Finite Group Databasebeta

← #14649679

Subgroups — #14649679

Order 2816.

566 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 566 conjugacy classes of subgroups — too many to draw. Only its 113 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13078415C211yesmaximal, characteristic
2#13071527C211yesmaximal, characteristic
3#13067181C211yesmaximal, characteristic, complemented
4#13067114C211yesmaximal, characteristic, complemented
5#13067008C211yesmaximal, characteristic
6#13066476C211yesmaximal, characteristic, complemented
7C11×#1303C211yesmaximal, characteristic, complemented
8C2×C4×D44—21no—
9C2×C4×D44C2211yescharacteristic
10#10623001C2211yescharacteristic
11C11×#431C2211yescharacteristic
12C11×#423C2211yescharacteristic
13C4×C11×C4⋊C4C2211yescharacteristic
14#10622744—21no—
15#10622734—21no—
16#10622602—22no—
17#10622549C2211yescharacteristic
18#10622541—21no—
19#10622538C2211yescharacteristic
20#10622460—22no—
21#10622459C412yescomplemented
22#10622455C412yescomplemented
23#10622280—21no—
24D11×#95—21no—
25#10622105—22no—
26#10622097—22no—
27#10622090—21no—
28#10622090—21no—
29C22×D44D411yescharacteristic
30C22×C4×D11—21no—
31C22×C4×D11—22no—
32C2×C11×M16—21no—
33C2×C11×C4⋊C4—21no—
34C2×C42×C11—21no—
35C2×C42×C11C2311yescharacteristic
36C2×(C2×D11)⋊C4—21no—
37C2×(C2×D11)⋊C4—22no—
38#66979—21no—
39C2×C4⋊Dic11—21no—
40C2×C4⋊Dic11D411yescharacteristic
41#66977—21no—
42#66977—21no—
43C2×Dic11⋊C4—22no—
44C4×D44—21no—
45C4×D44—21no—
46C4×D44—42no—
47C4×D44—42no—
48C4×D44C2×C412yes—
49C4×D44D412yes—
50#66923—21no—
51#66922C2×C411yescharacteristic, complemented
52#66922C2×C411yescharacteristic, complemented
53C4×Dic22—21no—
54C4×Dic22—21no—
55C11×C4⋊C8—21no—
56C11×C4⋊C8—21no—
57C11×C4⋊C8C2×C412yescomplemented
58C11×C22⋊C8—21no—
59C4×C8×C11—21no—
60C11×#95D411yescharacteristic
61C11×#95D411yescharacteristic
62C11⋊#95—22no—
63C11⋊#95—21no—
64C11⋊#95D412yes—
65C22⋊(C11⋊C8)—21no—
66#66885—22no—
67#66885—22no—
68#66882—22no—
69#66881—22no—
70C4⋊(C11⋊C8)—21no—
71C4×C11⋊C8—21no—
72#9175—111nomaximal, Sylow
73C23×D11—21no—
74C22×C4×C11—21no—
75C22×C4×C11—21no—
76C22×C4×C11C2×D411yescharacteristic
77C22×C4×C11C2×D411yescharacteristic
78C22×C4×C11C2×D411yescharacteristic
79C22×Dic11—21no—
80C22×Dic11—22no—
81C2×D44—21no—
82C2×D44—21no—
83C2×D44—21no—
84C2×D44C22⋊C412yes—
85C2×D44SD1612yes—
86C2×D44Q1612yes—
87C2×C4×D11—22no—
88C2×C4×D11—22no—
89C2×C4×D11—44no—
90C2×C4×D11—44no—
91C2×C4×D11—82no—
92C2×C4×D11—82no—
93C2×Dic22—21no—
94C2×Dic22—21no—
95C11×M16—41no—
96C11×M16—41no—
97C2×C8×C11—22no—
98C2×C8×C11—41no—
99C11×C4⋊C4—42no—
100C42×C11—41no—
101C42×C11—41no—
102C42×C11C22×C411yescharacteristic
103C42×C11C2×D411yescharacteristic
104C42×C11#4111yescharacteristic
105C42×C11#4111yescharacteristic
106C22⋊Dic11—41no—
107(C2×D11)⋊C4—22no—
108(C2×D11)⋊C4—22no—
109(C2×D11)⋊C4—44no—
110C4⋊Dic11—21no—
111C4⋊Dic11—21no—
112C4⋊Dic11—21no—
113C4⋊Dic11—21no—
114C4⋊Dic11—21no—
115C4⋊Dic11—41no—
116C4⋊Dic11—41no—
117C4⋊Dic11C22⋊C412yes—
118Dic11⋊C4—41no—
119Dic11⋊C4—41no—
120Dic11⋊C4—82no—
121C4×Dic11—41no—
122C2×C11⋊C8—41no—
123#3077—111no—
124#2349—111no—
125#1518—111no—
126#1503—111no—
127#1478—111no—
128#1303D1111yescharacteristic, complemented
129#1286—111no—
130C23×C11#12011yescharacteristic
131C22×D11—22no—
132C22×D11—22no—
133C22×D11—22no—
134C22×D11—42no—
135C22×D11—42no—
136C2×C4×C11—22no—
137C2×C4×C11—41no—
138C2×C4×C11—41no—
139C2×C4×C11—41no—
140C2×C4×C11—41no—
141C2×C4×C11—41no—
142C2×C4×C11—41no—
143C2×C4×C11—41no—
144C2×C4×C11C2×C22⋊C411yescharacteristic
145C2×C4×C11C4×D411yescharacteristic
146C2×C4×C11C4×D411yescharacteristic
147C2×C4×C11#12111yescharacteristic
148C2×C4×C11#12111yescharacteristic
149C2×C4×C11#12311yescharacteristic
150C2×C4×C11C2×SD1611yescharacteristic
151C2×C4×C11C2×Q1611yescharacteristic
152C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
153C2×C4×C11#13711yescharacteristic
154C2×Dic11—22no—
155C2×Dic11—42no—
156C2×Dic11—42no—
157C2×Dic11—42no—
158C2×Dic11—41no—
159C2×Dic11—41no—
160C2×Dic11—42no—
161D44—22no—
162D44—22no—
163D44—22no—
164D44#10314yes—
165C4×D11—82no—
166C4×D11—82no—
167C4×D11—88no—
168Dic22—81no—
169Dic22—81no—
170C8×C11—42no—
171C8×C11—81no—
172C11⋊C8—81no—
173#533—111no—
174C2×C4×D4—111no—
175C2×C4×D4—221no—
176#478—222no—
177#476—112no—
178#474—112no—
179#431—111no—
180#431C2×D1111yescharacteristic
181#428—221no—
182#423C2×D1111yescharacteristic
183#418—221no—
184#389—221no—
185#385—222no—
186#382—111no—
187#380—221no—
188C4×C4⋊C4C2×D1111yescharacteristic
189C2×#95—221no—
190#328—222no—
191#328—221no—
192#328—221no—
193D4⋊C8—222no—
194C22×C11—21no—
195C22×C11—21no—
196C22×C11#38611yescharacteristic
197C22×C11#45011yescharacteristic
198C22×C11#45111yescharacteristic
199C2×D11—24no—
200C2×D11—44no—
201C2×D11—44no—
202C2×D11—42no—
203C2×D11—42no—
204C4×C11—21no—
205C4×C11—21no—
206C4×C11—21no—
207C4×C11—21no—
208C4×C11—42no—
209C4×C11—81no—
210C4×C11C2×#10311yescharacteristic
211C4×C11#41711yescharacteristic
212C4×C11#48311yescharacteristic
213C4×C11#48411yescharacteristic
214Dic11—42no—
215Dic11—82no—
216Dic11—81no—
217Dic11—81no—
218C22×D4—111no—
219C23×C4—222no—
220C23×C4—221no—
221C2×M16—21no—
222C4⋊Q8—111no—
223C4⋊Q8—111no—
224#125—221no—
225C22⋊Q8—221no—
226C22⋊Q8—221no—
227C4×Q8—221no—
228C4×Q8—221no—
229C4×D4—112no—
230C4×D4—112no—
231C4×D4—221no—
232C4×D4—221no—
233C4×D4—442no—
234C4×D4—442no—
235#117—221no—
236C2×C4⋊C4—21no—
237C2×C4⋊C4—111no—
238C2×C4⋊C4—221no—
239C2×C4⋊C4—222no—
240C2×C22⋊C4—221no—
241C2×C22⋊C4—222no—
242C2×C42—21no—
243C2×C42C22×D1111yescharacteristic
244#107—222no—
245#106—222no—
246C4⋊C8—21no—
247C4⋊C8—21no—
248C4⋊C8—221no—
249C4⋊C8C4×D1112yescomplemented
250#102—222no—
251#102—222no—
252C22⋊C8—21no—
253C22⋊C8—221no—
254C4×C8—21no—
255C4×C8—221no—
256#95—112no—
257#95—222no—
258#95—221no—
259#95D4411yescharacteristic
260#95D4411yescharacteristic
261C2×C11—21no—
262C2×C11—21no—
263C2×C11#187211yescharacteristic
264C2×C11#190411yescharacteristic
265C2×C11#190611yescharacteristic
266D11—44no—
267C24—221no—
268C2×Q8—221no—
269C2×Q8—221no—
270C2×D4—112no—
271C2×D4—112no—
272C2×D4—112no—
273C2×D4—221no—
274C2×D4—221no—
275C2×D4—221no—
276C22×C4—21no—
277C22×C4—21no—
278C22×C4—221no—
279C22×C4—222no—
280C22×C4—222no—
281C22×C4—222no—
282C22×C4—444no—
283C22×C4—444no—
284C22×C4—882no—
285C22×C4—882no—
286C22×C4C2×D4411yescharacteristic
287C22×C4D4×D1111yescharacteristic
288C22×C4D4×D1111yescharacteristic
289M16—41no—
290M16—41no—
291C2×C8—22no—
292C2×C8—41no—
293C2×C8—441no—
294C4⋊C4—42no—
295C4⋊C4—112no—
296C4⋊C4—221no—
297C4⋊C4—221no—
298C4⋊C4—221no—
299C4⋊C4—221no—
300C4⋊C4—221no—
301C4⋊C4—441no—
302C4⋊C4—441no—
303C4⋊C4—441no—
304C4⋊C4—441no—
305C4⋊C4—882no—
306C22⋊C4—222no—
307C22⋊C4—222no—
308C22⋊C4—444no—
309C22⋊C4—441no—
310C42—41no—
311C42—41no—
312C42—441no—
313C42C2×C4×D1111yescharacteristic
314C42#433911yescharacteristic
315C42D4×D1111yescharacteristic
316C42#434311yescharacteristic
317C11#917511yescharacteristic, complemented, Sylow
318C23—222no—
319C23—222no—
320C23—222no—
321C23—442no—
322C23—442no—
323C23#6693511yescharacteristic
324Q8—881no—
325Q8—881no—
326D4—114no—
327D4—222no—
328D4—222no—
329D4—222no—
330C2×C4—22no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—41no—
338C2×C4—222no—
339C2×C4—442no—
340C2×C4—442no—
341C2×C4—442no—
342C2×C4—441no—
343C2×C4—441no—
344C2×C4—442no—
345C2×C4—882no—
346C2×C4—882no—
347C2×C4—888no—
348C2×C4C4×D4411yescharacteristic
349C2×C4C22⋊C4×D1111yescharacteristic
350C2×C4#6693711yescharacteristic
351C2×C4#6694611yescharacteristic
352C2×C4#6694711yescharacteristic
353C2×C4#6694811yescharacteristic
354C2×C4#6696411yescharacteristic
355C2×C4SD16×D1111yescharacteristic
356C2×C4#6696811yescharacteristic
357C2×C4Q16×D1111yescharacteristic
358C8—42no—
359C8—81no—
360C8—881no—
361C22—21no—
362C22—21no—
363C22—224no—
364C22—444no—
365C22—444no—
366C22—442no—
367C22—442no—
368C22#1062227811yescharacteristic
369C22#1062238911yescharacteristic
370C22#1062242111yescharacteristic
371C4—21no—
372C4—21no—
373C4—21no—
374C4—21no—
375C4—42no—
376C4—81no—
377C4—442no—
378C4—882no—
379C4—881no—
380C4—881no—
381C4#1062238411yescharacteristic
382C4D11×#10311yescharacteristic
383C4#1062247511yescharacteristic
384C4#1062249711yescharacteristic
385C2—21no—
386C2—21no—
387C2—444no—
388C2#1306892211yescharacteristic
389C2#1306910211yescharacteristic
390C2#1306911611yescharacteristic
subgroupG/H
centerC22#10622278
commutatorC42×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1303C2
socleC22×C11#386
prime radicalC22×D44D4
cosocleC2×C42×C11C23
hypercenter#1303D11
hypocenterC11#9175
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1303

Complements

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

NH ≅ G/Ntype
3. #13067181C2semidirect
4. #13067114C2semidirect
6. #13066476C2semidirect
7. C11×#1303C2semidirect
21. #10622459C4semidirect
22. #10622455C4semidirect
51. #66922C2×C4semidirect
52. #66922C2×C4semidirect
57. C11×C4⋊C8C2×C4semidirect
128. #1303D11semidirect
249. C4⋊C8C4×D11semidirect
317. C11#9175semidirect

Maximal subgroups

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

subgroupindex
#130784152
#130715272
#130671812
#130671142
#130670082
#130664762
C11×#13032
#917511