Finite Group Databasebeta

← #14908620

Subgroups — #14908620

Order 2816.

588 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13078265C211yesmaximal, characteristic
2#13077213C211yesmaximal, characteristic, complemented
3#13070810C212yesmaximal, complemented
4#13070809C212yesmaximal, complemented
5#13070803C212yesmaximal, complemented
6#13070798C212yesmaximal, complemented
7#13070405C211yesmaximal, characteristic, complemented
8#13070331C211yesmaximal, characteristic, complemented
9C2×#10622147C211yesmaximal, characteristic, complemented
10#13070229C211yesmaximal, characteristic, complemented
11C11×#2158C211yesmaximal, characteristic, complemented
12C22×D88C2211yescharacteristic
13C2×#66954C2211yescharacteristic
14#10623056—21no—
15#10623054—21no—
16C22×C11×C16C2211yescharacteristic
17C11×#427C2211yescharacteristic
18C11×#427C2211yescharacteristic
19C2×#66882C2211yescharacteristic
20C2×#66876C2211yescharacteristic
21#10622614—21no—
22#10622608—21no—
23#10622496C2212yes—
24#10622496C2212yes—
25#10622493C2212yescomplemented
26D11×#107C2212yescomplemented
27#10622478—22no—
28#10622474—22no—
29C11×#367C2211yescharacteristic, complemented
30C11×#367C2211yescharacteristic, complemented
31C11×#366C2211yescharacteristic, complemented
32C11×#366C2211yescharacteristic, complemented
33#10622147C2212yes—
34#10622147C2212yes—
35(C2×D11)⋊C16C2212yescomplemented
36(C2×D11)⋊C16C2212yescomplemented
37#10622129C2212yes—
38#10622129C2212yes—
39#10622128C2212yescomplemented
40#10622127C2212yescomplemented
41C2×#4339D411yescharacteristic
42C22×D44—21no—
43C22×C8×C11C2311yescharacteristic
44C11×#117—21no—
45C11×#117—21no—
46C2×C4⋊Dic11—21no—
47C2×#4318D411yescharacteristic
48C2×D88—22no—
49C2×D88—22no—
50C2×D88—21no—
51C2×D88C2312yes—
52#66954—22no—
53#66954—22no—
54C2×#4313D412yes—
55C2×C8×D11C2312yes—
56#66948—22no—
57#66948—22no—
58#66945—22no—
59C4⋊C4×D11—22no—
60#66935—42no—
61(C22⋊D11)⋊C4—42no—
62#66928—41no—
63#66927—41no—
64C4×D44—41no—
65C4×Dic22—41no—
66C2×C11×C16—22no—
67C2×C11×C16C2311yescharacteristic
68C2×C11×C16C2311yescharacteristic
69C11×#107C2311yescharacteristic
70C11×#107C2311yescharacteristic
71C11×#107C2311yescharacteristic
72C11×#107C2311yescharacteristic
73C11×#106—21no—
74C11×#106—21no—
75#66882—21no—
76#66882C2312yes—
77#66876—22no—
78C2×C11⋊C16C2312yes—
79#66873—22no—
80#66873—22no—
81#66872—22no—
82#66871—22no—
83#33650—111nomaximal, Sylow
84C23×D11—41no—
85C22×C4×C11C2×D411yescharacteristic
86C2×C22⋊D11D812yes—
87C22×Dic11—41no—
88#4339—22no—
89#4339—22no—
90C2×D44—22no—
91C2×D44—42no—
92C2×D44—42no—
93C2×D44—42no—
94C2×D44—41no—
95C2×D44—42no—
96C2×D44D811yescharacteristic
97C2×C4×D11—42no—
98C2×C4×D11C2×D412yes—
99C2×Dic22D811yescharacteristic
100C2×C8×C11C2×D411yescharacteristic
101C2×C8×C11#4112yes—
102C2×C8×C11#4112yes—
103C2×C8×C11C2411yescharacteristic
104C11×C4⋊C4—21no—
105C11×C4⋊C4—21no—
106C11×C4⋊C4—21no—
107C11×C4⋊C4—21no—
108C11×C22⋊C4—41no—
109C11×C22⋊C4—41no—
110C42×C11—41no—
111C42×C11—41no—
112(C2×D11)⋊C4—42no—
113(C2×D11)⋊C4—42no—
114(C2×D11)⋊C4—42no—
115C4⋊Dic11—22no—
116C4⋊Dic11—41no—
117Dic11⋊C4—42no—
118C4×Dic11—42no—
119#4318—22no—
120C2×C11⋊C8C2×D412yes—
121D88—22no—
122D88—22no—
123D88—42no—
124#4313—24no—
125C8×D11—22no—
126C8×D11—22no—
127C11×C16—21no—
128C11×C16—21no—
129C11⋊C16—22no—
130#3058—111no—
131#2913—111no—
132#2234—112no—
133#2234—112no—
134#2233—112no—
135#2232—112no—
136#2159—111no—
137#2158D1111yescharacteristic, complemented
138#2140—111no—
139C2×#357—111no—
140#2113—111no—
141C23×C11C2×D811yescharacteristic
142C22×D11—42no—
143C22×D11—82no—
144C22×D11—161no—
145C22×D11—161no—
146C22×D11C2×D812yes—
147C2×C4×C11—41no—
148C2×C4×C11—41no—
149C2×C4×C11—41no—
150C2×C4×C11—41no—
151C2×C4×C11#12312yes—
152C2×C4×C11C2×D811yescharacteristic
153C2×C4×C11#13712yes—
154C2×C4×C11C22×D411yescharacteristic
155C22⋊D11—24no—
156C2×Dic11—42no—
157C2×Dic11—161no—
158C2×Dic11C2×D812yes—
159D44—22no—
160D44—42no—
161D44—42no—
162D44—82no—
163D44—162no—
164D44—162no—
165C4×D11—22no—
166C4×D11—22no—
167C4×D11—162no—
168Dic22—22no—
169C8×C11#12312yes—
170C8×C11C2×#4111yescharacteristic
171C8×C11C2×#4111yescharacteristic
172C11⋊C8—22no—
173C22×D8—111no—
174C2×#131—111no—
175#535—221no—
176#520—221no—
177C2×M32—111no—
178C22×C16C2×D1111yescharacteristic
179#469—222no—
180#466—112no—
181#466—112no—
182#428—222no—
183#428—221no—
184#427—112no—
185#427C2×D1111yescharacteristic
186#427C2×D1111yescharacteristic
187C2×#107—111no—
188C2×#107—112no—
189#418—221no—
190#367—112no—
191#367C2×D1111yescharacteristic, complemented
192#367C2×D1111yescharacteristic, complemented
193#366—112no—
194#366C2×D1111yescharacteristic, complemented
195#366C2×D1111yescharacteristic, complemented
196#357—112no—
197#357—112no—
198#357—112no—
199#357—112no—
200C22⋊C16—112no—
201C22⋊C16—112no—
202C22×C11—21no—
203C22×C11—21no—
204C22×C11#48012yes—
205C22×C11C22×D811yescharacteristic
206C2×D11—22no—
207C2×D11—22no—
208C2×D11—22no—
209C2×D11—82no—
210C2×D11—82no—
211C2×D11—82no—
212C2×D11—164no—
213C4×C11—81no—
214C4×C11—81no—
215C4×C11—81no—
216C4×C11—81no—
217C4×C11#48012yes—
218C4×C11C2×#12311yescharacteristic
219C4×C11C2×#13711yescharacteristic
220Dic11—22no—
221Dic11—82no—
222C2×#41—111no—
223C22×D4—221no—
224C2×D8—112no—
225C2×D8—222no—
226C2×D8—221no—
227C2×D8—222no—
228#131—222no—
229#131—222no—
230C2×M16—111no—
231C2×M16—112no—
232C22×C8—112no—
233C22×C8C22×D1111yescharacteristic
234#127—441no—
235#124—441no—
236#121—222no—
237#121—222no—
238#120—442no—
239C4×Q8—441no—
240C4×D4—441no—
241C4×D4—442no—
242#117—21no—
243#117—21no—
244#117—222no—
245C2×C4⋊C4—222no—
246C2×C4⋊C4—221no—
247M32—222no—
248C2×C16—22no—
249C2×C16—112no—
250C2×C16C22×D1111yescharacteristic
251C2×C16C22×D1111yescharacteristic
252#107—112no—
253#107—222no—
254#107—221no—
255#107C22×D1111yescharacteristic
256#107C22×D1111yescharacteristic
257#107C22×D1111yescharacteristic
258#107C22×D1111yescharacteristic
259#106—21no—
260#106—21no—
261#106—222no—
262#102—222no—
263#102—222no—
264C2×C11—22no—
265C2×C11C2×#48011yescharacteristic
266C2×C11#341511yescharacteristic
267C2×C11#341611yescharacteristic
268D11—42no—
269D11—162no—
270C24—441no—
271#41—222no—
272#41—222no—
273C2×Q8—111no—
274C2×D4—112no—
275C2×D4—111no—
276C2×D4—222no—
277C2×D4—442no—
278C2×D4—442no—
279C2×D4—442no—
280C2×D4—441no—
281C2×D4—442no—
282C22×C4—112no—
283C22×C4—442no—
284C22×C4—441no—
285C22×C4D4×D1111yescharacteristic
286D8—222no—
287D8—222no—
288D8—442no—
289M16—222no—
290M16—224no—
291C2×C8—112no—
292C2×C8—222no—
293C2×C8—222no—
294C2×C8#433912yes—
295C2×C8D4×D1111yescharacteristic
296C2×C8#434312yes—
297C2×C8C23×D1111yescharacteristic
298C4⋊C4—21no—
299C4⋊C4—21no—
300C4⋊C4—21no—
301C4⋊C4—21no—
302C4⋊C4—222no—
303C4⋊C4—442no—
304C4⋊C4—441no—
305C22⋊C4—41no—
306C22⋊C4—41no—
307C22⋊C4—442no—
308C22⋊C4—442no—
309C22⋊C4—442no—
310C42—41no—
311C42—41no—
312C42—442no—
313C16—21no—
314C16—21no—
315C16—222no—
316C11#3365011yescharacteristic, complemented, Sylow
317C23—112no—
318C23—442no—
319C23—882no—
320C23—1761no—
321C23—1761no—
322C23D8×D1111yescharacteristic
323Q8—222no—
324D4—224no—
325D4—222no—
326D4—442no—
327D4—442no—
328D4—882no—
329D4—1762no—
330D4—1762no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—112no—
336C2×C4—222no—
337C2×C4—222no—
338C2×C4—442no—
339C2×C4—1762no—
340C2×C4—1761no—
341C2×C4#6694712yes—
342C2×C4D8×D1111yescharacteristic
343C2×C4#6697112yes—
344C2×C4C2×D4×D1111yescharacteristic
345C8—222no—
346C8#6694712yes—
347C8C2×#433911yescharacteristic
348C8C2×#434311yescharacteristic
349C22—21no—
350C22—21no—
351C22—222no—
352C22—222no—
353C22—222no—
354C22—882no—
355C22—882no—
356C22—882no—
357C22—1764no—
358C22#1062249512yes—
359C22C2×D8×D1111yescharacteristic
360C4—81no—
361C4—81no—
362C4—81no—
363C4—81no—
364C4—222no—
365C4—882no—
366C4#1062249512yes—
367C4C2×#6694711yescharacteristic
368C4C2×#6697111yescharacteristic
369C2—22no—
370C2—442no—
371C2—1762no—
372C2C2×#1062249511yescharacteristic
373C2#1308175411yescharacteristic
374C2#1308175911yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2158C2
socleC22×C11C22×D8
prime radical#13078265C2
hypercenter#2158D11
hypocenterC11#33650
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2158

Complements

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

NH ≅ G/Ntype
2. #13077213C2semidirect
3. #13070810C2semidirect
4. #13070809C2semidirect
5. #13070803C2semidirect
6. #13070798C2semidirect
7. #13070405C2semidirect
8. #13070331C2semidirect
9. C2×#10622147C2semidirect
10. #13070229C2semidirect
11. C11×#2158C2semidirect
25. #10622493C22semidirect
26. D11×#107C22semidirect
29. C11×#367C22semidirect
30. C11×#367C22semidirect
31. C11×#366C22semidirect
32. C11×#366C22semidirect
35. (C2×D11)⋊C16C22semidirect
36. (C2×D11)⋊C16C22semidirect
39. #10622128C22semidirect
40. #10622127C22semidirect
137. #2158D11semidirect
191. #367C2×D11semidirect
192. #367C2×D11semidirect
194. #366C2×D11semidirect
195. #366C2×D11semidirect
316. C11#33650semidirect

Maximal subgroups

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

subgroupindex
#130782652
#130772132
#130708102
#130708092
#130708032
#130707982
#130704052
#130703312
C2×#106221472
#130702292
C11×#21582
#3365011