Finite Group Databasebeta

← #28338145

Subgroups — #28338145

Order 13696.

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

normal subgroups only

This group has 250 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#20293178C211yesmaximal, characteristic
2#20292610C212yesmaximal, complemented
3#20292426C211yesmaximal, characteristic, complemented
4#20292423C212yesmaximal, complemented
5#356×C107C211yesmaximal, characteristic, complemented
6C2×#13133819C411yescharacteristic
7C2×#13133819C2211yescharacteristic
8M16×D107—22no—
9#16812106C411yescharacteristic
10#16812098C411yescharacteristic
11#16812098C2211yescharacteristic
12#16812084—22no—
13#16812071—22no—
14C42×D107C411yescharacteristic
15#16812028C2212yes—
16#16812025—22no—
17C4⋊Q8×C107C2211yescharacteristic
18#101×C107C2212yes—
19#13133819—41no—
20#13133819—41no—
21#13133819—41no—
22#13133819—41no—
23C2×D428—22no—
24C2×D428—21no—
25C2×D428C2×C411yescharacteristic
26C2×D428C2×C411yescharacteristic
27C2×D428D412yes—
28C2×C4×D107—21no—
29C2×C4×D107—21no—
30C2×C4×D107C2×C411yescharacteristic
31C2×C4×D107D412yes—
32#13133802—22no—
33#13133801—42no—
34C8×D107—42no—
35(C2×D107)⋊C4—22no—
36(C2×D107)⋊C4—22no—
37C4×Dic107—21no—
38C4×Dic107C2×C411yescharacteristic
39C2×Q8×C107C2×C411yescharacteristic
40C2×Q8×C107C2311yescharacteristic
41M16×C107—22no—
42C4⋊C4×C107—22no—
43C42×C107C2×C411yescharacteristic
44C22×D107—21no—
45C22×D107C22⋊C412yes—
46C22×D107C22⋊C411yescharacteristic
47Q8×C107—41no—
48Q8×C107—41no—
49C2×C4×C107—21no—
50C2×C4×C107—21no—
51C2×C4×C107C22×C411yescharacteristic
52C2×C4×C107C2×D412yes—
53C2×Dic107—21no—
54C2×Dic107C22⋊C411yescharacteristic
55D428—41no—
56D428—42no—
57D428—41no—
58D428—44no—
59D428—42no—
60C4×D107—22no—
61C4×D107—22no—
62C4×D107—21no—
63C4×D107—21no—
64C4×D107—42no—
65C4×D107—41no—
66C4×D107—41no—
67C8×C107—42no—
68C107⋊C8—42no—
69C22×C107C2×C22⋊C411yescharacteristic
70C2×D107—21no—
71C2×D107—22no—
72C2×D107—41no—
73C2×D107—42no—
74C2×D107—42no—
75C2×D107—41no—
76C4×C107—22no—
77C4×C107—22no—
78C4×C107—21no—
79C4×C107—41no—
80Dic107—41no—
81Dic107#9911yescharacteristic
82Dic107#9911yescharacteristic
83C2×C107—21no—
84C2×C107C2×#9911yescharacteristic
85D107—41no—
86D107—42no—
87D107—81no—
88#2132—1071nomaximal, Sylow
89C107#213211yescharacteristic, complemented, Sylow
90#532—1071no—
91#413—1072no—
92#356—1071no—
93#356D10711yescharacteristic, complemented
94#355—1072no—
95C2×#41—1071no—
96C2×#41—1071no—
97C2×M16—2142no—
98C4⋊Q8C2×D10711yescharacteristic
99#127—1071no—
100#124—1071no—
101#124—1071no—
102#121—2142no—
103C4×D4—2142no—
104C2×C42—1071no—
105#101—1072no—
106#101C2×D10712yes—
107#100—2142no—
108#41—4281no—
109#41—4281no—
110#41—4281no—
111#41—4281no—
112C2×Q8C4×D10711yescharacteristic
113C2×Q8C22×D10711yescharacteristic
114C2×D4—1071no—
115C2×D4—1071no—
116C2×D4—1072no—
117C2×D4—2142no—
118C2×D4—2141no—
119C22×C4—1071no—
120C22×C4—1072no—
121C22×C4—2141no—
122C22×C4—2141no—
123M16—22no—
124M16—4282no—
125M16—2142no—
126C2×C8—4282no—
127C4⋊C4—22no—
128C22⋊C4—2142no—
129C22⋊C4—2142no—
130C42—1071no—
131C42—2141no—
132C42C4×D10711yescharacteristic
133C23—1072no—
134C23—1071no—
135C23—2141no—
136Q8—41no—
137Q8—41no—
138D4—4281no—
139D4—4284no—
140D4—4282no—
141D4—4281no—
142D4—4282no—
143C2×C4—21no—
144C2×C4—21no—
145C2×C4—1071no—
146C2×C4—4282no—
147C2×C4—4281no—
148C2×C4—4281no—
149C2×C4—2142no—
150C2×C4—2142no—
151C2×C4—2141no—
152C2×C4—2141no—
153C2×C4—2141no—
154C2×C4C2×C4×D10711yescharacteristic
155C2×C4D4×D10712yes—
156C8—42no—
157C8—4282no—
158C22—4282no—
159C22—4281no—
160C22—4282no—
161C22—4281no—
162C22—2141no—
163C22—2142no—
164C22C22⋊C4×D10711yescharacteristic
165C4—22no—
166C4—22no—
167C4—21no—
168C4—41no—
169C4—1071no—
170C4—1071no—
171C4—4281no—
172C2—21no—
173C2—8561no—
174C2—4281no—
175C2—4282no—
176C2#99×D10711yescharacteristic
subgroupG/H
centerC2#99×D107
commutatorC2×C4×C107C22×C4
FrattiniC2×Q8C22×D107
Fitting#356×C107C2
socleC2×C107C2×#99
prime radical#20293178C2
cosocleC2×Q8×C107C23
hypercenter#356D107
hypocenterC107#2132
LCSG ▷ C2×C4×C107 ▷ C22×C107 ▷ C2×C107 ▷ C107
UCSC1 ◁ C2 ◁ C22 ◁ C2×Q8 ◁ #356

Complements

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

NH ≅ G/Ntype
2. #20292610C2semidirect
3. #20292426C2semidirect
4. #20292423C2semidirect
5. #356×C107C2semidirect
89. C107#2132semidirect
93. #356D107semidirect

Maximal subgroups

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

subgroupindex
#202931782
#202926102
#202924262
#202924232
#356×C1072
#2132107