Finite Group Databasebeta

← C2×D3×#455 #11661792

Subgroups — C2×D3×#455 #11661792

Order 768.

5110 conjugacy classes of subgroups.

The subgroup lattice has 1004 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D3×H(5,𝔽2)C211yesmaximal, characteristic
2C2×D3×#137C212yesmaximal, complemented
3C2×D3×#124C211yesmaximal, characteristic, complemented
4C2×C3×#455C211yesmaximal, characteristic, complemented
5C2×#5242C211yesmaximal, characteristic, complemented
6C2×#5202C212yesmaximal, complemented
7C2×#5061C211yesmaximal, characteristic, complemented
8D3×#455C2116yesmaximal, direct product factor
9C2×#4825C212yesmaximal, complemented
10C2×D3×#104C212yesmaximal, complemented
11C2×#4746C211yesmaximal, characteristic, complemented
12C2×D3×#100C211yesmaximal, characteristic, complemented
13C22×#455—31nomaximal, Sylow
14C2×C3×H(5,𝔽2)C2211yescharacteristic
15D3×H(5,𝔽2)—28no—
16D3×H(5,𝔽2)—24no—
17D3×H(5,𝔽2)C2218yes—
18C2×#1009—22no—
19C2×#1009C2212yes—
20C2×D3×#41—22no—
21C2×D3×#41C2212yes—
22C22×D3×Q8C2211yescharacteristic, complemented
23C2×#1004—22no—
24C2×#1004—22no—
25C2×#1004C2211yescharacteristic
26C22×D3×D4—22no—
27C22×D3×D4—22no—
28C22×D3×D4C2211yescharacteristic
29C2×C3×#137C2212yescomplemented
30C2×C3×#124C2211yescharacteristic, complemented
31C2×#951C2212yescomplemented
32C2×#947C2211yescharacteristic, complemented
33C2×#942C2212yescomplemented
34C2×#936C2211yescharacteristic, complemented
35D3×#137—28no—
36D3×#137C22116yescomplemented
37C2×#918—22no—
38C2×D3×Q16—22no—
39C2×#915—22no—
40C2×D3×SD16—22no—
41C2×#909C2212yescomplemented
42C2×D3×M16C2212yescomplemented
43D3×#124—24no—
44D3×#124C2218yescomplemented
45C2×#885—22no—
46C2×D3×C22⋊C4—22no—
47C2×#875C2211yescharacteristic, complemented
48C2×C42×D3C2211yescharacteristic, complemented
49C3×#455C2218yescomplemented
50C2×C3×#104C2212yescomplemented
51C2×C3×#100C2211yescharacteristic, complemented
52#5242C2218yescomplemented
53C2×#837C2212yescomplemented
54C2×#833C2211yescharacteristic, complemented
55#5202C22116yescomplemented
56C2×#825C2212yescomplemented
57C2×#823C2212yescomplemented
58#5061C2218yescomplemented
59C2×#805C2212yescomplemented
60#4825C22116yescomplemented
61D3×#104C22116yescomplemented
62#4746C2218yescomplemented
63D3×#100C2218yescomplemented
64C22×H(5,𝔽2)—31no—
65C22×#137—32no—
66C22×#124—31no—
67C2×#455—316no—
68C2×#455—32no—
69C2×#455—31no—
70C2×#455—31no—
71C2×#455—32no—
72C2×#455—31no—
73C2×#455D311yescharacteristic, direct product factor
74C22×#104—32no—
75C22×#100—31no—
76C24×D3—22no—
77C24×D3D412yes—
78C3×H(5,𝔽2)—24no—
79C3×H(5,𝔽2)—22no—
80C3×H(5,𝔽2)C2314yes—
81C2×C3×#41—22no—
82C2×C3×#41C2312yes—
83C22×C3×Q8C2311yescharacteristic, complemented
84C22×C3×D4—22no—
85C22×C3×D4—22no—
86C22×C3×D4C2311yescharacteristic
87C22×#67—22no—
88C22×#67—24no—
89C22×#67—22no—
90C22×#67D412yes—
91#1009—216no—
92#1009—24no—
93#1009—216no—
94#1009—24no—
95#1009—24no—
96#1009C2318yes—
97D3×#41—216no—
98D3×#41—216no—
99D3×#41—24no—
100D3×#41—24no—
101D3×#41D418yes—
102D3×#41C2318yes—
103C2×#239—22no—
104C2×#239D412yes—
105C2×D3×Q8—22no—
106C2×D3×Q8—22no—
107C2×D3×Q8—22no—
108C2×D3×Q8—24no—
109C2×D3×Q8D412yes—
110C2×D3×Q8C2314yescomplemented
111#1004—216no—
112#1004—216no—
113#1004—22no—
114#1004—216no—
115#1004—216no—
116#1004—24no—
117#1004C2314yes—
118C2×#237—24no—
119C2×#237—22no—
120C2×#237—22no—
121C2×#237D412yes—
122C2×D3×D4—24no—
123C2×D3×D4—24no—
124C2×D3×D4—24no—
125C2×D3×D4—216no—
126C2×D3×D4—216no—
127C2×D3×D4—22no—
128C2×D3×D4—24no—
129C2×D3×D4—216no—
130C2×D3×D4—22no—
131C2×D3×D4—216no—
132C2×D3×D4—22no—
133C2×D3×D4—22no—
134C2×D3×D4—22no—
135C2×D3×D4—24no—
136C2×D3×D4D414yes—
137C2×D3×D4D412yes—
138C2×D3×D4C2314yes—
139C2×#235—24no—
140C2×#235—22no—
141C2×#235—22no—
142C2×#235C2312yes—
143C22×D12—22no—
144C22×D12—22no—
145C22×D12C2311yescharacteristic
146C22×C4×D3—22no—
147C22×C4×D3—22no—
148C22×C4×D3—21no—
149C22×C4×D3—21no—
150C22×C4×D3C2311yescharacteristic
151C22×Dic6—21no—
152C22×Dic6C2311yescharacteristic, complemented
153C3×#137—24no—
154C3×#137C2318yescomplemented
155C2×C3×Q16—22no—
156C2×C3×SD16—22no—
157C2×C3×M16C2312yescomplemented
158C3×#124—22no—
159C3×#124C2314yescomplemented
160C2×C3×C22⋊C4—22no—
161C2×C3×C42C2311yescharacteristic, complemented
162C2×#217—22no—
163#951—24no—
164#951C2318yescomplemented
165#947—22no—
166#947C2314yescomplemented
167C2×#216—22no—
168C2×#216—22no—
169#942—24no—
170#942C2318yescomplemented
171C2×#215—22no—
172#936—22no—
173#936C2314yescomplemented
174C2×#214—22no—
175C2×(C2×D3)⋊C4—22no—
176C2×(C2×D3)⋊C4—22no—
177C2×C4×Dic3—21no—
178C2×C4×Dic3C2311yescharacteristic, complemented
179C2×#208C2312yescomplemented
180#918—216no—
181D3×Q16—216no—
182#915—216no—
183D3×SD16—216no—
184#909—24no—
185#909C2318yescomplemented
186D3×M16—24no—
187D3×M16C2318yescomplemented
188C2×Dic12—22no—
189C2×#204—22no—
190C2×ΓL(1,𝔽25)—22no—
191C2×D3×C8—22no—
192#885—216no—
193D3×C22⋊C4—216no—
194#875—22no—
195#875C2314yescomplemented
196C42×D3—22no—
197C42×D3C2314yescomplemented
198C3×#104C2318yescomplemented
199C3×#100C2314yescomplemented
200#837C2318yescomplemented
201#833C2314yescomplemented
202#825C2318yescomplemented
203#823C2318yescomplemented
204#805C2318yescomplemented
205C2×H(5,𝔽2)—38no—
206C2×H(5,𝔽2)—32no—
207C2×H(5,𝔽2)—31no—
208C2×H(5,𝔽2)—62no—
209C2×H(5,𝔽2)—62no—
210C2×H(5,𝔽2)—64no—
211C2×H(5,𝔽2)—62no—
212C2×H(5,𝔽2)—68no—
213C2×H(5,𝔽2)C2×D311yescharacteristic
214C22×#41—32no—
215C22×#41—62no—
216C23×Q8—31no—
217C23×D4—31no—
218C23×D4—62no—
219C23×D4—62no—
220C2×#137—32no—
221C2×#137—32no—
222C2×#137—316no—
223C2×#137—32no—
224C2×#137—62no—
225C2×#137—62no—
226C2×#137—68no—
227C2×#137C2×D312yescomplemented
228C22×Q16—62no—
229C22×SD16—62no—
230C22×M16—32no—
231C2×#124—31no—
232C2×#124—31no—
233C2×#124—38no—
234C2×#124—31no—
235C2×#124—62no—
236C2×#124—64no—
237C2×#124C2×D311yescharacteristic, complemented
238C22×C22⋊C4—62no—
239C22×C42—31no—
240#455—38no—
241#455—316no—
242#455—38no—
243#455—316no—
244#455—38no—
245#455C2×D318yesdirect product factor
246C2×#104—32no—
247C2×#104—32no—
248C2×#104—32no—
249C2×#104—316no—
250C2×#104C2×D312yescomplemented
251C2×#100—31no—
252C2×#100—32no—
253C2×#100—38no—
254C2×#100C2×D311yescharacteristic, complemented
255C24×C3—22no—
256C24×C3C2×D412yes—
257C23×D3—24no—
258C23×D3—22no—
259C23×D3—216no—
260C23×D3—22no—
261C23×D3—22no—
262C23×D3—22no—
263C23×D3—24no—
264C23×D3—48no—
265C23×D3—88no—
266C23×D3C2×D411yescharacteristic
267C23×D3C2×D418yes—
268C23×D3C2×D412yes—
269C3×#41—28no—
270C3×#41—28no—
271C3×#41—22no—
272C3×#41—22no—
273C3×#41C2×D414yes—
274C3×#41C2414yes—
275C2×C3×Q8—21no—
276C2×C3×Q8—22no—
277C2×C3×Q8—22no—
278C2×C3×Q8C2×D412yes—
279C2×C3×Q8C2412yescomplemented
280C2×C3×D4—24no—
281C2×C3×D4—28no—
282C2×C3×D4—28no—
283C2×C3×D4—22no—
284C2×C3×D4—28no—
285C2×C3×D4—28no—
286C2×C3×D4—22no—
287C2×C3×D4—22no—
288C2×C3×D4C2×D412yes—
289C2×C3×D4C2×D412yes—
290C2×C3×D4C2412yes—
291C22×C3×C4—22no—
292C22×C3×C4—22no—
293C22×C3×C4—21no—
294C22×C3×C4—21no—
295C22×C3×C4C2411yescharacteristic
296C2×#67—24no—
297C2×#67—24no—
298C2×#67—28no—
299C2×#67—216no—
300C2×#67—232no—
301C2×#67—22no—
302C2×#67—28no—
303C2×#67—22no—
304C2×#67—24no—
305C2×#67—22no—
306C2×#67—24no—
307C2×#67C2×D418yes—
308C22×Dic3—22no—
309C22×Dic3—22no—
310C22×Dic3—21no—
311C22×Dic3—21no—
312C22×Dic3C2×D411yescharacteristic
313#239—28no—
314#239—28no—
315#239—24no—
316#239C2×D418yes—
317D3×Q8—24no—
318D3×Q8—28no—
319D3×Q8—28no—
320D3×Q8—44no—
321D3×Q8—44no—
322D3×Q8C2×D418yes—
323#237—28no—
324#237—232no—
325#237—28no—
326#237—28no—
327#237—24no—
328#237—28no—
329#237C2×D418yes—
330D3×D4—232no—
331D3×D4—216no—
332D3×D4—232no—
333D3×D4—28no—
334D3×D4—28no—
335D3×D4—232no—
336D3×D4—28no—
337D3×D4—28no—
338D3×D4—216no—
339D3×D4—28no—
340D3×D4—28no—
341D3×D4—28no—
342D3×D4—24no—
343D3×D4—28no—
344D3×D4—28no—
345D3×D4—28no—
346D3×D4C2×D418yes—
347#235—28no—
348#235—232no—
349#235—22no—
350#235—22no—
351#235—28no—
352#235—28no—
353#235—28no—
354#235C2×D414yes—
355#235C2414yes—
356C2×D12—24no—
357C2×D12—216no—
358C2×D12—28no—
359C2×D12—22no—
360C2×D12—22no—
361C2×D12—22no—
362C2×D12—28no—
363C2×D12C2×D412yes—
364C2×D12C2×D412yes—
365C2×D12C2412yes—
366C2×C4×D3—24no—
367C2×C4×D3—216no—
368C2×C4×D3—22no—
369C2×C4×D3—22no—
370C2×C4×D3—22no—
371C2×C4×D3—28no—
372C2×C4×D3—28no—
373C2×C4×D3—24no—
374C2×C4×D3—24no—
375C2×C4×D3—44no—
376C2×C4×D3—41no—
377C2×C4×D3—42no—
378C2×C4×D3—41no—
379C2×C4×D3C2×D412yes—
380C2×C4×D3C2×D412yes—
381C2×C4×D3C2×D412yes—
382C2×C4×D3C2×D414yes—
383C2×C4×D3C2412yes—
384C2×Dic6—22no—
385C2×Dic6—22no—
386C2×Dic6—22no—
387C2×Dic6—21no—
388C2×Dic6—24no—
389C2×Dic6—42no—
390C2×Dic6—42no—
391C2×Dic6C2×D412yes—
392C2×Dic6C2412yescomplemented
393C3×Q16—28no—
394C3×SD16—28no—
395C3×M16—22no—
396C3×M16C2414yescomplemented
397C2×C3×C8—22no—
398C3×C22⋊C4—28no—
399C3×C42—21no—
400C3×C42C2412yescomplemented
401#217—28no—
402#216—28no—
403#216—28no—
404#215—28no—
405#214—28no—
406(C2×D3)⋊C4—28no—
407(C2×D3)⋊C4—28no—
408C4×Dic3—21no—
409C4×Dic3—24no—
410C4×Dic3C2412yescomplemented
411#208—22no—
412#208C2414yescomplemented
413C2×C3⋊C8—22no—
414Dic12—28no—
415#204—28no—
416ΓL(1,𝔽25)—28no—
417D3×C8—28no—
418C25—32no—
419C25—62no—
420H(5,𝔽2)—24no—
421H(5,𝔽2)—22no—
422H(5,𝔽2)—38no—
423H(5,𝔽2)—34no—
424H(5,𝔽2)—616no—
425H(5,𝔽2)—616no—
426H(5,𝔽2)—64no—
427H(5,𝔽2)—616no—
428H(5,𝔽2)—616no—
429H(5,𝔽2)—64no—
430H(5,𝔽2)—64no—
431H(5,𝔽2)—616no—
432H(5,𝔽2)—616no—
433H(5,𝔽2)—64no—
434H(5,𝔽2)—62no—
435H(5,𝔽2)C22×D314yes—
436C2×#41—22no—
437C2×#41—38no—
438C2×#41—38no—
439C2×#41—32no—
440C2×#41—32no—
441C2×#41—32no—
442C2×#41—62no—
443C2×#41—62no—
444C2×#41—64no—
445C2×#41—62no—
446C2×#41—64no—
447C2×#41—64no—
448C2×#41—62no—
449C2×#41—64no—
450C2×#41—616no—
451C2×#41—616no—
452C2×#41—62no—
453C2×#41C22×D312yes—
454C22×Q8—32no—
455C22×Q8—34no—
456C22×Q8—31no—
457C22×Q8—61no—
458C22×Q8—62no—
459C22×Q8—62no—
460C22×Q8—62no—
461C22×Q8—64no—
462C22×Q8C22×D311yescharacteristic, complemented
463C22×D4—22no—
464C22×D4—22no—
465C22×D4—32no—
466C22×D4—32no—
467C22×D4—34no—
468C22×D4—34no—
469C22×D4—31no—
470C22×D4—62no—
471C22×D4—62no—
472C22×D4—62no—
473C22×D4—62no—
474C22×D4—64no—
475C22×D4—616no—
476C22×D4—62no—
477C22×D4—62no—
478C22×D4—64no—
479C22×D4—616no—
480C22×D4—64no—
481C22×D4—64no—
482C22×D4—616no—
483C22×D4—64no—
484C22×D4—616no—
485C22×D4—64no—
486C22×D4—62no—
487C22×D4—62no—
488C22×D4—62no—
489C22×D4C22×D311yescharacteristic
490C23×C4—31no—
491C23×C4—62no—
492C23×C4—62no—
493C23×C4—61no—
494C23×C4—61no—
495#137—24no—
496#137—38no—
497#137—38no—
498#137—38no—
499#137—64no—
500#137—616no—
501#137—616no—
502#137—64no—
503#137—64no—
504#137C22×D318yescomplemented
505C2×Q16—22no—
506C2×Q16—62no—
507C2×Q16—616no—
508C2×Q16—62no—
509C2×Q16—62no—
510C2×SD16—22no—
511C2×SD16—62no—
512C2×SD16—616no—
513C2×SD16—62no—
514C2×SD16—62no—
515C2×M16—32no—
516C2×M16—38no—
517C2×M16—62no—
518C2×M16—64no—
519C2×M16C22×D312yescomplemented
520C22×C8—62no—
521#124—22no—
522#124—34no—
523#124—34no—
524#124—34no—
525#124—62no—
526#124—616no—
527#124—62no—
528#124—62no—
529#124C22×D314yescomplemented
530C2×C22⋊C4—22no—
531C2×C22⋊C4—616no—
532C2×C22⋊C4—62no—
533C2×C22⋊C4—62no—
534C2×C22⋊C4—62no—
535C2×C42—31no—
536C2×C42—34no—
537C2×C42—62no—
538C2×C42—61no—
539C2×C42C22×D311yescharacteristic, complemented
540#104—38no—
541#104—38no—
542#104—38no—
543#104C22×D318yescomplemented
544#100—34no—
545#100—38no—
546#100C22×D314yescomplemented
547C23×C3—28no—
548C23×C3—22no—
549C23×C3—22no—
550C23×C3—22no—
551C23×C3—44no—
552C23×C3—84no—
553C23×C3C22×D411yescharacteristic
554C23×C3C22×D414yes—
555C22×D3—24no—
556C22×D3—22no—
557C22×D3—22no—
558C22×D3—216no—
559C22×D3—28no—
560C22×D3—22no—
561C22×D3—28no—
562C22×D3—28no—
563C22×D3—28no—
564C22×D3—416no—
565C22×D3—48no—
566C22×D3—48no—
567C22×D3—44no—
568C22×D3—88no—
569C22×D3—84no—
570C22×D3—832no—
571C22×D3—88no—
572C22×D3—84no—
573C22×D3#12011yescharacteristic
574C22×D3#12012yes—
575C22×D3#12011yescharacteristic
576C22×D3C22×D412yes—
577C22×D3C22×D414yes—
578C3×Q8—22no—
579C3×Q8—24no—
580C3×Q8—42no—
581C3×Q8C22×D414yes—
582C3×D4—216no—
583C3×D4—24no—
584C3×D4—24no—
585C3×D4—24no—
586C3×D4—22no—
587C3×D4—24no—
588C3×D4C22×D414yes—
589C2×C3×C4—28no—
590C2×C3×C4—22no—
591C2×C3×C4—24no—
592C2×C3×C4—24no—
593C2×C3×C4—22no—
594C2×C3×C4—22no—
595C2×C3×C4—42no—
596C2×C3×C4—41no—
597C2×C3×C4—41no—
598C2×C3×C4C22×D411yescharacteristic
599C2×C3×C4C22×D412yes—
600C2×C3×C4C22×D412yes—
601C2×C3×C4C2511yescharacteristic
602#67—216no—
603#67—216no—
604#67—24no—
605#67—24no—
606#67—28no—
607#67—216no—
608#67—28no—
609C2×Dic3—28no—
610C2×Dic3—22no—
611C2×Dic3—28no—
612C2×Dic3—22no—
613C2×Dic3—22no—
614C2×Dic3—42no—
615C2×Dic3—41no—
616C2×Dic3—41no—
617C2×Dic3#12012yes—
618C2×Dic3#12012yes—
619C2×Dic3C22×D412yes—
620D12—216no—
621D12—28no—
622D12—24no—
623D12—22no—
624D12—24no—
625D12C22×D414yes—
626C4×D3—216no—
627C4×D3—28no—
628C4×D3—24no—
629C4×D3—24no—
630C4×D3—28no—
631C4×D3—48no—
632C4×D3—44no—
633C4×D3—44no—
634C4×D3#12014yes—
635C4×D3#12014yes—
636C4×D3C22×D414yes—
637C4×D3C22×D414yes—
638Dic6—22no—
639Dic6—28no—
640Dic6—24no—
641Dic6—42no—
642Dic6—48no—
643Dic6C22×D414yes—
644C3×C8—24no—
645C3⋊C8—24no—
646C24—22no—
647C24—31no—
648C24—38no—
649C24—32no—
650C24—62no—
651C24—62no—
652C24—62no—
653C24—64no—
654C24—616no—
655C24—62no—
656C24—64no—
657C24—128no—
658C24—248no—
659C24D3×D412yes—
660#41—28no—
661#41—28no—
662#41—22no—
663#41—22no—
664#41—38no—
665#41—38no—
666#41—34no—
667#41—34no—
668#41—68no—
669#41—68no—
670#41—68no—
671#41—632no—
672#41—68no—
673#41—68no—
674#41—68no—
675#41—64no—
676#41—64no—
677#41—68no—
678#41—632no—
679#41—68no—
680#41—68no—
681#41—68no—
682#41—62no—
683#41—62no—
684#41D3×D414yes—
685#41C23×D314yes—
686C2×Q8—21no—
687C2×Q8—22no—
688C2×Q8—22no—
689C2×Q8—38no—
690C2×Q8—32no—
691C2×Q8—32no—
692C2×Q8—62no—
693C2×Q8—64no—
694C2×Q8—64no—
695C2×Q8—68no—
696C2×Q8—68no—
697C2×Q8—61no—
698C2×Q8—62no—
699C2×Q8—62no—
700C2×Q8—122no—
701C2×Q8—122no—
702C2×Q8—124no—
703C2×Q8—124no—
704C2×Q8D3×D412yes—
705C2×Q8C23×D312yescomplemented
706C2×D4—24no—
707C2×D4—28no—
708C2×D4—28no—
709C2×D4—22no—
710C2×D4—28no—
711C2×D4—28no—
712C2×D4—22no—
713C2×D4—22no—
714C2×D4—38no—
715C2×D4—38no—
716C2×D4—32no—
717C2×D4—32no—
718C2×D4—32no—
719C2×D4—68no—
720C2×D4—62no—
721C2×D4—64no—
722C2×D4—616no—
723C2×D4—68no—
724C2×D4—68no—
725C2×D4—64no—
726C2×D4—68no—
727C2×D4—68no—
728C2×D4—68no—
729C2×D4—64no—
730C2×D4—62no—
731C2×D4—64no—
732C2×D4—68no—
733C2×D4—68no—
734C2×D4—68no—
735C2×D4—616no—
736C2×D4—632no—
737C2×D4—632no—
738C2×D4—632no—
739C2×D4—616no—
740C2×D4—68no—
741C2×D4—68no—
742C2×D4—62no—
743C2×D4—64no—
744C2×D4—64no—
745C2×D4—632no—
746C2×D4—616no—
747C2×D4—68no—
748C2×D4—62no—
749C2×D4—68no—
750C2×D4—68no—
751C2×D4—62no—
752C2×D4—62no—
753C2×D4D3×D412yes—
754C2×D4D3×D412yes—
755C2×D4C23×D312yes—
756C22×C4—22no—
757C22×C4—22no—
758C22×C4—21no—
759C22×C4—21no—
760C22×C4—31no—
761C22×C4—32no—
762C22×C4—32no—
763C22×C4—34no—
764C22×C4—32no—
765C22×C4—32no—
766C22×C4—62no—
767C22×C4—68no—
768C22×C4—68no—
769C22×C4—62no—
770C22×C4—616no—
771C22×C4—64no—
772C22×C4—64no—
773C22×C4—64no—
774C22×C4—62no—
775C22×C4—62no—
776C22×C4—62no—
777C22×C4—61no—
778C22×C4—61no—
779C22×C4—122no—
780C22×C4—121no—
781C22×C4—121no—
782C22×C4—124no—
783C22×C4C23×D311yescharacteristic
784Q16—28no—
785Q16—68no—
786Q16—68no—
787Q16—68no—
788SD16—28no—
789SD16—68no—
790SD16—68no—
791SD16—68no—
792M16—22no—
793M16—34no—
794M16—68no—
795M16—62no—
796M16C23×D314yescomplemented
797C2×C8—22no—
798C2×C8—68no—
799C2×C8—62no—
800C22⋊C4—28no—
801C22⋊C4—68no—
802C22⋊C4—68no—
803C22⋊C4—68no—
804C42—21no—
805C42—32no—
806C42—64no—
807C42—61no—
808C42C23×D312yescomplemented
809C22×C3—22no—
810C22×C3—24no—
811C22×C3—24no—
812C22×C3—44no—
813C22×C3—44no—
814C22×C3—44no—
815C22×C3—82no—
816C22×C3—88no—
817C22×C3C2×#12011yescharacteristic
818C22×C3C2×#12011yescharacteristic
819C22×C3C23×D411yescharacteristic
820C2×D3—22no—
821C2×D3—24no—
822C2×D3—24no—
823C2×D3—24no—
824C2×D3—24no—
825C2×D3—44no—
826C2×D3—44no—
827C2×D3—416no—
828C2×D3—416no—
829C2×D3—44no—
830C2×D3—88no—
831C2×D3—82no—
832C2×D3—816no—
833C2×D3—88no—
834C2×D3#45514yesdirect product factor
835C2×D3C2×#12012yes—
836C2×D3C2×#12012yes—
837C3×C4—24no—
838C3×C4—42no—
839C3×C4—42no—
840C3×C4C2×#12012yes—
841C3×C4C23×D412yes—
842Dic3—24no—
843Dic3—42no—
844Dic3—42no—
845Dic3C2×#12014yes—
846C23—28no—
847C23—22no—
848C23—22no—
849C23—22no—
850C23—31no—
851C23—32no—
852C23—32no—
853C23—31no—
854C23—34no—
855C23—44no—
856C23—64no—
857C23—68no—
858C23—68no—
859C23—68no—
860C23—68no—
861C23—616no—
862C23—62no—
863C23—62no—
864C23—62no—
865C23—84no—
866C23—124no—
867C23—128no—
868C23—128no—
869C23—1216no—
870C23—244no—
871C23—244no—
872C23—248no—
873C23—248no—
874C23—2432no—
875C23C2×D3×D411yescharacteristic
876C23C2×D3×D414yes—
877Q8—22no—
878Q8—24no—
879Q8—34no—
880Q8—42no—
881Q8—68no—
882Q8—62no—
883Q8—64no—
884Q8—128no—
885Q8—122no—
886Q8C2×D3×D414yes—
887D4—216no—
888D4—24no—
889D4—24no—
890D4—24no—
891D4—24no—
892D4—22no—
893D4—34no—
894D4—68no—
895D4—616no—
896D4—616no—
897D4—68no—
898D4—68no—
899D4—616no—
900D4—616no—
901D4—64no—
902D4—64no—
903D4—64no—
904D4—62no—
905D4—64no—
906D4C2×D3×D414yes—
907C2×C4—28no—
908C2×C4—22no—
909C2×C4—24no—
910C2×C4—24no—
911C2×C4—22no—
912C2×C4—22no—
913C2×C4—32no—
914C2×C4—32no—
915C2×C4—32no—
916C2×C4—34no—
917C2×C4—34no—
918C2×C4—34no—
919C2×C4—34no—
920C2×C4—42no—
921C2×C4—41no—
922C2×C4—41no—
923C2×C4—68no—
924C2×C4—68no—
925C2×C4—616no—
926C2×C4—68no—
927C2×C4—68no—
928C2×C4—62no—
929C2×C4—64no—
930C2×C4—64no—
931C2×C4—62no—
932C2×C4—62no—
933C2×C4—124no—
934C2×C4—124no—
935C2×C4—128no—
936C2×C4—122no—
937C2×C4—121no—
938C2×C4—121no—
939C2×C4C2×D3×D412yes—
940C2×C4C2×D3×D412yes—
941C2×C4C2×D3×D411yescharacteristic
942C2×C4C24×D311yescharacteristic
943C8—24no—
944C8—64no—
945C2×C3—21no—
946C2×C3—21no—
947C2×C3—44no—
948C2×C3—44no—
949C2×C3C2×#45512yescomplemented
950C2×C3C22×#12011yescharacteristic
951D3—22no—
952D3—44no—
953D3—44no—
954D3C2×#45514yesdirect product factor
955C22—22no—
956C22—24no—
957C22—24no—
958C22—32no—
959C22—34no—
960C22—32no—
961C22—44no—
962C22—44no—
963C22—44no—
964C22—64no—
965C22—64no—
966C22—62no—
967C22—64no—
968C22—64no—
969C22—82no—
970C22—88no—
971C22—124no—
972C22—1216no—
973C22—1216no—
974C22—124no—
975C22—124no—
976C22—242no—
977C22—248no—
978C22—248no—
979C22—2416no—
980C22D3×#12011yescharacteristic
981C22D3×#12011yescharacteristic
982C22C22×D3×D411yescharacteristic
983C4—24no—
984C4—34no—
985C4—42no—
986C4—42no—
987C4—64no—
988C4—122no—
989C4—122no—
990C4D3×#12012yes—
991C4C22×D3×D412yes—
992C3C22×#45511yescharacteristic, complemented, Sylow
993C2—21no—
994C2—21no—
995C2—34no—
996C2—44no—
997C2—44no—
998C2—62no—
999C2—124no—
1000C2—124no—
1001C2D3×#45512yesdirect product factor
1002C2C2×D3×#12011yescharacteristic
subgroupG/H
centerC22D3×#120
commutator, cosocleC2×C3×C4C25
FrattiniC2×C4C24×D3
FittingC2×C3×#455C2
socleC22×C3C2×#120
prime radicalC2×D3×H(5,𝔽2)C2
hypercenterC2×#455D3
hypocenterC3C22×#455
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#455

Complements

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

NH ≅ G/Ntype
2. C2×D3×#137C2semidirect
3. C2×D3×#124C2semidirect
4. C2×C3×#455C2semidirect
5. C2×#5242C2semidirect
6. C2×#5202C2semidirect
7. C2×#5061C2semidirect
8. D3×#455C2direct (N × H)
9. C2×#4825C2semidirect
10. C2×D3×#104C2semidirect
11. C2×#4746C2semidirect
12. C2×D3×#100C2semidirect
22. C22×D3×Q8C22semidirect
29. C2×C3×#137C22semidirect
30. C2×C3×#124C22semidirect
31. C2×#951C22semidirect
32. C2×#947C22semidirect
33. C2×#942C22semidirect
34. C2×#936C22semidirect
36. D3×#137C22semidirect
41. C2×#909C22semidirect
42. C2×D3×M16C22semidirect
44. D3×#124C22semidirect
47. C2×#875C22semidirect
48. C2×C42×D3C22semidirect
49. C3×#455C22semidirect
50. C2×C3×#104C22semidirect
51. C2×C3×#100C22semidirect
52. #5242C22semidirect
53. C2×#837C22semidirect
54. C2×#833C22semidirect
55. #5202C22semidirect
56. C2×#825C22semidirect
57. C2×#823C22semidirect
58. #5061C22semidirect
59. C2×#805C22semidirect
60. #4825C22semidirect
61. D3×#104C22semidirect
62. #4746C22semidirect
63. D3×#100C22semidirect
73. C2×#455D3direct (N × H)
83. C22×C3×Q8C23semidirect
110. C2×D3×Q8C23semidirect
152. C22×Dic6C23semidirect
154. C3×#137C23semidirect
157. C2×C3×M16C23semidirect
159. C3×#124C23semidirect
161. C2×C3×C42C23semidirect
164. #951C23semidirect
166. #947C23semidirect
170. #942C23semidirect
173. #936C23semidirect
178. C2×C4×Dic3C23semidirect
179. C2×#208C23semidirect
185. #909C23semidirect
187. D3×M16C23semidirect
195. #875C23semidirect
197. C42×D3C23semidirect
198. C3×#104C23semidirect
199. C3×#100C23semidirect
200. #837C23semidirect
201. #833C23semidirect
202. #825C23semidirect
203. #823C23semidirect
204. #805C23semidirect
227. C2×#137C2×D3semidirect
237. C2×#124C2×D3semidirect
245. #455C2×D3direct (N × H)
250. C2×#104C2×D3semidirect
254. C2×#100C2×D3semidirect
279. C2×C3×Q8C24semidirect
392. C2×Dic6C24semidirect
396. C3×M16C24semidirect
400. C3×C42C24semidirect
410. C4×Dic3C24semidirect
412. #208C24semidirect
462. C22×Q8C22×D3semidirect
504. #137C22×D3semidirect
519. C2×M16C22×D3semidirect
529. #124C22×D3semidirect
539. C2×C42C22×D3semidirect
543. #104C22×D3semidirect
546. #100C22×D3semidirect
705. C2×Q8C23×D3semidirect
796. M16C23×D3semidirect
808. C42C23×D3semidirect
834. C2×D3#455direct (N × H)
949. C2×C3C2×#455semidirect
954. D3C2×#455direct (N × H)
992. C3C22×#455semidirect
1001. C2D3×#455direct (N × H)

Maximal subgroups

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

subgroupindex
C2×D3×H(5,𝔽2)2
C2×D3×#1372
C2×D3×#1242
C2×C3×#4552
C2×#52422
C2×#52022
C2×#50612
D3×#4552
C2×#48252
C2×D3×#1042
C2×#47462
C2×D3×#1002
C22×#4553