Finite Group Databasebeta

← #679657

Subgroups — #679657

Order 512.

3630 conjugacy classes of subgroups.

The subgroup lattice has 950 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2856C211yesmaximal, characteristic
2C2×#2548C211yesmaximal, characteristic, complemented
3C2×#2355C211yesmaximal, characteristic, complemented
4C2×C4×C22⋊Q8C211yesmaximal, characteristic, complemented
5#15902C214yesmaximal, complemented
6#15338C214yesmaximal, complemented
7#15226C212yesmaximal, complemented
8#15222C212yesmaximal, complemented
9#15219C212yesmaximal, complemented
10#15215C212yesmaximal, complemented
11#14154C211yesmaximal, characteristic, complemented
12#14151C211yesmaximal, characteristic, complemented
13#14141C212yesmaximal, complemented
14#14022C212yesmaximal, complemented
15#13998C212yesmaximal, complemented
16#13998C212yesmaximal, complemented
17C4×#380C211yesmaximal, characteristic, complemented
18C22×#127C2211yescharacteristic
19C22×#124C2212yes—
20C22×C22⋊Q8C2211yescharacteristic
21C22×#121C2212yes—
22C22×#121C2212yes—
23C22×#121C2212yes—
24C22×C4×Q8C2211yescharacteristic
25C23×C42C2211yescharacteristic
26#2856—28no—
27#2548—28no—
28C2×#394C2214yes—
29#2355—28no—
30C4×C22⋊Q8—28no—
31C2×#391C2212yes—
32C2×#391C2211yescharacteristic
33C2×#390C2212yes—
34C2×#390C2212yes—
35C2×#390C2212yes—
36C2×#390C2212yes—
37C2×#390C2212yes—
38C2×#390C2212yes—
39C2×#390C2212yes—
40C2×#390C2212yes—
41C2×#390C2212yes—
42C2×#390C2212yes—
43C2×#390C2214yes—
44C2×#389C2211yescharacteristic
45C2×#389C2212yes—
46C2×#389C2212yes—
47C2×#388C2214yes—
48C2×#387C2212yes—
49C2×#387C2214yes—
50C2×#385C2212yes—
51C2×#384C2211yescharacteristic
52C2×#382C2212yes—
53C2×#380C2211yescharacteristic
54C2×#380C2211yescharacteristic
55C2×#380C2211yescharacteristic
56C2×C4×C4⋊C4C2212yes—
57C2×C4×C4⋊C4C2211yescharacteristic
58C2×C4×C4⋊C4C2212yes—
59C2×C4×C4⋊C4C2211yescharacteristic
60C2×C4×C4⋊C4C2211yescharacteristic
61C2×C4×C4⋊C4C2212yes—
62C2×C4×C22⋊C4C2212yes—
63C2×C4×C22⋊C4C2212yes—
64#1441C2214yes—
65#1440C2214yes—
66#1440C2214yes—
67#1440C2214yes—
68#1439C2214yes—
69#1439C2214yes—
70#1439C2214yes—
71#1439C2214yes—
72#1439C2214yes—
73#1439C2214yes—
74#1438C2214yes—
75#1438C2214yes—
76#1438C2214yes—
77#1438C2214yes—
78#1437C2214yes—
79#1437C2214yes—
80C4⋊#95C2212yes—
81C4⋊#95C2212yes—
82C4⋊#95C2211yescharacteristic
83C4⋊#95C2211yescharacteristic
84#1434C2212yes—
85C22⋊#95C2212yes—
86C4×#95C2212yes—
87C23×Q8C2311yescharacteristic
88C23×D4C2312yes—
89C23×D4C2312yes—
90C23×D4C2314yes—
91C23×D4C2312yes—
92C24×C4C2311yescharacteristic
93C24×C4C2311yescharacteristic
94C24×C4C2311yescharacteristic
95C2×#127—24no—
96C2×#127—24no—
97C2×#127—24no—
98C2×#124—28no—
99C2×#124—44no—
100C2×#124—44no—
101C2×C22⋊Q8—24no—
102C2×C22⋊Q8—24no—
103C2×C22⋊Q8—24no—
104C2×#121—28no—
105C2×#121—28no—
106C2×#121—28no—
107C2×#121—28no—
108C2×#121—28no—
109C2×#121—44no—
110C2×#121—44no—
111C2×#121—44no—
112C2×#121—44no—
113C2×C4×Q8—24no—
114C2×C4×Q8—24no—
115C2×C4×Q8D418yescomplemented
116C22×C4⋊C4C2312yes—
117C22×C4⋊C4C2311yescharacteristic
118C22×C4⋊C4C2311yescharacteristic
119C22×C4⋊C4C2311yescharacteristic
120C22×C4⋊C4C2311yescharacteristic
121C22×C4⋊C4C2312yes—
122C22×C4⋊C4C2312yes—
123C22×C4⋊C4C2311yescharacteristic
124C22×C4⋊C4C2312yes—
125C22×C4⋊C4C2312yes—
126C22×C4⋊C4C2311yescharacteristic
127C22×C4⋊C4C2311yescharacteristic
128C22×C4⋊C4C2314yes—
129C22×C4⋊C4C2312yes—
130C22×C22⋊C4C2312yes—
131C22×C22⋊C4C2314yes—
132C22×C22⋊C4C2314yes—
133C22×C22⋊C4C2314yes—
134C22×C22⋊C4C2312yes—
135C22×C22⋊C4C2314yes—
136C22×C22⋊C4C2312yes—
137C22×C22⋊C4C2314yes—
138C22×C22⋊C4C2314yes—
139C22×C22⋊C4C2314yes—
140C22×C22⋊C4C2314yes—
141C22×C22⋊C4C2312yes—
142C22×C22⋊C4C2314yes—
143C22×C22⋊C4C2314yes—
144C22×C22⋊C4C2314yes—
145C22×C42—24no—
146C22×C42—24no—
147C22×C42—24no—
148C22×C42C2311yescharacteristic
149C22×C42C2311yescharacteristic
150C22×C42C2311yescharacteristic
151C22×C42C2312yes—
152C22×C42C2312yes—
153C22×C42C2312yes—
154C22×C42C2312yes—
155C22×C42C2314yes—
156C22×C42C2311yescharacteristic
157#394—216no—
158#391—24no—
159#391—28no—
160#390—28no—
161#390—28no—
162#390—28no—
163#390—28no—
164#390—28no—
165#390—28no—
166#390—28no—
167#390—28no—
168#390—44no—
169#390—44no—
170#390—48no—
171#389—24no—
172#389—44no—
173#389—44no—
174#388—48no—
175#387—216no—
176#387—28no—
177#385—28no—
178#384D418yes—
179#382—28no—
180#380—24no—
181#380—24no—
182#380—24no—
183C4×C4⋊C4—28no—
184C4×C4⋊C4—28no—
185C4×C4⋊C4—24no—
186C4×C4⋊C4—24no—
187C4×C4⋊C4—28no—
188C4×C4⋊C4—24no—
189C4×C22⋊C4—28no—
190C4×C22⋊C4—44no—
191C2×#95C2312yes—
192C2×#95C2312yes—
193C2×#95C2312yes—
194C2×#95C2312yes—
195C2×#95C2312yes—
196C2×#95C2312yes—
197C2×#95C2312yes—
198C2×#95C2312yes—
199C2×#95C2314yes—
200C2×#95C2314yes—
201C2×#95C2314yes—
202C2×#95C2312yes—
203C2×#95C2312yes—
204C2×#95C2312yes—
205C2×#95C2312yes—
206C2×#95C2312yes—
207C2×#95C2314yes—
208C2×#95C2314yes—
209C2×#95C2314yes—
210C25C2414yes—
211C25C2411yescharacteristic
212C22×Q8—22no—
213C22×Q8—22no—
214C22×Q8—22no—
215C22×Q8—22no—
216C22×Q8—22no—
217C22×Q8—22no—
218C22×Q8C2×D414yes—
219C22×D4—28no—
220C22×D4—28no—
221C22×D4—28no—
222C22×D4—28no—
223C22×D4—24no—
224C22×D4—24no—
225C22×D4—24no—
226C22×D4—24no—
227C22×D4—24no—
228C22×D4—24no—
229C22×D4—24no—
230C22×D4—24no—
231C22×D4—24no—
232C22×D4—24no—
233C22×D4—24no—
234C22×D4—24no—
235C22×D4—24no—
236C22×D4—24no—
237C22×D4—24no—
238C22×D4—24no—
239C22×D4—24no—
240C22×D4—42no—
241C22×D4—42no—
242C22×D4—44no—
243C22×D4—44no—
244C22×D4—44no—
245C22×D4—42no—
246C22×D4—42no—
247C23×C4—22no—
248C23×C4—22no—
249C23×C4—22no—
250C23×C4—22no—
251C23×C4—22no—
252C23×C4—22no—
253C23×C4—22no—
254C23×C4—22no—
255C23×C4—22no—
256C23×C4—22no—
257C23×C4—22no—
258C23×C4—22no—
259C23×C4—22no—
260C23×C4—22no—
261C23×C4—22no—
262C23×C4—22no—
263C23×C4—22no—
264C23×C4—41no—
265C23×C4—41no—
266C23×C4#4114yes—
267C23×C4#4114yes—
268C23×C4C2412yes—
269C23×C4C2412yes—
270C23×C4C2412yes—
271C23×C4C2412yes—
272C23×C4C2412yes—
273C23×C4C2412yes—
274C23×C4C2414yes—
275C23×C4C2412yes—
276C23×C4C2412yes—
277C23×C4C2411yescharacteristic
278C23×C4C2411yescharacteristic
279C23×C4C2411yescharacteristic
280C23×C4C2411yescharacteristic
281C23×C4C2411yescharacteristic
282C23×C4C2411yescharacteristic
283#127—416no—
284#124—432no—
285C22⋊Q8—232no—
286#121—432no—
287#121—432no—
288#121—432no—
289C4×Q8—232no—
290C2×C4⋊C4—22no—
291C2×C4⋊C4—24no—
292C2×C4⋊C4—24no—
293C2×C4⋊C4—22no—
294C2×C4⋊C4—22no—
295C2×C4⋊C4—22no—
296C2×C4⋊C4—24no—
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—22no—
305C2×C4⋊C4—22no—
306C2×C4⋊C4—22no—
307C2×C4⋊C4—24no—
308C2×C4⋊C4—22no—
309C2×C4⋊C4—22no—
310C2×C4⋊C4—22no—
311C2×C4⋊C4—22no—
312C2×C4⋊C4—22no—
313C2×C4⋊C4—24no—
314C2×C4⋊C4—22no—
315C2×C4⋊C4—22no—
316C2×C4⋊C4—22no—
317C2×C4⋊C4—22no—
318C2×C4⋊C4—22no—
319C2×C4⋊C4—42no—
320C2×C4⋊C4—42no—
321C2×C4⋊C4—42no—
322C2×C4⋊C4—44no—
323C2×C4⋊C4—44no—
324C2×C4⋊C4—44no—
325C2×C4⋊C4C2×D414yes—
326C2×C4⋊C4C2×D418yes—
327C2×C4⋊C4C2×D418yes—
328C2×C4⋊C4C2×D418yes—
329C2×C4⋊C4C2×D418yes—
330C2×C4⋊C4#4114yes—
331C2×C4⋊C4#4114yes—
332C2×C22⋊C4—24no—
333C2×C22⋊C4—24no—
334C2×C22⋊C4—24no—
335C2×C22⋊C4—24no—
336C2×C22⋊C4—24no—
337C2×C22⋊C4—24no—
338C2×C22⋊C4—28no—
339C2×C22⋊C4—28no—
340C2×C22⋊C4—28no—
341C2×C22⋊C4—28no—
342C2×C22⋊C4—28no—
343C2×C22⋊C4—24no—
344C2×C22⋊C4—28no—
345C2×C22⋊C4—28no—
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—28no—
354C2×C22⋊C4—42no—
355C2×C22⋊C4—42no—
356C2×C22⋊C4—44no—
357C2×C22⋊C4—44no—
358C2×C22⋊C4—44no—
359C2×C22⋊C4—44no—
360C2×C22⋊C4—44no—
361C2×C22⋊C4—44no—
362C2×C22⋊C4—44no—
363C2×C22⋊C4—42no—
364C2×C22⋊C4—42no—
365C2×C22⋊C4—44no—
366C2×C22⋊C4—44no—
367C2×C22⋊C4—44no—
368C2×C22⋊C4—44no—
369C2×C22⋊C4—44no—
370C2×C22⋊C4—44no—
371C2×C22⋊C4—44no—
372C2×C22⋊C4—44no—
373C2×C22⋊C4—44no—
374C2×C22⋊C4—44no—
375C2×C22⋊C4—44no—
376C2×C22⋊C4—44no—
377C2×C42—24no—
378C2×C42—24no—
379C2×C42—24no—
380C2×C42—24no—
381C2×C42—24no—
382C2×C42—22no—
383C2×C42—22no—
384C2×C42—22no—
385C2×C42—22no—
386C2×C42—22no—
387C2×C42—22no—
388C2×C42—24no—
389C2×C42—24no—
390C2×C42—22no—
391C2×C42—22no—
392C2×C42—22no—
393C2×C42—24no—
394C2×C42—24no—
395C2×C42—24no—
396C2×C42—24no—
397C2×C42—28no—
398C2×C42—416no—
399C2×C42—44no—
400C2×C42—44no—
401C2×C42C2×D418yes—
402C2×C42C2×D414yes—
403C2×C42C2×D414yes—
404C2×C42#4114yes—
405#95—24no—
406#95—24no—
407#95—24no—
408#95—28no—
409#95—24no—
410#95—24no—
411#95—24no—
412#95—28no—
413#95—24no—
414#95—28no—
415#95—24no—
416#95—24no—
417#95—24no—
418#95—42no—
419#95—42no—
420#95—42no—
421#95—44no—
422#95—44no—
423#95—44no—
424C24—21no—
425C24—21no—
426C24—21no—
427C24—21no—
428C24—21no—
429C24—21no—
430C24—21no—
431C24—21no—
432C24—21no—
433C24—21no—
434C24—21no—
435C24—21no—
436C24—24no—
437C24—24no—
438C24—24no—
439C24—24no—
440C24—24no—
441C24—24no—
442C24—24no—
443C24—24no—
444C24—24no—
445C24—24no—
446C24—24no—
447C24—24no—
448C24—24no—
449C24—24no—
450C24—24no—
451C24C2×#4112yes—
452C24C2×#4112yes—
453C24H(5,𝔽2)12yes—
454C24C2511yescharacteristic
455C2×Q8—28no—
456C2×Q8—28no—
457C2×Q8—28no—
458C2×Q8—44no—
459C2×Q8—44no—
460C2×Q8—44no—
461C2×Q8—44no—
462C2×D4—416no—
463C2×D4—416no—
464C2×D4—416no—
465C2×D4—48no—
466C2×D4—48no—
467C2×D4—416no—
468C2×D4—48no—
469C2×D4—48no—
470C2×D4—48no—
471C2×D4—48no—
472C2×D4—48no—
473C2×D4—48no—
474C2×D4—48no—
475C2×D4—48no—
476C2×D4—48no—
477C2×D4—48no—
478C2×D4—48no—
479C2×D4—48no—
480C2×D4—48no—
481C2×D4—48no—
482C2×D4—48no—
483C2×D4—84no—
484C2×D4—84no—
485C2×D4—84no—
486C2×D4—84no—
487C2×D4—88no—
488C2×D4—88no—
489C2×D4—88no—
490C22×C4—21no—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—28no—
495C22×C4—21no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—21no—
500C22×C4—21no—
501C22×C4—22no—
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—21no—
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—24no—
515C22×C4—24no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—21no—
519C22×C4—22no—
520C22×C4—21no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—24no—
525C22×C4—24no—
526C22×C4—24no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—24no—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—21no—
543C22×C4—28no—
544C22×C4—28no—
545C22×C4—28no—
546C22×C4—28no—
547C22×C4—28no—
548C22×C4—28no—
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—22no—
577C22×C4—44no—
578C22×C4—44no—
579C22×C4—44no—
580C22×C4—44no—
581C22×C4—44no—
582C22×C4—44no—
583C22×C4—44no—
584C22×C4—44no—
585C22×C4—44no—
586C22×C4—44no—
587C22×C4—44no—
588C22×C4—44no—
589C22×C4—44no—
590C22×C4—44no—
591C22×C4C22×D418yes—
592C22×C4C22×D414yes—
593C22×C4C22×D414yes—
594C22×C4C22×D412yes—
595C22×C4C22×D412yes—
596C22×C4C22×D412yes—
597C22×C4C22×D412yes—
598C22×C4C22×D412yes—
599C22×C4C22×D412yes—
600C22×C4C2×#4112yes—
601C22×C4C2×#4114yes—
602C22×C4C2×#4114yes—
603C22×C4C2×#4112yes—
604C22×C4C2×#4112yes—
605C22×C4C2×#4112yes—
606C22×C4C2×#4112yes—
607C22×C4C2×#4112yes—
608C22×C4C2×#4112yes—
609C22×C4C2×#4112yes—
610C22×C4C2×#4112yes—
611C22×C4H(5,𝔽2)12yes—
612C22×C4H(5,𝔽2)12yes—
613C22×C4H(5,𝔽2)12yes—
614C22×C4H(5,𝔽2)12yes—
615C22×C42−1+412yes—
616C4⋊C4—216no—
617C4⋊C4—28no—
618C4⋊C4—216no—
619C4⋊C4—28no—
620C4⋊C4—216no—
621C4⋊C4—216no—
622C4⋊C4—28no—
623C4⋊C4—48no—
624C4⋊C4—48no—
625C4⋊C4—44no—
626C4⋊C4—44no—
627C4⋊C4—44no—
628C4⋊C4—44no—
629C4⋊C4—88no—
630C22⋊C4—216no—
631C22⋊C4—416no—
632C22⋊C4—416no—
633C22⋊C4—416no—
634C22⋊C4—416no—
635C22⋊C4—48no—
636C22⋊C4—48no—
637C22⋊C4—416no—
638C22⋊C4—416no—
639C22⋊C4—48no—
640C22⋊C4—88no—
641C22⋊C4—88no—
642C22⋊C4—88no—
643C22⋊C4—88no—
644C22⋊C4—88no—
645C42—216no—
646C42—44no—
647C42—44no—
648C42—44no—
649C42—48no—
650C42—48no—
651C42—48no—
652C42—88no—
653C42#121116yes—
654C23—22no—
655C23—22no—
656C23—22no—
657C23—22no—
658C23—22no—
659C23—22no—
660C23—22no—
661C23—22no—
662C23—22no—
663C23—22no—
664C23—22no—
665C23—22no—
666C23—22no—
667C23—22no—
668C23—22no—
669C23—22no—
670C23—22no—
671C23—22no—
672C23—41no—
673C23—41no—
674C23—41no—
675C23—41no—
676C23—41no—
677C23—41no—
678C23—41no—
679C23—41no—
680C23—41no—
681C23—41no—
682C23—41no—
683C23—41no—
684C23—41no—
685C23—41no—
686C23—41no—
687C23—41no—
688C23—44no—
689C23—44no—
690C23—44no—
691C23—44no—
692C23—44no—
693C23—44no—
694C23—44no—
695C23—44no—
696C23—44no—
697C23—44no—
698C23—44no—
699C23—44no—
700C23—44no—
701C23—44no—
702C23—44no—
703C23—44no—
704C23—44no—
705C23—44no—
706C23—44no—
707C23—44no—
708C23—44no—
709C23—44no—
710C23—44no—
711C23—44no—
712C23—44no—
713C23—44no—
714C23—44no—
715C23—44no—
716C23—44no—
717C23—44no—
718C23—44no—
719C23—44no—
720C23—44no—
721C23—44no—
722C23—44no—
723C23#55914yes—
724C23C23×D411yescharacteristic
725C23C23×D411yescharacteristic
726C23C22×#4111yescharacteristic
727C23C22×#4111yescharacteristic
728C23C22×#4111yescharacteristic
729C23C22×#4111yescharacteristic
730C23C22×#4111yescharacteristic
731C23C2×H(5,𝔽2)11yescharacteristic
732C23C2×H(5,𝔽2)11yescharacteristic
733C23C2×H(5,𝔽2)11yescharacteristic
734C23C2×H(5,𝔽2)11yescharacteristic
735C23C2×H(5,𝔽2)11yescharacteristic
736C23C2×2−1+411yescharacteristic
737C23#58511yescharacteristic
738C23#58511yescharacteristic
739Q8—416no—
740D4—816no—
741D4—832no—
742D4—816no—
743D4—816no—
744C2×C4—22no—
745C2×C4—22no—
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—22no—
755C2×C4—22no—
756C2×C4—24no—
757C2×C4—22no—
758C2×C4—22no—
759C2×C4—28no—
760C2×C4—28no—
761C2×C4—24no—
762C2×C4—22no—
763C2×C4—22no—
764C2×C4—24no—
765C2×C4—24no—
766C2×C4—28no—
767C2×C4—22no—
768C2×C4—24no—
769C2×C4—24no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—24no—
773C2×C4—24no—
774C2×C4—416no—
775C2×C4—41no—
776C2×C4—41no—
777C2×C4—41no—
778C2×C4—41no—
779C2×C4—41no—
780C2×C4—42no—
781C2×C4—41no—
782C2×C4—42no—
783C2×C4—42no—
784C2×C4—41no—
785C2×C4—41no—
786C2×C4—42no—
787C2×C4—42no—
788C2×C4—41no—
789C2×C4—42no—
790C2×C4—44no—
791C2×C4—42no—
792C2×C4—42no—
793C2×C4—42no—
794C2×C4—42no—
795C2×C4—41no—
796C2×C4—42no—
797C2×C4—41no—
798C2×C4—42no—
799C2×C4—42no—
800C2×C4—41no—
801C2×C4—42no—
802C2×C4—44no—
803C2×C4—44no—
804C2×C4—42no—
805C2×C4—44no—
806C2×C4—42no—
807C2×C4—416no—
808C2×C4—416no—
809C2×C4—42no—
810C2×C4—42no—
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—42no—
829C2×C4—42no—
830C2×C4—42no—
831C2×C4—42no—
832C2×C4—42no—
833C2×C4—42no—
834C2×C4—42no—
835C2×C4—42no—
836C2×C4—42no—
837C2×C4C2×#12114yes—
838C2×C4C2×#12114yes—
839C2×C4C2×#12114yes—
840C2×C4#52514yes—
841C2×C4#52914yes—
842C2×C4#53514yes—
843C2×C4#54214yes—
844C2×C4#54614yes—
845C2×C4#54614yes—
846C2×C4#54814yes—
847C2×C4#54814yes—
848C2×C4#55014yes—
849C2×C4#55014yes—
850C2×C4#55314yes—
851C2×C4#55514yes—
852C22—24no—
853C22—24no—
854C22—24no—
855C22—42no—
856C22—42no—
857C22—42no—
858C22—42no—
859C22—42no—
860C22—42no—
861C22—42no—
862C22—42no—
863C22—42no—
864C22—42no—
865C22—42no—
866C22—42no—
867C22—84no—
868C22—84no—
869C22—84no—
870C22—84no—
871C22—84no—
872C22—84no—
873C22—84no—
874C22—84no—
875C22—84no—
876C22—84no—
877C22—84no—
878C22—84no—
879C22—84no—
880C22—84no—
881C22—84no—
882C22C22×#12111yescharacteristic
883C22C2×#52511yescharacteristic
884C22C2×#52911yescharacteristic
885C22C2×#53511yescharacteristic
886C22C2×#54211yescharacteristic
887C22C2×#54611yescharacteristic
888C22C2×#54611yescharacteristic
889C22C2×#54811yescharacteristic
890C22C2×#54811yescharacteristic
891C22C2×#55011yescharacteristic
892C22C2×#55011yescharacteristic
893C22C2×#55311yescharacteristic
894C22C2×#55511yescharacteristic
895C22C2×#55911yescharacteristic
896C22#348011yescharacteristic
897C22#348011yescharacteristic
898C22#348111yescharacteristic
899C22#348411yescharacteristic
900C22#348711yescharacteristic
901C22#348811yescharacteristic
902C22#348811yescharacteristic
903C22#349411yescharacteristic
904C22#349411yescharacteristic
905C22#350611yescharacteristic
906C22#350711yescharacteristic
907C22#350811yescharacteristic
908C22#350811yescharacteristic
909C22#351411yescharacteristic
910C22#351711yescharacteristic
911C22#351911yescharacteristic
912C22#352211yescharacteristic
913C22#354311yescharacteristic
914C22#354611yescharacteristic
915C22#354811yescharacteristic
916C22#355411yescharacteristic
917C4—24no—
918C4—48no—
919C4—44no—
920C4—42no—
921C4—42no—
922C4—44no—
923C4—44no—
924C4—44no—
925C4—42no—
926C4—82no—
927C4—82no—
928C4—82no—
929C4—82no—
930C4#241418yes—
931C4#242618yes—
932C2—44no—
933C2—164no—
934C2C2×#242611yescharacteristic
935C2C2×#241411yescharacteristic
936C2#3556311yescharacteristic
937C2#3630211yescharacteristic
938C2#3649311yescharacteristic
939C2#3658011yescharacteristic
940C2#3658711yescharacteristic
941C2#3894111yescharacteristic
942C2#3913811yescharacteristic
943C2#3972511yescharacteristic
944C2#3973611yescharacteristic
945C2#5904911yescharacteristic
946C2#5905711yescharacteristic
947C2#5907811yescharacteristic
948C2#5914311yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC2×#2856C2
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×#2548C2semidirect
3. C2×#2355C2semidirect
4. C2×C4×C22⋊Q8C2semidirect
5. #15902C2semidirect
6. #15338C2semidirect
7. #15226C2semidirect
8. #15222C2semidirect
9. #15219C2semidirect
10. #15215C2semidirect
11. #14154C2semidirect
12. #14151C2semidirect
13. #14141C2semidirect
14. #14022C2semidirect
15. #13998C2semidirect
16. #13998C2semidirect
17. C4×#380C2semidirect
115. C2×C4×Q8D4semidirect

Maximal subgroups

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

subgroupindex
C2×#28562
C2×#25482
C2×#23552
C2×C4×C22⋊Q82
#159022
#153382
#152262
#152222
#152192
#152152
#141542
#141512
#141412
#140222
#139982
C4×#3802