Finite Group Databasebeta

← #28401650

Subgroups — #28401650

Order 14464.

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

normal subgroups only

This group has 364 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#20299209C211yesmaximal, characteristic, complemented
2#20299173C211yesmaximal, characteristic
3#20298990C211yesmaximal, characteristic, complemented
4#20298966C211yesmaximal, characteristic, complemented
5#20298953C211yesmaximal, characteristic, complemented
6#20298822C212yesmaximal, complemented
7#20298806C212yesmaximal, complemented
8#20298759C212yesmaximal
9#20298752C212yesmaximal, complemented
10#20298657C211yesmaximal, characteristic, complemented
11#494×C113C211yesmaximal, characteristic, complemented
12C2×#14268648C2211yescharacteristic
13C2×Q8×D113C2211yescharacteristic
14C2×#14268637C2212yes—
15C2×#14268634C2212yes—
16#16813620C2211yescharacteristic
17#16813617—22no—
18#16813614C2211yescharacteristic
19#16813612—22no—
20#16813611C2211yescharacteristic
21#16813610C2211yescharacteristic
22#16813607—22no—
23#16813600—22no—
24#16813598C2212yes—
25Q8×Dic113C2212yes—
26#16813579C2211yescharacteristic
27#16813551C2212yes—
28#16813547C2212yes—
29#16813546C2212yes—
30#16813546C2212yes—
31#16813544C2212yes—
32#16813534C2212yes—
33#16813533C2211yescharacteristic
34C2×Q16×C113C2212yes—
35C2×Q16×C113C2212yes—
36C4⋊Q8×C113C2211yescharacteristic
37C4⋊Q8×C113C2211yescharacteristic
38C4×C8×C113C2211yescharacteristic
39#14268648—42no—
40C2×Dic226—21no—
41C2×Dic226C2311yescharacteristic
42Q8×D113—42no—
43C2×D452—21no—
44C2×D452C2311yescharacteristic
45C2×C4×D113—21no—
46C2×C4×D113—21no—
47C2×C4×D113C2311yescharacteristic
48#14268637—42no—
49#14268634—42no—
50C2×#11744751C2312yes—
51C4⋊Dic113—22no—
52C4⋊Dic113C2312yes—
53#14268626—22no—
54#14268626—22no—
55#14268626—22no—
56#14268626D412yes—
57#14268624—22no—
58#14268624—22no—
59#14268624—22no—
60#14268624D412yes—
61C4×Dic113—22no—
62C4×Dic113C2311yescharacteristic
63C2×Q8×C113C2312yes—
64C2×Q8×C113C2311yescharacteristic
65C2×Q8×C113C2311yescharacteristic
66Q16×C113—42no—
67Q16×C113—42no—
68C2×C8×C113C2312yes—
69C4⋊C4×C113—22no—
70C4⋊C4×C113—22no—
71C42×C113C2311yescharacteristic
72C22×D113—21no—
73C22×D113C2×D411yescharacteristic
74Q8×C113—22no—
75Q8×C113—22no—
76Q8×C113—22no—
77Q8×C113—22no—
78C2×C4×C113—22no—
79C2×C4×C113—21no—
80C2×C4×C113—21no—
81C2×C4×C113C2×D412yes—
82C2×C4×C113C2411yescharacteristic
83C2×Dic113—22no—
84C2×Dic113—21no—
85C2×Dic113C2×D412yes—
86C2×Dic113C2×D411yescharacteristic
87D452—22no—
88D452—42no—
89C4×D113—22no—
90C4×D113—42no—
91C4×D113—42no—
92Dic226—22no—
93Dic226—42no—
94C8×C113—22no—
95#11744751—22no—
96C22×C113C22×D411yescharacteristic
97C2×D113—21no—
98C2×D113—22no—
99C2×D113—41no—
100C2×D113—42no—
101C4×C113—22no—
102C4×C113—41no—
103C4×C113—41no—
104C4×C113—42no—
105C4×C113H(5,𝔽2)12yes—
106Dic113—21no—
107Dic113—22no—
108Dic113—41no—
109Dic113—42no—
110C2×C113#53511yescharacteristic
111C2×C113#57812yes—
112D113—41no—
113D113—81no—
114#3223—1131nomaximal, Sylow
115C113#322311yescharacteristic, complemented, Sylow
116#541—1131no—
117#536—1131no—
118#497—1131no—
119#494D11311yescharacteristic, complemented
120#491—1131no—
121#488—1131no—
122#464—1132no—
123#462—1132no—
124#452—1132no—
125#451—1132no—
126#433—1131no—
127C2×#41—1131no—
128C22×Q8—1131no—
129C2×Q16—1132no—
130C2×Q16C2×D11312yes—
131C2×Q16C2×D11312yes—
132C2×SD16—1132no—
133C4⋊Q8—1131no—
134C4⋊Q8C2×D11311yescharacteristic
135C4⋊Q8C2×D11311yescharacteristic
136#126—2262no—
137#125—1131no—
138#125—2262no—
139#124—1131no—
140#124—1131no—
141#123—2262no—
142C22⋊Q8—1132no—
143C22⋊Q8—2262no—
144C4×Q8—1132no—
145#117—1131no—
146C4⋊C8—1132no—
147#103—1132no—
148#103—1132no—
149#103—1132no—
150#102—1132no—
151C22⋊C8—1132no—
152#97—1131no—
153C4×C8C2×D11311yescharacteristic
154#41—4522no—
155C2×Q8—1131no—
156C2×Q8—4522no—
157C2×Q8—2261no—
158C2×Q8C22×D11311yescharacteristic
159C2×Q8C22×D11311yescharacteristic
160C2×Q8C22×D11312yes—
161C2×D4—1131no—
162C2×D4—2261no—
163C22×C4—1131no—
164C22×C4—2261no—
165C22×C4—2261no—
166Q16—42no—
167Q16—42no—
168Q16—4522no—
169SD16—4522no—
170C2×C8—1132no—
171C2×C8C22×D11312yes—
172C4⋊C4—22no—
173C4⋊C4—22no—
174C4⋊C4—1132no—
175C4⋊C4—1132no—
176C4⋊C4—2262no—
177C4⋊C4—2262no—
178C4⋊C4—2262no—
179C4⋊C4—2262no—
180C22⋊C4—1132no—
181C22⋊C4—2262no—
182C22⋊C4—2262no—
183C22⋊C4—2262no—
184C42—1131no—
185C42—2262no—
186C42C22×D11311yescharacteristic
187C23—1131no—
188C23—2261no—
189Q8—22no—
190Q8—22no—
191Q8—22no—
192Q8—22no—
193Q8—4522no—
194Q8—2262no—
195D4—4522no—
196D4—2262no—
197C2×C4—22no—
198C2×C4—21no—
199C2×C4—21no—
200C2×C4—1132no—
201C2×C4—1131no—
202C2×C4—4522no—
203C2×C4—4522no—
204C2×C4—2262no—
205C2×C4—2261no—
206C2×C4—2262no—
207C2×C4D4×D11312yes—
208C2×C4C23×D11311yescharacteristic
209C8—22no—
210C8—2262no—
211C22—4522no—
212C22—4521no—
213C22—2262no—
214C22—2261no—
215C22C2×D4×D11311yescharacteristic
216C4—22no—
217C4—41no—
218C4—41no—
219C4—42no—
220C4—4522no—
221C4—4521no—
222C4—2262no—
223C4—2261no—
224C4#1681366712yes—
225C2—9041no—
226C2—4521no—
227C2#2029916111yescharacteristic
228C2#2029941112yes—
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#494×C113C2
socleC22×C113C22×D4
prime radicalC2×#14268648C22
hypercenter#494D113
hypocenterC113#3223
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C42 ◁ #494

Complements

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

NH ≅ G/Ntype
1. #20299209C2semidirect
3. #20298990C2semidirect
4. #20298966C2semidirect
5. #20298953C2semidirect
6. #20298822C2semidirect
7. #20298806C2semidirect
9. #20298752C2semidirect
10. #20298657C2semidirect
11. #494×C113C2semidirect
115. C113#3223semidirect
119. #494D113semidirect

Maximal subgroups

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

subgroupindex
#202992092
#202991732
#202989902
#202989662
#202989532
#202988222
#202988062
#202987592
#202987522
#202986572
#494×C1132
#3223113