Finite Group Databasebeta

← #14666125

Subgroups — #14666125

Order 2816.

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

normal subgroups only

This group has 398 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#13069840C211yesmaximal, characteristic, complemented
2#13067652C211yesmaximal, characteristic, complemented
3#13067550C211yesmaximal, characteristic
4#13066643C211yesmaximal, characteristic, complemented
5#13066619C211yesmaximal, characteristic, complemented
6#13066562C211yesmaximal, characteristic, complemented
7C11×#2795C211yesmaximal, characteristic, complemented
8#10623041C2211yescharacteristic
9C11×#400C2211yescharacteristic
10C11×#396—21no—
11C11×#394—21no—
12C11×#394C2211yescharacteristic
13C11×#388—21no—
14C11×#388—21no—
15C11×#388—21no—
16C11×#387—21no—
17C11×#384C2211yescharacteristic
18#10622830—21no—
19#10622581—21no—
20#10622579—21no—
21C2×#66869—21no—
22#10622168C2211yescharacteristic
23#10622166C2211yescharacteristic
24#10622166C2211yescharacteristic
25#10622089—21no—
26#10622089—21no—
27C22×D4×C11D411yescharacteristic
28C2×#4339—21no—
29C2×C11×C4⋊C4—21no—
30C2×C11×C4⋊C4—21no—
31C2×C11×C4⋊C4—21no—
32C2×C11×C4⋊C4D411yescharacteristic
33C2×C11×C4⋊C4D411yescharacteristic
34C2×C11×C4⋊C4C2311yescharacteristic
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×C11×C22⋊C4—21no—
41C2×C42×C11—21no—
42C2×C42×C11D411yescharacteristic
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×#95D411yescharacteristic
54C11×#95D411yescharacteristic
55#66896—41no—
56C22⋊(C11⋊C8)—21no—
57C22⋊(C11⋊C8)—21no—
58#66874—41no—
59#66873—41no—
60#66873—41no—
61#66872—41no—
62#66869—42no—
63#12144—111nomaximal, Sylow
64C24×C11—21no—
65C2×D4×C11—41no—
66C2×D4×C11—81no—
67C22×C4×C11—21no—
68C22×C4×C11—21no—
69C22×C4×C11—21no—
70C22×C4×C11—21no—
71C22×C4×C11—21no—
72C22×C4×C11C2×D411yescharacteristic
73C22×C4×C11C2×D411yescharacteristic
74C22×C4×C11C2×D411yescharacteristic
75C2×C22⋊D11—41no—
76#4339—41no—
77#4339—41no—
78#4339—41no—
79#4339—41no—
80C2×D44—21no—
81C2×D44—21no—
82C2×D44—21no—
83C2×C4×D11—41no—
84C2×Dic22—21no—
85C11×C4⋊C4—41no—
86C11×C4⋊C4—42no—
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—81no—
101#4323—82no—
102(C2×D11)⋊C4—41no—
103(C2×D11)⋊C4—41no—
104C4⋊Dic11—21no—
105C4⋊Dic11—21no—
106#4318—41no—
107#4318—41no—
108C2×C11⋊C8—41no—
109C2×C11⋊C8—41no—
110C2×C11⋊C8—41no—
111#2795D1111yescharacteristic, complemented
112#2039—111no—
113#1616—111no—
114#1598—111no—
115#1353—111no—
116#1345—111no—
117#1325—111no—
118C23×C11—41no—
119C23×C11—41no—
120C23×C11—41no—
121C23×C11—41no—
122C23×C11—41no—
123C23×C11—41no—
124C23×C11—41no—
125C23×C11#12011yescharacteristic
126C22×D11—41no—
127D4×C11—42no—
128D4×C11—81no—
129C2×C4×C11—21no—
130C2×C4×C11—21no—
131C2×C4×C11—22no—
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—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#13511yescharacteristic
151C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
152C22⋊D11—81no—
153C22⋊D11—81no—
154C2×Dic11—41no—
155D44—41no—
156D44—41no—
157D44—81no—
158D44—81no—
159C4×D11—81no—
160C4×D11—81no—
161Dic22—41no—
162Dic22—41no—
163C11⋊C8—81no—
164C11⋊C8—81no—
165C11⋊C8—81no—
166#537—111no—
167#481—221no—
168#447—221no—
169C2×#104—221no—
170#417—221no—
171#400C2×D1111yescharacteristic
172#396—21no—
173#394—21no—
174#394C2×D1111yescharacteristic
175#388—21no—
176#388—21no—
177#388—21no—
178#387—21no—
179#384C2×D1111yescharacteristic
180#343—111no—
181#327—221no—
182#327—221no—
183#324—111no—
184#324—111no—
185C22×C11—21no—
186C22×C11—21no—
187C22×C11—81no—
188C22×C11—81no—
189C22×C11—81no—
190C22×C11—81no—
191C22×C11—81no—
192C22×C11—81no—
193C22×C11—81no—
194C22×C11#44911yescharacteristic
195C22×C11#45411yescharacteristic
196C22×C11B(4,𝔽2)11yescharacteristic
197C2×D11—81no—
198C2×D11—81no—
199C2×D11—81no—
200C4×C11—21no—
201C4×C11—21no—
202C4×C11—42no—
203C4×C11—41no—
204C4×C11—41no—
205C4×C11—81no—
206C4×C11—81no—
207C4×C11—81no—
208C4×C11—81no—
209Dic11—81no—
210C2×#41—221no—
211C22×D4C22⋊D1111yescharacteristic
212C2×D8—441no—
213C2×M16—221no—
214C22⋊Q8—441no—
215#121—221no—
216#121—221no—
217#121—441no—
218C2×C4⋊C4—21no—
219C2×C4⋊C4—21no—
220C2×C4⋊C4—21no—
221C2×C4⋊C4C22⋊D1111yescharacteristic
222C2×C4⋊C4C22⋊D1111yescharacteristic
223C2×C4⋊C4C22×D1111yescharacteristic
224C2×C22⋊C4—21no—
225C2×C22⋊C4—21no—
226C2×C22⋊C4—21no—
227C2×C22⋊C4—21no—
228C2×C22⋊C4—21no—
229C2×C22⋊C4—21no—
230C2×C42—21no—
231C2×C42C22⋊D1111yescharacteristic
232#106—441no—
233#104—442no—
234#103—441no—
235#102—441no—
236#102—441no—
237#102—441no—
238C22⋊C8—221no—
239C22⋊C8—221no—
240#95—21no—
241#95—21no—
242#95—21no—
243#95—21no—
244#95C22⋊D1111yescharacteristic
245#95C22⋊D1111yescharacteristic
246C2×C11—21no—
247C2×C11—21no—
248C2×C11—161no—
249C2×C11#159711yescharacteristic
250C2×C11#220011yescharacteristic
251C2×C11#220411yescharacteristic
252D11—161no—
253C24—21no—
254#41—441no—
255#41—441no—
256#41—441no—
257#41—441no—
258C2×Q8—221no—
259C2×D4—41no—
260C2×D4—81no—
261C2×D4—221no—
262C2×D4—221no—
263C2×D4—221no—
264C2×D4—441no—
265C22×C4—21no—
266C22×C4—21no—
267C22×C4—21no—
268C22×C4—21no—
269C22×C4—21no—
270C22×C4—441no—
271C22×C4C2×C22⋊D1111yescharacteristic
272C22×C4C2×C22⋊D1111yescharacteristic
273C22×C4C2×C22⋊D1111yescharacteristic
274D8—882no—
275M16—441no—
276M16—441no—
277C2×C8—441no—
278C2×C8—441no—
279C2×C8—441no—
280C4⋊C4—41no—
281C4⋊C4—41no—
282C4⋊C4—41no—
283C4⋊C4—42no—
284C4⋊C4—81no—
285C4⋊C4—81no—
286C4⋊C4—221no—
287C4⋊C4—221no—
288C22⋊C4—42no—
289C22⋊C4—42no—
290C22⋊C4—41no—
291C22⋊C4—41no—
292C22⋊C4—81no—
293C22⋊C4—81no—
294C22⋊C4—81no—
295C22⋊C4—441no—
296C22⋊C4—441no—
297C42—21no—
298C42—21no—
299C42—81no—
300C11#1214411yescharacteristic, complemented, Sylow
301C23—41no—
302C23—41no—
303C23—41no—
304C23—41no—
305C23—41no—
306C23—41no—
307C23—41no—
308C23—441no—
309C23#6700611yescharacteristic
310Q8—441no—
311Q8—441no—
312D4—42no—
313D4—81no—
314D4—441no—
315D4—441no—
316D4—881no—
317D4—881no—
318D4—881no—
319D4—881no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—22no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—41no—
326C2×C4—41no—
327C2×C4—41no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—41no—
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—441no—
342C2×C4—881no—
343C2×C4—881no—
344C2×C4#6700211yescharacteristic
345C2×C4#6700311yescharacteristic
346C8—881no—
347C8—881no—
348C8—881no—
349C22—21no—
350C22—21no—
351C22—81no—
352C22—81no—
353C22—81no—
354C22—81no—
355C22—81no—
356C22—81no—
357C22—81no—
358C22—881no—
359C22—881no—
360C22—881no—
361C22#1062285111yescharacteristic
362C22#1062285711yescharacteristic
363C22#1062285811yescharacteristic
364C4—21no—
365C4—21no—
366C4—42no—
367C4—41no—
368C4—41no—
369C4—81no—
370C4—81no—
371C4—81no—
372C4—81no—
373C4—881no—
374C2—21no—
375C2—21no—
376C2—161no—
377C2—1761no—
378C2#1306754511yescharacteristic
379C2#1307062311yescharacteristic
380C2#1307064211yescharacteristic
subgroupG/H
centerC22#10622857
commutator, cosocleC2×C11×C4⋊C4C23
FrattiniC2×C4⋊C4C22×D11
FittingC11×#2795C2
socleC22×C11B(4,𝔽2)
prime radical#13067550C2
hypercenter#2795D11
hypocenterC11#12144
LCSG ▷ C2×C11×C4⋊C4 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #2795

Complements

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

NH ≅ G/Ntype
1. #13069840C2semidirect
2. #13067652C2semidirect
4. #13066643C2semidirect
5. #13066619C2semidirect
6. #13066562C2semidirect
7. C11×#2795C2semidirect
111. #2795D11semidirect
300. C11#12144semidirect

Maximal subgroups

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

subgroupindex
#130698402
#130676522
#130675502
#130666432
#130666192
#130665622
C11×#27952
#1214411