Finite Group Databasebeta

← #14827007

Subgroups — #14827007

Order 2816.

708 conjugacy classes of subgroups.

The subgroup lattice has 600 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13073187C211yesmaximal, characteristic
2#13071670C211yesmaximal, characteristic
3#13070155C211yesmaximal, characteristic
4#13069939C211yesmaximal, characteristic
5#13069861C211yesmaximal, characteristic
6#13069717C211yesmaximal, characteristic
7#13069474C211yesmaximal, characteristic
8#13069260C211yesmaximal, characteristic
9#13069255C211yesmaximal, characteristic
10#13069211C211yesmaximal, characteristic
11#13069170C211yesmaximal, characteristic
12#13068958C211yesmaximal, characteristic
13#13068957C211yesmaximal, characteristic
14#13068435C211yesmaximal, characteristic
15C11×#1803C211yesmaximal, characteristic
16C2×C4×Q8×C11C2211yescharacteristic
17C2×#66997C2211yescharacteristic
18C22×#4326C2211yescharacteristic
19C22×Dic44C2211yescharacteristic
20C2×#66940C2211yescharacteristic
21C2×C11×C4⋊C8C2211yescharacteristic
22C2×C11×#103C2211yescharacteristic
23C2×C11×#103C2211yescharacteristic
24C11×#384C2211yescharacteristic
25#10622843C2211yescharacteristic
26C2×#66899C2211yescharacteristic
27C2×#66880C2211yescharacteristic
28C2×#66880C2211yescharacteristic
29C2×C8×Dic11C2211yescharacteristic
30#10622599—21no—
31#10622598C2211yescharacteristic
32#10622595—21no—
33#10622594—21no—
34#10622591—21no—
35#10622591—21no—
36C4⋊C4×Dic11C2211yescharacteristic
37C4⋊C4×Dic11C2211yescharacteristic
38#10622587C2211yescharacteristic
39#10622587C2211yescharacteristic
40#10622585—21no—
41C2×#66874C2211yescharacteristic
42C2×#66874C2211yescharacteristic
43C2×#66874C2211yescharacteristic
44C2×#66871C2211yescharacteristic
45C2×#66871C2211yescharacteristic
46#10622546—21no—
47C4×Dic11⋊C4—21no—
48C4×Dic11⋊C4C2211yescharacteristic
49#10622542C2211yescharacteristic
50#10622542C2211yescharacteristic
51C11×#340C2211yescharacteristic
52C11×#340C2211yescharacteristic
53#10622189C2211yescharacteristic
54#10622188C2211yescharacteristic
55#10622188C2211yescharacteristic
56#10622188C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622162C2211yescharacteristic
59C22×Q8×C11C2311yescharacteristic
60C22×Dic22C2311yescharacteristic
61C22×Dic22C2311yescharacteristic
62C22×C8×C11C2311yescharacteristic
63C22×C8×C11C2311yescharacteristic
64C4×Q8×C11—22no—
65C4×Q8×C11—41no—
66C2×C11×C4⋊C4—21no—
67C2×C11×C4⋊C4—21no—
68C2×C11×C4⋊C4—21no—
69C2×C11×C4⋊C4C2311yescharacteristic
70C2×C11×C4⋊C4C2311yescharacteristic
71C2×C11×C4⋊C4C2311yescharacteristic
72C2×C42×C11—21no—
73C2×C42×C11C2311yescharacteristic
74#66997—22no—
75#66997—22no—
76C2×#4326—22no—
77C2×#4326—22no—
78C2×#4326—41no—
79C2×C4⋊Dic11—21no—
80C2×C4⋊Dic11C2311yescharacteristic
81C2×C4⋊Dic11C2311yescharacteristic
82C2×Dic11⋊C4—21no—
83C2×Dic11⋊C4—21no—
84C2×Dic11⋊C4—21no—
85C2×Dic11⋊C4D411yescharacteristic
86C2×Dic11⋊C4D411yescharacteristic
87C2×C4×Dic11—21no—
88C2×C4×Dic11—21no—
89C2×C4×Dic11—21no—
90C2×C4×Dic11C2311yescharacteristic
91C2×C4×Dic11C2311yescharacteristic
92C22×C11⋊C8C2311yescharacteristic
93C22×C11⋊C8C2311yescharacteristic
94C2×Dic44—22no—
95C2×Dic44—41no—
96C2×Dic44—41no—
97#66940—22no—
98#66940—41no—
99C11×C4⋊C8—41no—
100C11×#103—41no—
101C11×#103—41no—
102#66899—22no—
103C11⋊#95—21no—
104C11⋊#95—21no—
105C11⋊#95—21no—
106C11⋊#95—21no—
107C11⋊#95—21no—
108C11⋊#95—21no—
109C11⋊#95—21no—
110C11⋊#95—21no—
111C11⋊#95—21no—
112C11⋊#95—21no—
113C11⋊#95—21no—
114C11⋊#95—21no—
115C11⋊#95—21no—
116C11⋊#95D411yescharacteristic
117C11⋊#95D411yescharacteristic
118#66880—22no—
119#66880—41no—
120C8×Dic11—41no—
121#66874—22no—
122#66874—22no—
123#66874—41no—
124#66871—22no—
125#66871—41no—
126#27068—111nomaximal, Sylow
127C2×Q8×C11—21no—
128C2×Q8×C11—21no—
129C2×Q8×C11—21no—
130C2×Q8×C11—21no—
131C2×Q8×C11—21no—
132C2×Q8×C11#4112yes—
133C22×C4×C11—21no—
134C22×C4×C11—21no—
135C22×C4×C11—21no—
136C22×C4×C11—21no—
137C22×C4×C11C2×D411yescharacteristic
138C22×C4×C11C2×D411yescharacteristic
139C22×C4×C11C2411yescharacteristic
140C22×Dic11—21no—
141C22×Dic11—21no—
142C22×Dic11—21no—
143C22×Dic11—21no—
144C22×Dic11C2×D411yescharacteristic
145C22×Dic11C2×D411yescharacteristic
146C22×Dic11C2×D411yescharacteristic
147C22×Dic11C2×D411yescharacteristic
148C2×Dic22—21no—
149C2×Dic22—21no—
150C2×Dic22—21no—
151C2×Dic22—21no—
152C2×Dic22—21no—
153C2×Dic22—21no—
154C2×Dic22—21no—
155C2×Dic22—21no—
156C2×Dic22—21no—
157C2×Dic22—21no—
158C2×Dic22—21no—
159C2×Dic22#4112yes—
160C2×C8×C11—21no—
161C2×C8×C11—21no—
162C2×C8×C11—21no—
163C2×C8×C11—21no—
164C2×C8×C11—21no—
165C2×C8×C11—21no—
166C11×C4⋊C4—21no—
167C11×C4⋊C4—21no—
168C11×C4⋊C4—21no—
169C11×C4⋊C4—21no—
170C11×C4⋊C4—21no—
171C11×C4⋊C4—42no—
172C11×C4⋊C4—42no—
173C11×C4⋊C4—81no—
174C11×C4⋊C4#4112yes—
175C42×C11—21no—
176C42×C11—21no—
177C42×C11—42no—
178#4326—44no—
179C4⋊Dic11—21no—
180C4⋊Dic11—21no—
181C4⋊Dic11—21no—
182C4⋊Dic11—21no—
183C4⋊Dic11—81no—
184Dic11⋊C4—24no—
185Dic11⋊C4—24no—
186Dic11⋊C4—41no—
187Dic11⋊C4—42no—
188Dic11⋊C4Q1614yescomplemented
189C4×Dic11—21no—
190C4×Dic11—21no—
191C4×Dic11—21no—
192C4×Dic11—21no—
193C4×Dic11—42no—
194C4×Dic11—42no—
195C4×Dic11—81no—
196C2×C11⋊C8—21no—
197C2×C11⋊C8—21no—
198C2×C11⋊C8—21no—
199C2×C11⋊C8—21no—
200C2×C11⋊C8—21no—
201C2×C11⋊C8#4112yes—
202Dic44—44no—
203#2511—111no—
204#2365—111no—
205#2095—111no—
206#2056—111no—
207#2043—111no—
208#2016—111no—
209#1969—111no—
210#1928—111no—
211#1928—111no—
212#1921—111no—
213#1916—111no—
214#1878—111no—
215#1878—111no—
216#1803D1111yescharacteristic
217C4×#103—111no—
218C23×C11C22×D411yescharacteristic
219Q8×C11—22no—
220Q8×C11—22no—
221Q8×C11—41no—
222Q8×C11—41no—
223C2×C4×C11—21no—
224C2×C4×C11—21no—
225C2×C4×C11—22no—
226C2×C4×C11—22no—
227C2×C4×C11—21no—
228C2×C4×C11—21no—
229C2×C4×C11—21no—
230C2×C4×C11—41no—
231C2×C4×C11—41no—
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—41no—
240C2×C4×C11C2×Q1612yes—
241C2×C4×C11C2×#4111yescharacteristic
242C2×C4×C11C2×#4111yescharacteristic
243C2×C4×C11C2×#4111yescharacteristic
244C2×C4×C11C2×#4111yescharacteristic
245C2×C4×C11H(5,𝔽2)11yescharacteristic
246C2×C4×C11H(5,𝔽2)11yescharacteristic
247C2×Dic11—21no—
248C2×Dic11—21no—
249C2×Dic11—21no—
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—41no—
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×Dic11C2×Q1612yes—
270C2×Dic11C2×Q1612yes—
271Dic22—22no—
272Dic22—22no—
273Dic22—41no—
274Dic22—41no—
275Dic22—41no—
276Dic22—41no—
277Dic22—41no—
278Dic22—41no—
279C8×C11—41no—
280C8×C11—41no—
281C11⋊C8—22no—
282C11⋊C8—41no—
283C22×Q16—111no—
284C22×Q16—111no—
285C2×C4⋊Q8—111no—
286C2×C4×Q8—111no—
287C2×C4×Q8C2×D1111yescharacteristic
288C2×#107—111no—
289C2×#107—111no—
290C2×C4⋊C8C2×D1111yescharacteristic
291C2×#103—111no—
292C2×#103—111no—
293C2×#103—111no—
294C2×#103—111no—
295C2×#103—111no—
296C2×#103—111no—
297C2×#103C2×D1111yescharacteristic
298C2×#103C2×D1111yescharacteristic
299C2×C4×C8—111no—
300#400—221no—
301#400—221no—
302#391—111no—
303#391—111no—
304#391—111no—
305#391—111no—
306#391—111no—
307#389—111no—
308#389—221no—
309#387—221no—
310#387—221no—
311#387—221no—
312#387—221no—
313#384C2×D1111yescharacteristic
314C4×C4⋊C4—111no—
315C4×C4⋊C4—111no—
316C4×C4⋊C4—111no—
317C4×C4⋊C4—221no—
318#340—111no—
319#340—111no—
320#340C2×D1111yescharacteristic
321#340C2×D1111yescharacteristic
322#336—111no—
323#336—111no—
324#336—111no—
325#336—111no—
326C22×C11#52511yescharacteristic
327C22×C11#54611yescharacteristic
328C22×C11#55011yescharacteristic
329C22×C11C22×Q1611yescharacteristic
330C22×C11#57511yescharacteristic
331C22×C11#57711yescharacteristic
332C22×C11#57811yescharacteristic
333C4×C11—22no—
334C4×C11—42no—
335C4×C11—41no—
336C4×C11—42no—
337C4×C11—81no—
338C4×C11—81no—
339C4×C11#52911yescharacteristic
340C4×C11#53811yescharacteristic
341C4×C11#55111yescharacteristic
342C4×C11#55311yescharacteristic
343Dic11—22no—
344Dic11—22no—
345Dic11—41no—
346Dic11—42no—
347Dic11—41no—
348Dic11—81no—
349Dic11—81no—
350Dic11—81no—
351C22×Q8—111no—
352C22×Q8—111no—
353C22×Q8C22×D1111yescharacteristic
354C2×Q16—222no—
355C2×Q16—222no—
356C2×Q16—222no—
357C2×Q16—441no—
358C2×Q16—441no—
359C2×Q16—441no—
360C22×C8—111no—
361C22×C8—111no—
362C22×C8C22×D1111yescharacteristic
363C22×C8C22×D1111yescharacteristic
364C4⋊Q8—222no—
365C4⋊Q8—222no—
366C4×Q8—22no—
367C4×Q8—41no—
368C4×Q8—222no—
369C4×Q8—441no—
370C2×C4⋊C4—21no—
371C2×C4⋊C4—21no—
372C2×C4⋊C4—21no—
373C2×C4⋊C4—111no—
374C2×C4⋊C4—111no—
375C2×C4⋊C4—111no—
376C2×C4⋊C4—111no—
377C2×C4⋊C4—221no—
378C2×C4⋊C4—221no—
379C2×C4⋊C4—221no—
380C2×C4⋊C4—221no—
381C2×C4⋊C4C22×D1111yescharacteristic
382C2×C4⋊C4C22×D1111yescharacteristic
383C2×C4⋊C4C22×D1111yescharacteristic
384C2×C42—21no—
385C2×C42—111no—
386C2×C42—111no—
387C2×C42—221no—
388C2×C42—221no—
389C2×C42—221no—
390C2×C42C22×D1111yescharacteristic
391#107—222no—
392#107—441no—
393C4⋊C8—41no—
394#103—41no—
395#103—41no—
396#103—222no—
397#103—222no—
398#103—222no—
399#103—222no—
400#103—441no—
401#103—441no—
402C4×C8—441no—
403#95—111no—
404#95—111no—
405#95—221no—
406#95—221no—
407#95—221no—
408#95—221no—
409#95—221no—
410#95—221no—
411#95—221no—
412#95—221no—
413#95—221no—
414#95—221no—
415#95—221no—
416#95—221no—
417#95—221no—
418C2×C11#246711yescharacteristic
419C2×C11#310411yescharacteristic
420C2×C11#312111yescharacteristic
421C2×C11#329911yescharacteristic
422C2×C11#331511yescharacteristic
423C2×C11#339511yescharacteristic
424C2×C11#340111yescharacteristic
425C2×Q8—21no—
426C2×Q8—21no—
427C2×Q8—21no—
428C2×Q8—21no—
429C2×Q8—21no—
430C2×Q8—112no—
431C2×Q8—221no—
432C2×Q8—221no—
433C2×Q8—221no—
434C2×Q8—221no—
435C2×Q8—221no—
436C2×Q8—221no—
437C2×Q8—221no—
438C2×Q8—221no—
439C2×Q8—221no—
440C2×Q8—221no—
441C2×Q8—221no—
442C2×Q8#434312yes—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—111no—
448C22×C4—111no—
449C22×C4—111no—
450C22×C4—111no—
451C22×C4—221no—
452C22×C4—221no—
453C22×C4—221no—
454C22×C4—221no—
455C22×C4D4×D1111yescharacteristic
456C22×C4D4×D1111yescharacteristic
457C22×C4C23×D1111yescharacteristic
458Q16—444no—
459Q16—444no—
460C2×C8—21no—
461C2×C8—21no—
462C2×C8—21no—
463C2×C8—21no—
464C2×C8—21no—
465C2×C8—21no—
466C2×C8—112no—
467C2×C8—221no—
468C2×C8—221no—
469C2×C8—221no—
470C2×C8—221no—
471C2×C8—221no—
472C4⋊C4—21no—
473C4⋊C4—21no—
474C4⋊C4—21no—
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—42no—
478C4⋊C4—42no—
479C4⋊C4—81no—
480C4⋊C4—114no—
481C4⋊C4—224no—
482C4⋊C4—224no—
483C4⋊C4—221no—
484C4⋊C4—221no—
485C4⋊C4—221no—
486C4⋊C4—221no—
487C4⋊C4—441no—
488C4⋊C4—442no—
489C4⋊C4—881no—
490C4⋊C4#433912yes—
491C42—21no—
492C42—21no—
493C42—42no—
494C42—221no—
495C42—221no—
496C42—221no—
497C42—221no—
498C42—442no—
499C42—442no—
500C42—881no—
501C11#2706811yescharacteristic, complemented, Sylow
502C23C2×D4×D1111yescharacteristic
503Q8—22no—
504Q8—22no—
505Q8—41no—
506Q8—41no—
507Q8—222no—
508Q8—222no—
509Q8—441no—
510Q8—441no—
511Q8—441no—
512Q8—441no—
513Q8—441no—
514Q8—441no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—22no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—22no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—41no—
532C2×C4—112no—
533C2×C4—112no—
534C2×C4—221no—
535C2×C4—221no—
536C2×C4—221no—
537C2×C4—221no—
538C2×C4—221no—
539C2×C4—221no—
540C2×C4—221no—
541C2×C4—221no—
542C2×C4—221no—
543C2×C4—221no—
544C2×C4—222no—
545C2×C4—441no—
546C2×C4—441no—
547C2×C4—441no—
548C2×C4—441no—
549C2×C4—441no—
550C2×C4—441no—
551C2×C4—441no—
552C2×C4—441no—
553C2×C4—441no—
554C2×C4—441no—
555C2×C4—441no—
556C2×C4Q16×D1112yes—
557C2×C4C2×#433911yescharacteristic
558C2×C4#6703711yescharacteristic
559C2×C4#6703711yescharacteristic
560C2×C4C2×#434311yescharacteristic
561C2×C4#41×D1111yescharacteristic
562C2×C4#41×D1111yescharacteristic
563C8—41no—
564C8—41no—
565C8—222no—
566C8—441no—
567C22#1062302111yescharacteristic
568C22#1062313011yescharacteristic
569C22#1062315811yescharacteristic
570C22#1062329311yescharacteristic
571C22C2×Q16×D1111yescharacteristic
572C22#1062330411yescharacteristic
573C22#1062331011yescharacteristic
574C4—22no—
575C4—42no—
576C4—41no—
577C4—42no—
578C4—81no—
579C4—81no—
580C4—222no—
581C4—222no—
582C4—442no—
583C4—441no—
584C4—441no—
585C4—881no—
586C4—881no—
587C4—881no—
588C4#1062304511yescharacteristic
589C4#1062305911yescharacteristic
590C4#1062314411yescharacteristic
591C4#1062316811yescharacteristic
592C2#1307267411yescharacteristic
593C2#1307865711yescharacteristic
594C2#1307885211yescharacteristic
595C2#1308048811yescharacteristic
596C2#1308071311yescharacteristic
597C2#1308161811yescharacteristic
598C2#1308167511yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1803C2
socle, prime radicalC23×C11C22×D4
hypercenter#1803D11
hypocenterC11#27068
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1803

Complements

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

NH ≅ G/Ntype
188. Dic11⋊C4Q16semidirect
501. C11#27068semidirect

Maximal subgroups

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

subgroupindex
#130731872
#130716702
#130701552
#130699392
#130698612
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