Finite Group Databasebeta

← #14655616

Subgroups — #14655616

Order 2816.

578 conjugacy classes of subgroups; only the 105 normal subgroups are shown.

normal subgroups only

This group has 578 conjugacy classes of subgroups — too many to draw. Only its 105 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#13079012C211yesmaximal, characteristic, complemented
3#13069457C211yesmaximal, characteristic, complemented
4#13067297C211yesmaximal, characteristic, complemented
5#13067068C211yesmaximal, characteristic, complemented
6#13066453C211yesmaximal, characteristic, complemented
7C2×C11×#486C211yesmaximal, characteristic, complemented
8C2×C11×C4⋊Q8C2211yescharacteristic
9C2×C11×#127C2211yescharacteristic
10#10623008C2211yescharacteristic
11C11×#486—22no—
12C11×#486—22no—
13C2×C11×#102—22no—
14C2×C4×C8×C11C2211yescharacteristic
15#10622830—22no—
16C2×#66897—22no—
17#10622706—21no—
18#10622702—22no—
19#10622701—21no—
20#10622686—21no—
21#10622685—22no—
22#10622683—21no—
23#10622579—22no—
24#10622538C2211yescharacteristic
25#10622537C2211yescharacteristic
26C4×#4318C2211yescharacteristic
27#10622184—22no—
28#10622097—22no—
29C22×Q8×C11—21no—
30C22×D4×C11—21no—
31C22×D4×C11—21no—
32C22×D4×C11D412yes—
33C2×#4339—21no—
34C22×C8×C11—21no—
35C11×C4⋊Q8—21no—
36C11×C4⋊Q8—21no—
37C11×C4⋊Q8—21no—
38C11×C4⋊Q8D412yes—
39C11×#127—21no—
40C11×#127—21no—
41C11×#127—21no—
42C11×#127—21no—
43C2×C11×C4⋊C4—21no—
44C2×C11×C4⋊C4—21no—
45C2×C42×C11C2311yescharacteristic
46C2×#4323—24no—
47#66983—21no—
48#66983—21no—
49C2×#4318—21no—
50C2×#4318D412yes—
51#66928—21no—
52#66927D411yescharacteristic
53C4×D44—21no—
54C4×D44—21no—
55#66922D411yescharacteristic
56C11×#102—28no—
57C4×C8×C11—21no—
58C4×C8×C11D412yes—
59#66897—44no—
60#66896—24no—
61C22⋊(C11⋊C8)—21no—
62#66874—24no—
63#66873—24no—
64C4⋊(C11⋊C8)—21no—
65C4⋊(C11⋊C8)—21no—
66C4⋊(C11⋊C8)D412yes—
67#66867—21no—
68C4×C11⋊C8—21no—
69C4×C11⋊C8—21no—
70#10160—111nomaximal, Sylow
71C24×C11—22no—
72C2×Q8×C11—22no—
73C2×Q8×C11—41no—
74C2×Q8×C11—82no—
75C2×D4×C11—22no—
76C2×D4×C11—22no—
77C2×D4×C11—44no—
78C2×D4×C11—41no—
79C2×D4×C11—41no—
80C2×D4×C11—41no—
81C2×D4×C11—41no—
82C2×D4×C11—42no—
83C2×D4×C11—42no—
84C2×D4×C11—82no—
85C22×C4×C11—41no—
86C22×C4×C11C2×D411yescharacteristic
87C22×C4×C11C2×D411yescharacteristic
88C22×C4×C11#4111yescharacteristic
89C2×C22⋊D11—41no—
90#4339—42no—
91#4339—42no—
92C2×D44—21no—
93C2×D44—21no—
94C2×D44—21no—
95C2×C4×D11—41no—
96C2×Dic22—21no—
97C2×C8×C11—22no—
98C2×C8×C11—42no—
99C11×C4⋊C4—22no—
100C11×C4⋊C4—22no—
101C11×C4⋊C4—41no—
102C11×C4⋊C4—41no—
103C42×C11C2×D411yescharacteristic
104C42×C11C2×D411yescharacteristic
105C42×C11C2×D411yescharacteristic
106C42×C11C2×D411yescharacteristic
107#4323—84no—
108(C2×D11)⋊C4—41no—
109(C2×D11)⋊C4—41no—
110C4⋊Dic11—21no—
111C4⋊Dic11—21no—
112#4318—22no—
113#4318—22no—
114#4318—42no—
115C2×C11⋊C8—22no—
116C2×C11⋊C8—22no—
117C2×C11⋊C8—41no—
118#3205—111no—
119#3141—111no—
120C2×#486D1111yescharacteristic, complemented
121#1965—111no—
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—
131Q8×C11—82no—
132Q8×C11—82no—
133D4×C11—44no—
134D4×C11—44no—
135D4×C11—82no—
136D4×C11—82no—
137D4×C11—82no—
138D4×C11—81no—
139D4×C11—81no—
140C2×C4×C11—22no—
141C2×C4×C11—22no—
142C2×C4×C11—42no—
143C2×C4×C11—82no—
144C2×C4×C11#12011yescharacteristic
145C2×C4×C11#12011yescharacteristic
146C2×C4×C11#12011yescharacteristic
147C2×C4×C11#12111yescharacteristic
148C2×C4×C11#12111yescharacteristic
149C2×C4×C11#12711yescharacteristic
150C2×C4×C11#13512yes—
151C2×C4×C11AGL(1,ℤ/8)12yes—
152C22⋊D11—82no—
153C2×Dic11—41no—
154D44—42no—
155D44—42no—
156D44—42no—
157C4×D11—81no—
158C4×D11—81no—
159Dic22—42no—
160C8×C11—42no—
161C11⋊C8—42no—
162C11⋊C8—42no—
163C11⋊C8—81no—
164#532—111no—
165C2×C4⋊Q8C2×D1111yescharacteristic
166C2×#127C2×D1111yescharacteristic
167#493—221no—
168#489—222no—
169#487—221no—
170#486—22no—
171#486—22no—
172#486—221no—
173#486—221no—
174#459—222no—
175#447—222no—
176#431—111no—
177#423—111no—
178#417—222no—
179C2×#102—22no—
180C2×#100—222no—
181C4×M16—111no—
182C2×C4×C8C2×D1111yescharacteristic
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—82no—
199C4×C11#44912yes—
200C4×C11#45512yes—
201C4×C11#47212yes—
202C4×C11#49511yescharacteristic
203C4×C11#49611yescharacteristic
204Dic11—81no—
205C2×#41—221no—
206C22×Q8—21no—
207C22×D4—21no—
208C22×D4—21no—
209C22×D4C22⋊D1112yes—
210C2×D8—224no—
211C2×M16—112no—
212C2×M16—221no—
213C22×C8—21no—
214C4⋊Q8—21no—
215C4⋊Q8—21no—
216C4⋊Q8—21no—
217C4⋊Q8—111no—
218C4⋊Q8C22⋊D1112yes—
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—21no—
230C2×C4⋊C4—21no—
231C2×C42C22×D1111yescharacteristic
232C4⋊C8—112no—
233C4⋊C8—221no—
234C4⋊C8—221no—
235#103—224no—
236#102—28no—
237#102—224no—
238#102—224no—
239#100—444no—
240C22⋊C8—221no—
241#97—221no—
242C4×C8—21no—
243C4×C8—221no—
244C4×C8—221no—
245C4×C8C22⋊D1112yes—
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—22no—
256C2×Q8—41no—
257C2×Q8—82no—
258C2×Q8—221no—
259C2×D4—22no—
260C2×D4—22no—
261C2×D4—44no—
262C2×D4—42no—
263C2×D4—42no—
264C2×D4—41no—
265C2×D4—41no—
266C2×D4—41no—
267C2×D4—41no—
268C2×D4—82no—
269C2×D4—221no—
270C2×D4—221no—
271C2×D4—221no—
272C2×D4—441no—
273C22×C4—41no—
274C22×C4—441no—
275C22×C4D4×D1111yescharacteristic
276C22×C4#434111yescharacteristic
277C22×C4C2×C22⋊D1111yescharacteristic
278D8—884no—
279M16—222no—
280M16—222no—
281M16—442no—
282C2×C8—22no—
283C2×C8—42no—
284C2×C8—222no—
285C2×C8—222no—
286C2×C8—441no—
287C4⋊C4—22no—
288C4⋊C4—22no—
289C4⋊C4—41no—
290C4⋊C4—41no—
291C4⋊C4—221no—
292C4⋊C4—221no—
293C22⋊C4—441no—
294C22⋊C4—441no—
295C42D4×D1111yescharacteristic
296C42D4×D1111yescharacteristic
297C42C2×C22⋊D1111yescharacteristic
298C42C2×C22⋊D1111yescharacteristic
299C11#1016011yescharacteristic, complemented, Sylow
300C23—42no—
301C23—44no—
302C23—82no—
303C23—82no—
304C23—441no—
305C23#6699211yescharacteristic
306Q8—82no—
307Q8—82no—
308Q8—442no—
309D4—44no—
310D4—44no—
311D4—82no—
312D4—82no—
313D4—81no—
314D4—82no—
315D4—81no—
316D4—442no—
317D4—442no—
318D4—442no—
319D4—882no—
320C2×C4—22no—
321C2×C4—22no—
322C2×C4—42no—
323C2×C4—82no—
324C2×C4—441no—
325C2×C4—881no—
326C2×C4—881no—
327C2×C4#6696712yes—
328C2×C4#6696912yes—
329C2×C4#6699011yescharacteristic
330C2×C4#6699011yescharacteristic
331C2×C4#6699111yescharacteristic
332C2×C4#6699211yescharacteristic
333C2×C4#6699311yescharacteristic
334C2×C4#6700611yescharacteristic
335C8—42no—
336C8—442no—
337C8—442no—
338C8—881no—
339C22—21no—
340C22—21no—
341C22—82no—
342C22—82no—
343C22—82no—
344C22—164no—
345C22—881no—
346C22—881no—
347C22—881no—
348C22#1062277812yes—
349C22#1062283611yescharacteristic
350C4—21no—
351C4—21no—
352C4—82no—
353C4—881no—
354C4#1062267412yes—
355C4#1062277312yes—
356C4#1062278111yescharacteristic
357C4#1062278512yes—
358C4#1062278911yescharacteristic
359C2—22no—
360C2—162no—
361C2—1761no—
362C2#1306964511yescharacteristic
363C2#1306969011yescharacteristic
364C2#1306972311yescharacteristic
subgroupG/H
centerC22#10622836
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC2×C11×#486C2
socleC22×C11#392
prime radical#13079534C2
hypercenterC2×#486D11
hypocenterC11#10160
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#486

Complements

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

NH ≅ G/Ntype
2. #13079012C2semidirect
3. #13069457C2semidirect
4. #13067297C2semidirect
5. #13067068C2semidirect
6. #13066453C2semidirect
7. C2×C11×#486C2semidirect
120. C2×#486D11semidirect
299. C11#10160semidirect

Maximal subgroups

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

subgroupindex
#130795342
#130790122
#130694572
#130672972
#130670682
#130664532
C2×C11×#4862
#1016011