Finite Group Databasebeta

← #14666083

Subgroups — #14666083

Order 2816.

394 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 394 conjugacy classes of subgroups — too many to draw. Only its 59 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#13069867C211yesmaximal, characteristic
2#13067635C211yesmaximal, characteristic
3#13067601C211yesmaximal, characteristic
4#13066640C211yesmaximal, characteristic, complemented
5#13066616C211yesmaximal, characteristic, complemented
6#13066564C211yesmaximal, characteristic, complemented
7C11×#2834C211yesmaximal, characteristic, complemented
8#10623024C2211yescharacteristic
9C11×#401—21no—
10C11×#399C2211yescharacteristic
11C11×#398—21no—
12C11×#398—21no—
13C11×#398—21no—
14C11×#397—21no—
15C11×#397C2211yescharacteristic
16C11×#385—21no—
17C11×#385C2211yescharacteristic
18#10622826—21no—
19#10622581—21no—
20#10622580—21no—
21C2×#66870—21no—
22#10622164C2211yescharacteristic
23#10622163C2211yescharacteristic
24#10622163C2211yescharacteristic
25#10622089—21no—
26#10622089—21no—
27C23×C4×C11D411yescharacteristic
28C22×C22⋊D11—21no—
29C2×C11×C4⋊C4—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×C11×C22⋊C4—21no—
37C2×C11×C22⋊C4—21no—
38C2×C11×C22⋊C4D411yescharacteristic
39C2×C11×C22⋊C4C2311yescharacteristic
40C2×C22⋊Dic11—21no—
41#66983—21no—
42#66983—21no—
43C2×(C2×D11)⋊C4—41no—
44#66939—41no—
45#66935—41no—
46C11×#95—21no—
47C11×#95—21no—
48C11×#95—21no—
49C11×#95—21no—
50C11×#95—21no—
51C11×#95—21no—
52C11×#95—21no—
53C11×#95D411yescharacteristic
54C11×#95D411yescharacteristic
55C11⋊#95—41no—
56C22⋊(C11⋊C8)—21no—
57C22⋊(C11⋊C8)—21no—
58#66873—41no—
59#66873—41no—
60#66872—41no—
61#66871—41no—
62#66870—42no—
63#12138—111nomaximal, Sylow
64C24×C11C2×D411yescharacteristic
65C23×D11—21no—
66C22×C4×C11—21no—
67C22×C4×C11—21no—
68C22×C4×C11—21no—
69C22×C4×C11—21no—
70C22×C4×C11—21no—
71C22×C4×C11—21no—
72C22×C4×C11—41no—
73C22×C4×C11—81no—
74C22×C4×C11C2×D411yescharacteristic
75C22×C4×C11C2×D411yescharacteristic
76C2×C22⋊D11—41no—
77C2×C22⋊D11—41no—
78C2×C22⋊D11—41no—
79C2×C22⋊D11—41no—
80C2×C22⋊D11—41no—
81C2×C22⋊D11—41no—
82C22×Dic11—21no—
83C22×Dic11—41no—
84C2×D44—21no—
85C2×D44—21no—
86C11×C4⋊C4—41no—
87C11×C4⋊C4—41no—
88C11×C4⋊C4—81no—
89C11×C4⋊C4—81no—
90C11×C4⋊C4—81no—
91C11×C4⋊C4—81no—
92C11×C4⋊C4—81no—
93C11×C22⋊C4—21no—
94C11×C22⋊C4—21no—
95C11×C22⋊C4—41no—
96C11×C22⋊C4—41no—
97C11×C22⋊C4—41no—
98C11×C22⋊C4—81no—
99C22⋊Dic11—41no—
100C22⋊Dic11—41no—
101(C2×D11)⋊C4—41no—
102(C2×D11)⋊C4—41no—
103(C2×D11)⋊C4—82no—
104C4⋊Dic11—21no—
105C4⋊Dic11—21no—
106C2×C11⋊C8—41no—
107C2×C11⋊C8—41no—
108#2834D1111yescharacteristic, complemented
109#2044—111no—
110#1613—111no—
111#1607—111no—
112#1352—111no—
113#1344—111no—
114#1326—111no—
115C23×C11—21no—
116C23×C11—21no—
117C23×C11—41no—
118C23×C11—41no—
119C23×C11#12011yescharacteristic
120C23×C11#13511yescharacteristic
121C23×C11AGL(1,ℤ/8)11yescharacteristic
122C22×D11—41no—
123C22×D11—41no—
124C22×D11—41no—
125C22×D11—81no—
126C22×D11—81no—
127C2×C4×C11—21no—
128C2×C4×C11—21no—
129C2×C4×C11—41no—
130C2×C4×C11—41no—
131C2×C4×C11—41no—
132C2×C4×C11—41no—
133C2×C4×C11—41no—
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—41no—
141C2×C4×C11—42no—
142C2×C4×C11—41no—
143C2×C4×C11—41no—
144C2×C4×C11—41no—
145C2×C4×C11—41no—
146C2×C4×C11—41no—
147C2×C4×C11—41no—
148C2×C4×C11—41no—
149C2×C4×C11—41no—
150C2×C4×C11—81no—
151C22⋊D11—81no—
152C22⋊D11—81no—
153C22⋊D11—81no—
154C22⋊D11—81no—
155C2×Dic11—41no—
156C2×Dic11—41no—
157C2×Dic11—41no—
158C2×Dic11—81no—
159C2×Dic11—81no—
160C2×Dic11—81no—
161D44—81no—
162D44—81no—
163C11⋊C8—81no—
164C11⋊C8—81no—
165#534—111no—
166#481—221no—
167#480—221no—
168C2×#99—221no—
169#401—21no—
170#399C2×D1111yescharacteristic
171#398—21no—
172#398—21no—
173#398—21no—
174#397—21no—
175#397C2×D1111yescharacteristic
176#386—221no—
177#385—21no—
178#385C2×D1111yescharacteristic
179#342—111no—
180#327—221no—
181#327—221no—
182#323—111no—
183#323—111no—
184C22×C11—21no—
185C22×C11—21no—
186C22×C11—21no—
187C22×C11—21no—
188C22×C11—41no—
189C22×C11—41no—
190C22×C11—41no—
191C22×C11—41no—
192C22×C11—81no—
193C22×C11#44911yescharacteristic
194C22×C11#45411yescharacteristic
195C22×C11B(4,𝔽2)11yescharacteristic
196C2×D11—82no—
197C2×D11—81no—
198C2×D11—81no—
199C2×D11—81no—
200C2×D11—161no—
201C4×C11—41no—
202C4×C11—41no—
203C4×C11—81no—
204C4×C11—81no—
205C4×C11—81no—
206C4×C11—81no—
207C4×C11—81no—
208C4×C11—81no—
209Dic11—81no—
210Dic11—161no—
211C22×D4—221no—
212C23×C4C22⋊D1111yescharacteristic
213#123—441no—
214#121—221no—
215#121—221no—
216#120—441no—
217C2×C4⋊C4—21no—
218C2×C4⋊C4—21no—
219C2×C4⋊C4—21no—
220C2×C4⋊C4—21no—
221C2×C4⋊C4—21no—
222C2×C4⋊C4C22⋊D1111yescharacteristic
223C2×C4⋊C4C22⋊D1111yescharacteristic
224C2×C22⋊C4—21no—
225C2×C22⋊C4—21no—
226C2×C22⋊C4—221no—
227C2×C22⋊C4—441no—
228C2×C22⋊C4C22⋊D1111yescharacteristic
229C2×C22⋊C4C22×D1111yescharacteristic
230#107—441no—
231#106—441no—
232#102—441no—
233#102—441no—
234#99—442no—
235C22⋊C8—221no—
236C22⋊C8—221no—
237#95—21no—
238#95—21no—
239#95—21no—
240#95—21no—
241#95—21no—
242#95—21no—
243#95—21no—
244#95—441no—
245#95C22⋊D1111yescharacteristic
246#95C22⋊D1111yescharacteristic
247C2×C11—21no—
248C2×C11—21no—
249C2×C11—41no—
250C2×C11—41no—
251C2×C11#159711yescharacteristic
252C2×C11#220011yescharacteristic
253C2×C11#220111yescharacteristic
254D11—161no—
255C24—221no—
256C24C2×C22⋊D1111yescharacteristic
257C2×D4—221no—
258C2×D4—221no—
259C2×D4—441no—
260C2×D4—441no—
261C2×D4—441no—
262C2×D4—441no—
263C2×D4—441no—
264C2×D4—441no—
265C22×C4—21no—
266C22×C4—21no—
267C22×C4—21no—
268C22×C4—21no—
269C22×C4—21no—
270C22×C4—21no—
271C22×C4—41no—
272C22×C4—81no—
273C22×C4—221no—
274C22×C4—441no—
275C22×C4C2×C22⋊D1111yescharacteristic
276C22×C4C2×C22⋊D1111yescharacteristic
277C2×C8—441no—
278C2×C8—441no—
279C4⋊C4—41no—
280C4⋊C4—41no—
281C4⋊C4—81no—
282C4⋊C4—81no—
283C4⋊C4—81no—
284C4⋊C4—81no—
285C4⋊C4—81no—
286C4⋊C4—221no—
287C4⋊C4—221no—
288C22⋊C4—21no—
289C22⋊C4—21no—
290C22⋊C4—41no—
291C22⋊C4—41no—
292C22⋊C4—41no—
293C22⋊C4—81no—
294C22⋊C4—441no—
295C22⋊C4—441no—
296C22⋊C4—441no—
297C22⋊C4—441no—
298C22⋊C4—882no—
299C11#1213811yescharacteristic, complemented, Sylow
300C23—21no—
301C23—21no—
302C23—41no—
303C23—41no—
304C23—441no—
305C23—441no—
306C23—441no—
307C23—881no—
308C23—881no—
309C23#6700211yescharacteristic
310C23#6700311yescharacteristic
311C23#6700611yescharacteristic
312D4—881no—
313D4—881no—
314D4—881no—
315D4—881no—
316D4—881no—
317D4—881no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—41no—
321C2×C4—41no—
322C2×C4—41no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—41no—
326C2×C4—41no—
327C2×C4—41no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—42no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4—41no—
340C2×C4—41no—
341C2×C4—81no—
342C2×C4—441no—
343C2×C4—441no—
344C2×C4—441no—
345C2×C4—881no—
346C2×C4—881no—
347C2×C4—881no—
348C8—881no—
349C8—881no—
350C22—21no—
351C22—21no—
352C22—21no—
353C22—21no—
354C22—41no—
355C22—41no—
356C22—41no—
357C22—41no—
358C22—81no—
359C22—882no—
360C22—881no—
361C22—881no—
362C22—881no—
363C22—1761no—
364C22#1062285111yescharacteristic
365C22#1062285711yescharacteristic
366C22#1062285811yescharacteristic
367C4—41no—
368C4—41no—
369C4—81no—
370C4—81no—
371C4—81no—
372C4—81no—
373C4—81no—
374C4—81no—
375C4—881no—
376C4—1761no—
377C2—21no—
378C2—21no—
379C2—41no—
380C2—41no—
381C2—1761no—
382C2#1306754511yescharacteristic
383C2#1307062311yescharacteristic
384C2#1307062911yescharacteristic
subgroupG/H
centerC22#10622857
commutator, cosocleC2×C11×C22⋊C4C23
FrattiniC2×C22⋊C4C22×D11
FittingC11×#2834C2
socleC22×C11B(4,𝔽2)
prime radical#10623024C22
hypercenter#2834D11
hypocenterC11#12138
LCSG ▷ C2×C11×C22⋊C4 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C2×C22⋊C4 ◁ #2834

Complements

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

NH ≅ G/Ntype
4. #13066640C2semidirect
5. #13066616C2semidirect
6. #13066564C2semidirect
7. C11×#2834C2semidirect
108. #2834D11semidirect
299. C11#12138semidirect

Maximal subgroups

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

subgroupindex
#130698672
#130676352
#130676012
#130666402
#130666162
#130665642
C11×#28342
#1213811