Finite Group Databasebeta

← #14746016

Subgroups — #14746016

Order 2816.

584 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13081242C212yesmaximal, complemented
2#13081040C211yesmaximal, characteristic
3#13068233C211yesmaximal, characteristic, complemented
4#13068137C212yesmaximal, complemented
5#13068020C211yesmaximal, characteristic, complemented
6#13068012C211yesmaximal, characteristic, complemented
7#13067760C212yesmaximal, complemented
8#13067750C212yesmaximal, complemented
9#13067501C211yesmaximal, characteristic, complemented
10C8×#4325C211yesmaximal, characteristic, complemented
11C11×#3380C211yesmaximal, characteristic, complemented
12C11×#554C2212yes—
13#10623094C2212yes—
14C11×#500C2211yescharacteristic
15C11×#499—21no—
16C11×#478—22no—
17C11×#476C2212yes—
18C8×Q8×C11C2211yescharacteristic
19C4×C11×D8—21no—
20C4×C11×D8C2211yescharacteristic
21#10622770—21no—
22#10622705C2212yes—
23#10622697C2212yes—
24#10622691C2212yes—
25#10622662—22no—
26#10622658—22no—
27C4×#4325C2211yescharacteristic
28#10622634C2212yes—
29#10622625C2212yes—
30#10622621C2212yes—
31#10622580—22no—
32#10622577—22no—
33#10622493—21no—
34#10622397—22no—
35C8×D44C2211yescharacteristic
36#10622295C2211yescharacteristic
37#10622184C2212yes—
38Q8⋊(C11⋊C8)C2211yescharacteristic
39D4⋊(C11⋊C8)C2212yes—
40#10622121C2211yescharacteristic
41#10622119C2212yes—
42#10622118C2211yescharacteristic
43#10622096C2211yescharacteristic
44C8×C11⋊C8C2211yescharacteristic
45C2×C11×D8D411yescharacteristic
46C11×C4⋊Q8C2312yes—
47C11×#125—22no—
48C11×C22⋊Q8—22no—
49C11×C22⋊Q8—42no—
50C4×Q8×C11C2311yescharacteristic
51C4×D4×C11—22no—
52C4×D4×C11C2312yes—
53C2×C11×C4⋊C4—22no—
54C2×#4326—42no—
55C2×#4325D411yescharacteristic
56#66991—22no—
57#66983—22no—
58#66979—22no—
59C2×#4318—22no—
60C2×C8×D11—21no—
61#66945—22no—
62#66938—42no—
63C4×D44C2311yescharacteristic
64#66922C2312yes—
65C11×#107—21no—
66C11×#107—21no—
67C11×#107D411yescharacteristic
68C11×#106—22no—
69C11×C4⋊C8—21no—
70C11×C4⋊C8C2311yescharacteristic
71C11×#102—22no—
72C11×#102D412yes—
73C4×C8×C11—21no—
74C4×C8×C11C2311yescharacteristic
75#66899—22no—
76#66899D411yescharacteristic
77#66896—22no—
78C22⋊(C11⋊C8)—22no—
79(C2×D11)⋊C8—21no—
80#66882—21no—
81#66882—21no—
82#66873—22no—
83#66873D411yescharacteristic
84#66872—22no—
85#66872—22no—
86#66872D411yescharacteristic
87#66871—22no—
88#66871—22no—
89#66871—22no—
90C4⋊(C11⋊C8)C2311yescharacteristic
91C4⋊(C11⋊C8)C2312yes—
92C4×C11⋊C8C2311yescharacteristic
93C4×C11⋊C8C2311yescharacteristic
94#19957—111nomaximal, Sylow
95C2×Q8×C11—22no—
96C2×Q8×C11C2×D411yescharacteristic
97C2×D4×C11C2×D412yes—
98C22×C4×C11—22no—
99C22×C4×C11—42no—
100C2×C22⋊D11—42no—
101C2×D44C2×D411yescharacteristic
102C2×C4×D11—21no—
103C2×Dic22—22no—
104C11×D8—22no—
105C2×C8×C11—21no—
106C2×C8×C11C2×D411yescharacteristic
107C2×C8×C11C2×D411yescharacteristic
108C11×C4⋊C4—21no—
109C11×C4⋊C4—22no—
110C11×C4⋊C4—22no—
111C11×C4⋊C4—42no—
112C11×C4⋊C4—42no—
113C11×C4⋊C4C2×D411yescharacteristic
114C11×C4⋊C4C2×D412yes—
115C11×C22⋊C4—22no—
116C11×C22⋊C4—42no—
117C42×C11—21no—
118C42×C11C2411yescharacteristic
119C22⋊Dic11—42no—
120#4326—84no—
121#4325—22no—
122(C2×D11)⋊C4—21no—
123(C2×D11)⋊C4—42no—
124C4⋊Dic11—22no—
125C4⋊Dic11—22no—
126C4⋊Dic11C2×D411yescharacteristic
127C4×Dic11—42no—
128#4318—44no—
129C2×C11⋊C8—22no—
130C2×C11⋊C8—21no—
131C2×C11⋊C8—21no—
132C2×C11⋊C8C2×D411yescharacteristic
133C2×C11⋊C8C2×D411yescharacteristic
134C8×D11—42no—
135#3380D1111yescharacteristic, complemented
136#3357—112no—
137#3341—111no—
138#1713—111no—
139#1695—112no—
140#1676—111no—
141#1675—111no—
142#1634—112no—
143#1632—112no—
144#1589—111no—
145C8×SD16—111no—
146C23×C11—22no—
147C22×D11—21no—
148Q8×C11—21no—
149Q8×C11—21no—
150Q8×C11—82no—
151D4×C11—22no—
152D4×C11—22no—
153C2×C4×C11—22no—
154C2×C4×C11—21no—
155C2×C4×C11—21no—
156C2×C4×C11—42no—
157C2×C4×C11—42no—
158C2×C4×C11—42no—
159C2×C4×C11—162no—
160C2×C4×C11C22×D411yescharacteristic
161C2×C4×C11C22×D411yescharacteristic
162C2×C4×C11H(5,𝔽2)11yescharacteristic
163C22⋊D11—162no—
164C2×Dic11—21no—
165C2×Dic11—42no—
166D44—21no—
167D44—21no—
168C4×D11—41no—
169C4×D11—41no—
170Dic22—82no—
171C8×C11—21no—
172C8×C11—41no—
173C8×C11#13712yes—
174C11⋊C8—22no—
175C11⋊C8—21no—
176C11⋊C8—42no—
177C11⋊C8—41no—
178C11⋊C8#13512yes—
179#555—112no—
180#554C2×D1112yes—
181#500—112no—
182#500—111no—
183#500C2×D1111yescharacteristic
184#499—21no—
185#494—112no—
186#485—222no—
187#482—222no—
188#480—222no—
189#478—22no—
190#477—112no—
191#476—112no—
192#476—112no—
193#476C2×D1112yes—
194#468—222no—
195#466—221no—
196C8×Q8C2×D1111yescharacteristic
197C4×SD16—111no—
198C4×D8—21no—
199C4×D8C2×D1111yescharacteristic
200#436—112no—
201C8×D4—111no—
202#428—222no—
203#427—221no—
204#335—111no—
205#334—111no—
206#333—112no—
207#333—112no—
208Q8⋊C8—111no—
209D4⋊C8—112no—
210D4⋊C8—111no—
211C82—111no—
212C22×C11—42no—
213C22×C11—42no—
214C22×C11—42no—
215C22×C11D4211yescharacteristic
216C2×D11—41no—
217C2×D11—41no—
218C2×D11—41no—
219C4×C11—21no—
220C4×C11—42no—
221C4×C11—41no—
222C4×C11—41no—
223C4×C11—82no—
224C4×C11C2×#13511yescharacteristic
225C4×C11C2×#13711yescharacteristic
226C4×C11#57811yescharacteristic
227C4×C11#57811yescharacteristic
228Dic11—41no—
229Dic11—82no—
230C2×Q16—442no—
231C2×SD16—111no—
232C2×D8C22⋊D1111yescharacteristic
233C2×M16—222no—
234C22×C8—221no—
235C4⋊Q8—112no—
236C4⋊Q8C22×D1112yes—
237#125—22no—
238#124—442no—
239C22⋊Q8—22no—
240C22⋊Q8—42no—
241#121—222no—
242#121—222no—
243C4×Q8C22×D1111yescharacteristic
244C4×D4—22no—
245C4×D4—111no—
246C4×D4C22×D1112yes—
247#117—222no—
248#117—222no—
249C2×C4⋊C4—22no—
250#107—21no—
251#107—21no—
252#107—222no—
253#107—222no—
254#107—221no—
255#107—221no—
256#107—222no—
257#107C22⋊D1111yescharacteristic
258#106—22no—
259#106—111no—
260#106—222no—
261#106—222no—
262C4⋊C8—21no—
263C4⋊C8—112no—
264C4⋊C8—111no—
265C4⋊C8C22×D1111yescharacteristic
266#103—111no—
267#103—222no—
268#102—22no—
269#102—111no—
270#102—222no—
271#102—222no—
272#102C22⋊D1112yes—
273C22⋊C8—222no—
274C22⋊C8—221no—
275C4×C8—21no—
276C4×C8—111no—
277C4×C8—111no—
278C4×C8C22×D1111yescharacteristic
279C2×C11—82no—
280C2×C11#327611yescharacteristic
281C2×C11#328311yescharacteristic
282C2×C11#329211yescharacteristic
283D11—81no—
284C2×Q8—22no—
285C2×Q8—222no—
286C2×Q8D4×D1111yescharacteristic
287C2×D4—111no—
288C2×D4—442no—
289C2×D4C2×C22⋊D1112yes—
290C22×C4—22no—
291C22×C4—42no—
292C22×C4—221no—
293Q16—884no—
294SD16—222no—
295D8—22no—
296M16—444no—
297C2×C8—21no—
298C2×C8—111no—
299C2×C8—111no—
300C2×C8—221no—
301C2×C8—222no—
302C2×C8—221no—
303C2×C8—442no—
304C2×C8C2×C22⋊D1111yescharacteristic
305C2×C8C2×C22⋊D1111yescharacteristic
306C4⋊C4—21no—
307C4⋊C4—22no—
308C4⋊C4—22no—
309C4⋊C4—42no—
310C4⋊C4—42no—
311C4⋊C4—111no—
312C4⋊C4—222no—
313C4⋊C4—222no—
314C4⋊C4D4×D1111yescharacteristic
315C4⋊C4C2×C22⋊D1112yes—
316C22⋊C4—22no—
317C22⋊C4—42no—
318C22⋊C4—221no—
319C22⋊C4—442no—
320C22⋊C4—442no—
321C42—21no—
322C42—442no—
323C42C23×D1111yescharacteristic
324C11#1995711yescharacteristic, complemented, Sylow
325C23—22no—
326C23—221no—
327Q8—21no—
328Q8—21no—
329Q8—82no—
330Q8—882no—
331D4—22no—
332D4—22no—
333D4—221no—
334D4—221no—
335D4—1762no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—22no—
339C2×C4—42no—
340C2×C4—42no—
341C2×C4—42no—
342C2×C4—162no—
343C2×C4—221no—
344C2×C4—441no—
345C2×C4—441no—
346C2×C4—442no—
347C2×C4C2×D4×D1111yescharacteristic
348C2×C4#6703711yescharacteristic
349C2×C4C22×C22⋊D1111yescharacteristic
350C8—21no—
351C8—41no—
352C8—112no—
353C8—222no—
354C8—221no—
355C8—442no—
356C8—441no—
357C8#6699512yes—
358C22—42no—
359C22—42no—
360C22—42no—
361C22—441no—
362C22—441no—
363C22—441no—
364C22D4×C22⋊D1111yescharacteristic
365C4—21no—
366C4—42no—
367C4—41no—
368C4—41no—
369C4—82no—
370C4—441no—
371C4—882no—
372C4D11×#13511yescharacteristic
373C4#1062330211yescharacteristic
374C4C2×#6699511yescharacteristic
375C4#1062336911yescharacteristic
376C2—82no—
377C2—881no—
378C2#1308026211yescharacteristic
379C2#1308033211yescharacteristic
380C2#1308041311yescharacteristic
subgroupG/H
centerC22D4×C22⋊D11
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#3380C2
socleC22×C11D42
prime radical#13081040C2
hypercenter#3380D11
hypocenterC11#19957
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ #3380

Complements

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

NH ≅ G/Ntype
1. #13081242C2semidirect
3. #13068233C2semidirect
4. #13068137C2semidirect
5. #13068020C2semidirect
6. #13068012C2semidirect
7. #13067760C2semidirect
8. #13067750C2semidirect
9. #13067501C2semidirect
10. C8×#4325C2semidirect
11. C11×#3380C2semidirect
135. #3380D11semidirect
324. C11#19957semidirect

Maximal subgroups

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

subgroupindex
#130812422
#130810402
#130682332
#130681372
#130680202
#130680122
#130677602
#130677502
#130675012
C8×#43252
C11×#33802
#1995711