Finite Group Databasebeta

← #14909506

Subgroups — #14909506

Order 2816.

642 conjugacy classes of subgroups.

The subgroup lattice has 466 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622801C211yesmaximal, characteristic, complemented
2D11×#466C211yesmaximal, characteristic
3#13070812C212yesmaximal, complemented
4#13070802C211yesmaximal, characteristic, complemented
5#13070799C211yesmaximal, characteristic, complemented
6#13070715C212yesmaximal, complemented
7#13070709C212yesmaximal, complemented
8#13070543C212yesmaximal, complemented
9#13070533C211yesmaximal, characteristic, complemented
10D11×C22⋊C16C211yesmaximal, characteristic, complemented
11C11×#2185C211yesmaximal, characteristic, complemented
12C22×C11×Q16C2211yescharacteristic, complemented
13C2×#66999—21no—
14C2×D8×D11C2211yescharacteristic
15C22×C8×D11C2211yescharacteristic
16D11×#121—21no—
17C2×C11×SD32C2212yescomplemented
18C11×#466C2211yescharacteristic
19C2×#66899—21no—
20#10622801—21no—
21#10622801—21no—
22#10622801C2212yes—
23#10622801C2212yescomplemented
24C2×#66892C2212yescomplemented
25#10622770C2211yescharacteristic
26#10622728C2211yescharacteristic
27C2×#66882C2211yescharacteristic, complemented
28#10622651—21no—
29C2×C16×D11C2212yescomplemented
30#10622496C2211yescharacteristic
31D11×#107C2211yescharacteristic
32#10622388—21no—
33D11×#102—21no—
34C11×#358C2212yescomplemented
35C11×C22⋊C16C2211yescharacteristic, complemented
36#10622202C2212yescomplemented
37#10622200C2212yescomplemented
38C22⋊(C11⋊C16)C2211yescharacteristic, complemented
39#10622147C2212yescomplemented
40(C2×D11)⋊C16C2212yes—
41#10622143C2212yescomplemented
42#10622128C2212yescomplemented
43C22×Q8×C11—21no—
44C2×D4×D11—21no—
45C2×D4×D11—41no—
46C22×C4×D11D411yescharacteristic
47C2×C11×Q16—21no—
48C2×C11×Q16—42no—
49C2×C11×Q16C2312yes—
50C2×C11×D8C2311yescharacteristic
51C22×C8×C11C2311yescharacteristic
52C11×#121—21no—
53#66999—22no—
54#66999—22no—
55#66999—41no—
56#66999—41no—
57#66992—41no—
58#66991—21no—
59C2×#4323—21no—
60#66983—21no—
61C2×(C2×D11)⋊C4—41no—
62C2×C4⋊Dic11—21no—
63C2×Dic11⋊C4—41no—
64C22×C11⋊C8D411yescharacteristic
65D8×D11—42no—
66C2×D88C2311yescharacteristic
67C2×C8×D11—42no—
68C2×C8×D11D411yescharacteristic
69C2×C8×D11D411yescharacteristic
70C2×C8×D11C2311yescharacteristic
71C2×C8×D11C2311yescharacteristic
72#66948—21no—
73C4⋊C4×D11—21no—
74#66937—41no—
75C22⋊C4×D11—41no—
76C11×SD32—42no—
77C2×C11×C16C2312yes—
78C11×#107C2311yescharacteristic
79C11×#102—21no—
80#66899—22no—
81#66899—22no—
82#66896—21no—
83#66892—42no—
84#66885—21no—
85#66882—21no—
86#66882C2311yescharacteristic
87#66882C2312yes—
88C2×C11⋊C16C2312yes—
89#66873—21no—
90#66871—21no—
91C16×D11—42no—
92#33753—111nomaximal, Sylow
93C23×D11—41no—
94C23×D11D811yescharacteristic
95C2×Q8×C11—22no—
96C2×Q8×C11—42no—
97C2×Q8×C11—42no—
98C2×Q8×C11—41no—
99C2×D4×C11—21no—
100C2×D4×C11—41no—
101C22×C4×C11—41no—
102C22×C4×C11C2×D411yescharacteristic
103C2×C22⋊D11—41no—
104C2×C22⋊D11—41no—
105C2×C22⋊D11—41no—
106C22×Dic11—41no—
107C22×Dic11D811yescharacteristic
108D4×D11—42no—
109D4×D11—42no—
110D4×D11—84no—
111C2×D44—21no—
112C2×D44—41no—
113C2×C4×D11—41no—
114C2×C4×D11—41no—
115C2×C4×D11—41no—
116C2×C4×D11D811yescharacteristic
117C2×C4×D11D811yescharacteristic
118C2×C4×D11C2×D411yescharacteristic
119C2×C4×D11C2×D411yescharacteristic
120C11×Q16—22no—
121C11×Q16—22no—
122C11×Q16—42no—
123C11×D8—22no—
124C2×C8×C11—22no—
125C2×C8×C11C2×D411yescharacteristic
126C2×C8×C11C2411yescharacteristic
127C11×C4⋊C4—21no—
128C11×C22⋊C4—41no—
129C22⋊Dic11—41no—
130#4323—42no—
131(C2×D11)⋊C4—41no—
132(C2×D11)⋊C4—42no—
133(C2×D11)⋊C4—42no—
134(C2×D11)⋊C4—41no—
135C4⋊Dic11—21no—
136C4⋊Dic11—22no—
137C4⋊Dic11—41no—
138Dic11⋊C4—41no—
139Dic11⋊C4—42no—
140Dic11⋊C4—42no—
141C2×C11⋊C8—41no—
142C2×C11⋊C8C2×D411yescharacteristic
143C2×C11⋊C8C2×D411yescharacteristic
144D88—22no—
145C8×D11—22no—
146C8×D11—22no—
147C8×D11—41no—
148C8×D11—41no—
149C11×C16—22no—
150C11⋊C16—22no—
151C2×#467—111no—
152C2×#466—111no—
153#2235—112no—
154#2233—111no—
155#2233—111no—
156#2217—112no—
157#2217—112no—
158#2187—112no—
159#2185—111no—
160#2185D1111yescharacteristic, complemented
161C2×C22⋊C16—111no—
162C23×C11—41no—
163C23×C11C2×D811yescharacteristic
164C22×D11—41no—
165C22×D11—41no—
166C22×D11—41no—
167C22×D11—82no—
168C22×D11—82no—
169C22×D11—82no—
170C22×D11SD3214yescomplemented
171C22×D11C2×D811yescharacteristic
172C22×D11C2×D811yescharacteristic
173Q8×C11—42no—
174Q8×C11—42no—
175Q8×C11—82no—
176D4×C11—41no—
177D4×C11—41no—
178D4×C11—82no—
179C2×C4×C11—21no—
180C2×C4×C11—21no—
181C2×C4×C11—42no—
182C2×C4×C11—41no—
183C2×C4×C11—82no—
184C2×C4×C11C2×D811yescharacteristic
185C2×C4×C11C22×D411yescharacteristic
186C22⋊D11—82no—
187C22⋊D11—82no—
188C22⋊D11—82no—
189C2×Dic11—41no—
190C2×Dic11—42no—
191C2×Dic11—41no—
192C2×Dic11—82no—
193C2×Dic11C2×D811yescharacteristic
194C2×Dic11C2×D811yescharacteristic
195D44—41no—
196D44—41no—
197D44—82no—
198C4×D11—21no—
199C4×D11—21no—
200C4×D11—21no—
201C4×D11—21no—
202C4×D11—41no—
203C4×D11—41no—
204C4×D11—82no—
205C8×C11—21no—
206C8×C11H(5,𝔽2)12yes—
207C11⋊C8—21no—
208C11⋊C8—21no—
209C22×Q16C2×D1111yescharacteristic, complemented
210C22×D8—111no—
211C23×C8—111no—
212C2×C22⋊Q8—221no—
213C2×#121—221no—
214C2×SD32—112no—
215C2×SD32C2×D1112yescomplemented
216C22×C16—112no—
217#467—112no—
218#467—112no—
219#467—221no—
220#467—221no—
221#466—111no—
222#466—111no—
223#466—111no—
224#466—221no—
225#466—221no—
226#466C2×D1111yescharacteristic
227C2×#107—111no—
228C2×#107—111no—
229C2×#103—221no—
230C2×#102—221no—
231#367—112no—
232#367—112no—
233#358—112no—
234#358C2×D1112yescomplemented
235#357—112no—
236#357—112no—
237C22⋊C16—111no—
238C22⋊C16—112no—
239C22⋊C16C2×D1111yescharacteristic, complemented
240C22×C11—21no—
241C22×C11—21no—
242C22×C11—81no—
243C22×C11—81no—
244C22×C11—81no—
245C22×C11C2×SD3212yes—
246C22×C11C22×D811yescharacteristic
247C2×D11—21no—
248C2×D11—21no—
249C2×D11—21no—
250C2×D11—21no—
251C2×D11—44no—
252C2×D11—81no—
253C2×D11—81no—
254C2×D11—81no—
255C2×D11—164no—
256C2×D11C2×SD3212yes—
257C2×D11C2×SD3212yes—
258C4×C11—21no—
259C4×C11—81no—
260C4×C11—82no—
261C4×C11#53411yescharacteristic
262C4×C11#57511yescharacteristic
263Dic11—21no—
264Dic11—21no—
265Dic11—81no—
266Dic11—82no—
267C22×Q8—21no—
268C22×D4—221no—
269C22×D4—441no—
270C23×C4—111no—
271C2×Q16—21no—
272C2×Q16—42no—
273C2×Q16C22×D1112yes—
274C2×D8—111no—
275C2×D8—221no—
276C2×D8—442no—
277C2×D8C22×D1111yescharacteristic
278C22×C8—111no—
279C22×C8—111no—
280C22×C8—111no—
281C22×C8—111no—
282C22×C8—111no—
283C22×C8—442no—
284C22×C8C22×D1111yescharacteristic
285C22⋊Q8—222no—
286C22⋊Q8—222no—
287C22⋊Q8—441no—
288C22⋊Q8—441no—
289#121—21no—
290#121—221no—
291#121—221no—
292#121—221no—
293#121—441no—
294#121—441no—
295C2×C4⋊C4—221no—
296C2×C4⋊C4—221no—
297C2×C4⋊C4—441no—
298C2×C22⋊C4—441no—
299C2×C22⋊C4—441no—
300SD32—42no—
301SD32—442no—
302C2×C16—112no—
303C2×C16—442no—
304C2×C16C22×D1112yes—
305#107—112no—
306#107—111no—
307#107—221no—
308#107—221no—
309#107C22×D1111yescharacteristic
310#103—222no—
311#103—222no—
312#102—21no—
313#102—221no—
314#102—221no—
315#102—221no—
316C2×C11—22no—
317C2×C11—161no—
318C2×C11#318611yescharacteristic
319C2×C11C22×SD3211yescharacteristic
320C2×C11#341411yescharacteristic
321D11—22no—
322D11—22no—
323D11—161no—
324C24—111no—
325C24—441no—
326C2×Q8—22no—
327C2×Q8—42no—
328C2×Q8—42no—
329C2×Q8—41no—
330C2×D4—21no—
331C2×D4—41no—
332C2×D4—221no—
333C2×D4—441no—
334C2×D4—441no—
335C2×D4—442no—
336C2×D4—442no—
337C2×D4—441no—
338C2×D4—441no—
339C2×D4—884no—
340C22×C4—41no—
341C22×C4—111no—
342C22×C4—111no—
343C22×C4—111no—
344C22×C4—111no—
345C22×C4—111no—
346C22×C4—441no—
347C22×C4—441no—
348C22×C4—441no—
349C22×C4—441no—
350C22×C4D4×D1111yescharacteristic
351Q16—22no—
352Q16—22no—
353Q16—42no—
354D8—22no—
355D8—222no—
356D8—442no—
357C2×C8—22no—
358C2×C8—111no—
359C2×C8—111no—
360C2×C8—222no—
361C2×C8—222no—
362C2×C8—441no—
363C2×C8—441no—
364C2×C8—441no—
365C2×C8D4×D1111yescharacteristic
366C2×C8C23×D1111yescharacteristic
367C4⋊C4—21no—
368C4⋊C4—221no—
369C4⋊C4—222no—
370C4⋊C4—441no—
371C4⋊C4—442no—
372C4⋊C4—442no—
373C4⋊C4—441no—
374C22⋊C4—41no—
375C22⋊C4—441no—
376C22⋊C4—442no—
377C22⋊C4—442no—
378C22⋊C4—441no—
379C22⋊C4—441no—
380C16—22no—
381C16—222no—
382C11#3375311yescharacteristic, complemented, Sylow
383C23—41no—
384C23—111no—
385C23—111no—
386C23—114no—
387C23—441no—
388C23—441no—
389C23—441no—
390C23—882no—
391C23—882no—
392C23—882no—
393C23D8×D1111yescharacteristic
394Q8—42no—
395Q8—42no—
396Q8—82no—
397D4—41no—
398D4—41no—
399D4—82no—
400D4—441no—
401D4—441no—
402D4—882no—
403D4—882no—
404D4—882no—
405D4—882no—
406C2×C4—21no—
407C2×C4—21no—
408C2×C4—41no—
409C2×C4—42no—
410C2×C4—82no—
411C2×C4—111no—
412C2×C4—111no—
413C2×C4—221no—
414C2×C4—221no—
415C2×C4—221no—
416C2×C4—221no—
417C2×C4—441no—
418C2×C4—441no—
419C2×C4—441no—
420C2×C4—442no—
421C2×C4—441no—
422C2×C4—882no—
423C2×C4—882no—
424C2×C4D8×D1111yescharacteristic
425C2×C4C2×D4×D1111yescharacteristic
426C8—21no—
427C8—221no—
428C8—221no—
429C8#6703712yes—
430C22—21no—
431C22—21no—
432C22—81no—
433C22—81no—
434C22—81no—
435C22—112no—
436C22—112no—
437C22—221no—
438C22—221no—
439C22—221no—
440C22—221no—
441C22—444no—
442C22—881no—
443C22—881no—
444C22—881no—
445C22—1764no—
446C22D11×SD3212yes—
447C22C2×D8×D1111yescharacteristic
448C4—21no—
449C4—82no—
450C4—81no—
451C4—221no—
452C4—221no—
453C4—881no—
454C4—882no—
455C4#1062312011yescharacteristic
456C4#1062330411yescharacteristic
457C2—22no—
458C2—161no—
459C2—222no—
460C2—222no—
461C2—1761no—
462C2#1307936511yescharacteristic
463C2C2×D11×SD3211yescharacteristic
464C2#1308175111yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2185C2
socleC22×C11C22×D8
prime radicalD11×#466C2
hypercenter#2185D11
hypocenterC11#33753
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2185

Complements

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

NH ≅ G/Ntype
1. C2×#10622801C2semidirect
3. #13070812C2semidirect
4. #13070802C2semidirect
5. #13070799C2semidirect
6. #13070715C2semidirect
7. #13070709C2semidirect
8. #13070543C2semidirect
9. #13070533C2semidirect
10. D11×C22⋊C16C2semidirect
11. C11×#2185C2semidirect
12. C22×C11×Q16C22semidirect
17. C2×C11×SD32C22semidirect
23. #10622801C22semidirect
24. C2×#66892C22semidirect
27. C2×#66882C22semidirect
29. C2×C16×D11C22semidirect
34. C11×#358C22semidirect
35. C11×C22⋊C16C22semidirect
36. #10622202C22semidirect
37. #10622200C22semidirect
38. C22⋊(C11⋊C16)C22semidirect
39. #10622147C22semidirect
41. #10622143C22semidirect
42. #10622128C22semidirect
160. #2185D11semidirect
170. C22×D11SD32semidirect
209. C22×Q16C2×D11semidirect
215. C2×SD32C2×D11semidirect
234. #358C2×D11semidirect
239. C22⋊C16C2×D11semidirect
382. C11#33753semidirect

Maximal subgroups

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

subgroupindex
C2×#106228012
D11×#4662
#130708122
#130708022
#130707992
#130707152
#130707092
#130705432
#130705332
D11×C22⋊C162
C11×#21852
#3375311