Finite Group Databasebeta

← #28403610

Subgroups — #28403610

Order 14464.

350 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 350 conjugacy classes of subgroups — too many to draw. Only its 117 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#20299323C211yesmaximal, characteristic, complemented
2#20299322C211yesmaximal, characteristic
3#20298991C212yesmaximal
4#20298822C212yesmaximal
5#20298806C212yesmaximal, complemented
6#20298805C211yesmaximal, characteristic, complemented
7#20298800C211yesmaximal, characteristic
8#20298728C211yesmaximal, characteristic, complemented
9#20298705C212yesmaximal, complemented
10C4×#14268636C211yesmaximal, characteristic
11#494×C113C211yesmaximal, characteristic, complemented
12C2×#14268637C2212yes—
13C2×#14268636C2211yescharacteristic
14C2×#14268634C2212yes—
15#16813620C2212yes—
16#16813617—22no—
17#16813613—21no—
18#16813612—22no—
19#16813611C2212yes—
20#16813602—21no—
21Q8×Dic113C2212yes—
22Q8×Dic113C2212yes—
23C4×Dic226C2211yescharacteristic
24C4×Dic226C2211yescharacteristic
25#16813587—21no—
26C4×D452C2211yescharacteristic
27#16813580—21no—
28#16813554C2211yescharacteristic
29C4⋊#11744751C2211yescharacteristic
30#16813551C2212yes—
31#16813547C2211yescharacteristic
32#16813546C2212yes—
33#16813546C2212yes—
34#16813544C2211yescharacteristic
35#16813532C2212yes—
36C2×Q16×C113C2212yes—
37C2×Q16×C113C2212yes—
38C4⋊Q8×C113C2211yescharacteristic
39C4⋊Q8×C113C2211yescharacteristic
40C4×C8×C113C2211yescharacteristic
41C2×Dic226D411yescharacteristic
42C2×Dic226C2311yescharacteristic
43C2×D452C2311yescharacteristic
44C2×C4×D113—21no—
45#14268637—42no—
46#14268636—22no—
47#14268634—42no—
48C2×#11744751C2312yes—
49C4⋊Dic113—22no—
50C4⋊Dic113—22no—
51C4⋊Dic113D411yescharacteristic
52C4⋊Dic113C2311yescharacteristic
53C4⋊Dic113C2311yescharacteristic
54#14268626—21no—
55#14268626—22no—
56#14268626—22no—
57#14268626D412yes—
58#14268624—21no—
59#14268624—22no—
60#14268624—22no—
61C4×Dic113—21no—
62C4×Dic113—22no—
63C4×Dic113—22no—
64C4×Dic113C2312yes—
65C2×Q8×C113C2312yes—
66C2×Q8×C113C2312yes—
67Q16×C113—24no—
68Q16×C113—42no—
69C2×C8×C113C2311yescharacteristic
70C2×C8×C113C2311yescharacteristic
71C4⋊C4×C113—21no—
72C4⋊C4×C113—21no—
73C4⋊C4×C113—21no—
74C4⋊C4×C113—21no—
75C42×C113C2311yescharacteristic
76C22×D113—21no—
77Q8×C113—22no—
78Q8×C113—22no—
79Q8×C113—22no—
80Q8×C113—22no—
81C2×C4×C113—22no—
82C2×C4×C113—22no—
83C2×C4×C113C2×D411yescharacteristic
84C2×C4×C113C2×D411yescharacteristic
85C2×C4×C113C2411yescharacteristic
86C2×Dic113—21no—
87C2×Dic113—21no—
88C2×Dic113—21no—
89C2×Dic113C2×D412yes—
90C2×Dic113C2×D412yes—
91D452—21no—
92D452—21no—
93C4×D113—42no—
94Dic226—22no—
95Dic226—21no—
96Dic226—21no—
97C8×C113—21no—
98C8×C113#4112yes—
99#11744751—22no—
100C22×C113C22×D411yescharacteristic
101C2×D113—41no—
102C2×D113—41no—
103C2×D113—41no—
104C4×C113—21no—
105C4×C113—42no—
106C4×C113—42no—
107C4×C113#13712yes—
108C4×C113C2×#4111yescharacteristic
109C4×C113H(5,𝔽2)11yescharacteristic
110Dic113—22no—
111Dic113—22no—
112Dic113—41no—
113Dic113—41no—
114Dic113—41no—
115C2×C113#55011yescharacteristic
116C2×C113C2×#13711yescharacteristic
117C2×C113#57811yescharacteristic
118D113—81no—
119#3398—1131nomaximal, Sylow
120C113#339811yescharacteristic, complemented, Sylow
121#557—1131no—
122#556—1131no—
123#497—1132no—
124#494D11311yescharacteristic, complemented
125#464—1132no—
126#462—1132no—
127#462—1131no—
128#461—1131no—
129#446—1131no—
130#441—1132no—
131C4×SD16—1131no—
132C2×Q16—1132no—
133C2×Q16C2×D11312yes—
134C2×Q16C2×D11312yes—
135C2×SD16—1132no—
136C2×SD16—1131no—
137C4⋊Q8—1132no—
138C4⋊Q8C2×D11311yescharacteristic
139C4⋊Q8C2×D11311yescharacteristic
140#126—2262no—
141#125—2262no—
142#125—2261no—
143#124—1132no—
144C22⋊Q8—2261no—
145C4×Q8—1131no—
146C4×Q8—1132no—
147C4×Q8—1132no—
148C4×Q8—1131no—
149C4×Q8—2261no—
150C4×D4—1131no—
151#117—2261no—
152#106—1131no—
153C4⋊C8—1132no—
154C4⋊C8—1131no—
155#103—1132no—
156#103—1132no—
157#103—1131no—
158#102—1131no—
159#97—1132no—
160C4×C8C2×D11311yescharacteristic
161C2×Q8—1131no—
162C2×Q8—1131no—
163C2×Q8C22×D11312yes—
164C2×Q8C22×D11312yes—
165C2×D4—1131no—
166C22×C4—2261no—
167Q16—24no—
168Q16—42no—
169Q16—4522no—
170SD16—4522no—
171SD16—2262no—
172C2×C8—1132no—
173C2×C8C22×D11311yescharacteristic
174C2×C8C22×D11311yescharacteristic
175C4⋊C4—21no—
176C4⋊C4—21no—
177C4⋊C4—21no—
178C4⋊C4—21no—
179C4⋊C4—1131no—
180C4⋊C4—1132no—
181C4⋊C4—1131no—
182C4⋊C4—1131no—
183C4⋊C4—2262no—
184C4⋊C4—2262no—
185C4⋊C4—2262no—
186C4⋊C4—2262no—
187C4⋊C4—2261no—
188C22⋊C4—2262no—
189C22⋊C4—2262no—
190C22⋊C4—2261no—
191C42—1132no—
192C42—2262no—
193C42—2262no—
194C42—2261no—
195C42C22×D11311yescharacteristic
196C23—2261no—
197Q8—22no—
198Q8—22no—
199Q8—22no—
200Q8—22no—
201Q8—2261no—
202Q8—2261no—
203Q8—2262no—
204D4—2261no—
205D4—2261no—
206C2×C4—22no—
207C2×C4—22no—
208C2×C4—1132no—
209C2×C4—1132no—
210C2×C4—4522no—
211C2×C4—2261no—
212C2×C4—2261no—
213C2×C4—2261no—
214C2×C4D4×D11311yescharacteristic
215C2×C4D4×D11311yescharacteristic
216C2×C4C23×D11311yescharacteristic
217C8—21no—
218C8—2262no—
219C8#1426864612yes—
220C22—4521no—
221C22—4521no—
222C22—4521no—
223C22C2×D4×D11311yescharacteristic
224C4—21no—
225C4—42no—
226C4—42no—
227C4—4521no—
228C4—4521no—
229C4—4521no—
230C4—2262no—
231C4—2262no—
232C4#1681365412yes—
233C4C2×#1426864611yescharacteristic
234C4#1681366711yescharacteristic
235C2—9041no—
236C2#2029926811yescharacteristic
237C2C2×#1681365411yescharacteristic
238C2#2029941111yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#494×C113C2
socleC22×C113C22×D4
prime radicalC2×D452C23
hypercenter#494D113
hypocenterC113#3398
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C42 ◁ #494

Complements

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

NH ≅ G/Ntype
1. #20299323C2semidirect
5. #20298806C2semidirect
6. #20298805C2semidirect
8. #20298728C2semidirect
9. #20298705C2semidirect
11. #494×C113C2semidirect
120. C113#3398semidirect
124. #494D113semidirect

Maximal subgroups

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

subgroupindex
#202993232
#202993222
#202989912
#202988222
#202988062
#202988052
#202988002
#202987282
#202987052
C4×#142686362
#494×C1132
#3398113