Finite Group Databasebeta

← #14911370

Subgroups — #14911370

Order 2816.

502 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#13081048C211yesmaximal, characteristic, complemented
2#13080963C211yesmaximal, characteristic
3#13070889C211yesmaximal, characteristic, complemented
4#13070817C212yesmaximal, complemented
5#13070809C212yesmaximal, complemented
6#13070754C211yesmaximal, characteristic, complemented
7#13070732C212yesmaximal, complemented
8C4×#66892C211yesmaximal, characteristic, complemented
9#13070447C211yesmaximal, characteristic, complemented
10#13070403C212yesmaximal, complemented
11C11×#2225C211yesmaximal, characteristic, complemented
12#10623257—21no—
13#10623115—21no—
14C11×#500C2211yescharacteristic
15C4×C11×Q16C2211yescharacteristic
16#10622801C2212yes—
17C2×#66892C2211yescharacteristic
18#10622700—21no—
19#10622633—21no—
20C2×#66862C2212yes—
21#10622496C2212yes—
22#10622495—22no—
23#10622493C2212yes—
24D11×#107C2212yes—
25#10622427—22no—
26C4×D88C2211yescharacteristic
27C8×D44C2211yescharacteristic
28#10622295C2211yescharacteristic
29C11×#367C2212yes—
30C11×C4⋊C16C2211yescharacteristic
31C11×#358C2212yes—
32#10622202C2211yescharacteristic
33#10622147C2212yes—
34(C2×D11)⋊C16C2212yes—
35#10622142C2212yes—
36#10622129C2211yescharacteristic
37#10622128C2211yescharacteristic
38#10622127C2212yes—
39#10622127C2212yes—
40C4×C11⋊C16C2211yescharacteristic
41C2×#4343—41no—
42C2×C11×Q16C2311yescharacteristic
43C11×C4⋊Q8—21no—
44C4×Q8×C11—21no—
45#66999—22no—
46#66999—41no—
47C2×D88C2311yescharacteristic
48C2×C8×D11C2312yes—
49#66951—42no—
50#66948—22no—
51#66947—42no—
52#66945—22no—
53C4⋊C4×D11—22no—
54#66928—41no—
55C4×D44—21no—
56C4×D44D411yescharacteristic
57#66922—21no—
58C4×Dic22—41no—
59C2×C11×C16C2312yes—
60C11×#107—21no—
61C11×#107C2312yes—
62C11×#107C2311yescharacteristic
63C11×#103—21no—
64C4×C8×C11C2311yescharacteristic
65#66899—22no—
66#66892—22no—
67#66885—21no—
68(C2×D11)⋊C8D412yes—
69#66882—21no—
70#66882C2311yescharacteristic
71#66882C2312yes—
72C2×C11⋊C16C2311yescharacteristic
73C2×C11⋊C16C2311yescharacteristic
74#66873—22no—
75#66872—22no—
76#66871—22no—
77C4⋊(C11⋊C8)D411yescharacteristic
78#66862—24no—
79#33920—111nomaximal, Sylow
80C2×Q8×C11—21no—
81C2×Q8×C11—41no—
82#4343—84no—
83C2×D44—21no—
84C2×D44—42no—
85C2×D44D811yescharacteristic
86C2×C4×D11—42no—
87C2×C4×D11—41no—
88C2×C4×D11C2×D412yes—
89C2×Dic22—41no—
90C11×Q16—21no—
91C11×Q16—21no—
92C2×C8×C11C2×D411yescharacteristic
93C2×C8×C11C2411yescharacteristic
94C11×C4⋊C4—22no—
95C11×C4⋊C4—21no—
96C11×C4⋊C4—41no—
97C11×C4⋊C4—41no—
98C42×C11—41no—
99C42×C11C2×D411yescharacteristic
100(C2×D11)⋊C4—42no—
101(C2×D11)⋊C4—42no—
102(C2×D11)⋊C4—42no—
103(C2×D11)⋊C4—41no—
104(C2×D11)⋊C4D812yes—
105C4⋊Dic11—21no—
106C4⋊Dic11—22no—
107C4⋊Dic11—41no—
108C4⋊Dic11D811yescharacteristic
109Dic11⋊C4—42no—
110Dic11⋊C4—42no—
111C4×Dic11—42no—
112C2×C11⋊C8C2×D412yes—
113D88—21no—
114D88—21no—
115C8×D11—22no—
116C8×D11—22no—
117C11×C16—22no—
118C11⋊C16—21no—
119C11⋊C16#4112yescomplemented
120#3342—111no—
121#3334—111no—
122#2252—111no—
123#2236—112no—
124#2234—112no—
125#2225D1111yescharacteristic, complemented
126#2224—111no—
127#2220—112no—
128C4×SD32—111no—
129#2169—111no—
130#2159—112no—
131C22×D11—41no—
132C22×D11C2×D812yes—
133Q8×C11—41no—
134Q8×C11—41no—
135Q8×C11—82no—
136C2×C4×C11—41no—
137C2×C4×C11—41no—
138C2×C4×C11—42no—
139C2×C4×C11C2×D811yescharacteristic
140C2×C4×C11C2×D811yescharacteristic
141C2×C4×C11C22×D411yescharacteristic
142C2×Dic11—42no—
143C2×Dic11—41no—
144C2×Dic11C2×D812yes—
145D44—22no—
146D44—41no—
147D44—41no—
148D44—84no—
149C4×D11—22no—
150C4×D11—22no—
151C4×D11—84no—
152C4×D11—82no—
153Dic22—82no—
154C8×C11—21no—
155C8×C11C2×#4111yescharacteristic
156C8×C112−1+411yescharacteristic
157C11⋊C8—22no—
158#556—221no—
159#547—221no—
160C2×SD32—111no—
161C2×M32—112no—
162#500—111no—
163#500C2×D1111yescharacteristic
164#485—222no—
165#480—222no—
166#475—221no—
167#474—221no—
168#467—112no—
169#466—112no—
170C4×Q16C2×D1111yescharacteristic
171C4×D8—111no—
172C8×D4—111no—
173#427—112no—
174C2×#107—112no—
175#367—111no—
176#367C2×D1112yes—
177#366—112no—
178#366—112no—
179#366—112no—
180C4⋊C16C2×D1111yescharacteristic
181#358—111no—
182#358C2×D1112yes—
183#357—112no—
184#357—111no—
185C22⋊C16—112no—
186C4×C16—111no—
187C22×C11C22×D811yescharacteristic
188C2×D11—22no—
189C2×D11—22no—
190C2×D11—22no—
191C2×D11—81no—
192C2×D11—81no—
193C2×D11—81no—
194C4×C11—21no—
195C4×C11—81no—
196C4×C11—82no—
197C4×C11—81no—
198C4×C11#50912yes—
199C4×C11#54711yescharacteristic
200C4×C11#57811yescharacteristic
201Dic11—22no—
202Dic11—82no—
203Dic11—81no—
204C2×#41—441no—
205C2×Q16C22×D1111yescharacteristic
206C2×D8—111no—
207C22×C8—112no—
208C4⋊Q8—21no—
209C4⋊Q8—221no—
210#126—442no—
211#124—441no—
212#123—442no—
213C22⋊Q8—222no—
214C22⋊Q8—441no—
215#121—222no—
216C4×Q8—21no—
217C4×Q8—441no—
218C4×D4—111no—
219C4×D4—221no—
220#117—222no—
221C2×C4⋊C4—222no—
222SD32—222no—
223M32—224no—
224C2×C16—111no—
225C2×C16—111no—
226C2×C16C22×D1112yes—
227#107—21no—
228#107—112no—
229#107—111no—
230#107—222no—
231#107—221no—
232#107C22×D1111yescharacteristic
233#107C22×D1112yes—
234#106—222no—
235C4⋊C8—111no—
236#103—21no—
237#103—222no—
238#102—222no—
239#102—221no—
240C22⋊C8—112no—
241C4×C8C22×D1111yescharacteristic
242C2×C11#333411yescharacteristic
243C2×C11C2×#50911yescharacteristic
244C2×C11#341711yescharacteristic
245D11—42no—
246D11—161no—
247#41—884no—
248C2×Q8—21no—
249C2×Q8—41no—
250C2×Q8—441no—
251C2×D4—111no—
252C2×D4—221no—
253C2×D4—442no—
254C22×C4—112no—
255C22×C4—442no—
256C22×C4—441no—
257Q16—21no—
258Q16—21no—
259D8—221no—
260D8—221no—
261C2×C8—112no—
262C2×C8—222no—
263C2×C8—222no—
264C2×C8D4×D1111yescharacteristic
265C2×C8C23×D1111yescharacteristic
266C4⋊C4—22no—
267C4⋊C4—21no—
268C4⋊C4—41no—
269C4⋊C4—41no—
270C4⋊C4—111no—
271C4⋊C4—221no—
272C4⋊C4—222no—
273C4⋊C4—442no—
274C4⋊C4—442no—
275C4⋊C4—441no—
276C22⋊C4—112no—
277C22⋊C4—442no—
278C22⋊C4—442no—
279C22⋊C4—442no—
280C22⋊C4—441no—
281C42—41no—
282C42—442no—
283C42D4×D1111yescharacteristic
284C16—22no—
285C16—112no—
286C16—221no—
287C11#3392011yescharacteristic, complemented, Sylow
288C23—112no—
289C23—441no—
290Q8—41no—
291Q8—41no—
292Q8—82no—
293Q8—882no—
294D4—222no—
295D4—441no—
296D4—441no—
297D4—884no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—42no—
301C2×C4—112no—
302C2×C4—222no—
303C2×C4—222no—
304C2×C4—442no—
305C2×C4—441no—
306C2×C4—884no—
307C2×C4—882no—
308C2×C4D8×D1111yescharacteristic
309C2×C4D8×D1111yescharacteristic
310C2×C4C2×D4×D1111yescharacteristic
311C8—21no—
312C8—222no—
313C8#6704011yescharacteristic
314C8#41×D1111yescharacteristic
315C22—222no—
316C22—222no—
317C22—222no—
318C22—881no—
319C22—881no—
320C22—881no—
321C22C2×D8×D1111yescharacteristic
322C4—21no—
323C4—81no—
324C4—82no—
325C4—81no—
326C4—222no—
327C4—881no—
328C4—882no—
329C4#1062252712yes—
330C4#1062316211yescharacteristic
331C4#1062331011yescharacteristic
332C2—442no—
333C2—1761no—
334C2#1308096211yescharacteristic
335C2C2×#1062252711yescharacteristic
336C2#1308176811yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2225C2
socleC22×C11C22×D8
prime radical#13080963C2
hypercenter#2225D11
hypocenterC11#33920
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
1. #13081048C2semidirect
3. #13070889C2semidirect
4. #13070817C2semidirect
5. #13070809C2semidirect
6. #13070754C2semidirect
7. #13070732C2semidirect
8. C4×#66892C2semidirect
9. #13070447C2semidirect
10. #13070403C2semidirect
11. C11×#2225C2semidirect
119. C11⋊C16#41semidirect
125. #2225D11semidirect
287. C11#33920semidirect

Maximal subgroups

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

subgroupindex
#130810482
#130809632
#130708892
#130708172
#130708092
#130707542
#130707322
C4×#668922
#130704472
#130704032
C11×#22252
#3392011