Finite Group Databasebeta

← #14654698

Subgroups — #14654698

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#13079165C211yesmaximal, characteristic
2#13078746C211yesmaximal, characteristic
3#13067243C211yesmaximal, characteristic
4#13067166C211yesmaximal, characteristic
5#13067063C211yesmaximal, characteristic
6#13066480C211yesmaximal, characteristic
7C11×#2634C211yesmaximal, characteristic
8C2×C11×#125C2211yescharacteristic
9C2×C4×Q8×C11C2211yescharacteristic
10#10623001C2211yescharacteristic
11C11×#400—21no—
12C11×#400—21no—
13C11×#398—21no—
14C11×#395—21no—
15C11×#387—22no—
16C11×#383C2211yescharacteristic
17#10622841—21no—
18#10622678—21no—
19#10622678—21no—
20#10622677—22no—
21#10622644—21no—
22#10622643—22no—
23#10622633—21no—
24#10622584—21no—
25#10622577—21no—
26#10622577—21no—
27#10622539C2211yescharacteristic
28#10622539C2211yescharacteristic
29C4×#4318C2211yescharacteristic
30#10622181—22no—
31Q8⋊(C11⋊C8)—22no—
32#10622090—22no—
33C22×Q8×C11D411yescharacteristic
34C11×#125—21no—
35C11×#125—21no—
36C11×#125—21no—
37C11×#125—21no—
38C4×Q8×C11—21no—
39C4×Q8×C11—21no—
40C4×Q8×C11—21no—
41C4×Q8×C11—21no—
42C2×C11×C4⋊C4—22no—
43C2×C11×C4⋊C4—21no—
44C2×C11×C4⋊C4—21no—
45C2×C11×C4⋊C4—21no—
46C2×C11×C4⋊C4D411yescharacteristic
47C2×C11×C4⋊C4D411yescharacteristic
48C2×C11×C4⋊C4D411yescharacteristic
49C2×C42×C11—21no—
50C2×C42×C11C2311yescharacteristic
51C2×#4326—22no—
52#66979—21no—
53#66977—21no—
54#66977—21no—
55C2×#4318—21no—
56#66923—21no—
57#66922D411yescharacteristic
58#66922D411yescharacteristic
59C4×Dic22—21no—
60C4×Dic22—21no—
61C11×#95—22no—
62C11×#95—22no—
63C11×#95—22no—
64C11×#95—21no—
65C11×#95—21no—
66C11×#95D412yes—
67#66899—22no—
68C22⋊(C11⋊C8)—21no—
69C22⋊(C11⋊C8)—21no—
70#66874—22no—
71#66872—22no—
72#66872—22no—
73#66872—22no—
74#66871—22no—
75#66871—22no—
76C4⋊(C11⋊C8)—21no—
77C4⋊(C11⋊C8)—21no—
78#66867—21no—
79#66867—21no—
80#66867D412yes—
81C4×C11⋊C8D412yes—
82#10025—111nomaximal, Sylow
83C2×Q8×C11—21no—
84C2×Q8×C11—21no—
85C2×Q8×C11—42no—
86C22×C4×C11—21no—
87C22×C4×C11—22no—
88C22×C4×C11—21no—
89C22×C4×C11—21no—
90C22×C4×C11—21no—
91C22×C4×C11C2×D411yescharacteristic
92C22×C4×C11C2×D411yescharacteristic
93C22×C4×C11C2×D411yescharacteristic
94C2×Dic22—21no—
95C2×Dic22—21no—
96C11×C4⋊C4—21no—
97C11×C4⋊C4—21no—
98C11×C4⋊C4—21no—
99C11×C4⋊C4—21no—
100C11×C4⋊C4—21no—
101C11×C4⋊C4—21no—
102C11×C4⋊C4—44no—
103C11×C4⋊C4—41no—
104C11×C4⋊C4—41no—
105C11×C4⋊C4—41no—
106C11×C4⋊C4—41no—
107C11×C4⋊C4—41no—
108C11×C4⋊C4—41no—
109C42×C11—41no—
110C42×C11—41no—
111C42×C11C2×D411yescharacteristic
112C42×C11C2×D411yescharacteristic
113C42×C11C2×D411yescharacteristic
114C42×C11#4111yescharacteristic
115C22⋊Dic11—41no—
116#4326—44no—
117C4⋊Dic11—21no—
118C4⋊Dic11—21no—
119C4⋊Dic11—21no—
120C4⋊Dic11—21no—
121Dic11⋊C4—41no—
122Dic11⋊C4—41no—
123C4×Dic11—41no—
124#4318—24no—
125C2×C11⋊C8—22no—
126C2×C11⋊C8—22no—
127C2×C11⋊C8—41no—
128#3166—111no—
129#3113—111no—
130#2634D1111yescharacteristic
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—
140C2×C4×C11—22no—
141C2×C4×C11—22no—
142C2×C4×C11—41no—
143C2×C4×C11—41no—
144C2×C4×C11—41no—
145C2×C4×C11—41no—
146C2×C4×C11—42no—
147C2×C4×C11—42no—
148C2×C4×C11—42no—
149C2×C4×C11—42no—
150C2×C4×C11—41no—
151C2×C4×C11—41no—
152C2×C4×C11—41no—
153C2×C4×C11—42no—
154C2×C4×C11—42no—
155C2×C4×C11#12011yescharacteristic
156C2×C4×C11#12011yescharacteristic
157C2×C4×C11#12111yescharacteristic
158C2×C4×C11#12111yescharacteristic
159C2×C4×C11#12111yescharacteristic
160C2×C4×C11#12711yescharacteristic
161C2×Dic11—41no—
162C2×Dic11—41no—
163Dic22—42no—
164Dic22—81no—
165C11⋊C8—24no—
166C11⋊C8—42no—
167C11⋊C8—81no—
168#533—111no—
169C2×#125C2×D1111yescharacteristic
170C2×C4×Q8C2×D1111yescharacteristic
171#501—221no—
172#501—221no—
173#499—222no—
174#483—221no—
175#475—221no—
176#462—221no—
177#451—221no—
178#441—222no—
179#432—111no—
180#432—111no—
181#428—221no—
182#428—221no—
183C4×M16—111no—
184#400—21no—
185#400—21no—
186#398—21no—
187#395—21no—
188#387—22no—
189#383C2×D1111yescharacteristic
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—82no—
205C4×C11—81no—
206C4×C11—81no—
207C4×C11—81no—
208Dic11—81no—
209Dic11—81no—
210C22×Q8C22⋊D1111yescharacteristic
211C2×Q16—222no—
212C2×M16—221no—
213C4⋊Q8—111no—
214C4⋊Q8—111no—
215#125—21no—
216#125—21no—
217#125—21no—
218#125—21no—
219#125—221no—
220C22⋊Q8—221no—
221C22⋊Q8—221no—
222C4×Q8—21no—
223C4×Q8—21no—
224C4×Q8—21no—
225C4×Q8—21no—
226C4×Q8—221no—
227C4×Q8—221no—
228#117—221no—
229C2×C4⋊C4—22no—
230C2×C4⋊C4—21no—
231C2×C4⋊C4—21no—
232C2×C4⋊C4—21no—
233C2×C4⋊C4C22⋊D1111yescharacteristic
234C2×C4⋊C4C22⋊D1111yescharacteristic
235C2×C4⋊C4C22⋊D1111yescharacteristic
236C2×C42—21no—
237C2×C42C22×D1111yescharacteristic
238#107—222no—
239#107—222no—
240#106—222no—
241#106—222no—
242#106—222no—
243C4⋊C8—221no—
244C4⋊C8—221no—
245#103—222no—
246#103—222no—
247C22⋊C8—221no—
248C22⋊C8—221no—
249#97—112no—
250#97—221no—
251#97—221no—
252C4×C8—112no—
253#95—22no—
254#95—22no—
255#95—22no—
256#95—21no—
257#95—21no—
258#95C22⋊D1112yes—
259C2×C11—22no—
260C2×C11#200511yescharacteristic
261C2×C11#200911yescharacteristic
262C2×C11#201011yescharacteristic
263C2×Q8—21no—
264C2×Q8—21no—
265C2×Q8—42no—
266C2×Q8—221no—
267C2×Q8—221no—
268C22×C4—21no—
269C22×C4—22no—
270C22×C4—21no—
271C22×C4—21no—
272C22×C4—21no—
273C22×C4C2×C22⋊D1111yescharacteristic
274C22×C4C2×C22⋊D1111yescharacteristic
275C22×C4C2×C22⋊D1111yescharacteristic
276Q16—444no—
277M16—224no—
278C2×C8—222no—
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—44no—
288C4⋊C4—41no—
289C4⋊C4—41no—
290C4⋊C4—41no—
291C4⋊C4—41no—
292C4⋊C4—41no—
293C4⋊C4—41no—
294C4⋊C4—221no—
295C4⋊C4—221no—
296C4⋊C4—221no—
297C4⋊C4—221no—
298C4⋊C4—441no—
299C4⋊C4—441no—
300C22⋊C4—441no—
301C42—41no—
302C42—41no—
303C42—441no—
304C42D4×D1111yescharacteristic
305C42D4×D1111yescharacteristic
306C42D4×D1111yescharacteristic
307C42#434111yescharacteristic
308C11#1002511yescharacteristic, complemented, Sylow
309C23#6700611yescharacteristic
310Q8—22no—
311Q8—22no—
312Q8—41no—
313Q8—41no—
314Q8—442no—
315Q8—881no—
316C2×C4—22no—
317C2×C4—22no—
318C2×C4—41no—
319C2×C4—41no—
320C2×C4—41no—
321C2×C4—41no—
322C2×C4—42no—
323C2×C4—42no—
324C2×C4—42no—
325C2×C4—42no—
326C2×C4—41no—
327C2×C4—41no—
328C2×C4—41no—
329C2×C4—42no—
330C2×C4—42no—
331C2×C4—441no—
332C2×C4—441no—
333C2×C4#6699011yescharacteristic
334C2×C4#6699011yescharacteristic
335C2×C4#6699111yescharacteristic
336C2×C4#6699211yescharacteristic
337C2×C4#6699211yescharacteristic
338C2×C4#6699311yescharacteristic
339C8—224no—
340C8—442no—
341C8—881no—
342C22—21no—
343C22—21no—
344C22#1062283611yescharacteristic
345C22#1062285912yes—
346C4—21no—
347C4—21no—
348C4—21no—
349C4—21no—
350C4—21no—
351C4—21no—
352C4—42no—
353C4—82no—
354C4—81no—
355C4—81no—
356C4—81no—
357C4—881no—
358C4—881no—
359C2—22no—
360C2#1306965011yescharacteristic
361C2#1306967611yescharacteristic
362C2#1306968111yescharacteristic
subgroupG/H
centerC22#10622836
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#2634C2
socleC22×C11#392
prime radicalC23×C11#120
hypercenter#2634D11
hypocenterC11#10025
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2634

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
#130791652
#130787462
#130672432
#130671662
#130670632
#130664802
C11×#26342
#1002511