Finite Group Databasebeta

← #14769638

Subgroups — #14769638

Order 2816.

1450 conjugacy classes of subgroups.

The subgroup lattice has 566 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66972C211yesmaximal, characteristic
2C2×Q16×Dic11C211yesmaximal, characteristic, complemented
3#13071454C212yesmaximal, complemented
4#13069482C211yesmaximal, characteristic, complemented
5#13069480C211yesmaximal, characteristic, complemented
6#13068971C212yesmaximal, complemented
7#13068969C212yesmaximal, complemented
8#13068642C211yesmaximal, characteristic, complemented
9#13068555C212yesmaximal, complemented
10C8×(C2×D11)⋊C4C211yesmaximal, characteristic, complemented
11C2×C4×C11×Q16C211yesmaximal, characteristic, complemented
12C22×#4343C2212yes—
13C22×C11×Q16C2211yescharacteristic
14C2×C4×Q8×C11C2212yes—
15C2×Q8×Dic11C2212yes—
16C22×#4325C2212yes—
17C2×#66972—24no—
18C2×#66972—24no—
19C2×#66972C418yescomplemented
20C22×D88C2211yescharacteristic
21C22×C8×D11C2211yescharacteristic
22C4×C11×Q16—24no—
23C2×C11×#107C2211yescharacteristic
24C2×C11×#103C2212yes—
25C2×C4×C8×C11C2211yescharacteristic
26C2×#66899C2212yes—
27Q16×Dic11—24no—
28C2×#66885C2212yes—
29C2×(C2×D11)⋊C8C2211yescharacteristic
30C2×#66882C2211yescharacteristic
31C2×C8×Dic11C2211yescharacteristic
32#10622601—22no—
33#10622601C2212yes—
34#10622600—22no—
35#10622600C2212yes—
36C2×#66873C2212yes—
37#10622552—22no—
38#10622552C2212yes—
39C4×(C2×D11)⋊C4—22no—
40C4×(C2×D11)⋊C4C2211yescharacteristic
41#10622188C2211yescharacteristic
42#10622167C2212yes—
43#10622162C2211yescharacteristic
44C22×Q8×C11C2312yes—
45C2×#4343—24no—
46C2×#4343—24no—
47C2×#4343—24no—
48C2×#4343—42no—
49C2×#4343—42no—
50C2×#4343C2×C418yes—
51C22×D44—22no—
52C22×D44C2312yes—
53C22×C4×D11—22no—
54C22×C4×D11C2311yescharacteristic
55C2×C11×Q16C2×C414yes—
56C2×C11×Q16D414yes—
57C2×C11×Q16D414yes—
58C22×C8×C11C2311yescharacteristic
59C22×C8×C11C2311yescharacteristic
60C4×Q8×C11—24no—
61C4×Q8×C11—42no—
62C2×C11×C4⋊C4—22no—
63C2×C11×C4⋊C4C2312yes—
64C2×C42×C11—22no—
65C2×C42×C11C2311yescharacteristic
66Q8×Dic11—24no—
67Q8×Dic11—42no—
68C2×#4325—24no—
69C2×#4325—24no—
70C2×#4325C2×C418yes—
71C2×(C2×D11)⋊C4—22no—
72C2×(C2×D11)⋊C4—22no—
73C2×(C2×D11)⋊C4—22no—
74C2×(C2×D11)⋊C4—22no—
75C2×(C2×D11)⋊C4—22no—
76C2×(C2×D11)⋊C4D411yescharacteristic
77C2×(C2×D11)⋊C4D411yescharacteristic
78C2×C4⋊Dic11—22no—
79C2×C4⋊Dic11C2312yes—
80C2×C4×Dic11—22no—
81C2×C4×Dic11C2311yescharacteristic
82C22×C11⋊C8C2311yescharacteristic
83C22×C11⋊C8C2311yescharacteristic
84#66972—232no—
85C2×D88—22no—
86C2×D88—22no—
87C2×D88C2×C414yes—
88C2×C8×D11—22no—
89C2×C8×D11—22no—
90C2×C8×D11C2×C414yes—
91C11×#107—22no—
92C11×#103—24no—
93C4×C8×C11—22no—
94#66899—24no—
95C11⋊#95—22no—
96C11⋊#95D411yescharacteristic
97C11⋊#95D411yescharacteristic
98#66885—42no—
99(C2×D11)⋊C8—22no—
100#66882—22no—
101C8×Dic11—22no—
102#66873—42no—
103#22451—111nomaximal, Sylow
104C23×D11—22no—
105C23×D11C2×D411yescharacteristic
106C2×Q8×C11—22no—
107C2×Q8×C11—22no—
108C2×Q8×C11—22no—
109C2×Q8×C11C22×C414yes—
110C2×Q8×C11C2×D414yes—
111C2×Q8×C11C2×D414yes—
112C22×C4×C11—22no—
113C22×C4×C11—22no—
114C22×C4×C11C2×D411yescharacteristic
115C22×C4×C11C2×D411yescharacteristic
116C22×C4×C11C2411yescharacteristic
117C22×Dic11—22no—
118C22×Dic11C2×D411yescharacteristic
119C22×Dic11C2×D411yescharacteristic
120C22×Dic11C2×D411yescharacteristic
121#4343—216no—
122#4343—48no—
123#4343—48no—
124#4343—48no—
125C2×D44—28no—
126C2×D44—22no—
127C2×D44—22no—
128C2×D44—22no—
129C2×D44—22no—
130C2×D44—22no—
131C2×D44—44no—
132C2×D44—44no—
133C2×D44C22×C414yes—
134C2×C4×D11—28no—
135C2×C4×D11—21no—
136C2×C4×D11—21no—
137C2×C4×D11—21no—
138C2×C4×D11—21no—
139C2×C4×D11—44no—
140C2×C4×D11—44no—
141C2×C4×D11C22×C412yes—
142C2×C4×D11#4112yes—
143C11×Q16C22⋊C4116yescomplemented
144C2×C8×C11—21no—
145C2×C8×C11—21no—
146C2×C8×C11—21no—
147C2×C8×C11C22×C412yes—
148C2×C8×C11C2×D412yes—
149C2×C8×C11C2×D412yes—
150C11×C4⋊C4—22no—
151C11×C4⋊C4—22no—
152C11×C4⋊C4—44no—
153C42×C11—21no—
154C42×C11—21no—
155C42×C11—44no—
156#4325—216no—
157(C2×D11)⋊C4—22no—
158(C2×D11)⋊C4—22no—
159(C2×D11)⋊C4—44no—
160(C2×D11)⋊C4—44no—
161(C2×D11)⋊C4—82no—
162(C2×D11)⋊C4—82no—
163(C2×D11)⋊C4—82no—
164C4⋊Dic11—22no—
165C4⋊Dic11—22no—
166C4⋊Dic11—44no—
167C4×Dic11—21no—
168C4×Dic11—21no—
169C4×Dic11—44no—
170C2×C11⋊C8—21no—
171C2×C11⋊C8—21no—
172C2×C11⋊C8—21no—
173C2×C11⋊C8—21no—
174C2×C11⋊C8—21no—
175C2×C11⋊C8C22×C412yes—
176D88—28no—
177C8×D11—28no—
178C22×#135—111no—
179C2×C4×Q16—111no—
180C2×C4×Q16D1111yescharacteristic, complemented
181#2341—112no—
182#1970—111no—
183#1970—111no—
184#1880—112no—
185#1880—112no—
186#1808—111no—
187#1788—112no—
188C8×C22⋊C4—111no—
189C23×C11C22×D411yescharacteristic
190C22×D11—21no—
191C22×D11—21no—
192C22×D11—21no—
193C22×D11—21no—
194C22×D11—21no—
195C22×D11—21no—
196C22×D11—24no—
197C22×D11—42no—
198C22×D11—42no—
199C22×D11—42no—
200C22×D11—42no—
201C22×D11—42no—
202C22×D11—42no—
203C22×D11C4×D412yes—
204Q8×C11—24no—
205Q8×C11—24no—
206Q8×C11—24no—
207Q8×C11C2×C22⋊C418yes—
208C2×C4×C11—24no—
209C2×C4×C11—24no—
210C2×C4×C11—21no—
211C2×C4×C11—24no—
212C2×C4×C11—21no—
213C2×C4×C11—21no—
214C2×C4×C11—21no—
215C2×C4×C11—21no—
216C2×C4×C11—42no—
217C2×C4×C11—42no—
218C2×C4×C11—42no—
219C2×C4×C11#13512yescomplemented
220C2×C4×C11C23×C411yescharacteristic
221C2×C4×C11C22×D411yescharacteristic
222C2×C4×C11C22×D411yescharacteristic
223C2×C4×C11C2×#4111yescharacteristic
224C2×C4×C11H(5,𝔽2)11yescharacteristic
225C2×C4×C11H(5,𝔽2)11yescharacteristic
226C2×Dic11—21no—
227C2×Dic11—21no—
228C2×Dic11—21no—
229C2×Dic11—21no—
230C2×Dic11—21no—
231C2×Dic11—21no—
232C2×Dic11—21no—
233C2×Dic11—42no—
234C2×Dic11—42no—
235C2×Dic11—42no—
236C2×Dic11C4×D412yes—
237C2×Dic11#13512yescomplemented
238D44—24no—
239D44—24no—
240D44—416no—
241D44—42no—
242D44—42no—
243C4×D11—22no—
244C4×D11—22no—
245C4×D11—22no—
246C4×D11—22no—
247C4×D11—416no—
248C8×C11—41no—
249C8×C11C2×C22⋊C414yes—
250C11⋊C8—22no—
251C11⋊C8—41no—
252C22×#41—112no—
253C2×#135—118no—
254C2×#135—224no—
255C2×#135—224no—
256C22×Q16C2×D1111yescharacteristic
257C22×SD16—112no—
258C22×D8—111no—
259C23×C8—111no—
260C2×C4×Q8—112no—
261C2×C4×Q8C2×D1112yes—
262C4×Q16—24no—
263C4×Q16—224no—
264C2×#107—111no—
265C2×#107C2×D1111yescharacteristic
266C2×#103—112no—
267C2×#103C2×D1112yes—
268C2×#102—112no—
269C2×#102—112no—
270C2×C22⋊C8—111no—
271C2×C4×C8—111no—
272C2×C4×C8C2×D1111yescharacteristic
273#390—112no—
274#390—112no—
275#390—222no—
276#390—222no—
277#380—112no—
278#380—222no—
279C4×C22⋊C4—111no—
280C4×C22⋊C4—222no—
281#340—112no—
282#336—111no—
283#336—111no—
284C22×C11C2×C4×D411yescharacteristic
285C22×C11D4211yescharacteristic
286C22×C11D4211yescharacteristic
287C22×C11C2×#13511yescharacteristic
288C22×C11C2×#13511yescharacteristic
289C22×C11#57611yescharacteristic
290C22×C11#57811yescharacteristic
291C2×D11—22no—
292C2×D11—22no—
293C2×D11—22no—
294C2×D11—41no—
295C2×D11—41no—
296C2×D11—41no—
297C2×D11—41no—
298C2×D11—44no—
299C2×D11—44no—
300C2×D11—44no—
301C2×D11—82no—
302C2×D11—82no—
303C2×D11—82no—
304C2×D11—82no—
305C4×C11—28no—
306C4×C11—22no—
307C4×C11—41no—
308C4×C11—82no—
309C4×C11C22×C22⋊C411yescharacteristic
310C4×C11#51811yescharacteristic
311C4×C11#54611yescharacteristic
312C4×C11#54611yescharacteristic
313Dic11—22no—
314Dic11—22no—
315Dic11—41no—
316Dic11—82no—
317C2×#41—118no—
318C2×#41—224no—
319C2×#41—224no—
320C2×#41—224no—
321C2×#41—442no—
322C2×#41—442no—
323C22×Q8C22×D1112yes—
324C22×D4—112no—
325C22×D4—222no—
326C23×C4—111no—
327C23×C4—222no—
328#135—2232no—
329C2×Q16C4×D1114yes—
330C2×Q16D4414yes—
331C2×Q16C22⋊D1114yes—
332C2×SD16—118no—
333C2×SD16—224no—
334C2×SD16—224no—
335C2×D8—114no—
336C2×D8—222no—
337C2×D8—222no—
338C22×C8—111no—
339C22×C8—114no—
340C22×C8—111no—
341C22×C8—222no—
342C22×C8—222no—
343C22×C8C22×D1111yescharacteristic
344C22×C8C22×D1111yescharacteristic
345C4×Q8—24no—
346C4×Q8—42no—
347C4×Q8—224no—
348C4×Q8—442no—
349C2×C4⋊C4—22no—
350C2×C4⋊C4—112no—
351C2×C4⋊C4—222no—
352C2×C4⋊C4C22×D1112yes—
353C2×C22⋊C4—111no—
354C2×C22⋊C4—111no—
355C2×C22⋊C4—222no—
356C2×C22⋊C4—222no—
357C2×C22⋊C4—222no—
358C2×C22⋊C4—222no—
359C2×C22⋊C4—222no—
360C2×C42—22no—
361C2×C42—111no—
362C2×C42—222no—
363C2×C42C22×D1111yescharacteristic
364#107—22no—
365#107—222no—
366#103—24no—
367#103—224no—
368#102—442no—
369#102—442no—
370C22⋊C8—222no—
371C4×C8—22no—
372C4×C8—222no—
373#95—111no—
374#95—111no—
375#95—222no—
376C2×C11D4×C22⋊C411yescharacteristic
377C2×C11C4×#13511yescharacteristic
378C2×C11#295111yescharacteristic
379C2×C11#328511yescharacteristic
380C2×C11#328511yescharacteristic
381C2×C11#328711yescharacteristic
382C2×C11#328711yescharacteristic
383D11—42no—
384D11—84no—
385C24—111no—
386C24—222no—
387#41—2216no—
388#41—448no—
389#41—448no—
390#41—448no—
391C2×Q8—22no—
392C2×Q8—22no—
393C2×Q8—22no—
394C2×Q8C2×C4×D1114yes—
395C2×Q8C2×D4414yes—
396C2×Q8C2×C22⋊D1114yes—
397C2×D4—114no—
398C2×D4—228no—
399C2×D4—222no—
400C2×D4—222no—
401C2×D4—222no—
402C2×D4—222no—
403C2×D4—222no—
404C2×D4—444no—
405C2×D4—444no—
406C22×C4—22no—
407C22×C4—22no—
408C22×C4—111no—
409C22×C4—111no—
410C22×C4—112no—
411C22×C4—112no—
412C22×C4—111no—
413C22×C4—228no—
414C22×C4—221no—
415C22×C4—221no—
416C22×C4—221no—
417C22×C4—221no—
418C22×C4—222no—
419C22×C4—444no—
420C22×C4—444no—
421C22×C4D4×D1111yescharacteristic
422C22×C4D4×D1111yescharacteristic
423C22×C4C23×D1111yescharacteristic
424Q16(C2×D11)⋊C4116yescomplemented
425SD16—2216no—
426D8—228no—
427C2×C8—21no—
428C2×C8—21no—
429C2×C8—21no—
430C2×C8—112no—
431C2×C8—221no—
432C2×C8—221no—
433C2×C8—228no—
434C2×C8—221no—
435C2×C8—221no—
436C2×C8—221no—
437C2×C8C2×C4×D1112yes—
438C2×C8C2×D4412yes—
439C2×C8C2×C22⋊D1112yes—
440C4⋊C4—22no—
441C4⋊C4—22no—
442C4⋊C4—44no—
443C4⋊C4—222no—
444C4⋊C4—222no—
445C4⋊C4—444no—
446C22⋊C4—222no—
447C22⋊C4—222no—
448C22⋊C4—444no—
449C22⋊C4—444no—
450C22⋊C4—882no—
451C22⋊C4—882no—
452C22⋊C4—882no—
453C42—21no—
454C42—21no—
455C42—44no—
456C42—221no—
457C42—221no—
458C42—444no—
459C11#2245111yescharacteristic, complemented, Sylow
460C23—112no—
461C23—221no—
462C23—221no—
463C23—221no—
464C23—221no—
465C23—221no—
466C23—221no—
467C23—224no—
468C23—442no—
469C23—442no—
470C23—442no—
471C23—442no—
472C23—442no—
473C23—442no—
474C23C2×D4×D1111yescharacteristic
475Q8—24no—
476Q8—24no—
477Q8—24no—
478Q8C2×(C2×D11)⋊C418yes—
479D4—224no—
480D4—224no—
481D4—4416no—
482D4—442no—
483D4—442no—
484C2×C4—21no—
485C2×C4—24no—
486C2×C4—21no—
487C2×C4—24no—
488C2×C4—24no—
489C2×C4—21no—
490C2×C4—21no—
491C2×C4—21no—
492C2×C4—42no—
493C2×C4—42no—
494C2×C4—42no—
495C2×C4—112no—
496C2×C4—112no—
497C2×C4—221no—
498C2×C4—221no—
499C2×C4—221no—
500C2×C4—221no—
501C2×C4—222no—
502C2×C4—222no—
503C2×C4—222no—
504C2×C4—222no—
505C2×C4—221no—
506C2×C4—221no—
507C2×C4—221no—
508C2×C4—4416no—
509C2×C4—442no—
510C2×C4—442no—
511C2×C4—442no—
512C2×C4#6697212yescomplemented
513C2×C4C22×C4×D1111yescharacteristic
514C2×C4C22×D4411yescharacteristic
515C2×C4#6703711yescharacteristic
516C2×C4#41×D1111yescharacteristic
517C2×C4#6704211yescharacteristic
518C2×C4C22×C22⋊D1111yescharacteristic
519C8—41no—
520C8—222no—
521C8—441no—
522C8C2×(C2×D11)⋊C414yes—
523C22—222no—
524C22—222no—
525C22—222no—
526C22—441no—
527C22—441no—
528C22—441no—
529C22—441no—
530C22—444no—
531C22—444no—
532C22—444no—
533C22—882no—
534C22—882no—
535C22—882no—
536C22—882no—
537C22C4×D4×D1111yescharacteristic
538C22D4×D4411yescharacteristic
539C22C2×#6697211yescharacteristic
540C22#1062329711yescharacteristic
541C22D11×#13511yescharacteristic
542C22#1062330011yescharacteristic
543C22D4×C22⋊D1111yescharacteristic
544C4—22no—
545C4—28no—
546C4—41no—
547C4—82no—
548C4—222no—
549C4—222no—
550C4—441no—
551C4—882no—
552C4#1062307611yescharacteristic
553C4#1062308511yescharacteristic
554C4C22×(C2×D11)⋊C411yescharacteristic
555C4#1062336011yescharacteristic
556C2—442no—
557C2—884no—
558C2D4×(C2×D11)⋊C411yescharacteristic
559C2C4×#6697211yescharacteristic
560C2#1307749111yescharacteristic
561C2#1308035711yescharacteristic
562C2#1308035811yescharacteristic
563C2#1308037011yescharacteristic
564C2#1308037511yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC2×C4×C11×Q16C2
socleC23×C11C22×D4
prime radicalC22×#66972C2
cosocleC22×C4×C11C24
hypercenterC2×C4×Q16D11
hypocenterC11#22451
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×Q16

Complements

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

NH ≅ G/Ntype
2. C2×Q16×Dic11C2semidirect
3. #13071454C2semidirect
4. #13069482C2semidirect
5. #13069480C2semidirect
6. #13068971C2semidirect
7. #13068969C2semidirect
8. #13068642C2semidirect
9. #13068555C2semidirect
10. C8×(C2×D11)⋊C4C2semidirect
11. C2×C4×C11×Q16C2semidirect
19. C2×#66972C4semidirect
143. C11×Q16C22⋊C4semidirect
180. C2×C4×Q16D11semidirect
219. C2×C4×C11#135semidirect
237. C2×Dic11#135semidirect
424. Q16(C2×D11)⋊C4semidirect
459. C11#22451semidirect
512. C2×C4#66972semidirect

Maximal subgroups

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

subgroupindex
C22×#669722
C2×Q16×Dic112
#130714542
#130694822
#130694802
#130689712
#130689692
#130686422
#130685552
C8×(C2×D11)⋊C42
C2×C4×C11×Q162
#2245111