Finite Group Databasebeta

← #6374713

Subgroups — #6374713

Order 512.

3036 conjugacy classes of subgroups.

The subgroup lattice has 1199 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3455C211yesmaximal, characteristic
2#60124C211yesmaximal, characteristic, complemented
3#34109C211yesmaximal, characteristic, complemented
4#21901C214yesmaximal, complemented
5#21858C214yesmaximal, complemented
6#21845C211yesmaximal, characteristic, complemented
7#21844C211yesmaximal, characteristic, complemented
8#21816C211yesmaximal, characteristic, complemented
9#21815C211yesmaximal, characteristic, complemented
10#21774C212yesmaximal, complemented
11#21773C212yesmaximal, complemented
12#21419C214yesmaximal, complemented
13#21384C214yesmaximal, complemented
14#20748C212yesmaximal, complemented
15#20747C212yesmaximal, complemented
16#3455—22no—
17#3455—22no—
18#3455—21no—
19#3455—21no—
20#3455—21no—
21#3455—21no—
22#3455C414yescomplemented
23#3455C414yescomplemented
24#3455C2212yes—
25#3455C2212yes—
26#3455C2212yes—
27#3455C2212yes—
28C2×#542C412yescomplemented
29C2×#542C412yescomplemented
30C2×#541C412yescomplemented
31C2×#540C412yescomplemented
32C2×#539—21no—
33C2×#539—21no—
34C2×#538—21no—
35C2×#538—21no—
36C2×#533C2211yescharacteristic
37C2×#532C2211yescharacteristic
38C2×#529—22no—
39C2×#529—22no—
40C2×#525C2212yes—
41C2×C4×#41C2212yes—
42C22×#117C2211yescharacteristic
43#2924—22no—
44#2924—22no—
45#2924—22no—
46#2924—22no—
47#2921C2212yescomplemented
48#2921C2212yescomplemented
49#2920C2212yes—
50#2920C2211yescharacteristic
51#2920C2211yescharacteristic
52#2905C2212yescomplemented
53C2×#407C2212yes—
54#2873C2212yescomplemented
55#2347—21no—
56#2346—21no—
57#2345—21no—
58#2344—21no—
59#2343—21no—
60#2343—21no—
61#2342—21no—
62#2342—21no—
63#2298C2212yescomplemented
64#2298C2212yescomplemented
65#2296C2212yescomplemented
66#2283C2211yescharacteristic
67#2283C2211yescharacteristic
68#2280C2211yescharacteristic
69C4×#117C2211yescharacteristic
70C4×#117C2211yescharacteristic
71C4×#117C2212yescomplemented
72C2×C4×C22⋊C4C2211yescharacteristic
73#1995C2214yescomplemented
74#1994C2214yescomplemented
75#1986C2214yescomplemented
76#1986C2214yescomplemented
77#1980C2214yescomplemented
78#1980C2214yescomplemented
79#1963C2214yescomplemented
80#1962C2214yescomplemented
81#1897C2218yescomplemented
82#1896C2218yescomplemented
83#1871C2218yescomplemented
84#1871C2218yescomplemented
85#1826C2212yes—
86#1826C2212yes—
87#1826C2212yes—
88#1826C2212yes—
89#1806C2218yescomplemented
90#1806C2218yescomplemented
91#1789C2212yes—
92#1789C2212yes—
93#1789C2212yes—
94#1789C2212yes—
95#1759C2218yescomplemented
96C4×#104C2218yescomplemented
97C22×#41C2312yes—
98C24×C4C2311yescharacteristic
99C22×M16C2314yes—
100#542—22no—
101#542—22no—
102#542—22no—
103#542—22no—
104#542—22no—
105#542—22no—
106#542—22no—
107#542—22no—
108#542C2×C414yes—
109#542C2×C414yes—
110#542C2×C414yes—
111#542C2×C414yes—
112#542C2×C414yescomplemented
113#542C2×C414yescomplemented
114#542C2×C414yescomplemented
115#542C2×C414yescomplemented
116#541—22no—
117#541—22no—
118#541—22no—
119#541—22no—
120#541C2×C414yes—
121#541C2×C414yes—
122#541C2×C414yescomplemented
123#541C2×C414yescomplemented
124#540—22no—
125#540—22no—
126#540—22no—
127#540—22no—
128#540C2×C414yes—
129#540C2×C414yes—
130#540C2×C414yescomplemented
131#540C2×C414yescomplemented
132#539—24no—
133#539—24no—
134#539—24no—
135#539—24no—
136#539—22no—
137#539—22no—
138#539—22no—
139#539—22no—
140#539—22no—
141#539—22no—
142#539—22no—
143#539—22no—
144#538—24no—
145#538—24no—
146#538—24no—
147#538—24no—
148#538—22no—
149#538—22no—
150#538—22no—
151#538—22no—
152#538—22no—
153#538—22no—
154#538—22no—
155#538—22no—
156#533—21no—
157#533—21no—
158#533—21no—
159#533—21no—
160#533C2×C412yescomplemented
161#533C2×C412yescomplemented
162#533C2312yes—
163#533C2312yes—
164#532—21no—
165#532—21no—
166#532—21no—
167#532—21no—
168#532C2×C412yescomplemented
169#532C2×C412yescomplemented
170#532C2312yes—
171#532C2312yes—
172C2×C4⋊Q8C2×C411yescharacteristic, complemented
173C2×C4⋊Q8C2×C411yescharacteristic, complemented
174C2×C4⋊Q8C2×C411yescharacteristic, complemented
175C2×#127C2×C411yescharacteristic, complemented
176#529—24no—
177#529—24no—
178#529—24no—
179#529—24no—
180#529—24no—
181#529—24no—
182#529—24no—
183#529—24no—
184#529—24no—
185#529—24no—
186#529—24no—
187#529—24no—
188#529—24no—
189#529—24no—
190#529—24no—
191#529—24no—
192C2×#126—22no—
193C2×#126—22no—
194C2×#126—22no—
195C2×#126—22no—
196C2×#125—22no—
197C2×#125—22no—
198C2×#125C2×C412yescomplemented
199C2×#124—22no—
200C2×#124—22no—
201C2×#124C2×C412yescomplemented
202#525—22no—
203#525—22no—
204#525—22no—
205#525—22no—
206#525C2×C414yes—
207#525C2×C414yes—
208#525C2314yes—
209#525C2314yes—
210C2×#123—22no—
211C2×#123—22no—
212C2×#123—22no—
213C2×#123—22no—
214C2×#123—22no—
215C2×C22⋊Q8—21no—
216C2×C22⋊Q8—21no—
217C2×C22⋊Q8—22no—
218C2×C22⋊Q8—22no—
219C2×C22⋊Q8C2×C412yes—
220C2×C22⋊Q8C2×C412yes—
221C2×#121—21no—
222C2×#121—21no—
223C2×#121—22no—
224C2×#121—22no—
225C2×#121C2×C412yes—
226C2×#121C2×C412yes—
227C2×#120—22no—
228C4×#41—22no—
229C4×#41—22no—
230C4×#41—22no—
231C4×#41—22no—
232C4×#41C2×C414yescomplemented
233C4×#41C2×C414yescomplemented
234C4×#41C2314yes—
235C4×#41C2314yes—
236C2×C4×Q8—21no—
237C2×C4×Q8—21no—
238C2×C4×Q8C2×C412yescomplemented
239C2×C4×Q8C2×C412yescomplemented
240C2×C4×D4—22no—
241C2×C4×D4—22no—
242C2×C4×D4—22no—
243C2×C4×D4—22no—
244C2×C4×D4—21no—
245C2×C4×D4—21no—
246C2×C4×D4C2×C412yescomplemented
247C2×C4×D4C2×C412yescomplemented
248C2×#117—21no—
249C2×#117—21no—
250C2×#117—22no—
251C2×#117C2×C412yes—
252C2×#117C2×C412yes—
253C2×#117C2×C412yes—
254C2×#117C2×C412yes—
255C2×#117D412yes—
256C2×#117D412yes—
257C2×#117D412yes—
258C2×#117D412yes—
259C2×#117D411yescharacteristic
260C2×#117D411yescharacteristic
261C2×#117D411yescharacteristic
262C2×#117D411yescharacteristic
263C2×#117C2312yes—
264C2×#117C2312yes—
265C2×#117C2311yescharacteristic
266C2×#117C2311yescharacteristic
267C2×#117C2311yescharacteristic
268C2×#117C2311yescharacteristic
269C22×C4⋊C4D411yescharacteristic
270C22×C4⋊C4D411yescharacteristic
271C22×C22⋊C4—21no—
272C22×C22⋊C4D411yescharacteristic
273C22×C22⋊C4D411yescharacteristic
274C22×C42—22no—
275C22×C42C2312yes—
276C22×C42C2311yescharacteristic
277C22×C42C2311yescharacteristic
278#433—24no—
279#433—24no—
280#433—24no—
281#433—24no—
282#432—22no—
283#432—21no—
284#432—21no—
285#432—22no—
286#432—21no—
287#432—21no—
288#431—22no—
289#431—21no—
290#431—21no—
291#431—22no—
292#431—21no—
293#431—21no—
294#424—24no—
295#424—24no—
296#423C2314yes—
297#423C2312yes—
298#423C2312yes—
299C2×#104C2318yes—
300C2×#104C2318yes—
301C2×#104C2318yes—
302C2×#104C2318yes—
303#407—22no—
304#407—22no—
305#407C2312yes—
306#407C2312yes—
307#407C2314yes—
308C2×C22⋊C8—22no—
309C2×C22⋊C8—22no—
310#405—24no—
311#405—24no—
312C4×M16C2312yes—
313C4×M16C2312yes—
314C4×M16C2314yes—
315#389—22no—
316#389—22no—
317#388—22no—
318#388—22no—
319#388—22no—
320#388—22no—
321#387—22no—
322#387—22no—
323#387—22no—
324#387—22no—
325#385—22no—
326#385—22no—
327#383—21no—
328#383—21no—
329#382—21no—
330#382—21no—
331#381—21no—
332#381—21no—
333#381—21no—
334#380—21no—
335#380—21no—
336#380—21no—
337#380—21no—
338#379—21no—
339C4×C4⋊C4—22no—
340C4×C4⋊C4—22no—
341C4×C4⋊C4—21no—
342C4×C4⋊C4—21no—
343C4×C4⋊C4C2312yes—
344C4×C4⋊C4C2312yes—
345C4×C4⋊C4C2312yes—
346C4×C4⋊C4C2312yes—
347C4×C22⋊C4—21no—
348C4×C22⋊C4—21no—
349C4×C22⋊C4—21no—
350C4×C22⋊C4—21no—
351C4×C22⋊C4—22no—
352C4×C22⋊C4—22no—
353C4×C22⋊C4C2311yescharacteristic
354C4×C22⋊C4C2311yescharacteristic
355C4×C22⋊C4C2311yescharacteristic
356C4×C22⋊C4C2311yescharacteristic
357C4×C22⋊C4C2312yes—
358C4×C22⋊C4C2312yes—
359#376—21no—
360#376—21no—
361#376C2312yes—
362#376C2312yes—
363C2×#95—21no—
364C43C2312yes—
365C43C2312yes—
366#339C2318yes—
367#339C2318yes—
368#339C2318yes—
369#339C2318yes—
370C25C2×D411yescharacteristic
371C2×#41—22no—
372C2×#41—22no—
373C2×#41—48no—
374C2×#41C22×C414yes—
375C2×#41C2414yes—
376C22×Q8—21no—
377C22×Q8—21no—
378C22×Q8C22×C412yes—
379C22×D4—22no—
380C22×D4—22no—
381C22×D4—22no—
382C22×D4—21no—
383C22×D4—21no—
384C22×D4C22×C412yes—
385C23×C4—22no—
386C23×C4—22no—
387C23×C4—22no—
388C23×C4—22no—
389C23×C4—44no—
390C23×C4C22×C412yes—
391C23×C4C22×C412yes—
392C23×C4C2×D411yescharacteristic
393C23×C4C2×D411yescharacteristic
394C23×C4C2×D411yescharacteristic
395C23×C4C2×D411yescharacteristic
396C23×C4C2×D411yescharacteristic
397C23×C4C2×D412yes—
398C23×C4C2×D412yes—
399C23×C4C2×D411yescharacteristic
400C23×C4C2×D411yescharacteristic
401C23×C4C2411yescharacteristic
402C23×C4C2411yescharacteristic
403C23×C4C2411yescharacteristic
404C2×M16—24no—
405C2×M16—48no—
406C2×M16C2414yes—
407C2×M16C2414yes—
408C22×C8—24no—
409C4⋊Q8—21no—
410C4⋊Q8—21no—
411C4⋊Q8—21no—
412C4⋊Q8—21no—
413C4⋊Q8—21no—
414C4⋊Q8—21no—
415C4⋊Q8C22×C412yes—
416C4⋊Q8C22×C412yes—
417C4⋊Q8C22×C412yes—
418C4⋊Q8C22×C412yes—
419C4⋊Q8C22×C412yes—
420C4⋊Q8C22×C412yes—
421#127—21no—
422#127—21no—
423#127C22×C412yes—
424#127C22×C412yes—
425#126—24no—
426#126—24no—
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—24no—
437#126—24no—
438#126—24no—
439#126—24no—
440#126—24no—
441#125—24no—
442#125—24no—
443#125—24no—
444#125—24no—
445#125—24no—
446#125—24no—
447#125—24no—
448#125—24no—
449#125—22no—
450#125—22no—
451#125C22×C414yes—
452#125C22×C414yes—
453#124—24no—
454#124—24no—
455#124—24no—
456#124—24no—
457#124—24no—
458#124—24no—
459#124—24no—
460#124—24no—
461#124—22no—
462#124—22no—
463#124C22×C414yes—
464#124C22×C414yes—
465#123—24no—
466#123—24no—
467#123—24no—
468#123—24no—
469#123—24no—
470#123—24no—
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—24no—
480#123—24no—
481#123—24no—
482#123—24no—
483#123—24no—
484#123—24no—
485C22⋊Q8—22no—
486C22⋊Q8—22no—
487C22⋊Q8—22no—
488C22⋊Q8—22no—
489C22⋊Q8—22no—
490C22⋊Q8—22no—
491C22⋊Q8—22no—
492C22⋊Q8—22no—
493C22⋊Q8—22no—
494C22⋊Q8—22no—
495C22⋊Q8—22no—
496C22⋊Q8—22no—
497C22⋊Q8—24no—
498C22⋊Q8—24no—
499C22⋊Q8—24no—
500C22⋊Q8—24no—
501C22⋊Q8—24no—
502C22⋊Q8—24no—
503C22⋊Q8—24no—
504C22⋊Q8—24no—
505C22⋊Q8C22×C414yes—
506C22⋊Q8C22×C414yes—
507C22⋊Q8C22×C414yes—
508C22⋊Q8C22×C414yes—
509#121—22no—
510#121—22no—
511#121—22no—
512#121—22no—
513#121—22no—
514#121—22no—
515#121—22no—
516#121—22no—
517#121—22no—
518#121—22no—
519#121—22no—
520#121—22no—
521#121—24no—
522#121—24no—
523#121—24no—
524#121—24no—
525#121—24no—
526#121—24no—
527#121—24no—
528#121—24no—
529#121C22×C414yes—
530#121C22×C414yes—
531#121C22×C414yes—
532#121C22×C414yes—
533#120—24no—
534#120—24no—
535#120—24no—
536#120—24no—
537C4×Q8—22no—
538C4×Q8—22no—
539C4×Q8—22no—
540C4×Q8—22no—
541C4×Q8—22no—
542C4×Q8—22no—
543C4×Q8—22no—
544C4×Q8—22no—
545C4×Q8—22no—
546C4×Q8—22no—
547C4×Q8—22no—
548C4×Q8—22no—
549C4×Q8C22×C414yes—
550C4×Q8C22×C414yes—
551C4×Q8C22×C414yes—
552C4×Q8C22×C414yes—
553C4×D4—24no—
554C4×D4—24no—
555C4×D4—24no—
556C4×D4—24no—
557C4×D4—24no—
558C4×D4—24no—
559C4×D4—24no—
560C4×D4—24no—
561C4×D4—24no—
562C4×D4—24no—
563C4×D4—24no—
564C4×D4—24no—
565C4×D4—24no—
566C4×D4—24no—
567C4×D4—24no—
568C4×D4—24no—
569C4×D4—22no—
570C4×D4—22no—
571C4×D4—22no—
572C4×D4—22no—
573C4×D4—22no—
574C4×D4—22no—
575C4×D4—22no—
576C4×D4—22no—
577C4×D4—22no—
578C4×D4—22no—
579C4×D4—22no—
580C4×D4—22no—
581C4×D4C22×C414yes—
582C4×D4C22×C414yes—
583C4×D4C22×C414yes—
584C4×D4C22×C414yes—
585#117—22no—
586#117—22no—
587#117—24no—
588#117—24no—
589#117—24no—
590#117—24no—
591#117—44no—
592#117—44no—
593#117—44no—
594#117C22⋊C412yes—
595#117C22⋊C412yes—
596#117C22⋊C412yes—
597#117C22⋊C412yes—
598#117C22⋊C412yes—
599#117C22⋊C412yes—
600#117C22⋊C412yes—
601#117C22⋊C412yes—
602#117C22⋊C412yes—
603#117C22⋊C412yes—
604#117C22⋊C412yes—
605#117C22⋊C412yes—
606#117C22⋊C412yes—
607#117C22⋊C412yes—
608#117C22⋊C412yes—
609#117C22⋊C412yes—
610#117C22×C414yes—
611#117C22×C412yes—
612#117C22×C412yes—
613#117C22×C412yes—
614#117C22×C412yes—
615#117C22×C412yes—
616#117C22×C412yes—
617#117C22×C412yes—
618#117C22×C412yes—
619#117C2×D412yes—
620#117C2×D412yes—
621#117C2×D412yes—
622#117C2×D412yes—
623#117C2×D412yes—
624#117C2×D412yes—
625#117C2×D412yes—
626#117C2×D412yes—
627#117C2414yes—
628C2×C4⋊C4—22no—
629C2×C4⋊C4—22no—
630C2×C4⋊C4—21no—
631C2×C4⋊C4—21no—
632C2×C4⋊C4—22no—
633C2×C4⋊C4—22no—
634C2×C4⋊C4—22no—
635C2×C4⋊C4—22no—
636C2×C4⋊C4—21no—
637C2×C4⋊C4—21no—
638C2×C4⋊C4—22no—
639C2×C4⋊C4—22no—
640C2×C4⋊C4—22no—
641C2×C4⋊C4—22no—
642C2×C4⋊C4—22no—
643C2×C4⋊C4C22⋊C412yes—
644C2×C4⋊C4C22⋊C412yes—
645C2×C4⋊C4C22⋊C412yes—
646C2×C4⋊C4C22⋊C412yes—
647C2×C4⋊C4C22⋊C412yes—
648C2×C4⋊C4C22⋊C412yes—
649C2×C4⋊C4C22⋊C412yes—
650C2×C4⋊C4C22⋊C412yes—
651C2×C4⋊C4C22×C412yes—
652C2×C4⋊C4C22×C412yes—
653C2×C4⋊C4C2×D411yescharacteristic
654C2×C4⋊C4C2×D411yescharacteristic
655C2×C4⋊C4C2×D411yescharacteristic
656C2×C4⋊C4C2×D411yescharacteristic
657C2×C4⋊C4C2×D411yescharacteristic
658C2×C4⋊C4C2×D411yescharacteristic
659C2×C4⋊C4C2×D411yescharacteristic
660C2×C4⋊C4C2×D411yescharacteristic
661C2×C22⋊C4—22no—
662C2×C22⋊C4—22no—
663C2×C22⋊C4—21no—
664C2×C22⋊C4—22no—
665C2×C22⋊C4—22no—
666C2×C22⋊C4—22no—
667C2×C22⋊C4—22no—
668C2×C22⋊C4—22no—
669C2×C22⋊C4—22no—
670C2×C22⋊C4—22no—
671C2×C22⋊C4—21no—
672C2×C22⋊C4—22no—
673C2×C22⋊C4—21no—
674C2×C22⋊C4—21no—
675C2×C22⋊C4—22no—
676C2×C22⋊C4—22no—
677C2×C22⋊C4—44no—
678C2×C22⋊C4C22⋊C412yes—
679C2×C22⋊C4C22⋊C412yes—
680C2×C22⋊C4C22⋊C412yes—
681C2×C22⋊C4C22⋊C412yes—
682C2×C22⋊C4C22⋊C412yes—
683C2×C22⋊C4C22⋊C412yes—
684C2×C22⋊C4C22⋊C412yes—
685C2×C22⋊C4C22⋊C412yes—
686C2×C22⋊C4C2×D411yescharacteristic
687C2×C22⋊C4C2×D411yescharacteristic
688C2×C22⋊C4C2×D411yescharacteristic
689C2×C22⋊C4C2×D411yescharacteristic
690C2×C22⋊C4C2×D411yescharacteristic
691C2×C22⋊C4C2×D411yescharacteristic
692C2×C22⋊C4C2×D411yescharacteristic
693C2×C22⋊C4C2×D411yescharacteristic
694C2×C42—22no—
695C2×C42—22no—
696C2×C42—22no—
697C2×C42—24no—
698C2×C42—24no—
699C2×C42—24no—
700C2×C42—24no—
701C2×C42—22no—
702C2×C42—22no—
703C2×C42—22no—
704C2×C42—22no—
705C2×C42—22no—
706C2×C42—44no—
707C2×C42C22×C412yes—
708C2×C42C22×C412yes—
709C2×C42C22×C411yescharacteristic
710C2×C42C22×C411yescharacteristic
711C2×C42C22×C411yescharacteristic
712C2×C42C22×C411yescharacteristic
713C2×C42C2×D411yescharacteristic
714C2×C42C2×D411yescharacteristic
715C2×C42C2×D411yescharacteristic
716C2×C42C2×D411yescharacteristic
717C2×C42C2×D412yes—
718C2×C42C2×D411yescharacteristic
719C2×C42C2×D411yescharacteristic
720C2×C42C2×D412yes—
721C2×C42C2×D411yescharacteristic
722C2×C42C2×D411yescharacteristic
723C2×C42C2412yes—
724C2×C42C2412yes—
725C2×C42C2412yes—
726C2×C42C2412yes—
727C2×C42C2411yescharacteristic
728C2×C42C2411yescharacteristic
729C2×C42C2411yescharacteristic
730C2×C42C2411yescharacteristic
731C4⋊C8—24no—
732C4⋊C8—24no—
733C4⋊C8—22no—
734C4⋊C8—22no—
735C4⋊C8—22no—
736C4⋊C8—22no—
737#104—48no—
738#104—48no—
739#104—48no—
740#104—48no—
741C22⋊C8—22no—
742C22⋊C8—22no—
743C22⋊C8—22no—
744C22⋊C8—22no—
745C22⋊C8—24no—
746C22⋊C8—24no—
747#97—24no—
748#97—22no—
749#97—22no—
750C4×C8—24no—
751C4×C8—22no—
752C4×C8—22no—
753#95—21no—
754#95—21no—
755#95—22no—
756#95—22no—
757#95—22no—
758#95—21no—
759#95—21no—
760#95—22no—
761#95—22no—
762#95—22no—
763#95—22no—
764#95—22no—
765#95—22no—
766#95—22no—
767C24—22no—
768C24—42no—
769C24—42no—
770C24—81no—
771C24C2×C22⋊C412yes—
772C24C2×C22⋊C412yes—
773C24C22×D411yescharacteristic
774C24C22×D411yescharacteristic
775C24C22×D411yescharacteristic
776#41—28no—
777#41—28no—
778#41—44no—
779#41—44no—
780#41—48no—
781#41—48no—
782C2×Q8—22no—
783C2×Q8—22no—
784C2×Q8—22no—
785C2×Q8—22no—
786C2×Q8—22no—
787C2×Q8—44no—
788C2×Q8—82no—
789C2×Q8—82no—
790C2×Q8C23×C414yes—
791C2×D4—24no—
792C2×D4—24no—
793C2×D4—24no—
794C2×D4—24no—
795C2×D4—24no—
796C2×D4—24no—
797C2×D4—22no—
798C2×D4—22no—
799C2×D4—22no—
800C2×D4—22no—
801C2×D4—22no—
802C2×D4—44no—
803C2×D4—48no—
804C2×D4—82no—
805C2×D4—84no—
806C2×D4—82no—
807C2×D4—84no—
808C2×D4C23×C414yes—
809C22×C4—24no—
810C22×C4—24no—
811C22×C4—24no—
812C22×C4—22no—
813C22×C4—22no—
814C22×C4—22no—
815C22×C4—22no—
816C22×C4—24no—
817C22×C4—24no—
818C22×C4—24no—
819C22×C4—24no—
820C22×C4—24no—
821C22×C4—24no—
822C22×C4—22no—
823C22×C4—22no—
824C22×C4—22no—
825C22×C4—44no—
826C22×C4—44no—
827C22×C4—44no—
828C22×C4—44no—
829C22×C4—42no—
830C22×C4—42no—
831C22×C4—42no—
832C22×C4—42no—
833C22×C4—42no—
834C22×C4—48no—
835C22×C4—44no—
836C22×C4—44no—
837C22×C4—84no—
838C22×C4—81no—
839C22×C4—81no—
840C22×C4—84no—
841C22×C4—82no—
842C22×C4C2×C22⋊C412yes—
843C22×C4C2×C22⋊C411yescharacteristic
844C22×C4C2×C22⋊C411yescharacteristic
845C22×C4C2×C22⋊C412yes—
846C22×C4C2×C22⋊C411yescharacteristic
847C22×C4C2×C22⋊C411yescharacteristic
848C22×C4C2×C22⋊C412yes—
849C22×C4C2×C22⋊C412yes—
850C22×C4C2×C22⋊C411yescharacteristic
851C22×C4C2×C22⋊C411yescharacteristic
852C22×C4C2×C22⋊C411yescharacteristic
853C22×C4C2×C22⋊C411yescharacteristic
854C22×C4C2×C22⋊C412yes—
855C22×C4C2×C22⋊C412yes—
856C22×C4C2×C22⋊C412yes—
857C22×C4C2×C22⋊C412yes—
858C22×C4C2×C22⋊C412yes—
859C22×C4C2×C22⋊C412yes—
860C22×C4C23×C411yescharacteristic
861C22×C4C23×C411yescharacteristic
862C22×C4C23×C412yes—
863C22×C4C23×C412yes—
864C22×C4C22×D411yescharacteristic
865C22×C4C22×D411yescharacteristic
866C22×C4C22×D411yescharacteristic
867C22×C4C22×D411yescharacteristic
868C22×C4C22×D411yescharacteristic
869C22×C4C22×D412yes—
870C22×C4C22×D412yes—
871C22×C4C22×D411yescharacteristic
872C22×C4C22×D411yescharacteristic
873C22×C4C22×D411yescharacteristic
874C22×C4C22×D411yescharacteristic
875C22×C4C22×D411yescharacteristic
876C22×C4C22×D411yescharacteristic
877C22×C4C22×D411yescharacteristic
878C22×C4C22×D411yescharacteristic
879C22×C4C2511yescharacteristic
880M16—28no—
881M16—28no—
882M16—48no—
883C2×C8—24no—
884C2×C8—24no—
885C2×C8—48no—
886C4⋊C4—24no—
887C4⋊C4—24no—
888C4⋊C4—24no—
889C4⋊C4—24no—
890C4⋊C4—22no—
891C4⋊C4—22no—
892C4⋊C4—22no—
893C4⋊C4—22no—
894C4⋊C4—24no—
895C4⋊C4—24no—
896C4⋊C4—24no—
897C4⋊C4—24no—
898C4⋊C4—24no—
899C4⋊C4—24no—
900C4⋊C4—24no—
901C4⋊C4—24no—
902C4⋊C4—22no—
903C4⋊C4—22no—
904C4⋊C4—22no—
905C4⋊C4—22no—
906C4⋊C4—22no—
907C4⋊C4—22no—
908C4⋊C4—44no—
909C4⋊C4—44no—
910C4⋊C4—44no—
911C4⋊C4—82no—
912C4⋊C4—82no—
913C4⋊C4C2×C22⋊C412yes—
914C4⋊C4C2×C22⋊C412yes—
915C4⋊C4C2×C22⋊C412yes—
916C4⋊C4C2×C22⋊C412yes—
917C4⋊C4C2×C22⋊C412yes—
918C4⋊C4C2×C22⋊C412yes—
919C4⋊C4C2×C22⋊C412yes—
920C4⋊C4C2×C22⋊C412yes—
921C4⋊C4C2×C22⋊C412yes—
922C4⋊C4C2×C22⋊C412yes—
923C4⋊C4C2×C22⋊C412yes—
924C4⋊C4C2×C22⋊C412yes—
925C4⋊C4C2×C22⋊C412yes—
926C4⋊C4C2×C22⋊C412yes—
927C4⋊C4C2×C22⋊C412yes—
928C4⋊C4C2×C22⋊C412yes—
929C4⋊C4C23×C414yes—
930C4⋊C4C23×C414yes—
931C22⋊C4—24no—
932C22⋊C4—24no—
933C22⋊C4—24no—
934C22⋊C4—24no—
935C22⋊C4—24no—
936C22⋊C4—24no—
937C22⋊C4—24no—
938C22⋊C4—24no—
939C22⋊C4—24no—
940C22⋊C4—24no—
941C22⋊C4—24no—
942C22⋊C4—24no—
943C22⋊C4—24no—
944C22⋊C4—24no—
945C22⋊C4—24no—
946C22⋊C4—24no—
947C22⋊C4—24no—
948C22⋊C4—24no—
949C22⋊C4—24no—
950C22⋊C4—44no—
951C22⋊C4—42no—
952C22⋊C4—42no—
953C22⋊C4—42no—
954C22⋊C4—44no—
955C22⋊C4—82no—
956C22⋊C4C2×C22⋊C412yes—
957C22⋊C4C2×C22⋊C412yes—
958C22⋊C4C2×C22⋊C412yes—
959C22⋊C4C2×C22⋊C412yes—
960C22⋊C4C2×C22⋊C412yes—
961C22⋊C4C2×C22⋊C412yes—
962C22⋊C4C2×C22⋊C412yes—
963C22⋊C4C2×C22⋊C412yes—
964C22⋊C4C2×C22⋊C412yes—
965C22⋊C4C2×C22⋊C412yes—
966C22⋊C4C2×C22⋊C412yes—
967C22⋊C4C2×C22⋊C412yes—
968C22⋊C4C2×C22⋊C412yes—
969C22⋊C4C2×C22⋊C412yes—
970C22⋊C4C2×C22⋊C412yes—
971C22⋊C4C2×C22⋊C412yes—
972C42—24no—
973C42—24no—
974C42—24no—
975C42—24no—
976C42—24no—
977C42—24no—
978C42—24no—
979C42—24no—
980C42—24no—
981C42—24no—
982C42—44no—
983C42—44no—
984C42—44no—
985C42—82no—
986C42—82no—
987C42C2×C22⋊C412yes—
988C42C2×C22⋊C412yes—
989C42C2×C22⋊C411yescharacteristic
990C42C2×C22⋊C411yescharacteristic
991C42C2×C22⋊C411yescharacteristic
992C42C2×C22⋊C411yescharacteristic
993C42C2×C22⋊C412yes—
994C42C2×C22⋊C412yes—
995C42C2×C22⋊C411yescharacteristic
996C42C2×C22⋊C411yescharacteristic
997C42C2×C22⋊C411yescharacteristic
998C42C2×C22⋊C411yescharacteristic
999C42C23×C412yes—
1000C42C23×C412yes—
1001C42C23×C411yescharacteristic
1002C42C23×C411yescharacteristic
1003C42C23×C411yescharacteristic
1004C42C23×C411yescharacteristic
1005C42C22×D412yes—
1006C42C22×D411yescharacteristic
1007C42C22×D411yescharacteristic
1008C42C22×D412yes—
1009C42C22×D411yescharacteristic
1010C42C22×D411yescharacteristic
1011C23—22no—
1012C23—22no—
1013C23—22no—
1014C23—24no—
1015C23—22no—
1016C23—24no—
1017C23—41no—
1018C23—41no—
1019C23—41no—
1020C23—41no—
1021C23—41no—
1022C23—42no—
1023C23—42no—
1024C23—42no—
1025C23—42no—
1026C23—42no—
1027C23—44no—
1028C23—44no—
1029C23—44no—
1030C23—88no—
1031C23C22×C22⋊C412yes—
1032C23C22×C22⋊C412yes—
1033C23C22×C22⋊C411yescharacteristic
1034C23C22×C22⋊C411yescharacteristic
1035C23C23×D411yescharacteristic
1036Q8—24no—
1037Q8—24no—
1038Q8—44no—
1039Q8—82no—
1040Q8—82no—
1041Q8—82no—
1042Q8—82no—
1043D4—24no—
1044D4—24no—
1045D4—44no—
1046D4—48no—
1047D4—48no—
1048D4—82no—
1049D4—82no—
1050D4—82no—
1051D4—82no—
1052D4—84no—
1053D4—84no—
1054D4—84no—
1055D4—84no—
1056C2×C4—24no—
1057C2×C4—22no—
1058C2×C4—22no—
1059C2×C4—22no—
1060C2×C4—22no—
1061C2×C4—22no—
1062C2×C4—24no—
1063C2×C4—24no—
1064C2×C4—22no—
1065C2×C4—22no—
1066C2×C4—24no—
1067C2×C4—22no—
1068C2×C4—24no—
1069C2×C4—22no—
1070C2×C4—24no—
1071C2×C4—24no—
1072C2×C4—24no—
1073C2×C4—24no—
1074C2×C4—41no—
1075C2×C4—41no—
1076C2×C4—41no—
1077C2×C4—41no—
1078C2×C4—41no—
1079C2×C4—41no—
1080C2×C4—41no—
1081C2×C4—41no—
1082C2×C4—42no—
1083C2×C4—42no—
1084C2×C4—42no—
1085C2×C4—42no—
1086C2×C4—42no—
1087C2×C4—42no—
1088C2×C4—42no—
1089C2×C4—41no—
1090C2×C4—41no—
1091C2×C4—42no—
1092C2×C4—42no—
1093C2×C4—41no—
1094C2×C4—41no—
1095C2×C4—41no—
1096C2×C4—41no—
1097C2×C4—48no—
1098C2×C4—42no—
1099C2×C4—44no—
1100C2×C4—44no—
1101C2×C4—44no—
1102C2×C4—42no—
1103C2×C4—48no—
1104C2×C4—42no—
1105C2×C4—42no—
1106C2×C4—42no—
1107C2×C4—42no—
1108C2×C4—42no—
1109C2×C4—42no—
1110C2×C4—42no—
1111C2×C4—42no—
1112C2×C4—42no—
1113C2×C4—84no—
1114C2×C4—84no—
1115C2×C4—84no—
1116C2×C4—84no—
1117C2×C4—88no—
1118C2×C4C22×C22⋊C411yescharacteristic
1119C2×C4C22×C22⋊C412yes—
1120C2×C4C22×C22⋊C412yes—
1121C2×C4C22×C22⋊C412yes—
1122C2×C4C22×C22⋊C412yes—
1123C2×C4C22×C22⋊C411yescharacteristic
1124C2×C4C22×C22⋊C411yescharacteristic
1125C2×C4C22×C22⋊C411yescharacteristic
1126C2×C4C22×C22⋊C411yescharacteristic
1127C2×C4C22×C22⋊C411yescharacteristic
1128C2×C4C22×C22⋊C411yescharacteristic
1129C2×C4C22×C22⋊C411yescharacteristic
1130C2×C4C22×C22⋊C411yescharacteristic
1131C2×C4C22×C22⋊C411yescharacteristic
1132C2×C4C22×C22⋊C412yes—
1133C2×C4C22×C22⋊C412yes—
1134C2×C4C24×C411yescharacteristic
1135C2×C4C23×D411yescharacteristic
1136C2×C4#58514yes—
1137C8—44no—
1138C8—44no—
1139C22—21no—
1140C22—21no—
1141C22—21no—
1142C22—21no—
1143C22—21no—
1144C22—22no—
1145C22—22no—
1146C22—21no—
1147C22—22no—
1148C22—22no—
1149C22—21no—
1150C22—22no—
1151C22—22no—
1152C22—44no—
1153C22—44no—
1154C22—44no—
1155C22—44no—
1156C22—44no—
1157C22—82no—
1158C22—84no—
1159C22—88no—
1160C22—84no—
1161C22#290112yes—
1162C22C23×C22⋊C411yescharacteristic
1163C22#344912yes—
1164C4—22no—
1165C4—22no—
1166C4—21no—
1167C4—21no—
1168C4—21no—
1169C4—21no—
1170C4—22no—
1171C4—22no—
1172C4—21no—
1173C4—21no—
1174C4—21no—
1175C4—21no—
1176C4—21no—
1177C4—22no—
1178C4—22no—
1179C4—21no—
1180C4—44no—
1181C4—44no—
1182C4—44no—
1183C4—44no—
1184C4—82no—
1185C4—82no—
1186C4—82no—
1187C4#342812yes—
1188C4#344912yes—
1189C2—22no—
1190C2—22no—
1191C2—41no—
1192C2—42no—
1193C2—42no—
1194C2—84no—
1195C2#3404411yescharacteristic
1196C2C2×#290111yescharacteristic
1197C2#6009311yescharacteristic
subgroupG/H
centerC2×C4C23×D4
commutatorC2×C4C24×C4
Frattini, cosocleC22×C4C25
socleC22C23×C22⋊C4
prime radicalC2×#3455C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4 ◁ C22×#117 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #60124C2semidirect
3. #34109C2semidirect
4. #21901C2semidirect
5. #21858C2semidirect
6. #21845C2semidirect
7. #21844C2semidirect
8. #21816C2semidirect
9. #21815C2semidirect
10. #21774C2semidirect
11. #21773C2semidirect
12. #21419C2semidirect
13. #21384C2semidirect
14. #20748C2semidirect
15. #20747C2semidirect
22. #3455C4semidirect
23. #3455C4semidirect
28. C2×#542C4semidirect
29. C2×#542C4semidirect
30. C2×#541C4semidirect
31. C2×#540C4semidirect
47. #2921C22semidirect
48. #2921C22semidirect
52. #2905C22semidirect
54. #2873C22semidirect
63. #2298C22semidirect
64. #2298C22semidirect
65. #2296C22semidirect
71. C4×#117C22semidirect
73. #1995C22semidirect
74. #1994C22semidirect
75. #1986C22semidirect
76. #1986C22semidirect
77. #1980C22semidirect
78. #1980C22semidirect
79. #1963C22semidirect
80. #1962C22semidirect
81. #1897C22semidirect
82. #1896C22semidirect
83. #1871C22semidirect
84. #1871C22semidirect
89. #1806C22semidirect
90. #1806C22semidirect
95. #1759C22semidirect
96. C4×#104C22semidirect
112. #542C2×C4semidirect
113. #542C2×C4semidirect
114. #542C2×C4semidirect
115. #542C2×C4semidirect
122. #541C2×C4semidirect
123. #541C2×C4semidirect
130. #540C2×C4semidirect
131. #540C2×C4semidirect
160. #533C2×C4semidirect
161. #533C2×C4semidirect
168. #532C2×C4semidirect
169. #532C2×C4semidirect
172. C2×C4⋊Q8C2×C4semidirect
173. C2×C4⋊Q8C2×C4semidirect
174. C2×C4⋊Q8C2×C4semidirect
175. C2×#127C2×C4semidirect
198. C2×#125C2×C4semidirect
201. C2×#124C2×C4semidirect
232. C4×#41C2×C4semidirect
233. C4×#41C2×C4semidirect
238. C2×C4×Q8C2×C4semidirect
239. C2×C4×Q8C2×C4semidirect
246. C2×C4×D4C2×C4semidirect
247. C2×C4×D4C2×C4semidirect

Maximal subgroups

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

subgroupindex
C2×#34552
#601242
#341092
#219012
#218582
#218452
#218442
#218162
#218152
#217742
#217732
#214192
#213842
#207482
#207472