Finite Group Databasebeta

← #34098546

Subgroups — #34098546

Order 20096.

234 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 234 conjugacy classes of subgroups — too many to draw. Only its 67 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#23757805C211yesmaximal, characteristic
2C4⋊C8×D157C211yesmaximal, characteristic, complemented
3C4×#14578937C211yesmaximal, characteristic, complemented
4#23757005C211yesmaximal, characteristic, complemented
5#23757003C211yesmaximal, characteristic, complemented
6D4⋊#11929434C211yesmaximal, characteristic, complemented
7D4⋊C8×C157C211yesmaximal, characteristic, complemented
8C2×#14578937—21no—
9C2×C8×D157—21no—
10#19097764—21no—
11#19097762C411yescharacteristic
12#19097758C411yescharacteristic
13#19097753—21no—
14#19097751C411yescharacteristic
15#19097742C411yescharacteristic
16C4×Dic314C2211yescharacteristic
17C4×C22⋊D157—21no—
18#19097730—21no—
19C42×D157C2211yescharacteristic
20C4⋊#11929434C2211yescharacteristic
21#19097700—21no—
22#19097681—21no—
23C4×#11929434C2211yescharacteristic
24C4×D4×C157C2211yescharacteristic
25C4⋊C8×C157C2211yescharacteristic
26C4×C8×C157C2211yescharacteristic
27C2×Dic314C2×C411yescharacteristic
28C2×C22⋊D157—21no—
29C2×C4×D157C2×C411yescharacteristic
30C2×C4×D157D411yescharacteristic
31C2×C4×D157D411yescharacteristic
32#14578937—24no—
33C2×#11929434—21no—
34C2×#11929434—21no—
35C8×D157—42no—
36C4⋊Dic157—21no—
37C4⋊Dic157—21no—
38C4⋊Dic157C2×C411yescharacteristic
39#14578933—21no—
40#14578933—21no—
41C22⋊Dic157—21no—
42C22⋊Dic157—21no—
43C22⋊Dic157—21no—
44#14578931—21no—
45C4×Dic157—21no—
46C4×Dic157C2×C411yescharacteristic
47C4×Dic157D411yescharacteristic
48C4×Dic157D411yescharacteristic
49C2×D4×C157C2×C411yescharacteristic
50C22×C4×C157—21no—
51C2×C8×C157—21no—
52C2×C8×C157—21no—
53C4⋊C4×C157C2×C411yescharacteristic
54C22⋊C4×C157—21no—
55C42×C157C2311yescharacteristic
56C22×D157C22⋊C411yescharacteristic
57Dic314—21no—
58Dic314—21no—
59C22⋊D157—42no—
60C2×Dic157—21no—
61C2×Dic157—21no—
62C2×Dic157C22⋊C411yescharacteristic
63C2×Dic157C22⋊C411yescharacteristic
64C2×Dic157C22⋊C411yescharacteristic
65C4×D157—22no—
66C4×D157—21no—
67C4×D157—21no—
68C4×D157—21no—
69C4×D157—21no—
70#11929434—22no—
71#11929434—41no—
72C23×C157—21no—
73D4×C157—21no—
74D4×C157—21no—
75C2×C4×C157—21no—
76C2×C4×C157—41no—
77C2×C4×C157—41no—
78C2×C4×C157C22×C411yescharacteristic
79C2×C4×C157C2×D411yescharacteristic
80C2×C4×C157C2×D411yescharacteristic
81C8×C157—22no—
82C8×C157—41no—
83C22×C157—41no—
84C22×C157—41no—
85C22×C157—41no—
86C22×C157C2×C22⋊C411yescharacteristic
87C2×D157—21no—
88C2×D157—21no—
89C2×D157#10412yes—
90C4×C157—21no—
91C4×C157—41no—
92C4×C157#13111yescharacteristic
93C4×C157#13111yescharacteristic
94C4×C157AGL(1,ℤ/8)11yescharacteristic
95C4×C157#13711yescharacteristic
96Dic157—21no—
97Dic157—21no—
98Dic157—21no—
99Dic157—41no—
100Dic157—41no—
101C2×C157—81no—
102C2×C157#40811yescharacteristic
103C2×C157#41711yescharacteristic
104C2×C157C2×#10411yescharacteristic
105D157—22no—
106C157#148311yescharacteristic, complemented, Sylow
107#1483—1571nomaximal, Sylow
108#529—1571no—
109C2×C4⋊C8—1571no—
110C4×M16—1571no—
111Q8⋊C8—1571no—
112Q8⋊C8—1571no—
113D4⋊C8—1571no—
114D4⋊C8D15711yescharacteristic, complemented
115C2×M16—3141no—
116C22×C8—3141no—
117#126—3141no—
118#125—1571no—
119#124—1571no—
120#123—3141no—
121C22⋊Q8—1571no—
122#121—1571no—
123C4×Q8—1571no—
124C4×D4—3141no—
125C4×D4C2×D15711yescharacteristic
126#117—3141no—
127C2×C42—1571no—
128C4⋊C8—3141no—
129C4⋊C8—1571no—
130C4⋊C8C2×D15711yescharacteristic
131#97—3141no—
132C4×C8—1571no—
133C4×C8C2×D15711yescharacteristic
134C2×Q8—1571no—
135C2×D4—3141no—
136C2×D4C4×D15711yescharacteristic
137C22×C4—21no—
138C22×C4—1571no—
139C22×C4—1571no—
140C22×C4—1571no—
141M16—3144no—
142C2×C8—21no—
143C2×C8—21no—
144C2×C8—3141no—
145C2×C8—3141no—
146C2×C8—6282no—
147C4⋊C4—3141no—
148C4⋊C4—3141no—
149C4⋊C4—3141no—
150C4⋊C4—3141no—
151C4⋊C4—1571no—
152C4⋊C4C4×D15711yescharacteristic
153C22⋊C4—21no—
154C22⋊C4—3141no—
155C22⋊C4—3141no—
156C22⋊C4—3141no—
157C22⋊C4—3141no—
158C42—3141no—
159C42—1571no—
160C42—1571no—
161C42—1571no—
162C42C22×D15711yescharacteristic
163C23—21no—
164C23—1571no—
165Q8—3141no—
166Q8—3141no—
167D4—21no—
168D4—21no—
169D4—6282no—
170C2×C4—21no—
171C2×C4—41no—
172C2×C4—41no—
173C2×C4—3142no—
174C2×C4—3141no—
175C2×C4—3141no—
176C2×C4—3141no—
177C2×C4—3141no—
178C2×C4—3141no—
179C2×C4—3141no—
180C2×C4—1571no—
181C2×C4—1571no—
182C2×C4—1571no—
183C2×C4C2×C4×D15711yescharacteristic
184C2×C4D4×D15711yescharacteristic
185C2×C4D4×D15711yescharacteristic
186C8—22no—
187C8—41no—
188C8—3142no—
189C8—6281no—
190C22—41no—
191C22—41no—
192C22—41no—
193C22—3141no—
194C22—3141no—
195C22—1572no—
196C22C22⋊C4×D15711yescharacteristic
197C4—21no—
198C4—41no—
199C4—3141no—
200C4—3141no—
201C4—3141no—
202C4—6281no—
203C4—6281no—
204C4#1909777711yescharacteristic
205C4#1909777911yescharacteristic
206C4#1909779511yescharacteristic
207C4#1909780011yescharacteristic
208C2—81no—
209C2—3142no—
210C2#2375723811yescharacteristic
211C2#2375727111yescharacteristic
212C2#104×D15711yescharacteristic
subgroupG/H
centerC2×C4D4×D157
commutatorC2×C4×C157C22×C4
FrattiniC42C22×D157
FittingD4⋊C8×C157C2
socleC22×C157C2×C22⋊C4
prime radical#19097742C4
cosocleC42×C157C23
hypercenterD4⋊C8D157
hypocenterC157#1483
LCSG ▷ C2×C4×C157 ▷ C2×C157 ▷ C157
UCSC1 ◁ C2×C4 ◁ C42 ◁ D4⋊C8

Complements

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

NH ≅ G/Ntype
2. C4⋊C8×D157C2semidirect
3. C4×#14578937C2semidirect
4. #23757005C2semidirect
5. #23757003C2semidirect
6. D4⋊#11929434C2semidirect
7. D4⋊C8×C157C2semidirect
106. C157#1483semidirect
114. D4⋊C8D157semidirect

Maximal subgroups

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

subgroupindex
#237578052
C4⋊C8×D1572
C4×#145789372
#237570052
#237570032
D4⋊#119294342
D4⋊C8×C1572
#1483157