Finite Group Databasebeta

← #560375

Subgroups — #560375

Order 512.

2794 conjugacy classes of subgroups.

The subgroup lattice has 882 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2632C211yesmaximal, characteristic
2C2×Q8×C4⋊C4C211yesmaximal, characteristic, complemented
3C2×#2326C211yesmaximal, characteristic
4#14563C212yesmaximal
5#14554C212yesmaximal, complemented
6#14551C212yesmaximal, complemented
7#14529C212yesmaximal, complemented
8#14413C212yesmaximal, complemented
9#14405C212yesmaximal, complemented
10#14288C211yesmaximal, characteristic
11#14188C212yesmaximal, complemented
12#14186C212yesmaximal, complemented
13#14185C212yesmaximal
14#14172C212yesmaximal, complemented
15#14164C211yesmaximal, characteristic, complemented
16#14125C212yesmaximal, complemented
17#14118C212yesmaximal, complemented
18#13961C211yesmaximal, characteristic, complemented
19#13830C211yesmaximal, characteristic, complemented
20C22×#124C2211yescharacteristic
21C22×C4×Q8C2211yescharacteristic
22C22×C4×Q8C2211yescharacteristic
23C22×C4×Q8C2212yes—
24C22×C4×D4C2211yescharacteristic
25#2632C4116yescomplemented
26C2×#399C2212yes—
27C2×#395C2212yes—
28C2×#394C2212yes—
29C2×#393C2212yes—
30Q8×C4⋊C4—28no—
31#2326—28no—
32C2×#391C2211yescharacteristic
33C2×#390C2211yescharacteristic
34C2×#389C2212yes—
35C2×#389C2212yes—
36C2×#389C2212yes—
37C2×#389C2212yes—
38C2×#388C2212yes—
39C2×#388C2212yes—
40C2×#388C2212yes—
41C2×#388C2212yes—
42C2×#388C2212yes—
43C2×#388C2212yes—
44C2×#388C2212yes—
45C2×#387C2212yes—
46C2×#385C2212yes—
47C2×#385C2212yes—
48C2×#385C2212yes—
49C2×#385C2212yes—
50C2×#384C2212yes—
51C2×#384C2211yescharacteristic
52C2×#383C2211yescharacteristic
53C2×#383C2211yescharacteristic
54C2×C4×C4⋊C4C2212yes—
55C2×C4×C4⋊C4C2211yescharacteristic
56C2×C4×C22⋊C4C2212yes—
57C2×#376C2211yescharacteristic
58#1446C2211yescharacteristic
59#1446C2212yes—
60#1446C2211yescharacteristic
61#1445C2212yes—
62#1445C2211yescharacteristic
63#1445C2211yescharacteristic
64#1444C2211yescharacteristic
65#1444C2211yescharacteristic
66#1444C2212yes—
67#1442C2211yescharacteristic
68#1442C2212yes—
69#1442C2211yescharacteristic
70#1441C2212yes—
71#1441C2212yes—
72#1441C2212yes—
73#1440C2212yes—
74#1439C2212yes—
75#1439C2212yes—
76#1439C2212yes—
77#1439C2212yes—
78#1439C2212yes—
79#1439C2212yes—
80#1439C2212yes—
81#1438C2212yes—
82#1437C2212yes—
83#1437C2212yes—
84#1437C2212yes—
85#1437C2212yes—
86#1437C2212yes—
87#1436C2212yes—
88#1436C2212yes—
89#1436C2212yes—
90#1436C2212yes—
91#1436C2212yes—
92#1436C2212yes—
93#1436C2212yes—
94#1436C2212yes—
95#1436C2212yes—
96#1436C2212yes—
97#1436C2212yes—
98#1436C2212yes—
99#1436C2212yes—
100#1436C2212yes—
101#1436C2212yes—
102#1436C2212yes—
103#1436C2212yes—
104C4⋊#95C2212yes—
105#1434C2212yes—
106#1434C2212yes—
107#1434C2212yes—
108C22⋊#95C2212yes—
109C4×#95C2212yes—
110C23×Q8C2311yescharacteristic
111C23×Q8C2311yescharacteristic
112C23×D4C2311yescharacteristic
113C24×C4C2312yes—
114C2×#124—24no—
115C2×#124—24no—
116C2×#124C2×C418yes—
117C2×C4×Q8—24no—
118C2×C4×Q8—28no—
119C2×C4×Q8—24no—
120C2×C4×Q8—24no—
121C2×C4×Q8—42no—
122C2×C4×Q8—42no—
123C2×C4×Q8—44no—
124C2×C4×Q8—44no—
125C2×C4×Q8C2×C418yescomplemented
126C2×C4×D4—24no—
127C2×C4×D4—42no—
128C2×C4×D4—42no—
129C22×C4⋊C4C2311yescharacteristic
130C22×C4⋊C4C2312yes—
131C22×C4⋊C4C2312yes—
132C22×C4⋊C4C2312yes—
133C22×C4⋊C4C2312yes—
134C22×C4⋊C4C2311yescharacteristic
135C22×C4⋊C4C2312yes—
136C22×C4⋊C4C2312yes—
137C22×C4⋊C4C2311yescharacteristic
138C22×C4⋊C4C2312yes—
139C22×C4⋊C4C2312yes—
140C22×C4⋊C4C2312yes—
141C22×C4⋊C4C2312yes—
142C22×C4⋊C4C2311yescharacteristic
143C22×C4⋊C4C2312yes—
144C22×C4⋊C4C2311yescharacteristic
145C22×C4⋊C4C2312yes—
146C22×C22⋊C4C2312yes—
147C22×C22⋊C4C2312yes—
148C22×C22⋊C4C2312yes—
149C22×C22⋊C4C2312yes—
150C22×C22⋊C4C2312yes—
151C22×C22⋊C4C2312yes—
152C22×C22⋊C4C2312yes—
153C22×C22⋊C4C2312yes—
154C22×C22⋊C4C2312yes—
155C22×C22⋊C4C2312yes—
156C22×C22⋊C4C2312yes—
157C22×C22⋊C4C2312yes—
158C22×C22⋊C4C2312yes—
159C22×C42C2311yescharacteristic
160C22×C42C2312yes—
161C22×C42C2312yes—
162C22×C42C2312yes—
163C22×C42C2312yes—
164C22×C42C2312yes—
165C22×C42C2311yescharacteristic
166C22×C42C2312yes—
167C22×C42C2312yes—
168C22×C42C2311yescharacteristic
169#399C2×C4116yescomplemented
170#395C2×C4116yescomplemented
171#394C2×C4116yes—
172#393C2×C4116yescomplemented
173#391—24no—
174#390—24no—
175#389—28no—
176#389—28no—
177#389—28no—
178#389—44no—
179#388—28no—
180#388—28no—
181#388—44no—
182#388—44no—
183#388—44no—
184#388C2×C4116yescomplemented
185#388C2×C4116yescomplemented
186#387—44no—
187#385—28no—
188#385—28no—
189#385—44no—
190#385—44no—
191#384—28no—
192#384D418yes—
193#383—24no—
194#383C2×C418yescomplemented
195C4×C4⋊C4—28no—
196C4×C4⋊C4—24no—
197C4×C22⋊C4—44no—
198#376—24no—
199C2×#95C2312yes—
200C2×#95C2312yes—
201C2×#95C2312yes—
202C2×#95C2312yes—
203C2×#95C2312yes—
204C2×#95C2312yes—
205C2×#95C2311yescharacteristic
206C2×#95C2311yescharacteristic
207C2×#95C2312yes—
208C2×#95C2312yes—
209C2×#95C2312yes—
210C2×#95C2312yes—
211C2×#95C2312yes—
212C2×#95C2312yes—
213C2×#95C2312yes—
214C2×#95C2311yescharacteristic
215C2×#95C2311yescharacteristic
216C2×#95C2312yes—
217C2×#95C2311yescharacteristic
218C2×#95C2311yescharacteristic
219C2×#95C2312yes—
220C2×#95C2312yes—
221C2×#95C2312yes—
222C2×#95C2312yes—
223C2×#95C2312yes—
224C2×#95C2312yes—
225C2×#95C2312yes—
226C2×#95C2312yes—
227C2×#95C2312yes—
228C2×#95C2312yes—
229C2×#95C2312yes—
230C2×#95C2312yes—
231C2×#95C2312yes—
232C2×#95C2312yes—
233C2×#95C2312yes—
234C2×#95C2312yes—
235C2×#95C2312yes—
236C2×#95C2312yes—
237C2×#95C2312yes—
238C2×#95C2312yes—
239C2×#95C2312yes—
240C2×#95C2311yescharacteristic
241C2×#95C2311yescharacteristic
242C25C2412yes—
243C22×Q8—22no—
244C22×Q8—22no—
245C22×Q8—22no—
246C22×Q8—22no—
247C22×Q8—24no—
248C22×Q8—24no—
249C22×Q8—41no—
250C22×Q8—41no—
251C22×Q8—41no—
252C22×Q8—41no—
253C22×Q8C22×C414yes—
254C22×Q8C22×C414yes—
255C22×D4—22no—
256C22×D4—22no—
257C22×D4—41no—
258C22×D4—41no—
259C22×D4—41no—
260C22×D4—41no—
261C22×D4C22×C414yes—
262C23×C4—24no—
263C23×C4—24no—
264C23×C4—42no—
265C23×C4—42no—
266C23×C4—42no—
267C23×C4—42no—
268C23×C4—42no—
269C23×C4C2412yes—
270C23×C4C2411yescharacteristic
271C23×C4C2411yescharacteristic
272C23×C4C2412yes—
273C23×C4C2412yes—
274C23×C4C2412yes—
275C23×C4C2412yes—
276C23×C4C2412yes—
277C23×C4C2412yes—
278C23×C4C2412yes—
279C23×C4C2412yes—
280C23×C4C2411yescharacteristic
281C23×C4C2411yescharacteristic
282C23×C4C2412yes—
283C23×C4C2411yescharacteristic
284C23×C4C2411yescharacteristic
285C23×C4C2411yescharacteristic
286C23×C4C2412yes—
287#124—232no—
288C4×Q8—232no—
289C4×Q8—416no—
290C4×Q8—432no—
291C4×D4—416no—
292C2×C4⋊C4—24no—
293C2×C4⋊C4—22no—
294C2×C4⋊C4—22no—
295C2×C4⋊C4—24no—
296C2×C4⋊C4—22no—
297C2×C4⋊C4—24no—
298C2×C4⋊C4—24no—
299C2×C4⋊C4—24no—
300C2×C4⋊C4—24no—
301C2×C4⋊C4—22no—
302C2×C4⋊C4—24no—
303C2×C4⋊C4—24no—
304C2×C4⋊C4—24no—
305C2×C4⋊C4—24no—
306C2×C4⋊C4—24no—
307C2×C4⋊C4—24no—
308C2×C4⋊C4—24no—
309C2×C4⋊C4—42no—
310C2×C4⋊C4—42no—
311C2×C4⋊C4—42no—
312C2×C4⋊C4—42no—
313C2×C4⋊C4—42no—
314C2×C4⋊C4—41no—
315C2×C4⋊C4—41no—
316C2×C4⋊C4—41no—
317C2×C4⋊C4—41no—
318C2×C4⋊C4—42no—
319C2×C4⋊C4—42no—
320C2×C4⋊C4—42no—
321C2×C4⋊C4—42no—
322C2×C4⋊C4—42no—
323C2×C4⋊C4—42no—
324C2×C4⋊C4—42no—
325C2×C4⋊C4—42no—
326C2×C4⋊C4—42no—
327C2×C4⋊C4—42no—
328C2×C4⋊C4—42no—
329C2×C4⋊C4—42no—
330C2×C4⋊C4—42no—
331C2×C4⋊C4—42no—
332C2×C4⋊C4—42no—
333C2×C4⋊C4C22×C418yes—
334C2×C4⋊C4C22×C414yes—
335C2×C4⋊C4C22×C418yes—
336C2×C4⋊C4C22×C418yes—
337C2×C4⋊C4C2×D414yes—
338C2×C4⋊C4C2×D418yes—
339C2×C4⋊C4C2×D414yes—
340C2×C4⋊C4C2×D418yes—
341C2×C22⋊C4—24no—
342C2×C22⋊C4—24no—
343C2×C22⋊C4—24no—
344C2×C22⋊C4—24no—
345C2×C22⋊C4—24no—
346C2×C22⋊C4—24no—
347C2×C22⋊C4—24no—
348C2×C22⋊C4—24no—
349C2×C22⋊C4—24no—
350C2×C22⋊C4—24no—
351C2×C22⋊C4—24no—
352C2×C22⋊C4—24no—
353C2×C22⋊C4—24no—
354C2×C22⋊C4—24no—
355C2×C22⋊C4—42no—
356C2×C22⋊C4—42no—
357C2×C22⋊C4—42no—
358C2×C22⋊C4—42no—
359C2×C22⋊C4—42no—
360C2×C22⋊C4—42no—
361C2×C22⋊C4—42no—
362C2×C22⋊C4—42no—
363C2×C22⋊C4—42no—
364C2×C22⋊C4—42no—
365C2×C22⋊C4—42no—
366C2×C22⋊C4—42no—
367C2×C22⋊C4—42no—
368C2×C22⋊C4—42no—
369C2×C22⋊C4—42no—
370C2×C22⋊C4—42no—
371C2×C22⋊C4—42no—
372C2×C22⋊C4—42no—
373C2×C22⋊C4—42no—
374C2×C22⋊C4C22×C418yes—
375C2×C22⋊C4C22×C418yes—
376C2×C22⋊C4C22×C418yes—
377C2×C22⋊C4C22×C418yes—
378C2×C22⋊C4C22×C418yes—
379C2×C22⋊C4C22×C418yes—
380C2×C42—22no—
381C2×C42—24no—
382C2×C42—24no—
383C2×C42—22no—
384C2×C42—22no—
385C2×C42—24no—
386C2×C42—24no—
387C2×C42—24no—
388C2×C42—24no—
389C2×C42—22no—
390C2×C42—24no—
391C2×C42—24no—
392C2×C42—24no—
393C2×C42—42no—
394C2×C42—42no—
395C2×C42—42no—
396C2×C42—42no—
397C2×C42—42no—
398C2×C42—41no—
399C2×C42—41no—
400C2×C42—42no—
401C2×C42—42no—
402C2×C42—42no—
403C2×C42—42no—
404C2×C42—42no—
405C2×C42—42no—
406C2×C42C22×C418yes—
407C2×C42C22×C414yes—
408C2×C42C2×D414yes—
409C2×C42#4114yes—
410#95—22no—
411#95—22no—
412#95—22no—
413#95—22no—
414#95—24no—
415#95—24no—
416#95—24no—
417#95—24no—
418#95—24no—
419#95—24no—
420#95—22no—
421#95—22no—
422#95—24no—
423#95—24no—
424#95—24no—
425#95—24no—
426#95—24no—
427#95—24no—
428#95—24no—
429#95—24no—
430#95—24no—
431#95—42no—
432#95—42no—
433#95—42no—
434#95—42no—
435#95—42no—
436#95—42no—
437#95—42no—
438#95—42no—
439#95—42no—
440#95—42no—
441#95—42no—
442#95—42no—
443#95—42no—
444#95—42no—
445#95—42no—
446#95—42no—
447#95C22×C414yes—
448#95C22×C414yes—
449#95C22×C418yes—
450#95C22×C418yes—
451#95C22×C418yes—
452#95C22×C418yes—
453C24—22no—
454C24—22no—
455C24—22no—
456C24—22no—
457C24—22no—
458C24—22no—
459C24—22no—
460C24—22no—
461C24—22no—
462C24—22no—
463C24—22no—
464C24—22no—
465C24—22no—
466C24—22no—
467C24C23×C414yes—
468C24C2511yescharacteristic
469C2×Q8—28no—
470C2×Q8—28no—
471C2×Q8—216no—
472C2×Q8—28no—
473C2×Q8—28no—
474C2×Q8—216no—
475C2×Q8—44no—
476C2×Q8—44no—
477C2×Q8—44no—
478C2×Q8—44no—
479C2×Q8—44no—
480C2×Q8—44no—
481C2×D4—28no—
482C2×D4—44no—
483C2×D4—44no—
484C2×D4—44no—
485C2×D4—44no—
486C2×D4—44no—
487C2×D4—44no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—21no—
491C22×C4—21no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—21no—
498C22×C4—21no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—21no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—21no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—21no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—21no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—21no—
580C22×C4—22no—
581C22×C4—48no—
582C22×C4—48no—
583C22×C4—84no—
584C22×C4—84no—
585C22×C4—84no—
586C22×C4—84no—
587C22×C4—84no—
588C22×C4C23×C414yes—
589C22×C4C23×C414yes—
590C22×C4C23×C414yes—
591C22×C4C23×C414yes—
592C22×C4C23×C412yes—
593C22×C4C23×C412yes—
594C22×C4C23×C412yes—
595C22×C4C23×C414yes—
596C22×C4C22×D414yes—
597C22×C4C22×D414yes—
598C22×C4C22×D412yes—
599C22×C4C22×D412yes—
600C22×C4C22×D412yes—
601C22×C4C2×#4112yes—
602C22×C4C2×#4112yes—
603C22×C4C2×#4112yes—
604C22×C4H(5,𝔽2)12yes—
605C22×C4H(5,𝔽2)12yes—
606C22×C4H(5,𝔽2)14yes—
607C22×C42−1+414yes—
608C22×C42−1+414yes—
609C4⋊C4—28no—
610C4⋊C4—216no—
611C4⋊C4—28no—
612C4⋊C4—48no—
613C4⋊C4—48no—
614C4⋊C4—48no—
615C4⋊C4—44no—
616C4⋊C4—44no—
617C4⋊C4—48no—
618C4⋊C4—48no—
619C4⋊C4—48no—
620C4⋊C4—48no—
621C4⋊C4—44no—
622C4⋊C4—84no—
623C4⋊C4—84no—
624C4⋊C4—84no—
625C4⋊C4—84no—
626C22⋊C4—216no—
627C22⋊C4—216no—
628C22⋊C4—216no—
629C22⋊C4—216no—
630C22⋊C4—48no—
631C22⋊C4—48no—
632C22⋊C4—48no—
633C22⋊C4—48no—
634C22⋊C4—84no—
635C22⋊C4—84no—
636C22⋊C4—84no—
637C22⋊C4—84no—
638C22⋊C4—84no—
639C42—28no—
640C42—216no—
641C42—48no—
642C42—48no—
643C42—48no—
644C42—44no—
645C42—48no—
646C42—84no—
647C42—84no—
648C42C4×D4116yes—
649C23—24no—
650C23—24no—
651C23—24no—
652C23—24no—
653C23—24no—
654C23—24no—
655C23—24no—
656C23—42no—
657C23—42no—
658C23—42no—
659C23—42no—
660C23—42no—
661C23—42no—
662C23—42no—
663C23—42no—
664C23—42no—
665C23—42no—
666C23—42no—
667C23—42no—
668C23—42no—
669C23—42no—
670C23—42no—
671C23—42no—
672C23—42no—
673C23—42no—
674C23—42no—
675C23—42no—
676C23—42no—
677C23—42no—
678C23—42no—
679C23—42no—
680C23—42no—
681C23—42no—
682C23—42no—
683C23—42no—
684C23C24×C411yescharacteristic
685C23C23×D411yescharacteristic
686C23C22×#4111yescharacteristic
687C23C2×H(5,𝔽2)12yes—
688C23C2×H(5,𝔽2)11yescharacteristic
689C23C2×H(5,𝔽2)11yescharacteristic
690C23C2×2−1+412yes—
691C23C2×2−1+412yes—
692C23#58511yescharacteristic
693C23#58511yescharacteristic
694C23#58512yes—
695Q8—232no—
696Q8—416no—
697D4—416no—
698C2×C4—24no—
699C2×C4—24no—
700C2×C4—24no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—24no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—24no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—24no—
711C2×C4—22no—
712C2×C4—24no—
713C2×C4—24no—
714C2×C4—24no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—24no—
718C2×C4—24no—
719C2×C4—24no—
720C2×C4—24no—
721C2×C4—24no—
722C2×C4—24no—
723C2×C4—24no—
724C2×C4—24no—
725C2×C4—24no—
726C2×C4—24no—
727C2×C4—24no—
728C2×C4—24no—
729C2×C4—24no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—24no—
733C2×C4—24no—
734C2×C4—24no—
735C2×C4—24no—
736C2×C4—24no—
737C2×C4—24no—
738C2×C4—24no—
739C2×C4—24no—
740C2×C4—24no—
741C2×C4—24no—
742C2×C4—24no—
743C2×C4—42no—
744C2×C4—42no—
745C2×C4—42no—
746C2×C4—41no—
747C2×C4—41no—
748C2×C4—41no—
749C2×C4—41no—
750C2×C4—42no—
751C2×C4—42no—
752C2×C4—42no—
753C2×C4—42no—
754C2×C4—42no—
755C2×C4—42no—
756C2×C4—42no—
757C2×C4—42no—
758C2×C4—42no—
759C2×C4—42no—
760C2×C4—42no—
761C2×C4—42no—
762C2×C4—42no—
763C2×C4—42no—
764C2×C4—42no—
765C2×C4—42no—
766C2×C4—42no—
767C2×C4—42no—
768C2×C4—42no—
769C2×C4—42no—
770C2×C4—42no—
771C2×C4—42no—
772C2×C4—42no—
773C2×C4—42no—
774C2×C4—42no—
775C2×C4—42no—
776C2×C4—42no—
777C2×C4—42no—
778C2×C4—41no—
779C2×C4—42no—
780C2×C4—41no—
781C2×C4—42no—
782C2×C4—41no—
783C2×C4—41no—
784C2×C4—41no—
785C2×C4—41no—
786C2×C4—42no—
787C2×C4—42no—
788C2×C4—42no—
789C2×C4—42no—
790C2×C4—42no—
791C2×C4—42no—
792C2×C4—42no—
793C2×C4—42no—
794C2×C4—42no—
795C2×C4—42no—
796C2×C4—42no—
797C2×C4—42no—
798C2×C4—42no—
799C2×C4—42no—
800C2×C4—42no—
801C2×C4—42no—
802C2×C4—42no—
803C2×C4—42no—
804C2×C4—42no—
805C2×C4—42no—
806C2×C4—42no—
807C2×C4—42no—
808C2×C4—816no—
809C2×C4C2×C4×D414yes—
810C2×C4C2×C4×D414yes—
811C2×C4C2×C4×D414yes—
812C2×C4#52018yes—
813C22—44no—
814C22—44no—
815C22—44no—
816C22—44no—
817C22—44no—
818C22—44no—
819C22—44no—
820C22—82no—
821C22—82no—
822C22—82no—
823C22—82no—
824C22—82no—
825C22—82no—
826C22—82no—
827C22—82no—
828C22C22×C4×D411yescharacteristic
829C22C2×#52012yes—
830C22C4×H(5,𝔽2)11yescharacteristic
831C22C4×H(5,𝔽2)11yescharacteristic
832C22C4×2−1+412yes—
833C22#348411yescharacteristic
834C22#348411yescharacteristic
835C22#348511yescharacteristic
836C22#348611yescharacteristic
837C22#348611yescharacteristic
838C22#348711yescharacteristic
839C22#349212yes—
840C22#350611yescharacteristic
841C22#350611yescharacteristic
842C22#350712yes—
843C22#354112yes—
844C22#354212yes—
845C22#354412yes—
846C22#354612yes—
847C22#355012yes—
848C22#355712yes—
849C22#356112yes—
850C22#356512yes—
851C4—24no—
852C4—28no—
853C4—24no—
854C4—24no—
855C4—44no—
856C4—44no—
857C4—42no—
858C4—44no—
859C4—42no—
860C4—44no—
861C4—44no—
862C4—44no—
863C4—44no—
864C4—82no—
865C4—81no—
866C4—82no—
867C4—82no—
868C4—81no—
869C2—84no—
870C2#3420011yescharacteristic
871C2#3426511yescharacteristic
872C2#3426611yescharacteristic
873C2#3442212yes—
874C2#3442912yes—
875C2#5200511yescharacteristic
876C2#5201111yescharacteristic
877C2#5204312yes—
878C2#5204912yes—
879C2#5205811yescharacteristic
880C2#5207211yescharacteristic
subgroupG/H
center, Frattini, socle, cosocleC24C25
commutatorC23C24×C4
prime radicalC23×D4C23
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×Q8×C4⋊C4C2semidirect
5. #14554C2semidirect
6. #14551C2semidirect
7. #14529C2semidirect
8. #14413C2semidirect
9. #14405C2semidirect
11. #14188C2semidirect
12. #14186C2semidirect
14. #14172C2semidirect
15. #14164C2semidirect
16. #14125C2semidirect
17. #14118C2semidirect
18. #13961C2semidirect
19. #13830C2semidirect
25. #2632C4semidirect
125. C2×C4×Q8C2×C4semidirect
169. #399C2×C4semidirect
170. #395C2×C4semidirect
172. #393C2×C4semidirect
184. #388C2×C4semidirect
185. #388C2×C4semidirect
194. #383C2×C4semidirect

Maximal subgroups

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

subgroupindex
C2×#26322
C2×Q8×C4⋊C42
C2×#23262
#145632
#145542
#145512
#145292
#144132
#144052
#142882
#141882
#141862
#141852
#141722
#141642
#141252
#141182
#139612
#138302