Finite Group Databasebeta

← #28337525

Subgroups — #28337525

Order 13696.

394 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 394 conjugacy classes of subgroups — too many to draw. Only its 71 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#20293134C212yesmaximal, complemented
2#20292644C212yesmaximal, complemented
3#20292590C211yesmaximal, characteristic, complemented
4#20292384C211yesmaximal, characteristic, complemented
5#575×C107C211yesmaximal, characteristic, complemented
6C22×C4×D107C2211yescharacteristic
7C2×#13133802C2211yescharacteristic
8#16812090—22no—
9#16812085—22no—
10#16812080—22no—
11#16812077—22no—
12C4×C22⋊D107—24no—
13#16812068C2212yes—
14#16812036—24no—
15(C2×D107)⋊C8—22no—
16C2×#41×C107C2212yes—
17#137×C107—22no—
18AGL(1,ℤ/8)×C107—22no—
19#135×C107—22no—
20C2×M16×C107C2211yescharacteristic
21C23×D107D411yescharacteristic
22C2×C22⋊D107—24no—
23C22×Dic107D411yescharacteristic
24C2×C4×D107—22no—
25C2×C4×D107—22no—
26C2×C4×D107—21no—
27C2×C4×D107—21no—
28#13133802—22no—
29C2×C107⋊C8—21no—
30C4⋊Dic107—22no—
31Dic107⋊C4—24no—
32C22⋊Dic107—24no—
33C22⋊Dic107—22no—
34(C2×D107)⋊C4—24no—
35C4×Dic107D414yescomplemented
36#41×C107—22no—
37#41×C107—22no—
38#41×C107—22no—
39#41×C107—22no—
40C2×Q8×C107D412yescomplemented
41C2×D4×C107—22no—
42C2×D4×C107D412yescomplemented
43C22×C4×C107—22no—
44C22×C4×C107C2311yescharacteristic
45Q16×C107—22no—
46SD16×C107—24no—
47D8×C107—22no—
48M16×C107—22no—
49C2×C8×C107D412yescomplemented
50C23×C107—22no—
51C23×C107C2×D411yescharacteristic
52C22×D107—22no—
53C22×D107—21no—
54C22×D107—42no—
55Q8×C107—22no—
56Q8×C107—22no—
57D4×C107—22no—
58D4×C107—22no—
59D4×C107—42no—
60D4×C107—42no—
61C2×C4×C107—22no—
62C2×C4×C107—42no—
63C2×C4×C107—42no—
64C2×C4×C107C2×D412yes—
65C2×C4×C107C2×D412yes—
66C2×C4×C107C2×D411yescharacteristic
67C2×C4×C107#4111yescharacteristic
68C22⋊D107—48no—
69C2×Dic107—24no—
70C2×Dic107—22no—
71C2×Dic107—21no—
72C4×D107—41no—
73C4×D107—42no—
74C4×D107—41no—
75C8×C107—22no—
76C107⋊C8—41no—
77C22×C107—41no—
78C22×C107—44no—
79C22×C107—42no—
80C22×C107#12012yes—
81C22×C107#12111yescharacteristic
82C2×D107—24no—
83C2×D107—22no—
84C2×D107—42no—
85C2×D107—41no—
86C2×D107—41no—
87C4×C107—42no—
88C4×C107#12011yescharacteristic
89C4×C107#12112yes—
90C4×C107#12711yescharacteristic
91Dic107—44no—
92Dic107—41no—
93C2×C107—22no—
94C2×C107—21no—
95C2×C107—82no—
96C2×C107#39211yescharacteristic
97D107—42no—
98#2010—1071nomaximal, Sylow
99C107#201011yescharacteristic, complemented, Sylow
100#575D10711yescharacteristic, complemented
101#525—1072no—
102#421—1072no—
103#407—1071no—
104H(3,ℤ/4)—1071no—
105C2×#41C2×D10712yes—
106C23×C4—1071no—
107#137—22no—
108AGL(1,ℤ/8)—22no—
109#135—22no—
110C2×M16—1071no—
111C2×M16C2×D10711yescharacteristic
112#123—2142no—
113C22⋊Q8—2142no—
114#121—2142no—
115#120—2142no—
116C4×D4—2144no—
117#117—1072no—
118#104—2144no—
119C22⋊C8—2142no—
120C24—1071no—
121#41—22no—
122#41—22no—
123#41—22no—
124#41—22no—
125C2×Q8C22⋊D10712yescomplemented
126C2×D4—22no—
127C2×D4—2144no—
128C2×D4C22⋊D10712yescomplemented
129C22×C4—22no—
130C22×C4—1071no—
131C22×C4—2142no—
132C22×C4—2141no—
133C22×C4—2142no—
134C22×C4—2141no—
135C22×C4C22×D10711yescharacteristic
136Q16—22no—
137SD16—24no—
138D8—22no—
139M16—22no—
140M16—2142no—
141C2×C8—2141no—
142C2×C8C22⋊D10712yescomplemented
143C4⋊C4—2144no—
144C4⋊C4—2142no—
145C22⋊C4—2144no—
146C22⋊C4—2144no—
147C22⋊C4—2142no—
148C42—1074no—
149C23—22no—
150C23—4282no—
151C23—2142no—
152C23—2141no—
153C23D4×D10711yescharacteristic
154Q8—22no—
155Q8—22no—
156D4—22no—
157D4—22no—
158D4—42no—
159D4—42no—
160D4—4288no—
161C2×C4—22no—
162C2×C4—42no—
163C2×C4—42no—
164C2×C4—4281no—
165C2×C4—4282no—
166C2×C4—4281no—
167C2×C4—2144no—
168C2×C4—2142no—
169C2×C4—2141no—
170C2×C4D4×D10712yes—
171C2×C4C2×C22⋊D10712yes—
172C2×C4C2×C22⋊D10711yescharacteristic
173C2×C4#1313381711yescharacteristic
174C8—22no—
175C8—4281no—
176C22—41no—
177C22—44no—
178C22—42no—
179C22—4282no—
180C22—4281no—
181C22—4281no—
182C22—2144no—
183C22—2142no—
184C22#1681207712yes—
185C22#1681208011yescharacteristic
186C4—42no—
187C4—4284no—
188C4—4281no—
189C4#1681207811yescharacteristic
190C4#1681208112yes—
191C4#1681210511yescharacteristic
192C2—22no—
193C2—21no—
194C2—82no—
195C2—4282no—
196C2#2029253511yescharacteristic
subgroupG/H
centerC4#16812105
commutator, cosocleC22×C4×C107C23
FrattiniC22×C4C22×D107
Fitting#575×C107C2
socleC2×C107#392
hypercenter#575D107
hypocenterC107#2010
LCSG ▷ C22×C4×C107 ▷ C2×C107 ▷ C107
UCSC1 ◁ C4 ◁ C22×C4 ◁ #575

Complements

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

NH ≅ G/Ntype
1. #20293134C2semidirect
2. #20292644C2semidirect
3. #20292590C2semidirect
4. #20292384C2semidirect
5. #575×C107C2semidirect
35. C4×Dic107D4semidirect
40. C2×Q8×C107D4semidirect
42. C2×D4×C107D4semidirect
49. C2×C8×C107D4semidirect
99. C107#2010semidirect
100. #575D107semidirect
125. C2×Q8C22⋊D107semidirect
128. C2×D4C22⋊D107semidirect
142. C2×C8C22⋊D107semidirect

Maximal subgroups

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

subgroupindex
#202931342
#202926442
#202925902
#202923842
#575×C1072
#2010107