Finite Group Databasebeta

← #14656818

Subgroups — #14656818

Order 2816.

536 conjugacy classes of subgroups.

The subgroup lattice has 424 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13073647C211yesmaximal, characteristic, complemented
2#13069543C211yesmaximal, characteristic
3#13069542C211yesmaximal, characteristic
4#13069422C211yesmaximal, characteristic
5#13066500C211yesmaximal, characteristic, complemented
6#13066456C211yesmaximal, characteristic, complemented
7C11×#1279C211yesmaximal, characteristic, complemented
8C2×#66943—21no—
9C2×#66927C2211yescharacteristic
10C2×C11×C4⋊C8C2211yescharacteristic
11C2×C4×C8×C11C2211yescharacteristic
12C4×C11×C4⋊C4C2211yescharacteristic
13C2×#66885—22no—
14C2×#66885—21no—
15C2×#66885—21no—
16#10622598—21no—
17C2×#66873—21no—
18C2×#66873—21no—
19#10622548—21no—
20#10622548C2211yescharacteristic
21C4×C4⋊Dic11C2211yescharacteristic
22#10622541—21no—
23C2×C4⋊(C11⋊C8)C2211yescharacteristic
24#10622274—22no—
25C22×D44—21no—
26C22×D44—21no—
27C22×D44—21no—
28C22×C8×C11—21no—
29C22×C8×C11—21no—
30C2×C11×C4⋊C4D411yescharacteristic
31C2×C11×C4⋊C4D411yescharacteristic
32C2×C42×C11—21no—
33C2×C42×C11C2311yescharacteristic
34C2×C4⋊Dic11—22no—
35C2×C4⋊Dic11—21no—
36C2×C4⋊Dic11—21no—
37C2×C4⋊Dic11—22no—
38C2×C4⋊Dic11D411yescharacteristic
39C2×C4⋊Dic11D411yescharacteristic
40C2×C4⋊Dic11D412yes—
41C2×Dic11⋊C4—22no—
42C2×C4×Dic11—21no—
43C22×C11⋊C8—21no—
44#66943—42no—
45#66943—42no—
46#66927—21no—
47#66927—21no—
48#66927—21no—
49#66927Q812yes—
50C11×C4⋊C8—21no—
51C11×C4⋊C8—21no—
52C4×C8×C11—21no—
53C4×C8×C11—21no—
54C11×#95—21no—
55C11⋊#95—22no—
56C11⋊#95—21no—
57#66885—42no—
58#66885—42no—
59#66885—44no—
60#66873—42no—
61#66873—42no—
62C4⋊(C11⋊C8)—21no—
63C4⋊(C11⋊C8)—21no—
64#10354—111nomaximal, Sylow
65C23×D11—41no—
66C22×C4×C11—21no—
67C22×C4×C11—21no—
68C22×C4×C11C2×D411yescharacteristic
69C22×C4×C11C2×D411yescharacteristic
70C22×C4×C11C2×D411yescharacteristic
71C22×Dic11—21no—
72C22×Dic11—21no—
73C22×Dic11—22no—
74C2×D44—22no—
75C2×D44—22no—
76C2×D44—22no—
77C2×D44—42no—
78C2×D44—42no—
79C2×D44—41no—
80C2×D44—41no—
81C2×D44—41no—
82C2×D44—41no—
83C2×D44—41no—
84C2×D44—41no—
85C2×D44—41no—
86C2×D44—41no—
87C2×D44—41no—
88C2×D44—41no—
89C2×D44—41no—
90C2×C8×C11—22no—
91C2×C8×C11—41no—
92C2×C8×C11—41no—
93C2×C8×C11—41no—
94C2×C8×C11—41no—
95C2×C8×C11—41no—
96C11×C4⋊C4—21no—
97C11×C4⋊C4—21no—
98C11×C4⋊C4D812yes—
99C11×C4⋊C4SD1612yes—
100C42×C11—41no—
101C42×C11—41no—
102C42×C11C2×Q811yescharacteristic
103C42×C11#4111yescharacteristic
104C42×C11#4111yescharacteristic
105C42×C11#4111yescharacteristic
106C4⋊Dic11—21no—
107C4⋊Dic11—21no—
108C4⋊Dic11—21no—
109C4⋊Dic11—21no—
110C4⋊Dic11—42no—
111C4⋊Dic11—44no—
112C4⋊Dic11—41no—
113C4⋊Dic11—41no—
114C4⋊Dic11—41no—
115C4⋊Dic11—41no—
116C4⋊Dic11—82no—
117Dic11⋊C4—44no—
118C4×Dic11—41no—
119C4×Dic11—41no—
120C2×C11⋊C8—41no—
121C2×C11⋊C8—41no—
122C2×C11⋊C8—41no—
123#2552—111no—
124#1982—111no—
125#1982—111no—
126#1957—111no—
127#1296—111no—
128#1279—111no—
129#1279D1111yescharacteristic, complemented
130C23×C11#12011yescharacteristic
131C22×D11—42no—
132C22×D11—81no—
133C22×D11—81no—
134C22×D11—81no—
135C22×D11—81no—
136C22×D11—81no—
137C22×D11—81no—
138C2×C4×C11—21no—
139C2×C4×C11—21no—
140C2×C4×C11—22no—
141C2×C4×C11—22no—
142C2×C4×C11—41no—
143C2×C4×C11—41no—
144C2×C4×C11—41no—
145C2×C4×C11—41no—
146C2×C4×C11C22⋊Q811yescharacteristic
147C2×C4×C11C22⋊Q811yescharacteristic
148C2×C4×C11C22⋊Q811yescharacteristic
149C2×C4×C11#12411yescharacteristic
150C2×C4×C11#12411yescharacteristic
151C2×C4×C11#12411yescharacteristic
152C2×C4×C11C2×D811yescharacteristic
153C2×C4×C11C2×SD1611yescharacteristic
154C2×C4×C11#13511yescharacteristic
155C2×C4×C11#13511yescharacteristic
156C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
157C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
158C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
159C2×C4×C11#13711yescharacteristic
160C2×Dic11—41no—
161C2×Dic11—41no—
162C2×Dic11—42no—
163C2×Dic11—41no—
164C2×Dic11—41no—
165C2×Dic11—42no—
166C2×Dic11—42no—
167C2×Dic11—41no—
168C2×Dic11—41no—
169D44—44no—
170D44—42no—
171D44—42no—
172D44—42no—
173D44—42no—
174D44—82no—
175D44—81no—
176D44—81no—
177D44—81no—
178D44—81no—
179C8×C11—42no—
180C8×C11—81no—
181C11⋊C8—81no—
182C2×#127—111no—
183C2×#125—221no—
184C2×C4⋊C8—111no—
185C2×C4⋊C8C2×D1111yescharacteristic
186C2×#102—222no—
187C2×#102—221no—
188C2×#102—221no—
189C2×#102—221no—
190C2×#102—221no—
191C2×C4×C8C2×D1111yescharacteristic
192#398—222no—
193#389—221no—
194#389—221no—
195#384—111no—
196#384—221no—
197C4×C4⋊C4—111no—
198C4×C4⋊C4C2×D1111yescharacteristic
199C22×C11#39311yescharacteristic
200C22×C11#44711yescharacteristic
201C22×C11#44811yescharacteristic
202C22×C11#44911yescharacteristic
203C22×C11#44911yescharacteristic
204C22×C11#45311yescharacteristic
205C22×C11#45411yescharacteristic
206C2×D11—82no—
207C2×D11—82no—
208C2×D11—82no—
209C2×D11—161no—
210C2×D11—161no—
211C2×D11—161no—
212C2×D11—161no—
213C4×C11—21no—
214C4×C11—21no—
215C4×C11—42no—
216C4×C11—42no—
217C4×C11#47411yescharacteristic
218C4×C11#47611yescharacteristic
219C4×C11#47811yescharacteristic
220C4×C11#47811yescharacteristic
221C4×C11#48611yescharacteristic
222C4×C11#48811yescharacteristic
223C4×C11#48911yescharacteristic
224C4×C11#49011yescharacteristic
225Dic11—81no—
226Dic11—82no—
227Dic11—81no—
228C22×D4—221no—
229C22×D4—221no—
230C22×D4—221no—
231C22×C8—21no—
232C22×C8—21no—
233C22×C8—221no—
234#127—112no—
235#127—221no—
236#127—221no—
237#127—221no—
238#125—442no—
239#125—442no—
240C2×C4⋊C4—111no—
241C2×C4⋊C4—111no—
242C2×C4⋊C4—112no—
243C2×C4⋊C4—222no—
244C2×C4⋊C4—222no—
245C2×C4⋊C4—221no—
246C2×C4⋊C4—221no—
247C2×C4⋊C4—222no—
248C2×C4⋊C4D4411yescharacteristic
249C2×C4⋊C4D4411yescharacteristic
250C2×C42—21no—
251C2×C42—221no—
252C2×C42C22×D1111yescharacteristic
253C4⋊C8—21no—
254C4⋊C8—21no—
255C4⋊C8—221no—
256C4⋊C8—221no—
257#102—442no—
258#102—442no—
259#102—444no—
260#102—442no—
261#102—442no—
262C4×C8—21no—
263C4×C8—21no—
264#95—21no—
265#95—222no—
266#95—221no—
267C2×C11#162111yescharacteristic
268C2×C11#162211yescharacteristic
269C2×C11#162511yescharacteristic
270C2×C11#162611yescharacteristic
271C2×C11#202311yescharacteristic
272C2×C11#202511yescharacteristic
273C2×C11#202711yescharacteristic
274D11—162no—
275C24—441no—
276C2×D4—222no—
277C2×D4—222no—
278C2×D4—222no—
279C2×D4—442no—
280C2×D4—442no—
281C2×D4—441no—
282C2×D4—441no—
283C2×D4—441no—
284C2×D4—441no—
285C2×D4—441no—
286C2×D4—441no—
287C2×D4—441no—
288C2×D4—441no—
289C2×D4—441no—
290C2×D4—441no—
291C2×D4—441no—
292C22×C4—21no—
293C22×C4—21no—
294C22×C4—221no—
295C22×C4—221no—
296C22×C4—222no—
297C22×C4C2×D4411yescharacteristic
298C22×C4D4×D1111yescharacteristic
299C22×C4D4×D1111yescharacteristic
300C2×C8—22no—
301C2×C8—41no—
302C2×C8—41no—
303C2×C8—41no—
304C2×C8—41no—
305C2×C8—41no—
306C2×C8—441no—
307C2×C8—441no—
308C2×C8—441no—
309C4⋊C4—21no—
310C4⋊C4—21no—
311C4⋊C4—221no—
312C4⋊C4—221no—
313C4⋊C4—221no—
314C4⋊C4—221no—
315C4⋊C4—442no—
316C4⋊C4—444no—
317C4⋊C4—444no—
318C4⋊C4—441no—
319C4⋊C4—441no—
320C4⋊C4—441no—
321C4⋊C4—441no—
322C4⋊C4—882no—
323C4⋊C4#431412yes—
324C4⋊C4D8812yes—
325C42—41no—
326C42—41no—
327C42—441no—
328C42—441no—
329C42#433911yescharacteristic
330C42#433911yescharacteristic
331C42#434111yescharacteristic
332C42Q8×D1111yescharacteristic
333C11#1035411yescharacteristic, complemented, Sylow
334C23—442no—
335C23—881no—
336C23—881no—
337C23—881no—
338C23—881no—
339C23—881no—
340C23—881no—
341C23#6693511yescharacteristic
342D4—444no—
343D4—442no—
344D4—442no—
345D4—442no—
346D4—442no—
347D4—882no—
348D4—881no—
349D4—881no—
350D4—881no—
351D4—881no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—22no—
355C2×C4—22no—
356C2×C4—41no—
357C2×C4—41no—
358C2×C4—41no—
359C2×C4—41no—
360C2×C4—441no—
361C2×C4—441no—
362C2×C4—442no—
363C2×C4—441no—
364C2×C4—441no—
365C2×C4—442no—
366C2×C4—442no—
367C2×C4—441no—
368C2×C4—441no—
369C2×C4#6692811yescharacteristic
370C2×C4#6693811yescharacteristic
371C2×C4#6693811yescharacteristic
372C2×C4#6694911yescharacteristic
373C2×C4#6694911yescharacteristic
374C2×C4#6695011yescharacteristic
375C2×C4C2×#431411yescharacteristic
376C2×C4C2×D8811yescharacteristic
377C2×C4#6696111yescharacteristic
378C2×C4#6696211yescharacteristic
379C2×C4#6696411yescharacteristic
380C2×C4#6696711yescharacteristic
381C2×C4#6696911yescharacteristic
382C2×C4#6697211yescharacteristic
383C8—42no—
384C8—81no—
385C8—881no—
386C22—882no—
387C22—882no—
388C22—882no—
389C22—1761no—
390C22—1761no—
391C22—1761no—
392C22—1761no—
393C22#1062228611yescharacteristic
394C22#1062234511yescharacteristic
395C22#1062235111yescharacteristic
396C22#1062239411yescharacteristic
397C22#1062242411yescharacteristic
398C22#1062243511yescharacteristic
399C22#1062244011yescharacteristic
400C4—21no—
401C4—21no—
402C4—42no—
403C4—42no—
404C4—881no—
405C4—882no—
406C4—881no—
407C4#1062230711yescharacteristic
408C4#1062232711yescharacteristic
409C4#1062237711yescharacteristic
410C4#1062241311yescharacteristic
411C4#1062245511yescharacteristic
412C4#1062245911yescharacteristic
413C4#1062248411yescharacteristic
414C4#1062250411yescharacteristic
415C2—1762no—
416C2#1306768311yescharacteristic
417C2#1306769011yescharacteristic
418C2#1306770711yescharacteristic
419C2#1306771511yescharacteristic
420C2#1306975311yescharacteristic
421C2#1306976111yescharacteristic
422C2#1306977111yescharacteristic
subgroupG/H
centerC23#66935
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1279C2
socleC23×C11#120
prime radicalC2×#66927C22
hypercenter#1279D11
hypocenterC11#10354
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1279

Complements

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

NH ≅ G/Ntype
1. #13073647C2semidirect
5. #13066500C2semidirect
6. #13066456C2semidirect
7. C11×#1279C2semidirect
129. #1279D11semidirect
333. C11#10354semidirect

Maximal subgroups

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

subgroupindex
#130736472
#130695432
#130695422
#130694222
#130665002
#130664562
C11×#12792
#1035411