Finite Group Databasebeta

← #14642341

Subgroups — #14642341

Order 2816.

426 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 426 conjugacy classes of subgroups — too many to draw. Only its 103 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#13076983C211yesmaximal, characteristic
2#13068365C211yesmaximal, characteristic, complemented
3#13066438C212yesmaximal, complemented
4#13066436C212yesmaximal
5C11×#1831C211yesmaximal, characteristic, complemented
6C2×#66929—21no—
7C2×C11×C4⋊C8—21no—
8C43×C11C2211yescharacteristic
9#10622553—21no—
10#10622553—21no—
11#10622553—21no—
12#10622552C411yescharacteristic
13#10622552C411yescharacteristic
14#10622552C2211yescharacteristic
15#10622541C411yescharacteristic
16#10622541C411yescharacteristic
17#10622541C2211yescharacteristic
18C2×#66867—21no—
19C11×#336—21no—
20C11×#336C2212yes—
21#10622162—21no—
22#10622162C2212yes—
23C22×D44C2×C411yescharacteristic
24C22×C8×C11—22no—
25C2×C42×C11C2×C411yescharacteristic
26C2×C42×C11C2×C411yescharacteristic
27C2×C42×C11D411yescharacteristic
28C2×C42×C11D411yescharacteristic
29C2×C42×C11D411yescharacteristic
30C2×C42×C11D411yescharacteristic
31C2×C42×C11C2311yescharacteristic
32C2×(C2×D11)⋊C4—21no—
33C2×(C2×D11)⋊C4—21no—
34C2×(C2×D11)⋊C4—21no—
35C2×(C2×D11)⋊C4—21no—
36C2×(C2×D11)⋊C4—21no—
37C2×(C2×D11)⋊C4—21no—
38C2×C4⋊Dic11C2×C411yescharacteristic
39C2×C4⋊Dic11C2×C411yescharacteristic
40C2×C4⋊Dic11C2×C411yescharacteristic
41C2×Dic11⋊C4—21no—
42C2×Dic11⋊C4—21no—
43C2×Dic11⋊C4—21no—
44C22×C11⋊C8—22no—
45#66929—44no—
46C11×C4⋊C8—42no—
47C11⋊#95—21no—
48C11⋊#95—21no—
49C11⋊#95—21no—
50#66867—24no—
51#7706—111nomaximal, Sylow
52C23×D11—21no—
53C22×C4×C11C22⋊C411yescharacteristic
54C22×C4×C11C22⋊C411yescharacteristic
55C22×C4×C11C22⋊C411yescharacteristic
56C22×C4×C11C22⋊C411yescharacteristic
57C22×C4×C11C22×C411yescharacteristic
58C22×C4×C11C2×D411yescharacteristic
59C22×C4×C11C2×D411yescharacteristic
60C22×Dic11—21no—
61C22×Dic11—21no—
62C22×Dic11—21no—
63C2×D44—22no—
64C2×D44—41no—
65C2×D44—41no—
66C2×C8×C11—42no—
67C2×C8×C11—42no—
68C2×C8×C11—42no—
69C42×C11—22no—
70C42×C11—22no—
71C42×C11—21no—
72C42×C11—22no—
73C42×C11—21no—
74C42×C11—41no—
75C42×C11—41no—
76C42×C11—41no—
77(C2×D11)⋊C4—42no—
78(C2×D11)⋊C4—42no—
79(C2×D11)⋊C4—42no—
80(C2×D11)⋊C4—42no—
81(C2×D11)⋊C4—42no—
82(C2×D11)⋊C4—41no—
83(C2×D11)⋊C4—41no—
84C4⋊Dic11—22no—
85C4⋊Dic11—41no—
86C4⋊Dic11—41no—
87Dic11⋊C4—42no—
88Dic11⋊C4—42no—
89Dic11⋊C4—42no—
90C2×C11⋊C8—24no—
91C2×C11⋊C8—42no—
92C2×C11⋊C8—42no—
93#2860—111no—
94#1831D1111yescharacteristic, complemented
95#1745—111no—
96#1271—112no—
97#1270—112no—
98C23×C11C2×C22⋊C411yescharacteristic
99C22×D11—41no—
100C22×D11—41no—
101C22×D11—41no—
102C22×D11—41no—
103C22×D11—41no—
104C22×D11—41no—
105C22×D11—41no—
106C2×C4×C11—21no—
107C2×C4×C11—21no—
108C2×C4×C11—21no—
109C2×C4×C11—21no—
110C2×C4×C11—21no—
111C2×C4×C11—21no—
112C2×C4×C11—21no—
113C2×C4×C11—21no—
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—21no—
123C2×C4×C11#10412yes—
124C2×C4×C11#13112yes—
125C2×C4×C11AGL(1,ℤ/8)12yes—
126C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
127C2×C4×C11#13711yescharacteristic
128C2×Dic11—41no—
129C2×Dic11—41no—
130C2×Dic11—41no—
131C2×Dic11—41no—
132C2×Dic11—41no—
133C2×Dic11—41no—
134C2×Dic11—41no—
135C2×Dic11—41no—
136C2×Dic11—41no—
137D44—82no—
138C8×C11—82no—
139C11⋊C8—44no—
140C2×#126—221no—
141C2×C4⋊C8—21no—
142C2×#97—221no—
143#390—111no—
144#390—111no—
145#390—111no—
146#389—111no—
147#389—111no—
148#389—111no—
149#388—221no—
150#388—221no—
151#388—221no—
152C43C2×D1111yescharacteristic
153#336—21no—
154#336—112no—
155#336—221no—
156#336C2×D1112yes—
157C22×C11#40811yescharacteristic
158C22×C11#41011yescharacteristic
159C22×C11#41311yescharacteristic
160C22×C11#41711yescharacteristic
161C22×C11#41811yescharacteristic
162C22×C11C2×#10411yescharacteristic
163C22×C11#42111yescharacteristic
164C2×D11—81no—
165C2×D11—81no—
166C2×D11—81no—
167C2×D11—81no—
168C2×D11—81no—
169C2×D11—81no—
170C2×D11—81no—
171C4×C11—22no—
172C4×C11—22no—
173C4×C11—22no—
174C4×C11—21no—
175C4×C11—21no—
176C4×C11—41no—
177C4×C11—41no—
178C4×C11—41no—
179Dic11—81no—
180Dic11—81no—
181Dic11—81no—
182C22×D4—111no—
183C22×C8—22no—
184C22×C8—222no—
185#126—444no—
186C2×C4⋊C4—111no—
187C2×C4⋊C4—111no—
188C2×C4⋊C4—111no—
189C2×C4⋊C4—221no—
190C2×C4⋊C4—221no—
191C2×C4⋊C4—221no—
192C2×C22⋊C4—221no—
193C2×C22⋊C4—221no—
194C2×C22⋊C4—221no—
195C2×C22⋊C4—221no—
196C2×C22⋊C4—221no—
197C2×C22⋊C4—221no—
198C2×C42C4×D1111yescharacteristic
199C2×C42C4×D1111yescharacteristic
200C2×C42D4411yescharacteristic
201C2×C42D4411yescharacteristic
202C2×C42C22⋊D1111yescharacteristic
203C2×C42C22⋊D1111yescharacteristic
204C2×C42C22×D1111yescharacteristic
205C4⋊C8—42no—
206#97—224no—
207#95—221no—
208#95—221no—
209#95—221no—
210C2×C11#147311yescharacteristic
211C2×C11#148311yescharacteristic
212C2×C11#149611yescharacteristic
213C2×C11#150511yescharacteristic
214C2×C11#151211yescharacteristic
215C2×C11#152911yescharacteristic
216C2×C11#155711yescharacteristic
217D11—161no—
218C24—221no—
219C2×D4—222no—
220C2×D4—441no—
221C2×D4—441no—
222C22×C4—221no—
223C22×C4—221no—
224C22×C4—221no—
225C22×C4(C2×D11)⋊C411yescharacteristic
226C22×C4(C2×D11)⋊C411yescharacteristic
227C22×C4(C2×D11)⋊C411yescharacteristic
228C22×C4(C2×D11)⋊C411yescharacteristic
229C22×C4C2×C4×D1111yescharacteristic
230C22×C4C2×D4411yescharacteristic
231C22×C4C2×C22⋊D1111yescharacteristic
232C2×C8—42no—
233C2×C8—42no—
234C2×C8—42no—
235C2×C8—224no—
236C2×C8—442no—
237C2×C8—442no—
238C4⋊C4—222no—
239C4⋊C4—441no—
240C4⋊C4—441no—
241C4⋊C4—442no—
242C4⋊C4—442no—
243C4⋊C4—442no—
244C22⋊C4—442no—
245C22⋊C4—442no—
246C22⋊C4—442no—
247C22⋊C4—442no—
248C22⋊C4—442no—
249C22⋊C4—441no—
250C22⋊C4—441no—
251C42—22no—
252C42—22no—
253C42—22no—
254C42—21no—
255C42—21no—
256C42—41no—
257C42—41no—
258C42—41no—
259C11#770611yescharacteristic, complemented, Sylow
260C23—441no—
261C23—441no—
262C23—441no—
263C23—441no—
264C23—441no—
265C23—441no—
266C23—441no—
267C23C2×(C2×D11)⋊C411yescharacteristic
268D4—882no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
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—441no—
287C2×C4—441no—
288C2×C4—441no—
289C2×C4—441no—
290C2×C4—441no—
291C2×C4—441no—
292C2×C4—441no—
293C2×C4—441no—
294C2×C4—441no—
295C2×C4#6688912yes—
296C2×C4#6695412yes—
297C2×C4#6696112yes—
298C2×C4#6698511yescharacteristic
299C2×C4#6699511yescharacteristic
300C8—82no—
301C8—444no—
302C22—881no—
303C22—881no—
304C22—881no—
305C22—881no—
306C22—881no—
307C22—881no—
308C22—881no—
309C22#1062257911yescharacteristic
310C22#1062261811yescharacteristic
311C22#1062261911yescharacteristic
312C22#1062272311yescharacteristic
313C22#1062274411yescharacteristic
314C22#1062274511yescharacteristic
315C22C2×#6688911yescharacteristic
316C4—22no—
317C4—22no—
318C4—21no—
319C4—21no—
320C4—22no—
321C4—41no—
322C4—41no—
323C4—41no—
324C4—881no—
325C4—881no—
326C4—881no—
327C2—1761no—
328C2#1306698311yescharacteristic
329C2#1306702711yescharacteristic
330C2#1306708611yescharacteristic
331C2#1306712511yescharacteristic
332C2#1306715211yescharacteristic
333C2#1306722411yescharacteristic
334C2#1306733611yescharacteristic
subgroupG/H
centerC23C2×(C2×D11)⋊C4
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1831C2
socleC23×C11C2×C22⋊C4
prime radicalC22×D44C2×C4
cosocleC2×C42×C11C23
hypercenter#1831D11
hypocenterC11#7706
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C43 ◁ #1831

Complements

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

NH ≅ G/Ntype
2. #13068365C2semidirect
3. #13066438C2semidirect
5. C11×#1831C2semidirect
94. #1831D11semidirect
259. C11#7706semidirect

Maximal subgroups

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

subgroupindex
#130769832
#130683652
#130664382
#130664362
C11×#18312
#770611