Finite Group Databasebeta

← #14666481

Subgroups — #14666481

Order 2816.

380 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 380 conjugacy classes of subgroups — too many to draw. Only its 55 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#13076796C211yesmaximal, characteristic, complemented
2#13069663C211yesmaximal, characteristic
3#13067653C211yesmaximal, characteristic
4#13066644C211yesmaximal, characteristic, complemented
5#13066622C211yesmaximal, characteristic, complemented
6#13066549C211yesmaximal, characteristic, complemented
7C11×#1610C211yesmaximal, characteristic
8C11×#537C2211yescharacteristic
9C2×#67004—21no—
10C11×#480—21no—
11C11×#398C2211yescharacteristic
12C2×#66901—21no—
13#10622647—21no—
14#10622599C2211yescharacteristic
15#10622597—21no—
16#10622594—21no—
17#10622592—21no—
18#10622587C2211yescharacteristic
19C11⋊#401—21no—
20#10622273—21no—
21#10622272—21no—
22C11×#327—21no—
23C11×#324C2211yescharacteristic
24#10622175—21no—
25#10622168C2211yescharacteristic
26#10622166C2211yescharacteristic
27C2×C11×#41—21no—
28C22×Dic22D411yescharacteristic
29C11×C22⋊Q8—41no—
30C11×#121—21no—
31C11×#121—21no—
32C11×#121—41no—
33C2×C11×C4⋊C4—21no—
34C2×C11×C4⋊C4D411yescharacteristic
35C2×C11×C4⋊C4C2311yescharacteristic
36#67004—42no—
37#67004—42no—
38C2×#4326—41no—
39C2×#4324—41no—
40C2×C4⋊Dic11—21no—
41C2×C4⋊Dic11D411yescharacteristic
42C2×Dic11⋊C4—21no—
43C2×Dic11⋊C4—21no—
44C2×C4×Dic11D411yescharacteristic
45C2×#4318—21no—
46C11×#107—41no—
47C11×#102—41no—
48C11×C22⋊C8—21no—
49C11×#95—21no—
50C11×#95D411yescharacteristic
51#66901—42no—
52#66896—41no—
53C11⋊#95—21no—
54C11⋊#95—21no—
55C11⋊#95—21no—
56C11⋊#95—21no—
57C11⋊#95—21no—
58C11⋊#95—21no—
59C11⋊#95—21no—
60C11⋊#95—21no—
61C11⋊#95—21no—
62C11⋊#95D411yescharacteristic
63C22⋊(C11⋊C8)—21no—
64#66872—41no—
65#12201—111nomaximal, Sylow
66C11×#41—41no—
67C11×#41—41no—
68C11×#41—41no—
69C11×#41—41no—
70C2×Q8×C11—21no—
71C2×D4×C11—21no—
72C2×D4×C11—21no—
73C2×D4×C11—21no—
74C2×D4×C11—41no—
75C22×C4×C11—21no—
76C22×C4×C11—21no—
77C22×C4×C11—41no—
78C22×C4×C11C2×D411yescharacteristic
79C22×C4×C11C2×D411yescharacteristic
80C22×C4×C11C2×D411yescharacteristic
81C22×Dic11—21no—
82C22×Dic11—21no—
83C22×Dic11—21no—
84C22×Dic11—21no—
85C2×Dic22—21no—
86C2×Dic22—21no—
87C2×Dic22—41no—
88C2×Dic22—41no—
89C2×C8×C11—41no—
90C11×C4⋊C4—21no—
91C11×C4⋊C4—21no—
92C11×C4⋊C4—41no—
93C11×C4⋊C4—41no—
94C11×C4⋊C4—41no—
95C11×C4⋊C4—41no—
96C11×C22⋊C4—41no—
97C11×C22⋊C4—41no—
98#4326—44no—
99#4324—44no—
100C4⋊Dic11—41no—
101C4⋊Dic11—81no—
102Dic11⋊C4—81no—
103Dic11⋊C4—81no—
104C4×Dic11—41no—
105#4318—22no—
106#4318—41no—
107C2×C11⋊C8—41no—
108C2×C11⋊C8—41no—
109#2833—111no—
110#2007—111no—
111#1616—111no—
112#1610D1111yescharacteristic
113#1353—111no—
114#1346—111no—
115#1319—111no—
116C23×C11—41no—
117C23×C11#12011yescharacteristic
118Q8×C11—41no—
119Q8×C11—41no—
120D4×C11—41no—
121D4×C11—41no—
122D4×C11—81no—
123D4×C11—81no—
124D4×C11—81no—
125D4×C11—81no—
126C2×C4×C11—21no—
127C2×C4×C11—21no—
128C2×C4×C11—21no—
129C2×C4×C11—21no—
130C2×C4×C11—41no—
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—81no—
140C2×C4×C11—81no—
141C2×C4×C11#13511yescharacteristic
142C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
143C2×Dic11—41no—
144C2×Dic11—41no—
145C2×Dic11—41no—
146C2×Dic11—41no—
147C2×Dic11—42no—
148C2×Dic11—41no—
149C2×Dic11—41no—
150C2×Dic11—41no—
151C2×Dic11—41no—
152C2×Dic11—41no—
153C2×Dic11—41no—
154Dic22—42no—
155Dic22—81no—
156C8×C11—81no—
157C11⋊C8—42no—
158C11⋊C8—81no—
159C2×#137—221no—
160#537C2×D1111yescharacteristic
161#481—221no—
162#480—21no—
163C2×#104—221no—
164#401—221no—
165#400—111no—
166#400—221no—
167#400—221no—
168#398—221no—
169#398C2×D1111yescharacteristic
170#395—221no—
171#391—111no—
172#387—221no—
173#343—111no—
174#327—21no—
175#327—221no—
176#324—111no—
177#324C2×D1111yescharacteristic
178C22×C11—21no—
179C22×C11—21no—
180C22×C11—81no—
181C22×C11—81no—
182C22×C11—81no—
183C22×C11#44911yescharacteristic
184C22×C11#45311yescharacteristic
185C22×C11B(4,𝔽2)11yescharacteristic
186C4×C11—21no—
187C4×C11—21no—
188C4×C11—41no—
189C4×C11—41no—
190C4×C11—81no—
191C4×C11—81no—
192C4×C11—81no—
193Dic11—81no—
194Dic11—81no—
195Dic11—81no—
196Dic11—81no—
197C2×#41—21no—
198C22×Q8—111no—
199#137—442no—
200#137—442no—
201C2×Q16—441no—
202C2×SD16—441no—
203C2×M16—221no—
204C22⋊Q8—41no—
205#121—21no—
206#121—21no—
207#121—41no—
208C2×C4⋊C4—21no—
209C2×C4⋊C4—111no—
210C2×C4⋊C4—221no—
211C2×C4⋊C4—221no—
212C2×C4⋊C4—221no—
213C2×C4⋊C4C22⋊D1111yescharacteristic
214C2×C4⋊C4C22×D1111yescharacteristic
215C2×C42—111no—
216#107—41no—
217#106—441no—
218#104—442no—
219#102—41no—
220#102—441no—
221C22⋊C8—21no—
222C22⋊C8—221no—
223#95—21no—
224#95—111no—
225#95—221no—
226#95—221no—
227#95—221no—
228#95—221no—
229#95—221no—
230#95—221no—
231#95—221no—
232#95—221no—
233#95—221no—
234#95C22⋊D1111yescharacteristic
235C2×C11—21no—
236C2×C11—21no—
237C2×C11—161no—
238C2×C11#160011yescharacteristic
239C2×C11#220111yescharacteristic
240C2×C11#220311yescharacteristic
241#41—41no—
242#41—41no—
243#41—41no—
244#41—41no—
245C2×Q8—21no—
246C2×Q8—221no—
247C2×Q8—221no—
248C2×Q8—441no—
249C2×Q8—441no—
250C2×D4—21no—
251C2×D4—21no—
252C2×D4—21no—
253C2×D4—41no—
254C22×C4—21no—
255C22×C4—21no—
256C22×C4—41no—
257C22×C4—221no—
258C22×C4—221no—
259C22×C4—221no—
260C22×C4—221no—
261C22×C4D4×D1111yescharacteristic
262C22×C4D4×D1111yescharacteristic
263C22×C4C2×C22⋊D1111yescharacteristic
264Q16—444no—
265SD16—444no—
266M16—222no—
267M16—441no—
268C2×C8—41no—
269C2×C8—441no—
270C2×C8—441no—
271C4⋊C4—21no—
272C4⋊C4—21no—
273C4⋊C4—41no—
274C4⋊C4—41no—
275C4⋊C4—41no—
276C4⋊C4—41no—
277C4⋊C4—441no—
278C4⋊C4—881no—
279C4⋊C4—881no—
280C4⋊C4—881no—
281C22⋊C4—41no—
282C22⋊C4—41no—
283C42—441no—
284C11#1220111yescharacteristic, complemented, Sylow
285C23—41no—
286C23#6699011yescharacteristic
287Q8—41no—
288Q8—41no—
289Q8—442no—
290Q8—881no—
291D4—41no—
292D4—41no—
293D4—81no—
294D4—81no—
295D4—81no—
296D4—81no—
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—41no—
310C2×C4—81no—
311C2×C4—81no—
312C2×C4—441no—
313C2×C4—441no—
314C2×C4—441no—
315C2×C4—441no—
316C2×C4—442no—
317C2×C4—441no—
318C2×C4—441no—
319C2×C4—441no—
320C2×C4—441no—
321C2×C4—441no—
322C2×C4—441no—
323C2×C4#6696411yescharacteristic
324C2×C4#6696511yescharacteristic
325C8—81no—
326C8—442no—
327C8—881no—
328C22—21no—
329C22—21no—
330C22—81no—
331C22—81no—
332C22—81no—
333C22#1062264511yescharacteristic
334C22#1062277111yescharacteristic
335C22#1062281111yescharacteristic
336C4—21no—
337C4—21no—
338C4—41no—
339C4—41no—
340C4—81no—
341C4—81no—
342C4—81no—
343C4—881no—
344C4—881no—
345C4—881no—
346C4—881no—
347C2—21no—
348C2—21no—
349C2—161no—
350C2#1306755911yescharacteristic
351C2#1307062711yescharacteristic
352C2#1307063511yescharacteristic
subgroupG/H
centerC22#10622645
commutator, cosocleC2×C11×C4⋊C4C23
FrattiniC2×C4⋊C4C22×D11
FittingC11×#1610C2
socleC22×C11B(4,𝔽2)
prime radicalC11×#537C22
hypercenter#1610D11
hypocenterC11#12201
LCSG ▷ C2×C11×C4⋊C4 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #1610

Complements

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

NH ≅ G/Ntype
1. #13076796C2semidirect
4. #13066644C2semidirect
5. #13066622C2semidirect
6. #13066549C2semidirect
284. C11#12201semidirect

Maximal subgroups

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

subgroupindex
#130767962
#130696632
#130676532
#130666442
#130666222
#130665492
C11×#16102
#1220111