Finite Group Databasebeta

← #14909337

Subgroups — #14909337

Order 2816.

558 conjugacy classes of subgroups.

The subgroup lattice has 332 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079203C211yesmaximal, characteristic, complemented
2#13079196C211yesmaximal, characteristic
3#13070872C211yesmaximal, characteristic, complemented
4#13070845C211yesmaximal, characteristic, complemented
5#13070841C211yesmaximal, characteristic, complemented
6#13070713C214yesmaximal, complemented
7#13070467C214yesmaximal, complemented
8C4×C16×D11C211yesmaximal, characteristic, complemented
9C11×#2254C211yesmaximal, characteristic, complemented
10#10623259—21no—
11#10623256—21no—
12C11×#500C2211yescharacteristic
13C11×#500C2211yescharacteristic
14#10622706—21no—
15#10622701—21no—
16C2×#66864C2214yes—
17C2×C16×D11C2212yes—
18#10622500—21no—
19#10622500C2212yes—
20#10622496—21no—
21#10622496C2212yes—
22#10622486—21no—
23#10622486C2212yes—
24#10622485—21no—
25#10622485C2212yes—
26#10622312C2211yescharacteristic
27#10622308C2211yescharacteristic
28C4×C8×D11C2211yescharacteristic
29C11×#367C2214yes—
30C4×C11×C16C2211yescharacteristic
31C16×Dic11C2212yes—
32#10622130C2214yes—
33#10622129C2214yes—
34C4×C11⋊C16C2211yescharacteristic
35C2×#4343—41no—
36C11×C4⋊Q8—21no—
37C11×C4⋊Q8—21no—
38#67000—41no—
39#66999—41no—
40Q8×Dic11—41no—
41C2×Dic44—21no—
42C2×Dic44C2312yes—
43C2×D88—21no—
44C2×D88C2312yes—
45C2×C8×D11D411yescharacteristic
46C2×C8×D11C2311yescharacteristic
47#66950—22no—
48#66948—22no—
49#66948—41no—
50#66946—22no—
51#66946—41no—
52#66945—41no—
53#66943—41no—
54#66940—22no—
55#66927—21no—
56C42×D11D411yescharacteristic
57#66922—21no—
58C2×C11×C16C2312yes—
59C11×#107—21no—
60C11×#107—21no—
61C11×#107C2312yes—
62C11×#107C2312yes—
63C4×C8×C11C2311yescharacteristic
64C8×Dic11D411yescharacteristic
65C8×Dic11C2311yescharacteristic
66C2×C11⋊C16C2312yes—
67#66874—22no—
68#66874—22no—
69#66873—22no—
70#66873—22no—
71C4×C11⋊C8D411yescharacteristic
72#66864—28no—
73C16×D11—24no—
74#33736—111nomaximal, Sylow
75C2×Q8×C11—41no—
76C2×Q8×C11—41no—
77#4343—84no—
78C2×D44—22no—
79C2×D44—42no—
80C2×D44—41no—
81C2×D44—41no—
82C2×C4×D11—42no—
83C2×C4×D11D811yescharacteristic
84C2×C4×D11D811yescharacteristic
85C2×C4×D11C2×D411yescharacteristic
86C2×Dic22—22no—
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—
97C4⋊Dic11—42no—
98C4⋊Dic11—41no—
99C4⋊Dic11—41no—
100Dic11⋊C4—42no—
101C4×Dic11—42no—
102C4×Dic11D811yescharacteristic
103C4×Dic11D811yescharacteristic
104C4×Dic11C2×D411yescharacteristic
105C2×C11⋊C8C2×D411yescharacteristic
106C2×C11⋊C8C2×D411yescharacteristic
107Dic44—24no—
108Dic44—42no—
109D88—24no—
110D88—42no—
111C8×D11—22no—
112C8×D11—22no—
113C11×C16#4114yescomplemented
114C11⋊C16—22no—
115#3170—111no—
116#3169—111no—
117#2254D1111yescharacteristic, complemented
118#2248—111no—
119#2241—111no—
120#2240—111no—
121#2217—114no—
122C4×SD32—114no—
123C2×C4×C16—111no—
124C22×D11—42no—
125C22×D11C2×D811yescharacteristic
126Q8×C11—82no—
127Q8×C11—82no—
128C2×C4×C11—42no—
129C2×C4×C11—42no—
130C2×C4×C11C2×D811yescharacteristic
131C2×C4×C11C2×D811yescharacteristic
132C2×C4×C11C22×D411yescharacteristic
133C2×Dic11—42no—
134C2×Dic11C2×D811yescharacteristic
135C2×Dic11C2×D811yescharacteristic
136C2×Dic11C2×D811yescharacteristic
137D44—42no—
138D44—42no—
139D44—84no—
140D44—82no—
141D44—82no—
142C4×D11—21no—
143C4×D11—21no—
144C4×D11—22no—
145C4×D11—84no—
146C4×D11SD3214yescomplemented
147Dic22—42no—
148Dic22—42no—
149C8×C11#13512yes—
150C8×C11C2×#4112yes—
151C11⋊C8—21no—
152C11⋊C8—21no—
153#533—221no—
154#532—221no—
155C2×SD32—114no—
156C22×C16—112no—
157#500C2×D1111yescharacteristic
158#500C2×D1111yescharacteristic
159#494—111no—
160#493—111no—
161#487—221no—
162#486—221no—
163#467—112no—
164#467—221no—
165#466—112no—
166#466—221no—
167C4×Q16—112no—
168C4×Q16—221no—
169C4×D8—112no—
170C4×D8—221no—
171C2×C4×C8—111no—
172#367C2×D1114yes—
173#358—114no—
174#357—114no—
175C4×C16—112no—
176C4×C16—111no—
177C4×C16C2×D1111yescharacteristic
178C22×C11C22×D811yescharacteristic
179C2×D11—21no—
180C2×D11—21no—
181C2×D11—82no—
182C2×D11—82no—
183C2×D11—82no—
184C2×D11C2×SD3212yes—
185C4×C11—82no—
186C4×C11—82no—
187C4×C11C2×SD3212yes—
188C4×C11#50812yes—
189C4×C11#53211yescharacteristic
190C4×C11C2×#13511yescharacteristic
191Dic11—21no—
192Dic11—21no—
193Dic11—82no—
194Dic11C2×SD3212yes—
195C2×#41—441no—
196C2×Q16—112no—
197C2×Q16—221no—
198C2×D8—112no—
199C2×D8—221no—
200C22×C8—111no—
201C22×C8—111no—
202C4⋊Q8—21no—
203C4⋊Q8—21no—
204C4⋊Q8—221no—
205#127—221no—
206#125—441no—
207#124—441no—
208C22⋊Q8—222no—
209C22⋊Q8—441no—
210#121—222no—
211#121—441no—
212C4×Q8—222no—
213C4×Q8—441no—
214C4×D4—222no—
215C4×D4—441no—
216#117—441no—
217C2×C42—111no—
218SD32—228no—
219C2×C16—112no—
220C2×C16—224no—
221C2×C16C22×D1112yes—
222#107—21no—
223#107—21no—
224#107C22×D1112yes—
225#107C22×D1112yes—
226#103—222no—
227#103—222no—
228#102—222no—
229#102—222no—
230C4×C8—111no—
231C4×C8—111no—
232C4×C8—111no—
233C4×C8C22×D1111yescharacteristic
234C2×C11#316911yescharacteristic
235C2×C11C22×SD3211yescharacteristic
236C2×C11C2×#50811yescharacteristic
237D11—22no—
238D11—162no—
239#41—884no—
240C2×Q8—41no—
241C2×Q8—41no—
242C2×Q8—222no—
243C2×D4—222no—
244C2×D4—442no—
245C2×D4—441no—
246C2×D4—441no—
247C22×C4—111no—
248C22×C4—111no—
249C22×C4—111no—
250C22×C4—442no—
251Q16—224no—
252Q16—442no—
253D8—224no—
254D8—442no—
255C2×C8—111no—
256C2×C8—111no—
257C2×C8—222no—
258C2×C8—222no—
259C2×C8D4×D1111yescharacteristic
260C2×C8C23×D1111yescharacteristic
261C4⋊C4—22no—
262C4⋊C4—22no—
263C4⋊C4—41no—
264C4⋊C4—41no—
265C4⋊C4—442no—
266C4⋊C4—442no—
267C4⋊C4—441no—
268C4⋊C4—441no—
269C22⋊C4—442no—
270C22⋊C4—442no—
271C22⋊C4—442no—
272C42—111no—
273C42—111no—
274C42—111no—
275C42—442no—
276C42D4×D1111yescharacteristic
277C16—222no—
278C16#434314yescomplemented
279C11#3373611yescharacteristic, complemented, Sylow
280C23—111no—
281C23—442no—
282Q8—82no—
283Q8—82no—
284Q8—442no—
285Q8—442no—
286D4—442no—
287D4—442no—
288D4—884no—
289D4—882no—
290D4—882no—
291C2×C4—42no—
292C2×C4—42no—
293C2×C4—111no—
294C2×C4—114no—
295C2×C4—111no—
296C2×C4—111no—
297C2×C4—221no—
298C2×C4—221no—
299C2×C4—222no—
300C2×C4—442no—
301C2×C4—884no—
302C2×C4D8×D1111yescharacteristic
303C2×C4D8×D1111yescharacteristic
304C2×C4C2×D4×D1111yescharacteristic
305C8—221no—
306C8—221no—
307C8#6697212yes—
308C8C2×#434312yes—
309C22—112no—
310C22—221no—
311C22—221no—
312C22—882no—
313C22—882no—
314C22—882no—
315C22C2×D8×D1111yescharacteristic
316C4—82no—
317C4—82no—
318C4—112no—
319C4—221no—
320C4—221no—
321C4—882no—
322C4D11×SD3212yes—
323C4#1062252912yes—
324C4#1062325611yescharacteristic
325C4C2×#6697211yescharacteristic
326C2—222no—
327C2—1762no—
328C2#1307919611yescharacteristic
329C2C2×D11×SD3211yescharacteristic
330C2C2×#1062252911yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2254C2
socleC22×C11C22×D8
prime radical#13079196C2
hypercenter#2254D11
hypocenterC11#33736
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
1. #13079203C2semidirect
3. #13070872C2semidirect
4. #13070845C2semidirect
5. #13070841C2semidirect
6. #13070713C2semidirect
7. #13070467C2semidirect
8. C4×C16×D11C2semidirect
9. C11×#2254C2semidirect
113. C11×C16#41semidirect
117. #2254D11semidirect
146. C4×D11SD32semidirect
278. C16#4343semidirect
279. C11#33736semidirect

Maximal subgroups

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

subgroupindex
#130792032
#130791962
#130708722
#130708452
#130708412
#130707132
#130704672
C4×C16×D112
C11×#22542
#3373611