Finite Group Databasebeta

← C2×#24554 #6440546

Subgroups — C2×#24554 #6440546

Order 512.

3598 conjugacy classes of subgroups.

The subgroup lattice has 839 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#485C211yesmaximal, characteristic, complemented
2C23×C22⋊C8C211yesmaximal, characteristic
3C2×#2848C211yesmaximal, characteristic
4C2×#2280C211yesmaximal, characteristic
5#24554C2116yesmaximal, direct product factor
6C2×#2077C211yesmaximal, characteristic, complemented
7C2×#2075C211yesmaximal, characteristic, complemented
8C2×#2036C211yesmaximal, characteristic, complemented
9C2×#2035C211yesmaximal, characteristic, complemented
10C2×#1892C211yesmaximal, characteristic, complemented
11C2×#1892C211yesmaximal, characteristic, complemented
12C2×#1873C211yesmaximal, characteristic, complemented
13C2×#1854C211yesmaximal, characteristic, complemented
14C2×#1825C211yesmaximal, characteristic, complemented
15C2×#1808C211yesmaximal, characteristic, complemented
16C2×#1807C211yesmaximal, characteristic, complemented
17C25×C4C2211yescharacteristic
18C24×C8C2211yescharacteristic
19C24×C8C2211yescharacteristic
20C22×C22⋊Q8C2211yescharacteristic
21C22×C22⋊Q8C2211yescharacteristic
22C22×C22⋊Q8C2211yescharacteristic
23C22×#117C2211yescharacteristic
24C22×#117C2211yescharacteristic
25C2×#485—28no—
26C2×#485C2218yescomplemented
27C22×#107C2211yescharacteristic, complemented
28C22×#107C2211yescharacteristic, complemented
29C22×#106C2211yescharacteristic, complemented
30C22×#106C2211yescharacteristic, complemented
31C22×#103C2211yescharacteristic, complemented
32C22×#103C2211yescharacteristic, complemented
33C22×#103C2211yescharacteristic, complemented
34C22×#103C2211yescharacteristic, complemented
35C22×C22⋊C8—28no—
36C22×C22⋊C8C2211yescharacteristic
37C22×C22⋊C8C2211yescharacteristic
38C22×C22⋊C8C2211yescharacteristic
39C22×C22⋊C8C2218yes—
40C22×C22⋊C8C2211yescharacteristic
41#2848—24no—
42#2848C2218yes—
43C2×#385—21no—
44C2×#385—21no—
45C2×#385—21no—
46#2280—24no—
47#2280C2218yes—
48C2×#381—21no—
49C2×#380C2211yescharacteristic
50C2×#380C2211yescharacteristic
51C2×#380C2211yescharacteristic
52C2×#380C2211yescharacteristic
53C2×#380C2211yescharacteristic
54C2×#380C2211yescharacteristic
55C2×#380C2211yescharacteristic
56C2×#379—21no—
57C2×#379—21no—
58C2×C4×C22⋊C4—21no—
59C2×C4×C22⋊C4—21no—
60#2077C2218yescomplemented
61#2075C2218yescomplemented
62#2036C2218yescomplemented
63#2035C2218yescomplemented
64#1892C2218yescomplemented
65#1892C2218yescomplemented
66#1873C2218yescomplemented
67#1854C2218yescomplemented
68#1825C2218yescomplemented
69#1808C2218yescomplemented
70#1807C2218yescomplemented
71C2×#340C2211yescharacteristic, complemented
72C2×#340C2211yescharacteristic, complemented
73C2×#340C2211yescharacteristic, complemented
74C2×#340C2211yescharacteristic, complemented
75C2×#340C2211yescharacteristic, complemented
76C2×#340C2211yescharacteristic, complemented
77C2×#340C2211yescharacteristic, complemented
78C2×#340C2211yescharacteristic, complemented
79C26D411yescharacteristic
80C23×Q8C2311yescharacteristic
81C24×C4—24no—
82C24×C4—24no—
83C24×C4—24no—
84C24×C4—24no—
85C24×C4—42no—
86C24×C4—42no—
87C24×C4D414yes—
88C24×C4D411yescharacteristic
89C24×C4D411yescharacteristic
90C24×C4D411yescharacteristic
91C24×C4C2311yescharacteristic
92C24×C4C2314yes—
93C24×C4C2311yescharacteristic
94C24×C4C2311yescharacteristic
95C23×C8—24no—
96C23×C8—24no—
97C23×C8—24no—
98C23×C8—24no—
99C23×C8—42no—
100C23×C8—42no—
101C23×C8C2311yescharacteristic
102C23×C8C2311yescharacteristic
103C23×C8C2314yes—
104C23×C8C2314yes—
105C23×C8C2311yescharacteristic
106C23×C8C2311yescharacteristic
107C2×C22⋊Q8—22no—
108C2×C22⋊Q8—22no—
109C2×C22⋊Q8—22no—
110C2×C22⋊Q8—24no—
111C2×C22⋊Q8—24no—
112C2×C22⋊Q8—24no—
113C2×C22⋊Q8—24no—
114C2×C22⋊Q8—42no—
115C2×C22⋊Q8—42no—
116C2×C22⋊Q8C2314yes—
117C2×C22⋊Q8C2314yes—
118C2×C22⋊Q8C2314yes—
119C2×#117—22no—
120C2×#117—22no—
121C2×#117—24no—
122C2×#117—24no—
123C2×#117—42no—
124C2×#117—42no—
125C2×#117C2314yes—
126C2×#117C2314yes—
127C22×C4⋊C4—21no—
128C22×C4⋊C4—21no—
129C22×C4⋊C4—21no—
130C22×C4⋊C4C2311yescharacteristic
131C22×C4⋊C4C2311yescharacteristic
132C22×C4⋊C4C2311yescharacteristic
133C22×C4⋊C4C2311yescharacteristic
134C22×C4⋊C4C2311yescharacteristic
135C22×C4⋊C4C2311yescharacteristic
136C22×C4⋊C4C2311yescharacteristic
137C22×C22⋊C4—21no—
138C22×C22⋊C4—21no—
139C22×C22⋊C4—21no—
140C22×C22⋊C4—21no—
141C22×C22⋊C4—21no—
142C22×C22⋊C4—21no—
143C22×C22⋊C4—21no—
144C22×C22⋊C4—21no—
145C22×C22⋊C4—21no—
146C22×C22⋊C4—21no—
147C22×C22⋊C4—21no—
148C22×C22⋊C4—21no—
149C22×C42—21no—
150C22×C42—21no—
151#485—232no—
152C2×#107—24no—
153C2×#107—42no—
154C2×#107C2314yescomplemented
155C2×#107C2314yescomplemented
156C2×#106—24no—
157C2×#106—42no—
158C2×#106C2314yescomplemented
159C2×#106C2314yescomplemented
160C2×#103—24no—
161C2×#103—24no—
162C2×#103—42no—
163C2×#103—42no—
164C2×#103C2314yescomplemented
165C2×#103C2314yescomplemented
166C2×#103C2314yescomplemented
167C2×#103C2314yescomplemented
168C2×C22⋊C8—24no—
169C2×C22⋊C8—24no—
170C2×C22⋊C8—24no—
171C2×C22⋊C8—232no—
172C2×C22⋊C8D418yes—
173C2×C22⋊C8C2314yes—
174C2×C22⋊C8C2314yes—
175C2×C22⋊C8C2314yes—
176C2×C22⋊C8C2314yes—
177#385—28no—
178#385—28no—
179#385—28no—
180#381—28no—
181#380—22no—
182#380—22no—
183#380—22no—
184#380—22no—
185#380—22no—
186#380—22no—
187#380—22no—
188#380C2314yes—
189#380C2314yes—
190#380C2314yes—
191#380C2314yes—
192#380C2314yes—
193#380C2314yes—
194#380C2314yes—
195#379—28no—
196#379—28no—
197C4×C22⋊C4—28no—
198C4×C22⋊C4—28no—
199C2×#95—21no—
200C2×#95—21no—
201C2×#95—21no—
202C2×#95—21no—
203C2×#95—21no—
204C2×#95—21no—
205C2×#95—21no—
206#340C2314yescomplemented
207#340C2314yescomplemented
208#340C2314yescomplemented
209#340C2314yescomplemented
210#340C2314yescomplemented
211#340C2314yescomplemented
212#340C2314yescomplemented
213#340C2314yescomplemented
214C25—24no—
215C25—24no—
216C25—24no—
217C25—24no—
218C25—24no—
219C25—42no—
220C25—42no—
221C25C2×D411yescharacteristic
222C25C2×D411yescharacteristic
223C25C2×D414yes—
224C25C2×D411yescharacteristic
225C22×Q8—21no—
226C22×Q8—22no—
227C22×Q8—22no—
228C22×Q8—22no—
229C22×Q8—22no—
230C22×Q8—22no—
231C22×Q8—22no—
232C22×Q8C2412yes—
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—24no—
242C23×C4—24no—
243C23×C4—24no—
244C23×C4—216no—
245C23×C4—24no—
246C23×C4—24no—
247C23×C4—216no—
248C23×C4—24no—
249C23×C4—28no—
250C23×C4—22no—
251C23×C4—28no—
252C23×C4—28no—
253C23×C4—28no—
254C23×C4—22no—
255C23×C4—22no—
256C23×C4—22no—
257C23×C4—22no—
258C23×C4—22no—
259C23×C4—21no—
260C23×C4—21no—
261C23×C4—21no—
262C23×C4—21no—
263C23×C4—21no—
264C23×C4—21no—
265C23×C4—21no—
266C23×C4—21no—
267C23×C4—48no—
268C23×C4—44no—
269C23×C4—44no—
270C23×C4—42no—
271C23×C4—42no—
272C23×C4—42no—
273C23×C4—416no—
274C23×C4—416no—
275C23×C4—416no—
276C23×C4—416no—
277C23×C4C2×D412yes—
278C23×C4C2×D411yescharacteristic
279C23×C4C2×D414yes—
280C23×C4C2×D414yes—
281C23×C4C2×D414yes—
282C23×C4C2×D412yes—
283C23×C4C2×D411yescharacteristic
284C23×C4C2×D414yes—
285C23×C4C2×D412yes—
286C23×C4C2×D411yescharacteristic
287C23×C4#4114yes—
288C23×C4#4114yes—
289C23×C4#4114yes—
290C23×C4C2412yes—
291C23×C4C2412yes—
292C23×C4C2412yes—
293C23×C4C2411yescharacteristic
294C22×C8—22no—
295C22×C8—22no—
296C22×C8—22no—
297C22×C8—22no—
298C22×C8—22no—
299C22×C8—22no—
300C22×C8—28no—
301C22×C8—28no—
302C22×C8—22no—
303C22×C8—22no—
304C22×C8—22no—
305C22×C8—22no—
306C22×C8—28no—
307C22×C8—28no—
308C22×C8—44no—
309C22×C8—44no—
310C22×C8—416no—
311C22×C8—416no—
312C22×C8C2×D414yes—
313C22×C8C2×D414yes—
314C22×C8C2412yes—
315C22×C8C2412yes—
316C22×C8C2412yes—
317C22×C8C2412yes—
318C22⋊Q8—28no—
319C22⋊Q8—28no—
320C22⋊Q8—28no—
321C22⋊Q8—28no—
322C22⋊Q8—44no—
323C22⋊Q8—44no—
324C22⋊Q8—48no—
325C22⋊Q8—48no—
326C22⋊Q8—48no—
327#117—28no—
328#117—28no—
329#117—44no—
330#117—44no—
331#117—48no—
332#117—48no—
333C2×C4⋊C4—22no—
334C2×C4⋊C4—22no—
335C2×C4⋊C4—22no—
336C2×C4⋊C4—22no—
337C2×C4⋊C4—22no—
338C2×C4⋊C4—22no—
339C2×C4⋊C4—22no—
340C2×C4⋊C4—22no—
341C2×C4⋊C4—22no—
342C2×C4⋊C4—22no—
343C2×C4⋊C4—22no—
344C2×C4⋊C4—22no—
345C2×C4⋊C4—22no—
346C2×C4⋊C4—22no—
347C2×C4⋊C4—24no—
348C2×C4⋊C4—24no—
349C2×C4⋊C4—24no—
350C2×C4⋊C4—21no—
351C2×C4⋊C4—21no—
352C2×C4⋊C4—21no—
353C2×C4⋊C4—21no—
354C2×C4⋊C4—21no—
355C2×C4⋊C4—21no—
356C2×C4⋊C4—21no—
357C2×C4⋊C4—44no—
358C2×C4⋊C4—44no—
359C2×C4⋊C4—44no—
360C2×C4⋊C4C2412yes—
361C2×C4⋊C4C2412yes—
362C2×C4⋊C4C2412yes—
363C2×C4⋊C4C2412yes—
364C2×C4⋊C4C2412yes—
365C2×C4⋊C4C2412yes—
366C2×C4⋊C4C2412yes—
367C2×C22⋊C4—24no—
368C2×C22⋊C4—24no—
369C2×C22⋊C4—24no—
370C2×C22⋊C4—24no—
371C2×C22⋊C4—24no—
372C2×C22⋊C4—24no—
373C2×C22⋊C4—24no—
374C2×C22⋊C4—24no—
375C2×C22⋊C4—24no—
376C2×C22⋊C4—24no—
377C2×C22⋊C4—24no—
378C2×C22⋊C4—24no—
379C2×C22⋊C4—44no—
380C2×C22⋊C4—44no—
381C2×C22⋊C4—44no—
382C2×C22⋊C4—44no—
383C2×C22⋊C4—44no—
384C2×C22⋊C4—44no—
385C2×C22⋊C4—44no—
386C2×C22⋊C4—44no—
387C2×C22⋊C4—44no—
388C2×C22⋊C4—44no—
389C2×C22⋊C4—44no—
390C2×C22⋊C4—44no—
391C2×C42—24no—
392C2×C42—24no—
393C2×C42—44no—
394C2×C42—44no—
395#107—28no—
396#107—44no—
397#106—28no—
398#106—44no—
399#103—28no—
400#103—28no—
401#103—44no—
402#103—44no—
403C22⋊C8—28no—
404C22⋊C8—28no—
405C22⋊C8—28no—
406C22⋊C8C2×D4116yes—
407#95—24no—
408#95—24no—
409#95—24no—
410#95—24no—
411#95—24no—
412#95—24no—
413#95—24no—
414C24—22no—
415C24—22no—
416C24—22no—
417C24—22no—
418C24—232no—
419C24—28no—
420C24—22no—
421C24—22no—
422C24—22no—
423C24—22no—
424C24—22no—
425C24—28no—
426C24—28no—
427C24—22no—
428C24—22no—
429C24—22no—
430C24—22no—
431C24—22no—
432C24—22no—
433C24—22no—
434C24—28no—
435C24—28no—
436C24—44no—
437C24—44no—
438C24—416no—
439C24—416no—
440C24—416no—
441C24—416no—
442C24—416no—
443C24—416no—
444C24#12114yes—
445C24#12314yes—
446C24#13514yes—
447C24#13514yes—
448C24#13714yes—
449C24C22×D412yes—
450C24C22×D412yes—
451C24C22×D412yes—
452C24C22×D411yescharacteristic
453C2×Q8—22no—
454C2×Q8—22no—
455C2×Q8—22no—
456C2×Q8—22no—
457C2×Q8—22no—
458C2×Q8—22no—
459C2×Q8—42no—
460C2×Q8—42no—
461C2×Q8—42no—
462C2×Q8—44no—
463C2×Q8—44no—
464C2×Q8—44no—
465C2×Q8—44no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—24no—
471C22×C4—24no—
472C22×C4—24no—
473C22×C4—24no—
474C22×C4—28no—
475C22×C4—28no—
476C22×C4—28no—
477C22×C4—28no—
478C22×C4—28no—
479C22×C4—28no—
480C22×C4—28no—
481C22×C4—28no—
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—28no—
491C22×C4—22no—
492C22×C4—28no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—28no—
496C22×C4—28no—
497C22×C4—24no—
498C22×C4—28no—
499C22×C4—28no—
500C22×C4—24no—
501C22×C4—24no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—44no—
517C22×C4—44no—
518C22×C4—44no—
519C22×C4—416no—
520C22×C4—464no—
521C22×C4—416no—
522C22×C4—416no—
523C22×C4—416no—
524C22×C4—416no—
525C22×C4—416no—
526C22×C4—416no—
527C22×C4—44no—
528C22×C4—44no—
529C22×C4—44no—
530C22×C4—44no—
531C22×C4—42no—
532C22×C4—42no—
533C22×C4—42no—
534C22×C4—42no—
535C22×C4—42no—
536C22×C4—42no—
537C22×C4—42no—
538C22×C4—42no—
539C22×C4—42no—
540C22×C4—42no—
541C22×C4—42no—
542C22×C4—42no—
543C22×C4—42no—
544C22×C4—42no—
545C22×C4—42no—
546C22×C4—42no—
547C22×C4—42no—
548C22×C4—42no—
549C22×C4—42no—
550C22×C4—42no—
551C22×C4—42no—
552C22×C4—42no—
553C22×C4—42no—
554C22×C4—42no—
555C22×C4#12114yes—
556C22×C4#12118yes—
557C22×C4#12314yes—
558C22×C4#12318yes—
559C22×C4C22×D412yes—
560C22×C4C22×D412yes—
561C22×C4C22×D414yes—
562C22×C4C22×D412yes—
563C22×C4C22×D411yescharacteristic
564C22×C4C22×D412yes—
565C22×C4C2×#4114yes—
566C22×C4C2×#4114yes—
567C22×C4C2×#4114yes—
568C22×C4C2×#4112yes—
569C22×C4C2×#4112yes—
570C22×C4C2×#4112yes—
571C22×C4H(5,𝔽2)12yes—
572C22×C4H(5,𝔽2)12yes—
573C22×C4C2511yescharacteristic
574C2×C8—28no—
575C2×C8—28no—
576C2×C8—22no—
577C2×C8—22no—
578C2×C8—22no—
579C2×C8—22no—
580C2×C8—22no—
581C2×C8—22no—
582C2×C8—22no—
583C2×C8—22no—
584C2×C8—22no—
585C2×C8—22no—
586C2×C8—416no—
587C2×C8—416no—
588C2×C8—44no—
589C2×C8—44no—
590C2×C8C22×D414yes—
591C2×C8C22×D414yes—
592C4⋊C4—22no—
593C4⋊C4—22no—
594C4⋊C4—22no—
595C4⋊C4—22no—
596C4⋊C4—22no—
597C4⋊C4—22no—
598C4⋊C4—22no—
599C4⋊C4—22no—
600C4⋊C4—22no—
601C4⋊C4—22no—
602C4⋊C4—22no—
603C4⋊C4—22no—
604C4⋊C4—22no—
605C4⋊C4—22no—
606C4⋊C4—48no—
607C4⋊C4—42no—
608C4⋊C4—42no—
609C4⋊C4—42no—
610C4⋊C4—48no—
611C4⋊C4—42no—
612C4⋊C4—48no—
613C4⋊C4—42no—
614C4⋊C4—42no—
615C4⋊C4—42no—
616C22⋊C4—48no—
617C22⋊C4—48no—
618C22⋊C4—48no—
619C22⋊C4—48no—
620C22⋊C4—48no—
621C22⋊C4—48no—
622C22⋊C4—48no—
623C22⋊C4—48no—
624C22⋊C4—48no—
625C22⋊C4—48no—
626C22⋊C4—48no—
627C22⋊C4—48no—
628C42—48no—
629C42—48no—
630C23—28no—
631C23—22no—
632C23—28no—
633C23—22no—
634C23—28no—
635C23—28no—
636C23—28no—
637C23—28no—
638C23—22no—
639C23—22no—
640C23—232no—
641C23—28no—
642C23—22no—
643C23—22no—
644C23—22no—
645C23—28no—
646C23—22no—
647C23—22no—
648C23—28no—
649C23—28no—
650C23—28no—
651C23—28no—
652C23—22no—
653C23—22no—
654C23—22no—
655C23—22no—
656C23—22no—
657C23—22no—
658C23—22no—
659C23—416no—
660C23—416no—
661C23—416no—
662C23—416no—
663C23—416no—
664C23—4128no—
665C23—44no—
666C23—44no—
667C23—416no—
668C23—44no—
669C23—44no—
670C23—44no—
671C23—44no—
672C23—44no—
673C23—44no—
674C23#485116yescomplemented
675C23C2×#12114yes—
676C23C2×#12112yes—
677C23C2×#12314yes—
678C23C2×#12312yes—
679C23#53412yes—
680C23C2×#13514yes—
681C23C2×#13514yes—
682C23C2×#13512yes—
683C23C2×#13512yes—
684C23C2×#13714yes—
685C23C2×#13712yes—
686C23#57512yes—
687C23C23×D411yescharacteristic
688Q8—42no—
689Q8—42no—
690Q8—42no—
691Q8—42no—
692Q8—84no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—28no—
696C2×C4—28no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—216no—
700C2×C4—216no—
701C2×C4—24no—
702C2×C4—24no—
703C2×C4—24no—
704C2×C4—24no—
705C2×C4—24no—
706C2×C4—24no—
707C2×C4—24no—
708C2×C4—24no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—416no—
713C2×C4—416no—
714C2×C4—416no—
715C2×C4—44no—
716C2×C4—48no—
717C2×C4—42no—
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—84no—
746C2×C4—84no—
747C2×C4—84no—
748C2×C4—84no—
749C2×C4—84no—
750C2×C4—84no—
751C2×C4—84no—
752C2×C4—84no—
753C2×C4C2×#12114yes—
754C2×C4C2×#12112yes—
755C2×C4C2×#12314yes—
756C2×C4C2×#12312yes—
757C2×C4#53412yes—
758C2×C4#54614yes—
759C2×C4#54614yes—
760C2×C4#55114yes—
761C2×C4#55114yes—
762C2×C4C23×D411yescharacteristic
763C2×C4C22×#4111yescharacteristic
764C2×C4C22×#4111yescharacteristic
765C2×C4C22×#4111yescharacteristic
766C2×C4C2×H(5,𝔽2)11yescharacteristic
767C2×C4C2×H(5,𝔽2)11yescharacteristic
768C8—24no—
769C8—24no—
770C8—42no—
771C8—42no—
772C22—24no—
773C22—24no—
774C22—24no—
775C22—24no—
776C22—24no—
777C22—24no—
778C22—232no—
779C22—24no—
780C22—24no—
781C22—24no—
782C22—24no—
783C22—24no—
784C22—24no—
785C22—464no—
786C22—42no—
787C22—42no—
788C22—42no—
789C22—42no—
790C22—42no—
791C22—42no—
792C22—42no—
793C22—42no—
794C22—416no—
795C22—416no—
796C22#241214yes—
797C22#305014yes—
798C22#305614yes—
799C22C2×#48514yes—
800C22C2×#48518yescomplemented
801C22#309114yes—
802C22#319014yes—
803C22#319114yes—
804C22C22×#12111yescharacteristic
805C22C22×#12311yescharacteristic
806C22C2×#53411yescharacteristic
807C22C22×#13511yescharacteristic
808C22C22×#13511yescharacteristic
809C22C22×#13711yescharacteristic
810C22C2×#57511yescharacteristic
811C4—24no—
812C4—24no—
813C4—42no—
814C4—82no—
815C4—82no—
816C4—82no—
817C4—82no—
818C4—82no—
819C4—82no—
820C4—82no—
821C4—82no—
822C4#241214yes—
823C4C2×#54611yescharacteristic
824C4C2×#54611yescharacteristic
825C4C2×#55111yescharacteristic
826C4C2×#55111yescharacteristic
827C2—28no—
828C2—44no—
829C2—44no—
830C2#2455418yesdirect product factor
831C2C2×#241211yescharacteristic
832C2C2×#305011yescharacteristic
833C2C2×#305611yescharacteristic
834C2C22×#48511yescharacteristic
835C2C2×#309111yescharacteristic
836C2C2×#319011yescharacteristic
837C2C2×#319111yescharacteristic
subgroupG/H
center, socleC24C22×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC26D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24 ◁ C25×C4 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C22×#485C2semidirect
5. #24554C2direct (N × H)
6. C2×#2077C2semidirect
7. C2×#2075C2semidirect
8. C2×#2036C2semidirect
9. C2×#2035C2semidirect
10. C2×#1892C2semidirect
11. C2×#1892C2semidirect
12. C2×#1873C2semidirect
13. C2×#1854C2semidirect
14. C2×#1825C2semidirect
15. C2×#1808C2semidirect
16. C2×#1807C2semidirect
26. C2×#485C22semidirect
27. C22×#107C22semidirect
28. C22×#107C22semidirect
29. C22×#106C22semidirect
30. C22×#106C22semidirect
31. C22×#103C22semidirect
32. C22×#103C22semidirect
33. C22×#103C22semidirect
34. C22×#103C22semidirect
60. #2077C22semidirect
61. #2075C22semidirect
62. #2036C22semidirect
63. #2035C22semidirect
64. #1892C22semidirect
65. #1892C22semidirect
66. #1873C22semidirect
67. #1854C22semidirect
68. #1825C22semidirect
69. #1808C22semidirect
70. #1807C22semidirect
71. C2×#340C22semidirect
72. C2×#340C22semidirect
73. C2×#340C22semidirect
74. C2×#340C22semidirect
75. C2×#340C22semidirect
76. C2×#340C22semidirect
77. C2×#340C22semidirect
78. C2×#340C22semidirect
154. C2×#107C23semidirect
155. C2×#107C23semidirect
158. C2×#106C23semidirect
159. C2×#106C23semidirect
164. C2×#103C23semidirect
165. C2×#103C23semidirect
166. C2×#103C23semidirect
167. C2×#103C23semidirect
206. #340C23semidirect
207. #340C23semidirect
208. #340C23semidirect
209. #340C23semidirect
210. #340C23semidirect
211. #340C23semidirect
212. #340C23semidirect
213. #340C23semidirect
674. C23#485semidirect
800. C22C2×#485semidirect
830. C2#24554direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#4852
C23×C22⋊C82
C2×#28482
C2×#22802
#245542
C2×#20772
C2×#20752
C2×#20362
C2×#20352
C2×#18922
C2×#18732
C2×#18542
C2×#18252
C2×#18082
C2×#18072