Finite Group Databasebeta

← #6444009

Subgroups — #6444009

Order 512.

2596 conjugacy classes of subgroups.

The subgroup lattice has 851 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3092C212yesmaximal, complemented
2#34935C211yesmaximal, characteristic
3C2×D4×C4⋊C4C211yesmaximal, characteristic, complemented
4#25024C214yesmaximal, complemented
5#25022C214yesmaximal, complemented
6#25016C212yesmaximal, complemented
7#25014C212yesmaximal, complemented
8#25012C212yesmaximal, complemented
9#25010C212yesmaximal, complemented
10#23642C212yesmaximal, complemented
11#23482C212yesmaximal, complemented
12#21190C211yesmaximal, characteristic, complemented
13#21170C211yesmaximal, characteristic, complemented
14#20844C212yesmaximal, complemented
15#20800C211yesmaximal, characteristic, complemented
16#20648C211yesmaximal, characteristic, complemented
17C4×#417C211yesmaximal, characteristic, complemented
18C2×#525C2212yes—
19C2×C4×#41C2211yescharacteristic
20C22×C4×D4—21no—
21C22×C4×D4C2211yescharacteristic
22C23×C4⋊C4C2212yes—
23#3092—216no—
24C2×#484C2214yescomplemented
25C2×#481C2214yescomplemented
26C2×#483C2214yescomplemented
27C2×#480C2214yescomplemented
28C2×#428C2212yes—
29C2×#428C2212yes—
30C2×#428C2212yes—
31C2×#423C2211yescharacteristic
32C2×#417C2212yes—
33C2×#417C2211yescharacteristic
34C2×#417C2211yescharacteristic
35C2×#407C2212yes—
36C2×#407C2212yes—
37C2×C4×M16C2211yescharacteristic
38#2538C2211yescharacteristic
39#2538C2211yescharacteristic
40#2537C2211yescharacteristic
41#2537C2211yescharacteristic
42#2536C2212yes—
43#2535C2212yes—
44#2534—22no—
45#2486—21no—
46#2408—21no—
47#2392—22no—
48D4×C4⋊C4—22no—
49D4×C4⋊C4—21no—
50D4×C4⋊C4—21no—
51D4×C4⋊C4C2212yes—
52D4×C4⋊C4C2212yes—
53D4×C4⋊C4C2214yes—
54C4×#121—21no—
55C4×#121—21no—
56C2×#389—21no—
57C2×#385—22no—
58#2285C2211yescharacteristic
59C2×#384C2211yescharacteristic
60#2280C2212yes—
61C2×#380C2212yes—
62C2×C4×C4⋊C4C2211yescharacteristic
63#2077C2214yescomplemented
64#2077C2214yescomplemented
65#2076C2214yescomplemented
66#2075C2214yescomplemented
67#2036C2214yescomplemented
68#2035C2214yescomplemented
69#2034C2214yescomplemented
70#2033C2214yescomplemented
71#1955C2214yes—
72#1954C2212yes—
73#1954C2212yes—
74#1949C2214yescomplemented
75#1948C2212yescomplemented
76#1947C2212yescomplemented
77#1853C2214yescomplemented
78#1853C2214yescomplemented
79#1852C2214yescomplemented
80#1852C2214yescomplemented
81#1847C2214yescomplemented
82#1845C2212yescomplemented
83#1844C2212yescomplemented
84#1803C2212yescomplemented
85#1803C2212yescomplemented
86#1802C2212yescomplemented
87#1802C2212yescomplemented
88#1763C2212yescomplemented
89#1762C2212yescomplemented
90C4×#103C2212yescomplemented
91C4×#102C2212yescomplemented
92#1736C2211yescharacteristic
93#1736C2212yes—
94#1736C2212yes—
95#1736C2211yescharacteristic
96C22×#41C2311yescharacteristic
97C23×D4D411yescharacteristic
98C24×C4—22no—
99C24×C4C2312yes—
100C22×M16C2312yes—
101C22×M16C2311yescharacteristic
102C22×M16C2311yescharacteristic
103#525—28no—
104#525—44no—
105C2×#123—22no—
106C2×C22⋊Q8C2312yes—
107C2×C22⋊Q8C2312yes—
108C2×#121—21no—
109C2×#121—21no—
110C2×#121C2312yes—
111C2×#121C2312yes—
112C2×#120—22no—
113C4×#41—24no—
114C4×#41—24no—
115C2×C4×Q8C2311yescharacteristic
116C2×C4×Q8C2311yescharacteristic
117C2×C4×D4—24no—
118C2×C4×D4—22no—
119C2×C4×D4—22no—
120C2×C4×D4—22no—
121C2×C4×D4—22no—
122C2×C4×D4—21no—
123C2×C4×D4—21no—
124C2×C4×D4—24no—
125C2×C4×D4—24no—
126C2×C4×D4—48no—
127C2×C4×D4D412yes—
128C2×C4×D4D411yescharacteristic
129C2×C4×D4D411yescharacteristic
130C2×C4×D4C2311yescharacteristic
131C2×C4×D4C2311yescharacteristic
132C2×C4×D4C2311yescharacteristic
133C2×C4×D4C2311yescharacteristic
134C2×C4×D4C2312yes—
135C2×#117—21no—
136C2×#117C2312yes—
137C2×#117C2311yescharacteristic
138C22×C4⋊C4—28no—
139C22×C4⋊C4—22no—
140C22×C4⋊C4—22no—
141C22×C4⋊C4—22no—
142C22×C4⋊C4—21no—
143C22×C4⋊C4—21no—
144C22×C4⋊C4—44no—
145C22×C4⋊C4D411yescharacteristic
146C22×C4⋊C4C2312yes—
147C22×C4⋊C4C2311yescharacteristic
148C22×C4⋊C4C2314yes—
149C22×C4⋊C4C2314yes—
150C22×C4⋊C4C2311yescharacteristic
151C22×C22⋊C4—22no—
152C22×C22⋊C4D412yes—
153C22×C42—21no—
154C22×C42—21no—
155C22×C42C2311yescharacteristic
156#484—216no—
157#483—216no—
158#481—216no—
159#480—216no—
160#428—28no—
161#428—28no—
162#428—44no—
163C2×#107C2314yes—
164C2×#107C2314yes—
165C2×#107C2314yes—
166C2×#106C2314yes—
167C2×#106C2314yes—
168C2×#106C2314yes—
169#423—24no—
170C2×C4⋊C8C2312yes—
171C2×C4⋊C8C2312yes—
172#417—28no—
173#417—24no—
174#417D418yescomplemented
175C2×#103C2314yes—
176C2×#103C2312yes—
177C2×#103C2312yes—
178C2×#102C2314yes—
179C2×#102C2312yes—
180C2×#102C2312yes—
181#407—28no—
182#407—28no—
183C2×C22⋊C8C2314yes—
184C2×C22⋊C8C2314yes—
185C2×C22⋊C8C2314yes—
186C2×C22⋊C8C2314yes—
187C4×M16—24no—
188C2×#97C2312yes—
189C2×C4×C8C2312yes—
190#398—22no—
191#397—22no—
192#396—22no—
193#396—22no—
194#394—22no—
195#394—22no—
196#394—22no—
197#392—22no—
198#390—21no—
199#390—21no—
200#389—22no—
201#389—22no—
202#389—24no—
203#389—21no—
204#389—21no—
205#388—22no—
206#388—22no—
207#386—22no—
208#386—22no—
209#385—24no—
210#385—24no—
211#385—24no—
212#385—24no—
213#384—21no—
214#384—21no—
215#384C2312yes—
216#384C2312yes—
217#384C2311yescharacteristic
218#384C2311yescharacteristic
219#382C2312yes—
220#381—22no—
221#380—22no—
222#380—22no—
223#380—21no—
224#380—21no—
225#380—21no—
226#380—21no—
227#380C2312yes—
228#380C2314yes—
229#380C2312yes—
230#380C2314yes—
231#380C2312yes—
232#380C2312yes—
233#379—22no—
234C4×C4⋊C4—21no—
235C4×C4⋊C4—21no—
236C4×C4⋊C4—21no—
237C4×C4⋊C4—21no—
238C4×C4⋊C4C2312yes—
239C4×C4⋊C4C2312yes—
240C4×C22⋊C4—22no—
241C4×C22⋊C4—22no—
242C2×#95—21no—
243C2×#95—22no—
244#340C2314yes—
245#340C2314yes—
246#340C2312yes—
247#340C2314yes—
248#340C2312yes—
249#340C2314yes—
250#340C2312yes—
251#340C2312yes—
252C25C2×D412yes—
253C2×#41—22no—
254C2×#41—22no—
255C2×#41—22no—
256C2×#41—22no—
257C2×#41—22no—
258C2×#41C2×D414yes—
259C22×Q8C2411yescharacteristic
260C22×D4—24no—
261C22×D4—24no—
262C22×D4—21no—
263C22×D4—22no—
264C22×D4—22no—
265C22×D4—24no—
266C22×D4C2×D412yes—
267C22×D4C2×D411yescharacteristic
268C22×D4C2×D411yescharacteristic
269C22×D4C2411yescharacteristic
270C23×C4—21no—
271C23×C4—24no—
272C23×C4—21no—
273C23×C4—24no—
274C23×C4—24no—
275C23×C4—24no—
276C23×C4—24no—
277C23×C4—24no—
278C23×C4—21no—
279C23×C4—22no—
280C23×C4—24no—
281C23×C4—24no—
282C23×C4—21no—
283C23×C4—21no—
284C23×C4—48no—
285C23×C4—48no—
286C23×C4—84no—
287C23×C4C2×D412yes—
288C23×C4C2×D412yes—
289C23×C4C2×D412yes—
290C23×C4C2×D411yescharacteristic
291C23×C4C2×D411yescharacteristic
292C23×C4C2412yes—
293C23×C4C2412yes—
294C23×C4C2411yescharacteristic
295C2×M16—22no—
296C2×M16—22no—
297C2×M16—22no—
298C2×M16—22no—
299C2×M16—24no—
300C2×M16—24no—
301C2×M16—24no—
302C2×M16C2×D414yes—
303C2×M16#4114yes—
304C22×C8C2414yes—
305C22×C8C2412yes—
306C22×C8C2412yes—
307#123—48no—
308C22⋊Q8—24no—
309C22⋊Q8—24no—
310C22⋊Q8—42no—
311C22⋊Q8—42no—
312#121—24no—
313#121—24no—
314#121—42no—
315#121—42no—
316#121—44no—
317#121—44no—
318#120—48no—
319C4×Q8—22no—
320C4×Q8—22no—
321C4×Q8—22no—
322C4×Q8—22no—
323C4×D4—24no—
324C4×D4—24no—
325C4×D4—28no—
326C4×D4—22no—
327C4×D4—22no—
328C4×D4—24no—
329C4×D4—22no—
330C4×D4—22no—
331C4×D4—24no—
332C4×D4—22no—
333C4×D4—22no—
334C4×D4—22no—
335C4×D4—22no—
336C4×D4—48no—
337C4×D4—48no—
338C4×D4—416no—
339C4×D4—48no—
340C4×D4—48no—
341C4×D4—44no—
342C4×D4—44no—
343#117—24no—
344#117—22no—
345#117—22no—
346#117—24no—
347#117—44no—
348C2×C4⋊C4—24no—
349C2×C4⋊C4—21no—
350C2×C4⋊C4—22no—
351C2×C4⋊C4—24no—
352C2×C4⋊C4—22no—
353C2×C4⋊C4—24no—
354C2×C4⋊C4—22no—
355C2×C4⋊C4—28no—
356C2×C4⋊C4—28no—
357C2×C4⋊C4—22no—
358C2×C4⋊C4—24no—
359C2×C4⋊C4—24no—
360C2×C4⋊C4—22no—
361C2×C4⋊C4—22no—
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—22no—
370C2×C4⋊C4—22no—
371C2×C4⋊C4—21no—
372C2×C4⋊C4—21no—
373C2×C4⋊C4—44no—
374C2×C4⋊C4—44no—
375C2×C4⋊C4—48no—
376C2×C4⋊C4—48no—
377C2×C4⋊C4—48no—
378C2×C4⋊C4—44no—
379C2×C4⋊C4—82no—
380C2×C4⋊C4C2×D411yescharacteristic
381C2×C4⋊C4C2×D411yescharacteristic
382C2×C4⋊C4C2×D412yes—
383C2×C4⋊C4C2×D414yes—
384C2×C4⋊C4C2414yes—
385C2×C4⋊C4C2412yes—
386C2×C4⋊C4C2411yescharacteristic
387C2×C4⋊C4C2411yescharacteristic
388C2×C4⋊C4C2412yes—
389C2×C4⋊C4C2412yes—
390C2×C4⋊C4C2412yes—
391C2×C22⋊C4—28no—
392C2×C22⋊C4—24no—
393C2×C22⋊C4—24no—
394C2×C22⋊C4—21no—
395C2×C22⋊C4—22no—
396C2×C22⋊C4—22no—
397C2×C22⋊C4—22no—
398C2×C22⋊C4—22no—
399C2×C22⋊C4—22no—
400C2×C22⋊C4—21no—
401C2×C22⋊C4—21no—
402C2×C22⋊C4—22no—
403C2×C22⋊C4—22no—
404C2×C22⋊C4—22no—
405C2×C22⋊C4—22no—
406C2×C22⋊C4—48no—
407C2×C22⋊C4C2×D412yes—
408C2×C22⋊C4C2×D412yes—
409C2×C22⋊C4C2×D412yes—
410C2×C22⋊C4C2×D412yes—
411C2×C42—21no—
412C2×C42—22no—
413C2×C42—22no—
414C2×C42—22no—
415C2×C42—21no—
416C2×C42—21no—
417C2×C42—44no—
418C2×C42—44no—
419C2×C42C2×D411yescharacteristic
420C2×C42C2×D411yescharacteristic
421C2×C42#4114yes—
422C2×C42#4114yes—
423C2×C42C2411yescharacteristic
424C2×C42C2411yescharacteristic
425#107—28no—
426#107—28no—
427#107—44no—
428#106—28no—
429#106—28no—
430#106—44no—
431C4⋊C8—24no—
432C4⋊C8—24no—
433#103—28no—
434#103—24no—
435#103C2×D418yescomplemented
436#102—28no—
437#102—24no—
438#102C2×D418yescomplemented
439C22⋊C8—28no—
440C22⋊C8—28no—
441C22⋊C8—28no—
442C22⋊C8—28no—
443#97—24no—
444C4×C8—24no—
445#95—22no—
446#95—22no—
447#95—24no—
448#95—24no—
449#95—22no—
450#95—22no—
451#95—22no—
452#95—22no—
453#95—22no—
454#95—22no—
455C24—24no—
456C24—24no—
457C24—24no—
458C24—24no—
459C24—24no—
460C24—21no—
461C24—42no—
462C24—42no—
463C24C22×D412yes—
464C24C22×D412yes—
465C24C22×D411yescharacteristic
466#41—28no—
467#41—28no—
468#41—44no—
469#41—44no—
470C2×Q8—21no—
471C2×Q8—21no—
472C2×Q8—21no—
473C2×Q8—21no—
474C2×Q8—21no—
475C2×Q8C22×D412yes—
476C2×D4—232no—
477C2×D4—24no—
478C2×D4—24no—
479C2×D4—24no—
480C2×D4—24no—
481C2×D4—22no—
482C2×D4—22no—
483C2×D4—22no—
484C2×D4—22no—
485C2×D4—21no—
486C2×D4—21no—
487C2×D4—21no—
488C2×D4—21no—
489C2×D4—21no—
490C2×D4—42no—
491C2×D4—42no—
492C2×D4—44no—
493C2×D4—44no—
494C2×D4—44no—
495C2×D4—44no—
496C2×D4—82no—
497C2×D4—82no—
498C2×D4AGL(1,ℤ/8)14yes—
499C2×D4#13714yes—
500C2×D4C22×D412yes—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—24no—
504C22×C4—24no—
505C22×C4—24no—
506C22×C4—24no—
507C22×C4—22no—
508C22×C4—21no—
509C22×C4—24no—
510C22×C4—24no—
511C22×C4—24no—
512C22×C4—24no—
513C22×C4—24no—
514C22×C4—24no—
515C22×C4—24no—
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—21no—
530C22×C4—21no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—24no—
534C22×C4—41no—
535C22×C4—41no—
536C22×C4—48no—
537C22×C4—48no—
538C22×C4—42no—
539C22×C4—42no—
540C22×C4—42no—
541C22×C4—48no—
542C22×C4—48no—
543C22×C4—48no—
544C22×C4—42no—
545C22×C4—48no—
546C22×C4—42no—
547C22×C4—44no—
548C22×C4—44no—
549C22×C4—48no—
550C22×C4—42no—
551C22×C4—44no—
552C22×C4—42no—
553C22×C4—48no—
554C22×C4—42no—
555C22×C4—42no—
556C22×C4—42no—
557C22×C4—42no—
558C22×C4—81no—
559C22×C4—81no—
560C22×C4—84no—
561C22×C4—84no—
562C22×C4—832no—
563C22×C4#12314yes—
564C22×C4#12314yes—
565C22×C4C22×D412yes—
566C22×C4C22×D412yes—
567C22×C4C22×D411yescharacteristic
568C22×C4C22×D411yescharacteristic
569C22×C4C22×D411yescharacteristic
570C22×C4C22×D411yescharacteristic
571C22×C4C22×D411yescharacteristic
572C22×C4C22×D412yes—
573C22×C4C2×#4112yes—
574C22×C4C2×#4112yes—
575C22×C4C2×#4112yes—
576C22×C4H(5,𝔽2)12yes—
577C22×C42−1+412yes—
578C22×C4C2511yescharacteristic
579M16—28no—
580M16—28no—
581M16—48no—
582C2×C8—22no—
583C2×C8—22no—
584C2×C8—22no—
585C2×C8—22no—
586C2×C8—24no—
587C2×C8—24no—
588C2×C8—24no—
589C2×C8C22×D414yes—
590C2×C8C2×#4114yes—
591C4⋊C4—24no—
592C4⋊C4—22no—
593C4⋊C4—22no—
594C4⋊C4—24no—
595C4⋊C4—22no—
596C4⋊C4—24no—
597C4⋊C4—22no—
598C4⋊C4—22no—
599C4⋊C4—22no—
600C4⋊C4—21no—
601C4⋊C4—21no—
602C4⋊C4—21no—
603C4⋊C4—21no—
604C4⋊C4—22no—
605C4⋊C4—24no—
606C4⋊C4—22no—
607C4⋊C4—22no—
608C4⋊C4—48no—
609C4⋊C4—48no—
610C4⋊C4—44no—
611C4⋊C4—44no—
612C4⋊C4—44no—
613C4⋊C4—42no—
614C4⋊C4—42no—
615C4⋊C4—44no—
616C4⋊C4—42no—
617C4⋊C4—44no—
618C4⋊C4—42no—
619C4⋊C4—42no—
620C4⋊C4—81no—
621C4⋊C4—81no—
622C4⋊C4—82no—
623C4⋊C4—82no—
624C4⋊C4C22×D414yes—
625C22⋊C4—24no—
626C22⋊C4—24no—
627C22⋊C4—24no—
628C22⋊C4—24no—
629C22⋊C4—44no—
630C22⋊C4—44no—
631C22⋊C4—44no—
632C22⋊C4—44no—
633C22⋊C4—48no—
634C22⋊C4—42no—
635C22⋊C4—44no—
636C22⋊C4—48no—
637C22⋊C4—44no—
638C22⋊C4—44no—
639C22⋊C4—42no—
640C22⋊C4—42no—
641C22⋊C4—82no—
642C22⋊C4—82no—
643C42—44no—
644C42—42no—
645C42—42no—
646C42—42no—
647C42—44no—
648C42—44no—
649C42#12314yes—
650C42#12314yes—
651C42C2×#4112yes—
652C42C2×#4112yes—
653C42C2×#4112yes—
654C42C2×#4112yes—
655C23—21no—
656C23—21no—
657C23—21no—
658C23—21no—
659C23—216no—
660C23—22no—
661C23—22no—
662C23—22no—
663C23—22no—
664C23—22no—
665C23—22no—
666C23—22no—
667C23—22no—
668C23—22no—
669C23—22no—
670C23—22no—
671C23—22no—
672C23—22no—
673C23—48no—
674C23—48no—
675C23—48no—
676C23—48no—
677C23—48no—
678C23—48no—
679C23—41no—
680C23—41no—
681C23—41no—
682C23—41no—
683C23—41no—
684C23—41no—
685C23C2×#12312yes—
686C23D4212yes—
687C23#54712yes—
688C23C2×AGL(1,ℤ/8)14yes—
689C23C2×#13714yes—
690C23C23×D411yescharacteristic
691Q8—22no—
692Q8—22no—
693Q8—41no—
694Q8—41no—
695D4—216no—
696D4—28no—
697D4—28no—
698D4—22no—
699D4—22no—
700D4—48no—
701D4—41no—
702D4—41no—
703D4—88no—
704D4—88no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—28no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—24no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—44no—
721C2×C4—48no—
722C2×C4—42no—
723C2×C4—41no—
724C2×C4—48no—
725C2×C4—41no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—42no—
729C2×C4—48no—
730C2×C4—48no—
731C2×C4—48no—
732C2×C4—42no—
733C2×C4—42no—
734C2×C4—42no—
735C2×C4—42no—
736C2×C4—42no—
737C2×C4—42no—
738C2×C4—41no—
739C2×C4—42no—
740C2×C4—44no—
741C2×C4—41no—
742C2×C4—42no—
743C2×C4—42no—
744C2×C4—41no—
745C2×C4—41no—
746C2×C4—42no—
747C2×C4—42no—
748C2×C4—44no—
749C2×C4—42no—
750C2×C4—42no—
751C2×C4—44no—
752C2×C4—41no—
753C2×C4—42no—
754C2×C4—41no—
755C2×C4—42no—
756C2×C4—84no—
757C2×C4—816no—
758C2×C4—816no—
759C2×C4—84no—
760C2×C4—88no—
761C2×C4—84no—
762C2×C4C2×#12312yes—
763C2×C4C2×#12312yes—
764C2×C4C2×#12312yes—
765C2×C4C2×#12312yes—
766C2×C4C2×#12312yes—
767C2×C4#53214yes—
768C2×C4#54214yes—
769C2×C4D4212yes—
770C2×C4#54712yes—
771C2×C4#54714yes—
772C2×C4#55314yes—
773C2×C4C2×AGL(1,ℤ/8)12yes—
774C2×C4C2×#13712yes—
775C2×C4C23×D411yescharacteristic
776C2×C4C22×#4111yescharacteristic
777C2×C4C22×#4111yescharacteristic
778C2×C4C22×#4111yescharacteristic
779C2×C4C2×H(5,𝔽2)11yescharacteristic
780C2×C4C2×2−1+411yescharacteristic
781C8—24no—
782C8—24no—
783C8—44no—
784C22—22no—
785C22—22no—
786C22—22no—
787C22—22no—
788C22—22no—
789C22—22no—
790C22—24no—
791C22—24no—
792C22—24no—
793C22—24no—
794C22—24no—
795C22—24no—
796C22—432no—
797C22—42no—
798C22—42no—
799C22—42no—
800C22—42no—
801C22—42no—
802C22—42no—
803C22—42no—
804C22—42no—
805C22—42no—
806C22—42no—
807C22—42no—
808C22—81no—
809C22—81no—
810C22—81no—
811C22—81no—
812C22#242214yes—
813C22C22×#12311yescharacteristic
814C22C2×D4211yescharacteristic
815C22C2×#54711yescharacteristic
816C22C22×AGL(1,ℤ/8)11yescharacteristic
817C22C22×#13711yescharacteristic
818C22#358511yescharacteristic
819C22#358611yescharacteristic
820C4—22no—
821C4—22no—
822C4—22no—
823C4—42no—
824C4—42no—
825C4—42no—
826C4—44no—
827C4—82no—
828C4—81no—
829C4—81no—
830C4—84no—
831C4—82no—
832C4—82no—
833C4#242214yes—
834C4#309214yescomplemented
835C4C2×#53211yescharacteristic
836C4C2×#54211yescharacteristic
837C4C2×#54711yescharacteristic
838C4C2×#55311yescharacteristic
839C2—24no—
840C2—44no—
841C2—44no—
842C2—82no—
843C2C2×#242211yescharacteristic
844C2C2×#309211yescharacteristic
845C2#6051711yescharacteristic
846C2D4×AGL(1,ℤ/8)11yescharacteristic
847C2D4×#13711yescharacteristic
848C2#6125211yescharacteristic
849C2#6125411yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#34935C2
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. #25024C2semidirect
5. #25022C2semidirect
6. #25016C2semidirect
7. #25014C2semidirect
8. #25012C2semidirect
9. #25010C2semidirect
10. #23642C2semidirect
11. #23482C2semidirect
12. #21190C2semidirect
13. #21170C2semidirect
14. #20844C2semidirect
15. #20800C2semidirect
16. #20648C2semidirect
17. C4×#417C2semidirect
24. C2×#484C22semidirect
25. C2×#481C22semidirect
26. C2×#483C22semidirect
27. C2×#480C22semidirect
63. #2077C22semidirect
64. #2077C22semidirect
65. #2076C22semidirect
66. #2075C22semidirect
67. #2036C22semidirect
68. #2035C22semidirect
69. #2034C22semidirect
70. #2033C22semidirect
74. #1949C22semidirect
75. #1948C22semidirect
76. #1947C22semidirect
77. #1853C22semidirect
78. #1853C22semidirect
79. #1852C22semidirect
80. #1852C22semidirect
81. #1847C22semidirect
82. #1845C22semidirect
83. #1844C22semidirect
84. #1803C22semidirect
85. #1803C22semidirect
86. #1802C22semidirect
87. #1802C22semidirect
88. #1763C22semidirect
89. #1762C22semidirect
90. C4×#103C22semidirect
91. C4×#102C22semidirect
174. #417D4semidirect
435. #103C2×D4semidirect
438. #102C2×D4semidirect
834. C4#3092semidirect

Maximal subgroups

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

subgroupindex
C2×#30922
#349352
C2×D4×C4⋊C42
#250242
#250222
#250162
#250142
#250122
#250102
#236422
#234822
#211902
#211702
#208442
#208002
#206482
C4×#4172