Finite Group Databasebeta

← #28347931

Subgroups — #28347931

Order 13696.

346 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 346 conjugacy classes of subgroups — too many to draw. Only its 109 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#20293244C212yesmaximal, complemented
2#20292915C212yesmaximal, complemented
3#20292911C212yesmaximal, complemented
4#20292885C211yesmaximal, characteristic, complemented
5#20292854C212yesmaximal, complemented
6#20292848C212yesmaximal, complemented
7#20292840C212yesmaximal, complemented
8#20292655C211yesmaximal, characteristic, complemented
9#469×C107C211yesmaximal, characteristic
10C2×Dic428C2211yescharacteristic
11C2×#13133806C2212yes—
12C22×C107⋊C8C2211yescharacteristic
13#16812108C2212yes—
14#16812102—22no—
15#16812096—22no—
16#16812096C2212yes—
17#16812090—22no—
18#16812088C2212yes—
19#16812086—22no—
20#16812074C2212yes—
21D4×Dic107C2212yes—
22#16812068C2211yescharacteristic
23#16812041C2211yescharacteristic
24#16812040C2212yes—
25Dic107⋊C8C2212yes—
26Dic107⋊C8C2212yes—
27#16812034C2212yes—
28#16812032C2212yes—
29#16812030C2212yes—
30C2×D8×C107C2211yescharacteristic
31C2×M16×C107C2211yescharacteristic
32#121×C107C2212yes—
33#106×C107C2211yescharacteristic
34#102×C107C2212yes—
35C2×Dic214—22no—
36C2×Dic214C2312yes—
37C22×Dic107—22no—
38Dic428—41no—
39#13133806—42no—
40C2×C107⋊C8—41no—
41C2×C107⋊C8C2312yes—
42C4⋊Dic107D412yes—
43C4⋊Dic107C2312yes—
44Dic107⋊C4—22no—
45Dic107⋊C4—22no—
46Dic107⋊C4—22no—
47C22⋊Dic107—22no—
48C22⋊Dic107—22no—
49C22⋊Dic107—22no—
50C22⋊Dic107—22no—
51C22⋊Dic107D411yescharacteristic
52C22⋊Dic107D411yescharacteristic
53C4×Dic107—22no—
54C4×Dic107C2312yes—
55C2×D4×C107—22no—
56C2×D4×C107C2312yes—
57C22×C4×C107C2311yescharacteristic
58D8×C107—41no—
59M16×C107—41no—
60C2×C8×C107C2311yescharacteristic
61C2×C8×C107C2311yescharacteristic
62C4⋊C4×C107C2312yes—
63C22⋊C4×C107—22no—
64C23×C107—22no—
65C23×C107C2×D411yescharacteristic
66D4×C107—22no—
67D4×C107—22no—
68D4×C107—82no—
69C2×C4×C107—21no—
70C2×C4×C107—21no—
71C2×C4×C107—22no—
72C2×C4×C107C2×D411yescharacteristic
73C2×C4×C107C2411yescharacteristic
74C2×Dic107—22no—
75C2×Dic107—22no—
76C2×Dic107—82no—
77C2×Dic107C2×D412yes—
78C2×Dic107C2×D412yes—
79Dic214—22no—
80Dic214—22no—
81Dic214—82no—
82C8×C107—21no—
83C8×C107—21no—
84C107⋊C8—22no—
85C22×C107—21no—
86C22×C107—22no—
87C22×C107—42no—
88C22×C107—42no—
89C22×C107—42no—
90C22×C107C22×D411yescharacteristic
91C4×C107—21no—
92C4×C107—42no—
93C4×C107H(5,𝔽2)11yescharacteristic
94C4×C1072−1+411yescharacteristic
95Dic107—22no—
96Dic107—22no—
97Dic107—42no—
98Dic107—42no—
99C2×C107—41no—
100C2×C107—82no—
101C2×C107#53711yescharacteristic
102C2×C107#57712yes—
103#3263—1071nomaximal, Sylow
104C107#326311yescharacteristic, complemented, Sylow
105#542—1072no—
106#476—1072no—
107#475—1072no—
108#470—1071no—
109#469D10711yescharacteristic
110#465—1072no—
111#464—1072no—
112#463—1072no—
113#424—1071no—
114C2×Q16—1071no—
115C2×SD16—1072no—
116C2×D8C2×D10711yescharacteristic
117C2×M16C2×D10711yescharacteristic
118C22×C8—1071no—
119C4⋊Q8—1072no—
120#126—2142no—
121#124—1072no—
122#124—2142no—
123#123—2142no—
124C22⋊Q8—1072no—
125C22⋊Q8—2142no—
126#121C2×D10712yes—
127C4×Q8—1072no—
128C4×D4—1072no—
129#117—1071no—
130#106—1071no—
131#106—1072no—
132#106C2×D10711yescharacteristic
133C4⋊C8—1072no—
134C4⋊C8—1072no—
135#103—1072no—
136#103—1072no—
137#102—1072no—
138#102C2×D10712yes—
139C2×Q8—1072no—
140C2×Q8—2142no—
141C2×D4—22no—
142C2×D4C22×D10712yes—
143C22×C4—2142no—
144C22×C4C22×D10711yescharacteristic
145Q16—4281no—
146SD16—4282no—
147D8—41no—
148M16—41no—
149C2×C8—1072no—
150C2×C8—4281no—
151C2×C8C22×D10711yescharacteristic
152C2×C8C22×D10711yescharacteristic
153C4⋊C4—1072no—
154C4⋊C4—1072no—
155C4⋊C4—2142no—
156C4⋊C4—2142no—
157C4⋊C4—2142no—
158C4⋊C4C22×D10712yes—
159C22⋊C4—22no—
160C22⋊C4—1071no—
161C22⋊C4—1071no—
162C22⋊C4—2142no—
163C22⋊C4—2142no—
164C22⋊C4—2142no—
165C22⋊C4—2142no—
166C42—1072no—
167C42—2142no—
168C23—22no—
169C23D4×D10711yescharacteristic
170Q8—8562no—
171Q8—2142no—
172Q8—2142no—
173D4—22no—
174D4—22no—
175D4—82no—
176C2×C4—21no—
177C2×C4—21no—
178C2×C4—22no—
179C2×C4—8562no—
180C2×C4—1072no—
181C2×C4—1072no—
182C2×C4—2142no—
183C2×C4—2142no—
184C2×C4D4×D10711yescharacteristic
185C2×C4C23×D10711yescharacteristic
186C8—21no—
187C8—21no—
188C8—2142no—
189C22—22no—
190C22—21no—
191C22—42no—
192C22—42no—
193C22—42no—
194C22C2×D4×D10711yescharacteristic
195C4—21no—
196C4—42no—
197C4—4282no—
198C4—4282no—
199C4—2142no—
200C4—2142no—
201C4#1681215411yescharacteristic
202C4#1681215611yescharacteristic
203C2—41no—
204C2—82no—
205C2#2029320411yescharacteristic
206C2#2029343712yes—
subgroupG/H
centerC22C2×D4×D107
commutator, cosocleC2×C4×C107C24
FrattiniC2×C4C23×D107
Fitting, prime radical#469×C107C2
socleC22×C107C22×D4
hypercenter#469D107
hypocenterC107#3263
LCSG ▷ C2×C4×C107 ▷ C2×C107 ▷ C107
UCSC1 ◁ C22 ◁ C22×C4 ◁ #469

Complements

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

NH ≅ G/Ntype
1. #20293244C2semidirect
2. #20292915C2semidirect
3. #20292911C2semidirect
4. #20292885C2semidirect
5. #20292854C2semidirect
6. #20292848C2semidirect
7. #20292840C2semidirect
8. #20292655C2semidirect
104. C107#3263semidirect

Maximal subgroups

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

subgroupindex
#202932442
#202929152
#202929112
#202928852
#202928542
#202928482
#202928402
#202926552
#469×C1072
#3263107