Finite Group Databasebeta

← #14909806

Subgroups — #14909806

Order 2816.

586 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079110C211yesmaximal, characteristic, complemented
2#13070880C211yesmaximal, characteristic, complemented
3#13070871C211yesmaximal, characteristic, complemented
4#13070863C211yesmaximal, characteristic, complemented
5#13070850C211yesmaximal, characteristic, complemented
6#13070671C212yesmaximal, complemented
7#13070661C212yesmaximal, complemented
8#13070537C212yesmaximal, complemented
9#13070532C212yesmaximal, complemented
10#13070423C211yesmaximal, characteristic, complemented
11C11×#3176C211yesmaximal, characteristic, complemented
12C11×#540—21no—
13C2×#66962—21no—
14C22×Dic44C2211yescharacteristic
15C2×#66957C2211yescharacteristic
16#10623057—21no—
17C11×#499C2211yescharacteristic
18C11×#493C2211yescharacteristic
19C11×#490—21no—
20C11×#469—21no—
21C11×#466C2212yes—
22C11×#442—21no—
23C4×C11×D8C2212yes—
24C11×#405C2211yescharacteristic
25C2×#66891C2212yes—
26C2×#66891C2212yes—
27C2×#66891C2212yes—
28C2×#66890C2212yes—
29#10622328—21no—
30#10622328—21no—
31#10622312C2211yescharacteristic
32#10622312C2211yescharacteristic
33#10622309C2211yescharacteristic
34#10622309C2211yescharacteristic
35C22⋊(C11⋊C16)C2212yes—
36#10622130C2212yes—
37#10622130C2212yes—
38#10622130C2212yes—
39#10622129C2212yes—
40C4⋊(C11⋊C16)C2212yes—
41#10622099C2211yescharacteristic
42C4×C11⋊C16C2211yescharacteristic
43C2×#4339—21no—
44C22×Dic22—21no—
45C2×C11×D8—21no—
46C2×C11×D8C2312yes—
47C2×C11×M16D411yescharacteristic
48C22×C8×C11C2311yescharacteristic
49C11×#127—21no—
50C11×#125—21no—
51C11×#123—42no—
52C11×#121—22no—
53C11×#121—42no—
54C4×D4×C11—22no—
55C11×#117D411yescharacteristic
56#66962—44no—
57C2×Dic44—21no—
58C2×Dic44—21no—
59C2×Dic44—21no—
60C2×Dic44—42no—
61C2×Dic44C2311yescharacteristic
62C2×Dic44C2311yescharacteristic
63C2×Dic44C2311yescharacteristic
64#66957—42no—
65C2×D88C2311yescharacteristic
66C2×#4314—21no—
67C2×#4314—21no—
68C2×#4314—21no—
69#66950—42no—
70#66939—42no—
71#66928—21no—
72#66928—21no—
73#66922—21no—
74#66922—21no—
75C11×#107C2312yes—
76C11×#106—21no—
77C11×#102—22no—
78C11×#102—22no—
79C11×#97D411yescharacteristic
80C11×#97D411yescharacteristic
81C4×C8×C11C2311yescharacteristic
82C4×C8×C11C2311yescharacteristic
83#66891—42no—
84#66891—42no—
85#66891—42no—
86#66890—42no—
87C2×C11⋊C16C2312yes—
88C2×C11⋊C16C2312yes—
89#33787—111nomaximal, Sylow
90C2×D4×C11—22no—
91C2×D4×C11—42no—
92C2×D4×C11—42no—
93C22×C4×C11—42no—
94C22×C4×C11C2×D411yescharacteristic
95C2×C22⋊D11—41no—
96C22×Dic11—41no—
97#4339—42no—
98#4339—42no—
99C2×D44—21no—
100C2×C4×D11—41no—
101C2×Dic22—21no—
102C2×Dic22—21no—
103C2×Dic22—21no—
104C2×Dic22—42no—
105C2×Dic22—42no—
106C2×Dic22—41no—
107C11×D8—22no—
108C11×D8—22no—
109C11×D8—42no—
110C11×M16—22no—
111C2×C8×C11—22no—
112C2×C8×C11C2×D411yescharacteristic
113C2×C8×C11C2×D411yescharacteristic
114C2×C8×C11C2×D411yescharacteristic
115C2×C8×C11C2411yescharacteristic
116C11×C4⋊C4—22no—
117C11×C4⋊C4—42no—
118C11×C4⋊C4D812yes—
119C11×C22⋊C4—42no—
120C11×C22⋊C4—42no—
121C11×C22⋊C4D812yes—
122C42×C11C2×D411yescharacteristic
123C42×C11C2×D411yescharacteristic
124(C2×D11)⋊C4—42no—
125(C2×D11)⋊C4—42no—
126C4⋊Dic11—42no—
127C4⋊Dic11—42no—
128Dic44—22no—
129Dic44—22no—
130Dic44—22no—
131Dic44—42no—
132Dic44—42no—
133Dic44—42no—
134D88—22no—
135#4314—42no—
136#4314—42no—
137#4314—42no—
138C11⋊C16—22no—
139C11⋊C16—22no—
140#3176D1111yescharacteristic, complemented
141#3156—111no—
142#2250—111no—
143#2248—111no—
144#2245—111no—
145#2242—111no—
146#2210—112no—
147#2208—112no—
148#2186—112no—
149#2185—112no—
150#2164—111no—
151C23×C11—42no—
152C23×C11C2×D811yescharacteristic
153C22×D11—41no—
154D4×C11—42no—
155D4×C11—42no—
156D4×C11—162no—
157D4×C11—162no—
158C2×C4×C11—21no—
159C2×C4×C11—21no—
160C2×C4×C11—42no—
161C2×C4×C11—162no—
162C2×C4×C11C2×D812yes—
163C2×C4×C11C2×D812yes—
164C2×C4×C11C2×D811yescharacteristic
165C2×C4×C11C22×D411yescharacteristic
166C22⋊D11—82no—
167C2×Dic11—41no—
168C2×Dic11—41no—
169C2×Dic11—41no—
170C2×Dic11—82no—
171D44—41no—
172D44—41no—
173C4×D11—82no—
174Dic22—41no—
175Dic22—41no—
176Dic22—41no—
177Dic22—41no—
178Dic22—41no—
179Dic22—41no—
180Dic22—82no—
181C8×C11—21no—
182C8×C11—21no—
183C8×C11AGL(1,ℤ/8)12yes—
184C8×C11H(5,𝔽2)12yes—
185C2×#137—221no—
186C2×#135—111no—
187C22×Q16—111no—
188#540—21no—
189#536—221no—
190C2×SD32—112no—
191C2×SD32—112no—
192C2×SD32—112no—
193C2×D16—112no—
194#499C2×D1111yescharacteristic
195#497—221no—
196#497—221no—
197#495—111no—
198#495—111no—
199#494—111no—
200#494—111no—
201#493C2×D1111yescharacteristic
202#490—21no—
203#469—21no—
204#466C2×D1112yes—
205#442—21no—
206C4×D8C2×D1112yes—
207#405C2×D1111yescharacteristic
208C4⋊C16—112no—
209#358—112no—
210#358—112no—
211#358—112no—
212#357—112no—
213C22⋊C16—112no—
214#346—111no—
215C4×C16—111no—
216C22×C11—22no—
217C22×C11—21no—
218C22×C11—82no—
219C22×C11—82no—
220C22×C11—82no—
221C22×C11C22×D811yescharacteristic
222C2×D11—82no—
223C2×D11—81no—
224C4×C11—22no—
225C4×C11—22no—
226C4×C11—21no—
227C4×C11—82no—
228C4×C11#53511yescharacteristic
229C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
230Dic11—81no—
231Dic11—81no—
232Dic11—81no—
233C2×#41—221no—
234C22×Q8—221no—
235#137—444no—
236#135—442no—
237C2×Q16—111no—
238C2×Q16—111no—
239C2×Q16—111no—
240C2×Q16—221no—
241C2×Q16—221no—
242C2×Q16—221no—
243C2×Q16—442no—
244C2×SD16—221no—
245C2×SD16—221no—
246C2×SD16—221no—
247C2×D8—21no—
248C2×D8—111no—
249C2×D8C22×D1112yes—
250C2×M16C22⋊D1111yescharacteristic
251C22×C8C22×D1111yescharacteristic
252C4⋊Q8—221no—
253C4⋊Q8—221no—
254#127—21no—
255#125—21no—
256#124—221no—
257#124—221no—
258#123—42no—
259#123—442no—
260C22⋊Q8—442no—
261#121—22no—
262#121—42no—
263C4×D4—22no—
264#117C22⋊D1111yescharacteristic
265SD32—442no—
266SD32—442no—
267SD32—442no—
268D16—442no—
269C2×C16—112no—
270C2×C16—112no—
271#107C22×D1112yes—
272#106—21no—
273#102—22no—
274#102—22no—
275#97C22⋊D1111yescharacteristic
276#97C22⋊D1111yescharacteristic
277C4×C8C22×D1111yescharacteristic
278C4×C8C22×D1111yescharacteristic
279C2×C11—41no—
280C2×C11—162no—
281C2×C11#320511yescharacteristic
282C2×C11#341612yes—
283D11—161no—
284#41—442no—
285#41—442no—
286C2×Q8—221no—
287C2×Q8—221no—
288C2×Q8—221no—
289C2×Q8—442no—
290C2×Q8—442no—
291C2×Q8—441no—
292C2×D4—22no—
293C2×D4—42no—
294C2×D4—42no—
295C2×D4—221no—
296C2×D4—441no—
297C22×C4—42no—
298C22×C4—441no—
299C22×C4—441no—
300C22×C4C2×C22⋊D1111yescharacteristic
301Q16—222no—
302Q16—222no—
303Q16—222no—
304Q16—442no—
305Q16—442no—
306Q16—442no—
307SD16—442no—
308SD16—442no—
309SD16—442no—
310D8—22no—
311D8—22no—
312D8—42no—
313D8—222no—
314M16—22no—
315C2×C8—22no—
316C2×C8C2×C22⋊D1111yescharacteristic
317C2×C8C2×C22⋊D1111yescharacteristic
318C2×C8C2×C22⋊D1111yescharacteristic
319C2×C8C23×D1111yescharacteristic
320C4⋊C4—22no—
321C4⋊C4—42no—
322C4⋊C4—442no—
323C4⋊C4—442no—
324C4⋊C4#432312yes—
325C22⋊C4—42no—
326C22⋊C4—42no—
327C22⋊C4—442no—
328C22⋊C4—442no—
329C22⋊C4#432312yes—
330C42C2×C22⋊D1111yescharacteristic
331C42C2×C22⋊D1111yescharacteristic
332C16—222no—
333C16—222no—
334C11#3378711yescharacteristic, complemented, Sylow
335C23—42no—
336C23—441no—
337C23C2×#432311yescharacteristic
338Q8—441no—
339Q8—441no—
340Q8—441no—
341Q8—441no—
342Q8—441no—
343Q8—441no—
344Q8—882no—
345D4—42no—
346D4—42no—
347D4—162no—
348D4—162no—
349D4—441no—
350D4—441no—
351D4—882no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—42no—
355C2×C4—162no—
356C2×C4—441no—
357C2×C4—441no—
358C2×C4—441no—
359C2×C4—882no—
360C2×C4—882no—
361C2×C4C2×#432312yes—
362C2×C4C2×#432312yes—
363C2×C4C2×#432311yescharacteristic
364C2×C4C22×C22⋊D1111yescharacteristic
365C8—21no—
366C8—21no—
367C8#6700212yes—
368C8#6704212yes—
369C22—22no—
370C22—21no—
371C22—82no—
372C22—82no—
373C22—82no—
374C22—882no—
375C22—881no—
376C22C22×#432311yescharacteristic
377C4—22no—
378C4—22no—
379C4—21no—
380C4—82no—
381C4—881no—
382C4—881no—
383C4—881no—
384C4C2×#6700211yescharacteristic
385C4#1062336111yescharacteristic
386C2—41no—
387C2—162no—
388C2—1761no—
389C2#1307953111yescharacteristic
390C2#1308176312yes—
subgroupG/H
centerC22C22×#4323
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#3176C2
socleC22×C11C22×D8
hypercenter#3176D11
hypocenterC11#33787
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ #117 ◁ #405 ◁ #3176

Complements

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

NH ≅ G/Ntype
1. #13079110C2semidirect
2. #13070880C2semidirect
3. #13070871C2semidirect
4. #13070863C2semidirect
5. #13070850C2semidirect
6. #13070671C2semidirect
7. #13070661C2semidirect
8. #13070537C2semidirect
9. #13070532C2semidirect
10. #13070423C2semidirect
11. C11×#3176C2semidirect
140. #3176D11semidirect
334. C11#33787semidirect

Maximal subgroups

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

subgroupindex
#130791102
#130708802
#130708712
#130708632
#130708502
#130706712
#130706612
#130705372
#130705322
#130704232
C11×#31762
#3378711