Finite Group Databasebeta

← #14811870

Subgroups — #14811870

Order 2816.

734 conjugacy classes of subgroups.

The subgroup lattice has 450 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13073652C211yesmaximal, characteristic, complemented
2#13071567C211yesmaximal, characteristic
3#13069991C212yesmaximal
4#13069761C212yesmaximal
5#13069570C212yesmaximal, complemented
6#13069377C211yesmaximal, characteristic, complemented
7#13069334C211yesmaximal, characteristic, complemented
8#13069192C212yesmaximal, complemented
9#13068613C211yesmaximal, characteristic
10C4×#66885C211yesmaximal, characteristic
11C11×#1834C211yesmaximal, characteristic, complemented
12C2×#66945—21no—
13C2×#66943C2212yes—
14C2×C4×D44C2211yescharacteristic
15C2×C4×C8×C11C2211yescharacteristic
16C11×#384C2211yescharacteristic
17C11×#384C2211yescharacteristic
18C2×#66885C2211yescharacteristic
19C2×#66885C2211yescharacteristic
20C2×Dic11⋊C8C2212yes—
21#10622603—22no—
22#10622601C2212yes—
23#10622600—21no—
24#10622598—21no—
25#10622597—22no—
26#10622589—21no—
27C4⋊C4×Dic11C2212yes—
28#10622586C2212yes—
29C2×#66873C2212yes—
30C2×#66872C2212yes—
31C4×C4⋊Dic11C2211yescharacteristic
32C4×C4⋊Dic11C2211yescharacteristic
33C2×C4⋊(C11⋊C8)C2211yescharacteristic
34C11×#340C2212yes—
35C11×#340C2212yes—
36#10622189C2211yescharacteristic
37#10622189C2211yescharacteristic
38#10622188C2212yes—
39#10622167C2212yes—
40#10622167C2212yes—
41C22×D44C2311yescharacteristic
42C22×C4×D11—21no—
43C22×C8×C11C2311yescharacteristic
44C22×C8×C11C2311yescharacteristic
45C2×C11×C4⋊C4—21no—
46C2×C11×C4⋊C4—21no—
47C2×C11×C4⋊C4—21no—
48C2×C11×C4⋊C4—21no—
49C2×C11×C4⋊C4C2312yes—
50C2×C11×C4⋊C4C2312yes—
51C2×C42×C11C2311yescharacteristic
52C2×(C2×D11)⋊C4—21no—
53C2×(C2×D11)⋊C4—22no—
54C2×(C2×D11)⋊C4—22no—
55C2×C4⋊Dic11—22no—
56C2×C4⋊Dic11D411yescharacteristic
57C2×C4⋊Dic11D411yescharacteristic
58C2×C4⋊Dic11C2311yescharacteristic
59C2×C4⋊Dic11C2311yescharacteristic
60C2×C4⋊Dic11C2311yescharacteristic
61C2×Dic11⋊C4—22no—
62C2×Dic11⋊C4—22no—
63C2×C4×Dic11—21no—
64C2×C4×Dic11—22no—
65C2×C4×Dic11C2312yes—
66C22×C11⋊C8C2312yes—
67#66945—44no—
68#66943—24no—
69#66943—42no—
70C4×D44—22no—
71C4×D44Q814yes—
72C4×C8×C11—22no—
73C11⋊#95—21no—
74C11⋊#95—22no—
75C11⋊#95—22no—
76C11⋊#95D412yes—
77#66885—22no—
78#66885—22no—
79Dic11⋊C8—42no—
80#66873—42no—
81#66872—24no—
82C4⋊(C11⋊C8)—22no—
83#26021—111nomaximal, Sylow
84C23×D11—21no—
85C22×C4×C11—22no—
86C22×C4×C11—22no—
87C22×C4×C11C2×D411yescharacteristic
88C22×C4×C11C2×D411yescharacteristic
89C22×C4×C11C2411yescharacteristic
90C22×Dic11—21no—
91C22×Dic11—21no—
92C22×Dic11—21no—
93C22×Dic11C2×D412yes—
94C22×Dic11C2×D412yes—
95C2×D44—21no—
96C2×D44—21no—
97C2×D44—21no—
98C2×D44—21no—
99C2×D44—21no—
100C2×D44C2×Q812yes—
101C2×C4×D11—24no—
102C2×C4×D11—42no—
103C2×C4×D11—42no—
104C2×C8×C11—21no—
105C2×C8×C11—21no—
106C2×C8×C11—21no—
107C2×C8×C11—21no—
108C2×C8×C11—21no—
109C2×C8×C11—21no—
110C11×C4⋊C4—22no—
111C11×C4⋊C4—22no—
112C11×C4⋊C4—22no—
113C11×C4⋊C4—22no—
114C11×C4⋊C4—42no—
115C11×C4⋊C4—42no—
116C11×C4⋊C4—81no—
117C11×C4⋊C4—81no—
118C42×C11C2×Q812yes—
119C42×C11#4112yes—
120(C2×D11)⋊C4—24no—
121(C2×D11)⋊C4—44no—
122(C2×D11)⋊C4—82no—
123C4⋊Dic11—22no—
124C4⋊Dic11—22no—
125C4⋊Dic11—21no—
126C4⋊Dic11—21no—
127C4⋊Dic11—21no—
128C4⋊Dic11—44no—
129C4⋊Dic11C2×Q812yes—
130C4⋊Dic11#4112yes—
131C4⋊Dic11#4112yes—
132Dic11⋊C4—44no—
133Dic11⋊C4—82no—
134C4×Dic11—22no—
135C4×Dic11—22no—
136C4×Dic11—44no—
137C4×Dic11—42no—
138C2×C11⋊C8—22no—
139C2×C11⋊C8—22no—
140C2×C11⋊C8—22no—
141#2552—111no—
142#2354—111no—
143#2065—112no—
144#2025—112no—
145#1989—112no—
146#1948—111no—
147#1939—111no—
148#1919—112no—
149#1834D1111yescharacteristic, complemented
150#1802—111no—
151C4×#102—111no—
152C23×C11C22×D411yescharacteristic
153C22×D11—22no—
154C22×D11—41no—
155C22×D11—41no—
156C22×D11—41no—
157C22×D11—41no—
158C22×D11—41no—
159C22×D11—41no—
160C2×C4×C11—21no—
161C2×C4×C11—21no—
162C2×C4×C11—42no—
163C2×C4×C11—42no—
164C2×C4×C11—42no—
165C2×C4×C11—42no—
166C2×C4×C11—42no—
167C2×C4×C11—42no—
168C2×C4×C11C22⋊Q812yes—
169C2×C4×C11C22⋊Q812yes—
170C2×C4×C11#13512yes—
171C2×C4×C11AGL(1,ℤ/8)12yes—
172C2×C4×C11C22×Q811yescharacteristic
173C2×C4×C11C2×#4111yescharacteristic
174C2×C4×C11C2×#4111yescharacteristic
175C2×C4×C11C2×#4111yescharacteristic
176C2×C4×C11H(5,𝔽2)11yescharacteristic
177C2×C4×C112−1+411yescharacteristic
178C2×Dic11—22no—
179C2×Dic11—22no—
180C2×Dic11—22no—
181C2×Dic11—22no—
182C2×Dic11—22no—
183C2×Dic11—22no—
184C2×Dic11—22no—
185C2×Dic11—22no—
186C2×Dic11—22no—
187C2×Dic11—41no—
188C2×Dic11—41no—
189C2×Dic11—41no—
190C2×Dic11—41no—
191C2×Dic11—41no—
192C2×Dic11—41no—
193D44—22no—
194D44—22no—
195D44—41no—
196D44—41no—
197C4×D11—48no—
198C8×C11—41no—
199C8×C11—41no—
200C11⋊C8—42no—
201C2×#125—112no—
202C2×C4×D4—111no—
203C2×#117—221no—
204C2×#106—112no—
205C2×C4⋊C8—111no—
206C2×C4⋊C8—112no—
207C2×#102—111no—
208C2×#102—111no—
209C2×#102—112no—
210C2×C4×C8C2×D1111yescharacteristic
211#398—222no—
212#390—112no—
213#389—112no—
214#389—221no—
215#388—222no—
216#384—221no—
217#384C2×D1111yescharacteristic
218#384C2×D1111yescharacteristic
219#380—221no—
220C4×C4⋊C4—111no—
221C4×C4⋊C4—112no—
222C4×C4⋊C4—111no—
223#340—111no—
224#340—111no—
225#340—112no—
226#340—112no—
227#340C2×D1112yes—
228#340C2×D1112yes—
229#336—112no—
230C22×C11C2×C22⋊Q811yescharacteristic
231C22×C11#54611yescharacteristic
232C22×C11#54811yescharacteristic
233C22×C11C2×#13511yescharacteristic
234C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
235C22×C11#57711yescharacteristic
236C22×C11#57711yescharacteristic
237C2×D11—42no—
238C2×D11—42no—
239C2×D11—42no—
240C2×D11—81no—
241C2×D11—81no—
242C2×D11—81no—
243C2×D11—81no—
244C4×C11—22no—
245C4×C11—82no—
246C4×C11—82no—
247C4×C11#47814yes—
248C4×C11#53311yescharacteristic
249C4×C11#54411yescharacteristic
250C4×C11#55511yescharacteristic
251C4×C11#55611yescharacteristic
252Dic11—42no—
253Dic11—42no—
254Dic11—42no—
255Dic11—42no—
256Dic11—42no—
257C22×D4—111no—
258C23×C4—221no—
259C22×C8—112no—
260C22×C8C22×D1111yescharacteristic
261C22×C8C22×D1111yescharacteristic
262#125—224no—
263#125—442no—
264C4×D4—114no—
265C4×D4—222no—
266#117—444no—
267C2×C4⋊C4—21no—
268C2×C4⋊C4—21no—
269C2×C4⋊C4—21no—
270C2×C4⋊C4—21no—
271C2×C4⋊C4—111no—
272C2×C4⋊C4—111no—
273C2×C4⋊C4—111no—
274C2×C4⋊C4—111no—
275C2×C4⋊C4—111no—
276C2×C4⋊C4—222no—
277C2×C4⋊C4—222no—
278C2×C4⋊C4—222no—
279C2×C4⋊C4C22×D1112yes—
280C2×C4⋊C4C22×D1112yes—
281C2×C22⋊C4—221no—
282C2×C22⋊C4—222no—
283C2×C22⋊C4—222no—
284C2×C42—112no—
285C2×C42—222no—
286C2×C42—221no—
287C2×C42C22×D1111yescharacteristic
288#106—224no—
289C4⋊C8—222no—
290C4⋊C8—442no—
291#102—222no—
292#102—222no—
293#102—442no—
294C4×C8—22no—
295#95—112no—
296#95—222no—
297#95—222no—
298#95—221no—
299C2×C11#243911yescharacteristic
300C2×C11C2×#47811yescharacteristic
301C2×C11#308411yescharacteristic
302C2×C11#330311yescharacteristic
303C2×C11#333211yescharacteristic
304C2×C11#336011yescharacteristic
305C2×C11#336811yescharacteristic
306D11—82no—
307C24—221no—
308C2×D4—112no—
309C2×D4—221no—
310C2×D4—221no—
311C2×D4—221no—
312C2×D4—221no—
313C2×D4—221no—
314C22×C4—22no—
315C22×C4—22no—
316C22×C4—112no—
317C22×C4—112no—
318C22×C4—221no—
319C22×C4—221no—
320C22×C4—221no—
321C22×C4—224no—
322C22×C4—442no—
323C22×C4—442no—
324C22×C4D4×D1111yescharacteristic
325C22×C4D4×D1111yescharacteristic
326C22×C4C23×D1111yescharacteristic
327C2×C8—21no—
328C2×C8—21no—
329C2×C8—21no—
330C2×C8—21no—
331C2×C8—21no—
332C2×C8—21no—
333C2×C8—222no—
334C2×C8—222no—
335C2×C8—222no—
336C4⋊C4—22no—
337C4⋊C4—22no—
338C4⋊C4—22no—
339C4⋊C4—22no—
340C4⋊C4—42no—
341C4⋊C4—42no—
342C4⋊C4—81no—
343C4⋊C4—81no—
344C4⋊C4—112no—
345C4⋊C4—112no—
346C4⋊C4—112no—
347C4⋊C4—222no—
348C4⋊C4—222no—
349C4⋊C4—221no—
350C4⋊C4—221no—
351C4⋊C4—221no—
352C4⋊C4—444no—
353C4⋊C4—444no—
354C4⋊C4—882no—
355C22⋊C4—224no—
356C22⋊C4—444no—
357C22⋊C4—882no—
358C42—222no—
359C42—222no—
360C42—444no—
361C42—442no—
362C42#433912yes—
363C42Q8×D1112yes—
364C11#2602111yescharacteristic, complemented, Sylow
365C23—222no—
366C23—441no—
367C23—441no—
368C23—441no—
369C23—441no—
370C23—441no—
371C23—441no—
372C23C2×D4×D1111yescharacteristic
373D4—222no—
374D4—222no—
375D4—441no—
376D4—441no—
377C2×C4—21no—
378C2×C4—21no—
379C2×C4—42no—
380C2×C4—42no—
381C2×C4—42no—
382C2×C4—42no—
383C2×C4—42no—
384C2×C4—42no—
385C2×C4—222no—
386C2×C4—222no—
387C2×C4—222no—
388C2×C4—222no—
389C2×C4—222no—
390C2×C4—222no—
391C2×C4—222no—
392C2×C4—222no—
393C2×C4—222no—
394C2×C4—441no—
395C2×C4—441no—
396C2×C4—441no—
397C2×C4—441no—
398C2×C4—441no—
399C2×C4—441no—
400C2×C4—448no—
401C2×C4#6694912yes—
402C2×C4#6694912yes—
403C2×C4#6696412yes—
404C2×C4#6697212yes—
405C2×C4C2×#433911yescharacteristic
406C2×C4C2×Q8×D1111yescharacteristic
407C2×C4#41×D1111yescharacteristic
408C2×C4#41×D1111yescharacteristic
409C2×C4#6704211yescharacteristic
410C2×C4#6704311yescharacteristic
411C8—41no—
412C8—41no—
413C8—442no—
414C22—442no—
415C22—442no—
416C22—442no—
417C22—881no—
418C22—881no—
419C22—881no—
420C22—881no—
421C22C2×#6694911yescharacteristic
422C22#1062320711yescharacteristic
423C22#1062320811yescharacteristic
424C22C2×#6696411yescharacteristic
425C22#1062329311yescharacteristic
426C22#1062329311yescharacteristic
427C22C2×#6697211yescharacteristic
428C4—22no—
429C4—82no—
430C4—82no—
431C4—442no—
432C4—442no—
433C4—442no—
434C4—442no—
435C4—442no—
436C4#1062250414yes—
437C4#1062306311yescharacteristic
438C4#1062306411yescharacteristic
439C4#1062321911yescharacteristic
440C4#1062322011yescharacteristic
441C2—882no—
442C2#1307231011yescharacteristic
443C2C2×#1062250411yescharacteristic
444C2#1307848311yescharacteristic
445C2#1308054311yescharacteristic
446C2#1308094211yescharacteristic
447C2#1308127011yescharacteristic
448C2#1308135011yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1834C2
socleC23×C11C22×D4
prime radicalC22×D44C23
hypercenter#1834D11
hypocenterC11#26021
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1834

Complements

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

NH ≅ G/Ntype
1. #13073652C2semidirect
5. #13069570C2semidirect
6. #13069377C2semidirect
7. #13069334C2semidirect
8. #13069192C2semidirect
11. C11×#1834C2semidirect
149. #1834D11semidirect
364. C11#26021semidirect

Maximal subgroups

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

subgroupindex
#130736522
#130715672
#130699912
#130697612
#130695702
#130693772
#130693342
#130691922
#130686132
C4×#668852
C11×#18342
#2602111