Finite Group Databasebeta

← #28348266

Subgroups — #28348266

Order 13696.

444 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 444 conjugacy classes of subgroups — too many to draw. Only its 125 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#20293444C212yesmaximal, complemented
2#20293441C212yesmaximal, complemented
3#20293007C211yesmaximal, characteristic, complemented
4#20292903C212yesmaximal, complemented
5#20292902C212yesmaximal, complemented
6#20292811C214yesmaximal, complemented
7#20292745C211yesmaximal, characteristic, complemented
8#443×C107C211yesmaximal, characteristic, complemented
9#16812156C2214yes—
10#16812142—24no—
11#16812142C2214yes—
12#16812139C2214yes—
13#16812138—24no—
14#16812131—22no—
15#16812131C2211yescharacteristic
16#16812128—22no—
17C2×Dic428—22no—
18C2×Dic428C2212yes—
19C2×Dic428C2212yes—
20Q16×D107—22no—
21#16812115C2212yes—
22#16812109C2212yes—
23#16812045C2211yescharacteristic
24#16812037C2212yes—
25#16812027C2214yes—
26#135×C107C2211yescharacteristic
27#131×C107C2212yes—
28#108×C107C2211yescharacteristic
29#104×C107C2212yes—
30C4×C8×C107C2211yescharacteristic
31#13133818—24no—
32#13133818C2312yes—
33#13133817—24no—
34#13133817—44no—
35C2×Dic214—24no—
36C2×Dic214C2314yes—
37Q8×D107—24no—
38Dic428—24no—
39Dic428—22no—
40Dic428—22no—
41Dic428—22no—
42Dic428—22no—
43Dic428D411yescharacteristic
44#13133808—24no—
45#13133807—24no—
46#13133807D412yes—
47#13133806—24no—
48D856D411yescharacteristic
49#13133802C2312yes—
50#13133801—22no—
51C8×D107—22no—
52C4⋊Dic107—42no—
53#41×C107C2312yes—
54Q16×C107D411yescharacteristic
55SD16×C107D412yes—
56D8×C107D411yescharacteristic
57M16×C107—22no—
58M16×C107C2312yes—
59C2×C8×C107—22no—
60C2×C8×C107C2311yescharacteristic
61C2×C8×C107C2311yescharacteristic
62C42×C107C2311yescharacteristic
63Q8×C107C2×D412yes—
64D4×C107—22no—
65D4×C107C2×D412yes—
66C2×C4×C107—21no—
67C2×C4×C107—22no—
68C2×C4×C107C2411yescharacteristic
69C22⋊D107—22no—
70C22⋊D107—44no—
71C2×Dic107—24no—
72C2×Dic107—44no—
73D428C2×D412yes—
74C4×D107—22no—
75C4×D107—44no—
76Dic214—24no—
77Dic214—24no—
78Dic214—44no—
79Dic214C2×D412yes—
80C8×C107—22no—
81C8×C107C2×D411yescharacteristic
82C8×C107C2×D411yescharacteristic
83C8×C107C2×D411yescharacteristic
84C8×C107C2×D411yescharacteristic
85C107⋊C8—22no—
86C22×C107—22no—
87C22×C107H(5,𝔽2)11yescharacteristic
88C2×D107—22no—
89C4×C107—22no—
90C4×C107—22no—
91C4×C107C22×D411yescharacteristic
92C4×C107C22×D411yescharacteristic
93Dic107—22no—
94Dic107—44no—
95C2×C107—21no—
96C2×C107—42no—
97C2×C107D4211yescharacteristic
98D107—42no—
99#3293—1071nomaximal, Sylow
100C107#329311yescharacteristic, complemented, Sylow
101#578—1072no—
102#578—1072no—
103#494—1071no—
104#473—1072no—
105#473—1072no—
106#456—1074no—
107#443—1071no—
108#443D10711yescharacteristic, complemented
1092−1+4—1074no—
110#137—1074no—
111#137—1074no—
112#137—2144no—
113#137—2144no—
114#135—1071no—
115#135—2142no—
116#135—2142no—
117#135C2×D10711yescharacteristic
118C2×Q16—1072no—
119C2×Q16—1072no—
120C2×Q16—2142no—
121C2×Q16—2142no—
122#131—1072no—
123#131C2×D10712yes—
124C4⋊Q8—1072no—
125#108—1071no—
126#108C2×D10711yescharacteristic
127#104—1072no—
128#104C2×D10712yes—
129#101—1074no—
130C4×C8C2×D10711yescharacteristic
131#41—1072no—
132#41—4284no—
133#41—2144no—
134#41—2144no—
135#41C22×D10712yes—
136C2×Q8—1074no—
137C2×Q8—2144no—
138C2×Q8—2144no—
139Q16—1071no—
140Q16—2144no—
141Q16—2144no—
142Q16—2142no—
143Q16—2142no—
144Q16—2142no—
145Q16—2142no—
146Q16D42811yescharacteristic
147SD16—1072no—
148SD16—2144no—
149SD16—2144no—
150SD16D42812yes—
151D8—1071no—
152D8D42811yescharacteristic
153M16—22no—
154M16—1072no—
155M16—2142no—
156M16C22×D10712yes—
157C2×C8—22no—
158C2×C8—2142no—
159C2×C8C22×D10711yescharacteristic
160C2×C8C22×D10711yescharacteristic
161C4⋊C4—4282no—
162C42C22×D10711yescharacteristic
163Q8—1072no—
164Q8—4284no—
165Q8—2144no—
166Q8—2144no—
167Q8C2×D42812yes—
168D4—22no—
169D4—1072no—
170D4—4284no—
171D4—2142no—
172D4C2×D42812yes—
173C2×C4—21no—
174C2×C4—22no—
175C2×C4—4284no—
176C2×C4—4284no—
177C2×C4—2144no—
178C2×C4—2142no—
179C2×C4C23×D10711yescharacteristic
180C8—22no—
181C8—2142no—
182C8D4×D10711yescharacteristic
183C8D4×D10711yescharacteristic
184C8C2×D42811yescharacteristic
185C8C2×D42811yescharacteristic
186C22—22no—
187C22—2142no—
188C22#1681215511yescharacteristic
189C4—22no—
190C4—22no—
191C4—4284no—
192C4—2142no—
193C4C2×D4×D10711yescharacteristic
194C4C22×D42811yescharacteristic
195C2—21no—
196C2—42no—
197C2—4282no—
198C2D4×D42811yescharacteristic
subgroupG/H
centerC2D4×D428
commutator, cosocleC2×C4×C107C24
FrattiniC2×C4C23×D107
Fitting#443×C107C2
socleC2×C107D42
hypercenter#443D107
hypocenterC107#3293
LCSG ▷ C2×C4×C107 ▷ C2×C107 ▷ C107
UCSC1 ◁ C2 ◁ C2×C4 ◁ #443

Complements

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

NH ≅ G/Ntype
1. #20293444C2semidirect
2. #20293441C2semidirect
3. #20293007C2semidirect
4. #20292903C2semidirect
5. #20292902C2semidirect
6. #20292811C2semidirect
7. #20292745C2semidirect
8. #443×C107C2semidirect
100. C107#3293semidirect
108. #443D107semidirect

Maximal subgroups

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

subgroupindex
#202934442
#202934412
#202930072
#202929032
#202929022
#202928112
#202927452
#443×C1072
#3293107