Finite Group Databasebeta

← #6374591

Subgroups — #6374591

Order 512.

3256 conjugacy classes of subgroups.

The subgroup lattice has 1409 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3444C211yesmaximal, characteristic
2C2×#2920C211yesmaximal, characteristic, complemented
3C2×#2920C211yesmaximal, characteristic, complemented
4#21880C214yesmaximal, complemented
5#21879C212yesmaximal, complemented
6#21878C212yesmaximal, complemented
7#21831C212yesmaximal, complemented
8#21800C212yesmaximal, complemented
9#21754C214yesmaximal, complemented
10#21426C214yesmaximal, complemented
11#21425C212yesmaximal, complemented
12#21424C212yesmaximal, complemented
13#20728C214yesmaximal, complemented
14#3444—21no—
15#3444—21no—
16#3444—21no—
17#3444—21no—
18#3444—21no—
19#3444—21no—
20#3444—21no—
21#3444—21no—
22#3444—21no—
23#3444—21no—
24#3444—21no—
25#3444—21no—
26#3444—21no—
27#3444—21no—
28#3444—21no—
29#3444—21no—
30C2×#533C2211yescharacteristic
31C2×#533C2211yescharacteristic
32C2×#533C2211yescharacteristic
33C2×#532C2211yescharacteristic
34C2×#532C2211yescharacteristic
35C2×#532C2211yescharacteristic
36C2×#529C412yes—
37C2×#529C412yes—
38C2×#529C412yes—
39C2×#529C412yes—
40C2×#529C2212yes—
41C2×#529C2212yes—
42C2×#525C412yes—
43C2×#525C412yes—
44C2×#525C2212yes—
45C2×C4×#41C412yes—
46C2×C4×#41C412yes—
47C2×C4×#41C2212yes—
48C23×C42C2211yescharacteristic
49#2920—21no—
50#2920—21no—
51#2920—21no—
52#2920—21no—
53#2920—21no—
54#2920—21no—
55#2920—21no—
56#2920—21no—
57#2920C2212yes—
58#2920C2212yes—
59#2920C2212yes—
60#2920C2212yes—
61#2920C2212yes—
62#2920C2212yes—
63#2920C2212yes—
64#2920C2212yes—
65C2×#432—21no—
66C2×#432—21no—
67C2×#432—21no—
68C2×#432—21no—
69C2×#431—21no—
70C2×#431—21no—
71C2×#431—21no—
72C2×#431—21no—
73C2×#423C2212yes—
74C2×#423C2212yes—
75C2×#407C2212yes—
76C2×#407C2212yes—
77C2×C4×M16C2212yes—
78C2×C4×M16C2212yes—
79#1998C2218yescomplemented
80#1997C2214yescomplemented
81#1997C2214yescomplemented
82#1967C2218yescomplemented
83#1966C2214yescomplemented
84#1965C2214yescomplemented
85#1901C2218yes—
86#1901C2218yes—
87#1900C2218yes—
88#1900C2218yes—
89#1822C2218yes—
90#1801C2218yescomplemented
91#1800C2218yescomplemented
92#1785C2218yes—
93C4×#101C2218yescomplemented
94C4×#100C2218yescomplemented
95C22×#41C2×C412yes—
96C22×#41C2×C412yes—
97C22×#41C2312yes—
98C24×C4C2×C411yescharacteristic
99C24×C4C2×C411yescharacteristic
100C24×C4C2311yescharacteristic
101C22×M16C2314yes—
102C22×M16C2314yes—
103#533—21no—
104#533—21no—
105#533—21no—
106#533—21no—
107#533—21no—
108#533—21no—
109#533—21no—
110#533—21no—
111#533—21no—
112#533—21no—
113#533—21no—
114#533—21no—
115#533—21no—
116#533—21no—
117#533—21no—
118#533—21no—
119#533—21no—
120#533—21no—
121#533—21no—
122#533—21no—
123#533—21no—
124#533—21no—
125#533—21no—
126#533—21no—
127#532—21no—
128#532—21no—
129#532—21no—
130#532—21no—
131#532—21no—
132#532—21no—
133#532—21no—
134#532—21no—
135#532—21no—
136#532—21no—
137#532—21no—
138#532—21no—
139#532—21no—
140#532—21no—
141#532—21no—
142#532—21no—
143#532—21no—
144#532—21no—
145#532—21no—
146#532—21no—
147#532—21no—
148#532—21no—
149#532—21no—
150#532—21no—
151C2×C4⋊Q8C2311yescharacteristic
152C2×C4⋊Q8C2311yescharacteristic
153C2×C4⋊Q8C2311yescharacteristic
154C2×#127C2311yescharacteristic
155#529—22no—
156#529—22no—
157#529—22no—
158#529—22no—
159#529—22no—
160#529—22no—
161#529—22no—
162#529—22no—
163#529—22no—
164#529—22no—
165#529—22no—
166#529—22no—
167#529—22no—
168#529—22no—
169#529—22no—
170#529—22no—
171#529—22no—
172#529—22no—
173#529—22no—
174#529—22no—
175#529—22no—
176#529—22no—
177#529—22no—
178#529—22no—
179#529—22no—
180#529—22no—
181#529—22no—
182#529—22no—
183#529—22no—
184#529—22no—
185#529—22no—
186#529—22no—
187#529—22no—
188#529—22no—
189#529—22no—
190#529—22no—
191#529—22no—
192#529—22no—
193#529—22no—
194#529—22no—
195#529—22no—
196#529—22no—
197#529—22no—
198#529—22no—
199#529—22no—
200#529—22no—
201#529—22no—
202#529—22no—
203C2×#126C2×C414yes—
204C2×#126C2×C414yes—
205C2×#125C2×C412yes—
206C2×#125C2×C412yes—
207C2×#125C2312yes—
208C2×#124C2×C412yes—
209C2×#124C2×C412yes—
210C2×#124C2312yes—
211#525—22no—
212#525—22no—
213#525—22no—
214#525—22no—
215#525—22no—
216#525—22no—
217#525—22no—
218#525—22no—
219#525—22no—
220#525—22no—
221#525—22no—
222#525—22no—
223#525—22no—
224#525—22no—
225#525—22no—
226#525—22no—
227#525—22no—
228#525—22no—
229#525—22no—
230#525—22no—
231#525—22no—
232#525—22no—
233#525—22no—
234#525—22no—
235C2×#123C2×C414yes—
236C2×#123C2×C414yes—
237C2×#123C2×C414yes—
238C2×C22⋊Q8C2×C412yes—
239C2×C22⋊Q8C2×C412yes—
240C2×C22⋊Q8C2×C412yes—
241C2×C22⋊Q8C2×C412yes—
242C2×C22⋊Q8C2312yes—
243C2×C22⋊Q8C2312yes—
244C2×#121C2×C412yes—
245C2×#121C2×C412yes—
246C2×#121C2×C412yes—
247C2×#121C2×C412yes—
248C2×#121C2312yes—
249C2×#121C2312yes—
250C2×#120C2×C414yes—
251C4×#41—22no—
252C4×#41—22no—
253C4×#41—22no—
254C4×#41—22no—
255C4×#41—22no—
256C4×#41—22no—
257C4×#41—22no—
258C4×#41—22no—
259C4×#41—22no—
260C4×#41—22no—
261C4×#41—22no—
262C4×#41—22no—
263C4×#41—22no—
264C4×#41—22no—
265C4×#41—22no—
266C4×#41—22no—
267C4×#41—22no—
268C4×#41—22no—
269C4×#41—22no—
270C4×#41—22no—
271C4×#41—22no—
272C4×#41—22no—
273C4×#41—22no—
274C4×#41—22no—
275C2×C4×Q8C2×C412yes—
276C2×C4×Q8C2×C412yes—
277C2×C4×Q8C2×C412yes—
278C2×C4×Q8C2×C412yes—
279C2×C4×Q8C2312yes—
280C2×C4×Q8C2312yes—
281C2×C4×D4C2×C414yes—
282C2×C4×D4C2×C414yes—
283C2×C4×D4C2×C414yes—
284C2×C4×D4C2×C414yes—
285C2×C4×D4C2×C412yes—
286C2×C4×D4C2×C412yes—
287C2×C4×D4C2×C412yes—
288C2×C4×D4C2×C412yes—
289C2×C4×D4C2×C414yes—
290C2×C4×D4C2×C414yes—
291C2×C4×D4C2312yes—
292C2×C4×D4C2312yes—
293C2×#117C2×C412yes—
294C2×#117C2×C412yes—
295C2×#117C2×C414yes—
296C2×#117C2×C414yes—
297C2×#117C2×C414yes—
298C2×#117C2312yes—
299C22×C42C2×C414yes—
300C22×C42C2×C411yescharacteristic
301C22×C42C2×C411yescharacteristic
302C22×C42C2×C411yescharacteristic
303C22×C42C2×C411yescharacteristic
304C22×C42C2×C411yescharacteristic
305C22×C42C2×C411yescharacteristic
306C22×C42D411yescharacteristic
307C22×C42D411yescharacteristic
308C22×C42D411yescharacteristic
309C22×C42D411yescharacteristic
310C22×C42D411yescharacteristic
311C22×C42D411yescharacteristic
312C22×C42D411yescharacteristic
313C22×C42D411yescharacteristic
314C22×C42D411yescharacteristic
315C22×C42D411yescharacteristic
316C22×C42D411yescharacteristic
317C22×C42D411yescharacteristic
318C22×C42D411yescharacteristic
319C22×C42D411yescharacteristic
320C22×C42D411yescharacteristic
321C22×C42D411yescharacteristic
322C22×C42C2311yescharacteristic
323C22×C42C2311yescharacteristic
324C22×C42C2311yescharacteristic
325C22×C42C2311yescharacteristic
326C22×C42C2311yescharacteristic
327C22×C42C2311yescharacteristic
328#432—22no—
329#432—22no—
330#432—22no—
331#432—22no—
332#432—22no—
333#432—22no—
334#432—22no—
335#432—22no—
336#432—22no—
337#432—22no—
338#432—22no—
339#432—22no—
340#432—22no—
341#432—22no—
342#432—22no—
343#432—22no—
344#431—22no—
345#431—22no—
346#431—22no—
347#431—22no—
348#431—22no—
349#431—22no—
350#431—22no—
351#431—22no—
352#431—22no—
353#431—22no—
354#431—22no—
355#431—22no—
356#431—22no—
357#431—22no—
358#431—22no—
359#431—22no—
360#423—22no—
361#423—22no—
362#423—22no—
363#423—22no—
364#423C2314yes—
365#423C2314yes—
366#423C2314yes—
367#423C2314yes—
368C2×C4⋊C8—22no—
369C2×C4⋊C8—22no—
370C2×C4⋊C8—22no—
371C2×C4⋊C8—22no—
372C2×#101C23116yes—
373C2×#100C23116yes—
374#407—22no—
375#407—22no—
376#407—22no—
377#407—22no—
378#407C2314yes—
379#407C2314yes—
380#407C2314yes—
381#407C2314yes—
382C2×C22⋊C8—22no—
383C2×C22⋊C8—22no—
384C2×C22⋊C8—22no—
385C2×C22⋊C8—22no—
386C4×M16—22no—
387C4×M16—22no—
388C4×M16—22no—
389C4×M16—22no—
390C4×M16C2314yes—
391C4×M16C2314yes—
392C4×M16C2314yes—
393C4×M16C2314yes—
394C2×#97—22no—
395C2×#97—22no—
396C2×C4×C8—22no—
397C2×C4×C8—22no—
398#343C23116yes—
399#343C23116yes—
400C25C22×C411yescharacteristic
401C2×#41—22no—
402C2×#41—22no—
403C2×#41—22no—
404C2×#41—22no—
405C2×#41—22no—
406C2×#41—22no—
407C2×#41—22no—
408C2×#41—22no—
409C2×#41—22no—
410C2×#41—22no—
411C2×#41—22no—
412C2×#41—22no—
413C2×#41—48no—
414C2×#41—48no—
415C2×#41—48no—
416C22×Q8C22×C412yes—
417C22×Q8C22×C412yes—
418C22×Q8C2412yes—
419C22×D4C22×C414yes—
420C22×D4C22×C414yes—
421C22×D4C22×C414yes—
422C22×D4C22×C412yes—
423C22×D4C22×C412yes—
424C22×D4C2412yes—
425C23×C4—44no—
426C23×C4—44no—
427C23×C4—44no—
428C23×C4C22⋊C411yescharacteristic
429C23×C4C22⋊C411yescharacteristic
430C23×C4C22⋊C411yescharacteristic
431C23×C4C22⋊C411yescharacteristic
432C23×C4C22⋊C411yescharacteristic
433C23×C4C22⋊C411yescharacteristic
434C23×C4C22⋊C411yescharacteristic
435C23×C4C22⋊C411yescharacteristic
436C23×C4C22⋊C411yescharacteristic
437C23×C4C22⋊C411yescharacteristic
438C23×C4C22⋊C411yescharacteristic
439C23×C4C22⋊C411yescharacteristic
440C23×C4C22⋊C411yescharacteristic
441C23×C4C22⋊C411yescharacteristic
442C23×C4C22⋊C411yescharacteristic
443C23×C4C22⋊C411yescharacteristic
444C23×C4C22×C411yescharacteristic
445C23×C4C22×C411yescharacteristic
446C23×C4C22×C414yes—
447C23×C4C22×C414yes—
448C23×C4C22×C414yes—
449C23×C4C22×C411yescharacteristic
450C23×C4C22×C411yescharacteristic
451C23×C4C22×C411yescharacteristic
452C23×C4C22×C411yescharacteristic
453C23×C4C22×C411yescharacteristic
454C23×C4C22×C411yescharacteristic
455C23×C4C22×C411yescharacteristic
456C23×C4C22×C411yescharacteristic
457C23×C4C22×C411yescharacteristic
458C23×C4C22×C411yescharacteristic
459C23×C4C22×C411yescharacteristic
460C23×C4C22×C411yescharacteristic
461C23×C4C22×C411yescharacteristic
462C23×C4C2×D411yescharacteristic
463C23×C4C2×D411yescharacteristic
464C23×C4C2×D411yescharacteristic
465C23×C4C2×D411yescharacteristic
466C23×C4C2×D411yescharacteristic
467C23×C4C2×D411yescharacteristic
468C23×C4C2×D411yescharacteristic
469C23×C4C2×D411yescharacteristic
470C23×C4C2411yescharacteristic
471C23×C4C2411yescharacteristic
472C23×C4C2411yescharacteristic
473C2×M16—24no—
474C2×M16—24no—
475C2×M16—48no—
476C2×M16—48no—
477C2×M16C2418yes—
478C2×M16C2418yes—
479C22×C8—24no—
480C22×C8—24no—
481C4⋊Q8—21no—
482C4⋊Q8—21no—
483C4⋊Q8—21no—
484C4⋊Q8—21no—
485C4⋊Q8—21no—
486C4⋊Q8—21no—
487C4⋊Q8—21no—
488C4⋊Q8—21no—
489C4⋊Q8—21no—
490C4⋊Q8—21no—
491C4⋊Q8—21no—
492C4⋊Q8—21no—
493#127—21no—
494#127—21no—
495#127—21no—
496#127—21no—
497#126—24no—
498#126—24no—
499#126—24no—
500#126—24no—
501#126—24no—
502#126—24no—
503#126—24no—
504#126—24no—
505#125—22no—
506#125—22no—
507#125—22no—
508#125—22no—
509#125—22no—
510#125—22no—
511#125—22no—
512#125—22no—
513#125—22no—
514#125—22no—
515#125—22no—
516#125—22no—
517#124—22no—
518#124—22no—
519#124—22no—
520#124—22no—
521#124—22no—
522#124—22no—
523#124—22no—
524#124—22no—
525#124—22no—
526#124—22no—
527#124—22no—
528#124—22no—
529#123—24no—
530#123—24no—
531#123—24no—
532#123—24no—
533#123—24no—
534#123—24no—
535#123—24no—
536#123—24no—
537#123—24no—
538#123—24no—
539#123—24no—
540#123—24no—
541C22⋊Q8—22no—
542C22⋊Q8—22no—
543C22⋊Q8—22no—
544C22⋊Q8—22no—
545C22⋊Q8—22no—
546C22⋊Q8—22no—
547C22⋊Q8—22no—
548C22⋊Q8—22no—
549C22⋊Q8—22no—
550C22⋊Q8—22no—
551C22⋊Q8—22no—
552C22⋊Q8—22no—
553C22⋊Q8—22no—
554C22⋊Q8—22no—
555C22⋊Q8—22no—
556C22⋊Q8—22no—
557C22⋊Q8—22no—
558C22⋊Q8—22no—
559C22⋊Q8—22no—
560C22⋊Q8—22no—
561C22⋊Q8—22no—
562C22⋊Q8—22no—
563C22⋊Q8—22no—
564C22⋊Q8—22no—
565#121—22no—
566#121—22no—
567#121—22no—
568#121—22no—
569#121—22no—
570#121—22no—
571#121—22no—
572#121—22no—
573#121—22no—
574#121—22no—
575#121—22no—
576#121—22no—
577#121—22no—
578#121—22no—
579#121—22no—
580#121—22no—
581#121—22no—
582#121—22no—
583#121—22no—
584#121—22no—
585#121—22no—
586#121—22no—
587#121—22no—
588#121—22no—
589#120—24no—
590#120—24no—
591#120—24no—
592#120—24no—
593C4×Q8—22no—
594C4×Q8—22no—
595C4×Q8—22no—
596C4×Q8—22no—
597C4×Q8—22no—
598C4×Q8—22no—
599C4×Q8—22no—
600C4×Q8—22no—
601C4×Q8—22no—
602C4×Q8—22no—
603C4×Q8—22no—
604C4×Q8—22no—
605C4×Q8—22no—
606C4×Q8—22no—
607C4×Q8—22no—
608C4×Q8—22no—
609C4×Q8—22no—
610C4×Q8—22no—
611C4×Q8—22no—
612C4×Q8—22no—
613C4×Q8—22no—
614C4×Q8—22no—
615C4×Q8—22no—
616C4×Q8—22no—
617C4×D4—24no—
618C4×D4—24no—
619C4×D4—24no—
620C4×D4—24no—
621C4×D4—24no—
622C4×D4—24no—
623C4×D4—24no—
624C4×D4—24no—
625C4×D4—24no—
626C4×D4—24no—
627C4×D4—24no—
628C4×D4—24no—
629C4×D4—24no—
630C4×D4—24no—
631C4×D4—24no—
632C4×D4—24no—
633C4×D4—24no—
634C4×D4—24no—
635C4×D4—24no—
636C4×D4—24no—
637C4×D4—24no—
638C4×D4—24no—
639C4×D4—24no—
640C4×D4—24no—
641C4×D4—22no—
642C4×D4—22no—
643C4×D4—22no—
644C4×D4—22no—
645C4×D4—22no—
646C4×D4—22no—
647C4×D4—22no—
648C4×D4—22no—
649C4×D4—22no—
650C4×D4—22no—
651C4×D4—22no—
652C4×D4—22no—
653C4×D4—22no—
654C4×D4—22no—
655C4×D4—22no—
656C4×D4—22no—
657C4×D4—22no—
658C4×D4—22no—
659C4×D4—22no—
660C4×D4—22no—
661C4×D4—22no—
662C4×D4—22no—
663C4×D4—22no—
664C4×D4—22no—
665#117—22no—
666#117—22no—
667#117—22no—
668#117—22no—
669#117—22no—
670#117—22no—
671#117—22no—
672#117—22no—
673#117—22no—
674#117—22no—
675#117—22no—
676#117—22no—
677#117—24no—
678#117—24no—
679#117—24no—
680#117—24no—
681#117—24no—
682#117—24no—
683#117—24no—
684#117—24no—
685#117—24no—
686#117—24no—
687#117—24no—
688#117—24no—
689C2×C4⋊C4C22×C412yes—
690C2×C4⋊C4C22×C412yes—
691C2×C4⋊C4C22×C412yes—
692C2×C4⋊C4C22×C412yes—
693C2×C4⋊C4C22×C414yes—
694C2×C4⋊C4C22×C414yes—
695C2×C4⋊C4C22×C414yes—
696C2×C4⋊C4C22×C414yes—
697C2×C4⋊C4C22×C414yes—
698C2×C4⋊C4C22×C414yes—
699C2×C4⋊C4C2412yes—
700C2×C4⋊C4C2412yes—
701C2×C22⋊C4C22×C414yes—
702C2×C22⋊C4C22×C414yes—
703C2×C22⋊C4C22×C414yes—
704C2×C22⋊C4C22×C414yes—
705C2×C22⋊C4C22×C414yes—
706C2×C22⋊C4C22×C414yes—
707C2×C22⋊C4C22×C414yes—
708C2×C22⋊C4C22×C414yes—
709C2×C22⋊C4C22×C414yes—
710C2×C42—24no—
711C2×C42—24no—
712C2×C42—24no—
713C2×C42—24no—
714C2×C42C22⋊C411yescharacteristic
715C2×C42C22⋊C411yescharacteristic
716C2×C42C22⋊C411yescharacteristic
717C2×C42C22⋊C411yescharacteristic
718C2×C42C22⋊C411yescharacteristic
719C2×C42C22⋊C411yescharacteristic
720C2×C42C22⋊C411yescharacteristic
721C2×C42C22⋊C411yescharacteristic
722C2×C42C22⋊C411yescharacteristic
723C2×C42C22⋊C411yescharacteristic
724C2×C42C22⋊C411yescharacteristic
725C2×C42C22⋊C411yescharacteristic
726C2×C42C22⋊C411yescharacteristic
727C2×C42C22⋊C411yescharacteristic
728C2×C42C22⋊C411yescharacteristic
729C2×C42C22⋊C411yescharacteristic
730C2×C42C22⋊C411yescharacteristic
731C2×C42C22⋊C411yescharacteristic
732C2×C42C22⋊C411yescharacteristic
733C2×C42C22⋊C411yescharacteristic
734C2×C42C22⋊C411yescharacteristic
735C2×C42C22⋊C411yescharacteristic
736C2×C42C22⋊C411yescharacteristic
737C2×C42C22⋊C411yescharacteristic
738C2×C42C22⋊C411yescharacteristic
739C2×C42C22⋊C411yescharacteristic
740C2×C42C22⋊C411yescharacteristic
741C2×C42C22⋊C411yescharacteristic
742C2×C42C22⋊C411yescharacteristic
743C2×C42C22⋊C411yescharacteristic
744C2×C42C22⋊C411yescharacteristic
745C2×C42C22⋊C411yescharacteristic
746C2×C42C22⋊C411yescharacteristic
747C2×C42C22⋊C411yescharacteristic
748C2×C42C22⋊C411yescharacteristic
749C2×C42C22⋊C411yescharacteristic
750C2×C42C22⋊C411yescharacteristic
751C2×C42C22⋊C411yescharacteristic
752C2×C42C22⋊C411yescharacteristic
753C2×C42C22⋊C411yescharacteristic
754C2×C42C22⋊C411yescharacteristic
755C2×C42C22⋊C411yescharacteristic
756C2×C42C22⋊C411yescharacteristic
757C2×C42C22⋊C411yescharacteristic
758C2×C42C22⋊C411yescharacteristic
759C2×C42C22⋊C411yescharacteristic
760C2×C42C22⋊C411yescharacteristic
761C2×C42C22⋊C411yescharacteristic
762C2×C42C22×C414yes—
763C2×C42C22×C414yes—
764C2×C42C22×C414yes—
765C2×C42C22×C411yescharacteristic
766C2×C42C22×C411yescharacteristic
767C2×C42C22×C411yescharacteristic
768C2×C42C22×C411yescharacteristic
769C2×C42C22×C411yescharacteristic
770C2×C42C22×C411yescharacteristic
771C2×C42C22×C411yescharacteristic
772C2×C42C22×C411yescharacteristic
773C2×C42C22×C411yescharacteristic
774C2×C42C22×C411yescharacteristic
775C2×C42C22×C411yescharacteristic
776C2×C42C22×C411yescharacteristic
777C2×C42C2×D411yescharacteristic
778C2×C42C2×D411yescharacteristic
779C2×C42C2×D411yescharacteristic
780C2×C42C2×D411yescharacteristic
781C2×C42C2×D411yescharacteristic
782C2×C42C2×D411yescharacteristic
783C2×C42C2×D411yescharacteristic
784C2×C42C2×D411yescharacteristic
785C2×C42C2×D411yescharacteristic
786C2×C42C2×D411yescharacteristic
787C2×C42C2×D411yescharacteristic
788C2×C42C2×D411yescharacteristic
789C2×C42C2×D411yescharacteristic
790C2×C42C2×D411yescharacteristic
791C2×C42C2×D411yescharacteristic
792C2×C42C2×D411yescharacteristic
793C2×C42C2×D411yescharacteristic
794C2×C42C2×D411yescharacteristic
795C2×C42C2×D411yescharacteristic
796C2×C42C2×D411yescharacteristic
797C2×C42C2×D411yescharacteristic
798C2×C42C2×D411yescharacteristic
799C2×C42C2×D411yescharacteristic
800C2×C42C2×D411yescharacteristic
801C2×C42C2×D411yescharacteristic
802C2×C42C2×D411yescharacteristic
803C2×C42C2×D411yescharacteristic
804C2×C42C2×D411yescharacteristic
805C2×C42C2×D411yescharacteristic
806C2×C42C2×D411yescharacteristic
807C2×C42C2×D411yescharacteristic
808C2×C42C2×D411yescharacteristic
809C2×C42C2×D411yescharacteristic
810C2×C42C2×D411yescharacteristic
811C2×C42C2×D411yescharacteristic
812C2×C42C2×D411yescharacteristic
813C2×C42C2×D411yescharacteristic
814C2×C42C2×D411yescharacteristic
815C2×C42C2×D411yescharacteristic
816C2×C42C2×D411yescharacteristic
817C2×C42C2×D411yescharacteristic
818C2×C42C2×D411yescharacteristic
819C2×C42C2×D411yescharacteristic
820C2×C42C2×D411yescharacteristic
821C2×C42C2×D411yescharacteristic
822C2×C42C2×D411yescharacteristic
823C2×C42C2×D411yescharacteristic
824C2×C42C2×D411yescharacteristic
825C2×C42C2411yescharacteristic
826C2×C42C2411yescharacteristic
827C2×C42C2411yescharacteristic
828C2×C42C2411yescharacteristic
829C4⋊C8—24no—
830C4⋊C8—24no—
831C4⋊C8—24no—
832C4⋊C8—24no—
833C4⋊C8—24no—
834C4⋊C8—24no—
835C4⋊C8—24no—
836C4⋊C8—24no—
837#101—416no—
838#100—416no—
839C22⋊C8—24no—
840C22⋊C8—24no—
841C22⋊C8—24no—
842C22⋊C8—24no—
843C22⋊C8—24no—
844C22⋊C8—24no—
845C22⋊C8—24no—
846C22⋊C8—24no—
847#97—24no—
848#97—24no—
849#97—24no—
850#97—24no—
851C4×C8—24no—
852C4×C8—24no—
853C4×C8—24no—
854C4×C8—24no—
855C24—42no—
856C24—42no—
857C24—42no—
858C24C2×C22⋊C411yescharacteristic
859C24C2×C22⋊C411yescharacteristic
860C24C2×C22⋊C411yescharacteristic
861C24C2×C22⋊C411yescharacteristic
862C24C23×C411yescharacteristic
863C24C23×C411yescharacteristic
864C24C23×C414yes—
865C24C23×C411yescharacteristic
866#41—48no—
867#41—48no—
868#41—48no—
869#41—48no—
870#41—48no—
871#41—48no—
872#41—48no—
873#41—48no—
874#41—48no—
875#41—48no—
876#41—48no—
877#41—48no—
878C2×Q8—22no—
879C2×Q8—22no—
880C2×Q8—22no—
881C2×Q8—22no—
882C2×Q8—22no—
883C2×Q8—22no—
884C2×Q8—28no—
885C2×Q8—44no—
886C2×Q8—44no—
887C2×D4—24no—
888C2×D4—24no—
889C2×D4—24no—
890C2×D4—24no—
891C2×D4—24no—
892C2×D4—24no—
893C2×D4—22no—
894C2×D4—22no—
895C2×D4—22no—
896C2×D4—22no—
897C2×D4—22no—
898C2×D4—22no—
899C2×D4—28no—
900C2×D4—48no—
901C2×D4—44no—
902C2×D4—44no—
903C2×D4—48no—
904C2×D4—48no—
905C22×C4—24no—
906C22×C4—24no—
907C22×C4—24no—
908C22×C4—24no—
909C22×C4—24no—
910C22×C4—24no—
911C22×C4—24no—
912C22×C4—24no—
913C22×C4—24no—
914C22×C4—24no—
915C22×C4—24no—
916C22×C4—24no—
917C22×C4—24no—
918C22×C4—24no—
919C22×C4—24no—
920C22×C4—42no—
921C22×C4—42no—
922C22×C4—42no—
923C22×C4—42no—
924C22×C4—42no—
925C22×C4—42no—
926C22×C4—42no—
927C22×C4—42no—
928C22×C4—42no—
929C22×C4—42no—
930C22×C4—42no—
931C22×C4—42no—
932C22×C4—42no—
933C22×C4—42no—
934C22×C4—42no—
935C22×C4—42no—
936C22×C4—42no—
937C22×C4—42no—
938C22×C4—42no—
939C22×C4—42no—
940C22×C4—42no—
941C22×C4—42no—
942C22×C4—42no—
943C22×C4—42no—
944C22×C4—42no—
945C22×C4—42no—
946C22×C4—42no—
947C22×C4—42no—
948C22×C4—42no—
949C22×C4—42no—
950C22×C4—42no—
951C22×C4—42no—
952C22×C4—42no—
953C22×C4—48no—
954C22×C4—48no—
955C22×C4—48no—
956C22×C4C2×C22⋊C411yescharacteristic
957C22×C4C2×C22⋊C411yescharacteristic
958C22×C4C2×C22⋊C411yescharacteristic
959C22×C4C2×C22⋊C411yescharacteristic
960C22×C4C2×C22⋊C411yescharacteristic
961C22×C4C2×C22⋊C411yescharacteristic
962C22×C4C2×C22⋊C411yescharacteristic
963C22×C4C2×C22⋊C411yescharacteristic
964C22×C4C2×C22⋊C411yescharacteristic
965C22×C4C2×C22⋊C411yescharacteristic
966C22×C4C2×C22⋊C411yescharacteristic
967C22×C4C2×C22⋊C411yescharacteristic
968C22×C4C2×C22⋊C411yescharacteristic
969C22×C4C2×C22⋊C411yescharacteristic
970C22×C4C2×C22⋊C411yescharacteristic
971C22×C4C2×C22⋊C411yescharacteristic
972C22×C4C2×C22⋊C411yescharacteristic
973C22×C4C2×C22⋊C411yescharacteristic
974C22×C4C2×C22⋊C411yescharacteristic
975C22×C4C2×C22⋊C411yescharacteristic
976C22×C4C2×C22⋊C411yescharacteristic
977C22×C4C2×C22⋊C411yescharacteristic
978C22×C4C2×C22⋊C411yescharacteristic
979C22×C4C2×C22⋊C411yescharacteristic
980C22×C4C2×C22⋊C411yescharacteristic
981C22×C4C2×C22⋊C411yescharacteristic
982C22×C4C2×C22⋊C411yescharacteristic
983C22×C4C2×C22⋊C411yescharacteristic
984C22×C4C2×C22⋊C411yescharacteristic
985C22×C4C2×C22⋊C411yescharacteristic
986C22×C4C2×C22⋊C411yescharacteristic
987C22×C4C2×C22⋊C411yescharacteristic
988C22×C4C2×C22⋊C411yescharacteristic
989C22×C4C2×C22⋊C411yescharacteristic
990C22×C4C2×C22⋊C411yescharacteristic
991C22×C4C2×C22⋊C411yescharacteristic
992C22×C4C2×C22⋊C411yescharacteristic
993C22×C4C2×C22⋊C411yescharacteristic
994C22×C4C2×C22⋊C411yescharacteristic
995C22×C4C2×C22⋊C411yescharacteristic
996C22×C4C2×C22⋊C411yescharacteristic
997C22×C4C2×C22⋊C411yescharacteristic
998C22×C4C2×C22⋊C411yescharacteristic
999C22×C4C2×C22⋊C411yescharacteristic
1000C22×C4C2×C22⋊C411yescharacteristic
1001C22×C4C2×C22⋊C411yescharacteristic
1002C22×C4C2×C22⋊C411yescharacteristic
1003C22×C4C2×C22⋊C411yescharacteristic
1004C22×C4C2×C22⋊C411yescharacteristic
1005C22×C4C2×C22⋊C411yescharacteristic
1006C22×C4C2×C22⋊C411yescharacteristic
1007C22×C4C2×C22⋊C411yescharacteristic
1008C22×C4C2×C22⋊C411yescharacteristic
1009C22×C4C2×C22⋊C411yescharacteristic
1010C22×C4C2×C22⋊C411yescharacteristic
1011C22×C4C2×C22⋊C411yescharacteristic
1012C22×C4C2×C22⋊C411yescharacteristic
1013C22×C4C2×C22⋊C411yescharacteristic
1014C22×C4C2×C22⋊C411yescharacteristic
1015C22×C4C2×C22⋊C411yescharacteristic
1016C22×C4C23×C414yes—
1017C22×C4C23×C411yescharacteristic
1018C22×C4C23×C411yescharacteristic
1019C22×C4C23×C411yescharacteristic
1020C22×C4C23×C411yescharacteristic
1021C22×C4C23×C411yescharacteristic
1022C22×C4C23×C411yescharacteristic
1023C22×C4C23×C411yescharacteristic
1024C22×C4C23×C414yes—
1025C22×C4C23×C414yes—
1026C22×C4C23×C411yescharacteristic
1027C22×C4C23×C411yescharacteristic
1028C22×C4C23×C411yescharacteristic
1029C22×C4C23×C411yescharacteristic
1030C22×C4C22×D411yescharacteristic
1031C22×C4C22×D411yescharacteristic
1032C22×C4C22×D411yescharacteristic
1033C22×C4C22×D411yescharacteristic
1034C22×C4C22×D411yescharacteristic
1035C22×C4C22×D411yescharacteristic
1036C22×C4C22×D411yescharacteristic
1037C22×C4C22×D411yescharacteristic
1038C22×C4C22×D411yescharacteristic
1039C22×C4C22×D411yescharacteristic
1040C22×C4C22×D411yescharacteristic
1041C22×C4C22×D411yescharacteristic
1042C22×C4C2511yescharacteristic
1043M16—28no—
1044M16—216no—
1045M16—28no—
1046M16—48no—
1047M16—48no—
1048C2×C8—28no—
1049C2×C8—28no—
1050C2×C8—48no—
1051C2×C8—48no—
1052C4⋊C4—22no—
1053C4⋊C4—22no—
1054C4⋊C4—22no—
1055C4⋊C4—22no—
1056C4⋊C4—22no—
1057C4⋊C4—22no—
1058C4⋊C4—22no—
1059C4⋊C4—22no—
1060C4⋊C4—24no—
1061C4⋊C4—24no—
1062C4⋊C4—24no—
1063C4⋊C4—24no—
1064C4⋊C4—24no—
1065C4⋊C4—24no—
1066C4⋊C4—24no—
1067C4⋊C4—24no—
1068C4⋊C4—24no—
1069C4⋊C4—24no—
1070C4⋊C4—24no—
1071C4⋊C4—24no—
1072C4⋊C4—22no—
1073C4⋊C4—22no—
1074C4⋊C4—22no—
1075C4⋊C4—22no—
1076C22⋊C4—24no—
1077C22⋊C4—24no—
1078C22⋊C4—24no—
1079C22⋊C4—24no—
1080C22⋊C4—24no—
1081C22⋊C4—24no—
1082C22⋊C4—24no—
1083C22⋊C4—24no—
1084C22⋊C4—24no—
1085C22⋊C4—24no—
1086C22⋊C4—24no—
1087C22⋊C4—24no—
1088C22⋊C4—24no—
1089C22⋊C4—24no—
1090C22⋊C4—24no—
1091C22⋊C4—24no—
1092C22⋊C4—24no—
1093C22⋊C4—24no—
1094C42—24no—
1095C42—24no—
1096C42—24no—
1097C42—24no—
1098C42—24no—
1099C42—24no—
1100C42C2×C22⋊C411yescharacteristic
1101C42C2×C22⋊C411yescharacteristic
1102C42C2×C22⋊C411yescharacteristic
1103C42C2×C22⋊C411yescharacteristic
1104C42C2×C22⋊C411yescharacteristic
1105C42C2×C22⋊C411yescharacteristic
1106C42C2×C22⋊C411yescharacteristic
1107C42C2×C22⋊C411yescharacteristic
1108C42C2×C22⋊C411yescharacteristic
1109C42C2×C22⋊C411yescharacteristic
1110C42C2×C22⋊C411yescharacteristic
1111C42C2×C22⋊C411yescharacteristic
1112C42C2×C22⋊C411yescharacteristic
1113C42C2×C22⋊C411yescharacteristic
1114C42C2×C22⋊C411yescharacteristic
1115C42C2×C22⋊C411yescharacteristic
1116C42C2×C22⋊C411yescharacteristic
1117C42C2×C22⋊C411yescharacteristic
1118C42C2×C22⋊C411yescharacteristic
1119C42C2×C22⋊C411yescharacteristic
1120C42C2×C22⋊C411yescharacteristic
1121C42C2×C22⋊C411yescharacteristic
1122C42C2×C22⋊C411yescharacteristic
1123C42C2×C22⋊C411yescharacteristic
1124C42C2×C22⋊C411yescharacteristic
1125C42C2×C22⋊C411yescharacteristic
1126C42C2×C22⋊C411yescharacteristic
1127C42C2×C22⋊C411yescharacteristic
1128C42C2×C22⋊C411yescharacteristic
1129C42C2×C22⋊C411yescharacteristic
1130C42C2×C22⋊C411yescharacteristic
1131C42C2×C22⋊C411yescharacteristic
1132C42C2×C22⋊C411yescharacteristic
1133C42C2×C22⋊C411yescharacteristic
1134C42C2×C22⋊C411yescharacteristic
1135C42C2×C22⋊C411yescharacteristic
1136C42C2×C22⋊C411yescharacteristic
1137C42C2×C22⋊C411yescharacteristic
1138C42C2×C22⋊C411yescharacteristic
1139C42C2×C22⋊C411yescharacteristic
1140C42C2×C22⋊C411yescharacteristic
1141C42C2×C22⋊C411yescharacteristic
1142C42C2×C22⋊C411yescharacteristic
1143C42C2×C22⋊C411yescharacteristic
1144C42C2×C22⋊C411yescharacteristic
1145C42C2×C22⋊C411yescharacteristic
1146C42C2×C22⋊C411yescharacteristic
1147C42C2×C22⋊C411yescharacteristic
1148C42C22×D411yescharacteristic
1149C42C22×D411yescharacteristic
1150C42C22×D411yescharacteristic
1151C42C22×D411yescharacteristic
1152C42C22×D411yescharacteristic
1153C42C22×D411yescharacteristic
1154C42C22×D411yescharacteristic
1155C42C22×D411yescharacteristic
1156C42C22×D411yescharacteristic
1157C42C22×D411yescharacteristic
1158C42C22×D411yescharacteristic
1159C42C22×D411yescharacteristic
1160C42C22×D411yescharacteristic
1161C42C22×D411yescharacteristic
1162C42C22×D411yescharacteristic
1163C42C22×D411yescharacteristic
1164C23—22no—
1165C23—22no—
1166C23—22no—
1167C23—22no—
1168C23—22no—
1169C23—22no—
1170C23—22no—
1171C23—22no—
1172C23—22no—
1173C23—24no—
1174C23—28no—
1175C23—41no—
1176C23—41no—
1177C23—41no—
1178C23—41no—
1179C23—41no—
1180C23—41no—
1181C23—41no—
1182C23—41no—
1183C23—41no—
1184C23—41no—
1185C23—41no—
1186C23—41no—
1187C23—44no—
1188C23—44no—
1189C23—416no—
1190C23C22×C22⋊C411yescharacteristic
1191C23C22×C22⋊C411yescharacteristic
1192C23C22×C22⋊C411yescharacteristic
1193C23C22×C22⋊C411yescharacteristic
1194C23C22×C22⋊C411yescharacteristic
1195C23C22×C22⋊C411yescharacteristic
1196C23C24×C411yescharacteristic
1197Q8—44no—
1198Q8—44no—
1199Q8—44no—
1200Q8—44no—
1201Q8—44no—
1202Q8—44no—
1203D4—44no—
1204D4—44no—
1205D4—48no—
1206D4—48no—
1207D4—48no—
1208D4—48no—
1209D4—48no—
1210D4—48no—
1211D4—44no—
1212D4—44no—
1213D4—44no—
1214D4—44no—
1215C2×C4—22no—
1216C2×C4—22no—
1217C2×C4—22no—
1218C2×C4—22no—
1219C2×C4—22no—
1220C2×C4—22no—
1221C2×C4—22no—
1222C2×C4—22no—
1223C2×C4—22no—
1224C2×C4—22no—
1225C2×C4—22no—
1226C2×C4—22no—
1227C2×C4—22no—
1228C2×C4—22no—
1229C2×C4—22no—
1230C2×C4—22no—
1231C2×C4—22no—
1232C2×C4—22no—
1233C2×C4—22no—
1234C2×C4—22no—
1235C2×C4—22no—
1236C2×C4—22no—
1237C2×C4—22no—
1238C2×C4—22no—
1239C2×C4—22no—
1240C2×C4—22no—
1241C2×C4—22no—
1242C2×C4—22no—
1243C2×C4—22no—
1244C2×C4—22no—
1245C2×C4—22no—
1246C2×C4—22no—
1247C2×C4—22no—
1248C2×C4—22no—
1249C2×C4—22no—
1250C2×C4—22no—
1251C2×C4—22no—
1252C2×C4—22no—
1253C2×C4—22no—
1254C2×C4—22no—
1255C2×C4—22no—
1256C2×C4—22no—
1257C2×C4—22no—
1258C2×C4—22no—
1259C2×C4—22no—
1260C2×C4—24no—
1261C2×C4—24no—
1262C2×C4—24no—
1263C2×C4—28no—
1264C2×C4—41no—
1265C2×C4—41no—
1266C2×C4—41no—
1267C2×C4—41no—
1268C2×C4—41no—
1269C2×C4—41no—
1270C2×C4—41no—
1271C2×C4—41no—
1272C2×C4—41no—
1273C2×C4—41no—
1274C2×C4—41no—
1275C2×C4—41no—
1276C2×C4—41no—
1277C2×C4—41no—
1278C2×C4—41no—
1279C2×C4—41no—
1280C2×C4—41no—
1281C2×C4—41no—
1282C2×C4—41no—
1283C2×C4—41no—
1284C2×C4—41no—
1285C2×C4—41no—
1286C2×C4—41no—
1287C2×C4—41no—
1288C2×C4—41no—
1289C2×C4—41no—
1290C2×C4—41no—
1291C2×C4—41no—
1292C2×C4—41no—
1293C2×C4—41no—
1294C2×C4—41no—
1295C2×C4—41no—
1296C2×C4—41no—
1297C2×C4—41no—
1298C2×C4—41no—
1299C2×C4—41no—
1300C2×C4—48no—
1301C2×C4—48no—
1302C2×C4—48no—
1303C2×C4—48no—
1304C2×C4—48no—
1305C2×C4—48no—
1306C2×C4—44no—
1307C2×C4—44no—
1308C2×C4#41314yes—
1309C2×C4#41314yes—
1310C2×C4C22×C22⋊C411yescharacteristic
1311C2×C4C22×C22⋊C411yescharacteristic
1312C2×C4C22×C22⋊C411yescharacteristic
1313C2×C4C22×C22⋊C411yescharacteristic
1314C2×C4C22×C22⋊C411yescharacteristic
1315C2×C4C22×C22⋊C411yescharacteristic
1316C2×C4C22×C22⋊C411yescharacteristic
1317C2×C4C22×C22⋊C411yescharacteristic
1318C2×C4C22×C22⋊C411yescharacteristic
1319C2×C4C22×C22⋊C411yescharacteristic
1320C2×C4C22×C22⋊C411yescharacteristic
1321C2×C4C22×C22⋊C411yescharacteristic
1322C2×C4C22×C22⋊C411yescharacteristic
1323C2×C4C22×C22⋊C411yescharacteristic
1324C2×C4C22×C22⋊C411yescharacteristic
1325C2×C4C22×C22⋊C411yescharacteristic
1326C2×C4C22×C22⋊C411yescharacteristic
1327C2×C4C22×C22⋊C411yescharacteristic
1328C2×C4C22×C22⋊C411yescharacteristic
1329C2×C4C22×C22⋊C411yescharacteristic
1330C2×C4C22×C22⋊C411yescharacteristic
1331C2×C4C22×C22⋊C411yescharacteristic
1332C2×C4C23×D411yescharacteristic
1333C2×C4C23×D411yescharacteristic
1334C2×C4#58514yes—
1335C8—48no—
1336C8—48no—
1337C22—21no—
1338C22—21no—
1339C22—21no—
1340C22—21no—
1341C22—21no—
1342C22—21no—
1343C22—21no—
1344C22—21no—
1345C22—21no—
1346C22—21no—
1347C22—21no—
1348C22—21no—
1349C22—21no—
1350C22—21no—
1351C22—21no—
1352C22—21no—
1353C22—21no—
1354C22—21no—
1355C22—44no—
1356C22—44no—
1357C22—44no—
1358C22—44no—
1359C22—44no—
1360C22—44no—
1361C22—44no—
1362C22—44no—
1363C22—44no—
1364C22—44no—
1365C22—88no—
1366C22C2×#41312yes—
1367C22C2×#41312yes—
1368C22C23×C22⋊C411yescharacteristic
1369C22#342812yes—
1370C4—21no—
1371C4—21no—
1372C4—21no—
1373C4—21no—
1374C4—21no—
1375C4—21no—
1376C4—21no—
1377C4—21no—
1378C4—21no—
1379C4—21no—
1380C4—21no—
1381C4—21no—
1382C4—21no—
1383C4—21no—
1384C4—21no—
1385C4—21no—
1386C4—21no—
1387C4—21no—
1388C4—44no—
1389C4—44no—
1390C4—44no—
1391C4C2×#41312yes—
1392C4C2×#41312yes—
1393C4C2×#41312yes—
1394C4C2×#41312yes—
1395C4#344912yes—
1396C4#344912yes—
1397C2—22no—
1398C2—22no—
1399C2—22no—
1400C2—41no—
1401C2—41no—
1402C2—41no—
1403C2—41no—
1404C2—84no—
1405C2#3404411yescharacteristic
1406C2C22×#41311yescharacteristic
1407C2C22×#41311yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊C4
commutatorC23C24×C4
Frattini, cosocleC22×C4C25
socleC22C23×C22⋊C4
prime radicalC2×#3444C2
LCSG ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4 ◁ C23×C42 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C2×#2920C2semidirect
3. C2×#2920C2semidirect
4. #21880C2semidirect
5. #21879C2semidirect
6. #21878C2semidirect
7. #21831C2semidirect
8. #21800C2semidirect
9. #21754C2semidirect
10. #21426C2semidirect
11. #21425C2semidirect
12. #21424C2semidirect
13. #20728C2semidirect
79. #1998C22semidirect
80. #1997C22semidirect
81. #1997C22semidirect
82. #1967C22semidirect
83. #1966C22semidirect
84. #1965C22semidirect
90. #1801C22semidirect
91. #1800C22semidirect
93. C4×#101C22semidirect
94. C4×#100C22semidirect

Maximal subgroups

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

subgroupindex
C2×#34442
C2×#29202
#218802
#218792
#218782
#218312
#218002
#217542
#214262
#214252
#214242
#207282