Finite Group Databasebeta

← #5956092

Subgroups — #5956092

Order 512.

6162 conjugacy classes of subgroups.

The subgroup lattice has 986 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#525C211yesmaximal, characteristic
2C2×#2317C211yesmaximal, characteristic, complemented
3C2×#2311C211yesmaximal, characteristic, complemented
4C2×#2311C211yesmaximal, characteristic, complemented
5C2×#2280C211yesmaximal, characteristic, complemented
6C22×#380C211yesmaximal, characteristic, complemented
7#15236C212yesmaximal, complemented
8#15219C212yesmaximal, complemented
9#15182C212yesmaximal, complemented
10#15181C214yesmaximal, complemented
11#15130C212yesmaximal, complemented
12#15129C214yesmaximal, complemented
13#14912C214yesmaximal, complemented
14#14718C214yesmaximal, complemented
15#13795C211yesmaximal, characteristic, complemented
16C23×#41C2211yescharacteristic
17C25×C4C2211yescharacteristic
18C2×#525—28no—
19C2×#525—28no—
20C2×#525—28no—
21C22×#123C2212yes—
22C22×C22⋊Q8C2211yescharacteristic
23C22×C22⋊Q8C2211yescharacteristic
24C22×#121C2211yescharacteristic
25C22×#121C2211yescharacteristic
26C22×#120C2212yes—
27C22×C4×D4C2212yes—
28C22×C4×D4C2212yes—
29C22×#117C2211yescharacteristic
30C22×#117C2211yescharacteristic
31C22×#117C2211yescharacteristic
32C23×C4⋊C4C2211yescharacteristic
33C23×C4⋊C4C2211yescharacteristic
34C23×C22⋊C4C2212yes—
35C2×#394C2218yes—
36#2317—28no—
37#2311—28no—
38#2311—28no—
39C2×#391C2212yescomplemented
40C2×#391C2212yescomplemented
41C2×#390C2212yescomplemented
42C2×#390C2212yescomplemented
43C2×#389C2214yescomplemented
44C2×#386C2214yes—
45C2×#386C2214yes—
46C2×#385C2214yes—
47C2×#384C2212yescomplemented
48C2×#382C2212yescomplemented
49#2280—28no—
50C2×#381C2212yes—
51C2×#380—28no—
52C2×#380C2212yes—
53C2×#380C2212yes—
54C2×#380C2212yes—
55C2×#380C2212yes—
56C2×#380C2212yes—
57C2×#380C2212yes—
58C2×#380C2214yescomplemented
59C2×#380C2214yescomplemented
60C2×#379C2212yes—
61C2×C4×C22⋊C4C2212yes—
62C2×C4×C22⋊C4C2212yes—
63C22×#95C2212yes—
64#1442C2218yescomplemented
65#1441C2218yescomplemented
66#1440C2218yes—
67#1440C2218yescomplemented
68#1439C2218yes—
69#1439C2218yescomplemented
70#1438C2218yes—
71C4⋊#95C2214yescomplemented
72C4⋊#95C2212yescomplemented
73C4⋊#95C2212yescomplemented
74C22⋊#95C2214yes—
75C26C2311yescharacteristic
76C22×#41—24no—
77C22×#41—24no—
78C22×#41—24no—
79C22×#41—24no—
80C22×#41—24no—
81C22×#41—24no—
82C22×#41D418yes—
83C23×Q8C2311yescharacteristic
84C23×D4C2312yes—
85C23×D4C2311yescharacteristic
86C23×D4C2312yes—
87C23×D4C2312yes—
88C24×C4—24no—
89C24×C4—24no—
90C24×C4—24no—
91C24×C4—24no—
92C24×C4—24no—
93C24×C4—24no—
94C24×C4D418yes—
95C24×C4C2311yescharacteristic
96C24×C4C2311yescharacteristic
97C24×C4C2311yescharacteristic
98C24×C4C2311yescharacteristic
99C24×C4C2311yescharacteristic
100C24×C4C2312yes—
101C24×C4C2312yes—
102C24×C4C2312yes—
103C24×C4C2311yescharacteristic
104#525—2128no—
105C2×#123—28no—
106C2×#123—28no—
107C2×#123—28no—
108C2×C22⋊Q8—24no—
109C2×C22⋊Q8—24no—
110C2×C22⋊Q8—24no—
111C2×C22⋊Q8—24no—
112C2×C22⋊Q8—24no—
113C2×C22⋊Q8—24no—
114C2×#121—24no—
115C2×#121—24no—
116C2×#121—24no—
117C2×#121—24no—
118C2×#121—24no—
119C2×#121—24no—
120C2×#120—28no—
121C2×#120—28no—
122C2×#120—28no—
123C2×C4×D4—28no—
124C2×C4×D4—28no—
125C2×C4×D4—28no—
126C2×C4×D4—28no—
127C2×C4×D4—28no—
128C2×C4×D4—28no—
129C2×#117—24no—
130C2×#117—24no—
131C2×#117—24no—
132C2×#117—24no—
133C2×#117—24no—
134C2×#117—24no—
135C2×#117—24no—
136C2×#117D418yes—
137C2×#117D418yescomplemented
138C22×C4⋊C4—24no—
139C22×C4⋊C4—24no—
140C22×C4⋊C4—24no—
141C22×C4⋊C4—24no—
142C22×C4⋊C4—24no—
143C22×C4⋊C4—24no—
144C22×C4⋊C4C2312yes—
145C22×C4⋊C4C2312yes—
146C22×C4⋊C4C2312yes—
147C22×C4⋊C4C2312yes—
148C22×C4⋊C4C2312yes—
149C22×C4⋊C4C2312yes—
150C22×C4⋊C4C2312yes—
151C22×C4⋊C4C2311yescharacteristic
152C22×C4⋊C4C2311yescharacteristic
153C22×C4⋊C4C2312yes—
154C22×C4⋊C4C2318yes—
155C22×C22⋊C4—28no—
156C22×C22⋊C4—48no—
157C22×C22⋊C4C2314yes—
158C22×C22⋊C4C2312yes—
159C22×C22⋊C4C2312yes—
160C22×C22⋊C4C2312yes—
161C22×C22⋊C4C2312yes—
162C22×C22⋊C4C2312yes—
163C22×C22⋊C4C2314yes—
164C22×C22⋊C4C2314yes—
165C22×C22⋊C4C2312yes—
166C22×C22⋊C4C2312yes—
167C22×C22⋊C4C2318yes—
168C22×C22⋊C4C2318yes—
169C22×C22⋊C4C2314yes—
170C22×C42C2312yes—
171C22×C42C2312yes—
172C22×C42C2312yes—
173#394—416no—
174#391—28no—
175#391—28no—
176#390—28no—
177#390—28no—
178#389—216no—
179#386—216no—
180#386—216no—
181#385—216no—
182#384—28no—
183#382—28no—
184#381—28no—
185#380—216no—
186#380—28no—
187#380—28no—
188#380—28no—
189#380—28no—
190#380—216no—
191#380—28no—
192#380—28no—
193#379—28no—
194C4×C22⋊C4—28no—
195C4×C22⋊C4—28no—
196C2×#95—28no—
197C2×#95C2318yes—
198C2×#95C2318yes—
199C2×#95C2318yes—
200C2×#95C2314yes—
201C2×#95C2314yes—
202C2×#95C2314yes—
203C2×#95C2314yes—
204C2×#95C2318yes—
205C2×#95C2318yes—
206C25—22no—
207C25—22no—
208C25—24no—
209C25—24no—
210C25—22no—
211C25—22no—
212C25—22no—
213C25—22no—
214C25—42no—
215C25—42no—
216C25C2×D414yes—
217C25C2412yes—
218C25C2411yescharacteristic
219C25C2411yescharacteristic
220C25C2411yescharacteristic
221C2×#41—232no—
222C2×#41—232no—
223C2×#41—232no—
224C2×#41—416no—
225C2×#41—416no—
226C2×#41—416no—
227C2×#41—416no—
228C22×Q8—22no—
229C22×Q8—22no—
230C22×Q8—22no—
231C22×Q8—22no—
232C22×Q8—22no—
233C22×Q8—22no—
234C22×Q8C2×D414yes—
235C22×D4—24no—
236C22×D4—24no—
237C22×D4—24no—
238C22×D4—24no—
239C22×D4—24no—
240C22×D4—24no—
241C22×D4—24no—
242C22×D4—24no—
243C22×D4—24no—
244C22×D4—24no—
245C22×D4—28no—
246C22×D4—28no—
247C22×D4—24no—
248C22×D4—24no—
249C22×D4—22no—
250C22×D4—22no—
251C22×D4—22no—
252C22×D4—22no—
253C22×D4—22no—
254C22×D4—22no—
255C22×D4—44no—
256C22×D4—44no—
257C22×D4C2×D418yes—
258C22×D4C2×D414yes—
259C23×C4—22no—
260C23×C4—22no—
261C23×C4—22no—
262C23×C4—22no—
263C23×C4—22no—
264C23×C4—22no—
265C23×C4—232no—
266C23×C4—232no—
267C23×C4—232no—
268C23×C4—22no—
269C23×C4—22no—
270C23×C4—22no—
271C23×C4—22no—
272C23×C4—24no—
273C23×C4—24no—
274C23×C4—22no—
275C23×C4—22no—
276C23×C4—22no—
277C23×C4—22no—
278C23×C4—22no—
279C23×C4—22no—
280C23×C4—22no—
281C23×C4—22no—
282C23×C4—24no—
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—22no—
294C23×C4—22no—
295C23×C4—24no—
296C23×C4—24no—
297C23×C4—24no—
298C23×C4—24no—
299C23×C4—24no—
300C23×C4—24no—
301C23×C4—24no—
302C23×C4—24no—
303C23×C4—24no—
304C23×C4—44no—
305C23×C4—44no—
306C23×C4—44no—
307C23×C4—44no—
308C23×C4—416no—
309C23×C4—416no—
310C23×C4—416no—
311C23×C4—416no—
312C23×C4C2×D414yes—
313C23×C4C2×D414yes—
314C23×C4C2×D418yes—
315C23×C4C2×D414yes—
316C23×C4C2×D414yes—
317C23×C4C2×D414yes—
318C23×C4C2×D414yes—
319C23×C4C2×D414yes—
320C23×C4C2×D414yes—
321C23×C4C2×D414yes—
322C23×C4#4114yes—
323C23×C4#4114yes—
324C23×C4#4114yes—
325C23×C4C2414yes—
326C23×C4C2414yes—
327C23×C4C2414yes—
328C23×C4C2414yes—
329C23×C4C2412yes—
330C23×C4C2412yes—
331C23×C4C2411yescharacteristic
332C23×C4C2411yescharacteristic
333C23×C4C2412yes—
334C23×C4C2411yescharacteristic
335C23×C4C2411yescharacteristic
336#123—264no—
337C22⋊Q8—232no—
338C22⋊Q8—232no—
339#121—232no—
340#121—232no—
341#120—264no—
342C4×D4—264no—
343C4×D4—264no—
344#117—232no—
345#117—232no—
346#117—416no—
347C2×C4⋊C4—22no—
348C2×C4⋊C4—22no—
349C2×C4⋊C4—22no—
350C2×C4⋊C4—22no—
351C2×C4⋊C4—24no—
352C2×C4⋊C4—24no—
353C2×C4⋊C4—24no—
354C2×C4⋊C4—24no—
355C2×C4⋊C4—24no—
356C2×C4⋊C4—24no—
357C2×C4⋊C4—24no—
358C2×C4⋊C4—24no—
359C2×C4⋊C4—24no—
360C2×C4⋊C4—24no—
361C2×C4⋊C4—24no—
362C2×C4⋊C4—24no—
363C2×C4⋊C4—24no—
364C2×C4⋊C4—24no—
365C2×C4⋊C4—24no—
366C2×C4⋊C4—24no—
367C2×C4⋊C4—24no—
368C2×C4⋊C4—24no—
369C2×C4⋊C4—24no—
370C2×C4⋊C4—24no—
371C2×C4⋊C4—24no—
372C2×C4⋊C4—24no—
373C2×C4⋊C4—24no—
374C2×C4⋊C4—216no—
375C2×C4⋊C4—416no—
376C2×C4⋊C4—416no—
377C2×C4⋊C4—48no—
378C2×C4⋊C4—48no—
379C2×C4⋊C4C2×D414yes—
380C2×C4⋊C4C2×D414yes—
381C2×C4⋊C4C2×D418yes—
382C2×C22⋊C4—24no—
383C2×C22⋊C4—24no—
384C2×C22⋊C4—24no—
385C2×C22⋊C4—24no—
386C2×C22⋊C4—24no—
387C2×C22⋊C4—24no—
388C2×C22⋊C4—24no—
389C2×C22⋊C4—24no—
390C2×C22⋊C4—24no—
391C2×C22⋊C4—24no—
392C2×C22⋊C4—24no—
393C2×C22⋊C4—24no—
394C2×C22⋊C4—24no—
395C2×C22⋊C4—24no—
396C2×C22⋊C4—24no—
397C2×C22⋊C4—24no—
398C2×C22⋊C4—28no—
399C2×C22⋊C4—28no—
400C2×C22⋊C4—24no—
401C2×C22⋊C4—24no—
402C2×C22⋊C4—24no—
403C2×C22⋊C4—216no—
404C2×C22⋊C4—28no—
405C2×C22⋊C4—28no—
406C2×C22⋊C4—28no—
407C2×C22⋊C4—28no—
408C2×C22⋊C4—216no—
409C2×C22⋊C4—216no—
410C2×C22⋊C4—48no—
411C2×C22⋊C4—44no—
412C2×C22⋊C4—44no—
413C2×C22⋊C4—432no—
414C2×C22⋊C4—48no—
415C2×C22⋊C4—48no—
416C2×C22⋊C4—48no—
417C2×C22⋊C4—48no—
418C2×C22⋊C4C2×D418yes—
419C2×C22⋊C4C2×D418yes—
420C2×C42—24no—
421C2×C42—24no—
422C2×C42—24no—
423C2×C42—24no—
424C2×C42—24no—
425C2×C42—24no—
426C2×C42—24no—
427C2×C42C2×D418yes—
428C2×C42C2×D418yes—
429#95—28no—
430#95—28no—
431#95—28no—
432#95—28no—
433#95—216no—
434#95—216no—
435#95—216no—
436#95—48no—
437#95—48no—
438C24—22no—
439C24—22no—
440C24—22no—
441C24—22no—
442C24—216no—
443C24—216no—
444C24—28no—
445C24—28no—
446C24—28no—
447C24—21no—
448C24—21no—
449C24—21no—
450C24—21no—
451C24—21no—
452C24—21no—
453C24—21no—
454C24—21no—
455C24—21no—
456C24—21no—
457C24—21no—
458C24—21no—
459C24—22no—
460C24—22no—
461C24—22no—
462C24—22no—
463C24—22no—
464C24—22no—
465C24—28no—
466C24—28no—
467C24—22no—
468C24—22no—
469C24—22no—
470C24—22no—
471C24—22no—
472C24—22no—
473C24—24no—
474C24—24no—
475C24—24no—
476C24—24no—
477C24—44no—
478C24—44no—
479C24—48no—
480C24—48no—
481C24—48no—
482C24—48no—
483C24—48no—
484C24—48no—
485C24—48no—
486C24—48no—
487C24—48no—
488C24—48no—
489C24—44no—
490C24—44no—
491C24—44no—
492C24—44no—
493C24C22×D414yes—
494C24C22×D412yes—
495C24C22×D412yes—
496C24C22×D412yes—
497C24C22×D412yes—
498C24C22×D412yes—
499C24C22×D412yes—
500C24C2×#4112yes—
501C24C2×#4112yes—
502C24C2×#4112yes—
503C24H(5,𝔽2)14yes—
504C242−1+414yes—
505C24C2511yescharacteristic
506#41—4128no—
507C2×Q8—28no—
508C2×Q8—28no—
509C2×Q8—28no—
510C2×Q8—44no—
511C2×Q8—44no—
512C2×Q8—44no—
513C2×Q8—44no—
514C2×D4—216no—
515C2×D4—216no—
516C2×D4—216no—
517C2×D4—216no—
518C2×D4—216no—
519C2×D4—28no—
520C2×D4—28no—
521C2×D4—28no—
522C2×D4—416no—
523C2×D4—416no—
524C2×D4—416no—
525C2×D4—416no—
526C2×D4—48no—
527C2×D4—48no—
528C2×D4—48no—
529C2×D4—48no—
530C2×D4—48no—
531C2×D4—48no—
532C2×D4—48no—
533C2×D4—48no—
534C2×D4—44no—
535C2×D4—44no—
536C2×D4—44no—
537C2×D4—44no—
538C22×C4—28no—
539C22×C4—28no—
540C22×C4—28no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—22no—
544C22×C4—24no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—24no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—24no—
566C22×C4—24no—
567C22×C4—24no—
568C22×C4—24no—
569C22×C4—24no—
570C22×C4—24no—
571C22×C4—24no—
572C22×C4—24no—
573C22×C4—28no—
574C22×C4—28no—
575C22×C4—216no—
576C22×C4—28no—
577C22×C4—28no—
578C22×C4—28no—
579C22×C4—28no—
580C22×C4—28no—
581C22×C4—28no—
582C22×C4—216no—
583C22×C4—28no—
584C22×C4—28no—
585C22×C4—28no—
586C22×C4—28no—
587C22×C4—216no—
588C22×C4—24no—
589C22×C4—24no—
590C22×C4—24no—
591C22×C4—24no—
592C22×C4—24no—
593C22×C4—24no—
594C22×C4—24no—
595C22×C4—24no—
596C22×C4—24no—
597C22×C4—24no—
598C22×C4—28no—
599C22×C4—28no—
600C22×C4—24no—
601C22×C4—24no—
602C22×C4—28no—
603C22×C4—24no—
604C22×C4—28no—
605C22×C4—44no—
606C22×C4—44no—
607C22×C4—44no—
608C22×C4—44no—
609C22×C4—44no—
610C22×C4—44no—
611C22×C4—44no—
612C22×C4—44no—
613C22×C4—44no—
614C22×C4—44no—
615C22×C4—44no—
616C22×C4—44no—
617C22×C4—48no—
618C22×C4—48no—
619C22×C4—44no—
620C22×C4—44no—
621C22×C4—44no—
622C22×C4—44no—
623C22×C4—48no—
624C22×C4—44no—
625C22×C4—44no—
626C22×C4—44no—
627C22×C4—44no—
628C22×C4—48no—
629C22×C4—4128no—
630C22×C4—48no—
631C22×C4—48no—
632C22×C4—48no—
633C22×C4—48no—
634C22×C4—48no—
635C22×C4—48no—
636C22×C4—88no—
637C22×C4—88no—
638C22×C4—88no—
639C22×C4—88no—
640C22×C4#120116yes—
641C22×C4#121116yes—
642C22×C4#121116yes—
643C22×C4#121116yes—
644C22×C4#123116yes—
645C22×C4#123116yes—
646C22×C4#124116yes—
647C22×C4C22×D418yes—
648C22×C4C22×D414yes—
649C22×C4C22×D412yes—
650C22×C4C22×D412yes—
651C22×C4C22×D414yes—
652C22×C4C22×D414yes—
653C22×C4C22×D412yes—
654C22×C4C22×D412yes—
655C22×C4C22×D412yes—
656C22×C4C22×D412yes—
657C22×C4C22×D412yes—
658C22×C4C22×D412yes—
659C22×C4C22×D412yes—
660C22×C4C22×D412yes—
661C22×C4C2×#4112yes—
662C22×C4C2×#4112yes—
663C22×C4C2×#4112yes—
664C22×C4C2×#4112yes—
665C22×C4C2×#4112yes—
666C22×C4C2×#4112yes—
667C4⋊C4—216no—
668C4⋊C4—216no—
669C4⋊C4—28no—
670C4⋊C4—28no—
671C4⋊C4—216no—
672C4⋊C4—48no—
673C4⋊C4—48no—
674C4⋊C4—48no—
675C4⋊C4—48no—
676C4⋊C4—48no—
677C4⋊C4—816no—
678C22⋊C4—216no—
679C22⋊C4—216no—
680C22⋊C4—216no—
681C22⋊C4—216no—
682C22⋊C4—216no—
683C22⋊C4—216no—
684C22⋊C4—416no—
685C22⋊C4—416no—
686C22⋊C4—416no—
687C22⋊C4—48no—
688C22⋊C4—416no—
689C22⋊C4—816no—
690C22⋊C4—816no—
691C42—216no—
692C42—216no—
693C42—48no—
694C23—22no—
695C23—22no—
696C23—22no—
697C23—22no—
698C23—24no—
699C23—24no—
700C23—24no—
701C23—24no—
702C23—24no—
703C23—24no—
704C23—24no—
705C23—24no—
706C23—24no—
707C23—24no—
708C23—24no—
709C23—24no—
710C23—232no—
711C23—22no—
712C23—22no—
713C23—22no—
714C23—22no—
715C23—22no—
716C23—22no—
717C23—22no—
718C23—22no—
719C23—22no—
720C23—22no—
721C23—22no—
722C23—22no—
723C23—24no—
724C23—24no—
725C23—24no—
726C23—24no—
727C23—24no—
728C23—24no—
729C23—24no—
730C23—24no—
731C23—24no—
732C23—24no—
733C23—24no—
734C23—24no—
735C23—24no—
736C23—24no—
737C23—24no—
738C23—28no—
739C23—28no—
740C23—416no—
741C23—416no—
742C23—416no—
743C23—416no—
744C23—416no—
745C23—432no—
746C23—432no—
747C23—432no—
748C23—432no—
749C23—416no—
750C23—41no—
751C23—41no—
752C23—41no—
753C23—41no—
754C23—41no—
755C23—41no—
756C23—41no—
757C23—41no—
758C23—42no—
759C23—42no—
760C23—42no—
761C23—42no—
762C23—42no—
763C23—42no—
764C23—42no—
765C23—42no—
766C23—42no—
767C23—42no—
768C23—42no—
769C23—42no—
770C23—42no—
771C23—42no—
772C23—42no—
773C23—42no—
774C23—42no—
775C23—42no—
776C23—42no—
777C23—42no—
778C23—44no—
779C23—44no—
780C23—44no—
781C23—44no—
782C23—44no—
783C23—44no—
784C23—44no—
785C23—44no—
786C23—44no—
787C23—44no—
788C23C2×#12014yes—
789C23C2×#12114yes—
790C23C2×#12114yes—
791C23C2×#12114yes—
792C23C2×#12314yes—
793C23C2×#12314yes—
794C23C2×#12414yes—
795C23#53514yes—
796C23#53614yes—
797C23C23×D411yescharacteristic
798C23C23×D411yescharacteristic
799C23C23×D411yescharacteristic
800C23C23×D411yescharacteristic
801C23C22×#4111yescharacteristic
802C23C22×#4111yescharacteristic
803C23C22×#4111yescharacteristic
804C23C2×H(5,𝔽2)12yes—
805C23C2×2−1+412yes—
806C23#58512yes—
807C23#58512yes—
808Q8—416no—
809D4—432no—
810D4—432no—
811D4—432no—
812D4—416no—
813C2×C4—24no—
814C2×C4—24no—
815C2×C4—22no—
816C2×C4—22no—
817C2×C4—24no—
818C2×C4—28no—
819C2×C4—22no—
820C2×C4—22no—
821C2×C4—24no—
822C2×C4—22no—
823C2×C4—22no—
824C2×C4—24no—
825C2×C4—28no—
826C2×C4—28no—
827C2×C4—28no—
828C2×C4—28no—
829C2×C4—416no—
830C2×C4—41no—
831C2×C4—41no—
832C2×C4—41no—
833C2×C4—41no—
834C2×C4—42no—
835C2×C4—42no—
836C2×C4—41no—
837C2×C4—41no—
838C2×C4—42no—
839C2×C4—41no—
840C2×C4—41no—
841C2×C4—42no—
842C2×C4—42no—
843C2×C4—42no—
844C2×C4—42no—
845C2×C4—42no—
846C2×C4—44no—
847C2×C4—44no—
848C2×C4—44no—
849C2×C4—44no—
850C2×C4—44no—
851C2×C4—44no—
852C2×C4—416no—
853C2×C4—416no—
854C2×C4—416no—
855C2×C4—416no—
856C2×C4—432no—
857C2×C4—44no—
858C2×C4—44no—
859C2×C4—44no—
860C2×C4—44no—
861C2×C4—44no—
862C2×C4—44no—
863C2×C4—44no—
864C2×C4—44no—
865C2×C4—44no—
866C2×C4—48no—
867C2×C4—48no—
868C2×C4—48no—
869C2×C4—44no—
870C2×C4—44no—
871C2×C4—44no—
872C2×C4—44no—
873C2×C4—48no—
874C2×C4—816no—
875C2×C4—816no—
876C2×C4#394164yescomplemented
877C2×C4C2×#12014yes—
878C2×C4C2×#12014yes—
879C2×C4C2×#12114yes—
880C2×C4C2×#12114yes—
881C2×C4C2×#12114yes—
882C2×C4C2×#12114yes—
883C2×C4C2×#12114yes—
884C2×C4C2×#12114yes—
885C2×C4C2×#12314yes—
886C2×C4C2×#12314yes—
887C2×C4C2×#12314yes—
888C2×C4C2×#12314yes—
889C2×C4C2×#12414yes—
890C2×C4C2×#12414yes—
891C22—24no—
892C22—24no—
893C22—24no—
894C22—24no—
895C22—28no—
896C22—28no—
897C22—28no—
898C22—28no—
899C22—24no—
900C22—24no—
901C22—24no—
902C22—24no—
903C22—24no—
904C22—24no—
905C22—24no—
906C22—24no—
907C22—464no—
908C22—42no—
909C22—42no—
910C22—42no—
911C22—42no—
912C22—44no—
913C22—44no—
914C22—44no—
915C22—44no—
916C22—44no—
917C22—44no—
918C22—44no—
919C22—44no—
920C22—42no—
921C22—42no—
922C22—42no—
923C22—42no—
924C22—44no—
925C22—48no—
926C22—48no—
927C22—44no—
928C22—44no—
929C22—82no—
930C22—82no—
931C22—82no—
932C22—84no—
933C22—84no—
934C22—82no—
935C22C2×#39418yes—
936C22C22×#12011yescharacteristic
937C22C22×#12111yescharacteristic
938C22C22×#12111yescharacteristic
939C22C22×#12111yescharacteristic
940C22C22×#12311yescharacteristic
941C22C22×#12311yescharacteristic
942C22C22×#12411yescharacteristic
943C22C2×#53511yescharacteristic
944C22C2×#53611yescharacteristic
945C22#344911yescharacteristic
946C22#344911yescharacteristic
947C22#348812yes—
948C22#348812yes—
949C22#348812yes—
950C22#348912yes—
951C22#348912yes—
952C22#348912yes—
953C22#349212yes—
954C22#349212yes—
955C22#349312yes—
956C22#349312yes—
957C22#349412yes—
958C22#349512yes—
959C4—44no—
960C4—48no—
961C4—42no—
962C4—42no—
963C4—44no—
964C4—44no—
965C4—84no—
966C4—84no—
967C4—84no—
968C4C2×#39418yes—
969C4C2×#39418yes—
970C2—28no—
971C2—44no—
972C2—44no—
973C2—84no—
974C2C22×#39411yescharacteristic
975C2#3515711yescharacteristic
976C2#3522711yescharacteristic
977C2#3525011yescharacteristic
978C2#3525211yescharacteristic
979C2#3530511yescharacteristic
980C2#3530611yescharacteristic
981C2#3551612yes—
982C2#3551812yes—
983C2#3551812yes—
984C2#3554212yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC22×#525C2
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×#2317C2semidirect
3. C2×#2311C2semidirect
4. C2×#2311C2semidirect
5. C2×#2280C2semidirect
6. C22×#380C2semidirect
7. #15236C2semidirect
8. #15219C2semidirect
9. #15182C2semidirect
10. #15181C2semidirect
11. #15130C2semidirect
12. #15129C2semidirect
13. #14912C2semidirect
14. #14718C2semidirect
15. #13795C2semidirect
39. C2×#391C22semidirect
40. C2×#391C22semidirect
41. C2×#390C22semidirect
42. C2×#390C22semidirect
43. C2×#389C22semidirect
47. C2×#384C22semidirect
48. C2×#382C22semidirect
58. C2×#380C22semidirect
59. C2×#380C22semidirect
64. #1442C22semidirect
65. #1441C22semidirect
67. #1440C22semidirect
69. #1439C22semidirect
71. C4⋊#95C22semidirect
72. C4⋊#95C22semidirect
73. C4⋊#95C22semidirect
137. C2×#117D4semidirect
876. C2×C4#394semidirect

Maximal subgroups

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

subgroupindex
C22×#5252
C2×#23172
C2×#23112
C2×#22802
C22×#3802
#152362
#152192
#151822
#151812
#151302
#151292
#149122
#147182
#137952