Finite Group Databasebeta

← #14826893

Subgroups — #14826893

Order 2816.

672 conjugacy classes of subgroups.

The subgroup lattice has 594 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13073016C211yesmaximal, characteristic
2#13071641C211yesmaximal, characteristic
3#13070036C211yesmaximal, characteristic, complemented
4#13069996C211yesmaximal, characteristic, complemented
5#13069820C211yesmaximal, characteristic
6#13069813C211yesmaximal, characteristic
7#13069386C211yesmaximal, characteristic, complemented
8#13069354C211yesmaximal, characteristic, complemented
9#13069209C211yesmaximal, characteristic, complemented
10#13069202C211yesmaximal, characteristic, complemented
11#13068873C211yesmaximal, characteristic, complemented
12#13068817C211yesmaximal, characteristic
13#13068712C211yesmaximal, characteristic
14#13068447C211yesmaximal, characteristic, complemented
15C11×#1924C211yesmaximal, characteristic
16C2×#66979C2211yescharacteristic
17C2×#66977C2211yescharacteristic
18C2×C4×Dic22C2211yescharacteristic
19C2×C11×C4⋊C8C2211yescharacteristic
20C2×C11×C22⋊C8C2211yescharacteristic
21C2×C11×C22⋊C8C2211yescharacteristic
22C2×C11×#97C2211yescharacteristic
23C4×C11×C22⋊C4C2211yescharacteristic
24#10622825C2211yescharacteristic
25#10622825C2211yescharacteristic
26C2×#66882C2211yescharacteristic
27C2×#66882C2211yescharacteristic
28C2×#66881C2211yescharacteristic
29C2×#66881C2211yescharacteristic
30C2×#66880C2211yescharacteristic
31C2×#66880C2211yescharacteristic
32C2×#66880C2211yescharacteristic
33C2×#66880C2211yescharacteristic
34#10622565—21no—
35#10622558—21no—
36#10622558—21no—
37#10622557—21no—
38#10622549C2211yescharacteristic
39C4×C4⋊Dic11C2211yescharacteristic
40C4×C4⋊Dic11C2211yescharacteristic
41#10622542C2211yescharacteristic
42#10622541C2211yescharacteristic
43#10622541C2211yescharacteristic
44#10622541C2211yescharacteristic
45C11⋊#401—21no—
46#10622265—21no—
47#10622265—21no—
48#10622262—21no—
49C11×#336C2211yescharacteristic
50C11×#336C2211yescharacteristic
51#10622189C2211yescharacteristic
52#10622189C2211yescharacteristic
53#10622189C2211yescharacteristic
54#10622189C2211yescharacteristic
55#10622189C2211yescharacteristic
56#10622189C2211yescharacteristic
57#10622189C2211yescharacteristic
58#10622189C2211yescharacteristic
59C23×C4×C11C2311yescharacteristic
60C22×Dic22C2311yescharacteristic
61C22×C8×C11C2311yescharacteristic
62C22×C8×C11C2311yescharacteristic
63C22×C8×C11C2311yescharacteristic
64C22×C8×C11C2311yescharacteristic
65C2×C11×C22⋊C4D411yescharacteristic
66C2×C11×C22⋊C4D411yescharacteristic
67C2×C42×C11C2311yescharacteristic
68C2×C42×C11C2311yescharacteristic
69C2×C22⋊Dic11—21no—
70C2×C22⋊Dic11—21no—
71C2×C22⋊Dic11—21no—
72C2×C22⋊Dic11—21no—
73#66979—22no—
74#66979—41no—
75C2×C4⋊Dic11C2311yescharacteristic
76C2×C4⋊Dic11C2311yescharacteristic
77C2×C4⋊Dic11C2311yescharacteristic
78C2×C4⋊Dic11C2311yescharacteristic
79C2×C4⋊Dic11C2311yescharacteristic
80C2×C4⋊Dic11C2311yescharacteristic
81C2×C4⋊Dic11C2311yescharacteristic
82#66977—22no—
83#66977—22no—
84C2×Dic11⋊C4—21no—
85C2×Dic11⋊C4—21no—
86C2×Dic11⋊C4—21no—
87C2×Dic11⋊C4—21no—
88C2×Dic11⋊C4—21no—
89C2×C4×Dic11—21no—
90C2×C4×Dic11—21no—
91C2×C4×Dic11—21no—
92C2×C4×Dic11—21no—
93C4×Dic22—22no—
94C4×Dic22—41no—
95C11×C4⋊C8—22no—
96C11×C22⋊C8—22no—
97C11×C22⋊C8—41no—
98C11×#97—41no—
99C11×#95D411yescharacteristic
100C11×#95D411yescharacteristic
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⋊#95—21no—
111C11⋊#95—21no—
112#66882—22no—
113#66882—22no—
114#66881—22no—
115#66881—41no—
116#66880—22no—
117#66880—22no—
118#66880—22no—
119#66880—41no—
120#27061—111nomaximal, Sylow
121C24×C11C2×D411yescharacteristic
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×D411yescharacteristic
130C22×C4×C11C2×D411yescharacteristic
131C22×C4×C11C2×D411yescharacteristic
132C22×C4×C11C2×D411yescharacteristic
133C22×C4×C11C2411yescharacteristic
134C22×Dic11—21no—
135C22×Dic11—21no—
136C22×Dic11—21no—
137C22×Dic11—21no—
138C22×Dic11—21no—
139C22×Dic11—21no—
140C22×Dic11—21no—
141C22×Dic11—21no—
142C2×Dic22—21no—
143C2×Dic22—21no—
144C2×Dic22—21no—
145C2×Dic22—21no—
146C2×Dic22—21no—
147C2×Dic22#4112yes—
148C2×C8×C11—21no—
149C2×C8×C11—21no—
150C2×C8×C11—21no—
151C2×C8×C11—21no—
152C2×C8×C11—21no—
153C2×C8×C11—21no—
154C2×C8×C11—21no—
155C2×C8×C11—21no—
156C2×C8×C11—21no—
157C2×C8×C11—21no—
158C2×C8×C11—21no—
159C2×C8×C11#4112yes—
160C11×C22⋊C4—41no—
161C11×C22⋊C4—41no—
162C42×C11—21no—
163C42×C11—21no—
164C42×C11—21no—
165C42×C11—21no—
166C22⋊Dic11—24no—
167C22⋊Dic11—42no—
168C22⋊Dic11—42no—
169C22⋊Dic11—81no—
170C4⋊Dic11—21no—
171C4⋊Dic11—21no—
172C4⋊Dic11—21no—
173C4⋊Dic11—21no—
174C4⋊Dic11—21no—
175C4⋊Dic11—21no—
176C4⋊Dic11—21no—
177C4⋊Dic11—21no—
178C4⋊Dic11—21no—
179C4⋊Dic11—21no—
180C4⋊Dic11—21no—
181C4⋊Dic11—21no—
182C4⋊Dic11#4112yes—
183C4⋊Dic11#4112yes—
184Dic11⋊C4—24no—
185Dic11⋊C4—42no—
186Dic11⋊C4—42no—
187Dic11⋊C4—42no—
188Dic11⋊C4—81no—
189C4×Dic11—42no—
190C4×Dic11—42no—
191C4×Dic11—42no—
192C4×Dic11—81no—
193#2494—111no—
194#2362—111no—
195#2074—111no—
196#2066—111no—
197#2036—111no—
198#2035—111no—
199#1949—111no—
200#1943—111no—
201#1924D1111yescharacteristic
202#1921—111no—
203#1920—111no—
204#1863—111no—
205#1854—111no—
206#1825—111no—
207#1763—111no—
208C23×C11—21no—
209C23×C11—21no—
210C23×C11—21no—
211C23×C11—21no—
212C23×C11—21no—
213C23×C11—21no—
214C23×C11—21no—
215C23×C11C22×D411yescharacteristic
216C2×C4×C11—21no—
217C2×C4×C11—21no—
218C2×C4×C11—21no—
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—21no—
226C2×C4×C11—21no—
227C2×C4×C11—21no—
228C2×C4×C11—21no—
229C2×C4×C11—21no—
230C2×C4×C11—21no—
231C2×C4×C11—41no—
232C2×C4×C11—41no—
233C2×C4×C11—41no—
234C2×C4×C11—41no—
235C2×C4×C11C2×#4111yescharacteristic
236C2×C4×C11C2×#4111yescharacteristic
237C2×C4×C11C2×#4111yescharacteristic
238C2×C4×C11C2×#4111yescharacteristic
239C2×C4×C11H(5,𝔽2)11yescharacteristic
240C2×C4×C112−1+411yescharacteristic
241C2×Dic11—22no—
242C2×Dic11—22no—
243C2×Dic11—22no—
244C2×Dic11—41no—
245C2×Dic11—41no—
246C2×Dic11—41no—
247C2×Dic11—41no—
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—41no—
257C2×Dic11—41no—
258C2×Dic11—41no—
259C2×Dic11—41no—
260C2×Dic11—41no—
261C2×Dic11—41no—
262C2×Dic11—41no—
263C2×Dic11—41no—
264C2×Dic11—41no—
265Dic22—22no—
266Dic22—22no—
267Dic22—41no—
268Dic22—41no—
269C8×C11—22no—
270C8×C11—41no—
271C8×C11—41no—
272C8×C11—41no—
273C2×C22⋊Q8—111no—
274C2×C4×Q8—111no—
275C2×#117—111no—
276C2×#107—111no—
277C2×#107—111no—
278C2×#106—111no—
279C2×#106—111no—
280C2×C4⋊C8C2×D1111yescharacteristic
281C2×#103—111no—
282C2×#103—111no—
283C2×#103—111no—
284C2×#103—111no—
285C2×C22⋊C8C2×D1111yescharacteristic
286C2×C22⋊C8C2×D1111yescharacteristic
287C2×#97C2×D1111yescharacteristic
288#401—221no—
289#397—221no—
290#391—111no—
291#389—111no—
292#389—111no—
293#389—111no—
294#388—221no—
295#388—221no—
296#388—221no—
297#387—221no—
298#387—221no—
299#382—111no—
300#380—111no—
301#380—111no—
302C4×C4⋊C4—111no—
303C4×C4⋊C4—111no—
304C4×C4⋊C4—221no—
305C4×C22⋊C4C2×D1111yescharacteristic
306#340—111no—
307#340—111no—
308#340—111no—
309#340—111no—
310#340—111no—
311#340—111no—
312#340—111no—
313#340—111no—
314#336C2×D1111yescharacteristic
315#336C2×D1111yescharacteristic
316C22×C11—41no—
317C22×C11—41no—
318C22×C11—41no—
319C22×C11—41no—
320C22×C11—41no—
321C22×C11—41no—
322C22×C11—41no—
323C22×C11#52511yescharacteristic
324C22×C11#54611yescharacteristic
325C22×C11#54711yescharacteristic
326C22×C11#57511yescharacteristic
327C22×C11#57511yescharacteristic
328C22×C11#57711yescharacteristic
329C22×C11#57811yescharacteristic
330C4×C11—41no—
331C4×C11—41no—
332C4×C11—41no—
333C4×C11—41no—
334C4×C11—41no—
335C4×C11#52911yescharacteristic
336C4×C11#53911yescharacteristic
337C4×C11#55311yescharacteristic
338C4×C11#55611yescharacteristic
339Dic11—42no—
340Dic11—42no—
341Dic11—42no—
342Dic11—81no—
343Dic11—81no—
344Dic11—81no—
345Dic11—81no—
346Dic11—81no—
347C22×Q8—111no—
348C23×C4C22×D1111yescharacteristic
349C22×C8C22×D1111yescharacteristic
350C22×C8C22×D1111yescharacteristic
351C22×C8C22×D1111yescharacteristic
352C22×C8C22×D1111yescharacteristic
353C22⋊Q8—222no—
354C22⋊Q8—222no—
355C4×Q8—222no—
356C4×Q8—441no—
357#117—222no—
358#117—441no—
359C2×C4⋊C4—111no—
360C2×C4⋊C4—111no—
361C2×C4⋊C4—111no—
362C2×C4⋊C4—111no—
363C2×C4⋊C4—111no—
364C2×C4⋊C4—111no—
365C2×C4⋊C4—111no—
366C2×C4⋊C4—221no—
367C2×C4⋊C4—221no—
368C2×C4⋊C4—221no—
369C2×C4⋊C4—221no—
370C2×C4⋊C4—221no—
371C2×C22⋊C4—221no—
372C2×C22⋊C4—221no—
373C2×C22⋊C4—221no—
374C2×C22⋊C4—221no—
375C2×C22⋊C4D4411yescharacteristic
376C2×C22⋊C4D4411yescharacteristic
377C2×C42—221no—
378C2×C42—221no—
379C2×C42—221no—
380C2×C42—221no—
381C2×C42C22×D1111yescharacteristic
382C2×C42C22×D1111yescharacteristic
383#107—222no—
384#107—222no—
385#106—222no—
386#106—441no—
387C4⋊C8—22no—
388#103—222no—
389#103—222no—
390#103—222no—
391#103—441no—
392C22⋊C8—22no—
393C22⋊C8—41no—
394#97—41no—
395#95—221no—
396#95—221no—
397#95—221no—
398#95—221no—
399#95—221no—
400#95—221no—
401#95—221no—
402#95—221no—
403#95—221no—
404#95—221no—
405#95—221no—
406#95D4411yescharacteristic
407#95D4411yescharacteristic
408C2×C11—81no—
409C2×C11#246611yescharacteristic
410C2×C11#311111yescharacteristic
411C2×C11#312111yescharacteristic
412C2×C11#330711yescharacteristic
413C2×C11#332711yescharacteristic
414C2×C11#334911yescharacteristic
415C2×C11#335011yescharacteristic
416C24C2×D4411yescharacteristic
417C2×Q8—112no—
418C2×Q8—221no—
419C2×Q8—221no—
420C2×Q8—221no—
421C2×Q8—221no—
422C2×Q8—221no—
423C22×C4—21no—
424C22×C4—21no—
425C22×C4—21no—
426C22×C4—21no—
427C22×C4—21no—
428C22×C4—21no—
429C22×C4—221no—
430C22×C4—221no—
431C22×C4—221no—
432C22×C4—221no—
433C22×C4—221no—
434C22×C4—221no—
435C22×C4—221no—
436C22×C4—221no—
437C22×C4C2×D4411yescharacteristic
438C22×C4C2×D4411yescharacteristic
439C22×C4C2×D4411yescharacteristic
440C22×C4C2×D4411yescharacteristic
441C22×C4C2×D4411yescharacteristic
442C22×C4C23×D1111yescharacteristic
443C2×C8—21no—
444C2×C8—21no—
445C2×C8—21no—
446C2×C8—21no—
447C2×C8—21no—
448C2×C8—21no—
449C2×C8—21no—
450C2×C8—21no—
451C2×C8—21no—
452C2×C8—21no—
453C2×C8—21no—
454C2×C8#434112yes—
455C4⋊C4—112no—
456C4⋊C4—112no—
457C4⋊C4—224no—
458C4⋊C4—221no—
459C4⋊C4—221no—
460C4⋊C4—221no—
461C4⋊C4—221no—
462C4⋊C4—221no—
463C4⋊C4—221no—
464C4⋊C4—221no—
465C4⋊C4—221no—
466C4⋊C4—221no—
467C4⋊C4—221no—
468C4⋊C4—221no—
469C4⋊C4—221no—
470C4⋊C4—442no—
471C4⋊C4—442no—
472C4⋊C4—442no—
473C4⋊C4—881no—
474C22⋊C4—41no—
475C22⋊C4—41no—
476C22⋊C4—224no—
477C22⋊C4—442no—
478C22⋊C4—442no—
479C22⋊C4—881no—
480C42—21no—
481C42—21no—
482C42—21no—
483C42—21no—
484C42—442no—
485C42—442no—
486C42—442no—
487C42—881no—
488C11#2706111yescharacteristic, complemented, Sylow
489C23—21no—
490C23—21no—
491C23—21no—
492C23—21no—
493C23—21no—
494C23—21no—
495C23—21no—
496C23C22×D4411yescharacteristic
497Q8—222no—
498Q8—222no—
499Q8—441no—
500Q8—441no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—222no—
521C2×C4—222no—
522C2×C4—222no—
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—441no—
533C2×C4—441no—
534C2×C4—441no—
535C2×C4—441no—
536C2×C4—441no—
537C2×C4—441no—
538C2×C4—441no—
539C2×C4—441no—
540C2×C4—441no—
541C2×C4—441no—
542C2×C4—441no—
543C2×C4—441no—
544C2×C4C2×#434111yescharacteristic
545C2×C4#6703711yescharacteristic
546C2×C4#41×D1111yescharacteristic
547C2×C4#41×D1111yescharacteristic
548C2×C4#41×D1111yescharacteristic
549C2×C4#6704311yescharacteristic
550C8—22no—
551C8—41no—
552C8—41no—
553C8—41no—
554C22—41no—
555C22—41no—
556C22—41no—
557C22—41no—
558C22—41no—
559C22—41no—
560C22—41no—
561C22#1062305511yescharacteristic
562C22#1062308511yescharacteristic
563C22#1062308611yescharacteristic
564C22#1062327911yescharacteristic
565C22#1062327911yescharacteristic
566C22#1062328211yescharacteristic
567C22#1062328411yescharacteristic
568C4—41no—
569C4—41no—
570C4—41no—
571C4—41no—
572C4—41no—
573C4—442no—
574C4—442no—
575C4—442no—
576C4—881no—
577C4—881no—
578C4—881no—
579C4—881no—
580C4—881no—
581C4#1062313211yescharacteristic
582C4#1062319111yescharacteristic
583C4#1062321111yescharacteristic
584C4#1062323311yescharacteristic
585C2—81no—
586C2#1307265011yescharacteristic
587C2#1307872711yescharacteristic
588C2#1307884711yescharacteristic
589C2#1308059411yescharacteristic
590C2#1308088611yescharacteristic
591C2#1308114811yescharacteristic
592C2#1308116311yescharacteristic
subgroupG/H
centerC23C22×D44
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1924C2
socleC23×C11C22×D4
prime radicalC24×C11C2×D4
hypercenter#1924D11
hypocenterC11#27061
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #1924

Complements

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

NH ≅ G/Ntype
3. #13070036C2semidirect
4. #13069996C2semidirect
7. #13069386C2semidirect
8. #13069354C2semidirect
9. #13069209C2semidirect
10. #13069202C2semidirect
11. #13068873C2semidirect
14. #13068447C2semidirect
488. C11#27061semidirect

Maximal subgroups

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

subgroupindex
#130730162
#130716412
#130700362
#130699962
#130698202
#130698132
#130693862
#130693542
#130692092
#130692022
#130688732
#130688172
#130687122
#130684472
C11×#19242
#2706111