Finite Group Databasebeta

← #28335010

Subgroups — #28335010

Order 13696.

208 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 208 conjugacy classes of subgroups — too many to draw. Only its 61 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#20293179C211yesmaximal, characteristic
2#20292681C211yesmaximal, characteristic
3#20292494C211yesmaximal, characteristic
4#20292365C211yesmaximal, characteristic
5#20292364C211yesmaximal, characteristic
6#20292363C211yesmaximal, characteristic
7#328×C107C211yesmaximal, characteristic
8#16812108C411yescharacteristic, complemented
9#16812107C411yescharacteristic, complemented
10#16812099—21no—
11#16812088C2211yescharacteristic
12#16812086—21no—
13Q8×Dic107C411yescharacteristic, complemented
14#16812074—21no—
15#16812074C411yescharacteristic, complemented
16#16812065—21no—
17C2×C4×Dic107C2211yescharacteristic
18Dic107⋊C8—21no—
19C22⋊(C107⋊C8)C2211yescharacteristic
20#16812019—21no—
21C107⋊#95—21no—
22C107⋊#95—21no—
23C107⋊#95C2211yescharacteristic
24C22⋊Q8×C107C2211yescharacteristic
25C22⋊C8×C107C2211yescharacteristic
26#95×C107C2211yescharacteristic
27C2×Dic214—21no—
28C2×Dic214C2×C411yescharacteristic
29C22×Dic107—21no—
30C22×Dic107D411yescharacteristic
31C22×Dic107D411yescharacteristic
32C2×C107⋊C8—21no—
33C4⋊Dic107—21no—
34C4⋊Dic107C2×C411yescharacteristic
35Dic107⋊C4—21no—
36Dic107⋊C4—21no—
37Dic107⋊C4—21no—
38Dic107⋊C4—21no—
39Dic107⋊C4—21no—
40C22⋊Dic107—21no—
41C4×Dic107—21no—
42C4×Dic107—21no—
43C4×Dic107C2×C411yescharacteristic
44C4×Dic107C2×C411yescharacteristic
45C4×Dic107D411yescharacteristic
46C4×Dic107D411yescharacteristic
47C2×Q8×C107C2×C411yescharacteristic
48C22×C4×C107—21no—
49C22×C4×C107C2311yescharacteristic
50C2×C8×C107—21no—
51C4⋊C4×C107—21no—
52C4⋊C4×C107C2×C411yescharacteristic
53C22⋊C4×C107—21no—
54C23×C107C2×D411yescharacteristic
55Q8×C107—41no—
56C2×C4×C107—21no—
57C2×C4×C107—21no—
58C2×C4×C107—41no—
59C2×C4×C107—41no—
60C2×C4×C107—41no—
61C2×C4×C107—41no—
62C2×C4×C107C22×C411yescharacteristic
63C2×C4×C107C2×D411yescharacteristic
64C2×Dic107—21no—
65C2×Dic107—21no—
66C2×Dic107—21no—
67C2×Dic107—21no—
68C2×Dic107—41no—
69C2×Dic107—41no—
70C2×Dic107—41no—
71C2×Dic107—41no—
72C2×Dic107C22⋊C411yescharacteristic
73C2×Dic107C22⋊C411yescharacteristic
74C2×Dic107C22⋊C411yescharacteristic
75C2×Dic107C22⋊C411yescharacteristic
76Dic214—42no—
77Dic214—41no—
78C8×C107—41no—
79C107⋊C8—41no—
80C22×C107—21no—
81C22×C107—21no—
82C22×C107C2×C22⋊C411yescharacteristic
83C22×C107#13711yescharacteristic
84C22×C107#13711yescharacteristic
85C4×C107—21no—
86C4×C107—21no—
87C4×C107—41no—
88C4×C107—41no—
89C4×C107—81no—
90Dic107—21no—
91Dic107—21no—
92Dic107—21no—
93Dic107—21no—
94Dic107—41no—
95Dic107—41no—
96Dic107—81no—
97C2×C107—21no—
98C2×C107—21no—
99C2×C107#41011yescharacteristic
100C2×C107#41911yescharacteristic
101C2×C107#42111yescharacteristic
102#1515—1071nomaximal, Sylow
103C107#151511yescharacteristic, complemented, Sylow
104#533—1071no—
105#432—1071no—
106#383—1071no—
107#328—1071no—
108#328—1071no—
109#328—1071no—
110#328D10711yescharacteristic
111C4⋊Q8—1071no—
112C4⋊Q8—1071no—
113#125—2141no—
114C22⋊Q8—1071no—
115C22⋊Q8—2141no—
116C22⋊Q8C2×D10711yescharacteristic
117C4×Q8—1071no—
118C4×Q8—1071no—
119C4×Q8—2141no—
120#117—2141no—
121C2×C42—1071no—
122C4⋊C8—2141no—
123C22⋊C8—1071no—
124C22⋊C8C2×D10711yescharacteristic
125#97—2141no—
126#95—1071no—
127#95—2141no—
128#95—2141no—
129#95C2×D10711yescharacteristic
130C2×Q8—1071no—
131C2×Q8—2141no—
132C2×Q8C4×D10711yescharacteristic
133C22×C4—21no—
134C22×C4—1071no—
135C22×C4—1071no—
136C22×C4—2141no—
137C22×C4C22×D10711yescharacteristic
138C2×C8—21no—
139C2×C8—2141no—
140C4⋊C4—21no—
141C4⋊C4—1071no—
142C4⋊C4—2141no—
143C4⋊C4—2141no—
144C4⋊C4—2141no—
145C4⋊C4—2141no—
146C4⋊C4—2141no—
147C4⋊C4—2141no—
148C4⋊C4C4×D10711yescharacteristic
149C22⋊C4—21no—
150C22⋊C4—2141no—
151C42—1071no—
152C42—1071no—
153C42—1071no—
154C42—1071no—
155C42—2141no—
156C42—2141no—
157C23D4×D10711yescharacteristic
158Q8—41no—
159Q8—4281no—
160Q8—4282no—
161C2×C4—21no—
162C2×C4—21no—
163C2×C4—41no—
164C2×C4—41no—
165C2×C4—41no—
166C2×C4—41no—
167C2×C4—1071no—
168C2×C4—1071no—
169C2×C4—1071no—
170C2×C4—1071no—
171C2×C4—4281no—
172C2×C4—4281no—
173C2×C4—4281no—
174C2×C4—4281no—
175C2×C4—2141no—
176C2×C4—2141no—
177C2×C4—2141no—
178C2×C4—2141no—
179C2×C4C2×C4×D10711yescharacteristic
180C2×C4D4×D10711yescharacteristic
181C8—41no—
182C8—4281no—
183C22—21no—
184C22—21no—
185C22C22⋊C4×D10711yescharacteristic
186C22#1681213811yescharacteristic
187C22#1681214111yescharacteristic
188C4—21no—
189C4—21no—
190C4—41no—
191C4—41no—
192C4—81no—
193C4—8561no—
194C4—4281no—
195C4—4281no—
196C4—2141no—
197C4—2141no—
198C4—2141no—
199C4—2141no—
200C2—21no—
201C2—21no—
202C2#2029259911yescharacteristic
203C2#2029263411yescharacteristic
204C2#2029264211yescharacteristic
subgroupG/H
centerC22C22⋊C4×D107
commutatorC2×C4×C107C22×C4
FrattiniC22×C4C22×D107
Fitting#328×C107C2
socleC22×C107C2×C22⋊C4
prime radicalC23×C107C2×D4
cosocleC22×C4×C107C23
hypercenter#328D107
hypocenterC107#1515
LCSG ▷ C2×C4×C107 ▷ C22×C107 ▷ C107
UCSC1 ◁ C22 ◁ C22×C4 ◁ #328

Complements

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

NH ≅ G/Ntype
8. #16812108C4semidirect
9. #16812107C4semidirect
13. Q8×Dic107C4semidirect
15. #16812074C4semidirect
103. C107#1515semidirect

Maximal subgroups

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

subgroupindex
#202931792
#202926812
#202924942
#202923652
#202923642
#202923632
#328×C1072
#1515107