Finite Group Databasebeta

← #14664697

Subgroups — #14664697

Order 2816.

438 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 438 conjugacy classes of subgroups — too many to draw. Only its 83 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#13074096C211yesmaximal, characteristic
2#13068696C211yesmaximal, characteristic, complemented
3#13066644C212yesmaximal, complemented
4#13066620C212yesmaximal, complemented
5C2×C11×#324C211yesmaximal, characteristic, complemented
6C22×C11×C4⋊C4C2211yescharacteristic
7C2×#66983C411yescharacteristic
8C2×C11×C22⋊C8—21no—
9#10622826—21no—
10#10622826—21no—
11C4×C22⋊Dic11C411yescharacteristic
12#10622820—21no—
13#10622604C411yescharacteristic
14#10622604C2211yescharacteristic
15#10622603—21no—
16#10622603—21no—
17#10622599C411yescharacteristic
18#10622599C2211yescharacteristic
19C11×#324—21no—
20C11×#324C2212yes—
21#10622168—21no—
22#10622168C2212yes—
23C23×C4×C11C2×C411yescharacteristic
24C23×C4×C11D411yescharacteristic
25C23×C4×C11D411yescharacteristic
26C22×C22⋊D11—21no—
27C22×D44C2×C411yescharacteristic
28C22×C8×C11—41no—
29C2×C11×C4⋊C4—41no—
30C2×C11×C4⋊C4—41no—
31C2×C11×C4⋊C4C2×C411yescharacteristic
32C2×C11×C4⋊C4D411yescharacteristic
33C2×C11×C4⋊C4D411yescharacteristic
34C2×C11×C4⋊C4C2311yescharacteristic
35C2×C22⋊Dic11—21no—
36#66983—41no—
37#66983—41no—
38C2×(C2×D11)⋊C4—21no—
39C2×(C2×D11)⋊C4—21no—
40C2×(C2×D11)⋊C4—21no—
41C2×(C2×D11)⋊C4—21no—
42C2×(C2×D11)⋊C4—21no—
43C2×C4⋊Dic11C2×C411yescharacteristic
44C2×C4×Dic11—21no—
45C2×#4318—22no—
46C11×C22⋊C8—22no—
47C11×C22⋊C8—41no—
48C11⋊#95—21no—
49C11⋊#95—21no—
50C11⋊#95—21no—
51C11⋊#95—21no—
52C11⋊#95C2×C411yescharacteristic
53C11⋊#95C2×C411yescharacteristic
54C22⋊(C11⋊C8)—41no—
55C22⋊(C11⋊C8)—41no—
56#11852—111nomaximal, Sylow
57C24×C11C22⋊C411yescharacteristic
58C23×D11—21no—
59C22×C4×C11—21no—
60C22×C4×C11—21no—
61C22×C4×C11—21no—
62C22×C4×C11—21no—
63C22×C4×C11—21no—
64C22×C4×C11—21no—
65C22×C4×C11—22no—
66C22×C4×C11—41no—
67C22×C4×C11—81no—
68C22×C4×C11—81no—
69C22×C4×C11C22⋊C411yescharacteristic
70C22×C4×C11C22⋊C411yescharacteristic
71C22×C4×C11C22⋊C411yescharacteristic
72C22×C4×C11C22×C411yescharacteristic
73C22×C4×C11C2×D411yescharacteristic
74C22×C4×C11C2×D411yescharacteristic
75C2×C22⋊D11—42no—
76C2×C22⋊D11—42no—
77C2×C22⋊D11—41no—
78C2×C22⋊D11—41no—
79C22×Dic11—21no—
80C22×Dic11—21no—
81C22×Dic11—21no—
82C2×D44—41no—
83C2×D44—81no—
84C2×C8×C11—42no—
85C2×C8×C11—82no—
86C11×C4⋊C4—41no—
87C11×C4⋊C4—41no—
88C11×C4⋊C4—41no—
89C11×C4⋊C4—41no—
90C22⋊Dic11—42no—
91(C2×D11)⋊C4—42no—
92(C2×D11)⋊C4—42no—
93(C2×D11)⋊C4—42no—
94(C2×D11)⋊C4—81no—
95(C2×D11)⋊C4—81no—
96C4⋊Dic11—41no—
97C4×Dic11—81no—
98#4318—42no—
99#4318—42no—
100C2×C11⋊C8—42no—
101#2591—111no—
102#1821—111no—
103C2×#324D1111yescharacteristic, complemented
104#1353—112no—
105#1345—112no—
106C23×C11—22no—
107C23×C11—21no—
108C23×C11—21no—
109C23×C11—41no—
110C23×C11#9911yescharacteristic
111C23×C11#9911yescharacteristic
112C23×C11C2×C22⋊C411yescharacteristic
113C22×D11—41no—
114C22×D11—41no—
115C22×D11—41no—
116C22×D11—41no—
117C22×D11—41no—
118C22×D11—41no—
119C22×D11—41no—
120C2×C4×C11—21no—
121C2×C4×C11—21no—
122C2×C4×C11—21no—
123C2×C4×C11—21no—
124C2×C4×C11—21no—
125C2×C4×C11—21no—
126C2×C4×C11—21no—
127C2×C4×C11—21no—
128C2×C4×C11—21no—
129C2×C4×C11—42no—
130C2×C4×C11—42no—
131C2×C4×C11—42no—
132C2×C4×C11—41no—
133C2×C4×C11—41no—
134C2×C4×C11—41no—
135C2×C4×C11—41no—
136C2×C4×C11—81no—
137C2×C4×C11—81no—
138C2×C4×C11—81no—
139C2×C4×C11#13512yes—
140C22⋊D11—82no—
141C22⋊D11—82no—
142C2×Dic11—41no—
143C2×Dic11—41no—
144C2×Dic11—41no—
145C2×Dic11—41no—
146C2×Dic11—41no—
147C2×Dic11—41no—
148C2×Dic11—41no—
149C2×Dic11—41no—
150C2×Dic11—41no—
151D44—82no—
152C8×C11—82no—
153C11⋊C8—82no—
154C2×#121—111no—
155C22×C4⋊C4C2×D1111yescharacteristic
156#407—221no—
157C2×C22⋊C8—21no—
158#400—111no—
159#400—111no—
160#394—111no—
161#394—111no—
162#388—221no—
163#388—221no—
164#386—221no—
165#386—221no—
166C4×C22⋊C4—111no—
167#343—112no—
168#343—221no—
169#324—21no—
170#324C2×D1112yes—
171C22×C11—21no—
172C22×C11—21no—
173C22×C11—21no—
174C22×C11—21no—
175C22×C11—21no—
176C22×C11—21no—
177C22×C11—21no—
178C22×C11—42no—
179C22×C11—42no—
180C22×C11#35512yes—
181C22×C11C2×#9911yescharacteristic
182C22×C11#41611yescharacteristic
183C22×C11#42111yescharacteristic
184C2×D11—81no—
185C2×D11—81no—
186C2×D11—81no—
187C2×D11—81no—
188C2×D11—81no—
189C2×D11—81no—
190C2×D11—81no—
191C4×C11—22no—
192C4×C11—41no—
193C4×C11—41no—
194C4×C11—41no—
195C4×C11—41no—
196C4×C11—41no—
197Dic11—81no—
198Dic11—81no—
199Dic11—81no—
200C22×D4—111no—
201C22×D4—221no—
202C23×C4C4×D1111yescharacteristic
203C23×C4D4411yescharacteristic
204C23×C4C22⋊D1111yescharacteristic
205C2×M16—222no—
206C22×C8—41no—
207#121—441no—
208#121—441no—
209C2×C4⋊C4—41no—
210C2×C4⋊C4—41no—
211C2×C4⋊C4—111no—
212C2×C4⋊C4C4×D1111yescharacteristic
213C2×C4⋊C4D4411yescharacteristic
214C2×C4⋊C4C22⋊D1111yescharacteristic
215C2×C4⋊C4C22×D1111yescharacteristic
216C2×C22⋊C4—221no—
217C2×C22⋊C4—221no—
218C2×C22⋊C4—221no—
219C2×C22⋊C4—221no—
220C2×C22⋊C4—221no—
221C2×C22⋊C4—221no—
222C2×C42—221no—
223C22⋊C8—22no—
224C22⋊C8—41no—
225C22⋊C8—441no—
226C22⋊C8—441no—
227#95—111no—
228#95—111no—
229#95—221no—
230#95—221no—
231#95—221no—
232#95—221no—
233C2×C11—21no—
234C2×C11—21no—
235C2×C11—22no—
236C2×C11—41no—
237C2×C11#151611yescharacteristic
238C2×C11#212111yescharacteristic
239C2×C11C2×#35511yescharacteristic
240D11—161no—
241C24—221no—
242C24(C2×D11)⋊C411yescharacteristic
243C2×D4—441no—
244C2×D4—442no—
245C2×D4—442no—
246C2×D4—441no—
247C2×D4—441no—
248C2×D4—881no—
249C22×C4—21no—
250C22×C4—21no—
251C22×C4—21no—
252C22×C4—21no—
253C22×C4—21no—
254C22×C4—21no—
255C22×C4—22no—
256C22×C4—41no—
257C22×C4—81no—
258C22×C4—81no—
259C22×C4—221no—
260C22×C4—221no—
261C22×C4—221no—
262C22×C4(C2×D11)⋊C411yescharacteristic
263C22×C4(C2×D11)⋊C411yescharacteristic
264C22×C4(C2×D11)⋊C411yescharacteristic
265C22×C4C2×C4×D1111yescharacteristic
266C22×C4C2×D4411yescharacteristic
267C22×C4C2×C22⋊D1111yescharacteristic
268M16—442no—
269M16—442no—
270C2×C8—42no—
271C2×C8—82no—
272C2×C8—442no—
273C4⋊C4—41no—
274C4⋊C4—41no—
275C4⋊C4—41no—
276C4⋊C4—41no—
277C4⋊C4—441no—
278C22⋊C4—442no—
279C22⋊C4—442no—
280C22⋊C4—442no—
281C22⋊C4—442no—
282C22⋊C4—881no—
283C22⋊C4—881no—
284C42—881no—
285C11#1185211yescharacteristic, complemented, Sylow
286C23—21no—
287C23—21no—
288C23—22no—
289C23—41no—
290C23—441no—
291C23—441no—
292C23—441no—
293C23—441no—
294C23—441no—
295C23—441no—
296C23—441no—
297C23#6687011yescharacteristic
298C23#6687011yescharacteristic
299C23C2×(C2×D11)⋊C411yescharacteristic
300D4—882no—
301D4—882no—
302D4—882no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—42no—
313C2×C4—42no—
314C2×C4—42no—
315C2×C4—41no—
316C2×C4—41no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—81no—
320C2×C4—81no—
321C2×C4—81no—
322C2×C4—441no—
323C2×C4—441no—
324C2×C4—441no—
325C2×C4—441no—
326C2×C4—441no—
327C2×C4—441no—
328C2×C4—441no—
329C2×C4—441no—
330C2×C4—441no—
331C2×C4#6695712yes—
332C8—82no—
333C8—882no—
334C22—21no—
335C22—21no—
336C22—21no—
337C22—21no—
338C22—21no—
339C22—21no—
340C22—21no—
341C22—42no—
342C22—42no—
343C22—881no—
344C22—881no—
345C22—881no—
346C22—881no—
347C22—881no—
348C22—881no—
349C22—881no—
350C22#1062211512yes—
351C22C2×#6687011yescharacteristic
352C22#1062272611yescharacteristic
353C22#1062275211yescharacteristic
354C4—22no—
355C4—41no—
356C4—41no—
357C4—41no—
358C4—41no—
359C4—41no—
360C4—881no—
361C4—881no—
362C4—881no—
363C2—21no—
364C2—21no—
365C2—22no—
366C2—41no—
367C2—1761no—
368C2#1306717311yescharacteristic
369C2#1307026011yescharacteristic
370C2C2×#1062211511yescharacteristic
subgroupG/H
centerC22C2×#66870
commutatorC22×C4×C11C22×C4
FrattiniC2×C4⋊C4C22×D11
FittingC2×C11×#324C2
socleC22×C11C2×#99
prime radicalC2×#66983C4
cosocleC2×C11×C4⋊C4C23
hypercenterC2×#324D11
hypocenterC11#11852
LCSG ▷ C22×C4×C11 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C24 ◁ C22×C4⋊C4 ◁ C2×#324

Complements

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

NH ≅ G/Ntype
2. #13068696C2semidirect
3. #13066644C2semidirect
4. #13066620C2semidirect
5. C2×C11×#324C2semidirect
103. C2×#324D11semidirect
285. C11#11852semidirect

Maximal subgroups

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

subgroupindex
#130740962
#130686962
#130666442
#130666202
C2×C11×#3242
#1185211