Finite Group Databasebeta

← #14656214

Subgroups — #14656214

Order 2816.

604 conjugacy classes of subgroups; only the 105 normal subgroups are shown.

normal subgroups only

This group has 604 conjugacy classes of subgroups — too many to draw. Only its 105 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#13079554C211yesmaximal, characteristic
2#13073615C211yesmaximal, characteristic
3#13067285C211yesmaximal, characteristic
4#13067115C211yesmaximal, characteristic, complemented
5#13067011C211yesmaximal, characteristic, complemented
6#13066517C211yesmaximal, characteristic, complemented
7C11×#3078C211yesmaximal, characteristic, complemented
8C11×#533C2211yescharacteristic
9C2×C4×Q8×C11C2211yescharacteristic
10C2×#67000—21no—
11C2×#66927C2211yescharacteristic
12C11×#479—22no—
13C11×#477—21no—
14C11×#475—21no—
15C11×#428—21no—
16C11×#423C2211yescharacteristic
17C11×#419—21no—
18#10622701—21no—
19#10622698—21no—
20#10622659—22no—
21#10622640—22no—
22#10622604—22no—
23#10622601—21no—
24#10622552—22no—
25C4×C4⋊Dic11C2211yescharacteristic
26#10622538C2211yescharacteristic
27#10622538C2211yescharacteristic
28#10622176—22no—
29Q8⋊(C11⋊C8)—22no—
30#10622123—22no—
31C22×Q8×C11D411yescharacteristic
32C22×D44—21no—
33C22×D44—21no—
34C22×D44D412yes—
35C2×C11×M16—21no—
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
52#67000—42no—
53#67000—42no—
54C2×#4325—24no—
55C2×(C2×D11)⋊C4—24no—
56C2×(C2×D11)⋊C4—24no—
57C2×C4⋊Dic11—21no—
58C2×C4×Dic11—21no—
59#66927—21no—
60#66927—21no—
61#66927—21no—
62#66927—21no—
63C11×#107—22no—
64C11×#106—22no—
65C11×C4⋊C8—21no—
66C11×C4⋊C8D412yes—
67C11×#103—22no—
68C11×#103—22no—
69C11⋊#95D412yes—
70C22⋊(C11⋊C8)—21no—
71C22⋊(C11⋊C8)—21no—
72#66873—24no—
73C4⋊(C11⋊C8)—21no—
74C4⋊(C11⋊C8)D412yes—
75C4×C11⋊C8—21no—
76C4×C11⋊C8—21no—
77#10250—111nomaximal, Sylow
78C23×D11—22no—
79C2×Q8×C11—21no—
80C2×Q8×C11—21no—
81C2×Q8×C11—21no—
82C2×Q8×C11—21no—
83C2×Q8×C11—21no—
84C2×Q8×C11—21no—
85C2×Q8×C11—21no—
86C2×Q8×C11SD1612yescomplemented
87C22×C4×C11—21no—
88C22×C4×C11—21no—
89C22×C4×C11C2×D411yescharacteristic
90C22×C4×C11C2×D411yescharacteristic
91C22×C4×C11C2×D411yescharacteristic
92C22×Dic11—22no—
93C2×D44—22no—
94C2×D44—22no—
95C2×D44—44no—
96C2×D44—41no—
97C2×D44—41no—
98C2×D44—41no—
99C2×D44—41no—
100C2×D44—41no—
101C2×D44—41no—
102C2×D44—41no—
103C2×D44—41no—
104C2×D44—82no—
105C11×M16—41no—
106C11×M16—41no—
107C2×C8×C11—22no—
108C11×C4⋊C4—21no—
109C11×C4⋊C4—21no—
110C11×C4⋊C4—21no—
111C11×C4⋊C4—21no—
112C11×C4⋊C4—21no—
113C11×C4⋊C4—21no—
114C11×C4⋊C4—41no—
115C11×C4⋊C4—41no—
116C11×C4⋊C4—41no—
117C11×C4⋊C4—41no—
118C11×C22⋊C4—41no—
119C42×C11—41no—
120C42×C11—41no—
121C42×C11—41no—
122C42×C11C2×D411yescharacteristic
123C42×C11C2×D411yescharacteristic
124C42×C11C2×D411yescharacteristic
125C42×C11#4111yescharacteristic
126#4325—84no—
127(C2×D11)⋊C4—48no—
128(C2×D11)⋊C4—84no—
129C4⋊Dic11—42no—
130C4×Dic11—41no—
131C4×Dic11—41no—
132C2×C11⋊C8—22no—
133C2×C11⋊C8—41no—
134#3208—111no—
135#3078D1111yescharacteristic, complemented
136#2548—111no—
137#1545—111no—
138#1503—111no—
139#1479—111no—
140#1303—111no—
141C23×C11#12011yescharacteristic
142C22×D11—44no—
143C22×D11—44no—
144C22×D11—42no—
145C22×D11—42no—
146C22×D11—42no—
147Q8×C11—22no—
148Q8×C11—22no—
149Q8×C11—41no—
150Q8×C11—41no—
151Q8×C11—42no—
152Q8×C11—81no—
153C2×C4×C11—22no—
154C2×C4×C11—22no—
155C2×C4×C11—41no—
156C2×C4×C11—41no—
157C2×C4×C11—41no—
158C2×C4×C11—42no—
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×C4×C11C2×SD1611yescharacteristic
169C2×C4×C11#13511yescharacteristic
170C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
171C2×C4×C11#13711yescharacteristic
172C2×Dic11—42no—
173C2×Dic11—42no—
174C2×Dic11—42no—
175D44—44no—
176D44—82no—
177D44—82no—
178D44—82no—
179D44—81no—
180D44—81no—
181D44—81no—
182D44—81no—
183C8×C11—42no—
184C11⋊C8—42no—
185C11⋊C8—81no—
186#533C2×D1111yescharacteristic
187C2×#127—111no—
188C2×#124—221no—
189C2×C4×Q8C2×D1111yescharacteristic
190#492—221no—
191#486—221no—
192#479—22no—
193#477—21no—
194#475—21no—
195#460—222no—
196#450—222no—
197#431—111no—
198#431—111no—
199#428—21no—
200#423C2×D1111yescharacteristic
201#419—21no—
202#394—222no—
203#390—222no—
204#390—221no—
205C4×C4⋊C4—111no—
206#331—222no—
207#328—222no—
208Q8⋊C8—222no—
209C22×C11—21no—
210C22×C11—21no—
211C22×C11#39211yescharacteristic
212C22×C11#45011yescharacteristic
213C22×C11#45211yescharacteristic
214C2×D11—84no—
215C2×D11—84no—
216C2×D11—82no—
217C2×D11—82no—
218C2×D11—82no—
219C4×C11—21no—
220C4×C11—21no—
221C4×C11—21no—
222C4×C11—42no—
223C4×C11—81no—
224C4×C11—81no—
225C4×C11—81no—
226C4×C11#44811yescharacteristic
227C4×C11#44911yescharacteristic
228C4×C11#45512yes—
229C4×C11#46511yescharacteristic
230C4×C11#46811yescharacteristic
231Dic11—82no—
232C22×Q8C22⋊D1111yescharacteristic
233C22×D4—112no—
234C22×D4—221no—
235C22×D4—221no—
236C2×SD16—224no—
237C2×M16—21no—
238C4⋊Q8C22⋊D1111yescharacteristic
239C4⋊Q8C22⋊D1111yescharacteristic
240#127—221no—
241#127—221no—
242#127—221no—
243#127—221no—
244#125—21no—
245#124—442no—
246#124—442no—
247C22⋊Q8—21no—
248C22⋊Q8—21no—
249C4×Q8—21no—
250C4×Q8—21no—
251C4×Q8—21no—
252C4×Q8—21no—
253C4×Q8—21no—
254C4×Q8—21no—
255#117—21no—
256C2×C4⋊C4—21no—
257C2×C4⋊C4—221no—
258C2×C4⋊C4C22⋊D1111yescharacteristic
259C2×C22⋊C4—224no—
260C2×C22⋊C4—224no—
261C2×C42—21no—
262C2×C42—221no—
263C2×C42C22×D1111yescharacteristic
264#107—22no—
265#106—22no—
266C4⋊C8—21no—
267C4⋊C8—112no—
268C4⋊C8—221no—
269C4⋊C8C22⋊D1112yes—
270#103—22no—
271#103—22no—
272#102—224no—
273C22⋊C8—221no—
274C22⋊C8—221no—
275C4×C8—221no—
276C4×C8—221no—
277#95—112no—
278C2×C11—21no—
279C2×C11—21no—
280C2×C11#200011yescharacteristic
281C2×C11#200411yescharacteristic
282C2×C11#200811yescharacteristic
283D11—162no—
284C24—222no—
285C2×Q8—21no—
286C2×Q8—21no—
287C2×Q8—21no—
288C2×Q8—21no—
289C2×Q8—21no—
290C2×Q8—21no—
291C2×Q8—21no—
292C2×Q8#432512yescomplemented
293C2×D4—222no—
294C2×D4—222no—
295C2×D4—444no—
296C2×D4—441no—
297C2×D4—441no—
298C2×D4—441no—
299C2×D4—441no—
300C2×D4—441no—
301C2×D4—441no—
302C2×D4—441no—
303C2×D4—441no—
304C2×D4—882no—
305C22×C4—21no—
306C22×C4—21no—
307C22×C4—222no—
308C22×C4D4×D1111yescharacteristic
309C22×C4D4×D1111yescharacteristic
310C22×C4C2×C22⋊D1111yescharacteristic
311SD16—884no—
312M16—41no—
313M16—41no—
314C2×C8—22no—
315C2×C8—222no—
316C2×C8—441no—
317C4⋊C4—21no—
318C4⋊C4—21no—
319C4⋊C4—21no—
320C4⋊C4—21no—
321C4⋊C4—21no—
322C4⋊C4—21no—
323C4⋊C4—41no—
324C4⋊C4—41no—
325C4⋊C4—41no—
326C4⋊C4—41no—
327C4⋊C4—442no—
328C22⋊C4—41no—
329C22⋊C4—448no—
330C22⋊C4—884no—
331C42—41no—
332C42—41no—
333C42—41no—
334C42—441no—
335C42—441no—
336C42D4×D1111yescharacteristic
337C42#434111yescharacteristic
338C42C2×C22⋊D1111yescharacteristic
339C42C2×C22⋊D1111yescharacteristic
340C11#1025011yescharacteristic, complemented, Sylow
341C23—444no—
342C23—444no—
343C23—442no—
344C23—442no—
345C23—442no—
346C23#6699011yescharacteristic
347Q8—22no—
348Q8—22no—
349Q8—41no—
350Q8—41no—
351Q8—42no—
352Q8—81no—
353D4—444no—
354D4—882no—
355D4—882no—
356D4—882no—
357D4—881no—
358D4—881no—
359D4—881no—
360D4—881no—
361C2×C4—22no—
362C2×C4—22no—
363C2×C4—41no—
364C2×C4—41no—
365C2×C4—41no—
366C2×C4—42no—
367C2×C4—41no—
368C2×C4—41no—
369C2×C4—41no—
370C2×C4—442no—
371C2×C4—442no—
372C2×C4—442no—
373C2×C4#6699011yescharacteristic
374C2×C4#6699111yescharacteristic
375C2×C4#6699211yescharacteristic
376C2×C4#6699211yescharacteristic
377C2×C4#6699311yescharacteristic
378C2×C4C2×#432511yescharacteristic
379C2×C4#6699511yescharacteristic
380C2×C4#6700211yescharacteristic
381C2×C4#6700311yescharacteristic
382C2×C4#6700611yescharacteristic
383C8—42no—
384C8—442no—
385C8—881no—
386C22—21no—
387C22—21no—
388C22—884no—
389C22—884no—
390C22—882no—
391C22—882no—
392C22—882no—
393C22#1062265911yescharacteristic
394C22#1062266011yescharacteristic
395C22#1062283611yescharacteristic
396C4—21no—
397C4—21no—
398C4—21no—
399C4—42no—
400C4—81no—
401C4—81no—
402C4—81no—
403C4—882no—
404C4#1062266111yescharacteristic
405C4#1062266211yescharacteristic
406C4#1062281512yes—
407C4#1062284011yescharacteristic
408C4#1062285111yescharacteristic
409C2—21no—
410C2—21no—
411C2—1762no—
412C2#1306961711yescharacteristic
413C2#1306964211yescharacteristic
414C2#1306966611yescharacteristic
subgroupG/H
centerC22#10622836
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#3078C2
socleC22×C11#392
prime radicalC2×#66927C22
hypercenter#3078D11
hypocenterC11#10250
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3078

Complements

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

NH ≅ G/Ntype
4. #13067115C2semidirect
5. #13067011C2semidirect
6. #13066517C2semidirect
7. C11×#3078C2semidirect
86. C2×Q8×C11SD16semidirect
135. #3078D11semidirect
292. C2×Q8#4325semidirect
340. C11#10250semidirect

Maximal subgroups

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

subgroupindex
#130795542
#130736152
#130672852
#130671152
#130670112
#130665172
C11×#30782
#1025011