Finite Group Databasebeta

← #14654608

Subgroups — #14654608

Order 2816.

496 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 496 conjugacy classes of subgroups — too many to draw. Only its 85 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#13079822C211yesmaximal, characteristic
2#13078746C211yesmaximal, characteristic
3#13069559C211yesmaximal, characteristic
4#13067218C211yesmaximal, characteristic
5#13067063C211yesmaximal, characteristic
6#13066472C211yesmaximal, characteristic
7C11×#2584C211yesmaximal, characteristic
8C2×C11×#125C2211yescharacteristic
9C2×C4×Q8×C11C2211yescharacteristic
10#10623001C2211yescharacteristic
11C11×#398—21no—
12C11×#395—21no—
13C11×#389—21no—
14C11×#389—21no—
15C11×#389—22no—
16C4×C11×C4⋊C4C2211yescharacteristic
17#10622841—21no—
18#10622682—21no—
19#10622678—21no—
20#10622676—22no—
21#10622644—21no—
22#10622643—22no—
23#10622633—21no—
24#10622584—21no—
25#10622584—21no—
26#10622583—21no—
27#10622539C2211yescharacteristic
28#10622539C2211yescharacteristic
29C4×#4318C2211yescharacteristic
30#10622181—22no—
31Q8⋊(C11⋊C8)—22no—
32#10622161—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—21no—
43C2×C11×C4⋊C4—22no—
44C2×C11×C4⋊C4—21no—
45C2×C11×C4⋊C4—21no—
46C2×C11×C4⋊C4—21no—
47C2×C11×C4⋊C4—22no—
48C2×C11×C4⋊C4D411yescharacteristic
49C2×C11×C4⋊C4D411yescharacteristic
50C2×C11×C4⋊C4D411yescharacteristic
51C2×C42×C11—21no—
52C2×C42×C11D412yes—
53C2×C42×C11C2311yescharacteristic
54C2×#4326—22no—
55#66979—21no—
56#66977—21no—
57#66977—21no—
58C2×#4318—21no—
59#66923—21no—
60#66922D411yescharacteristic
61#66922D411yescharacteristic
62C4×Dic22—21no—
63C4×Dic22—21no—
64C11×#95—22no—
65C11×#95—22no—
66C11×#95—21no—
67#66899—22no—
68C22⋊(C11⋊C8)—21no—
69C22⋊(C11⋊C8)—21no—
70#66874—22no—
71#66874—22no—
72#66874—22no—
73#66872—22no—
74#66872—22no—
75#66871—22no—
76C4⋊(C11⋊C8)—21no—
77C4⋊(C11⋊C8)D412yes—
78#66867—21no—
79#66867—21no—
80#66867D412yes—
81C4×C11⋊C8—21no—
82#10011—111nomaximal, Sylow
83C2×Q8×C11—21no—
84C2×Q8×C11—21no—
85C2×Q8×C11—42no—
86C22×C4×C11—22no—
87C22×C4×C11—21no—
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—24no—
97C11×C4⋊C4—21no—
98C11×C4⋊C4—21no—
99C11×C4⋊C4—21no—
100C11×C4⋊C4—21no—
101C11×C4⋊C4—21no—
102C11×C4⋊C4—21no—
103C11×C4⋊C4—44no—
104C11×C4⋊C4—41no—
105C11×C4⋊C4—41no—
106C11×C4⋊C4—41no—
107C11×C4⋊C4—41no—
108C11×C4⋊C4—41no—
109C11×C4⋊C4—41no—
110C11×C4⋊C4—82no—
111C42×C11—42no—
112C42×C11—41no—
113C42×C11—41no—
114C42×C11C2×D411yescharacteristic
115C42×C11C2×D411yescharacteristic
116C42×C11C2×D411yescharacteristic
117C42×C11#4111yescharacteristic
118C22⋊Dic11—41no—
119#4326—44no—
120C4⋊Dic11—21no—
121C4⋊Dic11—21no—
122C4⋊Dic11—21no—
123C4⋊Dic11—21no—
124Dic11⋊C4—41no—
125Dic11⋊C4—41no—
126C4×Dic11—41no—
127#4318—22no—
128#4318—41no—
129C2×C11⋊C8—22no—
130C2×C11⋊C8—22no—
131C2×C11⋊C8—41no—
132#3236—111no—
133#3113—111no—
134#2584D1111yescharacteristic
135#1986—111no—
136#1528—111no—
137#1491—111no—
138#1285—111no—
139C23×C11#12011yescharacteristic
140Q8×C11—22no—
141Q8×C11—22no—
142Q8×C11—41no—
143Q8×C11—41no—
144C2×C4×C11—21no—
145C2×C4×C11—21no—
146C2×C4×C11—22no—
147C2×C4×C11—24no—
148C2×C4×C11—22no—
149C2×C4×C11—41no—
150C2×C4×C11—42no—
151C2×C4×C11—41no—
152C2×C4×C11—41no—
153C2×C4×C11—42no—
154C2×C4×C11—42no—
155C2×C4×C11—41no—
156C2×C4×C11—41no—
157C2×C4×C11—41no—
158C2×C4×C11—41no—
159C2×C4×C11—41no—
160C2×C4×C11—41no—
161C2×C4×C11—41no—
162C2×C4×C11#12011yescharacteristic
163C2×C4×C11#12011yescharacteristic
164C2×C4×C11#12111yescharacteristic
165C2×C4×C11#12111yescharacteristic
166C2×C4×C11#12111yescharacteristic
167C2×C4×C11#12711yescharacteristic
168C2×Dic11—41no—
169C2×Dic11—41no—
170Dic22—42no—
171Dic22—42no—
172C11⋊C8—42no—
173C11⋊C8—42no—
174C11⋊C8—42no—
175#533—111no—
176C2×#125C2×D1111yescharacteristic
177C2×C4×Q8C2×D1111yescharacteristic
178#501—221no—
179#491—221no—
180#484—221no—
181#483—221no—
182#483—221no—
183#479—222no—
184#475—221no—
185#462—221no—
186#451—221no—
187#441—222no—
188#432—111no—
189#432—111no—
190C4×M16—111no—
191#398—21no—
192#395—21no—
193#389—21no—
194#389—21no—
195#389—22no—
196C4×C4⋊C4C2×D1111yescharacteristic
197#339—222no—
198#330—222no—
199Q8⋊C8—222no—
200C22×C11—21no—
201C22×C11—21no—
202C22×C11#39211yescharacteristic
203C22×C11#45511yescharacteristic
204C22×C11#45611yescharacteristic
205C4×C11—21no—
206C4×C11—21no—
207C4×C11—21no—
208C4×C11—21no—
209C4×C11—21no—
210C4×C11—44no—
211C4×C11—42no—
212C4×C11—81no—
213C4×C11—81no—
214C4×C11—81no—
215C4×C11#45612yes—
216Dic11—81no—
217Dic11—81no—
218C22×Q8C22⋊D1111yescharacteristic
219C2×Q16—222no—
220C2×M16—221no—
221C4⋊Q8—111no—
222C4⋊Q8—111no—
223#125—21no—
224#125—21no—
225#125—21no—
226#125—21no—
227#125—221no—
228C22⋊Q8—221no—
229C22⋊Q8—221no—
230C4×Q8—21no—
231C4×Q8—21no—
232C4×Q8—21no—
233C4×Q8—21no—
234C4×Q8—221no—
235C4×Q8—221no—
236#117—221no—
237C2×C4⋊C4—21no—
238C2×C4⋊C4—22no—
239C2×C4⋊C4—21no—
240C2×C4⋊C4—21no—
241C2×C4⋊C4—21no—
242C2×C4⋊C4—22no—
243C2×C4⋊C4C22⋊D1111yescharacteristic
244C2×C4⋊C4C22⋊D1111yescharacteristic
245C2×C4⋊C4C22⋊D1111yescharacteristic
246C2×C42—21no—
247C2×C42C22⋊D1112yes—
248C2×C42C22×D1111yescharacteristic
249#107—222no—
250#106—222no—
251#106—222no—
252C4⋊C8—112no—
253C4⋊C8—221no—
254#103—222no—
255#103—222no—
256#103—222no—
257#103—222no—
258C22⋊C8—221no—
259C22⋊C8—221no—
260#97—112no—
261#97—221no—
262#97—221no—
263C4×C8—221no—
264#95—22no—
265#95—22no—
266#95—21no—
267C2×C11—21no—
268C2×C11—21no—
269C2×C11#200511yescharacteristic
270C2×C11#200711yescharacteristic
271C2×C11#201011yescharacteristic
272C2×Q8—21no—
273C2×Q8—21no—
274C2×Q8—42no—
275C2×Q8—221no—
276C2×Q8—221no—
277C22×C4—22no—
278C22×C4—21no—
279C22×C4—21no—
280C22×C4—21no—
281C22×C4—21no—
282C22×C4C2×C22⋊D1111yescharacteristic
283C22×C4C2×C22⋊D1111yescharacteristic
284C22×C4C2×C22⋊D1111yescharacteristic
285Q16—444no—
286M16—222no—
287M16—441no—
288C2×C8—222no—
289C2×C8—222no—
290C2×C8—441no—
291C4⋊C4—24no—
292C4⋊C4—21no—
293C4⋊C4—21no—
294C4⋊C4—21no—
295C4⋊C4—21no—
296C4⋊C4—21no—
297C4⋊C4—21no—
298C4⋊C4—44no—
299C4⋊C4—41no—
300C4⋊C4—41no—
301C4⋊C4—41no—
302C4⋊C4—41no—
303C4⋊C4—41no—
304C4⋊C4—41no—
305C4⋊C4—82no—
306C4⋊C4—221no—
307C4⋊C4—221no—
308C4⋊C4—221no—
309C4⋊C4—221no—
310C4⋊C4—441no—
311C4⋊C4—441no—
312C22⋊C4—441no—
313C42—42no—
314C42—41no—
315C42—41no—
316C42—441no—
317C42D4×D1111yescharacteristic
318C42D4×D1111yescharacteristic
319C42D4×D1111yescharacteristic
320C42#434111yescharacteristic
321C11#1001111yescharacteristic, complemented, Sylow
322C23#6700611yescharacteristic
323Q8—22no—
324Q8—22no—
325Q8—41no—
326Q8—41no—
327Q8—442no—
328Q8—442no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—22no—
332C2×C4—24no—
333C2×C4—22no—
334C2×C4—41no—
335C2×C4—42no—
336C2×C4—41no—
337C2×C4—41no—
338C2×C4—42no—
339C2×C4—42no—
340C2×C4—41no—
341C2×C4—41no—
342C2×C4—41no—
343C2×C4—41no—
344C2×C4—41no—
345C2×C4—41no—
346C2×C4—41no—
347C2×C4—441no—
348C2×C4—441no—
349C2×C4#6699011yescharacteristic
350C2×C4#6699011yescharacteristic
351C2×C4#6699111yescharacteristic
352C2×C4#6699211yescharacteristic
353C2×C4#6699211yescharacteristic
354C2×C4#6699311yescharacteristic
355C8—442no—
356C8—442no—
357C8—442no—
358C22—21no—
359C22—21no—
360C22#1062283611yescharacteristic
361C22#1062285511yescharacteristic
362C22#1062285911yescharacteristic
363C4—21no—
364C4—21no—
365C4—21no—
366C4—21no—
367C4—21no—
368C4—44no—
369C4—42no—
370C4—81no—
371C4—81no—
372C4—81no—
373C4—881no—
374C4—881no—
375C4#1062270812yes—
376C2—21no—
377C2—21no—
378C2#1306965211yescharacteristic
379C2#1306966311yescharacteristic
380C2#1306968111yescharacteristic
subgroupG/H
centerC22#10622836
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#2584C2
socleC22×C11#392
prime radicalC23×C11#120
hypercenter#2584D11
hypocenterC11#10011
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2584

Complements

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

NH ≅ G/Ntype
321. C11#10011semidirect

Maximal subgroups

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

subgroupindex
#130798222
#130787462
#130695592
#130672182
#130670632
#130664722
C11×#25842
#1001111