Finite Group Databasebeta

← #359222

Subgroups — #359222

Order 512.

1338 conjugacy classes of subgroups.

The subgroup lattice has 762 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2331C211yesmaximal, characteristic
2C2×#2058C211yesmaximal, characteristic
3C2×#1776C211yesmaximal, characteristic
4C2×C4×#106C211yesmaximal, characteristic
5#13783C211yesmaximal, characteristic
6#11384C211yesmaximal, characteristic
7#11328C211yesmaximal, characteristic
8#11327C211yesmaximal, characteristic
9#11325C211yesmaximal, characteristic
10#11220C211yesmaximal, characteristic
11#11220C211yesmaximal, characteristic
12#11208C211yesmaximal, characteristic
13#10703C211yesmaximal, characteristic
14C4×#340C211yesmaximal, characteristic
15#10694C211yesmaximal, characteristic
16C22×C4⋊Q8C2211yescharacteristic
17C22×#107C2211yescharacteristic
18C22×#106C2211yescharacteristic
19C22×#106C2211yescharacteristic
20C22×#106C2211yescharacteristic
21C22×#97C2211yescharacteristic
22C22×C4×C8C2211yescharacteristic
23#2331—24no—
24#2331—24no—
25C2×#391—21no—
26C2×#391—21no—
27C2×#389C2211yescharacteristic
28C2×#389C2211yescharacteristic
29C2×#389C2211yescharacteristic
30C2×#389C2211yescharacteristic
31C2×#387—21no—
32C2×#387—21no—
33C2×#382C2211yescharacteristic
34C2×C4×C4⋊C4C2211yescharacteristic
35C2×C4×C4⋊C4C2211yescharacteristic
36C2×C4×C4⋊C4C2211yescharacteristic
37C2×C4×C4⋊C4C2211yescharacteristic
38C2×#376C2211yescharacteristic
39#2058C418yescomplemented
40#1776—24no—
41C4×#106—24no—
42C2×#340C2211yescharacteristic
43C2×#340C2211yescharacteristic
44C2×#340C2211yescharacteristic
45C2×#340C2211yescharacteristic
46C2×#340C2211yescharacteristic
47C2×#340C2211yescharacteristic
48C2×#340C2211yescharacteristic
49C2×#340C2211yescharacteristic
50C2×#340C2211yescharacteristic
51C2×#340C2211yescharacteristic
52C2×#340C2211yescharacteristic
53C2×#340C2211yescharacteristic
54C2×#336C2211yescharacteristic
55C2×#336C2211yescharacteristic
56C2×#336C2211yescharacteristic
57C2×#336C2211yescharacteristic
58#1436—21no—
59#1436—21no—
60C4⋊#95—21no—
61C4⋊#95C2211yescharacteristic
62C4⋊#95C2211yescharacteristic
63#1434—21no—
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—22no—
73C2×C4⋊Q8—22no—
74C2×C4⋊Q8C2×C414yes—
75C22×C4⋊C4—21no—
76C22×C4⋊C4—21no—
77C22×C4⋊C4—21no—
78C22×C4⋊C4—21no—
79C22×C4⋊C4—21no—
80C22×C4⋊C4C2311yescharacteristic
81C22×C4⋊C4C2311yescharacteristic
82C22×C4⋊C4C2311yescharacteristic
83C22×C4⋊C4C2311yescharacteristic
84C22×C4⋊C4C2311yescharacteristic
85C22×C4⋊C4C2311yescharacteristic
86C22×C4⋊C4C2311yescharacteristic
87C22×C4⋊C4C2311yescharacteristic
88C22×C42—21no—
89C22×C42—21no—
90C22×C42—21no—
91C22×C42—21no—
92C22×C42C2311yescharacteristic
93C22×C42C2311yescharacteristic
94C22×C42C2311yescharacteristic
95C2×#107—22no—
96C2×#107—22no—
97C2×#107—22no—
98C2×#106—22no—
99C2×#106—22no—
100C2×#106—22no—
101C2×#106—22no—
102C2×#106—22no—
103C2×#106—22no—
104C2×#106—22no—
105C2×#106C2×C414yes—
106C2×#106C2×C414yes—
107C2×#97—22no—
108C2×#97—22no—
109C2×#97Q814yescomplemented
110C2×C4×C8—22no—
111C2×C4×C8—22no—
112C2×C4×C8Q814yescomplemented
113#391—28no—
114#391—28no—
115#389—22no—
116#389—22no—
117#389—22no—
118#389—22no—
119#389—22no—
120#389—22no—
121#389—22no—
122#389C2×C414yes—
123#387—28no—
124#387—28no—
125#382—22no—
126#382—22no—
127C4×C4⋊C4—22no—
128C4×C4⋊C4—22no—
129C4×C4⋊C4—22no—
130C4×C4⋊C4—22no—
131C4×C4⋊C4—22no—
132C4×C4⋊C4D414yes—
133C4×C4⋊C4D414yes—
134C4×C4⋊C4Q814yescomplemented
135#376—22no—
136#376—22no—
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×#95D411yescharacteristic
152C2×#95D411yescharacteristic
153C2×#95D411yescharacteristic
154C2×#95D411yescharacteristic
155#340—22no—
156#340—22no—
157#340—22no—
158#340—22no—
159#340—22no—
160#340—22no—
161#340—22no—
162#340—22no—
163#340—22no—
164#340—22no—
165#340C2×C414yes—
166#340C2×C414yes—
167#336—22no—
168#336—22no—
169#336—22no—
170#336C2×C414yes—
171C22×Q8—24no—
172C22×Q8—24no—
173C22×Q8—24no—
174C22×Q8—81no—
175C22×Q8—81no—
176C22×Q8—81no—
177C22×Q8—81no—
178C23×C4—21no—
179C23×C4—21no—
180C23×C4—21no—
181C23×C4—21no—
182C23×C4—21no—
183C23×C4—21no—
184C23×C4—21no—
185C23×C4—21no—
186C23×C4C2×D411yescharacteristic
187C23×C4C2×D411yescharacteristic
188C23×C4C2×D411yescharacteristic
189C23×C4C2×D411yescharacteristic
190C23×C4C2×D411yescharacteristic
191C23×C4C2×D411yescharacteristic
192C23×C4C2411yescharacteristic
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×C8—21no—
208C22×C8—21no—
209C22×C8—21no—
210C22×C8—21no—
211C22×C8—21no—
212C22×C8—21no—
213C22×C8C22×C412yes—
214C22×C8C22×C412yes—
215C22×C8C2×Q812yes—
216C22×C8C2×Q812yes—
217C22×C8C2×Q812yes—
218C22×C8C2×Q812yes—
219C22×C8#4112yes—
220C22×C8#4112yes—
221C4⋊Q8—28no—
222C4⋊Q8—28no—
223C4⋊Q8—28no—
224C4⋊Q8—28no—
225C2×C4⋊C4—24no—
226C2×C4⋊C4—24no—
227C2×C4⋊C4—24no—
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—21no—
250C2×C4⋊C4—21no—
251C2×C4⋊C4—21no—
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—24no—
263C2×C4⋊C4—24no—
264C2×C4⋊C4—24no—
265C2×C4⋊C4—24no—
266C2×C4⋊C4—81no—
267C2×C4⋊C4—81no—
268C2×C4⋊C4—81no—
269C2×C4⋊C4—81no—
270C2×C4⋊C4—81no—
271C2×C4⋊C4—81no—
272C2×C4⋊C4—81no—
273C2×C4⋊C4—81no—
274C2×C4⋊C4C22×C412yes—
275C2×C4⋊C4C22×C412yes—
276C2×C4⋊C4C22×C412yes—
277C2×C4⋊C4C22×C412yes—
278C2×C4⋊C4C2×D412yes—
279C2×C4⋊C4C2×D412yes—
280C2×C4⋊C4C2×D412yes—
281C2×C4⋊C4C2×D412yes—
282C2×C4⋊C4C2×Q812yes—
283C2×C4⋊C4C2×Q812yes—
284C2×C4⋊C4#4112yes—
285C2×C4⋊C4#4112yes—
286C2×C4⋊C4#4112yes—
287C2×C4⋊C4#4112yes—
288C2×C42—21no—
289C2×C42—21no—
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—24no—
299C2×C42—24no—
300C2×C42—24no—
301C2×C42—42no—
302C2×C42—81no—
303C2×C42—81no—
304C2×C42—81no—
305C2×C42—81no—
306C2×C42—81no—
307C2×C42—81no—
308C2×C42—81no—
309C2×C42—81no—
310C2×C42C22×C412yes—
311C2×C42C2×D412yes—
312C2×C42C2×D412yes—
313C2×C42C2×Q812yes—
314C2×C42C2×Q812yes—
315C2×C42C2×Q812yes—
316C2×C42#4112yes—
317C2×C42#4112yes—
318#107—28no—
319#106—28no—
320#106—28no—
321#106—28no—
322#97—28no—
323C4×C8—28no—
324#95—24no—
325#95—24no—
326#95—24no—
327#95—24no—
328#95—24no—
329#95—24no—
330#95—24no—
331#95—24no—
332#95—22no—
333#95—22no—
334#95—22no—
335#95—22no—
336#95—24no—
337#95—42no—
338#95—81no—
339#95—81no—
340#95—81no—
341#95—81no—
342C24C22×D411yescharacteristic
343C2×Q8—216no—
344C2×Q8—84no—
345C2×Q8—84no—
346C2×Q8—84no—
347C2×Q8—84no—
348C2×Q8—84no—
349C2×Q8—84no—
350C22×C4—21no—
351C22×C4—21no—
352C22×C4—21no—
353C22×C4—21no—
354C22×C4—21no—
355C22×C4—21no—
356C22×C4—21no—
357C22×C4—21no—
358C22×C4—22no—
359C22×C4—22no—
360C22×C4—22no—
361C22×C4—21no—
362C22×C4—21no—
363C22×C4—22no—
364C22×C4—22no—
365C22×C4—22no—
366C22×C4—22no—
367C22×C4—21no—
368C22×C4—21no—
369C22×C4—22no—
370C22×C4—22no—
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—21no—
381C22×C4—21no—
382C22×C4—22no—
383C22×C4—22no—
384C22×C4—22no—
385C22×C4—21no—
386C22×C4—22no—
387C22×C4—21no—
388C22×C4—21no—
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—21no—
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×C4C4×D412yes—
441C22×C4C4×D412yes—
442C22×C4#12012yes—
443C22×C4#12012yes—
444C22×C4C22⋊Q812yes—
445C22×C4C22⋊Q812yes—
446C22×C4C4⋊Q812yes—
447C22×C4C4⋊Q812yes—
448C22×C4C23×C411yescharacteristic
449C22×C4C22×D411yescharacteristic
450C22×C4C22×D411yescharacteristic
451C22×C4C22×Q811yescharacteristic
452C22×C4C22×Q811yescharacteristic
453C22×C4C22×Q811yescharacteristic
454C22×C4C2×#4111yescharacteristic
455C22×C4C2×#4111yescharacteristic
456C22×C4C2×#4111yescharacteristic
457C22×C4C2×#4111yescharacteristic
458C22×C4C2×#4111yescharacteristic
459C22×C4C2×#4111yescharacteristic
460C22×C4C2×#4111yescharacteristic
461C22×C4C2×#4111yescharacteristic
462C2×C8—22no—
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—22no—
476C2×C8—22no—
477C2×C8—22no—
478C2×C8—22no—
479C2×C8—22no—
480C2×C8—41no—
481C2×C8—41no—
482C2×C8—41no—
483C2×C8—41no—
484C2×C8—41no—
485C2×C8—41no—
486C2×C8—41no—
487C2×C8—41no—
488C2×C8C4×Q814yes—
489C2×C8C4×Q814yes—
490C4⋊C4—216no—
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—22no—
506C4⋊C4—22no—
507C4⋊C4—22no—
508C4⋊C4—22no—
509C4⋊C4—22no—
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—84no—
521C4⋊C4—84no—
522C4⋊C4—84no—
523C4⋊C4—84no—
524C4⋊C4C4×D414yes—
525C4⋊C4C4×D414yes—
526C4⋊C4C4×Q814yes—
527C42—22no—
528C42—22no—
529C42—22no—
530C42—22no—
531C42—41no—
532C42—41no—
533C42—41no—
534C42—41no—
535C42—84no—
536C42—84no—
537C42—84no—
538C42—84no—
539C42C22⋊Q814yes—
540C42C22⋊Q814yes—
541C42C4⋊Q814yes—
542C42C4⋊Q814yes—
543C23C2×C4×D411yescharacteristic
544C23C2×#12011yescharacteristic
545C23C2×C22⋊Q811yescharacteristic
546C23#52511yescharacteristic
547C23#52511yescharacteristic
548C23C2×C4⋊Q811yescharacteristic
549C23#53211yescharacteristic
550C23#57611yescharacteristic
551C23#57711yescharacteristic
552C23#57711yescharacteristic
553C23#57711yescharacteristic
554C23#57711yescharacteristic
555C23#57711yescharacteristic
556C23#57711yescharacteristic
557C23#57811yescharacteristic
558Q8—816no—
559C2×C4—22no—
560C2×C4—22no—
561C2×C4—22no—
562C2×C4—22no—
563C2×C4—22no—
564C2×C4—22no—
565C2×C4—22no—
566C2×C4—22no—
567C2×C4—22no—
568C2×C4—22no—
569C2×C4—22no—
570C2×C4—22no—
571C2×C4—22no—
572C2×C4—22no—
573C2×C4—22no—
574C2×C4—22no—
575C2×C4—22no—
576C2×C4—22no—
577C2×C4—24no—
578C2×C4—24no—
579C2×C4—24no—
580C2×C4—42no—
581C2×C4—42no—
582C2×C4—42no—
583C2×C4—41no—
584C2×C4—42no—
585C2×C4—42no—
586C2×C4—41no—
587C2×C4—41no—
588C2×C4—42no—
589C2×C4—42no—
590C2×C4—42no—
591C2×C4—41no—
592C2×C4—42no—
593C2×C4—42no—
594C2×C4—42no—
595C2×C4—42no—
596C2×C4—42no—
597C2×C4—42no—
598C2×C4—42no—
599C2×C4—42no—
600C2×C4—41no—
601C2×C4—41no—
602C2×C4—42no—
603C2×C4—42no—
604C2×C4—41no—
605C2×C4—41no—
606C2×C4—42no—
607C2×C4—42no—
608C2×C4—41no—
609C2×C4—42no—
610C2×C4—41no—
611C2×C4—41no—
612C2×C4—41no—
613C2×C4—42no—
614C2×C4—41no—
615C2×C4—41no—
616C2×C4—42no—
617C2×C4—42no—
618C2×C4—42no—
619C2×C4—42no—
620C2×C4—41no—
621C2×C4—41no—
622C2×C4—41no—
623C2×C4—41no—
624C2×C4—42no—
625C2×C4—42no—
626C2×C4—42no—
627C2×C4—41no—
628C2×C4—41no—
629C2×C4—42no—
630C2×C4—42no—
631C2×C4—41no—
632C2×C4—41no—
633C2×C4—42no—
634C2×C4—42no—
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#39514yes—
656C2×C4#39514yes—
657C2×C4C2×C4×D411yescharacteristic
658C2×C4C2×C4×D411yescharacteristic
659C2×C4C2×C4×Q811yescharacteristic
660C2×C4C2×C4×Q811yescharacteristic
661C2×C4C2×C4×Q811yescharacteristic
662C2×C4C4×#4111yescharacteristic
663C2×C4C2×C22⋊Q811yescharacteristic
664C2×C4C2×C22⋊Q811yescharacteristic
665C2×C4#52511yescharacteristic
666C2×C4#52511yescharacteristic
667C2×C4#52511yescharacteristic
668C2×C4#52511yescharacteristic
669C2×C4#52911yescharacteristic
670C2×C4#52911yescharacteristic
671C2×C4#52911yescharacteristic
672C2×C4C2×C4⋊Q811yescharacteristic
673C2×C4C2×C4⋊Q811yescharacteristic
674C2×C4#53211yescharacteristic
675C2×C4#53211yescharacteristic
676C2×C4#53311yescharacteristic
677C2×C4#53311yescharacteristic
678C2×C4#53311yescharacteristic
679C2×C4#53311yescharacteristic
680C2×C4#53311yescharacteristic
681C2×C4#53311yescharacteristic
682C2×C4#53311yescharacteristic
683C2×C4#53311yescharacteristic
684C2×C4#53311yescharacteristic
685C8—24no—
686C8—24no—
687C8—42no—
688C8—42no—
689C22C4×#12011yescharacteristic
690C22C4×C22⋊Q811yescharacteristic
691C22C4×C4⋊Q811yescharacteristic
692C22C2×#39511yescharacteristic
693C22#238811yescharacteristic
694C22#239611yescharacteristic
695C22#239911yescharacteristic
696C22#294611yescharacteristic
697C22#294711yescharacteristic
698C22#294911yescharacteristic
699C22#294911yescharacteristic
700C22#300911yescharacteristic
701C22#301011yescharacteristic
702C22#301211yescharacteristic
703C22#301311yescharacteristic
704C22#308111yescharacteristic
705C22#308211yescharacteristic
706C22#308411yescharacteristic
707C22#308411yescharacteristic
708C22#311811yescharacteristic
709C22#311811yescharacteristic
710C22#312111yescharacteristic
711C22#312111yescharacteristic
712C22#312311yescharacteristic
713C22#312511yescharacteristic
714C22#312511yescharacteristic
715C22#312611yescharacteristic
716C22#316311yescharacteristic
717C22#316311yescharacteristic
718C22#316311yescharacteristic
719C22#316411yescharacteristic
720C22#317311yescharacteristic
721C22#317311yescharacteristic
722C22#317811yescharacteristic
723C22#317911yescharacteristic
724C4—24no—
725C4—24no—
726C4—44no—
727C4—42no—
728C4—44no—
729C4—44no—
730C4—42no—
731C4—81no—
732C4—82no—
733C4—81no—
734C4—82no—
735C4—82no—
736C4—82no—
737C4—82no—
738C4C4×C22⋊Q811yescharacteristic
739C4C4×C22⋊Q811yescharacteristic
740C4C4×C4⋊Q811yescharacteristic
741C4C4×C4⋊Q811yescharacteristic
742C4#239611yescharacteristic
743C4#239611yescharacteristic
744C4#239911yescharacteristic
745C4#239911yescharacteristic
746C2C4×#39511yescharacteristic
747C2#2145911yescharacteristic
748C2#2146211yescharacteristic
749C2#2162311yescharacteristic
750C2#2162611yescharacteristic
751C2#2172411yescharacteristic
752C2#2173011yescharacteristic
753C2#2355611yescharacteristic
754C2#2355711yescharacteristic
755C2#2358111yescharacteristic
756C2#2358311yescharacteristic
757C2#2378611yescharacteristic
758C2#2378911yescharacteristic
759C2#2384211yescharacteristic
760C2#2384511yescharacteristic
subgroupG/H
center, socle, prime radicalC24C22×D4
commutatorC22×C4C23×C4
Frattini, cosocleC23×C4C24
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24 ◁ C2×#376 ◁ G
LECSG ▷ C23×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
39. #2058C4semidirect
109. C2×#97Q8semidirect
112. C2×C4×C8Q8semidirect
134. C4×C4⋊C4Q8semidirect

Maximal subgroups

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

subgroupindex
C2×#23312
C2×#20582
C2×#17762
C2×C4×#1062
#137832
#113842
#113282
#113272
#113252
#112202
#112082
#107032
C4×#3402
#106942