Finite Group Databasebeta

← #6393375

Subgroups — #6393375

Order 512.

3622 conjugacy classes of subgroups.

The subgroup lattice has 907 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3505C211yesmaximal, characteristic
2C2×#2972C211yesmaximal, characteristic, complemented
3C2×#2352C211yesmaximal, characteristic, complemented
4#22488C214yesmaximal, complemented
5#22486C214yesmaximal, complemented
6#22416C214yesmaximal, complemented
7#22414C214yesmaximal, complemented
8#21861C212yesmaximal, complemented
9#21763C212yesmaximal, complemented
10#21759C211yesmaximal, characteristic, complemented
11#21758C211yesmaximal, characteristic, complemented
12#21388C212yesmaximal, complemented
13#20908C212yesmaximal, complemented
14C2×#1874C211yesmaximal, characteristic, complemented
15C2×#1872C211yesmaximal, characteristic, complemented
16#3505—28no—
17#3505C4116yescomplemented
18C2×#553—22no—
19C2×#553C2212yes—
20C2×#552C2212yes—
21C2×#551—22no—
22C2×#548C2212yes—
23C2×#546C2212yes—
24C2×#539—21no—
25C2×#538—21no—
26C2×#534—21no—
27C2×#529C2212yes—
28C2×#525C2212yes—
29C22×C22⋊Q8C2211yescharacteristic
30C22×#121C2211yescharacteristic
31C2×#518—21no—
32C22×C4×D4C2211yescharacteristic
33C22×#117C2211yescharacteristic, complemented
34C23×C4⋊C4C2211yescharacteristic
35#2972—28no—
36C2×C8×D4C2214yes—
37C2×C8×D4C2214yescomplemented
38C2×#431C2212yescomplemented
39C2×#416C2214yescomplemented
40C22×#103C2212yescomplemented
41C22×#102C2212yescomplemented
42C22×C22⋊C8C2211yescharacteristic
43C22×C22⋊C8C2211yescharacteristic
44C22×C22⋊C8C2212yescomplemented
45#2352—22no—
46#2352—22no—
47#2352C2214yes—
48#2352C2214yescomplemented
49C2×#388—21no—
50C2×#387—21no—
51C2×#386—21no—
52C2×#382C2211yescharacteristic, complemented
53C2×#380C2211yescharacteristic
54C2×#380C2211yescharacteristic, complemented
55C2×C4×C4⋊C4C2211yescharacteristic, complemented
56C2×C4×C22⋊C4—21no—
57#1991C2214yescomplemented
58#1989C2214yescomplemented
59#1983C2214yescomplemented
60#1958C2214yescomplemented
61#1893C2214yescomplemented
62#1893C2214yescomplemented
63#1892C2214yescomplemented
64#1892C2214yescomplemented
65#1875C2214yescomplemented
66#1874C2212yes—
67#1874C2212yes—
68#1874C2212yes—
69#1874C2212yes—
70#1874C2214yescomplemented
71#1873C2214yescomplemented
72#1872C2212yescomplemented
73#1872C2212yescomplemented
74#1872C2212yescomplemented
75#1872C2212yescomplemented
76#1872C2214yescomplemented
77#1825C2214yescomplemented
78#1824C2212yescomplemented
79#1823C2212yescomplemented
80#1805C2214yescomplemented
81#1804C2214yescomplemented
82#1788C2214yescomplemented
83#1787C2212yescomplemented
84#1786C2212yescomplemented
85C4×#103C2214yescomplemented
86C4×#102C2214yescomplemented
87#1735C2214yescomplemented
88C2×#340C2212yescomplemented
89C2×#340C2212yescomplemented
90C22×#41C2312yes—
91C23×Q8C2311yescharacteristic
92C23×D4—21no—
93C23×D4D411yescharacteristic
94C23×D4C2311yescharacteristic
95C24×C4—21no—
96C24×C4C2311yescharacteristic
97C24×C4C2311yescharacteristic
98C23×C8C2312yes—
99C23×C8C2312yes—
100C23×C8C2314yes—
101#553—232no—
102#553—28no—
103#553C2×C4116yescomplemented
104#552—28no—
105#552C2×C4116yescomplemented
106#551—232no—
107#548—28no—
108#548C2×C4116yescomplemented
109#546—28no—
110#546C2×C4116yescomplemented
111#539—216no—
112#538—216no—
113#534—216no—
114#529—28no—
115#529C2×C4116yescomplemented
116C2×#126—22no—
117C2×#126—22no—
118C2×#126—22no—
119C2×#125—22no—
120C2×#125C2312yes—
121C2×#124—22no—
122C2×#124C2312yes—
123#525—28no—
124#525C2×C4116yescomplemented
125C2×#123—22no—
126C2×#123—22no—
127C2×#123—22no—
128C2×#123—22no—
129C2×#123—22no—
130C2×C22⋊Q8—21no—
131C2×C22⋊Q8—21no—
132C2×C22⋊Q8—24no—
133C2×C22⋊Q8—22no—
134C2×C22⋊Q8C2×C418yes—
135C2×C22⋊Q8C2312yes—
136C2×C22⋊Q8C2312yes—
137C2×C22⋊Q8C2312yes—
138C2×#121—22no—
139C2×#121—22no—
140C2×#121—21no—
141C2×#121—21no—
142C2×#121—24no—
143C2×#121—22no—
144C2×#121C2×C418yes—
145C2×#121C2312yes—
146C2×#121C2312yes—
147C2×#121C2312yes—
148C2×#120—22no—
149C2×#120—22no—
150#518—216no—
151C2×C4×Q8C2312yes—
152C2×C4×D4—22no—
153C2×C4×D4—22no—
154C2×C4×D4—22no—
155C2×C4×D4—22no—
156C2×C4×D4—22no—
157C2×C4×D4C2×C418yes—
158C2×C4×D4D418yes—
159C2×C4×D4D412yes—
160C2×C4×D4D412yes—
161C2×C4×D4C2312yes—
162C2×C4×D4C2312yes—
163C2×C4×D4C2312yes—
164C2×#117—22no—
165C2×#117—22no—
166C2×#117—22no—
167C2×#117—44no—
168C2×#117C2314yes—
169C2×#117C2312yes—
170C22×C4⋊C4—21no—
171C22×C4⋊C4—21no—
172C22×C4⋊C4—21no—
173C22×C4⋊C4—21no—
174C22×C4⋊C4—44no—
175C22×C4⋊C4D411yescharacteristic
176C22×C4⋊C4C2311yescharacteristic
177C22×C4⋊C4C2312yes—
178C22×C4⋊C4C2312yes—
179C22×C4⋊C4C2311yescharacteristic
180C22×C4⋊C4C2311yescharacteristic
181C22×C4⋊C4C2311yescharacteristic
182C22×C4⋊C4C2311yescharacteristic
183C22×C4⋊C4C2311yescharacteristic
184C22×C22⋊C4—21no—
185C22×C22⋊C4—21no—
186C22×C22⋊C4—22no—
187C22×C22⋊C4—21no—
188C22×C22⋊C4—21no—
189C22×C22⋊C4—21no—
190C22×C22⋊C4D411yescharacteristic
191C22×C22⋊C4D411yescharacteristic
192C22×C42—21no—
193C22×C42—21no—
194C22×C42C2311yescharacteristic
195C8×D4—216no—
196C8×D4—216no—
197#431—28no—
198C2×C4⋊C8C2314yes—
199#416—48no—
200C2×#103—44no—
201C2×#103C2314yes—
202C2×#103C2314yes—
203C2×#103C2314yes—
204C2×#103C2314yes—
205C2×#102—44no—
206C2×#102C2314yes—
207C2×#102C2314yes—
208C2×#102C2314yes—
209C2×#102C2314yes—
210C2×C22⋊C8—24no—
211C2×C22⋊C8—24no—
212C2×C22⋊C8—28no—
213C2×C22⋊C8C2312yes—
214C2×C22⋊C8C2312yes—
215C2×C22⋊C8C2314yes—
216C2×C22⋊C8C2312yes—
217C2×C22⋊C8C2312yes—
218C2×C4×C8C2314yes—
219#388—24no—
220#388—24no—
221#387—24no—
222#387—24no—
223#386—24no—
224#386—24no—
225#382—22no—
226#382C2314yes—
227#380—21no—
228#380—21no—
229#380—22no—
230#380C2312yes—
231#380C2312yes—
232#380C2314yes—
233C4×C4⋊C4—22no—
234C4×C4⋊C4C2314yes—
235C4×C22⋊C4—24no—
236C4×C22⋊C4—24no—
237C2×#95—21no—
238C2×#95—21no—
239C2×#95—21no—
240C2×#95—21no—
241C2×#95—21no—
242#340C2314yes—
243#340C2314yes—
244#340C2314yes—
245#340C2314yes—
246#340C2314yes—
247#340C2314yes—
248#340C2314yes—
249#340C2314yes—
250C25—21no—
251C25C2×D411yescharacteristic
252C25C2×D411yescharacteristic
253C2×#41—24no—
254C2×#41—44no—
255C2×#41—44no—
256C2×#41C22×C418yescomplemented
257C22×Q8—21no—
258C22×Q8—22no—
259C22×Q8—42no—
260C22×Q8—42no—
261C22×Q8C22×C414yes—
262C22×Q8C2412yes—
263C22×D4—24no—
264C22×D4—24no—
265C22×D4—28no—
266C22×D4—22no—
267C22×D4—22no—
268C22×D4—22no—
269C22×D4—22no—
270C22×D4—21no—
271C22×D4—22no—
272C22×D4—42no—
273C22×D4—42no—
274C22×D4—44no—
275C22×D4—44no—
276C22×D4C22⋊C418yes—
277C22×D4C22×C414yes—
278C22×D4C2×D412yes—
279C22×D4C2×D412yes—
280C22×D4C2412yes—
281C23×C4—21no—
282C23×C4—21no—
283C23×C4—21no—
284C23×C4—21no—
285C23×C4—22no—
286C23×C4—22no—
287C23×C4—21no—
288C23×C4—21no—
289C23×C4—21no—
290C23×C4—22no—
291C23×C4—22no—
292C23×C4—42no—
293C23×C4—42no—
294C23×C4—42no—
295C23×C4—42no—
296C23×C4—44no—
297C23×C4—44no—
298C23×C4—82no—
299C23×C4C22×C414yes—
300C23×C4C22×C414yes—
301C23×C4C2×D411yescharacteristic
302C23×C4C2×D411yescharacteristic
303C23×C4C2×D411yescharacteristic
304C23×C4C2×D411yescharacteristic
305C23×C4C2×D411yescharacteristic
306C23×C4C2×D411yescharacteristic
307C23×C4C2×D412yes—
308C23×C4C2×D414yes—
309C23×C4C2×D414yes—
310C23×C4C2411yescharacteristic
311C23×C4C2411yescharacteristic
312C23×C4C2411yescharacteristic
313C23×C4C2412yes—
314C22×C8—24no—
315C22×C8—24no—
316C22×C8—28no—
317C22×C8—42no—
318C22×C8—44no—
319C22×C8—42no—
320C22×C8—42no—
321C22×C8—42no—
322C22×C8—44no—
323C22×C8C2414yes—
324C22×C8C2414yes—
325#126—216no—
326#126—216no—
327#126—216no—
328#125—216no—
329#125—24no—
330#125C22×C418yescomplemented
331#124—216no—
332#124—24no—
333#124C22×C418yescomplemented
334#123—216no—
335#123—216no—
336#123—216no—
337#123—216no—
338#123—216no—
339C22⋊Q8—28no—
340C22⋊Q8—28no—
341C22⋊Q8—24no—
342C22⋊Q8—24no—
343C22⋊Q8—24no—
344C22⋊Q8—216no—
345C22⋊Q8C22×C418yes—
346C22⋊Q8C22×C418yes—
347C22⋊Q8C22×C418yescomplemented
348#121—216no—
349#121—216no—
350#121—28no—
351#121—28no—
352#121—24no—
353#121—24no—
354#121—24no—
355#121—216no—
356#121C22×C418yes—
357#121C22×C418yes—
358#121C22×C418yescomplemented
359#120—216no—
360#120—216no—
361C4×Q8—24no—
362C4×Q8C22×C418yescomplemented
363C4×D4—216no—
364C4×D4—216no—
365C4×D4—216no—
366C4×D4—216no—
367C4×D4—216no—
368C4×D4—24no—
369C4×D4C22⋊C4116yes—
370C4×D4C22⋊C4116yes—
371C4×D4C22×C418yes—
372C4×D4C22×C418yes—
373C4×D4C22×C418yescomplemented
374C4×D4C2×D418yes—
375C4×D4C2×D418yes—
376#117—24no—
377#117—216no—
378#117—216no—
379#117—28no—
380#117—44no—
381#117—48no—
382#117C22×C418yescomplemented
383C2×C4⋊C4—28no—
384C2×C4⋊C4—21no—
385C2×C4⋊C4—22no—
386C2×C4⋊C4—22no—
387C2×C4⋊C4—21no—
388C2×C4⋊C4—22no—
389C2×C4⋊C4—21no—
390C2×C4⋊C4—22no—
391C2×C4⋊C4—22no—
392C2×C4⋊C4—22no—
393C2×C4⋊C4—22no—
394C2×C4⋊C4—22no—
395C2×C4⋊C4—24no—
396C2×C4⋊C4—24no—
397C2×C4⋊C4—24no—
398C2×C4⋊C4—21no—
399C2×C4⋊C4—22no—
400C2×C4⋊C4—22no—
401C2×C4⋊C4—21no—
402C2×C4⋊C4—21no—
403C2×C4⋊C4—42no—
404C2×C4⋊C4—42no—
405C2×C4⋊C4—42no—
406C2×C4⋊C4—42no—
407C2×C4⋊C4—42no—
408C2×C4⋊C4—44no—
409C2×C4⋊C4—44no—
410C2×C4⋊C4—44no—
411C2×C4⋊C4C22⋊C418yes—
412C2×C4⋊C4C22×C414yes—
413C2×C4⋊C4C22×C414yes—
414C2×C4⋊C4C2×D412yes—
415C2×C4⋊C4C2×D412yes—
416C2×C4⋊C4C2412yes—
417C2×C4⋊C4C2412yes—
418C2×C4⋊C4C2412yes—
419C2×C4⋊C4C2412yes—
420C2×C4⋊C4C2412yes—
421C2×C4⋊C4C2412yes—
422C2×C22⋊C4—28no—
423C2×C22⋊C4—22no—
424C2×C22⋊C4—22no—
425C2×C22⋊C4—22no—
426C2×C22⋊C4—22no—
427C2×C22⋊C4—28no—
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—216no—
435C2×C22⋊C4—24no—
436C2×C22⋊C4—22no—
437C2×C22⋊C4—22no—
438C2×C22⋊C4—24no—
439C2×C22⋊C4—44no—
440C2×C22⋊C4—44no—
441C2×C22⋊C4—82no—
442C2×C22⋊C4C22⋊C418yes—
443C2×C22⋊C4C22⋊C418yes—
444C2×C22⋊C4C2×D412yes—
445C2×C22⋊C4C2×D412yes—
446C2×C22⋊C4C2×D412yes—
447C2×C22⋊C4C2×D412yes—
448C2×C42—22no—
449C2×C42—22no—
450C2×C42—24no—
451C2×C42—24no—
452C2×C42—44no—
453C2×C42—82no—
454C2×C42C22×C414yes—
455C2×C42C2×D412yes—
456C2×C42C2×D414yes—
457C2×C42C2412yes—
458C4⋊C8—28no—
459#103—28no—
460#103—44no—
461#103—44no—
462#103—44no—
463#102—28no—
464#102—44no—
465#102—44no—
466#102—44no—
467C22⋊C8—24no—
468C22⋊C8—24no—
469C22⋊C8—24no—
470C22⋊C8—24no—
471C22⋊C8—28no—
472C4×C8—28no—
473#95—24no—
474#95—24no—
475#95—24no—
476#95—22no—
477#95—22no—
478#95—24no—
479C24—22no—
480C24—22no—
481C24—22no—
482C24—24no—
483C24—41no—
484C24—41no—
485C24—41no—
486C24—41no—
487C24—41no—
488C24—41no—
489C24—41no—
490C24—41no—
491C24—42no—
492C24—42no—
493C24—81no—
494C24—81no—
495C24—81no—
496C24—81no—
497C24C2×C22⋊C414yes—
498C24C2×C22⋊C414yes—
499C24#13514yes—
500C24#13514yes—
501C24C22×D412yes—
502C24C22×D411yescharacteristic
503C24C22×D411yescharacteristic
504C24C22×D411yescharacteristic
505#41—416no—
506#41—88no—
507C2×Q8—24no—
508C2×Q8—22no—
509C2×Q8—24no—
510C2×Q8—24no—
511C2×Q8—48no—
512C2×Q8—81no—
513C2×Q8—81no—
514C2×Q8—84no—
515C2×Q8C23×C414yes—
516C2×D4—24no—
517C2×D4—24no—
518C2×D4—24no—
519C2×D4—24no—
520C2×D4—232no—
521C2×D4—28no—
522C2×D4—28no—
523C2×D4—28no—
524C2×D4—28no—
525C2×D4—24no—
526C2×D4—22no—
527C2×D4—24no—
528C2×D4—24no—
529C2×D4—48no—
530C2×D4—44no—
531C2×D4—44no—
532C2×D4—44no—
533C2×D4—44no—
534C2×D4—432no—
535C2×D4—84no—
536C2×D4—81no—
537C2×D4—81no—
538C2×D4—82no—
539C2×D4—82no—
540C2×D4—82no—
541C2×D4—82no—
542C2×D4C2×C22⋊C418yes—
543C2×D4C2×C22⋊C418yes—
544C2×D4C23×C414yes—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—24no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—24no—
555C22×C4—24no—
556C22×C4—24no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—24no—
562C22×C4—24no—
563C22×C4—28no—
564C22×C4—28no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—48no—
569C22×C4—48no—
570C22×C4—48no—
571C22×C4—48no—
572C22×C4—41no—
573C22×C4—41no—
574C22×C4—41no—
575C22×C4—41no—
576C22×C4—41no—
577C22×C4—42no—
578C22×C4—42no—
579C22×C4—41no—
580C22×C4—41no—
581C22×C4—41no—
582C22×C4—41no—
583C22×C4—41no—
584C22×C4—44no—
585C22×C4—44no—
586C22×C4—42no—
587C22×C4—42no—
588C22×C4—42no—
589C22×C4—42no—
590C22×C4—42no—
591C22×C4—42no—
592C22×C4—42no—
593C22×C4—42no—
594C22×C4—42no—
595C22×C4—42no—
596C22×C4—42no—
597C22×C4—42no—
598C22×C4—44no—
599C22×C4—44no—
600C22×C4—42no—
601C22×C4—82no—
602C22×C4—82no—
603C22×C4—82no—
604C22×C4—82no—
605C22×C4—81no—
606C22×C4—81no—
607C22×C4—82no—
608C22×C4—82no—
609C22×C4—81no—
610C22×C4—81no—
611C22×C4—816no—
612C22×C4C2×C22⋊C414yes—
613C22×C4C2×C22⋊C414yes—
614C22×C4C2×C22⋊C414yes—
615C22×C4C2×C22⋊C414yes—
616C22×C4C2×C22⋊C414yes—
617C22×C4C2×C22⋊C414yes—
618C22×C4C2×C22⋊C418yes—
619C22×C4C23×C412yes—
620C22×C4C23×C412yes—
621C22×C4C23×C412yes—
622C22×C4C23×C414yes—
623C22×C4C22×D412yes—
624C22×C4C22×D412yes—
625C22×C4C22×D412yes—
626C22×C4C22×D411yescharacteristic
627C22×C4C22×D411yescharacteristic
628C22×C4C22×D411yescharacteristic
629C22×C4C22×D412yes—
630C22×C4C22×D412yes—
631C22×C4C22×D412yes—
632C22×C4C22×D414yes—
633C22×C4C2511yescharacteristic
634C2×C8—24no—
635C2×C8—24no—
636C2×C8—24no—
637C2×C8—24no—
638C2×C8—24no—
639C2×C8—24no—
640C2×C8—84no—
641C2×C8—84no—
642C2×C8—88no—
643C4⋊C4—24no—
644C4⋊C4—28no—
645C4⋊C4—28no—
646C4⋊C4—24no—
647C4⋊C4—24no—
648C4⋊C4—28no—
649C4⋊C4—28no—
650C4⋊C4—28no—
651C4⋊C4—28no—
652C4⋊C4—22no—
653C4⋊C4—22no—
654C4⋊C4—22no—
655C4⋊C4—22no—
656C4⋊C4—24no—
657C4⋊C4—22no—
658C4⋊C4—24no—
659C4⋊C4—44no—
660C4⋊C4—44no—
661C4⋊C4—42no—
662C4⋊C4—42no—
663C4⋊C4—42no—
664C4⋊C4C2×C22⋊C418yes—
665C4⋊C4C2×C22⋊C418yes—
666C4⋊C4C23×C414yes—
667C4⋊C4C23×C414yes—
668C4⋊C4H(5,𝔽2)14yes—
669C22⋊C4—28no—
670C22⋊C4—28no—
671C22⋊C4—28no—
672C22⋊C4—28no—
673C22⋊C4—28no—
674C22⋊C4—28no—
675C22⋊C4—28no—
676C22⋊C4—28no—
677C22⋊C4—28no—
678C22⋊C4—28no—
679C22⋊C4—48no—
680C22⋊C4—44no—
681C22⋊C4—44no—
682C22⋊C4—84no—
683C22⋊C4C2×C22⋊C418yes—
684C22⋊C4C2×C22⋊C418yes—
685C22⋊C4C2×C22⋊C418yes—
686C22⋊C4C2×C22⋊C418yes—
687C42—28no—
688C42—28no—
689C42—48no—
690C42—84no—
691C42C2×C22⋊C418yes—
692C42C23×C414yes—
693C42C22×D414yes—
694C23—21no—
695C23—21no—
696C23—21no—
697C23—21no—
698C23—21no—
699C23—21no—
700C23—21no—
701C23—21no—
702C23—21no—
703C23—21no—
704C23—21no—
705C23—21no—
706C23—22no—
707C23—22no—
708C23—22no—
709C23—22no—
710C23—22no—
711C23—22no—
712C23—28no—
713C23—24no—
714C23—44no—
715C23—44no—
716C23—44no—
717C23—44no—
718C23—44no—
719C23—44no—
720C23—44no—
721C23—44no—
722C23—42no—
723C23—42no—
724C23—42no—
725C23—42no—
726C23—42no—
727C23—42no—
728C23—48no—
729C23—82no—
730C23—82no—
731C23—82no—
732C23—82no—
733C23—84no—
734C23—84no—
735C23—162no—
736C23—162no—
737C23—162no—
738C23—162no—
739C23#416116yescomplemented
740C23C22×C22⋊C414yes—
741C23C22×C22⋊C412yes—
742C23C22×C22⋊C412yes—
743C23C22×C22⋊C412yes—
744C23C2×#13512yes—
745C23C2×#13512yes—
746C23C2×#13512yes—
747C23C2×#13512yes—
748C23C2×#13512yes—
749C23C2×#13512yes—
750C23C23×D411yescharacteristic
751Q8—28no—
752Q8—44no—
753Q8—84no—
754D4—216no—
755D4—216no—
756D4—28no—
757D4—416no—
758D4—416no—
759D4—44no—
760D4—84no—
761D4—88no—
762D4—88no—
763C2×C4—22no—
764C2×C4—22no—
765C2×C4—28no—
766C2×C4—22no—
767C2×C4—21no—
768C2×C4—21no—
769C2×C4—21no—
770C2×C4—21no—
771C2×C4—22no—
772C2×C4—21no—
773C2×C4—21no—
774C2×C4—22no—
775C2×C4—22no—
776C2×C4—24no—
777C2×C4—24no—
778C2×C4—24no—
779C2×C4—28no—
780C2×C4—24no—
781C2×C4—24no—
782C2×C4—28no—
783C2×C4—24no—
784C2×C4—24no—
785C2×C4—24no—
786C2×C4—24no—
787C2×C4—24no—
788C2×C4—48no—
789C2×C4—44no—
790C2×C4—44no—
791C2×C4—44no—
792C2×C4—44no—
793C2×C4—44no—
794C2×C4—48no—
795C2×C4—42no—
796C2×C4—42no—
797C2×C4—42no—
798C2×C4—48no—
799C2×C4—42no—
800C2×C4—42no—
801C2×C4—42no—
802C2×C4—42no—
803C2×C4—42no—
804C2×C4—42no—
805C2×C4—42no—
806C2×C4—42no—
807C2×C4—42no—
808C2×C4—42no—
809C2×C4—42no—
810C2×C4—42no—
811C2×C4—42no—
812C2×C4—42no—
813C2×C4—88no—
814C2×C4—88no—
815C2×C4—84no—
816C2×C4—84no—
817C2×C4—88no—
818C2×C4—88no—
819C2×C4—84no—
820C2×C4—84no—
821C2×C4—84no—
822C2×C4C22×C22⋊C414yes—
823C2×C4C22×C22⋊C414yes—
824C2×C4C22×C22⋊C412yes—
825C2×C4C22×C22⋊C414yes—
826C2×C4C22×C22⋊C412yes—
827C2×C4C22×C22⋊C412yes—
828C2×C4C24×C411yescharacteristic
829C2×C4C23×D411yescharacteristic
830C2×C4C2×H(5,𝔽2)12yes—
831C2×C4#58512yes—
832C8—44no—
833C8—44no—
834C22—22no—
835C22—22no—
836C22—22no—
837C22—22no—
838C22—22no—
839C22—22no—
840C22—22no—
841C22—22no—
842C22—22no—
843C22—22no—
844C22—22no—
845C22—22no—
846C22—22no—
847C22—22no—
848C22—22no—
849C22—22no—
850C22—22no—
851C22—22no—
852C22—24no—
853C22—24no—
854C22—24no—
855C22—416no—
856C22—42no—
857C22—42no—
858C22—42no—
859C22—42no—
860C22—44no—
861C22—44no—
862C22—44no—
863C22—88no—
864C22—82no—
865C22—82no—
866C22—82no—
867C22—82no—
868C22—168no—
869C22C2×#41614yes—
870C22C2×#41614yes—
871C22C2×#41614yes—
872C22C23×C22⋊C411yescharacteristic
873C22#348411yescharacteristic
874C22#348511yescharacteristic
875C22C22×#13511yescharacteristic
876C22C22×#13511yescharacteristic
877C22#358511yescharacteristic
878C22#358611yescharacteristic
879C4—24no—
880C4—24no—
881C4—22no—
882C4—24no—
883C4—22no—
884C4—22no—
885C4—44no—
886C4—44no—
887C4—44no—
888C4—44no—
889C4—82no—
890C4—82no—
891C4—82no—
892C4C4×H(5,𝔽2)12yes—
893C4#349612yes—
894C2—24no—
895C2—24no—
896C2—24no—
897C2—44no—
898C2—84no—
899C2#3425611yescharacteristic
900C2C22×#41611yescharacteristic
901C2#6008911yescharacteristic
902C2#6156111yescharacteristic
903C2#6156411yescharacteristic
904C2#6169611yescharacteristic
905C2#6169911yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutatorC2×C4C24×C4
Frattini, cosocleC22×C4C25
prime radicalC2×#3505C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C22×C4×D4 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C2×#2972C2semidirect
3. C2×#2352C2semidirect
4. #22488C2semidirect
5. #22486C2semidirect
6. #22416C2semidirect
7. #22414C2semidirect
8. #21861C2semidirect
9. #21763C2semidirect
10. #21759C2semidirect
11. #21758C2semidirect
12. #21388C2semidirect
13. #20908C2semidirect
14. C2×#1874C2semidirect
15. C2×#1872C2semidirect
17. #3505C4semidirect
33. C22×#117C22semidirect
37. C2×C8×D4C22semidirect
38. C2×#431C22semidirect
39. C2×#416C22semidirect
40. C22×#103C22semidirect
41. C22×#102C22semidirect
44. C22×C22⋊C8C22semidirect
48. #2352C22semidirect
52. C2×#382C22semidirect
54. C2×#380C22semidirect
55. C2×C4×C4⋊C4C22semidirect
57. #1991C22semidirect
58. #1989C22semidirect
59. #1983C22semidirect
60. #1958C22semidirect
61. #1893C22semidirect
62. #1893C22semidirect
63. #1892C22semidirect
64. #1892C22semidirect
65. #1875C22semidirect
70. #1874C22semidirect
71. #1873C22semidirect
72. #1872C22semidirect
73. #1872C22semidirect
74. #1872C22semidirect
75. #1872C22semidirect
76. #1872C22semidirect
77. #1825C22semidirect
78. #1824C22semidirect
79. #1823C22semidirect
80. #1805C22semidirect
81. #1804C22semidirect
82. #1788C22semidirect
83. #1787C22semidirect
84. #1786C22semidirect
85. C4×#103C22semidirect
86. C4×#102C22semidirect
87. #1735C22semidirect
88. C2×#340C22semidirect
89. C2×#340C22semidirect
103. #553C2×C4semidirect
105. #552C2×C4semidirect
108. #548C2×C4semidirect
110. #546C2×C4semidirect
115. #529C2×C4semidirect
124. #525C2×C4semidirect
256. C2×#41C22×C4semidirect
330. #125C22×C4semidirect
333. #124C22×C4semidirect
347. C22⋊Q8C22×C4semidirect
358. #121C22×C4semidirect
362. C4×Q8C22×C4semidirect
373. C4×D4C22×C4semidirect
382. #117C22×C4semidirect
739. C23#416semidirect

Maximal subgroups

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

subgroupindex
C2×#35052
C2×#29722
C2×#23522
#224882
#224862
#224162
#224142
#218612
#217632
#217592
#217582
#213882
#209082
C2×#18742
C2×#18722