Finite Group Databasebeta

← #14666132

Subgroups — #14666132

Order 2816.

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

normal subgroups only

This group has 408 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#13069845C211yesmaximal, characteristic, complemented
2#13067584C211yesmaximal, characteristic, complemented
3#13067550C211yesmaximal, characteristic
4#13066646C211yesmaximal, characteristic, complemented
5#13066619C211yesmaximal, characteristic, complemented
6#13066560C211yesmaximal, characteristic, complemented
7C11×#2785C211yesmaximal, characteristic, complemented
8#10623041C2211yescharacteristic
9C11×#395C2211yescharacteristic
10C11×#394—21no—
11C11×#394C2211yescharacteristic
12C11×#393—21no—
13C11×#388—21no—
14C11×#388—21no—
15C11×#388—21no—
16C11×#382—21no—
17C11×#382C2211yescharacteristic
18#10622840—21no—
19#10622830—21no—
20#10622579—21no—
21C2×#66869—21no—
22#10622168C2211yescharacteristic
23#10622166C2211yescharacteristic
24#10622166C2211yescharacteristic
25#10622089—21no—
26#10622089—21no—
27C22×Q8×C11D411yescharacteristic
28C22×D4×C11D411yescharacteristic
29C2×#4339—21no—
30C2×C11×C4⋊C4—21no—
31C2×C11×C4⋊C4—21no—
32C2×C11×C4⋊C4D411yescharacteristic
33C2×C11×C4⋊C4C2311yescharacteristic
34C2×C11×C22⋊C4—21no—
35C2×C11×C22⋊C4—21no—
36C2×C11×C22⋊C4—21no—
37C2×C11×C22⋊C4—21no—
38C2×C11×C22⋊C4—21no—
39C2×C11×C22⋊C4—21no—
40C2×C42×C11—21no—
41C2×C42×C11D411yescharacteristic
42C2×#4325—41no—
43C2×#4323—41no—
44#66983—21no—
45#66983—21no—
46C2×#4318—21no—
47#66950—41no—
48#66948—41no—
49C11×#95—21no—
50C11×#95—21no—
51C11×#95—21no—
52C11×#95—21no—
53C11×#95—21no—
54C11×#95D411yescharacteristic
55C11×#95D411yescharacteristic
56#66899—41no—
57#66896—41no—
58C22⋊(C11⋊C8)—21no—
59C22⋊(C11⋊C8)—21no—
60#66874—41no—
61#66873—41no—
62#66869—42no—
63#12145—111nomaximal, Sylow
64C24×C11—21no—
65C2×Q8×C11—41no—
66C2×Q8×C11—81no—
67C2×D4×C11—41no—
68C2×D4×C11—81no—
69C22×C4×C11—21no—
70C22×C4×C11—21no—
71C22×C4×C11—21no—
72C22×C4×C11—21no—
73C22×C4×C11—21no—
74C22×C4×C11C2×D411yescharacteristic
75C22×C4×C11C2×D411yescharacteristic
76C22×C4×C11C2×D411yescharacteristic
77C2×C22⋊D11—41no—
78#4339—41no—
79#4339—41no—
80#4339—41no—
81#4339—41no—
82C2×D44—21no—
83C2×D44—21no—
84C2×D44—21no—
85C2×C4×D11—41no—
86C2×Dic22—21no—
87C11×C4⋊C4—41no—
88C11×C4⋊C4—41no—
89C11×C4⋊C4—81no—
90C11×C4⋊C4—81no—
91C11×C22⋊C4—42no—
92C11×C22⋊C4—42no—
93C11×C22⋊C4—41no—
94C11×C22⋊C4—41no—
95C11×C22⋊C4—81no—
96C11×C22⋊C4—81no—
97C11×C22⋊C4—81no—
98C42×C11—21no—
99C42×C11—21no—
100C42×C11—42no—
101#4325—82no—
102#4323—82no—
103(C2×D11)⋊C4—41no—
104(C2×D11)⋊C4—41no—
105C4⋊Dic11—21no—
106C4⋊Dic11—21no—
107#4318—41no—
108#4318—41no—
109C2×C11⋊C8—41no—
110C2×C11⋊C8—41no—
111C2×C11⋊C8—41no—
112#2785D1111yescharacteristic, complemented
113#2040—111no—
114#1604—111no—
115#1598—111no—
116#1354—111no—
117#1345—111no—
118#1324—111no—
119C23×C11—41no—
120C23×C11—41no—
121C23×C11—41no—
122C23×C11—41no—
123C23×C11—41no—
124C23×C11—41no—
125C23×C11—41no—
126C23×C11#12011yescharacteristic
127C22×D11—41no—
128Q8×C11—42no—
129Q8×C11—81no—
130D4×C11—42no—
131D4×C11—81no—
132C2×C4×C11—21no—
133C2×C4×C11—21no—
134C2×C4×C11—22no—
135C2×C4×C11—21no—
136C2×C4×C11—21no—
137C2×C4×C11—41no—
138C2×C4×C11—41no—
139C2×C4×C11—41no—
140C2×C4×C11—41no—
141C2×C4×C11—41no—
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—41no—
151C2×C4×C11—41no—
152C2×C4×C11—41no—
153C2×C4×C11#13511yescharacteristic
154C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
155C22⋊D11—81no—
156C22⋊D11—81no—
157C2×Dic11—41no—
158D44—41no—
159D44—41no—
160D44—81no—
161D44—81no—
162C4×D11—81no—
163C4×D11—81no—
164Dic22—41no—
165Dic22—41no—
166C11⋊C8—81no—
167C11⋊C8—81no—
168C11⋊C8—81no—
169#537—111no—
170#448—221no—
171#447—221no—
172C2×#104—221no—
173#417—221no—
174#395C2×D1111yescharacteristic
175#394—21no—
176#394C2×D1111yescharacteristic
177#393—21no—
178#388—21no—
179#388—21no—
180#388—21no—
181#382—21no—
182#382C2×D1111yescharacteristic
183#343—111no—
184#327—221no—
185#327—221no—
186#324—111no—
187#324—111no—
188C22×C11—21no—
189C22×C11—21no—
190C22×C11—81no—
191C22×C11—81no—
192C22×C11—81no—
193C22×C11—81no—
194C22×C11—81no—
195C22×C11—81no—
196C22×C11—81no—
197C22×C11#44911yescharacteristic
198C22×C11#45411yescharacteristic
199C22×C11B(4,𝔽2)11yescharacteristic
200C2×D11—81no—
201C2×D11—81no—
202C2×D11—81no—
203C4×C11—21no—
204C4×C11—21no—
205C4×C11—42no—
206C4×C11—41no—
207C4×C11—41no—
208C4×C11—81no—
209C4×C11—81no—
210C4×C11—81no—
211C4×C11—81no—
212Dic11—81no—
213C2×#41—221no—
214C22×Q8C22⋊D1111yescharacteristic
215C22×D4C22⋊D1111yescharacteristic
216C2×SD16—441no—
217C2×D8—441no—
218C2×M16—221no—
219C22⋊Q8—441no—
220#121—221no—
221#121—221no—
222#121—441no—
223C2×C4⋊C4—21no—
224C2×C4⋊C4—21no—
225C2×C4⋊C4C22⋊D1111yescharacteristic
226C2×C4⋊C4C22×D1111yescharacteristic
227C2×C22⋊C4—21no—
228C2×C22⋊C4—21no—
229C2×C22⋊C4—21no—
230C2×C22⋊C4—21no—
231C2×C22⋊C4—21no—
232C2×C22⋊C4—21no—
233C2×C42—21no—
234C2×C42C22⋊D1111yescharacteristic
235#104—442no—
236#103—441no—
237#103—441no—
238#102—441no—
239#102—441no—
240C22⋊C8—221no—
241C22⋊C8—221no—
242#95—21no—
243#95—21no—
244#95—21no—
245#95—21no—
246#95—21no—
247#95C22⋊D1111yescharacteristic
248#95C22⋊D1111yescharacteristic
249C2×C11—21no—
250C2×C11—21no—
251C2×C11—161no—
252C2×C11#159711yescharacteristic
253C2×C11#219911yescharacteristic
254C2×C11#220411yescharacteristic
255D11—161no—
256C24—21no—
257#41—441no—
258#41—441no—
259#41—441no—
260#41—441no—
261C2×Q8—41no—
262C2×Q8—81no—
263C2×Q8—221no—
264C2×D4—41no—
265C2×D4—81no—
266C2×D4—221no—
267C2×D4—221no—
268C2×D4—221no—
269C2×D4—441no—
270C22×C4—21no—
271C22×C4—21no—
272C22×C4—21no—
273C22×C4—21no—
274C22×C4—21no—
275C22×C4—441no—
276C22×C4C2×C22⋊D1111yescharacteristic
277C22×C4C2×C22⋊D1111yescharacteristic
278C22×C4C2×C22⋊D1111yescharacteristic
279SD16—882no—
280D8—882no—
281M16—441no—
282M16—441no—
283C2×C8—441no—
284C2×C8—441no—
285C2×C8—441no—
286C4⋊C4—41no—
287C4⋊C4—41no—
288C4⋊C4—81no—
289C4⋊C4—81no—
290C4⋊C4—221no—
291C4⋊C4—221no—
292C22⋊C4—42no—
293C22⋊C4—42no—
294C22⋊C4—41no—
295C22⋊C4—41no—
296C22⋊C4—81no—
297C22⋊C4—81no—
298C22⋊C4—81no—
299C22⋊C4—441no—
300C22⋊C4—441no—
301C42—21no—
302C42—21no—
303C42—42no—
304C11#1214511yescharacteristic, complemented, Sylow
305C23—41no—
306C23—41no—
307C23—41no—
308C23—41no—
309C23—41no—
310C23—41no—
311C23—41no—
312C23—441no—
313C23#6700611yescharacteristic
314Q8—42no—
315Q8—81no—
316Q8—441no—
317Q8—441no—
318D4—42no—
319D4—81no—
320D4—441no—
321D4—441no—
322D4—881no—
323D4—881no—
324D4—881no—
325D4—881no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—22no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—41no—
332C2×C4—41no—
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—41no—
342C2×C4—41no—
343C2×C4—41no—
344C2×C4—41no—
345C2×C4—41no—
346C2×C4—41no—
347C2×C4—441no—
348C2×C4—881no—
349C2×C4—881no—
350C2×C4#6700211yescharacteristic
351C2×C4#6700311yescharacteristic
352C8—881no—
353C8—881no—
354C8—881no—
355C22—21no—
356C22—21no—
357C22—81no—
358C22—81no—
359C22—81no—
360C22—81no—
361C22—81no—
362C22—81no—
363C22—81no—
364C22—881no—
365C22—881no—
366C22—881no—
367C22#1062285111yescharacteristic
368C22#1062285711yescharacteristic
369C22#1062285811yescharacteristic
370C4—21no—
371C4—21no—
372C4—42no—
373C4—41no—
374C4—41no—
375C4—81no—
376C4—81no—
377C4—81no—
378C4—81no—
379C4—881no—
380C2—21no—
381C2—21no—
382C2—161no—
383C2—1761no—
384C2#1306754511yescharacteristic
385C2#1307061711yescharacteristic
386C2#1307064211yescharacteristic
subgroupG/H
centerC22#10622857
commutator, cosocleC2×C11×C4⋊C4C23
FrattiniC2×C4⋊C4C22×D11
FittingC11×#2785C2
socleC22×C11B(4,𝔽2)
prime radical#13067550C2
hypercenter#2785D11
hypocenterC11#12145
LCSG ▷ C2×C11×C4⋊C4 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #2785

Complements

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

NH ≅ G/Ntype
1. #13069845C2semidirect
2. #13067584C2semidirect
4. #13066646C2semidirect
5. #13066619C2semidirect
6. #13066560C2semidirect
7. C11×#2785C2semidirect
112. #2785D11semidirect
304. C11#12145semidirect

Maximal subgroups

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

subgroupindex
#130698452
#130675842
#130675502
#130666462
#130666192
#130665602
C11×#27852
#1214511