Finite Group Databasebeta

← #14738965

Subgroups — #14738965

Order 2816.

662 conjugacy classes of subgroups.

The subgroup lattice has 434 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13078711C211yesmaximal, characteristic, complemented
2#13078612C211yesmaximal, characteristic
3#13077639C211yesmaximal, characteristic, complemented
4#13068050C212yesmaximal, complemented
5#13068036C212yesmaximal, complemented
6#13067978C212yesmaximal, complemented
7#13067954C212yesmaximal, complemented
8#13067396C211yesmaximal, characteristic, complemented
9#13067321C211yesmaximal, characteristic, complemented
10#13067281C211yesmaximal, characteristic, complemented
11C11×#3210C211yesmaximal, characteristic, complemented
12C11×#533C2211yescharacteristic
13C11×#532C2211yescharacteristic
14C2×C4×D44C2211yescharacteristic
15C11×#494C2211yescharacteristic, complemented
16C11×#492C2211yescharacteristic, complemented
17C11×#487C2211yescharacteristic, complemented
18C11×#486C2211yescharacteristic, complemented
19C11×#464—22no—
20C11×#452—22no—
21C11×#431C2211yescharacteristic
22#10622700C2212yes—
23#10622700C2212yes—
24#10622696C2212yes—
25#10622685C2212yes—
26#10622659—21no—
27#10622657—21no—
28#10622649—21no—
29#10622646—21no—
30#10622639—22no—
31C4×#4323—22no—
32#10622539C2211yescharacteristic
33#10622538C2211yescharacteristic
34#10622538C2211yescharacteristic
35#10622447—22no—
36D11×C22⋊C8—22no—
37C8×D44C2212yes—
38C8×D44C2212yes—
39#10622185C2212yescomplemented
40#10622185C2212yescomplemented
41#10622185C2212yescomplemented
42#10622182C2212yescomplemented
43#10622096C2212yescomplemented
44#10622095C2212yescomplemented
45C2×C11×#41—21no—
46C22×D44D411yescharacteristic
47C22×C4×D11—21no—
48C2×C11×Q16—22no—
49C2×C11×SD16—22no—
50C11×C4⋊Q8C2311yescharacteristic
51C11×C4⋊Q8C2311yescharacteristic
52C11×C4⋊Q8C2311yescharacteristic
53C11×#127C2311yescharacteristic
54C11×#125—21no—
55C11×#124—21no—
56C11×C22⋊Q8—21no—
57C11×C22⋊Q8—21no—
58C11×#121—21no—
59C11×#121—21no—
60C4×Q8×C11—21no—
61C4×Q8×C11—21no—
62C4×D4×C11—21no—
63C4×D4×C11—21no—
64C11×#117—21no—
65C2×C42×C11C2311yescharacteristic
66C2×#4325—22no—
67C2×#4323—22no—
68C2×(C2×D11)⋊C4—21no—
69C2×C4⋊Dic11D411yescharacteristic
70C2×C8×D11—22no—
71C2×C8×D11—22no—
72C4×D44—21no—
73C4×D44—21no—
74C4×D44D412yes—
75C4×D44C2312yes—
76C11×C4⋊C8D412yes—
77C11×#103—22no—
78C11×#102—22no—
79C11×C22⋊C8D412yes—
80C4×C8×C11C2311yescharacteristic
81C4×C8×C11C2311yescharacteristic
82#66899—22no—
83#66896—22no—
84C22⋊(C11⋊C8)—21no—
85C22⋊(C11⋊C8)—21no—
86C22⋊(C11⋊C8)—21no—
87(C2×D11)⋊C8—22no—
88(C2×D11)⋊C8—22no—
89#66873—22no—
90#66873—22no—
91#66871—22no—
92#66871—22no—
93C4⋊(C11⋊C8)C2312yes—
94C4⋊(C11⋊C8)C2312yes—
95C4⋊(C11⋊C8)C2312yes—
96#66867—21no—
97C4×C11⋊C8—21no—
98C4×C11⋊C8—21no—
99#19388—111nomaximal, Sylow
100C23×D11—21no—
101C11×#41—82no—
102C2×Q8×C11—21no—
103C2×Q8×C11—21no—
104C2×Q8×C11—21no—
105C2×D4×C11—21no—
106C2×D4×C11—21no—
107C2×D4×C11—21no—
108C2×D4×C11—41no—
109C22×C4×C11—41no—
110C22×C4×C11C2×D411yescharacteristic
111C22×C4×C11C2×D411yescharacteristic
112C22×C4×C11#4111yescharacteristic
113C22×Dic11—21no—
114C2×D44—24no—
115C2×D44—21no—
116C2×D44C2×D412yes—
117C2×C4×D11—22no—
118C2×C4×D11—22no—
119C2×C4×D11—82no—
120C11×Q16—82no—
121C11×SD16—82no—
122C2×C8×C11C2×D412yes—
123C2×C8×C11C2×D412yes—
124C11×C4⋊C4—21no—
125C11×C4⋊C4—21no—
126C11×C4⋊C4—21no—
127C11×C4⋊C4—21no—
128C11×C4⋊C4—21no—
129C11×C4⋊C4—21no—
130C11×C4⋊C4—41no—
131C11×C4⋊C4—41no—
132C11×C22⋊C4—41no—
133C11×C22⋊C4—41no—
134C11×C22⋊C4—41no—
135C42×C11—41no—
136C42×C11C2×D411yescharacteristic
137C42×C11C2×D411yescharacteristic
138C42×C11#4111yescharacteristic
139C42×C11C2411yescharacteristic
140#4325—44no—
141#4323—44no—
142(C2×D11)⋊C4—22no—
143(C2×D11)⋊C4—22no—
144C4⋊Dic11—21no—
145C4⋊Dic11C2×D412yes—
146C2×C11⋊C8—22no—
147C2×C11⋊C8—22no—
148C2×C11⋊C8—22no—
149C8×D11—82no—
150C8×D11—82no—
151#3210D1111yescharacteristic, complemented
152#3110—111no—
153#3100—111no—
154#2972—111no—
155#1681—112no—
156#1679—112no—
157#1669—112no—
158#1665—112no—
159#1572—111no—
160#1553—111no—
161#1544—111no—
162C23×C11—41no—
163C23×C11#12111yescharacteristic
164C22×D11—22no—
165C22×D11—24no—
166C22×D11—81no—
167C22×D11—81no—
168Q8×C11—42no—
169Q8×C11—42no—
170Q8×C11—42no—
171D4×C11—42no—
172D4×C11—42no—
173D4×C11—81no—
174D4×C11—82no—
175C2×C4×C11—22no—
176C2×C4×C11—22no—
177C2×C4×C11—41no—
178C2×C4×C11—41no—
179C2×C4×C11—41no—
180C2×C4×C11—41no—
181C2×C4×C11—82no—
182C2×C4×C11#12111yescharacteristic
183C2×C4×C11#12111yescharacteristic
184C2×C4×C11#12111yescharacteristic
185C2×C4×C11C22×D411yescharacteristic
186C2×C4×C11C22×D411yescharacteristic
187C2×C4×C11C2×#4111yescharacteristic
188C2×Dic11—22no—
189C2×Dic11—81no—
190D44—24no—
191D44—22no—
192D44#13514yes—
193C4×D11—42no—
194C4×D11—42no—
195C4×D11—82no—
196C8×C11—22no—
197C8×C11—22no—
198C11⋊C8—42no—
199C11⋊C8—42no—
200C11⋊C8—42no—
201#533C2×D1111yescharacteristic
202#532C2×D1111yescharacteristic
203C2×C4×D4—111no—
204#494C2×D1111yescharacteristic, complemented
205#492C2×D1111yescharacteristic, complemented
206#487C2×D1111yescharacteristic, complemented
207#486C2×D1111yescharacteristic, complemented
208#484—221no—
209#480—221no—
210#474—112no—
211#474—112no—
212#464—22no—
213#461—112no—
214#459—112no—
215#452—22no—
216#450—221no—
217#447—221no—
218#440—222no—
219C4×D8—222no—
220C8×D4—112no—
221C8×D4—112no—
222C8×D4—222no—
223#432—111no—
224#431—111no—
225#431—111no—
226#431C2×D1111yescharacteristic
227C2×C22⋊C8—222no—
228#335—112no—
229#334—112no—
230#332—112no—
231#332—112no—
232#332—112no—
233#331—112no—
234C22×C11—21no—
235C22×C11—21no—
236C22×C11—21no—
237C22×C11—81no—
238C22×C11—81no—
239C22×C11—81no—
240C22×C11C2×#12111yescharacteristic
241C2×D11—24no—
242C2×D11—42no—
243C2×D11—42no—
244C2×D11—84no—
245C4×C11—21no—
246C4×C11—21no—
247C4×C11—21no—
248C4×C11—21no—
249C4×C11—81no—
250C4×C11—81no—
251C4×C11—81no—
252C4×C11C2×#13512yes—
253C4×C11#57612yes—
254Dic11—42no—
255C2×#41—21no—
256C22×D4—111no—
257C23×C4—221no—
258C2×Q16—22no—
259C2×SD16—22no—
260C2×SD16—222no—
261C2×D8—222no—
262C22×C8—222no—
263C22×C8—222no—
264C4⋊Q8C22×D1111yescharacteristic
265C4⋊Q8C22×D1111yescharacteristic
266C4⋊Q8C22×D1111yescharacteristic
267#127C22×D1111yescharacteristic
268#125—21no—
269#124—21no—
270C22⋊Q8—21no—
271C22⋊Q8—21no—
272#121—21no—
273#121—21no—
274C4×Q8—21no—
275C4×Q8—21no—
276C4×D4—21no—
277C4×D4—21no—
278C4×D4—112no—
279C4×D4—112no—
280C4×D4—221no—
281C4×D4—221no—
282#117—21no—
283C2×C4⋊C4—111no—
284C2×C22⋊C4—221no—
285C2×C42C22×D1111yescharacteristic
286#107—222no—
287#107—222no—
288C4⋊C8—112no—
289C4⋊C8—112no—
290C4⋊C8—112no—
291C4⋊C8C22⋊D1112yes—
292#103—22no—
293#103—222no—
294#102—22no—
295#102—222no—
296#102—222no—
297#102—222no—
298C22⋊C8—221no—
299C22⋊C8—221no—
300C22⋊C8—221no—
301C22⋊C8—222no—
302C22⋊C8—222no—
303C22⋊C8C22⋊D1112yes—
304#97—221no—
305C4×C8—221no—
306C4×C8—221no—
307C4×C8C22×D1111yescharacteristic
308C4×C8C22×D1111yescharacteristic
309C2×C11—41no—
310C2×C11—161no—
311C2×C11#304111yescharacteristic
312C2×C11#305011yescharacteristic
313C2×C11#306911yescharacteristic
314D11—44no—
315C24—221no—
316#41—82no—
317C2×Q8—21no—
318C2×Q8—21no—
319C2×Q8—21no—
320C2×D4—21no—
321C2×D4—21no—
322C2×D4—21no—
323C2×D4—41no—
324C2×D4—112no—
325C2×D4—224no—
326C2×D4—221no—
327C22×C4—41no—
328C22×C4—221no—
329C22×C4—222no—
330C22×C4—222no—
331C22×C4—882no—
332C22×C4D4×D1111yescharacteristic
333C22×C4#434111yescharacteristic
334C22×C4C2×C22⋊D1111yescharacteristic
335Q16—82no—
336SD16—82no—
337SD16—444no—
338D8—444no—
339C2×C8—222no—
340C2×C8—222no—
341C2×C8—222no—
342C2×C8—882no—
343C2×C8—882no—
344C2×C8C2×C22⋊D1112yes—
345C2×C8C2×C22⋊D1112yes—
346C4⋊C4—21no—
347C4⋊C4—21no—
348C4⋊C4—21no—
349C4⋊C4—21no—
350C4⋊C4—21no—
351C4⋊C4—21no—
352C4⋊C4—41no—
353C4⋊C4—41no—
354C4⋊C4—112no—
355C4⋊C4—221no—
356C22⋊C4—41no—
357C22⋊C4—41no—
358C22⋊C4—41no—
359C22⋊C4—222no—
360C22⋊C4—222no—
361C42—41no—
362C42D4×D1111yescharacteristic
363C42#434111yescharacteristic
364C42C2×C22⋊D1111yescharacteristic
365C42C23×D1111yescharacteristic
366C11#1938811yescharacteristic, complemented, Sylow
367C23—41no—
368C23—224no—
369C23—222no—
370C23—881no—
371C23—881no—
372C23#6699111yescharacteristic
373Q8—42no—
374Q8—42no—
375Q8—42no—
376D4—42no—
377D4—42no—
378D4—81no—
379D4—82no—
380D4—114no—
381D4—224no—
382D4—222no—
383C2×C4—22no—
384C2×C4—22no—
385C2×C4—41no—
386C2×C4—41no—
387C2×C4—41no—
388C2×C4—41no—
389C2×C4—82no—
390C2×C4—222no—
391C2×C4—442no—
392C2×C4—442no—
393C2×C4—882no—
394C2×C4—881no—
395C2×C4#6699111yescharacteristic
396C2×C4#6699111yescharacteristic
397C2×C4#6699111yescharacteristic
398C2×C4C2×D4×D1111yescharacteristic
399C2×C4C2×#434111yescharacteristic
400C2×C4C22×C22⋊D1111yescharacteristic
401C8—22no—
402C8—22no—
403C8—442no—
404C8—442no—
405C8—442no—
406C22—21no—
407C22—21no—
408C22—21no—
409C22—81no—
410C22—81no—
411C22—81no—
412C22—224no—
413C22—442no—
414C22—442no—
415C22—884no—
416C22C2×#6699111yescharacteristic
417C4—21no—
418C4—21no—
419C4—21no—
420C4—21no—
421C4—81no—
422C4—81no—
423C4—81no—
424C4—442no—
425C4D11×#13512yes—
426C4#1062336612yes—
427C2—41no—
428C2—161no—
429C2—444no—
430C2#1307811511yescharacteristic
431C2#1307819311yescharacteristic
432C2#1307834911yescharacteristic
subgroupG/H
centerC22C2×#66991
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#3210C2
socleC22×C11C2×#121
prime radical#13078612C2
hypercenter#3210D11
hypocenterC11#19388
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3210

Complements

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

NH ≅ G/Ntype
1. #13078711C2semidirect
3. #13077639C2semidirect
4. #13068050C2semidirect
5. #13068036C2semidirect
6. #13067978C2semidirect
7. #13067954C2semidirect
8. #13067396C2semidirect
9. #13067321C2semidirect
10. #13067281C2semidirect
11. C11×#3210C2semidirect
15. C11×#494C22semidirect
16. C11×#492C22semidirect
17. C11×#487C22semidirect
18. C11×#486C22semidirect
39. #10622185C22semidirect
40. #10622185C22semidirect
41. #10622185C22semidirect
42. #10622182C22semidirect
43. #10622096C22semidirect
44. #10622095C22semidirect
151. #3210D11semidirect
204. #494C2×D11semidirect
205. #492C2×D11semidirect
206. #487C2×D11semidirect
207. #486C2×D11semidirect
366. C11#19388semidirect

Maximal subgroups

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

subgroupindex
#130787112
#130786122
#130776392
#130680502
#130680362
#130679782
#130679542
#130673962
#130673212
#130672812
C11×#32102
#1938811