Finite Group Databasebeta

← #6660936

Subgroups — #6660936

Order 512.

1936 conjugacy classes of subgroups.

The subgroup lattice has 832 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#36625C211yesmaximal, characteristic, complemented
2C2×#2854C211yesmaximal, characteristic
3#32743C212yesmaximal, complemented
4#32739C212yesmaximal, complemented
5#30360C214yesmaximal, complemented
6#29972C212yesmaximal, complemented
7#29956C212yesmaximal, complemented
8#29910C212yesmaximal, complemented
9#29644C212yesmaximal, complemented
10#29297C211yesmaximal, characteristic, complemented
11#29296C211yesmaximal, characteristic, complemented
12#29103C211yesmaximal, characteristic, complemented
13#29103C211yesmaximal, characteristic, complemented
14#27602C212yesmaximal, complemented
15#24605C214yesmaximal, complemented
16#24009C212yesmaximal
17#20714C211yesmaximal, characteristic, complemented
18C2×#533C2211yescharacteristic, complemented
19C22×#123—21no—
20C22×#121C2211yescharacteristic
21C23×C42C2211yescharacteristic
22C2×#482C2214yes—
23C2×#431C2212yescomplemented
24#2857C2211yescharacteristic
25#2857C2211yescharacteristic
26#2857C2211yescharacteristic, complemented
27#2857C2211yescharacteristic, complemented
28#2855—21no—
29#2855—21no—
30#2854—21no—
31#2854—21no—
32#2854—21no—
33#2854—21no—
34#2854C2212yes—
35#2854C2212yes—
36#2854C2212yes—
37#2854C2212yes—
38#2851C2212yes—
39#2851C2212yescomplemented
40#2848—21no—
41#2848—21no—
42C4×C22⋊Q8—21no—
43C4×C22⋊Q8—21no—
44C4×C22⋊Q8—21no—
45C4×C22⋊Q8—21no—
46#2296C2212yescomplemented
47C2×#390C2211yescharacteristic
48C2×#390C2211yescharacteristic
49C2×#389C2211yescharacteristic
50C2×#389C2211yescharacteristic
51C2×#388—21no—
52C2×#388—21no—
53C2×#386—21no—
54#2285C2211yescharacteristic, complemented
55#2280C2212yes—
56C2×#380C2211yescharacteristic
57#2101C2214yescomplemented
58#2092C2214yescomplemented
59#2088C2214yescomplemented
60#2087C2214yescomplemented
61#2084C2212yescomplemented
62#2083C2212yescomplemented
63#2077C2214yescomplemented
64#2076C2214yescomplemented
65#2071C2212yescomplemented
66#2071C2212yescomplemented
67#2067C2214yescomplemented
68#2065C2214yescomplemented
69#2059C2214yescomplemented
70#2058C2212yescomplemented
71#2057C2212yescomplemented
72#2034C2214yes—
73#2033C2214yes—
74#2025C2214yescomplemented
75#2023C2212yescomplemented
76#2023C2212yescomplemented
77#1942C2214yescomplemented
78#1941C2214yescomplemented
79#1934C2214yescomplemented
80#1934C2214yescomplemented
81#1875C2214yes—
82#1854C2214yescomplemented
83#1853C2212yes—
84#1853C2212yes—
85#1852C2212yes—
86#1852C2212yes—
87#1825C2214yescomplemented
88#1823C2212yes—
89#1823C2212yes—
90#1817C2212yescomplemented
91#1797C2212yes—
92#1797C2212yescomplemented
93#1786C2212yes—
94#1786C2212yes—
95#1779C2212yes—
96C4×C22⋊C8C2211yescharacteristic
97C4×C22⋊C8C2211yescharacteristic
98C4×C22⋊C8C2212yescomplemented
99C23×D4—21no—
100C23×D4C2311yescharacteristic
101C24×C4D411yescharacteristic
102C24×C4D411yescharacteristic
103C24×C4C2311yescharacteristic
104#533—44no—
105C2×C4⋊Q8C2311yescharacteristic
106C2×C4⋊Q8C2311yescharacteristic
107C2×#125C2312yes—
108C2×#123—22no—
109C2×#123—22no—
110C2×#123—22no—
111C2×#123—22no—
112C2×#123—48no—
113C2×C22⋊Q8—21no—
114C2×C22⋊Q8—21no—
115C2×C22⋊Q8—21no—
116C2×C22⋊Q8—21no—
117C2×C22⋊Q8—21no—
118C2×C22⋊Q8—21no—
119C2×#121—21no—
120C2×#121—21no—
121C2×#121—44no—
122C2×#121C2312yes—
123C2×#121C2312yes—
124C2×C4×Q8—21no—
125C2×C4×Q8—21no—
126C2×#117C2312yes—
127C2×#117C2312yes—
128C22×C4⋊C4—21no—
129C22×C4⋊C4—21no—
130C22×C4⋊C4C2311yescharacteristic
131C22×C4⋊C4C2311yescharacteristic
132C22×C4⋊C4C2311yescharacteristic
133C22×C22⋊C4—21no—
134C22×C22⋊C4—21no—
135C22×C22⋊C4—21no—
136C22×C22⋊C4—21no—
137C22×C22⋊C4—21no—
138C22×C22⋊C4—21no—
139C22×C42—44no—
140C22×C42D411yescharacteristic
141C22×C42D411yescharacteristic
142C22×C42D411yescharacteristic
143C22×C42D411yescharacteristic
144C22×C42D411yescharacteristic
145C22×C42D411yescharacteristic
146C22×C42C2311yescharacteristic
147C22×C42C2311yescharacteristic
148C22×C42C2311yescharacteristic
149C22×C42C2311yescharacteristic
150C22×C42C2311yescharacteristic
151C22×C42C2311yescharacteristic
152#482—48no—
153#431—44no—
154C2×#107C2314yes—
155C2×#107C2314yes—
156C2×#106C2314yes—
157C2×#106C2314yes—
158C2×C4⋊C8C2314yes—
159C2×#102C2314yes—
160C2×#102C2314yes—
161C2×#102C2314yes—
162C2×#102C2314yes—
163C2×C22⋊C8C2312yes—
164C2×C22⋊C8C2312yes—
165C2×C22⋊C8C2314yes—
166C2×C22⋊C8C2314yes—
167C2×C4×C8C2312yes—
168C2×C4×C8C2312yes—
169#391—21no—
170#391—21no—
171#391—21no—
172#391—21no—
173#390—21no—
174#390—21no—
175#390—21no—
176#390—21no—
177#390C2312yes—
178#390C2312yes—
179#390C2312yes—
180#390C2312yes—
181#389—21no—
182#389—21no—
183#389—21no—
184#389—21no—
185#389—21no—
186#389—21no—
187#389—21no—
188#389—21no—
189#389C2312yes—
190#389C2312yes—
191#389C2312yes—
192#389C2312yes—
193#389C2312yes—
194#389C2312yes—
195#389C2312yes—
196#389C2312yes—
197#388—22no—
198#388—22no—
199#388—22no—
200#388—22no—
201#388—22no—
202#388—22no—
203#388—22no—
204#388—22no—
205#387—22no—
206#387—22no—
207#387—22no—
208#387—22no—
209#386—22no—
210#386—22no—
211#386—22no—
212#386—22no—
213#385—22no—
214#385—22no—
215#385—22no—
216#385—22no—
217#385—22no—
218#385—22no—
219#384C2311yescharacteristic
220#384C2311yescharacteristic
221#382C2312yes—
222#381—22no—
223#380—21no—
224#380—21no—
225#380—21no—
226#380—21no—
227#380—21no—
228#380—21no—
229#380—21no—
230#380—21no—
231#380C2312yes—
232#380C2312yes—
233#380C2312yes—
234#380C2312yes—
235#380C2312yes—
236#380C2312yes—
237#379—22no—
238C4×C4⋊C4—21no—
239C4×C4⋊C4—21no—
240C4×C4⋊C4—22no—
241C4×C4⋊C4—22no—
242C4×C22⋊C4—22no—
243C4×C22⋊C4—22no—
244C2×#95—21no—
245C2×#95—21no—
246C2×#95—21no—
247#340C2314yes—
248#340C2314yes—
249#340C2314yes—
250#340C2314yes—
251#340C2314yes—
252#340C2314yes—
253#340C2314yes—
254#340C2314yes—
255#336C2314yes—
256#336C2312yes—
257#336C2312yes—
258C25—21no—
259C25C2×D411yescharacteristic
260C22×Q8—21no—
261C22×Q8—21no—
262C22×D4—22no—
263C22×D4—22no—
264C22×D4—21no—
265C22×D4—24no—
266C22×D4—42no—
267C22×D4—42no—
268C22×D4—44no—
269C22×D4—44no—
270C22×D4—44no—
271C22×D4C2412yes—
272C23×C4—24no—
273C23×C4—24no—
274C23×C4—24no—
275C23×C4—24no—
276C23×C4—21no—
277C23×C4—21no—
278C23×C4—21no—
279C23×C4—42no—
280C23×C4—42no—
281C23×C4—42no—
282C23×C4—42no—
283C23×C4—42no—
284C23×C4C2×D411yescharacteristic
285C23×C4C2×D411yescharacteristic
286C23×C4C2×D411yescharacteristic
287C23×C4C2×D411yescharacteristic
288C23×C4C2×D411yescharacteristic
289C23×C4C2×D411yescharacteristic
290C23×C4C2×D411yescharacteristic
291C23×C4C2×D411yescharacteristic
292C23×C4C2×D411yescharacteristic
293C23×C4C2×D411yescharacteristic
294C23×C4C2×D411yescharacteristic
295C23×C4C2×D411yescharacteristic
296C23×C4C2×D411yescharacteristic
297C23×C4C2×D411yescharacteristic
298C23×C4C2×D411yescharacteristic
299C23×C4C2411yescharacteristic
300C23×C4C2411yescharacteristic
301C23×C4C2411yescharacteristic
302C22×C8C2414yes—
303C22×C8C2414yes—
304C4⋊Q8—42no—
305C4⋊Q8—42no—
306#125—44no—
307#123—48no—
308#123—48no—
309#123—48no—
310#123—48no—
311C22⋊Q8—44no—
312C22⋊Q8—44no—
313C22⋊Q8—44no—
314C22⋊Q8—44no—
315C22⋊Q8—44no—
316C22⋊Q8—44no—
317#121—28no—
318#121—44no—
319#121—44no—
320#121—44no—
321C4×Q8—44no—
322C4×Q8—44no—
323#117—28no—
324#117—44no—
325C2×C4⋊C4—24no—
326C2×C4⋊C4—22no—
327C2×C4⋊C4—22no—
328C2×C4⋊C4—22no—
329C2×C4⋊C4—22no—
330C2×C4⋊C4—21no—
331C2×C4⋊C4—21no—
332C2×C4⋊C4—21no—
333C2×C4⋊C4—22no—
334C2×C4⋊C4—22no—
335C2×C4⋊C4—21no—
336C2×C4⋊C4—21no—
337C2×C4⋊C4—21no—
338C2×C4⋊C4—21no—
339C2×C4⋊C4—21no—
340C2×C4⋊C4—21no—
341C2×C4⋊C4—22no—
342C2×C4⋊C4—22no—
343C2×C4⋊C4—22no—
344C2×C4⋊C4—22no—
345C2×C4⋊C4—42no—
346C2×C4⋊C4—42no—
347C2×C4⋊C4—44no—
348C2×C4⋊C4—44no—
349C2×C4⋊C4C2412yes—
350C2×C4⋊C4C2412yes—
351C2×C4⋊C4C2412yes—
352C2×C4⋊C4C2412yes—
353C2×C4⋊C4C2412yes—
354C2×C4⋊C4C2412yes—
355C2×C4⋊C4C2412yes—
356C2×C22⋊C4—22no—
357C2×C22⋊C4—22no—
358C2×C22⋊C4—22no—
359C2×C22⋊C4—22no—
360C2×C22⋊C4—22no—
361C2×C22⋊C4—22no—
362C2×C22⋊C4—22no—
363C2×C22⋊C4—22no—
364C2×C22⋊C4—22no—
365C2×C22⋊C4—22no—
366C2×C22⋊C4—22no—
367C2×C22⋊C4—22no—
368C2×C22⋊C4—22no—
369C2×C22⋊C4—22no—
370C2×C22⋊C4—22no—
371C2×C22⋊C4—22no—
372C2×C22⋊C4—22no—
373C2×C22⋊C4—22no—
374C2×C22⋊C4—44no—
375C2×C22⋊C4—44no—
376C2×C22⋊C4—44no—
377C2×C22⋊C4—44no—
378C2×C22⋊C4—44no—
379C2×C22⋊C4—44no—
380C2×C42—24no—
381C2×C42—24no—
382C2×C42—22no—
383C2×C42—22no—
384C2×C42—42no—
385C2×C42—42no—
386C2×C42—42no—
387C2×C42—42no—
388C2×C42—42no—
389C2×C42—42no—
390C2×C42—42no—
391C2×C42—42no—
392C2×C42—42no—
393C2×C42—42no—
394C2×C42C2×D411yescharacteristic
395C2×C42C2×D411yescharacteristic
396C2×C42C2×D411yescharacteristic
397C2×C42C2×D411yescharacteristic
398C2×C42C2×D411yescharacteristic
399C2×C42C2×D411yescharacteristic
400C2×C42C2×D411yescharacteristic
401C2×C42C2×D411yescharacteristic
402C2×C42C2×D411yescharacteristic
403C2×C42C2×D411yescharacteristic
404C2×C42C2×D411yescharacteristic
405C2×C42C2×D411yescharacteristic
406C2×C42C2411yescharacteristic
407C2×C42C2411yescharacteristic
408C2×C42C2411yescharacteristic
409C2×C42C2411yescharacteristic
410#107—44no—
411#107—44no—
412#106—44no—
413#106—44no—
414C4⋊C8—44no—
415#102—44no—
416#102—44no—
417#102—44no—
418#102—44no—
419C22⋊C8—28no—
420C22⋊C8—24no—
421C22⋊C8—24no—
422C22⋊C8—44no—
423C4×C8—42no—
424C4×C8—42no—
425#95—22no—
426#95—22no—
427#95—22no—
428#95—22no—
429#95—22no—
430#95—22no—
431#95—22no—
432#95—22no—
433#95—22no—
434#95—22no—
435#95—22no—
436#95—22no—
437#95—22no—
438#95—22no—
439#95—22no—
440#95—22no—
441C24—22no—
442C24—22no—
443C24—22no—
444C24—22no—
445C24—22no—
446C24—22no—
447C24—41no—
448C24—41no—
449C24—42no—
450C24—42no—
451C24—42no—
452C24—42no—
453C24—42no—
454C24—42no—
455C24—42no—
456C24C22×D411yescharacteristic
457C24C22×D411yescharacteristic
458C24C22×D411yescharacteristic
459C2×Q8—42no—
460C2×Q8—42no—
461C2×Q8—42no—
462C2×Q8—42no—
463C2×Q8—42no—
464C2×Q8—42no—
465C2×D4—24no—
466C2×D4—24no—
467C2×D4—22no—
468C2×D4—22no—
469C2×D4—42no—
470C2×D4—42no—
471C2×D4—44no—
472C2×D4—44no—
473C2×D4—44no—
474C2×D4—44no—
475C2×D4—44no—
476C2×D4—44no—
477C2×D4—42no—
478C2×D4—88no—
479C2×D4—816no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—41no—
520C22×C4—41no—
521C22×C4—41no—
522C22×C4—41no—
523C22×C4—41no—
524C22×C4—41no—
525C22×C4—41no—
526C22×C4—41no—
527C22×C4—41no—
528C22×C4—41no—
529C22×C4—41no—
530C22×C4—41no—
531C22×C4—41no—
532C22×C4—41no—
533C22×C4—41no—
534C22×C4—41no—
535C22×C4—41no—
536C22×C4—41no—
537C22×C4—416no—
538C22×C4—416no—
539C22×C4—416no—
540C22×C4—42no—
541C22×C4—42no—
542C22×C4—42no—
543C22×C4—42no—
544C22×C4—42no—
545C22×C4—42no—
546C22×C4—42no—
547C22×C4—42no—
548C22×C4—42no—
549C22×C4#13514yes—
550C22×C4AGL(1,ℤ/8)14yes—
551C22×C4C22×D411yescharacteristic
552C22×C4C22×D411yescharacteristic
553C22×C4C22×D411yescharacteristic
554C22×C4C22×D411yescharacteristic
555C22×C4C22×D411yescharacteristic
556C22×C4C22×D411yescharacteristic
557C22×C4C22×D411yescharacteristic
558C22×C4C22×D411yescharacteristic
559C22×C4C22×D411yescharacteristic
560C22×C4C22×D411yescharacteristic
561C22×C4C22×D411yescharacteristic
562C22×C4H(5,𝔽2)14yes—
563C22×C42−1+414yes—
564C22×C4C2511yescharacteristic
565C2×C8—24no—
566C2×C8—24no—
567C2×C8—24no—
568C2×C8—24no—
569C2×C8—24no—
570C2×C8—24no—
571C4⋊C4—24no—
572C4⋊C4—24no—
573C4⋊C4—24no—
574C4⋊C4—24no—
575C4⋊C4—24no—
576C4⋊C4—24no—
577C4⋊C4—22no—
578C4⋊C4—22no—
579C4⋊C4—42no—
580C4⋊C4—42no—
581C4⋊C4—44no—
582C4⋊C4—44no—
583C4⋊C4—44no—
584C4⋊C4—44no—
585C4⋊C4—42no—
586C4⋊C4—42no—
587C4⋊C4—42no—
588C4⋊C4—42no—
589C4⋊C4—44no—
590C4⋊C4—42no—
591C4⋊C4—42no—
592C4⋊C4—44no—
593C4⋊C4—44no—
594C4⋊C4—44no—
595C4⋊C4—42no—
596C4⋊C4—44no—
597C4⋊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—44no—
610C22⋊C4—44no—
611C22⋊C4—44no—
612C22⋊C4—44no—
613C22⋊C4—44no—
614C22⋊C4—44no—
615C22⋊C4—44no—
616C42—22no—
617C42—22no—
618C42—22no—
619C42—22no—
620C42—22no—
621C42—22no—
622C42—22no—
623C42—22no—
624C42—41no—
625C42—41no—
626C42—41no—
627C42—41no—
628C42—41no—
629C42—41no—
630C42—41no—
631C42—41no—
632C42—44no—
633C42—44no—
634C23—21no—
635C23—21no—
636C23—21no—
637C23—21no—
638C23—28no—
639C23—21no—
640C23—21no—
641C23—21no—
642C23—21no—
643C23—21no—
644C23—21no—
645C23—21no—
646C23—21no—
647C23—21no—
648C23—21no—
649C23—21no—
650C23—21no—
651C23—44no—
652C23—44no—
653C23—44no—
654C23—44no—
655C23—44no—
656C23—44no—
657C23—42no—
658C23—42no—
659C23—42no—
660C23—42no—
661C23—42no—
662C23—42no—
663C23—42no—
664C23—84no—
665C23—84no—
666C23—84no—
667C23—84no—
668C23—84no—
669C23—84no—
670C23—84no—
671C23#53412yes—
672C23#53612yes—
673C23C2×#13512yes—
674C23C2×AGL(1,ℤ/8)12yes—
675C23#57512yes—
676C23C23×D411yescharacteristic
677Q8—84no—
678Q8—84no—
679D4—44no—
680D4—44no—
681D4—84no—
682D4—88no—
683D4—88no—
684C2×C4—28no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—21no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—21no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—28no—
700C2×C4—28no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—44no—
714C2×C4—44no—
715C2×C4—44no—
716C2×C4—44no—
717C2×C4—44no—
718C2×C4—44no—
719C2×C4—44no—
720C2×C4—44no—
721C2×C4—44no—
722C2×C4—44no—
723C2×C4—44no—
724C2×C4—44no—
725C2×C4—44no—
726C2×C4—44no—
727C2×C4—44no—
728C2×C4—42no—
729C2×C4—42no—
730C2×C4—42no—
731C2×C4—42no—
732C2×C4—42no—
733C2×C4—42no—
734C2×C4—42no—
735C2×C4—42no—
736C2×C4—42no—
737C2×C4—42no—
738C2×C4—42no—
739C2×C4—42no—
740C2×C4—42no—
741C2×C4—42no—
742C2×C4—42no—
743C2×C4—42no—
744C2×C4—42no—
745C2×C4—42no—
746C2×C4—42no—
747C2×C4—42no—
748C2×C4—42no—
749C2×C4—84no—
750C2×C4—84no—
751C2×C4—84no—
752C2×C4#53412yes—
753C2×C4#53612yes—
754C2×C4C2×#13512yes—
755C2×C4C2×#13512yes—
756C2×C4C2×AGL(1,ℤ/8)12yes—
757C2×C4C2×AGL(1,ℤ/8)12yes—
758C2×C4#57512yes—
759C2×C4C2×H(5,𝔽2)12yes—
760C2×C4C2×2−1+412yes—
761C2×C4#58512yes—
762C8—44no—
763C8—44no—
764C22—22no—
765C22—22no—
766C22—22no—
767C22—22no—
768C22—22no—
769C22—22no—
770C22—22no—
771C22—22no—
772C22—22no—
773C22—22no—
774C22—22no—
775C22—22no—
776C22—416no—
777C22—41no—
778C22—41no—
779C22—41no—
780C22—41no—
781C22—41no—
782C22—41no—
783C22—41no—
784C22—41no—
785C22—82no—
786C22—82no—
787C22—82no—
788C22—82no—
789C22—82no—
790C22—82no—
791C22—82no—
792C22—168no—
793C22#322814yes—
794C22C2×#53411yescharacteristic
795C22C2×#53611yescharacteristic
796C22#344911yescharacteristic
797C22C22×#13511yescharacteristic
798C22C22×AGL(1,ℤ/8)11yescharacteristic
799C22C2×#57511yescharacteristic
800C22C2×#57511yescharacteristic
801C4—22no—
802C4—22no—
803C4—22no—
804C4—22no—
805C4—22no—
806C4—22no—
807C4—22no—
808C4—41no—
809C4—41no—
810C4—41no—
811C4—41no—
812C4—82no—
813C4—82no—
814C4—82no—
815C4—82no—
816C4—82no—
817C4—82no—
818C4—82no—
819C4#353514yes—
820C2—24no—
821C2—42no—
822C2—42no—
823C2—162no—
824C2#3744111yescharacteristic
825C2#6073411yescharacteristic
826C2#6075011yescharacteristic
827C2C2×#322811yescharacteristic
828C2#6086611yescharacteristic
829C2#6094211yescharacteristic
830C2#6095111yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC22×#121C22
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. #36625C2semidirect
3. #32743C2semidirect
4. #32739C2semidirect
5. #30360C2semidirect
6. #29972C2semidirect
7. #29956C2semidirect
8. #29910C2semidirect
9. #29644C2semidirect
10. #29297C2semidirect
11. #29296C2semidirect
12. #29103C2semidirect
13. #29103C2semidirect
14. #27602C2semidirect
15. #24605C2semidirect
17. #20714C2semidirect
18. C2×#533C22semidirect
23. C2×#431C22semidirect
26. #2857C22semidirect
27. #2857C22semidirect
39. #2851C22semidirect
46. #2296C22semidirect
54. #2285C22semidirect
57. #2101C22semidirect
58. #2092C22semidirect
59. #2088C22semidirect
60. #2087C22semidirect
61. #2084C22semidirect
62. #2083C22semidirect
63. #2077C22semidirect
64. #2076C22semidirect
65. #2071C22semidirect
66. #2071C22semidirect
67. #2067C22semidirect
68. #2065C22semidirect
69. #2059C22semidirect
70. #2058C22semidirect
71. #2057C22semidirect
74. #2025C22semidirect
75. #2023C22semidirect
76. #2023C22semidirect
77. #1942C22semidirect
78. #1941C22semidirect
79. #1934C22semidirect
80. #1934C22semidirect
82. #1854C22semidirect
87. #1825C22semidirect
90. #1817C22semidirect
92. #1797C22semidirect
98. C4×C22⋊C8C22semidirect

Maximal subgroups

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

subgroupindex
#366252
C2×#28542
#327432
#327392
#303602
#299722
#299562
#299102
#296442
#292972
#292962
#291032
#276022
#246052
#240092
#207142