Finite Group Databasebeta

← #28389641

Subgroups — #28389641

Order 14464.

278 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 278 conjugacy classes of subgroups — too many to draw. Only its 57 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#20299270C211yesmaximal, characteristic, complemented
2#20298975C211yesmaximal, characteristic, complemented
3#20298798C211yesmaximal, characteristic, complemented
4#20298794C211yesmaximal, characteristic, complemented
5#20298341C211yesmaximal, characteristic, complemented
6#20298327C211yesmaximal, characteristic, complemented
7Q8⋊C8×C113C211yesmaximal, characteristic, complemented
8C2×#14268648—21no—
9C2×#14268634—21no—
10C2×D904—21no—
11C2×D904—22no—
12#16813619—21no—
13#16813619C2211yescharacteristic
14#16813619C2211yescharacteristic
15#16813597—22no—
16#16813597—21no—
17C4×D452—21no—
18C4×D452C2211yescharacteristic
19C4⋊#11744751C2211yescharacteristic
20#16813544—21no—
21#16813542—21no—
22C4×Q8×C113C2211yescharacteristic
23C4⋊C8×C113C2211yescharacteristic
24C4×C8×C113C2211yescharacteristic
25#14268648—42no—
26#14268648—42no—
27C2×D452—22no—
28C2×D452—21no—
29C2×D452—21no—
30C2×D452—21no—
31C2×D452—21no—
32C2×D452—21no—
33C2×D452—22no—
34C2×D452D411yescharacteristic
35C2×D452D412yes—
36C2×C4×D113—22no—
37C2×C4×D113—21no—
38#14268634—42no—
39D904—44no—
40D904—42no—
41C2×#11744751—21no—
42C4⋊Dic113D411yescharacteristic
43#14268624—22no—
44#14268624—21no—
45C2×Q8×C113D411yescharacteristic
46C2×C8×C113—21no—
47C2×C8×C113—21no—
48C4⋊C4×C113—21no—
49C4⋊C4×C113D411yescharacteristic
50C42×C113—21no—
51C42×C113C2311yescharacteristic
52C22×D113—21no—
53C22×D113—22no—
54C22×D113—41no—
55Q8×C113—21no—
56Q8×C113D812yescomplemented
57C2×C4×C113—21no—
58C2×C4×C113—21no—
59C2×C4×C113C2×D411yescharacteristic
60C2×C4×C113C2×D411yescharacteristic
61C2×C4×C113C2×D411yescharacteristic
62C2×Dic113—21no—
63D452—21no—
64D452—21no—
65D452—42no—
66D452—44no—
67D452—42no—
68D452—41no—
69D452—41no—
70D452—41no—
71D452—41no—
72D452—41no—
73D452—41no—
74D452—41no—
75D452—41no—
76D452—82no—
77C4×D113—44no—
78C4×D113—41no—
79C4×D113—41no—
80C8×C113—22no—
81C8×C113—41no—
82#11744751—41no—
83C22×C113#12011yescharacteristic
84C2×D113—42no—
85C2×D113—41no—
86C2×D113—41no—
87C2×D113—42no—
88C2×D113—42no—
89C2×D113—41no—
90C2×D113—81no—
91C2×D113—81no—
92C2×D113—81no—
93C4×C113—22no—
94C4×C113—21no—
95C4×C113—41no—
96C4×C113C2×D811yescharacteristic
97C4×C113#13511yescharacteristic
98C4×C113AGL(1,ℤ/8)11yescharacteristic
99C4×C113AGL(1,ℤ/8)11yescharacteristic
100Dic113—41no—
101C2×C113#44711yescharacteristic
102C2×C113#44911yescharacteristic
103C2×C113#45311yescharacteristic
104D113—81no—
105D113—82no—
106D113—161no—
107#1621—1131nomaximal, Sylow
108C113#162111yescharacteristic, complemented, Sylow
109#550—1131no—
110#493—1131no—
111#460—1131no—
112#459—1131no—
113#331—1131no—
114Q8⋊C8D11311yescharacteristic, complemented
115D4⋊C8—1131no—
116C2×#41—2261no—
117C2×SD16—2261no—
118C2×D8—2261no—
119C2×D8—2262no—
120#127—1131no—
121#127—1131no—
122#127—2261no—
123#121—2262no—
124#121—2261no—
125C4×Q8C2×D11311yescharacteristic
126C4×D4—1131no—
127C4×D4—2261no—
128C4⋊C8—1131no—
129C4⋊C8C2×D11311yescharacteristic
130#102—2261no—
131#102—2261no—
132C4×C8C2×D11311yescharacteristic
133#41—4522no—
134#41—4522no—
135C2×Q8D45211yescharacteristic
136C2×D4—1132no—
137C2×D4—1131no—
138C2×D4—2262no—
139C2×D4—2262no—
140C2×D4—2261no—
141C2×D4—2261no—
142C2×D4—2261no—
143C2×D4—2261no—
144C2×D4—2261no—
145C22×C4—2262no—
146C22×C4—2261no—
147SD16—4522no—
148D8—4524no—
149D8—4522no—
150C2×C8—21no—
151C2×C8—21no—
152C2×C8—2261no—
153C4⋊C4—21no—
154C4⋊C4—1131no—
155C4⋊C4D45211yescharacteristic
156C22⋊C4—2262no—
157C22⋊C4—2261no—
158C42—21no—
159C42C22×D11311yescharacteristic
160C23—4521no—
161C23—2261no—
162C23—2262no—
163Q8—21no—
164Q8D90412yescomplemented
165D4—9042no—
166D4—4522no—
167D4—4522no—
168D4—4524no—
169D4—4521no—
170D4—4521no—
171D4—4521no—
172D4—4521no—
173D4—4521no—
174D4—4521no—
175D4—4521no—
176D4—4521no—
177D4—2261no—
178D4—2261no—
179C2×C4—21no—
180C2×C4—21no—
181C2×C4—4524no—
182C2×C4—4521no—
183C2×C4—4521no—
184C2×C4—2261no—
185C2×C4D4×D11311yescharacteristic
186C2×C4D4×D11311yescharacteristic
187C2×C4C2×D45211yescharacteristic
188C8—22no—
189C8—41no—
190C8—4521no—
191C22—9041no—
192C22—9041no—
193C22—9041no—
194C22—4521no—
195C22—4522no—
196C22—4522no—
197C22—4521no—
198C22—4522no—
199C22—4521no—
200C22#1681359211yescharacteristic
201C4—21no—
202C4—22no—
203C4—41no—
204C4—4521no—
205C4C2×D90411yescharacteristic
206C4#1681364511yescharacteristic
207C4#1681364911yescharacteristic
208C4#1681365011yescharacteristic
209C2—18081no—
210C2—9041no—
211C2—9042no—
212C2#2029873411yescharacteristic
213C2#2029874611yescharacteristic
214C2#2029876711yescharacteristic
subgroupG/H
centerC22#16813592
commutator, cosocleC42×C113C23
FrattiniC42C22×D113
FittingQ8⋊C8×C113C2
socleC22×C113#120
hypercenterQ8⋊C8D113
hypocenterC113#1621
LCSG ▷ C42×C113 ▷ C22×C113 ▷ C113
UCSC1 ◁ C22 ◁ C42 ◁ Q8⋊C8

Complements

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

NH ≅ G/Ntype
1. #20299270C2semidirect
2. #20298975C2semidirect
3. #20298798C2semidirect
4. #20298794C2semidirect
5. #20298341C2semidirect
6. #20298327C2semidirect
7. Q8⋊C8×C113C2semidirect
56. Q8×C113D8semidirect
108. C113#1621semidirect
114. Q8⋊C8D113semidirect
164. Q8D904semidirect

Maximal subgroups

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

subgroupindex
#202992702
#202989752
#202987982
#202987942
#202983412
#202983272
Q8⋊C8×C1132
#1621113