Finite Group Databasebeta

← #6490841

Subgroups — #6490841

Order 512.

3658 conjugacy classes of subgroups.

The subgroup lattice has 1036 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#529C211yesmaximal, characteristic, complemented
2C2×#3211C212yesmaximal, complemented
3C2×#2850C211yesmaximal, characteristic, complemented
4#32909C212yesmaximal, complemented
5#32908C212yesmaximal, complemented
6#29666C214yesmaximal, complemented
7#25907C212yesmaximal, complemented
8#25724C212yesmaximal, complemented
9#25601C214yesmaximal, complemented
10#23937C212yesmaximal, complemented
11#23936C212yesmaximal, complemented
12#23921C211yesmaximal, characteristic, complemented
13#23919C211yesmaximal, characteristic, complemented
14#23919C211yesmaximal, characteristic, complemented
15#23918C211yesmaximal, characteristic
16#21861C212yesmaximal, complemented
17#20714C211yesmaximal, characteristic, complemented
18C2×#529—21no—
19C2×#529—21no—
20C2×#529—21no—
21C2×#529—21no—
22C2×#529—216no—
23C2×#529C2212yes—
24C2×#529C2212yes—
25C2×#529C2212yescomplemented
26C2×#529C2212yescomplemented
27C22×#126—21no—
28C22×#125C2211yescharacteristic, complemented
29C22×#124C2211yescharacteristic, complemented
30C22×#124C2211yescharacteristic, complemented
31C22×#123—21no—
32C22×C22⋊Q8C2211yescharacteristic
33C22×C22⋊Q8C2211yescharacteristic
34C22×#121C2211yescharacteristic
35C22×#121C2211yescharacteristic
36C22×C4×Q8C2211yescharacteristic, complemented
37C22×C4×D4—21no—
38C22×C4×D4C2211yescharacteristic, complemented
39C22×#117—21no—
40C23×C42C2211yescharacteristic
41#3211—216no—
42C2×#495C2214yescomplemented
43C2×#488C2214yescomplemented
44C2×#464C2214yescomplemented
45C2×#463C2214yescomplemented
46C2×#451C2212yescomplemented
47C2×#451C2212yescomplemented
48C2×#448C2212yes—
49C2×#448C2212yes—
50C2×#450C2212yescomplemented
51C2×#450C2212yescomplemented
52C2×#447C2212yes—
53C2×#447C2212yes—
54C2×#431C2212yescomplemented
55#2850—21no—
56#2850—21no—
57#2850—21no—
58#2850—21no—
59#2850C2212yes—
60#2850C2212yes—
61#2850C2212yescomplemented
62#2850C2212yescomplemented
63C2×#391C2211yescharacteristic, complemented
64C2×#390C2211yescharacteristic, complemented
65C2×#388—21no—
66C2×#388—21no—
67C2×#386—21no—
68C2×#386—21no—
69C2×#382C2211yescharacteristic, complemented
70#2026C2214yescomplemented
71#2025C2214yescomplemented
72#2015C2214yescomplemented
73#2012C2214yescomplemented
74#2001C2214yescomplemented
75#2000C2214yescomplemented
76#2000C2214yescomplemented
77#1999C2214yes—
78#1991C2214yescomplemented
79#1958C2214yescomplemented
80#1880C2214yescomplemented
81#1879C2214yescomplemented
82#1878C2214yescomplemented
83#1877C2214yescomplemented
84#1874C2212yes—
85#1874C2212yes—
86#1874C2212yes—
87#1874C2212yes—
88#1872C2212yescomplemented
89#1872C2212yescomplemented
90#1872C2212yescomplemented
91#1872C2212yescomplemented
92#1817C2212yescomplemented
93#1805C2214yescomplemented
94#1804C2214yescomplemented
95#1797C2212yescomplemented
96#1797C2212yescomplemented
97#1779C2211yescharacteristic
98#1779C2211yescharacteristic
99C4×C22⋊C8C2212yescomplemented
100C4×C22⋊C8C2212yescomplemented
101C23×Q8C2311yescharacteristic
102C23×Q8C2311yescharacteristic
103C23×D4—21no—
104C23×D4—21no—
105C23×D4C2311yescharacteristic
106C23×D4C2311yescharacteristic
107C24×C4—21no—
108C24×C4D411yescharacteristic
109C24×C4D411yescharacteristic
110C24×C4C2311yescharacteristic
111C22×Q16C2314yes—
112C22×SD16C2314yes—
113C22×SD16C2314yes—
114C22×D8C2314yes—
115#529—216no—
116#529—216no—
117#529—216no—
118#529—216no—
119#529—28no—
120#529—28no—
121#529—28no—
122#529—28no—
123#529—28no—
124#529—28no—
125#529—28no—
126#529D4116yescomplemented
127C2×#126—216no—
128C2×#126—22no—
129C2×#126—22no—
130C2×#126—22no—
131C2×#126—22no—
132C2×#125—28no—
133C2×#125—21no—
134C2×#125—21no—
135C2×#125C2312yes—
136C2×#125C2312yes—
137C2×#124—28no—
138C2×#124—21no—
139C2×#124—21no—
140C2×#124—21no—
141C2×#124—21no—
142C2×#124—28no—
143C2×#124C2312yes—
144C2×#124C2312yes—
145C2×#124C2312yes—
146C2×#124C2312yes—
147C2×#123—216no—
148C2×#123—22no—
149C2×#123—22no—
150C2×#123—22no—
151C2×#123—22no—
152C2×C22⋊Q8—21no—
153C2×C22⋊Q8—21no—
154C2×C22⋊Q8—28no—
155C2×C22⋊Q8—21no—
156C2×C22⋊Q8—21no—
157C2×C22⋊Q8—44no—
158C2×C22⋊Q8C2312yes—
159C2×C22⋊Q8C2312yes—
160C2×C22⋊Q8C2312yes—
161C2×C22⋊Q8C2312yes—
162C2×#121—21no—
163C2×#121—21no—
164C2×#121—28no—
165C2×#121—21no—
166C2×#121—21no—
167C2×#121—44no—
168C2×#121C2312yes—
169C2×#121C2312yes—
170C2×#121C2312yes—
171C2×#121C2312yes—
172C2×C4×Q8—28no—
173C2×C4×Q8—21no—
174C2×C4×Q8—21no—
175C2×C4×Q8C2312yes—
176C2×C4×Q8C2312yes—
177C2×C4×D4—216no—
178C2×C4×D4—22no—
179C2×C4×D4—22no—
180C2×C4×D4—22no—
181C2×C4×D4—22no—
182C2×C4×D4—28no—
183C2×C4×D4—21no—
184C2×C4×D4—21no—
185C2×C4×D4C2312yes—
186C2×C4×D4C2312yes—
187C2×#117—216no—
188C2×#117—22no—
189C2×#117—22no—
190C2×#117—22no—
191C2×#117—22no—
192C22×C4⋊C4—21no—
193C22×C4⋊C4—21no—
194C22×C4⋊C4—21no—
195C22×C4⋊C4—21no—
196C22×C4⋊C4—21no—
197C22×C4⋊C4C2311yescharacteristic
198C22×C4⋊C4C2311yescharacteristic
199C22×C4⋊C4C2311yescharacteristic
200C22×C4⋊C4C2311yescharacteristic
201C22×C22⋊C4—21no—
202C22×C22⋊C4—21no—
203C22×C22⋊C4—21no—
204C22×C22⋊C4—21no—
205C22×C22⋊C4—21no—
206C22×C22⋊C4—21no—
207C22×C22⋊C4—21no—
208C22×C22⋊C4—21no—
209C22×C22⋊C4—21no—
210C22×C22⋊C4—21no—
211C22×C22⋊C4—21no—
212C22×C42—21no—
213C22×C42—28no—
214C22×C42D411yescharacteristic
215C22×C42D411yescharacteristic
216C22×C42D411yescharacteristic
217C22×C42D411yescharacteristic
218C22×C42D411yescharacteristic
219C22×C42D411yescharacteristic
220C22×C42C2311yescharacteristic
221C22×C42C2311yescharacteristic
222C22×C42C2311yescharacteristic
223C22×C42C2311yescharacteristic
224C22×C42C2311yescharacteristic
225C22×C42C2311yescharacteristic
226#495—216no—
227#488—216no—
228#464—216no—
229#463—216no—
230#451—28no—
231#451—44no—
232#450—28no—
233#450—44no—
234#448—28no—
235#448—44no—
236#447—28no—
237#447—44no—
238#431—28no—
239C2×C4⋊C8C2314yes—
240C2×#103C2314yes—
241C2×#103C2314yes—
242C2×#103C2314yes—
243C2×#103C2314yes—
244C2×#102C2314yes—
245C2×#102C2314yes—
246C2×#102C2314yes—
247C2×#102C2314yes—
248C2×C22⋊C8C2312yes—
249C2×C22⋊C8C2312yes—
250C2×C22⋊C8C2312yes—
251C2×C22⋊C8C2312yes—
252C2×C22⋊C8C2312yes—
253C2×C22⋊C8C2312yes—
254C2×C4×C8C2314yes—
255#391—21no—
256#391—21no—
257#391C2312yes—
258#391C2312yes—
259#390—21no—
260#390—21no—
261#390C2312yes—
262#390C2312yes—
263#388—22no—
264#388—22no—
265#388—22no—
266#388—22no—
267#388—22no—
268#388—22no—
269#388—22no—
270#388—22no—
271#386—22no—
272#386—22no—
273#386—22no—
274#386—22no—
275#386—22no—
276#386—22no—
277#386—22no—
278#386—22no—
279#382—21no—
280#382—21no—
281#382C2312yes—
282#382C2312yes—
283C2×#95—21no—
284C2×#95—21no—
285C2×#95—21no—
286C2×#95—21no—
287#340C2314yes—
288#340C2314yes—
289#340C2314yes—
290#340C2314yes—
291#336C2314yes—
292#336C2314yes—
293C25—21no—
294C25—21no—
295C25C2×D411yescharacteristic
296C22×Q8—24no—
297C22×Q8—21no—
298C22×Q8—21no—
299C22×Q8—24no—
300C22×Q8—24no—
301C22×Q8—42no—
302C22×Q8—42no—
303C22×Q8—42no—
304C22×Q8C2412yes—
305C22×Q8C2412yes—
306C22×D4—28no—
307C22×D4—22no—
308C22×D4—22no—
309C22×D4—24no—
310C22×D4—22no—
311C22×D4—22no—
312C22×D4—21no—
313C22×D4—24no—
314C22×D4—21no—
315C22×D4—24no—
316C22×D4—42no—
317C22×D4—42no—
318C22×D4—42no—
319C22×D4—44no—
320C22×D4—44no—
321C22×D4—44no—
322C22×D4—44no—
323C22×D4—44no—
324C22×D4C2412yes—
325C22×D4C2412yes—
326C23×C4—28no—
327C23×C4—24no—
328C23×C4—21no—
329C23×C4—21no—
330C23×C4—21no—
331C23×C4—24no—
332C23×C4—24no—
333C23×C4—22no—
334C23×C4—22no—
335C23×C4—24no—
336C23×C4—24no—
337C23×C4—21no—
338C23×C4—21no—
339C23×C4—21no—
340C23×C4—42no—
341C23×C4—42no—
342C23×C4—42no—
343C23×C4—42no—
344C23×C4—44no—
345C23×C4—44no—
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×C4C2×D411yescharacteristic
357C23×C4C2×D411yescharacteristic
358C23×C4C2×D411yescharacteristic
359C23×C4C2×D411yescharacteristic
360C23×C4C2×D411yescharacteristic
361C23×C4C2411yescharacteristic
362C23×C4C2411yescharacteristic
363C23×C4C2411yescharacteristic
364C2×Q16—28no—
365C2×Q16—44no—
366C2×Q16—44no—
367C2×SD16—28no—
368C2×SD16—28no—
369C2×SD16—44no—
370C2×SD16—44no—
371C2×SD16—44no—
372C2×SD16—44no—
373C2×D8—28no—
374C2×D8—44no—
375C2×D8—44no—
376C22×C8C2414yes—
377C22×C8C2414yes—
378#126—216no—
379#126—216no—
380#126—216no—
381#126—216no—
382#125—28no—
383#125—28no—
384#125—24no—
385#125—24no—
386#125—24no—
387#125C2×D418yescomplemented
388#124—28no—
389#124—28no—
390#124—24no—
391#124—24no—
392#124—24no—
393#124—28no—
394#124—28no—
395#124—44no—
396#124—44no—
397#124C2×D418yescomplemented
398#123—216no—
399#123—216no—
400#123—216no—
401#123—216no—
402C22⋊Q8—28no—
403C22⋊Q8—28no—
404C22⋊Q8—24no—
405C22⋊Q8—24no—
406C22⋊Q8—24no—
407C22⋊Q8—24no—
408C22⋊Q8—24no—
409C22⋊Q8—42no—
410C22⋊Q8—42no—
411C22⋊Q8—44no—
412C22⋊Q8—44no—
413C22⋊Q8C2×D418yes—
414#121—28no—
415#121—28no—
416#121—24no—
417#121—24no—
418#121—24no—
419#121—24no—
420#121—24no—
421#121—42no—
422#121—42no—
423#121—44no—
424#121—44no—
425#121C2×D418yes—
426C4×Q8—28no—
427C4×Q8—28no—
428C4×Q8—24no—
429C4×Q8—24no—
430C4×Q8—24no—
431C4×Q8C2×D418yescomplemented
432C4×D4—216no—
433C4×D4—216no—
434C4×D4—28no—
435C4×D4—28no—
436C4×D4—216no—
437C4×D4—24no—
438C4×D4—216no—
439C4×D4—24no—
440C4×D4—24no—
441C4×D4C2×D418yescomplemented
442#117—216no—
443#117—216no—
444#117—216no—
445#117—216no—
446C2×C4⋊C4—28no—
447C2×C4⋊C4—28no—
448C2×C4⋊C4—28no—
449C2×C4⋊C4—28no—
450C2×C4⋊C4—22no—
451C2×C4⋊C4—22no—
452C2×C4⋊C4—22no—
453C2×C4⋊C4—22no—
454C2×C4⋊C4—22no—
455C2×C4⋊C4—22no—
456C2×C4⋊C4—22no—
457C2×C4⋊C4—22no—
458C2×C4⋊C4—21no—
459C2×C4⋊C4—21no—
460C2×C4⋊C4—24no—
461C2×C4⋊C4—24no—
462C2×C4⋊C4—22no—
463C2×C4⋊C4—22no—
464C2×C4⋊C4—21no—
465C2×C4⋊C4—21no—
466C2×C4⋊C4—42no—
467C2×C4⋊C4—42no—
468C2×C4⋊C4—44no—
469C2×C4⋊C4C2412yes—
470C2×C4⋊C4C2412yes—
471C2×C4⋊C4C2412yes—
472C2×C4⋊C4C2412yes—
473C2×C22⋊C4—28no—
474C2×C22⋊C4—28no—
475C2×C22⋊C4—28no—
476C2×C22⋊C4—28no—
477C2×C22⋊C4—28no—
478C2×C22⋊C4—22no—
479C2×C22⋊C4—22no—
480C2×C22⋊C4—22no—
481C2×C22⋊C4—22no—
482C2×C22⋊C4—22no—
483C2×C22⋊C4—22no—
484C2×C22⋊C4—22no—
485C2×C22⋊C4—22no—
486C2×C22⋊C4—22no—
487C2×C22⋊C4—22no—
488C2×C22⋊C4—22no—
489C2×C22⋊C4—22no—
490C2×C22⋊C4—22no—
491C2×C22⋊C4—22no—
492C2×C22⋊C4—22no—
493C2×C22⋊C4—22no—
494C2×C22⋊C4—22no—
495C2×C22⋊C4—22no—
496C2×C22⋊C4—22no—
497C2×C22⋊C4—22no—
498C2×C22⋊C4—22no—
499C2×C22⋊C4—22no—
500C2×C22⋊C4—44no—
501C2×C22⋊C4—44no—
502C2×C22⋊C4—44no—
503C2×C22⋊C4—44no—
504C2×C22⋊C4—44no—
505C2×C22⋊C4—44no—
506C2×C42—28no—
507C2×C42—24no—
508C2×C42—24no—
509C2×C42—22no—
510C2×C42—22no—
511C2×C42—24no—
512C2×C42—24no—
513C2×C42—24no—
514C2×C42—24no—
515C2×C42—24no—
516C2×C42—24no—
517C2×C42—24no—
518C2×C42—24no—
519C2×C42—24no—
520C2×C42C2×D411yescharacteristic
521C2×C42C2×D411yescharacteristic
522C2×C42C2×D411yescharacteristic
523C2×C42C2×D411yescharacteristic
524C2×C42C2×D411yescharacteristic
525C2×C42C2×D411yescharacteristic
526C2×C42C2×D411yescharacteristic
527C2×C42C2×D411yescharacteristic
528C2×C42C2×D411yescharacteristic
529C2×C42C2×D411yescharacteristic
530C2×C42C2×D411yescharacteristic
531C2×C42C2×D411yescharacteristic
532C2×C42C2×D418yes—
533C2×C42C2411yescharacteristic
534C2×C42C2411yescharacteristic
535C2×C42C2411yescharacteristic
536C2×C42C2411yescharacteristic
537C4⋊C8—28no—
538#103—28no—
539#103—28no—
540#103—44no—
541#103—44no—
542#102—28no—
543#102—28no—
544#102—44no—
545#102—44no—
546C22⋊C8—24no—
547C22⋊C8—24no—
548C22⋊C8—24no—
549C22⋊C8—24no—
550C22⋊C8—42no—
551C22⋊C8—42no—
552C4×C8—28no—
553#95—22no—
554#95—22no—
555#95—22no—
556#95—22no—
557#95—22no—
558#95—22no—
559#95—22no—
560#95—22no—
561C24—22no—
562C24—22no—
563C24—22no—
564C24—22no—
565C24—24no—
566C24—22no—
567C24—22no—
568C24—41no—
569C24—41no—
570C24—42no—
571C24—42no—
572C24—42no—
573C24—42no—
574C24—42no—
575C24—42no—
576C24—42no—
577C24—42no—
578C24—42no—
579C24—42no—
580C24—42no—
581C24—42no—
582C24—42no—
583C24#13514yes—
584C24C22×D411yescharacteristic
585C24C22×D411yescharacteristic
586C24C22×D411yescharacteristic
587C2×Q8—24no—
588C2×Q8—22no—
589C2×Q8—24no—
590C2×Q8—24no—
591C2×Q8—22no—
592C2×Q8—22no—
593C2×Q8—24no—
594C2×Q8—24no—
595C2×Q8—416no—
596C2×Q8—42no—
597C2×Q8—42no—
598C2×Q8—42no—
599C2×Q8—42no—
600C2×Q8—42no—
601C2×Q8—88no—
602C2×Q8C22×D414yes—
603C2×D4—28no—
604C2×D4—24no—
605C2×D4—28no—
606C2×D4—22no—
607C2×D4—24no—
608C2×D4—24no—
609C2×D4—22no—
610C2×D4—22no—
611C2×D4—24no—
612C2×D4—24no—
613C2×D4—416no—
614C2×D4—42no—
615C2×D4—42no—
616C2×D4—42no—
617C2×D4—432no—
618C2×D4—44no—
619C2×D4—44no—
620C2×D4—44no—
621C2×D4—44no—
622C2×D4—44no—
623C2×D4—44no—
624C2×D4—44no—
625C2×D4—44no—
626C2×D4—44no—
627C2×D4—44no—
628C2×D4—42no—
629C2×D4—42no—
630C2×D4—88no—
631C2×D4—816no—
632C2×D4C22×D414yes—
633C22×C4—22no—
634C22×C4—22no—
635C22×C4—22no—
636C22×C4—22no—
637C22×C4—22no—
638C22×C4—22no—
639C22×C4—22no—
640C22×C4—22no—
641C22×C4—22no—
642C22×C4—24no—
643C22×C4—24no—
644C22×C4—24no—
645C22×C4—28no—
646C22×C4—22no—
647C22×C4—22no—
648C22×C4—22no—
649C22×C4—22no—
650C22×C4—22no—
651C22×C4—22no—
652C22×C4—22no—
653C22×C4—22no—
654C22×C4—22no—
655C22×C4—22no—
656C22×C4—22no—
657C22×C4—22no—
658C22×C4—22no—
659C22×C4—22no—
660C22×C4—22no—
661C22×C4—22no—
662C22×C4—22no—
663C22×C4—22no—
664C22×C4—22no—
665C22×C4—22no—
666C22×C4—22no—
667C22×C4—22no—
668C22×C4—22no—
669C22×C4—28no—
670C22×C4—22no—
671C22×C4—22no—
672C22×C4—22no—
673C22×C4—22no—
674C22×C4—22no—
675C22×C4—22no—
676C22×C4—22no—
677C22×C4—22no—
678C22×C4—22no—
679C22×C4—22no—
680C22×C4—41no—
681C22×C4—41no—
682C22×C4—41no—
683C22×C4—41no—
684C22×C4—41no—
685C22×C4—41no—
686C22×C4—41no—
687C22×C4—41no—
688C22×C4—41no—
689C22×C4—41no—
690C22×C4—41no—
691C22×C4—41no—
692C22×C4—41no—
693C22×C4—41no—
694C22×C4—416no—
695C22×C4—416no—
696C22×C4—416no—
697C22×C4—432no—
698C22×C4—44no—
699C22×C4—44no—
700C22×C4—44no—
701C22×C4—42no—
702C22×C4—42no—
703C22×C4—42no—
704C22×C4—42no—
705C22×C4—42no—
706C22×C4—42no—
707C22×C4—44no—
708C22×C4—42no—
709C22×C4—42no—
710C22×C4—42no—
711C22×C4—42no—
712C22×C4—42no—
713C22×C4—42no—
714C22×C4—42no—
715C22×C4—42no—
716C22×C4—42no—
717C22×C4#12014yes—
718C22×C4#12014yes—
719C22×C4C22×D411yescharacteristic
720C22×C4C22×D411yescharacteristic
721C22×C4C22×D411yescharacteristic
722C22×C4C22×D411yescharacteristic
723C22×C4C22×D411yescharacteristic
724C22×C4C22×D411yescharacteristic
725C22×C4C22×D411yescharacteristic
726C22×C4C22×D411yescharacteristic
727C22×C4C22×D411yescharacteristic
728C22×C4C22×D414yes—
729C22×C4C22×D411yescharacteristic
730C22×C4C22×D411yescharacteristic
731C22×C4H(5,𝔽2)14yes—
732C22×C4C2511yescharacteristic
733Q16—88no—
734SD16—88no—
735SD16—88no—
736D8—88no—
737C2×C8—24no—
738C2×C8—24no—
739C2×C8—24no—
740C2×C8—24no—
741C2×C8—24no—
742C2×C8—24no—
743C4⋊C4—28no—
744C4⋊C4—28no—
745C4⋊C4—24no—
746C4⋊C4—28no—
747C4⋊C4—24no—
748C4⋊C4—28no—
749C4⋊C4—28no—
750C4⋊C4—28no—
751C4⋊C4—28no—
752C4⋊C4—28no—
753C4⋊C4—22no—
754C4⋊C4—22no—
755C4⋊C4—22no—
756C4⋊C4—22no—
757C4⋊C4—22no—
758C4⋊C4—22no—
759C4⋊C4—42no—
760C4⋊C4—42no—
761C4⋊C4—44no—
762C4⋊C4—44no—
763C4⋊C4C22×D414yes—
764C4⋊C4C22×D414yes—
765C22⋊C4—28no—
766C22⋊C4—28no—
767C22⋊C4—28no—
768C22⋊C4—28no—
769C22⋊C4—28no—
770C22⋊C4—28no—
771C22⋊C4—28no—
772C22⋊C4—28no—
773C22⋊C4—28no—
774C22⋊C4—28no—
775C22⋊C4—44no—
776C22⋊C4—44no—
777C22⋊C4—44no—
778C22⋊C4—44no—
779C22⋊C4—44no—
780C22⋊C4—44no—
781C22⋊C4—44no—
782C22⋊C4—44no—
783C22⋊C4—44no—
784C22⋊C4—44no—
785C22⋊C4—44no—
786C22⋊C4—44no—
787C42—28no—
788C42—22no—
789C42—22no—
790C42—22no—
791C42—22no—
792C42—22no—
793C42—22no—
794C42—22no—
795C42—22no—
796C42—22no—
797C42—22no—
798C42—28no—
799C42—22no—
800C42—22no—
801C42#12014yes—
802C42#12014yes—
803C42C22×D414yes—
804C42C22×D414yes—
805C23—21no—
806C23—21no—
807C23—21no—
808C23—21no—
809C23—21no—
810C23—21no—
811C23—21no—
812C23—21no—
813C23—21no—
814C23—21no—
815C23—21no—
816C23—28no—
817C23—28no—
818C23—21no—
819C23—21no—
820C23—21no—
821C23—24no—
822C23—44no—
823C23—44no—
824C23—44no—
825C23—44no—
826C23—44no—
827C23—48no—
828C23—48no—
829C23—48no—
830C23—42no—
831C23—42no—
832C23—42no—
833C23—42no—
834C23—42no—
835C23—42no—
836C23—42no—
837C23—42no—
838C23—42no—
839C23—42no—
840C23—42no—
841C23—42no—
842C23—42no—
843C23—84no—
844C23—84no—
845C23—84no—
846C23—84no—
847C23—84no—
848C23—84no—
849C23—84no—
850C23—84no—
851C23—84no—
852C23—84no—
853C23—84no—
854C23C2×#12012yes—
855C23#53512yes—
856C23C2×#13512yes—
857C23C2×#13512yes—
858C23C2×#13512yes—
859C23#57512yes—
860C23#57512yes—
861C23C23×D411yescharacteristic
862Q8—28no—
863Q8—48no—
864Q8—44no—
865Q8—44no—
866Q8—44no—
867Q8—84no—
868D4—28no—
869D4—48no—
870D4—416no—
871D4—416no—
872D4—44no—
873D4—44no—
874D4—44no—
875D4—84no—
876D4—88no—
877D4—88no—
878C2×C4—28no—
879C2×C4—21no—
880C2×C4—21no—
881C2×C4—21no—
882C2×C4—21no—
883C2×C4—21no—
884C2×C4—28no—
885C2×C4—21no—
886C2×C4—21no—
887C2×C4—21no—
888C2×C4—21no—
889C2×C4—21no—
890C2×C4—21no—
891C2×C4—21no—
892C2×C4—21no—
893C2×C4—21no—
894C2×C4—28no—
895C2×C4—28no—
896C2×C4—21no—
897C2×C4—21no—
898C2×C4—21no—
899C2×C4—21no—
900C2×C4—24no—
901C2×C4—24no—
902C2×C4—24no—
903C2×C4—21no—
904C2×C4—21no—
905C2×C4—21no—
906C2×C4—21no—
907C2×C4—21no—
908C2×C4—21no—
909C2×C4—21no—
910C2×C4—21no—
911C2×C4—44no—
912C2×C4—44no—
913C2×C4—44no—
914C2×C4—44no—
915C2×C4—44no—
916C2×C4—44no—
917C2×C4—44no—
918C2×C4—44no—
919C2×C4—44no—
920C2×C4—44no—
921C2×C4—44no—
922C2×C4—44no—
923C2×C4—416no—
924C2×C4—416no—
925C2×C4—48no—
926C2×C4—48no—
927C2×C4—48no—
928C2×C4—42no—
929C2×C4—42no—
930C2×C4—44no—
931C2×C4—42no—
932C2×C4—42no—
933C2×C4—42no—
934C2×C4—42no—
935C2×C4—44no—
936C2×C4—42no—
937C2×C4—42no—
938C2×C4—42no—
939C2×C4—42no—
940C2×C4—42no—
941C2×C4—42no—
942C2×C4—42no—
943C2×C4—42no—
944C2×C4—42no—
945C2×C4—84no—
946C2×C4—84no—
947C2×C4—84no—
948C2×C4C2×#12012yes—
949C2×C4C2×#12012yes—
950C2×C4C2×#12012yes—
951C2×C4C2×#12012yes—
952C2×C4C2×#12012yes—
953C2×C4#53512yes—
954C2×C4#57512yes—
955C2×C4C23×D412yes—
956C2×C4C2×H(5,𝔽2)12yes—
957C2×C4#58512yes—
958C8—44no—
959C8—44no—
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—416no—
976C22—41no—
977C22—41no—
978C22—41no—
979C22—41no—
980C22—44no—
981C22—44no—
982C22—44no—
983C22—816no—
984C22—82no—
985C22—82no—
986C22—82no—
987C22—82no—
988C22—82no—
989C22—82no—
990C22—82no—
991C22—82no—
992C22—82no—
993C22—82no—
994C22—82no—
995C22—168no—
996C22#300214yes—
997C22#321114yescomplemented
998C22C22×#12011yescharacteristic
999C22C2×#53511yescharacteristic
1000C22#344911yescharacteristic
1001C22C22×#13511yescharacteristic
1002C22C2×#57511yescharacteristic
1003C22C2×#57511yescharacteristic
1004C22C2×#57511yescharacteristic
1005C4—22no—
1006C4—22no—
1007C4—22no—
1008C4—22no—
1009C4—22no—
1010C4—22no—
1011C4—22no—
1012C4—41no—
1013C4—44no—
1014C4—41no—
1015C4—41no—
1016C4—44no—
1017C4—41no—
1018C4—44no—
1019C4—82no—
1020C4—82no—
1021C4—82no—
1022C4#348814yes—
1023C2—24no—
1024C2—24no—
1025C2—42no—
1026C2—84no—
1027C2—162no—
1028C2#3525011yescharacteristic
1029C2C2×#300211yescharacteristic
1030C2#6035911yescharacteristic
1031C2C2×#321111yescharacteristic
1032C2#6080511yescharacteristic
1033C2#6094511yescharacteristic
1034C2#6096411yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#23918C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C23×C42 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C22×#529C2semidirect
2. C2×#3211C2semidirect
3. C2×#2850C2semidirect
4. #32909C2semidirect
5. #32908C2semidirect
6. #29666C2semidirect
7. #25907C2semidirect
8. #25724C2semidirect
9. #25601C2semidirect
10. #23937C2semidirect
11. #23936C2semidirect
12. #23921C2semidirect
13. #23919C2semidirect
14. #23919C2semidirect
16. #21861C2semidirect
17. #20714C2semidirect
25. C2×#529C22semidirect
26. C2×#529C22semidirect
28. C22×#125C22semidirect
29. C22×#124C22semidirect
30. C22×#124C22semidirect
36. C22×C4×Q8C22semidirect
38. C22×C4×D4C22semidirect
42. C2×#495C22semidirect
43. C2×#488C22semidirect
44. C2×#464C22semidirect
45. C2×#463C22semidirect
46. C2×#451C22semidirect
47. C2×#451C22semidirect
50. C2×#450C22semidirect
51. C2×#450C22semidirect
54. C2×#431C22semidirect
61. #2850C22semidirect
62. #2850C22semidirect
63. C2×#391C22semidirect
64. C2×#390C22semidirect
69. C2×#382C22semidirect
70. #2026C22semidirect
71. #2025C22semidirect
72. #2015C22semidirect
73. #2012C22semidirect
74. #2001C22semidirect
75. #2000C22semidirect
76. #2000C22semidirect
78. #1991C22semidirect
79. #1958C22semidirect
80. #1880C22semidirect
81. #1879C22semidirect
82. #1878C22semidirect
83. #1877C22semidirect
88. #1872C22semidirect
89. #1872C22semidirect
90. #1872C22semidirect
91. #1872C22semidirect
92. #1817C22semidirect
93. #1805C22semidirect
94. #1804C22semidirect
95. #1797C22semidirect
96. #1797C22semidirect
99. C4×C22⋊C8C22semidirect
100. C4×C22⋊C8C22semidirect
126. #529D4semidirect
387. #125C2×D4semidirect
397. #124C2×D4semidirect
431. C4×Q8C2×D4semidirect
441. C4×D4C2×D4semidirect
997. C22#3211semidirect

Maximal subgroups

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

subgroupindex
C22×#5292
C2×#32112
C2×#28502
#329092
#329082
#296662
#259072
#257242
#256012
#239372
#239362
#239212
#239192
#239182
#218612
#207142