Finite Group Databasebeta

← #612917

Subgroups — #612917

Order 512.

3702 conjugacy classes of subgroups.

The subgroup lattice has 881 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2851C211yesmaximal, characteristic, complemented
2C2×#2566C211yesmaximal, characteristic, complemented
3C2×C4×#121C211yesmaximal, characteristic
4C22×C4×C4⋊C4C211yesmaximal, characteristic, complemented
5#15234C211yesmaximal, characteristic, complemented
6#15222C211yesmaximal, characteristic, complemented
7#15196C211yesmaximal, characteristic, complemented
8#15134C211yesmaximal, characteristic, complemented
9#14864C214yesmaximal, complemented
10#14729C214yesmaximal, complemented
11#14698C211yesmaximal, characteristic
12#14698C211yesmaximal, characteristic
13#14686C211yesmaximal, characteristic, complemented
14#14682C211yesmaximal, characteristic, complemented
15#14198C214yesmaximal, complemented
16#14160C211yesmaximal, characteristic, complemented
17#13975C214yesmaximal, complemented
18#13941C211yesmaximal, characteristic, complemented
19#13909C211yesmaximal, characteristic, complemented
20C22×#125C2211yescharacteristic
21C22×#121C2211yescharacteristic
22C22×C4×D4C2211yescharacteristic
23C22×C4×D4C2212yes—
24C23×C4⋊C4C2212yes—
25C23×C42C2211yescharacteristic
26C23×C42C2211yescharacteristic
27C23×C42C2211yescharacteristic
28#2851—28no—
29#2566—28no—
30C2×#396C2214yes—
31C2×#396C2214yes—
32C4×#121—28no—
33C2×#390C2211yescharacteristic
34C2×#390C2211yescharacteristic
35C2×#390C2211yescharacteristic
36C2×#390C2211yescharacteristic
37C2×#390C2211yescharacteristic
38C2×#389C2211yescharacteristic
39C2×#389C2211yescharacteristic
40C2×#389C2211yescharacteristic
41C2×#388C2212yes—
42C2×#387C2212yes—
43C2×#387C2212yes—
44C2×#386C2214yes—
45C2×#386C2212yes—
46C2×#386C2214yes—
47C2×#385C2212yes—
48C2×#385C2212yes—
49C2×#385C2214yes—
50C2×#384C2211yescharacteristic
51C2×#384C2211yescharacteristic
52C2×#382C2211yescharacteristic
53C2×#382C2211yescharacteristic
54C2×#382C2211yescharacteristic
55C2×#380C2211yescharacteristic
56C2×#380C2211yescharacteristic
57C2×#380C2211yescharacteristic
58C2×#380C2214yes—
59C2×C4×C4⋊C4—28no—
60C2×C4×C4⋊C4C2212yes—
61C2×C4×C4⋊C4C2211yescharacteristic
62C2×C4×C4⋊C4C2211yescharacteristic
63C2×C4×C4⋊C4C2211yescharacteristic
64C2×C4×C4⋊C4C2212yes—
65C2×C4×C4⋊C4C2211yescharacteristic
66C2×C4×C4⋊C4C2211yescharacteristic
67C2×C4×C22⋊C4C2212yes—
68C22×#95C2212yes—
69#1444C2214yes—
70#1442C2214yes—
71#1441C2214yes—
72#1441C2214yes—
73#1441C2214yes—
74#1441C2214yes—
75#1439C2214yes—
76#1439C2214yes—
77#1439C2214yes—
78#1439C2214yes—
79#1437C2214yes—
80#1437C2214yes—
81#1436C2214yes—
82#1436C2214yes—
83C4⋊#95C2214yes—
84C4⋊#95C2211yescharacteristic
85C4⋊#95C2211yescharacteristic
86C4⋊#95C2211yescharacteristic
87C4⋊#95C2211yescharacteristic
88C4⋊#95C2211yescharacteristic
89C4⋊#95C2211yescharacteristic
90C4⋊#95C2211yescharacteristic
91C4⋊#95C2211yescharacteristic
92#1434C2214yes—
93C22⋊#95C2214yes—
94C22⋊#95C2214yes—
95C23×D4C2312yes—
96C23×D4C2311yescharacteristic
97C24×C4C2311yescharacteristic
98C24×C4C2312yes—
99C24×C4C2311yescharacteristic
100C24×C4C2312yes—
101C24×C4C2311yescharacteristic
102C24×C4C2312yes—
103C2×#125—24no—
104C2×#125—24no—
105C2×#125—24no—
106C2×#121—24no—
107C2×#121—24no—
108C2×#121Q818yes—
109C2×C4×D4—28no—
110C2×C4×D4—24no—
111C2×C4×D4—24no—
112C2×C4×D4—24no—
113C2×C4×D4—48no—
114C22×C4⋊C4—28no—
115C22×C4⋊C4—28no—
116C22×C4⋊C4—28no—
117C22×C4⋊C4C2312yes—
118C22×C4⋊C4C2312yes—
119C22×C4⋊C4C2312yes—
120C22×C4⋊C4C2312yes—
121C22×C4⋊C4C2311yescharacteristic
122C22×C4⋊C4C2311yescharacteristic
123C22×C4⋊C4C2311yescharacteristic
124C22×C4⋊C4C2312yes—
125C22×C4⋊C4C2311yescharacteristic
126C22×C4⋊C4C2311yescharacteristic
127C22×C4⋊C4C2311yescharacteristic
128C22×C4⋊C4C2312yes—
129C22×C4⋊C4C2311yescharacteristic
130C22×C4⋊C4C2312yes—
131C22×C4⋊C4C2314yes—
132C22×C4⋊C4C2314yes—
133C22×C4⋊C4C2312yes—
134C22×C4⋊C4C2312yes—
135C22×C22⋊C4C2312yes—
136C22×C22⋊C4C2314yes—
137C22×C22⋊C4C2312yes—
138C22×C22⋊C4C2312yes—
139C22×C22⋊C4C2312yes—
140C22×C22⋊C4C2312yes—
141C22×C22⋊C4C2312yes—
142C22×C22⋊C4C2314yes—
143C22×C22⋊C4C2314yes—
144C22×C22⋊C4C2312yes—
145C22×C22⋊C4C2314yes—
146C22×C42—24no—
147C22×C42—24no—
148C22×C42—24no—
149C22×C42—24no—
150C22×C42—24no—
151C22×C42—24no—
152C22×C42—42no—
153C22×C42—42no—
154C22×C42D418yes—
155C22×C42C2311yescharacteristic
156C22×C42C2311yescharacteristic
157C22×C42C2312yes—
158C22×C42C2312yes—
159C22×C42C2311yescharacteristic
160C22×C42C2311yescharacteristic
161C22×C42C2311yescharacteristic
162C22×C42C2311yescharacteristic
163C22×C42C2311yescharacteristic
164C22×C42C2312yes—
165C22×C42C2311yescharacteristic
166#396—216no—
167#396—216no—
168#390—24no—
169#390—24no—
170#390—24no—
171#390—42no—
172#390—42no—
173#389—24no—
174#389—24no—
175#389—24no—
176#388—28no—
177#387—28no—
178#387—28no—
179#386—28no—
180#386—216no—
181#386—48no—
182#385—28no—
183#385—28no—
184#385—216no—
185#384—24no—
186#384—42no—
187#382—24no—
188#382—24no—
189#382—42no—
190#380—24no—
191#380—24no—
192#380—24no—
193#380—48no—
194C4×C4⋊C4—28no—
195C4×C4⋊C4—24no—
196C4×C4⋊C4—24no—
197C4×C4⋊C4—24no—
198C4×C4⋊C4—24no—
199C4×C4⋊C4—28no—
200C4×C4⋊C4D418yescomplemented
201C4×C22⋊C4—28no—
202C2×#95—28no—
203C2×#95C2314yes—
204C2×#95C2314yes—
205C2×#95C2312yes—
206C2×#95C2312yes—
207C2×#95C2312yes—
208C2×#95C2312yes—
209C2×#95C2312yes—
210C2×#95C2314yes—
211C2×#95C2314yes—
212C2×#95C2312yes—
213C2×#95C2312yes—
214C2×#95C2312yes—
215C2×#95C2312yes—
216C2×#95C2312yes—
217C2×#95C2312yes—
218C2×#95C2312yes—
219C2×#95C2314yes—
220C2×#95C2314yes—
221C2×#95C2314yes—
222C2×#95C2314yes—
223C2×#95C2314yes—
224C2×#95C2314yes—
225C2×#95C2312yes—
226C25C2412yes—
227C25C2411yescharacteristic
228C22×D4—24no—
229C22×D4—24no—
230C22×D4—28no—
231C22×D4—28no—
232C22×D4—22no—
233C22×D4—22no—
234C22×D4—22no—
235C22×D4—22no—
236C22×D4—22no—
237C22×D4—22no—
238C22×D4C2×Q818yes—
239C22×D4C2×Q814yes—
240C23×C4—24no—
241C23×C4—22no—
242C23×C4—22no—
243C23×C4—24no—
244C23×C4—22no—
245C23×C4—22no—
246C23×C4—22no—
247C23×C4—22no—
248C23×C4—24no—
249C23×C4—24no—
250C23×C4—24no—
251C23×C4—24no—
252C23×C4—24no—
253C23×C4—24no—
254C23×C4—22no—
255C23×C4—24no—
256C23×C4—24no—
257C23×C4—22no—
258C23×C4—24no—
259C23×C4—24no—
260C23×C4—24no—
261C23×C4—24no—
262C23×C4—24no—
263C23×C4—42no—
264C23×C4—42no—
265C23×C4—42no—
266C23×C4—42no—
267C23×C4—42no—
268C23×C4—44no—
269C23×C4—44no—
270C23×C4C2×D414yes—
271C23×C4C2×D414yes—
272C23×C4C2×D414yes—
273C23×C4C2×Q814yes—
274C23×C4#4118yes—
275C23×C4#4114yes—
276C23×C4C2412yes—
277C23×C4C2412yes—
278C23×C4C2412yes—
279C23×C4C2412yes—
280C23×C4C2412yes—
281C23×C4C2412yes—
282C23×C4C2411yescharacteristic
283C23×C4C2412yes—
284C23×C4C2412yes—
285C23×C4C2412yes—
286C23×C4C2412yes—
287C23×C4C2411yescharacteristic
288C23×C4C2411yescharacteristic
289C23×C4C2411yescharacteristic
290C23×C4C2411yescharacteristic
291C23×C4C2412yes—
292C23×C4C2411yescharacteristic
293#125—416no—
294#121—232no—
295C4×D4—432no—
296C4×D4—416no—
297C2×C4⋊C4—264no—
298C2×C4⋊C4—24no—
299C2×C4⋊C4—24no—
300C2×C4⋊C4—24no—
301C2×C4⋊C4—22no—
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—24no—
309C2×C4⋊C4—22no—
310C2×C4⋊C4—22no—
311C2×C4⋊C4—22no—
312C2×C4⋊C4—24no—
313C2×C4⋊C4—22no—
314C2×C4⋊C4—22no—
315C2×C4⋊C4—22no—
316C2×C4⋊C4—22no—
317C2×C4⋊C4—24no—
318C2×C4⋊C4—24no—
319C2×C4⋊C4—24no—
320C2×C4⋊C4—24no—
321C2×C4⋊C4—22no—
322C2×C4⋊C4—22no—
323C2×C4⋊C4—22no—
324C2×C4⋊C4—24no—
325C2×C4⋊C4—24no—
326C2×C4⋊C4—22no—
327C2×C4⋊C4—24no—
328C2×C4⋊C4—24no—
329C2×C4⋊C4—22no—
330C2×C4⋊C4—22no—
331C2×C4⋊C4—28no—
332C2×C4⋊C4—22no—
333C2×C4⋊C4—22no—
334C2×C4⋊C4—22no—
335C2×C4⋊C4—22no—
336C2×C4⋊C4—22no—
337C2×C4⋊C4—22no—
338C2×C4⋊C4—28no—
339C2×C4⋊C4—28no—
340C2×C4⋊C4—44no—
341C2×C4⋊C4—44no—
342C2×C4⋊C4—44no—
343C2×C4⋊C4—44no—
344C2×C4⋊C4—44no—
345C2×C4⋊C4—44no—
346C2×C4⋊C4C2×D418yes—
347C2×C4⋊C4C2×Q814yes—
348C2×C4⋊C4#4118yes—
349C2×C22⋊C4—24no—
350C2×C22⋊C4—24no—
351C2×C22⋊C4—24no—
352C2×C22⋊C4—24no—
353C2×C22⋊C4—24no—
354C2×C22⋊C4—28no—
355C2×C22⋊C4—28no—
356C2×C22⋊C4—28no—
357C2×C22⋊C4—24no—
358C2×C22⋊C4—24no—
359C2×C22⋊C4—24no—
360C2×C22⋊C4—24no—
361C2×C22⋊C4—28no—
362C2×C22⋊C4—24no—
363C2×C22⋊C4—28no—
364C2×C22⋊C4—28no—
365C2×C22⋊C4—28no—
366C2×C22⋊C4—28no—
367C2×C22⋊C4—28no—
368C2×C22⋊C4—28no—
369C2×C22⋊C4—44no—
370C2×C22⋊C4—44no—
371C2×C22⋊C4—44no—
372C2×C22⋊C4—44no—
373C2×C22⋊C4—44no—
374C2×C22⋊C4—44no—
375C2×C22⋊C4—44no—
376C2×C22⋊C4C2×Q818yes—
377C2×C42—22no—
378C2×C42—22no—
379C2×C42—22no—
380C2×C42—22no—
381C2×C42—22no—
382C2×C42—22no—
383C2×C42—22no—
384C2×C42—22no—
385C2×C42—22no—
386C2×C42—22no—
387C2×C42—232no—
388C2×C42—24no—
389C2×C42—24no—
390C2×C42—24no—
391C2×C42—22no—
392C2×C42—22no—
393C2×C42—24no—
394C2×C42—24no—
395C2×C42—22no—
396C2×C42—22no—
397C2×C42—22no—
398C2×C42—22no—
399C2×C42—416no—
400C2×C42—416no—
401C2×C42—44no—
402C2×C42—42no—
403C2×C42—42no—
404C2×C42C2×D414yes—
405C2×C42C2×D414yes—
406C2×C42C2×D414yes—
407C2×C42C2×D414yes—
408C2×C42C2×D414yes—
409C2×C42C2×D414yes—
410C2×C42C2×D414yes—
411C2×C42#4114yes—
412#95—24no—
413#95—24no—
414#95—24no—
415#95—24no—
416#95—24no—
417#95—24no—
418#95—24no—
419#95—24no—
420#95—24no—
421#95—24no—
422#95—28no—
423#95—24no—
424#95—24no—
425#95—28no—
426#95—28no—
427#95—28no—
428#95—44no—
429#95—44no—
430#95—44no—
431#95—44no—
432#95—44no—
433#95—44no—
434#95C2×D418yes—
435C24—21no—
436C24—21no—
437C24—22no—
438C24—21no—
439C24—21no—
440C24—22no—
441C24—22no—
442C24—22no—
443C24—24no—
444C24—24no—
445C24—22no—
446C24—22no—
447C24—22no—
448C24—24no—
449C24—22no—
450C24—24no—
451C24C22×D412yes—
452C24C22×Q814yes—
453C24C22×Q812yes—
454C24C2×#4112yes—
455C24C2×#4114yes—
456C24H(5,𝔽2)14yes—
457C24C2511yescharacteristic
458C2×D4—216no—
459C2×D4—232no—
460C2×D4—28no—
461C2×D4—28no—
462C2×D4—28no—
463C2×D4—48no—
464C2×D4—48no—
465C2×D4—416no—
466C2×D4—44no—
467C2×D4—44no—
468C2×D4—44no—
469C2×D4—44no—
470C22×C4—216no—
471C22×C4—216no—
472C22×C4—28no—
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—21no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—21no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—28no—
489C22×C4—28no—
490C22×C4—28no—
491C22×C4—28no—
492C22×C4—28no—
493C22×C4—28no—
494C22×C4—28no—
495C22×C4—28no—
496C22×C4—216no—
497C22×C4—28no—
498C22×C4—216no—
499C22×C4—21no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—24no—
504C22×C4—21no—
505C22×C4—22no—
506C22×C4—22no—
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—24no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—28no—
526C22×C4—216no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—24no—
537C22×C4—24no—
538C22×C4—24no—
539C22×C4—24no—
540C22×C4—24no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—24no—
545C22×C4—24no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—24no—
549C22×C4—24no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—24no—
555C22×C4—24no—
556C22×C4—24no—
557C22×C4—44no—
558C22×C4—48no—
559C22×C4—48no—
560C22×C4—48no—
561C22×C4—48no—
562C22×C4—48no—
563C22×C4—48no—
564C22×C4—48no—
565C22×C4—48no—
566C22×C4—48no—
567C22×C4—48no—
568C22×C4—48no—
569C22×C4—48no—
570C22×C4—48no—
571C22×C4—48no—
572C22×C4—48no—
573C22×C4—48no—
574C22×C4—88no—
575C22×C4—88no—
576C22×C4C22⋊Q8116yes—
577C22×C4C22×D414yes—
578C22×C4C22×D412yes—
579C22×C4C22×D412yes—
580C22×C4C22×D412yes—
581C22×C4C22×D412yes—
582C22×C4C22×D412yes—
583C22×C4C22×D412yes—
584C22×C4C22×D414yes—
585C22×C4C22×D412yes—
586C22×C4C22×D412yes—
587C22×C4C22×D412yes—
588C22×C4C22×Q814yes—
589C22×C4C22×Q812yes—
590C22×C4C22×Q812yes—
591C22×C4C2×#4114yes—
592C22×C4C2×#4114yes—
593C22×C4C2×#4112yes—
594C22×C4C2×#4112yes—
595C22×C4C2×#4112yes—
596C22×C4C2×#4114yes—
597C22×C4C2×#4114yes—
598C22×C4C2×#4114yes—
599C22×C4C2×#4112yes—
600C22×C4C2×#4112yes—
601C22×C4H(5,𝔽2)12yes—
602C22×C42−1+412yes—
603C4⋊C4—216no—
604C4⋊C4—216no—
605C4⋊C4—28no—
606C4⋊C4—216no—
607C4⋊C4—216no—
608C4⋊C4—48no—
609C4⋊C4—48no—
610C4⋊C4—44no—
611C4⋊C4—48no—
612C4⋊C4—48no—
613C4⋊C4—44no—
614C4⋊C4—44no—
615C4⋊C4—48no—
616C4⋊C4—44no—
617C4⋊C4—44no—
618C4⋊C4—44no—
619C4⋊C4—88no—
620C4⋊C4—88no—
621C22⋊C4—216no—
622C22⋊C4—48no—
623C22⋊C4—48no—
624C22⋊C4—48no—
625C22⋊C4—48no—
626C22⋊C4—48no—
627C22⋊C4—416no—
628C22⋊C4—48no—
629C22⋊C4—88no—
630C22⋊C4—88no—
631C22⋊C4—88no—
632C42—28no—
633C42—28no—
634C42—28no—
635C42—28no—
636C42—28no—
637C42—48no—
638C42—48no—
639C42—48no—
640C42—44no—
641C42—44no—
642C42#121116yes—
643C23—22no—
644C23—24no—
645C23—22no—
646C23—24no—
647C23—22no—
648C23—22no—
649C23—22no—
650C23—22no—
651C23—22no—
652C23—22no—
653C23—24no—
654C23—24no—
655C23—24no—
656C23—24no—
657C23—24no—
658C23—24no—
659C23—24no—
660C23—24no—
661C23—24no—
662C23—24no—
663C23—28no—
664C23—24no—
665C23—28no—
666C23—42no—
667C23—44no—
668C23—42no—
669C23—42no—
670C23—44no—
671C23—42no—
672C23—42no—
673C23—42no—
674C23—42no—
675C23—42no—
676C23—44no—
677C23—44no—
678C23—44no—
679C23—44no—
680C23—44no—
681C23—44no—
682C23—44no—
683C23—44no—
684C23C2×C22⋊Q814yes—
685C23#53214yes—
686C23#53514yes—
687C23#55318yes—
688C23#55418yes—
689C23C23×D411yescharacteristic
690C23C23×D411yescharacteristic
691C23C23×Q811yescharacteristic
692C23C22×#4111yescharacteristic
693C23C22×#4111yescharacteristic
694C23C22×#4112yes—
695C23C22×#4112yes—
696C23C2×H(5,𝔽2)12yes—
697C23C2×H(5,𝔽2)11yescharacteristic
698C23C2×2−1+411yescharacteristic
699C23#58512yes—
700D4—432no—
701D4—416no—
702C2×C4—232no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—24no—
706C2×C4—24no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—24no—
711C2×C4—24no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—24no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—24no—
720C2×C4—22no—
721C2×C4—24no—
722C2×C4—24no—
723C2×C4—24no—
724C2×C4—24no—
725C2×C4—24no—
726C2×C4—24no—
727C2×C4—232no—
728C2×C4—22no—
729C2×C4—24no—
730C2×C4—24no—
731C2×C4—24no—
732C2×C4—24no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—24no—
736C2×C4—24no—
737C2×C4—28no—
738C2×C4—24no—
739C2×C4—24no—
740C2×C4—24no—
741C2×C4—24no—
742C2×C4—432no—
743C2×C4—416no—
744C2×C4—432no—
745C2×C4—42no—
746C2×C4—42no—
747C2×C4—42no—
748C2×C4—42no—
749C2×C4—42no—
750C2×C4—42no—
751C2×C4—44no—
752C2×C4—42no—
753C2×C4—42no—
754C2×C4—42no—
755C2×C4—42no—
756C2×C4—42no—
757C2×C4—42no—
758C2×C4—42no—
759C2×C4—42no—
760C2×C4—42no—
761C2×C4—42no—
762C2×C4—42no—
763C2×C4—42no—
764C2×C4—42no—
765C2×C4—44no—
766C2×C4—42no—
767C2×C4—42no—
768C2×C4—42no—
769C2×C4—42no—
770C2×C4—42no—
771C2×C4—44no—
772C2×C4—42no—
773C2×C4—42no—
774C2×C4—42no—
775C2×C4—42no—
776C2×C4—42no—
777C2×C4—42no—
778C2×C4—42no—
779C2×C4—42no—
780C2×C4—42no—
781C2×C4—42no—
782C2×C4—44no—
783C2×C4—44no—
784C2×C4—44no—
785C2×C4—44no—
786C2×C4—44no—
787C2×C4—44no—
788C2×C4—44no—
789C2×C4—44no—
790C2×C4—44no—
791C2×C4—44no—
792C2×C4—816no—
793C2×C4C2×#12114yes—
794C2×C4C2×#12114yes—
795C2×C4C2×#12114yes—
796C2×C4C2×C22⋊Q814yes—
797C2×C4C2×C22⋊Q814yes—
798C2×C4#52518yes—
799C2×C4#53214yes—
800C2×C4#53714yes—
801C2×C4#54614yes—
802C2×C4D4×Q814yes—
803C2×C4#55214yes—
804C2×C4#55414yes—
805C22—24no—
806C22—24no—
807C22—28no—
808C22—28no—
809C22—24no—
810C22—24no—
811C22—24no—
812C22—24no—
813C22—28no—
814C22—28no—
815C22—44no—
816C22—44no—
817C22—44no—
818C22—48no—
819C22—48no—
820C22—82no—
821C22—82no—
822C22—84no—
823C22—84no—
824C22—82no—
825C22—82no—
826C22#256618yescomplemented
827C22C22×#12111yescharacteristic
828C22C22×C22⋊Q811yescharacteristic
829C22C2×#52512yes—
830C22C2×#53211yescharacteristic
831C22C2×#53211yescharacteristic
832C22#344412yes—
833C22C2×#53511yescharacteristic
834C22C2×#53711yescharacteristic
835C22#344911yescharacteristic
836C22C2×#54611yescharacteristic
837C22C2×D4×Q811yescharacteristic
838C22C2×#55211yescharacteristic
839C22C2×#55312yes—
840C22C2×#55412yes—
841C22C2×#55411yescharacteristic
842C22#347512yes—
843C22Q8×#4112yes—
844C22#348812yes—
845C22#349412yes—
846C22#350512yes—
847C22#350712yes—
848C22#351912yes—
849C22#352212yes—
850C4—24no—
851C4—24no—
852C4—28no—
853C4—24no—
854C4—24no—
855C4—44no—
856C4—44no—
857C4—44no—
858C4—44no—
859C4—42no—
860C4—82no—
861C4—82no—
862C4—82no—
863C4—82no—
864C4—82no—
865C4—82no—
866C4#241718yes—
867C2—28no—
868C2—84no—
869C2C2×#241711yescharacteristic
870C2C2×#256611yescharacteristic
871C2#3494711yescharacteristic
872C2#3510311yescharacteristic
873C2#3523811yescharacteristic
874C2#3525211yescharacteristic
875C2#3615712yes—
876C2#3620012yes—
877C2#3654412yes—
878C2#3657012yes—
879C2#3662411yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC22×#121C22
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×#2851C2semidirect
2. C2×#2566C2semidirect
4. C22×C4×C4⋊C4C2semidirect
5. #15234C2semidirect
6. #15222C2semidirect
7. #15196C2semidirect
8. #15134C2semidirect
9. #14864C2semidirect
10. #14729C2semidirect
13. #14686C2semidirect
14. #14682C2semidirect
15. #14198C2semidirect
16. #14160C2semidirect
17. #13975C2semidirect
18. #13941C2semidirect
19. #13909C2semidirect
200. C4×C4⋊C4D4semidirect
826. C22#2566semidirect

Maximal subgroups

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

subgroupindex
C2×#28512
C2×#25662
C2×C4×#1212
C22×C4×C4⋊C42
#152342
#152222
#151962
#151342
#148642
#147292
#146982
#146862
#146822
#141982
#141602
#139752
#139412
#139092