Finite Group Databasebeta

← #14654695

Subgroups — #14654695

Order 2816.

470 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 470 conjugacy classes of subgroups — too many to draw. Only its 81 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#13079169C211yesmaximal, characteristic
2#13074492C211yesmaximal, characteristic
3#13067242C211yesmaximal, characteristic
4#13067167C211yesmaximal, characteristic
5#13067063C211yesmaximal, characteristic
6#13066482C211yesmaximal, characteristic
7C11×#3113C211yesmaximal, characteristic
8C11×#533C2211yescharacteristic
9C2×C4×Q8×C11C2211yescharacteristic
10C2×#66923C2211yescharacteristic
11C11×#483—21no—
12C11×#475—21no—
13C11×#462—21no—
14C11×#451—21no—
15C11×#441—22no—
16C11×#432C2211yescharacteristic
17#10622842—21no—
18#10622693—21no—
19#10622693—21no—
20#10622677—22no—
21#10622608—21no—
22#10622608—21no—
23#10622599—21no—
24#10622596—21no—
25#10622595—21no—
26#10622550C2211yescharacteristic
27#10622546—22no—
28#10622539C2211yescharacteristic
29C4×#4318C2211yescharacteristic
30#10622176—22no—
31Q8⋊(C11⋊C8)—22no—
32#10622103—22no—
33C22×Q8×C11D411yescharacteristic
34C2×C11×Q16—22no—
35C11×C4⋊Q8D411yescharacteristic
36C11×C4⋊Q8D411yescharacteristic
37C11×#125—21no—
38C11×C22⋊Q8—21no—
39C11×C22⋊Q8—21no—
40C4×Q8×C11—21no—
41C4×Q8×C11—21no—
42C4×Q8×C11—21no—
43C4×Q8×C11—21no—
44C4×Q8×C11—21no—
45C4×Q8×C11—21no—
46C11×#117—21no—
47C2×C11×C4⋊C4—21no—
48C2×C11×C4⋊C4D411yescharacteristic
49C2×C42×C11—21no—
50C2×C42×C11C2311yescharacteristic
51C2×C4⋊Dic11D411yescharacteristic
52C2×C4⋊Dic11D411yescharacteristic
53C2×Dic11⋊C4—22no—
54C2×Dic11⋊C4—21no—
55C2×Dic11⋊C4—21no—
56C2×#4318—21no—
57#66923—21no—
58#66923—21no—
59#66923—21no—
60#66923—21no—
61C11×#106—22no—
62C11×C4⋊C8—21no—
63C11×#103—22no—
64C11×#103—22no—
65C11×C22⋊C8—21no—
66C11×#97D412yes—
67C11⋊#95—22no—
68C11⋊#95—22no—
69C11⋊#95—22no—
70C11⋊#95—21no—
71C11⋊#95—21no—
72C11⋊#95D412yes—
73C22⋊(C11⋊C8)—21no—
74#66872—22no—
75#66872—22no—
76#66871—22no—
77#66871—22no—
78C4⋊(C11⋊C8)—21no—
79#66867—21no—
80#66867—21no—
81C4×C11⋊C8D412yes—
82#10025—111nomaximal, Sylow
83C2×Q8×C11—21no—
84C2×Q8×C11—21no—
85C2×Q8×C11—21no—
86C2×Q8×C11—21no—
87C2×Q8×C11—42no—
88C22×C4×C11—21no—
89C22×C4×C11—21no—
90C22×C4×C11C2×D411yescharacteristic
91C22×C4×C11C2×D411yescharacteristic
92C22×C4×C11C2×D411yescharacteristic
93C22×Dic11—22no—
94C22×Dic11—21no—
95C22×Dic11—21no—
96C11×Q16—44no—
97C2×C8×C11—22no—
98C11×C4⋊C4—21no—
99C11×C4⋊C4—21no—
100C11×C4⋊C4—21no—
101C11×C4⋊C4—21no—
102C11×C4⋊C4—21no—
103C11×C4⋊C4—21no—
104C11×C4⋊C4—41no—
105C11×C4⋊C4—41no—
106C11×C4⋊C4—41no—
107C11×C4⋊C4—41no—
108C11×C22⋊C4—41no—
109C42×C11—41no—
110C42×C11—41no—
111C42×C11—41no—
112C42×C11C2×D411yescharacteristic
113C42×C11C2×D411yescharacteristic
114C42×C11C2×D411yescharacteristic
115C42×C11#4111yescharacteristic
116C4⋊Dic11—21no—
117C4⋊Dic11—21no—
118C4⋊Dic11—21no—
119C4⋊Dic11—21no—
120Dic11⋊C4—44no—
121Dic11⋊C4—41no—
122Dic11⋊C4—41no—
123Dic11⋊C4—41no—
124Dic11⋊C4—41no—
125#4318—24no—
126C2×C11⋊C8—22no—
127C2×C11⋊C8—41no—
128#3166—111no—
129#3113D1111yescharacteristic
130#2634—111no—
131#1534—111no—
132#1515—111no—
133#1491—111no—
134#1288—111no—
135C23×C11#12011yescharacteristic
136Q8×C11—22no—
137Q8×C11—22no—
138Q8×C11—41no—
139Q8×C11—41no—
140Q8×C11—42no—
141Q8×C11—81no—
142C2×C4×C11—22no—
143C2×C4×C11—22no—
144C2×C4×C11—41no—
145C2×C4×C11—41no—
146C2×C4×C11—41no—
147C2×C4×C11—41no—
148C2×C4×C11—41no—
149C2×C4×C11—41no—
150C2×C4×C11—41no—
151C2×C4×C11—42no—
152C2×C4×C11#12011yescharacteristic
153C2×C4×C11#12011yescharacteristic
154C2×C4×C11#12111yescharacteristic
155C2×C4×C11#12111yescharacteristic
156C2×C4×C11#12111yescharacteristic
157C2×C4×C11#12711yescharacteristic
158C2×Dic11—42no—
159C2×Dic11—42no—
160C2×Dic11—42no—
161C2×Dic11—42no—
162C2×Dic11—41no—
163C2×Dic11—41no—
164C2×Dic11—42no—
165C8×C11—42no—
166C11⋊C8—24no—
167C11⋊C8—81no—
168#533C2×D1111yescharacteristic
169C2×#125—111no—
170C2×C4×Q8C2×D1111yescharacteristic
171#501—221no—
172#501—221no—
173#499—222no—
174#483—21no—
175#475—21no—
176#462—21no—
177#451—21no—
178#441—22no—
179#432—111no—
180#432C2×D1111yescharacteristic
181#428—221no—
182#428—221no—
183C4×M16—111no—
184#400—221no—
185#400—221no—
186#398—221no—
187#395—221no—
188#387—222no—
189#383—111no—
190#330—222no—
191#328—222no—
192Q8⋊C8—222no—
193C22×C11—21no—
194C22×C11—21no—
195C22×C11#39211yescharacteristic
196C22×C11#45612yes—
197C4×C11—21no—
198C4×C11—21no—
199C4×C11—21no—
200C4×C11—21no—
201C4×C11—21no—
202C4×C11—21no—
203C4×C11—42no—
204C4×C11—81no—
205C4×C11—81no—
206C4×C11—81no—
207Dic11—82no—
208Dic11—81no—
209Dic11—81no—
210C22×Q8C22⋊D1111yescharacteristic
211C2×Q16—22no—
212C2×M16—221no—
213C4⋊Q8C22⋊D1111yescharacteristic
214C4⋊Q8C22⋊D1111yescharacteristic
215#125—21no—
216#125—221no—
217#125—221no—
218#125—221no—
219#125—221no—
220C22⋊Q8—21no—
221C22⋊Q8—21no—
222C4×Q8—21no—
223C4×Q8—21no—
224C4×Q8—21no—
225C4×Q8—21no—
226C4×Q8—21no—
227C4×Q8—21no—
228#117—21no—
229C2×C4⋊C4—21no—
230C2×C4⋊C4—111no—
231C2×C4⋊C4—111no—
232C2×C4⋊C4—222no—
233C2×C4⋊C4—221no—
234C2×C4⋊C4—221no—
235C2×C4⋊C4C22⋊D1111yescharacteristic
236C2×C42—21no—
237C2×C42C22×D1111yescharacteristic
238#107—222no—
239#107—222no—
240#106—22no—
241#106—222no—
242#106—222no—
243C4⋊C8—21no—
244C4⋊C8—221no—
245#103—22no—
246#103—22no—
247C22⋊C8—21no—
248C22⋊C8—221no—
249#97—221no—
250#97—221no—
251#97C22⋊D1112yes—
252C4×C8—112no—
253#95—112no—
254#95—222no—
255#95—222no—
256#95—222no—
257#95—221no—
258#95—221no—
259C2×C11—22no—
260C2×C11#200511yescharacteristic
261C2×C11#200911yescharacteristic
262C2×C11#201011yescharacteristic
263C2×Q8—21no—
264C2×Q8—21no—
265C2×Q8—21no—
266C2×Q8—21no—
267C2×Q8—42no—
268C22×C4—21no—
269C22×C4—21no—
270C22×C4—222no—
271C22×C4—221no—
272C22×C4—221no—
273C22×C4D4×D1111yescharacteristic
274C22×C4D4×D1111yescharacteristic
275C22×C4C2×C22⋊D1111yescharacteristic
276Q16—44no—
277M16—224no—
278C2×C8—22no—
279C2×C8—222no—
280C2×C8—441no—
281C4⋊C4—21no—
282C4⋊C4—21no—
283C4⋊C4—21no—
284C4⋊C4—21no—
285C4⋊C4—21no—
286C4⋊C4—21no—
287C4⋊C4—41no—
288C4⋊C4—41no—
289C4⋊C4—41no—
290C4⋊C4—41no—
291C4⋊C4—221no—
292C4⋊C4—221no—
293C4⋊C4—221no—
294C4⋊C4—221no—
295C4⋊C4—444no—
296C4⋊C4—441no—
297C4⋊C4—441no—
298C4⋊C4—441no—
299C4⋊C4—441no—
300C22⋊C4—41no—
301C42—41no—
302C42—41no—
303C42—41no—
304C42D4×D1111yescharacteristic
305C42#434111yescharacteristic
306C42C2×C22⋊D1111yescharacteristic
307C42C2×C22⋊D1111yescharacteristic
308C11#1002511yescharacteristic, complemented, Sylow
309C23#6699011yescharacteristic
310Q8—22no—
311Q8—22no—
312Q8—41no—
313Q8—41no—
314Q8—42no—
315Q8—81no—
316C2×C4—22no—
317C2×C4—22no—
318C2×C4—41no—
319C2×C4—41no—
320C2×C4—41no—
321C2×C4—41no—
322C2×C4—42no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—41no—
326C2×C4—442no—
327C2×C4—442no—
328C2×C4—442no—
329C2×C4—442no—
330C2×C4—442no—
331C2×C4—441no—
332C2×C4—441no—
333C2×C4#6699011yescharacteristic
334C2×C4#6699111yescharacteristic
335C2×C4#6699211yescharacteristic
336C2×C4#6699211yescharacteristic
337C2×C4#6699311yescharacteristic
338C2×C4#6700611yescharacteristic
339C8—42no—
340C8—224no—
341C8—881no—
342C22—21no—
343C22—21no—
344C22#1062281812yes—
345C22#1062283611yescharacteristic
346C4—21no—
347C4—21no—
348C4—21no—
349C4—21no—
350C4—21no—
351C4—21no—
352C4—42no—
353C4—81no—
354C4—81no—
355C4—81no—
356C4—882no—
357C4—881no—
358C4—881no—
359C2—22no—
360C2#1306964911yescharacteristic
361C2#1306967411yescharacteristic
362C2#1306968111yescharacteristic
subgroupG/H
centerC22#10622836
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#3113C2
socleC22×C11#392
prime radicalC23×C11#120
hypercenter#3113D11
hypocenterC11#10025
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3113

Complements

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

NH ≅ G/Ntype
308. C11#10025semidirect

Maximal subgroups

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

subgroupindex
#130791692
#130744922
#130672422
#130671672
#130670632
#130664822
C11×#31132
#1002511