Finite Group Databasebeta

← #14738966

Subgroups — #14738966

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#13079572C211yesmaximal, characteristic, complemented
2#13078715C211yesmaximal, characteristic, complemented
3#13077640C211yesmaximal, characteristic, complemented
4#13068051C212yesmaximal, complemented
5#13068037C212yesmaximal, complemented
6#13067979C212yesmaximal, complemented
7#13067955C212yesmaximal, complemented
8#13067394C211yesmaximal, characteristic, complemented
9#13067321C211yesmaximal, characteristic, complemented
10#13067280C211yesmaximal, characteristic, complemented
11C11×#3100C211yesmaximal, characteristic
12C11×#532C2211yescharacteristic
13C2×C4×D4×C11C2211yescharacteristic
14#10623001C2211yescharacteristic
15C11×#480—21no—
16C11×#474C2212yes—
17C11×#459C2212yes—
18C11×#447—21no—
19C4×C11×D8—22no—
20C11×#431C2211yescharacteristic
21#10622852—22no—
22#10622831—21no—
23C2×C22⋊(C11⋊C8)—22no—
24#10622705C2211yescharacteristic, complemented
25#10622694C2211yescharacteristic, complemented
26#10622689C2211yescharacteristic, complemented
27#10622683C2211yescharacteristic, complemented
28#10622667—22no—
29#10622632C2212yes—
30#10622631—22no—
31D4×C11⋊C8—22no—
32D4×C11⋊C8C2212yes—
33D4×C11⋊C8C2212yes—
34#10622620C2212yes—
35#10622583—21no—
36#10622539C2211yescharacteristic
37#10622538C2211yescharacteristic
38#10622538C2211yescharacteristic
39#10622185C2212yescomplemented
40#10622182C2212yescomplemented
41#10622124C2212yescomplemented
42#10622120C2212yescomplemented
43#10622118C2212yescomplemented
44#10622117C2212yescomplemented
45C2×C11×#41—21no—
46C22×D4×C11D411yescharacteristic
47C23×C4×C11—21no—
48C2×C11×D8—22no—
49C11×C4⋊Q8C2311yescharacteristic
50C11×#127C2311yescharacteristic
51C11×#124—21no—
52C11×#121—21no—
53C11×#121—21no—
54C4×D4×C11—21no—
55C4×D4×C11—21no—
56C4×D4×C11—21no—
57C4×D4×C11—21no—
58C4×D4×C11D412yes—
59C4×D4×C11C2312yes—
60C2×C11×C4⋊C4D411yescharacteristic
61C2×C11×C22⋊C4—21no—
62C2×C42×C11C2311yescharacteristic
63C2×#4326—22no—
64C2×#4324—22no—
65C2×#4324—22no—
66#66979—21no—
67#66977—21no—
68#66977—21no—
69C22×C11⋊C8—22no—
70C22×C11⋊C8—22no—
71#66923—21no—
72#66922C2311yescharacteristic
73#66922C2311yescharacteristic
74C4×Dic22—21no—
75C4×Dic22—21no—
76C11×#107—22no—
77C11×C4⋊C8C2312yes—
78C11×#102—22no—
79C11×#102—22no—
80C11×C22⋊C8—21no—
81C4×C8×C11—21no—
82#66899—22no—
83#66896—22no—
84#66896—22no—
85C22⋊(C11⋊C8)—21no—
86C22⋊(C11⋊C8)—21no—
87C22⋊(C11⋊C8)—22no—
88C22⋊(C11⋊C8)—22no—
89C22⋊(C11⋊C8)D412yes—
90#66874—22no—
91#66871—22no—
92C4⋊(C11⋊C8)D412yes—
93C4⋊(C11⋊C8)C2312yes—
94C4⋊(C11⋊C8)C2312yes—
95#66867—21no—
96C4×C11⋊C8—21no—
97C4×C11⋊C8C2311yescharacteristic
98C4×C11⋊C8C2311yescharacteristic
99#19388—111nomaximal, Sylow
100C24×C11—21no—
101C11×#41—82no—
102C2×Q8×C11—21no—
103C2×D4×C11—24no—
104C2×D4×C11—21no—
105C2×D4×C11—21no—
106C2×D4×C11—21no—
107C2×D4×C11—21no—
108C2×D4×C11—41no—
109C2×D4×C11C2×D412yes—
110C22×C4×C11—21no—
111C22×C4×C11—22no—
112C22×C4×C11—22no—
113C22×C4×C11—41no—
114C22×C4×C11—82no—
115C22×C4×C11C2×D411yescharacteristic
116C22×C4×C11C2×D411yescharacteristic
117C22×C4×C11#4111yescharacteristic
118C2×Dic22—21no—
119C2×Dic22—21no—
120C11×D8—44no—
121C2×C8×C11—22no—
122C11×C4⋊C4—21no—
123C11×C4⋊C4—21no—
124C11×C4⋊C4—21no—
125C11×C4⋊C4C2×D412yes—
126C11×C22⋊C4—22no—
127C11×C22⋊C4—22no—
128C11×C22⋊C4—41no—
129C11×C22⋊C4—41no—
130C42×C11C2×D411yescharacteristic
131C42×C11C2×D411yescharacteristic
132C42×C11#4111yescharacteristic
133C42×C11C2411yescharacteristic
134C22⋊Dic11—41no—
135#4326—82no—
136#4324—44no—
137#4324—82no—
138C4⋊Dic11—21no—
139C4⋊Dic11—21no—
140C4⋊Dic11—21no—
141C4⋊Dic11—21no—
142Dic11⋊C4—41no—
143Dic11⋊C4—41no—
144C4×Dic11—41no—
145C2×C11⋊C8—22no—
146C2×C11⋊C8—22no—
147C2×C11⋊C8—82no—
148C2×C11⋊C8—82no—
149C2×C11⋊C8C2×D412yes—
150C2×C11⋊C8C2×D412yes—
151#3210—111no—
152#3110—111no—
153#3100D1111yescharacteristic
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—24no—
163C23×C11—22no—
164C23×C11—41no—
165C23×C11—81no—
166C23×C11—81no—
167C23×C11#12111yescharacteristic
168Q8×C11—42no—
169D4×C11—24no—
170D4×C11—22no—
171D4×C11—42no—
172D4×C11—42no—
173D4×C11—81no—
174D4×C11—82no—
175D4×C11#13514yes—
176C2×C4×C11—22no—
177C2×C4×C11—22no—
178C2×C4×C11—22no—
179C2×C4×C11—41no—
180C2×C4×C11—42no—
181C2×C4×C11—42no—
182C2×C4×C11—41no—
183C2×C4×C11—82no—
184C2×C4×C11—82no—
185C2×C4×C11—81no—
186C2×C4×C11#12111yescharacteristic
187C2×C4×C11#12111yescharacteristic
188C2×C4×C11#12111yescharacteristic
189C2×C4×C11C22×D411yescharacteristic
190C2×C4×C11C22×D411yescharacteristic
191C2×C4×C11C2×#4111yescharacteristic
192C2×Dic11—41no—
193C2×Dic11—41no—
194Dic22—42no—
195Dic22—42no—
196C8×C11—42no—
197C11⋊C8—22no—
198C11⋊C8—22no—
199C11⋊C8—42no—
200C11⋊C8—42no—
201#533—111no—
202#532C2×D1111yescharacteristic
203C2×C4×D4C2×D1111yescharacteristic
204#494—111no—
205#492—111no—
206#487—111no—
207#486—111no—
208#484—221no—
209#480—21no—
210#474—112no—
211#474C2×D1112yes—
212#464—222no—
213#461—112no—
214#459C2×D1112yes—
215#452—222no—
216#450—221no—
217#447—21no—
218#440—222no—
219C4×D8—22no—
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—24no—
237C22×C11—21no—
238C22×C11—42no—
239C22×C11—42no—
240C22×C11—84no—
241C22×C11—81no—
242C22×C11—81no—
243C22×C11—81no—
244C22×C11C2×#12111yescharacteristic
245C4×C11—21no—
246C4×C11—21no—
247C4×C11—21no—
248C4×C11—21no—
249C4×C11—42no—
250C4×C11—81no—
251C4×C11C2×#13512yes—
252C4×C11#57612yes—
253Dic11—81no—
254Dic11—81no—
255C2×#41—21no—
256C22×D4C22⋊D1111yescharacteristic
257C23×C4—21no—
258C2×Q16—222no—
259C2×SD16—222no—
260C2×SD16—222no—
261C2×D8—22no—
262C22×C8—222no—
263C22×C8—222no—
264C4⋊Q8—111no—
265C4⋊Q8—111no—
266C4⋊Q8C22×D1111yescharacteristic
267#127C22×D1111yescharacteristic
268#125—221no—
269#124—21no—
270C22⋊Q8—221no—
271C22⋊Q8—221no—
272#121—21no—
273#121—21no—
274C4×Q8—221no—
275C4×Q8—221no—
276C4×D4—21no—
277C4×D4—21no—
278C4×D4—21no—
279C4×D4—21no—
280C4×D4C22⋊D1112yes—
281C4×D4C22×D1112yes—
282#117—221no—
283C2×C4⋊C4C22⋊D1111yescharacteristic
284C2×C22⋊C4—21no—
285C2×C42C22×D1111yescharacteristic
286#107—22no—
287#107—222no—
288C4⋊C8—112no—
289C4⋊C8—112no—
290C4⋊C8—112no—
291C4⋊C8C22×D1112yes—
292#103—222no—
293#103—222no—
294#102—22no—
295#102—22no—
296#102—222no—
297#102—222no—
298C22⋊C8—21no—
299C22⋊C8—112no—
300C22⋊C8—222no—
301C22⋊C8—222no—
302C22⋊C8—221no—
303C22⋊C8—221no—
304#97—221no—
305C4×C8—21no—
306C4×C8—111no—
307C4×C8—111no—
308C4×C8—221no—
309C2×C11—41no—
310C2×C11—44no—
311C2×C11—161no—
312C2×C11#304111yescharacteristic
313C2×C11#305011yescharacteristic
314C2×C11#306911yescharacteristic
315C24—21no—
316#41—82no—
317C2×Q8—21no—
318C2×Q8—221no—
319C2×Q8—221no—
320C2×D4—24no—
321C2×D4—21no—
322C2×D4—21no—
323C2×D4—21no—
324C2×D4—21no—
325C2×D4—41no—
326C2×D4C2×C22⋊D1112yes—
327C22×C4—21no—
328C22×C4—22no—
329C22×C4—22no—
330C22×C4—41no—
331C22×C4—82no—
332C22×C4D4×D1111yescharacteristic
333C22×C4#434111yescharacteristic
334C22×C4C2×C22⋊D1111yescharacteristic
335Q16—882no—
336SD16—444no—
337SD16—882no—
338D8—44no—
339C2×C8—22no—
340C2×C8—112no—
341C2×C8—112no—
342C2×C8—222no—
343C2×C8—222no—
344C2×C8—882no—
345C2×C8—882no—
346C4⋊C4—21no—
347C4⋊C4—21no—
348C4⋊C4—21no—
349C4⋊C4—221no—
350C4⋊C4—221no—
351C4⋊C4—221no—
352C4⋊C4—221no—
353C4⋊C4—441no—
354C4⋊C4—441no—
355C4⋊C4C2×C22⋊D1112yes—
356C22⋊C4—22no—
357C22⋊C4—22no—
358C22⋊C4—41no—
359C22⋊C4—41no—
360C22⋊C4—441no—
361C42—441no—
362C42D4×D1111yescharacteristic
363C42#434111yescharacteristic
364C42C2×C22⋊D1111yescharacteristic
365C42C23×D1111yescharacteristic
366C11#1938811yescharacteristic, complemented, Sylow
367C23—24no—
368C23—22no—
369C23—41no—
370C23—81no—
371C23—81no—
372C23#6699211yescharacteristic
373Q8—42no—
374Q8—442no—
375Q8—442no—
376D4—24no—
377D4—22no—
378D4—42no—
379D4—42no—
380D4—81no—
381D4—82no—
382D4#6700314yes—
383C2×C4—22no—
384C2×C4—22no—
385C2×C4—22no—
386C2×C4—41no—
387C2×C4—42no—
388C2×C4—42no—
389C2×C4—41no—
390C2×C4—82no—
391C2×C4—82no—
392C2×C4—81no—
393C2×C4—441no—
394C2×C4—441no—
395C2×C4#6699211yescharacteristic
396C2×C4#6699211yescharacteristic
397C2×C4#6699211yescharacteristic
398C2×C4C2×D4×D1111yescharacteristic
399C2×C4C2×#434111yescharacteristic
400C2×C4C22×C22⋊D1111yescharacteristic
401C8—42no—
402C8—222no—
403C8—222no—
404C8—442no—
405C8—442no—
406C22—21no—
407C22—21no—
408C22—21no—
409C22—24no—
410C22—42no—
411C22—42no—
412C22—84no—
413C22—81no—
414C22—81no—
415C22—81no—
416C22C2×#6699211yescharacteristic
417C4—21no—
418C4—21no—
419C4—21no—
420C4—21no—
421C4—42no—
422C4—81no—
423C4—881no—
424C4—881no—
425C4#1062328812yes—
426C4C2×#6700312yes—
427C2—41no—
428C2—44no—
429C2—161no—
430C2#1307811611yescharacteristic
431C2#1307819411yescharacteristic
432C2#1307835511yescharacteristic
subgroupG/H
centerC22C2×#66992
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
Fitting, prime radicalC11×#3100C2
socleC22×C11C2×#121
hypercenter#3100D11
hypocenterC11#19388
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3100

Complements

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

NH ≅ G/Ntype
1. #13079572C2semidirect
2. #13078715C2semidirect
3. #13077640C2semidirect
4. #13068051C2semidirect
5. #13068037C2semidirect
6. #13067979C2semidirect
7. #13067955C2semidirect
8. #13067394C2semidirect
9. #13067321C2semidirect
10. #13067280C2semidirect
24. #10622705C22semidirect
25. #10622694C22semidirect
26. #10622689C22semidirect
27. #10622683C22semidirect
39. #10622185C22semidirect
40. #10622182C22semidirect
41. #10622124C22semidirect
42. #10622120C22semidirect
43. #10622118C22semidirect
44. #10622117C22semidirect
366. C11#19388semidirect

Maximal subgroups

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

subgroupindex
#130795722
#130787152
#130776402
#130680512
#130680372
#130679792
#130679552
#130673942
#130673212
#130672802
C11×#31002
#1938811