Finite Group Databasebeta

← C2×#31002 #7503100

Subgroups — C2×#31002 #7503100

Order 512.

3024 conjugacy classes of subgroups.

The subgroup lattice has 822 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#461C211yesmaximal, characteristic, complemented
2C22×#448C211yesmaximal, characteristic
3C2×#2420C211yesmaximal, characteristic
4C2×#2434C211yesmaximal, characteristic, complemented
5#31002C2116yesmaximal, direct product factor
6C2×#2074C211yesmaximal, characteristic, complemented
7C2×#2068C211yesmaximal, characteristic, complemented
8C2×#2043C211yesmaximal, characteristic, complemented
9C2×#2036C211yesmaximal, characteristic, complemented
10C2×#2013C211yesmaximal, characteristic, complemented
11C2×#2000C211yesmaximal, characteristic
12C2×#1973C211yesmaximal, characteristic, complemented
13C2×#1960C211yesmaximal, characteristic, complemented
14C2×#1924C211yesmaximal, characteristic, complemented
15C2×#1877C211yesmaximal, characteristic, complemented
16C2×#1787C211yesmaximal, characteristic, complemented
17C24×Q8C2211yescharacteristic
18C23×SD16C2211yescharacteristic
19C23×SD16C2211yescharacteristic
20C23×SD16C2211yescharacteristic
21C22×C4⋊Q8C2211yescharacteristic
22C22×C4⋊Q8C2211yescharacteristic
23C22×C22⋊Q8C2211yescharacteristic
24C22×#121C2211yescharacteristic
25C22×C4×D4C2211yescharacteristic
26C2×#461—28no—
27C2×#461C2218yescomplemented
28C2×#448—28no—
29C2×#448C2218yes—
30C22×#107C2211yescharacteristic
31C22×C4⋊C8C2211yescharacteristic
32C22×#103C2211yescharacteristic
33C22×#103C2211yescharacteristic
34C22×#103C2211yescharacteristic
35C22×#103C2211yescharacteristic
36C22×#103C2211yescharacteristic
37C22×#103C2211yescharacteristic
38C22×#103C2211yescharacteristic
39C22×#103C2211yescharacteristic
40C22×#103C2211yescharacteristic
41C22×#102C2211yescharacteristic
42C22×C22⋊C8C2211yescharacteristic
43C22×C22⋊C8C2211yescharacteristic
44C22×#97C2211yescharacteristic
45#2434—24no—
46#2434C2218yescomplemented
47#2420—24no—
48#2420C2218yes—
49C2×#397—21no—
50C2×#395—21no—
51C2×#395—21no—
52C2×#394—21no—
53C2×#391C2211yescharacteristic
54C2×#391C2211yescharacteristic
55C2×#390C2211yescharacteristic
56C2×#389C2211yescharacteristic
57C2×#386—21no—
58C2×#385—21no—
59C2×#385—21no—
60C2×#382C2211yescharacteristic
61C2×#381—21no—
62C2×#380C2211yescharacteristic
63C2×C4×C22⋊C4C2211yescharacteristic
64#2074C2218yescomplemented
65#2068C2218yescomplemented
66#2043C2218yescomplemented
67#2036C2218yescomplemented
68#2013C2218yescomplemented
69#2000C2218yes—
70#1973C2218yescomplemented
71#1960C2218yescomplemented
72#1924C2218yescomplemented
73#1877C2218yescomplemented
74#1787C2218yescomplemented
75C2×#340C2211yescharacteristic
76C2×#340C2211yescharacteristic
77C2×#336C2211yescharacteristic
78C2×#336C2211yescharacteristic
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×D4—21no—
92C23×D4C2311yescharacteristic
93C24×C4—21no—
94C24×C4—21no—
95C24×C4C2311yescharacteristic
96C22×SD16—24no—
97C22×SD16—24no—
98C22×SD16—24no—
99C22×SD16—42no—
100C22×SD16—42no—
101C22×SD16—42no—
102C22×SD16—42no—
103C22×SD16—42no—
104C22×SD16D418yes—
105C22×SD16C2314yes—
106C22×SD16C2314yes—
107C22×SD16C2314yes—
108C23×C8C2311yescharacteristic
109C23×C8C2311yescharacteristic
110C23×C8C2311yescharacteristic
111C23×C8C2311yescharacteristic
112C2×C4⋊Q8—24no—
113C2×C4⋊Q8—24no—
114C2×C4⋊Q8—22no—
115C2×C4⋊Q8—22no—
116C2×C4⋊Q8—42no—
117C2×C4⋊Q8—42no—
118C2×C4⋊Q8C2314yes—
119C2×C4⋊Q8C2314yes—
120C2×C22⋊Q8—22no—
121C2×C22⋊Q8—42no—
122C2×C22⋊Q8—42no—
123C2×C22⋊Q8C2314yes—
124C2×#121—22no—
125C2×#121—24no—
126C2×#121—42no—
127C2×#121C2314yes—
128C2×C4×D4—24no—
129C2×C4×D4—22no—
130C2×C4×D4—42no—
131C2×C4×D4C2314yes—
132C22×C4⋊C4—21no—
133C22×C4⋊C4—21no—
134C22×C4⋊C4—21no—
135C22×C4⋊C4—21no—
136C22×C4⋊C4—21no—
137C22×C4⋊C4—21no—
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⋊C4D411yescharacteristic
149C22×C22⋊C4D411yescharacteristic
150C22×C42C2311yescharacteristic
151C22×C42C2311yescharacteristic
152#461—232no—
153#448—232no—
154C2×#107—42no—
155C2×#107C2314yes—
156C2×C4⋊C8—24no—
157C2×C4⋊C8C2314yes—
158C2×#103—24no—
159C2×#103—24no—
160C2×#103—24no—
161C2×#103—24no—
162C2×#103—42no—
163C2×#103—42no—
164C2×#103—42no—
165C2×#103—42no—
166C2×#103—42no—
167C2×#103C2314yes—
168C2×#103C2314yes—
169C2×#103C2314yes—
170C2×#103C2314yes—
171C2×#103C2314yes—
172C2×#103C2314yes—
173C2×#103C2314yes—
174C2×#103C2314yes—
175C2×#103C2314yes—
176C2×#102—42no—
177C2×#102C2314yes—
178C2×C22⋊C8—24no—
179C2×C22⋊C8—42no—
180C2×C22⋊C8C2314yes—
181C2×C22⋊C8C2314yes—
182C2×#97—42no—
183C2×#97C2314yes—
184#397—28no—
185#395—28no—
186#395—28no—
187#394—28no—
188#391—22no—
189#391—22no—
190#391C2314yes—
191#391C2314yes—
192#390—22no—
193#390C2314yes—
194#389—22no—
195#389C2314yes—
196#386—28no—
197#385—28no—
198#385—28no—
199#382—22no—
200#382C2314yes—
201#381—28no—
202#380—22no—
203#380C2314yes—
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
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—21no—
265C22×D4—22no—
266C22×D4—22no—
267C22×D4—22no—
268C22×D4—22no—
269C22×D4—22no—
270C22×D4—44no—
271C22×D4—44no—
272C22×D4—82no—
273C22×D4C2×D414yes—
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—24no—
284C23×C4—21no—
285C23×C4—21no—
286C23×C4—21no—
287C23×C4—21no—
288C23×C4—21no—
289C23×C4—24no—
290C23×C4—44no—
291C23×C4—44no—
292C23×C4—44no—
293C23×C4—44no—
294C23×C4—44no—
295C23×C4—82no—
296C23×C4C2×D412yes—
297C23×C4C2×D411yescharacteristic
298C23×C4C2×D411yescharacteristic
299C23×C4C2×D411yescharacteristic
300C23×C4C2×D411yescharacteristic
301C23×C4C2×D411yescharacteristic
302C23×C4C2412yes—
303C23×C4C2411yescharacteristic
304C2×SD16—28no—
305C2×SD16—28no—
306C2×SD16—28no—
307C2×SD16—416no—
308C2×SD16—44no—
309C2×SD16—44no—
310C2×SD16—44no—
311C2×SD16—44no—
312C2×SD16—44no—
313C2×SD16—416no—
314C2×SD16—416no—
315C2×SD16C2×D4116yes—
316C22×C8—22no—
317C22×C8—22no—
318C22×C8—22no—
319C22×C8—22no—
320C22×C8—22no—
321C22×C8—22no—
322C22×C8—22no—
323C22×C8—22no—
324C22×C8—22no—
325C22×C8—22no—
326C22×C8—22no—
327C22×C8C2×D414yes—
328C22×C8C2412yes—
329C22×C8C2412yes—
330C22×C8C2412yes—
331C22×C8C2412yes—
332C4⋊Q8—28no—
333C4⋊Q8—28no—
334C4⋊Q8—44no—
335C4⋊Q8—44no—
336C4⋊Q8—48no—
337C4⋊Q8—48no—
338C22⋊Q8—44no—
339C22⋊Q8—44no—
340C22⋊Q8—48no—
341#121—28no—
342#121—44no—
343#121—48no—
344C4×D4—28no—
345C4×D4—44no—
346C4×D4—48no—
347C2×C4⋊C4—22no—
348C2×C4⋊C4—22no—
349C2×C4⋊C4—22no—
350C2×C4⋊C4—22no—
351C2×C4⋊C4—22no—
352C2×C4⋊C4—22no—
353C2×C4⋊C4—22no—
354C2×C4⋊C4—22no—
355C2×C4⋊C4—24no—
356C2×C4⋊C4—24no—
357C2×C4⋊C4—24no—
358C2×C4⋊C4—24no—
359C2×C4⋊C4—24no—
360C2×C4⋊C4—21no—
361C2×C4⋊C4—21no—
362C2×C4⋊C4—21no—
363C2×C4⋊C4—21no—
364C2×C4⋊C4—24no—
365C2×C4⋊C4—44no—
366C2×C4⋊C4—44no—
367C2×C4⋊C4—44no—
368C2×C4⋊C4—44no—
369C2×C4⋊C4—44no—
370C2×C4⋊C4—82no—
371C2×C4⋊C4C2412yes—
372C2×C4⋊C4C2412yes—
373C2×C4⋊C4C2412yes—
374C2×C4⋊C4C2412yes—
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—24no—
382C2×C22⋊C4—24no—
383C2×C22⋊C4—44no—
384C2×C22⋊C4—44no—
385C2×C22⋊C4—44no—
386C2×C22⋊C4—82no—
387C2×C22⋊C4—82no—
388C2×C22⋊C4—82no—
389C2×C22⋊C4C2×D414yes—
390C2×C22⋊C4C2×D414yes—
391C2×C42—22no—
392C2×C42—22no—
393C2×C42—22no—
394C2×C42—22no—
395C2×C42C2×D412yes—
396C2×C42C2×D412yes—
397C2×C42C2412yes—
398C2×C42C2412yes—
399#107—44no—
400C4⋊C8—28no—
401#103—28no—
402#103—28no—
403#103—28no—
404#103—28no—
405#103—44no—
406#103—44no—
407#103—44no—
408#103—44no—
409#103—44no—
410#102—44no—
411C22⋊C8—28no—
412C22⋊C8—44no—
413#97—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#95C2×D414yes—
423#95C2×D414yes—
424C24—22no—
425C24—22no—
426C24—22no—
427C24—22no—
428C24—22no—
429C24—22no—
430C24—24no—
431C24—22no—
432C24—42no—
433C24—42no—
434C24—42no—
435C24—42no—
436C24—42no—
437C24—42no—
438C24#13714yes—
439C24C22×D412yes—
440C24C22×D411yescharacteristic
441C2×Q8—24no—
442C2×Q8—24no—
443C2×Q8—22no—
444C2×Q8—22no—
445C2×Q8—28no—
446C2×Q8—28no—
447C2×Q8—28no—
448C2×Q8—28no—
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—48no—
464C2×Q8—48no—
465C2×Q8—48no—
466C2×Q8—416no—
467C2×Q8—416no—
468C2×Q8—416no—
469C2×Q8—464no—
470C2×Q8—416no—
471C2×Q8—432no—
472C2×Q8—44no—
473C2×Q8—42no—
474C2×Q8—42no—
475C2×Q8—42no—
476C2×Q8—44no—
477C2×Q8—42no—
478C2×Q8—42no—
479C2×Q8—42no—
480C2×Q8—42no—
481C2×Q8—44no—
482C2×Q8—44no—
483C2×Q8—44no—
484C2×Q8—44no—
485C2×Q8—44no—
486C2×Q8—44no—
487C2×Q8C22×D414yes—
488C2×Q8C2×#4114yes—
489C2×D4—28no—
490C2×D4—24no—
491C2×D4—28no—
492C2×D4—22no—
493C2×D4—22no—
494C2×D4—22no—
495C2×D4—22no—
496C2×D4—22no—
497C2×D4—48no—
498C2×D4—48no—
499C2×D4—42no—
500C2×D4—44no—
501C2×D4—42no—
502C2×D4—44no—
503C2×D4—84no—
504C2×D4—816no—
505C2×D4C22×D414yes—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—24no—
512C22×C4—22no—
513C22×C4—22no—
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—24no—
525C22×C4—24no—
526C22×C4—24no—
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—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—48no—
539C22×C4—48no—
540C22×C4—48no—
541C22×C4—48no—
542C22×C4—432no—
543C22×C4—42no—
544C22×C4—42no—
545C22×C4—42no—
546C22×C4—42no—
547C22×C4—44no—
548C22×C4—44no—
549C22×C4—44no—
550C22×C4—44no—
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—42no—
566C22×C4—48no—
567C22×C4—84no—
568C22×C4—816no—
569C22×C4#13714yes—
570C22×C4C22×D412yes—
571C22×C4C22×D412yes—
572C22×C4C22×D412yes—
573C22×C4C22×D412yes—
574C22×C4C22×D412yes—
575C22×C4C22×D412yes—
576C22×C4C22×D411yescharacteristic
577C22×C4C2×#4112yes—
578C22×C4H(5,𝔽2)12yes—
579C22×C4H(5,𝔽2)12yes—
580C22×C4H(5,𝔽2)12yes—
581C22×C4H(5,𝔽2)12yes—
582C22×C4C2511yescharacteristic
583SD16—416no—
584SD16—416no—
585SD16—416no—
586C2×C8—28no—
587C2×C8—22no—
588C2×C8—22no—
589C2×C8—22no—
590C2×C8—22no—
591C2×C8—22no—
592C2×C8—22no—
593C2×C8—22no—
594C2×C8—22no—
595C2×C8—22no—
596C2×C8—22no—
597C2×C8—22no—
598C2×C8—44no—
599C2×C8—44no—
600C2×C8—44no—
601C2×C8C22×D414yes—
602C4⋊C4—22no—
603C4⋊C4—22no—
604C4⋊C4—22no—
605C4⋊C4—22no—
606C4⋊C4—22no—
607C4⋊C4—22no—
608C4⋊C4—22no—
609C4⋊C4—22no—
610C4⋊C4—48no—
611C4⋊C4—48no—
612C4⋊C4—48no—
613C4⋊C4—48no—
614C4⋊C4—48no—
615C4⋊C4—42no—
616C4⋊C4—42no—
617C4⋊C4—42no—
618C4⋊C4—42no—
619C4⋊C4—84no—
620C22⋊C4—28no—
621C22⋊C4—28no—
622C22⋊C4—48no—
623C22⋊C4—48no—
624C22⋊C4—48no—
625C22⋊C4—84no—
626C22⋊C4—84no—
627C22⋊C4—84no—
628C42—24no—
629C42—24no—
630C42—22no—
631C42—22no—
632C42—22no—
633C42—22no—
634C23—22no—
635C23—22no—
636C23—22no—
637C23—28no—
638C23—28no—
639C23—28no—
640C23—22no—
641C23—22no—
642C23—22no—
643C23—24no—
644C23—44no—
645C23—44no—
646C23—44no—
647C23—44no—
648C23—48no—
649C23—42no—
650C23—42no—
651C23—48no—
652C23—48no—
653C23—42no—
654C23—42no—
655C23—42no—
656C23—42no—
657C23—84no—
658C23—84no—
659C23—84no—
660C23—84no—
661C23#53512yes—
662C23D4212yes—
663C23#54612yes—
664C23C2×#13714yes—
665C23C2×#13712yes—
666C23C2×#13712yes—
667C23#57712yes—
668C23#57712yes—
669C23C23×D411yescharacteristic
670Q8—24no—
671Q8—24no—
672Q8—24no—
673Q8—24no—
674Q8—432no—
675Q8—42no—
676Q8—48no—
677Q8—48no—
678Q8—42no—
679Q8—42no—
680Q8—42no—
681Q8—42no—
682Q8—42no—
683Q8—42no—
684Q8—42no—
685Q8—84no—
686D4—24no—
687D4—24no—
688D4—48no—
689D4—42no—
690D4—42no—
691D4—816no—
692C2×C4—22no—
693C2×C4—28no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—24no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—24no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—432no—
710C2×C4—44no—
711C2×C4—44no—
712C2×C4—48no—
713C2×C4—48no—
714C2×C4—42no—
715C2×C4—42no—
716C2×C4—42no—
717C2×C4—42no—
718C2×C4—44no—
719C2×C4—44no—
720C2×C4—42no—
721C2×C4—48no—
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—42no—
737C2×C4—42no—
738C2×C4—42no—
739C2×C4—42no—
740C2×C4—816no—
741C2×C4—84no—
742C2×C4—84no—
743C2×C4—84no—
744C2×C4—84no—
745C2×C4—84no—
746C2×C4#53414yes—
747C2×C4#53512yes—
748C2×C4#53814yes—
749C2×C4D4212yes—
750C2×C4#54612yes—
751C2×C4#54614yes—
752C2×C4#56014yes—
753C2×C4C2×#13714yes—
754C2×C4C23×D411yescharacteristic
755C2×C4C22×#4111yescharacteristic
756C2×C4C2×H(5,𝔽2)11yescharacteristic
757C2×C4C2×H(5,𝔽2)11yescharacteristic
758C2×C4C2×H(5,𝔽2)11yescharacteristic
759C2×C4C2×H(5,𝔽2)11yescharacteristic
760C8—24no—
761C8—42no—
762C8—42no—
763C8—42no—
764C22—24no—
765C22—24no—
766C22—24no—
767C22—416no—
768C22—42no—
769C22—42no—
770C22—42no—
771C22—42no—
772C22—44no—
773C22—44no—
774C22—44no—
775C22—816no—
776C22—82no—
777C22—82no—
778C22—82no—
779C22—82no—
780C22#267814yes—
781C22#321814yes—
782C22#322114yes—
783C22#326614yes—
784C22#326614yes—
785C22#332014yes—
786C22#332914yes—
787C22C2×#53511yescharacteristic
788C22C2×D4211yescharacteristic
789C22C2×#54611yescharacteristic
790C22C22×#13711yescharacteristic
791C22C22×#13711yescharacteristic
792C22C2×#57711yescharacteristic
793C22C2×#57711yescharacteristic
794C4—24no—
795C4—42no—
796C4—42no—
797C4—44no—
798C4—44no—
799C4—42no—
800C4—42no—
801C4—82no—
802C4—82no—
803C4—82no—
804C4—82no—
805C4—82no—
806C4#267814yes—
807C4C2×#53411yescharacteristic
808C4C2×#53811yescharacteristic
809C4C2×#54611yescharacteristic
810C4C2×#56011yescharacteristic
811C2—44no—
812C2—84no—
813C2#3100218yesdirect product factor
814C2C2×#267811yescharacteristic
815C2C2×#321811yescharacteristic
816C2C2×#322111yescharacteristic
817C2C2×#326611yescharacteristic
818C2C2×#326611yescharacteristic
819C2C2×#332011yescharacteristic
820C2C2×#332911yescharacteristic
subgroupG/H
center, socleC24C22×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC22×#121C22
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×#461C2semidirect
4. C2×#2434C2semidirect
5. #31002C2direct (N × H)
6. C2×#2074C2semidirect
7. C2×#2068C2semidirect
8. C2×#2043C2semidirect
9. C2×#2036C2semidirect
10. C2×#2013C2semidirect
12. C2×#1973C2semidirect
13. C2×#1960C2semidirect
14. C2×#1924C2semidirect
15. C2×#1877C2semidirect
16. C2×#1787C2semidirect
27. C2×#461C22semidirect
46. #2434C22semidirect
64. #2074C22semidirect
65. #2068C22semidirect
66. #2043C22semidirect
67. #2036C22semidirect
68. #2013C22semidirect
70. #1973C22semidirect
71. #1960C22semidirect
72. #1924C22semidirect
73. #1877C22semidirect
74. #1787C22semidirect
813. C2#31002direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#4612
C22×#4482
C2×#24202
C2×#24342
#310022
C2×#20742
C2×#20682
C2×#20432
C2×#20362
C2×#20132
C2×#20002
C2×#19732
C2×#19602
C2×#19242
C2×#18772
C2×#17872