Finite Group Databasebeta

← #6343090

Subgroups — #6343090

Order 512.

2817 conjugacy classes of subgroups.

The subgroup lattice has 1145 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#62788C211yesmaximal, characteristic
2#60292C211yesmaximal, characteristic, complemented
3#60279C211yesmaximal, characteristic, complemented
4#17525C214yesmaximal, complemented
5#17524C214yesmaximal, complemented
6#17516C214yesmaximal, complemented
7#17514C214yesmaximal, complemented
8#17484C212yesmaximal, complemented
9#17477C211yesmaximal, characteristic, complemented
10#17469C212yesmaximal, complemented
11#17467C211yesmaximal, characteristic, complemented
12#17454C212yesmaximal, complemented
13#17449C211yesmaximal, characteristic, complemented
14#17439C212yesmaximal, complemented
15C2×#1479C211yesmaximal, 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#2993—22no—
44#2992—22no—
45#2991C2212yes—
46#2990C2212yes—
47#2989C2212yes—
48#2988C2212yes—
49#2986—21no—
50#2985—21no—
51#2981—21no—
52#2979—21no—
53#2976—22no—
54#2976—22no—
55#2969—22no—
56#2966—22no—
57#2965C2212yes—
58#2965C2214yes—
59C8×#41C2212yes—
60#2925C2214yes—
61#2922C2214yes—
62#2920C2211yescharacteristic
63#2920C2211yescharacteristic
64C2×#431C2211yescharacteristic
65C2×#431C2211yescharacteristic
66#1497C2212yes—
67#1497C2214yescomplemented
68#1496C2212yes—
69#1495C2212yes—
70#1495C2212yes—
71#1495C2214yescomplemented
72#1494C2214yescomplemented
73#1493C2214yescomplemented
74#1491C2214yes—
75#1491C2214yescomplemented
76#1489C2214yescomplemented
77#1488C2214yescomplemented
78#1487C2212yes—
79#1487C2212yes—
80#1487C2214yescomplemented
81#1485C2212yes—
82#1485C2214yescomplemented
83#1484C2212yes—
84#1483C2214yescomplemented
85#1482C2214yes—
86#1482C2214yescomplemented
87#1481C2214yescomplemented
88#1479C2214yes—
89#1479C2214yes—
90#1479C2212yes—
91#1479C2212yes—
92#1479C2214yescomplemented
93#1477C2212yes—
94#1477C2212yes—
95#1477C2214yescomplemented
96#1476C2212yes—
97#1476C2212yes—
98#1476C2214yescomplemented
99C2×Q8⋊C8C2211yescharacteristic
100C2×Q8⋊C8C2211yescharacteristic
101C2×Q8⋊C8C2211yescharacteristic
102C2×Q8⋊C8C2211yescharacteristic
103C2×Q8⋊C8C2214yescomplemented
104C2×2−1+4C2×C412yes—
105C23×Q8C2×C411yescharacteristic
106#559—21no—
107#559—22no—
108#559—22no—
109#559C2×C412yes—
110Q82—21no—
111Q82C2×C412yes—
112#557—21no—
113#557—21no—
114#557—22no—
115#557—22no—
116#557—22no—
117#557C2×C412yes—
118#557C2×C412yes—
119#557C2×C414yes—
120#556—21no—
121#556—24no—
122#556—22no—
123#556—22no—
124#556—22no—
125#556—24no—
126#556C2×C414yes—
127#556C2×C412yes—
128#554—21no—
129#554—22no—
130#554—24no—
131#554—22no—
132#554—24no—
133#554—22no—
134#554C2×C414yes—
135#554C2×C412yes—
136#553—24no—
137#553—22no—
138#553—24no—
139#553C2×C414yes—
140#552—24no—
141#552—22no—
142#552—24no—
143#552—22no—
144#552—24no—
145#552—24no—
146#552C2×C414yes—
147#552C2×C414yes—
148#550—21no—
149#550C2×C412yes—
150D4×Q8—21no—
151D4×Q8—22no—
152D4×Q8—22no—
153D4×Q8C2×C414yes—
154D4×Q8C2×C412yes—
155D4×Q8C2×C414yes—
156#548—22no—
157#548—22no—
158#548—22no—
159#548C2×C414yes—
160#548C2×C414yes—
161#548C2×C414yes—
162#547—24no—
163#547—24no—
164#547—22no—
165#547C2×C414yes—
166#544—22no—
167#544C2×C412yes—
168#542—24no—
169#542—24no—
170#542—22no—
171#542C2×C414yes—
172#541—24no—
173#541—24no—
174#541—22no—
175#541C2×C414yes—
176#539—24no—
177#539—22no—
178#539—22no—
179#539—24no—
180#537—22no—
181#537C2×C412yes—
182#536—24no—
183#536C2×C412yes—
184#536C2×C412yes—
185#533—22no—
186#533—22no—
187#533—24no—
188#533—22no—
189#533—22no—
190#533—24no—
191#533C2×C411yescharacteristic
192#533C2×C411yescharacteristic
193#533C2×C411yescharacteristic
194#533D411yescharacteristic
195#533D411yescharacteristic
196#533C2311yescharacteristic
197#533C2314yes—
198#532—22no—
199#532—22no—
200#532—22no—
201#532C2×C411yescharacteristic
202#532C2×C411yescharacteristic
203#532C2×C411yescharacteristic
204#532D411yescharacteristic
205#532D411yescharacteristic
206#532C2311yescharacteristic
207#529—24no—
208#529—24no—
209#529—22no—
210#529—22no—
211#529—22no—
212#529—22no—
213#529—24no—
214#529—24no—
215#529—24no—
216#529—22no—
217#529—24no—
218#529—21no—
219#529—21no—
220#529—21no—
221#529—21no—
222#529C2×C412yes—
223#529C2×C412yes—
224#529C2×C412yes—
225#529D412yes—
226#529D412yes—
227#529D412yes—
228#529D412yes—
229#529C2312yes—
230#529C2314yes—
231#525—21no—
232#525—21no—
233#525—24no—
234#525—24no—
235#525C2×C412yes—
236#525C2×C412yes—
237#525D412yes—
238#525D412yes—
239#520—24no—
240#520—22no—
241#520C2×C412yes—
242#520C2×C414yes—
243#520C2×C412yes—
244#519—22no—
245#519C2×C412yes—
246#519C2×C414yes—
247C4×#41—22no—
248C4×#41—24no—
249C4×#41—22no—
250C4×#41—24no—
251C4×#41—22no—
252C4×#41—21no—
253C4×#41—21no—
254C4×#41C2312yes—
255C4×#41C2314yes—
256C4×#41C2312yes—
257C4×#41C2312yes—
258C4×#41C2312yes—
259C2×C4×Q8—22no—
260C2×C4×Q8—21no—
261C2×C4×Q8—21no—
262C2×C4×Q8—21no—
263C2×C4×Q8—21no—
264C2×C4×Q8—21no—
265C2×C4×Q8—21no—
266C2×C4×Q8C2×C411yescharacteristic
267C2×C4×Q8C2×C411yescharacteristic
268C2×C4×Q8C2×C412yes—
269C2×C4×Q8C2×C412yes—
270C2×C4×Q8C2311yescharacteristic
271C2×C4×Q8C2311yescharacteristic
272C2×C4×Q8C2312yes—
273C2×C4×Q8C2312yes—
274C2×C4×Q8C2314yes—
275C22×C4⋊C4—21no—
276C22×C4⋊C4C2×C411yescharacteristic
277C22×C42—21no—
278C22×C42C2311yescharacteristic
279#446—24no—
280#446—22no—
281#446—22no—
282#446—22no—
283C8×Q8—22no—
284C8×Q8—22no—
285C8×Q8—22no—
286#436—24no—
287#436—22no—
288#436—22no—
289#436—24no—
290#436—22no—
291#435—24no—
292#435—24no—
293#435—24no—
294#435—24no—
295#435—24no—
296C8×D4—24no—
297C8×D4—22no—
298C8×D4—24no—
299C8×D4—22no—
300C8×D4—22no—
301#433—24no—
302#433—24no—
303#433—24no—
304#433—24no—
305#432—21no—
306#432—21no—
307#432—21no—
308#432C2312yes—
309#432C2314yes—
310#431—21no—
311#431—21no—
312#431—21no—
313#431—21no—
314#431—21no—
315#431C2312yes—
316#431C2312yes—
317#431C2312yes—
318#431C2314yes—
319#431C2312yes—
320#431C2312yes—
321#431C2312yes—
322#431C2312yes—
323#431C2314yes—
324#431C2314yes—
325#424—24no—
326#423—21no—
327#423C2311yescharacteristic
328#423C2311yescharacteristic
329#423C2314yes—
330C2×C4⋊C8—21no—
331C2×C4⋊C8C2311yescharacteristic
332C2×C4⋊C8C2311yescharacteristic
333C2×C4⋊C8C2314yes—
334#408—24no—
335#408—24no—
336#407—21no—
337#407—21no—
338C2×C22⋊C8—21no—
339C2×C22⋊C8—21no—
340#405—24no—
341C4×M16—21no—
342C4×M16C2312yes—
343C4×M16C2314yes—
344C2×C4×C8—21no—
345C2×C4×C8C2311yescharacteristic
346C2×C4×C8C2311yescharacteristic
347C2×C4×C8C2314yes—
348Q8⋊C8C2314yes—
349Q8⋊C8C2314yes—
350Q8⋊C8C2314yes—
351Q8⋊C8C2314yes—
352Q8⋊C8C2312yes—
353Q8⋊C8C2314yes—
354Q8⋊C8C2314yes—
355Q8⋊C8C2312yes—
356Q8⋊C8C2312yes—
357Q8⋊C8C2312yes—
358Q8⋊C8C2314yes—
359Q8⋊C8C2314yes—
360Q8⋊C8C2314yes—
361Q8⋊C8C2314yes—
362D4⋊C8C2312yes—
363D4⋊C8C2312yes—
364D4⋊C8C2312yes—
365D4⋊C8C2312yes—
366D4⋊C8C2314yes—
367D4⋊C8C2314yes—
3682−1+4—28no—
3692−1+4—44no—
370C2×#41—24no—
371C2×#41—22no—
372C2×#41—24no—
373C2×#41—21no—
374C2×#41—21no—
375C2×#41C22×C412yes—
376C2×#41C22×C414yes—
377C2×#41C22×C412yes—
378C2×#41C2×D412yes—
379C2×#41C2×D412yes—
380C22×Q8—22no—
381C22×Q8—21no—
382C22×Q8—21no—
383C22×Q8—21no—
384C22×Q8—24no—
385C22×Q8—42no—
386C22×Q8C22×C411yescharacteristic
387C22×Q8C22×C412yes—
388C22×Q8C22×C412yes—
389C22×Q8C22×C414yes—
390C22×Q8C22×C411yescharacteristic
391C23×C4—21no—
392C23×C4—21no—
393C23×C4C22×C411yescharacteristic
394C23×C4C2×D411yescharacteristic
395C23×C4C2×D411yescharacteristic
396C2×M16—21no—
397C2×M16—21no—
398C2×M16—22no—
399C2×M16—24no—
400C2×M16—24no—
401C22×C8—21no—
402C22×C8—21no—
403C22×C8—21no—
404C22×C8—21no—
405C22×C8—24no—
406C22×C8—24no—
407C4⋊Q8—22no—
408C4⋊Q8—22no—
409C4⋊Q8—24no—
410C4⋊Q8—22no—
411C4⋊Q8—22no—
412C4⋊Q8—24no—
413C4⋊Q8—24no—
414C4⋊Q8—24no—
415C4⋊Q8—22no—
416C4⋊Q8C22⋊C411yescharacteristic
417C4⋊Q8C22⋊C411yescharacteristic
418C4⋊Q8C22⋊C411yescharacteristic
419C4⋊Q8C22×C411yescharacteristic
420C4⋊Q8C22×C414yes—
421C4⋊Q8C22×C411yescharacteristic
422C4⋊Q8C22×C411yescharacteristic
423C4⋊Q8C22×C414yes—
424#127—22no—
425#127C22⋊C411yescharacteristic
426#127C22×C411yescharacteristic
427#126—24no—
428#126—24no—
429#126—24no—
430#126—24no—
431#126—24no—
432#126—24no—
433#126—24no—
434#126—24no—
435#126—24no—
436#126—22no—
437#126—22no—
438#126—24no—
439#126C22⋊C414yes—
440#126C22⋊C414yes—
441#125—24no—
442#125—24no—
443#125—22no—
444#125—22no—
445#125—24no—
446#125—24no—
447#125—22no—
448#125—24no—
449#125—24no—
450#125—24no—
451#125—24no—
452#125—24no—
453#125—21no—
454#125—21no—
455#125—24no—
456#125C22⋊C412yes—
457#125C22⋊C412yes—
458#125C22⋊C412yes—
459#125C22×C412yes—
460#125C22×C414yes—
461#124—22no—
462#124—22no—
463#124—22no—
464#124—24no—
465#124—24no—
466#124—24no—
467#124—24no—
468#124—21no—
469#124—21no—
470#124C22⋊C412yes—
471#124C22⋊C412yes—
472#124C22⋊C412yes—
473#124C22×C412yes—
474#124C22×C414yes—
475#123—24no—
476#123—24no—
477#123—24no—
478#123—22no—
479#123—22no—
480#123—22no—
481#123—24no—
482#123—24no—
483#123—24no—
484#123—24no—
485#123—24no—
486#123—24no—
487#123—24no—
488#123C22⋊C414yes—
489#123C22⋊C414yes—
490#123C22⋊C414yes—
491C22⋊Q8—22no—
492C22⋊Q8—24no—
493C22⋊Q8—21no—
494C22⋊Q8—21no—
495C22⋊Q8—21no—
496C22⋊Q8—21no—
497C22⋊Q8—24no—
498C22⋊Q8—24no—
499C22⋊Q8—22no—
500C22⋊Q8—24no—
501C22⋊Q8—22no—
502C22⋊Q8—24no—
503C22⋊Q8—24no—
504C22⋊Q8—24no—
505C22⋊Q8—24no—
506C22⋊Q8—24no—
507C22⋊Q8—24no—
508C22⋊Q8—24no—
509C22⋊Q8—24no—
510C22⋊Q8—24no—
511C22⋊Q8—24no—
512C22⋊Q8—24no—
513C22⋊Q8—24no—
514C22⋊Q8C22⋊C412yes—
515C22⋊Q8C22⋊C412yes—
516C22⋊Q8C22⋊C412yes—
517C22⋊Q8C22⋊C412yes—
518C22⋊Q8C22⋊C412yes—
519C22⋊Q8C22⋊C412yes—
520C22⋊Q8C22×C412yes—
521C22⋊Q8C22×C412yes—
522C22⋊Q8C22×C414yes—
523C22⋊Q8C22×C414yes—
524C22⋊Q8C22×C414yes—
525#121—24no—
526#121—24no—
527#121—24no—
528#121—24no—
529#121—24no—
530#121—22no—
531#121—21no—
532#121—21no—
533#121—21no—
534#121—21no—
535#121—24no—
536#121C22⋊C412yes—
537#121C22⋊C412yes—
538#121C22⋊C412yes—
539#121C22⋊C412yes—
540#121C22⋊C412yes—
541#121C22⋊C412yes—
542#121C22×C412yes—
543#121C22×C412yes—
544#121C22×C414yes—
545#120—22no—
546#120C22⋊C414yes—
547C4×Q8—22no—
548C4×Q8—22no—
549C4×Q8—22no—
550C4×Q8—22no—
551C4×Q8—24no—
552C4×Q8—24no—
553C4×Q8—22no—
554C4×Q8—24no—
555C4×Q8—22no—
556C4×Q8—22no—
557C4×Q8—22no—
558C4×Q8—22no—
559C4×Q8—21no—
560C4×Q8—21no—
561C4×Q8—21no—
562C4×Q8—22no—
563C4×Q8—21no—
564C4×Q8—22no—
565C4×Q8—21no—
566C4×Q8—21no—
567C4×Q8—21no—
568C4×Q8—21no—
569C4×Q8—21no—
570C4×Q8—22no—
571C4×Q8—22no—
572C4×Q8—21no—
573C4×Q8—21no—
574C4×Q8—22no—
575C4×Q8—22no—
576C4×Q8—24no—
577C4×Q8—24no—
578C4×Q8—21no—
579C4×Q8—24no—
580C4×Q8C22×C412yes—
581C4×Q8C22×C412yes—
582C4×Q8C22×C412yes—
583C4×Q8C22×C412yes—
584C4×Q8C22×C412yes—
585C4×Q8C22×C412yes—
586C4×Q8C22×C414yes—
587C4×Q8C22×C414yes—
588C4×Q8C22×C412yes—
589C4×Q8C22×C414yes—
590C4×Q8C22×C412yes—
591C4×Q8C22×C412yes—
592C4×Q8C2×D412yes—
593C4×Q8C2×D412yes—
594C4×Q8C2×D412yes—
595C4×Q8C2×D412yes—
596C4×Q8C2412yes—
597C4×Q8C2412yes—
598C4×Q8C2412yes—
599C4×D4—24no—
600C4×D4—22no—
601C4×D4—24no—
602C4×D4—24no—
603C4×D4—24no—
604C4×D4—22no—
605C4×D4—22no—
606C4×D4—22no—
607C4×D4—22no—
608C4×D4—22no—
609C4×D4—22no—
610C4×D4—22no—
611C4×D4—24no—
612C4×D4—24no—
613C4×D4—22no—
614C4×D4—24no—
615C4×D4—22no—
616C4×D4—22no—
617C4×D4—24no—
618C4×D4—24no—
619C4×D4—24no—
620C4×D4—24no—
621C4×D4—24no—
622C4×D4—24no—
623C4×D4—24no—
624C4×D4—21no—
625C4×D4—21no—
626C4×D4—21no—
627C4×D4—21no—
628C4×D4C22×C412yes—
629C4×D4C22×C414yes—
630C4×D4C22×C414yes—
631C4×D4C22×C414yes—
632C4×D4C22×C412yes—
633C4×D4C22×C412yes—
634C4×D4C2×D414yes—
635C4×D4C2×D414yes—
636C4×D4C2×D412yes—
637C4×D4C2×D414yes—
638C4×D4C2×D412yes—
639C4×D4C2×D414yes—
640C4×D4C2×D412yes—
641C4×D4C2×D412yes—
642C4×D4C2412yes—
643#117—21no—
644#117—21no—
645#117—24no—
646#117—24no—
647#117—22no—
648#117—24no—
649#117—24no—
650#117—24no—
651#117—24no—
652#117—24no—
653#117—24no—
654#117—22no—
655#117—22no—
656#117—24no—
657#117—22no—
658#117—24no—
659#117C22×C412yes—
660#117C22×C414yes—
661#117C22×C412yes—
662#117C22×C414yes—
663#117C2×D412yes—
664#117C2×D412yes—
665#117C2×D414yes—
666#117C2×D414yes—
667C2×C4⋊C4—21no—
668C2×C4⋊C4—21no—
669C2×C4⋊C4—22no—
670C2×C4⋊C4—22no—
671C2×C4⋊C4—21no—
672C2×C4⋊C4—21no—
673C2×C4⋊C4—21no—
674C2×C4⋊C4—21no—
675C2×C4⋊C4—21no—
676C2×C4⋊C4—22no—
677C2×C4⋊C4—22no—
678C2×C4⋊C4—24no—
679C2×C4⋊C4—24no—
680C2×C4⋊C4—22no—
681C2×C4⋊C4C22×C411yescharacteristic
682C2×C4⋊C4C22×C411yescharacteristic
683C2×C4⋊C4C22×C412yes—
684C2×C4⋊C4C22×C412yes—
685C2×C4⋊C4C22×C414yes—
686C2×C42—22no—
687C2×C42—21no—
688C2×C42—22no—
689C2×C42—21no—
690C2×C42—21no—
691C2×C42—22no—
692C2×C42—22no—
693C2×C42—21no—
694C2×C42—24no—
695C2×C42—22no—
696C2×C42—24no—
697C2×C42C22×C411yescharacteristic
698C2×C42C22×C411yescharacteristic
699C2×C42C22×C411yescharacteristic
700C2×C42C2×D411yescharacteristic
701C2×C42C2×D411yescharacteristic
702C2×C42C2×D411yescharacteristic
703C2×C42C2×D411yescharacteristic
704C2×C42C2×D411yescharacteristic
705C2×C42C2×D411yescharacteristic
706C2×C42C2411yescharacteristic
707C2×C42C2411yescharacteristic
708C2×C42C2411yescharacteristic
709C2×C42C2414yes—
710C4⋊C8—22no—
711C4⋊C8—22no—
712C4⋊C8—21no—
713C4⋊C8—21no—
714C4⋊C8—24no—
715C4⋊C8—22no—
716C4⋊C8—22no—
717C4⋊C8—21no—
718C4⋊C8—21no—
719C4⋊C8—24no—
720C4⋊C8—24no—
721C4⋊C8—24no—
722C4⋊C8C2412yes—
723C4⋊C8C2412yes—
724C4⋊C8C2412yes—
725C4⋊C8C2412yes—
726C22⋊C8—22no—
727C22⋊C8—22no—
728C22⋊C8—22no—
729C22⋊C8—22no—
730C22⋊C8—22no—
731C22⋊C8—22no—
732C22⋊C8—22no—
733C22⋊C8—22no—
734C22⋊C8—24no—
735C22⋊C8—24no—
736C22⋊C8—24no—
737C22⋊C8—24no—
738#97—22no—
739#97—22no—
740#97—24no—
741#97—24no—
742C4×C8—22no—
743C4×C8—22no—
744C4×C8—21no—
745C4×C8—21no—
746C4×C8—24no—
747C4×C8—22no—
748C4×C8—24no—
749C4×C8C2412yes—
750C4×C8C2412yes—
751C4×C8C2414yes—
752C24C2×C22⋊C411yescharacteristic
753#41—24no—
754#41—24no—
755#41—28no—
756#41—24no—
757#41—24no—
758#41—42no—
759#41—42no—
760#41—44no—
761#41—416no—
762#41—42no—
763#41—42no—
764#41—48no—
765#41—82no—
766#41—82no—
767#41—88no—
768C2×Q8—21no—
769C2×Q8—21no—
770C2×Q8—22no—
771C2×Q8—22no—
772C2×Q8—21no—
773C2×Q8—24no—
774C2×Q8—21no—
775C2×Q8—24no—
776C2×Q8—22no—
777C2×Q8—24no—
778C2×Q8—24no—
779C2×Q8—28no—
780C2×Q8—22no—
781C2×Q8—22no—
782C2×Q8—44no—
783C2×Q8—42no—
784C2×Q8—42no—
785C2×Q8—44no—
786C2×Q8—44no—
787C2×Q8—44no—
788C2×Q8—48no—
789C2×Q8C2×C22⋊C412yes—
790C2×Q8C2×C22⋊C412yes—
791C2×Q8C2×C22⋊C412yes—
792C2×Q8#13114yes—
793C2×Q8C23×C412yes—
794C2×Q8C23×C412yes—
795C2×Q8C23×C412yes—
796C2×D4—22no—
797C2×D4—22no—
798C2×D4—22no—
799C2×D4—24no—
800C2×D4—24no—
801C2×D4—21no—
802C2×D4—21no—
803C2×D4C2×C22⋊C414yes—
804C2×D4C2×C22⋊C412yes—
805C2×D4C2×C22⋊C414yes—
806C2×D4C2×C22⋊C412yes—
807C2×D4C2×C22⋊C414yes—
808C2×D4C2×C22⋊C412yes—
809C2×D4C23×C412yes—
810C22×C4—21no—
811C22×C4—22no—
812C22×C4—22no—
813C22×C4—22no—
814C22×C4—22no—
815C22×C4—22no—
816C22×C4—21no—
817C22×C4—24no—
818C22×C4—21no—
819C22×C4—22no—
820C22×C4—21no—
821C22×C4—24no—
822C22×C4—24no—
823C22×C4—22no—
824C22×C4—22no—
825C22×C4—24no—
826C22×C4—22no—
827C22×C4—41no—
828C22×C4—41no—
829C22×C4—44no—
830C22×C4—81no—
831C22×C4—82no—
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×C4C2×C22⋊C411yescharacteristic
839C22×C4C2×C22⋊C411yescharacteristic
840C22×C4C2×C22⋊C411yescharacteristic
841C22×C4C23×C411yescharacteristic
842C22×C4C23×C411yescharacteristic
843C22×C4C23×C414yes—
844C22×C4C23×C411yescharacteristic
845C22×C4C22×D411yescharacteristic
846C22×C4C22×D411yescharacteristic
847C22×C4C22×D411yescharacteristic
848C22×C4C22×D414yes—
849C22×C4C22×D411yescharacteristic
850C22×C4C22×D411yescharacteristic
851C22×C4C22×D411yescharacteristic
852C22×C4C22×D414yes—
853M16—81no—
854M16—84no—
855M16—81no—
856M16—84no—
857M16—82no—
858C2×C8—22no—
859C2×C8—22no—
860C2×C8—24no—
861C2×C8—22no—
862C2×C8—22no—
863C2×C8—22no—
864C2×C8—22no—
865C2×C8—81no—
866C2×C8—84no—
867C2×C8—81no—
868C2×C8—81no—
869C2×C8—84no—
870C2×C8—81no—
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×D414yes—
974C42C22×D411yescharacteristic
975C42C22×D411yescharacteristic
976C42C22×D411yescharacteristic
977C42C22×D411yescharacteristic
978C42C22×D411yescharacteristic
979C42C22×D414yes—
980C42C2511yescharacteristic
981C23—22no—
982C23—22no—
983C23—41no—
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—22no—
995Q8—22no—
996Q8—42no—
997Q8—42no—
998Q8—44no—
999Q8—44no—
1000Q8—48no—
1001Q8—42no—
1002Q8—42no—
1003Q8—81no—
1004Q8—84no—
1005Q8C2×#13114yes—
1006D4—28no—
1007D4—24no—
1008D4—22no—
1009D4—22no—
1010D4—42no—
1011D4—44no—
1012D4—42no—
1013D4—44no—
1014D4—48no—
1015D4—42no—
1016D4—44no—
1017D4—44no—
1018D4—44no—
1019D4—81no—
1020D4—84no—
1021C2×C4—22no—
1022C2×C4—24no—
1023C2×C4—22no—
1024C2×C4—21no—
1025C2×C4—21no—
1026C2×C4—24no—
1027C2×C4—21no—
1028C2×C4—21no—
1029C2×C4—24no—
1030C2×C4—21no—
1031C2×C4—21no—
1032C2×C4—22no—
1033C2×C4—22no—
1034C2×C4—21no—
1035C2×C4—21no—
1036C2×C4—24no—
1037C2×C4—21no—
1038C2×C4—21no—
1039C2×C4—24no—
1040C2×C4—22no—
1041C2×C4—22no—
1042C2×C4—22no—
1043C2×C4—22no—
1044C2×C4—22no—
1045C2×C4—22no—
1046C2×C4—41no—
1047C2×C4—44no—
1048C2×C4—41no—
1049C2×C4—41no—
1050C2×C4—41no—
1051C2×C4—41no—
1052C2×C4—41no—
1053C2×C4—41no—
1054C2×C4—41no—
1055C2×C4—41no—
1056C2×C4—48no—
1057C2×C4—44no—
1058C2×C4—44no—
1059C2×C4—48no—
1060C2×C4—44no—
1061C2×C4—42no—
1062C2×C4—42no—
1063C2×C4—42no—
1064C2×C4—44no—
1065C2×C4—82no—
1066C2×C4—84no—
1067C2×C4—81no—
1068C2×C4—82no—
1069C2×C4—81no—
1070C2×C4—84no—
1071C2×C4C22×C22⋊C411yescharacteristic
1072C2×C4C22×C22⋊C411yescharacteristic
1073C2×C4C22×C22⋊C411yescharacteristic
1074C2×C4C22×C22⋊C411yescharacteristic
1075C2×C4C22×C22⋊C414yes—
1076C2×C4C22×C22⋊C414yes—
1077C2×C4C22×C22⋊C414yes—
1078C2×C4C22×C22⋊C411yescharacteristic
1079C2×C4C22×C22⋊C411yescharacteristic
1080C2×C4C22×C22⋊C411yescharacteristic
1081C2×C4C22×C22⋊C411yescharacteristic
1082C2×C4C22×C22⋊C411yescharacteristic
1083C2×C4C2×#13112yes—
1084C2×C4#56812yes—
1085C2×C4C24×C411yescharacteristic
1086C2×C4C23×D411yescharacteristic
1087C2×C4C23×D411yescharacteristic
1088C8—42no—
1089C8—42no—
1090C8—44no—
1091C8—42no—
1092C8—42no—
1093C8—42no—
1094C8—42no—
1095C22—21no—
1096C22—21no—
1097C22—21no—
1098C22—21no—
1099C22—24no—
1100C22—21no—
1101C22—21no—
1102C22—24no—
1103C22—21no—
1104C22—21no—
1105C22—24no—
1106C22—44no—
1107C22—42no—
1108C22—42no—
1109C22—42no—
1110C22#288012yes—
1111C22C23×C22⋊C411yescharacteristic
1112C4—21no—
1113C4—21no—
1114C4—24no—
1115C4—24no—
1116C4—21no—
1117C4—21no—
1118C4—21no—
1119C4—24no—
1120C4—21no—
1121C4—21no—
1122C4—21no—
1123C4—21no—
1124C4—24no—
1125C4—42no—
1126C4—42no—
1127C4—42no—
1128C4—42no—
1129C4—42no—
1130C4—42no—
1131C4#288012yes—
1132C4C22×#13111yescharacteristic
1133C4C2×#56811yescharacteristic
1134C4#358611yescharacteristic
1135C4#358611yescharacteristic
1136C2—22no—
1137C2—44no—
1138C2—41no—
1139C2—41no—
1140C2—82no—
1141C2C2×#288011yescharacteristic
1142C2#6008811yescharacteristic
1143C2#6009311yescharacteristic
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. #60292C2semidirect
3. #60279C2semidirect
4. #17525C2semidirect
5. #17524C2semidirect
6. #17516C2semidirect
7. #17514C2semidirect
8. #17484C2semidirect
9. #17477C2semidirect
10. #17469C2semidirect
11. #17467C2semidirect
12. #17454C2semidirect
13. #17449C2semidirect
14. #17439C2semidirect
15. C2×#1479C2semidirect
67. #1497C22semidirect
71. #1495C22semidirect
72. #1494C22semidirect
73. #1493C22semidirect
75. #1491C22semidirect
76. #1489C22semidirect
77. #1488C22semidirect
80. #1487C22semidirect
82. #1485C22semidirect
84. #1483C22semidirect
86. #1482C22semidirect
87. #1481C22semidirect
92. #1479C22semidirect
95. #1477C22semidirect
98. #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
#602922
#602792
#175252
#175242
#175162
#175142
#174842
#174772
#174692
#174672
#174542
#174492
#174392
C2×#14792