Finite Group Databasebeta

← #6498402

Subgroups — #6498402

Order 512.

1934 conjugacy classes of subgroups.

The subgroup lattice has 810 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3231C211yesmaximal, characteristic, complemented
2C2×#3210C211yesmaximal, characteristic
3#36639C211yesmaximal, characteristic
4C4×#533C211yesmaximal, characteristic, complemented
5#33029C214yesmaximal, complemented
6#29833C214yesmaximal, complemented
7#28656C211yesmaximal, characteristic, complemented
8#28655C211yesmaximal, characteristic, complemented
9#28654C211yesmaximal, characteristic, complemented
10#28653C211yesmaximal, characteristic, complemented
11#28616C211yesmaximal, characteristic, complemented
12#28616C211yesmaximal, characteristic, complemented
13#28614C211yesmaximal, characteristic, complemented
14#28614C211yesmaximal, characteristic, complemented
15#28125C214yesmaximal, complemented
16#28122C214yesmaximal, complemented
17#21835C211yesmaximal, characteristic, complemented
18#21805C211yesmaximal, characteristic
19#20808C211yesmaximal, characteristic, complemented
20C2×#533C2211yescharacteristic
21C2×#533C2211yescharacteristic
22C2×#532C2211yescharacteristic
23#3231—28no—
24#3210—28no—
25C2×#500C2211yescharacteristic
26C2×#498C2211yescharacteristic
27C2×#494C2211yescharacteristic
28C2×#492C2211yescharacteristic
29C2×#487C2211yescharacteristic
30C2×#487C2211yescharacteristic
31C2×#487C2211yescharacteristic
32C2×#486C2211yescharacteristic
33C2×#485C2214yes—
34C2×#479C2214yes—
35C2×#464C2214yes—
36C2×#452C2214yes—
37C2×#431C2211yescharacteristic
38C2×#431C2211yescharacteristic
39#2862C2211yescharacteristic
40#2862C2211yescharacteristic
41#2861C2212yes—
42#2861C2212yes—
43#2858C2211yescharacteristic
44#2858C2211yescharacteristic
45#2850—21no—
46#2850—21no—
47#2850—21no—
48#2850—21no—
49C4×C4⋊Q8C2211yescharacteristic
50C4×C4⋊Q8C2211yescharacteristic
51C4×C4⋊Q8C2211yescharacteristic
52C4×C4⋊Q8C2211yescharacteristic
53C4×#125—21no—
54C4×#125—21no—
55C4×#124—21no—
56C4×#124—21no—
57C4×#124—21no—
58C4×#124—21no—
59C4×C22⋊Q8—21no—
60C4×C22⋊Q8—21no—
61C4×C22⋊Q8C2212yes—
62C4×C22⋊Q8C2212yes—
63#2297C2212yes—
64#2297C2212yes—
65#2296—21no—
66#2295—21no—
67#2295C2212yes—
68#2285C2211yescharacteristic
69C42×Q8—21no—
70C42×Q8C2212yes—
71C4×#117—21no—
72C2×C43C2211yescharacteristic
73#2068C2214yes—
74#2067C2214yes—
75#2066C2214yes—
76#2065C2214yes—
77#2056C2214yes—
78#2056C2214yes—
79#2055C2214yes—
80#2055C2214yes—
81#1990C2211yescharacteristic
82#1990C2211yescharacteristic
83#1990C2211yescharacteristic
84#1990C2211yescharacteristic
85#1989C2214yes—
86#1983C2214yes—
87#1957C2211yescharacteristic
88#1957C2211yescharacteristic
89#1956C2211yescharacteristic
90#1956C2211yescharacteristic
91#1928C2214yes—
92#1927C2214yes—
93#1926C2214yes—
94#1925C2214yes—
95#1880C2214yes—
96#1880C2214yes—
97#1878C2214yes—
98#1878C2214yes—
99#1842C2212yes—
100#1831C2212yes—
101#1825C2214yes—
102#1797C2212yes—
103#1797C2212yes—
104#1788C2214yes—
105C4×C4⋊C8C2211yescharacteristic
106C4×C4⋊C8C2211yescharacteristic
107C4×C4⋊C8C2211yescharacteristic
108C4×C4⋊C8C2211yescharacteristic
109C22×#41C2312yes—
110C22×Q16C2314yes—
111C22×SD16C2314yes—
112#533—24no—
113#533—24no—
114#533—24no—
115#533D418yes—
116#532—24no—
117#532—24no—
118C2×C4⋊Q8C2311yescharacteristic
119C2×C4⋊Q8C2311yescharacteristic
120C2×C4⋊Q8C2311yescharacteristic
121C2×C4⋊Q8C2311yescharacteristic
122C2×C4⋊Q8C2311yescharacteristic
123C2×#127C2311yescharacteristic
124C2×#125—21no—
125C2×#125C2312yes—
126C2×#124—21no—
127C2×#124—21no—
128C2×#124—21no—
129C2×#124—21no—
130C2×#124C2312yes—
131C2×C22⋊Q8—21no—
132C2×C22⋊Q8—21no—
133C2×C22⋊Q8—21no—
134C2×C22⋊Q8C2312yes—
135C2×#121—21no—
136C2×#121—21no—
137C2×C4×Q8—21no—
138C2×C4×Q8—21no—
139C2×C4×Q8—21no—
140C2×C4×Q8—21no—
141C2×C4×Q8—21no—
142C2×C4×Q8C2312yes—
143C2×C4×Q8C2312yes—
144C2×C4×Q8C2312yes—
145C2×C4×D4—21no—
146C2×C4×D4—21no—
147C2×#117—21no—
148C2×#117—21no—
149C2×#117C2312yes—
150C22×C42D411yescharacteristic
151C22×C42D411yescharacteristic
152C22×C42D411yescharacteristic
153C22×C42D411yescharacteristic
154C22×C42C2311yescharacteristic
155C22×C42C2311yescharacteristic
156C22×C42C2311yescharacteristic
157#500—24no—
158#498—24no—
159#494—24no—
160#492—24no—
161#487—24no—
162#487—24no—
163#487—24no—
164#486—24no—
165#485—216no—
166#479—216no—
167#464—216no—
168#452—216no—
169#431—24no—
170#431—24no—
171C2×#107C2314yes—
172C2×#106C2314yes—
173C2×C4⋊C8C2312yes—
174C2×C4⋊C8C2312yes—
175C2×C4⋊C8C2312yes—
176C2×C4⋊C8C2312yes—
177C2×C4⋊C8C2312yes—
178C2×C4⋊C8C2312yes—
179C2×#103C2314yes—
180C2×#103C2314yes—
181C2×#103C2314yes—
182C2×#103C2314yes—
183C2×#103C2314yes—
184C2×#102C2314yes—
185C2×#102C2314yes—
186C2×#102C2314yes—
187C2×C22⋊C8C2312yes—
188C2×C22⋊C8C2312yes—
189C2×C4×C8C2311yescharacteristic
190C2×C4×C8C2311yescharacteristic
191C2×C4×C8C2311yescharacteristic
192C2×C4×C8C2311yescharacteristic
193#391—21no—
194#391—21no—
195#391—21no—
196#391—21no—
197#391—21no—
198#391—21no—
199#391C2312yes—
200#391C2312yes—
201#391C2312yes—
202#391C2312yes—
203#391C2312yes—
204#391C2312yes—
205#390—21no—
206#390—21no—
207#390—21no—
208#390—21no—
209#390C2312yes—
210#390C2312yes—
211#390C2312yes—
212#390C2312yes—
213#389—21no—
214#389—21no—
215#389—21no—
216#389—21no—
217#389—21no—
218#389—21no—
219#389C2312yes—
220#389C2312yes—
221#388—22no—
222#388—22no—
223#388—22no—
224#388—22no—
225#388—22no—
226#388—22no—
227#388—22no—
228#388—22no—
229#387—22no—
230#387—22no—
231#387—22no—
232#387—22no—
233#386—22no—
234#386—22no—
235#386—22no—
236#386—22no—
237#385—22no—
238#385—22no—
239#384C2311yescharacteristic
240#384C2311yescharacteristic
241#382—21no—
242#382—21no—
243#382—21no—
244#382—21no—
245#382—21no—
246#380—21no—
247#380C2312yes—
248C4×C4⋊C4—21no—
249C4×C4⋊C4—21no—
250C4×C4⋊C4—21no—
251C4×C4⋊C4—21no—
252C4×C4⋊C4—22no—
253C4×C4⋊C4—22no—
254C4×C4⋊C4—22no—
255C4×C4⋊C4—22no—
256C4×C4⋊C4—21no—
257C4×C4⋊C4—21no—
258C4×C4⋊C4—21no—
259C4×C4⋊C4—22no—
260C4×C4⋊C4—22no—
261C4×C4⋊C4C2312yes—
262C4×C4⋊C4C2312yes—
263C4×C4⋊C4C2312yes—
264C4×C22⋊C4—22no—
265C4×C22⋊C4—22no—
266C4×C22⋊C4—22no—
267C4×C22⋊C4—22no—
268C4×C22⋊C4—22no—
269C4×C22⋊C4—22no—
270#376—22no—
271C43—22no—
272C43D411yescharacteristic
273C43D411yescharacteristic
274C43D411yescharacteristic
275C43D411yescharacteristic
276C43C2311yescharacteristic
277C43C2311yescharacteristic
278C43C2311yescharacteristic
279C43C2311yescharacteristic
280#340C2314yes—
281#340C2314yes—
282#340C2314yes—
283#340C2314yes—
284#336C2312yes—
285#336C2312yes—
286#336C2312yes—
287#336C2312yes—
288C2×#41—24no—
289C2×#41—24no—
290C2×#41—44no—
291C2×#41—44no—
292C22×Q8—21no—
293C22×Q8—21no—
294C22×Q8—21no—
295C22×Q8C2412yes—
296C22×Q8C2412yes—
297C22×D4—22no—
298C22×D4—21no—
299C22×D4—21no—
300C22×D4C2412yes—
301C23×C4—22no—
302C23×C4C2×D411yescharacteristic
303C23×C4C2×D411yescharacteristic
304C23×C4C2×D411yescharacteristic
305C23×C4C2×D411yescharacteristic
306C23×C4C2×D411yescharacteristic
307C23×C4C2×D411yescharacteristic
308C23×C4C2411yescharacteristic
309C2×Q16—28no—
310C2×Q16—44no—
311C2×Q16—44no—
312C2×SD16—28no—
313C2×SD16—44no—
314C2×SD16—44no—
315C22×C8C2412yes—
316C22×C8C2412yes—
317C22×C8C2412yes—
318C22×C8C2412yes—
319C4⋊Q8—22no—
320C4⋊Q8—22no—
321C4⋊Q8—22no—
322C4⋊Q8—22no—
323C4⋊Q8—22no—
324C4⋊Q8—22no—
325C4⋊Q8—22no—
326C4⋊Q8—22no—
327C4⋊Q8C2×D414yes—
328C4⋊Q8C2×D414yes—
329#127—22no—
330#127—22no—
331#125—28no—
332#125—24no—
333#125—24no—
334#124—24no—
335#124—24no—
336#124—44no—
337#124—44no—
338#124—44no—
339#124—44no—
340C22⋊Q8—28no—
341C22⋊Q8—24no—
342C22⋊Q8—44no—
343C22⋊Q8—44no—
344C22⋊Q8C2×D418yes—
345#121—44no—
346#121—44no—
347C4×Q8—28no—
348C4×Q8—24no—
349C4×Q8—44no—
350C4×Q8—44no—
351C4×Q8—44no—
352C4×Q8—44no—
353C4×Q8—44no—
354C4×Q8—44no—
355C4×Q8C2×D418yes—
356C4×D4—44no—
357C4×D4—44no—
358#117—28no—
359#117—24no—
360#117—24no—
361#117—44no—
362C2×C4⋊C4—21no—
363C2×C4⋊C4—21no—
364C2×C4⋊C4—21no—
365C2×C4⋊C4—22no—
366C2×C4⋊C4—22no—
367C2×C4⋊C4—21no—
368C2×C4⋊C4—21no—
369C2×C4⋊C4—21no—
370C2×C4⋊C4—21no—
371C2×C4⋊C4—22no—
372C2×C4⋊C4—22no—
373C2×C4⋊C4—21no—
374C2×C4⋊C4—21no—
375C2×C4⋊C4—21no—
376C2×C4⋊C4—21no—
377C2×C4⋊C4—22no—
378C2×C4⋊C4—22no—
379C2×C4⋊C4—22no—
380C2×C4⋊C4—22no—
381C2×C4⋊C4C2412yes—
382C2×C4⋊C4C2412yes—
383C2×C4⋊C4C2412yes—
384C2×C4⋊C4C2412yes—
385C2×C4⋊C4C2412yes—
386C2×C22⋊C4—22no—
387C2×C22⋊C4—22no—
388C2×C22⋊C4—22no—
389C2×C22⋊C4—22no—
390C2×C22⋊C4—22no—
391C2×C22⋊C4—22no—
392C2×C22⋊C4—22no—
393C2×C22⋊C4—22no—
394C2×C22⋊C4—22no—
395C2×C22⋊C4—22no—
396C2×C22⋊C4—22no—
397C2×C22⋊C4—22no—
398C2×C22⋊C4—22no—
399C2×C42—22no—
400C2×C42—24no—
401C2×C42—24no—
402C2×C42—22no—
403C2×C42—22no—
404C2×C42—22no—
405C2×C42—22no—
406C2×C42—22no—
407C2×C42—22no—
408C2×C42—42no—
409C2×C42—42no—
410C2×C42—42no—
411C2×C42—42no—
412C2×C42C2×D411yescharacteristic
413C2×C42C2×D411yescharacteristic
414C2×C42C2×D411yescharacteristic
415C2×C42C2×D411yescharacteristic
416C2×C42C2×D411yescharacteristic
417C2×C42C2×D411yescharacteristic
418C2×C42C2×D411yescharacteristic
419C2×C42C2×D411yescharacteristic
420C2×C42C2×D411yescharacteristic
421C2×C42C2×D411yescharacteristic
422C2×C42C2×D411yescharacteristic
423C2×C42C2×D411yescharacteristic
424C2×C42C2×D411yescharacteristic
425C2×C42C2×D411yescharacteristic
426C2×C42C2×D411yescharacteristic
427C2×C42C2×D411yescharacteristic
428C2×C42C2×D411yescharacteristic
429C2×C42C2×D411yescharacteristic
430C2×C42C2×D411yescharacteristic
431C2×C42C2×D411yescharacteristic
432C2×C42C2×D414yes—
433C2×C42C2×D411yescharacteristic
434C2×C42C2×D411yescharacteristic
435C2×C42#4114yes—
436C2×C42C2411yescharacteristic
437C2×C42C2411yescharacteristic
438C2×C42C2411yescharacteristic
439C2×C42C2411yescharacteristic
440C2×C42C2411yescharacteristic
441C2×C42C2411yescharacteristic
442#107—28no—
443#106—28no—
444C4⋊C8—24no—
445C4⋊C8—24no—
446C4⋊C8—42no—
447C4⋊C8—42no—
448C4⋊C8—42no—
449C4⋊C8—42no—
450#103—28no—
451#103—28no—
452#103—28no—
453#103—44no—
454#103—44no—
455#102—28no—
456#102—44no—
457#102—44no—
458C22⋊C8—24no—
459C22⋊C8—24no—
460C4×C8—22no—
461C4×C8—22no—
462C4×C8—22no—
463C4×C8—22no—
464#95—22no—
465#95—22no—
466#95—22no—
467#95—22no—
468#95—22no—
469#95—22no—
470#95—22no—
471#95—22no—
472#95—22no—
473#95—22no—
474#95—22no—
475#95—22no—
476#95—22no—
477#95—22no—
478#95—22no—
479#95—22no—
480#95—22no—
481#95—22no—
482C24—22no—
483C24C22×D411yescharacteristic
484#41—88no—
485#41—88no—
486C2×Q8—24no—
487C2×Q8—22no—
488C2×Q8—22no—
489C2×Q8—22no—
490C2×Q8—24no—
491C2×Q8—24no—
492C2×Q8—24no—
493C2×Q8—24no—
494C2×Q8—42no—
495C2×Q8—42no—
496C2×Q8—42no—
497C2×Q8—42no—
498C2×Q8—42no—
499C2×Q8—42no—
500C2×Q8—42no—
501C2×Q8—42no—
502C2×Q8C22×D414yes—
503C2×D4—22no—
504C2×D4—22no—
505C2×D4—24no—
506C2×D4—24no—
507C2×D4—44no—
508C2×D4—44no—
509C2×D4—44no—
510C2×D4—42no—
511C2×D4—42no—
512C2×D4—42no—
513C2×D4—42no—
514C2×D4—42no—
515C2×D4—42no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—41no—
534C22×C4—41no—
535C22×C4—41no—
536C22×C4—41no—
537C22×C4—41no—
538C22×C4—41no—
539C22×C4—41no—
540C22×C4—41no—
541C22×C4—44no—
542C22×C4—44no—
543C22×C4—44no—
544C22×C4#12114yes—
545C22×C4#12114yes—
546C22×C4C22×D411yescharacteristic
547C22×C4C22×D411yescharacteristic
548C22×C4C22×D411yescharacteristic
549C22×C4C22×D411yescharacteristic
550C22×C4C22×D411yescharacteristic
551C22×C4C22×D411yescharacteristic
552C22×C4C22×D411yescharacteristic
553C22×C4C22×D412yes—
554C22×C4C22×D411yescharacteristic
555C22×C4C22×D411yescharacteristic
556C22×C4C22×D411yescharacteristic
557C22×C4C22×D411yescharacteristic
558C22×C4C22×D411yescharacteristic
559C22×C4C22×D411yescharacteristic
560C22×C4C2×#4112yes—
561C22×C4C2511yescharacteristic
562Q16—88no—
563SD16—88no—
564C2×C8—22no—
565C2×C8—22no—
566C2×C8—22no—
567C2×C8—22no—
568C2×C8—22no—
569C2×C8—22no—
570C2×C8—22no—
571C2×C8—22no—
572C2×C8—22no—
573C2×C8—22no—
574C2×C8—22no—
575C2×C8—22no—
576C4⋊C4—24no—
577C4⋊C4—24no—
578C4⋊C4—24no—
579C4⋊C4—28no—
580C4⋊C4—28no—
581C4⋊C4—22no—
582C4⋊C4—22no—
583C4⋊C4—22no—
584C4⋊C4—22no—
585C4⋊C4—22no—
586C4⋊C4—24no—
587C4⋊C4—24no—
588C4⋊C4—44no—
589C4⋊C4—44no—
590C4⋊C4—44no—
591C4⋊C4—42no—
592C4⋊C4—42no—
593C4⋊C4—44no—
594C4⋊C4—44no—
595C4⋊C4—42no—
596C4⋊C4—42no—
597C4⋊C4—44no—
598C4⋊C4—42no—
599C4⋊C4—42no—
600C4⋊C4—42no—
601C4⋊C4—42no—
602C4⋊C4C22×D414yes—
603C22⋊C4—28no—
604C22⋊C4—44no—
605C22⋊C4—44no—
606C22⋊C4—44no—
607C22⋊C4—44no—
608C22⋊C4—44no—
609C22⋊C4—44no—
610C22⋊C4—44no—
611C22⋊C4—44no—
612C22⋊C4—44no—
613C22⋊C4—44no—
614C22⋊C4—44no—
615C22⋊C4—44no—
616C42—28no—
617C42—22no—
618C42—22no—
619C42—22no—
620C42—22no—
621C42—22no—
622C42—22no—
623C42—22no—
624C42—22no—
625C42—22no—
626C42—22no—
627C42—22no—
628C42—22no—
629C42—22no—
630C42—22no—
631C42—41no—
632C42—41no—
633C42—41no—
634C42—41no—
635C42—41no—
636C42—41no—
637C42—41no—
638C42—41no—
639C42—44no—
640C42—44no—
641C42—44no—
642C42—44no—
643C42—44no—
644C42—44no—
645C42#12114yes—
646C42#12114yes—
647C42#13514yes—
648C42#13714yes—
649C42C22×D412yes—
650C42C22×D412yes—
651C42C2×#4112yes—
652C42C2×#4112yes—
653C23—21no—
654C23—21no—
655C23—21no—
656C23—21no—
657C23—21no—
658C23—21no—
659C23—42no—
660C23—42no—
661C23—42no—
662C23—42no—
663C23—42no—
664C23—42no—
665C23—42no—
666C23C2×#12112yes—
667C23C23×D411yescharacteristic
668Q8—28no—
669Q8—44no—
670Q8—48no—
671Q8—44no—
672Q8—44no—
673Q8—84no—
674Q8—84no—
675D4—44no—
676D4—44no—
677D4—88no—
678D4—84no—
679D4—84no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—21no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—21no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—21no—
694C2×C4—24no—
695C2×C4—24no—
696C2×C4—28no—
697C2×C4—28no—
698C2×C4—24no—
699C2×C4—24no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—44no—
713C2×C4—44no—
714C2×C4—44no—
715C2×C4—44no—
716C2×C4—42no—
717C2×C4—42no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—42no—
725C2×C4—42no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—42no—
729C2×C4—42no—
730C2×C4—42no—
731C2×C4—42no—
732C2×C4—42no—
733C2×C4—42no—
734C2×C4—42no—
735C2×C4—88no—
736C2×C4C2×#12112yes—
737C2×C4C2×#12112yes—
738C2×C4C2×#12112yes—
739C2×C4C2×#12112yes—
740C2×C4C2×#12112yes—
741C2×C4C2×#13512yes—
742C2×C4C2×#13512yes—
743C2×C4C2×#13512yes—
744C2×C4C2×#13712yes—
745C2×C4C2×#13712yes—
746C2×C4C2×#13712yes—
747C2×C4#57512yes—
748C2×C4#57512yes—
749C2×C4C23×D411yescharacteristic
750C2×C4C22×#4111yescharacteristic
751C2×C4#58512yes—
752C2×C4#58512yes—
753C8—42no—
754C8—42no—
755C8—42no—
756C8—42no—
757C22—22no—
758C22—22no—
759C22—22no—
760C22—41no—
761C22—41no—
762C22—41no—
763C22—41no—
764C22—82no—
765C22—82no—
766C22—82no—
767C22—82no—
768C22—82no—
769C22—82no—
770C22—82no—
771C22C22×#12111yescharacteristic
772C22#344911yescharacteristic
773C22#344911yescharacteristic
774C22C22×#13511yescharacteristic
775C22C22×#13711yescharacteristic
776C22C2×#57511yescharacteristic
777C22C2×#57511yescharacteristic
778C4—22no—
779C4—22no—
780C4—22no—
781C4—22no—
782C4—22no—
783C4—22no—
784C4—22no—
785C4—41no—
786C4—41no—
787C4—41no—
788C4—41no—
789C4—44no—
790C4—44no—
791C4—82no—
792C4—82no—
793C4—82no—
794C4—82no—
795C4—82no—
796C4#303514yes—
797C4#303714yes—
798C4#350012yes—
799C4#351012yes—
800C2—42no—
801C2—162no—
802C2#3532711yescharacteristic
803C2C2×#303511yescharacteristic
804C2C2×#303711yescharacteristic
805C2#6094411yescharacteristic
806C2#6094711yescharacteristic
807C2#6096611yescharacteristic
808C2#6097211yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#532C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C2×C43 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#3231C2semidirect
4. C4×#533C2semidirect
5. #33029C2semidirect
6. #29833C2semidirect
7. #28656C2semidirect
8. #28655C2semidirect
9. #28654C2semidirect
10. #28653C2semidirect
11. #28616C2semidirect
12. #28616C2semidirect
13. #28614C2semidirect
14. #28614C2semidirect
15. #28125C2semidirect
16. #28122C2semidirect
17. #21835C2semidirect
19. #20808C2semidirect

Maximal subgroups

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

subgroupindex
C2×#32312
C2×#32102
#366392
C4×#5332
#330292
#298332
#286562
#286552
#286542
#286532
#286162
#286142
#281252
#281222
#218352
#218052
#208082