Finite Group Databasebeta

← #14737085

Subgroups — #14737085

Order 2816.

592 conjugacy classes of subgroups.

The subgroup lattice has 456 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079958C211yesmaximal, characteristic, complemented
2#13079928C211yesmaximal, characteristic
3#13078939C211yesmaximal, characteristic
4#13068198C212yesmaximal, complemented
5#13068184C212yesmaximal, complemented
6#13068046C212yesmaximal, complemented
7#13068032C212yesmaximal, complemented
8C2×#10622095C211yesmaximal, characteristic, complemented
9#13067307C211yesmaximal, characteristic, complemented
10#13067294C211yesmaximal, characteristic
11C11×#2960C211yesmaximal, characteristic, complemented
12C11×#533C2211yescharacteristic
13#10623008C2211yescharacteristic
14#10623001C2211yescharacteristic
15C11×#446—21no—
16C11×#446C2212yes—
17C8×Q8×C11—21no—
18C8×Q8×C11C2212yes—
19C11×#424—21no—
20C11×#423C2211yescharacteristic
21C11×#405—21no—
22C2×C4×C8×C11C2211yescharacteristic
23#10622726—21no—
24#10622726—21no—
25#10622704—21no—
26#10622703—21no—
27#10622697—21no—
28#10622696—21no—
29#10622664—22no—
30#10622661—22no—
31#10622644C2212yes—
32#10622640C2212yes—
33#10622634C2212yes—
34#10622633C2212yes—
35C2×C4⋊(C11⋊C8)C2211yescharacteristic
36C2×C4⋊(C11⋊C8)C2211yescharacteristic
37#10622310—21no—
38#10622310—21no—
39#10622307C2211yescharacteristic
40#10622307C2211yescharacteristic
41#10622294C2211yescharacteristic
42#10622294C2211yescharacteristic
43#10622124C2212yes—
44#10622123C2212yes—
45#10622120C2212yes—
46#10622119C2212yes—
47#10622095C2212yes—
48#10622095C2212yes—
49C2×#4339—21no—
50C2×C11×M16—21no—
51C22×C8×C11D411yescharacteristic
52C22×C8×C11D411yescharacteristic
53C11×C4⋊Q8D411yescharacteristic
54C11×C4⋊Q8D411yescharacteristic
55C11×#125—21no—
56C11×C22⋊Q8—21no—
57C11×C22⋊Q8D412yes—
58C4×Q8×C11—21no—
59C4×Q8×C11C2312yes—
60C11×#117—21no—
61C2×C42×C11C2311yescharacteristic
62C2×#4326—22no—
63C2×#4325—22no—
64#66983—21no—
65#66983—21no—
66#66979—21no—
67#66977—21no—
68#66977—21no—
69C22×C11⋊C8—21no—
70C22×C11⋊C8—21no—
71#66928—21no—
72#66927C2311yescharacteristic
73C4×D44—21no—
74C4×D44—21no—
75#66923—21no—
76#66922C2311yescharacteristic
77#66922C2311yescharacteristic
78#66922C2311yescharacteristic
79C4×Dic22—21no—
80C4×Dic22—21no—
81C11×C4⋊C8—22no—
82C11×C4⋊C8—22no—
83C11×C4⋊C8—21no—
84C11×C4⋊C8C2312yes—
85C11×#97—22no—
86C4×C8×C11—22no—
87C4×C8×C11D411yescharacteristic
88C4×C8×C11D411yescharacteristic
89C4×C8×C11C2311yescharacteristic
90C4×C8×C11C2311yescharacteristic
91#66899—22no—
92#66899—22no—
93#66885—21no—
94#66885—21no—
95#66885—21no—
96#66885—21no—
97#66880—21no—
98#66880—21no—
99#66880—21no—
100#66880—21no—
101#66874—22no—
102#66873—22no—
103#66872—22no—
104#66871—22no—
105C4⋊(C11⋊C8)—21no—
106C4⋊(C11⋊C8)—21no—
107C4⋊(C11⋊C8)C2312yes—
108C4⋊(C11⋊C8)C2312yes—
109#19216—111nomaximal, Sylow
110C2×Q8×C11—21no—
111C2×Q8×C11C2×D412yes—
112C22×C4×C11C2×D411yescharacteristic
113C22×C4×C11C2×D411yescharacteristic
114C22×C4×C11#4111yescharacteristic
115C2×C22⋊D11—41no—
116#4339—42no—
117#4339—42no—
118C2×D44—21no—
119C2×D44—21no—
120C2×D44—21no—
121C2×C4×D11—41no—
122C2×Dic22—21no—
123C2×Dic22—21no—
124C2×Dic22—21no—
125C11×M16—42no—
126C2×C8×C11—22no—
127C2×C8×C11—22no—
128C2×C8×C11—22no—
129C2×C8×C11C2×D411yescharacteristic
130C2×C8×C11C2×D411yescharacteristic
131C2×C8×C11C2×D411yescharacteristic
132C2×C8×C11C2×D411yescharacteristic
133C11×C4⋊C4—21no—
134C11×C4⋊C4—21no—
135C11×C4⋊C4—21no—
136C11×C4⋊C4—22no—
137C11×C4⋊C4—22no—
138C11×C4⋊C4C2×D412yes—
139C11×C22⋊C4—22no—
140C42×C11—22no—
141C42×C11C2×D411yescharacteristic
142C42×C11C2×D411yescharacteristic
143C42×C11#4111yescharacteristic
144C42×C11C2411yescharacteristic
145C22⋊Dic11—41no—
146#4326—82no—
147#4325—82no—
148(C2×D11)⋊C4—41no—
149(C2×D11)⋊C4—41no—
150C4⋊Dic11—21no—
151C4⋊Dic11—21no—
152C4⋊Dic11—21no—
153C4⋊Dic11—21no—
154C4⋊Dic11—21no—
155C4⋊Dic11—21no—
156Dic11⋊C4—41no—
157Dic11⋊C4—41no—
158C4×Dic11—41no—
159C2×C11⋊C8—22no—
160C2×C11⋊C8—22no—
161C2×C11⋊C8—81no—
162C2×C11⋊C8—81no—
163#3249—111no—
164#3246—111no—
165#3131—111no—
166#2960D1111yescharacteristic, complemented
167#1704—112no—
168#1702—112no—
169#1680—112no—
170#1678—112no—
171C2×#334—111no—
172#1550—111no—
173#1547—111no—
174C23×C11#12111yescharacteristic
175C22×D11—41no—
176Q8×C11—22no—
177Q8×C11—22no—
178Q8×C11—42no—
179C2×C4×C11—21no—
180C2×C4×C11—21no—
181C2×C4×C11—22no—
182C2×C4×C11—22no—
183C2×C4×C11—41no—
184C2×C4×C11#12111yescharacteristic
185C2×C4×C11#12111yescharacteristic
186C2×C4×C11#12111yescharacteristic
187C2×C4×C11#13512yes—
188C2×C4×C11#13712yes—
189C2×C4×C11C22×D411yescharacteristic
190C2×C4×C11C22×D411yescharacteristic
191C2×C4×C11C2×#4111yescharacteristic
192C22⋊D11—82no—
193C2×Dic11—41no—
194C2×Dic11—41no—
195C2×Dic11—41no—
196D44—41no—
197D44—41no—
198D44—41no—
199D44—41no—
200D44—81no—
201C4×D11—82no—
202Dic22—41no—
203Dic22—41no—
204Dic22—41no—
205Dic22—41no—
206Dic22—81no—
207C8×C11—21no—
208C8×C11—21no—
209C8×C11—21no—
210C8×C11—21no—
211C8×C11—42no—
212C11⋊C8—42no—
213C11⋊C8—42no—
214#533—111no—
215#533C2×D1111yescharacteristic
216#532—111no—
217#488—221no—
218#488—221no—
219#487—111no—
220#487—111no—
221#486—111no—
222#486—111no—
223#477—112no—
224#477—221no—
225#476—221no—
226#475—112no—
227#467—222no—
228#465—222no—
229#462—112no—
230#462—221no—
231#461—221no—
232#460—112no—
233#446—21no—
234#446C2×D1112yes—
235C8×Q8—21no—
236C8×Q8C2×D1112yes—
237#424—21no—
238#423C2×D1111yescharacteristic
239C2×C4⋊C8—111no—
240C2×C4⋊C8—111no—
241#416—221no—
242#416—221no—
243#405—21no—
244C2×C4×C8C2×D1111yescharacteristic
245#334—112no—
246#334—112no—
247#333—112no—
248#332—112no—
249#332—112no—
250#331—112no—
251C22×C11—21no—
252C22×C11—21no—
253C22×C11#46412yes—
254C22×C11C2×#12111yescharacteristic
255C2×D11—81no—
256C2×D11—81no—
257C2×D11—81no—
258C4×C11—21no—
259C4×C11—21no—
260C4×C11—21no—
261C4×C11—42no—
262C4×C11—42no—
263C4×C11#46412yes—
264C4×C11C2×#13511yescharacteristic
265C4×C11C2×#13711yescharacteristic
266C4×C11#57711yescharacteristic
267C4×C11#57711yescharacteristic
268Dic11—81no—
269Dic11—81no—
270Dic11—81no—
271C2×#41—221no—
272C2×Q16—222no—
273C2×SD16—222no—
274C2×M16—21no—
275C22×C8—221no—
276C22×C8—221no—
277C22×C8C22⋊D1111yescharacteristic
278C22×C8C22⋊D1111yescharacteristic
279C4⋊Q8—111no—
280C4⋊Q8—111no—
281C4⋊Q8—111no—
282C4⋊Q8D4411yescharacteristic
283C4⋊Q8D4411yescharacteristic
284#127—111no—
285#125—21no—
286#125—221no—
287#124—221no—
288C22⋊Q8—21no—
289C22⋊Q8—221no—
290C22⋊Q8—221no—
291C22⋊Q8D4412yes—
292#121—221no—
293#121—221no—
294C4×Q8—21no—
295C4×Q8—221no—
296C4×Q8—221no—
297C4×Q8C22×D1112yes—
298C4×D4—221no—
299C4×D4—221no—
300#117—21no—
301#117—221no—
302C2×C42C22×D1111yescharacteristic
303#107—222no—
304#106—222no—
305C4⋊C8—22no—
306C4⋊C8—22no—
307C4⋊C8—21no—
308C4⋊C8—112no—
309C4⋊C8—112no—
310C4⋊C8—221no—
311C4⋊C8—221no—
312C4⋊C8C22×D1112yes—
313#103—222no—
314#103—222no—
315#103—221no—
316#103—221no—
317#103—221no—
318#103—221no—
319#103—222no—
320#102—221no—
321#102—221no—
322#102—221no—
323#102—221no—
324#102—222no—
325#97—22no—
326C4×C8—22no—
327C4×C8C22⋊D1111yescharacteristic
328C4×C8C22⋊D1111yescharacteristic
329C4×C8C22×D1111yescharacteristic
330C4×C8C22×D1111yescharacteristic
331C2×C11—22no—
332C2×C11C2×#46411yescharacteristic
333C2×C11#306011yescharacteristic
334C2×C11#306711yescharacteristic
335D11—161no—
336#41—442no—
337#41—442no—
338C2×Q8—21no—
339C2×Q8—221no—
340C2×Q8—221no—
341C2×Q8—221no—
342C2×Q8C2×D4412yes—
343C2×D4—221no—
344C2×D4—221no—
345C2×D4—221no—
346C2×D4—441no—
347C22×C4—441no—
348C22×C4C2×D4411yescharacteristic
349C22×C4#433911yescharacteristic
350C22×C4C2×C22⋊D1111yescharacteristic
351Q16—882no—
352SD16—882no—
353M16—42no—
354C2×C8—22no—
355C2×C8—22no—
356C2×C8—22no—
357C2×C8—222no—
358C2×C8—222no—
359C2×C8—881no—
360C2×C8—881no—
361C2×C8C2×C22⋊D1111yescharacteristic
362C2×C8C2×C22⋊D1111yescharacteristic
363C2×C8C2×C22⋊D1111yescharacteristic
364C2×C8C2×C22⋊D1111yescharacteristic
365C4⋊C4—21no—
366C4⋊C4—21no—
367C4⋊C4—21no—
368C4⋊C4—22no—
369C4⋊C4—22no—
370C4⋊C4—221no—
371C4⋊C4—221no—
372C4⋊C4—221no—
373C4⋊C4—221no—
374C4⋊C4—221no—
375C4⋊C4—221no—
376C4⋊C4—441no—
377C4⋊C4—441no—
378C4⋊C4C2×D4412yes—
379C22⋊C4—22no—
380C22⋊C4—441no—
381C22⋊C4—441no—
382C22⋊C4—441no—
383C42—22no—
384C42—441no—
385C42C2×D4411yescharacteristic
386C42#433911yescharacteristic
387C42C2×C22⋊D1111yescharacteristic
388C42C23×D1111yescharacteristic
389C11#1921611yescharacteristic, complemented, Sylow
390C23—441no—
391C23#6698311yescharacteristic
392Q8—22no—
393Q8—22no—
394Q8—42no—
395Q8—441no—
396Q8—441no—
397Q8—441no—
398Q8—441no—
399Q8—881no—
400D4—441no—
401D4—441no—
402D4—441no—
403D4—441no—
404D4—881no—
405D4—882no—
406C2×C4—21no—
407C2×C4—21no—
408C2×C4—22no—
409C2×C4—22no—
410C2×C4—41no—
411C2×C4—441no—
412C2×C4—441no—
413C2×C4—441no—
414C2×C4—882no—
415C2×C4#6698311yescharacteristic
416C2×C4#6698311yescharacteristic
417C2×C4#6698311yescharacteristic
418C2×C4#6699512yes—
419C2×C4#6700312yes—
420C2×C4C22×D4411yescharacteristic
421C2×C4C2×#433911yescharacteristic
422C2×C4C22×C22⋊D1111yescharacteristic
423C8—21no—
424C8—21no—
425C8—21no—
426C8—21no—
427C8—42no—
428C8—442no—
429C8—442no—
430C22—21no—
431C22—21no—
432C22—881no—
433C22—881no—
434C22—881no—
435C22#1062264112yes—
436C22C2×#6698311yescharacteristic
437C4—21no—
438C4—21no—
439C4—21no—
440C4—42no—
441C4—42no—
442C4—881no—
443C4—881no—
444C4—881no—
445C4#1062264112yes—
446C4#1062328211yescharacteristic
447C4#1062328211yescharacteristic
448C4C2×#6699511yescharacteristic
449C4C2×#6700311yescharacteristic
450C2—22no—
451C2—1761no—
452C2C2×#1062264111yescharacteristic
453C2#1307827811yescharacteristic
454C2#1307833611yescharacteristic
subgroupG/H
centerC22C2×#66983
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#2960C2
socleC22×C11C2×#121
prime radical#10623008C22
hypercenter#2960D11
hypocenterC11#19216
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2960

Complements

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

NH ≅ G/Ntype
1. #13079958C2semidirect
4. #13068198C2semidirect
5. #13068184C2semidirect
6. #13068046C2semidirect
7. #13068032C2semidirect
8. C2×#10622095C2semidirect
9. #13067307C2semidirect
11. C11×#2960C2semidirect
166. #2960D11semidirect
389. C11#19216semidirect

Maximal subgroups

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

subgroupindex
#130799582
#130799282
#130789392
#130681982
#130681842
#130680462
#130680322
C2×#106220952
#130673072
#130672942
C11×#29602
#1921611