Finite Group Databasebeta

← #14726620

Subgroups — #14726620

Order 2816.

1166 conjugacy classes of subgroups; only the 183 normal subgroups are shown.

normal subgroups only

This group has 1166 conjugacy classes of subgroups — too many to draw. Only its 183 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#13078734C212yesmaximal, complemented
2#13071907C211yesmaximal, characteristic, complemented
3#13067619C214yesmaximal, complemented
4#13067585C214yesmaximal, complemented
5#13067124C212yesmaximal, complemented
6#13066960C211yesmaximal, characteristic, complemented
7C11×#3497C211yesmaximal, characteristic
8C2×C11×2−1+4—21no—
9C11×#550—22no—
10D4×Q8×C11—22no—
11C11×#548—24no—
12C11×#537—21no—
13C11×#537C2214yes—
14C11×#532—22no—
15C11×#532C2212yes—
16C2×C4×Q8×C11C2211yescharacteristic
17C2×C4×Dic22C2211yescharacteristic
18#10622842—21no—
19#10622704—22no—
20#10622688—22no—
21#10622653C2214yes—
22#10622646C2214yes—
23#10622631—24no—
24#10622596C2212yes—
25#10622593—21no—
26#10622592C2212yes—
27#10622545C2211yescharacteristic
28C4×Dic11⋊C4—22no—
29#10622539C2212yes—
30#10622175C2218yes—
31#10622166C2214yes—
32C11×2−1+4—48no—
33C2×C11×#41—24no—
34C2×C11×#41—24no—
35C2×C11×#41—22no—
36C22×Q8×C11—24no—
37C22×Q8×C11D411yescharacteristic
38C22×Dic22C2311yescharacteristic
39C11×C4⋊Q8—22no—
40C11×C4⋊Q8D412yes—
41C11×#127—22no—
42C11×#127D412yes—
43C11×#124—24no—
44C11×#124—22no—
45C11×C22⋊Q8—24no—
46C11×C22⋊Q8—28no—
47C11×#121—24no—
48C11×#121—28no—
49C11×#121—22no—
50C11×#121—24no—
51C11×#121C2314yes—
52C4×Q8×C11—22no—
53C4×Q8×C11—22no—
54C4×D4×C11—24no—
55C4×D4×C11—24no—
56C4×D4×C11—22no—
57C4×D4×C11D414yes—
58C2×C11×C4⋊C4D411yescharacteristic
59C2×C11×C4⋊C4C2312yes—
60C2×C42×C11D412yes—
61C2×C42×C11C2311yescharacteristic
62C2×#4324—24no—
63C2×C4⋊Dic11C2311yescharacteristic
64C2×Dic11⋊C4—21no—
65C2×Dic11⋊C4—22no—
66C2×Dic11⋊C4—22no—
67C2×C4×Dic11—21no—
68C2×C4×Dic11—21no—
69C4×Dic22—22no—
70C4×Dic22—22no—
71#66896—24no—
72C11⋊#95—22no—
73C11⋊#95—22no—
74C11⋊#95—21no—
75C11⋊#95C2312yes—
76C22⋊(C11⋊C8)C2314yes—
77#66874—24no—
78#66871—24no—
79C4⋊(C11⋊C8)—22no—
80#66867—22no—
81#18187—111nomaximal, Sylow
82C11×#41—48no—
83C11×#41—48no—
84C11×#41—416no—
85C11×#41—48no—
86C2×Q8×C11—24no—
87C2×Q8×C11—22no—
88C2×Q8×C11—22no—
89C2×Q8×C11—24no—
90C2×Q8×C11—416no—
91C2×D4×C11—24no—
92C2×D4×C11—24no—
93C2×D4×C11—24no—
94C2×D4×C11—22no—
95C2×D4×C11—22no—
96C2×D4×C11C2×D414yes—
97C22×C4×C11—28no—
98C22×C4×C11—24no—
99C22×C4×C11C2×D411yescharacteristic
100C22×C4×C11C2×D411yescharacteristic
101C22×C4×C11C2×D412yes—
102C22×C4×C11C2×D412yes—
103C22×C4×C11C2411yescharacteristic
104C22×Dic11—22no—
105C22×Dic11—21no—
106C22×Dic11—21no—
107C2×Dic22—22no—
108C2×Dic22—42no—
109C11×C4⋊C4—24no—
110C11×C4⋊C4—22no—
111C11×C4⋊C4—22no—
112C11×C4⋊C4—24no—
113C11×C4⋊C4C2×D414yes—
114C11×C22⋊C4—28no—
115C11×C22⋊C4—24no—
116C11×C22⋊C4—24no—
117C42×C11—22no—
118C42×C11—22no—
119C42×C11C2×D412yes—
120C42×C11C2×D412yes—
121#4324—48no—
122C4⋊Dic11—22no—
123Dic11⋊C4—44no—
124Dic11⋊C4—42no—
125Dic11⋊C4—44no—
126C4×Dic11—24no—
127C4×Dic11—41no—
128C4×Dic11—41no—
129C2×C11⋊C8—24no—
130#3497D1111yescharacteristic
131#3112—112no—
132#2399—111no—
133#1610—114no—
134#1604—114no—
135#1505—112no—
136#1467—111no—
137C23×C11—24no—
138C23×C11C22×D411yescharacteristic
139Q8×C11—28no—
140Q8×C11—44no—
141Q8×C11—48no—
142D4×C11—44no—
143D4×C11—44no—
144D4×C11—48no—
145D4×C11—48no—
146D4×C11—44no—
147D4×C11—84no—
148C2×C4×C11—22no—
149C2×C4×C11—22no—
150C2×C4×C11—22no—
151C2×C4×C11—22no—
152C2×C4×C11—22no—
153C2×C4×C11—24no—
154C2×C4×C11—41no—
155C2×C4×C11—48no—
156C2×C4×C11—416no—
157C2×C4×C11—42no—
158C2×C4×C11#12011yescharacteristic
159C2×C4×C11#12012yes—
160C2×C4×C11#12011yescharacteristic
161C2×C4×C11AGL(1,ℤ/8)14yes—
162C2×C4×C11C22×D412yes—
163C2×Dic11—24no—
164C2×Dic11—22no—
165C2×Dic11—42no—
166C2×Dic11—41no—
167C2×Dic11—41no—
168C2×Dic11—42no—
169C2×Dic11—41no—
170C2×Dic11—42no—
171Dic22—24no—
172Dic22—42no—
173C11⋊C8—44no—
174C2×2−1+4—21no—
175#550—22no—
176D4×Q8—22no—
177#548—24no—
178#537—21no—
179#537C2×D1114yes—
180#532—22no—
181#532C2×D1112yes—
182C2×C4×Q8—111no—
183C2×C4×Q8C2×D1111yescharacteristic
184#480—114no—
185#477—222no—
186#460—222no—
187#448—114no—
188#440—224no—
189#432—112no—
190#398—112no—
191#398—221no—
192#395—112no—
193#395—221no—
194C4×C4⋊C4—222no—
195#376—111no—
196#327—118no—
197#324—114no—
198C22×C11—21no—
199C22×C11—21no—
200C22×C11—44no—
201C22×C11—44no—
202C22×C11—44no—
203C22×C11C2×#12011yescharacteristic
204C22×C11C2×AGL(1,ℤ/8)12yes—
205C4×C11—22no—
206C4×C11—24no—
207C4×C11—21no—
208C4×C11—22no—
209C4×C11—44no—
210C4×C11—42no—
211C4×C11#45612yes—
212Dic11—44no—
213Dic11—42no—
214Dic11—81no—
2152−1+4—48no—
216C2×#41—24no—
217C2×#41—24no—
218C2×#41—22no—
219C22×Q8—24no—
220C22×Q8—111no—
221C22×Q8C22⋊D1111yescharacteristic
222C2×SD16—224no—
223C4⋊Q8—22no—
224C4⋊Q8C22⋊D1112yes—
225#127—22no—
226#127C22⋊D1112yes—
227#124—24no—
228#124—22no—
229C22⋊Q8—24no—
230C22⋊Q8—28no—
231#121—24no—
232#121—28no—
233#121—22no—
234#121—24no—
235#121C22×D1114yes—
236C4×Q8—22no—
237C4×Q8—22no—
238C4×Q8—222no—
239C4×Q8—222no—
240C4×D4—24no—
241C4×D4—24no—
242C4×D4—22no—
243C4×D4C22⋊D1114yes—
244C2×C4⋊C4—111no—
245C2×C4⋊C4—221no—
246C2×C4⋊C4—222no—
247C2×C4⋊C4—222no—
248C2×C4⋊C4C22⋊D1111yescharacteristic
249C2×C4⋊C4C22×D1112yes—
250C2×C42—221no—
251C2×C42—221no—
252C2×C42C22⋊D1112yes—
253C2×C42C22×D1111yescharacteristic
254#107—224no—
255C4⋊C8—222no—
256#103—224no—
257#102—224no—
258C22⋊C8—114no—
259#97—222no—
260#95—112no—
261#95—221no—
262#95—222no—
263#95—222no—
264C2×C11—22no—
265C2×C11—84no—
266C2×C11#300311yescharacteristic
267C2×C11C2×#45611yescharacteristic
268C2×C11#302511yescharacteristic
269#41—48no—
270#41—48no—
271#41—416no—
272#41—48no—
273C2×Q8—24no—
274C2×Q8—24no—
275C2×Q8—22no—
276C2×Q8—22no—
277C2×Q8—416no—
278C2×Q8—222no—
279C2×Q8—442no—
280C2×D4—24no—
281C2×D4—24no—
282C2×D4—24no—
283C2×D4—22no—
284C2×D4—22no—
285C2×D4C2×C22⋊D1114yes—
286C22×C4—28no—
287C22×C4—24no—
288C22×C4—222no—
289C22×C4—221no—
290C22×C4—221no—
291C22×C4C2×C22⋊D1112yes—
292C22×C4C2×C22⋊D1111yescharacteristic
293C22×C4C2×C22⋊D1111yescharacteristic
294C22×C4C2×C22⋊D1112yes—
295C22×C4C23×D1111yescharacteristic
296SD16—448no—
297C2×C8—224no—
298C4⋊C4—24no—
299C4⋊C4—22no—
300C4⋊C4—22no—
301C4⋊C4—24no—
302C4⋊C4—222no—
303C4⋊C4—444no—
304C4⋊C4—444no—
305C4⋊C4—442no—
306C4⋊C4C2×C22⋊D1114yes—
307C22⋊C4—28no—
308C22⋊C4—24no—
309C22⋊C4—24no—
310C42—22no—
311C42—22no—
312C42—224no—
313C42—441no—
314C42—441no—
315C42C2×C22⋊D1112yes—
316C42C2×C22⋊D1112yes—
317C11#1818711yescharacteristic, complemented, Sylow
318C23—24no—
319C23C22×C22⋊D1111yescharacteristic
320Q8—28no—
321Q8—48no—
322Q8—44no—
323Q8—224no—
324Q8—442no—
325D4—44no—
326D4—48no—
327D4—44no—
328D4—48no—
329D4—44no—
330D4—84no—
331C2×C4—22no—
332C2×C4—22no—
333C2×C4—22no—
334C2×C4—22no—
335C2×C4—22no—
336C2×C4—24no—
337C2×C4—41no—
338C2×C4—416no—
339C2×C4—48no—
340C2×C4—42no—
341C2×C4—224no—
342C2×C4—222no—
343C2×C4—442no—
344C2×C4—441no—
345C2×C4—442no—
346C2×C4—441no—
347C2×C4—442no—
348C2×C4—441no—
349C2×C4#6698514yes—
350C2×C4#6700611yescharacteristic
351C2×C4#6700612yes—
352C2×C4#6700611yescharacteristic
353C2×C4C22×C22⋊D1112yes—
354C8—444no—
355C22—21no—
356C22—21no—
357C22—44no—
358C22—44no—
359C22—44no—
360C22C2×#6698512yes—
361C22C2×#6700611yescharacteristic
362C4—24no—
363C4—22no—
364C4—21no—
365C4—22no—
366C4—44no—
367C4—42no—
368C4—444no—
369C4—442no—
370C4—881no—
371C4#1062285912yes—
372C2—22no—
373C2—84no—
374C2#1307784311yescharacteristic
375C2C2×#1062285911yescharacteristic
376C2#1307800811yescharacteristic
subgroupG/H
centerC22C2×#67006
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
Fitting, prime radicalC11×#3497C2
socleC22×C11C2×#120
hypercenter#3497D11
hypocenterC11#18187
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3497

Complements

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

NH ≅ G/Ntype
1. #13078734C2semidirect
2. #13071907C2semidirect
3. #13067619C2semidirect
4. #13067585C2semidirect
5. #13067124C2semidirect
6. #13066960C2semidirect
317. C11#18187semidirect

Maximal subgroups

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

subgroupindex
#130787342
#130719072
#130676192
#130675852
#130671242
#130669602
C11×#34972
#1818711