Finite Group Databasebeta

← C2×#14141 #514579

Subgroups — C2×#14141 #514579

Order 512.

6362 conjugacy classes of subgroups.

The subgroup lattice has 828 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#390C211yesmaximal, characteristic
2C22×#390C211yesmaximal, characteristic
3C22×#390C211yesmaximal, characteristic
4C22×#389C211yesmaximal, characteristic, complemented
5C22×#388C212yesmaximal, complemented
6C22×C4×C4⋊C4C211yesmaximal, characteristic, complemented
7#14141C2116yesmaximal, direct product factor
8C2×#1440C212yesmaximal, complemented
9C2×#1439C212yesmaximal, complemented
10C2×#1437C212yesmaximal, complemented
11C2×C4⋊#95C211yesmaximal, characteristic, complemented
12C2×C4×#95C211yesmaximal, characteristic, complemented
13C24×D4C2211yescharacteristic
14C23×C4⋊C4C2212yes—
15C23×C4⋊C4C2211yescharacteristic
16C23×C4⋊C4C2211yescharacteristic
17C23×C4⋊C4C2211yescharacteristic
18C23×C22⋊C4C2212yes—
19C23×C22⋊C4C2212yes—
20C23×C22⋊C4C2212yes—
21C23×C22⋊C4C2212yes—
22C23×C22⋊C4C2212yes—
23C23×C22⋊C4C2212yes—
24C23×C42C2211yescharacteristic
25C23×C42C2211yescharacteristic
26C23×C42C2212yes—
27C23×C42C2211yescharacteristic
28C2×#390—28no—
29C2×#390—28no—
30C2×#390C4116yescomplemented
31C2×#390C2218yes—
32C2×#390C2218yes—
33C2×#390C2218yes—
34C2×#389—28no—
35C2×#389C2218yescomplemented
36C2×#388—216no—
37C2×#388C22116yescomplemented
38C2×C4×C4⋊C4—28no—
39C2×C4×C4⋊C4C2218yescomplemented
40C22×#95C2211yescharacteristic
41C22×#95C2212yes—
42C22×#95C2211yescharacteristic
43C22×#95C2212yes—
44C22×#95C2212yes—
45C22×#95C2211yescharacteristic
46C22×#95C2212yes—
47C22×#95C2211yescharacteristic
48#1440C22116yescomplemented
49#1439C22116yescomplemented
50#1437C22116yescomplemented
51C4⋊#95C2218yescomplemented
52C4×#95C2218yescomplemented
53C26C2312yes—
54C23×D4—24no—
55C23×D4—24no—
56C23×D4—24no—
57C23×D4—24no—
58C23×D4—24no—
59C23×D4—24no—
60C23×D4C2×C418yes—
61C23×D4C2314yes—
62C24×C4C2311yescharacteristic
63C24×C4C2312yes—
64C24×C4C2311yescharacteristic
65C24×C4C2312yes—
66C24×C4C2312yes—
67C24×C4C2311yescharacteristic
68C24×C4C2311yescharacteristic
69C24×C4C2311yescharacteristic
70C24×C4C2311yescharacteristic
71C24×C4C2311yescharacteristic
72C22×C4⋊C4—24no—
73C22×C4⋊C4—24no—
74C22×C4⋊C4—24no—
75C22×C4⋊C4—24no—
76C22×C4⋊C4—24no—
77C22×C4⋊C4—24no—
78C22×C4⋊C4—28no—
79C22×C4⋊C4—28no—
80C22×C4⋊C4—44no—
81C22×C4⋊C4C2×C418yes—
82C22×C4⋊C4D418yes—
83C22×C4⋊C4D418yes—
84C22×C4⋊C4C2318yes—
85C22×C4⋊C4C2314yes—
86C22×C4⋊C4C2314yes—
87C22×C4⋊C4C2314yes—
88C22×C22⋊C4—28no—
89C22×C22⋊C4—28no—
90C22×C22⋊C4—28no—
91C22×C22⋊C4—28no—
92C22×C22⋊C4—28no—
93C22×C22⋊C4—28no—
94C22×C22⋊C4—28no—
95C22×C22⋊C4—28no—
96C22×C22⋊C4—28no—
97C22×C22⋊C4—28no—
98C22×C22⋊C4—44no—
99C22×C22⋊C4—44no—
100C22×C22⋊C4—44no—
101C22×C22⋊C4—44no—
102C22×C22⋊C4—44no—
103C22×C22⋊C4—44no—
104C22×C22⋊C4C2×C4116yes—
105C22×C22⋊C4C2×C4116yes—
106C22×C22⋊C4C2318yes—
107C22×C22⋊C4C2318yes—
108C22×C22⋊C4C2318yes—
109C22×C22⋊C4C2318yes—
110C22×C22⋊C4C2318yes—
111C22×C22⋊C4C2318yes—
112C22×C42—24no—
113C22×C42—24no—
114C22×C42—28no—
115C22×C42—28no—
116C22×C42—24no—
117C22×C42—24no—
118C22×C42—24no—
119C22×C42—24no—
120C22×C42—24no—
121C22×C42—24no—
122C22×C42—44no—
123C22×C42C2×C418yes—
124C22×C42C2314yes—
125C22×C42C2314yes—
126C22×C42C2318yes—
127C22×C42C2314yes—
128#390—232no—
129#390—232no—
130#390C2×C4164yescomplemented
131#389—232no—
132#388—264no—
133C4×C4⋊C4—232no—
134C2×#95—28no—
135C2×#95—28no—
136C2×#95—28no—
137C2×#95—24no—
138C2×#95—24no—
139C2×#95—24no—
140C2×#95—44no—
141C2×#95D418yescomplemented
142C2×#95C2314yes—
143C2×#95C2314yes—
144C2×#95C2314yes—
145C2×#95C2318yes—
146C2×#95C2318yes—
147C2×#95C2318yes—
148C2×#95C2318yes—
149C2×#95C2314yes—
150C25—24no—
151C25—24no—
152C25—24no—
153C25—24no—
154C25—24no—
155C25—24no—
156C25—24no—
157C25—24no—
158C25—24no—
159C25—24no—
160C25—24no—
161C25—24no—
162C25—24no—
163C25—24no—
164C25C22×C418yes—
165C25C2414yes—
166C25C2411yescharacteristic
167C22×D4—232no—
168C22×D4—232no—
169C22×D4—232no—
170C22×D4—28no—
171C22×D4—28no—
172C22×D4—28no—
173C22×D4—28no—
174C22×D4—28no—
175C22×D4—28no—
176C22×D4—416no—
177C22×D4—416no—
178C22×D4—416no—
179C22×D4—416no—
180C22×D4C22×C4116yes—
181C23×C4—22no—
182C23×C4—22no—
183C23×C4—22no—
184C23×C4—22no—
185C23×C4—22no—
186C23×C4—22no—
187C23×C4—22no—
188C23×C4—22no—
189C23×C4—24no—
190C23×C4—24no—
191C23×C4—24no—
192C23×C4—24no—
193C23×C4—22no—
194C23×C4—24no—
195C23×C4—22no—
196C23×C4—22no—
197C23×C4—24no—
198C23×C4—24no—
199C23×C4—24no—
200C23×C4—24no—
201C23×C4—24no—
202C23×C4—24no—
203C23×C4—24no—
204C23×C4—22no—
205C23×C4—22no—
206C23×C4—22no—
207C23×C4—22no—
208C23×C4—22no—
209C23×C4—22no—
210C23×C4—22no—
211C23×C4—22no—
212C23×C4—22no—
213C23×C4—22no—
214C23×C4—22no—
215C23×C4—22no—
216C23×C4—22no—
217C23×C4—22no—
218C23×C4—22no—
219C23×C4—22no—
220C23×C4—22no—
221C23×C4—22no—
222C23×C4—22no—
223C23×C4—24no—
224C23×C4—24no—
225C23×C4—24no—
226C23×C4—24no—
227C23×C4—24no—
228C23×C4—24no—
229C23×C4—22no—
230C23×C4—22no—
231C23×C4—22no—
232C23×C4—22no—
233C23×C4C22×C418yes—
234C23×C4C22×C414yes—
235C23×C4C22×C414yes—
236C23×C4C22×C414yes—
237C23×C4C2×D414yes—
238C23×C4C2×D418yes—
239C23×C4C2×D418yes—
240C23×C4C2×D414yes—
241C23×C4C2×D414yes—
242C23×C4C2×D414yes—
243C23×C4C2×D414yes—
244C23×C4#4114yes—
245C23×C4#4114yes—
246C23×C4#4114yes—
247C23×C4#4114yes—
248C23×C4#4114yes—
249C23×C4#4114yes—
250C23×C4#4114yes—
251C23×C4C2414yes—
252C23×C4C2412yes—
253C23×C4C2414yes—
254C23×C4C2412yes—
255C23×C4C2414yes—
256C23×C4C2412yes—
257C23×C4C2412yes—
258C23×C4C2412yes—
259C23×C4C2412yes—
260C23×C4C2412yes—
261C2×C4⋊C4—232no—
262C2×C4⋊C4—232no—
263C2×C4⋊C4—232no—
264C2×C4⋊C4—28no—
265C2×C4⋊C4—28no—
266C2×C4⋊C4—28no—
267C2×C4⋊C4—28no—
268C2×C4⋊C4—28no—
269C2×C4⋊C4—28no—
270C2×C4⋊C4—216no—
271C2×C4⋊C4—216no—
272C2×C4⋊C4—48no—
273C2×C4⋊C4—432no—
274C2×C4⋊C4C22×C4116yes—
275C2×C4⋊C4C2×D4116yes—
276C2×C4⋊C4C2×D4116yes—
277C2×C22⋊C4—264no—
278C2×C22⋊C4—216no—
279C2×C22⋊C4—216no—
280C2×C22⋊C4—216no—
281C2×C22⋊C4—216no—
282C2×C22⋊C4—216no—
283C2×C22⋊C4—216no—
284C2×C22⋊C4—216no—
285C2×C22⋊C4—216no—
286C2×C22⋊C4—216no—
287C2×C22⋊C4—216no—
288C2×C22⋊C4—432no—
289C2×C22⋊C4—48no—
290C2×C22⋊C4—48no—
291C2×C22⋊C4—48no—
292C2×C22⋊C4—48no—
293C2×C22⋊C4—48no—
294C2×C22⋊C4—48no—
295C2×C22⋊C4—432no—
296C2×C22⋊C4—432no—
297C2×C22⋊C4—432no—
298C2×C22⋊C4—432no—
299C2×C22⋊C4C22×C4132yes—
300C2×C22⋊C4C22×C4132yes—
301C2×C42—232no—
302C2×C42—28no—
303C2×C42—28no—
304C2×C42—216no—
305C2×C42—216no—
306C2×C42—28no—
307C2×C42—28no—
308C2×C42—28no—
309C2×C42—28no—
310C2×C42—28no—
311C2×C42—28no—
312C2×C42—48no—
313C2×C42—432no—
314C2×C42—416no—
315C2×C42—416no—
316C2×C42C22×C4116yes—
317#95—216no—
318#95—216no—
319#95—216no—
320#95—28no—
321#95—28no—
322#95—28no—
323#95—48no—
324#95C2×D4116yescomplemented
325C24—216no—
326C24—216no—
327C24—216no—
328C24—216no—
329C24—216no—
330C24—216no—
331C24—216no—
332C24—24no—
333C24—24no—
334C24—24no—
335C24—24no—
336C24—24no—
337C24—24no—
338C24—24no—
339C24—24no—
340C24—24no—
341C24—24no—
342C24—24no—
343C24—24no—
344C24—24no—
345C24—24no—
346C24—48no—
347C24—48no—
348C24—48no—
349C24—48no—
350C24—48no—
351C24—48no—
352C24—48no—
353C24—48no—
354C24—48no—
355C24—48no—
356C24—48no—
357C24—48no—
358C24—48no—
359C24—48no—
360C24—48no—
361C24—48no—
362C24—48no—
363C24—48no—
364C24—48no—
365C24—48no—
366C24—48no—
367C24—48no—
368C24—48no—
369C24—48no—
370C24—48no—
371C24—48no—
372C24—48no—
373C24—48no—
374C24C23×C418yes—
375C24C23×C412yes—
376C24C22×D412yes—
377C24C22×D412yes—
378C24C22×D412yes—
379C24C2×#4112yes—
380C24C2×#4112yes—
381C24C2×#4112yes—
382C24C2×#4112yes—
383C24C2×#4112yes—
384C24C2×#4112yes—
385C24C2×#4112yes—
386C24H(5,𝔽2)12yes—
387C24H(5,𝔽2)12yes—
388C24H(5,𝔽2)12yes—
389C242−1+412yes—
390C24C2511yescharacteristic
391C2×D4—232no—
392C2×D4—232no—
393C2×D4—232no—
394C2×D4—416no—
395C2×D4—416no—
396C2×D4—416no—
397C2×D4—416no—
398C2×D4—4128no—
399C22×C4—28no—
400C22×C4—28no—
401C22×C4—28no—
402C22×C4—28no—
403C22×C4—28no—
404C22×C4—28no—
405C22×C4—22no—
406C22×C4—22no—
407C22×C4—22no—
408C22×C4—22no—
409C22×C4—28no—
410C22×C4—216no—
411C22×C4—216no—
412C22×C4—28no—
413C22×C4—28no—
414C22×C4—216no—
415C22×C4—216no—
416C22×C4—216no—
417C22×C4—28no—
418C22×C4—28no—
419C22×C4—28no—
420C22×C4—28no—
421C22×C4—216no—
422C22×C4—28no—
423C22×C4—28no—
424C22×C4—216no—
425C22×C4—28no—
426C22×C4—28no—
427C22×C4—28no—
428C22×C4—216no—
429C22×C4—216no—
430C22×C4—28no—
431C22×C4—28no—
432C22×C4—28no—
433C22×C4—22no—
434C22×C4—22no—
435C22×C4—24no—
436C22×C4—24no—
437C22×C4—24no—
438C22×C4—24no—
439C22×C4—22no—
440C22×C4—22no—
441C22×C4—22no—
442C22×C4—22no—
443C22×C4—24no—
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—24no—
459C22×C4—24no—
460C22×C4—24no—
461C22×C4—24no—
462C22×C4—24no—
463C22×C4—24no—
464C22×C4—24no—
465C22×C4—22no—
466C22×C4—24no—
467C22×C4—24no—
468C22×C4—24no—
469C22×C4—24no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—24no—
477C22×C4—24no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—44no—
482C22×C4—44no—
483C22×C4—44no—
484C22×C4—44no—
485C22×C4—48no—
486C22×C4—48no—
487C22×C4—48no—
488C22×C4—44no—
489C22×C4—48no—
490C22×C4—44no—
491C22×C4—44no—
492C22×C4—44no—
493C22×C4—48no—
494C22×C4—48no—
495C22×C4—44no—
496C22×C4—44no—
497C22×C4—44no—
498C22×C4—44no—
499C22×C4—44no—
500C22×C4—48no—
501C22×C4—48no—
502C22×C4—44no—
503C22×C4—44no—
504C22×C4—48no—
505C22×C4—48no—
506C22×C4—44no—
507C22×C4—44no—
508C22×C4—44no—
509C22×C4—44no—
510C22×C4—44no—
511C22×C4—48no—
512C22×C4—48no—
513C22×C4#117116yes—
514C22×C4C4×D4116yes—
515C22×C4C4×D4116yes—
516C22×C4C4×D4116yes—
517C22×C4#121116yes—
518C22×C4#123116yes—
519C22×C4#124116yes—
520C22×C4#126116yes—
521C22×C4C23×C414yes—
522C22×C4C23×C418yes—
523C22×C4C23×C414yes—
524C22×C4C23×C414yes—
525C22×C4C22×D414yes—
526C22×C4C22×D418yes—
527C22×C4C22×D418yes—
528C22×C4C22×D414yes—
529C22×C4C22×D414yes—
530C22×C4C22×D414yes—
531C22×C4C22×D414yes—
532C22×C4C2×#4114yes—
533C22×C4C2×#4114yes—
534C22×C4C2×#4114yes—
535C22×C4C2×#4114yes—
536C22×C4C2×#4114yes—
537C22×C4C2×#4114yes—
538C22×C4C2×#4114yes—
539C4⋊C4—232no—
540C4⋊C4—232no—
541C4⋊C4—232no—
542C4⋊C4—432no—
543C22⋊C4—264no—
544C22⋊C4—432no—
545C22⋊C4—432no—
546C22⋊C4—432no—
547C22⋊C4—432no—
548C22⋊C4—432no—
549C42—232no—
550C42—432no—
551C42—416no—
552C42—416no—
553C23—28no—
554C23—28no—
555C23—28no—
556C23—28no—
557C23—28no—
558C23—28no—
559C23—28no—
560C23—432no—
561C23—432no—
562C23—432no—
563C23—432no—
564C23—432no—
565C23—44no—
566C23—44no—
567C23—44no—
568C23—44no—
569C23—44no—
570C23—44no—
571C23—44no—
572C23—44no—
573C23—44no—
574C23—44no—
575C23—44no—
576C23—44no—
577C23—44no—
578C23—44no—
579C23—44no—
580C23—44no—
581C23—44no—
582C23—44no—
583C23—44no—
584C23—44no—
585C23—44no—
586C23—44no—
587C23—44no—
588C23—44no—
589C23—44no—
590C23—44no—
591C23—44no—
592C23—44no—
593C23—432no—
594C23—432no—
595C23—816no—
596C23—816no—
597C23—816no—
598C23—816no—
599C23—816no—
600C23—816no—
601C23—816no—
602C23—816no—
603C23C2×#11714yes—
604C23C2×C4×D414yes—
605C23C2×C4×D414yes—
606C23C2×C4×D414yes—
607C23C4×#4114yes—
608C23#51814yes—
609C23#52014yes—
610C23C2×#12114yes—
611C23C2×#12314yes—
612C23C2×#12414yes—
613C23C2×#12614yes—
614C23#52914yes—
615C23#52914yes—
616C23#53214yes—
617C23#53214yes—
618C23#54014yes—
619C23#54014yes—
620C23#54214yes—
621C23#54214yes—
622C23D4214yes—
623C23D4214yes—
624C23#54614yes—
625C23#54614yes—
626C23#54714yes—
627C23#54814yes—
628C23#54814yes—
629C23#55014yes—
630C23#55014yes—
631C23#55014yes—
632C23#55314yes—
633C23#55314yes—
634C23#55514yes—
635C23#55614yes—
636C23#55914yes—
637C23#55914yes—
638C23C24×C411yescharacteristic
639C23C23×D411yescharacteristic
640C23C23×D411yescharacteristic
641C23C23×D411yescharacteristic
642C23C22×#4111yescharacteristic
643C23C22×#4111yescharacteristic
644C23C22×#4111yescharacteristic
645C23C22×#4111yescharacteristic
646C23C22×#4111yescharacteristic
647C23C22×#4111yescharacteristic
648C23C22×#4111yescharacteristic
649C23C2×H(5,𝔽2)11yescharacteristic
650C23C2×H(5,𝔽2)11yescharacteristic
651C23C2×H(5,𝔽2)11yescharacteristic
652C23C2×2−1+411yescharacteristic
653D4—464no—
654C2×C4—232no—
655C2×C4—24no—
656C2×C4—24no—
657C2×C4—24no—
658C2×C4—24no—
659C2×C4—24no—
660C2×C4—24no—
661C2×C4—24no—
662C2×C4—28no—
663C2×C4—28no—
664C2×C4—24no—
665C2×C4—24no—
666C2×C4—28no—
667C2×C4—28no—
668C2×C4—28no—
669C2×C4—24no—
670C2×C4—24no—
671C2×C4—24no—
672C2×C4—24no—
673C2×C4—28no—
674C2×C4—24no—
675C2×C4—24no—
676C2×C4—28no—
677C2×C4—24no—
678C2×C4—24no—
679C2×C4—24no—
680C2×C4—28no—
681C2×C4—28no—
682C2×C4—24no—
683C2×C4—24no—
684C2×C4—24no—
685C2×C4—416no—
686C2×C4—432no—
687C2×C4—42no—
688C2×C4—42no—
689C2×C4—42no—
690C2×C4—42no—
691C2×C4—44no—
692C2×C4—44no—
693C2×C4—416no—
694C2×C4—432no—
695C2×C4—416no—
696C2×C4—42no—
697C2×C4—44no—
698C2×C4—44no—
699C2×C4—42no—
700C2×C4—42no—
701C2×C4—42no—
702C2×C4—44no—
703C2×C4—44no—
704C2×C4—42no—
705C2×C4—42no—
706C2×C4—42no—
707C2×C4—42no—
708C2×C4—42no—
709C2×C4—44no—
710C2×C4—44no—
711C2×C4—44no—
712C2×C4—42no—
713C2×C4—44no—
714C2×C4—42no—
715C2×C4—42no—
716C2×C4—432no—
717C2×C4—42no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—42no—
721C2×C4—44no—
722C2×C4—44no—
723C2×C4—416no—
724C2×C4—416no—
725C2×C4#388164yescomplemented
726C2×C4C2×#11718yes—
727C2×C4C2×C4×D418yes—
728C2×C4C2×C4×D418yes—
729C2×C4C2×C4×D418yes—
730C2×C4C2×#12118yes—
731C2×C4C2×#12318yes—
732C2×C4C2×#12418yes—
733C2×C4C2×#12618yes—
734C22—48no—
735C22—48no—
736C22—48no—
737C22—48no—
738C22—48no—
739C22—48no—
740C22—48no—
741C22—864no—
742C22—84no—
743C22—84no—
744C22—84no—
745C22—84no—
746C22—84no—
747C22—84no—
748C22—84no—
749C22—84no—
750C22C2×#38818yes—
751C22#229318yes—
752C22#231918yes—
753C22#236118yes—
754C22#236318yes—
755C22#236618yes—
756C22#236718yes—
757C22#242618yes—
758C22#242818yes—
759C22#244518yes—
760C22#244818yes—
761C22#249018yes—
762C22#249118yes—
763C22#251218yes—
764C22#251318yes—
765C22C22×#11711yescharacteristic
766C22C22×C4×D411yescharacteristic
767C22C22×C4×D411yescharacteristic
768C22C22×C4×D411yescharacteristic
769C22C2×C4×#4111yescharacteristic
770C22C2×#51811yescharacteristic
771C22C2×#52011yescharacteristic
772C22C22×#12111yescharacteristic
773C22C22×#12311yescharacteristic
774C22C22×#12411yescharacteristic
775C22C22×#12611yescharacteristic
776C22C2×#52911yescharacteristic
777C22C2×#52911yescharacteristic
778C22C2×#53211yescharacteristic
779C22C2×#53211yescharacteristic
780C22C2×#54011yescharacteristic
781C22C2×#54011yescharacteristic
782C22C2×#54211yescharacteristic
783C22C2×#54211yescharacteristic
784C22C2×D4211yescharacteristic
785C22C2×D4211yescharacteristic
786C22C2×#54611yescharacteristic
787C22C2×#54611yescharacteristic
788C22C2×#54711yescharacteristic
789C22C2×#54811yescharacteristic
790C22C2×#54811yescharacteristic
791C22C2×#55011yescharacteristic
792C22C2×#55011yescharacteristic
793C22C2×#55011yescharacteristic
794C22C2×#55311yescharacteristic
795C22C2×#55311yescharacteristic
796C22C2×#55511yescharacteristic
797C22C2×#55611yescharacteristic
798C22C2×#55911yescharacteristic
799C22C2×#55911yescharacteristic
800C4—28no—
801C4—44no—
802C4—48no—
803C4—48no—
804C4—44no—
805C4—48no—
806C4—44no—
807C4—44no—
808C4—44no—
809C4C2×#388116yescomplemented
810C2—88no—
811C2#14141116yesdirect product factor
812C2C22×#38811yescharacteristic
813C2C2×#229311yescharacteristic
814C2C2×#231911yescharacteristic
815C2C2×#236111yescharacteristic
816C2C2×#236311yescharacteristic
817C2C2×#236611yescharacteristic
818C2C2×#236711yescharacteristic
819C2C2×#242811yescharacteristic
820C2C2×#244511yescharacteristic
821C2C2×#242611yescharacteristic
822C2C2×#244811yescharacteristic
823C2C2×#249111yescharacteristic
824C2C2×#251211yescharacteristic
825C2C2×#249011yescharacteristic
826C2C2×#251311yescharacteristic
subgroupG/H
center, socleC25C24
commutatorC23C24×C4
Frattini, cosocleC24C25
prime radicalC24×D4C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C25 ◁ G
LECSG ▷ C24 ▷ C1

Complements

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

NH ≅ G/Ntype
4. C22×#389C2semidirect
5. C22×#388C2semidirect
6. C22×C4×C4⋊C4C2semidirect
7. #14141C2direct (N × H)
8. C2×#1440C2semidirect
9. C2×#1439C2semidirect
10. C2×#1437C2semidirect
11. C2×C4⋊#95C2semidirect
12. C2×C4×#95C2semidirect
30. C2×#390C4semidirect
35. C2×#389C22semidirect
37. C2×#388C22semidirect
39. C2×C4×C4⋊C4C22semidirect
48. #1440C22semidirect
49. #1439C22semidirect
50. #1437C22semidirect
51. C4⋊#95C22semidirect
52. C4×#95C22semidirect
130. #390C2×C4semidirect
141. C2×#95D4semidirect
324. #95C2×D4semidirect
725. C2×C4#388semidirect
809. C4C2×#388semidirect
811. C2#14141direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#3902
C22×#3892
C22×#3882
C22×C4×C4⋊C42
#141412
C2×#14402
C2×#14392
C2×#14372
C2×C4⋊#952
C2×C4×#952