Finite Group Databasebeta

← #14775571

Subgroups — #14775571

Order 2816.

926 conjugacy classes of subgroups.

The subgroup lattice has 470 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622459C211yesmaximal, characteristic
2#13071672C211yesmaximal, characteristic, complemented
3#13071516C211yesmaximal, characteristic
4#13069576C211yesmaximal, characteristic, complemented
5#13069347C212yesmaximal, complemented
6#13069186C212yesmaximal, complemented
7#13068860C212yesmaximal
8#13068481C211yesmaximal, characteristic, complemented
9C4×#66873C211yesmaximal, characteristic
10#13068430C212yesmaximal
11C11×#1947C211yesmaximal, characteristic, complemented
12C2×#66946C2212yes—
13C2×C4⋊C4×D11—21no—
14C2×C4×D44C2211yescharacteristic
15C2×#66922C2211yescharacteristic
16C2×C4×Dic22—21no—
17C2×C11×#107C2212yes—
18C2×C11×C4⋊C8C2211yescharacteristic
19C11×#384C2211yescharacteristic
20C4×C11×C4⋊C4C2211yescharacteristic
21C2×#66885C2212yes—
22C2×#66882C2212yes—
23C2×C8×Dic11C2212yes—
24#10622602—22no—
25#10622600—21no—
26C4⋊C4×Dic11C2212yes—
27#10622586C2212yes—
28#10622586C2212yes—
29C2×#66873C2211yescharacteristic
30C2×#66873C2211yescharacteristic
31C4×C4⋊Dic11C2211yescharacteristic
32#10622542—21no—
33C2×C4×C11⋊C8C2211yescharacteristic
34#10622459C418yescomplemented
35#10622267—22no—
36C11×#340C2212yes—
37#10622188C2212yes—
38#10622167C2212yes—
39#10622167C2212yes—
40#10622167C2211yescharacteristic
41#10622167C2211yescharacteristic
42C22×D44C2311yescharacteristic
43C22×C4×D11—21no—
44C22×C4×D11—22no—
45C22×Dic22—21no—
46C22×C8×C11C2312yes—
47C2×C11×C4⋊C4—21no—
48C2×C11×C4⋊C4—21no—
49C2×C11×C4⋊C4C2312yes—
50C2×C11×C4⋊C4C2311yescharacteristic
51C2×C11×C4⋊C4C2311yescharacteristic
52C2×C42×C11—21no—
53C2×C42×C11C2311yescharacteristic
54C2×(C2×D11)⋊C4—21no—
55C2×(C2×D11)⋊C4—22no—
56C2×C4⋊Dic11—21no—
57C2×C4⋊Dic11D411yescharacteristic
58C2×C4⋊Dic11D411yescharacteristic
59C2×C4⋊Dic11C2312yes—
60C2×C4⋊Dic11C2311yescharacteristic
61C2×Dic11⋊C4—22no—
62C2×Dic11⋊C4—22no—
63C2×C4×Dic11—22no—
64C2×C4×Dic11C2312yes—
65C22×C11⋊C8C2311yescharacteristic
66C22×C11⋊C8C2311yescharacteristic
67#66946—24no—
68#66946—42no—
69C4⋊C4×D11—44no—
70C4×D44—22no—
71C4×D44C2×C414yes—
72#66922—22no—
73#66922C2×C414yescomplemented
74C4×Dic22—44no—
75C11×#107—42no—
76C11×C4⋊C8C2×C414yescomplemented
77C11×#95—21no—
78C11⋊#95—22no—
79C11⋊#95—22no—
80C11⋊#95—22no—
81C11⋊#95D412yes—
82#66885C2×C418yes—
83#66882C2×C418yescomplemented
84C8×Dic11—42no—
85#66873—22no—
86#66873Q814yescomplemented
87C4×C11⋊C8—22no—
88#22962—111nomaximal, Sylow
89C23×D11—21no—
90C22×C4×C11—21no—
91C22×C4×C11—21no—
92C22×C4×C11—22no—
93C22×C4×C11C2×D411yescharacteristic
94C22×C4×C11C2×D411yescharacteristic
95C22×C4×C11C2411yescharacteristic
96C22×Dic11—22no—
97C22×Dic11—21no—
98C22×Dic11C2×D412yes—
99C22×Dic11C2×D412yes—
100C2×D44—21no—
101C2×D44—21no—
102C2×D44—21no—
103C2×D44C22×C412yes—
104C2×D44C2×Q812yes—
105C2×D44#4112yes—
106C2×C4×D11—24no—
107C2×C4×D11—44no—
108C2×C4×D11—44no—
109C2×C4×D11—42no—
110C2×C4×D11—42no—
111C2×C4×D11—82no—
112C2×Dic22—24no—
113C2×Dic22—42no—
114C2×Dic22—42no—
115C2×C8×C11—22no—
116C2×C8×C11—22no—
117C2×C8×C11C22×C414yes—
118C11×C4⋊C4—21no—
119C11×C4⋊C4—21no—
120C11×C4⋊C4—22no—
121C11×C4⋊C4—21no—
122C11×C4⋊C4—22no—
123C11×C4⋊C4—42no—
124C11×C4⋊C4—81no—
125C11×C4⋊C4C2×Q812yes—
126C42×C11—42no—
127C42×C11C22×C412yes—
128C42×C11#4112yes—
129(C2×D11)⋊C4—24no—
130(C2×D11)⋊C4—44no—
131C4⋊Dic11—24no—
132C4⋊Dic11—22no—
133C4⋊Dic11—22no—
134C4⋊Dic11—21no—
135C4⋊Dic11D814yes—
136C4⋊Dic11C22×C412yes—
137C4⋊Dic11C22×C414yes—
138Dic11⋊C4—44no—
139Dic11⋊C4—44no—
140C4×Dic11—22no—
141C4×Dic11—22no—
142C4×Dic11—44no—
143C2×C11⋊C8—21no—
144C2×C11⋊C8—21no—
145C2×C11⋊C8—21no—
146C2×C11⋊C8—21no—
147C2×C11⋊C8—21no—
148C2×C11⋊C8C2×Q812yes—
149C2×#474—111no—
150#2365—111no—
151D4×C4⋊C4—111no—
152#1990—111no—
153#1947D1111yescharacteristic, complemented
154#1942—112no—
155#1918—112no—
156#1862—112no—
157C8×C4⋊C4—111no—
158C4×#102—111no—
159C4×#102—112no—
160C23×C11C22×D411yescharacteristic
161C22×D11—22no—
162C22×D11—22no—
163C22×D11—22no—
164C22×D11—41no—
165C22×D11—41no—
166C22×D11—41no—
167C22×D11—41no—
168C2×C4×C11—21no—
169C2×C4×C11—21no—
170C2×C4×C11—22no—
171C2×C4×C11—41no—
172C2×C4×C11—41no—
173C2×C4×C11—42no—
174C2×C4×C11—41no—
175C2×C4×C11—41no—
176C2×C4×C11—42no—
177C2×C4×C11—42no—
178C2×C4×C11—41no—
179C2×C4×C11C4×D412yes—
180C2×C4×C11C4×D412yes—
181C2×C4×C11C2×D812yes—
182C2×C4×C11#13512yes—
183C2×C4×C11C23×C411yescharacteristic
184C2×C4×C11C22×Q811yescharacteristic
185C2×C4×C11C2×#4111yescharacteristic
186C2×C4×C11C2×#4111yescharacteristic
187C2×C4×C11H(5,𝔽2)11yescharacteristic
188C2×C4×C112−1+411yescharacteristic
189C2×Dic11—22no—
190C2×Dic11—22no—
191C2×Dic11—24no—
192C2×Dic11—22no—
193C2×Dic11—22no—
194C2×Dic11—22no—
195C2×Dic11—22no—
196C2×Dic11—42no—
197C2×Dic11—41no—
198C2×Dic11—42no—
199C2×Dic11—41no—
200C2×Dic11C2×D814yes—
201D44—22no—
202D44—22no—
203D44—22no—
204D44C4×Q814yescomplemented
205C4×D11—48no—
206C4×D11—88no—
207Dic22—48no—
208C8×C11—24no—
209C11⋊C8—22no—
210C11⋊C8—41no—
211C2×C4⋊Q8—111no—
212C2×C4×Q8—221no—
213C2×C4×D4—112no—
214C2×C4×D4—111no—
215C22×C4⋊C4—221no—
216#474—118no—
217C2×#107—112no—
218C2×#107C2×D1112yes—
219C2×C4⋊C8C2×D1111yescharacteristic
220C2×#102—112no—
221C2×#102—111no—
222C2×#102—111no—
223C2×C4×C8—111no—
224C2×C4×C8—112no—
225#391—221no—
226#389—112no—
227#389—112no—
228#387—222no—
229#385—222no—
230#384C2×D1111yescharacteristic
231#380—221no—
232C4×C4⋊C4—111no—
233C4×C4⋊C4—112no—
234C4×C4⋊C4C2×D1111yescharacteristic
235#340—112no—
236#340—111no—
237#340—111no—
238#340—112no—
239#340C2×D1112yes—
240#336—112no—
241C22×C11C2×C4×D411yescharacteristic
242C22×C11#54611yescharacteristic
243C22×C11D4×Q811yescharacteristic
244C22×C11C22×D811yescharacteristic
245C22×C11C2×#13511yescharacteristic
246C22×C11#57711yescharacteristic
247C22×C11#57811yescharacteristic
248C2×D11—24no—
249C2×D11—42no—
250C2×D11—42no—
251C2×D11—42no—
252C2×D11—42no—
253C2×D11—42no—
254C2×D11—42no—
255C4×C11—22no—
256C4×C11—42no—
257C4×C11—81no—
258C4×C11—82no—
259C4×C11C4×D814yes—
260C4×C11C2×C4×Q811yescharacteristic
261C4×C11#52011yescharacteristic
262C4×C11#55211yescharacteristic
263C4×C11#55411yescharacteristic
264Dic11—24no—
265Dic11—44no—
266Dic11—42no—
267Dic11—42no—
268C22×Q8—221no—
269C22×D4—111no—
270C23×C4—222no—
271C23×C4—221no—
272C22×C8—111no—
273C22×C8—111no—
274C22×C8C22×D1112yes—
275C4⋊Q8—114no—
276C4⋊Q8—222no—
277C4×Q8—444no—
278C4×D4—114no—
279C4×D4—224no—
280C4×D4—222no—
281C4×D4—442no—
282C2×C4⋊C4—21no—
283C2×C4⋊C4—21no—
284C2×C4⋊C4—111no—
285C2×C4⋊C4—111no—
286C2×C4⋊C4—112no—
287C2×C4⋊C4—111no—
288C2×C4⋊C4—221no—
289C2×C4⋊C4—222no—
290C2×C4⋊C4—222no—
291C2×C4⋊C4—444no—
292C2×C4⋊C4C22×D1112yes—
293C2×C4⋊C4C22×D1111yescharacteristic
294C2×C4⋊C4C22×D1111yescharacteristic
295C2×C22⋊C4—221no—
296C2×C22⋊C4—222no—
297C2×C42—21no—
298C2×C42—112no—
299C2×C42—222no—
300C2×C42C22×D1111yescharacteristic
301#107—42no—
302#107—118no—
303C4⋊C8C4×D1114yescomplemented
304#102—118no—
305#102—114no—
306#102—222no—
307C4×C8—222no—
308C4×C8—442no—
309#95—21no—
310#95—112no—
311#95—222no—
312#95—222no—
313#95—222no—
314C2×C11#236011yescharacteristic
315C2×C11C2×C4×D811yescharacteristic
316C2×C11#294711yescharacteristic
317C2×C11#329411yescharacteristic
318C2×C11#330211yescharacteristic
319C2×C11Q8×D811yescharacteristic
320C2×C11#338111yescharacteristic
321D11—44no—
322C24—221no—
323C2×Q8—224no—
324C2×Q8—442no—
325C2×Q8—442no—
326C2×D4—112no—
327C2×D4—112no—
328C2×D4—112no—
329C2×D4—221no—
330C2×D4—221no—
331C2×D4—221no—
332C22×C4—21no—
333C22×C4—21no—
334C22×C4—22no—
335C22×C4—112no—
336C22×C4—112no—
337C22×C4—222no—
338C22×C4—221no—
339C22×C4—224no—
340C22×C4—444no—
341C22×C4—444no—
342C22×C4—442no—
343C22×C4—442no—
344C22×C4—882no—
345C22×C4D4×D1111yescharacteristic
346C22×C4D4×D1111yescharacteristic
347C22×C4C23×D1111yescharacteristic
348C2×C8—22no—
349C2×C8—22no—
350C2×C8—112no—
351C2×C8—221no—
352C2×C8—221no—
353C2×C8—221no—
354C2×C8—221no—
355C2×C8—221no—
356C2×C8C2×C4×D1114yes—
357C4⋊C4—21no—
358C4⋊C4—21no—
359C4⋊C4—22no—
360C4⋊C4—21no—
361C4⋊C4—22no—
362C4⋊C4—42no—
363C4⋊C4—81no—
364C4⋊C4—114no—
365C4⋊C4—114no—
366C4⋊C4—112no—
367C4⋊C4—224no—
368C4⋊C4—222no—
369C4⋊C4—221no—
370C4⋊C4—222no—
371C4⋊C4—444no—
372C4⋊C4—444no—
373C4⋊C4Q8×D1112yes—
374C22⋊C4—224no—
375C22⋊C4—444no—
376C42—42no—
377C42—222no—
378C42—222no—
379C42—444no—
380C42C2×C4×D1112yes—
381C42#434312yes—
382C11#2296211yescharacteristic, complemented, Sylow
383C23—222no—
384C23—222no—
385C23—222no—
386C23—441no—
387C23—441no—
388C23—441no—
389C23—441no—
390C23C2×D4×D1111yescharacteristic
391Q8—448no—
392D4—114no—
393D4—222no—
394D4—222no—
395D4—222no—
396C2×C4—21no—
397C2×C4—21no—
398C2×C4—22no—
399C2×C4—41no—
400C2×C4—41no—
401C2×C4—41no—
402C2×C4—42no—
403C2×C4—42no—
404C2×C4—41no—
405C2×C4—42no—
406C2×C4—41no—
407C2×C4—114no—
408C2×C4—222no—
409C2×C4—222no—
410C2×C4—222no—
411C2×C4—224no—
412C2×C4—222no—
413C2×C4—222no—
414C2×C4—222no—
415C2×C4—442no—
416C2×C4—441no—
417C2×C4—441no—
418C2×C4—442no—
419C2×C4—448no—
420C2×C4—888no—
421C2×C4#6694612yes—
422C2×C4#6694612yes—
423C2×C4D8×D1112yes—
424C2×C4#6697212yes—
425C2×C4C22×C4×D1111yescharacteristic
426C2×C4#6703711yescharacteristic
427C2×C4C2×Q8×D1111yescharacteristic
428C2×C4C2×#434311yescharacteristic
429C2×C4#41×D1111yescharacteristic
430C2×C4#6704311yescharacteristic
431C8—24no—
432C8—222no—
433C8—441no—
434C22—224no—
435C22—442no—
436C22—442no—
437C22—442no—
438C22—442no—
439C22—442no—
440C22—442no—
441C22C2×#6694611yescharacteristic
442C22#1062314311yescharacteristic
443C22#1062316311yescharacteristic
444C22C2×D8×D1111yescharacteristic
445C22C2×#6697211yescharacteristic
446C22#1062330611yescharacteristic
447C22#1062331011yescharacteristic
448C4—22no—
449C4—42no—
450C4—82no—
451C4—81no—
452C4—224no—
453C4—442no—
454C4—444no—
455C4—442no—
456C4#1062248514yes—
457C4#1062307711yescharacteristic
458C4C4×Q8×D1111yescharacteristic
459C4#1062322511yescharacteristic
460C4#1062326111yescharacteristic
461C2—444no—
462C2#1307162011yescharacteristic
463C2C2×#1062248511yescharacteristic
464C2#1307745711yescharacteristic
465C2#1308043211yescharacteristic
466C2#1308053611yescharacteristic
467C2#1308146611yescharacteristic
468C2#1308149011yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1947C2
socleC23×C11C22×D4
prime radicalC22×D44C23
cosocleC22×C4×C11C24
hypercenter#1947D11
hypocenterC11#22962
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1947

Complements

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

NH ≅ G/Ntype
2. #13071672C2semidirect
4. #13069576C2semidirect
5. #13069347C2semidirect
6. #13069186C2semidirect
8. #13068481C2semidirect
11. C11×#1947C2semidirect
34. #10622459C4semidirect
73. #66922C2×C4semidirect
76. C11×C4⋊C8C2×C4semidirect
83. #66882C2×C4semidirect
86. #66873Q8semidirect
153. #1947D11semidirect
204. D44C4×Q8semidirect
303. C4⋊C8C4×D11semidirect
382. C11#22962semidirect

Maximal subgroups

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

subgroupindex
C2×#106224592
#130716722
#130715162
#130695762
#130693472
#130691862
#130688602
#130684812
C4×#668732
#130684302
C11×#19472
#2296211