Finite Group Databasebeta

← #28392222

Subgroups — #28392222

Order 14464.

266 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 266 conjugacy classes of subgroups — too many to draw. Only its 55 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#20299163C211yesmaximal, characteristic
2#20298579C211yesmaximal, characteristic, complemented
3#20298570C211yesmaximal, characteristic, complemented
4#20298386C211yesmaximal, characteristic, complemented
5#20298385C211yesmaximal, characteristic, complemented
6#20298384C211yesmaximal, characteristic, complemented
7AΣL(1,𝔽16)×C113C211yesmaximal, characteristic, complemented
8C2×#14268646C2211yescharacteristic
9C22×C22⋊D113C411yescharacteristic, complemented
10M16×D113—21no—
11#16813618—21no—
12#16813608—21no—
13#16813595—21no—
14#16813594—21no—
15#16813592C411yescharacteristic, complemented
16#16813591C411yescharacteristic, complemented
17#16813590C2211yescharacteristic
18#16813578—21no—
19#16813578C411yescharacteristic, complemented
20#16813540—21no—
21#16813539C2211yescharacteristic
22#16813537C2211yescharacteristic
23#16813536—21no—
24#120×C113C2211yescharacteristic
25#100×C113C2211yescharacteristic
26#99×C113C2211yescharacteristic
27C23×D113C2×C411yescharacteristic
28#14268646—41no—
29#14268646—41no—
30C2×Dic226D411yescharacteristic
31C2×D452—21no—
32C2×C22⋊D113—21no—
33C2×C22⋊D113—21no—
34C2×C22⋊D113—21no—
35C2×C22⋊D113—21no—
36C2×C22⋊D113—41no—
37C2×C22⋊D113—41no—
38C2×C22⋊D113C2×C411yescharacteristic
39C2×C22⋊D113D411yescharacteristic
40C22×Dic113C2×C411yescharacteristic
41C22×Dic113D411yescharacteristic
42C2×C4×D113D411yescharacteristic
43#14268631—21no—
44#14268630—41no—
45C8×D113—41no—
46#14268626—21no—
47#14268626—41no—
48C22⋊Dic113—21no—
49C22⋊Dic113—21no—
50C22⋊Dic113C2×C411yescharacteristic
51#14268624—21no—
52#14268624—21no—
53C4×Dic113—21no—
54C4×Dic113—41no—
55C24×C113C2×C411yescharacteristic
56C2×D4×C113—21no—
57C2×D4×C113C2311yescharacteristic
58M16×C113—21no—
59C22⋊C4×C113—21no—
60C22⋊C4×C113—21no—
61C22⋊C4×C113C2×C411yescharacteristic
62C23×C113—21no—
63C23×C113—41no—
64C23×C113—81no—
65C23×C113C22×C411yescharacteristic
66C23×C113C2×D411yescharacteristic
67C22×D113—21no—
68C22×D113—41no—
69C22×D113—81no—
70C22×D113C22⋊C411yescharacteristic
71D4×C113—41no—
72D4×C113—81no—
73C2×C4×C113—21no—
74C2×C4×C113—41no—
75C2×C4×C113C2×D411yescharacteristic
76C22⋊D113—41no—
77C22⋊D113—41no—
78C22⋊D113—42no—
79C22⋊D113—41no—
80C22⋊D113—41no—
81C22⋊D113—81no—
82C22⋊D113—81no—
83C2×Dic113—21no—
84C2×Dic113—21no—
85C2×Dic113—21no—
86C2×Dic113—21no—
87C2×Dic113—21no—
88C2×Dic113—41no—
89C2×Dic113C22⋊C411yescharacteristic
90C2×Dic113C22⋊C411yescharacteristic
91C2×Dic113C22⋊C411yescharacteristic
92D452—81no—
93C4×D113—21no—
94C4×D113—21no—
95Dic226—41no—
96C8×C113—41no—
97#11744751—41no—
98C22×C113—21no—
99C22×C113—21no—
100C22×C113—41no—
101C22×C113—41no—
102C22×C113—41no—
103C22×C113—41no—
104C22×C113—41no—
105C22×C113—82no—
106C22×C113C2×C22⋊C411yescharacteristic
107C2×D113—21no—
108C2×D113—41no—
109C2×D113—41no—
110C2×D113—41no—
111C2×D113—41no—
112C2×D113—82no—
113C4×C113—21no—
114C4×C113—41no—
115C4×C113—81no—
116Dic113—21no—
117Dic113—21no—
118Dic113—41no—
119Dic113—81no—
120Dic113#9911yescharacteristic
121Dic113#9911yescharacteristic
122C2×C113—21no—
123C2×C113—41no—
124C2×C113—41no—
125C2×C113—81no—
126C2×C113C2×#9911yescharacteristic
127D113—41no—
128D113—81no—
129#2122—1131nomaximal, Sylow
130C113#212211yescharacteristic, complemented, Sylow
131#535—1131no—
132#413—1131no—
133#410—1131no—
134AΣL(1,𝔽16)—1131no—
135AΣL(1,𝔽16)—1131no—
136AΣL(1,𝔽16)—1131no—
137AΣL(1,𝔽16)D11311yescharacteristic, complemented
138C2×#41—1131no—
139C22×D4—1131no—
140C2×M16—2261no—
141#127—2261no—
142#124—2261no—
143#121—2261no—
144#121—2261no—
145#120—1131no—
146#120—1131no—
147#120—1131no—
148#120C2×D11311yescharacteristic
149#117—1131no—
150#117—2261no—
151#101—2261no—
152#100—1131no—
153#100C2×D11311yescharacteristic
154#99—1131no—
155#99—2261no—
156#99C2×D11311yescharacteristic
157C24—1131no—
158C24C4×D11311yescharacteristic
159#41—4521no—
160#41—4521no—
161C2×Q8—1131no—
162C2×D4—21no—
163C2×D4—1131no—
164C2×D4—1131no—
165C2×D4—4521no—
166C2×D4—4521no—
167C2×D4—2261no—
168C2×D4—2261no—
169C2×D4—2261no—
170C2×D4—2261no—
171C2×D4—2261no—
172C2×D4C22×D11311yescharacteristic
173C22×C4—1131no—
174C22×C4—1131no—
175C22×C4—1131no—
176M16—21no—
177M16—4521no—
178M16—2261no—
179C2×C8—4521no—
180C4⋊C4—4521no—
181C4⋊C4—2261no—
182C22⋊C4—21no—
183C22⋊C4—21no—
184C22⋊C4—1131no—
185C22⋊C4—2261no—
186C22⋊C4—2261no—
187C22⋊C4—2261no—
188C22⋊C4—2261no—
189C22⋊C4C4×D11311yescharacteristic
190C42—4521no—
191C42—2261no—
192C23—21no—
193C23—41no—
194C23—81no—
195C23—1131no—
196C23—9041no—
197C23—4521no—
198C23—2261no—
199C23C2×C4×D11311yescharacteristic
200C23D4×D11311yescharacteristic
201Q8—4521no—
202D4—41no—
203D4—81no—
204D4—9041no—
205D4—9041no—
206D4—9041no—
207D4—4521no—
208D4—4521no—
209D4—4521no—
210D4—4521no—
211D4—4522no—
212C2×C4—21no—
213C2×C4—41no—
214C2×C4—1131no—
215C2×C4—1131no—
216C2×C4—1131no—
217C2×C4—4521no—
218C2×C4—2261no—
219C2×C4—2261no—
220C2×C4—2261no—
221C2×C4—2261no—
222C2×C4—2261no—
223C2×C4—2261no—
224C2×C4—2261no—
225C2×C4D4×D11311yescharacteristic
226C8—41no—
227C8—4521no—
228C22—21no—
229C22—21no—
230C22—41no—
231C22—41no—
232C22—41no—
233C22—41no—
234C22—41no—
235C22—82no—
236C22—9042no—
237C22—4521no—
238C22—4521no—
239C22—4521no—
240C22—4521no—
241C22—2261no—
242C22C22⋊C4×D11311yescharacteristic
243C4—21no—
244C4—41no—
245C4—81no—
246C4—1131no—
247C4—1131no—
248C4—9041no—
249C4—4521no—
250C4—2261no—
251C4—2261no—
252C2—21no—
253C2—41no—
254C2—41no—
255C2—81no—
256C2—9041no—
257C2—4521no—
258C2#99×D11311yescharacteristic
subgroupG/H
centerC2#99×D113
commutatorC23×C113C22×C4
FrattiniC2×D4C22×D113
FittingAΣL(1,𝔽16)×C113C2
socleC2×C113C2×#99
prime radical#20299163C2
cosocleC2×D4×C113C23
hypercenterAΣL(1,𝔽16)D113
hypocenterC113#2122
LCSG ▷ C23×C113 ▷ C22×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ AΣL(1,𝔽16)

Complements

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

NH ≅ G/Ntype
2. #20298579C2semidirect
3. #20298570C2semidirect
4. #20298386C2semidirect
5. #20298385C2semidirect
6. #20298384C2semidirect
7. AΣL(1,𝔽16)×C113C2semidirect
9. C22×C22⋊D113C4semidirect
15. #16813592C4semidirect
16. #16813591C4semidirect
19. #16813578C4semidirect
130. C113#2122semidirect
137. AΣL(1,𝔽16)D113semidirect

Maximal subgroups

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

subgroupindex
#202991632
#202985792
#202985702
#202983862
#202983852
#202983842
AΣL(1,𝔽16)×C1132
#2122113