Finite Group Databasebeta

← #678234

Subgroups — #678234

Order 512.

3678 conjugacy classes of subgroups.

The subgroup lattice has 959 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2857C211yesmaximal, characteristic, complemented
2C2×#2568C211yesmaximal, characteristic, complemented
3C2×#2547C211yesmaximal, characteristic, complemented
4C2×#2538C211yesmaximal, characteristic, complemented
5C2×C4×C22⋊Q8C211yesmaximal, characteristic, complemented
6C2×C4×#121C211yesmaximal, characteristic
7#15808C214yesmaximal, complemented
8#15526C214yesmaximal, complemented
9#15223C212yesmaximal, complemented
10#15215C212yesmaximal
11#15193C212yesmaximal, complemented
12#15177C212yesmaximal, complemented
13#14153C212yesmaximal, complemented
14#13997C212yesmaximal, complemented
15#13997C212yesmaximal, complemented
16#13905C212yesmaximal, complemented
17C4⋊C42C211yesmaximal, characteristic, complemented
18C22×C4⋊Q8C2211yescharacteristic
19C22×#124C2212yes—
20C22×C22⋊Q8C2211yescharacteristic
21C22×C22⋊Q8C2212yes—
22C22×C22⋊Q8C2212yes—
23C22×#121C2211yescharacteristic
24C22×C4×Q8C2211yescharacteristic
25C22×C4×D4C2211yescharacteristic
26C22×C4×D4C2212yes—
27C23×C42C2211yescharacteristic
28#2857—28no—
29#2568—28no—
30#2547—28no—
31#2538—28no—
32C2×#400C2214yes—
33C2×#397C2214yes—
34C2×#396C2214yes—
35C4×C22⋊Q8—28no—
36C4×#121—28no—
37C2×#391C2212yes—
38C2×#391C2212yes—
39C2×#391C2212yes—
40C2×#391C2212yes—
41C2×#391C2212yes—
42C2×#391C2211yescharacteristic
43C2×#390C2211yescharacteristic
44C2×#390C2212yes—
45C2×#389C2212yes—
46C2×#389C2212yes—
47C2×#389C2211yescharacteristic
48C2×#389C2212yes—
49C2×#389C2211yescharacteristic
50C2×#388C2212yes—
51C2×#387C2212yes—
52C2×#386C2212yes—
53C2×#385C2212yes—
54C2×#384C2211yescharacteristic
55C2×#382C2212yes—
56C2×#380C2212yes—
57C2×#380C2212yes—
58C2×#380C2212yes—
59C2×#380C2211yescharacteristic
60C2×#380C2212yes—
61C2×#380C2212yes—
62C2×#380C2211yescharacteristic
63C2×C4×C4⋊C4C2212yes—
64C2×C4×C4⋊C4C2212yes—
65C2×C4×C4⋊C4C2212yes—
66C2×C4×C4⋊C4C2211yescharacteristic
67C2×C4×C4⋊C4C2211yescharacteristic
68C2×C4×C22⋊C4C2212yes—
69C2×C4×C22⋊C4C2212yes—
70#1445C2214yes—
71#1445C2214yes—
72#1445C2214yes—
73#1445C2214yes—
74#1444C2214yes—
75#1439C2214yes—
76#1439C2214yes—
77#1439C2214yes—
78#1439C2214yes—
79#1439C2214yes—
80#1438C2214yes—
81#1438C2214yes—
82#1437C2214yes—
83#1437C2214yes—
84#1437C2214yes—
85#1436C2214yes—
86C4⋊#95C2212yes—
87C4⋊#95C2212yes—
88C4⋊#95C2214yes—
89C23×Q8C2312yes—
90C23×Q8C2311yescharacteristic
91C23×D4C2311yescharacteristic
92C23×D4C2312yes—
93C24×C4C2312yes—
94C24×C4C2311yescharacteristic
95C24×C4C2311yescharacteristic
96C24×C4C2311yescharacteristic
97C2×C4⋊Q8—24no—
98C2×C4⋊Q8—24no—
99C2×C4⋊Q8—24no—
100C2×#124—28no—
101C2×#124—28no—
102C2×#124—44no—
103C2×C22⋊Q8—24no—
104C2×C22⋊Q8—24no—
105C2×C22⋊Q8—28no—
106C2×C22⋊Q8—28no—
107C2×C22⋊Q8—24no—
108C2×C22⋊Q8—28no—
109C2×C22⋊Q8—28no—
110C2×C22⋊Q8—44no—
111C2×C22⋊Q8—44no—
112C2×#121—24no—
113C2×#121—24no—
114C2×#121—24no—
115C2×C4×Q8—24no—
116C2×C4×Q8—24no—
117C2×C4×Q8—24no—
118C2×C4×D4—28no—
119C2×C4×D4—24no—
120C2×C4×D4—24no—
121C2×C4×D4—28no—
122C2×C4×D4—24no—
123C2×C4×D4—44no—
124C22×C4⋊C4C2312yes—
125C22×C4⋊C4C2312yes—
126C22×C4⋊C4C2311yescharacteristic
127C22×C4⋊C4C2311yescharacteristic
128C22×C4⋊C4C2312yes—
129C22×C4⋊C4C2312yes—
130C22×C4⋊C4C2314yes—
131C22×C4⋊C4C2312yes—
132C22×C4⋊C4C2314yes—
133C22×C4⋊C4C2312yes—
134C22×C4⋊C4C2311yescharacteristic
135C22×C4⋊C4C2311yescharacteristic
136C22×C4⋊C4C2312yes—
137C22×C4⋊C4C2312yes—
138C22×C4⋊C4C2311yescharacteristic
139C22×C4⋊C4C2311yescharacteristic
140C22×C4⋊C4C2312yes—
141C22×C22⋊C4C2312yes—
142C22×C22⋊C4C2312yes—
143C22×C22⋊C4C2312yes—
144C22×C22⋊C4C2314yes—
145C22×C22⋊C4C2314yes—
146C22×C22⋊C4C2314yes—
147C22×C22⋊C4C2312yes—
148C22×C22⋊C4C2312yes—
149C22×C22⋊C4C2314yes—
150C22×C22⋊C4C2312yes—
151C22×C22⋊C4C2312yes—
152C22×C22⋊C4C2314yes—
153C22×C42—24no—
154C22×C42—24no—
155C22×C42—24no—
156C22×C42C2311yescharacteristic
157C22×C42C2311yescharacteristic
158C22×C42C2311yescharacteristic
159C22×C42C2312yes—
160C22×C42C2312yes—
161C22×C42C2312yes—
162C22×C42C2314yes—
163C22×C42C2311yescharacteristic
164#400—216no—
165#397—216no—
166#396—216no—
167#391—28no—
168#391—28no—
169#391—28no—
170#391—24no—
171#391—28no—
172#391—28no—
173#390—28no—
174#390—24no—
175#389—28no—
176#389—28no—
177#389—28no—
178#389—24no—
179#389—24no—
180#388—28no—
181#387—28no—
182#386—28no—
183#385—28no—
184#384D418yescomplemented
185#382—28no—
186#380—28no—
187#380—28no—
188#380—28no—
189#380—28no—
190#380—28no—
191#380—24no—
192#380—24no—
193C4×C4⋊C4—28no—
194C4×C4⋊C4—44no—
195C4×C4⋊C4—44no—
196C4×C4⋊C4D418yes—
197C4×C4⋊C4D418yescomplemented
198C4×C22⋊C4—28no—
199C4×C22⋊C4—28no—
200C2×#95C2314yes—
201C2×#95C2314yes—
202C2×#95C2314yes—
203C2×#95C2314yes—
204C2×#95C2314yes—
205C2×#95C2314yes—
206C2×#95C2314yes—
207C2×#95C2312yes—
208C2×#95C2312yes—
209C2×#95C2312yes—
210C2×#95C2312yes—
211C2×#95C2314yes—
212C2×#95C2314yes—
213C2×#95C2312yes—
214C2×#95C2312yes—
215C2×#95C2314yes—
216C2×#95C2314yes—
217C2×#95C2314yes—
218C2×#95C2312yes—
219C2×#95C2312yes—
220C25C2412yes—
221C25C2411yescharacteristic
222C22×Q8—22no—
223C22×Q8—22no—
224C22×Q8—22no—
225C22×Q8—24no—
226C22×Q8—24no—
227C22×Q8—24no—
228C22×Q8—22no—
229C22×Q8—24no—
230C22×Q8—24no—
231C22×Q8—22no—
232C22×Q8—24no—
233C22×Q8—22no—
234C22×Q8—24no—
235C22×Q8#4114yes—
236C22×D4—24no—
237C22×D4—24no—
238C22×D4—24no—
239C22×D4—24no—
240C22×D4—24no—
241C22×D4—22no—
242C22×D4—22no—
243C22×D4—22no—
244C22×D4—22no—
245C22×D4—22no—
246C22×D4—22no—
247C22×D4—42no—
248C22×D4—42no—
249C22×D4#4114yes—
250C23×C4—22no—
251C23×C4—22no—
252C23×C4—22no—
253C23×C4—22no—
254C23×C4—22no—
255C23×C4—22no—
256C23×C4—22no—
257C23×C4—22no—
258C23×C4—22no—
259C23×C4—22no—
260C23×C4—22no—
261C23×C4—22no—
262C23×C4—22no—
263C23×C4—22no—
264C23×C4—22no—
265C23×C4—24no—
266C23×C4—24no—
267C23×C4—24no—
268C23×C4—22no—
269C23×C4—22no—
270C23×C4—24no—
271C23×C4—24no—
272C23×C4—24no—
273C23×C4—24no—
274C23×C4—41no—
275C23×C4—41no—
276C23×C4#4114yes—
277C23×C4#4114yes—
278C23×C4C2414yes—
279C23×C4C2412yes—
280C23×C4C2412yes—
281C23×C4C2414yes—
282C23×C4C2412yes—
283C23×C4C2412yes—
284C23×C4C2412yes—
285C23×C4C2412yes—
286C23×C4C2412yes—
287C23×C4C2411yescharacteristic
288C23×C4C2411yescharacteristic
289C23×C4C2411yescharacteristic
290C23×C4C2411yescharacteristic
291C23×C4C2411yescharacteristic
292C23×C4C2411yescharacteristic
293C4⋊Q8—416no—
294#124—432no—
295C22⋊Q8—232no—
296C22⋊Q8—432no—
297C22⋊Q8—432no—
298#121—232no—
299C4×Q8—416no—
300C4×D4—432no—
301C4×D4—416no—
302C2×C4⋊C4—24no—
303C2×C4⋊C4—22no—
304C2×C4⋊C4—22no—
305C2×C4⋊C4—24no—
306C2×C4⋊C4—24no—
307C2×C4⋊C4—22no—
308C2×C4⋊C4—22no—
309C2×C4⋊C4—24no—
310C2×C4⋊C4—24no—
311C2×C4⋊C4—24no—
312C2×C4⋊C4—24no—
313C2×C4⋊C4—22no—
314C2×C4⋊C4—22no—
315C2×C4⋊C4—22no—
316C2×C4⋊C4—22no—
317C2×C4⋊C4—22no—
318C2×C4⋊C4—24no—
319C2×C4⋊C4—22no—
320C2×C4⋊C4—22no—
321C2×C4⋊C4—22no—
322C2×C4⋊C4—22no—
323C2×C4⋊C4—22no—
324C2×C4⋊C4—24no—
325C2×C4⋊C4—24no—
326C2×C4⋊C4—24no—
327C2×C4⋊C4—28no—
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—24no—
335C2×C4⋊C4—24no—
336C2×C4⋊C4—24no—
337C2×C4⋊C4—28no—
338C2×C4⋊C4—28no—
339C2×C4⋊C4—24no—
340C2×C4⋊C4—42no—
341C2×C4⋊C4—42no—
342C2×C4⋊C4—42no—
343C2×C4⋊C4—42no—
344C2×C4⋊C4—44no—
345C2×C4⋊C4—44no—
346C2×C4⋊C4C2×D414yes—
347C2×C4⋊C4C2×D414yes—
348C2×C4⋊C4C2×D418yes—
349C2×C4⋊C4C2×D418yes—
350C2×C4⋊C4C2×D414yes—
351C2×C4⋊C4C2×D414yes—
352C2×C4⋊C4C2×D418yes—
353C2×C22⋊C4—24no—
354C2×C22⋊C4—24no—
355C2×C22⋊C4—24no—
356C2×C22⋊C4—24no—
357C2×C22⋊C4—24no—
358C2×C22⋊C4—24no—
359C2×C22⋊C4—24no—
360C2×C22⋊C4—28no—
361C2×C22⋊C4—28no—
362C2×C22⋊C4—28no—
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—28no—
370C2×C22⋊C4—28no—
371C2×C22⋊C4—28no—
372C2×C22⋊C4—28no—
373C2×C22⋊C4—24no—
374C2×C22⋊C4—24no—
375C2×C22⋊C4—24no—
376C2×C22⋊C4—28no—
377C2×C22⋊C4—24no—
378C2×C22⋊C4—28no—
379C2×C22⋊C4—42no—
380C2×C22⋊C4—42no—
381C2×C22⋊C4—42no—
382C2×C22⋊C4—42no—
383C2×C22⋊C4—44no—
384C2×C22⋊C4—44no—
385C2×C22⋊C4—44no—
386C2×C22⋊C4—44no—
387C2×C22⋊C4—44no—
388C2×C22⋊C4—44no—
389C2×C42—24no—
390C2×C42—24no—
391C2×C42—24no—
392C2×C42—24no—
393C2×C42—24no—
394C2×C42—24no—
395C2×C42—24no—
396C2×C42—22no—
397C2×C42—22no—
398C2×C42—22no—
399C2×C42—22no—
400C2×C42—22no—
401C2×C42—22no—
402C2×C42—22no—
403C2×C42—22no—
404C2×C42—22no—
405C2×C42—416no—
406C2×C42—44no—
407C2×C42—44no—
408C2×C42—44no—
409C2×C42C2×D418yes—
410C2×C42C2×D418yes—
411C2×C42C2×D414yes—
412C2×C42C2×D414yes—
413C2×C42C2×D414yes—
414#95—24no—
415#95—24no—
416#95—24no—
417#95—24no—
418#95—24no—
419#95—24no—
420#95—28no—
421#95—28no—
422#95—28no—
423#95—28no—
424#95—28no—
425#95—28no—
426#95—28no—
427#95—28no—
428#95—28no—
429#95—44no—
430#95—44no—
431#95—44no—
432#95C2×D418yes—
433#95C2×D418yes—
434C24—21no—
435C24—21no—
436C24—21no—
437C24—21no—
438C24—21no—
439C24—21no—
440C24—21no—
441C24—21no—
442C24—21no—
443C24—21no—
444C24—21no—
445C24—21no—
446C24—22no—
447C24—22no—
448C24—22no—
449C24—22no—
450C24—22no—
451C24—22no—
452C24—22no—
453C24—22no—
454C24—22no—
455C24—22no—
456C24—22no—
457C24—22no—
458C24—22no—
459C24—22no—
460C24C2×#4114yes—
461C24C2×#4112yes—
462C24C2×#4112yes—
463C242−1+412yes—
464C24C2511yescharacteristic
465C2×Q8—28no—
466C2×Q8—28no—
467C2×Q8—28no—
468C2×Q8—48no—
469C2×Q8—44no—
470C2×Q8—48no—
471C2×Q8—44no—
472C2×Q8—48no—
473C2×Q8—44no—
474C2×Q8—48no—
475C2×Q8—48no—
476C2×Q8—44no—
477C2×Q8—48no—
478C2×Q8—48no—
479C2×D4—216no—
480C2×D4—28no—
481C2×D4—28no—
482C2×D4—28no—
483C2×D4—48no—
484C2×D4—48no—
485C2×D4—48no—
486C2×D4—48no—
487C2×D4—48no—
488C2×D4—48no—
489C2×D4—44no—
490C2×D4—44no—
491C2×D4—44no—
492C2×D4—44no—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—21no—
497C22×C4—28no—
498C22×C4—21no—
499C22×C4—21no—
500C22×C4—21no—
501C22×C4—22no—
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—21no—
506C22×C4—22no—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—21no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—24no—
518C22×C4—24no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—21no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—24no—
528C22×C4—24no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—21no—
532C22×C4—22no—
533C22×C4—21no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—24no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—24no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—28no—
553C22×C4—28no—
554C22×C4—28no—
555C22×C4—28no—
556C22×C4—28no—
557C22×C4—28no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—24no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—24no—
565C22×C4—22no—
566C22×C4—24no—
567C22×C4—24no—
568C22×C4—22no—
569C22×C4—24no—
570C22×C4—22no—
571C22×C4—24no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—24no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—44no—
580C22×C4—44no—
581C22×C4—44no—
582C22×C4—44no—
583C22×C4—44no—
584C22×C4—44no—
585C22×C4—44no—
586C22×C4—44no—
587C22×C4—44no—
588C22×C4—44no—
589C22×C4—44no—
590C22×C4—44no—
591C22×C4—44no—
592C22×C4—44no—
593C22×C4—48no—
594C22×C4—48no—
595C22×C4—48no—
596C22×C4—48no—
597C22×C4—48no—
598C22×C4—48no—
599C22×C4—48no—
600C22×C4C22×D414yes—
601C22×C4C22×D414yes—
602C22×C4C22×D414yes—
603C22×C4C22×D414yes—
604C22×C4C22×D418yes—
605C22×C4C22×D412yes—
606C22×C4C22×D412yes—
607C22×C4C22×D412yes—
608C22×C4C22×D412yes—
609C22×C4C22×D412yes—
610C22×C4C22×D412yes—
611C22×C4C22×D412yes—
612C22×C4C22×D412yes—
613C22×C4C22×D412yes—
614C22×C4C2×#4114yes—
615C22×C4C2×#4112yes—
616C22×C4C2×#4112yes—
617C22×C4C2×#4112yes—
618C22×C4C2×#4112yes—
619C22×C4C2×#4112yes—
620C22×C4C2×#4112yes—
621C22×C4H(5,𝔽2)12yes—
622C22×C4H(5,𝔽2)12yes—
623C22×C42−1+412yes—
624C22×C42−1+412yes—
625C22×C42−1+412yes—
626C4⋊C4—216no—
627C4⋊C4—28no—
628C4⋊C4—28no—
629C4⋊C4—28no—
630C4⋊C4—28no—
631C4⋊C4—216no—
632C4⋊C4—216no—
633C4⋊C4—48no—
634C4⋊C4—48no—
635C4⋊C4—48no—
636C4⋊C4—416no—
637C4⋊C4—416no—
638C4⋊C4—44no—
639C4⋊C4—48no—
640C4⋊C4—44no—
641C4⋊C4—48no—
642C4⋊C4—48no—
643C22⋊C4—216no—
644C22⋊C4—216no—
645C22⋊C4—48no—
646C22⋊C4—48no—
647C22⋊C4—416no—
648C22⋊C4—48no—
649C22⋊C4—48no—
650C22⋊C4—416no—
651C22⋊C4—416no—
652C22⋊C4—416no—
653C22⋊C4—48no—
654C22⋊C4—88no—
655C42—216no—
656C42—216no—
657C42—44no—
658C42—44no—
659C42—44no—
660C42—48no—
661C42—88no—
662C42#127116yes—
663C23—22no—
664C23—22no—
665C23—22no—
666C23—22no—
667C23—22no—
668C23—22no—
669C23—22no—
670C23—22no—
671C23—22no—
672C23—22no—
673C23—22no—
674C23—22no—
675C23—22no—
676C23—22no—
677C23—22no—
678C23—22no—
679C23—22no—
680C23—22no—
681C23—24no—
682C23—24no—
683C23—24no—
684C23—24no—
685C23—24no—
686C23—24no—
687C23—24no—
688C23—41no—
689C23—41no—
690C23—41no—
691C23—41no—
692C23—41no—
693C23—41no—
694C23—41no—
695C23—41no—
696C23—41no—
697C23—41no—
698C23—41no—
699C23—41no—
700C23—41no—
701C23—41no—
702C23—41no—
703C23—41no—
704C23—42no—
705C23—42no—
706C23—42no—
707C23—42no—
708C23—42no—
709C23—42no—
710C23—42no—
711C23—42no—
712C23—42no—
713C23—42no—
714C23—42no—
715C23—42no—
716C23—42no—
717C23—42no—
718C23—42no—
719C23—42no—
720C23—42no—
721C23—42no—
722C23—42no—
723C23—42no—
724C23—42no—
725C23—42no—
726C23—42no—
727C23—42no—
728C23—42no—
729C23—42no—
730C23—42no—
731C23—42no—
732C23#55614yes—
733C23C23×D411yescharacteristic
734C23C23×D411yescharacteristic
735C23C23×D411yescharacteristic
736C23C22×#4111yescharacteristic
737C23C22×#4111yescharacteristic
738C23C22×#4111yescharacteristic
739C23C22×#4111yescharacteristic
740C23C2×H(5,𝔽2)11yescharacteristic
741C23C2×H(5,𝔽2)11yescharacteristic
742C23C2×2−1+411yescharacteristic
743C23C2×2−1+411yescharacteristic
744C23C2×2−1+411yescharacteristic
745C23C2×2−1+411yescharacteristic
746C23#58511yescharacteristic
747C23#58511yescharacteristic
748Q8—416no—
749Q8—816no—
750D4—432no—
751D4—416no—
752C2×C4—22no—
753C2×C4—22no—
754C2×C4—22no—
755C2×C4—22no—
756C2×C4—22no—
757C2×C4—22no—
758C2×C4—22no—
759C2×C4—24no—
760C2×C4—24no—
761C2×C4—24no—
762C2×C4—22no—
763C2×C4—24no—
764C2×C4—24no—
765C2×C4—24no—
766C2×C4—24no—
767C2×C4—24no—
768C2×C4—24no—
769C2×C4—22no—
770C2×C4—24no—
771C2×C4—28no—
772C2×C4—28no—
773C2×C4—22no—
774C2×C4—22no—
775C2×C4—22no—
776C2×C4—24no—
777C2×C4—28no—
778C2×C4—22no—
779C2×C4—22no—
780C2×C4—24no—
781C2×C4—24no—
782C2×C4—22no—
783C2×C4—24no—
784C2×C4—24no—
785C2×C4—416no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—42no—
790C2×C4—41no—
791C2×C4—41no—
792C2×C4—42no—
793C2×C4—41no—
794C2×C4—41no—
795C2×C4—42no—
796C2×C4—41no—
797C2×C4—41no—
798C2×C4—42no—
799C2×C4—42no—
800C2×C4—42no—
801C2×C4—42no—
802C2×C4—44no—
803C2×C4—42no—
804C2×C4—41no—
805C2×C4—41no—
806C2×C4—41no—
807C2×C4—44no—
808C2×C4—42no—
809C2×C4—42no—
810C2×C4—42no—
811C2×C4—42no—
812C2×C4—42no—
813C2×C4—42no—
814C2×C4—44no—
815C2×C4—42no—
816C2×C4—42no—
817C2×C4—42no—
818C2×C4—42no—
819C2×C4—44no—
820C2×C4—42no—
821C2×C4—42no—
822C2×C4—416no—
823C2×C4—416no—
824C2×C4—42no—
825C2×C4—44no—
826C2×C4—42no—
827C2×C4—42no—
828C2×C4—44no—
829C2×C4—42no—
830C2×C4—44no—
831C2×C4—44no—
832C2×C4—42no—
833C2×C4—44no—
834C2×C4—42no—
835C2×C4—42no—
836C2×C4—42no—
837C2×C4—44no—
838C2×C4—44no—
839C2×C4—42no—
840C2×C4—42no—
841C2×C4—42no—
842C2×C4—42no—
843C2×C4—42no—
844C2×C4—42no—
845C2×C4—816no—
846C2×C4#52514yes—
847C2×C4#52514yes—
848C2×C4C2×#12714yes—
849C2×C4C2×#12714yes—
850C2×C4C2×#12714yes—
851C2×C4#53714yes—
852C2×C4#53714yes—
853C2×C4#54614yes—
854C2×C4#54614yes—
855C2×C4#54614yes—
856C2×C4#54614yes—
857C2×C4#54814yes—
858C2×C4#54814yes—
859C2×C4#54814yes—
860C2×C4#54814yes—
861C22—24no—
862C22—24no—
863C22—24no—
864C22—42no—
865C22—42no—
866C22—42no—
867C22—42no—
868C22—42no—
869C22—42no—
870C22—42no—
871C22—42no—
872C22—42no—
873C22—42no—
874C22—42no—
875C22—42no—
876C22—44no—
877C22—44no—
878C22—44no—
879C22—44no—
880C22—44no—
881C22—44no—
882C22—44no—
883C22—82no—
884C22—82no—
885C22—82no—
886C22—82no—
887C22—82no—
888C22—82no—
889C22—82no—
890C22—82no—
891C22C2×#52511yescharacteristic
892C22C2×#52511yescharacteristic
893C22C22×#12711yescharacteristic
894C22C2×#53711yescharacteristic
895C22C2×#53711yescharacteristic
896C22C2×#54611yescharacteristic
897C22C2×#54611yescharacteristic
898C22C2×#54611yescharacteristic
899C22C2×#54611yescharacteristic
900C22C2×#54811yescharacteristic
901C22C2×#54811yescharacteristic
902C22C2×#54811yescharacteristic
903C22C2×#54811yescharacteristic
904C22C2×#55611yescharacteristic
905C22#347511yescharacteristic
906C22#348011yescharacteristic
907C22#348211yescharacteristic
908C22#348511yescharacteristic
909C22#348611yescharacteristic
910C22#348911yescharacteristic
911C22#348911yescharacteristic
912C22#348911yescharacteristic
913C22#348911yescharacteristic
914C22#350611yescharacteristic
915C22#350711yescharacteristic
916C22#350911yescharacteristic
917C22#351111yescharacteristic
918C22#351511yescharacteristic
919C22#351711yescharacteristic
920C22#352011yescharacteristic
921C22#352311yescharacteristic
922C22#354611yescharacteristic
923C22#355011yescharacteristic
924C22#355211yescharacteristic
925C22#355511yescharacteristic
926C4—24no—
927C4—44no—
928C4—42no—
929C4—44no—
930C4—44no—
931C4—42no—
932C4—42no—
933C4—44no—
934C4—48no—
935C4—44no—
936C4—82no—
937C4—82no—
938C4—84no—
939C4#254018yes—
940C4#254018yes—
941C2—44no—
942C2—84no—
943C2C2×#254011yescharacteristic
944C2C2×#254011yescharacteristic
945C2#3563411yescharacteristic
946C2#3616111yescharacteristic
947C2#3640411yescharacteristic
948C2#3650511yescharacteristic
949C2#3657911yescharacteristic
950C2#3890811yescharacteristic
951C2#3912711yescharacteristic
952C2#3946811yescharacteristic
953C2#3972711yescharacteristic
954C2#5903311yescharacteristic
955C2#5904211yescharacteristic
956C2#5907911yescharacteristic
957C2#5913411yescharacteristic
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×#2857C2semidirect
2. C2×#2568C2semidirect
3. C2×#2547C2semidirect
4. C2×#2538C2semidirect
5. C2×C4×C22⋊Q8C2semidirect
7. #15808C2semidirect
8. #15526C2semidirect
9. #15223C2semidirect
11. #15193C2semidirect
12. #15177C2semidirect
13. #14153C2semidirect
14. #13997C2semidirect
15. #13997C2semidirect
16. #13905C2semidirect
17. C4⋊C42C2semidirect
184. #384D4semidirect
197. C4×C4⋊C4D4semidirect

Maximal subgroups

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

subgroupindex
C2×#28572
C2×#25682
C2×#25472
C2×#25382
C2×C4×C22⋊Q82
C2×C4×#1212
#158082
#155262
#152232
#152152
#151932
#151772
#141532
#139972
#139052
C4⋊C422