Finite Group Databasebeta

← #14726634

Subgroups — #14726634

Order 2816.

902 conjugacy classes of subgroups; only the 183 normal subgroups are shown.

normal subgroups only

This group has 902 conjugacy classes of subgroups — too many to draw. Only its 183 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#13078742C212yesmaximal
2#13071907C211yesmaximal, characteristic
3#13067624C214yesmaximal
4#13067590C214yesmaximal
5#13067128C212yesmaximal
6#13066960C211yesmaximal, characteristic
7C11×#3502C211yesmaximal, characteristic
8Q82×C11—22no—
9C11×#557—22no—
10C11×#557—24no—
11C11×#544—21no—
12C11×#544C2214yes—
13C11×#533—22no—
14C11×#533C2212yes—
15C11×#519—21no—
16C2×C4×Q8×C11C2211yescharacteristic
17C2×C4×Dic22C2211yescharacteristic
18#10622842—21no—
19#10622707—22no—
20#10622703—22no—
21#10622663C2214yes—
22#10622656C2214yes—
23#10622643—24no—
24#10622596C2212yes—
25#10622593—21no—
26#10622592C2212yes—
27#10622545C2211yescharacteristic
28C4×Dic11⋊C4—22no—
29#10622539C2212yes—
30#10622176C2218yes—
31#10622166C2214yes—
32C22×Q8×C11D411yescharacteristic
33C22×Dic22C2311yescharacteristic
34C11×C4⋊Q8—22no—
35C11×C4⋊Q8—22no—
36C11×C4⋊Q8—24no—
37C11×C4⋊Q8—28no—
38C11×C4⋊Q8D412yes—
39C11×C4⋊Q8D412yes—
40C11×#125—24no—
41C11×#125—24no—
42C11×#125—28no—
43C11×#125—22no—
44C11×C22⋊Q8—22no—
45C11×C22⋊Q8—24no—
46C11×C22⋊Q8C2314yes—
47C4×Q8×C11—24no—
48C4×Q8×C11—24no—
49C4×Q8×C11—24no—
50C4×Q8×C11—24no—
51C4×Q8×C11—22no—
52C4×Q8×C11—22no—
53C4×Q8×C11—22no—
54C4×Q8×C11D414yes—
55C11×#117—24no—
56C11×#117—22no—
57C2×C11×C4⋊C4D411yescharacteristic
58C2×C11×C4⋊C4C2312yes—
59C2×C42×C11D412yes—
60C2×C42×C11C2311yescharacteristic
61C2×#4326—24no—
62C2×C4⋊Dic11C2311yescharacteristic
63C2×Dic11⋊C4—21no—
64C2×Dic11⋊C4—22no—
65C2×Dic11⋊C4—22no—
66C2×C4×Dic11—21no—
67C2×C4×Dic11—21no—
68C4×Dic22—22no—
69C4×Dic22—22no—
70#66899—24no—
71C11⋊#95—22no—
72C11⋊#95—22no—
73C11⋊#95—21no—
74C11⋊#95C2312yes—
75C22⋊(C11⋊C8)C2314yes—
76#66874—24no—
77#66872—24no—
78C4⋊(C11⋊C8)—22no—
79#66867—22no—
80#18189—111nomaximal, Sylow
81C2×Q8×C11—24no—
82C2×Q8×C11—22no—
83C2×Q8×C11—22no—
84C2×Q8×C11—24no—
85C2×Q8×C11C2×D414yes—
86C22×C4×C11C2×D411yescharacteristic
87C22×C4×C11C2×D411yescharacteristic
88C22×C4×C11C2×D412yes—
89C22×C4×C11C2×D412yes—
90C22×C4×C11C2411yescharacteristic
91C22×Dic11—22no—
92C22×Dic11—21no—
93C22×Dic11—21no—
94C2×Dic22—22no—
95C2×Dic22—42no—
96C11×C4⋊C4—24no—
97C11×C4⋊C4—24no—
98C11×C4⋊C4—24no—
99C11×C4⋊C4—28no—
100C11×C4⋊C4—22no—
101C11×C4⋊C4—22no—
102C11×C4⋊C4—22no—
103C11×C4⋊C4—22no—
104C11×C4⋊C4—24no—
105C11×C4⋊C4—24no—
106C11×C4⋊C4—24no—
107C11×C4⋊C4C2×D414yes—
108C11×C22⋊C4—24no—
109C42×C11—28no—
110C42×C11—22no—
111C42×C11—22no—
112C42×C11—24no—
113C42×C11C2×D412yes—
114C42×C11C2×D412yes—
115#4326—48no—
116C4⋊Dic11—22no—
117Dic11⋊C4—44no—
118Dic11⋊C4—42no—
119Dic11⋊C4—44no—
120C4×Dic11—24no—
121C4×Dic11—41no—
122C4×Dic11—41no—
123C2×C11⋊C8—24no—
124#3502D1111yescharacteristic
125#3113—112no—
126#2399—111no—
127#1611—114no—
128#1605—114no—
129#1506—112no—
130#1467—111no—
131C23×C11C22×D411yescharacteristic
132Q8×C11—28no—
133Q8×C11—44no—
134Q8×C11—44no—
135Q8×C11—84no—
136C2×C4×C11—22no—
137C2×C4×C11—22no—
138C2×C4×C11—22no—
139C2×C4×C11—22no—
140C2×C4×C11—24no—
141C2×C4×C11—24no—
142C2×C4×C11—22no—
143C2×C4×C11—41no—
144C2×C4×C11—42no—
145C2×C4×C11#12011yescharacteristic
146C2×C4×C11#12012yes—
147C2×C4×C11#12011yescharacteristic
148C2×C4×C11#13714yes—
149C2×C4×C11C22×D412yes—
150C2×Dic11—24no—
151C2×Dic11—22no—
152C2×Dic11—42no—
153C2×Dic11—41no—
154C2×Dic11—41no—
155C2×Dic11—42no—
156C2×Dic11—41no—
157C2×Dic11—42no—
158Dic22—24no—
159Dic22—42no—
160C11⋊C8—44no—
161Q82—22no—
162#557—22no—
163#557—24no—
164#544—21no—
165#544C2×D1114yes—
166#533—22no—
167#533C2×D1112yes—
168#519—21no—
169C2×C4×Q8—111no—
170C2×C4×Q8C2×D1111yescharacteristic
171#483—114no—
172#475—222no—
173#462—222no—
174#451—114no—
175#441—224no—
176#432—112no—
177#398—112no—
178#398—221no—
179#395—112no—
180#395—221no—
181C4×C4⋊C4—222no—
182#376—111no—
183#328—118no—
184#324—114no—
185C22×C11—21no—
186C22×C11—21no—
187C22×C11C2×#12011yescharacteristic
188C22×C11C2×#13712yes—
189C4×C11—22no—
190C4×C11—24no—
191C4×C11—21no—
192C4×C11—22no—
193C4×C11—44no—
194C4×C11—42no—
195C4×C11—44no—
196C4×C11#45612yes—
197Dic11—44no—
198Dic11—42no—
199Dic11—81no—
200C22×Q8—111no—
201C22×Q8C22⋊D1111yescharacteristic
202C2×Q16—224no—
203C4⋊Q8—22no—
204C4⋊Q8—22no—
205C4⋊Q8—24no—
206C4⋊Q8—28no—
207C4⋊Q8C22⋊D1112yes—
208C4⋊Q8C22⋊D1112yes—
209#125—24no—
210#125—24no—
211#125—28no—
212#125—22no—
213C22⋊Q8—22no—
214C22⋊Q8—24no—
215C22⋊Q8C22×D1114yes—
216C4×Q8—24no—
217C4×Q8—24no—
218C4×Q8—24no—
219C4×Q8—24no—
220C4×Q8—22no—
221C4×Q8—22no—
222C4×Q8—22no—
223C4×Q8—222no—
224C4×Q8—222no—
225C4×Q8C22⋊D1114yes—
226#117—24no—
227#117—22no—
228C2×C4⋊C4—111no—
229C2×C4⋊C4—221no—
230C2×C4⋊C4—222no—
231C2×C4⋊C4—222no—
232C2×C4⋊C4C22⋊D1111yescharacteristic
233C2×C4⋊C4C22×D1112yes—
234C2×C42—221no—
235C2×C42—221no—
236C2×C42C22⋊D1112yes—
237C2×C42C22×D1111yescharacteristic
238#106—224no—
239C4⋊C8—222no—
240#103—224no—
241#103—224no—
242C22⋊C8—114no—
243#97—222no—
244#95—112no—
245#95—221no—
246#95—222no—
247#95—222no—
248C2×C11—22no—
249C2×C11#300411yescharacteristic
250C2×C11C2×#45611yescharacteristic
251C2×C11#302511yescharacteristic
252C2×Q8—24no—
253C2×Q8—24no—
254C2×Q8—22no—
255C2×Q8—22no—
256C2×Q8—222no—
257C2×Q8—442no—
258C2×Q8C2×C22⋊D1114yes—
259C22×C4—222no—
260C22×C4—221no—
261C22×C4—221no—
262C22×C4C2×C22⋊D1112yes—
263C22×C4C2×C22⋊D1111yescharacteristic
264C22×C4C2×C22⋊D1111yescharacteristic
265C22×C4C2×C22⋊D1112yes—
266C22×C4C23×D1111yescharacteristic
267Q16—448no—
268C2×C8—224no—
269C4⋊C4—24no—
270C4⋊C4—24no—
271C4⋊C4—24no—
272C4⋊C4—28no—
273C4⋊C4—22no—
274C4⋊C4—22no—
275C4⋊C4—22no—
276C4⋊C4—22no—
277C4⋊C4—24no—
278C4⋊C4—24no—
279C4⋊C4—24no—
280C4⋊C4—222no—
281C4⋊C4—444no—
282C4⋊C4—444no—
283C4⋊C4—442no—
284C4⋊C4C2×C22⋊D1114yes—
285C22⋊C4—24no—
286C42—28no—
287C42—22no—
288C42—22no—
289C42—24no—
290C42—224no—
291C42—441no—
292C42—441no—
293C42C2×C22⋊D1112yes—
294C42C2×C22⋊D1112yes—
295C11#1818911yescharacteristic, complemented, Sylow
296C23C22×C22⋊D1111yescharacteristic
297Q8—28no—
298Q8—44no—
299Q8—44no—
300Q8—84no—
301Q8—224no—
302Q8—442no—
303C2×C4—22no—
304C2×C4—22no—
305C2×C4—22no—
306C2×C4—22no—
307C2×C4—24no—
308C2×C4—24no—
309C2×C4—22no—
310C2×C4—41no—
311C2×C4—42no—
312C2×C4—224no—
313C2×C4—222no—
314C2×C4—442no—
315C2×C4—441no—
316C2×C4—442no—
317C2×C4—441no—
318C2×C4—442no—
319C2×C4—441no—
320C2×C4#6699514yes—
321C2×C4#6700611yescharacteristic
322C2×C4#6700612yes—
323C2×C4#6700611yescharacteristic
324C2×C4C22×C22⋊D1112yes—
325C8—444no—
326C22—21no—
327C22—21no—
328C22C2×#6699512yes—
329C22C2×#6700611yescharacteristic
330C4—24no—
331C4—22no—
332C4—21no—
333C4—22no—
334C4—44no—
335C4—42no—
336C4—44no—
337C4—444no—
338C4—442no—
339C4—881no—
340C4#1062285912yes—
341C2—22no—
342C2#1307785011yescharacteristic
343C2C2×#1062285911yescharacteristic
344C2#1307800811yescharacteristic
subgroupG/H
centerC22C2×#67006
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#3502C2
socleC22×C11C2×#120
prime radicalC23×C11C22×D4
hypercenter#3502D11
hypocenterC11#18189
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3502

Complements

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

NH ≅ G/Ntype
295. C11#18189semidirect

Maximal subgroups

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

subgroupindex
#130787422
#130719072
#130676242
#130675902
#130671282
#130669602
C11×#35022
#1818911