Finite Group Databasebeta

← #14909812

Subgroups — #14909812

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#13079266C211yesmaximal, characteristic, complemented
2#13070883C211yesmaximal, characteristic, complemented
3#13070873C211yesmaximal, characteristic, complemented
4#13070861C211yesmaximal, characteristic, complemented
5#13070847C211yesmaximal, characteristic, complemented
6#13070668C212yesmaximal, complemented
7#13070658C212yesmaximal, complemented
8#13070539C212yesmaximal, complemented
9#13070533C212yesmaximal, complemented
10#13070423C211yesmaximal, characteristic, complemented
11C11×#3156C211yesmaximal, characteristic, complemented
12C2×C11×#137—21no—
13C2×C11×#135C2211yescharacteristic
14C22×C11×Q16C2211yescharacteristic
15C11×#536—21no—
16#10623066—21no—
17C11×#497—21no—
18C11×#497—21no—
19C11×#495C2211yescharacteristic
20C11×#495C2211yescharacteristic
21C11×#494C2211yescharacteristic
22C11×#494C2211yescharacteristic
23C11×#405C2211yescharacteristic
24C2×#66892C2212yes—
25C2×#66892C2212yes—
26C2×#66892C2212yes—
27C2×#66890C2212yes—
28#10622748—21no—
29#10622728C2212yes—
30#10622326—21no—
31#10622324—21no—
32#10622308C2211yescharacteristic
33C4×D88C2212yes—
34#10622296C2211yescharacteristic
35#10622202C2212yes—
36#10622202C2212yes—
37#10622202C2212yes—
38#10622200C2212yes—
39C22⋊(C11⋊C16)C2212yes—
40C4⋊(C11⋊C16)C2212yes—
41#10622099C2211yescharacteristic
42C4×C11⋊C16C2211yescharacteristic
43C2×C11×#41—21no—
44C22×Q8×C11—21no—
45C11×#137—44no—
46C11×#135—42no—
47C2×C11×Q16—21no—
48C2×C11×Q16—21no—
49C2×C11×Q16—21no—
50C2×C11×Q16—42no—
51C2×C11×Q16C2311yescharacteristic
52C2×C11×Q16C2311yescharacteristic
53C2×C11×Q16C2311yescharacteristic
54C2×C11×SD16—21no—
55C2×C11×SD16—21no—
56C2×C11×SD16—21no—
57C2×C11×D8C2311yescharacteristic
58C2×C11×M16D411yescharacteristic
59C22×C8×C11C2311yescharacteristic
60C11×C4⋊Q8—21no—
61C11×C4⋊Q8—21no—
62C11×#124—21no—
63C11×#124—21no—
64C11×#123—42no—
65C11×C22⋊Q8—42no—
66C11×#117D411yescharacteristic
67#66983—22no—
68C2×D88—21no—
69C2×D88C2312yes—
70#66947—42no—
71#66937—42no—
72#66927—21no—
73C4×D44—22no—
74#66923—21no—
75C11×#97D411yescharacteristic
76C11×#97D411yescharacteristic
77C4×C8×C11C2311yescharacteristic
78C4×C8×C11C2311yescharacteristic
79#66892—42no—
80#66892—42no—
81#66892—42no—
82#66890—42no—
83#66885—22no—
84#66885—22no—
85#66882C2312yes—
86#66881—21no—
87C2×C11⋊C16C2312yes—
88C2×C11⋊C16C2312yes—
89#33787—111nomaximal, Sylow
90C11×#41—42no—
91C11×#41—42no—
92C2×Q8×C11—21no—
93C2×Q8×C11—21no—
94C2×Q8×C11—21no—
95C2×Q8×C11—42no—
96C2×Q8×C11—42no—
97C2×Q8×C11—41no—
98C2×D4×C11—21no—
99C2×D4×C11—41no—
100C22×C4×C11—41no—
101C22×C4×C11—41no—
102C22×C4×C11C2×D411yescharacteristic
103C2×C22⋊D11—42no—
104C2×D44—22no—
105C2×D44—42no—
106C2×C4×D11—42no—
107C11×Q16—22no—
108C11×Q16—22no—
109C11×Q16—22no—
110C11×Q16—42no—
111C11×Q16—42no—
112C11×Q16—42no—
113C11×SD16—42no—
114C11×SD16—42no—
115C11×SD16—42no—
116C11×D8—22no—
117C11×M16—22no—
118C2×C8×C11—22no—
119C2×C8×C11C2×D411yescharacteristic
120C2×C8×C11C2×D411yescharacteristic
121C2×C8×C11C2×D411yescharacteristic
122C2×C8×C11C2411yescharacteristic
123C11×C4⋊C4—42no—
124C11×C4⋊C4—42no—
125C11×C4⋊C4D812yes—
126C11×C22⋊C4—42no—
127C11×C22⋊C4—42no—
128C11×C22⋊C4D812yes—
129C42×C11C2×D411yescharacteristic
130C42×C11C2×D411yescharacteristic
131(C2×D11)⋊C4—42no—
132(C2×D11)⋊C4—42no—
133C4⋊Dic11—22no—
134Dic11⋊C4—42no—
135D88—22no—
136D88—22no—
137D88—42no—
138C11⋊C16—22no—
139C11⋊C16—22no—
140#3176—111no—
141#3156D1111yescharacteristic, complemented
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—41no—
152C23×C11C2×D811yescharacteristic
153C22×D11—42no—
154Q8×C11—41no—
155Q8×C11—41no—
156Q8×C11—41no—
157Q8×C11—41no—
158Q8×C11—41no—
159Q8×C11—41no—
160Q8×C11—82no—
161D4×C11—41no—
162D4×C11—41no—
163D4×C11—82no—
164C2×C4×C11—21no—
165C2×C4×C11—21no—
166C2×C4×C11—41no—
167C2×C4×C11—41no—
168C2×C4×C11—41no—
169C2×C4×C11—82no—
170C2×C4×C11—82no—
171C2×C4×C11C2×D812yes—
172C2×C4×C11C2×D811yescharacteristic
173C2×C4×C11C2×D812yes—
174C2×C4×C11C22×D411yescharacteristic
175C22⋊D11—162no—
176C2×Dic11—42no—
177D44—42no—
178D44—42no—
179D44—162no—
180C4×D11—162no—
181C8×C11—21no—
182C8×C11—21no—
183C8×C11AGL(1,ℤ/8)12yes—
184C8×C11H(5,𝔽2)12yes—
185C2×#137—21no—
186C2×#135C2×D1111yescharacteristic
187C22×Q16C2×D1111yescharacteristic
188#540—221no—
189#536—21no—
190C2×SD32—112no—
191C2×SD32—112no—
192C2×SD32—112no—
193C2×D16—112no—
194#499—111no—
195#497—21no—
196#497—21no—
197#495C2×D1111yescharacteristic
198#495C2×D1111yescharacteristic
199#494C2×D1111yescharacteristic
200#494C2×D1111yescharacteristic
201#493—111no—
202#490—221no—
203#469—221no—
204#466—112no—
205#442—221no—
206C4×D8—112no—
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—81no—
220C22×C11C22×D811yescharacteristic
221C2×D11—82no—
222C2×D11—82no—
223C2×D11—82no—
224C4×C11—22no—
225C4×C11—22no—
226C4×C11—21no—
227C4×C11—81no—
228C4×C11—81no—
229C4×C11—81no—
230C4×C11#53511yescharacteristic
231C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
232Dic11—82no—
233C2×#41—21no—
234C22×Q8—21no—
235#137—44no—
236#135—42no—
237C2×Q16—21no—
238C2×Q16—21no—
239C2×Q16—21no—
240C2×Q16—42no—
241C2×Q16C22×D1111yescharacteristic
242C2×Q16C22×D1111yescharacteristic
243C2×Q16C22×D1111yescharacteristic
244C2×SD16—21no—
245C2×SD16—21no—
246C2×SD16—21no—
247C2×D8—112no—
248C2×D8—221no—
249C2×D8C22×D1111yescharacteristic
250C2×M16C22⋊D1111yescharacteristic
251C22×C8C22×D1111yescharacteristic
252C4⋊Q8—21no—
253C4⋊Q8—21no—
254#127—221no—
255#125—221no—
256#124—21no—
257#124—21no—
258#123—42no—
259#123—442no—
260C22⋊Q8—42no—
261#121—222no—
262#121—442no—
263C4×D4—222no—
264#117C22⋊D1111yescharacteristic
265SD32—442no—
266SD32—442no—
267SD32—442no—
268D16—442no—
269C2×C16—112no—
270C2×C16—112no—
271#107—112no—
272#106—221no—
273#102—222no—
274#102—222no—
275#97C22⋊D1111yescharacteristic
276#97C22⋊D1111yescharacteristic
277C4×C8C22×D1111yescharacteristic
278C4×C8C22×D1111yescharacteristic
279C2×C11—41no—
280C2×C11—161no—
281C2×C11#320511yescharacteristic
282C2×C11#341612yes—
283D11—162no—
284#41—42no—
285#41—42no—
286C2×Q8—21no—
287C2×Q8—21no—
288C2×Q8—21no—
289C2×Q8—42no—
290C2×Q8—42no—
291C2×Q8—41no—
292C2×D4—21no—
293C2×D4—41no—
294C2×D4—222no—
295C2×D4—442no—
296C2×D4—442no—
297C22×C4—41no—
298C22×C4—41no—
299C22×C4—442no—
300C22×C4C2×C22⋊D1111yescharacteristic
301Q16—22no—
302Q16—22no—
303Q16—22no—
304Q16—42no—
305Q16—42no—
306Q16—42no—
307SD16—42no—
308SD16—42no—
309SD16—42no—
310D8—22no—
311D8—222no—
312D8—222no—
313D8—442no—
314M16—22no—
315C2×C8—22no—
316C2×C8C2×C22⋊D1111yescharacteristic
317C2×C8C2×C22⋊D1111yescharacteristic
318C2×C8C2×C22⋊D1111yescharacteristic
319C2×C8C23×D1111yescharacteristic
320C4⋊C4—42no—
321C4⋊C4—42no—
322C4⋊C4—222no—
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—41no—
336C23—442no—
337C23C2×#432311yescharacteristic
338Q8—41no—
339Q8—41no—
340Q8—41no—
341Q8—41no—
342Q8—41no—
343Q8—41no—
344Q8—82no—
345D4—41no—
346D4—41no—
347D4—82no—
348D4—442no—
349D4—442no—
350D4—1762no—
351D4—1762no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—41no—
355C2×C4—41no—
356C2×C4—41no—
357C2×C4—82no—
358C2×C4—82no—
359C2×C4—442no—
360C2×C4—1762no—
361C2×C4C2×#432312yes—
362C2×C4C2×#432312yes—
363C2×C4C2×#432311yescharacteristic
364C2×C4C22×C22⋊D1111yescharacteristic
365C8—21no—
366C8—21no—
367C8#6698512yes—
368C8#6703712yes—
369C22—22no—
370C22—21no—
371C22—82no—
372C22—81no—
373C22—882no—
374C22—882no—
375C22—882no—
376C22C22×#432311yescharacteristic
377C4—22no—
378C4—22no—
379C4—21no—
380C4—81no—
381C4—81no—
382C4—81no—
383C4—882no—
384C4C2×#6698511yescharacteristic
385C4#1062333611yescharacteristic
386C2—41no—
387C2—161no—
388C2—1762no—
389C2#1307953411yescharacteristic
390C2#1308176012yes—
subgroupG/H
centerC22C22×#4323
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#3156C2
socleC22×C11C22×D8
hypercenter#3156D11
hypocenterC11#33787
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ #117 ◁ #405 ◁ #3156

Complements

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

NH ≅ G/Ntype
1. #13079266C2semidirect
2. #13070883C2semidirect
3. #13070873C2semidirect
4. #13070861C2semidirect
5. #13070847C2semidirect
6. #13070668C2semidirect
7. #13070658C2semidirect
8. #13070539C2semidirect
9. #13070533C2semidirect
10. #13070423C2semidirect
11. C11×#3156C2semidirect
141. #3156D11semidirect
334. C11#33787semidirect

Maximal subgroups

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

subgroupindex
#130792662
#130708832
#130708732
#130708612
#130708472
#130706682
#130706582
#130705392
#130705332
#130704232
C11×#31562
#3378711