Finite Group Databasebeta

← #28335090

Subgroups — #28335090

Order 13696.

200 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 200 conjugacy classes of subgroups — too many to draw. Only its 65 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#20292684C211yesmaximal, characteristic, complemented
3#20292368C212yesmaximal, complemented
4#20292366C212yesmaximal, complemented
5#432×C107C211yesmaximal, characteristic, complemented
6#16812103—21no—
7#16812101C2211yescharacteristic
8#16812097C2211yescharacteristic
9#16812092—21no—
10#16812088C411yescharacteristic
11#16812083C411yescharacteristic
12C4×Dic214C411yescharacteristic
13C4×D428C411yescharacteristic
14C4×C22⋊D107—21no—
15#16812066—21no—
16C4⋊(C107⋊C8)—21no—
17C22⋊(C107⋊C8)—21no—
18#16812020C2212yes—
19C2×C42×C107C2211yescharacteristic
20C4⋊C8×C107—21no—
21C22⋊C8×C107—21no—
22#97×C107C2212yes—
23C2×Dic214C2×C411yescharacteristic
24C2×D428C2×C411yescharacteristic
25C2×C22⋊D107—21no—
26C2×C4×D107—21no—
27C2×C107⋊C8—22no—
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—21no—
40C22×C4×C107C2×C411yescharacteristic
41C22×C4×C107D411yescharacteristic
42C22×C4×C107D411yescharacteristic
43C2×C8×C107—22no—
44C42×C107C2×C411yescharacteristic
45C42×C107D411yescharacteristic
46C42×C107D411yescharacteristic
47C42×C107C2311yescharacteristic
48C23×C107C22⋊C411yescharacteristic
49C22×D107—21no—
50C2×C4×C107—41no—
51C2×C4×C107—41no—
52C2×C4×C107—41no—
53C2×C4×C107C22⋊C411yescharacteristic
54C2×C4×C107C22⋊C411yescharacteristic
55C2×C4×C107C22⋊C411yescharacteristic
56C2×C4×C107C22×C411yescharacteristic
57C2×C4×C107C2×D411yescharacteristic
58C2×C4×C107C2×D411yescharacteristic
59C22⋊D107—42no—
60C2×Dic107—21no—
61C2×Dic107—21no—
62C2×Dic107—21no—
63D428—41no—
64C4×D107—42no—
65Dic214—41no—
66C8×C107—42no—
67C107⋊C8—42no—
68C22×C107—21no—
69C22×C107—21no—
70C22×C107—21no—
71C22×C107C2×C22⋊C411yescharacteristic
72C2×D107—41no—
73C2×D107—41no—
74C2×D107—41no—
75C4×C107—21no—
76C4×C107—21no—
77C4×C107—21no—
78C4×C107—21no—
79C4×C107—21no—
80C4×C107—21no—
81Dic107—41no—
82Dic107—41no—
83Dic107—41no—
84C2×C107—41no—
85C2×C107#41311yescharacteristic
86C2×C107#42111yescharacteristic
87C2×C107#42111yescharacteristic
88D107—81no—
89#1535—1071nomaximal, Sylow
90C107#153511yescharacteristic, complemented, Sylow
91#529—1071no—
92#432—1071no—
93#432D10711yescharacteristic, complemented
94#330—1072no—
95#329—1072no—
96#126—2141no—
97#125—1071no—
98#124—1071no—
99#123—2141no—
100C22⋊Q8—1071no—
101#121—1071no—
102C4×Q8—1071no—
103C4×D4—1071no—
104C4×D4—2141no—
105#117—2141no—
106C2×C42C2×D10711yescharacteristic
107C4⋊C8—21no—
108C4⋊C8—2141no—
109C22⋊C8—21no—
110C22⋊C8—2141no—
111#97—1072no—
112#97C2×D10712yes—
113C2×Q8—1071no—
114C2×D4—1071no—
115C2×D4—2141no—
116C22×C4—2141no—
117C22×C4C4×D10711yescharacteristic
118C22×C4D42811yescharacteristic
119C22×C4C22⋊D10711yescharacteristic
120C2×C8—22no—
121C2×C8—2142no—
122C4⋊C4—1071no—
123C4⋊C4—1071no—
124C4⋊C4—2141no—
125C4⋊C4—2141no—
126C4⋊C4—2141no—
127C4⋊C4—2141no—
128C22⋊C4—2141no—
129C22⋊C4—2141no—
130C22⋊C4—2141no—
131C22⋊C4—2141no—
132C22⋊C4—2141no—
133C42—2141no—
134C42C4×D10711yescharacteristic
135C42D42811yescharacteristic
136C42C22⋊D10711yescharacteristic
137C42C22×D10711yescharacteristic
138C23—2141no—
139C23(C2×D107)⋊C411yescharacteristic
140Q8—4281no—
141D4—4281no—
142D4—4282no—
143C2×C4—41no—
144C2×C4—41no—
145C2×C4—41no—
146C2×C4—4282no—
147C2×C4—2141no—
148C2×C4—2141no—
149C2×C4—2141no—
150C2×C4(C2×D107)⋊C411yescharacteristic
151C2×C4(C2×D107)⋊C411yescharacteristic
152C2×C4(C2×D107)⋊C411yescharacteristic
153C2×C4C2×C4×D10711yescharacteristic
154C2×C4C2×C22⋊D10711yescharacteristic
155C2×C4C2×D42811yescharacteristic
156C8—42no—
157C8—4282no—
158C22—21no—
159C22—21no—
160C22—21no—
161C22—4281no—
162C22—4281no—
163C22—4281no—
164C22C2×(C2×D107)⋊C411yescharacteristic
165C4—21no—
166C4—21no—
167C4—21no—
168C4—21no—
169C4—21no—
170C4—21no—
171C4—4281no—
172C4—4281no—
173C4—4281no—
174C2—41no—
175C2—8561no—
176C2#2029260911yescharacteristic
177C2#2029264311yescharacteristic
178C2#2029264511yescharacteristic
subgroupG/H
centerC22C2×(C2×D107)⋊C4
commutatorC2×C4×C107C22×C4
FrattiniC42C22×D107
Fitting#432×C107C2
socleC22×C107C2×C22⋊C4
prime radical#16812083C4
cosocleC42×C107C23
hypercenter#432D107
hypocenterC107#1535
LCSG ▷ C2×C4×C107 ▷ C22×C107 ▷ C107
UCSC1 ◁ C22 ◁ C2×C42 ◁ #432

Complements

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

NH ≅ G/Ntype
2. #20292684C2semidirect
3. #20292368C2semidirect
4. #20292366C2semidirect
5. #432×C107C2semidirect
90. C107#1535semidirect
93. #432D107semidirect

Maximal subgroups

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

subgroupindex
#202931612
#202926842
#202923682
#202923662
#432×C1072
#1535107