Finite Group Databasebeta

← #14911468

Subgroups — #14911468

Order 2816.

472 conjugacy classes of subgroups.

The subgroup lattice has 328 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13081605C211yesmaximal, characteristic
2#13070850C212yesmaximal
3#13070845C211yesmaximal, characteristic, complemented
4#13070777C212yesmaximal, complemented
5#13070750C211yesmaximal, characteristic
6#13070678C212yesmaximal
7#13070666C211yesmaximal, characteristic, complemented
8Q8×C11⋊C16C211yesmaximal, characteristic, complemented
9C4×#66893C212yesmaximal, complemented
10C4×#66892C211yesmaximal, characteristic
11C11×#3383C211yesmaximal, characteristic, complemented
12C11×#557—21no—
13#10623115—21no—
14C11×#500C2211yescharacteristic
15C11×#499C2212yes—
16C11×#479—22no—
17C11×#475—21no—
18C8×Q8×C11C2211yescharacteristic
19C4×C11×Q16C2211yescharacteristic
20C4×C11×Q16C2212yes—
21C2×#66893C2212yes—
22C2×#66892C2211yescharacteristic
23#10622458—22no—
24#10622454—21no—
25#10622312C2211yescharacteristic
26C4×Dic44C2212yes—
27#10622309C2212yes—
28C4×D88C2211yescharacteristic
29#10622202C2211yescharacteristic
30#10622130C2212yes—
31#10622130C2212yes—
32#10622130C2212yes—
33#10622129C2211yescharacteristic
34#10622129C2212yes—
35#10622128C2211yescharacteristic
36#10622127C2212yes—
37C4⋊(C11⋊C16)C2211yescharacteristic
38C4⋊(C11⋊C16)C2212yes—
39C4×C11⋊C16C2212yes—
40C4×C11⋊C16C2211yescharacteristic
41C2×C11×Q16C2311yescharacteristic
42C11×C4⋊Q8—21no—
43C11×C4⋊Q8—41no—
44C11×#125—22no—
45C11×#125—42no—
46C4×Q8×C11—21no—
47C4×Q8×C11—22no—
48C4×Q8×C11—41no—
49C4×Q8×C11D411yescharacteristic
50#66999—41no—
51C2×Dic44—21no—
52C2×Dic44C2312yes—
53C2×D88C2311yescharacteristic
54C2×#4314—22no—
55#66951—42no—
56#66945—41no—
57#66928—22no—
58C4×D44—21no—
59#66922—21no—
60C4×Dic22—22no—
61C11×#107—21no—
62C11×#107C2311yescharacteristic
63C11×#107C2312yes—
64C11×#106—22no—
65C11×C4⋊C8D411yescharacteristic
66C11×C4⋊C8D412yes—
67C11×#103—22no—
68C11×#103—21no—
69C4×C8×C11C2312yes—
70C4×C8×C11C2311yescharacteristic
71#66893—24no—
72#66892—22no—
73#66885—21no—
74#66882C2311yescharacteristic
75#66880—22no—
76C2×C11⋊C16C2311yescharacteristic
77C2×C11⋊C16C2312yes—
78C2×C11⋊C16C2311yescharacteristic
79#33931—111nomaximal, Sylow
80C2×Q8×C11—21no—
81C2×Q8×C11—41no—
82C2×Q8×C11D811yescharacteristic
83C2×D44—21no—
84C2×C4×D11—41no—
85C2×Dic22—22no—
86C11×Q16—21no—
87C11×Q16#4112yes—
88C2×C8×C11C2×D412yes—
89C2×C8×C11C2×D411yescharacteristic
90C2×C8×C11C2411yescharacteristic
91C11×C4⋊C4—21no—
92C11×C4⋊C4—22no—
93C11×C4⋊C4—41no—
94C11×C4⋊C4—42no—
95C11×C4⋊C4—42no—
96C11×C4⋊C4—42no—
97C11×C4⋊C4—41no—
98C11×C4⋊C4D811yescharacteristic
99C11×C4⋊C4D812yes—
100C42×C11—42no—
101C42×C11—41no—
102C42×C11C2×D412yes—
103C42×C11C2×D411yescharacteristic
104(C2×D11)⋊C4—41no—
105(C2×D11)⋊C4—42no—
106(C2×D11)⋊C4—42no—
107C4⋊Dic11—21no—
108C4⋊Dic11—41no—
109C4⋊Dic11—41no—
110Dic11⋊C4—42no—
111C4×Dic11—42no—
112Dic44—22no—
113Dic44—22no—
114Dic44—81no—
115D88—21no—
116D88—21no—
117#4314—82no—
118C11⋊C16—21no—
119C11⋊C16—22no—
120C11⋊C16—21no—
121#3393—111no—
122#3383D1111yescharacteristic, complemented
123#2242—112no—
124#2241—111no—
125#2229—112no—
126#2224—111no—
127#2211—112no—
128#2209—111no—
129Q8×C16—111no—
130C4×Q32—112no—
131C4×SD32—111no—
132C22×D11—41no—
133Q8×C11—22no—
134Q8×C11—22no—
135Q8×C11—41no—
136Q8×C11—82no—
137C2×C4×C11—41no—
138C2×C4×C11—41no—
139C2×C4×C11—42no—
140C2×C4×C11C2×D812yes—
141C2×C4×C11C2×D812yes—
142C2×C4×C11C2×D811yescharacteristic
143C2×C4×C11C2×D811yescharacteristic
144C2×C4×C11C22×D411yescharacteristic
145C2×Dic11—41no—
146C2×Dic11—42no—
147D44—41no—
148D44—41no—
149C4×D11—82no—
150Dic22—42no—
151Dic22—42no—
152C8×C11—22no—
153C8×C11—21no—
154C8×C11C2×#4111yescharacteristic
155C8×C112−1+411yescharacteristic
156#557—21no—
157#556—221no—
158C2×Q32—112no—
159C2×SD32—111no—
160#500C2×D1111yescharacteristic
161#499C2×D1112yes—
162#495—112no—
163#494—111no—
164#479—22no—
165#475—21no—
166#464—222no—
167#461—221no—
168C8×Q8C2×D1111yescharacteristic
169C4×Q16—112no—
170C4×Q16C2×D1111yescharacteristic
171C4×Q16C2×D1112yes—
172C4×D8—111no—
173#367—111no—
174#366—112no—
175C4⋊C16—111no—
176C4⋊C16—112no—
177#358—111no—
178#358—112no—
179#358—112no—
180#358—112no—
181#357—111no—
182#357—112no—
183C4×C16—111no—
184C4×C16—112no—
185C22×C11C22×D811yescharacteristic
186C2×D11—81no—
187C2×D11—81no—
188C2×D11—81no—
189C4×C11—22no—
190C4×C11—22no—
191C4×C11—21no—
192C4×C11—42no—
193C4×C11—82no—
194C4×C11—81no—
195C4×C11#50812yes—
196C4×C11#54811yescharacteristic
197C4×C11#57711yescharacteristic
198Dic11—82no—
199Dic11—81no—
200C2×Q16—112no—
201C2×Q16—221no—
202C2×Q16C22×D1111yescharacteristic
203C2×SD16—222no—
204C2×D8—111no—
205C4⋊Q8—21no—
206C4⋊Q8—41no—
207C4⋊Q8—221no—
208#126—442no—
209#125—22no—
210#125—42no—
211#124—222no—
212C22⋊Q8—441no—
213C4×Q8—21no—
214C4×Q8—22no—
215C4×Q8—41no—
216C4×Q8—222no—
217C4×Q8C22⋊D1111yescharacteristic
218C4×D4—221no—
219#117—441no—
220Q32—224no—
221SD32—222no—
222C2×C16—111no—
223C2×C16—112no—
224C2×C16—111no—
225#107—21no—
226#107—111no—
227#107C22×D1112yes—
228#107C22×D1111yescharacteristic
229#106—22no—
230C4⋊C8C22⋊D1111yescharacteristic
231C4⋊C8C22⋊D1112yes—
232#103—22no—
233#103—21no—
234#103—222no—
235#102—221no—
236C4×C8C22×D1111yescharacteristic
237C4×C8C22×D1112yes—
238C2×C11#335811yescharacteristic
239C2×C11C2×#50811yescharacteristic
240C2×C11#341711yescharacteristic
241D11—161no—
242C2×Q8—21no—
243C2×Q8—41no—
244C2×Q8—222no—
245C2×Q8#432311yescharacteristic
246C2×D4—221no—
247C22×C4—441no—
248Q16—21no—
249Q16—222no—
250Q16—222no—
251Q16—881no—
252Q16#434312yes—
253SD16—882no—
254D8—221no—
255D8—221no—
256C2×C8C2×C22⋊D1111yescharacteristic
257C2×C8C2×C22⋊D1112yes—
258C2×C8C23×D1111yescharacteristic
259C4⋊C4—21no—
260C4⋊C4—22no—
261C4⋊C4—41no—
262C4⋊C4—42no—
263C4⋊C4—42no—
264C4⋊C4—42no—
265C4⋊C4—41no—
266C4⋊C4—221no—
267C4⋊C4—441no—
268C4⋊C4—442no—
269C4⋊C4—441no—
270C4⋊C4#432311yescharacteristic
271C4⋊C4#432312yes—
272C22⋊C4—442no—
273C22⋊C4—441no—
274C22⋊C4—442no—
275C42—42no—
276C42—41no—
277C42—442no—
278C42C2×C22⋊D1111yescharacteristic
279C42C2×C22⋊D1112yes—
280C16—221no—
281C16—222no—
282C16—221no—
283C11#3393111yescharacteristic, complemented, Sylow
284C23—441no—
285Q8—22no—
286Q8—22no—
287Q8—41no—
288Q8—82no—
289Q8—442no—
290Q8—442no—
291D4—441no—
292D4—441no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—42no—
296C2×C4—441no—
297C2×C4—442no—
298C2×C4—882no—
299C2×C4C2×#432312yes—
300C2×C4C2×#432311yescharacteristic
301C2×C4C2×#432312yes—
302C2×C4C2×#432311yescharacteristic
303C2×C4C22×C22⋊D1111yescharacteristic
304C8—22no—
305C8—21no—
306C8C2×#434311yescharacteristic
307C8#6704011yescharacteristic
308C22—881no—
309C22—881no—
310C22—881no—
311C22C22×#432311yescharacteristic
312C4—22no—
313C4—22no—
314C4—21no—
315C4—42no—
316C4—82no—
317C4—81no—
318C4—881no—
319C4—882no—
320C4#1062280712yes—
321C4#1062334811yescharacteristic
322C4#1062336811yescharacteristic
323C2—1761no—
324C2#1308125111yescharacteristic
325C2C2×#1062280711yescharacteristic
326C2#1308176711yescharacteristic
subgroupG/H
centerC22C22×#4323
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#3383C2
socleC22×C11C22×D8
prime radicalC2×D88C23
hypercenter#3383D11
hypocenterC11#33931
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C4×Q8 ◁ C8×Q8 ◁ #3383

Complements

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

NH ≅ G/Ntype
3. #13070845C2semidirect
4. #13070777C2semidirect
7. #13070666C2semidirect
8. Q8×C11⋊C16C2semidirect
9. C4×#66893C2semidirect
11. C11×#3383C2semidirect
122. #3383D11semidirect
283. C11#33931semidirect

Maximal subgroups

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

subgroupindex
#130816052
#130708502
#130708452
#130707772
#130707502
#130706782
#130706662
Q8×C11⋊C162
C4×#668932
C4×#668922
C11×#33832
#3393111