Finite Group Databasebeta

← #221980

Subgroups — #221980

Order 512.

1471 conjugacy classes of subgroups.

The subgroup lattice has 850 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#36121C211yesmaximal, characteristic
2#22648C211yesmaximal, characteristic, complemented
3D4×C4⋊C8C211yesmaximal, characteristic, complemented
4C2×#1547C211yesmaximal, characteristic, complemented
5C22×#331C211yesmaximal, characteristic, complemented
6#9704C211yesmaximal, characteristic, complemented
7#9698C211yesmaximal, characteristic, complemented
8#9141C211yesmaximal, characteristic, complemented
9#9133C211yesmaximal, characteristic, complemented
10#9131C211yesmaximal, characteristic, complemented
11#9129C211yesmaximal, characteristic, complemented
12#8585C211yesmaximal, characteristic, complemented
13#8341C211yesmaximal, characteristic, complemented
14#8339C211yesmaximal, characteristic, complemented
15#8234C211yesmaximal, characteristic, complemented
16C2×#546—21no—
17C2×#532C2211yescharacteristic
18C22×#127C2211yescharacteristic
19C2×#435—21no—
20C2×C8×D4—21no—
21C2×#423C2211yescharacteristic, complemented
22C22×C4⋊C8C2211yescharacteristic
23C22×C4⋊C8C2211yescharacteristic
24C22×C4⋊C8C2211yescharacteristic, complemented
25#2858C2211yescharacteristic
26#2857C2211yescharacteristic
27#2856C2211yescharacteristic
28#2544—21no—
29#2445—21no—
30#2445C412yes—
31#2435—21no—
32#2431—21no—
33#2428—21no—
34#2428C412yes—
35#2408—21no—
36#2408C412yes—
37D4×C22⋊C4—21no—
38D4×C22⋊C4C412yes—
39C4×#127C2211yescharacteristic
40C42×D4C2211yescharacteristic
41#1940—21no—
42#1939—21no—
43#1851—21no—
44#1850—21no—
45#1850—21no—
46#1850—21no—
47#1842C2211yescharacteristic, complemented
48#1842C2211yescharacteristic, complemented
49#1797C2211yescharacteristic
50#1797C2211yescharacteristic
51#1797C2211yescharacteristic, complemented
52#1797C2211yescharacteristic, complemented
53#1767C2211yescharacteristic, complemented
54C4×C4⋊C8C2211yescharacteristic, complemented
55#1547—24no—
56C2×#332C2211yescharacteristic, complemented
57C2×#332C2211yescharacteristic, complemented
58C2×#332C2211yescharacteristic, complemented
59C2×#332C2211yescharacteristic, complemented
60C2×#331—24no—
61C2×#331C2211yescharacteristic
62C2×#331C2211yescharacteristic
63C2×#331C2211yescharacteristic
64C2×#331C2211yescharacteristic
65C2×#331C2211yescharacteristic
66C2×#331C2211yescharacteristic
67C2×#331C2211yescharacteristic
68C2×#331C2211yescharacteristic
69#1296C2211yescharacteristic, complemented
70#1296C2211yescharacteristic, complemented
71#1296C2211yescharacteristic, complemented
72#1296C2211yescharacteristic, complemented
73C22×#41—21no—
74C23×D4—21no—
75C23×D4—21no—
76C23×D4C2×C412yes—
77C22×M16—21no—
78C23×C8—21no—
79C23×C8—21no—
80C23×C8—21no—
81#546—44no—
82#546—44no—
83#532—22no—
84#532—22no—
85#532—41no—
86#532—41no—
87C2×C4⋊Q8C2311yescharacteristic
88C2×#127—22no—
89C2×#127—22no—
90C2×#127—21no—
91C2×#127—21no—
92C2×#127—41no—
93C2×#127—41no—
94C2×#127C2×C412yes—
95C2×#127C2311yescharacteristic
96C2×#127C2311yescharacteristic
97C2×#124—21no—
98C2×#124—21no—
99C2×#124—21no—
100C2×#123—22no—
101C2×C22⋊Q8—21no—
102C2×#121—21no—
103C2×#121—21no—
104C2×#121—21no—
105C2×#121—22no—
106C2×#121C2×C412yes—
107C2×#121C2×C412yes—
108C2×#120—22no—
109C2×C4×D4—21no—
110C2×C4×D4—21no—
111C2×C4×D4—21no—
112C2×C4×D4C2×C412yes—
113C2×C4×D4C2×C412yes—
114C2×C4×D4C2×C411yescharacteristic
115C2×C4×D4D411yescharacteristic
116C2×C4×D4D411yescharacteristic
117C22×C22⋊C4—22no—
118C22×C42C2311yescharacteristic
119C22×C42C2311yescharacteristic
120#435—44no—
121C8×D4—44no—
122#423—22no—
123#423—41no—
124C2×C4⋊C8—22no—
125C2×C4⋊C8—22no—
126C2×C4⋊C8—22no—
127C2×C4⋊C8—21no—
128C2×C4⋊C8—21no—
129C2×C4⋊C8—21no—
130C2×C4⋊C8—21no—
131C2×C4⋊C8—21no—
132C2×C4⋊C8—21no—
133C2×C4⋊C8—21no—
134C2×C4⋊C8—21no—
135C2×C4⋊C8—41no—
136C2×C4⋊C8—41no—
137C2×C4⋊C8—41no—
138C2×C4⋊C8C2311yescharacteristic
139C2×C4⋊C8C2311yescharacteristic
140C2×C4⋊C8C2311yescharacteristic
141C2×C4⋊C8C2311yescharacteristic
142C2×C4⋊C8C2311yescharacteristic
143C2×C4⋊C8C2311yescharacteristic
144C2×C4⋊C8C2311yescharacteristic
145C2×C4⋊C8C2311yescharacteristic
146C2×C22⋊C8—21no—
147C2×C22⋊C8—21no—
148C2×C22⋊C8—21no—
149C2×C22⋊C8—21no—
150C2×#97—21no—
151C2×C4×C8—21no—
152#394—22no—
153#394—22no—
154#394—22no—
155#394—22no—
156#392—22no—
157#392—22no—
158#391—21no—
159#390—21no—
160#390—21no—
161#390—21no—
162#390—21no—
163#390—21no—
164#390—21no—
165#390C2×C412yes—
166#390C2×C412yes—
167#390C2×C412yes—
168#390C2×C412yes—
169#389—21no—
170#389C2×C412yes—
171#386—22no—
172#386—22no—
173#386—22no—
174#386—22no—
175#384C2311yescharacteristic
176#380—21no—
177#380C2×C412yes—
178#379—22no—
179#379—22no—
180C4×C4⋊C4C2×C411yescharacteristic
181C4×C4⋊C4D411yescharacteristic
182C4×C4⋊C4D411yescharacteristic
183C4×C22⋊C4C2×C411yescharacteristic
184C4×C22⋊C4C2×C411yescharacteristic
185C4×C22⋊C4D411yescharacteristic
186C4×C22⋊C4D411yescharacteristic
187C4×C22⋊C4D411yescharacteristic
188C4×C22⋊C4D411yescharacteristic
189C43C2311yescharacteristic
190#336—21no—
191#336—21no—
192#336—21no—
193#336—21no—
194#336—21no—
195#336—21no—
196#332—22no—
197#332—22no—
198#332—41no—
199#332—41no—
200#331—22no—
201#331—22no—
202#331—22no—
203#331—22no—
204#331—22no—
205#331—41no—
206#331—41no—
207#331D414yescomplemented
208C25—22no—
209C2×#41—42no—
210C2×#41—42no—
211C2×#41—42no—
212C2×#41—42no—
213C2×#41—81no—
214C2×#41—81no—
215C22×Q8—21no—
216C22×D4—24no—
217C22×D4—22no—
218C22×D4—22no—
219C22×D4—22no—
220C22×D4—22no—
221C22×D4—22no—
222C22×D4—21no—
223C22×D4—21no—
224C22×D4—21no—
225C22×D4—21no—
226C22×D4—42no—
227C22×D4—42no—
228C22×D4—42no—
229C22×D4—42no—
230C22×D4—42no—
231C22×D4—44no—
232C22×D4—42no—
233C22×D4—42no—
234C22×D4—42no—
235C22×D4—42no—
236C22×D4—81no—
237C22×D4—81no—
238C22×D4—81no—
239C22×D4—81no—
240C22×D4—82no—
241C22×D4C22⋊C411yescharacteristic
242C22×D4C22×C412yes—
243C22×D4C22×C412yes—
244C23×C4—22no—
245C23×C4—22no—
246C23×C4C22×C411yescharacteristic
247C23×C4C22×C411yescharacteristic
248C23×C4C2×D411yescharacteristic
249C23×C4C2×D411yescharacteristic
250C23×C4C2×D411yescharacteristic
251C23×C4C2×D411yescharacteristic
252C2×M16—42no—
253C2×M16—42no—
254C2×M16—81no—
255C22×C8—21no—
256C22×C8—21no—
257C22×C8—21no—
258C22×C8—21no—
259C22×C8—21no—
260C22×C8—21no—
261C22×C8—21no—
262C22×C8—21no—
263C22×C8—42no—
264C22×C8—42no—
265C22×C8—42no—
266C22×C8—42no—
267C22×C8—42no—
268C22×C8—42no—
269C22×C8—81no—
270C22×C8—81no—
271C22×C8—81no—
272C4⋊Q8—21no—
273C4⋊Q8—21no—
274C4⋊Q8—21no—
275C4⋊Q8—21no—
276#127—24no—
277#127—21no—
278#127—21no—
279#127—21no—
280#127—21no—
281#127—21no—
282#127—21no—
283#127—42no—
284#127—42no—
285#127—42no—
286#127—42no—
287#127—42no—
288#127C2×D412yes—
289#127#4112yes—
290#124—42no—
291#124—42no—
292#124—42no—
293#124—42no—
294#124—81no—
295#124—81no—
296#123—48no—
297C22⋊Q8—42no—
298C22⋊Q8—42no—
299#121—24no—
300#121—42no—
301#121—42no—
302#121—42no—
303#121—42no—
304#121—42no—
305#121—48no—
306#121—81no—
307#121—81no—
308#121—82no—
309#120—48no—
310C4×D4—22no—
311C4×D4—22no—
312C4×D4—24no—
313C4×D4—42no—
314C4×D4—42no—
315C4×D4—42no—
316C4×D4—42no—
317C4×D4—42no—
318C4×D4—42no—
319C4×D4—81no—
320C4×D4—81no—
321C4×D4—82no—
322C4×D4D814yes—
323C4×D4SD1614yes—
324C2×C4⋊C4—22no—
325C2×C4⋊C4—21no—
326C2×C4⋊C4—21no—
327C2×C4⋊C4—21no—
328C2×C4⋊C4C22⋊C411yescharacteristic
329C2×C4⋊C4C22⋊C411yescharacteristic
330C2×C4⋊C4C22⋊C411yescharacteristic
331C2×C4⋊C4C22×C412yes—
332C2×C4⋊C4C22×C412yes—
333C2×C22⋊C4—22no—
334C2×C22⋊C4—22no—
335C2×C22⋊C4—22no—
336C2×C22⋊C4—22no—
337C2×C22⋊C4—22no—
338C2×C22⋊C4—22no—
339C2×C22⋊C4—22no—
340C2×C22⋊C4—22no—
341C2×C22⋊C4—22no—
342C2×C22⋊C4—22no—
343C2×C22⋊C4—22no—
344C2×C22⋊C4—22no—
345C2×C22⋊C4—22no—
346C2×C22⋊C4—48no—
347C2×C22⋊C4C22⋊C411yescharacteristic
348C2×C22⋊C4C22⋊C411yescharacteristic
349C2×C22⋊C4C22⋊C411yescharacteristic
350C2×C22⋊C4C22⋊C411yescharacteristic
351C2×C22⋊C4C22⋊C411yescharacteristic
352C2×C22⋊C4C22⋊C411yescharacteristic
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×C42C22×C411yescharacteristic
362C2×C42C22×C411yescharacteristic
363C2×C42C22×C411yescharacteristic
364C2×C42C22×C411yescharacteristic
365C2×C42C2×D411yescharacteristic
366C2×C42C2×D411yescharacteristic
367C2×C42C2×D411yescharacteristic
368C2×C42C2×D411yescharacteristic
369C2×C42C2×D411yescharacteristic
370C2×C42C2×D411yescharacteristic
371C2×C42C2×D411yescharacteristic
372C2×C42C2×D411yescharacteristic
373C2×C42C2411yescharacteristic
374C4⋊C8—21no—
375C4⋊C8—21no—
376C4⋊C8—21no—
377C4⋊C8—21no—
378C4⋊C8—21no—
379C4⋊C8—21no—
380C4⋊C8—21no—
381C4⋊C8—21no—
382C4⋊C8—21no—
383C4⋊C8—21no—
384C4⋊C8—21no—
385C4⋊C8—21no—
386C4⋊C8—21no—
387C4⋊C8—21no—
388C4⋊C8—42no—
389C4⋊C8—42no—
390C4⋊C8—42no—
391C4⋊C8—42no—
392C4⋊C8—42no—
393C4⋊C8—42no—
394C4⋊C8—81no—
395C4⋊C8—81no—
396C4⋊C8C2×D412yes—
397C4⋊C8C2×D412yes—
398C22⋊C8—42no—
399C22⋊C8—42no—
400C22⋊C8—42no—
401C22⋊C8—42no—
402#97—42no—
403C4×C8—42no—
404#95—22no—
405#95—22no—
406#95C22⋊C411yescharacteristic
407#95C22⋊C411yescharacteristic
408#95C22⋊C411yescharacteristic
409#95C22⋊C411yescharacteristic
410#95C22⋊C411yescharacteristic
411#95C22⋊C411yescharacteristic
412C24—22no—
413C24—22no—
414C24—44no—
415C24—44no—
416C24—44no—
417C24—44no—
418C24—82no—
419C24—82no—
420C24—82no—
421C24C2×C22⋊C411yescharacteristic
422C24C2×C22⋊C411yescharacteristic
423#41—84no—
424#41—84no—
425#41—84no—
426#41—84no—
427C2×Q8—41no—
428C2×Q8—41no—
429C2×Q8—41no—
430C2×Q8—41no—
431C2×Q8—41no—
432C2×Q8—41no—
433C2×D4—22no—
434C2×D4—22no—
435C2×D4—22no—
436C2×D4—22no—
437C2×D4—22no—
438C2×D4—22no—
439C2×D4—22no—
440C2×D4—22no—
441C2×D4—22no—
442C2×D4—42no—
443C2×D4—42no—
444C2×D4—44no—
445C2×D4—44no—
446C2×D4—44no—
447C2×D4—42no—
448C2×D4—42no—
449C2×D4—44no—
450C2×D4—44no—
451C2×D4—44no—
452C2×D4—44no—
453C2×D4—41no—
454C2×D4—41no—
455C2×D4—41no—
456C2×D4—41no—
457C2×D4—41no—
458C2×D4—41no—
459C2×D4—41no—
460C2×D4—41no—
461C2×D4—41no—
462C2×D4—41no—
463C2×D4—41no—
464C2×D4—41no—
465C2×D4—41no—
466C2×D4—41no—
467C2×D4—41no—
468C2×D4—41no—
469C2×D4—41no—
470C2×D4—41no—
471C2×D4—41no—
472C2×D4—41no—
473C2×D4—44no—
474C2×D4—44no—
475C2×D4—84no—
476C2×D4—84no—
477C2×D4—84no—
478C2×D4—84no—
479C2×D4—84no—
480C2×D4—84no—
481C2×D4—84no—
482C2×D4—84no—
483C2×D4—82no—
484C2×D4—82no—
485C2×D4—82no—
486C2×D4—88no—
487C2×D4—88no—
488C2×D4—82no—
489C2×D4—82no—
490C2×D4—82no—
491C2×D4#10214yes—
492C2×D4C4×D414yes—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—21no—
497C22×C4—21no—
498C22×C4—21no—
499C22×C4—21no—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—22no—
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—41no—
519C22×C4—41no—
520C22×C4—41no—
521C22×C4—44no—
522C22×C4—44no—
523C22×C4—44no—
524C22×C4—82no—
525C22×C4—82no—
526C22×C4—82no—
527C22×C4C2×C22⋊C411yescharacteristic
528C22×C4C2×C22⋊C411yescharacteristic
529C22×C4C2×C22⋊C411yescharacteristic
530C22×C4C2×C22⋊C411yescharacteristic
531C22×C4C2×C22⋊C411yescharacteristic
532C22×C4C2×C22⋊C411yescharacteristic
533C22×C4C2×C22⋊C411yescharacteristic
534C22×C4C2×C22⋊C411yescharacteristic
535C22×C4C2×C22⋊C411yescharacteristic
536C22×C4C2×C22⋊C411yescharacteristic
537C22×C4C2×D812yes—
538C22×C4C2×D812yes—
539C22×C4C2×SD1612yes—
540C22×C4C2×SD1612yes—
541C22×C4AGL(1,ℤ/8)12yes—
542C22×C4#13712yes—
543C22×C4C23×C411yescharacteristic
544C22×C4C22×D411yescharacteristic
545C22×C4C22×D411yescharacteristic
546M16—84no—
547C2×C8—22no—
548C2×C8—22no—
549C2×C8—41no—
550C2×C8—41no—
551C2×C8—41no—
552C2×C8—41no—
553C2×C8—41no—
554C2×C8—41no—
555C2×C8—41no—
556C2×C8—41no—
557C2×C8—41no—
558C2×C8—41no—
559C2×C8—41no—
560C2×C8—41no—
561C2×C8—41no—
562C2×C8—41no—
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—84no—
572C2×C8—84no—
573C2×C8—84no—
574C4⋊C4—22no—
575C4⋊C4—22no—
576C4⋊C4—22no—
577C4⋊C4—41no—
578C4⋊C4—42no—
579C4⋊C4—41no—
580C4⋊C4—41no—
581C4⋊C4—41no—
582C4⋊C4—41no—
583C4⋊C4—41no—
584C4⋊C4—41no—
585C4⋊C4—44no—
586C4⋊C4#10214yes—
587C22⋊C4—22no—
588C22⋊C4—22no—
589C22⋊C4—22no—
590C22⋊C4—41no—
591C22⋊C4—44no—
592C22⋊C4—44no—
593C22⋊C4—44no—
594C22⋊C4—44no—
595C22⋊C4—44no—
596C22⋊C4—44no—
597C22⋊C4—44no—
598C22⋊C4—82no—
599C22⋊C4—82no—
600C22⋊C4—82no—
601C22⋊C4—82no—
602C22⋊C4—82no—
603C22⋊C4—82no—
604C22⋊C4#10214yes—
605C22⋊C4#10214yes—
606C42—21no—
607C42—21no—
608C42—21no—
609C42—21no—
610C42—21no—
611C42—21no—
612C42—21no—
613C42—21no—
614C42—21no—
615C42—21no—
616C42—21no—
617C42—21no—
618C42—21no—
619C42—21no—
620C42—21no—
621C42—21no—
622C42—21no—
623C42—21no—
624C42—41no—
625C42—41no—
626C42C2×D812yes—
627C42C2×SD1612yes—
628C42C22×D411yescharacteristic
629C42C2×#4111yescharacteristic
630C42H(5,𝔽2)11yescharacteristic
631C42H(5,𝔽2)11yescharacteristic
632C23—21no—
633C23—21no—
634C23—21no—
635C23—21no—
636C23—21no—
637C23—21no—
638C23—21no—
639C23—21no—
640C23—21no—
641C23—21no—
642C23—24no—
643C23—42no—
644C23—42no—
645C23—42no—
646C23—42no—
647C23—42no—
648C23—42no—
649C23—42no—
650C23—42no—
651C23—42no—
652C23—42no—
653C23—42no—
654C23—42no—
655C23—42no—
656C23—88no—
657C23—88no—
658C23—88no—
659C23—88no—
660C23—164no—
661C23—164no—
662C23—164no—
663C23#41312yes—
664C23C2×#10212yes—
665C23C2×#10212yes—
666C23#41712yes—
667C23C22×C22⋊C411yescharacteristic
668Q8—81no—
669Q8—81no—
670Q8—81no—
671Q8—81no—
672D4—28no—
673D4—44no—
674D4—44no—
675D4—42no—
676D4—42no—
677D4—42no—
678D4—42no—
679D4—42no—
680D4—42no—
681D4—42no—
682D4—42no—
683D4—88no—
684D4—88no—
685D4—82no—
686D4—82no—
687D4—88no—
688D4—88no—
689D4—81no—
690D4—81no—
691D4—81no—
692D4—81no—
693D4—81no—
694D4—81no—
695D4—81no—
696D4—81no—
697D4—164no—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—21no—
723C2×C4—21no—
724C2×C4—21no—
725C2×C4—21no—
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—21no—
729C2×C4—21no—
730C2×C4—21no—
731C2×C4—21no—
732C2×C4—21no—
733C2×C4—21no—
734C2×C4—21no—
735C2×C4—21no—
736C2×C4—21no—
737C2×C4—42no—
738C2×C4—42no—
739C2×C4—41no—
740C2×C4—41no—
741C2×C4—41no—
742C2×C4—41no—
743C2×C4—42no—
744C2×C4—42no—
745C2×C4—42no—
746C2×C4—42no—
747C2×C4—42no—
748C2×C4—42no—
749C2×C4—81no—
750C2×C4—81no—
751C2×C4—88no—
752C2×C4—164no—
753C2×C4C2×#10212yes—
754C2×C4C2×#10212yes—
755C2×C4C2×#10212yes—
756C2×C4C2×#10212yes—
757C2×C4#41712yes—
758C2×C4C2×C4×D411yescharacteristic
759C2×C4#51811yescharacteristic
760C2×C4D4211yescharacteristic
761C2×C4D4211yescharacteristic
762C2×C4#54611yescharacteristic
763C2×C4#54611yescharacteristic
764C2×C4C22×D811yescharacteristic
765C2×C4C22×SD1611yescharacteristic
766C2×C4C2×AGL(1,ℤ/8)11yescharacteristic
767C2×C4C2×#13711yescharacteristic
768C2×C4#57611yescharacteristic
769C2×C4#57611yescharacteristic
770C2×C4#57711yescharacteristic
771C2×C4#57711yescharacteristic
772C8—42no—
773C8—42no—
774C8—81no—
775C8—81no—
776C8—81no—
777C8—81no—
778C8—81no—
779C8—81no—
780C22—22no—
781C22—22no—
782C22—22no—
783C22—22no—
784C22—22no—
785C22—22no—
786C22—22no—
787C22—22no—
788C22—22no—
789C22—41no—
790C22—41no—
791C22—41no—
792C22—41no—
793C22—44no—
794C22—44no—
795C22—44no—
796C22—82no—
797C22—82no—
798C22—82no—
799C22—82no—
800C22—82no—
801C22—82no—
802C22—82no—
803C22—82no—
804C22—82no—
805C22—82no—
806C22—82no—
807C22—1616no—
808C22#154714yescomplemented
809C22D4×C22⋊C411yescharacteristic
810C22C2×#41311yescharacteristic
811C22#288811yescharacteristic
812C22C22×#10211yescharacteristic
813C22C2×#41711yescharacteristic
814C22#289711yescharacteristic
815C22#289711yescharacteristic
816C4—22no—
817C4—22no—
818C4—21no—
819C4—21no—
820C4—22no—
821C4—22no—
822C4—22no—
823C4—41no—
824C4—41no—
825C4—41no—
826C4—41no—
827C4—41no—
828C4—82no—
829C4—82no—
830C4#326411yescharacteristic
831C4#326611yescharacteristic
832C4D4×D811yescharacteristic
833C4D4×SD1611yescharacteristic
834C4#329411yescharacteristic
835C4#329511yescharacteristic
836C4#330611yescharacteristic
837C4#331411yescharacteristic
838C2—24no—
839C2—42no—
840C2—84no—
841C2—162no—
842C2C2×#154711yescharacteristic
843C2#1772011yescharacteristic
844C2#1776211yescharacteristic
845C2#1777111yescharacteristic
846C2#2240811yescharacteristic
847C2D4×#10211yescharacteristic
848C2#2241911yescharacteristic
subgroupG/H
center, socleC23C22×C22⋊C4
commutatorC22×C4C23×C4
Frattini, cosocleC2×C42C24
prime radical#36121C2
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23 ◁ C42×D4 ◁ G
LECSG ▷ C2×C42 ▷ C22 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #22648C2semidirect
3. D4×C4⋊C8C2semidirect
4. C2×#1547C2semidirect
5. C22×#331C2semidirect
6. #9704C2semidirect
7. #9698C2semidirect
8. #9141C2semidirect
9. #9133C2semidirect
10. #9131C2semidirect
11. #9129C2semidirect
12. #8585C2semidirect
13. #8341C2semidirect
14. #8339C2semidirect
15. #8234C2semidirect
21. C2×#423C22semidirect
24. C22×C4⋊C8C22semidirect
47. #1842C22semidirect
48. #1842C22semidirect
51. #1797C22semidirect
52. #1797C22semidirect
53. #1767C22semidirect
54. C4×C4⋊C8C22semidirect
56. C2×#332C22semidirect
57. C2×#332C22semidirect
58. C2×#332C22semidirect
59. C2×#332C22semidirect
69. #1296C22semidirect
70. #1296C22semidirect
71. #1296C22semidirect
72. #1296C22semidirect
207. #331D4semidirect
808. C22#1547semidirect

Maximal subgroups

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

subgroupindex
#361212
#226482
D4×C4⋊C82
C2×#15472
C22×#3312
#97042
#96982
#91412
#91332
#91312
#91292
#85852
#83412
#83392
#82342