Finite Group Databasebeta

← #14911472

Subgroups — #14911472

Order 2816.

472 conjugacy classes of subgroups.

The subgroup lattice has 328 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13081606C211yesmaximal, characteristic
2#13081505C211yesmaximal, characteristic, complemented
3#13070849C212yesmaximal
4#13070843C211yesmaximal, characteristic, complemented
5#13070782C212yesmaximal, complemented
6#13070754C211yesmaximal, characteristic
7#13070680C212yesmaximal
8#13070518C211yesmaximal, characteristic, complemented
9Q32×Dic11C212yesmaximal, complemented
10C4×#66892C211yesmaximal, characteristic
11C11×#2209C211yesmaximal, characteristic, complemented
12#10623263—21no—
13#10623101—21no—
14C2×C11×Q32C2212yes—
15C11×#494C2211yescharacteristic
16C4×C11×Q16C2211yescharacteristic
17#10622804C2212yes—
18#10622798—22no—
19Q16×Dic11C2212yes—
20Q16×Dic11C2212yes—
21C2×#66892C2211yescharacteristic
22#10622696—21no—
23#10622633—21no—
24#10622491C2212yes—
25#10622409—22no—
26C4×D88C2211yescharacteristic
27#10622295C2211yescharacteristic
28C8×Dic22C2211yescharacteristic
29C11×C4⋊C16C2211yescharacteristic
30C11×#358C2212yes—
31#10622202C2212yes—
32#10622202C2212yes—
33#10622202C2211yescharacteristic
34#10622147C2212yes—
35#10622142C2212yes—
36Dic11⋊C16C2212yes—
37C16×Dic11C2212yes—
38#10622129C2211yescharacteristic
39#10622128C2211yescharacteristic
40C4×C11⋊C16C2211yescharacteristic
41C2×C11×Q16—21no—
42C2×C11×Q16C2312yes—
43C2×C11×Q16C2311yescharacteristic
44C11×C4⋊Q8—21no—
45C4×Q8×C11—21no—
46#67000—22no—
47Q8×Dic11—22no—
48Q8×Dic11—22no—
49C2×#4325—22no—
50C2×D88C2311yescharacteristic
51#66951—42no—
52#66950—41no—
53#66945—41no—
54#66943—22no—
55#66943—42no—
56C4×D44—21no—
57#66922—21no—
58#66922—41no—
59C4×Dic22—41no—
60C4×Dic22D411yescharacteristic
61C11×Q32—24no—
62C2×C11×C16C2312yes—
63C11×#107C2311yescharacteristic
64C11×#103—21no—
65C4×C8×C11C2311yescharacteristic
66#66899—22no—
67#66899—22no—
68#66892—22no—
69#66885—21no—
70#66882—21no—
71#66882C2312yes—
72#66882C2311yescharacteristic
73Dic11⋊C8D412yes—
74C8×Dic11C2312yes—
75C2×C11⋊C16C2311yescharacteristic
76C2×C11⋊C16C2311yescharacteristic
77#66872—22no—
78C4⋊(C11⋊C8)D411yescharacteristic
79#33931—111nomaximal, Sylow
80C2×Q8×C11—21no—
81C2×Q8×C11—22no—
82C2×D44—21no—
83C2×C4×D11—41no—
84C2×Dic22—41no—
85C2×Dic22D811yescharacteristic
86C11×Q16—21no—
87C11×Q16—22no—
88C11×Q16—22no—
89C11×Q16—81no—
90C11×Q16#4112yes—
91C2×C8×C11C2×D411yescharacteristic
92C2×C8×C11C2411yescharacteristic
93C11×C4⋊C4—21no—
94C11×C4⋊C4—41no—
95C11×C4⋊C4—41no—
96C11×C4⋊C4—41no—
97C42×C11—41no—
98C42×C11C2×D411yescharacteristic
99#4325—82no—
100(C2×D11)⋊C4—42no—
101(C2×D11)⋊C4—42no—
102(C2×D11)⋊C4—41no—
103C4⋊Dic11—22no—
104C4⋊Dic11—21no—
105C4⋊Dic11—42no—
106C4⋊Dic11—42no—
107C4⋊Dic11—42no—
108C4⋊Dic11—41no—
109C4⋊Dic11D811yescharacteristic
110Dic11⋊C4—42no—
111Dic11⋊C4D812yes—
112C4×Dic11—42no—
113C4×Dic11—42no—
114C4×Dic11C2×D412yes—
115C2×C11⋊C8C2×D412yes—
116D88—21no—
117D88—21no—
118C11×C16—22no—
119C11⋊C16—21no—
120C11⋊C16—21no—
121#3393—111no—
122#3383—111no—
123#2242—112no—
124#2241—111no—
125#2229—112no—
126#2224—111no—
127#2211—112no—
128#2209D1111yescharacteristic, complemented
129Q8×C16—111no—
130C4×Q32—112no—
131C4×SD32—111no—
132C22×D11—41no—
133Q8×C11—22no—
134Q8×C11—41no—
135Q8×C11—42no—
136Q8×C11—42no—
137C2×C4×C11—41no—
138C2×C4×C11—42no—
139C2×C4×C11—41no—
140C2×C4×C11C2×D811yescharacteristic
141C2×C4×C11C2×D811yescharacteristic
142C2×C4×C11C22×D411yescharacteristic
143C2×Dic11—41no—
144C2×Dic11—42no—
145C2×Dic11C2×D812yes—
146C2×Dic11C2×D812yes—
147D44—41no—
148D44—41no—
149C4×D11—82no—
150Dic22—22no—
151Dic22—82no—
152C8×C11—21no—
153C8×C11C2×#4111yescharacteristic
154C8×C112−1+411yescharacteristic
155C11⋊C8—22no—
156#557—221no—
157#556—221no—
158C2×Q32C2×D1112yes—
159C2×SD32—111no—
160#500—111no—
161#499—112no—
162#495—112no—
163#494C2×D1111yescharacteristic
164#479—222no—
165#475—221no—
166#464—222no—
167#461—221no—
168C8×Q8—111no—
169C4×Q16—112no—
170C4×Q16—112no—
171C4×Q16C2×D1111yescharacteristic
172C4×D8—111no—
173#367—111no—
174#366—112no—
175C4⋊C16—112no—
176C4⋊C16C2×D1111yescharacteristic
177#358—111no—
178#358—112no—
179#358—112no—
180#358C2×D1112yes—
181#357—112no—
182#357—111no—
183C4×C16—112no—
184C4×C16—111no—
185C22×C11C22×D811yescharacteristic
186C2×D11—81no—
187C2×D11—81no—
188C2×D11—81no—
189C4×C11—21no—
190C4×C11—42no—
191C4×C11—82no—
192C4×C11—81no—
193C4×C11#50812yes—
194C4×C11#54811yescharacteristic
195C4×C11#57711yescharacteristic
196Dic11—22no—
197Dic11—22no—
198Dic11—82no—
199Dic11—81no—
200C2×Q16—21no—
201C2×Q16C22×D1112yes—
202C2×Q16C22×D1111yescharacteristic
203C2×SD16—222no—
204C2×D8—111no—
205C4⋊Q8—21no—
206C4⋊Q8—221no—
207C4⋊Q8—441no—
208#126—442no—
209#125—222no—
210#125—442no—
211#124—222no—
212C22⋊Q8—441no—
213C4×Q8—21no—
214C4×Q8—111no—
215C4×Q8—222no—
216C4×Q8—222no—
217C4×Q8—441no—
218C4×D4—221no—
219#117—441no—
220Q32—24no—
221SD32—222no—
222C2×C16—111no—
223C2×C16—111no—
224C2×C16C22×D1112yes—
225#107—112no—
226#107—111no—
227#107—221no—
228#107C22×D1111yescharacteristic
229#106—222no—
230C4⋊C8—112no—
231C4⋊C8—111no—
232#103—21no—
233#103—222no—
234#103—222no—
235#102—221no—
236C4×C8—112no—
237C4×C8C22×D1111yescharacteristic
238C2×C11#335811yescharacteristic
239C2×C11C2×#50811yescharacteristic
240C2×C11#341711yescharacteristic
241D11—161no—
242C2×Q8—21no—
243C2×Q8—22no—
244C2×Q8—111no—
245C2×Q8—441no—
246C2×D4—221no—
247C22×C4—441no—
248Q16—22no—
249Q16—21no—
250Q16—22no—
251Q16—81no—
252Q16#434112yes—
253SD16—882no—
254D8—221no—
255D8—221no—
256C2×C8—112no—
257C2×C8D4×D1111yescharacteristic
258C2×C8C23×D1111yescharacteristic
259C4⋊C4—21no—
260C4⋊C4—41no—
261C4⋊C4—41no—
262C4⋊C4—41no—
263C4⋊C4—111no—
264C4⋊C4—112no—
265C4⋊C4—221no—
266C4⋊C4—222no—
267C4⋊C4—442no—
268C4⋊C4—442no—
269C4⋊C4—442no—
270C4⋊C4—442no—
271C4⋊C4—441no—
272C22⋊C4—442no—
273C22⋊C4—442no—
274C22⋊C4—441no—
275C42—41no—
276C42—112no—
277C42—442no—
278C42—442no—
279C42D4×D1111yescharacteristic
280C16—22no—
281C16—221no—
282C16—221no—
283C11#3393111yescharacteristic, complemented, Sylow
284C23—441no—
285Q8—22no—
286Q8—41no—
287Q8—42no—
288Q8—42no—
289Q8—222no—
290Q8—882no—
291D4—441no—
292D4—441no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—42no—
296C2×C4—112no—
297C2×C4—112no—
298C2×C4—441no—
299C2×C4—442no—
300C2×C4—882no—
301C2×C4D8×D1111yescharacteristic
302C2×C4D8×D1111yescharacteristic
303C2×C4C2×D4×D1111yescharacteristic
304C8—21no—
305C8—222no—
306C8C2×#434111yescharacteristic
307C8#6704311yescharacteristic
308C22—881no—
309C22—881no—
310C22—881no—
311C22C2×D8×D1111yescharacteristic
312C4—21no—
313C4—42no—
314C4—82no—
315C4—81no—
316C4—222no—
317C4—222no—
318C4—881no—
319C4—882no—
320C4#1062253212yes—
321C4#1062312911yescharacteristic
322C4#1062330611yescharacteristic
323C2—1761no—
324C2#1308124611yescharacteristic
325C2C2×#1062253211yescharacteristic
326C2#1308176811yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2209C2
socleC22×C11C22×D8
prime radicalC2×D88C23
hypercenter#2209D11
hypocenterC11#33931
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2209

Complements

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

NH ≅ G/Ntype
2. #13081505C2semidirect
4. #13070843C2semidirect
5. #13070782C2semidirect
8. #13070518C2semidirect
9. Q32×Dic11C2semidirect
11. C11×#2209C2semidirect
128. #2209D11semidirect
283. C11#33931semidirect

Maximal subgroups

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

subgroupindex
#130816062
#130815052
#130708492
#130708432
#130707822
#130707542
#130706802
#130705182
Q32×Dic112
C4×#668922
C11×#22092
#3393111