Finite Group Databasebeta

← #6472781

Subgroups — #6472781

Order 512.

3098 conjugacy classes of subgroups.

The subgroup lattice has 1042 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2848C211yesmaximal, characteristic
2C2×#2280C211yesmaximal, characteristic
3#32985C212yesmaximal, complemented
4#32984C212yesmaximal, complemented
5#29897C214yesmaximal, complemented
6#27602C212yesmaximal, complemented
7#27601C211yesmaximal, characteristic, complemented
8#27600C211yesmaximal, characteristic, complemented
9#24554C214yesmaximal, complemented
10#24552C212yesmaximal, complemented
11#24551C212yesmaximal, complemented
12#24010C212yesmaximal, complemented
13#24006C211yesmaximal, characteristic, complemented
14#24003C211yesmaximal, characteristic, complemented
15#21941C212yesmaximal, complemented
16#21762C212yesmaximal, complemented
17C2×#1779C211yesmaximal, characteristic
18C25×C4C2211yescharacteristic
19C22×C22⋊Q8C2211yescharacteristic
20C22×C22⋊Q8C2211yescharacteristic
21C22×C22⋊Q8C2211yescharacteristic
22C22×#117C2211yescharacteristic
23C22×#117C2211yescharacteristic
24C2×#484C2212yescomplemented
25C2×#485C2214yescomplemented
26C2×#483C2212yescomplemented
27C22×C22⋊C8C2212yes—
28C22×C22⋊C8C2212yes—
29C22×C22⋊C8C2212yes—
30#2848—21no—
31#2848—21no—
32#2848—21no—
33#2848—21no—
34#2848C2212yes—
35#2848C2212yes—
36#2848C2212yes—
37#2848C2212yes—
38C2×#385—21no—
39C2×#385—21no—
40C2×#385—21no—
41#2280—21no—
42#2280—21no—
43#2280—21no—
44#2280—21no—
45#2280C2212yes—
46#2280C2212yes—
47#2280C2212yes—
48#2280C2212yes—
49C2×#381—21no—
50C2×#380C2211yescharacteristic
51C2×#380C2211yescharacteristic
52C2×#380C2211yescharacteristic
53C2×#380C2211yescharacteristic
54C2×#380C2211yescharacteristic
55C2×#380C2211yescharacteristic
56C2×#380C2211yescharacteristic
57C2×#379—21no—
58C2×#379—21no—
59C2×C4×C22⋊C4—21no—
60C2×C4×C22⋊C4—21no—
61#2077C2214yescomplemented
62#2077C2214yescomplemented
63#2076C2214yescomplemented
64#2075C2214yescomplemented
65#2036C2214yescomplemented
66#2036C2214yescomplemented
67#2035C2214yescomplemented
68#2035C2214yescomplemented
69#1892C2214yescomplemented
70#1892C2214yescomplemented
71#1873C2214yescomplemented
72#1873C2214yescomplemented
73#1873C2214yescomplemented
74#1872C2212yescomplemented
75#1872C2212yescomplemented
76#1854C2214yescomplemented
77#1854C2214yescomplemented
78#1854C2214yescomplemented
79#1853C2212yescomplemented
80#1853C2212yescomplemented
81#1853C2212yescomplemented
82#1852C2212yescomplemented
83#1852C2212yescomplemented
84#1852C2212yescomplemented
85#1825C2214yescomplemented
86#1824C2212yescomplemented
87#1823C2212yescomplemented
88#1823C2212yescomplemented
89#1823C2212yescomplemented
90#1808C2214yescomplemented
91#1807C2214yescomplemented
92#1787C2212yescomplemented
93#1787C2212yescomplemented
94#1779C2211yescharacteristic
95#1779C2211yescharacteristic
96#1779C2212yes—
97#1779C2212yes—
98#1779C2212yes—
99C26D411yescharacteristic
100C23×Q8C2311yescharacteristic
101C24×C4—28no—
102C24×C4—44no—
103C24×C4—44no—
104C24×C4D411yescharacteristic
105C24×C4D411yescharacteristic
106C24×C4D411yescharacteristic
107C24×C4D411yescharacteristic
108C24×C4D411yescharacteristic
109C24×C4D411yescharacteristic
110C24×C4D411yescharacteristic
111C24×C4C2311yescharacteristic
112C24×C4C2311yescharacteristic
113C24×C4C2311yescharacteristic
114C24×C4C2311yescharacteristic
115C24×C4C2311yescharacteristic
116C24×C4C2311yescharacteristic
117C24×C4C2311yescharacteristic
118C23×C8C2314yes—
119C2×C22⋊Q8—21no—
120C2×C22⋊Q8—21no—
121C2×C22⋊Q8—21no—
122C2×C22⋊Q8—21no—
123C2×C22⋊Q8—21no—
124C2×C22⋊Q8—21no—
125C2×C22⋊Q8—28no—
126C2×C22⋊Q8—44no—
127C2×C22⋊Q8—44no—
128C2×C22⋊Q8C2312yes—
129C2×C22⋊Q8C2312yes—
130C2×C22⋊Q8C2312yes—
131C2×C22⋊Q8C2312yes—
132C2×C22⋊Q8C2312yes—
133C2×C22⋊Q8C2312yes—
134C2×#117—21no—
135C2×#117—21no—
136C2×#117—21no—
137C2×#117—21no—
138C2×#117—44no—
139C2×#117—44no—
140C2×#117C2312yes—
141C2×#117C2312yes—
142C2×#117C2312yes—
143C2×#117C2312yes—
144C22×C4⋊C4—21no—
145C22×C4⋊C4—21no—
146C22×C4⋊C4—21no—
147C22×C4⋊C4C2311yescharacteristic
148C22×C4⋊C4C2311yescharacteristic
149C22×C4⋊C4C2311yescharacteristic
150C22×C4⋊C4C2311yescharacteristic
151C22×C4⋊C4C2311yescharacteristic
152C22×C4⋊C4C2311yescharacteristic
153C22×C4⋊C4C2311yescharacteristic
154C22×C22⋊C4—21no—
155C22×C22⋊C4—21no—
156C22×C22⋊C4—21no—
157C22×C22⋊C4—21no—
158C22×C22⋊C4—21no—
159C22×C22⋊C4—21no—
160C22×C22⋊C4—21no—
161C22×C22⋊C4—21no—
162C22×C22⋊C4—21no—
163C22×C22⋊C4—21no—
164C22×C22⋊C4—21no—
165C22×C22⋊C4—21no—
166C22×C42—21no—
167C22×C42—21no—
168#485—48no—
169#484—44no—
170#483—44no—
171C2×#107C2314yescomplemented
172C2×#107C2314yescomplemented
173C2×#106C2314yescomplemented
174C2×#106C2314yescomplemented
175C2×#103C2314yescomplemented
176C2×#103C2314yescomplemented
177C2×#103C2314yescomplemented
178C2×#103C2314yescomplemented
179C2×C22⋊C8—28no—
180C2×C22⋊C8—44no—
181C2×C22⋊C8—44no—
182C2×C22⋊C8C2312yes—
183C2×C22⋊C8C2314yes—
184C2×C22⋊C8C2312yes—
185C2×C22⋊C8C2312yes—
186C2×C22⋊C8C2312yes—
187C2×C22⋊C8C2314yes—
188C2×C22⋊C8C2312yes—
189C2×C22⋊C8C2314yes—
190C2×C22⋊C8C2312yes—
191#385—22no—
192#385—22no—
193#385—22no—
194#385—22no—
195#385—22no—
196#385—22no—
197#385—22no—
198#385—22no—
199#385—22no—
200#385—22no—
201#385—22no—
202#385—22no—
203#381—22no—
204#381—22no—
205#381—22no—
206#381—22no—
207#380—21no—
208#380—21no—
209#380—21no—
210#380—21no—
211#380—21no—
212#380—21no—
213#380—21no—
214#380—21no—
215#380—21no—
216#380—21no—
217#380—21no—
218#380—21no—
219#380—21no—
220#380—21no—
221#380C2312yes—
222#380C2312yes—
223#380C2312yes—
224#380C2312yes—
225#380C2312yes—
226#380C2312yes—
227#380C2312yes—
228#380C2312yes—
229#380C2312yes—
230#380C2312yes—
231#380C2312yes—
232#380C2312yes—
233#380C2312yes—
234#380C2312yes—
235#379—22no—
236#379—22no—
237#379—22no—
238#379—22no—
239#379—22no—
240#379—22no—
241#379—22no—
242#379—22no—
243C4×C22⋊C4—22no—
244C4×C22⋊C4—22no—
245C4×C22⋊C4—22no—
246C4×C22⋊C4—22no—
247C4×C22⋊C4—22no—
248C4×C22⋊C4—22no—
249C4×C22⋊C4—22no—
250C4×C22⋊C4—22no—
251C2×#95—21no—
252C2×#95—21no—
253C2×#95—21no—
254C2×#95—21no—
255C2×#95—21no—
256C2×#95—21no—
257C2×#95—21no—
258#340C2314yescomplemented
259#340C2314yescomplemented
260#340C2314yescomplemented
261#340C2314yescomplemented
262#340C2314yescomplemented
263#340C2314yescomplemented
264#340C2314yescomplemented
265#340C2314yescomplemented
266C25—24no—
267C25—24no—
268C25—24no—
269C25—42no—
270C25—42no—
271C25—42no—
272C25—42no—
273C25C2×D411yescharacteristic
274C25C2×D411yescharacteristic
275C25C2×D411yescharacteristic
276C25C2×D411yescharacteristic
277C25C2×D411yescharacteristic
278C25C2×D411yescharacteristic
279C25C2×D411yescharacteristic
280C22×Q8—21no—
281C22×Q8—24no—
282C22×Q8—42no—
283C22×Q8—42no—
284C22×Q8C2412yes—
285C23×C4—24no—
286C23×C4—24no—
287C23×C4—24no—
288C23×C4—24no—
289C23×C4—24no—
290C23×C4—24no—
291C23×C4—24no—
292C23×C4—24no—
293C23×C4—24no—
294C23×C4—24no—
295C23×C4—24no—
296C23×C4—24no—
297C23×C4—24no—
298C23×C4—24no—
299C23×C4—24no—
300C23×C4—24no—
301C23×C4—24no—
302C23×C4—24no—
303C23×C4—24no—
304C23×C4—21no—
305C23×C4—21no—
306C23×C4—21no—
307C23×C4—21no—
308C23×C4—21no—
309C23×C4—21no—
310C23×C4—21no—
311C23×C4—21no—
312C23×C4—42no—
313C23×C4—42no—
314C23×C4—42no—
315C23×C4—42no—
316C23×C4—42no—
317C23×C4—42no—
318C23×C4—42no—
319C23×C4—42no—
320C23×C4—42no—
321C23×C4—42no—
322C23×C4—42no—
323C23×C4—42no—
324C23×C4—42no—
325C23×C4—42no—
326C23×C4—42no—
327C23×C4—42no—
328C23×C4—42no—
329C23×C4—42no—
330C23×C4—42no—
331C23×C4—42no—
332C23×C4—42no—
333C23×C4—42no—
334C23×C4—464no—
335C23×C4C2×D411yescharacteristic
336C23×C4C2×D411yescharacteristic
337C23×C4C2×D411yescharacteristic
338C23×C4C2×D411yescharacteristic
339C23×C4C2×D411yescharacteristic
340C23×C4C2×D411yescharacteristic
341C23×C4C2×D411yescharacteristic
342C23×C4C2×D411yescharacteristic
343C23×C4C2×D411yescharacteristic
344C23×C4C2×D411yescharacteristic
345C23×C4C2×D411yescharacteristic
346C23×C4C2×D411yescharacteristic
347C23×C4C2×D411yescharacteristic
348C23×C4C2×D411yescharacteristic
349C23×C4C2×D411yescharacteristic
350C23×C4C2×D411yescharacteristic
351C23×C4C2×D411yescharacteristic
352C23×C4C2×D411yescharacteristic
353C23×C4C2×D411yescharacteristic
354C23×C4C2×D411yescharacteristic
355C23×C4C2×D411yescharacteristic
356C23×C4#4118yes—
357C23×C4C2411yescharacteristic
358C23×C4C2411yescharacteristic
359C23×C4C2411yescharacteristic
360C23×C4C2411yescharacteristic
361C23×C4C2411yescharacteristic
362C23×C4C2411yescharacteristic
363C23×C4C2411yescharacteristic
364C22×C8—28no—
365C22×C8—44no—
366C22×C8—44no—
367C22×C8C2414yes—
368C22×C8C2414yes—
369C22⋊Q8—28no—
370C22⋊Q8—28no—
371C22⋊Q8—24no—
372C22⋊Q8—24no—
373C22⋊Q8—28no—
374C22⋊Q8—42no—
375C22⋊Q8—44no—
376C22⋊Q8—42no—
377C22⋊Q8—44no—
378C22⋊Q8—44no—
379C22⋊Q8—44no—
380C22⋊Q8—44no—
381C22⋊Q8—44no—
382C22⋊Q8—44no—
383#117—28no—
384#117—44no—
385#117—44no—
386#117—44no—
387#117—44no—
388#117—44no—
389#117—44no—
390#117—44no—
391C2×C4⋊C4—24no—
392C2×C4⋊C4—24no—
393C2×C4⋊C4—24no—
394C2×C4⋊C4—22no—
395C2×C4⋊C4—22no—
396C2×C4⋊C4—22no—
397C2×C4⋊C4—22no—
398C2×C4⋊C4—22no—
399C2×C4⋊C4—22no—
400C2×C4⋊C4—21no—
401C2×C4⋊C4—21no—
402C2×C4⋊C4—21no—
403C2×C4⋊C4—21no—
404C2×C4⋊C4—21no—
405C2×C4⋊C4—21no—
406C2×C4⋊C4—21no—
407C2×C4⋊C4—42no—
408C2×C4⋊C4—42no—
409C2×C4⋊C4—42no—
410C2×C4⋊C4—42no—
411C2×C4⋊C4—44no—
412C2×C4⋊C4—44no—
413C2×C4⋊C4—44no—
414C2×C4⋊C4C2412yes—
415C2×C4⋊C4C2412yes—
416C2×C4⋊C4C2412yes—
417C2×C4⋊C4C2412yes—
418C2×C4⋊C4C2412yes—
419C2×C4⋊C4C2412yes—
420C2×C4⋊C4C2412yes—
421C2×C22⋊C4—22no—
422C2×C22⋊C4—22no—
423C2×C22⋊C4—22no—
424C2×C22⋊C4—22no—
425C2×C22⋊C4—22no—
426C2×C22⋊C4—22no—
427C2×C22⋊C4—22no—
428C2×C22⋊C4—22no—
429C2×C22⋊C4—22no—
430C2×C22⋊C4—22no—
431C2×C22⋊C4—22no—
432C2×C22⋊C4—22no—
433C2×C22⋊C4—22no—
434C2×C22⋊C4—22no—
435C2×C22⋊C4—22no—
436C2×C22⋊C4—22no—
437C2×C22⋊C4—22no—
438C2×C22⋊C4—22no—
439C2×C22⋊C4—22no—
440C2×C22⋊C4—22no—
441C2×C22⋊C4—22no—
442C2×C22⋊C4—22no—
443C2×C22⋊C4—22no—
444C2×C22⋊C4—22no—
445C2×C22⋊C4—44no—
446C2×C22⋊C4—44no—
447C2×C22⋊C4—44no—
448C2×C22⋊C4—44no—
449C2×C22⋊C4—44no—
450C2×C22⋊C4—44no—
451C2×C22⋊C4—44no—
452C2×C22⋊C4—44no—
453C2×C22⋊C4—44no—
454C2×C22⋊C4—44no—
455C2×C22⋊C4—44no—
456C2×C22⋊C4—44no—
457C2×C42—22no—
458C2×C42—22no—
459C2×C42—22no—
460C2×C42—22no—
461C2×C42—44no—
462C2×C42—44no—
463#107—44no—
464#107—44no—
465#106—44no—
466#106—44no—
467#103—44no—
468#103—44no—
469#103—44no—
470#103—44no—
471C22⋊C8—24no—
472C22⋊C8—24no—
473C22⋊C8—28no—
474C22⋊C8—24no—
475C22⋊C8—24no—
476C22⋊C8—28no—
477C22⋊C8—42no—
478C22⋊C8—44no—
479C22⋊C8—42no—
480#95—22no—
481#95—22no—
482#95—22no—
483#95—22no—
484#95—22no—
485#95—22no—
486#95—22no—
487#95—22no—
488#95—22no—
489#95—22no—
490#95—22no—
491#95—22no—
492#95—22no—
493#95—22no—
494C24—22no—
495C24—22no—
496C24—22no—
497C24—22no—
498C24—22no—
499C24—22no—
500C24—22no—
501C24—22no—
502C24—22no—
503C24—22no—
504C24—22no—
505C24—22no—
506C24—22no—
507C24—22no—
508C24—22no—
509C24—22no—
510C24—22no—
511C24—22no—
512C24—22no—
513C24—22no—
514C24—22no—
515C24—22no—
516C24—22no—
517C24—22no—
518C24—22no—
519C24—22no—
520C24—22no—
521C24—22no—
522C24—22no—
523C24—22no—
524C24—41no—
525C24—41no—
526C24—41no—
527C24—41no—
528C24—41no—
529C24—41no—
530C24—41no—
531C24—41no—
532C24—41no—
533C24—41no—
534C24—41no—
535C24—41no—
536C24—41no—
537C24—41no—
538C24—41no—
539C24—41no—
540C24—416no—
541C24—416no—
542C24—416no—
543C24—416no—
544C24—416no—
545C24—416no—
546C24—416no—
547C24#12314yes—
548C24#13514yes—
549C24#13714yes—
550C24C22×D411yescharacteristic
551C24C22×D411yescharacteristic
552C24C22×D411yescharacteristic
553C24C22×D411yescharacteristic
554C24C22×D411yescharacteristic
555C24C22×D411yescharacteristic
556C24C22×D411yescharacteristic
557C2×Q8—24no—
558C2×Q8—22no—
559C2×Q8—22no—
560C2×Q8—24no—
561C2×Q8—42no—
562C2×Q8—42no—
563C2×Q8—42no—
564C2×Q8—88no—
565C22×C4—232no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—22no—
591C22×C4—22no—
592C22×C4—22no—
593C22×C4—22no—
594C22×C4—22no—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—22no—
598C22×C4—22no—
599C22×C4—22no—
600C22×C4—22no—
601C22×C4—22no—
602C22×C4—22no—
603C22×C4—22no—
604C22×C4—22no—
605C22×C4—22no—
606C22×C4—22no—
607C22×C4—22no—
608C22×C4—22no—
609C22×C4—22no—
610C22×C4—22no—
611C22×C4—22no—
612C22×C4—22no—
613C22×C4—22no—
614C22×C4—22no—
615C22×C4—22no—
616C22×C4—22no—
617C22×C4—22no—
618C22×C4—22no—
619C22×C4—22no—
620C22×C4—22no—
621C22×C4—22no—
622C22×C4—22no—
623C22×C4—22no—
624C22×C4—22no—
625C22×C4—22no—
626C22×C4—416no—
627C22×C4—41no—
628C22×C4—41no—
629C22×C4—41no—
630C22×C4—41no—
631C22×C4—41no—
632C22×C4—41no—
633C22×C4—41no—
634C22×C4—41no—
635C22×C4—41no—
636C22×C4—41no—
637C22×C4—41no—
638C22×C4—41no—
639C22×C4—41no—
640C22×C4—41no—
641C22×C4—41no—
642C22×C4—41no—
643C22×C4—41no—
644C22×C4—41no—
645C22×C4—41no—
646C22×C4—41no—
647C22×C4—41no—
648C22×C4—41no—
649C22×C4—41no—
650C22×C4—41no—
651C22×C4—416no—
652C22×C4—416no—
653C22×C4—416no—
654C22×C4—416no—
655C22×C4—416no—
656C22×C4—416no—
657C22×C4—416no—
658C22×C4—416no—
659C22×C4—416no—
660C22×C4—416no—
661C22×C4—416no—
662C22×C4—416no—
663C22×C4—42no—
664C22×C4—42no—
665C22×C4—42no—
666C22×C4—42no—
667C22×C4—42no—
668C22×C4—42no—
669C22×C4—42no—
670C22×C4—42no—
671C22×C4—42no—
672C22×C4—42no—
673C22×C4—42no—
674C22×C4—42no—
675C22×C4—42no—
676C22×C4—42no—
677C22×C4—42no—
678C22×C4—42no—
679C22×C4—42no—
680C22×C4—42no—
681C22×C4—42no—
682C22×C4—42no—
683C22×C4—42no—
684C22×C4—42no—
685C22×C4—42no—
686C22×C4—42no—
687C22×C4#12314yes—
688C22×C4#12314yes—
689C22×C4#12314yes—
690C22×C4C22×D411yescharacteristic
691C22×C4C22×D411yescharacteristic
692C22×C4C22×D411yescharacteristic
693C22×C4C22×D411yescharacteristic
694C22×C4C22×D411yescharacteristic
695C22×C4C22×D411yescharacteristic
696C22×C4C22×D411yescharacteristic
697C22×C4C2×#4114yes—
698C22×C4C2×#4114yes—
699C22×C4C2×#4114yes—
700C22×C4H(5,𝔽2)14yes—
701C22×C4H(5,𝔽2)14yes—
702C22×C4C2511yescharacteristic
703C2×C8—24no—
704C2×C8—24no—
705C2×C8—24no—
706C2×C8—24no—
707C2×C8—24no—
708C2×C8—24no—
709C2×C8—88no—
710C4⋊C4—24no—
711C4⋊C4—24no—
712C4⋊C4—24no—
713C4⋊C4—24no—
714C4⋊C4—24no—
715C4⋊C4—22no—
716C4⋊C4—24no—
717C4⋊C4—22no—
718C4⋊C4—42no—
719C4⋊C4—42no—
720C4⋊C4—42no—
721C4⋊C4—42no—
722C4⋊C4—44no—
723C4⋊C4—44no—
724C4⋊C4—42no—
725C4⋊C4—44no—
726C4⋊C4—44no—
727C4⋊C4—42no—
728C4⋊C4—42no—
729C4⋊C4—44no—
730C4⋊C4—44no—
731C22⋊C4—44no—
732C22⋊C4—44no—
733C22⋊C4—44no—
734C22⋊C4—44no—
735C22⋊C4—44no—
736C22⋊C4—44no—
737C22⋊C4—44no—
738C22⋊C4—44no—
739C22⋊C4—44no—
740C22⋊C4—44no—
741C22⋊C4—44no—
742C22⋊C4—44no—
743C22⋊C4—44no—
744C22⋊C4—44no—
745C22⋊C4—44no—
746C22⋊C4—44no—
747C22⋊C4—44no—
748C22⋊C4—44no—
749C22⋊C4—44no—
750C22⋊C4—44no—
751C22⋊C4—44no—
752C22⋊C4—44no—
753C22⋊C4—44no—
754C22⋊C4—44no—
755C42—44no—
756C42—44no—
757C42—44no—
758C42—44no—
759C23—21no—
760C23—21no—
761C23—21no—
762C23—21no—
763C23—21no—
764C23—21no—
765C23—21no—
766C23—21no—
767C23—21no—
768C23—21no—
769C23—21no—
770C23—21no—
771C23—28no—
772C23—28no—
773C23—28no—
774C23—28no—
775C23—28no—
776C23—28no—
777C23—28no—
778C23—21no—
779C23—21no—
780C23—21no—
781C23—21no—
782C23—21no—
783C23—21no—
784C23—21no—
785C23—21no—
786C23—21no—
787C23—21no—
788C23—28no—
789C23—28no—
790C23—21no—
791C23—21no—
792C23—21no—
793C23—21no—
794C23—21no—
795C23—21no—
796C23—21no—
797C23—21no—
798C23—21no—
799C23—21no—
800C23—21no—
801C23—21no—
802C23—21no—
803C23—21no—
804C23—44no—
805C23—44no—
806C23—44no—
807C23—44no—
808C23—44no—
809C23—44no—
810C23—44no—
811C23—44no—
812C23—44no—
813C23—44no—
814C23—44no—
815C23—44no—
816C23—44no—
817C23—44no—
818C23—44no—
819C23—44no—
820C23—44no—
821C23—44no—
822C23—44no—
823C23—44no—
824C23—44no—
825C23—44no—
826C23—44no—
827C23—44no—
828C23—44no—
829C23—44no—
830C23—44no—
831C23—44no—
832C23—44no—
833C23—44no—
834C23—44no—
835C23—44no—
836C23—44no—
837C23—44no—
838C23—44no—
839C23—44no—
840C23—4128no—
841C23—44no—
842C23—44no—
843C23—44no—
844C23—44no—
845C23C2×#12312yes—
846C23C2×#12312yes—
847C23C2×#12312yes—
848C23#53412yes—
849C23#53412yes—
850C23C2×#13512yes—
851C23C2×#13512yes—
852C23C2×#13512yes—
853C23C2×#13712yes—
854C23C2×#13712yes—
855C23C2×#13712yes—
856C23#57512yes—
857C23#57512yes—
858C23C23×D411yescharacteristic
859Q8—44no—
860Q8—44no—
861Q8—84no—
862C2×C4—28no—
863C2×C4—28no—
864C2×C4—28no—
865C2×C4—21no—
866C2×C4—21no—
867C2×C4—21no—
868C2×C4—21no—
869C2×C4—21no—
870C2×C4—21no—
871C2×C4—21no—
872C2×C4—21no—
873C2×C4—21no—
874C2×C4—21no—
875C2×C4—28no—
876C2×C4—28no—
877C2×C4—28no—
878C2×C4—28no—
879C2×C4—28no—
880C2×C4—21no—
881C2×C4—21no—
882C2×C4—21no—
883C2×C4—21no—
884C2×C4—21no—
885C2×C4—21no—
886C2×C4—44no—
887C2×C4—44no—
888C2×C4—44no—
889C2×C4—44no—
890C2×C4—44no—
891C2×C4—44no—
892C2×C4—44no—
893C2×C4—44no—
894C2×C4—44no—
895C2×C4—44no—
896C2×C4—44no—
897C2×C4—44no—
898C2×C4—44no—
899C2×C4—44no—
900C2×C4—44no—
901C2×C4—44no—
902C2×C4—44no—
903C2×C4—44no—
904C2×C4—44no—
905C2×C4—44no—
906C2×C4—42no—
907C2×C4—42no—
908C2×C4—42no—
909C2×C4—42no—
910C2×C4—42no—
911C2×C4—42no—
912C2×C4—42no—
913C2×C4—42no—
914C2×C4—42no—
915C2×C4—42no—
916C2×C4—42no—
917C2×C4—42no—
918C2×C4—42no—
919C2×C4—42no—
920C2×C4—42no—
921C2×C4—42no—
922C2×C4—42no—
923C2×C4—42no—
924C2×C4—42no—
925C2×C4—42no—
926C2×C4—42no—
927C2×C4—42no—
928C2×C4—42no—
929C2×C4—42no—
930C2×C4—84no—
931C2×C4—84no—
932C2×C4—84no—
933C2×C4—84no—
934C2×C4—84no—
935C2×C4—84no—
936C2×C4—84no—
937C2×C4—84no—
938C2×C4C2×#12312yes—
939C2×C4C2×#12312yes—
940C2×C4C2×#12312yes—
941C2×C4#53412yes—
942C2×C4#53412yes—
943C2×C4C22×#4112yes—
944C2×C4C2×H(5,𝔽2)12yes—
945C2×C4C2×H(5,𝔽2)12yes—
946C8—44no—
947C8—44no—
948C22—22no—
949C22—22no—
950C22—22no—
951C22—22no—
952C22—22no—
953C22—22no—
954C22—22no—
955C22—22no—
956C22—22no—
957C22—22no—
958C22—22no—
959C22—22no—
960C22—22no—
961C22—22no—
962C22—22no—
963C22—22no—
964C22—22no—
965C22—22no—
966C22—22no—
967C22—22no—
968C22—22no—
969C22—22no—
970C22—22no—
971C22—22no—
972C22—22no—
973C22—22no—
974C22—22no—
975C22—22no—
976C22—22no—
977C22—22no—
978C22—416no—
979C22—416no—
980C22—416no—
981C22—416no—
982C22—416no—
983C22—416no—
984C22—416no—
985C22—41no—
986C22—41no—
987C22—41no—
988C22—41no—
989C22—41no—
990C22—41no—
991C22—41no—
992C22—41no—
993C22—41no—
994C22—41no—
995C22—41no—
996C22—41no—
997C22—41no—
998C22—41no—
999C22—41no—
1000C22—41no—
1001C22#309114yes—
1002C22#309514yes—
1003C22#319014yes—
1004C22C22×#12311yescharacteristic
1005C22C2×#53411yescharacteristic
1006C22C2×#53411yescharacteristic
1007C22C22×#13511yescharacteristic
1008C22C22×#13711yescharacteristic
1009C22C2×#57511yescharacteristic
1010C22C2×#57511yescharacteristic
1011C4—22no—
1012C4—22no—
1013C4—22no—
1014C4—22no—
1015C4—22no—
1016C4—41no—
1017C4—41no—
1018C4—82no—
1019C4—82no—
1020C4—82no—
1021C4—82no—
1022C4—82no—
1023C4—82no—
1024C4—82no—
1025C4—82no—
1026C4#349014yes—
1027C2—24no—
1028C2—24no—
1029C2—24no—
1030C2—42no—
1031C2—42no—
1032C2—42no—
1033C2—42no—
1034C2#3499211yescharacteristic
1035C2C2×#309111yescharacteristic
1036C2C2×#309511yescharacteristic
1037C2C2×#319011yescharacteristic
1038C2#6073411yescharacteristic
1039C2#6075111yescharacteristic
1040C2#6075211yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC26D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C25×C4 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
3. #32985C2semidirect
4. #32984C2semidirect
5. #29897C2semidirect
6. #27602C2semidirect
7. #27601C2semidirect
8. #27600C2semidirect
9. #24554C2semidirect
10. #24552C2semidirect
11. #24551C2semidirect
12. #24010C2semidirect
13. #24006C2semidirect
14. #24003C2semidirect
15. #21941C2semidirect
16. #21762C2semidirect
24. C2×#484C22semidirect
25. C2×#485C22semidirect
26. C2×#483C22semidirect
61. #2077C22semidirect
62. #2077C22semidirect
63. #2076C22semidirect
64. #2075C22semidirect
65. #2036C22semidirect
66. #2036C22semidirect
67. #2035C22semidirect
68. #2035C22semidirect
69. #1892C22semidirect
70. #1892C22semidirect
71. #1873C22semidirect
72. #1873C22semidirect
73. #1873C22semidirect
74. #1872C22semidirect
75. #1872C22semidirect
76. #1854C22semidirect
77. #1854C22semidirect
78. #1854C22semidirect
79. #1853C22semidirect
80. #1853C22semidirect
81. #1853C22semidirect
82. #1852C22semidirect
83. #1852C22semidirect
84. #1852C22semidirect
85. #1825C22semidirect
86. #1824C22semidirect
87. #1823C22semidirect
88. #1823C22semidirect
89. #1823C22semidirect
90. #1808C22semidirect
91. #1807C22semidirect
92. #1787C22semidirect
93. #1787C22semidirect
171. C2×#107C23semidirect
172. C2×#107C23semidirect
173. C2×#106C23semidirect
174. C2×#106C23semidirect
175. C2×#103C23semidirect
176. C2×#103C23semidirect
177. C2×#103C23semidirect
178. C2×#103C23semidirect
258. #340C23semidirect
259. #340C23semidirect
260. #340C23semidirect
261. #340C23semidirect
262. #340C23semidirect
263. #340C23semidirect
264. #340C23semidirect
265. #340C23semidirect

Maximal subgroups

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

subgroupindex
C2×#28482
C2×#22802
#329852
#329842
#298972
#276022
#276012
#276002
#245542
#245522
#245512
#240102
#240062
#240032
#219412
#217622
C2×#17792