Finite Group Databasebeta

← #28403291

Subgroups — #28403291

Order 14464.

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

normal subgroups only

This group has 372 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#20299318C211yesmaximal, characteristic, complemented
2#20299263C211yesmaximal, characteristic, complemented
3#20298956C212yesmaximal, complemented
4#20298950C211yesmaximal, characteristic, complemented
5#20298892C212yesmaximal, complemented
6#20298812C212yesmaximal
7#20298804C211yesmaximal, characteristic, complemented
8#20298725C211yesmaximal, characteristic, complemented
9#20298697C212yesmaximal, complemented
10C4×#14268632C211yesmaximal, characteristic
11#474×C113C211yesmaximal, characteristic, complemented
12C2×Q8×D113—21no—
13C2×#14268636C2212yes—
14C2×#14268632C2211yescharacteristic
15#16813622C2211yescharacteristic
16#16813621C2212yes—
17#16813615—22no—
18#16813609C2212yes—
19#16813601—21no—
20#16813600—22no—
21#16813598—21no—
22C4×Dic226C2211yescharacteristic
23#16813587C2212yes—
24C4×D452C2211yescharacteristic
25#16813584C2212yes—
26#16813581—21no—
27#16813555C2211yescharacteristic
28#16813551C2212yes—
29#16813547C2212yes—
30#16813545C2212yes—
31#16813545C2212yes—
32#16813543C2211yescharacteristic
33#16813542C2211yescharacteristic
34#16813532C2212yes—
35C4×#11744751C2211yescharacteristic
36C4⋊Q8×C113C2211yescharacteristic
37C4×D4×C113C2211yescharacteristic
38#107×C113C2212yes—
39C4⋊C8×C113C2211yescharacteristic
40#102×C113C2212yes—
41C2×Dic226—22no—
42C2×Dic226D411yescharacteristic
43C2×Dic226C2312yes—
44Q8×D113—44no—
45C2×D452C2311yescharacteristic
46C2×C4×D113—21no—
47C2×C4×D113—22no—
48#14268636—24no—
49#14268632—22no—
50C2×#11744751C2311yescharacteristic
51C2×#11744751C2311yescharacteristic
52C4⋊Dic113—21no—
53C4⋊Dic113—21no—
54C4⋊Dic113D411yescharacteristic
55C4⋊Dic113C2311yescharacteristic
56#14268626—22no—
57#14268626—22no—
58#14268626D412yes—
59C22⋊Dic113—22no—
60C22⋊Dic113—22no—
61#14268624—21no—
62#14268624—22no—
63C4×Dic113—22no—
64C4×Dic113C2312yes—
65C2×Q8×C113—21no—
66C2×D4×C113C2311yescharacteristic
67C22×C4×C113—21no—
68C2×C8×C113C2312yes—
69C4⋊C4×C113—21no—
70C4⋊C4×C113C2312yes—
71C4⋊C4×C113C2311yescharacteristic
72C22⋊C4×C113—21no—
73C42×C113C2311yescharacteristic
74C23×C113—21no—
75C22×D113—21no—
76Q8×C113—42no—
77D4×C113—21no—
78D4×C113—21no—
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—22no—
86C2×Dic113—21no—
87C2×Dic113C2×D412yes—
88C2×Dic113C2×D412yes—
89D452—21no—
90D452#4112yes—
91C4×D113—44no—
92C4×D113—42no—
93Dic226—22no—
94Dic226—22no—
95Dic226—22no—
96Dic226—44no—
97C8×C113—22no—
98#11744751—21no—
99#11744751—21no—
100C22×C113—41no—
101C22×C113—41no—
102C22×C113—41no—
103C22×C113C22×D411yescharacteristic
104C2×D113—22no—
105C2×D113—41no—
106C2×D113—41no—
107C4×C113—21no—
108C4×C113—42no—
109C4×C113—41no—
110C4×C113AGL(1,ℤ/8)12yes—
111C4×C113C2×#4111yescharacteristic
112C4×C1132−1+411yescharacteristic
113Dic113—22no—
114Dic113—22no—
115Dic113—42no—
116Dic113—41no—
117C2×C113—81no—
118C2×C113#54811yescharacteristic
119C2×C113C2×AGL(1,ℤ/8)11yescharacteristic
120C2×C113#57811yescharacteristic
121D113—42no—
122#3367—1131nomaximal, Sylow
123C113#336711yescharacteristic, complemented, Sylow
124#556—1131no—
125D4×Q8—1131no—
126#489—1132no—
127#487—1131no—
128#477—1132no—
129#474D11311yescharacteristic, complemented
130#463—1132no—
131#461—1131no—
132#446—1131no—
133#440—1132no—
134C4×D8—1131no—
135C22×Q8—2261no—
136C2×SD16—1132no—
137C2×D8—1131no—
138C4⋊Q8—1132no—
139C4⋊Q8—1131no—
140C4⋊Q8C2×D11311yescharacteristic
141#126—2262no—
142#124—1132no—
143C22⋊Q8—2262no—
144C22⋊Q8—2261no—
145C22⋊Q8—2261no—
146C4×Q8—1131no—
147C4×Q8—1132no—
148C4×D4—1132no—
149C4×D4—1131no—
150C4×D4C2×D11311yescharacteristic
151#117—2261no—
152#107—1131no—
153#107C2×D11312yes—
154C4⋊C8—1132no—
155C4⋊C8C2×D11311yescharacteristic
156#103—1132no—
157#103—1132no—
158#103—1132no—
159#102—1131no—
160#102—1131no—
161#102C2×D11312yes—
162#97—1132no—
163C4×C8—1131no—
164C2×Q8—21no—
165C2×Q8—1131no—
166C2×Q8—1132no—
167C2×Q8—4524no—
168C2×Q8—2262no—
169C2×D4—1131no—
170C2×D4C22×D11311yescharacteristic
171C22×C4—21no—
172C22×C4—2262no—
173C22×C4—2261no—
174SD16—2264no—
175D8—2262no—
176C2×C8—1131no—
177C2×C8—1131no—
178C2×C8C22×D11312yes—
179C4⋊C4—21no—
180C4⋊C4—1131no—
181C4⋊C4—1132no—
182C4⋊C4—1131no—
183C4⋊C4—2262no—
184C4⋊C4—2262no—
185C4⋊C4—2261no—
186C4⋊C4—2261no—
187C4⋊C4C22×D11311yescharacteristic
188C4⋊C4C22×D11312yes—
189C22⋊C4—21no—
190C22⋊C4—2262no—
191C22⋊C4—2262no—
192C22⋊C4—2262no—
193C22⋊C4—2261no—
194C42—1132no—
195C42—2262no—
196C42C22×D11311yescharacteristic
197C23—21no—
198C23—2261no—
199Q8—42no—
200Q8—4524no—
201Q8—2262no—
202Q8—2262no—
203Q8—2262no—
204D4—21no—
205D4—21no—
206D4—1132no—
207D4—2261no—
208C2×C4—21no—
209C2×C4—22no—
210C2×C4—42no—
211C2×C4—1132no—
212C2×C4—1132no—
213C2×C4—4524no—
214C2×C4—4522no—
215C2×C4—2262no—
216C2×C4—2261no—
217C2×C4D4×D11311yescharacteristic
218C2×C4D4×D11311yescharacteristic
219C2×C4C23×D11311yescharacteristic
220C8—22no—
221C8—2261no—
222C8—2261no—
223C22—41no—
224C22—41no—
225C22—41no—
226C22—4521no—
227C22—4521no—
228C22—2262no—
229C22C2×D4×D11311yescharacteristic
230C4—21no—
231C4—41no—
232C4—42no—
233C4—4521no—
234C4—4522no—
235C4—2262no—
236C4—2262no—
237C4#1681364612yes—
238C4#41×D11311yescharacteristic
239C4#1681367011yescharacteristic
240C2—81no—
241C2—4522no—
242C2#2029925811yescharacteristic
243C2C2×#1681364611yescharacteristic
244C2#2029941411yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#474×C113C2
socleC22×C113C22×D4
prime radicalC2×#14268632C22
hypercenter#474D113
hypocenterC113#3367
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C42 ◁ #474

Complements

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

NH ≅ G/Ntype
1. #20299318C2semidirect
2. #20299263C2semidirect
3. #20298956C2semidirect
4. #20298950C2semidirect
5. #20298892C2semidirect
7. #20298804C2semidirect
8. #20298725C2semidirect
9. #20298697C2semidirect
11. #474×C113C2semidirect
123. C113#3367semidirect
129. #474D113semidirect

Maximal subgroups

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

subgroupindex
#202993182
#202992632
#202989562
#202989502
#202988922
#202988122
#202988042
#202987252
#202986972
C4×#142686322
#474×C1132
#3367113