Finite Group Databasebeta

← #14643013

Subgroups — #14643013

Order 2816.

434 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 434 conjugacy classes of subgroups — too many to draw. Only its 81 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#13075545C211yesmaximal, characteristic
2#13070145C211yesmaximal, characteristic
3#13070093C211yesmaximal, characteristic, complemented
4#13066439C211yesmaximal, characteristic, complemented
5#13066438C211yesmaximal, characteristic, complemented
6#13066436C211yesmaximal, characteristic
7C11×#2084C211yesmaximal, characteristic, complemented
8C2×#66947—21no—
9C2×C11×#106—21no—
10C11×#389C2211yescharacteristic
11C11×#384C2211yescharacteristic
12#10622606—21no—
13#10622602—21no—
14#10622597—21no—
15C2×#66873—21no—
16C2×#66872—21no—
17C2×#66871—21no—
18#10622552C2211yescharacteristic
19#10622541C2211yescharacteristic
20#10622287—21no—
21#10622281—21no—
22C11×#340—21no—
23C11×#336C2211yescharacteristic
24#10622167—21no—
25#10622162C2211yescharacteristic
26#10622162C2211yescharacteristic
27C22×D44D411yescharacteristic
28C22×C4×D11—21no—
29C22×C8×C11—21no—
30C2×C11×C4⋊C4—21no—
31C2×C11×C4⋊C4—21no—
32C2×C11×C4⋊C4—21no—
33C2×C11×C4⋊C4—21no—
34C2×C11×C4⋊C4D411yescharacteristic
35C2×C11×C4⋊C4D411yescharacteristic
36C2×C42×C11C2311yescharacteristic
37C2×(C2×D11)⋊C4—21no—
38C2×(C2×D11)⋊C4—21no—
39C2×(C2×D11)⋊C4—21no—
40C2×(C2×D11)⋊C4—21no—
41C2×(C2×D11)⋊C4—21no—
42C2×C4⋊Dic11D411yescharacteristic
43C2×C4⋊Dic11D411yescharacteristic
44C2×C4⋊Dic11D411yescharacteristic
45C2×Dic11⋊C4—21no—
46C2×Dic11⋊C4—21no—
47C22×C11⋊C8—21no—
48C22×C11⋊C8—21no—
49#66947—42no—
50#66947—42no—
51C11×#106—42no—
52C11×#95—21no—
53C11⋊#95—21no—
54C11⋊#95—21no—
55C11⋊#95—21no—
56C11⋊#95—21no—
57#66873—42no—
58#66872—42no—
59#66871—42no—
60#7819—111nomaximal, Sylow
61C23×D11—21no—
62C22×C4×C11—21no—
63C22×C4×C11—21no—
64C22×C4×C11—41no—
65C22×C4×C11C2×D411yescharacteristic
66C22×C4×C11C2×D411yescharacteristic
67C22×C4×C11C2×D411yescharacteristic
68C22×Dic11—21no—
69C22×Dic11—21no—
70C22×Dic11—21no—
71C2×D44—21no—
72C2×D44—41no—
73C2×D44—41no—
74C2×D44SD1612yes—
75C2×C4×D11—42no—
76C2×C4×D11—81no—
77C2×C4×D11—81no—
78C2×C8×C11—22no—
79C2×C8×C11—41no—
80C2×C8×C11—41no—
81C11×C4⋊C4—21no—
82C11×C4⋊C4—21no—
83C11×C4⋊C4—41no—
84C11×C4⋊C4—41no—
85C11×C4⋊C4—41no—
86C11×C4⋊C4—41no—
87C11×C4⋊C4—41no—
88C11×C4⋊C4—41no—
89C11×C4⋊C4—41no—
90C11×C4⋊C4—41no—
91C11×C4⋊C4—41no—
92C42×C11—41no—
93(C2×D11)⋊C4—42no—
94(C2×D11)⋊C4—42no—
95(C2×D11)⋊C4—42no—
96(C2×D11)⋊C4—41no—
97(C2×D11)⋊C4—41no—
98(C2×D11)⋊C4—41no—
99(C2×D11)⋊C4—41no—
100C4⋊Dic11—21no—
101C4⋊Dic11—21no—
102C4⋊Dic11—41no—
103C4⋊Dic11—41no—
104Dic11⋊C4—41no—
105Dic11⋊C4—41no—
106Dic11⋊C4—81no—
107C2×C11⋊C8—22no—
108C2×C11⋊C8—22no—
109C2×C11⋊C8—41no—
110C2×C11⋊C8—41no—
111C2×C11⋊C8—41no—
112C2×C11⋊C8—41no—
113#2724—111no—
114#2093—111no—
115#2084—111no—
116#2084D1111yescharacteristic, complemented
117#1271—111no—
118#1271—111no—
119#1270—111no—
120C23×C11#12011yescharacteristic
121C22×D11—22no—
122C22×D11—41no—
123C22×D11—41no—
124C22×D11—41no—
125C22×D11—41no—
126C22×D11—41no—
127C22×D11—41no—
128C2×C4×C11—21no—
129C2×C4×C11—21no—
130C2×C4×C11—21no—
131C2×C4×C11—21no—
132C2×C4×C11—21no—
133C2×C4×C11—21no—
134C2×C4×C11—41no—
135C2×C4×C11—41no—
136C2×C4×C11—41no—
137C2×C4×C11—41no—
138C2×C4×C11—41no—
139C2×C4×C11—41no—
140C2×C4×C11—81no—
141C2×C4×C11—81no—
142C2×C4×C11—81no—
143C2×C4×C11C2×SD1611yescharacteristic
144C2×C4×C11#13511yescharacteristic
145C2×C4×C11#13511yescharacteristic
146C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
147C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
148C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
149C2×Dic11—41no—
150C2×Dic11—41no—
151C2×Dic11—41no—
152C2×Dic11—41no—
153C2×Dic11—41no—
154C2×Dic11—41no—
155C2×Dic11—41no—
156C2×Dic11—41no—
157C2×Dic11—41no—
158D44—42no—
159D44—81no—
160C4×D11—84no—
161C8×C11—42no—
162C11⋊C8—42no—
163C11⋊C8—42no—
164C2×#123—221no—
165C2×#107—221no—
166C2×#106—21no—
167C2×#106—221no—
168C2×#102—221no—
169#398—221no—
170#397—221no—
171#397—221no—
172#390—111no—
173#389—111no—
174#389C2×D1111yescharacteristic
175#385—221no—
176#385—221no—
177#384C2×D1111yescharacteristic
178#340—21no—
179#340—221no—
180#336—111no—
181#336—111no—
182#336C2×D1111yescharacteristic
183C22×C11#44911yescharacteristic
184C22×C11#44911yescharacteristic
185C22×C11#45011yescharacteristic
186C22×C11#45311yescharacteristic
187C22×C11#45611yescharacteristic
188C22×C11#45611yescharacteristic
189C22×C11#45811yescharacteristic
190C2×D11—42no—
191C2×D11—42no—
192C2×D11—42no—
193C2×D11—81no—
194C2×D11—81no—
195C2×D11—81no—
196C2×D11—81no—
197C4×C11—21no—
198C4×C11—21no—
199C4×C11—21no—
200C4×C11—21no—
201C4×C11—21no—
202C4×C11—21no—
203C4×C11—81no—
204C4×C11—81no—
205C4×C11—161no—
206Dic11—81no—
207Dic11—81no—
208Dic11—81no—
209C22×D4—111no—
210C23×C4—221no—
211C22×C8—21no—
212C22×C8—221no—
213C22×C8—221no—
214#123—442no—
215#123—442no—
216C2×C4⋊C4—21no—
217C2×C4⋊C4—21no—
218C2×C4⋊C4—21no—
219C2×C4⋊C4—21no—
220C2×C4⋊C4—111no—
221C2×C4⋊C4—111no—
222C2×C4⋊C4—111no—
223C2×C4⋊C4—221no—
224C2×C4⋊C4—221no—
225C2×C4⋊C4C22⋊D1111yescharacteristic
226C2×C4⋊C4C22⋊D1111yescharacteristic
227C2×C22⋊C4—221no—
228C2×C22⋊C4—221no—
229C2×C22⋊C4—221no—
230C2×C22⋊C4—221no—
231C2×C22⋊C4—221no—
232C2×C42C22×D1111yescharacteristic
233#107—442no—
234#106—42no—
235#106—442no—
236#102—442no—
237#95—21no—
238#95—221no—
239#95—221no—
240#95—221no—
241#95—221no—
242C2×C11#160911yescharacteristic
243C2×C11#160911yescharacteristic
244C2×C11#161311yescharacteristic
245C2×C11#162011yescharacteristic
246C2×C11#165411yescharacteristic
247C2×C11#165411yescharacteristic
248C2×C11#166011yescharacteristic
249D11—82no—
250C24—221no—
251C2×D4—112no—
252C2×D4—221no—
253C2×D4—441no—
254C2×D4—441no—
255C22×C4—21no—
256C22×C4—21no—
257C22×C4—41no—
258C22×C4—221no—
259C22×C4—221no—
260C22×C4—221no—
261C22×C4—442no—
262C22×C4—881no—
263C22×C4—881no—
264C22×C4D4×D1111yescharacteristic
265C22×C4D4×D1111yescharacteristic
266C22×C4C2×C22⋊D1111yescharacteristic
267C2×C8—22no—
268C2×C8—41no—
269C2×C8—41no—
270C2×C8—222no—
271C2×C8—222no—
272C2×C8—441no—
273C2×C8—441no—
274C2×C8—441no—
275C2×C8—441no—
276C4⋊C4—21no—
277C4⋊C4—21no—
278C4⋊C4—41no—
279C4⋊C4—41no—
280C4⋊C4—41no—
281C4⋊C4—41no—
282C4⋊C4—41no—
283C4⋊C4—41no—
284C4⋊C4—41no—
285C4⋊C4—41no—
286C4⋊C4—41no—
287C4⋊C4—221no—
288C4⋊C4—221no—
289C4⋊C4—441no—
290C4⋊C4—441no—
291C4⋊C4—441no—
292C4⋊C4—441no—
293C4⋊C4—881no—
294C22⋊C4—442no—
295C22⋊C4—442no—
296C22⋊C4—442no—
297C22⋊C4—441no—
298C22⋊C4—441no—
299C22⋊C4—441no—
300C22⋊C4—441no—
301C42—41no—
302C11#781911yescharacteristic, complemented, Sylow
303C23—222no—
304C23—441no—
305C23—441no—
306C23—441no—
307C23—441no—
308C23—441no—
309C23—441no—
310C23#6699011yescharacteristic
311D4—442no—
312D4—881no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—41no—
320C2×C4—41no—
321C2×C4—41no—
322C2×C4—41no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—81no—
326C2×C4—81no—
327C2×C4—81no—
328C2×C4—441no—
329C2×C4—441no—
330C2×C4—441no—
331C2×C4—441no—
332C2×C4—441no—
333C2×C4—441no—
334C2×C4—441no—
335C2×C4—441no—
336C2×C4—441no—
337C2×C4—884no—
338C2×C4SD16×D1111yescharacteristic
339C2×C4#6696711yescharacteristic
340C2×C4#6696711yescharacteristic
341C2×C4#6696911yescharacteristic
342C2×C4#6698511yescharacteristic
343C2×C4#6700311yescharacteristic
344C8—42no—
345C8—442no—
346C8—442no—
347C22—442no—
348C22—442no—
349C22—442no—
350C22—881no—
351C22—881no—
352C22—881no—
353C22—881no—
354C22#1062265011yescharacteristic
355C22#1062266611yescharacteristic
356C22#1062270811yescharacteristic
357C22#1062278211yescharacteristic
358C22#1062278511yescharacteristic
359C22#1062281111yescharacteristic
360C22#1062281811yescharacteristic
361C4—21no—
362C4—21no—
363C4—21no—
364C4—21no—
365C4—21no—
366C4—21no—
367C4—81no—
368C4—81no—
369C4—161no—
370C4—881no—
371C4—881no—
372C4—881no—
373C2—882no—
374C2#1306761111yescharacteristic
375C2#1306761211yescharacteristic
376C2#1306763411yescharacteristic
377C2#1306767411yescharacteristic
378C2#1306789711yescharacteristic
379C2#1306789811yescharacteristic
380C2#1306792611yescharacteristic
subgroupG/H
centerC23#66990
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#2084C2
socleC23×C11#120
prime radicalC22×D44D4
hypercenter#2084D11
hypocenterC11#7819
LCSG ▷ C2×C42×C11 ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2084

Complements

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

NH ≅ G/Ntype
3. #13070093C2semidirect
4. #13066439C2semidirect
5. #13066438C2semidirect
7. C11×#2084C2semidirect
116. #2084D11semidirect
302. C11#7819semidirect

Maximal subgroups

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

subgroupindex
#130755452
#130701452
#130700932
#130664392
#130664382
#130664362
C11×#20842
#781911