Finite Group Databasebeta

← #14642343

Subgroups — #14642343

Order 2816.

426 conjugacy classes of subgroups.

The subgroup lattice has 336 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13068733C211yesmaximal, characteristic, complemented
2#13068365C211yesmaximal, characteristic, complemented
3#13066439C212yesmaximal, complemented
4#13066437C212yesmaximal
5C11×#2860C211yesmaximal, characteristic
6C2×C11×#126—21no—
7C11×#390C411yescharacteristic
8C11×#390C411yescharacteristic
9C11×#390C2211yescharacteristic
10C11×#389C411yescharacteristic
11C11×#389C411yescharacteristic
12C11×#389C2211yescharacteristic
13C11×#388—21no—
14C11×#388—21no—
15C11×#388—21no—
16C43×C11C2211yescharacteristic
17C2×C4⋊(C11⋊C8)—21no—
18C2×#66867—21no—
19#10622162—21no—
20#10622162—21no—
21#10622162C2212yes—
22#10622162C2212yes—
23C22×D4×C11C2×C411yescharacteristic
24C11×#126—44no—
25C2×C11×C4⋊C4—21no—
26C2×C11×C4⋊C4—21no—
27C2×C11×C4⋊C4—21no—
28C2×C11×C4⋊C4C2×C411yescharacteristic
29C2×C11×C4⋊C4C2×C411yescharacteristic
30C2×C11×C4⋊C4C2×C411yescharacteristic
31C2×C11×C22⋊C4—21no—
32C2×C11×C22⋊C4—21no—
33C2×C11×C22⋊C4—21no—
34C2×C11×C22⋊C4—21no—
35C2×C11×C22⋊C4—21no—
36C2×C11×C22⋊C4—21no—
37C2×C42×C11C2×C411yescharacteristic
38C2×C42×C11C2×C411yescharacteristic
39C2×C42×C11D411yescharacteristic
40C2×C42×C11D411yescharacteristic
41C2×C42×C11D411yescharacteristic
42C2×C42×C11D411yescharacteristic
43C2×C42×C11C2311yescharacteristic
44C22×C11⋊C8—22no—
45C22×C11⋊C8—22no—
46C11×#95—21no—
47C11×#95—21no—
48C11×#95—21no—
49C4⋊(C11⋊C8)—42no—
50#66867—24no—
51#7706—111nomaximal, Sylow
52C24×C11—21no—
53C2×D4×C11—22no—
54C2×D4×C11—41no—
55C2×D4×C11—41no—
56C22×C4×C11—21no—
57C22×C4×C11—21no—
58C22×C4×C11—21no—
59C22×C4×C11C22⋊C411yescharacteristic
60C22×C4×C11C22⋊C411yescharacteristic
61C22×C4×C11C22⋊C411yescharacteristic
62C22×C4×C11C22⋊C411yescharacteristic
63C22×C4×C11C22×C411yescharacteristic
64C22×C4×C11C2×D411yescharacteristic
65C22×C4×C11C2×D411yescharacteristic
66C11×C4⋊C4—22no—
67C11×C4⋊C4—42no—
68C11×C4⋊C4—42no—
69C11×C4⋊C4—41no—
70C11×C4⋊C4—41no—
71C11×C4⋊C4—42no—
72C11×C22⋊C4—42no—
73C11×C22⋊C4—42no—
74C11×C22⋊C4—42no—
75C11×C22⋊C4—42no—
76C11×C22⋊C4—41no—
77C11×C22⋊C4—42no—
78C11×C22⋊C4—41no—
79C42×C11—22no—
80C42×C11—22no—
81C42×C11—21no—
82C42×C11—22no—
83C42×C11—21no—
84C42×C11—41no—
85C42×C11—41no—
86C42×C11—41no—
87C2×C11⋊C8—24no—
88C2×C11⋊C8—42no—
89C2×C11⋊C8—42no—
90C2×C11⋊C8—42no—
91C2×C11⋊C8—42no—
92C2×C11⋊C8—42no—
93#2860D1111yescharacteristic
94#1831—111no—
95#1745—111no—
96#1271—112no—
97#1270—112no—
98C23×C11—41no—
99C23×C11—41no—
100C23×C11—41no—
101C23×C11—41no—
102C23×C11—41no—
103C23×C11—41no—
104C23×C11—41no—
105C23×C11C2×C22⋊C411yescharacteristic
106D4×C11—82no—
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—21no—
124C2×C4×C11—41no—
125C2×C4×C11—41no—
126C2×C4×C11—41no—
127C2×C4×C11—41no—
128C2×C4×C11—41no—
129C2×C4×C11—41no—
130C2×C4×C11—41no—
131C2×C4×C11—41no—
132C2×C4×C11—41no—
133C2×C4×C11#10412yes—
134C2×C4×C11#13112yes—
135C2×C4×C11AGL(1,ℤ/8)12yes—
136C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
137C2×C4×C11#13711yescharacteristic
138C11⋊C8—44no—
139C11⋊C8—82no—
140C2×#126—21no—
141C2×C4⋊C8—221no—
142C2×#97—221no—
143#390Dic1111yescharacteristic
144#390Dic1111yescharacteristic
145#390C2×D1111yescharacteristic
146#389Dic1111yescharacteristic
147#389Dic1111yescharacteristic
148#389C2×D1111yescharacteristic
149#388—21no—
150#388—21no—
151#388—21no—
152C43C2×D1111yescharacteristic
153#336—112no—
154#336—112no—
155#336—221no—
156#336—221no—
157C22×C11—81no—
158C22×C11—81no—
159C22×C11—81no—
160C22×C11—81no—
161C22×C11—81no—
162C22×C11—81no—
163C22×C11—81no—
164C22×C11#40811yescharacteristic
165C22×C11#41011yescharacteristic
166C22×C11#41311yescharacteristic
167C22×C11#41711yescharacteristic
168C22×C11#41811yescharacteristic
169C22×C11C2×#10411yescharacteristic
170C22×C11#42111yescharacteristic
171C4×C11—22no—
172C4×C11—22no—
173C4×C11—22no—
174C4×C11—21no—
175C4×C11—21no—
176C4×C11—41no—
177C4×C11—41no—
178C4×C11—41no—
179C4×C11—81no—
180C4×C11—81no—
181C4×C11—81no—
182C22×D4C2×Dic1111yescharacteristic
183C22×C8—222no—
184C22×C8—222no—
185#126—44no—
186C2×C4⋊C4—21no—
187C2×C4⋊C4—21no—
188C2×C4⋊C4—21no—
189C2×C4⋊C4C2×Dic1111yescharacteristic
190C2×C4⋊C4C2×Dic1111yescharacteristic
191C2×C4⋊C4C2×Dic1111yescharacteristic
192C2×C22⋊C4—21no—
193C2×C22⋊C4—21no—
194C2×C22⋊C4—21no—
195C2×C22⋊C4—21no—
196C2×C22⋊C4—21no—
197C2×C22⋊C4—21no—
198C2×C42C2×Dic1111yescharacteristic
199C2×C42C2×Dic1111yescharacteristic
200C2×C42C22⋊D1111yescharacteristic
201C2×C42C22⋊D1111yescharacteristic
202C2×C42C22⋊D1111yescharacteristic
203C2×C42C22⋊D1111yescharacteristic
204C2×C42C22×D1111yescharacteristic
205C4⋊C8—442no—
206#97—224no—
207#95—21no—
208#95—21no—
209#95—21no—
210C2×C11—161no—
211C2×C11#147311yescharacteristic
212C2×C11#148311yescharacteristic
213C2×C11#149611yescharacteristic
214C2×C11#150511yescharacteristic
215C2×C11#151211yescharacteristic
216C2×C11#152911yescharacteristic
217C2×C11#155711yescharacteristic
218C24—21no—
219C2×D4—22no—
220C2×D4—41no—
221C2×D4—41no—
222C22×C4—21no—
223C22×C4—21no—
224C22×C4—21no—
225C22×C4C22⋊Dic1111yescharacteristic
226C22×C4C22⋊Dic1111yescharacteristic
227C22×C4C22⋊Dic1111yescharacteristic
228C22×C4C22⋊Dic1111yescharacteristic
229C22×C4C22×Dic1111yescharacteristic
230C22×C4C2×C22⋊D1111yescharacteristic
231C22×C4C2×C22⋊D1111yescharacteristic
232C2×C8—224no—
233C2×C8—442no—
234C2×C8—442no—
235C2×C8—442no—
236C2×C8—442no—
237C2×C8—442no—
238C4⋊C4—22no—
239C4⋊C4—41no—
240C4⋊C4—41no—
241C4⋊C4—42no—
242C4⋊C4—42no—
243C4⋊C4—42no—
244C22⋊C4—42no—
245C22⋊C4—42no—
246C22⋊C4—42no—
247C22⋊C4—42no—
248C22⋊C4—42no—
249C22⋊C4—41no—
250C22⋊C4—41no—
251C42—22no—
252C42—22no—
253C42—22no—
254C42—21no—
255C42—21no—
256C42—41no—
257C42—41no—
258C42—41no—
259C11#770611yescharacteristic, complemented, Sylow
260C23—41no—
261C23—41no—
262C23—41no—
263C23—41no—
264C23—41no—
265C23—41no—
266C23—41no—
267C23C2×C22⋊Dic1111yescharacteristic
268D4—82no—
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—41no—
287C2×C4—41no—
288C2×C4—41no—
289C2×C4—41no—
290C2×C4—41no—
291C2×C4—41no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4#6690112yes—
296C2×C4#6698512yes—
297C2×C4#6700112yes—
298C2×C4#6700211yescharacteristic
299C2×C4#6700411yescharacteristic
300C8—444no—
301C8—882no—
302C22—81no—
303C22—81no—
304C22—81no—
305C22—81no—
306C22—81no—
307C22—81no—
308C22—81no—
309C22#1062282811yescharacteristic
310C22#1062284511yescharacteristic
311C22#1062284711yescharacteristic
312C22C2×#6690111yescharacteristic
313C22#1062284911yescharacteristic
314C22#1062285011yescharacteristic
315C22#1062285311yescharacteristic
316C4—22no—
317C4—22no—
318C4—21no—
319C4—21no—
320C4—22no—
321C4—41no—
322C4—41no—
323C4—41no—
324C4—81no—
325C4—81no—
326C4—81no—
327C2—161no—
328C2#1306698511yescharacteristic
329C2#1306702911yescharacteristic
330C2#1306708511yescharacteristic
331C2#1306712411yescharacteristic
332C2#1306715411yescharacteristic
333C2#1306722311yescharacteristic
334C2#1306733811yescharacteristic
subgroupG/H
centerC23C2×C22⋊Dic11
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#2860C2
socleC23×C11C2×C22⋊C4
prime radicalC22×D4×C11C2×C4
cosocleC2×C42×C11C23
hypercenter#2860D11
hypocenterC11#7706
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C43 ◁ #2860

Complements

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

NH ≅ G/Ntype
1. #13068733C2semidirect
2. #13068365C2semidirect
3. #13066439C2semidirect
259. C11#7706semidirect

Maximal subgroups

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

subgroupindex
#130687332
#130683652
#130664392
#130664372
C11×#28602
#770611