Finite Group Databasebeta

← #28401464

Subgroups — #28401464

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#20298941C212yesmaximal, complemented
3#20298938C212yesmaximal, complemented
4#20298854C212yesmaximal, complemented
5#20298839C211yesmaximal, characteristic, complemented
6#20298755C212yesmaximal, complemented
7#20298752C212yesmaximal, complemented
8#20298564C211yesmaximal, characteristic
9#467×C113C211yesmaximal, characteristic, complemented
10C2×#14268647C2211yescharacteristic
11C2×Q8×D113C2212yes—
12C2×Dic452C2211yescharacteristic
13C2×#14268637C2212yes—
14C2×#14268631C2211yescharacteristic
15#16813621—22no—
16#16813608—22no—
17#16813607—22no—
18#16813604—22no—
19#16813602C2212yes—
20#16813601C2212yes—
21#16813598C2212yes—
22#16813580C2212yes—
23#16813556C2211yescharacteristic
24#16813553C2212yes—
25#16813547C2212yes—
26#16813546C2212yes—
27#16813545C2212yes—
28#16813534C2212yes—
29#16813534C2212yes—
30C2×Q16×C113C2211yescharacteristic
31C22×C8×C113C2211yescharacteristic
32C22⋊Q8×C113C2212yes—
33#107×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—
48#14268631—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—
62C2×C8×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—21no—
95C22×C113—21no—
96C22×C113C22×D411yescharacteristic
97C2×D113—22no—
98C2×D113—22no—
99C2×D113—22no—
100C4×C113—21no—
101C4×C113—42no—
102C4×C113—42no—
103C4×C113H(5,𝔽2)11yescharacteristic
104C4×C113H(5,𝔽2)11yescharacteristic
105Dic113—22no—
106Dic113—42no—
107Dic113—42no—
108C2×C113—41no—
109C2×C113#53411yescharacteristic
110C2×C113#57811yescharacteristic
111C2×C113#57811yescharacteristic
112D113—42no—
113#3202—1131nomaximal, Sylow
114C113#320211yescharacteristic, complemented, Sylow
115#536—1132no—
116#485—1132no—
117#485—1132no—
118#470—1132no—
119#467—1131no—
120#467D11311yescharacteristic, complemented
121#451—1132no—
122#451—1132no—
123#408—1131no—
124C2×#41—1131no—
125C22×Q8—1132no—
126C2×Q16—1132no—
127C2×Q16—1131no—
128C2×Q16C2×D11311yescharacteristic
129C2×M16—1131no—
130C22×C8C2×D11311yescharacteristic
131C4⋊Q8—2262no—
132#124—2262no—
133#123—2262no—
134#123—2262no—
135C22⋊Q8—1132no—
136C22⋊Q8—1132no—
137C22⋊Q8—1132no—
138C22⋊Q8C2×D11312yes—
139#117—1132no—
140#107—1131no—
141#107C2×D11311yescharacteristic
142#106—1132no—
143#103—1132no—
144#103—1132no—
145#103—1132no—
146#103C2×D11312yes—
147C22⋊C8—1132no—
148C22⋊C8—1132no—
149#41—4521no—
150#41—4521no—
151C2×Q8—1131no—
152C2×Q8—1132no—
153C2×Q8—4522no—
154C2×Q8—4522no—
155C2×Q8—2262no—
156C2×Q8C22×D11312yes—
157C2×D4—1132no—
158C2×D4—1131no—
159C22×C4—1132no—
160C22×C4—2262no—
161C22×C4C22×D11311yescharacteristic
162Q16—41no—
163Q16—4521no—
164Q16—4522no—
165M16—4521no—
166C2×C8—41no—
167C2×C8—1132no—
168C2×C8C22×D11311yescharacteristic
169C2×C8C22×D11311yescharacteristic
170C4⋊C4—22no—
171C4⋊C4—1132no—
172C4⋊C4—2262no—
173C4⋊C4—2262no—
174C4⋊C4—2262no—
175C4⋊C4C22×D11312yes—
176C22⋊C4—22no—
177C22⋊C4—2262no—
178C22⋊C4—2262no—
179C22⋊C4—2262no—
180C22⋊C4—2262no—
181C42—2262no—
182C23—1132no—
183C23D4×D11311yescharacteristic
184Q8—22no—
185Q8—22no—
186Q8—4521no—
187Q8—4524no—
188Q8—2262no—
189Q8—2262no—
190D4—4521no—
191D4—4522no—
192C2×C4—21no—
193C2×C4—21no—
194C2×C4—22no—
195C2×C4—22no—
196C2×C4—1132no—
197C2×C4—4524no—
198C2×C4—2262no—
199C2×C4—2262no—
200C2×C4—2262no—
201C2×C4—2262no—
202C2×C4D4×D11311yescharacteristic
203C2×C4C23×D11311yescharacteristic
204C8—21no—
205C8—21no—
206C8—2262no—
207C22—21no—
208C22—21no—
209C22—21no—
210C22—2262no—
211C22—2262no—
212C22—2262no—
213C22C2×D4×D11311yescharacteristic
214C4—21no—
215C4—42no—
216C4—42no—
217C4—4522no—
218C4—4522no—
219C4—2262no—
220C4#1681366711yescharacteristic
221C4#1681366811yescharacteristic
222C2—41no—
223C2—4522no—
224C2#2029915611yescharacteristic
225C2#2029941111yescharacteristic
226C2#2029941211yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#467×C113C2
socleC22×C113C22×D4
prime radicalC2×#14268647C22
hypercenter#467D113
hypocenterC113#3202
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C22×C4 ◁ #467

Complements

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

NH ≅ G/Ntype
2. #20298941C2semidirect
3. #20298938C2semidirect
4. #20298854C2semidirect
5. #20298839C2semidirect
6. #20298755C2semidirect
7. #20298752C2semidirect
9. #467×C113C2semidirect
114. C113#3202semidirect
120. #467D113semidirect

Maximal subgroups

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

subgroupindex
#202991712
#202989412
#202989382
#202988542
#202988392
#202987552
#202987522
#202985642
#467×C1132
#3202113