Finite Group Databasebeta

← #14653554

Subgroups — #14653554

Order 2816.

578 conjugacy classes of subgroups.

The subgroup lattice has 354 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13069578C211yesmaximal, characteristic, complemented
2#13069423C211yesmaximal, characteristic
3#13069423C211yesmaximal, characteristic
4#13069419C211yesmaximal, characteristic, complemented
5#13068773C211yesmaximal, characteristic, complemented
6C2×#10622092C211yesmaximal, characteristic, complemented
7C2×C11×#486C211yesmaximal, characteristic
8C2×C11×C4⋊Q8C2211yescharacteristic
9C2×C11×#127C2211yescharacteristic
10C11×#486—22no—
11C11×#486C414yescomplemented
12C2×C11×#102—22no—
13C2×C4×C8×C11C2211yescharacteristic
14C2×#66899—22no—
15C2×#66896—22no—
16C2×#66896—22no—
17C2×#66881—22no—
18#10622548C2211yescharacteristic
19#10622548C2211yescharacteristic
20C2×C4×C11⋊C8C2211yescharacteristic
21C2×C4×C11⋊C8C2211yescharacteristic
22#10622167—22no—
23#10622092—22no—
24C22×Q8×C11—21no—
25C22×D4×C11—21no—
26C22×D4×C11—21no—
27C22×D4×C11—21no—
28C22×C8×C11D412yes—
29C11×C4⋊Q8—21no—
30C11×C4⋊Q8—21no—
31C11×C4⋊Q8—21no—
32C11×C4⋊Q8C2×C412yes—
33C11×#127—21no—
34C11×#127—21no—
35C11×#127—21no—
36C11×#127C2×C412yes—
37C2×C11×C4⋊C4—21no—
38C2×C11×C4⋊C4—21no—
39C2×C42×C11C2311yescharacteristic
40C2×C4⋊Dic11—21no—
41C2×C4⋊Dic11—21no—
42C2×C4⋊Dic11—21no—
43C2×C4⋊Dic11—21no—
44C2×C4⋊Dic11—21no—
45C2×C4⋊Dic11—21no—
46C22×C11⋊C8D412yes—
47C22×C11⋊C8D412yes—
48C11×#102—28no—
49C4×C8×C11C2×C412yes—
50C4×C8×C11D412yes—
51#66899—44no—
52#66896—44no—
53#66896—44no—
54#66881—44no—
55C4×C11⋊C8—21no—
56C4×C11⋊C8—21no—
57C4×C11⋊C8—21no—
58C4×C11⋊C8—21no—
59#9827—111nomaximal, Sylow
60C24×C11—41no—
61C2×Q8×C11—22no—
62C2×Q8×C11—41no—
63C2×Q8×C11—42no—
64C2×Q8×C11—42no—
65C2×D4×C11—22no—
66C2×D4×C11—22no—
67C2×D4×C11—22no—
68C2×D4×C11—41no—
69C2×D4×C11—41no—
70C2×D4×C11—41no—
71C2×D4×C11—42no—
72C2×D4×C11—42no—
73C2×D4×C11—42no—
74C2×D4×C11—42no—
75C2×D4×C11—42no—
76C2×D4×C11—42no—
77C22×C4×C11—41no—
78C22×C4×C11C2×D411yescharacteristic
79C22×C4×C11C2×D411yescharacteristic
80C22×C4×C11C2×D411yescharacteristic
81C22×Dic11—41no—
82C22×Dic11—41no—
83C2×C8×C11—22no—
84C2×C8×C11—22no—
85C2×C8×C11C22⋊C414yes—
86C11×C4⋊C4—22no—
87C11×C4⋊C4—22no—
88C11×C4⋊C4—41no—
89C11×C4⋊C4—41no—
90C42×C11C22×C411yescharacteristic
91C42×C11C2×D411yescharacteristic
92C42×C11#4111yescharacteristic
93C42×C11#4111yescharacteristic
94C4⋊Dic11—42no—
95C4⋊Dic11—42no—
96C4⋊Dic11—42no—
97C4⋊Dic11—42no—
98C4⋊Dic11—42no—
99C4⋊Dic11—42no—
100C2×C11⋊C8—22no—
101C2×C11⋊C8—22no—
102C2×C11⋊C8—22no—
103C2×C11⋊C8—22no—
104C2×C11⋊C8—22no—
105C2×C11⋊C8SD1614yes—
106C2×#486D1111yescharacteristic
107#1990—111no—
108#1957—111no—
109#1957—111no—
110#1956—111no—
111#1844—111no—
112C2×#322—111no—
113C23×C11—42no—
114C23×C11—81no—
115C23×C11—81no—
116C23×C11—81no—
117C23×C11—81no—
118C23×C11—81no—
119C23×C11—81no—
120C23×C11#12711yescharacteristic
121Q8×C11—44no—
122Q8×C11—82no—
123D4×C11—44no—
124D4×C11—44no—
125D4×C11—44no—
126D4×C11—82no—
127D4×C11—82no—
128D4×C11—82no—
129C2×C4×C11—42no—
130C2×C4×C11—81no—
131C2×C4×C11—81no—
132C2×C4×C11C2×C22⋊C411yescharacteristic
133C2×C4×C11C4×D411yescharacteristic
134C2×C4×C11C4×D411yescharacteristic
135C2×C4×C11#12111yescharacteristic
136C2×C4×C11#12111yescharacteristic
137C2×C4×C11#12411yescharacteristic
138C2×C4×C11C2×SD1612yes—
139C2×C4×C11#13512yes—
140C2×C4×C11AGL(1,ℤ/8)12yes—
141C2×C4×C11AGL(1,ℤ/8)12yes—
142C2×C4×C11AGL(1,ℤ/8)12yes—
143C2×C4×C11#13712yes—
144C2×Dic11—81no—
145C2×Dic11—81no—
146C2×Dic11—81no—
147C2×Dic11—81no—
148C2×Dic11—81no—
149C2×Dic11—81no—
150C8×C11—24no—
151C11⋊C8—24no—
152C11⋊C8—42no—
153C2×C4⋊Q8C2×D1111yescharacteristic
154C2×#127C2×D1111yescharacteristic
155#486—22no—
156#486Dic1114yescomplemented
157C2×#106—222no—
158C2×#103—222no—
159C2×#102—22no—
160C2×#102—222no—
161C2×#102—222no—
162C2×C4×C8—111no—
163C2×C4×C8—111no—
164C2×C4×C8C2×D1111yescharacteristic
165#384—111no—
166#384—111no—
167#340—222no—
168#322—222no—
169C22×C11—82no—
170C22×C11—82no—
171C22×C11—82no—
172C22×C11—161no—
173C22×C11—161no—
174C22×C11—161no—
175C22×C11—161no—
176C22×C11#39011yescharacteristic
177C22×C11#49211yescharacteristic
178C22×C11#49511yescharacteristic
179C22×C11#49611yescharacteristic
180C22×C11#49611yescharacteristic
181C22×C11#49611yescharacteristic
182C22×C11#49711yescharacteristic
183C4×C11—82no—
184C4×C11#41712yes—
185C4×C11C4×SD1612yes—
186C4×C11#44212yes—
187C4×C11#46512yes—
188C4×C11#46912yes—
189C4×C11#48912yes—
190Dic11—161no—
191Dic11—161no—
192C22×Q8—21no—
193C22×D4—21no—
194C22×D4—21no—
195C22×D4—21no—
196C22×C8—112no—
197C22×C8—112no—
198C22×C8C22⋊D1112yes—
199C4⋊Q8—21no—
200C4⋊Q8—21no—
201C4⋊Q8—21no—
202C4⋊Q8C2×Dic1112yes—
203#127—21no—
204#127—21no—
205#127—21no—
206#127C2×Dic1112yes—
207C2×C4⋊C4—21no—
208C2×C4⋊C4—21no—
209C2×C4⋊C4—221no—
210C2×C4⋊C4—221no—
211C2×C4⋊C4—221no—
212C2×C4⋊C4—221no—
213C2×C4⋊C4—221no—
214C2×C4⋊C4—221no—
215C2×C42C22×D1111yescharacteristic
216#106—444no—
217#103—444no—
218#102—28no—
219#102—444no—
220#102—444no—
221C4×C8—221no—
222C4×C8—221no—
223C4×C8—221no—
224C4×C8—221no—
225C4×C8C2×Dic1112yes—
226C4×C8C22⋊D1112yes—
227C2×C11—162no—
228C2×C11#171411yescharacteristic
229C2×C11#171511yescharacteristic
230C2×C11#171711yescharacteristic
231C2×C11#172011yescharacteristic
232C2×C11#195911yescharacteristic
233C2×C11#196811yescharacteristic
234C2×C11#197211yescharacteristic
235C24—41no—
236C2×Q8—22no—
237C2×Q8—41no—
238C2×Q8—42no—
239C2×Q8—42no—
240C2×D4—22no—
241C2×D4—22no—
242C2×D4—22no—
243C2×D4—42no—
244C2×D4—42no—
245C2×D4—42no—
246C2×D4—42no—
247C2×D4—41no—
248C2×D4—41no—
249C2×D4—41no—
250C2×D4—42no—
251C2×D4—42no—
252C22×C4—41no—
253C22×C4—441no—
254C22×C4—441no—
255C22×C4D4×D1111yescharacteristic
256C22×C4D4×D1111yescharacteristic
257C22×C4C2×C22⋊D1111yescharacteristic
258C2×C8—22no—
259C2×C8—22no—
260C2×C8—114no—
261C2×C8—222no—
262C2×C8—222no—
263C2×C8—222no—
264C2×C8—222no—
265C2×C8—222no—
266C2×C8C22⋊Dic1114yes—
267C4⋊C4—22no—
268C4⋊C4—22no—
269C4⋊C4—41no—
270C4⋊C4—41no—
271C4⋊C4—442no—
272C4⋊C4—442no—
273C4⋊C4—442no—
274C4⋊C4—442no—
275C4⋊C4—442no—
276C4⋊C4—442no—
277C42#434111yescharacteristic
278C42#434111yescharacteristic
279C42C22×Dic1111yescharacteristic
280C42C2×C22⋊D1111yescharacteristic
281C11#982711yescharacteristic, complemented, Sylow
282C23—42no—
283C23—81no—
284C23—81no—
285C23—81no—
286C23—81no—
287C23—81no—
288C23—81no—
289C23#6699311yescharacteristic
290Q8—44no—
291Q8—82no—
292D4—44no—
293D4—44no—
294D4—44no—
295D4—82no—
296D4—82no—
297D4—82no—
298C2×C4—42no—
299C2×C4—81no—
300C2×C4—81no—
301C2×C4—881no—
302C2×C4—881no—
303C2×C4—881no—
304C2×C4—881no—
305C2×C4—881no—
306C2×C4—881no—
307C2×C4#6696412yes—
308C2×C4#6696412yes—
309C2×C4SD16×D1112yes—
310C2×C4#6696912yes—
311C2×C4D4×Dic1111yescharacteristic
312C2×C4D4×Dic1111yescharacteristic
313C2×C4#6698911yescharacteristic
314C2×C4#6699111yescharacteristic
315C2×C4#6699111yescharacteristic
316C2×C4#6700212yes—
317C2×C4#6700412yes—
318C2×C4C2×C22⋊Dic1111yescharacteristic
319C8—24no—
320C8—224no—
321C8—442no—
322C22—82no—
323C22—82no—
324C22—82no—
325C22—161no—
326C22—161no—
327C22—161no—
328C22—161no—
329C22#1062267111yescharacteristic
330C22#1062267311yescharacteristic
331C22#1062276711yescharacteristic
332C22#1062276711yescharacteristic
333C22#1062278111yescharacteristic
334C22#1062278811yescharacteristic
335C22#1062283411yescharacteristic
336C4—82no—
337C4—1761no—
338C4—1761no—
339C4#1062266812yes—
340C4#1062276512yes—
341C4#1062277212yes—
342C4SD16×Dic1112yes—
343C4#1062278412yes—
344C4#1062284512yes—
345C2—162no—
346C2#1306823711yescharacteristic
347C2#1306824611yescharacteristic
348C2#1306825711yescharacteristic
349C2#1306827811yescharacteristic
350C2#1306943311yescharacteristic
351C2#1306947211yescharacteristic
352C2#1306949311yescharacteristic
subgroupG/H
centerC23#66993
commutatorC42×C11C22×C4
FrattiniC2×C42C22×D11
FittingC2×C11×#486C2
socleC23×C11#127
prime radicalC2×C11×#127C22
cosocleC2×C42×C11C23
hypercenterC2×#486D11
hypocenterC11#9827
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#486

Complements

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

NH ≅ G/Ntype
1. #13069578C2semidirect
4. #13069419C2semidirect
5. #13068773C2semidirect
6. C2×#10622092C2semidirect
11. C11×#486C4semidirect
156. #486Dic11semidirect
281. C11#9827semidirect

Maximal subgroups

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

subgroupindex
#130695782
#130694232
#130694192
#130687732
C2×#106220922
C2×C11×#4862
#982711