Finite Group Databasebeta

← #14642964

Subgroups — #14642964

Order 2816.

380 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 380 conjugacy classes of subgroups — too many to draw. Only its 83 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#13070174C211yesmaximal, characteristic, complemented
2#13070024C211yesmaximal, characteristic, complemented
3#13070019C211yesmaximal, characteristic
4#13066442C211yesmaximal, characteristic, complemented
5#13066439C211yesmaximal, characteristic, complemented
6#13066437C211yesmaximal, characteristic
7C11×#2808C211yesmaximal, characteristic
8C11×#397—21no—
9C11×#394—21no—
10C11×#393—21no—
11C11×#391C2211yescharacteristic
12C11×#390C2211yescharacteristic
13C11×#389C2211yescharacteristic
14C11×#388—21no—
15C11×#388—21no—
16C11×#387—21no—
17C2×#66899—21no—
18C2×#66896—21no—
19#10622548C2211yescharacteristic
20#10622167—21no—
21#10622167—21no—
22#10622167—21no—
23#10622167—21no—
24#10622162C2211yescharacteristic
25#10622162C2211yescharacteristic
26#10622162C2211yescharacteristic
27C22×Q8×C11D411yescharacteristic
28C22×D4×C11D411yescharacteristic
29C2×C11×C4⋊C4—21no—
30C2×C11×C4⋊C4D411yescharacteristic
31C2×C11×C4⋊C4D411yescharacteristic
32C2×C11×C4⋊C4D411yescharacteristic
33C2×C11×C4⋊C4D411yescharacteristic
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×C11C2311yescharacteristic
42C2×C4⋊Dic11—21no—
43C2×C4⋊Dic11—21no—
44C2×C4⋊Dic11—21no—
45C22×C11⋊C8—21no—
46C22×C11⋊C8—21no—
47C22×C11⋊C8—21no—
48C11×#95—21no—
49C11×#95—21no—
50C11×#95—21no—
51C11×#95—21no—
52C11×#95—21no—
53C11×#95—21no—
54#66899—42no—
55#66896—42no—
56#7811—111nomaximal, Sylow
57C24×C11—21no—
58C2×Q8×C11—21no—
59C2×Q8×C11—21no—
60C2×Q8×C11—41no—
61C2×Q8×C11—41no—
62C2×D4×C11—21no—
63C2×D4×C11—21no—
64C2×D4×C11—41no—
65C2×D4×C11—41no—
66C22×C4×C11—21no—
67C22×C4×C11—21no—
68C22×C4×C11—21no—
69C22×C4×C11—21no—
70C22×C4×C11—21no—
71C22×C4×C11C2×D411yescharacteristic
72C22×C4×C11C2×D411yescharacteristic
73C22×C4×C11C2×D411yescharacteristic
74C22×Dic11—41no—
75C11×C4⋊C4—21no—
76C11×C4⋊C4—21no—
77C11×C4⋊C4—41no—
78C11×C4⋊C4—41no—
79C11×C4⋊C4—41no—
80C11×C4⋊C4—41no—
81C11×C4⋊C4—41no—
82C11×C22⋊C4—41no—
83C11×C22⋊C4—41no—
84C11×C22⋊C4—41no—
85C11×C22⋊C4—41no—
86C11×C22⋊C4—81no—
87C11×C22⋊C4—81no—
88C11×C22⋊C4—81no—
89C11×C22⋊C4—81no—
90C42×C11—41no—
91C42×C11—81no—
92C4⋊Dic11—42no—
93C4⋊Dic11—41no—
94C4⋊Dic11—41no—
95C4⋊Dic11—41no—
96C4⋊Dic11—41no—
97C2×C11⋊C8—41no—
98C2×C11⋊C8—41no—
99C2×C11⋊C8—41no—
100C2×C11⋊C8—41no—
101C2×C11⋊C8—41no—
102C2×C11⋊C8—41no—
103C2×C11⋊C8—41no—
104C2×C11⋊C8—41no—
105C2×C11⋊C8—41no—
106#2808D1111yescharacteristic
107#2099—111no—
108#2072—111no—
109#2071—111no—
110#1272—111no—
111#1271—111no—
112#1270—111no—
113C23×C11—41no—
114C23×C11—41no—
115C23×C11—41no—
116C23×C11—41no—
117C23×C11—41no—
118C23×C11—41no—
119C23×C11—41no—
120C23×C11#12011yescharacteristic
121Q8×C11—42no—
122Q8×C11—81no—
123D4×C11—42no—
124D4×C11—81no—
125C2×C4×C11—21no—
126C2×C4×C11—21no—
127C2×C4×C11—21no—
128C2×C4×C11—21no—
129C2×C4×C11—21no—
130C2×C4×C11—21no—
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—41no—
142C2×C4×C11—41no—
143C2×C4×C11—41no—
144C2×C4×C11—41no—
145C2×C4×C11—41no—
146C2×C4×C11#13511yescharacteristic
147C2×C4×C11#13511yescharacteristic
148C2×C4×C11#13511yescharacteristic
149C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
150C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
151C2×C4×C11#13711yescharacteristic
152C2×Dic11—81no—
153C2×Dic11—81no—
154C2×Dic11—81no—
155C11⋊C8—81no—
156C11⋊C8—81no—
157C11⋊C8—81no—
158C2×#103—221no—
159C2×#102—221no—
160#397—21no—
161#394—21no—
162#393—21no—
163#391C2×D1111yescharacteristic
164#390C2×D1111yescharacteristic
165#389C2×D1111yescharacteristic
166#388—21no—
167#388—21no—
168#387—21no—
169#384—111no—
170#340—221no—
171#340—221no—
172#340—221no—
173#340—221no—
174#336—111no—
175#336—111no—
176#336—111no—
177C22×C11—81no—
178C22×C11—81no—
179C22×C11—81no—
180C22×C11—81no—
181C22×C11—81no—
182C22×C11—81no—
183C22×C11—81no—
184C22×C11#44911yescharacteristic
185C22×C11#44911yescharacteristic
186C22×C11#45211yescharacteristic
187C22×C11#45411yescharacteristic
188C22×C11#45511yescharacteristic
189C22×C11#45511yescharacteristic
190C22×C11#45811yescharacteristic
191C4×C11—21no—
192C4×C11—21no—
193C4×C11—21no—
194C4×C11—21no—
195C4×C11—21no—
196C4×C11—21no—
197C4×C11—81no—
198C4×C11—81no—
199C4×C11—81no—
200C4×C11—81no—
201C4×C11—81no—
202Dic11—161no—
203C22×Q8C22⋊D1111yescharacteristic
204C22×D4C22⋊D1111yescharacteristic
205C22×C8—221no—
206C22×C8—221no—
207C22×C8—221no—
208C2×C4⋊C4—21no—
209C2×C4⋊C4—221no—
210C2×C4⋊C4—221no—
211C2×C4⋊C4—221no—
212C2×C4⋊C4C22⋊D1111yescharacteristic
213C2×C4⋊C4C22⋊D1111yescharacteristic
214C2×C4⋊C4C22⋊D1111yescharacteristic
215C2×C4⋊C4C22⋊D1111yescharacteristic
216C2×C22⋊C4—21no—
217C2×C22⋊C4—21no—
218C2×C22⋊C4—21no—
219C2×C22⋊C4—21no—
220C2×C22⋊C4—21no—
221C2×C22⋊C4—21no—
222C2×C42—21no—
223C2×C42C22×D1111yescharacteristic
224#103—442no—
225#102—442no—
226#95—21no—
227#95—21no—
228#95—21no—
229#95—21no—
230#95—21no—
231#95—21no—
232C2×C11—161no—
233C2×C11#161211yescharacteristic
234C2×C11#161211yescharacteristic
235C2×C11#161511yescharacteristic
236C2×C11#162811yescharacteristic
237C2×C11#164011yescharacteristic
238C2×C11#164611yescharacteristic
239C2×C11#166211yescharacteristic
240C24—21no—
241C2×Q8—21no—
242C2×Q8—21no—
243C2×Q8—41no—
244C2×Q8—41no—
245C2×D4—21no—
246C2×D4—21no—
247C2×D4—41no—
248C2×D4—41no—
249C22×C4—21no—
250C22×C4—21no—
251C22×C4—21no—
252C22×C4—21no—
253C22×C4—21no—
254C22×C4—441no—
255C22×C4C2×C22⋊D1111yescharacteristic
256C22×C4C2×C22⋊D1111yescharacteristic
257C22×C4C2×C22⋊D1111yescharacteristic
258C2×C8—441no—
259C2×C8—441no—
260C2×C8—441no—
261C2×C8—441no—
262C2×C8—441no—
263C2×C8—441no—
264C2×C8—441no—
265C2×C8—441no—
266C2×C8—441no—
267C4⋊C4—21no—
268C4⋊C4—21no—
269C4⋊C4—41no—
270C4⋊C4—41no—
271C4⋊C4—41no—
272C4⋊C4—41no—
273C4⋊C4—41no—
274C4⋊C4—442no—
275C4⋊C4—441no—
276C4⋊C4—441no—
277C4⋊C4—441no—
278C4⋊C4—441no—
279C22⋊C4—41no—
280C22⋊C4—41no—
281C22⋊C4—41no—
282C22⋊C4—41no—
283C22⋊C4—81no—
284C22⋊C4—81no—
285C22⋊C4—81no—
286C22⋊C4—81no—
287C42—41no—
288C42—81no—
289C11#781111yescharacteristic, complemented, Sylow
290C23—41no—
291C23—41no—
292C23—41no—
293C23—41no—
294C23—41no—
295C23—41no—
296C23—41no—
297C23#6700611yescharacteristic
298Q8—42no—
299Q8—81no—
300D4—42no—
301D4—81no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—41no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—41no—
320C2×C4—41no—
321C2×C4—41no—
322C2×C4—41no—
323C2×C4—881no—
324C2×C4—881no—
325C2×C4—881no—
326C2×C4#6700211yescharacteristic
327C2×C4#6700211yescharacteristic
328C2×C4#6700311yescharacteristic
329C2×C4#6700311yescharacteristic
330C2×C4#6700311yescharacteristic
331C2×C4#6700411yescharacteristic
332C8—881no—
333C8—881no—
334C8—881no—
335C22—81no—
336C22—81no—
337C22—81no—
338C22—81no—
339C22—81no—
340C22—81no—
341C22—81no—
342C22#1062285111yescharacteristic
343C22#1062285111yescharacteristic
344C22#1062285211yescharacteristic
345C22#1062285511yescharacteristic
346C22#1062285511yescharacteristic
347C22#1062285611yescharacteristic
348C22#1062285811yescharacteristic
349C4—21no—
350C4—21no—
351C4—21no—
352C4—21no—
353C4—21no—
354C4—21no—
355C4—81no—
356C4—81no—
357C4—81no—
358C4—81no—
359C4—81no—
360C4—1761no—
361C2—161no—
362C2#1306763011yescharacteristic
363C2#1306763011yescharacteristic
364C2#1306764711yescharacteristic
365C2#1306772611yescharacteristic
366C2#1306780211yescharacteristic
367C2#1306784411yescharacteristic
368C2#1306793911yescharacteristic
subgroupG/H
centerC23#67006
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#2808C2
socleC23×C11#120
prime radicalC22×D4×C11D4
hypercenter#2808D11
hypocenterC11#7811
LCSG ▷ C2×C42×C11 ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2808

Complements

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

NH ≅ G/Ntype
1. #13070174C2semidirect
2. #13070024C2semidirect
4. #13066442C2semidirect
5. #13066439C2semidirect
289. C11#7811semidirect

Maximal subgroups

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

subgroupindex
#130701742
#130700242
#130700192
#130664422
#130664392
#130664372
C11×#28082
#781111