Finite Group Databasebeta

← #14911569

Subgroups — #14911569

Order 2816.

476 conjugacy classes of subgroups.

The subgroup lattice has 330 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13081620C211yesmaximal, characteristic, complemented
2#13081485C211yesmaximal, characteristic
3#13070860C212yesmaximal, complemented
4#13070778C212yesmaximal, complemented
5#13070765C211yesmaximal, characteristic, complemented
6#13070660C212yesmaximal
7#13070658C211yesmaximal, characteristic
8#13070524C211yesmaximal, characteristic, complemented
9#13070483C212yesmaximal
10C4×#66864C211yesmaximal, characteristic
11C11×#2241C211yesmaximal, characteristic, complemented
12#10623261—21no—
13#10623252—21no—
14C11×#500C2211yescharacteristic
15C11×#494C2211yescharacteristic
16Q16×Dic11C2212yes—
17#10622795—22no—
18#10622794C2212yes—
19C2×#66892C2212yes—
20#10622703—21no—
21#10622697—21no—
22C2×#66864C2211yescharacteristic
23#10622504—22no—
24#10622491C2212yes—
25#10622485C2212yes—
26C4×Dic44C2211yescharacteristic
27C4×D88C2211yescharacteristic
28C8×Dic22C2211yescharacteristic
29C11×#358C2212yes—
30C11×#358C2212yes—
31C4×C11×C16C2211yescharacteristic
32#10622202C2212yes—
33#10622147C2211yescharacteristic
34#10622143C2211yescharacteristic
35#10622141C2211yescharacteristic
36#10622140C2212yes—
37Dic11⋊C16C2212yes—
38#10622130C2212yes—
39#10622127C2212yes—
40C4⋊(C11⋊C16)C2211yescharacteristic
41C2×C11×Q16—21no—
42C2×C11×Q16C2312yes—
43C11×C4⋊Q8—21no—
44C11×C4⋊Q8—21no—
45#66999—42no—
46Q8×Dic11—22no—
47#66997—22no—
48C2×#4326—22no—
49C2×Dic44C2311yescharacteristic
50C2×D88C2311yescharacteristic
51#66950—41no—
52#66946—22no—
53C4⋊C4×D11—41no—
54#66943—22no—
55#66943—41no—
56#66942—42no—
57#66940—41no—
58C4×D44—21no—
59C4×Dic22—21no—
60C4×Dic22D411yescharacteristic
61C2×C11×C16C2311yescharacteristic
62C2×C11×C16C2311yescharacteristic
63C11×#107—21no—
64C11×#107C2312yes—
65C4×C8×C11C2311yescharacteristic
66#66899—22no—
67#66892—24no—
68#66885—21no—
69#66882C2311yescharacteristic
70#66882C2311yescharacteristic
71#66880—21no—
72Dic11⋊C8D412yes—
73C8×Dic11C2312yes—
74C2×C11⋊C16C2312yes—
75#66873—22no—
76#66872—22no—
77C4⋊(C11⋊C8)D411yescharacteristic
78#66864—22no—
79#33939—111nomaximal, Sylow
80C2×Q8×C11—22no—
81C2×Q8×C11—41no—
82C2×D44—21no—
83C2×C4×D11—42no—
84C2×C4×D11—41no—
85C2×Dic22—21no—
86C2×Dic22D811yescharacteristic
87C11×Q16—22no—
88C11×Q16—22no—
89C11×Q16—81no—
90C2×C8×C11C2×D411yescharacteristic
91C2×C8×C11C2411yescharacteristic
92C11×C4⋊C4—22no—
93C11×C4⋊C4—41no—
94C11×C4⋊C4—41no—
95C11×C4⋊C4—41no—
96C42×C11C2×D411yescharacteristic
97#4326—82no—
98(C2×D11)⋊C4—42no—
99(C2×D11)⋊C4—41no—
100C4⋊Dic11—21no—
101C4⋊Dic11—21no—
102C4⋊Dic11—42no—
103C4⋊Dic11—42no—
104C4⋊Dic11D811yescharacteristic
105Dic11⋊C4—42no—
106Dic11⋊C4—42no—
107Dic11⋊C4—42no—
108Dic11⋊C4—41no—
109Dic11⋊C4D812yes—
110C4×Dic11—42no—
111C4×Dic11—41no—
112C4×Dic11C2×D412yes—
113C2×C11⋊C8C2×D412yes—
114Dic44—21no—
115Dic44—21no—
116D88—21no—
117D88#4112yes—
118C11×C16—21no—
119C11×C16—21no—
120C11⋊C16—22no—
121#3395—111no—
122#3380—111no—
123#2245—112no—
124#2241D1111yescharacteristic, complemented
125#2229—112no—
126#2227—111no—
127#2208—111no—
128#2208—112no—
129#2183—111no—
130#2175—112no—
131C4×SD32—111no—
132C22×D11—41no—
133Q8×C11—42no—
134Q8×C11—42no—
135Q8×C11—161no—
136C2×C4×C11—42no—
137C2×C4×C11—42no—
138C2×C4×C11C2×D811yescharacteristic
139C2×C4×C11C2×D811yescharacteristic
140C2×C4×C11C22×D411yescharacteristic
141C2×Dic11—41no—
142C2×Dic11—41no—
143C2×Dic11—41no—
144C2×Dic11C2×D812yes—
145C2×Dic11C2×D812yes—
146D44—22no—
147D44—41no—
148C4×D11—82no—
149C4×D11—162no—
150Dic22—22no—
151Dic22—41no—
152Dic22—41no—
153C8×C11—21no—
154C8×C11C2×#4111yescharacteristic
155C8×C112−1+411yescharacteristic
156C11⋊C8—22no—
157#557—221no—
158#554—221no—
159C2×SD32—112no—
160C2×SD32—111no—
161#500C2×D1111yescharacteristic
162#499—112no—
163#494—112no—
164#494C2×D1111yescharacteristic
165#478—222no—
166#476—221no—
167#462—221no—
168#462—222no—
169C8×Q8—111no—
170C4×Q16—112no—
171C4×Q16—111no—
172C4×D8—112no—
173C4×D8—111no—
174#367—111no—
175#366—112no—
176C4⋊C16—112no—
177C4⋊C16—111no—
178#358—112no—
179#358—111no—
180#358—112no—
181#358C2×D1112yes—
182#358C2×D1112yes—
183#357—111no—
184#346—112no—
185C4×C16C2×D1111yescharacteristic
186C22×C11C22×D811yescharacteristic
187C2×D11—42no—
188C2×D11—81no—
189C2×D11—81no—
190C4×C11—21no—
191C4×C11—82no—
192C4×C11—82no—
193C4×C11#51012yes—
194C4×C11#54811yescharacteristic
195C4×C11#57711yescharacteristic
196Dic11—22no—
197Dic11—22no—
198Dic11—81no—
199Dic11—81no—
200Dic11—81no—
201C2×Q16—21no—
202C2×Q16—111no—
203C2×Q16—222no—
204C2×Q16C22×D1112yes—
205C2×D8—111no—
206C4⋊Q8—21no—
207C4⋊Q8—21no—
208C4⋊Q8—222no—
209#125—222no—
210#125—442no—
211#125—441no—
212C22⋊Q8—441no—
213C22⋊Q8—442no—
214C4×Q8—111no—
215C4×Q8—222no—
216C4×Q8—221no—
217C4×Q8—441no—
218C4×D4—222no—
219C4×D4—221no—
220C2×C4⋊C4—441no—
221SD32—222no—
222SD32—224no—
223C2×C16—112no—
224C2×C16C22×D1111yescharacteristic
225C2×C16C22×D1111yescharacteristic
226#107—21no—
227#107—111no—
228#107—111no—
229#107C22×D1112yes—
230#106—222no—
231C4⋊C8—112no—
232C4⋊C8—111no—
233#103—222no—
234#103—221no—
235#102—222no—
236#102—221no—
237C4×C8—112no—
238C4×C8C22×D1111yescharacteristic
239C2×C11#335811yescharacteristic
240C2×C11C2×#51011yescharacteristic
241C2×C11#341611yescharacteristic
242D11—82no—
243C2×Q8—22no—
244C2×Q8—41no—
245C2×Q8—111no—
246C2×Q8—221no—
247C2×D4—221no—
248C22×C4—442no—
249C22×C4—441no—
250Q16—22no—
251Q16—22no—
252Q16—81no—
253Q16—221no—
254Q16—221no—
255Q16—882no—
256D8—112no—
257D8—221no—
258C2×C8—112no—
259C2×C8D4×D1111yescharacteristic
260C2×C8C23×D1111yescharacteristic
261C4⋊C4—22no—
262C4⋊C4—41no—
263C4⋊C4—41no—
264C4⋊C4—41no—
265C4⋊C4—111no—
266C4⋊C4—112no—
267C4⋊C4—221no—
268C4⋊C4—221no—
269C4⋊C4—442no—
270C4⋊C4—442no—
271C4⋊C4—442no—
272C4⋊C4—442no—
273C4⋊C4—442no—
274C4⋊C4—441no—
275C22⋊C4—442no—
276C22⋊C4—441no—
277C42—112no—
278C42—442no—
279C42—441no—
280C42D4×D1111yescharacteristic
281C16—21no—
282C16—21no—
283C16—222no—
284C11#3393911yescharacteristic, complemented, Sylow
285C23—441no—
286Q8—42no—
287Q8—42no—
288Q8—161no—
289Q8—222no—
290Q8—441no—
291Q8—441no—
292D4—222no—
293D4—441no—
294C2×C4—42no—
295C2×C4—42no—
296C2×C4—112no—
297C2×C4—112no—
298C2×C4—441no—
299C2×C4—441no—
300C2×C4—441no—
301C2×C4—882no—
302C2×C4—1762no—
303C2×C4D8×D1111yescharacteristic
304C2×C4D8×D1111yescharacteristic
305C2×C4C2×D4×D1111yescharacteristic
306C8—21no—
307C8—222no—
308C8#41×D1111yescharacteristic
309C8#6704311yescharacteristic
310C22—442no—
311C22—881no—
312C22—881no—
313C22C2×D8×D1111yescharacteristic
314C4—21no—
315C4—82no—
316C4—82no—
317C4—222no—
318C4—222no—
319C4—881no—
320C4—881no—
321C4—881no—
322C4#1062253112yes—
323C4#1062320811yescharacteristic
324C4#1062329311yescharacteristic
325C2—882no—
326C2#1308124811yescharacteristic
327C2C2×#1062253111yescharacteristic
328C2#1308175811yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2241C2
socleC22×C11C22×D8
prime radicalC2×D88C23
hypercenter#2241D11
hypocenterC11#33939
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. #13081620C2semidirect
3. #13070860C2semidirect
4. #13070778C2semidirect
5. #13070765C2semidirect
8. #13070524C2semidirect
11. C11×#2241C2semidirect
124. #2241D11semidirect
284. C11#33939semidirect

Maximal subgroups

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

subgroupindex
#130816202
#130814852
#130708602
#130707782
#130707652
#130706602
#130706582
#130705242
#130704832
C4×#668642
C11×#22412
#3393911