Finite Group Databasebeta

← #28335568

Subgroups — #28335568

Order 13696.

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

normal subgroups only

This group has 216 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#20293351C211yesmaximal, characteristic, complemented
2#20292824C211yesmaximal, characteristic, complemented
3#20292819C211yesmaximal, characteristic
4#20292373C211yesmaximal, characteristic, complemented
5#20292359C211yesmaximal, characteristic, complemented
6#20292356C211yesmaximal, characteristic, complemented
7#486×C107C211yesmaximal, characteristic, complemented
8C2×#13133806—21no—
9C2×#13133803—21no—
10#16812104—22no—
11#16812098—21no—
12#16812089—21no—
13Q8×Dic107—21no—
14C4×Dic214C2211yescharacteristic
15C4×D428C2211yescharacteristic
16#16812067—21no—
17C4⋊(C107⋊C8)C2211yescharacteristic
18C4⋊(C107⋊C8)C2211yescharacteristic
19#16812030—21no—
20#16812030—21no—
21C4⋊Q8×C107C2211yescharacteristic
22#127×C107C2211yescharacteristic
23#102×C107—22no—
24C4×C8×C107C2211yescharacteristic
25C2×Dic214D411yescharacteristic
26C2×D428D411yescharacteristic
27C2×C4×D107—21no—
28#13133806—42no—
29#13133803—42no—
30C2×C107⋊C8—21no—
31C2×C107⋊C8—21no—
32C4⋊Dic107—22no—
33C4⋊Dic107D411yescharacteristic
34C4⋊Dic107D411yescharacteristic
35Dic107⋊C4—21no—
36(C2×D107)⋊C4—22no—
37(C2×D107)⋊C4—22no—
38(C2×D107)⋊C4—21no—
39C4×Dic107—22no—
40C4×Dic107—21no—
41C2×Q8×C107—21no—
42C2×D4×C107—21no—
43C2×D4×C107—21no—
44C2×D4×C107—21no—
45C2×C8×C107—21no—
46C4⋊C4×C107—21no—
47C4⋊C4×C107D412yes—
48C42×C107C2311yescharacteristic
49C23×C107—41no—
50C22×D107—21no—
51Q8×C107—41no—
52Q8×C107—41no—
53D4×C107—42no—
54D4×C107—41no—
55D4×C107—41no—
56D4×C107—41no—
57D4×C107—41no—
58C2×C4×C107—22no—
59C2×C4×C107C2×D411yescharacteristic
60C2×C4×C107C2×D411yescharacteristic
61C2×C4×C107C2×D411yescharacteristic
62C2×Dic107—21no—
63C2×Dic107—21no—
64C2×Dic107—21no—
65D428—21no—
66D428—21no—
67C4×D107—41no—
68C4×D107—41no—
69Dic214—21no—
70Dic214—21no—
71C8×C107—41no—
72C107⋊C8—41no—
73C107⋊C8—41no—
74C22×C107—81no—
75C22×C107—81no—
76C22×C107—81no—
77C22×C107#12011yescharacteristic
78C2×D107—41no—
79C2×D107—41no—
80C2×D107—41no—
81C4×C107—21no—
82C4×C107—42no—
83C4×C107#13511yescharacteristic
84C4×C107#13511yescharacteristic
85C4×C107AGL(1,ℤ/8)11yescharacteristic
86C4×C107AGL(1,ℤ/8)11yescharacteristic
87Dic107—41no—
88Dic107—41no—
89Dic107—41no—
90C2×C107—161no—
91C2×C107#44911yescharacteristic
92C2×C107#44911yescharacteristic
93C2×C107#45411yescharacteristic
94D107—81no—
95#1628—1071nomaximal, Sylow
96C107#162811yescharacteristic, complemented, Sylow
97#556—1071no—
98#486D10711yescharacteristic, complemented
99#460—1071no—
100#459—1071no—
101#332—1071no—
102Q8⋊C8—1071no—
103D4⋊C8—1071no—
104C2×SD16—2141no—
105C2×D8—2141no—
106C4⋊Q8C2×D10711yescharacteristic
107#127C2×D10711yescharacteristic
108#126—2142no—
109#124—2141no—
110C22⋊Q8—2141no—
111C4×Q8—1071no—
112C4×Q8—2141no—
113C4×D4—1071no—
114#117—2141no—
115C4⋊C8—1071no—
116C4⋊C8—1071no—
117#102—22no—
118#102—2141no—
119#102—2141no—
120C4×C8C2×D10711yescharacteristic
121C2×Q8—21no—
122C2×Q8—1071no—
123C2×D4—21no—
124C2×D4—21no—
125C2×D4—21no—
126C2×D4—1071no—
127C22×C4—2141no—
128SD16—4282no—
129D8—4282no—
130C2×C8—21no—
131C2×C8—2141no—
132C2×C8—2141no—
133C4⋊C4—21no—
134C4⋊C4—1071no—
135C4⋊C4—1071no—
136C4⋊C4—2142no—
137C4⋊C4—2141no—
138C4⋊C4C22⋊D10712yes—
139C22⋊C4—2142no—
140C22⋊C4—2142no—
141C22⋊C4—2141no—
142C42—2142no—
143C42—2141no—
144C42C22×D10711yescharacteristic
145C23—41no—
146C23—2141no—
147Q8—41no—
148Q8—41no—
149Q8—2141no—
150Q8—2141no—
151D4—42no—
152D4—41no—
153D4—41no—
154D4—41no—
155D4—41no—
156D4—2141no—
157D4—2141no—
158C2×C4—22no—
159C2×C4—4281no—
160C2×C4—4281no—
161C2×C4—2141no—
162C2×C4—2141no—
163C2×C4—2141no—
164C2×C4D4×D10711yescharacteristic
165C2×C4D4×D10711yescharacteristic
166C2×C4C2×C22⋊D10711yescharacteristic
167C8—41no—
168C8—4281no—
169C8—4281no—
170C22—81no—
171C22—81no—
172C22—81no—
173C22—4281no—
174C22—4281no—
175C22—4281no—
176C22#1681207711yescharacteristic
177C4—21no—
178C4—42no—
179C4—4281no—
180C4—4281no—
181C4—4281no—
182C4#1681212811yescharacteristic
183C4#1681213011yescharacteristic
184C4#1681213311yescharacteristic
185C4#1681213611yescharacteristic
186C2—161no—
187C2—8561no—
188C2#2029276911yescharacteristic
189C2#2029277111yescharacteristic
190C2#2029279911yescharacteristic
subgroupG/H
centerC22#16812077
commutator, cosocleC42×C107C23
FrattiniC42C22×D107
Fitting#486×C107C2
socleC22×C107#120
prime radical#20292819C2
hypercenter#486D107
hypocenterC107#1628
LCSG ▷ C42×C107 ▷ C22×C107 ▷ C107
UCSC1 ◁ C22 ◁ C42 ◁ #486

Complements

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

NH ≅ G/Ntype
1. #20293351C2semidirect
2. #20292824C2semidirect
4. #20292373C2semidirect
5. #20292359C2semidirect
6. #20292356C2semidirect
7. #486×C107C2semidirect
96. C107#1628semidirect
98. #486D107semidirect

Maximal subgroups

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

subgroupindex
#202933512
#202928242
#202928192
#202923732
#202923592
#202923562
#486×C1072
#1628107