Finite Group Databasebeta

← #15638625

Subgroups — #15638625

Order 2816.

2578 conjugacy classes of subgroups.

The subgroup lattice has 1002 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082455C211yesmaximal, characteristic, complemented
2C2×D4×D44C211yesmaximal, characteristic, complemented
3#13080759C214yesmaximal, complemented
4#13080639C214yesmaximal, complemented
5#13080116C214yesmaximal, complemented
6#13080101C214yesmaximal, complemented
7#13079636C212yesmaximal, complemented
8#13079432C212yesmaximal, complemented
9#13079374C211yesmaximal, characteristic, complemented
10#13079367C211yesmaximal, characteristic, complemented
11#13078756C212yesmaximal, complemented
12#13077846C212yesmaximal, complemented
13C2×#10622344C211yesmaximal, characteristic, complemented
14C2×#10622345C211yesmaximal, characteristic, complemented
15C11×#2973C211yesmaximal, characteristic, complemented
16C22×D4×D11—21no—
17C23×D44C2211yescharacteristic
18C23×D44C2211yescharacteristic, complemented
19C2×C4×D4×C11C2211yescharacteristic
20#10623335—21no—
21#10623322C2212yescomplemented
22C2×#66983C2211yescharacteristic
23C2×#66983C2211yescharacteristic, complemented
24C2×#66983C2211yescharacteristic, complemented
25C2×#66977C2211yescharacteristic, complemented
26C2×#66961C2214yescomplemented
27C22×D88C2212yescomplemented
28C22×#4314C2212yescomplemented
29#10623096C2212yescomplemented
30#10623087—22no—
31#10623083C2212yescomplemented
32#10623081C2212yescomplemented
33D4×D44—22no—
34D4×D44—22no—
35D4×D44C2214yes—
36D4×D44C2214yescomplemented
37#10623072C2212yescomplemented
38#10623071—22no—
39#10623046—21no—
40C2×#66948—21no—
41#10623025—21no—
42C2×#66935—21no—
43C2×#66935—21no—
44#10623017—21no—
45#10623010C2212yescomplemented
46C2×#66927C2211yescharacteristic, complemented
47C2×C4×D44C2211yescharacteristic, complemented
48C11×#435C2214yescomplemented
49C11×#435C2214yescomplemented
50C11×#432C2212yescomplemented
51C11×#407C2212yescomplemented
52C2×C11×C22⋊C8C2211yescharacteristic, complemented
53C2×C11×C22⋊C8C2211yescharacteristic, complemented
54#10622748C2214yescomplemented
55#10622747C2214yescomplemented
56#10622744C2214yescomplemented
57#10622728C2214yescomplemented
58#10622727C2214yescomplemented
59C2×#66885C2212yescomplemented
60C2×#66885C2212yescomplemented
61#10622461C2214yescomplemented
62#10622460C2214yescomplemented
63#10622457C2214yescomplemented
64#10622456C2214yescomplemented
65#10622351C2212yescomplemented
66#10622350C2214yescomplemented
67#10622349C2212yescomplemented
68#10622349C2212yescomplemented
69#10622348C2212yescomplemented
70#10622347C2214yescomplemented
71#10622345C2212yes—
72#10622345C2214yescomplemented
73#10622345C2214yescomplemented
74#10622345C2212yescomplemented
75#10622345C2212yescomplemented
76#10622345C2212yescomplemented
77#10622344C2212yescomplemented
78#10622344C2214yescomplemented
79#10622344C2214yescomplemented
80#10622344C2212yescomplemented
81#10622344C2212yescomplemented
82#10622334C2212yescomplemented
83#10622326C2214yescomplemented
84#10622325C2214yescomplemented
85#10622324C2214yescomplemented
86#10622323C2214yescomplemented
87C24×D11—21no—
88C24×D11—21no—
89C22×D4×C11D411yescharacteristic
90C23×C4×C11C2311yescharacteristic
91C23×C4×C11C2311yescharacteristic
92C22×C22⋊D11—21no—
93C22×C22⋊D11—21no—
94C22×C22⋊D11—21no—
95C2×D4×D11—24no—
96C2×D4×D11—24no—
97C2×D4×D11—48no—
98C2×#4339C2312yescomplemented
99C22×D44—21no—
100C22×D44—21no—
101C22×D44—21no—
102C22×D44—21no—
103C22×D44—21no—
104C22×D44—22no—
105C22×D44—21no—
106C22×D44—44no—
107C22×D44—44no—
108C22×D44C2311yescharacteristic
109C22×D44C2312yes—
110C22×D44C2312yes—
111C22×D44C2314yes—
112C22×D44C2311yescharacteristic
113C22×D44C2311yescharacteristic
114C22×D44C2311yescharacteristic, complemented
115C22×C4×D11—21no—
116C22×Dic22C2311yescharacteristic, complemented
117C2×C11×M16C2314yescomplemented
118C22×C8×C11C2312yescomplemented
119C22×C8×C11C2312yescomplemented
120C4×D4×C11D412yes—
121C4×D4×C11D412yes—
122C4×D4×C11C2312yes—
123C4×D4×C11C2312yes—
124C2×C11×C4⋊C4D411yescharacteristic
125C2×C11×C22⋊C4D411yescharacteristic
126C2×C11×C22⋊C4D411yescharacteristic
127C2×C42×C11C2311yescharacteristic
128#67006—22no—
129C2×C22⋊Dic11—21no—
130#66992—22no—
131#66992—22no—
132#66990—22no—
133#66988—22no—
134#66983—21no—
135#66983—21no—
136#66983—21no—
137#66983—21no—
138#66983—22no—
139#66983C2312yes—
140#66983C2312yes—
141#66983C2314yes—
142#66983C2312yes—
143#66983C2312yescomplemented
144#66983C2312yescomplemented
145#66982—22no—
146#66982—22no—
147C4×C22⋊D11—22no—
148C4×C22⋊D11—22no—
149C4×C22⋊D11—22no—
150C2×(C2×D11)⋊C4—21no—
151C2×(C2×D11)⋊C4—21no—
152C2×(C2×D11)⋊C4—21no—
153C2×(C2×D11)⋊C4—21no—
154#66979C2312yescomplemented
155C2×C4⋊Dic11C2311yescharacteristic
156C2×C4⋊Dic11C2311yescharacteristic, complemented
157C2×C4⋊Dic11C2311yescharacteristic, complemented
158#66977—21no—
159#66977—21no—
160#66977C2312yes—
161#66977C2312yescomplemented
162#66977C2312yescomplemented
163C2×Dic11⋊C4—21no—
164#66961—48no—
165C2×D88—44no—
166C2×D88C2314yes—
167C2×D88C2314yescomplemented
168C2×D88C2314yescomplemented
169C2×#4314—44no—
170C2×#4314C2314yes—
171C2×#4314C2314yescomplemented
172C2×#4314C2314yescomplemented
173#66951—22no—
174#66949—22no—
175#66948—24no—
176#66948—24no—
177#66947—22no—
178#66942—22no—
179#66938—22no—
180#66937—22no—
181#66936—22no—
182#66935—24no—
183#66935—24no—
184#66935—24no—
185#66935—24no—
186(C22⋊D11)⋊C4—22no—
187(C22⋊D11)⋊C4—22no—
188C22⋊C4×D11—22no—
189#66932—22no—
190#66930—22no—
191#66929—22no—
192#66928C2312yescomplemented
193#66927—22no—
194#66927C2314yes—
195C4×D44—22no—
196C4×D44C2314yes—
197C4×D44C2312yescomplemented
198#66925—22no—
199#66923C2312yescomplemented
200C4×Dic22C2312yescomplemented
201C11×C4⋊C8C2314yescomplemented
202C11×C22⋊C8C2312yes—
203C11×C22⋊C8C2312yes—
204C11×C22⋊C8C2312yescomplemented
205C11×C22⋊C8C2314yescomplemented
206C11×C22⋊C8C2312yescomplemented
207C11×#97C2314yescomplemented
208#66885C2314yes—
209#66885C2314yes—
210#66885C2314yescomplemented
211#66885C2314yescomplemented
212#66885C2314yescomplemented
213#66885C2314yescomplemented
214#66885C2314yescomplemented
215#66882C2314yescomplemented
216#66881C2314yescomplemented
217#66880C2314yescomplemented
218#61571—111nomaximal, Sylow
219C24×C11C2×D411yescharacteristic
220C24×C11C2×D411yescharacteristic
221C23×D11—21no—
222C23×D11—21no—
223C23×D11—21no—
224C23×D11—24no—
225C23×D11—22no—
226C23×D11—22no—
227C23×D11—21no—
228C23×D11—44no—
229C23×D11—44no—
230C23×D11—44no—
231C23×D11—44no—
232C23×D11—82no—
233C23×D11—82no—
234C2×D4×C11—24no—
235C2×D4×C11C2×D412yes—
236C2×D4×C11C2×D412yes—
237C22×C4×C11—42no—
238C22×C4×C11—42no—
239C22×C4×C11C2×D411yescharacteristic
240C22×C4×C11C2×D411yescharacteristic
241C22×C4×C11C2×D411yescharacteristic
242C22×C4×C11C2×D411yescharacteristic
243C22×C4×C11C2×D411yescharacteristic
244C22×C4×C11C2×D411yescharacteristic
245C22×C4×C11C2×D412yes—
246C22×C4×C11C2411yescharacteristic
247C22×C4×C11C2411yescharacteristic
248C22×C4×C11C2412yes—
249C22×C4×C11C2411yescharacteristic
250C2×C22⋊D11—22no—
251C2×C22⋊D11—24no—
252C2×C22⋊D11—22no—
253C2×C22⋊D11—22no—
254C2×C22⋊D11—22no—
255C2×C22⋊D11—22no—
256C2×C22⋊D11—22no—
257C2×C22⋊D11—44no—
258C2×C22⋊D11—44no—
259C2×C22⋊D11—44no—
260C22×Dic11—21no—
261C22×Dic11—21no—
262C22×Dic11—21no—
263C22×Dic11—21no—
264D4×D11—416no—
265D4×D11—416no—
266#4339—44no—
267C2×D44—24no—
268C2×D44—24no—
269C2×D44—24no—
270C2×D44—28no—
271C2×D44—21no—
272C2×D44—21no—
273C2×D44—21no—
274C2×D44—24no—
275C2×D44—24no—
276C2×D44—22no—
277C2×D44—22no—
278C2×D44—24no—
279C2×D44—21no—
280C2×D44—42no—
281C2×D44—42no—
282C2×D44—44no—
283C2×D44—42no—
284C2×D44—42no—
285C2×D44—44no—
286C2×D44—42no—
287C2×D44—44no—
288C2×D44—44no—
289C2×D44—44no—
290C2×D44—44no—
291C2×D44—48no—
292C2×D44—82no—
293C2×D44C2412yes—
294C2×D44C2412yes—
295C2×D44C2412yes—
296C2×D44C2412yes—
297C2×C4×D11—24no—
298C2×C4×D11—22no—
299C2×C4×D11—22no—
300C2×C4×D11—44no—
301C2×Dic22—21no—
302C2×Dic22—42no—
303C2×Dic22C2412yes—
304C11×M16—44no—
305C2×C8×C11—42no—
306C2×C8×C11—42no—
307C2×C8×C11C2414yes—
308C2×C8×C11C2414yes—
309C11×C4⋊C4C2×D412yes—
310C11×C4⋊C4C2×D412yes—
311C11×C22⋊C4C2×D412yes—
312C11×C22⋊C4C2×D412yes—
313C11×C22⋊C4C2×D412yes—
314C11×C22⋊C4C2×D412yes—
315C42×C11C2×D412yes—
316C42×C11C2412yes—
317C22⋊Dic11—22no—
318C22⋊Dic11—22no—
319C22⋊Dic11—22no—
320C22⋊Dic11—22no—
321(C2×D11)⋊C4—22no—
322(C2×D11)⋊C4—22no—
323(C2×D11)⋊C4—24no—
324(C2×D11)⋊C4—22no—
325(C2×D11)⋊C4—22no—
326(C2×D11)⋊C4—22no—
327(C2×D11)⋊C4—24no—
328(C2×D11)⋊C4—22no—
329(C2×D11)⋊C4—22no—
330(C2×D11)⋊C4—22no—
331C4⋊Dic11—21no—
332C4⋊Dic11—21no—
333C4⋊Dic11—21no—
334C4⋊Dic11C2412yes—
335C4⋊Dic11C2412yes—
336C4⋊Dic11C2412yes—
337Dic11⋊C4—22no—
338Dic11⋊C4—22no—
339Dic11⋊C4—22no—
340Dic11⋊C4—22no—
341Dic11⋊C4—22no—
342Dic11⋊C4—22no—
343C4×Dic11—22no—
344C4×Dic11—22no—
345D88—28no—
346D88—44no—
347D88—44no—
348#4314—28no—
349#4314—44no—
350#4314—44no—
351#3505—111no—
352C2×D42—111no—
353#3318—114no—
354#3310—114no—
355#3265—114no—
356#3264—114no—
357#3217—112no—
358#3194—112no—
359#3187—111no—
360#3186—111no—
361#3114—112no—
362#3003—112no—
363C2×#450—111no—
364C2×#447—111no—
365#2973D1111yescharacteristic, complemented
366C23×C11—22no—
367C23×C11—41no—
368C23×C11—41no—
369C23×C11—41no—
370C23×C11—41no—
371C23×C11AGL(1,ℤ/8)14yescomplemented
372C23×C11C22×D412yes—
373C23×C11C22×D411yescharacteristic
374C23×C11C22×D411yescharacteristic
375C23×C11C22×D411yescharacteristic
376C22×D11—24no—
377C22×D11—22no—
378C22×D11—22no—
379C22×D11—22no—
380C22×D11—22no—
381C22×D11—44no—
382C22×D11—44no—
383C22×D11—48no—
384C22×D11—42no—
385C22×D11—42no—
386C22×D11—42no—
387C22×D11—42no—
388C22×D11—42no—
389C22×D11—42no—
390C22×D11—48no—
391C22×D11—42no—
392C22×D11—42no—
393C22×D11—44no—
394C22×D11—44no—
395C22×D11—42no—
396C22×D11—82no—
397C22×D11—82no—
398C22×D11—84no—
399C22×D11—81no—
400C22×D11—81no—
401C22×D11—816no—
402C22×D11—816no—
403D4×C11—24no—
404D4×C11—24no—
405C2×C4×C11—22no—
406C2×C4×C11—22no—
407C2×C4×C11—22no—
408C2×C4×C11—24no—
409C2×C4×C11—22no—
410C2×C4×C11—41no—
411C2×C4×C11—42no—
412C2×C4×C11—41no—
413C2×C4×C11—41no—
414C2×C4×C11—41no—
415C2×C4×C11—41no—
416C2×C4×C11C22×D412yes—
417C2×C4×C11C22×D412yes—
418C2×C4×C11C22×D411yescharacteristic
419C2×C4×C11C22×D411yescharacteristic
420C2×C4×C11C22×D412yes—
421C2×C4×C11C22×D411yescharacteristic
422C2×C4×C11C2511yescharacteristic
423C22⋊D11—48no—
424C22⋊D11—44no—
425C22⋊D11—44no—
426C22⋊D11—44no—
427C22⋊D11—44no—
428C22⋊D11—82no—
429C22⋊D11—82no—
430C2×Dic11—22no—
431C2×Dic11—22no—
432C2×Dic11—22no—
433C2×Dic11—22no—
434C2×Dic11—42no—
435C2×Dic11—42no—
436C2×Dic11—81no—
437C2×Dic11—81no—
438D44—24no—
439D44—22no—
440D44—22no—
441D44—24no—
442D44—24no—
443D44—22no—
444D44—44no—
445D44—48no—
446D44—44no—
447D44—42no—
448D44—42no—
449D44—48no—
450D44—81no—
451D44—84no—
452D44H(5,𝔽2)14yes—
453C4×D11—48no—
454C4×D11—82no—
455C4×D11—82no—
456Dic22—24no—
457Dic22—81no—
458C8×C11—24no—
459C8×C11—24no—
460C23×D4—111no—
461C23×D4—111no—
462C23×D4—221no—
463C2×AGL(1,ℤ/8)—114no—
464C22×SD16—112no—
465C22×D8—112no—
466#553—112no—
467#553—222no—
468#552—112no—
469#551—222no—
470#548—112no—
471#546—112no—
472D42—114no—
473D42—114no—
474D42—222no—
475D42—222no—
476#539—221no—
477#538—221no—
478#534—221no—
479C2×#127—111no—
480#529—112no—
481#525—112no—
482C2×C22⋊Q8—111no—
483C2×#121—111no—
484C2×#121—111no—
485C2×#121—111no—
486C2×#121—221no—
487C2×#120—221no—
488C2×#120—221no—
489#518—221no—
490C2×C4×D4—111no—
491C2×C4×D4C2×D1111yescharacteristic
492#496—114no—
493#490—114no—
494#483—112no—
495#482—114no—
496#481—112no—
497#480—112no—
498#480—112no—
499#478—114no—
500#469—114no—
501#468—114no—
502#466—114no—
503#465—114no—
504#463—114no—
505#460—114no—
506#459—114no—
507#450—112no—
508#450—112no—
509#450—112no—
510#450—114no—
511#450—114no—
512#449—114no—
513#448—112no—
514#447—112no—
515#447—112no—
516#447—112no—
517#447—112no—
518#447—114no—
519#447—114no—
520#442—114no—
521#440—114no—
522#435C2×D1114yescomplemented
523#435C2×D1114yescomplemented
524#432C2×D1112yescomplemented
525#418—114no—
526C2×#102—112no—
527C2×#102—112no—
528#407C2×D1112yescomplemented
529C2×C22⋊C8C2×D1111yescharacteristic, complemented
530C2×C22⋊C8C2×D1111yescharacteristic, complemented
531C22×C11—21no—
532C22×C11—21no—
533C22×C11—21no—
534C22×C11—21no—
535C22×C11—21no—
536C22×C11—21no—
537C22×C11—22no—
538C22×C11—22no—
539C22×C11—22no—
540C22×C11—44no—
541C22×C11—44no—
542C22×C11C2×AGL(1,ℤ/8)12yes—
543C22×C11C2×AGL(1,ℤ/8)12yes—
544C22×C11C2×AGL(1,ℤ/8)12yes—
545C22×C11C23×D411yescharacteristic
546C2×D11—24no—
547C2×D11—48no—
548C2×D11—42no—
549C2×D11—42no—
550C2×D11—42no—
551C2×D11—42no—
552C2×D11—42no—
553C2×D11—42no—
554C2×D11—42no—
555C2×D11—42no—
556C2×D11—42no—
557C2×D11—42no—
558C2×D11—42no—
559C2×D11—88no—
560C2×D11—88no—
561C2×D11—816no—
562C2×D11—84no—
563C2×D11—84no—
564C2×D11—162no—
565C4×C11—22no—
566C4×C11—21no—
567C4×C11—21no—
568C4×C11—22no—
569C4×C11—21no—
570C4×C11—22no—
571C4×C11C2×H(5,𝔽2)12yes—
572Dic11—42no—
573Dic11—42no—
574Dic11—42no—
575Dic11—42no—
576C25—221no—
577C25—221no—
578C2×#41—112no—
579C22×Q8—111no—
580C22×D4—111no—
581C22×D4—112no—
582C22×D4—112no—
583C22×D4—114no—
584C22×D4—111no—
585C22×D4—111no—
586C22×D4—111no—
587C22×D4—221no—
588C22×D4—221no—
589C22×D4—221no—
590C22×D4—224no—
591C22×D4—224no—
592C22×D4—221no—
593C22×D4—221no—
594C22×D4—221no—
595C22×D4—221no—
596C22×D4—221no—
597C22×D4—222no—
598C22×D4—221no—
599C22×D4—444no—
600C22×D4—444no—
601C22×D4—448no—
602C22×D4D4411yescharacteristic
603C23×C4—221no—
604C23×C4C22×D1111yescharacteristic
605C23×C4C22×D1111yescharacteristic
606AGL(1,ℤ/8)—448no—
607C2×SD16—114no—
608C2×SD16—114no—
609C2×SD16—114no—
610C2×SD16—444no—
611C2×D8—114no—
612C2×D8—114no—
613C2×D8—114no—
614C2×D8—444no—
615C2×M16C22×D1114yescomplemented
616C22×C8C22×D1112yescomplemented
617C22×C8C22×D1112yescomplemented
618#127—114no—
619#127—222no—
620#126—222no—
621#126—222no—
622#126—222no—
623#125—112no—
624#125—222no—
625#124—112no—
626#124—222no—
627#123—222no—
628#123—222no—
629#123—222no—
630#123—222no—
631#123—222no—
632C22⋊Q8—112no—
633C22⋊Q8—112no—
634C22⋊Q8—112no—
635C22⋊Q8—221no—
636C22⋊Q8—221no—
637C22⋊Q8—222no—
638#121—112no—
639#121—112no—
640#121—112no—
641#121—114no—
642#121—112no—
643#121—112no—
644#121—222no—
645#121—222no—
646#121—221no—
647#121—221no—
648#121—221no—
649#121—222no—
650#121—221no—
651#121—224no—
652#121—224no—
653#121—222no—
654#120—222no—
655#120—222no—
656#120—224no—
657#120—224no—
658#120—224no—
659#120—224no—
660C4×Q8—112no—
661C4×D4—114no—
662C4×D4—112no—
663C4×D4—222no—
664C4×D4—222no—
665C4×D4—222no—
666C4×D4—222no—
667C4×D4—222no—
668C4×D4—222no—
669C4×D4D4412yes—
670C4×D4D4412yes—
671C4×D4C22×D1112yes—
672C4×D4C22×D1112yes—
673#117—112no—
674#117—222no—
675#117—222no—
676C2×C4⋊C4—111no—
677C2×C4⋊C4—111no—
678C2×C4⋊C4—111no—
679C2×C4⋊C4—221no—
680C2×C4⋊C4D4411yescharacteristic
681C2×C22⋊C4—221no—
682C2×C22⋊C4—221no—
683C2×C22⋊C4—221no—
684C2×C22⋊C4—221no—
685C2×C22⋊C4—221no—
686C2×C22⋊C4—222no—
687C2×C22⋊C4D4411yescharacteristic
688C2×C22⋊C4D4411yescharacteristic
689C2×C42C22×D1111yescharacteristic
690#107—114no—
691#106—114no—
692C4⋊C8C22×D1114yescomplemented
693#103—114no—
694#102—114no—
695#102—114no—
696#102—114no—
697#102—114no—
698#102—114no—
699#102—114no—
700#102—114no—
701C22⋊C8C22×D1112yes—
702C22⋊C8C22×D1112yes—
703C22⋊C8C22×D1112yescomplemented
704C22⋊C8C22×D1112yescomplemented
705C22⋊C8C22×D1114yescomplemented
706#97C22×D1114yescomplemented
707C2×C11—22no—
708C2×C11—22no—
709C2×C11—22no—
710C2×C11—42no—
711C2×C11#348411yescharacteristic
712C2×C11C22×AGL(1,ℤ/8)11yescharacteristic
713C2×C11#358511yescharacteristic
714D11—44no—
715D11—82no—
716D11—82no—
717D11—82no—
718C24—221no—
719C24—221no—
720C24—221no—
721C24—224no—
722C24—222no—
723C24—222no—
724C24—221no—
725C24—444no—
726C24—444no—
727C24—444no—
728C24—444no—
729C24—882no—
730C24—882no—
731C24C2×D4411yescharacteristic
732C24C2×D4411yescharacteristic
733#41—444no—
734C2×Q8—112no—
735C2×Q8—221no—
736C2×Q8—442no—
737C2×D4—24no—
738C2×D4—112no—
739C2×D4—112no—
740C2×D4—112no—
741C2×D4—112no—
742C2×D4—224no—
743C2×D4—224no—
744C2×D4—224no—
745C2×D4—228no—
746C2×D4—222no—
747C2×D4—222no—
748C2×D4—224no—
749C2×D4—222no—
750C2×D4—222no—
751C2×D4—222no—
752C2×D4—222no—
753C2×D4—221no—
754C2×D4—224no—
755C2×D4—222no—
756C2×D4—222no—
757C2×D4—224no—
758C2×D4—221no—
759C2×D4—221no—
760C2×D4—224no—
761C2×D4—221no—
762C2×D4—442no—
763C2×D4—442no—
764C2×D4—444no—
765C2×D4—442no—
766C2×D4—442no—
767C2×D4—442no—
768C2×D4—444no—
769C2×D4—448no—
770C2×D4—444no—
771C2×D4—444no—
772C2×D4—444no—
773C2×D4—444no—
774C2×D4—4416no—
775C2×D4—4416no—
776C2×D4—444no—
777C2×D4—444no—
778C2×D4—444no—
779C2×D4—882no—
780C2×D4C2×D4412yes—
781C2×D4C2×D4412yes—
782C22×C4—42no—
783C22×C4—42no—
784C22×C4—221no—
785C22×C4—221no—
786C22×C4—221no—
787C22×C4—221no—
788C22×C4—224no—
789C22×C4—222no—
790C22×C4—222no—
791C22×C4—444no—
792C22×C4C2×D4411yescharacteristic
793C22×C4C2×D4411yescharacteristic
794C22×C4C2×D4411yescharacteristic
795C22×C4C2×D4411yescharacteristic
796C22×C4C2×D4411yescharacteristic
797C22×C4C2×D4411yescharacteristic
798C22×C4C2×D4412yes—
799C22×C4C23×D1111yescharacteristic
800C22×C4C23×D1111yescharacteristic
801C22×C4C23×D1111yescharacteristic
802C22×C4C23×D1112yes—
803SD16—228no—
804SD16—444no—
805SD16—444no—
806D8—228no—
807D8—444no—
808D8—444no—
809M16—44no—
810C2×C8—42no—
811C2×C8—42no—
812C2×C8C23×D1114yes—
813C2×C8C23×D1114yes—
814C4⋊C4—112no—
815C4⋊C4—112no—
816C4⋊C4—112no—
817C4⋊C4—221no—
818C4⋊C4—221no—
819C4⋊C4—221no—
820C4⋊C4—222no—
821C4⋊C4—222no—
822C4⋊C4—222no—
823C4⋊C4—222no—
824C4⋊C4—222no—
825C4⋊C4—222no—
826C4⋊C4C2×D4412yes—
827C4⋊C4C2×D4412yes—
828C22⋊C4—222no—
829C22⋊C4—222no—
830C22⋊C4—222no—
831C22⋊C4—222no—
832C22⋊C4—222no—
833C22⋊C4—224no—
834C22⋊C4—222no—
835C22⋊C4—222no—
836C22⋊C4—224no—
837C22⋊C4—222no—
838C22⋊C4—222no—
839C22⋊C4—222no—
840C22⋊C4—222no—
841C22⋊C4—222no—
842C22⋊C4C2×D4412yes—
843C22⋊C4C2×D4412yes—
844C22⋊C4C2×D4412yes—
845C22⋊C4C2×D4412yes—
846C42—222no—
847C42—222no—
848C42C2×D4412yes—
849C42C23×D1112yes—
850C11#6157111yescharacteristic, complemented, Sylow
851C23—22no—
852C23—41no—
853C23—41no—
854C23—41no—
855C23—41no—
856C23—224no—
857C23—222no—
858C23—222no—
859C23—222no—
860C23—222no—
861C23—444no—
862C23—444no—
863C23—448no—
864C23—442no—
865C23—442no—
866C23—442no—
867C23—448no—
868C23—442no—
869C23—442no—
870C23—442no—
871C23—444no—
872C23—444no—
873C23—442no—
874C23—442no—
875C23—442no—
876C23—882no—
877C23—882no—
878C23—884no—
879C23—881no—
880C23—881no—
881C23—8816no—
882C23—8816no—
883C23#6696114yescomplemented
884C23C22×D4412yes—
885C23C22×D4411yescharacteristic
886C23C22×D4411yescharacteristic
887C23C22×D4411yescharacteristic
888Q8—224no—
889Q8—881no—
890D4—24no—
891D4—24no—
892D4—114no—
893D4—224no—
894D4—222no—
895D4—224no—
896D4—222no—
897D4—224no—
898D4—222no—
899D4—448no—
900D4—444no—
901D4—444no—
902D4—442no—
903D4—442no—
904D4—448no—
905D4—448no—
906D4—444no—
907D4—444no—
908D4—444no—
909D4—444no—
910D4—881no—
911D4—884no—
912D4—882no—
913D4—882no—
914C2×C4—22no—
915C2×C4—22no—
916C2×C4—22no—
917C2×C4—24no—
918C2×C4—22no—
919C2×C4—42no—
920C2×C4—41no—
921C2×C4—41no—
922C2×C4—41no—
923C2×C4—41no—
924C2×C4—41no—
925C2×C4—222no—
926C2×C4—222no—
927C2×C4—222no—
928C2×C4—222no—
929C2×C4—448no—
930C2×C4—442no—
931C2×C4—442no—
932C2×C4—882no—
933C2×C4—882no—
934C2×C4—881no—
935C2×C4—881no—
936C2×C4C22×D4412yes—
937C2×C4C22×D4412yes—
938C2×C4C22×D4411yescharacteristic
939C2×C4C22×D4412yes—
940C2×C4C22×D4411yescharacteristic
941C2×C4C22×D4411yescharacteristic
942C2×C4C24×D1111yescharacteristic
943C8—24no—
944C8—24no—
945C22—21no—
946C22—21no—
947C22—21no—
948C22—21no—
949C22—21no—
950C22—21no—
951C22—22no—
952C22—22no—
953C22—22no—
954C22—44no—
955C22—44no—
956C22—224no—
957C22—448no—
958C22—442no—
959C22—442no—
960C22—442no—
961C22—442no—
962C22—442no—
963C22—442no—
964C22—442no—
965C22—442no—
966C22—442no—
967C22—442no—
968C22—442no—
969C22—888no—
970C22—888no—
971C22—884no—
972C22—884no—
973C22—8816no—
974C22—1762no—
975C22C2×#6696112yes—
976C22C2×#6696112yes—
977C22C2×#6696112yes—
978C22C23×D4411yescharacteristic
979C4—22no—
980C4—21no—
981C4—22no—
982C4—21no—
983C4—21no—
984C4—22no—
985C4—442no—
986C4—442no—
987C4—442no—
988C4—442no—
989C4D11×H(5,𝔽2)12yes—
990C2—22no—
991C2—22no—
992C2—22no—
993C2—42no—
994C2—444no—
995C2—882no—
996C2—882no—
997C2—882no—
998C2#1308225211yescharacteristic
999C2C22×#6696111yescharacteristic
1000C2#1308339711yescharacteristic
subgroupG/H
centerC22C23×D44
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC11×#2973C2
socleC22×C11C23×D4
hypercenter#2973D11
hypocenterC11#61571
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C4×D4 ◁ #2973

Complements

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

NH ≅ G/Ntype
1. #13082455C2semidirect
2. C2×D4×D44C2semidirect
3. #13080759C2semidirect
4. #13080639C2semidirect
5. #13080116C2semidirect
6. #13080101C2semidirect
7. #13079636C2semidirect
8. #13079432C2semidirect
9. #13079374C2semidirect
10. #13079367C2semidirect
11. #13078756C2semidirect
12. #13077846C2semidirect
13. C2×#10622344C2semidirect
14. C2×#10622345C2semidirect
15. C11×#2973C2semidirect
18. C23×D44C22semidirect
21. #10623322C22semidirect
23. C2×#66983C22semidirect
24. C2×#66983C22semidirect
25. C2×#66977C22semidirect
26. C2×#66961C22semidirect
27. C22×D88C22semidirect
28. C22×#4314C22semidirect
29. #10623096C22semidirect
31. #10623083C22semidirect
32. #10623081C22semidirect
36. D4×D44C22semidirect
37. #10623072C22semidirect
45. #10623010C22semidirect
46. C2×#66927C22semidirect
47. C2×C4×D44C22semidirect
48. C11×#435C22semidirect
49. C11×#435C22semidirect
50. C11×#432C22semidirect
51. C11×#407C22semidirect
52. C2×C11×C22⋊C8C22semidirect
53. C2×C11×C22⋊C8C22semidirect
54. #10622748C22semidirect
55. #10622747C22semidirect
56. #10622744C22semidirect
57. #10622728C22semidirect
58. #10622727C22semidirect
59. C2×#66885C22semidirect
60. C2×#66885C22semidirect
61. #10622461C22semidirect
62. #10622460C22semidirect
63. #10622457C22semidirect
64. #10622456C22semidirect
65. #10622351C22semidirect
66. #10622350C22semidirect
67. #10622349C22semidirect
68. #10622349C22semidirect
69. #10622348C22semidirect
70. #10622347C22semidirect
72. #10622345C22semidirect
73. #10622345C22semidirect
74. #10622345C22semidirect
75. #10622345C22semidirect
76. #10622345C22semidirect
77. #10622344C22semidirect
78. #10622344C22semidirect
79. #10622344C22semidirect
80. #10622344C22semidirect
81. #10622344C22semidirect
82. #10622334C22semidirect
83. #10622326C22semidirect
84. #10622325C22semidirect
85. #10622324C22semidirect
86. #10622323C22semidirect
98. C2×#4339C23semidirect
114. C22×D44C23semidirect
116. C22×Dic22C23semidirect
117. C2×C11×M16C23semidirect
118. C22×C8×C11C23semidirect
119. C22×C8×C11C23semidirect
143. #66983C23semidirect
144. #66983C23semidirect
154. #66979C23semidirect
156. C2×C4⋊Dic11C23semidirect
157. C2×C4⋊Dic11C23semidirect
161. #66977C23semidirect
162. #66977C23semidirect
167. C2×D88C23semidirect
168. C2×D88C23semidirect
171. C2×#4314C23semidirect
172. C2×#4314C23semidirect
192. #66928C23semidirect
197. C4×D44C23semidirect
199. #66923C23semidirect
200. C4×Dic22C23semidirect
201. C11×C4⋊C8C23semidirect
204. C11×C22⋊C8C23semidirect
205. C11×C22⋊C8C23semidirect
206. C11×C22⋊C8C23semidirect
207. C11×#97C23semidirect
210. #66885C23semidirect
211. #66885C23semidirect
212. #66885C23semidirect
213. #66885C23semidirect
214. #66885C23semidirect
215. #66882C23semidirect
216. #66881C23semidirect
217. #66880C23semidirect
365. #2973D11semidirect
371. C23×C11AGL(1,ℤ/8)semidirect
522. #435C2×D11semidirect
523. #435C2×D11semidirect
524. #432C2×D11semidirect
528. #407C2×D11semidirect
529. C2×C22⋊C8C2×D11semidirect
530. C2×C22⋊C8C2×D11semidirect
615. C2×M16C22×D11semidirect
616. C22×C8C22×D11semidirect
617. C22×C8C22×D11semidirect
692. C4⋊C8C22×D11semidirect
703. C22⋊C8C22×D11semidirect
704. C22⋊C8C22×D11semidirect
705. C22⋊C8C22×D11semidirect
706. #97C22×D11semidirect
850. C11#61571semidirect
883. C23#66961semidirect

Maximal subgroups

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

subgroupindex
#130824552
C2×D4×D442
#130807592
#130806392
#130801162
#130801012
#130796362
#130794322
#130793742
#130793672
#130787562
#130778462
C2×#106223442
C2×#106223452
C11×#29732
#6157111