Finite Group Databasebeta

← #14643021

Subgroups — #14643021

Order 2816.

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

normal subgroups only

This group has 396 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#13070144C211yesmaximal, characteristic
2#13070092C211yesmaximal, characteristic, complemented
3#13070024C211yesmaximal, characteristic, complemented
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—
19C2×#66872—21no—
20C2×#66871—21no—
21#10622548C2211yescharacteristic
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#66872—42no—
57#66871—42no—
58#7820—111nomaximal, Sylow
59C24×C11—21no—
60C2×Q8×C11—21no—
61C2×Q8×C11—21no—
62C2×Q8×C11—41no—
63C2×Q8×C11—41no—
64C2×D4×C11—21no—
65C2×D4×C11—21no—
66C2×D4×C11—41no—
67C2×D4×C11—41no—
68C22×C4×C11—21no—
69C22×C4×C11—21no—
70C22×C4×C11—21no—
71C22×C4×C11—21no—
72C22×C4×C11—21no—
73C22×C4×C11C2×D411yescharacteristic
74C22×C4×C11C2×D411yescharacteristic
75C22×C4×C11C2×D411yescharacteristic
76C22×Dic11—41no—
77C11×C4⋊C4—21no—
78C11×C4⋊C4—21no—
79C11×C4⋊C4—41no—
80C11×C4⋊C4—41no—
81C11×C4⋊C4—41no—
82C11×C4⋊C4—41no—
83C11×C4⋊C4—41no—
84C11×C22⋊C4—41no—
85C11×C22⋊C4—41no—
86C11×C22⋊C4—41no—
87C11×C22⋊C4—41no—
88C11×C22⋊C4—81no—
89C11×C22⋊C4—81no—
90C11×C22⋊C4—81no—
91C11×C22⋊C4—81no—
92C42×C11—41no—
93C42×C11—81no—
94C4⋊Dic11—41no—
95C4⋊Dic11—41no—
96C4⋊Dic11—41no—
97C4⋊Dic11—41no—
98C4⋊Dic11—41no—
99C4⋊Dic11—41no—
100C2×C11⋊C8—22no—
101C2×C11⋊C8—22no—
102C2×C11⋊C8—41no—
103C2×C11⋊C8—41no—
104C2×C11⋊C8—41no—
105C2×C11⋊C8—41no—
106C2×C11⋊C8—41no—
107C2×C11⋊C8—41no—
108C2×C11⋊C8—41no—
109#2808D1111yescharacteristic
110#2093—111no—
111#2084—111no—
112#2072—111no—
113#1272—111no—
114#1271—111no—
115#1270—111no—
116C23×C11—41no—
117C23×C11—41no—
118C23×C11—41no—
119C23×C11—41no—
120C23×C11—41no—
121C23×C11—41no—
122C23×C11—41no—
123C23×C11#12011yescharacteristic
124Q8×C11—42no—
125Q8×C11—81no—
126D4×C11—42no—
127D4×C11—81no—
128C2×C4×C11—21no—
129C2×C4×C11—21no—
130C2×C4×C11—21no—
131C2×C4×C11—21no—
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#13511yescharacteristic
150C2×C4×C11#13511yescharacteristic
151C2×C4×C11#13511yescharacteristic
152C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
153C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
154C2×C4×C11#13711yescharacteristic
155C2×Dic11—81no—
156C2×Dic11—81no—
157C2×Dic11—81no—
158C11⋊C8—42no—
159C11⋊C8—42no—
160C11⋊C8—81no—
161C2×#107—221no—
162C2×#106—221no—
163C2×#103—221no—
164C2×#102—221no—
165#397—21no—
166#394—21no—
167#393—21no—
168#391C2×D1111yescharacteristic
169#390C2×D1111yescharacteristic
170#389C2×D1111yescharacteristic
171#388—21no—
172#388—21no—
173#387—21no—
174#384—111no—
175#340—221no—
176#340—221no—
177#336—111no—
178#336—111no—
179#336—111no—
180C22×C11—81no—
181C22×C11—81no—
182C22×C11—81no—
183C22×C11—81no—
184C22×C11—81no—
185C22×C11—81no—
186C22×C11—81no—
187C22×C11#44911yescharacteristic
188C22×C11#44911yescharacteristic
189C22×C11#45211yescharacteristic
190C22×C11#45311yescharacteristic
191C22×C11#45511yescharacteristic
192C22×C11#45611yescharacteristic
193C22×C11#45811yescharacteristic
194C4×C11—21no—
195C4×C11—21no—
196C4×C11—21no—
197C4×C11—21no—
198C4×C11—21no—
199C4×C11—21no—
200C4×C11—81no—
201C4×C11—81no—
202C4×C11—81no—
203C4×C11—81no—
204C4×C11—81no—
205Dic11—161no—
206C22×Q8C22⋊D1111yescharacteristic
207C22×D4C22⋊D1111yescharacteristic
208C22×C8—221no—
209C22×C8—221no—
210C22×C8—221no—
211C2×C4⋊C4—21no—
212C2×C4⋊C4—221no—
213C2×C4⋊C4—221no—
214C2×C4⋊C4—221no—
215C2×C4⋊C4C22⋊D1111yescharacteristic
216C2×C4⋊C4C22⋊D1111yescharacteristic
217C2×C4⋊C4C22⋊D1111yescharacteristic
218C2×C4⋊C4C22⋊D1111yescharacteristic
219C2×C22⋊C4—21no—
220C2×C22⋊C4—21no—
221C2×C22⋊C4—21no—
222C2×C22⋊C4—21no—
223C2×C22⋊C4—21no—
224C2×C22⋊C4—21no—
225C2×C42—21no—
226C2×C42C22×D1111yescharacteristic
227#107—442no—
228#106—442no—
229#103—442no—
230#102—442no—
231#95—21no—
232#95—21no—
233#95—21no—
234#95—21no—
235#95—21no—
236#95—21no—
237C2×C11—161no—
238C2×C11#160911yescharacteristic
239C2×C11#161211yescharacteristic
240C2×C11#161811yescharacteristic
241C2×C11#162011yescharacteristic
242C2×C11#164611yescharacteristic
243C2×C11#165211yescharacteristic
244C2×C11#166111yescharacteristic
245C24—21no—
246C2×Q8—21no—
247C2×Q8—21no—
248C2×Q8—41no—
249C2×Q8—41no—
250C2×D4—21no—
251C2×D4—21no—
252C2×D4—41no—
253C2×D4—41no—
254C22×C4—21no—
255C22×C4—21no—
256C22×C4—21no—
257C22×C4—21no—
258C22×C4—21no—
259C22×C4—441no—
260C22×C4C2×C22⋊D1111yescharacteristic
261C22×C4C2×C22⋊D1111yescharacteristic
262C22×C4C2×C22⋊D1111yescharacteristic
263C2×C8—222no—
264C2×C8—222no—
265C2×C8—441no—
266C2×C8—441no—
267C2×C8—441no—
268C2×C8—441no—
269C2×C8—441no—
270C2×C8—441no—
271C2×C8—441no—
272C4⋊C4—21no—
273C4⋊C4—21no—
274C4⋊C4—41no—
275C4⋊C4—41no—
276C4⋊C4—41no—
277C4⋊C4—41no—
278C4⋊C4—41no—
279C4⋊C4—441no—
280C4⋊C4—441no—
281C4⋊C4—441no—
282C4⋊C4—441no—
283C4⋊C4—441no—
284C4⋊C4—441no—
285C22⋊C4—41no—
286C22⋊C4—41no—
287C22⋊C4—41no—
288C22⋊C4—41no—
289C22⋊C4—81no—
290C22⋊C4—81no—
291C22⋊C4—81no—
292C22⋊C4—81no—
293C42—41no—
294C42—81no—
295C11#782011yescharacteristic, complemented, Sylow
296C23—41no—
297C23—41no—
298C23—41no—
299C23—41no—
300C23—41no—
301C23—41no—
302C23—41no—
303C23#6700611yescharacteristic
304Q8—42no—
305Q8—81no—
306D4—42no—
307D4—81no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
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—41no—
324C2×C4—41no—
325C2×C4—41no—
326C2×C4—41no—
327C2×C4—41no—
328C2×C4—41no—
329C2×C4—881no—
330C2×C4—881no—
331C2×C4—881no—
332C2×C4#6700211yescharacteristic
333C2×C4#6700211yescharacteristic
334C2×C4#6700311yescharacteristic
335C2×C4#6700311yescharacteristic
336C2×C4#6700311yescharacteristic
337C2×C4#6700411yescharacteristic
338C8—442no—
339C8—442no—
340C8—881no—
341C22—81no—
342C22—81no—
343C22—81no—
344C22—81no—
345C22—81no—
346C22—81no—
347C22—81no—
348C22#1062285111yescharacteristic
349C22#1062285111yescharacteristic
350C22#1062285211yescharacteristic
351C22#1062285411yescharacteristic
352C22#1062285511yescharacteristic
353C22#1062285611yescharacteristic
354C22#1062285911yescharacteristic
355C4—21no—
356C4—21no—
357C4—21no—
358C4—21no—
359C4—21no—
360C4—21no—
361C4—81no—
362C4—81no—
363C4—81no—
364C4—81no—
365C4—81no—
366C4—1761no—
367C2—161no—
368C2#1306761311yescharacteristic
369C2#1306763011yescharacteristic
370C2#1306766411yescharacteristic
371C2#1306767511yescharacteristic
372C2#1306784411yescharacteristic
373C2#1306788611yescharacteristic
374C2#1306793311yescharacteristic
subgroupG/H
centerC23#67006
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#2808C2
socleC23×C11#120
prime radicalC22×D4×C11D4
hypercenter#2808D11
hypocenterC11#7820
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
2. #13070092C2semidirect
3. #13070024C2semidirect
4. #13066442C2semidirect
5. #13066439C2semidirect
295. C11#7820semidirect

Maximal subgroups

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

subgroupindex
#130701442
#130700922
#130700242
#130664422
#130664392
#130664372
C11×#28082
#782011