Finite Group Databasebeta

← #28401630

Subgroups — #28401630

Order 14464.

388 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 388 conjugacy classes of subgroups — too many to draw. Only its 109 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#20299202C211yesmaximal, characteristic, complemented
2#20299168C211yesmaximal, characteristic, complemented
3#20298970C211yesmaximal, characteristic, complemented
4#20298967C211yesmaximal, characteristic, complemented
5#20298952C211yesmaximal, characteristic, complemented
6#20298811C212yesmaximal, complemented
7#20298801C212yesmaximal, complemented
8#20298740C212yesmaximal, complemented
9#20298735C212yesmaximal, complemented
10#20298660C211yesmaximal, characteristic, complemented
11#496×C113C211yesmaximal, characteristic, complemented
12C2×#14268646C2211yescharacteristic
13C2×Q8×D113C2211yescharacteristic
14C2×#14268635C2212yes—
15C2×#14268635C2212yes—
16#16813622C2211yescharacteristic
17#16813620C2211yescharacteristic
18#16813614C2211yescharacteristic
19#16813609C2211yescharacteristic
20#16813604—22no—
21#16813603—22no—
22#16813599—22no—
23#16813594—22no—
24#16813593C2212yes—
25D4×Dic113C2212yes—
26#16813579C2211yescharacteristic
27#16813551C2212yes—
28#16813547C2212yes—
29#16813547C2212yes—
30#16813546C2212yes—
31#16813543C2212yes—
32#16813534C2212yes—
33C4×#11744751C2211yescharacteristic
34C2×SD16×C113C2212yes—
35C2×D8×C113C2212yes—
36#127×C113C2211yescharacteristic
37#124×C113C2211yescharacteristic
38#97×C113C2211yescharacteristic
39#14268646—42no—
40C2×Dic226—21no—
41C2×Dic226C2311yescharacteristic
42C2×Dic226C2311yescharacteristic
43Q8×D113—42no—
44C2×C22⋊D113—21no—
45C2×C22⋊D113—22no—
46C22×Dic113—21no—
47C22×Dic113—22no—
48C2×C4×D113—21no—
49C2×C4×D113C2311yescharacteristic
50#14268635—42no—
51#14268635—42no—
52C2×#11744751C2312yes—
53C4⋊Dic113—22no—
54C4⋊Dic113C2312yes—
55#14268626—22no—
56#14268626—22no—
57#14268626D412yes—
58C22⋊Dic113—22no—
59C22⋊Dic113—22no—
60C22⋊Dic113—22no—
61#14268624D412yes—
62C4×Dic113C2311yescharacteristic
63C2×Q8×C113C2311yescharacteristic
64C2×D4×C113—22no—
65C2×D4×C113C2312yes—
66C2×D4×C113C2311yescharacteristic
67SD16×C113—42no—
68D8×C113—42no—
69C2×C8×C113C2312yes—
70C22⋊C4×C113—22no—
71C42×C113C2311yescharacteristic
72C23×C113—21no—
73C23×C113—22no—
74C22×D113C2×D411yescharacteristic
75Q8×C113—22no—
76D4×C113—22no—
77D4×C113—22no—
78D4×C113—22no—
79D4×C113—82no—
80C2×C4×C113—21no—
81C2×C4×C113C2×D412yes—
82C2×C4×C113C2411yescharacteristic
83C22⋊D113—42no—
84C22⋊D113—82no—
85C2×Dic113—22no—
86C2×Dic113—21no—
87C2×Dic113—21no—
88C2×Dic113—42no—
89C2×Dic113—82no—
90C2×Dic113C2×D412yes—
91C2×Dic113C2×D411yescharacteristic
92C4×D113—22no—
93C4×D113—42no—
94Dic226—22no—
95Dic226—22no—
96Dic226—42no—
97C8×C113—22no—
98#11744751—22no—
99C22×C113—41no—
100C22×C113—42no—
101C22×C113—42no—
102C22×C113—42no—
103C22×C113—42no—
104C22×C113C22×D411yescharacteristic
105C2×D113—21no—
106C2×D113—22no—
107C4×C113—22no—
108C4×C113—41no—
109C4×C113H(5,𝔽2)12yes—
110Dic113—21no—
111Dic113—22no—
112Dic113—41no—
113Dic113—41no—
114Dic113—42no—
115C2×C113—81no—
116C2×C113—82no—
117C2×C113#53511yescharacteristic
118C2×C113#57712yes—
119D113—41no—
120#3221—1131nomaximal, Sylow
121C113#322111yescharacteristic, complemented, Sylow
122#540—1131no—
123#536—1131no—
124#496D11311yescharacteristic, complemented
125#492—1131no—
126#491—1131no—
127#488—1131no—
128#463—1132no—
129#461—1132no—
130#449—1132no—
131#448—1132no—
132#433—1131no—
133C2×#41—1131no—
134C22×Q8—1131no—
135C2×SD16—1132no—
136C2×SD16—1132no—
137C2×SD16C2×D11312yes—
138C2×D8C2×D11312yes—
139C4⋊Q8—1131no—
140C4⋊Q8—1131no—
141#127C2×D11311yescharacteristic
142#125—1131no—
143#124—1131no—
144#124C2×D11311yescharacteristic
145#123—2262no—
146#123—2262no—
147C22⋊Q8—2262no—
148#121—1132no—
149#121—2262no—
150C4×D4—1132no—
151#117—1131no—
152C4⋊C8—1132no—
153#103—1132no—
154#103—1132no—
155#103—1132no—
156#102—1132no—
157C22⋊C8—1132no—
158#97C2×D11311yescharacteristic
159C4×C8—1131no—
160#41—4522no—
161C2×Q8—1131no—
162C2×Q8—1131no—
163C2×Q8—4522no—
164C2×Q8—2261no—
165C2×Q8C22×D11311yescharacteristic
166C2×D4—22no—
167C2×D4—2262no—
168C2×D4—2261no—
169C2×D4C22×D11311yescharacteristic
170C2×D4C22×D11312yes—
171C22×C4—1131no—
172C22×C4—2261no—
173C22×C4—2262no—
174C22×C4—2261no—
175SD16—42no—
176SD16—4522no—
177SD16—4522no—
178D8—42no—
179C2×C8—1132no—
180C2×C8C22×D11312yes—
181C4⋊C4—1132no—
182C4⋊C4—1132no—
183C4⋊C4—2262no—
184C4⋊C4—2262no—
185C4⋊C4—2262no—
186C22⋊C4—22no—
187C22⋊C4—1132no—
188C22⋊C4—2262no—
189C22⋊C4—2262no—
190C22⋊C4—2262no—
191C42—1131no—
192C42C22×D11311yescharacteristic
193C23—21no—
194C23—22no—
195C23—1131no—
196Q8—22no—
197Q8—4522no—
198Q8—2262no—
199Q8—2262no—
200D4—22no—
201D4—22no—
202D4—22no—
203D4—82no—
204D4—9042no—
205D4—4522no—
206C2×C4—21no—
207C2×C4—1132no—
208C2×C4—1131no—
209C2×C4—9042no—
210C2×C4—4522no—
211C2×C4—4522no—
212C2×C4—2262no—
213C2×C4—2261no—
214C2×C4—2261no—
215C2×C4—2262no—
216C2×C4D4×D11312yes—
217C2×C4C23×D11311yescharacteristic
218C8—22no—
219C8—2262no—
220C22—42no—
221C22—42no—
222C22—42no—
223C22—41no—
224C22—42no—
225C22—2262no—
226C22—2261no—
227C22C2×D4×D11311yescharacteristic
228C4—22no—
229C4—41no—
230C4—4522no—
231C4—4521no—
232C4—4521no—
233C4—2262no—
234C4—2261no—
235C4#1681366712yes—
236C2—82no—
237C2—81no—
238C2—4521no—
239C2#2029916111yescharacteristic
240C2#2029940812yes—
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#496×C113C2
socleC22×C113C22×D4
hypercenter#496D113
hypocenterC113#3221
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C42 ◁ #496

Complements

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

NH ≅ G/Ntype
1. #20299202C2semidirect
2. #20299168C2semidirect
3. #20298970C2semidirect
4. #20298967C2semidirect
5. #20298952C2semidirect
6. #20298811C2semidirect
7. #20298801C2semidirect
8. #20298740C2semidirect
9. #20298735C2semidirect
10. #20298660C2semidirect
11. #496×C113C2semidirect
121. C113#3221semidirect
124. #496D113semidirect

Maximal subgroups

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

subgroupindex
#202992022
#202991682
#202989702
#202989672
#202989522
#202988112
#202988012
#202987402
#202987352
#202986602
#496×C1132
#3221113