Finite Group Databasebeta

← #15623292

Subgroups — #15623292

Order 2816.

3350 conjugacy classes of subgroups.

The subgroup lattice has 864 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623353C211yesmaximal, characteristic, complemented
2C22×#66961C211yesmaximal, characteristic, complemented
3C22×#67002C211yesmaximal, characteristic, complemented
4#13081945C211yesmaximal, characteristic, complemented
5C2×#10623361C211yesmaximal, characteristic, complemented
6#13079103C214yesmaximal, complemented
7#13079101C214yesmaximal, complemented
8#13079095C214yesmaximal, complemented
9#13079093C214yesmaximal, complemented
10#13079083C214yesmaximal, complemented
11#13079064C214yesmaximal, complemented
12#13077034C211yesmaximal, characteristic, complemented
13C2×C11×#575C211yesmaximal, characteristic, complemented
14C22×C11×#41C2211yescharacteristic
15C22×C11×#41C2211yescharacteristic
16C22×#4339C2211yescharacteristic
17C23×D44C2211yescharacteristic
18C11×#575—28no—
19C2×C11×#137C2212yescomplemented
20C2×C11×#137C2212yescomplemented
21C2×C11×AGL(1,ℤ/8)C2212yescomplemented
22C2×C11×AGL(1,ℤ/8)C2212yescomplemented
23C2×C11×#135C2214yescomplemented
24C22×C11×M16C2211yescharacteristic
25#10623364—22no—
26#10623363C2214yescomplemented
27#10623361—22no—
28#10623361—22no—
29#10623361C2214yescomplemented
30#10623361C2214yescomplemented
31#10623361C2212yescomplemented
32#10623359—22no—
33#10623356C2212yescomplemented
34C2×#67004C2212yescomplemented
35#10623353—28no—
36C2×#67003C2214yescomplemented
37C2×#67002—28no—
38C2×#67002C2214yescomplemented
39C2×#67002C2214yescomplemented
40C2×#67002C2212yescomplemented
41#10623347C2212yescomplemented
42C2×#67000C2212yescomplemented
43C2×#66995C2212yescomplemented
44C22×#4325C2212yescomplemented
45#10623336C2212yescomplemented
46#10623335—22no—
47C2×#66993C2212yescomplemented
48C2×#66990—22no—
49C2×#66985C2212yescomplemented
50C22×#4323C2212yescomplemented
51#10623322—22no—
52C2×#66983—22no—
53C2×#66979C2211yescharacteristic
54C22×#4318C2211yescharacteristic
55C2×#66961—28no—
56C2×#66961C2214yescomplemented
57C2×#66961C2214yescomplemented
58C22×D88C2212yescomplemented
59C22×#4314C2212yescomplemented
60#10622804C2218yescomplemented
61#10622803C2218yescomplemented
62#10622789C2218yescomplemented
63#10622789C2218yescomplemented
64#10622788C2218yescomplemented
65#10622781C2218yescomplemented
66#10622767C2218yescomplemented
67#10622764C2218yescomplemented
68#10622735C2214yescomplemented
69M16×Dic11C2214yescomplemented
70#10622714C2214yescomplemented
71C24×D11—21no—
72C2×C11×#41—21no—
73C2×C11×#41—21no—
74C2×C11×#41—21no—
75C2×C11×#41—21no—
76C2×C11×#41—24no—
77C2×C11×#41—24no—
78C2×C11×#41—24no—
79C2×C11×#41—24no—
80C2×C11×#41C2312yes—
81C2×C11×#41C2312yes—
82C2×C11×#41C2312yes—
83C2×C11×#41C2312yes—
84C22×Q8×C11C2311yescharacteristic
85C22×Q8×C11C2311yescharacteristic
86C22×D4×C11—21no—
87C22×D4×C11—21no—
88C22×D4×C11C2311yescharacteristic
89C22×D4×C11C2311yescharacteristic
90C23×C4×C11—21no—
91C23×C4×C11—21no—
92C23×C4×C11C2311yescharacteristic
93C22×C22⋊D11—21no—
94C22×C22⋊D11—24no—
95C2×#4339—21no—
96C2×#4339—21no—
97C2×#4339—24no—
98C2×#4339—24no—
99C2×#4339C2312yes—
100C2×#4339C2312yes—
101C22×D44—24no—
102C22×D44—24no—
103C22×D44—21no—
104C22×D44—21no—
105C22×D44—21no—
106C22×D44C2312yes—
107C22×D44C2311yescharacteristic
108C22×D44C2312yes—
109C22×D44C2312yes—
110C22×C4×D11—21no—
111C22×Dic22C2311yescharacteristic
112C11×#137—28no—
113C11×#137—28no—
114C11×AGL(1,ℤ/8)—28no—
115C11×AGL(1,ℤ/8)—28no—
116C11×#135—216no—
117C2×C11×Q16C2314yescomplemented
118C2×C11×SD16C2314yescomplemented
119C2×C11×SD16C2314yescomplemented
120C2×C11×D8C2314yescomplemented
121C2×C11×M16D418yescomplemented
122C2×C11×M16C2312yes—
123C2×C11×M16C2312yes—
124C22×C8×C11C2312yes—
125#67006—24no—
126C2×C22⋊Dic11D412yes—
127#67004—28no—
128#67003—216no—
129#67002—216no—
130#67002—216no—
131#67002—28no—
132#67000—24no—
133#67000C2318yes—
134#67000C2314yescomplemented
135#66999—24no—
136#66997C2314yescomplemented
137C2×#4326C2314yescomplemented
138#66995—28no—
139C2×#4325—28no—
140C2×#4325C2318yes—
141C2×#4325C2314yescomplemented
142#66993—24no—
143#66993C2318yes—
144#66993C2314yescomplemented
145#66992—28no—
146#66991—24no—
147#66990—28no—
148#66990—28no—
149#66990—24no—
150#66989C2314yescomplemented
151#66988—24no—
152C2×#4324C2314yescomplemented
153#66985—28no—
154C2×#4323—28no—
155C2×#4323C2318yes—
156C2×#4323C2314yescomplemented
157#66983—28no—
158#66983—28no—
159#66983—24no—
160#66982—24no—
161C4×C22⋊D11—28no—
162C2×(C2×D11)⋊C4—24no—
163#66979D412yes—
164#66979D412yes—
165#66979C2312yes—
166#66979C2312yes—
167C2×C4⋊Dic11D412yes—
168#66977—24no—
169C2×C4×Dic11C2312yes—
170C2×#4318D418yescomplemented
171C2×#4318C2312yes—
172C2×#4318C2312yes—
173C22×C11⋊C8C2312yes—
174#66961—216no—
175#66961—216no—
176C2×D88—28no—
177C2×D88C2318yes—
178C2×#4314—28no—
179C2×#4314C2318yes—
180#66879C2318yescomplemented
181C8×Dic11C2318yescomplemented
182#60644—111nomaximal, Sylow
183C24×C11—21no—
184C24×C11—21no—
185C24×C11C2×D411yescharacteristic
186C23×D11—22no—
187C23×D11—21no—
188C23×D11—22no—
189C23×D11—22no—
190C23×D11—44no—
191C23×D11—84no—
192C11×#41—24no—
193C11×#41—24no—
194C11×#41—24no—
195C11×#41—24no—
196C11×#41—24no—
197C11×#41—24no—
198C11×#41—24no—
199C11×#41—24no—
200C11×#41—44no—
201C11×#41—44no—
202C11×#41—44no—
203C11×#41—44no—
204C2×Q8×C11—21no—
205C2×Q8×C11—21no—
206C2×Q8×C11—22no—
207C2×Q8×C11—22no—
208C2×Q8×C11—22no—
209C2×Q8×C11—22no—
210C2×Q8×C11C2412yes—
211C2×Q8×C11C2412yes—
212C2×D4×C11—22no—
213C2×D4×C11—22no—
214C2×D4×C11—22no—
215C2×D4×C11—22no—
216C2×D4×C11—22no—
217C2×D4×C11—22no—
218C2×D4×C11—22no—
219C2×D4×C11—22no—
220C2×D4×C11—21no—
221C2×D4×C11—21no—
222C2×D4×C11—44no—
223C2×D4×C11—44no—
224C2×D4×C11C2412yes—
225C2×D4×C11C2412yes—
226C22×C4×C11—21no—
227C22×C4×C11—21no—
228C22×C4×C11—22no—
229C22×C4×C11—22no—
230C22×C4×C11—22no—
231C22×C4×C11—22no—
232C22×C4×C11—44no—
233C22×C4×C11—44no—
234C22×C4×C11C2×D411yescharacteristic
235C22×C4×C11C2×D411yescharacteristic
236C22×C4×C11C2×D411yescharacteristic
237C22×C4×C11C2×D414yes—
238C22×C4×C11C2×D414yes—
239C22×C4×C11C2411yescharacteristic
240C22×C4×C11C2411yescharacteristic
241C22×C4×C11C2411yescharacteristic
242C2×C22⋊D11—28no—
243C2×C22⋊D11—216no—
244C2×C22⋊D11—22no—
245C2×C22⋊D11—22no—
246C2×C22⋊D11—44no—
247C2×C22⋊D11—88no—
248C22×Dic11—21no—
249C22×Dic11C2×D414yes—
250#4339—24no—
251#4339—24no—
252#4339—24no—
253#4339—24no—
254#4339—44no—
255#4339—44no—
256C2×D44—22no—
257C2×D44—22no—
258C2×D44—21no—
259C2×D44—22no—
260C2×D44—24no—
261C2×D44—22no—
262C2×D44—24no—
263C2×D44—24no—
264C2×D44—24no—
265C2×D44—24no—
266C2×D44—24no—
267C2×D44—22no—
268C2×D44—44no—
269C2×D44—44no—
270C2×D44—44no—
271C2×D44C2414yes—
272C2×D44C2412yes—
273C2×C4×D11—22no—
274C2×C4×D11—22no—
275C2×C4×D11—44no—
276C2×Dic22—22no—
277C2×Dic22—22no—
278C2×Dic22—21no—
279C2×Dic22C2412yes—
280C11×Q16—28no—
281C11×SD16—28no—
282C11×SD16—28no—
283C11×D8—28no—
284C11×M16C2×D418yes—
285C11×M16C2×D418yescomplemented
286C2×C8×C11C2×D418yescomplemented
287C2×C8×C11C2414yes—
288C22⋊Dic11—28no—
289C22⋊Dic11C2×D414yes—
290C22⋊Dic11C2×D414yes—
291#4326—28no—
292#4325—216no—
293#4325—28no—
294#4324—28no—
295#4323—216no—
296#4323—28no—
297(C2×D11)⋊C4—216no—
298(C2×D11)⋊C4—28no—
299C4⋊Dic11C2×D414yes—
300C4⋊Dic11C2×D414yes—
301Dic11⋊C4—28no—
302C4×Dic11C2×D414yes—
303C4×Dic11C2414yes—
304#4318C2×D418yes—
305#4318C2×D418yescomplemented
306C2×C11⋊C8C2×D418yescomplemented
307C2×C11⋊C8C2414yes—
308D88—216no—
309#4314—216no—
310C2×#575—111no—
311C2×#575D1111yescharacteristic, complemented
312C22×AGL(1,ℤ/8)—111no—
313C22×AGL(1,ℤ/8)—111no—
314#3449—111no—
315C2×#535—111no—
316#3155—114no—
317#3155—114no—
318#3154—114no—
319#3154—114no—
320#3153—114no—
321#3151—114no—
322#2873—111no—
323C23×C11—22no—
324C23×C11—22no—
325C23×C11—42no—
326C23×C11—44no—
327C23×C11—42no—
328C23×C11—42no—
329C23×C11—82no—
330C23×C11#12714yes—
331C23×C11C22×D411yescharacteristic
332C23×C11C22×D411yescharacteristic
333C23×C11C22×D411yescharacteristic
334C22×D11—22no—
335C22×D11—24no—
336C22×D11—48no—
337C22×D11—42no—
338C22×D11—44no—
339C22×D11—44no—
340C22×D11—44no—
341C22×D11—82no—
342C22×D11—84no—
343C22×D11—84no—
344C22×D11—816no—
345Q8×C11—22no—
346Q8×C11—22no—
347Q8×C11—22no—
348Q8×C11—22no—
349Q8×C11—42no—
350Q8×C11—42no—
351D4×C11—22no—
352D4×C11—22no—
353D4×C11—22no—
354D4×C11—22no—
355D4×C11—44no—
356D4×C11—44no—
357D4×C11—44no—
358D4×C11—44no—
359D4×C11—42no—
360D4×C11—42no—
361C2×C4×C11—22no—
362C2×C4×C11—22no—
363C2×C4×C11—42no—
364C2×C4×C11—42no—
365C2×C4×C11—44no—
366C2×C4×C11—44no—
367C2×C4×C11—44no—
368C2×C4×C11—44no—
369C2×C4×C11#12714yes—
370C2×C4×C11#12714yes—
371C2×C4×C11#12714yes—
372C2×C4×C11C22×D411yescharacteristic
373C2×C4×C11C22×D411yescharacteristic
374C2×C4×C11C22×D411yescharacteristic
375C2×C4×C11C22×D412yes—
376C2×C4×C11C22×D412yes—
377C2×C4×C11C22×D412yes—
378C2×C4×C11C22×D412yes—
379C2×C4×C11C22×D412yes—
380C2×C4×C11C22×D412yes—
381C2×C4×C11C2511yescharacteristic
382C22⋊D11—44no—
383C22⋊D11—44no—
384C22⋊D11—88no—
385C22⋊D11—816no—
386C2×Dic11—22no—
387C2×Dic11—44no—
388C2×Dic11—42no—
389C2×Dic11C22×D418yes—
390D44—24no—
391D44—22no—
392D44—24no—
393D44—22no—
394D44—44no—
395D44—44no—
396D44—44no—
397D44—42no—
398C4×D11—44no—
399C4×D11—44no—
400Dic22—22no—
401Dic22—22no—
402Dic22—42no—
403C8×C11C22×D418yes—
404C11⋊C8C22×D418yes—
405C22×#41—111no—
406C22×#41C2×D1111yescharacteristic
407C22×#41C2×D1111yescharacteristic
408C23×D4—111no—
409#575—28no—
410#575—228no—
411C2×#137—112no—
412C2×#137—112no—
413C2×#137C2×D1112yescomplemented
414C2×#137C2×D1112yescomplemented
415C2×AGL(1,ℤ/8)—114no—
416C2×AGL(1,ℤ/8)—114no—
417C2×AGL(1,ℤ/8)—112no—
418C2×AGL(1,ℤ/8)—112no—
419C2×AGL(1,ℤ/8)—114no—
420C2×AGL(1,ℤ/8)—114no—
421C2×AGL(1,ℤ/8)—228no—
422C2×AGL(1,ℤ/8)—228no—
423C2×AGL(1,ℤ/8)C2×D1112yescomplemented
424C2×AGL(1,ℤ/8)C2×D1112yescomplemented
425C2×#135—114no—
426C2×#135C2×D1114yescomplemented
427C22×SD16—112no—
428C22×SD16—112no—
429C22×D8—112no—
430C22×D8—112no—
431C22×M16—111no—
432C22×M16C2×D1111yescharacteristic
433#537—222no—
434#536—112no—
435#536—112no—
436#535—114no—
437#535—114no—
438#535—112no—
439#535—112no—
440#535—222no—
441#535—222no—
442#534—222no—
443#532—114no—
444C2×#127—112no—
445C2×#124—112no—
446#525—222no—
447#525—222no—
448C2×#121—222no—
449C2×#120—222no—
450C2×#117—111no—
451#497—118no—
452#496—118no—
453#496—118no—
454#496—118no—
455#495—118no—
456#495—118no—
457#493—118no—
458#492—118no—
459#405—114no—
460#405—114no—
461C4×M16—114no—
462C22×C11—22no—
463C22×C11—22no—
464C22×C11—22no—
465C22×C11—44no—
466C22×C11—44no—
467C22×C11—44no—
468C22×C11—42no—
469C22×C11—42no—
470C22×C11—84no—
471C22×C11—84no—
472C22×C11C2×#12712yes—
473C22×C11C2×#12712yes—
474C22×C11C2×#12712yes—
475C22×C11C23×D411yescharacteristic
476C2×D11—48no—
477C2×D11—44no—
478C2×D11—44no—
479C2×D11—42no—
480C2×D11—88no—
481C2×D11—84no—
482C2×D11—88no—
483C2×D11—88no—
484C4×C11—42no—
485C4×C11—42no—
486C4×C11C2×#12712yes—
487C4×C11C2×#12712yes—
488C4×C11C2×#12712yes—
489C4×C11C23×D411yescharacteristic
490C4×C11C23×D411yescharacteristic
491Dic11—28no—
492Dic11—42no—
493C25—221no—
494C2×#41—21no—
495C2×#41—21no—
496C2×#41—21no—
497C2×#41—21no—
498C2×#41—24no—
499C2×#41—24no—
500C2×#41—24no—
501C2×#41—24no—
502C2×#41—112no—
503C2×#41—112no—
504C2×#41—221no—
505C2×#41—221no—
506C2×#41—224no—
507C2×#41—224no—
508C2×#41C22×D1112yes—
509C2×#41C22×D1112yes—
510C2×#41C22×D1112yes—
511C2×#41C22×D1112yes—
512C22×Q8—111no—
513C22×Q8C22×D1111yescharacteristic
514C22×Q8C22×D1111yescharacteristic
515C22×D4—21no—
516C22×D4—21no—
517C22×D4—112no—
518C22×D4—111no—
519C22×D4—112no—
520C22×D4—112no—
521C22×D4—224no—
522C22×D4—221no—
523C22×D4—224no—
524C22×D4—221no—
525C22×D4—221no—
526C22×D4—221no—
527C22×D4—224no—
528C22×D4C22×D1111yescharacteristic
529C22×D4C22×D1111yescharacteristic
530C23×C4—21no—
531C23×C4—21no—
532C23×C4—221no—
533C23×C4C22×D1111yescharacteristic
534#137—28no—
535#137—28no—
536#137—228no—
537#137—228no—
538AGL(1,ℤ/8)—28no—
539AGL(1,ℤ/8)—28no—
540AGL(1,ℤ/8)—228no—
541AGL(1,ℤ/8)—2216no—
542AGL(1,ℤ/8)—2216no—
543AGL(1,ℤ/8)—228no—
544AGL(1,ℤ/8)—2216no—
545AGL(1,ℤ/8)—2216no—
546#135—216no—
547#135—2216no—
548C2×Q16—114no—
549C2×Q16C22×D1114yescomplemented
550C2×SD16—118no—
551C2×SD16—114no—
552C2×SD16—114no—
553C2×SD16—118no—
554C2×SD16—228no—
555C2×SD16—228no—
556C2×SD16C22×D1114yescomplemented
557C2×SD16C22×D1114yescomplemented
558C2×D8—118no—
559C2×D8—114no—
560C2×D8—118no—
561C2×D8—228no—
562C2×D8—228no—
563C2×D8C22×D1114yescomplemented
564C2×M16—118no—
565C2×M16—112no—
566C2×M16—112no—
567C2×M16C22⋊D1118yescomplemented
568C2×M16C22×D1112yes—
569C2×M16C22×D1112yes—
570C22×C8—112no—
571C22×C8C22×D1112yes—
572C4⋊Q8—114no—
573#127—118no—
574#127—114no—
575#127—224no—
576#124—118no—
577#124—114no—
578#124—114no—
579#124—224no—
580#123—224no—
581#123—224no—
582C22⋊Q8—224no—
583C22⋊Q8—224no—
584#121—228no—
585#121—228no—
586#121—224no—
587#121—224no—
588#121—228no—
589#120—228no—
590#120—228no—
591#120—224no—
592#120—224no—
593C4×D4—228no—
594#117—112no—
595#117—112no—
596#117—112no—
597#117—112no—
598C2×C4⋊C4—112no—
599C2×C22⋊C4—112no—
600C2×C22⋊C4—224no—
601C2×C42—112no—
602#97—118no—
603C4×C8—118no—
604C2×C11—22no—
605C2×C11—22no—
606C2×C11—22no—
607C2×C11—82no—
608C2×C11—82no—
609C2×C11C22×#12711yescharacteristic
610C2×C11#358512yes—
611D11—82no—
612D11—84no—
613C24—21no—
614C24—21no—
615C24—222no—
616C24—221no—
617C24—222no—
618C24—222no—
619C24—444no—
620C24—884no—
621C24D4×D1111yescharacteristic
622#41—24no—
623#41—24no—
624#41—24no—
625#41—24no—
626#41—24no—
627#41—24no—
628#41—24no—
629#41—24no—
630#41—44no—
631#41—44no—
632#41—44no—
633#41—44no—
634#41—224no—
635#41—224no—
636#41—224no—
637#41—224no—
638#41—444no—
639#41—444no—
640C2×Q8—21no—
641C2×Q8—21no—
642C2×Q8—22no—
643C2×Q8—22no—
644C2×Q8—22no—
645C2×Q8—22no—
646C2×Q8—112no—
647C2×Q8—221no—
648C2×Q8—222no—
649C2×Q8—222no—
650C2×Q8C23×D1112yes—
651C2×Q8C23×D1112yes—
652C2×D4—22no—
653C2×D4—22no—
654C2×D4—22no—
655C2×D4—22no—
656C2×D4—22no—
657C2×D4—22no—
658C2×D4—21no—
659C2×D4—21no—
660C2×D4—22no—
661C2×D4—22no—
662C2×D4—44no—
663C2×D4—44no—
664C2×D4—112no—
665C2×D4—114no—
666C2×D4—228no—
667C2×D4—2216no—
668C2×D4—222no—
669C2×D4—222no—
670C2×D4—224no—
671C2×D4—224no—
672C2×D4—224no—
673C2×D4—222no—
674C2×D4—222no—
675C2×D4—222no—
676C2×D4—221no—
677C2×D4—222no—
678C2×D4—222no—
679C2×D4—224no—
680C2×D4—224no—
681C2×D4—224no—
682C2×D4—444no—
683C2×D4—444no—
684C2×D4—444no—
685C2×D4—444no—
686C2×D4—888no—
687C2×D4C23×D1112yes—
688C2×D4C23×D1112yes—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—22no—
692C22×C4—22no—
693C22×C4—22no—
694C22×C4—22no—
695C22×C4—44no—
696C22×C4—44no—
697C22×C4—114no—
698C22×C4—221no—
699C22×C4—222no—
700C22×C4—222no—
701C22×C4—444no—
702C22×C4D4×D1111yescharacteristic
703C22×C4D4×D1111yescharacteristic
704C22×C4D4×D1111yescharacteristic
705C22×C4D4×D1114yes—
706C22×C4C2×C22⋊D1114yes—
707C22×C4C23×D1111yescharacteristic
708C22×C4C23×D1111yescharacteristic
709C22×C4C23×D1111yescharacteristic
710Q16—28no—
711Q16—228no—
712SD16—28no—
713SD16—28no—
714SD16—228no—
715SD16—2216no—
716SD16—228no—
717SD16—2216no—
718D8—28no—
719D8—2216no—
720D8—228no—
721D8—2216no—
722M16—118no—
723M16—118no—
724M16C2×C22⋊D1118yes—
725M16C2×C22⋊D1118yescomplemented
726C2×C8—118no—
727C2×C8—114no—
728C2×C8C2×C22⋊D1118yescomplemented
729C2×C8C23×D1114yes—
730C4⋊C4—114no—
731C4⋊C4—114no—
732C4⋊C4—228no—
733C22⋊C4—114no—
734C22⋊C4—114no—
735C22⋊C4—2216no—
736C22⋊C4—228no—
737C22⋊C4—228no—
738C42—114no—
739C42—114no—
740C11#6064411yescharacteristic, complemented, Sylow
741C23—22no—
742C23—22no—
743C23—42no—
744C23—44no—
745C23—42no—
746C23—42no—
747C23—82no—
748C23—222no—
749C23—224no—
750C23—448no—
751C23—442no—
752C23—444no—
753C23—444no—
754C23—444no—
755C23—882no—
756C23—884no—
757C23—884no—
758C23—8816no—
759C23#6699314yes—
760C23C2×D4×D1111yescharacteristic
761C23C2×D4×D1111yescharacteristic
762C23C2×D4×D1111yescharacteristic
763Q8—22no—
764Q8—22no—
765Q8—22no—
766Q8—22no—
767Q8—42no—
768Q8—42no—
769Q8—222no—
770Q8—222no—
771Q8—442no—
772D4—22no—
773D4—22no—
774D4—22no—
775D4—22no—
776D4—44no—
777D4—44no—
778D4—44no—
779D4—44no—
780D4—42no—
781D4—42no—
782D4—224no—
783D4—222no—
784D4—222no—
785D4—224no—
786D4—444no—
787D4—444no—
788D4—444no—
789D4—444no—
790D4—444no—
791D4—442no—
792D4—8816no—
793D4—888no—
794C2×C4—22no—
795C2×C4—22no—
796C2×C4—42no—
797C2×C4—42no—
798C2×C4—44no—
799C2×C4—44no—
800C2×C4—44no—
801C2×C4—44no—
802C2×C4—118no—
803C2×C4—222no—
804C2×C4—444no—
805C2×C4—442no—
806C2×C4—444no—
807C2×C4—444no—
808C2×C4#6699314yes—
809C2×C4#6699314yes—
810C2×C4#6699314yes—
811C2×C4C2×D4×D1111yescharacteristic
812C2×C4C2×D4×D1111yescharacteristic
813C2×C4C2×D4×D1111yescharacteristic
814C2×C4C2×D4×D1112yes—
815C2×C4C2×D4×D1112yes—
816C2×C4C2×D4×D1112yes—
817C2×C4C22×C22⋊D1112yes—
818C2×C4C22×C22⋊D1112yes—
819C2×C4C22×C22⋊D1112yes—
820C2×C4C24×D1111yescharacteristic
821C8—118no—
822C8C22×C22⋊D1118yes—
823C22—22no—
824C22—22no—
825C22—22no—
826C22—44no—
827C22—44no—
828C22—44no—
829C22—42no—
830C22—42no—
831C22—84no—
832C22—84no—
833C22—448no—
834C22—444no—
835C22—442no—
836C22—444no—
837C22—888no—
838C22—888no—
839C22—888no—
840C22—884no—
841C22C2×#6699312yes—
842C22C2×#6699312yes—
843C22C2×#6699312yes—
844C22C22×D4×D1111yescharacteristic
845C4—42no—
846C4—42no—
847C4—228no—
848C4—442no—
849C4C2×#6699312yes—
850C4C2×#6699312yes—
851C4C2×#6699312yes—
852C4C22×D4×D1111yescharacteristic
853C4C23×C22⋊D1111yescharacteristic
854C2—22no—
855C2—22no—
856C2—22no—
857C2—82no—
858C2—82no—
859C2—884no—
860C2—882no—
861C2C22×#6699311yescharacteristic
862C2#1308339312yes—
subgroupG/H
centerC22C22×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#575C2
socleC22×C11C23×D4
hypercenterC2×#575D11
hypocenterC11#60644
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#575

Complements

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

NH ≅ G/Ntype
1. C2×#10623353C2semidirect
2. C22×#66961C2semidirect
3. C22×#67002C2semidirect
4. #13081945C2semidirect
5. C2×#10623361C2semidirect
6. #13079103C2semidirect
7. #13079101C2semidirect
8. #13079095C2semidirect
9. #13079093C2semidirect
10. #13079083C2semidirect
11. #13079064C2semidirect
12. #13077034C2semidirect
13. C2×C11×#575C2semidirect
19. C2×C11×#137C22semidirect
20. C2×C11×#137C22semidirect
21. C2×C11×AGL(1,ℤ/8)C22semidirect
22. C2×C11×AGL(1,ℤ/8)C22semidirect
23. C2×C11×#135C22semidirect
26. #10623363C22semidirect
29. #10623361C22semidirect
30. #10623361C22semidirect
31. #10623361C22semidirect
33. #10623356C22semidirect
34. C2×#67004C22semidirect
36. C2×#67003C22semidirect
38. C2×#67002C22semidirect
39. C2×#67002C22semidirect
40. C2×#67002C22semidirect
41. #10623347C22semidirect
42. C2×#67000C22semidirect
43. C2×#66995C22semidirect
44. C22×#4325C22semidirect
45. #10623336C22semidirect
47. C2×#66993C22semidirect
49. C2×#66985C22semidirect
50. C22×#4323C22semidirect
56. C2×#66961C22semidirect
57. C2×#66961C22semidirect
58. C22×D88C22semidirect
59. C22×#4314C22semidirect
60. #10622804C22semidirect
61. #10622803C22semidirect
62. #10622789C22semidirect
63. #10622789C22semidirect
64. #10622788C22semidirect
65. #10622781C22semidirect
66. #10622767C22semidirect
67. #10622764C22semidirect
68. #10622735C22semidirect
69. M16×Dic11C22semidirect
70. #10622714C22semidirect
117. C2×C11×Q16C23semidirect
118. C2×C11×SD16C23semidirect
119. C2×C11×SD16C23semidirect
120. C2×C11×D8C23semidirect
121. C2×C11×M16D4semidirect
134. #67000C23semidirect
136. #66997C23semidirect
137. C2×#4326C23semidirect
141. C2×#4325C23semidirect
144. #66993C23semidirect
150. #66989C23semidirect
152. C2×#4324C23semidirect
156. C2×#4323C23semidirect
170. C2×#4318D4semidirect
180. #66879C23semidirect
181. C8×Dic11C23semidirect
285. C11×M16C2×D4semidirect
286. C2×C8×C11C2×D4semidirect
305. #4318C2×D4semidirect
306. C2×C11⋊C8C2×D4semidirect
311. C2×#575D11semidirect
413. C2×#137C2×D11semidirect
414. C2×#137C2×D11semidirect
423. C2×AGL(1,ℤ/8)C2×D11semidirect
424. C2×AGL(1,ℤ/8)C2×D11semidirect
426. C2×#135C2×D11semidirect
549. C2×Q16C22×D11semidirect
556. C2×SD16C22×D11semidirect
557. C2×SD16C22×D11semidirect
563. C2×D8C22×D11semidirect
567. C2×M16C22⋊D11semidirect
725. M16C2×C22⋊D11semidirect
728. C2×C8C2×C22⋊D11semidirect
740. C11#60644semidirect

Maximal subgroups

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

subgroupindex
C2×#106233532
C22×#669612
C22×#670022
#130819452
C2×#106233612
#130791032
#130791012
#130790952
#130790932
#130790832
#130790642
#130770342
C2×C11×#5752
#6064411