Finite Group Databasebeta

← #14826921

Subgroups — #14826921

Order 2816.

840 conjugacy classes of subgroups.

The subgroup lattice has 674 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13071680C211yesmaximal, characteristic
2#13070140C211yesmaximal, characteristic, complemented
3#13069931C211yesmaximal, characteristic, complemented
4#13069850C211yesmaximal, characteristic
5#13069703C211yesmaximal, characteristic
6#13069473C211yesmaximal, characteristic, complemented
7#13069254C211yesmaximal, characteristic, complemented
8#13069236C211yesmaximal, characteristic, complemented
9#13069191C211yesmaximal, characteristic, complemented
10#13069175C211yesmaximal, characteristic, complemented
11#13068953C211yesmaximal, characteristic, complemented
12#13068953C211yesmaximal, characteristic, complemented
13#13068623C211yesmaximal, characteristic, complemented
14C4×#66873C211yesmaximal, characteristic, complemented
15C11×#2514C211yesmaximal, characteristic, complemented
16C22×#4325C2211yescharacteristic
17C22×#4325C2211yescharacteristic
18C2×#66946—21no—
19C2×#66927C2211yescharacteristic
20C2×C4×D44C2211yescharacteristic
21C2×C4×D44C2211yescharacteristic
22C11×#401—21no—
23C11×#400—21no—
24C11×#391C2211yescharacteristic
25C11×#391C2211yescharacteristic
26C11×#391C2211yescharacteristic
27C11×#389C2211yescharacteristic
28C11×#387—21no—
29C11×#383—21no—
30C11×#382C2211yescharacteristic
31C4×C11×C4⋊C4C2211yescharacteristic
32C4×C11×C4⋊C4C2211yescharacteristic
33C2×#66899C2211yescharacteristic
34C2×#66899C2211yescharacteristic
35#10622601—21no—
36C2×#66873C2211yescharacteristic
37C2×#66873C2211yescharacteristic
38C2×#66873C2211yescharacteristic
39C2×#66873C2211yescharacteristic
40C2×#66873C2211yescharacteristic
41C2×#66873C2211yescharacteristic
42C2×#66872C2211yescharacteristic
43C2×#66871C2211yescharacteristic
44#10622552C2211yescharacteristic
45#10622552C2211yescharacteristic
46C4×C4⋊Dic11C2211yescharacteristic
47C2×C4⋊(C11⋊C8)C2211yescharacteristic
48C2×C4×C11⋊C8C2211yescharacteristic
49#10622278—21no—
50#10622278—21no—
51#10622167C2211yescharacteristic
52#10622167C2211yescharacteristic
53#10622167C2211yescharacteristic
54#10622167C2211yescharacteristic
55#10622162C2211yescharacteristic
56#10622162C2211yescharacteristic
57#10622162C2211yescharacteristic
58#10622162C2211yescharacteristic
59C22×Q8×C11C2311yescharacteristic
60C22×D44—21no—
61C22×D44—21no—
62C22×D44C2311yescharacteristic
63C22×D44C2311yescharacteristic
64C22×C4×D11—21no—
65C22×C4×D11—21no—
66C2×C11×C4⋊C4—21no—
67C2×C11×C4⋊C4D411yescharacteristic
68C2×C11×C4⋊C4D411yescharacteristic
69C2×C11×C4⋊C4C2311yescharacteristic
70C2×C11×C4⋊C4C2311yescharacteristic
71C2×C11×C4⋊C4C2311yescharacteristic
72C2×C42×C11—21no—
73C2×C42×C11C2311yescharacteristic
74C2×C42×C11C2311yescharacteristic
75C2×C42×C11C2311yescharacteristic
76C2×#4325—22no—
77C2×#4325—22no—
78C2×#4325—22no—
79C2×#4325—41no—
80C2×#4325—41no—
81C2×#4325—41no—
82C2×(C2×D11)⋊C4—21no—
83C2×(C2×D11)⋊C4—21no—
84C2×(C2×D11)⋊C4—21no—
85C2×(C2×D11)⋊C4—21no—
86C2×(C2×D11)⋊C4—21no—
87C2×(C2×D11)⋊C4—21no—
88C2×C4⋊Dic11C2311yescharacteristic
89C2×C4⋊Dic11C2311yescharacteristic
90C2×C4×Dic11—21no—
91C22×C11⋊C8C2311yescharacteristic
92C22×C11⋊C8C2311yescharacteristic
93C22×C11⋊C8C2311yescharacteristic
94C22×C11⋊C8C2311yescharacteristic
95#66946—44no—
96#66927—22no—
97#66927—22no—
98C4×D44—22no—
99C4×D44—22no—
100C4×D44—41no—
101C4×D44—41no—
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—
112C11×#95D411yescharacteristic
113C11×#95D411yescharacteristic
114#66899—22no—
115#66899—41no—
116C11⋊#95—21no—
117#66873—22no—
118#66873—22no—
119#66873—22no—
120#66873—41no—
121#66873—41no—
122#66873—41no—
123#66872—22no—
124#66871—41no—
125C4⋊(C11⋊C8)—41no—
126C4×C11⋊C8—41no—
127#27063—111nomaximal, Sylow
128C23×D11—21no—
129C23×D11—21no—
130C2×Q8×C11—21no—
131C2×Q8×C11—21no—
132C2×Q8×C11—21no—
133C2×Q8×C11—21no—
134C2×Q8×C11—21no—
135C2×Q8×C11—21no—
136C22×C4×C11—21no—
137C22×C4×C11—21no—
138C22×C4×C11—21no—
139C22×C4×C11—21no—
140C22×C4×C11C2×D411yescharacteristic
141C22×C4×C11C2×D411yescharacteristic
142C22×C4×C11C2×D411yescharacteristic
143C22×C4×C11C2×D411yescharacteristic
144C22×C4×C11C2×D411yescharacteristic
145C22×C4×C11C2×D411yescharacteristic
146C22×C4×C11C2411yescharacteristic
147C22×Dic11—21no—
148C22×Dic11—21no—
149C2×D44—24no—
150C2×D44—24no—
151C2×D44—21no—
152C2×D44—21no—
153C2×D44—21no—
154C2×D44—21no—
155C2×D44—21no—
156C2×D44—21no—
157C2×D44—21no—
158C2×D44—21no—
159C2×D44—21no—
160C2×D44—21no—
161C2×D44—42no—
162C2×D44—42no—
163C2×D44—81no—
164C2×D44—81no—
165C2×D44#4112yes—
166C2×D44#4112yes—
167C2×C4×D11—42no—
168C2×C4×D11—42no—
169C2×C4×D11—42no—
170C2×C4×D11—42no—
171C2×C4×D11—81no—
172C2×C4×D11—81no—
173C11×C4⋊C4—22no—
174C11×C4⋊C4—22no—
175C11×C4⋊C4—21no—
176C11×C4⋊C4—21no—
177C11×C4⋊C4—21no—
178C11×C4⋊C4—21no—
179C11×C4⋊C4—21no—
180C11×C4⋊C4—21no—
181C11×C4⋊C4—42no—
182C42×C11—21no—
183C42×C11—21no—
184C42×C11—21no—
185C42×C11—21no—
186C42×C11—21no—
187C42×C11—21no—
188C42×C11—42no—
189#4325—44no—
190#4325—44no—
191(C2×D11)⋊C4—42no—
192(C2×D11)⋊C4—42no—
193(C2×D11)⋊C4—42no—
194(C2×D11)⋊C4—42no—
195(C2×D11)⋊C4—81no—
196(C2×D11)⋊C4—81no—
197C4⋊Dic11—21no—
198C4⋊Dic11—21no—
199C4⋊Dic11—21no—
200C4⋊Dic11#4112yes—
201C4×Dic11—42no—
202C2×C11⋊C8—21no—
203C2×C11⋊C8—21no—
204C2×C11⋊C8—21no—
205C2×C11⋊C8—21no—
206C2×C11⋊C8—21no—
207C2×C11⋊C8—21no—
208C2×C11⋊C8—21no—
209C2×C11⋊C8—21no—
210C2×C11⋊C8—21no—
211C2×C11⋊C8—21no—
212C2×C11⋊C8—21no—
213C2×C11⋊C8#4112yes—
214#2514D1111yescharacteristic, complemented
215#2366—111no—
216#2092—111no—
217#2055—111no—
218#2041—111no—
219#2014—111no—
220#1968—111no—
221#1928—111no—
222#1925—111no—
223#1919—111no—
224#1916—111no—
225#1877—111no—
226#1877—111no—
227#1804—111no—
228C4×#102—111no—
229C23×C11C22×D411yescharacteristic
230C22×D11—22no—
231C22×D11—22no—
232C22×D11—41no—
233C22×D11—41no—
234C22×D11—41no—
235C22×D11—41no—
236C22×D11—41no—
237C22×D11—41no—
238C22×D11—41no—
239C22×D11—41no—
240C22×D11—41no—
241C22×D11—41no—
242C22×D11—41no—
243C22×D11—41no—
244Q8×C11—41no—
245Q8×C11—41no—
246Q8×C11—41no—
247Q8×C11—41no—
248C2×C4×C11—21no—
249C2×C4×C11—21no—
250C2×C4×C11—21no—
251C2×C4×C11—21no—
252C2×C4×C11—21no—
253C2×C4×C11—21no—
254C2×C4×C11—21no—
255C2×C4×C11—21no—
256C2×C4×C11—21no—
257C2×C4×C11—21no—
258C2×C4×C11—21no—
259C2×C4×C11—21no—
260C2×C4×C11—21no—
261C2×C4×C11—21no—
262C2×C4×C11—21no—
263C2×C4×C11—21no—
264C2×C4×C11—41no—
265C2×C4×C11—41no—
266C2×C4×C11—41no—
267C2×C4×C11—41no—
268C2×C4×C11—41no—
269C2×C4×C11—41no—
270C2×C4×C11—41no—
271C2×C4×C11—41no—
272C2×C4×C11—41no—
273C2×C4×C11—41no—
274C2×C4×C11—41no—
275C2×C4×C11—41no—
276C2×C4×C11#13512yes—
277C2×C4×C11AGL(1,ℤ/8)12yes—
278C2×C4×C11C2×#4111yescharacteristic
279C2×C4×C11C2×#4111yescharacteristic
280C2×C4×C11C2×#4111yescharacteristic
281C2×C4×C11C2×#4111yescharacteristic
282C2×C4×C11H(5,𝔽2)11yescharacteristic
283C2×C4×C11H(5,𝔽2)11yescharacteristic
284C2×Dic11—22no—
285C2×Dic11—41no—
286C2×Dic11—41no—
287C2×Dic11—41no—
288C2×Dic11—41no—
289C2×Dic11—41no—
290D44—22no—
291D44—22no—
292D44—22no—
293D44—22no—
294D44—48no—
295D44—41no—
296D44—41no—
297D44—41no—
298D44—41no—
299D44—84no—
300C4×D11—84no—
301C4×D11—84no—
302C11⋊C8—22no—
303C11⋊C8—41no—
304C11⋊C8—41no—
305C11⋊C8—41no—
306C22×SD16—111no—
307C22×SD16—111no—
308C2×#127—111no—
309C2×C4×D4—111no—
310C2×C4×D4—111no—
311C2×C4×D4—221no—
312C2×#107—111no—
313C2×#106—111no—
314C2×C4⋊C8—111no—
315C2×#103—111no—
316C2×#103—111no—
317C2×#102—111no—
318C2×#102—111no—
319C2×#102—111no—
320C2×#102—111no—
321C2×#102—111no—
322C2×#102—111no—
323C2×C4×C8—111no—
324#401—21no—
325#400—21no—
326#391C2×D1111yescharacteristic
327#391C2×D1111yescharacteristic
328#391C2×D1111yescharacteristic
329#390—111no—
330#390—111no—
331#390—221no—
332#389C2×D1111yescharacteristic
333#387—21no—
334#386—221no—
335#386—221no—
336#383—21no—
337#382C2×D1111yescharacteristic
338C4×C4⋊C4—111no—
339C4×C4⋊C4C2×D1111yescharacteristic
340C4×C4⋊C4C2×D1111yescharacteristic
341#340—111no—
342#340—111no—
343#340—111no—
344#340—111no—
345#336—111no—
346#336—111no—
347#336—111no—
348#336—111no—
349C22×C11#52511yescharacteristic
350C22×C11#54611yescharacteristic
351C22×C11#55011yescharacteristic
352C22×C11C2×#13511yescharacteristic
353C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
354C22×C11#57711yescharacteristic
355C22×C11#57711yescharacteristic
356C2×D11—42no—
357C2×D11—42no—
358C2×D11—42no—
359C2×D11—42no—
360C2×D11—42no—
361C2×D11—42no—
362C2×D11—81no—
363C2×D11—81no—
364C2×D11—81no—
365C2×D11—81no—
366C2×D11—81no—
367C2×D11—81no—
368C2×D11—81no—
369C2×D11—81no—
370C4×C11—22no—
371C4×C11—22no—
372C4×C11—41no—
373C4×C11—41no—
374C4×C11—41no—
375C4×C11—41no—
376C4×C11—81no—
377C4×C11—81no—
378C4×C11—81no—
379C4×C11—81no—
380C4×C11#52911yescharacteristic
381C4×C11#53811yescharacteristic
382C4×C11#55111yescharacteristic
383C4×C11#55311yescharacteristic
384Dic11—42no—
385Dic11—81no—
386C22×Q8C22×D1111yescharacteristic
387C22×D4—111no—
388C22×D4—111no—
389C22×D4—221no—
390C22×D4—221no—
391C23×C4—221no—
392C23×C4—221no—
393C2×SD16—222no—
394C2×SD16—222no—
395C2×SD16—222no—
396C2×SD16—441no—
397C2×SD16—441no—
398C2×SD16—441no—
399C22×C8—111no—
400C22×C8—111no—
401C22×C8—111no—
402C22×C8—111no—
403#127—222no—
404#127—222no—
405C4×D4—222no—
406C4×D4—222no—
407C4×D4—441no—
408C4×D4—441no—
409C4×D4—444no—
410C2×C4⋊C4—21no—
411C2×C4⋊C4—111no—
412C2×C4⋊C4—111no—
413C2×C4⋊C4C22⋊D1111yescharacteristic
414C2×C4⋊C4C22⋊D1111yescharacteristic
415C2×C4⋊C4C22×D1111yescharacteristic
416C2×C4⋊C4C22×D1111yescharacteristic
417C2×C4⋊C4C22×D1111yescharacteristic
418C2×C22⋊C4—221no—
419C2×C22⋊C4—221no—
420C2×C22⋊C4—221no—
421C2×C22⋊C4—221no—
422C2×C22⋊C4—221no—
423C2×C22⋊C4—221no—
424C2×C42—21no—
425C2×C42—221no—
426C2×C42C22×D1111yescharacteristic
427C2×C42C22×D1111yescharacteristic
428C2×C42C22×D1111yescharacteristic
429#107—441no—
430#106—222no—
431C4⋊C8—441no—
432#103—222no—
433#103—441no—
434#102—222no—
435#102—222no—
436#102—222no—
437#102—441no—
438#102—441no—
439#102—441no—
440C4×C8—441no—
441#95—21no—
442#95—21no—
443#95—21no—
444#95—21no—
445#95—21no—
446#95—21no—
447#95—21no—
448#95—21no—
449#95—21no—
450#95—21no—
451#95—221no—
452#95C22⋊D1111yescharacteristic
453#95C22⋊D1111yescharacteristic
454C2×C11#246711yescharacteristic
455C2×C11#310511yescharacteristic
456C2×C11#312311yescharacteristic
457C2×C11#330411yescharacteristic
458C2×C11#331011yescharacteristic
459C2×C11#339411yescharacteristic
460C2×C11#339711yescharacteristic
461D11—82no—
462D11—82no—
463C24—221no—
464C24—221no—
465C2×Q8—21no—
466C2×Q8—21no—
467C2×Q8—21no—
468C2×Q8—21no—
469C2×Q8—21no—
470C2×Q8—21no—
471C2×D4—112no—
472C2×D4—112no—
473C2×D4—224no—
474C2×D4—224no—
475C2×D4—221no—
476C2×D4—221no—
477C2×D4—221no—
478C2×D4—221no—
479C2×D4—221no—
480C2×D4—221no—
481C2×D4—221no—
482C2×D4—221no—
483C2×D4—221no—
484C2×D4—221no—
485C2×D4—442no—
486C2×D4—442no—
487C2×D4—881no—
488C2×D4—881no—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—221no—
494C22×C4—221no—
495C22×C4—442no—
496C22×C4—442no—
497C22×C4—442no—
498C22×C4—442no—
499C22×C4—881no—
500C22×C4—881no—
501C22×C4C2×C22⋊D1111yescharacteristic
502C22×C4C2×C22⋊D1111yescharacteristic
503C22×C4C2×C22⋊D1111yescharacteristic
504C22×C4C2×C22⋊D1111yescharacteristic
505C22×C4C2×C22⋊D1111yescharacteristic
506C22×C4C2×C22⋊D1111yescharacteristic
507C22×C4C23×D1111yescharacteristic
508SD16—444no—
509SD16—444no—
510C2×C8—112no—
511C2×C8—221no—
512C2×C8—221no—
513C2×C8—221no—
514C2×C8—221no—
515C2×C8—221no—
516C2×C8—221no—
517C2×C8—221no—
518C2×C8—221no—
519C2×C8—221no—
520C2×C8—221no—
521C2×C8—221no—
522C4⋊C4—22no—
523C4⋊C4—22no—
524C4⋊C4—21no—
525C4⋊C4—21no—
526C4⋊C4—21no—
527C4⋊C4—21no—
528C4⋊C4—21no—
529C4⋊C4—21no—
530C4⋊C4—42no—
531C4⋊C4—112no—
532C4⋊C4—221no—
533C4⋊C4—221no—
534C4⋊C4—221no—
535C22⋊C4—442no—
536C22⋊C4—442no—
537C22⋊C4—442no—
538C22⋊C4—442no—
539C22⋊C4—881no—
540C22⋊C4—881no—
541C42—21no—
542C42—21no—
543C42—21no—
544C42—21no—
545C42—21no—
546C42—21no—
547C42—42no—
548C42—442no—
549C11#2706311yescharacteristic, complemented, Sylow
550C23—222no—
551C23—222no—
552C23—441no—
553C23—441no—
554C23—441no—
555C23—441no—
556C23—441no—
557C23—441no—
558C23—441no—
559C23—441no—
560C23—441no—
561C23—441no—
562C23—441no—
563C23—441no—
564C23C22×C22⋊D1111yescharacteristic
565Q8—41no—
566Q8—41no—
567Q8—41no—
568Q8—41no—
569D4—222no—
570D4—222no—
571D4—222no—
572D4—222no—
573D4—448no—
574D4—441no—
575D4—441no—
576D4—441no—
577D4—441no—
578D4—884no—
579C2×C4—21no—
580C2×C4—21no—
581C2×C4—21no—
582C2×C4—21no—
583C2×C4—21no—
584C2×C4—21no—
585C2×C4—21no—
586C2×C4—21no—
587C2×C4—21no—
588C2×C4—21no—
589C2×C4—21no—
590C2×C4—21no—
591C2×C4—21no—
592C2×C4—21no—
593C2×C4—21no—
594C2×C4—21no—
595C2×C4—41no—
596C2×C4—41no—
597C2×C4—41no—
598C2×C4—41no—
599C2×C4—41no—
600C2×C4—41no—
601C2×C4—41no—
602C2×C4—41no—
603C2×C4—41no—
604C2×C4—41no—
605C2×C4—41no—
606C2×C4—41no—
607C2×C4—222no—
608C2×C4—441no—
609C2×C4—441no—
610C2×C4—441no—
611C2×C4—441no—
612C2×C4—441no—
613C2×C4—884no—
614C2×C4—884no—
615C2×C4#6700212yes—
616C2×C4#6700312yes—
617C2×C4#41×D1111yescharacteristic
618C2×C4#41×D1111yescharacteristic
619C2×C4#41×D1111yescharacteristic
620C2×C4#41×D1111yescharacteristic
621C2×C4#6704211yescharacteristic
622C2×C4#6704211yescharacteristic
623C8—222no—
624C8—441no—
625C8—441no—
626C8—441no—
627C22—442no—
628C22—442no—
629C22—442no—
630C22—442no—
631C22—442no—
632C22—442no—
633C22—881no—
634C22—881no—
635C22—881no—
636C22—881no—
637C22—881no—
638C22—881no—
639C22—881no—
640C22—881no—
641C22C2×#6700211yescharacteristic
642C22C2×#6700311yescharacteristic
643C22#1062335911yescharacteristic
644C22#1062336011yescharacteristic
645C22#1062336511yescharacteristic
646C22#1062336811yescharacteristic
647C22#1062336811yescharacteristic
648C4—22no—
649C4—22no—
650C4—41no—
651C4—41no—
652C4—41no—
653C4—41no—
654C4—81no—
655C4—81no—
656C4—81no—
657C4—81no—
658C4—442no—
659C4—881no—
660C4#1062323511yescharacteristic
661C4#1062323611yescharacteristic
662C4#1062323711yescharacteristic
663C4#1062324011yescharacteristic
664C2—882no—
665C2—882no—
666C2#1307266311yescharacteristic
667C2#1307865911yescharacteristic
668C2#1307886311yescharacteristic
669C2#1308054911yescharacteristic
670C2#1308063111yescharacteristic
671C2#1308161211yescharacteristic
672C2#1308163611yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2514C2
socleC23×C11C22×D4
prime radicalC2×#66927C22
hypercenter#2514D11
hypocenterC11#27063
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ #2514

Complements

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

NH ≅ G/Ntype
2. #13070140C2semidirect
3. #13069931C2semidirect
6. #13069473C2semidirect
7. #13069254C2semidirect
8. #13069236C2semidirect
9. #13069191C2semidirect
10. #13069175C2semidirect
11. #13068953C2semidirect
12. #13068953C2semidirect
13. #13068623C2semidirect
14. C4×#66873C2semidirect
15. C11×#2514C2semidirect
214. #2514D11semidirect
549. C11#27063semidirect

Maximal subgroups

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

subgroupindex
#130716802
#130701402
#130699312
#130698502
#130697032
#130694732
#130692542
#130692362
#130691912
#130691752
#130689532
#130686232
C4×#668732
C11×#25142
#2706311