Finite Group Databasebeta

← C2×#25636 #6449199

Subgroups — C2×#25636 #6449199

Order 512.

3670 conjugacy classes of subgroups.

The subgroup lattice has 838 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#556C211yesmaximal, characteristic, complemented
2C22×#495C211yesmaximal, characteristic
3C22×#464C211yesmaximal, characteristic, complemented
4C2×#2592C211yesmaximal, characteristic, complemented
5#25636C2116yesmaximal, direct product factor
6C2×#2016C211yesmaximal, characteristic, complemented
7C2×#2013C211yesmaximal, characteristic, complemented
8C2×#2015C211yesmaximal, characteristic, complemented
9C2×#2012C211yesmaximal, characteristic
10C2×#1984C211yesmaximal, characteristic, complemented
11C2×#1983C211yesmaximal, characteristic, complemented
12C2×#1880C211yesmaximal, characteristic, complemented
13C2×#1878C211yesmaximal, characteristic, complemented
14C2×#1879C211yesmaximal, characteristic
15C2×#1877C211yesmaximal, characteristic, complemented
16C2×C4×#103C211yesmaximal, characteristic, complemented
17C23×Q16C2211yescharacteristic
18C23×Q16C2211yescharacteristic
19C23×SD16C2211yescharacteristic
20C23×SD16C2211yescharacteristic
21C23×SD16C2211yescharacteristic
22C23×D8C2211yescharacteristic
23C2×#556—28no—
24C2×#556—28no—
25C2×#556—24no—
26C2×#556C2218yescomplemented
27C22×C4⋊Q8C2211yescharacteristic
28C22×#126—21no—
29C22×#126—21no—
30C22×#124C2211yescharacteristic
31C22×#124C2211yescharacteristic
32C22×#124C2211yescharacteristic
33C22×C22⋊Q8—21no—
34C22×C4×Q8C2211yescharacteristic
35C22×C4×Q8C2211yescharacteristic
36C22×C4×Q8C2211yescharacteristic
37C22×C4×D4C2211yescharacteristic
38C22×#117—21no—
39C2×#495—28no—
40C2×#495C2218yes—
41C2×#464—28no—
42C2×#464C2218yescomplemented
43C22×C4⋊C8C2211yescharacteristic
44C22×#103C2211yescharacteristic
45C22×#103C2211yescharacteristic
46C22×#103C2211yescharacteristic
47C22×#103C2211yescharacteristic
48C22×#103C2211yescharacteristic
49C22×#102C2211yescharacteristic
50C22×#102C2211yescharacteristic
51C22×#102C2211yescharacteristic
52C22×C4×C8C2211yescharacteristic
53#2592—24no—
54#2592C2218yescomplemented
55C2×#397—21no—
56C2×#393—21no—
57C2×#391C2211yescharacteristic
58C2×#391C2211yescharacteristic
59C2×#390C2211yescharacteristic
60C2×#390C2211yescharacteristic
61C2×#388—21no—
62C2×#388—21no—
63C2×C4×C4⋊C4C2211yescharacteristic
64#2016C2218yescomplemented
65#2015C2218yescomplemented
66#2013C2218yescomplemented
67#2012C2218yes—
68#1984C2218yescomplemented
69#1983C2218yescomplemented
70#1880C2218yescomplemented
71#1879C2218yes—
72#1878C2218yescomplemented
73#1877C2218yescomplemented
74C4×#103C2218yescomplemented
75C2×#340C2211yescharacteristic
76C2×#340C2211yescharacteristic
77C2×#336C2211yescharacteristic
78C2×#336C2211yescharacteristic
79C2×#336C2211yescharacteristic
80C2×#336C2211yescharacteristic
81C23×Q8D411yescharacteristic
82C23×Q8C2311yescharacteristic
83C23×Q8C2311yescharacteristic
84C23×Q8C2311yescharacteristic
85C23×D4C2311yescharacteristic
86C23×D4C2311yescharacteristic
87C24×C4—21no—
88C22×Q16—24no—
89C22×Q16—24no—
90C22×Q16—24no—
91C22×Q16—42no—
92C22×Q16—42no—
93C22×Q16—42no—
94C22×Q16C2314yes—
95C22×Q16C2314yes—
96C22×SD16—24no—
97C22×SD16—24no—
98C22×SD16—24no—
99C22×SD16—24no—
100C22×SD16—24no—
101C22×SD16—42no—
102C22×SD16—42no—
103C22×SD16—42no—
104C22×SD16—42no—
105C22×SD16C2314yes—
106C22×SD16C2314yes—
107C22×SD16C2314yes—
108C22×D8—24no—
109C22×D8—24no—
110C22×D8—42no—
111C22×D8C2314yes—
112C23×C8C2311yescharacteristic
113C23×C8C2311yescharacteristic
114C23×C8C2311yescharacteristic
115C23×C8C2311yescharacteristic
116#556—264no—
117#556—232no—
118#556—232no—
119C2×C4⋊Q8—24no—
120C2×C4⋊Q8—24no—
121C2×C4⋊Q8—22no—
122C2×C4⋊Q8C2314yes—
123C2×#126—216no—
124C2×#126—216no—
125C2×#126—28no—
126C2×#126—28no—
127C2×#124—24no—
128C2×#124—24no—
129C2×#124—22no—
130C2×#124—22no—
131C2×#124—24no—
132C2×#124—22no—
133C2×#124—24no—
134C2×#124—24no—
135C2×#124D418yes—
136C2×#124C2314yes—
137C2×#124C2314yes—
138C2×#124C2314yes—
139C2×C22⋊Q8—216no—
140C2×C22⋊Q8—28no—
141C2×C4×Q8—24no—
142C2×C4×Q8—24no—
143C2×C4×Q8—24no—
144C2×C4×Q8—22no—
145C2×C4×Q8—22no—
146C2×C4×Q8—24no—
147C2×C4×Q8—24no—
148C2×C4×Q8D418yes—
149C2×C4×Q8D414yes—
150C2×C4×Q8C2314yes—
151C2×C4×Q8C2314yes—
152C2×C4×Q8C2314yes—
153C2×C4×D4—24no—
154C2×C4×D4—24no—
155C2×C4×D4—22no—
156C2×C4×D4C2314yes—
157C2×#117—216no—
158C2×#117—28no—
159C22×C4⋊C4—21no—
160C22×C4⋊C4—21no—
161C22×C4⋊C4—21no—
162C22×C4⋊C4—21no—
163C22×C4⋊C4D411yescharacteristic
164C22×C4⋊C4D411yescharacteristic
165C22×C4⋊C4D411yescharacteristic
166C22×C4⋊C4C2311yescharacteristic
167C22×C4⋊C4C2311yescharacteristic
168C22×C4⋊C4C2311yescharacteristic
169C22×C22⋊C4—21no—
170C22×C22⋊C4—21no—
171C22×C22⋊C4—21no—
172C22×C22⋊C4—21no—
173C22×C22⋊C4—21no—
174C22×C22⋊C4—21no—
175C22×C22⋊C4—21no—
176C22×C22⋊C4—21no—
177C22×C22⋊C4—21no—
178C22×C22⋊C4—21no—
179C22×C22⋊C4—21no—
180C22×C42—21no—
181C22×C42—21no—
182C22×C42—21no—
183C22×C42C2311yescharacteristic
184C22×C42C2311yescharacteristic
185C22×C42C2311yescharacteristic
186#495—232no—
187#464—232no—
188C2×C4⋊C8—24no—
189C2×C4⋊C8C2314yes—
190C2×#103—24no—
191C2×#103—24no—
192C2×#103—24no—
193C2×#103—42no—
194C2×#103—42no—
195C2×#103C2314yes—
196C2×#103C2314yes—
197C2×#103C2314yes—
198C2×#103C2314yes—
199C2×#103C2314yes—
200C2×#102—24no—
201C2×#102—42no—
202C2×#102—42no—
203C2×#102C2314yes—
204C2×#102C2314yes—
205C2×#102C2314yes—
206C2×C4×C8—24no—
207C2×C4×C8C2314yes—
208#397—28no—
209#393—28no—
210#391—22no—
211#391—22no—
212#391C2314yes—
213#391C2314yes—
214#390—22no—
215#390—22no—
216#390C2314yes—
217#390C2314yes—
218#388—28no—
219#388—28no—
220C4×C4⋊C4—22no—
221C4×C4⋊C4C2314yes—
222C2×#95—21no—
223C2×#95—21no—
224C2×#95—21no—
225C2×#95—21no—
226C2×#95—21no—
227#340C2314yes—
228#340C2314yes—
229#336C2314yes—
230#336C2314yes—
231#336C2314yes—
232#336C2314yes—
233C25—21no—
234C25—21no—
235C22×Q8—24no—
236C22×Q8—24no—
237C22×Q8—22no—
238C22×Q8—22no—
239C22×Q8—21no—
240C22×Q8—21no—
241C22×Q8—21no—
242C22×Q8—22no—
243C22×Q8—22no—
244C22×Q8—22no—
245C22×Q8—22no—
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—42no—
257C22×Q8C2×D414yes—
258C22×Q8C2×D414yes—
259C22×Q8C2×D414yes—
260C22×Q8C2412yes—
261C22×Q8C2412yes—
262C22×Q8C2412yes—
263C22×D4—21no—
264C22×D4—22no—
265C22×D4—22no—
266C22×D4—22no—
267C22×D4—21no—
268C22×D4—22no—
269C22×D4—22no—
270C22×D4—22no—
271C22×D4—22no—
272C22×D4—22no—
273C22×D4—22no—
274C22×D4—22no—
275C22×D4—22no—
276C22×D4C2×D414yes—
277C22×D4C2412yes—
278C22×D4C2412yes—
279C23×C4—28no—
280C23×C4—21no—
281C23×C4—21no—
282C23×C4—21no—
283C23×C4—24no—
284C23×C4—21no—
285C23×C4—21no—
286C23×C4—21no—
287C23×C4—44no—
288C23×C4—44no—
289C23×C4C2×D411yescharacteristic
290C23×C4C2×D411yescharacteristic
291C23×C4C2×D411yescharacteristic
292C23×C4C2×D411yescharacteristic
293C23×C4C2×D411yescharacteristic
294C23×C4C2×D411yescharacteristic
295C23×C4C2411yescharacteristic
296C2×Q16—28no—
297C2×Q16—28no—
298C2×Q16—28no—
299C2×Q16—44no—
300C2×Q16—44no—
301C2×Q16—44no—
302C2×Q16—416no—
303C2×Q16—416no—
304C2×SD16—28no—
305C2×SD16—28no—
306C2×SD16—28no—
307C2×SD16—28no—
308C2×SD16—28no—
309C2×SD16—44no—
310C2×SD16—44no—
311C2×SD16—44no—
312C2×SD16—44no—
313C2×SD16—416no—
314C2×SD16—416no—
315C2×SD16—416no—
316C2×D8—28no—
317C2×D8—28no—
318C2×D8—44no—
319C2×D8—416no—
320C22×C8—22no—
321C22×C8—22no—
322C22×C8—22no—
323C22×C8—22no—
324C22×C8—22no—
325C22×C8—22no—
326C22×C8—22no—
327C22×C8—22no—
328C22×C8—22no—
329C22×C8—22no—
330C22×C8#4114yes—
331C22×C8#4114yes—
332C22×C8C2412yes—
333C22×C8C2412yes—
334C22×C8C2412yes—
335C22×C8C2412yes—
336C4⋊Q8—216no—
337C4⋊Q8—28no—
338C4⋊Q8—28no—
339#126—264no—
340#126—264no—
341#124—216no—
342#124—28no—
343#124—28no—
344#124—216no—
345#124—28no—
346#124—28no—
347#124—28no—
348#124—48no—
349#124C2×D4116yes—
350C22⋊Q8—264no—
351C4×Q8—216no—
352C4×Q8—28no—
353C4×Q8—28no—
354C4×Q8—216no—
355C4×Q8—216no—
356C4×Q8—28no—
357C4×Q8—28no—
358C4×Q8—28no—
359C4×Q8C2×D4116yes—
360C4×D4—216no—
361C4×D4—28no—
362C4×D4—28no—
363#117—264no—
364C2×C4⋊C4—28no—
365C2×C4⋊C4—28no—
366C2×C4⋊C4—28no—
367C2×C4⋊C4—28no—
368C2×C4⋊C4—24no—
369C2×C4⋊C4—24no—
370C2×C4⋊C4—24no—
371C2×C4⋊C4—24no—
372C2×C4⋊C4—24no—
373C2×C4⋊C4—24no—
374C2×C4⋊C4—24no—
375C2×C4⋊C4—21no—
376C2×C4⋊C4—22no—
377C2×C4⋊C4—22no—
378C2×C4⋊C4—22no—
379C2×C4⋊C4—22no—
380C2×C4⋊C4—22no—
381C2×C4⋊C4—21no—
382C2×C4⋊C4—21no—
383C2×C4⋊C4C2×D414yes—
384C2×C4⋊C4C2×D414yes—
385C2×C4⋊C4C2×D414yes—
386C2×C4⋊C4C2×D414yes—
387C2×C4⋊C4C2412yes—
388C2×C4⋊C4C2412yes—
389C2×C4⋊C4C2412yes—
390C2×C22⋊C4—28no—
391C2×C22⋊C4—28no—
392C2×C22⋊C4—28no—
393C2×C22⋊C4—28no—
394C2×C22⋊C4—28no—
395C2×C22⋊C4—24no—
396C2×C22⋊C4—24no—
397C2×C22⋊C4—24no—
398C2×C22⋊C4—24no—
399C2×C22⋊C4—24no—
400C2×C22⋊C4—24no—
401C2×C22⋊C4—24no—
402C2×C22⋊C4—24no—
403C2×C22⋊C4—24no—
404C2×C22⋊C4—24no—
405C2×C22⋊C4—24no—
406C2×C22⋊C4—44no—
407C2×C22⋊C4—44no—
408C2×C22⋊C4—44no—
409C2×C22⋊C4—44no—
410C2×C22⋊C4—82no—
411C2×C22⋊C4—82no—
412C2×C42—28no—
413C2×C42—28no—
414C2×C42—24no—
415C2×C42—24no—
416C2×C42—22no—
417C2×C42—22no—
418C2×C42—22no—
419C2×C42—22no—
420C2×C42—24no—
421C2×C42—82no—
422C2×C42C2×D412yes—
423C2×C42C2×D412yes—
424C2×C42C2×D412yes—
425C2×C42C2×D414yes—
426C2×C42C2×D414yes—
427C2×C42C2412yes—
428C2×C42C2412yes—
429C2×C42C2412yes—
430C4⋊C8—28no—
431#103—28no—
432#103—28no—
433#103—28no—
434#103—44no—
435#103—44no—
436#102—28no—
437#102—44no—
438#102—44no—
439C4×C8—28no—
440#95—24no—
441#95—24no—
442#95—24no—
443#95—24no—
444#95—24no—
445C24—24no—
446C24—22no—
447C24—22no—
448C24—42no—
449C24—42no—
450C24—42no—
451C24—42no—
452C24—42no—
453C24—42no—
454C24—42no—
455C24—42no—
456C24—42no—
457C24—42no—
458C24—42no—
459C24—42no—
460C24—42no—
461C24C22×D411yescharacteristic
462C2×Q8—28no—
463C2×Q8—24no—
464C2×Q8—24no—
465C2×Q8—28no—
466C2×Q8—22no—
467C2×Q8—22no—
468C2×Q8—28no—
469C2×Q8—28no—
470C2×Q8—28no—
471C2×Q8—28no—
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—22no—
481C2×Q8—22no—
482C2×Q8—22no—
483C2×Q8—22no—
484C2×Q8—22no—
485C2×Q8—22no—
486C2×Q8—44no—
487C2×Q8—416no—
488C2×Q8—42no—
489C2×Q8—44no—
490C2×Q8—44no—
491C2×Q8—44no—
492C2×Q8—44no—
493C2×Q8—42no—
494C2×Q8—42no—
495C2×Q8—42no—
496C2×Q8—42no—
497C2×Q8—42no—
498C2×Q8—42no—
499C2×Q8—44no—
500C2×Q8—44no—
501C2×Q8—44no—
502C2×Q8—44no—
503C2×Q8C22×D414yes—
504C2×Q8C22×D414yes—
505C2×D4—24no—
506C2×D4—28no—
507C2×D4—28no—
508C2×D4—22no—
509C2×D4—22no—
510C2×D4—22no—
511C2×D4—22no—
512C2×D4—22no—
513C2×D4—22no—
514C2×D4—22no—
515C2×D4—22no—
516C2×D4—22no—
517C2×D4—22no—
518C2×D4—22no—
519C2×D4—42no—
520C2×D4—44no—
521C2×D4—44no—
522C2×D4—44no—
523C2×D4—44no—
524C2×D4—44no—
525C2×D4—44no—
526C2×D4—42no—
527C2×D4—42no—
528C2×D4—42no—
529C2×D4—42no—
530C2×D4C22×D414yes—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—216no—
538C22×C4—22no—
539C22×C4—24no—
540C22×C4—22no—
541C22×C4—24no—
542C22×C4—24no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—432no—
557C22×C4—48no—
558C22×C4—42no—
559C22×C4—42no—
560C22×C4—42no—
561C22×C4—42no—
562C22×C4—42no—
563C22×C4—42no—
564C22×C4—48no—
565C22×C4—42no—
566C22×C4—42no—
567C22×C4—42no—
568C22×C4—42no—
569C22×C4—42no—
570C22×C4—42no—
571C22×C4—42no—
572C22×C4—42no—
573C22×C4—42no—
574C22×C4#12014yes—
575C22×C4#12014yes—
576C22×C4#13514yes—
577C22×C4C22×D412yes—
578C22×C4C22×D412yes—
579C22×C4C22×D412yes—
580C22×C4C22×D412yes—
581C22×C4C22×D412yes—
582C22×C4C22×D412yes—
583C22×C4C22×D411yescharacteristic
584C22×C4C22×D412yes—
585C22×C4C22×D412yes—
586C22×C4C2×#4112yes—
587C22×C4C2×#4112yes—
588C22×C4H(5,𝔽2)12yes—
589C22×C4H(5,𝔽2)12yes—
590C22×C4C2511yescharacteristic
591Q16—416no—
592Q16—416no—
593SD16—416no—
594SD16—416no—
595SD16—416no—
596D8—416no—
597C2×C8—28no—
598C2×C8—28no—
599C2×C8—22no—
600C2×C8—22no—
601C2×C8—22no—
602C2×C8—22no—
603C2×C8—22no—
604C2×C8—22no—
605C2×C8—22no—
606C2×C8—22no—
607C2×C8—22no—
608C2×C8—22no—
609C2×C8—44no—
610C2×C8—44no—
611C2×C8C2×#4114yes—
612C2×C8C2×#4114yes—
613C4⋊C4—216no—
614C4⋊C4—216no—
615C4⋊C4—216no—
616C4⋊C4—216no—
617C4⋊C4—28no—
618C4⋊C4—24no—
619C4⋊C4—28no—
620C4⋊C4—28no—
621C4⋊C4—22no—
622C4⋊C4—22no—
623C4⋊C4—22no—
624C4⋊C4—22no—
625C4⋊C4—22no—
626C4⋊C4—42no—
627C4⋊C4—42no—
628C4⋊C4C22×D414yes—
629C22⋊C4—216no—
630C22⋊C4—216no—
631C22⋊C4—216no—
632C22⋊C4—216no—
633C22⋊C4—216no—
634C22⋊C4—48no—
635C22⋊C4—48no—
636C22⋊C4—48no—
637C22⋊C4—48no—
638C22⋊C4—84no—
639C22⋊C4—84no—
640C42—216no—
641C42—216no—
642C42—24no—
643C42—24no—
644C42—22no—
645C42—22no—
646C42—22no—
647C42—22no—
648C42—84no—
649C42#12018yes—
650C42C22×D414yes—
651C42C22×D414yes—
652C23—24no—
653C23—48no—
654C23—42no—
655C23—42no—
656C23—48no—
657C23—48no—
658C23—42no—
659C23—42no—
660C23—42no—
661C23—42no—
662C23—42no—
663C23—42no—
664C23—42no—
665C23—42no—
666C23—42no—
667C23—42no—
668C23—42no—
669C23—84no—
670C23—84no—
671C23—84no—
672C23—84no—
673C23—84no—
674C23—84no—
675C23—84no—
676C23—84no—
677C23—84no—
678C23—84no—
679C23—84no—
680C23C2×#12012yes—
681C23#55012yes—
682C23#55012yes—
683C23C2×#13512yes—
684C23#57512yes—
685C23#57712yes—
686C23#57812yes—
687C23C23×D411yescharacteristic
688Q8—24no—
689Q8—24no—
690Q8—24no—
691Q8—24no—
692Q8—416no—
693Q8—42no—
694Q8—42no—
695Q8—48no—
696Q8—48no—
697Q8—42no—
698Q8—42no—
699Q8—42no—
700Q8—42no—
701Q8—42no—
702Q8—42no—
703Q8—84no—
704D4—24no—
705D4—24no—
706D4—42no—
707D4—42no—
708D4—42no—
709D4—42no—
710D4—48no—
711D4—42no—
712D4—42no—
713D4—84no—
714C2×C4—22no—
715C2×C4—28no—
716C2×C4—28no—
717C2×C4—28no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—24no—
725C2×C4—22no—
726C2×C4—24no—
727C2×C4—24no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—432no—
736C2×C4—48no—
737C2×C4—48no—
738C2×C4—42no—
739C2×C4—42no—
740C2×C4—42no—
741C2×C4—42no—
742C2×C4—44no—
743C2×C4—48no—
744C2×C4—44no—
745C2×C4—44no—
746C2×C4—42no—
747C2×C4—42no—
748C2×C4—42no—
749C2×C4—42no—
750C2×C4—42no—
751C2×C4—42no—
752C2×C4—42no—
753C2×C4—42no—
754C2×C4—42no—
755C2×C4—42no—
756C2×C4—42no—
757C2×C4—84no—
758C2×C4—84no—
759C2×C4—84no—
760C2×C4C2×#12014yes—
761C2×C4C2×#12014yes—
762C2×C4C2×#12012yes—
763C2×C4#53214yes—
764C2×C4#53514yes—
765C2×C4#54614yes—
766C2×C4#54614yes—
767C2×C4#55012yes—
768C2×C4#55012yes—
769C2×C4C2×#13514yes—
770C2×C4C23×D411yescharacteristic
771C2×C4C23×D411yescharacteristic
772C2×C4C22×#4111yescharacteristic
773C2×C4C22×#4111yescharacteristic
774C2×C4C2×H(5,𝔽2)11yescharacteristic
775C2×C4C2×H(5,𝔽2)11yescharacteristic
776C8—24no—
777C8—24no—
778C8—42no—
779C8—42no—
780C22—44no—
781C22—44no—
782C22—44no—
783C22—816no—
784C22—82no—
785C22—82no—
786C22—82no—
787C22—82no—
788C22—82no—
789C22—82no—
790C22—82no—
791C22—82no—
792C22—82no—
793C22—82no—
794C22—82no—
795C22—168no—
796C22#243114yes—
797C22#300214yes—
798C22#301314yes—
799C22#339314yes—
800C22#339414yes—
801C22#340114yes—
802C22#340214yes—
803C22C22×#12011yescharacteristic
804C22C2×#55011yescharacteristic
805C22C2×#55011yescharacteristic
806C22C22×#13511yescharacteristic
807C22C2×#57511yescharacteristic
808C22C2×#57711yescharacteristic
809C22C2×#57811yescharacteristic
810C4—24no—
811C4—24no—
812C4—24no—
813C4—44no—
814C4—44no—
815C4—42no—
816C4—44no—
817C4—42no—
818C4—42no—
819C4—82no—
820C4—82no—
821C4—82no—
822C4#243114yes—
823C4C2×#53211yescharacteristic
824C4C2×#53511yescharacteristic
825C4C2×#54611yescharacteristic
826C4C2×#54611yescharacteristic
827C2—84no—
828C2—162no—
829C2#2563618yesdirect product factor
830C2C2×#243111yescharacteristic
831C2C2×#300211yescharacteristic
832C2C2×#301311yescharacteristic
833C2C2×#339311yescharacteristic
834C2C2×#339411yescharacteristic
835C2C2×#340111yescharacteristic
836C2C2×#340211yescharacteristic
subgroupG/H
center, socleC24C22×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC23×D8C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24 ◁ C22×C4×Q8 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C22×#556C2semidirect
3. C22×#464C2semidirect
4. C2×#2592C2semidirect
5. #25636C2direct (N × H)
6. C2×#2016C2semidirect
7. C2×#2013C2semidirect
8. C2×#2015C2semidirect
10. C2×#1984C2semidirect
11. C2×#1983C2semidirect
12. C2×#1880C2semidirect
13. C2×#1878C2semidirect
15. C2×#1877C2semidirect
16. C2×C4×#103C2semidirect
26. C2×#556C22semidirect
42. C2×#464C22semidirect
54. #2592C22semidirect
64. #2016C22semidirect
65. #2015C22semidirect
66. #2013C22semidirect
68. #1984C22semidirect
69. #1983C22semidirect
70. #1880C22semidirect
72. #1878C22semidirect
73. #1877C22semidirect
74. C4×#103C22semidirect
829. C2#25636direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#5562
C22×#4952
C22×#4642
C2×#25922
#256362
C2×#20162
C2×#20132
C2×#20152
C2×#20122
C2×#19842
C2×#19832
C2×#18802
C2×#18782
C2×#18792
C2×#18772
C2×C4×#1032