Finite Group Databasebeta

← #14743166

Subgroups — #14743166

Order 2816.

736 conjugacy classes of subgroups.

The subgroup lattice has 650 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13080431C211yesmaximal, characteristic, complemented
2#13080334C211yesmaximal, characteristic, complemented
3#13080216C211yesmaximal, characteristic, complemented
4#13068286C211yesmaximal, characteristic, complemented
5#13068103C211yesmaximal, characteristic, complemented
6#13068053C211yesmaximal, characteristic, complemented
7#13068002C211yesmaximal, characteristic, complemented
8#13067959C211yesmaximal, characteristic, complemented
9#13067851C211yesmaximal, characteristic, complemented
10#13067850C211yesmaximal, characteristic, complemented
11#13067794C211yesmaximal, characteristic, complemented
12#13067705C211yesmaximal, characteristic, complemented
13#13067446C211yesmaximal, characteristic, complemented
14#13067438C211yesmaximal, characteristic, complemented
15C11×#3334C211yesmaximal, characteristic, complemented
16C11×#547C2211yescharacteristic
17C11×#547C2211yescharacteristic, complemented
18C2×#67003—21no—
19C2×#67002—21no—
20#10623082C2211yescharacteristic
21D4×D44C2211yescharacteristic
22C11×#500C2211yescharacteristic, complemented
23C11×#480—21no—
24C11×#480—21no—
25C11×#474C2211yescharacteristic
26C11×#474C2211yescharacteristic, complemented
27C11×#466—21no—
28C4×C11×D8C2211yescharacteristic
29C8×D4×C11C2211yescharacteristic, complemented
30C2×C11×#107—21no—
31#10622852—21no—
32#10622851—21no—
33#10622769—21no—
34#10622705C2211yescharacteristic, complemented
35#10622701C2211yescharacteristic
36#10622698C2211yescharacteristic
37#10622696C2211yescharacteristic
38#10622696C2211yescharacteristic
39#10622691C2211yescharacteristic, complemented
40#10622664—21no—
41#10622662—21no—
42#10622660—21no—
43#10622659—21no—
44#10622632C2211yescharacteristic, complemented
45#10622628C2211yescharacteristic
46#10622628C2211yescharacteristic
47C4×#4323C2211yescharacteristic
48#10622625C2211yescharacteristic
49D4×C11⋊C8C2211yescharacteristic, complemented
50#10622620C2211yescharacteristic
51#10622495—21no—
52#10622388—21no—
53D11×#102—21no—
54#10622307C2211yescharacteristic
55C8×D44C2211yescharacteristic
56#10622185C2211yescharacteristic, complemented
57#10622185C2211yescharacteristic, complemented
58D4⋊(C11⋊C8)C2211yescharacteristic
59D4⋊(C11⋊C8)C2211yescharacteristic, complemented
60D4⋊(C11⋊C8)C2211yescharacteristic, complemented
61#10622124C2211yescharacteristic, complemented
62#10622123C2211yescharacteristic
63#10622121C2211yescharacteristic
64#10622118C2211yescharacteristic, complemented
65#10622096C2211yescharacteristic, complemented
66#10622092C2211yescharacteristic, complemented
67C2×C11×#41—21no—
68C2×C11×#41—21no—
69C2×D4×D11—21no—
70C2×#4339—21no—
71C22×D44—21no—
72C2×C11×D8D411yescharacteristic
73C22×C8×C11—21no—
74C11×C4⋊Q8C2311yescharacteristic
75C11×C4⋊Q8C2311yescharacteristic
76C11×#123—41no—
77C11×#123—41no—
78C11×C22⋊Q8—21no—
79C11×C22⋊Q8—21no—
80C11×#121—21no—
81C11×#121—21no—
82C4×D4×C11C2311yescharacteristic
83C4×D4×C11C2311yescharacteristic
84C4×D4×C11C2311yescharacteristic
85C2×C11×C4⋊C4—21no—
86C2×C11×C4⋊C4—21no—
87#67003—44no—
88#67002—44no—
89C2×#4326—21no—
90C2×#4326—21no—
91C2×#4325—21no—
92C2×#4325—21no—
93C2×#4325—21no—
94C2×#4325—21no—
95#66991—21no—
96C2×#4324—21no—
97C2×#4323—21no—
98C2×#4323—21no—
99C2×#4323D411yescharacteristic
100#66983—21no—
101#66977—21no—
102C2×#4318—21no—
103C22×C11⋊C8—21no—
104C2×C8×D11—21no—
105#66948—21no—
106C4⋊C4×D11—21no—
107#66936—41no—
108#66935—41no—
109#66927C2311yescharacteristic
110C4×D44C2311yescharacteristic
111#66922C2311yescharacteristic
112C11×#107—21no—
113C11×#107—21no—
114C11×#107—21no—
115C11×#107—21no—
116C11×#107D411yescharacteristic
117C11×C4⋊C8C2311yescharacteristic
118C11×#102—21no—
119C11×#102—21no—
120C11×#102D411yescharacteristic
121C11×#102D411yescharacteristic
122C11×C22⋊C8—21no—
123C4×C8×C11C2311yescharacteristic
124#66899—21no—
125#66899—21no—
126#66896—21no—
127#66896D411yescharacteristic
128C22⋊(C11⋊C8)—21no—
129C22⋊(C11⋊C8)—21no—
130#66885—21no—
131#66885—21no—
132(C2×D11)⋊C8—21no—
133#66874—21no—
134#66873—21no—
135#66873—21no—
136#66873—41no—
137#66873D411yescharacteristic
138#66871—21no—
139#66871—41no—
140#66871D411yescharacteristic
141C4⋊(C11⋊C8)C2311yescharacteristic
142C4⋊(C11⋊C8)C2311yescharacteristic
143C4⋊(C11⋊C8)C2311yescharacteristic
144C4×C11⋊C8C2311yescharacteristic
145C4×C11⋊C8C2311yescharacteristic
146#19758—111nomaximal, Sylow
147C23×D11—41no—
148C11×#41—42no—
149C11×#41—42no—
150C11×#41—81no—
151C11×#41—81no—
152C2×Q8×C11—21no—
153C2×Q8×C11—21no—
154C2×D4×C11—41no—
155C2×D4×C11—41no—
156C2×D4×C11C2×D411yescharacteristic
157C2×D4×C11C2×D411yescharacteristic
158C2×D4×C11C2×D411yescharacteristic
159C22×C4×C11—21no—
160C22×C4×C11—21no—
161C22×C4×C11—21no—
162C22×C4×C11—41no—
163C22×C4×C11—41no—
164C2×C22⋊D11—41no—
165C2×C22⋊D11—41no—
166D4×D11—42no—
167D4×D11—81no—
168#4339—42no—
169#4339—81no—
170C2×D44—21no—
171C2×D44—21no—
172C2×D44—21no—
173C2×D44—41no—
174C2×D44—42no—
175C2×D44—81no—
176C2×D44C2×D411yescharacteristic
177C2×C4×D11—21no—
178C2×C4×D11—41no—
179C2×Dic22—21no—
180C11×D8—41no—
181C2×C8×C11—21no—
182C2×C8×C11—42no—
183C2×C8×C11C2×D411yescharacteristic
184C2×C8×C11C2×D411yescharacteristic
185C11×C4⋊C4—21no—
186C11×C4⋊C4—21no—
187C11×C4⋊C4—21no—
188C11×C4⋊C4—21no—
189C11×C4⋊C4—41no—
190C11×C4⋊C4—41no—
191C11×C4⋊C4C2×D411yescharacteristic
192C11×C4⋊C4C2×D411yescharacteristic
193C11×C4⋊C4C2×D411yescharacteristic
194C11×C22⋊C4—21no—
195C11×C22⋊C4—21no—
196C11×C22⋊C4—21no—
197C11×C22⋊C4—41no—
198C11×C22⋊C4—41no—
199C42×C11C2411yescharacteristic
200C22⋊Dic11—41no—
201#4326—42no—
202#4326—81no—
203#4325—42no—
204#4325—42no—
205#4325—42no—
206#4325—81no—
207#4324—42no—
208#4323—42no—
209#4323—81no—
210#4323D814yescomplemented
211(C2×D11)⋊C4—21no—
212(C2×D11)⋊C4—41no—
213C4⋊Dic11—21no—
214C4⋊Dic11—21no—
215C4⋊Dic11C2×D411yescharacteristic
216Dic11⋊C4—41no—
217#4318—42no—
218C2×C11⋊C8—21no—
219C2×C11⋊C8—21no—
220C2×C11⋊C8—21no—
221C2×C11⋊C8—21no—
222C2×C11⋊C8—42no—
223C2×C11⋊C8C2×D411yescharacteristic
224C2×C11⋊C8C2×D411yescharacteristic
225C8×D11—81no—
226#3334D1111yescharacteristic, complemented
227#3294—111no—
228#3283—111no—
229#3272—111no—
230#1722—111no—
231#1689—111no—
232#1681—111no—
233#1673—111no—
234#1665—111no—
235#1647—111no—
236#1647—111no—
237#1639—111no—
238#1625—111no—
239#1581—111no—
240#1580—111no—
241C23×C11—21no—
242C23×C11—21no—
243C23×C11—21no—
244C22×D11—21no—
245C22×D11—41no—
246C22×D11—82no—
247C22×D11—82no—
248C22×D11—161no—
249Q8×C11—41no—
250Q8×C11—41no—
251Q8×C11—41no—
252Q8×C11—41no—
253D4×C11—21no—
254D4×C11—21no—
255D4×C11—21no—
256D4×C11—21no—
257D4×C11—21no—
258D4×C11—82no—
259D4×C11—82no—
260D4×C11C2×D812yes—
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—82no—
273C2×C4×C11—82no—
274C2×C4×C11C22×D411yescharacteristic
275C2×C4×C11C22×D411yescharacteristic
276C2×C4×C11H(5,𝔽2)11yescharacteristic
277C22⋊D11—82no—
278C22⋊D11—82no—
279C2×Dic11—21no—
280C2×Dic11—41no—
281D44—21no—
282D44—41no—
283D44—41no—
284D44—41no—
285D44—41no—
286D44—81no—
287D44—82no—
288D44C2×D812yes—
289C4×D11—41no—
290C4×D11—41no—
291C4×D11—82no—
292Dic22—41no—
293Dic22—41no—
294C8×C11—21no—
295C8×C11—21no—
296C8×C11—41no—
297C11⋊C8—21no—
298C11⋊C8—41no—
299C11⋊C8—41no—
300C11⋊C8—41no—
301C11⋊C8—41no—
302C11⋊C8C2×D812yes—
303C2×AGL(1,ℤ/8)—221no—
304C2×#135—221no—
305#547—111no—
306#547C2×D1111yescharacteristic
307#547C2×D1111yescharacteristic, complemented
308D42—111no—
309#500—111no—
310#500C2×D1111yescharacteristic, complemented
311#494—111no—
312#492—111no—
313#486—111no—
314#486—111no—
315#480—21no—
316#480—21no—
317#480—221no—
318#474—111no—
319#474C2×D1111yescharacteristic
320#474C2×D1111yescharacteristic, complemented
321#468—221no—
322#467—221no—
323#466—21no—
324#466—221no—
325#461—111no—
326#461—111no—
327#461—111no—
328#459—111no—
329#459—111no—
330#452—221no—
331#452—221no—
332#450—221no—
333#449—221no—
334#447—221no—
335C4×D8—111no—
336C4×D8C2×D1111yescharacteristic
337#436—111no—
338C8×D4—111no—
339C8×D4—111no—
340C8×D4C2×D1111yescharacteristic, complemented
341C2×#107—21no—
342C2×#102—221no—
343#335—111no—
344#334—111no—
345#332—111no—
346#332—111no—
347#332—111no—
348#331—111no—
349D4⋊C8—111no—
350D4⋊C8—111no—
351D4⋊C8—111no—
352D4⋊C8—111no—
353#322—111no—
354C22×C11—22no—
355C22×C11—41no—
356C22×C11—41no—
357C22×C11—41no—
358C22×C11—41no—
359C22×C11—41no—
360C22×C11—41no—
361C22×C11—41no—
362C22×C11—41no—
363C22×C11D4211yescharacteristic
364C2×D11—22no—
365C2×D11—41no—
366C2×D11—41no—
367C2×D11—81no—
368C2×D11—81no—
369C2×D11—81no—
370C2×D11—164no—
371C4×C11—21no—
372C4×C11—41no—
373C4×C11—41no—
374C4×C11—41no—
375C4×C11—81no—
376C4×C11—81no—
377C4×C11C22×D811yescharacteristic
378C4×C11#57511yescharacteristic
379C4×C11#57611yescharacteristic
380C4×C11#57711yescharacteristic
381Dic11—41no—
382Dic11—81no—
383C2×#41—21no—
384C2×#41—21no—
385C2×#41—221no—
386C22×D4—221no—
387C22×D4—221no—
388AGL(1,ℤ/8)—444no—
389#135—444no—
390C2×Q16—221no—
391C2×Q16—221no—
392C2×SD16—221no—
393C2×SD16—221no—
394C2×SD16—221no—
395C2×SD16—221no—
396C2×SD16—221no—
397C2×D8—111no—
398C2×D8—221no—
399C2×D8—221no—
400C2×D8C22⋊D1111yescharacteristic
401C2×M16—221no—
402C22×C8—21no—
403C22×C8—221no—
404C22×C8—221no—
405C4⋊Q8—111no—
406C4⋊Q8C22×D1111yescharacteristic
407C4⋊Q8C22×D1111yescharacteristic
408#127—111no—
409#123—41no—
410#123—41no—
411#123—441no—
412C22⋊Q8—21no—
413C22⋊Q8—21no—
414C22⋊Q8—221no—
415#121—21no—
416#121—21no—
417#121—221no—
418#121—221no—
419#121—221no—
420#120—441no—
421C4×D4—111no—
422C4×D4C22×D1111yescharacteristic
423C4×D4C22×D1111yescharacteristic
424C4×D4C22×D1111yescharacteristic
425C2×C4⋊C4—21no—
426C2×C4⋊C4—21no—
427C2×C4⋊C4—221no—
428#107—21no—
429#107—21no—
430#107—21no—
431#107—21no—
432#107—111no—
433#107—221no—
434#107—441no—
435#107C22⋊D1111yescharacteristic
436C4⋊C8—111no—
437C4⋊C8—111no—
438C4⋊C8—111no—
439C4⋊C8C22×D1111yescharacteristic
440#103—221no—
441#103—221no—
442#103—221no—
443#102—21no—
444#102—21no—
445#102—111no—
446#102—111no—
447#102—221no—
448#102—221no—
449#102—221no—
450#102—221no—
451#102—221no—
452#102—441no—
453#102C22⋊D1111yescharacteristic
454#102C22⋊D1111yescharacteristic
455C22⋊C8—21no—
456C22⋊C8—221no—
457C22⋊C8—221no—
458C22⋊C8—221no—
459C4×C8—111no—
460C4×C8—111no—
461C4×C8C22×D1111yescharacteristic
462C2×C11—42no—
463C2×C11—81no—
464C2×C11—81no—
465C2×C11#326711yescharacteristic
466C2×C11D4×D811yescharacteristic
467C2×C11#328911yescharacteristic
468D11—42no—
469D11—161no—
470C24—441no—
471#41—42no—
472#41—42no—
473#41—81no—
474#41—81no—
475#41—442no—
476#41—881no—
477C2×Q8—21no—
478C2×Q8—21no—
479C2×Q8—221no—
480C2×D4—41no—
481C2×D4—41no—
482C2×D4—111no—
483C2×D4—221no—
484C2×D4—221no—
485C2×D4—221no—
486C2×D4—441no—
487C2×D4—442no—
488C2×D4—441no—
489C2×D4—442no—
490C2×D4—441no—
491C2×D4—881no—
492C2×D4—881no—
493C2×D4D4×D1111yescharacteristic
494C2×D4C2×C22⋊D1111yescharacteristic
495C2×D4C2×C22⋊D1111yescharacteristic
496C22×C4—21no—
497C22×C4—21no—
498C22×C4—21no—
499C22×C4—41no—
500C22×C4—41no—
501C22×C4—221no—
502C22×C4—441no—
503Q16—442no—
504Q16—881no—
505SD16—442no—
506SD16—442no—
507SD16—442no—
508SD16—442no—
509SD16—881no—
510D8—41no—
511D8—114no—
512D8—442no—
513D8—881no—
514M16—442no—
515C2×C8—21no—
516C2×C8—42no—
517C2×C8—111no—
518C2×C8—111no—
519C2×C8—221no—
520C2×C8—221no—
521C2×C8—221no—
522C2×C8—221no—
523C2×C8—442no—
524C2×C8—881no—
525C2×C8C2×C22⋊D1111yescharacteristic
526C2×C8C2×C22⋊D1111yescharacteristic
527C4⋊C4—21no—
528C4⋊C4—21no—
529C4⋊C4—21no—
530C4⋊C4—21no—
531C4⋊C4—41no—
532C4⋊C4—41no—
533C4⋊C4—111no—
534C4⋊C4—221no—
535C4⋊C4—221no—
536C4⋊C4—441no—
537C4⋊C4D4×D1111yescharacteristic
538C4⋊C4C2×C22⋊D1111yescharacteristic
539C4⋊C4C2×C22⋊D1111yescharacteristic
540C22⋊C4—21no—
541C22⋊C4—21no—
542C22⋊C4—21no—
543C22⋊C4—41no—
544C22⋊C4—41no—
545C22⋊C4—221no—
546C22⋊C4—441no—
547C22⋊C4—441no—
548C42C23×D1111yescharacteristic
549C11#1975811yescharacteristic, complemented, Sylow
550C23—21no—
551C23—21no—
552C23—21no—
553C23—221no—
554C23—441no—
555C23—882no—
556C23—882no—
557C23—1761no—
558Q8—41no—
559Q8—41no—
560Q8—41no—
561Q8—41no—
562Q8—441no—
563Q8—441no—
564D4—21no—
565D4—21no—
566D4—21no—
567D4—21no—
568D4—21no—
569D4—82no—
570D4—82no—
571D4—112no—
572D4—221no—
573D4—441no—
574D4—441no—
575D4—441no—
576D4—441no—
577D4—881no—
578D4—882no—
579D4—882no—
580D4—882no—
581D4D8×D1112yes—
582C2×C4—21no—
583C2×C4—21no—
584C2×C4—21no—
585C2×C4—41no—
586C2×C4—41no—
587C2×C4—41no—
588C2×C4—41no—
589C2×C4—41no—
590C2×C4—41no—
591C2×C4—41no—
592C2×C4—41no—
593C2×C4—82no—
594C2×C4—82no—
595C2×C4—221no—
596C2×C4—441no—
597C2×C4—441no—
598C2×C4—441no—
599C2×C4—882no—
600C2×C4C2×D4×D1111yescharacteristic
601C2×C4#6703711yescharacteristic
602C2×C4C22×C22⋊D1111yescharacteristic
603C8—21no—
604C8—21no—
605C8—41no—
606C8—112no—
607C8—221no—
608C8—441no—
609C8—441no—
610C8—441no—
611C8—441no—
612C22—22no—
613C22—41no—
614C22—41no—
615C22—41no—
616C22—41no—
617C22—41no—
618C22—41no—
619C22—41no—
620C22—41no—
621C22—222no—
622C22—441no—
623C22—441no—
624C22—881no—
625C22—881no—
626C22—881no—
627C22—1764no—
628C22D4×C22⋊D1111yescharacteristic
629C4—21no—
630C4—41no—
631C4—41no—
632C4—41no—
633C4—81no—
634C4—81no—
635C4—441no—
636C4—881no—
637C4C2×D8×D1111yescharacteristic
638C4#1062328811yescharacteristic
639C4#1062335311yescharacteristic
640C4#1062336811yescharacteristic
641C2—42no—
642C2—81no—
643C2—81no—
644C2—442no—
645C2—1761no—
646C2#1308014211yescharacteristic
647C2D8×C22⋊D1111yescharacteristic
648C2#1308038711yescharacteristic
subgroupG/H
centerC22D4×C22⋊D11
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#3334C2
socleC22×C11D42
hypercenter#3334D11
hypocenterC11#19758
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ #3334

Complements

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

NH ≅ G/Ntype
1. #13080431C2semidirect
2. #13080334C2semidirect
3. #13080216C2semidirect
4. #13068286C2semidirect
5. #13068103C2semidirect
6. #13068053C2semidirect
7. #13068002C2semidirect
8. #13067959C2semidirect
9. #13067851C2semidirect
10. #13067850C2semidirect
11. #13067794C2semidirect
12. #13067705C2semidirect
13. #13067446C2semidirect
14. #13067438C2semidirect
15. C11×#3334C2semidirect
17. C11×#547C22semidirect
22. C11×#500C22semidirect
26. C11×#474C22semidirect
29. C8×D4×C11C22semidirect
34. #10622705C22semidirect
39. #10622691C22semidirect
44. #10622632C22semidirect
49. D4×C11⋊C8C22semidirect
56. #10622185C22semidirect
57. #10622185C22semidirect
59. D4⋊(C11⋊C8)C22semidirect
60. D4⋊(C11⋊C8)C22semidirect
61. #10622124C22semidirect
64. #10622118C22semidirect
65. #10622096C22semidirect
66. #10622092C22semidirect
210. #4323D8semidirect
226. #3334D11semidirect
307. #547C2×D11semidirect
310. #500C2×D11semidirect
320. #474C2×D11semidirect
340. C8×D4C2×D11semidirect
549. C11#19758semidirect

Maximal subgroups

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

subgroupindex
#130804312
#130803342
#130802162
#130682862
#130681032
#130680532
#130680022
#130679592
#130678512
#130678502
#130677942
#130677052
#130674462
#130674382
C11×#33342
#1975811