Finite Group Databasebeta

← #4453558

Subgroups — #4453558

Order 512.

4148 conjugacy classes of subgroups.

The subgroup lattice has 911 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#540C211yesmaximal, characteristic
2C2×#2538C211yesmaximal, characteristic, complemented
3C2×#2580C211yesmaximal, characteristic, complemented
4C2×#2396C211yesmaximal, characteristic, complemented
5#16363C212yesmaximal, complemented
6#16360C212yesmaximal, complemented
7#16261C214yesmaximal, complemented
8#16257C214yesmaximal, complemented
9#16253C212yesmaximal, complemented
10#16251C212yesmaximal, complemented
11#15218C212yesmaximal, complemented
12#15127C212yesmaximal, complemented
13#15126C212yesmaximal, complemented
14#15126C212yesmaximal, complemented
15#14340C211yesmaximal, characteristic, complemented
16#13941C211yesmaximal, characteristic, complemented
17#13906C211yesmaximal, characteristic, complemented
18C2×#540—28no—
19C2×#540—28no—
20C2×#540—28no—
21C22×#127C2211yescharacteristic
22C22×#125C2211yescharacteristic
23C22×#123C2212yes—
24C22×#123C2212yes—
25C22×C22⋊Q8C2212yes—
26C22×#121C2211yescharacteristic
27C22×#121C2211yescharacteristic
28C22×#121C2212yes—
29C22×#121C2212yes—
30C22×C4×Q8C2211yescharacteristic
31C22×C4×D4C2211yescharacteristic
32C22×C4×D4C2211yescharacteristic
33C22×#117C2211yescharacteristic
34#2580—28no—
35#2538—28no—
36#2396—28no—
37C2×#400C2211yescharacteristic
38C2×#399C2212yes—
39C2×#399C2211yescharacteristic
40C2×#398C2212yes—
41C2×#396C2214yes—
42C2×#396C2212yes—
43C2×#395C2211yescharacteristic
44C2×#394C2214yes—
45C2×#394C2214yes—
46C2×#394C2214yes—
47C2×#394C2214yes—
48C2×#393C2212yes—
49C2×#393C2211yescharacteristic
50C2×#390C2212yes—
51C2×#390C2212yes—
52C2×#390C2212yes—
53C2×#390C2212yes—
54C2×#389C2212yes—
55C2×#389C2212yes—
56C2×#385C2214yes—
57C2×#384C2211yescharacteristic
58C2×#382C2211yescharacteristic
59C2×#380C2212yes—
60C2×#380C2212yes—
61C2×#380C2214yes—
62C2×C4×C4⋊C4C2212yes—
63C2×C4×C4⋊C4C2211yescharacteristic
64C2×C4×C22⋊C4C2212yes—
65#1444C2214yes—
66#1444C2214yes—
67#1441C2212yes—
68#1441C2212yes—
69#1441C2214yes—
70#1441C2214yes—
71#1440C2214yes—
72#1440C2214yes—
73#1439C2212yes—
74#1439C2212yes—
75#1439C2214yes—
76#1439C2214yes—
77#1439C2212yes—
78#1439C2212yes—
79#1439C2214yes—
80#1438C2214yes—
81#1438C2214yes—
82#1438C2214yes—
83#1438C2214yes—
84C4⋊#95C2212yes—
85C4⋊#95C2212yes—
86C4⋊#95C2212yes—
87C22⋊#95C2212yes—
88C22⋊#95C2212yes—
89C23×Q8C2311yescharacteristic
90C23×D4C2311yescharacteristic
91C23×D4C2311yescharacteristic
92C23×D4C2312yes—
93C23×D4C2312yes—
94C23×D4C2312yes—
95C23×D4C2312yes—
96C24×C4C2311yescharacteristic
97C24×C4C2312yes—
98C24×C4C2312yes—
99#540—2128no—
100C2×#127—24no—
101C2×#127—24no—
102C2×#127—24no—
103C2×#125—24no—
104C2×#125—24no—
105C2×#125—24no—
106C2×#123—28no—
107C2×#123—28no—
108C2×#123—28no—
109C2×#123—28no—
110C2×#123—28no—
111C2×#123—28no—
112C2×C22⋊Q8—28no—
113C2×C22⋊Q8—48no—
114C2×#121—24no—
115C2×#121—24no—
116C2×#121—28no—
117C2×#121—28no—
118C2×#121—24no—
119C2×#121—24no—
120C2×#121—24no—
121C2×#121—24no—
122C2×#121—28no—
123C2×#121—28no—
124C2×#121—28no—
125C2×#121—28no—
126C2×C4×Q8—24no—
127C2×C4×Q8—24no—
128C2×C4×Q8—24no—
129C2×C4×D4—24no—
130C2×C4×D4—24no—
131C2×C4×D4—24no—
132C2×C4×D4—24no—
133C2×C4×D4D418yes—
134C2×C4×D4D418yes—
135C2×#117—24no—
136C2×#117—24no—
137C2×#117D418yes—
138C22×C4⋊C4C2312yes—
139C22×C4⋊C4C2311yescharacteristic
140C22×C4⋊C4C2312yes—
141C22×C4⋊C4C2312yes—
142C22×C4⋊C4C2312yes—
143C22×C4⋊C4C2312yes—
144C22×C4⋊C4C2312yes—
145C22×C4⋊C4C2312yes—
146C22×C4⋊C4C2314yes—
147C22×C4⋊C4C2312yes—
148C22×C4⋊C4C2311yescharacteristic
149C22×C4⋊C4C2311yescharacteristic
150C22×C4⋊C4C2311yescharacteristic
151C22×C4⋊C4C2311yescharacteristic
152C22×C4⋊C4C2314yes—
153C22×C4⋊C4C2312yes—
154C22×C4⋊C4C2312yes—
155C22×C22⋊C4C2312yes—
156C22×C22⋊C4C2312yes—
157C22×C22⋊C4C2312yes—
158C22×C22⋊C4C2314yes—
159C22×C22⋊C4C2312yes—
160C22×C22⋊C4C2314yes—
161C22×C22⋊C4C2311yescharacteristic
162C22×C22⋊C4C2312yes—
163C22×C22⋊C4C2311yescharacteristic
164C22×C22⋊C4C2312yes—
165C22×C22⋊C4C2314yes—
166C22×C22⋊C4C2314yes—
167C22×C22⋊C4C2314yes—
168C22×C22⋊C4C2314yes—
169C22×C22⋊C4C2314yes—
170C22×C22⋊C4C2314yes—
171C22×C22⋊C4C2314yes—
172C22×C42C2312yes—
173C22×C42C2312yes—
174C22×C42C2311yescharacteristic
175C22×C42C2311yescharacteristic
176#400—24no—
177#399—28no—
178#399—24no—
179#398—28no—
180#396—28no—
181#396—216no—
182#395—24no—
183#394—48no—
184#394—48no—
185#394—48no—
186#394—48no—
187#393—28no—
188#393—24no—
189#390—28no—
190#390—28no—
191#390—44no—
192#390—44no—
193#389—28no—
194#389—28no—
195#385—216no—
196#384—24no—
197#382—24no—
198#380—28no—
199#380—48no—
200#380—44no—
201C4×C4⋊C4—28no—
202C4×C4⋊C4—24no—
203C4×C22⋊C4—28no—
204C2×#95C2312yes—
205C2×#95C2312yes—
206C2×#95C2311yescharacteristic
207C2×#95C2314yes—
208C2×#95C2314yes—
209C2×#95C2312yes—
210C2×#95C2311yescharacteristic
211C2×#95C2312yes—
212C2×#95C2314yes—
213C2×#95C2312yes—
214C2×#95C2312yes—
215C2×#95C2314yes—
216C2×#95C2314yes—
217C2×#95C2314yes—
218C2×#95C2314yes—
219C2×#95C2314yes—
220C2×#95C2314yes—
221C25C2412yes—
222C25C2412yes—
223C25C2411yescharacteristic
224C22×Q8—22no—
225C22×Q8—22no—
226C22×Q8—22no—
227C22×Q8—24no—
228C22×Q8—42no—
229C22×D4—24no—
230C22×D4—24no—
231C22×D4—24no—
232C22×D4—24no—
233C22×D4—24no—
234C22×D4—24no—
235C22×D4—24no—
236C22×D4—24no—
237C22×D4—22no—
238C22×D4—22no—
239C22×D4—22no—
240C22×D4—22no—
241C22×D4—24no—
242C22×D4—24no—
243C22×D4—24no—
244C22×D4—24no—
245C22×D4—22no—
246C22×D4—22no—
247C22×D4—22no—
248C22×D4—22no—
249C22×D4—22no—
250C22×D4—22no—
251C22×D4—22no—
252C22×D4—22no—
253C22×D4—44no—
254C22×D4—44no—
255C22×D4—44no—
256C22×D4—44no—
257C22×D4—44no—
258C22×D4—44no—
259C22×D4—44no—
260C22×D4—44no—
261C22×D4C2×D414yes—
262C22×D4C2×D414yes—
263C23×C4—22no—
264C23×C4—22no—
265C23×C4—22no—
266C23×C4—22no—
267C23×C4—22no—
268C23×C4—22no—
269C23×C4—24no—
270C23×C4—24no—
271C23×C4—24no—
272C23×C4—24no—
273C23×C4—44no—
274C23×C4—44no—
275C23×C4—44no—
276C23×C4—44no—
277C23×C4C2×D414yes—
278C23×C4C2×D418yes—
279C23×C4C2×D418yes—
280C23×C4C2412yes—
281C23×C4C2414yes—
282C23×C4C2414yes—
283C23×C4C2412yes—
284C23×C4C2411yescharacteristic
285C23×C4C2412yes—
286C23×C4C2412yes—
287C23×C4C2411yescharacteristic
288C23×C4C2411yescharacteristic
289C23×C4C2412yes—
290C23×C4C2412yes—
291C23×C4C2411yescharacteristic
292C23×C4C2411yescharacteristic
293C23×C4C2411yescharacteristic
294#127—232no—
295#125—232no—
296#123—264no—
297#123—264no—
298C22⋊Q8—432no—
299#121—232no—
300#121—232no—
301#121—264no—
302#121—264no—
303C4×Q8—416no—
304C4×D4—232no—
305C4×D4—232no—
306#117—232no—
307C2×C4⋊C4—22no—
308C2×C4⋊C4—22no—
309C2×C4⋊C4—22no—
310C2×C4⋊C4—22no—
311C2×C4⋊C4—22no—
312C2×C4⋊C4—22no—
313C2×C4⋊C4—22no—
314C2×C4⋊C4—22no—
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—22no—
322C2×C4⋊C4—24no—
323C2×C4⋊C4—24no—
324C2×C4⋊C4—24no—
325C2×C4⋊C4—22no—
326C2×C4⋊C4—22no—
327C2×C4⋊C4—24no—
328C2×C4⋊C4—28no—
329C2×C4⋊C4—24no—
330C2×C4⋊C4—24no—
331C2×C4⋊C4—24no—
332C2×C4⋊C4—24no—
333C2×C4⋊C4—24no—
334C2×C4⋊C4—28no—
335C2×C4⋊C4—24no—
336C2×C4⋊C4—24no—
337C2×C4⋊C4—24no—
338C2×C4⋊C4—24no—
339C2×C4⋊C4—24no—
340C2×C4⋊C4—24no—
341C2×C4⋊C4—24no—
342C2×C4⋊C4—24no—
343C2×C4⋊C4—28no—
344C2×C4⋊C4—42no—
345C2×C4⋊C4—42no—
346C2×C4⋊C4—42no—
347C2×C4⋊C4—44no—
348C2×C4⋊C4—44no—
349C2×C4⋊C4—44no—
350C2×C4⋊C4—44no—
351C2×C4⋊C4—44no—
352C2×C4⋊C4C2×D414yes—
353C2×C4⋊C4C2×D414yes—
354C2×C4⋊C4C2×D414yes—
355C2×C4⋊C4C2×D414yes—
356C2×C22⋊C4—24no—
357C2×C22⋊C4—24no—
358C2×C22⋊C4—22no—
359C2×C22⋊C4—22no—
360C2×C22⋊C4—22no—
361C2×C22⋊C4—22no—
362C2×C22⋊C4—24no—
363C2×C22⋊C4—24no—
364C2×C22⋊C4—24no—
365C2×C22⋊C4—24no—
366C2×C22⋊C4—24no—
367C2×C22⋊C4—24no—
368C2×C22⋊C4—24no—
369C2×C22⋊C4—24no—
370C2×C22⋊C4—28no—
371C2×C22⋊C4—24no—
372C2×C22⋊C4—24no—
373C2×C22⋊C4—28no—
374C2×C22⋊C4—28no—
375C2×C22⋊C4—24no—
376C2×C22⋊C4—28no—
377C2×C22⋊C4—24no—
378C2×C22⋊C4—28no—
379C2×C22⋊C4—28no—
380C2×C22⋊C4—28no—
381C2×C22⋊C4—28no—
382C2×C22⋊C4—44no—
383C2×C22⋊C4—42no—
384C2×C22⋊C4—42no—
385C2×C22⋊C4—44no—
386C2×C22⋊C4—44no—
387C2×C22⋊C4—44no—
388C2×C22⋊C4—44no—
389C2×C22⋊C4—44no—
390C2×C22⋊C4—44no—
391C2×C22⋊C4—44no—
392C2×C22⋊C4—44no—
393C2×C22⋊C4—44no—
394C2×C22⋊C4—44no—
395C2×C22⋊C4—44no—
396C2×C22⋊C4—44no—
397C2×C22⋊C4—44no—
398C2×C22⋊C4—44no—
399C2×C22⋊C4—44no—
400C2×C22⋊C4—44no—
401C2×C22⋊C4—44no—
402C2×C22⋊C4—44no—
403C2×C22⋊C4C2×D414yes—
404C2×C22⋊C4C2×D414yes—
405C2×C22⋊C4C2×D418yes—
406C2×C22⋊C4C2×D418yes—
407C2×C42—22no—
408C2×C42—22no—
409C2×C42—24no—
410C2×C42—24no—
411C2×C42—24no—
412C2×C42—24no—
413C2×C42—24no—
414C2×C42—24no—
415C2×C42C2×D414yes—
416C2×C42C2×D414yes—
417C2×C42C2×D414yes—
418C2×C42C2×D414yes—
419#95—24no—
420#95—24no—
421#95—24no—
422#95—22no—
423#95—22no—
424#95—24no—
425#95—28no—
426#95—24no—
427#95—24no—
428#95—28no—
429#95—28no—
430#95—44no—
431#95—44no—
432#95—44no—
433#95—44no—
434#95—44no—
435#95—44no—
436C24—21no—
437C24—21no—
438C24—22no—
439C24—22no—
440C24—22no—
441C24—22no—
442C24—24no—
443C24—24no—
444C24—22no—
445C24—24no—
446C24—22no—
447C24—24no—
448C24—21no—
449C24—22no—
450C24—22no—
451C24—21no—
452C24—21no—
453C24—21no—
454C24—22no—
455C24—22no—
456C24—22no—
457C24—22no—
458C24—22no—
459C24—22no—
460C24—24no—
461C24—24no—
462C24—22no—
463C24—24no—
464C24—22no—
465C24—24no—
466C24C22×D414yes—
467C24C22×D414yes—
468C24C22×D412yes—
469C24C2511yescharacteristic
470C2×Q8—28no—
471C2×Q8—48no—
472C2×Q8—48no—
473C2×Q8—44no—
474C2×Q8—44no—
475C2×D4—216no—
476C2×D4—216no—
477C2×D4—216no—
478C2×D4—216no—
479C2×D4—28no—
480C2×D4—28no—
481C2×D4—28no—
482C2×D4—28no—
483C2×D4—28no—
484C2×D4—28no—
485C2×D4—44no—
486C2×D4—44no—
487C2×D4—44no—
488C2×D4—44no—
489C2×D4—44no—
490C2×D4—44no—
491C2×D4—44no—
492C2×D4—44no—
493C2×D4—84no—
494C2×D4—84no—
495C2×D4—88no—
496C2×D4—88no—
497C2×D4—88no—
498C2×D4—84no—
499C2×D4—84no—
500C2×D4—88no—
501C2×D4—88no—
502C2×D4—88no—
503C2×D4—88no—
504C2×D4—88no—
505C2×D4—84no—
506C2×D4—84no—
507C2×D4—84no—
508C2×D4—84no—
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—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—24no—
528C22×C4—21no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—24no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—22no—
540C22×C4—24no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—24no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—28no—
548C22×C4—28no—
549C22×C4—28no—
550C22×C4—216no—
551C22×C4—216no—
552C22×C4—22no—
553C22×C4—24no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—24no—
557C22×C4—22no—
558C22×C4—24no—
559C22×C4—22no—
560C22×C4—24no—
561C22×C4—24no—
562C22×C4—22no—
563C22×C4—24no—
564C22×C4—24no—
565C22×C4—24no—
566C22×C4—24no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—24no—
571C22×C4—22no—
572C22×C4—24no—
573C22×C4—24no—
574C22×C4—24no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—24no—
579C22×C4—22no—
580C22×C4—48no—
581C22×C4—48no—
582C22×C4—416no—
583C22×C4—44no—
584C22×C4—44no—
585C22×C4—44no—
586C22×C4—44no—
587C22×C4—88no—
588C22×C4—88no—
589C22×C4—88no—
590C22×C4—84no—
591C22×C4—84no—
592C22×C4C22×D412yes—
593C22×C4C22×D412yes—
594C22×C4C22×D412yes—
595C22×C4C22×D414yes—
596C22×C4C22×D414yes—
597C22×C4C22×D412yes—
598C22×C4C22×D412yes—
599C22×C4C22×D412yes—
600C22×C4C22×D412yes—
601C22×C4C22×D412yes—
602C22×C4C22×D412yes—
603C22×C4C22×D412yes—
604C22×C4C22×D412yes—
605C22×C4C22×D412yes—
606C22×C4H(5,𝔽2)14yes—
607C22×C4H(5,𝔽2)14yes—
608C22×C4H(5,𝔽2)12yes—
609C22×C42−1+412yes—
610C22×C42−1+412yes—
611C22×C42−1+412yes—
612C4⋊C4—216no—
613C4⋊C4—216no—
614C4⋊C4—28no—
615C4⋊C4—28no—
616C4⋊C4—28no—
617C4⋊C4—28no—
618C4⋊C4—48no—
619C4⋊C4—48no—
620C4⋊C4—48no—
621C4⋊C4—416no—
622C4⋊C4—48no—
623C4⋊C4—48no—
624C4⋊C4—44no—
625C4⋊C4—48no—
626C4⋊C4—48no—
627C4⋊C4—84no—
628C4⋊C4—88no—
629C22⋊C4—216no—
630C22⋊C4—216no—
631C22⋊C4—28no—
632C22⋊C4—28no—
633C22⋊C4—216no—
634C22⋊C4—216no—
635C22⋊C4—416no—
636C22⋊C4—48no—
637C22⋊C4—48no—
638C22⋊C4—416no—
639C22⋊C4—88no—
640C22⋊C4—88no—
641C22⋊C4—88no—
642C22⋊C4—88no—
643C22⋊C4—88no—
644C22⋊C4—88no—
645C22⋊C4—88no—
646C42—28no—
647C42—48no—
648C42—48no—
649C42#120116yes—
650C23—22no—
651C23—24no—
652C23—24no—
653C23—22no—
654C23—24no—
655C23—24no—
656C23—22no—
657C23—24no—
658C23—24no—
659C23—24no—
660C23—24no—
661C23—24no—
662C23—24no—
663C23—28no—
664C23—28no—
665C23—24no—
666C23—24no—
667C23—41no—
668C23—41no—
669C23—42no—
670C23—42no—
671C23—42no—
672C23—42no—
673C23—41no—
674C23—41no—
675C23—42no—
676C23—42no—
677C23—42no—
678C23—42no—
679C23—41no—
680C23—42no—
681C23—41no—
682C23—42no—
683C23—44no—
684C23—44no—
685C23—44no—
686C23—44no—
687C23—42no—
688C23—44no—
689C23—42no—
690C23—44no—
691C23—42no—
692C23—41no—
693C23—42no—
694C23—41no—
695C23—42no—
696C23—44no—
697C23—44no—
698C23—42no—
699C23—44no—
700C23—44no—
701C23—42no—
702C23—44no—
703C23—44no—
704C23—42no—
705C23—42no—
706C23—44no—
707C23—44no—
708C23—44no—
709C23—44no—
710C23—44no—
711C23—42no—
712C23—44no—
713C23—44no—
714C23—42no—
715C23—44no—
716C23—44no—
717C23—42no—
718C23—44no—
719C23C23×D411yescharacteristic
720C23C23×D411yescharacteristic
721C23C23×D411yescharacteristic
722C23C2×H(5,𝔽2)11yescharacteristic
723C23C2×H(5,𝔽2)12yes—
724C23C2×H(5,𝔽2)12yes—
725C23C2×2−1+411yescharacteristic
726C23C2×2−1+411yescharacteristic
727C23C2×2−1+411yescharacteristic
728C23#58512yes—
729C23#58512yes—
730Q8—416no—
731D4—416no—
732D4—416no—
733D4—816no—
734D4—816no—
735D4—816no—
736D4—816no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—24no—
740C2×C4—24no—
741C2×C4—24no—
742C2×C4—24no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—24no—
749C2×C4—24no—
750C2×C4—22no—
751C2×C4—22no—
752C2×C4—24no—
753C2×C4—24no—
754C2×C4—24no—
755C2×C4—24no—
756C2×C4—24no—
757C2×C4—24no—
758C2×C4—24no—
759C2×C4—24no—
760C2×C4—28no—
761C2×C4—24no—
762C2×C4—24no—
763C2×C4—42no—
764C2×C4—41no—
765C2×C4—41no—
766C2×C4—42no—
767C2×C4—41no—
768C2×C4—41no—
769C2×C4—41no—
770C2×C4—41no—
771C2×C4—42no—
772C2×C4—42no—
773C2×C4—44no—
774C2×C4—44no—
775C2×C4—44no—
776C2×C4—42no—
777C2×C4—42no—
778C2×C4—42no—
779C2×C4—42no—
780C2×C4—42no—
781C2×C4—41no—
782C2×C4—42no—
783C2×C4—41no—
784C2×C4—42no—
785C2×C4—42no—
786C2×C4—416no—
787C2×C4—42no—
788C2×C4—42no—
789C2×C4—44no—
790C2×C4—44no—
791C2×C4—44no—
792C2×C4—42no—
793C2×C4—42no—
794C2×C4—44no—
795C2×C4—42no—
796C2×C4—42no—
797C2×C4—42no—
798C2×C4—44no—
799C2×C4—42no—
800C2×C4—42no—
801C2×C4—44no—
802C2×C4—42no—
803C2×C4—42no—
804C2×C4—44no—
805C2×C4—44no—
806C2×C4—44no—
807C2×C4—42no—
808C2×C4—44no—
809C2×C4—44no—
810C2×C4—44no—
811C2×C4—44no—
812C2×C4—42no—
813C2×C4—42no—
814C2×C4—44no—
815C2×C4—816no—
816C2×C4—816no—
817C2×C4C2×#12014yes—
818C2×C4C2×#12014yes—
819C2×C4C2×#12014yes—
820C2×C4#53614yes—
821C2×C4#53614yes—
822C2×C4#53614yes—
823C2×C4#53714yes—
824C2×C4#53714yes—
825C2×C4#53714yes—
826C22—42no—
827C22—44no—
828C22—44no—
829C22—44no—
830C22—44no—
831C22—44no—
832C22—44no—
833C22—44no—
834C22—42no—
835C22—44no—
836C22—44no—
837C22—42no—
838C22—44no—
839C22—44no—
840C22—44no—
841C22—48no—
842C22—48no—
843C22—81no—
844C22—82no—
845C22—84no—
846C22—84no—
847C22—81no—
848C22—82no—
849C22—84no—
850C22—84no—
851C22—81no—
852C22—82no—
853C22—81no—
854C22—82no—
855C22—82no—
856C22—84no—
857C22—82no—
858C22—84no—
859C22C22×#12011yescharacteristic
860C22C2×#53611yescharacteristic
861C22C2×#53611yescharacteristic
862C22C2×#53611yescharacteristic
863C22C2×#53711yescharacteristic
864C22C2×#53711yescharacteristic
865C22C2×#53711yescharacteristic
866C22#348411yescharacteristic
867C22#348511yescharacteristic
868C22#348812yes—
869C22#348812yes—
870C22#348812yes—
871C22#349612yes—
872C22#349811yescharacteristic
873C22#350011yescharacteristic
874C22#354312yes—
875C22#354712yes—
876C22#354812yes—
877C22#355412yes—
878C22#355412yes—
879C22#355712yes—
880C22#355912yes—
881C22#356212yes—
882C4—24no—
883C4—24no—
884C4—42no—
885C4—44no—
886C4—44no—
887C4—42no—
888C4—44no—
889C4—44no—
890C4—42no—
891C4—82no—
892C4—82no—
893C4—84no—
894C4—84no—
895C4#261618yes—
896C2—82no—
897C2—84no—
898C2—84no—
899C2C2×#261611yescharacteristic
900C2#3551211yescharacteristic
901C2#3551311yescharacteristic
902C2#3727412yes—
903C2#3727612yes—
904C2#4242511yescharacteristic
905C2#4243111yescharacteristic
906C2#4243912yes—
907C2#4244412yes—
908C2#4264511yescharacteristic
909C2#4265111yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC22×#540C2
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24 ◁ G
LECSG ▷ C24 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C2×#2538C2semidirect
3. C2×#2580C2semidirect
4. C2×#2396C2semidirect
5. #16363C2semidirect
6. #16360C2semidirect
7. #16261C2semidirect
8. #16257C2semidirect
9. #16253C2semidirect
10. #16251C2semidirect
11. #15218C2semidirect
12. #15127C2semidirect
13. #15126C2semidirect
14. #15126C2semidirect
15. #14340C2semidirect
16. #13941C2semidirect
17. #13906C2semidirect

Maximal subgroups

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

subgroupindex
C22×#5402
C2×#25382
C2×#25802
C2×#23962
#163632
#163602
#162612
#162572
#162532
#162512
#152182
#151272
#151262
#143402
#139412
#139062