Finite Group Databasebeta

← #28403609

Subgroups — #28403609

Order 14464.

350 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 350 conjugacy classes of subgroups — too many to draw. Only its 115 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#20299318C211yesmaximal, characteristic
3#20298989C212yesmaximal
4#20298977C211yesmaximal, characteristic, complemented
5#20298818C212yesmaximal
6#20298809C211yesmaximal, characteristic, complemented
7#20298807C212yesmaximal, complemented
8#20298725C211yesmaximal, characteristic, complemented
9#20298702C212yesmaximal, complemented
10C4×#14268635C211yesmaximal, characteristic
11#461×C113C211yesmaximal, characteristic
12C2×Dic452C2212yes—
13C2×#14268637C2212yes—
14C2×#14268637C2212yes—
15C2×#14268635C2211yescharacteristic
16#16813622C2211yescharacteristic
17#16813620C2212yes—
18#16813615—22no—
19#16813613—21no—
20#16813612—22no—
21#16813609C2212yes—
22#16813601—21no—
23Q8×Dic113C2212yes—
24C4×Dic226C2211yescharacteristic
25C4×Dic226C2211yescharacteristic
26#16813587—21no—
27#16813587C2212yes—
28#16813581—21no—
29#16813553C2211yescharacteristic
30#16813551C2212yes—
31#16813547C2212yes—
32#16813545C2211yescharacteristic
33#16813543C2211yescharacteristic
34#16813532C2212yes—
35C4×#11744751C2211yescharacteristic
36C2×SD16×C113C2212yes—
37C4⋊Q8×C113C2211yescharacteristic
38C4×D4×C113C2211yescharacteristic
39C4⋊C8×C113C2211yescharacteristic
40#103×C113C2212yes—
41C2×Dic226D411yescharacteristic
42C2×Dic226C2312yes—
43C2×Dic226C2311yescharacteristic
44Dic452—42no—
45#14268637—24no—
46#14268637—42no—
47#14268635—22no—
48C2×#11744751C2311yescharacteristic
49C2×#11744751C2311yescharacteristic
50C4⋊Dic113—21no—
51C4⋊Dic113—21no—
52C4⋊Dic113—22no—
53C4⋊Dic113D411yescharacteristic
54C4⋊Dic113C2311yescharacteristic
55#14268626—21no—
56#14268626—22no—
57#14268626—22no—
58#14268626—22no—
59#14268626D412yes—
60C22⋊Dic113—22no—
61C22⋊Dic113—22no—
62C4×Dic113—21no—
63C4×Dic113—22no—
64C4×Dic113—22no—
65C4×Dic113C2312yes—
66C2×Q8×C113C2312yes—
67C2×D4×C113C2311yescharacteristic
68C22×C4×C113—21no—
69SD16×C113—42no—
70C2×C8×C113C2312yes—
71C4⋊C4×C113—21no—
72C4⋊C4×C113—21no—
73C4⋊C4×C113C2311yescharacteristic
74C22⋊C4×C113—21no—
75C42×C113C2311yescharacteristic
76C23×C113—21no—
77Q8×C113—22no—
78Q8×C113—22no—
79D4×C113—21no—
80D4×C113—21no—
81C2×C4×C113—21no—
82C2×C4×C113—22no—
83C2×C4×C113—42no—
84C2×C4×C113C2×D411yescharacteristic
85C2×C4×C113C2×D411yescharacteristic
86C2×C4×C113C2411yescharacteristic
87C2×Dic113—21no—
88C2×Dic113—22no—
89C2×Dic113—21no—
90C2×Dic113C2×D412yes—
91C2×Dic113C2×D412yes—
92Dic226—22no—
93Dic226—21no—
94Dic226—22no—
95Dic226—22no—
96Dic226—21no—
97C8×C113—22no—
98#11744751—21no—
99#11744751#4112yes—
100C22×C113—41no—
101C22×C113—41no—
102C22×C113—41no—
103C22×C113C22×D411yescharacteristic
104C4×C113—21no—
105C4×C113—42no—
106C4×C113—41no—
107C4×C113#13712yes—
108C4×C113C2×#4111yescharacteristic
109C4×C113H(5,𝔽2)11yescharacteristic
110Dic113—22no—
111Dic113—22no—
112Dic113—41no—
113Dic113—42no—
114Dic113—41no—
115C2×C113—81no—
116C2×C113#55011yescharacteristic
117C2×C113C2×#13711yescharacteristic
118C2×C113#57811yescharacteristic
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—1131no—
127#462—1132no—
128#461D11311yescharacteristic
129#446—1131no—
130#441—1132no—
131C4×SD16—1131no—
132C2×Q16—1132no—
133C2×Q16—1132no—
134C2×Q16—1132no—
135C2×SD16—1131no—
136C2×SD16C2×D11312yes—
137C4⋊Q8—1132no—
138C4⋊Q8—1131no—
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×D4C2×D11311yescharacteristic
151#117—2261no—
152#106—1131no—
153C4⋊C8—1132no—
154C4⋊C8C2×D11311yescharacteristic
155#103—1132no—
156#103—1131no—
157#103C2×D11312yes—
158#102—1131no—
159#97—1132no—
160C4×C8—1131no—
161C2×Q8—1131no—
162C2×Q8—1132no—
163C2×Q8—1131no—
164C2×Q8C22×D11312yes—
165C2×D4C22×D11311yescharacteristic
166C22×C4—21no—
167Q16—4522no—
168Q16—4522no—
169Q16—2264no—
170SD16—42no—
171SD16—2262no—
172C2×C8—1131no—
173C2×C8—1131no—
174C2×C8C22×D11312yes—
175C4⋊C4—21no—
176C4⋊C4—21no—
177C4⋊C4—1131no—
178C4⋊C4—1132no—
179C4⋊C4—1131no—
180C4⋊C4—2262no—
181C4⋊C4—2262no—
182C4⋊C4—2262no—
183C4⋊C4—2262no—
184C4⋊C4—2261no—
185C4⋊C4—2261no—
186C4⋊C4—2261no—
187C4⋊C4C22×D11311yescharacteristic
188C22⋊C4—21no—
189C22⋊C4—2262no—
190C22⋊C4—2262no—
191C42—1132no—
192C42—2262no—
193C42—2262no—
194C42—2261no—
195C42C22×D11311yescharacteristic
196C23—21no—
197Q8—22no—
198Q8—22no—
199Q8—2261no—
200Q8—2262no—
201Q8—2261no—
202Q8—2262no—
203Q8—2262no—
204D4—21no—
205D4—21no—
206C2×C4—21no—
207C2×C4—22no—
208C2×C4—42no—
209C2×C4—1132no—
210C2×C4—1132no—
211C2×C4—2261no—
212C2×C4—2262no—
213C2×C4—2261no—
214C2×C4D4×D11311yescharacteristic
215C2×C4D4×D11311yescharacteristic
216C2×C4C23×D11311yescharacteristic
217C8—22no—
218C8—1132no—
219C8—2261no—
220C22—41no—
221C22—41no—
222C22—41no—
223C22C2×D4×D11311yescharacteristic
224C4—21no—
225C4—42no—
226C4—41no—
227C4—4522no—
228C4—4521no—
229C4—4521no—
230C4—2262no—
231C4—2262no—
232C4#1681365112yes—
233C4#41×D11311yescharacteristic
234C4#1681366711yescharacteristic
235C2—81no—
236C2#2029926611yescharacteristic
237C2C2×#1681365111yescharacteristic
238C2#2029941411yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#461×C113C2
socleC22×C113C22×D4
prime radicalC2×D4×C113C23
hypercenter#461D113
hypocenterC113#3398
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C42 ◁ #461

Complements

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

NH ≅ G/Ntype
1. #20299323C2semidirect
4. #20298977C2semidirect
6. #20298809C2semidirect
7. #20298807C2semidirect
8. #20298725C2semidirect
9. #20298702C2semidirect
120. C113#3398semidirect

Maximal subgroups

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

subgroupindex
#202993232
#202993182
#202989892
#202989772
#202988182
#202988092
#202988072
#202987252
#202987022
C4×#142686352
#461×C1132
#3398113