Finite Group Databasebeta

← #28335776

Subgroups — #28335776

Order 13696.

208 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 208 conjugacy classes of subgroups — too many to draw. Only its 45 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#20293375C211yesmaximal, characteristic
2#20293019C211yesmaximal, characteristic, complemented
3#20292989C211yesmaximal, characteristic, complemented
4#20292369C211yesmaximal, characteristic, complemented
5#20292366C211yesmaximal, characteristic, complemented
6#20292366C211yesmaximal, characteristic, complemented
7#501×C107C211yesmaximal, characteristic, complemented
8C2×#13133808—21no—
9C2×#13133805—21no—
10#16812097C2211yescharacteristic
11#16812097C2211yescharacteristic
12#16812094—21no—
13#16812094—21no—
14#16812087—21no—
15#16812087—21no—
16#16812084—21no—
17#16812084—21no—
18#16812032—21no—
19#16812029—21no—
20#16812020C2211yescharacteristic
21#16812020C2211yescharacteristic
22C4⋊Q8×C107C2211yescharacteristic
23#125×C107C2211yescharacteristic
24#107×C107—21no—
25#106×C107—21no—
26#97×C107C2211yescharacteristic
27C2×Dic214D411yescharacteristic
28C2×Dic214D411yescharacteristic
29C2×D428—21no—
30C2×D428—21no—
31C2×D428D411yescharacteristic
32C2×D428D411yescharacteristic
33C2×C4×D107—21no—
34C2×C4×D107—21no—
35#13133808—42no—
36#13133805—42no—
37C2×C107⋊C8—21no—
38C2×C107⋊C8—21no—
39Dic107⋊C4—21no—
40Dic107⋊C4—21no—
41(C2×D107)⋊C4—21no—
42(C2×D107)⋊C4—21no—
43(C2×D107)⋊C4—21no—
44(C2×D107)⋊C4—21no—
45(C2×D107)⋊C4—21no—
46(C2×D107)⋊C4—21no—
47C2×Q8×C107—21no—
48C2×C8×C107—21no—
49C4⋊C4×C107—21no—
50C4⋊C4×C107—21no—
51C4⋊C4×C107—21no—
52C4⋊C4×C107—21no—
53C4⋊C4×C107D411yescharacteristic
54C4⋊C4×C107D411yescharacteristic
55C42×C107C2311yescharacteristic
56C22×D107—21no—
57C22×D107—21no—
58Q8×C107—41no—
59Q8×C107—41no—
60C2×C4×C107—21no—
61C2×C4×C107—21no—
62C2×C4×C107—41no—
63C2×C4×C107C2×D411yescharacteristic
64C2×C4×C107C2×D411yescharacteristic
65C2×C4×C107C2×D411yescharacteristic
66C2×Dic107—21no—
67C2×Dic107—21no—
68D428—41no—
69D428—41no—
70D428—81no—
71D428—81no—
72C4×D107—81no—
73C4×D107—81no—
74Dic214—41no—
75Dic214—41no—
76C8×C107—22no—
77C107⋊C8—22no—
78C107⋊C8—41no—
79C22×C107#12011yescharacteristic
80C2×D107—41no—
81C2×D107—41no—
82C2×D107—41no—
83C2×D107—41no—
84C2×D107—41no—
85C2×D107—41no—
86C4×C107—21no—
87C4×C107—21no—
88C4×C107—21no—
89C4×C107—41no—
90C4×C107—41no—
91C4×C107—81no—
92Dic107—41no—
93Dic107—41no—
94C2×C107#45311yescharacteristic
95C2×C107#45511yescharacteristic
96C2×C107#45611yescharacteristic
97D107—81no—
98D107—81no—
99#1661—1071nomaximal, Sylow
100C107#166111yescharacteristic, complemented, Sylow
101#562—1071no—
102#501D10711yescharacteristic, complemented
103#497—1071no—
104#489—1071no—
105#330—1071no—
106#329—1071no—
107#329—1071no—
108C2×Q16—2141no—
109C2×SD16—2141no—
110C4⋊Q8C2×D10711yescharacteristic
111#125C2×D10711yescharacteristic
112#124—1071no—
113#124—1071no—
114#123—2141no—
115#123—2141no—
116C22⋊Q8—2141no—
117C22⋊Q8—2141no—
118#121—2141no—
119#121—2141no—
120#107—21no—
121#106—21no—
122#103—2141no—
123#102—2141no—
124#97—1071no—
125#97—1071no—
126#97C2×D10711yescharacteristic
127C2×Q8—21no—
128C2×Q8—1071no—
129C2×Q8—1071no—
130C2×D4—1071no—
131C2×D4—1071no—
132C2×D4—2141no—
133C2×D4—2141no—
134C22×C4—2141no—
135C22×C4—2141no—
136Q16—4282no—
137SD16—4282no—
138C2×C8—21no—
139C2×C8—2141no—
140C2×C8—2141no—
141C4⋊C4—21no—
142C4⋊C4—21no—
143C4⋊C4—21no—
144C4⋊C4—21no—
145C4⋊C4—2141no—
146C4⋊C4—2141no—
147C4⋊C4C22⋊D10711yescharacteristic
148C4⋊C4C22⋊D10711yescharacteristic
149C22⋊C4—2141no—
150C22⋊C4—2141no—
151C22⋊C4—2141no—
152C22⋊C4—2141no—
153C22⋊C4—2141no—
154C22⋊C4—2141no—
155C42C22×D10711yescharacteristic
156C23—2141no—
157C23—2141no—
158Q8—41no—
159Q8—41no—
160Q8—4281no—
161Q8—4281no—
162D4—8561no—
163D4—8561no—
164D4—4281no—
165D4—4281no—
166C2×C4—21no—
167C2×C4—21no—
168C2×C4—41no—
169C2×C4—8561no—
170C2×C4—8561no—
171C2×C4—2141no—
172C2×C4—2141no—
173C2×C4D4×D10711yescharacteristic
174C2×C4D4×D10711yescharacteristic
175C2×C4C2×C22⋊D10711yescharacteristic
176C8—22no—
177C8—4281no—
178C8—2142no—
179C22—4281no—
180C22—4281no—
181C22—4281no—
182C22—4281no—
183C22—4281no—
184C22—4281no—
185C22#1681207711yescharacteristic
186C4—21no—
187C4—21no—
188C4—21no—
189C4—41no—
190C4—41no—
191C4—81no—
192C4—4281no—
193C4—4281no—
194C2—8561no—
195C2—8561no—
196C2#2029279311yescharacteristic
197C2#2029280311yescharacteristic
198C2#2029280911yescharacteristic
subgroupG/H
centerC22#16812077
commutator, cosocleC42×C107C23
FrattiniC42C22×D107
Fitting#501×C107C2
socleC22×C107#120
prime radical#20293375C2
hypercenter#501D107
hypocenterC107#1661
LCSG ▷ C42×C107 ▷ C22×C107 ▷ C107
UCSC1 ◁ C22 ◁ C42 ◁ #501

Complements

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

NH ≅ G/Ntype
2. #20293019C2semidirect
3. #20292989C2semidirect
4. #20292369C2semidirect
5. #20292366C2semidirect
6. #20292366C2semidirect
7. #501×C107C2semidirect
100. C107#1661semidirect
102. #501D107semidirect

Maximal subgroups

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

subgroupindex
#202933752
#202930192
#202929892
#202923692
#202923662
#501×C1072
#1661107