Finite Group Databasebeta

← #28349547

Subgroups — #28349547

Order 13696.

380 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 380 conjugacy classes of subgroups — too many to draw. Only its 113 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#20293360C212yesmaximal, complemented
2#20293015C212yesmaximal, complemented
3#20293011C211yesmaximal, characteristic, complemented
4#20292848C212yesmaximal, complemented
5#20292842C212yesmaximal, complemented
6#20292821C212yesmaximal, complemented
7#20292757C211yesmaximal, characteristic, complemented
8#20292726C212yesmaximal, complemented
9C4×D8×C107C211yesmaximal, characteristic, complemented
10C2×Dic428C2211yescharacteristic
11C2×#13133807C2212yes—
12C2×#13133806C2212yes—
13C2×D856C2211yescharacteristic
14C2×#13133803C2212yes—
15#16812105C2212yes—
16#16812097C2212yes—
17#16812096C2212yes—
18#16812095—22no—
19#16812092—22no—
20#16812091—22no—
21C4×Dic214C2211yescharacteristic
22#16812074C2212yes—
23#16812071C2212yes—
24C4×C22⋊D107—22no—
25C4⋊(C107⋊C8)C2211yescharacteristic
26Dic107⋊C8C2212yes—
27#16812032C2212yes—
28#16812029C2212yes—
29#16812019C2212yes—
30C2×D8×C107C2211yescharacteristic
31C4×D4×C107C2212yes—
32#107×C107C2211yescharacteristic
33#102×C107C2212yes—
34C4×C8×C107C2211yescharacteristic
35C2×Dic214D411yescharacteristic
36C2×Dic214C2312yes—
37C2×D428C2312yes—
38C2×C22⋊D107—22no—
39C2×C22⋊D107—22no—
40C2×C4×D107—22no—
41Dic428—41no—
42#13133807—24no—
43#13133806—42no—
44D856—41no—
45#13133803—42no—
46C2×C107⋊C8C2312yes—
47C4⋊Dic107D411yescharacteristic
48Dic107⋊C4—22no—
49Dic107⋊C4D412yes—
50C22⋊Dic107—22no—
51C22⋊Dic107—22no—
52(C2×D107)⋊C4—22no—
53(C2×D107)⋊C4—22no—
54(C2×D107)⋊C4—22no—
55C4×Dic107—22no—
56C4×Dic107C2312yes—
57C2×D4×C107C2312yes—
58C22×C4×C107—22no—
59D8×C107—22no—
60C2×C8×C107C2311yescharacteristic
61C2×C8×C107C2311yescharacteristic
62C4⋊C4×C107C2312yes—
63C22⋊C4×C107—22no—
64C42×C107C2311yescharacteristic
65C23×C107—22no—
66C22×D107—22no—
67D4×C107—22no—
68D4×C107—22no—
69C2×C4×C107—22no—
70C2×C4×C107—82no—
71C2×C4×C107C2×D411yescharacteristic
72C2×C4×C107C2×D411yescharacteristic
73C2×C4×C107C2411yescharacteristic
74C22⋊D107—44no—
75C22⋊D107—82no—
76C2×Dic107—22no—
77C2×Dic107C2×D412yes—
78C2×Dic107C2×D412yes—
79D428—22no—
80D428—22no—
81C4×D107—82no—
82Dic214—22no—
83Dic214—22no—
84Dic214—41no—
85C8×C107—21no—
86C8×C107#4112yes—
87C107⋊C8—22no—
88C22×C107—42no—
89C22×C107—42no—
90C22×C107—42no—
91C22×C107C22×D411yescharacteristic
92C2×D107—42no—
93C2×D107—42no—
94C2×D107—42no—
95C4×C107—21no—
96C4×C107—21no—
97C4×C107—42no—
98C4×C107C2×#4111yescharacteristic
99C4×C107H(5,𝔽2)11yescharacteristic
100Dic107—22no—
101Dic107—22no—
102Dic107—42no—
103C2×C107—82no—
104C2×C107#55011yescharacteristic
105C2×C107#57511yescharacteristic
106C2×C107#57611yescharacteristic
107D107—82no—
108#3403—1071nomaximal, Sylow
109C107#340311yescharacteristic, complemented, Sylow
110#559—1072no—
111#496—1072no—
112#495—1071no—
113#464—1072no—
114#463—1072no—
115#459—1072no—
116#446—1071no—
117#440—1072no—
118C4×D8D10711yescharacteristic, complemented
119C2×Q16—1071no—
120C2×SD16—1072no—
121C2×SD16—1072no—
122C2×D8—1072no—
123C2×D8—1071no—
124C2×D8C2×D10711yescharacteristic
125#127—1072no—
126#124—1072no—
127#124—1072no—
128#124—2142no—
129#123—2142no—
130#123—2142no—
131C4×Q8—1071no—
132C4×Q8—1072no—
133C4×D4—1072no—
134C4×D4—2142no—
135C4×D4C2×D10712yes—
136#107C2×D10711yescharacteristic
137C4⋊C8—1072no—
138C4⋊C8—1071no—
139#103—1072no—
140#102—1072no—
141#102C2×D10712yes—
142#97—1072no—
143C4×C8C2×D10711yescharacteristic
144C2×Q8—1071no—
145C2×Q8—1072no—
146C2×D4—1072no—
147C2×D4—2142no—
148C2×D4—2142no—
149C2×D4C22×D10712yes—
150C22×C4—22no—
151C22×C4—2142no—
152Q16—4281no—
153SD16—4282no—
154SD16—2144no—
155D8—22no—
156D8—4281no—
157D8—4282no—
158C2×C8—1072no—
159C2×C8C22×D10711yescharacteristic
160C2×C8C22×D10711yescharacteristic
161C4⋊C4—1072no—
162C4⋊C4—1071no—
163C4⋊C4—2142no—
164C4⋊C4C22×D10712yes—
165C22⋊C4—22no—
166C22⋊C4—2142no—
167C22⋊C4—2142no—
168C22⋊C4—2142no—
169C22⋊C4—2142no—
170C22⋊C4—2142no—
171C42—1072no—
172C42—2142no—
173C42C22×D10711yescharacteristic
174C23—22no—
175C23—2142no—
176Q8—4281no—
177Q8—2142no—
178Q8—2142no—
179D4—22no—
180D4—22no—
181D4—8562no—
182D4—4284no—
183D4—2142no—
184D4—2142no—
185C2×C4—22no—
186C2×C4—82no—
187C2×C4—8562no—
188C2×C4—1072no—
189C2×C4—1072no—
190C2×C4—2142no—
191C2×C4D4×D10711yescharacteristic
192C2×C4D4×D10711yescharacteristic
193C2×C4C23×D10711yescharacteristic
194C8—21no—
195C8—2142no—
196C8#1313381812yes—
197C22—42no—
198C22—42no—
199C22—42no—
200C22—4282no—
201C22—4282no—
202C22—4282no—
203C22C2×D4×D10711yescharacteristic
204C4—21no—
205C4—21no—
206C4—42no—
207C4—4282no—
208C4—2142no—
209C4—2142no—
210C4C2×#1313381811yescharacteristic
211C4#1681215511yescharacteristic
212C2—82no—
213C2—8562no—
214C2#2029329811yescharacteristic
215C2#2029342411yescharacteristic
216C2#2029342811yescharacteristic
subgroupG/H
centerC22C2×D4×D107
commutator, cosocleC2×C4×C107C24
FrattiniC2×C4C23×D107
FittingC4×D8×C107C2
socleC22×C107C22×D4
hypercenterC4×D8D107
hypocenterC107#3403
LCSG ▷ C2×C4×C107 ▷ C2×C107 ▷ C107
UCSC1 ◁ C22 ◁ C42 ◁ C4×D8

Complements

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

NH ≅ G/Ntype
1. #20293360C2semidirect
2. #20293015C2semidirect
3. #20293011C2semidirect
4. #20292848C2semidirect
5. #20292842C2semidirect
6. #20292821C2semidirect
7. #20292757C2semidirect
8. #20292726C2semidirect
9. C4×D8×C107C2semidirect
109. C107#3403semidirect
118. C4×D8D107semidirect

Maximal subgroups

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

subgroupindex
#202933602
#202930152
#202930112
#202928482
#202928422
#202928212
#202927572
#202927262
C4×D8×C1072
#3403107