Finite Group Databasebeta

← #28346133

Subgroups — #28346133

Order 13696.

484 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 484 conjugacy classes of subgroups — too many to draw. Only its 141 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
1C2×#16812131C211yesmaximal, characteristic, complemented
2C2×#16812115C211yesmaximal, characteristic, complemented
3#20293208C212yesmaximal, complemented
4#20292874C214yesmaximal, complemented
5#20292869C212yesmaximal, complemented
6#20292864C212yesmaximal, complemented
7#20292626C212yesmaximal, complemented
8C2×#107×C107C211yesmaximal, characteristic, complemented
9C2×#13133818C2212yes—
10C2×#13133818C2211yescharacteristic
11#16812131—24no—
12C2×Dic428C2211yescharacteristic
13C2×#13133807C2212yes—
14C2×D856C2211yescharacteristic
15#16812115—24no—
16C2×#13133802C2211yescharacteristic
17C2×#13133801C2212yes—
18C2×C8×D107C2212yes—
19#16812089—22no—
20#16812089C2214yes—
21#16812084—22no—
22#16812084C2214yes—
23#16812083—24no—
24#16812032C2214yes—
25#16812029C2214yes—
26C22×C8×C107C2211yescharacteristic
27C2×C4⋊C4×C107C2212yes—
28#107×C107C2212yes—
29#107×C107C2212yes—
30#13133818—22no—
31#13133818—22no—
32#13133818—24no—
33#13133818—24no—
34C2×Dic214D411yescharacteristic
35C2×Dic214C2312yes—
36C2×D428—24no—
37C2×D428D411yescharacteristic
38C2×D428C2312yes—
39C2×C22⋊D107—22no—
40C2×C22⋊D107D412yes—
41C2×C4×D107—22no—
42C2×C4×D107C2312yes—
43Dic428—22no—
44#13133807—24no—
45D856—22no—
46#13133802—22no—
47#13133801—24no—
48C2×C107⋊C8C2312yes—
49C8×D107—24no—
50C4⋊Dic107—24no—
51(C2×D107)⋊C4—24no—
52(C2×D107)⋊C4—24no—
53C22×C4×C107—22no—
54C22×C4×C107C2311yescharacteristic
55C2×C8×C107D414yescomplemented
56C2×C8×C107C2311yescharacteristic
57C2×C8×C107C2311yescharacteristic
58C4⋊C4×C107—22no—
59C4⋊C4×C107C2314yes—
60C23×C107C2×D411yescharacteristic
61C22×D107—22no—
62C22×D107C2×D412yes—
63C2×C4×C107—24no—
64C2×C4×C107—82no—
65C2×C4×C107C2×D411yescharacteristic
66C2×C4×C107C2×D412yes—
67C2×C4×C107#4112yes—
68C2×C4×C107C2411yescharacteristic
69C22⋊D107—24no—
70C22⋊D107—44no—
71C2×Dic107—22no—
72C2×Dic107C2×D412yes—
73D428—22no—
74D428—22no—
75D428—22no—
76D428—84no—
77C4×D107—22no—
78C4×D107—22no—
79C4×D107—44no—
80Dic214—22no—
81Dic214—22no—
82Dic214—22no—
83C8×C107C2×D412yes—
84C8×C107C2×D412yes—
85C107⋊C8—22no—
86C22×C107—21no—
87C22×C107—21no—
88C22×C107#12112yes—
89C22×C107C22×D411yescharacteristic
90C2×D107—22no—
91C2×D107—22no—
92C2×D107—22no—
93C2×D107—42no—
94C2×D107—42no—
95C2×D107—42no—
96C4×C107—44no—
97C4×C107#12112yes—
98C4×C107C22×D411yescharacteristic
99C4×C107C2×#4111yescharacteristic
100Dic107—22no—
101Dic107—42no—
102C2×C107—22no—
103C2×C107C2×#12111yescharacteristic
104C2×C107#57611yescharacteristic
105C2×C107#57811yescharacteristic
106D107—42no—
107D107—82no—
108#3061—1071nomaximal, Sylow
109C107#306111yescharacteristic, complemented, Sylow
110C2×#135—1071no—
111C2×#131—1071no—
112#537—1072no—
113#468—1074no—
114#467—1072no—
115#466—1072no—
116C2×#107D10711yescharacteristic, complemented
117#417—1072no—
118C2×#41—1071no—
119C2×#41—1072no—
120#135—2144no—
121C2×Q16—1071no—
122C2×SD16—1072no—
123C2×D8—1071no—
124#131—2144no—
125C2×M16—1071no—
126C2×M16—1072no—
127C22×C8—1072no—
128C22×C8C2×D10711yescharacteristic
129C22⋊Q8—1074no—
130C22⋊Q8—2142no—
131#121—1074no—
132#121—2142no—
133#121—2144no—
134C2×C4⋊C4C2×D10712yes—
135#107C2×D10712yes—
136#107C2×D10712yes—
137#103—1074no—
138#102—1074no—
139#41—2144no—
140#41—2144no—
141#41—2142no—
142#41—2142no—
143C2×Q8—1071no—
144C2×Q8—1072no—
145C2×D4—1072no—
146C2×D4—1071no—
147C2×D4—1072no—
148C2×D4—2144no—
149C2×D4—2142no—
150C22×C4—22no—
151C22×C4—1072no—
152C22×C4—2142no—
153C22×C4C22×D10711yescharacteristic
154Q16—2142no—
155SD16—2144no—
156D8—2142no—
157M16—2142no—
158M16—2144no—
159C2×C8—1072no—
160C2×C8—2144no—
161C2×C8D42814yescomplemented
162C2×C8C22×D10711yescharacteristic
163C2×C8C22×D10711yescharacteristic
164C4⋊C4—22no—
165C4⋊C4—2144no—
166C4⋊C4C22×D10714yes—
167C22⋊C4—2144no—
168C22⋊C4—2144no—
169C23—1072no—
170C23—2142no—
171C23D4×D10711yescharacteristic
172Q8—2142no—
173Q8—2142no—
174Q8—2142no—
175D4—8564no—
176D4—4284no—
177D4—2144no—
178D4—2142no—
179D4—2142no—
180D4—2142no—
181C2×C4—24no—
182C2×C4—82no—
183C2×C4—1072no—
184C2×C4—4284no—
185C2×C4—2142no—
186C2×C4—2142no—
187C2×C4—2142no—
188C2×C4D4×D10711yescharacteristic
189C2×C4C2×D42812yes—
190C2×C4#1313381912yes—
191C2×C4C23×D10711yescharacteristic
192C8—2142no—
193C8C2×D42812yes—
194C8C2×D42812yes—
195C22—21no—
196C22—21no—
197C22—4282no—
198C22—4282no—
199C22—4282no—
200C22—2142no—
201C22—2142no—
202C22—2142no—
203C22#1681208412yes—
204C22C2×D4×D10711yescharacteristic
205C4—44no—
206C4—4282no—
207C4—2142no—
208C4#1681208412yes—
209C4C22×D42811yescharacteristic
210C4C2×#1313381911yescharacteristic
211C2—22no—
212C2—8562no—
213C2—4282no—
214C2C2×#1681208411yescharacteristic
215C2#2029342811yescharacteristic
216C2#2029344011yescharacteristic
subgroupG/H
centerC22C2×D4×D107
commutator, cosocleC2×C4×C107C24
FrattiniC2×C4C23×D107
FittingC2×#107×C107C2
socleC22×C107C22×D4
hypercenterC2×#107D107
hypocenterC107#3061
LCSG ▷ C2×C4×C107 ▷ C2×C107 ▷ C107
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#107

Complements

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

NH ≅ G/Ntype
1. C2×#16812131C2semidirect
2. C2×#16812115C2semidirect
3. #20293208C2semidirect
4. #20292874C2semidirect
5. #20292869C2semidirect
6. #20292864C2semidirect
7. #20292626C2semidirect
8. C2×#107×C107C2semidirect
55. C2×C8×C107D4semidirect
109. C107#3061semidirect
116. C2×#107D107semidirect
161. C2×C8D428semidirect

Maximal subgroups

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

subgroupindex
C2×#168121312
C2×#168121152
#202932082
#202928742
#202928692
#202928642
#202926262
C2×#107×C1072
#3061107