Finite Group Databasebeta

← #11661580

Subgroups — #11661580

Order 768.

5098 conjugacy classes of subgroups.

The subgroup lattice has 1026 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×#239C211yesmaximal, characteristic, complemented
2C2×#5777C212yesmaximal, complemented
3D3×#525C211yesmaximal, characteristic, complemented
4C3×#3004C211yesmaximal, characteristic, complemented
5#84059C211yesmaximal, characteristic, complemented
6#83980C212yesmaximal, complemented
7#82927C211yesmaximal, characteristic, complemented
8#80184C214yesmaximal, complemented
9#80182C214yesmaximal, complemented
10#80040C214yesmaximal, complemented
11#80038C214yesmaximal, complemented
12#78959C212yesmaximal, complemented
13#78956C212yesmaximal, complemented
14#78637C211yesmaximal, characteristic, complemented
15D3×#407C211yesmaximal, characteristic, complemented
16#60359—31nomaximal, Sylow
17C23×C3×Q8C2211yescharacteristic, complemented
18C2×D3×#41C2211yescharacteristic, complemented
19C22×#239—216no—
20C22×#239—21no—
21C22×#239—22no—
22C22×#239—21no—
23C22×#239—22no—
24C22×#239C2214yes—
25C22×#239C2212yes—
26C22×#239C2212yescomplemented
27C22×#239C2214yescomplemented
28C23×D12—21no—
29C23×D12C2211yescharacteristic, complemented
30C23×C4×D3—21no—
31C23×C4×D3C2211yescharacteristic
32C2×C3×#137C2212yescomplemented
33C3×#525C2211yescharacteristic
34#5828C2211yescharacteristic, complemented
35C2×#949C2212yescomplemented
36C2×#942C2212yescomplemented
37#5791C2211yescharacteristic
38#5777—216no—
39C2×#919C2214yescomplemented
40C2×#918C2214yescomplemented
41C2×#916C2214yescomplemented
42C2×#914C2214yescomplemented
43C2×#908C2212yescomplemented
44C2×D3×M16C2212yescomplemented
45#5656—21no—
46D3×#123—21no—
47#5627C2212yescomplemented
48D3×C22⋊Q8C2212yescomplemented
49#5606C2212yescomplemented
50D3×#121C2212yescomplemented
51D3×#120—21no—
52#5586—21no—
53#5547—22no—
54C4×D3×D4—22no—
55#5524C2211yescharacteristic, complemented
56D3×#117C2211yescharacteristic, complemented
57C3×#451C2214yescomplemented
58C3×#448C2214yescomplemented
59C3×#419C2212yescomplemented
60C3×#407C2211yescharacteristic, complemented
61#5228C2214yescomplemented
62#5227C2214yescomplemented
63#5225C2212yescomplemented
64#5207C2211yescharacteristic, complemented
65#5187C2218yescomplemented
66#5172C2218yescomplemented
67#5131C2212yescomplemented
68#5126C2212yescomplemented
69#5046C2214yescomplemented
70#5036C2214yescomplemented
71#5001C2212yescomplemented
72#4810C2218yescomplemented
73#4808C2218yescomplemented
74#4804C2218yescomplemented
75#4803C2218yescomplemented
76#4732C2214yescomplemented
77#4731C2214yescomplemented
78#4726C2214yescomplemented
79D3×C22⋊C8C2214yescomplemented
80C23×#41—31no—
81C2×#575—32no—
82C2×#525—31no—
83#3007—34no—
84#3006—34no—
85#3005—32no—
86#3005—32no—
87#3004—31no—
88#3004D311yescharacteristic, complemented
89#3003—31no—
90#3003—31no—
91#3002—34no—
92#3002—34no—
93#2896—32no—
94C2×#407—31no—
95C24×D3—21no—
96C24×D3D411yescharacteristic
97C2×C3×#41C2311yescharacteristic
98C22×C3×Q8—28no—
99C22×C3×Q8—22no—
100C22×C3×Q8—21no—
101C22×C3×Q8C2314yes—
102C22×C3×Q8C2312yes—
103C23×C3×C4—21no—
104C23×C3×C4C2311yescharacteristic
105C23×Dic3D411yescharacteristic
106D3×#41—28no—
107C2×#239—216no—
108C2×#239—232no—
109C2×#239—232no—
110C2×#239—216no—
111C2×#239—28no—
112C2×#239—232no—
113C2×#239—232no—
114C2×#239—28no—
115C2×#239—28no—
116C2×#239—24no—
117C2×#239—24no—
118C2×#239—22no—
119C2×#239—22no—
120C2×#239—24no—
121C2×#239—24no—
122C2×#239—24no—
123C2×#239D4116yescomplemented
124C2×#239C2318yes—
125C2×#239C2314yes—
126C2×#239C2314yes—
127C2×#239C2311yescharacteristic, complemented
128C2×D3×Q8C2311yescharacteristic, complemented
129C2×#237—21no—
130C2×#237C2311yescharacteristic, complemented
131C2×D3×D4—21no—
132C2×D3×D4—22no—
133C2×D3×D4C2311yescharacteristic, complemented
134C2×#235—21no—
135C2×#235C2311yescharacteristic
136C22×D12—216no—
137C22×D12—24no—
138C22×D12—22no—
139C22×D12—24no—
140C22×D12—22no—
141C22×D12—22no—
142C22×D12—21no—
143C22×D12—28no—
144C22×D12C2314yes—
145C22×D12C2312yes—
146C22×C4×D3—216no—
147C22×C4×D3—24no—
148C22×C4×D3—22no—
149C22×C4×D3—24no—
150C22×C4×D3—22no—
151C22×C4×D3—28no—
152C22×C4×D3—21no—
153C22×C4×D3D411yescharacteristic
154C22×C4×D3D411yescharacteristic
155C22×C4×D3D412yes—
156C22×C4×D3D412yes—
157C22×C4×D3C2311yescharacteristic
158C22×C4×D3C2312yes—
159C22×C4×D3C2312yes—
160C22×C4×D3C2311yescharacteristic
161C3×#137—28no—
162C2×C3×Q16C2314yescomplemented
163C2×C3×SD16C2314yescomplemented
164C2×C3×M16C2312yes—
165C3×#123—21no—
166C3×C22⋊Q8C2312yes—
167C3×#121C2312yes—
168C3×#120—21no—
169C3×C4×D4—22no—
170C3×#117C2311yescharacteristic
171#953—21no—
172#949—28no—
173#946C2312yescomplemented
174C2×#216C2314yescomplemented
175#942—28no—
176C2×#215C2314yescomplemented
177C2×#215C2314yescomplemented
178#939—22no—
179#938C2312yescomplemented
180#937—21no—
181#937—22no—
182#935—21no—
183D4×Dic3—22no—
184C2×#213C2314yescomplemented
185#930C2312yes—
186#929—21no—
187C4×#67—22no—
188C4×#67—22no—
189#926C2311yescharacteristic
190#924C2312yes—
191C2×#208C2312yes—
192#919—216no—
193#918—216no—
194#916—216no—
195#914—216no—
196#908—28no—
197D3×M16—28no—
198C2×D24C2314yescomplemented
199C2×#204C2314yescomplemented
200C2×ΓL(1,𝔽25)C2314yescomplemented
201C2×D3×C8C2314yescomplemented
202#897C2312yescomplemented
203#896—22no—
204#895C2312yescomplemented
205#894—22no—
206#893—22no—
207#892C2312yescomplemented
208D3×C4⋊C4—22no—
209D3×C4⋊C4C2312yescomplemented
210#886—21no—
211#884—22no—
212#883—22no—
213#882—21no—
214#882—22no—
215#67⋊C4—22no—
216#67⋊C4—22no—
217D3×C22⋊C4—21no—
218D3×C22⋊C4—22no—
219D3×C22⋊C4—22no—
220#878—22no—
221#877—21no—
222C4×D12—22no—
223#872—21no—
224C42×D3—21no—
225C3×#103C2318yescomplemented
226C3×C22⋊C8C2314yes—
227#835C2318yescomplemented
228#830C2314yes—
229#821C2318yescomplemented
230(C2×D3)⋊C8C2318yescomplemented
231#809C2318yescomplemented
232C22×#41—31no—
233C22×#41—32no—
234C22×#41—34no—
235C22×#41—34no—
236C22×#41—32no—
237C22×#41—62no—
238C22×#41—61no—
239C22×#41—61no—
240C22×#41—62no—
241C22×#41—616no—
242C23×Q8C2×D311yescharacteristic, complemented
243C23×D4—31no—
244C23×D4—61no—
245C24×C4—31no—
246C24×C4—61no—
247#575—616no—
248C2×#137—32no—
249C2×#137—34no—
250C2×#137C2×D312yescomplemented
251C2×AGL(1,ℤ/8)—32no—
252C2×AGL(1,ℤ/8)—34no—
253C2×AGL(1,ℤ/8)—32no—
254C2×#135—34no—
255C2×#135—34no—
256C22×M16—32no—
257#525—31no—
258#525—31no—
259#525—32no—
260#525—32no—
261#525—31no—
262#525—62no—
263#525—61no—
264#525—61no—
265#525C2×D311yescharacteristic
266C2×#123—61no—
267C2×C22⋊Q8—32no—
268C2×#121—32no—
269C2×#120—61no—
270C2×C4×D4—62no—
271C2×#117—31no—
272#452—38no—
273#452—38no—
274#451—34no—
275#451C2×D314yescomplemented
276#450—34no—
277#450—34no—
278#449—38no—
279#449—38no—
280#448—34no—
281#448C2×D314yescomplemented
282#447—34no—
283#447—34no—
284#419—32no—
285#419C2×D312yescomplemented
286#418—32no—
287#418—32no—
288#417—38no—
289#416—38no—
290#407—31no—
291#407—32no—
292#407—34no—
293#407C2×D311yescharacteristic, complemented
294C2×C22⋊C8—34no—
295C24×C3C2×D411yescharacteristic
296C23×D3—28no—
297C23×D3—24no—
298C23×D3—22no—
299C23×D3—24no—
300C23×D3—21no—
301C23×D3—44no—
302C23×D3—48no—
303C23×D3C2×D412yes—
304C23×D3C2×D412yes—
305C23×D3C2×D411yescharacteristic
306C23×D3C2×D411yescharacteristic
307C3×#41—24no—
308C2×C3×Q8—216no—
309C2×C3×Q8—28no—
310C2×C3×Q8—216no—
311C2×C3×Q8—24no—
312C2×C3×Q8—24no—
313C2×C3×Q8—22no—
314C2×C3×Q8C2×D418yescomplemented
315C2×C3×Q8C2411yescharacteristic
316C2×C3×Q8C2414yes—
317C2×C3×D4—22no—
318C2×C3×D4—21no—
319C2×C3×D4C2411yescharacteristic
320C22×C3×C4—28no—
321C22×C3×C4—24no—
322C22×C3×C4—22no—
323C22×C3×C4—24no—
324C22×C3×C4—21no—
325C22×C3×C4C2×D412yes—
326C22×C3×C4C2×D411yescharacteristic
327C22×C3×C4C2412yes—
328C22×C3×C4C2411yescharacteristic
329C2×#67—22no—
330C2×#67—21no—
331C2×#67—22no—
332C2×#67—21no—
333C2×#67—21no—
334C22×Dic3—24no—
335C22×Dic3—21no—
336C22×Dic3C2×D412yes—
337C22×Dic3C2×D412yes—
338C22×Dic3C2×D411yescharacteristic
339C22×Dic3C2×D411yescharacteristic
340#239—232no—
341#239—232no—
342#239—232no—
343#239—232no—
344#239—232no—
345#239—216no—
346#239—216no—
347#239—216no—
348#239—216no—
349#239—28no—
350#239—28no—
351#239—24no—
352#239C2×D4116yes—
353#239C2×D4116yescomplemented
354D3×Q8—24no—
355#237—24no—
356#237—44no—
357D3×D4—24no—
358D3×D4—48no—
359D3×D4—44no—
360#235—24no—
361#235—44no—
362C2×D12—216no—
363C2×D12—28no—
364C2×D12—232no—
365C2×D12—232no—
366C2×D12—216no—
367C2×D12—216no—
368C2×D12—28no—
369C2×D12—24no—
370C2×D12—24no—
371C2×D12—24no—
372C2×D12—22no—
373C2×D12—24no—
374C2×D12—216no—
375C2×D12—22no—
376C2×D12—21no—
377C2×D12C2×D418yescomplemented
378C2×D12C2411yescharacteristic
379C2×D12C2414yes—
380C2×C4×D3—216no—
381C2×C4×D3—232no—
382C2×C4×D3—232no—
383C2×C4×D3—24no—
384C2×C4×D3—24no—
385C2×C4×D3—216no—
386C2×C4×D3—24no—
387C2×C4×D3—28no—
388C2×C4×D3—24no—
389C2×C4×D3—24no—
390C2×C4×D3—28no—
391C2×C4×D3—28no—
392C2×C4×D3—28no—
393C2×C4×D3—28no—
394C2×C4×D3—22no—
395C2×C4×D3—21no—
396C2×C4×D3—21no—
397C2×C4×D3—21no—
398C2×C4×D3—44no—
399C2×C4×D3C2×D412yes—
400C2×C4×D3C2×D412yes—
401C2×C4×D3C2×D412yes—
402C2×C4×D3C2×D412yes—
403C2×C4×D3C2×D412yes—
404C2×C4×D3C2×D411yescharacteristic
405C2×C4×D3C2×D411yescharacteristic
406C2×C4×D3C2×D418yes—
407C2×C4×D3C2412yes—
408C2×C4×D3C2411yescharacteristic
409C2×C4×D3C2411yescharacteristic
410C2×Dic6—21no—
411C2×Dic6C2411yescharacteristic
412C3×Q16—28no—
413C3×SD16—28no—
414C3×M16—24no—
415C2×C3×C8C2414yes—
416C3×C4⋊C4—22no—
417C3×C4⋊C4C2412yes—
418C3×C22⋊C4—21no—
419C3×C22⋊C4—22no—
420C3×C22⋊C4—22no—
421C3×C42—21no—
422#217—21no—
423#217—22no—
424#217—22no—
425#216—28no—
426#215—28no—
427#215—28no—
428#213—28no—
429(C2×D3)⋊C4—22no—
430(C2×D3)⋊C4—22no—
431(C2×D3)⋊C4—22no—
432(C2×D3)⋊C4—22no—
433(C2×D3)⋊C4—22no—
434C4⋊Dic3—22no—
435C4⋊Dic3C2412yes—
436Dic3⋊C4—22no—
437Dic3⋊C4—22no—
438Dic3⋊C4—22no—
439C4×Dic3—21no—
440C4×Dic3—22no—
441#208—24no—
442C2×C3⋊C8C2414yes—
443D24—28no—
444#204—28no—
445ΓL(1,𝔽25)—28no—
446D3×C8—28no—
447C25—31no—
448C25—61no—
449C2×#41—316no—
450C2×#41—34no—
451C2×#41—34no—
452C2×#41—31no—
453C2×#41—38no—
454C2×#41—31no—
455C2×#41—31no—
456C2×#41—61no—
457C2×#41—61no—
458C2×#41—62no—
459C2×#41—62no—
460C2×#41—68no—
461C2×#41—64no—
462C2×#41—64no—
463C2×#41—64no—
464C2×#41—64no—
465C2×#41—64no—
466C2×#41—68no—
467C2×#41—68no—
468C2×#41—632no—
469C2×#41—632no—
470C2×#41—616no—
471C2×#41—632no—
472C2×#41—632no—
473C2×#41—616no—
474C2×#41—68no—
475C2×#41C22×D311yescharacteristic
476C22×Q8—28no—
477C22×Q8—22no—
478C22×Q8—21no—
479C22×Q8—31no—
480C22×Q8C22×D314yes—
481C22×Q8C22×D312yes—
482C22×D4—31no—
483C22×D4—32no—
484C22×D4—34no—
485C22×D4—68no—
486C22×D4—62no—
487C22×D4—64no—
488C22×D4—64no—
489C22×D4—62no—
490C22×D4—616no—
491C22×D4—62no—
492C22×D4—61no—
493C22×D4—62no—
494C22×D4—61no—
495C23×C4—21no—
496C23×C4—31no—
497C23×C4—31no—
498C23×C4—32no—
499C23×C4—31no—
500C23×C4—31no—
501C23×C4—32no—
502C23×C4—32no—
503C23×C4—32no—
504C23×C4—31no—
505C23×C4—68no—
506C23×C4—62no—
507C23×C4—64no—
508C23×C4—64no—
509C23×C4—62no—
510C23×C4—61no—
511C23×C4—616no—
512C23×C4C22×D311yescharacteristic
513#137—28no—
514#137—616no—
515#137—68no—
516AGL(1,ℤ/8)—68no—
517AGL(1,ℤ/8)—616no—
518AGL(1,ℤ/8)—68no—
519#135—616no—
520#135—616no—
521C2×Q16—34no—
522C2×Q16C22×D314yescomplemented
523C2×SD16—34no—
524C2×SD16—34no—
525C2×SD16—34no—
526C2×SD16C22×D314yescomplemented
527C2×D8—34no—
528C2×D8—34no—
529C2×M16—32no—
530C2×M16—34no—
531C2×M16—68no—
532C2×M16C22×D312yes—
533C22×C8—34no—
534#123—21no—
535#123—62no—
536#123—61no—
537#123—62no—
538#123—61no—
539#123—61no—
540C22⋊Q8—32no—
541C22⋊Q8—32no—
542C22⋊Q8—32no—
543C22⋊Q8—62no—
544C22⋊Q8—62no—
545C22⋊Q8C22×D312yes—
546#121—32no—
547#121—32no—
548#121—32no—
549#121—62no—
550#121—62no—
551#121C22×D312yes—
552#120—21no—
553#120—61no—
554#120—62no—
555#120—62no—
556#120—61no—
557#120—61no—
558C4×D4—22no—
559C4×D4—62no—
560C4×D4—62no—
561C4×D4—62no—
562C4×D4—62no—
563C4×D4—62no—
564C4×D4—62no—
565C4×D4—62no—
566#117—31no—
567#117—32no—
568#117—61no—
569#117—61no—
570#117C22×D311yescharacteristic
571C2×C4⋊C4—32no—
572C2×C4⋊C4—62no—
573C2×C22⋊C4—62no—
574C2×C22⋊C4—61no—
575C2×C22⋊C4—62no—
576C2×C42—61no—
577#103—38no—
578#103C22×D318yescomplemented
579#102—38no—
580#102—38no—
581C22⋊C8—34no—
582C22⋊C8—38no—
583C22⋊C8C22×D314yes—
584C23×C3—22no—
585C23×C3—24no—
586C23×C3—21no—
587C23×C3C22×D411yescharacteristic
588C23×C3C22×D412yes—
589C22×D3—216no—
590C22×D3—22no—
591C22×D3—28no—
592C22×D3—24no—
593C22×D3—24no—
594C22×D3—24no—
595C22×D3—24no—
596C22×D3—24no—
597C22×D3—21no—
598C22×D3—42no—
599C22×D3—42no—
600C22×D3—42no—
601C22×D3—42no—
602C22×D3—44no—
603C22×D3—416no—
604C22×D3—432no—
605C22×D3—48no—
606C22×D3—48no—
607C22×D3—48no—
608C22×D3—42no—
609C22×D3#12014yes—
610C22×D3C22×D412yes—
611C22×D3C22×D411yescharacteristic
612C22×D3C22×D411yescharacteristic
613C3×Q8—216no—
614C3×Q8—28no—
615C3×Q8—24no—
616C3×Q8—22no—
617C3×Q8C22×D418yes—
618C3×D4—22no—
619C3×D4—42no—
620C3×D4—44no—
621C2×C3×C4—216no—
622C2×C3×C4—28no—
623C2×C3×C4—22no—
624C2×C3×C4—24no—
625C2×C3×C4—24no—
626C2×C3×C4—24no—
627C2×C3×C4—22no—
628C2×C3×C4—21no—
629C2×C3×C4—42no—
630C2×C3×C4C22×D412yes—
631C2×C3×C4C22×D411yescharacteristic
632C2×C3×C4C22×D414yes—
633C2×C3×C4C2511yescharacteristic
634#67—44no—
635#67—42no—
636#67—44no—
637#67—42no—
638#67—42no—
639C2×Dic3—22no—
640C2×Dic3—24no—
641C2×Dic3—24no—
642C2×Dic3—22no—
643C2×Dic3—21no—
644C2×Dic3—42no—
645C2×Dic3#12014yes—
646C2×Dic3C22×D412yes—
647C2×Dic3C22×D411yescharacteristic
648C2×Dic3C22×D411yescharacteristic
649D12—232no—
650D12—216no—
651D12—216no—
652D12—216no—
653D12—28no—
654D12—24no—
655D12—22no—
656D12—44no—
657D12—42no—
658D12C22×D418yes—
659C4×D3—232no—
660C4×D3—24no—
661C4×D3—24no—
662C4×D3—24no—
663C4×D3—24no—
664C4×D3—216no—
665C4×D3—216no—
666C4×D3—24no—
667C4×D3—24no—
668C4×D3—44no—
669C4×D3—42no—
670C4×D3—42no—
671C4×D3—42no—
672C4×D3#12014yes—
673C4×D3#12014yes—
674C4×D3C22×D414yes—
675C4×D3C22×D414yes—
676Dic6—22no—
677Dic6—42no—
678C3×C8—24no—
679C3⋊C8—24no—
680C24—31no—
681C24—32no—
682C24—32no—
683C24—31no—
684C24—64no—
685C24—61no—
686C24—68no—
687C24—64no—
688C24—62no—
689C24—124no—
690C24—128no—
691C24D3×D411yescharacteristic
692#41—24no—
693#41—316no—
694#41—316no—
695#41—68no—
696#41—68no—
697#41—616no—
698#41—616no—
699#41—64no—
700#41—64no—
701#41—616no—
702#41—632no—
703#41—632no—
704#41—632no—
705#41—632no—
706#41—632no—
707#41—616no—
708#41—64no—
709#41—124no—
710#41—124no—
711C2×Q8—216no—
712C2×Q8—28no—
713C2×Q8—216no—
714C2×Q8—24no—
715C2×Q8—22no—
716C2×Q8—24no—
717C2×Q8—31no—
718C2×Q8—61no—
719C2×Q8—64no—
720C2×Q8D3×D418yescomplemented
721C2×Q8C23×D311yescharacteristic
722C2×Q8C23×D314yes—
723C2×D4—22no—
724C2×D4—21no—
725C2×D4—38no—
726C2×D4—34no—
727C2×D4—31no—
728C2×D4—616no—
729C2×D4—64no—
730C2×D4—64no—
731C2×D4—68no—
732C2×D4—616no—
733C2×D4—632no—
734C2×D4—632no—
735C2×D4—616no—
736C2×D4—68no—
737C2×D4—616no—
738C2×D4—62no—
739C2×D4—61no—
740C2×D4—64no—
741C2×D4—61no—
742C2×D4—62no—
743C2×D4—61no—
744C2×D4—62no—
745C2×D4—61no—
746C2×D4—64no—
747C2×D4—64no—
748C2×D4—62no—
749C2×D4—124no—
750C2×D4—128no—
751C2×D4C23×D311yescharacteristic
752C22×C4—28no—
753C22×C4—24no—
754C22×C4—22no—
755C22×C4—24no—
756C22×C4—21no—
757C22×C4—31no—
758C22×C4—31no—
759C22×C4—31no—
760C22×C4—38no—
761C22×C4—31no—
762C22×C4—31no—
763C22×C4—32no—
764C22×C4—32no—
765C22×C4—31no—
766C22×C4—32no—
767C22×C4—32no—
768C22×C4—32no—
769C22×C4—32no—
770C22×C4—32no—
771C22×C4—32no—
772C22×C4—64no—
773C22×C4—68no—
774C22×C4—68no—
775C22×C4—68no—
776C22×C4—68no—
777C22×C4—64no—
778C22×C4—64no—
779C22×C4—68no—
780C22×C4—616no—
781C22×C4—61no—
782C22×C4—64no—
783C22×C4—632no—
784C22×C4—632no—
785C22×C4—616no—
786C22×C4—62no—
787C22×C4—61no—
788C22×C4—64no—
789C22×C4—61no—
790C22×C4—64no—
791C22×C4—61no—
792C22×C4—124no—
793C22×C4D3×D412yes—
794C22×C4D3×D411yescharacteristic
795C22×C4C23×D312yes—
796C22×C4C23×D311yescharacteristic
797Q16—28no—
798Q16—68no—
799SD16—28no—
800SD16—68no—
801SD16—68no—
802SD16—68no—
803D8—68no—
804D8—68no—
805M16—24no—
806M16—68no—
807M16—64no—
808C2×C8—34no—
809C2×C8—68no—
810C2×C8C23×D314yes—
811C4⋊C4—22no—
812C4⋊C4—32no—
813C4⋊C4—62no—
814C4⋊C4—62no—
815C4⋊C4—62no—
816C4⋊C4—62no—
817C4⋊C4C23×D312yes—
818C22⋊C4—21no—
819C22⋊C4—22no—
820C22⋊C4—22no—
821C22⋊C4—62no—
822C22⋊C4—62no—
823C22⋊C4—62no—
824C22⋊C4—62no—
825C22⋊C4—62no—
826C22⋊C4—61no—
827C22⋊C4—62no—
828C22⋊C4—62no—
829C42—21no—
830C42—62no—
831C42—61no—
832C22×C3—28no—
833C22×C3—22no—
834C22×C3—22no—
835C22×C3—22no—
836C22×C3—41no—
837C22×C3—42no—
838C22×C3C2×#12012yes—
839C22×C3#57514yescomplemented
840C22×C3C23×D411yescharacteristic
841C2×D3—22no—
842C2×D3—22no—
843C2×D3—22no—
844C2×D3—28no—
845C2×D3—22no—
846C2×D3—22no—
847C2×D3—44no—
848C2×D3—48no—
849C2×D3—48no—
850C2×D3—44no—
851C2×D3—416no—
852C2×D3—432no—
853C2×D3—48no—
854C2×D3—41no—
855C2×D3—42no—
856C2×D3—84no—
857C2×D3C2×#12012yes—
858C2×D3C2×#12012yes—
859C3×C4—28no—
860C3×C4—22no—
861C3×C4—41no—
862C3×C4—42no—
863C3×C4C2×#12012yes—
864C3×C4C23×D412yes—
865Dic3—22no—
866Dic3—41no—
867Dic3—42no—
868Dic3C2×#12012yes—
869Dic3C2×#12012yes—
870C23—24no—
871C23—22no—
872C23—21no—
873C23—31no—
874C23—31no—
875C23—34no—
876C23—32no—
877C23—64no—
878C23—64no—
879C23—616no—
880C23—64no—
881C23—64no—
882C23—64no—
883C23—68no—
884C23—62no—
885C23—61no—
886C23—122no—
887C23—122no—
888C23—122no—
889C23—122no—
890C23—1216no—
891C23—1232no—
892C23—128no—
893C23—128no—
894C23—122no—
895C23—124no—
896C23—128no—
897C23C2×D3×D412yes—
898C23C2×D3×D411yescharacteristic
899Q8—216no—
900Q8—24no—
901Q8—28no—
902Q8—22no—
903Q8—62no—
904Q8—122no—
905Q8C2×D3×D418yes—
906D4—22no—
907D4—38no—
908D4—44no—
909D4—42no—
910D4—616no—
911D4—616no—
912D4—632no—
913D4—616no—
914D4—64no—
915D4—62no—
916D4—68no—
917D4—122no—
918D4—122no—
919D4—124no—
920D4—122no—
921D4—124no—
922D4—124no—
923D4—122no—
924C2×C4—216no—
925C2×C4—24no—
926C2×C4—28no—
927C2×C4—22no—
928C2×C4—24no—
929C2×C4—24no—
930C2×C4—22no—
931C2×C4—21no—
932C2×C4—31no—
933C2×C4—31no—
934C2×C4—34no—
935C2×C4—34no—
936C2×C4—34no—
937C2×C4—34no—
938C2×C4—34no—
939C2×C4—32no—
940C2×C4—42no—
941C2×C4—64no—
942C2×C4—64no—
943C2×C4—616no—
944C2×C4—616no—
945C2×C4—64no—
946C2×C4—64no—
947C2×C4—632no—
948C2×C4—64no—
949C2×C4—64no—
950C2×C4—62no—
951C2×C4—64no—
952C2×C4—64no—
953C2×C4—62no—
954C2×C4—61no—
955C2×C4—122no—
956C2×C4—122no—
957C2×C4—122no—
958C2×C4—124no—
959C2×C4—122no—
960C2×C4C2×D3×D412yes—
961C2×C4C2×D3×D414yes—
962C2×C4C2×D3×D411yescharacteristic
963C2×C4C24×D311yescharacteristic
964C8—24no—
965C8—64no—
966C2×C3—22no—
967C2×C3—24no—
968C2×C3—81no—
969C2×C3C22×#12011yescharacteristic
970C2×C3C2×#57512yes—
971D3—22no—
972D3—22no—
973D3—42no—
974D3—48no—
975D3—81no—
976C22—28no—
977C22—22no—
978C22—22no—
979C22—22no—
980C22—32no—
981C22—32no—
982C22—42no—
983C22—41no—
984C22—62no—
985C22—62no—
986C22—62no—
987C22—62no—
988C22—68no—
989C22—62no—
990C22—124no—
991C22—128no—
992C22—128no—
993C22—1232no—
994C22—124no—
995C22—1216no—
996C22—128no—
997C22—122no—
998C22—121no—
999C22—244no—
1000C22D3×#12012yes—
1001C22#577714yescomplemented
1002C22C22×D3×D411yescharacteristic
1003C4—28no—
1004C4—22no—
1005C4—32no—
1006C4—32no—
1007C4—42no—
1008C4—41no—
1009C4—62no—
1010C4—122no—
1011C4—121no—
1012C4D3×#12012yes—
1013C4C22×D3×D412yes—
1014C3#6035911yescharacteristic, complemented, Sylow
1015C2—24no—
1016C2—22no—
1017C2—62no—
1018C2—62no—
1019C2—81no—
1020C2—122no—
1021C2—128no—
1022C2—241no—
1023C2C2×D3×#12011yescharacteristic
1024C2C2×#577712yes—
subgroupG/H
centerC22C22×D3×D4
commutator, cosocleC2×C3×C4C25
FrattiniC2×C4C24×D3
FittingC3×#3004C2
socleC22×C3C23×D4
hypercenter#3004D3
hypocenterC3#60359
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C23×C4 ◁ #3004

Complements

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

NH ≅ G/Ntype
1. C23×#239C2semidirect
2. C2×#5777C2semidirect
3. D3×#525C2semidirect
4. C3×#3004C2semidirect
5. #84059C2semidirect
6. #83980C2semidirect
7. #82927C2semidirect
8. #80184C2semidirect
9. #80182C2semidirect
10. #80040C2semidirect
11. #80038C2semidirect
12. #78959C2semidirect
13. #78956C2semidirect
14. #78637C2semidirect
15. D3×#407C2semidirect
17. C23×C3×Q8C22semidirect
18. C2×D3×#41C22semidirect
26. C22×#239C22semidirect
27. C22×#239C22semidirect
29. C23×D12C22semidirect
32. C2×C3×#137C22semidirect
34. #5828C22semidirect
35. C2×#949C22semidirect
36. C2×#942C22semidirect
39. C2×#919C22semidirect
40. C2×#918C22semidirect
41. C2×#916C22semidirect
42. C2×#914C22semidirect
43. C2×#908C22semidirect
44. C2×D3×M16C22semidirect
47. #5627C22semidirect
48. D3×C22⋊Q8C22semidirect
49. #5606C22semidirect
50. D3×#121C22semidirect
55. #5524C22semidirect
56. D3×#117C22semidirect
57. C3×#451C22semidirect
58. C3×#448C22semidirect
59. C3×#419C22semidirect
60. C3×#407C22semidirect
61. #5228C22semidirect
62. #5227C22semidirect
63. #5225C22semidirect
64. #5207C22semidirect
65. #5187C22semidirect
66. #5172C22semidirect
67. #5131C22semidirect
68. #5126C22semidirect
69. #5046C22semidirect
70. #5036C22semidirect
71. #5001C22semidirect
72. #4810C22semidirect
73. #4808C22semidirect
74. #4804C22semidirect
75. #4803C22semidirect
76. #4732C22semidirect
77. #4731C22semidirect
78. #4726C22semidirect
79. D3×C22⋊C8C22semidirect
88. #3004D3semidirect
123. C2×#239D4semidirect
127. C2×#239C23semidirect
128. C2×D3×Q8C23semidirect
130. C2×#237C23semidirect
133. C2×D3×D4C23semidirect
162. C2×C3×Q16C23semidirect
163. C2×C3×SD16C23semidirect
173. #946C23semidirect
174. C2×#216C23semidirect
176. C2×#215C23semidirect
177. C2×#215C23semidirect
179. #938C23semidirect
184. C2×#213C23semidirect
198. C2×D24C23semidirect
199. C2×#204C23semidirect
200. C2×ΓL(1,𝔽25)C23semidirect
201. C2×D3×C8C23semidirect
202. #897C23semidirect
204. #895C23semidirect
207. #892C23semidirect
209. D3×C4⋊C4C23semidirect
225. C3×#103C23semidirect
227. #835C23semidirect
229. #821C23semidirect
230. (C2×D3)⋊C8C23semidirect
231. #809C23semidirect
242. C23×Q8C2×D3semidirect
250. C2×#137C2×D3semidirect
275. #451C2×D3semidirect
281. #448C2×D3semidirect
285. #419C2×D3semidirect
293. #407C2×D3semidirect
314. C2×C3×Q8C2×D4semidirect
353. #239C2×D4semidirect
377. C2×D12C2×D4semidirect
522. C2×Q16C22×D3semidirect
526. C2×SD16C22×D3semidirect
578. #103C22×D3semidirect
720. C2×Q8D3×D4semidirect
839. C22×C3#575semidirect
1001. C22#5777semidirect
1014. C3#60359semidirect

Maximal subgroups

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

subgroupindex
C23×#2392
C2×#57772
D3×#5252
C3×#30042
#840592
#839802
#829272
#801842
#801822
#800402
#800382
#789592
#789562
#786372
D3×#4072
#603593