Finite Group Databasebeta

← C2×#24169 #6448688

Subgroups — C2×#24169 #6448688

Order 512.

3502 conjugacy classes of subgroups.

The subgroup lattice has 806 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#542C211yesmaximal, characteristic
2C22×#475C211yesmaximal, characteristic, complemented
3C22×#464C211yesmaximal, characteristic, complemented
4C2×#2323C211yesmaximal, characteristic, complemented
5#24169C2116yesmaximal, direct product factor
6C2×#2034C211yesmaximal, characteristic
7C2×#2035C211yesmaximal, characteristic, complemented
8C2×#2001C211yesmaximal, characteristic, complemented
9C2×#2000C211yesmaximal, characteristic
10C2×#1987C211yesmaximal, characteristic, complemented
11C2×#1983C211yesmaximal, characteristic, complemented
12C2×#1878C211yesmaximal, characteristic, complemented
13C2×#1877C211yesmaximal, characteristic, complemented
14C2×#1865C211yesmaximal, characteristic, complemented
15C2×#1864C211yesmaximal, characteristic, complemented
16C2×#1798C211yesmaximal, characteristic, complemented
17C23×Q16C2211yescharacteristic
18C23×SD16C2211yescharacteristic
19C2×#542—28no—
20C2×#542—28no—
21C2×#542—24no—
22C2×#542C2218yes—
23C22×C4⋊Q8C2211yescharacteristic
24C22×#126—21no—
25C22×#124—21no—
26C22×#124C2211yescharacteristic
27C22×#123—21no—
28C22×C22⋊Q8—21no—
29C22×C22⋊Q8C2211yescharacteristic
30C22×C22⋊Q8C2211yescharacteristic
31C22×#121C2211yescharacteristic
32C22×C4×Q8C2211yescharacteristic
33C22×C4×Q8C2211yescharacteristic
34C22×C4×D4C2211yescharacteristic
35C22×#117C2211yescharacteristic
36C2×#475—28no—
37C2×#475C2218yescomplemented
38C2×#464—28no—
39C2×#464C2218yescomplemented
40C22×#106C2211yescharacteristic
41C22×#106C2211yescharacteristic
42C22×C4⋊C8C2211yescharacteristic
43C22×C4⋊C8C2211yescharacteristic
44C22×#103C2211yescharacteristic
45C22×#103C2211yescharacteristic
46C22×#103C2211yescharacteristic
47C22×#103C2211yescharacteristic
48C22×#103C2211yescharacteristic
49C22×#102C2211yescharacteristic
50C22×#102C2211yescharacteristic
51C22×#102C2211yescharacteristic
52C22×C22⋊C8C2211yescharacteristic
53C22×C22⋊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#2035C2218yescomplemented
65#2034C2218yes—
66#2001C2218yescomplemented
67#2000C2218yes—
68#1987C2218yescomplemented
69#1983C2218yescomplemented
70#1878C2218yescomplemented
71#1877C2218yescomplemented
72#1865C2218yescomplemented
73#1864C2218yescomplemented
74#1798C2218yescomplemented
75C2×#340C2211yescharacteristic
76C2×#340C2211yescharacteristic
77C2×#340C2211yescharacteristic
78C2×#340C2211yescharacteristic
79C2×#336C2211yescharacteristic
80C2×#336C2211yescharacteristic
81C23×Q8—21no—
82C23×Q8C2311yescharacteristic
83C23×Q8C2311yescharacteristic
84C23×D4—21no—
85C23×D4C2311yescharacteristic
86C24×C4—21no—
87C24×C4C2311yescharacteristic
88C22×Q16—24no—
89C22×Q16—24no—
90C22×Q16—42no—
91C22×Q16C2314yes—
92C22×SD16—24no—
93C22×SD16—24no—
94C22×SD16—42no—
95C22×SD16C2314yes—
96C23×C8C2311yescharacteristic
97C23×C8C2311yescharacteristic
98C23×C8C2311yescharacteristic
99C23×C8C2311yescharacteristic
100#542—264no—
101#542—232no—
102#542—232no—
103C2×C4⋊Q8—22no—
104C2×C4⋊Q8—24no—
105C2×C4⋊Q8D418yes—
106C2×C4⋊Q8C2314yes—
107C2×#126—216no—
108C2×#126—28no—
109C2×#124—216no—
110C2×#124—28no—
111C2×#124—22no—
112C2×#124—24no—
113C2×#124D418yes—
114C2×#124C2314yes—
115C2×#123—216no—
116C2×#123—28no—
117C2×C22⋊Q8—216no—
118C2×C22⋊Q8—24no—
119C2×C22⋊Q8—24no—
120C2×C22⋊Q8—22no—
121C2×C22⋊Q8—22no—
122C2×C22⋊Q8—28no—
123C2×C22⋊Q8—24no—
124C2×C22⋊Q8—24no—
125C2×C22⋊Q8C2314yes—
126C2×C22⋊Q8C2314yes—
127C2×#121—24no—
128C2×#121—22no—
129C2×#121—24no—
130C2×#121C2314yes—
131C2×C4×Q8—24no—
132C2×C4×Q8—24no—
133C2×C4×Q8—22no—
134C2×C4×Q8—22no—
135C2×C4×Q8—24no—
136C2×C4×Q8—24no—
137C2×C4×Q8C2314yes—
138C2×C4×Q8C2314yes—
139C2×C4×D4—24no—
140C2×C4×D4—24no—
141C2×C4×D4—22no—
142C2×C4×D4C2314yes—
143C2×#117—24no—
144C2×#117—24no—
145C2×#117D414yes—
146C2×#117C2314yes—
147C22×C4⋊C4—21no—
148C22×C4⋊C4—21no—
149C22×C4⋊C4—21no—
150C22×C4⋊C4—21no—
151C22×C4⋊C4—21no—
152C22×C4⋊C4—21no—
153C22×C4⋊C4D411yescharacteristic
154C22×C4⋊C4D411yescharacteristic
155C22×C4⋊C4C2311yescharacteristic
156C22×C4⋊C4C2311yescharacteristic
157C22×C4⋊C4C2311yescharacteristic
158C22×C4⋊C4C2311yescharacteristic
159C22×C4⋊C4C2311yescharacteristic
160C22×C22⋊C4—21no—
161C22×C22⋊C4—21no—
162C22×C22⋊C4—21no—
163C22×C22⋊C4—21no—
164C22×C22⋊C4—21no—
165C22×C22⋊C4—21no—
166C22×C22⋊C4—21no—
167C22×C22⋊C4D411yescharacteristic
168C22×C22⋊C4D411yescharacteristic
169C22×C42—21no—
170C22×C42—21no—
171C22×C42—21no—
172C22×C42C2311yescharacteristic
173C22×C42C2311yescharacteristic
174#475—232no—
175#464—232no—
176C2×#106—24no—
177C2×#106—24no—
178C2×#106C2314yes—
179C2×#106C2314yes—
180C2×C4⋊C8—24no—
181C2×C4⋊C8—24no—
182C2×C4⋊C8C2314yes—
183C2×C4⋊C8C2314yes—
184C2×#103—24no—
185C2×#103—24no—
186C2×#103—24no—
187C2×#103—24no—
188C2×#103—42no—
189C2×#103C2314yes—
190C2×#103C2314yes—
191C2×#103C2314yes—
192C2×#103C2314yes—
193C2×#103C2314yes—
194C2×#102—24no—
195C2×#102—24no—
196C2×#102—42no—
197C2×#102C2314yes—
198C2×#102C2314yes—
199C2×#102C2314yes—
200C2×C22⋊C8—42no—
201C2×C22⋊C8—42no—
202C2×C22⋊C8C2314yes—
203C2×C22⋊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—
228C25C2×D411yescharacteristic
229C22×Q8—28no—
230C22×Q8—22no—
231C22×Q8—21no—
232C22×Q8—21no—
233C22×Q8—24no—
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—82no—
244C22×Q8—82no—
245C22×Q8C2×D414yes—
246C22×Q8#4114yes—
247C22×Q8C2412yes—
248C22×Q8C2412yes—
249C22×D4—28no—
250C22×D4—24no—
251C22×D4—21no—
252C22×D4—22no—
253C22×D4—22no—
254C22×D4—22no—
255C22×D4—22no—
256C22×D4—22no—
257C22×D4—82no—
258C22×D4—82no—
259C22×D4C2×D414yes—
260C22×D4C2412yes—
261C23×C4—21no—
262C23×C4—21no—
263C23×C4—21no—
264C23×C4—21no—
265C23×C4—21no—
266C23×C4—28no—
267C23×C4—22no—
268C23×C4—22no—
269C23×C4—22no—
270C23×C4—22no—
271C23×C4—22no—
272C23×C4—22no—
273C23×C4—24no—
274C23×C4—21no—
275C23×C4—21no—
276C23×C4—82no—
277C23×C4—82no—
278C23×C4C2×D412yes—
279C23×C4C2×D411yescharacteristic
280C23×C4C2×D411yescharacteristic
281C23×C4C2×D411yescharacteristic
282C23×C4C2×D411yescharacteristic
283C23×C4C2×D411yescharacteristic
284C23×C4C2412yes—
285C23×C4C2411yescharacteristic
286C2×Q16—28no—
287C2×Q16—28no—
288C2×Q16—44no—
289C2×Q16—416no—
290C2×SD16—28no—
291C2×SD16—28no—
292C2×SD16—44no—
293C2×SD16—416no—
294C22×C8—22no—
295C22×C8—22no—
296C22×C8—22no—
297C22×C8—22no—
298C22×C8—22no—
299C22×C8—22no—
300C22×C8—22no—
301C22×C8—22no—
302C22×C8—22no—
303C22×C8—22no—
304C22×C8—22no—
305C22×C8—22no—
306C22×C8C2412yes—
307C22×C8C2412yes—
308C22×C8C2412yes—
309C22×C8C2412yes—
310C4⋊Q8—216no—
311C4⋊Q8—28no—
312C4⋊Q8C2×D4116yes—
313#126—264no—
314#124—264no—
315#124—216no—
316#124—28no—
317#124C2×D4116yes—
318#123—264no—
319C22⋊Q8—216no—
320C22⋊Q8—264no—
321C22⋊Q8—216no—
322C22⋊Q8—28no—
323C22⋊Q8—28no—
324C22⋊Q8—28no—
325C22⋊Q8—28no—
326#121—216no—
327#121—28no—
328#121—28no—
329C4×Q8—216no—
330C4×Q8—28no—
331C4×Q8—28no—
332C4×Q8—28no—
333C4×Q8—28no—
334C4×Q8—48no—
335C4×D4—216no—
336C4×D4—28no—
337C4×D4—28no—
338#117—216no—
339#117—28no—
340#117—28no—
341C2×C4⋊C4—28no—
342C2×C4⋊C4—28no—
343C2×C4⋊C4—28no—
344C2×C4⋊C4—28no—
345C2×C4⋊C4—24no—
346C2×C4⋊C4—24no—
347C2×C4⋊C4—24no—
348C2×C4⋊C4—24no—
349C2×C4⋊C4—24no—
350C2×C4⋊C4—24no—
351C2×C4⋊C4—21no—
352C2×C4⋊C4—22no—
353C2×C4⋊C4—21no—
354C2×C4⋊C4—22no—
355C2×C4⋊C4—21no—
356C2×C4⋊C4—22no—
357C2×C4⋊C4—22no—
358C2×C4⋊C4—22no—
359C2×C4⋊C4—22no—
360C2×C4⋊C4—22no—
361C2×C4⋊C4—24no—
362C2×C4⋊C4—21no—
363C2×C4⋊C4—21no—
364C2×C4⋊C4—24no—
365C2×C4⋊C4—44no—
366C2×C4⋊C4—82no—
367C2×C4⋊C4C2×D414yes—
368C2×C4⋊C4C2×D414yes—
369C2×C4⋊C4C2×D414yes—
370C2×C4⋊C4C2×D414yes—
371C2×C4⋊C4#4114yes—
372C2×C4⋊C4C2412yes—
373C2×C4⋊C4C2412yes—
374C2×C4⋊C4C2412yes—
375C2×C4⋊C4C2412yes—
376C2×C4⋊C4C2412yes—
377C2×C22⋊C4—28no—
378C2×C22⋊C4—28no—
379C2×C22⋊C4—28no—
380C2×C22⋊C4—28no—
381C2×C22⋊C4—24no—
382C2×C22⋊C4—24no—
383C2×C22⋊C4—28no—
384C2×C22⋊C4—28no—
385C2×C22⋊C4—24no—
386C2×C22⋊C4—24no—
387C2×C22⋊C4—24no—
388C2×C22⋊C4—24no—
389C2×C22⋊C4—24no—
390C2×C22⋊C4—24no—
391C2×C22⋊C4—24no—
392C2×C22⋊C4—82no—
393C2×C22⋊C4C2×D414yes—
394C2×C22⋊C4C2×D414yes—
395C2×C42—28no—
396C2×C42—22no—
397C2×C42—22no—
398C2×C42—24no—
399C2×C42—24no—
400C2×C42—24no—
401C2×C42—44no—
402C2×C42—82no—
403C2×C42C2×D412yes—
404C2×C42C2×D412yes—
405C2×C42C2×D414yes—
406C2×C42C2×D414yes—
407C2×C42C2412yes—
408C2×C42C2412yes—
409#106—28no—
410#106—28no—
411C4⋊C8—28no—
412C4⋊C8—28no—
413#103—28no—
414#103—28no—
415#103—28no—
416#103—28no—
417#103—44no—
418#102—28no—
419#102—28no—
420#102—44no—
421C22⋊C8—44no—
422C22⋊C8—44no—
423#95—24no—
424#95—24no—
425#95—24no—
426#95—24no—
427#95—24no—
428C24—22no—
429C24—24no—
430C24—22no—
431C24—22no—
432C24—22no—
433C24—22no—
434C24—22no—
435C24—22no—
436C24—22no—
437C24—42no—
438C24—42no—
439C24—42no—
440C24—42no—
441C24—42no—
442C24—42no—
443C24C22×D412yes—
444C24C22×D411yescharacteristic
445C2×Q8—24no—
446C2×Q8—216no—
447C2×Q8—24no—
448C2×Q8—22no—
449C2×Q8—22no—
450C2×Q8—28no—
451C2×Q8—28no—
452C2×Q8—28no—
453C2×Q8—28no—
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—42no—
463C2×Q8—42no—
464C2×Q8—42no—
465C2×Q8—42no—
466C2×Q8—44no—
467C2×Q8—44no—
468C2×Q8—44no—
469C2×Q8—44no—
470C2×Q8—816no—
471C2×Q8—84no—
472C2×Q8—84no—
473C2×Q8C22×D414yes—
474C2×Q8C2×#4114yes—
475C2×D4—216no—
476C2×D4—24no—
477C2×D4—28no—
478C2×D4—28no—
479C2×D4—22no—
480C2×D4—22no—
481C2×D4—22no—
482C2×D4—22no—
483C2×D4—22no—
484C2×D4—42no—
485C2×D4—42no—
486C2×D4—44no—
487C2×D4—44no—
488C2×D4—84no—
489C2×D4—84no—
490C2×D4—816no—
491C2×D4C22×D414yes—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—24no—
498C22×C4—22no—
499C22×C4—24no—
500C22×C4—22no—
501C22×C4—24no—
502C22×C4—24no—
503C22×C4—24no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—216no—
516C22×C4—24no—
517C22×C4—24no—
518C22×C4—24no—
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—42no—
528C22×C4—42no—
529C22×C4—42no—
530C22×C4—42no—
531C22×C4—42no—
532C22×C4—42no—
533C22×C4—42no—
534C22×C4—42no—
535C22×C4—42no—
536C22×C4—42no—
537C22×C4—44no—
538C22×C4—44no—
539C22×C4—44no—
540C22×C4—44no—
541C22×C4—42no—
542C22×C4—42no—
543C22×C4—42no—
544C22×C4—42no—
545C22×C4—42no—
546C22×C4—42no—
547C22×C4—84no—
548C22×C4—84no—
549C22×C4—816no—
550C22×C4#12014yes—
551C22×C4#12014yes—
552C22×C4C22×D412yes—
553C22×C4C22×D412yes—
554C22×C4C22×D412yes—
555C22×C4C22×D412yes—
556C22×C4C22×D412yes—
557C22×C4C22×D411yescharacteristic
558C22×C4C22×D412yes—
559C22×C4C22×D412yes—
560C22×C4C2×#4112yes—
561C22×C4C2×#4112yes—
562C22×C4H(5,𝔽2)12yes—
563C22×C42−1+412yes—
564C22×C4C2511yescharacteristic
565Q16—416no—
566SD16—416no—
567C2×C8—22no—
568C2×C8—22no—
569C2×C8—22no—
570C2×C8—22no—
571C2×C8—22no—
572C2×C8—22no—
573C2×C8—22no—
574C2×C8—22no—
575C2×C8—22no—
576C2×C8—22no—
577C2×C8—22no—
578C2×C8—22no—
579C2×C8—44no—
580C2×C8—44no—
581C2×C8—44no—
582C2×C8—44no—
583C4⋊C4—216no—
584C4⋊C4—216no—
585C4⋊C4—216no—
586C4⋊C4—216no—
587C4⋊C4—28no—
588C4⋊C4—28no—
589C4⋊C4—24no—
590C4⋊C4—24no—
591C4⋊C4—24no—
592C4⋊C4—22no—
593C4⋊C4—22no—
594C4⋊C4—22no—
595C4⋊C4—22no—
596C4⋊C4—22no—
597C4⋊C4—22no—
598C4⋊C4—22no—
599C4⋊C4—42no—
600C4⋊C4—48no—
601C4⋊C4—42no—
602C4⋊C4—84no—
603C4⋊C4C22×D414yes—
604C4⋊C4C22×D414yes—
605C4⋊C4C2×#4114yes—
606C22⋊C4—216no—
607C22⋊C4—216no—
608C22⋊C4—216no—
609C22⋊C4—216no—
610C22⋊C4—216no—
611C22⋊C4—216no—
612C22⋊C4—28no—
613C22⋊C4—28no—
614C22⋊C4—84no—
615C42—216no—
616C42—24no—
617C42—22no—
618C42—22no—
619C42—48no—
620C42—84no—
621C42#12018yes—
622C42C22×D414yes—
623C42C22×D414yes—
624C23—22no—
625C23—24no—
626C23—22no—
627C23—22no—
628C23—22no—
629C23—22no—
630C23—22no—
631C23—22no—
632C23—44no—
633C23—44no—
634C23—44no—
635C23—48no—
636C23—42no—
637C23—42no—
638C23—44no—
639C23—44no—
640C23—48no—
641C23—44no—
642C23—44no—
643C23—48no—
644C23—42no—
645C23—42no—
646C23—42no—
647C23—42no—
648C23—84no—
649C23—84no—
650C23—84no—
651C23—84no—
652C23C2×#12012yes—
653C23#52512yes—
654C23#53712yes—
655C23#57712yes—
656C23#57712yes—
657C23#57712yes—
658C23#57812yes—
659C23C23×D411yescharacteristic
660Q8—24no—
661Q8—24no—
662Q8—24no—
663Q8—24no—
664Q8—48no—
665Q8—48no—
666Q8—42no—
667Q8—42no—
668Q8—42no—
669Q8—42no—
670Q8—816no—
671D4—24no—
672D4—24no—
673D4—48no—
674D4—42no—
675D4—42no—
676D4—816no—
677C2×C4—28no—
678C2×C4—28no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—24no—
685C2×C4—22no—
686C2×C4—24no—
687C2×C4—22no—
688C2×C4—24no—
689C2×C4—24no—
690C2×C4—24no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—48no—
698C2×C4—44no—
699C2×C4—48no—
700C2×C4—48no—
701C2×C4—42no—
702C2×C4—42no—
703C2×C4—42no—
704C2×C4—42no—
705C2×C4—44no—
706C2×C4—48no—
707C2×C4—48no—
708C2×C4—44no—
709C2×C4—42no—
710C2×C4—42no—
711C2×C4—42no—
712C2×C4—42no—
713C2×C4—42no—
714C2×C4—42no—
715C2×C4—48no—
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—816no—
727C2×C4—84no—
728C2×C4—84no—
729C2×C4C2×#12014yes—
730C2×C4C2×#12014yes—
731C2×C4C2×#12012yes—
732C2×C4#52512yes—
733C2×C4#53712yes—
734C2×C4#54614yes—
735C2×C4#54714yes—
736C2×C4#54814yes—
737C2×C4#55014yes—
738C2×C4C23×D411yescharacteristic
739C2×C4C23×D411yescharacteristic
740C2×C4C22×#4111yescharacteristic
741C2×C4C22×#4111yescharacteristic
742C2×C4C2×H(5,𝔽2)11yescharacteristic
743C2×C4C2×2−1+411yescharacteristic
744C8—42no—
745C8—42no—
746C8—42no—
747C8—42no—
748C22—42no—
749C22—42no—
750C22—42no—
751C22—44no—
752C22—44no—
753C22—42no—
754C22—42no—
755C22—44no—
756C22—42no—
757C22—42no—
758C22—88no—
759C22—816no—
760C22—82no—
761C22—82no—
762C22—82no—
763C22—82no—
764C22#240714yes—
765C22#300914yes—
766C22#301314yes—
767C22#312114yes—
768C22#312514yes—
769C22#325814yes—
770C22#326314yes—
771C22C22×#12011yescharacteristic
772C22C2×#52511yescharacteristic
773C22C2×#53711yescharacteristic
774C22C2×#57711yescharacteristic
775C22C2×#57711yescharacteristic
776C22C2×#57711yescharacteristic
777C22C2×#57811yescharacteristic
778C4—24no—
779C4—24no—
780C4—44no—
781C4—42no—
782C4—44no—
783C4—44no—
784C4—42no—
785C4—44no—
786C4—44no—
787C4—42no—
788C4—82no—
789C4—82no—
790C4#240714yes—
791C4C2×#54611yescharacteristic
792C4C2×#54711yescharacteristic
793C4C2×#54811yescharacteristic
794C4C2×#55011yescharacteristic
795C2—82no—
796C2—84no—
797C2#2416918yesdirect product factor
798C2C2×#240711yescharacteristic
799C2C2×#300911yescharacteristic
800C2C2×#301311yescharacteristic
801C2C2×#312111yescharacteristic
802C2C2×#312511yescharacteristic
803C2C2×#325811yescharacteristic
804C2C2×#326311yescharacteristic
subgroupG/H
center, socleC24C22×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC22×#121C22
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×#475C2semidirect
3. C22×#464C2semidirect
4. C2×#2323C2semidirect
5. #24169C2direct (N × H)
7. C2×#2035C2semidirect
8. C2×#2001C2semidirect
10. C2×#1987C2semidirect
11. C2×#1983C2semidirect
12. C2×#1878C2semidirect
13. C2×#1877C2semidirect
14. C2×#1865C2semidirect
15. C2×#1864C2semidirect
16. C2×#1798C2semidirect
37. C2×#475C22semidirect
39. C2×#464C22semidirect
55. #2323C22semidirect
64. #2035C22semidirect
66. #2001C22semidirect
68. #1987C22semidirect
69. #1983C22semidirect
70. #1878C22semidirect
71. #1877C22semidirect
72. #1865C22semidirect
73. #1864C22semidirect
74. #1798C22semidirect
797. C2#24169direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#5422
C22×#4752
C22×#4642
C2×#23232
#241692
C2×#20342
C2×#20352
C2×#20012
C2×#20002
C2×#19872
C2×#19832
C2×#18782
C2×#18772
C2×#18652
C2×#18642
C2×#17982