Finite Group Databasebeta

← C2×#15220 #608538

Subgroups — C2×#15220 #608538

Order 512.

5494 conjugacy classes of subgroups.

The subgroup lattice has 816 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#389C211yesmaximal, characteristic, complemented
2C22×#389C211yesmaximal, characteristic, complemented
3C22×#382C211yesmaximal, characteristic, complemented
4C22×#380C211yesmaximal, characteristic
5C22×#380C211yesmaximal, characteristic
6C22×C4×C22⋊C4C211yesmaximal, characteristic
7#15220C2116yesmaximal, direct product factor
8C2×#1443C212yesmaximal, complemented
9C2×#1441C212yesmaximal, complemented
10C2×#1439C212yesmaximal
11C2×#1439C212yesmaximal
12C2×C4⋊#95C211yesmaximal, characteristic, complemented
13C25×C4C2211yescharacteristic
14C23×C4⋊C4C2211yescharacteristic
15C23×C4⋊C4C2211yescharacteristic
16C23×C4⋊C4C2212yes—
17C23×C4⋊C4C2211yescharacteristic
18C23×C4⋊C4C2211yescharacteristic
19C23×C4⋊C4C2212yes—
20C23×C22⋊C4C2211yescharacteristic
21C23×C22⋊C4C2211yescharacteristic
22C23×C22⋊C4C2212yes—
23C23×C22⋊C4C2212yes—
24C23×C42C2211yescharacteristic
25C23×C42C2211yescharacteristic
26C2×#389—28no—
27C2×#389—28no—
28C2×#389C2218yescomplemented
29C2×#389C2218yescomplemented
30C2×#382—28no—
31C2×#382C2218yescomplemented
32C2×#380—28no—
33C2×#380—28no—
34C2×#380C2218yes—
35C2×#380C2218yes—
36C2×C4×C22⋊C4—28no—
37C2×C4×C22⋊C4C2218yes—
38C22×#95C2212yes—
39C22×#95C2212yes—
40C22×#95C2212yes—
41C22×#95C2212yes—
42C22×#95C2212yes—
43C22×#95C2211yescharacteristic
44C22×#95C2212yes—
45C22×#95C2212yes—
46C22×#95C2211yescharacteristic
47C22×#95C2212yes—
48#1443C22116yescomplemented
49#1441C22116yescomplemented
50#1439C22116yes—
51#1439C22116yes—
52C4⋊#95C2218yescomplemented
53C26C2311yescharacteristic
54C24×C4—24no—
55C24×C4—24no—
56C24×C4—24no—
57C24×C4—24no—
58C24×C4—24no—
59C24×C4—24no—
60C24×C4Q818yes—
61C24×C4C2312yes—
62C24×C4C2312yes—
63C24×C4C2311yescharacteristic
64C24×C4C2311yescharacteristic
65C24×C4C2312yes—
66C24×C4C2312yes—
67C24×C4C2314yes—
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—24no—
79C22×C4⋊C4—28no—
80C22×C4⋊C4—28no—
81C22×C4⋊C4—24no—
82C22×C4⋊C4—28no—
83C22×C4⋊C4—24no—
84C22×C4⋊C4—24no—
85C22×C4⋊C4—44no—
86C22×C4⋊C4—44no—
87C22×C4⋊C4—44no—
88C22×C4⋊C4D418yes—
89C22×C4⋊C4D418yes—
90C22×C4⋊C4C2314yes—
91C22×C4⋊C4C2314yes—
92C22×C4⋊C4C2318yes—
93C22×C4⋊C4C2314yes—
94C22×C4⋊C4C2314yes—
95C22×C4⋊C4C2318yes—
96C22×C22⋊C4—24no—
97C22×C22⋊C4—24no—
98C22×C22⋊C4—24no—
99C22×C22⋊C4—24no—
100C22×C22⋊C4—24no—
101C22×C22⋊C4—24no—
102C22×C22⋊C4—28no—
103C22×C22⋊C4—28no—
104C22×C22⋊C4—28no—
105C22×C22⋊C4—28no—
106C22×C22⋊C4—44no—
107C22×C22⋊C4—44no—
108C22×C22⋊C4C2314yes—
109C22×C22⋊C4C2314yes—
110C22×C22⋊C4C2318yes—
111C22×C22⋊C4C2318yes—
112C22×C42—24no—
113C22×C42—24no—
114C22×C42—24no—
115C22×C42—24no—
116C22×C42—24no—
117C22×C42D418yes—
118C22×C42C2314yes—
119C22×C42C2314yes—
120#389—232no—
121#389—232no—
122#382—232no—
123#380—232no—
124#380—232no—
125C4×C22⋊C4—232no—
126C2×#95—24no—
127C2×#95—24no—
128C2×#95—28no—
129C2×#95—28no—
130C2×#95—28no—
131C2×#95—28no—
132C2×#95—28no—
133C2×#95—28no—
134C2×#95—28no—
135C2×#95—44no—
136C2×#95C2318yes—
137C2×#95C2318yes—
138C2×#95C2318yes—
139C2×#95C2318yes—
140C2×#95C2318yes—
141C2×#95C2314yes—
142C2×#95C2318yes—
143C2×#95C2318yes—
144C2×#95C2314yes—
145C2×#95C2318yes—
146C25—22no—
147C25—22no—
148C25—22no—
149C25—22no—
150C25—22no—
151C25—22no—
152C25—22no—
153C25—22no—
154C25—22no—
155C25—22no—
156C25—22no—
157C25—22no—
158C25C2×Q814yes—
159C25#4114yes—
160C25#4114yes—
161C25C2412yes—
162C25C2411yescharacteristic
163C23×C4—22no—
164C23×C4—22no—
165C23×C4—24no—
166C23×C4—24no—
167C23×C4—22no—
168C23×C4—22no—
169C23×C4—22no—
170C23×C4—22no—
171C23×C4—22no—
172C23×C4—22no—
173C23×C4—22no—
174C23×C4—22no—
175C23×C4—22no—
176C23×C4—22no—
177C23×C4—22no—
178C23×C4—22no—
179C23×C4—22no—
180C23×C4—24no—
181C23×C4—24no—
182C23×C4—24no—
183C23×C4—24no—
184C23×C4—24no—
185C23×C4—24no—
186C23×C4—22no—
187C23×C4—22no—
188C23×C4—22no—
189C23×C4—22no—
190C23×C4—22no—
191C23×C4—22no—
192C23×C4—22no—
193C23×C4—24no—
194C23×C4—24no—
195C23×C4—22no—
196C23×C4—22no—
197C23×C4—22no—
198C23×C4—24no—
199C23×C4—22no—
200C23×C4—22no—
201C23×C4—22no—
202C23×C4—24no—
203C23×C4—22no—
204C23×C4—22no—
205C23×C4—232no—
206C23×C4—232no—
207C23×C4—232no—
208C23×C4—28no—
209C23×C4—28no—
210C23×C4—28no—
211C23×C4—28no—
212C23×C4—28no—
213C23×C4—28no—
214C23×C4—24no—
215C23×C4—24no—
216C23×C4—24no—
217C23×C4—24no—
218C23×C4—24no—
219C23×C4—24no—
220C23×C4—24no—
221C23×C4—24no—
222C23×C4—24no—
223C23×C4—24no—
224C23×C4—24no—
225C23×C4—24no—
226C23×C4—24no—
227C23×C4—24no—
228C23×C4—416no—
229C23×C4—416no—
230C23×C4—416no—
231C23×C4—416no—
232C23×C4C2×D414yes—
233C23×C4C2×D418yes—
234C23×C4C2×D418yes—
235C23×C4C2×D414yes—
236C23×C4C2×D414yes—
237C23×C4C2×D414yes—
238C23×C4C2×D414yes—
239C23×C4C2×Q814yes—
240C23×C4C2×Q8116yes—
241C23×C4C2×Q814yes—
242C23×C4#4114yes—
243C23×C4#4114yes—
244C23×C4#4114yes—
245C23×C4#4114yes—
246C23×C4#4114yes—
247C23×C4C2414yes—
248C23×C4C2414yes—
249C23×C4C2414yes—
250C23×C4C2414yes—
251C23×C4C2412yes—
252C23×C4C2412yes—
253C23×C4C2412yes—
254C23×C4C2412yes—
255C23×C4C2412yes—
256C23×C4C2412yes—
257C2×C4⋊C4—232no—
258C2×C4⋊C4—232no—
259C2×C4⋊C4—28no—
260C2×C4⋊C4—28no—
261C2×C4⋊C4—28no—
262C2×C4⋊C4—28no—
263C2×C4⋊C4—28no—
264C2×C4⋊C4—28no—
265C2×C4⋊C4—28no—
266C2×C4⋊C4—216no—
267C2×C4⋊C4—216no—
268C2×C4⋊C4—28no—
269C2×C4⋊C4—216no—
270C2×C4⋊C4—28no—
271C2×C4⋊C4—28no—
272C2×C4⋊C4—48no—
273C2×C4⋊C4—48no—
274C2×C4⋊C4—48no—
275C2×C4⋊C4—432no—
276C2×C4⋊C4—432no—
277C2×C4⋊C4—416no—
278C2×C4⋊C4—416no—
279C2×C4⋊C4C2×D4116yes—
280C2×C4⋊C4C2×D4116yes—
281C2×C22⋊C4—232no—
282C2×C22⋊C4—232no—
283C2×C22⋊C4—28no—
284C2×C22⋊C4—28no—
285C2×C22⋊C4—28no—
286C2×C22⋊C4—28no—
287C2×C22⋊C4—28no—
288C2×C22⋊C4—28no—
289C2×C22⋊C4—216no—
290C2×C22⋊C4—216no—
291C2×C22⋊C4—216no—
292C2×C22⋊C4—216no—
293C2×C22⋊C4—48no—
294C2×C22⋊C4—48no—
295C2×C22⋊C4—432no—
296C2×C22⋊C4—432no—
297C2×C42—232no—
298C2×C42—28no—
299C2×C42—28no—
300C2×C42—28no—
301C2×C42—28no—
302C2×C42—28no—
303C2×C42—416no—
304C2×C42C2×D4116yes—
305#95—28no—
306#95—28no—
307#95—216no—
308#95—216no—
309#95—216no—
310#95—216no—
311#95—216no—
312#95—216no—
313#95—216no—
314#95—48no—
315C24—28no—
316C24—28no—
317C24—28no—
318C24—28no—
319C24—28no—
320C24—28no—
321C24—28no—
322C24—28no—
323C24—28no—
324C24—28no—
325C24—28no—
326C24—28no—
327C24—28no—
328C24—28no—
329C24—28no—
330C24—28no—
331C24—28no—
332C24—28no—
333C24—22no—
334C24—22no—
335C24—22no—
336C24—22no—
337C24—22no—
338C24—22no—
339C24—22no—
340C24—22no—
341C24—22no—
342C24—22no—
343C24—22no—
344C24—22no—
345C24—44no—
346C24—44no—
347C24—44no—
348C24—44no—
349C24—44no—
350C24—44no—
351C24—44no—
352C24—44no—
353C24—44no—
354C24—44no—
355C24—44no—
356C24—44no—
357C24—44no—
358C24—44no—
359C24—44no—
360C24—44no—
361C24#125116yes—
362C24C22×D412yes—
363C24C22×D412yes—
364C24C22×D412yes—
365C24C22×Q814yes—
366C24C22×Q812yes—
367C24C2×#4114yes—
368C24C2×#4114yes—
369C24C2×#4112yes—
370C24C2×#4112yes—
371C24C2×#4112yes—
372C24C2×#4112yes—
373C24C2×#4112yes—
374C24C2×#4112yes—
375C24C2×#4112yes—
376C24H(5,𝔽2)12yes—
377C24H(5,𝔽2)12yes—
378C242−1+412yes—
379C242−1+412yes—
380C24C2511yescharacteristic
381C22×C4—28no—
382C22×C4—28no—
383C22×C4—216no—
384C22×C4—216no—
385C22×C4—28no—
386C22×C4—28no—
387C22×C4—28no—
388C22×C4—28no—
389C22×C4—28no—
390C22×C4—28no—
391C22×C4—28no—
392C22×C4—28no—
393C22×C4—28no—
394C22×C4—216no—
395C22×C4—216no—
396C22×C4—28no—
397C22×C4—216no—
398C22×C4—216no—
399C22×C4—28no—
400C22×C4—28no—
401C22×C4—28no—
402C22×C4—22no—
403C22×C4—22no—
404C22×C4—22no—
405C22×C4—22no—
406C22×C4—22no—
407C22×C4—22no—
408C22×C4—22no—
409C22×C4—22no—
410C22×C4—24no—
411C22×C4—24no—
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—22no—
421C22×C4—22no—
422C22×C4—22no—
423C22×C4—24no—
424C22×C4—24no—
425C22×C4—24no—
426C22×C4—24no—
427C22×C4—24no—
428C22×C4—24no—
429C22×C4—22no—
430C22×C4—22no—
431C22×C4—22no—
432C22×C4—22no—
433C22×C4—24no—
434C22×C4—24no—
435C22×C4—22no—
436C22×C4—22no—
437C22×C4—22no—
438C22×C4—24no—
439C22×C4—22no—
440C22×C4—22no—
441C22×C4—24no—
442C22×C4—22no—
443C22×C4—22no—
444C22×C4—232no—
445C22×C4—232no—
446C22×C4—232no—
447C22×C4—24no—
448C22×C4—24no—
449C22×C4—24no—
450C22×C4—24no—
451C22×C4—24no—
452C22×C4—24no—
453C22×C4—24no—
454C22×C4—24no—
455C22×C4—24no—
456C22×C4—24no—
457C22×C4—24no—
458C22×C4—24no—
459C22×C4—24no—
460C22×C4—24no—
461C22×C4—44no—
462C22×C4—44no—
463C22×C4—44no—
464C22×C4—44no—
465C22×C4—44no—
466C22×C4—48no—
467C22×C4—44no—
468C22×C4—48no—
469C22×C4—48no—
470C22×C4—44no—
471C22×C4—44no—
472C22×C4—48no—
473C22×C4—48no—
474C22×C4—44no—
475C22×C4—44no—
476C22×C4—44no—
477C22×C4—44no—
478C22×C4—48no—
479C22×C4—44no—
480C22×C4—44no—
481C22×C4—44no—
482C22×C4—44no—
483C22×C4—44no—
484C22×C4—48no—
485C22×C4—48no—
486C22×C4—44no—
487C22×C4—44no—
488C22×C4—44no—
489C22×C4—416no—
490C22×C4—416no—
491C22×C4—416no—
492C22×C4—416no—
493C22×C4—4128no—
494C22×C4—48no—
495C22×C4—48no—
496C22×C4—48no—
497C22×C4—48no—
498C22×C4—48no—
499C22×C4—48no—
500C22×C4—48no—
501C22×C4—48no—
502C22×C4—48no—
503C22×C4—48no—
504C22×C4—48no—
505C22×C4—48no—
506C22×C4—48no—
507C22×C4—48no—
508C22×C4#121116yes—
509C22×C4#121116yes—
510C22×C4#121116yes—
511C22×C4C22⋊Q8116yes—
512C22×C4C22⋊Q8116yes—
513C22×C4C22⋊Q8116yes—
514C22×C4#126116yes—
515C22×C4C22×D414yes—
516C22×C4C22×D418yes—
517C22×C4C22×D418yes—
518C22×C4C22×D414yes—
519C22×C4C22×D414yes—
520C22×C4C22×D414yes—
521C22×C4C22×D414yes—
522C22×C4C22×Q814yes—
523C22×C4C22×Q814yes—
524C22×C4C2×#4114yes—
525C22×C4C2×#4114yes—
526C22×C4C2×#4114yes—
527C22×C4C2×#4114yes—
528C22×C4C2×#4114yes—
529C4⋊C4—232no—
530C4⋊C4—232no—
531C4⋊C4—432no—
532C4⋊C4—432no—
533C4⋊C4—416no—
534C4⋊C4—416no—
535C22⋊C4—232no—
536C22⋊C4—232no—
537C22⋊C4—432no—
538C22⋊C4—432no—
539C42—232no—
540C42—416no—
541C23—232no—
542C23—24no—
543C23—24no—
544C23—24no—
545C23—24no—
546C23—24no—
547C23—24no—
548C23—24no—
549C23—24no—
550C23—24no—
551C23—24no—
552C23—24no—
553C23—24no—
554C23—24no—
555C23—24no—
556C23—232no—
557C23—232no—
558C23—24no—
559C23—24no—
560C23—24no—
561C23—24no—
562C23—416no—
563C23—416no—
564C23—42no—
565C23—42no—
566C23—42no—
567C23—416no—
568C23—42no—
569C23—416no—
570C23—42no—
571C23—42no—
572C23—416no—
573C23—416no—
574C23—42no—
575C23—42no—
576C23—416no—
577C23—42no—
578C23—42no—
579C23—416no—
580C23—42no—
581C23—42no—
582C23—42no—
583C23—42no—
584C23—42no—
585C23—42no—
586C23—416no—
587C23—416no—
588C23—416no—
589C23—416no—
590C23C2×#12114yes—
591C23C2×#12114yes—
592C23C2×#12114yes—
593C23C2×C22⋊Q814yes—
594C23C2×C22⋊Q814yes—
595C23C2×C22⋊Q814yes—
596C23#52514yes—
597C23#52514yes—
598C23C2×#12518yes—
599C23C2×#12514yes—
600C23C2×#12614yes—
601C23#52914yes—
602C23#52914yes—
603C23#53314yes—
604C23#53514yes—
605C23#53614yes—
606C23#54214yes—
607C23#54214yes—
608C23#54414yes—
609C23#54414yes—
610C23#54614yes—
611C23#54614yes—
612C23#54614yes—
613C23#54714yes—
614C23#54814yes—
615C23#54814yes—
616C23#54814yes—
617C23#55014yes—
618C23#55214yes—
619C23#55214yes—
620C23#55214yes—
621C23#55314yes—
622C23#55314yes—
623C23#55314yes—
624C23#55514yes—
625C23#55614yes—
626C23C23×D411yescharacteristic
627C23C23×D411yescharacteristic
628C23C23×D411yescharacteristic
629C23C23×Q811yescharacteristic
630C23C22×#4111yescharacteristic
631C23C22×#4111yescharacteristic
632C23C22×#4111yescharacteristic
633C23C22×#4111yescharacteristic
634C23C22×#4111yescharacteristic
635C23C22×#4111yescharacteristic
636C23C22×#4111yescharacteristic
637C23C2×H(5,𝔽2)11yescharacteristic
638C23C2×H(5,𝔽2)11yescharacteristic
639C23C2×2−1+411yescharacteristic
640C23C2×2−1+411yescharacteristic
641C2×C4—24no—
642C2×C4—24no—
643C2×C4—28no—
644C2×C4—28no—
645C2×C4—24no—
646C2×C4—24no—
647C2×C4—24no—
648C2×C4—24no—
649C2×C4—24no—
650C2×C4—24no—
651C2×C4—24no—
652C2×C4—24no—
653C2×C4—24no—
654C2×C4—28no—
655C2×C4—28no—
656C2×C4—24no—
657C2×C4—28no—
658C2×C4—28no—
659C2×C4—24no—
660C2×C4—24no—
661C2×C4—24no—
662C2×C4—416no—
663C2×C4—42no—
664C2×C4—42no—
665C2×C4—42no—
666C2×C4—42no—
667C2×C4—42no—
668C2×C4—44no—
669C2×C4—416no—
670C2×C4—42no—
671C2×C4—416no—
672C2×C4—44no—
673C2×C4—44no—
674C2×C4—42no—
675C2×C4—42no—
676C2×C4—432no—
677C2×C4—44no—
678C2×C4—44no—
679C2×C4—42no—
680C2×C4—42no—
681C2×C4—42no—
682C2×C4—42no—
683C2×C4—44no—
684C2×C4—42no—
685C2×C4—42no—
686C2×C4—42no—
687C2×C4—42no—
688C2×C4—42no—
689C2×C4—44no—
690C2×C4—44no—
691C2×C4—42no—
692C2×C4—42no—
693C2×C4—42no—
694C2×C4—432no—
695C2×C4—416no—
696C2×C4—416no—
697C2×C4—464no—
698C2×C4—44no—
699C2×C4—44no—
700C2×C4—44no—
701C2×C4—44no—
702C2×C4—44no—
703C2×C4—44no—
704C2×C4—44no—
705C2×C4—44no—
706C2×C4—44no—
707C2×C4—44no—
708C2×C4—44no—
709C2×C4—44no—
710C2×C4—44no—
711C2×C4—44no—
712C2×C4—816no—
713C2×C4—816no—
714C2×C4#396164yes—
715C2×C4C2×#12118yes—
716C2×C4C2×#12118yes—
717C2×C4C2×#12118yes—
718C2×C4C2×C22⋊Q818yes—
719C2×C4C2×C22⋊Q818yes—
720C2×C4C2×C22⋊Q818yes—
721C2×C4C2×#12618yes—
722C22—28no—
723C22—28no—
724C22—28no—
725C22—44no—
726C22—44no—
727C22—44no—
728C22—464no—
729C22—44no—
730C22—44no—
731C22—44no—
732C22—44no—
733C22—44no—
734C22—44no—
735C22—44no—
736C22—44no—
737C22—44no—
738C22C2×#39618yes—
739C22#241418yes—
740C22#241518yes—
741C22#242618yes—
742C22#242718yes—
743C22#243918yes—
744C22#244118yes—
745C22#244218yes—
746C22#244218yes—
747C22#249418yes—
748C22#249518yes—
749C22#253518yes—
750C22#253618yes—
751C22#262818yes—
752C22#285118yes—
753C22C22×#12111yescharacteristic
754C22C22×#12111yescharacteristic
755C22C22×#12111yescharacteristic
756C22C22×C22⋊Q811yescharacteristic
757C22C22×C22⋊Q811yescharacteristic
758C22C22×C22⋊Q811yescharacteristic
759C22C2×#52511yescharacteristic
760C22C2×#52511yescharacteristic
761C22C22×#12511yescharacteristic
762C22C22×#12611yescharacteristic
763C22C2×#52911yescharacteristic
764C22C2×#52911yescharacteristic
765C22C2×#53311yescharacteristic
766C22C2×#53511yescharacteristic
767C22C2×#53611yescharacteristic
768C22C2×#54211yescharacteristic
769C22C2×#54211yescharacteristic
770C22C2×#54411yescharacteristic
771C22C2×#54411yescharacteristic
772C22C2×#54611yescharacteristic
773C22C2×#54611yescharacteristic
774C22C2×#54611yescharacteristic
775C22C2×#54711yescharacteristic
776C22C2×#54811yescharacteristic
777C22C2×#54811yescharacteristic
778C22C2×#54811yescharacteristic
779C22C2×#55011yescharacteristic
780C22C2×#55211yescharacteristic
781C22C2×#55211yescharacteristic
782C22C2×#55211yescharacteristic
783C22C2×#55311yescharacteristic
784C22C2×#55311yescharacteristic
785C22C2×#55311yescharacteristic
786C22C2×#55511yescharacteristic
787C22C2×#55611yescharacteristic
788C4—48no—
789C4—44no—
790C4—44no—
791C4—48no—
792C4—44no—
793C4—44no—
794C4—44no—
795C4—84no—
796C4—84no—
797C4C2×#396116yes—
798C2—48no—
799C2#15220116yesdirect product factor
800C2C22×#39611yescharacteristic
801C2C2×#262811yescharacteristic
802C2C2×#244211yescharacteristic
803C2C2×#244211yescharacteristic
804C2C2×#242711yescharacteristic
805C2C2×#242611yescharacteristic
806C2C2×#241411yescharacteristic
807C2C2×#243911yescharacteristic
808C2C2×#241511yescharacteristic
809C2C2×#244111yescharacteristic
810C2C2×#249511yescharacteristic
811C2C2×#249411yescharacteristic
812C2C2×#253511yescharacteristic
813C2C2×#253611yescharacteristic
814C2C2×#285111yescharacteristic
subgroupG/H
center, socleC25C24
commutator, Frattini, cosocleC24C25
prime radicalC26C23
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C25 ◁ G
LECSG ▷ C24 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C22×#389C2semidirect
2. C22×#389C2semidirect
3. C22×#382C2semidirect
7. #15220C2direct (N × H)
8. C2×#1443C2semidirect
9. C2×#1441C2semidirect
12. C2×C4⋊#95C2semidirect
28. C2×#389C22semidirect
29. C2×#389C22semidirect
31. C2×#382C22semidirect
48. #1443C22semidirect
49. #1441C22semidirect
52. C4⋊#95C22semidirect
799. C2#15220direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#3892
C22×#3822
C22×#3802
C22×C4×C22⋊C42
#152202
C2×#14432
C2×#14412
C2×#14392
C2×C4⋊#952