Finite Group Databasebeta

← C2×#25079 #6438739

Subgroups — C2×#25079 #6438739

Order 512.

3368 conjugacy classes of subgroups.

The subgroup lattice has 829 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#467C211yesmaximal, characteristic, complemented
2C22×#462C211yesmaximal, characteristic, complemented
3C22×#452C211yesmaximal, characteristic
4C22×#416C211yesmaximal, characteristic
5C2×#2432C211yesmaximal, characteristic
6C2×#2362C211yesmaximal, characteristic, complemented
7#25079C2116yesmaximal, direct product factor
8C2×#2067C211yesmaximal, characteristic, complemented
9C2×#2056C211yesmaximal, characteristic, complemented
10C2×#2043C211yesmaximal, characteristic, complemented
11C2×#2015C211yesmaximal, characteristic, complemented
12C2×#1983C211yesmaximal, characteristic, complemented
13C2×#1928C211yesmaximal, characteristic, complemented
14C2×#1880C211yesmaximal, characteristic, complemented
15C2×#1873C211yesmaximal, characteristic, complemented
16C2×#1850C211yesmaximal, characteristic, complemented
17C23×#41C2211yescharacteristic
18C23×Q16C2211yescharacteristic
19C23×Q16C2211yescharacteristic
20C23×SD16C2211yescharacteristic
21C24×C8C2211yescharacteristic
22C22×C4⋊Q8C2211yescharacteristic
23C22×#124C2211yescharacteristic
24C22×C22⋊Q8C2211yescharacteristic
25C22×C22⋊Q8C2211yescharacteristic
26C22×C4×Q8C2211yescharacteristic
27C22×#117C2211yescharacteristic
28C2×#467—28no—
29C2×#467C2218yescomplemented
30C2×#462—28no—
31C2×#462C2218yescomplemented
32C2×#452—28no—
33C2×#452C2218yes—
34C22×#107C2211yescharacteristic
35C22×C4⋊C8C2211yescharacteristic
36C22×C4⋊C8C2211yescharacteristic
37C2×#416—28no—
38C2×#416C2218yes—
39C22×#103C2211yescharacteristic
40C22×#103C2211yescharacteristic
41C22×#103C2211yescharacteristic
42C22×#103C2211yescharacteristic
43C22×#103C2211yescharacteristic
44C22×#103C2211yescharacteristic
45C22×#103C2211yescharacteristic
46C22×#102C2211yescharacteristic
47C22×#102C2211yescharacteristic
48C22×#102C2211yescharacteristic
49C22×C22⋊C8C2211yescharacteristic
50#2432—24no—
51#2432C2218yes—
52C2×#394—21no—
53C2×#394—21no—
54#2362—24no—
55#2362C2218yescomplemented
56C2×#391C2211yescharacteristic
57C2×#391C2211yescharacteristic
58C2×#390C2211yescharacteristic
59C2×#389C2211yescharacteristic
60C2×#388—21no—
61C2×#388—21no—
62C2×#387—21no—
63C2×#385—21no—
64C2×#385—21no—
65C2×C4×C4⋊C4—21no—
66C2×C4×C4⋊C4C2211yescharacteristic
67C2×C4×C22⋊C4C2211yescharacteristic
68#2067C2218yescomplemented
69#2056C2218yescomplemented
70#2043C2218yescomplemented
71#2015C2218yescomplemented
72#1983C2218yescomplemented
73#1928C2218yescomplemented
74#1880C2218yescomplemented
75#1873C2218yescomplemented
76#1850C2218yescomplemented
77C2×#340C2211yescharacteristic
78C2×#340C2211yescharacteristic
79C2×#336C2211yescharacteristic
80C2×#336C2211yescharacteristic
81C22×#41—22no—
82C22×#41—24no—
83C22×#41—24no—
84C22×#41—24no—
85C22×#41—24no—
86C22×#41—42no—
87C22×#41—42no—
88C22×#41C2314yes—
89C23×Q8C2311yescharacteristic
90C23×Q8C2311yescharacteristic
91C23×Q8C2311yescharacteristic
92C23×D4—21no—
93C23×D4C2311yescharacteristic
94C24×C4—21no—
95C24×C4C2311yescharacteristic
96C22×Q16—24no—
97C22×Q16—24no—
98C22×Q16—24no—
99C22×Q16—24no—
100C22×Q16—42no—
101C22×Q16—42no—
102C22×Q16C2314yes—
103C22×Q16C2314yes—
104C22×SD16—24no—
105C22×SD16—24no—
106C22×SD16—42no—
107C22×SD16C2314yes—
108C23×C8—24no—
109C23×C8—24no—
110C23×C8—42no—
111C23×C8C2311yescharacteristic
112C23×C8C2311yescharacteristic
113C23×C8C2311yescharacteristic
114C23×C8C2314yes—
115C23×C8C2311yescharacteristic
116C2×C4⋊Q8—24no—
117C2×C4⋊Q8—22no—
118C2×C4⋊Q8—42no—
119C2×C4⋊Q8C2314yes—
120C2×#124—24no—
121C2×#124—22no—
122C2×#124—42no—
123C2×#124C2314yes—
124C2×C22⋊Q8—22no—
125C2×C22⋊Q8—24no—
126C2×C22⋊Q8—22no—
127C2×C22⋊Q8—24no—
128C2×C22⋊Q8—24no—
129C2×C22⋊Q8D418yes—
130C2×C22⋊Q8C2314yes—
131C2×C22⋊Q8C2314yes—
132C2×C4×Q8—22no—
133C2×C4×Q8—24no—
134C2×C4×Q8—42no—
135C2×C4×Q8C2314yes—
136C2×#117—22no—
137C2×#117—24no—
138C2×#117—42no—
139C2×#117C2314yes—
140C22×C4⋊C4—21no—
141C22×C4⋊C4—21no—
142C22×C4⋊C4—21no—
143C22×C4⋊C4—21no—
144C22×C4⋊C4—21no—
145C22×C4⋊C4—21no—
146C22×C4⋊C4C2311yescharacteristic
147C22×C4⋊C4C2311yescharacteristic
148C22×C4⋊C4C2311yescharacteristic
149C22×C4⋊C4C2311yescharacteristic
150C22×C22⋊C4—21no—
151C22×C22⋊C4—21no—
152C22×C22⋊C4—21no—
153C22×C22⋊C4—21no—
154C22×C22⋊C4—21no—
155C22×C22⋊C4—21no—
156C22×C22⋊C4—21no—
157C22×C22⋊C4D411yescharacteristic
158C22×C22⋊C4D411yescharacteristic
159C22×C42—21no—
160C22×C42—21no—
161C22×C42—21no—
162C22×C42C2311yescharacteristic
163C22×C42C2311yescharacteristic
164#467—232no—
165#462—232no—
166#452—232no—
167C2×#107—24no—
168C2×#107C2314yes—
169C2×C4⋊C8—24no—
170C2×C4⋊C8—42no—
171C2×C4⋊C8C2314yes—
172C2×C4⋊C8C2314yes—
173#416—232no—
174C2×#103—24no—
175C2×#103—24no—
176C2×#103—24no—
177C2×#103—24no—
178C2×#103—24no—
179C2×#103—42no—
180C2×#103D418yes—
181C2×#103C2314yes—
182C2×#103C2314yes—
183C2×#103C2314yes—
184C2×#103C2314yes—
185C2×#103C2314yes—
186C2×#103C2314yes—
187C2×#103C2314yes—
188C2×#102—24no—
189C2×#102—24no—
190C2×#102—24no—
191C2×#102C2314yes—
192C2×#102C2314yes—
193C2×#102C2314yes—
194C2×C22⋊C8—24no—
195C2×C22⋊C8C2314yes—
196#394—28no—
197#394—28no—
198#391—22no—
199#391—22no—
200#391C2314yes—
201#391C2314yes—
202#390—22no—
203#390C2314yes—
204#389—22no—
205#389C2314yes—
206#388—28no—
207#388—28no—
208#387—28no—
209#385—28no—
210#385—28no—
211C4×C4⋊C4—22no—
212C4×C4⋊C4—28no—
213C4×C4⋊C4C2314yes—
214C4×C22⋊C4D414yes—
215C4×C22⋊C4C2314yes—
216C2×#95—21no—
217C2×#95—21no—
218C2×#95—21no—
219C2×#95—21no—
220C2×#95—21no—
221C2×#95—21no—
222C2×#95D411yescharacteristic
223C2×#95D411yescharacteristic
224#340C2314yes—
225#340C2314yes—
226#336C2314yes—
227#336C2314yes—
228C25—21no—
229C25C2×D411yescharacteristic
230C2×#41—232no—
231C2×#41—28no—
232C2×#41—28no—
233C2×#41—28no—
234C2×#41—28no—
235C2×#41—44no—
236C2×#41—44no—
237C2×#41—48no—
238C2×#41—416no—
239C2×#41—48no—
240C2×#41—416no—
241C2×#41—416no—
242C2×#41—48no—
243C22×Q8—21no—
244C22×Q8—21no—
245C22×Q8—21no—
246C22×Q8—22no—
247C22×Q8—22no—
248C22×Q8—22no—
249C22×Q8—22no—
250C22×Q8—22no—
251C22×Q8—22no—
252C22×Q8—22no—
253C22×Q8—22no—
254C22×Q8—22no—
255C22×Q8—22no—
256C22×Q8—22no—
257C22×Q8—22no—
258C22×Q8—22no—
259C22×Q8—22no—
260C22×Q8—22no—
261C22×Q8—22no—
262C22×Q8C2×D414yes—
263C22×Q8C2×D414yes—
264C22×Q8C2412yes—
265C22×Q8C2412yes—
266C22×Q8C2412yes—
267C22×D4—24no—
268C22×D4—22no—
269C22×D4—22no—
270C22×D4—21no—
271C22×D4—22no—
272C22×D4—22no—
273C22×D4—22no—
274C22×D4—44no—
275C22×D4—44no—
276C22×D4—44no—
277C22×D4#4114yes—
278C22×D4C2412yes—
279C23×C4—22no—
280C23×C4—22no—
281C23×C4—22no—
282C23×C4—22no—
283C23×C4—21no—
284C23×C4—21no—
285C23×C4—21no—
286C23×C4—21no—
287C23×C4—21no—
288C23×C4—21no—
289C23×C4—21no—
290C23×C4—24no—
291C23×C4—44no—
292C23×C4—44no—
293C23×C4—44no—
294C23×C4C2×D411yescharacteristic
295C23×C4C2×D411yescharacteristic
296C23×C4C2×D411yescharacteristic
297C23×C4C2×D412yes—
298C23×C4C2×D411yescharacteristic
299C23×C4C2×D414yes—
300C23×C4C2×D411yescharacteristic
301C23×C4#4114yes—
302C23×C4C2412yes—
303C23×C4C2411yescharacteristic
304C2×Q16—28no—
305C2×Q16—28no—
306C2×Q16—28no—
307C2×Q16—28no—
308C2×Q16—44no—
309C2×Q16—44no—
310C2×Q16—416no—
311C2×Q16—416no—
312C2×SD16—28no—
313C2×SD16—28no—
314C2×SD16—44no—
315C2×SD16—416no—
316C22×C8—22no—
317C22×C8—22no—
318C22×C8—22no—
319C22×C8—22no—
320C22×C8—28no—
321C22×C8—22no—
322C22×C8—22no—
323C22×C8—22no—
324C22×C8—22no—
325C22×C8—22no—
326C22×C8—22no—
327C22×C8—22no—
328C22×C8—28no—
329C22×C8—44no—
330C22×C8—416no—
331C22×C8C2×D414yes—
332C22×C8C2412yes—
333C22×C8C2412yes—
334C22×C8C2412yes—
335C22×C8C2412yes—
336C4⋊Q8—28no—
337C4⋊Q8—44no—
338C4⋊Q8—48no—
339#124—28no—
340#124—44no—
341#124—48no—
342C22⋊Q8—216no—
343C22⋊Q8—28no—
344C22⋊Q8—28no—
345C22⋊Q8—28no—
346C22⋊Q8—48no—
347C22⋊Q8C2×D4116yes—
348C4×Q8—28no—
349C4×Q8—44no—
350C4×Q8—48no—
351#117—28no—
352#117—44no—
353#117—48no—
354C2×C4⋊C4—28no—
355C2×C4⋊C4—24no—
356C2×C4⋊C4—21no—
357C2×C4⋊C4—21no—
358C2×C4⋊C4—22no—
359C2×C4⋊C4—22no—
360C2×C4⋊C4—22no—
361C2×C4⋊C4—22no—
362C2×C4⋊C4—22no—
363C2×C4⋊C4—22no—
364C2×C4⋊C4—24no—
365C2×C4⋊C4—24no—
366C2×C4⋊C4—24no—
367C2×C4⋊C4—24no—
368C2×C4⋊C4—24no—
369C2×C4⋊C4—21no—
370C2×C4⋊C4—21no—
371C2×C4⋊C4—44no—
372C2×C4⋊C4—44no—
373C2×C4⋊C4—44no—
374C2×C4⋊C4—44no—
375C2×C4⋊C4—44no—
376C2×C4⋊C4C2×D414yes—
377C2×C4⋊C4C2×D414yes—
378C2×C4⋊C4C2412yes—
379C2×C4⋊C4C2412yes—
380C2×C4⋊C4C2412yes—
381C2×C4⋊C4C2412yes—
382C2×C22⋊C4—28no—
383C2×C22⋊C4—24no—
384C2×C22⋊C4—24no—
385C2×C22⋊C4—24no—
386C2×C22⋊C4—24no—
387C2×C22⋊C4—24no—
388C2×C22⋊C4—24no—
389C2×C22⋊C4—24no—
390C2×C22⋊C4—24no—
391C2×C22⋊C4—42no—
392C2×C22⋊C4—44no—
393C2×C22⋊C4—44no—
394C2×C22⋊C4—44no—
395C2×C22⋊C4—44no—
396C2×C22⋊C4—44no—
397C2×C22⋊C4—44no—
398C2×C22⋊C4C2×D414yes—
399C2×C22⋊C4C2×D414yes—
400C2×C42—22no—
401C2×C42—22no—
402C2×C42—22no—
403C2×C42—22no—
404C2×C42—24no—
405C2×C42—24no—
406C2×C42—24no—
407C2×C42—44no—
408C2×C42—44no—
409C2×C42—44no—
410C2×C42C2×D412yes—
411C2×C42C2×D412yes—
412C2×C42C2412yes—
413C2×C42C2412yes—
414#107—28no—
415C4⋊C8—28no—
416C4⋊C8—44no—
417#103—28no—
418#103—28no—
419#103—28no—
420#103—28no—
421#103—28no—
422#103—44no—
423#103C2×D4116yes—
424#102—28no—
425#102—28no—
426#102—28no—
427C22⋊C8—28no—
428#95—24no—
429#95—24no—
430#95—24no—
431#95—24no—
432#95—24no—
433#95—24no—
434#95C2×D414yes—
435#95C2×D414yes—
436C24—22no—
437C24—22no—
438C24—22no—
439C24—22no—
440C24—22no—
441C24—22no—
442C24—24no—
443C24—22no—
444C24—42no—
445C24—42no—
446C24—42no—
447C24—42no—
448C24—42no—
449C24—42no—
450C24#12114yes—
451C24C22×D412yes—
452C24C22×D411yescharacteristic
453#41—232no—
454#41—416no—
455#41—416no—
456#41—464no—
457#41—416no—
458C2×Q8—24no—
459C2×Q8—24no—
460C2×Q8—22no—
461C2×Q8—22no—
462C2×Q8—28no—
463C2×Q8—28no—
464C2×Q8—28no—
465C2×Q8—28no—
466C2×Q8—22no—
467C2×Q8—22no—
468C2×Q8—22no—
469C2×Q8—22no—
470C2×Q8—22no—
471C2×Q8—22no—
472C2×Q8—22no—
473C2×Q8—22no—
474C2×Q8—22no—
475C2×Q8—22no—
476C2×Q8—22no—
477C2×Q8—22no—
478C2×Q8—22no—
479C2×Q8—22no—
480C2×Q8—42no—
481C2×Q8—42no—
482C2×Q8—44no—
483C2×Q8—44no—
484C2×Q8—44no—
485C2×Q8—42no—
486C2×Q8—42no—
487C2×Q8—42no—
488C2×Q8—44no—
489C2×Q8—42no—
490C2×Q8—42no—
491C2×Q8—44no—
492C2×Q8—44no—
493C2×Q8—44no—
494C2×Q8—44no—
495C2×Q8C22×D414yes—
496C2×Q8C22×D414yes—
497C2×D4—28no—
498C2×D4—28no—
499C2×D4—24no—
500C2×D4—22no—
501C2×D4—22no—
502C2×D4—22no—
503C2×D4—22no—
504C2×D4—22no—
505C2×D4—48no—
506C2×D4—48no—
507C2×D4—432no—
508C2×D4—48no—
509C2×D4—42no—
510C2×D4—44no—
511C2×D4—42no—
512C2×D4—44no—
513C2×D4C2×#4114yes—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—28no—
519C22×C4—28no—
520C22×C4—24no—
521C22×C4—28no—
522C22×C4—28no—
523C22×C4—24no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—24no—
529C22×C4—24no—
530C22×C4—22no—
531C22×C4—24no—
532C22×C4—24no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—48no—
549C22×C4—48no—
550C22×C4—432no—
551C22×C4—42no—
552C22×C4—42no—
553C22×C4—42no—
554C22×C4—42no—
555C22×C4—42no—
556C22×C4—42no—
557C22×C4—42no—
558C22×C4—42no—
559C22×C4—48no—
560C22×C4—42no—
561C22×C4—42no—
562C22×C4—42no—
563C22×C4—42no—
564C22×C4—42no—
565C22×C4—42no—
566C22×C4—42no—
567C22×C4—42no—
568C22×C4—42no—
569C22×C4#12114yes—
570C22×C4#12118yes—
571C22×C4#13514yes—
572C22×C4C22×D412yes—
573C22×C4C22×D412yes—
574C22×C4C22×D412yes—
575C22×C4C22×D412yes—
576C22×C4C22×D414yes—
577C22×C4C22×D412yes—
578C22×C4C22×D411yescharacteristic
579C22×C4C22×D412yes—
580C22×C4C22×D412yes—
581C22×C4C2×#4114yes—
582C22×C4C2×#4112yes—
583C22×C4C2×#4112yes—
584C22×C4H(5,𝔽2)12yes—
585C22×C4H(5,𝔽2)12yes—
586C22×C4C2511yescharacteristic
587Q16—416no—
588Q16—416no—
589SD16—416no—
590C2×C8—28no—
591C2×C8—22no—
592C2×C8—22no—
593C2×C8—22no—
594C2×C8—22no—
595C2×C8—22no—
596C2×C8—22no—
597C2×C8—22no—
598C2×C8—22no—
599C2×C8—22no—
600C2×C8—22no—
601C2×C8—22no—
602C2×C8—416no—
603C2×C8—44no—
604C2×C8—44no—
605C2×C8—44no—
606C2×C8C22×D414yes—
607C4⋊C4—216no—
608C4⋊C4—24no—
609C4⋊C4—24no—
610C4⋊C4—22no—
611C4⋊C4—22no—
612C4⋊C4—22no—
613C4⋊C4—22no—
614C4⋊C4—22no—
615C4⋊C4—22no—
616C4⋊C4—48no—
617C4⋊C4—48no—
618C4⋊C4—48no—
619C4⋊C4—42no—
620C4⋊C4—48no—
621C4⋊C4—42no—
622C4⋊C4—48no—
623C4⋊C4C22×D414yes—
624C4⋊C4C22×D414yes—
625C22⋊C4—216no—
626C22⋊C4—28no—
627C22⋊C4—44no—
628C22⋊C4—48no—
629C22⋊C4—48no—
630C22⋊C4—48no—
631C22⋊C4—48no—
632C22⋊C4—48no—
633C22⋊C4—48no—
634C42—24no—
635C42—24no—
636C42—22no—
637C42—22no—
638C42—22no—
639C42—22no—
640C42—48no—
641C42—48no—
642C42—48no—
643C23—28no—
644C23—22no—
645C23—22no—
646C23—28no—
647C23—28no—
648C23—22no—
649C23—22no—
650C23—22no—
651C23—22no—
652C23—24no—
653C23—44no—
654C23—44no—
655C23—44no—
656C23—44no—
657C23—42no—
658C23—48no—
659C23—42no—
660C23—48no—
661C23—48no—
662C23—42no—
663C23—42no—
664C23—42no—
665C23—42no—
666C23—84no—
667C23—84no—
668C23—84no—
669C23—84no—
670C23C2×#12114yes—
671C23C2×#12112yes—
672C23D4212yes—
673C23#54612yes—
674C23C2×#13512yes—
675C23#57512yes—
676C23#57812yes—
677C23#57812yes—
678C23C23×D411yescharacteristic
679Q8—24no—
680Q8—24no—
681Q8—24no—
682Q8—24no—
683Q8—42no—
684Q8—48no—
685Q8—48no—
686Q8—42no—
687Q8—42no—
688Q8—42no—
689Q8—42no—
690Q8—42no—
691Q8—42no—
692Q8—42no—
693Q8—84no—
694D4—24no—
695D4—24no—
696D4—432no—
697D4—48no—
698D4—42no—
699D4—42no—
700C2×C4—28no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—28no—
705C2×C4—22no—
706C2×C4—24no—
707C2×C4—216no—
708C2×C4—24no—
709C2×C4—24no—
710C2×C4—24no—
711C2×C4—24no—
712C2×C4—24no—
713C2×C4—22no—
714C2×C4—24no—
715C2×C4—24no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—432no—
725C2×C4—42no—
726C2×C4—48no—
727C2×C4—48no—
728C2×C4—42no—
729C2×C4—42no—
730C2×C4—42no—
731C2×C4—44no—
732C2×C4—48no—
733C2×C4—48no—
734C2×C4—44no—
735C2×C4—44no—
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—42no—
747C2×C4—42no—
748C2×C4—42no—
749C2×C4—84no—
750C2×C4—84no—
751C2×C4—84no—
752C2×C4C2×#12114yes—
753C2×C4C2×#12112yes—
754C2×C4#52514yes—
755C2×C4#53814yes—
756C2×C4D4212yes—
757C2×C4D4214yes—
758C2×C4#54612yes—
759C2×C4#54614yes—
760C2×C4C2×#13514yes—
761C2×C4C23×D411yescharacteristic
762C2×C4C23×D411yescharacteristic
763C2×C4C22×#4111yescharacteristic
764C2×C4C22×#4111yescharacteristic
765C2×C4C2×H(5,𝔽2)11yescharacteristic
766C2×C4C2×H(5,𝔽2)11yescharacteristic
767C8—24no—
768C8—42no—
769C8—42no—
770C8—42no—
771C22—24no—
772C22—24no—
773C22—24no—
774C22—42no—
775C22—42no—
776C22—42no—
777C22—42no—
778C22—416no—
779C22—44no—
780C22—44no—
781C22—44no—
782C22—82no—
783C22—82no—
784C22—82no—
785C22—816no—
786C22—82no—
787C22#242414yes—
788C22#303514yes—
789C22#304414yes—
790C22#326914yes—
791C22#328514yes—
792C22#330214yes—
793C22#331514yes—
794C22C22×#12111yescharacteristic
795C22C2×D4211yescharacteristic
796C22C2×#54611yescharacteristic
797C22C22×#13511yescharacteristic
798C22C2×#57511yescharacteristic
799C22C2×#57811yescharacteristic
800C22C2×#57811yescharacteristic
801C4—24no—
802C4—24no—
803C4—44no—
804C4—44no—
805C4—42no—
806C4—44no—
807C4—42no—
808C4—42no—
809C4—44no—
810C4—82no—
811C4—82no—
812C4—82no—
813C4#242414yes—
814C4C2×#52511yescharacteristic
815C4C2×#53811yescharacteristic
816C4C2×D4211yescharacteristic
817C4C2×#54611yescharacteristic
818C2—44no—
819C2—84no—
820C2#2507918yesdirect product factor
821C2C2×#242411yescharacteristic
822C2C2×#303511yescharacteristic
823C2C2×#304411yescharacteristic
824C2C2×#326911yescharacteristic
825C2C2×#328511yescharacteristic
826C2C2×#330211yescharacteristic
827C2C2×#331511yescharacteristic
subgroupG/H
center, socleC24C22×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC23×#41C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24 ◁ C2×C4×C22⋊C4 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C22×#467C2semidirect
2. C22×#462C2semidirect
6. C2×#2362C2semidirect
7. #25079C2direct (N × H)
8. C2×#2067C2semidirect
9. C2×#2056C2semidirect
10. C2×#2043C2semidirect
11. C2×#2015C2semidirect
12. C2×#1983C2semidirect
13. C2×#1928C2semidirect
14. C2×#1880C2semidirect
15. C2×#1873C2semidirect
16. C2×#1850C2semidirect
29. C2×#467C22semidirect
31. C2×#462C22semidirect
55. #2362C22semidirect
68. #2067C22semidirect
69. #2056C22semidirect
70. #2043C22semidirect
71. #2015C22semidirect
72. #1983C22semidirect
73. #1928C22semidirect
74. #1880C22semidirect
75. #1873C22semidirect
76. #1850C22semidirect
820. C2#25079direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#4672
C22×#4622
C22×#4522
C22×#4162
C2×#24322
C2×#23622
#250792
C2×#20672
C2×#20562
C2×#20432
C2×#20152
C2×#19832
C2×#19282
C2×#18802
C2×#18732
C2×#18502