Finite Group Databasebeta

← #367477

Subgroups — #367477

Order 512.

1274 conjugacy classes of subgroups.

The subgroup lattice has 820 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#1952C211yesmaximal, characteristic, complemented
2C2×#1855C211yesmaximal, characteristic
3#20844C211yesmaximal, characteristic
4C2×#1852C211yesmaximal, characteristic
5#20661C211yesmaximal, characteristic
6#20389C211yesmaximal, characteristic
7C22×#343C211yesmaximal, characteristic
8#11331C211yesmaximal, characteristic, complemented
9#11270C211yesmaximal, characteristic, complemented
10#11249C211yesmaximal, characteristic, complemented
11#11249C211yesmaximal, characteristic, complemented
12#10896C211yesmaximal, characteristic, complemented
13#10896C211yesmaximal, characteristic, complemented
14#10870C211yesmaximal, characteristic, complemented
15#10739C211yesmaximal, characteristic
16C23×M16C2211yescharacteristic
17C23×M16C2211yescharacteristic
18C23×C4⋊C4C2211yescharacteristic
19C22×#108C2211yescharacteristic
20C22×#108C2211yescharacteristic
21C2×#428C2211yescharacteristic
22C2×#428C2211yescharacteristic
23C2×#428C2211yescharacteristic
24C2×#428C2211yescharacteristic
25C22×#107C2211yescharacteristic
26C22×#107C2211yescharacteristic
27C2×#407C2211yescharacteristic
28C22×C22⋊C8C2211yescharacteristic
29C2×#405C2211yescharacteristic
30C2×#405C2211yescharacteristic
31#2280C2211yescharacteristic
32C2×#380C2211yescharacteristic
33#1952—24no—
34#1855C418yescomplemented
35#1853—21no—
36#1853—21no—
37#1852—21no—
38#1852—21no—
39#1852—21no—
40#1852—21no—
41#1852—21no—
42#1852—21no—
43#1809—21no—
44#1809—21no—
45#1808—21no—
46#1807—21no—
47#1753—21no—
48#1753—21no—
49#1752—21no—
50C8×C22⋊C4—21no—
51C2×#343—24no—
52C2×#343C2211yescharacteristic
53C2×#343C2211yescharacteristic
54C2×#343C2211yescharacteristic
55C2×#343C2211yescharacteristic
56C2×#343C2211yescharacteristic
57C2×#343C2211yescharacteristic
58C2×#343C2211yescharacteristic
59C2×#343C2211yescharacteristic
60C2×#341C2211yescharacteristic
61C2×#341C2211yescharacteristic
62#1736C2211yescharacteristic
63#1736C2211yescharacteristic
64#1736C2211yescharacteristic
65#1736C2211yescharacteristic
66C2×#340C2211yescharacteristic
67C2×#340C2211yescharacteristic
68#1729C2211yescharacteristic
69#1729C2211yescharacteristic
70C24×C4—21no—
71C24×C4C2311yescharacteristic
72C22×M16—21no—
73C22×M16—21no—
74C22×M16—22no—
75C22×M16—22no—
76C22×M16—22no—
77C22×M16—22no—
78C22×M16—22no—
79C22×M16—22no—
80C22×M16—41no—
81C22×M16—41no—
82C22×M16—41no—
83C22×M16—41no—
84C22×M16C2×C414yes—
85C22×M16Q814yes—
86C22×M16C2311yescharacteristic
87C22×M16C2311yescharacteristic
88C22×M16C2311yescharacteristic
89C22×M16C2311yescharacteristic
90C22×M16C2311yescharacteristic
91C22×M16C2311yescharacteristic
92C23×C8—21no—
93C23×C8—21no—
94C23×C8C2311yescharacteristic
95C23×C8C2311yescharacteristic
96C2×#117C2311yescharacteristic
97C2×#117C2311yescharacteristic
98C22×C4⋊C4—21no—
99C22×C4⋊C4—22no—
100C22×C4⋊C4—22no—
101C22×C4⋊C4—21no—
102C22×C4⋊C4—21no—
103C22×C4⋊C4—21no—
104C22×C4⋊C4—21no—
105C22×C4⋊C4—41no—
106C22×C4⋊C4—41no—
107C22×C4⋊C4C2311yescharacteristic
108C22×C4⋊C4C2311yescharacteristic
109C22×C4⋊C4C2311yescharacteristic
110C22×C4⋊C4C2311yescharacteristic
111C22×C22⋊C4—21no—
112C2×#108—22no—
113C2×#108—22no—
114C2×#108—41no—
115C2×#108—41no—
116C2×#108C2×C414yescomplemented
117C2×#108C2×C414yescomplemented
118#428—22no—
119#428—22no—
120#428—22no—
121#428—22no—
122#428—41no—
123#428—41no—
124#428—41no—
125#428—41no—
126C2×#107—21no—
127C2×#107—21no—
128C2×#107—21no—
129C2×#107—21no—
130C2×#107—21no—
131C2×#107—21no—
132C2×#107—21no—
133C2×#107—21no—
134C2×#107—22no—
135C2×#107—22no—
136C2×#107—41no—
137C2×#107—41no—
138C2×#106—21no—
139C2×#106—21no—
140C2×#106—21no—
141C2×#106—21no—
142#407—22no—
143#407C2×C414yes—
144C2×C22⋊C8—21no—
145C2×C22⋊C8—21no—
146C2×C22⋊C8C2×C414yes—
147C2×C22⋊C8D411yescharacteristic
148C2×C22⋊C8D411yescharacteristic
149C2×C22⋊C8D411yescharacteristic
150C2×C22⋊C8D411yescharacteristic
151C2×C22⋊C8Q814yes—
152#405—22no—
153#405—22no—
154#405—41no—
155#405—41no—
156C2×#97—21no—
157C2×#97—21no—
158C2×C4×C8—21no—
159C2×C4×C8—21no—
160#381—21no—
161#380—21no—
162#380—21no—
163#380—21no—
164#380—21no—
165#380D411yescharacteristic
166#380D411yescharacteristic
167#380D411yescharacteristic
168#380D411yescharacteristic
169#379—21no—
170C4×C22⋊C4—21no—
171C4×C22⋊C4—21no—
172C2×#95—21no—
173#343—22no—
174#343—22no—
175#343—22no—
176#343—22no—
177#343—22no—
178#343—41no—
179#343—41no—
180#343D414yes—
181#341C2×C414yescomplemented
182#341C2×C414yescomplemented
183#340—21no—
184#340—21no—
185#340—21no—
186#340—21no—
187#340—21no—
188#340—21no—
189#340—21no—
190#340—21no—
191#340—21no—
192#340—21no—
193#340—21no—
194#340—21no—
195#336—21no—
196#336—21no—
197#336—21no—
198#336—21no—
199C25#4111yescharacteristic
200C23×C4—21no—
201C23×C4—21no—
202C23×C4—21no—
203C23×C4—21no—
204C23×C4—21no—
205C23×C4—21no—
206C23×C4—21no—
207C23×C4—21no—
208C23×C4—24no—
209C23×C4—21no—
210C23×C4—21no—
211C23×C4—21no—
212C23×C4—21no—
213C23×C4—42no—
214C23×C4—41no—
215C23×C4—41no—
216C23×C4—82no—
217C23×C4—82no—
218C23×C4C22×C412yes—
219C23×C4C2×D411yescharacteristic
220C23×C4C2×D411yescharacteristic
221C23×C4C2×D411yescharacteristic
222C23×C4C2×D411yescharacteristic
223C23×C4C2×Q812yes—
224C23×C4C2×Q812yes—
225C23×C4#4112yes—
226C23×C4#4111yescharacteristic
227C23×C4C2411yescharacteristic
228C2×M16—21no—
229C2×M16—21no—
230C2×M16—21no—
231C2×M16—21no—
232C2×M16—21no—
233C2×M16—21no—
234C2×M16—24no—
235C2×M16—24no—
236C2×M16—21no—
237C2×M16—21no—
238C2×M16—21no—
239C2×M16—21no—
240C2×M16—21no—
241C2×M16—21no—
242C2×M16—21no—
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—28no—
257C2×M16—28no—
258C2×M16—42no—
259C2×M16—42no—
260C2×M16—42no—
261C2×M16—42no—
262C2×M16—44no—
263C2×M16—44no—
264C2×M16—44no—
265C2×M16—44no—
266C2×M16—44no—
267C2×M16—44no—
268C2×M16C22×C412yes—
269C2×M16C22×C412yes—
270C2×M16C22×C412yes—
271C2×M16C22×C412yes—
272C2×M16C2×D412yes—
273C2×M16C2×D412yes—
274C2×M16C2×Q812yes—
275C2×M16C2×Q812yes—
276C2×M16#4112yes—
277C2×M16#4112yes—
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×C8—24no—
289C22×C8—24no—
290C22×C8—21no—
291C22×C8—21no—
292C22×C8—21no—
293C22×C8—21no—
294C22×C8—42no—
295C22×C8—42no—
296C22×C8—42no—
297C22×C8—42no—
298C22×C8C22×C412yes—
299C22×C8C22×C412yes—
300C22×C8C2×D411yescharacteristic
301C22×C8C2×D411yescharacteristic
302C22×C8C2×D411yescharacteristic
303C22×C8C2×D411yescharacteristic
304C22×C8C2×Q812yes—
305C22×C8C2×Q812yes—
306#117—21no—
307#117—21no—
308#117—21no—
309#117—21no—
310#117—21no—
311#117—21no—
312#117—21no—
313#117—21no—
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—24no—
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—42no—
338C2×C4⋊C4—42no—
339C2×C4⋊C4—42no—
340C2×C4⋊C4—42no—
341C2×C4⋊C4—42no—
342C2×C4⋊C4—42no—
343C2×C4⋊C4—42no—
344C2×C4⋊C4—42no—
345C2×C4⋊C4—42no—
346C2×C4⋊C4—41no—
347C2×C4⋊C4—41no—
348C2×C4⋊C4C2×D412yes—
349C2×C4⋊C4C2×D411yescharacteristic
350C2×C4⋊C4C2×D411yescharacteristic
351C2×C4⋊C4C2×D411yescharacteristic
352C2×C4⋊C4C2×D411yescharacteristic
353C2×C4⋊C4#4112yes—
354C2×C22⋊C4—21no—
355C2×C22⋊C4—21no—
356C2×C22⋊C4—21no—
357C2×C22⋊C4—21no—
358C2×C22⋊C4—21no—
359C2×C22⋊C4—21no—
360C2×C22⋊C4—41no—
361C2×C22⋊C4—41no—
362C2×C22⋊C4—82no—
363C2×C42—21no—
364C2×C42—21no—
365#108—28no—
366#108—44no—
367#107—42no—
368#107—42no—
369#107—42no—
370#107—42no—
371#107—42no—
372#107—42no—
373#107—42no—
374#107—42no—
375#106—42no—
376#106—42no—
377#106—42no—
378#106—42no—
379C22⋊C8—24no—
380C22⋊C8—24no—
381C22⋊C8C4⋊C414yes—
382C22⋊C8C4⋊C414yes—
383C22⋊C8C4⋊C414yes—
384C22⋊C8C4⋊C414yes—
385#97—42no—
386#97—42no—
387C4×C8—42no—
388C4×C8—42no—
389#95—21no—
390#95—21no—
391#95—21no—
392#95—21no—
393#95—41no—
394#95—41no—
395C24—21no—
396C24—21no—
397C24—21no—
398C24—21no—
399C24—22no—
400C24—22no—
401C24—41no—
402C24—41no—
403C24C4×Q812yes—
404C24#12111yescharacteristic
405C24#12111yescharacteristic
406C24#12512yes—
407C24C2×#4111yescharacteristic
408C22×C4—21no—
409C22×C4—21no—
410C22×C4—21no—
411C22×C4—21no—
412C22×C4—22no—
413C22×C4—22no—
414C22×C4—22no—
415C22×C4—22no—
416C22×C4—22no—
417C22×C4—22no—
418C22×C4—22no—
419C22×C4—22no—
420C22×C4—21no—
421C22×C4—21no—
422C22×C4—21no—
423C22×C4—21no—
424C22×C4—21no—
425C22×C4—21no—
426C22×C4—21no—
427C22×C4—21no—
428C22×C4—21no—
429C22×C4—21no—
430C22×C4—22no—
431C22×C4—21no—
432C22×C4—21no—
433C22×C4—21no—
434C22×C4—21no—
435C22×C4—21no—
436C22×C4—21no—
437C22×C4—22no—
438C22×C4—22no—
439C22×C4—22no—
440C22×C4—22no—
441C22×C4—22no—
442C22×C4—22no—
443C22×C4—22no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—44no—
451C22×C4—44no—
452C22×C4—41no—
453C22×C4—41no—
454C22×C4—41no—
455C22×C4—41no—
456C22×C4—41no—
457C22×C4—41no—
458C22×C4—41no—
459C22×C4—41no—
460C22×C4—41no—
461C22×C4—41no—
462C22×C4—82no—
463C22×C4—82no—
464C22×C4—82no—
465C22×C4—88no—
466C22×C4—82no—
467C22×C4—81no—
468C22×C4—81no—
469C22×C4—81no—
470C22×C4—81no—
471C22×C4—88no—
472C22×C4—81no—
473C22×C4—81no—
474C22×C4—81no—
475C22×C4—81no—
476C22×C4C2×C4⋊C412yes—
477C22×C4C2×C4⋊C412yes—
478C22×C4C4×D412yes—
479C22×C4C4×D412yes—
480C22×C4C4×Q812yes—
481C22×C4#12111yescharacteristic
482C22×C4#12111yescharacteristic
483C22×C4C22⋊Q812yes—
484C22×C4C22⋊Q812yes—
485C22×C4#12512yes—
486C22×C4C4⋊Q812yes—
487C22×C4C4⋊Q812yes—
488C22×C4C23×C411yescharacteristic
489C22×C4C22×D411yescharacteristic
490C22×C4C22×D411yescharacteristic
491C22×C4C22×D411yescharacteristic
492C22×C4C22×Q811yescharacteristic
493C22×C4C22×Q811yescharacteristic
494C22×C4C2×#4111yescharacteristic
495C22×C4C2×#4111yescharacteristic
496C22×C4C2×#4111yescharacteristic
497C22×C4C2×#4111yescharacteristic
498C22×C4H(5,𝔽2)11yescharacteristic
499C22×C4H(5,𝔽2)11yescharacteristic
500C22×C4H(5,𝔽2)11yescharacteristic
501C22×C42−1+411yescharacteristic
502M16—22no—
503M16—22no—
504M16—22no—
505M16—22no—
506M16—22no—
507M16—22no—
508M16—22no—
509M16—22no—
510M16—22no—
511M16—22no—
512M16—22no—
513M16—22no—
514M16—22no—
515M16—22no—
516M16—48no—
517M16—48no—
518M16—41no—
519M16—41no—
520M16—41no—
521M16—41no—
522M16—41no—
523M16—41no—
524M16—41no—
525M16—41no—
526M16C4×D414yes—
527M16C22⋊Q814yes—
528C2×C8—22no—
529C2×C8—22no—
530C2×C8—22no—
531C2×C8—22no—
532C2×C8—22no—
533C2×C8—22no—
534C2×C8—21no—
535C2×C8—22no—
536C2×C8—21no—
537C2×C8—22no—
538C2×C8—21no—
539C2×C8—22no—
540C2×C8—21no—
541C2×C8—22no—
542C2×C8—21no—
543C2×C8—21no—
544C2×C8—21no—
545C2×C8—21no—
546C2×C8—22no—
547C2×C8—22no—
548C2×C8—22no—
549C2×C8—22no—
550C2×C8—22no—
551C2×C8—22no—
552C2×C8—22no—
553C2×C8—22no—
554C2×C8—48no—
555C2×C8—48no—
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×C8C2×C4⋊C412yes—
565C2×C8C2×C4⋊C412yes—
566C2×C8C2×C4⋊C412yes—
567C2×C8C2×C4⋊C412yes—
568C4⋊C4—21no—
569C4⋊C4—22no—
570C4⋊C4—21no—
571C4⋊C4—22no—
572C4⋊C4—21no—
573C4⋊C4—21no—
574C4⋊C4—22no—
575C4⋊C4—22no—
576C4⋊C4—21no—
577C4⋊C4—21no—
578C4⋊C4—21no—
579C4⋊C4—21no—
580C4⋊C4—44no—
581C4⋊C4—44no—
582C4⋊C4—41no—
583C4⋊C4—41no—
584C4⋊C4—41no—
585C4⋊C4—41no—
586C4⋊C4—41no—
587C4⋊C4—41no—
588C4⋊C4—41no—
589C4⋊C4—41no—
590C4⋊C4—41no—
591C4⋊C4—41no—
592C4⋊C4—41no—
593C4⋊C4—41no—
594C22⋊C4—41no—
595C22⋊C4—41no—
596C22⋊C4—41no—
597C22⋊C4—41no—
598C22⋊C4—42no—
599C22⋊C4—42no—
600C22⋊C4—81no—
601C22⋊C4—81no—
602C22⋊C4—82no—
603C22⋊C4—82no—
604C42—41no—
605C42—41no—
606C42—41no—
607C42—41no—
608C23—21no—
609C23—21no—
610C23—21no—
611C23—21no—
612C23—21no—
613C23—21no—
614C23—21no—
615C23—21no—
616C23—22no—
617C23—21no—
618C23—21no—
619C23—24no—
620C23—24no—
621C23—22no—
622C23—22no—
623C23—21no—
624C23—21no—
625C23—21no—
626C23—21no—
627C23—22no—
628C23—42no—
629C23—42no—
630C23—42no—
631C23—42no—
632C23—42no—
633C23—42no—
634C23—42no—
635C23—42no—
636C23—42no—
637C23—42no—
638C23#38912yes—
639C23#38912yes—
640C23#47212yes—
641C23#47312yes—
642C23C2×C4×Q811yescharacteristic
643C23C2×#12111yescharacteristic
644C23#52511yescharacteristic
645C23C2×#12511yescharacteristic
646C23#52911yescharacteristic
647C23#53811yescharacteristic
648C23#53911yescharacteristic
649C2×C4—22no—
650C2×C4—21no—
651C2×C4—21no—
652C2×C4—21no—
653C2×C4—21no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—41no—
674C2×C4—41no—
675C2×C4—42no—
676C2×C4—42no—
677C2×C4—41no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—88no—
688C2×C4—82no—
689C2×C4—82no—
690C2×C4—88no—
691C2×C4—81no—
692C2×C4—81no—
693C2×C4—81no—
694C2×C4—81no—
695C2×C4—82no—
696C2×C4—82no—
697C2×C4—81no—
698C2×C4—81no—
699C2×C4—81no—
700C2×C4—81no—
701C2×C4—81no—
702C2×C4—81no—
703C2×C4—161no—
704C2×C4—161no—
705C2×C4—161no—
706C2×C4—161no—
707C2×C4#38912yes—
708C2×C4#38912yes—
709C2×C4C22×C4⋊C411yescharacteristic
710C2×C4C2×C4×D411yescharacteristic
711C2×C4C2×C4×D411yescharacteristic
712C2×C4C4×#4111yescharacteristic
713C2×C4#51811yescharacteristic
714C2×C4#52011yescharacteristic
715C2×C4C2×C22⋊Q811yescharacteristic
716C2×C4C2×C22⋊Q811yescharacteristic
717C2×C4C2×C4⋊Q811yescharacteristic
718C2×C4#53311yescharacteristic
719C2×C4#54311yescharacteristic
720C2×C4#54411yescharacteristic
721C2×C4D4211yescharacteristic
722C2×C4D4211yescharacteristic
723C2×C4#54611yescharacteristic
724C2×C4#54611yescharacteristic
725C2×C4#54611yescharacteristic
726C2×C4#54611yescharacteristic
727C2×C4#54611yescharacteristic
728C2×C4#54711yescharacteristic
729C2×C4#54711yescharacteristic
730C2×C4D4×Q811yescharacteristic
731C2×C4#55111yescharacteristic
732C2×C4#55111yescharacteristic
733C2×C4#55211yescharacteristic
734C2×C4#55411yescharacteristic
735C2×C4#55411yescharacteristic
736C2×C4#55411yescharacteristic
737C8—22no—
738C8—22no—
739C8—22no—
740C8—22no—
741C8—24no—
742C8—24no—
743C8—42no—
744C8—42no—
745C8—42no—
746C8—42no—
747C22—21no—
748C22—21no—
749C22—22no—
750C22—21no—
751C22—21no—
752C22—22no—
753C22—21no—
754C22—21no—
755C22—22no—
756C22—21no—
757C22—21no—
758C22—22no—
759C22—22no—
760C22—21no—
761C22—21no—
762C22—21no—
763C22—21no—
764C22—22no—
765C22—22no—
766C22—22no—
767C22—22no—
768C22—44no—
769C22—44no—
770C22—44no—
771C22—44no—
772C22—41no—
773C22—41no—
774C22—41no—
775C22—41no—
776C22#195214yescomplemented
777C22C2×#38911yescharacteristic
778C22C4×C22⋊Q811yescharacteristic
779C22#232911yescharacteristic
780C22#242411yescharacteristic
781C22#242511yescharacteristic
782C22#247311yescharacteristic
783C22#250511yescharacteristic
784C22C2×#47211yescharacteristic
785C22C2×#47311yescharacteristic
786C22#306811yescharacteristic
787C22#306911yescharacteristic
788C4—22no—
789C4—22no—
790C4—81no—
791C4—82no—
792C4—82no—
793C4—81no—
794C4—81no—
795C4—81no—
796C4—161no—
797C4—161no—
798C4D4×C4⋊C411yescharacteristic
799C4#234911yescharacteristic
800C4#235811yescharacteristic
801C4#235911yescharacteristic
802C4#243711yescharacteristic
803C4#243811yescharacteristic
804C4#244011yescharacteristic
805C4#254911yescharacteristic
806C2—21no—
807C2—24no—
808C2—21no—
809C2—21no—
810C2—21no—
811C2—42no—
812C2#1400411yescharacteristic
813C2C2×#195211yescharacteristic
814C2#2118211yescharacteristic
815C2#2514011yescharacteristic
816C2#2514211yescharacteristic
817C2#2526411yescharacteristic
818C2#2526611yescharacteristic
subgroupG/H
center, socleC23C2×#121
commutatorC22×C4C23×C4
Frattini, cosocleC23×C4C24
prime radicalC25#41
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C24×C4 ◁ G
LECSG ▷ C23×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#1952C2semidirect
8. #11331C2semidirect
9. #11270C2semidirect
10. #11249C2semidirect
11. #11249C2semidirect
12. #10896C2semidirect
13. #10896C2semidirect
14. #10870C2semidirect
34. #1855C4semidirect
116. C2×#108C2×C4semidirect
117. C2×#108C2×C4semidirect
181. #341C2×C4semidirect
182. #341C2×C4semidirect
776. C22#1952semidirect

Maximal subgroups

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

subgroupindex
C2×#19522
C2×#18552
#208442
C2×#18522
#206612
#203892
C22×#3432
#113312
#112702
#112492
#108962
#108702
#107392