Finite Group Databasebeta

← #34098589

Subgroups — #34098589

Order 20096.

232 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 232 conjugacy classes of subgroups — too many to draw. Only its 75 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#23757827C211yesmaximal, characteristic
2#23757295C211yesmaximal, characteristic
3C4×C8×D157C211yesmaximal, characteristic
4#23757005C211yesmaximal, characteristic, complemented
5Q8⋊#11929434C211yesmaximal, characteristic, complemented
6#23757003C211yesmaximal, characteristic, complemented
7Q8⋊C8×C157C211yesmaximal, characteristic, complemented
8C2×#14578937—21no—
9C2×C8×D157—21no—
10#19097770C411yescharacteristic
11#19097769C411yescharacteristic
12#19097761—21no—
13#19097751C411yescharacteristic
14#19097749—21no—
15#19097747C411yescharacteristic
16C4×Dic314—21no—
17C4×Dic314C2211yescharacteristic
18#19097728—21no—
19C42×D157C2211yescharacteristic
20C4⋊#11929434C2211yescharacteristic
21#19097700—21no—
22C4×#11929434C2211yescharacteristic
23C8×Dic157—21no—
24C4×Q8×C157C2211yescharacteristic
25C4⋊C8×C157C2211yescharacteristic
26C4×C8×C157C2211yescharacteristic
27C2×Dic314—21no—
28C2×Dic314C2×C411yescharacteristic
29C2×C4×D157C2×C411yescharacteristic
30C2×C4×D157D411yescharacteristic
31C2×C4×D157D411yescharacteristic
32#14578937—42no—
33C2×#11929434—21no—
34C2×#11929434—21no—
35C8×D157—24no—
36C4⋊Dic157—21no—
37C4⋊Dic157C2×C411yescharacteristic
38#14578933—21no—
39#14578933—21no—
40#14578933—21no—
41#14578933—21no—
42#14578933—21no—
43#14578931—21no—
44#14578931—21no—
45C4×Dic157—21no—
46C4×Dic157C2×C411yescharacteristic
47C4×Dic157D411yescharacteristic
48C4×Dic157D411yescharacteristic
49C2×Q8×C157C2×C411yescharacteristic
50C2×C8×C157—21no—
51C2×C8×C157—21no—
52C4⋊C4×C157—21no—
53C4⋊C4×C157C2×C411yescharacteristic
54C42×C157—21no—
55C42×C157C2311yescharacteristic
56C22×D157C22⋊C411yescharacteristic
57Dic314—21no—
58Dic314—21no—
59Dic314—42no—
60C2×Dic157—21no—
61C2×Dic157—21no—
62C2×Dic157C22⋊C411yescharacteristic
63C2×Dic157C22⋊C411yescharacteristic
64C2×Dic157C22⋊C411yescharacteristic
65C4×D157—21no—
66C4×D157—21no—
67C4×D157—22no—
68C4×D157SD1612yes—
69C4×D157Q1612yes—
70#11929434—22no—
71#11929434—41no—
72Q8×C157—21no—
73Q8×C157—21no—
74C2×C4×C157—21no—
75C2×C4×C157—21no—
76C2×C4×C157C22×C411yescharacteristic
77C2×C4×C157C2×D411yescharacteristic
78C2×C4×C157C2×D411yescharacteristic
79C8×C157—22no—
80C8×C157—41no—
81C22×C157C2×C22⋊C411yescharacteristic
82C2×D157—21no—
83C2×D157—21no—
84C2×D157#10312yes—
85C4×C157—21no—
86C4×C157—41no—
87C4×C157—41no—
88C4×C157#13111yescharacteristic
89C4×C157#13111yescharacteristic
90C4×C157C2×SD1611yescharacteristic
91C4×C157C2×Q1611yescharacteristic
92Dic157—21no—
93Dic157—41no—
94Dic157—41no—
95Dic157#10312yes—
96Dic157#10412yes—
97C2×C157#40811yescharacteristic
98C2×C157C2×#10311yescharacteristic
99C2×C157C2×#10411yescharacteristic
100D157—22no—
101C157#149311yescharacteristic, complemented, Sylow
102#1493—1571nomaximal, Sylow
103#533—1571no—
104#423—1571no—
105C2×C4×C8—1571no—
106Q8⋊C8—1571no—
107Q8⋊C8—1571no—
108Q8⋊C8—1571no—
109Q8⋊C8D15711yescharacteristic, complemented
110C2×M16—3141no—
111C22×C8—3141no—
112C4⋊Q8—1571no—
113C4⋊Q8—1571no—
114#125—3141no—
115C22⋊Q8—3141no—
116C22⋊Q8—1571no—
117C22⋊Q8—1571no—
118C4×Q8—3141no—
119C4×Q8—1571no—
120C4×Q8C2×D15711yescharacteristic
121#117—3141no—
122C2×C42—1571no—
123C4⋊C8—3141no—
124C4⋊C8—1571no—
125C4⋊C8C2×D15711yescharacteristic
126C4×C8—3141no—
127C4×C8—1571no—
128C4×C8C2×D15711yescharacteristic
129C2×Q8—3141no—
130C2×Q8—1571no—
131C2×Q8C4×D15711yescharacteristic
132C22×C4—1571no—
133C22×C4—1571no—
134C22×C4—1571no—
135M16—6282no—
136C2×C8—21no—
137C2×C8—21no—
138C2×C8—3144no—
139C2×C8—3141no—
140C2×C8—3141no—
141C4⋊C4—21no—
142C4⋊C4—3141no—
143C4⋊C4—3141no—
144C4⋊C4—3141no—
145C4⋊C4—3141no—
146C4⋊C4—3141no—
147C4⋊C4—3141no—
148C4⋊C4—1571no—
149C4⋊C4C4×D15711yescharacteristic
150C22⋊C4—3141no—
151C22⋊C4—3141no—
152C42—21no—
153C42—3141no—
154C42—1571no—
155C42—1571no—
156C42—1571no—
157C42C22×D15711yescharacteristic
158C23—1571no—
159Q8—21no—
160Q8—21no—
161Q8—3141no—
162Q8—3141no—
163Q8—6282no—
164C2×C4—21no—
165C2×C4—21no—
166C2×C4—3142no—
167C2×C4—3141no—
168C2×C4—3141no—
169C2×C4—3141no—
170C2×C4—3141no—
171C2×C4—1571no—
172C2×C4—1571no—
173C2×C4—1571no—
174C2×C4—1572no—
175C2×C4—1572no—
176C2×C4C2×C4×D15711yescharacteristic
177C2×C4D4×D15711yescharacteristic
178C2×C4D4×D15711yescharacteristic
179C8—22no—
180C8—41no—
181C8—3142no—
182C8—6281no—
183C22—3141no—
184C22—3141no—
185C22—1572no—
186C22C22⋊C4×D15711yescharacteristic
187C4—21no—
188C4—41no—
189C4—41no—
190C4—3141no—
191C4—6281no—
192C4—6281no—
193C4—1572no—
194C4—1572no—
195C4#1909777711yescharacteristic
196C4#1909777911yescharacteristic
197C4SD16×D15711yescharacteristic
198C4Q16×D15711yescharacteristic
199C2—3142no—
200C2#2375723811yescharacteristic
201C2#103×D15711yescharacteristic
202C2#104×D15711yescharacteristic
subgroupG/H
centerC2×C4D4×D157
commutatorC2×C4×C157C22×C4
FrattiniC42C22×D157
FittingQ8⋊C8×C157C2
socleC22×C157C2×C22⋊C4
prime radicalC22×D157C22⋊C4
cosocleC42×C157C23
hypercenterQ8⋊C8D157
hypocenterC157#1493
LCSG ▷ C2×C4×C157 ▷ C2×C157 ▷ C157
UCSC1 ◁ C2×C4 ◁ C42 ◁ Q8⋊C8

Complements

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

NH ≅ G/Ntype
4. #23757005C2semidirect
5. Q8⋊#11929434C2semidirect
6. #23757003C2semidirect
7. Q8⋊C8×C157C2semidirect
101. C157#1493semidirect
109. Q8⋊C8D157semidirect

Maximal subgroups

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

subgroupindex
#237578272
#237572952
C4×C8×D1572
#237570052
Q8⋊#119294342
#237570032
Q8⋊C8×C1572
#1493157