Finite Group Databasebeta

← #6453715

Subgroups — #6453715

Order 512.

3830 conjugacy classes of subgroups.

The subgroup lattice has 1060 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3444C211yesmaximal, characteristic, complemented
2C2×#3101C211yesmaximal, characteristic, complemented
3C2×#3100C211yesmaximal, characteristic, complemented
4C2×C4×#121C211yesmaximal, characteristic, complemented
5#24300C212yesmaximal, complemented
6#24210C212yesmaximal, complemented
7#24153C212yesmaximal, complemented
8#24152C212yesmaximal, complemented
9#24066C212yesmaximal, complemented
10#24004C212yesmaximal, complemented
11#23936C212yesmaximal, complemented
12#23920C212yesmaximal, complemented
13#23569C214yesmaximal, complemented
14C4×#449C214yesmaximal, complemented
15#21386C211yesmaximal, characteristic, complemented
16#21385C211yesmaximal, characteristic, complemented
17#20714C211yesmaximal, characteristic, complemented
18#3444—28no—
19#3444—28no—
20C2×#533C2211yescharacteristic
21C2×#533C2211yescharacteristic, complemented
22C2×#533C2211yescharacteristic, complemented
23C2×#532C2211yescharacteristic
24C2×#532C2211yescharacteristic, complemented
25C2×#532C2211yescharacteristic, complemented
26C2×#529—21no—
27C2×#529—21no—
28C2×#529—21no—
29C2×#529—21no—
30C2×#529C2212yes—
31C2×#529C2212yescomplemented
32C2×#525—21no—
33C2×#525—21no—
34C2×#525C2212yes—
35C22×#121C2211yescharacteristic
36C2×C4×#41—21no—
37C2×C4×#41—21no—
38C2×C4×#41C2212yescomplemented
39C22×C4×D4—21no—
40C22×C4×D4C2211yescharacteristic
41C23×C42C2211yescharacteristic
42#3101—28no—
43#3100—28no—
44C2×#483C2212yes—
45C2×#480C2212yes—
46C2×#476C2212yescomplemented
47C2×#474C2212yescomplemented
48C2×#461C2212yescomplemented
49C2×#459C2212yescomplemented
50C2×#449C2214yes—
51C2×#450C2212yes—
52C2×#447C2212yes—
53C2×C4×SD16C2214yescomplemented
54C2×C4×D8C2214yescomplemented
55C2×#431C2211yescharacteristic
56C2×#431C2211yescharacteristic
57C4×#121—21no—
58C4×#121—21no—
59C4×#121—21no—
60C4×#121—21no—
61C4×#121C2212yes—
62C4×#121C2212yes—
63C4×#121C2212yes—
64C4×#121C2212yes—
65C2×#390C2211yescharacteristic
66C2×#389C2211yescharacteristic
67C2×#388—21no—
68C2×#386—21no—
69C2×#380C2211yescharacteristic
70C2×C4×C4⋊C4C2211yescharacteristic
71C2×C4×C22⋊C4—21no—
72#2059C2214yescomplemented
73#2042C2214yescomplemented
74#2036C2214yescomplemented
75#2034C2214yescomplemented
76#2025C2214yescomplemented
77#2012C2214yescomplemented
78#2000C2214yes—
79#1999C2214yes—
80#1988C2212yescomplemented
81#1987C2212yescomplemented
82#1982C2212yescomplemented
83#1981C2212yescomplemented
84#1880C2214yescomplemented
85#1879C2214yescomplemented
86#1875C2214yes—
87#1874C2212yes—
88#1874C2212yes—
89#1872C2212yes—
90#1872C2212yes—
91#1864C2214yescomplemented
92#1863C2214yescomplemented
93#1854C2214yescomplemented
94#1817C2212yes—
95#1797C2212yescomplemented
96#1797C2212yescomplemented
97#1788C2214yescomplemented
98#1779C2212yes—
99C4×#103C2214yescomplemented
100C4×#102C2214yescomplemented
101C4×C22⋊C8C2212yescomplemented
102C4×C22⋊C8C2212yescomplemented
103C22×#41—21no—
104C22×#41—21no—
105C22×#41C2312yes—
106C23×D4—21no—
107C23×D4C2311yescharacteristic
108C24×C4—21no—
109C24×C4D411yescharacteristic
110C24×C4D411yescharacteristic
111C24×C4C2311yescharacteristic
112C22×SD16C2314yes—
113C22×D8C2314yes—
114#533—24no—
115#533—24no—
116#533—24no—
117#533—24no—
118#533—24no—
119#533D418yescomplemented
120#532—24no—
121#532—24no—
122#532—24no—
123#532—24no—
124#532—24no—
125#532D418yescomplemented
126C2×C4⋊Q8C2311yescharacteristic
127C2×C4⋊Q8C2311yescharacteristic
128C2×C4⋊Q8C2311yescharacteristic
129C2×#127C2311yescharacteristic
130#529—216no—
131#529—216no—
132#529—216no—
133#529—216no—
134#529—28no—
135#529—28no—
136#529—28no—
137#529—28no—
138C2×#126—22no—
139C2×#126—22no—
140C2×#125—21no—
141C2×#125—21no—
142C2×#125C2312yes—
143C2×#124—21no—
144C2×#124—21no—
145C2×#124C2312yes—
146#525—216no—
147#525—216no—
148#525—28no—
149#525—28no—
150C2×#123—22no—
151C2×#123—22no—
152C2×#123—22no—
153C2×C22⋊Q8—21no—
154C2×C22⋊Q8—21no—
155C2×C22⋊Q8—21no—
156C2×C22⋊Q8—21no—
157C2×C22⋊Q8C2312yes—
158C2×C22⋊Q8C2312yes—
159C2×#121—21no—
160C2×#121—21no—
161C2×#121—21no—
162C2×#121—21no—
163C2×#121—21no—
164C2×#121—21no—
165C2×#121—28no—
166C2×#121C2312yes—
167C2×#121C2312yes—
168C2×#121C2312yes—
169C2×#121C2312yes—
170C2×#120—22no—
171C4×#41—216no—
172C4×#41—216no—
173C4×#41—28no—
174C4×#41—28no—
175C2×C4×Q8—21no—
176C2×C4×Q8—21no—
177C2×C4×Q8—21no—
178C2×C4×Q8—21no—
179C2×C4×Q8C2312yes—
180C2×C4×Q8C2312yes—
181C2×C4×D4—22no—
182C2×C4×D4—22no—
183C2×C4×D4—22no—
184C2×C4×D4—22no—
185C2×C4×D4—22no—
186C2×C4×D4—22no—
187C2×C4×D4—22no—
188C2×C4×D4—22no—
189C2×C4×D4—22no—
190C2×C4×D4—22no—
191C2×C4×D4—21no—
192C2×C4×D4—21no—
193C2×C4×D4—21no—
194C2×C4×D4—21no—
195C2×C4×D4—21no—
196C2×C4×D4—21no—
197C2×C4×D4—24no—
198C2×C4×D4—24no—
199C2×C4×D4—48no—
200C2×C4×D4C2312yes—
201C2×C4×D4C2312yes—
202C2×C4×D4C2312yes—
203C2×C4×D4C2312yes—
204C2×#117—21no—
205C2×#117—21no—
206C2×#117—22no—
207C2×#117—22no—
208C2×#117—22no—
209C2×#117C2312yes—
210C22×C4⋊C4—21no—
211C22×C4⋊C4C2311yescharacteristic
212C22×C4⋊C4C2311yescharacteristic
213C22×C4⋊C4C2311yescharacteristic
214C22×C22⋊C4—21no—
215C22×C22⋊C4—21no—
216C22×C22⋊C4—21no—
217C22×C22⋊C4—21no—
218C22×C22⋊C4—21no—
219C22×C42—24no—
220C22×C42—24no—
221C22×C42—22no—
222C22×C42—21no—
223C22×C42D411yescharacteristic
224C22×C42D411yescharacteristic
225C22×C42D411yescharacteristic
226C22×C42D411yescharacteristic
227C22×C42D411yescharacteristic
228C22×C42D411yescharacteristic
229C22×C42C2311yescharacteristic
230C22×C42C2311yescharacteristic
231C22×C42C2311yescharacteristic
232C22×C42C2311yescharacteristic
233C22×C42C2311yescharacteristic
234C22×C42C2311yescharacteristic
235#483—28no—
236#480—28no—
237#476—28no—
238#474—28no—
239#461—28no—
240#459—28no—
241#450—28no—
242#449—216no—
243#447—28no—
244C4×SD16—216no—
245C4×D8—216no—
246#431—24no—
247#431—24no—
248C2×#107C2314yes—
249C2×#106C2314yes—
250C2×C4⋊C8C2312yes—
251C2×C4⋊C8C2312yes—
252C2×#103C2314yes—
253C2×#103C2314yes—
254C2×#103C2314yes—
255C2×#102C2314yes—
256C2×#102C2314yes—
257C2×#102C2314yes—
258C2×#102C2314yes—
259C2×#102C2314yes—
260C2×C22⋊C8C2314yes—
261C2×C22⋊C8C2312yes—
262C2×C22⋊C8C2312yes—
263C2×C22⋊C8C2314yes—
264C2×C4×C8C2312yes—
265C2×C4×C8C2312yes—
266#390—21no—
267#390—21no—
268#390C2312yes—
269#390C2312yes—
270#389—21no—
271#389—21no—
272#389C2312yes—
273#389C2312yes—
274#388—22no—
275#388—22no—
276#388—22no—
277#388—22no—
278#386—22no—
279#386—22no—
280#386—22no—
281#386—22no—
282#380—21no—
283#380—21no—
284#380C2312yes—
285#380C2312yes—
286C4×C4⋊C4—21no—
287C4×C4⋊C4—21no—
288C4×C4⋊C4C2312yes—
289C4×C4⋊C4C2312yes—
290C4×C22⋊C4—22no—
291C4×C22⋊C4—22no—
292C4×C22⋊C4—22no—
293C4×C22⋊C4—22no—
294C2×#95—21no—
295C2×#95—21no—
296C2×#95—21no—
297#340C2314yes—
298#340C2314yes—
299#340C2314yes—
300#340C2314yes—
301#336C2314yes—
302#336C2314yes—
303C25—21no—
304C25C2×D411yescharacteristic
305C2×#41—28no—
306C2×#41—24no—
307C2×#41—24no—
308C2×#41—28no—
309C2×#41—28no—
310C2×#41—44no—
311C2×#41—44no—
312C2×#41—44no—
313C2×#41—44no—
314C2×#41—44no—
315C22×Q8—21no—
316C22×Q8—21no—
317C22×Q8C2412yes—
318C22×D4—28no—
319C22×D4—22no—
320C22×D4—22no—
321C22×D4—22no—
322C22×D4—22no—
323C22×D4—22no—
324C22×D4—24no—
325C22×D4—21no—
326C22×D4—21no—
327C22×D4—21no—
328C22×D4—22no—
329C22×D4—22no—
330C22×D4—42no—
331C22×D4—44no—
332C22×D4—44no—
333C22×D4C2412yes—
334C22×D4C2412yes—
335C23×C4—21no—
336C23×C4—24no—
337C23×C4—24no—
338C23×C4—24no—
339C23×C4—24no—
340C23×C4—22no—
341C23×C4—22no—
342C23×C4—22no—
343C23×C4—22no—
344C23×C4—22no—
345C23×C4—24no—
346C23×C4—21no—
347C23×C4—21no—
348C23×C4—22no—
349C23×C4—22no—
350C23×C4—42no—
351C23×C4—42no—
352C23×C4—42no—
353C23×C4—44no—
354C23×C4—44no—
355C23×C4—44no—
356C23×C4C2×D411yescharacteristic
357C23×C4C2×D411yescharacteristic
358C23×C4C2×D411yescharacteristic
359C23×C4C2×D411yescharacteristic
360C23×C4C2×D411yescharacteristic
361C23×C4C2×D411yescharacteristic
362C23×C4C2×D411yescharacteristic
363C23×C4C2×D411yescharacteristic
364C23×C4C2×D411yescharacteristic
365C23×C4C2×D411yescharacteristic
366C23×C4C2×D411yescharacteristic
367C23×C4C2×D411yescharacteristic
368C23×C4C2×D411yescharacteristic
369C23×C4C2×D411yescharacteristic
370C23×C4C2×D411yescharacteristic
371C23×C4C2411yescharacteristic
372C23×C4C2411yescharacteristic
373C23×C4C2411yescharacteristic
374C2×SD16—28no—
375C2×SD16—28no—
376C2×SD16—44no—
377C2×D8—28no—
378C2×D8—28no—
379C2×D8—44no—
380C22×C8C2414yes—
381C22×C8C2414yes—
382C4⋊Q8—22no—
383C4⋊Q8—22no—
384C4⋊Q8—22no—
385C4⋊Q8C2×D414yescomplemented
386C4⋊Q8C2×D414yescomplemented
387C4⋊Q8C2×D414yescomplemented
388#127—22no—
389#127C2×D414yescomplemented
390#126—216no—
391#126—216no—
392#125—28no—
393#125—24no—
394#125—24no—
395#125—28no—
396#124—28no—
397#124—24no—
398#124—24no—
399#124—28no—
400#123—216no—
401#123—216no—
402#123—216no—
403C22⋊Q8—28no—
404C22⋊Q8—28no—
405C22⋊Q8—28no—
406C22⋊Q8—24no—
407C22⋊Q8—28no—
408C22⋊Q8—24no—
409C22⋊Q8—24no—
410C22⋊Q8C2×D418yes—
411#121—28no—
412#121—28no—
413#121—28no—
414#121—28no—
415#121—28no—
416#121—24no—
417#121—24no—
418#121—28no—
419#121—24no—
420#121—24no—
421#121—24no—
422#121—24no—
423#121C2×D418yes—
424#121#4118yescomplemented
425#120—216no—
426C4×Q8—28no—
427C4×Q8—28no—
428C4×Q8—28no—
429C4×Q8—24no—
430C4×Q8—24no—
431C4×Q8—28no—
432C4×Q8—24no—
433C4×Q8C2×D418yescomplemented
434C4×D4—216no—
435C4×D4—216no—
436C4×D4—216no—
437C4×D4—216no—
438C4×D4—216no—
439C4×D4—216no—
440C4×D4—28no—
441C4×D4—28no—
442C4×D4—28no—
443C4×D4—24no—
444C4×D4—24no—
445C4×D4—28no—
446C4×D4—24no—
447C4×D4—24no—
448C4×D4—24no—
449C4×D4—24no—
450C4×D4—24no—
451C4×D4—48no—
452C4×D4—48no—
453C4×D4—48no—
454C4×D4—48no—
455C4×D4—44no—
456C4×D4—44no—
457C4×D4C2×D418yescomplemented
458#117—28no—
459#117—216no—
460#117—216no—
461#117—216no—
462#117—28no—
463#117—24no—
464#117—24no—
465C2×C4⋊C4—21no—
466C2×C4⋊C4—21no—
467C2×C4⋊C4—21no—
468C2×C4⋊C4—21no—
469C2×C4⋊C4—21no—
470C2×C4⋊C4—22no—
471C2×C4⋊C4—22no—
472C2×C4⋊C4—22no—
473C2×C4⋊C4—22no—
474C2×C4⋊C4—22no—
475C2×C4⋊C4—22no—
476C2×C4⋊C4—24no—
477C2×C4⋊C4—22no—
478C2×C4⋊C4—22no—
479C2×C4⋊C4—22no—
480C2×C4⋊C4—22no—
481C2×C4⋊C4—21no—
482C2×C4⋊C4—21no—
483C2×C4⋊C4—42no—
484C2×C4⋊C4—44no—
485C2×C4⋊C4C2412yes—
486C2×C4⋊C4C2412yes—
487C2×C4⋊C4C2412yes—
488C2×C4⋊C4C2412yes—
489C2×C4⋊C4C2412yes—
490C2×C22⋊C4—28no—
491C2×C22⋊C4—22no—
492C2×C22⋊C4—22no—
493C2×C22⋊C4—22no—
494C2×C22⋊C4—22no—
495C2×C22⋊C4—22no—
496C2×C22⋊C4—22no—
497C2×C22⋊C4—22no—
498C2×C22⋊C4—22no—
499C2×C22⋊C4—22no—
500C2×C22⋊C4—22no—
501C2×C22⋊C4—22no—
502C2×C22⋊C4—22no—
503C2×C22⋊C4—22no—
504C2×C22⋊C4—22no—
505C2×C22⋊C4—22no—
506C2×C22⋊C4—22no—
507C2×C22⋊C4—22no—
508C2×C22⋊C4—22no—
509C2×C22⋊C4—22no—
510C2×C22⋊C4—44no—
511C2×C22⋊C4—44no—
512C2×C22⋊C4—44no—
513C2×C22⋊C4—44no—
514C2×C42—216no—
515C2×C42—24no—
516C2×C42—24no—
517C2×C42—22no—
518C2×C42—22no—
519C2×C42—22no—
520C2×C42—22no—
521C2×C42—22no—
522C2×C42—24no—
523C2×C42—24no—
524C2×C42—24no—
525C2×C42—24no—
526C2×C42—22no—
527C2×C42—22no—
528C2×C42—22no—
529C2×C42—22no—
530C2×C42—22no—
531C2×C42—22no—
532C2×C42—22no—
533C2×C42—22no—
534C2×C42—22no—
535C2×C42—22no—
536C2×C42—44no—
537C2×C42C2×D411yescharacteristic
538C2×C42C2×D411yescharacteristic
539C2×C42C2×D411yescharacteristic
540C2×C42C2×D411yescharacteristic
541C2×C42C2×D411yescharacteristic
542C2×C42C2×D411yescharacteristic
543C2×C42C2×D411yescharacteristic
544C2×C42C2×D411yescharacteristic
545C2×C42C2×D411yescharacteristic
546C2×C42C2×D411yescharacteristic
547C2×C42C2×D411yescharacteristic
548C2×C42C2×D411yescharacteristic
549C2×C42C2×D414yes—
550C2×C42C2×D414yes—
551C2×C42C2411yescharacteristic
552C2×C42C2411yescharacteristic
553C2×C42C2411yescharacteristic
554C2×C42C2411yescharacteristic
555#107—28no—
556#106—28no—
557C4⋊C8—24no—
558C4⋊C8—24no—
559#103—28no—
560#103—28no—
561#103—44no—
562#102—28no—
563#102—28no—
564#102—28no—
565#102—28no—
566#102—44no—
567C22⋊C8—24no—
568C22⋊C8—24no—
569C22⋊C8—28no—
570C22⋊C8—44no—
571C4×C8—24no—
572C4×C8—24no—
573#95—22no—
574#95—22no—
575#95—22no—
576#95—22no—
577#95—22no—
578#95—22no—
579C24—22no—
580C24—22no—
581C24—22no—
582C24—24no—
583C24—22no—
584C24—22no—
585C24—22no—
586C24—22no—
587C24—41no—
588C24—41no—
589C24—42no—
590C24—42no—
591C24—42no—
592C24—42no—
593C24—42no—
594C24—42no—
595C24C22×D411yescharacteristic
596C24C22×D411yescharacteristic
597C24C22×D411yescharacteristic
598#41—416no—
599#41—416no—
600#41—432no—
601#41—432no—
602C2×Q8—24no—
603C2×Q8—24no—
604C2×Q8—22no—
605C2×Q8—24no—
606C2×Q8—24no—
607C2×Q8—42no—
608C2×Q8—42no—
609C2×Q8—42no—
610C2×Q8—42no—
611C2×Q8C22×D414yes—
612C2×D4—28no—
613C2×D4—28no—
614C2×D4—24no—
615C2×D4—28no—
616C2×D4—28no—
617C2×D4—28no—
618C2×D4—24no—
619C2×D4—24no—
620C2×D4—22no—
621C2×D4—22no—
622C2×D4—22no—
623C2×D4—24no—
624C2×D4—22no—
625C2×D4—24no—
626C2×D4—22no—
627C2×D4—22no—
628C2×D4—48no—
629C2×D4—48no—
630C2×D4—42no—
631C2×D4—42no—
632C2×D4—42no—
633C2×D4—44no—
634C2×D4—44no—
635C2×D4—432no—
636C2×D4—44no—
637C2×D4—44no—
638C2×D4—44no—
639C2×D4—44no—
640C2×D4—44no—
641C2×D4—44no—
642C2×D4—44no—
643C2×D4—44no—
644C2×D4—42no—
645C2×D4—42no—
646C2×D4—42no—
647C2×D4C22×D414yes—
648C2×D4C2×#4114yes—
649C22×C4—22no—
650C22×C4—22no—
651C22×C4—22no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—22no—
655C22×C4—22no—
656C22×C4—22no—
657C22×C4—28no—
658C22×C4—28no—
659C22×C4—24no—
660C22×C4—22no—
661C22×C4—22no—
662C22×C4—22no—
663C22×C4—22no—
664C22×C4—22no—
665C22×C4—22no—
666C22×C4—22no—
667C22×C4—22no—
668C22×C4—22no—
669C22×C4—22no—
670C22×C4—22no—
671C22×C4—22no—
672C22×C4—22no—
673C22×C4—22no—
674C22×C4—22no—
675C22×C4—22no—
676C22×C4—22no—
677C22×C4—22no—
678C22×C4—22no—
679C22×C4—22no—
680C22×C4—28no—
681C22×C4—22no—
682C22×C4—22no—
683C22×C4—22no—
684C22×C4—22no—
685C22×C4—22no—
686C22×C4—22no—
687C22×C4—22no—
688C22×C4—22no—
689C22×C4—22no—
690C22×C4—22no—
691C22×C4—22no—
692C22×C4—22no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—22no—
696C22×C4—22no—
697C22×C4—22no—
698C22×C4—22no—
699C22×C4—41no—
700C22×C4—41no—
701C22×C4—41no—
702C22×C4—41no—
703C22×C4—41no—
704C22×C4—41no—
705C22×C4—41no—
706C22×C4—41no—
707C22×C4—41no—
708C22×C4—41no—
709C22×C4—48no—
710C22×C4—48no—
711C22×C4—416no—
712C22×C4—44no—
713C22×C4—44no—
714C22×C4—42no—
715C22×C4—42no—
716C22×C4—44no—
717C22×C4—44no—
718C22×C4—44no—
719C22×C4—44no—
720C22×C4—416no—
721C22×C4—42no—
722C22×C4—42no—
723C22×C4—42no—
724C22×C4—42no—
725C22×C4—42no—
726C22×C4—42no—
727C22×C4—44no—
728C22×C4—44no—
729C22×C4—44no—
730C22×C4—44no—
731C22×C4—44no—
732C22×C4—44no—
733C22×C4—816no—
734C22×C4#12014yes—
735C22×C4#12014yes—
736C22×C4#13514yes—
737C22×C4AGL(1,ℤ/8)14yes—
738C22×C4C22×D411yescharacteristic
739C22×C4C22×D411yescharacteristic
740C22×C4C22×D411yescharacteristic
741C22×C4C22×D411yescharacteristic
742C22×C4C22×D411yescharacteristic
743C22×C4C22×D411yescharacteristic
744C22×C4C22×D411yescharacteristic
745C22×C4C22×D412yes—
746C22×C4C22×D412yes—
747C22×C4C22×D411yescharacteristic
748C22×C4C22×D411yescharacteristic
749C22×C4C22×D411yescharacteristic
750C22×C4C22×D411yescharacteristic
751C22×C4C2×#4114yes—
752C22×C4C2511yescharacteristic
753SD16—416no—
754D8—416no—
755C2×C8—24no—
756C2×C8—24no—
757C2×C8—24no—
758C2×C8—24no—
759C2×C8—24no—
760C2×C8—24no—
761C4⋊C4—24no—
762C4⋊C4—28no—
763C4⋊C4—28no—
764C4⋊C4—28no—
765C4⋊C4—28no—
766C4⋊C4—24no—
767C4⋊C4—24no—
768C4⋊C4—24no—
769C4⋊C4—24no—
770C4⋊C4—28no—
771C4⋊C4—28no—
772C4⋊C4—22no—
773C4⋊C4—22no—
774C4⋊C4—22no—
775C4⋊C4—22no—
776C4⋊C4—22no—
777C4⋊C4—22no—
778C4⋊C4—22no—
779C4⋊C4—42no—
780C4⋊C4—44no—
781C4⋊C4—44no—
782C4⋊C4—42no—
783C4⋊C4C22×D414yes—
784C4⋊C4C22×D414yes—
785C4⋊C4C2×#4114yes—
786C22⋊C4—28no—
787C22⋊C4—28no—
788C22⋊C4—28no—
789C22⋊C4—28no—
790C22⋊C4—28no—
791C22⋊C4—28no—
792C22⋊C4—28no—
793C22⋊C4—28no—
794C22⋊C4—28no—
795C22⋊C4—28no—
796C22⋊C4—28no—
797C22⋊C4—44no—
798C22⋊C4—44no—
799C22⋊C4—44no—
800C22⋊C4—44no—
801C22⋊C4—44no—
802C22⋊C4—44no—
803C22⋊C4—44no—
804C22⋊C4—44no—
805C42—28no—
806C42—28no—
807C42—22no—
808C42—22no—
809C42—22no—
810C42—22no—
811C42—22no—
812C42—22no—
813C42—22no—
814C42—22no—
815C42—22no—
816C42—22no—
817C42—28no—
818C42—21no—
819C42—21no—
820C42—21no—
821C42—21no—
822C42—44no—
823C42—44no—
824C42#12014yes—
825C42#12014yes—
826C42C22×D412yes—
827C42C22×D412yes—
828C42C22×D412yes—
829C42C22×D412yes—
830C23—21no—
831C23—21no—
832C23—21no—
833C23—21no—
834C23—28no—
835C23—21no—
836C23—21no—
837C23—21no—
838C23—21no—
839C23—21no—
840C23—21no—
841C23—21no—
842C23—21no—
843C23—21no—
844C23—21no—
845C23—21no—
846C23—21no—
847C23—24no—
848C23—24no—
849C23—44no—
850C23—44no—
851C23—44no—
852C23—44no—
853C23—44no—
854C23—48no—
855C23—48no—
856C23—48no—
857C23—44no—
858C23—42no—
859C23—42no—
860C23—42no—
861C23—42no—
862C23—42no—
863C23—42no—
864C23—42no—
865C23—42no—
866C23—42no—
867C23—42no—
868C23—42no—
869C23—42no—
870C23—84no—
871C23—84no—
872C23—84no—
873C23—84no—
874C23C2×#12012yes—
875C23#52512yes—
876C23C2×#13512yes—
877C23C2×AGL(1,ℤ/8)12yes—
878C23#57512yes—
879C23C23×D411yescharacteristic
880Q8—28no—
881Q8—48no—
882Q8—44no—
883Q8—48no—
884D4—24no—
885D4—28no—
886D4—24no—
887D4—48no—
888D4—48no—
889D4—416no—
890D4—416no—
891D4—416no—
892D4—416no—
893D4—416no—
894D4—42no—
895D4—42no—
896D4—44no—
897D4—48no—
898C2×C4—28no—
899C2×C4—21no—
900C2×C4—21no—
901C2×C4—21no—
902C2×C4—21no—
903C2×C4—21no—
904C2×C4—21no—
905C2×C4—21no—
906C2×C4—21no—
907C2×C4—21no—
908C2×C4—21no—
909C2×C4—24no—
910C2×C4—24no—
911C2×C4—24no—
912C2×C4—24no—
913C2×C4—21no—
914C2×C4—21no—
915C2×C4—21no—
916C2×C4—21no—
917C2×C4—24no—
918C2×C4—24no—
919C2×C4—24no—
920C2×C4—21no—
921C2×C4—24no—
922C2×C4—21no—
923C2×C4—21no—
924C2×C4—21no—
925C2×C4—21no—
926C2×C4—21no—
927C2×C4—21no—
928C2×C4—21no—
929C2×C4—44no—
930C2×C4—44no—
931C2×C4—44no—
932C2×C4—44no—
933C2×C4—44no—
934C2×C4—44no—
935C2×C4—44no—
936C2×C4—44no—
937C2×C4—416no—
938C2×C4—416no—
939C2×C4—48no—
940C2×C4—42no—
941C2×C4—42no—
942C2×C4—44no—
943C2×C4—42no—
944C2×C4—42no—
945C2×C4—42no—
946C2×C4—42no—
947C2×C4—42no—
948C2×C4—42no—
949C2×C4—42no—
950C2×C4—42no—
951C2×C4—44no—
952C2×C4—44no—
953C2×C4—44no—
954C2×C4—44no—
955C2×C4—416no—
956C2×C4—42no—
957C2×C4—42no—
958C2×C4—42no—
959C2×C4—42no—
960C2×C4—42no—
961C2×C4—42no—
962C2×C4—84no—
963C2×C4—84no—
964C2×C4—88no—
965C2×C4—88no—
966C2×C4#449116yescomplemented
967C2×C4C2×#12012yes—
968C2×C4C2×#12012yes—
969C2×C4C2×#12012yes—
970C2×C4C2×#12012yes—
971C2×C4C2×#12012yes—
972C2×C4#52512yes—
973C2×C4C2×#13512yes—
974C2×C4C2×#13512yes—
975C2×C4C2×AGL(1,ℤ/8)12yes—
976C2×C4C2×AGL(1,ℤ/8)12yes—
977C2×C4#57512yes—
978C2×C4C23×D411yescharacteristic
979C2×C4C23×D411yescharacteristic
980C2×C4C22×#4112yes—
981C2×C4#58512yes—
982C8—44no—
983C8—44no—
984C22—22no—
985C22—22no—
986C22—22no—
987C22—22no—
988C22—22no—
989C22—22no—
990C22—22no—
991C22—22no—
992C22—22no—
993C22—22no—
994C22—22no—
995C22—22no—
996C22—416no—
997C22—41no—
998C22—41no—
999C22—41no—
1000C22—41no—
1001C22—41no—
1002C22—41no—
1003C22—41no—
1004C22—41no—
1005C22—44no—
1006C22—44no—
1007C22—44no—
1008C22—44no—
1009C22—44no—
1010C22—44no—
1011C22—816no—
1012C22—82no—
1013C22—82no—
1014C22—82no—
1015C22—82no—
1016C22—82no—
1017C22—82no—
1018C22—82no—
1019C22—82no—
1020C22C2×#44914yes—
1021C22C22×#12011yescharacteristic
1022C22C2×#52511yescharacteristic
1023C22#344911yescharacteristic
1024C22C22×#13511yescharacteristic
1025C22C22×AGL(1,ℤ/8)11yescharacteristic
1026C22C2×#57511yescharacteristic
1027C22C2×#57511yescharacteristic
1028C4—22no—
1029C4—22no—
1030C4—22no—
1031C4—22no—
1032C4—22no—
1033C4—44no—
1034C4—41no—
1035C4—44no—
1036C4—41no—
1037C4—41no—
1038C4—44no—
1039C4—41no—
1040C4—44no—
1041C4—82no—
1042C4—82no—
1043C4C2×#44914yes—
1044C4C2×#44914yes—
1045C4D4×#4112yes—
1046C4D4×#4112yes—
1047C2—24no—
1048C2—42no—
1049C2—42no—
1050C2—84no—
1051C2—84no—
1052C2#3473611yescharacteristic
1053C2C22×#44911yescharacteristic
1054C2#6035911yescharacteristic
1055C2#6053611yescharacteristic
1056C2#6055811yescharacteristic
1057C2#6094211yescharacteristic
1058C2#6095111yescharacteristic
subgroupG/H
centerC22×C4C22×D4
commutator, Frattini, cosocleC22×C4C25
socleC23C23×D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C4 ◁ C23×C42 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#3444C2semidirect
2. C2×#3101C2semidirect
3. C2×#3100C2semidirect
4. C2×C4×#121C2semidirect
5. #24300C2semidirect
6. #24210C2semidirect
7. #24153C2semidirect
8. #24152C2semidirect
9. #24066C2semidirect
10. #24004C2semidirect
11. #23936C2semidirect
12. #23920C2semidirect
13. #23569C2semidirect
14. C4×#449C2semidirect
15. #21386C2semidirect
16. #21385C2semidirect
17. #20714C2semidirect
21. C2×#533C22semidirect
22. C2×#533C22semidirect
24. C2×#532C22semidirect
25. C2×#532C22semidirect
31. C2×#529C22semidirect
38. C2×C4×#41C22semidirect
46. C2×#476C22semidirect
47. C2×#474C22semidirect
48. C2×#461C22semidirect
49. C2×#459C22semidirect
53. C2×C4×SD16C22semidirect
54. C2×C4×D8C22semidirect
72. #2059C22semidirect
73. #2042C22semidirect
74. #2036C22semidirect
75. #2034C22semidirect
76. #2025C22semidirect
77. #2012C22semidirect
80. #1988C22semidirect
81. #1987C22semidirect
82. #1982C22semidirect
83. #1981C22semidirect
84. #1880C22semidirect
85. #1879C22semidirect
91. #1864C22semidirect
92. #1863C22semidirect
93. #1854C22semidirect
95. #1797C22semidirect
96. #1797C22semidirect
97. #1788C22semidirect
99. C4×#103C22semidirect
100. C4×#102C22semidirect
101. C4×C22⋊C8C22semidirect
102. C4×C22⋊C8C22semidirect
119. #533D4semidirect
125. #532D4semidirect
385. C4⋊Q8C2×D4semidirect
386. C4⋊Q8C2×D4semidirect
387. C4⋊Q8C2×D4semidirect
389. #127C2×D4semidirect
424. #121#41semidirect
433. C4×Q8C2×D4semidirect
457. C4×D4C2×D4semidirect
966. C2×C4#449semidirect

Maximal subgroups

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

subgroupindex
C2×#34442
C2×#31012
C2×#31002
C2×C4×#1212
#243002
#242102
#241532
#241522
#240662
#240042
#239362
#239202
#235692
C4×#4492
#213862
#213852
#207142