Finite Group Databasebeta

← #11661723

Subgroups — #11661723

Order 768.

5058 conjugacy classes of subgroups.

The subgroup lattice has 1190 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#1004C211yesmaximal, characteristic, complemented
2C2×#5762C212yesmaximal, complemented
3#85985C211yesmaximal, characteristic, complemented
4C2×C3×#450C211yesmaximal, characteristic, complemented
5#84038C211yesmaximal, characteristic, complemented
6#83859C212yesmaximal, complemented
7#82735C211yesmaximal, characteristic, complemented
8#80149C214yesmaximal, complemented
9#80148C214yesmaximal, complemented
10#80147C212yesmaximal, complemented
11#80146C212yesmaximal, complemented
12#80145C212yesmaximal, complemented
13D3×#450C212yesmaximal, complemented
14#78747C212yesmaximal, complemented
15#78742C212yesmaximal, complemented
16#78610C211yesmaximal, characteristic, complemented
17#78600C211yesmaximal, characteristic, complemented
18#60373—31nomaximal, Sylow
19C23×C3×D4C2211yescharacteristic
20C23×#67—22no—
21C2×#1007C2211yescharacteristic, complemented
22C2×#1004—216no—
23C2×#1004—21no—
24C2×#1004—22no—
25C2×#1004—21no—
26C2×#1004C2214yes—
27C2×#1004C2212yes—
28C2×#1004C2212yes—
29C22×#237—21no—
30C22×#237C2212yes—
31C22×D3×D4—21no—
32C22×D3×D4C2212yes—
33C22×#235C2211yescharacteristic
34C22×#235C2211yescharacteristic
35C22×C3×SD16C2212yescomplemented
36C2×C3×C22⋊Q8C2211yescharacteristic, complemented
37#5816C2211yescharacteristic, complemented
38C2×#942C2212yescomplemented
39C2×#932C2212yescomplemented
40#5791C2211yescharacteristic, complemented
41#5762—216no—
42C2×#916C2214yescomplemented
43C2×#915C2214yescomplemented
44C2×#914C2214yescomplemented
45C2×D3×SD16C2214yescomplemented
46C2×#904C2212yescomplemented
47C2×#901C2212yescomplemented
48#5633—21no—
49#5632—21no—
50#5631—21no—
51#5630—21no—
52#5629C2212yescomplemented
53#5628C2212yescomplemented
54#5627C2212yescomplemented
55D3×C22⋊Q8C2212yescomplemented
56#5510C2211yescharacteristic, complemented
57#5507—22no—
58#5504C2211yescharacteristic, complemented
59#5490—22no—
60C3×#450C2212yescomplemented
61C3×#450C2212yescomplemented
62C3×#450C2214yescomplemented
63C2×C3×#102C2212yescomplemented
64C2×C3×C22⋊C8C2211yescharacteristic, complemented
65#5218C2212yescomplemented
66#5218C2212yescomplemented
67#5217C2212yescomplemented
68#5217C2212yescomplemented
69#5215C2212yescomplemented
70#5207C2211yescharacteristic, complemented
71#5173C2214yescomplemented
72#5173C2214yescomplemented
73#5169C2214yescomplemented
74#5169C2214yescomplemented
75#5113C2212yescomplemented
76#5110C2212yescomplemented
77#5050C2212yescomplemented
78#5047C2214yescomplemented
79#5046C2212yescomplemented
80#4966C2212yescomplemented
81#4783C2214yescomplemented
82#4781C2214yescomplemented
83#4776C2214yescomplemented
84#4773C2214yescomplemented
85#4772C2214yescomplemented
86#4771C2214yescomplemented
87#4770C2214yescomplemented
88D3×#102C2214yescomplemented
89#4739C2211yescharacteristic, complemented
90#4738C2211yescharacteristic, complemented
91#4734C2212yescomplemented
92#4733C2212yescomplemented
93#4732C2211yescharacteristic, complemented
94#4731C2211yescharacteristic, complemented
95#4727C2214yescomplemented
96#4726C2212yescomplemented
97D3×C22⋊C8C2212yescomplemented
98C22×H(5,𝔽2)—31no—
99C2×#577—32no—
100#3489—31no—
101#3012—34no—
102#3012—32no—
103#3009—34no—
104#3009—32no—
105#3007—32no—
106#3007—31no—
107#3003—32no—
108#3003—31no—
109#3002—32no—
110#3002—31no—
111C2×#450—32no—
112C2×#450D311yescharacteristic, complemented
113#2897—32no—
114#2880—31no—
115C25×C3—21no—
116C24×D3—22no—
117C22×C3×Q8C2311yescharacteristic, complemented
118C22×C3×D4—28no—
119C22×C3×D4—21no—
120C22×C3×D4—21no—
121C22×C3×D4—21no—
122C22×C3×D4C2312yes—
123C22×C3×D4C2312yes—
124C22×C3×D4C2312yes—
125C23×C3×C4C2311yescharacteristic
126C22×#67—232no—
127C22×#67—21no—
128C22×#67—22no—
129C22×#67—24no—
130C22×#67—24no—
131C22×#67—24no—
132C22×#67—24no—
133C22×#67—22no—
134C22×#67D412yes—
135C23×Dic3—22no—
136#1007—28no—
137C2×#239—21no—
138C2×#239C2312yescomplemented
139C2×D3×Q8—21no—
140C2×D3×Q8C2312yescomplemented
141#1004—232no—
142#1004—216no—
143#1004—216no—
144#1004—28no—
145#1004—216no—
146#1004—216no—
147#1004—28no—
148#1004—28no—
149#1004D4116yescomplemented
150C2×#237—216no—
151C2×#237—216no—
152C2×#237—22no—
153C2×#237—22no—
154C2×#237—24no—
155C2×#237—22no—
156C2×#237—22no—
157C2×#237C2314yes—
158C2×#237C2314yes—
159C2×D3×D4—216no—
160C2×D3×D4—216no—
161C2×D3×D4—24no—
162C2×D3×D4—22no—
163C2×D3×D4—22no—
164C2×D3×D4—22no—
165C2×D3×D4—22no—
166C2×D3×D4C2314yes—
167C2×D3×D4C2314yes—
168C2×#235—21no—
169C2×#235—21no—
170C2×#235—28no—
171C2×#235—28no—
172C2×#235—22no—
173C2×#235D411yescharacteristic
174C2×#235D412yes—
175C2×#235D411yescharacteristic
176C2×#235C2312yes—
177C2×#235C2311yescharacteristic
178C2×#235C2311yescharacteristic
179C2×#235C2312yes—
180C2×#235C2312yes—
181C2×#235C2311yescharacteristic, complemented
182C22×D12D411yescharacteristic
183C22×D12C2311yescharacteristic
184C22×C4×D3—21no—
185C22×C4×D3C2312yes—
186C22×Dic6D411yescharacteristic
187C22×Dic6C2311yescharacteristic
188C2×C3×SD16—28no—
189C2×C3×SD16C2314yescomplemented
190C2×C3×SD16C2314yescomplemented
191C22×C3×C8C2312yescomplemented
192C3×C22⋊Q8—21no—
193C3×C22⋊Q8—21no—
194C3×C22⋊Q8C2312yes—
195C3×C22⋊Q8C2312yescomplemented
196C2×C3×C4⋊C4—21no—
197C2×C3×C4⋊C4C2311yescharacteristic, complemented
198C2×C3×C22⋊C4—21no—
199#953—21no—
200#947—21no—
201#946C2312yescomplemented
202#946C2312yescomplemented
203#944—21no—
204C2×#216C2314yescomplemented
205#942—28no—
206C2×#215C2314yescomplemented
207C2×#214C2314yescomplemented
208#932—28no—
209C2×#213C2314yescomplemented
210#930—22no—
211#930C2311yescharacteristic
212#930C2311yescharacteristic, complemented
213#929—21no—
214#929—22no—
215C4×#67—21no—
216C4×#67—21no—
217C4×#67—22no—
218#926C2311yescharacteristic, complemented
219#924C2311yescharacteristic
220#924C2311yescharacteristic, complemented
221C2×#208C2312yescomplemented
222#916—216no—
223#915—216no—
224#914—216no—
225D3×SD16—216no—
226C2×Dic12C2312yescomplemented
227#904—28no—
228C2×D24C2312yescomplemented
229C2×#204C2312yescomplemented
230C2×#204C2312yescomplemented
231#901—28no—
232C2×ΓL(1,𝔽25)C2314yescomplemented
233C2×D3×C8C2314yescomplemented
234#897—21no—
235#897C2312yescomplemented
236#896—22no—
237#896—22no—
238#895—21no—
239#895—22no—
240#895C2312yescomplemented
241#894—22no—
242#894—22no—
243#893—21no—
244#893—22no—
245#892C2312yescomplemented
246D3×C4⋊C4—22no—
247D3×C4⋊C4C2312yescomplemented
248#888—22no—
249#887—21no—
250#885—22no—
251#884—22no—
252#884—22no—
253#883—22no—
254#882—22no—
255#67⋊C4—22no—
256D3×C22⋊C4—22no—
257#878—22no—
258C3×#102C2314yescomplemented
259C3×#102C2314yescomplemented
260C3×C22⋊C8C2311yescharacteristic
261C3×C22⋊C8C2311yescharacteristic
262C3×C22⋊C8C2312yescomplemented
263#832C2314yescomplemented
264#832C2314yescomplemented
265#830C2312yes—
266#830C2312yescomplemented
267#821C2312yescomplemented
268#821C2312yescomplemented
269(C2×D3)⋊C8C2314yescomplemented
270(C2×D3)⋊C8C2314yescomplemented
271#816C2312yescomplemented
272#816C2312yescomplemented
273#810C2314yescomplemented
274#809C2314yescomplemented
275C2×2−1+4—31no—
276C2×H(5,𝔽2)—32no—
277C2×H(5,𝔽2)—34no—
278C2×H(5,𝔽2)—32no—
279C2×H(5,𝔽2)—62no—
280C2×H(5,𝔽2)—61no—
281C2×H(5,𝔽2)—61no—
282C2×H(5,𝔽2)—616no—
283C22×#41—31no—
284C22×#41—32no—
285C22×#41—31no—
286C22×#41—61no—
287C23×D4—32no—
288C23×D4—61no—
289C23×D4—62no—
290C23×D4C2×D311yescharacteristic
291#577—616no—
292C2×#137—32no—
293C2×#137—34no—
294C2×AGL(1,ℤ/8)—32no—
295C2×AGL(1,ℤ/8)—34no—
296C2×#135—34no—
297C2×#135—32no—
298C22×SD16—34no—
299C22×SD16C2×D312yescomplemented
300C2×#131—32no—
301D4×Q8—61no—
302#548—61no—
303#547—62no—
304#547—61no—
305#546—62no—
306#546—61no—
307#537—32no—
308#537—31no—
309#536—31no—
310#536—32no—
311#525—31no—
312#525—32no—
313C2×C22⋊Q8—32no—
314C2×C22⋊Q8C2×D311yescharacteristic, complemented
315#520—31no—
316#452—34no—
317#452—34no—
318#452—34no—
319#452—34no—
320#452—32no—
321#451—32no—
322#451—31no—
323#450—32no—
324#450—32no—
325#450—34no—
326#450—34no—
327#450—32no—
328#450—34no—
329#450—31no—
330#450C2×D312yescomplemented
331#450C2×D312yescomplemented
332#450C2×D314yescomplemented
333#449—34no—
334#449—32no—
335#448—31no—
336#447—32no—
337#447—32no—
338#447—34no—
339#447—31no—
340#418—32no—
341#418—34no—
342#417—32no—
343#417—34no—
344#416—32no—
345#416—34no—
346C2×#102—34no—
347C2×#102C2×D312yescomplemented
348#408—32no—
349#408—34no—
350#407—31no—
351#407—32no—
352C2×C22⋊C8—32no—
353C2×C22⋊C8C2×D311yescharacteristic, complemented
354C24×C3—28no—
355C24×C3—22no—
356C24×C3—22no—
357C24×C3—22no—
358C24×C3—82no—
359C24×C3—82no—
360C24×C3C2×D411yescharacteristic
361C23×D3—21no—
362C23×D3—216no—
363C23×D3—24no—
364C23×D3—24no—
365C23×D3—84no—
366C23×D3—84no—
367C23×D3C2×D412yes—
368C2×C3×Q8—21no—
369C2×C3×Q8—24no—
370C2×C3×Q8C2412yes—
371C2×C3×D4—28no—
372C2×C3×D4—28no—
373C2×C3×D4—28no—
374C2×C3×D4—28no—
375C2×C3×D4—28no—
376C2×C3×D4—22no—
377C2×C3×D4—22no—
378C2×C3×D4—22no—
379C2×C3×D4—24no—
380C2×C3×D4C2×D418yes—
381C2×C3×D4C2414yes—
382C22×C3×C4—24no—
383C22×C3×C4—21no—
384C22×C3×C4—21no—
385C22×C3×C4C2×D411yescharacteristic
386C22×C3×C4C2×D411yescharacteristic
387C22×C3×C4C2×D411yescharacteristic
388C22×C3×C4C2411yescharacteristic
389C22×C3×C4C2411yescharacteristic
390C22×C3×C4C2411yescharacteristic
391C2×#67—28no—
392C2×#67—216no—
393C2×#67—216no—
394C2×#67—232no—
395C2×#67—232no—
396C2×#67—232no—
397C2×#67—22no—
398C2×#67—22no—
399C2×#67—24no—
400C2×#67—24no—
401C2×#67—28no—
402C2×#67—232no—
403C2×#67—21no—
404C2×#67—21no—
405C2×#67—21no—
406C2×#67—24no—
407C2×#67—24no—
408C2×#67C2×D412yes—
409C2×#67C2×D412yes—
410C2×#67C2×D412yes—
411C2×#67C2×D412yes—
412C22×Dic3—216no—
413C22×Dic3—21no—
414C22×Dic3—24no—
415C22×Dic3—24no—
416C22×Dic3C2×D412yes—
417#239—28no—
418#239—44no—
419D3×Q8—28no—
420D3×Q8—44no—
421#237—216no—
422#237—216no—
423#237—216no—
424#237—232no—
425#237—28no—
426#237—28no—
427#237—216no—
428#237—28no—
429#237C2×D4116yes—
430D3×D4—232no—
431D3×D4—216no—
432D3×D4—216no—
433D3×D4—216no—
434D3×D4—28no—
435D3×D4—216no—
436D3×D4—28no—
437D3×D4—28no—
438D3×D4C2×D4116yes—
439#235—28no—
440#235—28no—
441#235—24no—
442#235—24no—
443#235—28no—
444#235—24no—
445#235—24no—
446#235—28no—
447#235—24no—
448#235—24no—
449#235—24no—
450#235—48no—
451#235C2×D418yes—
452#235C2×D418yes—
453C2×D12—21no—
454C2×D12—24no—
455C2×D12—24no—
456C2×D12—22no—
457C2×D12—22no—
458C2×D12C2×D412yes—
459C2×D12C2×D411yescharacteristic
460C2×D12C2×D411yescharacteristic
461C2×D12C2411yescharacteristic
462C2×D12C2412yes—
463C2×C4×D3—28no—
464C2×C4×D3—22no—
465C2×C4×D3—22no—
466C2×C4×D3—28no—
467C2×C4×D3—22no—
468C2×C4×D3—21no—
469C2×C4×D3—22no—
470C2×C4×D3—22no—
471C2×C4×D3C2×D412yes—
472C2×C4×D3C2×D412yes—
473C2×C4×D3C2412yes—
474C2×C4×D3C2412yes—
475C2×Dic6—21no—
476C2×Dic6—24no—
477C2×Dic6—24no—
478C2×Dic6—22no—
479C2×Dic6C2×D412yes—
480C2×Dic6C2×D411yescharacteristic
481C2×Dic6C2×D411yescharacteristic
482C2×Dic6C2411yescharacteristic
483C2×Dic6C2412yes—
484C3×SD16—28no—
485C3×SD16—28no—
486C2×C3×C8—24no—
487C2×C3×C8C2412yes—
488C2×C3×C8C2412yes—
489C3×C4⋊C4—21no—
490C3×C4⋊C4—22no—
491C3×C4⋊C4—22no—
492C3×C4⋊C4C2412yes—
493C3×C22⋊C4—22no—
494C3×C22⋊C4—22no—
495#217—21no—
496#217—21no—
497#217—21no—
498#216—28no—
499#215—28no—
500#214—28no—
501#213—28no—
502(C2×D3)⋊C4—22no—
503(C2×D3)⋊C4—22no—
504(C2×D3)⋊C4—22no—
505(C2×D3)⋊C4—22no—
506(C2×D3)⋊C4—21no—
507(C2×D3)⋊C4—21no—
508(C2×D3)⋊C4—22no—
509C4⋊Dic3—22no—
510C4⋊Dic3C2411yescharacteristic
511C4⋊Dic3C2411yescharacteristic
512Dic3⋊C4—21no—
513Dic3⋊C4—21no—
514Dic3⋊C4—22no—
515Dic3⋊C4—22no—
516Dic3⋊C4—22no—
517C4×Dic3—21no—
518C4×Dic3—22no—
519#208—24no—
520C2×C3⋊C8C2414yes—
521Dic12—24no—
522D24—24no—
523#204—24no—
524#204—24no—
525ΓL(1,𝔽25)—28no—
526D3×C8—28no—
527C25—21no—
528C25—62no—
5292−1+4—68no—
530H(5,𝔽2)—316no—
531H(5,𝔽2)—616no—
532H(5,𝔽2)—616no—
533H(5,𝔽2)—68no—
534H(5,𝔽2)—68no—
535H(5,𝔽2)—616no—
536H(5,𝔽2)—632no—
537H(5,𝔽2)—616no—
538H(5,𝔽2)—68no—
539C2×#41—31no—
540C2×#41—32no—
541C2×#41—31no—
542C2×#41—31no—
543C2×#41—32no—
544C2×#41—31no—
545C2×#41—32no—
546C2×#41—34no—
547C2×#41—34no—
548C2×#41—32no—
549C2×#41—31no—
550C2×#41—32no—
551C2×#41—62no—
552C2×#41—68no—
553C2×#41—68no—
554C2×#41—62no—
555C2×#41—62no—
556C2×#41—62no—
557C2×#41—64no—
558C2×#41—62no—
559C2×#41—616no—
560C2×#41—616no—
561C2×#41—61no—
562C2×#41—61no—
563C2×#41—61no—
564C22×Q8—31no—
565C22×Q8—32no—
566C22×Q8—31no—
567C22×Q8—61no—
568C22×Q8C22×D311yescharacteristic, complemented
569C22×D4—28no—
570C22×D4—21no—
571C22×D4—21no—
572C22×D4—21no—
573C22×D4—34no—
574C22×D4—32no—
575C22×D4—34no—
576C22×D4—31no—
577C22×D4—31no—
578C22×D4—62no—
579C22×D4—62no—
580C22×D4—62no—
581C22×D4—616no—
582C22×D4—62no—
583C22×D4—64no—
584C22×D4—62no—
585C22×D4—616no—
586C22×D4—64no—
587C22×D4—64no—
588C22×D4—64no—
589C22×D4—64no—
590C22×D4—62no—
591C22×D4—632no—
592C22×D4—61no—
593C22×D4C22×D312yes—
594C22×D4C22×D312yes—
595C22×D4C22×D312yes—
596C23×C4—32no—
597C23×C4—62no—
598C23×C4—61no—
599C23×C4C22×D311yescharacteristic
600#137—616no—
601#137—68no—
602AGL(1,ℤ/8)—616no—
603AGL(1,ℤ/8)—68no—
604#135—68no—
605#135—616no—
606C2×Q16—34no—
607C2×Q16—32no—
608C2×SD16—28no—
609C2×SD16—34no—
610C2×SD16—34no—
611C2×SD16—32no—
612C2×SD16—32no—
613C2×SD16—616no—
614C2×SD16C22×D314yescomplemented
615C2×SD16C22×D314yescomplemented
616C2×D8—34no—
617C2×D8—32no—
618#131—68no—
619C2×M16—32no—
620C2×M16—34no—
621C22×C8—34no—
622C22×C8C22×D312yescomplemented
623C4⋊Q8—62no—
624C4⋊Q8—61no—
625#124—62no—
626#124—61no—
627#123—62no—
628#123—62no—
629#123—62no—
630#123—62no—
631#123—61no—
632C22⋊Q8—21no—
633C22⋊Q8—21no—
634C22⋊Q8—32no—
635C22⋊Q8—32no—
636C22⋊Q8—31no—
637C22⋊Q8—31no—
638C22⋊Q8—32no—
639C22⋊Q8—62no—
640C22⋊Q8—62no—
641C22⋊Q8—62no—
642C22⋊Q8—61no—
643C22⋊Q8C22×D312yes—
644C22⋊Q8C22×D312yescomplemented
645#121—31no—
646#121—31no—
647#121—32no—
648#121—62no—
649#121—62no—
650#121—62no—
651#121—61no—
652#121—62no—
653#120—62no—
654#120—61no—
655C4×Q8—61no—
656C4×D4—62no—
657C4×D4—62no—
658C4×D4—61no—
659C4×D4—62no—
660C4×D4—61no—
661C4×D4—61no—
662#117—31no—
663#117—32no—
664C2×C4⋊C4—21no—
665C2×C4⋊C4—32no—
666C2×C4⋊C4—62no—
667C2×C4⋊C4C22×D311yescharacteristic, complemented
668C2×C22⋊C4—21no—
669C2×C22⋊C4—62no—
670#103—32no—
671#103—32no—
672#103—34no—
673#102—34no—
674#102—34no—
675#102—32no—
676#102—32no—
677#102—34no—
678#102C22×D314yescomplemented
679#102C22×D314yescomplemented
680C22⋊C8—32no—
681C22⋊C8—32no—
682C22⋊C8—34no—
683C22⋊C8—34no—
684C22⋊C8C22×D311yescharacteristic
685C22⋊C8C22×D311yescharacteristic
686C22⋊C8C22×D312yescomplemented
687C23×C3—28no—
688C23×C3—28no—
689C23×C3—22no—
690C23×C3—22no—
691C23×C3—24no—
692C23×C3—28no—
693C23×C3—41no—
694C23×C3—44no—
695C23×C3—44no—
696C23×C3—82no—
697C23×C3—82no—
698C23×C3—82no—
699C23×C3—82no—
700C23×C3—816no—
701C23×C3C22×D411yescharacteristic
702C23×C3C22×D411yescharacteristic
703C23×C3C22×D411yescharacteristic
704C22×D3—24no—
705C22×D3—24no—
706C22×D3—22no—
707C22×D3—216no—
708C22×D3—24no—
709C22×D3—216no—
710C22×D3—21no—
711C22×D3—42no—
712C22×D3—42no—
713C22×D3—42no—
714C22×D3—84no—
715C22×D3—84no—
716C22×D3—84no—
717C22×D3—84no—
718C22×D3—832no—
719C22×D3C22×D412yes—
720C22×D3C22×D412yes—
721C3×Q8—24no—
722C3×Q8—42no—
723C3×D4—28no—
724C3×D4—28no—
725C3×D4—28no—
726C3×D4—24no—
727C3×D4C22×D418yes—
728C2×C3×C4—22no—
729C2×C3×C4—22no—
730C2×C3×C4—22no—
731C2×C3×C4—22no—
732C2×C3×C4—22no—
733C2×C3×C4—22no—
734C2×C3×C4—22no—
735C2×C3×C4—42no—
736C2×C3×C4—81no—
737C2×C3×C4C22×D411yescharacteristic
738C2×C3×C4C22×D411yescharacteristic
739C2×C3×C4C22×D411yescharacteristic
740C2×C3×C4C22×D414yes—
741C2×C3×C4C2511yescharacteristic
742#67—28no—
743#67—216no—
744#67—216no—
745#67—24no—
746#67—28no—
747#67—24no—
748#67—216no—
749#67—24no—
750#67—216no—
751#67—42no—
752#67—42no—
753#67—81no—
754#67#12018yes—
755C2×Dic3—24no—
756C2×Dic3—216no—
757C2×Dic3—22no—
758C2×Dic3—24no—
759C2×Dic3—216no—
760C2×Dic3—21no—
761C2×Dic3—21no—
762C2×Dic3—21no—
763C2×Dic3C22×D412yes—
764C2×Dic3C22×D412yes—
765D12—24no—
766D12—24no—
767D12—22no—
768D12—22no—
769D12—22no—
770D12—44no—
771D12—82no—
772D12#12014yes—
773D12C22×D414yes—
774C4×D3—28no—
775C4×D3—24no—
776C4×D3—28no—
777C4×D3—24no—
778C4×D3—24no—
779C4×D3—44no—
780C4×D3—42no—
781C4×D3—44no—
782C4×D3—82no—
783C4×D3C22×D418yes—
784Dic6—24no—
785Dic6—22no—
786Dic6—22no—
787Dic6—24no—
788Dic6—22no—
789Dic6—44no—
790Dic6#12014yes—
791Dic6C22×D414yes—
792C3×C8—22no—
793C3×C8—22no—
794C3⋊C8—24no—
795C24—28no—
796C24—22no—
797C24—22no—
798C24—22no—
799C24—32no—
800C24—64no—
801C24—64no—
802C24—616no—
803C24—61no—
804C24—82no—
805C24—82no—
806C24—244no—
807C24—244no—
808C24D3×D411yescharacteristic
809#41—38no—
810#41—316no—
811#41—38no—
812#41—68no—
813#41—68no—
814#41—64no—
815#41—64no—
816#41—64no—
817#41—64no—
818#41—68no—
819#41—68no—
820#41—68no—
821#41—68no—
822#41—68no—
823#41—616no—
824#41—616no—
825#41—616no—
826#41—632no—
827#41—616no—
828#41—68no—
829#41—64no—
830#41—64no—
831#41—64no—
832#41—128no—
833#41—124no—
834C2×Q8—21no—
835C2×Q8—24no—
836C2×Q8—31no—
837C2×Q8—32no—
838C2×Q8—31no—
839C2×Q8—32no—
840C2×Q8—31no—
841C2×Q8—62no—
842C2×Q8—64no—
843C2×Q8—64no—
844C2×Q8—68no—
845C2×Q8—61no—
846C2×Q8—124no—
847C2×Q8C23×D312yes—
848C2×D4—28no—
849C2×D4—28no—
850C2×D4—28no—
851C2×D4—28no—
852C2×D4—28no—
853C2×D4—22no—
854C2×D4—22no—
855C2×D4—22no—
856C2×D4—24no—
857C2×D4—32no—
858C2×D4—316no—
859C2×D4—32no—
860C2×D4—32no—
861C2×D4—32no—
862C2×D4—31no—
863C2×D4—32no—
864C2×D4—31no—
865C2×D4—32no—
866C2×D4—31no—
867C2×D4—64no—
868C2×D4—64no—
869C2×D4—62no—
870C2×D4—62no—
871C2×D4—68no—
872C2×D4—64no—
873C2×D4—64no—
874C2×D4—68no—
875C2×D4—616no—
876C2×D4—616no—
877C2×D4—616no—
878C2×D4—632no—
879C2×D4—616no—
880C2×D4—68no—
881C2×D4—632no—
882C2×D4—64no—
883C2×D4—64no—
884C2×D4—616no—
885C2×D4—616no—
886C2×D4—68no—
887C2×D4—632no—
888C2×D4—632no—
889C2×D4—632no—
890C2×D4—62no—
891C2×D4—62no—
892C2×D4—68no—
893C2×D4—61no—
894C2×D4—61no—
895C2×D4—61no—
896C2×D4—61no—
897C2×D4D3×D418yes—
898C2×D4C23×D314yes—
899C22×C4—24no—
900C22×C4—21no—
901C22×C4—21no—
902C22×C4—32no—
903C22×C4—32no—
904C22×C4—32no—
905C22×C4—32no—
906C22×C4—32no—
907C22×C4—68no—
908C22×C4—62no—
909C22×C4—68no—
910C22×C4—62no—
911C22×C4—62no—
912C22×C4—64no—
913C22×C4—64no—
914C22×C4—616no—
915C22×C4—61no—
916C22×C4—62no—
917C22×C4—62no—
918C22×C4—61no—
919C22×C4D3×D411yescharacteristic
920C22×C4D3×D411yescharacteristic
921C22×C4D3×D411yescharacteristic
922C22×C4C23×D311yescharacteristic
923C22×C4C23×D311yescharacteristic
924C22×C4C23×D311yescharacteristic
925Q16—64no—
926Q16—68no—
927SD16—28no—
928SD16—28no—
929SD16—64no—
930SD16—64no—
931SD16—68no—
932SD16—68no—
933D8—64no—
934D8—68no—
935M16—68no—
936M16—64no—
937C2×C8—24no—
938C2×C8—34no—
939C2×C8—68no—
940C2×C8C23×D312yes—
941C2×C8C23×D312yes—
942C4⋊C4—22no—
943C4⋊C4—22no—
944C4⋊C4—21no—
945C4⋊C4—31no—
946C4⋊C4—31no—
947C4⋊C4—62no—
948C4⋊C4—62no—
949C4⋊C4—62no—
950C4⋊C4—62no—
951C4⋊C4—61no—
952C4⋊C4—61no—
953C4⋊C4C23×D312yes—
954C22⋊C4—22no—
955C22⋊C4—22no—
956C22⋊C4—62no—
957C22⋊C4—62no—
958C22⋊C4—62no—
959C22⋊C4—62no—
960C22⋊C4—62no—
961C22⋊C4—61no—
962C22⋊C4—61no—
963C22⋊C4—61no—
964C22⋊C4—61no—
965C22⋊C4—61no—
966C42—62no—
967C42—61no—
968C22×C3—21no—
969C22×C3—21no—
970C22×C3—21no—
971C22×C3—21no—
972C22×C3—21no—
973C22×C3—28no—
974C22×C3—21no—
975C22×C3—21no—
976C22×C3—44no—
977C22×C3—416no—
978C22×C3—44no—
979C22×C3—44no—
980C22×C3—88no—
981C22×C3—88no—
982C22×C3C2×#12012yes—
983C22×C3#57712yescomplemented
984C22×C3C23×D411yescharacteristic
985C2×D3—22no—
986C2×D3—22no—
987C2×D3—22no—
988C2×D3—22no—
989C2×D3—24no—
990C2×D3—22no—
991C2×D3—48no—
992C2×D3—48no—
993C2×D3—42no—
994C2×D3—42no—
995C2×D3—41no—
996C2×D3—41no—
997C2×D3—41no—
998C2×D3—816no—
999C2×D3—816no—
1000C2×D3C2×#12014yes—
1001C3×C4—21no—
1002C3×C4—21no—
1003C3×C4—42no—
1004C3×C4—42no—
1005C3×C4C2×#12012yes—
1006C3×C4C23×D412yes—
1007Dic3—22no—
1008Dic3—24no—
1009Dic3—41no—
1010Dic3—41no—
1011Dic3—41no—
1012Dic3C2×#12014yes—
1013C23—28no—
1014C23—28no—
1015C23—24no—
1016C23—22no—
1017C23—22no—
1018C23—28no—
1019C23—32no—
1020C23—32no—
1021C23—41no—
1022C23—44no—
1023C23—44no—
1024C23—64no—
1025C23—616no—
1026C23—64no—
1027C23—616no—
1028C23—62no—
1029C23—64no—
1030C23—61no—
1031C23—82no—
1032C23—82no—
1033C23—82no—
1034C23—82no—
1035C23—816no—
1036C23—122no—
1037C23—122no—
1038C23—122no—
1039C23—244no—
1040C23—244no—
1041C23—244no—
1042C23—244no—
1043C23—2432no—
1044C23C2×D3×D411yescharacteristic
1045C23C2×D3×D411yescharacteristic
1046C23C2×D3×D411yescharacteristic
1047Q8—24no—
1048Q8—34no—
1049Q8—34no—
1050Q8—42no—
1051Q8—64no—
1052Q8—64no—
1053Q8—62no—
1054Q8—62no—
1055Q8—62no—
1056Q8—124no—
1057D4—28no—
1058D4—28no—
1059D4—24no—
1060D4—28no—
1061D4—38no—
1062D4—34no—
1063D4—34no—
1064D4—64no—
1065D4—64no—
1066D4—64no—
1067D4—616no—
1068D4—64no—
1069D4—616no—
1070D4—616no—
1071D4—68no—
1072D4—616no—
1073D4—64no—
1074D4—68no—
1075D4—62no—
1076D4—62no—
1077D4—62no—
1078D4—124no—
1079D4—122no—
1080D4—122no—
1081D4—242no—
1082D4—241no—
1083D4C2×D3×D418yes—
1084C2×C4—22no—
1085C2×C4—22no—
1086C2×C4—22no—
1087C2×C4—22no—
1088C2×C4—22no—
1089C2×C4—22no—
1090C2×C4—22no—
1091C2×C4—32no—
1092C2×C4—38no—
1093C2×C4—32no—
1094C2×C4—42no—
1095C2×C4—64no—
1096C2×C4—64no—
1097C2×C4—68no—
1098C2×C4—64no—
1099C2×C4—616no—
1100C2×C4—64no—
1101C2×C4—616no—
1102C2×C4—62no—
1103C2×C4—64no—
1104C2×C4—68no—
1105C2×C4—61no—
1106C2×C4—61no—
1107C2×C4—61no—
1108C2×C4—81no—
1109C2×C4—124no—
1110C2×C4—124no—
1111C2×C4—122no—
1112C2×C4—242no—
1113C2×C4C2×D3×D411yescharacteristic
1114C2×C4C2×D3×D411yescharacteristic
1115C2×C4C2×D3×D414yes—
1116C2×C4C2×D3×D411yescharacteristic
1117C2×C4C24×D311yescharacteristic
1118C8—22no—
1119C8—22no—
1120C8—64no—
1121C2×C3—22no—
1122C2×C3—22no—
1123C2×C3—48no—
1124C2×C3—41no—
1125C2×C3C22×#12011yescharacteristic
1126C2×C3C2×#57711yescharacteristic
1127C2×C3#358511yescharacteristic
1128D3—24no—
1129D3—42no—
1130D3—44no—
1131D3—81no—
1132C22—21no—
1133C22—21no—
1134C22—21no—
1135C22—21no—
1136C22—21no—
1137C22—21no—
1138C22—21no—
1139C22—28no—
1140C22—34no—
1141C22—44no—
1142C22—416no—
1143C22—44no—
1144C22—44no—
1145C22—62no—
1146C22—62no—
1147C22—62no—
1148C22—62no—
1149C22—64no—
1150C22—62no—
1151C22—88no—
1152C22—88no—
1153C22—128no—
1154C22—128no—
1155C22—122no—
1156C22—122no—
1157C22—121no—
1158C22—121no—
1159C22—121no—
1160C22—2416no—
1161C22—2416no—
1162C22D3×#12012yes—
1163C22#576212yescomplemented
1164C22C22×D3×D411yescharacteristic
1165C4—21no—
1166C4—21no—
1167C4—34no—
1168C4—42no—
1169C4—42no—
1170C4—62no—
1171C4—64no—
1172C4—121no—
1173C4—121no—
1174C4—121no—
1175C4D3×#12012yes—
1176C4C22×D3×D412yes—
1177C3#6037311yescharacteristic, complemented, Sylow
1178C2—22no—
1179C2—22no—
1180C2—41no—
1181C2—48no—
1182C2—64no—
1183C2—122no—
1184C2—124no—
1185C2—241no—
1186C2C2×D3×#12011yescharacteristic
1187C2C2×#576211yescharacteristic
1188C2#8719211yescharacteristic
subgroupG/H
centerC22C22×D3×D4
commutator, cosocleC2×C3×C4C25
FrattiniC2×C4C24×D3
FittingC2×C3×#450C2
socleC22×C3C23×D4
hypercenterC2×#450D3
hypocenterC3#60373
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#450

Complements

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

NH ≅ G/Ntype
1. C22×#1004C2semidirect
2. C2×#5762C2semidirect
3. #85985C2semidirect
4. C2×C3×#450C2semidirect
5. #84038C2semidirect
6. #83859C2semidirect
7. #82735C2semidirect
8. #80149C2semidirect
9. #80148C2semidirect
10. #80147C2semidirect
11. #80146C2semidirect
12. #80145C2semidirect
13. D3×#450C2semidirect
14. #78747C2semidirect
15. #78742C2semidirect
16. #78610C2semidirect
17. #78600C2semidirect
21. C2×#1007C22semidirect
35. C22×C3×SD16C22semidirect
36. C2×C3×C22⋊Q8C22semidirect
37. #5816C22semidirect
38. C2×#942C22semidirect
39. C2×#932C22semidirect
40. #5791C22semidirect
42. C2×#916C22semidirect
43. C2×#915C22semidirect
44. C2×#914C22semidirect
45. C2×D3×SD16C22semidirect
46. C2×#904C22semidirect
47. C2×#901C22semidirect
52. #5629C22semidirect
53. #5628C22semidirect
54. #5627C22semidirect
55. D3×C22⋊Q8C22semidirect
56. #5510C22semidirect
58. #5504C22semidirect
60. C3×#450C22semidirect
61. C3×#450C22semidirect
62. C3×#450C22semidirect
63. C2×C3×#102C22semidirect
64. C2×C3×C22⋊C8C22semidirect
65. #5218C22semidirect
66. #5218C22semidirect
67. #5217C22semidirect
68. #5217C22semidirect
69. #5215C22semidirect
70. #5207C22semidirect
71. #5173C22semidirect
72. #5173C22semidirect
73. #5169C22semidirect
74. #5169C22semidirect
75. #5113C22semidirect
76. #5110C22semidirect
77. #5050C22semidirect
78. #5047C22semidirect
79. #5046C22semidirect
80. #4966C22semidirect
81. #4783C22semidirect
82. #4781C22semidirect
83. #4776C22semidirect
84. #4773C22semidirect
85. #4772C22semidirect
86. #4771C22semidirect
87. #4770C22semidirect
88. D3×#102C22semidirect
89. #4739C22semidirect
90. #4738C22semidirect
91. #4734C22semidirect
92. #4733C22semidirect
93. #4732C22semidirect
94. #4731C22semidirect
95. #4727C22semidirect
96. #4726C22semidirect
97. D3×C22⋊C8C22semidirect
112. C2×#450D3semidirect
117. C22×C3×Q8C23semidirect
138. C2×#239C23semidirect
140. C2×D3×Q8C23semidirect
149. #1004D4semidirect
181. C2×#235C23semidirect
189. C2×C3×SD16C23semidirect
190. C2×C3×SD16C23semidirect
191. C22×C3×C8C23semidirect
195. C3×C22⋊Q8C23semidirect
197. C2×C3×C4⋊C4C23semidirect
201. #946C23semidirect
202. #946C23semidirect
204. C2×#216C23semidirect
206. C2×#215C23semidirect
207. C2×#214C23semidirect
209. C2×#213C23semidirect
212. #930C23semidirect
218. #926C23semidirect
220. #924C23semidirect
221. C2×#208C23semidirect
226. C2×Dic12C23semidirect
228. C2×D24C23semidirect
229. C2×#204C23semidirect
230. C2×#204C23semidirect
232. C2×ΓL(1,𝔽25)C23semidirect
233. C2×D3×C8C23semidirect
235. #897C23semidirect
240. #895C23semidirect
245. #892C23semidirect
247. D3×C4⋊C4C23semidirect
258. C3×#102C23semidirect
259. C3×#102C23semidirect
262. C3×C22⋊C8C23semidirect
263. #832C23semidirect
264. #832C23semidirect
266. #830C23semidirect
267. #821C23semidirect
268. #821C23semidirect
269. (C2×D3)⋊C8C23semidirect
270. (C2×D3)⋊C8C23semidirect
271. #816C23semidirect
272. #816C23semidirect
273. #810C23semidirect
274. #809C23semidirect
299. C22×SD16C2×D3semidirect
314. C2×C22⋊Q8C2×D3semidirect
330. #450C2×D3semidirect
331. #450C2×D3semidirect
332. #450C2×D3semidirect
347. C2×#102C2×D3semidirect
353. C2×C22⋊C8C2×D3semidirect
568. C22×Q8C22×D3semidirect
614. C2×SD16C22×D3semidirect
615. C2×SD16C22×D3semidirect
622. C22×C8C22×D3semidirect
644. C22⋊Q8C22×D3semidirect
667. C2×C4⋊C4C22×D3semidirect
678. #102C22×D3semidirect
679. #102C22×D3semidirect
686. C22⋊C8C22×D3semidirect
983. C22×C3#577semidirect
1163. C22#5762semidirect
1177. C3#60373semidirect

Maximal subgroups

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

subgroupindex
C22×#10042
C2×#57622
#859852
C2×C3×#4502
#840382
#838592
#827352
#801492
#801482
#801472
#801462
#801452
D3×#4502
#787472
#787422
#786102
#786002
#603733