Finite Group Databasebeta

← #14911196

Subgroups — #14911196

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#13081047C211yesmaximal, characteristic, complemented
2#13070896C211yesmaximal, characteristic, complemented
3#13070824C212yesmaximal, complemented
4#13070804C212yesmaximal, complemented
5#13070765C211yesmaximal, characteristic, complemented
6#13070753C211yesmaximal, characteristic, complemented
7#13070710C212yesmaximal, complemented
8C4×#66891C211yesmaximal, characteristic, complemented
9D4×C11⋊C16C211yesmaximal, characteristic, complemented
10#13070398C212yesmaximal, complemented
11C11×#3341C211yesmaximal, characteristic
12C11×#555—21no—
13#10623073—21no—
14C11×#500C2211yescharacteristic
15C11×#482—22no—
16C11×#476—21no—
17C11×#466C2212yes—
18C4×C11×D8C2211yescharacteristic
19C8×D4×C11C2211yescharacteristic
20C11×#427C2212yes—
21C2×#66891C2211yescharacteristic
22#10622729C2212yes—
23#10622719C2212yes—
24C22×C11⋊C16C2212yes—
25#10622464—21no—
26#10622336—22no—
27C4×Dic44C2211yescharacteristic
28#10622295C2211yescharacteristic
29#10622200C2212yes—
30#10622200C2211yescharacteristic
31C22⋊(C11⋊C16)C2212yes—
32#10622130C2212yes—
33#10622130C2211yescharacteristic
34#10622128C2212yes—
35#10622128C2212yes—
36#10622128C2211yescharacteristic
37#10622127C2212yes—
38#10622127C2212yes—
39C4⋊(C11⋊C16)C2211yescharacteristic
40C4×C11⋊C16C2211yescharacteristic
41C2×C11×D8C2311yescharacteristic
42C22×C8×C11C2312yes—
43C11×C4⋊Q8—21no—
44C11×#124—42no—
45C11×#121—22no—
46C11×#121—41no—
47C4×D4×C11—21no—
48C4×D4×C11D411yescharacteristic
49C11×#117—22no—
50C11×#117—41no—
51#66989—41no—
52#66979—22no—
53#66977—22no—
54C2×Dic44C2311yescharacteristic
55#66940—41no—
56#66932—42no—
57#66922—21no—
58C4×Dic22—21no—
59C11×#107—21no—
60C11×#107C2312yes—
61C11×#107C2311yescharacteristic
62C11×#106—22no—
63C11×C4⋊C8D411yescharacteristic
64C11×#102—21no—
65C11×#102—22no—
66C11×C22⋊C8D412yes—
67C4×C8×C11C2311yescharacteristic
68#66891—22no—
69#66882—21no—
70#66882C2312yes—
71#66882C2311yescharacteristic
72#66881—22no—
73#66880—22no—
74#66880—21no—
75C2×C11⋊C16—24no—
76C2×C11⋊C16C2311yescharacteristic
77C2×C11⋊C16C2312yes—
78C2×C11⋊C16C2311yescharacteristic
79#33907—111nomaximal, Sylow
80C2×Q8×C11—41no—
81C2×D4×C11—21no—
82C2×D4×C11—42no—
83C2×D4×C11D811yescharacteristic
84C22×C4×C11—41no—
85C22×C4×C11C2×D412yes—
86C2×Dic22—21no—
87C2×Dic22—41no—
88C11×D8—21no—
89C11×D8—21no—
90C2×C8×C11—22no—
91C2×C8×C11—22no—
92C2×C8×C11C2×D412yes—
93C2×C8×C11C2×D411yescharacteristic
94C2×C8×C11C2411yescharacteristic
95C11×C4⋊C4—21no—
96C11×C4⋊C4—22no—
97C11×C4⋊C4—41no—
98C11×C4⋊C4D811yescharacteristic
99C11×C22⋊C4—42no—
100C11×C22⋊C4—42no—
101C11×C22⋊C4—41no—
102C11×C22⋊C4D812yes—
103C42×C11—42no—
104C42×C11C2×D411yescharacteristic
105C22⋊Dic11—42no—
106C22⋊Dic11—42no—
107C4⋊Dic11—21no—
108C4⋊Dic11—22no—
109C4⋊Dic11—41no—
110Dic11⋊C4—41no—
111Dic11⋊C4—42no—
112C4×Dic11—41no—
113C4×Dic11—42no—
114Dic44—21no—
115Dic44—21no—
116C11⋊C16—22no—
117C11⋊C16—21no—
118C11⋊C16#4112yes—
119#3342—111no—
120#3341D1111yescharacteristic
121#2254—111no—
122#2237—112no—
123#2234—112no—
124#2227—111no—
125#2224—111no—
126#2217—112no—
127C4×SD32—111no—
128D4×C16—111no—
129#2158—112no—
130C23×C11—41no—
131C23×C11C2×D812yes—
132Q8×C11—161no—
133D4×C11—22no—
134D4×C11—41no—
135D4×C11—41no—
136D4×C11—162no—
137C2×C4×C11—22no—
138C2×C4×C11—22no—
139C2×C4×C11—41no—
140C2×C4×C11—42no—
141C2×C4×C11—82no—
142C2×C4×C11C2×D812yes—
143C2×C4×C11C2×D811yescharacteristic
144C2×C4×C11C2×D811yescharacteristic
145C2×C4×C11C22×D411yescharacteristic
146C2×Dic11—41no—
147C2×Dic11—41no—
148C2×Dic11—42no—
149Dic22—41no—
150Dic22—41no—
151Dic22—82no—
152C8×C11—22no—
153C8×C11—21no—
154C8×C11C2×#4111yescharacteristic
155C8×C112−1+411yescharacteristic
156#556—221no—
157#555—21no—
158C2×SD32—111no—
159C22×C16—112no—
160#500—111no—
161#500C2×D1111yescharacteristic
162#485—222no—
163#482—22no—
164#476—21no—
165#475—221no—
166#467—112no—
167#466C2×D1112yes—
168C4×Q16—111no—
169C4×D8C2×D1111yescharacteristic
170C8×D4C2×D1111yescharacteristic
171#427—112no—
172#427C2×D1112yes—
173#367—111no—
174#367—112no—
175#367—112no—
176#366—112no—
177#366—112no—
178C4⋊C16—111no—
179#358—111no—
180#358—112no—
181#357—111no—
182#357—112no—
183C22⋊C16—112no—
184C4×C16—111no—
185C22×C11—22no—
186C22×C11—22no—
187C22×C11—22no—
188C22×C11—81no—
189C22×C11—81no—
190C22×C11—81no—
191C22×C11C22×D811yescharacteristic
192C4×C11—22no—
193C4×C11—21no—
194C4×C11—81no—
195C4×C11—82no—
196C4×C11#50812yes—
197C4×C11#54711yescharacteristic
198C4×C11#57811yescharacteristic
199Dic11—81no—
200Dic11—82no—
201Dic11—81no—
202C2×Q16—111no—
203C2×D8C22×D1111yescharacteristic
204C22×C8C22×D1112yes—
205C4⋊Q8—21no—
206C4⋊Q8—221no—
207#126—442no—
208#124—42no—
209#124—441no—
210C22⋊Q8—222no—
211#121—22no—
212#121—41no—
213C4×Q8—221no—
214C4×Q8—441no—
215C4×D4—21no—
216C4×D4C22⋊D1111yescharacteristic
217#117—22no—
218#117—41no—
219#117—222no—
220SD32—222no—
221C2×C16—111no—
222C2×C16—111no—
223C2×C16—112no—
224C2×C16—224no—
225#107—21no—
226#107—111no—
227#107—112no—
228#107—221no—
229#107C22×D1111yescharacteristic
230#107C22×D1112yes—
231#106—22no—
232#106—222no—
233C4⋊C8C22⋊D1111yescharacteristic
234#103—221no—
235#103—222no—
236#102—21no—
237#102—22no—
238C22⋊C8C22⋊D1112yes—
239C4×C8C22×D1111yescharacteristic
240C2×C11—42no—
241C2×C11—161no—
242C2×C11#333411yescharacteristic
243C2×C11C2×#50811yescharacteristic
244C2×C11#341611yescharacteristic
245C2×Q8—41no—
246C2×Q8—221no—
247C2×Q8—441no—
248C2×D4—21no—
249C2×D4—42no—
250C2×D4#432311yescharacteristic
251C22×C4—41no—
252C22×C4C2×C22⋊D1112yes—
253Q16—221no—
254Q16—221no—
255D8—21no—
256D8—21no—
257C2×C8—22no—
258C2×C8—22no—
259C2×C8C2×C22⋊D1111yescharacteristic
260C2×C8C2×C22⋊D1112yes—
261C2×C8C23×D1111yescharacteristic
262C4⋊C4—21no—
263C4⋊C4—22no—
264C4⋊C4—41no—
265C4⋊C4—221no—
266C4⋊C4—222no—
267C4⋊C4—441no—
268C4⋊C4—442no—
269C4⋊C4—441no—
270C4⋊C4#432311yescharacteristic
271C22⋊C4—42no—
272C22⋊C4—42no—
273C22⋊C4—41no—
274C22⋊C4—442no—
275C22⋊C4—442no—
276C22⋊C4#432312yes—
277C42—42no—
278C42—442no—
279C42—441no—
280C42C2×C22⋊D1111yescharacteristic
281C16—112no—
282C16—222no—
283C16—221no—
284C11#3390711yescharacteristic, complemented, Sylow
285C23—41no—
286C23C2×#432312yes—
287Q8—161no—
288Q8—441no—
289Q8—441no—
290Q8—882no—
291D4—22no—
292D4—41no—
293D4—41no—
294D4—162no—
295C2×C4—22no—
296C2×C4—22no—
297C2×C4—41no—
298C2×C4—42no—
299C2×C4—82no—
300C2×C4—441no—
301C2×C4—442no—
302C2×C4—441no—
303C2×C4C2×#432312yes—
304C2×C4C2×#432311yescharacteristic
305C2×C4C2×#432311yescharacteristic
306C2×C4C22×C22⋊D1111yescharacteristic
307C8—22no—
308C8—21no—
309C8#41×D1111yescharacteristic
310C8#6704311yescharacteristic
311C22—22no—
312C22—22no—
313C22—22no—
314C22—81no—
315C22—81no—
316C22—81no—
317C22C22×#432311yescharacteristic
318C4—22no—
319C4—21no—
320C4—81no—
321C4—82no—
322C4—881no—
323C4—882no—
324C4—881no—
325C4#1062280712yes—
326C4#1062335511yescharacteristic
327C4#1062336911yescharacteristic
328C2—42no—
329C2—161no—
330C2#1308095911yescharacteristic
331C2C2×#1062280711yescharacteristic
332C2#1308176311yescharacteristic
subgroupG/H
centerC22C22×#4323
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
Fitting, prime radicalC11×#3341C2
socleC22×C11C22×D8
hypercenter#3341D11
hypocenterC11#33907
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C4×D4 ◁ C8×D4 ◁ #3341

Complements

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

NH ≅ G/Ntype
1. #13081047C2semidirect
2. #13070896C2semidirect
3. #13070824C2semidirect
4. #13070804C2semidirect
5. #13070765C2semidirect
6. #13070753C2semidirect
7. #13070710C2semidirect
8. C4×#66891C2semidirect
9. D4×C11⋊C16C2semidirect
10. #13070398C2semidirect
284. C11#33907semidirect

Maximal subgroups

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

subgroupindex
#130810472
#130708962
#130708242
#130708042
#130707652
#130707532
#130707102
C4×#668912
D4×C11⋊C162
#130703982
C11×#33412
#3390711