Finite Group Databasebeta

← #28335715

Subgroups — #28335715

Order 13696.

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

normal subgroups only

This group has 200 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#20293347C211yesmaximal, characteristic
2#20293030C211yesmaximal, characteristic, complemented
3#20292909C211yesmaximal, characteristic, complemented
4#20292374C211yesmaximal, characteristic, complemented
5#20292357C211yesmaximal, characteristic, complemented
6D4⋊(C107⋊C8)C211yesmaximal, characteristic
7#461×C107C211yesmaximal, characteristic
8#16812109C2211yescharacteristic
9#16812102—22no—
10#16812096—21no—
11#16812088—21no—
12C4×Dic214C2211yescharacteristic
13#16812074—21no—
14#16812068—21no—
15#16812042—22no—
16#16812040—21no—
17C4⋊(C107⋊C8)C2211yescharacteristic
18#16812032—21no—
19C4×C107⋊C8C2211yescharacteristic
20C2×SD16×C107—21no—
21C4⋊Q8×C107C2211yescharacteristic
22C4×D4×C107C2211yescharacteristic
23C4⋊C8×C107C2211yescharacteristic
24#103×C107—21no—
25C2×Dic214—21no—
26C2×Dic214D411yescharacteristic
27C2×C107⋊C8—21no—
28C2×C107⋊C8—21no—
29C4⋊Dic107—21no—
30C4⋊Dic107D411yescharacteristic
31C4⋊Dic107D412yes—
32Dic107⋊C4—22no—
33Dic107⋊C4—21no—
34C22⋊Dic107—22no—
35C22⋊Dic107—22no—
36C4×Dic107—22no—
37C4×Dic107—21no—
38C2×Q8×C107—21no—
39C2×D4×C107D411yescharacteristic
40C22×C4×C107—21no—
41SD16×C107—42no—
42C2×C8×C107—21no—
43C4⋊C4×C107—21no—
44C4⋊C4×C107—21no—
45C4⋊C4×C107D411yescharacteristic
46C22⋊C4×C107—21no—
47C42×C107C2311yescharacteristic
48C23×C107—21no—
49Q8×C107—41no—
50Q8×C107—41no—
51D4×C107—21no—
52D4×C107—21no—
53C2×C4×C107—21no—
54C2×C4×C107—41no—
55C2×C4×C107—41no—
56C2×C4×C107—41no—
57C2×C4×C107C2×D411yescharacteristic
58C2×C4×C107C2×D411yescharacteristic
59C2×C4×C107C2×D411yescharacteristic
60C2×Dic107—21no—
61C2×Dic107—21no—
62C2×Dic107—22no—
63Dic214—21no—
64Dic214—21no—
65Dic214—41no—
66Dic214—41no—
67C8×C107—41no—
68C107⋊C8—22no—
69C107⋊C8—41no—
70C22×C107—41no—
71C22×C107—41no—
72C22×C107—41no—
73C22×C107#12011yescharacteristic
74C4×C107—21no—
75C4×C107—41no—
76C4×C107—81no—
77C4×C107#13511yescharacteristic
78C4×C107#13511yescharacteristic
79C4×C107AGL(1,ℤ/8)11yescharacteristic
80C4×C107#13711yescharacteristic
81Dic107—42no—
82Dic107—41no—
83Dic107—41no—
84C2×C107—81no—
85C2×C107#44911yescharacteristic
86C2×C107#45211yescharacteristic
87C2×C107#45611yescharacteristic
88#1650—1071nomaximal, Sylow
89C107#165011yescharacteristic, complemented, Sylow
90#556—1071no—
91#500—1071no—
92#475—1071no—
93#461D10711yescharacteristic
94#332—1071no—
95Q8⋊C8—1071no—
96D4⋊C8—1071no—
97C2×SD16—21no—
98C4⋊Q8—1071no—
99C4⋊Q8C2×D10711yescharacteristic
100#126—2142no—
101#124—2141no—
102C22⋊Q8—2141no—
103C4×Q8—1071no—
104C4×Q8—2141no—
105C4×D4C2×D10711yescharacteristic
106#117—2141no—
107#107—2142no—
108#106—2141no—
109C4⋊C8—1071no—
110C4⋊C8C2×D10711yescharacteristic
111#103—21no—
112#103—2141no—
113C4×C8—1071no—
114C2×Q8—21no—
115C2×Q8—1071no—
116C2×Q8—2141no—
117C2×D4C22⋊D10711yescharacteristic
118C22×C4—21no—
119SD16—42no—
120C2×C8—21no—
121C2×C8—2141no—
122C2×C8—2141no—
123C4⋊C4—21no—
124C4⋊C4—21no—
125C4⋊C4—1071no—
126C4⋊C4—1072no—
127C4⋊C4—2142no—
128C4⋊C4—2141no—
129C4⋊C4—2141no—
130C4⋊C4C22⋊D10711yescharacteristic
131C22⋊C4—21no—
132C22⋊C4—2142no—
133C22⋊C4—2142no—
134C42—2142no—
135C42—2141no—
136C42C22×D10711yescharacteristic
137C23—21no—
138Q8—41no—
139Q8—41no—
140Q8—4281no—
141Q8—4281no—
142Q8—2141no—
143Q8—2141no—
144D4—21no—
145D4—21no—
146C2×C4—21no—
147C2×C4—41no—
148C2×C4—41no—
149C2×C4—41no—
150C2×C4—2141no—
151C2×C4—2142no—
152C2×C4—2141no—
153C2×C4D4×D10711yescharacteristic
154C2×C4D4×D10711yescharacteristic
155C2×C4C2×C22⋊D10711yescharacteristic
156C8—41no—
157C8—4281no—
158C8—2142no—
159C22—41no—
160C22—41no—
161C22—41no—
162C22#1681207711yescharacteristic
163C4—21no—
164C4—41no—
165C4—81no—
166C4—4282no—
167C4—4281no—
168C4—4281no—
169C4#1681212911yescharacteristic
170C4#1681213011yescharacteristic
171C4#1681213511yescharacteristic
172C4#1681213811yescharacteristic
173C2—81no—
174C2#2029277011yescharacteristic
175C2#2029278611yescharacteristic
176C2#2029280811yescharacteristic
subgroupG/H
centerC22#16812077
commutator, cosocleC42×C107C23
FrattiniC42C22×D107
Fitting#461×C107C2
socleC22×C107#120
prime radicalC2×D4×C107D4
hypercenter#461D107
hypocenterC107#1650
LCSG ▷ C42×C107 ▷ C22×C107 ▷ C107
UCSC1 ◁ C22 ◁ C42 ◁ #461

Complements

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

NH ≅ G/Ntype
2. #20293030C2semidirect
3. #20292909C2semidirect
4. #20292374C2semidirect
5. #20292357C2semidirect
89. C107#1650semidirect

Maximal subgroups

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

subgroupindex
#202933472
#202930302
#202929092
#202923742
#202923572
D4⋊(C107⋊C8)2
#461×C1072
#1650107