Finite Group Databasebeta

← #14826270

Subgroups — #14826270

Order 2816.

742 conjugacy classes of subgroups.

The subgroup lattice has 602 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13072468C211yesmaximal, characteristic
2#13071703C211yesmaximal, characteristic, complemented
3#13069990C211yesmaximal, characteristic
4#13069947C211yesmaximal, characteristic, complemented
5#13069945C211yesmaximal, characteristic, complemented
6#13069750C211yesmaximal, characteristic
7#13069564C211yesmaximal, characteristic, complemented
8#13069360C211yesmaximal, characteristic, complemented
9#13069238C211yesmaximal, characteristic
10#13069204C211yesmaximal, characteristic, complemented
11#13069186C211yesmaximal, characteristic, complemented
12#13069183C211yesmaximal, characteristic, complemented
13#13068865C211yesmaximal, characteristic
14#13068443C211yesmaximal, characteristic
15C11×#1926C211yesmaximal, characteristic
16C2×D4×Dic11C2211yescharacteristic
17C2×#66941C2211yescharacteristic
18C2×#66931—21no—
19C2×#66922C2211yescharacteristic
20C2×C11×#106C2211yescharacteristic
21C2×C11×#102C2211yescharacteristic
22C2×C11×#102C2211yescharacteristic
23C11×#390C2211yescharacteristic
24C4×C11×C4⋊C4C2211yescharacteristic
25#10622834C2211yescharacteristic
26C2×#66896C2211yescharacteristic
27C2×#66896C2211yescharacteristic
28C2×#66882C2211yescharacteristic
29C2×#66882C2211yescharacteristic
30C2×#66879C2211yescharacteristic
31#10622598C2211yescharacteristic
32#10622598C2211yescharacteristic
33C4⋊C4×Dic11C2211yescharacteristic
34C4⋊C4×Dic11C2211yescharacteristic
35#10622586C2211yescharacteristic
36C2×#66872C2211yescharacteristic
37#10622563—21no—
38#10622561—21no—
39#10622560—21no—
40C4×Dic11⋊C4—21no—
41C4×Dic11⋊C4C2211yescharacteristic
42#10622542—21no—
43#10622541C2211yescharacteristic
44C2×C4⋊(C11⋊C8)C2211yescharacteristic
45#10622260—21no—
46#10622259—21no—
47C11×#340C2211yescharacteristic
48C11×#336C2211yescharacteristic
49#10622189C2211yescharacteristic
50#10622189C2211yescharacteristic
51#10622188C2211yescharacteristic
52#10622188C2211yescharacteristic
53#10622188C2211yescharacteristic
54#10622167C2211yescharacteristic
55#10622167C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59C22×D4×C11C2311yescharacteristic
60C23×Dic11—21no—
61C22×Dic22—21no—
62C22×Dic22—21no—
63C22×C8×C11C2311yescharacteristic
64C22×C8×C11C2311yescharacteristic
65C2×C11×C4⋊C4C2311yescharacteristic
66C2×C11×C4⋊C4C2311yescharacteristic
67C2×C11×C4⋊C4C2311yescharacteristic
68C2×C11×C22⋊C4—21no—
69C2×C11×C22⋊C4—21no—
70C2×C42×C11—21no—
71C2×C42×C11C2311yescharacteristic
72C2×C22⋊Dic11—21no—
73C2×C22⋊Dic11—21no—
74C2×C22⋊Dic11—21no—
75D4×Dic11—22no—
76D4×Dic11—41no—
77C2×C4⋊Dic11—21no—
78C2×C4⋊Dic11—21no—
79C2×C4⋊Dic11—21no—
80C2×C4⋊Dic11C2311yescharacteristic
81C2×C4⋊Dic11C2311yescharacteristic
82C2×C4⋊Dic11C2311yescharacteristic
83C2×C4⋊Dic11C2311yescharacteristic
84C2×Dic11⋊C4—21no—
85C2×Dic11⋊C4—21no—
86C2×Dic11⋊C4—21no—
87C2×Dic11⋊C4D411yescharacteristic
88C2×Dic11⋊C4D411yescharacteristic
89C2×C4×Dic11—21no—
90C2×C4×Dic11—21no—
91C2×C4×Dic11C2311yescharacteristic
92C2×C4×Dic11C2311yescharacteristic
93C22×C11⋊C8C2311yescharacteristic
94C22×C11⋊C8C2311yescharacteristic
95#66941—22no—
96#66941—22no—
97#66931—44no—
98#66922—22no—
99#66922—41no—
100C11×#106—22no—
101C11×#102—22no—
102C11×#102Q814yescomplemented
103C11×#95—21no—
104#66896—22no—
105#66896—41no—
106C11⋊#95—21no—
107C11⋊#95—21no—
108C11⋊#95—21no—
109C11⋊#95—21no—
110C11⋊#95—21no—
111C11⋊#95—21no—
112C11⋊#95D411yescharacteristic
113C11⋊#95D411yescharacteristic
114#66882—22no—
115#66882—41no—
116#66879—41no—
117#66872—22no—
118C4⋊(C11⋊C8)—41no—
119#27019—111nomaximal, Sylow
120C24×C11—21no—
121C2×D4×C11—21no—
122C2×D4×C11—21no—
123C2×D4×C11—21no—
124C2×D4×C11—21no—
125C2×D4×C11—21no—
126C2×D4×C11C2×Q812yes—
127C22×C4×C11—21no—
128C22×C4×C11—21no—
129C22×C4×C11—21no—
130C22×C4×C11C2×D411yescharacteristic
131C22×C4×C11C2×D411yescharacteristic
132C22×C4×C11C2411yescharacteristic
133C22×Dic11—21no—
134C22×Dic11—21no—
135C22×Dic11—21no—
136C22×Dic11—21no—
137C22×Dic11—42no—
138C22×Dic11—42no—
139C22×Dic11—81no—
140C22×Dic11C2×D411yescharacteristic
141C22×Dic11C2×D411yescharacteristic
142C22×Dic11C2×D411yescharacteristic
143C22×Dic11C2×D411yescharacteristic
144C2×Dic22—24no—
145C2×Dic22—42no—
146C2×Dic22—42no—
147C2×Dic22—81no—
148C2×Dic22—81no—
149C2×Dic22—81no—
150C2×C8×C11—21no—
151C2×C8×C11—21no—
152C2×C8×C11—21no—
153C2×C8×C11—21no—
154C2×C8×C11—21no—
155C2×C8×C11C2×Q812yes—
156C11×C4⋊C4—21no—
157C11×C4⋊C4—21no—
158C11×C4⋊C4—21no—
159C11×C4⋊C4—21no—
160C11×C4⋊C4C2×Q812yes—
161C11×C4⋊C4#4112yes—
162C11×C22⋊C4—42no—
163C11×C22⋊C4—42no—
164C42×C11—21no—
165C42×C11—21no—
166C42×C11—81no—
167C22⋊Dic11—42no—
168C22⋊Dic11—42no—
169C22⋊Dic11—81no—
170C4⋊Dic11—21no—
171C4⋊Dic11—21no—
172C4⋊Dic11—21no—
173C4⋊Dic11—21no—
174C4⋊Dic11—21no—
175C4⋊Dic11—21no—
176C4⋊Dic11—42no—
177C4⋊Dic11—42no—
178C4⋊Dic11—81no—
179C4⋊Dic11#4112yes—
180C4⋊Dic11#4112yes—
181Dic11⋊C4—24no—
182Dic11⋊C4—22no—
183Dic11⋊C4—22no—
184Dic11⋊C4—42no—
185Dic11⋊C4—81no—
186C4×Dic11—21no—
187C4×Dic11—21no—
188C4×Dic11—21no—
189C4×Dic11—21no—
190C4×Dic11—42no—
191C4×Dic11—81no—
192C2×C11⋊C8—21no—
193C2×C11⋊C8—21no—
194C2×C11⋊C8—21no—
195C2×C11⋊C8—21no—
196C2×C11⋊C8—21no—
197C2×C11⋊C8—21no—
198#2452—111no—
199#2369—111no—
200#2065—111no—
201#2058—111no—
202#2057—111no—
203#2023—111no—
204#1987—111no—
205#1944—111no—
206#1926D1111yescharacteristic
207#1925—111no—
208#1920—111no—
209#1918—111no—
210#1917—111no—
211#1862—111no—
212#1762—111no—
213C23×C11—22no—
214C23×C11—41no—
215C23×C11—41no—
216C23×C11—41no—
217C23×C11—41no—
218C23×C11—41no—
219C23×C11—41no—
220C23×C11C22×D411yescharacteristic
221D4×C11—22no—
222D4×C11—22no—
223D4×C11—41no—
224D4×C11—41no—
225C2×C4×C11—21no—
226C2×C4×C11—21no—
227C2×C4×C11—22no—
228C2×C4×C11—21no—
229C2×C4×C11—22no—
230C2×C4×C11—21no—
231C2×C4×C11—21no—
232C2×C4×C11—41no—
233C2×C4×C11—41no—
234C2×C4×C11—41no—
235C2×C4×C11—41no—
236C2×C4×C11—41no—
237C2×C4×C11—41no—
238C2×C4×C11—41no—
239C2×C4×C11#13712yes—
240C2×C4×C11C22×Q811yescharacteristic
241C2×C4×C11C2×#4111yescharacteristic
242C2×C4×C11C2×#4111yescharacteristic
243C2×C4×C11C2×#4111yescharacteristic
244C2×C4×C11H(5,𝔽2)11yescharacteristic
245C2×C4×C112−1+411yescharacteristic
246C2×Dic11—21no—
247C2×Dic11—21no—
248C2×Dic11—21no—
249C2×Dic11—22no—
250C2×Dic11—21no—
251C2×Dic11—21no—
252C2×Dic11—22no—
253C2×Dic11—21no—
254C2×Dic11—21no—
255C2×Dic11—21no—
256C2×Dic11—21no—
257C2×Dic11—21no—
258C2×Dic11—21no—
259C2×Dic11—41no—
260C2×Dic11—41no—
261C2×Dic11—41no—
262C2×Dic11—41no—
263C2×Dic11—41no—
264C2×Dic11—41no—
265C2×Dic11—41no—
266C2×Dic11—41no—
267C2×Dic11—41no—
268C2×Dic11—41no—
269C2×Dic11—84no—
270C2×Dic11AGL(1,ℤ/8)12yes—
271Dic22—84no—
272Dic22—84no—
273C8×C11—22no—
274C8×C11—41no—
275C11⋊C8—41no—
276C11⋊C8—41no—
277C2×C4⋊Q8—111no—
278C2×C4⋊Q8—111no—
279C2×C22⋊Q8—221no—
280C2×C4×D4—111no—
281C2×#107—111no—
282C2×#107—111no—
283C2×#106—111no—
284C2×#106C2×D1111yescharacteristic
285C2×C4⋊C8—111no—
286C2×#102—111no—
287C2×#102—111no—
288C2×#102C2×D1111yescharacteristic
289C2×#102C2×D1111yescharacteristic
290C2×#97—111no—
291#396—221no—
292#393—221no—
293#391—221no—
294#391—221no—
295#390—111no—
296#390C2×D1111yescharacteristic
297#389—111no—
298#389—111no—
299#389—111no—
300#389—111no—
301#389—221no—
302#385—221no—
303C4×C4⋊C4—111no—
304C4×C4⋊C4—111no—
305C4×C4⋊C4—111no—
306C4×C4⋊C4—221no—
307C4×C4⋊C4C2×D1111yescharacteristic
308#340—111no—
309#340—111no—
310#340—111no—
311#340—111no—
312#340—111no—
313#340—111no—
314#340—111no—
315#340C2×D1111yescharacteristic
316#336—111no—
317#336—111no—
318#336—111no—
319#336C2×D1111yescharacteristic
320C22×C11—42no—
321C22×C11—42no—
322C22×C11—42no—
323C22×C11—81no—
324C22×C11—81no—
325C22×C11—81no—
326C22×C11—81no—
327C22×C11#52511yescharacteristic
328C22×C11#54611yescharacteristic
329C22×C11D4×Q811yescharacteristic
330C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
331C22×C11C2×#13711yescharacteristic
332C22×C11#57611yescharacteristic
333C22×C11#57711yescharacteristic
334C4×C11—22no—
335C4×C11—42no—
336C4×C11—42no—
337C4×C11—41no—
338C4×C11—81no—
339C4×C11#53311yescharacteristic
340C4×C11#54211yescharacteristic
341C4×C11#55411yescharacteristic
342C4×C11#55611yescharacteristic
343Dic11—22no—
344Dic11—41no—
345Dic11—42no—
346Dic11—41no—
347Dic11—42no—
348Dic11—41no—
349Dic11—81no—
350Dic11—81no—
351C22×Q8—221no—
352C22×Q8—221no—
353C22×D4C22×D1111yescharacteristic
354C23×C4—221no—
355C22×C8—111no—
356C22×C8—111no—
357C22×C8C22×D1111yescharacteristic
358C22×C8C22×D1111yescharacteristic
359C4⋊Q8—222no—
360C4⋊Q8—222no—
361C4⋊Q8—222no—
362C4⋊Q8—441no—
363C22⋊Q8—444no—
364C4×D4—222no—
365C4×D4—441no—
366C2×C4⋊C4—111no—
367C2×C4⋊C4—111no—
368C2×C4⋊C4—111no—
369C2×C4⋊C4—111no—
370C2×C4⋊C4—111no—
371C2×C4⋊C4—111no—
372C2×C4⋊C4—221no—
373C2×C4⋊C4—221no—
374C2×C4⋊C4—221no—
375C2×C4⋊C4—221no—
376C2×C4⋊C4—221no—
377C2×C4⋊C4—221no—
378C2×C4⋊C4C22×D1111yescharacteristic
379C2×C4⋊C4C22×D1111yescharacteristic
380C2×C4⋊C4C22×D1111yescharacteristic
381C2×C22⋊C4—21no—
382C2×C22⋊C4—21no—
383C2×C22⋊C4—221no—
384C2×C22⋊C4—221no—
385C2×C22⋊C4—221no—
386C2×C42—21no—
387C2×C42—111no—
388C2×C42—111no—
389C2×C42—221no—
390C2×C42—221no—
391C2×C42C22×D1111yescharacteristic
392#107—222no—
393#107—441no—
394#106—22no—
395#106—222no—
396C4⋊C8—441no—
397#102—22no—
398#102—222no—
399#102—441no—
400#102Dic2214yescomplemented
401#97—441no—
402#95—21no—
403#95—111no—
404#95—111no—
405#95—221no—
406#95—221no—
407#95—221no—
408#95—221no—
409#95—221no—
410#95—221no—
411C2×C11—82no—
412C2×C11#246511yescharacteristic
413C2×C11#311211yescharacteristic
414C2×C11#311811yescharacteristic
415C2×C11#331611yescharacteristic
416C2×C11#332511yescharacteristic
417C2×C11#338411yescharacteristic
418C2×C11#338511yescharacteristic
419C24—21no—
420C2×Q8—224no—
421C2×Q8—442no—
422C2×Q8—442no—
423C2×Q8—881no—
424C2×Q8—881no—
425C2×Q8—881no—
426C2×D4—21no—
427C2×D4—21no—
428C2×D4—21no—
429C2×D4—21no—
430C2×D4—21no—
431C2×D4C2×Dic2212yes—
432C22×C4—21no—
433C22×C4—21no—
434C22×C4—21no—
435C22×C4—111no—
436C22×C4—111no—
437C22×C4—111no—
438C22×C4—111no—
439C22×C4—221no—
440C22×C4—221no—
441C22×C4—221no—
442C22×C4—221no—
443C22×C4—442no—
444C22×C4—442no—
445C22×C4—881no—
446C22×C4D4×D1111yescharacteristic
447C22×C4D4×D1111yescharacteristic
448C22×C4C23×D1111yescharacteristic
449C2×C8—21no—
450C2×C8—21no—
451C2×C8—21no—
452C2×C8—21no—
453C2×C8—21no—
454C2×C8—221no—
455C2×C8—221no—
456C2×C8—221no—
457C2×C8—221no—
458C2×C8—221no—
459C2×C8—221no—
460C2×C8C2×Dic2212yes—
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—112no—
466C4⋊C4—112no—
467C4⋊C4—222no—
468C4⋊C4—224no—
469C4⋊C4—222no—
470C4⋊C4—221no—
471C4⋊C4—221no—
472C4⋊C4—221no—
473C4⋊C4—221no—
474C4⋊C4—221no—
475C4⋊C4—221no—
476C4⋊C4—442no—
477C4⋊C4—442no—
478C4⋊C4—442no—
479C4⋊C4—881no—
480C4⋊C4—881no—
481C4⋊C4C2×Dic2212yes—
482C4⋊C4#434112yes—
483C22⋊C4—42no—
484C22⋊C4—42no—
485C22⋊C4—442no—
486C22⋊C4—442no—
487C22⋊C4—881no—
488C42—21no—
489C42—21no—
490C42—81no—
491C42—221no—
492C42—221no—
493C42—221no—
494C42—221no—
495C42—442no—
496C42—881no—
497C11#2701911yescharacteristic, complemented, Sylow
498C23—22no—
499C23—41no—
500C23—41no—
501C23—41no—
502C23—41no—
503C23—41no—
504C23—41no—
505C23C2×D4×D1111yescharacteristic
506Q8—884no—
507Q8—884no—
508D4—22no—
509D4—22no—
510D4—41no—
511D4—41no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—22no—
517C2×C4—22no—
518C2×C4—21no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—41no—
526C2×C4—112no—
527C2×C4—221no—
528C2×C4—221no—
529C2×C4—221no—
530C2×C4—221no—
531C2×C4—221no—
532C2×C4—221no—
533C2×C4—221no—
534C2×C4—221no—
535C2×C4—221no—
536C2×C4—222no—
537C2×C4—221no—
538C2×C4—221no—
539C2×C4—222no—
540C2×C4—441no—
541C2×C4—441no—
542C2×C4—441no—
543C2×C4—441no—
544C2×C4—441no—
545C2×C4—441no—
546C2×C4—441no—
547C2×C4—441no—
548C2×C4—441no—
549C2×C4—441no—
550C2×C4—884no—
551C2×C4#6696812yes—
552C2×C4C22×Dic2211yescharacteristic
553C2×C4C2×#434111yescharacteristic
554C2×C4#41×D1111yescharacteristic
555C2×C4#41×D1111yescharacteristic
556C2×C4#6704211yescharacteristic
557C2×C4#6704311yescharacteristic
558C8—22no—
559C8—41no—
560C8—441no—
561C8—441no—
562C22—42no—
563C22—42no—
564C22—42no—
565C22—81no—
566C22—81no—
567C22—81no—
568C22—81no—
569C22D4×Dic2211yescharacteristic
570C22#1062313711yescharacteristic
571C22#1062318511yescharacteristic
572C22C2×#6696811yescharacteristic
573C22#1062330011yescharacteristic
574C22D11×AGL(1,ℤ/8)11yescharacteristic
575C22#1062330611yescharacteristic
576C4—22no—
577C4—42no—
578C4—41no—
579C4—42no—
580C4—81no—
581C4—222no—
582C4—441no—
583C4—442no—
584C4—441no—
585C4—442no—
586C4—441no—
587C4—881no—
588C4—881no—
589C4#1062304811yescharacteristic
590C4#1062307411yescharacteristic
591C4#1062320211yescharacteristic
592C4#1062324111yescharacteristic
593C2—82no—
594C2#1307264211yescharacteristic
595C2#1307873711yescharacteristic
596C2#1307879711yescharacteristic
597C2#1308072511yescharacteristic
598C2#1308085611yescharacteristic
599C2#1308151611yescharacteristic
600C2#1308152411yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1926C2
socleC23×C11C22×D4
prime radicalC22×D4×C11C23
hypercenter#1926D11
hypocenterC11#27019
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1926

Complements

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

NH ≅ G/Ntype
2. #13071703C2semidirect
4. #13069947C2semidirect
5. #13069945C2semidirect
7. #13069564C2semidirect
8. #13069360C2semidirect
10. #13069204C2semidirect
11. #13069186C2semidirect
12. #13069183C2semidirect
102. C11×#102Q8semidirect
400. #102Dic22semidirect
497. C11#27019semidirect

Maximal subgroups

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

subgroupindex
#130724682
#130717032
#130699902
#130699472
#130699452
#130697502
#130695642
#130693602
#130692382
#130692042
#130691862
#130691832
#130688652
#130684432
C11×#19262
#2701911