Finite Group Databasebeta

← #14656407

Subgroups — #14656407

Order 2816.

690 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 690 conjugacy classes of subgroups — too many to draw. Only its 103 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#13079538C211yesmaximal, characteristic, complemented
2#13079531C211yesmaximal, characteristic
3#13076973C211yesmaximal, characteristic, complemented
4#13067298C211yesmaximal, characteristic, complemented
5#13067285C211yesmaximal, characteristic, complemented
6#13066449C211yesmaximal, characteristic, complemented
7C11×#1962C211yesmaximal, characteristic, complemented
8C11×#532C2211yescharacteristic
9C2×#66928—22no—
10C2×#66927C2211yescharacteristic
11C2×#66922C2211yescharacteristic
12C11×#423C2211yescharacteristic
13C2×C11×#104—22no—
14C43×C11C2211yescharacteristic
15#10622706—21no—
16#10622701—21no—
17#10622689—21no—
18#10622686—21no—
19#10622653—22no—
20#10622649—22no—
21#10622632—22no—
22#10622628—22no—
23#10622552—22no—
24#10622552—22no—
25#10622538C2211yescharacteristic
26#10622538C2211yescharacteristic
27#10622123—22no—
28#10622119—22no—
29C2×C11×#41—21no—
30C22×D44—21no—
31C22×D44—21no—
32C22×D44D412yes—
33C22×Dic22D412yes—
34C2×C11×M16—21no—
35C11×C4⋊Q8D411yescharacteristic
36C11×#127D411yescharacteristic
37C11×#124—21no—
38C11×#121—21no—
39C11×#121—21no—
40C4×D4×C11—21no—
41C4×D4×C11—21no—
42C2×C42×C11—21no—
43C2×C42×C11—21no—
44C2×C42×C11D412yes—
45C2×C42×C11C2311yescharacteristic
46C2×#4324—24no—
47C2×#4323—24no—
48C2×(C2×D11)⋊C4—28no—
49C2×C4⋊Dic11—21no—
50C2×C4⋊Dic11—21no—
51#66928—48no—
52#66927—21no—
53#66927—21no—
54#66927—21no—
55#66927—21no—
56#66922—21no—
57#66922—21no—
58#66922—21no—
59#66922—21no—
60C11×C4⋊C8—21no—
61C11×C4⋊C8—21no—
62C11×#104—44no—
63C22⋊(C11⋊C8)—21no—
64C22⋊(C11⋊C8)—21no—
65#66874—24no—
66#66873—24no—
67C4⋊(C11⋊C8)D412yes—
68C4⋊(C11⋊C8)D412yes—
69C4×C11⋊C8—21no—
70C4×C11⋊C8—21no—
71#10281—111nomaximal, Sylow
72C23×D11—22no—
73C11×#41—42no—
74C11×#41—42no—
75C2×Q8×C11—21no—
76C2×D4×C11—21no—
77C2×D4×C11—21no—
78C2×D4×C11—21no—
79C2×D4×C11—41no—
80C22×C4×C11—22no—
81C22×C4×C11—41no—
82C22×C4×C11C2×D411yescharacteristic
83C22×C4×C11C2×D411yescharacteristic
84C22×C4×C11C2×D411yescharacteristic
85C22×Dic11—22no—
86C2×D44—22no—
87C2×D44—22no—
88C2×D44—44no—
89C2×D44—44no—
90C2×D44—41no—
91C2×D44—41no—
92C2×D44—41no—
93C2×D44—41no—
94C2×D44—42no—
95C2×D44—42no—
96C2×Dic22—22no—
97C2×Dic22—22no—
98C2×Dic22—44no—
99C11×M16—42no—
100C2×C8×C11—41no—
101C11×C4⋊C4—21no—
102C11×C4⋊C4—21no—
103C11×C22⋊C4—41no—
104C11×C22⋊C4—41no—
105C42×C11—24no—
106C42×C11—22no—
107C42×C11—22no—
108C42×C11—42no—
109C42×C11C2×D411yescharacteristic
110C42×C11C2×D411yescharacteristic
111C42×C11C2×D411yescharacteristic
112C42×C11#4111yescharacteristic
113#4324—84no—
114#4323—84no—
115(C2×D11)⋊C4—416no—
116C4⋊Dic11—41no—
117C4⋊Dic11—41no—
118C4⋊Dic11—41no—
119C4⋊Dic11—41no—
120C2×C11⋊C8—22no—
121C2×C11⋊C8—22no—
122#3206—111no—
123#3205—111no—
124#2858—111no—
125#1962D1111yescharacteristic, complemented
126#1548—111no—
127#1545—111no—
128#1276—111no—
129C23×C11—41no—
130C23×C11#12011yescharacteristic
131C22×D11—44no—
132C22×D11—44no—
133C22×D11—42no—
134C22×D11—44no—
135Q8×C11—42no—
136D4×C11—42no—
137D4×C11—42no—
138D4×C11—42no—
139D4×C11—82no—
140C2×C4×C11—22no—
141C2×C4×C11—22no—
142C2×C4×C11—24no—
143C2×C4×C11—42no—
144C2×C4×C11—42no—
145C2×C4×C11—41no—
146C2×C4×C11—81no—
147C2×C4×C11—81no—
148C2×C4×C11#12011yescharacteristic
149C2×C4×C11#12011yescharacteristic
150C2×C4×C11#12111yescharacteristic
151C2×C4×C11#12111yescharacteristic
152C2×C4×C11#12111yescharacteristic
153C2×C4×C11#12711yescharacteristic
154C2×C4×C11#13512yes—
155C2×C4×C11AGL(1,ℤ/8)12yes—
156C2×Dic11—44no—
157C2×Dic11—42no—
158D44—44no—
159D44—82no—
160D44—82no—
161D44—82no—
162D44—82no—
163D44—81no—
164D44—81no—
165Dic22—44no—
166Dic22—82no—
167C8×C11—81no—
168C11⋊C8—42no—
169C11⋊C8—42no—
170#532C2×D1111yescharacteristic
171C2×C4⋊Q8—111no—
172C2×#127—111no—
173C2×#124—222no—
174#493—221no—
175#492—221no—
176#487—221no—
177#486—221no—
178#461—222no—
179#459—222no—
180#448—222no—
181#447—222no—
182#431—111no—
183#431—111no—
184#423C2×D1111yescharacteristic
185C2×#104—22no—
186#390—222no—
187#390—222no—
188C43C2×D1111yescharacteristic
189#333—222no—
190#331—222no—
191C22×C11—21no—
192C22×C11—21no—
193C22×C11—81no—
194C22×C11—81no—
195C22×C11—81no—
196C22×C11#39211yescharacteristic
197C22×C11#44912yes—
198C2×D11—88no—
199C2×D11—82no—
200C2×D11—82no—
201C2×D11—82no—
202C4×C11—21no—
203C4×C11—21no—
204C4×C11—44no—
205C4×C11—81no—
206C4×C11#45312yes—
207C4×C11#45512yes—
208C4×C11#46312yes—
209C4×C11#49511yescharacteristic
210C4×C11#49611yescharacteristic
211Dic11—82no—
212C2×#41—21no—
213C22×Q8—112no—
214C22×D4—112no—
215C22×D4—221no—
216C22×D4—221no—
217C2×SD16—224no—
218C2×D8—224no—
219C2×M16—21no—
220C4⋊Q8—221no—
221C4⋊Q8—221no—
222C4⋊Q8—221no—
223C4⋊Q8—221no—
224C4⋊Q8D4411yescharacteristic
225#127—221no—
226#127—221no—
227#127—221no—
228#127—221no—
229#127D4411yescharacteristic
230#124—21no—
231#124—448no—
232#121—21no—
233#121—21no—
234C4×D4—21no—
235C4×D4—21no—
236C2×C4⋊C4—221no—
237C2×C4⋊C4—221no—
238C2×C22⋊C4—228no—
239C2×C42—21no—
240C2×C42—21no—
241C2×C42C22⋊D1112yes—
242C2×C42C22×D1111yescharacteristic
243C4⋊C8—21no—
244C4⋊C8—21no—
245C4⋊C8—112no—
246C4⋊C8—112no—
247#104—44no—
248#103—224no—
249#102—224no—
250C22⋊C8—221no—
251C22⋊C8—221no—
252C4×C8—221no—
253C4×C8—221no—
254C2×C11—22no—
255C2×C11—161no—
256C2×C11#200211yescharacteristic
257C2×C11#200411yescharacteristic
258C2×C11#201211yescharacteristic
259D11—162no—
260C24—222no—
261#41—42no—
262#41—42no—
263C2×Q8—21no—
264C2×Q8—222no—
265C2×Q8—222no—
266C2×Q8—444no—
267C2×D4—21no—
268C2×D4—21no—
269C2×D4—21no—
270C2×D4—41no—
271C2×D4—222no—
272C2×D4—222no—
273C2×D4—444no—
274C2×D4—444no—
275C2×D4—441no—
276C2×D4—441no—
277C2×D4—441no—
278C2×D4—442no—
279C2×D4—441no—
280C2×D4—442no—
281C22×C4—22no—
282C22×C4—41no—
283C22×C4—222no—
284C22×C4D4×D1111yescharacteristic
285C22×C4D4×D1111yescharacteristic
286C22×C4C2×C22⋊D1111yescharacteristic
287SD16—884no—
288D8—884no—
289M16—42no—
290C2×C8—41no—
291C2×C8—222no—
292C2×C8—222no—
293C4⋊C4—21no—
294C4⋊C4—21no—
295C4⋊C4—441no—
296C4⋊C4—441no—
297C4⋊C4—441no—
298C4⋊C4—441no—
299C22⋊C4—41no—
300C22⋊C4—41no—
301C22⋊C4—4416no—
302C42—24no—
303C42—22no—
304C42—22no—
305C42—42no—
306C42C2×D4411yescharacteristic
307C42#433911yescharacteristic
308C42D4×D1111yescharacteristic
309C42D4×D1111yescharacteristic
310C11#1028111yescharacteristic, complemented, Sylow
311C23—41no—
312C23—444no—
313C23—444no—
314C23—442no—
315C23—444no—
316C23#6699011yescharacteristic
317Q8—42no—
318Q8—444no—
319Q8—882no—
320D4—42no—
321D4—42no—
322D4—42no—
323D4—82no—
324D4—444no—
325D4—882no—
326D4—882no—
327D4—882no—
328D4—881no—
329D4—881no—
330D4—882no—
331C2×C4—22no—
332C2×C4—22no—
333C2×C4—24no—
334C2×C4—42no—
335C2×C4—42no—
336C2×C4—41no—
337C2×C4—81no—
338C2×C4—81no—
339C2×C4—444no—
340C2×C4—442no—
341C2×C4#6693511yescharacteristic
342C2×C4#6693511yescharacteristic
343C2×C4#6693711yescharacteristic
344C2×C4#6693711yescharacteristic
345C2×C4#6698311yescharacteristic
346C2×C4#6698512yes—
347C2×C4#6699311yescharacteristic
348C2×C4#6700312yes—
349C8—81no—
350C8—442no—
351C8—442no—
352C22—21no—
353C22—21no—
354C22—81no—
355C22—81no—
356C22—81no—
357C22—888no—
358C22—882no—
359C22—882no—
360C22—882no—
361C22#1062257311yescharacteristic
362C22#1062265012yes—
363C4—21no—
364C4—21no—
365C4—44no—
366C4—81no—
367C4—882no—
368C4#1062243512yes—
369C4#1062243812yes—
370C4#1062262912yes—
371C4#1062267211yescharacteristic
372C4#1062268711yescharacteristic
373C2—22no—
374C2—161no—
375C2—1762no—
376C2#1306963011yescharacteristic
377C2#1306964411yescharacteristic
378C2#1306969211yescharacteristic
subgroupG/H
centerC22#10622573
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1962C2
socleC22×C11#392
prime radical#13079531C2
hypercenter#1962D11
hypocenterC11#10281
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1962

Complements

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

NH ≅ G/Ntype
1. #13079538C2semidirect
3. #13076973C2semidirect
4. #13067298C2semidirect
5. #13067285C2semidirect
6. #13066449C2semidirect
7. C11×#1962C2semidirect
125. #1962D11semidirect
310. C11#10281semidirect

Maximal subgroups

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

subgroupindex
#130795382
#130795312
#130769732
#130672982
#130672852
#130664492
C11×#19622
#1028111