Finite Group Databasebeta

← #674266

Subgroups — #674266

Order 512.

3810 conjugacy classes of subgroups.

The subgroup lattice has 942 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2857C211yesmaximal, characteristic, complemented
2C2×#2547C211yesmaximal, characteristic, complemented
3C2×#2427C212yesmaximal
4C2×D4×C4⋊C4C211yesmaximal, characteristic, complemented
5C2×C4×#121C211yesmaximal, characteristic
6#15390C214yesmaximal, complemented
7#15290C214yesmaximal, complemented
8#15189C212yesmaximal, complemented
9#15179C212yesmaximal, complemented
10#15132C212yesmaximal, complemented
11#15129C212yesmaximal, complemented
12#14155C211yesmaximal, characteristic, complemented
13#14151C211yesmaximal, characteristic, complemented
14#14027C212yesmaximal, complemented
15#13907C212yesmaximal, complemented
16#13872C212yesmaximal, complemented
17C4×#380C211yesmaximal, characteristic, complemented
18C22×C4⋊Q8C2211yescharacteristic
19C22×#124C2212yes—
20C22×C22⋊Q8C2212yes—
21C22×#121C2211yescharacteristic
22C22×C4×D4C2212yes—
23C22×C4×D4C2212yes—
24C22×C4×D4C2211yescharacteristic
25C23×C4⋊C4C2212yes—
26C23×C42C2211yescharacteristic
27#2857—28no—
28#2547—28no—
29#2427—216no—
30C2×#397C2214yes—
31C2×#397C2214yes—
32C2×#394C2214yes—
33D4×C4⋊C4—28no—
34C4×#121—28no—
35C2×#391C2212yes—
36C2×#391C2212yes—
37C2×#391C2212yes—
38C2×#391C2212yes—
39C2×#390C2211yescharacteristic
40C2×#389C2212yes—
41C2×#389C2212yes—
42C2×#389C2212yes—
43C2×#389C2212yes—
44C2×#389C2211yescharacteristic
45C2×#389C2212yes—
46C2×#388C2212yes—
47C2×#386C2212yes—
48C2×#386C2214yes—
49C2×#385C2214yes—
50C2×#384C2211yescharacteristic
51C2×#380C2212yes—
52C2×#380C2212yes—
53C2×#380C2211yescharacteristic
54C2×#380C2212yes—
55C2×#380C2212yes—
56C2×#380C2212yes—
57C2×#380C2211yescharacteristic
58C2×#380C2211yescharacteristic
59C2×#380C2214yes—
60C2×C4×C4⋊C4C2211yescharacteristic
61C2×C4×C4⋊C4C2211yescharacteristic
62C2×C4×C4⋊C4C2211yescharacteristic
63C2×C4×C22⋊C4C2212yes—
64C2×C4×C22⋊C4C2212yes—
65#1445C2214yes—
66#1443C2214yes—
67#1442C2214yes—
68#1441C2214yes—
69#1441C2214yes—
70#1441C2214yes—
71#1441C2214yes—
72#1441C2214yes—
73#1440C2214yes—
74#1440C2214yes—
75#1440C2214yes—
76#1439C2214yes—
77C4⋊#95C2212yes—
78C4⋊#95C2211yescharacteristic
79C4⋊#95C2212yes—
80C4⋊#95C2212yes—
81C4⋊#95C2212yes—
82C4⋊#95C2211yescharacteristic
83#1434C2212yes—
84C22⋊#95C2212yes—
85C22⋊#95C2214yes—
86C22⋊#95C2214yes—
87C4×#95C2212yes—
88C23×Q8C2312yes—
89C23×D4C2312yes—
90C23×D4C2311yescharacteristic
91C24×C4C2311yescharacteristic
92C24×C4C2312yes—
93C24×C4C2311yescharacteristic
94C24×C4C2311yescharacteristic
95C24×C4C2314yes—
96C2×C4⋊Q8—24no—
97C2×C4⋊Q8—24no—
98C2×C4⋊Q8—24no—
99C2×#124—28no—
100C2×#124—28no—
101C2×#124—28no—
102C2×C22⋊Q8—28no—
103C2×C22⋊Q8—28no—
104C2×C22⋊Q8—44no—
105C2×#121—24no—
106C2×#121—24no—
107C2×#121D418yes—
108C2×C4×D4—28no—
109C2×C4×D4—28no—
110C2×C4×D4—28no—
111C2×C4×D4—28no—
112C2×C4×D4—24no—
113C2×C4×D4—24no—
114C2×C4×D4—44no—
115C2×C4×D4—44no—
116C2×C4×D4D418yes—
117C22×C4⋊C4—28no—
118C22×C4⋊C4—28no—
119C22×C4⋊C4—44no—
120C22×C4⋊C4C2312yes—
121C22×C4⋊C4C2312yes—
122C22×C4⋊C4C2311yescharacteristic
123C22×C4⋊C4C2311yescharacteristic
124C22×C4⋊C4C2311yescharacteristic
125C22×C4⋊C4C2311yescharacteristic
126C22×C4⋊C4C2314yes—
127C22×C4⋊C4C2314yes—
128C22×C4⋊C4C2312yes—
129C22×C4⋊C4C2312yes—
130C22×C4⋊C4C2312yes—
131C22×C4⋊C4C2311yescharacteristic
132C22×C4⋊C4C2311yescharacteristic
133C22×C4⋊C4C2311yescharacteristic
134C22×C4⋊C4C2314yes—
135C22×C4⋊C4C2312yes—
136C22×C22⋊C4C2312yes—
137C22×C22⋊C4C2314yes—
138C22×C22⋊C4C2314yes—
139C22×C22⋊C4C2314yes—
140C22×C22⋊C4C2314yes—
141C22×C22⋊C4C2312yes—
142C22×C22⋊C4C2312yes—
143C22×C22⋊C4C2312yes—
144C22×C22⋊C4C2312yes—
145C22×C22⋊C4C2312yes—
146C22×C22⋊C4C2312yes—
147C22×C42—24no—
148C22×C42—24no—
149C22×C42—24no—
150C22×C42C2311yescharacteristic
151C22×C42C2311yescharacteristic
152C22×C42C2311yescharacteristic
153C22×C42C2312yes—
154C22×C42C2312yes—
155C22×C42C2312yes—
156C22×C42C2311yescharacteristic
157#397—216no—
158#397—216no—
159#394—216no—
160#391—28no—
161#391—28no—
162#391—28no—
163#391—44no—
164#390—24no—
165#389—28no—
166#389—28no—
167#389—28no—
168#389—28no—
169#389—24no—
170#389—44no—
171#388—28no—
172#386—216no—
173#386—28no—
174#385—216no—
175#384D418yescomplemented
176#380—28no—
177#380—28no—
178#380—24no—
179#380—28no—
180#380—28no—
181#380—28no—
182#380—24no—
183#380—24no—
184#380—216no—
185C4×C4⋊C4—24no—
186C4×C4⋊C4—24no—
187C4×C4⋊C4—24no—
188C4×C22⋊C4—28no—
189C4×C22⋊C4—28no—
190C2×#95C2314yes—
191C2×#95C2312yes—
192C2×#95C2312yes—
193C2×#95C2314yes—
194C2×#95C2314yes—
195C2×#95C2314yes—
196C2×#95C2312yes—
197C2×#95C2312yes—
198C2×#95C2312yes—
199C2×#95C2312yes—
200C2×#95C2314yes—
201C2×#95C2314yes—
202C2×#95C2312yes—
203C2×#95C2314yes—
204C2×#95C2314yes—
205C2×#95C2312yes—
206C2×#95C2312yes—
207C2×#95C2312yes—
208C2×#95C2312yes—
209C2×#95C2314yes—
210C2×#95C2314yes—
211C2×#95C2314yes—
212C2×#95C2314yes—
213C25C2412yes—
214C25C2411yescharacteristic
215C22×Q8—24no—
216C22×Q8—24no—
217C22×Q8—24no—
218C22×Q8—24no—
219C22×Q8—24no—
220C22×Q8—24no—
221C22×Q8—24no—
222C22×D4—24no—
223C22×D4—24no—
224C22×D4—24no—
225C22×D4—24no—
226C22×D4—22no—
227C22×D4—22no—
228C22×D4—22no—
229C22×D4—22no—
230C22×D4—42no—
231C22×D4—42no—
232C22×D4C2×D418yes—
233C22×D4C2×D414yes—
234C22×D4C2×D414yes—
235C22×D4#4114yes—
236C23×C4—22no—
237C23×C4—24no—
238C23×C4—22no—
239C23×C4—22no—
240C23×C4—22no—
241C23×C4—22no—
242C23×C4—22no—
243C23×C4—24no—
244C23×C4—24no—
245C23×C4—24no—
246C23×C4—22no—
247C23×C4—22no—
248C23×C4—22no—
249C23×C4—22no—
250C23×C4—24no—
251C23×C4—22no—
252C23×C4—22no—
253C23×C4—22no—
254C23×C4—22no—
255C23×C4—24no—
256C23×C4—22no—
257C23×C4—28no—
258C23×C4—22no—
259C23×C4—22no—
260C23×C4—28no—
261C23×C4—28no—
262C23×C4—41no—
263C23×C4—41no—
264C23×C4—44no—
265C23×C4—44no—
266C23×C4—44no—
267C23×C4—44no—
268C23×C4C2×D418yes—
269C23×C4C2×D414yes—
270C23×C4#4114yes—
271C23×C4C2414yes—
272C23×C4C2412yes—
273C23×C4C2412yes—
274C23×C4C2412yes—
275C23×C4C2412yes—
276C23×C4C2414yes—
277C23×C4C2412yes—
278C23×C4C2411yescharacteristic
279C23×C4C2412yes—
280C23×C4C2411yescharacteristic
281C23×C4C2412yes—
282C23×C4C2411yescharacteristic
283C23×C4C2411yescharacteristic
284C23×C4C2411yescharacteristic
285C23×C4C2411yescharacteristic
286C4⋊Q8—416no—
287#124—432no—
288C22⋊Q8—432no—
289#121—232no—
290C4×D4—232no—
291C4×D4—432no—
292C4×D4—432no—
293C2×C4⋊C4—22no—
294C2×C4⋊C4—24no—
295C2×C4⋊C4—22no—
296C2×C4⋊C4—22no—
297C2×C4⋊C4—24no—
298C2×C4⋊C4—22no—
299C2×C4⋊C4—22no—
300C2×C4⋊C4—22no—
301C2×C4⋊C4—24no—
302C2×C4⋊C4—24no—
303C2×C4⋊C4—28no—
304C2×C4⋊C4—24no—
305C2×C4⋊C4—28no—
306C2×C4⋊C4—28no—
307C2×C4⋊C4—24no—
308C2×C4⋊C4—24no—
309C2×C4⋊C4—24no—
310C2×C4⋊C4—24no—
311C2×C4⋊C4—22no—
312C2×C4⋊C4—22no—
313C2×C4⋊C4—22no—
314C2×C4⋊C4—22no—
315C2×C4⋊C4—28no—
316C2×C4⋊C4—24no—
317C2×C4⋊C4—24no—
318C2×C4⋊C4—24no—
319C2×C4⋊C4—22no—
320C2×C4⋊C4—22no—
321C2×C4⋊C4—22no—
322C2×C4⋊C4—22no—
323C2×C4⋊C4—22no—
324C2×C4⋊C4—22no—
325C2×C4⋊C4—22no—
326C2×C4⋊C4—22no—
327C2×C4⋊C4—28no—
328C2×C4⋊C4—432no—
329C2×C4⋊C4—44no—
330C2×C4⋊C4—42no—
331C2×C4⋊C4—42no—
332C2×C4⋊C4—42no—
333C2×C4⋊C4—44no—
334C2×C4⋊C4—44no—
335C2×C4⋊C4—44no—
336C2×C4⋊C4C2×D418yes—
337C2×C4⋊C4C2×D418yes—
338C2×C4⋊C4C2×D414yes—
339C2×C4⋊C4C2×D414yes—
340C2×C4⋊C4C2×D418yes—
341C2×C4⋊C4#4114yes—
342C2×C22⋊C4—24no—
343C2×C22⋊C4—24no—
344C2×C22⋊C4—24no—
345C2×C22⋊C4—24no—
346C2×C22⋊C4—24no—
347C2×C22⋊C4—28no—
348C2×C22⋊C4—28no—
349C2×C22⋊C4—28no—
350C2×C22⋊C4—28no—
351C2×C22⋊C4—28no—
352C2×C22⋊C4—28no—
353C2×C22⋊C4—24no—
354C2×C22⋊C4—24no—
355C2×C22⋊C4—24no—
356C2×C22⋊C4—24no—
357C2×C22⋊C4—28no—
358C2×C22⋊C4—28no—
359C2×C22⋊C4—24no—
360C2×C22⋊C4—24no—
361C2×C22⋊C4—28no—
362C2×C22⋊C4—24no—
363C2×C22⋊C4—28no—
364C2×C22⋊C4—24no—
365C2×C22⋊C4—24no—
366C2×C22⋊C4—24no—
367C2×C22⋊C4—42no—
368C2×C22⋊C4—42no—
369C2×C22⋊C4—44no—
370C2×C22⋊C4—42no—
371C2×C22⋊C4—42no—
372C2×C22⋊C4—44no—
373C2×C22⋊C4C2×D418yes—
374C2×C22⋊C4C2×D418yes—
375C2×C42—24no—
376C2×C42—24no—
377C2×C42—24no—
378C2×C42—24no—
379C2×C42—24no—
380C2×C42—22no—
381C2×C42—22no—
382C2×C42—22no—
383C2×C42—22no—
384C2×C42—22no—
385C2×C42—22no—
386C2×C42—24no—
387C2×C42—24no—
388C2×C42—22no—
389C2×C42—22no—
390C2×C42—22no—
391C2×C42—24no—
392C2×C42—24no—
393C2×C42—416no—
394C2×C42C2×D414yes—
395C2×C42C2×D414yes—
396C2×C42#4114yes—
397#95—24no—
398#95—24no—
399#95—24no—
400#95—24no—
401#95—24no—
402#95—24no—
403#95—24no—
404#95—28no—
405#95—28no—
406#95—28no—
407#95—28no—
408#95—28no—
409#95—28no—
410#95—28no—
411#95—28no—
412#95—24no—
413#95—24no—
414#95—24no—
415#95—42no—
416#95—44no—
417#95—44no—
418#95—44no—
419#95—44no—
420C24—21no—
421C24—22no—
422C24—21no—
423C24—21no—
424C24—22no—
425C24—22no—
426C24—21no—
427C24—22no—
428C24—21no—
429C24—21no—
430C24—21no—
431C24—22no—
432C24—22no—
433C24—22no—
434C24—22no—
435C24—21no—
436C24—21no—
437C24—21no—
438C24—22no—
439C24—22no—
440C24—21no—
441C24—22no—
442C24—22no—
443C24—21no—
444C24C22×D414yes—
445C24C22×D414yes—
446C24C22×D412yes—
447C24C2×#4114yes—
448C24C2×#4112yes—
449C242−1+412yes—
450C24C2511yescharacteristic
451C2×Q8—48no—
452C2×Q8—48no—
453C2×Q8—48no—
454C2×Q8—48no—
455C2×Q8—48no—
456C2×Q8—48no—
457C2×Q8—48no—
458C2×D4—216no—
459C2×D4—216no—
460C2×D4—28no—
461C2×D4—28no—
462C2×D4—28no—
463C2×D4—28no—
464C2×D4—28no—
465C2×D4—28no—
466C2×D4—48no—
467C2×D4—48no—
468C2×D4—48no—
469C2×D4—48no—
470C2×D4—48no—
471C2×D4#121116yes—
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—28no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—22no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—24no—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—21no—
492C22×C4—22no—
493C22×C4—21no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—24no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—24no—
501C22×C4—22no—
502C22×C4—24no—
503C22×C4—21no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—22no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—22no—
512C22×C4—21no—
513C22×C4—24no—
514C22×C4—22no—
515C22×C4—21no—
516C22×C4—22no—
517C22×C4—24no—
518C22×C4—22no—
519C22×C4—216no—
520C22×C4—28no—
521C22×C4—28no—
522C22×C4—28no—
523C22×C4—28no—
524C22×C4—216no—
525C22×C4—28no—
526C22×C4—216no—
527C22×C4—28no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—24no—
535C22×C4—24no—
536C22×C4—24no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—24no—
545C22×C4—24no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—24no—
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—24no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—44no—
564C22×C4—44no—
565C22×C4—416no—
566C22×C4—44no—
567C22×C4—44no—
568C22×C4—44no—
569C22×C4—416no—
570C22×C4—416no—
571C22×C4—44no—
572C22×C4—44no—
573C22×C4—44no—
574C22×C4—48no—
575C22×C4—44no—
576C22×C4—48no—
577C22×C4—44no—
578C22×C4—48no—
579C22×C4—44no—
580C22×C4—44no—
581C22×C4—44no—
582C22×C4—48no—
583C22×C4—44no—
584C22×C4—88no—
585C22×C4—88no—
586C22×C4—88no—
587C22×C4—88no—
588C22×C4C22×D414yes—
589C22×C4C22×D414yes—
590C22×C4C22×D412yes—
591C22×C4C22×D418yes—
592C22×C4C22×D412yes—
593C22×C4C22×D412yes—
594C22×C4C22×D412yes—
595C22×C4C22×D412yes—
596C22×C4C22×D412yes—
597C22×C4C22×D412yes—
598C22×C4C22×D412yes—
599C22×C4C2×#4112yes—
600C22×C4C2×#4114yes—
601C22×C4C2×#4112yes—
602C22×C4C2×#4112yes—
603C22×C4C2×#4112yes—
604C22×C4C2×#4112yes—
605C22×C4C2×#4112yes—
606C22×C4C2×#4112yes—
607C22×C4H(5,𝔽2)12yes—
608C22×C4H(5,𝔽2)12yes—
609C22×C42−1+412yes—
610C22×C42−1+412yes—
611C22×C42−1+412yes—
612C4⋊C4—28no—
613C4⋊C4—28no—
614C4⋊C4—216no—
615C4⋊C4—28no—
616C4⋊C4—216no—
617C4⋊C4—48no—
618C4⋊C4—416no—
619C4⋊C4—48no—
620C4⋊C4—416no—
621C4⋊C4—48no—
622C4⋊C4—48no—
623C4⋊C4—44no—
624C4⋊C4—44no—
625C4⋊C4—44no—
626C4⋊C4—44no—
627C4⋊C4—88no—
628C22⋊C4—216no—
629C22⋊C4—216no—
630C22⋊C4—48no—
631C22⋊C4—48no—
632C22⋊C4—416no—
633C22⋊C4—48no—
634C22⋊C4—48no—
635C22⋊C4—416no—
636C22⋊C4—416no—
637C22⋊C4—416no—
638C22⋊C4—48no—
639C42—44no—
640C42—44no—
641C42—44no—
642C42—48no—
643C42—48no—
644C42—48no—
645C42#121116yes—
646C23—24no—
647C23—22no—
648C23—22no—
649C23—24no—
650C23—22no—
651C23—24no—
652C23—22no—
653C23—24no—
654C23—22no—
655C23—24no—
656C23—24no—
657C23—24no—
658C23—22no—
659C23—24no—
660C23—22no—
661C23—24no—
662C23—24no—
663C23—22no—
664C23—24no—
665C23—24no—
666C23—22no—
667C23—24no—
668C23—22no—
669C23—24no—
670C23—22no—
671C23—24no—
672C23—22no—
673C23—24no—
674C23—22no—
675C23—22no—
676C23—22no—
677C23—24no—
678C23—22no—
679C23—24no—
680C23—22no—
681C23—22no—
682C23—41no—
683C23—42no—
684C23—41no—
685C23—42no—
686C23—41no—
687C23—42no—
688C23—41no—
689C23—41no—
690C23—41no—
691C23—42no—
692C23—41no—
693C23—41no—
694C23—41no—
695C23—42no—
696C23—42no—
697C23—41no—
698C23—41no—
699C23—42no—
700C23—42no—
701C23—42no—
702C23—42no—
703C23—42no—
704C23—41no—
705C23—41no—
706C23—42no—
707C23—42no—
708C23—41no—
709C23—41no—
710C23—42no—
711C23—42no—
712C23—41no—
713C23—42no—
714C23C2×#12118yes—
715C23#54714yes—
716C23C23×D411yescharacteristic
717C23C23×D411yescharacteristic
718C23C23×D411yescharacteristic
719C23C22×#4111yescharacteristic
720C23C22×#4111yescharacteristic
721C23C22×#4111yescharacteristic
722C23C22×#4111yescharacteristic
723C23C2×H(5,𝔽2)11yescharacteristic
724C23C2×H(5,𝔽2)11yescharacteristic
725C23C2×2−1+411yescharacteristic
726C23C2×2−1+411yescharacteristic
727C23C2×2−1+411yescharacteristic
728C23C2×2−1+411yescharacteristic
729C23#58511yescharacteristic
730C23#58511yescharacteristic
731Q8—816no—
732D4—232no—
733D4—432no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—24no—
742C2×C4—24no—
743C2×C4—22no—
744C2×C4—28no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—24no—
748C2×C4—24no—
749C2×C4—28no—
750C2×C4—22no—
751C2×C4—24no—
752C2×C4—24no—
753C2×C4—22no—
754C2×C4—24no—
755C2×C4—28no—
756C2×C4—22no—
757C2×C4—22no—
758C2×C4—22no—
759C2×C4—24no—
760C2×C4—24no—
761C2×C4—416no—
762C2×C4—41no—
763C2×C4—41no—
764C2×C4—41no—
765C2×C4—42no—
766C2×C4—41no—
767C2×C4—41no—
768C2×C4—42no—
769C2×C4—42no—
770C2×C4—42no—
771C2×C4—42no—
772C2×C4—41no—
773C2×C4—41no—
774C2×C4—41no—
775C2×C4—42no—
776C2×C4—44no—
777C2×C4—41no—
778C2×C4—42no—
779C2×C4—41no—
780C2×C4—42no—
781C2×C4—41no—
782C2×C4—42no—
783C2×C4—41no—
784C2×C4—44no—
785C2×C4—42no—
786C2×C4—44no—
787C2×C4—42no—
788C2×C4—44no—
789C2×C4—42no—
790C2×C4—416no—
791C2×C4—432no—
792C2×C4—416no—
793C2×C4—42no—
794C2×C4—42no—
795C2×C4—44no—
796C2×C4—44no—
797C2×C4—42no—
798C2×C4—44no—
799C2×C4—42no—
800C2×C4—44no—
801C2×C4—42no—
802C2×C4—42no—
803C2×C4—42no—
804C2×C4—42no—
805C2×C4—42no—
806C2×C4—44no—
807C2×C4—42no—
808C2×C4—44no—
809C2×C4—42no—
810C2×C4—44no—
811C2×C4—42no—
812C2×C4—42no—
813C2×C4—42no—
814C2×C4—42no—
815C2×C4—42no—
816C2×C4—42no—
817C2×C4—42no—
818C2×C4—42no—
819C2×C4—42no—
820C2×C4—42no—
821C2×C4—42no—
822C2×C4—42no—
823C2×C4—42no—
824C2×C4—42no—
825C2×C4—42no—
826C2×C4—42no—
827C2×C4—42no—
828C2×C4—832no—
829C2×C4C2×#12114yes—
830C2×C4C2×#12114yes—
831C2×C4C2×#12114yes—
832C2×C4C2×#12114yes—
833C2×C4#52914yes—
834C2×C4#53714yes—
835C2×C4#54214yes—
836C2×C4D4214yes—
837C2×C4#54614yes—
838C2×C4#54614yes—
839C2×C4#54714yes—
840C2×C4#54714yes—
841C2×C4#54814yes—
842C2×C4#54814yes—
843C2×C4#55314yes—
844C22—24no—
845C22—24no—
846C22—28no—
847C22—28no—
848C22—28no—
849C22—24no—
850C22—44no—
851C22—42no—
852C22—44no—
853C22—44no—
854C22—42no—
855C22—42no—
856C22—44no—
857C22—42no—
858C22—44no—
859C22—42no—
860C22—44no—
861C22—42no—
862C22—44no—
863C22—42no—
864C22—44no—
865C22—42no—
866C22—42no—
867C22—42no—
868C22—44no—
869C22—42no—
870C22—44no—
871C22—44no—
872C22—42no—
873C22—44no—
874C22C22×#12111yescharacteristic
875C22C22×#12111yescharacteristic
876C22C2×#52911yescharacteristic
877C22C2×#53711yescharacteristic
878C22C2×#54211yescharacteristic
879C22C2×D4211yescharacteristic
880C22C2×#54611yescharacteristic
881C22C2×#54611yescharacteristic
882C22C2×#54711yescharacteristic
883C22C2×#54711yescharacteristic
884C22C2×#54711yescharacteristic
885C22C2×#54811yescharacteristic
886C22C2×#54811yescharacteristic
887C22D4×#4111yescharacteristic
888C22C2×#55311yescharacteristic
889C22#347511yescharacteristic
890C22#348211yescharacteristic
891C22#348511yescharacteristic
892C22#348611yescharacteristic
893C22#348911yescharacteristic
894C22#348911yescharacteristic
895C22#349511yescharacteristic
896C22#349511yescharacteristic
897C22#349611yescharacteristic
898C22#349911yescharacteristic
899C22#350711yescharacteristic
900C22#351111yescharacteristic
901C22#351411yescharacteristic
902C22#351511yescharacteristic
903C22#352011yescharacteristic
904C22#352311yescharacteristic
905C22#354611yescharacteristic
906C22#355011yescharacteristic
907C22#355211yescharacteristic
908C22#355511yescharacteristic
909C4—24no—
910C4—42no—
911C4—44no—
912C4—42no—
913C4—44no—
914C4—42no—
915C4—48no—
916C4—44no—
917C4—82no—
918C4—82no—
919C4—84no—
920C4—82no—
921C4—82no—
922C4#241618yes—
923C4#242718yescomplemented
924C2—44no—
925C2—48no—
926C2C2×#241611yescharacteristic
927C2C2×#242711yescharacteristic
928C2#3563311yescharacteristic
929C2#3611611yescharacteristic
930C2#3615311yescharacteristic
931C2#3625911yescharacteristic
932C2#3644911yescharacteristic
933C2#3892311yescharacteristic
934C2#3914611yescharacteristic
935C2#3935011yescharacteristic
936C2#3946811yescharacteristic
937C2#5903511yescharacteristic
938C2#5904211yescharacteristic
939C2#5907911yescharacteristic
940C2#5912511yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC22×#121C22
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24 ◁ G
LECSG ▷ C24 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#2857C2semidirect
2. C2×#2547C2semidirect
4. C2×D4×C4⋊C4C2semidirect
6. #15390C2semidirect
7. #15290C2semidirect
8. #15189C2semidirect
9. #15179C2semidirect
10. #15132C2semidirect
11. #15129C2semidirect
12. #14155C2semidirect
13. #14151C2semidirect
14. #14027C2semidirect
15. #13907C2semidirect
16. #13872C2semidirect
17. C4×#380C2semidirect
175. #384D4semidirect
923. C4#2427semidirect

Maximal subgroups

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

subgroupindex
C2×#28572
C2×#25472
C2×#24272
C2×D4×C4⋊C42
C2×C4×#1212
#153902
#152902
#151892
#151792
#151322
#151292
#141552
#141512
#140272
#139072
#138722
C4×#3802