Finite Group Databasebeta

← #649067

Subgroups — #649067

Order 512.

4444 conjugacy classes of subgroups.

The subgroup lattice has 964 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2501C211yesmaximal, characteristic, complemented
2C2×#2416C211yesmaximal, characteristic
3C2×#2443C214yesmaximal, complemented
4C2×D4×C4⋊C4C211yesmaximal, characteristic, complemented
5C22×#384C211yesmaximal, characteristic, complemented
6#15765C214yesmaximal, complemented
7#15384C214yesmaximal, complemented
8#15155C211yesmaximal, characteristic, complemented
9#15150C211yesmaximal, characteristic, complemented
10#15145C211yesmaximal, characteristic, complemented
11#15130C211yesmaximal, characteristic, complemented
12#14777C214yesmaximal, complemented
13#14698C211yesmaximal, characteristic, complemented
14#14137C211yesmaximal, characteristic, complemented
15#14049C211yesmaximal, characteristic, complemented
16#14001C211yesmaximal, characteristic, complemented
17#13880C211yesmaximal, characteristic, complemented
18#13880C211yesmaximal, characteristic, complemented
19C4×#386C211yesmaximal, characteristic, complemented
20C22×#123C2214yes—
21C22×#121C2211yescharacteristic
22C22×#121C2212yes—
23C22×#121C2211yescharacteristic
24C22×C4×D4C2212yes—
25C22×C4×D4C2211yescharacteristic
26C23×C4⋊C4C2211yescharacteristic
27C23×C4⋊C4C2211yescharacteristic
28C23×C4⋊C4C2211yescharacteristic
29C23×C4⋊C4C2214yes—
30C23×C42C2211yescharacteristic
31#2501—28no—
32#2443—232no—
33#2416—28no—
34C2×#399C2214yes—
35C2×#399C2214yes—
36C2×#399C2214yes—
37C2×#398C2214yes—
38C2×#397C2214yes—
39C2×#396C2212yes—
40C2×#394C2212yes—
41C2×#394C2214yes—
42D4×C4⋊C4—28no—
43C2×#390C2211yescharacteristic
44C2×#390C2211yescharacteristic
45C2×#390C2211yescharacteristic
46C2×#390C2211yescharacteristic
47C2×#390C2211yescharacteristic
48C2×#389C2211yescharacteristic
49C2×#389C2212yes—
50C2×#388C2214yes—
51C2×#387C2214yes—
52C2×#386C2214yes—
53C2×#386C2214yes—
54C2×#386C2212yes—
55C2×#386C2212yes—
56C2×#385C2212yes—
57C2×#385C2214yes—
58C2×#385C2214yes—
59C2×#385C2212yes—
60C2×#384—28no—
61C2×#384C2214yes—
62C2×#384C2211yescharacteristic
63C2×#384C2211yescharacteristic
64C2×#384C2211yescharacteristic
65C2×#384C2211yescharacteristic
66C2×#384C2211yescharacteristic
67C2×#384C2211yescharacteristic
68C2×#384C2211yescharacteristic
69C2×#380C2211yescharacteristic
70C2×#380C2211yescharacteristic
71C2×#380C2211yescharacteristic
72C2×C4×C4⋊C4C2211yescharacteristic
73C2×C4×C22⋊C4C2211yescharacteristic
74C2×C4×C22⋊C4C2211yescharacteristic
75C2×C4×C22⋊C4C2211yescharacteristic
76#1445C2214yes—
77#1445C2214yes—
78#1444C2214yes—
79#1444C2214yes—
80#1444C2214yes—
81#1439C2214yes—
82#1439C2214yes—
83#1439C2214yes—
84#1437C2212yes—
85#1437C2214yes—
86#1436C2212yes—
87C4⋊#95C2211yescharacteristic
88C4⋊#95C2211yescharacteristic
89C4⋊#95C2211yescharacteristic
90C4⋊#95C2211yescharacteristic
91C4⋊#95C2211yescharacteristic
92C4⋊#95C2211yescharacteristic
93C22⋊#95C2212yes—
94C4×#95C2211yescharacteristic
95C4×#95C2211yescharacteristic
96C23×D4C2312yes—
97C23×D4C2311yescharacteristic
98C23×D4C2312yes—
99C23×D4C2311yescharacteristic
100C24×C4C2312yes—
101C24×C4C2311yescharacteristic
102C24×C4C2312yes—
103C24×C4C2312yes—
104C24×C4C2312yes—
105C24×C4C2311yescharacteristic
106C2×#123—216no—
107C2×#123—216no—
108C2×#123—48no—
109C2×#121—28no—
110C2×#121—216no—
111C2×#121—24no—
112C2×#121—24no—
113C2×#121—24no—
114C2×#121—24no—
115C2×#121—24no—
116C2×#121—42no—
117C2×C4×D4—24no—
118C2×C4×D4—24no—
119C2×C4×D4—28no—
120C2×C4×D4—216no—
121C2×C4×D4D418yes—
122C22×C4⋊C4—24no—
123C22×C4⋊C4—24no—
124C22×C4⋊C4—24no—
125C22×C4⋊C4—216no—
126C22×C4⋊C4—24no—
127C22×C4⋊C4—24no—
128C22×C4⋊C4—24no—
129C22×C4⋊C4—216no—
130C22×C4⋊C4—42no—
131C22×C4⋊C4—42no—
132C22×C4⋊C4—42no—
133C22×C4⋊C4—48no—
134C22×C4⋊C4C2312yes—
135C22×C4⋊C4C2314yes—
136C22×C4⋊C4C2312yes—
137C22×C4⋊C4C2311yescharacteristic
138C22×C4⋊C4C2311yescharacteristic
139C22×C4⋊C4C2311yescharacteristic
140C22×C4⋊C4C2311yescharacteristic
141C22×C4⋊C4C2311yescharacteristic
142C22×C4⋊C4C2312yes—
143C22×C4⋊C4C2314yes—
144C22×C4⋊C4C2314yes—
145C22×C4⋊C4C2312yes—
146C22×C4⋊C4C2312yes—
147C22×C4⋊C4C2314yes—
148C22×C4⋊C4C2311yescharacteristic
149C22×C4⋊C4C2314yes—
150C22×C4⋊C4C2311yescharacteristic
151C22×C4⋊C4C2311yescharacteristic
152C22×C4⋊C4C2312yes—
153C22×C4⋊C4C2314yes—
154C22×C22⋊C4C2312yes—
155C22×C22⋊C4C2312yes—
156C22×C22⋊C4C2312yes—
157C22×C22⋊C4C2314yes—
158C22×C22⋊C4C2312yes—
159C22×C22⋊C4C2314yes—
160C22×C22⋊C4C2312yes—
161C22×C22⋊C4C2312yes—
162C22×C22⋊C4C2314yes—
163C22×C22⋊C4C2311yescharacteristic
164C22×C22⋊C4C2312yes—
165C22×C22⋊C4C2312yes—
166C22×C22⋊C4C2311yescharacteristic
167C22×C22⋊C4C2312yes—
168C22×C22⋊C4C2312yes—
169C22×C22⋊C4C2314yes—
170C22×C42—24no—
171C22×C42—24no—
172C22×C42—24no—
173C22×C42C2312yes—
174C22×C42C2312yes—
175C22×C42C2311yescharacteristic
176C22×C42C2311yescharacteristic
177C22×C42C2311yescharacteristic
178C22×C42C2311yescharacteristic
179C22×C42C2311yescharacteristic
180#399—216no—
181#399—216no—
182#399—48no—
183#398—216no—
184#397—216no—
185#396—28no—
186#394—28no—
187#394—216no—
188#390—24no—
189#390—24no—
190#390—24no—
191#390—24no—
192#390—42no—
193#389—28no—
194#389—24no—
195#388—216no—
196#387—216no—
197#386—216no—
198#386—28no—
199#386—216no—
200#386D4116yescomplemented
201#385—28no—
202#385—28no—
203#385—216no—
204#385—216no—
205#384—24no—
206#384—24no—
207#384—24no—
208#384—216no—
209#384—24no—
210#384—24no—
211#384—42no—
212#384D418yescomplemented
213#380—24no—
214#380—24no—
215#380—24no—
216C4×C4⋊C4—24no—
217C4×C22⋊C4—24no—
218C4×C22⋊C4—24no—
219C4×C22⋊C4—24no—
220C2×#95C2314yes—
221C2×#95C2312yes—
222C2×#95C2312yes—
223C2×#95C2314yes—
224C2×#95C2314yes—
225C2×#95C2314yes—
226C2×#95C2314yes—
227C2×#95C2312yes—
228C2×#95C2312yes—
229C2×#95C2312yes—
230C2×#95C2312yes—
231C2×#95C2314yes—
232C2×#95C2312yes—
233C2×#95C2312yes—
234C2×#95C2312yes—
235C2×#95C2312yes—
236C2×#95C2312yes—
237C2×#95C2312yes—
238C25C2412yes—
239C25C2411yescharacteristic
240C25C2411yescharacteristic
241C22×D4—22no—
242C22×D4—22no—
243C22×D4—24no—
244C22×D4—24no—
245C22×D4—28no—
246C22×D4—24no—
247C22×D4—24no—
248C22×D4—28no—
249C22×D4—24no—
250C22×D4—28no—
251C22×D4—22no—
252C22×D4—24no—
253C22×D4—22no—
254C22×D4—22no—
255C22×D4—22no—
256C22×D4—22no—
257C22×D4—22no—
258C22×D4—22no—
259C22×D4—42no—
260C22×D4—44no—
261C22×D4C2×D414yes—
262C22×D4C2×D418yes—
263C23×C4—24no—
264C23×C4—24no—
265C23×C4—24no—
266C23×C4—22no—
267C23×C4—24no—
268C23×C4—22no—
269C23×C4—24no—
270C23×C4—22no—
271C23×C4—24no—
272C23×C4—22no—
273C23×C4—22no—
274C23×C4—22no—
275C23×C4—22no—
276C23×C4—22no—
277C23×C4—22no—
278C23×C4—22no—
279C23×C4—24no—
280C23×C4—24no—
281C23×C4—28no—
282C23×C4—28no—
283C23×C4—24no—
284C23×C4—28no—
285C23×C4—24no—
286C23×C4—24no—
287C23×C4—24no—
288C23×C4—44no—
289C23×C4—42no—
290C23×C4—42no—
291C23×C4—42no—
292C23×C4—44no—
293C23×C4—44no—
294C23×C4C2×D418yes—
295C23×C4C2×D414yes—
296C23×C4C2×D414yes—
297C23×C4#4114yes—
298C23×C4#4114yes—
299C23×C4C2412yes—
300C23×C4C2412yes—
301C23×C4C2412yes—
302C23×C4C2412yes—
303C23×C4C2412yes—
304C23×C4C2412yes—
305C23×C4C2412yes—
306C23×C4C2411yescharacteristic
307C23×C4C2411yescharacteristic
308C23×C4C2412yes—
309C23×C4C2412yes—
310C23×C4C2411yescharacteristic
311C23×C4C2412yes—
312C23×C4C2411yescharacteristic
313C23×C4C2412yes—
314C23×C4C2411yescharacteristic
315#123—464no—
316#121—416no—
317#121—432no—
318#121—416no—
319C4×D4—232no—
320C4×D4—432no—
321C2×C4⋊C4—22no—
322C2×C4⋊C4—22no—
323C2×C4⋊C4—28no—
324C2×C4⋊C4—22no—
325C2×C4⋊C4—22no—
326C2×C4⋊C4—22no—
327C2×C4⋊C4—22no—
328C2×C4⋊C4—28no—
329C2×C4⋊C4—22no—
330C2×C4⋊C4—22no—
331C2×C4⋊C4—22no—
332C2×C4⋊C4—24no—
333C2×C4⋊C4—28no—
334C2×C4⋊C4—24no—
335C2×C4⋊C4—28no—
336C2×C4⋊C4—28no—
337C2×C4⋊C4—22no—
338C2×C4⋊C4—22no—
339C2×C4⋊C4—22no—
340C2×C4⋊C4—28no—
341C2×C4⋊C4—24no—
342C2×C4⋊C4—24no—
343C2×C4⋊C4—24no—
344C2×C4⋊C4—28no—
345C2×C4⋊C4—28no—
346C2×C4⋊C4—24no—
347C2×C4⋊C4—24no—
348C2×C4⋊C4—28no—
349C2×C4⋊C4—22no—
350C2×C4⋊C4—28no—
351C2×C4⋊C4—24no—
352C2×C4⋊C4—28no—
353C2×C4⋊C4—28no—
354C2×C4⋊C4—22no—
355C2×C4⋊C4—22no—
356C2×C4⋊C4—22no—
357C2×C4⋊C4—22no—
358C2×C4⋊C4—22no—
359C2×C4⋊C4—22no—
360C2×C4⋊C4—22no—
361C2×C4⋊C4—28no—
362C2×C4⋊C4—22no—
363C2×C4⋊C4—24no—
364C2×C4⋊C4—28no—
365C2×C4⋊C4—416no—
366C2×C4⋊C4—416no—
367C2×C4⋊C4—416no—
368C2×C4⋊C4—464no—
369C2×C4⋊C4—44no—
370C2×C4⋊C4—42no—
371C2×C4⋊C4—42no—
372C2×C4⋊C4—44no—
373C2×C4⋊C4—42no—
374C2×C4⋊C4—44no—
375C2×C4⋊C4—44no—
376C2×C4⋊C4—44no—
377C2×C4⋊C4—44no—
378C2×C4⋊C4C2×D414yes—
379C2×C4⋊C4C2×D414yes—
380C2×C4⋊C4C2×D4116yes—
381C2×C4⋊C4C2×D414yes—
382C2×C22⋊C4—22no—
383C2×C22⋊C4—22no—
384C2×C22⋊C4—24no—
385C2×C22⋊C4—24no—
386C2×C22⋊C4—24no—
387C2×C22⋊C4—22no—
388C2×C22⋊C4—22no—
389C2×C22⋊C4—24no—
390C2×C22⋊C4—24no—
391C2×C22⋊C4—24no—
392C2×C22⋊C4—24no—
393C2×C22⋊C4—24no—
394C2×C22⋊C4—28no—
395C2×C22⋊C4—28no—
396C2×C22⋊C4—24no—
397C2×C22⋊C4—28no—
398C2×C22⋊C4—24no—
399C2×C22⋊C4—28no—
400C2×C22⋊C4—24no—
401C2×C22⋊C4—24no—
402C2×C22⋊C4—24no—
403C2×C22⋊C4—28no—
404C2×C22⋊C4—28no—
405C2×C22⋊C4—28no—
406C2×C22⋊C4—28no—
407C2×C22⋊C4—28no—
408C2×C22⋊C4—24no—
409C2×C22⋊C4—24no—
410C2×C22⋊C4—28no—
411C2×C22⋊C4—28no—
412C2×C22⋊C4—28no—
413C2×C22⋊C4—24no—
414C2×C22⋊C4—28no—
415C2×C22⋊C4—42no—
416C2×C22⋊C4—44no—
417C2×C22⋊C4—44no—
418C2×C22⋊C4—44no—
419C2×C22⋊C4—44no—
420C2×C22⋊C4C2×D414yes—
421C2×C22⋊C4C2×D414yes—
422C2×C22⋊C4C2×D418yes—
423C2×C22⋊C4C2×D418yes—
424C2×C22⋊C4C2×D418yes—
425C2×C42—232no—
426C2×C42—24no—
427C2×C42—22no—
428C2×C42—22no—
429C2×C42—22no—
430C2×C42—24no—
431C2×C42—24no—
432C2×C42—22no—
433C2×C42—22no—
434C2×C42—22no—
435C2×C42—24no—
436C2×C42—28no—
437C2×C42—22no—
438C2×C42—22no—
439C2×C42—22no—
440C2×C42—22no—
441C2×C42—22no—
442C2×C42—22no—
443C2×C42C2×D414yes—
444C2×C42C2×D414yes—
445C2×C42#4114yes—
446#95—24no—
447#95—24no—
448#95—24no—
449#95—24no—
450#95—24no—
451#95—28no—
452#95—28no—
453#95—28no—
454#95—28no—
455#95—28no—
456#95—24no—
457#95—28no—
458#95—24no—
459#95—24no—
460#95—24no—
461#95—24no—
462#95C2×D418yes—
463#95C2×D418yes—
464C24—21no—
465C24—21no—
466C24—21no—
467C24—22no—
468C24—21no—
469C24—22no—
470C24—21no—
471C24—21no—
472C24—21no—
473C24—21no—
474C24—22no—
475C24—21no—
476C24—22no—
477C24—21no—
478C24—22no—
479C24—22no—
480C24—24no—
481C24—22no—
482C24—22no—
483C24—22no—
484C24—22no—
485C24—24no—
486C24—22no—
487C24—24no—
488C24—24no—
489C24—22no—
490C24C22×D414yes—
491C24C22×D412yes—
492C24C22×D412yes—
493C24C22×D414yes—
494C24C2×#4112yes—
495C24C2×#4112yes—
496C242−1+414yes—
497C24C2511yescharacteristic
498C2×D4—28no—
499C2×D4—28no—
500C2×D4—216no—
501C2×D4—216no—
502C2×D4—48no—
503C2×D4—416no—
504C2×D4—48no—
505C2×D4—48no—
506C2×D4—48no—
507C2×D4—48no—
508C2×D4—416no—
509C2×D4—416no—
510C2×D4—44no—
511C2×D4—44no—
512C2×D4—44no—
513C2×D4—44no—
514C2×D4—44no—
515C2×D4—44no—
516C2×D4—44no—
517C2×D4—84no—
518C2×D4—88no—
519C2×D4#127116yes—
520C22×C4—216no—
521C22×C4—216no—
522C22×C4—216no—
523C22×C4—216no—
524C22×C4—216no—
525C22×C4—21no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—21no—
530C22×C4—22no—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—22no—
535C22×C4—21no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—28no—
541C22×C4—28no—
542C22×C4—216no—
543C22×C4—28no—
544C22×C4—216no—
545C22×C4—28no—
546C22×C4—28no—
547C22×C4—28no—
548C22×C4—21no—
549C22×C4—22no—
550C22×C4—24no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—24no—
554C22×C4—21no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—21no—
567C22×C4—24no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—24no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—21no—
578C22×C4—28no—
579C22×C4—28no—
580C22×C4—28no—
581C22×C4—24no—
582C22×C4—24no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—24no—
587C22×C4—24no—
588C22×C4—24no—
589C22×C4—22no—
590C22×C4—22no—
591C22×C4—22no—
592C22×C4—22no—
593C22×C4—22no—
594C22×C4—22no—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—24no—
598C22×C4—22no—
599C22×C4—24no—
600C22×C4—24no—
601C22×C4—22no—
602C22×C4—22no—
603C22×C4—24no—
604C22×C4—22no—
605C22×C4—24no—
606C22×C4—416no—
607C22×C4—48no—
608C22×C4—48no—
609C22×C4—48no—
610C22×C4—416no—
611C22×C4—416no—
612C22×C4—44no—
613C22×C4—44no—
614C22×C4—44no—
615C22×C4—44no—
616C22×C4—48no—
617C22×C4—48no—
618C22×C4—48no—
619C22×C4—88no—
620C22×C4—84no—
621C22×C4—84no—
622C22×C4—88no—
623C22×C4—84no—
624C22×C4—88no—
625C22×C4#123116yescomplemented
626C22×C4C22×D414yes—
627C22×C4C22×D414yes—
628C22×C4C22×D412yes—
629C22×C4C22×D412yes—
630C22×C4C22×D414yes—
631C22×C4C22×D414yes—
632C22×C4C22×D412yes—
633C22×C4C22×D414yes—
634C22×C4C22×D412yes—
635C22×C4C22×D414yes—
636C22×C4C22×D414yes—
637C22×C4C22×D414yes—
638C22×C4C22×D412yes—
639C22×C4C22×D412yes—
640C22×C4C2×#4112yes—
641C22×C4C2×#4112yes—
642C22×C4C2×#4114yes—
643C22×C4C2×#4112yes—
644C22×C4C2×#4112yes—
645C22×C4C2×#4112yes—
646C22×C4H(5,𝔽2)14yes—
647C22×C4H(5,𝔽2)12yes—
648C22×C42−1+414yes—
649C22×C42−1+412yes—
650C4⋊C4—28no—
651C4⋊C4—28no—
652C4⋊C4—28no—
653C4⋊C4—232no—
654C4⋊C4—416no—
655C4⋊C4—48no—
656C4⋊C4—48no—
657C4⋊C4—416no—
658C4⋊C4—48no—
659C4⋊C4—416no—
660C4⋊C4—44no—
661C4⋊C4—48no—
662C4⋊C4—48no—
663C4⋊C4—416no—
664C4⋊C4—44no—
665C4⋊C4—44no—
666C4⋊C4—44no—
667C4⋊C4—44no—
668C4⋊C4—84no—
669C4⋊C4—88no—
670C22⋊C4—28no—
671C22⋊C4—216no—
672C22⋊C4—28no—
673C22⋊C4—216no—
674C22⋊C4—216no—
675C22⋊C4—48no—
676C22⋊C4—416no—
677C22⋊C4—48no—
678C22⋊C4—48no—
679C22⋊C4—48no—
680C22⋊C4—48no—
681C22⋊C4—48no—
682C22⋊C4—416no—
683C22⋊C4—416no—
684C22⋊C4—84no—
685C22⋊C4—88no—
686C42—216no—
687C42—28no—
688C42—28no—
689C42—28no—
690C42—48no—
691C42—44no—
692C42—44no—
693C23—22no—
694C23—22no—
695C23—24no—
696C23—22no—
697C23—24no—
698C23—22no—
699C23—22no—
700C23—22no—
701C23—24no—
702C23—24no—
703C23—24no—
704C23—24no—
705C23—22no—
706C23—22no—
707C23—24no—
708C23—24no—
709C23—24no—
710C23—24no—
711C23—22no—
712C23—22no—
713C23—24no—
714C23—22no—
715C23—24no—
716C23—22no—
717C23—24no—
718C23—24no—
719C23—24no—
720C23—22no—
721C23—22no—
722C23—24no—
723C23—41no—
724C23—41no—
725C23—41no—
726C23—41no—
727C23—42no—
728C23—42no—
729C23—42no—
730C23—42no—
731C23—42no—
732C23—42no—
733C23—42no—
734C23—42no—
735C23—42no—
736C23—42no—
737C23—42no—
738C23—44no—
739C23—42no—
740C23—44no—
741C23—44no—
742C23—42no—
743C23—44no—
744C23—42no—
745C23—42no—
746C23—44no—
747C23—44no—
748C23—44no—
749C23—44no—
750C23—42no—
751C23—42no—
752C23—44no—
753C23—44no—
754C23—44no—
755C23—44no—
756C23C2×#12314yes—
757C23C2×#12714yes—
758C23C2×#12714yes—
759C23#53614yes—
760C23#54718yes—
761C23#54718yes—
762C23C23×D411yescharacteristic
763C23C23×D411yescharacteristic
764C23C23×D412yes—
765C23C22×#4111yescharacteristic
766C23C22×#4111yescharacteristic
767C23C22×#4111yescharacteristic
768C23C2×H(5,𝔽2)11yescharacteristic
769C23C2×H(5,𝔽2)12yes—
770C23C2×2−1+412yes—
771C23C2×2−1+411yescharacteristic
772C23C2×2−1+412yes—
773D4—232no—
774D4—816no—
775D4—816no—
776D4—88no—
777C2×C4—264no—
778C2×C4—22no—
779C2×C4—24no—
780C2×C4—24no—
781C2×C4—22no—
782C2×C4—22no—
783C2×C4—22no—
784C2×C4—24no—
785C2×C4—22no—
786C2×C4—24no—
787C2×C4—24no—
788C2×C4—24no—
789C2×C4—22no—
790C2×C4—24no—
791C2×C4—24no—
792C2×C4—22no—
793C2×C4—22no—
794C2×C4—24no—
795C2×C4—24no—
796C2×C4—24no—
797C2×C4—24no—
798C2×C4—24no—
799C2×C4—24no—
800C2×C4—232no—
801C2×C4—22no—
802C2×C4—22no—
803C2×C4—24no—
804C2×C4—22no—
805C2×C4—28no—
806C2×C4—24no—
807C2×C4—24no—
808C2×C4—28no—
809C2×C4—24no—
810C2×C4—24no—
811C2×C4—24no—
812C2×C4—22no—
813C2×C4—24no—
814C2×C4—22no—
815C2×C4—22no—
816C2×C4—24no—
817C2×C4—41no—
818C2×C4—42no—
819C2×C4—42no—
820C2×C4—41no—
821C2×C4—42no—
822C2×C4—41no—
823C2×C4—42no—
824C2×C4—41no—
825C2×C4—42no—
826C2×C4—42no—
827C2×C4—42no—
828C2×C4—44no—
829C2×C4—42no—
830C2×C4—44no—
831C2×C4—42no—
832C2×C4—42no—
833C2×C4—42no—
834C2×C4—42no—
835C2×C4—42no—
836C2×C4—42no—
837C2×C4—416no—
838C2×C4—42no—
839C2×C4—42no—
840C2×C4—42no—
841C2×C4—42no—
842C2×C4—42no—
843C2×C4—42no—
844C2×C4—42no—
845C2×C4—44no—
846C2×C4—44no—
847C2×C4—44no—
848C2×C4—42no—
849C2×C4—42no—
850C2×C4—42no—
851C2×C4—44no—
852C2×C4—42no—
853C2×C4—44no—
854C2×C4—44no—
855C2×C4—44no—
856C2×C4—42no—
857C2×C4—44no—
858C2×C4—44no—
859C2×C4—42no—
860C2×C4—42no—
861C2×C4—42no—
862C2×C4—44no—
863C2×C4—816no—
864C2×C4—816no—
865C2×C4—816no—
866C2×C4C2×#12314yes—
867C2×C4C2×#12314yes—
868C2×C4#52514yes—
869C2×C4C2×#12714yes—
870C2×C4#53914yes—
871C2×C4D4218yes—
872C2×C4D4214yes—
873C2×C4#54718yes—
874C2×C4#54714yes—
875C2×C4#54814yes—
876C2×C4#55314yes—
877C22—28no—
878C22—24no—
879C22—24no—
880C22—24no—
881C22—24no—
882C22—28no—
883C22—28no—
884C22—24no—
885C22—24no—
886C22—28no—
887C22—24no—
888C22—24no—
889C22—24no—
890C22—44no—
891C22—42no—
892C22—42no—
893C22—44no—
894C22—44no—
895C22—42no—
896C22—42no—
897C22—44no—
898C22—84no—
899C22—82no—
900C22—82no—
901C22—82no—
902C22—82no—
903C22—84no—
904C22—84no—
905C22—82no—
906C22—82no—
907C22—82no—
908C22—84no—
909C22#250118yescomplemented
910C22C22×#12311yescharacteristic
911C22C2×#52511yescharacteristic
912C22C22×#12711yescharacteristic
913C22C2×#53611yescharacteristic
914C22C2×#53911yescharacteristic
915C22C2×D4212yes—
916C22C2×D4211yescharacteristic
917C22C2×#54712yes—
918C22C2×#54712yes—
919C22C2×#54711yescharacteristic
920C22C2×#54712yes—
921C22C2×#54811yescharacteristic
922C22C2×#55311yescharacteristic
923C22#348612yes—
924C22#349212yes—
925C22#349212yes—
926C22#349812yes—
927C22#349811yescharacteristic
928C22#349911yescharacteristic
929C22#349912yes—
930C22#351112yes—
931C22#355212yes—
932C22#355212yes—
933C4—28no—
934C4—28no—
935C4—24no—
936C4—24no—
937C4—44no—
938C4—44no—
939C4—42no—
940C4—44no—
941C4—42no—
942C4—44no—
943C4—82no—
944C4—82no—
945C4—82no—
946C4—82no—
947C4—82no—
948C4#244318yescomplemented
949C2—28no—
950C2—44no—
951C2—162no—
952C2C2×#244311yescharacteristic
953C2C2×#250111yescharacteristic
954C2#3553011yescharacteristic
955C2#3610312yes—
956C2D4×#12711yescharacteristic
957C2#3617911yescharacteristic
958C2#3767511yescharacteristic
959C2#3786211yescharacteristic
960C2#3934812yes—
961C2#5912512yes—
962C2#5930412yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC2×#2416C2
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×#2501C2semidirect
3. C2×#2443C2semidirect
4. C2×D4×C4⋊C4C2semidirect
5. C22×#384C2semidirect
6. #15765C2semidirect
7. #15384C2semidirect
8. #15155C2semidirect
9. #15150C2semidirect
10. #15145C2semidirect
11. #15130C2semidirect
12. #14777C2semidirect
13. #14698C2semidirect
14. #14137C2semidirect
15. #14049C2semidirect
16. #14001C2semidirect
17. #13880C2semidirect
18. #13880C2semidirect
19. C4×#386C2semidirect
200. #386D4semidirect
212. #384D4semidirect
625. C22×C4#123semidirect
909. C22#2501semidirect
948. C4#2443semidirect

Maximal subgroups

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

subgroupindex
C2×#25012
C2×#24162
C2×#24432
C2×D4×C4⋊C42
C22×#3842
#157652
#153842
#151552
#151502
#151452
#151302
#147772
#146982
#141372
#140492
#140012
#138802
C4×#3862