Finite Group Databasebeta

← #6475283

Subgroups — #6475283

Order 512.

2262 conjugacy classes of subgroups.

The subgroup lattice has 876 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2851C211yesmaximal, characteristic, complemented
2C2×C4×#121C211yesmaximal, characteristic
3#33151C212yesmaximal, complemented
4#32959C212yesmaximal, complemented
5#29972C212yesmaximal, complemented
6#29956C212yesmaximal, complemented
7#29238C212yesmaximal, complemented
8#29237C212yesmaximal, complemented
9#29161C214yesmaximal, complemented
10#27684C212yesmaximal, complemented
11#24839C214yesmaximal, complemented
12#24305C212yesmaximal, complemented
13#21940C211yesmaximal, characteristic, complemented
14#21938C211yesmaximal, characteristic, complemented
15#21758C211yesmaximal, characteristic
16#21758C211yesmaximal, characteristic
17C2×#1797C211yesmaximal, characteristic, complemented
18C22×#125C2211yescharacteristic, complemented
19C22×#121C2211yescharacteristic
20C22×C4×D4—21no—
21C22×C4×D4C2211yescharacteristic
22C23×C42C2211yescharacteristic
23C2×#478C2214yescomplemented
24C22×C4⋊C8C2212yescomplemented
25C22×C22⋊C8C2211yescharacteristic
26C22×C22⋊C8C2211yescharacteristic
27#2851—21no—
28#2851—21no—
29#2851—21no—
30#2851—21no—
31#2851C2212yes—
32#2851C2212yes—
33#2851C2212yescomplemented
34#2851C2212yescomplemented
35C4×#121—21no—
36C4×#121—21no—
37C4×#121—21no—
38C4×#121—21no—
39C4×#121C2212yes—
40C4×#121C2212yes—
41C4×#121C2212yes—
42C4×#121C2212yes—
43C2×#390C2211yescharacteristic
44C2×#389C2211yescharacteristic
45C2×#389C2211yescharacteristic, complemented
46C2×#389C2211yescharacteristic, complemented
47C2×#388—21no—
48C2×#387—21no—
49C2×#387—21no—
50C2×#386—21no—
51C2×#385—21no—
52C2×#385—21no—
53C2×#382C2211yescharacteristic, complemented
54C2×#380C2211yescharacteristic
55C2×#380C2211yescharacteristic
56C2×#380C2211yescharacteristic
57C2×C4×C4⋊C4C2211yescharacteristic
58C2×C4×C22⋊C4—21no—
59#2101C2214yescomplemented
60#2092C2214yescomplemented
61#2088C2214yescomplemented
62#2087C2214yescomplemented
63#2067C2214yescomplemented
64#2065C2214yescomplemented
65#2059C2214yescomplemented
66#2025C2214yescomplemented
67#1989C2214yescomplemented
68#1949C2214yescomplemented
69#1921C2214yescomplemented
70#1919C2214yescomplemented
71#1893C2214yes—
72#1893C2214yes—
73#1874C2212yes—
74#1874C2212yes—
75#1874C2212yes—
76#1874C2212yes—
77#1864C2214yescomplemented
78#1862C2214yescomplemented
79#1853C2212yes—
80#1853C2212yes—
81#1853C2212yescomplemented
82#1853C2212yescomplemented
83#1852C2212yes—
84#1852C2212yes—
85#1852C2212yescomplemented
86#1852C2212yescomplemented
87#1823C2212yes—
88#1823C2212yes—
89#1808C2214yescomplemented
90#1807C2214yescomplemented
91#1804C2214yescomplemented
92#1797C2212yes—
93#1797C2212yes—
94#1797C2212yescomplemented
95#1797C2212yescomplemented
96#1786C2212yes—
97#1786C2212yes—
98C2×#336C2212yescomplemented
99C23×D4—21no—
100C23×D4C2311yescharacteristic
101C24×C4—21no—
102C24×C4D411yescharacteristic
103C24×C4D411yescharacteristic
104C24×C4C2311yescharacteristic
105C23×C8C2312yes—
106C23×C8C2312yes—
107C2×#125—21no—
108C2×#125—21no—
109C2×#125—44no—
110C2×#125C2312yes—
111C2×#125C2312yes—
112C2×#121—21no—
113C2×#121—21no—
114C2×#121—24no—
115C2×#121Q818yes—
116C2×#121C2312yes—
117C2×#121C2312yes—
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—44no—
125C2×C4×D4—48no—
126C2×C4×D4C2312yes—
127C2×C4×D4C2312yes—
128C22×C4⋊C4—21no—
129C22×C4⋊C4—21no—
130C22×C4⋊C4—21no—
131C22×C4⋊C4—21no—
132C22×C4⋊C4—21no—
133C22×C4⋊C4C2311yescharacteristic
134C22×C4⋊C4C2311yescharacteristic
135C22×C4⋊C4C2311yescharacteristic
136C22×C4⋊C4C2311yescharacteristic
137C22×C4⋊C4C2311yescharacteristic
138C22×C4⋊C4C2311yescharacteristic
139C22×C4⋊C4C2311yescharacteristic
140C22×C22⋊C4—21no—
141C22×C22⋊C4—21no—
142C22×C22⋊C4—21no—
143C22×C22⋊C4—21no—
144C22×C22⋊C4—21no—
145C22×C22⋊C4—21no—
146C22×C22⋊C4—21no—
147C22×C42—21no—
148C22×C42—44no—
149C22×C42D411yescharacteristic
150C22×C42D411yescharacteristic
151C22×C42D411yescharacteristic
152C22×C42D411yescharacteristic
153C22×C42D411yescharacteristic
154C22×C42D411yescharacteristic
155C22×C42C2311yescharacteristic
156C22×C42C2311yescharacteristic
157C22×C42C2311yescharacteristic
158C22×C42C2311yescharacteristic
159C22×C42C2311yescharacteristic
160C22×C42C2311yescharacteristic
161#478—48no—
162C2×#107C2314yes—
163C2×#107C2314yes—
164C2×#106C2314yes—
165C2×#106C2314yes—
166C2×C4⋊C8—44no—
167C2×C4⋊C8C2314yes—
168C2×C4⋊C8C2314yes—
169C2×#102C2314yes—
170C2×#102C2314yes—
171C2×#102C2314yes—
172C2×#102C2314yes—
173C2×C22⋊C8—24no—
174C2×C22⋊C8—24no—
175C2×C22⋊C8C2312yes—
176C2×C22⋊C8C2312yes—
177C2×C22⋊C8C2312yes—
178C2×C22⋊C8C2312yes—
179#390—21no—
180#390—21no—
181#390C2312yes—
182#390C2312yes—
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#388—22no—
196#388—22no—
197#388—22no—
198#388—22no—
199#387—22no—
200#387—22no—
201#387—22no—
202#387—22no—
203#387—22no—
204#387—22no—
205#387—22no—
206#387—22no—
207#386—22no—
208#386—22no—
209#386—22no—
210#386—22no—
211#385—22no—
212#385—22no—
213#385—22no—
214#385—22no—
215#385—22no—
216#385—22no—
217#385—22no—
218#385—22no—
219#382—21no—
220#382—21no—
221#382C2312yes—
222#382C2312yes—
223#380—21no—
224#380—21no—
225#380—21no—
226#380—21no—
227#380—21no—
228#380—21no—
229#380C2312yes—
230#380C2312yes—
231#380C2312yes—
232#380C2312yes—
233#380C2312yes—
234#380C2312yes—
235C4×C4⋊C4—21no—
236C4×C4⋊C4—21no—
237C4×C4⋊C4C2312yes—
238C4×C4⋊C4C2312yes—
239C4×C22⋊C4—22no—
240C4×C22⋊C4—22no—
241C4×C22⋊C4—22no—
242C4×C22⋊C4—22no—
243C2×#95—21no—
244C2×#95—21no—
245C2×#95—21no—
246C2×#95—21no—
247C2×#95—21no—
248C2×#95—21no—
249C2×#95—21no—
250C2×#95—21no—
251C2×#95—21no—
252#340C2314yes—
253#340C2314yes—
254#340C2314yes—
255#340C2314yes—
256#340C2314yes—
257#340C2314yes—
258#340C2314yes—
259#340C2314yes—
260#336C2314yes—
261#336C2314yes—
262C25—21no—
263C25C2×D411yescharacteristic
264C22×D4—28no—
265C22×D4—22no—
266C22×D4—22no—
267C22×D4—21no—
268C22×D4—22no—
269C22×D4—42no—
270C22×D4—42no—
271C22×D4—44no—
272C22×D4—44no—
273C22×D4C2×Q814yes—
274C22×D4C2412yes—
275C23×C4—24no—
276C23×C4—24no—
277C23×C4—21no—
278C23×C4—21no—
279C23×C4—21no—
280C23×C4—21no—
281C23×C4—21no—
282C23×C4—21no—
283C23×C4—21no—
284C23×C4—22no—
285C23×C4—22no—
286C23×C4—42no—
287C23×C4—42no—
288C23×C4—42no—
289C23×C4—42no—
290C23×C4—42no—
291C23×C4—42no—
292C23×C4—44no—
293C23×C4—44no—
294C23×C4—44no—
295C23×C4C2×D411yescharacteristic
296C23×C4C2×D411yescharacteristic
297C23×C4C2×D411yescharacteristic
298C23×C4C2×D411yescharacteristic
299C23×C4C2×D411yescharacteristic
300C23×C4C2×D411yescharacteristic
301C23×C4C2×D411yescharacteristic
302C23×C4C2×D411yescharacteristic
303C23×C4C2×D411yescharacteristic
304C23×C4C2×D411yescharacteristic
305C23×C4C2×D411yescharacteristic
306C23×C4C2×D411yescharacteristic
307C23×C4C2×D411yescharacteristic
308C23×C4C2×D411yescharacteristic
309C23×C4C2×D411yescharacteristic
310C23×C4C2×Q814yes—
311C23×C4#4114yes—
312C23×C4C2411yescharacteristic
313C23×C4C2411yescharacteristic
314C23×C4C2411yescharacteristic
315C22×C8—24no—
316C22×C8—24no—
317C22×C8—42no—
318C22×C8—42no—
319C22×C8—42no—
320C22×C8—42no—
321C22×C8C2414yes—
322C22×C8C2414yes—
323#125—28no—
324#125—44no—
325#125—44no—
326#125—44no—
327#121—28no—
328#121—28no—
329#121—24no—
330#121—24no—
331#121C2×Q818yes—
332#121C2×Q818yes—
333C4×D4—28no—
334C4×D4—44no—
335C4×D4—44no—
336C4×D4—44no—
337C4×D4—48no—
338C4×D4—48no—
339C4×D4—48no—
340C4×D4—48no—
341C2×C4⋊C4—21no—
342C2×C4⋊C4—22no—
343C2×C4⋊C4—22no—
344C2×C4⋊C4—22no—
345C2×C4⋊C4—22no—
346C2×C4⋊C4—22no—
347C2×C4⋊C4—22no—
348C2×C4⋊C4—22no—
349C2×C4⋊C4—22no—
350C2×C4⋊C4—22no—
351C2×C4⋊C4—22no—
352C2×C4⋊C4—22no—
353C2×C4⋊C4—21no—
354C2×C4⋊C4—21no—
355C2×C4⋊C4—21no—
356C2×C4⋊C4—21no—
357C2×C4⋊C4—21no—
358C2×C4⋊C4—21no—
359C2×C4⋊C4—42no—
360C2×C4⋊C4—42no—
361C2×C4⋊C4—42no—
362C2×C4⋊C4—42no—
363C2×C4⋊C4—42no—
364C2×C4⋊C4—42no—
365C2×C4⋊C4—44no—
366C2×C4⋊C4—44no—
367C2×C4⋊C4—44no—
368C2×C4⋊C4—44no—
369C2×C4⋊C4—44no—
370C2×C4⋊C4C2×Q814yes—
371C2×C4⋊C4C2412yes—
372C2×C4⋊C4C2412yes—
373C2×C4⋊C4C2412yes—
374C2×C4⋊C4C2412yes—
375C2×C4⋊C4C2412yes—
376C2×C4⋊C4C2412yes—
377C2×C4⋊C4C2412yes—
378C2×C22⋊C4—28no—
379C2×C22⋊C4—22no—
380C2×C22⋊C4—22no—
381C2×C22⋊C4—22no—
382C2×C22⋊C4—22no—
383C2×C22⋊C4—22no—
384C2×C22⋊C4—22no—
385C2×C22⋊C4—22no—
386C2×C22⋊C4—22no—
387C2×C22⋊C4—22no—
388C2×C22⋊C4—22no—
389C2×C22⋊C4—22no—
390C2×C22⋊C4—22no—
391C2×C22⋊C4—22no—
392C2×C22⋊C4—22no—
393C2×C22⋊C4—44no—
394C2×C22⋊C4—44no—
395C2×C22⋊C4—44no—
396C2×C22⋊C4—44no—
397C2×C22⋊C4—44no—
398C2×C22⋊C4—44no—
399C2×C42—24no—
400C2×C42—24no—
401C2×C42—24no—
402C2×C42—22no—
403C2×C42—22no—
404C2×C42—42no—
405C2×C42—42no—
406C2×C42—42no—
407C2×C42—42no—
408C2×C42—42no—
409C2×C42—42no—
410C2×C42—42no—
411C2×C42—42no—
412C2×C42—42no—
413C2×C42—44no—
414C2×C42C2×D411yescharacteristic
415C2×C42C2×D411yescharacteristic
416C2×C42C2×D411yescharacteristic
417C2×C42C2×D411yescharacteristic
418C2×C42C2×D411yescharacteristic
419C2×C42C2×D411yescharacteristic
420C2×C42C2×D411yescharacteristic
421C2×C42C2×D411yescharacteristic
422C2×C42C2×D411yescharacteristic
423C2×C42C2×D411yescharacteristic
424C2×C42C2×D411yescharacteristic
425C2×C42C2×D411yescharacteristic
426C2×C42C2411yescharacteristic
427C2×C42C2411yescharacteristic
428C2×C42C2411yescharacteristic
429C2×C42C2411yescharacteristic
430#107—44no—
431#107—44no—
432#106—44no—
433#106—44no—
434C4⋊C8—28no—
435C4⋊C8—44no—
436#102—44no—
437#102—44no—
438#102—44no—
439#102—44no—
440C22⋊C8—24no—
441C22⋊C8—24no—
442C22⋊C8—24no—
443C22⋊C8—24no—
444#95—22no—
445#95—22no—
446#95—22no—
447#95—22no—
448#95—22no—
449#95—22no—
450#95—22no—
451#95—22no—
452#95—22no—
453#95—22no—
454#95—22no—
455#95—22no—
456#95—22no—
457#95—22no—
458#95—22no—
459#95—22no—
460#95—22no—
461#95—22no—
462C24—24no—
463C24—22no—
464C24—41no—
465C24—41no—
466C24—41no—
467C24—41no—
468C24—42no—
469C24—42no—
470C24—42no—
471C24—42no—
472C24—42no—
473C24—42no—
474C24C22⋊Q814yes—
475C24#13514yes—
476C24AGL(1,ℤ/8)14yes—
477C24C22×D411yescharacteristic
478C24C22×D411yescharacteristic
479C24C22×D411yescharacteristic
480C2×D4—28no—
481C2×D4—28no—
482C2×D4—24no—
483C2×D4—22no—
484C2×D4—24no—
485C2×D4—24no—
486C2×D4—48no—
487C2×D4—42no—
488C2×D4—42no—
489C2×D4—48no—
490C2×D4—44no—
491C2×D4—44no—
492C2×D4—44no—
493C2×D4—44no—
494C2×D4—432no—
495C2×D4C22×Q814yes—
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—24no—
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—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—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—48no—
535C22×C4—48no—
536C22×C4—41no—
537C22×C4—41no—
538C22×C4—41no—
539C22×C4—41no—
540C22×C4—41no—
541C22×C4—41no—
542C22×C4—41no—
543C22×C4—41no—
544C22×C4—41no—
545C22×C4—41no—
546C22×C4—41no—
547C22×C4—41no—
548C22×C4—41no—
549C22×C4—41no—
550C22×C4—41no—
551C22×C4—41no—
552C22×C4—41no—
553C22×C4—41no—
554C22×C4—416no—
555C22×C4—416no—
556C22×C4—44no—
557C22×C4—44no—
558C22×C4—44no—
559C22×C4—44no—
560C22×C4—42no—
561C22×C4—42no—
562C22×C4—42no—
563C22×C4—42no—
564C22×C4—42no—
565C22×C4—42no—
566C22×C4—42no—
567C22×C4—42no—
568C22×C4—42no—
569C22×C4—42no—
570C22×C4—42no—
571C22×C4—42no—
572C22×C4—42no—
573C22×C4—42no—
574C22×C4—42no—
575C22×C4—42no—
576C22×C4—42no—
577C22×C4—42no—
578C22×C4—42no—
579C22×C4—42no—
580C22×C4—44no—
581C22×C4—44no—
582C22×C4—816no—
583C22×C4C22⋊Q814yes—
584C22×C4C22⋊Q814yes—
585C22×C4C22⋊Q814yes—
586C22×C4C22×D411yescharacteristic
587C22×C4C22×D411yescharacteristic
588C22×C4C22×D411yescharacteristic
589C22×C4C22×D411yescharacteristic
590C22×C4C22×D411yescharacteristic
591C22×C4C22×D411yescharacteristic
592C22×C4C22×D411yescharacteristic
593C22×C4C22×D411yescharacteristic
594C22×C4C22×D411yescharacteristic
595C22×C4C22×D411yescharacteristic
596C22×C4C22×D411yescharacteristic
597C22×C4C22×Q812yes—
598C22×C4C22×Q812yes—
599C22×C4C22×Q812yes—
600C22×C4C2×#4112yes—
601C22×C4C2×#4112yes—
602C22×C4C2×#4112yes—
603C22×C4C2511yescharacteristic
604C2×C8—24no—
605C2×C8—24no—
606C2×C8—24no—
607C2×C8—24no—
608C2×C8—24no—
609C2×C8—24no—
610C2×C8—84no—
611C2×C8—84no—
612C4⋊C4—24no—
613C4⋊C4—22no—
614C4⋊C4—24no—
615C4⋊C4—24no—
616C4⋊C4—24no—
617C4⋊C4—24no—
618C4⋊C4—24no—
619C4⋊C4—24no—
620C4⋊C4—42no—
621C4⋊C4—42no—
622C4⋊C4—42no—
623C4⋊C4—44no—
624C4⋊C4—44no—
625C4⋊C4—42no—
626C4⋊C4—44no—
627C4⋊C4—44no—
628C4⋊C4—42no—
629C4⋊C4—42no—
630C4⋊C4—44no—
631C4⋊C4—44no—
632C4⋊C4—44no—
633C4⋊C4—44no—
634C4⋊C4—44no—
635C4⋊C4—44no—
636C4⋊C4C22×Q814yes—
637C22⋊C4—28no—
638C22⋊C4—28no—
639C22⋊C4—44no—
640C22⋊C4—44no—
641C22⋊C4—44no—
642C22⋊C4—44no—
643C22⋊C4—44no—
644C22⋊C4—44no—
645C22⋊C4—44no—
646C22⋊C4—44no—
647C22⋊C4—44no—
648C22⋊C4—44no—
649C22⋊C4—44no—
650C22⋊C4—44no—
651C42—22no—
652C42—22no—
653C42—22no—
654C42—22no—
655C42—22no—
656C42—22no—
657C42—22no—
658C42—22no—
659C42—22no—
660C42—41no—
661C42—41no—
662C42—41no—
663C42—41no—
664C42—41no—
665C42—41no—
666C42—44no—
667C42—44no—
668C42H(5,𝔽2)14yes—
669C23—21no—
670C23—21no—
671C23—21no—
672C23—21no—
673C23—21no—
674C23—21no—
675C23—21no—
676C23—21no—
677C23—21no—
678C23—21no—
679C23—21no—
680C23—21no—
681C23—24no—
682C23—44no—
683C23—44no—
684C23—44no—
685C23—44no—
686C23—44no—
687C23—44no—
688C23—48no—
689C23—48no—
690C23—48no—
691C23—42no—
692C23—42no—
693C23—42no—
694C23—42no—
695C23—42no—
696C23—42no—
697C23—84no—
698C23—84no—
699C23—84no—
700C23—84no—
701C23#478116yescomplemented
702C23C2×C22⋊Q812yes—
703C23C2×C22⋊Q812yes—
704C23C2×C22⋊Q812yes—
705C23C2×#13512yes—
706C23C2×#13512yes—
707C23C2×#13512yes—
708C23C2×AGL(1,ℤ/8)12yes—
709C23C2×AGL(1,ℤ/8)12yes—
710C23C2×AGL(1,ℤ/8)12yes—
711C23C23×D411yescharacteristic
712D4—28no—
713D4—48no—
714D4—416no—
715D4—416no—
716D4—44no—
717C2×C4—28no—
718C2×C4—28no—
719C2×C4—21no—
720C2×C4—21no—
721C2×C4—21no—
722C2×C4—21no—
723C2×C4—21no—
724C2×C4—21no—
725C2×C4—21no—
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—21no—
729C2×C4—21no—
730C2×C4—21no—
731C2×C4—21no—
732C2×C4—21no—
733C2×C4—24no—
734C2×C4—24no—
735C2×C4—24no—
736C2×C4—24no—
737C2×C4—24no—
738C2×C4—24no—
739C2×C4—24no—
740C2×C4—21no—
741C2×C4—21no—
742C2×C4—21no—
743C2×C4—21no—
744C2×C4—21no—
745C2×C4—21no—
746C2×C4—21no—
747C2×C4—21no—
748C2×C4—21no—
749C2×C4—21no—
750C2×C4—21no—
751C2×C4—21no—
752C2×C4—44no—
753C2×C4—44no—
754C2×C4—44no—
755C2×C4—44no—
756C2×C4—44no—
757C2×C4—44no—
758C2×C4—44no—
759C2×C4—44no—
760C2×C4—44no—
761C2×C4—44no—
762C2×C4—44no—
763C2×C4—44no—
764C2×C4—44no—
765C2×C4—48no—
766C2×C4—42no—
767C2×C4—42no—
768C2×C4—42no—
769C2×C4—42no—
770C2×C4—42no—
771C2×C4—42no—
772C2×C4—42no—
773C2×C4—42no—
774C2×C4—42no—
775C2×C4—42no—
776C2×C4—42no—
777C2×C4—42no—
778C2×C4—42no—
779C2×C4—42no—
780C2×C4—42no—
781C2×C4—42no—
782C2×C4—42no—
783C2×C4—42no—
784C2×C4—42no—
785C2×C4—42no—
786C2×C4—88no—
787C2×C4—88no—
788C2×C4—84no—
789C2×C4—84no—
790C2×C4—84no—
791C2×C4—84no—
792C2×C4—84no—
793C2×C4—84no—
794C2×C4C2×C22⋊Q812yes—
795C2×C4C2×C22⋊Q812yes—
796C2×C4C2×C22⋊Q812yes—
797C2×C4#53412yes—
798C2×C4#53412yes—
799C2×C4#57512yes—
800C2×C4#57512yes—
801C2×C4C23×Q811yescharacteristic
802C2×C4C22×#4111yescharacteristic
803C2×C4C2×H(5,𝔽2)12yes—
804C2×C4#58512yes—
805C8—44no—
806C8—44no—
807C22—22no—
808C22—22no—
809C22—22no—
810C22—22no—
811C22—22no—
812C22—22no—
813C22—22no—
814C22—22no—
815C22—22no—
816C22—22no—
817C22—22no—
818C22—22no—
819C22—22no—
820C22—22no—
821C22—22no—
822C22—22no—
823C22—22no—
824C22—22no—
825C22—416no—
826C22—44no—
827C22—44no—
828C22—44no—
829C22—816no—
830C22—82no—
831C22—82no—
832C22—82no—
833C22—82no—
834C22C2×#47814yes—
835C22C2×#47814yes—
836C22C2×#47814yes—
837C22C22×C22⋊Q811yescharacteristic
838C22C2×#53411yescharacteristic
839C22#344911yescharacteristic
840C22C22×#13511yescharacteristic
841C22C22×AGL(1,ℤ/8)11yescharacteristic
842C22C2×#57511yescharacteristic
843C22C2×#57511yescharacteristic
844C4—22no—
845C4—22no—
846C4—22no—
847C4—22no—
848C4—22no—
849C4—22no—
850C4—22no—
851C4—44no—
852C4—41no—
853C4—41no—
854C4—41no—
855C4—41no—
856C4—82no—
857C4—82no—
858C4—82no—
859C4—82no—
860C4—82no—
861C4—82no—
862C4#350112yes—
863C4#350512yes—
864C2—24no—
865C2—24no—
866C2—24no—
867C2—84no—
868C2#3501011yescharacteristic
869C2C22×#47811yescharacteristic
870C2#6048411yescharacteristic
871C2#6073411yescharacteristic
872C2#6075011yescharacteristic
873C2#6094511yescharacteristic
874C2#6095811yescharacteristic
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. C2×#2851C2semidirect
3. #33151C2semidirect
4. #32959C2semidirect
5. #29972C2semidirect
6. #29956C2semidirect
7. #29238C2semidirect
8. #29237C2semidirect
9. #29161C2semidirect
10. #27684C2semidirect
11. #24839C2semidirect
12. #24305C2semidirect
13. #21940C2semidirect
14. #21938C2semidirect
17. C2×#1797C2semidirect
18. C22×#125C22semidirect
23. C2×#478C22semidirect
24. C22×C4⋊C8C22semidirect
33. #2851C22semidirect
34. #2851C22semidirect
45. C2×#389C22semidirect
46. C2×#389C22semidirect
53. C2×#382C22semidirect
59. #2101C22semidirect
60. #2092C22semidirect
61. #2088C22semidirect
62. #2087C22semidirect
63. #2067C22semidirect
64. #2065C22semidirect
65. #2059C22semidirect
66. #2025C22semidirect
67. #1989C22semidirect
68. #1949C22semidirect
69. #1921C22semidirect
70. #1919C22semidirect
77. #1864C22semidirect
78. #1862C22semidirect
81. #1853C22semidirect
82. #1853C22semidirect
85. #1852C22semidirect
86. #1852C22semidirect
89. #1808C22semidirect
90. #1807C22semidirect
91. #1804C22semidirect
94. #1797C22semidirect
95. #1797C22semidirect
98. C2×#336C22semidirect
701. C23#478semidirect

Maximal subgroups

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

subgroupindex
C2×#28512
C2×C4×#1212
#331512
#329592
#299722
#299562
#292382
#292372
#291612
#276842
#248392
#243052
#219402
#219382
#217582
C2×#17972