Finite Group Databasebeta

← #14810429

Subgroups — #14810429

Order 2816.

1320 conjugacy classes of subgroups.

The subgroup lattice has 576 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66941C211yesmaximal, characteristic, complemented
2C2×#10622378C212yesmaximal, complemented
3#13076915C211yesmaximal, characteristic
4#13069756C212yesmaximal, complemented
5#13069750C212yesmaximal, complemented
6#13069587C212yesmaximal, complemented
7#13068934C211yesmaximal, characteristic
8#13068923C211yesmaximal, characteristic, complemented
9#13068921C211yesmaximal, characteristic, complemented
10#13068380C211yesmaximal, characteristic, complemented
11C11×#1874C211yesmaximal, characteristic
12C23×Dic22—21no—
13C2×C11×#121C2211yescharacteristic
14C22×C11×C4⋊C4C2211yescharacteristic
15C2×#66989C2211yescharacteristic
16C22×C4⋊Dic11C2211yescharacteristic
17C2×#66977C2211yescharacteristic
18C22×Dic11⋊C4—21no—
19C22×C4×Dic11C2211yescharacteristic
20C2×#66941—21no—
21C2×#66941—21no—
22C2×#66941—28no—
23C2×#66941C2212yes—
24C2×#66941C2212yes—
25C2×C11×#102C2212yes—
26C2×C11×C22⋊C8C2211yescharacteristic
27#10622834C2211yescharacteristic
28#10622833—21no—
29#10622833—21no—
30C2×#66896C2212yes—
31C2×C22⋊(C11⋊C8)C2211yescharacteristic
32C2×#66880C2212yes—
33C2×#66879C2212yes—
34#10622590C2211yescharacteristic
35#10622587C2211yescharacteristic
36C2×#66874C2212yes—
37#10622558—21no—
38#10622558—21no—
39#10622378—28no—
40C11×#340C2212yes—
41#10622189C2212yes—
42#10622188C2212yes—
43#10622167C2212yes—
44#10622167C2212yes—
45C22×D4×C11—21no—
46C22×D4×C11C2311yescharacteristic
47C23×C4×C11—21no—
48C23×C4×C11C2311yescharacteristic
49C23×Dic11—21no—
50C23×Dic11D411yescharacteristic
51C23×Dic11D411yescharacteristic
52C22×Dic22—28no—
53C22×Dic22—22no—
54C22×Dic22—22no—
55C22×Dic22—44no—
56C22×Dic22—44no—
57C22×Dic22C2311yescharacteristic
58C22×C8×C11C2312yes—
59C11×#121—22no—
60C11×#121—22no—
61C2×C11×C4⋊C4—21no—
62C2×C11×C4⋊C4—24no—
63C2×C11×C4⋊C4C2311yescharacteristic
64C2×C11×C4⋊C4C2312yes—
65C2×C11×C22⋊C4—21no—
66C2×C22⋊Dic11—21no—
67C2×C22⋊Dic11—21no—
68C2×C22⋊Dic11—21no—
69C2×C22⋊Dic11—21no—
70C2×C22⋊Dic11—21no—
71#66989—24no—
72C2×C4⋊Dic11—21no—
73C2×C4⋊Dic11—24no—
74C2×C4⋊Dic11C2311yescharacteristic
75C2×C4⋊Dic11C2312yes—
76#66977—22no—
77#66977—22no—
78C2×Dic11⋊C4—28no—
79C2×Dic11⋊C4—22no—
80C2×Dic11⋊C4—22no—
81C2×Dic11⋊C4—21no—
82C2×C4×Dic11—24no—
83C2×C4×Dic11D411yescharacteristic
84C2×C4×Dic11D411yescharacteristic
85C2×C4×Dic11C2311yescharacteristic
86C2×C4×Dic11C2311yescharacteristic
87C22×C11⋊C8C2312yes—
88#66941—28no—
89#66941—28no—
90#66941—24no—
91#66941—24no—
92#66941—24no—
93#66941D418yescomplemented
94C11×#102—24no—
95C11×C22⋊C8—22no—
96#66896—24no—
97C11⋊#95—21no—
98C11⋊#95—21no—
99C11⋊#95—21no—
100C11⋊#95—21no—
101C22⋊(C11⋊C8)—22no—
102#66880—24no—
103#66879—24no—
104#66874—24no—
105#25908—111nomaximal, Sylow
106C24×C11—21no—
107C24×C11C2×D411yescharacteristic
108C2×D4×C11—22no—
109C2×D4×C11—21no—
110C2×D4×C11—21no—
111C2×D4×C11—22no—
112C2×D4×C11—42no—
113C2×D4×C11—42no—
114C2×D4×C11—42no—
115C22×C4×C11—22no—
116C22×C4×C11—22no—
117C22×C4×C11—24no—
118C22×C4×C11—22no—
119C22×C4×C11—21no—
120C22×C4×C11—42no—
121C22×C4×C11—42no—
122C22×C4×C11C2×D411yescharacteristic
123C22×C4×C11#4112yes—
124C22×C4×C11#4112yes—
125C22×C4×C11C2411yescharacteristic
126C22×Dic11—22no—
127C22×Dic11—22no—
128C22×Dic11—22no—
129C22×Dic11—22no—
130C22×Dic11—24no—
131C22×Dic11—22no—
132C22×Dic11—22no—
133C22×Dic11—22no—
134C22×Dic11—21no—
135C22×Dic11—21no—
136C22×Dic11—42no—
137C22×Dic11—42no—
138C22×Dic11C2×D411yescharacteristic
139C22×Dic11C2×D411yescharacteristic
140C22×Dic11C2×D411yescharacteristic
141C22×Dic11C2×D411yescharacteristic
142C2×Dic22—28no—
143C2×Dic22—28no—
144C2×Dic22—22no—
145C2×Dic22—21no—
146C2×Dic22—21no—
147C2×Dic22—22no—
148C2×Dic22—432no—
149C2×Dic22—44no—
150C2×Dic22—44no—
151C2×Dic22—44no—
152C2×Dic22—44no—
153C2×C8×C11—22no—
154C2×C8×C11—22no—
155C2×C8×C11—22no—
156C11×C4⋊C4—24no—
157C11×C4⋊C4—22no—
158C11×C4⋊C4—21no—
159C11×C4⋊C4—21no—
160C11×C4⋊C4C2×D414yes—
161C11×C22⋊C4—42no—
162C22⋊Dic11—42no—
163C22⋊Dic11—42no—
164C22⋊Dic11—42no—
165C22⋊Dic11—42no—
166C22⋊Dic11—42no—
167C4⋊Dic11—24no—
168C4⋊Dic11—22no—
169C4⋊Dic11—21no—
170C4⋊Dic11—21no—
171C4⋊Dic11C2×D414yes—
172Dic11⋊C4—28no—
173Dic11⋊C4—28no—
174Dic11⋊C4—42no—
175C4×Dic11—22no—
176C4×Dic11—22no—
177C4×Dic11—22no—
178C4×Dic11C2×D414yes—
179C2×C11⋊C8—22no—
180C2×C11⋊C8—22no—
181C2×C11⋊C8—22no—
182C22×C4⋊Q8—111no—
183C2×#489—112no—
184#2850—111no—
185#2024—112no—
186#2023—112no—
187#1993—112no—
188#1874—111no—
189#1874D1111yescharacteristic
190#1872—111no—
191#1872—111no—
192#1749—111no—
193C23×C11—21no—
194C23×C11—21no—
195C23×C11—21no—
196C23×C11—21no—
197C23×C11—41no—
198C23×C11—41no—
199C23×C11—41no—
200C23×C11—41no—
201C23×C11—41no—
202C23×C11—41no—
203C23×C11—41no—
204C23×C11#12412yes—
205C23×C11AGL(1,ℤ/8)12yes—
206C23×C11#13712yes—
207C23×C11C22×D411yescharacteristic
208D4×C11—42no—
209D4×C11—42no—
210D4×C11—84no—
211C2×C4×C11—21no—
212C2×C4×C11—21no—
213C2×C4×C11—24no—
214C2×C4×C11—24no—
215C2×C4×C11—24no—
216C2×C4×C11—48no—
217C2×C4×C11—42no—
218C2×C4×C11—42no—
219C2×C4×C11—41no—
220C2×C4×C11—41no—
221C2×C4×C11—41no—
222C2×C4×C11#12412yes—
223C2×C4×C11C22×D412yes—
224C2×C4×C11C2×#4111yescharacteristic
225C2×C4×C11C2×#4111yescharacteristic
226C2×C4×C112−1+412yes—
227C2×Dic11—28no—
228C2×Dic11—28no—
229C2×Dic11—21no—
230C2×Dic11—21no—
231C2×Dic11—21no—
232C2×Dic11—21no—
233C2×Dic11—21no—
234C2×Dic11—21no—
235C2×Dic11—21no—
236C2×Dic11—21no—
237C2×Dic11—24no—
238C2×Dic11—48no—
239C2×Dic11—42no—
240C2×Dic11—42no—
241C2×Dic11—41no—
242C2×Dic11—41no—
243C2×Dic11—41no—
244C2×Dic11—41no—
245C2×Dic11—41no—
246C2×Dic11—41no—
247C2×Dic11#12012yes—
248C2×Dic11#12012yes—
249C2×Dic11AGL(1,ℤ/8)12yes—
250C2×Dic11#13712yes—
251Dic22—416no—
252Dic22—416no—
253Dic22—42no—
254Dic22—42no—
255C8×C11—42no—
256C11⋊C8—42no—
257C23×Q8—221no—
258C2×C4⋊Q8—112no—
259C2×C4⋊Q8—112no—
260C2×C4⋊Q8—221no—
261C2×C4⋊Q8—221no—
262C2×C4⋊Q8—228no—
263C2×#124—111no—
264C2×C22⋊Q8—111no—
265C2×#121C2×D1111yescharacteristic
266C22×C4⋊C4—111no—
267C22×C4⋊C4—221no—
268C22×C4⋊C4C2×D1111yescharacteristic
269C22×C42—111no—
270#489—228no—
271C2×#103—112no—
272C2×#103—112no—
273C2×#102—112no—
274C2×#102C2×D1112yes—
275C2×C22⋊C8—111no—
276C2×C22⋊C8C2×D1111yescharacteristic
277C2×#97—112no—
278#391—111no—
279#390—111no—
280#388—221no—
281#388—221no—
282#386—221no—
283#386—221no—
284#382—111no—
285#340—112no—
286#340—112no—
287#340—112no—
288#340C2×D1112yes—
289#336—112no—
290C22×C11—22no—
291C22×C11—22no—
292C22×C11—22no—
293C22×C11—22no—
294C22×C11—22no—
295C22×C11—22no—
296C22×C11—81no—
297C22×C11—81no—
298C22×C11—81no—
299C22×C11—81no—
300C22×C11—81no—
301C22×C11—81no—
302C22×C11—81no—
303C22×C11#48914yescomplemented
304C22×C11C2×#12011yescharacteristic
305C22×C11C2×#12411yescharacteristic
306C22×C11#53611yescharacteristic
307C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
308C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
309C22×C11C2×#13711yescharacteristic
310C22×C11C2×#13711yescharacteristic
311C4×C11—22no—
312C4×C11—44no—
313C4×C11—81no—
314C4×C11#54812yes—
315C4×C11#54812yes—
316Dic11—22no—
317Dic11—22no—
318Dic11—22no—
319Dic11—22no—
320Dic11—44no—
321Dic11—81no—
322Dic11—81no—
323C22×Q8—111no—
324C22×Q8—222no—
325C22×Q8—222no—
326C22×Q8—228no—
327C22×Q8—444no—
328C22×Q8—444no—
329C22×D4—21no—
330C22×D4C22×D1111yescharacteristic
331C23×C4—21no—
332C23×C4—111no—
333C23×C4—111no—
334C23×C4—221no—
335C23×C4C22×D1111yescharacteristic
336C22×C8—112no—
337C22×C8C22×D1112yes—
338C4⋊Q8—118no—
339C4⋊Q8—224no—
340C4⋊Q8—224no—
341C4⋊Q8—228no—
342C4⋊Q8—228no—
343C4⋊Q8—224no—
344#124—224no—
345C22⋊Q8—222no—
346C22⋊Q8—222no—
347#121—22no—
348#121—22no—
349C2×C4⋊C4—21no—
350C2×C4⋊C4—24no—
351C2×C4⋊C4—112no—
352C2×C4⋊C4—111no—
353C2×C4⋊C4—224no—
354C2×C4⋊C4—222no—
355C2×C4⋊C4—222no—
356C2×C4⋊C4—228no—
357C2×C4⋊C4—221no—
358C2×C4⋊C4—221no—
359C2×C4⋊C4C22×D1111yescharacteristic
360C2×C4⋊C4C22×D1112yes—
361C2×C22⋊C4—21no—
362C2×C22⋊C4—221no—
363C2×C22⋊C4—221no—
364C2×C22⋊C4—221no—
365C2×C22⋊C4—221no—
366C2×C22⋊C4—221no—
367C2×C42—111no—
368C2×C42—111no—
369C2×C42—111no—
370C2×C42—111no—
371C2×C42—224no—
372#103—224no—
373#103—224no—
374#102—24no—
375#102—224no—
376C22⋊C8—22no—
377C22⋊C8—222no—
378#97—224no—
379#95—221no—
380#95—221no—
381#95—221no—
382#95—221no—
383C2×C11—24no—
384C2×C11—161no—
385C2×C11#243611yescharacteristic
386C2×C11#300311yescharacteristic
387C2×C11#300411yescharacteristic
388C2×C11C2×#48911yescharacteristic
389C2×C11#314111yescharacteristic
390C2×C11#323811yescharacteristic
391C2×C11#323911yescharacteristic
392C24—21no—
393C24D4×D1111yescharacteristic
394C2×Q8—228no—
395C2×Q8—228no—
396C2×Q8—221no—
397C2×Q8—222no—
398C2×Q8—221no—
399C2×Q8—222no—
400C2×Q8—444no—
401C2×Q8—4432no—
402C2×Q8—444no—
403C2×Q8—444no—
404C2×Q8—444no—
405C2×D4—21no—
406C2×D4—22no—
407C2×D4—21no—
408C2×D4—22no—
409C2×D4—42no—
410C2×D4—42no—
411C2×D4—42no—
412C22×C4—22no—
413C22×C4—22no—
414C22×C4—24no—
415C22×C4—22no—
416C22×C4—21no—
417C22×C4—42no—
418C22×C4—42no—
419C22×C4—111no—
420C22×C4—111no—
421C22×C4—111no—
422C22×C4—111no—
423C22×C4—222no—
424C22×C4—222no—
425C22×C4—222no—
426C22×C4—222no—
427C22×C4—222no—
428C22×C4—222no—
429C22×C4—224no—
430C22×C4—222no—
431C22×C4—221no—
432C22×C4—221no—
433C22×C4—442no—
434C22×C4—442no—
435C22×C4#433912yes—
436C22×C4D4×D1111yescharacteristic
437C22×C4#434112yes—
438C22×C4C23×D1111yescharacteristic
439C2×C8—22no—
440C2×C8—22no—
441C2×C8—22no—
442C2×C8—222no—
443C2×C8—222no—
444C2×C8—222no—
445C4⋊C4—24no—
446C4⋊C4—22no—
447C4⋊C4—21no—
448C4⋊C4—21no—
449C4⋊C4—114no—
450C4⋊C4—228no—
451C4⋊C4—228no—
452C4⋊C4—224no—
453C4⋊C4—222no—
454C4⋊C4—221no—
455C4⋊C4—221no—
456C4⋊C4—442no—
457C4⋊C4D4×D1114yes—
458C22⋊C4—42no—
459C22⋊C4—442no—
460C22⋊C4—442no—
461C22⋊C4—442no—
462C22⋊C4—442no—
463C22⋊C4—442no—
464C42—114no—
465C42—222no—
466C42—222no—
467C42—222no—
468C11#2590811yescharacteristic, complemented, Sylow
469C23—21no—
470C23—21no—
471C23—21no—
472C23—21no—
473C23—41no—
474C23—41no—
475C23—41no—
476C23—41no—
477C23—41no—
478C23—41no—
479C23—41no—
480C23#6693812yes—
481C23#6696412yes—
482C23#6696812yes—
483C23C2×D4×D1111yescharacteristic
484Q8—4416no—
485Q8—4416no—
486Q8—442no—
487Q8—442no—
488D4—42no—
489D4—42no—
490D4—84no—
491C2×C4—21no—
492C2×C4—21no—
493C2×C4—24no—
494C2×C4—24no—
495C2×C4—24no—
496C2×C4—48no—
497C2×C4—42no—
498C2×C4—42no—
499C2×C4—41no—
500C2×C4—41no—
501C2×C4—41no—
502C2×C4—112no—
503C2×C4—112no—
504C2×C4—112no—
505C2×C4—112no—
506C2×C4—228no—
507C2×C4—228no—
508C2×C4—221no—
509C2×C4—221no—
510C2×C4—221no—
511C2×C4—221no—
512C2×C4—221no—
513C2×C4—221no—
514C2×C4—221no—
515C2×C4—221no—
516C2×C4—224no—
517C2×C4—448no—
518C2×C4—442no—
519C2×C4—442no—
520C2×C4—441no—
521C2×C4—441no—
522C2×C4—441no—
523C2×C4—441no—
524C2×C4—441no—
525C2×C4—441no—
526C2×C4#6693812yes—
527C2×C4C2×#433911yescharacteristic
528C2×C4C2×D4×D1112yes—
529C2×C4C2×#434111yescharacteristic
530C2×C4#6704312yes—
531C8—42no—
532C8—442no—
533C22—22no—
534C22—22no—
535C22—22no—
536C22—22no—
537C22—22no—
538C22—22no—
539C22—81no—
540C22—81no—
541C22—81no—
542C22—81no—
543C22—81no—
544C22—81no—
545C22—81no—
546C22#1062237814yescomplemented
547C22C2×#6693811yescharacteristic
548C22D11×#12011yescharacteristic
549C22#1062317911yescharacteristic
550C22C2×#6696411yescharacteristic
551C22C2×#6696811yescharacteristic
552C22D11×AGL(1,ℤ/8)11yescharacteristic
553C22D11×#13711yescharacteristic
554C4—22no—
555C4—44no—
556C4—81no—
557C4—222no—
558C4—222no—
559C4—222no—
560C4—222no—
561C4—444no—
562C4—881no—
563C4—881no—
564C4#1062308312yes—
565C4#1062312912yes—
566C2—24no—
567C2—161no—
568C2#1307227211yescharacteristic
569C2#1307784011yescharacteristic
570C2#1307784711yescharacteristic
571C2C2×#1062237811yescharacteristic
572C2#1307900711yescharacteristic
573C2#1307983511yescharacteristic
574C2#1307984411yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1874C2
socleC23×C11C22×D4
prime radicalC2×C11×#121C22
hypercenter#1874D11
hypocenterC11#25908
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1874

Complements

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

NH ≅ G/Ntype
1. C22×#66941C2semidirect
2. C2×#10622378C2semidirect
4. #13069756C2semidirect
5. #13069750C2semidirect
6. #13069587C2semidirect
8. #13068923C2semidirect
9. #13068921C2semidirect
10. #13068380C2semidirect
93. #66941D4semidirect
303. C22×C11#489semidirect
468. C11#25908semidirect
546. C22#10622378semidirect

Maximal subgroups

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

subgroupindex
C22×#669412
C2×#106223782
#130769152
#130697562
#130697502
#130695872
#130689342
#130689232
#130689212
#130683802
C11×#18742
#2590811