Finite Group Databasebeta

← #6343407

Subgroups — #6343407

Order 512.

3131 conjugacy classes of subgroups.

The subgroup lattice has 1261 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3520C211yesmaximal, characteristic
2#60230C211yesmaximal, characteristic, complemented
3#34190C211yesmaximal, characteristic, complemented
4#17600C214yesmaximal, complemented
5#17598C218yesmaximal, complemented
6#17590C211yesmaximal, characteristic, complemented
7#17587C212yesmaximal, complemented
8#17580C211yesmaximal, characteristic, complemented
9#17578C212yesmaximal, complemented
10#17562C211yesmaximal, characteristic, complemented
11#17559C212yesmaximal, complemented
12#17554C211yesmaximal, characteristic, complemented
13C2×#1511C212yesmaximal, complemented
14#17548C214yesmaximal, complemented
15#3520—21no—
16#3520—22no—
17#3520—21no—
18#3520—21no—
19#3520—22no—
20#3520—21no—
21#3520C412yescomplemented
22#3520C412yescomplemented
23#3520C414yescomplemented
24#3520C2212yes—
25#3520C2214yes—
26#3520C2212yes—
27C2×#556C411yescharacteristic, complemented
28C2×#554—21no—
29C2×#552C412yescomplemented
30C2×#551—22no—
31C2×D4×Q8C411yescharacteristic, complemented
32C2×#548C412yescomplemented
33C2×#547C411yescharacteristic, complemented
34C2×#547C411yescharacteristic, complemented
35C2×#546—21no—
36C2×#542—21no—
37C2×#539—22no—
38C2×#533C2211yescharacteristic
39C2×#529C2211yescharacteristic
40C2×#525C2212yes—
41C22×C22⋊Q8C2212yes—
42C2×#520—21no—
43C22×C4×D4C2211yescharacteristic
44#2975—21no—
45#2974C2212yescomplemented
46#2974C2214yescomplemented
47#2974C2212yescomplemented
48#2973—22no—
49#2972—21no—
50D4×M16—21no—
51D4×M16—22no—
52D4×M16—21no—
53#2920C2211yescharacteristic
54#2920C2211yescharacteristic
55C2×#407C2212yes—
56C2×#407C2212yes—
57#2357—21no—
58#2353—22no—
59#2349—21no—
60#2344—21no—
61#2342—22no—
62D4×C22⋊C4—21no—
63#2319C2212yescomplemented
64#2318C2214yescomplemented
65#2283C2211yescharacteristic
66#2283C2211yescharacteristic
67#2280C2212yes—
68C2×#381C2212yes—
69#2275C2212yescomplemented
70#1521C2214yescomplemented
71#1520C2218yescomplemented
72#1518C2214yescomplemented
73#1516C2218yescomplemented
74#1515C2214yescomplemented
75#1513C2218yescomplemented
76#1512C2214yescomplemented
77#1511C2211yescharacteristic
78#1511C2212yes—
79#1511C2212yes—
80#1511C2212yes—
81#1511C2211yescharacteristic
82#1511C2212yes—
83#1511C2212yes—
84#1511C2218yescomplemented
85#1510C2211yescharacteristic
86#1510C2211yescharacteristic
87#1510C2212yes—
88#1509C2214yescomplemented
89#1508C2218yescomplemented
90#1506C2214yescomplemented
91#1504C2218yescomplemented
92#1503C2214yescomplemented
93#1501C2218yescomplemented
94#1500C2214yescomplemented
95C2×#328C2218yescomplemented
96C22×#41—21no—
97C22×#41C2×C412yescomplemented
98C23×Q8C2×C412yescomplemented
99C23×D4D411yescharacteristic
100C24×C4C2312yes—
101C22×M16—22no—
102C22×M16—22no—
103#556—21no—
104#556—21no—
105#556—22no—
106#556C2×C412yes—
107#556C2×C414yescomplemented
108#556C2×C412yescomplemented
109#554—22no—
110#554—24no—
111#554—22no—
112#554—22no—
113#554—24no—
114#554—22no—
115#552—22no—
116#552—22no—
117#552—22no—
118#552—22no—
119#552C2×C414yes—
120#552C2×C414yescomplemented
121#552C2×C414yescomplemented
122#552C2×C414yescomplemented
123#551—24no—
124#551—24no—
125#551—24no—
126#551—24no—
127#551—24no—
128#551—24no—
129#551—24no—
130#551—24no—
131D4×Q8—21no—
132D4×Q8—22no—
133D4×Q8—21no—
134D4×Q8C2×C412yes—
135D4×Q8C2×C412yescomplemented
136D4×Q8C2×C414yescomplemented
137#548—22no—
138#548—22no—
139#548—22no—
140#548—22no—
141#548C2×C414yes—
142#548C2×C414yescomplemented
143#548C2×C414yescomplemented
144#548C2×C414yescomplemented
145#547—21no—
146#547—22no—
147#547—21no—
148#547—21no—
149#547—21no—
150#547—22no—
151#547C2×C412yes—
152#547C2×C412yes—
153#547C2×C412yescomplemented
154#547C2×C414yescomplemented
155#547C2×C414yescomplemented
156#547C2×C412yescomplemented
157#546—22no—
158#546—24no—
159#546—22no—
160#546—22no—
161#546—24no—
162#546—22no—
163#542—22no—
164#542—22no—
165#542—24no—
166#542—22no—
167#542—24no—
168#542—22no—
169#539—24no—
170#539—24no—
171#539—24no—
172#539—24no—
173#539—24no—
174#539—24no—
175#539—24no—
176#539—24no—
177#533—21no—
178#533—21no—
179#533—21no—
180#533—21no—
181#533C2×C412yescomplemented
182#533C2×C412yescomplemented
183#533C2312yes—
184#533C2312yes—
185C2×C4⋊Q8—21no—
186C2×C4⋊Q8C2×C411yescharacteristic, complemented
187C2×C4⋊Q8C2×C411yescharacteristic, complemented
188#529—21no—
189#529—21no—
190#529—21no—
191#529—21no—
192#529C2×C412yescomplemented
193#529C2×C412yescomplemented
194#529C2312yes—
195#529C2312yes—
196C2×#126—22no—
197C2×#126—22no—
198C2×#126—21no—
199C2×#125—22no—
200C2×#125—21no—
201C2×#125C2×C411yescharacteristic, complemented
202C2×#124—21no—
203C2×#124—22no—
204C2×#124C2×C411yescharacteristic, complemented
205#525—22no—
206#525—22no—
207#525—22no—
208#525—22no—
209#525C2×C414yescomplemented
210#525C2×C414yescomplemented
211#525C2314yes—
212#525C2314yes—
213C2×#123—22no—
214C2×#123—22no—
215C2×#123—21no—
216C2×#123—22no—
217C2×#123—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⋊Q8—21no—
225C2×C22⋊Q8—22no—
226C2×C22⋊Q8—21no—
227C2×C22⋊Q8—22no—
228C2×C22⋊Q8C2×C412yescomplemented
229C2×C22⋊Q8C2×C412yescomplemented
230C2×C22⋊Q8C2×C414yescomplemented
231C2×C22⋊Q8C2×C414yescomplemented
232C2×C22⋊Q8C2×C412yescomplemented
233C2×C22⋊Q8C2311yescharacteristic
234C2×C22⋊Q8C2312yes—
235C2×C22⋊Q8C2314yes—
236C2×C22⋊Q8C2314yes—
237C2×#121—22no—
238C2×#121—21no—
239C2×#121C2×C412yescomplemented
240C2×#121C2311yescharacteristic
241C2×#120—22no—
242#520—22no—
243#520—24no—
244#520—22no—
245#520—22no—
246#520—24no—
247#520—22no—
248C2×C4×Q8—21no—
249C2×C4×Q8—21no—
250C2×C4×Q8C2×C411yescharacteristic, complemented
251C2×C4×Q8C2×C412yescomplemented
252C2×C4×D4—21no—
253C2×C4×D4—22no—
254C2×C4×D4—22no—
255C2×C4×D4—21no—
256C2×C4×D4—22no—
257C2×C4×D4—22no—
258C2×C4×D4C2×C411yescharacteristic
259C2×C4×D4C2×C411yescharacteristic
260C2×C4×D4C2×C412yes—
261C2×C4×D4C2×C411yescharacteristic
262C2×C4×D4C2×C411yescharacteristic
263C2×C4×D4C2×C412yes—
264C2×C4×D4C2×C411yescharacteristic, complemented
265C2×C4×D4D411yescharacteristic
266C2×C4×D4D412yes—
267C2×C4×D4D411yescharacteristic
268C2×C4×D4D411yescharacteristic
269C2×C4×D4D412yes—
270C2×C4×D4D411yescharacteristic
271C2×C4×D4D411yescharacteristic
272C2×C4×D4D412yes—
273C2×C4×D4D411yescharacteristic
274C2×C4×D4C2312yes—
275C2×C4×D4C2311yescharacteristic
276C2×C4×D4C2311yescharacteristic
277C2×#117—21no—
278C2×#117—22no—
279C2×#117—22no—
280C2×#117—21no—
281C2×#117C2×C412yescomplemented
282C22×C4⋊C4—22no—
283C22×C4⋊C4—21no—
284C22×C4⋊C4C2×C412yescomplemented
285C22×C4⋊C4D411yescharacteristic
286C22×C22⋊C4—22no—
287C22×C22⋊C4—22no—
288C22×C22⋊C4D412yes—
289C22×C42C2311yescharacteristic
290#436—22no—
291#436—24no—
292#436—22no—
293#435—24no—
294#435—24no—
295#435—24no—
296#435—24no—
297C8×D4—22no—
298C8×D4—24no—
299C8×D4—22no—
300#432—21no—
301#432—21no—
302#432C2312yes—
303#432C2312yes—
304#431—21no—
305#431—21no—
306#431C2312yes—
307#431C2312yes—
308#423—21no—
309#423—21no—
310#407—22no—
311#407—22no—
312#407—22no—
313#407—22no—
314#407C2311yescharacteristic
315#407C2312yes—
316#407C2311yescharacteristic
317#407C2314yes—
318#407C2314yes—
319C2×C22⋊C8—22no—
320C2×C22⋊C8—22no—
321C2×C22⋊C8C2314yes—
322C2×C22⋊C8C2314yes—
323C4×M16—21no—
324C4×M16—21no—
325#390—22no—
326#389—22no—
327#388—24no—
328#388—24no—
329#387—24no—
330#386—24no—
331#385—24no—
332#383—21no—
333#383C2312yes—
334#382—21no—
335#382C2312yes—
336#381—22no—
337#381—22no—
338#381C2314yes—
339#381C2311yescharacteristic
340#381C2312yes—
341#381C2311yescharacteristic
342#380—21no—
343#380—21no—
344#380—22no—
345#380C2314yes—
346#379—22no—
347C4×C4⋊C4—22no—
348C4×C4⋊C4—21no—
349C4×C4⋊C4C2312yes—
350C4×C22⋊C4—21no—
351C4×C22⋊C4—21no—
352C4×C22⋊C4—22no—
353C4×C22⋊C4—24no—
354C4×C22⋊C4C2314yes—
355#376—21no—
356#376C2312yes—
357C2×#95—22no—
358C2×#95C2314yes—
359#328C2314yes—
360#328C2318yes—
361#328C2318yes—
362#328C2318yes—
363#328C2314yes—
364#328C2318yes—
365#328C2318yes—
366#327C2314yes—
367#327C2314yes—
368#327C2318yes—
369C25C2×D412yes—
370C2×#41—22no—
371C2×#41—22no—
372C2×#41—24no—
373C2×#41—22no—
374C2×#41—22no—
375C2×#41—48no—
376C2×#41—84no—
377C2×#41C22×C414yes—
378C2×#41C22×C414yes—
379C22×Q8—21no—
380C22×Q8—22no—
381C22×Q8—22no—
382C22×Q8—22no—
383C22×Q8—84no—
384C22×Q8C22×C411yescharacteristic
385C22×Q8C22×C412yes—
386C22×Q8C22×C414yes—
387C22×Q8C22×C414yes—
388C22×D4—22no—
389C22×D4—21no—
390C22×D4—22no—
391C22×D4—44no—
392C22×D4C22⋊C411yescharacteristic
393C22×D4C22⋊C411yescharacteristic
394C22×D4C22⋊C412yes—
395C22×D4C22⋊C411yescharacteristic
396C22×D4C22⋊C411yescharacteristic
397C22×D4C22⋊C412yes—
398C22×D4C22×C411yescharacteristic
399C22×D4C2×D411yescharacteristic
400C22×D4C2×D412yes—
401C22×D4C2×D411yescharacteristic
402C23×C4—22no—
403C23×C4—22no—
404C23×C4—21no—
405C23×C4—22no—
406C23×C4—24no—
407C23×C4—84no—
408C23×C4C22×C412yes—
409C23×C4C22×C412yes—
410C23×C4C22×C412yes—
411C23×C4C22×C412yes—
412C23×C4C2×D411yescharacteristic
413C23×C4C2×D412yes—
414C23×C4C2×D411yescharacteristic
415C23×C4C2×D412yes—
416C23×C4C2×D412yes—
417C23×C4C2×D412yes—
418C23×C4C2×D412yes—
419C23×C4C2×D412yes—
420C23×C4C2×D412yes—
421C23×C4C2411yescharacteristic
422C23×C4C2412yes—
423C23×C4C2412yes—
424C2×M16—21no—
425C2×M16—22no—
426C2×M16—21no—
427C2×M16—24no—
428C2×M16—24no—
429C2×M16—84no—
430C2×M16—84no—
431C22×C8—24no—
432C22×C8—24no—
433C4⋊Q8—22no—
434C4⋊Q8—24no—
435C4⋊Q8—22no—
436C4⋊Q8—21no—
437C4⋊Q8—21no—
438C4⋊Q8—21no—
439C4⋊Q8—21no—
440C4⋊Q8C22×C412yes—
441C4⋊Q8C22×C412yes—
442C4⋊Q8C22×C412yes—
443C4⋊Q8C22×C412yes—
444#126—24no—
445#126—24no—
446#126—24no—
447#126—24no—
448#126—24no—
449#126—24no—
450#126—24no—
451#126—24no—
452#126—22no—
453#126—22no—
454#126—22no—
455#126—22no—
456#125—24no—
457#125—24no—
458#125—24no—
459#125—24no—
460#125—22no—
461#125—22no—
462#125—21no—
463#125—21no—
464#125—22no—
465#125—22no—
466#125C22×C412yes—
467#125C22×C412yes—
468#124—22no—
469#124—22no—
470#124—24no—
471#124—24no—
472#124—24no—
473#124—24no—
474#124—24no—
475#124—21no—
476#124—21no—
477#124C22×C412yes—
478#124C22×C412yes—
479#123—24no—
480#123—24no—
481#123—24no—
482#123—24no—
483#123—24no—
484#123—24no—
485#123—22no—
486#123—22no—
487#123—24no—
488#123—24no—
489#123—22no—
490#123—22no—
491#123—24no—
492#123—24no—
493#123—24no—
494#123—24no—
495#123—24no—
496#123—24no—
497#123—24no—
498#123—24no—
499C22⋊Q8—24no—
500C22⋊Q8—24no—
501C22⋊Q8—22no—
502C22⋊Q8—22no—
503C22⋊Q8—22no—
504C22⋊Q8—22no—
505C22⋊Q8—24no—
506C22⋊Q8—24no—
507C22⋊Q8—22no—
508C22⋊Q8—22no—
509C22⋊Q8—22no—
510C22⋊Q8—22no—
511C22⋊Q8—21no—
512C22⋊Q8—21no—
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—24no—
522C22⋊Q8—24no—
523C22⋊Q8—24no—
524C22⋊Q8—24no—
525C22⋊Q8—22no—
526C22⋊Q8—24no—
527C22⋊Q8—22no—
528C22⋊Q8—24no—
529C22⋊Q8—24no—
530C22⋊Q8—24no—
531C22⋊Q8—24no—
532C22⋊Q8C22×C412yes—
533C22⋊Q8C22×C414yes—
534C22⋊Q8C22×C414yes—
535C22⋊Q8C22×C414yes—
536C22⋊Q8C22×C414yes—
537C22⋊Q8C22×C414yes—
538C22⋊Q8C22×C414yes—
539C22⋊Q8C22×C414yes—
540C22⋊Q8C2412yes—
541C22⋊Q8C2414yes—
542#121—24no—
543#121—24no—
544#121—24no—
545#121—24no—
546#121—22no—
547#121—22no—
548#121—24no—
549#121—22no—
550#121—22no—
551#121—21no—
552#121—21no—
553#121C22×C414yes—
554#121C22×C414yes—
555#121C22×C412yes—
556#121C2412yes—
557#120—24no—
558#120—24no—
559#120—24no—
560#120—24no—
561C4×Q8—22no—
562C4×Q8—24no—
563C4×Q8—22no—
564C4×Q8—22no—
565C4×Q8—22no—
566C4×Q8—21no—
567C4×Q8—21no—
568C4×Q8—22no—
569C4×Q8—22no—
570C4×Q8—22no—
571C4×Q8—22no—
572C4×Q8C22×C412yes—
573C4×Q8C22×C412yes—
574C4×Q8C22×C414yes—
575C4×Q8C22×C414yes—
576C4×D4—22no—
577C4×D4—24no—
578C4×D4—22no—
579C4×D4—24no—
580C4×D4—24no—
581C4×D4—24no—
582C4×D4—24no—
583C4×D4—22no—
584C4×D4—22no—
585C4×D4—24no—
586C4×D4—24no—
587C4×D4—24no—
588C4×D4—24no—
589C4×D4—22no—
590C4×D4—22no—
591C4×D4—24no—
592C4×D4—24no—
593C4×D4—24no—
594C4×D4—24no—
595C4×D4—21no—
596C4×D4—21no—
597C4×D4—48no—
598C4×D4C22⋊C412yes—
599C4×D4C22⋊C411yescharacteristic
600C4×D4C22⋊C411yescharacteristic
601C4×D4C22⋊C412yes—
602C4×D4C22⋊C412yes—
603C4×D4C22⋊C412yes—
604C4×D4C22⋊C412yes—
605C4×D4C22⋊C411yescharacteristic
606C4×D4C22⋊C411yescharacteristic
607C4×D4C22⋊C412yes—
608C4×D4C22⋊C412yes—
609C4×D4C22⋊C411yescharacteristic
610C4×D4C22⋊C411yescharacteristic
611C4×D4C22⋊C411yescharacteristic
612C4×D4C22⋊C411yescharacteristic
613C4×D4C22⋊C412yes—
614C4×D4C22⋊C412yes—
615C4×D4C22⋊C412yes—
616C4×D4C22⋊C412yes—
617C4×D4C22⋊C412yes—
618C4×D4C22×C412yes—
619C4×D4C22×C412yes—
620C4×D4C22×C411yescharacteristic
621C4×D4C22×C411yescharacteristic
622C4×D4C22×C412yes—
623C4×D4C22×C411yescharacteristic
624C4×D4C22×C411yescharacteristic
625C4×D4C22×C412yes—
626C4×D4C22×C412yes—
627C4×D4C22×C412yes—
628C4×D4C22×C412yes—
629C4×D4C22×C412yes—
630C4×D4C2×D411yescharacteristic
631C4×D4C2×D412yes—
632C4×D4C2×D411yescharacteristic
633C4×D4C2×D412yes—
634C4×D4C2×D412yes—
635C4×D4C2×D412yes—
636C4×D4C2×D412yes—
637C4×D4C2×D411yescharacteristic
638C4×D4C2×D412yes—
639C4×D4C2×D411yescharacteristic
640#117—22no—
641#117—22no—
642#117—22no—
643#117—22no—
644#117—22no—
645#117—22no—
646#117—24no—
647#117—24no—
648#117—24no—
649#117—24no—
650#117—22no—
651#117—22no—
652#117—22no—
653#117—22no—
654#117—84no—
655#117C22×C414yes—
656#117C22×C414yes—
657C2×C4⋊C4—22no—
658C2×C4⋊C4—21no—
659C2×C4⋊C4—22no—
660C2×C4⋊C4—24no—
661C2×C4⋊C4—24no—
662C2×C4⋊C4—22no—
663C2×C4⋊C4—22no—
664C2×C4⋊C4—22no—
665C2×C4⋊C4—21no—
666C2×C4⋊C4—21no—
667C2×C4⋊C4—21no—
668C2×C4⋊C4—22no—
669C2×C4⋊C4—21no—
670C2×C4⋊C4—22no—
671C2×C4⋊C4—21no—
672C2×C4⋊C4—21no—
673C2×C4⋊C4—22no—
674C2×C4⋊C4—24no—
675C2×C4⋊C4—24no—
676C2×C4⋊C4—22no—
677C2×C4⋊C4—24no—
678C2×C4⋊C4—22no—
679C2×C4⋊C4—22no—
680C2×C4⋊C4—24no—
681C2×C4⋊C4—22no—
682C2×C4⋊C4C22⋊C411yescharacteristic
683C2×C4⋊C4C22⋊C412yes—
684C2×C4⋊C4C22⋊C411yescharacteristic
685C2×C4⋊C4C22⋊C411yescharacteristic
686C2×C4⋊C4C22⋊C411yescharacteristic
687C2×C4⋊C4C22⋊C412yes—
688C2×C4⋊C4C22×C411yescharacteristic
689C2×C4⋊C4C22×C412yes—
690C2×C4⋊C4C22×C414yes—
691C2×C4⋊C4C22×C414yes—
692C2×C4⋊C4C22×C411yescharacteristic
693C2×C4⋊C4C2×D411yescharacteristic
694C2×C4⋊C4C2×D412yes—
695C2×C4⋊C4C2×D411yescharacteristic
696C2×C22⋊C4—22no—
697C2×C22⋊C4—22no—
698C2×C22⋊C4—24no—
699C2×C22⋊C4—24no—
700C2×C22⋊C4—22no—
701C2×C22⋊C4—22no—
702C2×C22⋊C4—21no—
703C2×C22⋊C4—22no—
704C2×C22⋊C4—24no—
705C2×C22⋊C4—24no—
706C2×C22⋊C4—21no—
707C2×C22⋊C4—21no—
708C2×C22⋊C4—22no—
709C2×C22⋊C4—21no—
710C2×C22⋊C4—21no—
711C2×C22⋊C4—21no—
712C2×C22⋊C4—22no—
713C2×C22⋊C4—21no—
714C2×C22⋊C4—24no—
715C2×C22⋊C4—24no—
716C2×C22⋊C4—24no—
717C2×C22⋊C4—84no—
718C2×C22⋊C4C22⋊C412yes—
719C2×C22⋊C4C22⋊C412yes—
720C2×C22⋊C4C22⋊C412yes—
721C2×C22⋊C4C22⋊C412yes—
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×C42—22no—
731C2×C42—22no—
732C2×C42—21no—
733C2×C42—22no—
734C2×C42—24no—
735C2×C42—22no—
736C2×C42C22×C411yescharacteristic
737C2×C42C22×C411yescharacteristic
738C2×C42C22×C411yescharacteristic
739C2×C42C22×C411yescharacteristic
740C2×C42C2×D411yescharacteristic
741C2×C42C2×D411yescharacteristic
742C2×C42C2×D411yescharacteristic
743C2×C42C2×D411yescharacteristic
744C2×C42C2×D411yescharacteristic
745C2×C42C2×D411yescharacteristic
746C2×C42C2411yescharacteristic
747C2×C42C2411yescharacteristic
748C4⋊C8—22no—
749C4⋊C8—22no—
750C4⋊C8—22no—
751C4⋊C8—22no—
752C22⋊C8—21no—
753C22⋊C8—22no—
754C22⋊C8—21no—
755C22⋊C8—24no—
756C22⋊C8—24no—
757C22⋊C8—24no—
758C22⋊C8—24no—
759C22⋊C8C2412yes—
760C22⋊C8C2412yes—
761C22⋊C8C2414yes—
762#97—22no—
763#97—22no—
764C4×C8—22no—
765C4×C8—22no—
766#95—21no—
767#95—22no—
768#95—24no—
769#95—24no—
770#95—22no—
771#95—22no—
772#95—21no—
773#95—22no—
774#95—22no—
775#95C2412yes—
776#95C2414yes—
777#95C2412yes—
778C24—21no—
779C24—44no—
780C24—44no—
781C24—44no—
782C24C2×C22⋊C412yes—
783C24C2×C22⋊C412yes—
784C24C2×C22⋊C412yes—
785C24C2×C22⋊C412yes—
786C24C22×D411yescharacteristic
787C24C22×D412yes—
788C24C22×D412yes—
789#41—416no—
790#41—48no—
791#41—48no—
792#41—84no—
793#41—84no—
794#41—84no—
795#41—84no—
796C2×Q8—22no—
797C2×Q8—22no—
798C2×Q8—21no—
799C2×Q8—22no—
800C2×Q8—24no—
801C2×Q8—24no—
802C2×Q8—44no—
803C2×Q8—42no—
804C2×Q8—44no—
805C2×Q8—84no—
806C2×Q8—84no—
807C2×Q8—84no—
808C2×Q8—84no—
809C2×Q8—84no—
810C2×Q8C23×C412yes—
811C2×Q8C23×C414yes—
812C2×D4—24no—
813C2×D4—24no—
814C2×D4—24no—
815C2×D4—22no—
816C2×D4—24no—
817C2×D4—24no—
818C2×D4—22no—
819C2×D4—24no—
820C2×D4—24no—
821C2×D4—21no—
822C2×D4—42no—
823C2×D4—42no—
824C2×D4—42no—
825C2×D4—42no—
826C2×D4—44no—
827C2×D4—44no—
828C2×D4—44no—
829C2×D4—44no—
830C2×D4—48no—
831C2×D4—84no—
832C2×D4C2×C22⋊C412yes—
833C2×D4C2×C22⋊C411yescharacteristic
834C2×D4C2×C22⋊C412yes—
835C2×D4C2×C22⋊C412yes—
836C2×D4C2×C22⋊C411yescharacteristic
837C2×D4C2×C22⋊C411yescharacteristic
838C2×D4C2×C22⋊C412yes—
839C2×D4C2×C22⋊C412yes—
840C2×D4C2×C22⋊C412yes—
841C2×D4C2×C22⋊C411yescharacteristic
842C2×D4C23×C412yes—
843C22×C4—21no—
844C22×C4—22no—
845C22×C4—21no—
846C22×C4—22no—
847C22×C4—21no—
848C22×C4—24no—
849C22×C4—24no—
850C22×C4—24no—
851C22×C4—24no—
852C22×C4—22no—
853C22×C4—22no—
854C22×C4—24no—
855C22×C4—24no—
856C22×C4—22no—
857C22×C4—24no—
858C22×C4—22no—
859C22×C4—42no—
860C22×C4—44no—
861C22×C4—44no—
862C22×C4—44no—
863C22×C4—42no—
864C22×C4—44no—
865C22×C4—44no—
866C22×C4—42no—
867C22×C4—44no—
868C22×C4—48no—
869C22×C4—48no—
870C22×C4—84no—
871C22×C4—82no—
872C22×C4—82no—
873C22×C4—82no—
874C22×C4—82no—
875C22×C4—82no—
876C22×C4—82no—
877C22×C4—82no—
878C22×C4—82no—
879C22×C4—84no—
880C22×C4—84no—
881C22×C4—84no—
882C22×C4C2×C22⋊C411yescharacteristic
883C22×C4C2×C22⋊C412yes—
884C22×C4C2×C22⋊C411yescharacteristic
885C22×C4C2×C22⋊C412yes—
886C22×C4C2×C22⋊C411yescharacteristic
887C22×C4C2×C22⋊C411yescharacteristic
888C22×C4C2×C22⋊C411yescharacteristic
889C22×C4C2×C22⋊C411yescharacteristic
890C22×C4C2×C22⋊C411yescharacteristic
891C22×C4C2×C22⋊C411yescharacteristic
892C22×C4C2×C22⋊C412yes—
893C22×C4C2×C22⋊C412yes—
894C22×C4C2×C22⋊C412yes—
895C22×C4C2×C22⋊C412yes—
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×C4C23×C411yescharacteristic
903C22×C4C23×C411yescharacteristic
904C22×C4C23×C412yes—
905C22×C4C23×C412yes—
906C22×C4C23×C412yes—
907C22×C4C23×C412yes—
908C22×C4C22×D411yescharacteristic
909C22×C4C22×D411yescharacteristic
910C22×C4C22×D411yescharacteristic
911C22×C4C22×D411yescharacteristic
912C22×C4C22×D411yescharacteristic
913C22×C4C22×D411yescharacteristic
914C22×C4C22×D412yes—
915C22×C4C22×D412yes—
916C22×C4C22×D411yescharacteristic
917C22×C4C22×D412yes—
918C22×C4C22×D412yes—
919C22×C4C22×D412yes—
920C22×C4C22×D412yes—
921C22×C4C2511yescharacteristic
922M16—42no—
923M16—44no—
924M16—42no—
925M16—84no—
926M16—84no—
927C2×C8—22no—
928C2×C8—22no—
929C2×C8—24no—
930C2×C8—84no—
931C2×C8—84no—
932C4⋊C4—22no—
933C4⋊C4—24no—
934C4⋊C4—24no—
935C4⋊C4—21no—
936C4⋊C4—22no—
937C4⋊C4—22no—
938C4⋊C4—24no—
939C4⋊C4—24no—
940C4⋊C4—24no—
941C4⋊C4—22no—
942C4⋊C4—24no—
943C4⋊C4—24no—
944C4⋊C4—22no—
945C4⋊C4—22no—
946C4⋊C4—22no—
947C4⋊C4—22no—
948C4⋊C4—22no—
949C4⋊C4—22no—
950C4⋊C4—24no—
951C4⋊C4—24no—
952C4⋊C4—22no—
953C4⋊C4—22no—
954C4⋊C4—24no—
955C4⋊C4—24no—
956C4⋊C4—22no—
957C4⋊C4—22no—
958C4⋊C4—21no—
959C4⋊C4—22no—
960C4⋊C4—24no—
961C4⋊C4—44no—
962C4⋊C4—82no—
963C4⋊C4—84no—
964C4⋊C4C2×C22⋊C412yes—
965C4⋊C4C2×C22⋊C411yescharacteristic
966C4⋊C4C2×C22⋊C411yescharacteristic
967C4⋊C4C2×C22⋊C412yes—
968C4⋊C4C2×C22⋊C412yes—
969C4⋊C4C2×C22⋊C412yes—
970C4⋊C4C2×C22⋊C412yes—
971C4⋊C4C2×C22⋊C412yes—
972C4⋊C4C2×C22⋊C411yescharacteristic
973C4⋊C4C2×C22⋊C411yescharacteristic
974C4⋊C4C23×C412yes—
975C4⋊C4C23×C414yes—
976C4⋊C4C23×C412yes—
977C22⋊C4—22no—
978C22⋊C4—24no—
979C22⋊C4—24no—
980C22⋊C4—24no—
981C22⋊C4—24no—
982C22⋊C4—24no—
983C22⋊C4—24no—
984C22⋊C4—24no—
985C22⋊C4—24no—
986C22⋊C4—24no—
987C22⋊C4—22no—
988C22⋊C4—24no—
989C22⋊C4—22no—
990C22⋊C4—22no—
991C22⋊C4—22no—
992C22⋊C4—22no—
993C22⋊C4—22no—
994C22⋊C4—24no—
995C22⋊C4—24no—
996C22⋊C4—22no—
997C22⋊C4—22no—
998C22⋊C4—22no—
999C22⋊C4—42no—
1000C22⋊C4—44no—
1001C22⋊C4—42no—
1002C22⋊C4—48no—
1003C22⋊C4—84no—
1004C22⋊C4—84no—
1005C22⋊C4C2×C22⋊C412yes—
1006C22⋊C4C2×C22⋊C412yes—
1007C22⋊C4C2×C22⋊C412yes—
1008C22⋊C4C2×C22⋊C412yes—
1009C22⋊C4C2×C22⋊C412yes—
1010C22⋊C4C2×C22⋊C412yes—
1011C22⋊C4C2×C22⋊C412yes—
1012C22⋊C4C2×C22⋊C412yes—
1013C22⋊C4C2×C22⋊C412yes—
1014C22⋊C4C2×C22⋊C412yes—
1015C22⋊C4C2×C22⋊C412yes—
1016C22⋊C4C2×C22⋊C412yes—
1017C22⋊C4C2×C22⋊C412yes—
1018C22⋊C4C2×C22⋊C412yes—
1019C22⋊C4C2×C22⋊C412yes—
1020C22⋊C4C2×C22⋊C412yes—
1021C42—24no—
1022C42—24no—
1023C42—24no—
1024C42—24no—
1025C42—22no—
1026C42—22no—
1027C42—44no—
1028C42—82no—
1029C42—84no—
1030C42C2×C22⋊C411yescharacteristic
1031C42C2×C22⋊C411yescharacteristic
1032C42C2×C22⋊C411yescharacteristic
1033C42C2×C22⋊C411yescharacteristic
1034C42C2×C22⋊C411yescharacteristic
1035C42C2×C22⋊C411yescharacteristic
1036C42C2×C22⋊C411yescharacteristic
1037C42C2×C22⋊C411yescharacteristic
1038C42C23×C411yescharacteristic
1039C42C23×C411yescharacteristic
1040C42C23×C411yescharacteristic
1041C42C23×C411yescharacteristic
1042C42C22×D411yescharacteristic
1043C42C22×D411yescharacteristic
1044C42C22×D411yescharacteristic
1045C42C22×D411yescharacteristic
1046C23—22no—
1047C23—24no—
1048C23—22no—
1049C23—24no—
1050C23—24no—
1051C23—24no—
1052C23—24no—
1053C23—24no—
1054C23—24no—
1055C23—22no—
1056C23—41no—
1057C23—42no—
1058C23—42no—
1059C23—42no—
1060C23—42no—
1061C23—42no—
1062C23—42no—
1063C23—42no—
1064C23—42no—
1065C23—42no—
1066C23—42no—
1067C23—42no—
1068C23—42no—
1069C23—42no—
1070C23—42no—
1071C23—816no—
1072C23C22×C22⋊C412yes—
1073C23C22×C22⋊C412yes—
1074C23C22×C22⋊C411yescharacteristic
1075C23C22×C22⋊C412yes—
1076C23C22×C22⋊C411yescharacteristic
1077C23C22×C22⋊C412yes—
1078C23C23×D411yescharacteristic
1079Q8—42no—
1080Q8—44no—
1081Q8—42no—
1082Q8—44no—
1083Q8—44no—
1084Q8—44no—
1085Q8—84no—
1086Q8—84no—
1087D4—24no—
1088D4—24no—
1089D4—24no—
1090D4—22no—
1091D4—22no—
1092D4—22no—
1093D4—42no—
1094D4—42no—
1095D4—42no—
1096D4—42no—
1097D4—42no—
1098D4—44no—
1099D4—48no—
1100D4—44no—
1101D4—48no—
1102D4—84no—
1103D4—84no—
1104D4#42114yes—
1105C2×C4—22no—
1106C2×C4—22no—
1107C2×C4—22no—
1108C2×C4—22no—
1109C2×C4—24no—
1110C2×C4—24no—
1111C2×C4—22no—
1112C2×C4—22no—
1113C2×C4—22no—
1114C2×C4—22no—
1115C2×C4—24no—
1116C2×C4—22no—
1117C2×C4—24no—
1118C2×C4—22no—
1119C2×C4—42no—
1120C2×C4—42no—
1121C2×C4—42no—
1122C2×C4—42no—
1123C2×C4—42no—
1124C2×C4—42no—
1125C2×C4—41no—
1126C2×C4—41no—
1127C2×C4—41no—
1128C2×C4—41no—
1129C2×C4—42no—
1130C2×C4—42no—
1131C2×C4—42no—
1132C2×C4—42no—
1133C2×C4—42no—
1134C2×C4—42no—
1135C2×C4—42no—
1136C2×C4—42no—
1137C2×C4—42no—
1138C2×C4—42no—
1139C2×C4—42no—
1140C2×C4—42no—
1141C2×C4—42no—
1142C2×C4—42no—
1143C2×C4—41no—
1144C2×C4—41no—
1145C2×C4—41no—
1146C2×C4—41no—
1147C2×C4—41no—
1148C2×C4—41no—
1149C2×C4—41no—
1150C2×C4—44no—
1151C2×C4—42no—
1152C2×C4—44no—
1153C2×C4—48no—
1154C2×C4—42no—
1155C2×C4—44no—
1156C2×C4—42no—
1157C2×C4—48no—
1158C2×C4—44no—
1159C2×C4—42no—
1160C2×C4—42no—
1161C2×C4—42no—
1162C2×C4—44no—
1163C2×C4—42no—
1164C2×C4—44no—
1165C2×C4—44no—
1166C2×C4—42no—
1167C2×C4—42no—
1168C2×C4—84no—
1169C2×C4—84no—
1170C2×C4—84no—
1171C2×C4—84no—
1172C2×C4—168no—
1173C2×C4C22×C22⋊C411yescharacteristic
1174C2×C4C22×C22⋊C411yescharacteristic
1175C2×C4C22×C22⋊C411yescharacteristic
1176C2×C4C22×C22⋊C412yes—
1177C2×C4C22×C22⋊C412yes—
1178C2×C4C22×C22⋊C411yescharacteristic
1179C2×C4C22×C22⋊C411yescharacteristic
1180C2×C4C22×C22⋊C411yescharacteristic
1181C2×C4C22×C22⋊C411yescharacteristic
1182C2×C4C22×C22⋊C411yescharacteristic
1183C2×C4C22×C22⋊C411yescharacteristic
1184C2×C4C22×C22⋊C412yes—
1185C2×C4C22×C22⋊C412yes—
1186C2×C4C22×C22⋊C411yescharacteristic
1187C2×C4C24×C411yescharacteristic
1188C2×C4C23×D411yescharacteristic
1189C8—42no—
1190C8—42no—
1191C8—44no—
1192C22—21no—
1193C22—22no—
1194C22—21no—
1195C22—22no—
1196C22—21no—
1197C22—21no—
1198C22—21no—
1199C22—22no—
1200C22—22no—
1201C22—22no—
1202C22—21no—
1203C22—22no—
1204C22—22no—
1205C22—22no—
1206C22—21no—
1207C22—22no—
1208C22—22no—
1209C22—22no—
1210C22—48no—
1211C22—48no—
1212C22—44no—
1213C22—42no—
1214C22—42no—
1215C22—42no—
1216C22—84no—
1217C22—84no—
1218C22—84no—
1219C22—84no—
1220C22—84no—
1221C22#288312yes—
1222C22C2×#42114yes—
1223C22C23×C22⋊C411yescharacteristic
1224C22#358612yes—
1225C4—21no—
1226C4—21no—
1227C4—21no—
1228C4—21no—
1229C4—22no—
1230C4—22no—
1231C4—22no—
1232C4—22no—
1233C4—21no—
1234C4—21no—
1235C4—21no—
1236C4—21no—
1237C4—21no—
1238C4—21no—
1239C4—21no—
1240C4—44no—
1241C4—42no—
1242C4—42no—
1243C4—42no—
1244C4—44no—
1245C4—82no—
1246C4—84no—
1247C4—82no—
1248C4C2×#42112yes—
1249C2—22no—
1250C2—22no—
1251C2—24no—
1252C2—42no—
1253C2—42no—
1254C2—41no—
1255C2—42no—
1256C2—82no—
1257C2C2×#288311yescharacteristic
1258C2#6008811yescharacteristic
1259C2C22×#42111yescharacteristic
subgroupG/H
center, socleC22C23×C22⋊C4
commutatorC2×C4C24×C4
Frattini, cosocleC22×C4C25
prime radicalC2×#3520C2
LCSG ▷ C2×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22 ◁ C22×C4×D4 ◁ G
LECSG ▷ C22×C4 ▷ C22 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #60230C2semidirect
3. #34190C2semidirect
4. #17600C2semidirect
5. #17598C2semidirect
6. #17590C2semidirect
7. #17587C2semidirect
8. #17580C2semidirect
9. #17578C2semidirect
10. #17562C2semidirect
11. #17559C2semidirect
12. #17554C2semidirect
13. C2×#1511C2semidirect
14. #17548C2semidirect
21. #3520C4semidirect
22. #3520C4semidirect
23. #3520C4semidirect
27. C2×#556C4semidirect
29. C2×#552C4semidirect
31. C2×D4×Q8C4semidirect
32. C2×#548C4semidirect
33. C2×#547C4semidirect
34. C2×#547C4semidirect
45. #2974C22semidirect
46. #2974C22semidirect
47. #2974C22semidirect
63. #2319C22semidirect
64. #2318C22semidirect
69. #2275C22semidirect
70. #1521C22semidirect
71. #1520C22semidirect
72. #1518C22semidirect
73. #1516C22semidirect
74. #1515C22semidirect
75. #1513C22semidirect
76. #1512C22semidirect
84. #1511C22semidirect
88. #1509C22semidirect
89. #1508C22semidirect
90. #1506C22semidirect
91. #1504C22semidirect
92. #1503C22semidirect
93. #1501C22semidirect
94. #1500C22semidirect
95. C2×#328C22semidirect
97. C22×#41C2×C4semidirect
98. C23×Q8C2×C4semidirect
107. #556C2×C4semidirect
108. #556C2×C4semidirect
120. #552C2×C4semidirect
121. #552C2×C4semidirect
122. #552C2×C4semidirect
135. D4×Q8C2×C4semidirect
136. D4×Q8C2×C4semidirect
142. #548C2×C4semidirect
143. #548C2×C4semidirect
144. #548C2×C4semidirect
153. #547C2×C4semidirect
154. #547C2×C4semidirect
155. #547C2×C4semidirect
156. #547C2×C4semidirect
181. #533C2×C4semidirect
182. #533C2×C4semidirect
186. C2×C4⋊Q8C2×C4semidirect
187. C2×C4⋊Q8C2×C4semidirect
192. #529C2×C4semidirect
193. #529C2×C4semidirect
201. C2×#125C2×C4semidirect
204. C2×#124C2×C4semidirect
209. #525C2×C4semidirect
210. #525C2×C4semidirect
228. C2×C22⋊Q8C2×C4semidirect
229. C2×C22⋊Q8C2×C4semidirect
230. C2×C22⋊Q8C2×C4semidirect
231. C2×C22⋊Q8C2×C4semidirect
232. C2×C22⋊Q8C2×C4semidirect
239. C2×#121C2×C4semidirect
250. C2×C4×Q8C2×C4semidirect
251. C2×C4×Q8C2×C4semidirect
264. C2×C4×D4C2×C4semidirect
281. C2×#117C2×C4semidirect
284. 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
#602302
#341902
#176002
#175982
#175902
#175872
#175802
#175782
#175622
#175592
#175542
C2×#15112
#175482