Finite Group Databasebeta

← #14764681

Subgroups — #14764681

Order 2816.

606 conjugacy classes of subgroups.

The subgroup lattice has 332 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13071094C211yesmaximal, characteristic
2#13069557C211yesmaximal, characteristic
3#13069339C211yesmaximal, characteristic
4#13069337C211yesmaximal, characteristic
5#13069174C212yesmaximal
6#13069172C212yesmaximal
7#13068760C212yesmaximal
8#13068734C212yesmaximal
9C4⋊C8×Dic11C211yesmaximal, characteristic
10#13068364C211yesmaximal, characteristic
11C11×#1985C211yesmaximal, characteristic
12C2×C4×Q8×C11C2211yescharacteristic
13C2×C11×C4⋊C8C2211yescharacteristic
14C2×C11×#97C2211yescharacteristic
15#10622843C412yes—
16C2×Dic11⋊C8C2212yes—
17C2×Dic11⋊C8C2212yes—
18C2×C8×Dic11C2212yes—
19#10622598C412yes—
20#10622594C414yes—
21C4×C4⋊Dic11C2211yescharacteristic
22C4×C4⋊Dic11C2212yes—
23#10622545C2212yes—
24C42×Dic11C2211yescharacteristic
25C2×C4⋊(C11⋊C8)C2211yescharacteristic
26C2×#66867C2211yescharacteristic
27C11×#336C2212yes—
28C11×#336C2212yes—
29#10622188C2212yes—
30#10622188C2212yes—
31#10622188C2211yescharacteristic
32#10622188C2211yescharacteristic
33#10622188C2211yescharacteristic
34#10622188C2211yescharacteristic
35#10622188C2212yes—
36#10622162C2212yes—
37#10622162C2212yes—
38C22×Q8×C11C2×C411yescharacteristic
39C22×C8×C11C2311yescharacteristic
40C22×C8×C11C2311yescharacteristic
41C22×C8×C11C2312yes—
42C4×Q8×C11—22no—
43C4×Q8×C11—22no—
44C2×C11×C4⋊C4C2×C412yes—
45C2×C11×C4⋊C4C2×C411yescharacteristic
46C2×C42×C11C2312yes—
47C2×C42×C11C2311yescharacteristic
48C2×C4⋊Dic11C2×C414yes—
49C2×C4⋊Dic11C2×C412yes—
50C2×C4×Dic11C2×C412yes—
51C2×C4×Dic11C2×C412yes—
52C2×C4×Dic11C2311yescharacteristic
53C2×C4×Dic11C2311yescharacteristic
54C2×C4×Dic11C2312yes—
55C22×C11⋊C8C2311yescharacteristic
56C22×C11⋊C8C2311yescharacteristic
57C22×C11⋊C8C2312yes—
58C11×C4⋊C8—22no—
59C11×#97—22no—
60C11⋊#95C2×C414yes—
61C11⋊#95C2×C414yes—
62C11⋊#95C2×C414yes—
63C11⋊#95C2×C412yes—
64Dic11⋊C8—42no—
65Dic11⋊C8—42no—
66C8×Dic11—42no—
67C4⋊(C11⋊C8)—22no—
68#66867—22no—
69#22021—111nomaximal, Sylow
70C2×Q8×C11—22no—
71C2×Q8×C11—42no—
72C22×C4×C11C22×C412yes—
73C22×C4×C11C22×C412yes—
74C22×C4×C11C22×C411yescharacteristic
75C22×C4×C11C22×C411yescharacteristic
76C22×C4×C11C2411yescharacteristic
77C22×Dic11C22×C412yes—
78C22×Dic11C22×C414yes—
79C22×Dic11C22×C412yes—
80C2×C8×C11—21no—
81C2×C8×C11—21no—
82C2×C8×C11—22no—
83C2×C8×C11—22no—
84C2×C8×C11—21no—
85C2×C8×C11—21no—
86C2×C8×C11—21no—
87C2×C8×C11—21no—
88C2×C8×C11—22no—
89C11×C4⋊C4—22no—
90C11×C4⋊C4—24no—
91C42×C11—22no—
92C42×C11—22no—
93C42×C11#4112yes—
94C42×C11#4112yes—
95C4⋊Dic11—28no—
96C4⋊Dic11—42no—
97C4×Dic11—24no—
98C4×Dic11—21no—
99C4×Dic11—22no—
100C4×Dic11—21no—
101C4×Dic11—22no—
102C4×Dic11—21no—
103C4×Dic11—21no—
104C4×Dic11—42no—
105C2×C11⋊C8—21no—
106C2×C11⋊C8—21no—
107C2×C11⋊C8—22no—
108C2×C11⋊C8—22no—
109C2×C11⋊C8—21no—
110C2×C11⋊C8—21no—
111C2×C11⋊C8—21no—
112C2×C11⋊C8—22no—
113C2×C11⋊C8—21no—
114#2295—111no—
115#1985—111no—
116#1985D1111yescharacteristic
117#1940—111no—
118#1940—111no—
119#1916—112no—
120#1916—112no—
121#1840—112no—
122#1832—112no—
123C4×C4⋊C8—111no—
124#1745—111no—
125C23×C11C23×C411yescharacteristic
126Q8×C11—44no—
127C2×C4×C11—22no—
128C2×C4×C11—22no—
129C2×C4×C11—22no—
130C2×C4×C11—22no—
131C2×C4×C11—24no—
132C2×C4×C11—24no—
133C2×C4×C11#11712yes—
134C2×C4×C11#11712yes—
135C2×C4×C11C2×#4111yescharacteristic
136C2×C4×C11C2×#4111yescharacteristic
137C2×C4×C11H(5,𝔽2)11yescharacteristic
138C2×C4×C112−1+411yescharacteristic
139C2×C4×C112−1+411yescharacteristic
140C2×C4×C112−1+411yescharacteristic
141C2×Dic11—22no—
142C2×Dic11—22no—
143C2×Dic11—22no—
144C2×Dic11—24no—
145C2×Dic11—22no—
146C2×Dic11—24no—
147C2×Dic11—22no—
148C2×Dic11—24no—
149C2×Dic11#13114yes—
150C8×C11—41no—
151C8×C11—41no—
152C8×C11—42no—
153C11⋊C8—41no—
154C11⋊C8—42no—
155C11⋊C8—41no—
156C2×C4×Q8C2×D1111yescharacteristic
157C2×C4⋊C8—111no—
158C2×C4⋊C8—112no—
159C2×C4⋊C8—112no—
160C2×C4⋊C8C2×D1111yescharacteristic
161C2×#97—111no—
162C2×#97C2×D1111yescharacteristic
163C2×C4×C8—112no—
164#391—112no—
165#389—112no—
166#387—114no—
167C4×C4⋊C4—112no—
168C4×C4⋊C4—111no—
169#376—112no—
170C43—111no—
171#336—111no—
172#336—112no—
173#336—111no—
174#336—112no—
175#336—112no—
176#336—111no—
177#336—111no—
178#336—112no—
179#336—112no—
180#336C2×D1112yes—
181#336C2×D1112yes—
182C22×C11C2×#11711yescharacteristic
183C22×C11#51911yescharacteristic
184C22×C11#52011yescharacteristic
185C22×C11C2×#13112yes—
186C22×C11#56812yes—
187C4×C11—22no—
188C4×C11—22no—
189C4×C11—42no—
190C4×C11—42no—
191C4×C11#54111yescharacteristic
192C4×C11#54111yescharacteristic
193C4×C11#54211yescharacteristic
194C4×C11#54211yescharacteristic
195Dic11—24no—
196Dic11—42no—
197Dic11—44no—
198C22×Q8C4×D1111yescharacteristic
199C22×C8—111no—
200C22×C8—112no—
201C22×C8—111no—
202C22×C8C22×D1111yescharacteristic
203C22×C8C22×D1112yes—
204C22×C8C22×D1111yescharacteristic
205C4×Q8—22no—
206C4×Q8—22no—
207C2×C4⋊C4—114no—
208C2×C4⋊C4—112no—
209C2×C4⋊C4C4×D1112yes—
210C2×C4⋊C4C4×D1111yescharacteristic
211C2×C42—112no—
212C2×C42—111no—
213C2×C42—111no—
214C2×C42—112no—
215C2×C42—112no—
216C2×C42C22×D1112yes—
217C2×C42C22×D1111yescharacteristic
218C4⋊C8—22no—
219C4⋊C8—222no—
220C4⋊C8—442no—
221C4⋊C8—442no—
222#97—22no—
223#97—222no—
224C4×C8—442no—
225#95—114no—
226#95—114no—
227#95—112no—
228#95—114no—
229C2×C11#232011yescharacteristic
230C2×C11#292111yescharacteristic
231C2×C11#292211yescharacteristic
232C2×C11#298512yes—
233C2×C11#299212yes—
234C2×Q8—22no—
235C2×Q8—42no—
236C22×C4—112no—
237C22×C4—112no—
238C22×C4—114no—
239C22×C4C2×C4×D1112yes—
240C22×C4C2×C4×D1112yes—
241C22×C4C2×C4×D1111yescharacteristic
242C22×C4C2×C4×D1111yescharacteristic
243C22×C4C23×D1111yescharacteristic
244C2×C8—21no—
245C2×C8—21no—
246C2×C8—22no—
247C2×C8—21no—
248C2×C8—21no—
249C2×C8—22no—
250C2×C8—21no—
251C2×C8—21no—
252C2×C8—22no—
253C2×C8—221no—
254C2×C8—221no—
255C2×C8—222no—
256C2×C8—221no—
257C2×C8—221no—
258C2×C8—222no—
259C2×C8—222no—
260C2×C8—221no—
261C2×C8—221no—
262C4⋊C4—22no—
263C4⋊C4—24no—
264C4⋊C4—228no—
265C4⋊C4—442no—
266C42—22no—
267C42—22no—
268C42—224no—
269C42—221no—
270C42—221no—
271C42—222no—
272C42—221no—
273C42—222no—
274C42—221no—
275C42—442no—
276C42#434112yes—
277C42#434112yes—
278C11#2202111yescharacteristic, complemented, Sylow
279C23C22×C4×D1111yescharacteristic
280Q8—44no—
281C2×C4—22no—
282C2×C4—22no—
283C2×C4—22no—
284C2×C4—22no—
285C2×C4—24no—
286C2×C4—24no—
287C2×C4—114no—
288C2×C4—222no—
289C2×C4—222no—
290C2×C4—222no—
291C2×C4—224no—
292C2×C4—222no—
293C2×C4—224no—
294C2×C4—222no—
295C2×C4—224no—
296C2×C4#6693012yes—
297C2×C4#6693012yes—
298C2×C4C2×#434111yescharacteristic
299C2×C4C2×#434111yescharacteristic
300C2×C4#6704011yescharacteristic
301C2×C4#6704011yescharacteristic
302C2×C4#6704211yescharacteristic
303C2×C4#6704311yescharacteristic
304C8—41no—
305C8—41no—
306C8—42no—
307C8—441no—
308C8—442no—
309C8—441no—
310C22C2×#6693011yescharacteristic
311C22#1062310311yescharacteristic
312C22#1062310511yescharacteristic
313C22#1062327612yes—
314C22D11×#13112yes—
315C4—22no—
316C4—22no—
317C4—42no—
318C4—42no—
319C4—224no—
320C4—442no—
321C4—444no—
322C4#1062315611yescharacteristic
323C4#1062317411yescharacteristic
324C4#1062321311yescharacteristic
325C4#1062326211yescharacteristic
326C2#1307126111yescharacteristic
327C2#1307725111yescharacteristic
328C2#1307725611yescharacteristic
329C2#1307770912yes—
330C2#1307775412yes—
subgroupG/H
center, FrattiniC22×C4C23×D11
commutator, socle, prime radicalC23×C11C23×C4
FittingC11×#1985C2
cosocleC22×C4×C11C24
hypercenter#1985D11
hypocenterC11#22021
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ #1985

Complements

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

NH ≅ G/Ntype
278. C11#22021semidirect

Maximal subgroups

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

subgroupindex
#130710942
#130695572
#130693392
#130693372
#130691742
#130691722
#130687602
#130687342
C4⋊C8×Dic112
#130683642
C11×#19852
#2202111