Finite Group Databasebeta

← #10575753

Subgroups — #10575753

Order 512.

6207 conjugacy classes of subgroups.

The subgroup lattice has 1016 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#62813C211yesmaximal, characteristic, complemented
2C2×#3460C211yesmaximal, characteristic
3#60892C218yesmaximal, complemented
4#60890C2116yesmaximal, complemented
5#60888C218yesmaximal, complemented
6#60870C214yesmaximal, complemented
7#60868C214yesmaximal, complemented
8#60866C214yesmaximal, complemented
9#60864C214yesmaximal, complemented
10#60664C212yesmaximal, complemented
11#60619C212yesmaximal, complemented
12#60520C212yesmaximal, complemented
13#60518C212yesmaximal, complemented
14#60484C212yesmaximal, complemented
15C2×#3077C212yesmaximal, complemented
16#60125C211yesmaximal, characteristic, complemented
17#3504C2218yescomplemented
18#3503C2214yescomplemented
19#3503C2214yescomplemented
20#3502—21no—
21#3502—21no—
22#3501—22no—
23#3501—21no—
24#3501—22no—
25#3501—21no—
26Q8×#41—24no—
27Q8×#41—24no—
28#3460—24no—
29#3460—24no—
30#3460C2218yes—
31#3460C2218yes—
32#3458C2212yes—
33#3458C2214yescomplemented
34C2×#544C2211yescharacteristic
35C2×#542—21no—
36C2×#542C2212yes—
37C2×#540—21no—
38C2×#540C2212yes—
39C2×#538—22no—
40C2×#537C2211yescharacteristic
41C2×#535C2211yescharacteristic
42C2×#535C2211yescharacteristic
43C2×#533C2212yes—
44C2×#533C2214yescomplemented
45C2×#532—21no—
46C2×#532C2212yes—
47C2×#529—21no—
48C2×#529C2212yes—
49C2×#525—22no—
50#3428C2212yes—
51C2×C4×#41C2211yescharacteristic
52C2×C4×#41C2211yescharacteristic
53C22×C4×D4C2211yescharacteristic
54#3244C22132yescomplemented
55#3243C22132yescomplemented
56#3241C22132yescomplemented
57#3241C22132yescomplemented
58#3240C22116yescomplemented
59#3239C2218yescomplemented
60#3238C2218yescomplemented
61#3235C22116yescomplemented
62#3234C22116yescomplemented
63#3233C22116yescomplemented
64#3232C22116yescomplemented
65#3228C22116yescomplemented
66#3227C2218yescomplemented
67#3226C2218yescomplemented
68#3166C2218yescomplemented
69#3165C2218yescomplemented
70#3164C22116yescomplemented
71#3163C22116yescomplemented
72#3140C2218yes—
73#3138C2218yes—
74#3136C22116yescomplemented
75#3136C22116yescomplemented
76#3099C22116yescomplemented
77#3098C22116yescomplemented
78#3096C22116yescomplemented
79#3096C22116yescomplemented
80#3095C2218yescomplemented
81#3094C2218yes—
82#3094C2218yes—
83#3094C2218yescomplemented
84#3080C2218yescomplemented
85#3079C2214yescomplemented
86#3079C2214yescomplemented
87#3078C2214yescomplemented
88#3078C2214yescomplemented
89#3077C2218yes—
90#3077C2218yes—
91#3077C2218yescomplemented
92#3077C2218yescomplemented
93#3077C2214yescomplemented
94#3077C2214yescomplemented
95#3076C2218yescomplemented
96#3076C2218yescomplemented
97C2×#478C2218yescomplemented
98C2×#476C2214yescomplemented
99C2×#474C2214yescomplemented
100#2925C2218yescomplemented
101#2925C2218yescomplemented
102#2921C2214yescomplemented
103#2920C2214yescomplemented
104#2911C2214yes—
105C2×#428C2214yes—
106C2×#423C2212yes—
107#2896C2214yes—
108C2×#418C2214yes—
109#2879C2212yes—
110#2873C2212yes—
111C22×#41—22no—
112C22×#41C2311yescharacteristic
113C22×#41C2311yescharacteristic
114C23×D4C2311yescharacteristic
115C24×C4—21no—
116C22×M16C2314yes—
117Q82—24no—
118Q82—24no—
119#557—24no—
120#557—24no—
121#557—28no—
122#557—28no—
123#554—28no—
124#554—28no—
125#554—24no—
126#554—24no—
127#554—216no—
128#554—216no—
129#554—28no—
130#554—28no—
131D4×Q8—28no—
132D4×Q8—24no—
133D4×Q8—28no—
134D4×Q8—24no—
135#544—24no—
136#544—22no—
137#544—22no—
138#544—24no—
139#544—24no—
140#544C2318yes—
141#544C2318yes—
142#544C2318yes—
143#544C23116yescomplemented
144#544C23116yescomplemented
145#543—24no—
146#543—24no—
147#543—24no—
148#542—28no—
149#542—28no—
150#542—28no—
151#542C23116yes—
152#540—28no—
153#540—28no—
154#540—28no—
155#540C23116yes—
156#538—216no—
157#538—216no—
158#537—24no—
159#537C2318yes—
160#535—24no—
161#535—24no—
162#535C2318yes—
163#535C2318yes—
164#533—28no—
165#533—216no—
166#533—22no—
167#533—22no—
168#533—22no—
169#533—22no—
170#533—24no—
171#533—24no—
172#533—24no—
173#533—24no—
174#533C2314yes—
175#533C2314yes—
176#533C2314yes—
177#533C2314yes—
178#533C2318yes—
179#533C2318yescomplemented
180#533C2318yescomplemented
181#532—28no—
182#532—28no—
183#532—24no—
184#532—24no—
185#532C2318yes—
186#532C2318yes—
187C2×C4⋊Q8—21no—
188C2×C4⋊Q8C2312yes—
189C2×C4⋊Q8C2312yes—
190C2×C4⋊Q8C2312yes—
191C2×C4⋊Q8C2314yescomplemented
192C2×C4⋊Q8C2314yescomplemented
193C2×#127—21no—
194C2×#127C2312yes—
195#529—28no—
196#529—28no—
197#529—24no—
198#529—24no—
199#529C2318yes—
200#529C2318yes—
201C2×#126—22no—
202C2×#126—22no—
203C2×#125—21no—
204C2×#125C2314yes—
205C2×#125C2312yes—
206C2×#125C2318yescomplemented
207C2×#124—21no—
208C2×#124—22no—
209C2×#124—22no—
210C2×#124C2312yes—
211#525—216no—
212#525—216no—
213C2×#123—22no—
214C2×#123—22no—
215C2×#123—22no—
216C2×#123—22no—
217C2×C22⋊Q8—21no—
218C2×C22⋊Q8—22no—
219C2×C22⋊Q8—22no—
220C2×C22⋊Q8—24no—
221C2×C22⋊Q8—24no—
222C2×C22⋊Q8—22no—
223C2×C22⋊Q8—22no—
224C2×C22⋊Q8C2312yes—
225C2×#121—22no—
226C2×#121—21no—
227C2×#121—22no—
228C2×#121—21no—
229C2×#121—21no—
230C2×#121—22no—
231C2×#121—22no—
232C2×#121C2312yes—
233C2×#121C2312yes—
234C2×#121C2312yes—
235C2×#120—22no—
236C2×#120—22no—
237#520C2318yes—
238#520C2318yes—
239#519—22no—
240#518—24no—
241#518—22no—
242C4×#41—28no—
243C4×#41—22no—
244C4×#41—22no—
245C4×#41D414yes—
246C4×#41D414yes—
247C4×#41C2314yes—
248C4×#41C2314yes—
249C4×#41C2314yes—
250C4×#41C2314yes—
251C2×C4×Q8—22no—
252C2×C4×Q8—22no—
253C2×C4×Q8—24no—
254C2×C4×Q8—24no—
255C2×C4×Q8D411yescharacteristic
256C2×C4×Q8D411yescharacteristic
257C2×C4×Q8C2311yescharacteristic
258C2×C4×Q8C2311yescharacteristic
259C2×C4×D4—21no—
260C2×C4×D4—21no—
261C2×C4×D4—22no—
262C2×C4×D4—21no—
263C2×C4×D4—21no—
264C2×C4×D4—22no—
265C2×C4×D4—22no—
266C2×C4×D4—22no—
267C2×C4×D4D412yes—
268C2×C4×D4D411yescharacteristic
269C2×C4×D4D412yes—
270C2×C4×D4D411yescharacteristic
271C2×C4×D4C2314yes—
272C2×C4×D4C2312yes—
273C2×C4×D4C2312yes—
274C2×C4×D4C2311yescharacteristic
275C2×C4×D4C2311yescharacteristic
276C2×C4×D4C2314yes—
277C2×#117—21no—
278C2×#117—22no—
279C2×#117C2318yes—
280C2×#117C2314yes—
281C2×#117C2311yescharacteristic
282C2×#117C2311yescharacteristic
283C2×#117C2312yes—
284C22×C4⋊C4C2311yescharacteristic
285C22×C22⋊C4—21no—
286C22×C42—21no—
287C22×C42C2311yescharacteristic
288C22×C42C2312yes—
289#501C23116yescomplemented
290#501C23132yescomplemented
291#501C23116yescomplemented
292#500C23116yescomplemented
293#499C23132yescomplemented
294#498C23116yescomplemented
295#490C23132yes—
296#489C23116yes—
297#489C23116yes—
298#488C23132yes—
299#486C23116yes—
300#486C23116yes—
301#485C23132yescomplemented
302#484C23116yescomplemented
303#483C23116yescomplemented
304#482C23132yes—
305#482C23132yes—
306#482C23132yescomplemented
307#481C23116yes—
308#481C23116yes—
309#481C23116yescomplemented
310#480C23116yes—
311#480C23116yes—
312#480C23116yescomplemented
313#479C23116yescomplemented
314#479C23116yescomplemented
315#478C23132yes—
316#478C23132yes—
317#478C23116yescomplemented
318#478C23116yescomplemented
319#477C2318yescomplemented
320#477C2318yescomplemented
321#476C23116yes—
322#476C23116yes—
323#476C2318yescomplemented
324#476C2318yescomplemented
325#475C2318yescomplemented
326#475C2318yescomplemented
327#474C23116yes—
328#474C23116yes—
329#474C2318yescomplemented
330#474C2318yescomplemented
331#433C23132yescomplemented
332#432C2318yescomplemented
333#432C2318yescomplemented
334#431C2318yescomplemented
335#431C2318yescomplemented
336#428C23116yes—
337#428C23116yes—
338#428C2318yes—
339#428C2318yes—
340#428C2318yes—
341#428C2318yes—
342#427C23116yes—
343C2×#107C2318yes—
344C2×#106C2318yes—
345#423C2314yes—
346#423C2314yes—
347#423C2314yes—
348#423C2314yes—
349C2×C4⋊C8C2314yes—
350C2×C4⋊C8C2314yes—
351#419C2318yes—
352#418C23116yes—
353#418C2318yes—
354#418C23116yes—
355#417C2318yes—
356#417C2318yes—
357#416C23116yes—
358C2×#102C2318yes—
359C2×#102C2318yes—
360#408C23116yes—
361#407C2318yes—
362#405C23116yes—
363C4×M16C2318yes—
364C25—21no—
365C2×#41—22no—
366C2×#41—28no—
367C2×#41—28no—
368C2×#41—28no—
369C2×#41—28no—
370C2×#41—88no—
371C2×#41C2×D414yes—
372C2×#41C2414yes—
373C2×#41C2414yes—
374C22×Q8—22no—
375C22×Q8—22no—
376C22×Q8—24no—
377C22×Q8—24no—
378C22×Q8—22no—
379C22×Q8C2×D411yescharacteristic
380C22×Q8C2411yescharacteristic
381C22×D4—21no—
382C22×D4—22no—
383C22×D4—22no—
384C22×D4—22no—
385C22×D4—21no—
386C22×D4—22no—
387C22×D4—22no—
388C22×D4—22no—
389C22×D4—28no—
390C22×D4C2×D412yes—
391C22×D4C2×D411yescharacteristic
392C22×D4C2412yes—
393C22×D4C2411yescharacteristic
394C22×D4C2414yes—
395C23×C4—21no—
396C23×C4—22no—
397C23×C4—21no—
398C23×C4—21no—
399C23×C4—21no—
400C23×C4—22no—
401C23×C4—24no—
402C23×C4—24no—
403C23×C4—84no—
404C23×C4C2×D411yescharacteristic
405C23×C4C2×D412yes—
406C23×C4C2×D411yescharacteristic
407C23×C4C2×D412yes—
408C23×C4C2412yes—
409C23×C4C2411yescharacteristic
410C2×M16—216no—
411C2×M16C2418yes—
412C2×M16C2418yes—
413C22×C8C2418yes—
414C4⋊Q8—28no—
415C4⋊Q8—28no—
416C4⋊Q8—28no—
417C4⋊Q8—216no—
418C4⋊Q8—216no—
419C4⋊Q8—24no—
420C4⋊Q8—22no—
421C4⋊Q8—22no—
422C4⋊Q8—22no—
423C4⋊Q8—22no—
424C4⋊Q8—24no—
425C4⋊Q8—24no—
426C4⋊Q8—24no—
427C4⋊Q8—24no—
428C4⋊Q8C2414yes—
429C4⋊Q8C2414yes—
430C4⋊Q8C2418yes—
431C4⋊Q8C2414yes—
432C4⋊Q8C2414yes—
433C4⋊Q8C2418yes—
434C4⋊Q8C2418yes—
435#127—28no—
436#127—24no—
437#127C2418yes—
438#126—216no—
439#126—28no—
440#126—28no—
441#125—28no—
442#125—28no—
443#125—28no—
444#125—216no—
445#125—216no—
446#125—24no—
447#125—24no—
448#125—24no—
449#125—28no—
450#125—28no—
451#125C2418yes—
452#125C2418yes—
453#125C2418yes—
454#125C24116yes—
455#124—28no—
456#124—216no—
457#124—28no—
458#124—28no—
459#124—24no—
460#124C2418yes—
461#123—28no—
462#123—28no—
463#123—216no—
464#123—216no—
465#123—216no—
466C22⋊Q8—28no—
467C22⋊Q8—24no—
468C22⋊Q8—24no—
469C22⋊Q8—24no—
470C22⋊Q8—28no—
471C22⋊Q8—24no—
472C22⋊Q8—28no—
473C22⋊Q8—24no—
474C22⋊Q8—24no—
475C22⋊Q8—24no—
476C22⋊Q8—24no—
477C22⋊Q8—28no—
478C22⋊Q8—28no—
479C22⋊Q8—28no—
480C22⋊Q8—28no—
481C22⋊Q8—24no—
482C22⋊Q8—216no—
483C22⋊Q8—216no—
484C22⋊Q8—216no—
485C22⋊Q8—216no—
486C22⋊Q8—216no—
487C22⋊Q8—216no—
488C22⋊Q8—216no—
489C22⋊Q8—216no—
490C22⋊Q8C2418yes—
491#121—216no—
492#121—28no—
493#121—28no—
494#121—28no—
495#121—24no—
496#121—24no—
497#121—24no—
498#121—28no—
499#121—28no—
500#121—216no—
501#121—216no—
502#121C2418yes—
503#121C2418yes—
504#121C2418yes—
505#120—216no—
506#120—216no—
507C4×Q8—28no—
508C4×Q8—28no—
509C4×Q8—24no—
510C4×Q8—24no—
511C4×Q8—24no—
512C4×Q8—24no—
513C4×Q8—28no—
514C4×Q8—28no—
515C4×Q8—24no—
516C4×Q8—24no—
517C4×Q8—24no—
518C4×Q8—24no—
519C4×Q8—28no—
520C4×Q8—28no—
521C4×Q8—28no—
522C4×Q8—28no—
523C4×Q8—21no—
524C4×Q8—21no—
525C4×Q8—22no—
526C4×Q8C2×D414yes—
527C4×Q8C2×D414yes—
528C4×Q8C2×D414yes—
529C4×Q8C2×D414yes—
530C4×Q8C2412yes—
531C4×Q8C2412yes—
532C4×Q8C2414yes—
533C4×D4—216no—
534C4×D4—216no—
535C4×D4—28no—
536C4×D4—28no—
537C4×D4—24no—
538C4×D4—24no—
539C4×D4—24no—
540C4×D4—24no—
541C4×D4—28no—
542C4×D4—28no—
543C4×D4—24no—
544C4×D4—24no—
545C4×D4—22no—
546C4×D4—22no—
547C4×D4—24no—
548C4×D4—24no—
549C4×D4—24no—
550C4×D4—28no—
551C4×D4—28no—
552C4×D4—21no—
553C4×D4—21no—
554C4×D4—22no—
555C4×D4C2×D418yes—
556C4×D4C2×D418yes—
557C4×D4C2×D414yes—
558C4×D4C2×D414yes—
559C4×D4C2×D418yes—
560C4×D4C2×D418yes—
561C4×D4C2×D414yes—
562C4×D4C2×D414yes—
563C4×D4C2414yes—
564C4×D4C2414yes—
565C4×D4C2418yes—
566C4×D4C2412yes—
567C4×D4C2412yes—
568C4×D4C2414yes—
569#117—28no—
570#117—24no—
571#117—22no—
572#117—28no—
573#117—24no—
574#117—24no—
575#117—24no—
576#117—28no—
577#117—28no—
578#117C2×D414yes—
579#117C2×D418yes—
580#117C2418yes—
581#117C2414yes—
582#117C2418yes—
583#117C24116yes—
584#117C2414yes—
585#117C2418yes—
586C2×C4⋊C4—21no—
587C2×C4⋊C4—22no—
588C2×C4⋊C4—21no—
589C2×C4⋊C4—21no—
590C2×C4⋊C4—22no—
591C2×C4⋊C4—22no—
592C2×C4⋊C4—22no—
593C2×C4⋊C4—22no—
594C2×C4⋊C4—24no—
595C2×C4⋊C4—24no—
596C2×C4⋊C4—28no—
597C2×C4⋊C4—28no—
598C2×C4⋊C4—22no—
599C2×C4⋊C4—22no—
600C2×C4⋊C4—24no—
601C2×C4⋊C4—24no—
602C2×C4⋊C4C2×D411yescharacteristic
603C2×C4⋊C4C2×D411yescharacteristic
604C2×C4⋊C4C2×D412yes—
605C2×C4⋊C4C2×D412yes—
606C2×C4⋊C4C2412yes—
607C2×C4⋊C4C2414yes—
608C2×C4⋊C4C2411yescharacteristic
609C2×C4⋊C4C2411yescharacteristic
610C2×C4⋊C4C2414yes—
611C2×C4⋊C4C2414yes—
612C2×C4⋊C4C2418yes—
613C2×C4⋊C4C2418yes—
614C2×C22⋊C4—21no—
615C2×C22⋊C4—28no—
616C2×C22⋊C4—24no—
617C2×C22⋊C4—22no—
618C2×C22⋊C4—22no—
619C2×C22⋊C4—22no—
620C2×C22⋊C4—24no—
621C2×C22⋊C4—24no—
622C2×C22⋊C4—21no—
623C2×C22⋊C4—21no—
624C2×C22⋊C4—22no—
625C2×C22⋊C4—22no—
626C2×C22⋊C4—22no—
627C2×C22⋊C4—22no—
628C2×C22⋊C4—22no—
629C2×C22⋊C4C2×D412yes—
630C2×C22⋊C4C2×D412yes—
631C2×C22⋊C4C2×D412yes—
632C2×C42—21no—
633C2×C42—21no—
634C2×C42—28no—
635C2×C42—24no—
636C2×C42—21no—
637C2×C42—24no—
638C2×C42—24no—
639C2×C42C2×D412yes—
640C2×C42C2×D411yescharacteristic
641C2×C42C2×D411yescharacteristic
642C2×C42C2×D412yes—
643C2×C42C2×D412yes—
644C2×C42C2×D412yes—
645C2×C42C2×D414yes—
646C2×C42C2×D414yes—
647C2×C42C2411yescharacteristic
648C2×C42C2412yes—
649C2×C42C2411yescharacteristic
650C2×C42C2412yes—
651C2×C42C2412yes—
652C2×C42C2414yes—
653C2×C42C2414yes—
654#107C24132yes—
655#107C24116yes—
656#107C24116yes—
657#106C24132yes—
658#106C24116yes—
659#106C24116yes—
660C4⋊C8C2418yes—
661C4⋊C8C2418yes—
662C4⋊C8C2418yes—
663C4⋊C8C2418yes—
664#103C24116yes—
665#103C24116yes—
666#102C24132yes—
667#102C24132yes—
668#102C24116yes—
669#102C24116yes—
670C22⋊C8C24116yes—
671C22⋊C8C24116yes—
672#97C24116yes—
673C4×C8C24116yes—
674C24—22no—
675C24—21no—
676C24—24no—
677C24—44no—
678C24—82no—
679C24—82no—
680C24C22×D412yes—
681C24C22×D411yescharacteristic
682#41—216no—
683#41—28no—
684#41—28no—
685#41—28no—
686#41—28no—
687#41—48no—
688#41—816no—
689#41—816no—
690C2×Q8—24no—
691C2×Q8—21no—
692C2×Q8—24no—
693C2×Q8—24no—
694C2×Q8—24no—
695C2×Q8—28no—
696C2×Q8—24no—
697C2×Q8—28no—
698C2×Q8—28no—
699C2×Q8—24no—
700C2×Q8—84no—
701C2×Q8—88no—
702C2×Q8—84no—
703C2×Q8—84no—
704C2×Q8—88no—
705C2×Q8C22×D414yes—
706C2×Q8C2512yes—
707C2×D4—28no—
708C2×D4—24no—
709C2×D4—28no—
710C2×D4—28no—
711C2×D4—28no—
712C2×D4—24no—
713C2×D4—22no—
714C2×D4—24no—
715C2×D4—21no—
716C2×D4—28no—
717C2×D4—28no—
718C2×D4—28no—
719C2×D4—28no—
720C2×D4—28no—
721C2×D4—24no—
722C2×D4—44no—
723C2×D4—44no—
724C2×D4—48no—
725C2×D4—84no—
726C2×D4—84no—
727C2×D4—84no—
728C2×D4—84no—
729C2×D4—84no—
730C2×D4C22×D418yes—
731C2×D4C22×D414yes—
732C2×D4C2514yes—
733C2×D4C2512yes—
734C22×C4—28no—
735C22×C4—21no—
736C22×C4—21no—
737C22×C4—21no—
738C22×C4—22no—
739C22×C4—28no—
740C22×C4—28no—
741C22×C4—24no—
742C22×C4—24no—
743C22×C4—24no—
744C22×C4—24no—
745C22×C4—22no—
746C22×C4—22no—
747C22×C4—24no—
748C22×C4—24no—
749C22×C4—24no—
750C22×C4—28no—
751C22×C4—42no—
752C22×C4—44no—
753C22×C4—48no—
754C22×C4—44no—
755C22×C4—44no—
756C22×C4—88no—
757C22×C4—81no—
758C22×C4—82no—
759C22×C4—88no—
760C22×C4—82no—
761C22×C4—84no—
762C22×C4—82no—
763C22×C4C22×D414yes—
764C22×C4C22×D411yescharacteristic
765C22×C4C22×D412yes—
766C22×C4C22×D412yes—
767C22×C4C22×D414yes—
768C22×C4C22×D411yescharacteristic
769C22×C4C22×D411yescharacteristic
770C22×C4C22×D412yes—
771C22×C4C22×D412yes—
772C22×C4C22×D412yes—
773C22×C4C22×D411yescharacteristic
774C22×C4C22×D412yes—
775C22×C4C22×D412yes—
776C22×C4C22×D414yes—
777C22×C4C22×D414yes—
778C22×C4C22×D414yes—
779C22×C4C22×D412yes—
780C22×C4C22×D411yescharacteristic
781C22×C42−1+418yes—
782C22×C4C2514yes—
783C22×C4C2511yescharacteristic
784C22×C4C2512yes—
785M16—216no—
786M16—216no—
787C2×C8—216no—
788C2×C8C25116yes—
789C4⋊C4—28no—
790C4⋊C4—28no—
791C4⋊C4—24no—
792C4⋊C4—24no—
793C4⋊C4—22no—
794C4⋊C4—24no—
795C4⋊C4—24no—
796C4⋊C4—22no—
797C4⋊C4—22no—
798C4⋊C4—28no—
799C4⋊C4—28no—
800C4⋊C4—28no—
801C4⋊C4—28no—
802C4⋊C4—24no—
803C4⋊C4—28no—
804C4⋊C4—24no—
805C4⋊C4—28no—
806C4⋊C4—28no—
807C4⋊C4—216no—
808C4⋊C4—28no—
809C4⋊C4—216no—
810C4⋊C4—21no—
811C4⋊C4—21no—
812C4⋊C4—28no—
813C4⋊C4—28no—
814C4⋊C4—24no—
815C4⋊C4—24no—
816C4⋊C4C22×D414yes—
817C4⋊C4C22×D414yes—
818C4⋊C4C22×D418yes—
819C4⋊C4C22×D418yes—
820C4⋊C4C2518yes—
821C4⋊C4C2518yes—
822C4⋊C4C2514yes—
823C4⋊C4C2512yes—
824C4⋊C4C2512yes—
825C22⋊C4—28no—
826C22⋊C4—24no—
827C22⋊C4—216no—
828C22⋊C4—28no—
829C22⋊C4—28no—
830C22⋊C4—28no—
831C22⋊C4—24no—
832C22⋊C4—24no—
833C22⋊C4—24no—
834C22⋊C4—22no—
835C22⋊C4—22no—
836C22⋊C4—28no—
837C22⋊C4—28no—
838C22⋊C4—28no—
839C22⋊C4—28no—
840C22⋊C4—28no—
841C22⋊C4C22×D418yes—
842C22⋊C4C22×D418yes—
843C22⋊C4C22×D418yes—
844C42—22no—
845C42—22no—
846C42—28no—
847C42—24no—
848C42—24no—
849C42—216no—
850C42—28no—
851C42C22×D412yes—
852C42C22×D412yes—
853C42C22×D411yescharacteristic
854C42C22×D411yescharacteristic
855C42C22×D414yes—
856C42C22×D412yes—
857C42C22×D414yes—
858C42C22×D412yes—
859C42C22×D412yes—
860C42C22×D414yes—
861C42C22×D414yes—
862C42C22×D414yes—
863C42C2514yes—
864C42C2511yescharacteristic
865C42C2511yescharacteristic
866C42C2512yes—
867C23—24no—
868C23—24no—
869C23—22no—
870C23—41no—
871C23—41no—
872C23—42no—
873C23—42no—
874C23—44no—
875C23—42no—
876C23—42no—
877C23—44no—
878C23—42no—
879C23—44no—
880C23—48no—
881C23—84no—
882C23—84no—
883C23—816no—
884C23#53614yes—
885C23C23×D414yes—
886C23C23×D411yescharacteristic
887C23C23×D412yes—
888Q8—28no—
889Q8—24no—
890Q8—48no—
891Q8—48no—
892Q8—42no—
893Q8—84no—
894Q8—88no—
895Q8—84no—
896Q8—88no—
897Q8—88no—
898D4—216no—
899D4—28no—
900D4—24no—
901D4—28no—
902D4—48no—
903D4—44no—
904D4—48no—
905D4—42no—
906D4—88no—
907D4—88no—
908D4—88no—
909D4—88no—
910D4—88no—
911C2×C4—24no—
912C2×C4—22no—
913C2×C4—24no—
914C2×C4—28no—
915C2×C4—28no—
916C2×C4—28no—
917C2×C4—22no—
918C2×C4—22no—
919C2×C4—22no—
920C2×C4—28no—
921C2×C4—28no—
922C2×C4—24no—
923C2×C4—42no—
924C2×C4—41no—
925C2×C4—42no—
926C2×C4—44no—
927C2×C4—41no—
928C2×C4—41no—
929C2×C4—42no—
930C2×C4—44no—
931C2×C4—42no—
932C2×C4—42no—
933C2×C4—44no—
934C2×C4—48no—
935C2×C4—44no—
936C2×C4—44no—
937C2×C4—42no—
938C2×C4—42no—
939C2×C4—42no—
940C2×C4—48no—
941C2×C4—44no—
942C2×C4—48no—
943C2×C4—84no—
944C2×C4—88no—
945C2×C4—84no—
946C2×C4—84no—
947C2×C4—88no—
948C2×C4—84no—
949C2×C4—88no—
950C2×C4#53614yes—
951C2×C4#53618yes—
952C2×C4C23×D414yes—
953C2×C4C23×D411yescharacteristic
954C2×C4C23×D412yes—
955C2×C4C23×D411yescharacteristic
956C2×C4C23×D411yescharacteristic
957C2×C4C23×D414yes—
958C2×C4C23×D412yes—
959C2×C4C23×D414yes—
960C2×C4C23×D411yescharacteristic
961C2×C4C23×D411yescharacteristic
962C2×C4C23×D412yes—
963C2×C4C2×2−1+414yes—
964C2×C4C2×2−1+414yes—
965C2×C4C2×2−1+414yes—
966C2×C4C2611yescharacteristic
967C8—216no—
968C22—21no—
969C22—22no—
970C22—21no—
971C22—22no—
972C22—24no—
973C22—24no—
974C22—24no—
975C22—44no—
976C22—44no—
977C22—42no—
978C22—42no—
979C22—44no—
980C22—42no—
981C22—44no—
982C22—84no—
983C22—84no—
984C22—88no—
985C22—816no—
986C22C2×#53612yes—
987C22C2×#53614yes—
988C22C24×D411yescharacteristic
989C4—21no—
990C4—22no—
991C4—24no—
992C4—21no—
993C4—21no—
994C4—22no—
995C4—24no—
996C4—24no—
997C4—44no—
998C4—42no—
999C4—48no—
1000C4—42no—
1001C4—48no—
1002C4—42no—
1003C4C2×#53612yes—
1004C4C2×#53614yes—
1005C4#358512yes—
1006C4C22×2−1+412yes—
1007C2—22no—
1008C2—24no—
1009C2—44no—
1010C2—82no—
1011C2—84no—
1012C2C22×#53611yescharacteristic
1013C2C2×#358511yescharacteristic
1014C2#6309011yescharacteristic
subgroupG/H
center, socleC22C24×D4
commutator, Frattini, cosocleC2×C4C26
prime radicalC2×#3460C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22 ◁ C2×C4×#41 ◁ G
LECSG ▷ C2×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #62813C2semidirect
3. #60892C2semidirect
4. #60890C2semidirect
5. #60888C2semidirect
6. #60870C2semidirect
7. #60868C2semidirect
8. #60866C2semidirect
9. #60864C2semidirect
10. #60664C2semidirect
11. #60619C2semidirect
12. #60520C2semidirect
13. #60518C2semidirect
14. #60484C2semidirect
15. C2×#3077C2semidirect
16. #60125C2semidirect
17. #3504C22semidirect
18. #3503C22semidirect
19. #3503C22semidirect
33. #3458C22semidirect
44. C2×#533C22semidirect
54. #3244C22semidirect
55. #3243C22semidirect
56. #3241C22semidirect
57. #3241C22semidirect
58. #3240C22semidirect
59. #3239C22semidirect
60. #3238C22semidirect
61. #3235C22semidirect
62. #3234C22semidirect
63. #3233C22semidirect
64. #3232C22semidirect
65. #3228C22semidirect
66. #3227C22semidirect
67. #3226C22semidirect
68. #3166C22semidirect
69. #3165C22semidirect
70. #3164C22semidirect
71. #3163C22semidirect
74. #3136C22semidirect
75. #3136C22semidirect
76. #3099C22semidirect
77. #3098C22semidirect
78. #3096C22semidirect
79. #3096C22semidirect
80. #3095C22semidirect
83. #3094C22semidirect
84. #3080C22semidirect
85. #3079C22semidirect
86. #3079C22semidirect
87. #3078C22semidirect
88. #3078C22semidirect
91. #3077C22semidirect
92. #3077C22semidirect
93. #3077C22semidirect
94. #3077C22semidirect
95. #3076C22semidirect
96. #3076C22semidirect
97. C2×#478C22semidirect
98. C2×#476C22semidirect
99. C2×#474C22semidirect
100. #2925C22semidirect
101. #2925C22semidirect
102. #2921C22semidirect
103. #2920C22semidirect
143. #544C23semidirect
144. #544C23semidirect
179. #533C23semidirect
180. #533C23semidirect
191. C2×C4⋊Q8C23semidirect
192. C2×C4⋊Q8C23semidirect
206. C2×#125C23semidirect
289. #501C23semidirect
290. #501C23semidirect
291. #501C23semidirect
292. #500C23semidirect
293. #499C23semidirect
294. #498C23semidirect
301. #485C23semidirect
302. #484C23semidirect
303. #483C23semidirect
306. #482C23semidirect
309. #481C23semidirect
312. #480C23semidirect
313. #479C23semidirect
314. #479C23semidirect
317. #478C23semidirect
318. #478C23semidirect
319. #477C23semidirect
320. #477C23semidirect
323. #476C23semidirect
324. #476C23semidirect
325. #475C23semidirect
326. #475C23semidirect
329. #474C23semidirect
330. #474C23semidirect
331. #433C23semidirect
332. #432C23semidirect
333. #432C23semidirect
334. #431C23semidirect
335. #431C23semidirect

Maximal subgroups

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

subgroupindex
#628132
C2×#34602
#608922
#608902
#608882
#608702
#608682
#608662
#608642
#606642
#606192
#605202
#605182
#604842
C2×#30772
#601252