Finite Group Databasebeta

← #719375

Subgroups — #719375

Order 512.

4092 conjugacy classes of subgroups.

The subgroup lattice has 913 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2535C211yesmaximal, characteristic, complemented
2C2×#2416C212yesmaximal, complemented
3C2×#2392C211yesmaximal, characteristic, complemented
4C2×D4×C4⋊C4C211yesmaximal, characteristic, complemented
5C2×#2324C211yesmaximal, characteristic, complemented
6#17069C212yesmaximal, complemented
7#16821C212yesmaximal, complemented
8#15429C214yesmaximal, complemented
9#15274C214yesmaximal, complemented
10#15181C212yesmaximal, complemented
11#15126C212yesmaximal, complemented
12#15123C212yesmaximal, complemented
13#14806C212yesmaximal, complemented
14#14340C211yesmaximal, characteristic, complemented
15#13954C211yesmaximal, characteristic, complemented
16#13907C212yesmaximal, complemented
17#13906C211yesmaximal, characteristic, complemented
18C22×#121C2212yes—
19C22×#121C2211yescharacteristic
20C22×#121C2214yes—
21C22×C4×D4C2211yescharacteristic
22C22×C4×D4C2212yes—
23C22×C4×D4C2211yescharacteristic
24C22×C4×D4C2212yes—
25C22×#117C2211yescharacteristic
26C23×C4⋊C4C2212yes—
27#2535—28no—
28#2416—216no—
29#2392—28no—
30C2×#398C2211yescharacteristic
31C2×#397C2212yes—
32C2×#397C2211yescharacteristic
33C2×#396C2212yes—
34C2×#396C2214yes—
35C2×#394C2214yes—
36C2×#394C2212yes—
37C2×#394C2211yescharacteristic
38C2×#394C2214yes—
39C2×#392C2211yescharacteristic
40C2×#392C2212yes—
41D4×C4⋊C4—28no—
42#2324—28no—
43C2×#390C2212yes—
44C2×#390C2211yescharacteristic
45C2×#390C2212yes—
46C2×#389C2211yescharacteristic
47C2×#389C2212yes—
48C2×#389C2212yes—
49C2×#389C2212yes—
50C2×#388C2212yes—
51C2×#386C2212yes—
52C2×#386C2214yes—
53C2×#386C2214yes—
54C2×#385C2212yes—
55C2×#385C2214yes—
56C2×#384C2211yescharacteristic
57C2×#382C2211yescharacteristic
58C2×#380C2212yes—
59C2×#380C2211yescharacteristic
60C2×#380C2212yes—
61C2×#380C2212yes—
62C2×#380C2214yes—
63C2×#380C2214yes—
64C2×C4×C4⋊C4C2211yescharacteristic
65C2×C4×C4⋊C4C2211yescharacteristic
66C2×C4×C22⋊C4C2212yes—
67#1444C2214yes—
68#1442C2214yes—
69#1441C2212yes—
70#1441C2212yes—
71#1441C2214yes—
72#1441C2214yes—
73#1440C2214yes—
74#1439C2212yes—
75#1439C2212yes—
76#1439C2212yes—
77#1439C2214yes—
78#1439C2214yes—
79#1439C2214yes—
80#1439C2212yes—
81#1438C2214yes—
82#1438C2214yes—
83C4⋊#95C2212yes—
84C4⋊#95C2212yes—
85C4⋊#95C2212yes—
86C4⋊#95C2212yes—
87C22⋊#95C2214yes—
88C23×D4C2311yescharacteristic
89C23×D4C2311yescharacteristic
90C23×D4C2312yes—
91C23×D4C2314yes—
92C23×D4C2312yes—
93C24×C4C2312yes—
94C24×C4C2311yescharacteristic
95C24×C4C2314yes—
96C24×C4C2312yes—
97C2×#121—216no—
98C2×#121—28no—
99C2×#121—28no—
100C2×#121—24no—
101C2×#121—24no—
102C2×#121—48no—
103C2×#121—44no—
104C2×#121—48no—
105C2×#121D418yescomplemented
106C2×C4×D4—28no—
107C2×C4×D4—28no—
108C2×C4×D4—24no—
109C2×C4×D4—24no—
110C2×C4×D4—28no—
111C2×C4×D4—24no—
112C2×C4×D4—24no—
113C2×C4×D4—24no—
114C2×C4×D4—44no—
115C2×C4×D4—48no—
116C2×C4×D4D418yescomplemented
117C2×#117—24no—
118C2×#117—24no—
119C2×#117—24no—
120C22×C4⋊C4—28no—
121C22×C4⋊C4—28no—
122C22×C4⋊C4—28no—
123C22×C4⋊C4C2314yes—
124C22×C4⋊C4C2311yescharacteristic
125C22×C4⋊C4C2311yescharacteristic
126C22×C4⋊C4C2312yes—
127C22×C4⋊C4C2311yescharacteristic
128C22×C4⋊C4C2312yes—
129C22×C4⋊C4C2312yes—
130C22×C4⋊C4C2312yes—
131C22×C4⋊C4C2314yes—
132C22×C4⋊C4C2311yescharacteristic
133C22×C4⋊C4C2311yescharacteristic
134C22×C4⋊C4C2312yes—
135C22×C4⋊C4C2312yes—
136C22×C4⋊C4C2312yes—
137C22×C4⋊C4C2314yes—
138C22×C4⋊C4C2311yescharacteristic
139C22×C22⋊C4C2311yescharacteristic
140C22×C22⋊C4C2312yes—
141C22×C22⋊C4C2312yes—
142C22×C22⋊C4C2311yescharacteristic
143C22×C22⋊C4C2312yes—
144C22×C22⋊C4C2312yes—
145C22×C22⋊C4C2314yes—
146C22×C22⋊C4C2312yes—
147C22×C22⋊C4C2314yes—
148C22×C22⋊C4C2314yes—
149C22×C22⋊C4C2312yes—
150C22×C22⋊C4C2312yes—
151C22×C22⋊C4C2314yes—
152C22×C22⋊C4C2314yes—
153C22×C22⋊C4C2312yes—
154C22×C22⋊C4C2314yes—
155C22×C22⋊C4C2312yes—
156C22×C22⋊C4C2312yes—
157C22×C42C2311yescharacteristic
158C22×C42C2312yes—
159C22×C42C2312yes—
160C22×C42C2311yescharacteristic
161#398—24no—
162#397—24no—
163#397—28no—
164#396—28no—
165#396—216no—
166#394—24no—
167#394—216no—
168#394—28no—
169#394—48no—
170#392—24no—
171#392—28no—
172#390—28no—
173#390—24no—
174#390—28no—
175#389—24no—
176#389—28no—
177#389—28no—
178#389—44no—
179#388—28no—
180#386—216no—
181#386—216no—
182#386—28no—
183#385—28no—
184#385—216no—
185#384—24no—
186#382—24no—
187#380—28no—
188#380—28no—
189#380—24no—
190#380—28no—
191#380—48no—
192#380—48no—
193C4×C4⋊C4—24no—
194C4×C4⋊C4D418yescomplemented
195C4×C22⋊C4—28no—
196C2×#95C2312yes—
197C2×#95C2311yescharacteristic
198C2×#95C2311yescharacteristic
199C2×#95C2312yes—
200C2×#95C2314yes—
201C2×#95C2312yes—
202C2×#95C2314yes—
203C2×#95C2314yes—
204C2×#95C2312yes—
205C2×#95C2314yes—
206C2×#95C2314yes—
207C2×#95C2312yes—
208C2×#95C2312yes—
209C2×#95C2314yes—
210C2×#95C2314yes—
211C2×#95C2314yes—
212C2×#95C2314yes—
213C2×#95C2312yes—
214C25C2411yescharacteristic
215C25C2412yes—
216C25C2412yes—
217C22×D4—24no—
218C22×D4—24no—
219C22×D4—24no—
220C22×D4—24no—
221C22×D4—24no—
222C22×D4—28no—
223C22×D4—24no—
224C22×D4—28no—
225C22×D4—28no—
226C22×D4—28no—
227C22×D4—22no—
228C22×D4—22no—
229C22×D4—22no—
230C22×D4—24no—
231C22×D4—22no—
232C22×D4—22no—
233C22×D4—22no—
234C22×D4—24no—
235C22×D4—24no—
236C22×D4—22no—
237C22×D4—22no—
238C22×D4—42no—
239C22×D4—42no—
240C22×D4—44no—
241C22×D4—44no—
242C22×D4—44no—
243C22×D4—44no—
244C22×D4—44no—
245C22×D4C2×D414yes—
246C22×D4C2×D414yes—
247C22×D4C2×D418yes—
248C23×C4—24no—
249C23×C4—24no—
250C23×C4—22no—
251C23×C4—22no—
252C23×C4—24no—
253C23×C4—22no—
254C23×C4—24no—
255C23×C4—22no—
256C23×C4—22no—
257C23×C4—24no—
258C23×C4—24no—
259C23×C4—22no—
260C23×C4—28no—
261C23×C4—24no—
262C23×C4—28no—
263C23×C4—28no—
264C23×C4—28no—
265C23×C4—24no—
266C23×C4—24no—
267C23×C4—44no—
268C23×C4—44no—
269C23×C4—44no—
270C23×C4—44no—
271C23×C4—44no—
272C23×C4C2×D414yes—
273C23×C4C2×D418yes—
274C23×C4C2412yes—
275C23×C4C2411yescharacteristic
276C23×C4C2411yescharacteristic
277C23×C4C2414yes—
278C23×C4C2412yes—
279C23×C4C2414yes—
280C23×C4C2412yes—
281C23×C4C2411yescharacteristic
282C23×C4C2412yes—
283C23×C4C2412yes—
284C23×C4C2411yescharacteristic
285C23×C4C2411yescharacteristic
286C23×C4C2412yes—
287C23×C4C2411yescharacteristic
288#121—232no—
289#121—432no—
290#121—464no—
291C4×D4—232no—
292C4×D4—432no—
293C4×D4—432no—
294C4×D4—416no—
295#117—416no—
296C2×C4⋊C4—22no—
297C2×C4⋊C4—22no—
298C2×C4⋊C4—22no—
299C2×C4⋊C4—22no—
300C2×C4⋊C4—24no—
301C2×C4⋊C4—24no—
302C2×C4⋊C4—28no—
303C2×C4⋊C4—28no—
304C2×C4⋊C4—22no—
305C2×C4⋊C4—22no—
306C2×C4⋊C4—22no—
307C2×C4⋊C4—22no—
308C2×C4⋊C4—22no—
309C2×C4⋊C4—22no—
310C2×C4⋊C4—24no—
311C2×C4⋊C4—24no—
312C2×C4⋊C4—24no—
313C2×C4⋊C4—24no—
314C2×C4⋊C4—24no—
315C2×C4⋊C4—28no—
316C2×C4⋊C4—24no—
317C2×C4⋊C4—28no—
318C2×C4⋊C4—24no—
319C2×C4⋊C4—22no—
320C2×C4⋊C4—22no—
321C2×C4⋊C4—22no—
322C2×C4⋊C4—28no—
323C2×C4⋊C4—24no—
324C2×C4⋊C4—24no—
325C2×C4⋊C4—24no—
326C2×C4⋊C4—24no—
327C2×C4⋊C4—42no—
328C2×C4⋊C4—42no—
329C2×C4⋊C4—44no—
330C2×C4⋊C4—44no—
331C2×C4⋊C4—432no—
332C2×C4⋊C4—44no—
333C2×C4⋊C4—44no—
334C2×C4⋊C4—44no—
335C2×C4⋊C4—44no—
336C2×C4⋊C4—44no—
337C2×C4⋊C4C2×D414yes—
338C2×C4⋊C4C2×D414yes—
339C2×C4⋊C4C2×D414yes—
340C2×C4⋊C4C2×D414yes—
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—24no—
348C2×C22⋊C4—28no—
349C2×C22⋊C4—28no—
350C2×C22⋊C4—28no—
351C2×C22⋊C4—24no—
352C2×C22⋊C4—24no—
353C2×C22⋊C4—28no—
354C2×C22⋊C4—24no—
355C2×C22⋊C4—24no—
356C2×C22⋊C4—22no—
357C2×C22⋊C4—22no—
358C2×C22⋊C4—22no—
359C2×C22⋊C4—22no—
360C2×C22⋊C4—28no—
361C2×C22⋊C4—24no—
362C2×C22⋊C4—24no—
363C2×C22⋊C4—24no—
364C2×C22⋊C4—24no—
365C2×C22⋊C4—28no—
366C2×C22⋊C4—22no—
367C2×C22⋊C4—22no—
368C2×C22⋊C4—24no—
369C2×C22⋊C4—28no—
370C2×C22⋊C4—24no—
371C2×C22⋊C4—28no—
372C2×C22⋊C4—28no—
373C2×C22⋊C4—24no—
374C2×C22⋊C4—24no—
375C2×C22⋊C4—24no—
376C2×C22⋊C4—42no—
377C2×C22⋊C4—44no—
378C2×C22⋊C4—42no—
379C2×C22⋊C4—42no—
380C2×C22⋊C4—44no—
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⋊C4—44no—
390C2×C22⋊C4—44no—
391C2×C22⋊C4C2×D418yes—
392C2×C22⋊C4C2×D418yes—
393C2×C42—22no—
394C2×C42—22no—
395C2×C42—24no—
396C2×C42—24no—
397C2×C42—22no—
398C2×C42—24no—
399C2×C42—44no—
400C2×C42C2×D418yes—
401C2×C42C2×D414yes—
402C2×C42C2×D414yes—
403C2×C42#4114yes—
404#95—24no—
405#95—24no—
406#95—22no—
407#95—22no—
408#95—24no—
409#95—28no—
410#95—28no—
411#95—28no—
412#95—24no—
413#95—24no—
414#95—24no—
415#95—28no—
416#95—28no—
417#95—44no—
418#95—44no—
419#95—44no—
420#95—44no—
421#95C2×D418yes—
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—21no—
436C24—21no—
437C24—22no—
438C24—21no—
439C24—22no—
440C24—22no—
441C24—21no—
442C24—24no—
443C24—24no—
444C24—21no—
445C24—22no—
446C24—22no—
447C24—22no—
448C24—21no—
449C24—22no—
450C24—22no—
451C24—24no—
452C24—22no—
453C24—24no—
454C24C22×D414yes—
455C24C22×D412yes—
456C24C22×D414yes—
457C24H(5,𝔽2)14yes—
458C242−1+414yes—
459C24C2511yescharacteristic
460C2×D4—28no—
461C2×D4—28no—
462C2×D4—216no—
463C2×D4—216no—
464C2×D4—216no—
465C2×D4—28no—
466C2×D4—28no—
467C2×D4—216no—
468C2×D4—28no—
469C2×D4—28no—
470C2×D4—48no—
471C2×D4—48no—
472C2×D4—416no—
473C2×D4—48no—
474C2×D4—48no—
475C2×D4—48no—
476C2×D4—48no—
477C2×D4—416no—
478C2×D4—416no—
479C2×D4—416no—
480C2×D4—416no—
481C2×D4—44no—
482C2×D4—44no—
483C2×D4—44no—
484C2×D4—44no—
485C2×D4—84no—
486C2×D4—84no—
487C2×D4—88no—
488C2×D4—88no—
489C2×D4—88no—
490C2×D4—88no—
491C22×C4—22no—
492C22×C4—24no—
493C22×C4—22no—
494C22×C4—24no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—21no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—22no—
505C22×C4—21no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—24no—
510C22×C4—22no—
511C22×C4—21no—
512C22×C4—22no—
513C22×C4—22no—
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—216no—
523C22×C4—216no—
524C22×C4—28no—
525C22×C4—24no—
526C22×C4—22no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—24no—
534C22×C4—24no—
535C22×C4—24no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—22no—
540C22×C4—24no—
541C22×C4—24no—
542C22×C4—24no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—24no—
547C22×C4—24no—
548C22×C4—24no—
549C22×C4—24no—
550C22×C4—24no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—24no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—24no—
557C22×C4—22no—
558C22×C4—24no—
559C22×C4—24no—
560C22×C4—22no—
561C22×C4—416no—
562C22×C4—416no—
563C22×C4—416no—
564C22×C4—416no—
565C22×C4—48no—
566C22×C4—44no—
567C22×C4—48no—
568C22×C4—44no—
569C22×C4—44no—
570C22×C4—48no—
571C22×C4—48no—
572C22×C4—44no—
573C22×C4—416no—
574C22×C4—48no—
575C22×C4—88no—
576C22×C4—88no—
577C22×C4—84no—
578C22×C4—88no—
579C22×C4—84no—
580C22×C4—88no—
581C22×C4C22×D414yes—
582C22×C4C22×D412yes—
583C22×C4C22×D414yes—
584C22×C4C22×D412yes—
585C22×C4C22×D412yes—
586C22×C4C22×D414yes—
587C22×C4C22×D414yes—
588C22×C4C22×D412yes—
589C22×C4C22×D412yes—
590C22×C4C22×D412yes—
591C22×C4C22×D412yes—
592C22×C4C22×D412yes—
593C22×C4C2×#4112yes—
594C22×C4C2×#4112yes—
595C22×C4C2×#4114yes—
596C22×C4C2×#4112yes—
597C22×C4C2×#4112yes—
598C22×C4H(5,𝔽2)14yes—
599C22×C4H(5,𝔽2)12yes—
600C22×C42−1+412yes—
601C4⋊C4—28no—
602C4⋊C4—28no—
603C4⋊C4—48no—
604C4⋊C4—48no—
605C4⋊C4—416no—
606C4⋊C4—48no—
607C4⋊C4—416no—
608C4⋊C4—48no—
609C4⋊C4—44no—
610C4⋊C4—44no—
611C4⋊C4—44no—
612C4⋊C4—48no—
613C4⋊C4—84no—
614C4⋊C4—84no—
615C4⋊C4—88no—
616C4⋊C4#121116yes—
617C22⋊C4—216no—
618C22⋊C4—216no—
619C22⋊C4—48no—
620C22⋊C4—48no—
621C22⋊C4—48no—
622C22⋊C4—416no—
623C22⋊C4—416no—
624C22⋊C4—416no—
625C22⋊C4—416no—
626C22⋊C4—48no—
627C22⋊C4—44no—
628C22⋊C4—44no—
629C22⋊C4—48no—
630C22⋊C4—84no—
631C22⋊C4—84no—
632C22⋊C4—84no—
633C22⋊C4—88no—
634C22⋊C4—88no—
635C42—48no—
636C42—44no—
637C42—48no—
638C42#121116yescomplemented
639C23—24no—
640C23—24no—
641C23—24no—
642C23—24no—
643C23—24no—
644C23—24no—
645C23—24no—
646C23—24no—
647C23—24no—
648C23—24no—
649C23—24no—
650C23—24no—
651C23—24no—
652C23—24no—
653C23—24no—
654C23—24no—
655C23—24no—
656C23—24no—
657C23—24no—
658C23—22no—
659C23—22no—
660C23—24no—
661C23—22no—
662C23—24no—
663C23—24no—
664C23—28no—
665C23—24no—
666C23—28no—
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—41no—
684C23—42no—
685C23—41no—
686C23—42no—
687C23—44no—
688C23—42no—
689C23—41no—
690C23—42no—
691C23—41no—
692C23—42no—
693C23—42no—
694C23—41no—
695C23—42no—
696C23—41no—
697C23—44no—
698C23—42no—
699C23—42no—
700C23—44no—
701C23—42no—
702C23—41no—
703C23—41no—
704C23—42no—
705C23—44no—
706C23—42no—
707C23—44no—
708C23—42no—
709C23—42no—
710C23—44no—
711C23—42no—
712C23—44no—
713C23—42no—
714C23—44no—
715C23—44no—
716C23—42no—
717C23—44no—
718C23—42no—
719C23#53718yes—
720C23C23×D411yescharacteristic
721C23C23×D411yescharacteristic
722C23C23×D411yescharacteristic
723C23C22×#4111yescharacteristic
724C23C22×#4111yescharacteristic
725C23C2×H(5,𝔽2)11yescharacteristic
726C23C2×H(5,𝔽2)12yes—
727C23C2×H(5,𝔽2)12yes—
728C23C2×2−1+411yescharacteristic
729C23C2×2−1+412yes—
730C23#58512yes—
731D4—232no—
732D4—432no—
733D4—416no—
734D4—816no—
735D4—832no—
736C2×C4—24no—
737C2×C4—22no—
738C2×C4—24no—
739C2×C4—28no—
740C2×C4—22no—
741C2×C4—24no—
742C2×C4—24no—
743C2×C4—22no—
744C2×C4—24no—
745C2×C4—22no—
746C2×C4—24no—
747C2×C4—28no—
748C2×C4—22no—
749C2×C4—24no—
750C2×C4—24no—
751C2×C4—24no—
752C2×C4—22no—
753C2×C4—24no—
754C2×C4—22no—
755C2×C4—24no—
756C2×C4—24no—
757C2×C4—24no—
758C2×C4—24no—
759C2×C4—24no—
760C2×C4—42no—
761C2×C4—41no—
762C2×C4—41no—
763C2×C4—42no—
764C2×C4—42no—
765C2×C4—42no—
766C2×C4—41no—
767C2×C4—42no—
768C2×C4—41no—
769C2×C4—42no—
770C2×C4—42no—
771C2×C4—44no—
772C2×C4—42no—
773C2×C4—44no—
774C2×C4—432no—
775C2×C4—416no—
776C2×C4—41no—
777C2×C4—41no—
778C2×C4—42no—
779C2×C4—44no—
780C2×C4—42no—
781C2×C4—42no—
782C2×C4—44no—
783C2×C4—42no—
784C2×C4—44no—
785C2×C4—44no—
786C2×C4—44no—
787C2×C4—44no—
788C2×C4—42no—
789C2×C4—41no—
790C2×C4—44no—
791C2×C4—41no—
792C2×C4—42no—
793C2×C4—44no—
794C2×C4—44no—
795C2×C4—42no—
796C2×C4—42no—
797C2×C4—44no—
798C2×C4—42no—
799C2×C4—41no—
800C2×C4—44no—
801C2×C4—42no—
802C2×C4—41no—
803C2×C4—42no—
804C2×C4—42no—
805C2×C4—44no—
806C2×C4—44no—
807C2×C4—44no—
808C2×C4—42no—
809C2×C4—44no—
810C2×C4—42no—
811C2×C4—44no—
812C2×C4—832no—
813C2×C4—816no—
814C2×C4C2×#12114yes—
815C2×C4C2×#12114yes—
816C2×C4C2×#12118yes—
817C2×C4C2×#12114yes—
818C2×C4C2×#12114yes—
819C2×C4#53714yes—
820C2×C4D4214yes—
821C2×C4#54714yes—
822C2×C4#54714yes—
823C2×C4#55514yes—
824C22—28no—
825C22—28no—
826C22—28no—
827C22—44no—
828C22—44no—
829C22—44no—
830C22—44no—
831C22—44no—
832C22—44no—
833C22—44no—
834C22—44no—
835C22—44no—
836C22—44no—
837C22—44no—
838C22—44no—
839C22—44no—
840C22—48no—
841C22—42no—
842C22—44no—
843C22—42no—
844C22—44no—
845C22—44no—
846C22—42no—
847C22—44no—
848C22—48no—
849C22—81no—
850C22—82no—
851C22—82no—
852C22—84no—
853C22—81no—
854C22—82no—
855C22—82no—
856C22—84no—
857C22—81no—
858C22—82no—
859C22—82no—
860C22—81no—
861C22C22×#12111yescharacteristic
862C22C22×#12111yescharacteristic
863C22C2×#53712yes—
864C22C2×#53711yescharacteristic
865C22C2×D4211yescharacteristic
866C22C2×#54711yescharacteristic
867C22C2×#54711yescharacteristic
868C22C2×#55511yescharacteristic
869C22#348412yes—
870C22#348411yescharacteristic
871C22#348611yescharacteristic
872C22#348812yes—
873C22#348912yes—
874C22#349212yes—
875C22#349811yescharacteristic
876C22#350011yescharacteristic
877C22#350612yes—
878C22#351612yes—
879C22#351912yes—
880C22#353612yes—
881C22#354212yes—
882C22#355212yes—
883C22#355912yes—
884C4—28no—
885C4—24no—
886C4—24no—
887C4—44no—
888C4—42no—
889C4—44no—
890C4—44no—
891C4—82no—
892C4—84no—
893C4—84no—
894C4—81no—
895C4—81no—
896C4—82no—
897C4#253718yes—
898C2—48no—
899C2—82no—
900C2—84no—
901C2C2×#253711yescharacteristic
902C2#3522311yescharacteristic
903C2#3553311yescharacteristic
904C2#3569111yescharacteristic
905C2#3573711yescharacteristic
906C2#3764812yes—
907C2#3804212yes—
908C2#4242411yescharacteristic
909C2#4279411yescharacteristic
910C2#4492512yes—
911C2#4525512yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
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×#2535C2semidirect
2. C2×#2416C2semidirect
3. C2×#2392C2semidirect
4. C2×D4×C4⋊C4C2semidirect
5. C2×#2324C2semidirect
6. #17069C2semidirect
7. #16821C2semidirect
8. #15429C2semidirect
9. #15274C2semidirect
10. #15181C2semidirect
11. #15126C2semidirect
12. #15123C2semidirect
13. #14806C2semidirect
14. #14340C2semidirect
15. #13954C2semidirect
16. #13907C2semidirect
17. #13906C2semidirect
105. C2×#121D4semidirect
116. C2×C4×D4D4semidirect
194. C4×C4⋊C4D4semidirect
638. C42#121semidirect

Maximal subgroups

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

subgroupindex
C2×#25352
C2×#24162
C2×#23922
C2×D4×C4⋊C42
C2×#23242
#170692
#168212
#154292
#152742
#151812
#151262
#151232
#148062
#143402
#139542
#139072
#139062