Finite Group Databasebeta

← #28391642

Subgroups — #28391642

Order 14464.

394 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 394 conjugacy classes of subgroups — too many to draw. Only its 71 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#20299398C211yesmaximal, characteristic, complemented
2#20299110C212yesmaximal, complemented
3#20298616C212yesmaximal, complemented
4#20298561C211yesmaximal, characteristic, complemented
5H(3,ℤ/4)×C113C211yesmaximal, characteristic, complemented
6C2×#14268647C2212yes—
7C22×C4×D113C2211yescharacteristic
8#16813655—22no—
9#16813650—22no—
10#16813644—22no—
11C2×#14268631C2211yescharacteristic
12#16813606—22no—
13#16813602—22no—
14#16813597—22no—
15#16813592—22no—
16C4×D452—24no—
17#16813550—24no—
18#16813534—22no—
19C2×M16×C113C2211yescharacteristic
20#117×C113C2212yes—
21C23×D113D411yescharacteristic
22#14268647—22no—
23#14268647—22no—
24#14268647—22no—
25#14268647—22no—
26C2×Dic226D412yescomplemented
27C2×D452—24no—
28C2×D452D412yescomplemented
29C2×C22⋊D113—22no—
30C22×Dic113D411yescharacteristic
31C2×C4×D113—22no—
32C2×C4×D113—22no—
33C2×C4×D113—22no—
34C2×C4×D113—21no—
35C2×C4×D113—21no—
36Dic452—22no—
37#14268636—24no—
38D904—22no—
39#14268631—22no—
40C2×#11744751—21no—
41C4⋊Dic113—24no—
42#14268624—24no—
43#14268624—24no—
44C22×C4×C113C2311yescharacteristic
45M16×C113—22no—
46C2×C8×C113D412yescomplemented
47C4⋊C4×C113—22no—
48C22⋊C4×C113—22no—
49C42×C113D414yescomplemented
50C23×C113C2×D411yescharacteristic
51C22×D113—22no—
52C22×D113—21no—
53C22×D113—22no—
54C22×D113—42no—
55C2×C4×C113—24no—
56C2×C4×C113C2×D412yes—
57C2×C4×C113C2×D411yescharacteristic
58C2×C4×C113C2×D412yes—
59C2×C4×C113#4111yescharacteristic
60C22⋊D113—42no—
61C22⋊D113—42no—
62C2×Dic113—22no—
63C2×Dic113—22no—
64C2×Dic113—21no—
65D452—22no—
66D452—22no—
67D452—48no—
68C4×D113—41no—
69C4×D113—42no—
70C4×D113—42no—
71C4×D113—41no—
72C4×D113—42no—
73Dic226—22no—
74Dic226—22no—
75C8×C113—22no—
76#11744751—41no—
77C22×C113—41no—
78C22×C113#12012yes—
79C22×C113#12111yescharacteristic
80C2×D113—24no—
81C2×D113—22no—
82C2×D113—42no—
83C2×D113—41no—
84C2×D113—41no—
85C2×D113—44no—
86C2×D113—42no—
87C4×C113—44no—
88C4×C113#12011yescharacteristic
89C4×C113#12112yes—
90C4×C113#12711yescharacteristic
91Dic113—42no—
92Dic113—41no—
93C2×C113—22no—
94C2×C113—21no—
95C2×C113#39211yescharacteristic
96D113—42no—
97D113—82no—
98#2010—1131nomaximal, Sylow
99C113#201011yescharacteristic, complemented, Sylow
100#575—1131no—
101#525—1132no—
102#421—1132no—
103#407—1131no—
104H(3,ℤ/4)D11311yescharacteristic, complemented
105C2×#41—1132no—
106C23×C4—1131no—
107#137—2262no—
108AGL(1,ℤ/8)—2262no—
109#135—2262no—
110C2×M16—1131no—
111C2×M16C2×D11311yescharacteristic
112#123—2262no—
113C22⋊Q8—2262no—
114#121—2262no—
115#120—2262no—
116C4×D4—2264no—
117#117C2×D11312yes—
118#104—2264no—
119C22⋊C8—2262no—
120C24—1131no—
121#41—2262no—
122#41—2262no—
123#41—2262no—
124#41—2262no—
125C2×Q8—1132no—
126C2×D4—1132no—
127C2×D4—2264no—
128C2×D4—2262no—
129C22×C4—1131no—
130C22×C4—2262no—
131C22×C4—2261no—
132C22×C4—2262no—
133C22×C4—2262no—
134C22×C4—2261no—
135C22×C4C22×D11311yescharacteristic
136Q16—2262no—
137SD16—2264no—
138D8—2262no—
139M16—22no—
140M16—2262no—
141C2×C8—2261no—
142C2×C8D45212yescomplemented
143C4⋊C4—22no—
144C4⋊C4—2264no—
145C22⋊C4—22no—
146C22⋊C4—2264no—
147C22⋊C4—2264no—
148C42D45214yescomplemented
149C23—4522no—
150C23—2262no—
151C23—2262no—
152C23—2261no—
153C23D4×D11311yescharacteristic
154Q8—2262no—
155Q8—2262no—
156D4—4528no—
157D4—4522no—
158D4—4522no—
159D4—2262no—
160D4—2262no—
161C2×C4—24no—
162C2×C4—4521no—
163C2×C4—4522no—
164C2×C4—4522no—
165C2×C4—4521no—
166C2×C4—4522no—
167C2×C4—2262no—
168C2×C4—2262no—
169C2×C4—2261no—
170C2×C4D4×D11312yes—
171C2×C4C2×D45211yescharacteristic
172C2×C4C2×D45212yes—
173C2×C4#1426864811yescharacteristic
174C8—22no—
175C8—4521no—
176C22—41no—
177C22—4524no—
178C22—4522no—
179C22—4521no—
180C22—4522no—
181C22—4521no—
182C22—2264no—
183C22—2262no—
184C22#1681359212yes—
185C22#1681359711yescharacteristic
186C4—44no—
187C4—4521no—
188C4—4522no—
189C4#1681359211yescharacteristic
190C4#1681359712yes—
191C4#1681361911yescharacteristic
192C2—22no—
193C2—21no—
194C2—9042no—
195C2—4522no—
196C2#2029850811yescharacteristic
subgroupG/H
centerC4#16813619
commutator, cosocleC22×C4×C113C23
FrattiniC22×C4C22×D113
FittingH(3,ℤ/4)×C113C2
socleC2×C113#392
hypercenterH(3,ℤ/4)D113
hypocenterC113#2010
LCSG ▷ C22×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C4 ◁ C22×C4 ◁ H(3,ℤ/4)

Complements

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

NH ≅ G/Ntype
1. #20299398C2semidirect
2. #20299110C2semidirect
3. #20298616C2semidirect
4. #20298561C2semidirect
5. H(3,ℤ/4)×C113C2semidirect
26. C2×Dic226D4semidirect
28. C2×D452D4semidirect
46. C2×C8×C113D4semidirect
49. C42×C113D4semidirect
99. C113#2010semidirect
104. H(3,ℤ/4)D113semidirect
142. C2×C8D452semidirect
148. C42D452semidirect

Maximal subgroups

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

subgroupindex
#202993982
#202991102
#202986162
#202985612
H(3,ℤ/4)×C1132
#2010113