Finite Group Databasebeta

← #522130

Subgroups — #522130

Order 512.

3218 conjugacy classes of subgroups.

The subgroup lattice has 822 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2857C211yesmaximal, characteristic
2C2×#2365C211yesmaximal, characteristic, complemented
3C2×#2323C212yesmaximal
4C2×#2285C211yesmaximal, characteristic
5#14385C214yesmaximal, complemented
6#14369C214yesmaximal
7#14258C212yesmaximal
8#14155C211yesmaximal, characteristic, complemented
9#14151C211yesmaximal, characteristic, complemented
10#14021C212yesmaximal, complemented
11#14017C212yesmaximal, complemented
12#14005C212yesmaximal, complemented
13#13994C212yesmaximal
14#13981C212yesmaximal, complemented
15#13974C212yesmaximal
16C4⋊C42C211yesmaximal, characteristic, complemented
17C4×#380C211yesmaximal, characteristic
18C22×C4⋊Q8C2211yescharacteristic
19C22×C22⋊Q8C2212yes—
20C22×C4×Q8C2212yes—
21C22×#117C2212yes—
22C23×C42C2211yescharacteristic
23#2857C4116yescomplemented
24#2365—28no—
25#2323—216no—
26C2×#391C2212yes—
27C2×#391C2212yes—
28C2×#391C2212yes—
29C2×#391C2212yes—
30C2×#389C2214yes—
31C2×#389C2212yes—
32C2×#389C2212yes—
33C2×#389C2212yes—
34C2×#389C2212yes—
35C2×#389C2212yes—
36C2×#388C2214yes—
37C2×#388C2214yes—
38C2×#387C2214yes—
39C2×#387C2214yes—
40#2285—28no—
41C2×#384C2211yescharacteristic
42C2×#384C2211yescharacteristic
43C2×#384C2211yescharacteristic
44C2×#382C2212yes—
45C2×#380C2212yes—
46C2×#380C2211yescharacteristic
47C2×#380C2211yescharacteristic
48C2×#380C2211yescharacteristic
49C2×#380C2212yes—
50C2×#380C2212yes—
51C2×#380C2211yescharacteristic
52C2×C4×C4⋊C4C2212yes—
53C2×C4×C4⋊C4C2211yescharacteristic
54C2×C4×C4⋊C4C2211yescharacteristic
55C2×C4×C4⋊C4C2211yescharacteristic
56C2×C4×C4⋊C4C2212yes—
57C2×C4×C4⋊C4C2212yes—
58C2×C4×C4⋊C4C2212yes—
59C2×C4×C4⋊C4C2211yescharacteristic
60C2×C4×C22⋊C4C2212yes—
61#1445C2214yes—
62#1444C2214yes—
63#1443C2214yes—
64#1442C2214yes—
65#1442C2214yes—
66#1441C2214yes—
67#1441C2214yes—
68#1441C2214yes—
69#1440C2214yes—
70#1440C2214yes—
71#1436C2214yes—
72#1436C2214yes—
73#1436C2214yes—
74#1436C2214yes—
75C4⋊#95C2212yes—
76C4⋊#95C2212yes—
77C4⋊#95C2212yes—
78C4⋊#95C2212yes—
79C4⋊#95C2212yes—
80C4⋊#95C2212yes—
81C4⋊#95C2211yescharacteristic
82C4⋊#95C2211yescharacteristic
83#1434C2212yes—
84#1434C2214yes—
85C22⋊#95C2212yes—
86C4×#95C2212yes—
87C23×Q8C2312yes—
88C24×C4C2311yescharacteristic
89C24×C4C2311yescharacteristic
90C24×C4C2311yescharacteristic
91C2×C4⋊Q8—24no—
92C2×C4⋊Q8—24no—
93C2×C4⋊Q8C2×C418yes—
94C2×C22⋊Q8—28no—
95C2×C22⋊Q8—28no—
96C2×C22⋊Q8C2×C4116yes—
97C2×C4×Q8—28no—
98C2×C4×Q8—28no—
99C2×C4×Q8—44no—
100C2×#117—28no—
101C2×#117—28no—
102C2×#117—44no—
103C22×C4⋊C4C2311yescharacteristic
104C22×C4⋊C4C2311yescharacteristic
105C22×C4⋊C4C2311yescharacteristic
106C22×C4⋊C4C2311yescharacteristic
107C22×C4⋊C4C2312yes—
108C22×C4⋊C4C2312yes—
109C22×C4⋊C4C2314yes—
110C22×C4⋊C4C2312yes—
111C22×C4⋊C4C2312yes—
112C22×C4⋊C4C2312yes—
113C22×C4⋊C4C2314yes—
114C22×C4⋊C4C2312yes—
115C22×C4⋊C4C2312yes—
116C22×C4⋊C4C2312yes—
117C22×C4⋊C4C2311yescharacteristic
118C22×C4⋊C4C2311yescharacteristic
119C22×C4⋊C4C2311yescharacteristic
120C22×C4⋊C4C2311yescharacteristic
121C22×C4⋊C4C2314yes—
122C22×C4⋊C4C2312yes—
123C22×C22⋊C4C2312yes—
124C22×C22⋊C4C2312yes—
125C22×C22⋊C4C2314yes—
126C22×C22⋊C4C2312yes—
127C22×C22⋊C4C2312yes—
128C22×C42—24no—
129C22×C42—24no—
130C22×C42C2×C418yes—
131C22×C42C2312yes—
132C22×C42C2312yes—
133C22×C42C2312yes—
134C22×C42C2314yes—
135C22×C42C2311yescharacteristic
136C22×C42C2311yescharacteristic
137C22×C42C2311yescharacteristic
138C22×C42C2312yes—
139C22×C42C2314yes—
140C22×C42C2311yescharacteristic
141#391—28no—
142#391—28no—
143#391—44no—
144#391C2×C4116yes—
145#389—28no—
146#389—28no—
147#389—216no—
148#389—44no—
149#389C2×C4116yes—
150#389C2×C4116yes—
151#388—216no—
152#388—216no—
153#387—216no—
154#387—216no—
155#384—24no—
156#384—24no—
157#384C2×C418yes—
158#382—28no—
159#380—24no—
160#380—24no—
161#380—24no—
162#380—28no—
163#380C2×C4116yes—
164#380C2×C4116yes—
165#380D418yes—
166C4×C4⋊C4—28no—
167C4×C4⋊C4—28no—
168C4×C4⋊C4—24no—
169C4×C4⋊C4—28no—
170C4×C4⋊C4—24no—
171C4×C4⋊C4—24no—
172C4×C4⋊C4—44no—
173C4×C4⋊C4D418yes—
174C4×C22⋊C4—44no—
175C2×#95C2312yes—
176C2×#95C2312yes—
177C2×#95C2312yes—
178C2×#95C2312yes—
179C2×#95C2312yes—
180C2×#95C2312yes—
181C2×#95C2314yes—
182C2×#95C2314yes—
183C2×#95C2314yes—
184C2×#95C2314yes—
185C2×#95C2314yes—
186C2×#95C2312yes—
187C2×#95C2314yes—
188C2×#95C2312yes—
189C2×#95C2312yes—
190C2×#95C2314yes—
191C2×#95C2312yes—
192C2×#95C2314yes—
193C2×#95C2314yes—
194C2×#95C2314yes—
195C2×#95C2314yes—
196C2×#95C2314yes—
197C2×#95C2314yes—
198C2×#95C2314yes—
199C2×#95C2312yes—
200C2×#95C2312yes—
201C25C2411yescharacteristic
202C22×Q8—24no—
203C22×Q8—24no—
204C22×Q8—24no—
205C22×Q8—24no—
206C22×Q8—24no—
207C22×Q8—24no—
208C22×Q8C22×C418yes—
209C23×C4—22no—
210C23×C4—22no—
211C23×C4—22no—
212C23×C4—22no—
213C23×C4—22no—
214C23×C4—22no—
215C23×C4—22no—
216C23×C4—22no—
217C23×C4—22no—
218C23×C4—22no—
219C23×C4—22no—
220C23×C4—22no—
221C23×C4—22no—
222C23×C4—22no—
223C23×C4—41no—
224C23×C4—41no—
225C23×C4C22×C414yes—
226C23×C4C22×C414yes—
227C23×C4C22×C414yes—
228C23×C4C2×D414yes—
229C23×C4#4114yes—
230C23×C4C2412yes—
231C23×C4C2412yes—
232C23×C4C2412yes—
233C23×C4C2412yes—
234C23×C4C2414yes—
235C23×C4C2414yes—
236C23×C4C2411yescharacteristic
237C23×C4C2412yes—
238C23×C4C2412yes—
239C23×C4C2412yes—
240C23×C4C2412yes—
241C23×C4C2411yescharacteristic
242C23×C4C2411yescharacteristic
243C23×C4C2411yescharacteristic
244C23×C4C2411yescharacteristic
245C23×C4C2411yescharacteristic
246C4⋊Q8—232no—
247C22⋊Q8—264no—
248C4×Q8—432no—
249#117—432no—
250C2×C4⋊C4—22no—
251C2×C4⋊C4—24no—
252C2×C4⋊C4—28no—
253C2×C4⋊C4—24no—
254C2×C4⋊C4—24no—
255C2×C4⋊C4—24no—
256C2×C4⋊C4—28no—
257C2×C4⋊C4—24no—
258C2×C4⋊C4—24no—
259C2×C4⋊C4—22no—
260C2×C4⋊C4—22no—
261C2×C4⋊C4—22no—
262C2×C4⋊C4—24no—
263C2×C4⋊C4—24no—
264C2×C4⋊C4—22no—
265C2×C4⋊C4—22no—
266C2×C4⋊C4—22no—
267C2×C4⋊C4—22no—
268C2×C4⋊C4—24no—
269C2×C4⋊C4—24no—
270C2×C4⋊C4—24no—
271C2×C4⋊C4—24no—
272C2×C4⋊C4—28no—
273C2×C4⋊C4—28no—
274C2×C4⋊C4—24no—
275C2×C4⋊C4—24no—
276C2×C4⋊C4—22no—
277C2×C4⋊C4—22no—
278C2×C4⋊C4—22no—
279C2×C4⋊C4—22no—
280C2×C4⋊C4—22no—
281C2×C4⋊C4—22no—
282C2×C4⋊C4—22no—
283C2×C4⋊C4—22no—
284C2×C4⋊C4—24no—
285C2×C4⋊C4—24no—
286C2×C4⋊C4—22no—
287C2×C4⋊C4—22no—
288C2×C4⋊C4—22no—
289C2×C4⋊C4—22no—
290C2×C4⋊C4—28no—
291C2×C4⋊C4—42no—
292C2×C4⋊C4—42no—
293C2×C4⋊C4—42no—
294C2×C4⋊C4—42no—
295C2×C4⋊C4—42no—
296C2×C4⋊C4—42no—
297C2×C4⋊C4—44no—
298C2×C4⋊C4—44no—
299C2×C4⋊C4—44no—
300C2×C4⋊C4C22×C418yes—
301C2×C4⋊C4C22×C4116yes—
302C2×C4⋊C4C22×C418yes—
303C2×C4⋊C4C22×C418yes—
304C2×C4⋊C4C22×C418yes—
305C2×C4⋊C4C22×C418yes—
306C2×C4⋊C4C2×D414yes—
307C2×C4⋊C4C2×D414yes—
308C2×C4⋊C4C2×D414yes—
309C2×C4⋊C4C2×D414yes—
310C2×C22⋊C4—28no—
311C2×C22⋊C4—28no—
312C2×C22⋊C4—24no—
313C2×C22⋊C4—24no—
314C2×C22⋊C4—24no—
315C2×C22⋊C4—24no—
316C2×C22⋊C4—24no—
317C2×C22⋊C4—42no—
318C2×C22⋊C4—42no—
319C2×C22⋊C4—42no—
320C2×C22⋊C4—42no—
321C2×C22⋊C4—42no—
322C2×C22⋊C4—42no—
323C2×C22⋊C4C22×C4116yes—
324C2×C22⋊C4C2×D418yes—
325C2×C42—24no—
326C2×C42—22no—
327C2×C42—22no—
328C2×C42—22no—
329C2×C42—22no—
330C2×C42—22no—
331C2×C42—22no—
332C2×C42—24no—
333C2×C42—232no—
334C2×C42—24no—
335C2×C42—24no—
336C2×C42—28no—
337C2×C42—28no—
338C2×C42—24no—
339C2×C42—24no—
340C2×C42—24no—
341C2×C42—24no—
342C2×C42—24no—
343C2×C42—24no—
344C2×C42—24no—
345C2×C42—28no—
346C2×C42—44no—
347C2×C42—44no—
348C2×C42—44no—
349C2×C42C22×C414yes—
350C2×C42C22×C414yes—
351C2×C42C22×C414yes—
352C2×C42C22×C414yes—
353C2×C42C2×D418yes—
354C2×C42C2×D414yes—
355C2×C42#4114yes—
356#95—24no—
357#95—24no—
358#95—24no—
359#95—24no—
360#95—28no—
361#95—28no—
362#95—28no—
363#95—28no—
364#95—28no—
365#95—28no—
366#95—24no—
367#95—24no—
368#95—24no—
369#95—24no—
370#95—44no—
371#95—44no—
372#95—42no—
373#95—42no—
374#95—44no—
375#95—44no—
376#95—44no—
377#95—44no—
378#95C22×C4116yes—
379#95C22×C4116yes—
380#95C2×D418yes—
381#95C2×D418yes—
382C24—21no—
383C24—21no—
384C24—21no—
385C24—21no—
386C24—21no—
387C24—21no—
388C24—21no—
389C24—21no—
390C24—21no—
391C24—21no—
392C24—21no—
393C24—21no—
394C24C23×C412yes—
395C24C22×D412yes—
396C24C2×#4112yes—
397C24C2511yescharacteristic
398C2×Q8—216no—
399C2×Q8—216no—
400C2×Q8—216no—
401C2×Q8—48no—
402C2×Q8—48no—
403C2×Q8—48no—
404C2×Q8—48no—
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—28no—
418C22×C4—28no—
419C22×C4—28no—
420C22×C4—28no—
421C22×C4—28no—
422C22×C4—28no—
423C22×C4—21no—
424C22×C4—22no—
425C22×C4—24no—
426C22×C4—24no—
427C22×C4—24no—
428C22×C4—22no—
429C22×C4—22no—
430C22×C4—22no—
431C22×C4—21no—
432C22×C4—24no—
433C22×C4—24no—
434C22×C4—24no—
435C22×C4—21no—
436C22×C4—22no—
437C22×C4—24no—
438C22×C4—24no—
439C22×C4—22no—
440C22×C4—22no—
441C22×C4—22no—
442C22×C4—22no—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—24no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—24no—
459C22×C4—24no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—22no—
463C22×C4—24no—
464C22×C4—22no—
465C22×C4—28no—
466C22×C4—28no—
467C22×C4—28no—
468C22×C4—28no—
469C22×C4—28no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—44no—
499C22×C4—44no—
500C22×C4—44no—
501C22×C4—44no—
502C22×C4—44no—
503C22×C4—44no—
504C22×C4—44no—
505C22×C4—44no—
506C22×C4—44no—
507C22×C4C4×D4116yes—
508C22×C4C23×C412yes—
509C22×C4C23×C418yes—
510C22×C4C23×C418yes—
511C22×C4C23×C412yes—
512C22×C4C23×C412yes—
513C22×C4C23×C412yes—
514C22×C4C23×C412yes—
515C22×C4C23×C412yes—
516C22×C4C22×D414yes—
517C22×C4C22×D414yes—
518C22×C4C22×D414yes—
519C22×C4C22×D414yes—
520C22×C4C22×D412yes—
521C22×C4C22×D412yes—
522C22×C4C22×D412yes—
523C22×C4C22×D412yes—
524C22×C4C22×D412yes—
525C22×C4C2×#4112yes—
526C22×C4C2×#4112yes—
527C22×C4C2×#4112yes—
528C22×C4C2×#4112yes—
529C22×C4C2×#4112yes—
530C22×C4H(5,𝔽2)12yes—
531C22×C4H(5,𝔽2)12yes—
532C22×C42−1+412yes—
533C22×C42−1+412yes—
534C22×C42−1+412yes—
535C22×C42−1+412yes—
536C22×C42−1+412yes—
537C22×C42−1+412yes—
538C4⋊C4—216no—
539C4⋊C4—232no—
540C4⋊C4—216no—
541C4⋊C4—216no—
542C4⋊C4—216no—
543C4⋊C4—28no—
544C4⋊C4—28no—
545C4⋊C4—28no—
546C4⋊C4—28no—
547C4⋊C4—48no—
548C4⋊C4—48no—
549C4⋊C4—48no—
550C4⋊C4—48no—
551C4⋊C4—48no—
552C4⋊C4—416no—
553C4⋊C4—44no—
554C4⋊C4—44no—
555C4⋊C4—44no—
556C4⋊C4—44no—
557C4⋊C4—88no—
558C22⋊C4—232no—
559C22⋊C4—48no—
560C22⋊C4—48no—
561C22⋊C4—48no—
562C22⋊C4—48no—
563C42—28no—
564C42—28no—
565C42—28no—
566C42—216no—
567C42—416no—
568C42—48no—
569C42—48no—
570C42—48no—
571C42—88no—
572C42C4×D4116yes—
573C23—22no—
574C23—22no—
575C23—22no—
576C23—22no—
577C23—22no—
578C23—22no—
579C23—22no—
580C23—22no—
581C23—22no—
582C23—22no—
583C23—22no—
584C23—22no—
585C23—22no—
586C23—22no—
587C23—22no—
588C23—22no—
589C23—22no—
590C23—22no—
591C23—41no—
592C23—41no—
593C23—41no—
594C23—41no—
595C23—41no—
596C23—41no—
597C23—41no—
598C23—41no—
599C23—41no—
600C23—41no—
601C23—41no—
602C23—41no—
603C23—41no—
604C23—41no—
605C23—41no—
606C23—41no—
607C23C2×C4×D414yes—
608C23C24×C411yescharacteristic
609C23C23×D411yescharacteristic
610C23C23×D411yescharacteristic
611C23C22×#4111yescharacteristic
612C23C22×#4111yescharacteristic
613C23C2×H(5,𝔽2)11yescharacteristic
614C23C2×H(5,𝔽2)11yescharacteristic
615C23C2×2−1+411yescharacteristic
616C23C2×2−1+411yescharacteristic
617C23C2×2−1+411yescharacteristic
618C23C2×2−1+411yescharacteristic
619C23C2×2−1+411yescharacteristic
620C23C2×2−1+411yescharacteristic
621C23#58511yescharacteristic
622C23#58511yescharacteristic
623Q8—432no—
624C2×C4—22no—
625C2×C4—22no—
626C2×C4—22no—
627C2×C4—22no—
628C2×C4—22no—
629C2×C4—22no—
630C2×C4—22no—
631C2×C4—22no—
632C2×C4—22no—
633C2×C4—22no—
634C2×C4—22no—
635C2×C4—22no—
636C2×C4—22no—
637C2×C4—22no—
638C2×C4—22no—
639C2×C4—22no—
640C2×C4—22no—
641C2×C4—22no—
642C2×C4—232no—
643C2×C4—22no—
644C2×C4—28no—
645C2×C4—28no—
646C2×C4—28no—
647C2×C4—22no—
648C2×C4—28no—
649C2×C4—22no—
650C2×C4—28no—
651C2×C4—28no—
652C2×C4—24no—
653C2×C4—24no—
654C2×C4—24no—
655C2×C4—24no—
656C2×C4—24no—
657C2×C4—24no—
658C2×C4—24no—
659C2×C4—24no—
660C2×C4—24no—
661C2×C4—24no—
662C2×C4—24no—
663C2×C4—24no—
664C2×C4—416no—
665C2×C4—41no—
666C2×C4—42no—
667C2×C4—41no—
668C2×C4—41no—
669C2×C4—42no—
670C2×C4—41no—
671C2×C4—44no—
672C2×C4—44no—
673C2×C4—44no—
674C2×C4—44no—
675C2×C4—42no—
676C2×C4—42no—
677C2×C4—42no—
678C2×C4—44no—
679C2×C4—44no—
680C2×C4—42no—
681C2×C4—42no—
682C2×C4—42no—
683C2×C4—44no—
684C2×C4—44no—
685C2×C4—42no—
686C2×C4—42no—
687C2×C4—42no—
688C2×C4—42no—
689C2×C4—42no—
690C2×C4—42no—
691C2×C4—42no—
692C2×C4—42no—
693C2×C4—416no—
694C2×C4—42no—
695C2×C4—42no—
696C2×C4—42no—
697C2×C4—42no—
698C2×C4—42no—
699C2×C4—42no—
700C2×C4—42no—
701C2×C4—42no—
702C2×C4—42no—
703C2×C4—42no—
704C2×C4—42no—
705C2×C4—42no—
706C2×C4—42no—
707C2×C4—42no—
708C2×C4—42no—
709C2×C4—42no—
710C2×C4—42no—
711C2×C4—42no—
712C2×C4—42no—
713C2×C4—42no—
714C2×C4—42no—
715C2×C4—42no—
716C2×C4—42no—
717C2×C4—42no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4C2×C4×D414yes—
723C2×C4C2×C4×D414yes—
724C2×C4C2×C4×D414yes—
725C2×C4C2×C4×D414yes—
726C2×C4C2×C4×D414yes—
727C2×C4#51914yes—
728C2×C4#51914yes—
729C2×C4#52014yes—
730C2×C4#52014yes—
731C2×C4#53614yes—
732C2×C4#53714yes—
733C2×C4#54114yes—
734C2×C4#54214yes—
735C2×C4D4214yes—
736C2×C4#54714yes—
737C2×C4#54814yes—
738C2×C4#55314yes—
739C22—24no—
740C22—24no—
741C22—24no—
742C22—42no—
743C22—42no—
744C22—42no—
745C22—42no—
746C22—42no—
747C22—42no—
748C22—42no—
749C22—42no—
750C22—42no—
751C22—42no—
752C22—42no—
753C22—42no—
754C22C22×C4×D411yescharacteristic
755C22C22×C4×D411yescharacteristic
756C22C2×#51911yescharacteristic
757C22C2×#51911yescharacteristic
758C22C2×#52011yescharacteristic
759C22C2×#52011yescharacteristic
760C22#342811yescharacteristic
761C22C2×#53611yescharacteristic
762C22C2×#53711yescharacteristic
763C22C2×#54111yescharacteristic
764C22C2×#54211yescharacteristic
765C22C2×D4211yescharacteristic
766C22C2×#54711yescharacteristic
767C22C2×#54811yescharacteristic
768C22C2×#55311yescharacteristic
769C22#348911yescharacteristic
770C22#348911yescharacteristic
771C22#349511yescharacteristic
772C22#349511yescharacteristic
773C22#349611yescharacteristic
774C22#349711yescharacteristic
775C22#349911yescharacteristic
776C22#349911yescharacteristic
777C22#350611yescharacteristic
778C22#350711yescharacteristic
779C22#350911yescharacteristic
780C22#350911yescharacteristic
781C22#354711yescharacteristic
782C22#354711yescharacteristic
783C22#354811yescharacteristic
784C22#355011yescharacteristic
785C22#355011yescharacteristic
786C22#355511yescharacteristic
787C22#355511yescharacteristic
788C22#355611yescharacteristic
789C4—24no—
790C4—24no—
791C4—24no—
792C4—42no—
793C4—48no—
794C4—48no—
795C4—44no—
796C4—44no—
797C4—44no—
798C4—44no—
799C4—82no—
800C4—82no—
801C4—82no—
802C4—82no—
803C4#232318yescomplemented
804C4#236118yes—
805C2—44no—
806C2C2×#232311yescharacteristic
807C2C2×#236111yescharacteristic
808C2#3420311yescharacteristic
809C2#3420611yescharacteristic
810C2#3420911yescharacteristic
811C2#3437411yescharacteristic
812C2#3439411yescharacteristic
813C2#3934011yescharacteristic
814C2#3934311yescharacteristic
815C2#3935011yescharacteristic
816C2#3935311yescharacteristic
817C2#3972411yescharacteristic
818C2#3972711yescharacteristic
819C2#3973411yescharacteristic
820C2#3973711yescharacteristic
subgroupG/H
center, Frattini, socle, cosocleC24C25
commutatorC23C24×C4
prime radicalC25C24
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24 ◁ G
LECSG ▷ C24 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C2×#2365C2semidirect
5. #14385C2semidirect
8. #14155C2semidirect
9. #14151C2semidirect
10. #14021C2semidirect
11. #14017C2semidirect
12. #14005C2semidirect
14. #13981C2semidirect
16. C4⋊C42C2semidirect
23. #2857C4semidirect
803. C4#2323semidirect

Maximal subgroups

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

subgroupindex
C2×#28572
C2×#23652
C2×#23232
C2×#22852
#143852
#143692
#142582
#141552
#141512
#140212
#140172
#140052
#139942
#139812
#139742
C4⋊C422
C4×#3802