Finite Group Databasebeta

← #6444455

Subgroups — #6444455

Order 512.

2758 conjugacy classes of subgroups.

The subgroup lattice has 874 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3092C212yesmaximal, complemented
2#34936C211yesmaximal, characteristic
3C2×D4×C4⋊C4C211yesmaximal, characteristic, complemented
4#26244C214yesmaximal, complemented
5#26242C214yesmaximal, complemented
6#26236C212yesmaximal, complemented
7#26234C212yesmaximal, complemented
8#26232C212yesmaximal, complemented
9#26230C212yesmaximal, complemented
10#23482C212yesmaximal, complemented
11#23482C212yesmaximal, complemented
12#21258C211yesmaximal, characteristic, complemented
13#21200C211yesmaximal, characteristic, complemented
14#21190C211yesmaximal, characteristic, complemented
15#21171C211yesmaximal, characteristic, complemented
16#20909C212yesmaximal, complemented
17C4×#428C211yesmaximal, characteristic, complemented
18C2×#532C2211yescharacteristic
19C2×#525C2212yes—
20C2×#525C2212yes—
21C22×C4×D4—21no—
22C22×C4×D4C2211yescharacteristic
23C23×C4⋊C4C2212yes—
24#3092—216no—
25C2×#484C2214yescomplemented
26C2×#481C2214yescomplemented
27C2×#483C2214yescomplemented
28C2×#480C2214yescomplemented
29C2×#428C2212yes—
30C2×#428C2211yescharacteristic
31C2×#428C2211yescharacteristic
32C2×#423C2211yescharacteristic
33C2×#417C2212yes—
34C2×#417C2212yes—
35C2×#417C2212yes—
36C2×#417C2212yes—
37C2×#407C2212yes—
38C2×#407C2212yes—
39C2×C4×M16C2211yescharacteristic
40#2542C2211yescharacteristic
41#2542C2211yescharacteristic
42#2541C2211yescharacteristic
43#2541C2211yescharacteristic
44#2540C2212yes—
45#2540C2212yes—
46#2539—22no—
47#2501—21no—
48#2433—21no—
49#2397—22no—
50D4×C4⋊C4—21no—
51D4×C4⋊C4—21no—
52D4×C4⋊C4—22no—
53D4×C4⋊C4C2212yes—
54D4×C4⋊C4C2212yes—
55D4×C4⋊C4C2214yes—
56C4×#127—21no—
57C4×#127—21no—
58C2×#389—21no—
59C2×#385—22no—
60C2×#384C2211yescharacteristic
61C2×#380C2212yes—
62C4×#117C2211yescharacteristic
63C2×C4×C4⋊C4C2211yescharacteristic
64#2036C2214yescomplemented
65#2036C2214yescomplemented
66#2035C2214yescomplemented
67#2035C2214yescomplemented
68#2034C2214yescomplemented
69#2034C2214yescomplemented
70#2033C2214yescomplemented
71#2033C2214yescomplemented
72#1983C2214yescomplemented
73#1982C2212yescomplemented
74#1981C2212yescomplemented
75#1959C2214yescomplemented
76#1957C2212yescomplemented
77#1956C2212yescomplemented
78#1955C2214yes—
79#1954C2212yes—
80#1954C2212yes—
81#1948C2212yescomplemented
82#1948C2212yescomplemented
83#1947C2212yescomplemented
84#1947C2212yescomplemented
85#1874C2214yescomplemented
86#1874C2214yescomplemented
87#1872C2214yescomplemented
88#1872C2214yescomplemented
89#1776C2212yescomplemented
90#1776C2212yescomplemented
91C4×#107C2212yescomplemented
92C4×#106C2212yescomplemented
93#1736C2211yescharacteristic
94#1736C2212yes—
95#1736C2211yescharacteristic
96C22×#41C2312yes—
97C23×D4D411yescharacteristic
98C24×C4—22no—
99C24×C4C2312yes—
100C22×M16C2311yescharacteristic
101C22×M16C2312yes—
102C22×M16C2311yescharacteristic
103#532—24no—
104#532—24no—
105C2×C4⋊Q8C2311yescharacteristic
106C2×#127—21no—
107C2×#127—21no—
108C2×#127C2311yescharacteristic
109C2×#124C2312yes—
110#525—28no—
111#525—28no—
112#525—44no—
113#525—44no—
114C2×#123—22no—
115C2×#123—22no—
116C2×C22⋊Q8C2312yes—
117C2×C22⋊Q8C2312yes—
118C2×C22⋊Q8C2312yes—
119C2×C22⋊Q8C2312yes—
120C2×#121—21no—
121C2×#121—21no—
122C2×#121C2312yes—
123C2×#121C2312yes—
124C2×#121C2312yes—
125C2×#121C2312yes—
126C2×#120—22no—
127C2×#120—22no—
128C2×C4×D4—24no—
129C2×C4×D4—22no—
130C2×C4×D4—22no—
131C2×C4×D4—22no—
132C2×C4×D4—22no—
133C2×C4×D4—22no—
134C2×C4×D4—22no—
135C2×C4×D4—21no—
136C2×C4×D4—21no—
137C2×C4×D4—24no—
138C2×C4×D4—24no—
139C2×C4×D4—48no—
140C2×C4×D4D411yescharacteristic
141C2×C4×D4D411yescharacteristic
142C2×C4×D4D412yes—
143C2×C4×D4C2311yescharacteristic
144C2×C4×D4C2311yescharacteristic
145C2×C4×D4C2312yes—
146C2×#117C2311yescharacteristic
147C2×#117C2311yescharacteristic
148C22×C4⋊C4—28no—
149C22×C4⋊C4—22no—
150C22×C4⋊C4—22no—
151C22×C4⋊C4—22no—
152C22×C4⋊C4—21no—
153C22×C4⋊C4—21no—
154C22×C4⋊C4—44no—
155C22×C4⋊C4D411yescharacteristic
156C22×C4⋊C4C2312yes—
157C22×C4⋊C4C2311yescharacteristic
158C22×C4⋊C4C2314yes—
159C22×C4⋊C4C2314yes—
160C22×C4⋊C4C2311yescharacteristic
161C22×C22⋊C4—22no—
162C22×C22⋊C4D412yes—
163C22×C42—21no—
164C22×C42C2311yescharacteristic
165#484—216no—
166#483—216no—
167#481—216no—
168#480—216no—
169#428—28no—
170#428—24no—
171#428D418yescomplemented
172C2×#107C2314yes—
173C2×#107C2312yes—
174C2×#107C2312yes—
175C2×#106C2314yes—
176C2×#106C2312yes—
177C2×#106C2312yes—
178#423—24no—
179C2×C4⋊C8C2312yes—
180C2×C4⋊C8C2312yes—
181#417—28no—
182#417—28no—
183#417—44no—
184#417—44no—
185C2×#103C2314yes—
186C2×#103C2314yes—
187C2×#103C2314yes—
188C2×#103C2314yes—
189C2×#102C2314yes—
190C2×#102C2314yes—
191C2×#102C2314yes—
192C2×#102C2314yes—
193#407—28no—
194#407—44no—
195C2×C22⋊C8C2314yes—
196C2×C22⋊C8C2314yes—
197C2×C22⋊C8C2314yes—
198C2×C22⋊C8C2314yes—
199C4×M16—24no—
200C2×#97C2312yes—
201C2×C4×C8C2312yes—
202#399—22no—
203#399—22no—
204#399—22no—
205#399—22no—
206#392—22no—
207#392—22no—
208#392—22no—
209#392—22no—
210#390—21no—
211#390—21no—
212#390—21no—
213#390—21no—
214#390—22no—
215#390—22no—
216#390—22no—
217#390—22no—
218#389—22no—
219#389—22no—
220#389—24no—
221#385—24no—
222#385—24no—
223#385—24no—
224#385—24no—
225#384—21no—
226#384—21no—
227#384—21no—
228#384—21no—
229#384C2312yes—
230#384C2312yes—
231#380—22no—
232#380—22no—
233#380C2314yes—
234#380C2314yes—
235C4×C4⋊C4—21no—
236C4×C4⋊C4—21no—
237C4×C4⋊C4C2312yes—
238C4×C4⋊C4C2312yes—
239C4×C4⋊C4C2311yescharacteristic
240C4×C4⋊C4C2311yescharacteristic
241C4×C4⋊C4C2311yescharacteristic
242C4×C4⋊C4C2311yescharacteristic
243C4×C22⋊C4—21no—
244C4×C22⋊C4—21no—
245#376—21no—
246C2×#95—21no—
247C2×#95—22no—
248C43—21no—
249#340C2312yes—
250#340C2312yes—
251#340C2314yes—
252#340C2314yes—
253#340C2312yes—
254#340C2312yes—
255C25C2×D412yes—
256C2×#41—24no—
257C2×#41—24no—
258C2×#41—24no—
259C2×#41—24no—
260C2×#41—24no—
261C2×#41—24no—
262C22×Q8C2412yes—
263C22×D4—24no—
264C22×D4—24no—
265C22×D4—22no—
266C22×D4—22no—
267C22×D4—22no—
268C22×D4—22no—
269C22×D4—22no—
270C22×D4—24no—
271C22×D4—21no—
272C22×D4—21no—
273C22×D4C2×D412yes—
274C22×D4C2×D411yescharacteristic
275C22×D4C2×D411yescharacteristic
276C22×D4C2412yes—
277C23×C4—21no—
278C23×C4—24no—
279C23×C4—24no—
280C23×C4—24no—
281C23×C4—24no—
282C23×C4—24no—
283C23×C4—24no—
284C23×C4—21no—
285C23×C4—22no—
286C23×C4—24no—
287C23×C4—24no—
288C23×C4—22no—
289C23×C4—48no—
290C23×C4—48no—
291C23×C4—84no—
292C23×C4C2×D412yes—
293C23×C4C2×D412yes—
294C23×C4C2×D412yes—
295C23×C4C2×D411yescharacteristic
296C23×C4C2×D411yescharacteristic
297C23×C4C2412yes—
298C23×C4C2412yes—
299C23×C4C2411yescharacteristic
300C2×M16—22no—
301C2×M16—22no—
302C2×M16—24no—
303C2×M16—22no—
304C2×M16—24no—
305C2×M16—22no—
306C2×M16—24no—
307C2×M16—22no—
308C2×M16C2×D414yes—
309C22×C8C2412yes—
310C22×C8C2414yes—
311C22×C8C2412yes—
312C4⋊Q8—22no—
313C4⋊Q8—22no—
314#127—22no—
315#127—22no—
316#127—44no—
317#127—44no—
318#124—24no—
319#124—24no—
320#123—48no—
321#123—48no—
322C22⋊Q8—24no—
323C22⋊Q8—24no—
324C22⋊Q8—24no—
325C22⋊Q8—24no—
326C22⋊Q8—42no—
327C22⋊Q8—42no—
328C22⋊Q8—42no—
329C22⋊Q8—42no—
330#121—24no—
331#121—24no—
332#121—24no—
333#121—24no—
334#121—42no—
335#121—42no—
336#121—42no—
337#121—42no—
338#121—44no—
339#121—44no—
340#120—48no—
341#120—48no—
342C4×D4—24no—
343C4×D4—24no—
344C4×D4—28no—
345C4×D4—22no—
346C4×D4—22no—
347C4×D4—24no—
348C4×D4—24no—
349C4×D4—22no—
350C4×D4—22no—
351C4×D4—48no—
352C4×D4—48no—
353C4×D4—48no—
354C4×D4—48no—
355C4×D4—416no—
356C4×D4—48no—
357C4×D4—48no—
358C4×D4—44no—
359C4×D4—44no—
360#117—22no—
361#117—22no—
362#117C2×D414yes—
363#117#4114yes—
364C2×C4⋊C4—24no—
365C2×C4⋊C4—21no—
366C2×C4⋊C4—22no—
367C2×C4⋊C4—24no—
368C2×C4⋊C4—22no—
369C2×C4⋊C4—24no—
370C2×C4⋊C4—22no—
371C2×C4⋊C4—28no—
372C2×C4⋊C4—28no—
373C2×C4⋊C4—22no—
374C2×C4⋊C4—24no—
375C2×C4⋊C4—24no—
376C2×C4⋊C4—22no—
377C2×C4⋊C4—22no—
378C2×C4⋊C4—21no—
379C2×C4⋊C4—21no—
380C2×C4⋊C4—21no—
381C2×C4⋊C4—22no—
382C2×C4⋊C4—22no—
383C2×C4⋊C4—22no—
384C2×C4⋊C4—22no—
385C2×C4⋊C4—22no—
386C2×C4⋊C4—22no—
387C2×C4⋊C4—44no—
388C2×C4⋊C4—44no—
389C2×C4⋊C4—48no—
390C2×C4⋊C4—48no—
391C2×C4⋊C4—48no—
392C2×C4⋊C4—44no—
393C2×C4⋊C4—82no—
394C2×C4⋊C4C2×D411yescharacteristic
395C2×C4⋊C4C2×D411yescharacteristic
396C2×C4⋊C4C2×D412yes—
397C2×C4⋊C4C2×D414yes—
398C2×C4⋊C4C2414yes—
399C2×C4⋊C4C2412yes—
400C2×C4⋊C4C2412yes—
401C2×C4⋊C4C2411yescharacteristic
402C2×C4⋊C4C2411yescharacteristic
403C2×C4⋊C4C2411yescharacteristic
404C2×C4⋊C4C2411yescharacteristic
405C2×C22⋊C4—21no—
406C2×C22⋊C4—21no—
407C2×C22⋊C4—28no—
408C2×C22⋊C4—24no—
409C2×C22⋊C4—24no—
410C2×C22⋊C4—22no—
411C2×C22⋊C4—22no—
412C2×C22⋊C4—22no—
413C2×C22⋊C4—22no—
414C2×C22⋊C4—22no—
415C2×C22⋊C4—22no—
416C2×C22⋊C4—22no—
417C2×C22⋊C4—22no—
418C2×C22⋊C4—22no—
419C2×C22⋊C4—22no—
420C2×C22⋊C4—48no—
421C2×C22⋊C4C2×D412yes—
422C2×C22⋊C4C2×D412yes—
423C2×C22⋊C4C2×D412yes—
424C2×C22⋊C4C2×D412yes—
425C2×C42—21no—
426C2×C42—21no—
427C2×C42—22no—
428C2×C42—22no—
429C2×C42—21no—
430C2×C42—21no—
431C2×C42—21no—
432C2×C42—21no—
433C2×C42—44no—
434C2×C42C2×D411yescharacteristic
435C2×C42C2×D411yescharacteristic
436C2×C42#4114yes—
437C2×C42#4114yes—
438C2×C42C2411yescharacteristic
439C2×C42C2411yescharacteristic
440#107—28no—
441#107—24no—
442#107C2×D418yescomplemented
443#106—28no—
444#106—24no—
445#106C2×D418yescomplemented
446C4⋊C8—24no—
447C4⋊C8—24no—
448#103—28no—
449#103—28no—
450#103—44no—
451#103—44no—
452#102—28no—
453#102—28no—
454#102—44no—
455#102—44no—
456C22⋊C8—28no—
457C22⋊C8—28no—
458C22⋊C8—44no—
459C22⋊C8—44no—
460#97—24no—
461C4×C8—24no—
462#95—22no—
463#95—22no—
464#95—24no—
465#95—24no—
466#95—21no—
467#95—21no—
468#95—21no—
469#95—21no—
470C24—24no—
471C24—24no—
472C24—24no—
473C24—24no—
474C24—24no—
475C24—22no—
476C24—42no—
477C24—42no—
478C24C22×D412yes—
479C24C22×D412yes—
480C24C22×D411yescharacteristic
481#41—48no—
482#41—48no—
483#41—48no—
484#41—48no—
485C2×Q8—22no—
486C2×Q8—22no—
487C2×Q8—22no—
488C2×Q8—22no—
489C2×Q8—22no—
490C2×Q8—22no—
491C2×D4—232no—
492C2×D4—24no—
493C2×D4—24no—
494C2×D4—24no—
495C2×D4—22no—
496C2×D4—22no—
497C2×D4—22no—
498C2×D4—22no—
499C2×D4—22no—
500C2×D4—22no—
501C2×D4—22no—
502C2×D4—22no—
503C2×D4—22no—
504C2×D4—22no—
505C2×D4—44no—
506C2×D4—44no—
507C2×D4—44no—
508C2×D4—44no—
509C2×D4—44no—
510C2×D4—44no—
511C2×D4—44no—
512C2×D4—44no—
513C2×D4—44no—
514C2×D4—44no—
515C2×D4—44no—
516C2×D4—42no—
517C2×D4—42no—
518C2×D4—42no—
519C2×D4—42no—
520C2×D4—81no—
521C2×D4—81no—
522C2×D4—82no—
523C2×D4—82no—
524C2×D4—82no—
525C2×D4—82no—
526C2×D4AGL(1,ℤ/8)14yes—
527C2×D4#13714yes—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—24no—
531C22×C4—24no—
532C22×C4—24no—
533C22×C4—24no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—22no—
539C22×C4—24no—
540C22×C4—24no—
541C22×C4—24no—
542C22×C4—24no—
543C22×C4—24no—
544C22×C4—24no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—24no—
559C22×C4—22no—
560C22×C4—41no—
561C22×C4—41no—
562C22×C4—48no—
563C22×C4—48no—
564C22×C4—42no—
565C22×C4—42no—
566C22×C4—48no—
567C22×C4—48no—
568C22×C4—48no—
569C22×C4—48no—
570C22×C4—42no—
571C22×C4—44no—
572C22×C4—44no—
573C22×C4—48no—
574C22×C4—42no—
575C22×C4—44no—
576C22×C4—42no—
577C22×C4—48no—
578C22×C4—44no—
579C22×C4—44no—
580C22×C4—44no—
581C22×C4—84no—
582C22×C4—84no—
583C22×C4—832no—
584C22×C4#12314yes—
585C22×C4#12314yes—
586C22×C4C22×D412yes—
587C22×C4C22×D412yes—
588C22×C4C22×D411yescharacteristic
589C22×C4C22×D411yescharacteristic
590C22×C4C22×D411yescharacteristic
591C22×C4C22×D411yescharacteristic
592C22×C4C22×D411yescharacteristic
593C22×C4C22×D412yes—
594C22×C4C2×#4112yes—
595C22×C4C2×#4112yes—
596C22×C4C2×#4112yes—
597C22×C4H(5,𝔽2)12yes—
598C22×C4H(5,𝔽2)12yes—
599C22×C4C2511yescharacteristic
600M16—28no—
601M16—44no—
602M16—48no—
603C2×C8—22no—
604C2×C8—22no—
605C2×C8—24no—
606C2×C8—22no—
607C2×C8—24no—
608C2×C8—22no—
609C2×C8—24no—
610C2×C8—22no—
611C2×C8C22×D414yes—
612C4⋊C4—24no—
613C4⋊C4—22no—
614C4⋊C4—22no—
615C4⋊C4—24no—
616C4⋊C4—22no—
617C4⋊C4—21no—
618C4⋊C4—21no—
619C4⋊C4—21no—
620C4⋊C4—21no—
621C4⋊C4—24no—
622C4⋊C4—22no—
623C4⋊C4—22no—
624C4⋊C4—24no—
625C4⋊C4—48no—
626C4⋊C4—48no—
627C4⋊C4—44no—
628C4⋊C4—44no—
629C4⋊C4—44no—
630C4⋊C4—44no—
631C4⋊C4—44no—
632C4⋊C4—42no—
633C4⋊C4—42no—
634C4⋊C4—44no—
635C4⋊C4—42no—
636C4⋊C4—44no—
637C4⋊C4—82no—
638C4⋊C4—82no—
639C4⋊C4C22×D414yes—
640C4⋊C4C22×D412yes—
641C4⋊C4C22×D412yes—
642C4⋊C4C2×#4112yes—
643C4⋊C4C2×#4112yes—
644C22⋊C4—24no—
645C22⋊C4—24no—
646C22⋊C4—24no—
647C22⋊C4—24no—
648C22⋊C4—24no—
649C22⋊C4—24no—
650C22⋊C4—44no—
651C22⋊C4—44no—
652C22⋊C4—44no—
653C22⋊C4—44no—
654C22⋊C4—44no—
655C22⋊C4—44no—
656C22⋊C4—44no—
657C22⋊C4—44no—
658C22⋊C4—48no—
659C22⋊C4—48no—
660C22⋊C4—44no—
661C22⋊C4—44no—
662C42—24no—
663C42—24no—
664C42—44no—
665C42—44no—
666C42—42no—
667C42—42no—
668C42—81no—
669C42—81no—
670C42#12314yes—
671C42#12314yes—
672C42C2×#4112yes—
673C42C2×#4112yes—
674C42C2×#4112yes—
675C42C2×#4112yes—
676C23—21no—
677C23—21no—
678C23—21no—
679C23—21no—
680C23—216no—
681C23—22no—
682C23—22no—
683C23—22no—
684C23—22no—
685C23—22no—
686C23—22no—
687C23—22no—
688C23—22no—
689C23—22no—
690C23—22no—
691C23—22no—
692C23—22no—
693C23—48no—
694C23—48no—
695C23—48no—
696C23—48no—
697C23—48no—
698C23—48no—
699C23—42no—
700C23—42no—
701C23—42no—
702C23—42no—
703C23—42no—
704C23—42no—
705C23—42no—
706C23C2×#12312yes—
707C23D4212yes—
708C23#54612yes—
709C23C2×AGL(1,ℤ/8)14yes—
710C23C2×#13714yes—
711C23C23×D411yescharacteristic
712Q8—42no—
713Q8—42no—
714Q8—42no—
715Q8—42no—
716D4—216no—
717D4—28no—
718D4—28no—
719D4—42no—
720D4—42no—
721D4—42no—
722D4—42no—
723D4—84no—
724D4—88no—
725D4—88no—
726D4—88no—
727D4—88no—
728D4—88no—
729D4—84no—
730C2×C4—21no—
731C2×C4—21no—
732C2×C4—21no—
733C2×C4—21no—
734C2×C4—21no—
735C2×C4—21no—
736C2×C4—28no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—22no—
742C2×C4—22no—
743C2×C4—24no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—44no—
749C2×C4—48no—
750C2×C4—41no—
751C2×C4—41no—
752C2×C4—42no—
753C2×C4—41no—
754C2×C4—41no—
755C2×C4—48no—
756C2×C4—42no—
757C2×C4—41no—
758C2×C4—41no—
759C2×C4—41no—
760C2×C4—41no—
761C2×C4—42no—
762C2×C4—42no—
763C2×C4—42no—
764C2×C4—42no—
765C2×C4—42no—
766C2×C4—42no—
767C2×C4—48no—
768C2×C4—48no—
769C2×C4—42no—
770C2×C4—42no—
771C2×C4—44no—
772C2×C4—42no—
773C2×C4—42no—
774C2×C4—42no—
775C2×C4—44no—
776C2×C4—42no—
777C2×C4—42no—
778C2×C4—42no—
779C2×C4—44no—
780C2×C4—816no—
781C2×C4—816no—
782C2×C4—84no—
783C2×C4—88no—
784C2×C4—88no—
785C2×C4C2×#12312yes—
786C2×C4C2×#12312yes—
787C2×C4C2×#12312yes—
788C2×C4C2×#12312yes—
789C2×C4C2×#12312yes—
790C2×C4#53214yes—
791C2×C4#54014yes—
792C2×C4D4212yes—
793C2×C4#54612yes—
794C2×C4#55014yes—
795C2×C4#55914yes—
796C2×C4C2×AGL(1,ℤ/8)12yes—
797C2×C4C2×#13712yes—
798C2×C4C23×D411yescharacteristic
799C2×C4C22×#4111yescharacteristic
800C2×C4C22×#4111yescharacteristic
801C2×C4C22×#4111yescharacteristic
802C2×C4C2×H(5,𝔽2)11yescharacteristic
803C2×C4C2×H(5,𝔽2)11yescharacteristic
804C8—24no—
805C8—42no—
806C8—44no—
807C22—22no—
808C22—22no—
809C22—22no—
810C22—22no—
811C22—22no—
812C22—22no—
813C22—24no—
814C22—24no—
815C22—24no—
816C22—24no—
817C22—24no—
818C22—24no—
819C22—432no—
820C22—42no—
821C22—42no—
822C22—42no—
823C22—42no—
824C22—42no—
825C22—42no—
826C22—42no—
827C22—42no—
828C22—82no—
829C22—82no—
830C22—82no—
831C22—82no—
832C22—82no—
833C22—82no—
834C22—82no—
835C22#244514yes—
836C22C22×#12311yescharacteristic
837C22C2×D4211yescharacteristic
838C22C2×#54611yescharacteristic
839C22C22×AGL(1,ℤ/8)11yescharacteristic
840C22C22×#13711yescharacteristic
841C22#358511yescharacteristic
842C22#358611yescharacteristic
843C4—22no—
844C4—22no—
845C4—22no—
846C4—42no—
847C4—42no—
848C4—44no—
849C4—42no—
850C4—42no—
851C4—42no—
852C4—42no—
853C4—82no—
854C4—84no—
855C4—82no—
856C4#244514yes—
857C4#309214yescomplemented
858C4C2×#53211yescharacteristic
859C4C2×#54011yescharacteristic
860C4C2×#55011yescharacteristic
861C4C2×#55911yescharacteristic
862C2—24no—
863C2—44no—
864C2—44no—
865C2—162no—
866C2C2×#244511yescharacteristic
867C2C2×#309211yescharacteristic
868C2#6051711yescharacteristic
869C2D4×AGL(1,ℤ/8)11yescharacteristic
870C2D4×#13711yescharacteristic
871C2#6116111yescharacteristic
872C2#6116211yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#34936C2
LCSG ▷ C22×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
1. C2×#3092C2semidirect
3. C2×D4×C4⋊C4C2semidirect
4. #26244C2semidirect
5. #26242C2semidirect
6. #26236C2semidirect
7. #26234C2semidirect
8. #26232C2semidirect
9. #26230C2semidirect
10. #23482C2semidirect
11. #23482C2semidirect
12. #21258C2semidirect
13. #21200C2semidirect
14. #21190C2semidirect
15. #21171C2semidirect
16. #20909C2semidirect
17. C4×#428C2semidirect
25. C2×#484C22semidirect
26. C2×#481C22semidirect
27. C2×#483C22semidirect
28. C2×#480C22semidirect
64. #2036C22semidirect
65. #2036C22semidirect
66. #2035C22semidirect
67. #2035C22semidirect
68. #2034C22semidirect
69. #2034C22semidirect
70. #2033C22semidirect
71. #2033C22semidirect
72. #1983C22semidirect
73. #1982C22semidirect
74. #1981C22semidirect
75. #1959C22semidirect
76. #1957C22semidirect
77. #1956C22semidirect
81. #1948C22semidirect
82. #1948C22semidirect
83. #1947C22semidirect
84. #1947C22semidirect
85. #1874C22semidirect
86. #1874C22semidirect
87. #1872C22semidirect
88. #1872C22semidirect
89. #1776C22semidirect
90. #1776C22semidirect
91. C4×#107C22semidirect
92. C4×#106C22semidirect
171. #428D4semidirect
442. #107C2×D4semidirect
445. #106C2×D4semidirect
857. C4#3092semidirect

Maximal subgroups

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

subgroupindex
C2×#30922
#349362
C2×D4×C4⋊C42
#262442
#262422
#262362
#262342
#262322
#262302
#234822
#212582
#212002
#211902
#211712
#209092
C4×#4282