Finite Group Databasebeta

← #355446

Subgroups — #355446

Order 512.

1538 conjugacy classes of subgroups.

The subgroup lattice has 880 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2930C211yesmaximal, characteristic
2#20908C211yesmaximal, characteristic
3C2×#1871C211yesmaximal, characteristic
4C2×#1753C211yesmaximal, characteristic, complemented
5#20335C211yesmaximal, characteristic, complemented
6#10930C211yesmaximal, characteristic, complemented
7#10929C211yesmaximal, characteristic, complemented
8#10883C211yesmaximal, characteristic, complemented
9#10882C211yesmaximal, characteristic, complemented
10#10809C211yesmaximal, characteristic, complemented
11#10809C211yesmaximal, characteristic, complemented
12#10791C211yesmaximal, characteristic, complemented
13#10791C211yesmaximal, characteristic, complemented
14#10734C211yesmaximal, characteristic, complemented
15#10733C211yesmaximal, characteristic, complemented
16C22×#131C2211yescharacteristic
17C23×M16C2211yescharacteristic
18C23×M16C2211yescharacteristic
19C2×#525C2211yescharacteristic
20C22×#117C2211yescharacteristic
21#2930—24no—
22#2930C418yescomplemented
23C2×#436—21no—
24C2×#436—21no—
25C2×#435—21no—
26C2×#435—21no—
27C2×#424C2211yescharacteristic
28C22×#104C2211yescharacteristic
29C22×#104C2211yescharacteristic
30C2×#416C2211yescharacteristic
31C2×#416C2211yescharacteristic
32C2×#408C2211yescharacteristic
33C2×#407C2211yescharacteristic
34C22×C22⋊C8C2211yescharacteristic
35C2×#405C2211yescharacteristic
36C22×#97C2211yescharacteristic
37C22×C4×C8C2211yescharacteristic
38C2×C4×C22⋊C4C2211yescharacteristic
39#1875C412yescomplemented
40#1874C412yescomplemented
41#1873C412yescomplemented
42#1872C412yescomplemented
43#1871C418yescomplemented
44#1753—24no—
45C2×#341C2211yescharacteristic
46C2×#341C2211yescharacteristic
47C2×#341C2211yescharacteristic
48C2×#341C2211yescharacteristic
49#1735C2211yescharacteristic
50#1735C2211yescharacteristic
51C2×#339C2211yescharacteristic
52C2×#339C2211yescharacteristic
53C2×#339C2211yescharacteristic
54C2×#339C2211yescharacteristic
55C2×#339C2211yescharacteristic
56C2×#339C2211yescharacteristic
57#1729—21no—
58#1729—21no—
59#1729C2211yescharacteristic
60#1729C2211yescharacteristic
61#1729C2211yescharacteristic
62#1729C2211yescharacteristic
63#1728—21no—
64#1728—21no—
65C2×#336C2211yescharacteristic
66C2×#336C2211yescharacteristic
67C22×#41C2311yescharacteristic
68C24×C4C2311yescharacteristic
69C2×#131—22no—
70C2×#131—41no—
71C2×#131—41no—
72C2×#131—41no—
73C2×#131—41no—
74C2×#131C2×C414yescomplemented
75C22×M16—21no—
76C22×M16—22no—
77C22×M16—21no—
78C22×M16—41no—
79C22×M16—41no—
80C22×M16—41no—
81C22×M16—41no—
82C22×M16—41no—
83C22×M16—41no—
84C22×M16—41no—
85C22×M16—41no—
86C22×M16C2×C414yes—
87C22×M16C2×C414yes—
88C22×M16D411yescharacteristic
89C22×M16D411yescharacteristic
90C22×M16D411yescharacteristic
91C22×M16D411yescharacteristic
92C22×M16D414yes—
93C22×M16C2311yescharacteristic
94C22×M16C2311yescharacteristic
95C22×M16C2311yescharacteristic
96C22×M16C2311yescharacteristic
97C23×C8—21no—
98C23×C8—21no—
99C23×C8C2311yescharacteristic
100C23×C8C2311yescharacteristic
101C23×C8C2311yescharacteristic
102C23×C8C2311yescharacteristic
103#525—22no—
104#525—22no—
105#525C2×C414yes—
106#525C2×C414yes—
107C2×#123—21no—
108C2×C22⋊Q8C2×C411yescharacteristic
109C2×C22⋊Q8C2×C411yescharacteristic
110C2×#121C2×C411yescharacteristic
111C2×#121C2×C411yescharacteristic
112C2×#120—21no—
113C2×C4×D4—21no—
114C2×C4×D4—21no—
115C2×#117—21no—
116C2×#117—21no—
117C2×#117—41no—
118C2×#117—41no—
119C2×#117—41no—
120C2×#117—41no—
121C2×#117C2×C412yes—
122C2×#117C2311yescharacteristic
123C2×#117C2311yescharacteristic
124C2×#117C2311yescharacteristic
125C22×C4⋊C4C2×C412yes—
126C22×C22⋊C4—21no—
127C22×C22⋊C4—21no—
128C22×C42—21no—
129C22×C42C2311yescharacteristic
130C22×C42C2311yescharacteristic
131#436—28no—
132#436—28no—
133#435—28no—
134#435—28no—
135#424—22no—
136#424C2×C414yescomplemented
137C2×C4⋊C8—21no—
138C2×C4⋊C8—21no—
139C2×#104—41no—
140C2×#104—41no—
141C2×#104—41no—
142C2×#104—41no—
143C2×#104C2×C414yescomplemented
144C2×#104C2×C414yescomplemented
145#416—41no—
146#416—41no—
147#416—41no—
148#416—41no—
149C2×#103C2×C412yes—
150C2×#103C2×C412yes—
151C2×#102C2×C412yes—
152C2×#102C2×C412yes—
153#408—22no—
154#408C2×C414yescomplemented
155#407—22no—
156#407C2×C414yes—
157C2×C22⋊C8—22no—
158C2×C22⋊C8—21no—
159C2×C22⋊C8—21no—
160C2×C22⋊C8—22no—
161C2×C22⋊C8—21no—
162C2×C22⋊C8—21no—
163C2×C22⋊C8C2×C412yes—
164C2×C22⋊C8C2×C412yes—
165#405—22no—
166#405C2×C414yescomplemented
167C2×#97—21no—
168C2×#97—22no—
169C2×#97—41no—
170C2×#97—41no—
171C2×C4×C8—21no—
172C2×C4×C8—22no—
173C2×C4×C8—41no—
174C2×C4×C8—41no—
175C4×C22⋊C4—22no—
176C4×C22⋊C4C2×C414yes—
177C2×#95—21no—
178#341—41no—
179#341—41no—
180#341—41no—
181#341—41no—
182#340C2×C412yes—
183#340C2×C412yes—
184#340C2×C412yes—
185#340C2×C412yes—
186#339—41no—
187#339—41no—
188#339—41no—
189#339—41no—
190#339C2×C414yescomplemented
191#339C2×C414yescomplemented
192#336—22no—
193#336—22no—
194#336—21no—
195#336—21no—
196#336—21no—
197#336—21no—
198#336—21no—
199#336—21no—
200#336—21no—
201#336—21no—
202C25#4111yescharacteristic
203C2×#41—21no—
204C2×#41—21no—
205C2×#41—21no—
206C2×#41—21no—
207C2×#41—21no—
208C2×#41—21no—
209C2×#41—21no—
210C2×#41—21no—
211C2×#41—21no—
212C2×#41—21no—
213C2×#41C22×C412yes—
214C2×#41C22×C412yes—
215C22×Q8C22×C411yescharacteristic
216C22×D4—21no—
217C22×D4—21no—
218C22×D4—21no—
219C22×D4C22×C411yescharacteristic
220C23×C4—21no—
221C23×C4—21no—
222C23×C4—21no—
223C23×C4—21no—
224C23×C4—21no—
225C23×C4—21no—
226C23×C4—21no—
227C23×C4—21no—
228C23×C4—21no—
229C23×C4—21no—
230C23×C4—21no—
231C23×C4—22no—
232C23×C4C22×C412yes—
233C23×C4C22×C411yescharacteristic
234C23×C4C22×C411yescharacteristic
235C23×C4C22×C412yes—
236C23×C4C2×D412yes—
237C23×C4C2×D411yescharacteristic
238C23×C4C2×D411yescharacteristic
239C23×C4#4111yescharacteristic
240C23×C4#4112yes—
241C23×C4C2411yescharacteristic
242#131—44no—
243#131—44no—
244#131—44no—
245#131—44no—
246C2×M16—24no—
247C2×M16—21no—
248C2×M16—21no—
249C2×M16—21no—
250C2×M16—21no—
251C2×M16—24no—
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×M16—21no—
266C2×M16—21no—
267C2×M16—21no—
268C2×M16—44no—
269C2×M16—44no—
270C2×M16—44no—
271C2×M16—44no—
272C2×M16—41no—
273C2×M16—41no—
274C2×M16—41no—
275C2×M16—41no—
276C2×M16—41no—
277C2×M16—41no—
278C2×M16—41no—
279C2×M16—41no—
280C2×M16—42no—
281C2×M16—42no—
282C2×M16—44no—
283C2×M16—44no—
284C2×M16—44no—
285C2×M16—44no—
286C2×M16—42no—
287C2×M16—42no—
288C2×M16C22⋊C414yes—
289C2×M16C22⋊C414yes—
290C2×M16C22⋊C414yes—
291C2×M16C22⋊C414yes—
292C2×M16C22×C412yes—
293C2×M16C22×C412yes—
294C2×M16C22×C412yes—
295C2×M16C22×C412yes—
296C22×C8—21no—
297C22×C8—21no—
298C22×C8—21no—
299C22×C8—21no—
300C22×C8—21no—
301C22×C8—21no—
302C22×C8—21no—
303C22×C8—21no—
304C22×C8—24no—
305C22×C8—21no—
306C22×C8—21no—
307C22×C8—21no—
308C22×C8—21no—
309C22×C8—21no—
310C22×C8—21no—
311C22×C8—21no—
312C22×C8—21no—
313C22×C8—21no—
314C22×C8—21no—
315C22×C8—21no—
316C22×C8—21no—
317C22×C8—21no—
318C22×C8—21no—
319C22×C8—21no—
320C22×C8—21no—
321C22×C8—24no—
322C22×C8—42no—
323C22×C8—42no—
324C22×C8—42no—
325C22×C8—42no—
326C22×C8C22×C412yes—
327C22×C8C22×C412yes—
328C22×C8C22×C412yes—
329C22×C8C22×C412yes—
330C22×C8C2×D412yes—
331C22×C8C2×D412yes—
332C22×C8C2×D411yescharacteristic
333C22×C8C2×D411yescharacteristic
334C22×C8C2×D411yescharacteristic
335C22×C8C2×D411yescharacteristic
336#123—24no—
337#123—24no—
338C22⋊Q8—22no—
339C22⋊Q8—22no—
340C22⋊Q8C4214yes—
341C22⋊Q8C4214yes—
342#121—22no—
343#121—22no—
344#121C4214yes—
345#121C4214yes—
346#120—24no—
347#120—24no—
348C4×D4—24no—
349C4×D4—24no—
350C4×D4—24no—
351C4×D4—24no—
352#117—21no—
353#117—21no—
354#117—21no—
355#117—21no—
356#117—21no—
357#117—21no—
358#117—21no—
359#117—21no—
360#117—21no—
361#117—21no—
362#117—42no—
363#117—42no—
364#117—42no—
365#117—42no—
366#117—42no—
367#117—42no—
368#117C22×C412yes—
369#117C22×C412yes—
370C2×C4⋊C4—21no—
371C2×C4⋊C4—21no—
372C2×C4⋊C4—22no—
373C2×C4⋊C4—42no—
374C2×C4⋊C4—42no—
375C2×C4⋊C4C22×C412yes—
376C2×C4⋊C4C22×C412yes—
377C2×C4⋊C4C22×C411yescharacteristic
378C2×C4⋊C4C22×C411yescharacteristic
379C2×C22⋊C4—21no—
380C2×C22⋊C4—21no—
381C2×C22⋊C4—21no—
382C2×C22⋊C4—21no—
383C2×C22⋊C4—21no—
384C2×C22⋊C4—22no—
385C2×C22⋊C4—24no—
386C2×C22⋊C4—21no—
387C2×C22⋊C4—21no—
388C2×C22⋊C4—44no—
389C2×C22⋊C4—42no—
390C2×C22⋊C4—42no—
391C2×C42—21no—
392C2×C42—21no—
393C2×C42—21no—
394C2×C42—21no—
395C2×C42—21no—
396C2×C42—21no—
397C2×C42—21no—
398C2×C42—21no—
399C2×C42—21no—
400C2×C42—22no—
401C2×C42—21no—
402C2×C42—21no—
403C2×C42—21no—
404C2×C42—21no—
405C2×C42—42no—
406C2×C42—42no—
407C2×C42C22×C412yes—
408C2×C42C22×C412yes—
409C4⋊C8—24no—
410C4⋊C8—24no—
411#104—44no—
412#104—44no—
413#103—42no—
414#103—42no—
415#102—42no—
416#102—42no—
417C22⋊C8—24no—
418C22⋊C8—24no—
419C22⋊C8—24no—
420C22⋊C8—24no—
421C22⋊C8—24no—
422C22⋊C8—24no—
423#97—24no—
424#97—44no—
425C4×C8—24no—
426C4×C8—44no—
427#95—24no—
428C24—21no—
429C24—21no—
430C24—21no—
431C24—21no—
432C24—21no—
433C24—42no—
434C24—42no—
435C24#11712yes—
436C24C4×D411yescharacteristic
437C24C4×D411yescharacteristic
438C24C4×D412yes—
439C24C2×#4111yescharacteristic
440#41—22no—
441#41—22no—
442#41—22no—
443#41—22no—
444#41—22no—
445#41—22no—
446#41—22no—
447#41—22no—
448#41—41no—
449#41—41no—
450#41—41no—
451#41—41no—
452#41—41no—
453#41—41no—
454#41—41no—
455#41—41no—
456C2×Q8—21no—
457C2×Q8—21no—
458C2×Q8—21no—
459C2×Q8—21no—
460C2×Q8—21no—
461C2×Q8C2×C4212yes—
462C2×D4—22no—
463C2×D4—22no—
464C2×D4—24no—
465C2×D4—24no—
466C2×D4—21no—
467C2×D4—21no—
468C2×D4—21no—
469C2×D4—21no—
470C2×D4—21no—
471C2×D4—41no—
472C2×D4—41no—
473C2×D4—41no—
474C2×D4—41no—
475C2×D4—82no—
476C2×D4—82no—
477C2×D4C2×C4212yes—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—21no—
499C22×C4—21no—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—21no—
505C22×C4—21no—
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—24no—
515C22×C4—22no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—42no—
525C22×C4—41no—
526C22×C4—41no—
527C22×C4—41no—
528C22×C4—41no—
529C22×C4—41no—
530C22×C4—41no—
531C22×C4—44no—
532C22×C4—42no—
533C22×C4—42no—
534C22×C4—41no—
535C22×C4—41no—
536C22×C4—82no—
537C22×C4—82no—
538C22×C4C2×C4212yes—
539C22×C4C2×C4212yes—
540C22×C4C2×C22⋊C412yes—
541C22×C4C2×C22⋊C412yes—
542C22×C4#11712yes—
543C22×C4C4×D412yes—
544C22×C4C4×D412yes—
545C22×C4C4×D412yes—
546C22×C4C4×D412yes—
547C22×C4C4×D412yes—
548C22×C4C4×D411yescharacteristic
549C22×C4C4×D411yescharacteristic
550C22×C4C23×C411yescharacteristic
551C22×C4C23×C411yescharacteristic
552C22×C4C23×C411yescharacteristic
553C22×C4C22×D411yescharacteristic
554C22×C4C22×D411yescharacteristic
555C22×C4C2×#4111yescharacteristic
556C22×C4H(5,𝔽2)11yescharacteristic
557C22×C4H(5,𝔽2)11yescharacteristic
558C22×C4H(5,𝔽2)11yescharacteristic
559C22×C4H(5,𝔽2)11yescharacteristic
560C22×C4H(5,𝔽2)11yescharacteristic
561C22×C4H(5,𝔽2)11yescharacteristic
562C22×C42−1+411yescharacteristic
563C22×C42−1+411yescharacteristic
564M16—22no—
565M16—22no—
566M16—22no—
567M16—22no—
568M16—22no—
569M16—22no—
570M16—22no—
571M16—22no—
572M16—44no—
573M16—44no—
574M16—44no—
575M16—44no—
576M16—48no—
577M16—48no—
578M16—41no—
579M16—41no—
580M16—41no—
581M16—41no—
582M16—41no—
583M16—41no—
584M16—41no—
585M16—41no—
586C2×C8—22no—
587C2×C8—22no—
588C2×C8—22no—
589C2×C8—22no—
590C2×C8—22no—
591C2×C8—22no—
592C2×C8—21no—
593C2×C8—21no—
594C2×C8—21no—
595C2×C8—21no—
596C2×C8—21no—
597C2×C8—21no—
598C2×C8—21no—
599C2×C8—21no—
600C2×C8—22no—
601C2×C8—22no—
602C2×C8—22no—
603C2×C8—22no—
604C2×C8—22no—
605C2×C8—22no—
606C2×C8—22no—
607C2×C8—22no—
608C2×C8—22no—
609C2×C8—22no—
610C2×C8—22no—
611C2×C8—22no—
612C2×C8—48no—
613C2×C8—48no—
614C2×C8—41no—
615C2×C8—41no—
616C2×C8—41no—
617C2×C8—41no—
618C2×C8—41no—
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×C8C2×C22⋊C412yes—
631C2×C8C2×C22⋊C412yes—
632C2×C8C2×C22⋊C412yes—
633C2×C8C2×C22⋊C412yes—
634C4⋊C4—21no—
635C4⋊C4—21no—
636C4⋊C4—24no—
637C4⋊C4—24no—
638C4⋊C4—22no—
639C4⋊C4—22no—
640C4⋊C4—22no—
641C4⋊C4—22no—
642C4⋊C4—44no—
643C4⋊C4C2×C4212yes—
644C4⋊C4C2×C4212yes—
645C22⋊C4—22no—
646C22⋊C4—22no—
647C22⋊C4—24no—
648C22⋊C4—24no—
649C22⋊C4—24no—
650C22⋊C4—24no—
651C22⋊C4—48no—
652C22⋊C4—44no—
653C22⋊C4—41no—
654C22⋊C4—41no—
655C22⋊C4—41no—
656C22⋊C4—41no—
657C42—22no—
658C42—22no—
659C42—22no—
660C42—22no—
661C42—22no—
662C42—22no—
663C42—44no—
664C42—41no—
665C42—41no—
666C42—41no—
667C42—41no—
668C42—41no—
669C42—41no—
670C42—41no—
671C42—41no—
672C23—22no—
673C23—22no—
674C23—21no—
675C23—21no—
676C23—21no—
677C23—21no—
678C23—22no—
679C23—22no—
680C23—22no—
681C23—22no—
682C23—22no—
683C23—22no—
684C23—22no—
685C23—22no—
686C23—22no—
687C23—42no—
688C23—42no—
689C23—42no—
690C23—42no—
691C23—41no—
692C23—41no—
693C23—42no—
694C23—42no—
695C23—82no—
696C23—82no—
697C23—82no—
698C23—82no—
699C23C4×C22⋊C412yes—
700C23C4×C22⋊C412yes—
701C23C2×#11711yescharacteristic
702C23C2×C4×D411yescharacteristic
703C23C2×C4×D411yescharacteristic
704C23#53811yescharacteristic
705C23#53811yescharacteristic
706C23#53911yescharacteristic
707C23#53911yescharacteristic
708Q8—22no—
709Q8—22no—
710Q8—41no—
711Q8—41no—
712D4—22no—
713D4—22no—
714D4—42no—
715D4—42no—
716D4—42no—
717D4—42no—
718D4—41no—
719D4—41no—
720D4—84no—
721D4—84no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—21no—
725C2×C4—21no—
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—22no—
742C2×C4—22no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—24no—
747C2×C4—22no—
748C2×C4—22no—
749C2×C4—22no—
750C2×C4—44no—
751C2×C4—44no—
752C2×C4—42no—
753C2×C4—41no—
754C2×C4—41no—
755C2×C4—42no—
756C2×C4—42no—
757C2×C4—42no—
758C2×C4—42no—
759C2×C4—42no—
760C2×C4—42no—
761C2×C4—42no—
762C2×C4—42no—
763C2×C4—42no—
764C2×C4—42no—
765C2×C4—42no—
766C2×C4—42no—
767C2×C4—42no—
768C2×C4—42no—
769C2×C4—42no—
770C2×C4—42no—
771C2×C4—82no—
772C2×C4—82no—
773C2×C4—88no—
774C2×C4C4×C22⋊C412yes—
775C2×C4C4×C22⋊C412yes—
776C2×C4C22×C4211yescharacteristic
777C2×C4C22×C22⋊C411yescharacteristic
778C2×C4C2×C4×D411yescharacteristic
779C2×C4C2×C4×D411yescharacteristic
780C2×C4#51811yescharacteristic
781C2×C4#51811yescharacteristic
782C2×C4#51811yescharacteristic
783C2×C4#51811yescharacteristic
784C2×C4#51811yescharacteristic
785C2×C4#51811yescharacteristic
786C2×C4#52011yescharacteristic
787C2×C4#52011yescharacteristic
788C2×C4#52011yescharacteristic
789C2×C4#52011yescharacteristic
790C2×C4#52011yescharacteristic
791C2×C4#52011yescharacteristic
792C2×C4#53411yescharacteristic
793C2×C4#53411yescharacteristic
794C2×C4#53411yescharacteristic
795C2×C4#53411yescharacteristic
796C2×C4#53511yescharacteristic
797C2×C4#53611yescharacteristic
798C2×C4#53711yescharacteristic
799C2×C4#53711yescharacteristic
800C2×C4#53811yescharacteristic
801C2×C4#53811yescharacteristic
802C2×C4#53911yescharacteristic
803C2×C4#53911yescharacteristic
804C8—22no—
805C8—22no—
806C8—22no—
807C8—22no—
808C8—42no—
809C8—42no—
810C8—42no—
811C8—42no—
812C8—42no—
813C8—42no—
814C22—22no—
815C22—22no—
816C22—22no—
817C22—22no—
818C22—21no—
819C22—21no—
820C22—21no—
821C22—21no—
822C22—22no—
823C22—22no—
824C22—22no—
825C22—22no—
826C22—22no—
827C22—22no—
828C22—42no—
829C22—42no—
830C22—42no—
831C22—42no—
832C22—42no—
833C22—42no—
834C22—42no—
835C22—82no—
836C22—82no—
837C22—82no—
838C22—82no—
839C22—82no—
840C22—82no—
841C22C2×C4×C22⋊C411yescharacteristic
842C22#231811yescharacteristic
843C22#231811yescharacteristic
844C22#232111yescharacteristic
845C22#232211yescharacteristic
846C22#232511yescharacteristic
847C22#232511yescharacteristic
848C22#295612yes—
849C22#295712yes—
850C4—22no—
851C4—22no—
852C4—44no—
853C4—42no—
854C4—42no—
855C4—42no—
856C4—82no—
857C4—82no—
858C4—82no—
859C4#227511yescharacteristic
860C4#227511yescharacteristic
861C4#230811yescharacteristic
862C4#231111yescharacteristic
863C4#232111yescharacteristic
864C4#232211yescharacteristic
865C4#232511yescharacteristic
866C4#232511yescharacteristic
867C2—21no—
868C2—21no—
869C2—21no—
870C2—21no—
871C2—42no—
872C2—42no—
873C2—82no—
874C2#1378411yescharacteristic
875C2#2042111yescharacteristic
876C2#2042211yescharacteristic
877C2#2206212yes—
878C2#2209712yes—
subgroupG/H
centerC22×C4C22×D4
commutatorC2×C4C22×C42
Frattini, cosocleC23×C4C24
socleC23C2×C4×D4
prime radicalC2×#525C22
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C4 ◁ C23×M16 ◁ G
LECSG ▷ C23×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
4. C2×#1753C2semidirect
5. #20335C2semidirect
6. #10930C2semidirect
7. #10929C2semidirect
8. #10883C2semidirect
9. #10882C2semidirect
10. #10809C2semidirect
11. #10809C2semidirect
12. #10791C2semidirect
13. #10791C2semidirect
14. #10734C2semidirect
15. #10733C2semidirect
22. #2930C4semidirect
39. #1875C4semidirect
40. #1874C4semidirect
41. #1873C4semidirect
42. #1872C4semidirect
43. #1871C4semidirect
74. C2×#131C2×C4semidirect
136. #424C2×C4semidirect
143. C2×#104C2×C4semidirect
144. C2×#104C2×C4semidirect
154. #408C2×C4semidirect
166. #405C2×C4semidirect
190. #339C2×C4semidirect
191. #339C2×C4semidirect

Maximal subgroups

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

subgroupindex
C2×#29302
#209082
C2×#18712
C2×#17532
#203352
#109302
#109292
#108832
#108822
#108092
#107912
#107342
#107332