Finite Group Databasebeta

← #223516

Subgroups — #223516

Order 512.

1192 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
1C4×#547C211yesmaximal, characteristic
2#22751C211yesmaximal, characteristic, complemented
3#21102C211yesmaximal, characteristic, complemented
4#9873C211yesmaximal, characteristic, complemented
5#9864C211yesmaximal, characteristic, complemented
6#9078C211yesmaximal, characteristic, complemented
7#9076C211yesmaximal, characteristic, complemented
8#8944C211yesmaximal, characteristic, complemented
9#8943C211yesmaximal, characteristic, complemented
10#8707C211yesmaximal, characteristic, complemented
11#8706C211yesmaximal, characteristic, complemented
12#8565C211yesmaximal, characteristic, complemented
13#8170C211yesmaximal, characteristic, complemented
14#7904C211yesmaximal, characteristic, complemented
15#7901C211yesmaximal, characteristic, complemented
16C2×#547C411yescharacteristic
17C2×C4×#41—21no—
18C2×#432C2211yescharacteristic
19C2×#431C2211yescharacteristic
20C2×#423C2211yescharacteristic
21C2×C4×M16C2211yescharacteristic
22#2365C411yescharacteristic
23#2362—21no—
24#2361C411yescharacteristic
25#2361C411yescharacteristic
26#2359—21no—
27#2359—21no—
28#2354C411yescharacteristic
29D4×C4⋊C4C411yescharacteristic
30#2344C411yescharacteristic
31#2344C411yescharacteristic
32#2339—21no—
33C4×C4⋊Q8C2211yescharacteristic
34C4×C22⋊Q8—21no—
35C4×#123—21no—
36C4×#123—21no—
37C4×#121C2211yescharacteristic
38C4×#121C2211yescharacteristic
39C42×D4C2211yescharacteristic
40C42×D4C2211yescharacteristic
41C2×C4×C4⋊C4C2211yescharacteristic
42C2×C4×C4⋊C4C2211yescharacteristic
43#1924—21no—
44#1923—21no—
45#1917—21no—
46#1917—21no—
47#1870—21no—
48#1870—21no—
49#1851—21no—
50#1831C2211yescharacteristic
51#1797C2211yescharacteristic
52#1797C2211yescharacteristic
53C4×C4⋊C8C2211yescharacteristic
54C4×C4⋊C8C2211yescharacteristic
55#1753—21no—
56C4×C22⋊C8C2211yescharacteristic
57C4×C22⋊C8C2211yescharacteristic
58#1744C2211yescharacteristic
59C2×D4⋊C8C2211yescharacteristic
60C2×D4⋊C8C2211yescharacteristic
61C2×D4⋊C8C2211yescharacteristic
62C2×D4⋊C8C2211yescharacteristic
63#1279C2211yescharacteristic
64#1279C2211yescharacteristic
65#1279C2211yescharacteristic
66#1279C2211yescharacteristic
67#1279C2211yescharacteristic
68#1279C2211yescharacteristic
69#1279C2211yescharacteristic
70#1279C2211yescharacteristic
71#1279C2211yescharacteristic
72#1279C2211yescharacteristic
73#1279C2211yescharacteristic
74#1279C2211yescharacteristic
75C22×#41—21no—
76C22×M16—21no—
77C22×M16—21no—
78#547—24no—
79#547—24no—
80C2×C4⋊Q8C2×C411yescharacteristic
81C2×#123—21no—
82C2×#123—21no—
83C2×C22⋊Q8—21no—
84C2×#121C2×C411yescharacteristic
85C2×#121C2×C411yescharacteristic
86C4×#41—44no—
87C4×#41—44no—
88C2×C4×Q8—21no—
89C2×C4×Q8—21no—
90C2×C4×D4—21no—
91C2×C4×D4—21no—
92C2×C4×D4—21no—
93C2×C4×D4—21no—
94C2×C4×D4—21no—
95C2×C4×D4C2×C411yescharacteristic
96C2×C4×D4C2×C411yescharacteristic
97C2×C4×D4C2×C411yescharacteristic
98C2×C4×D4D411yescharacteristic
99C2×C4×D4D411yescharacteristic
100C2×C4×D4C2311yescharacteristic
101C2×#117—21no—
102C2×#117—21no—
103C2×#117—21no—
104C22×C4⋊C4C2×C411yescharacteristic
105C22×C4⋊C4C2×C411yescharacteristic
106C22×C4⋊C4C2×C411yescharacteristic
107C22×C4⋊C4C2×C411yescharacteristic
108C22×C42—21no—
109C22×C42—21no—
110C22×C42—21no—
111C22×C42C2311yescharacteristic
112C22×C42C2311yescharacteristic
113#432—22no—
114#432—41no—
115#431—22no—
116#431—41no—
117#423—22no—
118#423—41no—
119C2×C4⋊C8—21no—
120C2×C4⋊C8—21no—
121C2×C4⋊C8—21no—
122C2×C4⋊C8C2311yescharacteristic
123C2×C4⋊C8C2311yescharacteristic
124C2×C4⋊C8C2311yescharacteristic
125C2×C4⋊C8C2311yescharacteristic
126C2×C22⋊C8—21no—
127C2×C22⋊C8—21no—
128C2×C22⋊C8—21no—
129C2×C22⋊C8—21no—
130C2×C22⋊C8—21no—
131C2×C22⋊C8—21no—
132C4×M16—22no—
133C4×M16—41no—
134C2×#97—21no—
135C2×#97—21no—
136C2×C4×C8—21no—
137C2×C4×C8C2311yescharacteristic
138C2×C4×C8C2311yescharacteristic
139C2×C4×C8C2311yescharacteristic
140C2×C4×C8C2311yescharacteristic
141#391—21no—
142#391—21no—
143#390C2×C411yescharacteristic
144#390C2×C411yescharacteristic
145#389—21no—
146#389—21no—
147#389C2×C411yescharacteristic
148#389C2×C411yescharacteristic
149#389C2×C411yescharacteristic
150#389C2×C411yescharacteristic
151#388—21no—
152#388—21no—
153#388—21no—
154#388—21no—
155#388—21no—
156#388—21no—
157#387—21no—
158#387—21no—
159#387—21no—
160#387—21no—
161#387—21no—
162#387—21no—
163#386—21no—
164#386—21no—
165#386—21no—
166#386—21no—
167#385—21no—
168#385—21no—
169#385—21no—
170#385—21no—
171#384C2×C411yescharacteristic
172#381—21no—
173#381—21no—
174#380—21no—
175#380C2×C411yescharacteristic
176#380C2×C411yescharacteristic
177C4×C4⋊C4—21no—
178C4×C4⋊C4—21no—
179C4×C4⋊C4—21no—
180C4×C4⋊C4—21no—
181C4×C4⋊C4—21no—
182C4×C4⋊C4C2×C411yescharacteristic
183C4×C4⋊C4C2×C411yescharacteristic
184C4×C4⋊C4C2×C411yescharacteristic
185C4×C4⋊C4C2×C411yescharacteristic
186C4×C4⋊C4C2×C411yescharacteristic
187C4×C4⋊C4C2×C411yescharacteristic
188C4×C4⋊C4C2×C411yescharacteristic
189C4×C4⋊C4D411yescharacteristic
190C4×C4⋊C4D411yescharacteristic
191C4×C4⋊C4C2311yescharacteristic
192C4×C4⋊C4C2311yescharacteristic
193C4×C4⋊C4C2311yescharacteristic
194C4×C22⋊C4—21no—
195C4×C22⋊C4—21no—
196C4×C22⋊C4—21no—
197C4×C22⋊C4—21no—
198C4×C22⋊C4—21no—
199C4×C22⋊C4C2×C411yescharacteristic
200C4×C22⋊C4C2×C411yescharacteristic
201C4×C22⋊C4D411yescharacteristic
202C4×C22⋊C4D411yescharacteristic
203C4×C22⋊C4D411yescharacteristic
204C4×C22⋊C4D411yescharacteristic
205C2×#95—21no—
206C2×#95—21no—
207C43C2311yescharacteristic
208#336—21no—
209#336—21no—
210#336—21no—
211#336—21no—
212#336—21no—
213#336—21no—
214#336—21no—
215#336—21no—
216#336—21no—
217#336—21no—
218D4⋊C8—22no—
219D4⋊C8—22no—
220D4⋊C8—41no—
221D4⋊C8—41no—
222C2×#41—28no—
223C2×#41—44no—
224C2×#41—44no—
225C22×Q8—21no—
226C22×D4—21no—
227C22×D4—21no—
228C22×D4C22⋊C411yescharacteristic
229C22×D4C22×C411yescharacteristic
230C23×C4—21no—
231C23×C4—21no—
232C23×C4—21no—
233C23×C4—21no—
234C23×C4—21no—
235C23×C4—21no—
236C23×C4—21no—
237C23×C4C22×C411yescharacteristic
238C23×C4C22×C411yescharacteristic
239C23×C4C2×D411yescharacteristic
240C23×C4C2×D411yescharacteristic
241C23×C4C2×D411yescharacteristic
242C23×C4C2×D411yescharacteristic
243C2×M16—42no—
244C2×M16—42no—
245C2×M16—42no—
246C2×M16—42no—
247C2×M16—42no—
248C2×M16—81no—
249C22×C8—21no—
250C22×C8—21no—
251C22×C8—21no—
252C22×C8—21no—
253C22×C8—21no—
254C22×C8—21no—
255C22×C8—21no—
256C22×C8—21no—
257C4⋊Q8—22no—
258C4⋊Q8M1614yescomplemented
259#123—28no—
260#123—28no—
261C22⋊Q8—28no—
262#121—22no—
263#121—22no—
264#121—22no—
265#121—22no—
266C4×Q8—42no—
267C4×Q8—42no—
268C4×Q8—44no—
269C4×D4—22no—
270C4×D4—22no—
271C4×D4—22no—
272C4×D4—22no—
273C4×D4—22no—
274C4×D4—22no—
275C4×D4—21no—
276C4×D4—21no—
277C4×D4—21no—
278C4×D4—21no—
279C4×D4—41no—
280C4×D4—42no—
281C4×D4—44no—
282C4×D4—44no—
283C4×D4—42no—
284C4×D4—42no—
285C4×D4—44no—
286C4×D4—42no—
287C4×D4—42no—
288C4×D4M1614yescomplemented
289#117—44no—
290#117—44no—
291#117—44no—
292C2×C4⋊C4—21no—
293C2×C4⋊C4—21no—
294C2×C4⋊C4—21no—
295C2×C4⋊C4—22no—
296C2×C4⋊C4—22no—
297C2×C4⋊C4—22no—
298C2×C4⋊C4—22no—
299C2×C4⋊C4—22no—
300C2×C4⋊C4—22no—
301C2×C4⋊C4—21no—
302C2×C4⋊C4—21no—
303C2×C4⋊C4—21no—
304C2×C4⋊C4—21no—
305C2×C4⋊C4—21no—
306C2×C4⋊C4—21no—
307C2×C4⋊C4—21no—
308C2×C4⋊C4—21no—
309C2×C4⋊C4—41no—
310C2×C4⋊C4—41no—
311C2×C4⋊C4C22⋊C411yescharacteristic
312C2×C4⋊C4C22⋊C411yescharacteristic
313C2×C4⋊C4C22⋊C411yescharacteristic
314C2×C4⋊C4C22×C411yescharacteristic
315C2×C4⋊C4C22×C411yescharacteristic
316C2×C4⋊C4C22×C411yescharacteristic
317C2×C4⋊C4C22×C411yescharacteristic
318C2×C4⋊C4C22×C411yescharacteristic
319C2×C4⋊C4C22×C411yescharacteristic
320C2×C4⋊C4C22×C411yescharacteristic
321C2×C22⋊C4—21no—
322C2×C22⋊C4—21no—
323C2×C22⋊C4—21no—
324C2×C22⋊C4—21no—
325C2×C22⋊C4—21no—
326C2×C22⋊C4—21no—
327C2×C22⋊C4—21no—
328C2×C22⋊C4—21no—
329C2×C22⋊C4—21no—
330C2×C22⋊C4—21no—
331C2×C22⋊C4—21no—
332C2×C22⋊C4C22⋊C411yescharacteristic
333C2×C22⋊C4C22⋊C411yescharacteristic
334C2×C22⋊C4C22⋊C411yescharacteristic
335C2×C22⋊C4C22⋊C411yescharacteristic
336C2×C22⋊C4C22⋊C411yescharacteristic
337C2×C22⋊C4C22⋊C411yescharacteristic
338C2×C42—21no—
339C2×C42—21no—
340C2×C42—21no—
341C2×C42—21no—
342C2×C42—21no—
343C2×C42—21no—
344C2×C42—21no—
345C2×C42—21no—
346C2×C42—21no—
347C2×C42—21no—
348C2×C42—21no—
349C2×C42—21no—
350C2×C42—21no—
351C2×C42—21no—
352C2×C42—21no—
353C2×C42—21no—
354C2×C42—21no—
355C2×C42—42no—
356C2×C42—42no—
357C2×C42—42no—
358C2×C42—42no—
359C2×C42—42no—
360C2×C42—42no—
361C2×C42C22×C411yescharacteristic
362C2×C42C22×C411yescharacteristic
363C2×C42C22×C411yescharacteristic
364C2×C42C22×C411yescharacteristic
365C2×C42C2×D411yescharacteristic
366C2×C42C2×D411yescharacteristic
367C2×C42C2×D411yescharacteristic
368C2×C42C2×D411yescharacteristic
369C2×C42C2×D411yescharacteristic
370C2×C42C2×D411yescharacteristic
371C2×C42C2×D411yescharacteristic
372C2×C42C2×D411yescharacteristic
373C2×C42C2411yescharacteristic
374C4⋊C8—21no—
375C4⋊C8—21no—
376C4⋊C8—21no—
377C4⋊C8—21no—
378C4⋊C8—21no—
379C4⋊C8—21no—
380C4⋊C8—21no—
381C4⋊C8—42no—
382C4⋊C8—42no—
383C4⋊C8—42no—
384C4⋊C8#4112yescomplemented
385C22⋊C8—42no—
386C22⋊C8—42no—
387C22⋊C8—42no—
388C22⋊C8—42no—
389C22⋊C8—42no—
390C22⋊C8—81no—
391#97—42no—
392#97—42no—
393C4×C8—21no—
394C4×C8—21no—
395C4×C8—21no—
396C4×C8—21no—
397C4×C8—21no—
398C4×C8—21no—
399C4×C8—21no—
400C4×C8—81no—
401C4×C8#4112yescomplemented
402#95—21no—
403#95—21no—
404#95—21no—
405#95—21no—
406#95—21no—
407#95—21no—
408#95—21no—
409#95—21no—
410#95—21no—
411#95—21no—
412#95—21no—
413#95—21no—
414#95—21no—
415#95—21no—
416#95—21no—
417#95C22⋊C411yescharacteristic
418#95C22⋊C411yescharacteristic
419#95C22⋊C411yescharacteristic
420#95C22⋊C411yescharacteristic
421#95C22⋊C411yescharacteristic
422#95C22⋊C411yescharacteristic
423C24—21no—
424C24C2×C22⋊C411yescharacteristic
425C24C2×C22⋊C411yescharacteristic
426#41—432no—
427C2×Q8—24no—
428C2×Q8—42no—
429C2×Q8—42no—
430C2×D4—22no—
431C2×D4—22no—
432C2×D4—24no—
433C2×D4—24no—
434C2×D4—21no—
435C2×D4—21no—
436C2×D4—21no—
437C2×D4—21no—
438C2×D4—21no—
439C2×D4—22no—
440C2×D4—42no—
441C2×D4—42no—
442C2×D4—42no—
443C2×D4—42no—
444C2×D4C2×M1612yes—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—24no—
450C22×C4—24no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—22no—
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—24no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—41no—
483C22×C4—41no—
484C22×C4—41no—
485C22×C4—42no—
486C22×C4—42no—
487C22×C4—42no—
488C22×C4—42no—
489C22×C4—42no—
490C22×C4—42no—
491C22×C4—42no—
492C22×C4—42no—
493C22×C4—42no—
494C22×C4—42no—
495C22×C4—42no—
496C22×C4—42no—
497C22×C4—41no—
498C22×C4—41no—
499C22×C4—41no—
500C22×C4—41no—
501C22×C4—41no—
502C22×C4—41no—
503C22×C4—81no—
504C22×C4—81no—
505C22×C4—81no—
506C22×C4C2×C22⋊C411yescharacteristic
507C22×C4C2×C22⋊C411yescharacteristic
508C22×C4C2×C22⋊C411yescharacteristic
509C22×C4C2×C22⋊C411yescharacteristic
510C22×C4C2×C22⋊C411yescharacteristic
511C22×C4C2×C22⋊C411yescharacteristic
512C22×C4C2×C22⋊C411yescharacteristic
513C22×C4C2×C22⋊C411yescharacteristic
514C22×C4C2×C22⋊C411yescharacteristic
515C22×C4C2×C22⋊C411yescharacteristic
516C22×C4AGL(1,ℤ/8)12yes—
517C22×C4AGL(1,ℤ/8)12yes—
518C22×C4C23×C411yescharacteristic
519C22×C4C22×D411yescharacteristic
520C22×C4C22×D411yescharacteristic
521M16—48no—
522M16—84no—
523C2×C8—22no—
524C2×C8—22no—
525C2×C8—22no—
526C2×C8—41no—
527C2×C8—41no—
528C2×C8—41no—
529C2×C8—41no—
530C2×C8—41no—
531C2×C8—41no—
532C2×C8—41no—
533C2×C8—41no—
534C2×C8—41no—
535C2×C8—41no—
536C2×C8—41no—
537C2×C8—41no—
538C2×C8—41no—
539C2×C8—41no—
540C2×C8—41no—
541C2×C8—41no—
542C2×C8—41no—
543C2×C8—41no—
544C2×C8—41no—
545C2×C8—41no—
546C2×C8—41no—
547C4⋊C4—24no—
548C4⋊C4—24no—
549C4⋊C4—21no—
550C4⋊C4—21no—
551C4⋊C4—21no—
552C4⋊C4—21no—
553C4⋊C4—24no—
554C4⋊C4—22no—
555C4⋊C4—22no—
556C4⋊C4—21no—
557C4⋊C4—21no—
558C4⋊C4—21no—
559C4⋊C4—21no—
560C4⋊C4—21no—
561C4⋊C4—21no—
562C4⋊C4—41no—
563C4⋊C4—42no—
564C4⋊C4—42no—
565C4⋊C4—42no—
566C4⋊C4—42no—
567C4⋊C4—42no—
568C4⋊C4—42no—
569C4⋊C4—42no—
570C4⋊C4—81no—
571C4⋊C4C2×M1612yes—
572C4⋊C4C2×M1612yes—
573C4⋊C4C2×M1612yes—
574C4⋊C4#13112yes—
575C22⋊C4—24no—
576C22⋊C4—24no—
577C22⋊C4—22no—
578C22⋊C4—22no—
579C22⋊C4—24no—
580C22⋊C4—22no—
581C22⋊C4—22no—
582C22⋊C4—22no—
583C22⋊C4—41no—
584C22⋊C4—42no—
585C22⋊C4—42no—
586C22⋊C4—42no—
587C22⋊C4—42no—
588C22⋊C4—41no—
589C22⋊C4—41no—
590C22⋊C4—42no—
591C22⋊C4—81no—
592C22⋊C4—81no—
593C42—21no—
594C42—21no—
595C42—21no—
596C42—21no—
597C42—21no—
598C42—21no—
599C42—21no—
600C42—21no—
601C42—21no—
602C42—21no—
603C42—21no—
604C42—21no—
605C42—21no—
606C42—21no—
607C42—21no—
608C42—21no—
609C42—21no—
610C42—21no—
611C42—41no—
612C42—41no—
613C42—42no—
614C42—42no—
615C42—42no—
616C42—42no—
617C42—41no—
618C42—41no—
619C42—41no—
620C42—41no—
621C42—41no—
622C42—41no—
623C42—42no—
624C42—42no—
625C42C2×M1612yes—
626C42C2×M1612yes—
627C42C2×#4111yescharacteristic
628C42C2×#4111yescharacteristic
629C42H(5,𝔽2)11yescharacteristic
630C422−1+411yescharacteristic
631C23—21no—
632C23—21no—
633C23—21no—
634C23—21no—
635C23—21no—
636C23—21no—
637C23—21no—
638C23—21no—
639C23—21no—
640C23—21no—
641C23—21no—
642C23—21no—
643C23—22no—
644C23—41no—
645C23—41no—
646C23—41no—
647C23—41no—
648C23—41no—
649C23—41no—
650C23#41812yes—
651C23#42112yes—
652C23C22×C22⋊C411yescharacteristic
653Q8—48no—
654D4—28no—
655D4—22no—
656D4—22no—
657D4—48no—
658D4—48no—
659D4—41no—
660D4—41no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—21no—
666C2×C4—21no—
667C2×C4—21no—
668C2×C4—21no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—21no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—21no—
684C2×C4—21no—
685C2×C4—22no—
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—42no—
699C2×C4—42no—
700C2×C4—48no—
701C2×C4—48no—
702C2×C4—48no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—41no—
706C2×C4—41no—
707C2×C4—41no—
708C2×C4—41no—
709C2×C4—41no—
710C2×C4—41no—
711C2×C4—41no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—41no—
731C2×C4—41no—
732C2×C4—81no—
733C2×C4—81no—
734C2×C4—84no—
735C2×C4—84no—
736C2×C4—84no—
737C2×C4—81no—
738C2×C4—81no—
739C2×C4—81no—
740C2×C4—81no—
741C2×C4#40712yes—
742C2×C4#40712yes—
743C2×C4#41812yes—
744C2×C4C4×#4111yescharacteristic
745C2×C4#52011yescharacteristic
746C2×C4#54611yescharacteristic
747C2×C4#54611yescharacteristic
748C2×C4#54711yescharacteristic
749C2×C4#54711yescharacteristic
750C2×C4C22×M1611yescharacteristic
751C2×C4C22×M1611yescharacteristic
752C2×C4C2×#13111yescharacteristic
753C2×C4#56811yescharacteristic
754C2×C4C2×AGL(1,ℤ/8)11yescharacteristic
755C2×C4C2×AGL(1,ℤ/8)11yescharacteristic
756C2×C4#57711yescharacteristic
757C2×C4#57811yescharacteristic
758C8—42no—
759C8—42no—
760C8—42no—
761C8—81no—
762C8—81no—
763C8—81no—
764C8—81no—
765C8—81no—
766C22—22no—
767C22—22no—
768C22—22no—
769C22—22no—
770C22—22no—
771C22—22no—
772C22—41no—
773C22—41no—
774C22—41no—
775C22—41no—
776C22—41no—
777C22—41no—
778C22—41no—
779C22—41no—
780C22—42no—
781C22—42no—
782C22—42no—
783C22—81no—
784C22—81no—
785C22—81no—
786C22—81no—
787C22#233911yescharacteristic
788C22C2×#40711yescharacteristic
789C22#288011yescharacteristic
790C22C2×#41811yescharacteristic
791C22#289811yescharacteristic
792C22C2×#42111yescharacteristic
793C22#290111yescharacteristic
794C4—22no—
795C4—22no—
796C4—22no—
797C4—21no—
798C4—21no—
799C4—42no—
800C4—42no—
801C4—42no—
802C4—41no—
803C4—42no—
804C4—41no—
805C4—41no—
806C4—41no—
807C4—41no—
808C4—41no—
809C4—41no—
810C4—81no—
811C4—81no—
812C4—81no—
813C4#296511yescharacteristic
814C4#297111yescharacteristic
815C4#298911yescharacteristic
816C4#299111yescharacteristic
817C4#330611yescharacteristic
818C4#330811yescharacteristic
819C4#334311yescharacteristic
820C4#334511yescharacteristic
821C2—42no—
822C2—42no—
823C2—82no—
824C2#1744811yescharacteristic
825C2#1745411yescharacteristic
826C2#1751111yescharacteristic
827C2#1752411yescharacteristic
828C2#2247311yescharacteristic
829C2#2249511yescharacteristic
830C2#2250611yescharacteristic
subgroupG/H
centerC22×C4C22×D4
commutatorC22×C4C23×C4
Frattini, cosocleC2×C42C24
socleC23C22×C22⋊C4
prime radicalC2×#547C4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C4 ◁ C42×D4 ◁ G
LECSG ▷ C2×C42 ▷ C22 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #22751C2semidirect
3. #21102C2semidirect
4. #9873C2semidirect
5. #9864C2semidirect
6. #9078C2semidirect
7. #9076C2semidirect
8. #8944C2semidirect
9. #8943C2semidirect
10. #8707C2semidirect
11. #8706C2semidirect
12. #8565C2semidirect
13. #8170C2semidirect
14. #7904C2semidirect
15. #7901C2semidirect
258. C4⋊Q8M16semidirect
288. C4×D4M16semidirect
384. C4⋊C8#41semidirect
401. C4×C8#41semidirect

Maximal subgroups

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

subgroupindex
C4×#5472
#227512
#211022
#98732
#98642
#90782
#90762
#89442
#89432
#87072
#87062
#85652
#81702
#79042
#79012