Finite Group Databasebeta

← #28337528

Subgroups — #28337528

Order 13696.

394 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 394 conjugacy classes of subgroups — too many to draw. Only its 69 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#20293427C211yesmaximal, characteristic, complemented
2#20293138C212yesmaximal, complemented
3#20292643C212yesmaximal, complemented
4#20292384C211yesmaximal, characteristic, complemented
5#407×C107C211yesmaximal, characteristic, complemented
6C2×#13133818C2212yes—
7#16812142—22no—
8#16812137—22no—
9#16812131—22no—
10#16812092—22no—
11#16812088—22no—
12#16812083—22no—
13#16812078—22no—
14C4×C22⋊D107—24no—
15#16812068C2212yes—
16#16812035—24no—
17C23×C4×C107C2211yescharacteristic
18C2×M16×C107C2211yescharacteristic
19C2×M16×C107C2211yescharacteristic
20C22⋊C8×C107—22no—
21#13133818—22no—
22#13133818—22no—
23#13133818—22no—
24#13133818—22no—
25C2×Dic214D412yescomplemented
26C2×D428D412yescomplemented
27C2×C22⋊D107—24no—
28C2×C22⋊D107—22no—
29C2×C4×D107—22no—
30Dic428—22no—
31#13133807—24no—
32D856—22no—
33C4⋊Dic107—22no—
34Dic107⋊C4—24no—
35C22⋊Dic107—24no—
36C22⋊Dic107—22no—
37(C2×D107)⋊C4—24no—
38C4×Dic107D414yescomplemented
39C24×C107D411yescharacteristic
40C22×C4×C107—22no—
41C22×C4×C107—22no—
42C22×C4×C107—21no—
43C22×C4×C107—21no—
44C22×C4×C107D411yescharacteristic
45C22×C4×C107C2311yescharacteristic
46M16×C107—22no—
47M16×C107—22no—
48C2×C8×C107—21no—
49C2×C8×C107D412yescomplemented
50C23×C107—22no—
51C23×C107—21no—
52C23×C107—42no—
53C23×C107C2×D411yescharacteristic
54C22×D107—22no—
55C2×C4×C107—22no—
56C2×C4×C107—21no—
57C2×C4×C107—41no—
58C2×C4×C107—42no—
59C2×C4×C107—41no—
60C2×C4×C107C2×D412yes—
61C2×C4×C107C2×D412yes—
62C2×C4×C107C2×D411yescharacteristic
63C2×C4×C107#4111yescharacteristic
64C22⋊D107—48no—
65C22⋊D107—42no—
66C22⋊D107—42no—
67C2×Dic107—24no—
68C2×Dic107—22no—
69D428—22no—
70D428—22no—
71C4×D107—42no—
72C4×D107—42no—
73Dic214—22no—
74Dic214—22no—
75C8×C107—22no—
76C8×C107—41no—
77C22×C107—24no—
78C22×C107—22no—
79C22×C107—41no—
80C22×C107—42no—
81C22×C107—41no—
82C22×C107—41no—
83C22×C107#12012yes—
84C22×C107#12111yescharacteristic
85C2×D107—44no—
86C2×D107—42no—
87C4×C107—41no—
88C4×C107#12011yescharacteristic
89C4×C107#12112yes—
90C4×C107#12711yescharacteristic
91Dic107—44no—
92Dic107—42no—
93C2×C107—22no—
94C2×C107—21no—
95C2×C107—42no—
96C2×C107#39211yescharacteristic
97D107—82no—
98#2010—1071nomaximal, Sylow
99C107#201011yescharacteristic, complemented, Sylow
100#575—1071no—
101#525—1072no—
102#421—1072no—
103#407D10711yescharacteristic, complemented
104H(3,ℤ/4)—1071no—
105C2×#41—1072no—
106C23×C4C2×D10711yescharacteristic
107#137—2142no—
108AGL(1,ℤ/8)—2142no—
109#135—2142no—
110C2×M16C2×D10711yescharacteristic
111C2×M16C2×D10711yescharacteristic
112#123—2142no—
113C22⋊Q8—2142no—
114#121—2142no—
115#120—2142no—
116C4×D4—2144no—
117#117—1072no—
118#104—2144no—
119C22⋊C8—22no—
120C24D42811yescharacteristic
121#41—2142no—
122#41—2142no—
123#41—2142no—
124#41—2142no—
125C2×Q8—1072no—
126C2×D4—1072no—
127C2×D4—2144no—
128C2×D4—2142no—
129C22×C4—22no—
130C22×C4—22no—
131C22×C4—21no—
132C22×C4—21no—
133C22×C4—2142no—
134C22×C4D42811yescharacteristic
135C22×C4C22×D10711yescharacteristic
136Q16—2142no—
137SD16—2144no—
138D8—2142no—
139M16—22no—
140M16—22no—
141C2×C8—21no—
142C2×C8C22⋊D10712yescomplemented
143C4⋊C4—2144no—
144C4⋊C4—2142no—
145C22⋊C4—2144no—
146C22⋊C4—2144no—
147C22⋊C4—2142no—
148C42—1074no—
149C23—22no—
150C23—21no—
151C23—42no—
152C23—2142no—
153C23C2×D42811yescharacteristic
154Q8—2142no—
155Q8—2142no—
156D4—4288no—
157D4—4282no—
158D4—4282no—
159D4—2142no—
160D4—2142no—
161C2×C4—22no—
162C2×C4—21no—
163C2×C4—41no—
164C2×C4—42no—
165C2×C4—41no—
166C2×C4—4282no—
167C2×C4—4282no—
168C2×C4—2144no—
169C2×C4—2142no—
170C2×C4D4×D10712yes—
171C2×C4D4×D10712yes—
172C2×C4C2×C22⋊D10711yescharacteristic
173C2×C4#1313381811yescharacteristic
174C8—22no—
175C8—41no—
176C22—24no—
177C22—22no—
178C22—41no—
179C22—42no—
180C22—41no—
181C22—41no—
182C22—4284no—
183C22—4282no—
184C22#1681207912yes—
185C22#1681208311yescharacteristic
186C4—41no—
187C4—4284no—
188C4—4282no—
189C4#1681207711yescharacteristic
190C4#1681208212yes—
191C4#1681210511yescharacteristic
192C2—22no—
193C2—21no—
194C2—42no—
195C2—8562no—
196C2#2029253611yescharacteristic
subgroupG/H
centerC4#16812105
commutator, cosocleC22×C4×C107C23
FrattiniC22×C4C22×D107
Fitting#407×C107C2
socleC2×C107#392
hypercenter#407D107
hypocenterC107#2010
LCSG ▷ C22×C4×C107 ▷ C2×C107 ▷ C107
UCSC1 ◁ C4 ◁ C22×C4 ◁ #407

Complements

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

NH ≅ G/Ntype
1. #20293427C2semidirect
2. #20293138C2semidirect
3. #20292643C2semidirect
4. #20292384C2semidirect
5. #407×C107C2semidirect
25. C2×Dic214D4semidirect
26. C2×D428D4semidirect
38. C4×Dic107D4semidirect
49. C2×C8×C107D4semidirect
99. C107#2010semidirect
103. #407D107semidirect
142. C2×C8C22⋊D107semidirect

Maximal subgroups

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

subgroupindex
#202934272
#202931382
#202926432
#202923842
#407×C1072
#2010107