Finite Group Databasebeta

← #374334

Subgroups — #374334

Order 512.

2064 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×#2620C211yesmaximal, characteristic
2C2×#2317C211yesmaximal, characteristic, complemented
3C2×#1959C211yesmaximal, characteristic, complemented
4C2×#1958C211yesmaximal, characteristic, complemented
5C2×#1875C211yesmaximal, characteristic
6C2×#1873C211yesmaximal, characteristic, complemented
7C2×#1874C211yesmaximal, characteristic
8C2×#1872C211yesmaximal, characteristic, complemented
9C2×#1750C211yesmaximal, characteristic, complemented
10#11052C211yesmaximal, characteristic, complemented
11#11051C211yesmaximal, characteristic, complemented
12#11050C211yesmaximal, characteristic, complemented
13#11049C211yesmaximal, characteristic, complemented
14#10843C211yesmaximal, characteristic, complemented
15#10841C211yesmaximal, characteristic, complemented
16C22×#124C2211yescharacteristic
17C22×C22⋊Q8C2211yescharacteristic
18C22×#121C2211yescharacteristic
19C22×#117C2211yescharacteristic
20C22×#117C2211yescharacteristic
21C23×C4⋊C4C2211yescharacteristic
22C22×#103C2211yescharacteristic
23C22×#103C2211yescharacteristic
24C22×#103C2211yescharacteristic
25C22×#103C2211yescharacteristic
26C22×#102C2211yescharacteristic
27C22×#102C2211yescharacteristic
28C22×#102C2211yescharacteristic
29C22×#102C2211yescharacteristic
30C22×C22⋊C8C2211yescharacteristic
31C22×C22⋊C8C2211yescharacteristic
32C22×#97C2211yescharacteristic
33C22×C4×C8C2211yescharacteristic
34#2620—24no—
35#2620C418yescomplemented
36C2×#396—22no—
37C2×#394—22no—
38#2317—24no—
39#2317—24no—
40C2×#391C2211yescharacteristic
41C2×#390C2211yescharacteristic
42C2×#389—22no—
43C2×#385—22no—
44C2×#384C2211yescharacteristic
45C2×#384C2211yescharacteristic
46C2×#384C2211yescharacteristic
47C2×#382C2211yescharacteristic
48C2×#382C2211yescharacteristic
49#1959—24no—
50#1958—24no—
51#1875—24no—
52#1874—24no—
53#1873—24no—
54#1872—24no—
55#1750—24no—
56C2×#340C2211yescharacteristic
57C2×#340C2211yescharacteristic
58C2×#340C2211yescharacteristic
59C2×#340C2211yescharacteristic
60C2×#340C2211yescharacteristic
61C2×#340C2211yescharacteristic
62C2×#340C2211yescharacteristic
63C2×#340C2211yescharacteristic
64C2×#336C2211yescharacteristic
65C2×#336C2211yescharacteristic
66C23×Q8C2311yescharacteristic
67C23×D4—21no—
68C23×D4C2311yescharacteristic
69C24×C4—21no—
70C24×C4C2311yescharacteristic
71C23×C8C2311yescharacteristic
72C23×C8C2311yescharacteristic
73C23×C8C2311yescharacteristic
74C23×C8C2311yescharacteristic
75C2×#124—22no—
76C2×#124—22no—
77C2×#124—22no—
78C2×#124—22no—
79C2×#124—22no—
80C2×#124C2×C414yescomplemented
81C2×C22⋊Q8—22no—
82C2×C22⋊Q8—22no—
83C2×C22⋊Q8—22no—
84C2×C22⋊Q8—22no—
85C2×C22⋊Q8—22no—
86C2×C22⋊Q8C2×C414yes—
87C2×#121—22no—
88C2×#121—22no—
89C2×#121—22no—
90C2×#121—22no—
91C2×#121—22no—
92C2×#121C2×C414yes—
93C2×#117—22no—
94C2×#117—22no—
95C2×#117—22no—
96C2×#117—22no—
97C2×#117—22no—
98C2×#117—22no—
99C2×#117—22no—
100C2×#117—22no—
101C2×#117—41no—
102C2×#117—41no—
103C2×#117C2×C414yes—
104C2×#117D414yes—
105C22×C4⋊C4—21no—
106C22×C4⋊C4—21no—
107C22×C4⋊C4—22no—
108C22×C4⋊C4—22no—
109C22×C4⋊C4—22no—
110C22×C4⋊C4—22no—
111C22×C4⋊C4—22no—
112C22×C4⋊C4—22no—
113C22×C4⋊C4—22no—
114C22×C4⋊C4—41no—
115C22×C4⋊C4—41no—
116C22×C4⋊C4D412yes—
117C22×C4⋊C4C2311yescharacteristic
118C22×C4⋊C4C2311yescharacteristic
119C22×C4⋊C4C2311yescharacteristic
120C22×C4⋊C4C2311yescharacteristic
121C22×C4⋊C4C2311yescharacteristic
122C22×C4⋊C4C2311yescharacteristic
123C22×C22⋊C4—21no—
124C22×C22⋊C4—21no—
125C22×C22⋊C4—22no—
126C22×C22⋊C4—21no—
127C22×C22⋊C4—22no—
128C22×C22⋊C4D412yes—
129C22×C42—21no—
130C22×C42C2311yescharacteristic
131C22×C42C2311yescharacteristic
132C2×#103—22no—
133C2×#103—22no—
134C2×#103—22no—
135C2×#103—22no—
136C2×#103—22no—
137C2×#103—22no—
138C2×#103—22no—
139C2×#103—22no—
140C2×#103—41no—
141C2×#103—41no—
142C2×#103—41no—
143C2×#103—41no—
144C2×#102—22no—
145C2×#102—22no—
146C2×#102—22no—
147C2×#102—22no—
148C2×#102—22no—
149C2×#102—22no—
150C2×#102—22no—
151C2×#102—22no—
152C2×#102—41no—
153C2×#102—41no—
154C2×#102—41no—
155C2×#102—41no—
156C2×C22⋊C8—22no—
157C2×C22⋊C8—22no—
158C2×C22⋊C8—22no—
159C2×C22⋊C8—22no—
160C2×C22⋊C8D414yes—
161C2×C22⋊C8D414yes—
162C2×#97—22no—
163C2×#97—22no—
164C2×#97—22no—
165C2×C4×C8—22no—
166C2×C4×C8—22no—
167C2×C4×C8—22no—
168#396—216no—
169#394—216no—
170#391—22no—
171#391C2×C414yescomplemented
172#390—22no—
173#390C2×C414yescomplemented
174#389—216no—
175#385—216no—
176#384—22no—
177#384—22no—
178#384—22no—
179#384—22no—
180#384C2×C414yescomplemented
181#384D414yescomplemented
182#382—22no—
183#382—22no—
184#382—22no—
185#382D414yescomplemented
186C2×#95—22no—
187C2×#95—22no—
188C2×#95—22no—
189#340—22no—
190#340—22no—
191#340—22no—
192#340—22no—
193#340—22no—
194#340—22no—
195#340—22no—
196#340—22no—
197#336—22no—
198#336—22no—
199C25—21no—
200C25C2×D411yescharacteristic
201C22×Q8—21no—
202C22×Q8—21no—
203C22×Q8—21no—
204C22×Q8—21no—
205C22×Q8—21no—
206C22×Q8—21no—
207C22×Q8—21no—
208C22×Q8—21no—
209C22×Q8—21no—
210C22×Q8—21no—
211C22×Q8—21no—
212C22×Q8—21no—
213C22×Q8—21no—
214C22×Q8C22×C412yes—
215C22×D4—24no—
216C22×D4—21no—
217C22×D4—21no—
218C22×D4—21no—
219C22×D4—21no—
220C22×D4—21no—
221C22×D4—21no—
222C22×D4—21no—
223C22×D4—21no—
224C22×D4—21no—
225C22×D4—21no—
226C22×D4—21no—
227C22×D4—21no—
228C22×D4—21no—
229C22×D4—42no—
230C22×D4—42no—
231C22×D4—82no—
232C22×D4—82no—
233C22×D4C22×C412yes—
234C23×C4—21no—
235C23×C4—21no—
236C23×C4—21no—
237C23×C4—21no—
238C23×C4—21no—
239C23×C4—21no—
240C23×C4—21no—
241C23×C4—21no—
242C23×C4—21no—
243C23×C4—21no—
244C23×C4—21no—
245C23×C4—21no—
246C23×C4—21no—
247C23×C4—21no—
248C23×C4—21no—
249C23×C4—24no—
250C23×C4—42no—
251C23×C4—42no—
252C23×C4—82no—
253C23×C4—82no—
254C23×C4C22×C412yes—
255C23×C4C2×D412yes—
256C23×C4C2×D412yes—
257C23×C4C2×D411yescharacteristic
258C23×C4C2×D412yes—
259C23×C4C2×D412yes—
260C23×C4C2×D412yes—
261C23×C4#4112yes—
262C23×C4#4112yes—
263C23×C4C2411yescharacteristic
264C22×C8—21no—
265C22×C8—21no—
266C22×C8—21no—
267C22×C8—21no—
268C22×C8—21no—
269C22×C8—21no—
270C22×C8—21no—
271C22×C8—21no—
272C22×C8—21no—
273C22×C8—21no—
274C22×C8—21no—
275C22×C8—21no—
276C22×C8—21no—
277C22×C8—21no—
278C22×C8—21no—
279C22×C8—21no—
280C22×C8—21no—
281C22×C8—21no—
282C22×C8—21no—
283C22×C8—21no—
284C22×C8—21no—
285C22×C8—21no—
286C22×C8—21no—
287C22×C8—21no—
288C22×C8C2×D412yes—
289C22×C8C2×D412yes—
290C22×C8C2×D412yes—
291C22×C8C2×D412yes—
292#124—28no—
293#124—28no—
294#124—44no—
295#124—44no—
296C22⋊Q8—28no—
297C22⋊Q8—28no—
298C22⋊Q8—44no—
299C22⋊Q8—44no—
300#121—28no—
301#121—28no—
302#121—44no—
303#121—44no—
304#117—28no—
305#117—28no—
306#117—28no—
307#117—28no—
308#117—44no—
309#117—44no—
310#117—44no—
311#117—44no—
312C2×C4⋊C4—24no—
313C2×C4⋊C4—24no—
314C2×C4⋊C4—21no—
315C2×C4⋊C4—21no—
316C2×C4⋊C4—21no—
317C2×C4⋊C4—21no—
318C2×C4⋊C4—21no—
319C2×C4⋊C4—21no—
320C2×C4⋊C4—21no—
321C2×C4⋊C4—21no—
322C2×C4⋊C4—21no—
323C2×C4⋊C4—21no—
324C2×C4⋊C4—21no—
325C2×C4⋊C4—21no—
326C2×C4⋊C4—21no—
327C2×C4⋊C4—21no—
328C2×C4⋊C4—21no—
329C2×C4⋊C4—21no—
330C2×C4⋊C4—21no—
331C2×C4⋊C4—21no—
332C2×C4⋊C4—21no—
333C2×C4⋊C4—21no—
334C2×C4⋊C4—21no—
335C2×C4⋊C4—21no—
336C2×C4⋊C4—21no—
337C2×C4⋊C4—21no—
338C2×C4⋊C4—24no—
339C2×C4⋊C4—24no—
340C2×C4⋊C4—21no—
341C2×C4⋊C4—21no—
342C2×C4⋊C4—21no—
343C2×C4⋊C4—21no—
344C2×C4⋊C4—21no—
345C2×C4⋊C4—21no—
346C2×C4⋊C4—28no—
347C2×C4⋊C4—28no—
348C2×C4⋊C4—28no—
349C2×C4⋊C4—44no—
350C2×C4⋊C4—44no—
351C2×C4⋊C4—44no—
352C2×C4⋊C4—44no—
353C2×C4⋊C4—42no—
354C2×C4⋊C4—42no—
355C2×C4⋊C4—42no—
356C2×C4⋊C4—42no—
357C2×C4⋊C4—82no—
358C2×C4⋊C4—82no—
359C2×C4⋊C4—82no—
360C2×C4⋊C4—82no—
361C2×C4⋊C4—82no—
362C2×C4⋊C4—82no—
363C2×C4⋊C4C22⋊C418yes—
364C2×C4⋊C4C22×C412yes—
365C2×C4⋊C4C22×C412yes—
366C2×C4⋊C4C2×D412yes—
367C2×C4⋊C4C2×D412yes—
368C2×C4⋊C4C2×D412yes—
369C2×C4⋊C4C2×D412yes—
370C2×C22⋊C4—24no—
371C2×C22⋊C4—24no—
372C2×C22⋊C4—24no—
373C2×C22⋊C4—24no—
374C2×C22⋊C4—24no—
375C2×C22⋊C4—28no—
376C2×C22⋊C4—28no—
377C2×C22⋊C4—42no—
378C2×C22⋊C4—42no—
379C2×C22⋊C4—42no—
380C2×C22⋊C4—42no—
381C2×C22⋊C4—44no—
382C2×C22⋊C4—44no—
383C2×C22⋊C4—42no—
384C2×C22⋊C4—42no—
385C2×C22⋊C4—82no—
386C2×C22⋊C4—82no—
387C2×C22⋊C4C22⋊C418yes—
388C2×C42—21no—
389C2×C42—21no—
390C2×C42—21no—
391C2×C42—21no—
392C2×C42—24no—
393C2×C42—42no—
394C2×C42—42no—
395C2×C42C22×C412yes—
396C2×C42C22×C412yes—
397C2×C42C2×D412yes—
398C2×C42C2×D412yes—
399C2×C42C2×D412yes—
400C2×C42C2×D412yes—
401C2×C42#4112yes—
402C2×C42#4112yes—
403#103—44no—
404#103—44no—
405#103—44no—
406#103—44no—
407#102—44no—
408#102—44no—
409#102—44no—
410#102—44no—
411C22⋊C8—28no—
412C22⋊C8—28no—
413#97—44no—
414C4×C8—44no—
415#95—28no—
416#95—28no—
417#95—28no—
418C24—21no—
419C24—21no—
420C24—21no—
421C24—21no—
422C24—22no—
423C24—22no—
424C24—22no—
425C24—22no—
426C24—22no—
427C24—41no—
428C24—41no—
429C24—41no—
430C24—41no—
431C24—41no—
432C24—41no—
433C24—42no—
434C24—42no—
435C24—42no—
436C24—42no—
437C24C2×C22⋊C412yes—
438C24#12412yes—
439C24#12712yes—
440C24C22×D411yescharacteristic
441C2×Q8—22no—
442C2×Q8—22no—
443C2×Q8—22no—
444C2×Q8—22no—
445C2×Q8—22no—
446C2×Q8—22no—
447C2×Q8—41no—
448C2×Q8—41no—
449C2×Q8—41no—
450C2×Q8—41no—
451C2×Q8—41no—
452C2×Q8—41no—
453C2×Q8—41no—
454C2×Q8—41no—
455C2×Q8—41no—
456C2×Q8—41no—
457C2×Q8—41no—
458C2×Q8—41no—
459C2×Q8—41no—
460C2×Q8—41no—
461C2×Q8—41no—
462C2×Q8—41no—
463C2×Q8—41no—
464C2×Q8—41no—
465C2×Q8—41no—
466C2×Q8—41no—
467C2×Q8—41no—
468C2×Q8—41no—
469C2×D4—22no—
470C2×D4—22no—
471C2×D4—22no—
472C2×D4—22no—
473C2×D4—22no—
474C2×D4—22no—
475C2×D4—48no—
476C2×D4—41no—
477C2×D4—41no—
478C2×D4—41no—
479C2×D4—41no—
480C2×D4—41no—
481C2×D4—41no—
482C2×D4—41no—
483C2×D4—41no—
484C2×D4—41no—
485C2×D4—41no—
486C2×D4—41no—
487C2×D4—41no—
488C2×D4—41no—
489C2×D4—41no—
490C2×D4—41no—
491C2×D4—41no—
492C2×D4—41no—
493C2×D4—41no—
494C2×D4—41no—
495C2×D4—41no—
496C2×D4—41no—
497C2×D4—41no—
498C2×D4—88no—
499C2×D4—88no—
500C2×D4—84no—
501C2×D4—84no—
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—21no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—22no—
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—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—48no—
548C22×C4—41no—
549C22×C4—41no—
550C22×C4—41no—
551C22×C4—41no—
552C22×C4—41no—
553C22×C4—41no—
554C22×C4—41no—
555C22×C4—41no—
556C22×C4—41no—
557C22×C4—41no—
558C22×C4—41no—
559C22×C4—41no—
560C22×C4—41no—
561C22×C4—41no—
562C22×C4—41no—
563C22×C4—41no—
564C22×C4—41no—
565C22×C4—41no—
566C22×C4—42no—
567C22×C4—42no—
568C22×C4—42no—
569C22×C4—42no—
570C22×C4—42no—
571C22×C4—42no—
572C22×C4—42no—
573C22×C4—42no—
574C22×C4—42no—
575C22×C4—42no—
576C22×C4—42no—
577C22×C4—42no—
578C22×C4—88no—
579C22×C4—84no—
580C22×C4—84no—
581C22×C4—88no—
582C22×C4C2×C22⋊C414yes—
583C22×C4C2×C22⋊C414yes—
584C22×C4C2×C22⋊C412yes—
585C22×C4C4×D414yes—
586C22×C4C4×D414yes—
587C22×C4#12014yes—
588C22×C4#12114yes—
589C22×C4#12114yes—
590C22×C4#12314yes—
591C22×C4#12412yes—
592C22×C4#12712yes—
593C22×C4C23×C411yescharacteristic
594C22×C4C22×D411yescharacteristic
595C22×C4C22×D411yescharacteristic
596C22×C4C22×D411yescharacteristic
597C22×C4C22×D411yescharacteristic
598C22×C4C22×D411yescharacteristic
599C22×C4C2×#4111yescharacteristic
600C22×C4C2×#4111yescharacteristic
601C22×C4C2×#4111yescharacteristic
602C22×C4C2×#4111yescharacteristic
603C22×C4H(5,𝔽2)11yescharacteristic
604C22×C4H(5,𝔽2)11yescharacteristic
605C22×C42−1+411yescharacteristic
606C22×C42−1+411yescharacteristic
607C2×C8—22no—
608C2×C8—22no—
609C2×C8—22no—
610C2×C8—22no—
611C2×C8—22no—
612C2×C8—22no—
613C2×C8—22no—
614C2×C8—22no—
615C2×C8—22no—
616C2×C8—22no—
617C2×C8—22no—
618C2×C8—22no—
619C2×C8—41no—
620C2×C8—41no—
621C2×C8—41no—
622C2×C8—41no—
623C2×C8—41no—
624C2×C8—41no—
625C2×C8—41no—
626C2×C8—41no—
627C2×C8—41no—
628C2×C8—41no—
629C2×C8—41no—
630C2×C8—41no—
631C2×C8—41no—
632C2×C8—41no—
633C2×C8—41no—
634C2×C8—41no—
635C4⋊C4—216no—
636C4⋊C4—22no—
637C4⋊C4—22no—
638C4⋊C4—22no—
639C4⋊C4—22no—
640C4⋊C4—22no—
641C4⋊C4—22no—
642C4⋊C4—22no—
643C4⋊C4—22no—
644C4⋊C4—22no—
645C4⋊C4—22no—
646C4⋊C4—22no—
647C4⋊C4—22no—
648C4⋊C4—48no—
649C4⋊C4—41no—
650C4⋊C4—41no—
651C4⋊C4—41no—
652C4⋊C4—41no—
653C4⋊C4—41no—
654C4⋊C4—41no—
655C4⋊C4—41no—
656C4⋊C4—41no—
657C4⋊C4—41no—
658C4⋊C4—41no—
659C4⋊C4—41no—
660C4⋊C4—41no—
661C4⋊C4—48no—
662C4⋊C4—88no—
663C4⋊C4—88no—
664C4⋊C4—88no—
665C22⋊C4—216no—
666C22⋊C4—48no—
667C22⋊C4—48no—
668C22⋊C4—416no—
669C22⋊C4—48no—
670C22⋊C4—88no—
671C42—22no—
672C42—22no—
673C42—22no—
674C42—22no—
675C42—48no—
676C42C4×D414yes—
677C42C4×D414yes—
678C42#12114yes—
679C42#12114yes—
680C23—22no—
681C23—24no—
682C23—24no—
683C23—24no—
684C23—24no—
685C23—22no—
686C23—22no—
687C23—22no—
688C23—22no—
689C23—22no—
690C23—22no—
691C23—22no—
692C23—22no—
693C23—22no—
694C23—42no—
695C23—42no—
696C23—42no—
697C23—42no—
698C23—42no—
699C23—42no—
700C23—42no—
701C23—42no—
702C23—42no—
703C23—44no—
704C23—44no—
705C23—42no—
706C23—42no—
707C23—82no—
708C23—82no—
709C23—82no—
710C23—82no—
711C23—81no—
712C23—81no—
713C23—81no—
714C23—81no—
715C23—81no—
716C23—81no—
717C23—82no—
718C23—82no—
719C23—82no—
720C23—82no—
721C23—82no—
722C23—81no—
723C23—82no—
724C23—81no—
725C23#39014yes—
726C23C22×C22⋊C411yescharacteristic
727C23C2×#12011yescharacteristic
728C23C2×#12311yescharacteristic
729C23C2×#12411yescharacteristic
730C23C2×#12711yescharacteristic
731C23#53511yescharacteristic
732C23#53611yescharacteristic
733C23#57612yes—
734C23#57712yes—
735C23#57712yes—
736C23#57812yes—
737Q8—42no—
738Q8—42no—
739Q8—42no—
740Q8—42no—
741Q8—81no—
742Q8—81no—
743Q8—81no—
744Q8—81no—
745D4—42no—
746D4—42no—
747D4—42no—
748D4—42no—
749D4—816no—
750D4—81no—
751D4—81no—
752D4—81no—
753D4—81no—
754C2×C4—22no—
755C2×C4—24no—
756C2×C4—24no—
757C2×C4—24no—
758C2×C4—24no—
759C2×C4—22no—
760C2×C4—22no—
761C2×C4—24no—
762C2×C4—22no—
763C2×C4—24no—
764C2×C4—22no—
765C2×C4—22no—
766C2×C4—24no—
767C2×C4—24no—
768C2×C4—24no—
769C2×C4—24no—
770C2×C4—24no—
771C2×C4—24no—
772C2×C4—24no—
773C2×C4—24no—
774C2×C4—24no—
775C2×C4—24no—
776C2×C4—24no—
777C2×C4—42no—
778C2×C4—42no—
779C2×C4—42no—
780C2×C4—42no—
781C2×C4—42no—
782C2×C4—44no—
783C2×C4—44no—
784C2×C4—42no—
785C2×C4—42no—
786C2×C4—42no—
787C2×C4—42no—
788C2×C4—44no—
789C2×C4—44no—
790C2×C4—44no—
791C2×C4—44no—
792C2×C4—42no—
793C2×C4—42no—
794C2×C4—42no—
795C2×C4—42no—
796C2×C4—816no—
797C2×C4—82no—
798C2×C4—82no—
799C2×C4—81no—
800C2×C4—81no—
801C2×C4—81no—
802C2×C4—81no—
803C2×C4—81no—
804C2×C4—81no—
805C2×C4—81no—
806C2×C4—81no—
807C2×C4—81no—
808C2×C4—81no—
809C2×C4—81no—
810C2×C4—81no—
811C2×C4—81no—
812C2×C4—81no—
813C2×C4—82no—
814C2×C4—82no—
815C2×C4—82no—
816C2×C4—82no—
817C2×C4—81no—
818C2×C4—81no—
819C2×C4#38618yes—
820C2×C4#39014yes—
821C2×C4C2×C4×D411yescharacteristic
822C2×C4C2×C4×D411yescharacteristic
823C2×C4C2×C4×D411yescharacteristic
824C2×C4C2×C4×D411yescharacteristic
825C2×C4#52011yescharacteristic
826C2×C4#52011yescharacteristic
827C2×C4C2×#12111yescharacteristic
828C2×C4C2×#12111yescharacteristic
829C2×C4C2×#12111yescharacteristic
830C2×C4C2×#12111yescharacteristic
831C2×C4#53711yescharacteristic
832C2×C4#53711yescharacteristic
833C2×C4D4211yescharacteristic
834C2×C4D4211yescharacteristic
835C2×C4D4211yescharacteristic
836C2×C4D4211yescharacteristic
837C2×C4#54711yescharacteristic
838C2×C4#54711yescharacteristic
839C2×C4#54711yescharacteristic
840C2×C4#54711yescharacteristic
841C2×C4#54811yescharacteristic
842C2×C4#54811yescharacteristic
843C2×C4#54811yescharacteristic
844C2×C4#54811yescharacteristic
845C2×C4#55311yescharacteristic
846C2×C4#55311yescharacteristic
847C2×C4#55311yescharacteristic
848C2×C4#55311yescharacteristic
849C8—42no—
850C8—42no—
851C8—42no—
852C8—42no—
853C22—24no—
854C22—24no—
855C22—24no—
856C22—42no—
857C22—42no—
858C22—44no—
859C22—44no—
860C22—44no—
861C22—42no—
862C22—42no—
863C22—44no—
864C22—82no—
865C22—84no—
866C22—84no—
867C22—82no—
868C22—82no—
869C22—161no—
870C22—161no—
871C22—162no—
872C22—162no—
873C22—161no—
874C22—161no—
875C22C2×#38611yescharacteristic
876C22C2×#39011yescharacteristic
877C22#231111yescharacteristic
878C22#243311yescharacteristic
879C22#243611yescharacteristic
880C22#250111yescharacteristic
881C22#250411yescharacteristic
882C22#289712yes—
883C22#289812yes—
884C22#301212yes—
885C22#301312yes—
886C22#309812yes—
887C22#309912yes—
888C22#313612yes—
889C22#313712yes—
890C22#315411yescharacteristic
891C22#315411yescharacteristic
892C22#315511yescharacteristic
893C22#315611yescharacteristic
894C22#322412yes—
895C22#322512yes—
896C22#324312yes—
897C22#324412yes—
898C4—24no—
899C4—28no—
900C4—44no—
901C4—82no—
902C4—82no—
903C4—82no—
904C4—82no—
905C4—82no—
906C4—82no—
907C4—82no—
908C4#236111yescharacteristic
909C4#236111yescharacteristic
910C4#236111yescharacteristic
911C4#236111yescharacteristic
912C4#241611yescharacteristic
913C4#241611yescharacteristic
914C4#241611yescharacteristic
915C4#241611yescharacteristic
916C2—44no—
917C2—162no—
918C2#1413711yescharacteristic
919C2#2091512yes—
920C2#2120511yescharacteristic
921C2#2120611yescharacteristic
922C2#2187112yes—
923C2#2573611yescharacteristic
924C2#2573711yescharacteristic
925C2#2591612yes—
926C2#2792011yescharacteristic
927C2#2792111yescharacteristic
928C2#2798412yes—
subgroupG/H
center, socleC24C22×D4
commutatorC22×C4C23×C4
Frattini, cosocleC23×C4C24
prime radicalC22×#121C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24 ◁ C22×#117 ◁ G
LECSG ▷ C23×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C2×#2317C2semidirect
3. C2×#1959C2semidirect
4. C2×#1958C2semidirect
6. C2×#1873C2semidirect
8. C2×#1872C2semidirect
9. C2×#1750C2semidirect
10. #11052C2semidirect
11. #11051C2semidirect
12. #11050C2semidirect
13. #11049C2semidirect
14. #10843C2semidirect
15. #10841C2semidirect
35. #2620C4semidirect
80. C2×#124C2×C4semidirect
171. #391C2×C4semidirect
173. #390C2×C4semidirect
180. #384C2×C4semidirect
181. #384D4semidirect
185. #382D4semidirect

Maximal subgroups

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

subgroupindex
C2×#26202
C2×#23172
C2×#19592
C2×#19582
C2×#18752
C2×#18732
C2×#18742
C2×#18722
C2×#17502
#110522
#110512
#110502
#110492
#108432
#108412