Finite Group Databasebeta

← #10576130

Subgroups — #10576130

Order 512.

10236 conjugacy classes of subgroups.

The subgroup lattice has 1120 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3584C211yesmaximal, characteristic, complemented
2C22×#578C211yesmaximal, characteristic, complemented
3#62859C212yesmaximal, complemented
4#61091C214yesmaximal, complemented
5#61090C214yesmaximal, complemented
6#61083C218yesmaximal, complemented
7#61064C218yesmaximal, complemented
8#61060C218yesmaximal, complemented
9#61057C218yesmaximal, complemented
10#61053C214yesmaximal, complemented
11#61051C214yesmaximal, complemented
12C2×#3156C211yesmaximal, characteristic, complemented
13#60450C211yesmaximal, characteristic, complemented
14C2×#3059C211yesmaximal, characteristic, complemented
15#60427C212yesmaximal, complemented
16#60370C212yesmaximal, complemented
17#60368C212yesmaximal, complemented
18#60167C211yesmaximal, characteristic, complemented
19#60140C211yesmaximal, characteristic, complemented
20C2×#585C2212yes—
21C22×2−1+4C2212yescomplemented
22#3584—216no—
23C2×#578—216no—
24C2×#578C2212yes—
25C2×#578C2214yescomplemented
26C2×#578C2214yescomplemented
27C2×#578C2214yescomplemented
28C2×#578C2214yescomplemented
29C2×#578C2212yescomplemented
30C2×#577C2214yes—
31C2×#577C2214yescomplemented
32C2×#576C2212yes—
33C2×#576C2212yescomplemented
34C2×#575C2212yes—
35C2×#575C2214yescomplemented
36C22×#137C2212yescomplemented
37C22×#137C2214yescomplemented
38C22×#137C2212yescomplemented
39C22×#135C2211yescharacteristic
40C22×#135C2211yescharacteristic
41C22×#135C2212yescomplemented
42C22×#135C2214yescomplemented
43C23×Q16C2211yescharacteristic, complemented
44C23×Q16C2212yescomplemented
45C22×#131C2211yescharacteristic
46C22×#131C2211yescharacteristic, complemented
47#3500—24no—
48#3500C2218yescomplemented
49#3499—24no—
50#3499C2218yescomplemented
51#3489—28no—
52#3489C22116yescomplemented
53#3486C2218yescomplemented
54#3485—28no—
55#3485C2218yescomplemented
56#3449—24no—
57#3449C2211yescharacteristic
58#3449C2212yescomplemented
59C2×#536—24no—
60C2×#536C2212yes—
61C2×#536C2212yescomplemented
62#3428C2212yescomplemented
63D4×Q16C22116yescomplemented
64#3285C22116yescomplemented
65#3283C22116yescomplemented
66#3280C22116yescomplemented
67#3276C22132yescomplemented
68#3275C22132yescomplemented
69#3270C22132yescomplemented
70#3269C22132yescomplemented
71#3267C22132yescomplemented
72#3266C22132yescomplemented
73#3156C2214yescomplemented
74#3156C2214yescomplemented
75#3156C2214yescomplemented
76#3156C2214yescomplemented
77C2×#497C2214yescomplemented
78C2×#495C2212yescomplemented
79C2×#494C2212yescomplemented
80#3061C2214yescomplemented
81#3060C2214yescomplemented
82#3059C2214yescomplemented
83#3059C2214yescomplemented
84#3059C2214yescomplemented
85#3059C2214yescomplemented
86#3059C2212yescomplemented
87#3058C2212yescomplemented
88#3057C2214yescomplemented
89#3054C2214yescomplemented
90C2×#470C2214yescomplemented
91#3050C2214yescomplemented
92C2×#467C2214yescomplemented
93#3046C22116yescomplemented
94#3044C2218yescomplemented
95#3042C2218yescomplemented
96#3040C2218yescomplemented
97#3039C2218yescomplemented
98#3013C22116yescomplemented
99#3011C2218yescomplemented
100#3011C2218yescomplemented
101#3011C2218yescomplemented
102#3010C2218yescomplemented
103#3009C2218yescomplemented
104#3009C2218yescomplemented
105#3007C22116yescomplemented
106#3005C2218yescomplemented
107#3004C2218yescomplemented
108#2952C2214yescomplemented
109#2951C2214yescomplemented
110#2950C2212yescomplemented
111#2949C2214yescomplemented
112#2948C2212yescomplemented
113#2943C2214yescomplemented
114C4×#135C2214yescomplemented
115#2932C2214yescomplemented
116#2931C2214yescomplemented
117#2930C2214yescomplemented
118#2930C2214yescomplemented
119#2929C2214yescomplemented
120#2929C2214yescomplemented
121C2×#427C2211yescharacteristic, complemented
122#2905C2211yescharacteristic, complemented
123#2896C2212yescomplemented
124#2896C2212yescomplemented
125C2×#419C2212yescomplemented
126#2879C2211yescharacteristic
127#2879C2211yescharacteristic, complemented
128C2×#405C2211yescharacteristic, complemented
129#585—216no—
130#585—48no—
131C2×2−1+4—24no—
132C2×2−1+4—24no—
133C2×2−1+4—22no—
134C2×2−1+4—216no—
135C2×2−1+4—48no—
136C2×2−1+4C2318yes—
137C2×2−1+4C2318yes—
138C2×2−1+4C2314yes—
139C2×2−1+4C2314yes—
140C2×H(5,𝔽2)—24no—
141C2×H(5,𝔽2)—22no—
142C2×H(5,𝔽2)C2314yes—
143C2×H(5,𝔽2)C2314yes—
144C22×#41—24no—
145C22×#41—24no—
146C22×#41—22no—
147C22×#41—24no—
148C22×#41C2312yes—
149C22×#41C2314yes—
150C22×#41C2318yes—
151C22×#41C2312yes—
152C22×#41C2311yescharacteristic
153C22×#41C2311yescharacteristic
154C23×Q8—22no—
155C23×Q8C2312yes—
156C23×Q8C2314yes—
157#578—216no—
158#578—232no—
159#578—232no—
160#578—232no—
161#578—232no—
162#578—216no—
163#577—232no—
164#577—232no—
165#576—216no—
166#576—216no—
167#575—216no—
168#575—232no—
169C2×#137—216no—
170C2×#137—232no—
171C2×#137—48no—
172C2×#137C2314yes—
173C2×#137C2318yes—
174C2×#137C2318yes—
175C2×#137C23116yes—
176C2×#137C2314yes—
177C2×#137C2318yes—
178C2×#137C23116yes—
179C2×#137C2318yes—
180C2×#137C2318yes—
181C2×#137C2318yes—
182C2×AGL(1,ℤ/8)C2314yes—
183C2×AGL(1,ℤ/8)C2314yes—
184C2×AGL(1,ℤ/8)C2318yes—
185C2×AGL(1,ℤ/8)C2318yes—
186C2×#135—232no—
187C2×#135—216no—
188C2×#135—28no—
189C2×#135D4116yescomplemented
190C2×#135C2312yes—
191C2×#135C2312yes—
192C2×#135C2312yes—
193C2×#135C2312yes—
194C2×#135C2318yes—
195C2×#135C2318yes—
196C2×#135C2318yes—
197C2×#135C2318yes—
198C2×#135C2314yes—
199C2×#135C2314yes—
200C2×#135C2312yes—
201C2×#135C2312yes—
202C2×#135C2312yes—
203C2×#135C2312yes—
204C22×Q16—216no—
205C22×Q16—28no—
206C22×Q16C2311yescharacteristic
207C22×Q16C2312yes—
208C22×Q16C2312yes—
209C22×Q16C2312yes—
210C22×Q16C2312yes—
211C22×Q16C2312yes—
212C22×Q16C2312yes—
213C22×Q16C2314yes—
214C22×Q16C2318yes—
215C22×Q16C2318yes—
216C22×Q16C2314yes—
217C22×Q16C2314yes—
218C22×Q16C2311yescharacteristic
219C22×SD16C2312yes—
220C22×SD16C2314yes—
221C22×SD16C2318yes—
222C22×SD16C2314yes—
223C22×SD16C2312yes—
224C22×D8C2311yescharacteristic
225C22×D8C2314yes—
226C22×D8C2311yescharacteristic
227C2×#131—28no—
228C2×#131—28no—
229C2×#131C2312yes—
230C2×#131C2312yes—
231C2×#131C2312yes—
232C2×#131C2312yes—
233C2×#131C2312yes—
234C2×#131C2312yes—
235C2×#131C2312yes—
236C2×#131C2312yes—
237C22×M16C2311yescharacteristic
238C22×M16C2311yescharacteristic
239C22×M16C2311yescharacteristic
240C22×M16C2312yes—
241C22×M16C2312yes—
242C23×C8C2312yes—
243C23×C8C2312yes—
244C23×C8C2311yescharacteristic
245D4×Q8—216no—
246D4×Q8C23132yes—
247#548—216no—
248#548C23132yes—
249#547—232no—
250#547—216no—
251#547—232no—
252#547C23132yes—
253#546—232no—
254#546—216no—
255#546—232no—
256#546C23132yes—
257#537—216no—
258#537D414yes—
259#537C2318yes—
260#536—24no—
261#536—24no—
262#536—22no—
263#536—28no—
264#536—28no—
265#536—28no—
266#536—216no—
267#536—216no—
268#536—24no—
269#536—24no—
270#536D412yes—
271#536D412yes—
272#536C2318yes—
273#536C2318yes—
274#536C2318yes—
275#536C2318yes—
276#536C2314yes—
277#535—22no—
278#535—28no—
279#535D412yes—
280#535D412yes—
281#535C2314yes—
282#534—24no—
283#534—216no—
284#534D414yes—
285#532—24no—
286#532—28no—
287#532—28no—
288#532C2314yes—
289C2×C4⋊Q8—22no—
290C2×C4⋊Q8—28no—
291C2×C4⋊Q8C2314yes—
292C2×#124—22no—
293C2×#124—28no—
294C2×#124C2314yes—
295#525—24no—
296#525—216no—
297#525—216no—
298#525C2318yes—
299#525C2314yes—
300#525C2314yes—
301C2×#123—24no—
302C2×#123—216no—
303C2×#123—24no—
304C2×C22⋊Q8—216no—
305C2×C22⋊Q8—24no—
306C2×C22⋊Q8C2318yes—
307#520—24no—
308#520C2318yes—
309#519C2314yes—
310#518—24no—
311#518C2314yes—
312C4×#41—24no—
313C4×#41C2318yes—
314C2×#117—24no—
315C2×#117C2312yes—
316C2×#117C2311yescharacteristic
317#497C23116yes—
318#497C23116yes—
319#495C2318yes—
320#495C2318yes—
321#494C2318yes—
322#494C2318yes—
323#470C23116yes—
324#470C23116yes—
325#470C2318yes—
326#469C2318yes—
327#468C23116yes—
328#467C23116yes—
329#467C23116yes—
330#467C2318yes—
331#466C2318yes—
332#465C23116yes—
333#464C23132yes—
334#463C23132yes—
335#462C23132yes—
336#461C23132yes—
337#452C23132yes—
338#452C23132yes—
339#452C23132yes—
340#451C23132yes—
341#451C23132yes—
342#450C23132yes—
343#449C23132yes—
344#448C23132yes—
345#442C2318yes—
346#441C2318yes—
347#440C23116yes—
348C4×Q16C2318yes—
349C4×SD16C23116yes—
350C4×D8C2318yes—
351#436C23116yes—
352#435C23116yes—
353#435C23116yes—
354C8×D4C23116yes—
355#427C2312yes—
356#427C2312yes—
357#427C2312yes—
358#427C2312yes—
359C2×#107C2312yes—
360C2×#106C2312yes—
361#424C2314yes—
362#424C2314yes—
363#423C2314yes—
364#419C2318yes—
365#419C2318yes—
366#419C2314yes—
367#419C2314yes—
368#418C2314yes—
369#418C2314yes—
370#417C2318yes—
371#417C2318yes—
372#416C2318yes—
373#416C2318yes—
374C2×#103C2318yes—
375#408C2314yes—
376#408C2314yes—
377#408C2314yes—
378#408C2314yes—
379#407C2314yes—
380#407C2314yes—
381#405C2312yes—
382#405C2312yes—
383#405C2312yes—
384#405C2312yes—
385C2×#97C2312yes—
386C2×C4×C8C2312yes—
3872−1+4—216no—
3882−1+4—232no—
3892−1+4—232no—
3902−1+4—216no—
3912−1+4—416no—
3922−1+4—416no—
3932−1+4—48no—
3942−1+4—48no—
3952−1+4—416no—
3962−1+4—432no—
3972−1+4—432no—
398H(5,𝔽2)—216no—
399H(5,𝔽2)—216no—
400H(5,𝔽2)—432no—
401H(5,𝔽2)—48no—
402H(5,𝔽2)—48no—
403H(5,𝔽2)—416no—
404C2×#41—24no—
405C2×#41—24no—
406C2×#41—28no—
407C2×#41—28no—
408C2×#41—28no—
409C2×#41—24no—
410C2×#41—216no—
411C2×#41—216no—
412C2×#41—28no—
413C2×#41—24no—
414C2×#41—22no—
415C2×#41—22no—
416C2×#41—24no—
417C2×#41—24no—
418C2×#41—22no—
419C2×#41—22no—
420C2×#41—28no—
421C2×#41—28no—
422C2×#41—28no—
423C2×#41—24no—
424C2×#41—28no—
425C2×#41—24no—
426C2×#41—232no—
427C2×#41—216no—
428C2×#41—28no—
429C2×#41—28no—
430C2×#41—48no—
431C2×#41—416no—
432C2×#41—416no—
433C2×#41—432no—
434C2×#41—432no—
435C2×#41—432no—
436C2×#41C2×D4116yes—
437C2×#41C2×D412yes—
438C2×#41C2×D412yes—
439C2×#41C2×D412yes—
440C2×#41C2×D412yes—
441C2×#41C2414yes—
442C2×#41C2414yes—
443C2×#41C24116yes—
444C2×#41C2418yes—
445C2×#41C2418yes—
446C2×#41C2414yes—
447C2×#41C2414yes—
448C2×#41C2412yes—
449C2×#41C2412yes—
450C2×#41C2412yes—
451C2×#41C2412yes—
452C22×Q8—28no—
453C22×Q8—28no—
454C22×Q8—24no—
455C22×Q8—24no—
456C22×Q8—22no—
457C22×Q8—22no—
458C22×Q8—24no—
459C22×Q8—22no—
460C22×Q8—28no—
461C22×Q8—216no—
462C22×Q8—28no—
463C22×Q8—28no—
464C22×Q8—48no—
465C22×Q8—416no—
466C22×Q8C2×D411yescharacteristic
467C22×Q8C2×D411yescharacteristic
468C22×Q8C2414yes—
469C22×Q8C2414yes—
470C22×Q8C2412yes—
471C22×Q8C2414yes—
472C22×Q8C24116yes—
473C22×Q8C2418yes—
474C22×Q8C2412yes—
475C22×D4—22no—
476C22×D4—22no—
477C22×D4—24no—
478C22×D4—28no—
479C22×D4—28no—
480C22×D4—24no—
481C22×D4—28no—
482C22×D4—24no—
483C22×D4C2×D412yes—
484C22×D4C2×D411yescharacteristic
485C22×D4C2×D412yes—
486C22×D4C2×D411yescharacteristic
487C22×D4C2412yes—
488C22×D4C2418yes—
489C22×D4C2412yes—
490C23×C4—22no—
491C23×C4—22no—
492C23×C4—24no—
493C23×C4—28no—
494C23×C4—22no—
495C23×C4—24no—
496C23×C4C2412yes—
497C23×C4C2412yes—
498C23×C4C2411yescharacteristic
499#137—232no—
500#137—232no—
501#137—216no—
502#137—216no—
503#137—232no—
504#137—264no—
505#137—264no—
506#137—232no—
507#137—416no—
508#137—416no—
509AGL(1,ℤ/8)—216no—
510AGL(1,ℤ/8)—216no—
511AGL(1,ℤ/8)—232no—
512AGL(1,ℤ/8)—232no—
513#135—232no—
514#135—216no—
515#135—232no—
516#135—216no—
517#135—232no—
518#135—232no—
519#135—28no—
520#135—28no—
521#135—28no—
522#135—28no—
523#135C2×D4116yes—
524#135C2×D4116yes—
525#135C2×D4116yes—
526#135C2×D4116yes—
527C2×Q16—216no—
528C2×Q16—232no—
529C2×Q16—232no—
530C2×Q16—216no—
531C2×Q16—28no—
532C2×Q16—28no—
533C2×Q16—28no—
534C2×Q16—28no—
535C2×Q16—28no—
536C2×Q16—28no—
537C2×Q16—24no—
538C2×Q16—48no—
539C2×Q16C2×D418yes—
540C2×Q16C2414yes—
541C2×Q16C2414yes—
542C2×Q16C2412yes—
543C2×Q16C24116yes—
544C2×Q16C2414yes—
545C2×Q16C2414yes—
546C2×Q16C2418yes—
547C2×Q16C2412yes—
548C2×Q16C24116yes—
549C2×Q16C2412yes—
550C2×Q16C2412yes—
551C2×SD16—216no—
552C2×SD16—232no—
553C2×SD16—28no—
554C2×SD16—48no—
555C2×SD16C2×D4116yes—
556C2×SD16C2414yes—
557C2×SD16C2418yes—
558C2×SD16C2418yes—
559C2×SD16C2414yes—
560C2×SD16C24116yes—
561C2×SD16C24116yes—
562C2×SD16C2414yes—
563C2×SD16C2414yes—
564C2×D8—216no—
565C2×D8—24no—
566C2×D8C2×D418yes—
567C2×D8C2412yes—
568C2×D8C2418yes—
569C2×D8C2412yes—
570C2×D8C2412yes—
571C2×D8C2412yes—
572#131—28no—
573#131—28no—
574#131—28no—
575#131—28no—
576#131—28no—
577#131—28no—
578#131—28no—
579#131—28no—
580C2×M16—24no—
581C2×M16—24no—
582C2×M16—24no—
583C2×M16—28no—
584C2×M16—28no—
585C2×M16C2412yes—
586C2×M16C2412yes—
587C2×M16C2414yes—
588C2×M16C2414yes—
589C2×M16C2412yes—
590C2×M16C2412yes—
591C2×M16C2414yes—
592C2×M16C2414yes—
593C2×M16C2412yes—
594C2×M16C2412yes—
595C22×C8—28no—
596C22×C8—28no—
597C22×C8C2×D418yes—
598C22×C8C2412yes—
599C22×C8C2412yes—
600C22×C8C2414yes—
601C22×C8C2414yes—
602C22×C8C2414yes—
603C22×C8C2414yes—
604C22×C8C2412yes—
605C22×C8C2411yescharacteristic
606C22×C8C2411yescharacteristic
607C22×C8C2411yescharacteristic
608C22×C8C2411yescharacteristic
609C22×C8C2411yescharacteristic
610C22×C8C2411yescharacteristic
611C4⋊Q8—28no—
612C4⋊Q8—24no—
613C4⋊Q8—28no—
614C4⋊Q8—232no—
615C4⋊Q8—28no—
616C4⋊Q8C2×D414yes—
617C4⋊Q8C24116yes—
618#127—24no—
619#127C2×D414yes—
620#124—24no—
621#124—28no—
622#124—28no—
623#124—24no—
624#124—232no—
625#124—28no—
626#124C2×D414yes—
627#124C2×D414yes—
628#124C24116yes—
629#123—216no—
630#123—216no—
631#123—28no—
632#123—28no—
633#123—232no—
634#123—216no—
635#123—232no—
636#123—216no—
637#123—232no—
638#123C2×D418yes—
639#123C2×D418yes—
640C22⋊Q8—28no—
641C22⋊Q8—216no—
642C22⋊Q8—216no—
643C22⋊Q8—232no—
644C22⋊Q8—216no—
645C22⋊Q8—232no—
646C22⋊Q8—232no—
647C22⋊Q8C2×D418yes—
648C22⋊Q8C2×D418yes—
649C22⋊Q8C24132yes—
650C22⋊Q8C24116yes—
651#121—28no—
652#121—232no—
653#121—232no—
654#121—216no—
655#121—232no—
656#121C2×D418yes—
657#121C2×D418yes—
658#121C2×D4116yes—
659#121C24116yes—
660#120—28no—
661#120—232no—
662#120—28no—
663#120C2×D418yes—
664#120C2×D418yes—
665C4×Q8—28no—
666C4×Q8C24116yes—
667C4×D4—232no—
668C4×D4—216no—
669C4×D4—216no—
670C4×D4—28no—
671C4×D4—216no—
672C4×D4—232no—
673C4×D4C24116yes—
674C4×D4C24116yes—
675#117—22no—
676#117—22no—
677#117—28no—
678#117—28no—
679#117—28no—
680#117C2×D412yes—
681#117C2×D412yes—
682#117C2414yes—
683#117C2414yes—
684#117C2412yes—
685#117C2412yes—
686C2×C4⋊C4—28no—
687C2×C4⋊C4—28no—
688C2×C4⋊C4—28no—
689C2×C4⋊C4—232no—
690C2×C4⋊C4C2×D412yes—
691C2×C4⋊C4C2414yes—
692C2×C22⋊C4—22no—
693C2×C22⋊C4—28no—
694C2×C22⋊C4—28no—
695C2×C22⋊C4—28no—
696C2×C22⋊C4—232no—
697C2×C22⋊C4C2×D412yes—
698C2×C42—22no—
699C2×C42—28no—
700C2×C42C2412yes—
701#107C2414yes—
702#107C2414yes—
703#106C2414yes—
704#106C2414yes—
705C4⋊C8C24116yes—
706#103C24132yes—
707#103C24116yes—
708#103C24116yes—
709#102C24116yes—
710#102C24116yes—
711C22⋊C8C24116yes—
712C22⋊C8C24116yes—
713#97C2414yes—
714#97C2414yes—
715C4×C8C2414yes—
716C4×C8C2414yes—
717C24—22no—
718C24—28no—
719C24—22no—
720C24C22×D412yes—
721C24C22×D412yes—
722C24C22×D411yescharacteristic
723#41—28no—
724#41—28no—
725#41—216no—
726#41—216no—
727#41—28no—
728#41—28no—
729#41—24no—
730#41—24no—
731#41—24no—
732#41—24no—
733#41—28no—
734#41—24no—
735#41—24no—
736#41—28no—
737#41—24no—
738#41—24no—
739#41—216no—
740#41—216no—
741#41—232no—
742#41—28no—
743#41—28no—
744#41—28no—
745#41—28no—
746#41—432no—
747#41—48no—
748#41—48no—
749#41—416no—
750#41—432no—
751#41—432no—
752#41—432no—
753#41—416no—
754#41—432no—
755#41—432no—
756#41—416no—
757#41—432no—
758#41—464no—
759#41—464no—
760#41—416no—
761#41—416no—
762#41—48no—
763#41—48no—
764#41C22×D4116yes—
765#41C22×D4116yes—
766C2×Q8—24no—
767C2×Q8—24no—
768C2×Q8—22no—
769C2×Q8—24no—
770C2×Q8—216no—
771C2×Q8—24no—
772C2×Q8—28no—
773C2×Q8—24no—
774C2×Q8—22no—
775C2×Q8—24no—
776C2×Q8—216no—
777C2×Q8—232no—
778C2×Q8—28no—
779C2×Q8—24no—
780C2×Q8—28no—
781C2×Q8—28no—
782C2×Q8—28no—
783C2×Q8—24no—
784C2×Q8—28no—
785C2×Q8—28no—
786C2×Q8—416no—
787C2×Q8—416no—
788C2×Q8—48no—
789C2×Q8—432no—
790C2×Q8—432no—
791C2×Q8—432no—
792C2×Q8—416no—
793C2×Q8—416no—
794C2×Q8—48no—
795C2×Q8—48no—
796C2×Q8—48no—
797C2×Q8C22×D418yes—
798C2×Q8C22×D412yes—
799C2×Q8C22×D412yes—
800C2×Q8C22×D412yes—
801C2×Q8C22×D412yes—
802C2×Q8C2518yes—
803C2×Q8C2514yes—
804C2×Q8C2514yes—
805C2×D4—216no—
806C2×D4—28no—
807C2×D4—28no—
808C2×D4—24no—
809C2×D4—24no—
810C2×D4—216no—
811C2×D4—216no—
812C2×D4—24no—
813C2×D4—28no—
814C2×D4—24no—
815C2×D4—28no—
816C2×D4—216no—
817C2×D4—24no—
818C2×D4—24no—
819C2×D4—22no—
820C2×D4—24no—
821C2×D4—28no—
822C2×D4—22no—
823C2×D4—24no—
824C2×D4—24no—
825C2×D4—48no—
826C2×D4—416no—
827C2×D4—432no—
828C2×D4—416no—
829C2×D4—432no—
830C2×D4—432no—
831C2×D4—416no—
832C2×D4—48no—
833C2×D4C22×D414yes—
834C2×D4C22×D414yes—
835C2×D4C22×D414yes—
836C2×D4C22×D412yes—
837C2×D4C22×D414yes—
838C2×D4C22×D412yes—
839C2×D4C22×D412yes—
840C2×D4C22×D412yes—
841C2×D4C22×D418yes—
842C2×D4C22×D4116yes—
843C2×D4C2514yes—
844C2×D4C2514yes—
845C22×C4—22no—
846C22×C4—216no—
847C22×C4—24no—
848C22×C4—24no—
849C22×C4—24no—
850C22×C4—24no—
851C22×C4—24no—
852C22×C4—24no—
853C22×C4—24no—
854C22×C4—24no—
855C22×C4—22no—
856C22×C4—216no—
857C22×C4—28no—
858C22×C4—24no—
859C22×C4—24no—
860C22×C4—216no—
861C22×C4—28no—
862C22×C4—28no—
863C22×C4—24no—
864C22×C4—24no—
865C22×C4—216no—
866C22×C4—432no—
867C22×C4—416no—
868C22×C4—416no—
869C22×C4—48no—
870C22×C4—48no—
871C22×C4C22×D412yes—
872C22×C4C22×D414yes—
873C22×C4C22×D414yes—
874C22×C4C22×D412yes—
875C22×C4C22×D414yes—
876C22×C4C22×D411yescharacteristic
877C22×C4C22×D411yescharacteristic
878C22×C4C22×D411yescharacteristic
879C22×C4C22×D414yes—
880C22×C4H(5,𝔽2)14yes—
881C22×C4C2514yes—
882C22×C4C2514yes—
883C22×C4C2511yescharacteristic
884C22×C4C2511yescharacteristic
885C22×C4C2511yescharacteristic
886Q16—232no—
887Q16—216no—
888Q16—28no—
889Q16—28no—
890Q16—24no—
891Q16—28no—
892Q16—28no—
893Q16—24no—
894Q16—416no—
895Q16C22×D418yes—
896Q16C22×D418yes—
897SD16—216no—
898SD16—216no—
899SD16—232no—
900SD16—28no—
901SD16—28no—
902SD16—416no—
903SD16C22×D4116yes—
904SD16C22×D4116yes—
905D8—216no—
906D8—24no—
907D8—24no—
908D8C22×D418yes—
909D8C22×D418yes—
910M16—24no—
911M16—24no—
912M16—24no—
913M16—24no—
914M16—24no—
915M16—24no—
916M16—28no—
917M16—28no—
918M16—28no—
919M16—28no—
920C2×C8—24no—
921C2×C8—24no—
922C2×C8—24no—
923C2×C8—28no—
924C2×C8—28no—
925C2×C8—28no—
926C2×C8—28no—
927C2×C8C22×D414yes—
928C2×C8C22×D414yes—
929C2×C8C22×D414yes—
930C2×C8C22×D414yes—
931C2×C8C22×D414yes—
932C2×C8C22×D414yes—
933C2×C8C2514yes—
934C2×C8C2514yes—
935C2×C8C2514yes—
936C2×C8C2511yescharacteristic
937C2×C8C2511yescharacteristic
938C2×C8C2511yescharacteristic
939C2×C8C2511yescharacteristic
940C4⋊C4—24no—
941C4⋊C4—232no—
942C4⋊C4—232no—
943C4⋊C4—216no—
944C4⋊C4—216no—
945C4⋊C4C22×D414yes—
946C4⋊C4C22×D4116yes—
947C4⋊C4C22×D414yes—
948C4⋊C4C2518yes—
949C22⋊C4—24no—
950C22⋊C4—232no—
951C22⋊C4—24no—
952C22⋊C4—216no—
953C22⋊C4—232no—
954C22⋊C4—216no—
955C22⋊C4—216no—
956C22⋊C4C22×D414yes—
957C22⋊C4C22×D4116yes—
958C22⋊C4C22×D414yes—
959C22⋊C4C22×D4116yes—
960C42—24no—
961C42—216no—
962C42—24no—
963C42C22×D414yes—
964C42C2514yes—
965C23—24no—
966C23—24no—
967C23—28no—
968C23—24no—
969C23—24no—
970C23—42no—
971C23—44no—
972C23—44no—
973C23—416no—
974C23—44no—
975C23—84no—
976C23—84no—
977C23—816no—
978C23D4214yes—
979C23C23×D414yes—
980C23C23×D414yes—
981C23C23×D411yescharacteristic
982C23C23×D411yescharacteristic
983C23C23×D411yescharacteristic
984Q8—24no—
985Q8—24no—
986Q8—24no—
987Q8—28no—
988Q8—24no—
989Q8—24no—
990Q8—24no—
991Q8—28no—
992Q8—28no—
993Q8—24no—
994Q8—432no—
995Q8—416no—
996Q8—48no—
997Q8—48no—
998Q8—48no—
999Q8—44no—
1000Q8C23×D418yes—
1001D4—216no—
1002D4—216no—
1003D4—28no—
1004D4—28no—
1005D4—28no—
1006D4—28no—
1007D4—24no—
1008D4—24no—
1009D4—24no—
1010D4—24no—
1011D4—24no—
1012D4—28no—
1013D4—24no—
1014D4—24no—
1015D4—416no—
1016D4—416no—
1017D4—416no—
1018D4—416no—
1019D4—432no—
1020D4—48no—
1021D4—48no—
1022D4—44no—
1023D4—816no—
1024D4C23×D418yes—
1025C2×C4—24no—
1026C2×C4—28no—
1027C2×C4—24no—
1028C2×C4—24no—
1029C2×C4—24no—
1030C2×C4—24no—
1031C2×C4—24no—
1032C2×C4—24no—
1033C2×C4—216no—
1034C2×C4—216no—
1035C2×C4—28no—
1036C2×C4—28no—
1037C2×C4—28no—
1038C2×C4—28no—
1039C2×C4—24no—
1040C2×C4—44no—
1041C2×C4—416no—
1042C2×C4—416no—
1043C2×C4—416no—
1044C2×C4—432no—
1045C2×C4—432no—
1046C2×C4—48no—
1047C2×C4—44no—
1048C2×C4—48no—
1049C2×C4—48no—
1050C2×C4—48no—
1051C2×C4—48no—
1052C2×C4—816no—
1053C2×C4—84no—
1054C2×C4D4214yes—
1055C2×C4D4214yes—
1056C2×C4D4214yes—
1057C2×C4C23×D418yes—
1058C2×C4C23×D414yes—
1059C2×C4C23×D414yes—
1060C2×C4C23×D412yes—
1061C2×C4C23×D412yes—
1062C2×C4C23×D412yes—
1063C2×C4C23×D411yescharacteristic
1064C2×C4C23×D411yescharacteristic
1065C2×C4C23×D411yescharacteristic
1066C2×C4C2×H(5,𝔽2)12yes—
1067C2×C4C2×H(5,𝔽2)12yes—
1068C2×C4C2×H(5,𝔽2)12yes—
1069C2×C4C2611yescharacteristic
1070C8—24no—
1071C8—24no—
1072C8—24no—
1073C8C23×D412yes—
1074C8C23×D412yes—
1075C8C23×D412yes—
1076C8C23×D412yes—
1077C22—22no—
1078C22—22no—
1079C22—22no—
1080C22—28no—
1081C22—28no—
1082C22—24no—
1083C22—28no—
1084C22—24no—
1085C22—44no—
1086C22—48no—
1087C22—48no—
1088C22—48no—
1089C22—44no—
1090C22—84no—
1091C22—88no—
1092C22—164no—
1093C22—1616no—
1094C22C2×D4212yes—
1095C22C2×D4212yes—
1096C22C2×D4212yes—
1097C22C24×D411yescharacteristic
1098C4—28no—
1099C4—28no—
1100C4—24no—
1101C4—24no—
1102C4—48no—
1103C4—44no—
1104C4—48no—
1105C4C2×D4212yes—
1106C4C2×D4212yes—
1107C4C2×D4212yes—
1108C4C24×D411yescharacteristic
1109C4C22×H(5,𝔽2)11yescharacteristic
1110C2—22no—
1111C2—22no—
1112C2—22no—
1113C2—44no—
1114C2—44no—
1115C2—48no—
1116C2—84no—
1117C2C22×D4211yescharacteristic
1118C2#6309312yes—
subgroupG/H
center, socleC22C24×D4
commutator, Frattini, cosocleC2×C4C26
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22 ◁ #3449 ◁ G
LECSG ▷ C2×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#3584C2semidirect
2. C22×#578C2semidirect
3. #62859C2semidirect
4. #61091C2semidirect
5. #61090C2semidirect
6. #61083C2semidirect
7. #61064C2semidirect
8. #61060C2semidirect
9. #61057C2semidirect
10. #61053C2semidirect
11. #61051C2semidirect
12. C2×#3156C2semidirect
13. #60450C2semidirect
14. C2×#3059C2semidirect
15. #60427C2semidirect
16. #60370C2semidirect
17. #60368C2semidirect
18. #60167C2semidirect
19. #60140C2semidirect
21. C22×2−1+4C22semidirect
25. C2×#578C22semidirect
26. C2×#578C22semidirect
27. C2×#578C22semidirect
28. C2×#578C22semidirect
29. C2×#578C22semidirect
31. C2×#577C22semidirect
33. C2×#576C22semidirect
35. C2×#575C22semidirect
36. C22×#137C22semidirect
37. C22×#137C22semidirect
38. C22×#137C22semidirect
41. C22×#135C22semidirect
42. C22×#135C22semidirect
43. C23×Q16C22semidirect
44. C23×Q16C22semidirect
46. C22×#131C22semidirect
48. #3500C22semidirect
50. #3499C22semidirect
52. #3489C22semidirect
53. #3486C22semidirect
55. #3485C22semidirect
58. #3449C22semidirect
61. C2×#536C22semidirect
62. #3428C22semidirect
63. D4×Q16C22semidirect
64. #3285C22semidirect
65. #3283C22semidirect
66. #3280C22semidirect
67. #3276C22semidirect
68. #3275C22semidirect
69. #3270C22semidirect
70. #3269C22semidirect
71. #3267C22semidirect
72. #3266C22semidirect
73. #3156C22semidirect
74. #3156C22semidirect
75. #3156C22semidirect
76. #3156C22semidirect
77. C2×#497C22semidirect
78. C2×#495C22semidirect
79. C2×#494C22semidirect
80. #3061C22semidirect
81. #3060C22semidirect
82. #3059C22semidirect
83. #3059C22semidirect
84. #3059C22semidirect
85. #3059C22semidirect
86. #3059C22semidirect
87. #3058C22semidirect
88. #3057C22semidirect
89. #3054C22semidirect
90. C2×#470C22semidirect
91. #3050C22semidirect
92. C2×#467C22semidirect
93. #3046C22semidirect
94. #3044C22semidirect
95. #3042C22semidirect
96. #3040C22semidirect
97. #3039C22semidirect
98. #3013C22semidirect
99. #3011C22semidirect
100. #3011C22semidirect
101. #3011C22semidirect
102. #3010C22semidirect
103. #3009C22semidirect
104. #3009C22semidirect
105. #3007C22semidirect
106. #3005C22semidirect
107. #3004C22semidirect
108. #2952C22semidirect
109. #2951C22semidirect
110. #2950C22semidirect
111. #2949C22semidirect
112. #2948C22semidirect
113. #2943C22semidirect
114. C4×#135C22semidirect
115. #2932C22semidirect
116. #2931C22semidirect
117. #2930C22semidirect
118. #2930C22semidirect
119. #2929C22semidirect
120. #2929C22semidirect
121. C2×#427C22semidirect
122. #2905C22semidirect
123. #2896C22semidirect
124. #2896C22semidirect
125. C2×#419C22semidirect
127. #2879C22semidirect
128. C2×#405C22semidirect
189. C2×#135D4semidirect

Maximal subgroups

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

subgroupindex
C2×#35842
C22×#5782
#628592
#610912
#610902
#610832
#610642
#610602
#610572
#610532
#610512
C2×#31562
#604502
C2×#30592
#604272
#603702
#603682
#601672
#601402