Finite Group Databasebeta

← #28335569

Subgroups — #28335569

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#20293347C211yesmaximal, characteristic, complemented
2#20292973C211yesmaximal, characteristic, complemented
3#20292824C211yesmaximal, characteristic, complemented
4#20292374C211yesmaximal, characteristic, complemented
5#20292357C211yesmaximal, characteristic, complemented
6D4⋊(C107⋊C8)C211yesmaximal, characteristic, complemented
7#459×C107C211yesmaximal, characteristic
8C2×#13133806—21no—
9#16812109C2211yescharacteristic
10#16812102—22no—
11#16812096—21no—
12#16812088—21no—
13C4×Dic214C2211yescharacteristic
14#16812074—21no—
15#16812068—21no—
16C4⋊(C107⋊C8)C2211yescharacteristic
17#16812030—22no—
18#16812030—21no—
19C4×C107⋊C8C2211yescharacteristic
20C2×D8×C107—21no—
21#127×C107C2211yescharacteristic
22C4×D4×C107C2211yescharacteristic
23C4⋊C8×C107C2211yescharacteristic
24#102×C107—21no—
25C2×Dic214—21no—
26C2×Dic214D411yescharacteristic
27#13133806—42no—
28C2×C107⋊C8—21no—
29C2×C107⋊C8—21no—
30C4⋊Dic107—21no—
31C4⋊Dic107D411yescharacteristic
32C4⋊Dic107D412yes—
33Dic107⋊C4—22no—
34Dic107⋊C4—21no—
35C22⋊Dic107—22no—
36C22⋊Dic107—22no—
37C4×Dic107—22no—
38C4×Dic107—21no—
39C2×D4×C107—21no—
40C2×D4×C107—21no—
41C2×D4×C107—21no—
42C2×D4×C107D411yescharacteristic
43C22×C4×C107—21no—
44D8×C107—42no—
45C2×C8×C107—21no—
46C4⋊C4×C107D411yescharacteristic
47C22⋊C4×C107—21no—
48C42×C107C2311yescharacteristic
49C23×C107—21no—
50C23×C107—41no—
51D4×C107—21no—
52D4×C107—21no—
53D4×C107—42no—
54D4×C107—41no—
55D4×C107—41no—
56D4×C107—41no—
57D4×C107—41no—
58C2×C4×C107—21no—
59C2×C4×C107—41no—
60C2×C4×C107—41no—
61C2×C4×C107C2×D411yescharacteristic
62C2×C4×C107C2×D411yescharacteristic
63C2×C4×C107C2×D411yescharacteristic
64C2×Dic107—21no—
65C2×Dic107—21no—
66C2×Dic107—22no—
67Dic214—21no—
68Dic214—21no—
69Dic214—41no—
70Dic214—41no—
71C8×C107—41no—
72C107⋊C8—41no—
73C107⋊C8—41no—
74C22×C107—41no—
75C22×C107—41no—
76C22×C107—41no—
77C22×C107—81no—
78C22×C107—81no—
79C22×C107—81no—
80C22×C107#12011yescharacteristic
81C4×C107—21no—
82C4×C107—41no—
83C4×C107#13511yescharacteristic
84C4×C107#13511yescharacteristic
85C4×C107AGL(1,ℤ/8)11yescharacteristic
86C4×C107AGL(1,ℤ/8)11yescharacteristic
87Dic107—41no—
88Dic107—42no—
89Dic107—41no—
90C2×C107—81no—
91C2×C107—161no—
92C2×C107#44911yescharacteristic
93C2×C107#44911yescharacteristic
94C2×C107#45411yescharacteristic
95#1628—1071nomaximal, Sylow
96C107#162811yescharacteristic, complemented, Sylow
97#556—1071no—
98#486—1071no—
99#460—1071no—
100#459D10711yescharacteristic
101#332—1071no—
102Q8⋊C8—1071no—
103D4⋊C8—1071no—
104C2×SD16—2141no—
105C2×D8—21no—
106C4⋊Q8—1071no—
107#127C2×D10711yescharacteristic
108#126—2142no—
109#124—2141no—
110C22⋊Q8—2141no—
111C4×Q8—1071no—
112C4×Q8—2141no—
113C4×D4C2×D10711yescharacteristic
114#117—2141no—
115C4⋊C8—1071no—
116C4⋊C8C2×D10711yescharacteristic
117#102—21no—
118#102—2141no—
119#102—2142no—
120C4×C8—1071no—
121C2×Q8—1071no—
122C2×Q8—2141no—
123C2×D4—21no—
124C2×D4—21no—
125C2×D4—21no—
126C2×D4C22⋊D10711yescharacteristic
127C22×C4—21no—
128SD16—4282no—
129D8—42no—
130C2×C8—21no—
131C2×C8—2141no—
132C2×C8—2141no—
133C4⋊C4—1071no—
134C4⋊C4—1072no—
135C4⋊C4—2142no—
136C4⋊C4—2141no—
137C4⋊C4—2141no—
138C4⋊C4C22⋊D10711yescharacteristic
139C22⋊C4—21no—
140C22⋊C4—2142no—
141C22⋊C4—2142no—
142C42—2142no—
143C42—2141no—
144C42C22×D10711yescharacteristic
145C23—21no—
146C23—41no—
147Q8—4281no—
148Q8—4281no—
149Q8—2141no—
150Q8—2141no—
151D4—21no—
152D4—21no—
153D4—42no—
154D4—41no—
155D4—41no—
156D4—41no—
157D4—41no—
158C2×C4—21no—
159C2×C4—41no—
160C2×C4—41no—
161C2×C4—2141no—
162C2×C4—2142no—
163C2×C4—2141no—
164C2×C4D4×D10711yescharacteristic
165C2×C4D4×D10711yescharacteristic
166C2×C4C2×C22⋊D10711yescharacteristic
167C8—41no—
168C8—4281no—
169C8—4281no—
170C22—41no—
171C22—41no—
172C22—41no—
173C22—81no—
174C22—81no—
175C22—81no—
176C22#1681207711yescharacteristic
177C4—21no—
178C4—41no—
179C4—4281no—
180C4—4282no—
181C4—4281no—
182C4#1681212811yescharacteristic
183C4#1681212911yescharacteristic
184C4#1681213311yescharacteristic
185C4#1681213511yescharacteristic
186C2—81no—
187C2—161no—
188C2#2029276911yescharacteristic
189C2#2029277011yescharacteristic
190C2#2029279811yescharacteristic
subgroupG/H
centerC22#16812077
commutator, cosocleC42×C107C23
FrattiniC42C22×D107
Fitting, prime radical#459×C107C2
socleC22×C107#120
hypercenter#459D107
hypocenterC107#1628
LCSG ▷ C42×C107 ▷ C22×C107 ▷ C107
UCSC1 ◁ C22 ◁ C42 ◁ #459

Complements

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

NH ≅ G/Ntype
1. #20293347C2semidirect
2. #20292973C2semidirect
3. #20292824C2semidirect
4. #20292374C2semidirect
5. #20292357C2semidirect
6. D4⋊(C107⋊C8)C2semidirect
96. C107#1628semidirect

Maximal subgroups

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

subgroupindex
#202933472
#202929732
#202928242
#202923742
#202923572
D4⋊(C107⋊C8)2
#459×C1072
#1628107