Finite Group Databasebeta

← #14651575

Subgroups — #14651575

Order 2816.

818 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 818 conjugacy classes of subgroups — too many to draw. Only its 107 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#13071951C211yesmaximal, characteristic
2#13070973C211yesmaximal, characteristic, complemented
3#13068559C212yesmaximal
4#13066470C212yesmaximal, complemented
5C11×#1463C211yesmaximal, characteristic, complemented
6C22×#4339C2211yescharacteristic
7C22×C11×C4⋊C4C2211yescharacteristic
8C2×#66982—21no—
9C2×#66979—21no—
10C11×#407C2212yes—
11#10622826—21no—
12#10622824C2211yescharacteristic
13C4×C22⋊Dic11—21no—
14C4×C22⋊Dic11C2212yes—
15C2×#66889—24no—
16#10622604C412yescomplemented
17#10622602—22no—
18#10622592C412yescomplemented
19C4⋊C4×Dic11—24no—
20C11×#324—22no—
21C23×C4×C11D411yescharacteristic
22C23×C4×C11D411yescharacteristic
23C23×C4×C11C2311yescharacteristic
24C22×C22⋊D11—21no—
25C2×#4339—22no—
26C2×#4339—22no—
27C2×#4339—44no—
28C22×D44C2×C411yescharacteristic
29C22×C4×D11—21no—
30C22×Dic22C2×C411yescharacteristic
31C2×C11×M16—22no—
32C2×C11×C4⋊C4—22no—
33C2×C11×C4⋊C4—22no—
34C2×C11×C4⋊C4C2×C412yes—
35C2×C11×C4⋊C4D412yes—
36C2×C22⋊Dic11—22no—
37C2×C22⋊Dic11—21no—
38#66982—44no—
39C2×(C2×D11)⋊C4—22no—
40C2×(C2×D11)⋊C4—22no—
41#66979—28no—
42C2×C4⋊Dic11—22no—
43C2×Dic11⋊C4—22no—
44C2×C4×Dic11—22no—
45C2×C4×Dic11—22no—
46C2×C4×Dic11D414yes—
47C11×C22⋊C8—22no—
48C11×C22⋊C8—22no—
49C11⋊#95—22no—
50C11⋊#95—22no—
51C11⋊#95—22no—
52C11⋊#95—21no—
53C11⋊#95C2×C412yes—
54#66889—48no—
55#9476—111nomaximal, Sylow
56C24×C11C2×D411yescharacteristic
57C23×D11—21no—
58C22×C4×C11—21no—
59C22×C4×C11—21no—
60C22×C4×C11—24no—
61C22×C4×C11—21no—
62C22×C4×C11—21no—
63C22×C4×C11—42no—
64C22×C4×C11—42no—
65C22×C4×C11C22⋊C412yes—
66C22×C4×C11C22⋊C412yes—
67C22×C4×C11C22×C411yescharacteristic
68C22×C4×C11C2×D412yes—
69C22×C4×C11C2×D411yescharacteristic
70C22×C4×C11#4112yes—
71C2×C22⋊D11—24no—
72C2×C22⋊D11—42no—
73C2×C22⋊D11—41no—
74C2×C22⋊D11—41no—
75C22×Dic11—21no—
76C22×Dic11—22no—
77C22×Dic11—24no—
78#4339—28no—
79#4339—44no—
80#4339—44no—
81#4339—44no—
82C2×D44—22no—
83C2×D44—42no—
84C2×C4×D11—42no—
85C2×C4×D11—42no—
86C2×C4×D11—42no—
87C2×Dic22—22no—
88C2×Dic22—42no—
89C11×M16—44no—
90C2×C8×C11—42no—
91C11×C4⋊C4—24no—
92C11×C4⋊C4—24no—
93C22⋊Dic11—28no—
94C22⋊Dic11—42no—
95(C2×D11)⋊C4—44no—
96(C2×D11)⋊C4—44no—
97C4⋊Dic11—28no—
98Dic11⋊C4—44no—
99C4×Dic11—28no—
100C4×Dic11—44no—
101C4×Dic11—82no—
102#2406—111no—
103#2274—111no—
104#1789—112no—
105#1463D1111yescharacteristic, complemented
106#1284—112no—
107C23×C11—22no—
108C23×C11—22no—
109C23×C11—41no—
110C23×C11C2×C22⋊C411yescharacteristic
111C23×C11#12011yescharacteristic
112C23×C11#12311yescharacteristic
113C22×D11—22no—
114C22×D11—41no—
115C22×D11—42no—
116C22×D11—41no—
117C22×D11—42no—
118C2×C4×C11—22no—
119C2×C4×C11—22no—
120C2×C4×C11—24no—
121C2×C4×C11—22no—
122C2×C4×C11—22no—
123C2×C4×C11—24no—
124C2×C4×C11—22no—
125C2×C4×C11—41no—
126C2×C4×C11—41no—
127C2×C4×C11—42no—
128C2×C4×C11—42no—
129C2×C4×C11—42no—
130C2×C4×C11—81no—
131C2×C4×C11#10414yescomplemented
132C2×C4×C11C4×D412yes—
133C2×C4×C11#12112yes—
134C22⋊D11—44no—
135C22⋊D11—44no—
136C2×Dic11—28no—
137C2×Dic11—22no—
138C2×Dic11—41no—
139C2×Dic11—44no—
140C2×Dic11—41no—
141C2×Dic11—44no—
142C2×Dic11—42no—
143C2×Dic11—42no—
144C2×Dic11—42no—
145D44—24no—
146D44—42no—
147C4×D11—48no—
148Dic22—24no—
149Dic22—42no—
150C8×C11—82no—
151C22×#41—111no—
152C2×#123—221no—
153C2×#117—221no—
154C22×C4⋊C4C2×D1111yescharacteristic
155C2×#104—224no—
156#407C2×D1112yes—
157#395—112no—
158#394—112no—
159#386—221no—
160#385—222no—
161#381—111no—
162C4×C4⋊C4—224no—
163C4×C22⋊C4—112no—
164C4×C22⋊C4—221no—
165#324—22no—
166C22×C11—21no—
167C22×C11—21no—
168C22×C11—21no—
169C22×C11—21no—
170C22×C11—21no—
171C22×C11—21no—
172C22×C11—21no—
173C22×C11—44no—
174C22×C11#38611yescharacteristic
175C22×C11C2×#10412yes—
176C22×C11B(4,𝔽2)12yes—
177C2×D11—44no—
178C2×D11—42no—
179C2×D11—82no—
180C2×D11—81no—
181C2×D11—81no—
182C4×C11—22no—
183C4×C11—22no—
184C4×C11—24no—
185C4×C11—42no—
186Dic11—48no—
187Dic11—42no—
188Dic11—82no—
189C2×#41—222no—
190C2×#41—222no—
191C2×#41—444no—
192C22×Q8—111no—
193C22×D4—111no—
194C22×D4—221no—
195C23×C4—221no—
196C23×C4D4411yescharacteristic
197C23×C4D4411yescharacteristic
198C23×C4C22×D1111yescharacteristic
199C2×M16—22no—
200#123—444no—
201#117—228no—
202C2×C4⋊C4—22no—
203C2×C4⋊C4—22no—
204C2×C4⋊C4—222no—
205C2×C4⋊C4—222no—
206C2×C4⋊C4C4×D1112yes—
207C2×C4⋊C4C22⋊D1112yes—
208C2×C22⋊C4—222no—
209C2×C22⋊C4—221no—
210C2×C22⋊C4—222no—
211C2×C22⋊C4—222no—
212C2×C42—114no—
213C2×C42—222no—
214C2×C42—222no—
215#104—448no—
216C22⋊C8—22no—
217C22⋊C8—22no—
218#95—112no—
219#95—222no—
220#95—222no—
221#95—222no—
222#95—221no—
223C2×C11—22no—
224C2×C11—22no—
225C2×C11—41no—
226C2×C11#188911yescharacteristic
227C2×C11#189611yescharacteristic
228C2×C11#191211yescharacteristic
229D11—82no—
230C24—221no—
231C24C2×D4411yescharacteristic
232#41—228no—
233#41—444no—
234#41—444no—
235#41—444no—
236C2×Q8—222no—
237C2×Q8—442no—
238C2×D4—224no—
239C2×D4—222no—
240C2×D4—442no—
241C2×D4—442no—
242C2×D4—441no—
243C2×D4—441no—
244C22×C4—21no—
245C22×C4—21no—
246C22×C4—24no—
247C22×C4—21no—
248C22×C4—21no—
249C22×C4—42no—
250C22×C4—42no—
251C22×C4—224no—
252C22×C4—221no—
253C22×C4—222no—
254C22×C4—442no—
255C22×C4—442no—
256C22×C4—442no—
257C22×C4(C2×D11)⋊C412yes—
258C22×C4(C2×D11)⋊C412yes—
259C22×C4C2×C4×D1111yescharacteristic
260C22×C4D4×D1112yes—
261C22×C4#434112yes—
262C22×C4C2×C22⋊D1111yescharacteristic
263M16—44no—
264C2×C8—42no—
265C4⋊C4—24no—
266C4⋊C4—24no—
267C4⋊C4—228no—
268C4⋊C4—444no—
269C22⋊C4—228no—
270C22⋊C4—444no—
271C22⋊C4—442no—
272C22⋊C4—444no—
273C42—228no—
274C42—444no—
275C42—882no—
276C11#947611yescharacteristic, complemented, Sylow
277C23—22no—
278C23—22no—
279C23—41no—
280C23—222no—
281C23—441no—
282C23—442no—
283C23—442no—
284C23—441no—
285C23#6693511yescharacteristic
286C23#6693911yescharacteristic
287C23C2×(C2×D11)⋊C411yescharacteristic
288Q8—224no—
289Q8—442no—
290D4—224no—
291D4—442no—
292D4—444no—
293D4—444no—
294C2×C4—22no—
295C2×C4—22no—
296C2×C4—24no—
297C2×C4—22no—
298C2×C4—22no—
299C2×C4—24no—
300C2×C4—22no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—42no—
304C2×C4—42no—
305C2×C4—42no—
306C2×C4—81no—
307C2×C4—228no—
308C2×C4—222no—
309C2×C4—448no—
310C2×C4—441no—
311C2×C4—444no—
312C2×C4—441no—
313C2×C4—444no—
314C2×C4—442no—
315C2×C4—442no—
316C2×C4—442no—
317C2×C4#6688914yescomplemented
318C2×C4(C22⋊D11)⋊C412yes—
319C2×C4#6699212yes—
320C8—82no—
321C22—21no—
322C22—21no—
323C22—21no—
324C22—21no—
325C22—21no—
326C22—21no—
327C22—21no—
328C22—44no—
329C22—444no—
330C22—442no—
331C22—882no—
332C22—881no—
333C22—881no—
334C22#1062235412yes—
335C22#1062257111yescharacteristic
336C22C2×#6688912yes—
337C4—24no—
338C4—22no—
339C4—22no—
340C4—42no—
341C4—448no—
342C4—442no—
343C4—882no—
344C2—22no—
345C2—22no—
346C2—41no—
347C2—882no—
348C2#1306902211yescharacteristic
349C2#1306905711yescharacteristic
350C2#1306915111yescharacteristic
subgroupG/H
centerC22#10622571
commutatorC22×C4×C11C22×C4
FrattiniC23×C4C22×D11
FittingC11×#1463C2
socleC22×C11#386
prime radicalC22×#4339C22
cosocleC23×C4×C11C23
hypercenter#1463D11
hypocenterC11#9476
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1463

Complements

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

NH ≅ G/Ntype
2. #13070973C2semidirect
4. #13066470C2semidirect
5. C11×#1463C2semidirect
16. #10622604C4semidirect
18. #10622592C4semidirect
105. #1463D11semidirect
131. C2×C4×C11#104semidirect
276. C11#9476semidirect
317. C2×C4#66889semidirect

Maximal subgroups

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

subgroupindex
#130719512
#130709732
#130685592
#130664702
C11×#14632
#947611