Finite Group Databasebeta

← #28403227

Subgroups — #28403227

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#20299322C211yesmaximal, characteristic, complemented
2#20299305C211yesmaximal, characteristic, complemented
3#20298954C212yesmaximal, complemented
4#20298948C211yesmaximal, characteristic, complemented
5#20298903C212yesmaximal, complemented
6#20298889C211yesmaximal, characteristic, complemented
7#20298815C212yesmaximal
8#20298722C211yesmaximal, characteristic, complemented
9SD16×Dic113C212yesmaximal, complemented
10C4×#14268632C211yesmaximal, characteristic
11#461×C113C211yesmaximal, characteristic, complemented
12C2×#14268632C2211yescharacteristic
13#16813622C2211yescharacteristic
14#16813617—22no—
15#16813613C2212yes—
16#16813611C2212yes—
17#16813602—21no—
18#16813601—21no—
19#16813599—22no—
20Q8×Dic113C2212yes—
21C4×Dic226C2211yescharacteristic
22C4×D452C2211yescharacteristic
23D4×Dic113C2212yes—
24#16813580—21no—
25C2×C4⋊Dic113—21no—
26#16813555C2211yescharacteristic
27#16813554C2212yes—
28#16813551C2212yes—
29#16813546C2212yes—
30#16813546C2212yes—
31#16813544C2212yes—
32#16813543C2211yescharacteristic
33#16813542C2211yescharacteristic
34C4×#11744751C2211yescharacteristic
35C8×Dic113C2212yes—
36C2×SD16×C113C2212yes—
37C4⋊Q8×C113C2211yescharacteristic
38C4×D4×C113C2211yescharacteristic
39C4⋊C8×C113C2211yescharacteristic
40#103×C113C2212yes—
41C2×Dic226—21no—
42C2×Dic226D411yescharacteristic
43C2×D452C2311yescharacteristic
44C22×Dic113—22no—
45C2×C4×D113—21no—
46#14268632—22no—
47C2×#11744751C2311yescharacteristic
48C2×#11744751C2311yescharacteristic
49C4⋊Dic113—21no—
50C4⋊Dic113—22no—
51C4⋊Dic113—22no—
52C4⋊Dic113D411yescharacteristic
53C4⋊Dic113C2312yes—
54C4⋊Dic113C2311yescharacteristic
55#14268626—22no—
56#14268626D412yes—
57C22⋊Dic113—22no—
58#14268624—21no—
59#14268624—22no—
60#14268624—22no—
61C4×Dic113—22no—
62C4×Dic113C2312yes—
63C2×Q8×C113C2312yes—
64C2×D4×C113C2311yescharacteristic
65C22×C4×C113—21no—
66SD16×C113—24no—
67C2×C8×C113C2312yes—
68C4⋊C4×C113—21no—
69C4⋊C4×C113—21no—
70C4⋊C4×C113C2311yescharacteristic
71C22⋊C4×C113—21no—
72C42×C113C2311yescharacteristic
73C23×C113—21no—
74C22×D113—21no—
75Q8×C113—22no—
76Q8×C113—22no—
77D4×C113—21no—
78D4×C113#4112yes—
79C2×C4×C113—21no—
80C2×C4×C113—22no—
81C2×C4×C113—42no—
82C2×C4×C113C2×D411yescharacteristic
83C2×C4×C113C2×D411yescharacteristic
84C2×C4×C113C2411yescharacteristic
85C2×Dic113—21no—
86C2×Dic113—22no—
87C2×Dic113—82no—
88C2×Dic113C2×D412yes—
89C2×Dic113C2×D412yes—
90D452—21no—
91D452—21no—
92C4×D113—42no—
93Dic226—22no—
94Dic226—81no—
95C8×C113—22no—
96#11744751—21no—
97#11744751—21no—
98C22×C113—22no—
99C22×C113—41no—
100C22×C113—41no—
101C22×C113C22×D411yescharacteristic
102C2×D113—41no—
103C2×D113—41no—
104C2×D113—41no—
105C4×C113—21no—
106C4×C113—42no—
107C4×C113—41no—
108C4×C113#13512yes—
109C4×C113C2×#4111yescharacteristic
110C4×C1132−1+411yescharacteristic
111Dic113—22no—
112Dic113—22no—
113Dic113—41no—
114Dic113—42no—
115C2×C113—42no—
116C2×C113#54811yescharacteristic
117C2×C113C2×#13511yescharacteristic
118C2×C113#57711yescharacteristic
119D113—81no—
120#3360—1131nomaximal, Sylow
121C113#336011yescharacteristic, complemented, Sylow
122#556—1131no—
123#554—1131no—
124#488—1132no—
125#487—1131no—
126#479—1132no—
127#476—1131no—
128#463—1132no—
129#461D11311yescharacteristic, complemented
130C8×Q8—1131no—
131C4×SD16—1132no—
132C4×D8—1131no—
133C2×SD16C2×D11312yes—
134C2×D8—1131no—
135C4⋊Q8—1131no—
136C4⋊Q8C2×D11311yescharacteristic
137#126—2262no—
138#125—1132no—
139#124—1132no—
140C22⋊Q8—2262no—
141C22⋊Q8—2261no—
142C22⋊Q8—2261no—
143C4×Q8—1131no—
144C4×Q8—1132no—
145C4×D4—1132no—
146C4×D4—1131no—
147C4×D4C2×D11311yescharacteristic
148#117—2261no—
149C2×C4⋊C4—2261no—
150#107—1131no—
151#106—1132no—
152C4⋊C8—1132no—
153C4⋊C8C2×D11311yescharacteristic
154#103—1132no—
155#103—1132no—
156#103C2×D11312yes—
157#102—1131no—
158#102—1132no—
159#102—1131no—
160C4×C8—1132no—
161C4×C8—1131no—
162C2×Q8—1131no—
163C2×Q8—2261no—
164C2×Q8C22×D11312yes—
165C2×D4—1131no—
166C2×D4C22×D11311yescharacteristic
167C22×C4—21no—
168C22×C4—2262no—
169C22×C4—2261no—
170SD16—24no—
171D8—2262no—
172C2×C8—1131no—
173C2×C8—1131no—
174C2×C8C22×D11312yes—
175C4⋊C4—21no—
176C4⋊C4—21no—
177C4⋊C4—1131no—
178C4⋊C4—1132no—
179C4⋊C4—1132no—
180C4⋊C4—1131no—
181C4⋊C4—2262no—
182C4⋊C4—2262no—
183C4⋊C4—2262no—
184C4⋊C4—2261no—
185C4⋊C4C22×D11311yescharacteristic
186C22⋊C4—21no—
187C22⋊C4—2262no—
188C22⋊C4—2262no—
189C22⋊C4—2262no—
190C22⋊C4—2261no—
191C42—1132no—
192C42—2262no—
193C42C22×D11311yescharacteristic
194C23—21no—
195C23—2261no—
196Q8—22no—
197Q8—22no—
198Q8—9041no—
199Q8—2262no—
200D4—21no—
201D4—2261no—
202D4—2261no—
203D4#1426864612yes—
204C2×C4—22no—
205C2×C4—21no—
206C2×C4—42no—
207C2×C4—1132no—
208C2×C4—1132no—
209C2×C4—9042no—
210C2×C4—4522no—
211C2×C4—2261no—
212C2×C4—2262no—
213C2×C4D4×D11311yescharacteristic
214C2×C4D4×D11311yescharacteristic
215C2×C4C23×D11311yescharacteristic
216C8—22no—
217C8—2261no—
218C8—2261no—
219C22—22no—
220C22—41no—
221C22—41no—
222C22—4521no—
223C22—4521no—
224C22—4521no—
225C22C2×D4×D11311yescharacteristic
226C4—21no—
227C4—41no—
228C4—42no—
229C4—4521no—
230C4—4522no—
231C4—2262no—
232C4—2262no—
233C4#1681364312yes—
234C4C2×#1426864611yescharacteristic
235C4#1681366911yescharacteristic
236C2—42no—
237C2—9041no—
238C2#2029925411yescharacteristic
239C2C2×#1681364311yescharacteristic
240C2#2029940711yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#461×C113C2
socleC22×C113C22×D4
prime radicalC2×#14268632C22
hypercenter#461D113
hypocenterC113#3360
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. #20299322C2semidirect
2. #20299305C2semidirect
3. #20298954C2semidirect
4. #20298948C2semidirect
5. #20298903C2semidirect
6. #20298889C2semidirect
8. #20298722C2semidirect
9. SD16×Dic113C2semidirect
11. #461×C113C2semidirect
121. C113#3360semidirect
129. #461D113semidirect

Maximal subgroups

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

subgroupindex
#202993222
#202993052
#202989542
#202989482
#202989032
#202988892
#202988152
#202987222
SD16×Dic1132
C4×#142686322
#461×C1132
#3360113