C4⋊Dic157C2312yes—
46C4⋊Dic157C2312yes—
47#14578933—22no—
48#14578933—22no—
49#14578933—22no—
50C22⋊Dic157—21no—
51#14578931—22no—
52#14578931—22no—
53C4×Dic157—22no—
54C4×Dic157—22no—
55C4×Dic157—21no—
56C22×C4×C157C2311yescharacteristic
57C2×C8×C157C2312yes—
58C2×C8×C157C2312yes—
59C4⋊C4×C157D412yes—
60C22⋊C4×C157D412yes—
61C42×C157C2311yescharacteristic
62C42×C157C2311yescharacteristic
63C22×D157—22no—
64Dic314—24no—
65Dic314—22no—
66Dic314#4114yes—
67D628—22no—
68D628—22no—
69D628—82no—
70C22⋊D157—82no—
71C2×Dic157—24no—
72C2×Dic157—22no—
73C2×Dic157—22no—
74C2×Dic157—22no—
75C4×D157—82no—
76C23×C157C2×D411yescharacteristic
77C2×C4×C157—22no—
78C2×C4×C157C2×D412yes—
79C2×C4×C157C2×D412yes—
80C2×C4×C157C2×D411yescharacteristic
81C2×C4×C157C2411yescharacteristic
82C8×C157—22no—
83C8×C157—22no—
84C22×C157—21no—
85C22×C157—22no—
86C22×C157C22×D411yescharacteristic
87C2×D157—42no—
88C2×D157—42no—
89C2×D157—42no—
90C4×C157—21no—
91C4×C157—22no—
92C4×C157—22no—
93C4×C157C2×#4112yes—
94Dic157—24no—
95Dic157—42no—
96Dic157—42no—
97C2×C157—41no—
98C2×C157#52511yescharacteristic
99C2×C157#57712yes—
100D157—82no—
101C157#312611yescharacteristic, complemented, Sylow
102#3126—1571nomaximal, Sylow
103#540—1571no—
104#519—1571no—
105#482—1572no—
106#479—1572no—
107#460—1572no—
108#448—1572no—
109#440—1572no—
110C4×SD16—1572no—
111#433D15711yescharacteristic, complemented
112C22×Q8—1571no—
113C2×SD16—1572no—
114C2×SD16—1572no—
115#127—1571no—
116#125—1571no—
117#123—3142no—
118#121—3142no—
119#121—1572no—
120C4×Q8—3142no—
121C4×Q8—1572no—
122C4×Q8—1572no—
123C4×D4—1572no—
124#117—3142no—
125#117—1571no—
126#117C2×D15711yescharacteristic
127#107—1572no—
128#106—1572no—
129C4⋊C8C2×D15712yes—
130#103—1572no—
131#103—1572no—
132#102—1572no—
133#102—1572no—
134C22⋊C8C2×D15712yes—
135#97C2×D15711yescharacteristic
136C4×C8C2×D15711yescharacteristic
137C2×Q8—3144no—
138C2×Q8—3141no—
139C2×Q8—1572no—
140C2×D4—3142no—
141C2×D4—3142no—
142C2×D4—1572no—
143C22×C4—3141no—
144C22×C4—3142no—
145C22×C4C22×D15711yescharacteristic
146SD16—3144no—
147SD16—3144no—
148C2×C8C22×D15712yes—
149C2×C8C22×D15712yes—
150C4⋊C4—3142no—
151C4⋊C4—3142no—
152C4⋊C4—3142no—
153C4⋊C4—1572no—
154C4⋊C4—1572no—
155C4⋊C4D62812yes—
156C22⋊C4—3141no—
157C22⋊C4—3142no—
158C22⋊C4—3142no—
159C22⋊C4D62812yes—
160C42—3142no—
161C42—3142no—
162C42—3141no—
163C42C22×D15711yescharacteristic
164C42C22×D15711yescharacteristic
165C23—3142no—
166C23C2×D62811yescharacteristic
167Q8—3144no—
168Q8—3142no—
169Q8—1574no—
170D4—3142no—
171D4—3142no—
172D4—12562no—
173D4—12562no—
174C2×C4—22no—
175C2×C4—3144no—
176C2×C4—3142no—
177C2×C4—3142no—
178C2×C4—3142no—
179C2×C4—12562no—
180C2×C4C2×D62812yes—
181C2×C4C2×D62812yes—
182C2×C4C2×D62811yescharacteristic
183C2×C4C23×D15711yescharacteristic
184C8—22no—
185C8—22no—
186C22—22no—
187C22—21no—
188C22—6282no—
189C22—6282no—
190C22—6282no—
191C22C22×D62811yescharacteristic
192C4—22no—
193C4—22no—
194C4—21no—
195C4—3144no—
196C4—6282no—
197C4—6282no—
198C4#41×D15712yes—
199C2—41no—
200C2—12562no—
201C2#2375778511yescharacteristic
202C2#2375808512yes—
subgroupG/H
centerC22C22×D628
commutator, cosocleC2×C4×C157C24
FrattiniC2×C4C23×D157
Fitting#433×C157C2
socleC22×C157C22×D4
prime radical#23757878C2
hypercenter#433D157
hypocenterC157#3126
LCSG ▷ C2×C4×C157 ▷ C2×C157 ▷ C157
UCSC1 ◁ C22 ◁ #117 ◁ #433

Complements

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

NH ≅ G/Ntype
2. #23757750C2semidirect
3. #23757598C2semidirect
4. #23757581C2semidirect
5. #23757474C2semidirect
6. #23757414C2semidirect
7. #23757375C2semidirect
8. C4×#14578943C2semidirect
9. #433×C157C2semidirect
101. C157#3126semidirect
111. #433D157semidirect

Maximal subgroups

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

subgroupindex
#237578782
#237577502
#237575982
#237575812
#237574742
#237574142
#237573752
C4×#145789432
#433×C1572
#3126157