Finite Group Databasebeta

← #14666484

Subgroups — #14666484

Order 2816.

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

normal subgroups only

This group has 380 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#13069662C211yesmaximal, characteristic
2#13067652C211yesmaximal, characteristic
3#13067618C211yesmaximal, characteristic
4#13066643C211yesmaximal, characteristic, complemented
5#13066622C211yesmaximal, characteristic, complemented
6#13066550C211yesmaximal, characteristic, complemented
7C11×#2833C211yesmaximal, characteristic, complemented
8C2×#66995—21no—
9#10623041C2211yescharacteristic
10C11×#401—21no—
11C11×#400—21no—
12C11×#400—21no—
13C11×#400C2211yescharacteristic
14C11×#398—21no—
15C11×#398C2211yescharacteristic
16C11×#395—21no—
17C11×#391C2211yescharacteristic
18C11×#387—21no—
19#10622581—21no—
20#10622580—21no—
21C2×#66869—21no—
22#10622168C2211yescharacteristic
23#10622166C2211yescharacteristic
24#10622166C2211yescharacteristic
25#10622089—21no—
26#10622089—21no—
27C22×Q8×C11D411yescharacteristic
28C2×#4339—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×C11×C4⋊C4C2311yescharacteristic
36C2×C42×C11D411yescharacteristic
37C2×#4326—41no—
38#66995—42no—
39#66995—42no—
40C2×#4325—41no—
41#66983—21no—
42#66983—21no—
43C2×#4318—21no—
44#66950—41no—
45#66948—41no—
46C11×#95—21no—
47C11×#95—21no—
48C11×#95—21no—
49C11×#95—21no—
50C11×#95—21no—
51C11×#95—21no—
52C11×#95—21no—
53C11×#95—21no—
54C11×#95—21no—
55C11×#95—21no—
56C11×#95D411yescharacteristic
57C11×#95D411yescharacteristic
58C22⋊(C11⋊C8)—21no—
59C22⋊(C11⋊C8)—21no—
60#66873—41no—
61#66873—41no—
62#66872—41no—
63#66871—41no—
64#66869—42no—
65#12201—111nomaximal, Sylow
66C2×Q8×C11—21no—
67C2×Q8×C11—21no—
68C2×Q8×C11—41no—
69C2×Q8×C11—41no—
70C22×C4×C11—21no—
71C22×C4×C11—21no—
72C22×C4×C11—21no—
73C22×C4×C11—21no—
74C22×C4×C11—21no—
75C22×C4×C11—21no—
76C22×C4×C11C2×D411yescharacteristic
77C22×C4×C11C2×D411yescharacteristic
78C22×C4×C11C2×D411yescharacteristic
79C2×C22⋊D11—41no—
80#4339—41no—
81#4339—41no—
82#4339—41no—
83#4339—41no—
84C2×D44—21no—
85C2×D44—21no—
86C2×D44—21no—
87C2×C4×D11—41no—
88C2×Dic22—21no—
89C11×C4⋊C4—41no—
90C11×C4⋊C4—41no—
91C11×C4⋊C4—41no—
92C11×C4⋊C4—41no—
93C11×C4⋊C4—41no—
94C11×C4⋊C4—81no—
95C11×C4⋊C4—81no—
96C11×C4⋊C4—81no—
97C42×C11—41no—
98#4326—44no—
99#4325—44no—
100(C2×D11)⋊C4—41no—
101(C2×D11)⋊C4—41no—
102C4⋊Dic11—21no—
103C4⋊Dic11—21no—
104#4318—22no—
105#4318—41no—
106C2×C11⋊C8—41no—
107C2×C11⋊C8—41no—
108C2×C11⋊C8—41no—
109#2833D1111yescharacteristic, complemented
110#2007—111no—
111#1616—111no—
112#1610—111no—
113#1353—111no—
114#1346—111no—
115#1319—111no—
116C23×C11#12011yescharacteristic
117C22×D11—41no—
118Q8×C11—42no—
119Q8×C11—81no—
120C2×C4×C11—21no—
121C2×C4×C11—21no—
122C2×C4×C11—21no—
123C2×C4×C11—21no—
124C2×C4×C11—41no—
125C2×C4×C11—41no—
126C2×C4×C11—41no—
127C2×C4×C11—41no—
128C2×C4×C11—41no—
129C2×C4×C11—41no—
130C2×C4×C11—41no—
131C2×C4×C11—41no—
132C2×C4×C11—42no—
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#13511yescharacteristic
144C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
145C22⋊D11—81no—
146C22⋊D11—81no—
147C2×Dic11—41no—
148D44—41no—
149D44—41no—
150D44—81no—
151D44—81no—
152C4×D11—81no—
153C4×D11—81no—
154Dic22—41no—
155Dic22—41no—
156C11⋊C8—42no—
157C11⋊C8—81no—
158C11⋊C8—81no—
159C2×#137—221no—
160#537—111no—
161#481—221no—
162#480—221no—
163C2×#104—221no—
164#401—21no—
165#400—21no—
166#400—21no—
167#400C2×D1111yescharacteristic
168#398—21no—
169#398C2×D1111yescharacteristic
170#395—21no—
171#391C2×D1111yescharacteristic
172#387—21no—
173#343—111no—
174#327—221no—
175#327—221no—
176#324—111no—
177#324—111no—
178C22×C11—21no—
179C22×C11—21no—
180C22×C11#44911yescharacteristic
181C22×C11#45311yescharacteristic
182C22×C11B(4,𝔽2)11yescharacteristic
183C2×D11—81no—
184C2×D11—81no—
185C2×D11—81no—
186C4×C11—21no—
187C4×C11—21no—
188C4×C11—41no—
189C4×C11—41no—
190C4×C11—81no—
191C4×C11—81no—
192C4×C11—81no—
193C4×C11—81no—
194C4×C11—81no—
195C4×C11—81no—
196Dic11—81no—
197C2×#41—221no—
198C22×Q8C22⋊D1111yescharacteristic
199#137—442no—
200#137—442no—
201C2×Q16—441no—
202C2×SD16—441no—
203C2×M16—221no—
204C22⋊Q8—441no—
205#121—221no—
206#121—221no—
207#121—441no—
208C2×C4⋊C4—21no—
209C2×C4⋊C4—21no—
210C2×C4⋊C4—21no—
211C2×C4⋊C4—21no—
212C2×C4⋊C4C22⋊D1111yescharacteristic
213C2×C4⋊C4C22⋊D1111yescharacteristic
214C2×C4⋊C4C22×D1111yescharacteristic
215C2×C42C22⋊D1111yescharacteristic
216#107—441no—
217#106—441no—
218#104—442no—
219#102—441no—
220#102—441no—
221C22⋊C8—221no—
222C22⋊C8—221no—
223#95—21no—
224#95—21no—
225#95—21no—
226#95—21no—
227#95—21no—
228#95—21no—
229#95—21no—
230#95—21no—
231#95—21no—
232#95—21no—
233#95C22⋊D1111yescharacteristic
234#95C22⋊D1111yescharacteristic
235C2×C11—21no—
236C2×C11—21no—
237C2×C11#160011yescharacteristic
238C2×C11#220111yescharacteristic
239C2×C11#220311yescharacteristic
240D11—161no—
241#41—441no—
242#41—441no—
243#41—441no—
244#41—441no—
245C2×Q8—21no—
246C2×Q8—21no—
247C2×Q8—41no—
248C2×Q8—41no—
249C2×Q8—221no—
250C2×D4—221no—
251C2×D4—221no—
252C2×D4—221no—
253C2×D4—441no—
254C22×C4—21no—
255C22×C4—21no—
256C22×C4—21no—
257C22×C4—21no—
258C22×C4—21no—
259C22×C4—21no—
260C22×C4—441no—
261C22×C4C2×C22⋊D1111yescharacteristic
262C22×C4C2×C22⋊D1111yescharacteristic
263C22×C4C2×C22⋊D1111yescharacteristic
264Q16—444no—
265SD16—444no—
266M16—222no—
267M16—441no—
268C2×C8—441no—
269C2×C8—441no—
270C2×C8—441no—
271C4⋊C4—41no—
272C4⋊C4—41no—
273C4⋊C4—41no—
274C4⋊C4—41no—
275C4⋊C4—41no—
276C4⋊C4—81no—
277C4⋊C4—81no—
278C4⋊C4—81no—
279C4⋊C4—221no—
280C4⋊C4—221no—
281C22⋊C4—441no—
282C22⋊C4—441no—
283C42—41no—
284C11#1220111yescharacteristic, complemented, Sylow
285C23—441no—
286C23#6700611yescharacteristic
287Q8—42no—
288Q8—81no—
289Q8—441no—
290Q8—441no—
291D4—441no—
292D4—441no—
293D4—881no—
294D4—881no—
295D4—881no—
296D4—881no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—41no—
308C2×C4—41no—
309C2×C4—42no—
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—441no—
321C2×C4—881no—
322C2×C4—881no—
323C2×C4#6700211yescharacteristic
324C2×C4#6700311yescharacteristic
325C8—442no—
326C8—881no—
327C8—881no—
328C22—21no—
329C22—21no—
330C22—881no—
331C22—881no—
332C22—881no—
333C22#1062285111yescharacteristic
334C22#1062285411yescharacteristic
335C22#1062285711yescharacteristic
336C4—21no—
337C4—21no—
338C4—41no—
339C4—41no—
340C4—81no—
341C4—81no—
342C4—81no—
343C4—81no—
344C4—81no—
345C4—81no—
346C4—881no—
347C2—21no—
348C2—21no—
349C2—1761no—
350C2#1306756211yescharacteristic
351C2#1307062911yescharacteristic
352C2#1307063711yescharacteristic
subgroupG/H
centerC22#10622857
commutator, cosocleC2×C11×C4⋊C4C23
FrattiniC2×C4⋊C4C22×D11
FittingC11×#2833C2
socleC22×C11B(4,𝔽2)
prime radical#10623041C22
hypercenter#2833D11
hypocenterC11#12201
LCSG ▷ C2×C11×C4⋊C4 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #2833

Complements

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

NH ≅ G/Ntype
4. #13066643C2semidirect
5. #13066622C2semidirect
6. #13066550C2semidirect
7. C11×#2833C2semidirect
109. #2833D11semidirect
284. C11#12201semidirect

Maximal subgroups

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

subgroupindex
#130696622
#130676522
#130676182
#130666432
#130666222
#130665502
C11×#28332
#1220111