Finite Group Databasebeta

← #14911397

Subgroups — #14911397

Order 2816.

470 conjugacy classes of subgroups.

The subgroup lattice has 326 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13081046C211yesmaximal, characteristic
2#13081008C211yesmaximal, characteristic
3#13070827C212yesmaximal, complemented
4#13070815C212yesmaximal, complemented
5#13070765C211yesmaximal, characteristic, complemented
6#13070755C211yesmaximal, characteristic, complemented
7#13070725C212yesmaximal, complemented
8C4×Dic88C211yesmaximal, characteristic, complemented
9#13070449C211yesmaximal, characteristic
10#13070403C212yesmaximal, complemented
11C11×#2254C211yesmaximal, characteristic, complemented
12#10623263—21no—
13#10623261—21no—
14C11×#500C2211yescharacteristic
15C11×#500C2211yescharacteristic
16#10622707—21no—
17#10622704—21no—
18C2×Dic88C2211yescharacteristic
19C2×#66862C2212yes—
20#10622501—22no—
21#10622500C2212yes—
22#10622500C2212yes—
23#10622497—22no—
24#10622493C2212yes—
25D11×#107C2212yes—
26C4×Dic44C2211yescharacteristic
27C4×Dic44C2211yescharacteristic
28C8×D44C2211yescharacteristic
29C11×#367C2212yes—
30C11×#367C2212yes—
31C4×C11×C16C2211yescharacteristic
32(C2×D11)⋊C16C2212yes—
33#10622142C2211yescharacteristic
34#10622141C2211yescharacteristic
35#10622141C2211yescharacteristic
36#10622130C2212yes—
37#10622130C2212yes—
38#10622128C2212yes—
39#10622127C2212yes—
40C4⋊(C11⋊C16)C2211yescharacteristic
41C11×C4⋊Q8—21no—
42C11×C4⋊Q8—21no—
43#67000—41no—
44#66999—42no—
45Q8×Dic11—41no—
46C2×Dic44C2311yescharacteristic
47C2×Dic44C2311yescharacteristic
48C2×C8×D11C2312yes—
49#66951—42no—
50#66950—22no—
51#66950—22no—
52#66946—41no—
53#66945—22no—
54C4⋊C4×D11—22no—
55#66943—41no—
56C4×D44D411yescharacteristic
57C4×Dic22—21no—
58C4×Dic22—21no—
59C2×C11×C16C2311yescharacteristic
60C2×C11×C16C2311yescharacteristic
61C11×#107—21no—
62C11×#107—21no—
63C11×#107C2312yes—
64C11×#107C2312yes—
65C4×C8×C11C2311yescharacteristic
66(C2×D11)⋊C8D412yes—
67#66882C2311yescharacteristic
68#66882C2311yescharacteristic
69#66880—21no—
70#66880—21no—
71C2×C11⋊C16C2312yes—
72#66874—22no—
73#66874—22no—
74#66872—22no—
75#66871—22no—
76C4⋊(C11⋊C8)D411yescharacteristic
77Dic88—22no—
78#66862—24no—
79#33923—111nomaximal, Sylow
80C2×Q8×C11—41no—
81C2×Q8×C11—41no—
82C2×D44D811yescharacteristic
83C2×C4×D11—42no—
84C2×C4×D11C2×D412yes—
85C2×Dic22—21no—
86C2×Dic22—21no—
87C2×C8×C11C2×D411yescharacteristic
88C2×C8×C11C2411yescharacteristic
89C11×C4⋊C4—22no—
90C11×C4⋊C4—22no—
91C11×C4⋊C4—41no—
92C11×C4⋊C4—41no—
93C42×C11C2×D411yescharacteristic
94(C2×D11)⋊C4—42no—
95(C2×D11)⋊C4—42no—
96(C2×D11)⋊C4—42no—
97(C2×D11)⋊C4D812yes—
98C4⋊Dic11—21no—
99C4⋊Dic11—21no—
100C4⋊Dic11—42no—
101C4⋊Dic11—42no—
102C4⋊Dic11D811yescharacteristic
103Dic11⋊C4—42no—
104Dic11⋊C4—41no—
105Dic11⋊C4—41no—
106C4×Dic11—42no—
107C4×Dic11—41no—
108C4×Dic11—41no—
109C2×C11⋊C8C2×D412yes—
110Dic44—21no—
111Dic44—21no—
112Dic44—21no—
113Dic44—21no—
114C8×D11—22no—
115C8×D11—22no—
116C11×C16—21no—
117C11×C16#4112yes—
118C11⋊C16—22no—
119#3342—111no—
120#3338—111no—
121#2254D1111yescharacteristic, complemented
122#2237—112no—
123#2235—112no—
124#2227—111no—
125#2225—111no—
126#2219—112no—
127C4×Q32—111no—
128#2169—111no—
129#2159—112no—
130C22×D11C2×D812yes—
131Q8×C11—82no—
132Q8×C11—161no—
133C2×C4×C11—42no—
134C2×C4×C11—42no—
135C2×C4×C11C2×D811yescharacteristic
136C2×C4×C11C2×D811yescharacteristic
137C2×C4×C11C22×D411yescharacteristic
138C2×Dic11—41no—
139C2×Dic11—41no—
140C2×Dic11—41no—
141C2×Dic11—41no—
142C2×Dic11C2×D812yes—
143D44—22no—
144C4×D11—22no—
145C4×D11—22no—
146C4×D11—162no—
147Dic22—41no—
148Dic22—41no—
149Dic22—41no—
150Dic22—41no—
151C8×C11—21no—
152C8×C11C2×#4111yescharacteristic
153C8×C112−1+411yescharacteristic
154C11⋊C8—22no—
155#556—221no—
156#554—221no—
157C2×Q32—111no—
158C2×M32—112no—
159#500C2×D1111yescharacteristic
160#500C2×D1111yescharacteristic
161#485—222no—
162#484—222no—
163#477—221no—
164#475—221no—
165#467—112no—
166#467—112no—
167C4×Q16—111no—
168C4×Q16—111no—
169C8×D4—111no—
170#427—112no—
171C2×#107—112no—
172#367—112no—
173#367C2×D1112yes—
174#367C2×D1112yes—
175#366—111no—
176#366—112no—
177C4⋊C16—111no—
178#358—111no—
179#358—111no—
180#358—112no—
181#358—112no—
182C22⋊C16—112no—
183C4×C16C2×D1111yescharacteristic
184C22×C11C22×D811yescharacteristic
185C2×D11—22no—
186C2×D11—22no—
187C2×D11—22no—
188C4×C11—21no—
189C4×C11—82no—
190C4×C11—82no—
191C4×C11#51012yes—
192C4×C11#54711yescharacteristic
193C4×C11#57811yescharacteristic
194Dic11—22no—
195Dic11—81no—
196Dic11—81no—
197Dic11—81no—
198Dic11—81no—
199C2×Q16—111no—
200C2×Q16—111no—
201C22×C8—112no—
202C4⋊Q8—21no—
203C4⋊Q8—21no—
204#126—442no—
205#125—441no—
206#124—441no—
207C22⋊Q8—222no—
208C22⋊Q8—222no—
209C22⋊Q8—442no—
210C4×Q8—221no—
211C4×Q8—221no—
212C4×Q8—441no—
213C4×D4—111no—
214C4×D4—441no—
215#117—222no—
216C2×C4⋊C4—222no—
217Q32—222no—
218M32—224no—
219C2×C16—112no—
220C2×C16C22×D1111yescharacteristic
221C2×C16C22×D1111yescharacteristic
222#107—21no—
223#107—21no—
224#107—111no—
225#107—111no—
226#107—222no—
227#107C22×D1112yes—
228#107C22×D1112yes—
229#106—222no—
230C4⋊C8—111no—
231#103—222no—
232#103—222no—
233#103—221no—
234#103—221no—
235C22⋊C8—112no—
236C4×C8C22×D1111yescharacteristic
237C2×C11#333411yescharacteristic
238C2×C11C2×#51011yescharacteristic
239C2×C11#341611yescharacteristic
240D11—42no—
241C2×Q8—41no—
242C2×Q8—41no—
243C2×Q8—221no—
244C2×Q8—221no—
245C2×D4—111no—
246C22×C4—112no—
247C22×C4—442no—
248Q16—221no—
249Q16—221no—
250Q16—221no—
251Q16—221no—
252C2×C8—112no—
253C2×C8—222no—
254C2×C8—222no—
255C2×C8D4×D1111yescharacteristic
256C2×C8C23×D1111yescharacteristic
257C4⋊C4—22no—
258C4⋊C4—22no—
259C4⋊C4—41no—
260C4⋊C4—41no—
261C4⋊C4—111no—
262C4⋊C4—221no—
263C4⋊C4—221no—
264C4⋊C4—442no—
265C4⋊C4—442no—
266C4⋊C4—442no—
267C4⋊C4—441no—
268C4⋊C4—441no—
269C22⋊C4—112no—
270C22⋊C4—442no—
271C22⋊C4—442no—
272C22⋊C4—442no—
273C42—442no—
274C42—441no—
275C42—441no—
276C42D4×D1111yescharacteristic
277C16—21no—
278C16—222no—
279C16#434312yes—
280C11#3392311yescharacteristic, complemented, Sylow
281C23—112no—
282Q8—82no—
283Q8—161no—
284Q8—441no—
285Q8—441no—
286Q8—441no—
287Q8—441no—
288D4—222no—
289C2×C4—42no—
290C2×C4—42no—
291C2×C4—112no—
292C2×C4—222no—
293C2×C4—222no—
294C2×C4—441no—
295C2×C4—441no—
296C2×C4—441no—
297C2×C4—441no—
298C2×C4—1762no—
299C2×C4D8×D1111yescharacteristic
300C2×C4D8×D1111yescharacteristic
301C2×C4C2×D4×D1111yescharacteristic
302C8—21no—
303C8—222no—
304C8C2×#434311yescharacteristic
305C8#6704011yescharacteristic
306C22—222no—
307C22—222no—
308C22—222no—
309C22C2×D8×D1111yescharacteristic
310C4—21no—
311C4—82no—
312C4—82no—
313C4—222no—
314C4—881no—
315C4—881no—
316C4—881no—
317C4—881no—
318C4#1062252812yes—
319C4#1062325711yescharacteristic
320C4#1062329711yescharacteristic
321C2—442no—
322C2#1308096311yescharacteristic
323C2C2×#1062252811yescharacteristic
324C2#1308175811yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2254C2
socleC22×C11C22×D8
prime radicalC2×D44D8
hypercenter#2254D11
hypocenterC11#33923
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2254

Complements

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

NH ≅ G/Ntype
3. #13070827C2semidirect
4. #13070815C2semidirect
5. #13070765C2semidirect
6. #13070755C2semidirect
7. #13070725C2semidirect
8. C4×Dic88C2semidirect
10. #13070403C2semidirect
11. C11×#2254C2semidirect
121. #2254D11semidirect
280. C11#33923semidirect

Maximal subgroups

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

subgroupindex
#130810462
#130810082
#130708272
#130708152
#130707652
#130707552
#130707252
C4×Dic882
#130704492
#130704032
C11×#22542
#3392311