Finite Group Databasebeta

← #678228

Subgroups — #678228

Order 512.

3374 conjugacy classes of subgroups.

The subgroup lattice has 930 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2538C211yesmaximal, characteristic, complemented
2C2×#2354C211yesmaximal, characteristic, complemented
3C2×C4×C22⋊Q8C211yesmaximal, characteristic, complemented
4C2×C4×#121C211yesmaximal, characteristic
5#15839C214yesmaximal, complemented
6#15308C214yesmaximal, complemented
7#15219C212yesmaximal
8#15177C212yesmaximal, complemented
9#15147C212yesmaximal, complemented
10#15132C212yesmaximal, complemented
11#14686C211yesmaximal, characteristic, complemented
12#14150C212yesmaximal, complemented
13#14138C212yesmaximal, complemented
14#13993C212yesmaximal, complemented
15#13926C211yesmaximal, characteristic, complemented
16#13911C211yesmaximal, characteristic, complemented
17#13871C212yesmaximal, complemented
18C22×C22⋊Q8C2211yescharacteristic
19C22×C22⋊Q8C2212yes—
20C22×#121C2211yescharacteristic
21C22×C4×Q8C2211yescharacteristic
22C22×C4×D4C2212yes—
23C22×C4×D4C2211yescharacteristic
24C22×#117C2212yes—
25C23×C42C2211yescharacteristic
26#2538—28no—
27C2×#397C2214yes—
28C2×#396C2214yes—
29#2354—28no—
30C4×C22⋊Q8—28no—
31C4×#121—28no—
32C2×#391C2211yescharacteristic
33C2×#391C2212yes—
34C2×#390C2211yescharacteristic
35C2×#390C2212yes—
36C2×#390C2212yes—
37C2×#389C2211yescharacteristic
38C2×#389C2211yescharacteristic
39C2×#389C2212yes—
40C2×#388C2214yes—
41C2×#388C2212yes—
42C2×#387C2212yes—
43C2×#386C2212yes—
44C2×#385C2212yes—
45C2×#384C2211yescharacteristic
46C2×#384C2211yescharacteristic
47C2×#382C2212yes—
48C2×#380C2212yes—
49C2×#380C2212yes—
50C2×#380C2211yescharacteristic
51C2×#380C2212yes—
52C2×#380C2211yescharacteristic
53C2×#380C2212yes—
54C2×#380C2212yes—
55C2×C4×C4⋊C4C2212yes—
56C2×C4×C4⋊C4C2212yes—
57C2×C4×C4⋊C4C2211yescharacteristic
58C2×C4×C4⋊C4C2211yescharacteristic
59C2×C4×C22⋊C4C2212yes—
60C2×C4×C22⋊C4C2212yes—
61#1444C2214yes—
62#1443C2214yes—
63#1442C2214yes—
64#1442C2214yes—
65#1441C2214yes—
66#1440C2214yes—
67#1440C2214yes—
68#1440C2214yes—
69#1440C2214yes—
70#1439C2214yes—
71#1439C2214yes—
72#1438C2214yes—
73#1438C2214yes—
74#1437C2214yes—
75#1436C2214yes—
76#1436C2214yes—
77#1436C2214yes—
78C4⋊#95C2212yes—
79C4⋊#95C2212yes—
80C4⋊#95C2212yes—
81C4⋊#95C2212yes—
82C4⋊#95C2212yes—
83C4⋊#95C2212yes—
84C4⋊#95C2212yes—
85C4⋊#95C2212yes—
86C4⋊#95C2212yes—
87C23×Q8C2311yescharacteristic
88C23×D4C2311yescharacteristic
89C23×D4C2312yes—
90C24×C4C2312yes—
91C24×C4C2311yescharacteristic
92C24×C4C2311yescharacteristic
93C24×C4C2311yescharacteristic
94C2×C22⋊Q8—24no—
95C2×C22⋊Q8—24no—
96C2×C22⋊Q8—28no—
97C2×C22⋊Q8—28no—
98C2×C22⋊Q8—24no—
99C2×C22⋊Q8—44no—
100C2×#121—24no—
101C2×#121—24no—
102C2×#121—24no—
103C2×C4×Q8—24no—
104C2×C4×Q8—24no—
105C2×C4×Q8—24no—
106C2×C4×D4—28no—
107C2×C4×D4—28no—
108C2×C4×D4—24no—
109C2×C4×D4—24no—
110C2×C4×D4—44no—
111C2×C4×D4D418yes—
112C2×#117—28no—
113C2×#117—44no—
114C2×#117—44no—
115C22×C4⋊C4C2312yes—
116C22×C4⋊C4C2312yes—
117C22×C4⋊C4C2311yescharacteristic
118C22×C4⋊C4C2312yes—
119C22×C4⋊C4C2312yes—
120C22×C4⋊C4C2311yescharacteristic
121C22×C4⋊C4C2312yes—
122C22×C4⋊C4C2312yes—
123C22×C4⋊C4C2314yes—
124C22×C4⋊C4C2312yes—
125C22×C4⋊C4C2312yes—
126C22×C4⋊C4C2311yescharacteristic
127C22×C4⋊C4C2311yescharacteristic
128C22×C4⋊C4C2311yescharacteristic
129C22×C4⋊C4C2311yescharacteristic
130C22×C4⋊C4C2312yes—
131C22×C4⋊C4C2312yes—
132C22×C22⋊C4C2312yes—
133C22×C22⋊C4C2312yes—
134C22×C22⋊C4C2314yes—
135C22×C22⋊C4C2312yes—
136C22×C22⋊C4C2312yes—
137C22×C22⋊C4C2312yes—
138C22×C22⋊C4C2312yes—
139C22×C22⋊C4C2312yes—
140C22×C22⋊C4C2314yes—
141C22×C22⋊C4C2314yes—
142C22×C22⋊C4C2314yes—
143C22×C22⋊C4C2314yes—
144C22×C42—24no—
145C22×C42—24no—
146C22×C42—24no—
147C22×C42C2311yescharacteristic
148C22×C42C2311yescharacteristic
149C22×C42C2311yescharacteristic
150C22×C42C2312yes—
151C22×C42C2312yes—
152C22×C42C2312yes—
153C22×C42C2314yes—
154C22×C42C2311yescharacteristic
155#397—48no—
156#396—216no—
157#391—24no—
158#391—44no—
159#390—28no—
160#390—24no—
161#390—28no—
162#389—28no—
163#389—24no—
164#389—24no—
165#388—28no—
166#388—216no—
167#387—28no—
168#386—28no—
169#385—28no—
170#384—24no—
171#384—24no—
172#382—28no—
173#380—28no—
174#380—28no—
175#380—28no—
176#380—24no—
177#380—24no—
178#380—44no—
179#380—44no—
180C4×C4⋊C4—28no—
181C4×C4⋊C4—24no—
182C4×C4⋊C4—28no—
183C4×C4⋊C4D418yescomplemented
184C4×C22⋊C4—28no—
185C4×C22⋊C4—28no—
186C2×#95C2314yes—
187C2×#95C2314yes—
188C2×#95C2314yes—
189C2×#95C2314yes—
190C2×#95C2314yes—
191C2×#95C2312yes—
192C2×#95C2312yes—
193C2×#95C2312yes—
194C2×#95C2312yes—
195C2×#95C2312yes—
196C2×#95C2314yes—
197C2×#95C2312yes—
198C2×#95C2312yes—
199C2×#95C2314yes—
200C2×#95C2314yes—
201C2×#95C2314yes—
202C2×#95C2314yes—
203C2×#95C2314yes—
204C2×#95C2314yes—
205C2×#95C2314yes—
206C2×#95C2312yes—
207C25C2412yes—
208C25C2411yescharacteristic
209C22×Q8—22no—
210C22×Q8—22no—
211C22×Q8—22no—
212C22×Q8—22no—
213C22×Q8—22no—
214C22×Q8—22no—
215C22×Q8#4114yes—
216C22×D4—24no—
217C22×D4—24no—
218C22×D4—24no—
219C22×D4—24no—
220C22×D4—22no—
221C22×D4—22no—
222C22×D4—24no—
223C22×D4—22no—
224C22×D4—22no—
225C22×D4—22no—
226C22×D4—22no—
227C22×D4—42no—
228C22×D4—42no—
229C22×D4C2×D414yes—
230C23×C4—22no—
231C23×C4—24no—
232C23×C4—22no—
233C23×C4—22no—
234C23×C4—22no—
235C23×C4—22no—
236C23×C4—24no—
237C23×C4—24no—
238C23×C4—22no—
239C23×C4—22no—
240C23×C4—24no—
241C23×C4—22no—
242C23×C4—22no—
243C23×C4—22no—
244C23×C4—24no—
245C23×C4—24no—
246C23×C4—22no—
247C23×C4—22no—
248C23×C4—22no—
249C23×C4—22no—
250C23×C4—22no—
251C23×C4—22no—
252C23×C4—22no—
253C23×C4—41no—
254C23×C4—41no—
255C23×C4C2×D418yes—
256C23×C4#4114yes—
257C23×C4#4114yes—
258C23×C4C2414yes—
259C23×C4C2412yes—
260C23×C4C2414yes—
261C23×C4C2412yes—
262C23×C4C2412yes—
263C23×C4C2412yes—
264C23×C4C2412yes—
265C23×C4C2412yes—
266C23×C4C2411yescharacteristic
267C23×C4C2411yescharacteristic
268C23×C4C2412yes—
269C23×C4C2411yescharacteristic
270C23×C4C2411yescharacteristic
271C23×C4C2411yescharacteristic
272C23×C4C2411yescharacteristic
273C22⋊Q8—232no—
274C22⋊Q8—432no—
275#121—232no—
276C4×Q8—416no—
277C4×D4—232no—
278C4×D4—432no—
279#117—432no—
280C2×C4⋊C4—22no—
281C2×C4⋊C4—22no—
282C2×C4⋊C4—24no—
283C2×C4⋊C4—22no—
284C2×C4⋊C4—22no—
285C2×C4⋊C4—24no—
286C2×C4⋊C4—24no—
287C2×C4⋊C4—22no—
288C2×C4⋊C4—22no—
289C2×C4⋊C4—22no—
290C2×C4⋊C4—22no—
291C2×C4⋊C4—24no—
292C2×C4⋊C4—24no—
293C2×C4⋊C4—22no—
294C2×C4⋊C4—22no—
295C2×C4⋊C4—24no—
296C2×C4⋊C4—24no—
297C2×C4⋊C4—24no—
298C2×C4⋊C4—28no—
299C2×C4⋊C4—22no—
300C2×C4⋊C4—24no—
301C2×C4⋊C4—24no—
302C2×C4⋊C4—24no—
303C2×C4⋊C4—24no—
304C2×C4⋊C4—24no—
305C2×C4⋊C4—22no—
306C2×C4⋊C4—28no—
307C2×C4⋊C4—24no—
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—22no—
316C2×C4⋊C4—22no—
317C2×C4⋊C4—24no—
318C2×C4⋊C4—24no—
319C2×C4⋊C4—24no—
320C2×C4⋊C4—42no—
321C2×C4⋊C4—42no—
322C2×C4⋊C4—44no—
323C2×C4⋊C4—42no—
324C2×C4⋊C4—42no—
325C2×C4⋊C4—42no—
326C2×C4⋊C4—42no—
327C2×C4⋊C4C2×D414yes—
328C2×C4⋊C4C2×D414yes—
329C2×C4⋊C4C2×D414yes—
330C2×C4⋊C4#4114yes—
331C2×C22⋊C4—24no—
332C2×C22⋊C4—24no—
333C2×C22⋊C4—24no—
334C2×C22⋊C4—24no—
335C2×C22⋊C4—24no—
336C2×C22⋊C4—24no—
337C2×C22⋊C4—24no—
338C2×C22⋊C4—24no—
339C2×C22⋊C4—24no—
340C2×C22⋊C4—28no—
341C2×C22⋊C4—24no—
342C2×C22⋊C4—24no—
343C2×C22⋊C4—24no—
344C2×C22⋊C4—28no—
345C2×C22⋊C4—24no—
346C2×C22⋊C4—24no—
347C2×C22⋊C4—24no—
348C2×C22⋊C4—28no—
349C2×C22⋊C4—24no—
350C2×C22⋊C4—28no—
351C2×C22⋊C4—28no—
352C2×C22⋊C4—28no—
353C2×C22⋊C4—42no—
354C2×C22⋊C4—42no—
355C2×C22⋊C4—44no—
356C2×C22⋊C4—44no—
357C2×C22⋊C4—42no—
358C2×C22⋊C4—42no—
359C2×C22⋊C4—44no—
360C2×C22⋊C4—44no—
361C2×C22⋊C4—44no—
362C2×C22⋊C4—44no—
363C2×C22⋊C4—44no—
364C2×C22⋊C4—44no—
365C2×C22⋊C4—44no—
366C2×C22⋊C4C2×D418yes—
367C2×C42—24no—
368C2×C42—24no—
369C2×C42—28no—
370C2×C42—24no—
371C2×C42—24no—
372C2×C42—24no—
373C2×C42—22no—
374C2×C42—22no—
375C2×C42—22no—
376C2×C42—22no—
377C2×C42—22no—
378C2×C42—22no—
379C2×C42—24no—
380C2×C42—24no—
381C2×C42—22no—
382C2×C42—22no—
383C2×C42—22no—
384C2×C42—24no—
385C2×C42—44no—
386C2×C42—44no—
387C2×C42—416no—
388C2×C42C2×D418yes—
389C2×C42C2×D414yes—
390C2×C42C2×D414yes—
391C2×C42#4114yes—
392#95—24no—
393#95—24no—
394#95—24no—
395#95—24no—
396#95—24no—
397#95—28no—
398#95—24no—
399#95—24no—
400#95—28no—
401#95—28no—
402#95—28no—
403#95—28no—
404#95—28no—
405#95—44no—
406#95—44no—
407#95—44no—
408#95—44no—
409#95—44no—
410#95—44no—
411#95—44no—
412#95C2×D418yes—
413C24—21no—
414C24—21no—
415C24—21no—
416C24—21no—
417C24—21no—
418C24—21no—
419C24—21no—
420C24—21no—
421C24—21no—
422C24—21no—
423C24—21no—
424C24—21no—
425C24—22no—
426C24—22no—
427C24—22no—
428C24—22no—
429C24—22no—
430C24—22no—
431C24—22no—
432C24—22no—
433C24—22no—
434C24—22no—
435C24—22no—
436C24—22no—
437C24—22no—
438C24—22no—
439C24C22×D414yes—
440C24C2×#4112yes—
441C24C2×#4112yes—
442C242−1+412yes—
443C24C2511yescharacteristic
444C2×Q8—28no—
445C2×Q8—28no—
446C2×Q8—28no—
447C2×Q8—44no—
448C2×Q8—44no—
449C2×Q8—44no—
450C2×Q8—44no—
451C2×D4—216no—
452C2×D4—28no—
453C2×D4—28no—
454C2×D4—28no—
455C2×D4—48no—
456C2×D4—48no—
457C2×D4—48no—
458C2×D4—48no—
459C2×D4—48no—
460C2×D4—48no—
461C2×D4—44no—
462C2×D4—44no—
463C2×D4—44no—
464C2×D4—44no—
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—28no—
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—21no—
473C22×C4—22no—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—21no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—21no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—21no—
495C22×C4—22no—
496C22×C4—21no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—21no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—216no—
519C22×C4—28no—
520C22×C4—28no—
521C22×C4—28no—
522C22×C4—216no—
523C22×C4—216no—
524C22×C4—28no—
525C22×C4—28no—
526C22×C4—28no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—24no—
531C22×C4—24no—
532C22×C4—24no—
533C22×C4—24no—
534C22×C4—24no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—24no—
538C22×C4—24no—
539C22×C4—24no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—24no—
543C22×C4—22no—
544C22×C4—24no—
545C22×C4—24no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—24no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—24no—
553C22×C4—24no—
554C22×C4—22no—
555C22×C4—44no—
556C22×C4—44no—
557C22×C4—44no—
558C22×C4—44no—
559C22×C4—44no—
560C22×C4—44no—
561C22×C4—44no—
562C22×C4—44no—
563C22×C4—48no—
564C22×C4—48no—
565C22×C4—44no—
566C22×C4—44no—
567C22×C4—44no—
568C22×C4—44no—
569C22×C4—48no—
570C22×C4—44no—
571C22×C4—48no—
572C22×C4—44no—
573C22×C4C22×D414yes—
574C22×C4C22×D414yes—
575C22×C4C22×D414yes—
576C22×C4C22×D412yes—
577C22×C4C22×D412yes—
578C22×C4C22×D412yes—
579C22×C4C22×D412yes—
580C22×C4C22×D412yes—
581C22×C4C22×D412yes—
582C22×C4C2×#4112yes—
583C22×C4C2×#4114yes—
584C22×C4C2×#4114yes—
585C22×C4C2×#4112yes—
586C22×C4C2×#4112yes—
587C22×C4C2×#4112yes—
588C22×C4C2×#4112yes—
589C22×C4C2×#4112yes—
590C22×C4C2×#4112yes—
591C22×C4C2×#4112yes—
592C22×C4C2×#4112yes—
593C22×C4H(5,𝔽2)12yes—
594C22×C4H(5,𝔽2)12yes—
595C22×C4H(5,𝔽2)12yes—
596C22×C42−1+412yes—
597C22×C42−1+412yes—
598C4⋊C4—216no—
599C4⋊C4—28no—
600C4⋊C4—28no—
601C4⋊C4—28no—
602C4⋊C4—28no—
603C4⋊C4—48no—
604C4⋊C4—48no—
605C4⋊C4—416no—
606C4⋊C4—48no—
607C4⋊C4—44no—
608C4⋊C4—48no—
609C4⋊C4—48no—
610C4⋊C4—44no—
611C4⋊C4—48no—
612C4⋊C4—48no—
613C4⋊C4—84no—
614C4⋊C4—84no—
615C22⋊C4—216no—
616C22⋊C4—216no—
617C22⋊C4—216no—
618C22⋊C4—48no—
619C22⋊C4—48no—
620C22⋊C4—48no—
621C22⋊C4—48no—
622C22⋊C4—416no—
623C22⋊C4—416no—
624C22⋊C4—88no—
625C22⋊C4—88no—
626C22⋊C4—88no—
627C42—216no—
628C42—416no—
629C42—44no—
630C42—44no—
631C42—44no—
632C42—48no—
633C42—48no—
634C42#121116yes—
635C23—22no—
636C23—22no—
637C23—22no—
638C23—22no—
639C23—22no—
640C23—22no—
641C23—22no—
642C23—22no—
643C23—22no—
644C23—22no—
645C23—22no—
646C23—22no—
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—41no—
661C23—41no—
662C23—41no—
663C23—41no—
664C23—41no—
665C23—41no—
666C23—41no—
667C23—41no—
668C23—41no—
669C23—41no—
670C23—41no—
671C23—41no—
672C23—41no—
673C23—41no—
674C23—41no—
675C23—41no—
676C23—42no—
677C23—42no—
678C23—42no—
679C23—42no—
680C23—42no—
681C23—42no—
682C23—42no—
683C23—42no—
684C23—42no—
685C23—42no—
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#55614yes—
705C23C23×D411yescharacteristic
706C23C23×D411yescharacteristic
707C23C22×#4111yescharacteristic
708C23C22×#4111yescharacteristic
709C23C22×#4111yescharacteristic
710C23C22×#4111yescharacteristic
711C23C22×#4111yescharacteristic
712C23C2×H(5,𝔽2)11yescharacteristic
713C23C2×H(5,𝔽2)11yescharacteristic
714C23C2×H(5,𝔽2)11yescharacteristic
715C23C2×2−1+411yescharacteristic
716C23C2×2−1+411yescharacteristic
717C23C2×2−1+411yescharacteristic
718C23#58511yescharacteristic
719C23#58511yescharacteristic
720Q8—416no—
721D4—432no—
722D4—416no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—24no—
730C2×C4—22no—
731C2×C4—24no—
732C2×C4—24no—
733C2×C4—24no—
734C2×C4—22no—
735C2×C4—24no—
736C2×C4—22no—
737C2×C4—24no—
738C2×C4—24no—
739C2×C4—24no—
740C2×C4—24no—
741C2×C4—24no—
742C2×C4—22no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—24no—
746C2×C4—24no—
747C2×C4—22no—
748C2×C4—24no—
749C2×C4—22no—
750C2×C4—24no—
751C2×C4—22no—
752C2×C4—24no—
753C2×C4—416no—
754C2×C4—41no—
755C2×C4—41no—
756C2×C4—41no—
757C2×C4—42no—
758C2×C4—42no—
759C2×C4—42no—
760C2×C4—41no—
761C2×C4—42no—
762C2×C4—41no—
763C2×C4—42no—
764C2×C4—41no—
765C2×C4—42no—
766C2×C4—41no—
767C2×C4—41no—
768C2×C4—42no—
769C2×C4—42no—
770C2×C4—42no—
771C2×C4—41no—
772C2×C4—42no—
773C2×C4—42no—
774C2×C4—42no—
775C2×C4—41no—
776C2×C4—41no—
777C2×C4—42no—
778C2×C4—41no—
779C2×C4—42no—
780C2×C4—42no—
781C2×C4—42no—
782C2×C4—42no—
783C2×C4—42no—
784C2×C4—42no—
785C2×C4—42no—
786C2×C4—416no—
787C2×C4—416no—
788C2×C4—432no—
789C2×C4—42no—
790C2×C4—44no—
791C2×C4—44no—
792C2×C4—42no—
793C2×C4—42no—
794C2×C4—44no—
795C2×C4—44no—
796C2×C4—44no—
797C2×C4—44no—
798C2×C4—42no—
799C2×C4—42no—
800C2×C4—44no—
801C2×C4—44no—
802C2×C4—42no—
803C2×C4—42no—
804C2×C4—42no—
805C2×C4—42no—
806C2×C4—42no—
807C2×C4—44no—
808C2×C4—42no—
809C2×C4—44no—
810C2×C4—44no—
811C2×C4—42no—
812C2×C4—44no—
813C2×C4—42no—
814C2×C4—44no—
815C2×C4—42no—
816C2×C4—44no—
817C2×C4C2×#12114yes—
818C2×C4C2×#12114yes—
819C2×C4C2×#12114yes—
820C2×C4#52514yes—
821C2×C4#52514yes—
822C2×C4#53514yes—
823C2×C4#53614yes—
824C2×C4#54614yes—
825C2×C4#54614yes—
826C2×C4#54714yes—
827C2×C4#54814yes—
828C2×C4#55214yes—
829C2×C4#55314yes—
830C2×C4#55314yes—
831C2×C4#55614yes—
832C22—24no—
833C22—24no—
834C22—24no—
835C22—42no—
836C22—42no—
837C22—42no—
838C22—42no—
839C22—42no—
840C22—42no—
841C22—42no—
842C22—42no—
843C22—42no—
844C22—42no—
845C22—42no—
846C22—42no—
847C22—44no—
848C22—44no—
849C22—44no—
850C22—44no—
851C22—44no—
852C22—44no—
853C22—44no—
854C22—82no—
855C22—82no—
856C22—82no—
857C22—82no—
858C22—82no—
859C22—82no—
860C22—82no—
861C22—82no—
862C22C22×#12111yescharacteristic
863C22C2×#52511yescharacteristic
864C22C2×#52511yescharacteristic
865C22C2×#53511yescharacteristic
866C22C2×#53611yescharacteristic
867C22C2×#54611yescharacteristic
868C22C2×#54611yescharacteristic
869C22C2×#54711yescharacteristic
870C22C2×#54811yescharacteristic
871C22C2×#55211yescharacteristic
872C22C2×#55311yescharacteristic
873C22C2×#55311yescharacteristic
874C22C2×#55611yescharacteristic
875C22C2×#55611yescharacteristic
876C22#347511yescharacteristic
877C22#348011yescharacteristic
878C22#348311yescharacteristic
879C22#348811yescharacteristic
880C22#348811yescharacteristic
881C22#348911yescharacteristic
882C22#348911yescharacteristic
883C22#349211yescharacteristic
884C22#349311yescharacteristic
885C22#350611yescharacteristic
886C22#350711yescharacteristic
887C22#350811yescharacteristic
888C22#351111yescharacteristic
889C22#351711yescharacteristic
890C22#351811yescharacteristic
891C22#352011yescharacteristic
892C22#352311yescharacteristic
893C22#354711yescharacteristic
894C22#354811yescharacteristic
895C22#355211yescharacteristic
896C22#355411yescharacteristic
897C4—24no—
898C4—44no—
899C4—44no—
900C4—44no—
901C4—44no—
902C4—42no—
903C4—44no—
904C4—42no—
905C4—42no—
906C4—84no—
907C4—82no—
908C4—84no—
909C4—82no—
910C4#241518yes—
911C4#253518yes—
912C2—44no—
913C2—84no—
914C2C2×#241511yescharacteristic
915C2C2×#253511yescharacteristic
916C2#3551811yescharacteristic
917C2#3616111yescharacteristic
918C2#3641011yescharacteristic
919C2#3641111yescharacteristic
920C2#3657911yescharacteristic
921C2#3891111yescharacteristic
922C2#3892011yescharacteristic
923C2#3947011yescharacteristic
924C2#3972511yescharacteristic
925C2#5921111yescharacteristic
926C2#5921811yescharacteristic
927C2#5924311yescharacteristic
928C2#5930211yescharacteristic
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×#2538C2semidirect
2. C2×#2354C2semidirect
3. C2×C4×C22⋊Q8C2semidirect
5. #15839C2semidirect
6. #15308C2semidirect
8. #15177C2semidirect
9. #15147C2semidirect
10. #15132C2semidirect
11. #14686C2semidirect
12. #14150C2semidirect
13. #14138C2semidirect
14. #13993C2semidirect
15. #13926C2semidirect
16. #13911C2semidirect
17. #13871C2semidirect
183. C4×C4⋊C4D4semidirect

Maximal subgroups

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

subgroupindex
C2×#25382
C2×#23542
C2×C4×C22⋊Q82
C2×C4×#1212
#158392
#153082
#152192
#151772
#151472
#151322
#146862
#141502
#141382
#139932
#139262
#139112
#138712