Finite Group Databasebeta

← C2×#31023 #7503183

Subgroups — C2×#31023 #7503183

Order 512.

2938 conjugacy classes of subgroups.

The subgroup lattice has 817 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#485C211yesmaximal, characteristic, complemented
2C22×#451C211yesmaximal, characteristic, complemented
3C2×#2415C211yesmaximal, characteristic
4C2×#2409C211yesmaximal, characteristic
5#31023C2116yesmaximal, direct product factor
6C2×#2075C211yesmaximal, characteristic, complemented
7C2×#2066C211yesmaximal, characteristic, complemented
8C2×#2056C211yesmaximal, characteristic, complemented
9C2×#2035C211yesmaximal, characteristic, complemented
10C2×#2001C211yesmaximal, characteristic, complemented
11C2×#2001C211yesmaximal, characteristic, complemented
12C2×#1969C211yesmaximal, characteristic, complemented
13C2×#1954C211yesmaximal, characteristic
14C2×#1933C211yesmaximal, characteristic, complemented
15C2×#1873C211yesmaximal, characteristic, complemented
16C2×#1787C211yesmaximal, characteristic, complemented
17C24×Q8C2211yescharacteristic
18C23×Q16C2211yescharacteristic
19C23×Q16C2211yescharacteristic
20C22×C22⋊Q8C2211yescharacteristic
21C22×C22⋊Q8C2211yescharacteristic
22C22×C22⋊Q8C2211yescharacteristic
23C22×C22⋊Q8C2211yescharacteristic
24C22×C4×D4C2211yescharacteristic
25C22×#117C2211yescharacteristic
26C2×#485—28no—
27C2×#485C2218yescomplemented
28C2×#451—28no—
29C2×#451C2218yescomplemented
30C22×#107C2211yescharacteristic
31C22×#106C2211yescharacteristic
32C22×C4⋊C8C2211yescharacteristic
33C22×#103C2211yescharacteristic
34C22×#103C2211yescharacteristic
35C22×#103C2211yescharacteristic
36C22×#103C2211yescharacteristic
37C22×#103C2211yescharacteristic
38C22×#103C2211yescharacteristic
39C22×#103C2211yescharacteristic
40C22×#103C2211yescharacteristic
41C22×C22⋊C8C2211yescharacteristic
42C22×C22⋊C8C2211yescharacteristic
43C22×C22⋊C8C2211yescharacteristic
44C22×C22⋊C8C2211yescharacteristic
45C22×C4×C8C2211yescharacteristic
46#2415—24no—
47#2415C2218yes—
48#2409—24no—
49#2409C2218yes—
50C2×#397—21no—
51C2×#395—21no—
52C2×#394—21no—
53C2×#393—21no—
54C2×#391C2211yescharacteristic
55C2×#391C2211yescharacteristic
56C2×#391C2211yescharacteristic
57C2×#389—21no—
58C2×#389C2211yescharacteristic
59C2×#388—21no—
60C2×#386—21no—
61C2×#385—21no—
62C2×#380C2211yescharacteristic
63C2×#380C2211yescharacteristic
64#2075C2218yescomplemented
65#2066C2218yescomplemented
66#2056C2218yescomplemented
67#2035C2218yescomplemented
68#2001C2218yescomplemented
69#2001C2218yescomplemented
70#1969C2218yescomplemented
71#1954C2218yes—
72#1933C2218yescomplemented
73#1873C2218yescomplemented
74#1787C2218yescomplemented
75C2×#340C2211yescharacteristic
76C2×#340C2211yescharacteristic
77C2×#340C2211yescharacteristic
78C2×#340C2211yescharacteristic
79C23×Q8—21no—
80C23×Q8—22no—
81C23×Q8—24no—
82C23×Q8—24no—
83C23×Q8—42no—
84C23×Q8—42no—
85C23×Q8—42no—
86C23×Q8—42no—
87C23×Q8C2311yescharacteristic
88C23×Q8C2311yescharacteristic
89C23×Q8C2311yescharacteristic
90C23×Q8C2314yes—
91C23×D4D411yescharacteristic
92C24×C4—21no—
93C24×C4C2311yescharacteristic
94C24×C4C2311yescharacteristic
95C22×Q16—24no—
96C22×Q16—24no—
97C22×Q16—24no—
98C22×Q16—42no—
99C22×Q16—42no—
100C22×Q16—42no—
101C22×Q16C2314yes—
102C22×Q16C2314yes—
103C23×C8C2311yescharacteristic
104C23×C8C2311yescharacteristic
105C23×C8C2311yescharacteristic
106C23×C8C2311yescharacteristic
107C2×C22⋊Q8—22no—
108C2×C22⋊Q8—22no—
109C2×C22⋊Q8—22no—
110C2×C22⋊Q8—22no—
111C2×C22⋊Q8—24no—
112C2×C22⋊Q8—24no—
113C2×C22⋊Q8—24no—
114C2×C22⋊Q8—42no—
115C2×C22⋊Q8—42no—
116C2×C22⋊Q8—42no—
117C2×C22⋊Q8—42no—
118C2×C22⋊Q8—42no—
119C2×C22⋊Q8C2314yes—
120C2×C22⋊Q8C2314yes—
121C2×C22⋊Q8C2314yes—
122C2×C22⋊Q8C2314yes—
123C2×C4×D4—42no—
124C2×C4×D4—42no—
125C2×C4×D4D414yes—
126C2×C4×D4C2314yes—
127C2×#117—22no—
128C2×#117—24no—
129C2×#117—42no—
130C2×#117C2314yes—
131C22×C4⋊C4—21no—
132C22×C4⋊C4—21no—
133C22×C4⋊C4—21no—
134C22×C4⋊C4—21no—
135C22×C4⋊C4—21no—
136C22×C4⋊C4D411yescharacteristic
137C22×C4⋊C4C2311yescharacteristic
138C22×C4⋊C4C2311yescharacteristic
139C22×C4⋊C4C2311yescharacteristic
140C22×C4⋊C4C2311yescharacteristic
141C22×C4⋊C4C2311yescharacteristic
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×C22⋊C4D411yescharacteristic
150C22×C22⋊C4D411yescharacteristic
151C22×C42—21no—
152C22×C42C2311yescharacteristic
153#485—232no—
154#451—232no—
155C2×#107—24no—
156C2×#107C2314yes—
157C2×#106—24no—
158C2×#106C2314yes—
159C2×C4⋊C8—42no—
160C2×C4⋊C8C2314yes—
161C2×#103—24no—
162C2×#103—24no—
163C2×#103—42no—
164C2×#103—42no—
165C2×#103—42no—
166C2×#103—42no—
167C2×#103—42no—
168C2×#103D418yescomplemented
169C2×#103C2314yes—
170C2×#103C2314yes—
171C2×#103C2314yes—
172C2×#103C2314yes—
173C2×#103C2314yes—
174C2×#103C2314yes—
175C2×#103C2314yes—
176C2×#103C2314yes—
177C2×C22⋊C8—24no—
178C2×C22⋊C8—24no—
179C2×C22⋊C8—42no—
180C2×C22⋊C8—42no—
181C2×C22⋊C8C2314yes—
182C2×C22⋊C8C2314yes—
183C2×C22⋊C8C2314yes—
184C2×C22⋊C8C2314yes—
185C2×C4×C8—42no—
186C2×C4×C8C2314yes—
187#397—28no—
188#395—28no—
189#394—28no—
190#393—28no—
191#391—22no—
192#391—22no—
193#391—22no—
194#391C2314yes—
195#391C2314yes—
196#391C2314yes—
197#389—28no—
198#389—22no—
199#389C2314yes—
200#388—28no—
201#386—28no—
202#385—28no—
203#380—22no—
204#380—22no—
205#380C2314yes—
206#380C2314yes—
207C2×#95—21no—
208C2×#95—21no—
209C2×#95—21no—
210C2×#95—21no—
211C2×#95—21no—
212C2×#95—21no—
213C2×#95—21no—
214C2×#95—21no—
215C2×#95—21no—
216#340C2314yes—
217#340C2314yes—
218#340C2314yes—
219#340C2314yes—
220C25C2×D411yescharacteristic
221C25C2×D411yescharacteristic
222C22×Q8—21no—
223C22×Q8—21no—
224C22×Q8—21no—
225C22×Q8—24no—
226C22×Q8—22no—
227C22×Q8—22no—
228C22×Q8—28no—
229C22×Q8—28no—
230C22×Q8—22no—
231C22×Q8—22no—
232C22×Q8—22no—
233C22×Q8—22no—
234C22×Q8—22no—
235C22×Q8—22no—
236C22×Q8—22no—
237C22×Q8—22no—
238C22×Q8—22no—
239C22×Q8—22no—
240C22×Q8—22no—
241C22×Q8—22no—
242C22×Q8—22no—
243C22×Q8—22no—
244C22×Q8—44no—
245C22×Q8—44no—
246C22×Q8—44no—
247C22×Q8—44no—
248C22×Q8—44no—
249C22×Q8—44no—
250C22×Q8—48no—
251C22×Q8—48no—
252C22×Q8—44no—
253C22×Q8—48no—
254C22×Q8—416no—
255C22×Q8—416no—
256C22×Q8—416no—
257C22×Q8—416no—
258C22×Q8C2×D414yes—
259C22×Q8#4114yes—
260C22×Q8C2412yes—
261C22×Q8C2412yes—
262C22×Q8C2412yes—
263C22×D4—24no—
264C22×D4—24no—
265C22×D4—42no—
266C22×D4C2×D414yes—
267C23×C4—21no—
268C23×C4—21no—
269C23×C4—21no—
270C23×C4—22no—
271C23×C4—22no—
272C23×C4—22no—
273C23×C4—22no—
274C23×C4—22no—
275C23×C4—22no—
276C23×C4—22no—
277C23×C4—22no—
278C23×C4—22no—
279C23×C4—22no—
280C23×C4—22no—
281C23×C4—22no—
282C23×C4—24no—
283C23×C4—21no—
284C23×C4—21no—
285C23×C4—21no—
286C23×C4—21no—
287C23×C4—21no—
288C23×C4—44no—
289C23×C4—44no—
290C23×C4—44no—
291C23×C4C2×D412yes—
292C23×C4C2×D412yes—
293C23×C4C2×D411yescharacteristic
294C23×C4C2×D411yescharacteristic
295C23×C4C2×D411yescharacteristic
296C23×C4C2×D411yescharacteristic
297C23×C4C2412yes—
298C23×C4C2412yes—
299C23×C4C2411yescharacteristic
300C2×Q16—28no—
301C2×Q16—28no—
302C2×Q16—28no—
303C2×Q16—44no—
304C2×Q16—44no—
305C2×Q16—44no—
306C2×Q16—416no—
307C2×Q16—416no—
308C22×C8—22no—
309C22×C8—22no—
310C22×C8—22no—
311C22×C8—22no—
312C22×C8—22no—
313C22×C8—22no—
314C22×C8—22no—
315C22×C8—22no—
316C22×C8—22no—
317C22×C8—22no—
318C22×C8—22no—
319C22×C8C2×D414yes—
320C22×C8C2412yes—
321C22×C8C2412yes—
322C22×C8C2412yes—
323C22×C8C2412yes—
324C22⋊Q8—28no—
325C22⋊Q8—28no—
326C22⋊Q8—28no—
327C22⋊Q8—44no—
328C22⋊Q8—44no—
329C22⋊Q8—44no—
330C22⋊Q8—44no—
331C22⋊Q8—44no—
332C22⋊Q8—48no—
333C22⋊Q8—48no—
334C22⋊Q8—48no—
335C22⋊Q8—48no—
336C4×D4—48no—
337C4×D4—44no—
338C4×D4—44no—
339#117—28no—
340#117—44no—
341#117—48no—
342C2×C4⋊C4—21no—
343C2×C4⋊C4—22no—
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—22no—
352C2×C4⋊C4—24no—
353C2×C4⋊C4—24no—
354C2×C4⋊C4—24no—
355C2×C4⋊C4—24no—
356C2×C4⋊C4—24no—
357C2×C4⋊C4—21no—
358C2×C4⋊C4—21no—
359C2×C4⋊C4—21no—
360C2×C4⋊C4—21no—
361C2×C4⋊C4—42no—
362C2×C4⋊C4—44no—
363C2×C4⋊C4—44no—
364C2×C4⋊C4—44no—
365C2×C4⋊C4—44no—
366C2×C4⋊C4—44no—
367C2×C4⋊C4C2×D414yes—
368C2×C4⋊C4C2×D414yes—
369C2×C4⋊C4C2412yes—
370C2×C4⋊C4C2412yes—
371C2×C4⋊C4C2412yes—
372C2×C4⋊C4C2412yes—
373C2×C4⋊C4C2412yes—
374C2×C22⋊C4—24no—
375C2×C22⋊C4—24no—
376C2×C22⋊C4—24no—
377C2×C22⋊C4—24no—
378C2×C22⋊C4—24no—
379C2×C22⋊C4—24no—
380C2×C22⋊C4—24no—
381C2×C22⋊C4—42no—
382C2×C22⋊C4—42no—
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⋊C4C2×D414yes—
391C2×C22⋊C4C2×D414yes—
392C2×C42—22no—
393C2×C42—22no—
394C2×C42—24no—
395C2×C42—44no—
396C2×C42C2×D412yes—
397C2×C42C2412yes—
398#107—28no—
399#106—28no—
400C4⋊C8—44no—
401#103—28no—
402#103—28no—
403#103—44no—
404#103—44no—
405#103—44no—
406#103—44no—
407#103—44no—
408#103C2×D4116yescomplemented
409C22⋊C8—28no—
410C22⋊C8—28no—
411C22⋊C8—44no—
412C22⋊C8—44no—
413C4×C8—44no—
414#95—24no—
415#95—24no—
416#95—24no—
417#95—24no—
418#95—24no—
419#95—24no—
420#95—24no—
421#95—24no—
422#95—24no—
423C24—22no—
424C24—22no—
425C24—22no—
426C24—22no—
427C24—22no—
428C24—22no—
429C24—22no—
430C24—22no—
431C24—22no—
432C24—22no—
433C24—22no—
434C24—22no—
435C24—22no—
436C24#13514yes—
437C24C22×D412yes—
438C24C22×D412yes—
439C24C22×D411yescharacteristic
440C2×Q8—24no—
441C2×Q8—24no—
442C2×Q8—22no—
443C2×Q8—22no—
444C2×Q8—28no—
445C2×Q8—28no—
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—48no—
463C2×Q8—48no—
464C2×Q8—48no—
465C2×Q8—416no—
466C2×Q8—416no—
467C2×Q8—416no—
468C2×Q8—464no—
469C2×Q8—416no—
470C2×Q8—432no—
471C2×Q8—42no—
472C2×Q8—42no—
473C2×Q8—42no—
474C2×Q8—44no—
475C2×Q8—44no—
476C2×Q8—42no—
477C2×Q8—42no—
478C2×Q8—42no—
479C2×Q8—42no—
480C2×Q8—44no—
481C2×Q8—44no—
482C2×Q8—44no—
483C2×Q8—44no—
484C2×Q8—44no—
485C2×Q8—44no—
486C2×Q8C22×D414yes—
487C2×Q8C2×#4114yes—
488C2×D4—28no—
489C2×D4—28no—
490C2×D4—44no—
491C2×D4—416no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—24no—
499C22×C4—24no—
500C22×C4—22no—
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—24no—
510C22×C4—24no—
511C22×C4—24no—
512C22×C4—24no—
513C22×C4—24no—
514C22×C4—24no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
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—48no—
533C22×C4—48no—
534C22×C4—48no—
535C22×C4—432no—
536C22×C4—42no—
537C22×C4—42no—
538C22×C4—42no—
539C22×C4—42no—
540C22×C4—42no—
541C22×C4—42no—
542C22×C4—44no—
543C22×C4—44no—
544C22×C4—44no—
545C22×C4—44no—
546C22×C4—44no—
547C22×C4—44no—
548C22×C4—44no—
549C22×C4—44no—
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—42no—
563C22×C4—42no—
564C22×C4—42no—
565C22×C4#13714yes—
566C22×C4C22×D412yes—
567C22×C4C22×D412yes—
568C22×C4C22×D412yes—
569C22×C4C22×D412yes—
570C22×C4C22×D411yescharacteristic
571C22×C4C22×D412yes—
572C22×C4C2×#4112yes—
573C22×C4H(5,𝔽2)12yes—
574C22×C4H(5,𝔽2)12yes—
575C22×C4H(5,𝔽2)12yes—
576C22×C4H(5,𝔽2)12yes—
577C22×C4C2511yescharacteristic
578Q16—416no—
579Q16—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—22no—
605C4⋊C4—22no—
606C4⋊C4—44no—
607C4⋊C4—48no—
608C4⋊C4—48no—
609C4⋊C4—48no—
610C4⋊C4—48no—
611C4⋊C4—42no—
612C4⋊C4—42no—
613C4⋊C4—42no—
614C4⋊C4—42no—
615C4⋊C4—48no—
616C4⋊C4C22×D414yes—
617C22⋊C4—44no—
618C22⋊C4—44no—
619C22⋊C4—48no—
620C22⋊C4—48no—
621C22⋊C4—48no—
622C22⋊C4—48no—
623C22⋊C4—48no—
624C22⋊C4—48no—
625C22⋊C4—48no—
626C42—24no—
627C42—22no—
628C42—22no—
629C42—48no—
630C23—22no—
631C23—28no—
632C23—22no—
633C23—22no—
634C23—28no—
635C23—28no—
636C23—22no—
637C23—22no—
638C23—22no—
639C23—22no—
640C23—22no—
641C23—22no—
642C23—22no—
643C23—22no—
644C23—22no—
645C23—22no—
646C23—44no—
647C23—44no—
648C23—44no—
649C23—44no—
650C23—44no—
651C23—44no—
652C23—44no—
653C23—44no—
654C23—44no—
655C23—44no—
656C23—44no—
657C23#53412yes—
658C23D4212yes—
659C23#54612yes—
660C23C2×#13514yes—
661C23C2×#13512yes—
662C23C2×#13712yes—
663C23#57812yes—
664C23#57812yes—
665C23C23×D411yescharacteristic
666Q8—24no—
667Q8—24no—
668Q8—24no—
669Q8—24no—
670Q8—432no—
671Q8—48no—
672Q8—48no—
673Q8—42no—
674Q8—42no—
675Q8—42no—
676Q8—42no—
677Q8—42no—
678Q8—42no—
679Q8—42no—
680Q8—42no—
681Q8—84no—
682D4—416no—
683C2×C4—22no—
684C2×C4—28no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—24no—
691C2×C4—24no—
692C2×C4—22no—
693C2×C4—24no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—432no—
699C2×C4—42no—
700C2×C4—42no—
701C2×C4—44no—
702C2×C4—44no—
703C2×C4—48no—
704C2×C4—48no—
705C2×C4—44no—
706C2×C4—42no—
707C2×C4—42no—
708C2×C4—48no—
709C2×C4—42no—
710C2×C4—42no—
711C2×C4—48no—
712C2×C4—48no—
713C2×C4—42no—
714C2×C4—42no—
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—42no—
735C2×C4—42no—
736C2×C4—84no—
737C2×C4—84no—
738C2×C4—84no—
739C2×C4—84no—
740C2×C4—84no—
741C2×C4#53412yes—
742C2×C4#53514yes—
743C2×C4#53814yes—
744C2×C4D4212yes—
745C2×C4#54612yes—
746C2×C4#54614yes—
747C2×C4#56014yes—
748C2×C4C2×#13714yes—
749C2×C4C23×D411yescharacteristic
750C2×C4C22×#4111yescharacteristic
751C2×C4C2×H(5,𝔽2)11yescharacteristic
752C2×C4C2×H(5,𝔽2)11yescharacteristic
753C2×C4C2×H(5,𝔽2)11yescharacteristic
754C2×C4C2×H(5,𝔽2)11yescharacteristic
755C8—24no—
756C8—42no—
757C8—42no—
758C8—42no—
759C22—24no—
760C22—24no—
761C22—24no—
762C22—416no—
763C22—42no—
764C22—42no—
765C22—42no—
766C22—42no—
767C22—42no—
768C22—42no—
769C22—42no—
770C22—42no—
771C22—42no—
772C22—42no—
773C22—42no—
774C22—88no—
775C22#267814yes—
776C22#319014yes—
777C22#320214yes—
778C22#327614yes—
779C22#328514yes—
780C22#330014yes—
781C22#332814yes—
782C22C2×#53411yescharacteristic
783C22C2×D4211yescharacteristic
784C22C2×#54611yescharacteristic
785C22C22×#13511yescharacteristic
786C22C22×#13711yescharacteristic
787C22C2×#57811yescharacteristic
788C22C2×#57811yescharacteristic
789C4—24no—
790C4—42no—
791C4—44no—
792C4—42no—
793C4—42no—
794C4—44no—
795C4—44no—
796C4—82no—
797C4—82no—
798C4—82no—
799C4—82no—
800C4—82no—
801C4#267814yes—
802C4C2×#53511yescharacteristic
803C4C2×#53811yescharacteristic
804C4C2×#54611yescharacteristic
805C4C2×#56011yescharacteristic
806C2—44no—
807C2—82no—
808C2#3102318yesdirect product factor
809C2C2×#267811yescharacteristic
810C2C2×#319011yescharacteristic
811C2C2×#320211yescharacteristic
812C2C2×#327611yescharacteristic
813C2C2×#328511yescharacteristic
814C2C2×#330011yescharacteristic
815C2C2×#332811yescharacteristic
subgroupG/H
center, socleC24C22×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC23×D4D4
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×#451C2semidirect
5. #31023C2direct (N × H)
6. C2×#2075C2semidirect
7. C2×#2066C2semidirect
8. C2×#2056C2semidirect
9. C2×#2035C2semidirect
10. C2×#2001C2semidirect
11. C2×#2001C2semidirect
12. C2×#1969C2semidirect
14. C2×#1933C2semidirect
15. C2×#1873C2semidirect
16. C2×#1787C2semidirect
27. C2×#485C22semidirect
29. C2×#451C22semidirect
64. #2075C22semidirect
65. #2066C22semidirect
66. #2056C22semidirect
67. #2035C22semidirect
68. #2001C22semidirect
69. #2001C22semidirect
70. #1969C22semidirect
72. #1933C22semidirect
73. #1873C22semidirect
74. #1787C22semidirect
168. C2×#103D4semidirect
408. #103C2×D4semidirect
808. C2#31023direct (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×#4512
C2×#24152
C2×#24092
#310232
C2×#20752
C2×#20662
C2×#20562
C2×#20352
C2×#20012
C2×#19692
C2×#19542
C2×#19332
C2×#18732
C2×#17872