Finite Group Databasebeta

← #6343392

Subgroups — #6343392

Order 512.

3078 conjugacy classes of subgroups.

The subgroup lattice has 1254 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#62800C211yesmaximal, characteristic
2#60278C211yesmaximal, characteristic, complemented
3#34060C211yesmaximal, characteristic, complemented
4#17602C214yesmaximal, complemented
5#17599C214yesmaximal, complemented
6#17597C218yesmaximal, complemented
7#17576C212yesmaximal, complemented
8#17574C212yesmaximal, complemented
9#17563C212yesmaximal, complemented
10#17561C212yesmaximal, complemented
11#17546C211yesmaximal, characteristic, complemented
12#17544C211yesmaximal, characteristic, complemented
13#17533C211yesmaximal, characteristic, complemented
14C2×#1502C211yesmaximal, characteristic, complemented
15#3522C2212yes—
16#3519C2214yes—
17#3519C2212yes—
18#3517—21no—
19#3514—22no—
20#3514—21no—
21#3511C411yescharacteristic, complemented
22#3511C412yescomplemented
23#3508C411yescharacteristic, complemented
24#3508C412yescomplemented
25#3503C411yescharacteristic, complemented
26#3498C411yescharacteristic, complemented
27#3494—22no—
28#3494—21no—
29#3488—21no—
30#3483C412yescomplemented
31#3481C414yescomplemented
32#3481C412yescomplemented
33#3480—21no—
34D4×#41—22no—
35D4×#41—21no—
36#3460—21no—
37#3460—22no—
38#3444C2211yescharacteristic
39#3444C2212yes—
40C2×#532C2211yescharacteristic
41C2×#532C2212yes—
42C4×H(5,𝔽2)—21no—
43C2×C4×#41C2211yescharacteristic
44#2991—21no—
45#2990—22no—
46#2990—21no—
47#2984C2212yescomplemented
48#2974C2214yescomplemented
49#2974C2212yescomplemented
50#2965—21no—
51#2965—22no—
52C8×#41—21no—
53#2920C2211yescharacteristic, complemented
54#2920C2212yescomplemented
55C2×#431C2211yescharacteristic, complemented
56C2×#431C2212yescomplemented
57#2320C2212yescomplemented
58#2319C2212yescomplemented
59#2318C2214yescomplemented
60#2317—21no—
61#2314—22no—
62#2311—21no—
63#2295—21no—
64#2293—21no—
65#2290—22no—
66#2285C2212yescomplemented
67#2283C2212yescomplemented
68C4×#117C2211yescharacteristic, complemented
69C2×C4×C4⋊C4C2211yescharacteristic, complemented
70#1521C2218yescomplemented
71#1519C2218yescomplemented
72#1517C2218yescomplemented
73#1516C2218yescomplemented
74#1514C2218yescomplemented
75#1513C2218yescomplemented
76#1512C2218yescomplemented
77#1510C2218yescomplemented
78#1509C2214yescomplemented
79#1507C2214yescomplemented
80#1505C2214yescomplemented
81#1504C2214yescomplemented
82#1503C2211yescharacteristic, complemented
83#1503C2211yescharacteristic, complemented
84#1503C2212yescomplemented
85#1502C2212yescomplemented
86#1502C2212yescomplemented
87#1502C2214yescomplemented
88#1502C2211yescharacteristic, complemented
89#1502C2211yescharacteristic, complemented
90#1502C2212yescomplemented
91#1502C2212yescomplemented
92#1502C2212yescomplemented
93#1501C2214yescomplemented
94#1500C2214yescomplemented
95C2×#327C2214yescomplemented
96C2×H(5,𝔽2)—21no—
97C22×#41—21no—
98C22×#41—22no—
99C22×#41D411yescharacteristic
100#559—22no—
101#559—21no—
102#559C2×C414yescomplemented
103#559C2×C412yescomplemented
104Q82C2×C412yescomplemented
105#557—21no—
106#556—22no—
107#556—21no—
108#555—24no—
109#555—22no—
110#555C2×C414yes—
111#555C2×C412yescomplemented
112#554C2×C414yes—
113#554C2×C414yescomplemented
114#554C2×C412yescomplemented
115#554C2×C412yescomplemented
116#553—22no—
117#553—24no—
118#553—24no—
119#553—22no—
120#553C2×C414yes—
121#553C2×C414yes—
122#553C2×C414yescomplemented
123#551—24no—
124#551—24no—
125#551—24no—
126#550—22no—
127#550—21no—
128#550—21no—
129#550—22no—
130#550C2×C414yes—
131#550C2×C412yescomplemented
132#550C2×C412yescomplemented
133D4×Q8—22no—
134D4×Q8—21no—
135#548—22no—
136#548—22no—
137#548—22no—
138#548—22no—
139#547—21no—
140#547—22no—
141#547—24no—
142#547—22no—
143#546—24no—
144#546—22no—
145#546—22no—
146#546—22no—
147#546—22no—
148#546—24no—
149#546—24no—
150#546—24no—
151#546C2×C414yes—
152#546C2×C414yes—
153#546C2×C414yescomplemented
154D42—24no—
155D42—22no—
156D42—21no—
157D42—22no—
158D42C2×C414yes—
159D42C2×C412yescomplemented
160#544—21no—
161#544—22no—
162#542—22no—
163#542—24no—
164#542—22no—
165#542—22no—
166#542—22no—
167#540—22no—
168#540—24no—
169#540—22no—
170#540—22no—
171#540—22no—
172#538—24no—
173#538—24no—
174#538—24no—
175#537—21no—
176#537—22no—
177#535—21no—
178#535—22no—
179#535—21no—
180#535—22no—
181#533C2×C411yescharacteristic
182#533C2×C411yescharacteristic
183#533C2×C412yescomplemented
184#533C2×C412yescomplemented
185#533C2311yescharacteristic
186#532—22no—
187#532—24no—
188#532—22no—
189#532—21no—
190#532—21no—
191#532—22no—
192#532—21no—
193#532—22no—
194#532—22no—
195#532—21no—
196#532C2×C411yescharacteristic
197#532C2×C412yes—
198#532C2×C412yes—
199#532C2×C411yescharacteristic
200#532C2×C412yescomplemented
201#532C2×C414yescomplemented
202#532C2×C412yescomplemented
203#532C2×C412yescomplemented
204#532C2×C412yescomplemented
205#532C2312yes—
206#532C2311yescharacteristic
207#532C2312yes—
208#532C2314yes—
209C2×C4⋊Q8C2×C411yescharacteristic
210C2×C4⋊Q8C2×C412yescomplemented
211C2×#127C2×C411yescharacteristic
212C2×#127C2×C412yescomplemented
213#529—22no—
214#529—24no—
215#529—22no—
216#529—21no—
217#529—21no—
218#529—22no—
219#529—21no—
220#529—22no—
221#529—22no—
222#529—21no—
223#529C2×C412yes—
224#529C2×C414yescomplemented
225#529C2312yes—
226#529C2314yes—
227C2×#124—21no—
228C2×#124—22no—
229#525—21no—
230#525—22no—
231#525—21no—
232#525—22no—
233#525—24no—
234#525—24no—
235#525—24no—
236#525C2312yes—
237#525C2314yes—
238C2×#121—21no—
239C2×#121—22no—
240C2×#121C2312yes—
241C2×#121C2314yes—
242#520—21no—
243#520—22no—
244#520—21no—
245#520—22no—
246#518—24no—
247#518—22no—
248#518—21no—
249#518—22no—
250C4×#41—22no—
251C4×#41—21no—
252C4×#41—22no—
253C4×#41—21no—
254C4×#41—22no—
255C4×#41C2×C412yes—
256C4×#41C2×C412yes—
257C4×#41C2×C411yescharacteristic
258C4×#41C2×C411yescharacteristic
259C4×#41C2×C411yescharacteristic
260C4×#41C2×C411yescharacteristic
261C4×#41C2×C412yes—
262C4×#41C2×C414yescomplemented
263C4×#41D411yescharacteristic
264C4×#41D411yescharacteristic
265C4×#41D412yes—
266C4×#41D412yes—
267C4×#41D411yescharacteristic
268C4×#41D411yescharacteristic
269C2×C4×Q8D411yescharacteristic
270C2×C4×Q8C2311yescharacteristic
271C2×C4×D4—22no—
272C2×C4×D4—24no—
273C2×C4×D4—21no—
274C2×C4×D4—22no—
275C2×C4×D4C2×C412yes—
276C2×C4×D4C2×C414yescomplemented
277C2×C4×D4D412yes—
278C2×C4×D4D411yescharacteristic
279C2×C4×D4C2312yes—
280C2×C4×D4C2311yescharacteristic
281C2×#117—21no—
282C2×#117—22no—
283C2×#117D412yes—
284C2×#117D411yescharacteristic
285C22×C4⋊C4—21no—
286C22×C42—21no—
287C22×C42C2311yescharacteristic
288C22×C42C2312yes—
289#446—22no—
290#446—24no—
291C8×Q8—22no—
292#436—22no—
293#436—24no—
294#435—24no—
295#435—24no—
296#435—24no—
297C8×D4—24no—
298C8×D4—22no—
299#432—21no—
300#432—22no—
301#432C2312yes—
302#432C2314yes—
303#431—22no—
304#431—21no—
305#431—22no—
306#431—21no—
307#431—21no—
308#431—22no—
309#431C2311yescharacteristic
310#431C2311yescharacteristic
311#431C2312yes—
312#431C2312yes—
313#431C2314yes—
314#423—22no—
315#423—21no—
316C2×C4⋊C8—21no—
317C2×C4⋊C8—22no—
318#407C2312yes—
319#407C2314yes—
320C2×C22⋊C8C2312yes—
321C2×C22⋊C8C2314yes—
322C4×M16—22no—
323C4×M16—21no—
324C2×C4×C8—21no—
325C2×C4×C8—22no—
326#391—22no—
327#390—22no—
328#389—22no—
329#389—22no—
330#388—24no—
331#388—24no—
332#387—24no—
333#387—24no—
334#386—24no—
335#385—24no—
336#384—22no—
337#383C2314yes—
338#382—22no—
339#382C2314yes—
340#381C2314yes—
341#380—22no—
342#380—22no—
343#380C2314yes—
344C4×C4⋊C4—21no—
345C4×C4⋊C4—21no—
346C4×C4⋊C4—21no—
347C4×C4⋊C4—22no—
348C4×C4⋊C4C2312yes—
349C4×C4⋊C4C2312yes—
350C4×C4⋊C4C2311yescharacteristic
351C4×C4⋊C4C2311yescharacteristic
352C4×C22⋊C4—21no—
353C4×C22⋊C4—22no—
354C4×C22⋊C4C2312yes—
355#376—22no—
356#376C2312yes—
357C2×#95C2312yes—
358C43—21no—
359#328C2314yes—
360#328C2314yes—
361#328C2318yes—
362#327C2318yes—
363#327C2318yes—
364#327C2314yes—
365#327C2314yes—
366#327C2318yes—
367#327C2318yes—
368#327C2318yes—
369H(5,𝔽2)—48no—
370C2×#41—22no—
371C2×#41—21no—
372C2×#41—22no—
373C2×#41—22no—
374C2×#41—24no—
375C2×#41—22no—
376C2×#41—22no—
377C2×#41—22no—
378C2×#41—21no—
379C2×#41—22no—
380C2×#41—22no—
381C2×#41—24no—
382C2×#41—44no—
383C2×#41—82no—
384C2×#41—84no—
385C2×#41—82no—
386C2×#41—84no—
387C2×#41C22⋊C411yescharacteristic
388C2×#41C22⋊C411yescharacteristic
389C2×#41C22⋊C412yes—
390C2×#41C22⋊C412yes—
391C2×#41C22⋊C411yescharacteristic
392C2×#41C22⋊C411yescharacteristic
393C2×#41C22×C412yes—
394C2×#41C22×C414yes—
395C22×Q8—21no—
396C22×Q8—22no—
397C22×Q8C2×D411yescharacteristic
398C22×D4—22no—
399C22×D4—24no—
400C22×D4—24no—
401C22×D4—22no—
402C22×D4—21no—
403C22×D4—22no—
404C22×D4—21no—
405C22×D4—22no—
406C22×D4C22×C412yes—
407C22×D4C22×C414yes—
408C22×D4C2×D412yes—
409C22×D4C2×D411yescharacteristic
410C23×C4—22no—
411C23×C4—24no—
412C23×C4—22no—
413C23×C4C2×D411yescharacteristic
414C23×C4C2×D412yes—
415C23×C4C2×D411yescharacteristic
416C23×C4C2×D412yes—
417C23×C4C2411yescharacteristic
418C23×C4C2412yes—
419C2×M16—24no—
420C2×M16—22no—
421C22×C8—22no—
422C22×C8—24no—
423C4⋊Q8—24no—
424C4⋊Q8—22no—
425C4⋊Q8—21no—
426C4⋊Q8—21no—
427C4⋊Q8—22no—
428C4⋊Q8—22no—
429C4⋊Q8C22×C411yescharacteristic
430C4⋊Q8C22×C412yes—
431C4⋊Q8C22×C412yes—
432C4⋊Q8C22×C411yescharacteristic
433C4⋊Q8C22×C414yes—
434C4⋊Q8C22×C411yescharacteristic
435#127—24no—
436#127—22no—
437#127—21no—
438#127—21no—
439#127—22no—
440#127—22no—
441#127C22×C412yes—
442#127C22×C412yes—
443#127C22×C411yescharacteristic
444#127C22×C414yes—
445#126—24no—
446#126—24no—
447#126—24no—
448#126—22no—
449#126—24no—
450#126—24no—
451#126—22no—
452#125—24no—
453#125—22no—
454#125—21no—
455#125—22no—
456#125—21no—
457#125C22×C412yes—
458#125C22×C414yes—
459#124—22no—
460#124—24no—
461#124—24no—
462#124—24no—
463#124—24no—
464#124—22no—
465#124—22no—
466#124—22no—
467#124—22no—
468#124—24no—
469#124—21no—
470#124—22no—
471#124—22no—
472#124—21no—
473#124—24no—
474#124—22no—
475#124C22×C412yes—
476#124C22×C414yes—
477#123—22no—
478#123—24no—
479#123—22no—
480#123—24no—
481#123—24no—
482#123—22no—
483#123—24no—
484#123—24no—
485#123—24no—
486#123—24no—
487#123—24no—
488#123—24no—
489#123—24no—
490#123—24no—
491#123—24no—
492C22⋊Q8—22no—
493C22⋊Q8—24no—
494C22⋊Q8—21no—
495C22⋊Q8—21no—
496C22⋊Q8—21no—
497C22⋊Q8—22no—
498C22⋊Q8—22no—
499C22⋊Q8—22no—
500C22⋊Q8—21no—
501C22⋊Q8—24no—
502C22⋊Q8—24no—
503C22⋊Q8—24no—
504C22⋊Q8—24no—
505C22⋊Q8—24no—
506C22⋊Q8—24no—
507C22⋊Q8C22×C412yes—
508C22⋊Q8C22×C414yes—
509C22⋊Q8C2412yes—
510#121—24no—
511#121—24no—
512#121—24no—
513#121—24no—
514#121—22no—
515#121—22no—
516#121—22no—
517#121—22no—
518#121—22no—
519#121—24no—
520#121—21no—
521#121—21no—
522#121—21no—
523#121—22no—
524#121—22no—
525#121—22no—
526#121—22no—
527#121—21no—
528#121—22no—
529#121—24no—
530#121—24no—
531#121—22no—
532#121—22no—
533#121—24no—
534#121—24no—
535#121—22no—
536#121—24no—
537#121—22no—
538#121—24no—
539#121—24no—
540#121—24no—
541#121—24no—
542#121—24no—
543#121—24no—
544#121C22×C414yes—
545#121C22×C414yes—
546#121C22×C414yes—
547#121C22×C412yes—
548#121C22×C414yes—
549#121C2414yes—
550#121C2412yes—
551#120—22no—
552#120—24no—
553#120—24no—
554#120—24no—
555#120—24no—
556#120—24no—
557#120—24no—
558#120—24no—
559C4×Q8—22no—
560C4×Q8—21no—
561C4×Q8—22no—
562C4×Q8—21no—
563C4×Q8—21no—
564C4×Q8—22no—
565C4×Q8—22no—
566C4×Q8—21no—
567C4×Q8C22⋊C411yescharacteristic
568C4×Q8C22⋊C411yescharacteristic
569C4×Q8C22⋊C412yes—
570C4×Q8C22⋊C411yescharacteristic
571C4×Q8C22⋊C411yescharacteristic
572C4×Q8C22⋊C412yes—
573C4×Q8C22×C412yes—
574C4×Q8C22×C412yes—
575C4×Q8C22×C414yes—
576C4×Q8C22×C411yescharacteristic
577C4×Q8C22×C411yescharacteristic
578C4×Q8C22×C412yes—
579C4×Q8C2×D411yescharacteristic
580C4×Q8C2×D411yescharacteristic
581C4×Q8C2×D412yes—
582C4×D4—24no—
583C4×D4—22no—
584C4×D4—22no—
585C4×D4—24no—
586C4×D4—22no—
587C4×D4—22no—
588C4×D4—24no—
589C4×D4—24no—
590C4×D4—22no—
591C4×D4—24no—
592C4×D4—22no—
593C4×D4—24no—
594C4×D4—22no—
595C4×D4—24no—
596C4×D4—24no—
597C4×D4—22no—
598C4×D4—24no—
599C4×D4—22no—
600C4×D4—24no—
601C4×D4—24no—
602C4×D4—24no—
603C4×D4—22no—
604C4×D4—24no—
605C4×D4—22no—
606C4×D4—22no—
607C4×D4—22no—
608C4×D4—22no—
609C4×D4—22no—
610C4×D4—24no—
611C4×D4—24no—
612C4×D4—21no—
613C4×D4—22no—
614C4×D4—21no—
615C4×D4—21no—
616C4×D4—22no—
617C4×D4—22no—
618C4×D4—22no—
619C4×D4—21no—
620C4×D4—22no—
621C4×D4—24no—
622C4×D4C22⋊C412yes—
623C4×D4C22⋊C411yescharacteristic
624C4×D4C22⋊C412yes—
625C4×D4C22⋊C412yes—
626C4×D4C22⋊C412yes—
627C4×D4C22⋊C411yescharacteristic
628C4×D4C22⋊C412yes—
629C4×D4C22⋊C412yes—
630C4×D4C22⋊C411yescharacteristic
631C4×D4C22⋊C412yes—
632C4×D4C22⋊C412yes—
633C4×D4C22⋊C412yes—
634C4×D4C22⋊C411yescharacteristic
635C4×D4C22⋊C412yes—
636C4×D4C22×C414yes—
637C4×D4C22×C414yes—
638C4×D4C22×C412yes—
639C4×D4C22×C414yes—
640C4×D4C22×C414yes—
641C4×D4C22×C412yes—
642C4×D4C22×C414yes—
643C4×D4C22×C412yes—
644C4×D4C22×C411yescharacteristic
645C4×D4C22×C412yes—
646C4×D4C22×C412yes—
647C4×D4C22×C412yes—
648C4×D4C22×C412yes—
649C4×D4C22×C411yescharacteristic
650C4×D4C2×D412yes—
651C4×D4C2×D411yescharacteristic
652C4×D4C2×D412yes—
653C4×D4C2×D412yes—
654C4×D4C2×D412yes—
655C4×D4C2×D411yescharacteristic
656C4×D4C2×D412yes—
657#117—21no—
658#117—22no—
659#117—21no—
660#117—24no—
661#117—22no—
662#117—22no—
663#117—24no—
664#117—22no—
665#117—24no—
666#117—22no—
667#117—24no—
668#117—44no—
669#117—84no—
670#117C22⋊C412yes—
671#117C22⋊C411yescharacteristic
672#117C22⋊C412yes—
673#117C22⋊C411yescharacteristic
674#117C22⋊C412yes—
675#117C22⋊C412yes—
676#117C22⋊C412yes—
677#117C22⋊C412yes—
678#117C22⋊C412yes—
679#117C22⋊C412yes—
680#117C22⋊C411yescharacteristic
681#117C22⋊C412yes—
682#117C22⋊C411yescharacteristic
683#117C22⋊C412yes—
684#117C22×C412yes—
685#117C22×C414yes—
686C2×C4⋊C4—21no—
687C2×C4⋊C4—22no—
688C2×C4⋊C4—24no—
689C2×C4⋊C4—22no—
690C2×C4⋊C4—22no—
691C2×C4⋊C4—22no—
692C2×C4⋊C4—21no—
693C2×C4⋊C4—21no—
694C2×C4⋊C4—24no—
695C2×C4⋊C4—24no—
696C2×C4⋊C4—44no—
697C2×C4⋊C4C22×C412yes—
698C2×C4⋊C4C22×C414yes—
699C2×C4⋊C4C2×D412yes—
700C2×C4⋊C4C2×D411yescharacteristic
701C2×C4⋊C4C2×D412yes—
702C2×C4⋊C4C2×D411yescharacteristic
703C2×C22⋊C4—22no—
704C2×C22⋊C4—24no—
705C2×C22⋊C4—22no—
706C2×C22⋊C4—24no—
707C2×C22⋊C4—24no—
708C2×C22⋊C4—24no—
709C2×C22⋊C4—24no—
710C2×C22⋊C4—22no—
711C2×C22⋊C4—24no—
712C2×C22⋊C4—24no—
713C2×C22⋊C4C2×D412yes—
714C2×C22⋊C4C2×D412yes—
715C2×C22⋊C4C2×D412yes—
716C2×C42—22no—
717C2×C42—24no—
718C2×C42—21no—
719C2×C42—22no—
720C2×C42—22no—
721C2×C42—21no—
722C2×C42—22no—
723C2×C42—22no—
724C2×C42—82no—
725C2×C42C22×C411yescharacteristic
726C2×C42C22×C412yes—
727C2×C42C22×C411yescharacteristic
728C2×C42C22×C412yes—
729C2×C42C22×C411yescharacteristic
730C2×C42C22×C412yes—
731C2×C42C22×C411yescharacteristic
732C2×C42C22×C412yes—
733C2×C42C2×D411yescharacteristic
734C2×C42C2×D412yes—
735C2×C42C2×D411yescharacteristic
736C2×C42C2×D412yes—
737C2×C42C2×D411yescharacteristic
738C2×C42C2×D412yes—
739C2×C42C2×D411yescharacteristic
740C2×C42C2×D412yes—
741C2×C42C2×D412yes—
742C2×C42C2×D411yescharacteristic
743C2×C42C2×D412yes—
744C2×C42C2×D411yescharacteristic
745C2×C42C2411yescharacteristic
746C2×C42C2412yes—
747C2×C42C2411yescharacteristic
748C4⋊C8—21no—
749C4⋊C8—21no—
750C4⋊C8—22no—
751C4⋊C8—24no—
752C4⋊C8—22no—
753C4⋊C8—22no—
754C4⋊C8—24no—
755C22⋊C8—24no—
756C22⋊C8—22no—
757C22⋊C8—22no—
758C22⋊C8—24no—
759C22⋊C8C2412yes—
760C22⋊C8C2412yes—
761C22⋊C8C2414yes—
762#97—24no—
763#97—22no—
764C4×C8—21no—
765C4×C8—21no—
766C4×C8—22no—
767C4×C8—22no—
768C4×C8—24no—
769#95—22no—
770#95—24no—
771#95—24no—
772#95—22no—
773#95—24no—
774#95—24no—
775#95C2414yes—
776#95C2412yes—
777#95C2412yes—
778C24—24no—
779C24—22no—
780C24C22×D411yescharacteristic
781C24C22×D412yes—
782#41—24no—
783#41—24no—
784#41—44no—
785#41—44no—
786#41—42no—
787#41—42no—
788#41—48no—
789#41—48no—
790#41—44no—
791#41—42no—
792#41—42no—
793#41—44no—
794#41—44no—
795#41—84no—
796#41—88no—
797#41—82no—
798#41—84no—
799#41—82no—
800#41—84no—
801#41—84no—
802#41—84no—
803#41—84no—
804#41—82no—
805#41—84no—
806C2×Q8—21no—
807C2×Q8—21no—
808C2×Q8—22no—
809C2×Q8—24no—
810C2×Q8—22no—
811C2×Q8—42no—
812C2×Q8—82no—
813C2×Q8—84no—
814C2×Q8C2×C22⋊C411yescharacteristic
815C2×Q8C2×C22⋊C411yescharacteristic
816C2×Q8C2×C22⋊C412yes—
817C2×Q8C23×C412yes—
818C2×D4—24no—
819C2×D4—22no—
820C2×D4—22no—
821C2×D4—24no—
822C2×D4—22no—
823C2×D4—24no—
824C2×D4—24no—
825C2×D4—24no—
826C2×D4—24no—
827C2×D4—24no—
828C2×D4—22no—
829C2×D4—22no—
830C2×D4—21no—
831C2×D4—21no—
832C2×D4—22no—
833C2×D4—22no—
834C2×D4—24no—
835C2×D4—24no—
836C2×D4—22no—
837C2×D4—42no—
838C2×D4—48no—
839C2×D4—44no—
840C2×D4—416no—
841C2×D4—48no—
842C2×D4—44no—
843C2×D4—82no—
844C2×D4—84no—
845C2×D4—82no—
846C2×D4—84no—
847C2×D4—82no—
848C2×D4—84no—
849C2×D4—82no—
850C2×D4—84no—
851C2×D4C2×C22⋊C412yes—
852C2×D4C2×C22⋊C411yescharacteristic
853C2×D4C2×C22⋊C412yes—
854C2×D4C2×C22⋊C411yescharacteristic
855C2×D4C2×C22⋊C412yes—
856C2×D4C2×C22⋊C412yes—
857C2×D4C2×C22⋊C412yes—
858C2×D4C23×C414yes—
859C2×D4C23×C412yes—
860C22×C4—22no—
861C22×C4—24no—
862C22×C4—22no—
863C22×C4—24no—
864C22×C4—24no—
865C22×C4—24no—
866C22×C4—22no—
867C22×C4—24no—
868C22×C4—22no—
869C22×C4—22no—
870C22×C4—24no—
871C22×C4—22no—
872C22×C4—24no—
873C22×C4—24no—
874C22×C4—24no—
875C22×C4—24no—
876C22×C4—22no—
877C22×C4—24no—
878C22×C4—22no—
879C22×C4—44no—
880C22×C4—44no—
881C22×C4—84no—
882C22×C4—88no—
883C22×C4—81no—
884C22×C4—82no—
885C22×C4—82no—
886C22×C4—82no—
887C22×C4C2×C22⋊C411yescharacteristic
888C22×C4C2×C22⋊C412yes—
889C22×C4C2×C22⋊C411yescharacteristic
890C22×C4C2×C22⋊C411yescharacteristic
891C22×C4C2×C22⋊C412yes—
892C22×C4C2×C22⋊C412yes—
893C22×C4C2×C22⋊C411yescharacteristic
894C22×C4C2×C22⋊C411yescharacteristic
895C22×C4C2×C22⋊C412yes—
896C22×C4C2×C22⋊C412yes—
897C22×C4C2×C22⋊C411yescharacteristic
898C22×C4C2×C22⋊C411yescharacteristic
899C22×C4C2×C22⋊C412yes—
900C22×C4C2×C22⋊C412yes—
901C22×C4C2×C22⋊C412yes—
902C22×C4C2×C22⋊C411yescharacteristic
903C22×C4C23×C412yes—
904C22×C4C23×C411yescharacteristic
905C22×C4C23×C411yescharacteristic
906C22×C4C23×C412yes—
907C22×C4C22×D411yescharacteristic
908C22×C4C22×D412yes—
909C22×C4C22×D411yescharacteristic
910C22×C4C22×D411yescharacteristic
911C22×C4C22×D412yes—
912C22×C4C22×D411yescharacteristic
913C22×C4C22×D412yes—
914C22×C4C22×D411yescharacteristic
915C22×C4C22×D412yes—
916C22×C4C22×D412yes—
917C22×C4C22×D411yescharacteristic
918C22×C4C22×D411yescharacteristic
919C22×C4C2511yescharacteristic
920M16—84no—
921M16—82no—
922C2×C8—22no—
923C2×C8—22no—
924C2×C8—24no—
925C2×C8—82no—
926C2×C8—84no—
927C4⋊C4—24no—
928C4⋊C4—22no—
929C4⋊C4—22no—
930C4⋊C4—21no—
931C4⋊C4—22no—
932C4⋊C4—24no—
933C4⋊C4—22no—
934C4⋊C4—24no—
935C4⋊C4—21no—
936C4⋊C4—22no—
937C4⋊C4—21no—
938C4⋊C4—21no—
939C4⋊C4—22no—
940C4⋊C4—24no—
941C4⋊C4—22no—
942C4⋊C4—24no—
943C4⋊C4—22no—
944C4⋊C4—24no—
945C4⋊C4—22no—
946C4⋊C4—44no—
947C4⋊C4—44no—
948C4⋊C4—42no—
949C4⋊C4—42no—
950C4⋊C4—84no—
951C4⋊C4—84no—
952C4⋊C4C2×C22⋊C412yes—
953C4⋊C4C2×C22⋊C411yescharacteristic
954C4⋊C4C2×C22⋊C412yes—
955C4⋊C4C2×C22⋊C411yescharacteristic
956C4⋊C4C2×C22⋊C412yes—
957C4⋊C4C2×C22⋊C411yescharacteristic
958C4⋊C4C2×C22⋊C412yes—
959C4⋊C4C2×C22⋊C412yes—
960C4⋊C4C2×C22⋊C412yes—
961C4⋊C4C2×C22⋊C412yes—
962C4⋊C4C2×C22⋊C411yescharacteristic
963C4⋊C4C2×C22⋊C412yes—
964C4⋊C4C2×C22⋊C412yes—
965C4⋊C4C2×C22⋊C412yes—
966C4⋊C4C23×C414yes—
967C4⋊C4C23×C412yes—
968C4⋊C4C23×C412yes—
969C22⋊C4—24no—
970C22⋊C4—22no—
971C22⋊C4—22no—
972C22⋊C4—24no—
973C22⋊C4—22no—
974C22⋊C4—24no—
975C22⋊C4—22no—
976C22⋊C4—24no—
977C22⋊C4—24no—
978C22⋊C4—24no—
979C22⋊C4—24no—
980C22⋊C4—22no—
981C22⋊C4—24no—
982C22⋊C4—24no—
983C22⋊C4—24no—
984C22⋊C4—22no—
985C22⋊C4—24no—
986C22⋊C4—22no—
987C22⋊C4—24no—
988C22⋊C4—22no—
989C22⋊C4—24no—
990C22⋊C4—24no—
991C22⋊C4—22no—
992C22⋊C4—44no—
993C22⋊C4—84no—
994C22⋊C4—84no—
995C22⋊C4C2×C22⋊C412yes—
996C22⋊C4C2×C22⋊C412yes—
997C22⋊C4C2×C22⋊C412yes—
998C22⋊C4C2×C22⋊C412yes—
999C22⋊C4C2×C22⋊C412yes—
1000C22⋊C4C2×C22⋊C412yes—
1001C22⋊C4C2×C22⋊C412yes—
1002C22⋊C4C2×C22⋊C412yes—
1003C22⋊C4C2×C22⋊C412yes—
1004C22⋊C4C2×C22⋊C412yes—
1005C22⋊C4C2×C22⋊C412yes—
1006C22⋊C4C2×C22⋊C412yes—
1007C42—22no—
1008C42—24no—
1009C42—24no—
1010C42—22no—
1011C42—22no—
1012C42—44no—
1013C42—44no—
1014C42—42no—
1015C42—42no—
1016C42—82no—
1017C42—82no—
1018C42C2×C22⋊C411yescharacteristic
1019C42C2×C22⋊C412yes—
1020C42C2×C22⋊C411yescharacteristic
1021C42C2×C22⋊C412yes—
1022C42C2×C22⋊C411yescharacteristic
1023C42C2×C22⋊C412yes—
1024C42C2×C22⋊C411yescharacteristic
1025C42C2×C22⋊C412yes—
1026C42C2×C22⋊C411yescharacteristic
1027C42C2×C22⋊C412yes—
1028C42C2×C22⋊C412yes—
1029C42C2×C22⋊C411yescharacteristic
1030C42C2×C22⋊C412yes—
1031C42C2×C22⋊C411yescharacteristic
1032C42C2×C22⋊C411yescharacteristic
1033C42C2×C22⋊C412yes—
1034C42C23×C411yescharacteristic
1035C42C23×C411yescharacteristic
1036C42C23×C412yes—
1037C42C23×C412yes—
1038C42C23×C411yescharacteristic
1039C42C23×C411yescharacteristic
1040C42C22×D411yescharacteristic
1041C42C22×D412yes—
1042C42C22×D412yes—
1043C42C22×D411yescharacteristic
1044C42C22×D411yescharacteristic
1045C42C22×D411yescharacteristic
1046C23—22no—
1047C23—21no—
1048C23—21no—
1049C23—22no—
1050C23—22no—
1051C23—24no—
1052C23—22no—
1053C23—41no—
1054C23—42no—
1055C23—42no—
1056C23—48no—
1057C23—44no—
1058C23—82no—
1059C23—84no—
1060C23—82no—
1061C23—84no—
1062C23C22×C22⋊C412yes—
1063C23C22×C22⋊C411yescharacteristic
1064C23C22×C22⋊C412yes—
1065C23C22×C22⋊C411yescharacteristic
1066C23C23×D411yescharacteristic
1067Q8—22no—
1068Q8—22no—
1069Q8—42no—
1070Q8—42no—
1071Q8—42no—
1072Q8—44no—
1073Q8—42no—
1074Q8—82no—
1075Q8—84no—
1076D4—24no—
1077D4—24no—
1078D4—22no—
1079D4—22no—
1080D4—42no—
1081D4—42no—
1082D4—42no—
1083D4—44no—
1084D4—42no—
1085D4—48no—
1086D4—48no—
1087D4—44no—
1088D4—44no—
1089D4—42no—
1090D4—44no—
1091D4—42no—
1092D4—42no—
1093D4—44no—
1094D4—42no—
1095D4—44no—
1096D4—44no—
1097D4—82no—
1098D4—84no—
1099D4—82no—
1100D4—84no—
1101D4—84no—
1102D4—84no—
1103D4—84no—
1104D4—82no—
1105D4—84no—
1106C2×C4—22no—
1107C2×C4—21no—
1108C2×C4—22no—
1109C2×C4—21no—
1110C2×C4—22no—
1111C2×C4—22no—
1112C2×C4—24no—
1113C2×C4—22no—
1114C2×C4—24no—
1115C2×C4—22no—
1116C2×C4—24no—
1117C2×C4—22no—
1118C2×C4—24no—
1119C2×C4—22no—
1120C2×C4—22no—
1121C2×C4—22no—
1122C2×C4—22no—
1123C2×C4—24no—
1124C2×C4—24no—
1125C2×C4—22no—
1126C2×C4—22no—
1127C2×C4—22no—
1128C2×C4—24no—
1129C2×C4—41no—
1130C2×C4—42no—
1131C2×C4—41no—
1132C2×C4—42no—
1133C2×C4—42no—
1134C2×C4—41no—
1135C2×C4—42no—
1136C2×C4—42no—
1137C2×C4—42no—
1138C2×C4—41no—
1139C2×C4—41no—
1140C2×C4—42no—
1141C2×C4—41no—
1142C2×C4—42no—
1143C2×C4—48no—
1144C2×C4—44no—
1145C2×C4—48no—
1146C2×C4—44no—
1147C2×C4—42no—
1148C2×C4—42no—
1149C2×C4—42no—
1150C2×C4—42no—
1151C2×C4—44no—
1152C2×C4—44no—
1153C2×C4—44no—
1154C2×C4—42no—
1155C2×C4—42no—
1156C2×C4—84no—
1157C2×C4—84no—
1158C2×C4—84no—
1159C2×C4—82no—
1160C2×C4—84no—
1161C2×C4—82no—
1162C2×C4—84no—
1163C2×C4—88no—
1164C2×C4#42114yes—
1165C2×C4C22×C22⋊C411yescharacteristic
1166C2×C4C22×C22⋊C412yes—
1167C2×C4C22×C22⋊C412yes—
1168C2×C4C22×C22⋊C411yescharacteristic
1169C2×C4C22×C22⋊C411yescharacteristic
1170C2×C4C22×C22⋊C412yes—
1171C2×C4C22×C22⋊C411yescharacteristic
1172C2×C4C22×C22⋊C412yes—
1173C2×C4C22×C22⋊C411yescharacteristic
1174C2×C4C22×C22⋊C412yes—
1175C2×C4C22×C22⋊C412yes—
1176C2×C4C22×C22⋊C411yescharacteristic
1177C2×C4C22×C22⋊C411yescharacteristic
1178C2×C4C22×C22⋊C411yescharacteristic
1179C2×C4C22×C22⋊C411yescharacteristic
1180C2×C4C22×C22⋊C411yescharacteristic
1181C2×C4#57612yes—
1182C2×C4#57712yes—
1183C2×C4C24×C411yescharacteristic
1184C2×C4C23×D411yescharacteristic
1185C8—42no—
1186C8—42no—
1187C8—44no—
1188C22—21no—
1189C22—21no—
1190C22—21no—
1191C22—21no—
1192C22—21no—
1193C22—22no—
1194C22—22no—
1195C22—22no—
1196C22—21no—
1197C22—22no—
1198C22—21no—
1199C22—22no—
1200C22—22no—
1201C22—42no—
1202C22—42no—
1203C22—44no—
1204C22—42no—
1205C22—44no—
1206C22—42no—
1207C22—44no—
1208C22—42no—
1209C22—82no—
1210C22—82no—
1211C22—164no—
1212C22—168no—
1213C22C2×#42112yes—
1214C22C23×C22⋊C411yescharacteristic
1215C22C2×#57611yescharacteristic
1216C22C2×#57711yescharacteristic
1217C4—21no—
1218C4—21no—
1219C4—21no—
1220C4—22no—
1221C4—21no—
1222C4—22no—
1223C4—21no—
1224C4—22no—
1225C4—21no—
1226C4—22no—
1227C4—21no—
1228C4—21no—
1229C4—22no—
1230C4—22no—
1231C4—42no—
1232C4—44no—
1233C4—42no—
1234C4—42no—
1235C4—82no—
1236C4—82no—
1237C4—84no—
1238C4#289712yes—
1239C4#289712yes—
1240C4C2×#42112yes—
1241C4C2×#42112yes—
1242C2—21no—
1243C2—21no—
1244C2—22no—
1245C2—41no—
1246C2—42no—
1247C2—42no—
1248C2—84no—
1249C2—82no—
1250C2#6007011yescharacteristic
1251C2C2×#289711yescharacteristic
1252C2C22×#42111yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊C4
commutatorC2×C4C24×C4
Frattini, cosocleC22×C4C25
socleC22C23×C22⋊C4
prime radical#62800C2
LCSG ▷ C2×C4 ▷ C22 ▷ C1
UCSC1 ◁ C2×C4 ◁ C2×C4×#41 ◁ G
LECSG ▷ C22×C4 ▷ C22 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #60278C2semidirect
3. #34060C2semidirect
4. #17602C2semidirect
5. #17599C2semidirect
6. #17597C2semidirect
7. #17576C2semidirect
8. #17574C2semidirect
9. #17563C2semidirect
10. #17561C2semidirect
11. #17546C2semidirect
12. #17544C2semidirect
13. #17533C2semidirect
14. C2×#1502C2semidirect
21. #3511C4semidirect
22. #3511C4semidirect
23. #3508C4semidirect
24. #3508C4semidirect
25. #3503C4semidirect
26. #3498C4semidirect
30. #3483C4semidirect
31. #3481C4semidirect
32. #3481C4semidirect
47. #2984C22semidirect
48. #2974C22semidirect
49. #2974C22semidirect
53. #2920C22semidirect
54. #2920C22semidirect
55. C2×#431C22semidirect
56. C2×#431C22semidirect
57. #2320C22semidirect
58. #2319C22semidirect
59. #2318C22semidirect
66. #2285C22semidirect
67. #2283C22semidirect
68. C4×#117C22semidirect
69. C2×C4×C4⋊C4C22semidirect
70. #1521C22semidirect
71. #1519C22semidirect
72. #1517C22semidirect
73. #1516C22semidirect
74. #1514C22semidirect
75. #1513C22semidirect
76. #1512C22semidirect
77. #1510C22semidirect
78. #1509C22semidirect
79. #1507C22semidirect
80. #1505C22semidirect
81. #1504C22semidirect
82. #1503C22semidirect
83. #1503C22semidirect
84. #1503C22semidirect
85. #1502C22semidirect
86. #1502C22semidirect
87. #1502C22semidirect
88. #1502C22semidirect
89. #1502C22semidirect
90. #1502C22semidirect
91. #1502C22semidirect
92. #1502C22semidirect
93. #1501C22semidirect
94. #1500C22semidirect
95. C2×#327C22semidirect
102. #559C2×C4semidirect
103. #559C2×C4semidirect
104. Q82C2×C4semidirect
111. #555C2×C4semidirect
113. #554C2×C4semidirect
114. #554C2×C4semidirect
115. #554C2×C4semidirect
122. #553C2×C4semidirect
131. #550C2×C4semidirect
132. #550C2×C4semidirect
153. #546C2×C4semidirect
159. D42C2×C4semidirect
183. #533C2×C4semidirect
184. #533C2×C4semidirect
200. #532C2×C4semidirect
201. #532C2×C4semidirect
202. #532C2×C4semidirect
203. #532C2×C4semidirect
204. #532C2×C4semidirect
210. C2×C4⋊Q8C2×C4semidirect
212. C2×#127C2×C4semidirect
224. #529C2×C4semidirect
262. C4×#41C2×C4semidirect
276. C2×C4×D4C2×C4semidirect

Maximal subgroups

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

subgroupindex
#628002
#602782
#340602
#176022
#175992
#175972
#175762
#175742
#175632
#175612
#175462
#175442
#175332
C2×#15022