Finite Group Databasebeta

← #6394053

Subgroups — #6394053

Order 512.

2913 conjugacy classes of subgroups.

The subgroup lattice has 1232 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3515C211yesmaximal, characteristic
2#60263C211yesmaximal, characteristic, complemented
3M16×#41C211yesmaximal, characteristic, complemented
4#22517C212yesmaximal, complemented
5#22515C212yesmaximal, complemented
6#22482C214yesmaximal, complemented
7#22481C212yesmaximal, complemented
8#22480C214yesmaximal, complemented
9#22479C212yesmaximal, complemented
10#21880C211yesmaximal, characteristic, complemented
11#21880C212yesmaximal, complemented
12#21831C211yesmaximal, characteristic, complemented
13#21830C212yesmaximal, complemented
14#21426C212yesmaximal, complemented
15#21426C211yesmaximal, characteristic, complemented
16#21337C211yesmaximal, characteristic, complemented
17C2×#1998C212yesmaximal, complemented
18#3515—21no—
19#3515—22no—
20#3515—21no—
21#3515—21no—
22#3515—22no—
23#3515—21no—
24#3515—21no—
25#3515—22no—
26#3515—21no—
27#3515—21no—
28#3515—22no—
29#3515—21no—
30C2×#557C2211yescharacteristic
31C2×#554C2211yescharacteristic
32C2×#554C2211yescharacteristic
33C2×#553C2212yes—
34C2×#552C412yes—
35C2×#552C414yes—
36C2×#552C2212yes—
37C2×#547C412yes—
38C2×#547C2211yescharacteristic
39C2×#541C412yes—
40C2×#539C414yes—
41C2×#533C2211yescharacteristic
42C2×#529C2211yescharacteristic
43C2×#529C2212yes—
44C22×#125C2212yes—
45C2×#520C412yes—
46C2×C4×#41C2211yescharacteristic
47#2991—21no—
48#2990—21no—
49#2990—22no—
50#2989—22no—
51#2989—21no—
52#2988—21no—
53#2971—21no—
54#2970—21no—
55#2970—22no—
56#2965—22no—
57#2965—21no—
58C8×#41—21no—
59Q8×M16C2212yes—
60Q8×M16C2212yes—
61D4×M16C2212yes—
62D4×M16C2214yes—
63D4×M16C2212yes—
64D4×M16C2214yes—
65#2920C2212yes—
66#2920C2211yescharacteristic
67#2920C2212yes—
68#2920C2211yescharacteristic
69C2×#423C2212yes—
70C2×#423C2211yescharacteristic
71C2×C4×M16C2212yes—
72C2×C4×M16C2211yescharacteristic
73#1998C2211yescharacteristic
74#1998C2212yes—
75#1998C2212yes—
76#1998C2212yes—
77#1998C2214yes—
78#1998C2214yes—
79#1998C2212yes—
80#1998C2211yescharacteristic
81#1998C2212yes—
82#1998C2214yes—
83#1998C2214yes—
84#1997C2212yes—
85#1997C2212yes—
86#1997C2212yes—
87#1997C2212yes—
88#1967C2212yes—
89#1967C2211yescharacteristic
90#1967C2211yescharacteristic
91#1901C2212yes—
92#1901C2214yes—
93#1901C2212yes—
94#1901C2214yes—
95#1900C2214yes—
96#1900C2212yes—
97#1900C2214yes—
98#1900C2212yes—
99#1822C2214yes—
100#1821C2214yes—
101#1821C2214yes—
102#1801C2214yes—
103#1801C2212yes—
104#1800C2212yes—
105#1800C2214yes—
106C4×#101C2214yes—
107C4×#101C2212yes—
108C4×#100C2212yes—
109C4×#100C2214yes—
110#1742C2214yes—
111C2×#343C2214yes—
112C2×#343C2214yes—
113C22×#41C2×C412yes—
114C22×#41C2×C411yescharacteristic
115C22×M16C2314yes—
116C22×M16C2312yes—
117C22×M16C2314yes—
118C22×M16C2312yes—
119#557—21no—
120#557—21no—
121#557—22no—
122#557—22no—
123#557—21no—
124#557—21no—
125#554—21no—
126#554—21no—
127#554—21no—
128#554—21no—
129#554—22no—
130#554—22no—
131#554—21no—
132#554—21no—
133#554—22no—
134#554—22no—
135#554—21no—
136#554—21no—
137#553—22no—
138#553—22no—
139#553—22no—
140#553—22no—
141#553—22no—
142#553—22no—
143#553—22no—
144#553—22no—
145#552—22no—
146#552—22no—
147#552—22no—
148#552—22no—
149#552—22no—
150#552—22no—
151#552—22no—
152#552—22no—
153#552—24no—
154#552—24no—
155#552—24no—
156#552—24no—
157#552—24no—
158#552—24no—
159#552—24no—
160#552—24no—
161#552—22no—
162#552—22no—
163#552—22no—
164#552—22no—
165#552—24no—
166#552—24no—
167#547—22no—
168#547—22no—
169#547—24no—
170#547—24no—
171#547—22no—
172#547—22no—
173#547—21no—
174#547—21no—
175#547—22no—
176#547—22no—
177#547—21no—
178#547—21no—
179#541—22no—
180#541—22no—
181#541—22no—
182#541—22no—
183#541—24no—
184#541—24no—
185#539—24no—
186#539—24no—
187#539—24no—
188#539—24no—
189#539—24no—
190#539—24no—
191#539—24no—
192#539—24no—
193#533—21no—
194#533—21no—
195#533—21no—
196#533—21no—
197#533—21no—
198#533—21no—
199#533—21no—
200#533—21no—
201C2×C4⋊Q8C2×C412yes—
202C2×C4⋊Q8C2311yescharacteristic
203C2×C4⋊Q8C2311yescharacteristic
204#529—22no—
205#529—22no—
206#529—22no—
207#529—22no—
208#529—22no—
209#529—22no—
210#529—22no—
211#529—22no—
212#529—21no—
213#529—21no—
214#529—21no—
215#529—21no—
216#529—21no—
217#529—21no—
218#529—21no—
219#529—21no—
220C2×#126C2×C414yes—
221C2×#126C2×C412yes—
222C2×#126C2×C414yes—
223C2×#126C2×C414yes—
224C2×#125—22no—
225C2×#125—22no—
226C2×#125—22no—
227C2×#125—22no—
228C2×#125—22no—
229C2×#125—22no—
230C2×#125—22no—
231C2×#125—22no—
232C2×#125C2×C414yes—
233C2×#125C2×C414yes—
234C2×#125C2×C414yes—
235C2×#125C2×C414yes—
236C2×#125C2×C412yes—
237C2×#125C2311yescharacteristic
238C2×#125C2312yes—
239C2×#125C2312yes—
240C2×#125C2312yes—
241C2×#124C2311yescharacteristic
242C2×#123C2×C412yes—
243C2×#123C2×C414yes—
244C2×#123C2×C414yes—
245C2×#123C2×C414yes—
246C2×#123C2×C414yes—
247C2×C22⋊Q8C2×C412yes—
248C2×C22⋊Q8C2×C412yes—
249C2×C22⋊Q8C2×C414yes—
250C2×C22⋊Q8C2×C414yes—
251C2×C22⋊Q8C2×C412yes—
252C2×C22⋊Q8C2×C412yes—
253C2×C22⋊Q8C2311yescharacteristic
254C2×C22⋊Q8C2312yes—
255C2×#121C2×C414yes—
256C2×#121C2312yes—
257C2×#121C2311yescharacteristic
258#520—22no—
259#520—24no—
260#520—24no—
261#520—22no—
262#520—22no—
263#520—22no—
264C4×#41D411yescharacteristic
265C4×#41D412yes—
266C4×#41D411yescharacteristic
267C4×#41D411yescharacteristic
268C4×#41D412yes—
269C4×#41D411yescharacteristic
270C4×#41D411yescharacteristic
271C4×#41D412yes—
272C4×#41D411yescharacteristic
273C4×#41D411yescharacteristic
274C4×#41D412yes—
275C4×#41D411yescharacteristic
276C2×C4×Q8C2×C412yes—
277C2×C4×Q8C2×C412yes—
278C2×C4×Q8C2×C412yes—
279C2×C4×Q8C2×C411yescharacteristic
280C2×C4×Q8C2312yes—
281C2×C4×Q8C2311yescharacteristic
282C2×C4×Q8C2311yescharacteristic
283C2×C4×D4C2×C414yes—
284C2×C4×D4C2×C412yes—
285C2×C4×D4C2×C414yes—
286C2×C4×D4C2×C412yes—
287C2×C4×D4C2×C411yescharacteristic
288C2×C4×D4C2×C412yes—
289C2×C4×D4C2311yescharacteristic
290C2×C4×D4C2312yes—
291C2×C4×D4C2311yescharacteristic
292C2×C4×D4C2312yes—
293C2×#117C2×C412yes—
294C2×#117C2×C414yes—
295C2×#117C2×C414yes—
296C2×#117C2×C411yescharacteristic
297C2×#117C2×C412yes—
298C2×#117C2312yes—
299C22×C4⋊C4C2×C414yes—
300C22×C4⋊C4C2×C412yes—
301C22×C4⋊C4C2×C414yes—
302C22×C4⋊C4C2312yes—
303C22×C4⋊C4C2312yes—
304C22×C42C2312yes—
305C22×C42C2311yescharacteristic
306#446—24no—
307#446—22no—
308#446—24no—
309#446—22no—
310C8×Q8—22no—
311C8×Q8—22no—
312#436—22no—
313#436—24no—
314#436—22no—
315#436—24no—
316#435—24no—
317#435—24no—
318#435—24no—
319#435—24no—
320#435—24no—
321#435—24no—
322C8×D4—22no—
323C8×D4—24no—
324C8×D4—22no—
325C8×D4—24no—
326#432—22no—
327#432—21no—
328#432—22no—
329#432—21no—
330#432—22no—
331#432—21no—
332#432—22no—
333#432—21no—
334#431—22no—
335#431—21no—
336#431—22no—
337#431—21no—
338#431—22no—
339#431—21no—
340#431—22no—
341#431—21no—
342#423—22no—
343#423—21no—
344#423—22no—
345#423—21no—
346#423C2312yes—
347#423C2314yes—
348#423C2312yes—
349#423C2314yes—
350#423C2311yescharacteristic
351#423C2312yes—
352#423C2311yescharacteristic
353C2×C4⋊C8—22no—
354C2×C4⋊C8—21no—
355C2×C4⋊C8—22no—
356C2×C4⋊C8—21no—
357C2×#101C2312yes—
358C2×#101C2312yes—
359C2×#101C2314yes—
360C2×#100C2312yes—
361C2×#100C2314yes—
362C2×#100C2312yes—
363#407C2314yes—
364#407C2314yes—
365#407C2312yes—
366#407C2312yes—
367C4×M16—22no—
368C4×M16—21no—
369C4×M16—22no—
370C4×M16—21no—
371C4×M16C2311yescharacteristic
372C4×M16C2312yes—
373C4×M16C2311yescharacteristic
374C4×M16C2312yes—
375C4×M16C2314yes—
376C4×M16C2312yes—
377C4×M16C2314yes—
378C2×#97—22no—
379C2×#97—21no—
380C2×C4×C8—22no—
381C2×C4×C8—21no—
382#343C2314yes—
383#343C2314yes—
384#343C2314yes—
385#343C2314yes—
386#343C2314yes—
387#343C2314yes—
388#343C2312yes—
389#343C2312yes—
390#343C2314yes—
391#343C2314yes—
392#343C2312yes—
393#343C2314yes—
394#343C2312yes—
395#343C2314yes—
396C2×#41—22no—
397C2×#41—24no—
398C2×#41—22no—
399C2×#41—44no—
400C2×#41—48no—
401C2×#41C22⋊C411yescharacteristic
402C2×#41C22⋊C411yescharacteristic
403C2×#41C22⋊C412yes—
404C2×#41C22⋊C412yes—
405C2×#41C22⋊C411yescharacteristic
406C2×#41C22⋊C411yescharacteristic
407C22×Q8C22×C412yes—
408C22×Q8C22×C412yes—
409C22×Q8C22×C411yescharacteristic
410C22×Q8C2411yescharacteristic
411C22×D4C22×C411yescharacteristic
412C22×D4C22×C414yes—
413C22×D4C22×C412yes—
414C22×D4C22×C412yes—
415C22×D4C2411yescharacteristic
416C23×C4C22×C414yes—
417C23×C4C22×C412yes—
418C23×C4C22×C414yes—
419C23×C4C22×C414yes—
420C23×C4C22×C412yes—
421C23×C4C22×C411yescharacteristic
422C23×C4C22×C412yes—
423C23×C4C22×C411yescharacteristic
424C23×C4C2412yes—
425C23×C4C2411yescharacteristic
426C2×M16—24no—
427C2×M16—22no—
428C2×M16—24no—
429C2×M16—22no—
430C2×M16—28no—
431C2×M16—24no—
432C2×M16—44no—
433C2×M16—42no—
434C2×M16—44no—
435C2×M16—44no—
436C2×M16—44no—
437C2×M16C2412yes—
438C2×M16C2414yes—
439C2×M16C2414yes—
440C2×M16C2412yes—
441C2×M16C2412yes—
442C2×M16C2412yes—
443C22×C8—24no—
444C22×C8—22no—
445C22×C8—24no—
446C22×C8—22no—
447C4⋊Q8—22no—
448C4⋊Q8—22no—
449C4⋊Q8—24no—
450C4⋊Q8—21no—
451C4⋊Q8—21no—
452C4⋊Q8—21no—
453C4⋊Q8—21no—
454C4⋊Q8—21no—
455C4⋊Q8—21no—
456C4⋊Q8—21no—
457C4⋊Q8—21no—
458#126—24no—
459#126—24no—
460#126—24no—
461#126—24no—
462#126—24no—
463#126—24no—
464#126—24no—
465#126—24no—
466#126—24no—
467#126—24no—
468#126—24no—
469#126—24no—
470#126—22no—
471#126—22no—
472#126—22no—
473#126—22no—
474#125—24no—
475#125—24no—
476#125—24no—
477#125—24no—
478#125—24no—
479#125—24no—
480#125—24no—
481#125—24no—
482#125—24no—
483#125—22no—
484#125—22no—
485#125—24no—
486#125—24no—
487#125—24no—
488#125—24no—
489#125—24no—
490#125—24no—
491#125—24no—
492#125—24no—
493#125—21no—
494#125—21no—
495#125—21no—
496#125—21no—
497#125—22no—
498#125—22no—
499#125—22no—
500#125—22no—
501#125—22no—
502#125—22no—
503#125—22no—
504#125—22no—
505#125—22no—
506#125—22no—
507#125—22no—
508#125—22no—
509#124—21no—
510#124—21no—
511#124—21no—
512#124—21no—
513#123—24no—
514#123—24no—
515#123—24no—
516#123—24no—
517#123—22no—
518#123—22no—
519#123—22no—
520#123—22no—
521#123—24no—
522#123—24no—
523#123—24no—
524#123—24no—
525#123—24no—
526#123—24no—
527#123—24no—
528#123—24no—
529#123—24no—
530#123—24no—
531#123—24no—
532#123—24no—
533C22⋊Q8—22no—
534C22⋊Q8—22no—
535C22⋊Q8—24no—
536C22⋊Q8—22no—
537C22⋊Q8—22no—
538C22⋊Q8—22no—
539C22⋊Q8—22no—
540C22⋊Q8—22no—
541C22⋊Q8—22no—
542C22⋊Q8—22no—
543C22⋊Q8—22no—
544C22⋊Q8—21no—
545C22⋊Q8—21no—
546C22⋊Q8—21no—
547C22⋊Q8—21no—
548C22⋊Q8—22no—
549C22⋊Q8—22no—
550C22⋊Q8—22no—
551C22⋊Q8—22no—
552C22⋊Q8—24no—
553C22⋊Q8—24no—
554C22⋊Q8—24no—
555C22⋊Q8—24no—
556C22⋊Q8—24no—
557C22⋊Q8—22no—
558C22⋊Q8—22no—
559C22⋊Q8—24no—
560C22⋊Q8—24no—
561C22⋊Q8—24no—
562C22⋊Q8—24no—
563#121—24no—
564#121—24no—
565#121—24no—
566#121—24no—
567#121—22no—
568#121—22no—
569#121—22no—
570#121—22no—
571#121—21no—
572#121—21no—
573#121—21no—
574#121—21no—
575C4×Q8—24no—
576C4×Q8—22no—
577C4×Q8—22no—
578C4×Q8—22no—
579C4×Q8—22no—
580C4×Q8—22no—
581C4×Q8—22no—
582C4×Q8—22no—
583C4×Q8—22no—
584C4×Q8—22no—
585C4×Q8—22no—
586C4×Q8—22no—
587C4×Q8—22no—
588C4×Q8—22no—
589C4×Q8—22no—
590C4×Q8—21no—
591C4×Q8—21no—
592C4×Q8—21no—
593C4×Q8—21no—
594C4×Q8C22⋊C411yescharacteristic
595C4×Q8C22⋊C411yescharacteristic
596C4×Q8C22⋊C411yescharacteristic
597C4×Q8C22⋊C411yescharacteristic
598C4×Q8C22⋊C412yes—
599C4×Q8C22⋊C412yes—
600C4×Q8C2×D411yescharacteristic
601C4×Q8C2×D411yescharacteristic
602C4×Q8C2×D412yes—
603C4×Q8C2×D412yes—
604C4×Q8C2×D411yescharacteristic
605C4×Q8C2×D411yescharacteristic
606C4×D4—24no—
607C4×D4—22no—
608C4×D4—22no—
609C4×D4—24no—
610C4×D4—24no—
611C4×D4—24no—
612C4×D4—24no—
613C4×D4—22no—
614C4×D4—22no—
615C4×D4—22no—
616C4×D4—22no—
617C4×D4—24no—
618C4×D4—24no—
619C4×D4—24no—
620C4×D4—24no—
621C4×D4—21no—
622C4×D4—21no—
623C4×D4—21no—
624C4×D4—21no—
625C4×D4—22no—
626C4×D4—22no—
627C4×D4—22no—
628C4×D4—22no—
629C4×D4C22⋊C412yes—
630C4×D4C22⋊C411yescharacteristic
631C4×D4C22⋊C412yes—
632C4×D4C22⋊C411yescharacteristic
633C4×D4C22⋊C411yescharacteristic
634C4×D4C22⋊C411yescharacteristic
635C4×D4C22⋊C412yes—
636C4×D4C22⋊C412yes—
637C4×D4C22⋊C412yes—
638C4×D4C22⋊C412yes—
639C4×D4C22⋊C412yes—
640C4×D4C22⋊C412yes—
641C4×D4C22⋊C412yes—
642C4×D4C22⋊C412yes—
643C4×D4C2×D411yescharacteristic
644C4×D4C2×D411yescharacteristic
645C4×D4C2×D412yes—
646C4×D4C2×D412yes—
647C4×D4C2×D411yescharacteristic
648C4×D4C2×D411yescharacteristic
649C4×D4C2×D412yes—
650C4×D4C2×D412yes—
651C4×D4C2×D412yes—
652C4×D4C2×D412yes—
653C4×D4C2×D412yes—
654C4×D4C2×D412yes—
655C4×D4C2×D412yes—
656C4×D4C2×D412yes—
657#117—22no—
658#117—22no—
659#117—22no—
660#117—22no—
661#117—24no—
662#117—24no—
663#117—24no—
664#117—24no—
665#117—22no—
666#117—22no—
667#117—22no—
668#117—22no—
669#117—24no—
670#117—24no—
671#117—24no—
672#117—24no—
673#117C22⋊C411yescharacteristic
674#117C22⋊C411yescharacteristic
675#117C22⋊C411yescharacteristic
676#117C22⋊C411yescharacteristic
677#117C22⋊C412yes—
678#117C22⋊C412yes—
679#117C22⋊C412yes—
680#117C22⋊C412yes—
681#117C22⋊C412yes—
682#117C22⋊C412yes—
683#117C22⋊C412yes—
684#117C22⋊C412yes—
685#117C22⋊C412yes—
686#117C22⋊C412yes—
687C2×C4⋊C4—24no—
688C2×C4⋊C4—24no—
689C2×C4⋊C4—24no—
690C2×C4⋊C4—24no—
691C2×C4⋊C4—24no—
692C2×C4⋊C4—24no—
693C2×C4⋊C4—24no—
694C2×C4⋊C4—24no—
695C2×C4⋊C4—22no—
696C2×C4⋊C4—22no—
697C2×C4⋊C4—22no—
698C2×C4⋊C4—22no—
699C2×C4⋊C4—22no—
700C2×C4⋊C4—22no—
701C2×C4⋊C4—22no—
702C2×C4⋊C4—22no—
703C2×C4⋊C4—24no—
704C2×C4⋊C4—22no—
705C2×C4⋊C4—22no—
706C2×C4⋊C4C22×C414yes—
707C2×C4⋊C4C22×C412yes—
708C2×C4⋊C4C22×C412yes—
709C2×C4⋊C4C22×C414yes—
710C2×C4⋊C4C22×C412yes—
711C2×C4⋊C4C22×C414yes—
712C2×C4⋊C4C22×C414yes—
713C2×C4⋊C4C22×C414yes—
714C2×C4⋊C4C22×C414yes—
715C2×C4⋊C4C22×C414yes—
716C2×C4⋊C4C22×C414yes—
717C2×C4⋊C4C22×C412yes—
718C2×C4⋊C4C22×C414yes—
719C2×C4⋊C4C22×C412yes—
720C2×C4⋊C4C22×C412yes—
721C2×C4⋊C4C22×C414yes—
722C2×C4⋊C4C22×C411yescharacteristic
723C2×C4⋊C4C22×C412yes—
724C2×C4⋊C4C22×C411yescharacteristic
725C2×C4⋊C4C22×C412yes—
726C2×C4⋊C4C2411yescharacteristic
727C2×C4⋊C4C2411yescharacteristic
728C2×C4⋊C4C2412yes—
729C2×C4⋊C4C2412yes—
730C2×C22⋊C4C22×C412yes—
731C2×C22⋊C4C22×C412yes—
732C2×C22⋊C4C22×C414yes—
733C2×C22⋊C4C22×C412yes—
734C2×C22⋊C4C22×C414yes—
735C2×C22⋊C4C22×C414yes—
736C2×C22⋊C4C22×C412yes—
737C2×C22⋊C4C22×C414yes—
738C2×C22⋊C4C22×C412yes—
739C2×C22⋊C4C22×C412yes—
740C2×C22⋊C4C22×C412yes—
741C2×C22⋊C4C22×C412yes—
742C2×C42C22×C414yes—
743C2×C42C22×C414yes—
744C2×C42C22×C412yes—
745C2×C42C22×C412yes—
746C2×C42C22×C411yescharacteristic
747C2×C42C22×C411yescharacteristic
748C2×C42C22×C412yes—
749C2×C42C2×D412yes—
750C2×C42C2×D412yes—
751C2×C42C2×D412yes—
752C2×C42C2×D412yes—
753C2×C42C2×D412yes—
754C2×C42C2×D412yes—
755C2×C42C2×D412yes—
756C2×C42C2×D412yes—
757C2×C42C2×D411yescharacteristic
758C2×C42C2×D411yescharacteristic
759C2×C42C2×D411yescharacteristic
760C2×C42C2×D411yescharacteristic
761C2×C42C2×D411yescharacteristic
762C2×C42C2×D411yescharacteristic
763C2×C42C2×D411yescharacteristic
764C2×C42C2×D411yescharacteristic
765C2×C42C2412yes—
766C2×C42C2411yescharacteristic
767C2×C42C2411yescharacteristic
768C4⋊C8—21no—
769C4⋊C8—22no—
770C4⋊C8—21no—
771C4⋊C8—22no—
772C4⋊C8—24no—
773C4⋊C8—22no—
774C4⋊C8—24no—
775C4⋊C8—22no—
776C4⋊C8—21no—
777C4⋊C8—21no—
778C4⋊C8—24no—
779C4⋊C8—22no—
780C4⋊C8—24no—
781C4⋊C8—22no—
782#101—24no—
783#101—42no—
784#101—44no—
785#100—24no—
786#100—44no—
787#100—42no—
788C22⋊C8—24no—
789C22⋊C8—22no—
790C22⋊C8—24no—
791C22⋊C8—22no—
792C22⋊C8—24no—
793C22⋊C8—22no—
794C22⋊C8—24no—
795C22⋊C8—22no—
796#97—21no—
797#97—22no—
798#97—21no—
799#97—24no—
800#97—22no—
801#97—24no—
802#97—22no—
803C4×C8—21no—
804C4×C8—22no—
805C4×C8—21no—
806C4×C8—24no—
807C4×C8—22no—
808C4×C8—24no—
809C4×C8—22no—
810C24C23×C412yes—
811C24C23×C412yes—
812C24C23×C411yescharacteristic
813#41—24no—
814#41—24no—
815#41—44no—
816#41—44no—
817#41—42no—
818#41—42no—
819#41—416no—
820#41—48no—
821#41—48no—
822C2×Q8—22no—
823C2×Q8—22no—
824C2×Q8—22no—
825C2×Q8—22no—
826C2×Q8—21no—
827C2×Q8—21no—
828C2×Q8—22no—
829C2×Q8—22no—
830C2×Q8—42no—
831C2×Q8—44no—
832C2×Q8—82no—
833C2×Q8C2×C22⋊C411yescharacteristic
834C2×Q8C2×C22⋊C411yescharacteristic
835C2×Q8C2×C22⋊C412yes—
836C2×D4—24no—
837C2×D4—24no—
838C2×D4—24no—
839C2×D4—22no—
840C2×D4—22no—
841C2×D4—21no—
842C2×D4—21no—
843C2×D4—22no—
844C2×D4—22no—
845C2×D4—44no—
846C2×D4—48no—
847C2×D4—82no—
848C2×D4C2×C22⋊C412yes—
849C2×D4C2×C22⋊C411yescharacteristic
850C2×D4C2×C22⋊C412yes—
851C2×D4C2×C22⋊C412yes—
852C2×D4C2×C22⋊C412yes—
853C2×D4C2×C22⋊C412yes—
854C2×D4C2×C22⋊C411yescharacteristic
855C22×C4—24no—
856C22×C4—22no—
857C22×C4—24no—
858C22×C4—22no—
859C22×C4—24no—
860C22×C4—24no—
861C22×C4—24no—
862C22×C4—24no—
863C22×C4—22no—
864C22×C4—22no—
865C22×C4—24no—
866C22×C4—24no—
867C22×C4—42no—
868C22×C4—44no—
869C22×C4—44no—
870C22×C4—48no—
871C22×C4—82no—
872C22×C4—81no—
873C22×C4—84no—
874C22×C4—84no—
875C22×C4C2×C22⋊C412yes—
876C22×C4C2×C22⋊C412yes—
877C22×C4C2×C22⋊C411yescharacteristic
878C22×C4C2×C22⋊C411yescharacteristic
879C22×C4C2×C22⋊C412yes—
880C22×C4C2×C22⋊C412yes—
881C22×C4C2×C22⋊C412yes—
882C22×C4C2×C22⋊C412yes—
883C22×C4C2×C22⋊C412yes—
884C22×C4C2×C22⋊C412yes—
885C22×C4C2×C22⋊C411yescharacteristic
886C22×C4C2×C22⋊C411yescharacteristic
887C22×C4C2×C22⋊C411yescharacteristic
888C22×C4C2×C22⋊C411yescharacteristic
889C22×C4C2×C22⋊C411yescharacteristic
890C22×C4C2×C22⋊C411yescharacteristic
891C22×C4C23×C412yes—
892C22×C4C23×C411yescharacteristic
893C22×C4C23×C411yescharacteristic
894C22×C4C23×C412yes—
895C22×C4C23×C414yes—
896C22×C4C23×C414yes—
897C22×C4C23×C412yes—
898C22×C4C23×C412yes—
899C22×C4C23×C411yescharacteristic
900C22×C4C23×C412yes—
901C22×C4C23×C411yescharacteristic
902C22×C4C23×C411yescharacteristic
903C22×C4C23×C412yes—
904C22×C4C22×D412yes—
905C22×C4C22×D412yes—
906C22×C4C22×D412yes—
907C22×C4C22×D412yes—
908C22×C4C22×D411yescharacteristic
909C22×C4C22×D411yescharacteristic
910C22×C4C22×D411yescharacteristic
911C22×C4C22×D411yescharacteristic
912C22×C4C2511yescharacteristic
913M16—22no—
914M16—22no—
915M16—22no—
916M16—24no—
917M16—22no—
918M16—24no—
919M16—22no—
920M16—22no—
921M16—24no—
922M16—22no—
923M16—24no—
924M16—48no—
925M16—44no—
926M16—84no—
927M16—82no—
928M162−1+414yes—
929C2×C8—22no—
930C2×C8—22no—
931C2×C8—24no—
932C2×C8—22no—
933C2×C8—24no—
934C2×C8—22no—
935C2×C8—48no—
936C2×C8—44no—
937C2×C8—84no—
938C2×C8—82no—
939C4⋊C4—24no—
940C4⋊C4—24no—
941C4⋊C4—22no—
942C4⋊C4—22no—
943C4⋊C4—22no—
944C4⋊C4—22no—
945C4⋊C4—24no—
946C4⋊C4—24no—
947C4⋊C4—22no—
948C4⋊C4—22no—
949C4⋊C4—24no—
950C4⋊C4—24no—
951C4⋊C4—24no—
952C4⋊C4—24no—
953C4⋊C4—24no—
954C4⋊C4—24no—
955C4⋊C4—24no—
956C4⋊C4—24no—
957C4⋊C4—24no—
958C4⋊C4—24no—
959C4⋊C4—24no—
960C4⋊C4—24no—
961C4⋊C4—22no—
962C4⋊C4—22no—
963C4⋊C4—24no—
964C4⋊C4—24no—
965C4⋊C4—22no—
966C4⋊C4—22no—
967C4⋊C4—22no—
968C4⋊C4—22no—
969C4⋊C4—24no—
970C4⋊C4—24no—
971C4⋊C4—21no—
972C4⋊C4—21no—
973C4⋊C4—21no—
974C4⋊C4—21no—
975C4⋊C4—22no—
976C4⋊C4—22no—
977C4⋊C4—22no—
978C4⋊C4—22no—
979C4⋊C4C2×C22⋊C412yes—
980C4⋊C4C2×C22⋊C411yescharacteristic
981C4⋊C4C2×C22⋊C411yescharacteristic
982C4⋊C4C2×C22⋊C412yes—
983C4⋊C4C2×C22⋊C412yes—
984C4⋊C4C2×C22⋊C412yes—
985C4⋊C4C2×C22⋊C412yes—
986C4⋊C4C2×C22⋊C412yes—
987C4⋊C4C2×C22⋊C411yescharacteristic
988C4⋊C4C2×C22⋊C411yescharacteristic
989C4⋊C4C2×C22⋊C412yes—
990C4⋊C4C2×C22⋊C412yes—
991C4⋊C4C2×C22⋊C412yes—
992C4⋊C4C2×C22⋊C412yes—
993C22⋊C4—24no—
994C22⋊C4—24no—
995C22⋊C4—24no—
996C22⋊C4—24no—
997C22⋊C4—22no—
998C22⋊C4—22no—
999C22⋊C4—22no—
1000C22⋊C4—22no—
1001C22⋊C4—22no—
1002C22⋊C4—22no—
1003C22⋊C4—22no—
1004C22⋊C4—22no—
1005C22⋊C4—24no—
1006C22⋊C4—24no—
1007C22⋊C4—24no—
1008C22⋊C4—24no—
1009C22⋊C4—22no—
1010C22⋊C4—22no—
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—
1021C22⋊C4C2×C22⋊C412yes—
1022C22⋊C4C2×C22⋊C412yes—
1023C42—24no—
1024C42—24no—
1025C42—24no—
1026C42—24no—
1027C42—22no—
1028C42—22no—
1029C42C2×C22⋊C412yes—
1030C42C2×C22⋊C412yes—
1031C42C2×C22⋊C412yes—
1032C42C2×C22⋊C412yes—
1033C42C2×C22⋊C411yescharacteristic
1034C42C2×C22⋊C411yescharacteristic
1035C42C2×C22⋊C411yescharacteristic
1036C42C2×C22⋊C411yescharacteristic
1037C42C2×C22⋊C411yescharacteristic
1038C42C2×C22⋊C411yescharacteristic
1039C42C2×C22⋊C411yescharacteristic
1040C42C2×C22⋊C411yescharacteristic
1041C42C2×C22⋊C412yes—
1042C42C2×C22⋊C412yes—
1043C42C2×C22⋊C412yes—
1044C42C2×C22⋊C412yes—
1045C42C22×D411yescharacteristic
1046C42C22×D412yes—
1047C42C22×D412yes—
1048C42C22×D411yescharacteristic
1049C42C22×D411yescharacteristic
1050C42C22×D411yescharacteristic
1051C42C22×D412yes—
1052C42C22×D412yes—
1053C42C22×D411yescharacteristic
1054C42C22×D411yescharacteristic
1055C42C22×D411yescharacteristic
1056C42C22×D411yescharacteristic
1057C23—24no—
1058C23—24no—
1059C23—22no—
1060C23—22no—
1061C23—24no—
1062C23—42no—
1063C23—41no—
1064C23—41no—
1065C23—42no—
1066C23—42no—
1067C23C22×C22⋊C411yescharacteristic
1068C23C22×C22⋊C411yescharacteristic
1069C23C22×C22⋊C412yes—
1070C23C22×C22⋊C412yes—
1071C23C24×C411yescharacteristic
1072Q8—22no—
1073Q8—22no—
1074Q8—42no—
1075Q8—44no—
1076Q8—44no—
1077Q8—42no—
1078Q8—41no—
1079Q8—41no—
1080Q8—82no—
1081Q8—82no—
1082D4—24no—
1083D4—24no—
1084D4—24no—
1085D4—22no—
1086D4—42no—
1087D4—42no—
1088D4—48no—
1089D4—48no—
1090D4—42no—
1091D4—41no—
1092D4—41no—
1093D4—82no—
1094D4—82no—
1095D4#41314yes—
1096C2×C4—24no—
1097C2×C4—24no—
1098C2×C4—22no—
1099C2×C4—24no—
1100C2×C4—22no—
1101C2×C4—22no—
1102C2×C4—22no—
1103C2×C4—24no—
1104C2×C4—22no—
1105C2×C4—24no—
1106C2×C4—22no—
1107C2×C4—22no—
1108C2×C4—22no—
1109C2×C4—21no—
1110C2×C4—21no—
1111C2×C4—22no—
1112C2×C4—21no—
1113C2×C4—22no—
1114C2×C4—21no—
1115C2×C4—22no—
1116C2×C4—24no—
1117C2×C4—24no—
1118C2×C4—22no—
1119C2×C4—22no—
1120C2×C4—24no—
1121C2×C4—41no—
1122C2×C4—41no—
1123C2×C4—41no—
1124C2×C4—42no—
1125C2×C4—42no—
1126C2×C4—42no—
1127C2×C4—41no—
1128C2×C4—42no—
1129C2×C4—42no—
1130C2×C4—42no—
1131C2×C4—42no—
1132C2×C4—42no—
1133C2×C4—41no—
1134C2×C4—41no—
1135C2×C4—41no—
1136C2×C4—41no—
1137C2×C4—41no—
1138C2×C4—44no—
1139C2×C4—48no—
1140C2×C4—48no—
1141C2×C4—44no—
1142C2×C4—42no—
1143C2×C4—44no—
1144C2×C4—42no—
1145C2×C4—44no—
1146C2×C4—84no—
1147C2×C4—84no—
1148C2×C4—84no—
1149C2×C4—84no—
1150C2×C4C22×C22⋊C411yescharacteristic
1151C2×C4C22×C22⋊C411yescharacteristic
1152C2×C4C22×C22⋊C412yes—
1153C2×C4C22×C22⋊C412yes—
1154C2×C4C22×C22⋊C411yescharacteristic
1155C2×C4C22×C22⋊C411yescharacteristic
1156C2×C4C22×C22⋊C411yescharacteristic
1157C2×C4C22×C22⋊C411yescharacteristic
1158C2×C4C22×C22⋊C411yescharacteristic
1159C2×C4C22×C22⋊C412yes—
1160C2×C4C22×C22⋊C412yes—
1161C2×C4C22×C22⋊C411yescharacteristic
1162C2×C4C22×C22⋊C411yescharacteristic
1163C2×C4C22×C22⋊C412yes—
1164C2×C4C22×C22⋊C412yes—
1165C2×C4C22×C22⋊C411yescharacteristic
1166C2×C4C23×D411yescharacteristic
1167C2×C4C23×D411yescharacteristic
1168C2×C4C2×2−1+412yes—
1169C2×C4#58512yes—
1170C8—24no—
1171C8—44no—
1172C8—42no—
1173C8—42no—
1174C8—44no—
1175C8—42no—
1176C22—21no—
1177C22—21no—
1178C22—22no—
1179C22—22no—
1180C22—21no—
1181C22—21no—
1182C22—22no—
1183C22—22no—
1184C22—21no—
1185C22—21no—
1186C22—22no—
1187C22—21no—
1188C22—21no—
1189C22—48no—
1190C22—42no—
1191C22—42no—
1192C22—42no—
1193C22—82no—
1194C22—84no—
1195C22C2×#41314yes—
1196C22C23×C22⋊C411yescharacteristic
1197C22C4×2−1+412yes—
1198C4—21no—
1199C4—21no—
1200C4—21no—
1201C4—22no—
1202C4—22no—
1203C4—21no—
1204C4—21no—
1205C4—22no—
1206C4—22no—
1207C4—21no—
1208C4—21no—
1209C4—21no—
1210C4—22no—
1211C4—22no—
1212C4—21no—
1213C4—42no—
1214C4—44no—
1215C4—42no—
1216C4—44no—
1217C4—42no—
1218C4C2×#41312yes—
1219C4#348912yes—
1220C4#349911yescharacteristic
1221C4#350011yescharacteristic
1222C2—22no—
1223C2—24no—
1224C2—42no—
1225C2—41no—
1226C2—41no—
1227C2—82no—
1228C2#3425911yescharacteristic
1229C2C22×#41311yescharacteristic
1230C2#6007611yescharacteristic
subgroupG/H
center, socleC22C23×C22⋊C4
commutatorC23C24×C4
Frattini, cosocleC22×C4C25
prime radicalC2×#3515C2
LCSG ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22 ◁ C2×C4×#41 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #60263C2semidirect
3. M16×#41C2semidirect
4. #22517C2semidirect
5. #22515C2semidirect
6. #22482C2semidirect
7. #22481C2semidirect
8. #22480C2semidirect
9. #22479C2semidirect
10. #21880C2semidirect
11. #21880C2semidirect
12. #21831C2semidirect
13. #21830C2semidirect
14. #21426C2semidirect
15. #21426C2semidirect
16. #21337C2semidirect
17. C2×#1998C2semidirect

Maximal subgroups

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

subgroupindex
C2×#35152
#602632
M16×#412
#225172
#225152
#224822
#224812
#224802
#224792
#218802
#218312
#218302
#214262
#213372
C2×#19982