Finite Group Databasebeta

← #14655620

Subgroups — #14655620

Order 2816.

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

normal subgroups only

This group has 578 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#13079534C211yesmaximal, characteristic
2#13079010C211yesmaximal, characteristic, complemented
3C2×#10622683C211yesmaximal, characteristic, complemented
4#13067298C211yesmaximal, characteristic, complemented
5#13067066C211yesmaximal, characteristic, complemented
6#13066454C211yesmaximal, characteristic, complemented
7C11×#1965C211yesmaximal, characteristic, complemented
8C2×C11×#127C2211yescharacteristic
9#10623008C2211yescharacteristic
10C2×#66922C2211yescharacteristic
11C11×#423C2211yescharacteristic
12C2×C11×#100—22no—
13C4×C11×M16C2211yescharacteristic
14#10622830—22no—
15C2×#66896—22no—
16#10622746—22no—
17#10622686—21no—
18#10622685—22no—
19#10622683—22no—
20#10622683—21no—
21#10622683—22no—
22#10622538C2211yescharacteristic
23C2×C4×C11⋊C8C2211yescharacteristic
24#10622327—22no—
25#10622307—21no—
26#10622294—21no—
27#10622121—22no—
28#10622119—22no—
29C22×D4×C11—21no—
30C22×D4×C11—21no—
31C22×D4×C11D412yes—
32C2×#4339—21no—
33C22×Dic22—21no—
34C2×C11×M16—21no—
35C2×C11×M16D412yes—
36C11×#127—21no—
37C11×#127—21no—
38C11×#127—21no—
39C11×#127—21no—
40C2×C42×C11C2311yescharacteristic
41C2×#4323—24no—
42#66983—21no—
43#66983—21no—
44C2×C4⋊Dic11—21no—
45C2×C4⋊Dic11—21no—
46C22×C11⋊C8—21no—
47#66928—21no—
48#66927D411yescharacteristic
49C4×D44—21no—
50C4×D44—21no—
51#66922—21no—
52#66922—21no—
53#66922—21no—
54#66922D412yes—
55#66922D411yescharacteristic
56C11×C4⋊C8—21no—
57C11×C4⋊C8—21no—
58C11×#100—44no—
59C11×#97—21no—
60C4×C8×C11—21no—
61#66896—28no—
62#66896—24no—
63C22⋊(C11⋊C8)—21no—
64#66885—24no—
65#66880—24no—
66C4⋊(C11⋊C8)D412yes—
67C4×C11⋊C8—21no—
68C4×C11⋊C8—21no—
69C4×C11⋊C8D412yes—
70#10160—111nomaximal, Sylow
71C24×C11—22no—
72C2×D4×C11—22no—
73C2×D4×C11—22no—
74C2×D4×C11—44no—
75C2×D4×C11—41no—
76C2×D4×C11—41no—
77C2×D4×C11—41no—
78C2×D4×C11—41no—
79C2×D4×C11—42no—
80C2×D4×C11—42no—
81C2×D4×C11—82no—
82C22×C4×C11C2×D411yescharacteristic
83C22×C4×C11C2×D411yescharacteristic
84C22×C4×C11#4111yescharacteristic
85C2×C22⋊D11—41no—
86C22×Dic11—41no—
87#4339—42no—
88#4339—42no—
89C2×D44—21no—
90C2×D44—21no—
91C2×D44—21no—
92C2×C4×D11—41no—
93C2×Dic22—21no—
94C2×Dic22—22no—
95C2×Dic22—41no—
96C2×Dic22—82no—
97C11×M16—22no—
98C11×M16—22no—
99C11×M16—42no—
100C2×C8×C11—22no—
101C2×C8×C11—41no—
102C42×C11C2×D411yescharacteristic
103C42×C11C2×D411yescharacteristic
104C42×C11C2×D411yescharacteristic
105C42×C11C2×D411yescharacteristic
106#4323—84no—
107(C2×D11)⋊C4—41no—
108(C2×D11)⋊C4—41no—
109C4⋊Dic11—22no—
110C4⋊Dic11—22no—
111C4⋊Dic11—21no—
112C4⋊Dic11—21no—
113C4⋊Dic11—41no—
114C4⋊Dic11—41no—
115C2×C11⋊C8—22no—
116C2×C11⋊C8—22no—
117C2×C11⋊C8—42no—
118#3205—111no—
119#3141—111no—
120C2×#486—111no—
121#1965D1111yescharacteristic, complemented
122#1548—111no—
123#1492—111no—
124#1278—111no—
125C23×C11—42no—
126C23×C11—44no—
127C23×C11—82no—
128C23×C11—82no—
129C23×C11#12111yescharacteristic
130C22×D11—41no—
131D4×C11—44no—
132D4×C11—44no—
133D4×C11—82no—
134D4×C11—82no—
135D4×C11—82no—
136D4×C11—81no—
137D4×C11—81no—
138C2×C4×C11—22no—
139C2×C4×C11—22no—
140C2×C4×C11#12011yescharacteristic
141C2×C4×C11#12011yescharacteristic
142C2×C4×C11#12011yescharacteristic
143C2×C4×C11#12111yescharacteristic
144C2×C4×C11#12111yescharacteristic
145C2×C4×C11#12711yescharacteristic
146C2×C4×C11#13512yes—
147C2×C4×C11AGL(1,ℤ/8)12yes—
148C22⋊D11—82no—
149C2×Dic11—42no—
150C2×Dic11—41no—
151C2×Dic11—82no—
152D44—42no—
153D44—42no—
154D44—42no—
155C4×D11—81no—
156C4×D11—81no—
157Dic22—42no—
158Dic22—82no—
159Dic22—82no—
160C8×C11—42no—
161C8×C11—81no—
162C11⋊C8—42no—
163C11⋊C8—42no—
164#532—111no—
165C2×C4⋊Q8—111no—
166C2×#127C2×D1111yescharacteristic
167#493—221no—
168#489—222no—
169#487—221no—
170#486—221no—
171#486—222no—
172#486—222no—
173#486—221no—
174#459—222no—
175#447—222no—
176#431—111no—
177#423C2×D1111yescharacteristic
178#417—222no—
179C2×#102—222no—
180C2×#100—22no—
181C4×M16C2×D1111yescharacteristic
182C2×C4×C8—111no—
183#333—222no—
184D4⋊C8—222no—
185C22×C11—21no—
186C22×C11—21no—
187C22×C11—82no—
188C22×C11—82no—
189C22×C11—82no—
190C22×C11—164no—
191C22×C11#39211yescharacteristic
192C22×C11#46312yes—
193C2×D11—81no—
194C2×D11—81no—
195C2×D11—81no—
196C4×C11—21no—
197C4×C11—21no—
198C4×C11#44912yes—
199C4×C11#45512yes—
200C4×C11#47212yes—
201C4×C11#49511yescharacteristic
202C4×C11#49611yescharacteristic
203Dic11—81no—
204Dic11—82no—
205C2×#41—221no—
206C22×Q8—221no—
207C22×D4—21no—
208C22×D4—21no—
209C22×D4D4412yes—
210C2×D8—224no—
211C2×M16—21no—
212C2×M16C22⋊D1112yes—
213C22×C8—221no—
214C4⋊Q8—112no—
215C4⋊Q8—111no—
216C4⋊Q8—221no—
217C4⋊Q8—221no—
218C4⋊Q8—221no—
219#127—21no—
220#127—21no—
221#127—21no—
222#127—21no—
223#127—111no—
224#124—221no—
225#121—221no—
226#121—221no—
227C4×D4—221no—
228C4×D4—221no—
229C2×C4⋊C4—221no—
230C2×C4⋊C4—221no—
231C2×C42C22×D1111yescharacteristic
232C4⋊C8—21no—
233C4⋊C8—21no—
234C4⋊C8—112no—
235#103—224no—
236#102—224no—
237#102—228no—
238#102—224no—
239#100—44no—
240C22⋊C8—221no—
241#97—21no—
242C4×C8—21no—
243C4×C8—112no—
244C4×C8—221no—
245C4×C8—221no—
246C2×C11—22no—
247C2×C11—162no—
248C2×C11#200411yescharacteristic
249C2×C11#201211yescharacteristic
250C2×C11#201811yescharacteristic
251D11—161no—
252C24—22no—
253#41—442no—
254#41—442no—
255C2×Q8—222no—
256C2×Q8—221no—
257C2×Q8—441no—
258C2×Q8—882no—
259C2×D4—22no—
260C2×D4—22no—
261C2×D4—44no—
262C2×D4—41no—
263C2×D4—41no—
264C2×D4—42no—
265C2×D4—41no—
266C2×D4—41no—
267C2×D4—42no—
268C2×D4—82no—
269C2×D4—221no—
270C2×D4—221no—
271C2×D4—221no—
272C2×D4—441no—
273C22×C4—441no—
274C22×C4—441no—
275C22×C4C2×D4411yescharacteristic
276C22×C4#433911yescharacteristic
277C22×C4C2×C22⋊D1111yescharacteristic
278D8—884no—
279M16—22no—
280M16—22no—
281M16—42no—
282C2×C8—22no—
283C2×C8—41no—
284C2×C8—222no—
285C2×C8—222no—
286C2×C8—442no—
287C4⋊C4—222no—
288C4⋊C4—221no—
289C4⋊C4—221no—
290C4⋊C4—222no—
291C4⋊C4—441no—
292C4⋊C4—441no—
293C22⋊C4—441no—
294C22⋊C4—441no—
295C42D4×D1111yescharacteristic
296C42D4×D1111yescharacteristic
297C42D4×D1111yescharacteristic
298C42D4×D1111yescharacteristic
299C11#1016011yescharacteristic, complemented, Sylow
300C23—42no—
301C23—44no—
302C23—82no—
303C23—82no—
304C23—441no—
305C23#6698311yescharacteristic
306Q8—442no—
307Q8—882no—
308Q8—882no—
309D4—44no—
310D4—44no—
311D4—82no—
312D4—82no—
313D4—82no—
314D4—81no—
315D4—81no—
316D4—442no—
317D4—442no—
318D4—442no—
319D4—882no—
320C2×C4—22no—
321C2×C4—22no—
322C2×C4—441no—
323C2×C4—442no—
324C2×C4—882no—
325C2×C4—881no—
326C2×C4—881no—
327C2×C4#6693511yescharacteristic
328C2×C4#6693511yescharacteristic
329C2×C4#6693711yescharacteristic
330C2×C4#6693711yescharacteristic
331C2×C4#6698512yes—
332C2×C4#6699011yescharacteristic
333C2×C4#6699311yescharacteristic
334C2×C4#6700312yes—
335C8—42no—
336C8—81no—
337C8—442no—
338C8—442no—
339C22—21no—
340C22—21no—
341C22—82no—
342C22—82no—
343C22—82no—
344C22—164no—
345C22—881no—
346C22—881no—
347C22—881no—
348C22#1062257311yescharacteristic
349C22#1062262912yes—
350C4—21no—
351C4—21no—
352C4—881no—
353C4—882no—
354C4#1062235912yes—
355C4#1062236212yes—
356C4#1062265012yes—
357C4#1062267211yescharacteristic
358C4#1062268711yescharacteristic
359C2—22no—
360C2—162no—
361C2—1761no—
362C2#1306964711yescharacteristic
363C2#1306969211yescharacteristic
364C2#1306972411yescharacteristic
subgroupG/H
centerC22#10622573
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1965C2
socleC22×C11#392
prime radical#13079534C2
hypercenter#1965D11
hypocenterC11#10160
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1965

Complements

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

NH ≅ G/Ntype
2. #13079010C2semidirect
3. C2×#10622683C2semidirect
4. #13067298C2semidirect
5. #13067066C2semidirect
6. #13066454C2semidirect
7. C11×#1965C2semidirect
121. #1965D11semidirect
299. C11#10160semidirect

Maximal subgroups

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

subgroupindex
#130795342
#130790102
C2×#106226832
#130672982
#130670662
#130664542
C11×#19652
#1016011