Finite Group Databasebeta

← #14909750

Subgroups — #14909750

Order 2816.

598 conjugacy classes of subgroups.

The subgroup lattice has 352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622309C211yesmaximal, characteristic
2#13070885C212yesmaximal, complemented
3#13070855C212yesmaximal, complemented
4#13070678C214yesmaximal, complemented
5#13070549C212yesmaximal, complemented
6#13070544C212yesmaximal
7#13070419C211yesmaximal, characteristic, complemented
8C11×#3170C211yesmaximal, characteristic, complemented
9C11×#533—21no—
10C22×Dic44C2211yescharacteristic
11C22×D88C2211yescharacteristic
12C22×#4314—21no—
13C2×#66928—21no—
14C11×#500C2211yescharacteristic, complemented
15C11×#494C2211yescharacteristic, complemented
16C11×#487—21no—
17C11×#467—21no—
18C11×#467C2212yes—
19C4×C11×Q16—21no—
20C4×C11×Q16C2212yescomplemented
21C2×C4×C8×C11C2211yescharacteristic
22C2×#66893C2214yescomplemented
23C2×#66892C2214yes—
24#10622309—21no—
25#10622309—21no—
26#10622309C2212yes—
27#10622309C2212yes—
28C22⋊(C11⋊C16)C2212yes—
29#10622130C2214yescomplemented
30#10622129C2214yes—
31C4⋊(C11⋊C16)C2212yescomplemented
32#10622099C2212yescomplemented
33C22×D44—21no—
34C22×Dic22—21no—
35C2×C11×Q16—21no—
36C2×C11×Q16C2312yes—
37C22×C8×C11D411yescharacteristic
38C22×C8×C11C2311yescharacteristic
39C11×C4⋊Q8—21no—
40C11×C4⋊Q8—21no—
41C11×#125—41no—
42C11×C22⋊Q8—22no—
43C11×C22⋊Q8—41no—
44C4×Q8×C11—22no—
45C4×Q8×C11—41no—
46C11×#117—41no—
47C2×C42×C11D411yescharacteristic
48C2×(C2×D11)⋊C4—41no—
49C2×(C2×D11)⋊C4—41no—
50C2×Dic44—21no—
51C2×Dic44—42no—
52C2×Dic44C2312yes—
53C2×D88—21no—
54C2×D88—42no—
55C2×D88C2312yes—
56C2×#4314—22no—
57C2×#4314—22no—
58C2×#4314—44no—
59#66928—22no—
60#66928—22no—
61#66928—41no—
62#66928—41no—
63C11×#107—21no—
64C11×#107C2312yes—
65C11×#103—22no—
66C11×#103—22no—
67C4×C8×C11D411yescharacteristic
68C4×C8×C11D411yescharacteristic
69C4×C8×C11C2311yescharacteristic
70C4×C8×C11C2311yescharacteristic
71#66893—44no—
72#66892—44no—
73C2×C11⋊C16C2314yes—
74#33781—111nomaximal, Sylow
75C23×D11—41no—
76C2×Q8×C11—22no—
77C2×Q8×C11—41no—
78C22×C4×C11D811yescharacteristic
79C22×C4×C11D811yescharacteristic
80C22×C4×C11C2×D411yescharacteristic
81C22×Dic11—41no—
82C2×D44—22no—
83C2×D44—42no—
84C2×D44—42no—
85C2×D44—41no—
86C2×Dic22—22no—
87C2×Dic22—42no—
88C2×Dic22—42no—
89C2×Dic22—41no—
90C11×Q16—24no—
91C11×Q16—42no—
92C2×C8×C11—22no—
93C2×C8×C11—22no—
94C2×C8×C11C2×D411yescharacteristic
95C2×C8×C11C2×D411yescharacteristic
96C2×C8×C11C2×D411yescharacteristic
97C2×C8×C11C2411yescharacteristic
98C11×C4⋊C4—22no—
99C11×C4⋊C4—41no—
100C11×C4⋊C4—41no—
101C11×C4⋊C4—42no—
102C11×C4⋊C4—42no—
103C11×C4⋊C4—41no—
104C11×C22⋊C4—42no—
105C42×C11—42no—
106C42×C11D811yescharacteristic
107C42×C11D811yescharacteristic
108C42×C11C2×D411yescharacteristic
109C42×C11C2×D411yescharacteristic
110(C2×D11)⋊C4—42no—
111(C2×D11)⋊C4—42no—
112(C2×D11)⋊C4—42no—
113(C2×D11)⋊C4—42no—
114Dic44—24no—
115Dic44—42no—
116D88—24no—
117D88—42no—
118#4314—44no—
119#4314—44no—
120C11⋊C16—24no—
121#3170D1111yescharacteristic, complemented
122C2×#495—111no—
123#2251—112no—
124#2243—112no—
125#2211—114no—
126#2188—112no—
127#2187—112no—
128#2163—111no—
129C23×C11C2×D811yescharacteristic
130C22×D11—42no—
131C22×D11—82no—
132C22×D11—82no—
133C22×D11—82no—
134Q8×C11—42no—
135Q8×C11—42no—
136Q8×C11—82no—
137C2×C4×C11—22no—
138C2×C4×C11—21no—
139C2×C4×C11—21no—
140C2×C4×C11—41no—
141C2×C4×C11—42no—
142C2×C4×C11—42no—
143C2×C4×C11C2×D811yescharacteristic
144C2×C4×C11C2×D811yescharacteristic
145C2×C4×C11C2×D811yescharacteristic
146C2×C4×C11C2×D811yescharacteristic
147C2×C4×C11C2×D811yescharacteristic
148C2×C4×C11C22×D411yescharacteristic
149C2×Dic11—42no—
150C2×Dic11—82no—
151D44—42no—
152D44—42no—
153D44—82no—
154Dic22—42no—
155Dic22—42no—
156Dic22—82no—
157C8×C11—21no—
158C8×C11—21no—
159C8×C11AGL(1,ℤ/8)12yes—
160C8×C11H(5,𝔽2)12yes—
161C22×Q16—111no—
162C22×SD16—221no—
163C22×D8—111no—
164#533—21no—
165C2×#124—221no—
166C2×Q32—114no—
167C2×SD32—114no—
168#500C2×D1111yescharacteristic, complemented
169#495—112no—
170#495—112no—
171#495—221no—
172#495—221no—
173#494C2×D1111yescharacteristic, complemented
174#487—21no—
175#467—21no—
176#467C2×D1112yes—
177C4×Q16—21no—
178C4×Q16C2×D1112yescomplemented
179C2×C4×C8C2×D1111yescharacteristic
180C4⋊C16—112no—
181#358—114no—
182#357—114no—
183C22⋊C16—112no—
184#346—112no—
185C22×C11—21no—
186C22×C11—21no—
187C22×C11#51012yes—
188C22×C11C22×D811yescharacteristic
189C2×D11—82no—
190C2×D11—82no—
191C2×D11—82no—
192C2×D11—164no—
193C4×C11—21no—
194C4×C11—21no—
195C4×C11—21no—
196C4×C11—21no—
197C4×C11—21no—
198C4×C11—82no—
199C4×C11—82no—
200C4×C11#53511yescharacteristic
201C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
202Dic11—82no—
203C22×Q8—221no—
204C22×D4—221no—
205C2×Q16—21no—
206C2×Q16—112no—
207C2×Q16—221no—
208C2×Q16—442no—
209C2×Q16C22×D1112yes—
210C2×SD16—222no—
211C2×SD16—222no—
212C2×SD16—444no—
213C2×D8—112no—
214C2×D8—221no—
215C2×D8—442no—
216C22×C8C22⋊D1111yescharacteristic
217C22×C8C22×D1111yescharacteristic
218C4⋊Q8—21no—
219C4⋊Q8—21no—
220#125—41no—
221#124—222no—
222#124—222no—
223#124—441no—
224#124—441no—
225C22⋊Q8—22no—
226C22⋊Q8—41no—
227C4×Q8—22no—
228C4×Q8—41no—
229#117—41no—
230C2×C22⋊C4—441no—
231C2×C22⋊C4—441no—
232C2×C42C22⋊D1111yescharacteristic
233Q32—444no—
234SD32—444no—
235C2×C16—114no—
236#107—21no—
237#107C22×D1112yes—
238#103—22no—
239#103—22no—
240C4×C8C22⋊D1111yescharacteristic
241C4×C8C22⋊D1111yescharacteristic
242C4×C8C22×D1111yescharacteristic
243C4×C8C22×D1111yescharacteristic
244C2×C11—22no—
245C2×C11#320511yescharacteristic
246C2×C11C2×#51011yescharacteristic
247C2×C11#341411yescharacteristic
248D11—162no—
249C24—441no—
250C2×Q8—22no—
251C2×Q8—41no—
252C2×Q8—222no—
253C2×Q8—442no—
254C2×Q8—442no—
255C2×Q8—441no—
256C2×D4—222no—
257C2×D4—442no—
258C2×D4—442no—
259C2×D4—441no—
260C22×C4—441no—
261C22×C4#432311yescharacteristic
262C22×C4#432311yescharacteristic
263C22×C4C2×C22⋊D1111yescharacteristic
264Q16—24no—
265Q16—42no—
266Q16—224no—
267Q16—442no—
268SD16—444no—
269SD16—444no—
270D8—224no—
271D8—442no—
272C2×C8—22no—
273C2×C8—22no—
274C2×C8C2×C22⋊D1111yescharacteristic
275C2×C8C2×C22⋊D1111yescharacteristic
276C2×C8C2×C22⋊D1111yescharacteristic
277C2×C8C23×D1111yescharacteristic
278C4⋊C4—22no—
279C4⋊C4—41no—
280C4⋊C4—41no—
281C4⋊C4—42no—
282C4⋊C4—42no—
283C4⋊C4—41no—
284C22⋊C4—42no—
285C22⋊C4—442no—
286C22⋊C4—442no—
287C22⋊C4—442no—
288C22⋊C4—442no—
289C42—42no—
290C42#432311yescharacteristic
291C42#432311yescharacteristic
292C42C2×C22⋊D1111yescharacteristic
293C42C2×C22⋊D1111yescharacteristic
294C16—224no—
295C11#3378111yescharacteristic, complemented, Sylow
296C23—442no—
297C23—882no—
298C23—882no—
299C23—882no—
300C23C2×#432311yescharacteristic
301Q8—42no—
302Q8—42no—
303Q8—82no—
304Q8—442no—
305Q8—442no—
306Q8—882no—
307D4—442no—
308D4—442no—
309D4—882no—
310C2×C4—22no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—41no—
314C2×C4—42no—
315C2×C4—42no—
316C2×C4—442no—
317C2×C4—882no—
318C2×C4C2×#432311yescharacteristic
319C2×C4C2×#432311yescharacteristic
320C2×C4C2×#432311yescharacteristic
321C2×C4C2×#432311yescharacteristic
322C2×C4C2×#432311yescharacteristic
323C2×C4C22×C22⋊D1111yescharacteristic
324C8—21no—
325C8—21no—
326C8#6700212yes—
327C8#6704212yes—
328C22—21no—
329C22—21no—
330C22—882no—
331C22—882no—
332C22—882no—
333C22—1764no—
334C22#1062279212yes—
335C22C22×#432311yescharacteristic
336C4—21no—
337C4—21no—
338C4—21no—
339C4—21no—
340C4—21no—
341C4—82no—
342C4—82no—
343C4—882no—
344C4C2×#6700211yescharacteristic
345C4#1062336111yescharacteristic
346C2—22no—
347C2—1762no—
348C2#1307953111yescharacteristic
349C2C2×#1062279211yescharacteristic
350C2#1308175011yescharacteristic
subgroupG/H
centerC22C22×#4323
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#3170C2
socleC22×C11C22×D8
prime radicalC22×D88C22
hypercenter#3170D11
hypocenterC11#33781
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×C4×C8 ◁ #3170

Complements

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

NH ≅ G/Ntype
2. #13070885C2semidirect
3. #13070855C2semidirect
4. #13070678C2semidirect
5. #13070549C2semidirect
7. #13070419C2semidirect
8. C11×#3170C2semidirect
14. C11×#500C22semidirect
15. C11×#494C22semidirect
20. C4×C11×Q16C22semidirect
22. C2×#66893C22semidirect
29. #10622130C22semidirect
31. C4⋊(C11⋊C16)C22semidirect
32. #10622099C22semidirect
121. #3170D11semidirect
168. #500C2×D11semidirect
173. #494C2×D11semidirect
178. C4×Q16C2×D11semidirect
295. C11#33781semidirect

Maximal subgroups

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

subgroupindex
C2×#106223092
#130708852
#130708552
#130706782
#130705492
#130705442
#130704192
C11×#31702
#3378111