Finite Group Databasebeta

← #34099206

Subgroups — #34099206

Order 20096.

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

normal subgroups only

This group has 236 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#23757980C211yesmaximal, characteristic, complemented
2#23757645C211yesmaximal, characteristic, complemented
3#23757470C211yesmaximal, characteristic, complemented
4#23757021C211yesmaximal, characteristic, complemented
5#23757003C211yesmaximal, characteristic, complemented
6D4⋊#11929434C211yesmaximal, characteristic, complemented
7#459×C157C211yesmaximal, characteristic
8C2×#14578942—22no—
9C2×#14578942—21no—
10#19097771C2211yescharacteristic
11#19097762—21no—
12#19097750—21no—
13#19097748—22no—
14C4×Dic314C2211yescharacteristic
15D4×Dic157—21no—
16C2×C4⋊Dic157—21no—
17C4⋊#11929434C2211yescharacteristic
18#19097692—21no—
19C4×#11929434C2211yescharacteristic
20C2×D8×C157—21no—
21#127×C157C2211yescharacteristic
22C4×D4×C157C2211yescharacteristic
23C4⋊C8×C157C2211yescharacteristic
24#102×C157—21no—
25C2×Dic314D411yescharacteristic
26C2×Dic314D412yes—
27C22×Dic157—22no—
28#14578942—44no—
29#14578942—42no—
30C2×#11929434—21no—
31C2×#11929434—21no—
32C4⋊Dic157—22no—
33C4⋊Dic157—21no—
34C4⋊Dic157—21no—
35C4⋊Dic157D411yescharacteristic
36#14578933—22no—
37#14578933—21no—
38C22⋊Dic157—22no—
39C4×Dic157—21no—
40C2×D4×C157—21no—
41C2×D4×C157—21no—
42C2×D4×C157—21no—
43C2×D4×C157D411yescharacteristic
44C22×C4×C157—21no—
45D8×C157—42no—
46C2×C8×C157—21no—
47C4⋊C4×C157D411yescharacteristic
48C22⋊C4×C157—21no—
49C42×C157C2311yescharacteristic
50Dic314—21no—
51Dic314—21no—
52Dic314—42no—
53C2×Dic157—21no—
54C2×Dic157—22no—
55C2×Dic157—21no—
56C2×Dic157—82no—
57#11929434—22no—
58#11929434—41no—
59C23×C157—21no—
60C23×C157—41no—
61D4×C157—21no—
62D4×C157—42no—
63D4×C157—41no—
64D4×C157—41no—
65D4×C157—41no—
66D4×C157—41no—
67D4×C157SD1612yescomplemented
68C2×C4×C157—21no—
69C2×C4×C157—41no—
70C2×C4×C157—41no—
71C2×C4×C157C2×D411yescharacteristic
72C2×C4×C157C2×D411yescharacteristic
73C2×C4×C157C2×D411yescharacteristic
74C8×C157—41no—
75C22×C157—22no—
76C22×C157—41no—
77C22×C157—41no—
78C22×C157—81no—
79C22×C157—81no—
80C22×C157—81no—
81C22×C157#12011yescharacteristic
82C4×C157—21no—
83C4×C157—41no—
84C4×C157C2×SD1611yescharacteristic
85C4×C157#13511yescharacteristic
86C4×C157AGL(1,ℤ/8)11yescharacteristic
87C4×C157#13711yescharacteristic
88Dic157—41no—
89Dic157—41no—
90Dic157—42no—
91C2×C157—42no—
92C2×C157—161no—
93C2×C157#44811yescharacteristic
94C2×C157#44911yescharacteristic
95C2×C157#45311yescharacteristic
96C157#162211yescharacteristic, complemented, Sylow
97#1622—1571nomaximal, Sylow
98#554—1571no—
99#492—1571no—
100#460—1571no—
101#459D15711yescharacteristic
102#333—1571no—
103Q8⋊C8—1571no—
104D4⋊C8—1571no—
105C2×SD16—3141no—
106C2×SD16—3142no—
107C2×D8—21no—
108C4⋊Q8—1571no—
109#127C2×D15711yescharacteristic
110#125—3141no—
111C22⋊Q8—3142no—
112C22⋊Q8—3141no—
113C4×Q8—1571no—
114C4×D4—3141no—
115C4×D4C2×D15711yescharacteristic
116C2×C4⋊C4—3141no—
117C4⋊C8—1571no—
118C4⋊C8C2×D15711yescharacteristic
119#102—21no—
120#102—3141no—
121C4×C8—1571no—
122C2×Q8—1571no—
123C2×Q8—1572no—
124C2×D4—21no—
125C2×D4—21no—
126C2×D4—21no—
127C2×D4C22⋊D15711yescharacteristic
128C22×C4—21no—
129C22×C4—3142no—
130SD16—6284no—
131SD16—6282no—
132D8—42no—
133C2×C8—21no—
134C2×C8—3141no—
135C2×C8—3141no—
136C4⋊C4—3142no—
137C4⋊C4—3142no—
138C4⋊C4—3141no—
139C4⋊C4—3141no—
140C4⋊C4—3141no—
141C4⋊C4—1571no—
142C4⋊C4C22⋊D15711yescharacteristic
143C22⋊C4—21no—
144C22⋊C4—3142no—
145C42—3141no—
146C42C22×D15711yescharacteristic
147C23—21no—
148C23—41no—
149Q8—3141no—
150Q8—3141no—
151Q8—6282no—
152D4—21no—
153D4—42no—
154D4—41no—
155D4—41no—
156D4—41no—
157D4—41no—
158D4#1457894212yescomplemented
159C2×C4—21no—
160C2×C4—41no—
161C2×C4—41no—
162C2×C4—3141no—
163C2×C4—3141no—
164C2×C4—3142no—
165C2×C4—12562no—
166C2×C4D4×D15711yescharacteristic
167C2×C4D4×D15711yescharacteristic
168C2×C4C2×C22⋊D15711yescharacteristic
169C8—41no—
170C8—3142no—
171C8—6281no—
172C22—22no—
173C22—41no—
174C22—41no—
175C22—81no—
176C22—81no—
177C22—81no—
178C22#1909773911yescharacteristic
179C4—21no—
180C4—41no—
181C4—6281no—
182C4—6281no—
183C4—6282no—
184C4C2×#1457894211yescharacteristic
185C4#1909779011yescharacteristic
186C4#1909779511yescharacteristic
187C4#1909780111yescharacteristic
188C2—42no—
189C2—161no—
190C2#2375741111yescharacteristic
191C2#2375741511yescharacteristic
192C2#2375743911yescharacteristic
subgroupG/H
centerC22#19097739
commutator, cosocleC42×C157C23
FrattiniC42C22×D157
Fitting, prime radical#459×C157C2
socleC22×C157#120
hypercenter#459D157
hypocenterC157#1622
LCSG ▷ C42×C157 ▷ C22×C157 ▷ C157
UCSC1 ◁ C22 ◁ C42 ◁ #459

Complements

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

NH ≅ G/Ntype
1. #23757980C2semidirect
2. #23757645C2semidirect
3. #23757470C2semidirect
4. #23757021C2semidirect
5. #23757003C2semidirect
6. D4⋊#11929434C2semidirect
67. D4×C157SD16semidirect
96. C157#1622semidirect
158. D4#14578942semidirect

Maximal subgroups

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

subgroupindex
#237579802
#237576452
#237574702
#237570212
#237570032
D4⋊#119294342
#459×C1572
#1622157