Finite Group Databasebeta

← #72306648

Subgroups — #72306648

Order 1024.

7455 conjugacy classes of subgroups.

The subgroup lattice has 1113 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#62415C211yesmaximal, characteristic
2#6389868C212yesmaximal, complemented
3#6385980C212yesmaximal, complemented
4D8×#99C218yesmaximal, complemented
5#220244C218yesmaximal, complemented
6#205755C212yesmaximal, complemented
7#198480C214yesmaximal, complemented
8#188809C211yesmaximal, characteristic, complemented
9#185660C212yesmaximal, complemented
10#182081C211yesmaximal, characteristic, complemented
11C2×#3498C2212yes—
12#62415—24no—
13#62415—24no—
14#62415—24no—
15#62415—24no—
16C2×#3391C412yescomplemented
17C2×#3391C412yescomplemented
18C2×D4×D8C412yescomplemented
19C2×D4×D8C412yescomplemented
20C2×D4×D8C2214yes—
21C2×D4×D8C2214yes—
22C2×#3205C414yescomplemented
23C2×#3205C2212yes—
24C2×#3169C412yescomplemented
25C2×#3169C2211yescharacteristic
26C22×#493C412yescomplemented
27C22×#493C2211yescharacteristic
28C2×C8×#41C2211yescharacteristic
29#34364C2214yescomplemented
30#23188—24no—
31#23185—24no—
32C22⋊C4×D8C2218yescomplemented
33#22436C2218yescomplemented
34D4×#99—28no—
35D4×#99C22116yescomplemented
36#22276—24no—
37#21810C2214yescomplemented
38#21794C2214yescomplemented
39#21750—24no—
40#21697—24no—
41#20818C2212yescomplemented
42#20723C2211yescharacteristic
43#20723C2212yes—
44#20585—24no—
45#20476C2212yescomplemented
46#17595C2214yescomplemented
47#17363C2211yescharacteristic
48#9785C2218yescomplemented
49#9783C2218yescomplemented
50#9259C22132yescomplemented
51#8609C2214yescomplemented
52#8608C2214yescomplemented
53#8375C22116yescomplemented
54#8160C2214yescomplemented
55C8×#99C2214yescomplemented
56#7980C2212yescomplemented
57#7928C2212yescomplemented
58C22×H(5,𝔽2)—22no—
59C23×D8C2×C414yescomplemented
60C23×D8C2×C414yescomplemented
61C23×D8C2312yes—
62C23×D8C2312yes—
63#3498—28no—
64#3498—28no—
65#3498—44no—
66#3498—44no—
67C2×#550—22no—
68C2×#550C2×C414yescomplemented
69C2×D42—24no—
70C2×D42—22no—
71C2×D42C2×C414yescomplemented
72C2×D42C2318yes—
73C2×#535—22no—
74C2×#535—24no—
75C2×#532C2×C414yescomplemented
76C2×#532C2312yes—
77C22×#127C2×C414yescomplemented
78C22×#127C2312yes—
79C2×C4×#41C2311yescharacteristic
80#3391—28no—
81#3391—28no—
82#3391—28no—
83#3391—28no—
84D4×D8—28no—
85D4×D8—28no—
86D4×D8—28no—
87D4×D8—28no—
88D4×D8—216no—
89D4×D8—216no—
90D4×D8—216no—
91D4×D8—216no—
92#3205—216no—
93#3205—216no—
94#3205—28no—
95#3205—28no—
96#3169—24no—
97#3169—24no—
98#3169—24no—
99#3169—24no—
100#3169—22no—
101#3169—22no—
102#3169—22no—
103#3169—22no—
104C2×#500C2×C411yescharacteristic, complemented
105C2×#493—24no—
106C2×#493—24no—
107C2×#493—24no—
108C2×#493—24no—
109C2×#493C2×C412yes—
110C2×#493C2×C412yes—
111C2×#493C2×C412yes—
112C2×#493C2×C412yes—
113C2×#493C2×C414yescomplemented
114C2×#493C2×C414yescomplemented
115C2×#493C2×C414yescomplemented
116C2×#493C2×C411yescharacteristic, complemented
117C2×#493D414yes—
118C2×#493D414yes—
119C2×#493D414yes—
120C2×#493D414yes—
121C2×#486C2×C412yescomplemented
122C2×#486C2×C414yescomplemented
123C2×#466C2×C414yescomplemented
124C2×#466C2×C414yescomplemented
125C2×#466C2312yes—
126C2×#466C2312yes—
127C2×#459C2×C418yescomplemented
128C2×#459C2×C418yescomplemented
129C2×#459C2×C414yescomplemented
130C2×#459C2×C414yescomplemented
131C2×#447C2×C418yescomplemented
132C2×#447C2×C418yescomplemented
133C2×#447C2318yes—
134C8×#41—22no—
135C8×#41—22no—
136C8×#41—22no—
137C8×#41—22no—
138C2×C8×Q8C2×C411yescharacteristic, complemented
139C2×C8×Q8C2×C411yescharacteristic, complemented
140C2×#442—28no—
141C2×C4×D8—28no—
142C2×C4×D8C2×C412yescomplemented
143C2×C4×D8C2×C412yescomplemented
144C2×C4×D8C2×C414yescomplemented
145C2×C4×D8C2×C414yescomplemented
146C2×C8×D4C2×C411yescharacteristic, complemented
147C2×C8×D4C2×C411yescharacteristic, complemented
148C2×C8×D4C2312yes—
149C2×C8×D4C2312yes—
150C2×#432C2312yes—
151C2×#431C2×C412yescomplemented
152C2×#431C2311yescharacteristic
153C22×#99—216no—
154C22×C4×C8C2×C412yescomplemented
155C22×C4×C8C2311yescharacteristic
156#2380—44no—
157#2366—28no—
158D4×C22⋊C4—28no—
159D4×C22⋊C4C23116yes—
160#2328—28no—
161#2328—44no—
162#2308—28no—
163#2283C2314yes—
164#2283C2312yes—
165#1982—28no—
166#1972—28no—
167#1970—28no—
168#1964—28no—
169#1964C23116yes—
170#1961—28no—
171#1898—232no—
172#1879—216no—
173#1879—216no—
174#1846—22no—
175#1835—22no—
176#1820—22no—
177#1820D412yes—
178#1808C2314yes—
179#1807C2314yes—
180#1799D414yes—
181#1799C2318yes—
182#1786C23116yes—
183#1782—28no—
184#1782—22no—
185#1782D412yes—
186#1781—216no—
187C4×#107—22no—
188C4×#106—22no—
189#1770—22no—
190C8×C4⋊C4—22no—
191C4×#99—24no—
192C4×#99C2314yes—
193#1752C2314yes—
194C8×C22⋊C4C2314yes—
195#1746—22no—
196#1726—22no—
197#1519C23116yes—
198#1514—44no—
199#1505—44no—
200#1467—21no—
201#1466—21no—
202#1464—22no—
203#1459C2314yes—
204#1289C2318yes—
205#1282C2318yes—
206C2×H(5,𝔽2)—48no—
207C2×H(5,𝔽2)—48no—
208C2×H(5,𝔽2)—816no—
209C22×#41—24no—
210C22×#41—24no—
211C22×#41—22no—
212C22×#41C2×D411yescharacteristic
213C23×D4—28no—
214C23×D4—24no—
215C23×D4—24no—
216C23×D4—24no—
217C23×D4—22no—
218C23×D4—22no—
219C23×D4C22×C418yes—
220C23×D4C2414yes—
221C22×D8—28no—
222C22×D8—28no—
223C22×D8—28no—
224C22×D8—28no—
225C22×D8—84no—
226C22×D8—84no—
227C22×D8—88no—
228C22×D8—88no—
229C22×D8C22×C412yes—
230C22×D8C22×C412yes—
231C22×D8C22×C418yes—
232C22×D8C22×C418yes—
233C22×D8C22×C414yes—
234C22×D8C22×C414yes—
235C22×D8C22×C414yes—
236C22×D8C22×C414yes—
237C22×D8C2×D418yes—
238C22×D8C2×D418yes—
239C22×D8C2×D418yes—
240C22×D8C2×D418yes—
241C23×C8C22×C412yes—
242C23×C8C22×C412yes—
243C23×C8C2411yescharacteristic
244C23×C8C2411yescharacteristic
245#550—216no—
246#550—48no—
247#550—48no—
248#550—48no—
249D42—232no—
250D42—216no—
251D42—48no—
252D42—416no—
253D42—48no—
254D42—48no—
255D42—416no—
256D42—416no—
257#535—416no—
258#535—416no—
259#535—48no—
260#535—48no—
261#532—28no—
262#532—28no—
263#532—24no—
264#532—24no—
265#532—24no—
266#532—24no—
267#532—44no—
268#532—44no—
269C2×C4⋊Q8C22×C412yes—
270C2×#127—28no—
271C2×#127—28no—
272C2×#127—24no—
273C2×#127—24no—
274C2×#127—22no—
275C2×#127—22no—
276C2×#127—24no—
277C2×#127—24no—
278C2×#127—44no—
279C2×#127—44no—
280C2×#127C22×C412yes—
281C2×#127C22×C418yes—
282C2×#127C22×C414yes—
283C2×#127C22×C414yes—
284C2×#127C2×D418yes—
285C2×#127C2×D418yes—
286C2×#124—24no—
287C2×#124—22no—
288C2×#121—24no—
289C2×#121—22no—
290C2×#121—24no—
291C2×#121—28no—
292C2×#121—24no—
293C2×#121—28no—
294C2×#121C22×C418yes—
295C2×#121C2414yes—
296C2×#120—28no—
297C2×#120—28no—
298C2×#120—28no—
299C4×#41—22no—
300C4×#41—22no—
301C4×#41—22no—
302C4×#41—22no—
303C2×C4×Q8C22×C411yescharacteristic
304C2×C4×Q8#4111yescharacteristic
305C2×C4×D4—216no—
306C2×C4×D4—24no—
307C2×C4×D4—22no—
308C2×C4×D4—48no—
309C2×C4×D4C22×C414yes—
310C2×C4×D4C22×C418yes—
311C2×C4×D4C22×C411yescharacteristic
312C2×C4×D4C2×D412yes—
313C2×C4×D4#4111yescharacteristic
314C2×C4×D4C2412yes—
315C2×#117C2×D411yescharacteristic
316C2×#117#4112yes—
317C22×C22⋊C4—216no—
318C22×C42C22×C412yes—
319C22×C42C2411yescharacteristic
320#500—21no—
321#500—21no—
322#500—21no—
323#500—21no—
324#493—28no—
325#493—28no—
326#493—28no—
327#493—28no—
328#493—28no—
329#493—28no—
330#493—21no—
331#493—21no—
332#493—21no—
333#493—21no—
334#493C22⋊C418yes—
335#493C22⋊C418yes—
336#493C22⋊C418yes—
337#493C22⋊C418yes—
338#493C22⋊C414yes—
339#493C22⋊C414yes—
340#493C22⋊C414yes—
341#493C22⋊C414yes—
342#493C22⋊C418yes—
343#493C22⋊C418yes—
344#486—28no—
345#486—28no—
346#486—24no—
347#486—24no—
348#466—28no—
349#466—28no—
350#466—28no—
351#466—28no—
352#466—24no—
353#466—24no—
354#466—24no—
355#466—24no—
356#459—232no—
357#459—232no—
358#459—216no—
359#459—216no—
360#447—232no—
361#447—232no—
362#447—232no—
363C8×Q8—22no—
364C8×Q8—22no—
365C8×Q8—22no—
366C8×Q8—22no—
367#442—816no—
368C4×D8—28no—
369C4×D8—28no—
370C4×D8—28no—
371C4×D8—28no—
372C4×D8—24no—
373C4×D8—24no—
374C4×D8—24no—
375C4×D8—24no—
376C4×D8—816no—
377C8×D4—24no—
378C8×D4—24no—
379C8×D4—24no—
380C8×D4—24no—
381C8×D4—22no—
382C8×D4—22no—
383C8×D4—22no—
384C8×D4—22no—
385#432—22no—
386#432—22no—
387#432—22no—
388#432—22no—
389#431—22no—
390#431—22no—
391#431—24no—
392#431—24no—
393C2×#107—24no—
394C2×#107C22×C412yes—
395C2×#107C22×C412yes—
396C2×#106—24no—
397C2×C4⋊C8—22no—
398C2×C4⋊C8C22×C412yes—
399C2×C4⋊C8C22×C412yes—
400C2×C4⋊C8C22×C411yescharacteristic
401C2×C4⋊C8C22×C411yescharacteristic
402C2×#102—216no—
403C2×#102—216no—
404C2×#102C22×C414yes—
405C2×#102C22×C414yes—
406C2×#102C22×C418yes—
407C2×#102C22×C418yes—
408C2×#99—28no—
409C2×#99—232no—
410C2×#99—832no—
411C2×#99C2×D418yes—
412C2×C22⋊C8C22×C412yes—
413C2×C22⋊C8C22×C412yes—
414C2×C22⋊C8C2414yes—
415C2×C22⋊C8C2412yes—
416C2×#97—24no—
417C2×#97—22no—
418C2×C4×C8—22no—
419C2×C4×C8—22no—
420C2×C4×C8—22no—
421C2×C4×C8—22no—
422C2×C4×C8—24no—
423C2×C4×C8C22×C412yes—
424C2×C4×C8C22×C412yes—
425C2×C4×C8C22×C412yes—
426C2×C4×C8C22×C411yescharacteristic
427C2×C4×C8C22×C411yescharacteristic
428C2×C4×C8C22×C411yescharacteristic
429C2×C4×C8C22×C411yescharacteristic
430C2×C4×C8C2×D412yes—
431C2×C4×C8C2×D412yes—
432C2×C4×C8C2×D412yes—
433C2×C4×C8C2×D412yes—
434#390—216no—
435#390—48no—
436#386—416no—
437#386—416no—
438#386—416no—
439#386—416no—
440#383—22no—
441#383—24no—
442#382—22no—
443#382—24no—
444#381—24no—
445#381C2×D414yes—
446#380C2×D414yes—
447#380C2418yes—
448#379—216no—
449C4×C4⋊C4—22no—
450C4×C4⋊C4—24no—
451C4×C22⋊C4—24no—
452C4×C22⋊C4C2414yes—
453#376—22no—
454#376—24no—
455#342—28no—
456#342C2×D418yes—
457#340—24no—
458#340—24no—
459#336—24no—
460#336—24no—
461#327—416no—
462#324—24no—
463#323—24no—
464C25—24no—
465C25—28no—
466H(5,𝔽2)—832no—
467H(5,𝔽2)—864no—
468H(5,𝔽2)—832no—
469C2×#41—28no—
470C2×#41—22no—
471C2×#41—22no—
472C2×#41—48no—
473C2×#41—48no—
474C2×#41—416no—
475C2×#41—44no—
476C2×#41—44no—
477C2×#41—88no—
478C2×#41—88no—
479C2×#41—88no—
480C2×#41—816no—
481C22×Q8—22no—
482C22×Q8C4×D411yescharacteristic
483C22×D4—216no—
484C22×D4—24no—
485C22×D4—28no—
486C22×D4—24no—
487C22×D4—24no—
488C22×D4—24no—
489C22×D4—24no—
490C22×D4—28no—
491C22×D4—22no—
492C22×D4—22no—
493C22×D4—28no—
494C22×D4—28no—
495C22×D4—28no—
496C22×D4—28no—
497C22×D4—28no—
498C22×D4—28no—
499C22×D4—24no—
500C22×D4—28no—
501C22×D4—48no—
502C22×D4—48no—
503C22×D4—48no—
504C22×D4—48no—
505C22×D4—48no—
506C22×D4—416no—
507C22×D4—432no—
508C22×D4—432no—
509C22×D4—88no—
510C22×D4—88no—
511C22×D4—88no—
512C22×D4—84no—
513C22×D4—84no—
514C22×D4—88no—
515C22×D4—88no—
516C22×D4—816no—
517C22×D4—816no—
518C22×D4—164no—
519C22×D4—168no—
520C22×D4C4×D411yescharacteristic
521C22×D4C23×C414yes—
522C22×D4C23×C418yes—
523C22×D4C22×D412yes—
524C22×D4C22×D4116yes—
525C23×C4—28no—
526C23×C4—24no—
527C23×C4—416no—
528C23×C4C4×D412yes—
529C23×C4C4×D412yes—
530C23×C4C23×C412yes—
531C23×C4C22×D411yescharacteristic
532C23×C4C22×D411yescharacteristic
533C23×C4C2511yescharacteristic
534C2×D8—216no—
535C2×D8—216no—
536C2×D8—22no—
537C2×D8—22no—
538C2×D8—22no—
539C2×D8—22no—
540C2×D8—48no—
541C2×D8—48no—
542C2×D8—416no—
543C2×D8—416no—
544C2×D8—44no—
545C2×D8—44no—
546C2×D8—816no—
547C2×D8—816no—
548C2×D8—84no—
549C2×D8—84no—
550C2×D8—88no—
551C2×D8—88no—
552C2×D8—816no—
553C2×D8—816no—
554C2×D8—88no—
555C2×D8—88no—
556C2×D8C2×C22⋊C418yes—
557C2×D8C2×C22⋊C418yes—
558C2×D8C2×C22⋊C418yes—
559C2×D8C2×C22⋊C418yes—
560C2×D8C2×C22⋊C4116yes—
561C2×D8C2×C22⋊C4116yes—
562C22×C8—22no—
563C22×C8—22no—
564C22×C8—22no—
565C22×C8—22no—
566C22×C8—24no—
567C22×C8—42no—
568C22×C8—42no—
569C22×C8—44no—
570C22×C8—44no—
571C22×C8C23×C411yescharacteristic
572C22×C8C23×C411yescharacteristic
573C22×C8C23×C412yes—
574C22×C8C23×C412yes—
575C22×C8C23×C411yescharacteristic
576C22×C8C23×C411yescharacteristic
577C22×C8C22×D412yes—
578C22×C8C22×D412yes—
579C22×C8C22×D412yes—
580C22×C8C22×D412yes—
581C4⋊Q8—22no—
582C4⋊Q8—22no—
583C4⋊Q8—22no—
584C4⋊Q8—22no—
585#127—216no—
586#127—22no—
587#127—22no—
588#127—24no—
589#127—24no—
590#127—28no—
591#127—22no—
592#127—22no—
593#127—28no—
594#127—28no—
595#127—28no—
596#127—28no—
597#127—48no—
598#127—48no—
599#127—48no—
600#127—48no—
601#127—48no—
602#127C2×C22⋊C418yes—
603#127C2×C22⋊C418yes—
604#127C2×C22⋊C4116yes—
605#124—48no—
606#124—48no—
607#124—44no—
608#124—44no—
609#121—216no—
610#121—28no—
611#121—28no—
612#121—48no—
613#121—416no—
614#121—432no—
615#121—416no—
616#121—432no—
617#121—48no—
618#121—48no—
619#121—44no—
620#121—44no—
621#120—432no—
622#120—432no—
623#120—432no—
624C4×Q8—22no—
625C4×Q8—22no—
626C4×Q8—22no—
627C4×Q8—22no—
628C4×D4—24no—
629C4×D4—24no—
630C4×D4—24no—
631C4×D4—24no—
632C4×D4—216no—
633C4×D4—22no—
634C4×D4—28no—
635C4×D4—22no—
636C4×D4—28no—
637C4×D4—22no—
638C4×D4—22no—
639C4×D4—48no—
640C4×D4—48no—
641C4×D4—48no—
642C4×D4—44no—
643C4×D4—44no—
644C4×D4—816no—
645C4×D4—816no—
646C4×D4—1616no—
647#117—22no—
648#117—22no—
649#117—24no—
650#117—24no—
651C2×C4⋊C4—22no—
652C2×C4⋊C4—24no—
653C2×C4⋊C4—28no—
654C2×C4⋊C4C4×D411yescharacteristic
655C2×C4⋊C4C4×D411yescharacteristic
656C2×C4⋊C4C4×D412yes—
657C2×C4⋊C4C23×C414yes—
658C2×C4⋊C4C2×#4112yes—
659C2×C22⋊C4—28no—
660C2×C22⋊C4—28no—
661C2×C22⋊C4—24no—
662C2×C22⋊C4—24no—
663C2×C22⋊C4—28no—
664C2×C22⋊C4—416no—
665C2×C22⋊C4—416no—
666C2×C22⋊C4—416no—
667C2×C22⋊C4—832no—
668C2×C22⋊C4C4×D412yes—
669C2×C22⋊C4C22×D418yes—
670C2×C22⋊C4C22×D412yes—
671C2×C22⋊C4C2×#4112yes—
672C2×C42—22no—
673C2×C42—22no—
674C2×C42—22no—
675C2×C42—22no—
676C2×C42—24no—
677C2×C42—44no—
678C2×C42C4×D412yes—
679C2×C42C4×D412yes—
680C2×C42C23×C412yes—
681C2×C42C23×C411yescharacteristic
682C2×C42C23×C411yescharacteristic
683C2×C42C22×D412yes—
684C2×C42C22×D412yes—
685C2×C42C2×#4111yescharacteristic
686C2×C42C2×#4111yescharacteristic
687C2×C42H(5,𝔽2)12yes—
688C2×C42H(5,𝔽2)12yes—
689#107—22no—
690#107—22no—
691#107—22no—
692#107—22no—
693#107—48no—
694#106—48no—
695C4⋊C8—24no—
696C4⋊C8—24no—
697C4⋊C8—22no—
698C4⋊C8—22no—
699C4⋊C8—42no—
700C4⋊C8—42no—
701#102—216no—
702#102—216no—
703#102—28no—
704#102—28no—
705#102—816no—
706#102—816no—
707#99—216no—
708#99—416no—
709#99—832no—
710C22⋊C8—24no—
711C22⋊C8—24no—
712C22⋊C8—24no—
713C22⋊C8—24no—
714C22⋊C8—24no—
715#97—48no—
716#97—42no—
717#97—42no—
718C4×C8—22no—
719C4×C8—22no—
720C4×C8—22no—
721C4×C8—22no—
722C4×C8—22no—
723C4×C8—22no—
724C4×C8—48no—
725C4×C8C2×C22⋊C411yescharacteristic
726C4×C8C2×C22⋊C411yescharacteristic
727C4×C8C2×C22⋊C411yescharacteristic
728C4×C8C2×C22⋊C411yescharacteristic
729C4×C8C2×C22⋊C412yes—
730C4×C8C2×C22⋊C412yes—
731C4×C8C2×C22⋊C412yes—
732C4×C8C2×C22⋊C412yes—
733C4×C8C2×C22⋊C412yes—
734C4×C8C2×C22⋊C412yes—
735#95—24no—
736#95—24no—
737#95—24no—
738#95—24no—
739#95—28no—
740#95—44no—
741#95—44no—
742#95—44no—
743C24—28no—
744C24—216no—
745C24—24no—
746C24—416no—
747C24—416no—
748C24—416no—
749C24—88no—
750C24—164no—
751C24—164no—
752C24—168no—
753C24—168no—
754C24C2×C4×D412yes—
755C24C23×D411yescharacteristic
756#41—216no—
757#41—216no—
758#41—832no—
759#41—832no—
760#41—816no—
761#41—816no—
762#41—864no—
763C2×Q8—22no—
764C2×Q8—24no—
765C2×Q8—42no—
766C2×Q8—42no—
767C2×Q8—84no—
768C2×D4—24no—
769C2×D4—24no—
770C2×D4—24no—
771C2×D4—22no—
772C2×D4—28no—
773C2×D4—28no—
774C2×D4—216no—
775C2×D4—216no—
776C2×D4—28no—
777C2×D4—28no—
778C2×D4—24no—
779C2×D4—28no—
780C2×D4—24no—
781C2×D4—216no—
782C2×D4—416no—
783C2×D4—416no—
784C2×D4—48no—
785C2×D4—48no—
786C2×D4—44no—
787C2×D4—44no—
788C2×D4—416no—
789C2×D4—416no—
790C2×D4—416no—
791C2×D4—416no—
792C2×D4—416no—
793C2×D4—48no—
794C2×D4—416no—
795C2×D4—42no—
796C2×D4—42no—
797C2×D4—42no—
798C2×D4—42no—
799C2×D4—416no—
800C2×D4—816no—
801C2×D4—88no—
802C2×D4—84no—
803C2×D4—84no—
804C2×D4—84no—
805C2×D4—88no—
806C2×D4—88no—
807C2×D4—88no—
808C2×D4—816no—
809C2×D4—88no—
810C2×D4—832no—
811C2×D4—832no—
812C2×D4—84no—
813C2×D4—816no—
814C2×D4—816no—
815C2×D4—88no—
816C2×D4—864no—
817C2×D4—864no—
818C2×D4—864no—
819C2×D4—1616no—
820C2×D4—164no—
821C2×D4—168no—
822C2×D4—164no—
823C2×D4—168no—
824C2×D4—1616no—
825C2×D4—1616no—
826C2×D4—168no—
827C2×D4—168no—
828C2×D4C22×C22⋊C4116yes—
829C2×D4#57618yes—
830C22×C4—24no—
831C22×C4—24no—
832C22×C4—22no—
833C22×C4—22no—
834C22×C4—24no—
835C22×C4—22no—
836C22×C4—22no—
837C22×C4—22no—
838C22×C4—22no—
839C22×C4—24no—
840C22×C4—28no—
841C22×C4—41no—
842C22×C4—41no—
843C22×C4—42no—
844C22×C4—42no—
845C22×C4—42no—
846C22×C4—44no—
847C22×C4—416no—
848C22×C4—48no—
849C22×C4—416no—
850C22×C4—48no—
851C22×C4—88no—
852C22×C4—88no—
853C22×C4—1616no—
854C22×C4—1616no—
855C22×C4—1616no—
856C22×C4C2×C4×D411yescharacteristic
857C22×C4C2×C4×D411yescharacteristic
858C22×C4C2×C4×D411yescharacteristic
859C22×C4C2×C4×D412yes—
860C22×C4C2×C4×D412yes—
861C22×C4C2×C4×D412yes—
862C22×C4C2×C4×D411yescharacteristic
863C22×C4D4212yes—
864C22×C4D4212yes—
865C22×C4D4212yes—
866C22×C4D4212yes—
867C22×C4C24×C411yescharacteristic
868C22×C4C23×D412yes—
869C22×C4C22×#4111yescharacteristic
870C22×C4C2×H(5,𝔽2)12yes—
871D8—216no—
872D8—216no—
873D8—48no—
874D8—48no—
875D8—416no—
876D8—416no—
877D8—44no—
878D8—44no—
879D8—44no—
880D8—44no—
881D8—816no—
882D8—816no—
883C2×C8—24no—
884C2×C8—24no—
885C2×C8—22no—
886C2×C8—22no—
887C2×C8—22no—
888C2×C8—22no—
889C2×C8—41no—
890C2×C8—41no—
891C2×C8—42no—
892C2×C8—42no—
893C2×C8—44no—
894C2×C8—44no—
895C2×C8—44no—
896C2×C8—44no—
897C2×C8—42no—
898C2×C8—42no—
899C2×C8—44no—
900C2×C8—44no—
901C2×C8—44no—
902C2×C8C22×C22⋊C411yescharacteristic
903C2×C8C22×C22⋊C411yescharacteristic
904C2×C8C22×C22⋊C412yes—
905C2×C8C22×C22⋊C412yes—
906C2×C8C22×C22⋊C411yescharacteristic
907C2×C8C22×C22⋊C411yescharacteristic
908C4⋊C4—24no—
909C4⋊C4—22no—
910C4⋊C4—22no—
911C4⋊C4—24no—
912C4⋊C4—24no—
913C4⋊C4—24no—
914C4⋊C4—48no—
915C4⋊C4—48no—
916C4⋊C4—48no—
917C4⋊C4—42no—
918C4⋊C4—42no—
919C22⋊C4—24no—
920C22⋊C4—24no—
921C22⋊C4—24no—
922C22⋊C4—216no—
923C22⋊C4—416no—
924C22⋊C4—416no—
925C22⋊C4—48no—
926C22⋊C4—48no—
927C22⋊C4—416no—
928C22⋊C4—1616no—
929C22⋊C4—1616no—
930C22⋊C4—1616no—
931C42—22no—
932C42—22no—
933C42—22no—
934C42—22no—
935C42—22no—
936C42—22no—
937C42—44no—
938C42—44no—
939C42—88no—
940C42C22×C22⋊C411yescharacteristic
941C42C22×C22⋊C411yescharacteristic
942C42C22×C22⋊C412yes—
943C42#51811yescharacteristic
944C42#51811yescharacteristic
945C42#51812yes—
946C42#54612yes—
947C42#54612yes—
948C42#54612yes—
949C42#54612yes—
950C23—22no—
951C23—22no—
952C23—216no—
953C23—41no—
954C23—41no—
955C23—42no—
956C23—42no—
957C23—48no—
958C23—48no—
959C23—416no—
960C23—416no—
961C23—44no—
962C23—48no—
963C23—816no—
964C23—816no—
965C23—88no—
966C23—88no—
967C23—832no—
968C23—84no—
969C23—84no—
970C23—1616no—
971C23—1616no—
972C23—3216no—
973C23—3216no—
974C23—3216no—
975C23#294814yes—
976C23C22×C4×D411yescharacteristic
977C23C2×D4212yes—
978C23C2×#57614yes—
979Q8—28no—
980Q8—84no—
981Q8—84no—
982D4—28no—
983D4—216no—
984D4—216no—
985D4—216no—
986D4—44no—
987D4—44no—
988D4—416no—
989D4—816no—
990D4—88no—
991D4—88no—
992D4—88no—
993D4—816no—
994D4—816no—
995D4—88no—
996D4—832no—
997D4—84no—
998D4—84no—
999D4—84no—
1000D4—84no—
1001D4—832no—
1002D4—816no—
1003D4—84no—
1004D4—1616no—
1005D4—1616no—
1006C2×C4—28no—
1007C2×C4—28no—
1008C2×C4—22no—
1009C2×C4—22no—
1010C2×C4—22no—
1011C2×C4—22no—
1012C2×C4—24no—
1013C2×C4—24no—
1014C2×C4—22no—
1015C2×C4—22no—
1016C2×C4—21no—
1017C2×C4—21no—
1018C2×C4—24no—
1019C2×C4—22no—
1020C2×C4—22no—
1021C2×C4—22no—
1022C2×C4—41no—
1023C2×C4—42no—
1024C2×C4—41no—
1025C2×C4—42no—
1026C2×C4—44no—
1027C2×C4—44no—
1028C2×C4—42no—
1029C2×C4—42no—
1030C2×C4—44no—
1031C2×C4—42no—
1032C2×C4—42no—
1033C2×C4—48no—
1034C2×C4—48no—
1035C2×C4—48no—
1036C2×C4—44no—
1037C2×C4—48no—
1038C2×C4—832no—
1039C2×C4—816no—
1040C2×C4—88no—
1041C2×C4—88no—
1042C2×C4—88no—
1043C2×C4—3232no—
1044C2×C4D4×C22⋊C411yescharacteristic
1045C2×C4D4×C22⋊C411yescharacteristic
1046C2×C4D4×C22⋊C411yescharacteristic
1047C2×C4D4×C22⋊C412yes—
1048C2×C4D4×C22⋊C412yes—
1049C2×C4D4×C22⋊C411yescharacteristic
1050C2×C4#294814yes—
1051C2×C4C23×C22⋊C411yescharacteristic
1052C2×C4C2×#51811yescharacteristic
1053C2×C4C2×#54612yes—
1054C8—21no—
1055C8—21no—
1056C8—22no—
1057C8—22no—
1058C8—42no—
1059C8—42no—
1060C8—84no—
1061C8#288312yes—
1062C8#288312yes—
1063C22—22no—
1064C22—21no—
1065C22—22no—
1066C22—21no—
1067C22—24no—
1068C22—44no—
1069C22—44no—
1070C22—44no—
1071C22—42no—
1072C22—42no—
1073C22—416no—
1074C22—416no—
1075C22—416no—
1076C22—84no—
1077C22—84no—
1078C22—84no—
1079C22—1616no—
1080C22—1616no—
1081C22—168no—
1082C22—168no—
1083C22—168no—
1084C22—3232no—
1085C22C2×D4×C22⋊C411yescharacteristic
1086C22C2×#294812yes—
1087C22#6104914yes—
1088C4—22no—
1089C4—21no—
1090C4—21no—
1091C4—21no—
1092C4—22no—
1093C4—24no—
1094C4—21no—
1095C4—22no—
1096C4—42no—
1097C4—42no—
1098C4—88no—
1099C4—84no—
1100C4—168no—
1101C4#2245512yes—
1102C4C2×#288311yescharacteristic
1103C4C2×#288311yescharacteristic
1104C2—24no—
1105C2—22no—
1106C2—44no—
1107C2—816no—
1108C2—164no—
1109C2#637901511yescharacteristic
1110C2#637913411yescharacteristic
1111C2C2×#2245511yescharacteristic
subgroupG/H
center, socleC22C2×D4×C22⋊C4
commutatorC22×C4C24×C4
Frattini, cosocleC23×C4C25
prime radicalC2×#62415C2
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22 ◁ C22×C42 ◁ G
LECSG ▷ C23×C4 ▷ C22 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #6389868C2semidirect
3. #6385980C2semidirect
4. D8×#99C2semidirect
5. #220244C2semidirect
6. #205755C2semidirect
7. #198480C2semidirect
8. #188809C2semidirect
9. #185660C2semidirect
10. #182081C2semidirect
16. C2×#3391C4semidirect
17. C2×#3391C4semidirect
18. C2×D4×D8C4semidirect
19. C2×D4×D8C4semidirect
22. C2×#3205C4semidirect
24. C2×#3169C4semidirect
26. C22×#493C4semidirect
29. #34364C22semidirect
32. C22⋊C4×D8C22semidirect
33. #22436C22semidirect
35. D4×#99C22semidirect
37. #21810C22semidirect
38. #21794C22semidirect
41. #20818C22semidirect
45. #20476C22semidirect
46. #17595C22semidirect
48. #9785C22semidirect
49. #9783C22semidirect
50. #9259C22semidirect
51. #8609C22semidirect
52. #8608C22semidirect
53. #8375C22semidirect
54. #8160C22semidirect
55. C8×#99C22semidirect
56. #7980C22semidirect
57. #7928C22semidirect
59. C23×D8C2×C4semidirect
60. C23×D8C2×C4semidirect
68. C2×#550C2×C4semidirect
71. C2×D42C2×C4semidirect
75. C2×#532C2×C4semidirect
77. C22×#127C2×C4semidirect
104. C2×#500C2×C4semidirect
113. C2×#493C2×C4semidirect
114. C2×#493C2×C4semidirect
115. C2×#493C2×C4semidirect
116. C2×#493C2×C4semidirect
121. C2×#486C2×C4semidirect
122. C2×#486C2×C4semidirect
123. C2×#466C2×C4semidirect
124. C2×#466C2×C4semidirect
127. C2×#459C2×C4semidirect
128. C2×#459C2×C4semidirect
129. C2×#459C2×C4semidirect
130. C2×#459C2×C4semidirect
131. C2×#447C2×C4semidirect
132. C2×#447C2×C4semidirect
138. C2×C8×Q8C2×C4semidirect
139. C2×C8×Q8C2×C4semidirect
142. C2×C4×D8C2×C4semidirect
143. C2×C4×D8C2×C4semidirect
144. C2×C4×D8C2×C4semidirect
145. C2×C4×D8C2×C4semidirect
146. C2×C8×D4C2×C4semidirect
147. C2×C8×D4C2×C4semidirect
151. C2×#431C2×C4semidirect
154. C22×C4×C8C2×C4semidirect

Maximal subgroups

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

subgroupindex
C2×#624152
#63898682
#63859802
D8×#992
#2202442
#2057552
#1984802
#1888092
#1856602
#1820812