Finite Group Databasebeta

← #34098537

Subgroups — #34098537

Order 20096.

216 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 216 conjugacy classes of subgroups — too many to draw. Only its 73 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#23757324C211yesmaximal, characteristic
3C4⋊C8×D157C211yesmaximal, characteristic
4#23757005C211yesmaximal, characteristic, complemented
5Q8⋊#11929434C211yesmaximal, characteristic, complemented
6#23757003C211yesmaximal, characteristic, complemented
7Q8⋊C8×C157C211yesmaximal, characteristic, complemented
8C2×C8×D157—21no—
9#19097770C411yescharacteristic
10#19097769C411yescharacteristic
11#19097761—21no—
12#19097751C411yescharacteristic
13#19097749—21no—
14#19097747C411yescharacteristic
15C4×Dic314—21no—
16C4×Dic314C2211yescharacteristic
17#19097728—21no—
18C42×D157C2211yescharacteristic
19C4⋊#11929434C2211yescharacteristic
20#19097700—21no—
21#19097700—21no—
22#19097683—21no—
23C4×#11929434C2211yescharacteristic
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
32C2×#11929434—21no—
33C2×#11929434—21no—
34C8×D157—42no—
35C4⋊Dic157—21no—
36C4⋊Dic157C2×C411yescharacteristic
37#14578933—21no—
38#14578933—21no—
39#14578933—21no—
40#14578933—21no—
41#14578933—21no—
42#14578931—21no—
43#14578931—21no—
44C4×Dic157—21no—
45C4×Dic157C2×C411yescharacteristic
46C4×Dic157D411yescharacteristic
47C4×Dic157D411yescharacteristic
48C2×Q8×C157C2×C411yescharacteristic
49C2×C8×C157—21no—
50C2×C8×C157—21no—
51C4⋊C4×C157—21no—
52C4⋊C4×C157C2×C411yescharacteristic
53C42×C157—21no—
54C42×C157C2311yescharacteristic
55C22×D157C22⋊C411yescharacteristic
56Dic314—21no—
57Dic314—21no—
58Dic314—42no—
59C2×Dic157—21no—
60C2×Dic157—21no—
61C2×Dic157C22⋊C411yescharacteristic
62C2×Dic157C22⋊C411yescharacteristic
63C2×Dic157C22⋊C411yescharacteristic
64C4×D157—21no—
65C4×D157—21no—
66C4×D157—41no—
67C4×D157SD1612yes—
68C4×D157Q1612yes—
69#11929434—41no—
70#11929434—41no—
71Q8×C157—21no—
72Q8×C157—21no—
73C2×C4×C157—21no—
74C2×C4×C157—21no—
75C2×C4×C157C22×C411yescharacteristic
76C2×C4×C157C2×D411yescharacteristic
77C2×C4×C157C2×D411yescharacteristic
78C8×C157—41no—
79C8×C157—41no—
80C22×C157C2×C22⋊C411yescharacteristic
81C2×D157—21no—
82C2×D157—21no—
83C2×D157#10312yes—
84C4×C157—21no—
85C4×C157—41no—
86C4×C157—41no—
87C4×C157#13111yescharacteristic
88C4×C157#13111yescharacteristic
89C4×C157C2×SD1611yescharacteristic
90C4×C157C2×Q1611yescharacteristic
91Dic157—21no—
92Dic157—21no—
93Dic157—41no—
94Dic157—41no—
95Dic157#10312yes—
96C2×C157#40811yescharacteristic
97C2×C157C2×#10311yescharacteristic
98C2×C157#42111yescharacteristic
99D157—22no—
100C157#148111yescharacteristic, complemented, Sylow
101#1481—1571nomaximal, Sylow
102#533—1571no—
103#431—1571no—
104C2×C4⋊C8—1571no—
105Q8⋊C8—1571no—
106Q8⋊C8—1571no—
107Q8⋊C8—1571no—
108Q8⋊C8D15711yescharacteristic, complemented
109C22×C8—3141no—
110C4⋊Q8—1571no—
111C4⋊Q8—1571no—
112#125—3141no—
113C22⋊Q8—3141no—
114C22⋊Q8—1571no—
115C22⋊Q8—1571no—
116C4×Q8—3141no—
117C4×Q8—1571no—
118C4×Q8C2×D15711yescharacteristic
119#117—3141no—
120C2×C42—1571no—
121C4⋊C8—3141no—
122C4⋊C8—3141no—
123C4⋊C8—1571no—
124C4⋊C8C2×D15711yescharacteristic
125C22⋊C8—3141no—
126C4×C8—1571no—
127C4×C8C2×D15711yescharacteristic
128C2×Q8—3141no—
129C2×Q8—1571no—
130C2×Q8C4×D15711yescharacteristic
131C22×C4—1571no—
132C22×C4—1571no—
133C22×C4—1571no—
134C2×C8—21no—
135C2×C8—21no—
136C2×C8—3141no—
137C2×C8—3141no—
138C2×C8—6282no—
139C4⋊C4—21no—
140C4⋊C4—3141no—
141C4⋊C4—3141no—
142C4⋊C4—3141no—
143C4⋊C4—3141no—
144C4⋊C4—3141no—
145C4⋊C4—3141no—
146C4⋊C4—1571no—
147C4⋊C4C4×D15711yescharacteristic
148C22⋊C4—3141no—
149C22⋊C4—3141no—
150C42—21no—
151C42—3141no—
152C42—1571no—
153C42—1571no—
154C42—1571no—
155C42C22×D15711yescharacteristic
156C23—1571no—
157Q8—21no—
158Q8—21no—
159Q8—3141no—
160Q8—3141no—
161Q8—6282no—
162C2×C4—21no—
163C2×C4—21no—
164C2×C4—3141no—
165C2×C4—3141no—
166C2×C4—3141no—
167C2×C4—3141no—
168C2×C4—6281no—
169C2×C4—1571no—
170C2×C4—1571no—
171C2×C4—1571no—
172C2×C4—1572no—
173C2×C4—1572no—
174C2×C4C2×C4×D15711yescharacteristic
175C2×C4D4×D15711yescharacteristic
176C2×C4D4×D15711yescharacteristic
177C8—41no—
178C8—41no—
179C8—6281no—
180C8—6281no—
181C22—3141no—
182C22—3141no—
183C22—1572no—
184C22C22⋊C4×D15711yescharacteristic
185C4—21no—
186C4—41no—
187C4—41no—
188C4—3141no—
189C4—3141no—
190C4—6281no—
191C4—6281no—
192C4—1572no—
193C4#1909777711yescharacteristic
194C4#1909777911yescharacteristic
195C4SD16×D15711yescharacteristic
196C4Q16×D15711yescharacteristic
197C2—3142no—
198C2#2375723811yescharacteristic
199C2#103×D15711yescharacteristic
200C2#2375728811yescharacteristic
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#1481
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
100. C157#1481semidirect
108. Q8⋊C8D157semidirect

Maximal subgroups

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

subgroupindex
#237578272
#237573242
C4⋊C8×D1572
#237570052
Q8⋊#119294342
#237570032
Q8⋊C8×C1572
#1481157