Finite Group Databasebeta

← #380342

Subgroups — #380342

Order 512.

1308 conjugacy classes of subgroups.

The subgroup lattice has 800 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2295C211yesmaximal, characteristic
2C2×#1949C211yesmaximal, characteristic
3C2×#1805C211yesmaximal, characteristic
4C2×#1805C211yesmaximal, characteristic
5#14707C211yesmaximal, characteristic
6#11328C211yesmaximal, characteristic
7#11327C211yesmaximal, characteristic
8#11293C211yesmaximal, characteristic
9#11292C211yesmaximal, characteristic
10#11124C211yesmaximal, characteristic
11#11122C211yesmaximal, characteristic
12#11067C211yesmaximal, characteristic
13#11067C211yesmaximal, characteristic
14#10850C211yesmaximal, characteristic
15#10832C211yesmaximal, characteristic
16C22×C4×Q8C2211yescharacteristic
17C22×#107C2211yescharacteristic
18C22×#106C2211yescharacteristic
19C22×C4⋊C8C2211yescharacteristic
20C22×C4⋊C8C2211yescharacteristic
21C22×#103C2211yescharacteristic
22C22×#103C2211yescharacteristic
23C22×#103C2211yescharacteristic
24C22×#103C2211yescharacteristic
25#2295—24no—
26#2295—24no—
27C2×#391C2211yescharacteristic
28C2×#391C2211yescharacteristic
29C2×#389C2211yescharacteristic
30C2×#389C2211yescharacteristic
31C2×#389C2211yescharacteristic
32C2×#389C2211yescharacteristic
33C2×#387—21no—
34C2×#387—21no—
35C2×#382C2211yescharacteristic
36C2×#382C2211yescharacteristic
37C2×C4×C4⋊C4—21no—
38C2×C4×C4⋊C4C2211yescharacteristic
39C2×#376—21no—
40C2×C43C2211yescharacteristic
41#1949—24no—
42#1805—24no—
43#1805C418yescomplemented
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—
60#1436—21no—
61#1436—21no—
62C4⋊#95C2211yescharacteristic
63C4⋊#95C2211yescharacteristic
64C23×Q8C2311yescharacteristic
65C23×C8C2311yescharacteristic
66C23×C8C2311yescharacteristic
67C23×C8C2311yescharacteristic
68C23×C8C2311yescharacteristic
69C2×C4×Q8—22no—
70C2×C4×Q8—22no—
71C2×C4×Q8—22no—
72C2×C4×Q8C2×C414yes—
73C2×C4×Q8D414yes—
74C2×C4×Q8Q814yes—
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×C42—21no—
88C22×C42—21no—
89C22×C42D411yescharacteristic
90C22×C42D411yescharacteristic
91C22×C42D411yescharacteristic
92C22×C42D411yescharacteristic
93C22×C42C2311yescharacteristic
94C22×C42C2311yescharacteristic
95C22×C42C2311yescharacteristic
96C2×#107—22no—
97C2×#107—41no—
98C2×#107—41no—
99C2×#106—22no—
100C2×#106—41no—
101C2×#106—41no—
102C2×C4⋊C8—22no—
103C2×C4⋊C8—22no—
104C2×C4⋊C8—22no—
105C2×C4⋊C8—22no—
106C2×C4⋊C8—22no—
107C2×C4⋊C8C2×C414yes—
108C2×#103—22no—
109C2×#103—22no—
110C2×#103—41no—
111C2×#103—41no—
112C2×#103—41no—
113C2×#103—41no—
114C2×#103—41no—
115C2×#103—41no—
116C2×#103—41no—
117C2×#103—41no—
118C2×#103C2×C414yes—
119C2×#103C2×C414yes—
120#391—22no—
121#391—22no—
122#391—22no—
123#391—22no—
124#389—22no—
125#389—22no—
126#389—22no—
127#389—22no—
128#389—41no—
129#389—41no—
130#389—41no—
131#389—41no—
132#387—28no—
133#387—28no—
134#382—22no—
135#382—22no—
136#382—22no—
137#382C2×C414yes—
138C4×C4⋊C4—28no—
139C4×C4⋊C4—22no—
140C4×C4⋊C4D414yes—
141#376—28no—
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×#95—21no—
153C2×#95—21no—
154C2×#95—21no—
155C2×#95—21no—
156C2×#95—21no—
157C2×#95—21no—
158C2×#95—21no—
159C43—22no—
160C43—22no—
161#340—22no—
162#340—22no—
163#340—22no—
164#340—22no—
165#340—41no—
166#340—41no—
167#340—41no—
168#340—41no—
169#340C2×C414yes—
170#340C2×C414yes—
171#336—41no—
172#336—41no—
173#336—41no—
174#336—41no—
175C22×Q8—21no—
176C22×Q8—21no—
177C22×Q8—21no—
178C22×Q8—21no—
179C22×Q8—21no—
180C22×Q8—21no—
181C22×Q8—21no—
182C22×Q8—21no—
183C22×Q8—21no—
184C22×Q8—21no—
185C22×Q8—21no—
186C22×Q8C22×C412yes—
187C22×Q8C2×D412yes—
188C22×Q8C2×Q812yes—
189C23×C4—21no—
190C23×C4—21no—
191C23×C4—21no—
192C23×C4—21no—
193C23×C4—21no—
194C23×C4—21no—
195C23×C4—21no—
196C23×C4—21no—
197C23×C4C2×D411yescharacteristic
198C23×C4C2×D411yescharacteristic
199C23×C4C2×D411yescharacteristic
200C23×C4C2×D411yescharacteristic
201C23×C4C2×D411yescharacteristic
202C23×C4C2×D411yescharacteristic
203C23×C4C2411yescharacteristic
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×C8—21no—
214C22×C8—21no—
215C22×C8—21no—
216C22×C8—21no—
217C22×C8—21no—
218C22×C8—21no—
219C22×C8—21no—
220C22×C8—21no—
221C22×C8—21no—
222C22×C8—21no—
223C22×C8—21no—
224C22×C8—21no—
225C22×C8—21no—
226C22×C8—21no—
227C22×C8—21no—
228C22×C8—21no—
229C22×C8—21no—
230C22×C8C22×C412yes—
231C22×C8C22×C412yes—
232C4×Q8—28no—
233C4×Q8—28no—
234C4×Q8—28no—
235C4×Q8C4⋊C4116yescomplemented
236C2×C4⋊C4—24no—
237C2×C4⋊C4—24no—
238C2×C4⋊C4—24no—
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—24no—
259C2×C4⋊C4—24no—
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—21no—
269C2×C4⋊C4—21no—
270C2×C4⋊C4—21no—
271C2×C4⋊C4—21no—
272C2×C4⋊C4—21no—
273C2×C4⋊C4—21no—
274C2×C4⋊C4—21no—
275C2×C4⋊C4—21no—
276C2×C4⋊C4—42no—
277C2×C4⋊C4—42no—
278C2×C4⋊C4—42no—
279C2×C4⋊C4—42no—
280C2×C4⋊C4—42no—
281C2×C4⋊C4—42no—
282C2×C4⋊C4—42no—
283C2×C4⋊C4—42no—
284C2×C4⋊C4—42no—
285C2×C4⋊C4—42no—
286C2×C4⋊C4C22×C412yes—
287C2×C4⋊C4C22×C412yes—
288C2×C4⋊C4C22×C412yes—
289C2×C4⋊C4C2×D412yes—
290C2×C4⋊C4C2×D412yes—
291C2×C4⋊C4C2×D412yes—
292C2×C4⋊C4C2×Q812yes—
293C2×C42—24no—
294C2×C42—24no—
295C2×C42—22no—
296C2×C42—24no—
297C2×C42—22no—
298C2×C42—22no—
299C2×C42—22no—
300C2×C42—22no—
301C2×C42—22no—
302C2×C42—24no—
303C2×C42—22no—
304C2×C42—22no—
305C2×C42—21no—
306C2×C42—21no—
307C2×C42—21no—
308C2×C42—21no—
309C2×C42—21no—
310C2×C42—21no—
311C2×C42—21no—
312C2×C42—21no—
313C2×C42—21no—
314C2×C42—21no—
315C2×C42—21no—
316C2×C42—21no—
317C2×C42—41no—
318C2×C42—41no—
319C2×C42—41no—
320C2×C42—41no—
321C2×C42—42no—
322C2×C42—42no—
323C2×C42C22×C412yes—
324C2×C42C2×D412yes—
325C2×C42C2×D412yes—
326C2×C42C2×Q812yes—
327C2×C42#4112yes—
328C2×C42#4112yes—
329#107—44no—
330#106—44no—
331C4⋊C8—28no—
332C4⋊C8—44no—
333#103—44no—
334#103—44no—
335#103—44no—
336#103—44no—
337#95—24no—
338#95—24no—
339#95—24no—
340#95—24no—
341#95—24no—
342#95—24no—
343#95—24no—
344#95—24no—
345#95—24no—
346#95—42no—
347#95—42no—
348#95—42no—
349#95—42no—
350#95—42no—
351#95—42no—
352#95—42no—
353#95—42no—
354C24C22×D411yescharacteristic
355C2×Q8—22no—
356C2×Q8—22no—
357C2×Q8—22no—
358C2×Q8—22no—
359C2×Q8—22no—
360C2×Q8—22no—
361C2×Q8—22no—
362C2×Q8—22no—
363C2×Q8—22no—
364C2×Q8—22no—
365C2×Q8—22no—
366C2×Q8—22no—
367C2×Q8—22no—
368C2×Q8—22no—
369C2×Q8—22no—
370C2×Q8—41no—
371C2×Q8—41no—
372C2×Q8—41no—
373C2×Q8—41no—
374C2×Q8—41no—
375C2×Q8—41no—
376C2×Q8—41no—
377C2×Q8—41no—
378C2×Q8—41no—
379C2×Q8—41no—
380C2×Q8—41no—
381C2×Q8—41no—
382C2×Q8C2×C4⋊C414yes—
383C22×C4—21no—
384C22×C4—21no—
385C22×C4—21no—
386C22×C4—21no—
387C22×C4—21no—
388C22×C4—21no—
389C22×C4—21no—
390C22×C4—21no—
391C22×C4—22no—
392C22×C4—22no—
393C22×C4—21no—
394C22×C4—21no—
395C22×C4—22no—
396C22×C4—21no—
397C22×C4—21no—
398C22×C4—22no—
399C22×C4—22no—
400C22×C4—22no—
401C22×C4—21no—
402C22×C4—21no—
403C22×C4—21no—
404C22×C4—21no—
405C22×C4—21no—
406C22×C4—21no—
407C22×C4—21no—
408C22×C4—21no—
409C22×C4—21no—
410C22×C4—21no—
411C22×C4—21no—
412C22×C4—21no—
413C22×C4—21no—
414C22×C4—21no—
415C22×C4—21no—
416C22×C4—21no—
417C22×C4—21no—
418C22×C4—21no—
419C22×C4—21no—
420C22×C4—21no—
421C22×C4—22no—
422C22×C4—22no—
423C22×C4—22no—
424C22×C4—22no—
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×C4—41no—
444C22×C4—41no—
445C22×C4—41no—
446C22×C4—41no—
447C22×C4—41no—
448C22×C4—41no—
449C22×C4—41no—
450C22×C4—41no—
451C22×C4—41no—
452C22×C4—41no—
453C22×C4—41no—
454C22×C4—41no—
455C22×C4—41no—
456C22×C4—41no—
457C22×C4—41no—
458C22×C4—41no—
459C22×C4—41no—
460C22×C4—41no—
461C22×C4—41no—
462C22×C4—41no—
463C22×C4—41no—
464C22×C4—41no—
465C22×C4—41no—
466C22×C4—41no—
467C22×C4—41no—
468C22×C4—41no—
469C22×C4—41no—
470C22×C4—41no—
471C22×C4C4×D412yes—
472C22×C4C4×D412yes—
473C22×C4#12012yes—
474C22×C4#12012yes—
475C22×C4C22⋊Q812yes—
476C22×C4C22⋊Q812yes—
477C22×C4#13512yes—
478C22×C4#13512yes—
479C22×C4#13712yes—
480C22×C4#13712yes—
481C22×C4C23×C411yescharacteristic
482C22×C4C22×D411yescharacteristic
483C22×C4C22×D411yescharacteristic
484C22×C4C22×Q811yescharacteristic
485C22×C4C2×#4111yescharacteristic
486C22×C4C2×#4111yescharacteristic
487C22×C4H(5,𝔽2)11yescharacteristic
488C22×C4H(5,𝔽2)11yescharacteristic
489C22×C4H(5,𝔽2)11yescharacteristic
490C22×C4H(5,𝔽2)11yescharacteristic
491C22×C42−1+411yescharacteristic
492C22×C42−1+411yescharacteristic
493C22×C42−1+411yescharacteristic
494C22×C42−1+411yescharacteristic
495C2×C8—22no—
496C2×C8—22no—
497C2×C8—22no—
498C2×C8—22no—
499C2×C8—22no—
500C2×C8—22no—
501C2×C8—41no—
502C2×C8—41no—
503C2×C8—41no—
504C2×C8—41no—
505C2×C8—41no—
506C2×C8—41no—
507C2×C8—41no—
508C2×C8—41no—
509C2×C8—41no—
510C2×C8—41no—
511C2×C8—41no—
512C2×C8—41no—
513C2×C8—41no—
514C2×C8—41no—
515C2×C8—41no—
516C2×C8—41no—
517C2×C8—41no—
518C2×C8—41no—
519C2×C8—41no—
520C2×C8—41no—
521C2×C8—41no—
522C2×C8—41no—
523C4⋊C4—22no—
524C4⋊C4—22no—
525C4⋊C4—22no—
526C4⋊C4—216no—
527C4⋊C4—22no—
528C4⋊C4—22no—
529C4⋊C4—22no—
530C4⋊C4—22no—
531C4⋊C4—22no—
532C4⋊C4—22no—
533C4⋊C4—22no—
534C4⋊C4—22no—
535C4⋊C4—48no—
536C4⋊C4—48no—
537C4⋊C4—41no—
538C4⋊C4—41no—
539C4⋊C4—41no—
540C4⋊C4—41no—
541C4⋊C4—41no—
542C4⋊C4—41no—
543C4⋊C4—41no—
544C4⋊C4—41no—
545C4⋊C4—41no—
546C4⋊C4—41no—
547C4⋊C4—41no—
548C4⋊C4—41no—
549C4⋊C4—41no—
550C4⋊C4—41no—
551C4⋊C4—41no—
552C4⋊C4—41no—
553C4⋊C4—84no—
554C4⋊C4—84no—
555C4⋊C4C2×C4⋊C414yes—
556C42—28no—
557C42—216no—
558C42—44no—
559C42—44no—
560C42—44no—
561C42—48no—
562C42—41no—
563C42—41no—
564C42—41no—
565C42—41no—
566C42—41no—
567C42—41no—
568C42—41no—
569C42—41no—
570C42C2×C4⋊C414yes—
571C42C4×D414yes—
572C42C22⋊Q814yes—
573C42#12314yes—
574C23C2×C4×D411yescharacteristic
575C23C2×#12011yescharacteristic
576C23C2×C22⋊Q811yescharacteristic
577C23#53511yescharacteristic
578C23#53611yescharacteristic
579C23#53711yescharacteristic
580C23#53711yescharacteristic
581C23C2×#13511yescharacteristic
582C23C2×#13511yescharacteristic
583C23C2×#13711yescharacteristic
584C23C2×#13711yescharacteristic
585C23#57511yescharacteristic
586C23#57511yescharacteristic
587C23#57511yescharacteristic
588C23#57511yescharacteristic
589Q8—24no—
590Q8—24no—
591Q8—42no—
592Q8—42no—
593Q8—42no—
594Q8—42no—
595Q8—42no—
596Q8—42no—
597C2×C4—22no—
598C2×C4—22no—
599C2×C4—22no—
600C2×C4—22no—
601C2×C4—22no—
602C2×C4—22no—
603C2×C4—22no—
604C2×C4—22no—
605C2×C4—22no—
606C2×C4—22no—
607C2×C4—22no—
608C2×C4—22no—
609C2×C4—22no—
610C2×C4—22no—
611C2×C4—22no—
612C2×C4—22no—
613C2×C4—22no—
614C2×C4—22no—
615C2×C4—22no—
616C2×C4—22no—
617C2×C4—22no—
618C2×C4—22no—
619C2×C4—22no—
620C2×C4—22no—
621C2×C4—24no—
622C2×C4—24no—
623C2×C4—42no—
624C2×C4—42no—
625C2×C4—42no—
626C2×C4—42no—
627C2×C4—41no—
628C2×C4—41no—
629C2×C4—42no—
630C2×C4—41no—
631C2×C4—41no—
632C2×C4—42no—
633C2×C4—42no—
634C2×C4—42no—
635C2×C4—42no—
636C2×C4—42no—
637C2×C4—41no—
638C2×C4—41no—
639C2×C4—41no—
640C2×C4—41no—
641C2×C4—41no—
642C2×C4—41no—
643C2×C4—41no—
644C2×C4—41no—
645C2×C4—41no—
646C2×C4—41no—
647C2×C4—42no—
648C2×C4—42no—
649C2×C4—41no—
650C2×C4—41no—
651C2×C4—42no—
652C2×C4—42no—
653C2×C4—42no—
654C2×C4—42no—
655C2×C4—42no—
656C2×C4—42no—
657C2×C4—42no—
658C2×C4—42no—
659C2×C4—42no—
660C2×C4—42no—
661C2×C4—42no—
662C2×C4—42no—
663C2×C4—81no—
664C2×C4—81no—
665C2×C4—81no—
666C2×C4—81no—
667C2×C4—81no—
668C2×C4—81no—
669C2×C4—81no—
670C2×C4—81no—
671C2×C4—81no—
672C2×C4—81no—
673C2×C4—81no—
674C2×C4—81no—
675C2×C4—81no—
676C2×C4—81no—
677C2×C4—81no—
678C2×C4—81no—
679C2×C4—81no—
680C2×C4—81no—
681C2×C4—81no—
682C2×C4—81no—
683C2×C4—81no—
684C2×C4—81no—
685C2×C4—81no—
686C2×C4—81no—
687C2×C4—81no—
688C2×C4—81no—
689C2×C4—81no—
690C2×C4—81no—
691C2×C4—81no—
692C2×C4—81no—
693C2×C4#38514yes—
694C2×C4#38514yes—
695C2×C4C22×C4⋊C411yescharacteristic
696C2×C4C2×C4×D411yescharacteristic
697C2×C4#51811yescharacteristic
698C2×C4#51911yescharacteristic
699C2×C4#52011yescharacteristic
700C2×C4#52011yescharacteristic
701C2×C4C2×C22⋊Q811yescharacteristic
702C2×C4C2×#12311yescharacteristic
703C2×C4#53511yescharacteristic
704C2×C4#53511yescharacteristic
705C2×C4#53611yescharacteristic
706C2×C4#53611yescharacteristic
707C2×C4#53711yescharacteristic
708C2×C4#53711yescharacteristic
709C2×C4#53711yescharacteristic
710C2×C4#53711yescharacteristic
711C2×C4#54011yescharacteristic
712C2×C4#54011yescharacteristic
713C2×C4#54111yescharacteristic
714C2×C4#54111yescharacteristic
715C2×C4#54211yescharacteristic
716C2×C4#54211yescharacteristic
717C2×C4#54211yescharacteristic
718C2×C4#54211yescharacteristic
719C2×C4#54411yescharacteristic
720C2×C4#54411yescharacteristic
721C2×C4#54411yescharacteristic
722C2×C4#54411yescharacteristic
723C8—42no—
724C8—42no—
725C8—81no—
726C8—81no—
727C22C2×#38511yescharacteristic
728C22#232311yescharacteristic
729C22#232411yescharacteristic
730C22#261511yescharacteristic
731C22#261611yescharacteristic
732C22#262811yescharacteristic
733C22#262911yescharacteristic
734C22C4×#13511yescharacteristic
735C22#294311yescharacteristic
736C22C4×#13711yescharacteristic
737C22C4×#13711yescharacteristic
738C22#300211yescharacteristic
739C22#300211yescharacteristic
740C22#300411yescharacteristic
741C22#300511yescharacteristic
742C22#307611yescharacteristic
743C22#307611yescharacteristic
744C22#307811yescharacteristic
745C22#307811yescharacteristic
746C22#321011yescharacteristic
747C22#321111yescharacteristic
748C22#321511yescharacteristic
749C22#321911yescharacteristic
750C22#323111yescharacteristic
751C22#323211yescharacteristic
752C22#323611yescharacteristic
753C22#324011yescharacteristic
754C22#324811yescharacteristic
755C22#324811yescharacteristic
756C22#325011yescharacteristic
757C22#325011yescharacteristic
758C22#325211yescharacteristic
759C22#325211yescharacteristic
760C22#325611yescharacteristic
761C22#325611yescharacteristic
762C4—24no—
763C4—24no—
764C4—44no—
765C4—44no—
766C4—42no—
767C4—42no—
768C4—42no—
769C4—42no—
770C4—82no—
771C4—82no—
772C4—82no—
773C4—82no—
774C4—161no—
775C4—161no—
776C4#231611yescharacteristic
777C4#231711yescharacteristic
778C4#232311yescharacteristic
779C4#232411yescharacteristic
780C4#262411yescharacteristic
781C4#262511yescharacteristic
782C4#262811yescharacteristic
783C4#262911yescharacteristic
784C2#1426411yescharacteristic
785C2#2087211yescharacteristic
786C2#2087411yescharacteristic
787C2#2211511yescharacteristic
788C2#2212111yescharacteristic
789C2#2215011yescharacteristic
790C2#2215611yescharacteristic
791C2#2966611yescharacteristic
792C2#2966811yescharacteristic
793C2#2969311yescharacteristic
794C2#2969511yescharacteristic
795C2#2998511yescharacteristic
796C2#2998911yescharacteristic
797C2#3000111yescharacteristic
798C2#3000111yescharacteristic
subgroupG/H
center, socle, prime radicalC24C22×D4
commutatorC22×C4C23×C4
Frattini, cosocleC23×C4C24
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24 ◁ C2×C43 ◁ G
LECSG ▷ C23×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
43. #1805C4semidirect
235. C4×Q8C4⋊C4semidirect

Maximal subgroups

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

subgroupindex
C2×#22952
C2×#19492
C2×#18052
#147072
#113282
#113272
#112932
#112922
#111242
#111222
#110672
#108502
#108322