Finite Group Databasebeta

← #6343635

Subgroups — #6343635

Order 512.

3101 conjugacy classes of subgroups.

The subgroup lattice has 1251 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#62800C211yesmaximal, characteristic
2#60127C211yesmaximal, characteristic, complemented
3#34191C211yesmaximal, characteristic, complemented
4#17610C214yesmaximal, complemented
5#17604C218yesmaximal, complemented
6#17603C214yesmaximal, complemented
7#17589C212yesmaximal, complemented
8#17588C212yesmaximal, complemented
9#17585C211yesmaximal, characteristic, complemented
10#17583C211yesmaximal, characteristic, complemented
11#17574C211yesmaximal, characteristic, complemented
12#17573C211yesmaximal, characteristic, complemented
13#17571C212yesmaximal, complemented
14C2×#1517C212yesmaximal, complemented
15#3522—21no—
16#3519—22no—
17#3519—21no—
18#3517—21no—
19#3514—21no—
20#3514—22no—
21#3511C412yescomplemented
22#3511C411yescharacteristic, complemented
23#3508C412yescomplemented
24#3508C411yescharacteristic, complemented
25#3503C411yescharacteristic, complemented
26#3498C411yescharacteristic, complemented
27#3494C2214yes—
28#3494C2212yes—
29#3488C2212yes—
30#3483—21no—
31#3481—21no—
32#3481—22no—
33#3480—21no—
34D4×#41—21no—
35D4×#41—22no—
36#3460C414yescomplemented
37#3460C412yescomplemented
38#3444C2212yes—
39#3444C2211yescharacteristic
40C2×#532C2212yes—
41C2×#532C2211yescharacteristic
42C4×H(5,𝔽2)C412yescomplemented
43C2×C4×#41C2211yescharacteristic
44#2925—22no—
45#2925—21no—
46#2924C2214yescomplemented
47#2924C2212yescomplemented
48#2922—22no—
49#2922—21no—
50#2920C2211yescharacteristic, complemented
51#2920C2212yescomplemented
52C2×#431C2212yescomplemented
53C2×#431C2211yescharacteristic, complemented
54#2906—21no—
55#2880C2212yes—
56C4×#131—21no—
57#2355—21no—
58#2352—22no—
59D4×C4⋊C4—21no—
60#2346C2212yescomplemented
61#2343C2214yescomplemented
62#2339C2212yes—
63#2320—21no—
64#2318—22no—
65#2285C2211yescharacteristic, complemented
66#2283C2211yescharacteristic, complemented
67#2283C2212yescomplemented
68C2×#382C2212yescomplemented
69#2275—21no—
70#1521C2214yescomplemented
71#1519C2214yescomplemented
72#1518C2211yescharacteristic, complemented
73#1518C2212yescomplemented
74#1518C2211yescharacteristic, complemented
75#1517C2211yescharacteristic, complemented
76#1517C2212yescomplemented
77#1517C2212yescomplemented
78#1517C2212yescomplemented
79#1517C2218yescomplemented
80#1517C2212yescomplemented
81#1517C2211yescharacteristic, complemented
82#1517C2212yescomplemented
83#1516C2218yescomplemented
84#1514C2214yescomplemented
85#1513C2214yescomplemented
86#1512C2218yescomplemented
87#1510C2218yescomplemented
88#1509C2214yescomplemented
89#1507C2214yescomplemented
90#1505C2218yescomplemented
91#1504C2218yescomplemented
92#1502C2214yescomplemented
93#1501C2214yescomplemented
94#1500C2218yescomplemented
95C2×#327C2218yescomplemented
96C2×H(5,𝔽2)C2×C412yes—
97C22×#41—22no—
98C22×#41—21no—
99C22×#41C2311yescharacteristic
100C2×#131—22no—
101#559—21no—
102#559—22no—
103#559—21no—
104#559—22no—
105Q82—21no—
106#557—21no—
107#556—21no—
108#556—22no—
109#555—21no—
110#555—22no—
111#555—22no—
112#555—24no—
113#554—21no—
114#554—22no—
115#554—22no—
116#554—21no—
117#553—22no—
118#553—22no—
119#553—22no—
120#553—22no—
121#553—24no—
122#553—22no—
123#553—24no—
124#551—24no—
125#551—24no—
126#551—24no—
127#550—22no—
128#550—21no—
129#550—21no—
130#550—21no—
131#550—22no—
132#550—21no—
133#550—22no—
134D4×Q8—22no—
135D4×Q8—21no—
136#548—22no—
137#548—22no—
138#548—22no—
139#548—22no—
140#547—21no—
141#547—22no—
142#547—24no—
143#547—22no—
144#546—22no—
145#546—24no—
146#546—22no—
147#546—22no—
148#546—22no—
149#546—22no—
150#546—22no—
151#546—22no—
152#546—24no—
153#546—24no—
154#546—24no—
155D42—22no—
156D42—24no—
157D42—22no—
158D42—21no—
159D42—22no—
160D42—21no—
161#544C2×C414yescomplemented
162#544C2×C412yescomplemented
163#542—22no—
164#542—24no—
165#542C2×C414yescomplemented
166#542C2×C414yescomplemented
167#542C2×C414yescomplemented
168#540—22no—
169#540—24no—
170#540C2×C414yescomplemented
171#540C2×C414yescomplemented
172#540C2×C414yescomplemented
173#538—24no—
174#538—24no—
175#538—24no—
176#537C2×C414yes—
177#537C2×C412yes—
178#535C2×C412yes—
179#535C2×C414yes—
180#535C2×C414yescomplemented
181#535C2×C412yescomplemented
182#533C2×C412yescomplemented
183#533C2×C411yescharacteristic, complemented
184#533C2×C412yescomplemented
185#533C2×C411yescharacteristic, complemented
186#533C2311yescharacteristic
187#532—22no—
188#532—24no—
189#532—22no—
190#532—21no—
191#532—21no—
192#532—22no—
193#532—21no—
194#532—22no—
195#532—21no—
196#532—22no—
197#532C2×C412yescomplemented
198#532C2×C411yescharacteristic, complemented
199#532C2×C414yescomplemented
200#532C2×C412yescomplemented
201#532C2×C412yescomplemented
202#532C2×C412yescomplemented
203#532C2×C412yescomplemented
204#532C2×C412yescomplemented
205#532C2×C411yescharacteristic, complemented
206#532C2311yescharacteristic
207#532C2312yes—
208#532C2312yes—
209#532C2314yes—
210C2×C4⋊Q8C2×C412yescomplemented
211C2×C4⋊Q8C2×C411yescharacteristic, complemented
212C2×#127C2×C412yescomplemented
213C2×#127C2×C411yescharacteristic, complemented
214#529—22no—
215#529—24no—
216#529—22no—
217#529—21no—
218#529—22no—
219#529—21no—
220#529—21no—
221#529—22no—
222#529—21no—
223#529—22no—
224#529C2×C414yescomplemented
225#529C2×C412yescomplemented
226#529C2314yes—
227#529C2312yes—
228C2×#124—22no—
229C2×#124—21no—
230#525—22no—
231#525—21no—
232#525—22no—
233#525—21no—
234#525—24no—
235#525—24no—
236#525—24no—
237#525C2312yes—
238#525C2314yes—
239C2×#121—22no—
240C2×#121—21no—
241C2×#121C2314yes—
242C2×#121C2312yes—
243#520—22no—
244#520C2×C412yes—
245#520C2×C414yescomplemented
246#520C2×C412yescomplemented
247#518—24no—
248#518—22no—
249#518C2×C414yescomplemented
250#518C2×C412yescomplemented
251C4×#41—22no—
252C4×#41—22no—
253C4×#41—21no—
254C4×#41—21no—
255C4×#41—22no—
256C4×#41C2×C411yescharacteristic
257C4×#41C2×C412yes—
258C4×#41C2×C411yescharacteristic
259C4×#41C2×C411yescharacteristic
260C4×#41C2×C412yes—
261C4×#41C2×C411yescharacteristic
262C4×#41C2×C414yescomplemented
263C4×#41C2×C412yescomplemented
264C4×#41D411yescharacteristic
265C4×#41D411yescharacteristic
266C4×#41D412yes—
267C4×#41D411yescharacteristic
268C4×#41D412yes—
269C4×#41D411yescharacteristic
270C2×C4×Q8D411yescharacteristic
271C2×C4×Q8D411yescharacteristic
272C2×C4×D4—24no—
273C2×C4×D4—22no—
274C2×C4×D4—22no—
275C2×C4×D4—22no—
276C2×C4×D4—21no—
277C2×C4×D4C2×C414yescomplemented
278C2×C4×D4C2×C412yescomplemented
279C2×C4×D4D412yes—
280C2×C4×D4D411yescharacteristic
281C2×C4×D4D412yes—
282C2×C4×D4D411yescharacteristic
283C2×#117—21no—
284C2×#117C2312yes—
285C2×#117C2311yescharacteristic
286C22×C4⋊C4—22no—
287C22×C42C2312yes—
288C22×C42C2311yescharacteristic
289#433—24no—
290#433—24no—
291#433—24no—
292#432—21no—
293#432—22no—
294#432C2314yes—
295#432C2312yes—
296#431—21no—
297#431—22no—
298#431—21no—
299#431—22no—
300#431—21no—
301#431—22no—
302#431C2311yescharacteristic
303#431C2312yes—
304#431C2311yescharacteristic
305#431C2314yes—
306#431C2312yes—
307#424—24no—
308#424—22no—
309#423—22no—
310#423—21no—
311C2×C4⋊C8—22no—
312C2×C4⋊C8—21no—
313#408—24no—
314#408—22no—
315#407C2314yes—
316#407C2312yes—
317C2×C22⋊C8C2314yes—
318C2×C22⋊C8C2312yes—
319#405—24no—
320#405—22no—
321C4×M16—22no—
322C4×M16—21no—
323C2×C4×C8—22no—
324C2×C4×C8—21no—
325#391—22no—
326#389—22no—
327#388—24no—
328#387—24no—
329#387—24no—
330#386—24no—
331#385—24no—
332#384—21no—
333#383—22no—
334#383C2312yes—
335#382—22no—
336#382—22no—
337#382C2314yes—
338#382C2311yescharacteristic
339#382C2312yes—
340#382C2311yescharacteristic
341#381—21no—
342#381C2314yes—
343#380—21no—
344#380—22no—
345#380—21no—
346#380C2312yes—
347C4×C4⋊C4—22no—
348C4×C4⋊C4—21no—
349C4×C4⋊C4—21no—
350C4×C4⋊C4—22no—
351C4×C4⋊C4C2312yes—
352C4×C22⋊C4—22no—
353C4×C22⋊C4—24no—
354C4×C22⋊C4C2312yes—
355#376—21no—
356#376C2314yes—
357C2×#95—22no—
358C2×#95C2314yes—
359#328C2314yes—
360#328C2318yes—
361#328C2314yes—
362#327C2314yes—
363#327C2318yes—
364#327C2318yes—
365#327C2318yes—
366#327C2318yes—
367#327C2314yes—
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—22no—
379C2×#41—21no—
380C2×#41—22no—
381C2×#41—24no—
382C2×#41—44no—
383C2×#41—84no—
384C2×#41—82no—
385C2×#41—84no—
386C2×#41—82no—
387C2×#41C22×C414yes—
388C2×#41C22×C412yes—
389C2×#41C22×C411yescharacteristic
390C2×#41C22×C412yes—
391C2×#41C22×C411yescharacteristic
392C2×#41C2×D411yescharacteristic
393C2×#41C2×D412yes—
394C2×#41C2×D411yescharacteristic
395C22×Q8—21no—
396C22×Q8—22no—
397C22×Q8C2×D411yescharacteristic
398C22×D4—24no—
399C22×D4—22no—
400C22×D4—24no—
401C22×D4—22no—
402C22×D4—21no—
403C22×D4—22no—
404C22×D4—21no—
405C22×D4—22no—
406C22×D4C22×C414yes—
407C22×D4C22×C412yes—
408C22×D4C2×D411yescharacteristic
409C22×D4C2×D412yes—
410C23×C4—22no—
411C23×C4—24no—
412C23×C4—24no—
413C23×C4C2×D412yes—
414C23×C4C2×D411yescharacteristic
415C23×C4C2×D412yes—
416C23×C4C2×D411yescharacteristic
417C23×C4C2412yes—
418C23×C4C2411yescharacteristic
419#131—48no—
420C2×M16—24no—
421C2×M16—22no—
422C22×C8—24no—
423C22×C8—22no—
424C4⋊Q8—24no—
425C4⋊Q8—22no—
426C4⋊Q8—22no—
427C4⋊Q8—21no—
428C4⋊Q8—22no—
429C4⋊Q8—21no—
430C4⋊Q8C22×C411yescharacteristic
431C4⋊Q8C22×C411yescharacteristic
432C4⋊Q8C22×C412yes—
433C4⋊Q8C22×C412yes—
434C4⋊Q8C22×C414yes—
435C4⋊Q8C22×C411yescharacteristic
436#127—22no—
437#127—24no—
438#127—22no—
439#127—21no—
440#127—22no—
441#127—21no—
442#127C22×C411yescharacteristic
443#127C22×C412yes—
444#127C22×C412yes—
445#127C22×C414yes—
446#126—24no—
447#126—24no—
448#126—24no—
449#126—22no—
450#126—24no—
451#126—22no—
452#126—24no—
453#125—24no—
454#125—22no—
455#125—21no—
456#125—22no—
457#125—21no—
458#125C22×C414yes—
459#125C22×C412yes—
460#124—22no—
461#124—24no—
462#124—24no—
463#124—24no—
464#124—24no—
465#124—22no—
466#124—24no—
467#124—22no—
468#124—22no—
469#124—22no—
470#124—21no—
471#124—22no—
472#124—21no—
473#124—22no—
474#124—24no—
475#124—22no—
476#124C22×C414yes—
477#124C22×C412yes—
478#123—22no—
479#123—24no—
480#123—22no—
481#123—24no—
482#123—24no—
483#123—22no—
484#123—24no—
485#123—24no—
486#123—24no—
487#123—24no—
488#123—24no—
489#123—24no—
490#123—24no—
491#123—24no—
492#123—24no—
493C22⋊Q8—22no—
494C22⋊Q8—24no—
495C22⋊Q8—21no—
496C22⋊Q8—22no—
497C22⋊Q8—21no—
498C22⋊Q8—22no—
499C22⋊Q8—21no—
500C22⋊Q8—22no—
501C22⋊Q8—21no—
502C22⋊Q8—24no—
503C22⋊Q8—24no—
504C22⋊Q8—24no—
505C22⋊Q8—24no—
506C22⋊Q8—24no—
507C22⋊Q8—24no—
508C22⋊Q8C22×C412yes—
509C22⋊Q8C22×C414yes—
510C22⋊Q8C2412yes—
511#121—24no—
512#121—24no—
513#121—24no—
514#121—22no—
515#121—24no—
516#121—22no—
517#121—24no—
518#121—22no—
519#121—22no—
520#121—22no—
521#121—21no—
522#121—22no—
523#121—21no—
524#121—22no—
525#121—21no—
526#121—22no—
527#121—21no—
528#121—22no—
529#121—24no—
530#121—22no—
531#121—22no—
532#121—24no—
533#121—22no—
534#121—24no—
535#121—24no—
536#121—22no—
537#121—24no—
538#121—22no—
539#121—24no—
540#121—24no—
541#121—24no—
542#121—24no—
543#121—24no—
544#121—24no—
545#121C22×C414yes—
546#121C22×C414yes—
547#121C22×C414yes—
548#121C22×C412yes—
549#121C22×C414yes—
550#121C2412yes—
551#121C2414yes—
552#120—24no—
553#120—22no—
554#120—24no—
555#120—24no—
556#120—24no—
557#120—24no—
558#120—24no—
559#120—24no—
560C4×Q8—22no—
561C4×Q8—22no—
562C4×Q8—21no—
563C4×Q8—22no—
564C4×Q8—21no—
565C4×Q8—22no—
566C4×Q8—21no—
567C4×Q8—21no—
568C4×Q8C22⋊C411yescharacteristic
569C4×Q8C22⋊C411yescharacteristic
570C4×Q8C22⋊C411yescharacteristic
571C4×Q8C22⋊C412yes—
572C4×Q8C22⋊C411yescharacteristic
573C4×Q8C22⋊C412yes—
574C4×Q8C22⋊C411yescharacteristic
575C4×Q8C22⋊C411yescharacteristic
576C4×Q8C22⋊C411yescharacteristic
577C4×Q8C22⋊C412yes—
578C4×Q8C22⋊C411yescharacteristic
579C4×Q8C22⋊C412yes—
580C4×Q8C22×C412yes—
581C4×Q8C22×C414yes—
582C4×Q8C22×C412yes—
583C4×D4—24no—
584C4×D4—22no—
585C4×D4—22no—
586C4×D4—24no—
587C4×D4—22no—
588C4×D4—24no—
589C4×D4—22no—
590C4×D4—24no—
591C4×D4—24no—
592C4×D4—22no—
593C4×D4—22no—
594C4×D4—24no—
595C4×D4—22no—
596C4×D4—24no—
597C4×D4—24no—
598C4×D4—22no—
599C4×D4—24no—
600C4×D4—22no—
601C4×D4—24no—
602C4×D4—24no—
603C4×D4—24no—
604C4×D4—24no—
605C4×D4—22no—
606C4×D4—24no—
607C4×D4—22no—
608C4×D4—22no—
609C4×D4—22no—
610C4×D4—22no—
611C4×D4—24no—
612C4×D4—22no—
613C4×D4—22no—
614C4×D4—21no—
615C4×D4—22no—
616C4×D4—21no—
617C4×D4—22no—
618C4×D4—21no—
619C4×D4—21no—
620C4×D4—22no—
621C4×D4—22no—
622C4×D4—24no—
623C4×D4—48no—
624C4×D4C22⋊C412yes—
625C4×D4C22⋊C411yescharacteristic
626C4×D4C22⋊C412yes—
627C4×D4C22⋊C411yescharacteristic
628C4×D4C22⋊C412yes—
629C4×D4C22⋊C412yes—
630C4×D4C22⋊C412yes—
631C4×D4C22⋊C411yescharacteristic
632C4×D4C22⋊C412yes—
633C4×D4C22⋊C412yes—
634C4×D4C22⋊C412yes—
635C4×D4C22⋊C412yes—
636C4×D4C22⋊C411yescharacteristic
637C4×D4C22⋊C412yes—
638C4×D4C22⋊C412yes—
639C4×D4C22⋊C411yescharacteristic
640C4×D4C22⋊C412yes—
641C4×D4C22⋊C411yescharacteristic
642C4×D4C22⋊C412yes—
643C4×D4C22⋊C412yes—
644C4×D4C22⋊C412yes—
645C4×D4C22⋊C412yes—
646C4×D4C22⋊C412yes—
647C4×D4C22⋊C412yes—
648C4×D4C22⋊C411yescharacteristic
649C4×D4C22⋊C412yes—
650C4×D4C22⋊C411yescharacteristic
651C4×D4C22⋊C412yes—
652C4×D4C22×C412yes—
653C4×D4C22×C414yes—
654C4×D4C22×C414yes—
655C4×D4C22×C414yes—
656C4×D4C22×C414yes—
657C4×D4C22×C414yes—
658C4×D4C22×C412yes—
659#117—21no—
660#117—22no—
661#117—21no—
662#117—24no—
663#117—22no—
664#117—24no—
665#117—22no—
666#117—24no—
667#117—22no—
668#117—24no—
669#117—22no—
670#117—82no—
671#117C22×C412yes—
672#117C22×C414yes—
673#117C22×C412yes—
674#117C22×C411yescharacteristic
675#117C22×C412yes—
676#117C22×C411yescharacteristic
677#117C22×C412yes—
678#117C22×C412yes—
679#117C22×C412yes—
680#117C2×D412yes—
681#117C2×D412yes—
682#117C2×D412yes—
683#117C2×D411yescharacteristic
684#117C2×D412yes—
685#117C2×D411yescharacteristic
686#117C2×D412yes—
687C2×C4⋊C4—21no—
688C2×C4⋊C4—22no—
689C2×C4⋊C4—24no—
690C2×C4⋊C4—22no—
691C2×C4⋊C4—21no—
692C2×C4⋊C4—22no—
693C2×C4⋊C4—22no—
694C2×C4⋊C4—21no—
695C2×C4⋊C4—24no—
696C2×C4⋊C4—22no—
697C2×C4⋊C4—84no—
698C2×C4⋊C4C22×C414yes—
699C2×C4⋊C4C22×C412yes—
700C2×C4⋊C4C2×D412yes—
701C2×C4⋊C4C2×D411yescharacteristic
702C2×C4⋊C4C2×D411yescharacteristic
703C2×C4⋊C4C2×D412yes—
704C2×C22⋊C4—22no—
705C2×C22⋊C4—24no—
706C2×C22⋊C4—24no—
707C2×C22⋊C4—22no—
708C2×C22⋊C4—24no—
709C2×C22⋊C4—24no—
710C2×C22⋊C4—24no—
711C2×C22⋊C4—24no—
712C2×C22⋊C4—22no—
713C2×C22⋊C4—22no—
714C2×C22⋊C4C2×D412yes—
715C2×C22⋊C4C2×D412yes—
716C2×C22⋊C4C2×D412yes—
717C2×C42—24no—
718C2×C42—22no—
719C2×C42—22no—
720C2×C42—22no—
721C2×C42—24no—
722C2×C42C22×C412yes—
723C2×C42C22×C411yescharacteristic
724C2×C42C22×C412yes—
725C2×C42C22×C411yescharacteristic
726C2×C42C22×C412yes—
727C2×C42C22×C411yescharacteristic
728C2×C42C22×C412yes—
729C2×C42C22×C411yescharacteristic
730C2×C42C2×D412yes—
731C2×C42C2×D411yescharacteristic
732C2×C42C2×D411yescharacteristic
733C2×C42C2×D412yes—
734C2×C42C2×D412yes—
735C2×C42C2×D411yescharacteristic
736C2×C42C2×D411yescharacteristic
737C2×C42C2×D412yes—
738C2×C42C2×D412yes—
739C2×C42C2×D411yescharacteristic
740C2×C42C2×D411yescharacteristic
741C2×C42C2×D412yes—
742C2×C42C2412yes—
743C2×C42C2411yescharacteristic
744C2×C42C2411yescharacteristic
745C4⋊C8—21no—
746C4⋊C8—22no—
747C4⋊C8—21no—
748C4⋊C8—22no—
749C4⋊C8—24no—
750C4⋊C8—22no—
751C4⋊C8—24no—
752C22⋊C8—22no—
753C22⋊C8—24no—
754C22⋊C8—22no—
755C22⋊C8—24no—
756C22⋊C8C2412yes—
757C22⋊C8C2414yes—
758C22⋊C8C2412yes—
759#97—24no—
760#97—22no—
761C4×C8—21no—
762C4×C8—22no—
763C4×C8—21no—
764C4×C8—24no—
765C4×C8—22no—
766#95—21no—
767#95—22no—
768#95—24no—
769#95—24no—
770#95—22no—
771#95—21no—
772#95—24no—
773#95—22no—
774#95—24no—
775#95C2412yes—
776#95C2414yes—
777#95C2412yes—
778C24—22no—
779C24—24no—
780C24C22×D412yes—
781C24C22×D411yescharacteristic
782#41—24no—
783#41—24no—
784#41—44no—
785#41—44no—
786#41—42no—
787#41—42no—
788#41—48no—
789#41—44no—
790#41—48no—
791#41—42no—
792#41—44no—
793#41—42no—
794#41—44no—
795#41—88no—
796#41—84no—
797#41—82no—
798#41—84no—
799#41—82no—
800#41—84no—
801#41—84no—
802#41—84no—
803#41—84no—
804#41—84no—
805#41—82no—
806C2×Q8—21no—
807C2×Q8—22no—
808C2×Q8—21no—
809C2×Q8—24no—
810C2×Q8—22no—
811C2×Q8—42no—
812C2×Q8—84no—
813C2×Q8—82no—
814C2×Q8C2×C22⋊C411yescharacteristic
815C2×Q8C2×C22⋊C411yescharacteristic
816C2×Q8C2×C22⋊C412yes—
817C2×Q8C23×C412yes—
818C2×D4—24no—
819C2×D4—22no—
820C2×D4—24no—
821C2×D4—24no—
822C2×D4—22no—
823C2×D4—22no—
824C2×D4—24no—
825C2×D4—24no—
826C2×D4—24no—
827C2×D4—24no—
828C2×D4—24no—
829C2×D4—22no—
830C2×D4—22no—
831C2×D4—21no—
832C2×D4—22no—
833C2×D4—21no—
834C2×D4—22no—
835C2×D4—24no—
836C2×D4—24no—
837C2×D4—22no—
838C2×D4—48no—
839C2×D4—44no—
840C2×D4—44no—
841C2×D4—416no—
842C2×D4—48no—
843C2×D4—84no—
844C2×D4—82no—
845C2×D4—84no—
846C2×D4—82no—
847C2×D4—84no—
848C2×D4—82no—
849C2×D4—84no—
850C2×D4—82no—
851C2×D4C2×C22⋊C412yes—
852C2×D4C2×C22⋊C412yes—
853C2×D4C2×C22⋊C412yes—
854C2×D4C2×C22⋊C411yescharacteristic
855C2×D4C2×C22⋊C412yes—
856C2×D4C2×C22⋊C412yes—
857C2×D4C2×C22⋊C411yescharacteristic
858C2×D4C23×C412yes—
859C2×D4C23×C414yes—
860C22×C4—24no—
861C22×C4—22no—
862C22×C4—24no—
863C22×C4—22no—
864C22×C4—22no—
865C22×C4—24no—
866C22×C4—24no—
867C22×C4—22no—
868C22×C4—24no—
869C22×C4—22no—
870C22×C4—24no—
871C22×C4—22no—
872C22×C4—24no—
873C22×C4—24no—
874C22×C4—24no—
875C22×C4—22no—
876C22×C4—22no—
877C22×C4—24no—
878C22×C4—42no—
879C22×C4—44no—
880C22×C4—48no—
881C22×C4—88no—
882C22×C4—84no—
883C22×C4—82no—
884C22×C4—81no—
885C22×C4—84no—
886C22×C4—84no—
887C22×C4C2×C22⋊C411yescharacteristic
888C22×C4C2×C22⋊C412yes—
889C22×C4C2×C22⋊C411yescharacteristic
890C22×C4C2×C22⋊C412yes—
891C22×C4C2×C22⋊C411yescharacteristic
892C22×C4C2×C22⋊C412yes—
893C22×C4C2×C22⋊C411yescharacteristic
894C22×C4C2×C22⋊C412yes—
895C22×C4C2×C22⋊C411yescharacteristic
896C22×C4C2×C22⋊C412yes—
897C22×C4C2×C22⋊C411yescharacteristic
898C22×C4C2×C22⋊C412yes—
899C22×C4C2×C22⋊C411yescharacteristic
900C22×C4C2×C22⋊C412yes—
901C22×C4C2×C22⋊C411yescharacteristic
902C22×C4C2×C22⋊C412yes—
903C22×C4C23×C412yes—
904C22×C4C23×C411yescharacteristic
905C22×C4C23×C412yes—
906C22×C4C23×C411yescharacteristic
907C22×C4C22×D411yescharacteristic
908C22×C4C22×D412yes—
909C22×C4C22×D411yescharacteristic
910C22×C4C22×D412yes—
911C22×C4C22×D411yescharacteristic
912C22×C4C22×D411yescharacteristic
913C22×C4C22×D412yes—
914C22×C4C22×D412yes—
915C22×C4C22×D411yescharacteristic
916C22×C4C22×D411yescharacteristic
917C22×C4C22×D412yes—
918C22×C4C22×D411yescharacteristic
919C22×C4C2511yescharacteristic
920M16—48no—
921M16—44no—
922C2×C8—22no—
923C2×C8—24no—
924C2×C8—22no—
925C2×C8—48no—
926C2×C8—44no—
927C4⋊C4—22no—
928C4⋊C4—21no—
929C4⋊C4—22no—
930C4⋊C4—24no—
931C4⋊C4—24no—
932C4⋊C4—22no—
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—24no—
944C4⋊C4—22no—
945C4⋊C4—22no—
946C4⋊C4—44no—
947C4⋊C4—42no—
948C4⋊C4—44no—
949C4⋊C4—42no—
950C4⋊C4—84no—
951C4⋊C4—82no—
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⋊C411yescharacteristic
960C4⋊C4C2×C22⋊C412yes—
961C4⋊C4C2×C22⋊C412yes—
962C4⋊C4C2×C22⋊C412yes—
963C4⋊C4C2×C22⋊C412yes—
964C4⋊C4C2×C22⋊C412yes—
965C4⋊C4C2×C22⋊C412yes—
966C4⋊C4C23×C412yes—
967C4⋊C4C23×C414yes—
968C4⋊C4C23×C412yes—
969C22⋊C4—22no—
970C22⋊C4—24no—
971C22⋊C4—22no—
972C22⋊C4—24no—
973C22⋊C4—22no—
974C22⋊C4—22no—
975C22⋊C4—24no—
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—24no—
985C22⋊C4—22no—
986C22⋊C4—22no—
987C22⋊C4—24no—
988C22⋊C4—22no—
989C22⋊C4—24no—
990C22⋊C4—22no—
991C22⋊C4—24no—
992C22⋊C4—48no—
993C22⋊C4—82no—
994C22⋊C4—82no—
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—22no—
1010C42—24no—
1011C42—22no—
1012C42—44no—
1013C42—82no—
1014C42—84no—
1015C42C2×C22⋊C412yes—
1016C42C2×C22⋊C411yescharacteristic
1017C42C2×C22⋊C412yes—
1018C42C2×C22⋊C411yescharacteristic
1019C42C2×C22⋊C412yes—
1020C42C2×C22⋊C411yescharacteristic
1021C42C2×C22⋊C411yescharacteristic
1022C42C2×C22⋊C412yes—
1023C42C2×C22⋊C412yes—
1024C42C2×C22⋊C411yescharacteristic
1025C42C2×C22⋊C412yes—
1026C42C2×C22⋊C412yes—
1027C42C2×C22⋊C411yescharacteristic
1028C42C2×C22⋊C411yescharacteristic
1029C42C2×C22⋊C411yescharacteristic
1030C42C2×C22⋊C412yes—
1031C42C23×C411yescharacteristic
1032C42C23×C411yescharacteristic
1033C42C23×C412yes—
1034C42C23×C411yescharacteristic
1035C42C23×C412yes—
1036C42C23×C411yescharacteristic
1037C42C22×D411yescharacteristic
1038C42C22×D412yes—
1039C42C22×D411yescharacteristic
1040C42C22×D411yescharacteristic
1041C42C22×D411yescharacteristic
1042C42C22×D412yes—
1043C23—24no—
1044C23—22no—
1045C23—22no—
1046C23—21no—
1047C23—21no—
1048C23—24no—
1049C23—22no—
1050C23—42no—
1051C23—41no—
1052C23—41no—
1053C23—44no—
1054C23—48no—
1055C23—84no—
1056C23—82no—
1057C23—84no—
1058C23—82no—
1059C23C22×C22⋊C411yescharacteristic
1060C23C22×C22⋊C411yescharacteristic
1061C23C22×C22⋊C412yes—
1062C23C22×C22⋊C412yes—
1063C23C23×D411yescharacteristic
1064Q8—22no—
1065Q8—22no—
1066Q8—42no—
1067Q8—42no—
1068Q8—42no—
1069Q8—42no—
1070Q8—44no—
1071Q8—82no—
1072Q8—84no—
1073D4—24no—
1074D4—24no—
1075D4—24no—
1076D4—22no—
1077D4—42no—
1078D4—42no—
1079D4—42no—
1080D4—44no—
1081D4—48no—
1082D4—42no—
1083D4—44no—
1084D4—44no—
1085D4—48no—
1086D4—42no—
1087D4—44no—
1088D4—42no—
1089D4—44no—
1090D4—44no—
1091D4—42no—
1092D4—44no—
1093D4—84no—
1094D4—82no—
1095D4—82no—
1096D4—84no—
1097D4—84no—
1098D4—84no—
1099D4—84no—
1100D4—84no—
1101D4—82no—
1102D4#41014yes—
1103C2×C4—24no—
1104C2×C4—24no—
1105C2×C4—21no—
1106C2×C4—22no—
1107C2×C4—21no—
1108C2×C4—22no—
1109C2×C4—22no—
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—24no—
1123C2×C4—22no—
1124C2×C4—42no—
1125C2×C4—41no—
1126C2×C4—41no—
1127C2×C4—41no—
1128C2×C4—42no—
1129C2×C4—42no—
1130C2×C4—42no—
1131C2×C4—41no—
1132C2×C4—41no—
1133C2×C4—42no—
1134C2×C4—41no—
1135C2×C4—42no—
1136C2×C4—41no—
1137C2×C4—42no—
1138C2×C4—41no—
1139C2×C4—42no—
1140C2×C4—41no—
1141C2×C4—48no—
1142C2×C4—44no—
1143C2×C4—44no—
1144C2×C4—48no—
1145C2×C4—42no—
1146C2×C4—42no—
1147C2×C4—42no—
1148C2×C4—44no—
1149C2×C4—44no—
1150C2×C4—42no—
1151C2×C4—44no—
1152C2×C4—42no—
1153C2×C4—42no—
1154C2×C4—84no—
1155C2×C4—84no—
1156C2×C4—84no—
1157C2×C4—84no—
1158C2×C4—82no—
1159C2×C4—84no—
1160C2×C4—82no—
1161C2×C4—168no—
1162C2×C4C22×C22⋊C412yes—
1163C2×C4C22×C22⋊C412yes—
1164C2×C4C22×C22⋊C411yescharacteristic
1165C2×C4C22×C22⋊C411yescharacteristic
1166C2×C4C22×C22⋊C411yescharacteristic
1167C2×C4C22×C22⋊C411yescharacteristic
1168C2×C4C22×C22⋊C412yes—
1169C2×C4C22×C22⋊C411yescharacteristic
1170C2×C4C22×C22⋊C412yes—
1171C2×C4C22×C22⋊C411yescharacteristic
1172C2×C4C22×C22⋊C412yes—
1173C2×C4C22×C22⋊C412yes—
1174C2×C4C22×C22⋊C411yescharacteristic
1175C2×C4C22×C22⋊C411yescharacteristic
1176C2×C4C22×C22⋊C411yescharacteristic
1177C2×C4C22×C22⋊C411yescharacteristic
1178C2×C4#57612yes—
1179C2×C4#57712yes—
1180C2×C4C24×C411yescharacteristic
1181C2×C4C23×D411yescharacteristic
1182C8—42no—
1183C8—44no—
1184C8—42no—
1185C22—21no—
1186C22—22no—
1187C22—21no—
1188C22—22no—
1189C22—21no—
1190C22—21no—
1191C22—22no—
1192C22—21no—
1193C22—22no—
1194C22—21no—
1195C22—22no—
1196C22—21no—
1197C22—21no—
1198C22—44no—
1199C22—44no—
1200C22—44no—
1201C22—42no—
1202C22—42no—
1203C22—44no—
1204C22—42no—
1205C22—44no—
1206C22—81no—
1207C22—81no—
1208C22—168no—
1209C22—164no—
1210C22C2×#41014yes—
1211C22C23×C22⋊C411yescharacteristic
1212C22C2×#57611yescharacteristic
1213C22C2×#57711yescharacteristic
1214C4—21no—
1215C4—21no—
1216C4—22no—
1217C4—21no—
1218C4—22no—
1219C4—21no—
1220C4—22no—
1221C4—21no—
1222C4—22no—
1223C4—21no—
1224C4—21no—
1225C4—22no—
1226C4—21no—
1227C4—22no—
1228C4—21no—
1229C4—42no—
1230C4—42no—
1231C4—44no—
1232C4—42no—
1233C4—82no—
1234C4—84no—
1235C4—82no—
1236C4C2×#41012yes—
1237C4#289712yes—
1238C4#289712yes—
1239C2—21no—
1240C2—21no—
1241C2—24no—
1242C2—42no—
1243C2—41no—
1244C2—41no—
1245C2—82no—
1246C2—84no—
1247C2C22×#41011yescharacteristic
1248C2C2×#289711yescharacteristic
1249C2#6009311yescharacteristic
subgroupG/H
center, socleC22C23×C22⋊C4
commutatorC2×C4C24×C4
Frattini, cosocleC22×C4C25
prime radical#62800C2
LCSG ▷ C2×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22 ◁ C2×C4×#41 ◁ G
LECSG ▷ C22×C4 ▷ C22 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #60127C2semidirect
3. #34191C2semidirect
4. #17610C2semidirect
5. #17604C2semidirect
6. #17603C2semidirect
7. #17589C2semidirect
8. #17588C2semidirect
9. #17585C2semidirect
10. #17583C2semidirect
11. #17574C2semidirect
12. #17573C2semidirect
13. #17571C2semidirect
14. C2×#1517C2semidirect
21. #3511C4semidirect
22. #3511C4semidirect
23. #3508C4semidirect
24. #3508C4semidirect
25. #3503C4semidirect
26. #3498C4semidirect
36. #3460C4semidirect
37. #3460C4semidirect
42. C4×H(5,𝔽2)C4semidirect
46. #2924C22semidirect
47. #2924C22semidirect
50. #2920C22semidirect
51. #2920C22semidirect
52. C2×#431C22semidirect
53. C2×#431C22semidirect
60. #2346C22semidirect
61. #2343C22semidirect
65. #2285C22semidirect
66. #2283C22semidirect
67. #2283C22semidirect
68. C2×#382C22semidirect
70. #1521C22semidirect
71. #1519C22semidirect
72. #1518C22semidirect
73. #1518C22semidirect
74. #1518C22semidirect
75. #1517C22semidirect
76. #1517C22semidirect
77. #1517C22semidirect
78. #1517C22semidirect
79. #1517C22semidirect
80. #1517C22semidirect
81. #1517C22semidirect
82. #1517C22semidirect
83. #1516C22semidirect
84. #1514C22semidirect
85. #1513C22semidirect
86. #1512C22semidirect
87. #1510C22semidirect
88. #1509C22semidirect
89. #1507C22semidirect
90. #1505C22semidirect
91. #1504C22semidirect
92. #1502C22semidirect
93. #1501C22semidirect
94. #1500C22semidirect
95. C2×#327C22semidirect
161. #544C2×C4semidirect
162. #544C2×C4semidirect
165. #542C2×C4semidirect
166. #542C2×C4semidirect
167. #542C2×C4semidirect
170. #540C2×C4semidirect
171. #540C2×C4semidirect
172. #540C2×C4semidirect
180. #535C2×C4semidirect
181. #535C2×C4semidirect
182. #533C2×C4semidirect
183. #533C2×C4semidirect
184. #533C2×C4semidirect
185. #533C2×C4semidirect
197. #532C2×C4semidirect
198. #532C2×C4semidirect
199. #532C2×C4semidirect
200. #532C2×C4semidirect
201. #532C2×C4semidirect
202. #532C2×C4semidirect
203. #532C2×C4semidirect
204. #532C2×C4semidirect
205. #532C2×C4semidirect
210. C2×C4⋊Q8C2×C4semidirect
211. C2×C4⋊Q8C2×C4semidirect
212. C2×#127C2×C4semidirect
213. C2×#127C2×C4semidirect
224. #529C2×C4semidirect
225. #529C2×C4semidirect
245. #520C2×C4semidirect
246. #520C2×C4semidirect
249. #518C2×C4semidirect
250. #518C2×C4semidirect
262. C4×#41C2×C4semidirect
263. C4×#41C2×C4semidirect
277. C2×C4×D4C2×C4semidirect
278. 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
#601272
#341912
#176102
#176042
#176032
#175892
#175882
#175852
#175832
#175742
#175732
#175712
C2×#15172