Finite Group Databasebeta

← #370598

Subgroups — #370598

Order 512.

1282 conjugacy classes of subgroups.

The subgroup lattice has 761 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#501C211yesmaximal, characteristic
2C2×#1944C211yesmaximal, characteristic
3C2×C4×#106C211yesmaximal, characteristic
4#14054C211yesmaximal, characteristic
5#14053C211yesmaximal, characteristic
6#11385C211yesmaximal, characteristic
7#11384C211yesmaximal, characteristic
8#11220C211yesmaximal, characteristic
9#11219C211yesmaximal, characteristic
10#10908C211yesmaximal, characteristic
11#10907C211yesmaximal, characteristic
12#10863C211yesmaximal, characteristic
13#10863C211yesmaximal, characteristic
14#10862C211yesmaximal, characteristic
15#10696C211yesmaximal, characteristic
16C22×C4⋊Q8C2211yescharacteristic
17C22×#125C2211yescharacteristic
18C2×#501—24no—
19C2×#501—24no—
20C2×#501C418yescomplemented
21C22×#107C2211yescharacteristic
22C22×#107C2211yescharacteristic
23C22×#107C2211yescharacteristic
24C22×#106C2211yescharacteristic
25C22×#106C2211yescharacteristic
26C22×#106C2211yescharacteristic
27C22×#97C2211yescharacteristic
28C22×#97C2211yescharacteristic
29C22×C4×C8C2211yescharacteristic
30C2×#391—21no—
31C2×#389C2211yescharacteristic
32C2×#389C2211yescharacteristic
33C2×C4×C4⋊C4C2211yescharacteristic
34C2×C4×C4⋊C4C2211yescharacteristic
35#1944—24no—
36C4×#106—24no—
37C2×#340C2211yescharacteristic
38C2×#340C2211yescharacteristic
39C2×#340C2211yescharacteristic
40C2×#340C2211yescharacteristic
41C2×#340C2211yescharacteristic
42C2×#340C2211yescharacteristic
43C2×#340C2211yescharacteristic
44C2×#340C2211yescharacteristic
45C2×#340C2211yescharacteristic
46C2×#340C2211yescharacteristic
47C2×#336C2211yescharacteristic
48C2×#336C2211yescharacteristic
49C2×#336C2211yescharacteristic
50#1446—21no—
51#1445—21no—
52#1441—21no—
53#1441—21no—
54#1436—21no—
55#1436—21no—
56C4⋊#95—21no—
57C4⋊#95C2211yescharacteristic
58C4⋊#95C2211yescharacteristic
59C4⋊#95C2211yescharacteristic
60C4⋊#95C2211yescharacteristic
61C4⋊#95C2211yescharacteristic
62C4⋊#95C2211yescharacteristic
63C4×#95C2211yescharacteristic
64C23×Q8—21no—
65C23×C8C2311yescharacteristic
66C23×C8C2311yescharacteristic
67C23×C8C2311yescharacteristic
68C23×C8C2311yescharacteristic
69C2×C4⋊Q8—22no—
70C2×C4⋊Q8—22no—
71C2×C4⋊Q8—22no—
72C2×C4⋊Q8—41no—
73C2×C4⋊Q8—41no—
74C2×C4⋊Q8C2×C414yes—
75C2×#125—22no—
76C2×#125—22no—
77C2×#125—22no—
78C2×#125—41no—
79C2×#125—41no—
80C2×#125C2×C414yes—
81C22×C4⋊C4—21no—
82C22×C4⋊C4—21no—
83C22×C4⋊C4—21no—
84C22×C4⋊C4—21no—
85C22×C4⋊C4—21no—
86C22×C4⋊C4C2311yescharacteristic
87C22×C4⋊C4C2311yescharacteristic
88C22×C4⋊C4C2311yescharacteristic
89C22×C4⋊C4C2311yescharacteristic
90C22×C4⋊C4C2311yescharacteristic
91C22×C4⋊C4C2311yescharacteristic
92C22×C4⋊C4C2311yescharacteristic
93C22×C4⋊C4C2311yescharacteristic
94C22×C42—21no—
95C22×C42—21no—
96C22×C42C2311yescharacteristic
97C22×C42C2311yescharacteristic
98C22×C42C2311yescharacteristic
99#501—232no—
100C2×#107—22no—
101C2×#107—22no—
102C2×#107—22no—
103C2×#107—22no—
104C2×#107—22no—
105C2×#107—22no—
106C2×#107—22no—
107C2×#107C2×C414yes—
108C2×#107C2×C414yes—
109C2×#106—22no—
110C2×#106—22no—
111C2×#106—22no—
112C2×#106—22no—
113C2×#106C2×C414yes—
114C2×#106C2×C414yes—
115C2×#106D414yes—
116C2×#106D414yes—
117C2×#106Q814yescomplemented
118C2×#97—22no—
119C2×#97—22no—
120C2×#97—22no—
121C2×#97—22no—
122C2×#97—22no—
123C2×#97C2×C414yes—
124C2×C4×C8—22no—
125C2×C4×C8—22no—
126C2×C4×C8Q814yescomplemented
127#391—44no—
128#389—22no—
129#389—22no—
130#389—41no—
131#389—41no—
132C4×C4⋊C4—22no—
133C4×C4⋊C4—22no—
134C4×C4⋊C4—41no—
135C4×C4⋊C4—41no—
136C2×#95—21no—
137C2×#95—21no—
138C2×#95—21no—
139C2×#95—21no—
140C2×#95—21no—
141C2×#95—21no—
142C2×#95—21no—
143C2×#95—21no—
144C2×#95—21no—
145C2×#95—21no—
146C2×#95—21no—
147C2×#95—21no—
148C2×#95—21no—
149C2×#95—21no—
150C2×#95—21no—
151C2×#95—21no—
152C2×#95D411yescharacteristic
153C2×#95D411yescharacteristic
154C2×#95D411yescharacteristic
155C2×#95D411yescharacteristic
156#340—22no—
157#340—22no—
158#340—22no—
159#340—22no—
160#340—22no—
161#340—22no—
162#340—41no—
163#340—41no—
164#340—41no—
165#340—41no—
166#336—22no—
167#336—22no—
168#336Q814yescomplemented
169C22×Q8—24no—
170C22×Q8—42no—
171C22×Q8—42no—
172C22×Q8—42no—
173C22×Q8—42no—
174C22×Q8—81no—
175C22×Q8—81no—
176C23×C4—21no—
177C23×C4—21no—
178C23×C4—21no—
179C23×C4—21no—
180C23×C4—21no—
181C23×C4—21no—
182C23×C4—21no—
183C23×C4—21no—
184C23×C4C2×D411yescharacteristic
185C23×C4C2×D411yescharacteristic
186C23×C4C2×D411yescharacteristic
187C23×C4C2×D411yescharacteristic
188C23×C4C2×D411yescharacteristic
189C23×C4C2×D411yescharacteristic
190C23×C4C2411yescharacteristic
191C22×C8—21no—
192C22×C8—21no—
193C22×C8—21no—
194C22×C8—21no—
195C22×C8—21no—
196C22×C8—21no—
197C22×C8—21no—
198C22×C8—21no—
199C22×C8—21no—
200C22×C8—21no—
201C22×C8—21no—
202C22×C8—21no—
203C22×C8—21no—
204C22×C8—21no—
205C22×C8—21no—
206C22×C8—21no—
207C22×C8C22×C412yes—
208C22×C8C22×C412yes—
209C22×C8C2×D412yes—
210C22×C8C2×D412yes—
211C22×C8C2×Q812yes—
212C22×C8C2×Q812yes—
213C22×C8C2×Q812yes—
214C22×C8C2×Q812yes—
215C22×C8C2×Q812yes—
216C22×C8#4112yes—
217C22×C8#4112yes—
218C22×C8#4112yes—
219C4⋊Q8—28no—
220C4⋊Q8—44no—
221C4⋊Q8—44no—
222C4⋊Q8—44no—
223#125—28no—
224#125—44no—
225#125—44no—
226#125—44no—
227C2×C4⋊C4—21no—
228C2×C4⋊C4—21no—
229C2×C4⋊C4—21no—
230C2×C4⋊C4—21no—
231C2×C4⋊C4—21no—
232C2×C4⋊C4—21no—
233C2×C4⋊C4—21no—
234C2×C4⋊C4—21no—
235C2×C4⋊C4—21no—
236C2×C4⋊C4—21no—
237C2×C4⋊C4—21no—
238C2×C4⋊C4—21no—
239C2×C4⋊C4—21no—
240C2×C4⋊C4—21no—
241C2×C4⋊C4—21no—
242C2×C4⋊C4—21no—
243C2×C4⋊C4—21no—
244C2×C4⋊C4—21no—
245C2×C4⋊C4—21no—
246C2×C4⋊C4—21no—
247C2×C4⋊C4—21no—
248C2×C4⋊C4—21no—
249C2×C4⋊C4—24no—
250C2×C4⋊C4—24no—
251C2×C4⋊C4—24no—
252C2×C4⋊C4—21no—
253C2×C4⋊C4—21no—
254C2×C4⋊C4—21no—
255C2×C4⋊C4—21no—
256C2×C4⋊C4—21no—
257C2×C4⋊C4—21no—
258C2×C4⋊C4—21no—
259C2×C4⋊C4—21no—
260C2×C4⋊C4—21no—
261C2×C4⋊C4—21no—
262C2×C4⋊C4—21no—
263C2×C4⋊C4—21no—
264C2×C4⋊C4—21no—
265C2×C4⋊C4—21no—
266C2×C4⋊C4—21no—
267C2×C4⋊C4—21no—
268C2×C4⋊C4—42no—
269C2×C4⋊C4—42no—
270C2×C4⋊C4—42no—
271C2×C4⋊C4—42no—
272C2×C4⋊C4—42no—
273C2×C4⋊C4—42no—
274C2×C4⋊C4—42no—
275C2×C4⋊C4—42no—
276C2×C4⋊C4—42no—
277C2×C4⋊C4—42no—
278C2×C4⋊C4—81no—
279C2×C4⋊C4—81no—
280C2×C4⋊C4C22×C412yes—
281C2×C4⋊C4C22×C412yes—
282C2×C4⋊C4C22×C412yes—
283C2×C4⋊C4C22×C412yes—
284C2×C4⋊C4C2×D412yes—
285C2×C4⋊C4C2×D412yes—
286C2×C4⋊C4C2×D412yes—
287C2×C4⋊C4C2×D412yes—
288C2×C4⋊C4C2×Q812yes—
289C2×C4⋊C4C2×Q812yes—
290C2×C42—21no—
291C2×C42—21no—
292C2×C42—21no—
293C2×C42—21no—
294C2×C42—21no—
295C2×C42—21no—
296C2×C42—21no—
297C2×C42—21no—
298C2×C42—21no—
299C2×C42—21no—
300C2×C42—21no—
301C2×C42—21no—
302C2×C42—21no—
303C2×C42—21no—
304C2×C42—42no—
305C2×C42—42no—
306C2×C42—42no—
307C2×C42—42no—
308C2×C42—81no—
309C2×C42—81no—
310C2×C42C22×C412yes—
311C2×C42C2×Q812yes—
312C2×C42C2×Q812yes—
313C2×C42#4112yes—
314#107—28no—
315#107—28no—
316#107—44no—
317#106—28no—
318#106—28no—
319#106C22⋊C4116yes—
320#97—28no—
321#97—44no—
322C4×C8—28no—
323#95—22no—
324#95—22no—
325#95—41no—
326#95—41no—
327#95—42no—
328#95—42no—
329#95—42no—
330#95—42no—
331#95—42no—
332#95—42no—
333#95—42no—
334#95—42no—
335#95—42no—
336#95—42no—
337#95—81no—
338#95—81no—
339#95—81no—
340#95—81no—
341#95—81no—
342#95—81no—
343C24C22×D411yescharacteristic
344C2×Q8—48no—
345C2×Q8—48no—
346C2×Q8—84no—
347C2×Q8—84no—
348C2×Q8—84no—
349C2×Q8—84no—
350C2×Q8—84no—
351C22×C4—21no—
352C22×C4—21no—
353C22×C4—21no—
354C22×C4—21no—
355C22×C4—22no—
356C22×C4—22no—
357C22×C4—21no—
358C22×C4—22no—
359C22×C4—22no—
360C22×C4—22no—
361C22×C4—22no—
362C22×C4—21no—
363C22×C4—21no—
364C22×C4—21no—
365C22×C4—21no—
366C22×C4—21no—
367C22×C4—21no—
368C22×C4—21no—
369C22×C4—21no—
370C22×C4—21no—
371C22×C4—21no—
372C22×C4—21no—
373C22×C4—21no—
374C22×C4—21no—
375C22×C4—21no—
376C22×C4—21no—
377C22×C4—21no—
378C22×C4—21no—
379C22×C4—22no—
380C22×C4—22no—
381C22×C4—21no—
382C22×C4—21no—
383C22×C4—21no—
384C22×C4—21no—
385C22×C4—21no—
386C22×C4—21no—
387C22×C4—22no—
388C22×C4—22no—
389C22×C4—21no—
390C22×C4—21no—
391C22×C4—21no—
392C22×C4—21no—
393C22×C4—21no—
394C22×C4—21no—
395C22×C4—21no—
396C22×C4—21no—
397C22×C4—41no—
398C22×C4—41no—
399C22×C4—41no—
400C22×C4—41no—
401C22×C4—41no—
402C22×C4—41no—
403C22×C4—41no—
404C22×C4—41no—
405C22×C4—41no—
406C22×C4—41no—
407C22×C4—41no—
408C22×C4—41no—
409C22×C4—41no—
410C22×C4—41no—
411C22×C4—41no—
412C22×C4—41no—
413C22×C4—41no—
414C22×C4—41no—
415C22×C4—41no—
416C22×C4—41no—
417C22×C4—41no—
418C22×C4—41no—
419C22×C4—41no—
420C22×C4—41no—
421C22×C4—41no—
422C22×C4—41no—
423C22×C4—41no—
424C22×C4—41no—
425C22×C4—41no—
426C22×C4—41no—
427C22×C4—41no—
428C22×C4—41no—
429C22×C4—41no—
430C22×C4—41no—
431C22×C4—41no—
432C22×C4—41no—
433C22×C4—41no—
434C22×C4—41no—
435C22×C4—41no—
436C22×C4—41no—
437C22×C4—41no—
438C22×C4—41no—
439C22×C4—41no—
440C22×C4—41no—
441C22×C4—41no—
442C22×C4—41no—
443C22×C4C4×D412yes—
444C22×C4C4×D412yes—
445C22×C4C4⋊Q812yes—
446C22×C4C4⋊Q812yes—
447C22×C4AGL(1,ℤ/8)12yes—
448C22×C4#13712yes—
449C22×C4C23×C411yescharacteristic
450C22×C4C22×D411yescharacteristic
451C22×C4C22×D411yescharacteristic
452C22×C4C22×Q811yescharacteristic
453C22×C4C22×Q811yescharacteristic
454C22×C4C22×Q811yescharacteristic
455C22×C4C2×#4111yescharacteristic
456C22×C4C2×#4111yescharacteristic
457C22×C4C2×#4111yescharacteristic
458C22×C4C2×#4111yescharacteristic
459C22×C4H(5,𝔽2)11yescharacteristic
460C22×C4H(5,𝔽2)11yescharacteristic
461C22×C42−1+411yescharacteristic
462C22×C42−1+411yescharacteristic
463C2×C8—22no—
464C2×C8—22no—
465C2×C8—22no—
466C2×C8—22no—
467C2×C8—22no—
468C2×C8—22no—
469C2×C8—22no—
470C2×C8—22no—
471C2×C8—22no—
472C2×C8—22no—
473C2×C8—22no—
474C2×C8—22no—
475C2×C8—41no—
476C2×C8—41no—
477C2×C8—41no—
478C2×C8—41no—
479C2×C8—41no—
480C2×C8—41no—
481C2×C8—41no—
482C2×C8—41no—
483C2×C8C2×C22⋊C414yes—
484C2×C8C4×Q814yes—
485C2×C8C4×Q814yes—
486C2×C8C4×Q814yes—
487C2×C8C22⋊Q814yes—
488C2×C8C22⋊Q814yes—
489C2×C8#12414yes—
490C2×C8C4⋊Q814yes—
491C4⋊C4—22no—
492C4⋊C4—22no—
493C4⋊C4—22no—
494C4⋊C4—22no—
495C4⋊C4—22no—
496C4⋊C4—22no—
497C4⋊C4—22no—
498C4⋊C4—22no—
499C4⋊C4—22no—
500C4⋊C4—22no—
501C4⋊C4—22no—
502C4⋊C4—22no—
503C4⋊C4—22no—
504C4⋊C4—22no—
505C4⋊C4—48no—
506C4⋊C4—48no—
507C4⋊C4—48no—
508C4⋊C4—41no—
509C4⋊C4—41no—
510C4⋊C4—41no—
511C4⋊C4—41no—
512C4⋊C4—41no—
513C4⋊C4—41no—
514C4⋊C4—41no—
515C4⋊C4—41no—
516C4⋊C4—41no—
517C4⋊C4—41no—
518C4⋊C4—41no—
519C4⋊C4—41no—
520C4⋊C4—41no—
521C4⋊C4—41no—
522C4⋊C4—41no—
523C4⋊C4—41no—
524C4⋊C4—84no—
525C4⋊C4—84no—
526C4⋊C4C2×C22⋊C414yes—
527C4⋊C4C2×C22⋊C414yes—
528C42—22no—
529C42—22no—
530C42—22no—
531C42—22no—
532C42—22no—
533C42—22no—
534C42—22no—
535C42—22no—
536C42—41no—
537C42—41no—
538C42—41no—
539C42—41no—
540C42—84no—
541C42—84no—
542C23C2×C4×D411yescharacteristic
543C23C2×C4⋊Q811yescharacteristic
544C23#53211yescharacteristic
545C23D4211yescharacteristic
546C23D4211yescharacteristic
547C23#54711yescharacteristic
548C23D4×Q811yescharacteristic
549C23C2×AGL(1,ℤ/8)11yescharacteristic
550C23C2×#13711yescharacteristic
551C23#57511yescharacteristic
552C23#57511yescharacteristic
553C23#57611yescharacteristic
554C23#57711yescharacteristic
555C23#57711yescharacteristic
556C23#57811yescharacteristic
557Q8—816no—
558C2×C4—22no—
559C2×C4—22no—
560C2×C4—22no—
561C2×C4—22no—
562C2×C4—22no—
563C2×C4—22no—
564C2×C4—22no—
565C2×C4—22no—
566C2×C4—24no—
567C2×C4—24no—
568C2×C4—22no—
569C2×C4—22no—
570C2×C4—22no—
571C2×C4—22no—
572C2×C4—22no—
573C2×C4—22no—
574C2×C4—22no—
575C2×C4—41no—
576C2×C4—41no—
577C2×C4—42no—
578C2×C4—42no—
579C2×C4—42no—
580C2×C4—42no—
581C2×C4—42no—
582C2×C4—41no—
583C2×C4—42no—
584C2×C4—41no—
585C2×C4—41no—
586C2×C4—41no—
587C2×C4—42no—
588C2×C4—41no—
589C2×C4—41no—
590C2×C4—42no—
591C2×C4—42no—
592C2×C4—41no—
593C2×C4—42no—
594C2×C4—41no—
595C2×C4—41no—
596C2×C4—42no—
597C2×C4—41no—
598C2×C4—42no—
599C2×C4—41no—
600C2×C4—41no—
601C2×C4—41no—
602C2×C4—41no—
603C2×C4—42no—
604C2×C4—42no—
605C2×C4—42no—
606C2×C4—42no—
607C2×C4—42no—
608C2×C4—42no—
609C2×C4—41no—
610C2×C4—41no—
611C2×C4—41no—
612C2×C4—41no—
613C2×C4—42no—
614C2×C4—42no—
615C2×C4—42no—
616C2×C4—42no—
617C2×C4—42no—
618C2×C4—42no—
619C2×C4—41no—
620C2×C4—41no—
621C2×C4—41no—
622C2×C4—41no—
623C2×C4—41no—
624C2×C4—41no—
625C2×C4—81no—
626C2×C4—81no—
627C2×C4—81no—
628C2×C4—81no—
629C2×C4—81no—
630C2×C4—81no—
631C2×C4—81no—
632C2×C4—81no—
633C2×C4—81no—
634C2×C4—81no—
635C2×C4—81no—
636C2×C4—81no—
637C2×C4—81no—
638C2×C4—81no—
639C2×C4—81no—
640C2×C4—81no—
641C2×C4—81no—
642C2×C4—81no—
643C2×C4—81no—
644C2×C4—81no—
645C2×C4—81no—
646C2×C4—81no—
647C2×C4—81no—
648C2×C4—81no—
649C2×C4—81no—
650C2×C4—81no—
651C2×C4—81no—
652C2×C4—81no—
653C2×C4—81no—
654C2×C4—81no—
655C2×C4#50114yescomplemented
656C2×C4C22×C22⋊C411yescharacteristic
657C2×C4C2×C4×Q811yescharacteristic
658C2×C4C2×C4×Q811yescharacteristic
659C2×C4C2×C4×Q811yescharacteristic
660C2×C4#51811yescharacteristic
661C2×C4#51911yescharacteristic
662C2×C4C2×C22⋊Q811yescharacteristic
663C2×C4C2×C22⋊Q811yescharacteristic
664C2×C4C2×#12411yescharacteristic
665C2×C4C2×C4⋊Q811yescharacteristic
666C2×C4#53311yescharacteristic
667C2×C4#53311yescharacteristic
668C2×C4#54211yescharacteristic
669C2×C4#54211yescharacteristic
670C2×C4#54411yescharacteristic
671C2×C4#54411yescharacteristic
672C2×C4#54611yescharacteristic
673C2×C4#54611yescharacteristic
674C2×C4#54811yescharacteristic
675C2×C4#54811yescharacteristic
676C2×C4D4×Q811yescharacteristic
677C2×C4D4×Q811yescharacteristic
678C2×C4#55411yescharacteristic
679C2×C4#55411yescharacteristic
680C2×C4#55511yescharacteristic
681C2×C4#55611yescharacteristic
682C2×C4#55711yescharacteristic
683C2×C4Q8211yescharacteristic
684C8—24no—
685C8—42no—
686C8—42no—
687C8#39118yescomplemented
688C22C4×C4⋊Q811yescharacteristic
689C22D4×C22⋊C411yescharacteristic
690C22#236511yescharacteristic
691C22#244011yescharacteristic
692C22#245211yescharacteristic
693C22#249111yescharacteristic
694C22#255111yescharacteristic
695C22C4×AGL(1,ℤ/8)11yescharacteristic
696C22C4×#13711yescharacteristic
697C22#294611yescharacteristic
698C22#294711yescharacteristic
699C22C2×#50111yescharacteristic
700C22#316211yescharacteristic
701C22#316311yescharacteristic
702C22#316411yescharacteristic
703C22#317111yescharacteristic
704C22#317211yescharacteristic
705C22#317811yescharacteristic
706C22#317911yescharacteristic
707C22#326511yescharacteristic
708C22#326611yescharacteristic
709C22#326811yescharacteristic
710C22#326911yescharacteristic
711C22#327411yescharacteristic
712C22#327511yescharacteristic
713C22#327511yescharacteristic
714C22#327611yescharacteristic
715C22#334411yescharacteristic
716C22#334511yescharacteristic
717C22#334711yescharacteristic
718C22#334911yescharacteristic
719C22#338511yescharacteristic
720C22#338611yescharacteristic
721C22#338811yescharacteristic
722C22#338811yescharacteristic
723C4—24no—
724C4—42no—
725C4—44no—
726C4—42no—
727C4—44no—
728C4—42no—
729C4—82no—
730C4—82no—
731C4—81no—
732C4—81no—
733C4—82no—
734C4—82no—
735C4—161no—
736C4—161no—
737C4C2×#39111yescharacteristic
738C4#233111yescharacteristic
739C4Q8×C22⋊C411yescharacteristic
740C4#236911yescharacteristic
741C4#243911yescharacteristic
742C4#245111yescharacteristic
743C4#249211yescharacteristic
744C4#255011yescharacteristic
745C2#1405311yescharacteristic
746C2C4×#50111yescharacteristic
747C2#2173011yescharacteristic
748C2#2244311yescharacteristic
749C2#2244411yescharacteristic
750C2#2316811yescharacteristic
751C2#2316911yescharacteristic
752C2#2606811yescharacteristic
753C2#2606911yescharacteristic
754C2#2648611yescharacteristic
755C2#2648711yescharacteristic
756C2#2779311yescharacteristic
757C2#2779411yescharacteristic
758C2#2881511yescharacteristic
759C2#2881611yescharacteristic
subgroupG/H
center, socle, prime radicalC24C22×D4
commutatorC22×C4C23×C4
Frattini, cosocleC23×C4C24
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24 ◁ C4×#95 ◁ G
LECSG ▷ C23×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
20. C2×#501C4semidirect
117. C2×#106Q8semidirect
126. C2×C4×C8Q8semidirect
168. #336Q8semidirect
655. C2×C4#501semidirect
687. C8#391semidirect

Maximal subgroups

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

subgroupindex
C22×#5012
C2×#19442
C2×C4×#1062
#140542
#140532
#113852
#113842
#112202
#112192
#109082
#109072
#108632
#108622
#106962