Finite Group Databasebeta

← #674400

Subgroups — #674400

Order 512.

3614 conjugacy classes of subgroups.

The subgroup lattice has 926 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2547C212yesmaximal, complemented
2C2×#2551C211yesmaximal, characteristic, complemented
3C2×#2491C212yesmaximal
4C2×C4×#121C211yesmaximal, characteristic
5#15632C214yesmaximal, complemented
6#15311C214yesmaximal, complemented
7#15138C212yesmaximal, complemented
8#15132C212yesmaximal, complemented
9#15129C212yesmaximal, complemented
10#15125C212yesmaximal, complemented
11#14686C211yesmaximal, characteristic, complemented
12#14053C212yesmaximal, complemented
13#13974C212yesmaximal, complemented
14#13906C211yesmaximal, characteristic, complemented
15#13906C211yesmaximal, characteristic, complemented
16C4⋊C42C211yesmaximal, characteristic, complemented
17C4×#380C211yesmaximal, characteristic, complemented
18C22×C4⋊Q8C2212yes—
19C22×C4⋊Q8C2212yes—
20C22×#124C2214yes—
21C22×#121C2211yescharacteristic
22C22×C4×D4C2211yescharacteristic
23C22×C4×D4C2212yes—
24C23×C42C2211yescharacteristic
25#2551—28no—
26#2547—216no—
27#2491—216no—
28C2×#397C2214yes—
29C2×#397C2214yes—
30C2×#395C2214yes—
31C2×#394C2214yes—
32C2×#393C2214yes—
33C4×#121—28no—
34C2×#391C2214yes—
35C2×#390C2211yescharacteristic
36C2×#390C2212yes—
37C2×#390C2212yes—
38C2×#389C2212yes—
39C2×#389C2212yes—
40C2×#389C2211yescharacteristic
41C2×#388C2212yes—
42C2×#388C2214yes—
43C2×#386C2212yes—
44C2×#384C2211yescharacteristic
45C2×#384C2211yescharacteristic
46C2×#380C2212yes—
47C2×#380C2211yescharacteristic
48C2×#380C2212yes—
49C2×#380C2212yes—
50C2×#380C2211yescharacteristic
51C2×#380C2212yes—
52C2×#380C2212yes—
53C2×#380C2212yes—
54C2×#380C2212yes—
55C2×#380C2211yescharacteristic
56C2×C4×C4⋊C4C2211yescharacteristic
57C2×C4×C4⋊C4C2211yescharacteristic
58C2×C4×C4⋊C4C2212yes—
59C2×C4×C4⋊C4C2212yes—
60C2×C4×C4⋊C4C2211yescharacteristic
61C2×C4×C22⋊C4C2212yes—
62C2×C4×C22⋊C4C2212yes—
63#1446C2214yes—
64#1443C2214yes—
65#1442C2214yes—
66#1441C2214yes—
67#1440C2214yes—
68#1440C2214yes—
69#1440C2214yes—
70#1439C2214yes—
71#1439C2214yes—
72#1439C2214yes—
73#1436C2214yes—
74#1436C2214yes—
75C4⋊#95C2212yes—
76C4⋊#95C2211yescharacteristic
77C4⋊#95C2212yes—
78C4⋊#95C2212yes—
79C4⋊#95C2212yes—
80C4⋊#95C2212yes—
81C4⋊#95C2212yes—
82C4⋊#95C2212yes—
83C4⋊#95C2211yescharacteristic
84#1434C2212yes—
85C22⋊#95C2212yes—
86C4×#95C2212yes—
87C23×Q8C2314yes—
88C23×D4C2311yescharacteristic
89C23×D4C2312yes—
90C24×C4C2312yes—
91C24×C4C2311yescharacteristic
92C24×C4C2311yescharacteristic
93C24×C4C2311yescharacteristic
94C2×C4⋊Q8—28no—
95C2×C4⋊Q8—28no—
96C2×C4⋊Q8—28no—
97C2×C4⋊Q8—28no—
98C2×C4⋊Q8—28no—
99C2×C4⋊Q8—44no—
100C2×#124—216no—
101C2×#124—216no—
102C2×#124—48no—
103C2×#121—24no—
104C2×#121—24no—
105C2×#121D418yes—
106C2×C4×D4—28no—
107C2×C4×D4—28no—
108C2×C4×D4—24no—
109C2×C4×D4—24no—
110C2×C4×D4—24no—
111C2×C4×D4—44no—
112C22×C4⋊C4C2314yes—
113C22×C4⋊C4C2311yescharacteristic
114C22×C4⋊C4C2312yes—
115C22×C4⋊C4C2312yes—
116C22×C4⋊C4C2311yescharacteristic
117C22×C4⋊C4C2312yes—
118C22×C4⋊C4C2312yes—
119C22×C4⋊C4C2314yes—
120C22×C4⋊C4C2312yes—
121C22×C4⋊C4C2311yescharacteristic
122C22×C4⋊C4C2311yescharacteristic
123C22×C4⋊C4C2311yescharacteristic
124C22×C4⋊C4C2311yescharacteristic
125C22×C4⋊C4C2312yes—
126C22×C4⋊C4C2312yes—
127C22×C4⋊C4C2311yescharacteristic
128C22×C22⋊C4C2314yes—
129C22×C22⋊C4C2312yes—
130C22×C22⋊C4C2314yes—
131C22×C22⋊C4C2312yes—
132C22×C22⋊C4C2314yes—
133C22×C22⋊C4C2312yes—
134C22×C22⋊C4C2312yes—
135C22×C22⋊C4C2314yes—
136C22×C22⋊C4C2312yes—
137C22×C22⋊C4C2312yes—
138C22×C22⋊C4C2312yes—
139C22×C22⋊C4C2314yes—
140C22×C42—24no—
141C22×C42—24no—
142C22×C42—24no—
143C22×C42C2311yescharacteristic
144C22×C42C2311yescharacteristic
145C22×C42C2311yescharacteristic
146C22×C42C2312yes—
147C22×C42C2312yes—
148C22×C42C2314yes—
149C22×C42C2312yes—
150C22×C42C2311yescharacteristic
151#397—216no—
152#397—216no—
153#395—216no—
154#394—216no—
155#393—216no—
156#391—216no—
157#390—28no—
158#390—28no—
159#390—24no—
160#389—28no—
161#389—24no—
162#389—28no—
163#388—216no—
164#388—28no—
165#386—28no—
166#384—24no—
167#384—24no—
168#380—28no—
169#380—28no—
170#380—28no—
171#380—28no—
172#380—24no—
173#380—24no—
174#380—28no—
175#380—44no—
176#380—44no—
177#380D418yescomplemented
178C4×C4⋊C4—28no—
179C4×C4⋊C4—28no—
180C4×C4⋊C4—24no—
181C4×C4⋊C4—24no—
182C4×C4⋊C4D418yes—
183C4×C22⋊C4—28no—
184C4×C22⋊C4—28no—
185C2×#95C2312yes—
186C2×#95C2314yes—
187C2×#95C2314yes—
188C2×#95C2312yes—
189C2×#95C2314yes—
190C2×#95C2314yes—
191C2×#95C2314yes—
192C2×#95C2314yes—
193C2×#95C2314yes—
194C2×#95C2312yes—
195C2×#95C2312yes—
196C2×#95C2312yes—
197C2×#95C2312yes—
198C2×#95C2314yes—
199C2×#95C2312yes—
200C2×#95C2312yes—
201C2×#95C2312yes—
202C2×#95C2314yes—
203C2×#95C2314yes—
204C2×#95C2314yes—
205C2×#95C2312yes—
206C2×#95C2312yes—
207C25C2412yes—
208C25C2411yescharacteristic
209C22×Q8—28no—
210C22×Q8—28no—
211C22×Q8—28no—
212C22×Q8—28no—
213C22×Q8—44no—
214C22×Q8—44no—
215C22×Q8—44no—
216C22×D4—24no—
217C22×D4—24no—
218C22×D4—24no—
219C22×D4—22no—
220C22×D4—22no—
221C22×D4—22no—
222C22×D4—24no—
223C22×D4—22no—
224C22×D4—22no—
225C22×D4—22no—
226C22×D4—42no—
227C22×D4—42no—
228C22×D4C2×D414yes—
229C22×D4C2×D418yes—
230C23×C4—22no—
231C23×C4—22no—
232C23×C4—22no—
233C23×C4—22no—
234C23×C4—22no—
235C23×C4—22no—
236C23×C4—22no—
237C23×C4—22no—
238C23×C4—22no—
239C23×C4—22no—
240C23×C4—22no—
241C23×C4—22no—
242C23×C4—22no—
243C23×C4—22no—
244C23×C4—22no—
245C23×C4—24no—
246C23×C4—24no—
247C23×C4—22no—
248C23×C4—24no—
249C23×C4—24no—
250C23×C4—24no—
251C23×C4—22no—
252C23×C4—24no—
253C23×C4—24no—
254C23×C4—41no—
255C23×C4—41no—
256C23×C4C2×D414yes—
257C23×C4C2×D414yes—
258C23×C4C2414yes—
259C23×C4C2414yes—
260C23×C4C2412yes—
261C23×C4C2412yes—
262C23×C4C2412yes—
263C23×C4C2412yes—
264C23×C4C2412yes—
265C23×C4C2411yescharacteristic
266C23×C4C2411yescharacteristic
267C23×C4C2412yes—
268C23×C4C2411yescharacteristic
269C23×C4C2412yes—
270C23×C4C2411yescharacteristic
271C23×C4C2411yescharacteristic
272C23×C4C2411yescharacteristic
273C4⋊Q8—432no—
274C4⋊Q8—432no—
275#124—464no—
276#121—232no—
277C4×D4—432no—
278C4×D4—416no—
279C2×C4⋊C4—22no—
280C2×C4⋊C4—22no—
281C2×C4⋊C4—22no—
282C2×C4⋊C4—22no—
283C2×C4⋊C4—22no—
284C2×C4⋊C4—22no—
285C2×C4⋊C4—22no—
286C2×C4⋊C4—22no—
287C2×C4⋊C4—22no—
288C2×C4⋊C4—24no—
289C2×C4⋊C4—24no—
290C2×C4⋊C4—24no—
291C2×C4⋊C4—24no—
292C2×C4⋊C4—24no—
293C2×C4⋊C4—24no—
294C2×C4⋊C4—28no—
295C2×C4⋊C4—28no—
296C2×C4⋊C4—28no—
297C2×C4⋊C4—28no—
298C2×C4⋊C4—24no—
299C2×C4⋊C4—24no—
300C2×C4⋊C4—22no—
301C2×C4⋊C4—22no—
302C2×C4⋊C4—28no—
303C2×C4⋊C4—24no—
304C2×C4⋊C4—22no—
305C2×C4⋊C4—24no—
306C2×C4⋊C4—22no—
307C2×C4⋊C4—24no—
308C2×C4⋊C4—24no—
309C2×C4⋊C4—24no—
310C2×C4⋊C4—22no—
311C2×C4⋊C4—24no—
312C2×C4⋊C4—24no—
313C2×C4⋊C4—24no—
314C2×C4⋊C4—42no—
315C2×C4⋊C4—44no—
316C2×C4⋊C4—42no—
317C2×C4⋊C4—42no—
318C2×C4⋊C4—42no—
319C2×C4⋊C4—42no—
320C2×C4⋊C4C2×D414yes—
321C2×C4⋊C4C2×D414yes—
322C2×C4⋊C4C2×D414yes—
323C2×C4⋊C4C2×D414yes—
324C2×C4⋊C4C2×D414yes—
325C2×C4⋊C4#4114yes—
326C2×C4⋊C4#4114yes—
327C2×C22⋊C4—24no—
328C2×C22⋊C4—24no—
329C2×C22⋊C4—24no—
330C2×C22⋊C4—24no—
331C2×C22⋊C4—24no—
332C2×C22⋊C4—28no—
333C2×C22⋊C4—28no—
334C2×C22⋊C4—28no—
335C2×C22⋊C4—28no—
336C2×C22⋊C4—24no—
337C2×C22⋊C4—28no—
338C2×C22⋊C4—28no—
339C2×C22⋊C4—24no—
340C2×C22⋊C4—24no—
341C2×C22⋊C4—24no—
342C2×C22⋊C4—24no—
343C2×C22⋊C4—28no—
344C2×C22⋊C4—28no—
345C2×C22⋊C4—24no—
346C2×C22⋊C4—24no—
347C2×C22⋊C4—24no—
348C2×C22⋊C4—24no—
349C2×C22⋊C4—28no—
350C2×C22⋊C4—24no—
351C2×C22⋊C4—28no—
352C2×C22⋊C4—42no—
353C2×C22⋊C4—42no—
354C2×C22⋊C4—44no—
355C2×C22⋊C4—42no—
356C2×C22⋊C4—42no—
357C2×C22⋊C4—44no—
358C2×C22⋊C4—44no—
359C2×C22⋊C4—44no—
360C2×C22⋊C4—44no—
361C2×C22⋊C4C2×D418yes—
362C2×C22⋊C4C2×D418yes—
363C2×C42—24no—
364C2×C42—24no—
365C2×C42—28no—
366C2×C42—28no—
367C2×C42—24no—
368C2×C42—24no—
369C2×C42—22no—
370C2×C42—24no—
371C2×C42—22no—
372C2×C42—22no—
373C2×C42—24no—
374C2×C42—24no—
375C2×C42—22no—
376C2×C42—22no—
377C2×C42—22no—
378C2×C42—22no—
379C2×C42—22no—
380C2×C42—22no—
381C2×C42—24no—
382C2×C42—44no—
383C2×C42—416no—
384C2×C42C2×D418yes—
385C2×C42C2×D414yes—
386C2×C42#4114yes—
387C2×C42#4114yes—
388#95—24no—
389#95—24no—
390#95—24no—
391#95—24no—
392#95—28no—
393#95—24no—
394#95—28no—
395#95—28no—
396#95—28no—
397#95—28no—
398#95—28no—
399#95—28no—
400#95—24no—
401#95—24no—
402#95—28no—
403#95—24no—
404#95—44no—
405#95—42no—
406#95—44no—
407#95—44no—
408#95C2×D418yes—
409#95C2×D418yes—
410C24—21no—
411C24—21no—
412C24—21no—
413C24—21no—
414C24—21no—
415C24—21no—
416C24—21no—
417C24—21no—
418C24—21no—
419C24—21no—
420C24—21no—
421C24—21no—
422C24—22no—
423C24—22no—
424C24—22no—
425C24—22no—
426C24—22no—
427C24—22no—
428C24—22no—
429C24—22no—
430C24—22no—
431C24—22no—
432C24—22no—
433C24—22no—
434C24—22no—
435C24—22no—
436C24C22×D414yes—
437C24C22×D412yes—
438C24C22×D412yes—
439C24H(5,𝔽2)12yes—
440C24C2511yescharacteristic
441C2×Q8—416no—
442C2×Q8—416no—
443C2×Q8—416no—
444C2×Q8—416no—
445C2×Q8—88no—
446C2×Q8—88no—
447C2×Q8—88no—
448C2×D4—216no—
449C2×D4—216no—
450C2×D4—28no—
451C2×D4—28no—
452C2×D4—28no—
453C2×D4—48no—
454C2×D4—48no—
455C2×D4—48no—
456C2×D4—48no—
457C2×D4—48no—
458C2×D4—44no—
459C2×D4—44no—
460C2×D4—44no—
461C2×D4—44no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—22no—
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—22no—
470C22×C4—28no—
471C22×C4—22no—
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—22no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—21no—
491C22×C4—21no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—21no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—21no—
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—22no—
509C22×C4—21no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—21no—
513C22×C4—28no—
514C22×C4—28no—
515C22×C4—28no—
516C22×C4—28no—
517C22×C4—28no—
518C22×C4—28no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—24no—
522C22×C4—24no—
523C22×C4—22no—
524C22×C4—24no—
525C22×C4—24no—
526C22×C4—24no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—24no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—24no—
534C22×C4—24no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—24no—
538C22×C4—24no—
539C22×C4—24no—
540C22×C4—22no—
541C22×C4—24no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—24no—
546C22×C4—24no—
547C22×C4—44no—
548C22×C4—44no—
549C22×C4—44no—
550C22×C4—44no—
551C22×C4—44no—
552C22×C4—44no—
553C22×C4—44no—
554C22×C4—44no—
555C22×C4—44no—
556C22×C4—44no—
557C22×C4—44no—
558C22×C4—44no—
559C22×C4—44no—
560C22×C4—44no—
561C22×C4—48no—
562C22×C4—48no—
563C22×C4—48no—
564C22×C4—48no—
565C22×C4—48no—
566C22×C4—48no—
567C22×C4—48no—
568C22×C4C22×D412yes—
569C22×C4C22×D412yes—
570C22×C4C22×D414yes—
571C22×C4C22×D414yes—
572C22×C4C22×D414yes—
573C22×C4C22×D414yes—
574C22×C4C22×D414yes—
575C22×C4C22×D412yes—
576C22×C4C22×D412yes—
577C22×C4C22×D412yes—
578C22×C4C22×D412yes—
579C22×C4C22×D412yes—
580C22×C4C2×#4114yes—
581C22×C4C2×#4114yes—
582C22×C4C2×#4112yes—
583C22×C4C2×#4112yes—
584C22×C4C2×#4112yes—
585C22×C4C2×#4112yes—
586C22×C4C2×#4112yes—
587C22×C4C2×#4112yes—
588C22×C4C2×#4112yes—
589C22×C4C2×#4112yes—
590C22×C4H(5,𝔽2)12yes—
591C22×C42−1+412yes—
592C22×C42−1+412yes—
593C22×C42−1+412yes—
594C22×C42−1+412yes—
595C4⋊C4—28no—
596C4⋊C4—28no—
597C4⋊C4—28no—
598C4⋊C4—28no—
599C4⋊C4—48no—
600C4⋊C4—416no—
601C4⋊C4—416no—
602C4⋊C4—48no—
603C4⋊C4—44no—
604C4⋊C4—48no—
605C4⋊C4—48no—
606C4⋊C4—48no—
607C4⋊C4—44no—
608C4⋊C4—84no—
609C4⋊C4—84no—
610C4⋊C4#121116yes—
611C22⋊C4—216no—
612C22⋊C4—216no—
613C22⋊C4—48no—
614C22⋊C4—48no—
615C22⋊C4—48no—
616C22⋊C4—416no—
617C22⋊C4—48no—
618C22⋊C4—416no—
619C22⋊C4—416no—
620C22⋊C4—416no—
621C22⋊C4—48no—
622C22⋊C4—88no—
623C42—216no—
624C42—416no—
625C42—48no—
626C42—44no—
627C42—44no—
628C42—44no—
629C42—48no—
630C42#124116yescomplemented
631C23—22no—
632C23—22no—
633C23—22no—
634C23—22no—
635C23—22no—
636C23—22no—
637C23—22no—
638C23—22no—
639C23—22no—
640C23—22no—
641C23—22no—
642C23—22no—
643C23—22no—
644C23—22no—
645C23—22no—
646C23—22no—
647C23—22no—
648C23—22no—
649C23—24no—
650C23—24no—
651C23—24no—
652C23—24no—
653C23—24no—
654C23—24no—
655C23—24no—
656C23—41no—
657C23—41no—
658C23—41no—
659C23—41no—
660C23—41no—
661C23—41no—
662C23—41no—
663C23—41no—
664C23—41no—
665C23—41no—
666C23—41no—
667C23—41no—
668C23—41no—
669C23—41no—
670C23—41no—
671C23—41no—
672C23—42no—
673C23—42no—
674C23—42no—
675C23—42no—
676C23—42no—
677C23—42no—
678C23—42no—
679C23—42no—
680C23—42no—
681C23—42no—
682C23—42no—
683C23—42no—
684C23—42no—
685C23—42no—
686C23—42no—
687C23—42no—
688C23—42no—
689C23—42no—
690C23—42no—
691C23—42no—
692C23—42no—
693C23—42no—
694C23—42no—
695C23—42no—
696C23—42no—
697C23—42no—
698C23—42no—
699C23—42no—
700C23D4214yes—
701C23C23×D411yescharacteristic
702C23C23×D411yescharacteristic
703C23C23×D411yescharacteristic
704C23C22×#4111yescharacteristic
705C23C22×#4111yescharacteristic
706C23C22×#4111yescharacteristic
707C23C22×#4111yescharacteristic
708C23C2×H(5,𝔽2)11yescharacteristic
709C23C2×H(5,𝔽2)11yescharacteristic
710C23C2×2−1+411yescharacteristic
711C23C2×2−1+411yescharacteristic
712C23C2×2−1+411yescharacteristic
713C23C2×2−1+411yescharacteristic
714C23#58511yescharacteristic
715C23#58511yescharacteristic
716Q8—832no—
717D4—432no—
718D4—416no—
719C2×C4—24no—
720C2×C4—24no—
721C2×C4—24no—
722C2×C4—22no—
723C2×C4—24no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—24no—
730C2×C4—24no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—24no—
734C2×C4—24no—
735C2×C4—24no—
736C2×C4—24no—
737C2×C4—22no—
738C2×C4—24no—
739C2×C4—24no—
740C2×C4—22no—
741C2×C4—22no—
742C2×C4—22no—
743C2×C4—24no—
744C2×C4—24no—
745C2×C4—24no—
746C2×C4—24no—
747C2×C4—22no—
748C2×C4—24no—
749C2×C4—22no—
750C2×C4—22no—
751C2×C4—24no—
752C2×C4—416no—
753C2×C4—42no—
754C2×C4—42no—
755C2×C4—41no—
756C2×C4—41no—
757C2×C4—41no—
758C2×C4—41no—
759C2×C4—41no—
760C2×C4—42no—
761C2×C4—41no—
762C2×C4—41no—
763C2×C4—41no—
764C2×C4—41no—
765C2×C4—41no—
766C2×C4—42no—
767C2×C4—42no—
768C2×C4—42no—
769C2×C4—41no—
770C2×C4—41no—
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—416no—
782C2×C4—416no—
783C2×C4—44no—
784C2×C4—42no—
785C2×C4—44no—
786C2×C4—42no—
787C2×C4—42no—
788C2×C4—44no—
789C2×C4—44no—
790C2×C4—42no—
791C2×C4—44no—
792C2×C4—42no—
793C2×C4—44no—
794C2×C4—42no—
795C2×C4—42no—
796C2×C4—44no—
797C2×C4—42no—
798C2×C4—44no—
799C2×C4—42no—
800C2×C4—42no—
801C2×C4—44no—
802C2×C4—42no—
803C2×C4—44no—
804C2×C4—42no—
805C2×C4—44no—
806C2×C4—44no—
807C2×C4—42no—
808C2×C4—44no—
809C2×C4—44no—
810C2×C4—42no—
811C2×C4—816no—
812C2×C4C2×#12118yes—
813C2×C4C2×#12114yes—
814C2×C4C2×#12414yes—
815C2×C4C2×#12414yes—
816C2×C4C2×#12414yes—
817C2×C4#53214yes—
818C2×C4#53614yes—
819C2×C4#54214yes—
820C2×C4D4214yes—
821C2×C4#54714yes—
822C2×C4#54714yes—
823C2×C4#54714yes—
824C2×C4#54814yes—
825C2×C4#55514yes—
826C2×C4#55614yes—
827C2×C4#55614yes—
828C22—24no—
829C22—24no—
830C22—24no—
831C22—42no—
832C22—42no—
833C22—42no—
834C22—42no—
835C22—42no—
836C22—42no—
837C22—42no—
838C22—42no—
839C22—42no—
840C22—42no—
841C22—42no—
842C22—42no—
843C22—44no—
844C22—44no—
845C22—44no—
846C22—44no—
847C22—44no—
848C22—44no—
849C22—44no—
850C22—82no—
851C22—82no—
852C22—82no—
853C22—82no—
854C22—82no—
855C22—82no—
856C22—82no—
857C22—82no—
858C22C22×#12111yescharacteristic
859C22C22×#12411yescharacteristic
860C22C2×#53211yescharacteristic
861C22C2×#53611yescharacteristic
862C22C2×#54211yescharacteristic
863C22C2×D4211yescharacteristic
864C22C2×D4211yescharacteristic
865C22C2×#54711yescharacteristic
866C22C2×#54711yescharacteristic
867C22C2×#54711yescharacteristic
868C22C2×#54811yescharacteristic
869C22D4×#4111yescharacteristic
870C22D4×#4111yescharacteristic
871C22C2×#55511yescharacteristic
872C22C2×#55611yescharacteristic
873C22C2×#55611yescharacteristic
874C22#348211yescharacteristic
875C22#348811yescharacteristic
876C22#348911yescharacteristic
877C22#349211yescharacteristic
878C22#349311yescharacteristic
879C22#349411yescharacteristic
880C22#349511yescharacteristic
881C22#349611yescharacteristic
882C22#349711yescharacteristic
883C22#349911yescharacteristic
884C22#349911yescharacteristic
885C22#351811yescharacteristic
886C22#351811yescharacteristic
887C22#351911yescharacteristic
888C22#352211yescharacteristic
889C22#354411yescharacteristic
890C22#354711yescharacteristic
891C22#355011yescharacteristic
892C22#355511yescharacteristic
893C4—24no—
894C4—28no—
895C4—44no—
896C4—42no—
897C4—44no—
898C4—44no—
899C4—42no—
900C4—42no—
901C4—44no—
902C4—84no—
903C4—82no—
904C4—82no—
905C4—84no—
906C4#249118yescomplemented
907C4#254718yescomplemented
908C2—44no—
909C2—84no—
910C2C2×#249111yescharacteristic
911C2C2×#254711yescharacteristic
912C2#3554211yescharacteristic
913C2D4×#12111yescharacteristic
914C2#3612611yescharacteristic
915C2#3644411yescharacteristic
916C2#3647311yescharacteristic
917C2#3912511yescharacteristic
918C2#3915811yescharacteristic
919C2#3934311yescharacteristic
920C2#3935011yescharacteristic
921C2#5922911yescharacteristic
922C2#5923411yescharacteristic
923C2#5924411yescharacteristic
924C2#5931311yescharacteristic
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×#2547C2semidirect
2. C2×#2551C2semidirect
5. #15632C2semidirect
6. #15311C2semidirect
7. #15138C2semidirect
8. #15132C2semidirect
9. #15129C2semidirect
10. #15125C2semidirect
11. #14686C2semidirect
12. #14053C2semidirect
13. #13974C2semidirect
14. #13906C2semidirect
15. #13906C2semidirect
16. C4⋊C42C2semidirect
17. C4×#380C2semidirect
177. #380D4semidirect
630. C42#124semidirect
906. C4#2491semidirect
907. C4#2547semidirect

Maximal subgroups

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

subgroupindex
C2×#25472
C2×#25512
C2×#24912
C2×C4×#1212
#156322
#153112
#151382
#151322
#151292
#151252
#146862
#140532
#139742
#139062
C4⋊C422
C4×#3802