Finite Group Databasebeta

← #14782899

Subgroups — #14782899

Order 2816.

774 conjugacy classes of subgroups.

The subgroup lattice has 604 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13077203C211yesmaximal, characteristic
2C2×#10622494C211yesmaximal, characteristic
3D11×#428C211yesmaximal, characteristic
4#13077177C211yesmaximal, characteristic
5#13070130C211yesmaximal, characteristic, complemented
6#13070129C211yesmaximal, characteristic, complemented
7#13070128C211yesmaximal, characteristic, complemented
8#13070126C211yesmaximal, characteristic, complemented
9#13070125C211yesmaximal, characteristic, complemented
10#13070124C211yesmaximal, characteristic, complemented
11#13070122C211yesmaximal, characteristic, complemented
12#13068353C211yesmaximal, characteristic
13D11×#343C211yesmaximal, characteristic
14#13068341C211yesmaximal, characteristic
15C11×#2089C211yesmaximal, characteristic, complemented
16C2×M16×D11C2211yescharacteristic
17C2×M16×D11C2211yescharacteristic
18C2×M16×D11C2211yescharacteristic
19C22×#4313C2211yescharacteristic
20D11×#117C2211yescharacteristic
21C2×#66945C2211yescharacteristic
22C2×C4⋊C4×D11C2211yescharacteristic
23C11×#428C2211yescharacteristic
24C11×#428C2211yescharacteristic
25C2×C11×#107C2211yescharacteristic
26C11×#424C2211yescharacteristic
27#10622734C2211yescharacteristic
28#10622734C2211yescharacteristic
29#10622732C2211yescharacteristic
30C2×#66881C2211yescharacteristic
31#10622715C2211yescharacteristic
32#10622612C2211yescharacteristic
33#10622608C2211yescharacteristic
34#10622608C2211yescharacteristic
35#10622577C2211yescharacteristic
36#10622577C2211yescharacteristic
37C2×#66872C2211yescharacteristic
38C2×#66871C2211yescharacteristic
39#10622494—22no—
40#10622494—22no—
41#10622494—21no—
42#10622494—21no—
43#10622493—21no—
44D11×#107—21no—
45#10622474—21no—
46#10622474—21no—
47#10622473—21no—
48D11×#106—21no—
49#10622452—22no—
50#10622450—22no—
51C11×#343C2211yescharacteristic
52C11×#343C2211yescharacteristic
53C11×#341C2211yescharacteristic
54#10622196C2211yescharacteristic
55#10622196C2211yescharacteristic
56#10622192C2211yescharacteristic
57#10622192C2211yescharacteristic
58#10622192C2211yescharacteristic
59#10622192C2211yescharacteristic
60#10622190C2211yescharacteristic
61#10622168C2211yescharacteristic
62#10622168C2211yescharacteristic
63C22×C4×D11—21no—
64C22×C4×D11C2311yescharacteristic
65C2×C11×M16C2311yescharacteristic
66C2×C11×M16C2311yescharacteristic
67C2×C11×M16C2311yescharacteristic
68C22×C8×C11C2311yescharacteristic
69C11×#117C2311yescharacteristic
70C2×C11×C4⋊C4C2311yescharacteristic
71C2×C11×C4⋊C4C2311yescharacteristic
72C2×(C2×D11)⋊C4—21no—
73#66979C2311yescharacteristic
74C2×C4⋊Dic11C2311yescharacteristic
75C2×C4⋊Dic11C2311yescharacteristic
76C2×Dic11⋊C4—21no—
77C2×C4×Dic11—21no—
78C2×#4318C2311yescharacteristic
79C2×#4318C2311yescharacteristic
80C2×#4318C2311yescharacteristic
81C22×C11⋊C8C2311yescharacteristic
82M16×D11—22no—
83M16×D11—22no—
84M16×D11—22no—
85M16×D11—22no—
86M16×D11Q814yes—
87M16×D11Q814yes—
88C2×#4313—21no—
89C2×#4313—21no—
90C2×#4313—22no—
91C2×#4313—22no—
92C2×#4313—21no—
93C2×#4313D412yes—
94C2×#4313D412yes—
95C2×C8×D11—21no—
96C2×C8×D11—21no—
97C2×C8×D11—21no—
98#66945—21no—
99#66945—21no—
100#66945—21no—
101#66945—21no—
102#66945D411yescharacteristic
103#66945D411yescharacteristic
104C4⋊C4×D11—21no—
105C4⋊C4×D11—21no—
106C4⋊C4×D11—21no—
107C4⋊C4×D11—21no—
108C4⋊C4×D11D411yescharacteristic
109C4⋊C4×D11D411yescharacteristic
110C22⋊C4×D11—21no—
111#66930—21no—
112#66925—21no—
113C42×D11—21no—
114C11×#107—22no—
115C11×#107—21no—
116C11×#107—21no—
117C11×#106—21no—
118C11×#106—21no—
119C11×C4⋊C8—22no—
120#66882—21no—
121#66882—21no—
122#66881—22no—
123#66881—21no—
124#66881—21no—
125Dic11⋊C8—22no—
126Dic11⋊C8—22no—
127#66872—21no—
128#66872—21no—
129#66872—21no—
130#66872—21no—
131#66872—22no—
132#66871—21no—
133#66871—21no—
134#66871—21no—
135#66871—21no—
136#66871—22no—
137C4⋊(C11⋊C8)—22no—
138#23675—111nomaximal, Sylow
139C23×D11#4111yescharacteristic
140C22×C4×C11—21no—
141C22×C4×C11—21no—
142C22×C4×C11C2411yescharacteristic
143C22×Dic11—21no—
144C22×Dic11—21no—
145C22×Dic11#4111yescharacteristic
146C2×C4×D11—21no—
147C2×C4×D11—21no—
148C2×C4×D11—41no—
149C2×C4×D11—41no—
150C2×C4×D11—82no—
151C2×C4×D11C2×D411yescharacteristic
152C2×C4×D11C2×D411yescharacteristic
153C2×C4×D11C2×D411yescharacteristic
154C2×C4×D11C2×D411yescharacteristic
155C2×C4×D11C2×Q812yes—
156C2×C4×D11C2×Q812yes—
157C2×C4×D11#4112yes—
158C2×C4×D11#4112yes—
159C11×M16—21no—
160C11×M16—21no—
161C11×M16—21no—
162C11×M16—21no—
163C11×M16C2×Q812yes—
164C11×M16C2×Q812yes—
165C2×C8×C11—21no—
166C2×C8×C11—21no—
167C2×C8×C11—21no—
168C2×C8×C11—21no—
169C2×C8×C11—21no—
170C2×C8×C11C2×D412yes—
171C11×C4⋊C4—21no—
172C11×C4⋊C4—21no—
173C11×C4⋊C4—21no—
174C11×C4⋊C4—21no—
175C11×C4⋊C4C2×D411yescharacteristic
176C11×C4⋊C4C2×D411yescharacteristic
177C11×C22⋊C4—21no—
178C42×C11—21no—
179C22⋊Dic11—21no—
180(C2×D11)⋊C4—21no—
181(C2×D11)⋊C4—21no—
182(C2×D11)⋊C4—41no—
183(C2×D11)⋊C4—41no—
184C4⋊Dic11—21no—
185C4⋊Dic11—21no—
186C4⋊Dic11—21no—
187C4⋊Dic11—21no—
188C4⋊Dic11C2×D411yescharacteristic
189C4⋊Dic11C2×D411yescharacteristic
190Dic11⋊C4—21no—
191Dic11⋊C4—21no—
192Dic11⋊C4—41no—
193Dic11⋊C4—41no—
194C4×Dic11—21no—
195C4×Dic11—21no—
196C4×Dic11—21no—
197C4×Dic11—41no—
198C4×Dic11—41no—
199#4318—21no—
200#4318—21no—
201#4318—21no—
202#4318—21no—
203#4318C2×Q812yes—
204#4318C2×Q812yes—
205C2×C11⋊C8—21no—
206C2×C11⋊C8—21no—
207C2×C11⋊C8—21no—
208C2×C11⋊C8—21no—
209C2×C11⋊C8—21no—
210C2×C11⋊C8C2×D412yes—
211#4313—24no—
212#4313—24no—
213#4313—24no—
214#4313—24no—
215#4313—42no—
216C8×D11—24no—
217C8×D11—24no—
218C8×D11—42no—
219#2911—111no—
220C2×#428—111no—
221C2×#428—111no—
222#2905—111no—
223#2090—111no—
224#2090—111no—
225#2090—111no—
226#2090—111no—
227#2089—111no—
228#2089—111no—
229#2089—111no—
230#2089D1111yescharacteristic, complemented
231#1742—111no—
232C2×#343—111no—
233#1738—111no—
234C23×C11C2×#4111yescharacteristic
235C22×D11—41no—
236C22×D11—41no—
237C22×D11#12111yescharacteristic
238C22×D11#12111yescharacteristic
239C22×D11#12512yes—
240C22×D11#12512yes—
241C2×C4×C11—21no—
242C2×C4×C11—21no—
243C2×C4×C11—41no—
244C2×C4×C11—41no—
245C2×C4×C11—81no—
246C2×C4×C11—81no—
247C2×C4×C11C22×D411yescharacteristic
248C2×C4×C11C22×D411yescharacteristic
249C2×C4×C11C22×Q811yescharacteristic
250C2×C4×C11C22×Q811yescharacteristic
251C2×C4×C11C2×#4111yescharacteristic
252C2×C4×C11C2×#4111yescharacteristic
253C2×Dic11—21no—
254C2×Dic11—21no—
255C2×Dic11—41no—
256C2×Dic11—41no—
257C2×Dic11—81no—
258C2×Dic11—81no—
259C2×Dic11#12111yescharacteristic
260C2×Dic11#12111yescharacteristic
261C2×Dic11#12512yes—
262C2×Dic11#12512yes—
263C4×D11—81no—
264C4×D11—81no—
265C4×D11—82no—
266C4×D11—82no—
267C4×D11C22⋊Q812yes—
268C4×D11C22⋊Q812yes—
269C4×D11C22⋊Q812yes—
270C4×D11C22⋊Q812yes—
271C4×D11#12312yes—
272C4×D11#12312yes—
273C4×D11C4⋊Q812yes—
274C4×D11C4⋊Q812yes—
275C8×C11—22no—
276C8×C11—22no—
277C8×C11—22no—
278C8×C11—41no—
279C11⋊C8—22no—
280C11⋊C8—22no—
281C11⋊C8—22no—
282C11⋊C8—41no—
283C22×M16—111no—
284C22×M16—111no—
285C22×M16—111no—
286C22×M16—111no—
287C2×#117—111no—
288C2×#117—111no—
289C22×C4⋊C4—111no—
290#428—111no—
291#428—111no—
292#428—111no—
293#428—111no—
294#428—111no—
295#428—111no—
296#428—221no—
297#428—221no—
298#428—221no—
299#428—221no—
300#428—222no—
301#428—222no—
302#428C2×D1111yescharacteristic
303#428C2×D1111yescharacteristic
304#427—221no—
305#427—221no—
306C2×#107—111no—
307C2×#107—221no—
308C2×#107C2×D1111yescharacteristic
309C2×#106—111no—
310C2×#106—111no—
311C2×#106—221no—
312#424—111no—
313#424—111no—
314#424—111no—
315#424—222no—
316#424C2×D1111yescharacteristic
317#423—222no—
318#343—111no—
319#343—111no—
320#343—111no—
321#343—111no—
322#343—111no—
323#343—111no—
324#343C2×D1111yescharacteristic
325#343C2×D1111yescharacteristic
326#341—111no—
327#341—111no—
328#341—111no—
329#341C2×D1111yescharacteristic
330C22×C11—21no—
331C22×C11—21no—
332C22×C11C2×#12111yescharacteristic
333C22×C11C2×#12511yescharacteristic
334C22×C11C2×#12511yescharacteristic
335C2×D11—21no—
336C2×D11—21no—
337C2×D11—21no—
338C2×D11—21no—
339C2×D11—42no—
340C2×D11—42no—
341C2×D11#39812yes—
342C2×D11#39812yes—
343C4×C11—41no—
344C4×C11—41no—
345C4×C11—81no—
346C4×C11—81no—
347C4×C11C2×C22⋊Q811yescharacteristic
348C4×C11C2×C22⋊Q811yescharacteristic
349C4×C11C2×#12311yescharacteristic
350C4×C11C2×C4⋊Q811yescharacteristic
351Dic11—41no—
352Dic11—41no—
353Dic11—81no—
354Dic11—81no—
355Dic11#39812yes—
356Dic11#39812yes—
357C23×C4—111no—
358C23×C4—221no—
359C2×M16—112no—
360C2×M16—112no—
361C2×M16—111no—
362C2×M16—111no—
363C2×M16—114no—
364C2×M16—114no—
365C2×M16—111no—
366C2×M16—222no—
367C2×M16—222no—
368C2×M16—221no—
369C2×M16—221no—
370C2×M16—221no—
371C2×M16—222no—
372C2×M16—222no—
373C2×M16—222no—
374C2×M16—222no—
375C2×M16C22×D1111yescharacteristic
376C2×M16C22×D1111yescharacteristic
377C2×M16C22×D1111yescharacteristic
378C22×C8—111no—
379C22×C8—221no—
380C22×C8—221no—
381C22×C8—221no—
382C22×C8C22×D1111yescharacteristic
383#117—111no—
384#117—111no—
385#117—111no—
386#117—221no—
387#117—221no—
388#117—221no—
389#117—221no—
390#117—221no—
391#117—221no—
392#117C22×D1111yescharacteristic
393C2×C4⋊C4—111no—
394C2×C4⋊C4—111no—
395C2×C4⋊C4—111no—
396C2×C4⋊C4—111no—
397C2×C4⋊C4—221no—
398C2×C4⋊C4—221no—
399C2×C4⋊C4—221no—
400C2×C4⋊C4—221no—
401C2×C4⋊C4—221no—
402C2×C4⋊C4C22×D1111yescharacteristic
403C2×C4⋊C4C22×D1111yescharacteristic
404C2×C22⋊C4—221no—
405C2×C22⋊C4—221no—
406C2×C42—221no—
407C2×C42—221no—
408#107—22no—
409#107—21no—
410#107—21no—
411#107—221no—
412#107—221no—
413#107—222no—
414#107—221no—
415#107—221no—
416#107—221no—
417#107—221no—
418#106—21no—
419#106—21no—
420#106—221no—
421#106—221no—
422#106—222no—
423#106—221no—
424#106—221no—
425#106—222no—
426#106—221no—
427#106—221no—
428C4⋊C8—22no—
429C4⋊C8—222no—
430C4⋊C8—222no—
431C4⋊C8—222no—
432C2×C11—21no—
433C2×C11—21no—
434C2×C11C2×#39811yescharacteristic
435C2×C11#306811yescharacteristic
436C2×C11#306911yescharacteristic
437D11—22no—
438D11—22no—
439C24—111no—
440C22×C4—21no—
441C22×C4—21no—
442C22×C4—111no—
443C22×C4—111no—
444C22×C4—111no—
445C22×C4—111no—
446C22×C4—111no—
447C22×C4—112no—
448C22×C4—112no—
449C22×C4—112no—
450C22×C4—112no—
451C22×C4—221no—
452C22×C4—221no—
453C22×C4—221no—
454C22×C4—221no—
455C22×C4—441no—
456C22×C4—441no—
457C22×C4—882no—
458C22×C4C23×D1111yescharacteristic
459M16—21no—
460M16—21no—
461M16—21no—
462M16—21no—
463M16—112no—
464M16—112no—
465M16—224no—
466M16—224no—
467M16—224no—
468M16—224no—
469M16—221no—
470M16—221no—
471M16—221no—
472M16—221no—
473M16—442no—
474M16Q8×D1112yes—
475M16Q8×D1112yes—
476C2×C8—21no—
477C2×C8—21no—
478C2×C8—21no—
479C2×C8—21no—
480C2×C8—21no—
481C2×C8—112no—
482C2×C8—224no—
483C2×C8—224no—
484C2×C8—221no—
485C2×C8—221no—
486C2×C8—221no—
487C2×C8—221no—
488C2×C8—221no—
489C2×C8—442no—
490C2×C8D4×D1112yes—
491C4⋊C4—21no—
492C4⋊C4—21no—
493C4⋊C4—21no—
494C4⋊C4—21no—
495C4⋊C4—111no—
496C4⋊C4—111no—
497C4⋊C4—221no—
498C4⋊C4—221no—
499C4⋊C4—221no—
500C4⋊C4—221no—
501C4⋊C4—221no—
502C4⋊C4—221no—
503C4⋊C4—441no—
504C4⋊C4—441no—
505C4⋊C4D4×D1111yescharacteristic
506C4⋊C4D4×D1111yescharacteristic
507C22⋊C4—21no—
508C22⋊C4—221no—
509C22⋊C4—221no—
510C22⋊C4—221no—
511C22⋊C4—441no—
512C22⋊C4—441no—
513C42—21no—
514C42—221no—
515C42—221no—
516C42—221no—
517C42—441no—
518C42—441no—
519C11#2367511yescharacteristic, complemented, Sylow
520C23—111no—
521C23—111no—
522C23—112no—
523C23—112no—
524C23—441no—
525C23—441no—
526C23#41×D1111yescharacteristic
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—81no—
532C2×C4—81no—
533C2×C4—111no—
534C2×C4—111no—
535C2×C4—112no—
536C2×C4—112no—
537C2×C4—112no—
538C2×C4—112no—
539C2×C4—112no—
540C2×C4—112no—
541C2×C4—112no—
542C2×C4—112no—
543C2×C4—112no—
544C2×C4—112no—
545C2×C4—221no—
546C2×C4—221no—
547C2×C4—441no—
548C2×C4—441no—
549C2×C4—881no—
550C2×C4—881no—
551C2×C4—882no—
552C2×C4—882no—
553C2×C4—881no—
554C2×C4—881no—
555C2×C4C2×D4×D1111yescharacteristic
556C2×C4C2×D4×D1111yescharacteristic
557C2×C4C2×Q8×D1111yescharacteristic
558C2×C4C2×Q8×D1111yescharacteristic
559C2×C4#41×D1111yescharacteristic
560C2×C4#41×D1111yescharacteristic
561C8—22no—
562C8—22no—
563C8—22no—
564C8—41no—
565C8—222no—
566C8—222no—
567C8—222no—
568C8—441no—
569C22—21no—
570C22—21no—
571C22—112no—
572C22—112no—
573C22—221no—
574C22—221no—
575C22—221no—
576C22—221no—
577C22—442no—
578C22—442no—
579C22D11×#12111yescharacteristic
580C22D11×#12511yescharacteristic
581C22D11×#12511yescharacteristic
582C4—41no—
583C4—41no—
584C4—81no—
585C4—81no—
586C4—112no—
587C4—112no—
588C4—441no—
589C4—441no—
590C4—881no—
591C4—881no—
592C4D11×C22⋊Q811yescharacteristic
593C4D11×C22⋊Q811yescharacteristic
594C4D11×#12311yescharacteristic
595C4D11×C4⋊Q811yescharacteristic
596C2—21no—
597C2—21no—
598C2—222no—
599C2—222no—
600C2D11×#39811yescharacteristic
601C2#1307834211yescharacteristic
602C2#1307835111yescharacteristic
subgroupG/H
centerC22D11×#121
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2089C2
socleC22×C11C2×#121
prime radicalC23×D11#41
hypercenter#2089D11
hypocenterC11#23675
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ #2089

Complements

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

NH ≅ G/Ntype
5. #13070130C2semidirect
6. #13070129C2semidirect
7. #13070128C2semidirect
8. #13070126C2semidirect
9. #13070125C2semidirect
10. #13070124C2semidirect
11. #13070122C2semidirect
15. C11×#2089C2semidirect
230. #2089D11semidirect
519. C11#23675semidirect

Maximal subgroups

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

subgroupindex
#130772032
C2×#106224942
D11×#4282
#130771772
#130701302
#130701292
#130701282
#130701262
#130701252
#130701242
#130701222
#130683532
D11×#3432
#130683412
C11×#20892
#2367511