Finite Group Databasebeta

← #28338151

Subgroups — #28338151

Order 13696.

262 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 262 conjugacy classes of subgroups — too many to draw. Only its 55 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#20293195C211yesmaximal, characteristic
2#20292610C212yesmaximal, complemented
3#20292424C211yesmaximal, characteristic, complemented
4#20292423C212yesmaximal, complemented
5#355×C107C211yesmaximal, characteristic, complemented
6C2×#13133819C2211yescharacteristic
7C2×D4×D107C411yescharacteristic
8M16×D107—22no—
9#16812106C411yescharacteristic
10#16812105C411yescharacteristic
11#16812098C2211yescharacteristic
12#16812082—22no—
13#16812079—22no—
14#16812066C411yescharacteristic
15#16812028C2212yescomplemented
16#16812025—22no—
17#124×C107C2211yescharacteristic
18#101×C107C2212yescomplemented
19C23×D107—21no—
20#13133819—42no—
21C2×D428—22no—
22C2×D428C2×C411yescharacteristic
23C2×D428C2×C411yescharacteristic
24C2×D428D412yes—
25C2×C22⋊D107—22no—
26C2×C22⋊D107—21no—
27D4×D107—42no—
28C2×C4×D107C2×C411yescharacteristic
29C2×C4×D107D412yes—
30#13133802—22no—
31#13133801—42no—
32C8×D107—42no—
33Dic107⋊C4—21no—
34(C2×D107)⋊C4—21no—
35(C2×D107)⋊C4—22no—
36C4×Dic107C2×C411yescharacteristic
37C2×Q8×C107C2311yescharacteristic
38C2×D4×C107C2×C411yescharacteristic
39M16×C107—22no—
40C22⋊C4×C107—22no—
41C42×C107C2×C411yescharacteristic
42C23×C107—21no—
43C22×D107—21no—
44C22×D107—42no—
45C22×D107—82no—
46C22×D107C22⋊C411yescharacteristic
47C22×D107C22⋊C412yes—
48Q8×C107—41no—
49D4×C107—41no—
50C2×C4×C107—21no—
51C2×C4×C107C22×C411yescharacteristic
52C2×C4×C107C2×D412yes—
53C22⋊D107—42no—
54C22⋊D107—82no—
55C2×Dic107—21no—
56C2×Dic107C22⋊C411yescharacteristic
57D428—41no—
58D428—42no—
59D428—41no—
60D428—82no—
61C4×D107—22no—
62C4×D107—22no—
63C4×D107—22no—
64C8×C107—42no—
65C107⋊C8—42no—
66C22×C107—42no—
67C22×C107—41no—
68C22×C107C2×C22⋊C411yescharacteristic
69C2×D107—21no—
70C2×D107—22no—
71C2×D107—42no—
72C2×D107—41no—
73C2×D107—42no—
74C2×D107—41no—
75C2×D107—84no—
76C4×C107—22no—
77C4×C107—21no—
78C4×C107—41no—
79Dic107—41no—
80Dic107#9912yes—
81C2×C107—21no—
82C2×C107—81no—
83C2×C107C2×#9911yescharacteristic
84D107—42no—
85D107—41no—
86D107—81no—
87#2134—1071nomaximal, Sylow
88C107#213411yescharacteristic, complemented, Sylow
89#535—1071no—
90#413—1072no—
91#355—1071no—
92#355—1072no—
93#355D10711yescharacteristic, complemented
94C2×#41—1071no—
95C22×D4—1071no—
96C2×M16—2142no—
97#127—1071no—
98#127—1071no—
99#124—1071no—
100#124C2×D10711yescharacteristic
101#121—2142no—
102#120—2142no—
103#117—1071no—
104#101—1072no—
105#101C2×D10712yescomplemented
106#100—2142no—
107C24—2141no—
108#41—4282no—
109C2×Q8C22×D10711yescharacteristic
110C2×D4—1071no—
111C2×D4—1071no—
112C2×D4—1072no—
113C2×D4—4282no—
114C2×D4—2142no—
115C2×D4—2141no—
116C2×D4—2142no—
117C2×D4C4×D10711yescharacteristic
118C22×C4—1071no—
119C22×C4—1072no—
120M16—22no—
121M16—4282no—
122M16—2142no—
123C2×C8—4282no—
124C4⋊C4—2141no—
125C22⋊C4—22no—
126C22⋊C4—2141no—
127C22⋊C4—2142no—
128C42—1071no—
129C42C4×D10711yescharacteristic
130C23—21no—
131C23—8562no—
132C23—1071no—
133C23—1072no—
134C23—4282no—
135C23—2141no—
136Q8—41no—
137D4—41no—
138D4—8562no—
139D4—8562no—
140D4—4281no—
141D4—4282no—
142D4—4281no—
143D4—4282no—
144C2×C4—21no—
145C2×C4—1071no—
146C2×C4—2142no—
147C2×C4—2142no—
148C2×C4—2142no—
149C2×C4—2141no—
150C2×C4C2×C4×D10711yescharacteristic
151C2×C4D4×D10712yes—
152C8—42no—
153C8—4282no—
154C22—42no—
155C22—41no—
156C22—8564no—
157C22—4282no—
158C22—4282no—
159C22—4281no—
160C22—4281no—
161C22—2141no—
162C22—2142no—
163C22C22⋊C4×D10711yescharacteristic
164C4—22no—
165C4—21no—
166C4—41no—
167C4—1072no—
168C4—4281no—
169C2—21no—
170C2—81no—
171C2—8561no—
172C2—4281no—
173C2—4282no—
174C2#99×D10711yescharacteristic
subgroupG/H
centerC2#99×D107
commutatorC2×C4×C107C22×C4
FrattiniC2×Q8C22×D107
Fitting#355×C107C2
socleC2×C107C2×#99
prime radical#20293195C2
cosocleC2×Q8×C107C23
hypercenter#355D107
hypocenterC107#2134
LCSG ▷ C2×C4×C107 ▷ C22×C107 ▷ C2×C107 ▷ C107
UCSC1 ◁ C2 ◁ C22 ◁ C2×Q8 ◁ #355

Complements

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

NH ≅ G/Ntype
2. #20292610C2semidirect
3. #20292424C2semidirect
4. #20292423C2semidirect
5. #355×C107C2semidirect
15. #16812028C22semidirect
18. #101×C107C22semidirect
88. C107#2134semidirect
93. #355D107semidirect
105. #101C2×D107semidirect

Maximal subgroups

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

subgroupindex
#202931952
#202926102
#202924242
#202924232
#355×C1072
#2134107