Finite Group Databasebeta

← #14908615

Subgroups — #14908615

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#13078260C211yesmaximal, characteristic
2#13077213C211yesmaximal, characteristic, complemented
3#13070806C212yesmaximal, complemented
4#13070805C212yesmaximal, complemented
5#13070800C212yesmaximal, complemented
6#13070795C212yesmaximal, complemented
7#13070404C211yesmaximal, characteristic, complemented
8#13070398C211yesmaximal, characteristic, complemented
9C2×#10622200C211yesmaximal, characteristic, complemented
10#13070231C211yesmaximal, characteristic, complemented
11C11×#2140C211yesmaximal, characteristic, complemented
12C22×C11×D8C2211yescharacteristic
13#10623336—21no—
14C2×#66954C2211yescharacteristic
15#10623054—21no—
16C2×C11×M32C2211yescharacteristic
17C11×#427C2211yescharacteristic
18#10622828—21no—
19#10622772—22no—
20#10622770C2212yes—
21#10622770C2212yes—
22#10622719C2211yescharacteristic
23C2×#66882C2211yescharacteristic
24C22×C11⋊C16C2211yescharacteristic
25#10622608—21no—
26#10622493C2212yescomplemented
27D11×#107C2212yescomplemented
28#10622474—22no—
29C11×#357C2212yes—
30C11×#357C2212yes—
31#10622200C2212yes—
32#10622200C2212yes—
33(C2×D11)⋊C16C2212yescomplemented
34(C2×D11)⋊C16C2212yescomplemented
35#10622143C2212yescomplemented
36#10622142C2212yescomplemented
37#10622128C2211yescharacteristic, complemented
38#10622128C2211yescharacteristic, complemented
39#10622127C2211yescharacteristic, complemented
40#10622127C2211yescharacteristic, complemented
41C22×D4×C11—21no—
42C2×#4339D411yescharacteristic
43C2×C11×D8—21no—
44C2×C11×D8—22no—
45C2×C11×D8—22no—
46C2×C11×D8C2312yes—
47C22×C8×C11C2311yescharacteristic
48C11×#117—21no—
49#67006—42no—
50#66993—41no—
51#66991—22no—
52#66991—22no—
53#66989—41no—
54#66979—21no—
55C2×C4⋊Dic11—21no—
56C2×#4318D411yescharacteristic
57#66954—22no—
58#66954—22no—
59C2×#4313D412yes—
60C2×C8×D11C2312yes—
61#66945—22no—
62C4⋊C4×D11—22no—
63(C22⋊D11)⋊C4—42no—
64C4×D44—41no—
65C4×Dic22—41no—
66C11×M32—22no—
67C2×C11×C16C2312yes—
68C11×#107C2311yescharacteristic
69C11×#107C2311yescharacteristic
70C11×#106—21no—
71#66896—22no—
72#66896—22no—
73#66882—21no—
74#66882C2312yes—
75#66882C2311yescharacteristic
76#66882C2311yescharacteristic
77#66881—21no—
78C2×C11⋊C16—22no—
79C2×C11⋊C16C2311yescharacteristic
80C2×C11⋊C16C2311yescharacteristic
81#66872—22no—
82#66871—22no—
83#33650—111nomaximal, Sylow
84C24×C11—41no—
85C2×D4×C11—22no—
86C2×D4×C11—42no—
87C2×D4×C11—41no—
88C2×D4×C11—42no—
89C22×C4×C11C2×D411yescharacteristic
90C2×C22⋊D11—42no—
91C2×C22⋊D11—42no—
92C2×C22⋊D11D812yes—
93C22×Dic11—41no—
94#4339—22no—
95#4339—22no—
96C2×D44D811yescharacteristic
97C2×C4×D11—42no—
98C2×C4×D11C2×D412yes—
99C2×Dic22D811yescharacteristic
100C11×D8—22no—
101C11×D8—22no—
102C11×D8—42no—
103C2×C8×C11C2×D411yescharacteristic
104C2×C8×C11#4112yes—
105C2×C8×C11#4112yes—
106C2×C8×C11C2411yescharacteristic
107C11×C4⋊C4—21no—
108C11×C4⋊C4—21no—
109C11×C22⋊C4—41no—
110C42×C11—41no—
111C22⋊Dic11—42no—
112C22⋊Dic11—42no—
113C22⋊Dic11—41no—
114(C2×D11)⋊C4—42no—
115C4⋊Dic11—22no—
116C4⋊Dic11—21no—
117C4⋊Dic11—21no—
118C4⋊Dic11—41no—
119Dic11⋊C4—42no—
120C4×Dic11—42no—
121C4×Dic11—41no—
122#4318—22no—
123C2×C11⋊C8C2×D412yes—
124#4313—24no—
125C8×D11—22no—
126C8×D11—22no—
127C11×C16—22no—
128C11⋊C16—21no—
129C11⋊C16—21no—
130#3058—111no—
131#2913—111no—
132#2234—112no—
133#2234—112no—
134#2233—112no—
135#2232—112no—
136#2159—111no—
137#2158—111no—
138#2140D1111yescharacteristic, complemented
139C2×#357—111no—
140#2113—111no—
141C23×C11—42no—
142C23×C11—82no—
143C23×C11—161no—
144C23×C11—161no—
145C23×C11C2×D811yescharacteristic
146C22×D11C2×D812yes—
147D4×C11—42no—
148D4×C11—42no—
149D4×C11—82no—
150C2×C4×C11—41no—
151C2×C4×C11—41no—
152C2×C4×C11#12312yes—
153C2×C4×C11C2×D811yescharacteristic
154C2×C4×C11#13712yes—
155C2×C4×C11C22×D411yescharacteristic
156C22⋊D11—24no—
157C22⋊D11—162no—
158C22⋊D11—162no—
159C2×Dic11—42no—
160C2×Dic11—41no—
161C2×Dic11—41no—
162C2×Dic11—161no—
163C2×Dic11C2×D812yes—
164D44—22no—
165C4×D11—22no—
166C4×D11—22no—
167C4×D11—162no—
168Dic22—22no—
169C8×C11#12312yes—
170C8×C11C2×#4111yescharacteristic
171C8×C11C2×#4111yescharacteristic
172C11⋊C8—22no—
173C22×D8C2×D1111yescharacteristic
174C2×#131—111no—
175#535—221no—
176#520—221no—
177C2×M32C2×D1111yescharacteristic
178C22×C16—111no—
179#469—222no—
180#466—112no—
181#466—112no—
182#428—222no—
183#428—221no—
184#427—111no—
185#427—112no—
186#427C2×D1111yescharacteristic
187C2×#107—111no—
188C2×#107—112no—
189#418—221no—
190#367—112no—
191#367—111no—
192#367—111no—
193#366—112no—
194#366—111no—
195#366—111no—
196#357—112no—
197#357—112no—
198#357C2×D1112yes—
199#357C2×D1112yes—
200C22⋊C16—112no—
201C22⋊C16—112no—
202C22×C11—21no—
203C22×C11—21no—
204C22×C11—82no—
205C22×C11—82no—
206C22×C11—82no—
207C22×C11—164no—
208C22×C11#48012yes—
209C22×C11C22×D811yescharacteristic
210C2×D11—22no—
211C2×D11—22no—
212C2×D11—22no—
213C4×C11—81no—
214C4×C11—81no—
215C4×C11#48012yes—
216C4×C11C2×#12311yescharacteristic
217C4×C11C2×#13711yescharacteristic
218Dic11—22no—
219Dic11—82no—
220Dic11—81no—
221Dic11—81no—
222C2×#41—111no—
223C22×D4—21no—
224C2×D8—22no—
225C2×D8—21no—
226C2×D8—22no—
227C2×D8C22×D1112yes—
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—222no—
244#117—221no—
245C2×C4⋊C4—222no—
246C2×C4⋊C4—221no—
247M32—22no—
248C2×C16—111no—
249C2×C16—111no—
250C2×C16—222no—
251C2×C16C22×D1112yes—
252#107—112no—
253#107—111no—
254#107—111no—
255#107—222no—
256#107—221no—
257#107C22×D1111yescharacteristic
258#107C22×D1111yescharacteristic
259#106—21no—
260#106—222no—
261#106—221no—
262#102—222no—
263#102—222no—
264C2×C11—22no—
265C2×C11—162no—
266C2×C11C2×#48011yescharacteristic
267C2×C11#341511yescharacteristic
268C2×C11#341611yescharacteristic
269D11—42no—
270C24—41no—
271#41—222no—
272#41—222no—
273C2×Q8—111no—
274C2×D4—22no—
275C2×D4—42no—
276C2×D4—41no—
277C2×D4—42no—
278C2×D4—112no—
279C2×D4—111no—
280C2×D4—442no—
281C2×D4—442no—
282C22×C4—112no—
283C22×C4—442no—
284C22×C4—441no—
285C22×C4D4×D1111yescharacteristic
286D8—22no—
287D8—22no—
288D8—42no—
289M16—222no—
290M16—224no—
291C2×C8—112no—
292C2×C8—222no—
293C2×C8—222no—
294C2×C8#433912yes—
295C2×C8D4×D1111yescharacteristic
296C2×C8#434112yes—
297C2×C8C23×D1111yescharacteristic
298C4⋊C4—21no—
299C4⋊C4—21no—
300C4⋊C4—221no—
301C4⋊C4—221no—
302C4⋊C4—222no—
303C4⋊C4—442no—
304C4⋊C4—441no—
305C22⋊C4—41no—
306C22⋊C4—442no—
307C22⋊C4—442no—
308C22⋊C4—442no—
309C22⋊C4—441no—
310C42—41no—
311C42—442no—
312C42—441no—
313C16—22no—
314C16—221no—
315C16—221no—
316C11#3365011yescharacteristic, complemented, Sylow
317C23—42no—
318C23—82no—
319C23—112no—
320C23—161no—
321C23—161no—
322C23D8×D1111yescharacteristic
323Q8—222no—
324D4—42no—
325D4—42no—
326D4—82no—
327D4—224no—
328D4—222no—
329D4—1762no—
330D4—1762no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—112no—
334C2×C4—222no—
335C2×C4—222no—
336C2×C4—441no—
337C2×C4—441no—
338C2×C4—442no—
339C2×C4—1762no—
340C2×C4—1761no—
341C2×C4#6693612yes—
342C2×C4D8×D1111yescharacteristic
343C2×C4#6696812yes—
344C2×C4C2×D4×D1111yescharacteristic
345C8—222no—
346C8#6693612yes—
347C8C2×#433911yescharacteristic
348C8C2×#434111yescharacteristic
349C22—21no—
350C22—21no—
351C22—82no—
352C22—82no—
353C22—82no—
354C22—164no—
355C22—222no—
356C22—222no—
357C22—222no—
358C22#1062238712yes—
359C22C2×D8×D1111yescharacteristic
360C4—81no—
361C4—81no—
362C4—222no—
363C4—882no—
364C4—881no—
365C4—881no—
366C4#1062238712yes—
367C4C2×#6693611yescharacteristic
368C4C2×#6696811yescharacteristic
369C2—22no—
370C2—162no—
371C2—442no—
372C2C2×#1062238711yescharacteristic
373C2#1308175611yescharacteristic
374C2#1308176211yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2140C2
socleC22×C11C22×D8
prime radical#13078260C2
hypercenter#2140D11
hypocenterC11#33650
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2140

Complements

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

NH ≅ G/Ntype
2. #13077213C2semidirect
3. #13070806C2semidirect
4. #13070805C2semidirect
5. #13070800C2semidirect
6. #13070795C2semidirect
7. #13070404C2semidirect
8. #13070398C2semidirect
9. C2×#10622200C2semidirect
10. #13070231C2semidirect
11. C11×#2140C2semidirect
26. #10622493C22semidirect
27. D11×#107C22semidirect
33. (C2×D11)⋊C16C22semidirect
34. (C2×D11)⋊C16C22semidirect
35. #10622143C22semidirect
36. #10622142C22semidirect
37. #10622128C22semidirect
38. #10622128C22semidirect
39. #10622127C22semidirect
40. #10622127C22semidirect
138. #2140D11semidirect
316. C11#33650semidirect

Maximal subgroups

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

subgroupindex
#130782602
#130772132
#130708062
#130708052
#130708002
#130707952
#130704042
#130703982
C2×#106222002
#130702312
C11×#21402
#3365011