Finite Group Databasebeta

← #14642942

Subgroups — #14642942

Order 2816.

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

normal subgroups only

This group has 404 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#13075576C211yesmaximal, characteristic
2#13070173C211yesmaximal, characteristic, complemented
3#13070020C211yesmaximal, characteristic
4#13066439C211yesmaximal, characteristic, complemented
5#13066438C211yesmaximal, characteristic, complemented
6#13066436C211yesmaximal, characteristic
7C11×#2084C211yesmaximal, characteristic, complemented
8C2×#66951—21no—
9C2×C11×#106—21no—
10C11×#389C2211yescharacteristic
11C11×#384C2211yescharacteristic
12#10622607—21no—
13#10622605—21no—
14#10622603—21no—
15C2×#66873—21no—
16#10622552C2211yescharacteristic
17#10622541C2211yescharacteristic
18#10622285—21no—
19#10622260—21no—
20C11×#340—21no—
21C11×#336C2211yescharacteristic
22#10622167—21no—
23#10622167—21no—
24#10622167—21no—
25#10622162C2211yescharacteristic
26#10622162C2211yescharacteristic
27C22×D44D411yescharacteristic
28C22×C8×C11—21no—
29C2×C11×C4⋊C4—21no—
30C2×C11×C4⋊C4—21no—
31C2×C11×C4⋊C4—21no—
32C2×C11×C4⋊C4—21no—
33C2×C11×C4⋊C4D411yescharacteristic
34C2×C11×C4⋊C4D411yescharacteristic
35C2×C42×C11C2311yescharacteristic
36C2×(C2×D11)⋊C4—21no—
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—
47C2×Dic11⋊C4—21no—
48C2×C4×Dic11—21no—
49C22×C11⋊C8—21no—
50C22×C11⋊C8—21no—
51#66951—42no—
52#66951—42no—
53C11×#106—42no—
54C11×#95—21no—
55C11⋊#95—21no—
56C11⋊#95—21no—
57#66873—42no—
58#7808—111nomaximal, Sylow
59C23×D11—21no—
60C22×C4×C11—21no—
61C22×C4×C11—21no—
62C22×C4×C11—41no—
63C22×C4×C11C2×D411yescharacteristic
64C22×C4×C11C2×D411yescharacteristic
65C22×C4×C11C2×D411yescharacteristic
66C22×Dic11—21no—
67C22×Dic11—21no—
68C22×Dic11—21no—
69C2×D44—21no—
70C2×D44—21no—
71C2×D44—41no—
72C2×D44—41no—
73C2×C8×C11—22no—
74C2×C8×C11—41no—
75C2×C8×C11—41no—
76C11×C4⋊C4—21no—
77C11×C4⋊C4—21no—
78C11×C4⋊C4—41no—
79C11×C4⋊C4—42no—
80C11×C4⋊C4—41no—
81C11×C4⋊C4—41no—
82C11×C4⋊C4—41no—
83C11×C4⋊C4—41no—
84C11×C4⋊C4—41no—
85C11×C4⋊C4—41no—
86C42×C11—41no—
87(C2×D11)⋊C4—42no—
88(C2×D11)⋊C4—42no—
89(C2×D11)⋊C4—41no—
90(C2×D11)⋊C4—41no—
91(C2×D11)⋊C4—41no—
92(C2×D11)⋊C4—41no—
93(C2×D11)⋊C4—81no—
94(C2×D11)⋊C4—81no—
95C4⋊Dic11—21no—
96C4⋊Dic11—41no—
97C4⋊Dic11—41no—
98C4⋊Dic11SD1612yes—
99Dic11⋊C4—42no—
100Dic11⋊C4—41no—
101Dic11⋊C4—41no—
102Dic11⋊C4—81no—
103C4×Dic11—42no—
104C2×C11⋊C8—41no—
105C2×C11⋊C8—41no—
106C2×C11⋊C8—41no—
107C2×C11⋊C8—41no—
108C2×C11⋊C8—41no—
109C2×C11⋊C8—41no—
110#2727—111no—
111#2099—111no—
112#2084D1111yescharacteristic, complemented
113#2071—111no—
114#1271—111no—
115#1271—111no—
116#1270—111no—
117C23×C11#12011yescharacteristic
118C22×D11—41no—
119C22×D11—41no—
120C22×D11—41no—
121C22×D11—41no—
122C22×D11—41no—
123C22×D11—41no—
124C22×D11—41no—
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—81no—
138C2×C4×C11—81no—
139C2×C4×C11—81no—
140C2×C4×C11C2×SD1611yescharacteristic
141C2×C4×C11#13511yescharacteristic
142C2×C4×C11#13511yescharacteristic
143C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
144C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
145C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
146C2×Dic11—22no—
147C2×Dic11—41no—
148C2×Dic11—41no—
149C2×Dic11—41no—
150C2×Dic11—41no—
151C2×Dic11—41no—
152C2×Dic11—41no—
153C2×Dic11—41no—
154C2×Dic11—41no—
155D44—42no—
156D44—81no—
157C8×C11—42no—
158C11⋊C8—81no—
159C11⋊C8—81no—
160C2×#126—221no—
161C2×#106—21no—
162C2×#102—221no—
163#399—221no—
164#396—221no—
165#394—221no—
166#390—111no—
167#389—111no—
168#389—221no—
169#389C2×D1111yescharacteristic
170#388—221no—
171#384C2×D1111yescharacteristic
172#340—21no—
173#340—221no—
174#340—221no—
175#340—221no—
176#336—111no—
177#336—111no—
178#336C2×D1111yescharacteristic
179C22×C11#44911yescharacteristic
180C22×C11#44911yescharacteristic
181C22×C11#45011yescharacteristic
182C22×C11#45411yescharacteristic
183C22×C11#45511yescharacteristic
184C22×C11#45611yescharacteristic
185C22×C11#45811yescharacteristic
186C2×D11—81no—
187C2×D11—81no—
188C2×D11—81no—
189C2×D11—81no—
190C2×D11—81no—
191C2×D11—81no—
192C2×D11—81no—
193C4×C11—21no—
194C4×C11—21no—
195C4×C11—21no—
196C4×C11—21no—
197C4×C11—21no—
198C4×C11—21no—
199C4×C11—81no—
200C4×C11—81no—
201C4×C11—161no—
202Dic11—42no—
203Dic11—81no—
204Dic11—81no—
205C22×D4—111no—
206C22×C8—21no—
207C22×C8—221no—
208C22×C8—221no—
209#126—442no—
210#126—442no—
211C2×C4⋊C4—21no—
212C2×C4⋊C4—21no—
213C2×C4⋊C4—21no—
214C2×C4⋊C4—21no—
215C2×C4⋊C4—111no—
216C2×C4⋊C4—111no—
217C2×C4⋊C4—111no—
218C2×C4⋊C4—221no—
219C2×C4⋊C4—221no—
220C2×C4⋊C4—221no—
221C2×C4⋊C4C22⋊D1111yescharacteristic
222C2×C4⋊C4C22⋊D1111yescharacteristic
223C2×C22⋊C4—221no—
224C2×C22⋊C4—221no—
225C2×C22⋊C4—221no—
226C2×C22⋊C4—221no—
227C2×C22⋊C4—221no—
228C2×C22⋊C4—221no—
229C2×C42—221no—
230C2×C42C22×D1111yescharacteristic
231#106—42no—
232#102—442no—
233#95—21no—
234#95—221no—
235#95—221no—
236C2×C11#160911yescharacteristic
237C2×C11#161211yescharacteristic
238C2×C11#161611yescharacteristic
239C2×C11#162811yescharacteristic
240C2×C11#164211yescharacteristic
241C2×C11#165411yescharacteristic
242C2×C11#166411yescharacteristic
243D11—161no—
244C24—221no—
245C2×D4—221no—
246C2×D4—221no—
247C2×D4—441no—
248C2×D4—441no—
249C22×C4—21no—
250C22×C4—21no—
251C22×C4—41no—
252C22×C4—221no—
253C22×C4—221no—
254C22×C4—221no—
255C22×C4D4×D1111yescharacteristic
256C22×C4D4×D1111yescharacteristic
257C22×C4C2×C22⋊D1111yescharacteristic
258C2×C8—22no—
259C2×C8—41no—
260C2×C8—41no—
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—42no—
271C4⋊C4—41no—
272C4⋊C4—41no—
273C4⋊C4—41no—
274C4⋊C4—41no—
275C4⋊C4—41no—
276C4⋊C4—41no—
277C4⋊C4—112no—
278C4⋊C4—221no—
279C4⋊C4—441no—
280C4⋊C4—441no—
281C4⋊C4—442no—
282C4⋊C4—441no—
283C4⋊C4—441no—
284C4⋊C4—881no—
285C22⋊C4—442no—
286C22⋊C4—442no—
287C22⋊C4—441no—
288C22⋊C4—441no—
289C22⋊C4—441no—
290C22⋊C4—441no—
291C22⋊C4—881no—
292C22⋊C4—881no—
293C42—41no—
294C42—442no—
295C11#780811yescharacteristic, complemented, Sylow
296C23—441no—
297C23—441no—
298C23—441no—
299C23—441no—
300C23—441no—
301C23—441no—
302C23—441no—
303C23#6699011yescharacteristic
304D4—442no—
305D4—881no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—41no—
317C2×C4—41no—
318C2×C4—81no—
319C2×C4—81no—
320C2×C4—81no—
321C2×C4—222no—
322C2×C4—441no—
323C2×C4—441no—
324C2×C4—441no—
325C2×C4—441no—
326C2×C4—441no—
327C2×C4—441no—
328C2×C4—441no—
329C2×C4—441no—
330C2×C4SD16×D1111yescharacteristic
331C2×C4#6696711yescharacteristic
332C2×C4#6696711yescharacteristic
333C2×C4#6696911yescharacteristic
334C2×C4#6698511yescharacteristic
335C2×C4#6700311yescharacteristic
336C8—42no—
337C8—881no—
338C8—881no—
339C22—881no—
340C22—881no—
341C22—881no—
342C22—881no—
343C22—881no—
344C22—881no—
345C22—881no—
346C22#1062265011yescharacteristic
347C22#1062266611yescharacteristic
348C22#1062270811yescharacteristic
349C22#1062278211yescharacteristic
350C22#1062278511yescharacteristic
351C22#1062281411yescharacteristic
352C22#1062281511yescharacteristic
353C4—21no—
354C4—21no—
355C4—21no—
356C4—21no—
357C4—21no—
358C4—21no—
359C4—81no—
360C4—81no—
361C4—161no—
362C4—442no—
363C4—881no—
364C4—881no—
365C2—1761no—
366C2#1306761111yescharacteristic
367C2#1306762911yescharacteristic
368C2#1306765111yescharacteristic
369C2#1306772511yescharacteristic
370C2#1306781411yescharacteristic
371C2#1306789711yescharacteristic
372C2#1306794811yescharacteristic
subgroupG/H
centerC23#66990
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#2084C2
socleC23×C11#120
prime radicalC22×D44D4
hypercenter#2084D11
hypocenterC11#7808
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
2. #13070173C2semidirect
4. #13066439C2semidirect
5. #13066438C2semidirect
7. C11×#2084C2semidirect
112. #2084D11semidirect
295. C11#7808semidirect

Maximal subgroups

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

subgroupindex
#130755762
#130701732
#130700202
#130664392
#130664382
#130664362
C11×#20842
#780811