Finite Group Databasebeta

← #14664390

Subgroups — #14664390

Order 2816.

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

normal subgroups only

This group has 460 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
1C4×#66898C211yesmaximal, characteristic
2#13066954C211yesmaximal, characteristic
3#13066637C214yesmaximal, complemented
4C11×#2563C211yesmaximal, characteristic
5C2×C11×C4⋊Q8C411yescharacteristic, complemented
6C2×C4×D4×C11C2211yescharacteristic
7C11×#393C412yescomplemented
8C11×#393C2212yes—
9C11×#390—21no—
10C11×#382—21no—
11C11×#380—21no—
12C11×#380—21no—
13C4×C11×C4⋊C4C411yescharacteristic, complemented
14C2×#66898—21no—
15C4×C22⋊Dic11—21no—
16#10622820—21no—
17#10622166—21no—
18#10622164C2212yes—
19#10622163C2212yes—
20C22×Q8×C11C2×C412yes—
21C22×D4×C11D411yescharacteristic
22C23×C4×C11D411yescharacteristic
23C23×C4×C11D411yescharacteristic
24C11×C4⋊Q8—41no—
25C11×C4⋊Q8—41no—
26C4×D4×C11—41no—
27C4×D4×C11—41no—
28C2×C11×C4⋊C4—21no—
29C2×C11×C4⋊C4—21no—
30C2×C11×C4⋊C4—21no—
31C2×C11×C4⋊C4D411yescharacteristic
32C2×C11×C22⋊C4—22no—
33C2×C11×C22⋊C4—22no—
34C2×C11×C22⋊C4C2×C411yescharacteristic
35C2×C11×C22⋊C4C2311yescharacteristic
36C2×C42×C11—21no—
37C2×C42×C11C2×C411yescharacteristic
38C2×C22⋊Dic11—22no—
39C2×C4×Dic11—41no—
40C2×#4318—41no—
41C11×#95—22no—
42C11×#95—22no—
43C11×#95C2×C412yes—
44#66898—24no—
45C11⋊#95—41no—
46C22⋊(C11⋊C8)—22no—
47C22⋊(C11⋊C8)—41no—
48#11787—111nomaximal, Sylow
49C24×C11C22⋊C411yescharacteristic
50C24×C11C2×D411yescharacteristic
51C2×Q8×C11—42no—
52C2×Q8×C11—82no—
53C2×D4×C11—22no—
54C2×D4×C11—22no—
55C2×D4×C11—41no—
56C22×C4×C11—21no—
57C22×C4×C11—21no—
58C22×C4×C11—21no—
59C22×C4×C11—21no—
60C22×C4×C11—22no—
61C22×C4×C11—22no—
62C22×C4×C11—42no—
63C22×C4×C11—42no—
64C22×C4×C11C22⋊C411yescharacteristic
65C22×C4×C11C22⋊C411yescharacteristic
66C22×C4×C11C22⋊C411yescharacteristic
67C22×C4×C11C22×C411yescharacteristic
68C22×C4×C11C2×D411yescharacteristic
69C22×Dic11—42no—
70C11×C4⋊C4—41no—
71C11×C4⋊C4—42no—
72C11×C4⋊C4—42no—
73C11×C4⋊C4—41no—
74C11×C4⋊C4—41no—
75C11×C22⋊C4—41no—
76C11×C22⋊C4—41no—
77C11×C22⋊C4—82no—
78C11×C22⋊C4—82no—
79C42×C11—21no—
80C42×C11—21no—
81C42×C11—42no—
82C22⋊Dic11—24no—
83C22⋊Dic11—42no—
84C4×Dic11—82no—
85#4318—82no—
86C2×C11⋊C8—42no—
87#2563D1111yescharacteristic
88C4×#99—111no—
89#1465—111no—
90#1351—114no—
91C23×C11—21no—
92C23×C11—21no—
93C23×C11—21no—
94C23×C11—21no—
95C23×C11—21no—
96C23×C11—41no—
97C23×C11—41no—
98C23×C11—41no—
99C23×C11—41no—
100C23×C11C2×C22⋊C411yescharacteristic
101C23×C11#13712yes—
102Q8×C11—84no—
103D4×C11—44no—
104C2×C4×C11—21no—
105C2×C4×C11—21no—
106C2×C4×C11—22no—
107C2×C4×C11—21no—
108C2×C4×C11—21no—
109C2×C4×C11—21no—
110C2×C4×C11—42no—
111C2×C4×C11—42no—
112C2×C4×C11—41no—
113C2×C4×C11—41no—
114C2×C4×C11—41no—
115C2×C4×C11—42no—
116C2×C4×C11—42no—
117C2×C4×C11—42no—
118C2×C4×C11—42no—
119C2×C4×C11—42no—
120C2×C4×C11—42no—
121C2×C4×C11—81no—
122C2×C4×C11—81no—
123C2×C4×C11#9911yescharacteristic
124C2×C4×C11#9911yescharacteristic
125C2×C4×C11#10412yes—
126C2×Dic11—44no—
127C2×Dic11—82no—
128C2×Dic11—82no—
129C11⋊C8—82no—
130C2×C4⋊Q8Dic1111yescharacteristic, complemented
131C2×C4×D4C2×D1111yescharacteristic
132C2×#99—221no—
133#407—221no—
134#393Dic1112yescomplemented
135#393C2×D1112yes—
136#390—21no—
137#382—21no—
138#380—21no—
139#380—21no—
140C4×C4⋊C4Dic1111yescharacteristic, complemented
141C4×C22⋊C4—221no—
142#342—112no—
143#324—221no—
144#323—112no—
145C22×C11—21no—
146C22×C11—21no—
147C22×C11—22no—
148C22×C11—42no—
149C22×C11—42no—
150C22×C11—41no—
151C22×C11—41no—
152C22×C11—41no—
153C22×C11—41no—
154C22×C11—41no—
155C22×C11—81no—
156C22×C11—81no—
157C22×C11C2×#9911yescharacteristic
158C22×C11#41911yescharacteristic
159C22×C11C2×#10411yescharacteristic
160C4×C11—21no—
161C4×C11—22no—
162C4×C11—41no—
163C4×C11—41no—
164C4×C11—41no—
165C4×C11—82no—
166C4×C11—82no—
167C4×C11#35412yes—
168Dic11—84no—
169C22×Q8C2×Dic1112yes—
170C22×D4C22⋊D1111yescharacteristic
171C23×C4C22⋊D1111yescharacteristic
172C23×C4C22⋊D1111yescharacteristic
173C2×M16—441no—
174C4⋊Q8—41no—
175C4⋊Q8—41no—
176C4×D4—41no—
177C4×D4—41no—
178C2×C4⋊C4—21no—
179C2×C4⋊C4—21no—
180C2×C4⋊C4—21no—
181C2×C4⋊C4C22⋊D1111yescharacteristic
182C2×C22⋊C4—22no—
183C2×C22⋊C4—22no—
184C2×C22⋊C4—222no—
185C2×C22⋊C4C2×Dic1111yescharacteristic
186C2×C22⋊C4C22×D1111yescharacteristic
187C2×C42—21no—
188C2×C42—441no—
189C2×C42C2×Dic1111yescharacteristic
190#99—224no—
191C22⋊C8—222no—
192C22⋊C8—441no—
193#95—22no—
194#95—22no—
195#95—441no—
196#95C2×Dic1112yes—
197C2×C11—21no—
198C2×C11—21no—
199C2×C11—42no—
200C2×C11—81no—
201C2×C11#150811yescharacteristic
202C2×C11#212211yescharacteristic
203C2×C11C2×#35411yescharacteristic
204C24C22⋊Dic1111yescharacteristic
205C24C2×C22⋊D1111yescharacteristic
206C2×Q8—42no—
207C2×Q8—82no—
208C2×D4—22no—
209C2×D4—22no—
210C2×D4—41no—
211C22×C4—21no—
212C22×C4—21no—
213C22×C4—21no—
214C22×C4—21no—
215C22×C4—22no—
216C22×C4—22no—
217C22×C4—42no—
218C22×C4—42no—
219C22×C4—442no—
220C22×C4C22⋊Dic1111yescharacteristic
221C22×C4C22⋊Dic1111yescharacteristic
222C22×C4C22⋊Dic1111yescharacteristic
223C22×C4C22×Dic1111yescharacteristic
224C22×C4C2×C22⋊D1111yescharacteristic
225M16—882no—
226C2×C8—442no—
227C4⋊C4—41no—
228C4⋊C4—42no—
229C4⋊C4—42no—
230C4⋊C4—41no—
231C4⋊C4—41no—
232C22⋊C4—41no—
233C22⋊C4—41no—
234C22⋊C4—82no—
235C22⋊C4—82no—
236C22⋊C4—224no—
237C22⋊C4—442no—
238C42—21no—
239C42—21no—
240C42—42no—
241C42—882no—
242C11#1178711yescharacteristic, complemented, Sylow
243C23—21no—
244C23—21no—
245C23—21no—
246C23—21no—
247C23—21no—
248C23—41no—
249C23—41no—
250C23—41no—
251C23—41no—
252C23#6699512yes—
253C23C2×C22⋊Dic1111yescharacteristic
254Q8—84no—
255D4—44no—
256C2×C4—21no—
257C2×C4—21no—
258C2×C4—22no—
259C2×C4—21no—
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—42no—
263C2×C4—42no—
264C2×C4—41no—
265C2×C4—41no—
266C2×C4—41no—
267C2×C4—42no—
268C2×C4—42no—
269C2×C4—42no—
270C2×C4—42no—
271C2×C4—42no—
272C2×C4—42no—
273C2×C4—81no—
274C2×C4—81no—
275C2×C4—444no—
276C2×C4—882no—
277C2×C4—882no—
278C2×C4#6689811yescharacteristic
279C2×C4#6689811yescharacteristic
280C2×C4#6690112yes—
281C8—882no—
282C22—21no—
283C22—21no—
284C22—22no—
285C22—42no—
286C22—42no—
287C22—41no—
288C22—41no—
289C22—41no—
290C22—41no—
291C22—41no—
292C22—81no—
293C22—81no—
294C22C2×#6689811yescharacteristic
295C22#1062283811yescharacteristic
296C22C2×#6690111yescharacteristic
297C4—22no—
298C4—21no—
299C4—41no—
300C4—41no—
301C4—41no—
302C4—82no—
303C4—82no—
304C4—884no—
305C4#1062217912yes—
306C2—21no—
307C2—21no—
308C2—42no—
309C2—81no—
310C2#1306713611yescharacteristic
311C2#1307026611yescharacteristic
312C2C2×#1062217911yescharacteristic
subgroupG/H
centerC22C2×#66898
commutatorC22×C4×C11C22×C4
FrattiniC2×C22⋊C4C22×D11
FittingC11×#2563C2
socleC22×C11C2×#99
prime radicalC22×D4×C11D4
cosocleC2×C11×C22⋊C4C23
hypercenter#2563D11
hypocenterC11#11787
LCSG ▷ C22×C4×C11 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ #2563

Complements

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

NH ≅ G/Ntype
3. #13066637C2semidirect
5. C2×C11×C4⋊Q8C4semidirect
7. C11×#393C4semidirect
13. C4×C11×C4⋊C4C4semidirect
130. C2×C4⋊Q8Dic11semidirect
134. #393Dic11semidirect
140. C4×C4⋊C4Dic11semidirect
242. C11#11787semidirect

Maximal subgroups

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

subgroupindex
C4×#668982
#130669542
#130666372
C11×#25632
#1178711