Finite Group Databasebeta

← #7505971

Subgroups — #7505971

Order 512.

2705 conjugacy classes of subgroups.

The subgroup lattice has 889 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2486C211yesmaximal, characteristic, complemented
2#34736C211yesmaximal, characteristic
3#31683C212yesmaximal, complemented
4#31681C212yesmaximal, complemented
5#31679C214yesmaximal, complemented
6#31674C214yesmaximal, complemented
7#31668C212yesmaximal, complemented
8#31666C212yesmaximal, complemented
9#23642C212yesmaximal, complemented
10#23617C212yesmaximal, complemented
11#23482C212yesmaximal, complemented
12#21190C211yesmaximal, characteristic, complemented
13#21093C212yesmaximal, complemented
14#20909C212yesmaximal, complemented
15#20601C212yesmaximal, complemented
16C23×#41C2211yescharacteristic
17C2×#525C2212yes—
18C22×#123—21no—
19C22×C4×D4C2211yescharacteristic
20C23×C4⋊C4C2211yescharacteristic, complemented
21C2×#428C2212yescomplemented
22C2×#423C2211yescharacteristic, complemented
23C2×#417C2212yes—
24C2×#417C2212yes—
25C2×#417C2212yes—
26C2×#417C2212yes—
27C2×#407C2212yes—
28C2×#407C2212yescomplemented
29C2×C4×M16C2211yescharacteristic, complemented
30#2486—21no—
31#2486—21no—
32#2486—21no—
33#2486—21no—
34#2486C2212yes—
35#2486C2212yes—
36#2486C2212yescomplemented
37#2486C2212yescomplemented
38#2409C2211yescharacteristic
39#2409C2211yescharacteristic
40#2408C2211yescharacteristic
41#2408C2211yescharacteristic
42#2407C2212yes—
43#2407C2212yes—
44#2406—21no—
45#2405—21no—
46#2404—21no—
47#2403—21no—
48C2×#398—21no—
49C2×#397—21no—
50#2388—21no—
51#2388—21no—
52C4×#120—21no—
53C4×#120—21no—
54#2297C2212yes—
55C2×#389C2212yescomplemented
56#2280C2211yescharacteristic
57C2×#381—21no—
58C2×#380C2212yes—
59C2×#380C2211yescharacteristic, complemented
60#2077C2214yescomplemented
61#2077C2214yescomplemented
62#2076C2214yescomplemented
63#2075C2214yescomplemented
64#2068C2214yescomplemented
65#2067C2214yescomplemented
66#2066C2214yescomplemented
67#2065C2214yescomplemented
68#2036C2214yescomplemented
69#2035C2214yescomplemented
70#2034C2214yescomplemented
71#2033C2214yescomplemented
72#1955C2212yes—
73#1955C2212yescomplemented
74#1954C2212yes—
75#1954C2212yescomplemented
76#1936C2214yescomplemented
77#1935C2214yescomplemented
78#1934C2214yescomplemented
79#1933C2214yescomplemented
80#1874C2214yescomplemented
81#1874C2214yescomplemented
82#1872C2214yescomplemented
83#1872C2214yescomplemented
84#1788C2214yescomplemented
85#1788C2214yescomplemented
86#1787C2214yescomplemented
87#1786C2214yescomplemented
88#1736C2212yescomplemented
89#1736C2212yescomplemented
90#1736C2212yescomplemented
91C22×#41—21no—
92C22×#41—21no—
93C22×#41—28no—
94C22×#41—42no—
95C22×#41—42no—
96C22×#41—44no—
97C22×#41C2312yes—
98C22×#41C2312yes—
99C23×Q8C2311yescharacteristic
100C23×D4—21no—
101C23×D4D411yescharacteristic
102C23×D4C2311yescharacteristic
103C24×C4—21no—
104C24×C4—21no—
105C24×C4C2311yescharacteristic
106C24×C4C2311yescharacteristic
107C22×M16C2312yes—
108C22×M16C2312yes—
109#525—28no—
110#525—44no—
111C2×#123—22no—
112C2×#123—22no—
113C2×#123—22no—
114C2×#123—22no—
115C2×#123—22no—
116C2×#123—48no—
117C2×C22⋊Q8C2312yes—
118C2×C22⋊Q8C2312yes—
119C2×#121C2312yes—
120C2×#121C2312yes—
121C2×#120—22no—
122C2×#120—21no—
123C2×#120—21no—
124C2×C4×D4—22no—
125C2×C4×D4—22no—
126C2×C4×D4—42no—
127C2×C4×D4—42no—
128C2×C4×D4D411yescharacteristic
129C2×C4×D4D411yescharacteristic
130C2×C4×D4D411yescharacteristic
131C2×C4×D4D411yescharacteristic
132C2×C4×D4C2311yescharacteristic
133C2×C4×D4C2311yescharacteristic
134C2×C4×D4C2311yescharacteristic
135C2×C4×D4C2311yescharacteristic
136C2×#117C2312yes—
137C22×C4⋊C4—21no—
138C22×C4⋊C4—22no—
139C22×C4⋊C4—21no—
140C22×C4⋊C4—21no—
141C22×C4⋊C4—42no—
142C22×C4⋊C4—42no—
143C22×C4⋊C4D411yescharacteristic
144C22×C4⋊C4C2312yes—
145C22×C4⋊C4C2312yes—
146C22×C4⋊C4C2312yes—
147C22×C4⋊C4C2312yes—
148C22×C22⋊C4—22no—
149C22×C22⋊C4—21no—
150C22×C22⋊C4D411yescharacteristic
151C22×C22⋊C4D411yescharacteristic
152C22×C42C2311yescharacteristic
153#428—44no—
154C2×#107C2314yes—
155C2×#106C2314yes—
156#423—42no—
157C2×C4⋊C8C2312yes—
158C2×C4⋊C8C2312yes—
159#417—28no—
160#417—44no—
161#417—44no—
162#417—44no—
163C2×#103C2314yes—
164C2×#103C2314yes—
165C2×#103C2314yes—
166C2×#103C2314yes—
167C2×#102C2314yes—
168C2×#102C2314yes—
169C2×#102C2314yes—
170C2×#102C2314yes—
171#407—44no—
172#407—44no—
173C2×C22⋊C8C2314yes—
174C2×C22⋊C8C2314yes—
175C2×C22⋊C8C2314yes—
176C2×C22⋊C8C2314yes—
177C4×M16—42no—
178C2×#97C2312yes—
179C2×C4×C8C2312yes—
180#398—22no—
181#398—22no—
182#398—22no—
183#398—22no—
184#397—22no—
185#397—22no—
186#397—22no—
187#397—22no—
188#395—21no—
189#395—21no—
190#394—21no—
191#394—21no—
192#394—22no—
193#394—22no—
194#393—21no—
195#393—21no—
196#392—22no—
197#392—22no—
198#392—21no—
199#392—21no—
200#391C2312yes—
201#391C2312yes—
202#390C2312yes—
203#390C2312yes—
204#389—22no—
205#389—22no—
206#389C2314yes—
207#389C2314yes—
208#386—21no—
209#386—21no—
210#386—22no—
211#386—22no—
212#386—22no—
213#386—22no—
214#385—22no—
215#385—22no—
216#385—21no—
217#385—21no—
218#381—21no—
219#381—22no—
220#381—22no—
221#381—22no—
222#381—22no—
223#380—22no—
224#380—22no—
225#380—21no—
226#380—21no—
227#380C2311yescharacteristic
228#380C2314yes—
229#380C2312yes—
230#380C2314yes—
231#380C2311yescharacteristic
232#380C2312yes—
233#380C2312yes—
234#379—21no—
235#379—21no—
236#379—21no—
237C4×C22⋊C4—21no—
238C4×C22⋊C4—21no—
239C4×C22⋊C4—22no—
240C4×C22⋊C4—22no—
241C2×#95—21no—
242C2×#95—22no—
243C2×#95—22no—
244#340C2314yes—
245#340C2314yes—
246#340C2314yes—
247#340C2314yes—
248#340C2314yes—
249#340C2314yes—
250C25—21no—
251C25C2×D411yescharacteristic
252C25C2×D411yescharacteristic
253C2×#41—24no—
254C2×#41—24no—
255C2×#41—24no—
256C2×#41—24no—
257C2×#41—24no—
258C2×#41—24no—
259C2×#41—24no—
260C2×#41—48no—
261C2×#41—42no—
262C2×#41—42no—
263C2×#41—42no—
264C2×#41—42no—
265C2×#41—48no—
266C2×#41—44no—
267C2×#41—44no—
268C2×#41—416no—
269C2×#41—432no—
270C2×#41—416no—
271C2×#41#4118yes—
272C22×Q8—21no—
273C22×Q8—24no—
274C22×Q8—42no—
275C22×Q8—41no—
276C22×Q8—41no—
277C22×Q8C2412yes—
278C22×D4—22no—
279C22×D4—24no—
280C22×D4—24no—
281C22×D4—22no—
282C22×D4—22no—
283C22×D4—22no—
284C22×D4—21no—
285C22×D4—42no—
286C22×D4—41no—
287C22×D4—41no—
288C22×D4—42no—
289C22×D4—42no—
290C22×D4—48no—
291C22×D4—44no—
292C22×D4C2×D411yescharacteristic
293C22×D4C2×D411yescharacteristic
294C22×D4C2×D411yescharacteristic
295C22×D4C2×D411yescharacteristic
296C22×D4C2412yes—
297C23×C4—22no—
298C23×C4—24no—
299C23×C4—24no—
300C23×C4—22no—
301C23×C4—22no—
302C23×C4—22no—
303C23×C4—22no—
304C23×C4—24no—
305C23×C4—24no—
306C23×C4—22no—
307C23×C4—22no—
308C23×C4—22no—
309C23×C4—22no—
310C23×C4—21no—
311C23×C4—22no—
312C23×C4—48no—
313C23×C4—44no—
314C23×C4—44no—
315C23×C4—44no—
316C23×C4—44no—
317C23×C4C2×D411yescharacteristic
318C23×C4C2×D411yescharacteristic
319C23×C4C2×D411yescharacteristic
320C23×C4C2×D411yescharacteristic
321C23×C4C2×D411yescharacteristic
322C23×C4C2×D411yescharacteristic
323C23×C4C2×D411yescharacteristic
324C23×C4C2×D411yescharacteristic
325C23×C4C2411yescharacteristic
326C23×C4C2411yescharacteristic
327C23×C4C2411yescharacteristic
328C23×C4C2411yescharacteristic
329C23×C4C2411yescharacteristic
330C2×M16—24no—
331C2×M16—24no—
332C2×M16—24no—
333C2×M16—24no—
334C2×M16—24no—
335C2×M16—24no—
336C22×C8C2414yes—
337C22×C8C2414yes—
338#123—48no—
339#123—48no—
340#123—48no—
341#123—48no—
342#123—48no—
343C22⋊Q8—24no—
344C22⋊Q8—24no—
345C22⋊Q8—42no—
346C22⋊Q8—42no—
347#121—24no—
348#121—24no—
349#121—42no—
350#121—42no—
351#120—48no—
352#120—44no—
353#120—44no—
354C4×D4—42no—
355C4×D4—42no—
356C4×D4—42no—
357C4×D4—42no—
358C4×D4—41no—
359C4×D4—41no—
360C4×D4—41no—
361C4×D4—41no—
362C4×D4—41no—
363C4×D4—41no—
364C4×D4—41no—
365C4×D4—41no—
366C4×D4—48no—
367C4×D4—48no—
368#117—24no—
369#117—24no—
370C2×C4⋊C4—24no—
371C2×C4⋊C4—24no—
372C2×C4⋊C4—24no—
373C2×C4⋊C4—24no—
374C2×C4⋊C4—22no—
375C2×C4⋊C4—22no—
376C2×C4⋊C4—22no—
377C2×C4⋊C4—24no—
378C2×C4⋊C4—24no—
379C2×C4⋊C4—22no—
380C2×C4⋊C4—22no—
381C2×C4⋊C4—22no—
382C2×C4⋊C4—42no—
383C2×C4⋊C4—42no—
384C2×C4⋊C4—42no—
385C2×C4⋊C4—42no—
386C2×C4⋊C4—42no—
387C2×C4⋊C4—44no—
388C2×C4⋊C4—44no—
389C2×C4⋊C4—44no—
390C2×C4⋊C4—48no—
391C2×C4⋊C4C2×D411yescharacteristic
392C2×C4⋊C4C2×D411yescharacteristic
393C2×C4⋊C4C2×D411yescharacteristic
394C2×C4⋊C4C2×D411yescharacteristic
395C2×C4⋊C4C2414yes—
396C2×C4⋊C4C2414yes—
397C2×C4⋊C4C2412yes—
398C2×C4⋊C4C2412yes—
399C2×C22⋊C4—22no—
400C2×C22⋊C4—22no—
401C2×C22⋊C4—24no—
402C2×C22⋊C4—24no—
403C2×C22⋊C4—22no—
404C2×C22⋊C4—22no—
405C2×C22⋊C4—22no—
406C2×C22⋊C4—21no—
407C2×C22⋊C4—21no—
408C2×C22⋊C4—22no—
409C2×C22⋊C4—22no—
410C2×C22⋊C4—22no—
411C2×C22⋊C4—22no—
412C2×C22⋊C4—22no—
413C2×C22⋊C4—22no—
414C2×C22⋊C4—22no—
415C2×C22⋊C4—42no—
416C2×C22⋊C4—42no—
417C2×C22⋊C4—44no—
418C2×C22⋊C4—48no—
419C2×C22⋊C4C2×D411yescharacteristic
420C2×C22⋊C4C2×D411yescharacteristic
421C2×C22⋊C4C2×D411yescharacteristic
422C2×C22⋊C4C2×D411yescharacteristic
423C2×C22⋊C4C2×D411yescharacteristic
424C2×C22⋊C4C2×D411yescharacteristic
425C2×C22⋊C4C2×D411yescharacteristic
426C2×C22⋊C4C2×D411yescharacteristic
427C2×C42—22no—
428C2×C42—22no—
429C2×C42—22no—
430C2×C42C2×D411yescharacteristic
431C2×C42C2×D411yescharacteristic
432C2×C42C2411yescharacteristic
433C2×C42C2411yescharacteristic
434#107—44no—
435#106—44no—
436C4⋊C8—42no—
437C4⋊C8—42no—
438#103—28no—
439#103—44no—
440#103—44no—
441#103—44no—
442#102—28no—
443#102—44no—
444#102—44no—
445#102—44no—
446C22⋊C8—44no—
447C22⋊C8—44no—
448C22⋊C8—44no—
449C22⋊C8—44no—
450#97—42no—
451C4×C8—42no—
452#95—24no—
453#95—24no—
454#95—22no—
455#95—22no—
456#95—24no—
457#95—24no—
458#95—22no—
459#95—21no—
460#95—21no—
461#95—22no—
462#95—22no—
463#95—22no—
464#95—22no—
465C24—22no—
466C24—22no—
467C24—22no—
468C24—24no—
469C24—22no—
470C24—22no—
471C24—22no—
472C24—24no—
473C24—42no—
474C24—41no—
475C24—42no—
476C24—44no—
477C24—42no—
478C24—42no—
479C24—42no—
480C24—82no—
481C24C22×D411yescharacteristic
482C24C22×D411yescharacteristic
483C24C22×D411yescharacteristic
484C24C22×D411yescharacteristic
485C24C22×D411yescharacteristic
486#41—216no—
487#41—216no—
488#41—48no—
489#41—48no—
490#41—48no—
491#41—432no—
492#41—48no—
493#41—432no—
494#41—48no—
495#41—48no—
496C2×Q8—22no—
497C2×Q8—22no—
498C2×Q8—22no—
499C2×Q8—22no—
500C2×Q8—22no—
501C2×Q8—44no—
502C2×Q8—42no—
503C2×Q8—44no—
504C2×Q8—48no—
505C2×Q8—44no—
506C2×Q8C2×#4114yes—
507C2×D4—28no—
508C2×D4—22no—
509C2×D4—22no—
510C2×D4—22no—
511C2×D4—22no—
512C2×D4—22no—
513C2×D4—22no—
514C2×D4—22no—
515C2×D4—22no—
516C2×D4—22no—
517C2×D4—22no—
518C2×D4—41no—
519C2×D4—41no—
520C2×D4—41no—
521C2×D4—41no—
522C2×D4—41no—
523C2×D4—41no—
524C2×D4—44no—
525C2×D4—44no—
526C2×D4—42no—
527C2×D4—44no—
528C2×D4—48no—
529C2×D4—44no—
530C2×D4—416no—
531C2×D4—44no—
532C2×D4—432no—
533C2×D4—44no—
534C2×D4—44no—
535C2×D4—44no—
536C2×D4—44no—
537C2×D4—44no—
538C2×D4—44no—
539C2×D4—44no—
540C2×D4—82no—
541C2×D4—82no—
542C2×D4AGL(1,ℤ/8)14yes—
543C2×D4C2×#4114yes—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—24no—
548C22×C4—24no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—24no—
556C22×C4—24no—
557C22×C4—28no—
558C22×C4—24no—
559C22×C4—24no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—24no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—24no—
581C22×C4—41no—
582C22×C4—44no—
583C22×C4—42no—
584C22×C4—44no—
585C22×C4—44no—
586C22×C4—44no—
587C22×C4—42no—
588C22×C4—432no—
589C22×C4—44no—
590C22×C4—48no—
591C22×C4—48no—
592C22×C4—44no—
593C22×C4—44no—
594C22×C4—44no—
595C22×C4—44no—
596C22×C4—44no—
597C22×C4—44no—
598C22×C4—44no—
599C22×C4—44no—
600C22×C4—44no—
601C22×C4—44no—
602C22×C4—44no—
603C22×C4—44no—
604C22×C4—44no—
605C22×C4—44no—
606C22×C4—44no—
607C22×C4—44no—
608C22×C4—44no—
609C22×C4—816no—
610C22×C4C22×D411yescharacteristic
611C22×C4C22×D411yescharacteristic
612C22×C4C22×D411yescharacteristic
613C22×C4C22×D411yescharacteristic
614C22×C4C22×D411yescharacteristic
615C22×C4C22×D411yescharacteristic
616C22×C4C22×D411yescharacteristic
617C22×C4C22×D411yescharacteristic
618C22×C4C22×D411yescharacteristic
619C22×C4C2×#4114yes—
620C22×C4H(5,𝔽2)12yes—
621C22×C4H(5,𝔽2)12yes—
622C22×C4H(5,𝔽2)14yes—
623C22×C4C2511yescharacteristic
624M16—48no—
625M16—48no—
626C2×C8—24no—
627C2×C8—24no—
628C2×C8—24no—
629C2×C8—24no—
630C2×C8—24no—
631C2×C8—24no—
632C4⋊C4—24no—
633C4⋊C4—22no—
634C4⋊C4—22no—
635C4⋊C4—24no—
636C4⋊C4—24no—
637C4⋊C4—24no—
638C4⋊C4—22no—
639C4⋊C4—22no—
640C4⋊C4—41no—
641C4⋊C4—41no—
642C4⋊C4—41no—
643C4⋊C4—41no—
644C4⋊C4—44no—
645C4⋊C4—44no—
646C4⋊C4—44no—
647C4⋊C4—44no—
648C4⋊C4—48no—
649C4⋊C4—44no—
650C4⋊C4—44no—
651C4⋊C4—48no—
652C22⋊C4—41no—
653C22⋊C4—41no—
654C22⋊C4—41no—
655C22⋊C4—41no—
656C22⋊C4—41no—
657C22⋊C4—41no—
658C22⋊C4—41no—
659C22⋊C4—41no—
660C22⋊C4—44no—
661C22⋊C4—44no—
662C22⋊C4—44no—
663C22⋊C4—44no—
664C22⋊C4—44no—
665C22⋊C4—44no—
666C22⋊C4—48no—
667C22⋊C4—42no—
668C22⋊C4—44no—
669C22⋊C4—44no—
670C22⋊C4—48no—
671C22⋊C4—42no—
672C22⋊C4—44no—
673C22⋊C4—82no—
674C22⋊C4—82no—
675C22⋊C4—82no—
676C42—22no—
677C42—22no—
678C42—21no—
679C42—21no—
680C42—21no—
681C42—21no—
682C42—44no—
683C23—22no—
684C23—21no—
685C23—21no—
686C23—28no—
687C23—22no—
688C23—22no—
689C23—22no—
690C23—21no—
691C23—21no—
692C23—21no—
693C23—22no—
694C23—22no—
695C23—22no—
696C23—21no—
697C23—21no—
698C23—21no—
699C23—22no—
700C23—21no—
701C23—24no—
702C23—22no—
703C23—21no—
704C23—21no—
705C23—48no—
706C23—48no—
707C23—44no—
708C23—48no—
709C23—44no—
710C23—44no—
711C23—48no—
712C23—42no—
713C23—42no—
714C23—42no—
715C23—42no—
716C23—44no—
717C23—42no—
718C23—42no—
719C23—82no—
720C23—84no—
721C23—88no—
722C23—84no—
723C23—88no—
724C23—84no—
725C23#53412yes—
726C23#54614yes—
727C23C2×AGL(1,ℤ/8)12yes—
728C23C2×AGL(1,ℤ/8)12yes—
729C23#57512yes—
730C23C23×D411yescharacteristic
731Q8—24no—
732Q8—24no—
733Q8—48no—
734Q8—42no—
735Q8—42no—
736D4—24no—
737D4—24no—
738D4—44no—
739D4—44no—
740D4—44no—
741D4—44no—
742D4—48no—
743D4—416no—
744D4—416no—
745D4—42no—
746D4—42no—
747D4—88no—
748D4—88no—
749C2×C4—21no—
750C2×C4—21no—
751C2×C4—22no—
752C2×C4—22no—
753C2×C4—21no—
754C2×C4—21no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—21no—
759C2×C4—21no—
760C2×C4—22no—
761C2×C4—22no—
762C2×C4—24no—
763C2×C4—22no—
764C2×C4—22no—
765C2×C4—21no—
766C2×C4—21no—
767C2×C4—44no—
768C2×C4—48no—
769C2×C4—416no—
770C2×C4—42no—
771C2×C4—42no—
772C2×C4—44no—
773C2×C4—44no—
774C2×C4—42no—
775C2×C4—42no—
776C2×C4—42no—
777C2×C4—42no—
778C2×C4—44no—
779C2×C4—44no—
780C2×C4—44no—
781C2×C4—44no—
782C2×C4—416no—
783C2×C4—41no—
784C2×C4—41no—
785C2×C4—41no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—41no—
791C2×C4—42no—
792C2×C4—42no—
793C2×C4—44no—
794C2×C4—44no—
795C2×C4—42no—
796C2×C4—42no—
797C2×C4—44no—
798C2×C4—44no—
799C2×C4—44no—
800C2×C4—42no—
801C2×C4—42no—
802C2×C4—44no—
803C2×C4—82no—
804C2×C4—88no—
805C2×C4—88no—
806C2×C4—88no—
807C2×C4—88no—
808C2×C4#53412yes—
809C2×C4#53818yes—
810C2×C4#54614yes—
811C2×C4#55114yes—
812C2×C4#56014yes—
813C2×C4C2×AGL(1,ℤ/8)12yes—
814C2×C4C22×#4112yes—
815C2×C4C2×H(5,𝔽2)11yescharacteristic
816C2×C4C2×H(5,𝔽2)12yes—
817C2×C4C2×H(5,𝔽2)11yescharacteristic
818C8—44no—
819C8—44no—
820C22—22no—
821C22—22no—
822C22—24no—
823C22—24no—
824C22—22no—
825C22—22no—
826C22—22no—
827C22—24no—
828C22—24no—
829C22—24no—
830C22—416no—
831C22—41no—
832C22—41no—
833C22—41no—
834C22—41no—
835C22—41no—
836C22—41no—
837C22—42no—
838C22—42no—
839C22—42no—
840C22—41no—
841C22—41no—
842C22—44no—
843C22—41no—
844C22—44no—
845C22—42no—
846C22—44no—
847C22—42no—
848C22—88no—
849C22—816no—
850C22—82no—
851C22—82no—
852C22—82no—
853C22—82no—
854C22#269714yes—
855C22C2×#53411yescharacteristic
856C22C2×#54612yes—
857C22C22×AGL(1,ℤ/8)11yescharacteristic
858C22C2×#57511yescharacteristic
859C22#358612yes—
860C4—22no—
861C4—41no—
862C4—41no—
863C4—41no—
864C4—41no—
865C4—41no—
866C4—41no—
867C4—41no—
868C4—44no—
869C4—84no—
870C4—84no—
871C4—82no—
872C4—82no—
873C4#269714yes—
874C4C2×#53812yes—
875C4C2×#55111yescharacteristic
876C4C2×#56011yescharacteristic
877C2—24no—
878C2—42no—
879C2—42no—
880C2—42no—
881C2—81no—
882C2—84no—
883C2C2×#269711yescharacteristic
884C2#6075011yescharacteristic
885C2#6075411yescharacteristic
886C2#6116112yes—
887C2#6116312yes—
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#34736C2
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×#2486C2semidirect
3. #31683C2semidirect
4. #31681C2semidirect
5. #31679C2semidirect
6. #31674C2semidirect
7. #31668C2semidirect
8. #31666C2semidirect
9. #23642C2semidirect
10. #23617C2semidirect
11. #23482C2semidirect
12. #21190C2semidirect
13. #21093C2semidirect
14. #20909C2semidirect
15. #20601C2semidirect
20. C23×C4⋊C4C22semidirect
21. C2×#428C22semidirect
22. C2×#423C22semidirect
28. C2×#407C22semidirect
29. C2×C4×M16C22semidirect
36. #2486C22semidirect
37. #2486C22semidirect
55. C2×#389C22semidirect
59. C2×#380C22semidirect
60. #2077C22semidirect
61. #2077C22semidirect
62. #2076C22semidirect
63. #2075C22semidirect
64. #2068C22semidirect
65. #2067C22semidirect
66. #2066C22semidirect
67. #2065C22semidirect
68. #2036C22semidirect
69. #2035C22semidirect
70. #2034C22semidirect
71. #2033C22semidirect
73. #1955C22semidirect
75. #1954C22semidirect
76. #1936C22semidirect
77. #1935C22semidirect
78. #1934C22semidirect
79. #1933C22semidirect
80. #1874C22semidirect
81. #1874C22semidirect
82. #1872C22semidirect
83. #1872C22semidirect
84. #1788C22semidirect
85. #1788C22semidirect
86. #1787C22semidirect
87. #1786C22semidirect
88. #1736C22semidirect
89. #1736C22semidirect
90. #1736C22semidirect

Maximal subgroups

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

subgroupindex
C2×#24862
#347362
#316832
#316812
#316792
#316742
#316682
#316662
#236422
#236172
#234822
#211902
#210932
#209092
#206012