Finite Group Databasebeta

← C2×#15754 #609402

Subgroups — C2×#15754 #609402

Order 512.

3162 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
1C22×#400C211yesmaximal, characteristic
2C22×#387C211yesmaximal, characteristic
3#15754C2116yesmaximal, direct product factor
4C2×#1445C211yesmaximal, characteristic
5C2×#1444C211yesmaximal, characteristic
6C2×#1443C211yesmaximal, characteristic
7C2×#1443C211yesmaximal, characteristic
8C2×#1443C211yesmaximal, characteristic
9C2×#1442C211yesmaximal, characteristic
10C2×#1441C211yesmaximal, characteristic
11C2×#1441C211yesmaximal, characteristic
12C2×#1436C211yesmaximal, characteristic
13C2×#1436C211yesmaximal, characteristic
14C2×#1434C211yesmaximal, characteristic
15C2×#1434C211yesmaximal, characteristic
16C2×#1434C211yesmaximal, characteristic
17C23×C4⋊C4C2211yescharacteristic
18C23×C4⋊C4C2211yescharacteristic
19C23×C4⋊C4C2211yescharacteristic
20C23×C4⋊C4C2211yescharacteristic
21C23×C4⋊C4C2211yescharacteristic
22C23×C42C2211yescharacteristic
23C23×C42C2211yescharacteristic
24C2×#400—28no—
25C2×#400C2218yes—
26C2×#387—28no—
27C2×#387C2218yes—
28C22×#95C2211yescharacteristic
29C22×#95C2211yescharacteristic
30C22×#95C2211yescharacteristic
31C22×#95C2211yescharacteristic
32C22×#95C2211yescharacteristic
33C22×#95C2211yescharacteristic
34C22×#95C2211yescharacteristic
35C22×#95C2211yescharacteristic
36C22×#95C2211yescharacteristic
37C22×#95C2211yescharacteristic
38C22×#95C2211yescharacteristic
39C22×#95C2211yescharacteristic
40C22×#95C2211yescharacteristic
41C22×#95C2211yescharacteristic
42C22×#95C2211yescharacteristic
43C22×#95C2211yescharacteristic
44C22×#95C2211yescharacteristic
45C22×#95C2211yescharacteristic
46C22×#95C2211yescharacteristic
47C22×#95C2211yescharacteristic
48C22×#95C2211yescharacteristic
49C22×#95C2211yescharacteristic
50C22×#95C2211yescharacteristic
51C22×#95C2211yescharacteristic
52C22×#95C2211yescharacteristic
53C22×#95C2211yescharacteristic
54C22×#95C2211yescharacteristic
55C22×#95C2211yescharacteristic
56#1445C2218yes—
57#1444C2218yes—
58#1443C2218yes—
59#1443C2218yes—
60#1443C2218yes—
61#1442C2218yes—
62#1441C2218yes—
63#1441C2218yes—
64#1436C2218yes—
65#1436C2218yes—
66#1434C2218yes—
67#1434C2218yes—
68#1434C2218yes—
69C24×C4C2311yescharacteristic
70C24×C4C2311yescharacteristic
71C24×C4C2311yescharacteristic
72C24×C4C2311yescharacteristic
73C24×C4C2311yescharacteristic
74C24×C4C2311yescharacteristic
75C24×C4C2311yescharacteristic
76C24×C4C2311yescharacteristic
77C24×C4C2311yescharacteristic
78C24×C4C2311yescharacteristic
79C24×C4C2311yescharacteristic
80C24×C4C2311yescharacteristic
81C24×C4C2311yescharacteristic
82C24×C4C2311yescharacteristic
83C24×C4C2311yescharacteristic
84C22×C4⋊C4—24no—
85C22×C4⋊C4—24no—
86C22×C4⋊C4—24no—
87C22×C4⋊C4—24no—
88C22×C4⋊C4—24no—
89C22×C4⋊C4—24no—
90C22×C4⋊C4—24no—
91C22×C4⋊C4—24no—
92C22×C4⋊C4—24no—
93C22×C4⋊C4—24no—
94C22×C4⋊C4—24no—
95C22×C4⋊C4—42no—
96C22×C4⋊C4—42no—
97C22×C4⋊C4—42no—
98C22×C4⋊C4—42no—
99C22×C4⋊C4C2314yes—
100C22×C4⋊C4C2314yes—
101C22×C4⋊C4C2314yes—
102C22×C4⋊C4C2314yes—
103C22×C4⋊C4C2314yes—
104C22×C42—24no—
105C22×C42—24no—
106C22×C42—24no—
107C22×C42—24no—
108C22×C42—42no—
109C22×C42—42no—
110C22×C42C2314yes—
111C22×C42C2314yes—
112#400—232no—
113#387—232no—
114C2×#95—24no—
115C2×#95—24no—
116C2×#95—24no—
117C2×#95—24no—
118C2×#95—24no—
119C2×#95—24no—
120C2×#95—24no—
121C2×#95—24no—
122C2×#95—24no—
123C2×#95—24no—
124C2×#95—24no—
125C2×#95—24no—
126C2×#95—24no—
127C2×#95—24no—
128C2×#95—24no—
129C2×#95—24no—
130C2×#95—24no—
131C2×#95—24no—
132C2×#95—24no—
133C2×#95—24no—
134C2×#95—24no—
135C2×#95—42no—
136C2×#95—42no—
137C2×#95—42no—
138C2×#95—42no—
139C2×#95—42no—
140C2×#95—42no—
141C2×#95D418yes—
142C2×#95C2314yes—
143C2×#95C2314yes—
144C2×#95C2314yes—
145C2×#95C2314yes—
146C2×#95C2314yes—
147C2×#95C2314yes—
148C2×#95C2314yes—
149C2×#95C2314yes—
150C2×#95C2314yes—
151C2×#95C2314yes—
152C2×#95C2314yes—
153C2×#95C2314yes—
154C2×#95C2314yes—
155C2×#95C2314yes—
156C2×#95C2314yes—
157C2×#95C2314yes—
158C2×#95C2314yes—
159C2×#95C2314yes—
160C2×#95C2314yes—
161C2×#95C2314yes—
162C2×#95C2314yes—
163C2×#95C2314yes—
164C2×#95C2314yes—
165C2×#95C2314yes—
166C2×#95C2314yes—
167C2×#95C2314yes—
168C2×#95C2314yes—
169C2×#95C2314yes—
170C25C2411yescharacteristic
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—22no—
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—22no—
190C23×C4—22no—
191C23×C4—22no—
192C23×C4—22no—
193C23×C4—22no—
194C23×C4—22no—
195C23×C4—22no—
196C23×C4—22no—
197C23×C4—22no—
198C23×C4—22no—
199C23×C4—22no—
200C23×C4—22no—
201C23×C4—22no—
202C23×C4—22no—
203C23×C4—22no—
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—22no—
224C23×C4—22no—
225C23×C4—22no—
226C23×C4—22no—
227C23×C4—22no—
228C23×C4—22no—
229C23×C4—22no—
230C23×C4—22no—
231C23×C4—22no—
232C23×C4—22no—
233C23×C4—22no—
234C23×C4—22no—
235C23×C4—22no—
236C23×C4—22no—
237C23×C4—22no—
238C23×C4—22no—
239C23×C4—22no—
240C23×C4—22no—
241C23×C4—22no—
242C23×C4—22no—
243C23×C4—22no—
244C23×C4—22no—
245C23×C4—22no—
246C23×C4—22no—
247C23×C4—22no—
248C23×C4—22no—
249C23×C4—22no—
250C23×C4—22no—
251C23×C4—22no—
252C23×C4—22no—
253C23×C4—22no—
254C23×C4—22no—
255C23×C4—22no—
256C23×C4—22no—
257C23×C4—22no—
258C23×C4—22no—
259C23×C4—22no—
260C23×C4—22no—
261C23×C4—22no—
262C23×C4—22no—
263C23×C4—22no—
264C23×C4—22no—
265C23×C4C2×D414yes—
266C23×C4C2×D414yes—
267C23×C4C2×D414yes—
268C23×C4#4114yes—
269C23×C4#4114yes—
270C23×C4#4114yes—
271C23×C4#4114yes—
272C23×C4#4114yes—
273C23×C4#4114yes—
274C23×C4#4114yes—
275C23×C4#4114yes—
276C23×C4C2412yes—
277C23×C4C2412yes—
278C23×C4C2412yes—
279C23×C4C2412yes—
280C23×C4C2412yes—
281C23×C4C2412yes—
282C23×C4C2412yes—
283C23×C4C2412yes—
284C23×C4C2412yes—
285C23×C4C2412yes—
286C23×C4C2412yes—
287C23×C4C2412yes—
288C23×C4C2412yes—
289C23×C4C2412yes—
290C23×C4C2412yes—
291C2×C4⋊C4—232no—
292C2×C4⋊C4—28no—
293C2×C4⋊C4—28no—
294C2×C4⋊C4—28no—
295C2×C4⋊C4—28no—
296C2×C4⋊C4—28no—
297C2×C4⋊C4—28no—
298C2×C4⋊C4—28no—
299C2×C4⋊C4—28no—
300C2×C4⋊C4—28no—
301C2×C4⋊C4—28no—
302C2×C4⋊C4—28no—
303C2×C4⋊C4—44no—
304C2×C4⋊C4—44no—
305C2×C4⋊C4—44no—
306C2×C4⋊C4—44no—
307C2×C4⋊C4—416no—
308C2×C4⋊C4—416no—
309C2×C4⋊C4—416no—
310C2×C4⋊C4—416no—
311C2×C42—28no—
312C2×C42—28no—
313C2×C42—28no—
314C2×C42—28no—
315C2×C42—44no—
316C2×C42—44no—
317C2×C42—416no—
318C2×C42—416no—
319#95—28no—
320#95—28no—
321#95—28no—
322#95—28no—
323#95—28no—
324#95—28no—
325#95—28no—
326#95—28no—
327#95—28no—
328#95—28no—
329#95—28no—
330#95—28no—
331#95—28no—
332#95—28no—
333#95—28no—
334#95—28no—
335#95—28no—
336#95—28no—
337#95—28no—
338#95—28no—
339#95—28no—
340#95—44no—
341#95—44no—
342#95—44no—
343#95—44no—
344#95—44no—
345#95—44no—
346#95C2×D4116yes—
347C24C22×D412yes—
348C24C2×#4112yes—
349C24C2×#4112yes—
350C24C2×#4112yes—
351C24C2×#4112yes—
352C24C2×#4112yes—
353C24C2×#4112yes—
354C24C2×#4112yes—
355C24C2×#4112yes—
356C24H(5,𝔽2)12yes—
357C24H(5,𝔽2)12yes—
358C242−1+412yes—
359C242−1+412yes—
360C242−1+412yes—
361C242−1+412yes—
362C24C2511yescharacteristic
363C22×C4—28no—
364C22×C4—28no—
365C22×C4—28no—
366C22×C4—28no—
367C22×C4—28no—
368C22×C4—28no—
369C22×C4—28no—
370C22×C4—28no—
371C22×C4—28no—
372C22×C4—28no—
373C22×C4—28no—
374C22×C4—28no—
375C22×C4—28no—
376C22×C4—28no—
377C22×C4—28no—
378C22×C4—28no—
379C22×C4—28no—
380C22×C4—28no—
381C22×C4—28no—
382C22×C4—28no—
383C22×C4—28no—
384C22×C4—28no—
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—28no—
395C22×C4—28no—
396C22×C4—22no—
397C22×C4—22no—
398C22×C4—22no—
399C22×C4—22no—
400C22×C4—22no—
401C22×C4—22no—
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—22no—
411C22×C4—22no—
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—22no—
424C22×C4—22no—
425C22×C4—22no—
426C22×C4—22no—
427C22×C4—22no—
428C22×C4—22no—
429C22×C4—22no—
430C22×C4—22no—
431C22×C4—22no—
432C22×C4—22no—
433C22×C4—22no—
434C22×C4—22no—
435C22×C4—22no—
436C22×C4—22no—
437C22×C4—22no—
438C22×C4—22no—
439C22×C4—22no—
440C22×C4—22no—
441C22×C4—22no—
442C22×C4—22no—
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—22no—
463C22×C4—22no—
464C22×C4—22no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—44no—
491C22×C4—44no—
492C22×C4—44no—
493C22×C4—44no—
494C22×C4—44no—
495C22×C4—44no—
496C22×C4—44no—
497C22×C4—44no—
498C22×C4—44no—
499C22×C4—44no—
500C22×C4—44no—
501C22×C4—44no—
502C22×C4—44no—
503C22×C4—44no—
504C22×C4—44no—
505C22×C4—44no—
506C22×C4—44no—
507C22×C4—44no—
508C22×C4—44no—
509C22×C4—44no—
510C22×C4—44no—
511C22×C4—44no—
512C22×C4—44no—
513C22×C4—44no—
514C22×C4—44no—
515C22×C4—44no—
516C22×C4—44no—
517C22×C4—44no—
518C22×C4—44no—
519C22×C4—44no—
520C22×C4—44no—
521C22×C4—44no—
522C22×C4—44no—
523C22×C4—44no—
524C22×C4—44no—
525C22×C4—44no—
526C22×C4—44no—
527C22×C4—44no—
528C22×C4—44no—
529C22×C4—44no—
530C22×C4—44no—
531C22×C4—44no—
532C22×C4—44no—
533C22×C4—44no—
534C22×C4—44no—
535C22×C4—44no—
536C22×C4—44no—
537C22×C4—44no—
538C22×C4—44no—
539C22×C4—44no—
540C22×C4—44no—
541C22×C4—44no—
542C22×C4—44no—
543C22×C4—44no—
544C22×C4—44no—
545C22×C4—44no—
546C22×C4—44no—
547C22×C4—44no—
548C22×C4—44no—
549C22×C4—44no—
550C22×C4—44no—
551C22×C4—44no—
552C22×C4—44no—
553C22×C4—44no—
554C22×C4—44no—
555C22×C4—44no—
556C22×C4—44no—
557C22×C4—44no—
558C22×C4—44no—
559C22×C4—44no—
560C22×C4—44no—
561C22×C4—44no—
562C22×C4C22×D414yes—
563C22×C4C22×D414yes—
564C22×C4C22×D414yes—
565C22×C4C2×#4114yes—
566C22×C4C2×#4114yes—
567C22×C4C2×#4114yes—
568C22×C4C2×#4114yes—
569C22×C4C2×#4114yes—
570C22×C4C2×#4114yes—
571C22×C4C2×#4114yes—
572C22×C4C2×#4114yes—
573C4⋊C4—232no—
574C4⋊C4—416no—
575C4⋊C4—416no—
576C4⋊C4—416no—
577C4⋊C4—416no—
578C42—416no—
579C42—416no—
580C23#52514yes—
581C23#52914yes—
582C23#52914yes—
583C23#52914yes—
584C23#52914yes—
585C23#53214yes—
586C23#53614yes—
587C23#53914yes—
588C23#53914yes—
589C23#54014yes—
590C23#54114yes—
591C23#54114yes—
592C23#54114yes—
593C23#54214yes—
594C23#54214yes—
595C23#54614yes—
596C23#54614yes—
597C23#54714yes—
598C23#54814yes—
599C23#55114yes—
600C23#55114yes—
601C23#55214yes—
602C23#55214yes—
603C23#55214yes—
604C23#55214yes—
605C23#55214yes—
606C23#55214yes—
607C23#55214yes—
608C23#55314yes—
609C23#55314yes—
610C23#55614yes—
611C23#55614yes—
612C23#55614yes—
613C23#56314yes—
614C23#56314yes—
615C23C23×D411yescharacteristic
616C23C22×#4111yescharacteristic
617C23C22×#4111yescharacteristic
618C23C22×#4111yescharacteristic
619C23C22×#4111yescharacteristic
620C23C22×#4111yescharacteristic
621C23C22×#4111yescharacteristic
622C23C22×#4111yescharacteristic
623C23C22×#4111yescharacteristic
624C23C2×H(5,𝔽2)11yescharacteristic
625C23C2×H(5,𝔽2)11yescharacteristic
626C23C2×2−1+411yescharacteristic
627C23C2×2−1+411yescharacteristic
628C23C2×2−1+411yescharacteristic
629C23C2×2−1+411yescharacteristic
630C2×C4—24no—
631C2×C4—24no—
632C2×C4—24no—
633C2×C4—24no—
634C2×C4—24no—
635C2×C4—24no—
636C2×C4—24no—
637C2×C4—24no—
638C2×C4—24no—
639C2×C4—24no—
640C2×C4—24no—
641C2×C4—24no—
642C2×C4—24no—
643C2×C4—24no—
644C2×C4—24no—
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—24no—
655C2×C4—24no—
656C2×C4—24no—
657C2×C4—24no—
658C2×C4—24no—
659C2×C4—24no—
660C2×C4—24no—
661C2×C4—24no—
662C2×C4—24no—
663C2×C4—416no—
664C2×C4—42no—
665C2×C4—42no—
666C2×C4—42no—
667C2×C4—42no—
668C2×C4—42no—
669C2×C4—42no—
670C2×C4—42no—
671C2×C4—42no—
672C2×C4—42no—
673C2×C4—42no—
674C2×C4—42no—
675C2×C4—42no—
676C2×C4—42no—
677C2×C4—42no—
678C2×C4—42no—
679C2×C4—42no—
680C2×C4—42no—
681C2×C4—42no—
682C2×C4—42no—
683C2×C4—42no—
684C2×C4—42no—
685C2×C4—42no—
686C2×C4—416no—
687C2×C4—42no—
688C2×C4—42no—
689C2×C4—42no—
690C2×C4—42no—
691C2×C4—42no—
692C2×C4—42no—
693C2×C4—42no—
694C2×C4—416no—
695C2×C4—42no—
696C2×C4—42no—
697C2×C4—42no—
698C2×C4—42no—
699C2×C4—42no—
700C2×C4—42no—
701C2×C4—42no—
702C2×C4—42no—
703C2×C4—42no—
704C2×C4—42no—
705C2×C4—42no—
706C2×C4—42no—
707C2×C4—416no—
708C2×C4—416no—
709C2×C4—416no—
710C2×C4—416no—
711C2×C4—416no—
712C2×C4—42no—
713C2×C4—42no—
714C2×C4—42no—
715C2×C4—416no—
716C2×C4—416no—
717C2×C4—416no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—42no—
725C2×C4—42no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—42no—
729C2×C4—42no—
730C2×C4—42no—
731C2×C4—42no—
732C2×C4—42no—
733C2×C4—42no—
734C2×C4—42no—
735C2×C4—42no—
736C2×C4—42no—
737C2×C4—42no—
738C2×C4—42no—
739C2×C4—42no—
740C2×C4—42no—
741C2×C4—42no—
742C2×C4—42no—
743C2×C4—42no—
744C2×C4—42no—
745C2×C4—42no—
746C2×C4—88no—
747C2×C4—88no—
748C2×C4—88no—
749C2×C4—88no—
750C22#245718yes—
751C22#247518yes—
752C22#252118yes—
753C22#252418yes—
754C22#253018yes—
755C22#253318yes—
756C22#255818yes—
757C22#257318yes—
758C22#260418yes—
759C22#269018yes—
760C22#269818yes—
761C22#273818yes—
762C22#276618yes—
763C22#278918yes—
764C22#279318yes—
765C22C2×#52511yescharacteristic
766C22C2×#52911yescharacteristic
767C22C2×#52911yescharacteristic
768C22C2×#52911yescharacteristic
769C22C2×#52911yescharacteristic
770C22C2×#53211yescharacteristic
771C22C2×#53611yescharacteristic
772C22C2×#53911yescharacteristic
773C22C2×#53911yescharacteristic
774C22C2×#54011yescharacteristic
775C22C2×#54111yescharacteristic
776C22C2×#54111yescharacteristic
777C22C2×#54111yescharacteristic
778C22C2×#54211yescharacteristic
779C22C2×#54211yescharacteristic
780C22C2×#54611yescharacteristic
781C22C2×#54611yescharacteristic
782C22C2×#54711yescharacteristic
783C22C2×#54811yescharacteristic
784C22C2×#55111yescharacteristic
785C22C2×#55111yescharacteristic
786C22C2×#55211yescharacteristic
787C22C2×#55211yescharacteristic
788C22C2×#55211yescharacteristic
789C22C2×#55211yescharacteristic
790C22C2×#55211yescharacteristic
791C22C2×#55211yescharacteristic
792C22C2×#55211yescharacteristic
793C22C2×#55311yescharacteristic
794C22C2×#55311yescharacteristic
795C22C2×#55611yescharacteristic
796C22C2×#55611yescharacteristic
797C22C2×#55611yescharacteristic
798C22C2×#56311yescharacteristic
799C22C2×#56311yescharacteristic
800C4—44no—
801C4—44no—
802C4—44no—
803C4—44no—
804C4—44no—
805C4—44no—
806C4—44no—
807C4—44no—
808C4—44no—
809C4—44no—
810C4—44no—
811C4—82no—
812C4—82no—
813C4—82no—
814C4—82no—
815C2#15754116yesdirect product factor
816C2C2×#245711yescharacteristic
817C2C2×#247511yescharacteristic
818C2C2×#252111yescharacteristic
819C2C2×#252411yescharacteristic
820C2C2×#253011yescharacteristic
821C2C2×#253311yescharacteristic
822C2C2×#255811yescharacteristic
823C2C2×#257311yescharacteristic
824C2C2×#260411yescharacteristic
825C2C2×#269011yescharacteristic
826C2C2×#269811yescharacteristic
827C2C2×#273811yescharacteristic
828C2C2×#276611yescharacteristic
829C2C2×#278911yescharacteristic
830C2C2×#279311yescharacteristic
subgroupG/H
center, socle, prime radicalC25C24
commutator, Frattini, cosocleC24C25
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C25 ◁ G
LECSG ▷ C24 ▷ C1

Complements

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

NH ≅ G/Ntype
3. #15754C2direct (N × H)
815. C2#15754direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#4002
C22×#3872
#157542
C2×#14452
C2×#14442
C2×#14432
C2×#14422
C2×#14412
C2×#14362
C2×#14342