Finite Group Databasebeta

← #15622207

Subgroups — #15622207

Order 2816.

2428 conjugacy classes of subgroups.

The subgroup lattice has 910 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623008C211yesmaximal, characteristic, complemented
2#13078767C214yesmaximal, complemented
3#13078738C212yesmaximal, complemented
4#13078707C212yesmaximal, complemented
5#13078676C214yesmaximal, complemented
6#13078647C212yesmaximal, complemented
7#13078616C212yesmaximal, complemented
8#13078556C212yesmaximal, complemented
9#13078431C212yesmaximal, complemented
10#13078096C212yesmaximal, complemented
11#13077868C212yesmaximal, complemented
12C4×#67002C214yesmaximal, complemented
13#13077249C211yesmaximal, characteristic, complemented
14C2×C4×C11×#41C211yesmaximal, characteristic, complemented
15C22×C11×#41C2211yescharacteristic
16C22×#4339—21no—
17C4×C11×#41—21no—
18C4×C11×#41—21no—
19C4×C11×#41—21no—
20C4×C11×#41—21no—
21C4×C11×#41C2212yes—
22C4×C11×#41C2212yes—
23C4×C11×#41C2212yescomplemented
24C4×C11×#41C2212yescomplemented
25C2×C4×Q8×C11C2211yescharacteristic, complemented
26C2×C4×Q8×C11C2211yescharacteristic, complemented
27C2×C4×D4×C11—21no—
28C2×C4×D4×C11—21no—
29C2×C4×D4×C11C2211yescharacteristic, complemented
30C2×C4×D4×C11C2211yescharacteristic, complemented
31C2×C11×#117—21no—
32C2×C11×#117C2211yescharacteristic
33C22×C42×C11—21no—
34C22×C42×C11C2211yescharacteristic
35C2×#67002C2214yes—
36C2×#66983—21no—
37C2×#66983C2212yes—
38#10623008—21no—
39#10623008—21no—
40#10623008—21no—
41#10623008—21no—
42#10623008C2212yes—
43#10623008C2212yes—
44#10623008C2212yescomplemented
45#10623008C2212yescomplemented
46C2×#66928—21no—
47C2×#66927C2211yescharacteristic, complemented
48C2×C4×D44—21no—
49C2×C4×D44C2212yescomplemented
50C2×#66922C2211yescharacteristic, complemented
51#10622851C2218yescomplemented
52#10622845C2214yes—
53#10622840C2214yescomplemented
54#10622830C2214yescomplemented
55#10622820C2212yes—
56#10622640C2214yescomplemented
57#10622640C2214yescomplemented
58#10622639C2218yescomplemented
59C4×#4325C2218yescomplemented
60#10622634C2214yescomplemented
61#10622633C2214yescomplemented
62#10622628C2214yescomplemented
63#10622628C2214yescomplemented
64#10622627C2218yescomplemented
65C4×#4323C2218yescomplemented
66#10622621C2214yescomplemented
67#10622620C2214yescomplemented
68#10622616C2218yescomplemented
69#10622614C2214yescomplemented
70#10622608C2214yescomplemented
71#10622581C2214yescomplemented
72#10622580C2214yescomplemented
73#10622539C2212yescomplemented
74#10622539C2212yescomplemented
75#10622538C2212yescomplemented
76#10622538C2212yescomplemented
77#10622537C2212yescomplemented
78C4×#4318C2212yescomplemented
79C2×C11×#41—28no—
80C2×C11×#41—21no—
81C2×C11×#41—21no—
82C2×C11×#41C2312yes—
83C2×C11×#41C2312yes—
84C22×Q8×C11C2311yescharacteristic
85C22×D4×C11—21no—
86C22×D4×C11C2311yescharacteristic
87C23×C4×C11—21no—
88C23×C4×C11—21no—
89C23×C4×C11—21no—
90C23×C4×C11D411yescharacteristic
91C23×C4×C11D411yescharacteristic
92C23×C4×C11C2311yescharacteristic
93C22×C22⋊D11—22no—
94C2×#4339—22no—
95C2×#4339—22no—
96C2×#4339—22no—
97C2×#4339—22no—
98C2×#4339—48no—
99C22×D44—21no—
100C22×D44—21no—
101C22×D44C2312yes—
102C22×C4×D11—22no—
103C22×Dic22—21no—
104C4×Q8×C11—21no—
105C4×Q8×C11—21no—
106C4×Q8×C11—21no—
107C4×Q8×C11—21no—
108C4×Q8×C11C2312yes—
109C4×Q8×C11C2312yes—
110C4×Q8×C11C2312yes—
111C4×Q8×C11C2312yes—
112C4×D4×C11—22no—
113C4×D4×C11—22no—
114C4×D4×C11—22no—
115C4×D4×C11—22no—
116C4×D4×C11—22no—
117C4×D4×C11—22no—
118C4×D4×C11—22no—
119C4×D4×C11—22no—
120C4×D4×C11—21no—
121C4×D4×C11—21no—
122C4×D4×C11—21no—
123C4×D4×C11—21no—
124C4×D4×C11C2312yes—
125C4×D4×C11C2312yes—
126C4×D4×C11C2312yes—
127C4×D4×C11C2312yes—
128C11×#117—21no—
129C11×#117—21no—
130C11×#117—22no—
131C11×#117—22no—
132C11×#117—22no—
133C11×#117—22no—
134C11×#117C2312yes—
135C11×#117C2312yes—
136C2×C11×C4⋊C4—21no—
137C2×C11×C4⋊C4—21no—
138C2×C11×C4⋊C4C2311yescharacteristic
139C2×C11×C4⋊C4C2311yescharacteristic
140C2×C11×C22⋊C4—21no—
141C2×C11×C22⋊C4—21no—
142C2×C11×C22⋊C4—21no—
143C2×C42×C11—21no—
144C2×C42×C11—21no—
145C2×C42×C11—21no—
146C2×C42×C11—22no—
147C2×C42×C11—22no—
148C2×C42×C11—22no—
149C2×C42×C11—22no—
150C2×C42×C11D411yescharacteristic
151C2×C42×C11D411yescharacteristic
152C2×C42×C11D411yescharacteristic
153C2×C42×C11D411yescharacteristic
154C2×C42×C11D411yescharacteristic
155C2×C42×C11D411yescharacteristic
156C2×C42×C11C2311yescharacteristic
157C2×C42×C11C2311yescharacteristic
158C2×C42×C11C2311yescharacteristic
159C2×C42×C11C2311yescharacteristic
160C2×C42×C11C2311yescharacteristic
161C2×C42×C11C2311yescharacteristic
162#67002—216no—
163C2×#4325C2318yes—
164C2×#4323C2318yes—
165#66983—22no—
166#66983—22no—
167#66983—22no—
168#66983—22no—
169#66983—22no—
170#66983—22no—
171#66983C2314yes—
172#66983C2314yes—
173C2×(C2×D11)⋊C4—22no—
174C2×(C2×D11)⋊C4—22no—
175C2×C4⋊Dic11—21no—
176C2×C4⋊Dic11C2312yes—
177C2×#4318C2314yes—
178#66928—22no—
179#66928—22no—
180#66928—22no—
181#66928—22no—
182#66927—21no—
183#66927—21no—
184#66927C2312yes—
185#66927C2312yes—
186C4×D44—22no—
187C4×D44—22no—
188C4×D44—22no—
189C4×D44—22no—
190C4×D44—22no—
191C4×D44—22no—
192C4×D44C2314yes—
193C4×D44C2314yes—
194#66922—21no—
195#66922—21no—
196#66922C2312yes—
197#66922C2312yes—
198#66899C2318yes—
199#66896C2318yes—
200C22⋊(C11⋊C8)C2314yes—
201C22⋊(C11⋊C8)C2314yes—
202#66873C2318yes—
203#66873C2318yes—
204#66872C2318yes—
205#66871C2318yes—
206C4⋊(C11⋊C8)C2314yes—
207C4⋊(C11⋊C8)C2314yes—
208#66867C2314yes—
209C4×C11⋊C8C2314yes—
210#60561—111nomaximal, Sylow
211C24×C11—21no—
212C24×C11C2×D411yescharacteristic
213C23×D11—22no—
214C11×#41—28no—
215C11×#41—28no—
216C11×#41—24no—
217C11×#41—24no—
218C11×#41—24no—
219C11×#41#4118yescomplemented
220C2×Q8×C11—24no—
221C2×Q8×C11—21no—
222C2×Q8×C11C2412yes—
223C2×D4×C11—28no—
224C2×D4×C11—22no—
225C2×D4×C11—22no—
226C2×D4×C11—24no—
227C2×D4×C11—21no—
228C2×D4×C11C2412yes—
229C22×C4×C11—28no—
230C22×C4×C11—21no—
231C22×C4×C11—24no—
232C22×C4×C11—22no—
233C22×C4×C11—22no—
234C22×C4×C11—24no—
235C22×C4×C11—21no—
236C22×C4×C11—21no—
237C22×C4×C11—22no—
238C22×C4×C11—22no—
239C22×C4×C11—22no—
240C22×C4×C11—22no—
241C22×C4×C11—42no—
242C22×C4×C11—44no—
243C22×C4×C11—44no—
244C22×C4×C11C2×D411yescharacteristic
245C22×C4×C11C2×D411yescharacteristic
246C22×C4×C11C2×D411yescharacteristic
247C22×C4×C11C2×D411yescharacteristic
248C22×C4×C11C2×D411yescharacteristic
249C22×C4×C11C2×D411yescharacteristic
250C22×C4×C11C2×D411yescharacteristic
251C22×C4×C11C2×D411yescharacteristic
252C22×C4×C11C2×D411yescharacteristic
253C22×C4×C11C2×D411yescharacteristic
254C22×C4×C11C2×D411yescharacteristic
255C22×C4×C11C2×D411yescharacteristic
256C22×C4×C11C2×D411yescharacteristic
257C22×C4×C11C2×D411yescharacteristic
258C22×C4×C11C2×D411yescharacteristic
259C22×C4×C11C2411yescharacteristic
260C22×C4×C11C2411yescharacteristic
261C22×C4×C11C2411yescharacteristic
262C2×C22⋊D11—24no—
263C2×C22⋊D11—24no—
264C2×C22⋊D11—48no—
265C22×Dic11—22no—
266#4339—48no—
267#4339—48no—
268#4339—48no—
269#4339—48no—
270C2×D44—22no—
271C2×D44—22no—
272C2×D44—22no—
273C2×D44—22no—
274C2×D44—22no—
275C2×D44—28no—
276C2×D44—44no—
277C2×D44—44no—
278C2×D44C2414yes—
279C2×C4×D11—24no—
280C2×C4×D11—24no—
281C2×C4×D11—48no—
282C2×Dic22—22no—
283C2×Dic22—22no—
284C2×Dic22—44no—
285C11×C4⋊C4—22no—
286C11×C4⋊C4—22no—
287C11×C4⋊C4—22no—
288C11×C4⋊C4—22no—
289C11×C4⋊C4—21no—
290C11×C4⋊C4—21no—
291C11×C4⋊C4C2412yes—
292C11×C4⋊C4C2412yes—
293C11×C22⋊C4—22no—
294C11×C22⋊C4—22no—
295C11×C22⋊C4—22no—
296C11×C22⋊C4—22no—
297C11×C22⋊C4—22no—
298C11×C22⋊C4—22no—
299C42×C11—22no—
300C42×C11—22no—
301C42×C11—22no—
302C42×C11—22no—
303C42×C11—22no—
304C42×C11—22no—
305C42×C11C2×D411yescharacteristic
306C42×C11C2×D411yescharacteristic
307C42×C11C2×D411yescharacteristic
308C42×C11C2×D411yescharacteristic
309C42×C11C2×D411yescharacteristic
310C42×C11C2×D411yescharacteristic
311C42×C11C2×D411yescharacteristic
312C42×C11C2×D411yescharacteristic
313C42×C11C2×D411yescharacteristic
314C42×C11C2×D411yescharacteristic
315C42×C11C2×D411yescharacteristic
316C42×C11C2×D411yescharacteristic
317C42×C11C2411yescharacteristic
318C42×C11C2411yescharacteristic
319C42×C11C2411yescharacteristic
320C42×C11C2411yescharacteristic
321#4325—216no—
322#4323—216no—
323(C2×D11)⋊C4—24no—
324(C2×D11)⋊C4—24no—
325(C2×D11)⋊C4—24no—
326(C2×D11)⋊C4—24no—
327C4⋊Dic11—22no—
328C4⋊Dic11—22no—
329C4⋊Dic11—22no—
330C4⋊Dic11C2414yes—
331#4318—28no—
332C2×C11⋊C8C2418yes—
333C2×#532—111no—
334C2×C4×#41D1111yescharacteristic, complemented
335#3115—114no—
336#3112—112no—
337#3109—112no—
338#3106—114no—
339#3103—112no—
340#3100—112no—
341#3094—112no—
342#3079—112no—
343#3038—112no—
344#3006—112no—
345C4×AGL(1,ℤ/8)—114no—
346#2920—111no—
347C23×C11—24no—
348C23×C11—22no—
349C23×C11—22no—
350C23×C11—22no—
351C23×C11—41no—
352C23×C11—42no—
353C23×C11—42no—
354C23×C11C22×D411yescharacteristic
355C23×C11C22×D411yescharacteristic
356C23×C11C22×D411yescharacteristic
357C22×D11—24no—
358C22×D11—44no—
359C22×D11—44no—
360C22×D11—44no—
361Q8×C11—24no—
362Q8×C11—22no—
363Q8×C11C2×#4114yescomplemented
364D4×C11—28no—
365D4×C11—24no—
366D4×C11—28no—
367D4×C11—22no—
368D4×C11C2×#4114yescomplemented
369C2×C4×C11—24no—
370C2×C4×C11—28no—
371C2×C4×C11—22no—
372C2×C4×C11—22no—
373C2×C4×C11—22no—
374C2×C4×C11—22no—
375C2×C4×C11—28no—
376C2×C4×C11—22no—
377C2×C4×C11—22no—
378C2×C4×C11—22no—
379C2×C4×C11—22no—
380C2×C4×C11—22no—
381C2×C4×C11—22no—
382C2×C4×C11—22no—
383C2×C4×C11—22no—
384C2×C4×C11—22no—
385C2×C4×C11—22no—
386C2×C4×C11—22no—
387C2×C4×C11—22no—
388C2×C4×C11—41no—
389C2×C4×C11—41no—
390C2×C4×C11—41no—
391C2×C4×C11—44no—
392C2×C4×C11—42no—
393C2×C4×C11—42no—
394C2×C4×C11—44no—
395C2×C4×C11—44no—
396C2×C4×C11—44no—
397C2×C4×C11AGL(1,ℤ/8)14yescomplemented
398C2×C4×C11C22×D411yescharacteristic
399C2×C4×C11C22×D411yescharacteristic
400C2×C4×C11C22×D411yescharacteristic
401C2×C4×C11C22×D411yescharacteristic
402C2×C4×C11C22×D411yescharacteristic
403C2×C4×C11C22×D411yescharacteristic
404C2×C4×C11C22×D411yescharacteristic
405C2×C4×C11C22×D411yescharacteristic
406C2×C4×C11C22×D411yescharacteristic
407C2×C4×C11C22×D411yescharacteristic
408C2×C4×C11C22×D411yescharacteristic
409C2×C4×C11C2×#4114yes—
410C2×C4×C11C2511yescharacteristic
411C22⋊D11—48no—
412C22⋊D11—48no—
413C2×Dic11—24no—
414C2×Dic11—44no—
415D44—28no—
416D44—44no—
417D44—44no—
418D44—44no—
419D44—44no—
420D44—44no—
421C4×D11—48no—
422C4×D11—48no—
423Dic22—44no—
424Dic22—44no—
425C11⋊C8—28no—
426C22×#41—221no—
427C22×#41C2×D1111yescharacteristic
428C2×AGL(1,ℤ/8)—114no—
429#532—112no—
430#532—112no—
431#532—112no—
432#532—112no—
433#532—221no—
434#532—221no—
435#532—221no—
436#532—221no—
437C2×C4⋊Q8—111no—
438C2×#127—111no—
439C2×#124—221no—
440C2×#121—112no—
441C2×#121—221no—
442C4×#41—21no—
443C4×#41—21no—
444C4×#41—21no—
445C4×#41—21no—
446C4×#41C2×D1112yes—
447C4×#41C2×D1112yes—
448C4×#41C2×D1112yescomplemented
449C4×#41C2×D1112yescomplemented
450C2×C4×Q8C2×D1111yescharacteristic, complemented
451C2×C4×Q8C2×D1111yescharacteristic, complemented
452C2×C4×D4—21no—
453C2×C4×D4—21no—
454C2×C4×D4—112no—
455C2×C4×D4—221no—
456C2×C4×D4C2×D1111yescharacteristic, complemented
457C2×C4×D4C2×D1111yescharacteristic, complemented
458C2×#117—21no—
459C2×#117C2×D1111yescharacteristic
460C22×C42—21no—
461C22×C42C2×D1111yescharacteristic
462#482—118no—
463#481—114no—
464#480—114no—
465#477—114no—
466#476—114no—
467#475—114no—
468#474—114no—
469#460—114no—
470#460—114no—
471#459—114no—
472#459—114no—
473#449—118no—
474#448—114no—
475#447—114no—
476#442—118no—
477#440—118no—
478C4×SD16—118no—
479C4×D8—118no—
480#432—112no—
481#432—112no—
482#431—112no—
483#431—112no—
484#428—114no—
485#423—112no—
486#418—114no—
487#417—114no—
488#407—112no—
489C4×M16—112no—
490C22×C11—21no—
491C22×C11—21no—
492C22×C11—21no—
493C22×C11—21no—
494C22×C11—21no—
495C22×C11—24no—
496C22×C11—21no—
497C22×C11—21no—
498C22×C11—44no—
499C22×C11—48no—
500C22×C11—42no—
501C22×C11—42no—
502C22×C11#52512yes—
503C22×C11C2×AGL(1,ℤ/8)12yes—
504C22×C11C23×D411yescharacteristic
505C2×D11—44no—
506C2×D11—44no—
507C2×D11—44no—
508C2×D11—88no—
509C4×C11—21no—
510C4×C11—24no—
511C4×C11—21no—
512C4×C11—21no—
513C4×C11—21no—
514C4×C11—21no—
515C4×C11—21no—
516C4×C11—21no—
517C4×C11—42no—
518C4×C11—42no—
519C4×C11#52512yes—
520C4×C11C2×AGL(1,ℤ/8)12yes—
521C4×C11C2×AGL(1,ℤ/8)12yes—
522C4×C11#57512yes—
523C4×C11C22×#4112yes—
524Dic11—44no—
525C2×#41—28no—
526C2×#41—21no—
527C2×#41—21no—
528C2×#41—222no—
529C2×#41—222no—
530C2×#41—222no—
531C2×#41—222no—
532C2×#41—448no—
533C2×#41C22×D1112yes—
534C2×#41C22×D1112yes—
535C22×Q8—221no—
536C22×Q8C22×D1111yescharacteristic
537C22×D4—21no—
538C22×D4—112no—
539C22×D4—222no—
540C22×D4—221no—
541C22×D4—221no—
542C22×D4C22×D1111yescharacteristic
543C23×C4—21no—
544C23×C4—21no—
545C23×C4—21no—
546C23×C4—222no—
547C23×C4C22⋊D1111yescharacteristic
548C23×C4C22⋊D1111yescharacteristic
549C23×C4C22×D1111yescharacteristic
550AGL(1,ℤ/8)—2216no—
551C2×SD16—118no—
552C2×D8—118no—
553C2×M16—114no—
554C4⋊Q8—112no—
555C4⋊Q8—112no—
556C4⋊Q8—221no—
557C4⋊Q8—221no—
558#127—112no—
559#127—112no—
560#127—221no—
561#127—221no—
562#124—222no—
563#124—222no—
564#124—222no—
565#124—222no—
566#121—114no—
567#121—114no—
568#121—222no—
569#121—222no—
570#121—222no—
571#121—222no—
572#121—222no—
573#121—222no—
574C4×Q8—21no—
575C4×Q8—21no—
576C4×Q8—21no—
577C4×Q8—21no—
578C4×Q8C22×D1112yes—
579C4×Q8C22×D1112yes—
580C4×Q8C22×D1112yes—
581C4×Q8C22×D1112yes—
582C4×D4—22no—
583C4×D4—22no—
584C4×D4—22no—
585C4×D4—22no—
586C4×D4—22no—
587C4×D4—22no—
588C4×D4—22no—
589C4×D4—22no—
590C4×D4—21no—
591C4×D4—21no—
592C4×D4—21no—
593C4×D4—21no—
594C4×D4—114no—
595C4×D4—114no—
596C4×D4—222no—
597C4×D4—222no—
598C4×D4—222no—
599C4×D4—222no—
600C4×D4—222no—
601C4×D4—222no—
602C4×D4C22×D1112yes—
603C4×D4C22×D1112yes—
604C4×D4C22×D1112yes—
605C4×D4C22×D1112yes—
606#117—21no—
607#117—21no—
608#117—22no—
609#117—22no—
610#117—22no—
611#117—22no—
612#117C22×D1112yes—
613#117C22×D1112yes—
614C2×C4⋊C4—21no—
615C2×C4⋊C4—21no—
616C2×C4⋊C4—112no—
617C2×C4⋊C4—221no—
618C2×C4⋊C4C22×D1111yescharacteristic
619C2×C4⋊C4C22×D1111yescharacteristic
620C2×C22⋊C4—21no—
621C2×C22⋊C4—21no—
622C2×C22⋊C4—21no—
623C2×C22⋊C4—222no—
624C2×C22⋊C4—222no—
625C2×C42—21no—
626C2×C42—21no—
627C2×C42—21no—
628C2×C42—22no—
629C2×C42—22no—
630C2×C42—22no—
631C2×C42—22no—
632C2×C42C22⋊D1111yescharacteristic
633C2×C42C22⋊D1111yescharacteristic
634C2×C42C22⋊D1111yescharacteristic
635C2×C42C22⋊D1111yescharacteristic
636C2×C42C22⋊D1111yescharacteristic
637C2×C42C22⋊D1111yescharacteristic
638C2×C42C22×D1111yescharacteristic
639C2×C42C22×D1111yescharacteristic
640C2×C42C22×D1111yescharacteristic
641C2×C42C22×D1111yescharacteristic
642C2×C42C22×D1111yescharacteristic
643C2×C42C22×D1111yescharacteristic
644#107—118no—
645#106—118no—
646C4⋊C8—114no—
647C4⋊C8—114no—
648#103—118no—
649#102—118no—
650#102—118no—
651#102—118no—
652C22⋊C8—114no—
653C22⋊C8—114no—
654#97—114no—
655C4×C8—114no—
656C2×C11—22no—
657C2×C11—22no—
658C2×C11—41no—
659C2×C11—44no—
660C2×C11C2×#52511yescharacteristic
661C2×C11C22×AGL(1,ℤ/8)11yescharacteristic
662C2×C11C2×#57511yescharacteristic
663D11—84no—
664C24—21no—
665C24—222no—
666C24C2×C22⋊D1111yescharacteristic
667#41—28no—
668#41—28no—
669#41—24no—
670#41—24no—
671#41—24no—
672#41—448no—
673#41—448no—
674#41—448no—
675#41—448no—
676#41#433918yescomplemented
677C2×Q8—24no—
678C2×Q8—21no—
679C2×Q8—222no—
680C2×Q8—222no—
681C2×Q8—444no—
682C2×Q8C23×D1112yes—
683C2×D4—28no—
684C2×D4—22no—
685C2×D4—22no—
686C2×D4—24no—
687C2×D4—21no—
688C2×D4—114no—
689C2×D4—224no—
690C2×D4—224no—
691C2×D4—228no—
692C2×D4—222no—
693C2×D4—222no—
694C2×D4—222no—
695C2×D4—222no—
696C2×D4—222no—
697C2×D4—444no—
698C2×D4—444no—
699C2×D4—448no—
700C2×D4C23×D1112yes—
701C22×C4—28no—
702C22×C4—21no—
703C22×C4—24no—
704C22×C4—24no—
705C22×C4—22no—
706C22×C4—22no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—22no—
710C22×C4—22no—
711C22×C4—22no—
712C22×C4—22no—
713C22×C4—42no—
714C22×C4—44no—
715C22×C4—44no—
716C22×C4—222no—
717C22×C4—224no—
718C22×C4—224no—
719C22×C4—448no—
720C22×C4C2×C22⋊D1111yescharacteristic
721C22×C4C2×C22⋊D1111yescharacteristic
722C22×C4C2×C22⋊D1111yescharacteristic
723C22×C4C2×C22⋊D1111yescharacteristic
724C22×C4C2×C22⋊D1111yescharacteristic
725C22×C4C2×C22⋊D1111yescharacteristic
726C22×C4C2×C22⋊D1111yescharacteristic
727C22×C4C2×C22⋊D1111yescharacteristic
728C22×C4C2×C22⋊D1111yescharacteristic
729C22×C4C2×C22⋊D1111yescharacteristic
730C22×C4C2×C22⋊D1111yescharacteristic
731C22×C4C2×C22⋊D1111yescharacteristic
732C22×C4C2×C22⋊D1111yescharacteristic
733C22×C4C2×C22⋊D1111yescharacteristic
734C22×C4C2×C22⋊D1111yescharacteristic
735C22×C4C23×D1111yescharacteristic
736C22×C4C23×D1111yescharacteristic
737C22×C4C23×D1111yescharacteristic
738SD16—2216no—
739D8—2216no—
740M16—228no—
741C2×C8—118no—
742C4⋊C4—22no—
743C4⋊C4—22no—
744C4⋊C4—22no—
745C4⋊C4—22no—
746C4⋊C4—21no—
747C4⋊C4—21no—
748C4⋊C4—114no—
749C4⋊C4—222no—
750C4⋊C4—222no—
751C4⋊C4—222no—
752C4⋊C4C23×D1112yes—
753C4⋊C4C23×D1112yes—
754C22⋊C4—22no—
755C22⋊C4—22no—
756C22⋊C4—22no—
757C22⋊C4—22no—
758C22⋊C4—22no—
759C22⋊C4—22no—
760C22⋊C4—224no—
761C22⋊C4—224no—
762C22⋊C4—224no—
763C22⋊C4—224no—
764C42—22no—
765C42—22no—
766C42—22no—
767C42—22no—
768C42—22no—
769C42—22no—
770C42C2×C22⋊D1111yescharacteristic
771C42C2×C22⋊D1111yescharacteristic
772C42C2×C22⋊D1111yescharacteristic
773C42C2×C22⋊D1111yescharacteristic
774C42C2×C22⋊D1111yescharacteristic
775C42C2×C22⋊D1111yescharacteristic
776C42C2×C22⋊D1111yescharacteristic
777C42C2×C22⋊D1111yescharacteristic
778C42C2×C22⋊D1111yescharacteristic
779C42C2×C22⋊D1111yescharacteristic
780C42C2×C22⋊D1111yescharacteristic
781C42C2×C22⋊D1111yescharacteristic
782C42C23×D1111yescharacteristic
783C42C23×D1111yescharacteristic
784C42C23×D1111yescharacteristic
785C42C23×D1111yescharacteristic
786C11#6056111yescharacteristic, complemented, Sylow
787C23—24no—
788C23—22no—
789C23—22no—
790C23—22no—
791C23—41no—
792C23—42no—
793C23—42no—
794C23—224no—
795C23—444no—
796C23—444no—
797C23—444no—
798C23C22×C22⋊D1111yescharacteristic
799C23C22×C22⋊D1111yescharacteristic
800C23C22×C22⋊D1111yescharacteristic
801Q8—24no—
802Q8—22no—
803Q8—444no—
804Q8—444no—
805Q8C2×#433914yescomplemented
806D4—28no—
807D4—24no—
808D4—28no—
809D4—22no—
810D4—228no—
811D4—444no—
812D4—444no—
813D4—448no—
814D4—448no—
815D4—444no—
816D4—444no—
817D4—444no—
818D4C2×#433914yescomplemented
819C2×C4—24no—
820C2×C4—28no—
821C2×C4—22no—
822C2×C4—22no—
823C2×C4—22no—
824C2×C4—22no—
825C2×C4—28no—
826C2×C4—22no—
827C2×C4—22no—
828C2×C4—22no—
829C2×C4—22no—
830C2×C4—22no—
831C2×C4—22no—
832C2×C4—22no—
833C2×C4—22no—
834C2×C4—22no—
835C2×C4—22no—
836C2×C4—22no—
837C2×C4—22no—
838C2×C4—41no—
839C2×C4—41no—
840C2×C4—41no—
841C2×C4—44no—
842C2×C4—42no—
843C2×C4—42no—
844C2×C4—44no—
845C2×C4—44no—
846C2×C4—44no—
847C2×C4—224no—
848C2×C4—448no—
849C2×C4—444no—
850C2×C4—448no—
851C2×C4#6700214yescomplemented
852C2×C4C2×#433914yes—
853C2×C4C22×C22⋊D1111yescharacteristic
854C2×C4C22×C22⋊D1111yescharacteristic
855C2×C4C22×C22⋊D1111yescharacteristic
856C2×C4C22×C22⋊D1111yescharacteristic
857C2×C4C22×C22⋊D1111yescharacteristic
858C2×C4C22×C22⋊D1111yescharacteristic
859C2×C4C22×C22⋊D1111yescharacteristic
860C2×C4C22×C22⋊D1111yescharacteristic
861C2×C4C22×C22⋊D1111yescharacteristic
862C2×C4C22×C22⋊D1111yescharacteristic
863C2×C4C22×C22⋊D1111yescharacteristic
864C2×C4C24×D1111yescharacteristic
865C8—228no—
866C22—21no—
867C22—21no—
868C22—21no—
869C22—21no—
870C22—21no—
871C22—24no—
872C22—21no—
873C22—21no—
874C22—44no—
875C22—48no—
876C22—42no—
877C22—42no—
878C22—444no—
879C22—444no—
880C22—444no—
881C22—888no—
882C22#1062332212yes—
883C22C2×#6700212yes—
884C22C23×C22⋊D1111yescharacteristic
885C4—21no—
886C4—24no—
887C4—21no—
888C4—21no—
889C4—21no—
890C4—21no—
891C4—21no—
892C4—21no—
893C4—42no—
894C4—42no—
895C4—444no—
896C4#1062332212yes—
897C4C2×#6700212yes—
898C4C2×#6700212yes—
899C4#1062335312yes—
900C4C22×#433912yes—
901C2—22no—
902C2—22no—
903C2—41no—
904C2—44no—
905C2—884no—
906C2C2×#1062332211yescharacteristic
907C2C22×#6700211yescharacteristic
908C2C2×#1062335311yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C4×C11×#41C2
socleC22×C11C23×D4
hypercenterC2×C4×#41D11
hypocenterC11#60561
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C22×C42 ◁ C2×C4×#41

Complements

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

NH ≅ G/Ntype
1. C2×#10623008C2semidirect
2. #13078767C2semidirect
3. #13078738C2semidirect
4. #13078707C2semidirect
5. #13078676C2semidirect
6. #13078647C2semidirect
7. #13078616C2semidirect
8. #13078556C2semidirect
9. #13078431C2semidirect
10. #13078096C2semidirect
11. #13077868C2semidirect
12. C4×#67002C2semidirect
13. #13077249C2semidirect
14. C2×C4×C11×#41C2semidirect
23. C4×C11×#41C22semidirect
24. C4×C11×#41C22semidirect
25. C2×C4×Q8×C11C22semidirect
26. C2×C4×Q8×C11C22semidirect
29. C2×C4×D4×C11C22semidirect
30. C2×C4×D4×C11C22semidirect
44. #10623008C22semidirect
45. #10623008C22semidirect
47. C2×#66927C22semidirect
49. C2×C4×D44C22semidirect
50. C2×#66922C22semidirect
51. #10622851C22semidirect
53. #10622840C22semidirect
54. #10622830C22semidirect
56. #10622640C22semidirect
57. #10622640C22semidirect
58. #10622639C22semidirect
59. C4×#4325C22semidirect
60. #10622634C22semidirect
61. #10622633C22semidirect
62. #10622628C22semidirect
63. #10622628C22semidirect
64. #10622627C22semidirect
65. C4×#4323C22semidirect
66. #10622621C22semidirect
67. #10622620C22semidirect
68. #10622616C22semidirect
69. #10622614C22semidirect
70. #10622608C22semidirect
71. #10622581C22semidirect
72. #10622580C22semidirect
73. #10622539C22semidirect
74. #10622539C22semidirect
75. #10622538C22semidirect
76. #10622538C22semidirect
77. #10622537C22semidirect
78. C4×#4318C22semidirect
219. C11×#41#41semidirect
334. C2×C4×#41D11semidirect
363. Q8×C11C2×#41semidirect
368. D4×C11C2×#41semidirect
397. C2×C4×C11AGL(1,ℤ/8)semidirect
448. C4×#41C2×D11semidirect
449. C4×#41C2×D11semidirect
450. C2×C4×Q8C2×D11semidirect
451. C2×C4×Q8C2×D11semidirect
456. C2×C4×D4C2×D11semidirect
457. C2×C4×D4C2×D11semidirect
676. #41#4339semidirect
786. C11#60561semidirect
805. Q8C2×#4339semidirect
818. D4C2×#4339semidirect
851. C2×C4#67002semidirect

Maximal subgroups

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

subgroupindex
C2×#106230082
#130787672
#130787382
#130787072
#130786762
#130786472
#130786162
#130785562
#130784312
#130780962
#130778682
C4×#670022
#130772492
C2×C4×C11×#412
#6056111