Finite Group Databasebeta

← #359191

Subgroups — #359191

Order 512.

1408 conjugacy classes of subgroups.

The subgroup lattice has 807 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2331C211yesmaximal, characteristic
2C2×#2024C211yesmaximal, characteristic
3C2×#1763C211yesmaximal, characteristic
4C2×C4×#103C211yesmaximal, characteristic
5#13786C211yesmaximal, characteristic
6#11384C211yesmaximal, characteristic
7#11293C211yesmaximal, characteristic
8#11292C211yesmaximal, characteristic
9#11268C211yesmaximal, characteristic
10#11067C211yesmaximal, characteristic
11#11067C211yesmaximal, characteristic
12#11052C211yesmaximal, characteristic
13#10703C211yesmaximal, characteristic
14C4×#340C211yesmaximal, characteristic
15#10694C211yesmaximal, characteristic
16C22×C4⋊Q8C2211yescharacteristic
17C22×C4×Q8C2211yescharacteristic
18C22×#103C2211yescharacteristic
19C22×#103C2211yescharacteristic
20C22×#103C2211yescharacteristic
21C22×#103C2211yescharacteristic
22C22×#97C2211yescharacteristic
23C22×C4×C8C2211yescharacteristic
24#2331—24no—
25#2331—24no—
26C2×#391—21no—
27C2×#391—21no—
28C2×#391C2211yescharacteristic
29C2×#391C2211yescharacteristic
30C2×#389C2211yescharacteristic
31C2×#389C2211yescharacteristic
32C2×#387—21no—
33C2×#387—21no—
34C2×#382C2211yescharacteristic
35C2×C4×C4⋊C4C2211yescharacteristic
36C2×C4×C4⋊C4C2211yescharacteristic
37C2×C4×C4⋊C4C2211yescharacteristic
38C2×#376C2211yescharacteristic
39#2024C418yescomplemented
40#1763—24no—
41C4×#103—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⋊#95C2211yescharacteristic
61C4⋊#95C2211yescharacteristic
62#1434—21no—
63#1434—21no—
64C23×Q8—21no—
65C23×Q8C2311yescharacteristic
66C23×C8C2311yescharacteristic
67C23×C8C2311yescharacteristic
68C23×C8C2311yescharacteristic
69C23×C8C2311yescharacteristic
70C2×C4⋊Q8—22no—
71C2×C4⋊Q8—22no—
72C2×C4⋊Q8—22no—
73C2×C4⋊Q8—22no—
74C2×C4⋊Q8—22no—
75C2×C4⋊Q8C2×C414yes—
76C2×C4×Q8—22no—
77C2×C4×Q8—22no—
78C2×C4×Q8—22no—
79C2×C4×Q8—22no—
80C2×C4×Q8—22no—
81C2×C4×Q8Q814yescomplemented
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×C42—21no—
94C22×C42—21no—
95C22×C42—21no—
96C22×C42—21no—
97C22×C42C2311yescharacteristic
98C22×C42C2311yescharacteristic
99C22×C42C2311yescharacteristic
100C2×#103—22no—
101C2×#103—22no—
102C2×#103—22no—
103C2×#103—22no—
104C2×#103—22no—
105C2×#103—22no—
106C2×#103—22no—
107C2×#103—22no—
108C2×#103—22no—
109C2×#103—22no—
110C2×#103C2×C414yes—
111C2×#103C2×C414yes—
112C2×#97—22no—
113C2×#97—22no—
114C2×#97—22no—
115C2×C4×C8—22no—
116C2×C4×C8—22no—
117C2×C4×C8—22no—
118#391—28no—
119#391—28no—
120#391—22no—
121#391—22no—
122#391—22no—
123#391C2×C414yes—
124#389—22no—
125#389—22no—
126#389—22no—
127#389—22no—
128#387—28no—
129#387—28no—
130#382—22no—
131#382—22no—
132C4×C4⋊C4—22no—
133C4×C4⋊C4—22no—
134C4×C4⋊C4—22no—
135C4×C4⋊C4—22no—
136C4×C4⋊C4D414yes—
137C4×C4⋊C4D414yes—
138#376—22no—
139#376—22no—
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×#95—21no—
153C2×#95—21no—
154C2×#95—21no—
155C2×#95D411yescharacteristic
156C2×#95D411yescharacteristic
157C2×#95D411yescharacteristic
158C2×#95D411yescharacteristic
159#340—22no—
160#340—22no—
161#340—22no—
162#340—22no—
163#340—22no—
164#340—22no—
165#340—22no—
166#340—22no—
167#340—22no—
168#340—22no—
169#340C2×C414yes—
170#340C2×C414yes—
171#336—22no—
172#336—22no—
173#336—22no—
174#336C2×C414yes—
175C22×Q8—24no—
176C22×Q8—24no—
177C22×Q8—24no—
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×Q8—21no—
187C22×Q8—21no—
188C22×Q8—21no—
189C22×Q8—81no—
190C22×Q8—81no—
191C22×Q8—81no—
192C22×Q8—81no—
193C22×Q8C22×C412yes—
194C22×Q8C2×Q812yes—
195C22×Q8#4112yes—
196C23×C4—21no—
197C23×C4—21no—
198C23×C4—21no—
199C23×C4—21no—
200C23×C4—21no—
201C23×C4—21no—
202C23×C4—21no—
203C23×C4—21no—
204C23×C4C2×D411yescharacteristic
205C23×C4C2×D411yescharacteristic
206C23×C4C2×D411yescharacteristic
207C23×C4C2×D411yescharacteristic
208C23×C4C2×D411yescharacteristic
209C23×C4C2×D411yescharacteristic
210C23×C4C2411yescharacteristic
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×C8—21no—
231C22×C8—21no—
232C22×C8—21no—
233C22×C8—21no—
234C22×C8—21no—
235C22×C8C22×C412yes—
236C22×C8C22×C412yes—
237C22×C8#4112yes—
238C22×C8#4112yes—
239C4⋊Q8—28no—
240C4⋊Q8—28no—
241C4⋊Q8—28no—
242C4⋊Q8—28no—
243C4×Q8—28no—
244C4×Q8—28no—
245C4×Q8—44no—
246C4×Q8—44no—
247C2×C4⋊C4—24no—
248C2×C4⋊C4—24no—
249C2×C4⋊C4—24no—
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—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—24no—
277C2×C4⋊C4—21no—
278C2×C4⋊C4—21no—
279C2×C4⋊C4—21no—
280C2×C4⋊C4—21no—
281C2×C4⋊C4—21no—
282C2×C4⋊C4—24no—
283C2×C4⋊C4—24no—
284C2×C4⋊C4—42no—
285C2×C4⋊C4—42no—
286C2×C4⋊C4—81no—
287C2×C4⋊C4—81no—
288C2×C4⋊C4—81no—
289C2×C4⋊C4—81no—
290C2×C4⋊C4C22×C412yes—
291C2×C4⋊C4C22×C412yes—
292C2×C4⋊C4C22×C412yes—
293C2×C4⋊C4C2×D412yes—
294C2×C4⋊C4C2×D412yes—
295C2×C4⋊C4C2×D412yes—
296C2×C4⋊C4C2×D412yes—
297C2×C4⋊C4C2×Q812yes—
298C2×C4⋊C4#4112yes—
299C2×C4⋊C4#4112yes—
300C2×C4⋊C4#4112yes—
301C2×C42—21no—
302C2×C42—21no—
303C2×C42—21no—
304C2×C42—21no—
305C2×C42—24no—
306C2×C42—21no—
307C2×C42—21no—
308C2×C42—21no—
309C2×C42—21no—
310C2×C42—21no—
311C2×C42—21no—
312C2×C42—24no—
313C2×C42—24no—
314C2×C42—42no—
315C2×C42—42no—
316C2×C42—42no—
317C2×C42—81no—
318C2×C42—81no—
319C2×C42—81no—
320C2×C42—81no—
321C2×C42—81no—
322C2×C42—81no—
323C2×C42C22×C412yes—
324C2×C42C2×D412yes—
325C2×C42C2×D412yes—
326C2×C42C2×Q812yes—
327C2×C42#4112yes—
328C2×C42#4112yes—
329C2×C42#4112yes—
330C2×C42#4112yes—
331#103—28no—
332#103—28no—
333#103—28no—
334#103—28no—
335#97—44no—
336C4×C8—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—24no—
347#95—22no—
348#95—22no—
349#95—22no—
350#95—22no—
351#95—42no—
352#95—81no—
353#95—81no—
354#95—81no—
355#95—81no—
356C24C22×D411yescharacteristic
357C2×Q8—216no—
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—22no—
371C2×Q8—22no—
372C2×Q8—22no—
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×Q8—41no—
383C2×Q8—41no—
384C2×Q8—41no—
385C2×Q8—84no—
386C2×Q8—84no—
387C2×Q8—84no—
388C2×Q8—84no—
389C2×Q8—84no—
390C2×Q8—84no—
391C2×Q8C4×Q814yes—
392C22×C4—21no—
393C22×C4—21no—
394C22×C4—21no—
395C22×C4—21no—
396C22×C4—21no—
397C22×C4—21no—
398C22×C4—21no—
399C22×C4—21no—
400C22×C4—22no—
401C22×C4—22no—
402C22×C4—22no—
403C22×C4—21no—
404C22×C4—21no—
405C22×C4—22no—
406C22×C4—22no—
407C22×C4—22no—
408C22×C4—22no—
409C22×C4—21no—
410C22×C4—21no—
411C22×C4—22no—
412C22×C4—22no—
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—21no—
423C22×C4—21no—
424C22×C4—22no—
425C22×C4—22no—
426C22×C4—22no—
427C22×C4—21no—
428C22×C4—21no—
429C22×C4—22no—
430C22×C4—21no—
431C22×C4—21no—
432C22×C4—21no—
433C22×C4—21no—
434C22×C4—21no—
435C22×C4—21no—
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—21no—
439C22×C4—21no—
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×C4—41no—
472C22×C4—41no—
473C22×C4—41no—
474C22×C4—41no—
475C22×C4—41no—
476C22×C4—41no—
477C22×C4—41no—
478C22×C4—41no—
479C22×C4—41no—
480C22×C4—41no—
481C22×C4—41no—
482C22×C4C4×D412yes—
483C22×C4C4×D412yes—
484C22×C4#12012yes—
485C22×C4#12012yes—
486C22×C4C22⋊Q812yes—
487C22×C4C22⋊Q812yes—
488C22×C4#12412yes—
489C22×C4#12412yes—
490C22×C4C23×C411yescharacteristic
491C22×C4C22×D411yescharacteristic
492C22×C4C22×D411yescharacteristic
493C22×C4C22×Q811yescharacteristic
494C22×C4C2×#4111yescharacteristic
495C22×C4C2×#4111yescharacteristic
496C22×C4C2×#4111yescharacteristic
497C22×C4C2×#4111yescharacteristic
498C22×C4C2×#4111yescharacteristic
499C22×C4C2×#4111yescharacteristic
500C22×C4C2×#4111yescharacteristic
501C22×C4C2×#4111yescharacteristic
502C22×C4C2×#4111yescharacteristic
503C22×C4C2×#4111yescharacteristic
504C2×C8—22no—
505C2×C8—22no—
506C2×C8—22no—
507C2×C8—22no—
508C2×C8—22no—
509C2×C8—22no—
510C2×C8—22no—
511C2×C8—22no—
512C2×C8—22no—
513C2×C8—22no—
514C2×C8—22no—
515C2×C8—22no—
516C2×C8—41no—
517C2×C8—41no—
518C2×C8—41no—
519C2×C8—41no—
520C2×C8—41no—
521C2×C8—41no—
522C2×C8—41no—
523C2×C8—41no—
524C2×C8—41no—
525C2×C8—41no—
526C2×C8—41no—
527C2×C8—41no—
528C2×C8—41no—
529C2×C8—41no—
530C2×C8—41no—
531C2×C8—41no—
532C4⋊C4—216no—
533C4⋊C4—22no—
534C4⋊C4—22no—
535C4⋊C4—22no—
536C4⋊C4—22no—
537C4⋊C4—22no—
538C4⋊C4—22no—
539C4⋊C4—22no—
540C4⋊C4—22no—
541C4⋊C4—22no—
542C4⋊C4—22no—
543C4⋊C4—22no—
544C4⋊C4—22no—
545C4⋊C4—22no—
546C4⋊C4—22no—
547C4⋊C4—22no—
548C4⋊C4—22no—
549C4⋊C4—41no—
550C4⋊C4—41no—
551C4⋊C4—41no—
552C4⋊C4—41no—
553C4⋊C4—41no—
554C4⋊C4—41no—
555C4⋊C4—41no—
556C4⋊C4—41no—
557C4⋊C4—41no—
558C4⋊C4—41no—
559C4⋊C4—48no—
560C4⋊C4—84no—
561C4⋊C4—84no—
562C4⋊C4C4×D414yes—
563C4⋊C4C4×D414yes—
564C42—22no—
565C42—22no—
566C42—22no—
567C42—22no—
568C42—41no—
569C42—41no—
570C42—41no—
571C42—41no—
572C42—48no—
573C42—84no—
574C42—84no—
575C42—84no—
576C42C22⋊Q814yes—
577C42C22⋊Q814yes—
578C42#12414yes—
579C42#12414yes—
580C23C2×C4×D411yescharacteristic
581C23C2×#12011yescharacteristic
582C23C2×C22⋊Q811yescharacteristic
583C23#52511yescharacteristic
584C23#52511yescharacteristic
585C23C2×#12411yescharacteristic
586C23#53211yescharacteristic
587C23#57611yescharacteristic
588C23#57711yescharacteristic
589C23#57711yescharacteristic
590C23#57711yescharacteristic
591C23#57711yescharacteristic
592C23#57811yescharacteristic
593C23#57811yescharacteristic
594C23#57811yescharacteristic
595Q8—24no—
596Q8—24no—
597Q8—42no—
598Q8—42no—
599Q8—42no—
600Q8—42no—
601Q8—42no—
602Q8—42no—
603Q8—816no—
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—22no—
622C2×C4—24no—
623C2×C4—24no—
624C2×C4—24no—
625C2×C4—41no—
626C2×C4—42no—
627C2×C4—42no—
628C2×C4—41no—
629C2×C4—41no—
630C2×C4—42no—
631C2×C4—42no—
632C2×C4—41no—
633C2×C4—42no—
634C2×C4—42no—
635C2×C4—42no—
636C2×C4—42no—
637C2×C4—42no—
638C2×C4—42no—
639C2×C4—42no—
640C2×C4—42no—
641C2×C4—42no—
642C2×C4—42no—
643C2×C4—41no—
644C2×C4—41no—
645C2×C4—42no—
646C2×C4—42no—
647C2×C4—41no—
648C2×C4—41no—
649C2×C4—42no—
650C2×C4—42no—
651C2×C4—42no—
652C2×C4—42no—
653C2×C4—41no—
654C2×C4—41no—
655C2×C4—41no—
656C2×C4—42no—
657C2×C4—41no—
658C2×C4—42no—
659C2×C4—42no—
660C2×C4—41no—
661C2×C4—41no—
662C2×C4—42no—
663C2×C4—42no—
664C2×C4—42no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—41no—
668C2×C4—41no—
669C2×C4—42no—
670C2×C4—42no—
671C2×C4—42no—
672C2×C4—41no—
673C2×C4—41no—
674C2×C4—42no—
675C2×C4—42no—
676C2×C4—41no—
677C2×C4—41no—
678C2×C4—42no—
679C2×C4—42no—
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—81no—
694C2×C4—81no—
695C2×C4—81no—
696C2×C4—81no—
697C2×C4—81no—
698C2×C4—81no—
699C2×C4—81no—
700C2×C4#39314yes—
701C2×C4#39314yes—
702C2×C4C2×C4×D411yescharacteristic
703C2×C4C2×C4×D411yescharacteristic
704C2×C4C2×C4×Q811yescharacteristic
705C2×C4C4×#4111yescharacteristic
706C2×C4C4×#4111yescharacteristic
707C2×C4C4×#4111yescharacteristic
708C2×C4C2×C22⋊Q811yescharacteristic
709C2×C4C2×C22⋊Q811yescharacteristic
710C2×C4#52511yescharacteristic
711C2×C4#52511yescharacteristic
712C2×C4#52511yescharacteristic
713C2×C4#52511yescharacteristic
714C2×C4C2×#12411yescharacteristic
715C2×C4C2×#12411yescharacteristic
716C2×C4#52911yescharacteristic
717C2×C4#52911yescharacteristic
718C2×C4#52911yescharacteristic
719C2×C4#52911yescharacteristic
720C2×C4#52911yescharacteristic
721C2×C4#52911yescharacteristic
722C2×C4#52911yescharacteristic
723C2×C4#52911yescharacteristic
724C2×C4#52911yescharacteristic
725C2×C4#53211yescharacteristic
726C2×C4#53211yescharacteristic
727C2×C4#53311yescharacteristic
728C2×C4#53311yescharacteristic
729C2×C4#53311yescharacteristic
730C8—42no—
731C8—42no—
732C8—42no—
733C8—42no—
734C22C4×#12011yescharacteristic
735C22C4×C22⋊Q811yescharacteristic
736C22C4×#12411yescharacteristic
737C22C2×#39311yescharacteristic
738C22#238811yescharacteristic
739C22#239611yescharacteristic
740C22#239811yescharacteristic
741C22#294611yescharacteristic
742C22#294711yescharacteristic
743C22#294911yescharacteristic
744C22#295011yescharacteristic
745C22#300911yescharacteristic
746C22#301111yescharacteristic
747C22#301211yescharacteristic
748C22#301311yescharacteristic
749C22#308211yescharacteristic
750C22#308211yescharacteristic
751C22#308311yescharacteristic
752C22#308411yescharacteristic
753C22#311811yescharacteristic
754C22#312111yescharacteristic
755C22#312111yescharacteristic
756C22#312111yescharacteristic
757C22#312311yescharacteristic
758C22#312411yescharacteristic
759C22#312511yescharacteristic
760C22#312711yescharacteristic
761C22#313611yescharacteristic
762C22#313711yescharacteristic
763C22#313711yescharacteristic
764C22#313711yescharacteristic
765C22#317311yescharacteristic
766C22#317511yescharacteristic
767C22#317811yescharacteristic
768C22#317811yescharacteristic
769C4—24no—
770C4—24no—
771C4—44no—
772C4—42no—
773C4—44no—
774C4—44no—
775C4—42no—
776C4—82no—
777C4—81no—
778C4—82no—
779C4—81no—
780C4—82no—
781C4—82no—
782C4—82no—
783C4C4×C22⋊Q811yescharacteristic
784C4C4×C22⋊Q811yescharacteristic
785C4C4×#12411yescharacteristic
786C4C4×#12411yescharacteristic
787C4#239611yescharacteristic
788C4#239611yescharacteristic
789C4#239811yescharacteristic
790C4#239811yescharacteristic
791C2C4×#39311yescharacteristic
792C2#2145911yescharacteristic
793C2#2146311yescharacteristic
794C2#2162511yescharacteristic
795C2#2162611yescharacteristic
796C2#2164511yescharacteristic
797C2#2165411yescharacteristic
798C2#2345711yescharacteristic
799C2#2345811yescharacteristic
800C2#2358111yescharacteristic
801C2#2358511yescharacteristic
802C2#2378811yescharacteristic
803C2#2378911yescharacteristic
804C2#2382711yescharacteristic
805C2#2382911yescharacteristic
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. #2024C4semidirect
81. C2×C4×Q8Q8semidirect

Maximal subgroups

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

subgroupindex
C2×#23312
C2×#20242
C2×#17632
C2×C4×#1032
#137862
#113842
#112932
#112922
#112682
#110672
#110522
#107032
C4×#3402
#106942