Finite Group Databasebeta

← C2×#14016 #514317

Subgroups — C2×#14016 #514317

Order 512.

9506 conjugacy classes of subgroups.

The subgroup lattice has 832 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C4×D4C211yesmaximal, characteristic
2C22×#386C211yesmaximal, characteristic
3C22×#386C211yesmaximal, characteristic
4C22×#385C211yesmaximal, characteristic, complemented
5C23×#95C211yesmaximal, characteristic, complemented
6#14016C2116yesmaximal, direct product factor
7C2×#1442C212yesmaximal, complemented
8C2×#1439C212yesmaximal, complemented
9C2×#1436C212yesmaximal, complemented
10C2×C22⋊#95C212yesmaximal, complemented
11C2×C22⋊#95C211yesmaximal, characteristic, complemented
12C2×C22⋊#95C211yesmaximal, characteristic, complemented
13C24×D4C2211yescharacteristic
14C25×C4C2211yescharacteristic
15C25×C4C2211yescharacteristic
16C25×C4C2211yescharacteristic
17C25×C4C2211yescharacteristic
18C22×C4×D4—28no—
19C22×C4×D4—28no—
20C22×C4×D4—28no—
21C22×C4×D4C2218yes—
22C23×C4⋊C4C2211yescharacteristic
23C23×C4⋊C4C2212yes—
24C23×C22⋊C4C2211yescharacteristic
25C23×C22⋊C4C2211yescharacteristic
26C23×C22⋊C4C2212yes—
27C23×C22⋊C4C2211yescharacteristic
28C23×C22⋊C4C2211yescharacteristic
29C23×C22⋊C4C2212yes—
30C23×C42C2211yescharacteristic
31C2×#386—28no—
32C2×#386C4116yescomplemented
33C2×#386C2218yes—
34C2×#386C2218yes—
35C2×#385—28no—
36C2×#385C2218yescomplemented
37C22×#95—28no—
38C22×#95C2212yes—
39C22×#95C2212yes—
40C22×#95C2212yes—
41C22×#95C2212yes—
42C22×#95C2212yes—
43C22×#95C2212yes—
44C22×#95C2212yes—
45C22×#95C2212yes—
46C22×#95C2212yes—
47C22×#95C2218yescomplemented
48#1442C22116yescomplemented
49#1439C22116yescomplemented
50#1436C22116yescomplemented
51C22⋊#95C2218yescomplemented
52C22⋊#95C2218yescomplemented
53C22⋊#95C22116yescomplemented
54C26C2311yescharacteristic
55C26C2311yescharacteristic
56C23×D4—24no—
57C23×D4—24no—
58C23×D4—24no—
59C23×D4—24no—
60C23×D4C2×C418yes—
61C23×D4D418yes—
62C23×D4Q818yes—
63C23×D4C2314yes—
64C24×C4—24no—
65C24×C4—24no—
66C24×C4—24no—
67C24×C4—24no—
68C24×C4—24no—
69C24×C4—24no—
70C24×C4—24no—
71C24×C4—24no—
72C24×C4—28no—
73C24×C4—28no—
74C24×C4—24no—
75C24×C4—24no—
76C24×C4—28no—
77C24×C4—44no—
78C24×C4—44no—
79C24×C4—44no—
80C24×C4—44no—
81C24×C4—44no—
82C24×C4C2×C418yescomplemented
83C24×C4D418yes—
84C24×C4C2312yes—
85C24×C4C2312yes—
86C24×C4C2312yes—
87C24×C4C2311yescharacteristic
88C24×C4C2311yescharacteristic
89C24×C4C2311yescharacteristic
90C24×C4C2312yes—
91C24×C4C2314yes—
92C24×C4C2314yes—
93C24×C4C2314yes—
94C24×C4C2311yescharacteristic
95C24×C4C2311yescharacteristic
96C24×C4C2314yes—
97C2×C4×D4—2128no—
98C2×C4×D4—232no—
99C2×C4×D4—232no—
100C2×C4×D4—232no—
101C22×C4⋊C4—24no—
102C22×C4⋊C4—24no—
103C22×C4⋊C4—24no—
104C22×C4⋊C4—28no—
105C22×C4⋊C4—28no—
106C22×C4⋊C4—44no—
107C22×C4⋊C4C2314yes—
108C22×C4⋊C4C2318yes—
109C22×C22⋊C4—24no—
110C22×C22⋊C4—24no—
111C22×C22⋊C4—24no—
112C22×C22⋊C4—24no—
113C22×C22⋊C4—24no—
114C22×C22⋊C4—24no—
115C22×C22⋊C4—24no—
116C22×C22⋊C4—28no—
117C22×C22⋊C4—24no—
118C22×C22⋊C4—24no—
119C22×C22⋊C4—24no—
120C22×C22⋊C4—28no—
121C22×C22⋊C4—44no—
122C22×C22⋊C4—44no—
123C22×C22⋊C4—44no—
124C22×C22⋊C4C2×C418yescomplemented
125C22×C22⋊C4C2×C4116yescomplemented
126C22×C22⋊C4D418yes—
127C22×C22⋊C4C2314yes—
128C22×C22⋊C4C2314yes—
129C22×C22⋊C4C2318yes—
130C22×C22⋊C4C2314yes—
131C22×C22⋊C4C2314yes—
132C22×C22⋊C4C2318yes—
133C22×C42—24no—
134C22×C42—24no—
135C22×C42—24no—
136C22×C42C2314yes—
137#386—232no—
138#386C2×C4164yescomplemented
139#385—232no—
140C2×#95—28no—
141C2×#95—28no—
142C2×#95—232no—
143C2×#95—28no—
144C2×#95—28no—
145C2×#95—28no—
146C2×#95—44no—
147C2×#95—44no—
148C2×#95—44no—
149C2×#95C2×C4116yescomplemented
150C2×#95C2318yes—
151C2×#95C2318yes—
152C2×#95C2318yes—
153C2×#95C2318yes—
154C2×#95C2318yes—
155C2×#95C2318yes—
156C2×#95C2318yes—
157C2×#95C2318yes—
158C2×#95C2318yes—
159C25—24no—
160C25—24no—
161C25—24no—
162C25—24no—
163C25—22no—
164C25—22no—
165C25—24no—
166C25—24no—
167C25—22no—
168C25—22no—
169C25—24no—
170C25—24no—
171C25C22×C414yes—
172C25C22×C414yes—
173C25C2×D414yes—
174C25C2×D414yes—
175C25C2×D414yes—
176C25C2×D414yes—
177C25C2×Q814yes—
178C25C2×Q814yes—
179C25#4114yes—
180C25#4114yes—
181C25C2412yes—
182C25C2412yes—
183C25C2411yescharacteristic
184C22×D4—232no—
185C22×D4—232no—
186C22×D4—232no—
187C22×D4—232no—
188C22×D4—232no—
189C22×D4—232no—
190C22×D4—28no—
191C22×D4—28no—
192C22×D4—28no—
193C22×D4—28no—
194C22×D4C4⋊C4164yescomplemented
195C22×D4C22×C4116yes—
196C22×D4C2×D4116yes—
197C22×D4C2×Q8116yes—
198C23×C4—22no—
199C23×C4—22no—
200C23×C4—22no—
201C23×C4—22no—
202C23×C4—22no—
203C23×C4—22no—
204C23×C4—24no—
205C23×C4—232no—
206C23×C4—232no—
207C23×C4—232no—
208C23×C4—232no—
209C23×C4—22no—
210C23×C4—22no—
211C23×C4—22no—
212C23×C4—22no—
213C23×C4—22no—
214C23×C4—22no—
215C23×C4—24no—
216C23×C4—24no—
217C23×C4—24no—
218C23×C4—28no—
219C23×C4—28no—
220C23×C4—28no—
221C23×C4—28no—
222C23×C4—24no—
223C23×C4—28no—
224C23×C4—24no—
225C23×C4—24no—
226C23×C4—24no—
227C23×C4—24no—
228C23×C4—24no—
229C23×C4—28no—
230C23×C4—24no—
231C23×C4—24no—
232C23×C4—24no—
233C23×C4—24no—
234C23×C4—24no—
235C23×C4—24no—
236C23×C4—24no—
237C23×C4—24no—
238C23×C4—24no—
239C23×C4—24no—
240C23×C4—24no—
241C23×C4—24no—
242C23×C4—24no—
243C23×C4—24no—
244C23×C4—24no—
245C23×C4—232no—
246C23×C4—28no—
247C23×C4—28no—
248C23×C4—216no—
249C23×C4—216no—
250C23×C4—24no—
251C23×C4—28no—
252C23×C4—28no—
253C23×C4—24no—
254C23×C4—24no—
255C23×C4—24no—
256C23×C4—24no—
257C23×C4—24no—
258C23×C4—24no—
259C23×C4—216no—
260C23×C4—432no—
261C23×C4—416no—
262C23×C4—48no—
263C23×C4—48no—
264C23×C4—48no—
265C23×C4—48no—
266C23×C4—48no—
267C23×C4—432no—
268C23×C4—432no—
269C23×C4—432no—
270C23×C4—432no—
271C23×C4—432no—
272C23×C4—432no—
273C23×C4—416no—
274C23×C4—416no—
275C23×C4—416no—
276C23×C4—416no—
277C23×C4—432no—
278C23×C4—416no—
279C23×C4—416no—
280C23×C4C22×C418yes—
281C23×C4C22×C418yes—
282C23×C4C22×C414yes—
283C23×C4C22×C4116yescomplemented
284C23×C4C2×D414yes—
285C23×C4C2×D414yes—
286C23×C4C2×D414yes—
287C23×C4C2×D4116yes—
288C23×C4C2×D414yes—
289C23×C4C2×D414yes—
290C23×C4C2×Q814yes—
291C23×C4#4118yes—
292C23×C4#4118yes—
293C23×C4C2414yes—
294C23×C4C2414yes—
295C23×C4C2414yes—
296C23×C4C2412yes—
297C23×C4C2412yes—
298C23×C4C2412yes—
299C23×C4C2414yes—
300C23×C4C2412yes—
301C23×C4C2412yes—
302C4×D4—2256no—
303C2×C4⋊C4—232no—
304C2×C4⋊C4—28no—
305C2×C4⋊C4—28no—
306C2×C4⋊C4—28no—
307C2×C4⋊C4—216no—
308C2×C4⋊C4—216no—
309C2×C4⋊C4—48no—
310C2×C4⋊C4—432no—
311C2×C22⋊C4—232no—
312C2×C22⋊C4—232no—
313C2×C22⋊C4—232no—
314C2×C22⋊C4—28no—
315C2×C22⋊C4—28no—
316C2×C22⋊C4—28no—
317C2×C22⋊C4—28no—
318C2×C22⋊C4—28no—
319C2×C22⋊C4—28no—
320C2×C22⋊C4—28no—
321C2×C22⋊C4—216no—
322C2×C22⋊C4—28no—
323C2×C22⋊C4—28no—
324C2×C22⋊C4—28no—
325C2×C22⋊C4—216no—
326C2×C22⋊C4—432no—
327C2×C22⋊C4—48no—
328C2×C22⋊C4—48no—
329C2×C22⋊C4—48no—
330C2×C22⋊C4—432no—
331C2×C22⋊C4—416no—
332C2×C22⋊C4C22×C4116yescomplemented
333C2×C22⋊C4C22×C4132yescomplemented
334C2×C22⋊C4C2×D4116yes—
335C2×C42—232no—
336C2×C42—28no—
337C2×C42—28no—
338C2×C42—28no—
339#95—216no—
340#95—216no—
341#95—216no—
342#95—216no—
343#95—216no—
344#95—48no—
345#95—48no—
346#95—48no—
347#95C22×C4132yescomplemented
348C24—216no—
349C24—216no—
350C24—28no—
351C24—28no—
352C24—216no—
353C24—28no—
354C24—28no—
355C24—216no—
356C24—216no—
357C24—216no—
358C24—216no—
359C24—216no—
360C24—216no—
361C24—216no—
362C24—216no—
363C24—216no—
364C24—24no—
365C24—24no—
366C24—24no—
367C24—24no—
368C24—28no—
369C24—28no—
370C24—216no—
371C24—216no—
372C24—28no—
373C24—28no—
374C24—28no—
375C24—28no—
376C24—216no—
377C24—216no—
378C24—216no—
379C24—216no—
380C24—22no—
381C24—22no—
382C24—24no—
383C24—24no—
384C24—22no—
385C24—22no—
386C24—24no—
387C24—24no—
388C24—44no—
389C24—44no—
390C24—48no—
391C24—44no—
392C24—44no—
393C24—48no—
394C24—48no—
395C24—48no—
396C24—48no—
397C24—48no—
398C24C2×C4⋊C4116yes—
399C24C2×C4⋊C4116yes—
400C24C4×D4116yes—
401C24C4×D4116yes—
402C24#120116yes—
403C24C22⋊Q8116yes—
404C24C22⋊Q8116yes—
405C24#123116yes—
406C24C23×C414yes—
407C24C23×C414yes—
408C24C23×C412yes—
409C24C22×D414yes—
410C24C22×D414yes—
411C24C22×D414yes—
412C24C22×D414yes—
413C24C22×D412yes—
414C24C22×D412yes—
415C24C22×D412yes—
416C24C22×Q814yes—
417C24C22×Q814yes—
418C24C22×Q812yes—
419C24C2×#4114yes—
420C24C2×#4114yes—
421C24C2×#4112yes—
422C24C2×#4112yes—
423C24C2×#4114yes—
424C24C2×#4114yes—
425C24H(5,𝔽2)14yes—
426C24H(5,𝔽2)14yes—
427C24C2511yescharacteristic
428C2×D4—232no—
429C2×D4—232no—
430C2×D4—232no—
431C2×D4—232no—
432C2×D4—232no—
433C2×D4—232no—
434C2×D4—2256no—
435C2×D4C2×C4⋊C4164yescomplemented
436C22×C4—28no—
437C22×C4—28no—
438C22×C4—28no—
439C22×C4—28no—
440C22×C4—28no—
441C22×C4—28no—
442C22×C4—28no—
443C22×C4—28no—
444C22×C4—216no—
445C22×C4—216no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—24no—
453C22×C4—232no—
454C22×C4—232no—
455C22×C4—216no—
456C22×C4—216no—
457C22×C4—232no—
458C22×C4—216no—
459C22×C4—216no—
460C22×C4—216no—
461C22×C4—216no—
462C22×C4—28no—
463C22×C4—28no—
464C22×C4—28no—
465C22×C4—232no—
466C22×C4—28no—
467C22×C4—216no—
468C22×C4—28no—
469C22×C4—216no—
470C22×C4—216no—
471C22×C4—216no—
472C22×C4—216no—
473C22×C4—24no—
474C22×C4—24no—
475C22×C4—24no—
476C22×C4—24no—
477C22×C4—24no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—24no—
485C22×C4—24no—
486C22×C4—24no—
487C22×C4—24no—
488C22×C4—24no—
489C22×C4—24no—
490C22×C4—24no—
491C22×C4—24no—
492C22×C4—24no—
493C22×C4—24no—
494C22×C4—24no—
495C22×C4—24no—
496C22×C4—24no—
497C22×C4—24no—
498C22×C4—24no—
499C22×C4—24no—
500C22×C4—24no—
501C22×C4—24no—
502C22×C4—24no—
503C22×C4—232no—
504C22×C4—24no—
505C22×C4—24no—
506C22×C4—24no—
507C22×C4—24no—
508C22×C4—24no—
509C22×C4—24no—
510C22×C4—24no—
511C22×C4—432no—
512C22×C4—416no—
513C22×C4—432no—
514C22×C4—4128no—
515C22×C4—432no—
516C22×C4—432no—
517C22×C4—432no—
518C22×C4—432no—
519C22×C4—432no—
520C22×C4—4128no—
521C22×C4—416no—
522C22×C4—4128no—
523C22×C4—4128no—
524C22×C4—416no—
525C22×C4—416no—
526C22×C4—416no—
527C22×C4—432no—
528C22×C4—416no—
529C22×C4—48no—
530C22×C4—44no—
531C22×C4—44no—
532C22×C4—48no—
533C22×C4—44no—
534C22×C4—44no—
535C22×C4—48no—
536C22×C4—48no—
537C22×C4—48no—
538C22×C4—48no—
539C22×C4—48no—
540C22×C4—48no—
541C22×C4—48no—
542C22×C4—48no—
543C22×C4—48no—
544C22×C4—48no—
545C22×C4—48no—
546C22×C4—48no—
547C22×C4—48no—
548C22×C4—48no—
549C22×C4—416no—
550C22×C4—48no—
551C22×C4—48no—
552C22×C4—48no—
553C22×C4—48no—
554C22×C4—48no—
555C22×C4—48no—
556C22×C4—48no—
557C22×C4C2×C4⋊C4116yes—
558C22×C4#123116yes—
559C22×C4C23×C418yes—
560C22×C4C23×C418yes—
561C22×C4C23×C414yes—
562C22×C4C22×D414yes—
563C22×C4C22×D414yes—
564C22×C4C22×D414yes—
565C22×C4C22×D414yes—
566C22×C4C22×D414yes—
567C22×C4C22×Q814yes—
568C22×C4C2×#4118yes—
569C22×C4C2×#4118yes—
570C4⋊C4—232no—
571C4⋊C4—432no—
572C22⋊C4—232no—
573C22⋊C4—232no—
574C22⋊C4—232no—
575C22⋊C4—432no—
576C22⋊C4—432no—
577C22⋊C4—416no—
578C42—232no—
579C23—232no—
580C23—232no—
581C23—264no—
582C23—264no—
583C23—28no—
584C23—28no—
585C23—232no—
586C23—232no—
587C23—24no—
588C23—24no—
589C23—28no—
590C23—24no—
591C23—24no—
592C23—28no—
593C23—28no—
594C23—28no—
595C23—28no—
596C23—28no—
597C23—264no—
598C23—28no—
599C23—28no—
600C23—28no—
601C23—28no—
602C23—264no—
603C23—232no—
604C23—232no—
605C23—264no—
606C23—24no—
607C23—24no—
608C23—28no—
609C23—28no—
610C23—24no—
611C23—24no—
612C23—24no—
613C23—24no—
614C23—28no—
615C23—28no—
616C23—28no—
617C23—28no—
618C23—232no—
619C23—416no—
620C23—416no—
621C23—432no—
622C23—416no—
623C23—416no—
624C23—42no—
625C23—42no—
626C23—44no—
627C23—42no—
628C23—42no—
629C23—44no—
630C23—44no—
631C23—44no—
632C23—432no—
633C23—44no—
634C23—44no—
635C23—432no—
636C23—416no—
637C23—416no—
638C23#385164yes—
639C23C22×C4⋊C418yes—
640C23C22×C4⋊C418yes—
641C23C22×C4⋊C414yes—
642C23C2×C4×D418yes—
643C23C2×C4×D418yes—
644C23C2×C4×D414yes—
645C23C2×C4×D414yes—
646C23C4×#4118yes—
647C23#51818yes—
648C23C2×#12018yes—
649C23C2×#12014yes—
650C23C2×C22⋊Q818yes—
651C23C2×C22⋊Q818yes—
652C23C2×C22⋊Q814yes—
653C23C2×C22⋊Q814yes—
654C23C2×#12318yes—
655C23C2×#12314yes—
656C23C2×#12314yes—
657C23#52514yes—
658C23#52918yes—
659C23#53414yes—
660C23#53514yes—
661C23#53818yes—
662C23#54618yes—
663C23#54618yes—
664C23#54618yes—
665C23#54618yes—
666C23#55318yes—
667C23#55318yes—
668C23#55418yes—
669C23#55418yes—
670C23C24×C411yescharacteristic
671C23C23×D411yescharacteristic
672C23C23×D411yescharacteristic
673C23C23×D411yescharacteristic
674C23C23×Q811yescharacteristic
675C23C22×#4111yescharacteristic
676C23C22×#4111yescharacteristic
677C23C22×#4112yes—
678C23C22×#4112yes—
679C23C2×H(5,𝔽2)12yes—
680C23C2×H(5,𝔽2)12yes—
681D4—2128no—
682C2×C4—24no—
683C2×C4—24no—
684C2×C4—232no—
685C2×C4—24no—
686C2×C4—24no—
687C2×C4—24no—
688C2×C4—24no—
689C2×C4—24no—
690C2×C4—24no—
691C2×C4—28no—
692C2×C4—28no—
693C2×C4—232no—
694C2×C4—28no—
695C2×C4—28no—
696C2×C4—28no—
697C2×C4—28no—
698C2×C4—28no—
699C2×C4—28no—
700C2×C4—24no—
701C2×C4—24no—
702C2×C4—24no—
703C2×C4—24no—
704C2×C4—28no—
705C2×C4—24no—
706C2×C4—28no—
707C2×C4—28no—
708C2×C4—28no—
709C2×C4—28no—
710C2×C4—464no—
711C2×C4—464no—
712C2×C4—464no—
713C2×C4—464no—
714C2×C4—432no—
715C2×C4—432no—
716C2×C4—416no—
717C2×C4—432no—
718C2×C4—416no—
719C2×C4—416no—
720C2×C4—44no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—44no—
724C2×C4—42no—
725C2×C4—42no—
726C2×C4—44no—
727C2×C4—44no—
728C2×C4—44no—
729C2×C4—44no—
730C2×C4—44no—
731C2×C4—44no—
732C2×C4—44no—
733C2×C4—44no—
734C2×C4—44no—
735C2×C4—44no—
736C2×C4—44no—
737C2×C4—44no—
738C2×C4—44no—
739C2×C4—44no—
740C2×C4—44no—
741C2×C4—44no—
742C2×C4—44no—
743C2×C4—44no—
744C2×C4—44no—
745C2×C4—44no—
746C2×C4—44no—
747C2×C4—816no—
748C2×C4C22×C4⋊C418yes—
749C2×C4C2×#12318yes—
750C22—28no—
751C22—28no—
752C22—216no—
753C22—216no—
754C22—28no—
755C22—216no—
756C22—216no—
757C22—28no—
758C22—2128no—
759C22—28no—
760C22—28no—
761C22—216no—
762C22—28no—
763C22—44no—
764C22—44no—
765C22—48no—
766C22—44no—
767C22—48no—
768C22—48no—
769C22—44no—
770C22—464no—
771C22—44no—
772C22—44no—
773C22C2×#385116yes—
774C22C2×#38518yes—
775C22C4×#12318yes—
776C22#232118yes—
777C22#2349116yes—
778C22#2364116yes—
779C22#240418yes—
780C22#240518yes—
781C22#2444116yes—
782C22#2450116yes—
783C22#248718yes—
784C22#257918yes—
785C22C23×C4⋊C411yescharacteristic
786C22C22×C4×D411yescharacteristic
787C22C22×C4×D411yescharacteristic
788C22C2×C4×#4112yes—
789C22C2×#51812yes—
790C22C22×#12011yescharacteristic
791C22C22×C22⋊Q811yescharacteristic
792C22C22×C22⋊Q811yescharacteristic
793C22C22×#12311yescharacteristic
794C22C22×#12311yescharacteristic
795C22C2×#52511yescharacteristic
796C22C2×#52912yes—
797C22C2×#53411yescharacteristic
798C22C2×#53511yescharacteristic
799C22C2×#53812yes—
800C22C2×#54612yes—
801C22C2×#54612yes—
802C22C2×#54612yes—
803C22C2×#54612yes—
804C22C2×#55312yes—
805C22C2×#55312yes—
806C22C2×#55412yes—
807C22C2×#55412yes—
808C4—28no—
809C4—28no—
810C4—48no—
811C4—48no—
812C4—44no—
813C4—44no—
814C4—44no—
815C4—48no—
816C4—84no—
817C2—216no—
818C2—48no—
819C2#14016116yesdirect product factor
820C2C22×#38511yescharacteristic
821C2C2×C4×#12311yescharacteristic
822C2C2×#232111yescharacteristic
823C2C2×#234912yes—
824C2C2×#236412yes—
825C2C2×#240511yescharacteristic
826C2C2×#244412yes—
827C2C2×#245012yes—
828C2C2×#240411yescharacteristic
829C2C2×#248711yescharacteristic
830C2C2×#257911yescharacteristic
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×#385C2semidirect
5. C23×#95C2semidirect
6. #14016C2direct (N × H)
7. C2×#1442C2semidirect
8. C2×#1439C2semidirect
9. C2×#1436C2semidirect
10. C2×C22⋊#95C2semidirect
11. C2×C22⋊#95C2semidirect
12. C2×C22⋊#95C2semidirect
32. C2×#386C4semidirect
36. C2×#385C22semidirect
47. C22×#95C22semidirect
48. #1442C22semidirect
49. #1439C22semidirect
50. #1436C22semidirect
51. C22⋊#95C22semidirect
52. C22⋊#95C22semidirect
53. C22⋊#95C22semidirect
82. C24×C4C2×C4semidirect
124. C22×C22⋊C4C2×C4semidirect
125. C22×C22⋊C4C2×C4semidirect
138. #386C2×C4semidirect
149. C2×#95C2×C4semidirect
194. C22×D4C4⋊C4semidirect
283. C23×C4C22×C4semidirect
332. C2×C22⋊C4C22×C4semidirect
333. C2×C22⋊C4C22×C4semidirect
347. #95C22×C4semidirect
435. C2×D4C2×C4⋊C4semidirect
819. C2#14016direct (N × H)

Maximal subgroups

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

subgroupindex
C23×C4×D42
C22×#3862
C22×#3852
C23×#952
#140162
C2×#14422
C2×#14392
C2×#14362
C2×C22⋊#952