Finite Group Databasebeta

← #28335605

Subgroups — #28335605

Order 13696.

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

normal subgroups only

This group has 218 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#20293342C211yesmaximal, characteristic
2#20293006C211yesmaximal, characteristic, complemented
3#20292914C211yesmaximal, characteristic, complemented
4#20292375C211yesmaximal, characteristic, complemented
5D4⋊(C107⋊C8)C211yesmaximal, characteristic, complemented
6#20292354C211yesmaximal, characteristic, complemented
7#476×C107C211yesmaximal, characteristic, complemented
8C2×#13133808—22no—
9#16812109C2211yescharacteristic
10#16812095—22no—
11#16812083—21no—
12#16812080—21no—
13C4×D428C2211yescharacteristic
14#16812068—21no—
15#16812067—21no—
16#16812040—21no—
17C4⋊(C107⋊C8)C2211yescharacteristic
18#16812029—21no—
19C4×C107⋊C8C2211yescharacteristic
20C4⋊Q8×C107C2211yescharacteristic
21C4×D4×C107C2211yescharacteristic
22#106×C107—21no—
23C4⋊C8×C107C2211yescharacteristic
24#102×C107—21no—
25C2×Dic214D412yes—
26C2×D428D411yescharacteristic
27C2×C22⋊D107—22no—
28C2×C4×D107—21no—
29#13133808—44no—
30C2×C107⋊C8—21no—
31C2×C107⋊C8—21no—
32C4⋊Dic107—21no—
33C4⋊Dic107—21no—
34C4⋊Dic107D411yescharacteristic
35C22⋊Dic107—22no—
36(C2×D107)⋊C4—22no—
37(C2×D107)⋊C4—21no—
38C4×Dic107—22no—
39C2×Q8×C107—21no—
40C2×D4×C107D411yescharacteristic
41C22×C4×C107—21no—
42C2×C8×C107—21no—
43C4⋊C4×C107—21no—
44C4⋊C4×C107—21no—
45C4⋊C4×C107D411yescharacteristic
46C22⋊C4×C107—21no—
47C42×C107C2311yescharacteristic
48C23×C107—21no—
49C22×D107—21no—
50Q8×C107—42no—
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
60C22⋊D107—82no—
61C2×Dic107—21no—
62C2×Dic107—22no—
63D428—21no—
64D428—21no—
65C4×D107—41no—
66C4×D107—41no—
67Dic214—42no—
68C8×C107—41no—
69C107⋊C8—22no—
70C107⋊C8—41no—
71C22×C107—41no—
72C22×C107—41no—
73C22×C107—41no—
74C22×C107#12011yescharacteristic
75C2×D107—41no—
76C2×D107—41no—
77C2×D107—41no—
78C4×C107—21no—
79C4×C107—41no—
80C4×C107—81no—
81C4×C107#13511yescharacteristic
82C4×C107#13511yescharacteristic
83C4×C107#13711yescharacteristic
84C4×C107#13711yescharacteristic
85Dic107—41no—
86Dic107—42no—
87C2×C107—81no—
88C2×C107#45211yescharacteristic
89C2×C107#45211yescharacteristic
90C2×C107#45311yescharacteristic
91D107—81no—
92#1634—1071nomaximal, Sylow
93C107#163411yescharacteristic, complemented, Sylow
94#555—1071no—
95#494—1071no—
96#476—1071no—
97#476D10711yescharacteristic, complemented
98#333—1071no—
99D4⋊C8—1071no—
100D4⋊C8—1071no—
101C2×Q16—2142no—
102C4⋊Q8—1071no—
103C4⋊Q8C2×D10711yescharacteristic
104#124—2142no—
105#121—2141no—
106#121—2141no—
107C4×D4—1071no—
108C4×D4C2×D10711yescharacteristic
109#117—2141no—
110#117—2141no—
111#106—21no—
112#106—2141no—
113C4⋊C8—1071no—
114C4⋊C8C2×D10711yescharacteristic
115#102—21no—
116#102—2141no—
117C4×C8—1071no—
118C2×Q8—21no—
119C2×Q8—1072no—
120C2×D4—1071no—
121C2×D4—2142no—
122C2×D4C22⋊D10711yescharacteristic
123C22×C4—21no—
124C22×C4—2141no—
125Q16—4284no—
126C2×C8—21no—
127C2×C8—2141no—
128C2×C8—2141no—
129C4⋊C4—21no—
130C4⋊C4—21no—
131C4⋊C4—1071no—
132C4⋊C4—2141no—
133C4⋊C4—2141no—
134C4⋊C4C22⋊D10711yescharacteristic
135C22⋊C4—21no—
136C22⋊C4—2142no—
137C22⋊C4—2142no—
138C22⋊C4—2141no—
139C42—2142no—
140C42C22×D10711yescharacteristic
141C23—21no—
142C23—2141no—
143Q8—42no—
144Q8—4282no—
145D4—21no—
146D4—21no—
147D4—8562no—
148D4—2141no—
149D4—2141no—
150C2×C4—21no—
151C2×C4—41no—
152C2×C4—41no—
153C2×C4—41no—
154C2×C4—4281no—
155C2×C4—4281no—
156C2×C4—2141no—
157C2×C4—2142no—
158C2×C4D4×D10711yescharacteristic
159C2×C4D4×D10711yescharacteristic
160C2×C4C2×C22⋊D10711yescharacteristic
161C8—41no—
162C8—4281no—
163C8—2142no—
164C22—41no—
165C22—41no—
166C22—41no—
167C22—4281no—
168C22—4281no—
169C22—4281no—
170C22#1681207711yescharacteristic
171C4—21no—
172C4—41no—
173C4—81no—
174C4—4281no—
175C4—4282no—
176C4#1681212911yescharacteristic
177C4#1681213011yescharacteristic
178C4#1681213811yescharacteristic
179C4#1681214011yescharacteristic
180C2—81no—
181C2—8561no—
182C2#2029278611yescharacteristic
183C2#2029278711yescharacteristic
184C2#2029279311yescharacteristic
subgroupG/H
centerC22#16812077
commutator, cosocleC42×C107C23
FrattiniC42C22×D107
Fitting#476×C107C2
socleC22×C107#120
prime radical#20293342C2
hypercenter#476D107
hypocenterC107#1634
LCSG ▷ C42×C107 ▷ C22×C107 ▷ C107
UCSC1 ◁ C22 ◁ C42 ◁ #476

Complements

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

NH ≅ G/Ntype
2. #20293006C2semidirect
3. #20292914C2semidirect
4. #20292375C2semidirect
5. D4⋊(C107⋊C8)C2semidirect
6. #20292354C2semidirect
7. #476×C107C2semidirect
93. C107#1634semidirect
97. #476D107semidirect

Maximal subgroups

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

subgroupindex
#202933422
#202930062
#202929142
#202923752
D4⋊(C107⋊C8)2
#202923542
#476×C1072
#1634107