Finite Group Databasebeta

← #14656784

Subgroups — #14656784

Order 2816.

588 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#13073642C211yesmaximal, characteristic, complemented
2#13069543C211yesmaximal, characteristic
3#13069542C211yesmaximal, characteristic
4#13069422C211yesmaximal, characteristic
5#13066500C211yesmaximal, characteristic, complemented
6#13066456C211yesmaximal, characteristic, complemented
7C11×#1279C211yesmaximal, characteristic, complemented
8C2×#66941—21no—
9C2×#66927C2211yescharacteristic
10C2×#66922—21no—
11C2×C11×C4⋊C8C2211yescharacteristic
12C2×C4×C8×C11C2211yescharacteristic
13C4×C11×C4⋊C4C2211yescharacteristic
14C2×#66885—22no—
15C2×#66885—21no—
16C2×#66885—21no—
17#10622598—21no—
18C2×#66873—21no—
19C2×#66873—21no—
20#10622548C2211yescharacteristic
21C4×C4⋊Dic11C2211yescharacteristic
22#10622541—21no—
23C2×C4⋊(C11⋊C8)C2211yescharacteristic
24#10622269—22no—
25C22×D44—21no—
26C22×D44—21no—
27C22×D44—21no—
28C22×Dic22—22no—
29C22×C8×C11—21no—
30C22×C8×C11—21no—
31C2×C11×C4⋊C4D411yescharacteristic
32C2×C11×C4⋊C4D411yescharacteristic
33C2×C42×C11—21no—
34C2×C42×C11C2311yescharacteristic
35C2×C4⋊Dic11—22no—
36C2×C4⋊Dic11—21no—
37C2×C4⋊Dic11—21no—
38C2×C4⋊Dic11D411yescharacteristic
39C2×C4⋊Dic11D411yescharacteristic
40C2×C4⋊Dic11D412yes—
41C2×Dic11⋊C4—22no—
42C2×C4×Dic11—21no—
43C22×C11⋊C8—21no—
44#66941—42no—
45#66941—42no—
46#66927—21no—
47#66927—21no—
48#66927—21no—
49#66927Q812yescomplemented
50#66922—42no—
51#66922—42no—
52C11×C4⋊C8—21no—
53C11×C4⋊C8—21no—
54C4×C8×C11—21no—
55C4×C8×C11—21no—
56C11×#95—21no—
57C11⋊#95—22no—
58C11⋊#95—21no—
59#66885—44no—
60#66885—42no—
61#66885—42no—
62#66873—42no—
63#66873—42no—
64C4⋊(C11⋊C8)—21no—
65C4⋊(C11⋊C8)—21no—
66#10348—111nomaximal, Sylow
67C23×D11—41no—
68C22×C4×C11—21no—
69C22×C4×C11—21no—
70C22×C4×C11C2×D411yescharacteristic
71C22×C4×C11C2×D411yescharacteristic
72C22×C4×C11C2×D411yescharacteristic
73C22×Dic11—21no—
74C22×Dic11—21no—
75C22×Dic11—22no—
76C2×D44—22no—
77C2×D44—22no—
78C2×D44—22no—
79C2×D44—42no—
80C2×D44—42no—
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×D44—41no—
91C2×D44—41no—
92C2×Dic22—44no—
93C2×Dic22—44no—
94C2×Dic22—82no—
95C2×C8×C11—22no—
96C2×C8×C11—41no—
97C2×C8×C11—41no—
98C2×C8×C11—41no—
99C2×C8×C11—41no—
100C2×C8×C11—41no—
101C11×C4⋊C4—21no—
102C11×C4⋊C4—21no—
103C11×C4⋊C4D812yes—
104C11×C4⋊C4SD1612yes—
105C42×C11—41no—
106C42×C11—41no—
107C42×C11C2×Q811yescharacteristic
108C42×C11#4111yescharacteristic
109C42×C11#4111yescharacteristic
110C42×C11#4111yescharacteristic
111C4⋊Dic11—21no—
112C4⋊Dic11—21no—
113C4⋊Dic11—42no—
114C4⋊Dic11—44no—
115C4⋊Dic11—41no—
116C4⋊Dic11—41no—
117C4⋊Dic11—41no—
118C4⋊Dic11—41no—
119C4⋊Dic11D812yes—
120C4⋊Dic11SD1612yes—
121Dic11⋊C4—44no—
122C4×Dic11—41no—
123C4×Dic11—41no—
124C2×C11⋊C8—41no—
125C2×C11⋊C8—41no—
126C2×C11⋊C8—41no—
127#2551—111no—
128#1982—111no—
129#1982—111no—
130#1957—111no—
131#1296—111no—
132#1279—111no—
133#1279D1111yescharacteristic, complemented
134C23×C11#12011yescharacteristic
135C22×D11—42no—
136C22×D11—81no—
137C22×D11—81no—
138C22×D11—81no—
139C22×D11—81no—
140C22×D11—81no—
141C22×D11—81no—
142C2×C4×C11—21no—
143C2×C4×C11—21no—
144C2×C4×C11—22no—
145C2×C4×C11—22no—
146C2×C4×C11—41no—
147C2×C4×C11—41no—
148C2×C4×C11—41no—
149C2×C4×C11—41no—
150C2×C4×C11C22⋊Q811yescharacteristic
151C2×C4×C11C22⋊Q811yescharacteristic
152C2×C4×C11C22⋊Q811yescharacteristic
153C2×C4×C11#12411yescharacteristic
154C2×C4×C11#12411yescharacteristic
155C2×C4×C11#12411yescharacteristic
156C2×C4×C11C2×D811yescharacteristic
157C2×C4×C11C2×D811yescharacteristic
158C2×C4×C11C2×SD1611yescharacteristic
159C2×C4×C11C2×SD1611yescharacteristic
160C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
161C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
162C2×C4×C11#13711yescharacteristic
163C2×C4×C11#13711yescharacteristic
164C2×Dic11—22no—
165C2×Dic11—22no—
166C2×Dic11—41no—
167C2×Dic11—41no—
168C2×Dic11—41no—
169C2×Dic11—41no—
170C2×Dic11—42no—
171C2×Dic11—42no—
172C2×Dic11—42no—
173D44—44no—
174D44—42no—
175D44—42no—
176D44—42no—
177D44—42no—
178D44—82no—
179D44—81no—
180D44—81no—
181D44—81no—
182D44—81no—
183Dic22—88no—
184C8×C11—42no—
185C8×C11—81no—
186C11⋊C8—81no—
187C2×C4⋊Q8—221no—
188C2×C4⋊Q8—221no—
189C2×#127—111no—
190C2×C4⋊C8—111no—
191C2×C4⋊C8C2×D1111yescharacteristic
192C2×#102—222no—
193C2×#102—221no—
194C2×#102—221no—
195C2×#102—221no—
196C2×#102—221no—
197C2×C4×C8C2×D1111yescharacteristic
198#395—222no—
199#389—221no—
200#389—221no—
201#384—111no—
202C4×C4⋊C4—111no—
203C4×C4⋊C4C2×D1111yescharacteristic
204C22×C11#39311yescharacteristic
205C22×C11#44711yescharacteristic
206C22×C11#44711yescharacteristic
207C22×C11#44811yescharacteristic
208C22×C11#44811yescharacteristic
209C22×C11#45311yescharacteristic
210C22×C11#45411yescharacteristic
211C2×D11—82no—
212C2×D11—82no—
213C2×D11—82no—
214C2×D11—161no—
215C2×D11—161no—
216C2×D11—161no—
217C2×D11—161no—
218C4×C11—21no—
219C4×C11—21no—
220C4×C11—42no—
221C4×C11—42no—
222C4×C11#47411yescharacteristic
223C4×C11#47411yescharacteristic
224C4×C11#47611yescharacteristic
225C4×C11#47611yescharacteristic
226C4×C11#48611yescharacteristic
227C4×C11#48611yescharacteristic
228C4×C11#48911yescharacteristic
229C4×C11#48911yescharacteristic
230Dic11—42no—
231Dic11—42no—
232Dic11—82no—
233C22×Q8—222no—
234C22×D4—221no—
235C22×D4—221no—
236C22×D4—221no—
237C22×C8—21no—
238C22×C8—21no—
239C22×C8—221no—
240C4⋊Q8—442no—
241C4⋊Q8—442no—
242C4⋊Q8—442no—
243C4⋊Q8—442no—
244#127—112no—
245#127—221no—
246#127—221no—
247#127—221no—
248C2×C4⋊C4—111no—
249C2×C4⋊C4—111no—
250C2×C4⋊C4—112no—
251C2×C4⋊C4—222no—
252C2×C4⋊C4—222no—
253C2×C4⋊C4—221no—
254C2×C4⋊C4—221no—
255C2×C4⋊C4D4411yescharacteristic
256C2×C4⋊C4D4411yescharacteristic
257C2×C42—21no—
258C2×C42—221no—
259C2×C42C22×D1111yescharacteristic
260C4⋊C8—21no—
261C4⋊C8—21no—
262C4⋊C8—221no—
263C4⋊C8—221no—
264#102—442no—
265#102—442no—
266#102—444no—
267#102—442no—
268#102—442no—
269C4×C8—21no—
270C4×C8—21no—
271#95—21no—
272#95—222no—
273#95—221no—
274C2×C11#161911yescharacteristic
275C2×C11#162311yescharacteristic
276C2×C11#162711yescharacteristic
277C2×C11#162711yescharacteristic
278C2×C11#202311yescharacteristic
279C2×C11#202311yescharacteristic
280C2×C11#202711yescharacteristic
281D11—162no—
282C24—441no—
283C2×Q8—444no—
284C2×Q8—444no—
285C2×Q8—882no—
286C2×D4—222no—
287C2×D4—222no—
288C2×D4—222no—
289C2×D4—442no—
290C2×D4—442no—
291C2×D4—441no—
292C2×D4—441no—
293C2×D4—441no—
294C2×D4—441no—
295C2×D4—441no—
296C2×D4—441no—
297C2×D4—441no—
298C2×D4—441no—
299C2×D4—441no—
300C2×D4—441no—
301C2×D4—441no—
302C22×C4—21no—
303C22×C4—21no—
304C22×C4—221no—
305C22×C4—221no—
306C22×C4—222no—
307C22×C4C2×D4411yescharacteristic
308C22×C4D4×D1111yescharacteristic
309C22×C4D4×D1111yescharacteristic
310C2×C8—22no—
311C2×C8—41no—
312C2×C8—41no—
313C2×C8—41no—
314C2×C8—41no—
315C2×C8—41no—
316C2×C8—441no—
317C2×C8—441no—
318C2×C8—441no—
319C4⋊C4—21no—
320C4⋊C4—21no—
321C4⋊C4—112no—
322C4⋊C4—112no—
323C4⋊C4—221no—
324C4⋊C4—221no—
325C4⋊C4—442no—
326C4⋊C4—444no—
327C4⋊C4—444no—
328C4⋊C4—441no—
329C4⋊C4—441no—
330C4⋊C4—441no—
331C4⋊C4—441no—
332C4⋊C4#431412yes—
333C4⋊C4D8812yes—
334C42—41no—
335C42—41no—
336C42—441no—
337C42—441no—
338C42#433911yescharacteristic
339C42#433911yescharacteristic
340C42#434111yescharacteristic
341C42Q8×D1111yescharacteristic
342C11#1034811yescharacteristic, complemented, Sylow
343C23—442no—
344C23—881no—
345C23—881no—
346C23—881no—
347C23—881no—
348C23—881no—
349C23—881no—
350C23#6693511yescharacteristic
351Q8—888no—
352D4—444no—
353D4—442no—
354D4—442no—
355D4—442no—
356D4—442no—
357D4—882no—
358D4—881no—
359D4—881no—
360D4—881no—
361D4—881no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—22no—
365C2×C4—22no—
366C2×C4—41no—
367C2×C4—41no—
368C2×C4—41no—
369C2×C4—41no—
370C2×C4—222no—
371C2×C4—222no—
372C2×C4—441no—
373C2×C4—441no—
374C2×C4—441no—
375C2×C4—441no—
376C2×C4—442no—
377C2×C4—442no—
378C2×C4—442no—
379C2×C4#6692811yescharacteristic
380C2×C4#6693811yescharacteristic
381C2×C4#6693811yescharacteristic
382C2×C4#6694911yescharacteristic
383C2×C4#6694911yescharacteristic
384C2×C4#6695011yescharacteristic
385C2×C4C2×#431411yescharacteristic
386C2×C4C2×D8811yescharacteristic
387C2×C4#6696111yescharacteristic
388C2×C4#6696211yescharacteristic
389C2×C4D8×D1111yescharacteristic
390C2×C4SD16×D1111yescharacteristic
391C2×C4#6696711yescharacteristic
392C2×C4#6697111yescharacteristic
393C8—42no—
394C8—81no—
395C8—881no—
396C22—882no—
397C22—882no—
398C22—882no—
399C22—1761no—
400C22—1761no—
401C22—1761no—
402C22—1761no—
403C22#1062228611yescharacteristic
404C22#1062234511yescharacteristic
405C22#1062235111yescharacteristic
406C22#1062238611yescharacteristic
407C22#1062241911yescharacteristic
408C22#1062243511yescharacteristic
409C22#1062244011yescharacteristic
410C4—21no—
411C4—21no—
412C4—42no—
413C4—42no—
414C4—442no—
415C4—442no—
416C4—882no—
417C4#1062230711yescharacteristic
418C4#1062232711yescharacteristic
419C4#1062237311yescharacteristic
420C4#1062240811yescharacteristic
421C4#1062245511yescharacteristic
422C4#1062245911yescharacteristic
423C4#1062248311yescharacteristic
424C4#1062250311yescharacteristic
425C2—1762no—
426C2#1306767211yescharacteristic
427C2#1306769611yescharacteristic
428C2#1306772111yescharacteristic
429C2#1306772211yescharacteristic
430C2#1306975111yescharacteristic
431C2#1306975311yescharacteristic
432C2#1306977111yescharacteristic
subgroupG/H
centerC23#66935
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1279C2
socleC23×C11#120
prime radicalC2×#66927C22
hypercenter#1279D11
hypocenterC11#10348
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. #13073642C2semidirect
5. #13066500C2semidirect
6. #13066456C2semidirect
7. C11×#1279C2semidirect
49. #66927Q8semidirect
133. #1279D11semidirect
342. C11#10348semidirect

Maximal subgroups

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

subgroupindex
#130736422
#130695432
#130695422
#130694222
#130665002
#130664562
C11×#12792
#1034811