Finite Group Databasebeta

← #664148

Subgroups — #664148

Order 512.

4270 conjugacy classes of subgroups.

The subgroup lattice has 923 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2854C211yesmaximal, characteristic, complemented
2C2×#2501C212yesmaximal, complemented
3C2×#2501C211yesmaximal, characteristic, complemented
4C2×#2486C211yesmaximal, characteristic, complemented
5C2×#2416C211yesmaximal, characteristic
6C2×C4×#123C211yesmaximal, characteristic, complemented
7C22×#389C211yesmaximal, characteristic, complemented
8#15765C214yesmaximal, complemented
9#15696C214yesmaximal, complemented
10#15148C212yesmaximal, complemented
11#15135C212yesmaximal, complemented
12#15069C212yesmaximal, complemented
13#14926C212yesmaximal, complemented
14#13998C212yesmaximal, complemented
15#13996C212yesmaximal, complemented
16#13910C212yesmaximal, complemented
17C22⋊C4×C4⋊C4C211yesmaximal, characteristic, complemented
18C22×#123C2212yes—
19C22×#123C2212yes—
20C22×#123C2212yes—
21C22×#123C2211yescharacteristic
22C22×#123C2212yes—
23C22×#121C2211yescharacteristic
24C22×#121C2211yescharacteristic
25C22×#121C2212yes—
26C22×C4×D4C2211yescharacteristic
27C23×C4⋊C4C2211yescharacteristic
28C23×C4⋊C4C2212yes—
29C23×C4⋊C4C2211yescharacteristic
30C23×C42C2211yescharacteristic
31#2854—28no—
32#2501—28no—
33#2501—216no—
34#2486—28no—
35#2416—28no—
36C2×#399C2214yes—
37C2×#399C2214yes—
38C2×#399C2214yes—
39C2×#398C2212yes—
40C2×#397C2212yes—
41C2×#396C2212yes—
42C2×#394C2212yes—
43C4×#123—28no—
44C2×#390C2212yes—
45C2×#390C2211yescharacteristic
46C2×#390C2212yes—
47C2×#390C2214yes—
48C2×#389—28no—
49C2×#389C2212yes—
50C2×#389C2212yes—
51C2×#389C2212yes—
52C2×#389C2214yes—
53C2×#389C2211yescharacteristic
54C2×#389C2212yes—
55C2×#388C2214yes—
56C2×#388C2212yes—
57C2×#387C2212yes—
58C2×#386C2212yes—
59C2×#386C2211yescharacteristic
60C2×#386C2212yes—
61C2×#385C2211yescharacteristic
62C2×#384C2212yes—
63C2×#384C2214yes—
64C2×#381C2212yes—
65C2×#381C2211yescharacteristic
66C2×#380C2211yescharacteristic
67C2×#380C2212yes—
68C2×#380C2211yescharacteristic
69C2×C4×C4⋊C4C2212yes—
70C2×C4×C4⋊C4C2212yes—
71C2×C4×C22⋊C4C2212yes—
72C2×C4×C22⋊C4C2212yes—
73C2×C4×C22⋊C4C2211yescharacteristic
74C22×#95C2212yes—
75#1445C2214yes—
76#1444C2214yes—
77#1444C2214yes—
78#1444C2214yes—
79#1439C2214yes—
80#1439C2214yes—
81#1439C2214yes—
82#1439C2214yes—
83#1439C2214yes—
84#1438C2214yes—
85#1437C2214yes—
86#1436C2214yes—
87C4⋊#95C2212yes—
88C4⋊#95C2214yes—
89C22⋊#95C2212yes—
90C23×D4C2312yes—
91C23×D4C2311yescharacteristic
92C23×D4C2311yescharacteristic
93C23×D4C2312yes—
94C24×C4C2312yes—
95C24×C4C2311yescharacteristic
96C24×C4C2311yescharacteristic
97C24×C4C2311yescharacteristic
98C24×C4C2312yes—
99C24×C4C2311yescharacteristic
100C2×#123—28no—
101C2×#123—28no—
102C2×#123—24no—
103C2×#123—28no—
104C2×#123—28no—
105C2×#123—28no—
106C2×#123—28no—
107C2×#123—28no—
108C2×#123—24no—
109C2×#123—28no—
110C2×#123—44no—
111C2×#123—44no—
112C2×#123—44no—
113C2×#123—44no—
114C2×#123D418yescomplemented
115C2×#121—28no—
116C2×#121—24no—
117C2×#121—28no—
118C2×#121—24no—
119C2×#121—24no—
120C2×#121—24no—
121C2×#121—28no—
122C2×#121—44no—
123C2×C4×D4—24no—
124C2×C4×D4—24no—
125C2×C4×D4—24no—
126C22×C4⋊C4—28no—
127C22×C4⋊C4—24no—
128C22×C4⋊C4—28no—
129C22×C4⋊C4—24no—
130C22×C4⋊C4—28no—
131C22×C4⋊C4—24no—
132C22×C4⋊C4—44no—
133C22×C4⋊C4D418yes—
134C22×C4⋊C4C2311yescharacteristic
135C22×C4⋊C4C2312yes—
136C22×C4⋊C4C2314yes—
137C22×C4⋊C4C2312yes—
138C22×C4⋊C4C2311yescharacteristic
139C22×C4⋊C4C2312yes—
140C22×C4⋊C4C2314yes—
141C22×C4⋊C4C2314yes—
142C22×C4⋊C4C2314yes—
143C22×C4⋊C4C2314yes—
144C22×C4⋊C4C2312yes—
145C22×C4⋊C4C2312yes—
146C22×C4⋊C4C2312yes—
147C22×C4⋊C4C2311yescharacteristic
148C22×C4⋊C4C2312yes—
149C22×C4⋊C4C2314yes—
150C22×C4⋊C4C2311yescharacteristic
151C22×C22⋊C4C2311yescharacteristic
152C22×C22⋊C4C2312yes—
153C22×C22⋊C4C2312yes—
154C22×C22⋊C4C2314yes—
155C22×C22⋊C4C2311yescharacteristic
156C22×C22⋊C4C2312yes—
157C22×C22⋊C4C2312yes—
158C22×C22⋊C4C2314yes—
159C22×C22⋊C4C2314yes—
160C22×C22⋊C4C2314yes—
161C22×C22⋊C4C2312yes—
162C22×C22⋊C4C2312yes—
163C22×C22⋊C4C2311yescharacteristic
164C22×C22⋊C4C2312yes—
165C22×C22⋊C4C2312yes—
166C22×C22⋊C4C2314yes—
167C22×C22⋊C4C2311yescharacteristic
168C22×C42—24no—
169C22×C42—24no—
170C22×C42—24no—
171C22×C42C2312yes—
172C22×C42C2312yes—
173C22×C42C2311yescharacteristic
174C22×C42C2314yes—
175C22×C42C2312yes—
176#399—216no—
177#399—216no—
178#399—216no—
179#398—28no—
180#397—28no—
181#396—28no—
182#394—28no—
183#390—28no—
184#390—24no—
185#390—216no—
186#390—28no—
187#389—28no—
188#389—24no—
189#389—28no—
190#389—28no—
191#389—216no—
192#389—28no—
193#388—216no—
194#388—28no—
195#387—28no—
196#386—28no—
197#386—28no—
198#386—24no—
199#385—24no—
200#384—216no—
201#384—28no—
202#381—28no—
203#381—24no—
204#380—24no—
205#380—28no—
206#380D418yescomplemented
207C4×C4⋊C4—28no—
208C4×C4⋊C4—28no—
209C4×C22⋊C4—28no—
210C4×C22⋊C4—28no—
211C4×C22⋊C4D418yescomplemented
212C2×#95—28no—
213C2×#95C2312yes—
214C2×#95C2312yes—
215C2×#95C2314yes—
216C2×#95C2314yes—
217C2×#95C2314yes—
218C2×#95C2314yes—
219C2×#95C2314yes—
220C2×#95C2314yes—
221C2×#95C2312yes—
222C2×#95C2314yes—
223C2×#95C2312yes—
224C2×#95C2312yes—
225C2×#95C2312yes—
226C2×#95C2314yes—
227C2×#95C2312yes—
228C2×#95C2312yes—
229C25C2412yes—
230C25C2411yescharacteristic
231C25C2411yescharacteristic
232C22×D4—22no—
233C22×D4—22no—
234C22×D4—22no—
235C22×D4—22no—
236C22×D4—22no—
237C22×D4—22no—
238C22×D4—24no—
239C22×D4—24no—
240C22×D4—24no—
241C22×D4—24no—
242C22×D4—24no—
243C22×D4—24no—
244C22×D4—24no—
245C22×D4—24no—
246C22×D4—22no—
247C22×D4—22no—
248C22×D4—22no—
249C22×D4—24no—
250C22×D4—24no—
251C22×D4—28no—
252C22×D4—24no—
253C22×D4—42no—
254C22×D4—44no—
255C22×D4C2×D414yes—
256C23×C4—24no—
257C23×C4—24no—
258C23×C4—22no—
259C23×C4—24no—
260C23×C4—22no—
261C23×C4—22no—
262C23×C4—22no—
263C23×C4—22no—
264C23×C4—22no—
265C23×C4—24no—
266C23×C4—22no—
267C23×C4—28no—
268C23×C4—24no—
269C23×C4—24no—
270C23×C4—24no—
271C23×C4—24no—
272C23×C4—24no—
273C23×C4—22no—
274C23×C4—22no—
275C23×C4—24no—
276C23×C4—24no—
277C23×C4—24no—
278C23×C4—22no—
279C23×C4—22no—
280C23×C4—22no—
281C23×C4—24no—
282C23×C4—24no—
283C23×C4—44no—
284C23×C4—42no—
285C23×C4C2×D414yes—
286C23×C4C2×D418yes—
287C23×C4C2×D414yes—
288C23×C4C2×D414yes—
289C23×C4C2×D414yes—
290C23×C4C2411yescharacteristic
291C23×C4C2414yes—
292C23×C4C2411yescharacteristic
293C23×C4C2412yes—
294C23×C4C2414yes—
295C23×C4C2412yes—
296C23×C4C2412yes—
297C23×C4C2412yes—
298C23×C4C2411yescharacteristic
299C23×C4C2412yes—
300C23×C4C2411yescharacteristic
301C23×C4C2412yes—
302C23×C4C2412yes—
303C23×C4C2411yescharacteristic
304#123—232no—
305#123—432no—
306#123—432no—
307#123—432no—
308#123—432no—
309#121—432no—
310#121—416no—
311#121—416no—
312C4×D4—416no—
313C2×C4⋊C4—24no—
314C2×C4⋊C4—28no—
315C2×C4⋊C4—24no—
316C2×C4⋊C4—24no—
317C2×C4⋊C4—24no—
318C2×C4⋊C4—24no—
319C2×C4⋊C4—232no—
320C2×C4⋊C4—24no—
321C2×C4⋊C4—28no—
322C2×C4⋊C4—24no—
323C2×C4⋊C4—28no—
324C2×C4⋊C4—28no—
325C2×C4⋊C4—24no—
326C2×C4⋊C4—24no—
327C2×C4⋊C4—24no—
328C2×C4⋊C4—28no—
329C2×C4⋊C4—24no—
330C2×C4⋊C4—22no—
331C2×C4⋊C4—22no—
332C2×C4⋊C4—22no—
333C2×C4⋊C4—22no—
334C2×C4⋊C4—24no—
335C2×C4⋊C4—22no—
336C2×C4⋊C4—22no—
337C2×C4⋊C4—24no—
338C2×C4⋊C4—28no—
339C2×C4⋊C4—28no—
340C2×C4⋊C4—28no—
341C2×C4⋊C4—28no—
342C2×C4⋊C4—28no—
343C2×C4⋊C4—28no—
344C2×C4⋊C4—28no—
345C2×C4⋊C4—24no—
346C2×C4⋊C4—28no—
347C2×C4⋊C4—24no—
348C2×C4⋊C4—44no—
349C2×C4⋊C4—44no—
350C2×C4⋊C4—42no—
351C2×C4⋊C4—42no—
352C2×C4⋊C4—44no—
353C2×C4⋊C4—44no—
354C2×C4⋊C4—44no—
355C2×C4⋊C4—44no—
356C2×C4⋊C4—432no—
357C2×C4⋊C4—416no—
358C2×C4⋊C4C2×D414yes—
359C2×C4⋊C4C2×D418yes—
360C2×C4⋊C4C2×D418yes—
361C2×C4⋊C4C2×D418yes—
362C2×C4⋊C4C2×D414yes—
363C2×C4⋊C4#4118yes—
364C2×C22⋊C4—24no—
365C2×C22⋊C4—22no—
366C2×C22⋊C4—22no—
367C2×C22⋊C4—24no—
368C2×C22⋊C4—24no—
369C2×C22⋊C4—24no—
370C2×C22⋊C4—22no—
371C2×C22⋊C4—22no—
372C2×C22⋊C4—22no—
373C2×C22⋊C4—24no—
374C2×C22⋊C4—28no—
375C2×C22⋊C4—22no—
376C2×C22⋊C4—22no—
377C2×C22⋊C4—22no—
378C2×C22⋊C4—24no—
379C2×C22⋊C4—24no—
380C2×C22⋊C4—24no—
381C2×C22⋊C4—24no—
382C2×C22⋊C4—24no—
383C2×C22⋊C4—24no—
384C2×C22⋊C4—24no—
385C2×C22⋊C4—28no—
386C2×C22⋊C4—28no—
387C2×C22⋊C4—28no—
388C2×C22⋊C4—28no—
389C2×C22⋊C4—28no—
390C2×C22⋊C4—28no—
391C2×C22⋊C4—24no—
392C2×C22⋊C4—28no—
393C2×C22⋊C4—28no—
394C2×C22⋊C4—28no—
395C2×C22⋊C4—24no—
396C2×C22⋊C4—28no—
397C2×C22⋊C4—24no—
398C2×C22⋊C4—42no—
399C2×C22⋊C4—44no—
400C2×C22⋊C4—42no—
401C2×C22⋊C4—42no—
402C2×C22⋊C4—44no—
403C2×C22⋊C4—44no—
404C2×C22⋊C4—44no—
405C2×C22⋊C4—44no—
406C2×C22⋊C4—44no—
407C2×C22⋊C4C2×D414yes—
408C2×C22⋊C4C2×D418yes—
409C2×C22⋊C4C2×D418yes—
410C2×C22⋊C4C2×D414yes—
411C2×C22⋊C4C2×D414yes—
412C2×C22⋊C4#4114yes—
413C2×C42—24no—
414C2×C42—24no—
415C2×C42—22no—
416C2×C42—22no—
417C2×C42—22no—
418C2×C42—24no—
419C2×C42—28no—
420C2×C42—24no—
421C2×C42—24no—
422C2×C42—24no—
423C2×C42—24no—
424C2×C42—24no—
425C2×C42—28no—
426C2×C42—44no—
427C2×C42—416no—
428C2×C42C2×D418yes—
429#95—28no—
430#95—28no—
431#95—24no—
432#95—24no—
433#95—28no—
434#95—24no—
435#95—24no—
436#95—28no—
437#95—24no—
438#95—28no—
439#95—28no—
440#95—24no—
441#95—28no—
442#95—44no—
443#95C2×D418yes—
444#95C2×D418yes—
445C24—22no—
446C24—22no—
447C24—22no—
448C24—22no—
449C24—21no—
450C24—21no—
451C24—21no—
452C24—21no—
453C24—22no—
454C24—21no—
455C24—21no—
456C24—22no—
457C24—22no—
458C24—22no—
459C24—22no—
460C24—22no—
461C24—22no—
462C24—22no—
463C24—22no—
464C24—24no—
465C24—22no—
466C24—22no—
467C24—24no—
468C24—24no—
469C24—24no—
470C24C22×D412yes—
471C24C22×D412yes—
472C24C22×D412yes—
473C24C22×D412yes—
474C24C22×D412yes—
475C24C2×#4112yes—
476C24H(5,𝔽2)12yes—
477C24H(5,𝔽2)12yes—
478C24C2511yescharacteristic
479C2×D4—28no—
480C2×D4—28no—
481C2×D4—28no—
482C2×D4—48no—
483C2×D4—416no—
484C2×D4—44no—
485C2×D4—44no—
486C2×D4—44no—
487C2×D4—44no—
488C2×D4—48no—
489C2×D4—48no—
490C2×D4—48no—
491C2×D4—48no—
492C2×D4—48no—
493C2×D4—48no—
494C2×D4—48no—
495C2×D4—48no—
496C2×D4—44no—
497C2×D4—44no—
498C2×D4—44no—
499C2×D4—48no—
500C2×D4—48no—
501C2×D4—84no—
502C2×D4—88no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—24no—
512C22×C4—28no—
513C22×C4—28no—
514C22×C4—216no—
515C22×C4—216no—
516C22×C4—28no—
517C22×C4—28no—
518C22×C4—28no—
519C22×C4—216no—
520C22×C4—28no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—21no—
526C22×C4—22no—
527C22×C4—24no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—22no—
533C22×C4—24no—
534C22×C4—22no—
535C22×C4—24no—
536C22×C4—21no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—24no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—21no—
543C22×C4—22no—
544C22×C4—21no—
545C22×C4—22no—
546C22×C4—24no—
547C22×C4—22no—
548C22×C4—24no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—24no—
552C22×C4—24no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—216no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—22no—
563C22×C4—24no—
564C22×C4—22no—
565C22×C4—24no—
566C22×C4—24no—
567C22×C4—24no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—24no—
572C22×C4—22no—
573C22×C4—24no—
574C22×C4—24no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—48no—
581C22×C4—416no—
582C22×C4—416no—
583C22×C4—48no—
584C22×C4—48no—
585C22×C4—44no—
586C22×C4—44no—
587C22×C4—44no—
588C22×C4—44no—
589C22×C4—44no—
590C22×C4—44no—
591C22×C4—48no—
592C22×C4—48no—
593C22×C4—48no—
594C22×C4—48no—
595C22×C4—48no—
596C22×C4—48no—
597C22×C4—48no—
598C22×C4—44no—
599C22×C4—44no—
600C22×C4—44no—
601C22×C4—48no—
602C22×C4—48no—
603C22×C4#127116yes—
604C22×C4C22×D414yes—
605C22×C4C22×D418yes—
606C22×C4C22×D414yes—
607C22×C4C22×D414yes—
608C22×C4C22×D412yes—
609C22×C4C22×D414yes—
610C22×C4C22×D414yes—
611C22×C4C22×D414yes—
612C22×C4C22×D412yes—
613C22×C4C22×D412yes—
614C22×C4C22×D412yes—
615C22×C4C22×D412yes—
616C22×C4C22×D412yes—
617C22×C4C22×D412yes—
618C22×C4C2×#4114yes—
619C22×C4C2×#4118yes—
620C22×C4C2×#4114yes—
621C22×C42−1+414yes—
622C22×C42−1+414yes—
623C4⋊C4—216no—
624C4⋊C4—216no—
625C4⋊C4—28no—
626C4⋊C4—216no—
627C4⋊C4—48no—
628C4⋊C4—416no—
629C4⋊C4—416no—
630C4⋊C4—48no—
631C4⋊C4—416no—
632C4⋊C4—416no—
633C4⋊C4—416no—
634C4⋊C4—416no—
635C4⋊C4—48no—
636C4⋊C4—48no—
637C4⋊C4—44no—
638C4⋊C4—44no—
639C4⋊C4#123116yescomplemented
640C22⋊C4—28no—
641C22⋊C4—216no—
642C22⋊C4—216no—
643C22⋊C4—416no—
644C22⋊C4—48no—
645C22⋊C4—48no—
646C22⋊C4—416no—
647C22⋊C4—48no—
648C22⋊C4—416no—
649C22⋊C4—416no—
650C22⋊C4—44no—
651C22⋊C4—416no—
652C22⋊C4—48no—
653C22⋊C4—44no—
654C22⋊C4—48no—
655C22⋊C4—84no—
656C22⋊C4#121116yescomplemented
657C42—216no—
658C42—416no—
659C42—48no—
660C42—48no—
661C42—44no—
662C23—22no—
663C23—22no—
664C23—24no—
665C23—24no—
666C23—24no—
667C23—24no—
668C23—22no—
669C23—22no—
670C23—24no—
671C23—24no—
672C23—24no—
673C23—24no—
674C23—24no—
675C23—24no—
676C23—24no—
677C23—24no—
678C23—22no—
679C23—22no—
680C23—22no—
681C23—24no—
682C23—24no—
683C23—41no—
684C23—41no—
685C23—41no—
686C23—41no—
687C23—42no—
688C23—42no—
689C23—41no—
690C23—41no—
691C23—42no—
692C23—41no—
693C23—41no—
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—44no—
709C23—44no—
710C23—42no—
711C23—42no—
712C23—44no—
713C23—44no—
714C23—42no—
715C23—42no—
716C23—44no—
717C23—44no—
718C23—44no—
719C23—44no—
720C23—44no—
721C23—44no—
722C23—44no—
723C23—44no—
724C23C2×#12114yes—
725C23C2×#12714yes—
726C23#53514yes—
727C23D4214yes—
728C23D4214yes—
729C23#55014yes—
730C23#55014yes—
731C23C23×D411yescharacteristic
732C23C23×D411yescharacteristic
733C23C23×D411yescharacteristic
734C23C23×D411yescharacteristic
735C23C22×#4111yescharacteristic
736C23C22×#4112yes—
737C23C2×H(5,𝔽2)11yescharacteristic
738C23C2×H(5,𝔽2)11yescharacteristic
739C23C2×2−1+412yes—
740C23C2×2−1+412yes—
741C23#58512yes—
742D4—416no—
743D4—816no—
744D4—816no—
745D4—88no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—24no—
749C2×C4—24no—
750C2×C4—24no—
751C2×C4—24no—
752C2×C4—24no—
753C2×C4—28no—
754C2×C4—24no—
755C2×C4—24no—
756C2×C4—24no—
757C2×C4—24no—
758C2×C4—28no—
759C2×C4—24no—
760C2×C4—232no—
761C2×C4—24no—
762C2×C4—22no—
763C2×C4—24no—
764C2×C4—24no—
765C2×C4—28no—
766C2×C4—24no—
767C2×C4—24no—
768C2×C4—22no—
769C2×C4—24no—
770C2×C4—22no—
771C2×C4—24no—
772C2×C4—28no—
773C2×C4—24no—
774C2×C4—24no—
775C2×C4—24no—
776C2×C4—24no—
777C2×C4—24no—
778C2×C4—28no—
779C2×C4—432no—
780C2×C4—416no—
781C2×C4—42no—
782C2×C4—42no—
783C2×C4—41no—
784C2×C4—42no—
785C2×C4—41no—
786C2×C4—42no—
787C2×C4—42no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—44no—
791C2×C4—44no—
792C2×C4—42no—
793C2×C4—42no—
794C2×C4—42no—
795C2×C4—44no—
796C2×C4—42no—
797C2×C4—44no—
798C2×C4—42no—
799C2×C4—44no—
800C2×C4—42no—
801C2×C4—42no—
802C2×C4—44no—
803C2×C4—416no—
804C2×C4—44no—
805C2×C4—42no—
806C2×C4—41no—
807C2×C4—41no—
808C2×C4—41no—
809C2×C4—42no—
810C2×C4—44no—
811C2×C4—44no—
812C2×C4—42no—
813C2×C4—41no—
814C2×C4—44no—
815C2×C4—42no—
816C2×C4—44no—
817C2×C4—42no—
818C2×C4—42no—
819C2×C4—42no—
820C2×C4—44no—
821C2×C4—44no—
822C2×C4—42no—
823C2×C4—42no—
824C2×C4—41no—
825C2×C4—41no—
826C2×C4—42no—
827C2×C4—42no—
828C2×C4—816no—
829C2×C4—88no—
830C2×C4C2×#12118yes—
831C2×C4C2×#12318yes—
832C2×C4C2×#12314yes—
833C2×C4C2×#12714yes—
834C2×C4C2×#12714yes—
835C2×C4#53614yes—
836C2×C4#54718yes—
837C2×C4#54718yes—
838C22—24no—
839C22—24no—
840C22—28no—
841C22—28no—
842C22—28no—
843C22—24no—
844C22—24no—
845C22—24no—
846C22—28no—
847C22—24no—
848C22—42no—
849C22—44no—
850C22—42no—
851C22—44no—
852C22—42no—
853C22—81no—
854C22—81no—
855C22—82no—
856C22—82no—
857C22—81no—
858C22—81no—
859C22—82no—
860C22—82no—
861C22—82no—
862C22—84no—
863C22—84no—
864C22—84no—
865C22—82no—
866C22—82no—
867C22—82no—
868C22—84no—
869C22—82no—
870C22#254118yes—
871C22C22×#12111yescharacteristic
872C22C22×#12311yescharacteristic
873C22C22×#12711yescharacteristic
874C22C2×#53511yescharacteristic
875C22C2×#53611yescharacteristic
876C22C2×D4211yescharacteristic
877C22C2×D4211yescharacteristic
878C22C2×#54712yes—
879C22C2×#54712yes—
880C22C2×#55011yescharacteristic
881C22C2×#55011yescharacteristic
882C22D4×#4112yes—
883C22#348212yes—
884C22#348511yescharacteristic
885C22#348611yescharacteristic
886C22#348912yes—
887C22#348912yes—
888C22#349912yes—
889C22#351312yes—
890C22#351512yes—
891C22#352212yes—
892C22#354412yes—
893C22#355912yes—
894C4—28no—
895C4—24no—
896C4—28no—
897C4—44no—
898C4—44no—
899C4—42no—
900C4—44no—
901C4—48no—
902C4—44no—
903C4—81no—
904C4—84no—
905C4—82no—
906C4—81no—
907C4#250118yescomplemented
908C2—28no—
909C2—82no—
910C2—162no—
911C2C2×#250111yescharacteristic
912C2C2×#254111yescharacteristic
913C2#3563411yescharacteristic
914C2D4×#12311yescharacteristic
915C2#3625912yes—
916C2#3648311yescharacteristic
917C2#3804112yes—
918C2#3913411yescharacteristic
919C2#3933711yescharacteristic
920C2#5904712yes—
921C2#5911212yes—
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×#2854C2semidirect
2. C2×#2501C2semidirect
3. C2×#2501C2semidirect
4. C2×#2486C2semidirect
6. C2×C4×#123C2semidirect
7. C22×#389C2semidirect
8. #15765C2semidirect
9. #15696C2semidirect
10. #15148C2semidirect
11. #15135C2semidirect
12. #15069C2semidirect
13. #14926C2semidirect
14. #13998C2semidirect
15. #13996C2semidirect
16. #13910C2semidirect
17. C22⋊C4×C4⋊C4C2semidirect
114. C2×#123D4semidirect
206. #380D4semidirect
211. C4×C22⋊C4D4semidirect
639. C4⋊C4#123semidirect
656. C22⋊C4#121semidirect
907. C4#2501semidirect

Maximal subgroups

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

subgroupindex
C2×#28542
C2×#25012
C2×#24862
C2×#24162
C2×C4×#1232
C22×#3892
#157652
#156962
#151482
#151352
#150692
#149262
#139982
#139962
#139102
C22⋊C4×C4⋊C42