Finite Group Databasebeta

← #14811843

Subgroups — #14811843

Order 2816.

696 conjugacy classes of subgroups.

The subgroup lattice has 584 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13072341C211yesmaximal, characteristic
2#13071501C211yesmaximal, characteristic
3#13070189C211yesmaximal, characteristic, complemented
4#13070120C211yesmaximal, characteristic, complemented
5#13070116C211yesmaximal, characteristic, complemented
6#13069953C211yesmaximal, characteristic, complemented
7#13069572C211yesmaximal, characteristic, complemented
8#13069383C211yesmaximal, characteristic, complemented
9#13069197C211yesmaximal, characteristic, complemented
10#13069193C211yesmaximal, characteristic, complemented
11#13068811C211yesmaximal, characteristic
12#13068798C211yesmaximal, characteristic
13#13068647C211yesmaximal, characteristic
14#13068337C211yesmaximal, characteristic
15C11×#1825C211yesmaximal, characteristic
16C2×C11×#117C2211yescharacteristic
17C22×C4⋊Dic11C2211yescharacteristic
18C22×#4318C2211yescharacteristic
19C2×#66943C2211yescharacteristic
20C2×C11×C22⋊C8C2211yescharacteristic
21C11×#380C2211yescharacteristic
22#10622825C2211yescharacteristic
23C4×C22⋊Dic11C2211yescharacteristic
24C2×#66881C2211yescharacteristic
25C2×#66881C2211yescharacteristic
26C2×Dic11⋊C8C2211yescharacteristic
27C2×Dic11⋊C8C2211yescharacteristic
28#10622598C2211yescharacteristic
29#10622598C2211yescharacteristic
30#10622598C2211yescharacteristic
31#10622590C2211yescharacteristic
32C4⋊C4×Dic11C2211yescharacteristic
33C4⋊C4×Dic11C2211yescharacteristic
34#10622586C2211yescharacteristic
35C2×#66872C2211yescharacteristic
36C2×#66871C2211yescharacteristic
37#10622564—21no—
38#10622564—21no—
39#10622563—21no—
40#10622555—21no—
41#10622549—21no—
42#10622545—21no—
43#10622274—21no—
44#10622273—21no—
45C11×#340C2211yescharacteristic
46C11×#340C2211yescharacteristic
47C11×#340C2211yescharacteristic
48C11×#340C2211yescharacteristic
49#10622189C2211yescharacteristic
50#10622189C2211yescharacteristic
51#10622188C2211yescharacteristic
52#10622188C2211yescharacteristic
53#10622167C2211yescharacteristic
54#10622167C2211yescharacteristic
55#10622167C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59C23×C4×C11C2311yescharacteristic
60C23×Dic11—21no—
61C22×C8×C11C2311yescharacteristic
62C22×C8×C11C2311yescharacteristic
63C11×#117—22no—
64C11×#117Q814yes—
65C2×C11×C4⋊C4C2311yescharacteristic
66C2×C11×C4⋊C4C2311yescharacteristic
67C2×C11×C4⋊C4C2311yescharacteristic
68C2×C11×C4⋊C4C2311yescharacteristic
69C2×C11×C22⋊C4—21no—
70C2×C11×C22⋊C4—21no—
71C2×C42×C11—21no—
72C2×C22⋊Dic11—21no—
73C2×C22⋊Dic11D411yescharacteristic
74C2×C22⋊Dic11D411yescharacteristic
75C2×C4⋊Dic11—22no—
76C2×C4⋊Dic11—21no—
77C2×C4⋊Dic11—21no—
78C2×C4⋊Dic11—21no—
79C2×C4⋊Dic11—21no—
80C2×C4⋊Dic11—21no—
81C2×C4⋊Dic11—41no—
82C2×C4⋊Dic11C2311yescharacteristic
83C2×C4⋊Dic11C2311yescharacteristic
84C2×C4⋊Dic11C2311yescharacteristic
85C2×C4⋊Dic11C2311yescharacteristic
86C2×Dic11⋊C4—21no—
87C2×Dic11⋊C4—21no—
88C2×C4×Dic11—21no—
89C2×C4×Dic11—21no—
90C2×C4×Dic11C2311yescharacteristic
91C2×C4×Dic11C2311yescharacteristic
92C2×#4318—22no—
93C2×#4318—22no—
94C2×#4318—41no—
95C22×C11⋊C8C2311yescharacteristic
96C22×C11⋊C8C2311yescharacteristic
97#66943—22no—
98#66943—41no—
99C11×C22⋊C8—22no—
100C11×#95—21no—
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⋊#95—21no—
110C11⋊#95D411yescharacteristic
111C11⋊#95D411yescharacteristic
112#66881—22no—
113#66881—41no—
114Dic11⋊C8—22no—
115Dic11⋊C8—41no—
116#66872—22no—
117#66871—41no—
118#26019—111nomaximal, Sylow
119C24×C11C2×D411yescharacteristic
120C22×C4×C11—21no—
121C22×C4×C11—21no—
122C22×C4×C11—21no—
123C22×C4×C11—21no—
124C22×C4×C11—21no—
125C22×C4×C11—21no—
126C22×C4×C11—21no—
127C22×C4×C11—21no—
128C22×C4×C11C2×D411yescharacteristic
129C22×C4×C11C2×Q812yes—
130C22×C4×C11#4112yes—
131C22×C4×C11C2411yescharacteristic
132C22×Dic11—21no—
133C22×Dic11—21no—
134C22×Dic11—21no—
135C22×Dic11—21no—
136C22×Dic11—42no—
137C22×Dic11—42no—
138C22×Dic11—81no—
139C22×Dic11C2×D411yescharacteristic
140C22×Dic11C2×D411yescharacteristic
141C22×Dic11C2×D411yescharacteristic
142C22×Dic11C2×D411yescharacteristic
143C2×C8×C11—21no—
144C2×C8×C11—21no—
145C2×C8×C11—21no—
146C2×C8×C11—21no—
147C2×C8×C11—21no—
148C2×C8×C11—21no—
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⋊C4C2×Q812yes—
156C11×C4⋊C4C2×Q812yes—
157C11×C22⋊C4—24no—
158C11×C22⋊C4—42no—
159C42×C11—24no—
160C22⋊Dic11—41no—
161C22⋊Dic11—41no—
162C22⋊Dic11—81no—
163C4⋊Dic11—21no—
164C4⋊Dic11—21no—
165C4⋊Dic11—21no—
166C4⋊Dic11—21no—
167C4⋊Dic11—21no—
168C4⋊Dic11—21no—
169C4⋊Dic11—21no—
170C4⋊Dic11—42no—
171C4⋊Dic11—42no—
172C4⋊Dic11—81no—
173C4⋊Dic11—81no—
174C4⋊Dic11—81no—
175C4⋊Dic11#4112yes—
176Dic11⋊C4—42no—
177Dic11⋊C4—81no—
178C4×Dic11—21no—
179C4×Dic11—21no—
180C4×Dic11—21no—
181C4×Dic11—21no—
182C4×Dic11—42no—
183C4×Dic11—42no—
184#4318—44no—
185C2×C11⋊C8—21no—
186C2×C11⋊C8—21no—
187C2×C11⋊C8—21no—
188C2×C11⋊C8—21no—
189C2×C11⋊C8—21no—
190C2×C11⋊C8#4112yes—
191#2442—111no—
192#2346—111no—
193#2101—111no—
194#2088—111no—
195#2088—111no—
196#2059—111no—
197#1989—111no—
198#1949—111no—
199#1919—111no—
200#1919—111no—
201#1853—111no—
202#1851—111no—
203#1825D1111yescharacteristic
204#1809—111no—
205#1736—111no—
206C23×C11—21no—
207C23×C11—21no—
208C23×C11—21no—
209C23×C11—21no—
210C23×C11—21no—
211C23×C11—21no—
212C23×C11C22⋊Q812yes—
213C23×C11C22×D411yescharacteristic
214C2×C4×C11—21no—
215C2×C4×C11—21no—
216C2×C4×C11—22no—
217C2×C4×C11—22no—
218C2×C4×C11—22no—
219C2×C4×C11—22no—
220C2×C4×C11—22no—
221C2×C4×C11—22no—
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×C11—41no—
229C2×C4×C11—41no—
230C2×C4×C11—41no—
231C2×C4×C11—41no—
232C2×C4×C11C22⋊Q812yes—
233C2×C4×C11C22×Q811yescharacteristic
234C2×C4×C11C2×#4111yescharacteristic
235C2×C4×C11C2×#4111yescharacteristic
236C2×C4×C11C2×#4111yescharacteristic
237C2×C4×C11H(5,𝔽2)11yescharacteristic
238C2×C4×C112−1+411yescharacteristic
239C2×Dic11—21no—
240C2×Dic11—21no—
241C2×Dic11—22no—
242C2×Dic11—21no—
243C2×Dic11—21no—
244C2×Dic11—21no—
245C2×Dic11—21no—
246C2×Dic11—21no—
247C2×Dic11—21no—
248C2×Dic11—21no—
249C2×Dic11—21no—
250C2×Dic11—21no—
251C2×Dic11—21no—
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×Dic11—41no—
262C2×Dic11—41no—
263C2×Dic11—84no—
264C8×C11—41no—
265C8×C11—41no—
266C11⋊C8—22no—
267C11⋊C8—41no—
268C22×M16—111no—
269C2×#125—111no—
270C2×#117C2×D1111yescharacteristic
271C22×C4⋊C4—111no—
272C2×#107—111no—
273C2×#106—111no—
274C2×#106—111no—
275C2×#106—111no—
276C2×C4⋊C8—111no—
277C2×C4⋊C8—111no—
278C2×C22⋊C8C2×D1111yescharacteristic
279#400—221no—
280#398—221no—
281#389—111no—
282#389—111no—
283#389—111no—
284#389—111no—
285#388—221no—
286#388—221no—
287#385—221no—
288#382—111no—
289#382—221no—
290#380—111no—
291#380—221no—
292#380C2×D1111yescharacteristic
293C4×C4⋊C4—111no—
294C4×C4⋊C4—111no—
295C4×C22⋊C4—111no—
296#376—221no—
297#340—111no—
298#340—111no—
299#340—111no—
300#340—111no—
301#340—111no—
302#340—111no—
303#340—111no—
304#340—111no—
305#340C2×D1111yescharacteristic
306#340C2×D1111yescharacteristic
307#340C2×D1111yescharacteristic
308#340C2×D1111yescharacteristic
309#336—111no—
310#336—111no—
311C22×C11—22no—
312C22×C11—22no—
313C22×C11—22no—
314C22×C11—41no—
315C22×C11—41no—
316C22×C11—41no—
317C22×C11—41no—
318C22×C11C2×C22⋊Q811yescharacteristic
319C22×C11#54611yescharacteristic
320C22×C11#54711yescharacteristic
321C22×C11#57511yescharacteristic
322C22×C11#57511yescharacteristic
323C22×C11#57711yescharacteristic
324C22×C11#57711yescharacteristic
325C4×C11—22no—
326C4×C11—42no—
327C4×C11—42no—
328C4×C11—81no—
329C4×C11—81no—
330C4×C11#53311yescharacteristic
331C4×C11#54411yescharacteristic
332C4×C11#55111yescharacteristic
333C4×C11#55211yescharacteristic
334Dic11—41no—
335Dic11—41no—
336Dic11—41no—
337Dic11—41no—
338Dic11—42no—
339Dic11—81no—
340Dic11—81no—
341Dic11—81no—
342C23×C4—221no—
343C23×C4C22×D1111yescharacteristic
344C2×M16—222no—
345C2×M16—222no—
346C2×M16—441no—
347C22×C8—111no—
348C22×C8—111no—
349C22×C8C22×D1111yescharacteristic
350C22×C8C22×D1111yescharacteristic
351#125—222no—
352#125—441no—
353#117—22no—
354#117Dic2214yes—
355C2×C4⋊C4—111no—
356C2×C4⋊C4—111no—
357C2×C4⋊C4—111no—
358C2×C4⋊C4—111no—
359C2×C4⋊C4—222no—
360C2×C4⋊C4—221no—
361C2×C4⋊C4—221no—
362C2×C4⋊C4—221no—
363C2×C4⋊C4—221no—
364C2×C4⋊C4—221no—
365C2×C4⋊C4—221no—
366C2×C4⋊C4—221no—
367C2×C4⋊C4—441no—
368C2×C4⋊C4C22×D1111yescharacteristic
369C2×C4⋊C4C22×D1111yescharacteristic
370C2×C4⋊C4C22×D1111yescharacteristic
371C2×C4⋊C4C22×D1111yescharacteristic
372C2×C22⋊C4—21no—
373C2×C22⋊C4—21no—
374C2×C22⋊C4—111no—
375C2×C22⋊C4—111no—
376C2×C22⋊C4—221no—
377C2×C42—21no—
378C2×C42—111no—
379C2×C42—111no—
380C2×C42—221no—
381C2×C42—221no—
382#107—441no—
383#106—222no—
384#106—222no—
385#106—441no—
386C4⋊C8—222no—
387C4⋊C8—441no—
388C22⋊C8—22no—
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—
399#95—221no—
400#95—221no—
401C2×C11—42no—
402C2×C11#243811yescharacteristic
403C2×C11#308011yescharacteristic
404C2×C11#308411yescharacteristic
405C2×C11#332111yescharacteristic
406C2×C11#332311yescharacteristic
407C2×C11#334811yescharacteristic
408C2×C11#335111yescharacteristic
409C24D4×D1111yescharacteristic
410C22×C4—21no—
411C22×C4—21no—
412C22×C4—21no—
413C22×C4—21no—
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—221no—
424C22×C4—221no—
425C22×C4—221no—
426C22×C4—442no—
427C22×C4—442no—
428C22×C4—881no—
429C22×C4C2×Dic2212yes—
430C22×C4D4×D1111yescharacteristic
431C22×C4#434112yes—
432C22×C4C23×D1111yescharacteristic
433M16—444no—
434C2×C8—21no—
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—
446C4⋊C4—21no—
447C4⋊C4—21no—
448C4⋊C4—21no—
449C4⋊C4—21no—
450C4⋊C4—21no—
451C4⋊C4—21no—
452C4⋊C4—112no—
453C4⋊C4—221no—
454C4⋊C4—221no—
455C4⋊C4—221no—
456C4⋊C4—221no—
457C4⋊C4—221no—
458C4⋊C4—221no—
459C4⋊C4—221no—
460C4⋊C4—442no—
461C4⋊C4—442no—
462C4⋊C4—442no—
463C4⋊C4—881no—
464C4⋊C4—881no—
465C4⋊C4—881no—
466C4⋊C4—881no—
467C4⋊C4C2×Dic2212yes—
468C4⋊C4C2×Dic2212yes—
469C22⋊C4—24no—
470C22⋊C4—42no—
471C22⋊C4—441no—
472C22⋊C4—441no—
473C22⋊C4—881no—
474C42—24no—
475C42—221no—
476C42—221no—
477C42—221no—
478C42—221no—
479C42—442no—
480C42—442no—
481C11#2601911yescharacteristic, complemented, Sylow
482C23—21no—
483C23—21no—
484C23—21no—
485C23—21no—
486C23—21no—
487C23—21no—
488C23#6693112yes—
489C23C2×D4×D1111yescharacteristic
490C2×C4—21no—
491C2×C4—21no—
492C2×C4—22no—
493C2×C4—22no—
494C2×C4—22no—
495C2×C4—22no—
496C2×C4—22no—
497C2×C4—22no—
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—41no—
507C2×C4—41no—
508C2×C4—221no—
509C2×C4—221no—
510C2×C4—221no—
511C2×C4—221no—
512C2×C4—221no—
513C2×C4—221no—
514C2×C4—221no—
515C2×C4—221no—
516C2×C4—221no—
517C2×C4—221no—
518C2×C4—222no—
519C2×C4—221no—
520C2×C4—221no—
521C2×C4—441no—
522C2×C4—441no—
523C2×C4—441no—
524C2×C4—441no—
525C2×C4—441no—
526C2×C4—441no—
527C2×C4—441no—
528C2×C4—441no—
529C2×C4—441no—
530C2×C4—441no—
531C2×C4—441no—
532C2×C4—884no—
533C2×C4#6693112yes—
534C2×C4C22×Dic2211yescharacteristic
535C2×C4C2×#434111yescharacteristic
536C2×C4#41×D1111yescharacteristic
537C2×C4#41×D1111yescharacteristic
538C2×C4#6704211yescharacteristic
539C2×C4#6704311yescharacteristic
540C8—41no—
541C8—41no—
542C8—222no—
543C8—441no—
544C22—22no—
545C22—22no—
546C22—22no—
547C22—41no—
548C22—41no—
549C22—41no—
550C22—41no—
551C22C2×#6693111yescharacteristic
552C22#1062318511yescharacteristic
553C22#1062318611yescharacteristic
554C22#1062330111yescharacteristic
555C22#1062330111yescharacteristic
556C22#1062330411yescharacteristic
557C22#1062330811yescharacteristic
558C4—22no—
559C4—42no—
560C4—42no—
561C4—81no—
562C4—81no—
563C4—441no—
564C4—441no—
565C4—441no—
566C4—441no—
567C4—442no—
568C4—881no—
569C4—881no—
570C4—881no—
571C4#1062304811yescharacteristic
572C4#1062305011yescharacteristic
573C4#1062318111yescharacteristic
574C4#1062318911yescharacteristic
575C2—42no—
576C2#1307229411yescharacteristic
577C2#1307843611yescharacteristic
578C2#1307847611yescharacteristic
579C2#1308080511yescharacteristic
580C2#1308083011yescharacteristic
581C2#1308112411yescharacteristic
582C2#1308116911yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1825C2
socleC23×C11C22×D4
prime radicalC24×C11C2×D4
hypercenter#1825D11
hypocenterC11#26019
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1825

Complements

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

NH ≅ G/Ntype
3. #13070189C2semidirect
4. #13070120C2semidirect
5. #13070116C2semidirect
6. #13069953C2semidirect
7. #13069572C2semidirect
8. #13069383C2semidirect
9. #13069197C2semidirect
10. #13069193C2semidirect
481. C11#26019semidirect

Maximal subgroups

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

subgroupindex
#130723412
#130715012
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