Finite Group Databasebeta

← #14654641

Subgroups — #14654641

Order 2816.

528 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 528 conjugacy classes of subgroups — too many to draw. Only its 101 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#13078651C211yesmaximal, characteristic
2#13071907C211yesmaximal, characteristic
3#13069598C211yesmaximal, characteristic
4#13067046C211yesmaximal, characteristic
5#13067045C211yesmaximal, characteristic
6#13066444C211yesmaximal, characteristic
7C11×#3104C211yesmaximal, characteristic
8C11×#533C2211yescharacteristic
9C2×C4×Q8×C11C2211yescharacteristic
10C2×C4×Dic22C2211yescharacteristic
11C11×#484—21no—
12C11×#477—21no—
13C11×#462—21no—
14C11×#451—21no—
15C4×C11×Q16—22no—
16C11×#431C2211yescharacteristic
17#10622842—21no—
18#10622704—21no—
19#10622703—21no—
20#10622663—21no—
21#10622657—21no—
22C4×#4326—22no—
23#10622596—21no—
24#10622593—21no—
25#10622592—21no—
26#10622545C2211yescharacteristic
27C4×Dic11⋊C4—22no—
28#10622538C2211yescharacteristic
29#10622537C2211yescharacteristic
30Q8⋊(C11⋊C8)—22no—
31#10622170—22no—
32#10622094—22no—
33C22×Q8×C11D411yescharacteristic
34C22×Dic22D411yescharacteristic
35C2×C11×Q16—22no—
36C11×C4⋊Q8D411yescharacteristic
37C11×C4⋊Q8D411yescharacteristic
38C11×#125—21no—
39C11×C22⋊Q8—21no—
40C11×C22⋊Q8—21no—
41C4×Q8×C11—21no—
42C4×Q8×C11—21no—
43C4×Q8×C11—21no—
44C4×Q8×C11—21no—
45C4×Q8×C11—21no—
46C4×Q8×C11—21no—
47C11×#117—21no—
48C2×C11×C4⋊C4—21no—
49C2×C11×C4⋊C4D411yescharacteristic
50C2×C42×C11—21no—
51C2×C42×C11C2311yescharacteristic
52C2×#4326—22no—
53C2×C4⋊Dic11D411yescharacteristic
54C2×Dic11⋊C4—22no—
55C2×Dic11⋊C4—22no—
56C2×Dic11⋊C4—21no—
57C2×C4×Dic11—21no—
58C2×C4×Dic11D412yes—
59C2×#4318—21no—
60C4×Dic22—21no—
61C4×Dic22—21no—
62C4×Dic22—21no—
63C4×Dic22—21no—
64C11×#107—22no—
65C11×C4⋊C8—21no—
66C11×#103—22no—
67C11×#103—22no—
68C11×C22⋊C8—21no—
69C4×C8×C11D412yes—
70#66899—22no—
71C11⋊#95—22no—
72C11⋊#95—22no—
73C11⋊#95—21no—
74C11⋊#95—21no—
75C22⋊(C11⋊C8)—21no—
76#66874—22no—
77#66871—22no—
78C4⋊(C11⋊C8)—21no—
79C4⋊(C11⋊C8)—21no—
80C4⋊(C11⋊C8)—21no—
81C4×C11⋊C8D412yes—
82#10017—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—
96C2×Dic22—21no—
97C2×Dic22—21no—
98C2×Dic22—42no—
99C11×Q16—44no—
100C2×C8×C11—22no—
101C11×C4⋊C4—21no—
102C11×C4⋊C4—21no—
103C11×C4⋊C4—21no—
104C11×C4⋊C4—21no—
105C11×C4⋊C4—21no—
106C11×C4⋊C4—21no—
107C11×C4⋊C4—41no—
108C11×C4⋊C4—41no—
109C11×C4⋊C4—41no—
110C11×C4⋊C4—41no—
111C11×C22⋊C4—41no—
112C42×C11—41no—
113C42×C11—41no—
114C42×C11—41no—
115C42×C11C2×D411yescharacteristic
116C42×C11C2×D411yescharacteristic
117C42×C11C2×D411yescharacteristic
118C42×C11#4111yescharacteristic
119#4326—44no—
120C4⋊Dic11—21no—
121C4⋊Dic11—21no—
122Dic11⋊C4—44no—
123Dic11⋊C4—44no—
124Dic11⋊C4—41no—
125Dic11⋊C4—41no—
126C4×Dic11—22no—
127C4×Dic11—41no—
128C4×Dic11—41no—
129C4×Dic11Q1614yescomplemented
130#4318—42no—
131C2×C11⋊C8—22no—
132C2×C11⋊C8—41no—
133#3104—111no—
134#3104D1111yescharacteristic
135#2399—111no—
136#1995—111no—
137#1487—111no—
138#1487—111no—
139#1274—111no—
140C23×C11#12011yescharacteristic
141Q8×C11—22no—
142Q8×C11—22no—
143Q8×C11—41no—
144Q8×C11—41no—
145Q8×C11—42no—
146Q8×C11—42no—
147C2×C4×C11—22no—
148C2×C4×C11—41no—
149C2×C4×C11—41no—
150C2×C4×C11—41no—
151C2×C4×C11—41no—
152C2×C4×C11—42no—
153C2×C4×C11—41no—
154C2×C4×C11—41no—
155C2×C4×C11—41no—
156C2×C4×C11#12011yescharacteristic
157C2×C4×C11#12011yescharacteristic
158C2×C4×C11#12111yescharacteristic
159C2×C4×C11#12111yescharacteristic
160C2×C4×C11#12111yescharacteristic
161C2×C4×C11#12711yescharacteristic
162C2×C4×C11C2×Q1612yes—
163C2×C4×C11#13712yes—
164C2×Dic11—22no—
165C2×Dic11—24no—
166C2×Dic11—42no—
167C2×Dic11—42no—
168C2×Dic11—41no—
169C2×Dic11—41no—
170C2×Dic11—42no—
171C2×Dic11—41no—
172Dic22—22no—
173Dic22—22no—
174Dic22—41no—
175Dic22—41no—
176C8×C11—42no—
177C11⋊C8—42no—
178C11⋊C8—81no—
179#533C2×D1111yescharacteristic
180C2×C4×Q8—111no—
181C2×C4×Q8C2×D1111yescharacteristic
182#484—21no—
183#484—221no—
184#477—21no—
185#477—221no—
186#462—21no—
187#462—221no—
188#451—21no—
189#451—221no—
190C4×Q16—22no—
191C4×Q16—222no—
192#431—111no—
193#431C2×D1111yescharacteristic
194#423—111no—
195#398—221no—
196#398—221no—
197#395—221no—
198#395—221no—
199C4×C4⋊C4—222no—
200#376—111no—
201#339—222no—
202Q8⋊C8—222no—
203Q8⋊C8—222no—
204C22×C11—21no—
205C22×C11—21no—
206C22×C11#39211yescharacteristic
207C22×C11#45112yes—
208C4×C11—21no—
209C4×C11—21no—
210C4×C11—21no—
211C4×C11—21no—
212C4×C11—42no—
213C4×C11—81no—
214C4×C11—81no—
215C4×C11—81no—
216C4×C11#46212yes—
217C4×C11#49411yescharacteristic
218C4×C11#49711yescharacteristic
219Dic11—44no—
220Dic11—42no—
221Dic11—81no—
222C22×Q8—111no—
223C22×Q8C22⋊D1111yescharacteristic
224C2×Q16—22no—
225C2×Q16—222no—
226C2×M16—221no—
227C4⋊Q8C22⋊D1111yescharacteristic
228C4⋊Q8C22⋊D1111yescharacteristic
229#125—21no—
230C22⋊Q8—21no—
231C22⋊Q8—21no—
232C4×Q8—21no—
233C4×Q8—21no—
234C4×Q8—21no—
235C4×Q8—21no—
236C4×Q8—21no—
237C4×Q8—21no—
238C4×Q8—221no—
239C4×Q8—221no—
240C4×Q8—221no—
241C4×Q8—221no—
242#117—21no—
243C2×C4⋊C4—21no—
244C2×C4⋊C4—111no—
245C2×C4⋊C4—222no—
246C2×C4⋊C4—222no—
247C2×C4⋊C4—221no—
248C2×C4⋊C4C22⋊D1111yescharacteristic
249C2×C42—21no—
250C2×C42—112no—
251C2×C42—221no—
252C2×C42C22×D1111yescharacteristic
253#107—22no—
254#107—222no—
255C4⋊C8—21no—
256C4⋊C8—221no—
257C4⋊C8—221no—
258C4⋊C8—221no—
259#103—22no—
260#103—22no—
261#103—222no—
262#103—222no—
263C22⋊C8—21no—
264C22⋊C8—221no—
265C4×C8—112no—
266C4×C8C22⋊D1112yes—
267#95—222no—
268#95—222no—
269#95—221no—
270#95—221no—
271C2×C11—22no—
272C2×C11#201011yescharacteristic
273C2×C11#201011yescharacteristic
274C2×C11#201611yescharacteristic
275C2×Q8—21no—
276C2×Q8—21no—
277C2×Q8—21no—
278C2×Q8—21no—
279C2×Q8—42no—
280C2×Q8—221no—
281C2×Q8—221no—
282C2×Q8—442no—
283C22×C4—21no—
284C22×C4—21no—
285C22×C4—222no—
286C22×C4—221no—
287C22×C4—221no—
288C22×C4D4×D1111yescharacteristic
289C22×C4D4×D1111yescharacteristic
290C22×C4C2×C22⋊D1111yescharacteristic
291Q16—44no—
292Q16—444no—
293M16—442no—
294C2×C8—22no—
295C2×C8—222no—
296C2×C8—441no—
297C4⋊C4—21no—
298C4⋊C4—21no—
299C4⋊C4—21no—
300C4⋊C4—21no—
301C4⋊C4—21no—
302C4⋊C4—21no—
303C4⋊C4—41no—
304C4⋊C4—41no—
305C4⋊C4—41no—
306C4⋊C4—41no—
307C4⋊C4—221no—
308C4⋊C4—221no—
309C4⋊C4—444no—
310C4⋊C4—444no—
311C4⋊C4—441no—
312C4⋊C4—441no—
313C22⋊C4—41no—
314C42—41no—
315C42—41no—
316C42—41no—
317C42—114no—
318C42—222no—
319C42—441no—
320C42—441no—
321C42D4×D1111yescharacteristic
322C42#434111yescharacteristic
323C42C2×C22⋊D1111yescharacteristic
324C42C2×C22⋊D1111yescharacteristic
325C11#1001711yescharacteristic, complemented, Sylow
326C23#6699011yescharacteristic
327Q8—22no—
328Q8—22no—
329Q8—41no—
330Q8—41no—
331Q8—42no—
332Q8—42no—
333Q8—222no—
334Q8—222no—
335Q8—441no—
336Q8—441no—
337C2×C4—22no—
338C2×C4—41no—
339C2×C4—41no—
340C2×C4—41no—
341C2×C4—41no—
342C2×C4—42no—
343C2×C4—41no—
344C2×C4—41no—
345C2×C4—41no—
346C2×C4—222no—
347C2×C4—224no—
348C2×C4—442no—
349C2×C4—442no—
350C2×C4—441no—
351C2×C4—441no—
352C2×C4—442no—
353C2×C4—441no—
354C2×C4Q16×D1112yes—
355C2×C4#6697112yes—
356C2×C4#6699011yescharacteristic
357C2×C4#6699111yescharacteristic
358C2×C4#6699211yescharacteristic
359C2×C4#6699211yescharacteristic
360C2×C4#6699311yescharacteristic
361C2×C4#6700611yescharacteristic
362C8—42no—
363C8—442no—
364C8—881no—
365C22—21no—
366C22—21no—
367C22#1062279912yes—
368C22#1062283611yescharacteristic
369C4—21no—
370C4—21no—
371C4—21no—
372C4—21no—
373C4—42no—
374C4—81no—
375C4—81no—
376C4—81no—
377C4—444no—
378C4—442no—
379C4—881no—
380C4#1062279411yescharacteristic
381C4#1062279512yes—
382C4#1062280311yescharacteristic
383C2—22no—
384C2#1306968011yescharacteristic
385C2#1306968111yescharacteristic
386C2#1306971411yescharacteristic
subgroupG/H
centerC2×C4#66993
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#3104C2
socleC22×C11#392
prime radicalC23×C11#120
hypercenter#3104D11
hypocenterC11#10017
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #3104

Complements

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

NH ≅ G/Ntype
129. C4×Dic11Q16semidirect
325. C11#10017semidirect

Maximal subgroups

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

subgroupindex
#130786512
#130719072
#130695982
#130670462
#130670452
#130664442
C11×#31042
#1001711