Finite Group Databasebeta

← C2×#30986 #7503083

Subgroups — C2×#30986 #7503083

Order 512.

3138 conjugacy classes of subgroups.

The subgroup lattice has 828 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#461C211yesmaximal, characteristic, complemented
2C22×#448C211yesmaximal, characteristic
3C2×#2434C211yesmaximal, characteristic, complemented
4C2×#2422C211yesmaximal, characteristic
5#30986C2116yesmaximal, direct product factor
6C2×#2072C211yesmaximal, characteristic, complemented
7C2×#2066C211yesmaximal, characteristic, complemented
8C2×#2043C211yesmaximal, characteristic, complemented
9C2×#2035C211yesmaximal, characteristic, complemented
10C2×#2013C211yesmaximal, characteristic, complemented
11C2×#2000C211yesmaximal, characteristic
12C2×#1968C211yesmaximal, characteristic, complemented
13C2×#1956C211yesmaximal, characteristic, complemented
14C2×#1923C211yesmaximal, 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×#123—21no—
24C22×C22⋊Q8C2211yescharacteristic
25C22×#121C2211yescharacteristic
26C22×C4×D4C2211yescharacteristic
27C2×#461—28no—
28C2×#461C2218yescomplemented
29C2×#448—28no—
30C2×#448C2218yes—
31C22×#106C2211yescharacteristic
32C22×C4⋊C8C2211yescharacteristic
33C22×#103C2211yescharacteristic
34C22×#103C2211yescharacteristic
35C22×#103C2211yescharacteristic
36C22×#103C2211yescharacteristic
37C22×#103C2211yescharacteristic
38C22×#103C2211yescharacteristic
39C22×#103C2211yescharacteristic
40C22×#103C2211yescharacteristic
41C22×#103C2211yescharacteristic
42C22×#102C2211yescharacteristic
43C22×C22⋊C8C2211yescharacteristic
44C22×C22⋊C8C2211yescharacteristic
45C22×C4×C8C2211yescharacteristic
46#2434—24no—
47#2434C2218yescomplemented
48#2422—24no—
49#2422C2218yes—
50C2×#397—21no—
51C2×#395—21no—
52C2×#395—21no—
53C2×#394—21no—
54C2×#391C2211yescharacteristic
55C2×#391C2211yescharacteristic
56C2×#390C2211yescharacteristic
57C2×#389C2211yescharacteristic
58C2×#385—21no—
59C2×#385—21no—
60C2×#385—21no—
61C2×#384C2211yescharacteristic
62C2×#380C2211yescharacteristic
63C2×C4×C22⋊C4C2211yescharacteristic
64#2072C2218yescomplemented
65#2066C2218yescomplemented
66#2043C2218yescomplemented
67#2035C2218yescomplemented
68#2013C2218yescomplemented
69#2000C2218yes—
70#1968C2218yescomplemented
71#1956C2218yescomplemented
72#1923C2218yescomplemented
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×#123—28no—
121C2×#123—48no—
122C2×C22⋊Q8—22no—
123C2×C22⋊Q8—42no—
124C2×C22⋊Q8—42no—
125C2×C22⋊Q8C2314yes—
126C2×#121—22no—
127C2×#121—24no—
128C2×#121—42no—
129C2×#121C2314yes—
130C2×C4×D4—24no—
131C2×C4×D4—22no—
132C2×C4×D4—42no—
133C2×C4×D4C2314yes—
134C22×C4⋊C4—21no—
135C22×C4⋊C4—21no—
136C22×C4⋊C4—21no—
137C22×C4⋊C4—21no—
138C22×C4⋊C4—21no—
139C22×C4⋊C4—21no—
140C22×C4⋊C4—21no—
141C22×C4⋊C4—21no—
142C22×C4⋊C4C2311yescharacteristic
143C22×C4⋊C4C2311yescharacteristic
144C22×C4⋊C4C2311yescharacteristic
145C22×C4⋊C4C2311yescharacteristic
146C22×C22⋊C4—21no—
147C22×C22⋊C4—21no—
148C22×C22⋊C4—21no—
149C22×C22⋊C4—21no—
150C22×C22⋊C4—21no—
151C22×C22⋊C4—21no—
152C22×C22⋊C4D411yescharacteristic
153C22×C22⋊C4D411yescharacteristic
154C22×C42C2311yescharacteristic
155C22×C42C2311yescharacteristic
156#461—232no—
157#448—232no—
158C2×#106—42no—
159C2×#106C2314yes—
160C2×C4⋊C8—24no—
161C2×C4⋊C8C2314yes—
162C2×#103—24no—
163C2×#103—24no—
164C2×#103—24no—
165C2×#103—24no—
166C2×#103—42no—
167C2×#103—42no—
168C2×#103—42no—
169C2×#103—42no—
170C2×#103—42no—
171C2×#103C2314yes—
172C2×#103C2314yes—
173C2×#103C2314yes—
174C2×#103C2314yes—
175C2×#103C2314yes—
176C2×#103C2314yes—
177C2×#103C2314yes—
178C2×#103C2314yes—
179C2×#103C2314yes—
180C2×#102—42no—
181C2×#102C2314yes—
182C2×C22⋊C8—24no—
183C2×C22⋊C8—42no—
184C2×C22⋊C8C2314yes—
185C2×C22⋊C8C2314yes—
186C2×C4×C8—42no—
187C2×C4×C8C2314yes—
188#397—28no—
189#395—28no—
190#395—28no—
191#394—28no—
192#391—22no—
193#391—22no—
194#391C2314yes—
195#391C2314yes—
196#390—22no—
197#390C2314yes—
198#389—22no—
199#389C2314yes—
200#385—28no—
201#385—28no—
202#385—28no—
203#384—22no—
204#384C2314yes—
205#380—22no—
206#380C2314yes—
207C4×C22⋊C4D414yes—
208C4×C22⋊C4C2314yes—
209C2×#95—21no—
210C2×#95—21no—
211C2×#95—21no—
212C2×#95—21no—
213C2×#95—21no—
214C2×#95—21no—
215C2×#95D411yescharacteristic
216C2×#95D411yescharacteristic
217#340C2314yes—
218#340C2314yes—
219#336C2314yes—
220#336C2314yes—
221C25—21no—
222C25C2×D411yescharacteristic
223C22×Q8—21no—
224C22×Q8—21no—
225C22×Q8—21no—
226C22×Q8—24no—
227C22×Q8—22no—
228C22×Q8—22no—
229C22×Q8—28no—
230C22×Q8—28no—
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—22no—
245C22×Q8—44no—
246C22×Q8—44no—
247C22×Q8—44no—
248C22×Q8—44no—
249C22×Q8—44no—
250C22×Q8—44no—
251C22×Q8—48no—
252C22×Q8—48no—
253C22×Q8—44no—
254C22×Q8—48no—
255C22×Q8—416no—
256C22×Q8—416no—
257C22×Q8—416no—
258C22×Q8—416no—
259C22×Q8C2×D414yes—
260C22×Q8#4114yes—
261C22×Q8C2412yes—
262C22×Q8C2412yes—
263C22×Q8C2412yes—
264C22×D4—24no—
265C22×D4—21no—
266C22×D4—22no—
267C22×D4—22no—
268C22×D4—22no—
269C22×D4—22no—
270C22×D4—22no—
271C22×D4—44no—
272C22×D4—44no—
273C22×D4—82no—
274C22×D4C2×D414yes—
275C22×D4C2412yes—
276C23×C4—21no—
277C23×C4—21no—
278C23×C4—22no—
279C23×C4—22no—
280C23×C4—22no—
281C23×C4—22no—
282C23×C4—22no—
283C23×C4—22no—
284C23×C4—24no—
285C23×C4—21no—
286C23×C4—21no—
287C23×C4—21no—
288C23×C4—21no—
289C23×C4—21no—
290C23×C4—24no—
291C23×C4—44no—
292C23×C4—44no—
293C23×C4—44no—
294C23×C4—44no—
295C23×C4—44no—
296C23×C4—82no—
297C23×C4C2×D412yes—
298C23×C4C2×D411yescharacteristic
299C23×C4C2×D411yescharacteristic
300C23×C4C2×D411yescharacteristic
301C23×C4C2×D411yescharacteristic
302C23×C4C2×D411yescharacteristic
303C23×C4C2412yes—
304C23×C4C2411yescharacteristic
305C2×SD16—28no—
306C2×SD16—28no—
307C2×SD16—28no—
308C2×SD16—416no—
309C2×SD16—44no—
310C2×SD16—44no—
311C2×SD16—44no—
312C2×SD16—44no—
313C2×SD16—44no—
314C2×SD16—416no—
315C2×SD16—416no—
316C2×SD16C2×D4116yes—
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×C8—22no—
328C22×C8C2×D414yes—
329C22×C8C2412yes—
330C22×C8C2412yes—
331C22×C8C2412yes—
332C22×C8C2412yes—
333C4⋊Q8—28no—
334C4⋊Q8—28no—
335C4⋊Q8—44no—
336C4⋊Q8—44no—
337C4⋊Q8—48no—
338C4⋊Q8—48no—
339#123—432no—
340C22⋊Q8—44no—
341C22⋊Q8—44no—
342C22⋊Q8—48no—
343#121—28no—
344#121—44no—
345#121—48no—
346C4×D4—28no—
347C4×D4—44no—
348C4×D4—48no—
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—22no—
356C2×C4⋊C4—22no—
357C2×C4⋊C4—24no—
358C2×C4⋊C4—24no—
359C2×C4⋊C4—24no—
360C2×C4⋊C4—24no—
361C2×C4⋊C4—24no—
362C2×C4⋊C4—24no—
363C2×C4⋊C4—24no—
364C2×C4⋊C4—21no—
365C2×C4⋊C4—21no—
366C2×C4⋊C4—21no—
367C2×C4⋊C4—21no—
368C2×C4⋊C4—24no—
369C2×C4⋊C4—44no—
370C2×C4⋊C4—44no—
371C2×C4⋊C4—44no—
372C2×C4⋊C4—44no—
373C2×C4⋊C4—44no—
374C2×C4⋊C4—44no—
375C2×C4⋊C4—44no—
376C2×C4⋊C4—82no—
377C2×C4⋊C4C2412yes—
378C2×C4⋊C4C2412yes—
379C2×C4⋊C4C2412yes—
380C2×C4⋊C4C2412yes—
381C2×C22⋊C4—24no—
382C2×C22⋊C4—24no—
383C2×C22⋊C4—24no—
384C2×C22⋊C4—24no—
385C2×C22⋊C4—24no—
386C2×C22⋊C4—24no—
387C2×C22⋊C4—24no—
388C2×C22⋊C4—44no—
389C2×C22⋊C4—44no—
390C2×C22⋊C4—44no—
391C2×C22⋊C4—44no—
392C2×C22⋊C4—44no—
393C2×C22⋊C4—44no—
394C2×C22⋊C4SD1618yescomplemented
395C2×C22⋊C4C2×D414yes—
396C2×C22⋊C4C2×D414yes—
397C2×C42—22no—
398C2×C42—22no—
399C2×C42—22no—
400C2×C42—22no—
401C2×C42C2×D412yes—
402C2×C42C2×D412yes—
403C2×C42C2412yes—
404C2×C42C2412yes—
405#106—44no—
406C4⋊C8—28no—
407#103—28no—
408#103—28no—
409#103—28no—
410#103—28no—
411#103—44no—
412#103—44no—
413#103—44no—
414#103—44no—
415#103—44no—
416#102—44no—
417C22⋊C8—28no—
418C22⋊C8—44no—
419C4×C8—44no—
420#95—24no—
421#95—24no—
422#95—24no—
423#95—24no—
424#95—24no—
425#95—24no—
426#95C2×D414yes—
427#95C2×D414yes—
428C24—22no—
429C24—22no—
430C24—22no—
431C24—22no—
432C24—22no—
433C24—22no—
434C24—24no—
435C24—22no—
436C24—42no—
437C24—42no—
438C24—42no—
439C24—42no—
440C24—42no—
441C24—42no—
442C24C2×SD1614yes—
443C24C22×D412yes—
444C24C22×D411yescharacteristic
445C2×Q8—24no—
446C2×Q8—24no—
447C2×Q8—22no—
448C2×Q8—22no—
449C2×Q8—28no—
450C2×Q8—28no—
451C2×Q8—28no—
452C2×Q8—28no—
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—22no—
465C2×Q8—22no—
466C2×Q8—22no—
467C2×Q8—48no—
468C2×Q8—48no—
469C2×Q8—48no—
470C2×Q8—416no—
471C2×Q8—416no—
472C2×Q8—416no—
473C2×Q8—464no—
474C2×Q8—416no—
475C2×Q8—432no—
476C2×Q8—44no—
477C2×Q8—42no—
478C2×Q8—42no—
479C2×Q8—42no—
480C2×Q8—44no—
481C2×Q8—42no—
482C2×Q8—42no—
483C2×Q8—42no—
484C2×Q8—42no—
485C2×Q8—44no—
486C2×Q8—44no—
487C2×Q8—44no—
488C2×Q8—44no—
489C2×Q8—44no—
490C2×Q8—44no—
491C2×Q8C22×D414yes—
492C2×Q8C2×#4114yes—
493C2×D4—28no—
494C2×D4—24no—
495C2×D4—28no—
496C2×D4—22no—
497C2×D4—22no—
498C2×D4—22no—
499C2×D4—22no—
500C2×D4—22no—
501C2×D4—48no—
502C2×D4—48no—
503C2×D4—42no—
504C2×D4—44no—
505C2×D4—42no—
506C2×D4—44no—
507C2×D4—84no—
508C2×D4—816no—
509C2×D4C22×D414yes—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—24no—
520C22×C4—24no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—24no—
527C22×C4—24no—
528C22×C4—24no—
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—22no—
539C22×C4—22no—
540C22×C4—48no—
541C22×C4—48no—
542C22×C4—48no—
543C22×C4—48no—
544C22×C4—432no—
545C22×C4—42no—
546C22×C4—42no—
547C22×C4—42no—
548C22×C4—42no—
549C22×C4—44no—
550C22×C4—44no—
551C22×C4—44no—
552C22×C4—44no—
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—42no—
567C22×C4—42no—
568C22×C4—48no—
569C22×C4—84no—
570C22×C4—816no—
571C22×C4C2×SD1614yes—
572C22×C4C2×SD1614yes—
573C22×C4#13714yes—
574C22×C4C22×D412yes—
575C22×C4C22×D412yes—
576C22×C4C22×D412yes—
577C22×C4C22×D412yes—
578C22×C4C22×D412yes—
579C22×C4C22×D412yes—
580C22×C4C22×D411yescharacteristic
581C22×C4C2×#4112yes—
582C22×C4H(5,𝔽2)12yes—
583C22×C4H(5,𝔽2)12yes—
584C22×C4H(5,𝔽2)12yes—
585C22×C4H(5,𝔽2)12yes—
586C22×C4C2511yescharacteristic
587SD16—416no—
588SD16—416no—
589SD16—416no—
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—22no—
602C2×C8—44no—
603C2×C8—44no—
604C2×C8—44no—
605C2×C8C22×D414yes—
606C4⋊C4—22no—
607C4⋊C4—22no—
608C4⋊C4—22no—
609C4⋊C4—22no—
610C4⋊C4—22no—
611C4⋊C4—22no—
612C4⋊C4—22no—
613C4⋊C4—22no—
614C4⋊C4—48no—
615C4⋊C4—48no—
616C4⋊C4—48no—
617C4⋊C4—48no—
618C4⋊C4—48no—
619C4⋊C4—42no—
620C4⋊C4—42no—
621C4⋊C4—42no—
622C4⋊C4—42no—
623C4⋊C4—48no—
624C4⋊C4—48no—
625C4⋊C4—84no—
626C22⋊C4—28no—
627C22⋊C4—48no—
628C22⋊C4—48no—
629C22⋊C4—48no—
630C22⋊C4—48no—
631C22⋊C4—48no—
632C22⋊C4—48no—
633C22⋊C4C2×SD16116yescomplemented
634C42—24no—
635C42—24no—
636C42—22no—
637C42—22no—
638C42—22no—
639C42—22no—
640C23—22no—
641C23—28no—
642C23—22no—
643C23—22no—
644C23—28no—
645C23—28no—
646C23—22no—
647C23—22no—
648C23—22no—
649C23—24no—
650C23—44no—
651C23—44no—
652C23—44no—
653C23—44no—
654C23—48no—
655C23—42no—
656C23—42no—
657C23—48no—
658C23—48no—
659C23—42no—
660C23—42no—
661C23—42no—
662C23—42no—
663C23—84no—
664C23—84no—
665C23—84no—
666C23—84no—
667C23#53512yes—
668C23D4212yes—
669C23#54612yes—
670C23C22×SD1614yes—
671C23C22×SD1612yes—
672C23C2×#13712yes—
673C23#57712yes—
674C23#57812yes—
675C23C23×D411yescharacteristic
676Q8—24no—
677Q8—24no—
678Q8—24no—
679Q8—24no—
680Q8—432no—
681Q8—42no—
682Q8—48no—
683Q8—48no—
684Q8—42no—
685Q8—42no—
686Q8—42no—
687Q8—42no—
688Q8—42no—
689Q8—42no—
690Q8—42no—
691Q8—84no—
692D4—24no—
693D4—24no—
694D4—48no—
695D4—42no—
696D4—42no—
697D4—816no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—28no—
702C2×C4—28no—
703C2×C4—28no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—24no—
711C2×C4—24no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—432no—
716C2×C4—44no—
717C2×C4—48no—
718C2×C4—48no—
719C2×C4—42no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—44no—
724C2×C4—42no—
725C2×C4—48no—
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—42no—
741C2×C4—42no—
742C2×C4—42no—
743C2×C4—42no—
744C2×C4—816no—
745C2×C4—84no—
746C2×C4—84no—
747C2×C4—84no—
748C2×C4—84no—
749C2×C4—84no—
750C2×C4#53414yes—
751C2×C4#53512yes—
752C2×C4#53814yes—
753C2×C4D4212yes—
754C2×C4#54612yes—
755C2×C4#54614yes—
756C2×C4#56014yes—
757C2×C4C22×SD1614yes—
758C2×C4C22×SD1614yes—
759C2×C4C2×#13714yes—
760C2×C4C23×D411yescharacteristic
761C2×C4C22×#4111yescharacteristic
762C2×C4C2×H(5,𝔽2)11yescharacteristic
763C2×C4C2×H(5,𝔽2)11yescharacteristic
764C2×C4C2×H(5,𝔽2)11yescharacteristic
765C2×C4C2×H(5,𝔽2)11yescharacteristic
766C8—24no—
767C8—42no—
768C8—42no—
769C8—42no—
770C22—24no—
771C22—24no—
772C22—24no—
773C22—416no—
774C22—42no—
775C22—42no—
776C22—42no—
777C22—42no—
778C22—44no—
779C22—44no—
780C22—44no—
781C22—816no—
782C22—82no—
783C22—82no—
784C22—82no—
785C22—82no—
786C22#267814yes—
787C22#320614yes—
788C22#322514yes—
789C22#327614yes—
790C22D4×SD1614yes—
791C22#329814yes—
792C22#332014yes—
793C22C2×#53511yescharacteristic
794C22C2×D4211yescharacteristic
795C22C2×#54611yescharacteristic
796C22C23×SD1611yescharacteristic
797C22C22×#13711yescharacteristic
798C22C2×#57711yescharacteristic
799C22C2×#57811yescharacteristic
800C4—24no—
801C4—24no—
802C4—24no—
803C4—42no—
804C4—42no—
805C4—44no—
806C4—44no—
807C4—82no—
808C4—82no—
809C4—82no—
810C4—82no—
811C4—82no—
812C4#267814yes—
813C4C2×#53411yescharacteristic
814C4C2×#53811yescharacteristic
815C4C2×#54611yescharacteristic
816C4C2×#56011yescharacteristic
817C2—44no—
818C2—84no—
819C2#3098618yesdirect product factor
820C2C2×#267811yescharacteristic
821C2C2×#320611yescharacteristic
822C2C2×#322511yescharacteristic
823C2C2×#327611yescharacteristic
824C2C2×D4×SD1611yescharacteristic
825C2C2×#329811yescharacteristic
826C2C2×#332011yescharacteristic
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
3. C2×#2434C2semidirect
5. #30986C2direct (N × H)
6. C2×#2072C2semidirect
7. C2×#2066C2semidirect
8. C2×#2043C2semidirect
9. C2×#2035C2semidirect
10. C2×#2013C2semidirect
12. C2×#1968C2semidirect
13. C2×#1956C2semidirect
14. C2×#1923C2semidirect
15. C2×#1877C2semidirect
16. C2×#1787C2semidirect
28. C2×#461C22semidirect
47. #2434C22semidirect
64. #2072C22semidirect
65. #2066C22semidirect
66. #2043C22semidirect
67. #2035C22semidirect
68. #2013C22semidirect
70. #1968C22semidirect
71. #1956C22semidirect
72. #1923C22semidirect
73. #1877C22semidirect
74. #1787C22semidirect
394. C2×C22⋊C4SD16semidirect
633. C22⋊C4C2×SD16semidirect
819. C2#30986direct (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×#24342
C2×#24222
#309862
C2×#20722
C2×#20662
C2×#20432
C2×#20352
C2×#20132
C2×#20002
C2×#19682
C2×#19562
C2×#19232
C2×#18772
C2×#17872