Finite Group Databasebeta

← #6494926

Subgroups — #6494926

Order 512.

1768 conjugacy classes of subgroups.

The subgroup lattice has 831 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#36645C211yesmaximal, characteristic, complemented
2C4×#529C211yesmaximal, characteristic
3#33198C211yesmaximal, characteristic, complemented
4#33197C211yesmaximal, characteristic, complemented
5#33196C211yesmaximal, characteristic, complemented
6#33195C211yesmaximal, characteristic, complemented
7#29997C212yesmaximal, complemented
8#29995C212yesmaximal, complemented
9#29289C212yesmaximal, complemented
10#29288C212yesmaximal, complemented
11#28282C212yesmaximal, complemented
12#28281C212yesmaximal, complemented
13#24838C212yesmaximal, complemented
14#24837C212yesmaximal, complemented
15#24836C212yesmaximal
16#24835C212yesmaximal
17#21962C212yesmaximal, complemented
18#21887C212yesmaximal
19C2×#1842C211yesmaximal, characteristic, complemented
20C2×#533—21no—
21C2×#529C2211yescharacteristic
22C2×#477C2212yes—
23C2×#475C2212yes—
24C2×#476C2212yes—
25C2×#474C2212yes—
26C22×C4⋊C8C2212yes—
27C22×C4⋊C8C2212yes—
28C22×C4⋊C8C2212yes—
29#2868C2211yescharacteristic
30#2868C2211yescharacteristic
31#2862—21no—
32#2859—21no—
33#2859C2212yes—
34#2857—21no—
35#2857—21no—
36#2857C2212yes—
37#2857C2212yes—
38C4×C4⋊Q8—21no—
39C4×C4⋊Q8—21no—
40C4×C4⋊Q8C2212yes—
41C4×C4⋊Q8C2212yes—
42C4×#125C2211yescharacteristic
43C4×#125C2211yescharacteristic
44C4×#126—21no—
45C4×#126—21no—
46C4×#124C2211yescharacteristic
47C4×#124C2211yescharacteristic
48C4×C22⋊Q8C2211yescharacteristic
49C4×C22⋊Q8C2211yescharacteristic
50C4×#123—21no—
51C4×#123—21no—
52C4×#121C2211yescharacteristic
53C4×#121C2211yescharacteristic
54#2298—21no—
55#2295C2211yescharacteristic
56#2293C2211yescharacteristic
57#2290—21no—
58#2285—21no—
59#2285C2212yes—
60#2283C2211yescharacteristic
61C42×Q8C2211yescharacteristic
62C42×D4—21no—
63C42×D4C2211yescharacteristic
64C4×#117—21no—
65C2×C43C2211yescharacteristic
66#2088C2214yes—
67#2088C2214yes—
68#2087C2214yes—
69#2086C2214yes—
70#2068C2214yes—
71#2067C2214yes—
72#2066C2214yes—
73#2065C2214yes—
74#1989C2214yes—
75#1988C2212yes—
76#1988C2212yes—
77#1987C2212yes—
78#1987C2212yes—
79#1983C2214yes—
80#1949C2214yes—
81#1949C2214yes—
82#1948C2212yes—
83#1948C2212yes—
84#1948C2212yes—
85#1948C2212yes—
86#1947C2212yes—
87#1947C2212yes—
88#1947C2212yes—
89#1947C2212yes—
90#1893C2214yes—
91#1892C2214yes—
92#1842C2212yes—
93#1842C2212yes—
94#1842C2212yes—
95#1842C2211yescharacteristic
96#1842C2211yescharacteristic
97#1808C2214yes—
98#1807C2214yes—
99#1803C2212yes—
100#1803C2212yes—
101#1803C2212yes—
102#1803C2212yes—
103#1802C2212yes—
104#1802C2212yes—
105#1802C2212yes—
106#1802C2212yes—
107C23×C8C2314yes—
108#533—48no—
109C2×C4⋊Q8—21no—
110C2×C4⋊Q8—21no—
111C2×C4⋊Q8—21no—
112C2×C4⋊Q8—21no—
113C2×C4⋊Q8C2312yes—
114C2×C4⋊Q8C2312yes—
115#529—24no—
116#529Q818yescomplemented
117C2×#126—21no—
118C2×#125—22no—
119C2×#125C2311yescharacteristic
120C2×#124C2311yescharacteristic
121C2×#123—21no—
122C2×C22⋊Q8—22no—
123C2×C22⋊Q8—22no—
124C2×C22⋊Q8C2311yescharacteristic
125C2×#121C2311yescharacteristic
126C2×C4×Q8—22no—
127C2×C4×Q8—22no—
128C2×C4×Q8C2311yescharacteristic
129C2×C4×Q8C2311yescharacteristic
130C2×C4×Q8C2311yescharacteristic
131C2×C4×D4—21no—
132C2×C4×D4—21no—
133C2×C4×D4—21no—
134C2×C4×D4C2311yescharacteristic
135C2×C4×D4C2311yescharacteristic
136C2×C4×D4C2311yescharacteristic
137C2×#117—22no—
138C2×#117—21no—
139C2×#117—21no—
140C22×C42—21no—
141C22×C42D411yescharacteristic
142C22×C42D411yescharacteristic
143C22×C42D411yescharacteristic
144C22×C42D411yescharacteristic
145C22×C42C2311yescharacteristic
146C22×C42C2311yescharacteristic
147C22×C42C2311yescharacteristic
148#477—44no—
149#476—44no—
150#475—44no—
151#474—44no—
152C2×#107C2314yes—
153C2×#107C2314yes—
154C2×#106C2314yes—
155C2×#106C2314yes—
156C2×C4⋊C8—28no—
157C2×C4⋊C8—44no—
158C2×C4⋊C8—44no—
159C2×C4⋊C8C2312yes—
160C2×C4⋊C8C2312yes—
161C2×C4⋊C8C2312yes—
162C2×C4⋊C8C2312yes—
163C2×C4⋊C8C2312yes—
164C2×C4⋊C8C2312yes—
165C2×C4⋊C8C2314yes—
166C2×C4⋊C8C2314yes—
167C2×C4⋊C8C2314yes—
168C2×#103C2314yes—
169C2×#103C2314yes—
170C2×#102C2314yes—
171C2×#102C2314yes—
172#391—22no—
173#391—22no—
174#391—22no—
175#391—22no—
176#391C2311yescharacteristic
177#391C2311yescharacteristic
178#390C2311yescharacteristic
179#390C2311yescharacteristic
180#389—22no—
181#389—22no—
182#389—22no—
183#389—22no—
184#389—22no—
185#389—22no—
186#389C2311yescharacteristic
187#389C2311yescharacteristic
188#389C2311yescharacteristic
189#389C2311yescharacteristic
190#389C2314yes—
191#389C2314yes—
192#388—21no—
193#388—21no—
194#388—21no—
195#388—21no—
196#388—21no—
197#388—21no—
198#388—21no—
199#388—21no—
200#387—21no—
201#387—21no—
202#387—21no—
203#387—21no—
204#387—21no—
205#387—21no—
206#387—21no—
207#387—21no—
208#386—21no—
209#386—21no—
210#385—21no—
211#385—21no—
212#384—21no—
213#384—21no—
214#384—21no—
215#384—21no—
216#384C2312yes—
217#384C2312yes—
218#384C2312yes—
219#384C2312yes—
220#383—21no—
221#382—22no—
222#382—22no—
223#382C2311yescharacteristic
224#382C2311yescharacteristic
225#381—21no—
226#380—22no—
227#380—22no—
228#380—22no—
229#380C2311yescharacteristic
230#380C2314yes—
231#380C2311yescharacteristic
232C4×C4⋊C4—21no—
233C4×C4⋊C4—21no—
234C4×C4⋊C4—21no—
235C4×C4⋊C4—21no—
236C4×C4⋊C4—21no—
237C4×C4⋊C4—21no—
238C4×C4⋊C4—21no—
239C4×C4⋊C4—21no—
240C4×C4⋊C4—22no—
241C4×C4⋊C4—22no—
242C4×C4⋊C4—22no—
243C4×C4⋊C4—21no—
244C4×C4⋊C4—21no—
245C4×C4⋊C4C2311yescharacteristic
246C4×C4⋊C4C2311yescharacteristic
247C4×C4⋊C4C2311yescharacteristic
248C4×C4⋊C4C2311yescharacteristic
249C4×C4⋊C4C2314yes—
250C4×C4⋊C4C2311yescharacteristic
251C4×C4⋊C4C2311yescharacteristic
252C4×C22⋊C4—21no—
253C4×C22⋊C4—21no—
254C4×C22⋊C4—21no—
255C4×C22⋊C4—21no—
256C4×C22⋊C4—21no—
257C4×C22⋊C4—21no—
258C4×C22⋊C4—21no—
259C4×C22⋊C4—21no—
260C4×C22⋊C4—21no—
261C4×C22⋊C4—21no—
262C4×C22⋊C4—21no—
263C4×C22⋊C4—21no—
264C4×C22⋊C4—21no—
265#376—21no—
266#376—21no—
267C43—21no—
268C43D411yescharacteristic
269C43D411yescharacteristic
270C43D411yescharacteristic
271C43D411yescharacteristic
272C43C2311yescharacteristic
273C43C2311yescharacteristic
274C43C2311yescharacteristic
275C43C2311yescharacteristic
276#340C2314yes—
277#340C2314yes—
278#340C2314yes—
279#340C2314yes—
280#340C2314yes—
281#340C2314yes—
282#340C2314yes—
283#340C2314yes—
284C22×Q8—22no—
285C22×Q8—22no—
286C22×Q8C2411yescharacteristic
287C22×D4—21no—
288C22×D4C2411yescharacteristic
289C23×C4—21no—
290C23×C4—21no—
291C23×C4—21no—
292C23×C4C2×D411yescharacteristic
293C23×C4C2×D411yescharacteristic
294C23×C4C2×D411yescharacteristic
295C23×C4C2×D411yescharacteristic
296C23×C4C2×D411yescharacteristic
297C23×C4C2×D411yescharacteristic
298C23×C4C2411yescharacteristic
299C22×C8—28no—
300C22×C8—44no—
301C22×C8—44no—
302C22×C8C2414yes—
303C22×C8C2414yes—
304C4⋊Q8—24no—
305C4⋊Q8—24no—
306C4⋊Q8—24no—
307C4⋊Q8—24no—
308C4⋊Q8—44no—
309C4⋊Q8—44no—
310C4⋊Q8—44no—
311C4⋊Q8—44no—
312#126—28no—
313#125—22no—
314#125—48no—
315#125C2×Q814yes—
316#124—22no—
317#124C2×Q814yes—
318#123—28no—
319C22⋊Q8—22no—
320C22⋊Q8—48no—
321C22⋊Q8—48no—
322C22⋊Q8C2×Q814yes—
323#121—22no—
324#121C2×Q814yes—
325C4×Q8—22no—
326C4×Q8—22no—
327C4×Q8—22no—
328C4×Q8—22no—
329C4×Q8—22no—
330C4×Q8—48no—
331C4×Q8—48no—
332C4×Q8C2×Q814yes—
333C4×D4—28no—
334C4×D4—22no—
335C4×D4—22no—
336C4×D4—22no—
337C4×D4—22no—
338C4×D4—22no—
339C4×D4—44no—
340C4×D4—44no—
341C4×D4C2×Q814yes—
342#117—28no—
343#117—44no—
344#117—48no—
345C2×C4⋊C4—21no—
346C2×C4⋊C4—21no—
347C2×C4⋊C4—21no—
348C2×C4⋊C4—21no—
349C2×C4⋊C4—22no—
350C2×C4⋊C4—22no—
351C2×C4⋊C4—21no—
352C2×C4⋊C4—21no—
353C2×C4⋊C4—21no—
354C2×C4⋊C4—21no—
355C2×C4⋊C4—24no—
356C2×C4⋊C4—24no—
357C2×C4⋊C4—22no—
358C2×C4⋊C4—22no—
359C2×C4⋊C4—21no—
360C2×C4⋊C4—21no—
361C2×C4⋊C4—22no—
362C2×C4⋊C4—22no—
363C2×C4⋊C4—22no—
364C2×C4⋊C4—22no—
365C2×C4⋊C4—22no—
366C2×C4⋊C4—22no—
367C2×C4⋊C4C2411yescharacteristic
368C2×C4⋊C4C2411yescharacteristic
369C2×C4⋊C4C2411yescharacteristic
370C2×C4⋊C4C2411yescharacteristic
371C2×C4⋊C4C2414yes—
372C2×C4⋊C4C2414yes—
373C2×C4⋊C4C2411yescharacteristic
374C2×C4⋊C4C2411yescharacteristic
375C2×C22⋊C4—21no—
376C2×C22⋊C4—21no—
377C2×C22⋊C4—21no—
378C2×C22⋊C4—21no—
379C2×C22⋊C4—21no—
380C2×C22⋊C4—24no—
381C2×C22⋊C4—21no—
382C2×C22⋊C4—21no—
383C2×C22⋊C4—21no—
384C2×C22⋊C4—21no—
385C2×C22⋊C4—21no—
386C2×C22⋊C4—21no—
387C2×C22⋊C4—21no—
388C2×C22⋊C4—21no—
389C2×C42—24no—
390C2×C42—24no—
391C2×C42—21no—
392C2×C42—24no—
393C2×C42—22no—
394C2×C42—22no—
395C2×C42—22no—
396C2×C42—22no—
397C2×C42—24no—
398C2×C42—21no—
399C2×C42—21no—
400C2×C42—21no—
401C2×C42—21no—
402C2×C42—21no—
403C2×C42—21no—
404C2×C42—21no—
405C2×C42—21no—
406C2×C42—42no—
407C2×C42—44no—
408C2×C42C2×D411yescharacteristic
409C2×C42C2×D411yescharacteristic
410C2×C42C2×D411yescharacteristic
411C2×C42C2×D411yescharacteristic
412C2×C42C2×D411yescharacteristic
413C2×C42C2×D411yescharacteristic
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×C42C2×D411yescharacteristic
427C2×C42C2×D411yescharacteristic
428C2×C42C2×D411yescharacteristic
429C2×C42C2×D411yescharacteristic
430C2×C42C2×Q814yes—
431C2×C42#4114yes—
432C2×C42C2411yescharacteristic
433C2×C42C2411yescharacteristic
434C2×C42C2411yescharacteristic
435C2×C42C2411yescharacteristic
436C2×C42C2411yescharacteristic
437C2×C42C2411yescharacteristic
438#107—44no—
439#107—44no—
440#106—44no—
441#106—44no—
442C4⋊C8—24no—
443C4⋊C8—24no—
444C4⋊C8—28no—
445C4⋊C8—24no—
446C4⋊C8—24no—
447C4⋊C8—24no—
448C4⋊C8—24no—
449C4⋊C8—44no—
450C4⋊C8—44no—
451#103—44no—
452#103—44no—
453#102—44no—
454#102—44no—
455#95—21no—
456#95—21no—
457#95—21no—
458#95—21no—
459#95—21no—
460#95—21no—
461#95—21no—
462#95—21no—
463#95—21no—
464#95—21no—
465#95—21no—
466#95—21no—
467#95—21no—
468#95—21no—
469#95—21no—
470#95—21no—
471#95—21no—
472#95—21no—
473#95—21no—
474#95—21no—
475#95—24no—
476#95—24no—
477#95—24no—
478#95—24no—
479C24—21no—
480C24C22×D411yescharacteristic
481C2×Q8—21no—
482C2×Q8—21no—
483C2×Q8—21no—
484C2×Q8—21no—
485C2×Q8—21no—
486C2×Q8—44no—
487C2×Q8—44no—
488C2×Q8—44no—
489C2×Q8—44no—
490C2×Q8—44no—
491C2×Q8—44no—
492C2×Q8C22×Q812yes—
493C2×D4—24no—
494C2×D4—21no—
495C2×D4—21no—
496C2×D4—21no—
497C2×D4—21no—
498C2×D4—21no—
499C2×D4—42no—
500C2×D4—42no—
501C2×D4C22×Q812yes—
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—21no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—24no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—24no—
527C22×C4—24no—
528C22×C4—41no—
529C22×C4—41no—
530C22×C4—42no—
531C22×C4—42no—
532C22×C4—42no—
533C22×C4—42no—
534C22×C4—42no—
535C22×C4—42no—
536C22×C4—42no—
537C22×C4—42no—
538C22×C4C22⋊Q814yes—
539C22×C4C22⋊Q814yes—
540C22×C4AGL(1,ℤ/8)14yes—
541C22×C4#13714yes—
542C22×C4C22×D411yescharacteristic
543C22×C4C22×D411yescharacteristic
544C22×C4C22×D411yescharacteristic
545C22×C4C22×D411yescharacteristic
546C22×C4C22×D411yescharacteristic
547C22×C4C22×D411yescharacteristic
548C22×C4C22×D411yescharacteristic
549C22×C4C22×D411yescharacteristic
550C22×C4C22×D411yescharacteristic
551C22×C4C22×D411yescharacteristic
552C22×C4C22×D411yescharacteristic
553C22×C4C22×D411yescharacteristic
554C22×C4C22×D411yescharacteristic
555C22×C4C22×Q812yes—
556C22×C4C2×#4112yes—
557C22×C4C2511yescharacteristic
558C2×C8—24no—
559C2×C8—24no—
560C2×C8—24no—
561C2×C8—24no—
562C2×C8—24no—
563C2×C8—24no—
564C2×C8—88no—
565C4⋊C4—24no—
566C4⋊C4—24no—
567C4⋊C4—24no—
568C4⋊C4—24no—
569C4⋊C4—21no—
570C4⋊C4—21no—
571C4⋊C4—24no—
572C4⋊C4—24no—
573C4⋊C4—21no—
574C4⋊C4—21no—
575C4⋊C4—21no—
576C4⋊C4—21no—
577C4⋊C4—21no—
578C4⋊C4—21no—
579C4⋊C4—21no—
580C4⋊C4—21no—
581C4⋊C4—24no—
582C4⋊C4—24no—
583C4⋊C4—42no—
584C4⋊C4—42no—
585C4⋊C4—44no—
586C4⋊C4—44no—
587C4⋊C4—48no—
588C4⋊C4—44no—
589C4⋊C4—44no—
590C4⋊C4—42no—
591C4⋊C4—42no—
592C4⋊C4—44no—
593C4⋊C4—44no—
594C4⋊C4—44no—
595C4⋊C4—44no—
596C4⋊C4—42no—
597C4⋊C4—48no—
598C4⋊C4—44no—
599C4⋊C4—42no—
600C4⋊C4—44no—
601C4⋊C4C22×Q812yes—
602C4⋊C4C22×Q812yes—
603C22⋊C4—24no—
604C22⋊C4—24no—
605C22⋊C4—24no—
606C22⋊C4—24no—
607C22⋊C4—24no—
608C22⋊C4—42no—
609C22⋊C4—42no—
610C22⋊C4—48no—
611C22⋊C4—42no—
612C22⋊C4—42no—
613C22⋊C4—42no—
614C22⋊C4—42no—
615C22⋊C4—42no—
616C22⋊C4—42no—
617C42—24no—
618C42—22no—
619C42—22no—
620C42—22no—
621C42—22no—
622C42—22no—
623C42—22no—
624C42—22no—
625C42—22no—
626C42—22no—
627C42—22no—
628C42—22no—
629C42—22no—
630C42—22no—
631C42—22no—
632C42—22no—
633C42—22no—
634C42—22no—
635C42—21no—
636C42—21no—
637C42—21no—
638C42—21no—
639C42—41no—
640C42—41no—
641C42—48no—
642C42—42no—
643C42—42no—
644C42—42no—
645C42—42no—
646C42—42no—
647C42—42no—
648C42—42no—
649C42—42no—
650C42C22⋊Q814yes—
651C42C22⋊Q814yes—
652C42#13514yes—
653C42C22×Q812yes—
654C42C22×Q812yes—
655C42C2×#4112yes—
656C42C2×#4112yes—
657C42H(5,𝔽2)12yes—
658C42H(5,𝔽2)12yes—
659C422−1+412yes—
660C422−1+412yes—
661C23—21no—
662C23—21no—
663C23—21no—
664C23—21no—
665C23—22no—
666C23—41no—
667C23—41no—
668C23—41no—
669C23—41no—
670C23—41no—
671C23—41no—
672C23C2×C22⋊Q812yes—
673C23C2×AGL(1,ℤ/8)12yes—
674C23C2×#13712yes—
675C23C23×D411yescharacteristic
676Q8—22no—
677Q8—22no—
678Q8—41no—
679Q8—41no—
680Q8—88no—
681Q8—88no—
682D4—22no—
683D4—22no—
684D4—48no—
685D4—41no—
686D4—41no—
687C2×C4—28no—
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—21no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—28no—
705C2×C4—28no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—28no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—21no—
715C2×C4—21no—
716C2×C4—21no—
717C2×C4—21no—
718C2×C4—21no—
719C2×C4—21no—
720C2×C4—44no—
721C2×C4—44no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—48no—
729C2×C4—41no—
730C2×C4—41no—
731C2×C4—41no—
732C2×C4—41no—
733C2×C4—44no—
734C2×C4—44no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—44no—
738C2×C4—41no—
739C2×C4—44no—
740C2×C4—44no—
741C2×C4—41no—
742C2×C4—41no—
743C2×C4—41no—
744C2×C4—41no—
745C2×C4—41no—
746C2×C4—44no—
747C2×C4—84no—
748C2×C4—84no—
749C2×C4C2×C22⋊Q812yes—
750C2×C4C2×C22⋊Q812yes—
751C2×C4C2×C22⋊Q812yes—
752C2×C4C2×C22⋊Q812yes—
753C2×C4C2×C22⋊Q812yes—
754C2×C4#53712yes—
755C2×C4#53712yes—
756C2×C4#53712yes—
757C2×C4#53712yes—
758C2×C4C2×#13512yes—
759C2×C4C2×#13512yes—
760C2×C4C2×#13512yes—
761C2×C4C2×AGL(1,ℤ/8)12yes—
762C2×C4C2×AGL(1,ℤ/8)12yes—
763C2×C4C2×#13712yes—
764C2×C4C2×#13712yes—
765C2×C4#57512yes—
766C2×C4C23×Q811yescharacteristic
767C2×C4C22×#4111yescharacteristic
768C2×C4C2×H(5,𝔽2)11yescharacteristic
769C2×C4C2×H(5,𝔽2)11yescharacteristic
770C2×C4C2×2−1+411yescharacteristic
771C2×C4C2×2−1+411yescharacteristic
772C8—44no—
773C8—44no—
774C22—22no—
775C22—22no—
776C22—22no—
777C22—22no—
778C22—22no—
779C22—22no—
780C22—42no—
781C22—42no—
782C22—42no—
783C22—81no—
784C22—81no—
785C22—81no—
786C22—81no—
787C22#307914yes—
788C22C22×C22⋊Q811yescharacteristic
789C22C2×#53711yescharacteristic
790C22C2×#53711yescharacteristic
791C22C22×#13511yescharacteristic
792C22C22×AGL(1,ℤ/8)11yescharacteristic
793C22C22×#13711yescharacteristic
794C22C2×#57511yescharacteristic
795C4—22no—
796C4—22no—
797C4—22no—
798C4—22no—
799C4—22no—
800C4—22no—
801C4—22no—
802C4—22no—
803C4—42no—
804C4—42no—
805C4—42no—
806C4—41no—
807C4—41no—
808C4—81no—
809C4—84no—
810C4—81no—
811C4—81no—
812C4—84no—
813C4—81no—
814C4#307614yes—
815C4#324714yes—
816C4#324814yes—
817C4#350311yescharacteristic
818C4#350311yescharacteristic
819C4#350811yescharacteristic
820C4#350911yescharacteristic
821C2—24no—
822C2—82no—
823C2#3528011yescharacteristic
824C2C2×#307611yescharacteristic
825C2C2×#307911yescharacteristic
826C2C2×#324711yescharacteristic
827C2C2×#324811yescharacteristic
828C2#6091611yescharacteristic
829C2#6091811yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#121C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C2×C43 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #36645C2semidirect
3. #33198C2semidirect
4. #33197C2semidirect
5. #33196C2semidirect
6. #33195C2semidirect
7. #29997C2semidirect
8. #29995C2semidirect
9. #29289C2semidirect
10. #29288C2semidirect
11. #28282C2semidirect
12. #28281C2semidirect
13. #24838C2semidirect
14. #24837C2semidirect
17. #21962C2semidirect
19. C2×#1842C2semidirect
116. #529Q8semidirect

Maximal subgroups

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

subgroupindex
#366452
C4×#5292
#331982
#331972
#331962
#331952
#299972
#299952
#292892
#292882
#282822
#282812
#248382
#248372
#248362
#248352
#219622
#218872
C2×#18422