Finite Group Databasebeta

← #28334918

Subgroups — #28334918

Order 13696.

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

normal subgroups only

This group has 230 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#20293159C211yesmaximal, characteristic
2#20292683C211yesmaximal, characteristic, complemented
3C4×C8×D107C211yesmaximal, characteristic, complemented
4#20292359C211yesmaximal, characteristic, complemented
5#20292357C211yesmaximal, characteristic, complemented
6D4⋊(C107⋊C8)C211yesmaximal, characteristic, complemented
7D4⋊C8×C107C211yesmaximal, characteristic, complemented
8C2×C8×D107—21no—
9#16812102—21no—
10#16812100C411yescharacteristic
11#16812096C411yescharacteristic
12#16812091—21no—
13#16812089C411yescharacteristic
14#16812080C411yescharacteristic
15C4×Dic214C2211yescharacteristic
16C4×C22⋊D107—21no—
17#16812068—21no—
18C42×D107C2211yescharacteristic
19C4⋊(C107⋊C8)C2211yescharacteristic
20(C2×D107)⋊C8—21no—
21#16812019—21no—
22C4×C107⋊C8C2211yescharacteristic
23C8×Dic107—21no—
24C4×D4×C107C2211yescharacteristic
25C4⋊C8×C107C2211yescharacteristic
26C4×C8×C107C2211yescharacteristic
27C2×Dic214C2×C411yescharacteristic
28C2×C22⋊D107—21no—
29C2×C4×D107C2×C411yescharacteristic
30C2×C4×D107D411yescharacteristic
31C2×C4×D107D411yescharacteristic
32C2×C107⋊C8—21no—
33C2×C107⋊C8—21no—
34C8×D107—24no—
35C4⋊Dic107—21no—
36C4⋊Dic107—21no—
37C4⋊Dic107C2×C411yescharacteristic
38Dic107⋊C4—21no—
39Dic107⋊C4—21no—
40C22⋊Dic107—21no—
41C22⋊Dic107—21no—
42C22⋊Dic107—21no—
43(C2×D107)⋊C4—21no—
44C4×Dic107—21no—
45C4×Dic107C2×C411yescharacteristic
46C4×Dic107D411yescharacteristic
47C4×Dic107D411yescharacteristic
48C2×D4×C107C2×C411yescharacteristic
49C22×C4×C107—21no—
50C2×C8×C107—21no—
51C2×C8×C107—21no—
52C4⋊C4×C107C2×C411yescharacteristic
53C22⋊C4×C107—21no—
54C42×C107C2311yescharacteristic
55C23×C107—21no—
56C22×D107C22⋊C411yescharacteristic
57D4×C107—21no—
58D4×C107—21no—
59C2×C4×C107—21no—
60C2×C4×C107—41no—
61C2×C4×C107—41no—
62C2×C4×C107C22×C411yescharacteristic
63C2×C4×C107C2×D411yescharacteristic
64C2×C4×C107C2×D411yescharacteristic
65C22⋊D107—42no—
66C2×Dic107—21no—
67C2×Dic107—21no—
68C2×Dic107C22⋊C411yescharacteristic
69C2×Dic107C22⋊C411yescharacteristic
70C2×Dic107C22⋊C411yescharacteristic
71C4×D107—22no—
72C4×D107—21no—
73C4×D107—21no—
74C4×D107—21no—
75C4×D107—21no—
76Dic214—21no—
77Dic214—21no—
78C8×C107—22no—
79C8×C107—41no—
80C107⋊C8—22no—
81C107⋊C8—41no—
82C22×C107—41no—
83C22×C107—41no—
84C22×C107—41no—
85C22×C107C2×C22⋊C411yescharacteristic
86C2×D107—21no—
87C2×D107—21no—
88C2×D107#10412yes—
89C4×C107—21no—
90C4×C107—41no—
91C4×C107#13111yescharacteristic
92C4×C107#13111yescharacteristic
93C4×C107#13511yescharacteristic
94C4×C107#13511yescharacteristic
95Dic107—21no—
96Dic107—21no—
97Dic107—21no—
98Dic107—41no—
99Dic107—41no—
100C2×C107—81no—
101C2×C107#40811yescharacteristic
102C2×C107#41611yescharacteristic
103C2×C107C2×#10411yescharacteristic
104D107—22no—
105#1494—1071nomaximal, Sylow
106C107#149411yescharacteristic, complemented, Sylow
107#529—1071no—
108#432—1071no—
109C2×C4×C8—1071no—
110Q8⋊C8—1071no—
111Q8⋊C8—1071no—
112D4⋊C8—1071no—
113D4⋊C8D10711yescharacteristic, complemented
114C22×C8—2141no—
115#126—2141no—
116#125—1071no—
117#124—1071no—
118#123—2141no—
119C22⋊Q8—1071no—
120#121—1071no—
121C4×Q8—1071no—
122C4×D4—2141no—
123C4×D4C2×D10711yescharacteristic
124#117—2141no—
125C2×C42—1071no—
126C4⋊C8—1071no—
127C4⋊C8C2×D10711yescharacteristic
128C22⋊C8—2141no—
129#97—2141no—
130C4×C8—1071no—
131C4×C8—2141no—
132C4×C8C2×D10711yescharacteristic
133C2×Q8—1071no—
134C2×D4—2141no—
135C2×D4C4×D10711yescharacteristic
136C22×C4—21no—
137C22×C4—1071no—
138C22×C4—1071no—
139C22×C4—1071no—
140C2×C8—21no—
141C2×C8—21no—
142C2×C8—2144no—
143C2×C8—2141no—
144C2×C8—2141no—
145C4⋊C4—1071no—
146C4⋊C4—2141no—
147C4⋊C4—2141no—
148C4⋊C4—2141no—
149C4⋊C4—2141no—
150C4⋊C4C4×D10711yescharacteristic
151C22⋊C4—21no—
152C22⋊C4—2141no—
153C22⋊C4—2141no—
154C22⋊C4—2141no—
155C22⋊C4—2141no—
156C42—1071no—
157C42—1071no—
158C42—1071no—
159C42—2141no—
160C42C22×D10711yescharacteristic
161C23—21no—
162C23—1071no—
163Q8—2141no—
164Q8—2141no—
165D4—21no—
166D4—21no—
167D4—4282no—
168C2×C4—21no—
169C2×C4—41no—
170C2×C4—41no—
171C2×C4—1071no—
172C2×C4—1071no—
173C2×C4—1071no—
174C2×C4—2142no—
175C2×C4—2141no—
176C2×C4—2141no—
177C2×C4—2141no—
178C2×C4—2141no—
179C2×C4—2141no—
180C2×C4—2141no—
181C2×C4C2×C4×D10711yescharacteristic
182C2×C4D4×D10711yescharacteristic
183C2×C4D4×D10711yescharacteristic
184C8—22no—
185C8—41no—
186C8—4281no—
187C8—2142no—
188C22—41no—
189C22—41no—
190C22—41no—
191C22—1072no—
192C22—2141no—
193C22—2141no—
194C22C22⋊C4×D10711yescharacteristic
195C4—21no—
196C4—41no—
197C4—4281no—
198C4—4281no—
199C4—2141no—
200C4—2141no—
201C4—2141no—
202C4#1681211511yescharacteristic
203C4#1681211711yescharacteristic
204C4#1681212811yescharacteristic
205C4#1681213011yescharacteristic
206C2—81no—
207C2—2142no—
208C2#2029259211yescharacteristic
209C2#2029262011yescharacteristic
210C2#104×D10711yescharacteristic
subgroupG/H
centerC2×C4D4×D107
commutatorC2×C4×C107C22×C4
FrattiniC42C22×D107
FittingD4⋊C8×C107C2
socleC22×C107C2×C22⋊C4
prime radical#16812080C4
cosocleC42×C107C23
hypercenterD4⋊C8D107
hypocenterC107#1494
LCSG ▷ C2×C4×C107 ▷ C2×C107 ▷ C107
UCSC1 ◁ C2×C4 ◁ C42 ◁ D4⋊C8

Complements

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

NH ≅ G/Ntype
2. #20292683C2semidirect
3. C4×C8×D107C2semidirect
4. #20292359C2semidirect
5. #20292357C2semidirect
6. D4⋊(C107⋊C8)C2semidirect
7. D4⋊C8×C107C2semidirect
106. C107#1494semidirect
113. D4⋊C8D107semidirect

Maximal subgroups

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

subgroupindex
#202931592
#202926832
C4×C8×D1072
#202923592
#202923572
D4⋊(C107⋊C8)2
D4⋊C8×C1072
#1494107