Finite Group Databasebeta

← #14909146

Subgroups — #14909146

Order 2816.

622 conjugacy classes of subgroups.

The subgroup lattice has 346 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D11×#500C211yesmaximal, characteristic, complemented
2#13079045C211yesmaximal, characteristic
3#13070854C214yesmaximal, complemented
4#13070843C211yesmaximal, characteristic, complemented
5#13070841C211yesmaximal, characteristic, complemented
6#13070840C211yesmaximal, characteristic, complemented
7#13070327C214yesmaximal, complemented
8C4×#66862C211yesmaximal, characteristic, complemented
9C11×#2241C211yesmaximal, characteristic, complemented
10C2×#66972—21no—
11C2×#66972C2212yes—
12#10623256—21no—
13D11×C4⋊Q8—21no—
14C11×#500C2211yescharacteristic
15C11×#494C2211yescharacteristic
16#10622804—21no—
17#10622804C2212yes—
18#10622698—21no—
19#10622691—21no—
20C2×#66862C2212yes—
21D11×#107—21no—
22D11×#107C2212yes—
23#10622487—21no—
24#10622487C2212yes—
25#10622308C2211yescharacteristic
26C4×C8×D11C2211yescharacteristic
27#10622295C2211yescharacteristic
28C11×#358C2214yes—
29C4×C11×C16C2211yescharacteristic
30#10622202C2214yes—
31#10622147C2214yes—
32#10622140C2212yes—
33#10622129C2214yes—
34C4×C11⋊C16C2211yescharacteristic
35C2×#4343—22no—
36C2×Q8×D11—41no—
37C2×C11×Q16—21no—
38C2×C11×Q16C2312yes—
39C11×C4⋊Q8—21no—
40C11×C4⋊Q8—21no—
41#67000—22no—
42#66997—41no—
43C2×#4325—22no—
44C2×#4325—22no—
45#66972—28no—
46#66972—44no—
47C2×D88—21no—
48C2×D88C2312yes—
49C2×C8×D11D411yescharacteristic
50C2×C8×D11C2311yescharacteristic
51#66948—41no—
52#66948—41no—
53#66946—41no—
54#66946—41no—
55C4⋊C4×D11—22no—
56C4⋊C4×D11—41no—
57#66941—22no—
58#66941—41no—
59#66927—21no—
60C42×D11D411yescharacteristic
61#66922—21no—
62C2×C11×C16C2312yes—
63C11×#107—21no—
64C11×#107C2312yes—
65C4×C8×C11C2311yescharacteristic
66#66882—21no—
67#66882C2312yes—
68C8×Dic11D411yescharacteristic
69C8×Dic11C2311yescharacteristic
70C2×C11⋊C16C2312yes—
71#66871—22no—
72#66871—22no—
73C4×C11⋊C8D411yescharacteristic
74#66862—24no—
75#33707—111nomaximal, Sylow
76C2×Q8×C11—22no—
77C2×Q8×C11—41no—
78#4343—44no—
79#4343—44no—
80Q8×D11—84no—
81C2×D44—22no—
82C2×D44—42no—
83C2×D44—41no—
84C2×D44—41no—
85C2×C4×D11—42no—
86C2×C4×D11—42no—
87C2×C4×D11D811yescharacteristic
88C2×C4×D11D811yescharacteristic
89C2×C4×D11C2×D411yescharacteristic
90C2×Dic22—42no—
91C2×Dic22—41no—
92C11×Q16—24no—
93C11×Q16—42no—
94C2×C8×C11C2×D411yescharacteristic
95C2×C8×C11C2411yescharacteristic
96C11×C4⋊C4—22no—
97C11×C4⋊C4—41no—
98C11×C4⋊C4—41no—
99C11×C4⋊C4—41no—
100C42×C11C2×D411yescharacteristic
101#4325—44no—
102#4325—44no—
103(C2×D11)⋊C4—42no—
104(C2×D11)⋊C4—42no—
105C4⋊Dic11—22no—
106C4⋊Dic11—41no—
107Dic11⋊C4—42no—
108Dic11⋊C4—42no—
109C4×Dic11D811yescharacteristic
110C4×Dic11D811yescharacteristic
111C4×Dic11C2×D411yescharacteristic
112C2×C11⋊C8C2×D411yescharacteristic
113C2×C11⋊C8C2×D411yescharacteristic
114D88—24no—
115D88—42no—
116C8×D11SD1614yes—
117C8×D11#4114yes—
118C11×C16—22no—
119C11⋊C16—22no—
120C2×#500—111no—
121#3147—111no—
122#2243—114no—
123#2241—111no—
124#2241D1111yescharacteristic, complemented
125#2240—111no—
126#2240—111no—
127#2139—114no—
128C4×M32—111no—
129C22×D11—42no—
130C22×D11C2×D811yescharacteristic
131Q8×C11—42no—
132Q8×C11—42no—
133Q8×C11—82no—
134C2×C4×C11—42no—
135C2×C4×C11—42no—
136C2×C4×C11C2×D811yescharacteristic
137C2×C4×C11C2×D811yescharacteristic
138C2×C4×C11C22×D411yescharacteristic
139C2×Dic11—42no—
140C2×Dic11C2×D811yescharacteristic
141C2×Dic11C2×D811yescharacteristic
142C2×Dic11C2×D811yescharacteristic
143D44—42no—
144D44—42no—
145D44—84no—
146D44—82no—
147D44—82no—
148C4×D11—22no—
149C4×D11—22no—
150C4×D11—84no—
151C4×D11—84no—
152C4×D11#12412yes—
153C4×D11C2×SD1612yes—
154Dic22—84no—
155Dic22—82no—
156C8×C11C2×SD1612yes—
157C8×C11C2×#4112yes—
158C11⋊C8#12412yes—
159C11⋊C8C2×SD1612yes—
160C2×#135—112no—
161C2×#135—221no—
162#532—221no—
163C2×C4⋊Q8—221no—
164C2×M32—112no—
165#500—112no—
166#500—111no—
167#500—221no—
168#500—221no—
169#500C2×D1111yescharacteristic
170#495—112no—
171#495—221no—
172#494C2×D1111yescharacteristic
173#493—111no—
174#492—221no—
175C2×#107—112no—
176C2×#107—221no—
177C2×C4×C8—111no—
178#358—114no—
179#358C2×D1114yes—
180#357—114no—
181#357—114no—
182#346—112no—
183C4×C16—111no—
184C4×C16C2×D1111yescharacteristic
185C22×C11C22×D811yescharacteristic
186C2×D11—21no—
187C2×D11—21no—
188C2×D11—82no—
189C2×D11—82no—
190C2×D11—82no—
191C2×D11#48612yes—
192C4×C11—82no—
193C4×C11—82no—
194C4×C11#50912yes—
195C4×C11#51012yes—
196C4×C11C2×#12411yescharacteristic
197C4×C11C22×SD1611yescharacteristic
198Dic11—21no—
199Dic11—21no—
200Dic11—82no—
201Dic11#48612yes—
202C2×#41—222no—
203C22×Q8—441no—
204#135—228no—
205#135—444no—
206C2×Q16—21no—
207C2×Q16C22×D1112yes—
208C2×SD16—222no—
209C2×SD16—222no—
210C2×D8—112no—
211C2×D8—221no—
212C22×C8—111no—
213C22×C8—111no—
214C4⋊Q8—21no—
215C4⋊Q8—21no—
216C4⋊Q8—222no—
217C4⋊Q8—221no—
218C4⋊Q8—441no—
219C4⋊Q8—441no—
220#127—221no—
221#124—222no—
222#121—441no—
223#121—441no—
224C4×D4—441no—
225C4×D4—441no—
226C2×C4⋊C4—222no—
227C2×C4⋊C4—441no—
228C2×C42—111no—
229M32—224no—
230C2×C16—112no—
231C2×C16C22×D1112yes—
232#107—21no—
233#107—112no—
234#107—222no—
235#107—222no—
236#107—221no—
237#107C22×D1112yes—
238C4×C8—111no—
239C4×C8—111no—
240C4×C8—111no—
241C4×C8C22×D1111yescharacteristic
242C2×C11C2×#48611yescharacteristic
243C2×C11C2×#50911yescharacteristic
244C2×C11C2×#51011yescharacteristic
245D11—22no—
246D11—162no—
247#41—444no—
248#41—444no—
249C2×Q8—22no—
250C2×Q8—41no—
251C2×Q8—442no—
252C2×Q8—441no—
253C2×Q8—884no—
254C2×D4—222no—
255C2×D4—442no—
256C2×D4—441no—
257C2×D4—441no—
258C22×C4—111no—
259C22×C4—111no—
260C22×C4—111no—
261C22×C4—442no—
262C22×C4—442no—
263Q16—24no—
264Q16—42no—
265SD16—444no—
266SD16—444no—
267D8—224no—
268D8—442no—
269C2×C8—111no—
270C2×C8—111no—
271C2×C8—114no—
272C2×C8—114no—
273C2×C8D4×D1111yescharacteristic
274C2×C8C23×D1111yescharacteristic
275C4⋊C4—22no—
276C4⋊C4—41no—
277C4⋊C4—41no—
278C4⋊C4—41no—
279C4⋊C4—222no—
280C4⋊C4—442no—
281C4⋊C4—442no—
282C4⋊C4—441no—
283C22⋊C4—442no—
284C22⋊C4—442no—
285C42—111no—
286C42—111no—
287C42—111no—
288C42D4×D1111yescharacteristic
289C16—22no—
290C16—222no—
291C11#3370711yescharacteristic, complemented, Sylow
292C23—111no—
293C23—442no—
294Q8—42no—
295Q8—42no—
296Q8—82no—
297Q8—884no—
298Q8—882no—
299D4—442no—
300D4—442no—
301D4—884no—
302D4—882no—
303D4—882no—
304C2×C4—42no—
305C2×C4—42no—
306C2×C4—111no—
307C2×C4—112no—
308C2×C4—112no—
309C2×C4—111no—
310C2×C4—111no—
311C2×C4—222no—
312C2×C4—222no—
313C2×C4—442no—
314C2×C4—884no—
315C2×C4—884no—
316C2×C4D8×D1111yescharacteristic
317C2×C4D8×D1111yescharacteristic
318C2×C4C2×D4×D1111yescharacteristic
319C8—112no—
320C8—112no—
321C8SD16×D1112yes—
322C8#41×D1112yes—
323C22—112no—
324C22—221no—
325C22—221no—
326C22—882no—
327C22—882no—
328C22—882no—
329C22C2×D8×D1111yescharacteristic
330C4—82no—
331C4—82no—
332C4—112no—
333C4—221no—
334C4—221no—
335C4—882no—
336C4#1062252712yes—
337C4#1062253112yes—
338C4D11×#12411yescharacteristic
339C4C2×SD16×D1111yescharacteristic
340C2—222no—
341C2—1762no—
342C2D11×#48611yescharacteristic
343C2C2×#1062252711yescharacteristic
344C2C2×#1062253111yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2241C2
socleC22×C11C22×D8
prime radical#13079045C2
hypercenter#2241D11
hypocenterC11#33707
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2241

Complements

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

NH ≅ G/Ntype
1. D11×#500C2semidirect
3. #13070854C2semidirect
4. #13070843C2semidirect
5. #13070841C2semidirect
6. #13070840C2semidirect
7. #13070327C2semidirect
8. C4×#66862C2semidirect
9. C11×#2241C2semidirect
124. #2241D11semidirect
291. C11#33707semidirect

Maximal subgroups

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

subgroupindex
D11×#5002
#130790452
#130708542
#130708432
#130708412
#130708402
#130703272
C4×#668622
C11×#22412
#3370711