Finite Group Databasebeta

← #14826894

Subgroups — #14826894

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#13073012C211yesmaximal, characteristic
2#13071643C211yesmaximal, characteristic
3#13070038C211yesmaximal, characteristic, complemented
4#13069998C211yesmaximal, characteristic, complemented
5#13069819C211yesmaximal, characteristic
6#13069813C211yesmaximal, characteristic
7#13069383C211yesmaximal, characteristic, complemented
8#13069353C211yesmaximal, characteristic, complemented
9#13069226C211yesmaximal, characteristic
10#13069206C211yesmaximal, characteristic, complemented
11#13069200C211yesmaximal, characteristic, complemented
12#13068871C211yesmaximal, characteristic, complemented
13#13068815C211yesmaximal, characteristic
14#13068445C211yesmaximal, characteristic, complemented
15C11×#1825C211yesmaximal, characteristic
16C2×C11×#117C2211yescharacteristic
17C2×#66977C2211yescharacteristic
18C2×#66940C2211yescharacteristic
19C2×C11×C22⋊C8C2211yescharacteristic
20C11×#380C2211yescharacteristic
21#10622825C2211yescharacteristic
22C4×C22⋊Dic11C2211yescharacteristic
23C2×C22⋊(C11⋊C8)C2211yescharacteristic
24C2×#66881C2211yescharacteristic
25C2×#66880C2211yescharacteristic
26C2×#66880C2211yescharacteristic
27C2×#66879C2211yescharacteristic
28C2×Dic11⋊C8C2211yescharacteristic
29#10622598C2211yescharacteristic
30#10622590C2211yescharacteristic
31C4⋊C4×Dic11C2211yescharacteristic
32C4⋊C4×Dic11C2211yescharacteristic
33#10622587C2211yescharacteristic
34#10622586C2211yescharacteristic
35#10622586C2211yescharacteristic
36C2×#66874C2211yescharacteristic
37C2×#66874C2211yescharacteristic
38C2×#66872C2211yescharacteristic
39C2×#66871C2211yescharacteristic
40C2×#66871C2211yescharacteristic
41#10622565—21no—
42#10622564—21no—
43#10622558—21no—
44#10622557—21no—
45#10622546—21no—
46C4×Dic11⋊C4—21no—
47C11⋊#401—21no—
48#10622266—21no—
49C11×#340C2211yescharacteristic
50C11×#340C2211yescharacteristic
51C11×#340C2211yescharacteristic
52C11×#340C2211yescharacteristic
53#10622189C2211yescharacteristic
54#10622188C2211yescharacteristic
55#10622188C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59C23×C4×C11C2311yescharacteristic
60C22×Dic22C2311yescharacteristic
61C22×C8×C11C2311yescharacteristic
62C22×C8×C11C2311yescharacteristic
63C11×#117—22no—
64C11×#117—41no—
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⋊Dic11—21no—
74C2×C22⋊Dic11D411yescharacteristic
75C2×C22⋊Dic11D411yescharacteristic
76C2×C4⋊Dic11—21no—
77C2×C4⋊Dic11C2311yescharacteristic
78C2×C4⋊Dic11C2311yescharacteristic
79C2×C4⋊Dic11C2311yescharacteristic
80#66977—22no—
81#66977—22no—
82C2×Dic11⋊C4—21no—
83C2×Dic11⋊C4—21no—
84C2×Dic11⋊C4—21no—
85C2×Dic11⋊C4—21no—
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#66940—22no—
94#66940—41no—
95C11×C22⋊C8—41no—
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
109C22⋊(C11⋊C8)—22no—
110#66881—22no—
111#66880—22no—
112#66880—41no—
113#66879—41no—
114Dic11⋊C8—22no—
115#66874—22no—
116#66874—22no—
117#66872—41no—
118#66871—22no—
119#66871—22no—
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×C11—21no—
129C22×C4×C11—21no—
130C22×C4×C11—21no—
131C22×C4×C11—21no—
132C22×C4×C11C2×D411yescharacteristic
133C22×C4×C11C2411yescharacteristic
134C22×Dic11—21no—
135C22×Dic11—21no—
136C22×Dic11—21no—
137C22×Dic11—21no—
138C22×Dic11C2×D411yescharacteristic
139C22×Dic11C2×D411yescharacteristic
140C22×Dic11C2×D411yescharacteristic
141C22×Dic11C2×D411yescharacteristic
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—
154C11×C4⋊C4—21no—
155C11×C4⋊C4—21no—
156C11×C4⋊C4—21no—
157C11×C4⋊C4—21no—
158C11×C4⋊C4—21no—
159C11×C4⋊C4—21no—
160C11×C4⋊C4—21no—
161C11×C4⋊C4#4112yes—
162C11×C22⋊C4—42no—
163C11×C22⋊C4—42no—
164C42×C11—42no—
165C22⋊Dic11—24no—
166C22⋊Dic11—41no—
167C22⋊Dic11—41no—
168C22⋊Dic11—81no—
169C4⋊Dic11—21no—
170C4⋊Dic11—21no—
171C4⋊Dic11—21no—
172C4⋊Dic11—21no—
173C4⋊Dic11—21no—
174C4⋊Dic11—42no—
175C4⋊Dic11#4112yes—
176Dic11⋊C4—24no—
177Dic11⋊C4—42no—
178Dic11⋊C4—42no—
179Dic11⋊C4—81no—
180C4×Dic11—21no—
181C4×Dic11—21no—
182C4×Dic11—21no—
183C4×Dic11—21no—
184C4×Dic11—42no—
185C4×Dic11—42no—
186C4×Dic11—81no—
187C2×C11⋊C8—21no—
188C2×C11⋊C8—21no—
189C2×C11⋊C8—21no—
190C2×C11⋊C8—21no—
191C2×C11⋊C8—21no—
192C2×C11⋊C8#4112yes—
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#1924—111no—
202#1921—111no—
203#1920—111no—
204#1863—111no—
205#1854—111no—
206#1825D1111yescharacteristic
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—22no—
218C2×C4×C11—21no—
219C2×C4×C11—21no—
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×C11—41no—
229C2×C4×C11—41no—
230C2×C4×C11—41no—
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—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—21no—
253C2×Dic11—21no—
254C2×Dic11—21no—
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—41no—
270C8×C11—41no—
271C11⋊C8—22no—
272C11⋊C8—41no—
273C2×C22⋊Q8—111no—
274C2×C4×Q8—111no—
275C2×#117C2×D1111yescharacteristic
276C2×#107—111no—
277C2×#107—111no—
278C2×#106—111no—
279C2×#106—111no—
280C2×C4⋊C8—111no—
281C2×#103—111no—
282C2×#103—111no—
283C2×#103—111no—
284C2×#103—111no—
285C2×C22⋊C8—111no—
286C2×C22⋊C8C2×D1111yescharacteristic
287C2×#97—111no—
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#380C2×D1111yescharacteristic
302C4×C4⋊C4—111no—
303C4×C4⋊C4—111no—
304C4×C4⋊C4—221no—
305C4×C22⋊C4—111no—
306#340—111no—
307#340—111no—
308#340—111no—
309#340—111no—
310#340C2×D1111yescharacteristic
311#340C2×D1111yescharacteristic
312#340C2×D1111yescharacteristic
313#340C2×D1111yescharacteristic
314#336—111no—
315#336—111no—
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—42no—
332C4×C11—81no—
333C4×C11—81no—
334C4×C11—81no—
335C4×C11#52911yescharacteristic
336C4×C11#53911yescharacteristic
337C4×C11#55311yescharacteristic
338C4×C11#55611yescharacteristic
339Dic11—41no—
340Dic11—41no—
341Dic11—42no—
342Dic11—42no—
343Dic11—41no—
344Dic11—41no—
345Dic11—81no—
346Dic11—81no—
347C22×Q8—111no—
348C23×C4C22×D1111yescharacteristic
349C22×C8—111no—
350C22×C8—111no—
351C22×C8C22×D1111yescharacteristic
352C22×C8C22×D1111yescharacteristic
353C22⋊Q8—222no—
354C22⋊Q8—222no—
355C4×Q8—222no—
356C4×Q8—441no—
357#117—22no—
358#117—41no—
359C2×C4⋊C4—111no—
360C2×C4⋊C4—111no—
361C2×C4⋊C4—111no—
362C2×C4⋊C4—221no—
363C2×C4⋊C4—221no—
364C2×C4⋊C4—221no—
365C2×C4⋊C4—221no—
366C2×C4⋊C4—221no—
367C2×C4⋊C4C22×D1111yescharacteristic
368C2×C4⋊C4C22×D1111yescharacteristic
369C2×C4⋊C4C22×D1111yescharacteristic
370C2×C4⋊C4C22×D1111yescharacteristic
371C2×C22⋊C4—21no—
372C2×C22⋊C4—21no—
373C2×C22⋊C4—111no—
374C2×C22⋊C4—111no—
375C2×C22⋊C4—221no—
376C2×C22⋊C4—221no—
377C2×C42—21no—
378C2×C42—111no—
379C2×C42—111no—
380C2×C42—221no—
381C2×C42—221no—
382C2×C42—221no—
383#107—222no—
384#107—222no—
385#106—222no—
386#106—441no—
387C4⋊C8—222no—
388#103—222no—
389#103—222no—
390#103—222no—
391#103—441no—
392C22⋊C8—41no—
393C22⋊C8—222no—
394#97—441no—
395#95—21no—
396#95—111no—
397#95—111no—
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#95—221no—
407#95—221no—
408C2×C11—81no—
409C2×C11#246611yescharacteristic
410C2×C11#311111yescharacteristic
411C2×C11#312111yescharacteristic
412C2×C11#330711yescharacteristic
413C2×C11#332711yescharacteristic
414C2×C11#334911yescharacteristic
415C2×C11#335011yescharacteristic
416C24D4×D1111yescharacteristic
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—21no—
430C22×C4—21no—
431C22×C4—21no—
432C22×C4—21no—
433C22×C4—111no—
434C22×C4—111no—
435C22×C4—111no—
436C22×C4—111no—
437C22×C4—221no—
438C22×C4—221no—
439C22×C4—221no—
440C22×C4—221no—
441C22×C4D4×D1111yescharacteristic
442C22×C4C23×D1111yescharacteristic
443C2×C8—21no—
444C2×C8—21no—
445C2×C8—21no—
446C2×C8—21no—
447C2×C8—21no—
448C2×C8—21no—
449C2×C8—112no—
450C2×C8—221no—
451C2×C8—221no—
452C2×C8—221no—
453C2×C8—221no—
454C2×C8—221no—
455C4⋊C4—21no—
456C4⋊C4—21no—
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—112no—
463C4⋊C4—224no—
464C4⋊C4—221no—
465C4⋊C4—221no—
466C4⋊C4—221no—
467C4⋊C4—221no—
468C4⋊C4—221no—
469C4⋊C4—442no—
470C4⋊C4—442no—
471C4⋊C4—442no—
472C4⋊C4—881no—
473C4⋊C4#433912yes—
474C22⋊C4—42no—
475C22⋊C4—42no—
476C22⋊C4—224no—
477C22⋊C4—441no—
478C22⋊C4—441no—
479C22⋊C4—881no—
480C42—42no—
481C42—221no—
482C42—221no—
483C42—221no—
484C42—221no—
485C42—442no—
486C42—442no—
487C42—881no—
488C11#2706111yescharacteristic, complemented, Sylow
489C23—21no—
490C23—21no—
491C23—21no—
492C23—21no—
493C23—21no—
494C23—21no—
495C23—21no—
496C23C2×D4×D1111yescharacteristic
497Q8—222no—
498Q8—222no—
499Q8—441no—
500Q8—441no—
501C2×C4—21no—
502C2×C4—22no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—41no—
506C2×C4—41no—
507C2×C4—41no—
508C2×C4—41no—
509C2×C4—41no—
510C2×C4—41no—
511C2×C4—41no—
512C2×C4—41no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—221no—
521C2×C4—221no—
522C2×C4—221no—
523C2×C4—221no—
524C2×C4—221no—
525C2×C4—221no—
526C2×C4—221no—
527C2×C4—221no—
528C2×C4—221no—
529C2×C4—221no—
530C2×C4—221no—
531C2×C4—221no—
532C2×C4—222no—
533C2×C4—222no—
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×#433911yescharacteristic
545C2×C4#6703711yescharacteristic
546C2×C4#41×D1111yescharacteristic
547C2×C4#41×D1111yescharacteristic
548C2×C4#41×D1111yescharacteristic
549C2×C4#6704311yescharacteristic
550C8—41no—
551C8—41no—
552C8—222no—
553C8—441no—
554C22—41no—
555C22—41no—
556C22—41no—
557C22—41no—
558C22—41no—
559C22—41no—
560C22—41no—
561C22#1062302111yescharacteristic
562C22#1062318611yescharacteristic
563C22#1062318711yescharacteristic
564C22#1062329911yescharacteristic
565C22#1062330111yescharacteristic
566C22#1062330411yescharacteristic
567C22#1062331011yescharacteristic
568C4—41no—
569C4—42no—
570C4—81no—
571C4—81no—
572C4—81no—
573C4—442no—
574C4—441no—
575C4—441no—
576C4—441no—
577C4—441no—
578C4—442no—
579C4—881no—
580C4—881no—
581C4#1062305911yescharacteristic
582C4#1062306411yescharacteristic
583C4#1062319111yescharacteristic
584C4#1062319211yescharacteristic
585C2—81no—
586C2#1307265111yescharacteristic
587C2#1307872011yescharacteristic
588C2#1307884811yescharacteristic
589C2#1308058811yescharacteristic
590C2#1308088511yescharacteristic
591C2#1308115011yescharacteristic
592C2#1308115411yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1825C2
socleC23×C11C22×D4
prime radicalC24×C11C2×D4
hypercenter#1825D11
hypocenterC11#27061
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. #13070038C2semidirect
4. #13069998C2semidirect
7. #13069383C2semidirect
8. #13069353C2semidirect
10. #13069206C2semidirect
11. #13069200C2semidirect
12. #13068871C2semidirect
14. #13068445C2semidirect
488. C11#27061semidirect

Maximal subgroups

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

subgroupindex
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#130698192
#130698132
#130693832
#130693532
#130692262
#130692062
#130692002
#130688712
#130688152
#130684452
C11×#18252
#2706111