Finite Group Databasebeta

← #377542

Subgroups — #377542

Order 512.

1200 conjugacy classes of subgroups.

The subgroup lattice has 787 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2066C211yesmaximal, characteristic
2C2×#1863C211yesmaximal, characteristic
3C2×#1767C211yesmaximal, characteristic
4#14699C211yesmaximal, characteristic
5C4×#391C211yesmaximal, characteristic
6#11232C211yesmaximal, characteristic
7#11227C211yesmaximal, characteristic
8#11077C211yesmaximal, characteristic
9#10928C211yesmaximal, characteristic
10#10928C211yesmaximal, characteristic
11#10908C211yesmaximal, characteristic
12#10885C211yesmaximal, characteristic
13#10863C211yesmaximal, characteristic
14#10821C211yesmaximal, characteristic
15#10789C211yesmaximal, 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×#387—21no—
32C2×C4×C4⋊C4C2211yescharacteristic
33C2×C43C2211yescharacteristic
34#2066C418yescomplemented
35#1863—24no—
36#1767—24no—
37C2×#340C2211yescharacteristic
38C2×#340C2211yescharacteristic
39C2×#340C2211yescharacteristic
40C2×#340C2211yescharacteristic
41C2×#340C2211yescharacteristic
42C2×#340C2211yescharacteristic
43C2×#340C2211yescharacteristic
44C2×#340C2211yescharacteristic
45C2×#340C2211yescharacteristic
46C2×#340C2211yescharacteristic
47C2×#336C2211yescharacteristic
48C2×#336C2211yescharacteristic
49#1436—21no—
50#1436—21no—
51#1436—21no—
52#1436—21no—
53C4⋊#95C2211yescharacteristic
54C4⋊#95C2211yescharacteristic
55C4⋊#95C2211yescharacteristic
56C4⋊#95C2211yescharacteristic
57C4⋊#95C2211yescharacteristic
58C4⋊#95C2211yescharacteristic
59#1434—21no—
60C4×#95—21no—
61C4×#95—21no—
62C23×Q8C2311yescharacteristic
63C23×C8C2311yescharacteristic
64C23×C8C2311yescharacteristic
65C23×C8C2311yescharacteristic
66C23×C8C2311yescharacteristic
67C2×C4×Q8—22no—
68C2×C4×Q8—22no—
69C2×C4×Q8—22no—
70C2×C4×Q8—22no—
71C2×C4×Q8—41no—
72C2×C4×Q8—41no—
73C22×C4⋊C4—21no—
74C22×C4⋊C4—21no—
75C22×C4⋊C4—21no—
76C22×C4⋊C4C2311yescharacteristic
77C22×C4⋊C4C2311yescharacteristic
78C22×C4⋊C4C2311yescharacteristic
79C22×C4⋊C4C2311yescharacteristic
80C22×C4⋊C4C2311yescharacteristic
81C22×C4⋊C4C2311yescharacteristic
82C22×C4⋊C4C2311yescharacteristic
83C22×C42—21no—
84C22×C42—21no—
85C22×C42D411yescharacteristic
86C22×C42D411yescharacteristic
87C22×C42D411yescharacteristic
88C22×C42D411yescharacteristic
89C22×C42C2311yescharacteristic
90C22×C42C2311yescharacteristic
91C22×C42C2311yescharacteristic
92C2×#107—22no—
93C2×#107—22no—
94C2×#107—41no—
95C2×#106—41no—
96C2×#106—41no—
97C2×#106C2×C414yes—
98C2×C4⋊C8—22no—
99C2×C4⋊C8—22no—
100C2×C4⋊C8—22no—
101C2×C4⋊C8—22no—
102C2×C4⋊C8—22no—
103C2×C4⋊C8C2×C414yes—
104C2×#103—22no—
105C2×#103—22no—
106C2×#103—22no—
107C2×#103—22no—
108C2×#103—22no—
109C2×#103—22no—
110C2×#103—41no—
111C2×#103—41no—
112C2×#103—41no—
113C2×#103—41no—
114C2×#103C2×C414yes—
115C2×#103C2×C414yes—
116C2×#97—22no—
117C2×#97—22no—
118C2×#97—22no—
119C2×#97—22no—
120C2×#97—41no—
121C2×#97—41no—
122#391—22no—
123#391—22no—
124#391C2×C414yes—
125#391Q814yes—
126#389—22no—
127#389—22no—
128#389—22no—
129#389C2×C414yes—
130#387—44no—
131C4×C4⋊C4—41no—
132C4×C4⋊C4—41no—
133C2×#95—21no—
134C2×#95—21no—
135C2×#95—21no—
136C2×#95—21no—
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×#95—21no—
152C43—22no—
153C43—22no—
154#340—22no—
155#340—22no—
156#340—22no—
157#340—22no—
158#340—41no—
159#340—41no—
160#340—41no—
161#340—41no—
162#340—41no—
163#340C2×C414yes—
164#336—22no—
165#336D414yes—
166C22×Q8—21no—
167C22×Q8—21no—
168C22×Q8—21no—
169C22×Q8—21no—
170C22×Q8—21no—
171C22×Q8—21no—
172C22×Q8—21no—
173C22×Q8—21no—
174C22×Q8—21no—
175C22×Q8—21no—
176C22×Q8—21no—
177C22×Q8C22×C412yes—
178C22×Q8C2×Q812yes—
179C22×Q8#4112yes—
180C23×C4—21no—
181C23×C4—21no—
182C23×C4—21no—
183C23×C4—21no—
184C23×C4—21no—
185C23×C4—21no—
186C23×C4—21no—
187C23×C4—21no—
188C23×C4C2×D411yescharacteristic
189C23×C4C2×D411yescharacteristic
190C23×C4C2×D411yescharacteristic
191C23×C4C2×D411yescharacteristic
192C23×C4C2×D411yescharacteristic
193C23×C4C2×D411yescharacteristic
194C23×C4C2411yescharacteristic
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×C8—21no—
214C22×C8—21no—
215C22×C8—21no—
216C22×C8—21no—
217C22×C8C22×C412yes—
218C22×C8C22×C412yes—
219C22×C8C2×D412yes—
220C22×C8C2×D412yes—
221C22×C8#4112yes—
222C22×C8#4112yes—
223C4×Q8—44no—
224C4×Q8—44no—
225C4×Q8—44no—
226C4×Q8—44no—
227C2×C4⋊C4—21no—
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—24no—
248C2×C4⋊C4—24no—
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—21no—
263C2×C4⋊C4—21no—
264C2×C4⋊C4—21no—
265C2×C4⋊C4—21no—
266C2×C4⋊C4—42no—
267C2×C4⋊C4—42no—
268C2×C4⋊C4—42no—
269C2×C4⋊C4—42no—
270C2×C4⋊C4—42no—
271C2×C4⋊C4—42no—
272C2×C4⋊C4—42no—
273C2×C4⋊C4C22×C412yes—
274C2×C4⋊C4C22×C412yes—
275C2×C4⋊C4C22×C412yes—
276C2×C4⋊C4C2×Q812yes—
277C2×C4⋊C4#4112yes—
278C2×C42—21no—
279C2×C42—21no—
280C2×C42—21no—
281C2×C42—21no—
282C2×C42—21no—
283C2×C42—21no—
284C2×C42—21no—
285C2×C42—21no—
286C2×C42—21no—
287C2×C42—21no—
288C2×C42—21no—
289C2×C42—21no—
290C2×C42—24no—
291C2×C42—22no—
292C2×C42—22no—
293C2×C42—22no—
294C2×C42—22no—
295C2×C42—22no—
296C2×C42—22no—
297C2×C42—22no—
298C2×C42—22no—
299C2×C42—41no—
300C2×C42—41no—
301C2×C42—41no—
302C2×C42—41no—
303C2×C42—42no—
304C2×C42—42no—
305C2×C42—42no—
306C2×C42—42no—
307C2×C42—42no—
308C2×C42C22×C412yes—
309C2×C42C2×D412yes—
310C2×C42C2×Q812yes—
311C2×C42#4112yes—
312C2×C42#4112yes—
313C2×C42#4112yes—
314#107—44no—
315#106—44no—
316C4⋊C8—28no—
317C4⋊C8—28no—
318#103—28no—
319#103—44no—
320#103—44no—
321#103—44no—
322#97—44no—
323#97—44no—
324#95—24no—
325#95—24no—
326#95—24no—
327#95—24no—
328#95—24no—
329#95—42no—
330#95—42no—
331#95—42no—
332#95—42no—
333#95—42no—
334#95—42no—
335#95—42no—
336#95—42no—
337#95—42no—
338#95—42no—
339#95—42no—
340#95—42no—
341#95—42no—
342#95—42no—
343C24C22×D411yescharacteristic
344C2×Q8—22no—
345C2×Q8—22no—
346C2×Q8—22no—
347C2×Q8—22no—
348C2×Q8—22no—
349C2×Q8—22no—
350C2×Q8—22no—
351C2×Q8—22no—
352C2×Q8—22no—
353C2×Q8—22no—
354C2×Q8—22no—
355C2×Q8—22no—
356C2×Q8—22no—
357C2×Q8—22no—
358C2×Q8—22no—
359C2×Q8—41no—
360C2×Q8—41no—
361C2×Q8—41no—
362C2×Q8—41no—
363C2×Q8—41no—
364C2×Q8—41no—
365C2×Q8—41no—
366C2×Q8—41no—
367C2×Q8—41no—
368C2×Q8—41no—
369C2×Q8—41no—
370C2×Q8—41no—
371C2×Q8C4×Q814yes—
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—22no—
381C22×C4—21no—
382C22×C4—21no—
383C22×C4—21no—
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—21no—
399C22×C4—21no—
400C22×C4—21no—
401C22×C4—21no—
402C22×C4—21no—
403C22×C4—21no—
404C22×C4—21no—
405C22×C4—21no—
406C22×C4—21no—
407C22×C4—22no—
408C22×C4—22no—
409C22×C4—22no—
410C22×C4—22no—
411C22×C4—22no—
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—41no—
457C22×C4—41no—
458C22×C4—41no—
459C22×C4—41no—
460C22×C4C4×D412yes—
461C22×C4C4×D412yes—
462C22×C4#12112yes—
463C22×C4#12112yes—
464C22×C4C22⋊Q812yes—
465C22×C4C22⋊Q812yes—
466C22×C4AGL(1,ℤ/8)12yes—
467C22×C4#13712yes—
468C22×C4#13712yes—
469C22×C4#13712yes—
470C22×C4C23×C411yescharacteristic
471C22×C4C22×D411yescharacteristic
472C22×C4C22×Q811yescharacteristic
473C22×C4C2×#4111yescharacteristic
474C22×C4C2×#4111yescharacteristic
475C22×C4C2×#4111yescharacteristic
476C22×C4C2×#4111yescharacteristic
477C22×C4C2×#4111yescharacteristic
478C22×C4C2×#4111yescharacteristic
479C22×C4C2×#4111yescharacteristic
480C22×C4H(5,𝔽2)11yescharacteristic
481C22×C4H(5,𝔽2)11yescharacteristic
482C22×C4H(5,𝔽2)11yescharacteristic
483C22×C42−1+411yescharacteristic
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—41no—
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×C8—41no—
509C2×C8—41no—
510C2×C8—41no—
511C2×C8C4×D414yes—
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—48no—
523C4⋊C4—41no—
524C4⋊C4—41no—
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—48no—
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—84no—
543C42—22no—
544C42—22no—
545C42—22no—
546C42—22no—
547C42—22no—
548C42—22no—
549C42—22no—
550C42—22no—
551C42—22no—
552C42—22no—
553C42—22no—
554C42—22no—
555C42—44no—
556C42—44no—
557C42—44no—
558C42—48no—
559C42—44no—
560C42—84no—
561C23C2×C4×D411yescharacteristic
562C23C2×#12111yescharacteristic
563C23C2×C22⋊Q811yescharacteristic
564C23#52511yescharacteristic
565C23#53211yescharacteristic
566C23#53511yescharacteristic
567C23#53711yescharacteristic
568C23C2×AGL(1,ℤ/8)11yescharacteristic
569C23C2×#13711yescharacteristic
570C23C2×#13711yescharacteristic
571C23C2×#13711yescharacteristic
572C23#57511yescharacteristic
573C23#57511yescharacteristic
574C23#57511yescharacteristic
575C23#57511yescharacteristic
576Q8—24no—
577Q8—24no—
578Q8—42no—
579Q8—42no—
580Q8—42no—
581Q8—42no—
582Q8—42no—
583Q8—42no—
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—22no—
603C2×C4—22no—
604C2×C4—22no—
605C2×C4—22no—
606C2×C4—22no—
607C2×C4—22no—
608C2×C4—24no—
609C2×C4—42no—
610C2×C4—42no—
611C2×C4—41no—
612C2×C4—42no—
613C2×C4—41no—
614C2×C4—41no—
615C2×C4—41no—
616C2×C4—42no—
617C2×C4—42no—
618C2×C4—41no—
619C2×C4—41no—
620C2×C4—41no—
621C2×C4—41no—
622C2×C4—41no—
623C2×C4—41no—
624C2×C4—41no—
625C2×C4—41no—
626C2×C4—41no—
627C2×C4—41no—
628C2×C4—41no—
629C2×C4—41no—
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—42no—
642C2×C4—42no—
643C2×C4—42no—
644C2×C4—42no—
645C2×C4—42no—
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—81no—
676C2×C4—81no—
677C2×C4—81no—
678C2×C4—81no—
679C2×C4—81no—
680C2×C4#44014yes—
681C2×C4#47014yes—
682C2×C4C2×C4×D411yescharacteristic
683C2×C4C2×C4×Q811yescharacteristic
684C2×C4C4×#4111yescharacteristic
685C2×C4C4×#4111yescharacteristic
686C2×C4#51811yescharacteristic
687C2×C4#52011yescharacteristic
688C2×C4#52511yescharacteristic
689C2×C4#52911yescharacteristic
690C2×C4#52911yescharacteristic
691C2×C4#53311yescharacteristic
692C2×C4#54011yescharacteristic
693C2×C4#54211yescharacteristic
694C2×C4#54611yescharacteristic
695C2×C4#54611yescharacteristic
696C2×C4#54611yescharacteristic
697C2×C4D4×Q811yescharacteristic
698C2×C4#55111yescharacteristic
699C2×C4#55111yescharacteristic
700C2×C4#55111yescharacteristic
701C2×C4#55211yescharacteristic
702C2×C4#55211yescharacteristic
703C2×C4#55311yescharacteristic
704C2×C4#55311yescharacteristic
705C2×C4#55311yescharacteristic
706C2×C4#55411yescharacteristic
707C2×C4#55411yescharacteristic
708C2×C4#55411yescharacteristic
709C2×C4#55611yescharacteristic
710C8—24no—
711C8—42no—
712C8—42no—
713C8—42no—
714C22C4×#12111yescharacteristic
715C22C4×C22⋊Q811yescharacteristic
716C22#232411yescharacteristic
717C22#241111yescharacteristic
718C22#241711yescharacteristic
719C22#256611yescharacteristic
720C22#260111yescharacteristic
721C22C2×#44011yescharacteristic
722C22#294311yescharacteristic
723C22C4×#13711yescharacteristic
724C22C4×#13711yescharacteristic
725C22C2×#47011yescharacteristic
726C22#305411yescharacteristic
727C22#305511yescharacteristic
728C22#305611yescharacteristic
729C22#307811yescharacteristic
730C22#307811yescharacteristic
731C22#307911yescharacteristic
732C22#308011yescharacteristic
733C22#311111yescharacteristic
734C22#311311yescharacteristic
735C22#311511yescharacteristic
736C22#311711yescharacteristic
737C22#317211yescharacteristic
738C22#317211yescharacteristic
739C22#318011yescharacteristic
740C22#318111yescharacteristic
741C22#321411yescharacteristic
742C22#321511yescharacteristic
743C22#321811yescharacteristic
744C22#321911yescharacteristic
745C22#325211yescharacteristic
746C22#325211yescharacteristic
747C22#325411yescharacteristic
748C22#325611yescharacteristic
749C4—24no—
750C4—24no—
751C4—42no—
752C4—42no—
753C4—42no—
754C4—44no—
755C4—42no—
756C4—82no—
757C4—82no—
758C4—82no—
759C4—82no—
760C4—82no—
761C4—161no—
762C4—161no—
763C4#236011yescharacteristic
764C4#236411yescharacteristic
765C4#236811yescharacteristic
766C4#237311yescharacteristic
767C4#245711yescharacteristic
768C4#246511yescharacteristic
769C4#251511yescharacteristic
770C4#252211yescharacteristic
771C2#1419811yescharacteristic
772C2#2152811yescharacteristic
773C2C4×#47011yescharacteristic
774C2#2161511yescharacteristic
775C2#2161811yescharacteristic
776C2#2215211yescharacteristic
777C2#2215611yescharacteristic
778C2#2450811yescharacteristic
779C2#2451011yescharacteristic
780C2#2484211yescharacteristic
781C2#2484611yescharacteristic
782C2#2919611yescharacteristic
783C2#2919811yescharacteristic
784C2#2944611yescharacteristic
785C2#2945111yescharacteristic
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
34. #2066C4semidirect

Maximal subgroups

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

subgroupindex
C2×#20662
C2×#18632
C2×#17672
#146992
C4×#3912
#112322
#112272
#110772
#109282
#109082
#108852
#108632
#108212
#107892