Finite Group Databasebeta

← #28402442

Subgroups — #28402442

Order 14464.

420 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

normal subgroups only

This group has 420 conjugacy classes of subgroups — too many to draw. Only its 123 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#20299263C211yesmaximal, characteristic, complemented
2#20299253C211yesmaximal, characteristic
3#20298948C211yesmaximal, characteristic, complemented
4#20298927C212yesmaximal, complemented
5#20298884C211yesmaximal, characteristic, complemented
6#20298824C212yesmaximal, complemented
7#20298735C212yesmaximal, complemented
8C4×#14268635C211yesmaximal, characteristic, complemented
9#20298663C211yesmaximal, characteristic, complemented
10#103×D113C212yesmaximal, complemented
11#461×C113C211yesmaximal, characteristic, complemented
12C2×#14268647—21no—
13C2×Q8×D113C2212yes—
14C2×#14268635C2211yescharacteristic
15C2×C8×D113C2212yes—
16#16813622C2211yescharacteristic
17#16813621—21no—
18#16813604—22no—
19#16813601—21no—
20#16813600—22no—
21#16813598C2212yes—
22#16813593C2212yes—
23C4×Dic226C2211yescharacteristic
24C4×D452C2211yescharacteristic
25#16813584—21no—
26C4⋊C4×D113C2212yes—
27#16813554C2212yes—
28#16813553C2211yescharacteristic
29#16813547C2212yes—
30#16813546C2212yes—
31#16813546C2212yes—
32#16813545C2211yescharacteristic
33#16813543C2211yescharacteristic
34#16813534C2212yes—
35C4×#11744751C2211yescharacteristic
36C2×SD16×C113C2212yes—
37C4⋊Q8×C113C2211yescharacteristic
38C4×D4×C113C2211yescharacteristic
39C4⋊C8×C113C2211yescharacteristic
40#103×C113C2212yes—
41#14268647—44no—
42C2×Dic226—21no—
43C2×Dic226—22no—
44C2×Dic226C2311yescharacteristic
45Q8×D113—24no—
46Q8×D113—42no—
47C2×D452D411yescharacteristic
48C2×C22⋊D113—22no—
49C2×C4×D113—22no—
50C2×C4×D113—22no—
51C2×C4×D113C2312yes—
52#14268635—22no—
53C2×#11744751C2311yescharacteristic
54C2×#11744751C2311yescharacteristic
55C8×D113—42no—
56C4⋊Dic113—21no—
57C4⋊Dic113D411yescharacteristic
58C4⋊Dic113C2312yes—
59C4⋊Dic113C2311yescharacteristic
60#14268626—21no—
61#14268626—22no—
62#14268626—22no—
63C22⋊Dic113—22no—
64#14268624—22no—
65#14268624D412yes—
66C4×Dic113—21no—
67C2×Q8×C113C2312yes—
68C2×D4×C113C2311yescharacteristic
69C22×C4×C113—21no—
70SD16×C113—42no—
71C2×C8×C113C2312yes—
72C4⋊C4×C113—21no—
73C4⋊C4×C113—21no—
74C4⋊C4×C113C2311yescharacteristic
75C22⋊C4×C113—21no—
76C42×C113C2311yescharacteristic
77C23×C113—21no—
78C22×D113C2×D412yes—
79Q8×C113—22no—
80Q8×C113—22no—
81D4×C113—21no—
82D4×C113—21no—
83C2×C4×C113—21no—
84C2×C4×C113—22no—
85C2×C4×C113—42no—
86C2×C4×C113C2×D411yescharacteristic
87C2×C4×C113C2×D411yescharacteristic
88C2×C4×C113C2411yescharacteristic
89C22⋊D113—44no—
90C2×Dic113—21no—
91C2×Dic113—21no—
92C2×Dic113—22no—
93C2×Dic113C2×D412yes—
94D452SD1614yescomplemented
95C4×D113—22no—
96C4×D113—22no—
97C4×D113—44no—
98C4×D113—44no—
99Dic226—21no—
100Dic226—44no—
101Dic226—42no—
102Dic226#4112yescomplemented
103C8×C113—22no—
104#11744751—21no—
105#11744751—21no—
106C22×C113—41no—
107C22×C113—41no—
108C22×C113—41no—
109C22×C113C22×D411yescharacteristic
110C2×D113—22no—
111C2×D113—22no—
112C2×D113C2×SD1614yes—
113C4×C113—21no—
114C4×C113—42no—
115C4×C113—41no—
116C4×C113C2×SD1612yes—
117C4×C113C2×#4111yescharacteristic
118C4×C113H(5,𝔽2)11yescharacteristic
119Dic113—22no—
120Dic113—22no—
121Dic113—42no—
122Dic113—41no—
123C2×C113—81no—
124C2×C113#54611yescharacteristic
125C2×C113C22×SD1611yescharacteristic
126C2×C113#57811yescharacteristic
127D113—24no—
128#3298—1131nomaximal, Sylow
129C113#329811yescharacteristic, complemented, Sylow
130D4×Q8—1131no—
131#547—1131no—
132#487—1131no—
133#483—1132no—
134#475—1131no—
135#465—1132no—
136#461D11311yescharacteristic, complemented
137#448—1132no—
138C4×SD16—1131no—
139C8×D4—1131no—
140C2×#103—1132no—
141C2×#41—2261no—
142C22×Q8—1132no—
143C2×SD16—1131no—
144C2×SD16C2×D11312yes—
145C22×C8—1132no—
146C4⋊Q8—1131no—
147C4⋊Q8—2261no—
148C4⋊Q8C2×D11311yescharacteristic
149#123—2262no—
150C22⋊Q8—1132no—
151C22⋊Q8—2262no—
152C22⋊Q8—2261no—
153#121—1132no—
154C4×Q8—1131no—
155C4×D4—1131no—
156C4×D4—2261no—
157C4×D4C2×D11311yescharacteristic
158C2×C4⋊C4—1132no—
159#106—1132no—
160#106—1131no—
161C4⋊C8C2×D11311yescharacteristic
162#103—1132no—
163#103—1132no—
164#103—1132no—
165#103—1131no—
166#103C2×D11312yes—
167#102—1131no—
168C22⋊C8—1132no—
169C4×C8—1131no—
170#41—4524no—
171C2×Q8—1131no—
172C2×Q8—4522no—
173C2×Q8—2262no—
174C2×Q8—2264no—
175C2×Q8—2261no—
176C2×Q8C22×D11312yes—
177C2×D4—1131no—
178C2×D4—2262no—
179C2×D4C22×D11311yescharacteristic
180C22×C4—21no—
181C22×C4—1132no—
182C22×C4—2262no—
183C22×C4—2262no—
184SD16—42no—
185SD16—2262no—
186C2×C8—1131no—
187C2×C8—1131no—
188C2×C8—4522no—
189C2×C8C22×D11312yes—
190C4⋊C4—21no—
191C4⋊C4—21no—
192C4⋊C4—1131no—
193C4⋊C4—1131no—
194C4⋊C4—1132no—
195C4⋊C4—2262no—
196C4⋊C4—2262no—
197C4⋊C4—2261no—
198C4⋊C4—2261no—
199C4⋊C4C22×D11311yescharacteristic
200C22⋊C4—21no—
201C22⋊C4—1132no—
202C22⋊C4—2262no—
203C22⋊C4—2262no—
204C42—2261no—
205C42C22×D11311yescharacteristic
206C23—21no—
207C23—1132no—
208Q8—22no—
209Q8—22no—
210Q8—1132no—
211Q8—4524no—
212Q8—4522no—
213Q8—2261no—
214D4—21no—
215D4—21no—
216D4—1134no—
217D4—4524no—
218C2×C4—21no—
219C2×C4—22no—
220C2×C4—42no—
221C2×C4—1132no—
222C2×C4—4524no—
223C2×C4—4524no—
224C2×C4—2261no—
225C2×C4—2262no—
226C2×C4—2261no—
227C2×C4—2262no—
228C2×C4—2262no—
229C2×C4D4×D11311yescharacteristic
230C2×C4D4×D11311yescharacteristic
231C2×C4C23×D11311yescharacteristic
232C8—22no—
233C8—2261no—
234C8—2261no—
235C22—41no—
236C22—41no—
237C22—41no—
238C22—1134no—
239C22—2262no—
240C22—2262no—
241C22C2×D4×D11311yescharacteristic
242C4—21no—
243C4—41no—
244C4—42no—
245C4—4522no—
246C4—4521no—
247C4—2262no—
248C4—2262no—
249C4SD16×D11312yes—
250C4#41×D11311yescharacteristic
251C4#1681366711yescharacteristic
252C2—81no—
253C2—2264no—
254C2#2029924511yescharacteristic
255C2C2×SD16×D11311yescharacteristic
256C2#2029941411yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#461×C113C2
socleC22×C113C22×D4
prime radical#20299253C2
hypercenter#461D113
hypocenterC113#3298
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. #20299263C2semidirect
3. #20298948C2semidirect
4. #20298927C2semidirect
5. #20298884C2semidirect
6. #20298824C2semidirect
7. #20298735C2semidirect
8. C4×#14268635C2semidirect
9. #20298663C2semidirect
10. #103×D113C2semidirect
11. #461×C113C2semidirect
94. D452SD16semidirect
102. Dic226#41semidirect
129. C113#3298semidirect
136. #461D113semidirect

Maximal subgroups

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

subgroupindex
#202992632
#202992532
#202989482
#202989272
#202988842
#202988242
#202987352
C4×#142686352
#202986632
#103×D1132
#461×C1132
#3298113