Finite Group Databasebeta

← #6343161

Subgroups — #6343161

Order 512.

2865 conjugacy classes of subgroups.

The subgroup lattice has 1139 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#62788C211yesmaximal, characteristic
2#60269C211yesmaximal, characteristic, complemented
3#60210C211yesmaximal, characteristic, complemented
4#17524C214yesmaximal, complemented
5#17519C214yesmaximal, complemented
6#17515C212yesmaximal, complemented
7#17514C212yesmaximal, complemented
8#17510C212yesmaximal, complemented
9#17509C212yesmaximal, complemented
10#17506C214yesmaximal, complemented
11#17504C211yesmaximal, characteristic, complemented
12#17488C211yesmaximal, characteristic, complemented
13#17454C214yesmaximal, complemented
14C2×#1491C211yesmaximal, characteristic, complemented
15C2×#1487C211yesmaximal, characteristic, complemented
16#3523—21no—
17#3523C412yes—
18#3522—21no—
19#3522C412yes—
20#3516—22no—
21#3516C414yes—
22#3507—22no—
23#3507C411yescharacteristic
24#3507C411yescharacteristic
25#3502C411yescharacteristic
26#3497C411yescharacteristic
27#3492—22no—
28#3492C412yes—
29#3486C412yes—
30#3482—22no—
31#3482C2214yes—
32#3480—21no—
33#3480C2212yes—
34Q8×#41—21no—
35Q8×#41C2212yes—
36#3461—22no—
37#3461C2212yes—
38#3444—22no—
39#3444C2211yescharacteristic
40#3444C2211yescharacteristic
41C4×2−1+4C2212yes—
42C22×C4×Q8C2211yescharacteristic
43#2995—22no—
44#2992—22no—
45#2990C2214yes—
46#2989C2214yes—
47#2969—22no—
48#2968—22no—
49#2965C2214yes—
50#2965C2212yes—
51C8×#41C2212yes—
52#2962—21no—
53#2961—21no—
54#2935—21no—
55#2933—22no—
56#2933—22no—
57#2932—21no—
58#2925C2212yes—
59#2922C2212yes—
60C2×#432C2211yescharacteristic
61C2×#431C2211yescharacteristic
62#2906C2212yes—
63C2×#423C2211yescharacteristic
64C4×#131C2212yes—
65C2×C4×M16C2211yescharacteristic
66#1497C2214yescomplemented
67#1495C2214yescomplemented
68#1494C2214yes—
69#1494C2214yescomplemented
70#1493C2212yes—
71#1493C2214yescomplemented
72#1492C2212yes—
73#1491C2212yes—
74#1491C2212yes—
75#1491C2212yes—
76#1491C2212yes—
77#1491C2214yescomplemented
78#1489C2214yes—
79#1489C2214yescomplemented
80#1488C2214yes—
81#1488C2214yescomplemented
82#1487C2212yes—
83#1487C2212yes—
84#1487C2212yes—
85#1487C2212yes—
86#1487C2214yescomplemented
87#1485C2214yescomplemented
88#1483C2212yes—
89#1483C2212yes—
90#1483C2214yescomplemented
91#1482C2214yescomplemented
92#1481C2211yescharacteristic
93#1481C2211yescharacteristic
94#1481C2214yescomplemented
95#1480C2211yescharacteristic
96#1480C2211yescharacteristic
97#1479C2214yescomplemented
98#1477C2214yescomplemented
99#1476C2214yescomplemented
100C2×Q8⋊C8C2214yes—
101C2×Q8⋊C8C2212yes—
102C2×Q8⋊C8C2212yes—
103C2×Q8⋊C8C2214yescomplemented
104C2×2−1+4C2×C412yes—
105C23×Q8C2×C411yescharacteristic
106C2×#131—22no—
107C2×#131—22no—
108C22×M16—21no—
109C22×M16—21no—
110#559—21no—
111#559—22no—
112#559—22no—
113#559C2×C412yes—
114Q82—21no—
115Q82C2×C412yes—
116#557—21no—
117#557—21no—
118#557—22no—
119#557—22no—
120#557—22no—
121#557C2×C412yes—
122#557C2×C412yes—
123#557C2×C414yes—
124#556—21no—
125#556—24no—
126#556—22no—
127#556—22no—
128#556—22no—
129#556—24no—
130#556C2×C414yes—
131#556C2×C412yes—
132#554—21no—
133#554—22no—
134#554—24no—
135#554—22no—
136#554—24no—
137#554—22no—
138#554C2×C414yes—
139#554C2×C412yes—
140#553—24no—
141#553—22no—
142#553—24no—
143#553C2×C414yes—
144#552—24no—
145#552—22no—
146#552—24no—
147#552—22no—
148#552—24no—
149#552—24no—
150#552C2×C414yes—
151#552C2×C414yes—
152#550—21no—
153#550C2×C412yes—
154D4×Q8—21no—
155D4×Q8—22no—
156D4×Q8—22no—
157D4×Q8C2×C414yes—
158D4×Q8C2×C412yes—
159D4×Q8C2×C414yes—
160#548—22no—
161#548—22no—
162#548—22no—
163#548C2×C414yes—
164#548C2×C414yes—
165#548C2×C414yes—
166#547—24no—
167#547—24no—
168#547—22no—
169#547C2×C414yes—
170#544—22no—
171#544C2×C412yes—
172#542—24no—
173#542—24no—
174#542—22no—
175#542C2×C414yes—
176#541—24no—
177#541—24no—
178#541—22no—
179#541C2×C414yes—
180#539—24no—
181#539—22no—
182#539—22no—
183#539—24no—
184#537—22no—
185#537C2×C412yes—
186#536—24no—
187#536C2×C412yes—
188#536C2×C412yes—
189#533—22no—
190#533—22no—
191#533—24no—
192#533—22no—
193#533—22no—
194#533—24no—
195#533C2×C411yescharacteristic
196#533C2×C411yescharacteristic
197#533C2×C411yescharacteristic
198#533D411yescharacteristic
199#533D411yescharacteristic
200#533C2311yescharacteristic
201#533C2314yes—
202#532—22no—
203#532—22no—
204#532—22no—
205#532C2×C411yescharacteristic
206#532C2×C411yescharacteristic
207#532C2×C411yescharacteristic
208#532D411yescharacteristic
209#532D411yescharacteristic
210#532C2311yescharacteristic
211#529—24no—
212#529—24no—
213#529—22no—
214#529—22no—
215#529—22no—
216#529—22no—
217#529—24no—
218#529—24no—
219#529—24no—
220#529—22no—
221#529—24no—
222#529—21no—
223#529—21no—
224#529—21no—
225#529—21no—
226#529C2×C412yes—
227#529C2×C412yes—
228#529C2×C412yes—
229#529D412yes—
230#529D412yes—
231#529D412yes—
232#529D412yes—
233#529C2312yes—
234#529C2314yes—
235#525—21no—
236#525—21no—
237#525—24no—
238#525—24no—
239#525C2×C412yes—
240#525C2×C412yes—
241#525D412yes—
242#525D412yes—
243#520—24no—
244#520—22no—
245#520C2×C412yes—
246#520C2×C414yes—
247#520C2×C412yes—
248#519—22no—
249#519C2×C412yes—
250#519C2×C414yes—
251C4×#41—22no—
252C4×#41—24no—
253C4×#41—22no—
254C4×#41—24no—
255C4×#41—22no—
256C4×#41—21no—
257C4×#41—21no—
258C4×#41C2312yes—
259C4×#41C2314yes—
260C4×#41C2312yes—
261C4×#41C2312yes—
262C4×#41C2312yes—
263C2×C4×Q8—22no—
264C2×C4×Q8—21no—
265C2×C4×Q8—21no—
266C2×C4×Q8—21no—
267C2×C4×Q8—21no—
268C2×C4×Q8—21no—
269C2×C4×Q8—21no—
270C2×C4×Q8C2×C411yescharacteristic
271C2×C4×Q8C2×C411yescharacteristic
272C2×C4×Q8C2×C412yes—
273C2×C4×Q8C2×C412yes—
274C2×C4×Q8C2311yescharacteristic
275C2×C4×Q8C2311yescharacteristic
276C2×C4×Q8C2312yes—
277C2×C4×Q8C2312yes—
278C2×C4×Q8C2314yes—
279C22×C4⋊C4—21no—
280C22×C4⋊C4C2×C411yescharacteristic
281C22×C42—21no—
282C22×C42C2311yescharacteristic
283#446—24no—
284#446—24no—
285#446—24no—
286#446—22no—
287C8×Q8—22no—
288#436—24no—
289#436—24no—
290#436—22no—
291#435—24no—
292#435—24no—
293#435—24no—
294#435—24no—
295#435—24no—
296#435—24no—
297#435—24no—
298C8×D4—24no—
299C8×D4—24no—
300C8×D4—22no—
301#433—24no—
302#433—24no—
303#432—21no—
304#432—21no—
305#432C2312yes—
306#432C2312yes—
307#432C2314yes—
308#431—21no—
309#431—21no—
310#431C2314yes—
311#431C2311yescharacteristic
312#431C2311yescharacteristic
313#431C2312yes—
314#431C2314yes—
315#431C2314yes—
316#424—22no—
317#424—24no—
318#424—22no—
319#423—21no—
320#423—21no—
321#423C2312yes—
322#423C2312yes—
323#423C2314yes—
324C2×C4⋊C8—21no—
325C2×C4⋊C8—21no—
326C2×C4⋊C8C2312yes—
327C2×C4⋊C8C2311yescharacteristic
328C2×C4⋊C8C2314yes—
329C2×C4⋊C8C2311yescharacteristic
330#408—22no—
331#408—22no—
332C2×C22⋊C8—21no—
333C2×C22⋊C8—21no—
334#405—22no—
335#405—24no—
336#405—22no—
337C4×M16—21no—
338C4×M16—21no—
339C4×M16C2311yescharacteristic
340C4×M16C2311yescharacteristic
341C4×M16C2312yes—
342C4×M16C2314yes—
343C2×#97—21no—
344C2×#97—21no—
345C2×C4×C8C2312yes—
346C2×C4×C8C2312yes—
347C2×C4×C8C2314yes—
348Q8⋊C8C2312yes—
349Q8⋊C8C2314yes—
350Q8⋊C8C2312yes—
351Q8⋊C8C2312yes—
352Q8⋊C8C2314yes—
353Q8⋊C8C2312yes—
354Q8⋊C8C2312yes—
355Q8⋊C8C2314yes—
356Q8⋊C8C2312yes—
357Q8⋊C8C2312yes—
358Q8⋊C8C2314yes—
359Q8⋊C8C2312yes—
360Q8⋊C8C2314yes—
361Q8⋊C8C2314yes—
362Q8⋊C8C2314yes—
363Q8⋊C8C2314yes—
364D4⋊C8C2314yes—
365D4⋊C8C2314yes—
366D4⋊C8C2314yes—
367D4⋊C8C2314yes—
3682−1+4—48no—
369C2×#41—24no—
370C2×#41—22no—
371C2×#41—24no—
372C2×#41—21no—
373C2×#41—21no—
374C2×#41C22×C414yes—
375C2×#41C22×C412yes—
376C2×#41C22×C412yes—
377C2×#41C2×D412yes—
378C2×#41C2×D412yes—
379C22×Q8—22no—
380C22×Q8—21no—
381C22×Q8—21no—
382C22×Q8—21no—
383C22×Q8—44no—
384C22×Q8C22×C411yescharacteristic
385C22×Q8C22×C412yes—
386C22×Q8C22×C412yes—
387C22×Q8C22×C414yes—
388C22×Q8C22×C411yescharacteristic
389C23×C4—21no—
390C23×C4—21no—
391C23×C4C22×C411yescharacteristic
392C23×C4C2×D411yescharacteristic
393C23×C4C2×D411yescharacteristic
394#131—48no—
395#131—84no—
396C2×M16—21no—
397C2×M16—22no—
398C2×M16—21no—
399C2×M16—22no—
400C2×M16—24no—
401C2×M16—22no—
402C2×M16—24no—
403C2×M16—44no—
404C2×M16—82no—
405C22×C8—22no—
406C22×C8—21no—
407C22×C8—22no—
408C22×C8—24no—
409C22×C8—21no—
410C22×C8—22no—
411C22×C8—24no—
412C4⋊Q8—22no—
413C4⋊Q8—22no—
414C4⋊Q8—24no—
415C4⋊Q8—22no—
416C4⋊Q8—22no—
417C4⋊Q8—24no—
418C4⋊Q8—24no—
419C4⋊Q8—24no—
420C4⋊Q8—22no—
421C4⋊Q8C22⋊C411yescharacteristic
422C4⋊Q8C22⋊C411yescharacteristic
423C4⋊Q8C22⋊C411yescharacteristic
424C4⋊Q8C22×C411yescharacteristic
425C4⋊Q8C22×C414yes—
426C4⋊Q8C22×C411yescharacteristic
427C4⋊Q8C22×C411yescharacteristic
428C4⋊Q8C22×C414yes—
429#127—22no—
430#127C22⋊C411yescharacteristic
431#127C22×C411yescharacteristic
432#126—24no—
433#126—24no—
434#126—24no—
435#126—24no—
436#126—24no—
437#126—24no—
438#126—24no—
439#126—24no—
440#126—24no—
441#126—22no—
442#126—22no—
443#126—24no—
444#126C22⋊C414yes—
445#126C22⋊C414yes—
446#125—24no—
447#125—24no—
448#125—22no—
449#125—22no—
450#125—24no—
451#125—24no—
452#125—22no—
453#125—24no—
454#125—24no—
455#125—24no—
456#125—24no—
457#125—24no—
458#125—21no—
459#125—21no—
460#125—24no—
461#125C22⋊C412yes—
462#125C22⋊C412yes—
463#125C22⋊C412yes—
464#125C22×C412yes—
465#125C22×C414yes—
466#124—22no—
467#124—22no—
468#124—22no—
469#124—24no—
470#124—24no—
471#124—24no—
472#124—24no—
473#124—21no—
474#124—21no—
475#124C22⋊C412yes—
476#124C22⋊C412yes—
477#124C22⋊C412yes—
478#124C22×C412yes—
479#124C22×C414yes—
480#123—24no—
481#123—24no—
482#123—24no—
483#123—22no—
484#123—22no—
485#123—22no—
486#123—24no—
487#123—24no—
488#123—24no—
489#123—24no—
490#123—24no—
491#123—24no—
492#123—24no—
493#123C22⋊C414yes—
494#123C22⋊C414yes—
495#123C22⋊C414yes—
496C22⋊Q8—22no—
497C22⋊Q8—24no—
498C22⋊Q8—21no—
499C22⋊Q8—21no—
500C22⋊Q8—21no—
501C22⋊Q8—21no—
502C22⋊Q8—24no—
503C22⋊Q8—24no—
504C22⋊Q8—22no—
505C22⋊Q8—24no—
506C22⋊Q8—22no—
507C22⋊Q8—24no—
508C22⋊Q8—24no—
509C22⋊Q8—24no—
510C22⋊Q8—24no—
511C22⋊Q8—24no—
512C22⋊Q8—24no—
513C22⋊Q8—24no—
514C22⋊Q8—24no—
515C22⋊Q8—24no—
516C22⋊Q8—24no—
517C22⋊Q8—24no—
518C22⋊Q8—24no—
519C22⋊Q8C22⋊C412yes—
520C22⋊Q8C22⋊C412yes—
521C22⋊Q8C22⋊C412yes—
522C22⋊Q8C22⋊C412yes—
523C22⋊Q8C22⋊C412yes—
524C22⋊Q8C22⋊C412yes—
525C22⋊Q8C22×C412yes—
526C22⋊Q8C22×C412yes—
527C22⋊Q8C22×C414yes—
528C22⋊Q8C22×C414yes—
529C22⋊Q8C22×C414yes—
530#121—24no—
531#121—24no—
532#121—24no—
533#121—24no—
534#121—24no—
535#121—22no—
536#121—21no—
537#121—21no—
538#121—21no—
539#121—21no—
540#121—24no—
541#121C22⋊C412yes—
542#121C22⋊C412yes—
543#121C22⋊C412yes—
544#121C22⋊C412yes—
545#121C22⋊C412yes—
546#121C22⋊C412yes—
547#121C22×C412yes—
548#121C22×C412yes—
549#121C22×C414yes—
550#120—22no—
551#120C22⋊C414yes—
552C4×Q8—22no—
553C4×Q8—22no—
554C4×Q8—22no—
555C4×Q8—22no—
556C4×Q8—24no—
557C4×Q8—24no—
558C4×Q8—22no—
559C4×Q8—24no—
560C4×Q8—22no—
561C4×Q8—22no—
562C4×Q8—22no—
563C4×Q8—22no—
564C4×Q8—21no—
565C4×Q8—21no—
566C4×Q8—21no—
567C4×Q8—22no—
568C4×Q8—21no—
569C4×Q8—22no—
570C4×Q8—21no—
571C4×Q8—21no—
572C4×Q8—21no—
573C4×Q8—21no—
574C4×Q8—21no—
575C4×Q8—22no—
576C4×Q8—22no—
577C4×Q8—21no—
578C4×Q8—21no—
579C4×Q8—22no—
580C4×Q8—22no—
581C4×Q8—24no—
582C4×Q8—24no—
583C4×Q8—24no—
584C4×Q8—21no—
585C4×Q8C22×C412yes—
586C4×Q8C22×C412yes—
587C4×Q8C22×C412yes—
588C4×Q8C22×C412yes—
589C4×Q8C22×C412yes—
590C4×Q8C22×C412yes—
591C4×Q8C22×C414yes—
592C4×Q8C22×C414yes—
593C4×Q8C22×C412yes—
594C4×Q8C22×C414yes—
595C4×Q8C22×C412yes—
596C4×Q8C22×C412yes—
597C4×Q8C2×D412yes—
598C4×Q8C2×D412yes—
599C4×Q8C2×D412yes—
600C4×Q8C2×D412yes—
601C4×Q8C2412yes—
602C4×Q8C2412yes—
603C4×Q8C2412yes—
604C4×D4—24no—
605C4×D4—22no—
606C4×D4—24no—
607C4×D4—24no—
608C4×D4—24no—
609C4×D4—22no—
610C4×D4—22no—
611C4×D4—22no—
612C4×D4—22no—
613C4×D4—22no—
614C4×D4—22no—
615C4×D4—22no—
616C4×D4—24no—
617C4×D4—24no—
618C4×D4—22no—
619C4×D4—24no—
620C4×D4—22no—
621C4×D4—22no—
622C4×D4—24no—
623C4×D4—24no—
624C4×D4—24no—
625C4×D4—24no—
626C4×D4—24no—
627C4×D4—24no—
628C4×D4—24no—
629C4×D4—21no—
630C4×D4—21no—
631C4×D4—21no—
632C4×D4—21no—
633C4×D4C22×C412yes—
634C4×D4C22×C414yes—
635C4×D4C22×C414yes—
636C4×D4C22×C414yes—
637C4×D4C22×C412yes—
638C4×D4C22×C412yes—
639C4×D4C2×D414yes—
640C4×D4C2×D414yes—
641C4×D4C2×D412yes—
642C4×D4C2×D414yes—
643C4×D4C2×D412yes—
644C4×D4C2×D414yes—
645C4×D4C2×D412yes—
646C4×D4C2×D412yes—
647C4×D4C2412yes—
648#117—21no—
649#117—21no—
650#117—24no—
651#117—24no—
652#117—22no—
653#117—24no—
654#117—24no—
655#117—24no—
656#117—24no—
657#117—24no—
658#117—24no—
659#117—22no—
660#117—24no—
661#117—22no—
662#117—22no—
663#117—24no—
664#117C22×C412yes—
665#117C22×C414yes—
666#117C22×C412yes—
667#117C22×C414yes—
668#117C2×D412yes—
669#117C2×D412yes—
670#117C2×D414yes—
671#117C2×D414yes—
672C2×C4⋊C4—21no—
673C2×C4⋊C4—21no—
674C2×C4⋊C4—22no—
675C2×C4⋊C4—22no—
676C2×C4⋊C4—21no—
677C2×C4⋊C4—21no—
678C2×C4⋊C4—21no—
679C2×C4⋊C4—21no—
680C2×C4⋊C4—21no—
681C2×C4⋊C4—22no—
682C2×C4⋊C4—22no—
683C2×C4⋊C4—24no—
684C2×C4⋊C4—24no—
685C2×C4⋊C4—22no—
686C2×C4⋊C4C22×C411yescharacteristic
687C2×C4⋊C4C22×C411yescharacteristic
688C2×C4⋊C4C22×C412yes—
689C2×C4⋊C4C22×C412yes—
690C2×C4⋊C4C22×C414yes—
691C2×C42—22no—
692C2×C42—21no—
693C2×C42—22no—
694C2×C42—21no—
695C2×C42—21no—
696C2×C42—22no—
697C2×C42—22no—
698C2×C42—21no—
699C2×C42—24no—
700C2×C42—22no—
701C2×C42—24no—
702C2×C42C22×C411yescharacteristic
703C2×C42C22×C411yescharacteristic
704C2×C42C22×C411yescharacteristic
705C2×C42C2×D411yescharacteristic
706C2×C42C2×D411yescharacteristic
707C2×C42C2×D411yescharacteristic
708C2×C42C2×D411yescharacteristic
709C2×C42C2×D411yescharacteristic
710C2×C42C2×D411yescharacteristic
711C2×C42C2411yescharacteristic
712C2×C42C2411yescharacteristic
713C2×C42C2411yescharacteristic
714C2×C42C2414yes—
715C4⋊C8—22no—
716C4⋊C8—22no—
717C4⋊C8—21no—
718C4⋊C8—22no—
719C4⋊C8—21no—
720C4⋊C8—22no—
721C4⋊C8—21no—
722C4⋊C8—24no—
723C4⋊C8—21no—
724C4⋊C8—24no—
725C4⋊C8—24no—
726C4⋊C8—24no—
727C4⋊C8C2412yes—
728C4⋊C8C2414yes—
729C4⋊C8C2412yes—
730C22⋊C8—21no—
731C22⋊C8—21no—
732C22⋊C8—22no—
733C22⋊C8—22no—
734C22⋊C8—22no—
735C22⋊C8—24no—
736C22⋊C8—24no—
737C22⋊C8—24no—
738C22⋊C8—24no—
739#97—21no—
740#97—21no—
741#97—22no—
742#97—22no—
743#97—22no—
744#97—24no—
745#97—24no—
746C4×C8—22no—
747C4×C8—22no—
748C4×C8—24no—
749C4×C8—24no—
750C4×C8C2412yes—
751C4×C8C2412yes—
752C4×C8C2412yes—
753C4×C8C2412yes—
754C24C2×C22⋊C411yescharacteristic
755#41—24no—
756#41—24no—
757#41—28no—
758#41—44no—
759#41—44no—
760#41—44no—
761#41—44no—
762#41—416no—
763#41—48no—
764#41—42no—
765#41—42no—
766#41—82no—
767#41—88no—
768C2×Q8—24no—
769C2×Q8—21no—
770C2×Q8—21no—
771C2×Q8—22no—
772C2×Q8—22no—
773C2×Q8—21no—
774C2×Q8—24no—
775C2×Q8—21no—
776C2×Q8—24no—
777C2×Q8—24no—
778C2×Q8—24no—
779C2×Q8—28no—
780C2×Q8—42no—
781C2×Q8—42no—
782C2×Q8—42no—
783C2×Q8—44no—
784C2×Q8—44no—
785C2×Q8—44no—
786C2×Q8—44no—
787C2×Q8—48no—
788C2×Q8C2×C22⋊C412yes—
789C2×Q8C2×C22⋊C412yes—
790C2×Q8C2×C22⋊C412yes—
791C2×Q8C23×C412yes—
792C2×Q8C23×C412yes—
793C2×Q8C23×C412yes—
794C2×D4—22no—
795C2×D4—22no—
796C2×D4—22no—
797C2×D4—24no—
798C2×D4—24no—
799C2×D4—21no—
800C2×D4—21no—
801C2×D4C2×C22⋊C414yes—
802C2×D4C2×C22⋊C412yes—
803C2×D4C2×C22⋊C414yes—
804C2×D4C2×C22⋊C414yes—
805C2×D4C2×C22⋊C412yes—
806C2×D4C2×C22⋊C412yes—
807C2×D4C23×C412yes—
808C22×C4—21no—
809C22×C4—22no—
810C22×C4—22no—
811C22×C4—22no—
812C22×C4—22no—
813C22×C4—22no—
814C22×C4—21no—
815C22×C4—24no—
816C22×C4—21no—
817C22×C4—22no—
818C22×C4—21no—
819C22×C4—24no—
820C22×C4—24no—
821C22×C4—22no—
822C22×C4—22no—
823C22×C4—24no—
824C22×C4—22no—
825C22×C4—42no—
826C22×C4—42no—
827C22×C4—44no—
828C22×C4—82no—
829C22×C4C2×C22⋊C411yescharacteristic
830C22×C4C2×C22⋊C411yescharacteristic
831C22×C4C2×C22⋊C411yescharacteristic
832C22×C4C2×C22⋊C411yescharacteristic
833C22×C4C2×C22⋊C411yescharacteristic
834C22×C4C2×C22⋊C411yescharacteristic
835C22×C4C2×C22⋊C411yescharacteristic
836C22×C4C2×C22⋊C411yescharacteristic
837C22×C4C2×C22⋊C411yescharacteristic
838C22×C4C23×C411yescharacteristic
839C22×C4C23×C411yescharacteristic
840C22×C4C23×C411yescharacteristic
841C22×C4C23×C414yes—
842C22×C4C22×D411yescharacteristic
843C22×C4C22×D411yescharacteristic
844C22×C4C22×D411yescharacteristic
845C22×C4C22×D414yes—
846C22×C4C22×D411yescharacteristic
847C22×C4C22×D411yescharacteristic
848C22×C4C22×D414yes—
849C22×C4C22×D411yescharacteristic
850M16—24no—
851M16—44no—
852M16—48no—
853M16—42no—
854M16—44no—
855M16—82no—
856M16—84no—
857C2×C8—22no—
858C2×C8—22no—
859C2×C8—22no—
860C2×C8—22no—
861C2×C8—22no—
862C2×C8—24no—
863C2×C8—22no—
864C2×C8—44no—
865C2×C8—48no—
866C2×C8—44no—
867C2×C8—42no—
868C2×C8—42no—
869C2×C8—82no—
870C2×C8—84no—
871C4⋊C4—22no—
872C4⋊C4—21no—
873C4⋊C4—22no—
874C4⋊C4—22no—
875C4⋊C4—22no—
876C4⋊C4—22no—
877C4⋊C4—22no—
878C4⋊C4—21no—
879C4⋊C4—22no—
880C4⋊C4—22no—
881C4⋊C4—24no—
882C4⋊C4—24no—
883C4⋊C4—24no—
884C4⋊C4—22no—
885C4⋊C4—24no—
886C4⋊C4—22no—
887C4⋊C4—21no—
888C4⋊C4—21no—
889C4⋊C4—21no—
890C4⋊C4—24no—
891C4⋊C4—21no—
892C4⋊C4—24no—
893C4⋊C4—24no—
894C4⋊C4—24no—
895C4⋊C4—22no—
896C4⋊C4—24no—
897C4⋊C4—24no—
898C4⋊C4—22no—
899C4⋊C4—24no—
900C4⋊C4—22no—
901C4⋊C4—24no—
902C4⋊C4—22no—
903C4⋊C4—22no—
904C4⋊C4—22no—
905C4⋊C4C2×C22⋊C412yes—
906C4⋊C4C2×C22⋊C414yes—
907C4⋊C4C2×C22⋊C412yes—
908C4⋊C4C2×C22⋊C414yes—
909C4⋊C4C2×C22⋊C414yes—
910C4⋊C4C2×C22⋊C412yes—
911C4⋊C4C2×C22⋊C412yes—
912C4⋊C4C2×C22⋊C412yes—
913C4⋊C4C2×C22⋊C414yes—
914C4⋊C4C2×C22⋊C414yes—
915C4⋊C4C2×C22⋊C412yes—
916C4⋊C4C2×C22⋊C414yes—
917C4⋊C4C23×C412yes—
918C4⋊C4C23×C412yes—
919C4⋊C4C23×C412yes—
920C4⋊C4C23×C412yes—
921C22⋊C4—22no—
922C22⋊C4—22no—
923C22⋊C4—24no—
924C22⋊C4—22no—
925C22⋊C4—24no—
926C22⋊C4—24no—
927C22⋊C4—24no—
928C22⋊C4—22no—
929C22⋊C4—24no—
930C22⋊C4—22no—
931C22⋊C4—22no—
932C22⋊C4—24no—
933C22⋊C4—24no—
934C22⋊C4—24no—
935C22⋊C4—22no—
936C22⋊C4—22no—
937C22⋊C4—22no—
938C22⋊C4C2×C22⋊C414yes—
939C22⋊C4C2×C22⋊C414yes—
940C22⋊C4C2×C22⋊C414yes—
941C22⋊C4C2×C22⋊C414yes—
942C22⋊C4C2×C22⋊C414yes—
943C22⋊C4C2×C22⋊C414yes—
944C22⋊C4C2×C22⋊C414yes—
945C22⋊C4C2×C22⋊C414yes—
946C22⋊C4C2×C22⋊C414yes—
947C42—22no—
948C42—22no—
949C42—22no—
950C42—22no—
951C42—22no—
952C42—22no—
953C42—24no—
954C42—22no—
955C42—24no—
956C42—24no—
957C42—24no—
958C42—22no—
959C42—22no—
960C42—22no—
961C42—22no—
962C42C2×C22⋊C411yescharacteristic
963C42C2×C22⋊C411yescharacteristic
964C42C2×C22⋊C411yescharacteristic
965C42C2×C22⋊C411yescharacteristic
966C42C2×C22⋊C411yescharacteristic
967C42C2×C22⋊C411yescharacteristic
968C42C23×C411yescharacteristic
969C42C23×C411yescharacteristic
970C42C23×C411yescharacteristic
971C42C23×C414yes—
972C42C22×D411yescharacteristic
973C42C22×D411yescharacteristic
974C42C22×D414yes—
975C42C22×D411yescharacteristic
976C42C22×D414yes—
977C42C22×D411yescharacteristic
978C42C22×D411yescharacteristic
979C42C22×D411yescharacteristic
980C42C2511yescharacteristic
981C23—22no—
982C23—22no—
983C23—22no—
984C23—41no—
985C23C22×C22⋊C414yes—
986C23C22×C22⋊C411yescharacteristic
987C23C22×C22⋊C411yescharacteristic
988C23C22×C22⋊C411yescharacteristic
989Q8—24no—
990Q8—24no—
991Q8—22no—
992Q8—22no—
993Q8—22no—
994Q8—24no—
995Q8—42no—
996Q8—42no—
997Q8—44no—
998Q8—44no—
999Q8—48no—
1000Q8—42no—
1001Q8—42no—
1002Q8—81no—
1003Q8—84no—
1004Q8#56814yes—
1005D4—28no—
1006D4—28no—
1007D4—24no—
1008D4—24no—
1009D4—42no—
1010D4—42no—
1011D4—44no—
1012D4—48no—
1013D4—44no—
1014D4—44no—
1015D4—44no—
1016D4—42no—
1017D4—81no—
1018D4—84no—
1019C2×C4—24no—
1020C2×C4—22no—
1021C2×C4—22no—
1022C2×C4—22no—
1023C2×C4—22no—
1024C2×C4—22no—
1025C2×C4—22no—
1026C2×C4—22no—
1027C2×C4—22no—
1028C2×C4—22no—
1029C2×C4—24no—
1030C2×C4—24no—
1031C2×C4—21no—
1032C2×C4—24no—
1033C2×C4—21no—
1034C2×C4—21no—
1035C2×C4—21no—
1036C2×C4—24no—
1037C2×C4—22no—
1038C2×C4—22no—
1039C2×C4—22no—
1040C2×C4—22no—
1041C2×C4—22no—
1042C2×C4—22no—
1043C2×C4—41no—
1044C2×C4—44no—
1045C2×C4—41no—
1046C2×C4—41no—
1047C2×C4—41no—
1048C2×C4—41no—
1049C2×C4—41no—
1050C2×C4—41no—
1051C2×C4—48no—
1052C2×C4—44no—
1053C2×C4—44no—
1054C2×C4—48no—
1055C2×C4—44no—
1056C2×C4—42no—
1057C2×C4—44no—
1058C2×C4—42no—
1059C2×C4—42no—
1060C2×C4—82no—
1061C2×C4—84no—
1062C2×C4—81no—
1063C2×C4—82no—
1064C2×C4—81no—
1065C2×C4—84no—
1066C2×C4C22×C22⋊C411yescharacteristic
1067C2×C4C22×C22⋊C411yescharacteristic
1068C2×C4C22×C22⋊C411yescharacteristic
1069C2×C4C22×C22⋊C411yescharacteristic
1070C2×C4C22×C22⋊C414yes—
1071C2×C4C22×C22⋊C414yes—
1072C2×C4C22×C22⋊C414yes—
1073C2×C4C22×C22⋊C411yescharacteristic
1074C2×C4C22×C22⋊C411yescharacteristic
1075C2×C4C22×C22⋊C411yescharacteristic
1076C2×C4C22×C22⋊C411yescharacteristic
1077C2×C4C22×C22⋊C411yescharacteristic
1078C2×C4#57712yes—
1079C2×C4#57812yes—
1080C2×C4C24×C411yescharacteristic
1081C2×C4C23×D411yescharacteristic
1082C2×C4C23×D411yescharacteristic
1083C8—24no—
1084C8—42no—
1085C8—42no—
1086C8—42no—
1087C8—42no—
1088C8—44no—
1089C8—42no—
1090C22—21no—
1091C22—21no—
1092C22—21no—
1093C22—21no—
1094C22—21no—
1095C22—24no—
1096C22—21no—
1097C22—24no—
1098C22—21no—
1099C22—24no—
1100C22—44no—
1101C22—42no—
1102C22—42no—
1103C22—42no—
1104C22#289812yes—
1105C22#290112yes—
1106C22C23×C22⋊C411yescharacteristic
1107C4—24no—
1108C4—21no—
1109C4—24no—
1110C4—21no—
1111C4—21no—
1112C4—21no—
1113C4—21no—
1114C4—24no—
1115C4—21no—
1116C4—21no—
1117C4—21no—
1118C4—21no—
1119C4—24no—
1120C4—42no—
1121C4—42no—
1122C4—42no—
1123C4—42no—
1124C4—42no—
1125C4—42no—
1126C4#289812yes—
1127C4C2×#56812yes—
1128C4C2×#57711yescharacteristic
1129C4C2×#57811yescharacteristic
1130C2—22no—
1131C2—22no—
1132C2—44no—
1133C2—41no—
1134C2—82no—
1135C2#6006411yescharacteristic
1136C2C2×#289811yescharacteristic
1137C2C2×#290111yescharacteristic
subgroupG/H
centerC2×C4C23×D4
commutatorC2×C4C24×C4
Frattini, cosocleC42C25
socleC22C23×C22⋊C4
prime radical#62788C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4 ◁ #3444 ◁ G
LECSG ▷ C42 ▷ C22 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #60269C2semidirect
3. #60210C2semidirect
4. #17524C2semidirect
5. #17519C2semidirect
6. #17515C2semidirect
7. #17514C2semidirect
8. #17510C2semidirect
9. #17509C2semidirect
10. #17506C2semidirect
11. #17504C2semidirect
12. #17488C2semidirect
13. #17454C2semidirect
14. C2×#1491C2semidirect
15. C2×#1487C2semidirect
66. #1497C22semidirect
67. #1495C22semidirect
69. #1494C22semidirect
71. #1493C22semidirect
77. #1491C22semidirect
79. #1489C22semidirect
81. #1488C22semidirect
86. #1487C22semidirect
87. #1485C22semidirect
90. #1483C22semidirect
91. #1482C22semidirect
94. #1481C22semidirect
97. #1479C22semidirect
98. #1477C22semidirect
99. #1476C22semidirect
103. C2×Q8⋊C8C22semidirect

Maximal subgroups

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

subgroupindex
#627882
#602692
#602102
#175242
#175192
#175152
#175142
#175102
#175092
#175062
#175042
#174882
#174542
C2×#14912
C2×#14872