Finite Group Databasebeta

← #530361

Subgroups — #530361

Order 512.

3914 conjugacy classes of subgroups.

The subgroup lattice has 941 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D4×C4⋊C4C211yesmaximal, characteristic, complemented
2C2×#2324C212yesmaximal
3C2×C4×#121C211yesmaximal, characteristic
4C2×#2285C211yesmaximal, characteristic, complemented
5#14686C211yesmaximal, characteristic, complemented
6#14403C214yesmaximal, complemented
7#14401C214yesmaximal, complemented
8#14264C212yesmaximal, complemented
9#14045C212yesmaximal, complemented
10#14018C212yesmaximal, complemented
11#13910C211yesmaximal, characteristic, complemented
12#13906C211yesmaximal, characteristic, complemented
13#13906C212yesmaximal, complemented
14#13880C212yesmaximal, complemented
15#13876C212yesmaximal, complemented
16#13872C212yesmaximal, complemented
17C4⋊C42C211yesmaximal, characteristic, complemented
18C22×#121C2211yescharacteristic
19C22×C4×D4C2212yes—
20C22×C4×D4C2211yescharacteristic
21C22×C4×D4C2212yes—
22C22×#117C2212yes—
23C23×C4⋊C4C2212yes—
24C23×C42C2211yescharacteristic
25D4×C4⋊C4—28no—
26#2324—216no—
27C4×#121C4116yescomplemented
28C2×#390C2214yes—
29C2×#390C2212yes—
30C2×#390C2211yescharacteristic
31C2×#389C2212yes—
32C2×#389C2212yes—
33C2×#389C2212yes—
34C2×#389C2211yescharacteristic
35C2×#388C2214yes—
36C2×#388C2212yes—
37C2×#386C2214yes—
38C2×#386C2212yes—
39C2×#385C2214yes—
40C2×#385C2214yes—
41C2×#385C2214yes—
42#2285—28no—
43C2×#384C2211yescharacteristic
44C2×#384C2211yescharacteristic
45C2×#384C2211yescharacteristic
46C2×#384C2211yescharacteristic
47C2×#384C2212yes—
48C2×#382C2212yes—
49C2×#380C2212yes—
50C2×#380C2211yescharacteristic
51C2×#380C2212yes—
52C2×#380C2212yes—
53C2×#380C2211yescharacteristic
54C2×#380C2212yes—
55C2×#380C2212yes—
56C2×#380C2212yes—
57C2×#380C2212yes—
58C2×#380C2211yescharacteristic
59C2×C4×C4⋊C4C2212yes—
60C2×C4×C4⋊C4C2211yescharacteristic
61C2×C4×C4⋊C4C2212yes—
62C2×C4×C4⋊C4C2212yes—
63C2×C4×C4⋊C4C2211yescharacteristic
64C2×C4×C4⋊C4C2211yescharacteristic
65C2×C4×C22⋊C4C2212yes—
66#1444C2214yes—
67#1444C2214yes—
68#1444C2214yes—
69#1442C2214yes—
70#1441C2214yes—
71#1439C2214yes—
72#1439C2214yes—
73#1439C2214yes—
74#1439C2214yes—
75#1439C2214yes—
76#1436C2214yes—
77#1436C2214yes—
78C4⋊#95C2212yes—
79C4⋊#95C2212yes—
80C4⋊#95C2212yes—
81C4⋊#95C2212yes—
82C4⋊#95C2214yes—
83C4⋊#95C2212yes—
84C4⋊#95C2212yes—
85C4⋊#95C2212yes—
86C22⋊#95C2214yes—
87C23×D4C2311yescharacteristic
88C23×D4C2312yes—
89C24×C4C2311yescharacteristic
90C24×C4C2312yes—
91C24×C4C2311yescharacteristic
92C24×C4C2311yescharacteristic
93C24×C4C2314yes—
94C2×#121C2×C418yes—
95C2×#121D418yes—
96C2×#121Q818yes—
97C2×C4×D4—28no—
98C2×C4×D4—24no—
99C2×C4×D4—28no—
100C2×C4×D4—24no—
101C2×C4×D4—44no—
102C2×C4×D4—44no—
103C2×C4×D4—44no—
104C2×C4×D4C2×C418yes—
105C2×C4×D4C2×C4116yescomplemented
106C2×#117—28no—
107C2×#117—28no—
108C2×#117—44no—
109C22×C4⋊C4—28no—
110C22×C4⋊C4—44no—
111C22×C4⋊C4—44no—
112C22×C4⋊C4C2312yes—
113C22×C4⋊C4C2312yes—
114C22×C4⋊C4C2312yes—
115C22×C4⋊C4C2311yescharacteristic
116C22×C4⋊C4C2312yes—
117C22×C4⋊C4C2311yescharacteristic
118C22×C4⋊C4C2312yes—
119C22×C4⋊C4C2312yes—
120C22×C4⋊C4C2312yes—
121C22×C4⋊C4C2312yes—
122C22×C4⋊C4C2311yescharacteristic
123C22×C4⋊C4C2311yescharacteristic
124C22×C4⋊C4C2311yescharacteristic
125C22×C4⋊C4C2311yescharacteristic
126C22×C4⋊C4C2314yes—
127C22×C4⋊C4C2312yes—
128C22×C4⋊C4C2312yes—
129C22×C4⋊C4C2314yes—
130C22×C4⋊C4C2314yes—
131C22×C4⋊C4C2312yes—
132C22×C4⋊C4C2311yescharacteristic
133C22×C22⋊C4C2312yes—
134C22×C22⋊C4C2312yes—
135C22×C22⋊C4C2314yes—
136C22×C22⋊C4C2312yes—
137C22×C22⋊C4C2312yes—
138C22×C22⋊C4C2314yes—
139C22×C22⋊C4C2314yes—
140C22×C22⋊C4C2314yes—
141C22×C22⋊C4C2312yes—
142C22×C22⋊C4C2312yes—
143C22×C22⋊C4C2312yes—
144C22×C42—24no—
145C22×C42—24no—
146C22×C42C2×C418yescomplemented
147C22×C42C2312yes—
148C22×C42C2311yescharacteristic
149C22×C42C2311yescharacteristic
150C22×C42C2311yescharacteristic
151C22×C42C2312yes—
152C22×C42C2312yes—
153C22×C42C2314yes—
154C22×C42C2311yescharacteristic
155#390—28no—
156#390—216no—
157#390C2×C418yes—
158#389—28no—
159#389—28no—
160#389—44no—
161#389C2×C418yescomplemented
162#388—216no—
163#388C2×C4116yescomplemented
164#386—216no—
165#386C2×C4116yescomplemented
166#385—216no—
167#385—216no—
168#385—48no—
169#384—24no—
170#384—24no—
171#384—24no—
172#384—24no—
173#384—44no—
174#382—28no—
175#380—28no—
176#380—28no—
177#380—24no—
178#380—24no—
179#380—28no—
180#380—44no—
181#380—44no—
182#380—44no—
183#380—44no—
184#380C2×C418yescomplemented
185C4×C4⋊C4—28no—
186C4×C4⋊C4—28no—
187C4×C4⋊C4—24no—
188C4×C4⋊C4—44no—
189C4×C4⋊C4C2×C418yescomplemented
190C4×C4⋊C4D418yescomplemented
191C4×C22⋊C4C2×C4116yescomplemented
192C2×#95C2312yes—
193C2×#95C2314yes—
194C2×#95C2312yes—
195C2×#95C2314yes—
196C2×#95C2314yes—
197C2×#95C2314yes—
198C2×#95C2314yes—
199C2×#95C2312yes—
200C2×#95C2314yes—
201C2×#95C2314yes—
202C2×#95C2314yes—
203C2×#95C2314yes—
204C2×#95C2314yes—
205C2×#95C2314yes—
206C2×#95C2312yes—
207C2×#95C2312yes—
208C2×#95C2312yes—
209C2×#95C2312yes—
210C25C2411yescharacteristic
211C25C2412yes—
212C22×D4—22no—
213C22×D4—22no—
214C22×D4—22no—
215C22×D4—22no—
216C22×D4—42no—
217C22×D4—42no—
218C22×D4—42no—
219C22×D4—42no—
220C22×D4C22×C414yes—
221C22×D4C22×C418yes—
222C22×D4C2×D414yes—
223C22×D4C2×D418yes—
224C22×D4C2×Q814yes—
225C22×D4C2×Q818yes—
226C23×C4—22no—
227C23×C4—22no—
228C23×C4—22no—
229C23×C4—22no—
230C23×C4—24no—
231C23×C4—22no—
232C23×C4—22no—
233C23×C4—24no—
234C23×C4—22no—
235C23×C4—22no—
236C23×C4—24no—
237C23×C4—24no—
238C23×C4—22no—
239C23×C4—22no—
240C23×C4—24no—
241C23×C4—22no—
242C23×C4—22no—
243C23×C4—22no—
244C23×C4—22no—
245C23×C4—24no—
246C23×C4—28no—
247C23×C4—28no—
248C23×C4—41no—
249C23×C4—41no—
250C23×C4—44no—
251C23×C4—44no—
252C23×C4—44no—
253C23×C4—44no—
254C23×C4—44no—
255C23×C4C22×C418yes—
256C23×C4C22×C414yes—
257C23×C4C22×C414yes—
258C23×C4C22×C414yes—
259C23×C4C2×D414yes—
260C23×C4C2×Q814yes—
261C23×C4C2412yes—
262C23×C4C2412yes—
263C23×C4C2414yes—
264C23×C4C2414yes—
265C23×C4C2412yes—
266C23×C4C2412yes—
267C23×C4C2411yescharacteristic
268C23×C4C2412yes—
269C23×C4C2412yes—
270C23×C4C2411yescharacteristic
271C23×C4C2412yes—
272C23×C4C2411yescharacteristic
273C23×C4C2411yescharacteristic
274C23×C4C2411yescharacteristic
275C23×C4C2411yescharacteristic
276#121C4⋊C4164yescomplemented
277C4×D4—232no—
278C4×D4—432no—
279C4×D4—432no—
280#117—432no—
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—22no—
289C2×C4⋊C4—24no—
290C2×C4⋊C4—28no—
291C2×C4⋊C4—24no—
292C2×C4⋊C4—24no—
293C2×C4⋊C4—24no—
294C2×C4⋊C4—24no—
295C2×C4⋊C4—24no—
296C2×C4⋊C4—24no—
297C2×C4⋊C4—24no—
298C2×C4⋊C4—24no—
299C2×C4⋊C4—22no—
300C2×C4⋊C4—22no—
301C2×C4⋊C4—24no—
302C2×C4⋊C4—24no—
303C2×C4⋊C4—24no—
304C2×C4⋊C4—24no—
305C2×C4⋊C4—24no—
306C2×C4⋊C4—24no—
307C2×C4⋊C4—24no—
308C2×C4⋊C4—22no—
309C2×C4⋊C4—22no—
310C2×C4⋊C4—24no—
311C2×C4⋊C4—22no—
312C2×C4⋊C4—24no—
313C2×C4⋊C4—24no—
314C2×C4⋊C4—22no—
315C2×C4⋊C4—24no—
316C2×C4⋊C4—24no—
317C2×C4⋊C4—28no—
318C2×C4⋊C4—24no—
319C2×C4⋊C4—432no—
320C2×C4⋊C4—44no—
321C2×C4⋊C4—44no—
322C2×C4⋊C4—42no—
323C2×C4⋊C4—42no—
324C2×C4⋊C4—42no—
325C2×C4⋊C4—42no—
326C2×C4⋊C4—42no—
327C2×C4⋊C4—42no—
328C2×C4⋊C4—42no—
329C2×C4⋊C4—42no—
330C2×C4⋊C4—44no—
331C2×C4⋊C4—42no—
332C2×C4⋊C4—42no—
333C2×C4⋊C4—44no—
334C2×C4⋊C4—44no—
335C2×C4⋊C4—44no—
336C2×C4⋊C4—44no—
337C2×C4⋊C4C22×C414yes—
338C2×C4⋊C4C22×C414yes—
339C2×C4⋊C4C22×C418yes—
340C2×C4⋊C4C22×C414yes—
341C2×C4⋊C4C2×D414yes—
342C2×C4⋊C4C2×D414yes—
343C2×C4⋊C4C2×D414yes—
344C2×C4⋊C4C2×Q814yes—
345C2×C22⋊C4—24no—
346C2×C22⋊C4—24no—
347C2×C22⋊C4—24no—
348C2×C22⋊C4—24no—
349C2×C22⋊C4—24no—
350C2×C22⋊C4—24no—
351C2×C22⋊C4—28no—
352C2×C22⋊C4—24no—
353C2×C22⋊C4—24no—
354C2×C22⋊C4—28no—
355C2×C22⋊C4—28no—
356C2×C22⋊C4—28no—
357C2×C22⋊C4—28no—
358C2×C22⋊C4—42no—
359C2×C22⋊C4—42no—
360C2×C22⋊C4—42no—
361C2×C22⋊C4—42no—
362C2×C22⋊C4—42no—
363C2×C22⋊C4—42no—
364C2×C22⋊C4—44no—
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⋊C4C22×C418yes—
372C2×C22⋊C4C22×C418yes—
373C2×C22⋊C4C22×C418yes—
374C2×C22⋊C4C22×C418yes—
375C2×C22⋊C4C22×C418yes—
376C2×C22⋊C4C2×D418yes—
377C2×C22⋊C4C2×Q818yes—
378C2×C42—24no—
379C2×C42—22no—
380C2×C42—22no—
381C2×C42—22no—
382C2×C42—22no—
383C2×C42—22no—
384C2×C42—22no—
385C2×C42—24no—
386C2×C42—24no—
387C2×C42—24no—
388C2×C42—232no—
389C2×C42—24no—
390C2×C42—24no—
391C2×C42—24no—
392C2×C42—28no—
393C2×C42—44no—
394C2×C42—44no—
395C2×C42C22×C418yes—
396C2×C42C22×C414yes—
397C2×C42C22×C414yes—
398C2×C42C22×C414yes—
399C2×C42C22×C414yes—
400C2×C42C2×D418yes—
401C2×C42C2×D414yes—
402C2×C42#4114yes—
403#95—24no—
404#95—24no—
405#95—24no—
406#95—28no—
407#95—28no—
408#95—28no—
409#95—28no—
410#95—28no—
411#95—44no—
412#95—44no—
413#95—44no—
414#95—44no—
415#95—44no—
416#95—44no—
417#95C22×C418yes—
418#95C22×C418yes—
419#95C22×C418yes—
420#95C2×D418yes—
421C24—21no—
422C24—22no—
423C24—22no—
424C24—21no—
425C24—22no—
426C24—21no—
427C24—21no—
428C24—21no—
429C24—22no—
430C24—22no—
431C24—21no—
432C24—21no—
433C24—22no—
434C24—22no—
435C24—22no—
436C24—21no—
437C24—21no—
438C24—22no—
439C24—21no—
440C24—22no—
441C24—22no—
442C24—22no—
443C24—21no—
444C24—21no—
445C24C23×C414yes—
446C24C23×C412yes—
447C24C22×D412yes—
448C24C22×D414yes—
449C24C22×Q814yes—
450C24C22×Q812yes—
451C24C2511yescharacteristic
452C2×D4—28no—
453C2×D4—28no—
454C2×D4—28no—
455C2×D4—28no—
456C2×D4—28no—
457C2×D4—28no—
458C2×D4—48no—
459C2×D4—48no—
460C2×D4—48no—
461C2×D4—48no—
462C2×D4—48no—
463C2×D4—48no—
464C2×D4C2×C4⋊C4116yes—
465C2×D4C2×C4⋊C4132yescomplemented
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—22no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—22no—
482C22×C4—28no—
483C22×C4—28no—
484C22×C4—28no—
485C22×C4—28no—
486C22×C4—28no—
487C22×C4—28no—
488C22×C4—21no—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—21no—
493C22×C4—22no—
494C22×C4—21no—
495C22×C4—22no—
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—22no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—21no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—28no—
519C22×C4—28no—
520C22×C4—216no—
521C22×C4—28no—
522C22×C4—216no—
523C22×C4—28no—
524C22×C4—216no—
525C22×C4—28no—
526C22×C4—22no—
527C22×C4—24no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—24no—
531C22×C4—24no—
532C22×C4—22no—
533C22×C4—24no—
534C22×C4—24no—
535C22×C4—24no—
536C22×C4—22no—
537C22×C4—24no—
538C22×C4—22no—
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—22no—
548C22×C4—24no—
549C22×C4—22no—
550C22×C4—24no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—24no—
554C22×C4—44no—
555C22×C4—44no—
556C22×C4—44no—
557C22×C4—44no—
558C22×C4—44no—
559C22×C4—416no—
560C22×C4—416no—
561C22×C4—48no—
562C22×C4—44no—
563C22×C4—48no—
564C22×C4—44no—
565C22×C4—48no—
566C22×C4—44no—
567C22×C4—48no—
568C22×C4—44no—
569C22×C4—88no—
570C22×C4—88no—
571C22×C4—88no—
572C22×C4—88no—
573C22×C4—88no—
574C22×C4C2×C4⋊C4116yescomplemented
575C22×C4C23×C414yes—
576C22×C4C23×C414yes—
577C22×C4C23×C412yes—
578C22×C4C23×C412yes—
579C22×C4C23×C414yes—
580C22×C4C23×C412yes—
581C22×C4C23×C412yes—
582C22×C4C23×C412yes—
583C22×C4C23×C412yes—
584C22×C4C22×D414yes—
585C22×C4C22×D414yes—
586C22×C4C22×D414yes—
587C22×C4C22×D412yes—
588C22×C4C22×D412yes—
589C22×C4C22×D412yes—
590C22×C4C22×D412yes—
591C22×C4C22×D412yes—
592C22×C4C22×Q812yes—
593C22×C4C22×Q814yes—
594C22×C4C22×Q812yes—
595C22×C4C2×#4112yes—
596C22×C4C2×#4112yes—
597C22×C4C2×#4112yes—
598C22×C4H(5,𝔽2)12yes—
599C22×C4H(5,𝔽2)12yes—
600C22×C4H(5,𝔽2)12yes—
601C22×C4H(5,𝔽2)12yes—
602C22×C4H(5,𝔽2)12yes—
603C22×C42−1+412yes—
604C22×C42−1+412yes—
605C22×C42−1+412yes—
606C4⋊C4—28no—
607C4⋊C4—28no—
608C4⋊C4—28no—
609C4⋊C4—28no—
610C4⋊C4—48no—
611C4⋊C4—48no—
612C4⋊C4—48no—
613C4⋊C4—48no—
614C4⋊C4—48no—
615C4⋊C4—416no—
616C4⋊C4—44no—
617C4⋊C4—48no—
618C4⋊C4—44no—
619C4⋊C4—48no—
620C4⋊C4—48no—
621C4⋊C4—48no—
622C4⋊C4—84no—
623C4⋊C4—84no—
624C4⋊C4—88no—
625C4⋊C4—88no—
626C4⋊C4C2×C4⋊C4116yescomplemented
627C22⋊C4—216no—
628C22⋊C4—216no—
629C22⋊C4—48no—
630C22⋊C4—48no—
631C22⋊C4—48no—
632C22⋊C4—48no—
633C22⋊C4—416no—
634C22⋊C4—88no—
635C22⋊C4—88no—
636C22⋊C4—88no—
637C22⋊C4C2×C4⋊C4132yescomplemented
638C42—28no—
639C42—28no—
640C42—28no—
641C42—216no—
642C42—216no—
643C42—48no—
644C42—88no—
645C42C4×D4116yes—
646C23—24no—
647C23—22no—
648C23—22no—
649C23—24no—
650C23—24no—
651C23—22no—
652C23—22no—
653C23—24no—
654C23—22no—
655C23—24no—
656C23—22no—
657C23—24no—
658C23—22no—
659C23—24no—
660C23—22no—
661C23—24no—
662C23—22no—
663C23—24no—
664C23—22no—
665C23—24no—
666C23—24no—
667C23—24no—
668C23—22no—
669C23—22no—
670C23—22no—
671C23—24no—
672C23—24no—
673C23—22no—
674C23—22no—
675C23—22no—
676C23—24no—
677C23—24no—
678C23—22no—
679C23—24no—
680C23—24no—
681C23—22no—
682C23—42no—
683C23—41no—
684C23—41no—
685C23—42no—
686C23—42no—
687C23—41no—
688C23—42no—
689C23—41no—
690C23—41no—
691C23—42no—
692C23—41no—
693C23—42no—
694C23—41no—
695C23—42no—
696C23—41no—
697C23—42no—
698C23—42no—
699C23—41no—
700C23—41no—
701C23—42no—
702C23—41no—
703C23—42no—
704C23—42no—
705C23—41no—
706C23—42no—
707C23—41no—
708C23—41no—
709C23—42no—
710C23—41no—
711C23—42no—
712C23—41no—
713C23—42no—
714C23C22×C4⋊C418yes—
715C23C22×C4⋊C414yes—
716C23C24×C411yescharacteristic
717C23C23×D411yescharacteristic
718C23C23×D411yescharacteristic
719C23C23×Q811yescharacteristic
720C23C22×#4111yescharacteristic
721C23C2×H(5,𝔽2)11yescharacteristic
722C23C2×H(5,𝔽2)11yescharacteristic
723C23C2×H(5,𝔽2)11yescharacteristic
724C23C2×H(5,𝔽2)11yescharacteristic
725C23C2×H(5,𝔽2)11yescharacteristic
726C23C2×2−1+411yescharacteristic
727C23C2×2−1+411yescharacteristic
728C23C2×2−1+411yescharacteristic
729C23#58511yescharacteristic
730C23#58511yescharacteristic
731D4—232no—
732D4—432no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—24no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—24no—
741C2×C4—22no—
742C2×C4—22no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—22no—
749C2×C4—22no—
750C2×C4—22no—
751C2×C4—22no—
752C2×C4—22no—
753C2×C4—24no—
754C2×C4—24no—
755C2×C4—24no—
756C2×C4—24no—
757C2×C4—232no—
758C2×C4—22no—
759C2×C4—24no—
760C2×C4—24no—
761C2×C4—22no—
762C2×C4—24no—
763C2×C4—24no—
764C2×C4—24no—
765C2×C4—22no—
766C2×C4—24no—
767C2×C4—24no—
768C2×C4—24no—
769C2×C4—24no—
770C2×C4—24no—
771C2×C4—24no—
772C2×C4—24no—
773C2×C4—416no—
774C2×C4—42no—
775C2×C4—41no—
776C2×C4—41no—
777C2×C4—42no—
778C2×C4—41no—
779C2×C4—42no—
780C2×C4—41no—
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—416no—
795C2×C4—432no—
796C2×C4—44no—
797C2×C4—42no—
798C2×C4—42no—
799C2×C4—44no—
800C2×C4—42no—
801C2×C4—42no—
802C2×C4—44no—
803C2×C4—44no—
804C2×C4—42no—
805C2×C4—44no—
806C2×C4—42no—
807C2×C4—44no—
808C2×C4—44no—
809C2×C4—42no—
810C2×C4—42no—
811C2×C4—44no—
812C2×C4—42no—
813C2×C4—44no—
814C2×C4—44no—
815C2×C4—42no—
816C2×C4—42no—
817C2×C4—44no—
818C2×C4—42no—
819C2×C4—42no—
820C2×C4—44no—
821C2×C4—42no—
822C2×C4—44no—
823C2×C4—44no—
824C2×C4—832no—
825C2×C4C22×C4⋊C414yes—
826C2×C4C22×C4⋊C418yes—
827C2×C4C22×C4⋊C414yes—
828C2×C4C2×C4×D414yes—
829C2×C4C2×C4×D414yes—
830C2×C4C2×C4×D414yes—
831C2×C4#51814yes—
832C2×C4#52014yes—
833C2×C4#52014yes—
834C2×C4#52014yes—
835C2×C4#53514yes—
836C2×C4#53714yes—
837C2×C4#54014yes—
838C2×C4#54214yes—
839C2×C4D4214yes—
840C2×C4#54714yes—
841C2×C4D4×Q814yes—
842C2×C4#55414yes—
843C22—24no—
844C22—28no—
845C22—24no—
846C22—28no—
847C22—28no—
848C22—24no—
849C22—44no—
850C22—42no—
851C22—42no—
852C22—44no—
853C22—42no—
854C22—44no—
855C22—42no—
856C22—44no—
857C22—42no—
858C22—44no—
859C22—42no—
860C22—44no—
861C22—44no—
862C22—42no—
863C22—42no—
864C22—44no—
865C22—42no—
866C22—44no—
867C22—42no—
868C22—44no—
869C22—42no—
870C22—44no—
871C22—42no—
872C22—44no—
873C22C23×C4⋊C411yescharacteristic
874C22C22×C4×D411yescharacteristic
875C22C2×#51811yescharacteristic
876C22C2×#52011yescharacteristic
877C22C2×#52011yescharacteristic
878C22C2×#52011yescharacteristic
879C22#342811yescharacteristic
880C22C2×#53511yescharacteristic
881C22C2×#53711yescharacteristic
882C22C2×#54011yescharacteristic
883C22C2×#54211yescharacteristic
884C22C2×D4211yescharacteristic
885C22C2×#54711yescharacteristic
886C22C2×D4×Q811yescharacteristic
887C22C2×#55411yescharacteristic
888C22#348811yescharacteristic
889C22#348911yescharacteristic
890C22#349411yescharacteristic
891C22#349511yescharacteristic
892C22#349611yescharacteristic
893C22#349611yescharacteristic
894C22#349811yescharacteristic
895C22#349911yescharacteristic
896C22#350111yescharacteristic
897C22#350111yescharacteristic
898C22#350311yescharacteristic
899C22#350311yescharacteristic
900C22#354611yescharacteristic
901C22#354711yescharacteristic
902C22#354811yescharacteristic
903C22#354811yescharacteristic
904C22#354911yescharacteristic
905C22#355011yescharacteristic
906C22#355411yescharacteristic
907C22#355511yescharacteristic
908C4—24no—
909C4—28no—
910C4—24no—
911C4—24no—
912C4—42no—
913C4—44no—
914C4—44no—
915C4—44no—
916C4—44no—
917C4—82no—
918C4—82no—
919C4—84no—
920C4—84no—
921C4#232418yescomplemented
922C4D4×C4⋊C418yes—
923C2—44no—
924C2—48no—
925C2C2×#232411yescharacteristic
926C2C2×D4×C4⋊C411yescharacteristic
927C2#3418111yescharacteristic
928C2#3418311yescharacteristic
929C2#3420211yescharacteristic
930C2#3436811yescharacteristic
931C2#3438311yescharacteristic
932C2#3934011yescharacteristic
933C2#3934211yescharacteristic
934C2#3935011yescharacteristic
935C2#3935211yescharacteristic
936C2#3959611yescharacteristic
937C2#3959811yescharacteristic
938C2#3960611yescharacteristic
939C2#3960811yescharacteristic
subgroupG/H
center, Frattini, socle, cosocleC24C25
commutatorC23C24×C4
prime radicalC22×#121C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24 ◁ G
LECSG ▷ C24 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×D4×C4⋊C4C2semidirect
4. C2×#2285C2semidirect
5. #14686C2semidirect
6. #14403C2semidirect
7. #14401C2semidirect
8. #14264C2semidirect
9. #14045C2semidirect
10. #14018C2semidirect
11. #13910C2semidirect
12. #13906C2semidirect
13. #13906C2semidirect
14. #13880C2semidirect
15. #13876C2semidirect
16. #13872C2semidirect
17. C4⋊C42C2semidirect
27. C4×#121C4semidirect
105. C2×C4×D4C2×C4semidirect
146. C22×C42C2×C4semidirect
161. #389C2×C4semidirect
163. #388C2×C4semidirect
165. #386C2×C4semidirect
184. #380C2×C4semidirect
189. C4×C4⋊C4C2×C4semidirect
190. C4×C4⋊C4D4semidirect
191. C4×C22⋊C4C2×C4semidirect
276. #121C4⋊C4semidirect
465. C2×D4C2×C4⋊C4semidirect
574. C22×C4C2×C4⋊C4semidirect
626. C4⋊C4C2×C4⋊C4semidirect
637. C22⋊C4C2×C4⋊C4semidirect
921. C4#2324semidirect

Maximal subgroups

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

subgroupindex
C2×D4×C4⋊C42
C2×#23242
C2×C4×#1212
C2×#22852
#146862
#144032
#144012
#142642
#140452
#140182
#139102
#139062
#138802
#138762
#138722
C4⋊C422