Finite Group Databasebeta

← #423977

Subgroups — #423977

Order 512.

1330 conjugacy classes of subgroups.

The subgroup lattice has 783 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#498C211yesmaximal, characteristic
2C2×#2084C211yesmaximal, characteristic
3C2×#2058C211yesmaximal, characteristic
4C2×#1948C211yesmaximal, characteristic
5#15143C211yesmaximal, characteristic
6#14053C211yesmaximal, characteristic
7#11384C211yesmaximal, characteristic
8#11323C211yesmaximal, characteristic
9#11323C211yesmaximal, characteristic
10#11257C211yesmaximal, characteristic
11#11231C211yesmaximal, characteristic
12#11220C211yesmaximal, characteristic
13#10908C211yesmaximal, characteristic
14#10880C211yesmaximal, characteristic
15#10876C211yesmaximal, characteristic
16C22×C4⋊Q8C2211yescharacteristic
17C22×C4⋊Q8C2211yescharacteristic
18C2×#498—24no—
19C2×#498—24no—
20C2×#498—24no—
21C22×#106C2211yescharacteristic
22C22×#106C2211yescharacteristic
23C22×#106C2211yescharacteristic
24C22×#106C2211yescharacteristic
25C22×#106C2211yescharacteristic
26C22×#106C2211yescharacteristic
27C22×C4⋊C8C2211yescharacteristic
28C22×C4×C8C2211yescharacteristic
29C2×#395—21no—
30C2×#395—21no—
31C2×#391—21no—
32C2×#389C2211yescharacteristic
33C2×#389C2211yescharacteristic
34C2×#384C2211yescharacteristic
35C2×#384C2211yescharacteristic
36C2×C4×C4⋊C4C2211yescharacteristic
37#2084—24no—
38#2058—24no—
39#1948—24no—
40C2×#340C2211yescharacteristic
41C2×#340C2211yescharacteristic
42C2×#340C2211yescharacteristic
43C2×#340C2211yescharacteristic
44C2×#340C2211yescharacteristic
45C2×#340C2211yescharacteristic
46C2×#340C2211yescharacteristic
47C2×#340C2211yescharacteristic
48C2×#340C2211yescharacteristic
49C2×#340C2211yescharacteristic
50C2×#336C2211yescharacteristic
51C2×#336C2211yescharacteristic
52C2×#336C2211yescharacteristic
53C2×#336C2211yescharacteristic
54#1446—21no—
55#1444—21no—
56#1444—21no—
57#1441—21no—
58#1436—21no—
59C4⋊#95C2211yescharacteristic
60C4⋊#95C2211yescharacteristic
61C4⋊#95C2211yescharacteristic
62C4⋊#95C2211yescharacteristic
63C4⋊#95C2211yescharacteristic
64C4×#95C2211yescharacteristic
65C23×Q8—21no—
66C23×Q8—21no—
67C23×C8C2311yescharacteristic
68C23×C8C2311yescharacteristic
69C23×C8C2311yescharacteristic
70C23×C8C2311yescharacteristic
71C2×C4⋊Q8—22no—
72C2×C4⋊Q8—22no—
73C2×C4⋊Q8—22no—
74C2×C4⋊Q8—22no—
75C2×C4⋊Q8—22no—
76C2×C4⋊Q8—22no—
77C2×C4⋊Q8—22no—
78C2×C4⋊Q8—41no—
79C2×C4⋊Q8—41no—
80C2×C4⋊Q8—41no—
81C2×C4⋊Q8—41no—
82C2×C4⋊Q8D414yes—
83C22×C4⋊C4—21no—
84C22×C4⋊C4—21no—
85C22×C4⋊C4—21no—
86C22×C4⋊C4—21no—
87C22×C4⋊C4—21no—
88C22×C4⋊C4—21no—
89C22×C4⋊C4—21no—
90C22×C4⋊C4—21no—
91C22×C4⋊C4C2311yescharacteristic
92C22×C4⋊C4C2311yescharacteristic
93C22×C4⋊C4C2311yescharacteristic
94C22×C4⋊C4C2311yescharacteristic
95C22×C4⋊C4C2311yescharacteristic
96C22×C4⋊C4C2311yescharacteristic
97C22×C4⋊C4C2311yescharacteristic
98C22×C4⋊C4C2311yescharacteristic
99C22×C42—21no—
100C22×C42C2311yescharacteristic
101C22×C42C2311yescharacteristic
102C22×C42C2311yescharacteristic
103#498—232no—
104C2×#106—22no—
105C2×#106—22no—
106C2×#106—22no—
107C2×#106—22no—
108C2×#106—22no—
109C2×#106—22no—
110C2×#106—22no—
111C2×#106—22no—
112C2×#106—22no—
113C2×#106—22no—
114C2×#106—22no—
115C2×#106—22no—
116C2×#106—22no—
117C2×#106—22no—
118C2×#106—41no—
119C2×#106—41no—
120C2×#106D414yes—
121C2×#106D414yes—
122C2×C4⋊C8—22no—
123C2×C4⋊C8—22no—
124C2×C4⋊C8Q814yescomplemented
125C2×C4×C8—22no—
126C2×C4×C8—22no—
127C2×C4×C8—22no—
128#395—44no—
129#395—44no—
130#391—44no—
131#389—22no—
132#389—22no—
133#389—22no—
134#389—41no—
135#384—22no—
136#384—22no—
137#384—41no—
138#384—41no—
139C4×C4⋊C4—22no—
140C4×C4⋊C4—41no—
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×#95D411yescharacteristic
155C2×#95D411yescharacteristic
156C2×#95D411yescharacteristic
157C2×#95D411yescharacteristic
158#340—22no—
159#340—22no—
160#340—22no—
161#340—22no—
162#340—22no—
163#340—22no—
164#340—22no—
165#340—41no—
166#340—41no—
167#340Q814yescomplemented
168#336—22no—
169#336—22no—
170#336—22no—
171#336Q814yescomplemented
172C22×Q8—24no—
173C22×Q8—42no—
174C22×Q8—42no—
175C22×Q8—42no—
176C22×Q8—42no—
177C22×Q8—42no—
178C22×Q8—42no—
179C22×Q8—42no—
180C22×Q8—42no—
181C22×Q8—42no—
182C22×Q8—81no—
183C22×Q8—81no—
184C22×Q8—81no—
185C22×Q8—81no—
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×C8C2×D412yes—
222C22×C8C2×D412yes—
223C22×C8C2×Q812yes—
224C22×C8C2×Q812yes—
225C22×C8C2×Q812yes—
226C22×C8C2×Q812yes—
227C22×C8C2×Q812yes—
228C22×C8#4112yes—
229C4⋊Q8—28no—
230C4⋊Q8—28no—
231C4⋊Q8—44no—
232C4⋊Q8—44no—
233C4⋊Q8—44no—
234C4⋊Q8—44no—
235C4⋊Q8—44no—
236C4⋊Q8—44no—
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—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—21no—
277C2×C4⋊C4—21no—
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⋊C4—42no—
287C2×C4⋊C4—42no—
288C2×C4⋊C4—42no—
289C2×C4⋊C4—42no—
290C2×C4⋊C4—42no—
291C2×C4⋊C4—42no—
292C2×C4⋊C4—42no—
293C2×C4⋊C4—42no—
294C2×C4⋊C4—42no—
295C2×C4⋊C4—42no—
296C2×C4⋊C4—81no—
297C2×C4⋊C4—81no—
298C2×C4⋊C4—81no—
299C2×C4⋊C4—81no—
300C2×C4⋊C4—81no—
301C2×C4⋊C4C2×D412yes—
302C2×C4⋊C4C2×D412yes—
303C2×C4⋊C4C2×D412yes—
304C2×C4⋊C4C2×D412yes—
305C2×C4⋊C4C2×D412yes—
306C2×C4⋊C4C2×D412yes—
307C2×C4⋊C4C2×Q812yes—
308C2×C4⋊C4C2×Q812yes—
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—21no—
318C2×C42—21no—
319C2×C42—21no—
320C2×C42—21no—
321C2×C42—21no—
322C2×C42—21no—
323C2×C42—42no—
324C2×C42—42no—
325C2×C42—81no—
326C2×C42C2×D412yes—
327C2×C42C2×Q812yes—
328C2×C42C2×Q812yes—
329C2×C42#4112yes—
330#106—28no—
331#106—28no—
332#106—28no—
333#106—28no—
334#106—44no—
335#106—44no—
336C4⋊C8—28no—
337C4×C8—28no—
338#95—22no—
339#95—22no—
340#95—42no—
341#95—42no—
342#95—42no—
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—81no—
352#95—81no—
353#95SD1614yes—
354#95SD1614yes—
355C24C22×D411yescharacteristic
356C2×Q8—48no—
357C2×Q8—48no—
358C2×Q8—48no—
359C2×Q8—84no—
360C2×Q8—84no—
361C2×Q8—84no—
362C2×Q8—84no—
363C2×Q8—84no—
364C2×Q8—84no—
365C2×Q8—84no—
366C2×Q8—84no—
367C2×Q8—84no—
368C2×Q8—84no—
369C2×Q8—84no—
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—21no—
380C22×C4—21no—
381C22×C4—21no—
382C22×C4—22no—
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—21no—
398C22×C4—21no—
399C22×C4—21no—
400C22×C4—21no—
401C22×C4—21no—
402C22×C4—21no—
403C22×C4—22no—
404C22×C4—22no—
405C22×C4—22no—
406C22×C4—22no—
407C22×C4—22no—
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×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#12112yes—
457C22×C4#12112yes—
458C22×C4C4⋊Q812yes—
459C22×C4C4⋊Q812yes—
460C22×C4C2×SD1612yes—
461C22×C4C2×SD1612yes—
462C22×C4C2×SD1612yes—
463C22×C4C2×SD1612yes—
464C22×C4C2×SD1612yes—
465C22×C4C2×SD1612yes—
466C22×C4AGL(1,ℤ/8)12yes—
467C22×C4#13712yes—
468C22×C4C22×D411yescharacteristic
469C22×C4C22×D411yescharacteristic
470C22×C4C22×D411yescharacteristic
471C22×C4C22×Q811yescharacteristic
472C22×C4C22×Q811yescharacteristic
473C22×C4C22×Q811yescharacteristic
474C22×C4C2×#4111yescharacteristic
475C22×C4C2×#4111yescharacteristic
476C22×C4H(5,𝔽2)11yescharacteristic
477C22×C4H(5,𝔽2)11yescharacteristic
478C22×C42−1+411yescharacteristic
479C22×C42−1+411yescharacteristic
480C22×C42−1+411yescharacteristic
481C22×C42−1+411yescharacteristic
482C2×C8—22no—
483C2×C8—22no—
484C2×C8—22no—
485C2×C8—22no—
486C2×C8—22no—
487C2×C8—22no—
488C2×C8—22no—
489C2×C8—22no—
490C2×C8—22no—
491C2×C8—22no—
492C2×C8—22no—
493C2×C8—22no—
494C2×C8—22no—
495C2×C8—22no—
496C2×C8—22no—
497C2×C8—22no—
498C2×C8—22no—
499C2×C8—22no—
500C2×C8—41no—
501C2×C8—41no—
502C2×C8—41no—
503C2×C8—41no—
504C2×C8—41no—
505C2×C8—41no—
506C2×C8—41no—
507C2×C8—41no—
508C2×C8C22⋊Q814yes—
509C2×C8C4⋊Q814yes—
510C4⋊C4—22no—
511C4⋊C4—22no—
512C4⋊C4—22no—
513C4⋊C4—22no—
514C4⋊C4—22no—
515C4⋊C4—22no—
516C4⋊C4—22no—
517C4⋊C4—22no—
518C4⋊C4—22no—
519C4⋊C4—22no—
520C4⋊C4—22no—
521C4⋊C4—22no—
522C4⋊C4—22no—
523C4⋊C4—48no—
524C4⋊C4—48no—
525C4⋊C4—41no—
526C4⋊C4—41no—
527C4⋊C4—41no—
528C4⋊C4—41no—
529C4⋊C4—41no—
530C4⋊C4—41no—
531C4⋊C4—41no—
532C4⋊C4—41no—
533C4⋊C4—41no—
534C4⋊C4—41no—
535C4⋊C4—41no—
536C4⋊C4—41no—
537C4⋊C4—41no—
538C4⋊C4—41no—
539C4⋊C4—41no—
540C4⋊C4—41no—
541C4⋊C4—41no—
542C4⋊C4—41no—
543C4⋊C4—84no—
544C4⋊C4—84no—
545C4⋊C4—84no—
546C4⋊C4—84no—
547C4⋊C4—84no—
548C4⋊C4—84no—
549C4⋊C4#12014yes—
550C42—22no—
551C42—22no—
552C42—22no—
553C42—22no—
554C42—22no—
555C42—22no—
556C42—22no—
557C42—22no—
558C42—41no—
559C42—41no—
560C42—41no—
561C42—41no—
562C42—84no—
563C23C2×#12111yescharacteristic
564C23C2×C4⋊Q811yescharacteristic
565C23#53611yescharacteristic
566C23D4211yescharacteristic
567C23D4211yescharacteristic
568C23#54711yescharacteristic
569C23D4×Q811yescharacteristic
570C23C22×SD1611yescharacteristic
571C23C22×SD1611yescharacteristic
572C23C2×AGL(1,ℤ/8)11yescharacteristic
573C23C2×#13711yescharacteristic
574C23#57711yescharacteristic
575C23#57711yescharacteristic
576C23#57711yescharacteristic
577C23#57711yescharacteristic
578Q8—816no—
579Q8—816no—
580C2×C4—22no—
581C2×C4—22no—
582C2×C4—22no—
583C2×C4—22no—
584C2×C4—22no—
585C2×C4—22no—
586C2×C4—22no—
587C2×C4—22no—
588C2×C4—22no—
589C2×C4—22no—
590C2×C4—22no—
591C2×C4—22no—
592C2×C4—22no—
593C2×C4—22no—
594C2×C4—22no—
595C2×C4—22no—
596C2×C4—22no—
597C2×C4—22no—
598C2×C4—22no—
599C2×C4—22no—
600C2×C4—22no—
601C2×C4—22no—
602C2×C4—24no—
603C2×C4—22no—
604C2×C4—22no—
605C2×C4—22no—
606C2×C4—22no—
607C2×C4—22no—
608C2×C4—41no—
609C2×C4—41no—
610C2×C4—41no—
611C2×C4—41no—
612C2×C4—41no—
613C2×C4—41no—
614C2×C4—41no—
615C2×C4—41no—
616C2×C4—41no—
617C2×C4—41no—
618C2×C4—41no—
619C2×C4—41no—
620C2×C4—42no—
621C2×C4—42no—
622C2×C4—42no—
623C2×C4—42no—
624C2×C4—42no—
625C2×C4—42no—
626C2×C4—42no—
627C2×C4—42no—
628C2×C4—42no—
629C2×C4—42no—
630C2×C4—42no—
631C2×C4—42no—
632C2×C4—42no—
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—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—81no—
656C2×C4—81no—
657C2×C4—81no—
658C2×C4—81no—
659C2×C4—81no—
660C2×C4—81no—
661C2×C4—81no—
662C2×C4—81no—
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#46014yes—
676C2×C4#46114yes—
677C2×C4#49814yescomplemented
678C2×C4C2×#12011yescharacteristic
679C2×C4C2×C22⋊Q811yescharacteristic
680C2×C4C2×C4⋊Q811yescharacteristic
681C2×C4#53311yescharacteristic
682C2×C4#53411yescharacteristic
683C2×C4#53611yescharacteristic
684C2×C4#53611yescharacteristic
685C2×C4#54111yescharacteristic
686C2×C4#54211yescharacteristic
687C2×C4#54411yescharacteristic
688C2×C4#54411yescharacteristic
689C2×C4#54411yescharacteristic
690C2×C4#54611yescharacteristic
691C2×C4#54611yescharacteristic
692C2×C4#54811yescharacteristic
693C2×C4#54811yescharacteristic
694C2×C4D4×Q811yescharacteristic
695C2×C4D4×Q811yescharacteristic
696C2×C4D4×Q811yescharacteristic
697C2×C4D4×Q811yescharacteristic
698C2×C4D4×Q811yescharacteristic
699C2×C4D4×Q811yescharacteristic
700C2×C4#55411yescharacteristic
701C2×C4#55711yescharacteristic
702C2×C4#55711yescharacteristic
703C2×C4Q8211yescharacteristic
704C2×C4#56311yescharacteristic
705C2×C4#56311yescharacteristic
706C8—24no—
707C8—24no—
708C8—42no—
709C8—42no—
710C22#241011yescharacteristic
711C22#242911yescharacteristic
712C22#244011yescharacteristic
713C22#254611yescharacteristic
714C22#255111yescharacteristic
715C22#267411yescharacteristic
716C22#267711yescharacteristic
717C22C2×#46111yescharacteristic
718C22C2×#46011yescharacteristic
719C22#304211yescharacteristic
720C22#304311yescharacteristic
721C22C2×#49811yescharacteristic
722C22#316311yescharacteristic
723C22#316311yescharacteristic
724C22#316511yescharacteristic
725C22#322711yescharacteristic
726C22#322911yescharacteristic
727C22#324411yescharacteristic
728C22#324411yescharacteristic
729C22#326511yescharacteristic
730C22#326511yescharacteristic
731C22#326611yescharacteristic
732C22#326611yescharacteristic
733C22D4×SD1611yescharacteristic
734C22D4×SD1611yescharacteristic
735C22D4×SD1611yescharacteristic
736C22D4×SD1611yescharacteristic
737C22#333511yescharacteristic
738C22#333511yescharacteristic
739C22#335411yescharacteristic
740C22#335611yescharacteristic
741C22Q8×SD1611yescharacteristic
742C22Q8×SD1611yescharacteristic
743C22#338411yescharacteristic
744C22#338711yescharacteristic
745C4—24no—
746C4—24no—
747C4—24no—
748C4—44no—
749C4—42no—
750C4—42no—
751C4—42no—
752C4—82no—
753C4—82no—
754C4—82no—
755C4—82no—
756C4—82no—
757C4—161no—
758C4—161no—
759C4#240911yescharacteristic
760C4#243411yescharacteristic
761C4#245111yescharacteristic
762C4#255011yescharacteristic
763C4#271311yescharacteristic
764C4#271311yescharacteristic
765C4#272911yescharacteristic
766C4#273411yescharacteristic
767C2#1531811yescharacteristic
768C2#2435611yescharacteristic
769C2#2435811yescharacteristic
770C2#2545111yescharacteristic
771C2#2545311yescharacteristic
772C2#2606011yescharacteristic
773C2#2607211yescharacteristic
774C2#2868711yescharacteristic
775C2#2869611yescharacteristic
776C2#2880911yescharacteristic
777C2#2881911yescharacteristic
778C2#3077511yescharacteristic
779C2#3077711yescharacteristic
780C2#3094911yescharacteristic
781C2#3095411yescharacteristic
subgroupG/H
center, socle, prime radicalC24C22×D4
commutator, Frattini, cosocleC23×C4C24
LCSG ▷ C23×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
124. C2×C4⋊C8Q8semidirect
167. #340Q8semidirect
171. #336Q8semidirect
677. C2×C4#498semidirect

Maximal subgroups

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

subgroupindex
C22×#4982
C2×#20842
C2×#20582
C2×#19482
#151432
#140532
#113842
#113232
#112572
#112312
#112202
#109082
#108802
#108762