Finite Group Databasebeta

← #359413

Subgroups — #359413

Order 512.

1348 conjugacy classes of subgroups.

The subgroup lattice has 799 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2066C211yesmaximal, characteristic
2C2×#1776C211yesmaximal, characteristic
3C2×#1767C211yesmaximal, characteristic
4C2×#1763C211yesmaximal, characteristic
5C2×#1763C211yesmaximal, characteristic
6C4×#391C211yesmaximal, characteristic
7C4×#389C211yesmaximal, characteristic
8#11316C211yesmaximal, characteristic
9#11232C211yesmaximal, characteristic
10#11227C211yesmaximal, characteristic
11#11220C211yesmaximal, characteristic
12#11124C211yesmaximal, characteristic
13#11077C211yesmaximal, characteristic
14#11067C211yesmaximal, characteristic
15#10703C211yesmaximal, characteristic
16C22×C4×Q8C2211yescharacteristic
17C22×#107C2211yescharacteristic
18C22×#106C2211yescharacteristic
19C22×C4⋊C8C2211yescharacteristic
20C22×C4⋊C8C2211yescharacteristic
21C22×#103C2211yescharacteristic
22C22×#103C2211yescharacteristic
23C22×#103C2211yescharacteristic
24C22×#103C2211yescharacteristic
25C22×#97C2211yescharacteristic
26C22×#97C2211yescharacteristic
27C2×#391C2211yescharacteristic
28C2×#391C2211yescharacteristic
29C2×#389C2211yescharacteristic
30C2×#389C2211yescharacteristic
31C2×C4×C4⋊C4—21no—
32C2×C4×C4⋊C4C2211yescharacteristic
33C2×C4×C4⋊C4C2211yescharacteristic
34C2×C4×C4⋊C4C2211yescharacteristic
35C2×C43C2211yescharacteristic
36#2066C418yescomplemented
37#1776—24no—
38#1767—24no—
39#1763—24no—
40#1763—24no—
41C2×#340C2211yescharacteristic
42C2×#340C2211yescharacteristic
43C2×#340C2211yescharacteristic
44C2×#340C2211yescharacteristic
45C2×#340C2211yescharacteristic
46C2×#340C2211yescharacteristic
47C2×#340C2211yescharacteristic
48C2×#340C2211yescharacteristic
49C2×#340C2211yescharacteristic
50C2×#340C2211yescharacteristic
51C2×#336C2211yescharacteristic
52C2×#336C2211yescharacteristic
53#1436—21no—
54#1436—21no—
55#1436—21no—
56#1436—21no—
57C4⋊#95C2211yescharacteristic
58C4⋊#95C2211yescharacteristic
59C4⋊#95C2211yescharacteristic
60C4⋊#95C2211yescharacteristic
61C4×#95—21no—
62C4×#95—21no—
63C4×#95—21no—
64C23×Q8C2311yescharacteristic
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×Q8Q814yes—
75C22×C4⋊C4—21no—
76C22×C4⋊C4—21no—
77C22×C4⋊C4—21no—
78C22×C4⋊C4C2311yescharacteristic
79C22×C4⋊C4C2311yescharacteristic
80C22×C4⋊C4C2311yescharacteristic
81C22×C4⋊C4C2311yescharacteristic
82C22×C4⋊C4C2311yescharacteristic
83C22×C4⋊C4C2311yescharacteristic
84C22×C4⋊C4C2311yescharacteristic
85C22×C42—21no—
86C22×C42—21no—
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—22no—
98C2×#107—22no—
99C2×#106—22no—
100C2×#106—22no—
101C2×#106C2×C414yes—
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—22no—
111C2×#103—22no—
112C2×#103—22no—
113C2×#103—22no—
114C2×#103—22no—
115C2×#103—22no—
116C2×#103—22no—
117C2×#103—22no—
118C2×#103C2×C414yes—
119C2×#103C2×C414yes—
120C2×#97—22no—
121C2×#97—22no—
122C2×#97—22no—
123C2×#97—22no—
124C2×#97—22no—
125C2×#97D414yes—
126#391—22no—
127#391—22no—
128#391—22no—
129#391C2×C414yes—
130#389—22no—
131#389—22no—
132#389—22no—
133#389C2×C414yes—
134C4×C4⋊C4—22no—
135C4×C4⋊C4—22no—
136C4×C4⋊C4—22no—
137C4×C4⋊C4—22no—
138C4×C4⋊C4—22no—
139C4×C4⋊C4—44no—
140C4×C4⋊C4D414yes—
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×#95—21no—
156C2×#95—21no—
157C2×#95—21no—
158C43—22no—
159C43—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#336—22no—
171#336—22no—
172C22×Q8—21no—
173C22×Q8—21no—
174C22×Q8—21no—
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×Q8C22×C412yes—
184C22×Q8C2×Q812yes—
185C22×Q8#4112yes—
186C23×C4—21no—
187C23×C4—21no—
188C23×C4—21no—
189C23×C4—21no—
190C23×C4—21no—
191C23×C4—21no—
192C23×C4—21no—
193C23×C4—21no—
194C23×C4C2×D411yescharacteristic
195C23×C4C2×D411yescharacteristic
196C23×C4C2×D411yescharacteristic
197C23×C4C2×D411yescharacteristic
198C23×C4C2×D411yescharacteristic
199C23×C4C2×D411yescharacteristic
200C23×C4C2411yescharacteristic
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×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×C8C22×C412yes—
224C22×C8C22×C412yes—
225C22×C8C2×D412yes—
226C22×C8C2×D412yes—
227C22×C8#4112yes—
228C22×C8#4112yes—
229C4×Q8—28no—
230C4×Q8—28no—
231C4×Q8—44no—
232C4×Q8—44no—
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—24no—
261C2×C4⋊C4—24no—
262C2×C4⋊C4—24no—
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—42no—
270C2×C4⋊C4—42no—
271C2×C4⋊C4—42no—
272C2×C4⋊C4—42no—
273C2×C4⋊C4—42no—
274C2×C4⋊C4—42no—
275C2×C4⋊C4C22×C412yes—
276C2×C4⋊C4C22×C412yes—
277C2×C4⋊C4C22×C412yes—
278C2×C4⋊C4C2×D412yes—
279C2×C4⋊C4C2×D412yes—
280C2×C4⋊C4C2×Q812yes—
281C2×C4⋊C4#4112yes—
282C2×C4⋊C4#4112yes—
283C2×C4⋊C4#4112yes—
284C2×C42—21no—
285C2×C42—21no—
286C2×C42—21no—
287C2×C42—21no—
288C2×C42—22no—
289C2×C42—22no—
290C2×C42—22no—
291C2×C42—22no—
292C2×C42—24no—
293C2×C42—24no—
294C2×C42—22no—
295C2×C42—22no—
296C2×C42—22no—
297C2×C42—22no—
298C2×C42—21no—
299C2×C42—21no—
300C2×C42—21no—
301C2×C42—21no—
302C2×C42—21no—
303C2×C42—21no—
304C2×C42—41no—
305C2×C42—41no—
306C2×C42—41no—
307C2×C42—41no—
308C2×C42—42no—
309C2×C42—42no—
310C2×C42—42no—
311C2×C42—42no—
312C2×C42—42no—
313C2×C42—42no—
314C2×C42—42no—
315C2×C42—42no—
316C2×C42—42no—
317C2×C42—42no—
318C2×C42C22×C412yes—
319C2×C42C2×D412yes—
320C2×C42C2×D412yes—
321C2×C42C2×Q812yes—
322C2×C42#4112yes—
323C2×C42#4112yes—
324C2×C42#4112yes—
325C2×C42#4112yes—
326#107—28no—
327#106—28no—
328C4⋊C8—28no—
329C4⋊C8—28no—
330#103—28no—
331#103—28no—
332#103—28no—
333#103—28no—
334#97—28no—
335#97—44no—
336#95—24no—
337#95—24no—
338#95—24no—
339#95—24no—
340#95—24no—
341#95—24no—
342#95—24no—
343#95—42no—
344#95—42no—
345#95—42no—
346#95—42no—
347#95—42no—
348#95—42no—
349#95—42no—
350#95—42no—
351#95—42no—
352#95—42no—
353C24C22×D411yescharacteristic
354C2×Q8—22no—
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—41no—
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×Q8C4×Q814yes—
382C22×C4—21no—
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—21no—
392C22×C4—21no—
393C22×C4—21no—
394C22×C4—22no—
395C22×C4—22no—
396C22×C4—22no—
397C22×C4—21no—
398C22×C4—21no—
399C22×C4—21no—
400C22×C4—22no—
401C22×C4—21no—
402C22×C4—21no—
403C22×C4—21no—
404C22×C4—22no—
405C22×C4—22no—
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—22no—
419C22×C4—22no—
420C22×C4—22no—
421C22×C4—22no—
422C22×C4—22no—
423C22×C4—22no—
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×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×C4C4×D412yes—
469C22×C4C4×D412yes—
470C22×C4#12112yes—
471C22×C4#12112yes—
472C22×C4#12112yes—
473C22×C4#12112yes—
474C22×C4C22⋊Q812yes—
475C22×C4C22⋊Q812yes—
476C22×C4AGL(1,ℤ/8)12yes—
477C22×C4#13712yes—
478C22×C4#13712yes—
479C22×C4#13712yes—
480C22×C4C23×C411yescharacteristic
481C22×C4C22×D411yescharacteristic
482C22×C4C22×D411yescharacteristic
483C22×C4C22×Q811yescharacteristic
484C22×C4C2×#4111yescharacteristic
485C22×C4C2×#4111yescharacteristic
486C22×C4C2×#4111yescharacteristic
487C22×C4C2×#4111yescharacteristic
488C22×C4C2×#4111yescharacteristic
489C22×C4C2×#4111yescharacteristic
490C22×C4C2×#4111yescharacteristic
491C22×C4C2×#4111yescharacteristic
492C22×C4C2×#4111yescharacteristic
493C22×C4C2×#4111yescharacteristic
494C2×C8—22no—
495C2×C8—22no—
496C2×C8—22no—
497C2×C8—22no—
498C2×C8—22no—
499C2×C8—22no—
500C2×C8—22no—
501C2×C8—22no—
502C2×C8—22no—
503C2×C8—22no—
504C2×C8—22no—
505C2×C8—22no—
506C2×C8—22no—
507C2×C8—22no—
508C2×C8—22no—
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×C8C4×D414yes—
522C4⋊C4—22no—
523C4⋊C4—22no—
524C4⋊C4—22no—
525C4⋊C4—22no—
526C4⋊C4—22no—
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—22no—
536C4⋊C4—22no—
537C4⋊C4—48no—
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—48no—
551C4⋊C4—48no—
552C4⋊C4C4×D414yes—
553C42—22no—
554C42—22no—
555C42—22no—
556C42—22no—
557C42—44no—
558C42—44no—
559C42—44no—
560C42—44no—
561C42—48no—
562C42—41no—
563C42—41no—
564C42—41no—
565C42—41no—
566C42—48no—
567C42—84no—
568C42—84no—
569C42#12114yes—
570C42C22⋊Q814yes—
571C42C22⋊Q814yes—
572C42#12614yes—
573C23C2×C4×D411yescharacteristic
574C23C2×#12111yescharacteristic
575C23C2×#12111yescharacteristic
576C23C2×C22⋊Q811yescharacteristic
577C23#52511yescharacteristic
578C23#52511yescharacteristic
579C23#53211yescharacteristic
580C23C2×AGL(1,ℤ/8)11yescharacteristic
581C23C2×#13711yescharacteristic
582C23C2×#13711yescharacteristic
583C23C2×#13711yescharacteristic
584C23#57511yescharacteristic
585C23#57511yescharacteristic
586C23#57511yescharacteristic
587C23#57511yescharacteristic
588Q8—24no—
589Q8—24no—
590Q8—42no—
591Q8—42no—
592Q8—42no—
593Q8—42no—
594Q8—42no—
595Q8—42no—
596C2×C4—22no—
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—22no—
622C2×C4—22no—
623C2×C4—24no—
624C2×C4—24no—
625C2×C4—42no—
626C2×C4—41no—
627C2×C4—41no—
628C2×C4—41no—
629C2×C4—41no—
630C2×C4—42no—
631C2×C4—42no—
632C2×C4—41no—
633C2×C4—41no—
634C2×C4—42no—
635C2×C4—42no—
636C2×C4—42no—
637C2×C4—41no—
638C2×C4—41no—
639C2×C4—42no—
640C2×C4—42no—
641C2×C4—42no—
642C2×C4—42no—
643C2×C4—41no—
644C2×C4—41no—
645C2×C4—41no—
646C2×C4—41no—
647C2×C4—42no—
648C2×C4—42no—
649C2×C4—42no—
650C2×C4—42no—
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—42no—
664C2×C4—42no—
665C2×C4—42no—
666C2×C4—42no—
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#39614yes—
692C2×C4#39614yes—
693C2×C4#44014yes—
694C2×C4C2×C4×D411yescharacteristic
695C2×C4C2×C4×D411yescharacteristic
696C2×C4C2×C4×Q811yescharacteristic
697C2×C4C4×#4111yescharacteristic
698C2×C4C4×#4111yescharacteristic
699C2×C4C4×#4111yescharacteristic
700C2×C4C2×#12111yescharacteristic
701C2×C4C2×C22⋊Q811yescharacteristic
702C2×C4C2×C22⋊Q811yescharacteristic
703C2×C4#52511yescharacteristic
704C2×C4#52511yescharacteristic
705C2×C4#52511yescharacteristic
706C2×C4#52511yescharacteristic
707C2×C4C2×#12611yescharacteristic
708C2×C4#52911yescharacteristic
709C2×C4#52911yescharacteristic
710C2×C4#52911yescharacteristic
711C2×C4#52911yescharacteristic
712C2×C4#52911yescharacteristic
713C2×C4#52911yescharacteristic
714C2×C4#52911yescharacteristic
715C2×C4#52911yescharacteristic
716C2×C4#52911yescharacteristic
717C2×C4#53211yescharacteristic
718C2×C4#53211yescharacteristic
719C2×C4#53311yescharacteristic
720C2×C4#53311yescharacteristic
721C2×C4#53311yescharacteristic
722C8—24no—
723C8—42no—
724C8—42no—
725C8—42no—
726C22C4×#12111yescharacteristic
727C22C4×#12111yescharacteristic
728C22C4×C22⋊Q811yescharacteristic
729C22C2×#39611yescharacteristic
730C22#239211yescharacteristic
731C22#239211yescharacteristic
732C22#239611yescharacteristic
733C22C2×#44011yescharacteristic
734C22#294311yescharacteristic
735C22C4×#13711yescharacteristic
736C22C4×#13711yescharacteristic
737C22#303611yescharacteristic
738C22#303711yescharacteristic
739C22#303911yescharacteristic
740C22#304011yescharacteristic
741C22#305511yescharacteristic
742C22#305611yescharacteristic
743C22#305611yescharacteristic
744C22#305611yescharacteristic
745C22#307811yescharacteristic
746C22#307811yescharacteristic
747C22#307911yescharacteristic
748C22#308011yescharacteristic
749C22#311011yescharacteristic
750C22#311111yescharacteristic
751C22#311111yescharacteristic
752C22#311311yescharacteristic
753C22#311511yescharacteristic
754C22#311611yescharacteristic
755C22#311711yescharacteristic
756C22#311711yescharacteristic
757C22#318011yescharacteristic
758C22#318111yescharacteristic
759C22#318311yescharacteristic
760C22#318511yescharacteristic
761C4—24no—
762C4—24no—
763C4—24no—
764C4—44no—
765C4—42no—
766C4—44no—
767C4—42no—
768C4—42no—
769C4—82no—
770C4—82no—
771C4—82no—
772C4—82no—
773C4—82no—
774C4—82no—
775C4C4×#12111yescharacteristic
776C4C4×C22⋊Q811yescharacteristic
777C4C4×C22⋊Q811yescharacteristic
778C4C4×#12611yescharacteristic
779C4#239211yescharacteristic
780C4#239611yescharacteristic
781C4#239611yescharacteristic
782C4#240111yescharacteristic
783C2C4×#39611yescharacteristic
784C2#2150411yescharacteristic
785C2#2150811yescharacteristic
786C2#2152811yescharacteristic
787C2#2153911yescharacteristic
788C2#2161511yescharacteristic
789C2#2161811yescharacteristic
790C2#2361711yescharacteristic
791C2#2361911yescharacteristic
792C2#2368511yescharacteristic
793C2#2368611yescharacteristic
794C2#2370911yescharacteristic
795C2#2371111yescharacteristic
796C2#2378211yescharacteristic
797C2#2378511yescharacteristic
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
36. #2066C4semidirect

Maximal subgroups

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

subgroupindex
C2×#20662
C2×#17762
C2×#17672
C2×#17632
C4×#3912
C4×#3892
#113162
#112322
#112272
#112202
#111242
#110772
#110672
#107032