Finite Group Databasebeta

← #14737851

Subgroups — #14737851

Order 2816.

582 conjugacy classes of subgroups.

The subgroup lattice has 334 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079202C211yesmaximal, characteristic
2#13078421C212yesmaximal
3#13068198C214yesmaximal, complemented
4#13068144C212yesmaximal, complemented
5#13068110C212yesmaximal, complemented
6#13067372C211yesmaximal, characteristic
7#13067304C212yesmaximal
8C2×C11×#446C211yesmaximal, characteristic
9C2×C4×Q8×C11C2211yescharacteristic
10#10623001C2212yes—
11C11×#446—21no—
12C11×#446—21no—
13C11×#446C2212yes—
14C11×#446C2212yes—
15C2×C11×C4⋊C8—21no—
16C2×C11×C4⋊C8C2211yescharacteristic
17C2×C11×#97—21no—
18C2×C4×C8×C11C2211yescharacteristic
19#10622838—22no—
20#10622729—21no—
21#10622729—21no—
22#10622635—24no—
23#10622634C2214yes—
24#10622633C2214yes—
25#10622577—22no—
26#10622537C2212yes—
27#10622312C2211yescharacteristic
28C4×Dic44—21no—
29C4×Dic44—21no—
30#10622295C2211yescharacteristic
31#10622294C2212yes—
32#10622120C2214yes—
33#10622119C2214yes—
34#10622095C2212yes—
35#10622095C2212yes—
36C22×Q8×C11D411yescharacteristic
37C22×C8×C11—21no—
38C22×C8×C11D411yescharacteristic
39C22×C8×C11D411yescharacteristic
40C4×Q8×C11—21no—
41C4×Q8×C11—21no—
42C4×Q8×C11D412yes—
43C4×Q8×C11C2312yes—
44C2×C11×C4⋊C4—21no—
45C2×C11×C4⋊C4D411yescharacteristic
46C2×C42×C11—21no—
47C2×C42×C11C2311yescharacteristic
48#66979—22no—
49#66977—22no—
50#66977—22no—
51C2×#4318—22no—
52C2×Dic44—21no—
53C2×Dic44—21no—
54#66923—22no—
55#66922C2312yes—
56#66922C2312yes—
57C4×Dic22—22no—
58C4×Dic22—22no—
59C11×C4⋊C8—22no—
60C11×C4⋊C8—22no—
61C11×C4⋊C8—21no—
62C11×C4⋊C8C2312yes—
63C11×#97—22no—
64C11×#97—22no—
65C4×C8×C11D411yescharacteristic
66C4×C8×C11D411yescharacteristic
67C4×C8×C11C2311yescharacteristic
68C4×C8×C11C2311yescharacteristic
69#66899—24no—
70#66899—24no—
71#66882—21no—
72#66882—21no—
73#66880—22no—
74#66880—22no—
75#66872—24no—
76#66871—24no—
77C4⋊(C11⋊C8)—22no—
78C4⋊(C11⋊C8)C2314yes—
79#19287—111nomaximal, Sylow
80C2×Q8×C11—21no—
81C2×Q8×C11—24no—
82C2×Q8×C11C2×D412yes—
83C22×C4×C11—21no—
84C22×C4×C11—21no—
85C22×C4×C11C2×D411yescharacteristic
86C22×C4×C11C2×D411yescharacteristic
87C22×C4×C11#4111yescharacteristic
88C2×Dic22—22no—
89C2×Dic22—22no—
90C2×C8×C11—22no—
91C2×C8×C11—22no—
92C2×C8×C11—41no—
93C2×C8×C11—42no—
94C2×C8×C11C2×D411yescharacteristic
95C2×C8×C11C2×D411yescharacteristic
96C2×C8×C11C2×D411yescharacteristic
97C2×C8×C11C2×D411yescharacteristic
98C11×C4⋊C4—22no—
99C11×C4⋊C4—21no—
100C11×C4⋊C4—22no—
101C11×C4⋊C4C2×D412yes—
102C42×C11—22no—
103C42×C11—22no—
104C42×C11C2×D411yescharacteristic
105C42×C11C2×D411yescharacteristic
106C42×C11#4111yescharacteristic
107C42×C11C2411yescharacteristic
108C22⋊Dic11—42no—
109C4⋊Dic11—22no—
110C4⋊Dic11—22no—
111C4⋊Dic11—22no—
112C4⋊Dic11—22no—
113Dic11⋊C4—42no—
114Dic11⋊C4—42no—
115C4×Dic11—42no—
116#4318—44no—
117C2×C11⋊C8—24no—
118Dic44—42no—
119Dic44—42no—
120#3170—111no—
121#3078—112no—
122C2×#446D1111yescharacteristic
123#1704—114no—
124#1696—112no—
125#1690—112no—
126#1566—111no—
127#1550—112no—
128C23×C11#12111yescharacteristic
129Q8×C11—24no—
130Q8×C11—42no—
131C2×C4×C11—21no—
132C2×C4×C11—21no—
133C2×C4×C11—22no—
134C2×C4×C11—22no—
135C2×C4×C11—41no—
136C2×C4×C11—42no—
137C2×C4×C11—42no—
138C2×C4×C11#12111yescharacteristic
139C2×C4×C11#12111yescharacteristic
140C2×C4×C11#12111yescharacteristic
141C2×C4×C11#13714yes—
142C2×C4×C11C22×D411yescharacteristic
143C2×C4×C11C22×D411yescharacteristic
144C2×C4×C11C2×#4111yescharacteristic
145C2×Dic11—42no—
146C2×Dic11—42no—
147Dic22—42no—
148Dic22—42no—
149Dic22—82no—
150C8×C11—21no—
151C8×C11—21no—
152C8×C11—21no—
153C8×C11—42no—
154C8×C11#13712yes—
155C11⋊C8—44no—
156#533—112no—
157C2×C4×Q8C2×D1111yescharacteristic
158#500—111no—
159#494—111no—
160#487—112no—
161#479—224no—
162#477—114no—
163#475—114no—
164#467—221no—
165#467—221no—
166#446—21no—
167#446—21no—
168#446C2×D1112yes—
169#446C2×D1112yes—
170C4×Q16—221no—
171C4×Q16—221no—
172#428—222no—
173#423—112no—
174C2×C4⋊C8—21no—
175C2×C4⋊C8C2×D1111yescharacteristic
176#419—222no—
177C2×#97—21no—
178C2×C4×C8C2×D1111yescharacteristic
179#334—112no—
180#334—112no—
181#333—114no—
182#332—114no—
183C22×C11—21no—
184C22×C11—21no—
185C22×C11#47012yes—
186C22×C11C2×#12111yescharacteristic
187C4×C11—21no—
188C4×C11—21no—
189C4×C11—21no—
190C4×C11—42no—
191C4×C11—42no—
192C4×C11#47012yes—
193C4×C11C2×#13712yes—
194C4×C11C2×#13711yescharacteristic
195C4×C11#57511yescharacteristic
196Dic11—82no—
197Dic11—82no—
198C22×Q8D4411yescharacteristic
199C2×Q16—221no—
200C2×Q16—221no—
201C2×M16—222no—
202C22×C8—21no—
203C22×C8C22⋊D1111yescharacteristic
204C22×C8C22⋊D1111yescharacteristic
205C4⋊Q8—112no—
206C4⋊Q8—112no—
207#125—222no—
208C22⋊Q8—222no—
209C22⋊Q8—222no—
210C4×Q8—21no—
211C4×Q8—21no—
212C4×Q8—222no—
213C4×Q8—222no—
214C4×Q8D4412yes—
215C4×Q8C22×D1112yes—
216#117—222no—
217C2×C4⋊C4—21no—
218C2×C4⋊C4D4411yescharacteristic
219C2×C42—21no—
220C2×C42C22×D1111yescharacteristic
221#107—221no—
222#107—221no—
223#107—224no—
224#106—224no—
225C4⋊C8—22no—
226C4⋊C8—22no—
227C4⋊C8—21no—
228C4⋊C8—114no—
229C4⋊C8—222no—
230C4⋊C8C22×D1112yes—
231#103—224no—
232#103—224no—
233#103—222no—
234#103—222no—
235#97—22no—
236#97—22no—
237C4×C8C22⋊D1111yescharacteristic
238C4×C8C22⋊D1111yescharacteristic
239C4×C8C22×D1111yescharacteristic
240C4×C8C22×D1111yescharacteristic
241C2×C11—22no—
242C2×C11#303711yescharacteristic
243C2×C11C2×#47011yescharacteristic
244C2×C11#306711yescharacteristic
245C2×Q8—21no—
246C2×Q8—24no—
247C2×Q8—222no—
248C2×Q8—222no—
249C2×Q8C2×D4412yes—
250C22×C4—21no—
251C22×C4—21no—
252C22×C4C2×D4411yescharacteristic
253C22×C4#433911yescharacteristic
254C22×C4C2×C22⋊D1111yescharacteristic
255Q16—442no—
256Q16—442no—
257M16—444no—
258C2×C8—22no—
259C2×C8—22no—
260C2×C8—41no—
261C2×C8—42no—
262C2×C8—224no—
263C2×C8C2×C22⋊D1111yescharacteristic
264C2×C8C2×C22⋊D1111yescharacteristic
265C2×C8C2×C22⋊D1111yescharacteristic
266C2×C8C2×C22⋊D1111yescharacteristic
267C4⋊C4—22no—
268C4⋊C4—21no—
269C4⋊C4—22no—
270C4⋊C4—222no—
271C4⋊C4—222no—
272C4⋊C4—222no—
273C4⋊C4—222no—
274C4⋊C4—442no—
275C4⋊C4—442no—
276C4⋊C4C2×D4412yes—
277C22⋊C4—442no—
278C42—22no—
279C42—22no—
280C42—442no—
281C42C2×D4411yescharacteristic
282C42#433911yescharacteristic
283C42C2×C22⋊D1111yescharacteristic
284C42C23×D1111yescharacteristic
285C11#1928711yescharacteristic, complemented, Sylow
286C23#6698311yescharacteristic
287Q8—24no—
288Q8—42no—
289Q8—442no—
290Q8—442no—
291Q8—882no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—22no—
295C2×C4—22no—
296C2×C4—41no—
297C2×C4—42no—
298C2×C4—42no—
299C2×C4—442no—
300C2×C4—442no—
301C2×C4#6696214yes—
302C2×C4#6698311yescharacteristic
303C2×C4#6698311yescharacteristic
304C2×C4#6698311yescharacteristic
305C2×C4C22×D4411yescharacteristic
306C2×C4C2×#433911yescharacteristic
307C2×C4C22×C22⋊D1111yescharacteristic
308C8—21no—
309C8—21no—
310C8—21no—
311C8—42no—
312C8—444no—
313C8#6699512yes—
314C22—21no—
315C22—21no—
316C22#1062275012yes—
317C22C2×#6698311yescharacteristic
318C4—21no—
319C4—21no—
320C4—21no—
321C4—42no—
322C4—42no—
323C4—882no—
324C4—882no—
325C4#1062275012yes—
326C4C2×#6696212yes—
327C4C2×#6699511yescharacteristic
328C4#1062335311yescharacteristic
329C2—22no—
330C2#1307808811yescharacteristic
331C2C2×#1062275011yescharacteristic
332C2#1307833611yescharacteristic
subgroupG/H
centerC22C2×#66983
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC2×C11×#446C2
socleC22×C11C2×#121
prime radicalC23×C11#121
hypercenterC2×#446D11
hypocenterC11#19287
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#446

Complements

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

NH ≅ G/Ntype
3. #13068198C2semidirect
4. #13068144C2semidirect
5. #13068110C2semidirect
285. C11#19287semidirect

Maximal subgroups

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

subgroupindex
#130792022
#130784212
#130681982
#130681442
#130681102
#130673722
#130673042
C2×C11×#4462
#1928711