Finite Group Databasebeta

← #28335083

Subgroups — #28335083

Order 13696.

248 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 248 conjugacy classes of subgroups — too many to draw. Only its 59 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#124×D107C211yesmaximal, characteristic
2#20292682C212yesmaximal, complemented
3#20292367C211yesmaximal, characteristic, complemented
4#20292366C212yesmaximal, complemented
5#329×C107C211yesmaximal, characteristic, complemented
6C2×Q8×D107C411yescharacteristic
7C2×D4×D107C411yescharacteristic
8#16812098C411yescharacteristic
9#16812097C2211yescharacteristic
10#16812096C411yescharacteristic
11#16812095—22no—
12C22⋊C4×D107—22no—
13C42×D107C2211yescharacteristic
14Dic107⋊C8—22no—
15(C2×D107)⋊C8—22no—
16#16812020C2212yescomplemented
17#124×C107C2211yescharacteristic
18#97×C107C2212yescomplemented
19C23×D107—21no—
20C2×Dic214—21no—
21C2×Dic214C2×C411yescharacteristic
22Q8×D107—42no—
23C2×D428C2×C411yescharacteristic
24C2×C22⋊D107—21no—
25D4×D107—42no—
26C2×C4×D107—21no—
27C2×C4×D107C2×C411yescharacteristic
28C2×C4×D107D412yes—
29C2×C107⋊C8—22no—
30C22⋊Dic107—22no—
31(C2×D107)⋊C4—22no—
32(C2×D107)⋊C4—22no—
33C4×Dic107C2×C411yescharacteristic
34C4×Dic107D412yes—
35C2×Q8×C107C2×C411yescharacteristic
36C2×D4×C107C2×C411yescharacteristic
37C2×C8×C107—22no—
38C22⋊C4×C107—22no—
39C42×C107C2311yescharacteristic
40C23×C107—21no—
41C22×D107—21no—
42C22×D107—44no—
43C22×D107—42no—
44C22×D107C22⋊C411yescharacteristic
45Q8×C107—41no—
46D4×C107—41no—
47C2×C4×C107—21no—
48C2×C4×C107C22×C411yescharacteristic
49C2×C4×C107C2×D412yes—
50C22⋊D107—42no—
51C2×Dic107—21no—
52C2×Dic107C22⋊C412yes—
53C2×Dic107C22⋊C411yescharacteristic
54D428—41no—
55C4×D107—22no—
56C4×D107—42no—
57C4×D107—42no—
58Dic214—42no—
59Dic214—41no—
60C8×C107—42no—
61C107⋊C8—42no—
62C22×C107—41no—
63C22×C107—42no—
64C22×C107C2×C22⋊C411yescharacteristic
65C2×D107—22no—
66C2×D107—41no—
67C2×D107—42no—
68C2×D107—84no—
69C2×D107#10012yes—
70C4×C107—21no—
71C4×C107—22no—
72C4×C107—41no—
73Dic107—21no—
74Dic107—22no—
75Dic107—41no—
76C2×C107—81no—
77C2×C107C2×#10011yescharacteristic
78C2×C107#42112yes—
79D107—22no—
80D107—81no—
81#1533—1071nomaximal, Sylow
82C107#153311yescharacteristic, complemented, Sylow
83C2×#124—1071no—
84#432—1072no—
85#329—1071no—
86#329—1072no—
87#329D10711yescharacteristic, complemented
88C22×Q8—1071no—
89C22×D4—1071no—
90#124—1071no—
91#124—1071no—
92#124—1071no—
93#124—2142no—
94#124C2×D10711yescharacteristic
95C2×C22⋊C4—2142no—
96C2×C42—1071no—
97C4⋊C8—2142no—
98C22⋊C8—2142no—
99#97—1072no—
100#97C2×D10712yescomplemented
101C24—2141no—
102C2×Q8—1071no—
103C2×Q8—4282no—
104C2×Q8—2141no—
105C2×Q8C4×D10711yescharacteristic
106C2×D4—1071no—
107C2×D4—4282no—
108C2×D4—2141no—
109C2×D4C4×D10711yescharacteristic
110C22×C4—1072no—
111C22×C4—1071no—
112C22×C4—2141no—
113C2×C8—22no—
114C2×C8—2142no—
115C22⋊C4—22no—
116C22⋊C4—2142no—
117C22⋊C4—2142no—
118C22⋊C4—2142no—
119C42—1071no—
120C42—1072no—
121C42C22×D10711yescharacteristic
122C23—21no—
123C23—1071no—
124C23—4282no—
125C23—4284no—
126C23—2141no—
127Q8—41no—
128Q8—4281no—
129Q8—4282no—
130D4—41no—
131D4—4281no—
132D4—4282no—
133C2×C4—21no—
134C2×C4—1072no—
135C2×C4—1071no—
136C2×C4—4282no—
137C2×C4—4282no—
138C2×C4—2142no—
139C2×C4—2141no—
140C2×C4C2×C4×D10711yescharacteristic
141C2×C4D4×D10712yes—
142C8—42no—
143C8—4282no—
144C22—42no—
145C22—41no—
146C22—8564no—
147C22—1072no—
148C22—4282no—
149C22—4281no—
150C22—2142no—
151C22C22⋊C4×D10711yescharacteristic
152C4—22no—
153C4—21no—
154C4—41no—
155C4—4281no—
156C4—2142no—
157C4—2141no—
158C2—81no—
159C2—8561no—
160C2—2142no—
161C2#100×D10711yescharacteristic
162C2#2029264212yes—
subgroupG/H
centerC22C22⋊C4×D107
commutatorC2×C4×C107C22×C4
FrattiniC42C22×D107
Fitting#329×C107C2
socleC22×C107C2×C22⋊C4
prime radicalC2×D4×D107C4
cosocleC42×C107C23
hypercenter#329D107
hypocenterC107#1533
LCSG ▷ C2×C4×C107 ▷ C22×C107 ▷ C107
UCSC1 ◁ C22 ◁ C42 ◁ #329

Complements

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

NH ≅ G/Ntype
2. #20292682C2semidirect
3. #20292367C2semidirect
4. #20292366C2semidirect
5. #329×C107C2semidirect
16. #16812020C22semidirect
18. #97×C107C22semidirect
82. C107#1533semidirect
87. #329D107semidirect
100. #97C2×D107semidirect

Maximal subgroups

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

subgroupindex
#124×D1072
#202926822
#202923672
#202923662
#329×C1072
#1533107