Finite Group Databasebeta

← #28403607

Subgroups — #28403607

Order 14464.

350 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 350 conjugacy classes of subgroups — too many to draw. Only its 125 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#20299327C211yesmaximal, characteristic, complemented
2#20299321C211yesmaximal, characteristic
3#20298992C212yesmaximal
4#20298978C211yesmaximal, characteristic, complemented
5#20298821C212yesmaximal
6#20298809C212yesmaximal, complemented
7#20298809C211yesmaximal, characteristic, complemented
8#20298804C211yesmaximal, characteristic
9#20298706C212yesmaximal, complemented
10C4×#14268636C211yesmaximal, characteristic
11#446×C113C211yesmaximal, characteristic, complemented
12C2×Dic452C2212yes—
13C2×Dic452C2212yes—
14C2×Dic452C2212yes—
15C2×#14268636C2211yescharacteristic
16C2×#14268636C2212yes—
17#16813622C2211yescharacteristic
18#16813622C2211yescharacteristic
19#16813622C2212yes—
20#16813617—22no—
21#16813613—21no—
22#16813613—22no—
23#16813610C2212yes—
24#16813598—21no—
25Q8×Dic113—21no—
26C4×Dic226C2212yes—
27C4×Dic226C2211yescharacteristic
28C4×Dic226C2212yes—
29C4×D452C2211yescharacteristic
30#16813580—21no—
31#16813554C2211yescharacteristic
32#16813547C2212yes—
33#16813547C2211yescharacteristic
34#16813547C2212yes—
35#16813544C2211yescharacteristic
36C4×Q8×C113C2211yescharacteristic
37C4⋊C8×C113C2211yescharacteristic
38C4⋊C8×C113C2212yes—
39#97×C113C2212yes—
40C4×C8×C113C2211yescharacteristic
41C2×Dic226C2312yes—
42C2×Dic226C2311yescharacteristic
43C2×Dic226C2312yes—
44C2×D452C2311yescharacteristic
45C2×C4×D113—21no—
46Dic452—24no—
47Dic452—42no—
48Dic452—42no—
49#14268636—22no—
50#14268636—42no—
51C4⋊Dic113—21no—
52C4⋊Dic113—22no—
53C4⋊Dic113—21no—
54C4⋊Dic113—22no—
55C4⋊Dic113—21no—
56C4⋊Dic113—21no—
57C4⋊Dic113C2311yescharacteristic
58C4⋊Dic113C2311yescharacteristic
59#14268626—22no—
60#14268626—22no—
61#14268626—21no—
62#14268624—22no—
63#14268624—21no—
64#14268624—22no—
65C4×Dic113—22no—
66C4×Dic113—22no—
67C4×Dic113—21no—
68C2×Q8×C113D411yescharacteristic
69C2×C8×C113C2312yes—
70C2×C8×C113C2311yescharacteristic
71C2×C8×C113C2311yescharacteristic
72C4⋊C4×C113D411yescharacteristic
73C4⋊C4×C113D412yes—
74C42×C113C2311yescharacteristic
75C42×C113C2312yes—
76C22×D113—21no—
77Q8×C113—22no—
78C2×C4×C113C2×D412yes—
79C2×C4×C113C2×D411yescharacteristic
80C2×C4×C113C2×D412yes—
81C2×C4×C113C2×D411yescharacteristic
82C2×C4×C113C2411yescharacteristic
83C2×Dic113—21no—
84C2×Dic113—21no—
85C2×Dic113—22no—
86C2×Dic113—21no—
87C2×Dic113—22no—
88D452—21no—
89D452—21no—
90C4×D113—42no—
91Dic226—21no—
92Dic226—22no—
93Dic226—22no—
94Dic226—22no—
95Dic226—22no—
96Dic226—21no—
97C8×C113—22no—
98C8×C113—21no—
99C8×C113#4112yes—
100C22×C113C22×D411yescharacteristic
101C2×D113—41no—
102C2×D113—41no—
103C2×D113—41no—
104C4×C113—22no—
105C4×C113—22no—
106C4×C113—21no—
107C4×C113#13712yes—
108C4×C113C2×#4111yescharacteristic
109C4×C113H(5,𝔽2)11yescharacteristic
110Dic113—41no—
111Dic113—42no—
112Dic113—42no—
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#494—1131no—
125#464—1132no—
126#462—1132no—
127#462—1131no—
128#461—1131no—
129#446D11311yescharacteristic, complemented
130#441—1132no—
131C4×SD16—1131no—
132C2×Q16—1132no—
133C2×Q16—1132no—
134C2×Q16—1132no—
135C2×SD16—1132no—
136C2×SD16—1131no—
137C4⋊Q8—1131no—
138C4⋊Q8—1131no—
139C4⋊Q8—1132no—
140#126—2262no—
141#125—2261no—
142#125—2262no—
143#124—1132no—
144C22⋊Q8—2261no—
145C4×Q8—1132no—
146C4×Q8—1131no—
147C4×Q8—1132no—
148C4×Q8—2261no—
149C4×Q8C2×D11311yescharacteristic
150C4×D4—1131no—
151#117—2261no—
152#106—1131no—
153C4⋊C8C2×D11311yescharacteristic
154C4⋊C8C2×D11312yes—
155#103—1131no—
156#103—1132no—
157#103—1132no—
158#102—1131no—
159#97C2×D11312yes—
160C4×C8C2×D11311yescharacteristic
161C2×Q8—1132no—
162C2×Q8—1131no—
163C2×Q8—1132no—
164C2×Q8D45211yescharacteristic
165C2×D4—1131no—
166C22×C4—2261no—
167Q16—4522no—
168Q16—4522no—
169Q16—2264no—
170SD16—4522no—
171SD16—2262no—
172C2×C8C22×D11311yescharacteristic
173C2×C8C22×D11312yes—
174C2×C8C22×D11311yescharacteristic
175C4⋊C4—1131no—
176C4⋊C4—1131no—
177C4⋊C4—2261no—
178C4⋊C4—2262no—
179C4⋊C4—2262no—
180C4⋊C4—2261no—
181C4⋊C4—2262no—
182C4⋊C4—2261no—
183C4⋊C4—2262no—
184C4⋊C4—2261no—
185C4⋊C4—2261no—
186C4⋊C4D45211yescharacteristic
187C4⋊C4D45212yes—
188C22⋊C4—2262no—
189C22⋊C4—2261no—
190C22⋊C4—2262no—
191C42—2262no—
192C42—2262no—
193C42—2261no—
194C42C22×D11311yescharacteristic
195C42C22×D11312yes—
196C23—2261no—
197Q8—22no—
198Q8—2261no—
199Q8—2262no—
200Q8—2262no—
201Q8—2262no—
202Q8—2262no—
203Q8—2261no—
204D4—2261no—
205D4—2261no—
206C2×C4—4522no—
207C2×C4—2261no—
208C2×C4—2261no—
209C2×C4—2262no—
210C2×C4—2261no—
211C2×C4—2262no—
212C2×C4C2×D45212yes—
213C2×C4C2×D45212yes—
214C2×C4C2×D45211yescharacteristic
215C2×C4C2×D45211yescharacteristic
216C2×C4C23×D11311yescharacteristic
217C8—22no—
218C8—21no—
219C8#1426864812yes—
220C22—4521no—
221C22—4521no—
222C22—4521no—
223C22C22×D45211yescharacteristic
224C4—22no—
225C4—22no—
226C4—21no—
227C4—4522no—
228C4—4521no—
229C4—4522no—
230C4—4521no—
231C4—4521no—
232C4#1681365512yes—
233C4C2×#1426864811yescharacteristic
234C4#1681366811yescharacteristic
235C2—9041no—
236C2#2029927011yescharacteristic
237C2C2×#1681365511yescharacteristic
238C2#2029941511yescharacteristic
subgroupG/H
centerC22C22×D452
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#446×C113C2
socleC22×C113C22×D4
prime radicalC2×D452C23
hypercenter#446D113
hypocenterC113#3398
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C4×Q8 ◁ #446

Complements

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

NH ≅ G/Ntype
1. #20299327C2semidirect
4. #20298978C2semidirect
6. #20298809C2semidirect
7. #20298809C2semidirect
9. #20298706C2semidirect
11. #446×C113C2semidirect
120. C113#3398semidirect
129. #446D113semidirect

Maximal subgroups

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

subgroupindex
#202993272
#202993212
#202989922
#202989782
#202988212
#202988092
#202988042
#202987062
C4×#142686362
#446×C1132
#3398113