Finite Group Databasebeta

← C2×#23582 #6432024

Subgroups — C2×#23582 #6432024

Order 512.

3838 conjugacy classes of subgroups.

The subgroup lattice has 846 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#540C211yesmaximal, characteristic
2C22×#440C211yesmaximal, characteristic, complemented
3C22×C4×SD16C211yesmaximal, characteristic, complemented
4C2×#2323C211yesmaximal, characteristic, complemented
5#23582C2116yesmaximal, direct product factor
6C2×#2059C211yesmaximal, characteristic, complemented
7C2×#2041C211yesmaximal, characteristic, complemented
8C2×#2034C211yesmaximal, characteristic, complemented
9C2×#2033C211yesmaximal, characteristic, complemented
10C2×#2026C211yesmaximal, characteristic, complemented
11C2×#2014C211yesmaximal, characteristic, complemented
12C2×#2000C211yesmaximal, characteristic, complemented
13C2×#2000C211yesmaximal, characteristic, complemented
14C2×#1762C211yesmaximal, characteristic, complemented
15C2×C4×#102C211yesmaximal, characteristic, complemented
16C2×#1750C211yesmaximal, characteristic, complemented
17C23×SD16C2211yescharacteristic
18C23×SD16C2211yescharacteristic
19C2×#540—28no—
20C2×#540—28no—
21C2×#540—24no—
22C2×#540C2218yes—
23C22×#127C2211yescharacteristic
24C22×#125C2211yescharacteristic
25C22×#123—21no—
26C22×#123—21no—
27C22×C22⋊Q8C2211yescharacteristic
28C22×#121—21no—
29C22×#121—21no—
30C22×#121C2211yescharacteristic
31C22×#121C2211yescharacteristic
32C22×C4×Q8C2211yescharacteristic
33C22×C4×D4C2211yescharacteristic
34C22×C4×D4C2211yescharacteristic
35C22×#117C2211yescharacteristic
36C2×#440—28no—
37C2×#440C2218yescomplemented
38C2×C4×SD16—28no—
39C2×C4×SD16C2218yescomplemented
40C22×#107C2211yescharacteristic
41C22×#106C2211yescharacteristic
42C22×#103C2211yescharacteristic
43C22×#103C2211yescharacteristic
44C22×#102C2211yescharacteristic
45C22×#102C2211yescharacteristic
46C22×#102C2211yescharacteristic
47C22×#102C2211yescharacteristic
48C22×#102C2211yescharacteristic
49C22×#102C2211yescharacteristic
50C22×C22⋊C8C2211yescharacteristic
51C22×C22⋊C8C2211yescharacteristic
52C22×#97C2211yescharacteristic
53C22×C4×C8C2211yescharacteristic
54#2323—24no—
55#2323C2218yescomplemented
56C2×#391C2211yescharacteristic
57C2×#389—21no—
58C2×#389C2211yescharacteristic
59C2×#388—21no—
60C2×#388—21no—
61C2×#387—21no—
62C2×#380C2211yescharacteristic
63C2×C4×C4⋊C4C2211yescharacteristic
64#2059C2218yescomplemented
65#2041C2218yescomplemented
66#2034C2218yescomplemented
67#2033C2218yescomplemented
68#2026C2218yescomplemented
69#2014C2218yescomplemented
70#2000C2218yescomplemented
71#2000C2218yescomplemented
72#1762C2218yescomplemented
73C4×#102C2218yescomplemented
74#1750C2218yescomplemented
75C2×#340C2211yescharacteristic
76C2×#340C2211yescharacteristic
77C2×#340C2211yescharacteristic
78C2×#340C2211yescharacteristic
79C2×#336C2211yescharacteristic
80C2×#336C2211yescharacteristic
81C23×Q8C2311yescharacteristic
82C23×D4—21no—
83C23×D4—21no—
84C23×D4—21no—
85C23×D4—21no—
86C23×D4C2311yescharacteristic
87C23×D4C2311yescharacteristic
88C24×C4—21no—
89C24×C4—21no—
90C24×C4C2311yescharacteristic
91C22×SD16—24no—
92C22×SD16—24no—
93C22×SD16—24no—
94C22×SD16—24no—
95C22×SD16—24no—
96C22×SD16—24no—
97C22×SD16C2314yes—
98C22×SD16C2314yes—
99C23×C8C2311yescharacteristic
100C23×C8C2311yescharacteristic
101C23×C8C2311yescharacteristic
102C23×C8C2311yescharacteristic
103#540—264no—
104#540—232no—
105#540—232no—
106C2×#127—24no—
107C2×#127—24no—
108C2×#127—22no—
109C2×#127C2314yes—
110C2×#125—24no—
111C2×#125—24no—
112C2×#125—22no—
113C2×#125C2314yes—
114C2×#123—216no—
115C2×#123—216no—
116C2×#123—28no—
117C2×#123—28no—
118C2×C22⋊Q8—24no—
119C2×C22⋊Q8—22no—
120C2×C22⋊Q8—24no—
121C2×C22⋊Q8C2314yes—
122C2×#121—216no—
123C2×#121—216no—
124C2×#121—24no—
125C2×#121—24no—
126C2×#121—22no—
127C2×#121—22no—
128C2×#121—24no—
129C2×#121—24no—
130C2×#121—28no—
131C2×#121—28no—
132C2×#121C2314yes—
133C2×#121C2314yes—
134C2×C4×Q8—22no—
135C2×C4×Q8—24no—
136C2×C4×Q8—24no—
137C2×C4×Q8C2314yes—
138C2×C4×D4—22no—
139C2×C4×D4—22no—
140C2×C4×D4—24no—
141C2×C4×D4—24no—
142C2×C4×D4D418yes—
143C2×C4×D4D418yes—
144C2×C4×D4C2314yes—
145C2×C4×D4C2314yes—
146C2×#117—24no—
147C2×#117—24no—
148C2×#117D414yes—
149C2×#117C2314yes—
150C22×C4⋊C4—21no—
151C22×C4⋊C4—21no—
152C22×C4⋊C4—21no—
153C22×C4⋊C4—21no—
154C22×C4⋊C4—21no—
155C22×C4⋊C4D411yescharacteristic
156C22×C4⋊C4D411yescharacteristic
157C22×C4⋊C4C2311yescharacteristic
158C22×C4⋊C4C2311yescharacteristic
159C22×C4⋊C4C2311yescharacteristic
160C22×C4⋊C4C2311yescharacteristic
161C22×C4⋊C4C2311yescharacteristic
162C22×C22⋊C4—21no—
163C22×C22⋊C4—21no—
164C22×C22⋊C4—21no—
165C22×C22⋊C4—21no—
166C22×C22⋊C4—21no—
167C22×C22⋊C4—21no—
168C22×C22⋊C4D411yescharacteristic
169C22×C22⋊C4D411yescharacteristic
170C22×C42—21no—
171C22×C42—21no—
172C22×C42C2311yescharacteristic
173C22×C42C2311yescharacteristic
174#440—232no—
175C4×SD16—232no—
176C2×#107—24no—
177C2×#107C2314yes—
178C2×#106—24no—
179C2×#106C2314yes—
180C2×#103—24no—
181C2×#103—24no—
182C2×#103C2314yes—
183C2×#103C2314yes—
184C2×#102—24no—
185C2×#102—24no—
186C2×#102—24no—
187C2×#102—24no—
188C2×#102—24no—
189C2×#102—24no—
190C2×#102C2314yes—
191C2×#102C2314yes—
192C2×#102C2314yes—
193C2×#102C2314yes—
194C2×#102C2314yes—
195C2×#102C2314yes—
196C2×C22⋊C8—24no—
197C2×C22⋊C8—24no—
198C2×C22⋊C8C2314yes—
199C2×C22⋊C8C2314yes—
200C2×#97—24no—
201C2×#97C2314yes—
202C2×C4×C8—24no—
203C2×C4×C8C2314yes—
204#391—22no—
205#391C2314yes—
206#389—28no—
207#389—22no—
208#389C2314yes—
209#388—28no—
210#388—28no—
211#387—28no—
212#380—22no—
213#380C2314yes—
214C4×C4⋊C4—22no—
215C4×C4⋊C4C2314yes—
216C2×#95—21no—
217C2×#95—21no—
218C2×#95—21no—
219C2×#95—21no—
220C2×#95—21no—
221#340C2314yes—
222#340C2314yes—
223#340C2314yes—
224#340C2314yes—
225#336C2314yes—
226#336C2314yes—
227C25—21no—
228C25—21no—
229C25C2×D411yescharacteristic
230C22×Q8—21no—
231C22×Q8—22no—
232C22×Q8—22no—
233C22×Q8—22no—
234C22×Q8—22no—
235C22×Q8—22no—
236C22×Q8#4114yes—
237C22×Q8C2412yes—
238C22×D4—28no—
239C22×D4—28no—
240C22×D4—28no—
241C22×D4—28no—
242C22×D4—24no—
243C22×D4—24no—
244C22×D4—21no—
245C22×D4—21no—
246C22×D4—22no—
247C22×D4—22no—
248C22×D4—24no—
249C22×D4—24no—
250C22×D4—22no—
251C22×D4—22no—
252C22×D4—22no—
253C22×D4—22no—
254C22×D4—22no—
255C22×D4—22no—
256C22×D4—22no—
257C22×D4—22no—
258C22×D4—82no—
259C22×D4—82no—
260C22×D4—82no—
261C22×D4—82no—
262C22×D4—82no—
263C22×D4—82no—
264C22×D4—82no—
265C22×D4—82no—
266C22×D4C2×D414yes—
267C22×D4C2×D414yes—
268C22×D4C2412yes—
269C22×D4C2412yes—
270C23×C4—21no—
271C23×C4—21no—
272C23×C4—21no—
273C23×C4—21no—
274C23×C4—22no—
275C23×C4—22no—
276C23×C4—22no—
277C23×C4—22no—
278C23×C4—22no—
279C23×C4—22no—
280C23×C4—28no—
281C23×C4—28no—
282C23×C4—24no—
283C23×C4—24no—
284C23×C4—21no—
285C23×C4—21no—
286C23×C4—82no—
287C23×C4—82no—
288C23×C4—82no—
289C23×C4—82no—
290C23×C4C2×D412yes—
291C23×C4C2×D411yescharacteristic
292C23×C4C2×D411yescharacteristic
293C23×C4C2×D411yescharacteristic
294C23×C4C2×D411yescharacteristic
295C23×C4C2×D411yescharacteristic
296C23×C4C2412yes—
297C23×C4C2411yescharacteristic
298C2×SD16—232no—
299C2×SD16—232no—
300C2×SD16—28no—
301C2×SD16—28no—
302C2×SD16—28no—
303C2×SD16—28no—
304C2×SD16—28no—
305C2×SD16—28no—
306C22×C8—22no—
307C22×C8—22no—
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#4114yes—
317C22×C8#4114yes—
318C22×C8C2412yes—
319C22×C8C2412yes—
320C22×C8C2412yes—
321C22×C8C2412yes—
322#127—216no—
323#127—28no—
324#127—28no—
325#125—216no—
326#125—28no—
327#125—28no—
328#123—264no—
329#123—264no—
330C22⋊Q8—216no—
331C22⋊Q8—28no—
332C22⋊Q8—28no—
333#121—216no—
334#121—216no—
335#121—264no—
336#121—264no—
337#121—28no—
338#121—28no—
339#121—28no—
340#121—28no—
341C4×Q8—28no—
342C4×Q8—28no—
343C4×Q8—48no—
344C4×D4—216no—
345C4×D4—216no—
346C4×D4—28no—
347C4×D4—28no—
348C4×D4C2×D4116yes—
349C4×D4C2×D4116yes—
350#117—216no—
351#117—28no—
352#117—28no—
353C2×C4⋊C4—28no—
354C2×C4⋊C4—28no—
355C2×C4⋊C4—28no—
356C2×C4⋊C4—24no—
357C2×C4⋊C4—24no—
358C2×C4⋊C4—24no—
359C2×C4⋊C4—24no—
360C2×C4⋊C4—24no—
361C2×C4⋊C4—21no—
362C2×C4⋊C4—21no—
363C2×C4⋊C4—22no—
364C2×C4⋊C4—22no—
365C2×C4⋊C4—21no—
366C2×C4⋊C4—22no—
367C2×C4⋊C4—22no—
368C2×C4⋊C4—22no—
369C2×C4⋊C4—22no—
370C2×C4⋊C4—22no—
371C2×C4⋊C4—24no—
372C2×C4⋊C4—21no—
373C2×C4⋊C4—21no—
374C2×C4⋊C4—24no—
375C2×C4⋊C4—44no—
376C2×C4⋊C4—82no—
377C2×C4⋊C4C2×D414yes—
378C2×C4⋊C4C2×D414yes—
379C2×C4⋊C4C2×D414yes—
380C2×C4⋊C4C2×D414yes—
381C2×C4⋊C4#4114yes—
382C2×C4⋊C4C2412yes—
383C2×C4⋊C4C2412yes—
384C2×C4⋊C4C2412yes—
385C2×C4⋊C4C2412yes—
386C2×C4⋊C4C2412yes—
387C2×C22⋊C4—28no—
388C2×C22⋊C4—28no—
389C2×C22⋊C4—28no—
390C2×C22⋊C4—24no—
391C2×C22⋊C4—28no—
392C2×C22⋊C4—28no—
393C2×C22⋊C4—24no—
394C2×C22⋊C4—24no—
395C2×C22⋊C4—24no—
396C2×C22⋊C4—24no—
397C2×C22⋊C4—24no—
398C2×C22⋊C4—24no—
399C2×C22⋊C4—24no—
400C2×C22⋊C4—82no—
401C2×C22⋊C4C2×D414yes—
402C2×C22⋊C4C2×D414yes—
403C2×C42—22no—
404C2×C42—22no—
405C2×C42—24no—
406C2×C42—24no—
407C2×C42—44no—
408C2×C42—82no—
409C2×C42C2×D412yes—
410C2×C42C2×D412yes—
411C2×C42C2×D414yes—
412C2×C42C2×D414yes—
413C2×C42C2412yes—
414C2×C42C2412yes—
415#107—28no—
416#106—28no—
417#103—28no—
418#103—28no—
419#102—28no—
420#102—28no—
421#102—28no—
422#102—28no—
423#102—28no—
424#102—28no—
425C22⋊C8—28no—
426C22⋊C8—28no—
427#97—28no—
428C4×C8—28no—
429#95—24no—
430#95—24no—
431#95—24no—
432#95—24no—
433#95—24no—
434C24—22no—
435C24—24no—
436C24—24no—
437C24—22no—
438C24—22no—
439C24—22no—
440C24—22no—
441C24—22no—
442C24—22no—
443C24—22no—
444C24—22no—
445C24—42no—
446C24—42no—
447C24—42no—
448C24—42no—
449C24—42no—
450C24—42no—
451C24—42no—
452C24—42no—
453C24—42no—
454C24—42no—
455C24—42no—
456C24—42no—
457C24C22×D412yes—
458C24C22×D411yescharacteristic
459C2×Q8—24no—
460C2×Q8—22no—
461C2×Q8—28no—
462C2×Q8—28no—
463C2×Q8—22no—
464C2×Q8—22no—
465C2×Q8—22no—
466C2×Q8—22no—
467C2×Q8—42no—
468C2×Q8—44no—
469C2×Q8—44no—
470C2×Q8—42no—
471C2×Q8C2×#4114yes—
472C2×D4—216no—
473C2×D4—216no—
474C2×D4—216no—
475C2×D4—216no—
476C2×D4—24no—
477C2×D4—24no—
478C2×D4—28no—
479C2×D4—28no—
480C2×D4—28no—
481C2×D4—28no—
482C2×D4—22no—
483C2×D4—22no—
484C2×D4—22no—
485C2×D4—22no—
486C2×D4—22no—
487C2×D4—22no—
488C2×D4—22no—
489C2×D4—22no—
490C2×D4—22no—
491C2×D4—22no—
492C2×D4—42no—
493C2×D4—42no—
494C2×D4—44no—
495C2×D4—44no—
496C2×D4—42no—
497C2×D4—42no—
498C2×D4—44no—
499C2×D4—44no—
500C2×D4—84no—
501C2×D4—84no—
502C2×D4—84no—
503C2×D4—84no—
504C2×D4—84no—
505C2×D4—84no—
506C2×D4—84no—
507C2×D4—84no—
508C2×D4—816no—
509C2×D4—816no—
510C2×D4—816no—
511C2×D4—816no—
512C2×D4C22×D414yes—
513C2×D4C22×D414yes—
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—24no—
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—24no—
536C22×C4—24no—
537C22×C4—24no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—216no—
545C22×C4—216no—
546C22×C4—22no—
547C22×C4—22no—
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—44no—
557C22×C4—44no—
558C22×C4—44no—
559C22×C4—44no—
560C22×C4—42no—
561C22×C4—42no—
562C22×C4—42no—
563C22×C4—42no—
564C22×C4—42no—
565C22×C4—42no—
566C22×C4—816no—
567C22×C4—816no—
568C22×C4—84no—
569C22×C4—84no—
570C22×C4—84no—
571C22×C4—84no—
572C22×C4#12014yes—
573C22×C4#12014yes—
574C22×C4C22×D412yes—
575C22×C4C22×D412yes—
576C22×C4C22×D412yes—
577C22×C4C22×D412yes—
578C22×C4C22×D412yes—
579C22×C4C22×D411yescharacteristic
580C22×C4C22×D412yes—
581C22×C4C22×D412yes—
582C22×C4C2×#4112yes—
583C22×C4C2×#4112yes—
584C22×C4C2×#4112yes—
585C22×C4C2×#4112yes—
586C22×C4C2511yescharacteristic
587SD16—232no—
588SD16—232no—
589C2×C8—28no—
590C2×C8—28no—
591C2×C8—22no—
592C2×C8—22no—
593C2×C8—22no—
594C2×C8—22no—
595C2×C8—22no—
596C2×C8—22no—
597C2×C8—22no—
598C2×C8—22no—
599C2×C8—22no—
600C2×C8—22no—
601C2×C8—44no—
602C2×C8—44no—
603C2×C8C2×#4114yes—
604C2×C8C2×#4114yes—
605C4⋊C4—216no—
606C4⋊C4—216no—
607C4⋊C4—216no—
608C4⋊C4—28no—
609C4⋊C4—28no—
610C4⋊C4—24no—
611C4⋊C4—24no—
612C4⋊C4—24no—
613C4⋊C4—22no—
614C4⋊C4—22no—
615C4⋊C4—22no—
616C4⋊C4—22no—
617C4⋊C4—22no—
618C4⋊C4—22no—
619C4⋊C4—22no—
620C4⋊C4—42no—
621C4⋊C4—48no—
622C4⋊C4—42no—
623C4⋊C4—84no—
624C4⋊C4C22×D414yes—
625C4⋊C4C22×D414yes—
626C4⋊C4C2×#4114yes—
627C22⋊C4—216no—
628C22⋊C4—216no—
629C22⋊C4—216no—
630C22⋊C4—216no—
631C22⋊C4—216no—
632C22⋊C4—28no—
633C22⋊C4—28no—
634C22⋊C4—84no—
635C42—24no—
636C42—22no—
637C42—22no—
638C42—48no—
639C42—84no—
640C42#12018yes—
641C42C22×D414yes—
642C42C22×D414yes—
643C23—22no—
644C23—24no—
645C23—24no—
646C23—22no—
647C23—22no—
648C23—22no—
649C23—22no—
650C23—22no—
651C23—22no—
652C23—44no—
653C23—44no—
654C23—44no—
655C23—48no—
656C23—48no—
657C23—44no—
658C23—44no—
659C23—42no—
660C23—42no—
661C23—42no—
662C23—42no—
663C23—48no—
664C23—44no—
665C23—48no—
666C23—48no—
667C23—44no—
668C23—48no—
669C23—42no—
670C23—42no—
671C23—42no—
672C23—42no—
673C23—42no—
674C23—42no—
675C23—42no—
676C23—42no—
677C23—84no—
678C23—84no—
679C23—84no—
680C23—84no—
681C23—84no—
682C23—84no—
683C23—84no—
684C23—84no—
685C23C2×#12012yes—
686C23#52512yes—
687C23#53212yes—
688C23#57612yes—
689C23#57712yes—
690C23#57712yes—
691C23#57712yes—
692C23C23×D411yescharacteristic
693Q8—24no—
694Q8—24no—
695Q8—48no—
696Q8—42no—
697Q8—42no—
698D4—24no—
699D4—24no—
700D4—24no—
701D4—24no—
702D4—48no—
703D4—48no—
704D4—42no—
705D4—42no—
706D4—42no—
707D4—42no—
708D4—816no—
709D4—816no—
710D4—816no—
711D4—816no—
712C2×C4—28no—
713C2×C4—28no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—24no—
722C2×C4—24no—
723C2×C4—24no—
724C2×C4—24no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—48no—
732C2×C4—44no—
733C2×C4—48no—
734C2×C4—42no—
735C2×C4—42no—
736C2×C4—44no—
737C2×C4—48no—
738C2×C4—44no—
739C2×C4—48no—
740C2×C4—42no—
741C2×C4—42no—
742C2×C4—42no—
743C2×C4—42no—
744C2×C4—42no—
745C2×C4—42no—
746C2×C4—48no—
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—816no—
758C2×C4—816no—
759C2×C4—84no—
760C2×C4—84no—
761C2×C4C2×#12014yes—
762C2×C4C2×#12014yes—
763C2×C4C2×#12012yes—
764C2×C4#52512yes—
765C2×C4#52514yes—
766C2×C4#52514yes—
767C2×C4#53212yes—
768C2×C4#53214yes—
769C2×C4#53214yes—
770C2×C4C23×D411yescharacteristic
771C2×C4C23×D411yescharacteristic
772C2×C4C22×#4111yescharacteristic
773C2×C4C22×#4111yescharacteristic
774C2×C4C22×#4111yescharacteristic
775C2×C4C22×#4111yescharacteristic
776C8—24no—
777C8—24no—
778C8—42no—
779C8—42no—
780C22—42no—
781C22—42no—
782C22—42no—
783C22—42no—
784C22—44no—
785C22—42no—
786C22—44no—
787C22—44no—
788C22—42no—
789C22—44no—
790C22—42no—
791C22—44no—
792C22—44no—
793C22—82no—
794C22—82no—
795C22—82no—
796C22—82no—
797C22—88no—
798C22—816no—
799C22—816no—
800C22—82no—
801C22—82no—
802C22—82no—
803C22—82no—
804C22#238814yes—
805C22#300914yes—
806C22#301214yes—
807C22#311914yes—
808C22#312614yes—
809C22#317414yes—
810C22#317914yes—
811C22C22×#12011yescharacteristic
812C22C2×#52511yescharacteristic
813C22C2×#53211yescharacteristic
814C22C2×#57611yescharacteristic
815C22C2×#57711yescharacteristic
816C22C2×#57711yescharacteristic
817C22C2×#57711yescharacteristic
818C4—24no—
819C4—24no—
820C4—44no—
821C4—42no—
822C4—44no—
823C4—42no—
824C4—44no—
825C4—42no—
826C4—44no—
827C4—82no—
828C4—82no—
829C4#238814yes—
830C4C2×#52511yescharacteristic
831C4C2×#52511yescharacteristic
832C4C2×#53211yescharacteristic
833C4C2×#53211yescharacteristic
834C2—82no—
835C2—84no—
836C2—84no—
837C2#2358218yesdirect product factor
838C2C2×#238811yescharacteristic
839C2C2×#300911yescharacteristic
840C2C2×#301211yescharacteristic
841C2C2×#311911yescharacteristic
842C2C2×#312611yescharacteristic
843C2C2×#317411yescharacteristic
844C2C2×#317911yescharacteristic
subgroupG/H
center, socleC24C22×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC22×#540C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24 ◁ C22×#117 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C22×#440C2semidirect
3. C22×C4×SD16C2semidirect
4. C2×#2323C2semidirect
5. #23582C2direct (N × H)
6. C2×#2059C2semidirect
7. C2×#2041C2semidirect
8. C2×#2034C2semidirect
9. C2×#2033C2semidirect
10. C2×#2026C2semidirect
11. C2×#2014C2semidirect
12. C2×#2000C2semidirect
13. C2×#2000C2semidirect
14. C2×#1762C2semidirect
15. C2×C4×#102C2semidirect
16. C2×#1750C2semidirect
37. C2×#440C22semidirect
39. C2×C4×SD16C22semidirect
55. #2323C22semidirect
64. #2059C22semidirect
65. #2041C22semidirect
66. #2034C22semidirect
67. #2033C22semidirect
68. #2026C22semidirect
69. #2014C22semidirect
70. #2000C22semidirect
71. #2000C22semidirect
72. #1762C22semidirect
73. C4×#102C22semidirect
74. #1750C22semidirect
837. C2#23582direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#5402
C22×#4402
C22×C4×SD162
C2×#23232
#235822
C2×#20592
C2×#20412
C2×#20342
C2×#20332
C2×#20262
C2×#20142
C2×#20002
C2×#17622
C2×C4×#1022
C2×#17502