Finite Group Databasebeta

← #10576381

Subgroups — #10576381

Order 512.

7616 conjugacy classes of subgroups.

The subgroup lattice has 1452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#62814C211yesmaximal, characteristic, complemented
2C2×#3487C211yesmaximal, characteristic, complemented
3#61190C218yesmaximal, complemented
4#61189C218yesmaximal, complemented
5#61178C218yesmaximal, complemented
6#61170C218yesmaximal, complemented
7#61160C218yesmaximal, complemented
8#61158C218yesmaximal, complemented
9#60619C211yesmaximal, characteristic, complemented
10#60518C211yesmaximal, characteristic, complemented
11#60511C211yesmaximal, characteristic, complemented
12#60491C211yesmaximal, characteristic, complemented
13#60454C211yesmaximal, characteristic, complemented
14#60444C211yesmaximal, characteristic, complemented
15#60426C211yesmaximal, characteristic, complemented
16#60368C211yesmaximal, characteristic, complemented
17C2×#3005C211yesmaximal, characteristic, complemented
18#60169C211yesmaximal, characteristic, complemented
19#60141C211yesmaximal, characteristic, complemented
20#60088C211yesmaximal, characteristic, complemented
21C2×#2896C211yesmaximal, characteristic, complemented
22C22×2−1+4C2211yescharacteristic
23C23×#41C2211yescharacteristic
24C2×#575C2211yescharacteristic
25C22×#137C2211yescharacteristic
26C22×AGL(1,ℤ/8)C2211yescharacteristic
27C2×#568C2211yescharacteristic
28C23×M16C2211yescharacteristic
29#3495—22no—
30#3495C2214yescomplemented
31#3494—22no—
32#3494C2214yescomplemented
33#3493C2214yescomplemented
34#3492C2214yescomplemented
35#3491—22no—
36#3490—22no—
37#3487—24no—
38#3487—22no—
39#3487—22no—
40#3487C2218yes—
41#3487C2214yescomplemented
42#3487C2214yescomplemented
43#3475—24no—
44#3475C2218yescomplemented
45C2×#550—22no—
46C2×#550C2214yescomplemented
47C2×#548—22no—
48C2×#548C2214yescomplemented
49#3458C2211yescharacteristic
50#3455—22no—
51#3449C2211yescharacteristic
52C2×#535—22no—
53C2×#535C2211yescharacteristic
54C2×#535C2211yescharacteristic
55#3444—22no—
56C2×#525—22no—
57C2×#525C2211yescharacteristic
58C2×#525C2211yescharacteristic
59C2×#525C2211yescharacteristic
60#3428C2211yescharacteristic
61#3428C2211yescharacteristic
62C2×#519C2211yescharacteristic
63C22×#117C2211yescharacteristic
64#3333C22116yescomplemented
65#3332C22116yescomplemented
66#3327C22116yescomplemented
67#3326C22116yescomplemented
68#3321C22116yescomplemented
69#3317C22116yescomplemented
70#3317C22116yescomplemented
71#3316C22116yescomplemented
72#3313C22116yescomplemented
73#3309C22116yescomplemented
74#3309C22116yescomplemented
75#3308C22116yescomplemented
76#3305C22116yescomplemented
77#3304C22116yescomplemented
78#3301C22116yescomplemented
79#3300C22116yescomplemented
80#3140C2214yescomplemented
81#3138C2214yescomplemented
82#3136C2218yescomplemented
83#3136C2218yescomplemented
84#3096C2218yescomplemented
85#3096C2218yescomplemented
86#3095C2214yescomplemented
87#3094C2214yescomplemented
88#3094C2218yescomplemented
89#3093C2214yescomplemented
90#3092C2214yescomplemented
91#3091C2218yescomplemented
92#3082C2218yescomplemented
93#3082C2218yescomplemented
94#3078C2218yescomplemented
95#3062C2218yescomplemented
96#3058C2214yescomplemented
97#3057C2214yescomplemented
98#3056C2214yescomplemented
99#3056C2214yescomplemented
100#3055C2214yescomplemented
101#3055C2214yescomplemented
102#3055C2218yescomplemented
103#3054C2214yescomplemented
104#3050C2214yescomplemented
105#3045C2218yescomplemented
106#3043C2214yescomplemented
107#3041C2214yescomplemented
108#3040C2214yescomplemented
109#3038C2214yescomplemented
110#3013C2218yescomplemented
111#3011C2214yescomplemented
112#3010C2214yescomplemented
113#3005C2218yes—
114#3005C2214yescomplemented
115#3005C2214yescomplemented
116#3005C2214yescomplemented
117#3004C2214yescomplemented
118C2×#452C2214yescomplemented
119C2×#449C2214yescomplemented
120#2950C2214yescomplemented
121#2949C2214yescomplemented
122#2947C2218yescomplemented
123C4×#137C2218yescomplemented
124D4×M16C2218yescomplemented
125#2933C2218yescomplemented
126#2930C2214yescomplemented
127#2929C2214yescomplemented
128#2911C2211yescharacteristic
129#2911C2211yescharacteristic
130#2911C2211yescharacteristic
131#2905C2211yescharacteristic
132#2898C2218yescomplemented
133#2898C2218yescomplemented
134#2896C2211yescharacteristic
135#2896C2211yescharacteristic
136#2896C2211yescharacteristic
137#2896C2211yescharacteristic
138#2896C2218yescomplemented
139#2896C2218yescomplemented
140#2896C2214yescomplemented
141C2×#417C2214yescomplemented
142C2×#419C2211yescharacteristic
143C2×#419C2211yescharacteristic
144C2×#419C2211yescharacteristic
145C2×#419C2214yescomplemented
146C2×#418C2211yescharacteristic
147C2×#418C2211yescharacteristic
148C2×#418C2211yescharacteristic
149C2×#416C2214yescomplemented
150#2879C2211yescharacteristic
151C2×#407C2211yescharacteristic
152#2873C2211yescharacteristic
153C2×2−1+4—22no—
154C2×2−1+4—22no—
155C2×2−1+4—28no—
156C2×2−1+4—44no—
157C2×2−1+4C2314yes—
158C2×2−1+4C2314yes—
159C22×#41—22no—
160C22×#41—21no—
161C22×#41—22no—
162C22×#41—22no—
163C22×#41—21no—
164C22×#41—21no—
165C22×#41—28no—
166C22×#41—44no—
167C22×#41C2311yescharacteristic
168C22×#41C2311yescharacteristic
169C22×#41C2312yes—
170C22×#41C2312yes—
171C22×#41C2314yes—
172C22×#41C2314yes—
173C22×#41C2312yes—
174C22×#41C2311yescharacteristic
175C23×Q8—21no—
176C23×Q8C2312yes—
177C23×Q8C2311yescharacteristic
178C23×D4—21no—
179C23×D4C2311yescharacteristic
180C24×C4—21no—
181C24×C4C2311yescharacteristic
182#575—44no—
183C2×#137—28no—
184C2×#137C2314yes—
185C2×#137C2314yes—
186C2×#137C2312yes—
187C2×#137C2312yes—
188C2×AGL(1,ℤ/8)—44no—
189C2×AGL(1,ℤ/8)C2314yes—
190C2×AGL(1,ℤ/8)C2312yes—
191C2×AGL(1,ℤ/8)C2314yes—
192C2×AGL(1,ℤ/8)C2312yes—
193C2×#135C2314yes—
194C22×Q16C2312yes—
195C22×SD16C2312yes—
196C22×SD16C2312yes—
197C22×D8C2312yes—
198#568—44no—
199C2×#131C2314yes—
200C2×#131C2314yes—
201C22×M16—44no—
202C22×M16C2311yescharacteristic
203C22×M16C2311yescharacteristic
204C22×M16C2311yescharacteristic
205C22×M16C2311yescharacteristic
206C22×M16C2314yes—
207C22×M16C2312yes—
208C22×M16C2314yes—
209C22×M16C2314yes—
210C23×C8C2312yes—
211#556—24no—
212#556C2318yescomplemented
213#555—24no—
214#555C2318yescomplemented
215#554—24no—
216#554C2318yescomplemented
217#553—24no—
218#553—24no—
219#553C2318yescomplemented
220#553C2318yescomplemented
221#552—28no—
222#552—24no—
223#552—24no—
224#552—28no—
225#552C2318yescomplemented
226#552C2318yescomplemented
227#551—28no—
228#551—28no—
229#551—28no—
230#551—28no—
231#550—28no—
232#550—28no—
233#550—28no—
234#550—28no—
235#550—28no—
236#550—28no—
237#550C23116yes—
238#550C23116yes—
239#548—28no—
240#548—28no—
241#548—28no—
242#548—28no—
243#548—28no—
244#548—28no—
245#548C23116yes—
246#548C23116yes—
247#547—24no—
248#547C2318yescomplemented
249#546—28no—
250#546—28no—
251#544—22no—
252#544C2314yes—
253#544C2314yes—
254#543—22no—
255#542—24no—
256#542—24no—
257#541—24no—
258#540—24no—
259#539—28no—
260#538—28no—
261#537C2314yes—
262#536—21no—
263#536C2312yes—
264#535—22no—
265#535—22no—
266#535—21no—
267#535—216no—
268#535—28no—
269#535—28no—
270#535—22no—
271#535—22no—
272#535C2314yes—
273#535C2314yes—
274#535C2314yes—
275#535C2314yes—
276#535C2312yes—
277#534—22no—
278#533—24no—
279#533—22no—
280#533—22no—
281#533C2314yes—
282#532—22no—
283#532—24no—
284C2×#127—24no—
285C2×#127—21no—
286C2×#127C2312yes—
287#529—28no—
288#529—24no—
289#529—24no—
290#529—28no—
291#529—28no—
292#529—28no—
293C2×#124—21no—
294C2×#124—24no—
295C2×#124C2312yes—
296#525—22no—
297#525—21no—
298#525—21no—
299#525—22no—
300#525—21no—
301#525—21no—
302#525—22no—
303#525—216no—
304#525—28no—
305#525—28no—
306#525—28no—
307#525D412yes—
308#525D412yes—
309#525D414yes—
310#525C2314yes—
311#525C2312yes—
312#525C2312yes—
313#525C2314yes—
314#525C2312yes—
315#525C2312yes—
316#525C2314yes—
317#525C2312yes—
318#525C2312yes—
319#525C2314yes—
320C2×#123—21no—
321C2×#123—21no—
322C2×#123D412yes—
323C2×C22⋊Q8—24no—
324C2×C22⋊Q8D412yes—
325C2×C22⋊Q8C2312yes—
326C2×C22⋊Q8C2312yes—
327C2×#121—24no—
328C2×#121—22no—
329C2×#121—24no—
330C2×#121—24no—
331C2×#121D412yes—
332C2×#121C2312yes—
333C2×#121C2314yes—
334C2×#121C2312yes—
335C2×#120—21no—
336C2×#120—21no—
337C2×#120—22no—
338C2×#120—22no—
339C2×#120D412yes—
340#520—22no—
341#520C2314yes—
342#520C2314yes—
343#520C2314yes—
344#519—21no—
345#519—22no—
346#519—22no—
347#519C2314yes—
348#519C2314yes—
349#519C2312yes—
350#518—22no—
351#518—21no—
352#518—22no—
353#518C2312yes—
354C4×#41—22no—
355C4×#41—22no—
356C4×#41—28no—
357C4×#41—22no—
358C4×#41C2314yes—
359C2×C4×Q8—22no—
360C2×C4×Q8C2314yes—
361C2×C4×D4—22no—
362C2×C4×D4—22no—
363C2×C4×D4—24no—
364C2×C4×D4—24no—
365C2×C4×D4C2314yes—
366C2×#117—21no—
367C2×#117—22no—
368C2×#117—21no—
369C2×#117—22no—
370C2×#117—22no—
371C2×#117—22no—
372C2×#117C2314yes—
373C2×#117C2312yes—
374C2×#117C2314yes—
375C2×#117C2314yes—
376C2×#117C2311yescharacteristic
377C2×#117C2311yescharacteristic
378C2×#117C2311yescharacteristic
379C2×#117C2311yescharacteristic
380C2×#117C2311yescharacteristic
381C22×C4⋊C4C2312yes—
382C22×C22⋊C4—21no—
383C22×C42—21no—
384#490C23116yescomplemented
385#489C23116yescomplemented
386#488C23116yescomplemented
387#486C23116yescomplemented
388#485C2318yescomplemented
389#485C2318yescomplemented
390#484C2318yescomplemented
391#483C2318yescomplemented
392#482C2318yescomplemented
393#482C2318yescomplemented
394#482C23116yescomplemented
395#482C23116yescomplemented
396#481C2318yescomplemented
397#481C23116yescomplemented
398#480C2318yescomplemented
399#480C23116yescomplemented
400#479C23116yescomplemented
401#479C23116yescomplemented
402#477C23116yescomplemented
403#475C23116yescomplemented
404#470C2318yescomplemented
405#469C2318yescomplemented
406#469C23116yescomplemented
407#468C2318yescomplemented
408#468C23116yescomplemented
409#468C2318yescomplemented
410#467C2318yescomplemented
411#466C23116yescomplemented
412#466C2318yescomplemented
413#465C23116yescomplemented
414#465C2318yescomplemented
415#465C2318yescomplemented
416#464C23116yescomplemented
417#463C23116yescomplemented
418#460C23116yescomplemented
419#459C23116yescomplemented
420#452C23116yes—
421#452C23116yes—
422#452C23116yescomplemented
423#451C23116yescomplemented
424#449C23116yes—
425#449C23116yes—
426#449C23116yescomplemented
427#448C23116yescomplemented
428#441C23116yescomplemented
429#440C23116yescomplemented
430C4×Q16C23116yescomplemented
431C4×SD16C23116yescomplemented
432#436C23116yescomplemented
433#435C23116yescomplemented
434#435C23116yescomplemented
435C8×D4C23116yescomplemented
436#428C2314yes—
437#428C2314yes—
438#428C2314yes—
439#428C2314yes—
440#428C2314yes—
441#428C2314yes—
442#427C2314yes—
443#427C2314yes—
444#427C2314yes—
445#424C2314yes—
446#424C2314yes—
447#423C2314yes—
448#419C2314yes—
449#419C2314yes—
450#419C2314yes—
451#419C2314yes—
452#419C2312yes—
453#419C2312yes—
454#419C2312yes—
455#419C2314yes—
456#419C2314yes—
457#419C2312yes—
458#419C23116yescomplemented
459#418C2312yes—
460#418C2314yes—
461#418C2314yes—
462#418C2312yes—
463#418C2314yes—
464#418C2314yes—
465#418C2314yes—
466#418C2312yes—
467#418C2314yes—
468#418C2312yes—
469#417C23116yes—
470#417C23116yes—
471#417C2314yes—
472#417C2314yes—
473#417C2314yes—
474#417C2314yes—
475#417C23116yescomplemented
476#416C2314yes—
477#416C2314yes—
478#416C2314yes—
479#416C23116yes—
480#416C23116yes—
481#416C2314yes—
482#416C23116yescomplemented
483C2×#103C2314yes—
484C2×#103C2314yes—
485C2×#103C2314yes—
486C2×#103C23116yescomplemented
487C2×#102C2314yes—
488C2×#102C2314yes—
489C2×#102C2314yes—
490#408C2314yes—
491#408C2314yes—
492#407C2312yes—
493#407C2312yes—
494#407C2314yes—
495#407C2314yes—
496C2×C22⋊C8C2314yes—
497#405C2314yes—
498#405C2314yes—
499C4×M16C2314yes—
500C25—21no—
501C25C2×D411yescharacteristic
5022−1+4—216no—
5032−1+4—216no—
5042−1+4—48no—
5052−1+4—48no—
5062−1+4—416no—
5072−1+4—416no—
508C2×#41—28no—
509C2×#41—28no—
510C2×#41—24no—
511C2×#41—24no—
512C2×#41—28no—
513C2×#41—21no—
514C2×#41—21no—
515C2×#41—21no—
516C2×#41—21no—
517C2×#41—24no—
518C2×#41—24no—
519C2×#41—24no—
520C2×#41—24no—
521C2×#41—24no—
522C2×#41—24no—
523C2×#41—24no—
524C2×#41—24no—
525C2×#41—24no—
526C2×#41—216no—
527C2×#41—216no—
528C2×#41—28no—
529C2×#41—28no—
530C2×#41—28no—
531C2×#41—24no—
532C2×#41—24no—
533C2×#41—24no—
534C2×#41—24no—
535C2×#41—44no—
536C2×#41—48no—
537C2×#41—48no—
538C2×#41—44no—
539C2×#41—44no—
540C2×#41—416no—
541C2×#41—416no—
542C2×#41—416no—
543C2×#41—48no—
544C2×#41—48no—
545C2×#41—48no—
546C2×#41C2×D412yes—
547C2×#41C2×D412yes—
548C2×#41C2412yes—
549C2×#41C2412yes—
550C2×#41C2412yes—
551C2×#41C2412yes—
552C2×#41C2418yes—
553C2×#41C2418yes—
554C2×#41C2418yes—
555C2×#41C2412yes—
556C2×#41C2412yes—
557C22×Q8—24no—
558C22×Q8—24no—
559C22×Q8—21no—
560C22×Q8—21no—
561C22×Q8—21no—
562C22×Q8—22no—
563C22×Q8—24no—
564C22×Q8—24no—
565C22×Q8—28no—
566C22×Q8—44no—
567C22×Q8—48no—
568C22×Q8C2×D411yescharacteristic
569C22×Q8#4118yescomplemented
570C22×Q8C2411yescharacteristic
571C22×Q8C2411yescharacteristic
572C22×Q8C2418yes—
573C22×Q8C2412yes—
574C22×Q8C2412yes—
575C22×Q8C2412yes—
576C22×D4—21no—
577C22×D4—21no—
578C22×D4—24no—
579C22×D4—22no—
580C22×D4—24no—
581C22×D4—22no—
582C22×D4—22no—
583C22×D4—24no—
584C22×D4—22no—
585C22×D4—22no—
586C22×D4—21no—
587C22×D4—21no—
588C22×D4—21no—
589C22×D4—24no—
590C22×D4—24no—
591C22×D4—24no—
592C22×D4—48no—
593C22×D4C2×D412yes—
594C22×D4C2×D411yescharacteristic
595C22×D4C2×D414yes—
596C22×D4C2411yescharacteristic
597C22×D4C2412yes—
598C22×D4C2411yescharacteristic
599C22×D4C2412yes—
600C22×D4C2412yes—
601C23×C4—21no—
602C23×C4—24no—
603C23×C4—24no—
604C23×C4—22no—
605C23×C4—22no—
606C23×C4—21no—
607C23×C4—22no—
608C23×C4—21no—
609C23×C4—24no—
610C23×C4—22no—
611C23×C4—24no—
612C23×C4—22no—
613C23×C4—48no—
614C23×C4C2×D412yes—
615C23×C4C2×D412yes—
616C23×C4C2×D411yescharacteristic
617C23×C4C2×D411yescharacteristic
618C23×C4C2×D411yescharacteristic
619C23×C4C2411yescharacteristic
620C23×C4C2412yes—
621C23×C4C2412yes—
622C23×C4C2412yes—
623C23×C4C2411yescharacteristic
624C23×C4C2411yescharacteristic
625#137—216no—
626#137—216no—
627#137—44no—
628#137—44no—
629AGL(1,ℤ/8)—48no—
630AGL(1,ℤ/8)—48no—
631AGL(1,ℤ/8)—44no—
632AGL(1,ℤ/8)—44no—
633#135—48no—
634C2×Q16—28no—
635C2×Q16C2418yes—
636C2×Q16C2414yes—
637C2×SD16—28no—
638C2×SD16—44no—
639C2×SD16C2418yes—
640C2×SD16C2418yes—
641C2×SD16C2414yes—
642C2×SD16C2414yes—
643C2×D8—44no—
644C2×D8C2418yes—
645C2×D8C2414yes—
646#131—48no—
647#131—48no—
648C2×M16—24no—
649C2×M16—24no—
650C2×M16—24no—
651C2×M16—24no—
652C2×M16—44no—
653C2×M16—48no—
654C2×M16—48no—
655C2×M16—48no—
656C2×M16C2412yes—
657C2×M16C2412yes—
658C2×M16C2412yes—
659C2×M16C2412yes—
660C2×M16C2412yes—
661C2×M16C2412yes—
662C2×M16C2412yes—
663C2×M16C2412yes—
664C2×M16C2418yes—
665C2×M16C2418yes—
666C22×C8—44no—
667C22×C8C2412yes—
668C22×C8C2412yes—
669C22×C8C2412yes—
670C22×C8C2412yes—
671C22×C8C2418yes—
672C22×C8C2418yes—
673C4⋊Q8—22no—
674C4⋊Q8—24no—
675C4⋊Q8—24no—
676C4⋊Q8C2418yes—
677#127—216no—
678#127—216no—
679#127—24no—
680#127—24no—
681#127—22no—
682#127—24no—
683#127C2418yes—
684#126—28no—
685#126—28no—
686#126—28no—
687#126—28no—
688#126—28no—
689#126—28no—
690#125—24no—
691#125—28no—
692#125—28no—
693#125—28no—
694#125—24no—
695#125C2418yes—
696#124—24no—
697#124—24no—
698#124—22no—
699#124—22no—
700#124—28no—
701#124—216no—
702#124—216no—
703#124—28no—
704#124—28no—
705#124—24no—
706#124C2418yes—
707#123—28no—
708#123—24no—
709#123—28no—
710#123—22no—
711#123—24no—
712#123—22no—
713#123—22no—
714#123—22no—
715#123—24no—
716#123—24no—
717#123—28no—
718#123—28no—
719#123—28no—
720#123—28no—
721#123C2×D414yes—
722#123C2×D414yes—
723#123C2×D418yes—
724C22⋊Q8—24no—
725C22⋊Q8—22no—
726C22⋊Q8—22no—
727C22⋊Q8—22no—
728C22⋊Q8—22no—
729C22⋊Q8—28no—
730C22⋊Q8—216no—
731C22⋊Q8—216no—
732C22⋊Q8—28no—
733C22⋊Q8—28no—
734C22⋊Q8—28no—
735C22⋊Q8—28no—
736C22⋊Q8—28no—
737C22⋊Q8C2×D414yes—
738C22⋊Q8C2×D414yes—
739C22⋊Q8C2×D414yes—
740C22⋊Q8C2×D414yes—
741C22⋊Q8C2414yes—
742C22⋊Q8C2414yes—
743C22⋊Q8C2414yes—
744C22⋊Q8C2414yes—
745C22⋊Q8C2418yes—
746#121—216no—
747#121—216no—
748#121—28no—
749#121—28no—
750#121—24no—
751#121—28no—
752#121—28no—
753#121—22no—
754#121—22no—
755#121—22no—
756#121—22no—
757#121—28no—
758#121—28no—
759#121—28no—
760#121—216no—
761#121—216no—
762#121—216no—
763#121—216no—
764#121C2×D414yes—
765#121C2×D414yes—
766#121C2×D414yes—
767#121C2×D414yes—
768#121C2414yes—
769#121C2414yes—
770#121C2414yes—
771#121C2414yes—
772#121C24116yes—
773#121C2418yes—
774#120—22no—
775#120—24no—
776#120—22no—
777#120—22no—
778#120—22no—
779#120—24no—
780#120—24no—
781#120—28no—
782#120—28no—
783#120—24no—
784#120—28no—
785#120—28no—
786#120C2×D414yes—
787#120C2×D414yes—
788#120C2×D418yes—
789C4×Q8—24no—
790C4×Q8—24no—
791C4×Q8—28no—
792C4×Q8—28no—
793C4×Q8—24no—
794C4×Q8—28no—
795C4×Q8—28no—
796C4×Q8—28no—
797C4×Q8C24116yes—
798C4×Q8C2418yes—
799C4×D4—28no—
800C4×D4—24no—
801C4×D4—28no—
802C4×D4—24no—
803C4×D4—28no—
804C4×D4—24no—
805C4×D4—24no—
806C4×D4—24no—
807C4×D4—24no—
808C4×D4—24no—
809C4×D4—24no—
810C4×D4—24no—
811C4×D4—24no—
812C4×D4—28no—
813C4×D4—28no—
814C4×D4—216no—
815C4×D4—216no—
816C4×D4—24no—
817C4×D4—216no—
818C4×D4—216no—
819C4×D4—28no—
820C4×D4—28no—
821C4×D4—28no—
822C4×D4C2×D418yes—
823C4×D4C2×D418yes—
824C4×D4C2418yes—
825C4×D4C2418yes—
826C4×D4C2418yes—
827#117—21no—
828#117—21no—
829#117—21no—
830#117—24no—
831#117—21no—
832#117—24no—
833#117—24no—
834#117—24no—
835#117—22no—
836#117—22no—
837#117—21no—
838#117—24no—
839#117—21no—
840#117—24no—
841#117—21no—
842#117—21no—
843#117—24no—
844#117—28no—
845#117—24no—
846#117—28no—
847#117—28no—
848#117—28no—
849#117—28no—
850#117—24no—
851#117C2×D412yes—
852#117C2×D412yes—
853#117C2412yes—
854#117C2412yes—
855#117C2412yes—
856#117C2412yes—
857#117C2412yes—
858#117C2414yes—
859#117C2414yes—
860#117C2412yes—
861#117C2412yes—
862#117C2412yes—
863#117C2418yes—
864#117C2412yes—
865#117C2412yes—
866C2×C4⋊C4—22no—
867C2×C4⋊C4—22no—
868C2×C4⋊C4—22no—
869C2×C4⋊C4—24no—
870C2×C4⋊C4—22no—
871C2×C4⋊C4—22no—
872C2×C4⋊C4—24no—
873C2×C4⋊C4C2×D412yes—
874C2×C4⋊C4C2×D414yes—
875C2×C4⋊C4C2412yes—
876C2×C4⋊C4C2412yes—
877C2×C4⋊C4C2414yes—
878C2×C4⋊C4C2414yes—
879C2×C4⋊C4C2412yes—
880C2×C4⋊C4C2412yes—
881C2×C4⋊C4C2418yes—
882C2×C22⋊C4—21no—
883C2×C22⋊C4—21no—
884C2×C22⋊C4—22no—
885C2×C22⋊C4—24no—
886C2×C22⋊C4—24no—
887C2×C22⋊C4—21no—
888C2×C22⋊C4—21no—
889C2×C22⋊C4—24no—
890C2×C22⋊C4—22no—
891C2×C22⋊C4—22no—
892C2×C22⋊C4—22no—
893C2×C22⋊C4—24no—
894C2×C22⋊C4—24no—
895C2×C22⋊C4—22no—
896C2×C22⋊C4—24no—
897C2×C22⋊C4C2×D412yes—
898C2×C22⋊C4C2×D414yes—
899C2×C22⋊C4C2×D414yes—
900C2×C42—21no—
901C2×C42—24no—
902C2×C42—22no—
903C2×C42—24no—
904C2×C42—21no—
905C2×C42—24no—
906C2×C42—21no—
907C2×C42—21no—
908C2×C42—24no—
909C2×C42—24no—
910C2×C42C2412yes—
911#107C2418yes—
912#107C2418yes—
913#107C2418yes—
914#106C2418yes—
915#106C2418yes—
916#106C2418yes—
917C4⋊C8C24116yes—
918#103C24116yes—
919#103C24116yes—
920#103C24116yes—
921#103C2418yes—
922#103C2418yes—
923#103C2418yes—
924#103C2418yes—
925#102C24116yes—
926#102C24116yes—
927#102C24116yes—
928#102C2418yes—
929#102C2418yes—
930#102C2418yes—
931#102C2418yes—
932C22⋊C8C2418yes—
933C22⋊C8C2418yes—
934C22⋊C8C24116yes—
935#97C2418yes—
936C4×C8C2418yes—
937C24—24no—
938C24—22no—
939C24—21no—
940C24—21no—
941C24—22no—
942C24—22no—
943C24—44no—
944C24—82no—
945C24—84no—
946C24C22×D412yes—
947C24C22×D412yes—
948C24C22×D412yes—
949C24C22×D411yescharacteristic
950C24C22×D411yescharacteristic
951C24C22×D411yescharacteristic
952#41—28no—
953#41—28no—
954#41—24no—
955#41—24no—
956#41—24no—
957#41—24no—
958#41—216no—
959#41—216no—
960#41—216no—
961#41—24no—
962#41—24no—
963#41—24no—
964#41—24no—
965#41—24no—
966#41—24no—
967#41—24no—
968#41—24no—
969#41—48no—
970#41—48no—
971#41—48no—
972#41—432no—
973#41—432no—
974#41—416no—
975#41—416no—
976#41—416no—
977#41—416no—
978#41—416no—
979#41—416no—
980#41—416no—
981#41—416no—
982#41—416no—
983#41—44no—
984#41—44no—
985#41—44no—
986#41—44no—
987#41—816no—
988C2×Q8—28no—
989C2×Q8—28no—
990C2×Q8—28no—
991C2×Q8—24no—
992C2×Q8—22no—
993C2×Q8—22no—
994C2×Q8—22no—
995C2×Q8—21no—
996C2×Q8—28no—
997C2×Q8—21no—
998C2×Q8—28no—
999C2×Q8—24no—
1000C2×Q8—24no—
1001C2×Q8—24no—
1002C2×Q8—216no—
1003C2×Q8—22no—
1004C2×Q8—22no—
1005C2×Q8—22no—
1006C2×Q8—22no—
1007C2×Q8—48no—
1008C2×Q8—48no—
1009C2×Q8—416no—
1010C2×Q8—416no—
1011C2×Q8—416no—
1012C2×Q8C22×D412yes—
1013C2×Q8C22×D412yes—
1014C2×Q8C2×#4118yes—
1015C2×Q8C2×#4118yes—
1016C2×Q8C2×#4118yes—
1017C2×Q8C2512yes—
1018C2×Q8C2512yes—
1019C2×Q8C2514yes—
1020C2×D4—28no—
1021C2×D4—22no—
1022C2×D4—22no—
1023C2×D4—24no—
1024C2×D4—22no—
1025C2×D4—22no—
1026C2×D4—28no—
1027C2×D4—28no—
1028C2×D4—28no—
1029C2×D4—24no—
1030C2×D4—28no—
1031C2×D4—216no—
1032C2×D4—24no—
1033C2×D4—24no—
1034C2×D4—24no—
1035C2×D4—21no—
1036C2×D4—22no—
1037C2×D4—22no—
1038C2×D4—22no—
1039C2×D4—21no—
1040C2×D4—216no—
1041C2×D4—22no—
1042C2×D4—24no—
1043C2×D4—24no—
1044C2×D4—24no—
1045C2×D4—22no—
1046C2×D4—22no—
1047C2×D4—24no—
1048C2×D4—24no—
1049C2×D4—24no—
1050C2×D4—22no—
1051C2×D4—416no—
1052C2×D4—48no—
1053C2×D4—48no—
1054C2×D4—416no—
1055C2×D4—48no—
1056C2×D4—44no—
1057C2×D4—44no—
1058C2×D4—44no—
1059C2×D4—44no—
1060C2×D4—44no—
1061C2×D4—84no—
1062C2×D4—88no—
1063C2×D4—88no—
1064C2×D4—84no—
1065C2×D4—84no—
1066C2×D4C22×D414yes—
1067C2×D4C22×D414yes—
1068C2×D4C22×D412yes—
1069C2×D4C22×D412yes—
1070C2×D4C22×D418yes—
1071C2×D4C22×D418yes—
1072C2×D4C2514yes—
1073C2×D4C2512yes—
1074C2×D4C2512yes—
1075C22×C4—24no—
1076C22×C4—28no—
1077C22×C4—22no—
1078C22×C4—22no—
1079C22×C4—22no—
1080C22×C4—28no—
1081C22×C4—28no—
1082C22×C4—24no—
1083C22×C4—24no—
1084C22×C4—24no—
1085C22×C4—24no—
1086C22×C4—22no—
1087C22×C4—22no—
1088C22×C4—24no—
1089C22×C4—22no—
1090C22×C4—24no—
1091C22×C4—24no—
1092C22×C4—22no—
1093C22×C4—24no—
1094C22×C4—22no—
1095C22×C4—24no—
1096C22×C4—21no—
1097C22×C4—21no—
1098C22×C4—28no—
1099C22×C4—22no—
1100C22×C4—24no—
1101C22×C4—22no—
1102C22×C4—22no—
1103C22×C4—28no—
1104C22×C4—22no—
1105C22×C4—22no—
1106C22×C4—28no—
1107C22×C4—22no—
1108C22×C4—22no—
1109C22×C4—28no—
1110C22×C4—28no—
1111C22×C4—28no—
1112C22×C4—416no—
1113C22×C4—416no—
1114C22×C4—48no—
1115C22×C4—48no—
1116C22×C4—48no—
1117C22×C4—48no—
1118C22×C4—44no—
1119C22×C4—44no—
1120C22×C4—84no—
1121C22×C4C22×D412yes—
1122C22×C4C22×D412yes—
1123C22×C4C22×D411yescharacteristic
1124C22×C4C22×D414yes—
1125C22×C4C22×D412yes—
1126C22×C4C22×D412yes—
1127C22×C4C22×D412yes—
1128C22×C4C22×D412yes—
1129C22×C4C22×D411yescharacteristic
1130C22×C4C22×D412yes—
1131C22×C4C22×D412yes—
1132C22×C4C22×D412yes—
1133C22×C4C22×D414yes—
1134C22×C4C22×D411yescharacteristic
1135C22×C4C22×D411yescharacteristic
1136C22×C4C22×D411yescharacteristic
1137C22×C4C2×#4114yes—
1138C22×C4H(5,𝔽2)14yes—
1139C22×C4C2512yes—
1140C22×C4C2514yes—
1141C22×C4C2512yes—
1142C22×C4C2511yescharacteristic
1143C22×C4C2511yescharacteristic
1144C22×C4C2511yescharacteristic
1145Q16—216no—
1146Q16—44no—
1147SD16—216no—
1148SD16—48no—
1149SD16—44no—
1150SD16—44no—
1151D8—48no—
1152D8—44no—
1153M16—24no—
1154M16—24no—
1155M16—24no—
1156M16—24no—
1157M16—24no—
1158M16—24no—
1159M16—24no—
1160M16—24no—
1161M16—48no—
1162M16—48no—
1163C2×C8—24no—
1164C2×C8—24no—
1165C2×C8—24no—
1166C2×C8—24no—
1167C2×C8—48no—
1168C2×C8—48no—
1169C2×C8C2514yes—
1170C2×C8C2514yes—
1171C2×C8C2514yes—
1172C2×C8C2514yes—
1173C4⋊C4—22no—
1174C4⋊C4—22no—
1175C4⋊C4—24no—
1176C4⋊C4—24no—
1177C4⋊C4—24no—
1178C4⋊C4—28no—
1179C4⋊C4—216no—
1180C4⋊C4—24no—
1181C4⋊C4—24no—
1182C4⋊C4—24no—
1183C4⋊C4—22no—
1184C4⋊C4—28no—
1185C4⋊C4—22no—
1186C4⋊C4—28no—
1187C4⋊C4—28no—
1188C4⋊C4—28no—
1189C4⋊C4—28no—
1190C4⋊C4C22×D414yes—
1191C4⋊C4C22×D418yes—
1192C4⋊C4C22×D414yes—
1193C4⋊C4C22×D418yes—
1194C4⋊C4C2514yes—
1195C4⋊C4C2514yes—
1196C4⋊C4C2514yes—
1197C4⋊C4C2514yes—
1198C22⋊C4—22no—
1199C22⋊C4—22no—
1200C22⋊C4—22no—
1201C22⋊C4—22no—
1202C22⋊C4—22no—
1203C22⋊C4—24no—
1204C22⋊C4—24no—
1205C22⋊C4—22no—
1206C22⋊C4—22no—
1207C22⋊C4—24no—
1208C22⋊C4—22no—
1209C22⋊C4—28no—
1210C22⋊C4—24no—
1211C22⋊C4—24no—
1212C22⋊C4—24no—
1213C22⋊C4—28no—
1214C22⋊C4—24no—
1215C22⋊C4—28no—
1216C22⋊C4—24no—
1217C22⋊C4—24no—
1218C22⋊C4—216no—
1219C22⋊C4—216no—
1220C22⋊C4—24no—
1221C22⋊C4—28no—
1222C22⋊C4C22×D414yes—
1223C22⋊C4C22×D414yes—
1224C22⋊C4C22×D418yes—
1225C22⋊C4C22×D418yes—
1226C22⋊C4C22×D418yes—
1227C22⋊C4C22×D418yes—
1228C42—22no—
1229C42—24no—
1230C42—22no—
1231C42—22no—
1232C42—22no—
1233C42—24no—
1234C42—22no—
1235C42—28no—
1236C42—28no—
1237C42—216no—
1238C42—22no—
1239C42—22no—
1240C42—22no—
1241C42C22×D414yes—
1242C42C2514yes—
1243C23—22no—
1244C23—22no—
1245C23—24no—
1246C23—24no—
1247C23—24no—
1248C23—22no—
1249C23—24no—
1250C23—22no—
1251C23—42no—
1252C23—42no—
1253C23—42no—
1254C23—44no—
1255C23—42no—
1256C23—42no—
1257C23—42no—
1258C23—42no—
1259C23—44no—
1260C23—48no—
1261C23—42no—
1262C23—44no—
1263C23—44no—
1264C23—44no—
1265C23—42no—
1266C23—84no—
1267C23—84no—
1268C23—82no—
1269C23—88no—
1270C23—816no—
1271C23#54614yes—
1272C23C23×D412yes—
1273C23C23×D412yes—
1274C23C23×D414yes—
1275C23C23×D411yescharacteristic
1276C23C23×D411yescharacteristic
1277C23C23×D411yescharacteristic
1278Q8—24no—
1279Q8—28no—
1280Q8—28no—
1281Q8—28no—
1282Q8—24no—
1283Q8—24no—
1284Q8—22no—
1285Q8—22no—
1286Q8—22no—
1287Q8—22no—
1288Q8—416no—
1289Q8—42no—
1290Q8—42no—
1291Q8—88no—
1292Q8C22×#4118yes—
1293D4—28no—
1294D4—28no—
1295D4—22no—
1296D4—24no—
1297D4—22no—
1298D4—22no—
1299D4—24no—
1300D4—22no—
1301D4—24no—
1302D4—24no—
1303D4—48no—
1304D4—48no—
1305D4—416no—
1306D4—416no—
1307D4—416no—
1308D4—48no—
1309D4—44no—
1310D4—44no—
1311D4—44no—
1312D4—44no—
1313D4—44no—
1314D4—44no—
1315D4—44no—
1316D4—42no—
1317D4—42no—
1318D4—816no—
1319D4—84no—
1320D4—816no—
1321D4—84no—
1322D4—84no—
1323D4—88no—
1324C2×C4—24no—
1325C2×C4—24no—
1326C2×C4—24no—
1327C2×C4—22no—
1328C2×C4—22no—
1329C2×C4—28no—
1330C2×C4—28no—
1331C2×C4—28no—
1332C2×C4—24no—
1333C2×C4—22no—
1334C2×C4—22no—
1335C2×C4—24no—
1336C2×C4—22no—
1337C2×C4—24no—
1338C2×C4—22no—
1339C2×C4—24no—
1340C2×C4—24no—
1341C2×C4—24no—
1342C2×C4—24no—
1343C2×C4—24no—
1344C2×C4—24no—
1345C2×C4—28no—
1346C2×C4—24no—
1347C2×C4—24no—
1348C2×C4—22no—
1349C2×C4—24no—
1350C2×C4—24no—
1351C2×C4—22no—
1352C2×C4—44no—
1353C2×C4—416no—
1354C2×C4—416no—
1355C2×C4—416no—
1356C2×C4—416no—
1357C2×C4—48no—
1358C2×C4—44no—
1359C2×C4—42no—
1360C2×C4—42no—
1361C2×C4—44no—
1362C2×C4—44no—
1363C2×C4—44no—
1364C2×C4—44no—
1365C2×C4—88no—
1366C2×C4—82no—
1367C2×C4—84no—
1368C2×C4—82no—
1369C2×C4—82no—
1370C2×C4—88no—
1371C2×C4#54614yes—
1372C2×C4#54614yes—
1373C2×C4#54614yes—
1374C2×C4C23×D412yes—
1375C2×C4C23×D418yes—
1376C2×C4C23×D414yes—
1377C2×C4C23×D412yes—
1378C2×C4C23×D411yescharacteristic
1379C2×C4C23×D411yescharacteristic
1380C2×C4C23×D411yescharacteristic
1381C2×C4C22×#4112yes—
1382C2×C4C22×#4112yes—
1383C2×C4C22×#4112yes—
1384C2×C4C2×H(5,𝔽2)12yes—
1385C2×C4C2×H(5,𝔽2)12yes—
1386C2×C4C2×H(5,𝔽2)12yes—
1387C2×C4C2611yescharacteristic
1388C8—24no—
1389C8—24no—
1390C8—24no—
1391C8—24no—
1392C22—22no—
1393C22—22no—
1394C22—22no—
1395C22—22no—
1396C22—22no—
1397C22—28no—
1398C22—22no—
1399C22—22no—
1400C22—22no—
1401C22—22no—
1402C22—24no—
1403C22—44no—
1404C22—44no—
1405C22—44no—
1406C22—44no—
1407C22—44no—
1408C22—48no—
1409C22—42no—
1410C22—44no—
1411C22—42no—
1412C22—84no—
1413C22—84no—
1414C22—84no—
1415C22—84no—
1416C22—88no—
1417C22—88no—
1418C22—88no—
1419C22—162no—
1420C22C2×#54612yes—
1421C22C2×#54612yes—
1422C22C2×#54612yes—
1423C22C24×D411yescharacteristic
1424C4—28no—
1425C4—22no—
1426C4—22no—
1427C4—28no—
1428C4—24no—
1429C4—44no—
1430C4—44no—
1431C4—44no—
1432C4—44no—
1433C4—42no—
1434C4—42no—
1435C4C2×#54612yes—
1436C4C2×#54612yes—
1437C4C2×#54612yes—
1438C4C23×#4111yescharacteristic
1439C4C22×H(5,𝔽2)11yescharacteristic
1440C2—22no—
1441C2—22no—
1442C2—22no—
1443C2—42no—
1444C2—42no—
1445C2—44no—
1446C2—82no—
1447C2—84no—
1448C2—82no—
1449C2C22×#54611yescharacteristic
1450C2#6309012yes—
subgroupG/H
center, socleC22C24×D4
commutator, Frattini, cosocleC2×C4C26
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22 ◁ C2×#525 ◁ G
LECSG ▷ C2×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #62814C2semidirect
2. C2×#3487C2semidirect
3. #61190C2semidirect
4. #61189C2semidirect
5. #61178C2semidirect
6. #61170C2semidirect
7. #61160C2semidirect
8. #61158C2semidirect
9. #60619C2semidirect
10. #60518C2semidirect
11. #60511C2semidirect
12. #60491C2semidirect
13. #60454C2semidirect
14. #60444C2semidirect
15. #60426C2semidirect
16. #60368C2semidirect
17. C2×#3005C2semidirect
18. #60169C2semidirect
19. #60141C2semidirect
20. #60088C2semidirect
21. C2×#2896C2semidirect
30. #3495C22semidirect
32. #3494C22semidirect
33. #3493C22semidirect
34. #3492C22semidirect
41. #3487C22semidirect
42. #3487C22semidirect
44. #3475C22semidirect
46. C2×#550C22semidirect
48. C2×#548C22semidirect
64. #3333C22semidirect
65. #3332C22semidirect
66. #3327C22semidirect
67. #3326C22semidirect
68. #3321C22semidirect
69. #3317C22semidirect
70. #3317C22semidirect
71. #3316C22semidirect
72. #3313C22semidirect
73. #3309C22semidirect
74. #3309C22semidirect
75. #3308C22semidirect
76. #3305C22semidirect
77. #3304C22semidirect
78. #3301C22semidirect
79. #3300C22semidirect
80. #3140C22semidirect
81. #3138C22semidirect
82. #3136C22semidirect
83. #3136C22semidirect
84. #3096C22semidirect
85. #3096C22semidirect
86. #3095C22semidirect
87. #3094C22semidirect
88. #3094C22semidirect
89. #3093C22semidirect
90. #3092C22semidirect
91. #3091C22semidirect
92. #3082C22semidirect
93. #3082C22semidirect
94. #3078C22semidirect
95. #3062C22semidirect
96. #3058C22semidirect
97. #3057C22semidirect
98. #3056C22semidirect
99. #3056C22semidirect
100. #3055C22semidirect
101. #3055C22semidirect
102. #3055C22semidirect
103. #3054C22semidirect
104. #3050C22semidirect
105. #3045C22semidirect
106. #3043C22semidirect
107. #3041C22semidirect
108. #3040C22semidirect
109. #3038C22semidirect
110. #3013C22semidirect
111. #3011C22semidirect
112. #3010C22semidirect
114. #3005C22semidirect
115. #3005C22semidirect
116. #3005C22semidirect
117. #3004C22semidirect
118. C2×#452C22semidirect
119. C2×#449C22semidirect
120. #2950C22semidirect
121. #2949C22semidirect
122. #2947C22semidirect
123. C4×#137C22semidirect
124. D4×M16C22semidirect
125. #2933C22semidirect
126. #2930C22semidirect
127. #2929C22semidirect
132. #2898C22semidirect
133. #2898C22semidirect
138. #2896C22semidirect
139. #2896C22semidirect
140. #2896C22semidirect
141. C2×#417C22semidirect
145. C2×#419C22semidirect
149. C2×#416C22semidirect
212. #556C23semidirect
214. #555C23semidirect
216. #554C23semidirect
219. #553C23semidirect
220. #553C23semidirect
225. #552C23semidirect
226. #552C23semidirect
248. #547C23semidirect
384. #490C23semidirect
385. #489C23semidirect
386. #488C23semidirect
387. #486C23semidirect
388. #485C23semidirect
389. #485C23semidirect
390. #484C23semidirect
391. #483C23semidirect
392. #482C23semidirect
393. #482C23semidirect
394. #482C23semidirect
395. #482C23semidirect
396. #481C23semidirect
397. #481C23semidirect
398. #480C23semidirect
399. #480C23semidirect
400. #479C23semidirect
401. #479C23semidirect
402. #477C23semidirect
403. #475C23semidirect
404. #470C23semidirect
405. #469C23semidirect
406. #469C23semidirect
407. #468C23semidirect
408. #468C23semidirect
409. #468C23semidirect
410. #467C23semidirect
411. #466C23semidirect
412. #466C23semidirect
413. #465C23semidirect
414. #465C23semidirect
415. #465C23semidirect
416. #464C23semidirect
417. #463C23semidirect
418. #460C23semidirect
419. #459C23semidirect
422. #452C23semidirect
423. #451C23semidirect
426. #449C23semidirect
427. #448C23semidirect
428. #441C23semidirect
429. #440C23semidirect
430. C4×Q16C23semidirect
431. C4×SD16C23semidirect
432. #436C23semidirect
433. #435C23semidirect
434. #435C23semidirect
435. C8×D4C23semidirect
458. #419C23semidirect
475. #417C23semidirect
482. #416C23semidirect
486. C2×#103C23semidirect
569. C22×Q8#41semidirect

Maximal subgroups

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

subgroupindex
#628142
C2×#34872
#611902
#611892
#611782
#611702
#611602
#611582
#606192
#605182
#605112
#604912
#604542
#604442
#604262
#603682
C2×#30052
#601692
#601412
#600882
C2×#28962