Finite Group Databasebeta

← #28335686

Subgroups — #28335686

Order 13696.

212 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 212 conjugacy classes of subgroups — too many to draw. Only its 53 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#20293343C211yesmaximal, characteristic
2#20292904C211yesmaximal, characteristic, complemented
3#20292829C211yesmaximal, characteristic, complemented
4#20292376C211yesmaximal, characteristic, complemented
5#20292356C211yesmaximal, characteristic, complemented
6#20292356C211yesmaximal, characteristic, complemented
7#487×C107C211yesmaximal, characteristic, complemented
8C2×#13133805—21no—
9#16812098—22no—
10#16812084—21no—
11#16812084—21no—
12C4×D428C2211yescharacteristic
13C4×D428C2211yescharacteristic
14#16812067—21no—
15#16812067—21no—
16#16812042—21no—
17C4⋊(C107⋊C8)C2211yescharacteristic
18C4⋊(C107⋊C8)C2211yescharacteristic
19#16812033—21no—
20#16812029—21no—
21C4⋊Q8×C107C2211yescharacteristic
22C4⋊Q8×C107C2211yescharacteristic
23#103×C107—22no—
24C4×C8×C107C2211yescharacteristic
25C2×D428—22no—
26C2×D428D411yescharacteristic
27C2×D428D411yescharacteristic
28C2×C4×D107—21no—
29C2×C4×D107—21no—
30#13133805—42no—
31C2×C107⋊C8—21no—
32C2×C107⋊C8—21no—
33C4⋊Dic107D411yescharacteristic
34C4⋊Dic107D411yescharacteristic
35(C2×D107)⋊C4—22no—
36(C2×D107)⋊C4—22no—
37(C2×D107)⋊C4—21no—
38(C2×D107)⋊C4—21no—
39C4×Dic107—22no—
40C2×Q8×C107—21no—
41C2×Q8×C107D412yes—
42C2×C8×C107—21no—
43C4⋊C4×C107—21no—
44C4⋊C4×C107—21no—
45C4⋊C4×C107—21no—
46C4⋊C4×C107—21no—
47C42×C107C2311yescharacteristic
48C22×D107—21no—
49C22×D107—21no—
50Q8×C107—42no—
51Q8×C107—41no—
52Q8×C107—41no—
53C2×C4×C107—22no—
54C2×C4×C107—41no—
55C2×C4×C107C2×D411yescharacteristic
56C2×C4×C107C2×D411yescharacteristic
57C2×C4×C107C2×D411yescharacteristic
58C2×Dic107—21no—
59C2×Dic107—21no—
60D428—21no—
61D428—21no—
62D428—21no—
63D428—21no—
64D428—82no—
65C4×D107—41no—
66C4×D107—41no—
67C4×D107—41no—
68C4×D107—41no—
69C8×C107—41no—
70C107⋊C8—41no—
71C107⋊C8—41no—
72C22×C107#12011yescharacteristic
73C2×D107—41no—
74C2×D107—41no—
75C2×D107—41no—
76C2×D107—41no—
77C2×D107—41no—
78C2×D107—41no—
79C4×C107—21no—
80C4×C107—42no—
81C4×C107—81no—
82C4×C107#13511yescharacteristic
83C4×C107#13511yescharacteristic
84C4×C107AGL(1,ℤ/8)11yescharacteristic
85C4×C107#13711yescharacteristic
86Dic107—41no—
87Dic107—41no—
88C2×C107#44911yescharacteristic
89C2×C107#45211yescharacteristic
90C2×C107#45511yescharacteristic
91D107—81no—
92D107—81no—
93#1646—1071nomaximal, Sylow
94C107#164611yescharacteristic, complemented, Sylow
95#555—1071no—
96#487D10711yescharacteristic, complemented
97#474—1071no—
98#461—1071no—
99#333—1071no—
100D4⋊C8—1071no—
101D4⋊C8—1071no—
102C2×SD16—2141no—
103C4⋊Q8C2×D10711yescharacteristic
104C4⋊Q8C2×D10711yescharacteristic
105#124—2142no—
106#121—2141no—
107#121—2141no—
108C4×D4—1071no—
109C4×D4—1071no—
110#117—2141no—
111#117—2141no—
112#107—2141no—
113C4⋊C8—1071no—
114C4⋊C8—1071no—
115#103—22no—
116#103—2141no—
117#102—2141no—
118C4×C8C2×D10711yescharacteristic
119C2×Q8—21no—
120C2×Q8C22⋊D10712yes—
121C2×D4—1071no—
122C2×D4—1071no—
123C2×D4—2142no—
124C22×C4—2141no—
125C22×C4—2141no—
126SD16—4282no—
127C2×C8—21no—
128C2×C8—2141no—
129C2×C8—2141no—
130C4⋊C4—21no—
131C4⋊C4—21no—
132C4⋊C4—21no—
133C4⋊C4—21no—
134C4⋊C4—1071no—
135C4⋊C4—1071no—
136C22⋊C4—2142no—
137C22⋊C4—2142no—
138C22⋊C4—2141no—
139C22⋊C4—2141no—
140C42—2142no—
141C42C22×D10711yescharacteristic
142C23—2141no—
143C23—2141no—
144Q8—42no—
145Q8—41no—
146Q8—41no—
147D4—8562no—
148D4—2141no—
149D4—2141no—
150D4—2141no—
151D4—2141no—
152C2×C4—22no—
153C2×C4—41no—
154C2×C4—4281no—
155C2×C4—4281no—
156C2×C4—4281no—
157C2×C4—4281no—
158C2×C4—2141no—
159C2×C4—2141no—
160C2×C4D4×D10711yescharacteristic
161C2×C4D4×D10711yescharacteristic
162C2×C4C2×C22⋊D10711yescharacteristic
163C8—41no—
164C8—4281no—
165C8—4281no—
166C22—4281no—
167C22—4281no—
168C22—4281no—
169C22—4281no—
170C22—4281no—
171C22—4281no—
172C22#1681207711yescharacteristic
173C4—21no—
174C4—42no—
175C4—81no—
176C4—4281no—
177C4—4281no—
178C4#1681213011yescharacteristic
179C4#1681213211yescharacteristic
180C4#1681213611yescharacteristic
181C4#1681214111yescharacteristic
182C2—8561no—
183C2—8561no—
184C2#2029277111yescharacteristic
185C2#2029278811yescharacteristic
186C2#2029280411yescharacteristic
subgroupG/H
centerC22#16812077
commutator, cosocleC42×C107C23
FrattiniC42C22×D107
Fitting#487×C107C2
socleC22×C107#120
prime radical#20293343C2
hypercenter#487D107
hypocenterC107#1646
LCSG ▷ C42×C107 ▷ C22×C107 ▷ C107
UCSC1 ◁ C22 ◁ C42 ◁ #487

Complements

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

NH ≅ G/Ntype
2. #20292904C2semidirect
3. #20292829C2semidirect
4. #20292376C2semidirect
5. #20292356C2semidirect
6. #20292356C2semidirect
7. #487×C107C2semidirect
94. C107#1646semidirect
96. #487D107semidirect

Maximal subgroups

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

subgroupindex
#202933432
#202929042
#202928292
#202923762
#202923562
#487×C1072
#1646107