Finite Group Databasebeta

← #14651466

Subgroups — #14651466

Order 2816.

448 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 448 conjugacy classes of subgroups — too many to draw. Only its 95 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#13077700C211yesmaximal, characteristic
2#13073824C211yesmaximal, characteristic
3#13067334C211yesmaximal, characteristic
4#13067332C211yesmaximal, characteristic
5#13066959C211yesmaximal, characteristic
6#13066472C211yesmaximal, characteristic
7C11×#1285C211yesmaximal, characteristic
8C2×#66922C2211yescharacteristic
9C2×C4×Dic22C2211yescharacteristic
10C11×#432C2211yescharacteristic
11C11×#432C2211yescharacteristic
12C4×C11×C4⋊C4C2211yescharacteristic
13#10622598—21no—
14#10622598—21no—
15#10622548C412yes—
16#10622542C412yes—
17#10622539C2211yescharacteristic
18#10622539C2211yescharacteristic
19#10622441—22no—
20#10622332—21no—
21#10622331—21no—
22#10622314—22no—
23#10622269—21no—
24#10622269—21no—
25#10622124—22no—
26#10622120—22no—
27#10622107—21no—
28#10622107—21no—
29C22×Dic22—21no—
30C22×Dic22C2×C411yescharacteristic
31C2×C11×C4⋊C4—21no—
32C2×C42×C11C2×C412yes—
33C2×C42×C11C2311yescharacteristic
34C2×C4⋊Dic11—21no—
35C2×C4⋊Dic11—22no—
36C2×C4⋊Dic11—22no—
37C2×C4⋊Dic11C2×C412yes—
38C2×C4⋊Dic11C2×C411yescharacteristic
39C2×Dic11⋊C4D411yescharacteristic
40C2×Dic11⋊C4D411yescharacteristic
41C2×C4×Dic11D411yescharacteristic
42C2×C4×Dic11D411yescharacteristic
43#66922—21no—
44#66922—21no—
45#66922—21no—
46#66922—21no—
47C4×Dic22—21no—
48C4×Dic22—21no—
49C4×Dic22—21no—
50C4×Dic22—21no—
51C11×C4⋊C8—21no—
52C11×C4⋊C8D412yes—
53C11×C22⋊C8—21no—
54C11×C22⋊C8—21no—
55C11×#97—21no—
56C11×#97—21no—
57C11×#95—21no—
58C11⋊#95—22no—
59C11⋊#95—22no—
60C22⋊(C11⋊C8)—21no—
61C22⋊(C11⋊C8)—21no—
62#66879—22no—
63Dic11⋊C8—22no—
64Dic11⋊C8—22no—
65C8×Dic11—22no—
66C4⋊(C11⋊C8)—21no—
67C4⋊(C11⋊C8)D412yes—
68#66867—21no—
69#66867—21no—
70#9454—111nomaximal, Sylow
71C22×C4×C11—22no—
72C22×C4×C11C22×C411yescharacteristic
73C22×C4×C11C2×D411yescharacteristic
74C22×C4×C11C2×D411yescharacteristic
75C22×Dic11—22no—
76C22×Dic11C22⋊C411yescharacteristic
77C22×Dic11C22⋊C411yescharacteristic
78C22×Dic11C22⋊C411yescharacteristic
79C22×Dic11C22⋊C411yescharacteristic
80C2×Dic22—22no—
81C2×Dic22—21no—
82C2×Dic22—21no—
83C2×Dic22—41no—
84C2×Dic22—41no—
85C2×Dic22—41no—
86C2×Dic22—82no—
87C2×C8×C11—22no—
88C2×C8×C11—41no—
89C11×C4⋊C4—24no—
90C42×C11—42no—
91C42×C11C2×D411yescharacteristic
92C42×C11C2×D411yescharacteristic
93C42×C11#4111yescharacteristic
94C42×C11#4111yescharacteristic
95C4⋊Dic11—21no—
96C4⋊Dic11—21no—
97C4⋊Dic11—22no—
98C4⋊Dic11—22no—
99C4⋊Dic11—41no—
100C4⋊Dic11—41no—
101C4⋊Dic11—82no—
102C4⋊Dic11—82no—
103Dic11⋊C4—21no—
104Dic11⋊C4—21no—
105Dic11⋊C4—21no—
106Dic11⋊C4—21no—
107C4×Dic11—21no—
108C4×Dic11—21no—
109C4×Dic11—21no—
110C4×Dic11—21no—
111C2×C11⋊C8—22no—
112C2×C11⋊C8—41no—
113#2983—111no—
114#2567—111no—
115#1556—111no—
116#1556—111no—
117#1467—111no—
118#1285—111no—
119#1285D1111yescharacteristic
120C23×C11C2×C22⋊C411yescharacteristic
121C2×C4×C11—21no—
122C2×C4×C11—21no—
123C2×C4×C11—22no—
124C2×C4×C11—24no—
125C2×C4×C11—41no—
126C2×C4×C11—42no—
127C2×C4×C11—42no—
128C2×C4×C11C4×D411yescharacteristic
129C2×C4×C11C4×D411yescharacteristic
130C2×C4×C11#12011yescharacteristic
131C2×C4×C11#12111yescharacteristic
132C2×C4×C11#12111yescharacteristic
133C2×C4×C11#12311yescharacteristic
134C2×Dic11—21no—
135C2×Dic11—21no—
136C2×Dic11—21no—
137C2×Dic11—21no—
138C2×Dic11—21no—
139C2×Dic11—21no—
140C2×Dic11—21no—
141C2×Dic11—41no—
142C2×Dic11—41no—
143C2×Dic11—42no—
144C2×Dic11—42no—
145C2×Dic11—42no—
146C2×Dic11#10112yes—
147Dic22—42no—
148Dic22—42no—
149Dic22—82no—
150Dic22—82no—
151C8×C11—42no—
152C8×C11—81no—
153C11⋊C8—42no—
154C11⋊C8—81no—
155C2×C4⋊Q8—111no—
156C2×C4×Q8—111no—
157#446—222no—
158#446—222no—
159#432—111no—
160#432—111no—
161#432—221no—
162#432C2×D1111yescharacteristic
163#432C2×D1111yescharacteristic
164#431—221no—
165#395—221no—
166#395—221no—
167#391—112no—
168#389—221no—
169#389—221no—
170#384—112no—
171C4×C4⋊C4C2×D1111yescharacteristic
172#332—222no—
173#332—222no—
174#324—221no—
175#324—221no—
176C22×C11—21no—
177C22×C11—21no—
178C22×C11#38611yescharacteristic
179C22×C11C2×#10111yescharacteristic
180C22×C11#41311yescharacteristic
181C4×C11—21no—
182C4×C11—21no—
183C4×C11—21no—
184C4×C11—21no—
185C4×C11—21no—
186C4×C11—44no—
187C4×C11#45612yes—
188Dic11—22no—
189Dic11—41no—
190Dic11—41no—
191Dic11—41no—
192Dic11—82no—
193C22×Q8—111no—
194C22×Q8—221no—
195C4⋊Q8—221no—
196C4⋊Q8—221no—
197C4⋊Q8—221no—
198C4⋊Q8—221no—
199C4×Q8—221no—
200C4×Q8—221no—
201C4×Q8—221no—
202C4×Q8—221no—
203C2×C4⋊C4—21no—
204C2×C4⋊C4—111no—
205C2×C4⋊C4—111no—
206C2×C4⋊C4—111no—
207C2×C4⋊C4—112no—
208C2×C4⋊C4—221no—
209C2×C4⋊C4—222no—
210C2×C4⋊C4—222no—
211C2×C42—111no—
212C2×C42—111no—
213C2×C42C4×D1112yes—
214C2×C42C22×D1111yescharacteristic
215C4⋊C8—21no—
216C4⋊C8—112no—
217C4⋊C8—222no—
218C4⋊C8—222no—
219C4⋊C8—221no—
220C4⋊C8D4412yes—
221C22⋊C8—21no—
222C22⋊C8—21no—
223C22⋊C8—221no—
224C22⋊C8—221no—
225#97—21no—
226#97—21no—
227#97—222no—
228#97—221no—
229#97—221no—
230C4×C8—222no—
231#95—21no—
232#95—222no—
233#95—222no—
234C2×C11—21no—
235C2×C11—21no—
236C2×C11#188611yescharacteristic
237C2×C11#190111yescharacteristic
238C2×C11#191011yescharacteristic
239C2×Q8—222no—
240C2×Q8—221no—
241C2×Q8—221no—
242C2×Q8—441no—
243C2×Q8—441no—
244C2×Q8—441no—
245C2×Q8—882no—
246C22×C4—22no—
247C22×C4—111no—
248C22×C4—111no—
249C22×C4—111no—
250C22×C4—111no—
251C22×C4—222no—
252C22×C4C2×C4×D1111yescharacteristic
253C22×C4D4×D1111yescharacteristic
254C22×C4D4×D1111yescharacteristic
255C2×C8—22no—
256C2×C8—41no—
257C2×C8—222no—
258C2×C8—441no—
259C4⋊C4—24no—
260C4⋊C4—221no—
261C4⋊C4—221no—
262C4⋊C4—221no—
263C4⋊C4—221no—
264C4⋊C4—221no—
265C4⋊C4—221no—
266C4⋊C4—222no—
267C4⋊C4—222no—
268C4⋊C4—441no—
269C4⋊C4—441no—
270C4⋊C4—882no—
271C4⋊C4—882no—
272C42—42no—
273C42—221no—
274C42—221no—
275C42—221no—
276C42—221no—
277C42C2×D4411yescharacteristic
278C42#433911yescharacteristic
279C42D4×D1111yescharacteristic
280C42#434311yescharacteristic
281C11#945411yescharacteristic, complemented, Sylow
282C23C22⋊C4×D1111yescharacteristic
283Q8—442no—
284Q8—442no—
285Q8—882no—
286Q8—882no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—22no—
290C2×C4—24no—
291C2×C4—41no—
292C2×C4—42no—
293C2×C4—42no—
294C2×C4—112no—
295C2×C4—221no—
296C2×C4—221no—
297C2×C4—221no—
298C2×C4—221no—
299C2×C4—221no—
300C2×C4—221no—
301C2×C4—221no—
302C2×C4—441no—
303C2×C4—441no—
304C2×C4—442no—
305C2×C4—442no—
306C2×C4—442no—
307C2×C4C4×D4411yescharacteristic
308C2×C4#6693511yescharacteristic
309C2×C4#6693711yescharacteristic
310C2×C4#6694611yescharacteristic
311C2×C4#6694711yescharacteristic
312C2×C4#6694811yescharacteristic
313C8—42no—
314C8—81no—
315C8—442no—
316C8—881no—
317C22—21no—
318C22—21no—
319C22#1062227811yescharacteristic
320C22#1062235811yescharacteristic
321C22D11×#10111yescharacteristic
322C4—21no—
323C4—21no—
324C4—21no—
325C4—21no—
326C4—21no—
327C4—44no—
328C4—222no—
329C4—441no—
330C4—441no—
331C4—441no—
332C4—882no—
333C4#1062243912yes—
334C2—21no—
335C2—21no—
336C2#1306900811yescharacteristic
337C2#1306908311yescharacteristic
338C2#1306914211yescharacteristic
subgroupG/H
centerC22#10622278
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1285C2
socleC22×C11#386
prime radicalC23×C11C2×C22⋊C4
cosocleC2×C42×C11C23
hypercenter#1285D11
hypocenterC11#9454
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1285

Complements

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

NH ≅ G/Ntype
281. C11#9454semidirect

Maximal subgroups

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

subgroupindex
#130777002
#130738242
#130673342
#130673322
#130669592
#130664722
C11×#12852
#945411