Finite Group Databasebeta

← #14646805

Subgroups — #14646805

Order 2816.

404 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 404 conjugacy classes of subgroups — too many to draw. Only its 109 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#13077328C211yesmaximal, characteristic
2#13067374C211yesmaximal, characteristic, complemented
3#13067371C211yesmaximal, characteristic, complemented
4#13067351C211yesmaximal, characteristic
5C11⋊#1309C211yesmaximal, characteristic, complemented
6C11⋊#1309C211yesmaximal, characteristic, complemented
7C11×#1560C211yesmaximal, characteristic
8C11×#532C2211yescharacteristic
9C2×#67001C412yes—
10C11×#423C2211yescharacteristic
11C11×#423C2211yescharacteristic
12#10622847C412yes—
13#10622625—21no—
14#10622625—21no—
15D4×C11⋊C8—21no—
16D4×C11⋊C8—21no—
17#10622537C2211yescharacteristic
18#10622537C2211yescharacteristic
19#10622537C2211yescharacteristic
20C2×C4×C11⋊C8C2211yescharacteristic
21C11×#333—21no—
22C11×#331—21no—
23#10622184—21no—
24#10622182—21no—
25#10622118—21no—
26#10622118—21no—
27#10622117—21no—
28#10622117—21no—
29C2×C11×#41C2×C412yes—
30C2×C11×M16—21no—
31C2×C11×M16—21no—
32C11×C4⋊Q8D411yescharacteristic
33C11×#127D411yescharacteristic
34C11×#124Q812yes—
35C11×#121—21no—
36C11×#121—21no—
37C4×D4×C11—21no—
38C4×D4×C11—21no—
39C2×C42×C11C2311yescharacteristic
40#67001—44no—
41C2×#4318—22no—
42C2×#4318—21no—
43C2×#4318—21no—
44C2×#4318C2×C412yes—
45C22×C11⋊C8—22no—
46C22×C11⋊C8C2×C411yescharacteristic
47C22×C11⋊C8C2×C411yescharacteristic
48C11×C4⋊C8—21no—
49C11×C4⋊C8—21no—
50C11×C4⋊C8—21no—
51C11×C4⋊C8—21no—
52C22⋊(C11⋊C8)—22no—
53C22⋊(C11⋊C8)—22no—
54C4⋊(C11⋊C8)—21no—
55C4⋊(C11⋊C8)—21no—
56C4⋊(C11⋊C8)—21no—
57C4⋊(C11⋊C8)—21no—
58C4⋊(C11⋊C8)—21no—
59C4⋊(C11⋊C8)—21no—
60C4×C11⋊C8D411yescharacteristic
61C4×C11⋊C8D411yescharacteristic
62C4×C11⋊C8D411yescharacteristic
63C4×C11⋊C8D411yescharacteristic
64#8640—111nomaximal, Sylow
65C11×#41—42no—
66C11×#41—42no—
67C2×Q8×C11C4⋊C412yes—
68C2×D4×C11—22no—
69C2×D4×C11—21no—
70C2×D4×C11—21no—
71C2×D4×C11C4⋊C412yes—
72C22×C4×C11—22no—
73C22×C4×C11C22×C411yescharacteristic
74C22×C4×C11#4111yescharacteristic
75C22×C4×C11#4111yescharacteristic
76C11×M16—81no—
77C11×M16—81no—
78C2×C8×C11—41no—
79C2×C8×C11—41no—
80C11×C4⋊C4—21no—
81C11×C4⋊C4—21no—
82C11×C22⋊C4—22no—
83C11×C22⋊C4—22no—
84C42×C11C2×D411yescharacteristic
85C42×C11C2×D411yescharacteristic
86C42×C11C2×D411yescharacteristic
87C42×C11C2×Q811yescharacteristic
88#4318—42no—
89#4318—44no—
90#4318—81no—
91#4318—81no—
92C2×C11⋊C8—22no—
93C2×C11⋊C8—22no—
94C2×C11⋊C8—41no—
95C2×C11⋊C8—44no—
96C2×C11⋊C8—41no—
97C2×C11⋊C8—41no—
98C2×C11⋊C8C22⋊C411yescharacteristic
99C2×C11⋊C8C22⋊C411yescharacteristic
100C2×C11⋊C8C22⋊C411yescharacteristic
101C2×C11⋊C8C22⋊C411yescharacteristic
102#2931—111no—
103#1567—111no—
104#1566—111no—
105#1560—111no—
106#1560D1111yescharacteristic
107#1309—111no—
108#1309—111no—
109C23×C11—22no—
110C23×C11#11711yescharacteristic
111Q8×C11—42no—
112D4×C11—42no—
113D4×C11—44no—
114D4×C11—41no—
115D4×C11—41no—
116D4×C11—41no—
117D4×C11—41no—
118C2×C4×C11—21no—
119C2×C4×C11—21no—
120C2×C4×C11—21no—
121C2×C4×C11—21no—
122C2×C4×C11—21no—
123C2×C4×C11—21no—
124C2×C4×C11—22no—
125C2×C4×C11—42no—
126C2×C4×C11—42no—
127C2×C4×C11C2×C22⋊C411yescharacteristic
128C2×C4×C11C2×C4⋊C411yescharacteristic
129C2×C4×C11#12111yescharacteristic
130C2×C4×C11#12111yescharacteristic
131C2×C4×C11C22⋊Q811yescharacteristic
132C2×C4×C11C22⋊Q811yescharacteristic
133C8×C11—81no—
134C8×C11—81no—
135C11⋊C8—21no—
136C11⋊C8—21no—
137C11⋊C8—21no—
138C11⋊C8—42no—
139C11⋊C8—81no—
140C11⋊C8—81no—
141C11⋊C8#10012yes—
142C2×#131—112no—
143#532C2×D1111yescharacteristic
144#436—221no—
145#436—221no—
146C8×D4—221no—
147C8×D4—221no—
148#423—111no—
149#423—111no—
150#423—111no—
151#423C2×D1111yescharacteristic
152#423C2×D1111yescharacteristic
153#408—112no—
154C2×C4×C8—111no—
155#335—221no—
156#335—221no—
157#334—221no—
158#334—221no—
159#333—21no—
160#333—221no—
161#331—21no—
162#331—221no—
163C22×C11—21no—
164C22×C11—21no—
165C22×C11—21no—
166C22×C11—42no—
167C22×C11—42no—
168C22×C11—42no—
169C22×C11#38011yescharacteristic
170C4×C11—21no—
171C4×C11—21no—
172C4×C11—21no—
173C4×C11—42no—
174C4×C11C2×#10011yescharacteristic
175C4×C11#41311yescharacteristic
176C4×C11#47111yescharacteristic
177C4×C11#47111yescharacteristic
178C4×C11#47211yescharacteristic
179C4×C11#47311yescharacteristic
180C2×#41C4×D1112yes—
181#131—444no—
182C2×M16—21no—
183C2×M16—21no—
184C2×M16—112no—
185C2×M16—222no—
186C2×M16—221no—
187C2×M16—221no—
188C22×C8—111no—
189C22×C8—111no—
190C22×C8—222no—
191C4⋊Q8C22⋊D1111yescharacteristic
192#127C22⋊D1111yescharacteristic
193#124Dic2212yes—
194#121—21no—
195#121—21no—
196C4×D4—21no—
197C4×D4—21no—
198C2×C42C22×D1111yescharacteristic
199C4⋊C8—21no—
200C4⋊C8—21no—
201C4⋊C8—21no—
202C4⋊C8—21no—
203C4⋊C8—221no—
204C4⋊C8—221no—
205C4⋊C8—221no—
206C4⋊C8—221no—
207C4⋊C8—221no—
208C4⋊C8—221no—
209C22⋊C8—222no—
210C22⋊C8—222no—
211C4×C8—111no—
212C4×C8—111no—
213C4×C8—111no—
214C4×C8—111no—
215C2×C11—41no—
216C2×C11—82no—
217C2×C11#180011yescharacteristic
218C2×C11#181511yescharacteristic
219C2×C11#181611yescharacteristic
220#41—42no—
221#41—42no—
222C2×Q8Dic11⋊C412yes—
223C2×D4—22no—
224C2×D4—21no—
225C2×D4—21no—
226C2×D4Dic11⋊C412yes—
227C22×C4—22no—
228C22×C4C2×C4×D1111yescharacteristic
229C22×C4#434111yescharacteristic
230C22×C4#434111yescharacteristic
231M16—81no—
232M16—81no—
233M16—444no—
234M16—442no—
235M16—881no—
236M16—881no—
237C2×C8—41no—
238C2×C8—41no—
239C2×C8—111no—
240C2×C8—111no—
241C2×C8—111no—
242C2×C8—111no—
243C2×C8—222no—
244C2×C8—222no—
245C2×C8—441no—
246C2×C8—444no—
247C2×C8—441no—
248C2×C8—441no—
249C4⋊C4—21no—
250C4⋊C4—21no—
251C22⋊C4—22no—
252C22⋊C4—22no—
253C42C2×Dic2211yescharacteristic
254C42D4×D1111yescharacteristic
255C42D4×D1111yescharacteristic
256C42C2×C22⋊D1111yescharacteristic
257C11#864011yescharacteristic, complemented, Sylow
258C23—22no—
259C23#6693011yescharacteristic
260Q8—42no—
261D4—42no—
262D4—44no—
263D4—41no—
264D4—41no—
265D4—41no—
266D4—41no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—22no—
274C2×C4—42no—
275C2×C4—42no—
276C2×C4#6693111yescharacteristic
277C2×C4#6693111yescharacteristic
278C2×C4C22⋊C4×D1111yescharacteristic
279C2×C4C2×Dic11⋊C411yescharacteristic
280C2×C4#6699211yescharacteristic
281C2×C4#6699211yescharacteristic
282C8—81no—
283C8—81no—
284C8—112no—
285C8—221no—
286C8—221no—
287C8—221no—
288C8—442no—
289C8—881no—
290C8—881no—
291C22—21no—
292C22—21no—
293C22—21no—
294C22—42no—
295C22—42no—
296C22—42no—
297C22#1062255511yescharacteristic
298C4—21no—
299C4—21no—
300C4—21no—
301C4—42no—
302C4D11×#10011yescharacteristic
303C4#1062235811yescharacteristic
304C4#1062281211yescharacteristic
305C4#1062281311yescharacteristic
306C4#1062281611yescharacteristic
307C4#1062281711yescharacteristic
308C2—41no—
309C2—82no—
310C2#1306860611yescharacteristic
311C2#1306867311yescharacteristic
312C2#1306867811yescharacteristic
subgroupG/H
centerC22#10622555
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1560C2
socleC22×C11#380
prime radicalC11×#532C22
cosocleC2×C42×C11C23
hypercenter#1560D11
hypocenterC11#8640
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1560

Complements

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

NH ≅ G/Ntype
2. #13067374C2semidirect
3. #13067371C2semidirect
5. C11⋊#1309C2semidirect
6. C11⋊#1309C2semidirect
257. C11#8640semidirect

Maximal subgroups

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

subgroupindex
#130773282
#130673742
#130673712
#130673512
C11⋊#13092
C11×#15602
#864011