Finite Group Databasebeta

← #14911478

Subgroups — #14911478

Order 2816.

484 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#13081626C211yesmaximal, characteristic
2#13081509C211yesmaximal, characteristic, complemented
3#13070849C212yesmaximal, complemented
4#13070841C211yesmaximal, characteristic
5#13070772C212yesmaximal, complemented
6#13070681C212yesmaximal, complemented
7#13070657C211yesmaximal, characteristic
8#13070518C211yesmaximal, characteristic, complemented
9C4×#66893C211yesmaximal, characteristic, complemented
10#13070467C212yesmaximal, complemented
11C11×#2225C211yesmaximal, characteristic, complemented
12#10623252—21no—
13#10623116—21no—
14C11×#500C2211yescharacteristic
15C4×C11×Q16C2211yescharacteristic
16#10622804C2212yes—
17C2×#66893C2211yescharacteristic
18#10622707—21no—
19#10622640—21no—
20C2×#66864C2212yes—
21#10622491C2212yes—
22#10622490—22no—
23#10622486C2212yes—
24#10622485C2212yes—
25#10622432—22no—
26C4×Dic44C2211yescharacteristic
27#10622308C2211yescharacteristic
28C8×Dic22C2211yescharacteristic
29C11×#367C2212yes—
30C11×C4⋊C16C2211yescharacteristic
31C11×#358C2212yes—
32#10622202C2211yescharacteristic
33#10622147C2212yes—
34Dic11⋊C16C2212yes—
35C16×Dic11C2212yes—
36#10622130C2211yescharacteristic
37#10622129C2212yes—
38#10622129C2212yes—
39#10622127C2211yescharacteristic
40C4×C11⋊C16C2211yescharacteristic
41C2×C11×Q16C2311yescharacteristic
42C11×C4⋊Q8—21no—
43C4×Q8×C11—21no—
44#67000—22no—
45Q8×Dic11—41no—
46#66997—41no—
47C2×#4325—22no—
48C2×Dic44C2311yescharacteristic
49C2×D88—21no—
50C2×D88C2312yes—
51#66947—42no—
52#66946—22no—
53#66943—22no—
54#66942—42no—
55#66940—22no—
56#66928—41no—
57#66927—21no—
58C4×D44—41no—
59C4×Dic22—21no—
60C4×Dic22D411yescharacteristic
61C2×C11×C16C2312yes—
62C11×#107—21no—
63C11×#107C2312yes—
64C11×#107C2311yescharacteristic
65C11×#103—21no—
66C4×C8×C11C2311yescharacteristic
67#66893—22no—
68#66882C2311yescharacteristic
69#66880—21no—
70Dic11⋊C8D412yes—
71C8×Dic11C2312yes—
72C2×C11⋊C16C2311yescharacteristic
73C2×C11⋊C16C2311yescharacteristic
74#66874—22no—
75#66873—22no—
76#66872—22no—
77C4⋊(C11⋊C8)D411yescharacteristic
78#66864—24no—
79#33932—111nomaximal, Sylow
80C2×Q8×C11—21no—
81C2×Q8×C11—41no—
82C2×D44—22no—
83C2×D44—41no—
84C2×D44—41no—
85C2×C4×D11—42no—
86C2×Dic22—21no—
87C2×Dic22D811yescharacteristic
88C11×Q16—21no—
89C11×Q16—21no—
90C2×C8×C11C2×D411yescharacteristic
91C2×C8×C11C2411yescharacteristic
92C11×C4⋊C4—22no—
93C11×C4⋊C4—21no—
94C11×C4⋊C4—41no—
95C11×C4⋊C4—41no—
96C42×C11—41no—
97C42×C11C2×D411yescharacteristic
98#4325—82no—
99(C2×D11)⋊C4—42no—
100(C2×D11)⋊C4—42no—
101(C2×D11)⋊C4—42no—
102C4⋊Dic11—21no—
103C4⋊Dic11—42no—
104C4⋊Dic11D811yescharacteristic
105Dic11⋊C4—42no—
106Dic11⋊C4—42no—
107Dic11⋊C4—41no—
108Dic11⋊C4D812yes—
109C4×Dic11—42no—
110C4×Dic11—41no—
111C4×Dic11C2×D412yes—
112C2×C11⋊C8C2×D412yes—
113Dic44—21no—
114Dic44#4112yes—
115D88—22no—
116D88—22no—
117D88—81no—
118C11×C16—22no—
119C11⋊C16—21no—
120C11⋊C16—21no—
121#3396—111no—
122#3383—111no—
123#2242—112no—
124#2240—111no—
125#2228—112no—
126#2225D1111yescharacteristic, complemented
127#2211—112no—
128#2207—111no—
129Q8×C16—111no—
130C4×Q32—111no—
131C4×SD32—112no—
132C22×D11—42no—
133Q8×C11—41no—
134Q8×C11—41no—
135Q8×C11—82no—
136C2×C4×C11—42no—
137C2×C4×C11—41no—
138C2×C4×C11—41no—
139C2×C4×C11C2×D811yescharacteristic
140C2×C4×C11C2×D811yescharacteristic
141C2×C4×C11C22×D411yescharacteristic
142C2×Dic11—41no—
143C2×Dic11—41no—
144C2×Dic11C2×D812yes—
145C2×Dic11C2×D812yes—
146D44—42no—
147D44—42no—
148D44—82no—
149D44—161no—
150C4×D11—162no—
151Dic22—22no—
152Dic22—22no—
153Dic22—41no—
154C8×C11—21no—
155C8×C11C2×#4111yescharacteristic
156C8×C112−1+411yescharacteristic
157C11⋊C8—22no—
158#559—221no—
159#557—221no—
160C2×Q32—111no—
161C2×SD32—112no—
162#500C2×D1111yescharacteristic
163#499—112no—
164#495—112no—
165#493—111no—
166#479—222no—
167#475—221no—
168#463—222no—
169#460—221no—
170C8×Q8—111no—
171C4×Q16—112no—
172C4×Q16—111no—
173C4×Q16C2×D1111yescharacteristic
174C4×D8—112no—
175#367C2×D1112yes—
176#366—111no—
177C4⋊C16—112no—
178C4⋊C16C2×D1111yescharacteristic
179#358—111no—
180#358—111no—
181#358C2×D1112yes—
182#357—112no—
183#357—112no—
184#357—112no—
185C4×C16—112no—
186C4×C16—111no—
187C22×C11C22×D811yescharacteristic
188C2×D11—82no—
189C2×D11—82no—
190C2×D11—82no—
191C4×C11—21no—
192C4×C11—81no—
193C4×C11—82no—
194C4×C11—81no—
195C4×C11#50812yes—
196C4×C11#54811yescharacteristic
197C4×C11#57711yescharacteristic
198Dic11—22no—
199Dic11—22no—
200Dic11—42no—
201Dic11—81no—
202C2×Q16—111no—
203C2×Q16C22×D1111yescharacteristic
204C2×SD16—222no—
205C2×D8—112no—
206C2×D8—221no—
207C4⋊Q8—21no—
208C4⋊Q8—441no—
209#127—221no—
210#125—222no—
211#125—442no—
212#124—222no—
213#124—441no—
214#123—442no—
215C4×Q8—21no—
216C4×Q8—111no—
217C4×Q8—222no—
218C4×Q8—221no—
219C4×Q8—441no—
220C4×D4—222no—
221C4×D4—441no—
222Q32—222no—
223SD32—224no—
224C2×C16—111no—
225C2×C16—111no—
226C2×C16C22×D1112yes—
227#107—21no—
228#107—111no—
229#107C22×D1112yes—
230#107C22×D1111yescharacteristic
231#106—222no—
232C4⋊C8—112no—
233C4⋊C8—111no—
234#103—21no—
235#103—222no—
236#103—221no—
237#102—222no—
238C4×C8—112no—
239C4×C8C22×D1111yescharacteristic
240C2×C11#335811yescharacteristic
241C2×C11C2×#50811yescharacteristic
242C2×C11#341611yescharacteristic
243D11—162no—
244C2×Q8—21no—
245C2×Q8—41no—
246C2×Q8—111no—
247C2×Q8—221no—
248C2×D4—222no—
249C2×D4—441no—
250C2×D4—441no—
251C22×C4—442no—
252Q16—21no—
253Q16—21no—
254Q16—112no—
255Q16—221no—
256SD16—882no—
257D8—222no—
258D8—222no—
259D8—881no—
260C2×C8—112no—
261C2×C8D4×D1111yescharacteristic
262C2×C8C23×D1111yescharacteristic
263C4⋊C4—21no—
264C4⋊C4—22no—
265C4⋊C4—41no—
266C4⋊C4—41no—
267C4⋊C4—111no—
268C4⋊C4—112no—
269C4⋊C4—221no—
270C4⋊C4—442no—
271C4⋊C4—442no—
272C4⋊C4—442no—
273C4⋊C4—441no—
274C22⋊C4—442no—
275C22⋊C4—442no—
276C22⋊C4—442no—
277C42—41no—
278C42—112no—
279C42—442no—
280C42—441no—
281C42D4×D1111yescharacteristic
282C16—22no—
283C16—221no—
284C16—221no—
285C11#3393211yescharacteristic, complemented, Sylow
286C23—442no—
287Q8—41no—
288Q8—41no—
289Q8—82no—
290Q8—222no—
291Q8—222no—
292Q8—441no—
293D4—442no—
294D4—442no—
295D4—882no—
296D4—1761no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—42no—
300C2×C4—112no—
301C2×C4—112no—
302C2×C4—441no—
303C2×C4—441no—
304C2×C4—1762no—
305C2×C4D8×D1111yescharacteristic
306C2×C4D8×D1111yescharacteristic
307C2×C4C2×D4×D1111yescharacteristic
308C8—21no—
309C8—222no—
310C8#6704011yescharacteristic
311C8#41×D1111yescharacteristic
312C22—882no—
313C22—882no—
314C22—882no—
315C22C2×D8×D1111yescharacteristic
316C4—21no—
317C4—82no—
318C4—81no—
319C4—81no—
320C4—222no—
321C4—222no—
322C4—442no—
323C4—881no—
324C4#1062252912yes—
325C4#1062316411yescharacteristic
326C4#1062330911yescharacteristic
327C2—1762no—
328C2#1308125011yescharacteristic
329C2C2×#1062252911yescharacteristic
330C2#1308176111yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2225C2
socleC22×C11C22×D8
prime radical#10622308C22
hypercenter#2225D11
hypocenterC11#33932
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2225

Complements

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

NH ≅ G/Ntype
2. #13081509C2semidirect
3. #13070849C2semidirect
5. #13070772C2semidirect
6. #13070681C2semidirect
8. #13070518C2semidirect
9. C4×#66893C2semidirect
10. #13070467C2semidirect
11. C11×#2225C2semidirect
126. #2225D11semidirect
285. C11#33932semidirect

Maximal subgroups

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

subgroupindex
#130816262
#130815092
#130708492
#130708412
#130707722
#130706812
#130706572
#130705182
C4×#668932
#130704672
C11×#22252
#3393211