Finite Group Databasebeta

← #28401466

Subgroups — #28401466

Order 14464.

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

normal subgroups only

This group has 378 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#20299171C212yesmaximal
2#20298942C212yesmaximal, complemented
3#20298937C212yesmaximal, complemented
4#20298856C211yesmaximal, characteristic, complemented
5#20298837C212yesmaximal, complemented
6#20298755C212yesmaximal, complemented
7#20298752C212yesmaximal, complemented
8#20298566C211yesmaximal, characteristic
9#470×C113C211yesmaximal, characteristic, complemented
10C2×#14268647C2211yescharacteristic
11C2×Q8×D113C2212yes—
12C2×Dic452C2211yescharacteristic
13C2×#14268637C2212yes—
14C22×#11744751C2211yescharacteristic
15#16813621—22no—
16#16813608—22no—
17#16813607—22no—
18#16813604—22no—
19#16813602C2212yes—
20#16813601C2212yes—
21#16813598C2212yes—
22#16813580C2212yes—
23#16813555C2212yes—
24#16813554C2211yescharacteristic
25#16813547C2212yes—
26#16813546C2212yes—
27#16813545C2212yes—
28#16813534C2212yes—
29#16813534C2212yes—
30C2×Q16×C113C2211yescharacteristic
31C2×M16×C113C2211yescharacteristic
32C22⋊Q8×C113C2212yes—
33#106×C113C2211yescharacteristic
34#103×C113C2212yes—
35#14268647—41no—
36#14268647—41no—
37C2×Dic226—22no—
38C2×Dic226D411yescharacteristic
39C2×Dic226C2312yes—
40Q8×D113—42no—
41Q8×D113—42no—
42C2×D452D411yescharacteristic
43C2×C22⋊D113D412yes—
44C2×C4×D113—22no—
45C2×C4×D113C2312yes—
46Dic452—41no—
47#14268637—42no—
48C2×#11744751—41no—
49C2×#11744751C2312yes—
50C4⋊Dic113—22no—
51C4⋊Dic113C2312yes—
52#14268626—22no—
53#14268626—22no—
54C22⋊Dic113—22no—
55#14268624—22no—
56#14268624—22no—
57#14268624—22no—
58C4×Dic113—22no—
59C2×Q8×C113C2312yes—
60C22×C4×C113C2311yescharacteristic
61Q16×C113—41no—
62M16×C113—41no—
63C2×C8×C113C2311yescharacteristic
64C2×C8×C113C2311yescharacteristic
65C4⋊C4×C113—22no—
66C4⋊C4×C113C2312yes—
67C22⋊C4×C113—22no—
68C23×C113C2×D411yescharacteristic
69C22×D113C2×D412yes—
70Q8×C113—22no—
71Q8×C113—22no—
72C2×C4×C113—21no—
73C2×C4×C113—21no—
74C2×C4×C113—22no—
75C2×C4×C113—22no—
76C2×C4×C113C2×D411yescharacteristic
77C2×C4×C113C2411yescharacteristic
78C22⋊D113—42no—
79C2×Dic113—22no—
80C2×Dic113—22no—
81C2×Dic113C2×D412yes—
82D452—41no—
83C4×D113—22no—
84C4×D113—22no—
85C4×D113—44no—
86Dic226—22no—
87Dic226—22no—
88Dic226—41no—
89Dic226—44no—
90C8×C113—21no—
91C8×C113—21no—
92#11744751—22no—
93C22×C113—21no—
94C22×C113—22no—
95C22×C113C22×D411yescharacteristic
96C2×D113—22no—
97C2×D113—24no—
98C4×C113—21no—
99C4×C113—42no—
100C4×C113—42no—
101C4×C113H(5,𝔽2)11yescharacteristic
102C4×C113H(5,𝔽2)11yescharacteristic
103Dic113—22no—
104Dic113—42no—
105Dic113—42no—
106C2×C113—41no—
107C2×C113#53411yescharacteristic
108C2×C113#57812yes—
109D113—42no—
110#3202—1131nomaximal, Sylow
111C113#320211yescharacteristic, complemented, Sylow
112#536—1132no—
113#485—1132no—
114#485—1132no—
115#470—1131no—
116#470D11311yescharacteristic, complemented
117#467—1132no—
118#451—1132no—
119#451—1132no—
120#408—1131no—
121C2×#41—1131no—
122C22×Q8—1132no—
123C2×Q16—1132no—
124C2×Q16—1131no—
125C2×Q16C2×D11311yescharacteristic
126C2×M16C2×D11311yescharacteristic
127C22×C8—1131no—
128C4⋊Q8—2262no—
129#124—2262no—
130#123—2262no—
131#123—2262no—
132C22⋊Q8—1132no—
133C22⋊Q8—1132no—
134C22⋊Q8—1132no—
135C22⋊Q8C2×D11312yes—
136#117—1132no—
137#107—1132no—
138#106—1131no—
139#106C2×D11311yescharacteristic
140#103—1132no—
141#103—1132no—
142#103—1132no—
143#103C2×D11312yes—
144C22⋊C8—1132no—
145C22⋊C8—1132no—
146#41—4521no—
147#41—4521no—
148C2×Q8—1131no—
149C2×Q8—1132no—
150C2×Q8—4522no—
151C2×Q8—4522no—
152C2×Q8—2262no—
153C2×Q8C22×D11312yes—
154C2×D4—1132no—
155C2×D4—1131no—
156C22×C4—1132no—
157C22×C4—2262no—
158C22×C4C22×D11311yescharacteristic
159Q16—41no—
160Q16—4521no—
161Q16—4522no—
162M16—41no—
163C2×C8—1132no—
164C2×C8—4521no—
165C2×C8C22×D11311yescharacteristic
166C2×C8C22×D11311yescharacteristic
167C4⋊C4—22no—
168C4⋊C4—1132no—
169C4⋊C4—2262no—
170C4⋊C4—2262no—
171C4⋊C4—2262no—
172C4⋊C4C22×D11312yes—
173C22⋊C4—22no—
174C22⋊C4—2262no—
175C22⋊C4—2262no—
176C22⋊C4—2262no—
177C22⋊C4—2262no—
178C42—2262no—
179C23—1132no—
180C23D4×D11311yescharacteristic
181Q8—22no—
182Q8—22no—
183Q8—4521no—
184Q8—4524no—
185Q8—2262no—
186Q8—2262no—
187D4—4521no—
188D4—4522no—
189C2×C4—21no—
190C2×C4—21no—
191C2×C4—22no—
192C2×C4—22no—
193C2×C4—1132no—
194C2×C4—4524no—
195C2×C4—2262no—
196C2×C4—2262no—
197C2×C4—2262no—
198C2×C4—2262no—
199C2×C4D4×D11311yescharacteristic
200C2×C4C23×D11311yescharacteristic
201C8—21no—
202C8—21no—
203C8—2262no—
204C22—21no—
205C22—22no—
206C22—2262no—
207C22—2264no—
208C22C2×D4×D11311yescharacteristic
209C4—21no—
210C4—42no—
211C4—42no—
212C4—4522no—
213C4—4522no—
214C4—2262no—
215C4#1681366711yescharacteristic
216C4#1681366811yescharacteristic
217C2—41no—
218C2—4522no—
219C2#2029915611yescharacteristic
220C2#2029941412yes—
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#470×C113C2
socleC22×C113C22×D4
prime radicalC2×#14268647C22
hypercenter#470D113
hypocenterC113#3202
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C22×C4 ◁ #470

Complements

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

NH ≅ G/Ntype
2. #20298942C2semidirect
3. #20298937C2semidirect
4. #20298856C2semidirect
5. #20298837C2semidirect
6. #20298755C2semidirect
7. #20298752C2semidirect
9. #470×C113C2semidirect
111. C113#3202semidirect
116. #470D113semidirect

Maximal subgroups

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

subgroupindex
#202991712
#202989422
#202989372
#202988562
#202988372
#202987552
#202987522
#202985662
#470×C1132
#3202113