Finite Group Databasebeta

← #366957

Subgroups — #366957

Order 512.

1386 conjugacy classes of subgroups.

The subgroup lattice has 848 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#34947C211yesmaximal, characteristic
2C2×#1995C211yesmaximal, characteristic, complemented
3C2×#1986C211yesmaximal, characteristic, complemented
4#21146C211yesmaximal, characteristic, complemented
5C2×#1806C211yesmaximal, characteristic
6C2×#1759C211yesmaximal, characteristic
7#13759C211yesmaximal, characteristic, complemented
8#11370C211yesmaximal, characteristic, complemented
9#11370C211yesmaximal, characteristic, complemented
10#11053C211yesmaximal, characteristic
11#11053C211yesmaximal, characteristic
12#10924C211yesmaximal, characteristic
13#10923C211yesmaximal, characteristic
14#10840C211yesmaximal, characteristic, complemented
15#10839C211yesmaximal, characteristic, complemented
16C2×#533C2211yescharacteristic
17C2×C4×#41C2211yescharacteristic
18C2×#423C2211yescharacteristic
19C2×#423C2211yescharacteristic
20C2×#423C2211yescharacteristic
21C22×#104C2211yescharacteristic
22C22×#104C2211yescharacteristic
23C22×#104C2211yescharacteristic
24C22×#104C2211yescharacteristic
25C2×C4×M16C2211yescharacteristic
26#2568C411yescharacteristic, complemented
27#2567C411yescharacteristic, complemented
28#2566C411yescharacteristic, complemented
29#2566C411yescharacteristic, complemented
30#2565C411yescharacteristic, complemented
31#2565C411yescharacteristic, complemented
32#2564—22no—
33#2563C411yescharacteristic, complemented
34#2542C411yescharacteristic, complemented
35#2417—22no—
36#2396—22no—
37C4×C22⋊Q8—22no—
38#2297C2211yescharacteristic
39#2297C2211yescharacteristic
40#2285C2211yescharacteristic
41#2285C2211yescharacteristic
42C2×C4×C4⋊C4C2211yescharacteristic
43C2×C4×C4⋊C4C2211yescharacteristic
44C2×#376C2211yescharacteristic
45C2×#376C2211yescharacteristic
46C2×C43C2211yescharacteristic
47#1995—24no—
48#1986—24no—
49#1940—22no—
50#1939—22no—
51#1806—24no—
52#1759—24no—
53C2×#339C2211yescharacteristic
54C2×#339C2211yescharacteristic
55C2×#339C2211yescharacteristic
56C2×#339C2211yescharacteristic
57C2×#339C2211yescharacteristic
58C2×#339C2211yescharacteristic
59C2×#339C2211yescharacteristic
60C2×#339C2211yescharacteristic
61C2×#339C2211yescharacteristic
62C2×#339C2211yescharacteristic
63C2×#339C2211yescharacteristic
64C2×#339C2211yescharacteristic
65#1728C2211yescharacteristic
66#1728C2211yescharacteristic
67#1436—22no—
68#1436—22no—
69C4×#95C2211yescharacteristic
70C4×#95C2211yescharacteristic
71C22×#41C2311yescharacteristic
72C22×M16C2311yescharacteristic
73C22×M16C2311yescharacteristic
74C22×M16C2311yescharacteristic
75C22×M16C2311yescharacteristic
76#533—22no—
77#533—22no—
78#533—22no—
79#533—22no—
80C2×C4⋊Q8C2×C411yescharacteristic
81C2×C4⋊Q8C2×C411yescharacteristic
82C2×#125C2×C411yescharacteristic
83C2×#125C2×C411yescharacteristic
84C2×C22⋊Q8—21no—
85C2×C22⋊Q8—21no—
86C2×C22⋊Q8—22no—
87C4×#41—22no—
88C4×#41—22no—
89C4×#41—22no—
90C4×#41—22no—
91C2×C4×Q8—21no—
92C2×C4×Q8—21no—
93C2×C4×Q8C2×C411yescharacteristic
94C2×C4×Q8C2×C411yescharacteristic
95C2×C4×D4—21no—
96C2×C4×D4—21no—
97C2×C4×D4C2×C411yescharacteristic
98C2×C4×D4C2×C411yescharacteristic
99C2×#117—21no—
100C2×#117C2311yescharacteristic
101C2×#117C2311yescharacteristic
102C2×#117C2311yescharacteristic
103C22×C4⋊C4—21no—
104C22×C4⋊C4D412yes—
105C22×C42—21no—
106C22×C42—22no—
107C22×C42C2311yescharacteristic
108C22×C42C2311yescharacteristic
109C22×C42C2311yescharacteristic
110C22×C42C2311yescharacteristic
111C22×C42C2311yescharacteristic
112C22×C42C2311yescharacteristic
113C22×C42C2311yescharacteristic
114#423—22no—
115#423—22no—
116#423—22no—
117#423—22no—
118#423—41no—
119#423—41no—
120C2×C4⋊C8—21no—
121C2×C4⋊C8—22no—
122C2×C4⋊C8—22no—
123C2×C4⋊C8—21no—
124C2×#104—22no—
125C2×#104—22no—
126C2×#104—22no—
127C2×#104—22no—
128C2×#104—22no—
129C2×#104—22no—
130C2×#104—22no—
131C2×#104—22no—
132C2×#104—22no—
133C2×#104—41no—
134C2×#104—41no—
135C2×#104Q814yescomplemented
136C4×M16—22no—
137C4×M16—22no—
138C2×#97—21no—
139C2×C4×C8—21no—
140#400—22no—
141#399—22no—
142#398—22no—
143#398—22no—
144#396—22no—
145#396—22no—
146#395—22no—
147#393—22no—
148#391—22no—
149#391C2×C411yescharacteristic
150#391C2×C411yescharacteristic
151#391C2×C411yescharacteristic
152#391C2×C411yescharacteristic
153#390C2×C411yescharacteristic
154#390C2×C411yescharacteristic
155#390C2×C411yescharacteristic
156#390C2×C411yescharacteristic
157#389—22no—
158#387—22no—
159#387—22no—
160#386—22no—
161#386—22no—
162#385—22no—
163#385—22no—
164#384C2×C411yescharacteristic
165#384C2×C411yescharacteristic
166#384C2×C411yescharacteristic
167#384C2×C411yescharacteristic
168#382C2×C411yescharacteristic
169#382C2×C411yescharacteristic
170#382C2×C411yescharacteristic
171#382C2×C411yescharacteristic
172#380—22no—
173#380—22no—
174#380—22no—
175C4×C4⋊C4—22no—
176C4×C4⋊C4—22no—
177C4×C4⋊C4—22no—
178C4×C4⋊C4C2×C411yescharacteristic
179C4×C4⋊C4C2×C411yescharacteristic
180C4×C4⋊C4C2×C411yescharacteristic
181C4×C4⋊C4C2×C411yescharacteristic
182C4×C4⋊C4D414yes—
183C4×C4⋊C4D412yes—
184C4×C4⋊C4D412yes—
185C4×C22⋊C4—22no—
186C4×C22⋊C4—22no—
187#376—22no—
188#376—22no—
189#376—41no—
190#376D414yes—
191C2×#95—21no—
192C2×#95—21no—
193C2×#95—21no—
194C2×#95—22no—
195C2×#95—22no—
196C2×#95—22no—
197C2×#95D412yes—
198C43—22no—
199C43—41no—
200#339—22no—
201#339—22no—
202#339—22no—
203#339—22no—
204#339—22no—
205#339—22no—
206#339—22no—
207#339—22no—
208#339—22no—
209#339—22no—
210#339—22no—
211#339—22no—
212#336—22no—
213#336—22no—
214C2×#41—21no—
215C2×#41—21no—
216C2×#41—21no—
217C2×#41—21no—
218C2×#41—21no—
219C2×#41—21no—
220C2×#41—21no—
221C2×#41—21no—
222C2×#41—21no—
223C2×#41—21no—
224C2×#41C2×Q812yes—
225C2×#41#4112yes—
226C22×Q8—21no—
227C22×Q8—21no—
228C22×Q8C22×C411yescharacteristic
229C22×D4—21no—
230C22×D4C22×C411yescharacteristic
231C23×C4—21no—
232C23×C4—21no—
233C23×C4—21no—
234C23×C4—21no—
235C23×C4—21no—
236C23×C4—21no—
237C23×C4—21no—
238C23×C4C2×D412yes—
239C23×C4C2×D412yes—
240C23×C4C2×D411yescharacteristic
241C23×C4C2×D411yescharacteristic
242C23×C4C2411yescharacteristic
243C2×M16—21no—
244C2×M16—21no—
245C2×M16—21no—
246C2×M16—21no—
247C2×M16—21no—
248C2×M16—21no—
249C2×M16—21no—
250C2×M16—21no—
251C2×M16—21no—
252C2×M16—21no—
253C2×M16—21no—
254C2×M16—21no—
255C2×M16—21no—
256C2×M16—21no—
257C2×M16—21no—
258C2×M16—21no—
259C2×M16—21no—
260C2×M16—21no—
261C2×M16—21no—
262C2×M16—21no—
263C2×M16—21no—
264C2×M16—21no—
265C2×M16C2×Q812yes—
266C2×M16#4112yes—
267C22×C8—21no—
268C22×C8—21no—
269C22×C8—21no—
270C22×C8—21no—
271C4⋊Q8—22no—
272C4⋊Q8—22no—
273C4⋊Q8—22no—
274C4⋊Q8—22no—
275#125—22no—
276#125—22no—
277#125—22no—
278#125—22no—
279C22⋊Q8—48no—
280C22⋊Q8—42no—
281C22⋊Q8—42no—
282C22⋊Q8—42no—
283C22⋊Q8—42no—
284C4×Q8—22no—
285C4×Q8—22no—
286C4×Q8—22no—
287C4×Q8—22no—
288C4×Q8—42no—
289C4×Q8—42no—
290C4×Q8—42no—
291C4×Q8—42no—
292C4×D4—22no—
293C4×D4—22no—
294C4×D4—22no—
295C4×D4—22no—
296C4×D4—42no—
297C4×D4—42no—
298C4×D4—42no—
299C4×D4—42no—
300#117—21no—
301#117—21no—
302#117—21no—
303#117—21no—
304#117—21no—
305#117—21no—
306#117—21no—
307#117—21no—
308#117—21no—
309#117—21no—
310#117—21no—
311#117—21no—
312#117—42no—
313#117—42no—
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—22no—
323C2×C4⋊C4—22no—
324C2×C4⋊C4—24no—
325C2×C4⋊C4—22no—
326C2×C4⋊C4—22no—
327C2×C4⋊C4—44no—
328C2×C4⋊C4—44no—
329C2×C4⋊C4C22⋊C412yes—
330C2×C4⋊C4C22⋊C412yes—
331C2×C4⋊C4C22⋊C412yes—
332C2×C4⋊C4C22⋊C412yes—
333C2×C4⋊C4C22×C411yescharacteristic
334C2×C4⋊C4C22×C411yescharacteristic
335C2×C4⋊C4C22×C411yescharacteristic
336C2×C4⋊C4C22×C411yescharacteristic
337C2×C4⋊C4C22×C411yescharacteristic
338C2×C4⋊C4C22×C411yescharacteristic
339C2×C22⋊C4—21no—
340C2×C22⋊C4—21no—
341C2×C22⋊C4—21no—
342C2×C22⋊C4—21no—
343C2×C22⋊C4—21no—
344C2×C22⋊C4—22no—
345C2×C22⋊C4—22no—
346C2×C22⋊C4—22no—
347C2×C22⋊C4—22no—
348C2×C42—21no—
349C2×C42—21no—
350C2×C42—21no—
351C2×C42—21no—
352C2×C42—21no—
353C2×C42—21no—
354C2×C42—21no—
355C2×C42—21no—
356C2×C42—21no—
357C2×C42—21no—
358C2×C42—21no—
359C2×C42—21no—
360C2×C42—21no—
361C2×C42—21no—
362C2×C42—21no—
363C2×C42—21no—
364C2×C42—21no—
365C2×C42—21no—
366C2×C42—21no—
367C2×C42—21no—
368C2×C42—21no—
369C2×C42—21no—
370C2×C42—21no—
371C2×C42—21no—
372C2×C42—21no—
373C2×C42—21no—
374C2×C42—21no—
375C2×C42—21no—
376C2×C42—21no—
377C2×C42—21no—
378C2×C42—21no—
379C2×C42—44no—
380C2×C42—44no—
381C2×C42—44no—
382C2×C42—42no—
383C2×C42—42no—
384C2×C42C22×C411yescharacteristic
385C2×C42C22×C411yescharacteristic
386C2×C42C22×C411yescharacteristic
387C2×C42C22×C411yescharacteristic
388C2×C42C22×C411yescharacteristic
389C2×C42C22×C411yescharacteristic
390C2×C42C2×D412yes—
391C2×C42C2×D412yes—
392C2×C42C2×D412yes—
393C2×C42C2×D412yes—
394C2×C42C2×D412yes—
395C2×C42C2×D412yes—
396C2×C42C2×D412yes—
397C2×C42C2×D412yes—
398C2×C42C2×D411yescharacteristic
399C2×C42C2×D411yescharacteristic
400C2×C42C2×Q812yes—
401C2×C42#4112yes—
402C2×C42#4112yes—
403C2×C42#4112yes—
404C4⋊C8—44no—
405C4⋊C8—44no—
406C4⋊C8—42no—
407C4⋊C8—42no—
408#104—28no—
409#104—28no—
410#104—44no—
411#104—44no—
412#97—42no—
413C4×C8—42no—
414#95—22no—
415#95—22no—
416#95—22no—
417#95—22no—
418#95—22no—
419#95—22no—
420#95—22no—
421#95—22no—
422#95—24no—
423#95—24no—
424#95—24no—
425#95—44no—
426#95—44no—
427#95—44no—
428#95C22⋊C412yes—
429#95C22⋊C412yes—
430#95C22⋊C412yes—
431#95C22⋊C412yes—
432C24—21no—
433C24C22×D411yescharacteristic
434#41—22no—
435#41—22no—
436#41—22no—
437#41—22no—
438#41—22no—
439#41—22no—
440#41—22no—
441#41—22no—
442#41—41no—
443#41—41no—
444#41—41no—
445#41—41no—
446#41—41no—
447#41—41no—
448#41—41no—
449#41—41no—
450C2×Q8—21no—
451C2×Q8—21no—
452C2×Q8—21no—
453C2×Q8—21no—
454C2×Q8—21no—
455C2×Q8—44no—
456C2×Q8—42no—
457C2×Q8—42no—
458C2×Q8—82no—
459C2×Q8C4×Q812yes—
460C2×D4—22no—
461C2×D4—22no—
462C2×D4—21no—
463C2×D4—21no—
464C2×D4—21no—
465C2×D4—21no—
466C2×D4—21no—
467C2×D4—41no—
468C2×D4—41no—
469C2×D4—41no—
470C2×D4—41no—
471C2×D4C4×Q812yes—
472C22×C4—24no—
473C22×C4—21no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—24no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—42no—
494C22×C4—42no—
495C22×C4—42no—
496C22×C4—42no—
497C22×C4—42no—
498C22×C4—44no—
499C22×C4—42no—
500C22×C4—42no—
501C22×C4—42no—
502C22×C4—41no—
503C22×C4—41no—
504C22×C4—41no—
505C22×C4—41no—
506C22×C4—41no—
507C22×C4—41no—
508C22×C4—42no—
509C22×C4—42no—
510C22×C4—42no—
511C22×C4—42no—
512C22×C4—41no—
513C22×C4—41no—
514C22×C4—41no—
515C22×C4—41no—
516C22×C4—42no—
517C22×C4—42no—
518C22×C4—82no—
519C22×C4C2×C22⋊C412yes—
520C22×C4C2×C22⋊C412yes—
521C22×C4C2×C22⋊C412yes—
522C22×C4C2×C22⋊C411yescharacteristic
523C22×C4C2×C22⋊C411yescharacteristic
524C22×C4C2×C22⋊C411yescharacteristic
525C22×C4C2×C22⋊C411yescharacteristic
526C22×C4C2×C22⋊C412yes—
527C22×C4#12112yes—
528C22×C4#12112yes—
529C22×C4#12112yes—
530C22×C4#12112yes—
531C22×C4C23×C411yescharacteristic
532C22×C4C22×D411yescharacteristic
533C22×C4C22×D411yescharacteristic
534C22×C4C22×D411yescharacteristic
535C22×C4C22×Q811yescharacteristic
536C22×C4C2×#4111yescharacteristic
537C22×C4C2×#4111yescharacteristic
538C22×C4C2×#4111yescharacteristic
539C22×C4C2×#4111yescharacteristic
540C22×C4C2×#4111yescharacteristic
541C22×C4H(5,𝔽2)11yescharacteristic
542C22×C42−1+411yescharacteristic
543C22×C42−1+411yescharacteristic
544C22×C42−1+411yescharacteristic
545M16—22no—
546M16—22no—
547M16—22no—
548M16—22no—
549M16—41no—
550M16—41no—
551M16—41no—
552M16—41no—
553M16—41no—
554M16—41no—
555M16—41no—
556M16—41no—
557M16—41no—
558M16—41no—
559M16—41no—
560M16—41no—
561C2×C8—22no—
562C2×C8—22no—
563C2×C8—41no—
564C2×C8—41no—
565C2×C8—41no—
566C2×C8—41no—
567C2×C8—41no—
568C2×C8—41no—
569C2×C8—41no—
570C2×C8—41no—
571C2×C8—41no—
572C2×C8—41no—
573C4⋊C4—24no—
574C4⋊C4—24no—
575C4⋊C4—21no—
576C4⋊C4—21no—
577C4⋊C4—21no—
578C4⋊C4—21no—
579C4⋊C4—21no—
580C4⋊C4—21no—
581C4⋊C4—21no—
582C4⋊C4—21no—
583C4⋊C4—21no—
584C4⋊C4—21no—
585C4⋊C4—21no—
586C4⋊C4—21no—
587C4⋊C4—42no—
588C4⋊C4—42no—
589C4⋊C4—48no—
590C4⋊C4—44no—
591C4⋊C4—42no—
592C4⋊C4—42no—
593C4⋊C4—42no—
594C4⋊C4—42no—
595C4⋊C4—42no—
596C4⋊C4—42no—
597C4⋊C4—42no—
598C4⋊C4—42no—
599C4⋊C4—44no—
600C4⋊C4—82no—
601C4⋊C4—82no—
602C22⋊C4—44no—
603C22⋊C4—41no—
604C22⋊C4—41no—
605C22⋊C4—41no—
606C22⋊C4—41no—
607C22⋊C4—41no—
608C22⋊C4—41no—
609C22⋊C4—42no—
610C22⋊C4—42no—
611C22⋊C4—44no—
612C22⋊C4—82no—
613C22⋊C4—82no—
614C42—21no—
615C42—21no—
616C42—21no—
617C42—21no—
618C42—21no—
619C42—21no—
620C42—21no—
621C42—21no—
622C42—22no—
623C42—22no—
624C42—22no—
625C42—22no—
626C42—22no—
627C42—22no—
628C42—22no—
629C42—22no—
630C42—22no—
631C42—22no—
632C42—22no—
633C42—22no—
634C42—22no—
635C42—416no—
636C42—41no—
637C42—41no—
638C42—41no—
639C42—41no—
640C42—41no—
641C42—41no—
642C42—41no—
643C42—41no—
644C42—41no—
645C42—41no—
646C42—41no—
647C42—41no—
648C42—42no—
649C42—42no—
650C42C4×D412yes—
651C42C4×D412yes—
652C42C4×D412yes—
653C42C4×D412yes—
654C42C22⋊Q814yescomplemented
655C42#12412yes—
656C42#12412yes—
657C42#12712yes—
658C42#12712yes—
659C23—22no—
660C23—22no—
661C23—22no—
662C23—41no—
663C23—42no—
664C23—42no—
665C23—41no—
666C23C22×C22⋊C411yescharacteristic
667C23C2×#12111yescharacteristic
668C23C2×#12111yescharacteristic
669C23#54611yescharacteristic
670C23#54711yescharacteristic
671C23#54811yescharacteristic
672C23D4×Q811yescharacteristic
673Q8—22no—
674Q8—22no—
675Q8—41no—
676Q8—41no—
677Q8—84no—
678Q8—84no—
679D4—22no—
680D4—22no—
681D4—42no—
682D4—42no—
683D4—42no—
684D4—42no—
685D4—41no—
686D4—41no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—24no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—24no—
705C2×C4—42no—
706C2×C4—42no—
707C2×C4—42no—
708C2×C4—42no—
709C2×C4—44no—
710C2×C4—44no—
711C2×C4—44no—
712C2×C4—44no—
713C2×C4—44no—
714C2×C4—44no—
715C2×C4—42no—
716C2×C4—42no—
717C2×C4—42no—
718C2×C4—41no—
719C2×C4—42no—
720C2×C4—41no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—42no—
725C2×C4—42no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—42no—
729C2×C4—42no—
730C2×C4—42no—
731C2×C4—42no—
732C2×C4—42no—
733C2×C4—42no—
734C2×C4—42no—
735C2×C4—42no—
736C2×C4—42no—
737C2×C4—41no—
738C2×C4—41no—
739C2×C4—41no—
740C2×C4—41no—
741C2×C4—41no—
742C2×C4—41no—
743C2×C4—84no—
744C2×C4—84no—
745C2×C4—82no—
746C2×C4—82no—
747C2×C4—82no—
748C2×C4—82no—
749C2×C4—82no—
750C2×C4—82no—
751C2×C4#39012yes—
752C2×C4#39012yes—
753C2×C4#39012yes—
754C2×C4#39012yes—
755C2×C4#42114yes—
756C2×C4C2×C4×D411yescharacteristic
757C2×C4C2×C4×D411yescharacteristic
758C2×C4C2×C4×Q811yescharacteristic
759C2×C4C4×#4111yescharacteristic
760C2×C4#51911yescharacteristic
761C2×C4#52011yescharacteristic
762C2×C4C2×C22⋊Q811yescharacteristic
763C2×C4#52511yescharacteristic
764C2×C4C2×#12411yescharacteristic
765C2×C4#52911yescharacteristic
766C2×C4C2×#12711yescharacteristic
767C2×C4#53311yescharacteristic
768C2×C4#53611yescharacteristic
769C2×C4#53711yescharacteristic
770C2×C4#54111yescharacteristic
771C2×C4#54211yescharacteristic
772C2×C4#54611yescharacteristic
773C2×C4#54611yescharacteristic
774C2×C4#54711yescharacteristic
775C2×C4#54711yescharacteristic
776C2×C4#54811yescharacteristic
777C2×C4#54811yescharacteristic
778C2×C4D4×Q811yescharacteristic
779C2×C4D4×Q811yescharacteristic
780C2×C4#55211yescharacteristic
781C2×C4#55211yescharacteristic
782C2×C4#55411yescharacteristic
783C2×C4#55611yescharacteristic
784C8—42no—
785C8—42no—
786C8—81no—
787C8—81no—
788C22—22no—
789C22—22no—
790C22—21no—
791C22—21no—
792C22—21no—
793C22—21no—
794C22—22no—
795C22—22no—
796C22—44no—
797C22—42no—
798C22—81no—
799C22—81no—
800C22—82no—
801C22C2×#39011yescharacteristic
802C22#233911yescharacteristic
803C22Q8×C22⋊C411yescharacteristic
804C22#241511yescharacteristic
805C22#241711yescharacteristic
806C22#242711yescharacteristic
807C22#242911yescharacteristic
808C22C2×#42112yes—
809C22#290112yes—
810C4—22no—
811C4—22no—
812C4—22no—
813C4—22no—
814C4—24no—
815C4—44no—
816C4—44no—
817C4—42no—
818C4—42no—
819C4—42no—
820C4—42no—
821C4—82no—
822C4—82no—
823C4—81no—
824C4—81no—
825C4—81no—
826C4—81no—
827C4—81no—
828C4—81no—
829C4C4×C22⋊Q811yescharacteristic
830C4#232311yescharacteristic
831C4#236011yescharacteristic
832C4#236211yescharacteristic
833C4#248911yescharacteristic
834C4#249211yescharacteristic
835C4#254011yescharacteristic
836C4#254211yescharacteristic
837C2—21no—
838C2—21no—
839C2—21no—
840C2—21no—
841C2—82no—
842C2#1399711yescharacteristic
843C2#2120911yescharacteristic
844C2#2121011yescharacteristic
845C2#2250612yes—
846C2#2252912yes—
subgroupG/H
centerC22×C4C22×D4
commutatorC22×C4C23×C4
Frattini, cosocleC23×C4C24
socleC23C22×C22⋊C4
prime radicalC22×#41C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C4 ◁ C2×C4×C4⋊C4 ◁ G
LECSG ▷ C23×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C2×#1995C2semidirect
3. C2×#1986C2semidirect
4. #21146C2semidirect
7. #13759C2semidirect
8. #11370C2semidirect
9. #11370C2semidirect
14. #10840C2semidirect
15. #10839C2semidirect
26. #2568C4semidirect
27. #2567C4semidirect
28. #2566C4semidirect
29. #2566C4semidirect
30. #2565C4semidirect
31. #2565C4semidirect
33. #2563C4semidirect
34. #2542C4semidirect
135. C2×#104Q8semidirect
654. C42C22⋊Q8semidirect

Maximal subgroups

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

subgroupindex
#349472
C2×#19952
C2×#19862
#211462
C2×#18062
C2×#17592
#137592
#113702
#110532
#109242
#109232
#108402
#108392