Finite Group Databasebeta

← #361984

Subgroups — #361984

Order 512.

2206 conjugacy classes of subgroups.

The subgroup lattice has 809 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#121C211yesmaximal, characteristic
2C2×#1964C212yesmaximal
3C2×#1799C214yesmaximal, complemented
4#14686C211yesmaximal, characteristic, complemented
5C4×#380C211yesmaximal, characteristic, complemented
6#11043C214yesmaximal, complemented
7#10854C212yesmaximal, complemented
8C22×#121C2211yescharacteristic
9C22×C4×D4C411yescharacteristic, complemented
10C22×C4×D4C2212yes—
11C23×C42C2211yescharacteristic
12C22×#99C2218yes—
13C4×#121—21no—
14C4×#121—21no—
15C4×#121—21no—
16C4×#121—21no—
17C4×#121—21no—
18C4×#121—21no—
19C4×#121—21no—
20C4×#121—21no—
21C2×#390C411yescharacteristic, complemented
22C2×#389C411yescharacteristic, complemented
23C2×#388C412yescomplemented
24C2×#386C2212yes—
25C2×#384—21no—
26C2×#380C2212yes—
27C2×#380C2212yes—
28C2×#380C2212yes—
29C2×#380C2212yes—
30C2×#380C2211yescharacteristic
31C2×C4×C4⋊C4—21no—
32C2×C4×C4⋊C4C411yescharacteristic, complemented
33C2×C4×C22⋊C4C412yescomplemented
34C2×C4×C22⋊C4C2212yes—
35#1964—28no—
36#1799—216no—
37C2×#342C2218yes—
38C4⋊#95—21no—
39C4⋊#95—21no—
40C4⋊#95—21no—
41C4⋊#95—21no—
42#1434—21no—
43C22⋊#95C2212yes—
44C4×#95—21no—
45C23×D4C2×C411yescharacteristic
46C23×D4C2312yes—
47C24×C4C2×C412yes—
48C24×C4C2311yescharacteristic
49C24×C4C2311yescharacteristic
50C24×C4C2311yescharacteristic
51C2×#121—21no—
52C2×#121—21no—
53C2×#121—21no—
54C2×#121—21no—
55C2×#121—22no—
56C2×#121—22no—
57C2×#121D414yes—
58C2×#121Q814yes—
59C2×C4×D4—28no—
60C2×C4×D4—22no—
61C2×C4×D4—22no—
62C2×C4×D4—22no—
63C2×C4×D4—22no—
64C2×C4×D4—28no—
65C2×C4×D4—21no—
66C2×C4×D4—21no—
67C2×C4×D4—21no—
68C2×C4×D4—21no—
69C2×C4×D4—44no—
70C22×C4⋊C4—22no—
71C22×C4⋊C4—22no—
72C22×C4⋊C4—22no—
73C22×C4⋊C4—22no—
74C22×C4⋊C4C2×C412yes—
75C22×C4⋊C4C2×C411yescharacteristic
76C22×C4⋊C4C2×C411yescharacteristic
77C22×C4⋊C4C2×C411yescharacteristic
78C22×C22⋊C4C2×C412yes—
79C22×C22⋊C4C2×C412yes—
80C22×C22⋊C4C2×C412yes—
81C22×C22⋊C4C2×C412yes—
82C22×C22⋊C4C2314yes—
83C22×C22⋊C4C2312yes—
84C22×C22⋊C4C2314yes—
85C22×C42—22no—
86C22×C42—44no—
87C22×C42C2×C412yes—
88C22×C42C2×C411yescharacteristic
89C22×C42C2×C411yescharacteristic
90C22×C42C2×C411yescharacteristic
91C22×C42C2×C411yescharacteristic
92C22×C42D411yescharacteristic
93C22×C42D411yescharacteristic
94C22×C42D411yescharacteristic
95C22×C42D411yescharacteristic
96C22×C42D411yescharacteristic
97C22×C42D411yescharacteristic
98C22×C42D411yescharacteristic
99C22×C42D411yescharacteristic
100C2×#99—216no—
101C2×#99—216no—
102C2×#99—48no—
103#390—21no—
104#390—21no—
105#390—21no—
106#390—21no—
107#389—21no—
108#389—21no—
109#389—21no—
110#389—21no—
111#388—22no—
112#388—22no—
113#388—22no—
114#388—22no—
115#386—22no—
116#386—22no—
117#386—22no—
118#386—22no—
119#384—44no—
120#380—21no—
121#380—21no—
122#380—21no—
123#380—21no—
124#380—24no—
125#380—28no—
126#380—24no—
127#380—24no—
128#380—44no—
129#380D418yescomplemented
130C4×C4⋊C4—21no—
131C4×C4⋊C4—21no—
132C4×C4⋊C4—21no—
133C4×C4⋊C4—21no—
134C4×C4⋊C4—44no—
135C4×C22⋊C4—22no—
136C4×C22⋊C4—22no—
137C4×C22⋊C4—22no—
138C4×C22⋊C4—22no—
139C4×C22⋊C4—24no—
140C4×C22⋊C4—24no—
141C2×#95—22no—
142C2×#95—22no—
143C2×#95—22no—
144C2×#95—22no—
145C2×#95—22no—
146C2×#95—22no—
147C2×#95—22no—
148C2×#95C2×C412yes—
149C2×#95C2×C412yes—
150C2×#95C2×C412yes—
151#342—216no—
152C25C22×C412yes—
153C25C2411yescharacteristic
154C22×D4—22no—
155C22×D4—22no—
156C22×D4—24no—
157C22×D4—24no—
158C22×D4—22no—
159C22×D4—22no—
160C22×D4—24no—
161C22×D4—24no—
162C22×D4—21no—
163C22×D4—21no—
164C22×D4—22no—
165C22×D4—42no—
166C22×D4—42no—
167C22×D4C4⋊C414yescomplemented
168C22×D4C2×D414yes—
169C22×D4C2×Q814yes—
170C23×C4—22no—
171C23×C4—22no—
172C23×C4—24no—
173C23×C4—22no—
174C23×C4—22no—
175C23×C4—28no—
176C23×C4—24no—
177C23×C4—42no—
178C23×C4—42no—
179C23×C4—42no—
180C23×C4—42no—
181C23×C4—42no—
182C23×C4—42no—
183C23×C4—44no—
184C23×C4—44no—
185C23×C4C22×C412yes—
186C23×C4C22×C411yescharacteristic
187C23×C4C22×C411yescharacteristic
188C23×C4C22×C411yescharacteristic
189C23×C4C22×C411yescharacteristic
190C23×C4C22×C412yes—
191C23×C4C22×C412yes—
192C23×C4C22×C411yescharacteristic
193C23×C4C22×C411yescharacteristic
194C23×C4C2×D411yescharacteristic
195C23×C4C2×D411yescharacteristic
196C23×C4C2×D411yescharacteristic
197C23×C4C2×D411yescharacteristic
198C23×C4C2×D411yescharacteristic
199C23×C4C2×D411yescharacteristic
200C23×C4C2×D411yescharacteristic
201C23×C4C2×D411yescharacteristic
202C23×C4C2×D411yescharacteristic
203C23×C4C2×D411yescharacteristic
204C23×C4C2×D411yescharacteristic
205C23×C4C2×D411yescharacteristic
206C23×C4C2×D412yes—
207C23×C4C2×D414yes—
208C23×C4C2×Q812yes—
209C23×C4#4112yes—
210C23×C4#4112yes—
211C23×C4#4114yes—
212#121—24no—
213#121—24no—
214#121—24no—
215#121—24no—
216#121—24no—
217#121—24no—
218#121—24no—
219#121—24no—
220C4×D4—44no—
221C4×D4—44no—
222C4×D4—44no—
223C4×D4—48no—
224C4×D4—48no—
225C4×D4—44no—
226C4×D4—44no—
227C4×D4—44no—
228C4×D4—44no—
229C4×D4—44no—
230C2×C4⋊C4—21no—
231C2×C4⋊C4—21no—
232C2×C4⋊C4—22no—
233C2×C4⋊C4—21no—
234C2×C4⋊C4—21no—
235C2×C4⋊C4—22no—
236C2×C4⋊C4—22no—
237C2×C4⋊C4—21no—
238C2×C4⋊C4—21no—
239C2×C4⋊C4—28no—
240C2×C4⋊C4—28no—
241C2×C4⋊C4—44no—
242C2×C4⋊C4—44no—
243C2×C4⋊C4—42no—
244C2×C4⋊C4—42no—
245C2×C4⋊C4—44no—
246C2×C4⋊C4—44no—
247C2×C4⋊C4—44no—
248C2×C4⋊C4—44no—
249C2×C4⋊C4—44no—
250C2×C4⋊C4—44no—
251C2×C4⋊C4—44no—
252C2×C4⋊C4—44no—
253C2×C4⋊C4—44no—
254C2×C4⋊C4C4⋊C414yescomplemented
255C2×C22⋊C4—22no—
256C2×C22⋊C4—22no—
257C2×C22⋊C4—24no—
258C2×C22⋊C4—24no—
259C2×C22⋊C4—24no—
260C2×C22⋊C4—24no—
261C2×C22⋊C4—24no—
262C2×C22⋊C4—24no—
263C2×C22⋊C4—22no—
264C2×C22⋊C4—22no—
265C2×C22⋊C4—24no—
266C2×C22⋊C4—24no—
267C2×C22⋊C4—22no—
268C2×C22⋊C4—22no—
269C2×C22⋊C4—22no—
270C2×C22⋊C4—22no—
271C2×C22⋊C4—22no—
272C2×C22⋊C4—22no—
273C2×C22⋊C4—28no—
274C2×C22⋊C4—28no—
275C2×C22⋊C4—24no—
276C2×C22⋊C4—24no—
277C2×C22⋊C4—28no—
278C2×C22⋊C4—44no—
279C2×C22⋊C4—44no—
280C2×C22⋊C4C4⋊C418yescomplemented
281C2×C22⋊C4C2×D418yes—
282C2×C42—24no—
283C2×C42—24no—
284C2×C42—24no—
285C2×C42—22no—
286C2×C42—22no—
287C2×C42—28no—
288C2×C42—42no—
289C2×C42—42no—
290C2×C42—42no—
291C2×C42—42no—
292C2×C42—42no—
293C2×C42—42no—
294C2×C42—42no—
295C2×C42—42no—
296C2×C42—42no—
297C2×C42—44no—
298C2×C42—44no—
299C2×C42—44no—
300C2×C42C22⋊C411yescharacteristic
301C2×C42C22⋊C411yescharacteristic
302C2×C42C22⋊C411yescharacteristic
303C2×C42C22⋊C411yescharacteristic
304C2×C42C22⋊C411yescharacteristic
305C2×C42C22⋊C411yescharacteristic
306C2×C42C22⋊C411yescharacteristic
307C2×C42C22⋊C411yescharacteristic
308C2×C42C22⋊C411yescharacteristic
309C2×C42C22⋊C411yescharacteristic
310C2×C42C22⋊C411yescharacteristic
311C2×C42C22⋊C411yescharacteristic
312C2×C42C22⋊C411yescharacteristic
313C2×C42C22⋊C411yescharacteristic
314C2×C42C22⋊C411yescharacteristic
315C2×C42C22⋊C411yescharacteristic
316#99—432no—
317#95—22no—
318#95—22no—
319#95—22no—
320#95—22no—
321#95—22no—
322#95—22no—
323#95—28no—
324#95—44no—
325#95—44no—
326#95—44no—
327#95—44no—
328#95—44no—
329#95—44no—
330C24—22no—
331C24—22no—
332C24—24no—
333C24—24no—
334C24—41no—
335C24—41no—
336C24—41no—
337C24—41no—
338C24—42no—
339C24—42no—
340C24—42no—
341C24—42no—
342C24C2×C4⋊C414yes—
343C24C23×C411yescharacteristic
344C24C22×D411yescharacteristic
345C24C22×D411yescharacteristic
346C24C22×D411yescharacteristic
347C24C22×D412yes—
348C24C22×Q811yescharacteristic
349C24C2×#4111yescharacteristic
350C24C2×#4111yescharacteristic
351C24C2×#4112yes—
352C24H(5,𝔽2)12yes—
353C242−1+412yes—
354C2×D4—24no—
355C2×D4—24no—
356C2×D4—24no—
357C2×D4—24no—
358C2×D4—28no—
359C2×D4—28no—
360C2×D4—28no—
361C2×D4—28no—
362C2×D4—24no—
363C2×D4—24no—
364C2×D4—42no—
365C2×D4—42no—
366C2×D4—48no—
367C2×D4—48no—
368C2×D4—44no—
369C2×D4—42no—
370C2×D4—42no—
371C2×D4—42no—
372C2×D4—42no—
373C2×D4—44no—
374C2×D4—44no—
375C2×D4—44no—
376C2×D4—44no—
377C2×D4—44no—
378C2×D4—42no—
379C2×D4—42no—
380C22×C4—21no—
381C22×C4—21no—
382C22×C4—22no—
383C22×C4—22no—
384C22×C4—22no—
385C22×C4—22no—
386C22×C4—22no—
387C22×C4—22no—
388C22×C4—22no—
389C22×C4—22no—
390C22×C4—22no—
391C22×C4—22no—
392C22×C4—22no—
393C22×C4—22no—
394C22×C4—22no—
395C22×C4—22no—
396C22×C4—22no—
397C22×C4—22no—
398C22×C4—24no—
399C22×C4—22no—
400C22×C4—22no—
401C22×C4—24no—
402C22×C4—21no—
403C22×C4—21no—
404C22×C4—22no—
405C22×C4—22no—
406C22×C4—22no—
407C22×C4—22no—
408C22×C4—22no—
409C22×C4—22no—
410C22×C4—22no—
411C22×C4—22no—
412C22×C4—28no—
413C22×C4—24no—
414C22×C4—24no—
415C22×C4—44no—
416C22×C4—48no—
417C22×C4—44no—
418C22×C4—44no—
419C22×C4—44no—
420C22×C4—48no—
421C22×C4—41no—
422C22×C4—41no—
423C22×C4—41no—
424C22×C4—41no—
425C22×C4—41no—
426C22×C4—41no—
427C22×C4—41no—
428C22×C4—41no—
429C22×C4—41no—
430C22×C4—41no—
431C22×C4—41no—
432C22×C4—41no—
433C22×C4—41no—
434C22×C4—41no—
435C22×C4—41no—
436C22×C4—41no—
437C22×C4—41no—
438C22×C4—41no—
439C22×C4—48no—
440C22×C4—48no—
441C22×C4—44no—
442C22×C4—44no—
443C22×C4—44no—
444C22×C4—44no—
445C22×C4—44no—
446C22×C4—44no—
447C22×C4—44no—
448C22×C4—44no—
449C22×C4—44no—
450C22×C4—44no—
451C22×C4—44no—
452C22×C4—44no—
453C22×C4—42no—
454C22×C4—42no—
455C22×C4—42no—
456C22×C4—42no—
457C22×C4—44no—
458C22×C4—44no—
459C22×C4—44no—
460C22×C4—44no—
461C22×C4—44no—
462C22×C4—44no—
463C22×C4—44no—
464C22×C4—816no—
465C22×C4C2×C22⋊C411yescharacteristic
466C22×C4C2×C22⋊C411yescharacteristic
467C22×C4C2×C22⋊C411yescharacteristic
468C22×C4C2×C22⋊C411yescharacteristic
469C22×C4C2×C22⋊C411yescharacteristic
470C22×C4C2×C22⋊C411yescharacteristic
471C22×C4C2×C22⋊C411yescharacteristic
472C22×C4C2×C22⋊C411yescharacteristic
473C22×C4C2×C22⋊C411yescharacteristic
474C22×C4C2×C22⋊C411yescharacteristic
475C22×C4C2×C22⋊C411yescharacteristic
476C22×C4C2×C22⋊C411yescharacteristic
477C22×C4C2×C4⋊C414yes—
478C22×C4C2×C4⋊C412yes—
479C22×C4C2×C4⋊C412yes—
480C22×C4#11712yes—
481C22×C4#11712yes—
482C22×C4C4×D414yes—
483C22×C4C4×D414yes—
484C22×C4#12112yes—
485C22×C4#12112yes—
486C22×C4#12114yes—
487C22×C4#12112yes—
488C22×C4#12112yes—
489C22×C4#12114yes—
490C22×C4C22⋊Q812yes—
491C22×C4C22⋊Q812yes—
492C22×C4C22⋊Q812yes—
493C22×C4C22⋊Q812yes—
494C22×C4#12412yes—
495C22×C4#12412yes—
496C22×C4#12712yes—
497C22×C4#12712yes—
498C4⋊C4—24no—
499C4⋊C4—24no—
500C4⋊C4—42no—
501C4⋊C4—416no—
502C4⋊C4—42no—
503C4⋊C4—44no—
504C4⋊C4—44no—
505C4⋊C4—42no—
506C4⋊C4—42no—
507C4⋊C4—88no—
508C4⋊C4—88no—
509C4⋊C4—88no—
510C22⋊C4—28no—
511C22⋊C4—28no—
512C22⋊C4—28no—
513C22⋊C4—28no—
514C22⋊C4—44no—
515C22⋊C4—44no—
516C22⋊C4—44no—
517C22⋊C4—42no—
518C22⋊C4—42no—
519C22⋊C4—44no—
520C22⋊C4—44no—
521C22⋊C4—44no—
522C22⋊C4—44no—
523C22⋊C4—44no—
524C22⋊C4—44no—
525C22⋊C4—48no—
526C22⋊C4—48no—
527C42—22no—
528C42—22no—
529C42—22no—
530C42—22no—
531C42—22no—
532C42—22no—
533C42—22no—
534C42—22no—
535C42—22no—
536C42—41no—
537C42—41no—
538C42—41no—
539C42—41no—
540C42—41no—
541C42—41no—
542C42—44no—
543C42—44no—
544C42—88no—
545C42#9914yescomplemented
546C23—21no—
547C23—21no—
548C23—21no—
549C23—21no—
550C23—21no—
551C23—21no—
552C23—21no—
553C23—21no—
554C23—21no—
555C23—21no—
556C23—21no—
557C23—21no—
558C23—24no—
559C23—28no—
560C23—41no—
561C23—42no—
562C23—41no—
563C23—41no—
564C23—41no—
565C23—42no—
566C23—42no—
567C23—42no—
568C23—41no—
569C23—42no—
570C23—41no—
571C23—41no—
572C23—41no—
573C23—42no—
574C23—42no—
575C23—42no—
576C23—44no—
577C23—44no—
578C23—44no—
579C23—44no—
580C23—42no—
581C23—44no—
582C23—42no—
583C23—42no—
584C23—42no—
585C23—42no—
586C23—42no—
587C23—84no—
588C23—84no—
589C23—84no—
590C23—84no—
591C23C22×C22⋊C411yescharacteristic
592C23C22×C4⋊C411yescharacteristic
593C23C2×#11711yescharacteristic
594C23C2×C4×D412yes—
595C23#52012yes—
596C23C2×#12111yescharacteristic
597C23C2×#12111yescharacteristic
598C23C2×#12112yes—
599C23C2×C22⋊Q811yescharacteristic
600C23C2×C22⋊Q811yescharacteristic
601C23C2×#12411yescharacteristic
602C23C2×#12711yescharacteristic
603C23#53511yescharacteristic
604C23#53611yescharacteristic
605C23#53712yes—
606C23D4212yes—
607C23#54712yes—
608C23#54712yes—
609C23D4×Q812yes—
610C23#55012yes—
611C23#55412yes—
612C23#55512yes—
613C23#55612yes—
614D4—48no—
615D4—44no—
616D4—48no—
617D4—48no—
618D4—44no—
619D4—44no—
620D4—44no—
621D4—48no—
622C2×C4—24no—
623C2×C4—24no—
624C2×C4—21no—
625C2×C4—21no—
626C2×C4—21no—
627C2×C4—21no—
628C2×C4—21no—
629C2×C4—21no—
630C2×C4—21no—
631C2×C4—21no—
632C2×C4—21no—
633C2×C4—21no—
634C2×C4—21no—
635C2×C4—21no—
636C2×C4—21no—
637C2×C4—21no—
638C2×C4—21no—
639C2×C4—21no—
640C2×C4—24no—
641C2×C4—24no—
642C2×C4—24no—
643C2×C4—24no—
644C2×C4—24no—
645C2×C4—24no—
646C2×C4—28no—
647C2×C4—24no—
648C2×C4—28no—
649C2×C4—24no—
650C2×C4—21no—
651C2×C4—21no—
652C2×C4—28no—
653C2×C4—21no—
654C2×C4—21no—
655C2×C4—21no—
656C2×C4—21no—
657C2×C4—24no—
658C2×C4—42no—
659C2×C4—42no—
660C2×C4—44no—
661C2×C4—42no—
662C2×C4—42no—
663C2×C4—44no—
664C2×C4—42no—
665C2×C4—42no—
666C2×C4—42no—
667C2×C4—42no—
668C2×C4—44no—
669C2×C4—44no—
670C2×C4—44no—
671C2×C4—44no—
672C2×C4—42no—
673C2×C4—42no—
674C2×C4—42no—
675C2×C4—44no—
676C2×C4—42no—
677C2×C4—48no—
678C2×C4—48no—
679C2×C4—42no—
680C2×C4—42no—
681C2×C4—42no—
682C2×C4—42no—
683C2×C4—48no—
684C2×C4—42no—
685C2×C4—42no—
686C2×C4—88no—
687C2×C4—84no—
688C2×C4—84no—
689C2×C4—84no—
690C2×C4—84no—
691C2×C4—88no—
692C2×C4—84no—
693C2×C4—84no—
694C2×C4—84no—
695C2×C4—84no—
696C2×C4—84no—
697C2×C4—84no—
698C2×C4—84no—
699C2×C4—84no—
700C2×C4—84no—
701C2×C4#38012yes—
702C2×C4#38012yes—
703C2×C4#38012yes—
704C2×C4#38012yes—
705C2×C4#39012yes—
706C2×C4#39012yes—
707C2×C4#39012yes—
708C2×C4#39012yes—
709C2×C4C2×#9912yes—
710C2×C4C2×#9912yes—
711C2×C4C2×#9912yes—
712C2×C4#41012yes—
713C2×C4#41012yes—
714C2×C4#41012yes—
715C22—21no—
716C22—21no—
717C22—22no—
718C22—22no—
719C22—21no—
720C22—22no—
721C22—22no—
722C22—21no—
723C22—21no—
724C22—21no—
725C22—21no—
726C22—21no—
727C22—21no—
728C22—21no—
729C22—21no—
730C22—21no—
731C22—21no—
732C22—21no—
733C22—21no—
734C22—21no—
735C22—22no—
736C22—21no—
737C22—22no—
738C22—21no—
739C22—22no—
740C22—21no—
741C22—22no—
742C22—21no—
743C22—42no—
744C22—42no—
745C22—42no—
746C22—42no—
747C22—42no—
748C22—42no—
749C22—42no—
750C22—42no—
751C22—44no—
752C22—44no—
753C22—44no—
754C22—88no—
755C22—88no—
756C22—82no—
757C22—82no—
758C22—82no—
759C22—82no—
760C22C2×#38011yescharacteristic
761C22C2×#39011yescharacteristic
762C22#231111yescharacteristic
763C22D4×C4⋊C412yes—
764C22#235412yes—
765C22#253712yes—
766C22#253812yes—
767C22#254111yescharacteristic
768C22#254211yescharacteristic
769C22#254711yescharacteristic
770C22#256311yescharacteristic
771C22C22×#9911yescharacteristic
772C22C2×#41011yescharacteristic
773C22C2×#41011yescharacteristic
774C22C2×#41011yescharacteristic
775C4—22no—
776C4—22no—
777C4—22no—
778C4—22no—
779C4—22no—
780C4—22no—
781C4—22no—
782C4—22no—
783C4—44no—
784C4—41no—
785C4—41no—
786C4—88no—
787C4—82no—
788C4—82no—
789C4—164no—
790C4#179914yescomplemented
791C4#196414yescomplemented
792C2—22no—
793C2—21no—
794C2—22no—
795C2—22no—
796C2—21no—
797C2—22no—
798C2—21no—
799C2—21no—
800C2—84no—
801C2#1390611yescharacteristic
802C2C2×#179911yescharacteristic
803C2#2063211yescharacteristic
804C2C2×#196411yescharacteristic
805C2#2121211yescharacteristic
806C2#2187411yescharacteristic
807C2#2187511yescharacteristic
subgroupG/H
center, socleC23C22×C22⋊C4
commutatorC24C23×C4
Frattini, cosocleC25C24
prime radicalC22×#121C22
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C23×C42 ◁ G
LECSG ▷ C25 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
3. C2×#1799C2semidirect
4. #14686C2semidirect
5. C4×#380C2semidirect
6. #11043C2semidirect
7. #10854C2semidirect
9. C22×C4×D4C4semidirect
21. C2×#390C4semidirect
22. C2×#389C4semidirect
23. C2×#388C4semidirect
32. C2×C4×C4⋊C4C4semidirect
33. C2×C4×C22⋊C4C4semidirect
129. #380D4semidirect
167. C22×D4C4⋊C4semidirect
254. C2×C4⋊C4C4⋊C4semidirect
280. C2×C22⋊C4C4⋊C4semidirect
545. C42#99semidirect
790. C4#1799semidirect
791. C4#1964semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#1212
C2×#19642
C2×#17992
#146862
C4×#3802
#110432
#108542