Finite Group Databasebeta

← #14771425

Subgroups — #14771425

Order 2816.

822 conjugacy classes of subgroups.

The subgroup lattice has 304 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13071493C212yesmaximal
2#13069350C212yesmaximal, complemented
3#13069210C214yesmaximal, complemented
4#13068706C212yesmaximal
5#13068645C211yesmaximal, characteristic
6#107×Dic11C212yesmaximal, complemented
7C8×C22⋊Dic11C211yesmaximal, characteristic
8C22×C11×#107C211yesmaximal, characteristic
9C23×C8×C11C2211yescharacteristic
10C22×C11×C4⋊C4C2212yes—
11C2×C11×#107C418yescomplemented
12C2×C11×#107C2211yescharacteristic
13C2×C11×#107C2212yes—
14C2×C11×#107C2211yescharacteristic
15#10622825—22no—
16#10622825C2212yes—
17C4×C22⋊Dic11—22no—
18C4×C22⋊Dic11C2211yescharacteristic
19C2×C22⋊(C11⋊C8)C2211yescharacteristic
20C2×#66882C2212yes—
21C2×C8×Dic11C2212yes—
22#10622598C2214yes—
23#10622594—24no—
24C4⋊C4×Dic11C2214yes—
25#10622189C2212yes—
26#10622188C2212yes—
27#10622167C2214yes—
28#10622167C2214yes—
29C23×C4×C11—22no—
30C23×C4×C11C2311yescharacteristic
31C22×C8×C11—24no—
32C22×C8×C11C2×C414yes—
33C22×C8×C11C2311yescharacteristic
34C22×C8×C11C2311yescharacteristic
35C2×C11×C4⋊C4—22no—
36C2×C11×C4⋊C4—24no—
37C2×C11×C4⋊C4C2×C418yes—
38C2×C11×C4⋊C4C2312yes—
39C2×C11×C4⋊C4C2312yes—
40C2×C22⋊Dic11—22no—
41C2×C22⋊Dic11D411yescharacteristic
42C2×C22⋊Dic11D411yescharacteristic
43C2×C4⋊Dic11—24no—
44C2×C4⋊Dic11C2314yes—
45C2×C4×Dic11—24no—
46C2×C4×Dic11C2312yes—
47C22×C11⋊C8C2312yes—
48C11×#107C2×C418yes—
49C11×#107C2×C414yes—
50C11×#107C2×C414yes—
51C11⋊#95—22no—
52C11⋊#95—24no—
53C11⋊#95—24no—
54C11⋊#95D412yes—
55C22⋊(C11⋊C8)—22no—
56#66882—24no—
57C8×Dic11—24no—
58#22612—111nomaximal, Sylow
59C24×C11C2×D411yescharacteristic
60C22×C4×C11—22no—
61C22×C4×C11—22no—
62C22×C4×C11—22no—
63C22×C4×C11—22no—
64C22×C4×C11—28no—
65C22×C4×C11—84no—
66C22×C4×C11C22×C412yes—
67C22×C4×C11C2×D411yescharacteristic
68C22×C4×C11#4112yes—
69C22×C4×C11C2411yescharacteristic
70C22×Dic11—24no—
71C22×Dic11C2×D412yes—
72C22×Dic11C2×D412yes—
73C2×C8×C11—28no—
74C2×C8×C11—22no—
75C2×C8×C11C22×C412yes—
76C2×C8×C11C22×C412yes—
77C2×C8×C11#4114yes—
78C11×C4⋊C4—28no—
79C11×C4⋊C4—22no—
80C11×C4⋊C4—22no—
81C11×C4⋊C4C22×C414yes—
82C11×C4⋊C4C22×C414yes—
83C22⋊Dic11—22no—
84C22⋊Dic11—44no—
85C22⋊Dic11Q1614yes—
86C4⋊Dic11—24no—
87C4⋊Dic11—24no—
88C4⋊Dic11—84no—
89C4×Dic11—22no—
90C4×Dic11—22no—
91C4×Dic11—84no—
92C2×C11⋊C8—22no—
93C2×C11⋊C8—22no—
94C2×C11⋊C8—22no—
95C22×#107D1111yescharacteristic
96#2345—112no—
97#1942—112no—
98#1921—114no—
99#1824—112no—
100#1808—111no—
101C4×#107—112no—
102C8×C22⋊C4—111no—
103C23×C11—22no—
104C23×C11—22no—
105C23×C11C4×D412yes—
106C23×C11C2×Q1612yes—
107C23×C11#13512yes—
108C23×C11C22×D411yescharacteristic
109C2×C4×C11—22no—
110C2×C4×C11—22no—
111C2×C4×C11—22no—
112C2×C4×C11—24no—
113C2×C4×C11—24no—
114C2×C4×C11—24no—
115C2×C4×C11—44no—
116C2×C4×C11—44no—
117C2×C4×C11—88no—
118C2×C4×C11C4×D412yes—
119C2×C4×C11C23×C411yescharacteristic
120C2×C4×C11C2×#4112yes—
121C2×C4×C11C2×#4111yescharacteristic
122C2×C4×C112−1+412yes—
123C2×Dic11—22no—
124C2×Dic11—22no—
125C2×Dic11—22no—
126C2×Dic11—22no—
127C2×Dic11—22no—
128C2×Dic11—44no—
129C2×Dic11—44no—
130C2×Dic11—44no—
131C2×Dic11C2×Q1614yes—
132C8×C11—22no—
133C8×C11#11714yes—
134C11⋊C8—42no—
135C23×C8C2×D1111yescharacteristic
136C22×C4⋊C4C2×D1112yes—
137C2×#107—112no—
138C2×#107Dic1118yescomplemented
139C2×#107C2×D1112yes—
140C2×#107C2×D1111yescharacteristic
141C2×#107C2×D1111yescharacteristic
142C2×C22⋊C8—111no—
143C2×C4×C8—112no—
144#389—114no—
145#387—224no—
146#380—112no—
147#380—222no—
148C4×C4⋊C4—114no—
149C4×C22⋊C4—111no—
150C4×C22⋊C4—222no—
151#340—112no—
152#340—114no—
153#340—114no—
154#336—112no—
155C22×C11—24no—
156C22×C11—24no—
157C22×C11—22no—
158C22×C11—22no—
159C22×C11C4×Q1614yes—
160C22×C11C2×C4×D411yescharacteristic
161C22×C11#54712yes—
162C22×C11C22×Q1611yescharacteristic
163C22×C11C2×#13511yescharacteristic
164C22×C11#57612yes—
165C4×C11—22no—
166C4×C11—44no—
167C4×C11—44no—
168C4×C11C2×#11711yescharacteristic
169C4×C11#51911yescharacteristic
170C4×C11#55212yes—
171Dic11—24no—
172Dic11—42no—
173Dic11—84no—
174C23×C4—22no—
175C23×C4C22×D1111yescharacteristic
176C22×C8—24no—
177C22×C8—112no—
178C22×C8C2×Dic1114yes—
179C22×C8C22×D1111yescharacteristic
180C22×C8C22×D1111yescharacteristic
181C2×C4⋊C4—22no—
182C2×C4⋊C4—24no—
183C2×C4⋊C4—114no—
184C2×C4⋊C4—224no—
185C2×C4⋊C4C2×Dic1118yes—
186C2×C4⋊C4C22×D1112yes—
187C2×C4⋊C4C22×D1112yes—
188C2×C22⋊C4—111no—
189C2×C22⋊C4—111no—
190C2×C22⋊C4—222no—
191C2×C42—112no—
192C2×C42—224no—
193#107—224no—
194#107C2×Dic1118yes—
195#107C2×Dic1114yes—
196#107C2×Dic1114yes—
197C22⋊C8—222no—
198C4×C8—224no—
199#95—112no—
200#95—224no—
201#95—224no—
202#95—222no—
203C2×C11—24no—
204C2×C11#234411yescharacteristic
205C2×C11C2×C4×Q1611yescharacteristic
206C2×C11#294811yescharacteristic
207C2×C11#333812yes—
208C2×C11#333912yes—
209C24D4×D1111yescharacteristic
210C22×C4—22no—
211C22×C4—22no—
212C22×C4—22no—
213C22×C4—22no—
214C22×C4—28no—
215C22×C4—84no—
216C22×C4—112no—
217C22×C4—112no—
218C22×C4—224no—
219C22×C4D4×D1111yescharacteristic
220C22×C4#434112yes—
221C22×C4C22×Dic1112yes—
222C22×C4C23×D1111yescharacteristic
223C2×C8—22no—
224C2×C8—28no—
225C2×C8—222no—
226C2×C8—222no—
227C2×C8—222no—
228C2×C8#433914yes—
229C2×C8C22×Dic1112yes—
230C2×C8C22×Dic1112yes—
231C4⋊C4—28no—
232C4⋊C4—22no—
233C4⋊C4—22no—
234C4⋊C4—224no—
235C4⋊C4—224no—
236C4⋊C4—884no—
237C4⋊C4C22×Dic1114yes—
238C4⋊C4C22×Dic1114yes—
239C22⋊C4—114no—
240C22⋊C4—222no—
241C22⋊C4—444no—
242C42—222no—
243C42—222no—
244C42—884no—
245C11#2261211yescharacteristic, complemented, Sylow
246C23—22no—
247C23—22no—
248C23Q16×D1112yes—
249C23#6697212yes—
250C23D4×Dic1112yes—
251C23C2×D4×D1111yescharacteristic
252C2×C4—22no—
253C2×C4—24no—
254C2×C4—22no—
255C2×C4—22no—
256C2×C4—24no—
257C2×C4—24no—
258C2×C4—44no—
259C2×C4—44no—
260C2×C4—88no—
261C2×C4—114no—
262C2×C4—222no—
263C2×C4—222no—
264C2×C4—222no—
265C2×C4—222no—
266C2×C4—222no—
267C2×C4—444no—
268C2×C4—444no—
269C2×C4—444no—
270C2×C4D4×Dic1112yes—
271C2×C4C2×#433912yes—
272C2×C4C2×#434111yescharacteristic
273C2×C4#6704012yes—
274C2×C4C23×Dic1111yescharacteristic
275C8—22no—
276C8—442no—
277C8#6697914yes—
278C22—22no—
279C22—24no—
280C22—24no—
281C22—22no—
282C22Q16×Dic1114yes—
283C22#1062303812yes—
284C22#1062328812yes—
285C22C2×Q16×D1111yescharacteristic
286C22C2×#6697211yescharacteristic
287C22C2×D4×Dic1111yescharacteristic
288C4—22no—
289C4—44no—
290C4—44no—
291C4—224no—
292C4—442no—
293C4—884no—
294C4#1062304412yes—
295C4C2×#6697911yescharacteristic
296C4#1062334311yescharacteristic
297C2—24no—
298C2#1307148511yescharacteristic
299C2C2×Q16×Dic1111yescharacteristic
300C2#1307746811yescharacteristic
301C2#1308100612yes—
302C2#1308101412yes—
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC22×C11×#107C2
socleC23×C11C22×D4
prime radicalC24×C11C2×D4
cosocleC22×C4×C11C24
hypercenterC22×#107D11
hypocenterC11#22612
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×#107

Complements

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

NH ≅ G/Ntype
2. #13069350C2semidirect
3. #13069210C2semidirect
6. #107×Dic11C2semidirect
11. C2×C11×#107C4semidirect
138. C2×#107Dic11semidirect
245. C11#22612semidirect

Maximal subgroups

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

subgroupindex
#130714932
#130693502
#130692102
#130687062
#130686452
#107×Dic112
C8×C22⋊Dic112
C22×C11×#1072
#2261211