Finite Group Databasebeta

← #28334948

Subgroups — #28334948

Order 13696.

238 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 238 conjugacy classes of subgroups — too many to draw. Only its 73 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#20293161C211yesmaximal, characteristic
2#20292473C211yesmaximal, characteristic, complemented
3#20292365C212yesmaximal, complemented
4#20292362C212yesmaximal
5#431×C107C211yesmaximal, characteristic, complemented
6#16812103—21no—
7#16812101C411yescharacteristic, complemented
8#16812097C411yescharacteristic, complemented
9#16812092—21no—
10#16812088C2211yescharacteristic
11#16812083C2211yescharacteristic
12C4×Dic214C411yescharacteristic, complemented
13C4×D428C411yescharacteristic, complemented
14C4×C22⋊D107—21no—
15#16812066—21no—
16C2×C4×Dic107—21no—
17C107⋊#95—21no—
18C107⋊#95C2212yes—
19C2×C42×C107C2211yescharacteristic
20C4⋊C8×C107—21no—
21C22⋊C8×C107C2212yes—
22C4×C8×C107—21no—
23C2×Dic214C2×C411yescharacteristic
24C2×D428C2×C411yescharacteristic
25C2×C22⋊D107—21no—
26C22×Dic107—22no—
27C2×C4×D107—21no—
28C4⋊Dic107C2×C411yescharacteristic
29C4⋊Dic107C2×C411yescharacteristic
30Dic107⋊C4—21no—
31Dic107⋊C4—21no—
32Dic107⋊C4—21no—
33Dic107⋊C4—21no—
34C22⋊Dic107—21no—
35(C2×D107)⋊C4—21no—
36(C2×D107)⋊C4—21no—
37(C2×D107)⋊C4—21no—
38(C2×D107)⋊C4—21no—
39C4×Dic107—24no—
40C4×Dic107—21no—
41C22×C4×C107D411yescharacteristic
42C22×C4×C107D411yescharacteristic
43C22×C4×C107C2311yescharacteristic
44C2×C8×C107—22no—
45C42×C107C2×C411yescharacteristic
46C42×C107C2×C411yescharacteristic
47C42×C107D411yescharacteristic
48C42×C107D411yescharacteristic
49C23×C107C2×D411yescharacteristic
50C22×D107—21no—
51C2×C4×C107—22no—
52C2×C4×C107—22no—
53C2×C4×C107—41no—
54C2×C4×C107C22⋊C411yescharacteristic
55C2×C4×C107C22⋊C411yescharacteristic
56C2×C4×C107C22⋊C411yescharacteristic
57C2×C4×C107C22⋊C411yescharacteristic
58C2×C4×C107C22×C411yescharacteristic
59C2×C4×C107C2×D411yescharacteristic
60C22⋊D107—42no—
61C2×Dic107—24no—
62C2×Dic107—21no—
63C2×Dic107—21no—
64C2×Dic107—21no—
65C2×Dic107—42no—
66C2×Dic107—42no—
67D428—41no—
68C4×D107—42no—
69Dic214—41no—
70C8×C107—42no—
71C22×C107—21no—
72C22×C107—21no—
73C22×C107C2×C22⋊C411yescharacteristic
74C22×C107#13512yes—
75C2×D107—41no—
76C2×D107—41no—
77C2×D107—41no—
78C4×C107—21no—
79C4×C107—21no—
80C4×C107—21no—
81C4×C107—21no—
82C4×C107—21no—
83C4×C107#10412yes—
84Dic107—44no—
85Dic107—41no—
86Dic107—41no—
87Dic107—41no—
88C2×C107—22no—
89C2×C107#41011yescharacteristic
90C2×C107#41611yescharacteristic
91C2×C107C2×#10411yescharacteristic
92D107—81no—
93#1500—1071nomaximal, Sylow
94C107#150011yescharacteristic, complemented, Sylow
95#529—1071no—
96#431D10711yescharacteristic, complemented
97#376—1071no—
98#328—1072no—
99#327—1072no—
100#126—2141no—
101#125—1071no—
102#124—1071no—
103#123—2141no—
104C22⋊Q8—1071no—
105#121—1071no—
106C4×Q8—1071no—
107C4×D4—1071no—
108C4×D4—2141no—
109#117—2141no—
110C2×C42—2141no—
111C2×C42C2×D10711yescharacteristic
112C4⋊C8—21no—
113C22⋊C8C2×D10712yes—
114C4×C8—21no—
115#95—1072no—
116#95—2141no—
117C2×Q8—1071no—
118C2×D4—1071no—
119C2×D4—2141no—
120C22×C4—2142no—
121C22×C4—2141no—
122C22×C4D42811yescharacteristic
123C22×C4D42811yescharacteristic
124C22×C4C22×D10711yescharacteristic
125C2×C8—22no—
126C4⋊C4—1071no—
127C4⋊C4—1071no—
128C4⋊C4—2141no—
129C4⋊C4—2141no—
130C4⋊C4—2141no—
131C4⋊C4—2141no—
132C22⋊C4—2141no—
133C22⋊C4—2141no—
134C22⋊C4—2141no—
135C22⋊C4—2141no—
136C22⋊C4—2141no—
137C42—2144no—
138C42—2141no—
139C42C4×D10711yescharacteristic
140C42C4×D10711yescharacteristic
141C42C22⋊D10711yescharacteristic
142C42C22⋊D10711yescharacteristic
143C23—2141no—
144C23C2×D42811yescharacteristic
145Q8—4281no—
146D4—4281no—
147D4—4282no—
148C2×C4—22no—
149C2×C4—22no—
150C2×C4—41no—
151C2×C4—4282no—
152C2×C4—4282no—
153C2×C4—4282no—
154C2×C4—2144no—
155C2×C4—2141no—
156C2×C4—2141no—
157C2×C4—2141no—
158C2×C4(C2×D107)⋊C411yescharacteristic
159C2×C4(C2×D107)⋊C411yescharacteristic
160C2×C4(C2×D107)⋊C411yescharacteristic
161C2×C4(C2×D107)⋊C411yescharacteristic
162C2×C4C2×C4×D10711yescharacteristic
163C2×C4C2×C22⋊D10711yescharacteristic
164C8—42no—
165C22—21no—
166C22—21no—
167C22—4281no—
168C22—4281no—
169C22—4281no—
170C22C2×(C2×D107)⋊C411yescharacteristic
171C22#1681213112yes—
172C4—21no—
173C4—21no—
174C4—21no—
175C4—21no—
176C4—21no—
177C4—4284no—
178C4—4281no—
179C4—4281no—
180C4—4281no—
181C4#1681203512yes—
182C2—22no—
183C2—8561no—
184C2#2029260011yescharacteristic
185C2#2029262411yescharacteristic
186C2C2×#1681203511yescharacteristic
subgroupG/H
centerC2×C4(C2×D107)⋊C4
commutatorC2×C4×C107C22×C4
FrattiniC22×C4C22×D107
Fitting#431×C107C2
socleC22×C107C2×C22⋊C4
prime radical#16812083C22
cosocleC22×C4×C107C23
hypercenter#431D107
hypocenterC107#1500
LCSG ▷ C2×C4×C107 ▷ C22×C107 ▷ C107
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #431

Complements

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

NH ≅ G/Ntype
2. #20292473C2semidirect
3. #20292365C2semidirect
5. #431×C107C2semidirect
7. #16812101C4semidirect
8. #16812097C4semidirect
12. C4×Dic214C4semidirect
13. C4×D428C4semidirect
94. C107#1500semidirect
96. #431D107semidirect

Maximal subgroups

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

subgroupindex
#202931612
#202924732
#202923652
#202923622
#431×C1072
#1500107