Finite Group Databasebeta

← #14666517

Subgroups — #14666517

Order 2816.

388 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 388 conjugacy classes of subgroups — too many to draw. Only its 57 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#13076654C211yesmaximal, characteristic
2#13069782C211yesmaximal, characteristic
3#13067607C211yesmaximal, characteristic
4#13066617C211yesmaximal, characteristic
5#13066616C211yesmaximal, characteristic
6#13066545C211yesmaximal, characteristic
7C11×#1608C211yesmaximal, characteristic
8C11×#543C2211yescharacteristic
9C2×#66931—21no—
10C11×#483—21no—
11C11×#397C2211yescharacteristic
12#10622656—21no—
13#10622592—21no—
14#10622566C2211yescharacteristic
15#10622565—21no—
16#10622556—21no—
17#10622556C2211yescharacteristic
18#10622273—21no—
19#10622271—21no—
20#10622269—21no—
21C11×#328—21no—
22C11×#323C2211yescharacteristic
23#10622176—21no—
24#10622164—21no—
25#10622164C2211yescharacteristic
26#10622163C2211yescharacteristic
27C23×Dic11D411yescharacteristic
28C22×Dic22—21no—
29C11×C22⋊Q8—21no—
30C11×C22⋊Q8—21no—
31C11×C22⋊Q8—41no—
32C11×C22⋊Q8—41no—
33C2×C11×C4⋊C4D411yescharacteristic
34C2×C11×C22⋊C4—21no—
35C2×C11×C22⋊C4—21no—
36C2×C11×C22⋊C4C2311yescharacteristic
37C2×C22⋊Dic11—21no—
38C2×C22⋊Dic11—21no—
39C2×C22⋊Dic11D411yescharacteristic
40C2×C4⋊Dic11—21no—
41C2×C4⋊Dic11D411yescharacteristic
42C2×Dic11⋊C4—21no—
43C2×Dic11⋊C4—21no—
44C2×Dic11⋊C4—21no—
45#66931—42no—
46#66931—42no—
47C11×#106—41no—
48C11×#103—41no—
49C11×C22⋊C8—21no—
50C11×#95—21no—
51C11×#95D411yescharacteristic
52#66899—41no—
53C11⋊#95—21no—
54C11⋊#95—21no—
55C11⋊#95—21no—
56C11⋊#95—21no—
57C11⋊#95—21no—
58C11⋊#95—21no—
59C11⋊#95—41no—
60C11⋊#95—41no—
61C11⋊#95D411yescharacteristic
62C22⋊(C11⋊C8)—21no—
63#66872—41no—
64#12207—111nomaximal, Sylow
65C24×C11C2×D411yescharacteristic
66C2×Q8×C11—21no—
67C2×Q8×C11—21no—
68C22×C4×C11—21no—
69C22×C4×C11—21no—
70C22×C4×C11—21no—
71C22×C4×C11—21no—
72C22×C4×C11C2×D411yescharacteristic
73C22×C4×C11C2×D411yescharacteristic
74C22×Dic11—21no—
75C22×Dic11—21no—
76C22×Dic11—21no—
77C22×Dic11—21no—
78C22×Dic11—21no—
79C22×Dic11—41no—
80C22×Dic11—41no—
81C22×Dic11—41no—
82C22×Dic11SD1612yes—
83C2×Dic22—42no—
84C2×Dic22—81no—
85C2×Dic22—81no—
86C2×C8×C11—41no—
87C11×C4⋊C4—21no—
88C11×C4⋊C4—21no—
89C11×C4⋊C4—41no—
90C11×C4⋊C4—41no—
91C11×C4⋊C4—41no—
92C11×C22⋊C4—41no—
93C11×C22⋊C4—41no—
94C11×C22⋊C4—41no—
95C11×C22⋊C4—41no—
96C11×C22⋊C4—41no—
97C22⋊Dic11—41no—
98C22⋊Dic11—41no—
99C22⋊Dic11—41no—
100C22⋊Dic11—41no—
101C22⋊Dic11—41no—
102C4⋊Dic11—41no—
103C4⋊Dic11—42no—
104Dic11⋊C4—42no—
105Dic11⋊C4—42no—
106Dic11⋊C4—81no—
107C2×C11⋊C8—41no—
108#2817—111no—
109#2030—111no—
110#1608—111no—
111#1608D1111yescharacteristic
112#1344—111no—
113#1344—111no—
114#1317—111no—
115C23×C11—21no—
116C23×C11—21no—
117C23×C11—41no—
118C23×C11—41no—
119C23×C11#12011yescharacteristic
120C23×C11C2×SD1611yescharacteristic
121C23×C11AGL(1,ℤ/8)11yescharacteristic
122Q8×C11—81no—
123Q8×C11—81no—
124C2×C4×C11—21no—
125C2×C4×C11—21no—
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—41no—
133C2×C4×C11—41no—
134C2×C4×C11—41no—
135C2×C4×C11—41no—
136C2×C4×C11—81no—
137C2×C4×C11—81no—
138C2×Dic11—22no—
139C2×Dic11—41no—
140C2×Dic11—41no—
141C2×Dic11—42no—
142C2×Dic11—41no—
143C2×Dic11—41no—
144C2×Dic11—41no—
145C2×Dic11—41no—
146C2×Dic11—41no—
147C2×Dic11—41no—
148C2×Dic11—41no—
149C2×Dic11—41no—
150C2×Dic11—41no—
151C2×Dic11—81no—
152C2×Dic11—81no—
153C2×Dic11—81no—
154C2×Dic11—81no—
155Dic22—84no—
156C8×C11—81no—
157C11⋊C8—81no—
158#543C2×D1111yescharacteristic
159C2×C22⋊Q8—221no—
160#483—21no—
161#483—221no—
162#400—221no—
163#400—221no—
164#397—111no—
165#397—221no—
166#397C2×D1111yescharacteristic
167#395—221no—
168#395—221no—
169#381—111no—
170#381—221no—
171#342—111no—
172#342—221no—
173#328—21no—
174#328—221no—
175#323—111no—
176#323C2×D1111yescharacteristic
177C22×C11—21no—
178C22×C11—21no—
179C22×C11—21no—
180C22×C11—21no—
181C22×C11—41no—
182C22×C11—41no—
183C22×C11—41no—
184C22×C11—41no—
185C22×C11—81no—
186C22×C11#45011yescharacteristic
187C22×C11#45511yescharacteristic
188C22×C11B(4,𝔽2)11yescharacteristic
189C4×C11—41no—
190C4×C11—41no—
191C4×C11—81no—
192C4×C11—81no—
193C4×C11—81no—
194C4×C11—81no—
195Dic11—42no—
196Dic11—81no—
197Dic11—81no—
198Dic11—81no—
199Dic11—161no—
200C22×Q8—221no—
201C23×C4—111no—
202C22⋊Q8—21no—
203C22⋊Q8—21no—
204C22⋊Q8—41no—
205C22⋊Q8—41no—
206C22⋊Q8—442no—
207C22⋊Q8—442no—
208C2×C4⋊C4—111no—
209C2×C4⋊C4—221no—
210C2×C4⋊C4—221no—
211C2×C4⋊C4—221no—
212C2×C4⋊C4—221no—
213C2×C4⋊C4C22⋊D1111yescharacteristic
214C2×C22⋊C4—21no—
215C2×C22⋊C4—21no—
216C2×C22⋊C4—111no—
217C2×C22⋊C4—221no—
218C2×C22⋊C4—221no—
219C2×C22⋊C4C22×D1111yescharacteristic
220#106—41no—
221#106—441no—
222#103—41no—
223#103—441no—
224C22⋊C8—21no—
225C22⋊C8—221no—
226#95—21no—
227#95—111no—
228#95—221no—
229#95—221no—
230#95—221no—
231#95—221no—
232#95—221no—
233#95—221no—
234#95—441no—
235#95—441no—
236#95C22⋊D1111yescharacteristic
237C2×C11—21no—
238C2×C11—21no—
239C2×C11—41no—
240C2×C11—41no—
241C2×C11#160111yescharacteristic
242C2×C11#220111yescharacteristic
243C2×C11#220111yescharacteristic
244C24D4×D1111yescharacteristic
245C2×Q8—21no—
246C2×Q8—21no—
247C2×Q8—442no—
248C2×Q8—881no—
249C2×Q8—881no—
250C22×C4—21no—
251C22×C4—21no—
252C22×C4—21no—
253C22×C4—21no—
254C22×C4—112no—
255C22×C4—221no—
256C22×C4—221no—
257C22×C4—221no—
258C22×C4—221no—
259C22×C4—221no—
260C22×C4—441no—
261C22×C4—441no—
262C22×C4—441no—
263C22×C4D4×D1111yescharacteristic
264C22×C4C2×C22⋊D1111yescharacteristic
265C2×C8—41no—
266C2×C8—441no—
267C4⋊C4—21no—
268C4⋊C4—21no—
269C4⋊C4—41no—
270C4⋊C4—41no—
271C4⋊C4—41no—
272C4⋊C4—441no—
273C4⋊C4—442no—
274C4⋊C4—442no—
275C4⋊C4—442no—
276C4⋊C4—881no—
277C22⋊C4—41no—
278C22⋊C4—41no—
279C22⋊C4—41no—
280C22⋊C4—41no—
281C22⋊C4—41no—
282C22⋊C4—441no—
283C22⋊C4—441no—
284C22⋊C4—441no—
285C22⋊C4—441no—
286C22⋊C4—441no—
287C11#1220711yescharacteristic, complemented, Sylow
288C23—21no—
289C23—21no—
290C23—41no—
291C23—41no—
292C23SD16×D1111yescharacteristic
293C23#6696711yescharacteristic
294C23#6699011yescharacteristic
295Q8—81no—
296Q8—81no—
297Q8—884no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—41no—
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—222no—
313C2×C4—441no—
314C2×C4—441no—
315C2×C4—442no—
316C2×C4—441no—
317C2×C4—441no—
318C2×C4—441no—
319C2×C4—441no—
320C2×C4—441no—
321C2×C4—441no—
322C2×C4—441no—
323C2×C4—441no—
324C2×C4—441no—
325C2×C4—881no—
326C2×C4—881no—
327C2×C4—881no—
328C2×C4—881no—
329C8—81no—
330C8—881no—
331C22—21no—
332C22—21no—
333C22—21no—
334C22—21no—
335C22—41no—
336C22—41no—
337C22—41no—
338C22—41no—
339C22—81no—
340C22#1062264511yescharacteristic
341C22#1062278211yescharacteristic
342C22#1062281511yescharacteristic
343C4—41no—
344C4—41no—
345C4—81no—
346C4—81no—
347C4—81no—
348C4—81no—
349C4—442no—
350C4—881no—
351C4—881no—
352C4—881no—
353C4—1761no—
354C2—21no—
355C2—21no—
356C2—41no—
357C2—41no—
358C2#1306756611yescharacteristic
359C2#1307062711yescharacteristic
360C2#1307062811yescharacteristic
subgroupG/H
centerC22#10622645
commutator, cosocleC2×C11×C22⋊C4C23
FrattiniC2×C22⋊C4C22×D11
FittingC11×#1608C2
socleC22×C11B(4,𝔽2)
prime radicalC24×C11C2×D4
hypercenter#1608D11
hypocenterC11#12207
LCSG ▷ C2×C11×C22⋊C4 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C2×C22⋊C4 ◁ #1608

Complements

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

NH ≅ G/Ntype
287. C11#12207semidirect

Maximal subgroups

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

subgroupindex
#130766542
#130697822
#130676072
#130666172
#130666162
#130665452
C11×#16082
#1220711