Finite Group Databasebeta

← #873681

Subgroups — #873681

Order 512.

3636 conjugacy classes of subgroups.

The subgroup lattice has 976 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2850C211yesmaximal, characteristic, complemented
2C2×#2538C211yesmaximal, characteristic, complemented
3C2×#2432C211yesmaximal, characteristic, complemented
4C2×#2407C211yesmaximal, characteristic
5#16533C214yesmaximal, complemented
6#15496C214yesmaximal, complemented
7#15328C214yesmaximal, complemented
8#15240C211yesmaximal, characteristic, complemented
9#15236C211yesmaximal, characteristic, complemented
10#15233C211yesmaximal, characteristic, complemented
11#15219C211yesmaximal, characteristic, complemented
12#15178C211yesmaximal, characteristic, complemented
13#15136C211yesmaximal, characteristic, complemented
14#14702C211yesmaximal, characteristic, complemented
15#14526C214yesmaximal, complemented
16#14026C211yesmaximal, characteristic, complemented
17#14024C211yesmaximal, characteristic, complemented
18#13937C211yesmaximal, characteristic, complemented
19C4×#386C211yesmaximal, characteristic, complemented
20C23×#41C2211yescharacteristic
21C22×C4⋊Q8C2211yescharacteristic
22C22×#124C2211yescharacteristic
23C22×C22⋊Q8C2211yescharacteristic
24C22×C22⋊Q8C2211yescharacteristic
25C22×C22⋊Q8C2211yescharacteristic
26C22×#121C2211yescharacteristic
27C22×C4×Q8C2211yescharacteristic
28C22×C4×D4C2211yescharacteristic
29C23×C42C2211yescharacteristic
30#2850—28no—
31#2538—28no—
32#2432—28no—
33#2407—28no—
34C2×#397C2214yes—
35C2×#396C2212yes—
36C2×#396C2212yes—
37C2×#394C2214yes—
38C2×#394C2212yes—
39C2×#392C2212yes—
40C2×#391C2211yescharacteristic
41C2×#391C2211yescharacteristic
42C2×#391C2211yescharacteristic
43C2×#391C2211yescharacteristic
44C2×#391C2211yescharacteristic
45C2×#391C2211yescharacteristic
46C2×#390C2211yescharacteristic
47C2×#390C2211yescharacteristic
48C2×#390C2211yescharacteristic
49C2×#390C2212yes—
50C2×#390C2211yescharacteristic
51C2×#389C2212yes—
52C2×#388C2214yes—
53C2×#386C2214yes—
54C2×#386C2212yes—
55C2×#386C2212yes—
56C2×#385C2212yes—
57C2×#385C2214yes—
58C2×#384C2211yescharacteristic
59C2×#382C2211yescharacteristic
60C2×#382C2211yescharacteristic
61C2×#380C2211yescharacteristic
62C2×#380C2211yescharacteristic
63C2×#380C2211yescharacteristic
64C2×C4×C22⋊C4C2211yescharacteristic
65C2×C4×C22⋊C4C2211yescharacteristic
66C2×C4×C22⋊C4C2211yescharacteristic
67#1445C2214yes—
68#1445C2214yes—
69#1444C2214yes—
70#1443C2214yes—
71#1442C2214yes—
72#1441C2214yes—
73#1440C2214yes—
74#1440C2214yes—
75#1440C2214yes—
76#1439C2214yes—
77#1439C2214yes—
78#1439C2214yes—
79#1438C2214yes—
80#1438C2214yes—
81#1437C2214yes—
82#1437C2212yes—
83#1436C2214yes—
84#1436C2214yes—
85#1436C2212yes—
86C4⋊#95C2211yescharacteristic
87C4⋊#95C2211yescharacteristic
88C4⋊#95C2211yescharacteristic
89C4⋊#95C2211yescharacteristic
90C22⋊#95C2214yes—
91C22⋊#95C2214yes—
92C22⋊#95C2212yes—
93C4×#95C2211yescharacteristic
94C4×#95C2211yescharacteristic
95C22×#41—24no—
96C22×#41—24no—
97C22×#41—24no—
98C22×#41—42no—
99C22×#41—42no—
100C22×#41—42no—
101C22×#41—42no—
102C23×Q8C2311yescharacteristic
103C23×Q8C2311yescharacteristic
104C23×D4C2311yescharacteristic
105C23×D4C2312yes—
106C23×D4C2311yescharacteristic
107C23×D4C2312yes—
108C24×C4C2311yescharacteristic
109C24×C4C2311yescharacteristic
110C24×C4C2312yes—
111C24×C4C2312yes—
112C2×C4⋊Q8—24no—
113C2×C4⋊Q8—24no—
114C2×C4⋊Q8—42no—
115C2×#124—42no—
116C2×#124—42no—
117C2×#124D418yescomplemented
118C2×C22⋊Q8—24no—
119C2×C22⋊Q8—24no—
120C2×C22⋊Q8—24no—
121C2×C22⋊Q8—24no—
122C2×C22⋊Q8—24no—
123C2×C22⋊Q8—24no—
124C2×C22⋊Q8—42no—
125C2×C22⋊Q8—42no—
126C2×C22⋊Q8—42no—
127C2×#121—24no—
128C2×#121—24no—
129C2×#121—42no—
130C2×C4×Q8—24no—
131C2×C4×Q8—42no—
132C2×C4×Q8—42no—
133C2×C4×D4—42no—
134C2×C4×D4—42no—
135C2×C4×D4D418yes—
136C22×C4⋊C4C2312yes—
137C22×C4⋊C4C2311yescharacteristic
138C22×C4⋊C4C2311yescharacteristic
139C22×C4⋊C4C2311yescharacteristic
140C22×C4⋊C4C2311yescharacteristic
141C22×C4⋊C4C2311yescharacteristic
142C22×C4⋊C4C2312yes—
143C22×C4⋊C4C2314yes—
144C22×C4⋊C4C2312yes—
145C22×C4⋊C4C2312yes—
146C22×C4⋊C4C2312yes—
147C22×C4⋊C4C2312yes—
148C22×C4⋊C4C2311yescharacteristic
149C22×C22⋊C4C2312yes—
150C22×C22⋊C4C2312yes—
151C22×C22⋊C4C2312yes—
152C22×C22⋊C4C2312yes—
153C22×C22⋊C4C2314yes—
154C22×C22⋊C4C2312yes—
155C22×C22⋊C4C2312yes—
156C22×C22⋊C4C2314yes—
157C22×C22⋊C4C2312yes—
158C22×C22⋊C4C2312yes—
159C22×C22⋊C4C2312yes—
160C22×C22⋊C4C2312yes—
161C22×C22⋊C4C2312yes—
162C22×C22⋊C4C2312yes—
163C22×C22⋊C4C2314yes—
164C22×C22⋊C4C2311yescharacteristic
165C22×C22⋊C4C2314yes—
166C22×C22⋊C4C2311yescharacteristic
167C22×C42—24no—
168C22×C42—42no—
169C22×C42—42no—
170C22×C42C2311yescharacteristic
171C22×C42C2311yescharacteristic
172C22×C42C2311yescharacteristic
173C22×C42C2311yescharacteristic
174C22×C42C2311yescharacteristic
175C22×C42C2312yes—
176C22×C42C2312yes—
177#397—216no—
178#396—28no—
179#396—28no—
180#394—28no—
181#394—216no—
182#392—28no—
183#391—24no—
184#391—24no—
185#391—24no—
186#391—42no—
187#391—42no—
188#391—42no—
189#390—24no—
190#390—24no—
191#390—28no—
192#390—24no—
193#390—42no—
194#389—28no—
195#388—216no—
196#386—216no—
197#386—28no—
198#386—28no—
199#385—28no—
200#385—216no—
201#384—24no—
202#382—24no—
203#382—42no—
204#380—24no—
205#380—24no—
206#380—24no—
207C4×C22⋊C4—24no—
208C4×C22⋊C4—42no—
209C4×C22⋊C4—42no—
210C2×#95C2312yes—
211C2×#95C2314yes—
212C2×#95C2312yes—
213C2×#95C2312yes—
214C2×#95C2312yes—
215C2×#95C2314yes—
216C2×#95C2314yes—
217C2×#95C2312yes—
218C2×#95C2312yes—
219C2×#95C2314yes—
220C2×#95C2314yes—
221C2×#95C2312yes—
222C2×#95C2312yes—
223C2×#95C2312yes—
224C2×#95C2312yes—
225C2×#95C2314yes—
226C2×#95C2314yes—
227C2×#95C2314yes—
228C2×#95C2314yes—
229C2×#95C2312yes—
230C2×#95C2314yes—
231C2×#95C2314yes—
232C2×#95C2312yes—
233C25C2411yescharacteristic
234C25C2412yes—
235C25C2411yescharacteristic
236C2×#41—416no—
237C2×#41—416no—
238C2×#41—416no—
239C2×#41—416no—
240C2×#41—416no—
241C2×#41—416no—
242C2×#41—416no—
243C22×Q8—22no—
244C22×Q8—22no—
245C22×Q8—22no—
246C22×Q8—22no—
247C22×Q8—22no—
248C22×Q8—22no—
249C22×Q8—22no—
250C22×Q8—22no—
251C22×Q8—22no—
252C22×Q8—22no—
253C22×Q8—22no—
254C22×Q8—22no—
255C22×Q8C2×D414yes—
256C22×Q8#4114yes—
257C22×D4—24no—
258C22×D4—24no—
259C22×D4—24no—
260C22×D4—24no—
261C22×D4—24no—
262C22×D4—28no—
263C22×D4—22no—
264C22×D4—22no—
265C22×D4—24no—
266C22×D4—24no—
267C22×D4—22no—
268C22×D4—22no—
269C22×D4—22no—
270C22×D4—22no—
271C22×D4—41no—
272C22×D4—41no—
273C22×D4—42no—
274C22×D4—42no—
275C22×D4—42no—
276C22×D4—42no—
277C22×D4—42no—
278C22×D4—44no—
279C22×D4C2×D414yes—
280C22×D4C2×D414yes—
281C23×C4—22no—
282C23×C4—22no—
283C23×C4—22no—
284C23×C4—22no—
285C23×C4—22no—
286C23×C4—22no—
287C23×C4—22no—
288C23×C4—22no—
289C23×C4—22no—
290C23×C4—22no—
291C23×C4—22no—
292C23×C4—22no—
293C23×C4—24no—
294C23×C4—24no—
295C23×C4—24no—
296C23×C4—24no—
297C23×C4—24no—
298C23×C4—24no—
299C23×C4—42no—
300C23×C4—42no—
301C23×C4—42no—
302C23×C4—42no—
303C23×C4—42no—
304C23×C4—42no—
305C23×C4—42no—
306C23×C4—42no—
307C23×C4C2×D414yes—
308C23×C4C2×D414yes—
309C23×C4C2412yes—
310C23×C4C2412yes—
311C23×C4C2412yes—
312C23×C4C2412yes—
313C23×C4C2412yes—
314C23×C4C2412yes—
315C23×C4C2412yes—
316C23×C4C2411yescharacteristic
317C23×C4C2411yescharacteristic
318C23×C4C2412yes—
319C23×C4C2411yescharacteristic
320C23×C4C2412yes—
321C23×C4C2412yes—
322C23×C4C2412yes—
323C23×C4C2411yescharacteristic
324C23×C4C2411yescharacteristic
325C4⋊Q8—416no—
326#124—416no—
327C22⋊Q8—416no—
328C22⋊Q8—416no—
329C22⋊Q8—416no—
330#121—416no—
331C4×Q8—416no—
332C4×D4—416no—
333C2×C4⋊C4—22no—
334C2×C4⋊C4—24no—
335C2×C4⋊C4—22no—
336C2×C4⋊C4—22no—
337C2×C4⋊C4—22no—
338C2×C4⋊C4—22no—
339C2×C4⋊C4—22no—
340C2×C4⋊C4—22no—
341C2×C4⋊C4—24no—
342C2×C4⋊C4—24no—
343C2×C4⋊C4—24no—
344C2×C4⋊C4—24no—
345C2×C4⋊C4—24no—
346C2×C4⋊C4—22no—
347C2×C4⋊C4—28no—
348C2×C4⋊C4—24no—
349C2×C4⋊C4—24no—
350C2×C4⋊C4—22no—
351C2×C4⋊C4—28no—
352C2×C4⋊C4—28no—
353C2×C4⋊C4—22no—
354C2×C4⋊C4—22no—
355C2×C4⋊C4—22no—
356C2×C4⋊C4—22no—
357C2×C4⋊C4—22no—
358C2×C4⋊C4—22no—
359C2×C4⋊C4—24no—
360C2×C4⋊C4—41no—
361C2×C4⋊C4—41no—
362C2×C4⋊C4—42no—
363C2×C4⋊C4—42no—
364C2×C4⋊C4—42no—
365C2×C4⋊C4—42no—
366C2×C4⋊C4—42no—
367C2×C4⋊C4—44no—
368C2×C4⋊C4—44no—
369C2×C4⋊C4C2×D414yes—
370C2×C22⋊C4—24no—
371C2×C22⋊C4—24no—
372C2×C22⋊C4—24no—
373C2×C22⋊C4—24no—
374C2×C22⋊C4—28no—
375C2×C22⋊C4—28no—
376C2×C22⋊C4—24no—
377C2×C22⋊C4—24no—
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—24no—
386C2×C22⋊C4—28no—
387C2×C22⋊C4—28no—
388C2×C22⋊C4—28no—
389C2×C22⋊C4—24no—
390C2×C22⋊C4—24no—
391C2×C22⋊C4—24no—
392C2×C22⋊C4—24no—
393C2×C22⋊C4—42no—
394C2×C22⋊C4—44no—
395C2×C22⋊C4—44no—
396C2×C22⋊C4—42no—
397C2×C22⋊C4—41no—
398C2×C22⋊C4—41no—
399C2×C22⋊C4—41no—
400C2×C22⋊C4—41no—
401C2×C22⋊C4—42no—
402C2×C22⋊C4—42no—
403C2×C22⋊C4—42no—
404C2×C22⋊C4—42no—
405C2×C22⋊C4—44no—
406C2×C22⋊C4—44no—
407C2×C22⋊C4—42no—
408C2×C22⋊C4—42no—
409C2×C22⋊C4—44no—
410C2×C22⋊C4—44no—
411C2×C22⋊C4—44no—
412C2×C22⋊C4—44no—
413C2×C22⋊C4—44no—
414C2×C22⋊C4—44no—
415C2×C22⋊C4—44no—
416C2×C22⋊C4C2×D414yes—
417C2×C22⋊C4C2×D414yes—
418C2×C22⋊C4C2×D4116yes—
419C2×C42—22no—
420C2×C42—22no—
421C2×C42—22no—
422C2×C42—22no—
423C2×C42—24no—
424C2×C42—22no—
425C2×C42—24no—
426C2×C42—22no—
427C2×C42—22no—
428C2×C42—22no—
429C2×C42—22no—
430C2×C42—22no—
431C2×C42—22no—
432C2×C42—22no—
433C2×C42—22no—
434C2×C42—416no—
435C2×C42—42no—
436C2×C42—42no—
437C2×C42—42no—
438C2×C42—42no—
439C2×C42C2×D414yes—
440C2×C42C2×D414yes—
441#95—24no—
442#95—24no—
443#95—24no—
444#95—24no—
445#95—28no—
446#95—24no—
447#95—28no—
448#95—28no—
449#95—24no—
450#95—24no—
451#95—28no—
452#95—28no—
453#95—42no—
454#95—44no—
455#95—44no—
456#95—42no—
457#95—42no—
458#95—42no—
459#95—44no—
460#95—44no—
461#95—44no—
462#95—44no—
463#95#4118yescomplemented
464C24—21no—
465C24—21no—
466C24—22no—
467C24—21no—
468C24—21no—
469C24—21no—
470C24—21no—
471C24—22no—
472C24—22no—
473C24—21no—
474C24—22no—
475C24—24no—
476C24—22no—
477C24—21no—
478C24—22no—
479C24—21no—
480C24—21no—
481C24—22no—
482C24—22no—
483C24—22no—
484C24—21no—
485C24—21no—
486C24—22no—
487C24—22no—
488C24—24no—
489C24—24no—
490C24—22no—
491C24—22no—
492C24—24no—
493C24C22×D412yes—
494C24C22×D414yes—
495C24C22×D412yes—
496C242−1+414yes—
497C24C2511yescharacteristic
498#41—4128no—
499C2×Q8—28no—
500C2×Q8—28no—
501C2×Q8—28no—
502C2×Q8—28no—
503C2×Q8—28no—
504C2×Q8—28no—
505C2×Q8—44no—
506C2×Q8—44no—
507C2×Q8—44no—
508C2×Q8—44no—
509C2×Q8—44no—
510C2×Q8—44no—
511C2×Q8—44no—
512C2×Q8—44no—
513C2×D4—28no—
514C2×D4—28no—
515C2×D4—28no—
516C2×D4—28no—
517C2×D4—28no—
518C2×D4—44no—
519C2×D4—48no—
520C2×D4—48no—
521C2×D4—48no—
522C2×D4—48no—
523C2×D4—48no—
524C2×D4—48no—
525C2×D4—48no—
526C2×D4—48no—
527C2×D4—48no—
528C2×D4—48no—
529C2×D4—416no—
530C2×D4—48no—
531C2×D4—44no—
532C2×D4—44no—
533C2×D4—44no—
534C2×D4—44no—
535C2×D4—84no—
536C2×D4—88no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—21no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—21no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—21no—
550C22×C4—22no—
551C22×C4—21no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—21no—
569C22×C4—22no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—22no—
573C22×C4—21no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—28no—
587C22×C4—28no—
588C22×C4—28no—
589C22×C4—28no—
590C22×C4—28no—
591C22×C4—28no—
592C22×C4—22no—
593C22×C4—22no—
594C22×C4—22no—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—22no—
598C22×C4—22no—
599C22×C4—22no—
600C22×C4—24no—
601C22×C4—22no—
602C22×C4—24no—
603C22×C4—24no—
604C22×C4—22no—
605C22×C4—22no—
606C22×C4—22no—
607C22×C4—22no—
608C22×C4—22no—
609C22×C4—22no—
610C22×C4—22no—
611C22×C4—22no—
612C22×C4—22no—
613C22×C4—22no—
614C22×C4—22no—
615C22×C4—24no—
616C22×C4—24no—
617C22×C4—24no—
618C22×C4—22no—
619C22×C4—24no—
620C22×C4—24no—
621C22×C4—22no—
622C22×C4—24no—
623C22×C4—24no—
624C22×C4—48no—
625C22×C4—48no—
626C22×C4—48no—
627C22×C4—48no—
628C22×C4—48no—
629C22×C4—48no—
630C22×C4—48no—
631C22×C4—48no—
632C22×C4—48no—
633C22×C4—48no—
634C22×C4—48no—
635C22×C4—48no—
636C22×C4—48no—
637C22×C4—48no—
638C22×C4—44no—
639C22×C4—44no—
640C22×C4—44no—
641C22×C4—44no—
642C22×C4—44no—
643C22×C4—44no—
644C22×C4—44no—
645C22×C4—44no—
646C22×C4C22×D414yes—
647C22×C4C22×D412yes—
648C22×C4C22×D412yes—
649C22×C4C22×D414yes—
650C22×C4C22×D412yes—
651C22×C4C22×D412yes—
652C22×C4C22×D412yes—
653C22×C4C22×D412yes—
654C22×C4C2×#4114yes—
655C22×C4C2×#4114yes—
656C22×C4C2×#4114yes—
657C22×C4C2×#4114yes—
658C22×C4C2×#4112yes—
659C22×C4H(5,𝔽2)12yes—
660C22×C4H(5,𝔽2)12yes—
661C22×C4H(5,𝔽2)12yes—
662C22×C4H(5,𝔽2)12yes—
663C4⋊C4—44no—
664C4⋊C4—48no—
665C4⋊C4—48no—
666C4⋊C4—48no—
667C4⋊C4—416no—
668C4⋊C4—48no—
669C4⋊C4—48no—
670C4⋊C4—44no—
671C4⋊C4—44no—
672C4⋊C4—44no—
673C4⋊C4—44no—
674C4⋊C4—44no—
675C4⋊C4—84no—
676C22⋊C4—44no—
677C22⋊C4—44no—
678C22⋊C4—416no—
679C22⋊C4—48no—
680C22⋊C4—416no—
681C22⋊C4—416no—
682C22⋊C4—48no—
683C22⋊C4—48no—
684C22⋊C4—48no—
685C22⋊C4—48no—
686C22⋊C4—48no—
687C22⋊C4—48no—
688C22⋊C4—48no—
689C22⋊C4—84no—
690C22⋊C4—84no—
691C22⋊C4—84no—
692C22⋊C4—84no—
693C22⋊C4—88no—
694C42—28no—
695C42—28no—
696C42—48no—
697C42—48no—
698C42—44no—
699C42—44no—
700C42—44no—
701C23—22no—
702C23—22no—
703C23—22no—
704C23—22no—
705C23—24no—
706C23—22no—
707C23—22no—
708C23—24no—
709C23—24no—
710C23—24no—
711C23—24no—
712C23—24no—
713C23—22no—
714C23—24no—
715C23—22no—
716C23—22no—
717C23—22no—
718C23—24no—
719C23—22no—
720C23—24no—
721C23—28no—
722C23—28no—
723C23—22no—
724C23—22no—
725C23—41no—
726C23—41no—
727C23—41no—
728C23—42no—
729C23—42no—
730C23—42no—
731C23—42no—
732C23—41no—
733C23—42no—
734C23—42no—
735C23—42no—
736C23—42no—
737C23—41no—
738C23—42no—
739C23—42no—
740C23—41no—
741C23—42no—
742C23—41no—
743C23—42no—
744C23—42no—
745C23—44no—
746C23—42no—
747C23—42no—
748C23—42no—
749C23—42no—
750C23—44no—
751C23—44no—
752C23—42no—
753C23—44no—
754C23—42no—
755C23—42no—
756C23—42no—
757C23—44no—
758C23—44no—
759C23—42no—
760C23—41no—
761C23—42no—
762C23—44no—
763C23—42no—
764C23—44no—
765C23—44no—
766C23—42no—
767C23—44no—
768C23—42no—
769C23#53614yes—
770C23C23×D411yescharacteristic
771C23C23×D411yescharacteristic
772C23C22×#4112yes—
773C23C22×#4111yescharacteristic
774C23C2×H(5,𝔽2)11yescharacteristic
775C23C2×H(5,𝔽2)11yescharacteristic
776C23C2×H(5,𝔽2)11yescharacteristic
777C23C2×H(5,𝔽2)11yescharacteristic
778C23C2×2−1+412yes—
779C23#58512yes—
780C23#58512yes—
781Q8—416no—
782Q8—416no—
783D4—416no—
784D4—432no—
785D4—416no—
786D4—816no—
787C2×C4—22no—
788C2×C4—22no—
789C2×C4—24no—
790C2×C4—24no—
791C2×C4—24no—
792C2×C4—22no—
793C2×C4—24no—
794C2×C4—22no—
795C2×C4—22no—
796C2×C4—24no—
797C2×C4—22no—
798C2×C4—24no—
799C2×C4—22no—
800C2×C4—24no—
801C2×C4—22no—
802C2×C4—24no—
803C2×C4—24no—
804C2×C4—22no—
805C2×C4—24no—
806C2×C4—24no—
807C2×C4—24no—
808C2×C4—24no—
809C2×C4—24no—
810C2×C4—22no—
811C2×C4—22no—
812C2×C4—24no—
813C2×C4—24no—
814C2×C4—24no—
815C2×C4—432no—
816C2×C4—432no—
817C2×C4—41no—
818C2×C4—42no—
819C2×C4—42no—
820C2×C4—41no—
821C2×C4—42no—
822C2×C4—42no—
823C2×C4—41no—
824C2×C4—41no—
825C2×C4—42no—
826C2×C4—42no—
827C2×C4—42no—
828C2×C4—41no—
829C2×C4—41no—
830C2×C4—42no—
831C2×C4—42no—
832C2×C4—42no—
833C2×C4—42no—
834C2×C4—42no—
835C2×C4—42no—
836C2×C4—41no—
837C2×C4—41no—
838C2×C4—42no—
839C2×C4—42no—
840C2×C4—42no—
841C2×C4—42no—
842C2×C4—42no—
843C2×C4—42no—
844C2×C4—42no—
845C2×C4—42no—
846C2×C4—42no—
847C2×C4—416no—
848C2×C4—416no—
849C2×C4—42no—
850C2×C4—42no—
851C2×C4—42no—
852C2×C4—42no—
853C2×C4—42no—
854C2×C4—42no—
855C2×C4—42no—
856C2×C4—42no—
857C2×C4—42no—
858C2×C4—44no—
859C2×C4—44no—
860C2×C4—44no—
861C2×C4—44no—
862C2×C4—42no—
863C2×C4—42no—
864C2×C4—42no—
865C2×C4—42no—
866C2×C4—42no—
867C2×C4—42no—
868C2×C4—42no—
869C2×C4—44no—
870C2×C4—44no—
871C2×C4—44no—
872C2×C4—42no—
873C2×C4—42no—
874C2×C4—42no—
875C2×C4—44no—
876C2×C4—42no—
877C2×C4—42no—
878C2×C4—44no—
879C2×C4—42no—
880C2×C4—44no—
881C2×C4#53214yes—
882C2×C4#53414yes—
883C2×C4#53414yes—
884C2×C4#53814yes—
885C2×C4D4214yes—
886C2×C4#54614yes—
887C2×C4#54614yes—
888C2×C4#56014yes—
889C22—24no—
890C22—24no—
891C22—24no—
892C22—42no—
893C22—42no—
894C22—44no—
895C22—42no—
896C22—42no—
897C22—44no—
898C22—44no—
899C22—44no—
900C22—42no—
901C22—42no—
902C22—44no—
903C22—42no—
904C22—44no—
905C22—42no—
906C22—42no—
907C22—44no—
908C22—42no—
909C22—48no—
910C22—42no—
911C22—48no—
912C22—82no—
913C22—82no—
914C22—82no—
915C22—84no—
916C22—82no—
917C22—82no—
918C22—84no—
919C22—82no—
920C22—82no—
921C22—82no—
922C22C2×#53211yescharacteristic
923C22C2×#53411yescharacteristic
924C22C2×#53411yescharacteristic
925C22C2×#53611yescharacteristic
926C22C2×#53811yescharacteristic
927C22C2×D4211yescharacteristic
928C22C2×#54611yescharacteristic
929C22C2×#54611yescharacteristic
930C22D4×#4112yes—
931C22#348012yes—
932C22#348912yes—
933C22#350011yescharacteristic
934C22#350011yescharacteristic
935C22#350612yes—
936C22#351612yes—
937C22#351712yes—
938C22#352012yes—
939C22#352012yes—
940C22C2×#56011yescharacteristic
941C22#353912yes—
942C22#354112yes—
943C22#355112yes—
944C22#356112yes—
945C4—24no—
946C4—42no—
947C4—42no—
948C4—42no—
949C4—44no—
950C4—44no—
951C4—44no—
952C4—44no—
953C4—44no—
954C4—82no—
955C4—82no—
956C4—82no—
957C4—82no—
958C4—82no—
959C4—82no—
960C4#266818yes—
961C2—44no—
962C2—82no—
963C2—84no—
964C2#3508511yescharacteristic
965C2#3612511yescharacteristic
966C2#3641911yescharacteristic
967C2#3741811yescharacteristic
968C2#3767611yescharacteristic
969C2#3808311yescharacteristic
970C2#3921512yes—
971C2#3988412yes—
972C2#4572112yes—
973C2C2×#266811yescharacteristic
974C2#5904312yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC2×#2407C2
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×#2850C2semidirect
2. C2×#2538C2semidirect
3. C2×#2432C2semidirect
5. #16533C2semidirect
6. #15496C2semidirect
7. #15328C2semidirect
8. #15240C2semidirect
9. #15236C2semidirect
10. #15233C2semidirect
11. #15219C2semidirect
12. #15178C2semidirect
13. #15136C2semidirect
14. #14702C2semidirect
15. #14526C2semidirect
16. #14026C2semidirect
17. #14024C2semidirect
18. #13937C2semidirect
19. C4×#386C2semidirect
117. C2×#124D4semidirect
463. #95#41semidirect

Maximal subgroups

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

subgroupindex
C2×#28502
C2×#25382
C2×#24322
C2×#24072
#165332
#154962
#153282
#152402
#152362
#152332
#152192
#151782
#151362
#147022
#145262
#140262
#140242
#139372
C4×#3862