Finite Group Databasebeta

← #28335491

Subgroups — #28335491

Order 13696.

208 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 208 conjugacy classes of subgroups — too many to draw. Only its 49 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#20293226C211yesmaximal, characteristic
2#20292945C211yesmaximal, characteristic
3#20292565C211yesmaximal, characteristic, complemented
4#20292364C211yesmaximal, characteristic, complemented
5#20292362C211yesmaximal, characteristic
6#20292352C211yesmaximal, characteristic, complemented
7#484×C107C211yesmaximal, characteristic, complemented
8#16812104—21no—
9#16812100—21no—
10#16812094—21no—
11#16812093—21no—
12#16812085—21no—
13#16812083C2211yescharacteristic
14(C22⋊D107)⋊C4—21no—
15C2×Dic107⋊C4C2211yescharacteristic
16#16812040—21no—
17#16812029—21no—
18C22⋊(C107⋊C8)C2211yescharacteristic
19C107⋊#95—21no—
20C107⋊#95—21no—
21C107⋊#95C2211yescharacteristic
22C22⋊Q8×C107C2211yescharacteristic
23C2×C4⋊C4×C107C2211yescharacteristic
24#107×C107—21no—
25#103×C107—21no—
26C22⋊C8×C107C2211yescharacteristic
27C2×D428D411yescharacteristic
28C2×C22⋊D107—21no—
29C22×Dic107—21no—
30C22×Dic107D411yescharacteristic
31C22×Dic107D411yescharacteristic
32C2×C4×D107—21no—
33C2×C107⋊C8—21no—
34C4⋊Dic107—21no—
35C4⋊Dic107—21no—
36C4⋊Dic107D411yescharacteristic
37Dic107⋊C4—21no—
38Dic107⋊C4—21no—
39Dic107⋊C4—21no—
40(C2×D107)⋊C4—21no—
41(C2×D107)⋊C4—21no—
42(C2×D107)⋊C4—21no—
43(C2×D107)⋊C4—21no—
44C4×Dic107—21no—
45C2×Q8×C107D411yescharacteristic
46C22×C4×C107—21no—
47C22×C4×C107C2311yescharacteristic
48C2×C8×C107—21no—
49C4⋊C4×C107—21no—
50C4⋊C4×C107—21no—
51C4⋊C4×C107—21no—
52C4⋊C4×C107D411yescharacteristic
53C22⋊C4×C107—21no—
54C23×C107C2×D411yescharacteristic
55C22×D107—21no—
56Q8×C107—41no—
57C2×C4×C107—21no—
58C2×C4×C107—21no—
59C2×C4×C107—41no—
60C2×C4×C107—42no—
61C2×C4×C107—41no—
62C2×C4×C107C2×D411yescharacteristic
63C2×C4×C107C2×D411yescharacteristic
64C22⋊D107—41no—
65C22⋊D107—41no—
66C2×Dic107—21no—
67C2×Dic107—21no—
68C2×Dic107—21no—
69C2×Dic107—21no—
70C2×Dic107—21no—
71C2×Dic107—41no—
72C2×Dic107—41no—
73C2×Dic107—41no—
74C2×Dic107—41no—
75D428—41no—
76C4×D107—81no—
77C8×C107—41no—
78C107⋊C8—41no—
79C22×C107—21no—
80C22×C107—21no—
81C22×C107#12011yescharacteristic
82C22×C107#13511yescharacteristic
83C22×C107#13711yescharacteristic
84C2×D107—41no—
85C2×D107—41no—
86C2×D107—41no—
87C4×C107—21no—
88C4×C107—21no—
89C4×C107—41no—
90C4×C107—41no—
91C4×C107—81no—
92Dic107—41no—
93Dic107—41no—
94Dic107—41no—
95Dic107—81no—
96C2×C107—21no—
97C2×C107—21no—
98C2×C107#45211yescharacteristic
99C2×C107#45411yescharacteristic
100C2×C107#45811yescharacteristic
101D107—81no—
102#1615—1071nomaximal, Sylow
103C107#161511yescharacteristic, complemented, Sylow
104#539—1071no—
105#484D10711yescharacteristic, complemented
106#481—1071no—
107#400—1071no—
108#328—1071no—
109#327—1071no—
110#324—1071no—
111#126—2141no—
112#125—2141no—
113#123—2141no—
114#123—2141no—
115C22⋊Q8—2141no—
116C22⋊Q8C2×D10711yescharacteristic
117#121—1071no—
118C4×D4—2141no—
119C2×C4⋊C4—1071no—
120C2×C4⋊C4C2×D10711yescharacteristic
121#107—21no—
122#106—2141no—
123#103—21no—
124#102—2141no—
125C22⋊C8—1071no—
126C22⋊C8C2×D10711yescharacteristic
127#95—1071no—
128#95—2141no—
129#95—2141no—
130C2×Q8C22⋊D10711yescharacteristic
131C2×D4—1071no—
132C2×D4—2141no—
133C22×C4—21no—
134C22×C4—1071no—
135C22×C4—1071no—
136C22×C4—2141no—
137C22×C4—2141no—
138C22×C4C22×D10711yescharacteristic
139C2×C8—21no—
140C2×C8—2141no—
141C4⋊C4—21no—
142C4⋊C4—21no—
143C4⋊C4—21no—
144C4⋊C4—1071no—
145C4⋊C4—2141no—
146C4⋊C4—2141no—
147C4⋊C4—2141no—
148C4⋊C4—2141no—
149C4⋊C4—2141no—
150C4⋊C4C22⋊D10711yescharacteristic
151C22⋊C4—21no—
152C22⋊C4—2141no—
153C22⋊C4—2141no—
154C22⋊C4—2141no—
155C22⋊C4—2141no—
156C42—2141no—
157C23—2141no—
158C23D4×D10711yescharacteristic
159Q8—41no—
160D4—4281no—
161D4—4281no—
162D4—4281no—
163C2×C4—21no—
164C2×C4—21no—
165C2×C4—41no—
166C2×C4—42no—
167C2×C4—41no—
168C2×C4—8561no—
169C2×C4—4281no—
170C2×C4—4281no—
171C2×C4—4281no—
172C2×C4—4281no—
173C2×C4—2141no—
174C2×C4—2141no—
175C2×C4—2141no—
176C2×C4—2141no—
177C2×C4—2141no—
178C2×C4D4×D10711yescharacteristic
179C2×C4C2×C22⋊D10711yescharacteristic
180C8—41no—
181C8—4281no—
182C22—21no—
183C22—21no—
184C22—4281no—
185C22—4281no—
186C22—4281no—
187C22#1681207711yescharacteristic
188C22#1681213211yescharacteristic
189C22#1681214111yescharacteristic
190C4—21no—
191C4—21no—
192C4—41no—
193C4—41no—
194C4—81no—
195C4—8561no—
196C4—4281no—
197C4—4281no—
198C4—4281no—
199C2—21no—
200C2—21no—
201C2—8561no—
202C2#2029278811yescharacteristic
203C2#2029279811yescharacteristic
204C2#2029281611yescharacteristic
subgroupG/H
centerC22#16812077
commutator, cosocleC22×C4×C107C23
FrattiniC22×C4C22×D107
Fitting#484×C107C2
socleC22×C107#120
prime radical#16812083C22
hypercenter#484D107
hypocenterC107#1615
LCSG ▷ C22×C4×C107 ▷ C22×C107 ▷ C107
UCSC1 ◁ C22 ◁ C22×C4 ◁ #484

Complements

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

NH ≅ G/Ntype
3. #20292565C2semidirect
4. #20292364C2semidirect
6. #20292352C2semidirect
7. #484×C107C2semidirect
103. C107#1615semidirect
105. #484D107semidirect

Maximal subgroups

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

subgroupindex
#202932262
#202929452
#202925652
#202923642
#202923622
#202923522
#484×C1072
#1615107