Finite Group Databasebeta

← C2×#30520 #7501025

Subgroups — C2×#30520 #7501025

Order 512.

2948 conjugacy classes of subgroups.

The subgroup lattice has 816 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#487C211yesmaximal, characteristic, complemented
2C22×#452C211yesmaximal, characteristic
3C2×#2492C211yesmaximal, characteristic, complemented
4C2×#2432C211yesmaximal, characteristic
5#30520C2116yesmaximal, direct product factor
6C2×#2056C211yesmaximal, characteristic, complemented
7C2×#2035C211yesmaximal, characteristic, complemented
8C2×#2023C211yesmaximal, characteristic, complemented
9C2×#2016C211yesmaximal, characteristic, complemented
10C2×#2015C211yesmaximal, characteristic, complemented
11C2×#2001C211yesmaximal, characteristic, complemented
12C2×#1983C211yesmaximal, characteristic, complemented
13C2×#1968C211yesmaximal, characteristic, complemented
14C2×#1927C211yesmaximal, characteristic, complemented
15C2×#1923C211yesmaximal, characteristic, complemented
16C2×#1788C211yesmaximal, characteristic
17C23×#41C2211yescharacteristic
18C23×Q16C2211yescharacteristic
19C23×Q16C2211yescharacteristic
20C23×SD16C2211yescharacteristic
21C22×C4⋊Q8C2211yescharacteristic
22C22×C4⋊Q8C2211yescharacteristic
23C22×#124C2211yescharacteristic
24C22×C22⋊Q8C2211yescharacteristic
25C22×C22⋊Q8C2211yescharacteristic
26C2×#487—28no—
27C2×#487C2218yescomplemented
28C2×#452—28no—
29C2×#452C2218yes—
30C22×#106C2211yescharacteristic
31C22×C4⋊C8C2211yescharacteristic
32C22×#103C2211yescharacteristic
33C22×#103C2211yescharacteristic
34C22×#103C2211yescharacteristic
35C22×#103C2211yescharacteristic
36C22×#103C2211yescharacteristic
37C22×#103C2211yescharacteristic
38C22×#103C2211yescharacteristic
39C22×#102C2211yescharacteristic
40C22×#102C2211yescharacteristic
41C22×#102C2211yescharacteristic
42C22×C22⋊C8C2211yescharacteristic
43C22×C22⋊C8C2211yescharacteristic
44C22×C4×C8C2211yescharacteristic
45#2492—24no—
46#2492C2218yescomplemented
47#2432—24no—
48#2432C2218yes—
49C2×#400—21no—
50C2×#394—21no—
51C2×#394—21no—
52C2×#393—21no—
53C2×#391—21no—
54C2×#391C2211yescharacteristic
55C2×#391C2211yescharacteristic
56C2×#391C2211yescharacteristic
57C2×#390C2211yescharacteristic
58C2×#388—21no—
59C2×#385—21no—
60C2×#385—21no—
61C2×#380C2211yescharacteristic
62C2×C4×C4⋊C4C2211yescharacteristic
63C2×C4×C22⋊C4C2211yescharacteristic
64#2056C2218yescomplemented
65#2035C2218yescomplemented
66#2023C2218yescomplemented
67#2016C2218yescomplemented
68#2015C2218yescomplemented
69#2001C2218yescomplemented
70#1983C2218yescomplemented
71#1968C2218yescomplemented
72#1927C2218yescomplemented
73#1923C2218yescomplemented
74#1788C2218yes—
75C2×#340C2211yescharacteristic
76C2×#340C2211yescharacteristic
77C2×#336C2211yescharacteristic
78C2×#336C2211yescharacteristic
79C22×#41—22no—
80C22×#41—24no—
81C22×#41—24no—
82C22×#41—42no—
83C22×#41—42no—
84C22×#41—42no—
85C22×#41—42no—
86C22×#41C2314yes—
87C23×Q8—21no—
88C23×Q8C2311yescharacteristic
89C23×Q8C2311yescharacteristic
90C23×Q8C2311yescharacteristic
91C23×D4—21no—
92C23×D4C2311yescharacteristic
93C24×C4—21no—
94C24×C4C2311yescharacteristic
95C22×Q16—24no—
96C22×Q16—42no—
97C22×Q16—42no—
98C22×Q16—42no—
99C22×Q16—42no—
100C22×Q16—42no—
101C22×Q16C2314yes—
102C22×Q16C2314yes—
103C22×SD16—24no—
104C22×SD16—24no—
105C22×SD16—42no—
106C22×SD16C2314yes—
107C23×C8C2311yescharacteristic
108C23×C8C2311yescharacteristic
109C23×C8C2311yescharacteristic
110C23×C8C2311yescharacteristic
111C2×C4⋊Q8—24no—
112C2×C4⋊Q8—24no—
113C2×C4⋊Q8—22no—
114C2×C4⋊Q8—22no—
115C2×C4⋊Q8—42no—
116C2×C4⋊Q8—42no—
117C2×C4⋊Q8C2314yes—
118C2×C4⋊Q8C2314yes—
119C2×#124—24no—
120C2×#124—22no—
121C2×#124—42no—
122C2×#124C2314yes—
123C2×C22⋊Q8—22no—
124C2×C22⋊Q8—22no—
125C2×C22⋊Q8—24no—
126C2×C22⋊Q8—42no—
127C2×C22⋊Q8—42no—
128C2×C22⋊Q8—42no—
129C2×C22⋊Q8C2314yes—
130C2×C22⋊Q8C2314yes—
131C22×C4⋊C4—21no—
132C22×C4⋊C4—21no—
133C22×C4⋊C4—21no—
134C22×C4⋊C4—21no—
135C22×C4⋊C4—21no—
136C22×C4⋊C4C2311yescharacteristic
137C22×C4⋊C4C2311yescharacteristic
138C22×C4⋊C4C2311yescharacteristic
139C22×C4⋊C4C2311yescharacteristic
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⋊C4D411yescharacteristic
148C22×C22⋊C4D411yescharacteristic
149C22×C42—21no—
150C22×C42C2311yescharacteristic
151C22×C42C2311yescharacteristic
152#487—232no—
153#452—232no—
154C2×#106—42no—
155C2×#106C2314yes—
156C2×C4⋊C8—42no—
157C2×C4⋊C8C2314yes—
158C2×#103—24no—
159C2×#103—24no—
160C2×#103—24no—
161C2×#103—42no—
162C2×#103—42no—
163C2×#103—42no—
164C2×#103D418yes—
165C2×#103C2314yes—
166C2×#103C2314yes—
167C2×#103C2314yes—
168C2×#103C2314yes—
169C2×#103C2314yes—
170C2×#103C2314yes—
171C2×#103C2314yes—
172C2×#102—24no—
173C2×#102—42no—
174C2×#102—42no—
175C2×#102C2314yes—
176C2×#102C2314yes—
177C2×#102C2314yes—
178C2×C22⋊C8—24no—
179C2×C22⋊C8—42no—
180C2×C22⋊C8C2314yes—
181C2×C22⋊C8C2314yes—
182C2×C4×C8—24no—
183C2×C4×C8C2314yes—
184#400—28no—
185#394—28no—
186#394—28no—
187#393—28no—
188#391—22no—
189#391—22no—
190#391—22no—
191#391—28no—
192#391C2314yes—
193#391C2314yes—
194#391C2314yes—
195#390—22no—
196#390C2314yes—
197#388—28no—
198#385—28no—
199#385—28no—
200#380—22no—
201#380C2314yes—
202C4×C4⋊C4—22no—
203C4×C4⋊C4C2314yes—
204C4×C22⋊C4D414yes—
205C4×C22⋊C4C2314yes—
206C2×#95—21no—
207C2×#95—21no—
208C2×#95—21no—
209C2×#95—21no—
210C2×#95—21no—
211C2×#95—21no—
212C2×#95—21no—
213C2×#95—21no—
214C2×#95D411yescharacteristic
215C2×#95D411yescharacteristic
216#340C2314yes—
217#340C2314yes—
218#336C2314yes—
219#336C2314yes—
220C25—21no—
221C25C2×D411yescharacteristic
222C2×#41—28no—
223C2×#41—28no—
224C2×#41—44no—
225C2×#41—44no—
226C2×#41—44no—
227C2×#41—44no—
228C2×#41—48no—
229C2×#41—48no—
230C2×#41—48no—
231C2×#41—416no—
232C2×#41—416no—
233C2×#41—416no—
234C2×#41—416no—
235C22×Q8—21no—
236C22×Q8—21no—
237C22×Q8—21no—
238C22×Q8—24no—
239C22×Q8—22no—
240C22×Q8—22no—
241C22×Q8—22no—
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—44no—
257C22×Q8—44no—
258C22×Q8—82no—
259C22×Q8C2×D414yes—
260C22×Q8C2412yes—
261C22×Q8C2412yes—
262C22×Q8C2412yes—
263C22×D4—24no—
264C22×D4—22no—
265C22×D4—21no—
266C22×D4—22no—
267C22×D4—22no—
268C22×D4—22no—
269C22×D4—22no—
270C22×D4—44no—
271C22×D4—44no—
272C22×D4—44no—
273C22×D4#4114yes—
274C22×D4C2412yes—
275C23×C4—21no—
276C23×C4—21no—
277C23×C4—22no—
278C23×C4—22no—
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—24no—
289C23×C4—44no—
290C23×C4—44no—
291C23×C4—44no—
292C23×C4C2×D412yes—
293C23×C4C2×D411yescharacteristic
294C23×C4C2×D411yescharacteristic
295C23×C4C2×D411yescharacteristic
296C23×C4C2×D411yescharacteristic
297C23×C4C2×D411yescharacteristic
298C23×C4C2412yes—
299C23×C4C2411yescharacteristic
300C2×Q16—28no—
301C2×Q16—44no—
302C2×Q16—44no—
303C2×Q16—44no—
304C2×Q16—44no—
305C2×Q16—44no—
306C2×Q16—416no—
307C2×Q16—416no—
308C2×SD16—28no—
309C2×SD16—28no—
310C2×SD16—44no—
311C2×SD16—416no—
312C22×C8—22no—
313C22×C8—22no—
314C22×C8—22no—
315C22×C8—22no—
316C22×C8—22no—
317C22×C8—22no—
318C22×C8—22no—
319C22×C8—22no—
320C22×C8—22no—
321C22×C8—22no—
322C22×C8—22no—
323C22×C8C2×D414yes—
324C22×C8C2412yes—
325C22×C8C2412yes—
326C22×C8C2412yes—
327C22×C8C2412yes—
328C4⋊Q8—28no—
329C4⋊Q8—28no—
330C4⋊Q8—44no—
331C4⋊Q8—48no—
332C4⋊Q8—44no—
333C4⋊Q8—48no—
334#124—28no—
335#124—44no—
336#124—48no—
337C22⋊Q8—28no—
338C22⋊Q8—44no—
339C22⋊Q8—44no—
340C22⋊Q8—44no—
341C22⋊Q8—48no—
342C22⋊Q8—48no—
343C2×C4⋊C4—21no—
344C2×C4⋊C4—22no—
345C2×C4⋊C4—22no—
346C2×C4⋊C4—22no—
347C2×C4⋊C4—22no—
348C2×C4⋊C4—22no—
349C2×C4⋊C4—22no—
350C2×C4⋊C4—22no—
351C2×C4⋊C4—24no—
352C2×C4⋊C4—24no—
353C2×C4⋊C4—24no—
354C2×C4⋊C4—24no—
355C2×C4⋊C4—24no—
356C2×C4⋊C4—21no—
357C2×C4⋊C4—21no—
358C2×C4⋊C4—21no—
359C2×C4⋊C4—44no—
360C2×C4⋊C4—44no—
361C2×C4⋊C4—44no—
362C2×C4⋊C4—44no—
363C2×C4⋊C4—44no—
364C2×C4⋊C4C2×D414yes—
365C2×C4⋊C4C2412yes—
366C2×C4⋊C4C2412yes—
367C2×C4⋊C4C2412yes—
368C2×C4⋊C4C2412yes—
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—44no—
379C2×C22⋊C4—44no—
380C2×C22⋊C4—44no—
381C2×C22⋊C4—44no—
382C2×C22⋊C4—44no—
383C2×C22⋊C4—44no—
384C2×C22⋊C4—82no—
385C2×C22⋊C4C2×D414yes—
386C2×C22⋊C4C2×D414yes—
387C2×C42—22no—
388C2×C42—22no—
389C2×C42—22no—
390C2×C42—22no—
391C2×C42—24no—
392C2×C42—82no—
393C2×C42C2×D412yes—
394C2×C42C2×D412yes—
395C2×C42C2412yes—
396C2×C42C2412yes—
397#106—44no—
398C4⋊C8—44no—
399#103—28no—
400#103—28no—
401#103—28no—
402#103—44no—
403#103—44no—
404#103—44no—
405#103C2×D4116yes—
406#102—28no—
407#102—44no—
408#102—44no—
409C22⋊C8—28no—
410C22⋊C8—44no—
411C4×C8—28no—
412#95—24no—
413#95—24no—
414#95—24no—
415#95—24no—
416#95—24no—
417#95—24no—
418#95—24no—
419#95—24no—
420#95C2×D414yes—
421#95C2×D414yes—
422C24—22no—
423C24—22no—
424C24—24no—
425C24—22no—
426C24—22no—
427C24—22no—
428C24—22no—
429C24—22no—
430C24—22no—
431C24—42no—
432C24—42no—
433C24—42no—
434C24—42no—
435C24—42no—
436C24—42no—
437C24C22×D412yes—
438C24C22×D411yescharacteristic
439#41—416no—
440#41—416no—
441#41—416no—
442#41—464no—
443#41—416no—
444C2×Q8—24no—
445C2×Q8—22no—
446C2×Q8—28no—
447C2×Q8—28no—
448C2×Q8—22no—
449C2×Q8—22no—
450C2×Q8—22no—
451C2×Q8—22no—
452C2×Q8—22no—
453C2×Q8—22no—
454C2×Q8—22no—
455C2×Q8—22no—
456C2×Q8—22no—
457C2×Q8—22no—
458C2×Q8—22no—
459C2×Q8—22no—
460C2×Q8—22no—
461C2×Q8—22no—
462C2×Q8—22no—
463C2×Q8—22no—
464C2×Q8—48no—
465C2×Q8—42no—
466C2×Q8—42no—
467C2×Q8—42no—
468C2×Q8—44no—
469C2×Q8—42no—
470C2×Q8—42no—
471C2×Q8—42no—
472C2×Q8—42no—
473C2×Q8—42no—
474C2×Q8—44no—
475C2×Q8—48no—
476C2×Q8—44no—
477C2×Q8—44no—
478C2×Q8—44no—
479C2×Q8—44no—
480C2×Q8—44no—
481C2×Q8—44no—
482C2×Q8—44no—
483C2×Q8—44no—
484C2×Q8—84no—
485C2×Q8—816no—
486C2×Q8C22×D414yes—
487C2×D4—28no—
488C2×D4—28no—
489C2×D4—24no—
490C2×D4—22no—
491C2×D4—22no—
492C2×D4—22no—
493C2×D4—22no—
494C2×D4—22no—
495C2×D4—48no—
496C2×D4—48no—
497C2×D4—48no—
498C2×D4—432no—
499C2×D4—42no—
500C2×D4—44no—
501C2×D4—42no—
502C2×D4—44no—
503C2×D4C2×#4114yes—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—24no—
510C22×C4—22no—
511C22×C4—24no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—24no—
522C22×C4—24no—
523C22×C4—24no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—48no—
536C22×C4—48no—
537C22×C4—48no—
538C22×C4—432no—
539C22×C4—42no—
540C22×C4—42no—
541C22×C4—42no—
542C22×C4—42no—
543C22×C4—44no—
544C22×C4—44no—
545C22×C4—44no—
546C22×C4—44no—
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—42no—
556C22×C4—42no—
557C22×C4—42no—
558C22×C4—42no—
559C22×C4—42no—
560C22×C4—42no—
561C22×C4—42no—
562C22×C4#13514yes—
563C22×C4#13714yes—
564C22×C4C22×D412yes—
565C22×C4C22×D412yes—
566C22×C4C22×D412yes—
567C22×C4C22×D412yes—
568C22×C4C22×D412yes—
569C22×C4C22×D411yescharacteristic
570C22×C4C22×D412yes—
571C22×C4C2×#4112yes—
572C22×C4H(5,𝔽2)12yes—
573C22×C4H(5,𝔽2)12yes—
574C22×C4H(5,𝔽2)12yes—
575C22×C4H(5,𝔽2)12yes—
576C22×C4C2511yescharacteristic
577Q16—416no—
578Q16—416no—
579SD16—416no—
580C2×C8—28no—
581C2×C8—22no—
582C2×C8—22no—
583C2×C8—22no—
584C2×C8—22no—
585C2×C8—22no—
586C2×C8—22no—
587C2×C8—22no—
588C2×C8—22no—
589C2×C8—22no—
590C2×C8—22no—
591C2×C8—22no—
592C2×C8—44no—
593C2×C8—44no—
594C2×C8—44no—
595C2×C8C22×D414yes—
596C4⋊C4—24no—
597C4⋊C4—22no—
598C4⋊C4—22no—
599C4⋊C4—22no—
600C4⋊C4—22no—
601C4⋊C4—22no—
602C4⋊C4—22no—
603C4⋊C4—22no—
604C4⋊C4—48no—
605C4⋊C4—48no—
606C4⋊C4—48no—
607C4⋊C4—48no—
608C4⋊C4—48no—
609C4⋊C4—42no—
610C4⋊C4—42no—
611C4⋊C4—42no—
612C4⋊C4C22×D414yes—
613C22⋊C4—28no—
614C22⋊C4—28no—
615C22⋊C4—48no—
616C22⋊C4—48no—
617C22⋊C4—48no—
618C22⋊C4—48no—
619C22⋊C4—48no—
620C22⋊C4—48no—
621C22⋊C4—84no—
622C42—24no—
623C42—24no—
624C42—22no—
625C42—22no—
626C42—22no—
627C42—22no—
628C42—84no—
629C23—22no—
630C23—22no—
631C23—24no—
632C23—22no—
633C23—22no—
634C23—22no—
635C23—22no—
636C23—22no—
637C23—44no—
638C23—48no—
639C23—48no—
640C23—44no—
641C23—42no—
642C23—42no—
643C23—44no—
644C23—44no—
645C23—44no—
646C23—44no—
647C23—44no—
648C23—48no—
649C23—42no—
650C23—42no—
651C23—42no—
652C23—42no—
653C23—84no—
654C23—84no—
655C23—84no—
656C23—84no—
657C23#53512yes—
658C23D4212yes—
659C23#54612yes—
660C23C2×#13512yes—
661C23C2×#13712yes—
662C23#57712yes—
663C23#57812yes—
664C23C23×D411yescharacteristic
665Q8—24no—
666Q8—24no—
667Q8—48no—
668Q8—42no—
669Q8—42no—
670Q8—42no—
671Q8—42no—
672Q8—42no—
673Q8—42no—
674Q8—42no—
675Q8—42no—
676Q8—42no—
677Q8—42no—
678Q8—816no—
679Q8—84no—
680Q8—84no—
681D4—24no—
682D4—24no—
683D4—432no—
684D4—48no—
685D4—42no—
686D4—42no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—28no—
690C2×C4—28no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—24no—
695C2×C4—22no—
696C2×C4—24no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—432no—
705C2×C4—44no—
706C2×C4—44no—
707C2×C4—48no—
708C2×C4—42no—
709C2×C4—42no—
710C2×C4—48no—
711C2×C4—44no—
712C2×C4—42no—
713C2×C4—42no—
714C2×C4—48no—
715C2×C4—42no—
716C2×C4—42no—
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—84no—
735C2×C4—84no—
736C2×C4—84no—
737C2×C4—84no—
738C2×C4—84no—
739C2×C4#53512yes—
740C2×C4#53514yes—
741C2×C4#53814yes—
742C2×C4D4212yes—
743C2×C4#54612yes—
744C2×C4#54614yes—
745C2×C4H(3,𝔽4)14yes—
746C2×C4C2×#13514yes—
747C2×C4C2×#13714yes—
748C2×C4C23×D411yescharacteristic
749C2×C4C22×#4111yescharacteristic
750C2×C4C2×H(5,𝔽2)11yescharacteristic
751C2×C4C2×H(5,𝔽2)11yescharacteristic
752C2×C4C2×H(5,𝔽2)11yescharacteristic
753C2×C4C2×H(5,𝔽2)11yescharacteristic
754C8—24no—
755C8—42no—
756C8—42no—
757C8—42no—
758C22—42no—
759C22—42no—
760C22—42no—
761C22—44no—
762C22—42no—
763C22—42no—
764C22—42no—
765C22—44no—
766C22—42no—
767C22—44no—
768C22—88no—
769C22—816no—
770C22—82no—
771C22—82no—
772C22—82no—
773C22—82no—
774C22#267014yes—
775C22#321014yes—
776C22#322514yes—
777C22#327014yes—
778C22#328214yes—
779C22#330214yes—
780C22#333114yes—
781C22C2×#53511yescharacteristic
782C22C2×D4211yescharacteristic
783C22C2×#54611yescharacteristic
784C22C22×#13511yescharacteristic
785C22C22×#13711yescharacteristic
786C22C2×#57711yescharacteristic
787C22C2×#57811yescharacteristic
788C4—24no—
789C4—24no—
790C4—44no—
791C4—42no—
792C4—44no—
793C4—42no—
794C4—42no—
795C4—82no—
796C4—82no—
797C4—82no—
798C4—82no—
799C4—82no—
800C4#267014yes—
801C4C2×#53511yescharacteristic
802C4C2×#53811yescharacteristic
803C4C2×#54611yescharacteristic
804C4C2×H(3,𝔽4)11yescharacteristic
805C2—82no—
806C2—84no—
807C2#3052018yesdirect product factor
808C2C2×#267011yescharacteristic
809C2C2×#321011yescharacteristic
810C2C2×#322511yescharacteristic
811C2C2×#327011yescharacteristic
812C2C2×#328211yescharacteristic
813C2C2×#330211yescharacteristic
814C2C2×#333111yescharacteristic
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×#487C2semidirect
3. C2×#2492C2semidirect
5. #30520C2direct (N × H)
6. C2×#2056C2semidirect
7. C2×#2035C2semidirect
8. C2×#2023C2semidirect
9. C2×#2016C2semidirect
10. C2×#2015C2semidirect
11. C2×#2001C2semidirect
12. C2×#1983C2semidirect
13. C2×#1968C2semidirect
14. C2×#1927C2semidirect
15. C2×#1923C2semidirect
27. C2×#487C22semidirect
46. #2492C22semidirect
64. #2056C22semidirect
65. #2035C22semidirect
66. #2023C22semidirect
67. #2016C22semidirect
68. #2015C22semidirect
69. #2001C22semidirect
70. #1983C22semidirect
71. #1968C22semidirect
72. #1927C22semidirect
73. #1923C22semidirect
807. C2#30520direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#4872
C22×#4522
C2×#24922
C2×#24322
#305202
C2×#20562
C2×#20352
C2×#20232
C2×#20162
C2×#20152
C2×#20012
C2×#19832
C2×#19682
C2×#19272
C2×#19232
C2×#17882