Finite Group Databasebeta

← #14911198

Subgroups — #14911198

Order 2816.

480 conjugacy classes of subgroups.

The subgroup lattice has 334 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13081048C211yesmaximal, characteristic, complemented
2#13081040C211yesmaximal, characteristic
3#13070898C211yesmaximal, characteristic, complemented
4#13070822C212yesmaximal, complemented
5#13070806C212yesmaximal, complemented
6#13070768C211yesmaximal, characteristic, complemented
7#13070753C211yesmaximal, characteristic, complemented
8#13070709C212yesmaximal, complemented
9C16×D44C211yesmaximal, characteristic, complemented
10#13070399C212yesmaximal, complemented
11C4×C11×SD32C211yesmaximal, characteristic, complemented
12#10623115—21no—
13#10623094—21no—
14C2×C11×SD32C2211yescharacteristic
15C4×C11×Q16C2211yescharacteristic
16C4×C11×D8C2211yescharacteristic
17#10622801C2212yes—
18#10622770C2212yes—
19#10622633—21no—
20#10622621—21no—
21C2×C16×D11C2212yes—
22#10622493C2212yes—
23#10622493C2212yes—
24#10622427—22no—
25#10622397—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#10622143C2212yes—
37#10622143C2212yes—
38#10622127C2212yes—
39#10622127C2212yes—
40C4⋊(C11⋊C16)C2211yescharacteristic
41C2×C11×Q16C2311yescharacteristic
42C2×C11×D8C2311yescharacteristic
43C4×Q8×C11—21no—
44C4×D4×C11—21no—
45#66999—22no—
46#66991—22no—
47#66983—41no—
48#66979—41no—
49C2×C8×D11C2312yes—
50#66951—42no—
51#66945—22no—
52#66945—22no—
53#66938—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#66872—22no—
77C4⋊(C11⋊C8)D411yescharacteristic
78C16×D11—24no—
79#33907—111nomaximal, Sylow
80C2×Q8×C11—21no—
81C2×D4×C11—21no—
82C22×C4×C11—41no—
83C2×C22⋊D11—42no—
84C2×D44D811yescharacteristic
85C2×C4×D11C2×D412yes—
86C2×Dic22—41no—
87C2×Dic22—41no—
88C11×Q16—21no—
89C11×Q16—21no—
90C11×D8—21no—
91C11×D8—21no—
92C2×C8×C11C2×D411yescharacteristic
93C2×C8×C11C2411yescharacteristic
94C11×C4⋊C4—21no—
95C11×C4⋊C4—21no—
96C11×C4⋊C4—41no—
97C11×C22⋊C4—41no—
98C42×C11—41no—
99C42×C11C2×D411yescharacteristic
100C22⋊Dic11—42no—
101(C2×D11)⋊C4—42no—
102(C2×D11)⋊C4—42no—
103(C2×D11)⋊C4—42no—
104(C2×D11)⋊C4D812yes—
105C4⋊Dic11—22no—
106C4⋊Dic11—22no—
107C4⋊Dic11—41no—
108C4⋊Dic11—41no—
109C4⋊Dic11D811yescharacteristic
110Dic11⋊C4—42no—
111C4×Dic11—42no—
112C4×Dic11—42no—
113C2×C11⋊C8C2×D412yes—
114C8×D11—22no—
115C8×D11—22no—
116C11×C16—21no—
117C11×C16#4112yes—
118C11⋊C16—22no—
119#3342—111no—
120#3341—111no—
121#2254—111no—
122#2237—112no—
123#2234—112no—
124#2227—111no—
125#2224—111no—
126#2217—112no—
127C4×SD32D1111yescharacteristic, complemented
128D4×C16—111no—
129#2158—112no—
130C23×C11—41no—
131C22×D11C2×D812yes—
132Q8×C11—41no—
133Q8×C11—41no—
134D4×C11—41no—
135D4×C11—41no—
136C2×C4×C11—41no—
137C2×C4×C11—41no—
138C2×C4×C11—41no—
139C2×C4×C11—82no—
140C2×C4×C11C2×D811yescharacteristic
141C2×C4×C11C2×D811yescharacteristic
142C2×C4×C11C22×D411yescharacteristic
143C22⋊D11—162no—
144C2×Dic11—42no—
145C2×Dic11—42no—
146C2×Dic11C2×D812yes—
147D44—22no—
148C4×D11—22no—
149C4×D11—22no—
150Dic22—82no—
151Dic22—161no—
152C8×C11—21no—
153C8×C11C2×#4111yescharacteristic
154C8×C112−1+411yescharacteristic
155C11⋊C8—22no—
156#556—221no—
157#555—221no—
158C2×SD32C2×D1111yescharacteristic
159C22×C16—112no—
160#500—111no—
161#500—111no—
162#485—222no—
163#482—222no—
164#476—221no—
165#475—221no—
166#467—112no—
167#466—112no—
168C4×Q16C2×D1111yescharacteristic
169C4×D8C2×D1111yescharacteristic
170C8×D4—111no—
171#427—112no—
172#427—112no—
173#367—112no—
174#367—112no—
175#367C2×D1111yescharacteristic
176#366—112no—
177#366—112no—
178C4⋊C16—111no—
179#358—112no—
180#358C2×D1111yescharacteristic
181#357—112no—
182#357C2×D1111yescharacteristic
183C22⋊C16—112no—
184C4×C16C2×D1111yescharacteristic
185C22×C11—81no—
186C22×C11—81no—
187C22×C11—81no—
188C22×C11C22×D811yescharacteristic
189C2×D11—22no—
190C2×D11—22no—
191C2×D11—22no—
192C4×C11—21no—
193C4×C11—81no—
194C4×C11—81no—
195C4×C11—81no—
196C4×C11#50812yes—
197C4×C11#54711yescharacteristic
198C4×C11#57811yescharacteristic
199Dic11—22no—
200Dic11—82no—
201Dic11—82no—
202C2×Q16C22×D1111yescharacteristic
203C2×D8C22×D1111yescharacteristic
204C22×C8—112no—
205C4⋊Q8—221no—
206C4⋊Q8—221no—
207#126—442no—
208#124—441no—
209#124—442no—
210C22⋊Q8—222no—
211#121—222no—
212#121—441no—
213C4×Q8—21no—
214C4×Q8—441no—
215C4×D4—21no—
216C4×D4—111no—
217#117—222no—
218#117—222no—
219#117—441no—
220SD32—22no—
221C2×C16—112no—
222C2×C16—224no—
223C2×C16C22×D1111yescharacteristic
224C2×C16C22×D1111yescharacteristic
225#107—112no—
226#107—112no—
227#107—221no—
228#107—221no—
229#107C22×D1111yescharacteristic
230#107C22×D1111yescharacteristic
231#106—222no—
232#106—222no—
233C4⋊C8—111no—
234#103—21no—
235#103—222no—
236#102—21no—
237#102—222no—
238C22⋊C8—112no—
239C4×C8C22×D1111yescharacteristic
240C2×C11—161no—
241C2×C11#333411yescharacteristic
242C2×C11C2×#50811yescharacteristic
243C2×C11#341611yescharacteristic
244D11—42no—
245C2×Q8—21no—
246C2×Q8—441no—
247C2×Q8—441no—
248C2×D4—21no—
249C2×D4—111no—
250C2×D4—442no—
251C22×C4—41no—
252C22×C4—112no—
253Q16—21no—
254Q16—21no—
255D8—21no—
256D8—21no—
257C2×C8—112no—
258C2×C8—222no—
259C2×C8—222no—
260C2×C8D4×D1111yescharacteristic
261C2×C8C23×D1111yescharacteristic
262C4⋊C4—21no—
263C4⋊C4—21no—
264C4⋊C4—41no—
265C4⋊C4—111no—
266C4⋊C4—222no—
267C4⋊C4—222no—
268C4⋊C4—442no—
269C4⋊C4—441no—
270C4⋊C4—441no—
271C22⋊C4—41no—
272C22⋊C4—112no—
273C22⋊C4—442no—
274C22⋊C4—442no—
275C22⋊C4—442no—
276C22⋊C4—442no—
277C42—41no—
278C42—442no—
279C42—442no—
280C42D4×D1111yescharacteristic
281C16—21no—
282C16—222no—
283C16#433912yes—
284C11#3390711yescharacteristic, complemented, Sylow
285C23—41no—
286C23—112no—
287Q8—41no—
288Q8—41no—
289Q8—882no—
290Q8—1761no—
291D4—41no—
292D4—41no—
293D4—222no—
294D4—1762no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4—82no—
299C2×C4—112no—
300C2×C4—222no—
301C2×C4—222no—
302C2×C4—442no—
303C2×C4—442no—
304C2×C4D8×D1111yescharacteristic
305C2×C4D8×D1111yescharacteristic
306C2×C4C2×D4×D1111yescharacteristic
307C8—21no—
308C8—222no—
309C8C2×#433911yescharacteristic
310C8#6704311yescharacteristic
311C22—81no—
312C22—81no—
313C22—81no—
314C22—222no—
315C22—222no—
316C22—222no—
317C22C2×D8×D1111yescharacteristic
318C4—21no—
319C4—81no—
320C4—81no—
321C4—81no—
322C4—222no—
323C4—882no—
324C4—882no—
325C4#1062252912yes—
326C4#1062308211yescharacteristic
327C4#1062330211yescharacteristic
328C2—161no—
329C2—442no—
330C2#1308096511yescharacteristic
331C2C2×#1062252911yescharacteristic
332C2#1308175911yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC4×C11×SD32C2
socleC22×C11C22×D8
prime radical#13081040C2
hypercenterC4×SD32D11
hypocenterC11#33907
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. #13070898C2semidirect
4. #13070822C2semidirect
5. #13070806C2semidirect
6. #13070768C2semidirect
7. #13070753C2semidirect
8. #13070709C2semidirect
9. C16×D44C2semidirect
10. #13070399C2semidirect
11. C4×C11×SD32C2semidirect
127. C4×SD32D11semidirect
284. C11#33907semidirect

Maximal subgroups

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

subgroupindex
#130810482
#130810402
#130708982
#130708222
#130708062
#130707682
#130707532
#130707092
C16×D442
#130703992
C4×C11×SD322
#3390711