Finite Group Databasebeta

← #14812740

Subgroups — #14812740

Order 2816.

714 conjugacy classes of subgroups.

The subgroup lattice has 586 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13073857C211yesmaximal, characteristic, complemented
2#13071564C211yesmaximal, characteristic
3#13070139C211yesmaximal, characteristic
4#13070137C211yesmaximal, characteristic
5#13070002C211yesmaximal, characteristic
6#13069386C211yesmaximal, characteristic, complemented
7#13069381C211yesmaximal, characteristic, complemented
8#13069378C211yesmaximal, characteristic, complemented
9#13069331C211yesmaximal, characteristic, complemented
10#13069206C211yesmaximal, characteristic, complemented
11#13069205C211yesmaximal, characteristic, complemented
12#13068774C211yesmaximal, characteristic, complemented
13#13068614C211yesmaximal, characteristic
14#102×Dic11C211yesmaximal, characteristic
15C11×#2067C211yesmaximal, characteristic
16C2×D4×Dic11C2211yescharacteristic
17C2×#66930—21no—
18C2×C11×#107C2211yescharacteristic
19C2×C11×C4⋊C8C2211yescharacteristic
20C2×C11×#102C2211yescharacteristic
21C2×C11×#102C2211yescharacteristic
22C11×#390C2211yescharacteristic
23C11×#389C2211yescharacteristic
24#10622834C2211yescharacteristic
25C2×#66896C2211yescharacteristic
26C2×#66896C2211yescharacteristic
27C2×#66882C2211yescharacteristic
28C2×#66881C2211yescharacteristic
29C2×Dic11⋊C8C2211yescharacteristic
30C2×Dic11⋊C8C2211yescharacteristic
31C2×C8×Dic11C2211yescharacteristic
32#10622595—21no—
33#10622590C2211yescharacteristic
34#10622589C2211yescharacteristic
35#10622589C2211yescharacteristic
36C4⋊C4×Dic11C2211yescharacteristic
37C4⋊C4×Dic11C2211yescharacteristic
38#10622586C2211yescharacteristic
39#10622585—21no—
40C2×#66872C2211yescharacteristic
41C2×#66871C2211yescharacteristic
42C2×#66871C2211yescharacteristic
43#10622558—21no—
44#10622557—21no—
45#10622555—21no—
46#10622549C2211yescharacteristic
47C4×C4⋊Dic11C2211yescharacteristic
48C4×Dic11⋊C4C2211yescharacteristic
49#10622271—21no—
50#10622263—21no—
51C11×#340C2211yescharacteristic
52#10622189C2211yescharacteristic
53#10622189C2211yescharacteristic
54#10622188C2211yescharacteristic
55#10622167C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622162C2211yescharacteristic
59C22×D4×C11C2311yescharacteristic
60C23×Dic11—21no—
61C22×C8×C11C2311yescharacteristic
62C22×C8×C11C2311yescharacteristic
63C2×C11×C4⋊C4—21no—
64C2×C11×C4⋊C4C2311yescharacteristic
65C2×C11×C4⋊C4C2311yescharacteristic
66C2×C11×C4⋊C4C2311yescharacteristic
67C2×C11×C22⋊C4—21no—
68C2×C11×C22⋊C4—21no—
69C2×C42×C11C2311yescharacteristic
70C2×C22⋊Dic11—21no—
71C2×C22⋊Dic11—21no—
72C2×C22⋊Dic11—21no—
73D4×Dic11—22no—
74D4×Dic11Q814yes—
75C2×C4⋊Dic11C2311yescharacteristic
76C2×C4⋊Dic11C2311yescharacteristic
77C2×C4⋊Dic11C2311yescharacteristic
78C2×C4⋊Dic11C2311yescharacteristic
79C2×Dic11⋊C4—21no—
80C2×Dic11⋊C4—21no—
81C2×Dic11⋊C4—21no—
82C2×Dic11⋊C4—21no—
83C2×Dic11⋊C4—21no—
84C2×Dic11⋊C4D411yescharacteristic
85C2×Dic11⋊C4D411yescharacteristic
86C2×C4×Dic11—21no—
87C2×C4×Dic11—21no—
88C2×C4×Dic11—21no—
89C2×C4×Dic11C2311yescharacteristic
90C2×C4×Dic11C2311yescharacteristic
91C22×C11⋊C8C2311yescharacteristic
92C22×C11⋊C8C2311yescharacteristic
93#66930—44no—
94C11×#107—41no—
95C11×C4⋊C8—22no—
96C11×#102—22no—
97C11×#102—41no—
98C11×#95—21no—
99#66896—22no—
100#66896—41no—
101C11⋊#95—21no—
102C11⋊#95—21no—
103C11⋊#95—21no—
104C11⋊#95—21no—
105C11⋊#95—21no—
106C11⋊#95—21no—
107C11⋊#95—21no—
108C11⋊#95—21no—
109C11⋊#95D411yescharacteristic
110C11⋊#95D411yescharacteristic
111#66882—41no—
112#66881—41no—
113Dic11⋊C8—22no—
114Dic11⋊C8—22no—
115C8×Dic11—22no—
116#66872—41no—
117#66871—22no—
118#66871—22no—
119#26087—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—24no—
134C22×Dic11—21no—
135C22×Dic11—21no—
136C22×Dic11—21no—
137C22×Dic11—21no—
138C22×Dic11—42no—
139C22×Dic11—42no—
140C22×Dic11C2×D411yescharacteristic
141C22×Dic11C2×D411yescharacteristic
142C22×Dic11C2×D411yescharacteristic
143C22×Dic11C2×D411yescharacteristic
144C2×C8×C11—21no—
145C2×C8×C11—21no—
146C2×C8×C11—21no—
147C2×C8×C11—21no—
148C2×C8×C11—21no—
149C2×C8×C11#4112yes—
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—81no—
157C11×C22⋊C4—42no—
158C11×C22⋊C4—81no—
159C42×C11—21no—
160C42×C11—21no—
161C22⋊Dic11—24no—
162C22⋊Dic11—42no—
163C22⋊Dic11—81no—
164C4⋊Dic11—21no—
165C4⋊Dic11—21no—
166C4⋊Dic11—21no—
167C4⋊Dic11—21no—
168C4⋊Dic11—21no—
169C4⋊Dic11—21no—
170C4⋊Dic11—21no—
171C4⋊Dic11C2×Q812yes—
172Dic11⋊C4—22no—
173Dic11⋊C4—22no—
174Dic11⋊C4—42no—
175Dic11⋊C4—42no—
176Dic11⋊C4—81no—
177Dic11⋊C4—81no—
178Dic11⋊C4—81no—
179C4×Dic11—21no—
180C4×Dic11—21no—
181C4×Dic11—42no—
182C4×Dic11—42no—
183C4×Dic11—42no—
184C4×Dic11C2×Q812yes—
185C4×Dic11#4112yes—
186C2×C11⋊C8—21no—
187C2×C11⋊C8—21no—
188C2×C11⋊C8—21no—
189C2×C11⋊C8—21no—
190C2×C11⋊C8—21no—
191C2×C11⋊C8#4112yes—
192#2571—111no—
193#2354—111no—
194#2092—111no—
195#2092—111no—
196#2067—111no—
197#2067D1111yescharacteristic
198#1949—111no—
199#1949—111no—
200#1948—111no—
201#1939—111no—
202#1921—111no—
203#1921—111no—
204#1845—111no—
205#1802—111no—
206C4×#102—111no—
207C23×C11—22no—
208C23×C11—41no—
209C23×C11—41no—
210C23×C11—41no—
211C23×C11—41no—
212C23×C11—41no—
213C23×C11—41no—
214C23×C11C22×D411yescharacteristic
215D4×C11—22no—
216D4×C11—22no—
217D4×C11—41no—
218D4×C11—41no—
219C2×C4×C11—21no—
220C2×C4×C11—21no—
221C2×C4×C11—21no—
222C2×C4×C11—21no—
223C2×C4×C11—21no—
224C2×C4×C11—21no—
225C2×C4×C11—41no—
226C2×C4×C11—41no—
227C2×C4×C11—41no—
228C2×C4×C11—41no—
229C2×C4×C11—41no—
230C2×C4×C11—41no—
231C2×C4×C11—41no—
232C2×C4×C11—41no—
233C2×C4×C11—41no—
234C2×C4×C11C22×Q811yescharacteristic
235C2×C4×C11C2×#4111yescharacteristic
236C2×C4×C11C2×#4111yescharacteristic
237C2×C4×C11C2×#4111yescharacteristic
238C2×C4×C11H(5,𝔽2)11yescharacteristic
239C2×C4×C112−1+411yescharacteristic
240C2×Dic11—21no—
241C2×Dic11—21no—
242C2×Dic11—22no—
243C2×Dic11—21no—
244C2×Dic11—21no—
245C2×Dic11—21no—
246C2×Dic11—21no—
247C2×Dic11—21no—
248C2×Dic11—21no—
249C2×Dic11—41no—
250C2×Dic11—41no—
251C2×Dic11—48no—
252C2×Dic11—41no—
253C2×Dic11—41no—
254C2×Dic11—41no—
255C2×Dic11—41no—
256C2×Dic11—41no—
257C2×Dic11—41no—
258C2×Dic11—41no—
259C2×Dic11—41no—
260C2×Dic11—41no—
261C2×Dic11C22⋊Q812yes—
262C2×Dic11C22⋊Q812yes—
263C2×Dic11#13512yes—
264C2×Dic11AGL(1,ℤ/8)12yes—
265C8×C11—22no—
266C8×C11—41no—
267C11⋊C8—22no—
268C11⋊C8—41no—
269C2×C4×D4—111no—
270C2×#117—221no—
271C2×#107—111no—
272C2×#107—111no—
273C2×#107—111no—
274C2×#107C2×D1111yescharacteristic
275C2×#106—111no—
276C2×#106—111no—
277C2×C4⋊C8—111no—
278C2×C4⋊C8—111no—
279C2×C4⋊C8C2×D1111yescharacteristic
280C2×#102—111no—
281C2×#102—111no—
282C2×#102C2×D1111yescharacteristic
283C2×#102C2×D1111yescharacteristic
284C2×C4×C8—111no—
285#400—221no—
286#400—221no—
287#390—111no—
288#390C2×D1111yescharacteristic
289#389—111no—
290#389—221no—
291#389C2×D1111yescharacteristic
292#388—221no—
293#388—221no—
294#384—111no—
295#384—111no—
296#382—111no—
297#382—111no—
298#382—221no—
299#380—221no—
300C4×C4⋊C4—111no—
301C4×C4⋊C4—111no—
302C4×C4⋊C4—111no—
303C4×C4⋊C4—111no—
304#340—111no—
305#340—111no—
306#340—111no—
307#340—111no—
308#340—111no—
309#340C2×D1111yescharacteristic
310#336—111no—
311#336—111no—
312C22×C11—42no—
313C22×C11—42no—
314C22×C11—42no—
315C22×C11—81no—
316C22×C11—81no—
317C22×C11—81no—
318C22×C11—81no—
319C22×C11C2×C22⋊Q811yescharacteristic
320C22×C11#54711yescharacteristic
321C22×C11#55011yescharacteristic
322C22×C11C2×#13511yescharacteristic
323C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
324C22×C11#57611yescharacteristic
325C22×C11#57811yescharacteristic
326C4×C11—41no—
327C4×C11—41no—
328C4×C11—81no—
329C4×C11—81no—
330C4×C11—81no—
331C4×C11#53311yescharacteristic
332C4×C11#54411yescharacteristic
333C4×C11#55211yescharacteristic
334C4×C11#55311yescharacteristic
335Dic11—22no—
336Dic11—42no—
337Dic11—41no—
338Dic11—41no—
339Dic11—81no—
340Dic11—81no—
341Dic11—81no—
342Dic11#47814yes—
343C22×D4C22×D1111yescharacteristic
344C23×C4—221no—
345C22×C8—111no—
346C22×C8—111no—
347C22×C8C22×D1111yescharacteristic
348C22×C8C22×D1111yescharacteristic
349C4×D4—114no—
350C4×D4—222no—
351#117—444no—
352C2×C4⋊C4—21no—
353C2×C4⋊C4—111no—
354C2×C4⋊C4—111no—
355C2×C4⋊C4—111no—
356C2×C4⋊C4—111no—
357C2×C4⋊C4—111no—
358C2×C4⋊C4—111no—
359C2×C4⋊C4—221no—
360C2×C4⋊C4—221no—
361C2×C4⋊C4—221no—
362C2×C4⋊C4—221no—
363C2×C4⋊C4—221no—
364C2×C4⋊C4C22×D1111yescharacteristic
365C2×C4⋊C4C22×D1111yescharacteristic
366C2×C4⋊C4C22×D1111yescharacteristic
367C2×C22⋊C4—21no—
368C2×C22⋊C4—21no—
369C2×C22⋊C4—221no—
370C2×C22⋊C4—221no—
371C2×C22⋊C4—221no—
372C2×C42—111no—
373C2×C42—111no—
374C2×C42—221no—
375C2×C42—221no—
376C2×C42—221no—
377C2×C42C22×D1111yescharacteristic
378#107—41no—
379#107—222no—
380#107—222no—
381#107—441no—
382#106—441no—
383#106—441no—
384C4⋊C8—22no—
385C4⋊C8—222no—
386C4⋊C8—222no—
387#102—22no—
388#102—41no—
389#102—222no—
390#102—441no—
391C4×C8—222no—
392#95—21no—
393#95—111no—
394#95—111no—
395#95—221no—
396#95—221no—
397#95—221no—
398#95—221no—
399#95—221no—
400#95—221no—
401#95—221no—
402#95—221no—
403C2×C11—82no—
404C2×C11#244111yescharacteristic
405C2×C11C2×#47811yescharacteristic
406C2×C11#308311yescharacteristic
407C2×C11#334111yescharacteristic
408C2×C11#335311yescharacteristic
409C2×C11#339311yescharacteristic
410C2×C11#339911yescharacteristic
411C24—21no—
412C2×D4—21no—
413C2×D4—21no—
414C2×D4—21no—
415C2×D4—21no—
416C2×D4—21no—
417C2×D4Q8×D1112yes—
418C22×C4—21no—
419C22×C4—21no—
420C22×C4—21no—
421C22×C4—111no—
422C22×C4—111no—
423C22×C4—111no—
424C22×C4—111no—
425C22×C4—224no—
426C22×C4—221no—
427C22×C4—221no—
428C22×C4—221no—
429C22×C4—221no—
430C22×C4—442no—
431C22×C4—442no—
432C22×C4D4×D1111yescharacteristic
433C22×C4D4×D1111yescharacteristic
434C22×C4C23×D1111yescharacteristic
435C2×C8—21no—
436C2×C8—21no—
437C2×C8—21no—
438C2×C8—21no—
439C2×C8—21no—
440C2×C8—112no—
441C2×C8—221no—
442C2×C8—221no—
443C2×C8—221no—
444C2×C8—221no—
445C2×C8—221no—
446C2×C8#434112yes—
447C4⋊C4—21no—
448C4⋊C4—21no—
449C4⋊C4—21no—
450C4⋊C4—21no—
451C4⋊C4—21no—
452C4⋊C4—21no—
453C4⋊C4—81no—
454C4⋊C4—112no—
455C4⋊C4—222no—
456C4⋊C4—222no—
457C4⋊C4—221no—
458C4⋊C4—221no—
459C4⋊C4—221no—
460C4⋊C4—221no—
461C4⋊C4—221no—
462C4⋊C4—221no—
463C4⋊C4—221no—
464C4⋊C4—442no—
465C4⋊C4—442no—
466C4⋊C4—881no—
467C4⋊C4—881no—
468C4⋊C4—881no—
469C22⋊C4—42no—
470C22⋊C4—81no—
471C22⋊C4—224no—
472C22⋊C4—442no—
473C22⋊C4—881no—
474C42—21no—
475C42—21no—
476C42—112no—
477C42—112no—
478C42—221no—
479C42—221no—
480C42—442no—
481C42—442no—
482C42—442no—
483C11#2608711yescharacteristic, complemented, Sylow
484C23—22no—
485C23—41no—
486C23—41no—
487C23—41no—
488C23—41no—
489C23—41no—
490C23—41no—
491C23C2×D4×D1111yescharacteristic
492D4—22no—
493D4—22no—
494D4—41no—
495D4—41no—
496C2×C4—21no—
497C2×C4—21no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—41no—
503C2×C4—41no—
504C2×C4—41no—
505C2×C4—41no—
506C2×C4—41no—
507C2×C4—41no—
508C2×C4—41no—
509C2×C4—41no—
510C2×C4—41no—
511C2×C4—112no—
512C2×C4—112no—
513C2×C4—112no—
514C2×C4—112no—
515C2×C4—221no—
516C2×C4—221no—
517C2×C4—221no—
518C2×C4—221no—
519C2×C4—221no—
520C2×C4—221no—
521C2×C4—221no—
522C2×C4—221no—
523C2×C4—222no—
524C2×C4—448no—
525C2×C4—441no—
526C2×C4—441no—
527C2×C4—441no—
528C2×C4—441no—
529C2×C4—441no—
530C2×C4—441no—
531C2×C4—441no—
532C2×C4—441no—
533C2×C4—441no—
534C2×C4—441no—
535C2×C4—441no—
536C2×C4C2×#434111yescharacteristic
537C2×C4#6703711yescharacteristic
538C2×C4C2×Q8×D1111yescharacteristic
539C2×C4#41×D1111yescharacteristic
540C2×C4#41×D1111yescharacteristic
541C2×C4#6704311yescharacteristic
542C8—22no—
543C8—41no—
544C8—222no—
545C8—441no—
546C22—42no—
547C22—42no—
548C22—42no—
549C22—81no—
550C22—81no—
551C22—81no—
552C22—81no—
553C22#1062313011yescharacteristic
554C22#1062314211yescharacteristic
555C22D11×C22⋊Q811yescharacteristic
556C22#1062328811yescharacteristic
557C22D11×#13511yescharacteristic
558C22D11×AGL(1,ℤ/8)11yescharacteristic
559C22#1062331011yescharacteristic
560C4—41no—
561C4—41no—
562C4—81no—
563C4—81no—
564C4—81no—
565C4—114no—
566C4—222no—
567C4—442no—
568C4—441no—
569C4—441no—
570C4—881no—
571C4—881no—
572C4—881no—
573C4#1062313211yescharacteristic
574C4#1062315311yescharacteristic
575C4#1062315411yescharacteristic
576C4#1062323911yescharacteristic
577C2—82no—
578C2#1307232411yescharacteristic
579C2D11×#47811yescharacteristic
580C2#1307846211yescharacteristic
581C2#1308103511yescharacteristic
582C2#1308119511yescharacteristic
583C2#1308159911yescharacteristic
584C2#1308166111yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2067C2
socleC23×C11C22×D4
prime radicalC22×D4×C11C23
hypercenter#2067D11
hypocenterC11#26087
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2067

Complements

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

NH ≅ G/Ntype
1. #13073857C2semidirect
6. #13069386C2semidirect
7. #13069381C2semidirect
8. #13069378C2semidirect
9. #13069331C2semidirect
10. #13069206C2semidirect
11. #13069205C2semidirect
12. #13068774C2semidirect
483. C11#26087semidirect

Maximal subgroups

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

subgroupindex
#130738572
#130715642
#130701392
#130701372
#130700022
#130693862
#130693812
#130693782
#130693312
#130692062
#130692052
#130687742
#130686142
#102×Dic112
C11×#20672
#2608711