Finite Group Databasebeta

← #14770359

Subgroups — #14770359

Order 2816.

1314 conjugacy classes of subgroups.

The subgroup lattice has 508 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623258C211yesmaximal, characteristic
2C2×C8×Dic22C211yesmaximal, characteristic, complemented
3#13071528C211yesmaximal, characteristic, complemented
4#13069575C212yesmaximal, complemented
5#13069569C211yesmaximal, characteristic, complemented
6#13069566C212yesmaximal, complemented
7#13068615C212yesmaximal
8#13068613C211yesmaximal, characteristic
9C4×#66885C211yesmaximal, characteristic
10#13068430C212yesmaximal
11C11×#1990C211yesmaximal, characteristic, complemented
12C22×Q8×D11—21no—
13C2×C11×C4⋊Q8C2211yescharacteristic
14C2×#66999—21no—
15#10623258—24no—
16#10623258C418yescomplemented
17C2×#66949—22no—
18C2×#66946C2212yes—
19C2×#66941C2212yes—
20C2×#66940—21no—
21C2×C4×D44C2211yescharacteristic
22C2×C4×Dic22C2211yescharacteristic
23C2×C4×C8×C11C2211yescharacteristic
24C11×#384C2211yescharacteristic
25C2×#66885C2211yescharacteristic
26C2×#66885C2211yescharacteristic
27C2×Dic11⋊C8C2212yes—
28C2×C8×Dic11C2212yes—
29#10622589C2212yes—
30C4⋊C4×Dic11C2212yes—
31#10622586—21no—
32#10622585—22no—
33C2×#66873C2212yes—
34C4×C4⋊Dic11C2211yescharacteristic
35C2×C4⋊(C11⋊C8)C2211yescharacteristic
36C8×Dic22—24no—
37C11×#340C2212yes—
38C11×#340C2212yes—
39#10622189C2211yescharacteristic
40#10622189C2211yescharacteristic
41#10622167C2212yes—
42#10622167C2212yes—
43#10622167C2212yes—
44C22×Q8×C11—21no—
45C2×Q8×D11—28no—
46C2×Q8×D11—44no—
47C2×Q8×D11—44no—
48C22×D44C2311yescharacteristic
49C22×C4×D11—21no—
50C22×C4×D11—22no—
51C22×Dic22—22no—
52C22×Dic22D411yescharacteristic
53C22×C8×C11C2311yescharacteristic
54C22×C8×C11C2311yescharacteristic
55C11×C4⋊Q8—22no—
56C11×C4⋊Q8C2×C414yes—
57C2×C11×C4⋊C4—21no—
58C2×C11×C4⋊C4—21no—
59C2×C11×C4⋊C4—21no—
60C2×C11×C4⋊C4C2312yes—
61C2×C11×C4⋊C4C2312yes—
62C2×C42×C11C2311yescharacteristic
63#66999—28no—
64C2×(C2×D11)⋊C4—21no—
65C2×(C2×D11)⋊C4—22no—
66C2×C4⋊Dic11D411yescharacteristic
67C2×C4⋊Dic11C2311yescharacteristic
68C2×C4⋊Dic11C2311yescharacteristic
69C2×C4⋊Dic11C2311yescharacteristic
70C2×Dic11⋊C4—22no—
71C2×Dic11⋊C4—22no—
72C2×Dic11⋊C4—22no—
73C2×Dic11⋊C4D412yes—
74C2×C4×Dic11—21no—
75C2×C4×Dic11—22no—
76C2×C4×Dic11C2312yes—
77C22×C11⋊C8C2312yes—
78#66949—216no—
79#66946—24no—
80#66946C2×C418yes—
81#66941—24no—
82#66941C2×C418yes—
83#66940—44no—
84C4×D44—22no—
85C4×D44C2×C414yes—
86C4×Dic22C2×C414yes—
87C4×Dic22D414yes—
88C4×C8×C11—22no—
89C11⋊#95—21no—
90C11⋊#95—22no—
91#66885—22no—
92#66885Q814yescomplemented
93Dic11⋊C8—24no—
94C8×Dic11—24no—
95#66873—24no—
96C4⋊(C11⋊C8)—22no—
97Q8×#102—111nomaximal, Sylow
98C23×D11—21no—
99C2×Q8×C11—24no—
100C2×Q8×C11—42no—
101C2×Q8×C11—42no—
102C22×C4×C11—22no—
103C22×C4×C11—22no—
104C22×C4×C11C2×D411yescharacteristic
105C22×C4×C11C2×D411yescharacteristic
106C22×C4×C11C2411yescharacteristic
107C22×Dic11—21no—
108C22×Dic11—21no—
109C22×Dic11—21no—
110C22×Dic11C2×D412yes—
111C22×Dic11C2×D412yes—
112Q8×D11—432no—
113C2×D44—21no—
114C2×D44—21no—
115C2×D44—21no—
116C2×D44C22×C412yes—
117C2×D44C2×Q812yes—
118C2×D44#4112yes—
119C2×C4×D11—28no—
120C2×C4×D11—24no—
121C2×C4×D11—44no—
122C2×C4×D11—44no—
123C2×C4×D11—42no—
124C2×C4×D11—42no—
125C2×Dic22—28no—
126C2×Dic22—44no—
127C2×Dic22—44no—
128C2×Dic22C22⋊C414yes—
129C2×Dic22D814yes—
130C2×Dic22SD1614yes—
131C2×C8×C11—21no—
132C2×C8×C11—21no—
133C2×C8×C11—21no—
134C2×C8×C11—21no—
135C2×C8×C11—21no—
136C2×C8×C11C2×Q812yescomplemented
137C11×C4⋊C4—24no—
138C11×C4⋊C4—22no—
139C11×C4⋊C4—22no—
140C11×C4⋊C4—22no—
141C11×C4⋊C4—42no—
142C11×C4⋊C4—81no—
143C11×C4⋊C4C22×C414yes—
144C42×C11C22×C412yes—
145C42×C11C2×D412yes—
146(C2×D11)⋊C4—28no—
147(C2×D11)⋊C4—24no—
148C4⋊Dic11—21no—
149C4⋊Dic11—21no—
150C4⋊Dic11—21no—
151C4⋊Dic11—21no—
152C4⋊Dic11C22⋊C414yes—
153C4⋊Dic11C22×C412yes—
154C4⋊Dic11C2×Q812yescomplemented
155Dic11⋊C4—28no—
156Dic11⋊C4—44no—
157Dic11⋊C4—82no—
158Dic11⋊C4C22⋊C418yes—
159C4×Dic11—44no—
160C4×Dic11—42no—
161C4×Dic11C22×C414yes—
162C4×Dic11C2×D414yes—
163C2×C11⋊C8—22no—
164C2×C11⋊C8—22no—
165C2×C11⋊C8—22no—
166C2×D4×Q8—111no—
167C2×C8×Q8—111no—
168Q8×C4⋊C4—111no—
169#1990—112no—
170#1990D1111yescharacteristic, complemented
171#1988—112no—
172#1988—111no—
173#1802—111no—
174#1802—112no—
175C4×#102—111no—
176C4×#102—112no—
177C23×C11C22×D411yescharacteristic
178C22×D11—22no—
179C22×D11—22no—
180C22×D11—22no—
181C22×D11—41no—
182C22×D11—41no—
183C22×D11—41no—
184C22×D11—41no—
185Q8×C11—48no—
186C2×C4×C11—21no—
187C2×C4×C11—21no—
188C2×C4×C11—24no—
189C2×C4×C11—42no—
190C2×C4×C11—42no—
191C2×C4×C11—42no—
192C2×C4×C11—42no—
193C2×C4×C11—42no—
194C2×C4×C11C2×C22⋊C412yes—
195C2×C4×C11C2×C22⋊C412yes—
196C2×C4×C11C2×D812yes—
197C2×C4×C11C2×SD1612yes—
198C2×C4×C11C23×C411yescharacteristic
199C2×C4×C11C22×D411yescharacteristic
200C2×C4×C11C22×Q811yescharacteristic
201C2×C4×C11C2×#4111yescharacteristic
202C2×C4×C112−1+411yescharacteristic
203C2×C4×C112−1+411yescharacteristic
204C2×Dic11—22no—
205C2×Dic11—22no—
206C2×Dic11—22no—
207C2×Dic11—22no—
208C2×Dic11—41no—
209C2×Dic11—41no—
210C2×Dic11—41no—
211C2×Dic11—41no—
212C2×Dic11—41no—
213C2×Dic11—41no—
214C2×Dic11—41no—
215C2×Dic11C2×C22⋊C414yes—
216C2×Dic11C2×C22⋊C414yes—
217C2×Dic11C2×D814yes—
218C2×Dic11C2×SD1614yes—
219D44—22no—
220D44—22no—
221D44—22no—
222D44C4×Q814yescomplemented
223C4×D11—48no—
224C4×D11—416no—
225Dic22—416no—
226Dic22#102116yescomplemented
227C8×C11—22no—
228C8×C11—41no—
229C11⋊C8—42no—
230C23×Q8—221no—
231D4×Q8—118no—
232D4×Q8—224no—
233C2×C4⋊Q8—112no—
234C2×C4⋊Q8C2×D1111yescharacteristic
235C2×C22⋊Q8—222no—
236C2×C22⋊Q8—221no—
237C2×C4×Q8—111no—
238C2×C4×Q8—221no—
239C2×C4×D4—112no—
240C2×C4×D4—111no—
241C8×Q8—224no—
242C2×C4⋊C8—112no—
243C2×C4⋊C8—111no—
244C2×#102—111no—
245C2×#102—111no—
246C2×#102—112no—
247C2×C4×C8—112no—
248C2×C4×C8C2×D1111yescharacteristic
249#389—222no—
250#389—221no—
251#384—112no—
252#384C2×D1111yescharacteristic
253C4×C4⋊C4—112no—
254C4×C4⋊C4—111no—
255#340—111no—
256#340—111no—
257#340—112no—
258#340—112no—
259#340—112no—
260#340C2×D1112yes—
261#340C2×D1112yes—
262C22×C11C22×C22⋊C411yescharacteristic
263C22×C11#54811yescharacteristic
264C22×C11D4×Q811yescharacteristic
265C22×C11C22×D811yescharacteristic
266C22×C11C22×SD1611yescharacteristic
267C22×C11#57711yescharacteristic
268C22×C11#57811yescharacteristic
269C2×D11—24no—
270C2×D11—42no—
271C2×D11—42no—
272C2×D11—42no—
273C2×D11—42no—
274C2×D11—42no—
275C2×D11—42no—
276C4×C11—22no—
277C4×C11—44no—
278C4×C11—82no—
279C4×C11C2×#10214yes—
280C4×C11C2×C4×Q811yescharacteristic
281C4×C11#51911yescharacteristic
282C4×C11#54811yescharacteristic
283C4×C11D4×Q811yescharacteristic
284Dic11—24no—
285Dic11—42no—
286Dic11—42no—
287Dic11—81no—
288Dic11C2×#10218yes—
289C22×Q8—21no—
290C22×Q8—111no—
291C22×Q8—222no—
292C22×Q8—228no—
293C22×Q8—444no—
294C22×Q8—444no—
295C22×D4—111no—
296C23×C4—222no—
297C23×C4—221no—
298C22×C8—112no—
299C22×C8C22×D1111yescharacteristic
300C22×C8C22×D1111yescharacteristic
301C4⋊Q8—22no—
302C4⋊Q8—118no—
303C4⋊Q8—224no—
304C4⋊Q8C4×D1114yes—
305C22⋊Q8—2216no—
306C22⋊Q8—228no—
307C4×Q8—114no—
308C4×Q8—114no—
309C4×Q8—444no—
310C4×D4—118no—
311C4×D4—114no—
312C4×D4—224no—
313C4×D4—222no—
314C2×C4⋊C4—21no—
315C2×C4⋊C4—21no—
316C2×C4⋊C4—21no—
317C2×C4⋊C4—112no—
318C2×C4⋊C4—111no—
319C2×C4⋊C4—111no—
320C2×C4⋊C4—111no—
321C2×C4⋊C4—111no—
322C2×C4⋊C4—222no—
323C2×C4⋊C4—222no—
324C2×C4⋊C4—222no—
325C2×C4⋊C4C22×D1112yes—
326C2×C4⋊C4C22×D1112yes—
327C2×C22⋊C4—222no—
328C2×C22⋊C4—221no—
329C2×C42—112no—
330C2×C42—222no—
331C2×C42—221no—
332C2×C42C22×D1111yescharacteristic
333C4⋊C8—224no—
334C4⋊C8—222no—
335#102—114no—
336#102—224no—
337#102—222no—
338C4×C8—22no—
339C4×C8—224no—
340#95—222no—
341#95—221no—
342C2×C11Q8×C22⋊C411yescharacteristic
343C2×C11C22×#10211yescharacteristic
344C2×C11#289811yescharacteristic
345C2×C11#335811yescharacteristic
346C2×C11#335911yescharacteristic
347C2×C11Q8×D811yescharacteristic
348C2×C11Q8×SD1611yescharacteristic
349D11—44no—
350C24—221no—
351C2×Q8—24no—
352C2×Q8—42no—
353C2×Q8—42no—
354C2×Q8—114no—
355C2×Q8—114no—
356C2×Q8—114no—
357C2×Q8—228no—
358C2×Q8—444no—
359C2×Q8—444no—
360C2×Q8—4432no—
361C2×D4—112no—
362C2×D4—112no—
363C2×D4—112no—
364C2×D4—221no—
365C2×D4—221no—
366C2×D4—221no—
367C22×C4—22no—
368C22×C4—22no—
369C22×C4—112no—
370C22×C4—112no—
371C22×C4—228no—
372C22×C4—221no—
373C22×C4—221no—
374C22×C4—224no—
375C22×C4—221no—
376C22×C4—444no—
377C22×C4—444no—
378C22×C4—442no—
379C22×C4—442no—
380C22×C4D4×D1111yescharacteristic
381C22×C4D4×D1111yescharacteristic
382C22×C4C23×D1111yescharacteristic
383C2×C8—21no—
384C2×C8—21no—
385C2×C8—21no—
386C2×C8—21no—
387C2×C8—21no—
388C2×C8—222no—
389C2×C8—222no—
390C2×C8—222no—
391C2×C8Q8×D1112yescomplemented
392C4⋊C4—24no—
393C4⋊C4—22no—
394C4⋊C4—22no—
395C4⋊C4—22no—
396C4⋊C4—42no—
397C4⋊C4—81no—
398C4⋊C4—118no—
399C4⋊C4—114no—
400C4⋊C4—112no—
401C4⋊C4—112no—
402C4⋊C4—228no—
403C4⋊C4—221no—
404C4⋊C4—221no—
405C4⋊C4—221no—
406C4⋊C4—221no—
407C4⋊C4—444no—
408C4⋊C4—882no—
409C4⋊C4C2×C4×D1114yes—
410C22⋊C4—228no—
411C22⋊C4—224no—
412C42—114no—
413C42—114no—
414C42—444no—
415C42—442no—
416C42C2×C4×D1112yes—
417C42D4×D1112yes—
418C11Q8×#10211yescharacteristic, complemented, Sylow
419C23—222no—
420C23—222no—
421C23—222no—
422C23—441no—
423C23—441no—
424C23—441no—
425C23—441no—
426C23C2×D4×D1111yescharacteristic
427Q8—48no—
428Q8—1116no—
429Q8—4416no—
430D4—114no—
431D4—222no—
432D4—222no—
433D4—222no—
434C2×C4—21no—
435C2×C4—21no—
436C2×C4—24no—
437C2×C4—42no—
438C2×C4—42no—
439C2×C4—42no—
440C2×C4—42no—
441C2×C4—42no—
442C2×C4—114no—
443C2×C4—114no—
444C2×C4—114no—
445C2×C4—114no—
446C2×C4—222no—
447C2×C4—222no—
448C2×C4—222no—
449C2×C4—222no—
450C2×C4—4416no—
451C2×C4—441no—
452C2×C4—441no—
453C2×C4—441no—
454C2×C4—441no—
455C2×C4—448no—
456C2×C4—441no—
457C2×C4—441no—
458C2×C4—441no—
459C2×C4C22⋊C4×D1112yes—
460C2×C4C22⋊C4×D1112yes—
461C2×C4D8×D1112yes—
462C2×C4SD16×D1112yes—
463C2×C4C22×C4×D1111yescharacteristic
464C2×C4C2×D4×D1111yescharacteristic
465C2×C4C2×Q8×D1111yescharacteristic
466C2×C4#6704011yescharacteristic
467C2×C4#41×D1111yescharacteristic
468C2×C4#6704311yescharacteristic
469C8—22no—
470C8—41no—
471C8—442no—
472C22—224no—
473C22—442no—
474C22—442no—
475C22—442no—
476C22—442no—
477C22—442no—
478C22—442no—
479C22C2×C22⋊C4×D1111yescharacteristic
480C22#1062320811yescharacteristic
481C22#1062325811yescharacteristic
482C22C2×D8×D1111yescharacteristic
483C22C2×SD16×D1111yescharacteristic
484C22#1062329311yescharacteristic
485C22#1062329711yescharacteristic
486C4—22no—
487C4—44no—
488C4—82no—
489C4—118no—
490C4—224no—
491C4—442no—
492C4—442no—
493C4—881no—
494C4D11×#10214yes—
495C4C4×Q8×D1111yescharacteristic
496C4#1062310311yescharacteristic
497C4#1062316311yescharacteristic
498C4#1062316411yescharacteristic
499C2—444no—
500C2#1307145011yescharacteristic
501C2C2×D11×#10211yescharacteristic
502C2#1307714411yescharacteristic
503C2#1308124811yescharacteristic
504C2#1308125511yescharacteristic
505C2#1308146811yescharacteristic
506C2#1308147311yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1990C2
socleC23×C11C22×D4
prime radicalC22×D44C23
cosocleC22×C4×C11C24
hypercenter#1990D11
hypocenterC11Q8×#102
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1990

Complements

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

NH ≅ G/Ntype
2. C2×C8×Dic22C2semidirect
3. #13071528C2semidirect
4. #13069575C2semidirect
5. #13069569C2semidirect
6. #13069566C2semidirect
11. C11×#1990C2semidirect
16. #10623258C4semidirect
92. #66885Q8semidirect
136. C2×C8×C11C2×Q8semidirect
154. C4⋊Dic11C2×Q8semidirect
170. #1990D11semidirect
222. D44C4×Q8semidirect
226. Dic22#102semidirect
391. C2×C8Q8×D11semidirect
418. C11Q8×#102semidirect

Maximal subgroups

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

subgroupindex
C2×#106232582
C2×C8×Dic222
#130715282
#130695752
#130695692
#130695662
#130686152
#130686132
C4×#668852
#130684302
C11×#19902
Q8×#10211