Finite Group Databasebeta

← #361910

Subgroups — #361910

Order 512.

1804 conjugacy classes of subgroups.

The subgroup lattice has 833 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#442C211yesmaximal, characteristic
2C2×#1836C211yesmaximal, characteristic, complemented
3C2×#1804C211yesmaximal, characteristic, complemented
4C2×#1802C211yesmaximal, characteristic, complemented
5C2×#1771C211yesmaximal, characteristic, complemented
6#13941C211yesmaximal, characteristic, complemented
7#13906C211yesmaximal, characteristic, complemented
8#11378C211yesmaximal, characteristic, complemented
9#11378C211yesmaximal, characteristic, complemented
10#11022C211yesmaximal, characteristic
11#11022C211yesmaximal, characteristic
12#10927C211yesmaximal, characteristic, complemented
13#10927C211yesmaximal, characteristic, complemented
14#10925C211yesmaximal, characteristic, complemented
15#10925C211yesmaximal, characteristic, complemented
16C23×D8C2211yescharacteristic
17C22×C4×D4C2211yescharacteristic
18C22×C4×D4C2211yescharacteristic
19C2×#442—24no—
20C2×#442—24no—
21C2×#442C418yescomplemented
22C22×#106C2211yescharacteristic
23C22×C4⋊C8C2211yescharacteristic
24C22×#102C2211yescharacteristic
25C22×#102C2211yescharacteristic
26C22×#102C2211yescharacteristic
27C22×#102C2211yescharacteristic
28C22×#102C2211yescharacteristic
29C22×#102C2211yescharacteristic
30C22×#97C2211yescharacteristic
31C22×#97C2211yescharacteristic
32C22×C4×C8C2211yescharacteristic
33C2×#390C2211yescharacteristic
34C2×#390C2211yescharacteristic
35C2×#390C2211yescharacteristic
36C2×#390C2211yescharacteristic
37C2×#384C2211yescharacteristic
38C2×#382C2211yescharacteristic
39C2×#380—22no—
40C2×C4×C4⋊C4C2211yescharacteristic
41#1836—24no—
42#1804—24no—
43#1802—24no—
44#1771—24no—
45C2×#340C2211yescharacteristic
46C2×#340C2211yescharacteristic
47C2×#340C2211yescharacteristic
48C2×#340C2211yescharacteristic
49C2×#340C2211yescharacteristic
50C2×#340C2211yescharacteristic
51C2×#340C2211yescharacteristic
52C2×#340C2211yescharacteristic
53C2×#336C2211yescharacteristic
54C2×#336C2211yescharacteristic
55#1439—22no—
56#1439—22no—
57C4⋊#95C2211yescharacteristic
58C4⋊#95C2211yescharacteristic
59C4⋊#95C2211yescharacteristic
60C4⋊#95C2211yescharacteristic
61C22⋊#95—22no—
62C23×D4C2311yescharacteristic
63C23×D4C2311yescharacteristic
64C24×C4—21no—
65C24×C4—21no—
66C22×D8—22no—
67C22×D8—22no—
68C22×D8—22no—
69C22×D8—22no—
70C22×D8—22no—
71C22×D8—22no—
72C22×D8C2×C414yes—
73C23×C8C2311yescharacteristic
74C23×C8C2311yescharacteristic
75C23×C8C2311yescharacteristic
76C23×C8C2311yescharacteristic
77C2×C4×D4—22no—
78C2×C4×D4—22no—
79C2×C4×D4—22no—
80C2×C4×D4—22no—
81C2×C4×D4—22no—
82C2×C4×D4—22no—
83C2×C4×D4—22no—
84C2×C4×D4—22no—
85C2×C4×D4—22no—
86C2×C4×D4—22no—
87C2×C4×D4C2×C414yes—
88C2×C4×D4C2×C414yes—
89C22×C4⋊C4—21no—
90C22×C4⋊C4—21no—
91C22×C4⋊C4D412yes—
92C22×C4⋊C4C2311yescharacteristic
93C22×C4⋊C4C2311yescharacteristic
94C22×C4⋊C4C2311yescharacteristic
95C22×C4⋊C4C2311yescharacteristic
96C22×C4⋊C4C2311yescharacteristic
97C22×C4⋊C4C2311yescharacteristic
98C22×C22⋊C4—21no—
99C22×C22⋊C4—21no—
100C22×C22⋊C4—22no—
101C22×C22⋊C4—22no—
102C22×C22⋊C4—22no—
103C22×C22⋊C4—22no—
104C22×C42C2311yescharacteristic
105C22×C42C2311yescharacteristic
106C22×C42C2311yescharacteristic
107#442—232no—
108C2×#106—22no—
109C2×#106—22no—
110C2×#106C2×C414yes—
111C2×C4⋊C8—22no—
112C2×C4⋊C8—22no—
113C2×C4⋊C8D414yes—
114C2×#102—22no—
115C2×#102—22no—
116C2×#102—22no—
117C2×#102—22no—
118C2×#102—22no—
119C2×#102—22no—
120C2×#102—22no—
121C2×#102—22no—
122C2×#102—22no—
123C2×#102—22no—
124C2×#102—22no—
125C2×#102—22no—
126C2×#102—41no—
127C2×#102—41no—
128C2×#102—41no—
129C2×#102—41no—
130C2×#102C2×C414yes—
131C2×#102C2×C414yes—
132C2×#97—22no—
133C2×#97—41no—
134C2×#97—41no—
135C2×#97C2×C414yes—
136C2×#97D414yes—
137C2×#97D414yes—
138C2×C4×C8—22no—
139C2×C4×C8—41no—
140C2×C4×C8—41no—
141#390—22no—
142#390—22no—
143#390—22no—
144#390—22no—
145#390—41no—
146#390—41no—
147#390—41no—
148#390—41no—
149#384—22no—
150#384—22no—
151#382—22no—
152#382—22no—
153#380—48no—
154C4×C4⋊C4—22no—
155C4×C4⋊C4—22no—
156C2×#95—21no—
157C2×#95—22no—
158C2×#95—22no—
159C2×#95—21no—
160C2×#95—22no—
161C2×#95—22no—
162C2×#95D412yes—
163#340—22no—
164#340—22no—
165#340—22no—
166#340—22no—
167#340—22no—
168#340—22no—
169#340—22no—
170#340—22no—
171#336—22no—
172#336—22no—
173C25—21no—
174C25—21no—
175C22×D4—21no—
176C22×D4—21no—
177C22×D4—21no—
178C22×D4—21no—
179C22×D4—21no—
180C22×D4—21no—
181C22×D4—21no—
182C22×D4—21no—
183C22×D4—21no—
184C22×D4—21no—
185C22×D4—21no—
186C22×D4—21no—
187C22×D4—21no—
188C22×D4—21no—
189C22×D4—21no—
190C22×D4—21no—
191C22×D4—21no—
192C22×D4—21no—
193C22×D4—21no—
194C22×D4—21no—
195C22×D4—21no—
196C22×D4—21no—
197C22×D4C22×C412yes—
198C22×D4C22×C412yes—
199C22×D4#4112yes—
200C22×D4#4112yes—
201C22×D4#4112yes—
202C22×D4#4112yes—
203C23×C4—21no—
204C23×C4—21no—
205C23×C4—24no—
206C23×C4—24no—
207C23×C4—21no—
208C23×C4—21no—
209C23×C4—21no—
210C23×C4—21no—
211C23×C4—44no—
212C23×C4—44no—
213C23×C4—42no—
214C23×C4—42no—
215C23×C4—42no—
216C23×C4—42no—
217C23×C4—82no—
218C23×C4—82no—
219C23×C4C2×D412yes—
220C23×C4C2×D412yes—
221C23×C4C2×D411yescharacteristic
222C23×C4C2×D411yescharacteristic
223C23×C4C2411yescharacteristic
224C2×D8—28no—
225C2×D8—28no—
226C2×D8—28no—
227C2×D8—28no—
228C2×D8—28no—
229C2×D8—28no—
230C2×D8—28no—
231C22×C8—21no—
232C22×C8—21no—
233C22×C8—21no—
234C22×C8—21no—
235C22×C8—21no—
236C22×C8—21no—
237C22×C8—21no—
238C22×C8—21no—
239C22×C8—21no—
240C22×C8—21no—
241C22×C8—21no—
242C22×C8—21no—
243C22×C8—21no—
244C22×C8—21no—
245C22×C8—21no—
246C22×C8—21no—
247C22×C8—21no—
248C22×C8—21no—
249C22×C8—21no—
250C22×C8—21no—
251C22×C8C22×C412yes—
252C22×C8C22×C412yes—
253C22×C8C2×D412yes—
254C22×C8C2×D412yes—
255C22×C8C2×D412yes—
256C22×C8C2×D412yes—
257C22×C8C2×D412yes—
258C22×C8C2×D412yes—
259C4×D4—28no—
260C4×D4—28no—
261C4×D4—28no—
262C4×D4—28no—
263C4×D4—44no—
264C4×D4—44no—
265C4×D4—44no—
266C4×D4—44no—
267C2×C4⋊C4—21no—
268C2×C4⋊C4—21no—
269C2×C4⋊C4—21no—
270C2×C4⋊C4—21no—
271C2×C4⋊C4—21no—
272C2×C4⋊C4—21no—
273C2×C4⋊C4—21no—
274C2×C4⋊C4—21no—
275C2×C4⋊C4—24no—
276C2×C4⋊C4—24no—
277C2×C4⋊C4—21no—
278C2×C4⋊C4—21no—
279C2×C4⋊C4—21no—
280C2×C4⋊C4—21no—
281C2×C4⋊C4—21no—
282C2×C4⋊C4—21no—
283C2×C4⋊C4—21no—
284C2×C4⋊C4—21no—
285C2×C4⋊C4—21no—
286C2×C4⋊C4—21no—
287C2×C4⋊C4—21no—
288C2×C4⋊C4—21no—
289C2×C4⋊C4—21no—
290C2×C4⋊C4—21no—
291C2×C4⋊C4—21no—
292C2×C4⋊C4—21no—
293C2×C4⋊C4—21no—
294C2×C4⋊C4—21no—
295C2×C4⋊C4—21no—
296C2×C4⋊C4—21no—
297C2×C4⋊C4—21no—
298C2×C4⋊C4—21no—
299C2×C4⋊C4—21no—
300C2×C4⋊C4—21no—
301C2×C4⋊C4—21no—
302C2×C4⋊C4—21no—
303C2×C4⋊C4—42no—
304C2×C4⋊C4—44no—
305C2×C4⋊C4—42no—
306C2×C4⋊C4—42no—
307C2×C4⋊C4—82no—
308C2×C4⋊C4C22×C412yes—
309C2×C4⋊C4C22×C412yes—
310C2×C22⋊C4—24no—
311C2×C22⋊C4—24no—
312C2×C22⋊C4—42no—
313C2×C22⋊C4—42no—
314C2×C22⋊C4—42no—
315C2×C22⋊C4—42no—
316C2×C22⋊C4—44no—
317C2×C22⋊C4—44no—
318C2×C22⋊C4—44no—
319C2×C22⋊C4—44no—
320C2×C22⋊C4—44no—
321C2×C22⋊C4—44no—
322C2×C22⋊C4—44no—
323C2×C22⋊C4—44no—
324C2×C22⋊C4—82no—
325C2×C22⋊C4—82no—
326C2×C22⋊C4—82no—
327C2×C22⋊C4—82no—
328C2×C42—21no—
329C2×C42—21no—
330C2×C42—21no—
331C2×C42—21no—
332C2×C42—21no—
333C2×C42—21no—
334C2×C42—21no—
335C2×C42—21no—
336C2×C42—21no—
337C2×C42—21no—
338C2×C42—21no—
339C2×C42—21no—
340C2×C42C22×C412yes—
341C2×C42C2×D412yes—
342C2×C42C2×D412yes—
343C2×C42C2×D412yes—
344C2×C42#4112yes—
345C2×C42#4112yes—
346#106—28no—
347C4⋊C8—28no—
348#102—28no—
349#102—28no—
350#102—44no—
351#102—44no—
352#102—44no—
353#102—44no—
354#97—44no—
355#97C22⋊C4116yescomplemented
356C4×C8—44no—
357#95—24no—
358#95—44no—
359#95—42no—
360#95—42no—
361#95—44no—
362#95—82no—
363#95—82no—
364C24—22no—
365C24—22no—
366C24—22no—
367C24—22no—
368C24—22no—
369C24—22no—
370C24—41no—
371C24—41no—
372C24—41no—
373C24—41no—
374C24—41no—
375C24—41no—
376C24—41no—
377C24—41no—
378C24—42no—
379C24—42no—
380C24—42no—
381C24—42no—
382C24—42no—
383C24—42no—
384C24—42no—
385C24—42no—
386C24C22×D411yescharacteristic
387C2×D4—22no—
388C2×D4—22no—
389C2×D4—22no—
390C2×D4—22no—
391C2×D4—22no—
392C2×D4—22no—
393C2×D4—22no—
394C2×D4—22no—
395C2×D4—22no—
396C2×D4—22no—
397C2×D4—22no—
398C2×D4—22no—
399C2×D4—22no—
400C2×D4—22no—
401C2×D4—22no—
402C2×D4—22no—
403C2×D4—22no—
404C2×D4—22no—
405C2×D4—22no—
406C2×D4—22no—
407C2×D4—22no—
408C2×D4—22no—
409C2×D4—22no—
410C2×D4—22no—
411C2×D4—22no—
412C2×D4—22no—
413C2×D4—22no—
414C2×D4—22no—
415C2×D4—22no—
416C2×D4—22no—
417C2×D4—41no—
418C2×D4—41no—
419C2×D4—41no—
420C2×D4—41no—
421C2×D4—41no—
422C2×D4—41no—
423C2×D4—41no—
424C2×D4—41no—
425C2×D4—41no—
426C2×D4—41no—
427C2×D4—41no—
428C2×D4—41no—
429C2×D4—41no—
430C2×D4—41no—
431C2×D4—41no—
432C2×D4—41no—
433C2×D4—41no—
434C2×D4—41no—
435C2×D4—41no—
436C2×D4—41no—
437C2×D4—41no—
438C2×D4—41no—
439C2×D4—41no—
440C2×D4—41no—
441C2×D4#11714yes—
442C2×D4#11714yes—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—416no—
463C22×C4—41no—
464C22×C4—41no—
465C22×C4—41no—
466C22×C4—41no—
467C22×C4—42no—
468C22×C4—42no—
469C22×C4—42no—
470C22×C4—42no—
471C22×C4—48no—
472C22×C4—48no—
473C22×C4—41no—
474C22×C4—41no—
475C22×C4—41no—
476C22×C4—41no—
477C22×C4—41no—
478C22×C4—41no—
479C22×C4—41no—
480C22×C4—41no—
481C22×C4—41no—
482C22×C4—41no—
483C22×C4—41no—
484C22×C4—41no—
485C22×C4—42no—
486C22×C4—42no—
487C22×C4—42no—
488C22×C4—42no—
489C22×C4—42no—
490C22×C4—42no—
491C22×C4—42no—
492C22×C4—42no—
493C22×C4—88no—
494C22×C4—84no—
495C22×C4—84no—
496C22×C4—88no—
497C22×C4—84no—
498C22×C4—84no—
499C22×C4—88no—
500C22×C4C4×D412yes—
501C22×C4C4×D412yes—
502C22×C4#12112yes—
503C22×C4#12112yes—
504C22×C4#12712yes—
505C22×C4#12712yes—
506C22×C4AGL(1,ℤ/8)14yes—
507C22×C4C23×C411yescharacteristic
508C22×C4C22×D411yescharacteristic
509C22×C4C22×D411yescharacteristic
510C22×C4C22×D411yescharacteristic
511C22×C4C2×#4111yescharacteristic
512C22×C4C2×#4111yescharacteristic
513C22×C4C2×#4111yescharacteristic
514C22×C4C2×#4111yescharacteristic
515C22×C4C2×#4111yescharacteristic
516C22×C4C2×#4111yescharacteristic
517C22×C4H(5,𝔽2)11yescharacteristic
518C22×C4H(5,𝔽2)11yescharacteristic
519C22×C42−1+411yescharacteristic
520C22×C42−1+411yescharacteristic
521D8—232no—
522C2×C8—22no—
523C2×C8—22no—
524C2×C8—22no—
525C2×C8—22no—
526C2×C8—22no—
527C2×C8—22no—
528C2×C8—22no—
529C2×C8—22no—
530C2×C8—22no—
531C2×C8—22no—
532C2×C8—22no—
533C2×C8—22no—
534C2×C8—22no—
535C2×C8—22no—
536C2×C8—22no—
537C2×C8—22no—
538C2×C8—22no—
539C2×C8—22no—
540C2×C8—41no—
541C2×C8—41no—
542C2×C8—41no—
543C2×C8—41no—
544C2×C8—41no—
545C2×C8—41no—
546C2×C8—41no—
547C2×C8—41no—
548C2×C8C2×C22⋊C414yes—
549C2×C8C2×C22⋊C414yes—
550C4⋊C4—22no—
551C4⋊C4—22no—
552C4⋊C4—22no—
553C4⋊C4—22no—
554C4⋊C4—48no—
555C4⋊C4—41no—
556C4⋊C4—41no—
557C4⋊C4—41no—
558C4⋊C4—41no—
559C4⋊C4—41no—
560C4⋊C4—41no—
561C4⋊C4—41no—
562C4⋊C4—41no—
563C4⋊C4—41no—
564C4⋊C4—41no—
565C4⋊C4—41no—
566C4⋊C4—41no—
567C4⋊C4—41no—
568C4⋊C4—41no—
569C4⋊C4—41no—
570C4⋊C4—41no—
571C4⋊C4—41no—
572C4⋊C4—41no—
573C4⋊C4—41no—
574C4⋊C4—41no—
575C4⋊C4—84no—
576C4⋊C4—84no—
577C22⋊C4—48no—
578C22⋊C4—48no—
579C22⋊C4—88no—
580C22⋊C4—88no—
581C22⋊C4—88no—
582C22⋊C4—88no—
583C42—41no—
584C42—41no—
585C42—41no—
586C42—41no—
587C42—41no—
588C42—41no—
589C42—41no—
590C42—41no—
591C42C2×C22⋊C414yes—
592C42C4×D414yes—
593C42#12114yes—
594C42#12414yes—
595C23—24no—
596C23—24no—
597C23—44no—
598C23—44no—
599C23—44no—
600C23—42no—
601C23—42no—
602C23—44no—
603C23—44no—
604C23—44no—
605C23—44no—
606C23—44no—
607C23—42no—
608C23—42no—
609C23—42no—
610C23—42no—
611C23—44no—
612C23—44no—
613C23—42no—
614C23—42no—
615C23—42no—
616C23—42no—
617C23—42no—
618C23—42no—
619C23—44no—
620C23—44no—
621C23—82no—
622C23—82no—
623C23—82no—
624C23—82no—
625C23—81no—
626C23—81no—
627C23—81no—
628C23—81no—
629C23—81no—
630C23—81no—
631C23—81no—
632C23—81no—
633C23—82no—
634C23—82no—
635C23—82no—
636C23—82no—
637C23—82no—
638C23—82no—
639C23—82no—
640C23—82no—
641C23C2×C4×D411yescharacteristic
642C23C2×#12111yescharacteristic
643C23C2×#12711yescharacteristic
644C23#54611yescharacteristic
645C23#54611yescharacteristic
646C23#54811yescharacteristic
647C23#54811yescharacteristic
648C23C2×AGL(1,ℤ/8)12yes—
649C23#57512yes—
650C23#57612yes—
651C23#57712yes—
652D4—24no—
653D4—24no—
654D4—24no—
655D4—24no—
656D4—42no—
657D4—42no—
658D4—42no—
659D4—42no—
660D4—42no—
661D4—42no—
662D4—42no—
663D4—42no—
664D4—42no—
665D4—42no—
666D4—42no—
667D4—42no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—24no—
673C2×C4—24no—
674C2×C4—24no—
675C2×C4—24no—
676C2×C4—24no—
677C2×C4—24no—
678C2×C4—24no—
679C2×C4—42no—
680C2×C4—42no—
681C2×C4—42no—
682C2×C4—42no—
683C2×C4—44no—
684C2×C4—44no—
685C2×C4—42no—
686C2×C4—42no—
687C2×C4—42no—
688C2×C4—42no—
689C2×C4—42no—
690C2×C4—42no—
691C2×C4—42no—
692C2×C4—42no—
693C2×C4—42no—
694C2×C4—816no—
695C2×C4—816no—
696C2×C4—81no—
697C2×C4—81no—
698C2×C4—81no—
699C2×C4—81no—
700C2×C4—82no—
701C2×C4—82no—
702C2×C4—82no—
703C2×C4—82no—
704C2×C4—82no—
705C2×C4—82no—
706C2×C4—81no—
707C2×C4—81no—
708C2×C4—81no—
709C2×C4—81no—
710C2×C4—81no—
711C2×C4—81no—
712C2×C4—81no—
713C2×C4—81no—
714C2×C4—82no—
715C2×C4—81no—
716C2×C4—81no—
717C2×C4—81no—
718C2×C4—81no—
719C2×C4—82no—
720C2×C4—82no—
721C2×C4—82no—
722C2×C4#39014yes—
723C2×C4#39014yes—
724C2×C4C22×C22⋊C411yescharacteristic
725C2×C4C2×#11711yescharacteristic
726C2×C4C2×#11711yescharacteristic
727C2×C4C2×C4×D411yescharacteristic
728C2×C4#52011yescharacteristic
729C2×C4#52011yescharacteristic
730C2×C4C2×#12111yescharacteristic
731C2×C4#52511yescharacteristic
732C2×C4#52511yescharacteristic
733C2×C4#52511yescharacteristic
734C2×C4#52511yescharacteristic
735C2×C4C2×#12411yescharacteristic
736C2×C4#53511yescharacteristic
737C2×C4#53611yescharacteristic
738C2×C4#53711yescharacteristic
739C2×C4#53711yescharacteristic
740C2×C4#54611yescharacteristic
741C2×C4#54611yescharacteristic
742C2×C4#54811yescharacteristic
743C2×C4#54811yescharacteristic
744C2×C4#55211yescharacteristic
745C2×C4#55211yescharacteristic
746C2×C4#55211yescharacteristic
747C2×C4#55211yescharacteristic
748C2×C4#55311yescharacteristic
749C2×C4#55311yescharacteristic
750C2×C4#55311yescharacteristic
751C2×C4#55311yescharacteristic
752C8—24no—
753C8—24no—
754C8—42no—
755C8—42no—
756C22—44no—
757C22—44no—
758C22—48no—
759C22—48no—
760C22—82no—
761C22—82no—
762C22—82no—
763C22—82no—
764C22—82no—
765C22—82no—
766C22—82no—
767C22—82no—
768C22—84no—
769C22—84no—
770C22—82no—
771C22—82no—
772C22—82no—
773C22—82no—
774C22—84no—
775C22—84no—
776C22—84no—
777C22—84no—
778C22C2×#39011yescharacteristic
779C22#235211yescharacteristic
780C22#235211yescharacteristic
781C22#253511yescharacteristic
782C22#253611yescharacteristic
783C22#254011yescharacteristic
784C22#254011yescharacteristic
785C22C4×AGL(1,ℤ/8)12yes—
786C22#294612yes—
787C22#305512yes—
788C22#306212yes—
789C22#315111yescharacteristic
790C22#315311yescharacteristic
791C22#315411yescharacteristic
792C22#315511yescharacteristic
793C22#330612yes—
794C22#330712yes—
795C22#331812yes—
796C22#331912yes—
797C22#336612yes—
798C22#337012yes—
799C22#337312yes—
800C22#337612yes—
801C4—24no—
802C4—24no—
803C4—44no—
804C4—82no—
805C4—82no—
806C4—82no—
807C4—161no—
808C4—161no—
809C4—161no—
810C4—161no—
811C4#228011yescharacteristic
812C4#231111yescharacteristic
813C4#235211yescharacteristic
814C4#235211yescharacteristic
815C4#253511yescharacteristic
816C4#253611yescharacteristic
817C4#256211yescharacteristic
818C4#256211yescharacteristic
819C2—84no—
820C2—84no—
821C2#1390511yescharacteristic
822C2#2123511yescharacteristic
823C2#2123611yescharacteristic
824C2#2277412yes—
825C2#2278012yes—
826C2#2815212yes—
827C2#2819712yes—
828C2#2842111yescharacteristic
829C2#2842211yescharacteristic
830C2#2842911yescharacteristic
831C2#2843011yescharacteristic
subgroupG/H
center, socleC24C22×D4
commutatorC22×C4C23×C4
Frattini, cosocleC23×C4C24
prime radicalC23×D8C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24 ◁ 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×#1836C2semidirect
3. C2×#1804C2semidirect
4. C2×#1802C2semidirect
5. C2×#1771C2semidirect
6. #13941C2semidirect
7. #13906C2semidirect
8. #11378C2semidirect
9. #11378C2semidirect
12. #10927C2semidirect
13. #10927C2semidirect
14. #10925C2semidirect
15. #10925C2semidirect
21. C2×#442C4semidirect
355. #97C22⋊C4semidirect

Maximal subgroups

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

subgroupindex
C22×#4422
C2×#18362
C2×#18042
C2×#18022
C2×#17712
#139412
#139062
#113782
#110222
#109272
#109252