Finite Group Databasebeta

← #6394041

Subgroups — #6394041

Order 512.

3350 conjugacy classes of subgroups.

The subgroup lattice has 1313 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3520C211yesmaximal, characteristic
2#34194C211yesmaximal, characteristic, complemented
3#34126C211yesmaximal, characteristic, complemented
4#22513C214yesmaximal, complemented
5#22477C218yesmaximal, complemented
6#22476C214yesmaximal, complemented
7#21875C211yesmaximal, characteristic, complemented
8#21874C212yesmaximal, complemented
9#21826C211yesmaximal, characteristic, complemented
10#21825C212yesmaximal, complemented
11#21421C211yesmaximal, characteristic, complemented
12#21420C212yesmaximal, complemented
13#21332C211yesmaximal, characteristic, complemented
14C2×#1996C212yesmaximal, complemented
15#3520—22no—
16#3520—21no—
17#3520—21no—
18#3520—21no—
19#3520—22no—
20#3520—22no—
21#3520—21no—
22#3520—21no—
23#3520—21no—
24#3520—21no—
25#3520—22no—
26#3520—21no—
27C2×#556C411yescharacteristic, complemented
28C2×#554C2212yes—
29C2×#552C412yescomplemented
30C2×#551C2214yes—
31C2×D4×Q8C411yescharacteristic, complemented
32C2×#548C412yescomplemented
33C2×#547C411yescharacteristic, complemented
34C2×#547C411yescharacteristic, complemented
35C2×#546C2212yes—
36C2×#542C412yescomplemented
37C2×#539C414yescomplemented
38C2×#533C2211yescharacteristic
39C2×#529C2211yescharacteristic
40C2×#525C2212yes—
41C22×C22⋊Q8C2212yes—
42C2×#520C412yescomplemented
43C22×C4×D4C2211yescharacteristic
44#2357—21no—
45#2354—21no—
46#2353—22no—
47#2352—22no—
48#2349—21no—
49D4×C4⋊C4—21no—
50#2345C2212yes—
51#2345C2212yes—
52#2342C2214yes—
53#2342C2214yes—
54D4×C22⋊C4C2212yes—
55D4×C22⋊C4C2212yes—
56#2319—21no—
57#2318—22no—
58#2293—21no—
59#2290—22no—
60#2285C2211yescharacteristic
61#2283C2211yescharacteristic
62#2283C2211yescharacteristic
63#2280C2212yes—
64#2280C2212yes—
65C2×#380C2212yes—
66#2275—21no—
67C42×D4—21no—
68C4×#117C2211yescharacteristic
69C2×C4×C22⋊C4C2212yes—
70#1996C2211yescharacteristic
71#1996C2212yes—
72#1996C2212yes—
73#1996C2212yes—
74#1996C2218yes—
75#1996C2212yes—
76#1996C2214yes—
77#1996C2211yescharacteristic
78#1996C2212yes—
79#1996C2218yes—
80#1996C2214yes—
81#1964C2211yescharacteristic
82#1964C2212yes—
83#1964C2211yescharacteristic
84#1899C2214yes—
85#1899C2214yes—
86#1898C2218yes—
87#1898C2218yes—
88#1820C2214yes—
89#1819C2218yes—
90#1799C2218yes—
91#1799C2214yes—
92C4×#99C2218yes—
93C4×#99C2214yes—
94#1740C2214yes—
95C2×#342C2218yes—
96C22×#41C2×C412yes—
97C22×#41C2×C412yescomplemented
98C23×Q8C2×C412yescomplemented
99C23×D4C2311yescharacteristic
100C24×C4C2312yes—
101#556—21no—
102#556—21no—
103#556—22no—
104#556—21no—
105#556—21no—
106#556—22no—
107#554—22no—
108#554—22no—
109#554—24no—
110#554—24no—
111#554—22no—
112#554—22no—
113#552—22no—
114#552—22no—
115#552—22no—
116#552—22no—
117#552—22no—
118#552—22no—
119#552—22no—
120#552—22no—
121#551—24no—
122#551—24no—
123#551—24no—
124#551—24no—
125#551—24no—
126#551—24no—
127#551—24no—
128#551—24no—
129D4×Q8—22no—
130D4×Q8—21no—
131D4×Q8—22no—
132D4×Q8—21no—
133D4×Q8—21no—
134D4×Q8—21no—
135#548—22no—
136#548—22no—
137#548—22no—
138#548—22no—
139#548—22no—
140#548—22no—
141#548—22no—
142#548—22no—
143#547—22no—
144#547—21no—
145#547—21no—
146#547—22no—
147#547—21no—
148#547—21no—
149#547—21no—
150#547—21no—
151#547—22no—
152#547—21no—
153#547—21no—
154#547—22no—
155#546—22no—
156#546—22no—
157#546—24no—
158#546—24no—
159#546—22no—
160#546—22no—
161#542—22no—
162#542—22no—
163#542—22no—
164#542—22no—
165#542—24no—
166#542—24no—
167#539—24no—
168#539—24no—
169#539—24no—
170#539—24no—
171#539—24no—
172#539—24no—
173#539—24no—
174#539—24no—
175#533—21no—
176#533—21no—
177#533—21no—
178#533—21no—
179#533—21no—
180#533—21no—
181#533—21no—
182#533—21no—
183C2×C4⋊Q8C2×C411yescharacteristic, complemented
184C2×C4⋊Q8C2×C411yescharacteristic, complemented
185C2×C4⋊Q8C2×C412yescomplemented
186#529—21no—
187#529—21no—
188#529—21no—
189#529—21no—
190#529—21no—
191#529—21no—
192#529—21no—
193#529—21no—
194C2×#126C2×C412yescomplemented
195C2×#126C2×C414yescomplemented
196C2×#126C2×C414yescomplemented
197C2×#125C2×C411yescharacteristic, complemented
198C2×#125C2×C412yescomplemented
199C2×#125C2×C414yescomplemented
200C2×#124C2×C412yes—
201C2×#124C2×C411yescharacteristic, complemented
202C2×#124C2×C414yescomplemented
203#525—22no—
204#525—22no—
205#525—22no—
206#525—22no—
207#525—22no—
208#525—22no—
209#525—22no—
210#525—22no—
211C2×#123C2×C414yes—
212C2×#123C2×C414yescomplemented
213C2×#123C2×C414yescomplemented
214C2×#123C2×C414yescomplemented
215C2×#123C2312yes—
216C2×C22⋊Q8—22no—
217C2×C22⋊Q8—22no—
218C2×C22⋊Q8—22no—
219C2×C22⋊Q8—22no—
220C2×C22⋊Q8—22no—
221C2×C22⋊Q8—22no—
222C2×C22⋊Q8—22no—
223C2×C22⋊Q8—22no—
224C2×C22⋊Q8C2×C414yescomplemented
225C2×C22⋊Q8C2×C412yescomplemented
226C2×C22⋊Q8C2×C412yescomplemented
227C2×C22⋊Q8C2×C412yescomplemented
228C2×C22⋊Q8C2×C414yescomplemented
229C2×C22⋊Q8C2×C414yescomplemented
230C2×C22⋊Q8C2×C412yescomplemented
231C2×C22⋊Q8C2311yescharacteristic
232C2×C22⋊Q8C2312yes—
233C2×C22⋊Q8C2314yes—
234C2×C22⋊Q8C2312yes—
235C2×#121C2×C414yes—
236C2×#121C2×C412yes—
237C2×#121C2×C412yescomplemented
238C2×#121C2311yescharacteristic
239C2×#120C2314yes—
240#520—24no—
241#520—22no—
242#520—24no—
243#520—22no—
244#520—22no—
245#520—22no—
246C2×C4×Q8C2×C412yescomplemented
247C2×C4×Q8C2×C412yescomplemented
248C2×C4×Q8C2×C411yescharacteristic, complemented
249C2×C4×Q8C2×C412yescomplemented
250C2×C4×D4—22no—
251C2×C4×D4—22no—
252C2×C4×D4C2×C412yes—
253C2×C4×D4C2×C411yescharacteristic
254C2×C4×D4C2×C412yes—
255C2×C4×D4C2×C411yescharacteristic
256C2×C4×D4C2×C411yescharacteristic
257C2×C4×D4C2×C411yescharacteristic
258C2×C4×D4C2×C412yes—
259C2×C4×D4C2×C414yescomplemented
260C2×C4×D4C2×C414yescomplemented
261C2×C4×D4C2×C411yescharacteristic, complemented
262C2×C4×D4D412yes—
263C2×C4×D4D411yescharacteristic
264C2×C4×D4D411yescharacteristic
265C2×C4×D4D411yescharacteristic
266C2×C4×D4D412yes—
267C2×C4×D4D412yes—
268C2×C4×D4D411yescharacteristic
269C2×C4×D4D411yescharacteristic
270C2×C4×D4D411yescharacteristic
271C2×C4×D4D411yescharacteristic
272C2×C4×D4D412yes—
273C2×C4×D4D411yescharacteristic
274C2×C4×D4C2314yes—
275C2×C4×D4C2312yes—
276C2×#117—22no—
277C2×#117—22no—
278C2×#117C2×C412yescomplemented
279C2×#117C2×C414yescomplemented
280C2×#117C2×C412yescomplemented
281C2×#117C2312yes—
282C2×#117C2312yes—
283C2×#117C2312yes—
284C22×C4⋊C4—22no—
285C22×C4⋊C4C2×C414yescomplemented
286C22×C4⋊C4C2×C412yescomplemented
287C22×C4⋊C4C2×C412yescomplemented
288C22×C4⋊C4C2311yescharacteristic
289C22×C22⋊C4C2314yes—
290C22×C22⋊C4C2314yes—
291C22×C22⋊C4C2314yes—
292C22×C22⋊C4C2312yes—
293C22×C42—22no—
294C22×C42C2311yescharacteristic
295C2×#99C2314yes—
296C2×#99C2314yes—
297C2×#99C2318yes—
298#390—22no—
299#390—22no—
300#389—22no—
301#389—22no—
302#388—24no—
303#388—24no—
304#388—24no—
305#388—24no—
306#387—24no—
307#387—24no—
308#386—24no—
309#386—24no—
310#385—24no—
311#385—24no—
312#384—21no—
313#383—21no—
314#383—21no—
315#382—21no—
316#382—21no—
317#382—21no—
318#381—22no—
319#381—22no—
320#381C2312yes—
321#381C2312yes—
322#380—22no—
323#380—22no—
324#380—22no—
325#380—22no—
326#380C2312yes—
327#380C2312yes—
328#380C2314yes—
329#380C2314yes—
330#380C2311yescharacteristic
331#380C2312yes—
332#380C2311yescharacteristic
333#379C2314yes—
334#379C2314yes—
335C4×C4⋊C4—22no—
336C4×C4⋊C4—22no—
337C4×C4⋊C4—21no—
338C4×C4⋊C4—21no—
339C4×C4⋊C4—21no—
340C4×C4⋊C4—21no—
341C4×C4⋊C4—21no—
342C4×C4⋊C4—21no—
343C4×C22⋊C4—22no—
344C4×C22⋊C4—22no—
345C4×C22⋊C4—22no—
346C4×C22⋊C4—22no—
347C4×C22⋊C4—24no—
348C4×C22⋊C4—24no—
349C4×C22⋊C4C2312yes—
350C4×C22⋊C4C2312yes—
351C4×C22⋊C4C2314yes—
352C4×C22⋊C4C2314yes—
353C4×C22⋊C4C2311yescharacteristic
354C4×C22⋊C4C2312yes—
355C4×C22⋊C4C2311yescharacteristic
356#376—21no—
357#376—21no—
358#376—21no—
359C2×#95—22no—
360C2×#95—22no—
361C43—21no—
362#342C2318yes—
363#342C2318yes—
364#342C2318yes—
365#342C2314yes—
366#342C2318yes—
367#342C2318yes—
368#342C2314yes—
369C25C2412yes—
370C2×#41—22no—
371C2×#41—24no—
372C2×#41—22no—
373C2×#41—22no—
374C2×#41—22no—
375C2×#41—22no—
376C2×#41—22no—
377C2×#41—48no—
378C2×#41—84no—
379C22×Q8—22no—
380C22×Q8—22no—
381C22×Q8—22no—
382C22×Q8—22no—
383C22×Q8—84no—
384C22×Q8C22×C412yes—
385C22×Q8C22×C411yescharacteristic
386C22×Q8C22×C412yes—
387C22×Q8C22×C414yes—
388C22×D4—44no—
389C22×D4C22×C411yescharacteristic
390C22×D4C22×C414yes—
391C22×D4C22×C411yescharacteristic
392C22×D4C22×C414yes—
393C22×D4C22×C412yes—
394C22×D4C22×C411yescharacteristic
395C22×D4C2×D411yescharacteristic
396C22×D4C2×D411yescharacteristic
397C22×D4C2×D412yes—
398C22×D4C2×D412yes—
399C22×D4C2×D411yescharacteristic
400C22×D4C2×D411yescharacteristic
401C22×D4C2412yes—
402C23×C4—24no—
403C23×C4—24no—
404C23×C4—84no—
405C23×C4C22×C414yes—
406C23×C4C22×C412yes—
407C23×C4C22×C414yes—
408C23×C4C22×C414yes—
409C23×C4C22×C412yes—
410C23×C4C22×C412yes—
411C23×C4C22×C412yes—
412C23×C4C22×C412yes—
413C23×C4C2×D412yes—
414C23×C4C2×D412yes—
415C23×C4C2×D412yes—
416C23×C4C2×D412yes—
417C23×C4C2×D412yes—
418C23×C4C2×D412yes—
419C23×C4C2×D412yes—
420C23×C4C2×D412yes—
421C23×C4C2411yescharacteristic
422C23×C4C2411yescharacteristic
423C23×C4C2411yescharacteristic
424C23×C4C2412yes—
425C4⋊Q8—24no—
426C4⋊Q8—22no—
427C4⋊Q8—22no—
428C4⋊Q8—21no—
429C4⋊Q8—21no—
430C4⋊Q8—21no—
431C4⋊Q8—21no—
432C4⋊Q8—21no—
433C4⋊Q8—21no—
434C4⋊Q8—21no—
435C4⋊Q8—21no—
436#126—24no—
437#126—24no—
438#126—24no—
439#126—24no—
440#126—24no—
441#126—24no—
442#126—24no—
443#126—24no—
444#126—22no—
445#126—22no—
446#126—22no—
447#126—22no—
448#125—24no—
449#125—24no—
450#125—24no—
451#125—24no—
452#125—21no—
453#125—21no—
454#125—21no—
455#125—21no—
456#125—22no—
457#125—22no—
458#125—22no—
459#125—22no—
460#124—22no—
461#124—22no—
462#124—24no—
463#124—24no—
464#124—24no—
465#124—24no—
466#124—24no—
467#124—21no—
468#124—21no—
469#124—21no—
470#124—21no—
471#123—24no—
472#123—24no—
473#123—24no—
474#123—24no—
475#123—24no—
476#123—24no—
477#123—24no—
478#123—24no—
479#123—22no—
480#123—22no—
481#123—22no—
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—
491C22⋊Q8—24no—
492C22⋊Q8—24no—
493C22⋊Q8—24no—
494C22⋊Q8—24no—
495C22⋊Q8—22no—
496C22⋊Q8—22no—
497C22⋊Q8—22no—
498C22⋊Q8—22no—
499C22⋊Q8—22no—
500C22⋊Q8—22no—
501C22⋊Q8—22no—
502C22⋊Q8—22no—
503C22⋊Q8—22no—
504C22⋊Q8—22no—
505C22⋊Q8—22no—
506C22⋊Q8—22no—
507C22⋊Q8—21no—
508C22⋊Q8—21no—
509C22⋊Q8—21no—
510C22⋊Q8—21no—
511C22⋊Q8—22no—
512C22⋊Q8—22no—
513C22⋊Q8—22no—
514C22⋊Q8—22no—
515C22⋊Q8—24no—
516C22⋊Q8—24no—
517C22⋊Q8—24no—
518C22⋊Q8—24no—
519C22⋊Q8—22no—
520C22⋊Q8—22no—
521C22⋊Q8—22no—
522C22⋊Q8—22no—
523C22⋊Q8—24no—
524C22⋊Q8—24no—
525C22⋊Q8—24no—
526C22⋊Q8—24no—
527C22⋊Q8—24no—
528C22⋊Q8—22no—
529C22⋊Q8—22no—
530C22⋊Q8—24no—
531C22⋊Q8—24no—
532C22⋊Q8—24no—
533C22⋊Q8—24no—
534#121—24no—
535#121—24no—
536#121—24no—
537#121—24no—
538#121—22no—
539#121—22no—
540#121—24no—
541#121—22no—
542#121—22no—
543#121—22no—
544#121—22no—
545#121—21no—
546#121—21no—
547#121—21no—
548#121—21no—
549#120—24no—
550#120—24no—
551#120—24no—
552#120—24no—
553C4×Q8—24no—
554C4×Q8—22no—
555C4×Q8—22no—
556C4×Q8—22no—
557C4×Q8—22no—
558C4×Q8—22no—
559C4×Q8—22no—
560C4×Q8—21no—
561C4×Q8—21no—
562C4×Q8—21no—
563C4×Q8—21no—
564C4×Q8—22no—
565C4×Q8—22no—
566C4×Q8—22no—
567C4×Q8—22no—
568C4×D4—24no—
569C4×D4—22no—
570C4×D4—22no—
571C4×D4—24no—
572C4×D4—24no—
573C4×D4—24no—
574C4×D4—24no—
575C4×D4—24no—
576C4×D4—24no—
577C4×D4—24no—
578C4×D4—24no—
579C4×D4—22no—
580C4×D4—22no—
581C4×D4—22no—
582C4×D4—22no—
583C4×D4—24no—
584C4×D4—24no—
585C4×D4—24no—
586C4×D4—24no—
587C4×D4—21no—
588C4×D4—21no—
589C4×D4—21no—
590C4×D4—21no—
591C4×D4—48no—
592C4×D4—48no—
593C4×D4C22⋊C412yes—
594C4×D4C22⋊C411yescharacteristic
595C4×D4C22⋊C412yes—
596C4×D4C22⋊C411yescharacteristic
597C4×D4C22⋊C411yescharacteristic
598C4×D4C22⋊C411yescharacteristic
599C4×D4C22⋊C412yes—
600C4×D4C22⋊C412yes—
601C4×D4C22⋊C412yes—
602C4×D4C22⋊C412yes—
603C4×D4C22⋊C412yes—
604C4×D4C22⋊C412yes—
605C4×D4C22⋊C412yes—
606C4×D4C22⋊C412yes—
607C4×D4C22⋊C411yescharacteristic
608C4×D4C22⋊C411yescharacteristic
609C4×D4C22⋊C411yescharacteristic
610C4×D4C22⋊C411yescharacteristic
611C4×D4C22⋊C412yes—
612C4×D4C22⋊C412yes—
613C4×D4C22⋊C412yes—
614C4×D4C22⋊C411yescharacteristic
615C4×D4C22⋊C411yescharacteristic
616C4×D4C22⋊C412yes—
617C4×D4C22⋊C411yescharacteristic
618C4×D4C22⋊C411yescharacteristic
619C4×D4C22⋊C411yescharacteristic
620C4×D4C22⋊C411yescharacteristic
621C4×D4C22⋊C412yes—
622C4×D4C22⋊C411yescharacteristic
623C4×D4C22⋊C411yescharacteristic
624C4×D4C22⋊C412yes—
625C4×D4C22⋊C412yes—
626C4×D4C22⋊C412yes—
627C4×D4C22⋊C412yes—
628C4×D4C22⋊C412yes—
629C4×D4C22⋊C412yes—
630C4×D4C22⋊C412yes—
631C4×D4C22⋊C412yes—
632C4×D4C22⋊C412yes—
633#117—22no—
634#117—22no—
635#117—22no—
636#117—22no—
637#117—22no—
638#117—22no—
639#117—22no—
640#117—22no—
641#117—24no—
642#117—24no—
643#117—24no—
644#117—24no—
645#117—22no—
646#117—22no—
647#117—22no—
648#117—22no—
649#117—24no—
650#117—42no—
651#117—44no—
652#117—84no—
653#117—84no—
654C2×C4⋊C4—24no—
655C2×C4⋊C4—24no—
656C2×C4⋊C4—24no—
657C2×C4⋊C4—24no—
658C2×C4⋊C4—22no—
659C2×C4⋊C4—22no—
660C2×C4⋊C4—22no—
661C2×C4⋊C4—22no—
662C2×C4⋊C4—24no—
663C2×C4⋊C4—22no—
664C2×C4⋊C4—22no—
665C2×C4⋊C4—21no—
666C2×C4⋊C4—22no—
667C2×C4⋊C4—21no—
668C2×C4⋊C4—22no—
669C2×C4⋊C4—22no—
670C2×C4⋊C4—22no—
671C2×C4⋊C4—24no—
672C2×C4⋊C4—24no—
673C2×C4⋊C4—22no—
674C2×C4⋊C4—84no—
675C2×C4⋊C4C22×C412yes—
676C2×C4⋊C4C22×C414yes—
677C2×C4⋊C4C22×C411yescharacteristic
678C2×C4⋊C4C22×C412yes—
679C2×C4⋊C4C22×C412yes—
680C2×C4⋊C4C22×C414yes—
681C2×C4⋊C4C22×C414yes—
682C2×C4⋊C4C22×C414yes—
683C2×C4⋊C4C22×C412yes—
684C2×C4⋊C4C22×C411yescharacteristic
685C2×C4⋊C4C22×C412yes—
686C2×C4⋊C4C22×C412yes—
687C2×C4⋊C4C22×C414yes—
688C2×C4⋊C4C22×C412yes—
689C2×C4⋊C4C22×C414yes—
690C2×C4⋊C4C22×C412yes—
691C2×C4⋊C4C22×C411yescharacteristic
692C2×C4⋊C4C22×C412yes—
693C2×C4⋊C4C22×C411yescharacteristic
694C2×C4⋊C4C2×D411yescharacteristic
695C2×C4⋊C4C2×D411yescharacteristic
696C2×C4⋊C4C2×D412yes—
697C2×C4⋊C4C2×D412yes—
698C2×C4⋊C4C2×D411yescharacteristic
699C2×C4⋊C4C2×D411yescharacteristic
700C2×C22⋊C4—24no—
701C2×C22⋊C4—24no—
702C2×C22⋊C4—24no—
703C2×C22⋊C4—24no—
704C2×C22⋊C4—28no—
705C2×C22⋊C4—24no—
706C2×C22⋊C4—24no—
707C2×C22⋊C4—24no—
708C2×C22⋊C4—24no—
709C2×C22⋊C4—24no—
710C2×C22⋊C4—24no—
711C2×C22⋊C4—44no—
712C2×C22⋊C4—48no—
713C2×C22⋊C4C22×C414yes—
714C2×C22⋊C4C22×C414yes—
715C2×C22⋊C4C22×C414yes—
716C2×C22⋊C4C22×C412yes—
717C2×C22⋊C4C22×C412yes—
718C2×C22⋊C4C22×C414yes—
719C2×C22⋊C4C22×C412yes—
720C2×C22⋊C4C22×C412yes—
721C2×C22⋊C4C22×C414yes—
722C2×C22⋊C4C22×C412yes—
723C2×C22⋊C4C22×C412yes—
724C2×C22⋊C4C22×C412yes—
725C2×C22⋊C4C22×C412yes—
726C2×C22⋊C4C2×D412yes—
727C2×C22⋊C4C2×D412yes—
728C2×C22⋊C4C2×D412yes—
729C2×C22⋊C4C2×D412yes—
730C2×C22⋊C4C2×D412yes—
731C2×C22⋊C4C2×D412yes—
732C2×C22⋊C4C2×D412yes—
733C2×C22⋊C4C2×D412yes—
734C2×C22⋊C4C2412yes—
735C2×C22⋊C4C2414yes—
736C2×C22⋊C4C2414yes—
737C2×C22⋊C4C2412yes—
738C2×C22⋊C4C2412yes—
739C2×C22⋊C4C2412yes—
740C2×C22⋊C4C2414yes—
741C2×C22⋊C4C2412yes—
742C2×C42—21no—
743C2×C42—22no—
744C2×C42—22no—
745C2×C42—22no—
746C2×C42—22no—
747C2×C42—21no—
748C2×C42—24no—
749C2×C42—22no—
750C2×C42—24no—
751C2×C42—84no—
752C2×C42C22×C414yes—
753C2×C42C22×C414yes—
754C2×C42C22×C412yes—
755C2×C42C22×C411yescharacteristic
756C2×C42C22×C411yescharacteristic
757C2×C42C22×C411yescharacteristic
758C2×C42C22×C411yescharacteristic
759C2×C42C2×D411yescharacteristic
760C2×C42C2×D411yescharacteristic
761C2×C42C2×D411yescharacteristic
762C2×C42C2×D411yescharacteristic
763C2×C42C2×D411yescharacteristic
764C2×C42C2×D411yescharacteristic
765C2×C42C2×D411yescharacteristic
766C2×C42C2×D411yescharacteristic
767#99—28no—
768#99—48no—
769#99—44no—
770#95—21no—
771#95—21no—
772#95—22no—
773#95—24no—
774#95—22no—
775#95—24no—
776#95—21no—
777#95—22no—
778#95—21no—
779#95—22no—
780#95—22no—
781#95—22no—
782#95—24no—
783#95—22no—
784#95—24no—
785#95—22no—
786#95—22no—
787#95—22no—
788C24—24no—
789C24—24no—
790C24—44no—
791C24—82no—
792C24C23×C412yes—
793C24C23×C412yes—
794C24C23×C412yes—
795C24C22×D412yes—
796C24C22×D412yes—
797C24C22×D412yes—
798C24C22×D412yes—
799C24C2511yescharacteristic
800#41—416no—
801#41—48no—
802#41—48no—
803#41—84no—
804#41—84no—
805#41—84no—
806#41—84no—
807C2×Q8—22no—
808C2×Q8—22no—
809C2×Q8—21no—
810C2×Q8—21no—
811C2×Q8—22no—
812C2×Q8—22no—
813C2×Q8—24no—
814C2×Q8—24no—
815C2×Q8—42no—
816C2×Q8—44no—
817C2×Q8—44no—
818C2×Q8—84no—
819C2×Q8—84no—
820C2×Q8—84no—
821C2×Q8—84no—
822C2×Q8—84no—
823C2×D4—24no—
824C2×D4—24no—
825C2×D4—24no—
826C2×D4—24no—
827C2×D4—24no—
828C2×D4—22no—
829C2×D4—22no—
830C2×D4—24no—
831C2×D4—24no—
832C2×D4—24no—
833C2×D4—24no—
834C2×D4—21no—
835C2×D4—21no—
836C2×D4—42no—
837C2×D4—42no—
838C2×D4—42no—
839C2×D4—42no—
840C2×D4—44no—
841C2×D4—44no—
842C2×D4—44no—
843C2×D4—48no—
844C2×D4—84no—
845C2×D4C2×C22⋊C412yes—
846C2×D4C2×C22⋊C411yescharacteristic
847C2×D4C2×C22⋊C412yes—
848C2×D4C2×C22⋊C412yes—
849C2×D4C2×C22⋊C411yescharacteristic
850C2×D4C2×C22⋊C411yescharacteristic
851C2×D4C2×C22⋊C412yes—
852C2×D4C2×C22⋊C412yes—
853C2×D4C2×C22⋊C412yes—
854C2×D4C2×C22⋊C411yescharacteristic
855C22×C4—22no—
856C22×C4—22no—
857C22×C4—24no—
858C22×C4—24no—
859C22×C4—22no—
860C22×C4—24no—
861C22×C4—24no—
862C22×C4—22no—
863C22×C4—22no—
864C22×C4—24no—
865C22×C4—24no—
866C22×C4—22no—
867C22×C4—24no—
868C22×C4—22no—
869C22×C4—22no—
870C22×C4—24no—
871C22×C4—44no—
872C22×C4—44no—
873C22×C4—44no—
874C22×C4—44no—
875C22×C4—42no—
876C22×C4—44no—
877C22×C4—44no—
878C22×C4—42no—
879C22×C4—44no—
880C22×C4—48no—
881C22×C4—48no—
882C22×C4—48no—
883C22×C4—48no—
884C22×C4—82no—
885C22×C4—82no—
886C22×C4—82no—
887C22×C4—82no—
888C22×C4—82no—
889C22×C4—82no—
890C22×C4—82no—
891C22×C4—84no—
892C22×C4—84no—
893C22×C4—84no—
894C22×C4—84no—
895C22×C4—84no—
896C22×C4C2×C22⋊C412yes—
897C22×C4C2×C22⋊C412yes—
898C22×C4C2×C22⋊C412yes—
899C22×C4C2×C22⋊C412yes—
900C22×C4C2×C22⋊C412yes—
901C22×C4C2×C22⋊C412yes—
902C22×C4C2×C22⋊C412yes—
903C22×C4C2×C22⋊C412yes—
904C22×C4C2×C22⋊C412yes—
905C22×C4C2×C22⋊C412yes—
906C22×C4C2×C22⋊C412yes—
907C22×C4C2×C22⋊C412yes—
908C22×C4C2×C22⋊C412yes—
909C22×C4C2×C22⋊C412yes—
910C22×C4C2×C22⋊C412yes—
911C22×C4C2×C22⋊C412yes—
912C22×C4C23×C412yes—
913C22×C4C23×C411yescharacteristic
914C22×C4C23×C411yescharacteristic
915C22×C4C23×C411yescharacteristic
916C22×C4C23×C411yescharacteristic
917C22×C4C23×C414yes—
918C22×C4C23×C412yes—
919C22×C4C23×C414yes—
920C22×C4C23×C412yes—
921C22×C4C23×C411yescharacteristic
922C22×C4C23×C412yes—
923C22×C4C23×C411yescharacteristic
924C22×C4C23×C412yes—
925C22×C4C22×D411yescharacteristic
926C22×C4C22×D411yescharacteristic
927C22×C4C22×D411yescharacteristic
928C22×C4C22×D411yescharacteristic
929C22×C4C22×D411yescharacteristic
930C22×C4C22×D411yescharacteristic
931C22×C4C22×D411yescharacteristic
932C22×C4C22×D411yescharacteristic
933C22×C4C22×D411yescharacteristic
934C22×C4C22×D411yescharacteristic
935C22×C4C22×D411yescharacteristic
936C22×C4C22×D411yescharacteristic
937C22×C4C22×D412yes—
938C22×C4C22×D412yes—
939C22×C4C22×D412yes—
940C22×C4C22×D412yes—
941C4⋊C4—22no—
942C4⋊C4—22no—
943C4⋊C4—24no—
944C4⋊C4—24no—
945C4⋊C4—21no—
946C4⋊C4—21no—
947C4⋊C4—22no—
948C4⋊C4—22no—
949C4⋊C4—22no—
950C4⋊C4—22no—
951C4⋊C4—24no—
952C4⋊C4—24no—
953C4⋊C4—24no—
954C4⋊C4—24no—
955C4⋊C4—24no—
956C4⋊C4—24no—
957C4⋊C4—22no—
958C4⋊C4—22no—
959C4⋊C4—21no—
960C4⋊C4—21no—
961C4⋊C4—22no—
962C4⋊C4—22no—
963C4⋊C4—22no—
964C4⋊C4—22no—
965C4⋊C4—24no—
966C4⋊C4—24no—
967C4⋊C4—22no—
968C4⋊C4—22no—
969C4⋊C4—24no—
970C4⋊C4—24no—
971C4⋊C4—22no—
972C4⋊C4—22no—
973C4⋊C4—44no—
974C4⋊C4—42no—
975C4⋊C4—44no—
976C4⋊C4—42no—
977C4⋊C4—44no—
978C4⋊C4—44no—
979C4⋊C4—82no—
980C4⋊C4—84no—
981C4⋊C4—84no—
982C4⋊C4C2×C22⋊C412yes—
983C4⋊C4C2×C22⋊C411yescharacteristic
984C4⋊C4C2×C22⋊C411yescharacteristic
985C4⋊C4C2×C22⋊C412yes—
986C4⋊C4C2×C22⋊C412yes—
987C4⋊C4C2×C22⋊C412yes—
988C4⋊C4C2×C22⋊C412yes—
989C4⋊C4C2×C22⋊C412yes—
990C4⋊C4C2×C22⋊C411yescharacteristic
991C4⋊C4C2×C22⋊C411yescharacteristic
992C22⋊C4—24no—
993C22⋊C4—24no—
994C22⋊C4—24no—
995C22⋊C4—24no—
996C22⋊C4—24no—
997C22⋊C4—24no—
998C22⋊C4—24no—
999C22⋊C4—24no—
1000C22⋊C4—22no—
1001C22⋊C4—22no—
1002C22⋊C4—24no—
1003C22⋊C4—24no—
1004C22⋊C4—22no—
1005C22⋊C4—22no—
1006C22⋊C4—22no—
1007C22⋊C4—22no—
1008C22⋊C4—22no—
1009C22⋊C4—22no—
1010C22⋊C4—22no—
1011C22⋊C4—24no—
1012C22⋊C4—24no—
1013C22⋊C4—22no—
1014C22⋊C4—22no—
1015C22⋊C4—24no—
1016C22⋊C4—24no—
1017C22⋊C4—22no—
1018C22⋊C4—24no—
1019C22⋊C4—22no—
1020C22⋊C4—24no—
1021C22⋊C4—28no—
1022C22⋊C4—48no—
1023C22⋊C4—48no—
1024C22⋊C4—48no—
1025C22⋊C4—84no—
1026C22⋊C4—84no—
1027C22⋊C4—84no—
1028C22⋊C4C2×C22⋊C412yes—
1029C22⋊C4C2×C22⋊C412yes—
1030C22⋊C4C2×C22⋊C412yes—
1031C22⋊C4C2×C22⋊C412yes—
1032C22⋊C4C2×C22⋊C412yes—
1033C22⋊C4C2×C22⋊C412yes—
1034C22⋊C4C2×C22⋊C412yes—
1035C22⋊C4C2×C22⋊C412yes—
1036C22⋊C4C2×C22⋊C412yes—
1037C22⋊C4C2×C22⋊C412yes—
1038C22⋊C4C2×C22⋊C412yes—
1039C22⋊C4C2×C22⋊C412yes—
1040C22⋊C4C2×C22⋊C412yes—
1041C22⋊C4C2×C22⋊C412yes—
1042C22⋊C4C2×C22⋊C412yes—
1043C22⋊C4C2×C22⋊C412yes—
1044C22⋊C42−1+414yes—
1045C42—24no—
1046C42—24no—
1047C42—24no—
1048C42—24no—
1049C42—22no—
1050C42—22no—
1051C42—44no—
1052C42—42no—
1053C42—44no—
1054C42—42no—
1055C42—44no—
1056C42—44no—
1057C42—82no—
1058C42—84no—
1059C42—84no—
1060C42C2×C22⋊C411yescharacteristic
1061C42C2×C22⋊C411yescharacteristic
1062C42C2×C22⋊C411yescharacteristic
1063C42C2×C22⋊C411yescharacteristic
1064C42C2×C22⋊C411yescharacteristic
1065C42C2×C22⋊C411yescharacteristic
1066C42C2×C22⋊C411yescharacteristic
1067C42C2×C22⋊C411yescharacteristic
1068C42C2×C22⋊C411yescharacteristic
1069C42C2×C22⋊C411yescharacteristic
1070C42C2×C22⋊C411yescharacteristic
1071C42C2×C22⋊C411yescharacteristic
1072C42C2×C22⋊C411yescharacteristic
1073C42C2×C22⋊C411yescharacteristic
1074C42C2×C22⋊C411yescharacteristic
1075C42C2×C22⋊C411yescharacteristic
1076C23—24no—
1077C23—24no—
1078C23—24no—
1079C23—24no—
1080C23—24no—
1081C23—22no—
1082C23—22no—
1083C23—24no—
1084C23—24no—
1085C23—22no—
1086C23—22no—
1087C23—22no—
1088C23—24no—
1089C23—42no—
1090C23—42no—
1091C23—42no—
1092C23—41no—
1093C23—41no—
1094C23—42no—
1095C23—42no—
1096C23—42no—
1097C23—42no—
1098C23—42no—
1099C23—42no—
1100C23—42no—
1101C23—42no—
1102C23—88no—
1103C23—88no—
1104C23C22×C22⋊C412yes—
1105C23C22×C22⋊C412yes—
1106C23C22×C22⋊C412yes—
1107C23C22×C22⋊C412yes—
1108C23C24×C411yescharacteristic
1109C23C23×D411yescharacteristic
1110C23C23×D411yescharacteristic
1111C23C2×2−1+412yes—
1112C23#58512yes—
1113Q8—42no—
1114Q8—44no—
1115Q8—44no—
1116Q8—44no—
1117Q8—42no—
1118Q8—44no—
1119Q8—84no—
1120Q8—84no—
1121D4—24no—
1122D4—24no—
1123D4—24no—
1124D4—22no—
1125D4—22no—
1126D4—22no—
1127D4—42no—
1128D4—42no—
1129D4—42no—
1130D4—42no—
1131D4—48no—
1132D4—48no—
1133D4—44no—
1134D4—42no—
1135D4—42no—
1136D4—42no—
1137D4—84no—
1138D4—84no—
1139D4#41014yes—
1140C2×C4—22no—
1141C2×C4—22no—
1142C2×C4—22no—
1143C2×C4—22no—
1144C2×C4—21no—
1145C2×C4—21no—
1146C2×C4—21no—
1147C2×C4—21no—
1148C2×C4—22no—
1149C2×C4—22no—
1150C2×C4—22no—
1151C2×C4—22no—
1152C2×C4—22no—
1153C2×C4—22no—
1154C2×C4—24no—
1155C2×C4—24no—
1156C2×C4—24no—
1157C2×C4—24no—
1158C2×C4—22no—
1159C2×C4—24no—
1160C2×C4—22no—
1161C2×C4—24no—
1162C2×C4—22no—
1163C2×C4—24no—
1164C2×C4—24no—
1165C2×C4—42no—
1166C2×C4—42no—
1167C2×C4—42no—
1168C2×C4—42no—
1169C2×C4—41no—
1170C2×C4—42no—
1171C2×C4—41no—
1172C2×C4—41no—
1173C2×C4—42no—
1174C2×C4—42no—
1175C2×C4—42no—
1176C2×C4—42no—
1177C2×C4—42no—
1178C2×C4—42no—
1179C2×C4—42no—
1180C2×C4—42no—
1181C2×C4—42no—
1182C2×C4—42no—
1183C2×C4—42no—
1184C2×C4—42no—
1185C2×C4—42no—
1186C2×C4—41no—
1187C2×C4—41no—
1188C2×C4—41no—
1189C2×C4—44no—
1190C2×C4—42no—
1191C2×C4—42no—
1192C2×C4—48no—
1193C2×C4—48no—
1194C2×C4—44no—
1195C2×C4—42no—
1196C2×C4—44no—
1197C2×C4—44no—
1198C2×C4—42no—
1199C2×C4—44no—
1200C2×C4—42no—
1201C2×C4—42no—
1202C2×C4—42no—
1203C2×C4—42no—
1204C2×C4—42no—
1205C2×C4—44no—
1206C2×C4—44no—
1207C2×C4—44no—
1208C2×C4—42no—
1209C2×C4—42no—
1210C2×C4—44no—
1211C2×C4—42no—
1212C2×C4—44no—
1213C2×C4—42no—
1214C2×C4—84no—
1215C2×C4—84no—
1216C2×C4—84no—
1217C2×C4—84no—
1218C2×C4—816no—
1219C2×C4—168no—
1220C2×C4C22×C22⋊C411yescharacteristic
1221C2×C4C22×C22⋊C411yescharacteristic
1222C2×C4C22×C22⋊C411yescharacteristic
1223C2×C4C22×C22⋊C412yes—
1224C2×C4C22×C22⋊C412yes—
1225C2×C4C22×C22⋊C411yescharacteristic
1226C2×C4C22×C22⋊C411yescharacteristic
1227C2×C4C22×C22⋊C411yescharacteristic
1228C2×C4C22×C22⋊C411yescharacteristic
1229C2×C4C22×C22⋊C411yescharacteristic
1230C2×C4C22×C22⋊C411yescharacteristic
1231C2×C4C22×C22⋊C411yescharacteristic
1232C2×C4C22×C22⋊C412yes—
1233C2×C4C22×C22⋊C412yes—
1234C2×C4C22×C22⋊C411yescharacteristic
1235C2×C4C22×C22⋊C411yescharacteristic
1236C22—21no—
1237C22—21no—
1238C22—21no—
1239C22—21no—
1240C22—21no—
1241C22—21no—
1242C22—22no—
1243C22—22no—
1244C22—22no—
1245C22—22no—
1246C22—22no—
1247C22—22no—
1248C22—22no—
1249C22—22no—
1250C22—22no—
1251C22—22no—
1252C22—22no—
1253C22—42no—
1254C22—42no—
1255C22—48no—
1256C22—44no—
1257C22—44no—
1258C22—48no—
1259C22—42no—
1260C22—42no—
1261C22—42no—
1262C22—84no—
1263C22—82no—
1264C22—82no—
1265C22—84no—
1266C22—84no—
1267C22C2×#41014yes—
1268C22C23×C22⋊C411yescharacteristic
1269C22C4×2−1+412yes—
1270C22#348912yes—
1271C22#349911yescharacteristic
1272C22#350011yescharacteristic
1273C4—21no—
1274C4—21no—
1275C4—21no—
1276C4—21no—
1277C4—21no—
1278C4—21no—
1279C4—22no—
1280C4—22no—
1281C4—22no—
1282C4—22no—
1283C4—21no—
1284C4—21no—
1285C4—21no—
1286C4—21no—
1287C4—44no—
1288C4—42no—
1289C4—44no—
1290C4—44no—
1291C4—42no—
1292C4—42no—
1293C4—82no—
1294C4—82no—
1295C4—84no—
1296C4—84no—
1297C4—82no—
1298C4C2×#41012yes—
1299C4#288312yes—
1300C2—22no—
1301C2—21no—
1302C2—21no—
1303C2—22no—
1304C2—24no—
1305C2—42no—
1306C2—42no—
1307C2—42no—
1308C2—82no—
1309C2#3425911yescharacteristic
1310C2C22×#41011yescharacteristic
1311C2C2×#288311yescharacteristic
subgroupG/H
center, socleC22C23×C22⋊C4
commutatorC23C24×C4
Frattini, cosocleC24C25
prime radicalC2×#3520C2
LCSG ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22 ◁ C22×C4×D4 ◁ G
LECSG ▷ C24 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #34194C2semidirect
3. #34126C2semidirect
4. #22513C2semidirect
5. #22477C2semidirect
6. #22476C2semidirect
7. #21875C2semidirect
8. #21874C2semidirect
9. #21826C2semidirect
10. #21825C2semidirect
11. #21421C2semidirect
12. #21420C2semidirect
13. #21332C2semidirect
14. C2×#1996C2semidirect
27. C2×#556C4semidirect
29. C2×#552C4semidirect
31. C2×D4×Q8C4semidirect
32. C2×#548C4semidirect
33. C2×#547C4semidirect
34. C2×#547C4semidirect
36. C2×#542C4semidirect
37. C2×#539C4semidirect
42. C2×#520C4semidirect
97. C22×#41C2×C4semidirect
98. C23×Q8C2×C4semidirect
183. C2×C4⋊Q8C2×C4semidirect
184. C2×C4⋊Q8C2×C4semidirect
185. C2×C4⋊Q8C2×C4semidirect
194. C2×#126C2×C4semidirect
195. C2×#126C2×C4semidirect
196. C2×#126C2×C4semidirect
197. C2×#125C2×C4semidirect
198. C2×#125C2×C4semidirect
199. C2×#125C2×C4semidirect
201. C2×#124C2×C4semidirect
202. C2×#124C2×C4semidirect
212. C2×#123C2×C4semidirect
213. C2×#123C2×C4semidirect
214. C2×#123C2×C4semidirect
224. C2×C22⋊Q8C2×C4semidirect
225. C2×C22⋊Q8C2×C4semidirect
226. C2×C22⋊Q8C2×C4semidirect
227. C2×C22⋊Q8C2×C4semidirect
228. C2×C22⋊Q8C2×C4semidirect
229. C2×C22⋊Q8C2×C4semidirect
230. C2×C22⋊Q8C2×C4semidirect
237. C2×#121C2×C4semidirect
246. C2×C4×Q8C2×C4semidirect
247. C2×C4×Q8C2×C4semidirect
248. C2×C4×Q8C2×C4semidirect
249. C2×C4×Q8C2×C4semidirect
259. C2×C4×D4C2×C4semidirect
260. C2×C4×D4C2×C4semidirect
261. C2×C4×D4C2×C4semidirect
278. C2×#117C2×C4semidirect
279. C2×#117C2×C4semidirect
280. C2×#117C2×C4semidirect
285. C22×C4⋊C4C2×C4semidirect
286. C22×C4⋊C4C2×C4semidirect
287. C22×C4⋊C4C2×C4semidirect

Maximal subgroups

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

subgroupindex
C2×#35202
#341942
#341262
#225132
#224772
#224762
#218752
#218742
#218262
#218252
#214212
#214202
#213322
C2×#19962