Finite Group Databasebeta

← #28335089

Subgroups — #28335089

Order 13696.

200 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 200 conjugacy classes of subgroups — too many to draw. Only its 57 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#20293156C211yesmaximal, characteristic
2#20292682C211yesmaximal, characteristic, complemented
3#20292682C211yesmaximal, characteristic, complemented
4#20292368C211yesmaximal, characteristic, complemented
5#20292368C211yesmaximal, characteristic, complemented
6#20292367C211yesmaximal, characteristic, complemented
7#329×C107C211yesmaximal, characteristic, complemented
8#16812102—21no—
9#16812101C2211yescharacteristic
10#16812091—21no—
11#16812085C411yescharacteristic
12#16812080C411yescharacteristic
13Q8×Dic107C411yescharacteristic
14D4×Dic107C411yescharacteristic
15(C22⋊D107)⋊C4—21no—
16#16812065—21no—
17C42×D107C2211yescharacteristic
18Dic107⋊C8—21no—
19Dic107⋊C8—21no—
20(C2×D107)⋊C8—21no—
21(C2×D107)⋊C8—21no—
22#16812020C2211yescharacteristic
23#16812020C2211yescharacteristic
24#124×C107C2211yescharacteristic
25#97×C107C2211yescharacteristic
26#97×C107C2211yescharacteristic
27C2×C22⋊D107—21no—
28C22×Dic107—21no—
29C2×C4×D107C2×C411yescharacteristic
30C2×C4×D107D411yescharacteristic
31C2×C4×D107D411yescharacteristic
32C2×C107⋊C8—21no—
33C2×C107⋊C8—21no—
34C4⋊Dic107—21no—
35C4⋊Dic107C2×C411yescharacteristic
36C4⋊Dic107C2×C411yescharacteristic
37Dic107⋊C4—21no—
38Dic107⋊C4—21no—
39Dic107⋊C4—21no—
40C22⋊Dic107—21no—
41C22⋊Dic107—21no—
42(C2×D107)⋊C4—21no—
43C4×Dic107—21no—
44C4×Dic107C2×C411yescharacteristic
45C4×Dic107D411yescharacteristic
46C4×Dic107D411yescharacteristic
47C2×Q8×C107C2×C411yescharacteristic
48C2×D4×C107C2×C411yescharacteristic
49C2×C8×C107—21no—
50C2×C8×C107—21no—
51C22⋊C4×C107—21no—
52C22⋊C4×C107—21no—
53C42×C107C2311yescharacteristic
54C23×C107—21no—
55C22×D107C22⋊C411yescharacteristic
56Q8×C107—41no—
57D4×C107—41no—
58C2×C4×C107—21no—
59C2×C4×C107C22×C411yescharacteristic
60C2×C4×C107C2×D411yescharacteristic
61C2×C4×C107C2×D411yescharacteristic
62C22⋊D107—42no—
63C2×Dic107—21no—
64C2×Dic107—21no—
65C2×Dic107—42no—
66C2×Dic107C22⋊C411yescharacteristic
67C2×Dic107C22⋊C411yescharacteristic
68C2×Dic107C22⋊C411yescharacteristic
69C4×D107—41no—
70C4×D107—41no—
71C4×D107—41no—
72C8×C107—41no—
73C8×C107—41no—
74C107⋊C8—41no—
75C107⋊C8—41no—
76C22×C107—41no—
77C22×C107—41no—
78C22×C107—41no—
79C22×C107C2×C22⋊C411yescharacteristic
80C2×D107—21no—
81C2×D107—21no—
82C2×D107—21no—
83C4×C107—21no—
84C4×C107—21no—
85C4×C107—21no—
86C4×C107—41no—
87Dic107—21no—
88Dic107—21no—
89Dic107—21no—
90Dic107—41no—
91Dic107—41no—
92C2×C107—81no—
93C2×C107#41311yescharacteristic
94C2×C107#42111yescharacteristic
95C2×C107#42111yescharacteristic
96D107—41no—
97#1535—1071nomaximal, Sylow
98C107#153511yescharacteristic, complemented, Sylow
99#529—1071no—
100#432—1071no—
101#432—1071no—
102#330—1071no—
103#330—1071no—
104#329—1071no—
105#329D10711yescharacteristic, complemented
106#126—2141no—
107#125—1071no—
108#124C2×D10711yescharacteristic
109#123—2141no—
110C22⋊Q8—1071no—
111#121—1071no—
112C4×Q8—1071no—
113C4×D4—1071no—
114C4×D4—2141no—
115#117—2141no—
116C2×C42—1071no—
117C4⋊C8—2141no—
118C4⋊C8—2141no—
119C22⋊C8—2141no—
120C22⋊C8—2141no—
121#97—1071no—
122#97—1071no—
123#97C2×D10711yescharacteristic
124#97C2×D10711yescharacteristic
125C2×Q8C4×D10711yescharacteristic
126C2×D4—2141no—
127C2×D4C4×D10711yescharacteristic
128C22×C4—1071no—
129C22×C4—1071no—
130C22×C4—1071no—
131C22×C4—2141no—
132C2×C8—21no—
133C2×C8—21no—
134C2×C8—2141no—
135C2×C8—2141no—
136C4⋊C4—1071no—
137C4⋊C4—1071no—
138C4⋊C4—2141no—
139C4⋊C4—2141no—
140C4⋊C4—2141no—
141C4⋊C4—2141no—
142C22⋊C4—21no—
143C22⋊C4—21no—
144C22⋊C4—2141no—
145C22⋊C4—2141no—
146C22⋊C4—2141no—
147C42—1071no—
148C42—1071no—
149C42—1071no—
150C42—2141no—
151C42C22×D10711yescharacteristic
152C23—21no—
153C23—1071no—
154Q8—41no—
155D4—41no—
156D4—4282no—
157C2×C4—21no—
158C2×C4—1071no—
159C2×C4—1071no—
160C2×C4—1071no—
161C2×C4—4281no—
162C2×C4—4281no—
163C2×C4—4281no—
164C2×C4—4282no—
165C2×C4—2141no—
166C2×C4—2141no—
167C2×C4C2×C4×D10711yescharacteristic
168C2×C4D4×D10711yescharacteristic
169C2×C4D4×D10711yescharacteristic
170C8—41no—
171C8—41no—
172C8—4281no—
173C8—4281no—
174C22—41no—
175C22—41no—
176C22—41no—
177C22—2141no—
178C22—2141no—
179C22—2141no—
180C22C22⋊C4×D10711yescharacteristic
181C4—21no—
182C4—21no—
183C4—21no—
184C4—41no—
185C4—4281no—
186C4—4281no—
187C4—2141no—
188C4—2141no—
189C4—2141no—
190C2—81no—
191C2—4281no—
192C2#2029260811yescharacteristic
193C2#2029264211yescharacteristic
194C2#2029264211yescharacteristic
subgroupG/H
centerC22C22⋊C4×D107
commutatorC2×C4×C107C22×C4
FrattiniC42C22×D107
Fitting#329×C107C2
socleC22×C107C2×C22⋊C4
prime radical#16812080C4
cosocleC42×C107C23
hypercenter#329D107
hypocenterC107#1535
LCSG ▷ C2×C4×C107 ▷ C22×C107 ▷ C107
UCSC1 ◁ C22 ◁ C42 ◁ #329

Complements

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

NH ≅ G/Ntype
2. #20292682C2semidirect
3. #20292682C2semidirect
4. #20292368C2semidirect
5. #20292368C2semidirect
6. #20292367C2semidirect
7. #329×C107C2semidirect
98. C107#1535semidirect
105. #329D107semidirect

Maximal subgroups

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

subgroupindex
#202931562
#202926822
#202923682
#202923672
#329×C1072
#1535107