Finite Group Databasebeta

← #28403223

Subgroups — #28403223

Order 14464.

350 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 350 conjugacy classes of subgroups — too many to draw. Only its 125 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#20299321C211yesmaximal, characteristic, complemented
2#20298955C212yesmaximal, complemented
3#20298950C211yesmaximal, characteristic, complemented
4#20298902C212yesmaximal, complemented
5#20298885C211yesmaximal, characteristic, complemented
6#20298813C212yesmaximal
7#20298803C211yesmaximal, characteristic, complemented
8Q8×#11744751C211yesmaximal, characteristic, complemented
9C4×#14268635C212yesmaximal, complemented
10C4×#14268632C211yesmaximal, characteristic
11#554×C113C211yesmaximal, characteristic, complemented
12C2×#14268635C2212yes—
13C2×#14268632C2211yescharacteristic
14#16813622C2211yescharacteristic
15#16813617—22no—
16#16813610C2212yes—
17#16813598—21no—
18C4×Dic226C2212yes—
19C4×D452C2211yescharacteristic
20#16813580—21no—
21#16813555C2211yescharacteristic
22#16813553C2212yes—
23C4⋊#11744751C2211yescharacteristic
24C4⋊#11744751C2212yes—
25#16813545C2212yes—
26#16813545C2212yes—
27#16813545C2212yes—
28#16813543C2211yescharacteristic
29#16813542C2212yes—
30#16813542C2211yescharacteristic
31C4×#11744751C2211yescharacteristic
32C4×#11744751C2212yes—
33C4⋊Q8×C113C2211yescharacteristic
34#125×C113C2212yes—
35C22⋊Q8×C113—21no—
36C22⋊Q8×C113—22no—
37C4×Q8×C113C2211yescharacteristic
38C4×D4×C113C2211yescharacteristic
39C4×D4×C113C2212yes—
40C2×C4⋊C4×C113—21no—
41C2×Dic226C2312yes—
42C2×D452C2311yescharacteristic
43C2×C4×D113—21no—
44#14268635—24no—
45#14268632—22no—
46C2×#11744751C2311yescharacteristic
47C2×#11744751C2312yes—
48C2×#11744751C2311yescharacteristic
49C4⋊Dic113—21no—
50C4⋊Dic113—21no—
51C4⋊Dic113C2311yescharacteristic
52#14268626—22no—
53#14268624—22no—
54#14268624—21no—
55#14268624—22no—
56C4×Dic113—22no—
57C2×Q8×C113—21no—
58C2×Q8×C113D411yescharacteristic
59C2×D4×C113C2311yescharacteristic
60C22×C4×C113—21no—
61C22×C4×C113—22no—
62C4⋊C4×C113—22no—
63C4⋊C4×C113—21no—
64C4⋊C4×C113—22no—
65C4⋊C4×C113D411yescharacteristic
66C4⋊C4×C113D412yes—
67C4⋊C4×C113C2311yescharacteristic
68C4⋊C4×C113C2312yes—
69C22⋊C4×C113—21no—
70C22⋊C4×C113—22no—
71C42×C113C2311yescharacteristic
72C42×C113C2312yes—
73C23×C113—21no—
74C22×D113—21no—
75Q8×C113—22no—
76Q8×C113—81no—
77D4×C113—21no—
78D4×C113#4112yes—
79C2×C4×C113—21no—
80C2×C4×C113—22no—
81C2×C4×C113—42no—
82C2×C4×C113—82no—
83C2×C4×C113C2×D412yes—
84C2×C4×C113C2×D411yescharacteristic
85C2×C4×C113C2×D412yes—
86C2×C4×C113C2×D411yescharacteristic
87C2×C4×C113C2411yescharacteristic
88C2×Dic113—21no—
89C2×Dic113—22no—
90D452—21no—
91D452—21no—
92C4×D113—42no—
93Dic226—22no—
94Dic226—22no—
95#11744751—21no—
96#11744751—22no—
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—22no—
106C4×C113—22no—
107C4×C113—21no—
108C4×C113—41no—
109C4×C113—42no—
110C4×C113#13512yes—
111C4×C113C2×#4111yescharacteristic
112C4×C1132−1+411yescharacteristic
113Dic113—42no—
114Dic113—41no—
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#554D11311yescharacteristic, complemented
124#488—1132no—
125#487—1131no—
126#479—1132no—
127#476—1131no—
128#463—1132no—
129#461—1131no—
130C8×Q8—1131no—
131C4×SD16—1132no—
132C4×D8—1131no—
133C2×SD16—1132no—
134C2×D8—1131no—
135C4⋊Q8—1131no—
136C4⋊Q8C2×D11311yescharacteristic
137#126—2262no—
138#125C2×D11312yes—
139#124—1132no—
140C22⋊Q8—21no—
141C22⋊Q8—22no—
142C22⋊Q8—2261no—
143C4×Q8—1132no—
144C4×Q8C2×D11311yescharacteristic
145C4×D4—1131no—
146C4×D4C2×D11311yescharacteristic
147C4×D4C2×D11312yes—
148#117—2261no—
149C2×C4⋊C4—21no—
150#107—1131no—
151#106—1132no—
152C4⋊C8—1131no—
153C4⋊C8—1132no—
154#103—1132no—
155#103—1132no—
156#103—1132no—
157#102—1131no—
158#102—1131no—
159#102—1132no—
160C4×C8—1131no—
161C4×C8—1132no—
162C2×Q8—21no—
163C2×Q8—1132no—
164C2×Q8C22⋊D11311yescharacteristic
165C2×D4—1131no—
166C2×D4C22×D11311yescharacteristic
167C22×C4—21no—
168C22×C4—22no—
169C22×C4—2261no—
170SD16—2264no—
171D8—2262no—
172C2×C8—1131no—
173C2×C8—1132no—
174C2×C8—1131no—
175C4⋊C4—22no—
176C4⋊C4—21no—
177C4⋊C4—22no—
178C4⋊C4—1131no—
179C4⋊C4—2261no—
180C4⋊C4—2262no—
181C4⋊C4—2261no—
182C4⋊C4C22⋊D11311yescharacteristic
183C4⋊C4C22⋊D11312yes—
184C4⋊C4C22×D11312yes—
185C4⋊C4C22×D11311yescharacteristic
186C22⋊C4—21no—
187C22⋊C4—22no—
188C22⋊C4—2262no—
189C22⋊C4—2261no—
190C22⋊C4—2262no—
191C42—2262no—
192C42C22×D11311yescharacteristic
193C42C22×D11312yes—
194C23—21no—
195C23—2261no—
196Q8—22no—
197Q8—81no—
198Q8—2262no—
199Q8—2262no—
200D4—21no—
201D4—2261no—
202D4—2261no—
203D4#1426864812yes—
204C2×C4—21no—
205C2×C4—22no—
206C2×C4—42no—
207C2×C4—82no—
208C2×C4—4522no—
209C2×C4—2261no—
210C2×C4—2262no—
211C2×C4C2×C22⋊D11312yes—
212C2×C4C2×C22⋊D11312yes—
213C2×C4C2×C22⋊D11311yescharacteristic
214C2×C4C2×C22⋊D11311yescharacteristic
215C2×C4C23×D11311yescharacteristic
216C8—2261no—
217C8—2262no—
218C8—2261no—
219C22—22no—
220C22—41no—
221C22—41no—
222C22—4521no—
223C22—4521no—
224C22—4521no—
225C22C22×C22⋊D11311yescharacteristic
226C4—22no—
227C4—22no—
228C4—21no—
229C4—41no—
230C4—42no—
231C4—4521no—
232C4—4522no—
233C4#1681364212yes—
234C4C2×#1426864811yescharacteristic
235C4#1681367011yescharacteristic
236C2—42no—
237C2—9041no—
238C2#2029925911yescharacteristic
239C2C2×#1681364211yescharacteristic
240C2#2029940911yescharacteristic
subgroupG/H
centerC22C22×C22⋊D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#554×C113C2
socleC22×C113C22×D4
prime radicalC2×#14268632C22
hypercenter#554D113
hypocenterC113#3360
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C4×Q8 ◁ #554

Complements

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

NH ≅ G/Ntype
1. #20299321C2semidirect
2. #20298955C2semidirect
3. #20298950C2semidirect
4. #20298902C2semidirect
5. #20298885C2semidirect
7. #20298803C2semidirect
8. Q8×#11744751C2semidirect
9. C4×#14268635C2semidirect
11. #554×C113C2semidirect
121. C113#3360semidirect
123. #554D113semidirect

Maximal subgroups

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

subgroupindex
#202993212
#202989552
#202989502
#202989022
#202988852
#202988132
#202988032
Q8×#117447512
C4×#142686352
C4×#142686322
#554×C1132
#3360113