Finite Group Databasebeta

← #14804505

Subgroups — #14804505

Order 2816.

1102 conjugacy classes of subgroups.

The subgroup lattice has 562 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622391C212yesmaximal, complemented
2C2×#10622632C211yesmaximal, characteristic, complemented
3C2×C8×D44C211yesmaximal, characteristic, complemented
4#13073565C211yesmaximal, characteristic, complemented
5#13073529C211yesmaximal, characteristic
6#13069815C212yesmaximal, complemented
7#13069620C212yesmaximal, complemented
8#13069418C211yesmaximal, characteristic, complemented
9#13069379C211yesmaximal, characteristic, complemented
10#13069038C212yesmaximal, complemented
11C4×C11×#102C211yesmaximal, characteristic, complemented
12C2×C4×D4×C11C2211yescharacteristic
13C2×#66991C2212yes—
14C22×#4324C2212yes—
15C2×#66983—21no—
16C22×C8×D11C2212yes—
17C2×#66950C2212yes—
18C2×#66950C2212yes—
19C2×C4×D44C2211yescharacteristic
20C2×#66922C2211yescharacteristic
21C2×C11×#102C2211yescharacteristic
22C2×C11×#102C2211yescharacteristic
23C2×C4×C8×C11C2211yescharacteristic
24C4×C11×C4⋊C4C2211yescharacteristic
25#10622825—21no—
26C2×(C2×D11)⋊C8C2212yes—
27C2×#66880C2212yes—
28C2×#66880C2212yes—
29#10622632—24no—
30#10622600C2212yes—
31C2×#66874C2212yes—
32C2×#66872C2212yes—
33#10622574—22no—
34#10622552—21no—
35#10622548—21no—
36#10622548C2211yescharacteristic
37C2×C4⋊(C11⋊C8)C2211yescharacteristic
38#10622391—28no—
39C8×D44—24no—
40#10622290—22no—
41C11×#340C2211yescharacteristic
42C11×#340C2211yescharacteristic
43#10622167C2212yes—
44C22×D4×C11C2311yescharacteristic
45C23×C4×C11—21no—
46C22×C22⋊D11—22no—
47C22×D44D411yescharacteristic
48C22×C4×D11C2312yes—
49C22×Dic22C2312yes—
50C22×C8×C11C2311yescharacteristic
51C22×C8×C11C2311yescharacteristic
52C4×D4×C11—22no—
53C4×D4×C11—22no—
54C2×C11×C4⋊C4C2311yescharacteristic
55C2×C11×C4⋊C4C2311yescharacteristic
56C2×C11×C4⋊C4C2311yescharacteristic
57C2×C11×C22⋊C4—21no—
58C2×C42×C11—21no—
59C2×C42×C11C2311yescharacteristic
60C2×C22⋊Dic11—22no—
61#66991—24no—
62#66991—42no—
63C2×#4324—24no—
64C2×#4324—24no—
65C2×#4324—42no—
66#66983—44no—
67C2×(C2×D11)⋊C4—22no—
68C2×(C2×D11)⋊C4—22no—
69C2×(C2×D11)⋊C4—22no—
70C2×(C2×D11)⋊C4D412yes—
71C2×C4⋊Dic11—21no—
72C2×C4⋊Dic11—21no—
73C2×C4⋊Dic11—21no—
74C2×C4⋊Dic11—22no—
75C2×C4⋊Dic11—22no—
76C2×C4⋊Dic11—21no—
77C2×C4⋊Dic11D411yescharacteristic
78C2×C4⋊Dic11C2312yes—
79C22×C11⋊C8C2312yes—
80C2×C8×D11—24no—
81C2×C8×D11—24no—
82C2×C8×D11—42no—
83#66950—24no—
84#66950—24no—
85#66950—42no—
86#66950—42no—
87C4×D44—22no—
88C4×D44—22no—
89#66922—22no—
90#66922—22no—
91C11×#102—22no—
92C11×#102D414yescomplemented
93C4×C8×C11—22no—
94C11×#95—21no—
95C11⋊#95—22no—
96(C2×D11)⋊C8—24no—
97#66880—24no—
98#66880—42no—
99#66874—24no—
100#66872—24no—
101C4⋊(C11⋊C8)D414yescomplemented
102#25385—111nomaximal, Sylow
103C24×C11—21no—
104C23×D11C2×D412yes—
105C2×D4×C11—21no—
106C2×D4×C11—21no—
107C2×D4×C11—21no—
108C2×D4×C11—21no—
109C2×D4×C11—21no—
110C2×D4×C11C2×D412yes—
111C22×C4×C11—21no—
112C22×C4×C11—21no—
113C22×C4×C11—21no—
114C22×C4×C11—42no—
115C22×C4×C11—42no—
116C22×C4×C11—42no—
117C22×C4×C11C2×D411yescharacteristic
118C22×C4×C11C2×D411yescharacteristic
119C22×C4×C11C2411yescharacteristic
120C2×C22⋊D11—44no—
121C2×C22⋊D11—44no—
122C2×C22⋊D11—82no—
123C22×Dic11—22no—
124C22×Dic11—22no—
125C22×Dic11C2×D412yes—
126C2×D44—22no—
127C2×D44—22no—
128C2×D44SD1614yescomplemented
129C2×C4×D11—22no—
130C2×C4×D11—22no—
131C2×C4×D11—22no—
132C2×C4×D11—22no—
133C2×C4×D11—22no—
134C2×C4×D11—22no—
135C2×Dic22—22no—
136C2×Dic22—22no—
137C2×Dic22—22no—
138C2×Dic22—22no—
139C2×Dic22—22no—
140C2×Dic22—22no—
141C2×C8×C11—21no—
142C2×C8×C11—21no—
143C2×C8×C11—21no—
144C2×C8×C11—21no—
145C2×C8×C11—21no—
146C2×C8×C11C2×D412yes—
147C11×C4⋊C4—21no—
148C11×C4⋊C4—21no—
149C11×C4⋊C4—21no—
150C11×C4⋊C4—21no—
151C11×C4⋊C4C2×D412yes—
152C11×C4⋊C4#4112yes—
153C11×C22⋊C4—42no—
154C42×C11—42no—
155C42×C11C2×D412yes—
156C42×C11#4112yes—
157C22⋊Dic11—44no—
158#4324—48no—
159(C2×D11)⋊C4—24no—
160(C2×D11)⋊C4—44no—
161(C2×D11)⋊C4—44no—
162(C2×D11)⋊C4—44no—
163C4⋊Dic11—22no—
164C4⋊Dic11—22no—
165C4⋊Dic11—22no—
166C4⋊Dic11—44no—
167C4⋊Dic11—44no—
168C4⋊Dic11—42no—
169C4⋊Dic11—42no—
170C4⋊Dic11—42no—
171C4⋊Dic11—81no—
172C2×C11⋊C8—22no—
173C2×C11⋊C8—22no—
174C2×C11⋊C8C2×D414yes—
175C8×D11—48no—
176C2×#465—112no—
177C2×#461—111no—
178C2×C8×D4—111no—
179#2542—111no—
180#2537—111no—
181#2035—112no—
182#2000—112no—
183#1956—111no—
184#1948—111no—
185#1892—112no—
186C4×#102D1111yescharacteristic, complemented
187C23×C11—22no—
188C23×C11—41no—
189C23×C11—41no—
190C23×C11—41no—
191C23×C11—41no—
192C23×C11—41no—
193C23×C11—41no—
194C23×C11C22×D411yescharacteristic
195C22×D11—22no—
196C22×D11—22no—
197C22×D11—22no—
198C22×D11—22no—
199C22×D11—22no—
200C22×D11—22no—
201C22×D11C2×SD1614yes—
202D4×C11—22no—
203D4×C11—22no—
204D4×C11—41no—
205D4×C11—41no—
206C2×C4×C11—21no—
207C2×C4×C11—21no—
208C2×C4×C11—22no—
209C2×C4×C11—22no—
210C2×C4×C11—41no—
211C2×C4×C11—41no—
212C2×C4×C11—41no—
213C2×C4×C11—41no—
214C2×C4×C11—41no—
215C2×C4×C11—41no—
216C2×C4×C11—41no—
217C2×C4×C11—84no—
218C2×C4×C11#12112yes—
219C2×C4×C11#12112yes—
220C2×C4×C11C2×SD1612yes—
221C2×C4×C11#13512yes—
222C2×C4×C11C22×D411yescharacteristic
223C2×C4×C11C22×D411yescharacteristic
224C2×C4×C11C2×#4111yescharacteristic
225C2×C4×C11C2×#4111yescharacteristic
226C2×C4×C11H(5,𝔽2)11yescharacteristic
227C2×C4×C11H(5,𝔽2)11yescharacteristic
228C22⋊D11—88no—
229C2×Dic11—22no—
230C2×Dic11—22no—
231C2×Dic11—22no—
232C2×Dic11—42no—
233C2×Dic11—42no—
234C2×Dic11—42no—
235C2×Dic11—42no—
236C2×Dic11—42no—
237C2×Dic11—42no—
238D44—28no—
239C4×D11—42no—
240C4×D11—42no—
241C4×D11—42no—
242C4×D11—42no—
243Dic22—42no—
244Dic22—42no—
245Dic22—42no—
246Dic22—42no—
247C8×C11—22no—
248C8×C11—41no—
249C11⋊C8—24no—
250C22×SD16—112no—
251C23×C8—112no—
252C2×C4⋊Q8—111no—
253C2×C22⋊Q8—112no—
254C2×C22⋊Q8—112no—
255C2×#121—112no—
256C2×#121—221no—
257C2×C4×D4—111no—
258C2×C4×D4C2×D1111yescharacteristic
259#465—228no—
260#461—224no—
261C8×D4—224no—
262C2×#106—112no—
263C2×C4⋊C8—111no—
264C2×#103—112no—
265C2×#103—112no—
266C2×#103—112no—
267C2×#102C2×D1111yescharacteristic
268C2×#102C2×D1111yescharacteristic
269C2×C22⋊C8—112no—
270C2×C4×C8C2×D1111yescharacteristic
271#399—222no—
272#394—222no—
273#390—221no—
274#384—111no—
275#384—221no—
276#380—112no—
277#380—221no—
278C4×C4⋊C4C2×D1111yescharacteristic
279#340—112no—
280#340C2×D1111yescharacteristic
281#340C2×D1111yescharacteristic
282C22×C11—42no—
283C22×C11—42no—
284C22×C11—42no—
285C22×C11—81no—
286C22×C11—81no—
287C22×C11—81no—
288C22×C11—81no—
289C22×C11C2×#12111yescharacteristic
290C22×C11D4211yescharacteristic
291C22×C11#54611yescharacteristic
292C22×C11C22×SD1611yescharacteristic
293C22×C11C2×#13511yescharacteristic
294C22×C11#57711yescharacteristic
295C22×C11#57811yescharacteristic
296C2×D11—24no—
297C2×D11—24no—
298C2×D11—24no—
299C2×D11—42no—
300C2×D11—42no—
301C2×D11—42no—
302C2×D11—42no—
303C4×C11—22no—
304C4×C11—42no—
305C4×C11—42no—
306C4×C11—81no—
307C4×C11#46514yescomplemented
308C4×C11#53211yescharacteristic
309C4×C11#54011yescharacteristic
310C4×C11D4211yescharacteristic
311C4×C11#55011yescharacteristic
312Dic11—42no—
313Dic11—82no—
314Dic11—82no—
315C22×Q8—112no—
316C22×D4—111no—
317C22×D4—222no—
318C22×D4C22×D1111yescharacteristic
319C23×C4—21no—
320C23×C4—112no—
321C2×SD16—224no—
322C2×SD16—224no—
323C2×SD16—442no—
324C22×C8—112no—
325C22×C8—224no—
326C22×C8—224no—
327C22×C8—442no—
328C22×C8C22×D1111yescharacteristic
329C22×C8C22×D1111yescharacteristic
330C4⋊Q8—222no—
331C4⋊Q8—222no—
332C22⋊Q8—224no—
333C22⋊Q8—224no—
334C22⋊Q8—442no—
335C22⋊Q8—442no—
336#121—224no—
337#121—442no—
338#121—444no—
339C4×D4—22no—
340C4×D4—22no—
341C4×D4—222no—
342C4×D4—222no—
343C2×C4⋊C4—111no—
344C2×C4⋊C4—112no—
345C2×C4⋊C4—222no—
346C2×C4⋊C4—222no—
347C2×C4⋊C4—221no—
348C2×C4⋊C4—221no—
349C2×C4⋊C4—221no—
350C2×C4⋊C4—221no—
351C2×C4⋊C4C22×D1111yescharacteristic
352C2×C4⋊C4C22×D1111yescharacteristic
353C2×C4⋊C4C22×D1111yescharacteristic
354C2×C22⋊C4—21no—
355C2×C22⋊C4—112no—
356C2×C22⋊C4—222no—
357C2×C22⋊C4—222no—
358C2×C22⋊C4—222no—
359C2×C22⋊C4—222no—
360C2×C42—21no—
361C2×C42C22×D1111yescharacteristic
362#106—224no—
363C4⋊C8—114no—
364#103—224no—
365#103—224no—
366#103—442no—
367#102—22no—
368#102D4414yescomplemented
369C22⋊C8—224no—
370C4×C8—22no—
371#95—21no—
372#95—222no—
373C2×C11—82no—
374C2×C11#242811yescharacteristic
375C2×C11C2×#46511yescharacteristic
376C2×C11#306311yescharacteristic
377C2×C11D4×SD1611yescharacteristic
378C2×C11#328311yescharacteristic
379C2×C11#329811yescharacteristic
380C2×C11#330311yescharacteristic
381D11—44no—
382C24—21no—
383C24—112no—
384C2×Q8—222no—
385C2×Q8—222no—
386C2×Q8—222no—
387C2×Q8—222no—
388C2×Q8—222no—
389C2×Q8—222no—
390C2×D4—21no—
391C2×D4—21no—
392C2×D4—21no—
393C2×D4—21no—
394C2×D4—21no—
395C2×D4—114no—
396C2×D4—222no—
397C2×D4—222no—
398C2×D4—444no—
399C2×D4—444no—
400C2×D4—882no—
401C2×D4C2×D4412yes—
402C22×C4—21no—
403C22×C4—21no—
404C22×C4—21no—
405C22×C4—42no—
406C22×C4—42no—
407C22×C4—42no—
408C22×C4—112no—
409C22×C4—222no—
410C22×C4—222no—
411C22×C4—222no—
412C22×C4—222no—
413C22×C4—222no—
414C22×C4—222no—
415C22×C4—222no—
416C22×C4—222no—
417C22×C4D4×D1111yescharacteristic
418C22×C4D4×D1111yescharacteristic
419C22×C4C23×D1111yescharacteristic
420SD16—448no—
421C2×C8—21no—
422C2×C8—21no—
423C2×C8—21no—
424C2×C8—21no—
425C2×C8—21no—
426C2×C8—114no—
427C2×C8—222no—
428C2×C8—222no—
429C2×C8—448no—
430C2×C8C2×D4412yes—
431C4⋊C4—21no—
432C4⋊C4—21no—
433C4⋊C4—21no—
434C4⋊C4—21no—
435C4⋊C4—222no—
436C4⋊C4—222no—
437C4⋊C4—222no—
438C4⋊C4—444no—
439C4⋊C4—444no—
440C4⋊C4—442no—
441C4⋊C4—442no—
442C4⋊C4—442no—
443C4⋊C4—881no—
444C4⋊C4C2×D4412yes—
445C4⋊C4#433912yes—
446C22⋊C4—42no—
447C22⋊C4—224no—
448C22⋊C4—444no—
449C22⋊C4—444no—
450C22⋊C4—444no—
451C22⋊C4—444no—
452C42—42no—
453C42#433912yes—
454C42D4×D1112yes—
455C11#2538511yescharacteristic, complemented, Sylow
456C23—22no—
457C23—41no—
458C23—41no—
459C23—41no—
460C23—41no—
461C23—41no—
462C23—41no—
463C23—114no—
464C23—222no—
465C23—222no—
466C23—222no—
467C23—222no—
468C23—222no—
469C23—222no—
470C23C2×D4×D1111yescharacteristic
471Q8—442no—
472Q8—442no—
473Q8—442no—
474Q8—442no—
475D4—22no—
476D4—22no—
477D4—41no—
478D4—41no—
479D4—228no—
480D4—888no—
481C2×C4—21no—
482C2×C4—21no—
483C2×C4—22no—
484C2×C4—22no—
485C2×C4—41no—
486C2×C4—41no—
487C2×C4—41no—
488C2×C4—41no—
489C2×C4—41no—
490C2×C4—41no—
491C2×C4—41no—
492C2×C4—84no—
493C2×C4—222no—
494C2×C4—222no—
495C2×C4—222no—
496C2×C4—442no—
497C2×C4—442no—
498C2×C4—442no—
499C2×C4—442no—
500C2×C4—442no—
501C2×C4—442no—
502C2×C4—442no—
503C2×C4—442no—
504C2×C4—442no—
505C2×C4—442no—
506C2×C4#6693712yes—
507C2×C4#6693712yes—
508C2×C4#6696512yes—
509C2×C4SD16×D1112yes—
510C2×C4C22×D4411yescharacteristic
511C2×C4C2×#433911yescharacteristic
512C2×C4C2×#433911yescharacteristic
513C2×C4C2×D4×D1111yescharacteristic
514C2×C4#6704211yescharacteristic
515C2×C4#6704211yescharacteristic
516C8—22no—
517C8—41no—
518C8—224no—
519C22—42no—
520C22—42no—
521C22—42no—
522C22—81no—
523C22—81no—
524C22—81no—
525C22—81no—
526C22—224no—
527C22—224no—
528C22—224no—
529C22—442no—
530C22—442no—
531C22—442no—
532C22—442no—
533C22C2×#6693711yescharacteristic
534C22D4×D4411yescharacteristic
535C22#1062308111yescharacteristic
536C22C2×#6696511yescharacteristic
537C22C2×SD16×D1111yescharacteristic
538C22#1062330111yescharacteristic
539C22#1062330211yescharacteristic
540C4—22no—
541C4—42no—
542C4—42no—
543C4—81no—
544C4—442no—
545C4—882no—
546C4—882no—
547C4#1062239114yescomplemented
548C4#1062300811yescharacteristic
549C4#1062306611yescharacteristic
550C4D4×D4411yescharacteristic
551C4#1062308411yescharacteristic
552C2—82no—
553C2—444no—
554C2#1307220411yescharacteristic
555C2C2×#1062239111yescharacteristic
556C2#1307831011yescharacteristic
557C2SD16×D4411yescharacteristic
558C2#1308033711yescharacteristic
559C2#1308048311yescharacteristic
560C2#1308054611yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC4×C11×#102C2
socleC23×C11C22×D4
prime radical#13073529C2
hypercenterC4×#102D11
hypocenterC11#25385
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C4×#102

Complements

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

NH ≅ G/Ntype
1. C2×#10622391C2semidirect
2. C2×#10622632C2semidirect
3. C2×C8×D44C2semidirect
4. #13073565C2semidirect
6. #13069815C2semidirect
7. #13069620C2semidirect
8. #13069418C2semidirect
9. #13069379C2semidirect
10. #13069038C2semidirect
11. C4×C11×#102C2semidirect
92. C11×#102D4semidirect
101. C4⋊(C11⋊C8)D4semidirect
128. C2×D44SD16semidirect
186. C4×#102D11semidirect
307. C4×C11#465semidirect
368. #102D44semidirect
455. C11#25385semidirect
547. C4#10622391semidirect

Maximal subgroups

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

subgroupindex
C2×#106223912
C2×#106226322
C2×C8×D442
#130735652
#130735292
#130698152
#130696202
#130694182
#130693792
#130690382
C4×C11×#1022
#2538511