Finite Group Databasebeta

← #873798

Subgroups — #873798

Order 512.

3184 conjugacy classes of subgroups.

The subgroup lattice has 899 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2858C211yesmaximal, characteristic
2C2×#2545C211yesmaximal, characteristic, complemented
3C2×#2544C211yesmaximal, characteristic
4C2×#2446C211yesmaximal, characteristic, complemented
5#16292C214yesmaximal, complemented
6#15508C214yesmaximal, complemented
7#15381C214yesmaximal, complemented
8#15243C211yesmaximal, characteristic, complemented
9#15243C211yesmaximal, characteristic, complemented
10#15243C211yesmaximal, characteristic, complemented
11#15217C211yesmaximal, characteristic, complemented
12#15190C211yesmaximal, characteristic, complemented
13#15140C211yesmaximal, characteristic
14#14703C211yesmaximal, characteristic, complemented
15#14573C214yesmaximal, complemented
16#14027C211yesmaximal, characteristic, complemented
17#14027C211yesmaximal, characteristic, complemented
18#14026C211yesmaximal, characteristic, complemented
19C4×#387C211yesmaximal, characteristic, complemented
20C22×C4⋊Q8C2211yescharacteristic
21C22×C4⋊Q8C2211yescharacteristic
22C22×C4⋊Q8C2211yescharacteristic
23C22×#127C2211yescharacteristic
24C22×#124C2211yescharacteristic
25C22×#124C2211yescharacteristic
26C22×#124C2211yescharacteristic
27C22×#124C2211yescharacteristic
28C22×#124C2211yescharacteristic
29C22×#124C2211yescharacteristic
30C22×C4×Q8C2211yescharacteristic
31C22×C4×D4C2211yescharacteristic
32#2858—28no—
33#2545—28no—
34#2544—28no—
35#2446—28no—
36C2×#400C2212yes—
37C2×#398C2212yes—
38C2×#396C2214yes—
39C2×#394C2212yes—
40C2×#394C2214yes—
41C2×#394C2212yes—
42C2×#391C2211yescharacteristic
43C2×#391C2211yescharacteristic
44C2×#391C2211yescharacteristic
45C2×#391C2211yescharacteristic
46C2×#391C2211yescharacteristic
47C2×#391C2211yescharacteristic
48C2×#391C2211yescharacteristic
49C2×#391C2211yescharacteristic
50C2×#390C2214yes—
51C2×#390C2214yes—
52C2×#390C2211yescharacteristic
53C2×#390C2211yescharacteristic
54C2×#390C2211yescharacteristic
55C2×#390C2211yescharacteristic
56C2×#390C2211yescharacteristic
57C2×#389C2211yescharacteristic
58C2×#388C2214yes—
59C2×#387C2212yes—
60C2×#387C2212yes—
61C2×#387C2212yes—
62C2×#386C2212yes—
63C2×#386C2212yes—
64C2×C4×C4⋊C4C2211yescharacteristic
65C2×C4×C4⋊C4C2211yescharacteristic
66C2×C43C2211yescharacteristic
67#1444C2214yes—
68#1444C2214yes—
69#1440C2214yes—
70#1440C2214yes—
71#1440C2214yes—
72#1439C2214yes—
73#1439C2214yes—
74#1439C2214yes—
75#1439C2214yes—
76#1439C2214yes—
77#1439C2214yes—
78#1439C2214yes—
79#1439C2214yes—
80#1438C2214yes—
81#1437C2214yes—
82#1436C2212yes—
83#1436C2214yes—
84#1436C2212yes—
85C4⋊#95C2211yescharacteristic
86C4⋊#95C2211yescharacteristic
87#1434C2214yes—
88#1434C2212yes—
89C22⋊#95C2214yes—
90C22⋊#95C2214yes—
91C4×#95C2211yescharacteristic
92C4×#95C2211yescharacteristic
93C4×#95C2211yescharacteristic
94C4×#95C2211yescharacteristic
95C23×Q8C2311yescharacteristic
96C23×Q8C2311yescharacteristic
97C23×Q8C2311yescharacteristic
98C23×D4C2311yescharacteristic
99C23×D4C2311yescharacteristic
100C23×D4C2312yes—
101C23×D4C2312yes—
102C24×C4C2312yes—
103C2×C4⋊Q8—24no—
104C2×C4⋊Q8—24no—
105C2×C4⋊Q8—24no—
106C2×C4⋊Q8—42no—
107C2×C4⋊Q8—42no—
108C2×C4⋊Q8—42no—
109C2×C4⋊Q8—42no—
110C2×C4⋊Q8—42no—
111C2×C4⋊Q8—42no—
112C2×#127—24no—
113C2×#127—24no—
114C2×#127—42no—
115C2×#124—24no—
116C2×#124—24no—
117C2×#124—24no—
118C2×#124—24no—
119C2×#124—24no—
120C2×#124—24no—
121C2×#124—24no—
122C2×#124—24no—
123C2×#124—42no—
124C2×#124—42no—
125C2×#124—42no—
126C2×#124—42no—
127C2×#124—42no—
128C2×#124—42no—
129C2×#124—42no—
130C2×#124—42no—
131C2×#124—42no—
132C2×#124D418yes—
133C2×C4×Q8—24no—
134C2×C4×Q8—24no—
135C2×C4×Q8—42no—
136C2×C4×D4—24no—
137C2×C4×D4—42no—
138C2×C4×D4—42no—
139C22×C4⋊C4C2312yes—
140C22×C4⋊C4C2311yescharacteristic
141C22×C4⋊C4C2311yescharacteristic
142C22×C4⋊C4C2311yescharacteristic
143C22×C4⋊C4C2312yes—
144C22×C4⋊C4C2312yes—
145C22×C4⋊C4C2312yes—
146C22×C4⋊C4C2312yes—
147C22×C4⋊C4C2311yescharacteristic
148C22×C4⋊C4C2311yescharacteristic
149C22×C4⋊C4C2314yes—
150C22×C4⋊C4C2314yes—
151C22×C22⋊C4C2312yes—
152C22×C22⋊C4C2314yes—
153C22×C22⋊C4C2312yes—
154C22×C22⋊C4C2314yes—
155C22×C22⋊C4C2314yes—
156C22×C22⋊C4C2312yes—
157C22×C22⋊C4C2312yes—
158C22×C22⋊C4C2314yes—
159C22×C22⋊C4C2312yes—
160C22×C22⋊C4C2314yes—
161C22×C22⋊C4C2314yes—
162C22×C22⋊C4C2312yes—
163C22×C22⋊C4C2312yes—
164C22×C22⋊C4C2314yes—
165C22×C22⋊C4C2314yes—
166C22×C42C2311yescharacteristic
167C22×C42C2311yescharacteristic
168C22×C42C2312yes—
169C22×C42C2312yes—
170C22×C42C2312yes—
171C22×C42C2311yescharacteristic
172C22×C42C2311yescharacteristic
173C22×C42C2311yescharacteristic
174C22×C42C2311yescharacteristic
175C22×C42C2311yescharacteristic
176#400—28no—
177#398—28no—
178#396—216no—
179#394—28no—
180#394—28no—
181#394—216no—
182#391—24no—
183#391—24no—
184#391—24no—
185#391—24no—
186#391—24no—
187#391—24no—
188#391—42no—
189#391—42no—
190#390—24no—
191#390—216no—
192#390—216no—
193#390—24no—
194#390—42no—
195#390—42no—
196#390—42no—
197#389—24no—
198#388—216no—
199#387—28no—
200#387—28no—
201#387—28no—
202#386—28no—
203#386—28no—
204C4×C4⋊C4—24no—
205C4×C4⋊C4D418yes—
206C2×#95C2312yes—
207C2×#95C2312yes—
208C2×#95C2314yes—
209C2×#95C2312yes—
210C2×#95C2312yes—
211C2×#95C2312yes—
212C2×#95C2312yes—
213C2×#95C2312yes—
214C2×#95C2312yes—
215C2×#95C2312yes—
216C2×#95C2312yes—
217C2×#95C2312yes—
218C2×#95C2312yes—
219C2×#95C2314yes—
220C2×#95C2312yes—
221C2×#95C2312yes—
222C2×#95C2312yes—
223C2×#95C2312yes—
224C2×#95C2312yes—
225C2×#95C2314yes—
226C2×#95C2314yes—
227C2×#95C2314yes—
228C2×#95C2314yes—
229C2×#95C2311yescharacteristic
230C2×#95C2311yescharacteristic
231C2×#95C2312yes—
232C43—24no—
233C25C2412yes—
234C25C2412yes—
235C22×Q8—22no—
236C22×Q8—22no—
237C22×Q8—22no—
238C22×Q8—22no—
239C22×Q8—22no—
240C22×Q8—22no—
241C22×Q8—22no—
242C22×Q8—22no—
243C22×Q8—22no—
244C22×Q8—22no—
245C22×Q8—22no—
246C22×Q8—22no—
247C22×Q8—22no—
248C22×Q8—22no—
249C22×Q8—22no—
250C22×Q8—22no—
251C22×Q8—22no—
252C22×Q8—22no—
253C22×Q8—22no—
254C22×Q8—22no—
255C22×Q8C2×D414yes—
256C22×D4—24no—
257C22×D4—24no—
258C22×D4—22no—
259C22×D4—22no—
260C22×D4—22no—
261C22×D4—24no—
262C22×D4—24no—
263C22×D4—22no—
264C22×D4—22no—
265C22×D4—28no—
266C22×D4—22no—
267C22×D4—22no—
268C22×D4—22no—
269C22×D4—22no—
270C22×D4—22no—
271C22×D4—22no—
272C22×D4—22no—
273C22×D4—22no—
274C22×D4—28no—
275C22×D4—42no—
276C22×D4—42no—
277C22×D4—44no—
278C22×D4—44no—
279C22×D4C2×D414yes—
280C23×C4—24no—
281C23×C4—42no—
282C23×C4—42no—
283C23×C4—44no—
284C23×C4—44no—
285C23×C4C2412yes—
286C23×C4C2412yes—
287C23×C4C2412yes—
288C23×C4C2412yes—
289C23×C4C2412yes—
290C23×C4C2412yes—
291C23×C4C2411yescharacteristic
292C23×C4C2411yescharacteristic
293C23×C4C2411yescharacteristic
294C23×C4C2412yes—
295C23×C4C2411yescharacteristic
296C23×C4C2412yes—
297C23×C4C2412yes—
298C23×C4C2412yes—
299C23×C4C2411yescharacteristic
300C23×C4C2411yescharacteristic
301C23×C4C2411yescharacteristic
302C4⋊Q8—416no—
303C4⋊Q8—416no—
304C4⋊Q8—416no—
305#127—416no—
306#124—416no—
307#124—416no—
308#124—416no—
309#124—416no—
310#124—416no—
311#124—416no—
312C4×Q8—416no—
313C4×D4—416no—
314C2×C4⋊C4—24no—
315C2×C4⋊C4—24no—
316C2×C4⋊C4—22no—
317C2×C4⋊C4—22no—
318C2×C4⋊C4—22no—
319C2×C4⋊C4—24no—
320C2×C4⋊C4—24no—
321C2×C4⋊C4—24no—
322C2×C4⋊C4—24no—
323C2×C4⋊C4—28no—
324C2×C4⋊C4—24no—
325C2×C4⋊C4—24no—
326C2×C4⋊C4—24no—
327C2×C4⋊C4—24no—
328C2×C4⋊C4—22no—
329C2×C4⋊C4—24no—
330C2×C4⋊C4—22no—
331C2×C4⋊C4—28no—
332C2×C4⋊C4—22no—
333C2×C4⋊C4—22no—
334C2×C4⋊C4—22no—
335C2×C4⋊C4—22no—
336C2×C4⋊C4—42no—
337C2×C4⋊C4—42no—
338C2×C4⋊C4—42no—
339C2×C4⋊C4—42no—
340C2×C4⋊C4—44no—
341C2×C4⋊C4—44no—
342C2×C4⋊C4—44no—
343C2×C4⋊C4—44no—
344C2×C4⋊C4—44no—
345C2×C4⋊C4C2×D414yes—
346C2×C4⋊C4C2×D414yes—
347C2×C22⋊C4—24no—
348C2×C22⋊C4—28no—
349C2×C22⋊C4—24no—
350C2×C22⋊C4—28no—
351C2×C22⋊C4—24no—
352C2×C22⋊C4—24no—
353C2×C22⋊C4—24no—
354C2×C22⋊C4—24no—
355C2×C22⋊C4—28no—
356C2×C22⋊C4—28no—
357C2×C22⋊C4—24no—
358C2×C22⋊C4—28no—
359C2×C22⋊C4—28no—
360C2×C22⋊C4—28no—
361C2×C22⋊C4—24no—
362C2×C22⋊C4—24no—
363C2×C22⋊C4—28no—
364C2×C22⋊C4—28no—
365C2×C22⋊C4—28no—
366C2×C22⋊C4—44no—
367C2×C22⋊C4—42no—
368C2×C22⋊C4—42no—
369C2×C22⋊C4—44no—
370C2×C22⋊C4—44no—
371C2×C22⋊C4—44no—
372C2×C22⋊C4—42no—
373C2×C22⋊C4—44no—
374C2×C22⋊C4—42no—
375C2×C22⋊C4—44no—
376C2×C22⋊C4—42no—
377C2×C22⋊C4—42no—
378C2×C22⋊C4—44no—
379C2×C22⋊C4—42no—
380C2×C22⋊C4—42no—
381C2×C22⋊C4—44no—
382C2×C22⋊C4—44no—
383C2×C22⋊C4—44no—
384C2×C22⋊C4—44no—
385C2×C22⋊C4—44no—
386C2×C22⋊C4—44no—
387C2×C22⋊C4—44no—
388C2×C22⋊C4—44no—
389C2×C22⋊C4C2×D4116yes—
390C2×C42—22no—
391C2×C42—22no—
392C2×C42—22no—
393C2×C42—22no—
394C2×C42—22no—
395C2×C42—22no—
396C2×C42—22no—
397C2×C42—22no—
398C2×C42—22no—
399C2×C42—22no—
400C2×C42—24no—
401C2×C42—24no—
402C2×C42—22no—
403C2×C42—24no—
404C2×C42—24no—
405C2×C42—24no—
406C2×C42—22no—
407C2×C42—22no—
408C2×C42—22no—
409C2×C42—22no—
410C2×C42—22no—
411C2×C42—24no—
412C2×C42—42no—
413C2×C42—42no—
414C2×C42—42no—
415C2×C42C2×D414yes—
416C2×C42C2×D414yes—
417C2×C42C2×D414yes—
418C2×C42C2×D414yes—
419C2×C42#4114yes—
420#95—24no—
421#95—24no—
422#95—24no—
423#95—24no—
424#95—24no—
425#95—24no—
426#95—24no—
427#95—24no—
428#95—24no—
429#95—28no—
430#95—24no—
431#95—24no—
432#95—24no—
433#95—24no—
434#95—28no—
435#95—24no—
436#95—42no—
437#95—42no—
438#95—44no—
439#95—44no—
440#95—42no—
441#95—44no—
442#95—44no—
443#95C2×D414yes—
444#95C2×D414yes—
445#95#4118yes—
446C24—22no—
447C24—22no—
448C24—24no—
449C24—22no—
450C24—22no—
451C24—22no—
452C24—22no—
453C24—24no—
454C24—24no—
455C24—24no—
456C24—22no—
457C24—22no—
458C24—24no—
459C24—22no—
460C24—22no—
461C24—22no—
462C24—22no—
463C24—22no—
464C24—24no—
465C24—24no—
466C24—24no—
467C24C22×D414yes—
468C24C2511yescharacteristic
469C2×Q8—28no—
470C2×Q8—28no—
471C2×Q8—28no—
472C2×Q8—44no—
473C2×Q8—44no—
474C2×Q8—44no—
475C2×Q8—44no—
476C2×Q8—44no—
477C2×Q8—44no—
478C2×Q8—44no—
479C2×Q8—44no—
480C2×Q8—44no—
481C2×Q8—44no—
482C2×Q8—44no—
483C2×Q8—44no—
484C2×Q8—44no—
485C2×Q8—44no—
486C2×Q8—44no—
487C2×Q8—44no—
488C2×Q8—44no—
489C2×Q8—44no—
490C2×D4—28no—
491C2×D4—28no—
492C2×D4—28no—
493C2×D4—48no—
494C2×D4—48no—
495C2×D4—416no—
496C2×D4—416no—
497C2×D4—48no—
498C2×D4—44no—
499C2×D4—44no—
500C2×D4—44no—
501C2×D4—48no—
502C2×D4—44no—
503C2×D4—44no—
504C2×D4—44no—
505C2×D4—44no—
506C2×D4—44no—
507C2×D4—44no—
508C2×D4—44no—
509C2×D4—44no—
510C2×D4—84no—
511C2×D4—84no—
512C2×D4—88no—
513C2×D4—88no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—21no—
521C22×C4—22no—
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—21no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—22no—
539C22×C4—21no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
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—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—24no—
577C22×C4—24no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—22no—
591C22×C4—24no—
592C22×C4—24no—
593C22×C4—24no—
594C22×C4—24no—
595C22×C4—48no—
596C22×C4—84no—
597C22×C4—84no—
598C22×C4—88no—
599C22×C4—88no—
600C22×C4C22×D412yes—
601C22×C4C22×D412yes—
602C22×C4C22×D414yes—
603C22×C4C22×D412yes—
604C22×C4C22×D412yes—
605C22×C4C22×D414yes—
606C22×C4C22×D412yes—
607C22×C4C22×D412yes—
608C22×C4C22×D412yes—
609C22×C4C22×D412yes—
610C22×C4C2×#4114yes—
611C22×C4C2×#4114yes—
612C22×C4C2×#4114yes—
613C22×C4C2×#4114yes—
614C22×C4C2×#4112yes—
615C22×C4H(5,𝔽2)12yes—
616C22×C4H(5,𝔽2)12yes—
617C22×C4H(5,𝔽2)12yes—
618C22×C4H(5,𝔽2)12yes—
619C22×C42−1+414yes—
620C4⋊C4—28no—
621C4⋊C4—28no—
622C4⋊C4—48no—
623C4⋊C4—48no—
624C4⋊C4—48no—
625C4⋊C4—48no—
626C4⋊C4—416no—
627C4⋊C4—416no—
628C4⋊C4—48no—
629C4⋊C4—44no—
630C4⋊C4—44no—
631C4⋊C4—44no—
632C22⋊C4—416no—
633C22⋊C4—416no—
634C22⋊C4—416no—
635C22⋊C4—48no—
636C22⋊C4—48no—
637C22⋊C4—416no—
638C22⋊C4—48no—
639C22⋊C4—416no—
640C22⋊C4—48no—
641C22⋊C4—48no—
642C22⋊C4—84no—
643C22⋊C4—84no—
644C22⋊C4—88no—
645C22⋊C4—88no—
646C22⋊C4—88no—
647C42—28no—
648C42—28no—
649C42—28no—
650C42—28no—
651C42—28no—
652C42—48no—
653C42—48no—
654C42—48no—
655C42—44no—
656C42—44no—
657C23—24no—
658C23—24no—
659C23—24no—
660C23—28no—
661C23—28no—
662C23—42no—
663C23—42no—
664C23—42no—
665C23—42no—
666C23—42no—
667C23—44no—
668C23—42no—
669C23—42no—
670C23—44no—
671C23—44no—
672C23—44no—
673C23—44no—
674C23—44no—
675C23—42no—
676C23—44no—
677C23—44no—
678C23—44no—
679C23—44no—
680C23—42no—
681C23—42no—
682C23—42no—
683C23—42no—
684C23—42no—
685C23—42no—
686C23—42no—
687C23—42no—
688C23—44no—
689C23—44no—
690C23—44no—
691C23—42no—
692C23—42no—
693C23—44no—
694C23—44no—
695C23—44no—
696C23—44no—
697C23—44no—
698C23—42no—
699C23—44no—
700C23—44no—
701C23—44no—
702C23—44no—
703C23C23×D411yescharacteristic
704C23C23×D411yescharacteristic
705C23C22×#4112yes—
706C23C22×#4111yescharacteristic
707C23C2×H(5,𝔽2)11yescharacteristic
708C23C2×H(5,𝔽2)11yescharacteristic
709C23C2×H(5,𝔽2)11yescharacteristic
710C23C2×H(5,𝔽2)11yescharacteristic
711C23C2×2−1+412yes—
712C23#58512yes—
713C23#58512yes—
714Q8—416no—
715Q8—88no—
716Q8—88no—
717D4—416no—
718D4—816no—
719D4—816no—
720D4—88no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—24no—
724C2×C4—24no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—24no—
728C2×C4—24no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—24no—
732C2×C4—24no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—24no—
740C2×C4—24no—
741C2×C4—24no—
742C2×C4—24no—
743C2×C4—24no—
744C2×C4—24no—
745C2×C4—24no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—22no—
749C2×C4—22no—
750C2×C4—24no—
751C2×C4—24no—
752C2×C4—24no—
753C2×C4—24no—
754C2×C4—24no—
755C2×C4—24no—
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—42no—
779C2×C4—42no—
780C2×C4—42no—
781C2×C4—42no—
782C2×C4—42no—
783C2×C4—42no—
784C2×C4—42no—
785C2×C4—42no—
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—44no—
802C2×C4—44no—
803C2×C4—42no—
804C2×C4—42no—
805C2×C4—42no—
806C2×C4—42no—
807C2×C4—44no—
808C2×C4—44no—
809C2×C4—42no—
810C2×C4—42no—
811C2×C4—44no—
812C2×C4—44no—
813C2×C4—816no—
814C2×C4#53214yes—
815C2×C4#53414yes—
816C2×C4#53514yes—
817C2×C4#53614yes—
818C2×C4#54014yes—
819C2×C4D4214yes—
820C2×C4#54614yes—
821C2×C4#55014yes—
822C2×C4#56014yes—
823C22—48no—
824C22—44no—
825C22—44no—
826C22—44no—
827C22—48no—
828C22—82no—
829C22—82no—
830C22—84no—
831C22—84no—
832C22—82no—
833C22—82no—
834C22—84no—
835C22—82no—
836C22—82no—
837C22—82no—
838C22—82no—
839C22—84no—
840C22—82no—
841C22—84no—
842C22—84no—
843C22—82no—
844C22—82no—
845C22C2×#53211yescharacteristic
846C22C2×#53411yescharacteristic
847C22C2×#53511yescharacteristic
848C22C2×#53611yescharacteristic
849C22C2×#54011yescharacteristic
850C22C2×D4211yescharacteristic
851C22C2×#54611yescharacteristic
852C22C2×#55011yescharacteristic
853C22D4×#4112yes—
854C22#348012yes—
855C22#348912yes—
856C22#350011yescharacteristic
857C22#350011yescharacteristic
858C22#350712yes—
859C22#351112yes—
860C22#351112yes—
861C22#351412yes—
862C22#351412yes—
863C22C2×#56011yescharacteristic
864C22#355412yes—
865C22#356112yes—
866C22#356212yes—
867C22#356212yes—
868C4—24no—
869C4—24no—
870C4—44no—
871C4—42no—
872C4—42no—
873C4—42no—
874C4—44no—
875C4—44no—
876C4—44no—
877C4—44no—
878C4—42no—
879C4—82no—
880C4—82no—
881C4—82no—
882C4—82no—
883C4—82no—
884C4#267318yes—
885C2—84no—
886C2—162no—
887C2#3529811yescharacteristic
888C2#3612411yescharacteristic
889C2#3659711yescharacteristic
890C2#3742411yescharacteristic
891C2#3767611yescharacteristic
892C2#3974611yescharacteristic
893C2#3986412yes—
894C2#4002512yes—
895C2#4604812yes—
896C2C2×#267311yescharacteristic
897C2#5914612yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC22×#127C22
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×#2545C2semidirect
4. C2×#2446C2semidirect
5. #16292C2semidirect
6. #15508C2semidirect
7. #15381C2semidirect
8. #15243C2semidirect
9. #15243C2semidirect
10. #15243C2semidirect
11. #15217C2semidirect
12. #15190C2semidirect
14. #14703C2semidirect
15. #14573C2semidirect
16. #14027C2semidirect
17. #14027C2semidirect
18. #14026C2semidirect
19. C4×#387C2semidirect

Maximal subgroups

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

subgroupindex
C2×#28582
C2×#25452
C2×#25442
C2×#24462
#162922
#155082
#153812
#152432
#152172
#151902
#151402
#147032
#145732
#140272
#140262
C4×#3872