Finite Group Databasebeta

← #7632631

Subgroups — #7632631

Order 512.

23126 conjugacy classes of subgroups.

The subgroup lattice has 1088 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#585C211yesmaximal, characteristic, complemented
2C2×#3500C211yesmaximal, characteristic, complemented
3C2×#3498C211yesmaximal, characteristic, complemented
4C2×#3488C211yesmaximal, characteristic, complemented
5#36429C214yesmaximal, complemented
6#36212C2112yesmaximal, complemented
7#35757C214yesmaximal, complemented
8#35680C2112yesmaximal, complemented
9#35676C213yesmaximal, complemented
10#35660C213yesmaximal, complemented
11#35527C213yesmaximal, complemented
12#35513C213yesmaximal, complemented
13#35250C213yesmaximal, complemented
14#35149C213yesmaximal, complemented
15#34738C213yesmaximal, complemented
16C2×#2431C213yesmaximal, complemented
17#34259C211yesmaximal, characteristic, complemented
18#34258C211yesmaximal, characteristic, complemented
19C22⋊C4×#41C211yesmaximal, characteristic, complemented
20C2×#585—216no—
21C2×#585—216no—
22C2×#585—216no—
23C22×2−1+4C2211yescharacteristic
24C22×2−1+4C2213yescomplemented
25C22×2−1+4C2212yescomplemented
26C22×H(5,𝔽2)C2211yescharacteristic
27C22×H(5,𝔽2)C2211yescharacteristic, complemented
28C22×H(5,𝔽2)C2216yescomplemented
29C22×H(5,𝔽2)C2213yescomplemented
30C23×#41C2211yescharacteristic
31C23×#41C2213yescomplemented
32C23×#41C2212yescomplemented
33C23×#41C2216yescomplemented
34C23×#41C2213yescomplemented
35#3500—216no—
36#3498—216no—
37#3488—216no—
38C2×#550C2212yescomplemented
39C2×#550C2214yescomplemented
40C2×#548C2212yescomplemented
41C2×#548C2214yescomplemented
42C2×#546C2216yescomplemented
43C2×#546C22112yescomplemented
44C2×D42C2216yescomplemented
45C2×D42C22112yescomplemented
46C2×#537C2213yescomplemented
47C2×#536C2213yescomplemented
48C2×#535C2213yescomplemented
49C2×#535C2213yescomplemented
50C2×#535C2213yescomplemented
51C2×#535C2213yescomplemented
52C2×#532C2213yescomplemented
53C2×#532C2213yescomplemented
54C22×#127C2213yescomplemented
55C22×#124C2213yescomplemented
56C2×#525C2213yescomplemented
57C22×#121C2213yescomplemented
58C2×#520C2211yescharacteristic, complemented
59C2×C4×#41C2211yescharacteristic, complemented
60C2×C4×#41C2211yescharacteristic, complemented
61#2849C22112yescomplemented
62#2847C22112yescomplemented
63#2615C22112yescomplemented
64#2613C22112yescomplemented
65#2436C2216yescomplemented
66#2436C2213yescomplemented
67#2436C22112yescomplemented
68#2435C2213yescomplemented
69#2434C2213yescomplemented
70#2433C22112yescomplemented
71#2433C2213yescomplemented
72#2433C2216yescomplemented
73#2432C2216yescomplemented
74#2432C2213yescomplemented
75#2432C2211yescharacteristic, complemented
76#2431C2216yescomplemented
77#2431C2216yescomplemented
78#2431C2216yescomplemented
79#2431C22112yescomplemented
80#2431C22112yescomplemented
81#2431C2216yescomplemented
82#2431C22112yescomplemented
83#2431C22112yescomplemented
84#2431C2213yescomplemented
85#2431C2213yescomplemented
86#2430C22124yescomplemented
87#2430C22112yescomplemented
88#2410C22112yescomplemented
89#2410C22124yescomplemented
90#2409C22112yescomplemented
91#2408C22112yescomplemented
92#2407C22112yescomplemented
93#2407C22112yescomplemented
94#2407C22112yescomplemented
95#2407C22112yescomplemented
96#2404C22124yescomplemented
97#2404C22112yescomplemented
98#2403C22112yescomplemented
99#2403C22124yescomplemented
100#2388C22112yescomplemented
101C2×#392C22112yescomplemented
102#2341C2212yescomplemented
103#2341C2214yescomplemented
104Q8×C22⋊C4C2212yescomplemented
105Q8×C22⋊C4C2214yescomplemented
106#2339C2216yescomplemented
107#2339C22112yescomplemented
108D4×C22⋊C4C2216yescomplemented
109D4×C22⋊C4C22112yescomplemented
110#2311C2213yescomplemented
111#2311C2213yescomplemented
112#2310C2213yescomplemented
113#2309C2213yescomplemented
114C4×#120C22112yescomplemented
115#2297C2213yescomplemented
116#2297C2213yescomplemented
117#2297C2213yescomplemented
118#2297C2213yescomplemented
119C2×#391C2213yescomplemented
120C2×#390C2213yescomplemented
121C2×#386C22112yescomplemented
122#2280C2213yescomplemented
123C2×C4×C22⋊C4C2213yescomplemented
124#585—2512no—
125C2×2−1+4—28no—
126C2×2−1+4—28no—
127C2×2−1+4—224no—
128C2×2−1+4—224no—
129C2×2−1+4—216no—
130C2×2−1+4—224no—
131C2×2−1+4—216no—
132C2×2−1+4—216no—
133C2×2−1+4D4116yescomplemented
134C2×H(5,𝔽2)—28no—
135C2×H(5,𝔽2)—28no—
136C2×H(5,𝔽2)—28no—
137C2×H(5,𝔽2)—28no—
138C2×H(5,𝔽2)—28no—
139C2×H(5,𝔽2)—224no—
140C2×H(5,𝔽2)—224no—
141C2×H(5,𝔽2)—248no—
142C2×H(5,𝔽2)—224no—
143C2×H(5,𝔽2)—248no—
144C2×H(5,𝔽2)—248no—
145C2×H(5,𝔽2)D4116yescomplemented
146C22×#41—28no—
147C22×#41—28no—
148C22×#41—224no—
149C22×#41—224no—
150C22×#41—248no—
151C22×#41—216no—
152C22×#41—248no—
153C22×#41—216no—
154C22×#41—224no—
155C22×#41—216no—
156C22×#41—224no—
157C22×#41—248no—
158C22×#41—224no—
159C22×#41—224no—
160C22×#41D4116yescomplemented
161C22×#41C2316yes—
162C22×#41C2316yes—
163C22×#41C2313yes—
164C22×#41C2311yescharacteristic
165C22×#41C2316yes—
166C22×#41C23112yes—
167C22×#41C2316yes—
168C22×#41C2316yes—
169C22×#41C2316yes—
170C22×#41C2316yes—
171C22×#41C2313yes—
172C22×#41C2312yes—
173C22×#41C2313yes—
174C22×#41C2311yescharacteristic
175C22×#41C2313yes—
176C22×#41C2313yes—
177C22×#41C2313yes—
178C22×#41C2312yes—
179C22×#41C2316yes—
180C22×#41C2311yescharacteristic
181C23×Q8C2316yes—
182C23×Q8C2313yes—
183C23×Q8C2313yes—
184C23×Q8C2311yescharacteristic
185C23×Q8C2312yes—
186C23×D4C2316yes—
187C23×D4C23112yes—
188C23×D4C2316yes—
189C23×D4C2316yes—
190C23×D4C2313yes—
191C23×D4C2313yes—
192C23×D4C2316yes—
193C23×D4C2313yes—
194C23×D4C2313yes—
195C23×D4C2316yes—
196C23×D4C23112yes—
197C23×D4C2316yes—
198C24×C4C2316yes—
199C24×C4C2316yes—
200C24×C4C2313yes—
201#550—216no—
202#550—232no—
203#548—216no—
204#548—232no—
205#546—248no—
206#546—296no—
207D42—248no—
208D42—296no—
209#537—224no—
210#536—224no—
211#535—224no—
212#535—224no—
213#535—224no—
214#535—224no—
215#532—224no—
216#532—224no—
217C2×C4⋊Q8C2311yescharacteristic
218C2×C4⋊Q8C2313yes—
219C2×#127—224no—
220C2×#127C2313yes—
221C2×#127C2316yes—
222C2×#127C23112yes—
223C2×#127C2313yes—
224C2×#127C2316yes—
225C2×#124—224no—
226C2×#124C2313yes—
227C2×#124C2316yes—
228C2×#124C23112yes—
229C2×#124C2311yescharacteristic
230C2×#124C2313yes—
231C2×#124C2313yes—
232C2×#124C2316yes—
233#525—224no—
234C2×#123C2316yes—
235C2×#123C23112yes—
236C2×C22⋊Q8C23112yes—
237C2×C22⋊Q8C2316yes—
238C2×C22⋊Q8C2311yescharacteristic
239C2×C22⋊Q8C2313yes—
240C2×#121—224no—
241C2×#121C2316yes—
242C2×#121C23112yes—
243C2×#121C23112yes—
244C2×#121C2316yes—
245C2×#121C23112yes—
246C2×#121C2316yes—
247C2×#121C2313yes—
248C2×#121C2316yes—
249C2×#121C23112yes—
250C2×#121C23112yes—
251C2×#121C23112yes—
252C2×#121C2313yes—
253C2×#120C23112yes—
254C2×#120C2316yes—
255C2×#120C23112yes—
256C2×#120C23112yes—
257C2×#120C23112yes—
258C2×#120C23112yes—
259C2×#120C23124yes—
260#520—28no—
261C4×#41—28no—
262C4×#41—28no—
263C2×C4×Q8C2312yes—
264C2×C4×Q8C2312yes—
265C2×C4×Q8C2312yes—
266C2×C4×D4C2316yes—
267C2×C4×D4C2316yes—
268C2×C4×D4C2316yes—
269C2×C4×D4C2316yes—
270C2×C4×D4C23112yes—
271C2×C4×D4C23112yes—
272C2×C4×D4C2316yes—
273C2×#117C2313yes—
274C2×#117C2313yes—
275C2×#117C2313yes—
276C22×C4⋊C4C2313yes—
277C22×C22⋊C4C23112yes—
278C22×C22⋊C4C2316yes—
279C22×C22⋊C4C2316yes—
280C22×C22⋊C4C23112yes—
281C22×C42C2313yes—
282C22×C42C2313yes—
283#395C23112yes—
284#394C23112yes—
285#394C23124yes—
286#394C2314yes—
287#394C23112yes—
288#393C23124yes—
289#393C23112yes—
290#392C23124yes—
291#392C23124yes—
292#392C23112yes—
293#392C23124yes—
294#392C23112yes—
295#392C23124yes—
296#392C23124yes—
297#392C23112yes—
298#391C2313yes—
299#391C2316yes—
300#391C23112yes—
301#391C2313yes—
302#391C2316yes—
303#391C23112yes—
304#391C2316yes—
305#391C2313yes—
306#391C2311yescharacteristic
307#390C2313yes—
308#390C2316yes—
309#390C23112yes—
310#390C2313yes—
311#390C2316yes—
312#390C23112yes—
313#390C2316yes—
314#390C2313yes—
315#390C2311yescharacteristic
316#386C23112yes—
317#386C23112yes—
318#386C23112yes—
319#386C23124yes—
320#386C23124yes—
321#386C23124yes—
322#386C23112yes—
323#386C23112yes—
324#386C23112yes—
325#386C23112yes—
326#386C23124yes—
327#386C23112yes—
328#386C23124yes—
329#386C23112yes—
330#385C23112yes—
331#385C23124yes—
332#385C23112yes—
333#385C2314yes—
334#381C23112yes—
335#381C2316yes—
336#380C23112yes—
337#380C23112yes—
338#380C2316yes—
339#380C2316yes—
340#379C23112yes—
341#379C2316yes—
342#379C23112yes—
343C4×C22⋊C4C2316yes—
344C4×C22⋊C4C23112yes—
345C4×C22⋊C4C23112yes—
346C4×C22⋊C4C2316yes—
347C4×C22⋊C4C2311yescharacteristic
348C4×C22⋊C4C2313yes—
349C4×C22⋊C4C2313yes—
350C4×C22⋊C4C2313yes—
351C4×C22⋊C4C2316yes—
352C2×#95C23112yes—
353C2×#95C2316yes—
354C25C2416yes—
355C25C2416yes—
356C25C2413yes—
357C25C2416yes—
3582−1+4—2384no—
3592−1+4—2256no—
3602−1+4—2128no—
361H(5,𝔽2)—2384no—
362H(5,𝔽2)—2768no—
363H(5,𝔽2)—2128no—
364H(5,𝔽2)—464no—
365C2×#41—2256no—
366C2×#41—2768no—
367C2×#41—2384no—
368C2×#41—2384no—
369C2×#41—2128no—
370C2×#41—224no—
371C2×#41—24no—
372C2×#41—212no—
373C2×#41—24no—
374C2×#41—24no—
375C2×#41—224no—
376C2×#41—224no—
377C2×#41—224no—
378C2×#41—224no—
379C2×#41—28no—
380C2×#41—28no—
381C2×#41—28no—
382C2×#41—28no—
383C2×#41—28no—
384C2×#41—224no—
385C2×#41—224no—
386C2×#41—224no—
387C2×#41—24no—
388C2×#41—212no—
389C2×#41—212no—
390C2×#41—212no—
391C2×#41—248no—
392C2×#41—248no—
393C2×#41—224no—
394C2×#41—224no—
395C2×#41—224no—
396C2×#41—224no—
397C2×#41—224no—
398C2×#41—224no—
399C2×#41—224no—
400C2×#41—224no—
401C2×#41—212no—
402C2×#41—24no—
403C2×#41—248no—
404C2×#41—224no—
405C2×#41—224no—
406C2×#41—224no—
407C2×#41—224no—
408C2×#41—224no—
409C2×#41—224no—
410C2×#41—224no—
411C2×#41—212no—
412C2×#41—212no—
413C2×#41—212no—
414C2×#41—212no—
415C2×#41—212no—
416C2×#41—212no—
417C2×#41—212no—
418C2×#41—212no—
419C2×#41—212no—
420C2×#41C2×D418yes—
421C2×#41C2×D418yes—
422C2×#41C2×D418yes—
423C2×#41C2×D4124yescomplemented
424C2×#41C2×D4124yescomplemented
425C2×#41C2×D4124yescomplemented
426C2×#41C2×D4124yescomplemented
427C2×#41C2×D4148yescomplemented
428C2×#41C2×D418yescomplemented
429C2×#41C2×D4116yescomplemented
430C22×Q8—224no—
431C22×Q8—224no—
432C22×Q8—212no—
433C22×Q8—212no—
434C22×Q8—24no—
435C22×Q8—28no—
436C22×Q8—28no—
437C22×Q8—24no—
438C22×Q8—224no—
439C22×Q8—212no—
440C22×Q8—212no—
441C22×Q8—212no—
442C22×Q8C2×D4124yescomplemented
443C22×Q8C2×D4116yescomplemented
444C22×Q8C2×D418yescomplemented
445C22×Q8C2411yescharacteristic
446C22×Q8C2416yes—
447C22×Q8C2413yes—
448C22×Q8C2416yes—
449C22×Q8C2411yescharacteristic
450C22×Q8C2413yes—
451C22×Q8C2411yescharacteristic
452C22×D4—224no—
453C22×D4—248no—
454C22×D4—224no—
455C22×D4—224no—
456C22×D4—248no—
457C22×D4—224no—
458C22×D4—248no—
459C22×D4—224no—
460C22×D4—224no—
461C22×D4—224no—
462C22×D4—212no—
463C22×D4—212no—
464C22×D4—212no—
465C22×D4—224no—
466C22×D4—224no—
467C22×D4—212no—
468C22×D4—224no—
469C22×D4—248no—
470C22×D4—224no—
471C22×D4—224no—
472C22×D4—224no—
473C22×D4—224no—
474C22×D4—224no—
475C22×D4—212no—
476C22×D4—212no—
477C22×D4—212no—
478C22×D4—212no—
479C22×D4—212no—
480C22×D4—212no—
481C22×D4—424no—
482C22×D4—812no—
483C22×D4—812no—
484C22×D4C2×D4124yescomplemented
485C22×D4C2×D4148yescomplemented
486C22×D4C2×D4124yescomplemented
487C22×D4C2416yes—
488C22×D4C2416yes—
489C22×D4C2413yes—
490C22×D4C2416yes—
491C22×D4C24112yes—
492C22×D4C2412yes—
493C22×D4C2416yes—
494C22×D4C24112yes—
495C22×D4C2416yes—
496C22×D4C2416yes—
497C22×D4C2416yes—
498C22×D4C2413yes—
499C22×D4C2416yes—
500C22×D4C2411yescharacteristic
501C22×D4C2413yes—
502C22×D4C24112yes—
503C22×D4C2416yes—
504C22×D4C2416yes—
505C22×D4C24112yes—
506C22×D4C24124yes—
507C22×D4C2413yes—
508C23×C4—224no—
509C23×C4—224no—
510C23×C4—224no—
511C23×C4—224no—
512C23×C4—224no—
513C23×C4—224no—
514C23×C4—212no—
515C23×C4—212no—
516C23×C4C2×D4124yescomplemented
517C23×C4C2416yes—
518C23×C4C2412yes—
519C23×C4C2416yes—
520C23×C4C2416yes—
521C23×C4C24112yes—
522C23×C4C2416yes—
523C23×C4C2413yes—
524C23×C4C2416yes—
525C23×C4C2413yes—
526C23×C4C2416yes—
527C23×C4C2416yes—
528C23×C4C2413yes—
529C23×C4C2411yescharacteristic
530C23×C4C2413yes—
531C23×C4C2416yes—
532C23×C4C2416yes—
533C23×C4C2413yes—
534C4⋊Q8—24no—
535C4⋊Q8—212no—
536#127—212no—
537#127—224no—
538#127—248no—
539#127—212no—
540#127—224no—
541#124—212no—
542#124—224no—
543#124—248no—
544#124—212no—
545#124—224no—
546#124—24no—
547#124—212no—
548#123—224no—
549#123—248no—
550C22⋊Q8—248no—
551C22⋊Q8—224no—
552C22⋊Q8—24no—
553C22⋊Q8—212no—
554#121—248no—
555#121—248no—
556#121—248no—
557#121—248no—
558#121—224no—
559#121—212no—
560#121—224no—
561#121—224no—
562#121—224no—
563#121—212no—
564#121—248no—
565#121—248no—
566#120—224no—
567#120—248no—
568#120—248no—
569#120—248no—
570#120—248no—
571#120—424no—
572#120—824no—
573C4×Q8—28no—
574C4×Q8—28no—
575C4×Q8—28no—
576C4×D4—224no—
577C4×D4—224no—
578C4×D4—224no—
579C4×D4—224no—
580C4×D4—224no—
581C4×D4—248no—
582C4×D4—248no—
583#117—212no—
584#117—212no—
585#117—212no—
586C2×C4⋊C4—212no—
587C2×C4⋊C4C2413yes—
588C2×C4⋊C4C2416yes—
589C2×C4⋊C4C2411yescharacteristic
590C2×C4⋊C4C2416yes—
591C2×C4⋊C4C2416yes—
592C2×C4⋊C4C2414yes—
593C2×C4⋊C4C2412yes—
594C2×C4⋊C4C2416yes—
595C2×C4⋊C4C24112yes—
596C2×C22⋊C4—224no—
597C2×C22⋊C4—248no—
598C2×C22⋊C4—412no—
599C2×C22⋊C4—812no—
600C2×C22⋊C4C2412yes—
601C2×C22⋊C4C2416yes—
602C2×C22⋊C4C24112yes—
603C2×C22⋊C4C2416yes—
604C2×C22⋊C4C24112yes—
605C2×C22⋊C4C24124yes—
606C2×C22⋊C4C2416yes—
607C2×C22⋊C4C2416yes—
608C2×C22⋊C4C2416yes—
609C2×C22⋊C4C2412yes—
610C2×C22⋊C4C2414yes—
611C2×C22⋊C4C24112yes—
612C2×C22⋊C4C24112yes—
613C2×C22⋊C4C2416yes—
614C2×C22⋊C4C2416yes—
615C2×C22⋊C4C2414yes—
616C2×C22⋊C4C24112yes—
617C2×C22⋊C4C24124yes—
618C2×C22⋊C4C2416yes—
619C2×C22⋊C4C2416yes—
620C2×C22⋊C4C24112yes—
621C2×C22⋊C4C24112yes—
622C2×C22⋊C4C24112yes—
623C2×C42—212no—
624C2×C42—212no—
625C2×C42C2413yes—
626C2×C42C2413yes—
627C2×C42C2416yes—
628C2×C42C2416yes—
629C2×C42C2416yes—
630C2×C42C2411yescharacteristic
631C2×C42C2411yescharacteristic
632#95C2412yes—
633#95C24112yes—
634#95C2416yes—
635#95C2416yes—
636#95C2416yes—
637#95C24124yes—
638#95C2414yes—
639#95C24112yes—
640#95C24112yes—
641#95C24112yes—
642C24—212no—
643C24—212no—
644C24—212no—
645C24—26no—
646C24—212no—
647C24—212no—
648C24—26no—
649C24—212no—
650C24—212no—
651C24—212no—
652C24—46no—
653C24—412no—
654C24—412no—
655C24—46no—
656C24—412no—
657C24—412no—
658C24—412no—
659C24—412no—
660C24C22×D4124yes—
661C24C22×D4112yes—
662C24C2516yes—
663C24C2511yescharacteristic
664C24C2513yes—
665C24C2512yes—
666C24C2516yes—
667C24C2513yes—
668#41—2192no—
669#41—2192no—
670#41—232no—
671#41—296no—
672#41—2384no—
673#41—2192no—
674#41—2192no—
675#41—2192no—
676#41—2192no—
677#41—2192no—
678#41—232no—
679#41—264no—
680#41—296no—
681#41—2192no—
682#41—296no—
683#41—296no—
684#41—296no—
685#41—432no—
686#41—448no—
687#41#120164yescomplemented
688C2×Q8—2192no—
689C2×Q8—296no—
690C2×Q8—264no—
691C2×Q8—232no—
692C2×Q8—296no—
693C2×Q8—212no—
694C2×Q8—212no—
695C2×Q8—212no—
696C2×Q8—22no—
697C2×Q8—26no—
698C2×Q8—26no—
699C2×Q8—212no—
700C2×Q8—26no—
701C2×Q8—212no—
702C2×Q8—22no—
703C2×Q8—26no—
704C2×Q8—22no—
705C2×Q8—22no—
706C2×Q8—22no—
707C2×Q8C22×D4112yes—
708C2×Q8C22×D4124yes—
709C2×Q8C22×D414yes—
710C2×Q8C22×D4112yes—
711C2×Q8C22×D414yes—
712C2×Q8C22×D414yes—
713C2×Q8C22×D414yes—
714C2×D4—2384no—
715C2×D4—2192no—
716C2×D4—2192no—
717C2×D4—2192no—
718C2×D4—296no—
719C2×D4—212no—
720C2×D4—224no—
721C2×D4—212no—
722C2×D4—224no—
723C2×D4—24no—
724C2×D4—212no—
725C2×D4—212no—
726C2×D4—24no—
727C2×D4—212no—
728C2×D4—212no—
729C2×D4—212no—
730C2×D4—212no—
731C2×D4—212no—
732C2×D4—212no—
733C2×D4—2192no—
734C2×D4—296no—
735C2×D4—212no—
736C2×D4—224no—
737C2×D4—212no—
738C2×D4—212no—
739C2×D4—212no—
740C2×D4—212no—
741C2×D4—224no—
742C2×D4—248no—
743C2×D4—224no—
744C2×D4—296no—
745C2×D4—212no—
746C2×D4—224no—
747C2×D4—212no—
748C2×D4—24no—
749C2×D4—26no—
750C2×D4—22no—
751C2×D4—26no—
752C2×D4—212no—
753C2×D4—212no—
754C2×D4—26no—
755C2×D4—22no—
756C2×D4—26no—
757C2×D4—26no—
758C2×D4—212no—
759C2×D4—212no—
760C2×D4—212no—
761C2×D4—26no—
762C2×D4—26no—
763C2×D4—224no—
764C2×D4—412no—
765C2×D4—412no—
766C2×D4—412no—
767C2×D4—412no—
768C2×D4—412no—
769C2×D4—424no—
770C2×D4—424no—
771C2×D4—424no—
772C2×D4—496no—
773C2×D4—448no—
774C2×D4—896no—
775C2×D4—848no—
776C2×D4C22×D4124yes—
777C2×D4C22×D4124yes—
778C2×D4C22×D4124yes—
779C2×D4C22×D4112yes—
780C2×D4C22×D4124yes—
781C2×D4C22×D414yes—
782C2×D4C22×D4112yes—
783C2×D4C22×D4112yes—
784C2×D4C22×D4112yes—
785C2×D4C22×D4112yes—
786C22×C4—2192no—
787C22×C4—2192no—
788C22×C4—212no—
789C22×C4—24no—
790C22×C4—26no—
791C22×C4—26no—
792C22×C4—224no—
793C22×C4—212no—
794C22×C4—212no—
795C22×C4—212no—
796C22×C4—296no—
797C22×C4—212no—
798C22×C4—24no—
799C22×C4—212no—
800C22×C4—24no—
801C22×C4—22no—
802C22×C4—22no—
803C22×C4—26no—
804C22×C4—26no—
805C22×C4—224no—
806C22×C4—212no—
807C22×C4—224no—
808C22×C4—212no—
809C22×C4—26no—
810C22×C4—26no—
811C22×C4—212no—
812C22×C4—26no—
813C22×C4—212no—
814C22×C4—212no—
815C22×C4—212no—
816C22×C4—26no—
817C22×C4—212no—
818C22×C4—212no—
819C22×C4—212no—
820C22×C4—212no—
821C22×C4—212no—
822C22×C4—212no—
823C22×C4—212no—
824C22×C4—46no—
825C22×C4—46no—
826C22×C4—46no—
827C22×C4—412no—
828C22×C4C22×D4112yes—
829C22×C4C22×D4124yes—
830C22×C4C22×D4112yes—
831C22×C4C22×D4124yes—
832C22×C4C22×D4124yes—
833C22×C4C22×D4112yes—
834C22×C4C22×D414yes—
835C22×C4C22×D4112yes—
836C22×C4C22×D4112yes—
837C22×C4C22×D4112yes—
838C22×C4C22×D4112yes—
839C22×C4C2516yes—
840C22×C4C2512yes—
841C22×C4C2516yes—
842C22×C4C2512yes—
843C22×C4C2516yes—
844C22×C4C2512yes—
845C22×C4C2511yescharacteristic
846C22×C4C2516yes—
847C22×C4C2513yes—
848C22×C4C2512yes—
849C22×C4C2512yes—
850C22×C4C2511yescharacteristic
851C22×C4C2513yes—
852C4⋊C4—26no—
853C4⋊C4—212no—
854C4⋊C4—22no—
855C4⋊C4—212no—
856C4⋊C4—212no—
857C4⋊C4—28no—
858C4⋊C4—24no—
859C4⋊C4—212no—
860C4⋊C4—224no—
861C22⋊C4—212no—
862C22⋊C4—212no—
863C22⋊C4—212no—
864C22⋊C4—24no—
865C22⋊C4—28no—
866C22⋊C4—224no—
867C22⋊C4—212no—
868C22⋊C4—212no—
869C22⋊C4—224no—
870C22⋊C4—224no—
871C22⋊C4—248no—
872C22⋊C4—224no—
873C22⋊C4—212no—
874C22⋊C4—24no—
875C22⋊C4—212no—
876C22⋊C4—28no—
877C22⋊C4—46no—
878C22⋊C4—46no—
879C22⋊C4—412no—
880C22⋊C4—424no—
881C22⋊C4—412no—
882C22⋊C4—412no—
883C22⋊C4—412no—
884C42—22no—
885C42—22no—
886C42—26no—
887C42—26no—
888C42—212no—
889C42—212no—
890C42—212no—
891C23—26no—
892C23—26no—
893C23—248no—
894C23—22no—
895C23—23no—
896C23—21no—
897C23—26no—
898C23—23no—
899C23—21no—
900C23—26no—
901C23—22no—
902C23—22no—
903C23—26no—
904C23—24no—
905C23—212no—
906C23—212no—
907C23—24no—
908C23—26no—
909C23—22no—
910C23—248no—
911C23—224no—
912C23—26no—
913C23—26no—
914C23—26no—
915C23—212no—
916C23—212no—
917C23—412no—
918C23—448no—
919C23—412no—
920C23—424no—
921C23—812no—
922C23—812no—
923C23—824no—
924C23—812no—
925C23—812no—
926C23—824no—
927C23—824no—
928C23—812no—
929C23—812no—
930C23—824no—
931C23—812no—
932C23—824no—
933C23—812no—
934C23C23×D4112yes—
935C23C23×D416yes—
936C23C23×D414yes—
937C23C23×D412yes—
938C23C23×D416yes—
939C23C23×D416yes—
940C23C23×D416yes—
941C23C2611yescharacteristic
942Q8—248no—
943Q8—224no—
944Q8—248no—
945Q8—28no—
946Q8—224no—
947Q8—44no—
948Q8C2×#120116yes—
949D4—296no—
950D4—248no—
951D4—216no—
952D4—248no—
953D4—248no—
954D4—248no—
955D4—248no—
956D4—224no—
957D4—248no—
958D4—28no—
959D4—224no—
960D4—448no—
961D4—424no—
962D4—424no—
963D4—424no—
964D4—412no—
965D4—824no—
966D4—812no—
967D4—848no—
968D4—824no—
969D4C2×#120148yes—
970C2×C4—248no—
971C2×C4—216no—
972C2×C4—248no—
973C2×C4—296no—
974C2×C4—22no—
975C2×C4—21no—
976C2×C4—21no—
977C2×C4—26no—
978C2×C4—23no—
979C2×C4—22no—
980C2×C4—23no—
981C2×C4—26no—
982C2×C4—22no—
983C2×C4—22no—
984C2×C4—224no—
985C2×C4—248no—
986C2×C4—224no—
987C2×C4—28no—
988C2×C4—248no—
989C2×C4—248no—
990C2×C4—224no—
991C2×C4—224no—
992C2×C4—22no—
993C2×C4—22no—
994C2×C4—26no—
995C2×C4—26no—
996C2×C4—26no—
997C2×C4—22no—
998C2×C4—22no—
999C2×C4—22no—
1000C2×C4—22no—
1001C2×C4—26no—
1002C2×C4—24no—
1003C2×C4—26no—
1004C2×C4—22no—
1005C2×C4—26no—
1006C2×C4—212no—
1007C2×C4—26no—
1008C2×C4—424no—
1009C2×C4—424no—
1010C2×C4—812no—
1011C2×C4—812no—
1012C2×C4C2×#120148yes—
1013C2×C4C23×D412yes—
1014C2×C4C23×D4112yes—
1015C2×C4C23×D416yes—
1016C2×C4C23×D414yes—
1017C2×C4C23×D412yes—
1018C2×C4C23×D412yes—
1019C2×C4C23×D416yes—
1020C2×C4C23×D416yes—
1021C2×C4C23×D416yes—
1022C2×C4C23×D412yes—
1023C2×C4#58514yescomplemented
1024C22—212no—
1025C22—212no—
1026C22—26no—
1027C22—26no—
1028C22—224no—
1029C22—28no—
1030C22—26no—
1031C22—22no—
1032C22—22no—
1033C22—26no—
1034C22—212no—
1035C22—24no—
1036C22—26no—
1037C22—22no—
1038C22—42no—
1039C22—46no—
1040C22—44no—
1041C22—42no—
1042C22—46no—
1043C22—412no—
1044C22—42no—
1045C22—46no—
1046C22—46no—
1047C22—42no—
1048C22—412no—
1049C22—412no—
1050C22—46no—
1051C22—46no—
1052C22—46no—
1053C22—824no—
1054C22—848no—
1055C22—848no—
1056C22—1624no—
1057C22C22×#120112yes—
1058C22C24×D411yescharacteristic
1059C22C24×D411yescharacteristic
1060C22C24×D411yescharacteristic
1061C22C2×#58512yes—
1062C22H(7,𝔽2)12yes—
1063C4—24no—
1064C4—22no—
1065C4—212no—
1066C4—24no—
1067C4—26no—
1068C4—46no—
1069C4—42no—
1070C4—46no—
1071C4—42no—
1072C4—46no—
1073C4—42no—
1074C4C22×#120112yes—
1075C4C22×#12014yes—
1076C2—212no—
1077C2—412no—
1078C2—44no—
1079C2—46no—
1080C2—42no—
1081C2—86no—
1082C2C23×#12011yescharacteristic
1083C2#6281211yescharacteristic
1084C2#6285211yescharacteristic
1085C2#6298712yes—
1086C2#6300312yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C22×#585C2semidirect
2. C2×#3500C2semidirect
3. C2×#3498C2semidirect
4. C2×#3488C2semidirect
5. #36429C2semidirect
6. #36212C2semidirect
7. #35757C2semidirect
8. #35680C2semidirect
9. #35676C2semidirect
10. #35660C2semidirect
11. #35527C2semidirect
12. #35513C2semidirect
13. #35250C2semidirect
14. #35149C2semidirect
15. #34738C2semidirect
16. C2×#2431C2semidirect
17. #34259C2semidirect
18. #34258C2semidirect
19. C22⋊C4×#41C2semidirect
24. C22×2−1+4C22semidirect
25. C22×2−1+4C22semidirect
27. C22×H(5,𝔽2)C22semidirect
28. C22×H(5,𝔽2)C22semidirect
29. C22×H(5,𝔽2)C22semidirect
31. C23×#41C22semidirect
32. C23×#41C22semidirect
33. C23×#41C22semidirect
34. C23×#41C22semidirect
38. C2×#550C22semidirect
39. C2×#550C22semidirect
40. C2×#548C22semidirect
41. C2×#548C22semidirect
42. C2×#546C22semidirect
43. C2×#546C22semidirect
44. C2×D42C22semidirect
45. C2×D42C22semidirect
46. C2×#537C22semidirect
47. C2×#536C22semidirect
48. C2×#535C22semidirect
49. C2×#535C22semidirect
50. C2×#535C22semidirect
51. C2×#535C22semidirect
52. C2×#532C22semidirect
53. C2×#532C22semidirect
54. C22×#127C22semidirect
55. C22×#124C22semidirect
56. C2×#525C22semidirect
57. C22×#121C22semidirect
58. C2×#520C22semidirect
59. C2×C4×#41C22semidirect
60. C2×C4×#41C22semidirect
61. #2849C22semidirect
62. #2847C22semidirect
63. #2615C22semidirect
64. #2613C22semidirect
65. #2436C22semidirect
66. #2436C22semidirect
67. #2436C22semidirect
68. #2435C22semidirect
69. #2434C22semidirect
70. #2433C22semidirect
71. #2433C22semidirect
72. #2433C22semidirect
73. #2432C22semidirect
74. #2432C22semidirect
75. #2432C22semidirect
76. #2431C22semidirect
77. #2431C22semidirect
78. #2431C22semidirect
79. #2431C22semidirect
80. #2431C22semidirect
81. #2431C22semidirect
82. #2431C22semidirect
83. #2431C22semidirect
84. #2431C22semidirect
85. #2431C22semidirect
86. #2430C22semidirect
87. #2430C22semidirect
88. #2410C22semidirect
89. #2410C22semidirect
90. #2409C22semidirect
91. #2408C22semidirect
92. #2407C22semidirect
93. #2407C22semidirect
94. #2407C22semidirect
95. #2407C22semidirect
96. #2404C22semidirect
97. #2404C22semidirect
98. #2403C22semidirect
99. #2403C22semidirect
100. #2388C22semidirect
101. C2×#392C22semidirect
102. #2341C22semidirect
103. #2341C22semidirect
104. Q8×C22⋊C4C22semidirect
105. Q8×C22⋊C4C22semidirect
106. #2339C22semidirect
107. #2339C22semidirect
108. D4×C22⋊C4C22semidirect
109. D4×C22⋊C4C22semidirect
110. #2311C22semidirect
111. #2311C22semidirect
112. #2310C22semidirect
113. #2309C22semidirect
114. C4×#120C22semidirect
115. #2297C22semidirect
116. #2297C22semidirect
117. #2297C22semidirect
118. #2297C22semidirect
119. C2×#391C22semidirect
120. C2×#390C22semidirect
121. C2×#386C22semidirect
122. #2280C22semidirect
123. C2×C4×C22⋊C4C22semidirect
133. C2×2−1+4D4semidirect
145. C2×H(5,𝔽2)D4semidirect
160. C22×#41D4semidirect
423. C2×#41C2×D4semidirect
424. C2×#41C2×D4semidirect
425. C2×#41C2×D4semidirect
426. C2×#41C2×D4semidirect
427. C2×#41C2×D4semidirect
428. C2×#41C2×D4semidirect
429. C2×#41C2×D4semidirect
442. C22×Q8C2×D4semidirect
443. C22×Q8C2×D4semidirect
444. C22×Q8C2×D4semidirect
484. C22×D4C2×D4semidirect
485. C22×D4C2×D4semidirect
486. C22×D4C2×D4semidirect
516. C23×C4C2×D4semidirect
687. #41#120semidirect
1023. C2×C4#585semidirect

Maximal subgroups

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

subgroupindex
C22×#5852
C2×#35002
C2×#34982
C2×#34882
#364292
#362122
#357572
#356802
#356762
#356602
#355272
#355132
#352502
#351492
#347382
C2×#24312
#342592
#342582
C22⋊C4×#412