Finite Group Databasebeta

← #14795291

Subgroups — #14795291

Order 2816.

658 conjugacy classes of subgroups.

The subgroup lattice has 618 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622676C211yesmaximal, characteristic, complemented
2C4×#67004C211yesmaximal, characteristic
3#13077282C211yesmaximal, characteristic
4#13070064C211yesmaximal, characteristic
5#13070059C211yesmaximal, characteristic
6#13069913C211yesmaximal, characteristic
7#13069913C211yesmaximal, characteristic
8#13069610C211yesmaximal, characteristic, complemented
9#13069398C211yesmaximal, characteristic, complemented
10#13069393C211yesmaximal, characteristic, complemented
11#13069389C211yesmaximal, characteristic, complemented
12#13069270C211yesmaximal, characteristic, complemented
13#13069270C211yesmaximal, characteristic, complemented
14#13068609C211yesmaximal, characteristic, complemented
15C11×#3080C211yesmaximal, characteristic
16C2×C11×#125C2211yescharacteristic
17C4×C11×#41C2211yescharacteristic
18C2×#67004C2211yescharacteristic
19C2×C4×Dic22C2211yescharacteristic
20C11×#479—21no—
21C11×#479—21no—
22C11×#478—21no—
23C11×#478—21no—
24C11×#428C2211yescharacteristic
25C11×#428C2211yescharacteristic
26C11×#423C2211yescharacteristic
27C11×#417C2211yescharacteristic
28C11×#417C2211yescharacteristic
29#10622847C2211yescharacteristic
30#10622847C2211yescharacteristic
31#10622845C2211yescharacteristic
32C2×#66888C2211yescharacteristic
33C2×#66888C2211yescharacteristic
34C2×#66886C2211yescharacteristic
35C2×#66886C2211yescharacteristic
36#10622676—21no—
37#10622676—21no—
38#10622676—21no—
39#10622676—21no—
40#10622643—21no—
41C4×#4326—21no—
42#10622631—21no—
43C4×#4324—21no—
44#10622617C2211yescharacteristic
45#10622613—21no—
46#10622613—21no—
47#10622610C2211yescharacteristic
48#10622610C2211yescharacteristic
49#10622608C2211yescharacteristic
50C2×#66874C2211yescharacteristic
51C2×#66874C2211yescharacteristic
52C2×#66872C2211yescharacteristic
53C2×#66871C2211yescharacteristic
54#10622539—21no—
55#10622538—21no—
56#10622537C2211yescharacteristic
57C2×C4⋊(C11⋊C8)C2211yescharacteristic
58C4×#4318C2211yescharacteristic
59#10622196C2211yescharacteristic
60#10622196C2211yescharacteristic
61#10622192C2211yescharacteristic
62#10622192C2211yescharacteristic
63#10622168C2211yescharacteristic
64#10622168C2211yescharacteristic
65#10622168C2211yescharacteristic
66#10622168C2211yescharacteristic
67C2×C11×#41C2311yescharacteristic
68C22×Dic22C2311yescharacteristic
69C2×C11×M16C2311yescharacteristic
70C2×C11×M16C2311yescharacteristic
71C11×#125—21no—
72C11×#125—21no—
73C11×#125—21no—
74C11×#125—21no—
75C4×Q8×C11D411yescharacteristic
76C4×Q8×C11D411yescharacteristic
77C4×D4×C11—21no—
78C4×D4×C11—21no—
79C4×D4×C11D411yescharacteristic
80C4×D4×C11D411yescharacteristic
81C11×#117—21no—
82C11×#117C2311yescharacteristic
83C2×C11×C4⋊C4—21no—
84C2×C11×C4⋊C4—21no—
85C2×C11×C4⋊C4C2311yescharacteristic
86C2×C11×C4⋊C4C2311yescharacteristic
87C2×C42×C11—21no—
88C2×C42×C11C2311yescharacteristic
89#67004—22no—
90#67004—22no—
91C2×#4326—21no—
92C2×#4324—21no—
93C2×C4⋊Dic11C2311yescharacteristic
94C2×Dic11⋊C4—21no—
95C2×C4×Dic11—21no—
96C2×#4318C2311yescharacteristic
97C2×#4318C2311yescharacteristic
98C2×#4318C2311yescharacteristic
99C2×#4318C2311yescharacteristic
100C22×C11⋊C8C2311yescharacteristic
101C22×C11⋊C8C2311yescharacteristic
102C4×Dic22—21no—
103C4×Dic22—21no—
104C4×Dic22—21no—
105C4×Dic22—21no—
106C11×#107—21no—
107C11×#107—21no—
108C11×#106—21no—
109C11×#106—21no—
110C11×C4⋊C8—21no—
111C11×C4⋊C8—21no—
112C11×#103—21no—
113C11×#103—21no—
114C11×#102—21no—
115C11×#102—21no—
116#66899—21no—
117#66896—21no—
118C22⋊(C11⋊C8)—21no—
119C22⋊(C11⋊C8)—21no—
120C22⋊(C11⋊C8)—21no—
121C22⋊(C11⋊C8)—21no—
122#66888—22no—
123#66888—22no—
124#66886—22no—
125#66886—22no—
126#66874—21no—
127#66874—21no—
128#66874—21no—
129#66874—21no—
130#66874—21no—
131#66874—21no—
132#66872—21no—
133#66872—21no—
134#66872—21no—
135#66871—21no—
136#66871—21no—
137#66871—21no—
138C4⋊(C11⋊C8)—21no—
139C4⋊(C11⋊C8)—21no—
140C4⋊(C11⋊C8)D411yescharacteristic
141C4⋊(C11⋊C8)D411yescharacteristic
142C4⋊(C11⋊C8)D411yescharacteristic
143C4⋊(C11⋊C8)D411yescharacteristic
144#66867—21no—
145#66867—21no—
146#66867—21no—
147C4×C11⋊C8—21no—
148C4×C11⋊C8—21no—
149C4×C11⋊C8—21no—
150#24725—111nomaximal, Sylow
151C11×#41—21no—
152C11×#41—21no—
153C11×#41—21no—
154C11×#41—21no—
155C2×Q8×C11C2×D411yescharacteristic
156C2×D4×C11—21no—
157C2×D4×C11C2×D411yescharacteristic
158C22×C4×C11—21no—
159C22×C4×C11—21no—
160C22×C4×C11—21no—
161C22×C4×C11—21no—
162C22×C4×C11—21no—
163C22×C4×C11#4111yescharacteristic
164C22×C4×C11#4111yescharacteristic
165C22×C4×C11C2411yescharacteristic
166C22×Dic11—21no—
167C22×Dic11—21no—
168C2×Dic22—21no—
169C2×Dic22—21no—
170C2×Dic22—21no—
171C2×Dic22—21no—
172C2×Dic22—21no—
173C2×Dic22#4112yes—
174C11×M16—21no—
175C11×M16—21no—
176C11×M16—21no—
177C11×M16—21no—
178C2×C8×C11—21no—
179C2×C8×C11—21no—
180C11×C4⋊C4—21no—
181C11×C4⋊C4—21no—
182C11×C4⋊C4—21no—
183C11×C4⋊C4—21no—
184C11×C4⋊C4—21no—
185C11×C4⋊C4—21no—
186C11×C4⋊C4—41no—
187C11×C4⋊C4—41no—
188C11×C4⋊C4—41no—
189C11×C4⋊C4—41no—
190C11×C4⋊C4C2×D411yescharacteristic
191C11×C4⋊C4C2×D411yescharacteristic
192C11×C22⋊C4—21no—
193C11×C22⋊C4—21no—
194C11×C22⋊C4—21no—
195C42×C11—21no—
196C42×C11—21no—
197C42×C11—21no—
198C42×C11C2×D411yescharacteristic
199C42×C11C2×D411yescharacteristic
200C42×C11C2×D411yescharacteristic
201C42×C11C2×D411yescharacteristic
202#4326—24no—
203#4324—24no—
204C4⋊Dic11—21no—
205C4⋊Dic11—21no—
206Dic11⋊C4—41no—
207Dic11⋊C4—41no—
208C4×Dic11—41no—
209C4×Dic11—41no—
210#4318—21no—
211#4318—21no—
212#4318—21no—
213#4318—21no—
214#4318—21no—
215#4318—21no—
216#4318—21no—
217#4318#4112yes—
218C2×C11⋊C8—21no—
219C2×C11⋊C8—21no—
220C2×C11⋊C8—21no—
221C2×C11⋊C8—21no—
222C2×C11⋊C8—21no—
223C2×C11⋊C8—21no—
224C2×C11⋊C8—21no—
225C2×C11⋊C8—21no—
226C2×C11⋊C8C2×D411yescharacteristic
227C2×C11⋊C8C2×D411yescharacteristic
228C2×C11⋊C8C2×D411yescharacteristic
229C2×C11⋊C8C2×D411yescharacteristic
230#3080D1111yescharacteristic
231C2×#479—111no—
232C4×#137—111no—
233#2925—111no—
234#2079—111no—
235#2078—111no—
236#2052—111no—
237#2052—111no—
238#1998—111no—
239#1952—111no—
240#1951—111no—
241#1950—111no—
242#1930—111no—
243#1930—111no—
244#1801—111no—
245C23×C11—21no—
246C23×C11C2×#4111yescharacteristic
247Q8×C11—21no—
248Q8×C11—21no—
249D4×C11—21no—
250D4×C11—21no—
251D4×C11—41no—
252D4×C11—41no—
253C2×C4×C11—21no—
254C2×C4×C11—21no—
255C2×C4×C11—21no—
256C2×C4×C11—41no—
257C2×C4×C11—41no—
258C2×C4×C11—42no—
259C2×C4×C11—41no—
260C2×C4×C11—41no—
261C2×C4×C11—41no—
262C2×C4×C11—41no—
263C2×C4×C11—81no—
264C2×C4×C11—81no—
265C2×C4×C11—81no—
266C2×C4×C11#12111yescharacteristic
267C2×C4×C11#12111yescharacteristic
268C2×C4×C11#12111yescharacteristic
269C2×C4×C11#12111yescharacteristic
270C2×C4×C11C22×D411yescharacteristic
271C2×C4×C11C22×D411yescharacteristic
272C2×C4×C11C2×#4111yescharacteristic
273C2×C4×C11C2×#4111yescharacteristic
274C2×C4×C112−1+411yescharacteristic
275C2×C4×C112−1+411yescharacteristic
276C2×Dic11—22no—
277C2×Dic11—41no—
278C2×Dic11—41no—
279C2×Dic11—41no—
280C2×Dic11—81no—
281Dic22—22no—
282Dic22—22no—
283Dic22—41no—
284Dic22—41no—
285C8×C11—41no—
286C8×C11—41no—
287C11⋊C8—22no—
288C11⋊C8—21no—
289C11⋊C8—21no—
290C11⋊C8—21no—
291C11⋊C8—21no—
292C11⋊C8—41no—
293C11⋊C8—41no—
294C11⋊C8—41no—
295C2×#137—111no—
296C2×#125C2×D1111yescharacteristic
297C4×#41C2×D1111yescharacteristic
298C2×C4×Q8—111no—
299#479—21no—
300#479—21no—
301#479—221no—
302#479—221no—
303#479—221no—
304#479—221no—
305#478—21no—
306#478—21no—
307#441—221no—
308#440—221no—
309C4×Q16—221no—
310C4×SD16—221no—
311#433—221no—
312#433—221no—
313#432—221no—
314#431—221no—
315C2×#108—111no—
316C2×#108—111no—
317#428—111no—
318#428C2×D1111yescharacteristic
319#428C2×D1111yescharacteristic
320C2×#107—111no—
321C2×#106—111no—
322#423—111no—
323#423C2×D1111yescharacteristic
324C2×C4⋊C8—111no—
325#419—111no—
326#417—111no—
327#417C2×D1111yescharacteristic
328#417C2×D1111yescharacteristic
329C2×#103—111no—
330C2×#103—111no—
331C2×#101—111no—
332C2×#101—111no—
333#408—111no—
334#408—111no—
335#405—111no—
336#405—111no—
337C4×M16—111no—
338#343—111no—
339#343—111no—
340#343—111no—
341#343—111no—
342#343—111no—
343#343—111no—
344#341—111no—
345#341—111no—
346C22×C11—21no—
347C22×C11—21no—
348C22×C11—41no—
349C22×C11—41no—
350C22×C11—41no—
351C22×C11C2×#12111yescharacteristic
352C22×C11#55211yescharacteristic
353C22×C11#55611yescharacteristic
354C4×C11—21no—
355C4×C11—21no—
356C4×C11—21no—
357C4×C11—21no—
358C4×C11—41no—
359C4×C11—41no—
360C4×C11—41no—
361C4×C11—81no—
362C4×C11—81no—
363C4×C11#52511yescharacteristic
364C4×C11#53611yescharacteristic
365C4×C11#54711yescharacteristic
366C4×C11#54811yescharacteristic
367Dic11—42no—
368Dic11—81no—
369C2×#41C22×D1111yescharacteristic
370C22×Q8—111no—
371#137—222no—
372#137—222no—
373C2×Q16—221no—
374C2×SD16—221no—
375C2×M16—111no—
376C2×M16—111no—
377C2×M16—111no—
378C2×M16—111no—
379C2×M16C22×D1111yescharacteristic
380C2×M16C22×D1111yescharacteristic
381C22×C8—111no—
382C22×C8—111no—
383#125—21no—
384#125—21no—
385#125—21no—
386#125—21no—
387C4×Q8—221no—
388C4×Q8—221no—
389C4×Q8—221no—
390C4×Q8—221no—
391C4×Q8C22⋊D1111yescharacteristic
392C4×Q8C22⋊D1111yescharacteristic
393C4×D4—21no—
394C4×D4—21no—
395C4×D4C22⋊D1111yescharacteristic
396C4×D4C22⋊D1111yescharacteristic
397#117—21no—
398#117C22×D1111yescharacteristic
399C2×C4⋊C4—21no—
400C2×C4⋊C4—21no—
401C2×C4⋊C4—111no—
402C2×C4⋊C4—221no—
403C2×C4⋊C4C22×D1111yescharacteristic
404C2×C4⋊C4C22×D1111yescharacteristic
405C2×C42—21no—
406C2×C42—221no—
407C2×C42C22×D1111yescharacteristic
408#108—222no—
409#108—222no—
410#107—21no—
411#107—21no—
412#107—221no—
413#107—221no—
414#107—221no—
415#106—21no—
416#106—21no—
417#106—221no—
418#106—221no—
419#106—221no—
420C4⋊C8—21no—
421C4⋊C8—21no—
422C4⋊C8—111no—
423C4⋊C8—111no—
424C4⋊C8—111no—
425C4⋊C8—111no—
426C4⋊C8—221no—
427C4⋊C8—221no—
428#103—21no—
429#103—21no—
430#103—221no—
431#103—221no—
432#103—221no—
433#103—221no—
434#103—221no—
435#103—221no—
436#103—221no—
437#102—21no—
438#102—21no—
439#102—221no—
440#101—222no—
441#101—222no—
442C22⋊C8—221no—
443C22⋊C8—221no—
444C22⋊C8—221no—
445C22⋊C8—221no—
446#97—221no—
447#97—221no—
448#97—221no—
449C4×C8—221no—
450C4×C8—221no—
451C4×C8—221no—
452C2×C11—21no—
453C2×C11—21no—
454C2×C11—81no—
455C2×C11#241511yescharacteristic
456C2×C11#306711yescharacteristic
457C2×C11#306911yescharacteristic
458#41—21no—
459#41—21no—
460#41—21no—
461#41—21no—
462C2×Q8—112no—
463C2×Q8—221no—
464C2×Q8—221no—
465C2×Q8—221no—
466C2×Q8—221no—
467C2×Q8—221no—
468C2×Q8C2×C22⋊D1111yescharacteristic
469C2×D4—21no—
470C2×D4C2×C22⋊D1111yescharacteristic
471C22×C4—21no—
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—221no—
477C22×C4—221no—
478C22×C4#434111yescharacteristic
479C22×C4#434111yescharacteristic
480C22×C4C23×D1111yescharacteristic
481Q16—224no—
482SD16—224no—
483M16—21no—
484M16—21no—
485M16—21no—
486M16—21no—
487M16—112no—
488M16—221no—
489M16—221no—
490M16—221no—
491M16—221no—
492M16—221no—
493M16—221no—
494M16—221no—
495C2×C8—21no—
496C2×C8—21no—
497C2×C8—111no—
498C2×C8—111no—
499C2×C8—111no—
500C2×C8—111no—
501C2×C8—221no—
502C2×C8—221no—
503C2×C8—221no—
504C2×C8—221no—
505C2×C8—221no—
506C2×C8—221no—
507C2×C8—221no—
508C2×C8—221no—
509C4⋊C4—21no—
510C4⋊C4—21no—
511C4⋊C4—21no—
512C4⋊C4—21no—
513C4⋊C4—21no—
514C4⋊C4—21no—
515C4⋊C4—41no—
516C4⋊C4—41no—
517C4⋊C4—41no—
518C4⋊C4—41no—
519C4⋊C4—221no—
520C4⋊C4—221no—
521C4⋊C4—441no—
522C4⋊C4—441no—
523C4⋊C4C2×C22⋊D1111yescharacteristic
524C4⋊C4C2×C22⋊D1111yescharacteristic
525C22⋊C4—21no—
526C22⋊C4—21no—
527C22⋊C4—21no—
528C42—21no—
529C42—21no—
530C42—21no—
531C42—441no—
532C42—441no—
533C42D4×D1111yescharacteristic
534C42D4×D1111yescharacteristic
535C42C2×C22⋊D1111yescharacteristic
536C42C2×C22⋊D1111yescharacteristic
537C11#2472511yescharacteristic, complemented, Sylow
538C23—21no—
539C23C2×#434111yescharacteristic
540Q8—21no—
541Q8—21no—
542Q8—222no—
543Q8—222no—
544Q8—441no—
545Q8—441no—
546D4—21no—
547D4—21no—
548D4—41no—
549D4—41no—
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—21no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—42no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—81no—
561C2×C4—81no—
562C2×C4—81no—
563C2×C4—222no—
564C2×C4—441no—
565C2×C4—441no—
566C2×C4—441no—
567C2×C4—881no—
568C2×C4#6699211yescharacteristic
569C2×C4#6699211yescharacteristic
570C2×C4#6699211yescharacteristic
571C2×C4#6699211yescharacteristic
572C2×C4C2×D4×D1111yescharacteristic
573C2×C4#6704011yescharacteristic
574C2×C4#6704011yescharacteristic
575C2×C4#41×D1111yescharacteristic
576C2×C4#41×D1111yescharacteristic
577C2×C4C22×C22⋊D1111yescharacteristic
578C8—41no—
579C8—41no—
580C8—222no—
581C8—221no—
582C8—221no—
583C8—221no—
584C8—221no—
585C8—441no—
586C8—441no—
587C8—441no—
588C22—21no—
589C22—21no—
590C22—41no—
591C22—41no—
592C22—41no—
593C22#1062317011yescharacteristic
594C22#1062317211yescharacteristic
595C22C2×#6699211yescharacteristic
596C4—21no—
597C4—21no—
598C4—21no—
599C4—21no—
600C4—41no—
601C4—41no—
602C4—41no—
603C4—81no—
604C4—81no—
605C4—442no—
606C4—881no—
607C4#1062316211yescharacteristic
608C4#1062316411yescharacteristic
609C4#1062334711yescharacteristic
610C4#1062335911yescharacteristic
611C2—21no—
612C2—21no—
613C2—81no—
614C2#1307204611yescharacteristic
615C2#1307833311yescharacteristic
616C2#1307835511yescharacteristic
subgroupG/H
centerC22C2×#66992
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#3080C2
socleC22×C11C2×#121
prime radicalC2×C11×#41C23
hypercenter#3080D11
hypocenterC11#24725
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3080

Complements

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

NH ≅ G/Ntype
1. C2×#10622676C2semidirect
8. #13069610C2semidirect
9. #13069398C2semidirect
10. #13069393C2semidirect
11. #13069389C2semidirect
12. #13069270C2semidirect
13. #13069270C2semidirect
14. #13068609C2semidirect
537. C11#24725semidirect

Maximal subgroups

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

subgroupindex
C2×#106226762
C4×#670042
#130772822
#130700642
#130700592
#130699132
#130696102
#130693982
#130693932
#130693892
#130692702
#130686092
C11×#30802
#2472511