Finite Group Databasebeta

← #14656428

Subgroups — #14656428

Order 2816.

678 conjugacy classes of subgroups; only the 111 normal subgroups are shown.

normal subgroups only

This group has 678 conjugacy classes of subgroups — too many to draw. Only its 111 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#13079734C211yesmaximal, characteristic, complemented
2#13079531C211yesmaximal, characteristic
3#13076973C211yesmaximal, characteristic, complemented
4#13067289C211yesmaximal, 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#10622701—21no—
16#10622691—21no—
17#10622686—21no—
18#10622683—21no—
19#10622649—22no—
20#10622646—22no—
21#10622628—22no—
22#10622620—22no—
23#10622552—22no—
24#10622552—22no—
25#10622538C2211yescharacteristic
26#10622538C2211yescharacteristic
27#10622123—22no—
28#10622120—22no—
29C2×C11×#41—21no—
30C22×D44—21no—
31C22×D44—21no—
32C22×D44D412yes—
33C22×Dic22—21no—
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×#4323—24no—
47C2×(C2×D11)⋊C4—28no—
48C2×C4⋊Dic11—21no—
49C2×C4⋊Dic11D412yes—
50#66928—44no—
51#66928—44no—
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—
63#66896—24no—
64C22⋊(C11⋊C8)—21no—
65C22⋊(C11⋊C8)—21no—
66#66873—24no—
67#66871—24no—
68C4⋊(C11⋊C8)D412yes—
69C4⋊(C11⋊C8)D412yes—
70C4×C11⋊C8—21no—
71C4×C11⋊C8—21no—
72#10284—111nomaximal, Sylow
73C23×D11—22no—
74C11×#41—42no—
75C11×#41—42no—
76C2×Q8×C11—21no—
77C2×D4×C11—21no—
78C2×D4×C11—21no—
79C2×D4×C11—21no—
80C2×D4×C11—41no—
81C22×C4×C11—22no—
82C22×C4×C11—41no—
83C22×C4×C11C2×D411yescharacteristic
84C22×C4×C11C2×D411yescharacteristic
85C22×C4×C11C2×D411yescharacteristic
86C22×Dic11—22no—
87C2×D44—22no—
88C2×D44—22no—
89C2×D44—44no—
90C2×D44—44no—
91C2×D44—41no—
92C2×D44—41no—
93C2×D44—41no—
94C2×D44—41no—
95C2×D44—42no—
96C2×D44—42no—
97C2×Dic22—41no—
98C2×Dic22—41no—
99C2×Dic22—42no—
100C2×Dic22—42no—
101C11×M16—42no—
102C2×C8×C11—41no—
103C11×C4⋊C4—21no—
104C11×C4⋊C4—21no—
105C11×C22⋊C4—41no—
106C11×C22⋊C4—41no—
107C42×C11—22no—
108C42×C11—42no—
109C42×C11—42no—
110C42×C11D814yescomplemented
111C42×C11C2×D411yescharacteristic
112C42×C11C2×D411yescharacteristic
113C42×C11C2×D411yescharacteristic
114C42×C11#4111yescharacteristic
115#4323—84no—
116(C2×D11)⋊C4—416no—
117C4⋊Dic11—22no—
118C4⋊Dic11—22no—
119C4⋊Dic11—41no—
120C4⋊Dic11—41no—
121C2×C11⋊C8—22no—
122C2×C11⋊C8—22no—
123#3226—111no—
124#3205—111no—
125#2858—111no—
126#1962D1111yescharacteristic, complemented
127#1546—111no—
128#1545—111no—
129#1276—111no—
130C23×C11—41no—
131C23×C11#12011yescharacteristic
132C22×D11—44no—
133C22×D11—44no—
134C22×D11—42no—
135C22×D11—44no—
136Q8×C11—42no—
137D4×C11—42no—
138D4×C11—42no—
139D4×C11—42no—
140D4×C11—82no—
141C2×C4×C11—22no—
142C2×C4×C11—22no—
143C2×C4×C11—24no—
144C2×C4×C11—42no—
145C2×C4×C11—42no—
146C2×C4×C11—41no—
147C2×C4×C11—81no—
148C2×C4×C11—81no—
149C2×C4×C11#12011yescharacteristic
150C2×C4×C11#12011yescharacteristic
151C2×C4×C11#12111yescharacteristic
152C2×C4×C11#12111yescharacteristic
153C2×C4×C11#12111yescharacteristic
154C2×C4×C11#12711yescharacteristic
155C2×C4×C11C2×D812yes—
156C2×C4×C11AGL(1,ℤ/8)12yes—
157C2×Dic11—42no—
158C2×Dic11—44no—
159D44—44no—
160D44—82no—
161D44—82no—
162D44—82no—
163D44—82no—
164D44—81no—
165D44—81no—
166Dic22—82no—
167Dic22—81no—
168Dic22—81no—
169C8×C11—81no—
170C11⋊C8—42no—
171C11⋊C8—42no—
172#532C2×D1111yescharacteristic
173C2×C4⋊Q8—111no—
174C2×#127—111no—
175C2×#124—222no—
176#500—221no—
177#493—221no—
178#486—221no—
179#486—221no—
180#480—222no—
181#474—222no—
182#459—222no—
183#447—222no—
184#431—111no—
185#431—111no—
186#423C2×D1111yescharacteristic
187C2×#104—22no—
188#390—222no—
189#390—222no—
190C43C2×D1111yescharacteristic
191#332—222no—
192#331—222no—
193C22×C11—21no—
194C22×C11—21no—
195C22×C11—81no—
196C22×C11—81no—
197C22×C11—81no—
198C22×C11#39211yescharacteristic
199C22×C11#44712yes—
200C2×D11—88no—
201C2×D11—82no—
202C2×D11—82no—
203C2×D11—82no—
204C4×C11—21no—
205C4×C11—21no—
206C4×C11—44no—
207C4×C11—81no—
208C4×C11#45412yes—
209C4×C11#45512yes—
210C4×C11#45912yes—
211C4×C11#49311yescharacteristic
212C4×C11#49611yescharacteristic
213Dic11—82no—
214C2×#41—21no—
215C22×Q8—221no—
216C22×D4—112no—
217C22×D4—221no—
218C22×D4—221no—
219C2×D8—224no—
220C2×M16—21no—
221C4⋊Q8—221no—
222C4⋊Q8—221no—
223C4⋊Q8—221no—
224C4⋊Q8—221no—
225C4⋊Q8D4411yescharacteristic
226#127—221no—
227#127—221no—
228#127—221no—
229#127—221no—
230#127D4411yescharacteristic
231#124—21no—
232#124—444no—
233#124—444no—
234#121—21no—
235#121—21no—
236C4×D4—21no—
237C4×D4—21no—
238C2×C4⋊C4—112no—
239C2×C4⋊C4—221no—
240C2×C22⋊C4—228no—
241C2×C42—21no—
242C2×C42—21no—
243C2×C42C22⋊D1112yes—
244C2×C42C22×D1111yescharacteristic
245#107—224no—
246C4⋊C8—21no—
247C4⋊C8—21no—
248C4⋊C8—112no—
249C4⋊C8—112no—
250#104—44no—
251#102—224no—
252#102—224no—
253C22⋊C8—221no—
254C22⋊C8—221no—
255C4×C8—221no—
256C4×C8—221no—
257C2×C11—22no—
258C2×C11—161no—
259C2×C11#200311yescharacteristic
260C2×C11#200411yescharacteristic
261C2×C11#201111yescharacteristic
262D11—162no—
263C24—222no—
264#41—42no—
265#41—42no—
266C2×Q8—21no—
267C2×Q8—441no—
268C2×Q8—442no—
269C2×Q8—441no—
270C2×Q8—442no—
271C2×D4—21no—
272C2×D4—21no—
273C2×D4—21no—
274C2×D4—41no—
275C2×D4—222no—
276C2×D4—222no—
277C2×D4—444no—
278C2×D4—444no—
279C2×D4—441no—
280C2×D4—441no—
281C2×D4—441no—
282C2×D4—442no—
283C2×D4—441no—
284C2×D4—442no—
285C22×C4—22no—
286C22×C4—41no—
287C22×C4—222no—
288C22×C4D4×D1111yescharacteristic
289C22×C4D4×D1111yescharacteristic
290C22×C4C2×C22⋊D1111yescharacteristic
291D8—884no—
292M16—42no—
293C2×C8—41no—
294C2×C8—222no—
295C2×C8—222no—
296C4⋊C4—21no—
297C4⋊C4—21no—
298C4⋊C4—222no—
299C4⋊C4—222no—
300C4⋊C4—441no—
301C4⋊C4—441no—
302C22⋊C4—41no—
303C22⋊C4—41no—
304C22⋊C4—4416no—
305C42—22no—
306C42—42no—
307C42—42no—
308C42#432314yescomplemented
309C42C2×D4411yescharacteristic
310C42#433911yescharacteristic
311C42D4×D1111yescharacteristic
312C42D4×D1111yescharacteristic
313C11#1028411yescharacteristic, complemented, Sylow
314C23—41no—
315C23—444no—
316C23—444no—
317C23—442no—
318C23—444no—
319C23#6699011yescharacteristic
320Q8—42no—
321Q8—882no—
322Q8—881no—
323Q8—881no—
324D4—42no—
325D4—42no—
326D4—42no—
327D4—82no—
328D4—444no—
329D4—882no—
330D4—882no—
331D4—882no—
332D4—881no—
333D4—881no—
334D4—882no—
335C2×C4—22no—
336C2×C4—22no—
337C2×C4—24no—
338C2×C4—42no—
339C2×C4—42no—
340C2×C4—41no—
341C2×C4—81no—
342C2×C4—81no—
343C2×C4—442no—
344C2×C4—444no—
345C2×C4#6693511yescharacteristic
346C2×C4#6693511yescharacteristic
347C2×C4#6693711yescharacteristic
348C2×C4#6693711yescharacteristic
349C2×C4#6698311yescharacteristic
350C2×C4C2×#432312yes—
351C2×C4#6699311yescharacteristic
352C2×C4#6700212yes—
353C8—81no—
354C8—442no—
355C8—442no—
356C22—21no—
357C22—21no—
358C22—81no—
359C22—81no—
360C22—81no—
361C22—888no—
362C22—882no—
363C22—882no—
364C22—882no—
365C22#1062257311yescharacteristic
366C22#1062264912yes—
367C4—21no—
368C4—21no—
369C4—44no—
370C4—81no—
371C4—882no—
372C4#1062243812yes—
373C4#1062244012yes—
374C4#1062262812yes—
375C4#1062267111yescharacteristic
376C4#1062268611yescharacteristic
377C2—22no—
378C2—161no—
379C2—1762no—
380C2#1306963711yescharacteristic
381C2#1306964411yescharacteristic
382C2#1306968611yescharacteristic
subgroupG/H
centerC22#10622573
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1962C2
socleC22×C11#392
prime radical#13079531C2
hypercenter#1962D11
hypocenterC11#10284
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. #13079734C2semidirect
3. #13076973C2semidirect
4. #13067289C2semidirect
5. #13067285C2semidirect
6. #13066449C2semidirect
7. C11×#1962C2semidirect
110. C42×C11D8semidirect
126. #1962D11semidirect
308. C42#4323semidirect
313. C11#10284semidirect

Maximal subgroups

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

subgroupindex
#130797342
#130795312
#130769732
#130672892
#130672852
#130664492
C11×#19622
#1028411