Finite Group Databasebeta

← C2×#26243 #6444439

Subgroups — C2×#26243 #6444439

Order 512.

2626 conjugacy classes of subgroups.

The subgroup lattice has 804 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#485C211yesmaximal, characteristic, complemented
2C22×#482C211yesmaximal, characteristic, complemented
3C2×#2540C211yesmaximal, characteristic
4C2×#2354C211yesmaximal, characteristic, complemented
5#26243C2116yesmaximal, direct product factor
6C2×#2036C211yesmaximal, characteristic, complemented
7C2×#2036C211yesmaximal, characteristic, complemented
8C2×#2033C211yesmaximal, characteristic, complemented
9C2×#2033C211yesmaximal, characteristic, complemented
10C2×#1983C211yesmaximal, characteristic, complemented
11C2×#1959C211yesmaximal, characteristic, complemented
12C2×#1955C211yesmaximal, characteristic, complemented
13C2×#1947C211yesmaximal, characteristic, complemented
14C2×#1875C211yesmaximal, characteristic, complemented
15C2×#1873C211yesmaximal, characteristic, complemented
16C2×#1776C211yesmaximal, characteristic, complemented
17C22×#124C2211yescharacteristic
18C22×C22⋊Q8C2211yescharacteristic
19C22×C22⋊Q8C2211yescharacteristic
20C22×#121C2211yescharacteristic
21C22×#121C2211yescharacteristic
22C22×C4×D4C2211yescharacteristic
23C22×#117C2211yescharacteristic
24C22×#117C2211yescharacteristic
25C2×#485—28no—
26C2×#485C2218yescomplemented
27C2×#482—28no—
28C2×#482C2218yescomplemented
29C22×#107C2211yescharacteristic
30C22×#107C2211yescharacteristic
31C22×#107C2211yescharacteristic
32C22×#106C2211yescharacteristic
33C22×C4⋊C8C2211yescharacteristic
34C22×#103C2211yescharacteristic
35C22×#103C2211yescharacteristic
36C22×#103C2211yescharacteristic
37C22×#103C2211yescharacteristic
38C22×#102C2211yescharacteristic
39C22×#102C2211yescharacteristic
40C22×#102C2211yescharacteristic
41C22×#102C2211yescharacteristic
42C22×C22⋊C8C2211yescharacteristic
43C22×C22⋊C8C2211yescharacteristic
44C22×C22⋊C8C2211yescharacteristic
45C22×C22⋊C8C2211yescharacteristic
46C22×#97C2211yescharacteristic
47#2540—24no—
48#2540C2218yes—
49C2×#399—21no—
50C2×#392—21no—
51#2354—24no—
52#2354C2218yescomplemented
53C2×#390—21no—
54C2×#390—21no—
55C2×#390—21no—
56C2×#388—21no—
57C2×#388—21no—
58C2×#384C2211yescharacteristic
59C2×#380C2211yescharacteristic
60C2×#380C2211yescharacteristic
61C2×C4×C4⋊C4—21no—
62C2×C4×C4⋊C4C2211yescharacteristic
63C2×C4×C4⋊C4C2211yescharacteristic
64#2036C2218yescomplemented
65#2036C2218yescomplemented
66#2033C2218yescomplemented
67#2033C2218yescomplemented
68#1983C2218yescomplemented
69#1959C2218yescomplemented
70#1955C2218yescomplemented
71#1947C2218yescomplemented
72#1875C2218yescomplemented
73#1873C2218yescomplemented
74#1776C2218yescomplemented
75C2×#340C2211yescharacteristic
76C2×#340C2211yescharacteristic
77C2×#340C2211yescharacteristic
78C2×#340C2211yescharacteristic
79C23×Q8C2311yescharacteristic
80C23×D4—21no—
81C23×D4—21no—
82C23×D4D411yescharacteristic
83C23×D4C2311yescharacteristic
84C24×C4C2311yescharacteristic
85C24×C4C2311yescharacteristic
86C23×C8C2311yescharacteristic
87C23×C8C2311yescharacteristic
88C23×C8C2311yescharacteristic
89C23×C8C2311yescharacteristic
90C2×#124—22no—
91C2×#124—24no—
92C2×#124—24no—
93C2×#124C2314yes—
94C2×C22⋊Q8—22no—
95C2×C22⋊Q8—22no—
96C2×C22⋊Q8—24no—
97C2×C22⋊Q8—24no—
98C2×C22⋊Q8—42no—
99C2×C22⋊Q8—42no—
100C2×C22⋊Q8C2314yes—
101C2×C22⋊Q8C2314yes—
102C2×#121—22no—
103C2×#121—22no—
104C2×#121—24no—
105C2×#121—24no—
106C2×#121—42no—
107C2×#121—42no—
108C2×#121C2314yes—
109C2×#121C2314yes—
110C2×C4×D4—24no—
111C2×C4×D4—24no—
112C2×C4×D4D414yes—
113C2×C4×D4C2314yes—
114C2×#117—22no—
115C2×#117—22no—
116C2×#117—24no—
117C2×#117—24no—
118C2×#117—42no—
119C2×#117—42no—
120C2×#117C2314yes—
121C2×#117C2314yes—
122C22×C4⋊C4—21no—
123C22×C4⋊C4—21no—
124C22×C4⋊C4—21no—
125C22×C4⋊C4—21no—
126C22×C4⋊C4D411yescharacteristic
127C22×C4⋊C4C2311yescharacteristic
128C22×C4⋊C4C2311yescharacteristic
129C22×C4⋊C4C2311yescharacteristic
130C22×C4⋊C4C2311yescharacteristic
131C22×C4⋊C4C2311yescharacteristic
132C22×C4⋊C4C2311yescharacteristic
133C22×C22⋊C4—21no—
134C22×C22⋊C4—21no—
135C22×C22⋊C4—21no—
136C22×C22⋊C4—21no—
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⋊C4D411yescharacteristic
144C22×C22⋊C4D411yescharacteristic
145C22×C42—21no—
146C22×C42—21no—
147C22×C42—21no—
148C22×C42—21no—
149C22×C42C2311yescharacteristic
150#485—232no—
151#482—232no—
152C2×#107—24no—
153C2×#107—24no—
154C2×#107—24no—
155C2×#107C2314yes—
156C2×#107C2314yes—
157C2×#107C2314yes—
158C2×#106D418yescomplemented
159C2×#106C2314yes—
160C2×C4⋊C8—24no—
161C2×C4⋊C8C2314yes—
162C2×#103—24no—
163C2×#103—24no—
164C2×#103—42no—
165C2×#103—42no—
166C2×#103C2314yes—
167C2×#103C2314yes—
168C2×#103C2314yes—
169C2×#103C2314yes—
170C2×#102—24no—
171C2×#102—24no—
172C2×#102—42no—
173C2×#102—42no—
174C2×#102C2314yes—
175C2×#102C2314yes—
176C2×#102C2314yes—
177C2×#102C2314yes—
178C2×C22⋊C8—24no—
179C2×C22⋊C8—24no—
180C2×C22⋊C8—42no—
181C2×C22⋊C8—42no—
182C2×C22⋊C8C2314yes—
183C2×C22⋊C8C2314yes—
184C2×C22⋊C8C2314yes—
185C2×C22⋊C8C2314yes—
186C2×#97—24no—
187C2×#97C2314yes—
188#399—28no—
189#392—28no—
190#390—28no—
191#390—28no—
192#390—28no—
193#388—28no—
194#388—28no—
195#384—22no—
196#384C2314yes—
197#380—22no—
198#380—22no—
199#380C2314yes—
200#380C2314yes—
201C4×C4⋊C4—28no—
202C4×C4⋊C4—22no—
203C4×C4⋊C4—22no—
204C4×C4⋊C4C2314yes—
205C4×C4⋊C4C2314yes—
206C2×#95—21no—
207C2×#95—21no—
208C2×#95—21no—
209C2×#95—21no—
210#340C2314yes—
211#340C2314yes—
212#340C2314yes—
213#340C2314yes—
214C25—21no—
215C25C2×D411yescharacteristic
216C25C2×D411yescharacteristic
217C22×Q8—21no—
218C22×Q8—22no—
219C22×Q8—22no—
220C22×Q8—22no—
221C22×Q8—22no—
222C22×Q8—22no—
223C22×Q8—22no—
224C22×Q8C2412yes—
225C22×D4—24no—
226C22×D4—24no—
227C22×D4—24no—
228C22×D4—22no—
229C22×D4—21no—
230C22×D4—22no—
231C22×D4—22no—
232C22×D4—22no—
233C22×D4—22no—
234C22×D4—22no—
235C22×D4—42no—
236C22×D4—42no—
237C22×D4—44no—
238C22×D4—44no—
239C22×D4—44no—
240C22×D4—44no—
241C22×D4—82no—
242C22×D4—82no—
243C22×D4C2×D414yes—
244C22×D4C2412yes—
245C23×C4—21no—
246C23×C4—21no—
247C23×C4—21no—
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—21no—
261C23×C4—21no—
262C23×C4—21no—
263C23×C4—21no—
264C23×C4C2×D412yes—
265C23×C4C2×D412yes—
266C23×C4C2×D411yescharacteristic
267C23×C4C2×D411yescharacteristic
268C23×C4C2×D411yescharacteristic
269C23×C4C2×D411yescharacteristic
270C23×C4C2412yes—
271C23×C4C2412yes—
272C23×C4C2411yescharacteristic
273C22×C8—22no—
274C22×C8—22no—
275C22×C8—22no—
276C22×C8—22no—
277C22×C8—22no—
278C22×C8—22no—
279C22×C8—22no—
280C22×C8—22no—
281C22×C8—22no—
282C22×C8—22no—
283C22×C8—22no—
284C22×C8C2×D414yes—
285C22×C8C2412yes—
286C22×C8C2412yes—
287C22×C8C2412yes—
288C22×C8C2412yes—
289#124—28no—
290#124—28no—
291#124—48no—
292C22⋊Q8—28no—
293C22⋊Q8—28no—
294C22⋊Q8—44no—
295C22⋊Q8—44no—
296C22⋊Q8—48no—
297C22⋊Q8—48no—
298#121—28no—
299#121—28no—
300#121—44no—
301#121—44no—
302#121—48no—
303#121—48no—
304C4×D4—216no—
305C4×D4—28no—
306C4×D4—28no—
307#117—28no—
308#117—28no—
309#117—44no—
310#117—44no—
311#117—48no—
312#117—48no—
313C2×C4⋊C4—24no—
314C2×C4⋊C4—21no—
315C2×C4⋊C4—21no—
316C2×C4⋊C4—21no—
317C2×C4⋊C4—22no—
318C2×C4⋊C4—22no—
319C2×C4⋊C4—22no—
320C2×C4⋊C4—22no—
321C2×C4⋊C4—22no—
322C2×C4⋊C4—22no—
323C2×C4⋊C4—22no—
324C2×C4⋊C4—22no—
325C2×C4⋊C4—22no—
326C2×C4⋊C4—24no—
327C2×C4⋊C4—24no—
328C2×C4⋊C4—24no—
329C2×C4⋊C4—21no—
330C2×C4⋊C4—21no—
331C2×C4⋊C4—21no—
332C2×C4⋊C4—24no—
333C2×C4⋊C4—44no—
334C2×C4⋊C4—44no—
335C2×C4⋊C4—44no—
336C2×C4⋊C4—82no—
337C2×C4⋊C4C2×D414yes—
338C2×C4⋊C4C2×D414yes—
339C2×C4⋊C4C2×D414yes—
340C2×C4⋊C4#4114yes—
341C2×C4⋊C4C2412yes—
342C2×C4⋊C4C2412yes—
343C2×C4⋊C4C2412yes—
344C2×C4⋊C4C2412yes—
345C2×C4⋊C4C2412yes—
346C2×C4⋊C4C2412yes—
347C2×C22⋊C4—24no—
348C2×C22⋊C4—24no—
349C2×C22⋊C4—24no—
350C2×C22⋊C4—24no—
351C2×C22⋊C4—24no—
352C2×C22⋊C4—24no—
353C2×C22⋊C4—24no—
354C2×C22⋊C4—24no—
355C2×C22⋊C4—24no—
356C2×C22⋊C4—24no—
357C2×C22⋊C4—24no—
358C2×C22⋊C4—24no—
359C2×C22⋊C4—44no—
360C2×C22⋊C4—44no—
361C2×C22⋊C4—44no—
362C2×C22⋊C4—44no—
363C2×C22⋊C4—44no—
364C2×C22⋊C4—44no—
365C2×C22⋊C4—44no—
366C2×C22⋊C4—44no—
367C2×C22⋊C4—82no—
368C2×C22⋊C4—82no—
369C2×C22⋊C4C2×D414yes—
370C2×C22⋊C4C2×D414yes—
371C2×C42—24no—
372C2×C42—24no—
373C2×C42—24no—
374C2×C42—24no—
375C2×C42—44no—
376C2×C42—44no—
377C2×C42—44no—
378C2×C42—82no—
379C2×C42C2×D412yes—
380C2×C42#4114yes—
381C2×C42#4114yes—
382C2×C42C2412yes—
383#107—28no—
384#107—28no—
385#107—28no—
386#106C2×D4116yescomplemented
387C4⋊C8—28no—
388#103—28no—
389#103—28no—
390#103—44no—
391#103—44no—
392#102—28no—
393#102—28no—
394#102—44no—
395#102—44no—
396C22⋊C8—28no—
397C22⋊C8—28no—
398C22⋊C8—44no—
399C22⋊C8—44no—
400#97—28no—
401#95—24no—
402#95—24no—
403#95—24no—
404#95—24no—
405C24—22no—
406C24—22no—
407C24—22no—
408C24—22no—
409C24—22no—
410C24—22no—
411C24—22no—
412C24—22no—
413C24—22no—
414C24—22no—
415C24—22no—
416C24—22no—
417C24—22no—
418C24—22no—
419C24—22no—
420C24—42no—
421C24—42no—
422C24—42no—
423C24—42no—
424C24—42no—
425C24—42no—
426C24—42no—
427C24C22×D412yes—
428C24C22×D412yes—
429C24C22×D411yescharacteristic
430C2×Q8—22no—
431C2×Q8—22no—
432C2×Q8—22no—
433C2×Q8—22no—
434C2×Q8—22no—
435C2×Q8—22no—
436C2×Q8—42no—
437C2×Q8—42no—
438C2×Q8—42no—
439C2×Q8—44no—
440C2×Q8—44no—
441C2×Q8—44no—
442C2×Q8—44no—
443C2×D4—28no—
444C2×D4—22no—
445C2×D4—22no—
446C2×D4—22no—
447C2×D4—22no—
448C2×D4—22no—
449C2×D4—22no—
450C2×D4—44no—
451C2×D4—44no—
452C2×D4—416no—
453C2×D4—48no—
454C2×D4—48no—
455C2×D4—48no—
456C2×D4—48no—
457C2×D4—42no—
458C2×D4—44no—
459C2×D4—44no—
460C2×D4—42no—
461C2×D4—42no—
462C2×D4—44no—
463C2×D4—44no—
464C2×D4—84no—
465C2×D4—84no—
466C2×D4—816no—
467C2×D4—816no—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—24no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—24no—
478C22×C4—24no—
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—22no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—42no—
507C22×C4—42no—
508C22×C4—42no—
509C22×C4—42no—
510C22×C4—42no—
511C22×C4—42no—
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—42no—
521C22×C4—42no—
522C22×C4—42no—
523C22×C4—42no—
524C22×C4—42no—
525C22×C4—42no—
526C22×C4—42no—
527C22×C4—42no—
528C22×C4—42no—
529C22×C4—42no—
530C22×C4—42no—
531C22×C4—42no—
532C22×C4#12314yes—
533C22×C4#12314yes—
534C22×C4C22×D412yes—
535C22×C4C22×D412yes—
536C22×C4C22×D412yes—
537C22×C4C22×D412yes—
538C22×C4C22×D411yescharacteristic
539C22×C4C22×D412yes—
540C22×C4C2×#4112yes—
541C22×C4C2×#4112yes—
542C22×C4C2×#4112yes—
543C22×C4H(5,𝔽2)12yes—
544C22×C4H(5,𝔽2)12yes—
545C22×C4C2511yescharacteristic
546C2×C8—28no—
547C2×C8—22no—
548C2×C8—22no—
549C2×C8—22no—
550C2×C8—22no—
551C2×C8—22no—
552C2×C8—22no—
553C2×C8—22no—
554C2×C8—22no—
555C2×C8—22no—
556C2×C8—22no—
557C2×C8—22no—
558C2×C8—44no—
559C2×C8—44no—
560C2×C8—44no—
561C2×C8C22×D414yes—
562C4⋊C4—28no—
563C4⋊C4—24no—
564C4⋊C4—24no—
565C4⋊C4—24no—
566C4⋊C4—22no—
567C4⋊C4—22no—
568C4⋊C4—22no—
569C4⋊C4—22no—
570C4⋊C4—22no—
571C4⋊C4—22no—
572C4⋊C4—22no—
573C4⋊C4—22no—
574C4⋊C4—22no—
575C4⋊C4—48no—
576C4⋊C4—48no—
577C4⋊C4—48no—
578C4⋊C4—42no—
579C4⋊C4—42no—
580C4⋊C4—42no—
581C4⋊C4—84no—
582C4⋊C4C22×D414yes—
583C4⋊C4C22×D414yes—
584C4⋊C4C2×#4114yes—
585C22⋊C4—28no—
586C22⋊C4—28no—
587C22⋊C4—48no—
588C22⋊C4—48no—
589C22⋊C4—48no—
590C22⋊C4—48no—
591C22⋊C4—48no—
592C22⋊C4—48no—
593C22⋊C4—48no—
594C22⋊C4—48no—
595C22⋊C4—84no—
596C22⋊C4—84no—
597C42—48no—
598C42—48no—
599C42—48no—
600C42—84no—
601C42#12318yes—
602C42C2×#4114yes—
603C42C2×#4114yes—
604C23—22no—
605C23—22no—
606C23—22no—
607C23—22no—
608C23—22no—
609C23—22no—
610C23—22no—
611C23—22no—
612C23—22no—
613C23—22no—
614C23—22no—
615C23—22no—
616C23—22no—
617C23—22no—
618C23—44no—
619C23—44no—
620C23—44no—
621C23—44no—
622C23—44no—
623C23—44no—
624C23—44no—
625C23—44no—
626C23—44no—
627C23—44no—
628C23—44no—
629C23—44no—
630C23—44no—
631C23—44no—
632C23—42no—
633C23—42no—
634C23—42no—
635C23—42no—
636C23—42no—
637C23—42no—
638C23—42no—
639C23—84no—
640C23—84no—
641C23—84no—
642C23—84no—
643C23—84no—
644C23—84no—
645C23—84no—
646C23C2×#12312yes—
647C23D4212yes—
648C23#54612yes—
649C23#57512yes—
650C23#57512yes—
651C23#57612yes—
652C23#57812yes—
653C23C23×D411yescharacteristic
654Q8—42no—
655Q8—42no—
656Q8—42no—
657Q8—42no—
658Q8—84no—
659D4—416no—
660D4—42no—
661D4—42no—
662D4—42no—
663D4—42no—
664D4—816no—
665D4—816no—
666D4—84no—
667C2×C4—28no—
668C2×C4—28no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—24no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—24no—
679C2×C4—24no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—44no—
683C2×C4—44no—
684C2×C4—48no—
685C2×C4—48no—
686C2×C4—48no—
687C2×C4—42no—
688C2×C4—42no—
689C2×C4—42no—
690C2×C4—42no—
691C2×C4—42no—
692C2×C4—42no—
693C2×C4—42no—
694C2×C4—42no—
695C2×C4—42no—
696C2×C4—42no—
697C2×C4—42no—
698C2×C4—42no—
699C2×C4—48no—
700C2×C4—48no—
701C2×C4—42no—
702C2×C4—42no—
703C2×C4—42no—
704C2×C4—42no—
705C2×C4—42no—
706C2×C4—42no—
707C2×C4—42no—
708C2×C4—42no—
709C2×C4—42no—
710C2×C4—42no—
711C2×C4—42no—
712C2×C4—42no—
713C2×C4—42no—
714C2×C4—42no—
715C2×C4—84no—
716C2×C4—84no—
717C2×C4—84no—
718C2×C4—84no—
719C2×C4C2×#12314yes—
720C2×C4C2×#12314yes—
721C2×C4C2×#12312yes—
722C2×C4#53214yes—
723C2×C4#54014yes—
724C2×C4D4212yes—
725C2×C4#54612yes—
726C2×C4#55014yes—
727C2×C4#55914yes—
728C2×C4C23×D411yescharacteristic
729C2×C4C22×#4111yescharacteristic
730C2×C4C22×#4111yescharacteristic
731C2×C4C22×#4111yescharacteristic
732C2×C4C2×H(5,𝔽2)11yescharacteristic
733C2×C4C2×H(5,𝔽2)11yescharacteristic
734C8—24no—
735C8—42no—
736C8—42no—
737C8—42no—
738C22—42no—
739C22—42no—
740C22—42no—
741C22—42no—
742C22—42no—
743C22—42no—
744C22—42no—
745C22—42no—
746C22—42no—
747C22—42no—
748C22—42no—
749C22—42no—
750C22—42no—
751C22—42no—
752C22—88no—
753C22—88no—
754C22—82no—
755C22—82no—
756C22—82no—
757C22—82no—
758C22—82no—
759C22—82no—
760C22—82no—
761C22—168no—
762C22#244514yes—
763C22#309314yes—
764C22#309814yes—
765C22#326814yes—
766C22#326914yes—
767C22#331314yes—
768C22#331914yes—
769C22C22×#12311yescharacteristic
770C22C2×D4211yescharacteristic
771C22C2×#54611yescharacteristic
772C22C2×#57511yescharacteristic
773C22C2×#57511yescharacteristic
774C22C2×#57611yescharacteristic
775C22C2×#57811yescharacteristic
776C4—24no—
777C4—24no—
778C4—44no—
779C4—44no—
780C4—42no—
781C4—42no—
782C4—44no—
783C4—82no—
784C4—82no—
785C4—82no—
786C4—82no—
787C4#244514yes—
788C4C2×#53211yescharacteristic
789C4C2×#54011yescharacteristic
790C4C2×#55011yescharacteristic
791C4C2×#55911yescharacteristic
792C2—82no—
793C2—82no—
794C2—162no—
795C2#2624318yesdirect product factor
796C2C2×#244511yescharacteristic
797C2C2×#309311yescharacteristic
798C2C2×#309811yescharacteristic
799C2C2×#326811yescharacteristic
800C2C2×#326911yescharacteristic
801C2C2×#331911yescharacteristic
802C2C2×#331311yescharacteristic
subgroupG/H
center, socleC24C22×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#2540C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24 ◁ C22×C4×D4 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C22×#485C2semidirect
2. C22×#482C2semidirect
4. C2×#2354C2semidirect
5. #26243C2direct (N × H)
6. C2×#2036C2semidirect
7. C2×#2036C2semidirect
8. C2×#2033C2semidirect
9. C2×#2033C2semidirect
10. C2×#1983C2semidirect
11. C2×#1959C2semidirect
12. C2×#1955C2semidirect
13. C2×#1947C2semidirect
14. C2×#1875C2semidirect
15. C2×#1873C2semidirect
16. C2×#1776C2semidirect
26. C2×#485C22semidirect
28. C2×#482C22semidirect
52. #2354C22semidirect
64. #2036C22semidirect
65. #2036C22semidirect
66. #2033C22semidirect
67. #2033C22semidirect
68. #1983C22semidirect
69. #1959C22semidirect
70. #1955C22semidirect
71. #1947C22semidirect
72. #1875C22semidirect
73. #1873C22semidirect
74. #1776C22semidirect
158. C2×#106D4semidirect
386. #106C2×D4semidirect
795. C2#26243direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#4852
C22×#4822
C2×#25402
C2×#23542
#262432
C2×#20362
C2×#20332
C2×#19832
C2×#19592
C2×#19552
C2×#19472
C2×#18752
C2×#18732
C2×#17762