Finite Group Databasebeta

← #14804506

Subgroups — #14804506

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×#10622420C212yesmaximal, complemented
2C2×#10622696C211yesmaximal, characteristic, complemented
3C2×C8×D44C211yesmaximal, characteristic, complemented
4#13073570C211yesmaximal, characteristic, complemented
5#13073532C211yesmaximal, characteristic
6#13069810C212yesmaximal, complemented
7#13069618C212yesmaximal, complemented
8#13069377C211yesmaximal, characteristic, complemented
9#13069036C212yesmaximal, complemented
10C4×#66885C211yesmaximal, characteristic, complemented
11C11×#1956C211yesmaximal, characteristic, complemented
12C2×C11×C4⋊Q8C2211yescharacteristic
13C2×#66999C2212yes—
14C2×#66999C2212yes—
15C22×#4325C2212yes—
16C22×C8×D11C2212yes—
17C2×#66948—21no—
18C2×#66948C2212yes—
19C2×C4×D44C2211yescharacteristic
20C2×C4×D44C2211yescharacteristic
21C2×C11×#103C2212yes—
22C2×C11×#103C2212yes—
23C2×C4×C8×C11C2211yescharacteristic
24C11×#384C2211yescharacteristic
25C2×#66899C2212yes—
26C2×#66885C2211yescharacteristic
27C2×#66885C2211yescharacteristic
28C2×(C2×D11)⋊C8C2212yes—
29#10622696—24no—
30#10622605—22no—
31#10622604—22no—
32#10622601—21no—
33#10622600—21no—
34#10622600C2212yes—
35#10622589—21no—
36C2×#66872C2212yes—
37C4×C4⋊Dic11C2211yescharacteristic
38C2×C4⋊(C11⋊C8)C2211yescharacteristic
39#10622420—28no—
40C8×D44—24no—
41#10622189C2211yescharacteristic
42#10622189C2211yescharacteristic
43#10622167C2212yes—
44C22×Q8×C11C2312yes—
45C22×D44—22no—
46C22×D44D411yescharacteristic
47C22×D44C2311yescharacteristic
48C22×C4×D11—21no—
49C22×C4×D11C2312yes—
50C22×C8×C11C2311yescharacteristic
51C22×C8×C11C2311yescharacteristic
52C11×C4⋊Q8—22no—
53C11×C4⋊Q8—22no—
54C2×C11×C4⋊C4—21no—
55C2×C11×C4⋊C4—21no—
56C2×C11×C4⋊C4—21no—
57C2×C11×C4⋊C4—21no—
58C2×C11×C4⋊C4C2312yes—
59C2×C42×C11C2311yescharacteristic
60#66999—24no—
61#66999—24no—
62#66999—42no—
63#66999—42no—
64C2×#4325—24no—
65C2×#4325—24no—
66C2×#4325—42no—
67C2×(C2×D11)⋊C4—22no—
68C2×(C2×D11)⋊C4—22no—
69C2×(C2×D11)⋊C4—22no—
70C2×(C2×D11)⋊C4—21no—
71C2×(C2×D11)⋊C4—22no—
72C2×(C2×D11)⋊C4D412yes—
73C2×C4⋊Dic11D411yescharacteristic
74C2×C4⋊Dic11C2311yescharacteristic
75C2×C4⋊Dic11C2311yescharacteristic
76C2×C4⋊Dic11C2311yescharacteristic
77C2×Dic11⋊C4—22no—
78C2×Dic11⋊C4—22no—
79C2×C4×Dic11—21no—
80C22×C11⋊C8C2312yes—
81C2×C8×D11—24no—
82C2×C8×D11—24no—
83C2×C8×D11—42no—
84#66948—24no—
85#66948—42no—
86#66948—44no—
87C4×D44—22no—
88C4×D44—22no—
89C4×D44—22no—
90C4×D44—22no—
91C11×#103—24no—
92C11×#103—42no—
93C4×C8×C11—22no—
94#66899—24no—
95C11⋊#95—21no—
96C11⋊#95—22no—
97#66885—22no—
98#66885D414yescomplemented
99(C2×D11)⋊C8—24no—
100#66872—24no—
101C4⋊(C11⋊C8)D414yescomplemented
102#25385—111nomaximal, Sylow
103C23×D11—21no—
104C23×D11C2×D412yes—
105C2×Q8×C11—22no—
106C2×Q8×C11—22no—
107C2×Q8×C11—22no—
108C2×Q8×C11—22no—
109C2×Q8×C11—22no—
110C2×Q8×C11—22no—
111C22×C4×C11—22no—
112C22×C4×C11—22no—
113C22×C4×C11C2×D411yescharacteristic
114C22×C4×C11C2×D411yescharacteristic
115C22×C4×C11C2411yescharacteristic
116C22×Dic11—21no—
117C22×Dic11—21no—
118C22×Dic11—21no—
119C22×Dic11C2×D412yes—
120C2×D44—22no—
121C2×D44—22no—
122C2×D44—21no—
123C2×D44—21no—
124C2×D44—21no—
125C2×D44—21no—
126C2×D44—21no—
127C2×D44—44no—
128C2×D44—44no—
129C2×D44—82no—
130C2×D44SD1614yescomplemented
131C2×D44C2×D412yes—
132C2×C4×D11—22no—
133C2×C4×D11—22no—
134C2×C4×D11—22no—
135C2×C4×D11—22no—
136C2×C4×D11—22no—
137C2×C4×D11—22no—
138C2×C4×D11—42no—
139C2×C4×D11—42no—
140C2×C4×D11—42no—
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—22no—
148C11×C4⋊C4—22no—
149C11×C4⋊C4—42no—
150C11×C4⋊C4—42no—
151C11×C4⋊C4—42no—
152C11×C4⋊C4—81no—
153C42×C11C2×D412yes—
154C42×C11#4112yes—
155#4325—48no—
156(C2×D11)⋊C4—24no—
157(C2×D11)⋊C4—44no—
158(C2×D11)⋊C4—44no—
159(C2×D11)⋊C4—44no—
160(C2×D11)⋊C4—44no—
161(C2×D11)⋊C4—42no—
162C4⋊Dic11—22no—
163C4⋊Dic11—21no—
164C4⋊Dic11—21no—
165C4⋊Dic11—21no—
166C4⋊Dic11—21no—
167C4⋊Dic11C2×D412yes—
168C4⋊Dic11#4112yes—
169Dic11⋊C4—44no—
170Dic11⋊C4—44no—
171C4×Dic11—42no—
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#1956D1111yescharacteristic, complemented
184#1948—111no—
185#1892—112no—
186C4×#102—111no—
187C23×C11C22×D411yescharacteristic
188C22×D11—22no—
189C22×D11—22no—
190C22×D11—22no—
191C22×D11—22no—
192C22×D11—22no—
193C22×D11—22no—
194C22×D11—22no—
195C22×D11—41no—
196C22×D11—41no—
197C22×D11—41no—
198C22×D11—41no—
199C22×D11—41no—
200C22×D11—41no—
201C22×D11C2×SD1614yes—
202Q8×C11—42no—
203Q8×C11—42no—
204Q8×C11—42no—
205Q8×C11—42no—
206C2×C4×C11—21no—
207C2×C4×C11—21no—
208C2×C4×C11—42no—
209C2×C4×C11—42no—
210C2×C4×C11—42no—
211C2×C4×C11—42no—
212C2×C4×C11—42no—
213C2×C4×C11—42no—
214C2×C4×C11#12112yes—
215C2×C4×C11#12112yes—
216C2×C4×C11C2×SD1612yes—
217C2×C4×C11#13512yes—
218C2×C4×C11C22×D411yescharacteristic
219C2×C4×C11C22×D411yescharacteristic
220C2×C4×C11C2×#4111yescharacteristic
221C2×C4×C11C2×#4111yescharacteristic
222C2×C4×C11H(5,𝔽2)11yescharacteristic
223C2×C4×C11H(5,𝔽2)11yescharacteristic
224C2×Dic11—22no—
225C2×Dic11—22no—
226C2×Dic11—22no—
227C2×Dic11—22no—
228C2×Dic11—22no—
229C2×Dic11—41no—
230C2×Dic11—41no—
231C2×Dic11—41no—
232C2×Dic11—41no—
233C2×Dic11—41no—
234C2×Dic11—41no—
235C2×Dic11—41no—
236D44—22no—
237D44—22no—
238D44—28no—
239D44—41no—
240D44—41no—
241D44—88no—
242C4×D11—42no—
243C4×D11—42no—
244C4×D11—42no—
245C4×D11—42no—
246C4×D11—84no—
247C8×C11—22no—
248C8×C11—41no—
249C11⋊C8—24no—
250C22×SD16—112no—
251C23×C8—112no—
252C2×C4⋊Q8C2×D1111yescharacteristic
253C2×C22⋊Q8—112no—
254C2×C22⋊Q8—112no—
255C2×#121—112no—
256C2×#121—221no—
257C2×C4×D4—111no—
258C2×C4×D4—111no—
259#465—228no—
260#461—224no—
261C8×D4—224no—
262C2×#106—112no—
263C2×C4⋊C8—111no—
264C2×#103—112no—
265C2×#103C2×D1112yes—
266C2×#103C2×D1112yes—
267C2×#102—111no—
268C2×#102—111no—
269C2×C22⋊C8—112no—
270C2×C4×C8C2×D1111yescharacteristic
271#399—222no—
272#394—222no—
273#390—221no—
274#384—221no—
275#384C2×D1111yescharacteristic
276#380—112no—
277#380—221no—
278C4×C4⋊C4—111no—
279#340—111no—
280#340—111no—
281#340—112no—
282C22×C11C2×#12111yescharacteristic
283C22×C11D4211yescharacteristic
284C22×C11#54611yescharacteristic
285C22×C11C22×SD1611yescharacteristic
286C22×C11C2×#13511yescharacteristic
287C22×C11#57711yescharacteristic
288C22×C11#57811yescharacteristic
289C2×D11—24no—
290C2×D11—24no—
291C2×D11—24no—
292C2×D11—42no—
293C2×D11—42no—
294C2×D11—42no—
295C2×D11—42no—
296C2×D11—42no—
297C2×D11—42no—
298C2×D11—42no—
299C2×D11—81no—
300C2×D11—81no—
301C2×D11—81no—
302C2×D11—81no—
303C4×C11—22no—
304C4×C11—82no—
305C4×C11—82no—
306C4×C11#46514yescomplemented
307C4×C11#53211yescharacteristic
308C4×C11#54011yescharacteristic
309C4×C11D4211yescharacteristic
310C4×C11#55011yescharacteristic
311Dic11—42no—
312Dic11—42no—
313Dic11—42no—
314Dic11—81no—
315C22×Q8C22×D1112yes—
316C22×D4—111no—
317C22×D4—111no—
318C22×D4—222no—
319C23×C4—112no—
320C23×C4—221no—
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—22no—
331C4⋊Q8—22no—
332C22⋊Q8—224no—
333C22⋊Q8—224no—
334C22⋊Q8—442no—
335C22⋊Q8—442no—
336#121—224no—
337#121—442no—
338#121—444no—
339C4×D4—222no—
340C4×D4—222no—
341C4×D4—222no—
342C4×D4—222no—
343C2×C4⋊C4—21no—
344C2×C4⋊C4—21no—
345C2×C4⋊C4—21no—
346C2×C4⋊C4—21no—
347C2×C4⋊C4—111no—
348C2×C4⋊C4—111no—
349C2×C4⋊C4—111no—
350C2×C4⋊C4—111no—
351C2×C4⋊C4—222no—
352C2×C4⋊C4—222no—
353C2×C4⋊C4C22×D1112yes—
354C2×C22⋊C4—112no—
355C2×C22⋊C4—222no—
356C2×C22⋊C4—222no—
357C2×C22⋊C4—222no—
358C2×C22⋊C4—222no—
359C2×C22⋊C4—221no—
360C2×C42—221no—
361C2×C42C22×D1111yescharacteristic
362#106—224no—
363C4⋊C8—114no—
364#103—24no—
365#103—42no—
366#103—224no—
367#102—114no—
368#102—222no—
369C22⋊C8—224no—
370C4×C8—22no—
371#95—222no—
372#95—221no—
373C2×C11#242811yescharacteristic
374C2×C11C2×#46511yescharacteristic
375C2×C11#306311yescharacteristic
376C2×C11D4×SD1611yescharacteristic
377C2×C11#328311yescharacteristic
378C2×C11#329811yescharacteristic
379C2×C11#330311yescharacteristic
380D11—44no—
381D11—82no—
382C24—112no—
383C24—221no—
384C2×Q8—22no—
385C2×Q8—22no—
386C2×Q8—22no—
387C2×Q8—22no—
388C2×Q8—22no—
389C2×Q8—22no—
390C2×D4—114no—
391C2×D4—112no—
392C2×D4—222no—
393C2×D4—222no—
394C2×D4—221no—
395C2×D4—221no—
396C2×D4—221no—
397C2×D4—221no—
398C2×D4—221no—
399C2×D4—444no—
400C2×D4—444no—
401C2×D4—882no—
402C22×C4—22no—
403C22×C4—22no—
404C22×C4—112no—
405C22×C4—221no—
406C22×C4—221no—
407C22×C4—222no—
408C22×C4—222no—
409C22×C4—222no—
410C22×C4—222no—
411C22×C4—222no—
412C22×C4—222no—
413C22×C4—221no—
414C22×C4—442no—
415C22×C4—442no—
416C22×C4—442no—
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×C8D4×D1112yes—
431C4⋊C4—22no—
432C4⋊C4—22no—
433C4⋊C4—42no—
434C4⋊C4—42no—
435C4⋊C4—42no—
436C4⋊C4—81no—
437C4⋊C4—112no—
438C4⋊C4—112no—
439C4⋊C4—222no—
440C4⋊C4—221no—
441C4⋊C4—221no—
442C4⋊C4—221no—
443C4⋊C4—221no—
444C4⋊C4—444no—
445C4⋊C4—444no—
446C22⋊C4—224no—
447C22⋊C4—444no—
448C22⋊C4—444no—
449C22⋊C4—444no—
450C22⋊C4—444no—
451C22⋊C4—442no—
452C42—442no—
453C42#433912yes—
454C42D4×D1112yes—
455C11#2538511yescharacteristic, complemented, Sylow
456C23—114no—
457C23—222no—
458C23—222no—
459C23—222no—
460C23—222no—
461C23—222no—
462C23—222no—
463C23—222no—
464C23—441no—
465C23—441no—
466C23—441no—
467C23—441no—
468C23—441no—
469C23—441no—
470C23C2×D4×D1111yescharacteristic
471Q8—42no—
472Q8—42no—
473Q8—42no—
474Q8—42no—
475D4—222no—
476D4—222no—
477D4—228no—
478D4—441no—
479D4—441no—
480D4—888no—
481C2×C4—21no—
482C2×C4—21no—
483C2×C4—42no—
484C2×C4—42no—
485C2×C4—42no—
486C2×C4—42no—
487C2×C4—42no—
488C2×C4—42no—
489C2×C4—222no—
490C2×C4—222no—
491C2×C4—222no—
492C2×C4—222no—
493C2×C4—222no—
494C2×C4—441no—
495C2×C4—441no—
496C2×C4—441no—
497C2×C4—441no—
498C2×C4—442no—
499C2×C4—442no—
500C2×C4—442no—
501C2×C4—442no—
502C2×C4—441no—
503C2×C4—441no—
504C2×C4—441no—
505C2×C4—884no—
506C2×C4#6693712yes—
507C2×C4#6693712yes—
508C2×C4SD16×D1112yes—
509C2×C4#6697212yes—
510C2×C4C2×#433911yescharacteristic
511C2×C4C2×D4×D1111yescharacteristic
512C2×C4C2×D4×D1111yescharacteristic
513C2×C4#6703711yescharacteristic
514C2×C4#41×D1111yescharacteristic
515C2×C4#6704211yescharacteristic
516C8—22no—
517C8—41no—
518C8—224no—
519C22—224no—
520C22—224no—
521C22—224no—
522C22—442no—
523C22—442no—
524C22—442no—
525C22—442no—
526C22—442no—
527C22—442no—
528C22—442no—
529C22—881no—
530C22—881no—
531C22—881no—
532C22—881no—
533C22C2×#6693711yescharacteristic
534C22#1062320711yescharacteristic
535C22#1062324811yescharacteristic
536C22C2×SD16×D1111yescharacteristic
537C22#1062329311yescharacteristic
538C22C2×#6697211yescharacteristic
539C22#1062329711yescharacteristic
540C4—22no—
541C4—82no—
542C4—82no—
543C4—442no—
544C4—442no—
545C4—442no—
546C4—881no—
547C4#1062242014yescomplemented
548C4#1062307911yescharacteristic
549C4#1062309311yescharacteristic
550C4#1062313011yescharacteristic
551C4#1062314011yescharacteristic
552C2—444no—
553C2—882no—
554C2#1307220511yescharacteristic
555C2C2×#1062242011yescharacteristic
556C2#1307830511yescharacteristic
557C2#1308031111yescharacteristic
558C2#1308033611yescharacteristic
559C2#1308048011yescharacteristic
560C2#1308054311yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1956C2
socleC23×C11C22×D4
prime radical#13073532C2
hypercenter#1956D11
hypocenterC11#25385
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1956

Complements

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

NH ≅ G/Ntype
1. C2×#10622420C2semidirect
2. C2×#10622696C2semidirect
3. C2×C8×D44C2semidirect
4. #13073570C2semidirect
6. #13069810C2semidirect
7. #13069618C2semidirect
8. #13069377C2semidirect
9. #13069036C2semidirect
10. C4×#66885C2semidirect
11. C11×#1956C2semidirect
98. #66885D4semidirect
101. C4⋊(C11⋊C8)D4semidirect
130. C2×D44SD16semidirect
183. #1956D11semidirect
306. C4×C11#465semidirect
455. C11#25385semidirect
547. C4#10622420semidirect

Maximal subgroups

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

subgroupindex
C2×#106224202
C2×#106226962
C2×C8×D442
#130735702
#130735322
#130698102
#130696182
#130693772
#130690362
C4×#668852
C11×#19562
#2538511