Finite Group Databasebeta

← #14911428

Subgroups — #14911428

Order 2816.

486 conjugacy classes of subgroups.

The subgroup lattice has 338 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13081484C211yesmaximal, characteristic, complemented
2#13070847C212yesmaximal, complemented
3#13070843C211yesmaximal, characteristic, complemented
4#13070780C212yesmaximal, complemented
5#13070763C211yesmaximal, characteristic, complemented
6#13070668C212yesmaximal
7#13070658C211yesmaximal, characteristic, complemented
8Q8×C11⋊C16C211yesmaximal, characteristic, complemented
9C4×#66892C212yesmaximal, complemented
10C4×#66890C211yesmaximal, characteristic
11C11×#3393C211yesmaximal, characteristic, complemented
12C11×#556—21no—
13#10623110—21no—
14C11×#495C2212yes—
15C11×#494C2211yescharacteristic
16C11×#464—22no—
17C11×#461—21no—
18C8×Q8×C11C2211yescharacteristic
19C4×C11×Q16C2212yes—
20C4×C11×D8C2211yescharacteristic
21C2×#66892C2212yes—
22C2×#66890C2211yescharacteristic
23#10622460—22no—
24#10622455—21no—
25C4×D88C2211yescharacteristic
26C4×D88C2212yes—
27#10622296C2212yes—
28#10622295C2211yescharacteristic
29#10622202C2212yes—
30#10622202C2212yes—
31#10622202C2212yes—
32#10622200C2212yes—
33#10622200C2211yescharacteristic
34#10622129C2211yescharacteristic
35#10622128C2212yes—
36#10622127C2211yescharacteristic
37C4⋊(C11⋊C16)C2211yescharacteristic
38C4⋊(C11⋊C16)C2212yes—
39C4×C11⋊C16C2211yescharacteristic
40C4×C11⋊C16C2212yes—
41C2×C11×Q16—21no—
42C2×C11×Q16C2312yes—
43C2×C11×SD16—22no—
44C2×C11×D8C2311yescharacteristic
45C11×C4⋊Q8—21no—
46C11×#126—42no—
47C11×#124—22no—
48C11×C22⋊Q8—41no—
49C4×Q8×C11—22no—
50C4×Q8×C11D411yescharacteristic
51C4×D4×C11—21no—
52C11×#117—41no—
53#66999—41no—
54C2×D88C2311yescharacteristic
55#66949—42no—
56C4⋊C4×D11—41no—
57C4×D44—21no—
58C4×D44—22no—
59#66923—22no—
60#66922—21no—
61C11×#107C2311yescharacteristic
62C11×C4⋊C8D411yescharacteristic
63C11×C4⋊C8D412yes—
64C11×#103—22no—
65C11×#102—21no—
66C4×C8×C11C2311yescharacteristic
67C4×C8×C11C2312yes—
68#66892—24no—
69#66890—22no—
70#66885—22no—
71#66885—21no—
72#66882—21no—
73#66882C2312yes—
74#66882C2311yescharacteristic
75#66881—22no—
76C2×C11⋊C16C2311yescharacteristic
77C2×C11⋊C16C2312yes—
78C2×C11⋊C16C2311yescharacteristic
79#33927—111nomaximal, Sylow
80C2×Q8×C11—22no—
81C2×Q8×C11D811yescharacteristic
82C2×D4×C11—21no—
83C22×C4×C11—41no—
84C2×D44—21no—
85C2×C4×D11—41no—
86C2×C4×D11—42no—
87C2×Dic22—41no—
88C11×Q16—22no—
89C11×Q16—22no—
90C11×Q16—81no—
91C11×SD16—82no—
92C11×D8—21no—
93C11×D8—21no—
94C2×C8×C11C2×D412yes—
95C2×C8×C11C2×D411yescharacteristic
96C2×C8×C11C2411yescharacteristic
97C11×C4⋊C4—21no—
98C11×C4⋊C4—41no—
99C11×C4⋊C4—42no—
100C11×C4⋊C4—41no—
101C11×C4⋊C4D811yescharacteristic
102C11×C4⋊C4D812yes—
103C11×C22⋊C4—42no—
104C11×C22⋊C4—41no—
105C11×C22⋊C4—42no—
106C42×C11—42no—
107C42×C11C2×D411yescharacteristic
108C42×C11C2×D412yes—
109(C2×D11)⋊C4—41no—
110(C2×D11)⋊C4—42no—
111C4⋊Dic11—21no—
112C4⋊Dic11—22no—
113C4⋊Dic11—41no—
114Dic11⋊C4—42no—
115Dic11⋊C4—42no—
116D88—21no—
117D88#4112yes—
118C11⋊C16—21no—
119C11⋊C16—22no—
120C11⋊C16—21no—
121#3393D1111yescharacteristic, complemented
122#3380—111no—
123#2242—112no—
124#2241—111no—
125#2229—112no—
126#2226—111no—
127#2210—112no—
128#2208—111no—
129Q8×C16—111no—
130C4×SD32—112no—
131C4×D16—111no—
132C23×C11—41no—
133C22×D11—41no—
134Q8×C11—22no—
135Q8×C11—42no—
136Q8×C11—42no—
137D4×C11—41no—
138D4×C11—41no—
139C2×C4×C11—41no—
140C2×C4×C11—42no—
141C2×C4×C11—82no—
142C2×C4×C11C2×D812yes—
143C2×C4×C11C2×D812yes—
144C2×C4×C11C2×D811yescharacteristic
145C2×C4×C11C2×D811yescharacteristic
146C2×C4×C11C22×D411yescharacteristic
147C2×Dic11—41no—
148C2×Dic11—42no—
149D44—22no—
150D44—41no—
151C4×D11—82no—
152C4×D11—162no—
153Dic22—161no—
154C8×C11—22no—
155C8×C11—21no—
156C8×C11C2×#4111yescharacteristic
157C8×C112−1+411yescharacteristic
158#556—21no—
159#554—221no—
160C2×SD32—112no—
161C2×D16—111no—
162#500—111no—
163#499—112no—
164#495C2×D1112yes—
165#494C2×D1111yescharacteristic
166#478—222no—
167#476—221no—
168#464—22no—
169#461—21no—
170C8×Q8C2×D1111yescharacteristic
171C4×Q16C2×D1112yes—
172C4×D8—111no—
173C4×D8—112no—
174C4×D8C2×D1111yescharacteristic
175#367—112no—
176#366—111no—
177C4⋊C16—111no—
178C4⋊C16—112no—
179#358—112no—
180#358—112no—
181#358—112no—
182#357—111no—
183#357—112no—
184#357—111no—
185C4×C16—111no—
186C4×C16—112no—
187C22×C11—81no—
188C22×C11—81no—
189C22×C11—81no—
190C22×C11C22×D811yescharacteristic
191C2×D11—42no—
192C2×D11—81no—
193C2×D11—81no—
194C4×C11—22no—
195C4×C11—21no—
196C4×C11—22no—
197C4×C11—82no—
198C4×C11—81no—
199C4×C11#50812yes—
200C4×C11#54811yescharacteristic
201C4×C11#57711yescharacteristic
202Dic11—81no—
203Dic11—82no—
204C2×Q16—21no—
205C2×Q16C22×D1112yes—
206C2×SD16—22no—
207C2×D8—111no—
208C2×D8C22×D1111yescharacteristic
209C4⋊Q8—21no—
210C4⋊Q8—221no—
211#126—42no—
212#125—222no—
213#124—22no—
214C22⋊Q8—41no—
215C22⋊Q8—441no—
216C22⋊Q8—442no—
217C4×Q8—22no—
218C4×Q8C22⋊D1111yescharacteristic
219C4×D4—21no—
220C4×D4—221no—
221C4×D4—222no—
222#117—41no—
223C2×C4⋊C4—441no—
224SD32—224no—
225D16—222no—
226C2×C16—111no—
227C2×C16—112no—
228C2×C16—111no—
229#107—111no—
230#107—112no—
231#107—221no—
232#107C22×D1111yescharacteristic
233#106—222no—
234C4⋊C8C22⋊D1111yescharacteristic
235C4⋊C8C22⋊D1112yes—
236#103—22no—
237#102—21no—
238#102—222no—
239#102—221no—
240C4×C8C22×D1111yescharacteristic
241C4×C8C22×D1112yes—
242C2×C11—161no—
243C2×C11#335811yescharacteristic
244C2×C11C2×#50811yescharacteristic
245C2×C11#341611yescharacteristic
246D11—82no—
247C2×Q8—22no—
248C2×Q8—441no—
249C2×Q8#432311yescharacteristic
250C2×D4—21no—
251C2×D4—221no—
252C22×C4—41no—
253C22×C4—441no—
254C22×C4—442no—
255Q16—22no—
256Q16—22no—
257Q16—81no—
258SD16—82no—
259D8—21no—
260D8—21no—
261D8—112no—
262D8—221no—
263C2×C8C2×C22⋊D1111yescharacteristic
264C2×C8C2×C22⋊D1112yes—
265C2×C8C23×D1111yescharacteristic
266C4⋊C4—21no—
267C4⋊C4—41no—
268C4⋊C4—42no—
269C4⋊C4—41no—
270C4⋊C4—221no—
271C4⋊C4—222no—
272C4⋊C4—442no—
273C4⋊C4—441no—
274C4⋊C4—442no—
275C4⋊C4#432311yescharacteristic
276C4⋊C4#432312yes—
277C22⋊C4—42no—
278C22⋊C4—41no—
279C22⋊C4—42no—
280C22⋊C4—441no—
281C22⋊C4—442no—
282C42—42no—
283C42C2×C22⋊D1111yescharacteristic
284C42C2×C22⋊D1112yes—
285C16—221no—
286C16—222no—
287C16—221no—
288C11#3392711yescharacteristic, complemented, Sylow
289C23—41no—
290C23—441no—
291Q8—22no—
292Q8—42no—
293Q8—42no—
294Q8—1761no—
295D4—41no—
296D4—41no—
297D4—222no—
298D4—441no—
299C2×C4—41no—
300C2×C4—42no—
301C2×C4—82no—
302C2×C4—441no—
303C2×C4—442no—
304C2×C4—882no—
305C2×C4—1762no—
306C2×C4C2×#432312yes—
307C2×C4C2×#432312yes—
308C2×C4C2×#432311yescharacteristic
309C2×C4C2×#432311yescharacteristic
310C2×C4C22×C22⋊D1111yescharacteristic
311C8—22no—
312C8—21no—
313C8#41×D1111yescharacteristic
314C8#6704311yescharacteristic
315C22—81no—
316C22—81no—
317C22—81no—
318C22—442no—
319C22—881no—
320C22—881no—
321C22C22×#432311yescharacteristic
322C4—22no—
323C4—22no—
324C4—21no—
325C4—81no—
326C4—82no—
327C4—881no—
328C4—882no—
329C4#1062280712yes—
330C4#1062336211yescharacteristic
331C4#1062336711yescharacteristic
332C2—161no—
333C2—882no—
334C2#1308124711yescharacteristic
335C2C2×#1062280711yescharacteristic
336C2#1308176011yescharacteristic
subgroupG/H
centerC22C22×#4323
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#3393C2
socleC22×C11C22×D8
prime radicalC2×#66890C22
hypercenter#3393D11
hypocenterC11#33927
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C4×Q8 ◁ C8×Q8 ◁ #3393

Complements

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

NH ≅ G/Ntype
1. #13081484C2semidirect
2. #13070847C2semidirect
3. #13070843C2semidirect
4. #13070780C2semidirect
5. #13070763C2semidirect
7. #13070658C2semidirect
8. Q8×C11⋊C16C2semidirect
9. C4×#66892C2semidirect
11. C11×#3393C2semidirect
121. #3393D11semidirect
288. C11#33927semidirect

Maximal subgroups

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

subgroupindex
#130814842
#130708472
#130708432
#130707802
#130707632
#130706682
#130706582
Q8×C11⋊C162
C4×#668922
C4×#668902
C11×#33932
#3392711