Finite Group Databasebeta

← #14911432

Subgroups — #14911432

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#13081605C211yesmaximal, characteristic, complemented
2#13070850C212yesmaximal, complemented
3#13070845C211yesmaximal, characteristic, complemented
4#13070777C212yesmaximal, complemented
5#13070760C211yesmaximal, characteristic, complemented
6#13070671C212yesmaximal
7#13070661C211yesmaximal, characteristic, complemented
8Q8×C11⋊C16C211yesmaximal, characteristic, complemented
9C4×#66891C212yesmaximal, complemented
10C4×#66890C211yesmaximal, characteristic
11C11×#3380C211yesmaximal, characteristic, complemented
12C11×#554—21no—
13#10623115—21no—
14C11×#500C2211yescharacteristic
15C11×#499C2212yes—
16C11×#478—22no—
17C11×#476—21no—
18C8×Q8×C11C2211yescharacteristic
19C4×C11×D8C2211yescharacteristic
20C4×C11×D8C2212yes—
21C2×#66891C2212yes—
22C2×#66890C2211yescharacteristic
23#10622458—22no—
24#10622454—21no—
25#10622312C2211yescharacteristic
26C4×Dic44C2212yes—
27#10622309C2212yes—
28C4×D88C2211yescharacteristic
29#10622200C2211yescharacteristic
30#10622130C2212yes—
31#10622130C2212yes—
32#10622130C2212yes—
33#10622129C2211yescharacteristic
34#10622129C2212yes—
35#10622128C2212yes—
36#10622127C2211yescharacteristic
37C4⋊(C11⋊C16)C2211yescharacteristic
38C4⋊(C11⋊C16)C2212yes—
39C4×C11⋊C16C2212yes—
40C4×C11⋊C16C2211yescharacteristic
41C2×C11×D8C2311yescharacteristic
42C11×C4⋊Q8—21no—
43C11×#125—22no—
44C11×C22⋊Q8—41no—
45C11×C22⋊Q8—42no—
46C4×Q8×C11D411yescharacteristic
47C4×D4×C11—21no—
48C4×D4×C11—22no—
49C2×C11×C4⋊C4—41no—
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×#102—22no—
68C11×#102—21no—
69C4×C8×C11C2312yes—
70C4×C8×C11C2311yescharacteristic
71#66891—24no—
72#66890—22no—
73#66885—21no—
74#66882C2311yescharacteristic
75#66880—22no—
76C2×C11⋊C16C2311yescharacteristic
77C2×C11⋊C16C2312yes—
78C2×C11⋊C16C2311yescharacteristic
79#33927—111nomaximal, Sylow
80C2×Q8×C11—41no—
81C2×Q8×C11D811yescharacteristic
82C2×D4×C11—21no—
83C22×C4×C11—41no—
84C22×C4×C11—42no—
85C2×D44—21no—
86C2×C4×D11—41no—
87C2×Dic22—22no—
88C11×D8—21no—
89C11×D8#4112yes—
90C2×C8×C11C2×D412yes—
91C2×C8×C11C2×D411yescharacteristic
92C2×C8×C11C2411yescharacteristic
93C11×C4⋊C4—21no—
94C11×C4⋊C4—22no—
95C11×C4⋊C4—42no—
96C11×C4⋊C4—41no—
97C11×C4⋊C4—42no—
98C11×C4⋊C4D811yescharacteristic
99C11×C4⋊C4D812yes—
100C11×C22⋊C4—41no—
101C11×C22⋊C4—42no—
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#3380D1111yescharacteristic, complemented
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—161no—
136D4×C11—22no—
137D4×C11—41no—
138C2×C4×C11—41no—
139C2×C4×C11—42no—
140C2×C4×C11—82no—
141C2×C4×C11—162no—
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—41no—
150D44—41no—
151C4×D11—82no—
152Dic22—42no—
153Dic22—42no—
154C8×C11—22no—
155C8×C11—21no—
156C8×C11C2×#4111yescharacteristic
157C8×C112−1+411yescharacteristic
158#556—221no—
159#554—21no—
160C2×SD32—112no—
161C2×D16—111no—
162#500C2×D1111yescharacteristic
163#499C2×D1112yes—
164#495—112no—
165#494—111no—
166#478—22no—
167#476—21no—
168#464—222no—
169#461—221no—
170C8×Q8C2×D1111yescharacteristic
171C4×Q16—112no—
172C4×D8—111no—
173C4×D8C2×D1111yescharacteristic
174C4×D8C2×D1112yes—
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—111no—
184#357—112no—
185C4×C16—111no—
186C4×C16—112no—
187C22×C11—42no—
188C22×C11—81no—
189C22×C11—81no—
190C22×C11C22×D811yescharacteristic
191C2×D11—81no—
192C2×D11—81no—
193C2×D11—81no—
194C4×C11—22no—
195C4×C11—22no—
196C4×C11—21no—
197C4×C11—81no—
198C4×C11—82no—
199C4×C11#50812yes—
200C4×C11#54811yescharacteristic
201C4×C11#57711yescharacteristic
202Dic11—82no—
203Dic11—81no—
204C2×Q16—112no—
205C2×Q16—221no—
206C2×SD16—222no—
207C2×D8—111no—
208C2×D8C22×D1111yescharacteristic
209C4⋊Q8—21no—
210C4⋊Q8—221no—
211#126—442no—
212#125—22no—
213#124—222no—
214C22⋊Q8—41no—
215C22⋊Q8—42no—
216C22⋊Q8—441no—
217C4×Q8—222no—
218C4×Q8C22⋊D1111yescharacteristic
219C4×D4—21no—
220C4×D4—22no—
221C4×D4—221no—
222#117—441no—
223C2×C4⋊C4—41no—
224SD32—224no—
225D16—222no—
226C2×C16—111no—
227C2×C16—112no—
228C2×C16—111no—
229#107—21no—
230#107—111no—
231#107C22×D1111yescharacteristic
232#107C22×D1112yes—
233#106—22no—
234C4⋊C8C22⋊D1111yescharacteristic
235C4⋊C8C22⋊D1112yes—
236#103—222no—
237#102—22no—
238#102—21no—
239#102—221no—
240C4×C8C22×D1111yescharacteristic
241C4×C8C22×D1112yes—
242C2×C11—82no—
243C2×C11#335811yescharacteristic
244C2×C11C2×#50811yescharacteristic
245C2×C11#341611yescharacteristic
246D11—161no—
247C2×Q8—41no—
248C2×Q8—222no—
249C2×Q8#432311yescharacteristic
250C2×D4—21no—
251C2×D4—221no—
252C22×C4—41no—
253C22×C4—42no—
254C22×C4—441no—
255Q16—222no—
256Q16—222no—
257Q16—881no—
258SD16—882no—
259D8—21no—
260D8—221no—
261D8—221no—
262D8#434312yes—
263C2×C8C2×C22⋊D1111yescharacteristic
264C2×C8C2×C22⋊D1112yes—
265C2×C8C23×D1111yescharacteristic
266C4⋊C4—21no—
267C4⋊C4—22no—
268C4⋊C4—42no—
269C4⋊C4—41no—
270C4⋊C4—42no—
271C4⋊C4—221no—
272C4⋊C4—441no—
273C4⋊C4—442no—
274C4⋊C4—441no—
275C4⋊C4#432311yescharacteristic
276C4⋊C4#432312yes—
277C22⋊C4—41no—
278C22⋊C4—42no—
279C22⋊C4—442no—
280C22⋊C4—441no—
281C22⋊C4—442no—
282C42—442no—
283C42C2×C22⋊D1111yescharacteristic
284C42C2×C22⋊D1112yes—
285C16—221no—
286C16—222no—
287C16—221no—
288C11#3392711yescharacteristic, complemented, Sylow
289C23—41no—
290C23—441no—
291Q8—22no—
292Q8—161no—
293Q8—442no—
294Q8—442no—
295D4—22no—
296D4—41no—
297D4—441no—
298D4—441no—
299C2×C4—41no—
300C2×C4—42no—
301C2×C4—82no—
302C2×C4—162no—
303C2×C4—441no—
304C2×C4—442no—
305C2×C4—882no—
306C2×C4C2×#432312yes—
307C2×C4C2×#432312yes—
308C2×C4C2×#432311yescharacteristic
309C2×C4C2×#432311yescharacteristic
310C2×C4C22×C22⋊D1111yescharacteristic
311C8—22no—
312C8—21no—
313C8C2×#434311yescharacteristic
314C8#6704011yescharacteristic
315C22—42no—
316C22—81no—
317C22—81no—
318C22—881no—
319C22—881no—
320C22—881no—
321C22C22×#432311yescharacteristic
322C4—22no—
323C4—22no—
324C4—21no—
325C4—81no—
326C4—82no—
327C4—881no—
328C4—882no—
329C4#1062280712yes—
330C4#1062334811yescharacteristic
331C4#1062336811yescharacteristic
332C2—82no—
333C2—1761no—
334C2#1308125111yescharacteristic
335C2C2×#1062280711yescharacteristic
336C2#1308176311yescharacteristic
subgroupG/H
centerC22C22×#4323
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#3380C2
socleC22×C11C22×D8
prime radicalC2×#66890C22
hypercenter#3380D11
hypocenterC11#33927
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C4×Q8 ◁ C8×Q8 ◁ #3380

Complements

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

NH ≅ G/Ntype
1. #13081605C2semidirect
2. #13070850C2semidirect
3. #13070845C2semidirect
4. #13070777C2semidirect
5. #13070760C2semidirect
7. #13070661C2semidirect
8. Q8×C11⋊C16C2semidirect
9. C4×#66891C2semidirect
11. C11×#3380C2semidirect
122. #3380D11semidirect
288. C11#33927semidirect

Maximal subgroups

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

subgroupindex
#130816052
#130708502
#130708452
#130707772
#130707602
#130706712
#130706612
Q8×C11⋊C162
C4×#668912
C4×#668902
C11×#33802
#3392711