Finite Group Databasebeta

← #4307608

Subgroups — #4307608

Order 512.

5444 conjugacy classes of subgroups.

The subgroup lattice has 837 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#548C211yesmaximal, characteristic
2C2×Q8×C4⋊C4C211yesmaximal, characteristic, complemented
3C2×#2341C211yesmaximal, characteristic, complemented
4C2×#2341C211yesmaximal, characteristic, complemented
5C2×Q8×C22⋊C4C211yesmaximal, characteristic, complemented
6C2×Q8×C22⋊C4C211yesmaximal, characteristic, complemented
7#15226C213yesmaximal, complemented
8#15217C213yesmaximal, complemented
9#15182C213yesmaximal, complemented
10#15179C213yesmaximal, complemented
11#15130C213yesmaximal, complemented
12#15129C213yesmaximal, complemented
13#15126C213yesmaximal, complemented
14C4×#394C213yesmaximal, complemented
15Q8×#95C211yesmaximal, characteristic, complemented
16C23×#41C2211yescharacteristic
17C24×Q8C2211yescharacteristic
18C2×#548—28no—
19C2×#548—28no—
20C2×#548—28no—
21C22×#124C2213yes—
22C22×C22⋊Q8C2213yes—
23C22×#121C2213yes—
24C22×C4×Q8C2211yescharacteristic
25C22×C4×Q8C2211yescharacteristic
26C22×C4×Q8C2211yescharacteristic
27C22×C4×Q8C2211yescharacteristic
28C22×C4×Q8C2211yescharacteristic
29C22×C4×D4C2213yes—
30C2×#394C2213yes—
31C2×#394C2216yes—
32Q8×C4⋊C4—28no—
33#2341—28no—
34#2341—28no—
35Q8×C22⋊C4—28no—
36Q8×C22⋊C4—28no—
37C2×#391C2213yes—
38C2×#391C2213yes—
39C2×#391C2213yes—
40C2×#391C2213yes—
41C2×#390C2213yes—
42C2×#390C2213yes—
43C2×#390C2213yes—
44C2×#390C2213yes—
45C2×#389C2213yes—
46C2×#389C2213yes—
47C2×#384C2213yes—
48C2×#380C2213yes—
49C2×#380C2213yes—
50C2×#380C2213yes—
51C2×#380C2213yes—
52C2×C4×C4⋊C4C2213yes—
53C2×C4×C22⋊C4C2213yes—
54C2×C4×C22⋊C4C2213yes—
55C2×C4×C22⋊C4C2213yes—
56C2×C4×C22⋊C4C2213yes—
57#1442C2213yes—
58#1441C2216yes—
59#1441C2213yes—
60#1440C2216yes—
61#1440C2213yes—
62#1440C2216yes—
63#1440C2213yes—
64#1439C2216yes—
65#1439C2216yes—
66#1439C2216yes—
67#1439C2211yescharacteristic
68#1439C2213yes—
69#1438C2213yes—
70C4⋊#95C2213yes—
71C4⋊#95C2213yes—
72C4⋊#95C2213yes—
73C4×#95C2213yes—
74C22×#41—24no—
75C22×#41—24no—
76C22×#41—24no—
77C22×#41—24no—
78C22×#41—24no—
79C22×#41—24no—
80C22×#41D418yes—
81C23×Q8—24no—
82C23×Q8—24no—
83C23×Q8—24no—
84C23×Q8—24no—
85C23×Q8—24no—
86C23×Q8—24no—
87C23×Q8D418yes—
88C23×Q8C2313yes—
89C23×Q8C2311yescharacteristic
90C23×D4C2313yes—
91C23×D4C2313yes—
92C24×C4C2313yes—
93C24×C4C2313yes—
94#548—2128no—
95C2×#124—212no—
96C2×#124—212no—
97C2×#124—212no—
98C2×C22⋊Q8—212no—
99C2×C22⋊Q8—212no—
100C2×C22⋊Q8—212no—
101C2×#121—212no—
102C2×#121—212no—
103C2×#121—212no—
104C2×C4×Q8—24no—
105C2×C4×Q8—24no—
106C2×C4×Q8—24no—
107C2×C4×Q8—24no—
108C2×C4×Q8—24no—
109C2×C4×Q8—24no—
110C2×C4×Q8—24no—
111C2×C4×Q8—24no—
112C2×C4×Q8—24no—
113C2×C4×Q8—24no—
114C2×C4×Q8—24no—
115C2×C4×Q8—24no—
116C2×C4×Q8—24no—
117C2×C4×Q8D418yes—
118C2×C4×Q8D418yescomplemented
119C2×C4×D4—212no—
120C2×C4×D4—212no—
121C2×C4×D4—212no—
122C22×C4⋊C4C2313yes—
123C22×C4⋊C4C2313yes—
124C22×C4⋊C4C2313yes—
125C22×C4⋊C4C2313yes—
126C22×C4⋊C4C2311yescharacteristic
127C22×C4⋊C4C2313yes—
128C22×C4⋊C4C2313yes—
129C22×C4⋊C4C2313yes—
130C22×C4⋊C4C2316yes—
131C22×C22⋊C4C2313yes—
132C22×C22⋊C4C2313yes—
133C22×C22⋊C4C2311yescharacteristic
134C22×C22⋊C4C2313yes—
135C22×C22⋊C4C2316yes—
136C22×C22⋊C4C2311yescharacteristic
137C22×C22⋊C4C2313yes—
138C22×C22⋊C4C2313yes—
139C22×C22⋊C4C2313yes—
140C22×C22⋊C4C2313yes—
141C22×C22⋊C4C2311yescharacteristic
142C22×C22⋊C4C2316yes—
143C22×C22⋊C4C2316yes—
144C22×C42C2313yes—
145C22×C42C2313yes—
146C22×C42C2313yes—
147C22×C42C2313yes—
148C22×C42C2313yes—
149#394—212no—
150#394—412no—
151#391—212no—
152#391—212no—
153#391—212no—
154#391—212no—
155#390—212no—
156#390—212no—
157#390—212no—
158#390—212no—
159#389—212no—
160#389—212no—
161#384—212no—
162#380—212no—
163#380—212no—
164#380—212no—
165#380—212no—
166C4×C4⋊C4—212no—
167C4×C22⋊C4—212no—
168C4×C22⋊C4—212no—
169C4×C22⋊C4—212no—
170C4×C22⋊C4—212no—
171C2×#95C2313yes—
172C2×#95C2311yescharacteristic
173C2×#95C2313yes—
174C2×#95C2313yes—
175C2×#95C2313yes—
176C2×#95C2316yes—
177C2×#95C2313yes—
178C2×#95C2316yes—
179C2×#95C2313yes—
180C2×#95C2311yescharacteristic
181C2×#95C2311yescharacteristic
182C2×#95C2313yes—
183C2×#95C2313yes—
184C2×#95C2313yes—
185C2×#95C2316yes—
186C2×#95C2313yes—
187C2×#95C2313yes—
188C25C2413yes—
189C25C2411yescharacteristic
190C2×#41—232no—
191C2×#41—232no—
192C2×#41—232no—
193C2×#41—416no—
194C2×#41—416no—
195C2×#41—416no—
196C2×#41—416no—
197C22×Q8—232no—
198C22×Q8—232no—
199C22×Q8—232no—
200C22×Q8—26no—
201C22×Q8—26no—
202C22×Q8—26no—
203C22×Q8—26no—
204C22×Q8—26no—
205C22×Q8—26no—
206C22×Q8—416no—
207C22×Q8—416no—
208C22×Q8—416no—
209C22×Q8—416no—
210C22×Q8C2×D4112yes—
211C22×Q8C2×D414yes—
212C22×Q8C2×D414yes—
213C22×Q8C2×D414yes—
214C22×Q8C2×D414yes—
215C22×Q8#4114yes—
216C22×Q8#4114yes—
217C22×Q8#4114yes—
218C22×D4—26no—
219C22×D4—26no—
220C22×D4—26no—
221C22×D4—26no—
222C22×D4—26no—
223C22×D4—26no—
224C22×D4—26no—
225C22×D4—26no—
226C22×D4—26no—
227C22×D4—26no—
228C22×D4—26no—
229C22×D4—43no—
230C22×D4—43no—
231C22×D4C2×D4112yes—
232C23×C4—26no—
233C23×C4—26no—
234C23×C4—26no—
235C23×C4—26no—
236C23×C4—26no—
237C23×C4—26no—
238C23×C4—26no—
239C23×C4—26no—
240C23×C4—26no—
241C23×C4—26no—
242C23×C4—26no—
243C23×C4—26no—
244C23×C4C2×D4112yes—
245C23×C4C2×D4112yes—
246C23×C4C2413yes—
247C23×C4C2413yes—
248C23×C4C2413yes—
249C23×C4C2413yes—
250C23×C4C2411yescharacteristic
251C23×C4C2413yes—
252C23×C4C2413yes—
253C23×C4C2411yescharacteristic
254C23×C4C2411yescharacteristic
255C23×C4C2411yescharacteristic
256C23×C4C2411yescharacteristic
257C23×C4C2411yescharacteristic
258C23×C4C2413yes—
259#124—296no—
260C22⋊Q8—296no—
261#121—296no—
262C4×Q8—232no—
263C4×Q8—232no—
264C4×Q8—416no—
265C4×Q8—416no—
266C4×Q8—416no—
267C4×D4—296no—
268C2×C4⋊C4—26no—
269C2×C4⋊C4—26no—
270C2×C4⋊C4—26no—
271C2×C4⋊C4—26no—
272C2×C4⋊C4—26no—
273C2×C4⋊C4—26no—
274C2×C4⋊C4—22no—
275C2×C4⋊C4—26no—
276C2×C4⋊C4—22no—
277C2×C4⋊C4—22no—
278C2×C4⋊C4—26no—
279C2×C4⋊C4—26no—
280C2×C4⋊C4—26no—
281C2×C4⋊C4—26no—
282C2×C4⋊C4—26no—
283C2×C4⋊C4—26no—
284C2×C4⋊C4—26no—
285C2×C4⋊C4—26no—
286C2×C4⋊C4—26no—
287C2×C4⋊C4—26no—
288C2×C4⋊C4—26no—
289C2×C4⋊C4—212no—
290C2×C4⋊C4—43no—
291C2×C4⋊C4—46no—
292C2×C4⋊C4—46no—
293C2×C4⋊C4C2×D4112yes—
294C2×C4⋊C4C2×D4112yes—
295C2×C22⋊C4—22no—
296C2×C22⋊C4—26no—
297C2×C22⋊C4—212no—
298C2×C22⋊C4—22no—
299C2×C22⋊C4—22no—
300C2×C22⋊C4—22no—
301C2×C22⋊C4—26no—
302C2×C22⋊C4—26no—
303C2×C22⋊C4—212no—
304C2×C22⋊C4—212no—
305C2×C22⋊C4—22no—
306C2×C22⋊C4—22no—
307C2×C22⋊C4—22no—
308C2×C22⋊C4—22no—
309C2×C22⋊C4—26no—
310C2×C22⋊C4—26no—
311C2×C22⋊C4—26no—
312C2×C22⋊C4—26no—
313C2×C22⋊C4—26no—
314C2×C22⋊C4—26no—
315C2×C22⋊C4—26no—
316C2×C22⋊C4—26no—
317C2×C22⋊C4—26no—
318C2×C22⋊C4—26no—
319C2×C22⋊C4—26no—
320C2×C22⋊C4—26no—
321C2×C22⋊C4—26no—
322C2×C22⋊C4—26no—
323C2×C22⋊C4—212no—
324C2×C22⋊C4—212no—
325C2×C22⋊C4—43no—
326C2×C22⋊C4—43no—
327C2×C22⋊C4—43no—
328C2×C22⋊C4—43no—
329C2×C22⋊C4—46no—
330C2×C22⋊C4—46no—
331C2×C22⋊C4—46no—
332C2×C22⋊C4—46no—
333C2×C22⋊C4#4114yescomplemented
334C2×C42—26no—
335C2×C42—26no—
336C2×C42—26no—
337C2×C42—26no—
338C2×C42—26no—
339C2×C42—26no—
340C2×C42—26no—
341C2×C42—26no—
342C2×C42—26no—
343C2×C42—26no—
344C2×C42—26no—
345C2×C42—26no—
346C2×C42—26no—
347C2×C42C2×D4112yes—
348C2×C42C2×D4112yes—
349#95—22no—
350#95—22no—
351#95—26no—
352#95—26no—
353#95—26no—
354#95—26no—
355#95—26no—
356#95—26no—
357#95—26no—
358#95—26no—
359#95—212no—
360#95—212no—
361#95—26no—
362#95—22no—
363#95—43no—
364#95—43no—
365#95—46no—
366C24—21no—
367C24—21no—
368C24—21no—
369C24—21no—
370C24—21no—
371C24—21no—
372C24—21no—
373C24—21no—
374C24—21no—
375C24—21no—
376C24—21no—
377C24—21no—
378C24—23no—
379C24—23no—
380C24—23no—
381C24—23no—
382C24—23no—
383C24—23no—
384C24—23no—
385C24—23no—
386C24—23no—
387C24—23no—
388C24—23no—
389C24—23no—
390C24—23no—
391C24—23no—
392C24C22×D416yes—
393C24C22×D412yes—
394C24C2×#4112yes—
395C24H(5,𝔽2)12yes—
396C24C2511yescharacteristic
397#41—4128no—
398C2×Q8—224no—
399C2×Q8—224no—
400C2×Q8—224no—
401C2×Q8—4128no—
402C2×Q8—412no—
403C2×Q8—412no—
404C2×Q8—412no—
405C2×Q8—412no—
406C2×Q8#120116yes—
407C2×Q8#121116yes—
408C2×Q8#121116yes—
409C2×Q8#121116yes—
410C2×Q8#123116yes—
411C2×Q8#123116yes—
412C2×Q8#124116yes—
413C2×D4—224no—
414C2×D4—224no—
415C2×D4—224no—
416C2×D4—224no—
417C2×D4—412no—
418C2×D4—412no—
419C2×D4—412no—
420C2×D4—412no—
421C2×D4—412no—
422C2×D4—412no—
423C2×D4—412no—
424C2×D4—412no—
425C2×D4—412no—
426C2×D4—412no—
427C22×C4—21no—
428C22×C4—21no—
429C22×C4—21no—
430C22×C4—21no—
431C22×C4—21no—
432C22×C4—23no—
433C22×C4—21no—
434C22×C4—21no—
435C22×C4—21no—
436C22×C4—21no—
437C22×C4—23no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—23no—
444C22×C4—23no—
445C22×C4—23no—
446C22×C4—23no—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—23no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—23no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—23no—
457C22×C4—23no—
458C22×C4—23no—
459C22×C4—23no—
460C22×C4—23no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—23no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—23no—
473C22×C4—21no—
474C22×C4—23no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—23no—
478C22×C4—23no—
479C22×C4—224no—
480C22×C4—224no—
481C22×C4—224no—
482C22×C4—224no—
483C22×C4—224no—
484C22×C4—224no—
485C22×C4—23no—
486C22×C4—23no—
487C22×C4—23no—
488C22×C4—23no—
489C22×C4—23no—
490C22×C4—23no—
491C22×C4—23no—
492C22×C4—23no—
493C22×C4—23no—
494C22×C4—23no—
495C22×C4—23no—
496C22×C4—23no—
497C22×C4—23no—
498C22×C4—23no—
499C22×C4—23no—
500C22×C4—23no—
501C22×C4—23no—
502C22×C4—23no—
503C22×C4—23no—
504C22×C4—23no—
505C22×C4—23no—
506C22×C4—412no—
507C22×C4—412no—
508C22×C4—412no—
509C22×C4—412no—
510C22×C4—412no—
511C22×C4—412no—
512C22×C4—412no—
513C22×C4—412no—
514C22×C4C22×D416yes—
515C22×C4C22×D416yes—
516C22×C4C22×D412yes—
517C22×C4C22×D412yes—
518C22×C4C22×D416yes—
519C22×C4C22×D412yes—
520C22×C4C22×D416yes—
521C22×C4C22×D416yes—
522C22×C4C22×D416yes—
523C22×C4C22×D416yes—
524C22×C4C2×#4112yes—
525C22×C4C2×#4112yes—
526C22×C4C2×#4116yes—
527C22×C4C2×#4116yes—
528C22×C4C2×#4116yes—
529C22×C42−1+412yes—
530C22×C42−1+412yes—
531C22×C42−1+412yes—
532C4⋊C4—28no—
533C4⋊C4—224no—
534C4⋊C4—224no—
535C4⋊C4—224no—
536C4⋊C4—412no—
537C4⋊C4—412no—
538C4⋊C4—412no—
539C4⋊C4—412no—
540C4⋊C4—812no—
541C22⋊C4—28no—
542C22⋊C4—28no—
543C22⋊C4—224no—
544C22⋊C4—248no—
545C22⋊C4—28no—
546C22⋊C4—412no—
547C22⋊C4—412no—
548C22⋊C4—412no—
549C22⋊C4—412no—
550C22⋊C4—412no—
551C22⋊C4—412no—
552C22⋊C4—812no—
553C22⋊C4—812no—
554C42—224no—
555C42—224no—
556C42—412no—
557C42—412no—
558C42—412no—
559C23—22no—
560C23—22no—
561C23—22no—
562C23—22no—
563C23—22no—
564C23—22no—
565C23—22no—
566C23—22no—
567C23—22no—
568C23—22no—
569C23—22no—
570C23—22no—
571C23—22no—
572C23—22no—
573C23—22no—
574C23—22no—
575C23—22no—
576C23—22no—
577C23—26no—
578C23—26no—
579C23—26no—
580C23—26no—
581C23—26no—
582C23—26no—
583C23—26no—
584C23—41no—
585C23—41no—
586C23—41no—
587C23—41no—
588C23—41no—
589C23—41no—
590C23—41no—
591C23—41no—
592C23—41no—
593C23—41no—
594C23—41no—
595C23—41no—
596C23—41no—
597C23—41no—
598C23—41no—
599C23—41no—
600C23—43no—
601C23—43no—
602C23—43no—
603C23—43no—
604C23—43no—
605C23—43no—
606C23—43no—
607C23—43no—
608C23—43no—
609C23—43no—
610C23—43no—
611C23—43no—
612C23—43no—
613C23—43no—
614C23—43no—
615C23—43no—
616C23—43no—
617C23—43no—
618C23—43no—
619C23—43no—
620C23—43no—
621C23—43no—
622C23—43no—
623C23—43no—
624C23—43no—
625C23—43no—
626C23—43no—
627C23—43no—
628C23#55014yes—
629C23C23×D411yescharacteristic
630C23C23×D411yescharacteristic
631C23C23×D411yescharacteristic
632C23C23×D411yescharacteristic
633C23C22×#4111yescharacteristic
634C23C22×#4111yescharacteristic
635C23C22×#4111yescharacteristic
636C23C22×#4111yescharacteristic
637C23C2×H(5,𝔽2)11yescharacteristic
638C23C2×2−1+411yescharacteristic
639C23C2×2−1+411yescharacteristic
640C23C2×2−1+411yescharacteristic
641C23#58511yescharacteristic
642C23#58511yescharacteristic
643C23#58511yescharacteristic
644Q8—448no—
645Q8#394164yescomplemented
646D4—448no—
647D4—448no—
648C2×C4—22no—
649C2×C4—22no—
650C2×C4—22no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—26no—
656C2×C4—26no—
657C2×C4—22no—
658C2×C4—26no—
659C2×C4—22no—
660C2×C4—26no—
661C2×C4—22no—
662C2×C4—26no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—26no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—26no—
672C2×C4—26no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—26no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—43no—
684C2×C4—43no—
685C2×C4—41no—
686C2×C4—43no—
687C2×C4—41no—
688C2×C4—43no—
689C2×C4—43no—
690C2×C4—43no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—43no—
694C2×C4—43no—
695C2×C4—43no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—43no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—41no—
706C2×C4—41no—
707C2×C4—41no—
708C2×C4—43no—
709C2×C4—43no—
710C2×C4—448no—
711C2×C4—448no—
712C2×C4—43no—
713C2×C4—43no—
714C2×C4—43no—
715C2×C4—43no—
716C2×C4—43no—
717C2×C4—43no—
718C2×C4—43no—
719C2×C4—43no—
720C2×C4—43no—
721C2×C4—43no—
722C2×C4—43no—
723C2×C4—43no—
724C2×C4—43no—
725C2×C4—43no—
726C2×C4—43no—
727C2×C4—43no—
728C2×C4—43no—
729C2×C4—43no—
730C2×C4—43no—
731C2×C4—43no—
732C2×C4—43no—
733C2×C4C2×#120112yes—
734C2×C4C2×#121112yes—
735C2×C4C2×#121112yes—
736C2×C4C2×#121112yes—
737C2×C4C2×#123112yes—
738C2×C4C2×#123112yes—
739C2×C4C2×#124112yes—
740C2×C4#54814yescomplemented
741C22—24no—
742C22—24no—
743C22—24no—
744C22—42no—
745C22—42no—
746C22—42no—
747C22—42no—
748C22—42no—
749C22—42no—
750C22—42no—
751C22—42no—
752C22—42no—
753C22—42no—
754C22—42no—
755C22—42no—
756C22—46no—
757C22—46no—
758C22—46no—
759C22—46no—
760C22—46no—
761C22—46no—
762C22—46no—
763C22—83no—
764C22—83no—
765C22—83no—
766C22—83no—
767C22—83no—
768C22—83no—
769C22—83no—
770C22—83no—
771C22C22×#12011yescharacteristic
772C22C22×#12111yescharacteristic
773C22C22×#12111yescharacteristic
774C22C22×#12111yescharacteristic
775C22C22×#12311yescharacteristic
776C22C22×#12311yescharacteristic
777C22C22×#12411yescharacteristic
778C22C2×#54811yescharacteristic
779C22C2×#55011yescharacteristic
780C22D4×#4111yescharacteristic
781C22D4×#4111yescharacteristic
782C22#348011yescharacteristic
783C22#348211yescharacteristic
784C22#348211yescharacteristic
785C22#348611yescharacteristic
786C22#348611yescharacteristic
787C22#348711yescharacteristic
788C22#348811yescharacteristic
789C22#348811yescharacteristic
790C22#348811yescharacteristic
791C22#348911yescharacteristic
792C22#348911yescharacteristic
793C22#349711yescharacteristic
794C22#349711yescharacteristic
795C22#349711yescharacteristic
796C22#349911yescharacteristic
797C22#351611yescharacteristic
798C22#351611yescharacteristic
799C22#351811yescharacteristic
800C22#351811yescharacteristic
801C22#352211yescharacteristic
802C22#352211yescharacteristic
803C22#352211yescharacteristic
804C22#352411yescharacteristic
805C22#352411yescharacteristic
806C4—24no—
807C4—46no—
808C4—42no—
809C4—42no—
810C4—42no—
811C4—42no—
812C4—42no—
813C4—46no—
814C4—46no—
815C4—83no—
816C4—83no—
817C4—83no—
818C4C2×#394124yes—
819C2—44no—
820C2—86no—
821C2C22×#39411yescharacteristic
822C2#3568711yescharacteristic
823C2#3577111yescharacteristic
824C2#3580111yescharacteristic
825C2#3583111yescharacteristic
826C2#3583111yescharacteristic
827C2#3594811yescharacteristic
828C2#3599611yescharacteristic
829C2#3642911yescharacteristic
830C2#3643211yescharacteristic
831C2#3643411yescharacteristic
832C2#3644411yescharacteristic
833C2#3646711yescharacteristic
834C2#3648311yescharacteristic
835C2#3657611yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC22×#548C2
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24 ◁ G
LECSG ▷ C24 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C2×Q8×C4⋊C4C2semidirect
3. C2×#2341C2semidirect
4. C2×#2341C2semidirect
5. C2×Q8×C22⋊C4C2semidirect
6. C2×Q8×C22⋊C4C2semidirect
7. #15226C2semidirect
8. #15217C2semidirect
9. #15182C2semidirect
10. #15179C2semidirect
11. #15130C2semidirect
12. #15129C2semidirect
13. #15126C2semidirect
14. C4×#394C2semidirect
15. Q8×#95C2semidirect
118. C2×C4×Q8D4semidirect
333. C2×C22⋊C4#41semidirect
645. Q8#394semidirect
740. C2×C4#548semidirect

Maximal subgroups

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

subgroupindex
C22×#5482
C2×Q8×C4⋊C42
C2×#23412
C2×Q8×C22⋊C42
#152262
#152172
#151822
#151792
#151302
#151292
#151262
C4×#3942
Q8×#952