Finite Group Databasebeta

← #28392218

Subgroups — #28392218

Order 14464.

280 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 280 conjugacy classes of subgroups — too many to draw. Only its 65 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#20299157C211yesmaximal, characteristic
2C2×#16813539C211yesmaximal, characteristic, complemented
3#20298387C212yesmaximal, complemented
4#20298384C212yesmaximal, complemented
5C2×#99×C113C211yesmaximal, characteristic, complemented
6C22×C22⋊D113C411yescharacteristic, complemented
7C2×#14268631—21no—
8#16813605—21no—
9#16813603C411yescharacteristic, complemented
10#16813603C2211yescharacteristic
11#16813594—21no—
12#16813594—21no—
13#16813591—21no—
14#16813590C411yescharacteristic, complemented
15#16813590C2211yescharacteristic
16C2×C22⋊Dic113C411yescharacteristic, complemented
17#16813539—21no—
18#16813539C2212yes—
19C22×D4×C113C2211yescharacteristic
20C2×C22⋊C4×C113—21no—
21#99×C113—21no—
22#99×C113C2212yes—
23C23×D113C2×C411yescharacteristic, complemented
24C2×C22⋊D113—21no—
25C2×C22⋊D113—21no—
26C2×C22⋊D113—21no—
27C2×C22⋊D113—21no—
28C2×C22⋊D113—41no—
29C2×C22⋊D113—41no—
30C22×Dic113—21no—
31C22×Dic113C2×C411yescharacteristic, complemented
32#14268631—22no—
33#14268631—41no—
34C2×#11744751—41no—
35#14268626—21no—
36#14268626—21no—
37C22⋊Dic113—21no—
38C22⋊Dic113—21no—
39C22⋊Dic113—21no—
40C22⋊Dic113C2×C411yescharacteristic, complemented
41C22⋊Dic113C2×C411yescharacteristic, complemented
42#14268624—21no—
43#14268624—21no—
44C24×C113C2×C411yescharacteristic
45C24×C113D411yescharacteristic
46C2×D4×C113—41no—
47C2×D4×C113—41no—
48C2×D4×C113C2×C411yescharacteristic
49C2×D4×C113D411yescharacteristic
50C2×D4×C113D411yescharacteristic
51C2×D4×C113C2311yescharacteristic
52C22×C4×C113—41no—
53C22×C4×C113D411yescharacteristic
54C22⋊C4×C113—22no—
55C22⋊C4×C113—41no—
56C23×C113—21no—
57C23×C113—21no—
58C23×C113—21no—
59C23×C113—21no—
60C23×C113—81no—
61C23×C113—81no—
62C23×C113C22⋊C411yescharacteristic
63C23×C113C22⋊C411yescharacteristic
64C23×C113C22⋊C411yescharacteristic
65C23×C113C22×C411yescharacteristic
66C23×C113C2×D411yescharacteristic
67C22×D113—21no—
68C22×D113—41no—
69C22×D113—81no—
70D4×C113—41no—
71D4×C113—41no—
72D4×C113—41no—
73D4×C113—41no—
74C2×C4×C113—21no—
75C2×C4×C113—21no—
76C2×C4×C113—42no—
77C2×C4×C113—82no—
78C2×C4×C113C22⋊C411yescharacteristic
79C2×C4×C113C2×D411yescharacteristic
80C22⋊D113—42no—
81C22⋊D113—41no—
82C22⋊D113—41no—
83C22⋊D113—81no—
84C22⋊D113—81no—
85C2×Dic113—21no—
86C2×Dic113—21no—
87C2×Dic113—21no—
88C2×Dic113—41no—
89C2×Dic113—81no—
90#11744751—42no—
91C22×C113—21no—
92C22×C113—21no—
93C22×C113—21no—
94C22×C113—21no—
95C22×C113—41no—
96C22×C113—41no—
97C22×C113—41no—
98C22×C113—41no—
99C22×C113—41no—
100C22×C113—42no—
101C22×C113—81no—
102C22×C113—81no—
103C22×C113—81no—
104C22×C113#9911yescharacteristic
105C22×C113#9911yescharacteristic
106C22×C113C2×C22⋊C411yescharacteristic
107C2×D113—41no—
108C2×D113—41no—
109C2×D113—41no—
110C2×D113—82no—
111C4×C113—21no—
112C4×C113—21no—
113C4×C113—82no—
114Dic113—41no—
115Dic113—41no—
116Dic113—41no—
117C2×C113—21no—
118C2×C113—21no—
119C2×C113—21no—
120C2×C113—41no—
121C2×C113—41no—
122C2×C113—41no—
123C2×C113—41no—
124C2×C113C2×#9911yescharacteristic
125D113—81no—
126#2121—1131nomaximal, Sylow
127C113#212111yescharacteristic, complemented, Sylow
128#534—1131no—
129C2×#100—1131no—
130C2×#99D11311yescharacteristic, complemented
131#352—1132no—
132AΣL(1,𝔽16)—1132no—
133C22×D4—1131no—
134C22×D4C2×D11311yescharacteristic
135C2×M16—2261no—
136#123—1131no—
137#123—1131no—
138#123—2261no—
139#121—2261no—
140#121—2261no—
141#120—1131no—
142#120—1131no—
143#120—2261no—
144C2×C22⋊C4—21no—
145C2×C22⋊C4—1131no—
146#100—1132no—
147#100—2261no—
148#99—21no—
149#99C2×D11312yes—
150C24—1131no—
151C24C4×D11311yescharacteristic
152C24C22⋊D11311yescharacteristic
153C2×D4—41no—
154C2×D4—41no—
155C2×D4—4521no—
156C2×D4—4521no—
157C2×D4—2261no—
158C2×D4—2261no—
159C2×D4—2261no—
160C2×D4—2261no—
161C2×D4C4×D11311yescharacteristic
162C2×D4D45211yescharacteristic
163C2×D4C22⋊D11311yescharacteristic
164C2×D4C22×D11311yescharacteristic
165C22×C4—41no—
166C22×C4—1131no—
167C22×C4—2261no—
168C22×C4D45211yescharacteristic
169M16—4521no—
170M16—2262no—
171C2×C8—4521no—
172C4⋊C4—2261no—
173C4⋊C4—2261no—
174C22⋊C4—22no—
175C22⋊C4—41no—
176C22⋊C4—1131no—
177C22⋊C4—1131no—
178C22⋊C4—2261no—
179C22⋊C4—2261no—
180C22⋊C4—2261no—
181C22⋊C4—2261no—
182C22⋊C4—2261no—
183C23—21no—
184C23—21no—
185C23—21no—
186C23—21no—
187C23—81no—
188C23—81no—
189C23—9041no—
190C23—4521no—
191C23—2261no—
192C23#1426862411yescharacteristic
193C23#1426862411yescharacteristic
194C23#1426862411yescharacteristic
195C23C2×C4×D11311yescharacteristic
196C23C2×C22⋊D11311yescharacteristic
197D4—41no—
198D4—41no—
199D4—41no—
200D4—41no—
201D4—9041no—
202D4—9041no—
203D4—4522no—
204D4—4521no—
205D4—4521no—
206C2×C4—21no—
207C2×C4—21no—
208C2×C4—42no—
209C2×C4—82no—
210C2×C4—9041no—
211C2×C4—4521no—
212C2×C4—2261no—
213C2×C4—2261no—
214C2×C4—2261no—
215C2×C4#1426862411yescharacteristic
216C2×C4C2×D45211yescharacteristic
217C8—4522no—
218C22—21no—
219C22—21no—
220C22—21no—
221C22—21no—
222C22—41no—
223C22—41no—
224C22—41no—
225C22—41no—
226C22—41no—
227C22—42no—
228C22—81no—
229C22—81no—
230C22—81no—
231C22—9042no—
232C22—4521no—
233C22—4521no—
234C22—4521no—
235C22#1681353611yescharacteristic
236C22#1681353611yescharacteristic
237C22C2×#1426862411yescharacteristic
238C4—21no—
239C4—21no—
240C4—82no—
241C4—4521no—
242C4—4521no—
243C4—4521no—
244C2—21no—
245C2—21no—
246C2—21no—
247C2—41no—
248C2—41no—
249C2—41no—
250C2—41no—
251C2—9041no—
252C2C2×#1681353611yescharacteristic
subgroupG/H
centerC2C2×#16813536
commutatorC23×C113C22×C4
FrattiniC2×D4C22×D113
FittingC2×#99×C113C2
socleC2×C113C2×#99
prime radical#20299157C2
cosocleC2×D4×C113C23
hypercenterC2×#99D113
hypocenterC113#2121
LCSG ▷ C23×C113 ▷ C22×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C2 ◁ C23 ◁ C22×D4 ◁ C2×#99

Complements

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

NH ≅ G/Ntype
2. C2×#16813539C2semidirect
3. #20298387C2semidirect
4. #20298384C2semidirect
5. C2×#99×C113C2semidirect
6. C22×C22⋊D113C4semidirect
9. #16813603C4semidirect
14. #16813590C4semidirect
16. C2×C22⋊Dic113C4semidirect
23. C23×D113C2×C4semidirect
31. C22×Dic113C2×C4semidirect
40. C22⋊Dic113C2×C4semidirect
41. C22⋊Dic113C2×C4semidirect
127. C113#2121semidirect
130. C2×#99D113semidirect

Maximal subgroups

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

subgroupindex
#202991572
C2×#168135392
#202983872
#202983842
C2×#99×C1132
#2121113