Finite Group Databasebeta

← #28335472

Subgroups — #28335472

Order 13696.

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

normal subgroups only

This group has 232 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#20293214C211yesmaximal, characteristic
2#20292957C211yesmaximal, characteristic, complemented
3#20292553C211yesmaximal, characteristic, complemented
4#20292365C211yesmaximal, characteristic, complemented
5#20292361C211yesmaximal, characteristic, complemented
6#20292350C211yesmaximal, characteristic, complemented
7#480×C107C211yesmaximal, characteristic, complemented
8#16812104—21no—
9#16812095—21no—
10#16812093—21no—
11#16812088C2211yescharacteristic
12#16812081—21no—
13#16812077—21no—
14D4×Dic107—21no—
15C2×(C2×D107)⋊C4—21no—
16C2×(C2×D107)⋊C4C2211yescharacteristic
17#16812040—21no—
18#16812032—21no—
19C22⋊(C107⋊C8)C2211yescharacteristic
20C107⋊#95—21no—
21C107⋊#95C2211yescharacteristic
22#121×C107C2211yescharacteristic
23C2×C4⋊C4×C107C2211yescharacteristic
24#107×C107—21no—
25#102×C107—21no—
26C22⋊C8×C107C2211yescharacteristic
27C23×D107D411yescharacteristic
28C2×Dic214D411yescharacteristic
29C2×C22⋊D107—21no—
30C2×C22⋊D107—21no—
31C22×Dic107—21no—
32C22×Dic107—21no—
33C22×Dic107D411yescharacteristic
34C2×C107⋊C8—21no—
35C4⋊Dic107—21no—
36C4⋊Dic107D411yescharacteristic
37Dic107⋊C4—21no—
38C22⋊Dic107—21no—
39C22⋊Dic107—21no—
40(C2×D107)⋊C4—21no—
41(C2×D107)⋊C4—21no—
42(C2×D107)⋊C4—21no—
43(C2×D107)⋊C4—21no—
44(C2×D107)⋊C4—42no—
45C4×Dic107—21no—
46C2×D4×C107—21no—
47C2×D4×C107D411yescharacteristic
48C22×C4×C107—21no—
49C22×C4×C107C2311yescharacteristic
50C2×C8×C107—21no—
51C4⋊C4×C107—21no—
52C4⋊C4×C107—21no—
53C4⋊C4×C107D411yescharacteristic
54C22⋊C4×C107—21no—
55C23×C107—21no—
56C23×C107C2×D411yescharacteristic
57C22×D107—21no—
58C22×D107—21no—
59C22×D107—21no—
60C22×D107—41no—
61C22×D107—41no—
62D4×C107—41no—
63D4×C107—41no—
64D4×C107—41no—
65C2×C4×C107—21no—
66C2×C4×C107—41no—
67C2×C4×C107—41no—
68C2×C4×C107—41no—
69C2×C4×C107—41no—
70C2×C4×C107C2×D411yescharacteristic
71C2×C4×C107C2×D411yescharacteristic
72C22⋊D107—81no—
73C22⋊D107—81no—
74C2×Dic107—21no—
75C2×Dic107—21no—
76C2×Dic107—21no—
77C2×Dic107—41no—
78C2×Dic107—41no—
79C2×Dic107—41no—
80C2×Dic107—41no—
81C2×Dic107—81no—
82Dic214—41no—
83C8×C107—41no—
84C107⋊C8—41no—
85C22×C107—21no—
86C22×C107—21no—
87C22×C107—41no—
88C22×C107—41no—
89C22×C107—41no—
90C22×C107#12011yescharacteristic
91C22×C107#13511yescharacteristic
92C22×C107AGL(1,ℤ/8)11yescharacteristic
93C2×D107—42no—
94C2×D107—41no—
95C2×D107—41no—
96C2×D107—41no—
97C2×D107—81no—
98C4×C107—21no—
99C4×C107—21no—
100C4×C107—41no—
101C4×C107—81no—
102Dic107—41no—
103Dic107—41no—
104Dic107—41no—
105Dic107—81no—
106C2×C107—21no—
107C2×C107—21no—
108C2×C107—81no—
109C2×C107#44911yescharacteristic
110C2×C107#45511yescharacteristic
111C2×C107#45811yescharacteristic
112D107—81no—
113#1612—1071nomaximal, Sylow
114C107#161211yescharacteristic, complemented, Sylow
115#538—1071no—
116#483—1071no—
117#480D10711yescharacteristic, complemented
118#397—1071no—
119#328—1071no—
120#327—1071no—
121#323—1071no—
122#126—2141no—
123#124—2141no—
124#123—2141no—
125C22⋊Q8—1071no—
126#121—2141no—
127#121C2×D10711yescharacteristic
128#120—2141no—
129C4×D4—2141no—
130C2×C4⋊C4C2×D10711yescharacteristic
131C2×C22⋊C4—1071no—
132C2×C22⋊C4—2141no—
133#107—21no—
134#106—2141no—
135#103—2141no—
136#102—21no—
137C22⋊C8—1071no—
138C22⋊C8C2×D10711yescharacteristic
139#95—1071no—
140#95—2141no—
141C24—1071no—
142C2×Q8—1071no—
143C2×D4—21no—
144C2×D4—2141no—
145C2×D4—2141no—
146C2×D4C22⋊D10711yescharacteristic
147C22×C4—21no—
148C22×C4—1071no—
149C22×C4—2141no—
150C22×C4—2141no—
151C22×C4C22×D10711yescharacteristic
152C2×C8—21no—
153C2×C8—2141no—
154C4⋊C4—21no—
155C4⋊C4—21no—
156C4⋊C4—1071no—
157C4⋊C4—2141no—
158C4⋊C4—2141no—
159C4⋊C4C22⋊D10711yescharacteristic
160C22⋊C4—21no—
161C22⋊C4—4282no—
162C22⋊C4—2141no—
163C22⋊C4—2141no—
164C22⋊C4—2141no—
165C22⋊C4—2141no—
166C22⋊C4—2141no—
167C22⋊C4—2141no—
168C42—2141no—
169C23—21no—
170C23—4281no—
171C23—4281no—
172C23—2141no—
173C23—2141no—
174C23—2141no—
175C23D4×D10711yescharacteristic
176Q8—4281no—
177D4—41no—
178D4—41no—
179D4—41no—
180D4—8561no—
181D4—8561no—
182C2×C4—21no—
183C2×C4—41no—
184C2×C4—41no—
185C2×C4—41no—
186C2×C4—41no—
187C2×C4—8561no—
188C2×C4—4281no—
189C2×C4—4281no—
190C2×C4—4281no—
191C2×C4—4281no—
192C2×C4—2141no—
193C2×C4—2141no—
194C2×C4—2141no—
195C2×C4D4×D10711yescharacteristic
196C2×C4C2×C22⋊D10711yescharacteristic
197C8—41no—
198C8—4281no—
199C22—21no—
200C22—21no—
201C22—41no—
202C22—41no—
203C22—41no—
204C22—8561no—
205C22—4282no—
206C22—4281no—
207C22—4281no—
208C22—4281no—
209C22#1681207711yescharacteristic
210C22#1681212811yescharacteristic
211C22#1681213311yescharacteristic
212C4—21no—
213C4—21no—
214C4—41no—
215C4—81no—
216C4—8561no—
217C4—4281no—
218C4—4281no—
219C4—4281no—
220C2—21no—
221C2—21no—
222C2—81no—
223C2—8561no—
224C2#2029276911yescharacteristic
225C2#2029280311yescharacteristic
226C2#2029281611yescharacteristic
subgroupG/H
centerC22#16812077
commutator, cosocleC22×C4×C107C23
FrattiniC22×C4C22×D107
Fitting#480×C107C2
socleC22×C107#120
prime radical#20293214C2
hypercenter#480D107
hypocenterC107#1612
LCSG ▷ C22×C4×C107 ▷ C22×C107 ▷ C107
UCSC1 ◁ C22 ◁ C22×C4 ◁ #480

Complements

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

NH ≅ G/Ntype
2. #20292957C2semidirect
3. #20292553C2semidirect
4. #20292365C2semidirect
5. #20292361C2semidirect
6. #20292350C2semidirect
7. #480×C107C2semidirect
114. C107#1612semidirect
117. #480D107semidirect

Maximal subgroups

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

subgroupindex
#202932142
#202929572
#202925532
#202923652
#202923612
#202923502
#480×C1072
#1612107