Finite Group Databasebeta

← #14647155

Subgroups — #14647155

Order 2816.

544 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13068684C211yesmaximal, characteristic
2#13066843C211yesmaximal, characteristic
3#13066494C212yesmaximal
4#13066494C212yesmaximal
5C11×#2283C211yesmaximal, characteristic
6C22×C42×C11C2211yescharacteristic
7C11×#383—21no—
8C11×#382C411yescharacteristic, complemented
9C11×#382C411yescharacteristic, complemented
10C11×#381—21no—
11C11×#380C2211yescharacteristic
12C11×#380C2211yescharacteristic
13C4×C11×C4⋊C4C411yescharacteristic, complemented
14C4×C11×C4⋊C4C411yescharacteristic, complemented
15C4×C11×C22⋊C4—21no—
16C11×#376—21no—
17C2×C11⋊#95—21no—
18C2×C11⋊#95—21no—
19C2×C11⋊#95C2212yes—
20C2×C22⋊(C11⋊C8)C2212yes—
21#10622162—21no—
22#10622162—21no—
23C23×C4×C11D411yescharacteristic
24C23×C4×C11D411yescharacteristic
25C23×C4×C11C2311yescharacteristic
26C23×Dic11—22no—
27C2×C11×C4⋊C4C2×C411yescharacteristic
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×C42×C11—24no—
34C2×C42×C11—21no—
35C2×C42×C11—21no—
36C2×C42×C11C2×C411yescharacteristic
37C2×C42×C11C2×C411yescharacteristic
38C2×C42×C11D411yescharacteristic
39C2×C42×C11D411yescharacteristic
40C22×C11⋊C8—22no—
41C11×#95—21no—
42C11×#95—21no—
43C11×#95—21no—
44C11×#95—21no—
45C11×#95—21no—
46C11×#95—21no—
47C11×#95—21no—
48C11×#95—21no—
49C11⋊#95—24no—
50C11⋊#95—24no—
51C11⋊#95—42no—
52C22⋊(C11⋊C8)—24no—
53#8714—111nomaximal, Sylow
54C24×C11C2×D411yescharacteristic
55C22×C4×C11—22no—
56C22×C4×C11—22no—
57C22×C4×C11—22no—
58C22×C4×C11—21no—
59C22×C4×C11—21no—
60C22×C4×C11—22no—
61C22×C4×C11—21no—
62C22×C4×C11—21no—
63C22×C4×C11—21no—
64C22×C4×C11—21no—
65C22×C4×C11—41no—
66C22×C4×C11—41no—
67C22×C4×C11—41no—
68C22×C4×C11C22⋊C411yescharacteristic
69C22×C4×C11C22⋊C411yescharacteristic
70C22×C4×C11C22⋊C411yescharacteristic
71C22×C4×C11C22⋊C411yescharacteristic
72C22×C4×C11C22×C411yescharacteristic
73C22×C4×C11C2×D411yescharacteristic
74C22×C4×C11#4114yes—
75C22×Dic11—24no—
76C22×Dic11—42no—
77C22×Dic11—42no—
78C22×Dic11—42no—
79C22×Dic11—42no—
80C22×Dic11—42no—
81C22×Dic11—42no—
82C11×C4⋊C4—41no—
83C11×C4⋊C4—41no—
84C11×C4⋊C4—41no—
85C11×C4⋊C4—41no—
86C11×C22⋊C4—42no—
87C11×C22⋊C4—41no—
88C11×C22⋊C4—41no—
89C42×C11—22no—
90C42×C11—22no—
91C42×C11—22no—
92C42×C11—22no—
93C42×C11—42no—
94C42×C11—42no—
95C2×C11⋊C8—42no—
96C2×C11⋊C8—42no—
97C2×C11⋊C8—42no—
98#2283D1111yescharacteristic
99#1817—111no—
100#1434—111no—
101#1294—112no—
102#1294—112no—
103C23×C11—21no—
104C23×C11—21no—
105C23×C11—21no—
106C23×C11—21no—
107C23×C11C2×C22⋊C411yescharacteristic
108C23×C11#12312yes—
109C23×C11#13512yes—
110C23×C11AGL(1,ℤ/8)11yescharacteristic
111C23×C11#13711yescharacteristic
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—21no—
125C2×C4×C11—21no—
126C2×C4×C11—21no—
127C2×C4×C11—44no—
128C2×C4×C11—44no—
129C2×C4×C11—42no—
130C2×C4×C11—42no—
131C2×C4×C11—41no—
132C2×C4×C11—41no—
133C2×C4×C11—41no—
134C2×C4×C11—41no—
135C2×C4×C11—41no—
136C2×C4×C11—41no—
137C2×C4×C11—41no—
138C2×C4×C11—41no—
139C2×C4×C11—41no—
140C2×C4×C11—41no—
141C2×C4×C11—41no—
142C2×C4×C11—41no—
143C2×C4×C11#10412yes—
144C2×C4×C11#11712yes—
145C2×C4×C11#12312yes—
146C2×Dic11—44no—
147C2×Dic11—44no—
148C2×Dic11—44no—
149C2×Dic11—82no—
150C2×Dic11—82no—
151C2×Dic11—82no—
152C2×Dic11—82no—
153C11⋊C8—82no—
154C22×C42C2×D1111yescharacteristic
155C2×C22⋊C8—112no—
156#383—21no—
157#382Dic1111yescharacteristic, complemented
158#382Dic1111yescharacteristic, complemented
159#381—21no—
160#380C2×D1111yescharacteristic
161#380C2×D1111yescharacteristic
162C4×C4⋊C4Dic1111yescharacteristic, complemented
163C4×C4⋊C4Dic1111yescharacteristic, complemented
164C4×C22⋊C4—21no—
165#376—21no—
166C2×#95—112no—
167C2×#95—221no—
168C2×#95—221no—
169#336—221no—
170#336—221no—
171C22×C11—22no—
172C22×C11—22no—
173C22×C11—22no—
174C22×C11—21no—
175C22×C11—21no—
176C22×C11—21no—
177C22×C11—21no—
178C22×C11—22no—
179C22×C11#38111yescharacteristic
180C22×C11#41011yescharacteristic
181C22×C11#41011yescharacteristic
182C22×C11#41611yescharacteristic
183C22×C11#41711yescharacteristic
184C22×C11C2×#10411yescharacteristic
185C22×C11#42111yescharacteristic
186C22×C11#48212yes—
187C22×C11#48512yes—
188C4×C11—22no—
189C4×C11—22no—
190C4×C11—22no—
191C4×C11—41no—
192C4×C11—41no—
193C4×C11—41no—
194C4×C11—81no—
195C4×C11—81no—
196C4×C11—81no—
197C4×C11—81no—
198Dic11—84no—
199C23×C4—222no—
200C23×C4C22⋊D1111yescharacteristic
201C23×C4C22⋊D1111yescharacteristic
202C23×C4C22×D1111yescharacteristic
203C22×C8—222no—
204C2×C4⋊C4C2×Dic1111yescharacteristic
205C2×C4⋊C4C2×Dic1111yescharacteristic
206C2×C4⋊C4C2×Dic1111yescharacteristic
207C2×C4⋊C4C2×Dic1111yescharacteristic
208C2×C22⋊C4—21no—
209C2×C22⋊C4—21no—
210C2×C42—24no—
211C2×C42—21no—
212C2×C42—21no—
213C2×C42C2×Dic1111yescharacteristic
214C2×C42C2×Dic1111yescharacteristic
215C2×C42C22⋊D1111yescharacteristic
216C2×C42C22⋊D1111yescharacteristic
217C22⋊C8—224no—
218#95—21no—
219#95—21no—
220#95—21no—
221#95—21no—
222#95—21no—
223#95—21no—
224#95—21no—
225#95—21no—
226#95—224no—
227#95—224no—
228#95—442no—
229C2×C11—22no—
230C2×C11—22no—
231C2×C11#150011yescharacteristic
232C2×C11#150911yescharacteristic
233C2×C11#151211yescharacteristic
234C2×C11#152111yescharacteristic
235C2×C11#182011yescharacteristic
236C2×C11#182511yescharacteristic
237C2×C11#182611yescharacteristic
238C24C2×C22⋊D1111yescharacteristic
239C22×C4—22no—
240C22×C4—22no—
241C22×C4—21no—
242C22×C4—22no—
243C22×C4—21no—
244C22×C4—22no—
245C22×C4—21no—
246C22×C4—21no—
247C22×C4—21no—
248C22×C4—21no—
249C22×C4—41no—
250C22×C4—41no—
251C22×C4—41no—
252C22×C4—224no—
253C22×C4—442no—
254C22×C4—442no—
255C22×C4—442no—
256C22×C4—442no—
257C22×C4—442no—
258C22×C4—442no—
259C22×C4C22⋊Dic1111yescharacteristic
260C22×C4C22⋊Dic1111yescharacteristic
261C22×C4C22⋊Dic1111yescharacteristic
262C22×C4C22⋊Dic1111yescharacteristic
263C22×C4#433914yes—
264C22×C4C22×Dic1111yescharacteristic
265C22×C4C2×C22⋊D1111yescharacteristic
266C2×C8—442no—
267C2×C8—442no—
268C2×C8—442no—
269C4⋊C4—41no—
270C4⋊C4—41no—
271C4⋊C4—41no—
272C4⋊C4—41no—
273C22⋊C4—41no—
274C22⋊C4—42no—
275C22⋊C4—41no—
276C42—22no—
277C42—22no—
278C42—22no—
279C42—22no—
280C42—42no—
281C42—42no—
282C11#871411yescharacteristic, complemented, Sylow
283C23—21no—
284C23—21no—
285C23—21no—
286C23—21no—
287C23#6698212yes—
288C23#6700211yescharacteristic
289C23#6700312yes—
290C23#6700411yescharacteristic
291C23C2×C22⋊Dic1111yescharacteristic
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—44no—
308C2×C4—44no—
309C2×C4—42no—
310C2×C4—42no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—41no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—41no—
320C2×C4—41no—
321C2×C4—41no—
322C2×C4—41no—
323C2×C4—444no—
324C2×C4—444no—
325C2×C4—444no—
326C2×C4—882no—
327C2×C4—882no—
328C2×C4—882no—
329C2×C4—882no—
330C2×C4#6690112yes—
331C2×C4#6697912yes—
332C2×C4#6698212yes—
333C8—882no—
334C22—22no—
335C22—21no—
336C22—21no—
337C22—21no—
338C22—21no—
339C22—22no—
340C22—22no—
341C22—22no—
342C22#1062260912yes—
343C22#1062261612yes—
344C22#1062282411yescharacteristic
345C22#1062284511yescharacteristic
346C22#1062284611yescharacteristic
347C22C2×#6690111yescharacteristic
348C22#1062284911yescharacteristic
349C22#1062285311yescharacteristic
350C22#1062285311yescharacteristic
351C4—22no—
352C4—22no—
353C4—22no—
354C4—41no—
355C4—41no—
356C4—41no—
357C4—81no—
358C4—81no—
359C4—81no—
360C4—81no—
361C4—884no—
362C2—22no—
363C2—22no—
364C2#1306710211yescharacteristic
365C2#1306714111yescharacteristic
366C2#1306715411yescharacteristic
367C2#1306719311yescharacteristic
368C2#1306869311yescharacteristic
369C2#1306871111yescharacteristic
370C2#1306871511yescharacteristic
subgroupG/H
centerC23C2×C22⋊Dic11
commutatorC22×C4×C11C22×C4
FrattiniC23×C4C22×D11
FittingC11×#2283C2
socleC23×C11C2×C22⋊C4
prime radicalC24×C11C2×D4
cosocleC23×C4×C11C23
hypercenter#2283D11
hypocenterC11#8714
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C42 ◁ #2283

Complements

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

NH ≅ G/Ntype
8. C11×#382C4semidirect
9. C11×#382C4semidirect
13. C4×C11×C4⋊C4C4semidirect
14. C4×C11×C4⋊C4C4semidirect
157. #382Dic11semidirect
158. #382Dic11semidirect
162. C4×C4⋊C4Dic11semidirect
163. C4×C4⋊C4Dic11semidirect
282. C11#8714semidirect

Maximal subgroups

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

subgroupindex
#130686842
#130668432
#130664942
C11×#22832
#871411