Finite Group Databasebeta

← #14911369

Subgroups — #14911369

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#13080965C211yesmaximal, characteristic
3#13070891C211yesmaximal, characteristic, complemented
4#13070817C212yesmaximal, complemented
5#13070805C212yesmaximal, complemented
6#13070758C211yesmaximal, characteristic, complemented
7#13070753C211yesmaximal, characteristic, complemented
8#13070726C212yesmaximal, complemented
9#13070449C211yesmaximal, characteristic, complemented
10#13070403C212yesmaximal, complemented
11C4×C11×SD32C211yesmaximal, characteristic, complemented
12#10623115—21no—
13#10623082—21no—
14C2×C11×SD32C2211yescharacteristic
15C4×C11×Q16C2211yescharacteristic
16C4×C11×D8C2211yescharacteristic
17#10622801C2212yes—
18#10622770C2212yes—
19#10622633—21no—
20#10622620—21no—
21C2×#66862C2212yes—
22#10622493C2212yes—
23D11×#107C2212yes—
24#10622427—22no—
25#10622387—22no—
26C8×D44C2211yescharacteristic
27#10622295C2211yescharacteristic
28#10622295C2211yescharacteristic
29C11×#367C2211yescharacteristic
30C11×#358C2211yescharacteristic
31C11×#357C2211yescharacteristic
32C4×C11×C16C2211yescharacteristic
33#10622202C2212yes—
34#10622200C2212yes—
35(C2×D11)⋊C16C2212yes—
36#10622142C2212yes—
37#10622142C2212yes—
38#10622128C2212yes—
39#10622127C2212yes—
40C4⋊(C11⋊C16)C2211yescharacteristic
41C2×#4339—41no—
42C2×C11×Q16C2311yescharacteristic
43C2×C11×D8C2311yescharacteristic
44C4×Q8×C11—21no—
45C4×D4×C11—21no—
46#66999—22no—
47#66991—22no—
48#66977—41no—
49C2×C8×D11C2312yes—
50#66951—42no—
51#66945—22no—
52C4⋊C4×D11—22no—
53#66936—42no—
54#66928—41no—
55C4×D44D411yescharacteristic
56#66922—21no—
57#66922—21no—
58C4×Dic22—41no—
59C11×SD32—22no—
60C2×C11×C16C2311yescharacteristic
61C2×C11×C16C2311yescharacteristic
62C11×#107C2311yescharacteristic
63C11×#107C2311yescharacteristic
64C11×#103—21no—
65C11×#102—21no—
66C4×C8×C11C2311yescharacteristic
67#66899—22no—
68#66896—22no—
69(C2×D11)⋊C8D412yes—
70#66882—21no—
71#66882—21no—
72#66882C2312yes—
73#66882C2312yes—
74C2×C11⋊C16C2312yes—
75#66872—22no—
76#66871—22no—
77C4⋊(C11⋊C8)D411yescharacteristic
78#66862—24no—
79#33920—111nomaximal, Sylow
80C2×Q8×C11—21no—
81C2×D4×C11—21no—
82C22×C4×C11—41no—
83C2×C22⋊D11—42no—
84#4339—84no—
85C2×D44D811yescharacteristic
86C2×C4×D11—42no—
87C2×C4×D11C2×D412yes—
88C2×Dic22—41no—
89C2×Dic22—41no—
90C11×Q16—21no—
91C11×Q16—21no—
92C11×D8—21no—
93C11×D8—21no—
94C2×C8×C11C2×D411yescharacteristic
95C2×C8×C11C2411yescharacteristic
96C11×C4⋊C4—21no—
97C11×C4⋊C4—21no—
98C11×C4⋊C4—41no—
99C11×C22⋊C4—41no—
100C42×C11—41no—
101C42×C11C2×D411yescharacteristic
102C22⋊Dic11—42no—
103(C2×D11)⋊C4—42no—
104(C2×D11)⋊C4—42no—
105(C2×D11)⋊C4D812yes—
106C4⋊Dic11—22no—
107C4⋊Dic11—22no—
108C4⋊Dic11—41no—
109C4⋊Dic11—41no—
110C4⋊Dic11D811yescharacteristic
111Dic11⋊C4—42no—
112Dic11⋊C4—42no—
113C4×Dic11—42no—
114C2×C11⋊C8C2×D412yes—
115C8×D11—22no—
116C8×D11—22no—
117C11×C16—21no—
118C11×C16#4112yescomplemented
119C11⋊C16—22no—
120#3342—111no—
121#3334—111no—
122#2252—111no—
123#2236—112no—
124#2234—112no—
125#2225—111no—
126#2224—111no—
127#2220—112no—
128C4×SD32D1111yescharacteristic, complemented
129#2169—111no—
130#2159—112no—
131C23×C11—41no—
132C22×D11C2×D812yes—
133Q8×C11—41no—
134Q8×C11—41no—
135D4×C11—41no—
136D4×C11—41no—
137C2×C4×C11—41no—
138C2×C4×C11—41no—
139C2×C4×C11—41no—
140C2×C4×C11—82no—
141C2×C4×C11C2×D811yescharacteristic
142C2×C4×C11C2×D811yescharacteristic
143C2×C4×C11C22×D411yescharacteristic
144C22⋊D11—84no—
145C2×Dic11—42no—
146C2×Dic11—42no—
147C2×Dic11C2×D812yes—
148D44—22no—
149C4×D11—22no—
150C4×D11—22no—
151C4×D11—84no—
152Dic22—82no—
153Dic22—82no—
154C8×C11—21no—
155C8×C11C2×#4111yescharacteristic
156C8×C112−1+411yescharacteristic
157C11⋊C8—22no—
158#556—221no—
159#547—221no—
160C2×SD32C2×D1111yescharacteristic
161C2×M32—112no—
162#500—111no—
163#500—111no—
164#485—222no—
165#480—222no—
166#475—221no—
167#474—221no—
168#467—112no—
169#466—112no—
170C4×Q16C2×D1111yescharacteristic
171C4×D8C2×D1111yescharacteristic
172C8×D4—111no—
173#427—112no—
174C2×#107—112no—
175#367—112no—
176#367C2×D1111yescharacteristic
177#366—112no—
178#366—112no—
179#366—112no—
180C4⋊C16—111no—
181#358—112no—
182#358C2×D1111yescharacteristic
183#357—112no—
184#357C2×D1111yescharacteristic
185C22⋊C16—112no—
186C4×C16C2×D1111yescharacteristic
187C22×C11—81no—
188C22×C11—81no—
189C22×C11—81no—
190C22×C11C22×D811yescharacteristic
191C2×D11—22no—
192C2×D11—22no—
193C2×D11—22no—
194C4×C11—21no—
195C4×C11—81no—
196C4×C11—81no—
197C4×C11—81no—
198C4×C11#50912yes—
199C4×C11#54711yescharacteristic
200C4×C11#57811yescharacteristic
201Dic11—22no—
202Dic11—82no—
203Dic11—82no—
204C2×#41—441no—
205C2×Q16C22×D1111yescharacteristic
206C2×D8C22×D1111yescharacteristic
207C22×C8—112no—
208C4⋊Q8—221no—
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—21no—
219C4×D4—111no—
220#117—222no—
221C2×C4⋊C4—222no—
222SD32—22no—
223M32—224no—
224C2×C16—112no—
225C2×C16C22×D1111yescharacteristic
226C2×C16C22×D1111yescharacteristic
227#107—112no—
228#107—112no—
229#107—222no—
230#107—221no—
231#107—221no—
232#107C22×D1111yescharacteristic
233#107C22×D1111yescharacteristic
234#106—222no—
235C4⋊C8—111no—
236#103—21no—
237#103—222no—
238#102—21no—
239#102—222no—
240C22⋊C8—112no—
241C4×C8C22×D1111yescharacteristic
242C2×C11—161no—
243C2×C11#333411yescharacteristic
244C2×C11C2×#50911yescharacteristic
245C2×C11#341711yescharacteristic
246D11—42no—
247#41—884no—
248C2×Q8—21no—
249C2×Q8—441no—
250C2×Q8—441no—
251C2×D4—21no—
252C2×D4—111no—
253C2×D4—442no—
254C22×C4—41no—
255C22×C4—112no—
256C22×C4—442no—
257Q16—21no—
258Q16—21no—
259D8—21no—
260D8—21no—
261C2×C8—112no—
262C2×C8—222no—
263C2×C8—222no—
264C2×C8D4×D1111yescharacteristic
265C2×C8C23×D1111yescharacteristic
266C4⋊C4—21no—
267C4⋊C4—21no—
268C4⋊C4—41no—
269C4⋊C4—111no—
270C4⋊C4—222no—
271C4⋊C4—222no—
272C4⋊C4—442no—
273C4⋊C4—442no—
274C4⋊C4—441no—
275C4⋊C4—441no—
276C22⋊C4—41no—
277C22⋊C4—112no—
278C22⋊C4—442no—
279C22⋊C4—442no—
280C22⋊C4—442no—
281C42—41no—
282C42—442no—
283C42D4×D1111yescharacteristic
284C16—21no—
285C16—222no—
286C16#433912yescomplemented
287C11#3392011yescharacteristic, complemented, Sylow
288C23—41no—
289C23—112no—
290Q8—41no—
291Q8—41no—
292Q8—882no—
293Q8—882no—
294D4—41no—
295D4—41no—
296D4—222no—
297D4—884no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—82no—
302C2×C4—112no—
303C2×C4—222no—
304C2×C4—222no—
305C2×C4—442no—
306C2×C4—442no—
307C2×C4—884no—
308C2×C4D8×D1111yescharacteristic
309C2×C4D8×D1111yescharacteristic
310C2×C4C2×D4×D1111yescharacteristic
311C8—21no—
312C8—222no—
313C8C2×#433911yescharacteristic
314C8#6704311yescharacteristic
315C22—81no—
316C22—81no—
317C22—81no—
318C22—222no—
319C22—222no—
320C22—222no—
321C22C2×D8×D1111yescharacteristic
322C4—21no—
323C4—81no—
324C4—81no—
325C4—81no—
326C4—222no—
327C4—882no—
328C4—882no—
329C4#1062252712yes—
330C4#1062308211yescharacteristic
331C4#1062330211yescharacteristic
332C2—161no—
333C2—442no—
334C2#1308096511yescharacteristic
335C2C2×#1062252711yescharacteristic
336C2#1308176611yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC4×C11×SD32C2
socleC22×C11C22×D8
prime radical#13080965C2
hypercenterC4×SD32D11
hypocenterC11#33920
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ C4×SD32

Complements

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

NH ≅ G/Ntype
1. #13081048C2semidirect
3. #13070891C2semidirect
4. #13070817C2semidirect
5. #13070805C2semidirect
6. #13070758C2semidirect
7. #13070753C2semidirect
8. #13070726C2semidirect
9. #13070449C2semidirect
10. #13070403C2semidirect
11. C4×C11×SD32C2semidirect
118. C11×C16#41semidirect
128. C4×SD32D11semidirect
286. C16#4339semidirect
287. C11#33920semidirect

Maximal subgroups

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

subgroupindex
#130810482
#130809652
#130708912
#130708172
#130708052
#130707582
#130707532
#130707262
#130704492
#130704032
C4×C11×SD322
#3392011