Finite Group Databasebeta

← #14656221

Subgroups — #14656221

Order 2816.

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

normal subgroups only

This group has 524 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#13079757C211yesmaximal, characteristic
2#13073601C211yesmaximal, characteristic
3#13067289C211yesmaximal, characteristic
4#13067115C211yesmaximal, characteristic
5#13067011C211yesmaximal, characteristic
6#13066517C211yesmaximal, characteristic
7C11×#3078C211yesmaximal, characteristic
8C11×#533C2211yescharacteristic
9C2×C4×Q8×C11C2211yescharacteristic
10C2×#66997—21no—
11C2×#66922C2211yescharacteristic
12C11×#479—22no—
13C11×#477—21no—
14C11×#475—21no—
15C11×#428—21no—
16C11×#423C2211yescharacteristic
17C11×#419—21no—
18#10622694—21no—
19#10622692—21no—
20#10622656—22no—
21#10622633—22no—
22#10622596—22no—
23#10622587—21no—
24C4×C4⋊Dic11C2211yescharacteristic
25#10622541—22no—
26#10622538C2211yescharacteristic
27#10622538C2211yescharacteristic
28#10622176—22no—
29Q8⋊(C11⋊C8)—22no—
30#10622120—22no—
31C22×Q8×C11D411yescharacteristic
32C22×Dic22—21no—
33C2×C11×M16—21no—
34C11×C4⋊Q8D411yescharacteristic
35C11×C4⋊Q8D411yescharacteristic
36C11×#125—21no—
37C11×C22⋊Q8—21no—
38C11×C22⋊Q8—21no—
39C4×Q8×C11—21no—
40C4×Q8×C11—21no—
41C4×Q8×C11—21no—
42C4×Q8×C11—21no—
43C4×Q8×C11—21no—
44C4×Q8×C11—21no—
45C11×#117—21no—
46C2×C11×C4⋊C4—21no—
47C2×C11×C4⋊C4D411yescharacteristic
48C2×C42×C11—21no—
49C2×C42×C11C2311yescharacteristic
50#66997—42no—
51#66997—42no—
52C2×C4⋊Dic11—21no—
53C2×C4⋊Dic11—21no—
54C2×C4⋊Dic11D412yes—
55C2×Dic11⋊C4—24no—
56C2×C4×Dic11—21no—
57#66922—21no—
58#66922—21no—
59#66922—21no—
60#66922—21no—
61C11×#107—22no—
62C11×#106—22no—
63C11×C4⋊C8—21no—
64C11×C4⋊C8D412yes—
65C11×#103—22no—
66C11×#103—22no—
67#66899—24no—
68C11⋊#95—24no—
69C11⋊#95D412yes—
70C22⋊(C11⋊C8)—21no—
71C22⋊(C11⋊C8)—21no—
72#66872—24no—
73C4⋊(C11⋊C8)—21no—
74C4⋊(C11⋊C8)D412yes—
75C4×C11⋊C8—21no—
76C4×C11⋊C8—21no—
77#10251—111nomaximal, Sylow
78C2×Q8×C11—21no—
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×C11SD1612yes—
86C22×C4×C11—21no—
87C22×C4×C11—21no—
88C22×C4×C11C2×D411yescharacteristic
89C22×C4×C11C2×D411yescharacteristic
90C22×C4×C11C2×D411yescharacteristic
91C22×Dic11—22no—
92C22×Dic11—22no—
93C2×Dic22—41no—
94C2×Dic22—41no—
95C2×Dic22—41no—
96C2×Dic22—41no—
97C2×Dic22—41no—
98C2×Dic22—41no—
99C11×M16—41no—
100C11×M16—41no—
101C2×C8×C11—22no—
102C11×C4⋊C4—21no—
103C11×C4⋊C4—21no—
104C11×C4⋊C4—21no—
105C11×C4⋊C4—21no—
106C11×C4⋊C4—21no—
107C11×C4⋊C4—21no—
108C11×C4⋊C4—41no—
109C11×C4⋊C4—41no—
110C11×C4⋊C4—41no—
111C11×C4⋊C4—41no—
112C11×C22⋊C4—41no—
113C42×C11—41no—
114C42×C11—41no—
115C42×C11—41no—
116C42×C11C2×D411yescharacteristic
117C42×C11C2×D411yescharacteristic
118C42×C11C2×D411yescharacteristic
119C42×C11#4111yescharacteristic
120C4⋊Dic11—24no—
121C4⋊Dic11—22no—
122C4⋊Dic11—22no—
123C4⋊Dic11—41no—
124C4⋊Dic11—41no—
125Dic11⋊C4—48no—
126C4×Dic11—41no—
127C4×Dic11—41no—
128C2×C11⋊C8—22no—
129C2×C11⋊C8—41no—
130#3229—111no—
131#3078D1111yescharacteristic
132#2546—111no—
133#1546—111no—
134#1503—111no—
135#1479—111no—
136#1303—111no—
137C23×C11#12011yescharacteristic
138Q8×C11—22no—
139Q8×C11—22no—
140Q8×C11—41no—
141Q8×C11—41no—
142Q8×C11—42no—
143Q8×C11—81no—
144C2×C4×C11—22no—
145C2×C4×C11—22no—
146C2×C4×C11—41no—
147C2×C4×C11—41no—
148C2×C4×C11—41no—
149C2×C4×C11—42no—
150C2×C4×C11—41no—
151C2×C4×C11—41no—
152C2×C4×C11—41no—
153C2×C4×C11#12011yescharacteristic
154C2×C4×C11#12011yescharacteristic
155C2×C4×C11#12111yescharacteristic
156C2×C4×C11#12111yescharacteristic
157C2×C4×C11#12111yescharacteristic
158C2×C4×C11#12711yescharacteristic
159C2×C4×C11C2×SD1611yescharacteristic
160C2×C4×C11#13511yescharacteristic
161C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
162C2×C4×C11#13711yescharacteristic
163C2×Dic11—24no—
164C2×Dic11—42no—
165C2×Dic11—42no—
166C2×Dic11—42no—
167C2×Dic11—42no—
168C2×Dic11—42no—
169Dic22—81no—
170Dic22—81no—
171Dic22—81no—
172Dic22—81no—
173C8×C11—42no—
174C11⋊C8—42no—
175C11⋊C8—81no—
176#533C2×D1111yescharacteristic
177C2×C4⋊Q8—111no—
178C2×C4⋊Q8—221no—
179C2×C4×Q8C2×D1111yescharacteristic
180#498—221no—
181#487—221no—
182#483—222no—
183#479—22no—
184#477—21no—
185#475—21no—
186#475—222no—
187#431—111no—
188#431—111no—
189#428—21no—
190#423C2×D1111yescharacteristic
191#419—21no—
192#398—222no—
193#391—221no—
194#389—222no—
195C4×C4⋊C4—111no—
196#332—222no—
197#328—222no—
198Q8⋊C8—222no—
199C22×C11—21no—
200C22×C11—21no—
201C22×C11#39211yescharacteristic
202C22×C11#45011yescharacteristic
203C22×C11#45211yescharacteristic
204C4×C11—21no—
205C4×C11—21no—
206C4×C11—21no—
207C4×C11—42no—
208C4×C11—81no—
209C4×C11—81no—
210C4×C11—81no—
211C4×C11#44811yescharacteristic
212C4×C11#44911yescharacteristic
213C4×C11#45612yes—
214C4×C11#46511yescharacteristic
215C4×C11#46811yescharacteristic
216Dic11—44no—
217Dic11—82no—
218C22×Q8—221no—
219C22×Q8C22⋊D1111yescharacteristic
220C2×M16—21no—
221C4⋊Q8—221no—
222C4⋊Q8—221no—
223C4⋊Q8—221no—
224C4⋊Q8—221no—
225C4⋊Q8—442no—
226C4⋊Q8—442no—
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—
238#117—21no—
239C2×C4⋊C4—21no—
240C2×C4⋊C4—112no—
241C2×C4⋊C4—221no—
242C2×C4⋊C4—224no—
243C2×C4⋊C4—221no—
244C2×C4⋊C4C22⋊D1111yescharacteristic
245C2×C42—21no—
246C2×C42—221no—
247C2×C42C22×D1111yescharacteristic
248#107—22no—
249#106—22no—
250#106—224no—
251C4⋊C8—21no—
252C4⋊C8—112no—
253C4⋊C8—221no—
254C4⋊C8C22⋊D1112yes—
255#103—22no—
256#103—22no—
257#103—224no—
258C22⋊C8—221no—
259C22⋊C8—221no—
260C4×C8—221no—
261C4×C8—221no—
262#95—112no—
263#95—224no—
264C2×C11—21no—
265C2×C11—21no—
266C2×C11#200011yescharacteristic
267C2×C11#200511yescharacteristic
268C2×C11#200911yescharacteristic
269C2×Q8—21no—
270C2×Q8—21no—
271C2×Q8—21no—
272C2×Q8—21no—
273C2×Q8—21no—
274C2×Q8—21no—
275C2×Q8—21no—
276C2×Q8—441no—
277C2×Q8—441no—
278C2×Q8—441no—
279C2×Q8—441no—
280C2×Q8—441no—
281C2×Q8—441no—
282C2×Q8#432512yes—
283C22×C4—21no—
284C22×C4—21no—
285C22×C4—222no—
286C22×C4—222no—
287C22×C4D4×D1111yescharacteristic
288C22×C4D4×D1111yescharacteristic
289C22×C4C2×C22⋊D1111yescharacteristic
290M16—41no—
291M16—41no—
292C2×C8—22no—
293C2×C8—222no—
294C2×C8—441no—
295C4⋊C4—21no—
296C4⋊C4—21no—
297C4⋊C4—21no—
298C4⋊C4—21no—
299C4⋊C4—21no—
300C4⋊C4—21no—
301C4⋊C4—41no—
302C4⋊C4—41no—
303C4⋊C4—41no—
304C4⋊C4—41no—
305C4⋊C4—224no—
306C4⋊C4—222no—
307C4⋊C4—222no—
308C4⋊C4—448no—
309C4⋊C4—441no—
310C4⋊C4—441no—
311C22⋊C4—41no—
312C42—41no—
313C42—41no—
314C42—41no—
315C42—441no—
316C42—441no—
317C42D4×D1111yescharacteristic
318C42#434111yescharacteristic
319C42C2×C22⋊D1111yescharacteristic
320C42C2×C22⋊D1111yescharacteristic
321C11#1025111yescharacteristic, complemented, Sylow
322C23#6699011yescharacteristic
323Q8—22no—
324Q8—22no—
325Q8—41no—
326Q8—41no—
327Q8—42no—
328Q8—81no—
329Q8—881no—
330Q8—881no—
331Q8—881no—
332Q8—881no—
333C2×C4—22no—
334C2×C4—22no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—41no—
338C2×C4—42no—
339C2×C4—41no—
340C2×C4—41no—
341C2×C4—41no—
342C2×C4—224no—
343C2×C4—442no—
344C2×C4—442no—
345C2×C4—442no—
346C2×C4—442no—
347C2×C4—442no—
348C2×C4#6699011yescharacteristic
349C2×C4#6699111yescharacteristic
350C2×C4#6699211yescharacteristic
351C2×C4#6699211yescharacteristic
352C2×C4#6699311yescharacteristic
353C2×C4C2×#432511yescharacteristic
354C2×C4#6699511yescharacteristic
355C2×C4#6700211yescharacteristic
356C2×C4#6700311yescharacteristic
357C2×C4#6700611yescharacteristic
358C8—42no—
359C8—442no—
360C8—881no—
361C22—21no—
362C22—21no—
363C22#1062265911yescharacteristic
364C22#1062266011yescharacteristic
365C22#1062283611yescharacteristic
366C4—21no—
367C4—21no—
368C4—21no—
369C4—42no—
370C4—81no—
371C4—81no—
372C4—81no—
373C4—444no—
374C4—882no—
375C4#1062266111yescharacteristic
376C4#1062266211yescharacteristic
377C4#1062281812yes—
378C4#1062284011yescharacteristic
379C4#1062285111yescharacteristic
380C2—21no—
381C2—21no—
382C2#1306961711yescharacteristic
383C2#1306964911yescharacteristic
384C2#1306967311yescharacteristic
subgroupG/H
centerC22#10622836
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#3078C2
socleC22×C11#392
prime radicalC23×C11#120
hypercenter#3078D11
hypocenterC11#10251
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
321. C11#10251semidirect

Maximal subgroups

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

subgroupindex
#130797572
#130736012
#130672892
#130671152
#130670112
#130665172
C11×#30782
#1025111