Finite Group Databasebeta

← #14651767

Subgroups — #14651767

Order 2816.

478 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 478 conjugacy classes of subgroups — too many to draw. Only its 99 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#13072899C211yesmaximal, characteristic
2#13068699C211yesmaximal, characteristic
3#13066945C212yesmaximal
4#13066525C212yesmaximal
5C11×#2921C211yesmaximal, characteristic
6C2×C11×#117C2211yescharacteristic
7C22×Dic11⋊C4C2211yescharacteristic
8C11×#433—24no—
9C11×#423—21no—
10C11×#407C2212yes—
11C4×C11×M16—21no—
12#10622824C2211yescharacteristic
13#10622820C2212yes—
14#10622595—21no—
15#10622593—21no—
16#10622559C411yescharacteristic
17#10622559C411yescharacteristic
18#10622556C411yescharacteristic
19#10622556C411yescharacteristic
20#10622546—21no—
21#10622546—21no—
22#10622168—21no—
23#10622168—21no—
24#10622107—24no—
25C23×C4×C11C2311yescharacteristic
26C23×Dic11C2×C411yescharacteristic
27C23×Dic11C2×C411yescharacteristic
28C2×C11×M16—22no—
29C11×#117—22no—
30C11×#117—22no—
31C2×C11×C4⋊C4D411yescharacteristic
32C2×C11×C4⋊C4D411yescharacteristic
33C2×C11×C22⋊C4C2×C411yescharacteristic
34C2×C11×C22⋊C4C2×C411yescharacteristic
35C2×C42×C11D411yescharacteristic
36C2×C42×C11D411yescharacteristic
37C2×C22⋊Dic11C2×C411yescharacteristic
38C2×C22⋊Dic11C2×C411yescharacteristic
39C2×Dic11⋊C4—21no—
40C2×Dic11⋊C4—21no—
41C2×Dic11⋊C4—21no—
42C2×Dic11⋊C4—21no—
43C2×Dic11⋊C4—22no—
44C2×Dic11⋊C4—22no—
45C2×#4318—22no—
46C11×C4⋊C8—24no—
47C11×C22⋊C8—22no—
48C11×C22⋊C8D414yes—
49C11×#97—22no—
50C4×C8×C11—22no—
51C11⋊#95—21no—
52C11⋊#95—21no—
53C11⋊#95—21no—
54C11⋊#95—21no—
55C11⋊#95—21no—
56C11⋊#95—21no—
57C11⋊#95—21no—
58C11⋊#95—21no—
59C22⋊(C11⋊C8)—22no—
60C22⋊(C11⋊C8)—22no—
61#9514—111nomaximal, Sylow
62C24×C11C22×C411yescharacteristic
63C22×C4×C11—41no—
64C22×C4×C11—41no—
65C22×C4×C11C22⋊C411yescharacteristic
66C22×C4×C11C22⋊C411yescharacteristic
67C22×C4×C11C22⋊C411yescharacteristic
68C22×C4×C11C22⋊C411yescharacteristic
69C22×C4×C11C2×D411yescharacteristic
70C22×C4×C11C2×D411yescharacteristic
71C22×C4×C11C2×D412yes—
72C22×C4×C11#4112yes—
73C22×Dic11—21no—
74C22×Dic11—21no—
75C22×Dic11—21no—
76C22×Dic11—21no—
77C22×Dic11—22no—
78C22×Dic11—22no—
79C22×Dic11—41no—
80C22×Dic11—41no—
81C22×Dic11—42no—
82C11×M16—42no—
83C11×M16—42no—
84C2×C8×C11—24no—
85C11×C4⋊C4—22no—
86C11×C4⋊C4—22no—
87C11×C22⋊C4—22no—
88C11×C22⋊C4—22no—
89C42×C11—21no—
90C42×C11—21no—
91C42×C11—21no—
92C42×C11—21no—
93C22⋊Dic11—41no—
94C22⋊Dic11—41no—
95Dic11⋊C4—42no—
96Dic11⋊C4—42no—
97Dic11⋊C4—41no—
98Dic11⋊C4—42no—
99Dic11⋊C4—41no—
100#4318—42no—
101#4318—42no—
102C2×C11⋊C8—42no—
103#2921D1111yescharacteristic
104#2484—111no—
105#1822—111no—
106#1463—112no—
107#1306—112no—
108C23×C11—21no—
109C23×C11—21no—
110C23×C11—41no—
111C23×C11—41no—
112C23×C11C2×C22⋊C411yescharacteristic
113C23×C11C4×D412yes—
114C2×C4×C11—21no—
115C2×C4×C11—21no—
116C2×C4×C11—21no—
117C2×C4×C11—21no—
118C2×C4×C11—21no—
119C2×C4×C11—21no—
120C2×C4×C11—21no—
121C2×C4×C11—21no—
122C2×C4×C11—42no—
123C2×C4×C11—42no—
124C2×C4×C11—41no—
125C2×C4×C11—41no—
126C2×C4×C11—41no—
127C2×C4×C11—41no—
128C2×C4×C11#12011yescharacteristic
129C2×C4×C11#12112yes—
130C2×C4×C11#12311yescharacteristic
131C2×Dic11—22no—
132C2×Dic11—24no—
133C2×Dic11—41no—
134C2×Dic11—42no—
135C2×Dic11—41no—
136C2×Dic11—41no—
137C2×Dic11—41no—
138C2×Dic11—41no—
139C2×Dic11—41no—
140C2×Dic11—41no—
141C2×Dic11—41no—
142C2×Dic11—41no—
143C2×Dic11—41no—
144C2×Dic11—41no—
145C2×Dic11—82no—
146C8×C11—44no—
147C11⋊C8—82no—
148C2×#117C2×D1111yescharacteristic
149C22×C4⋊C4—111no—
150#433—24no—
151#423—21no—
152#407—112no—
153#407C2×D1112yes—
154C4×M16—21no—
155#400—221no—
156#398—221no—
157#387—221no—
158#387—221no—
159#385—111no—
160#385—111no—
161#381—111no—
162#381—111no—
163#381—111no—
164#343—221no—
165#343—221no—
166#324—224no—
167C22×C11—21no—
168C22×C11—21no—
169C22×C11—22no—
170C22×C11—22no—
171C22×C11—22no—
172C22×C11—42no—
173C22×C11—42no—
174C22×C11#38611yescharacteristic
175C22×C11#41011yescharacteristic
176C22×C11#41011yescharacteristic
177C4×C11—21no—
178C4×C11—22no—
179C4×C11—21no—
180C4×C11—41no—
181C4×C11—41no—
182C4×C11—41no—
183C4×C11—41no—
184Dic11—42no—
185Dic11—81no—
186Dic11—81no—
187Dic11—81no—
188C23×C4—111no—
189C23×C4—111no—
190C23×C4C22×D1111yescharacteristic
191C2×M16—22no—
192C2×M16—222no—
193#117—22no—
194#117—22no—
195C2×C4⋊C4—221no—
196C2×C4⋊C4—221no—
197C2×C4⋊C4—221no—
198C2×C4⋊C4—222no—
199C2×C4⋊C4—222no—
200C2×C4⋊C4—221no—
201C2×C4⋊C4D4411yescharacteristic
202C2×C4⋊C4D4411yescharacteristic
203C2×C22⋊C4—111no—
204C2×C22⋊C4—111no—
205C2×C22⋊C4C4×D1111yescharacteristic
206C2×C22⋊C4C4×D1111yescharacteristic
207C2×C42C22⋊D1111yescharacteristic
208C2×C42C22⋊D1111yescharacteristic
209C4⋊C8—24no—
210C22⋊C8—22no—
211C22⋊C8—222no—
212C22⋊C8—222no—
213C22⋊C8C22⋊D1114yes—
214#97—22no—
215C4×C8—22no—
216#95—221no—
217#95—221no—
218#95—221no—
219#95—221no—
220#95—221no—
221#95—221no—
222#95—221no—
223#95—221no—
224C2×C11—21no—
225C2×C11—21no—
226C2×C11—42no—
227C2×C11#189111yescharacteristic
228C2×C11#189911yescharacteristic
229C2×C11#191511yescharacteristic
230C24C2×C4×D1111yescharacteristic
231C22×C4—41no—
232C22×C4—41no—
233C22×C4—221no—
234C22×C4—222no—
235C22×C4—221no—
236C22×C4—221no—
237C22×C4—221no—
238C22×C4—222no—
239C22×C4—442no—
240C22×C4—441no—
241C22×C4—441no—
242C22×C4(C2×D11)⋊C411yescharacteristic
243C22×C4(C2×D11)⋊C411yescharacteristic
244C22×C4(C2×D11)⋊C411yescharacteristic
245C22×C4(C2×D11)⋊C411yescharacteristic
246C22×C4C2×D4411yescharacteristic
247C22×C4#433912yes—
248C22×C4C2×C22⋊D1111yescharacteristic
249C22×C4C2×C22⋊D1112yes—
250M16—42no—
251M16—42no—
252M16—442no—
253M16—442no—
254C2×C8—24no—
255C2×C8—442no—
256C4⋊C4—22no—
257C4⋊C4—22no—
258C4⋊C4—442no—
259C4⋊C4—442no—
260C4⋊C4—441no—
261C4⋊C4—442no—
262C4⋊C4—441no—
263C22⋊C4—22no—
264C22⋊C4—22no—
265C22⋊C4—441no—
266C22⋊C4—441no—
267C42—21no—
268C42—21no—
269C42—21no—
270C42—21no—
271C11#951411yescharacteristic, complemented, Sylow
272C23—21no—
273C23—21no—
274C23—41no—
275C23—41no—
276C23C2×(C2×D11)⋊C411yescharacteristic
277C23C4×C22⋊D1112yes—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—42no—
287C2×C4—42no—
288C2×C4—41no—
289C2×C4—41no—
290C2×C4—41no—
291C2×C4—41no—
292C2×C4—222no—
293C2×C4—224no—
294C2×C4—441no—
295C2×C4—442no—
296C2×C4—441no—
297C2×C4—441no—
298C2×C4—441no—
299C2×C4—441no—
300C2×C4—441no—
301C2×C4—441no—
302C2×C4—441no—
303C2×C4—441no—
304C2×C4—441no—
305C2×C4—441no—
306C2×C4—882no—
307C2×C4#6698211yescharacteristic
308C2×C4#6698312yes—
309C2×C4#6700611yescharacteristic
310C8—44no—
311C8—882no—
312C22—21no—
313C22—21no—
314C22—22no—
315C22—22no—
316C22—22no—
317C22—42no—
318C22—42no—
319C22#1062261911yescharacteristic
320C22#1062261911yescharacteristic
321C22#1062282611yescharacteristic
322C4—21no—
323C4—22no—
324C4—21no—
325C4—41no—
326C4—41no—
327C4—41no—
328C4—41no—
329C4—442no—
330C4—881no—
331C4—881no—
332C4—881no—
333C2—21no—
334C2—21no—
335C2—42no—
336C2#1306903411yescharacteristic
337C2#1306907411yescharacteristic
338C2#1306916811yescharacteristic
subgroupG/H
centerC22#10622826
commutator, prime radicalC24×C11C22×C4
FrattiniC23×C4C22×D11
FittingC11×#2921C2
socleC22×C11#386
cosocleC23×C4×C11C23
hypercenter#2921D11
hypocenterC11#9514
LCSG ▷ C24×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2921

Complements

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

NH ≅ G/Ntype
271. C11#9514semidirect

Maximal subgroups

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

subgroupindex
#130728992
#130686992
#130669452
#130665252
C11×#29212
#951411