Finite Group Databasebeta

← #14812828

Subgroups — #14812828

Order 2816.

678 conjugacy classes of subgroups.

The subgroup lattice has 580 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13073851C211yesmaximal, characteristic, complemented
2#13071591C211yesmaximal, characteristic
3#13070141C211yesmaximal, characteristic
4#13070134C211yesmaximal, characteristic
5#13069985C211yesmaximal, characteristic
6#13069985C211yesmaximal, characteristic
7#13069385C211yesmaximal, characteristic, complemented
8#13069382C211yesmaximal, characteristic, complemented
9#13069376C211yesmaximal, characteristic, complemented
10#13069334C211yesmaximal, characteristic, complemented
11#13069210C211yesmaximal, characteristic, complemented
12#13069189C211yesmaximal, characteristic, complemented
13#13068623C211yesmaximal, characteristic
14C4×#66885C211yesmaximal, characteristic
15C11×#1846C211yesmaximal, characteristic, complemented
16C2×C4×D44C2211yescharacteristic
17C2×C11×#107C2211yescharacteristic
18C2×C11×#107C2211yescharacteristic
19C2×C11×#106C2211yescharacteristic
20C2×C11×#106C2211yescharacteristic
21C2×C4×C8×C11C2211yescharacteristic
22C11×#382C2211yescharacteristic
23C11×#382C2211yescharacteristic
24C2×#66885C2211yescharacteristic
25C2×#66885C2211yescharacteristic
26C2×Dic11⋊C8C2211yescharacteristic
27C2×Dic11⋊C8C2211yescharacteristic
28#10622601C2211yescharacteristic
29#10622601C2211yescharacteristic
30#10622598C2211yescharacteristic
31#10622598C2211yescharacteristic
32#10622590C2211yescharacteristic
33#10622589C2211yescharacteristic
34C4⋊C4×Dic11C2211yescharacteristic
35C4⋊C4×Dic11C2211yescharacteristic
36C2×#66873C2211yescharacteristic
37C2×#66873C2211yescharacteristic
38C2×#66872C2211yescharacteristic
39C2×#66871C2211yescharacteristic
40C4×C4⋊Dic11C2211yescharacteristic
41C4×C4⋊Dic11C2211yescharacteristic
42C2×C4⋊(C11⋊C8)C2211yescharacteristic
43#10622283—21no—
44#10622283—21no—
45#10622279—21no—
46#10622277—21no—
47#10622274—21no—
48#10622273—21no—
49#10622268—21no—
50#10622267—21no—
51#10622189C2211yescharacteristic
52#10622189C2211yescharacteristic
53#10622188C2211yescharacteristic
54#10622188C2211yescharacteristic
55#10622167C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59C22×D44C2311yescharacteristic
60C22×C4×D11—21no—
61C22×C8×C11C2311yescharacteristic
62C22×C8×C11C2311yescharacteristic
63C2×C11×C4⋊C4C2311yescharacteristic
64C2×C11×C4⋊C4C2311yescharacteristic
65C2×C11×C4⋊C4C2311yescharacteristic
66C2×C11×C4⋊C4C2311yescharacteristic
67C2×C42×C11C2311yescharacteristic
68C2×(C2×D11)⋊C4—21no—
69C2×(C2×D11)⋊C4—21no—
70C2×(C2×D11)⋊C4—21no—
71C2×(C2×D11)⋊C4—21no—
72C2×(C2×D11)⋊C4—21no—
73C2×C4⋊Dic11—21no—
74C2×C4⋊Dic11—21no—
75C2×C4⋊Dic11D411yescharacteristic
76C2×C4⋊Dic11D411yescharacteristic
77C2×C4⋊Dic11C2311yescharacteristic
78C2×C4⋊Dic11C2311yescharacteristic
79C2×C4⋊Dic11C2311yescharacteristic
80C2×Dic11⋊C4—21no—
81C2×Dic11⋊C4—21no—
82C2×C4×Dic11—21no—
83C2×C4×Dic11—21no—
84C2×C4×Dic11—21no—
85C2×C4×Dic11C2311yescharacteristic
86C2×C4×Dic11C2311yescharacteristic
87C22×C11⋊C8C2311yescharacteristic
88C22×C11⋊C8C2311yescharacteristic
89C4×D44—22no—
90C4×D44Q814yes—
91C11×#107—22no—
92C11×#107—22no—
93C11×#106—41no—
94C11×#106—41no—
95C4×C8×C11—22no—
96C11×#95—21no—
97C11×#95—21no—
98C11×#95—21no—
99C11×#95—21no—
100C11⋊#95—21no—
101C11⋊#95—21no—
102C11⋊#95—21no—
103C11⋊#95—21no—
104C11⋊#95—21no—
105C11⋊#95—21no—
106C11⋊#95—21no—
107C11⋊#95D411yescharacteristic
108C11⋊#95D411yescharacteristic
109#66885—22no—
110#66885—22no—
111Dic11⋊C8—22no—
112Dic11⋊C8—22no—
113#66873—41no—
114#66873—41no—
115#66872—41no—
116#66871—41no—
117C4⋊(C11⋊C8)—22no—
118#26094—111nomaximal, Sylow
119C23×D11—21no—
120C22×C4×C11—21no—
121C22×C4×C11—21no—
122C22×C4×C11—21no—
123C22×C4×C11—21no—
124C22×C4×C11C2×D411yescharacteristic
125C22×C4×C11C2×D411yescharacteristic
126C22×C4×C11C2411yescharacteristic
127C22×Dic11—21no—
128C22×Dic11—21no—
129C22×Dic11—21no—
130C22×Dic11C2×D411yescharacteristic
131C22×Dic11C2×D411yescharacteristic
132C22×Dic11C2×D411yescharacteristic
133C22×Dic11C2×D411yescharacteristic
134C2×D44—21no—
135C2×D44—21no—
136C2×D44—21no—
137C2×D44—21no—
138C2×D44—21no—
139C2×D44C2×Q812yes—
140C2×C4×D11—24no—
141C2×C4×D11—81no—
142C2×C4×D11—81no—
143C2×C8×C11—21no—
144C2×C8×C11—21no—
145C2×C8×C11—21no—
146C2×C8×C11—21no—
147C2×C8×C11#4112yes—
148C2×C8×C11#4112yes—
149C11×C4⋊C4—21no—
150C11×C4⋊C4—21no—
151C11×C4⋊C4—21no—
152C11×C4⋊C4—21no—
153C11×C4⋊C4—21no—
154C11×C4⋊C4—21no—
155C11×C4⋊C4—21no—
156C11×C4⋊C4—21no—
157C42×C11C2×Q812yes—
158C42×C11#4112yes—
159(C2×D11)⋊C4—24no—
160(C2×D11)⋊C4—42no—
161(C2×D11)⋊C4—42no—
162(C2×D11)⋊C4—81no—
163(C2×D11)⋊C4—81no—
164C4⋊Dic11—22no—
165C4⋊Dic11—21no—
166C4⋊Dic11—21no—
167C4⋊Dic11—21no—
168C4⋊Dic11—21no—
169C4⋊Dic11—21no—
170C4⋊Dic11—41no—
171C4⋊Dic11—42no—
172C4⋊Dic11—81no—
173C4⋊Dic11C2×Q812yes—
174Dic11⋊C4—42no—
175Dic11⋊C4—81no—
176C4×Dic11—21no—
177C4×Dic11—21no—
178C4×Dic11—21no—
179C4×Dic11—21no—
180C4×Dic11—81no—
181C4×Dic11—81no—
182C4×Dic11—81no—
183C2×C11⋊C8—21no—
184C2×C11⋊C8—21no—
185C2×C11⋊C8—21no—
186C2×C11⋊C8—21no—
187C2×C11⋊C8—21no—
188C2×C11⋊C8—21no—
189#2570—111no—
190#2357—111no—
191#2093—111no—
192#2092—111no—
193#2065—111no—
194#2065—111no—
195#1949—111no—
196#1949—111no—
197#1948—111no—
198#1939—111no—
199#1921—111no—
200#1918—111no—
201#1846D1111yescharacteristic, complemented
202#1804—111no—
203C4×#102—111no—
204C23×C11C22×D411yescharacteristic
205C22×D11—22no—
206C22×D11—41no—
207C22×D11—41no—
208C22×D11—41no—
209C22×D11—41no—
210C22×D11—41no—
211C22×D11—41no—
212C2×C4×C11—21no—
213C2×C4×C11—21no—
214C2×C4×C11—21no—
215C2×C4×C11—21no—
216C2×C4×C11—41no—
217C2×C4×C11—41no—
218C2×C4×C11—41no—
219C2×C4×C11—41no—
220C2×C4×C11—41no—
221C2×C4×C11—41no—
222C2×C4×C11—41no—
223C2×C4×C11—41no—
224C2×C4×C11—41no—
225C2×C4×C11—41no—
226C2×C4×C11—41no—
227C2×C4×C11—41no—
228C2×C4×C11C22⋊Q812yes—
229C2×C4×C11C22⋊Q812yes—
230C2×C4×C11C22×Q811yescharacteristic
231C2×C4×C11C2×#4111yescharacteristic
232C2×C4×C11C2×#4111yescharacteristic
233C2×C4×C11C2×#4111yescharacteristic
234C2×C4×C11H(5,𝔽2)11yescharacteristic
235C2×C4×C112−1+411yescharacteristic
236C2×Dic11—21no—
237C2×Dic11—21no—
238C2×Dic11—22no—
239C2×Dic11—21no—
240C2×Dic11—21no—
241C2×Dic11—21no—
242C2×Dic11—21no—
243C2×Dic11—21no—
244C2×Dic11—21no—
245C2×Dic11—21no—
246C2×Dic11—21no—
247C2×Dic11—21no—
248C2×Dic11—41no—
249C2×Dic11—41no—
250C2×Dic11—41no—
251C2×Dic11—41no—
252C2×Dic11—41no—
253C2×Dic11—41no—
254C2×Dic11—41no—
255C2×Dic11—41no—
256C2×Dic11#13512yes—
257D44—22no—
258D44—22no—
259D44—41no—
260D44—41no—
261C4×D11—84no—
262C8×C11—22no—
263C8×C11—22no—
264C11⋊C8—41no—
265C11⋊C8—41no—
266C2×C4×D4—111no—
267C2×#107—111no—
268C2×#107C2×D1111yescharacteristic
269C2×#107C2×D1111yescharacteristic
270C2×#106—111no—
271C2×#106C2×D1111yescharacteristic
272C2×#106C2×D1111yescharacteristic
273C2×C4⋊C8—111no—
274C2×C4⋊C8—111no—
275C2×C4⋊C8—111no—
276C2×#102—111no—
277C2×#102—111no—
278C2×#102—111no—
279C2×#102—111no—
280C2×C4×C8C2×D1111yescharacteristic
281#400—221no—
282#398—221no—
283#390—111no—
284#390—111no—
285#389—111no—
286#389—111no—
287#388—221no—
288#388—221no—
289#387—221no—
290#387—221no—
291#384—111no—
292#382—111no—
293#382C2×D1111yescharacteristic
294#382C2×D1111yescharacteristic
295#381—221no—
296C4×C4⋊C4—111no—
297C4×C4⋊C4—111no—
298C4×C4⋊C4—111no—
299C4×C4⋊C4—111no—
300C4×C22⋊C4—221no—
301#340—111no—
302#340—111no—
303#340—111no—
304#340—111no—
305#340—111no—
306#340—111no—
307#336—111no—
308#336—111no—
309C22×C11C2×C22⋊Q811yescharacteristic
310C22×C11#54711yescharacteristic
311C22×C11#55011yescharacteristic
312C22×C11C2×#13511yescharacteristic
313C22×C11#57511yescharacteristic
314C22×C11#57611yescharacteristic
315C22×C11#57711yescharacteristic
316C2×D11—42no—
317C2×D11—42no—
318C2×D11—42no—
319C2×D11—81no—
320C2×D11—81no—
321C2×D11—81no—
322C2×D11—81no—
323C4×C11—22no—
324C4×C11—22no—
325C4×C11—81no—
326C4×C11—81no—
327C4×C11—81no—
328C4×C11—81no—
329C4×C11#53311yescharacteristic
330C4×C11#54411yescharacteristic
331C4×C11#55211yescharacteristic
332C4×C11#55311yescharacteristic
333Dic11—22no—
334Dic11—42no—
335Dic11—41no—
336Dic11—41no—
337Dic11—41no—
338Dic11—81no—
339Dic11—81no—
340C22×D4—111no—
341C23×C4—221no—
342C22×C8—111no—
343C22×C8—111no—
344C22×C8C22×D1111yescharacteristic
345C22×C8C22×D1111yescharacteristic
346C4×D4—114no—
347C4×D4—222no—
348C2×C4⋊C4—111no—
349C2×C4⋊C4—111no—
350C2×C4⋊C4—111no—
351C2×C4⋊C4—111no—
352C2×C4⋊C4—111no—
353C2×C4⋊C4—221no—
354C2×C4⋊C4—221no—
355C2×C4⋊C4—221no—
356C2×C4⋊C4—221no—
357C2×C4⋊C4C22×D1111yescharacteristic
358C2×C4⋊C4C22×D1111yescharacteristic
359C2×C4⋊C4C22×D1111yescharacteristic
360C2×C4⋊C4C22×D1111yescharacteristic
361C2×C22⋊C4—221no—
362C2×C22⋊C4—221no—
363C2×C22⋊C4—221no—
364C2×C22⋊C4—221no—
365C2×C22⋊C4—221no—
366C2×C42—111no—
367C2×C42—111no—
368C2×C42—221no—
369C2×C42—221no—
370C2×C42—221no—
371C2×C42C22×D1111yescharacteristic
372#107—22no—
373#107—22no—
374#107—441no—
375#106—41no—
376#106—41no—
377#106—441no—
378C4⋊C8—222no—
379C4⋊C8—222no—
380C4⋊C8—222no—
381#102—222no—
382#102—222no—
383#102—441no—
384#102—441no—
385C4×C8—22no—
386#95—21no—
387#95—21no—
388#95—21no—
389#95—21no—
390#95—111no—
391#95—111no—
392#95—221no—
393#95—221no—
394#95—221no—
395#95—221no—
396#95—221no—
397#95—221no—
398#95—221no—
399C2×C11#244111yescharacteristic
400C2×C11#307611yescharacteristic
401C2×C11#308111yescharacteristic
402C2×C11#333711yescharacteristic
403C2×C11#335511yescharacteristic
404C2×C11#339611yescharacteristic
405C2×C11#340111yescharacteristic
406D11—82no—
407C24—221no—
408C2×D4—112no—
409C2×D4—221no—
410C2×D4—221no—
411C2×D4—221no—
412C2×D4—221no—
413C2×D4—221no—
414C22×C4—21no—
415C22×C4—21no—
416C22×C4—21no—
417C22×C4—21no—
418C22×C4—111no—
419C22×C4—111no—
420C22×C4—111no—
421C22×C4—111no—
422C22×C4—221no—
423C22×C4—224no—
424C22×C4—221no—
425C22×C4—221no—
426C22×C4—881no—
427C22×C4—881no—
428C22×C4D4×D1111yescharacteristic
429C22×C4D4×D1111yescharacteristic
430C22×C4C23×D1111yescharacteristic
431C2×C8—21no—
432C2×C8—21no—
433C2×C8—21no—
434C2×C8—21no—
435C2×C8—221no—
436C2×C8—221no—
437C2×C8—221no—
438C2×C8—221no—
439C2×C8—221no—
440C2×C8—221no—
441C2×C8#434112yes—
442C2×C8#434312yes—
443C4⋊C4—21no—
444C4⋊C4—21no—
445C4⋊C4—21no—
446C4⋊C4—21no—
447C4⋊C4—21no—
448C4⋊C4—21no—
449C4⋊C4—21no—
450C4⋊C4—21no—
451C4⋊C4—112no—
452C4⋊C4—222no—
453C4⋊C4—221no—
454C4⋊C4—221no—
455C4⋊C4—221no—
456C4⋊C4—221no—
457C4⋊C4—221no—
458C4⋊C4—441no—
459C4⋊C4—442no—
460C4⋊C4—442no—
461C4⋊C4—881no—
462C4⋊C4—881no—
463C22⋊C4—224no—
464C22⋊C4—442no—
465C22⋊C4—442no—
466C22⋊C4—881no—
467C22⋊C4—881no—
468C42—221no—
469C42—221no—
470C42—221no—
471C42—221no—
472C42—881no—
473C42—881no—
474C42—881no—
475C42#433912yes—
476C42Q8×D1112yes—
477C11#2609411yescharacteristic, complemented, Sylow
478C23—222no—
479C23—441no—
480C23—441no—
481C23—441no—
482C23—441no—
483C23—441no—
484C23—441no—
485C23C2×D4×D1111yescharacteristic
486D4—222no—
487D4—222no—
488D4—441no—
489D4—441no—
490C2×C4—21no—
491C2×C4—21no—
492C2×C4—21no—
493C2×C4—21no—
494C2×C4—41no—
495C2×C4—41no—
496C2×C4—41no—
497C2×C4—41no—
498C2×C4—41no—
499C2×C4—41no—
500C2×C4—41no—
501C2×C4—41no—
502C2×C4—41no—
503C2×C4—41no—
504C2×C4—41no—
505C2×C4—41no—
506C2×C4—112no—
507C2×C4—221no—
508C2×C4—221no—
509C2×C4—221no—
510C2×C4—221no—
511C2×C4—221no—
512C2×C4—222no—
513C2×C4—221no—
514C2×C4—221no—
515C2×C4—221no—
516C2×C4—221no—
517C2×C4—221no—
518C2×C4—221no—
519C2×C4—441no—
520C2×C4—441no—
521C2×C4—441no—
522C2×C4—441no—
523C2×C4—441no—
524C2×C4—441no—
525C2×C4—441no—
526C2×C4—441no—
527C2×C4—884no—
528C2×C4#6694912yes—
529C2×C4#6694912yes—
530C2×C4C2×#433911yescharacteristic
531C2×C4C2×#434111yescharacteristic
532C2×C4#6703711yescharacteristic
533C2×C4C2×Q8×D1111yescharacteristic
534C2×C4C2×#434311yescharacteristic
535C2×C4#6704011yescharacteristic
536C8—22no—
537C8—22no—
538C8—441no—
539C8—441no—
540C22—442no—
541C22—442no—
542C22—442no—
543C22—881no—
544C22—881no—
545C22—881no—
546C22—881no—
547C22C2×#6694911yescharacteristic
548C22#1062324911yescharacteristic
549C22#1062325711yescharacteristic
550C22D11×#13511yescharacteristic
551C22#1062329911yescharacteristic
552C22#1062330011yescharacteristic
553C22#1062330111yescharacteristic
554C4—22no—
555C4—22no—
556C4—81no—
557C4—81no—
558C4—81no—
559C4—81no—
560C4—222no—
561C4—441no—
562C4—441no—
563C4—441no—
564C4—442no—
565C4—881no—
566C4—881no—
567C4#1062304411yescharacteristic
568C4#1062304511yescharacteristic
569C4#1062325911yescharacteristic
570C4#1062326011yescharacteristic
571C2—882no—
572C2#1307233211yescharacteristic
573C2#1307840211yescharacteristic
574C2#1307845011yescharacteristic
575C2#1308099411yescharacteristic
576C2#1308122011yescharacteristic
577C2#1308162511yescharacteristic
578C2#1308168811yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1846C2
socleC23×C11C22×D4
prime radicalC22×D44C23
hypercenter#1846D11
hypocenterC11#26094
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1846

Complements

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

NH ≅ G/Ntype
1. #13073851C2semidirect
7. #13069385C2semidirect
8. #13069382C2semidirect
9. #13069376C2semidirect
10. #13069334C2semidirect
11. #13069210C2semidirect
12. #13069189C2semidirect
15. C11×#1846C2semidirect
201. #1846D11semidirect
477. C11#26094semidirect

Maximal subgroups

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

subgroupindex
#130738512
#130715912
#130701412
#130701342
#130699852
#130693852
#130693822
#130693762
#130693342
#130692102
#130691892
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C4×#668852
C11×#18462
#2609411