Finite Group Databasebeta

← #15620750

Subgroups — #15620750

Order 2816.

2750 conjugacy classes of subgroups.

The subgroup lattice has 858 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623353C211yesmaximal, characteristic, complemented
2#13081945C211yesmaximal, characteristic, complemented
3C2×#10623358C211yesmaximal, characteristic, complemented
4#13078170C214yesmaximal, complemented
5#13078164C214yesmaximal, complemented
6#13078159C214yesmaximal, complemented
7#13078153C214yesmaximal, complemented
8#13078085C214yesmaximal, complemented
9#13078077C214yesmaximal, complemented
10#13077179C211yesmaximal, characteristic, complemented
11C2×#10622746C211yesmaximal, characteristic, complemented
12C2×#10622845C211yesmaximal, characteristic, complemented
13C2×C11×#575C211yesmaximal, characteristic, complemented
14C22×C11×#41C2211yescharacteristic
15C22×C11×#41C2211yescharacteristic
16C22×#4339C2211yescharacteristic
17C11×#575—28no—
18C2×C11×#137C2212yescomplemented
19C2×C11×#137C2212yescomplemented
20C2×C11×AGL(1,ℤ/8)C2212yescomplemented
21C2×C11×AGL(1,ℤ/8)C2212yescomplemented
22C2×C11×#135C2214yes—
23C22×C11×M16C2211yescharacteristic
24#10623364—21no—
25#10623364—21no—
26#10623363C2214yes—
27#10623361C2212yescomplemented
28#10623359—22no—
29#10623358—22no—
30#10623358—22no—
31#10623358C2214yescomplemented
32#10623358C2214yescomplemented
33#10623356C2212yescomplemented
34C2×#67004C2212yescomplemented
35#10623353—28no—
36C2×#67003C2214yes—
37C2×#67002C2212yescomplemented
38#10623347C2212yescomplemented
39C2×Q8×Dic11C2212yescomplemented
40C2×#66995C2212yescomplemented
41#10623336C2212yescomplemented
42#10623335—22no—
43C2×D4×Dic11—22no—
44C2×D4×Dic11C2212yescomplemented
45C2×#66985C2212yescomplemented
46#10623322—22no—
47C2×#66979—21no—
48C2×#66979C2211yescharacteristic
49C22×C4⋊Dic11—21no—
50C22×C4⋊Dic11C2211yescharacteristic
51C22×#4318C2211yescharacteristic
52#10622845C2214yescomplemented
53#10622845C2214yescomplemented
54C2×#66899C2212yescomplemented
55C2×#66896C2212yescomplemented
56#10622798C2218yescomplemented
57#10622795C2218yescomplemented
58#10622779C2218yescomplemented
59#10622778C2218yescomplemented
60#10622776C2218yescomplemented
61#10622775C2218yescomplemented
62#10622766C2218yescomplemented
63#10622763C2218yescomplemented
64#10622746C2214yescomplemented
65#10622746C2214yescomplemented
66#10622732C2214yescomplemented
67#10622731C2214yescomplemented
68C2×#66885C2212yescomplemented
69C2×#66880C2212yescomplemented
70#10622715C2214yescomplemented
71C2×C11×#41—21no—
72C2×C11×#41—21no—
73C2×C11×#41—21no—
74C2×C11×#41—21no—
75C2×C11×#41—24no—
76C2×C11×#41—24no—
77C2×C11×#41—24no—
78C2×C11×#41D418yescomplemented
79C2×C11×#41C2312yes—
80C2×C11×#41C2312yes—
81C2×C11×#41C2312yes—
82C2×C11×#41C2312yes—
83C22×Q8×C11C2311yescharacteristic
84C22×Q8×C11C2311yescharacteristic
85C22×D4×C11—21no—
86C22×D4×C11—21no—
87C22×D4×C11C2311yescharacteristic
88C22×D4×C11C2311yescharacteristic
89C23×C4×C11—21no—
90C23×C4×C11—21no—
91C23×C4×C11C2311yescharacteristic
92C22×C22⋊D11—21no—
93C23×Dic11—21no—
94C23×Dic11—22no—
95C2×#4339—21no—
96C2×#4339—21no—
97C2×#4339—24no—
98C2×#4339—24no—
99C2×#4339C2312yes—
100C2×#4339C2312yes—
101C22×D44C2311yescharacteristic
102C22×C4×D11—21no—
103C22×Dic22C2311yescharacteristic
104C11×#137—28no—
105C11×#137—28no—
106C11×AGL(1,ℤ/8)—28no—
107C11×AGL(1,ℤ/8)—28no—
108C11×#135—216no—
109C2×C11×Q16C2314yes—
110C2×C11×SD16C2314yes—
111C2×C11×SD16C2314yes—
112C2×C11×D8C2314yes—
113C2×C11×M16—24no—
114C2×C11×M16C2312yes—
115C2×C11×M16C2312yes—
116C22×C8×C11C2312yes—
117#67006—24no—
118C2×C22⋊Dic11—22no—
119C2×C22⋊Dic11D412yes—
120#67004—28no—
121#67003—216no—
122#67002—28no—
123#67000C2314yes—
124#66999—22no—
125#66999—22no—
126Q8×Dic11—24no—
127Q8×Dic11C2318yes—
128#66997C2314yes—
129C2×#4326C2314yes—
130#66995—28no—
131C2×#4325C2314yes—
132#66993C2314yes—
133#66992—24no—
134#66992—24no—
135#66991—22no—
136#66991—22no—
137#66990—24no—
138#66989C2314yes—
139#66988—24no—
140D4×Dic11—28no—
141D4×Dic11—28no—
142D4×Dic11—24no—
143D4×Dic11C2318yes—
144C2×#4324C2314yes—
145#66985—28no—
146C2×#4323C2314yes—
147#66983—22no—
148#66983—22no—
149#66982—24no—
150C4×C22⋊D11—24no—
151C4×C22⋊D11—24no—
152#66979—24no—
153#66979—24no—
154#66979D412yes—
155#66979D412yes—
156#66979C2312yes—
157#66979C2312yes—
158C2×C4⋊Dic11—21no—
159C2×C4⋊Dic11—21no—
160C2×C4⋊Dic11—21no—
161C2×C4⋊Dic11—22no—
162C2×C4⋊Dic11—24no—
163C2×C4⋊Dic11—24no—
164C2×C4⋊Dic11D411yescharacteristic
165C2×C4⋊Dic11D411yescharacteristic
166C2×C4⋊Dic11C2312yes—
167C2×C4⋊Dic11C2312yes—
168C2×C4⋊Dic11C2312yes—
169#66977—22no—
170#66977—22no—
171C2×C4×Dic11—22no—
172C2×C4×Dic11C2312yes—
173C2×#4318—24no—
174C2×#4318C2312yes—
175C2×#4318C2312yes—
176C22×C11⋊C8C2312yes—
177#66899C2318yes—
178#66896C2318yes—
179#66885C2318yes—
180#66880C2318yes—
181Dic11⋊C8C2318yes—
182Dic11⋊C8C2318yes—
183#60425—111nomaximal, Sylow
184C24×C11—21no—
185C24×C11—21no—
186C24×C11C2×D411yescharacteristic
187C23×D11—21no—
188C11×#41—28no—
189C11×#41—28no—
190C11×#41—24no—
191C11×#41—24no—
192C11×#41—24no—
193C11×#41—24no—
194C11×#41—24no—
195C11×#41—24no—
196C11×#41—44no—
197C11×#41—44no—
198C11×#41C2×D418yes—
199C11×#41C2×D418yes—
200C2×Q8×C11—21no—
201C2×Q8×C11—21no—
202C2×Q8×C11—22no—
203C2×Q8×C11—22no—
204C2×Q8×C11—22no—
205C2×Q8×C11C2×D414yes—
206C2×Q8×C11C2412yes—
207C2×Q8×C11C2412yes—
208C2×D4×C11—28no—
209C2×D4×C11—22no—
210C2×D4×C11—22no—
211C2×D4×C11—22no—
212C2×D4×C11—22no—
213C2×D4×C11—21no—
214C2×D4×C11—22no—
215C2×D4×C11—21no—
216C2×D4×C11—22no—
217C2×D4×C11—22no—
218C2×D4×C11—44no—
219C2×D4×C11C2×D414yes—
220C2×D4×C11C2412yes—
221C2×D4×C11C2412yes—
222C22×C4×C11—21no—
223C22×C4×C11—28no—
224C22×C4×C11—22no—
225C22×C4×C11—22no—
226C22×C4×C11—21no—
227C22×C4×C11—22no—
228C22×C4×C11—22no—
229C22×C4×C11—44no—
230C22×C4×C11C2×D411yescharacteristic
231C22×C4×C11C2×D411yescharacteristic
232C22×C4×C11C2×D411yescharacteristic
233C22×C4×C11C2×D414yes—
234C22×C4×C11#4114yes—
235C22×C4×C11C2411yescharacteristic
236C22×C4×C11C2411yescharacteristic
237C22×C4×C11C2411yescharacteristic
238C2×C22⋊D11—24no—
239C2×C22⋊D11—24no—
240C2×C22⋊D11—22no—
241C2×C22⋊D11—22no—
242C2×C22⋊D11—44no—
243C22×Dic11—28no—
244C22×Dic11—22no—
245C22×Dic11—21no—
246C22×Dic11—22no—
247C22×Dic11—22no—
248C22×Dic11—82no—
249C22×Dic11—84no—
250C22×Dic11C2×D412yes—
251C22×Dic11C2×D412yes—
252#4339—24no—
253#4339—24no—
254#4339—24no—
255#4339—24no—
256#4339—44no—
257#4339—44no—
258C2×D44—21no—
259C2×D44—22no—
260C2×D44—22no—
261C2×D44C2412yes—
262C2×C4×D11—22no—
263C2×C4×D11—22no—
264C2×C4×D11—44no—
265C2×Dic22—22no—
266C2×Dic22—21no—
267C2×Dic22—22no—
268C2×Dic22C2412yes—
269C11×Q16—28no—
270C11×SD16—28no—
271C11×SD16—28no—
272C11×D8—28no—
273C11×M16—24no—
274C11×M16—24no—
275C2×C8×C11—24no—
276C2×C8×C11C2414yes—
277C22⋊Dic11—24no—
278C22⋊Dic11—24no—
279C22⋊Dic11—28no—
280C22⋊Dic11C2×D414yes—
281C22⋊Dic11C2×D414yes—
282#4326—28no—
283#4325—28no—
284#4324—28no—
285#4323—28no—
286(C2×D11)⋊C4—24no—
287(C2×D11)⋊C4—24no—
288C4⋊Dic11—28no—
289C4⋊Dic11—22no—
290C4⋊Dic11—22no—
291C4⋊Dic11—22no—
292C4⋊Dic11C2×D412yes—
293C4⋊Dic11C2×D412yes—
294C4⋊Dic11C2×D412yes—
295C4⋊Dic11C2×D412yes—
296C4⋊Dic11C2414yes—
297Dic11⋊C4—24no—
298Dic11⋊C4—24no—
299C4×Dic11—28no—
300C4×Dic11C2×D414yes—
301C4×Dic11C2414yes—
302#4318—24no—
303#4318—24no—
304C2×C11⋊C8—24no—
305C2×C11⋊C8C2414yes—
306C2×#575—111no—
307C2×#575D1111yescharacteristic, complemented
308#3449—111no—
309C2×#520—111no—
310#3046—114no—
311#3046—114no—
312#3045—114no—
313#3045—114no—
314#3037—114no—
315#3036—114no—
316#2905—111no—
317C2×#417—111no—
318C2×#417—111no—
319C23×C11—24no—
320C23×C11—22no—
321C23×C11—22no—
322C23×C11—41no—
323C23×C11—41no—
324C23×C11—42no—
325C23×C11—42no—
326C23×C11—42no—
327C23×C11—81no—
328C23×C11—81no—
329C23×C11#12114yes—
330C23×C11C22×D411yescharacteristic
331C23×C11C22×D411yescharacteristic
332C23×C11C22×D411yescharacteristic
333C22×D11—22no—
334C22×D11—42no—
335C22×D11—81no—
336C22×D11—81no—
337Q8×C11—24no—
338Q8×C11—22no—
339Q8×C11—22no—
340Q8×C11—22no—
341Q8×C11—42no—
342Q8×C11C22×D414yes—
343D4×C11—28no—
344D4×C11—28no—
345D4×C11—24no—
346D4×C11—22no—
347D4×C11—22no—
348D4×C11—22no—
349D4×C11—44no—
350D4×C11—44no—
351D4×C11—42no—
352D4×C11C22×D414yes—
353C2×C4×C11—24no—
354C2×C4×C11—22no—
355C2×C4×C11—28no—
356C2×C4×C11—28no—
357C2×C4×C11—22no—
358C2×C4×C11—42no—
359C2×C4×C11—44no—
360C2×C4×C11—44no—
361C2×C4×C11#12114yes—
362C2×C4×C11#12114yes—
363C2×C4×C11#12114yes—
364C2×C4×C11C22×D411yescharacteristic
365C2×C4×C11C22×D411yescharacteristic
366C2×C4×C11C22×D411yescharacteristic
367C2×C4×C11C22×D412yes—
368C2×C4×C11C22×D412yes—
369C2×C4×C11C22×D412yes—
370C2×C4×C11C2×#4112yes—
371C2×C4×C11C2×#4112yes—
372C2×C4×C11C2×#4112yes—
373C2×C4×C11C2511yescharacteristic
374C22⋊D11—44no—
375C22⋊D11—44no—
376C22⋊D11—84no—
377C22⋊D11—84no—
378C2×Dic11—24no—
379C2×Dic11—22no—
380C2×Dic11—42no—
381C2×Dic11—42no—
382C2×Dic11—44no—
383C2×Dic11—42no—
384C2×Dic11—88no—
385C2×Dic11—82no—
386C2×Dic11—82no—
387C2×Dic11C22×D414yes—
388C2×Dic11C22×D414yes—
389D44—22no—
390D44—22no—
391D44—42no—
392C4×D11—44no—
393C4×D11—44no—
394Dic22—22no—
395Dic22—22no—
396Dic22—42no—
397C8×C11—24no—
398C11⋊C8—24no—
399C22×#41—111no—
400C22×#41C2×D1111yescharacteristic
401C22×#41C2×D1111yescharacteristic
402#575—28no—
403#575—228no—
404C2×#137—112no—
405C2×#137—112no—
406C2×#137C2×D1112yescomplemented
407C2×#137C2×D1112yescomplemented
408C2×AGL(1,ℤ/8)—112no—
409C2×AGL(1,ℤ/8)—112no—
410C2×AGL(1,ℤ/8)C2×D1112yescomplemented
411C2×AGL(1,ℤ/8)C2×D1112yescomplemented
412C2×#135—114no—
413C2×#135C2×D1114yes—
414C22×M16—111no—
415C22×M16C2×D1111yescharacteristic
416#537—221no—
417#537—221no—
418#536—112no—
419#536—112no—
420#535—112no—
421#535—112no—
422#534—222no—
423#532—114no—
424#525—222no—
425#525—222no—
426#520—114no—
427#520—114no—
428#520—222no—
429#520—222no—
430C2×C4×Q8—112no—
431C2×C4×D4—112no—
432C2×C4×D4—222no—
433C2×#117—111no—
434C2×#117—221no—
435C22×C4⋊C4—111no—
436C22×C4⋊C4—221no—
437#464—118no—
438#464—118no—
439#463—118no—
440#463—118no—
441#462—118no—
442#461—118no—
443#460—118no—
444#459—118no—
445#424—114no—
446#424—114no—
447#423—114no—
448#417—114no—
449#417—114no—
450#417—114no—
451#417—114no—
452C2×#103—112no—
453C2×#103—112no—
454C2×#102—112no—
455C2×#102—112no—
456C22×C11—21no—
457C22×C11—21no—
458C22×C11—21no—
459C22×C11—21no—
460C22×C11—21no—
461C22×C11—21no—
462C22×C11—24no—
463C22×C11—44no—
464C22×C11—48no—
465C22×C11—42no—
466C22×C11—42no—
467C22×C11—42no—
468C22×C11—42no—
469C22×C11—42no—
470C22×C11—84no—
471C22×C11C2×#12112yes—
472C22×C11C2×#12112yes—
473C22×C11C2×#12112yes—
474C22×C11C23×D411yescharacteristic
475C2×D11—42no—
476C2×D11—42no—
477C2×D11—42no—
478C2×D11—84no—
479C4×C11—24no—
480C4×C11—42no—
481C4×C11C2×#12112yes—
482C4×C11C2×#12112yes—
483C4×C11C2×#12112yes—
484C4×C11C23×D411yescharacteristic
485C4×C11C22×#4111yescharacteristic
486Dic11—24no—
487Dic11—24no—
488Dic11—44no—
489Dic11—42no—
490C2×#41—21no—
491C2×#41—21no—
492C2×#41—21no—
493C2×#41—21no—
494C2×#41—24no—
495C2×#41—24no—
496C2×#41—24no—
497C2×#41—112no—
498C2×#41—112no—
499C2×#41—221no—
500C2×#41—221no—
501C2×#41—224no—
502C2×#41—224no—
503C2×#41C22⋊D1118yescomplemented
504C2×#41C22×D1112yes—
505C2×#41C22×D1112yes—
506C2×#41C22×D1112yes—
507C2×#41C22×D1112yes—
508C22×Q8—111no—
509C22×Q8C22×D1111yescharacteristic
510C22×Q8C22×D1111yescharacteristic
511C22×D4—21no—
512C22×D4—21no—
513C22×D4—111no—
514C22×D4—221no—
515C22×D4C22×D1111yescharacteristic
516C22×D4C22×D1111yescharacteristic
517C23×C4—21no—
518C23×C4—21no—
519C23×C4—222no—
520C23×C4—221no—
521C23×C4—221no—
522C23×C4C22×D1111yescharacteristic
523#137—28no—
524#137—28no—
525#137—228no—
526#137—228no—
527AGL(1,ℤ/8)—28no—
528AGL(1,ℤ/8)—28no—
529AGL(1,ℤ/8)—228no—
530AGL(1,ℤ/8)—228no—
531#135—216no—
532#135—2216no—
533C2×Q16—114no—
534C2×Q16C22×D1114yes—
535C2×SD16—114no—
536C2×SD16—114no—
537C2×SD16C22×D1114yes—
538C2×SD16C22×D1114yes—
539C2×D8—114no—
540C2×D8C22×D1114yes—
541C2×M16—24no—
542C2×M16—112no—
543C2×M16—112no—
544C2×M16—224no—
545C2×M16C22×D1112yes—
546C2×M16C22×D1112yes—
547C22×C8—112no—
548C22×C8C22×D1112yes—
549C4⋊Q8—114no—
550#127—114no—
551#124—114no—
552#124—114no—
553#123—224no—
554#123—224no—
555C22⋊Q8—222no—
556C22⋊Q8—222no—
557C22⋊Q8—222no—
558C22⋊Q8—222no—
559#121—222no—
560#121—222no—
561#121—222no—
562#121—222no—
563#121—224no—
564#121—224no—
565#120—224no—
566#120—224no—
567C4×Q8—118no—
568C4×Q8—224no—
569C4×D4—118no—
570C4×D4—224no—
571C4×D4—224no—
572C4×D4—224no—
573C4×D4—228no—
574C4×D4—228no—
575#117—112no—
576#117—112no—
577#117—112no—
578#117—112no—
579#117—224no—
580#117—224no—
581C2×C4⋊C4—111no—
582C2×C4⋊C4—111no—
583C2×C4⋊C4—112no—
584C2×C4⋊C4—112no—
585C2×C4⋊C4—112no—
586C2×C4⋊C4—224no—
587C2×C4⋊C4—224no—
588C2×C4⋊C4—222no—
589C2×C4⋊C4—221no—
590C2×C4⋊C4—221no—
591C2×C4⋊C4—221no—
592C2×C22⋊C4—112no—
593C2×C22⋊C4—222no—
594C2×C42—112no—
595C2×C42—222no—
596C4⋊C8—118no—
597C4⋊C8—118no—
598#103—118no—
599#103—118no—
600#102—118no—
601#102—118no—
602C2×C11—22no—
603C2×C11—22no—
604C2×C11—22no—
605C2×C11—44no—
606C2×C11—82no—
607C2×C11C22×#12111yescharacteristic
608C2×C11#358511yescharacteristic
609C2×C11#358611yescharacteristic
610D11—82no—
611C24—21no—
612C24—21no—
613C24—221no—
614C24D4×D1111yescharacteristic
615#41—28no—
616#41—28no—
617#41—24no—
618#41—24no—
619#41—24no—
620#41—24no—
621#41—24no—
622#41—24no—
623#41—44no—
624#41—44no—
625#41—224no—
626#41—224no—
627#41—224no—
628#41—224no—
629#41—444no—
630#41—444no—
631#41C2×C22⋊D1118yes—
632#41C2×C22⋊D1118yes—
633C2×Q8—21no—
634C2×Q8—21no—
635C2×Q8—22no—
636C2×Q8—22no—
637C2×Q8—22no—
638C2×Q8—112no—
639C2×Q8—221no—
640C2×Q8—222no—
641C2×Q8—222no—
642C2×Q8C2×C22⋊D1114yes—
643C2×Q8C23×D1112yes—
644C2×Q8C23×D1112yes—
645C2×D4—28no—
646C2×D4—22no—
647C2×D4—22no—
648C2×D4—22no—
649C2×D4—22no—
650C2×D4—21no—
651C2×D4—21no—
652C2×D4—22no—
653C2×D4—22no—
654C2×D4—22no—
655C2×D4—44no—
656C2×D4—112no—
657C2×D4—224no—
658C2×D4—224no—
659C2×D4—222no—
660C2×D4—222no—
661C2×D4—221no—
662C2×D4—222no—
663C2×D4—222no—
664C2×D4—444no—
665C2×D4C2×C22⋊D1114yes—
666C2×D4C23×D1112yes—
667C2×D4C23×D1112yes—
668C22×C4—21no—
669C22×C4—28no—
670C22×C4—22no—
671C22×C4—22no—
672C22×C4—21no—
673C22×C4—22no—
674C22×C4—22no—
675C22×C4—44no—
676C22×C4—112no—
677C22×C4—112no—
678C22×C4—228no—
679C22×C4—222no—
680C22×C4—221no—
681C22×C4—222no—
682C22×C4—222no—
683C22×C4—222no—
684C22×C4—222no—
685C22×C4—444no—
686C22×C4—884no—
687C22×C4—882no—
688C22×C4D4×D1111yescharacteristic
689C22×C4D4×D1111yescharacteristic
690C22×C4D4×D1111yescharacteristic
691C22×C4#434114yes—
692C22×C4C2×C22⋊D1114yes—
693C22×C4C23×D1111yescharacteristic
694C22×C4C23×D1111yescharacteristic
695C22×C4C23×D1111yescharacteristic
696Q16—28no—
697Q16—228no—
698SD16—28no—
699SD16—28no—
700SD16—228no—
701SD16—228no—
702D8—28no—
703D8—228no—
704M16—24no—
705M16—24no—
706M16—224no—
707M16—224no—
708C2×C8—24no—
709C2×C8—114no—
710C2×C8—224no—
711C2×C8C23×D1114yes—
712C4⋊C4—112no—
713C4⋊C4—112no—
714C4⋊C4—112no—
715C4⋊C4—112no—
716C4⋊C4—114no—
717C4⋊C4—228no—
718C4⋊C4—224no—
719C4⋊C4—224no—
720C4⋊C4—222no—
721C4⋊C4—222no—
722C4⋊C4—222no—
723C22⋊C4—114no—
724C22⋊C4—114no—
725C22⋊C4—224no—
726C22⋊C4—224no—
727C22⋊C4—228no—
728C22⋊C4—224no—
729C22⋊C4—224no—
730C42—114no—
731C42—114no—
732C42—228no—
733C11#6042511yescharacteristic, complemented, Sylow
734C23—24no—
735C23—22no—
736C23—22no—
737C23—41no—
738C23—41no—
739C23—42no—
740C23—42no—
741C23—42no—
742C23—81no—
743C23—81no—
744C23—222no—
745C23—442no—
746C23—881no—
747C23—881no—
748C23#6699214yes—
749C23C2×D4×D1111yescharacteristic
750C23C2×D4×D1111yescharacteristic
751C23C2×D4×D1111yescharacteristic
752Q8—24no—
753Q8—22no—
754Q8—22no—
755Q8—22no—
756Q8—42no—
757Q8—222no—
758Q8—222no—
759Q8—442no—
760Q8C22×C22⋊D1114yes—
761D4—28no—
762D4—28no—
763D4—24no—
764D4—22no—
765D4—22no—
766D4—22no—
767D4—44no—
768D4—44no—
769D4—42no—
770D4—222no—
771D4—222no—
772D4—444no—
773D4—444no—
774D4—442no—
775D4—884no—
776D4—884no—
777D4C22×C22⋊D1114yes—
778C2×C4—24no—
779C2×C4—22no—
780C2×C4—28no—
781C2×C4—28no—
782C2×C4—22no—
783C2×C4—42no—
784C2×C4—44no—
785C2×C4—44no—
786C2×C4—114no—
787C2×C4—114no—
788C2×C4—224no—
789C2×C4—222no—
790C2×C4—442no—
791C2×C4—442no—
792C2×C4—444no—
793C2×C4—442no—
794C2×C4—444no—
795C2×C4—444no—
796C2×C4—888no—
797C2×C4—882no—
798C2×C4—882no—
799C2×C4#6699214yes—
800C2×C4#6699214yes—
801C2×C4#6699214yes—
802C2×C4C2×D4×D1111yescharacteristic
803C2×C4C2×D4×D1111yescharacteristic
804C2×C4C2×D4×D1111yescharacteristic
805C2×C4C2×#434112yes—
806C2×C4C2×#434112yes—
807C2×C4C2×#434112yes—
808C2×C4C22×C22⋊D1112yes—
809C2×C4C22×C22⋊D1112yes—
810C2×C4C22×C22⋊D1112yes—
811C2×C4C24×D1111yescharacteristic
812C8—24no—
813C8—224no—
814C22—21no—
815C22—21no—
816C22—21no—
817C22—21no—
818C22—21no—
819C22—21no—
820C22—24no—
821C22—44no—
822C22—48no—
823C22—42no—
824C22—42no—
825C22—42no—
826C22—42no—
827C22—42no—
828C22—84no—
829C22—442no—
830C22—442no—
831C22—442no—
832C22—884no—
833C22C2×#6699212yes—
834C22C2×#6699212yes—
835C22C2×#6699212yes—
836C22C22×D4×D1111yescharacteristic
837C4—24no—
838C4—42no—
839C4—224no—
840C4—224no—
841C4—444no—
842C4—442no—
843C4C2×#6699212yes—
844C4C2×#6699212yes—
845C4C2×#6699212yes—
846C4C22×#434111yescharacteristic
847C4C23×C22⋊D1111yescharacteristic
848C2—22no—
849C2—22no—
850C2—22no—
851C2—44no—
852C2—82no—
853C2—882no—
854C2C22×#6699211yescharacteristic
855C2#1308339311yescharacteristic
856C2#1308340011yescharacteristic
subgroupG/H
centerC22C22×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#575C2
socleC22×C11C23×D4
hypercenterC2×#575D11
hypocenterC11#60425
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. #13081945C2semidirect
3. C2×#10623358C2semidirect
4. #13078170C2semidirect
5. #13078164C2semidirect
6. #13078159C2semidirect
7. #13078153C2semidirect
8. #13078085C2semidirect
9. #13078077C2semidirect
10. #13077179C2semidirect
11. C2×#10622746C2semidirect
12. C2×#10622845C2semidirect
13. C2×C11×#575C2semidirect
18. C2×C11×#137C22semidirect
19. C2×C11×#137C22semidirect
20. C2×C11×AGL(1,ℤ/8)C22semidirect
21. C2×C11×AGL(1,ℤ/8)C22semidirect
27. #10623361C22semidirect
31. #10623358C22semidirect
32. #10623358C22semidirect
33. #10623356C22semidirect
34. C2×#67004C22semidirect
37. C2×#67002C22semidirect
38. #10623347C22semidirect
39. C2×Q8×Dic11C22semidirect
40. C2×#66995C22semidirect
41. #10623336C22semidirect
44. C2×D4×Dic11C22semidirect
45. C2×#66985C22semidirect
52. #10622845C22semidirect
53. #10622845C22semidirect
54. C2×#66899C22semidirect
55. C2×#66896C22semidirect
56. #10622798C22semidirect
57. #10622795C22semidirect
58. #10622779C22semidirect
59. #10622778C22semidirect
60. #10622776C22semidirect
61. #10622775C22semidirect
62. #10622766C22semidirect
63. #10622763C22semidirect
64. #10622746C22semidirect
65. #10622746C22semidirect
66. #10622732C22semidirect
67. #10622731C22semidirect
68. C2×#66885C22semidirect
69. C2×#66880C22semidirect
70. #10622715C22semidirect
78. C2×C11×#41D4semidirect
307. C2×#575D11semidirect
406. C2×#137C2×D11semidirect
407. C2×#137C2×D11semidirect
410. C2×AGL(1,ℤ/8)C2×D11semidirect
411. C2×AGL(1,ℤ/8)C2×D11semidirect
503. C2×#41C22⋊D11semidirect
733. C11#60425semidirect

Maximal subgroups

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

subgroupindex
C2×#106233532
#130819452
C2×#106233582
#130781702
#130781642
#130781592
#130781532
#130780852
#130780772
#130771792
C2×#106227462
C2×#106228452
C2×C11×#5752
#6042511