Finite Group Databasebeta

← #519312

Subgroups — #519312

Order 512.

4122 conjugacy classes of subgroups.

The subgroup lattice has 947 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2354C211yesmaximal, characteristic, complemented
2C2×#2352C212yesmaximal, complemented
3C2×C4×#121C211yesmaximal, characteristic
4C22×C4×C4⋊C4C211yesmaximal, characteristic, complemented
5#14698C212yesmaximal
6#14686C211yesmaximal, characteristic, complemented
7#14119C214yesmaximal, complemented
8#14042C212yesmaximal, complemented
9#14022C212yesmaximal, complemented
10#13999C214yesmaximal, complemented
11#13911C211yesmaximal, characteristic, complemented
12#13906C211yesmaximal, characteristic, complemented
13#13875C212yesmaximal, complemented
14#13872C212yesmaximal, complemented
15C4⋊C42C211yesmaximal, characteristic, complemented
16#13801C212yesmaximal, complemented
17C4×#380C212yesmaximal, complemented
18C22×#121C2211yescharacteristic
19C22×C4×D4C2212yes—
20C22×C4×D4C2211yescharacteristic
21C22×#117C2212yes—
22C23×C4⋊C4C2211yescharacteristic
23C23×C4⋊C4C2211yescharacteristic
24C23×C42C2212yes—
25C23×C42C2211yescharacteristic
26#2354—28no—
27#2352—216no—
28C4×#121C4116yescomplemented
29C2×#390C2212yes—
30C2×#390C2212yes—
31C2×#390C2211yescharacteristic
32C2×#389C2211yescharacteristic
33C2×#388C2214yes—
34C2×#388C2214yes—
35C2×#388C2212yes—
36C2×#387C2214yes—
37C2×#386C2214yes—
38C2×#386C2214yes—
39C2×#386C2212yes—
40C2×#384C2211yescharacteristic
41C2×#384C2211yescharacteristic
42C2×#382C2212yes—
43C2×#380C2212yes—
44C2×#380C2212yes—
45C2×#380C2212yes—
46C2×#380C2212yes—
47C2×#380C2212yes—
48C2×#380C2212yes—
49C2×#380C2211yescharacteristic
50C2×C4×C4⋊C4—28no—
51C2×C4×C4⋊C4C2212yes—
52C2×C4×C4⋊C4C2211yescharacteristic
53C2×C4×C4⋊C4C2212yes—
54C2×C4×C4⋊C4C2212yes—
55C2×C4×C4⋊C4C2211yescharacteristic
56C2×C4×C4⋊C4C2212yes—
57C2×C4×C4⋊C4C2211yescharacteristic
58C2×C4×C4⋊C4C2212yes—
59C2×C4×C4⋊C4C2211yescharacteristic
60C2×C4×C4⋊C4C2211yescharacteristic
61C2×C4×C22⋊C4C2214yes—
62C2×C4×C22⋊C4C2212yes—
63C22×#95C2212yes—
64#1443C2214yes—
65#1442C2214yes—
66#1441C2214yes—
67#1440C2214yes—
68#1439C2214yes—
69#1439C2214yes—
70#1437C2214yes—
71#1437C2214yes—
72#1437C2214yes—
73#1436C2214yes—
74C4⋊#95C2212yes—
75C4⋊#95C2212yes—
76C4⋊#95C2212yes—
77C4⋊#95C2212yes—
78C4⋊#95C2212yes—
79C4⋊#95C2212yes—
80C4⋊#95C2212yes—
81C4⋊#95C2212yes—
82C4⋊#95C2212yes—
83#1434C2214yes—
84#1434C2214yes—
85C22⋊#95C2214yes—
86C4×#95C2214yes—
87C23×D4C2312yes—
88C23×D4C2311yescharacteristic
89C24×C4C2312yes—
90C24×C4C2312yes—
91C24×C4C2311yescharacteristic
92C24×C4C2312yes—
93C24×C4C2311yescharacteristic
94C24×C4C2311yescharacteristic
95C2×#121—24no—
96C2×#121—24no—
97C2×#121C2×C418yes—
98C2×C4×D4—28no—
99C2×C4×D4—28no—
100C2×C4×D4—24no—
101C2×C4×D4—24no—
102C2×C4×D4C2×C4116yes—
103C2×C4×D4C2×C418yescomplemented
104C2×#117—28no—
105C2×#117—28no—
106C2×#117—28no—
107C22×C4⋊C4—24no—
108C22×C4⋊C4—24no—
109C22×C4⋊C4—24no—
110C22×C4⋊C4—24no—
111C22×C4⋊C4—24no—
112C22×C4⋊C4D418yescomplemented
113C22×C4⋊C4C2312yes—
114C22×C4⋊C4C2312yes—
115C22×C4⋊C4C2312yes—
116C22×C4⋊C4C2312yes—
117C22×C4⋊C4C2312yes—
118C22×C4⋊C4C2311yescharacteristic
119C22×C4⋊C4C2312yes—
120C22×C4⋊C4C2311yescharacteristic
121C22×C4⋊C4C2311yescharacteristic
122C22×C4⋊C4C2311yescharacteristic
123C22×C4⋊C4C2311yescharacteristic
124C22×C4⋊C4C2312yes—
125C22×C4⋊C4C2311yescharacteristic
126C22×C4⋊C4C2312yes—
127C22×C4⋊C4C2312yes—
128C22×C4⋊C4C2311yescharacteristic
129C22×C22⋊C4C2314yes—
130C22×C22⋊C4C2314yes—
131C22×C22⋊C4C2312yes—
132C22×C22⋊C4C2312yes—
133C22×C22⋊C4C2312yes—
134C22×C22⋊C4C2312yes—
135C22×C22⋊C4C2314yes—
136C22×C22⋊C4C2314yes—
137C22×C22⋊C4C2314yes—
138C22×C22⋊C4C2312yes—
139C22×C42—24no—
140C22×C42—24no—
141C22×C42—28no—
142C22×C42—28no—
143C22×C42—44no—
144C22×C42C2×C418yes—
145C22×C42C2312yes—
146C22×C42C2314yes—
147C22×C42C2312yes—
148C22×C42C2312yes—
149C22×C42C2311yescharacteristic
150C22×C42C2311yescharacteristic
151C22×C42C2311yescharacteristic
152C22×C42C2312yes—
153C22×C42C2312yes—
154C22×C42C2314yes—
155C22×C42C2311yescharacteristic
156#390—28no—
157#390—44no—
158#390C2×C418yescomplemented
159#389C2×C418yescomplemented
160#388—216no—
161#388—216no—
162#388C2×C4116yescomplemented
163#387—216no—
164#386—216no—
165#386—48no—
166#386C2×C4116yes—
167#384—24no—
168#384—24no—
169#382—28no—
170#380—28no—
171#380—28no—
172#380—28no—
173#380—28no—
174#380—28no—
175#380—44no—
176#380C2×C418yes—
177C4×C4⋊C4—28no—
178C4×C4⋊C4—24no—
179C4×C4⋊C4—24no—
180C4×C4⋊C4—28no—
181C4×C4⋊C4—28no—
182C4×C4⋊C4—24no—
183C4×C4⋊C4—28no—
184C4×C4⋊C4—44no—
185C4×C4⋊C4C2×C418yescomplemented
186C4×C4⋊C4D418yescomplemented
187C4×C22⋊C4—216no—
188C4×C22⋊C4C2×C4116yescomplemented
189C2×#95—28no—
190C2×#95C2314yes—
191C2×#95C2314yes—
192C2×#95C2314yes—
193C2×#95C2312yes—
194C2×#95C2314yes—
195C2×#95C2314yes—
196C2×#95C2314yes—
197C2×#95C2314yes—
198C2×#95C2314yes—
199C2×#95C2312yes—
200C2×#95C2312yes—
201C2×#95C2314yes—
202C2×#95C2314yes—
203C2×#95C2314yes—
204C2×#95C2314yes—
205C2×#95C2314yes—
206C2×#95C2312yes—
207C2×#95C2312yes—
208C2×#95C2312yes—
209C2×#95C2312yes—
210C25C2412yes—
211C25C2411yescharacteristic
212C22×D4—24no—
213C22×D4—24no—
214C22×D4—24no—
215C22×D4—24no—
216C22×D4—24no—
217C22×D4—24no—
218C22×D4—22no—
219C22×D4—22no—
220C22×D4—22no—
221C22×D4—22no—
222C22×D4—22no—
223C22×D4—22no—
224C22×D4C22×C418yes—
225C22×D4C22×C414yes—
226C23×C4—22no—
227C23×C4—22no—
228C23×C4—22no—
229C23×C4—22no—
230C23×C4—22no—
231C23×C4—22no—
232C23×C4—22no—
233C23×C4—22no—
234C23×C4—24no—
235C23×C4—24no—
236C23×C4—22no—
237C23×C4—22no—
238C23×C4—24no—
239C23×C4—24no—
240C23×C4—24no—
241C23×C4—24no—
242C23×C4—24no—
243C23×C4—22no—
244C23×C4—24no—
245C23×C4—24no—
246C23×C4—24no—
247C23×C4—24no—
248C23×C4—24no—
249C23×C4—24no—
250C23×C4—22no—
251C23×C4—24no—
252C23×C4—24no—
253C23×C4—42no—
254C23×C4—41no—
255C23×C4—41no—
256C23×C4—42no—
257C23×C4—42no—
258C23×C4—42no—
259C23×C4C22×C418yes—
260C23×C4C22×C414yes—
261C23×C4C22×C414yes—
262C23×C4C22×C414yes—
263C23×C4C2×D418yes—
264C23×C4C2×D414yes—
265C23×C4#4114yes—
266C23×C4#4114yes—
267C23×C4#4114yes—
268C23×C4C2414yes—
269C23×C4C2414yes—
270C23×C4C2412yes—
271C23×C4C2412yes—
272C23×C4C2411yescharacteristic
273C23×C4C2412yes—
274C23×C4C2412yes—
275C23×C4C2412yes—
276C23×C4C2412yes—
277C23×C4C2411yescharacteristic
278C23×C4C2411yescharacteristic
279C23×C4C2411yescharacteristic
280C23×C4C2412yes—
281C23×C4C2411yescharacteristic
282C23×C4C2411yescharacteristic
283#121—232no—
284C4×D4—264no—
285C4×D4—232no—
286#117—432no—
287C2×C4⋊C4—232no—
288C2×C4⋊C4—24no—
289C2×C4⋊C4—24no—
290C2×C4⋊C4—22no—
291C2×C4⋊C4—22no—
292C2×C4⋊C4—22no—
293C2×C4⋊C4—24no—
294C2×C4⋊C4—24no—
295C2×C4⋊C4—24no—
296C2×C4⋊C4—24no—
297C2×C4⋊C4—22no—
298C2×C4⋊C4—22no—
299C2×C4⋊C4—22no—
300C2×C4⋊C4—22no—
301C2×C4⋊C4—24no—
302C2×C4⋊C4—22no—
303C2×C4⋊C4—22no—
304C2×C4⋊C4—22no—
305C2×C4⋊C4—22no—
306C2×C4⋊C4—22no—
307C2×C4⋊C4—232no—
308C2×C4⋊C4—24no—
309C2×C4⋊C4—24no—
310C2×C4⋊C4—24no—
311C2×C4⋊C4—24no—
312C2×C4⋊C4—24no—
313C2×C4⋊C4—24no—
314C2×C4⋊C4—24no—
315C2×C4⋊C4—24no—
316C2×C4⋊C4—24no—
317C2×C4⋊C4—24no—
318C2×C4⋊C4—24no—
319C2×C4⋊C4—24no—
320C2×C4⋊C4—24no—
321C2×C4⋊C4—24no—
322C2×C4⋊C4—42no—
323C2×C4⋊C4—42no—
324C2×C4⋊C4—42no—
325C2×C4⋊C4—42no—
326C2×C4⋊C4C22×C418yes—
327C2×C4⋊C4C22×C414yes—
328C2×C4⋊C4C22×C414yes—
329C2×C4⋊C4C22×C414yes—
330C2×C4⋊C4C2×D414yes—
331C2×C4⋊C4C2×D414yes—
332C2×C4⋊C4C2×D418yes—
333C2×C4⋊C4C2×D414yes—
334C2×C4⋊C4C2×D414yes—
335C2×C4⋊C4#4114yes—
336C2×C4⋊C4#4114yes—
337C2×C22⋊C4—24no—
338C2×C22⋊C4—24no—
339C2×C22⋊C4—24no—
340C2×C22⋊C4—24no—
341C2×C22⋊C4—24no—
342C2×C22⋊C4—24no—
343C2×C22⋊C4—24no—
344C2×C22⋊C4—24no—
345C2×C22⋊C4—28no—
346C2×C22⋊C4—28no—
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⋊C4C22×C418yes—
363C2×C22⋊C4C22×C418yes—
364C2×C22⋊C4C22×C418yes—
365C2×C22⋊C4C22×C418yes—
366C2×C22⋊C4C22×C418yes—
367C2×C42—24no—
368C2×C42—22no—
369C2×C42—22no—
370C2×C42—22no—
371C2×C42—24no—
372C2×C42—22no—
373C2×C42—22no—
374C2×C42—22no—
375C2×C42—24no—
376C2×C42—24no—
377C2×C42—232no—
378C2×C42—28no—
379C2×C42—28no—
380C2×C42—24no—
381C2×C42—24no—
382C2×C42—24no—
383C2×C42—28no—
384C2×C42—24no—
385C2×C42—24no—
386C2×C42—24no—
387C2×C42—24no—
388C2×C42—28no—
389C2×C42—432no—
390C2×C42—42no—
391C2×C42—42no—
392C2×C42—44no—
393C2×C42—44no—
394C2×C42C22×C418yes—
395C2×C42C22×C414yes—
396C2×C42C22×C414yes—
397C2×C42C22×C414yes—
398C2×C42C22×C414yes—
399C2×C42C2×D418yes—
400C2×C42C2×D414yes—
401C2×C42#4114yes—
402#95—24no—
403#95—24no—
404#95—24no—
405#95—28no—
406#95—28no—
407#95—28no—
408#95—28no—
409#95—28no—
410#95—28no—
411#95—28no—
412#95—28no—
413#95—44no—
414#95—44no—
415#95—44no—
416#95—44no—
417#95—44no—
418#95C22×C418yes—
419#95C22×C418yes—
420#95C22×C418yes—
421#95C2×D418yes—
422C24—21no—
423C24—21no—
424C24—21no—
425C24—21no—
426C24—21no—
427C24—21no—
428C24—21no—
429C24—21no—
430C24—22no—
431C24—22no—
432C24—22no—
433C24—22no—
434C24—22no—
435C24—22no—
436C24—22no—
437C24—22no—
438C24—22no—
439C24—22no—
440C24—22no—
441C24—22no—
442C24—22no—
443C24—22no—
444C24C23×C414yes—
445C24C23×C412yes—
446C24C22×D412yes—
447C24C2×#4112yes—
448C24C2×#4112yes—
449C24C2×#4112yes—
450C24H(5,𝔽2)12yes—
451C242−1+412yes—
452C24C2511yescharacteristic
453C2×D4—216no—
454C2×D4—216no—
455C2×D4—216no—
456C2×D4—28no—
457C2×D4—28no—
458C2×D4—28no—
459C2×D4—48no—
460C2×D4—48no—
461C2×D4—48no—
462C2×D4—48no—
463C2×D4—44no—
464C2×D4—44no—
465C2×D4—44no—
466C2×D4—44no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—22no—
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—22no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—28no—
484C22×C4—28no—
485C22×C4—28no—
486C22×C4—28no—
487C22×C4—28no—
488C22×C4—28no—
489C22×C4—28no—
490C22×C4—28no—
491C22×C4—28no—
492C22×C4—28no—
493C22×C4—28no—
494C22×C4—28no—
495C22×C4—216no—
496C22×C4—28no—
497C22×C4—216no—
498C22×C4—21no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—22no—
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—22no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—21no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—21no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—28no—
541C22×C4—216no—
542C22×C4—216no—
543C22×C4—216no—
544C22×C4—216no—
545C22×C4—24no—
546C22×C4—24no—
547C22×C4—24no—
548C22×C4—24no—
549C22×C4—24no—
550C22×C4—24no—
551C22×C4—24no—
552C22×C4—24no—
553C22×C4—24no—
554C22×C4—24no—
555C22×C4—24no—
556C22×C4—24no—
557C22×C4—24no—
558C22×C4—24no—
559C22×C4—44no—
560C22×C4—48no—
561C22×C4—48no—
562C22×C4—48no—
563C22×C4—48no—
564C22×C4—44no—
565C22×C4—48no—
566C22×C4—44no—
567C22×C4—44no—
568C22×C4—44no—
569C22×C4—48no—
570C22×C4—48no—
571C22×C4—48no—
572C22×C4—48no—
573C22×C4—48no—
574C22×C4—48no—
575C22×C4—48no—
576C22×C4—48no—
577C22×C4—48no—
578C22×C4—48no—
579C22×C4#117116yescomplemented
580C22×C4C4×D4116yes—
581C22×C4C23×C412yes—
582C22×C4C23×C414yes—
583C22×C4C23×C414yes—
584C22×C4C23×C414yes—
585C22×C4C23×C412yes—
586C22×C4C23×C412yes—
587C22×C4C23×C412yes—
588C22×C4C23×C412yes—
589C22×C4C23×C412yes—
590C22×C4C22×D414yes—
591C22×C4C22×D414yes—
592C22×C4C22×D412yes—
593C22×C4C22×D412yes—
594C22×C4C22×D414yes—
595C22×C4C22×D414yes—
596C22×C4C22×D412yes—
597C22×C4C22×D412yes—
598C22×C4C22×D412yes—
599C22×C4C2×#4114yes—
600C22×C4C2×#4112yes—
601C22×C4C2×#4112yes—
602C22×C4C2×#4112yes—
603C22×C4C2×#4112yes—
604C22×C4C2×#4114yes—
605C22×C4C2×#4112yes—
606C22×C4C2×#4112yes—
607C22×C4C2×#4112yes—
608C22×C4C2×#4112yes—
609C22×C4C2×#4112yes—
610C22×C4C2×#4112yes—
611C22×C4C2×#4112yes—
612C22×C4H(5,𝔽2)12yes—
613C22×C42−1+412yes—
614C4⋊C4—216no—
615C4⋊C4—28no—
616C4⋊C4—216no—
617C4⋊C4—28no—
618C4⋊C4—28no—
619C4⋊C4—216no—
620C4⋊C4—28no—
621C4⋊C4—28no—
622C4⋊C4—28no—
623C4⋊C4—48no—
624C4⋊C4—48no—
625C4⋊C4—48no—
626C4⋊C4—48no—
627C4⋊C4—84no—
628C4⋊C4—84no—
629C4⋊C4#121116yescomplemented
630C22⋊C4—216no—
631C22⋊C4—216no—
632C22⋊C4—216no—
633C22⋊C4—216no—
634C22⋊C4—48no—
635C22⋊C4—416no—
636C22⋊C4—416no—
637C22⋊C4—88no—
638C22⋊C4—88no—
639C22⋊C4—88no—
640C42—28no—
641C42—28no—
642C42—28no—
643C42—216no—
644C42—216no—
645C42—48no—
646C42—48no—
647C42—416no—
648C42—48no—
649C42—88no—
650C42C4×D4116yes—
651C23—22no—
652C23—22no—
653C23—22no—
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—22no—
673C23—22no—
674C23—22no—
675C23—22no—
676C23—22no—
677C23—22no—
678C23—22no—
679C23—24no—
680C23—24no—
681C23—24no—
682C23—24no—
683C23—24no—
684C23—24no—
685C23—24no—
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—
700C23—42no—
701C23—42no—
702C23—42no—
703C23—42no—
704C23—42no—
705C23—42no—
706C23—42no—
707C23—42no—
708C23—42no—
709C23—42no—
710C23—42no—
711C23—42no—
712C23—42no—
713C23—42no—
714C23C2×#11714yes—
715C23C2×C4×D414yes—
716C23#52014yes—
717C23#54714yes—
718C23#55014yes—
719C23#55514yes—
720C23#55614yes—
721C23C24×C411yescharacteristic
722C23C23×D411yescharacteristic
723C23C23×D411yescharacteristic
724C23C22×#4111yescharacteristic
725C23C22×#4111yescharacteristic
726C23C22×#4111yescharacteristic
727C23C22×#4111yescharacteristic
728C23C22×#4111yescharacteristic
729C23C22×#4111yescharacteristic
730C23C2×H(5,𝔽2)11yescharacteristic
731C23C2×H(5,𝔽2)11yescharacteristic
732C23C2×2−1+411yescharacteristic
733C23C2×2−1+411yescharacteristic
734C23#58511yescharacteristic
735C23#58511yescharacteristic
736D4—432no—
737D4—416no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—22no—
742C2×C4—22no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—24no—
749C2×C4—22no—
750C2×C4—24no—
751C2×C4—22no—
752C2×C4—22no—
753C2×C4—22no—
754C2×C4—24no—
755C2×C4—22no—
756C2×C4—24no—
757C2×C4—22no—
758C2×C4—22no—
759C2×C4—22no—
760C2×C4—24no—
761C2×C4—24no—
762C2×C4—232no—
763C2×C4—232no—
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—22no—
773C2×C4—24no—
774C2×C4—22no—
775C2×C4—24no—
776C2×C4—24no—
777C2×C4—24no—
778C2×C4—24no—
779C2×C4—24no—
780C2×C4—24no—
781C2×C4—24no—
782C2×C4—24no—
783C2×C4—24no—
784C2×C4—24no—
785C2×C4—432no—
786C2×C4—416no—
787C2×C4—432no—
788C2×C4—42no—
789C2×C4—42no—
790C2×C4—42no—
791C2×C4—42no—
792C2×C4—42no—
793C2×C4—42no—
794C2×C4—42no—
795C2×C4—42no—
796C2×C4—42no—
797C2×C4—42no—
798C2×C4—42no—
799C2×C4—42no—
800C2×C4—42no—
801C2×C4—42no—
802C2×C4—42no—
803C2×C4—41no—
804C2×C4—42no—
805C2×C4—41no—
806C2×C4—41no—
807C2×C4—41no—
808C2×C4—42no—
809C2×C4—42no—
810C2×C4—42no—
811C2×C4—42no—
812C2×C4—42no—
813C2×C4—42no—
814C2×C4—42no—
815C2×C4—42no—
816C2×C4—432no—
817C2×C4—44no—
818C2×C4—44no—
819C2×C4—44no—
820C2×C4—44no—
821C2×C4—44no—
822C2×C4—44no—
823C2×C4—44no—
824C2×C4—44no—
825C2×C4—44no—
826C2×C4—44no—
827C2×C4—44no—
828C2×C4—44no—
829C2×C4—44no—
830C2×C4—44no—
831C2×C4C2×#11714yes—
832C2×C4C2×#11714yes—
833C2×C4C2×C4×D414yes—
834C2×C4C2×C4×D414yes—
835C2×C4C2×C4×D414yes—
836C2×C4C2×C4×D414yes—
837C2×C4C2×C4×D414yes—
838C2×C4C4×#4114yes—
839C2×C4#52014yes—
840C2×C4C2×#12118yes—
841C2×C4C2×#12114yes—
842C2×C4#52514yes—
843C2×C4#52914yes—
844C2×C4#53214yes—
845C2×C4#54614yes—
846C2×C4#54814yes—
847C2×C4#55214yes—
848C2×C4#55314yes—
849C22—24no—
850C22—24no—
851C22—24no—
852C22—24no—
853C22—24no—
854C22—24no—
855C22—24no—
856C22—24no—
857C22—24no—
858C22—24no—
859C22—24no—
860C22—24no—
861C22—24no—
862C22—24no—
863C22—44no—
864C22—44no—
865C22—44no—
866C22—44no—
867C22—44no—
868C22—44no—
869C22—44no—
870C22—82no—
871C22—82no—
872C22—82no—
873C22—82no—
874C22—82no—
875C22—82no—
876C22—82no—
877C22—82no—
878C22#235418yescomplemented
879C22C22×#11711yescharacteristic
880C22C22×C4×D411yescharacteristic
881C22C22×C4×D411yescharacteristic
882C22C2×C4×#4111yescharacteristic
883C22C2×#52011yescharacteristic
884C22C2×#52011yescharacteristic
885C22#342811yescharacteristic
886C22C22×#12111yescharacteristic
887C22C2×#52511yescharacteristic
888C22C2×#52911yescharacteristic
889C22C2×#53211yescharacteristic
890C22C2×#54611yescharacteristic
891C22C2×#54711yescharacteristic
892C22C2×#54811yescharacteristic
893C22C2×#55011yescharacteristic
894C22C2×#55211yescharacteristic
895C22C2×#55311yescharacteristic
896C22C2×#55511yescharacteristic
897C22C2×#55611yescharacteristic
898C22#347511yescharacteristic
899C22#347511yescharacteristic
900C22#348011yescharacteristic
901C22#348011yescharacteristic
902C22#348811yescharacteristic
903C22#348911yescharacteristic
904C22#349411yescharacteristic
905C22#349511yescharacteristic
906C22#349611yescharacteristic
907C22#349711yescharacteristic
908C22#350611yescharacteristic
909C22#350711yescharacteristic
910C22#351911yescharacteristic
911C22#352011yescharacteristic
912C22#352211yescharacteristic
913C22#352311yescharacteristic
914C4—28no—
915C4—24no—
916C4—24no—
917C4—24no—
918C4—44no—
919C4—44no—
920C4—44no—
921C4—44no—
922C4—42no—
923C4—44no—
924C4—44no—
925C4—84no—
926C4—84no—
927C4C4×#12118yes—
928C4#235218yescomplemented
929C2—28no—
930C2—84no—
931C2C2×C4×#12111yescharacteristic
932C2C2×#235211yescharacteristic
933C2C2×#235411yescharacteristic
934C2#3412111yescharacteristic
935C2#3420211yescharacteristic
936C2#3420611yescharacteristic
937C2#3424311yescharacteristic
938C2#3615311yescharacteristic
939C2#3616011yescharacteristic
940C2#3617611yescharacteristic
941C2#3618611yescharacteristic
942C2#3657611yescharacteristic
943C2#3657911yescharacteristic
944C2#3658611yescharacteristic
945C2#3659611yescharacteristic
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×#2354C2semidirect
2. C2×#2352C2semidirect
4. C22×C4×C4⋊C4C2semidirect
6. #14686C2semidirect
7. #14119C2semidirect
8. #14042C2semidirect
9. #14022C2semidirect
10. #13999C2semidirect
11. #13911C2semidirect
12. #13906C2semidirect
13. #13875C2semidirect
14. #13872C2semidirect
15. C4⋊C42C2semidirect
16. #13801C2semidirect
17. C4×#380C2semidirect
28. C4×#121C4semidirect
103. C2×C4×D4C2×C4semidirect
112. C22×C4⋊C4D4semidirect
158. #390C2×C4semidirect
159. #389C2×C4semidirect
162. #388C2×C4semidirect
185. C4×C4⋊C4C2×C4semidirect
186. C4×C4⋊C4D4semidirect
188. C4×C22⋊C4C2×C4semidirect
579. C22×C4#117semidirect
629. C4⋊C4#121semidirect
878. C22#2354semidirect
928. C4#2352semidirect

Maximal subgroups

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

subgroupindex
C2×#23542
C2×#23522
C2×C4×#1212
C22×C4×C4⋊C42
#146982
#146862
#141192
#140422
#140222
#139992
#139112
#139062
#138752
#138722
C4⋊C422
#138012
C4×#3802