Finite Group Databasebeta

← #28401652

Subgroups — #28401652

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#20299168C211yesmaximal, characteristic
3#20298977C211yesmaximal, characteristic, complemented
4#20298967C211yesmaximal, characteristic, complemented
5#20298952C211yesmaximal, characteristic, complemented
6#20298818C212yesmaximal, complemented
7#20298806C212yesmaximal, complemented
8#20298757C212yesmaximal
9#20298752C212yesmaximal, complemented
10#20298660C211yesmaximal, characteristic, complemented
11#497×C113C211yesmaximal, characteristic, complemented
12C2×#14268646C2211yescharacteristic
13C2×Q8×D113C2211yescharacteristic
14C2×#14268637C2212yes—
15C2×#14268637C2212yes—
16#16813622C2211yescharacteristic
17#16813620C2211yescharacteristic
18#16813617—22no—
19#16813614C2211yescharacteristic
20#16813612—22no—
21#16813609C2211yescharacteristic
22#16813604—22no—
23#16813599—22no—
24#16813598C2212yes—
25Q8×Dic113C2212yes—
26#16813579C2211yescharacteristic
27#16813551C2212yes—
28#16813547C2212yes—
29#16813547C2212yes—
30#16813546C2212yes—
31#16813543C2212yes—
32#16813534C2212yes—
33C4×#11744751C2211yescharacteristic
34C2×Q16×C113C2212yes—
35C2×SD16×C113C2212yes—
36C4⋊Q8×C113C2211yescharacteristic
37#124×C113C2211yescharacteristic
38#97×C113C2211yescharacteristic
39#14268646—42no—
40C2×Dic226—21no—
41C2×Dic226C2311yescharacteristic
42C2×Dic226C2311yescharacteristic
43Q8×D113—42no—
44C2×C22⋊D113—21no—
45C22×Dic113—21no—
46C2×C4×D113—21no—
47C2×C4×D113C2311yescharacteristic
48#14268637—42no—
49#14268637—42no—
50C2×#11744751C2312yes—
51C4⋊Dic113—22no—
52C4⋊Dic113—22no—
53C4⋊Dic113C2312yes—
54#14268626—22no—
55#14268626—22no—
56#14268626—22no—
57#14268626D412yes—
58C22⋊Dic113—22no—
59#14268624—22no—
60#14268624D412yes—
61C4×Dic113—22no—
62C4×Dic113C2311yescharacteristic
63C2×Q8×C113C2312yes—
64C2×Q8×C113C2311yescharacteristic
65C2×D4×C113C2311yescharacteristic
66Q16×C113—42no—
67SD16×C113—42no—
68C2×C8×C113C2312yes—
69C4⋊C4×C113—22no—
70C22⋊C4×C113—22no—
71C42×C113C2311yescharacteristic
72C23×C113—21no—
73C22×D113C2×D411yescharacteristic
74Q8×C113—22no—
75Q8×C113—22no—
76Q8×C113—22no—
77D4×C113—22no—
78C2×C4×C113—21no—
79C2×C4×C113—22no—
80C2×C4×C113C2×D412yes—
81C2×C4×C113C2411yescharacteristic
82C22⋊D113—42no—
83C2×Dic113—22no—
84C2×Dic113—21no—
85C2×Dic113—21no—
86C2×Dic113—42no—
87C2×Dic113C2×D412yes—
88C2×Dic113C2×D411yescharacteristic
89C4×D113—22no—
90C4×D113—42no—
91Dic226—22no—
92Dic226—22no—
93Dic226—42no—
94C8×C113—22no—
95#11744751—22no—
96C22×C113—41no—
97C22×C113—42no—
98C22×C113C22×D411yescharacteristic
99C2×D113—21no—
100C2×D113—22no—
101C4×C113—22no—
102C4×C113—41no—
103C4×C113—42no—
104C4×C113H(5,𝔽2)12yes—
105Dic113—21no—
106Dic113—22no—
107Dic113—41no—
108Dic113—41no—
109Dic113—42no—
110C2×C113—81no—
111C2×C113#53511yescharacteristic
112C2×C113#57812yes—
113D113—41no—
114#3223—1131nomaximal, Sylow
115C113#322311yescharacteristic, complemented, Sylow
116#541—1131no—
117#536—1131no—
118#497D11311yescharacteristic, complemented
119#494—1131no—
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×Q16—1132no—
131C2×Q16C2×D11312yes—
132C2×SD16C2×D11312yes—
133C4⋊Q8—1131no—
134C4⋊Q8—1131no—
135C4⋊Q8C2×D11311yescharacteristic
136#126—2262no—
137#125—1131no—
138#125—2262no—
139#124—1131no—
140#124C2×D11311yescharacteristic
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#97C2×D11311yescharacteristic
153C4×C8—1131no—
154#41—4522no—
155C2×Q8—1131no—
156C2×Q8—1131no—
157C2×Q8—4522no—
158C2×Q8—2261no—
159C2×Q8C22×D11311yescharacteristic
160C2×Q8C22×D11312yes—
161C2×D4—2261no—
162C2×D4C22×D11311yescharacteristic
163C22×C4—1131no—
164C22×C4—2261no—
165C22×C4—2261no—
166Q16—42no—
167Q16—4522no—
168Q16—4522no—
169SD16—42no—
170C2×C8—1132no—
171C2×C8C22×D11312yes—
172C4⋊C4—22no—
173C4⋊C4—1132no—
174C4⋊C4—1132no—
175C4⋊C4—2262no—
176C4⋊C4—2262no—
177C4⋊C4—2262no—
178C4⋊C4—2262no—
179C4⋊C4—2262no—
180C22⋊C4—22no—
181C22⋊C4—1132no—
182C22⋊C4—2262no—
183C22⋊C4—2262no—
184C42—1131no—
185C42—2262no—
186C42C22×D11311yescharacteristic
187C23—21no—
188C23—1131no—
189Q8—22no—
190Q8—22no—
191Q8—22no—
192Q8—4522no—
193Q8—2262no—
194Q8—2262no—
195D4—22no—
196D4—4522no—
197C2×C4—22no—
198C2×C4—21no—
199C2×C4—1132no—
200C2×C4—1131no—
201C2×C4—4522no—
202C2×C4—4522no—
203C2×C4—2262no—
204C2×C4—2261no—
205C2×C4—2261no—
206C2×C4—2262no—
207C2×C4D4×D11312yes—
208C2×C4C23×D11311yescharacteristic
209C8—22no—
210C8—2262no—
211C22—42no—
212C22—41no—
213C22—2262no—
214C22—2261no—
215C22C2×D4×D11311yescharacteristic
216C4—22no—
217C4—41no—
218C4—42no—
219C4—4522no—
220C4—4521no—
221C4—4521no—
222C4—2262no—
223C4—2261no—
224C4#1681366712yes—
225C2—81no—
226C2—4521no—
227C2#2029916111yescharacteristic
228C2#2029941412yes—
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#497×C113C2
socleC22×C113C22×D4
prime radicalC2×#14268646C22
hypercenter#497D113
hypocenterC113#3223
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C42 ◁ #497

Complements

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

NH ≅ G/Ntype
1. #20299209C2semidirect
3. #20298977C2semidirect
4. #20298967C2semidirect
5. #20298952C2semidirect
6. #20298818C2semidirect
7. #20298806C2semidirect
9. #20298752C2semidirect
10. #20298660C2semidirect
11. #497×C113C2semidirect
115. C113#3223semidirect
118. #497D113semidirect

Maximal subgroups

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

subgroupindex
#202992092
#202991682
#202989772
#202989672
#202989522
#202988182
#202988062
#202987572
#202987522
#202986602
#497×C1132
#3223113