Finite Group Databasebeta

← #11661740

Subgroups — #11661740

Order 768.

4782 conjugacy classes of subgroups.

The subgroup lattice has 1172 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#1010C211yesmaximal, characteristic, complemented
2C2×#5775C212yesmaximal, complemented
3#85949C211yesmaximal, characteristic, complemented
4C3×#3006C211yesmaximal, characteristic, complemented
5#84080C211yesmaximal, characteristic, complemented
6#83948C212yesmaximal, complemented
7C2×#5040C211yesmaximal, characteristic, complemented
8#80088C214yesmaximal, complemented
9#80086C214yesmaximal, complemented
10#80039C212yesmaximal, complemented
11D3×#448C212yesmaximal, complemented
12#80003C212yesmaximal, complemented
13#80001C212yesmaximal, complemented
14#78887C212yesmaximal, complemented
15#78883C212yesmaximal, complemented
16#78645C211yesmaximal, characteristic, complemented
17#78631C211yesmaximal, characteristic, complemented
18#60374—31nomaximal, Sylow
19C22×C3×#41C2211yescharacteristic, complemented
20C2×#1010—216no—
21C2×#1010—21no—
22C2×#1010—21no—
23C2×#1010—22no—
24C2×#1010C2212yes—
25C2×#1010C2212yescomplemented
26C2×#1010C2214yescomplemented
27C22×D3×Q8C2212yescomplemented
28C2×#1004C2211yescharacteristic, complemented
29C22×#237—22no—
30C22×#237C2212yescomplemented
31C22×#235—21no—
32C22×#235C2211yescharacteristic
33C23×Dic6—21no—
34C23×Dic6C2211yescharacteristic, complemented
35C2×C3×AGL(1,ℤ/8)C2212yescomplemented
36C2×C3×#121C2211yescharacteristic
37C2×#950C2212yescomplemented
38#5805C2211yescharacteristic, complemented
39D4×#67—22no—
40C22×#214C2212yescomplemented
41#5791C2211yescharacteristic
42#5775—216no—
43C2×#915C2214yescomplemented
44C2×D3×SD16C2214yescomplemented
45C2×#912C2214yescomplemented
46C2×#911C2214yescomplemented
47C2×#909C2212yescomplemented
48C2×#907C2212yescomplemented
49#5612—21no—
50#5609—21no—
51#5608C2212yescomplemented
52#5607C2212yescomplemented
53#5606C2212yes—
54D3×#121C2212yes—
55#5599—21no—
56#5598—21no—
57#5510C2211yescharacteristic, complemented
58#5504C2211yescharacteristic, complemented
59#5490—22no—
60C3×#449C2214yescomplemented
61C3×#448C2212yescomplemented
62C3×#447C2212yescomplemented
63C3×#417C2212yescomplemented
64C3×#407C2211yescharacteristic, complemented
65#5239C2212yescomplemented
66#5238C2212yescomplemented
67#5233C2212yescomplemented
68#5228C2211yescharacteristic, complemented
69#5227C2211yescharacteristic, complemented
70#5218C2211yescharacteristic, complemented
71#5217C2211yescharacteristic, complemented
72C2×#830C2211yescharacteristic, complemented
73#5170C2214yescomplemented
74#5170C2214yescomplemented
75#5158C2214yescomplemented
76#5158C2214yescomplemented
77#5129C2212yescomplemented
78#5120C2212yescomplemented
79#5040C2212yescomplemented
80#5040C2212yescomplemented
81#5040C2214yescomplemented
82C2×#810C2212yescomplemented
83#4809C2214yescomplemented
84#4806C2214yescomplemented
85#4802C2214yescomplemented
86D3×#103C2214yescomplemented
87#4783C2214yescomplemented
88#4781C2214yescomplemented
89#4772C2214yescomplemented
90#4771C2214yescomplemented
91#4739C2212yescomplemented
92#4739C2212yescomplemented
93#4738C2212yescomplemented
94#4738C2212yescomplemented
95#4727C2214yescomplemented
96#4726C2212yescomplemented
97D3×C22⋊C8C2212yescomplemented
98C22×2−1+4—31no—
99C2×#577—32no—
100#3488—31no—
101#3013—34no—
102#3013—32no—
103#3010—34no—
104#3010—32no—
105#3006—32no—
106#3006D311yescharacteristic, complemented
107#3004—32no—
108#3004—31no—
109#3002—32no—
110#3002—31no—
111C2×#448—32no—
112C2×#448—31no—
113#2898—32no—
114#2880—31no—
115C2×C3×#41—28no—
116C2×C3×#41—21no—
117C2×C3×#41—21no—
118C2×C3×#41C2312yes—
119C2×C3×#41C2312yes—
120C22×C3×Q8C2311yescharacteristic
121C22×C3×D4—21no—
122C22×C3×D4—21no—
123C22×C3×D4C2311yescharacteristic
124C22×C3×D4C2311yescharacteristic
125C23×C3×C4—21no—
126C23×C3×C4C2311yescharacteristic
127C22×#67—22no—
128C22×#67—22no—
129C22×#67D412yes—
130C23×Dic3—21no—
131C23×Dic3—22no—
132#1010—232no—
133#1010—216no—
134#1010—216no—
135#1010—28no—
136#1010—216no—
137#1010—216no—
138#1010—28no—
139#1010—28no—
140#1010D4116yescomplemented
141C2×D3×Q8—216no—
142C2×D3×Q8—22no—
143C2×D3×Q8—22no—
144C2×D3×Q8C2314yes—
145C2×D3×Q8C2314yes—
146#1004—28no—
147C2×#237—232no—
148C2×#237—24no—
149C2×#237—24no—
150C2×#237—24no—
151C2×#237—24no—
152C2×#237—216no—
153C2×#237—22no—
154C2×#237—22no—
155C2×#237—21no—
156C2×#237C2314yes—
157C2×#237C2312yes—
158C2×#237C2314yes—
159C2×D3×D4—22no—
160C2×D3×D4—21no—
161C2×D3×D4C2312yes—
162C2×#235—216no—
163C2×#235—28no—
164C2×#235—22no—
165C2×#235—24no—
166C2×#235—22no—
167C2×#235D412yes—
168C2×#235D411yescharacteristic
169C2×#235D411yescharacteristic
170C2×#235C2311yescharacteristic
171C2×#235C2312yes—
172C2×#235C2311yescharacteristic
173C2×#235C2311yescharacteristic
174C22×D12D411yescharacteristic
175C22×C4×D3—22no—
176C22×C4×D3C2312yes—
177C22×Dic6—216no—
178C22×Dic6—21no—
179C22×Dic6—21no—
180C22×Dic6—21no—
181C22×Dic6—22no—
182C22×Dic6—22no—
183C22×Dic6—24no—
184C22×Dic6—22no—
185C22×Dic6—28no—
186C22×Dic6D411yescharacteristic
187C22×Dic6C2312yes—
188C22×Dic6C2312yes—
189C22×Dic6C2312yes—
190C3×AGL(1,ℤ/8)—28no—
191C2×C3×SD16C2314yes—
192C2×C3×D8C2314yes—
193C2×C3×M16C2312yes—
194C3×#121—21no—
195C3×#121—21no—
196C3×#121C2312yes—
197C3×#121C2312yes—
198C2×C3×C4⋊C4C2311yescharacteristic
199C2×C3×C22⋊C4—21no—
200#953—21no—
201#953—22no—
202#950—28no—
203C2×#216C2312yes—
204C2×#215C2312yes—
205#940—22no—
206#940—21no—
207#939—22no—
208#939—22no—
209#938—22no—
210#938C2312yes—
211#938C2312yes—
212#937—22no—
213#937—22no—
214#936—21no—
215D4×Dic3—22no—
216C2×#214—28no—
217C2×#214C2314yes—
218C2×#214C2314yes—
219C2×#214C2312yes—
220C2×#213C2312yes—
221#930—22no—
222#930C2311yescharacteristic
223#930C2311yescharacteristic
224#929—21no—
225C4×#67—21no—
226C4×#67—21no—
227C4×#67—22no—
228#926C2311yescharacteristic
229#924C2311yescharacteristic
230#924C2311yescharacteristic
231C22×C3⋊C8C2312yes—
232#915—216no—
233D3×SD16—216no—
234#912—216no—
235#911—216no—
236#909—28no—
237#907—28no—
238C2×Dic12C2314yes—
239C2×#204C2314yes—
240C2×ΓL(1,𝔽25)C2314yes—
241C2×D3×C8C2314yes—
242#897—21no—
243#897C2312yes—
244#895—21no—
245#895C2312yes—
246#893—21no—
247#892C2312yes—
248D3×C4⋊C4C2312yes—
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×#103C2314yes—
259C3×#102C2314yes—
260C3×C22⋊C8C2312yes—
261C3×C22⋊C8C2312yes—
262#835C2312yes—
263#835C2312yes—
264#832C2312yes—
265#832C2312yes—
266#830C2311yescharacteristic
267#830C2311yescharacteristic
268#830C2312yes—
269(C2×D3)⋊C8C2314yes—
270(C2×D3)⋊C8C2314yes—
271#816C2314yes—
272#816C2314yes—
273#810C2314yes—
274#810C2314yes—
275C2×2−1+4—32no—
276C2×2−1+4—34no—
277C2×2−1+4—32no—
278C2×2−1+4—61no—
279C2×2−1+4—62no—
280C2×2−1+4—61no—
281C2×2−1+4—616no—
282C2×H(5,𝔽2)—31no—
283C22×#41—31no—
284C22×#41—32no—
285C22×#41—61no—
286C22×#41—62no—
287C22×#41C2×D311yescharacteristic, complemented
288C23×Q8—32no—
289C23×Q8—31no—
290C23×Q8—61no—
291#577—616no—
292C2×#137—34no—
293C2×#137—32no—
294C2×AGL(1,ℤ/8)—34no—
295C2×AGL(1,ℤ/8)C2×D312yescomplemented
296C2×#135—32no—
297C2×#135—34no—
298C22×SD16—32no—
299C22×SD16—34no—
300C2×#131—32no—
301#550—61no—
302#548—61no—
303#546—62no—
304#546—61no—
305D42—61no—
306D42—62no—
307#537—32no—
308#537—31no—
309#535—31no—
310#535—32no—
311#525—31no—
312#525—32no—
313C2×#121—32no—
314C2×#121C2×D311yescharacteristic
315#520—31no—
316#452—32no—
317#452—34no—
318#451—31no—
319#451—34no—
320#451—32no—
321#451—32no—
322#450—31no—
323#449—32no—
324#449—34no—
325#449—34no—
326#449—34no—
327#449C2×D314yescomplemented
328#448—31no—
329#448—34no—
330#448—34no—
331#448—32no—
332#448—32no—
333#448—34no—
334#448—34no—
335#448—32no—
336#448—32no—
337#448C2×D312yescomplemented
338#447—31no—
339#447C2×D312yescomplemented
340#419—32no—
341#419—34no—
342#417—34no—
343#417C2×D312yescomplemented
344#416—32no—
345#416—34no—
346C2×#103—32no—
347C2×#103—34no—
348#408—32no—
349#408—34no—
350#407—32no—
351#407C2×D311yescharacteristic, complemented
352C2×C22⋊C8—31no—
353C2×C22⋊C8—32no—
354C24×C3—21no—
355C24×C3—21no—
356C24×C3C2×D411yescharacteristic
357C23×D3—22no—
358C23×D3C2×D412yes—
359C3×#41—28no—
360C3×#41—28no—
361C3×#41—24no—
362C3×#41—24no—
363C3×#41—24no—
364C3×#41C2×D418yescomplemented
365C2×C3×Q8—24no—
366C2×C3×Q8—21no—
367C2×C3×Q8C2412yes—
368C2×C3×D4—28no—
369C2×C3×D4—22no—
370C2×C3×D4—22no—
371C2×C3×D4—24no—
372C2×C3×D4—22no—
373C2×C3×D4—22no—
374C2×C3×D4—21no—
375C2×C3×D4—24no—
376C2×C3×D4—21no—
377C2×C3×D4—82no—
378C2×C3×D4C2412yes—
379C2×C3×D4C2412yes—
380C22×C3×C4—28no—
381C22×C3×C4—21no—
382C22×C3×C4—22no—
383C22×C3×C4—22no—
384C22×C3×C4—24no—
385C22×C3×C4—21no—
386C22×C3×C4C2×D411yescharacteristic
387C22×C3×C4C2×D411yescharacteristic
388C22×C3×C4C2×D411yescharacteristic
389C22×C3×C4C2411yescharacteristic
390C22×C3×C4C2411yescharacteristic
391C22×C3×C4C2411yescharacteristic
392C2×#67—216no—
393C2×#67—24no—
394C2×#67—24no—
395C2×#67—28no—
396C2×#67—21no—
397C2×#67—21no—
398C2×#67—22no—
399C2×#67—21no—
400C2×#67—22no—
401C2×#67—22no—
402C2×#67—22no—
403C2×#67—48no—
404C2×#67C2×D412yes—
405C2×#67C2×D412yes—
406C2×#67C2×D412yes—
407C2×#67C2×D412yes—
408C22×Dic3—28no—
409C22×Dic3—216no—
410C22×Dic3—22no—
411C22×Dic3—22no—
412C22×Dic3—22no—
413C22×Dic3—24no—
414C22×Dic3—24no—
415C22×Dic3—22no—
416C22×Dic3C2×D412yes—
417D3×Q8—216no—
418D3×Q8—216no—
419D3×Q8—28no—
420D3×Q8—28no—
421D3×Q8—28no—
422D3×Q8C2×D4116yescomplemented
423#237—232no—
424#237—232no—
425#237—216no—
426#237—216no—
427#237—232no—
428#237—28no—
429#237—232no—
430#237—28no—
431#237—28no—
432#237—28no—
433#237—44no—
434#237C2×D4116yescomplemented
435D3×D4—28no—
436D3×D4—44no—
437D3×D4—84no—
438#235—232no—
439#235—216no—
440#235—24no—
441#235—28no—
442#235—216no—
443#235—24no—
444#235—28no—
445#235—24no—
446#235—24no—
447#235C2×D418yes—
448C2×D12—24no—
449C2×D12—22no—
450C2×D12C2×D412yes—
451C2×D12C2×D411yescharacteristic
452C2×D12C2×D411yescharacteristic
453C2×D12C2411yescharacteristic
454C2×C4×D3—216no—
455C2×C4×D3—24no—
456C2×C4×D3—24no—
457C2×C4×D3—28no—
458C2×C4×D3—21no—
459C2×C4×D3—22no—
460C2×C4×D3C2×D412yes—
461C2×C4×D3C2×D412yes—
462C2×C4×D3C2412yes—
463C2×C4×D3C2412yes—
464C2×Dic6—28no—
465C2×Dic6—216no—
466C2×Dic6—28no—
467C2×Dic6—232no—
468C2×Dic6—216no—
469C2×Dic6—28no—
470C2×Dic6—22no—
471C2×Dic6—22no—
472C2×Dic6—22no—
473C2×Dic6—24no—
474C2×Dic6—24no—
475C2×Dic6—24no—
476C2×Dic6—24no—
477C2×Dic6—216no—
478C2×Dic6—28no—
479C2×Dic6—28no—
480C2×Dic6C2×D412yes—
481C2×Dic6C2×D411yescharacteristic
482C2×Dic6C2×D411yescharacteristic
483C2×Dic6C2×D418yescomplemented
484C2×Dic6C2411yescharacteristic
485C2×Dic6C2414yes—
486C3×SD16—28no—
487C3×D8—28no—
488C3×M16—24no—
489C2×C3×C8C2414yes—
490C3×C4⋊C4—21no—
491C3×C4⋊C4C2412yes—
492C3×C22⋊C4—22no—
493C3×C22⋊C4—22no—
494#217—21no—
495#217—21no—
496#217—21no—
497#217—22no—
498#217—22no—
499#216—24no—
500#215—24no—
501#214—24no—
502#214—28no—
503#214—28no—
504#213—24no—
505(C2×D3)⋊C4—22no—
506(C2×D3)⋊C4—22no—
507(C2×D3)⋊C4—21no—
508(C2×D3)⋊C4—21no—
509(C2×D3)⋊C4—22no—
510C4⋊Dic3—22no—
511C4⋊Dic3C2411yescharacteristic
512C4⋊Dic3C2411yescharacteristic
513Dic3⋊C4—21no—
514Dic3⋊C4—21no—
515Dic3⋊C4—22no—
516C4×Dic3—21no—
517C4×Dic3—22no—
518C2×C3⋊C8—24no—
519C2×C3⋊C8C2412yes—
520C2×C3⋊C8C2412yes—
521Dic12—28no—
522#204—28no—
523ΓL(1,𝔽25)—28no—
524D3×C8—28no—
5252−1+4—316no—
5262−1+4—616no—
5272−1+4—68no—
5282−1+4—616no—
5292−1+4—68no—
5302−1+4—616no—
5312−1+4—616no—
5322−1+4—632no—
5332−1+4—68no—
534H(5,𝔽2)—68no—
535C2×#41—28no—
536C2×#41—21no—
537C2×#41—21no—
538C2×#41—31no—
539C2×#41—32no—
540C2×#41—31no—
541C2×#41—31no—
542C2×#41—32no—
543C2×#41—31no—
544C2×#41—34no—
545C2×#41—32no—
546C2×#41—34no—
547C2×#41—31no—
548C2×#41—62no—
549C2×#41—64no—
550C2×#41—62no—
551C2×#41—68no—
552C2×#41—616no—
553C2×#41—62no—
554C2×#41—62no—
555C2×#41—64no—
556C2×#41—64no—
557C2×#41—64no—
558C2×#41—64no—
559C2×#41—61no—
560C2×#41—616no—
561C2×#41—632no—
562C2×#41C22×D312yes—
563C2×#41C22×D312yes—
564C22×Q8—31no—
565C22×Q8—34no—
566C22×Q8—34no—
567C22×Q8—32no—
568C22×Q8—32no—
569C22×Q8—32no—
570C22×Q8—62no—
571C22×Q8—68no—
572C22×Q8—62no—
573C22×Q8—64no—
574C22×Q8—62no—
575C22×Q8—616no—
576C22×Q8—62no—
577C22×Q8—62no—
578C22×Q8—616no—
579C22×Q8—61no—
580C22×Q8—61no—
581C22×Q8—61no—
582C22×Q8C22×D311yescharacteristic
583C22×D4—21no—
584C22×D4—21no—
585C22×D4—32no—
586C22×D4—32no—
587C22×D4—31no—
588C22×D4—61no—
589C22×D4—62no—
590C22×D4—62no—
591C22×D4—62no—
592C22×D4C22×D311yescharacteristic
593C22×D4C22×D311yescharacteristic
594C23×C4—21no—
595C23×C4—32no—
596C23×C4—62no—
597C23×C4—62no—
598C23×C4—61no—
599C23×C4C22×D311yescharacteristic
600#137—68no—
601#137—616no—
602AGL(1,ℤ/8)—28no—
603AGL(1,ℤ/8)—616no—
604#135—616no—
605#135—68no—
606C2×Q16—32no—
607C2×Q16—34no—
608C2×SD16—32no—
609C2×SD16—34no—
610C2×SD16—34no—
611C2×SD16—32no—
612C2×SD16—34no—
613C2×SD16—616no—
614C2×SD16—68no—
615C2×SD16C22×D314yes—
616C2×D8—32no—
617C2×D8C22×D314yes—
618#131—68no—
619C2×M16—34no—
620C2×M16C22×D312yes—
621C22×C8—32no—
622C22×C8—34no—
623#127—62no—
624#127—61no—
625#124—62no—
626#124—61no—
627#123—62no—
628#123—61no—
629C22⋊Q8—31no—
630C22⋊Q8—31no—
631C22⋊Q8—32no—
632C22⋊Q8—62no—
633C22⋊Q8—61no—
634#121—21no—
635#121—21no—
636#121—32no—
637#121—32no—
638#121—31no—
639#121—31no—
640#121—32no—
641#121—62no—
642#121—62no—
643#121—61no—
644#121—62no—
645#121—62no—
646#121—62no—
647#121—62no—
648#121C22×D312yes—
649#121C22×D312yes—
650#120—62no—
651#120—62no—
652#120—62no—
653#120—62no—
654#120—61no—
655C4×Q8—61no—
656C4×D4—62no—
657C4×D4—61no—
658C4×D4—62no—
659C4×D4—62no—
660C4×D4—61no—
661C4×D4—61no—
662#117—31no—
663#117—32no—
664C2×C4⋊C4—32no—
665C2×C4⋊C4C22×D311yescharacteristic
666C2×C22⋊C4—21no—
667C2×C22⋊C4—62no—
668#103—32no—
669#103—32no—
670#103—34no—
671#103—34no—
672#103—34no—
673#103—34no—
674#103C22×D314yes—
675#102—32no—
676#102—32no—
677#102C22×D314yes—
678C22⋊C8—31no—
679C22⋊C8—31no—
680C22⋊C8—32no—
681C22⋊C8—34no—
682C22⋊C8—34no—
683C22⋊C8C22×D312yes—
684C22⋊C8C22×D312yes—
685C23×C3—24no—
686C23×C3—22no—
687C23×C3—22no—
688C23×C3—22no—
689C23×C3—22no—
690C23×C3—41no—
691C23×C3—42no—
692C23×C3—42no—
693C23×C3—42no—
694C23×C3—81no—
695C23×C3—81no—
696C23×C3C22×D411yescharacteristic
697C23×C3C22×D411yescharacteristic
698C23×C3C22×D411yescharacteristic
699C22×D3—24no—
700C22×D3—24no—
701C22×D3—21no—
702C22×D3—42no—
703C22×D3—44no—
704C22×D3—82no—
705C22×D3—82no—
706C22×D3C22×D412yes—
707C22×D3C22×D412yes—
708C3×Q8—24no—
709C3×Q8—22no—
710C3×Q8C22×D414yes—
711C3×D4—28no—
712C3×D4—24no—
713C3×D4—28no—
714C3×D4—22no—
715C3×D4—24no—
716C3×D4—44no—
717C3×D4—42no—
718C3×D4—82no—
719C3×D4C22×D414yes—
720C2×C3×C4—24no—
721C2×C3×C4—28no—
722C2×C3×C4—22no—
723C2×C3×C4—22no—
724C2×C3×C4—22no—
725C2×C3×C4—28no—
726C2×C3×C4—22no—
727C2×C3×C4—22no—
728C2×C3×C4—22no—
729C2×C3×C4—22no—
730C2×C3×C4—81no—
731C2×C3×C4C22×D411yescharacteristic
732C2×C3×C4C22×D411yescharacteristic
733C2×C3×C4C22×D411yescharacteristic
734C2×C3×C4C22×D414yes—
735C2×C3×C4C2511yescharacteristic
736#67—216no—
737#67—24no—
738#67—24no—
739#67—216no—
740#67—24no—
741#67—42no—
742#67—42no—
743#67—44no—
744#67—44no—
745#67—82no—
746#67—82no—
747#67—81no—
748#67#12018yes—
749C2×Dic3—28no—
750C2×Dic3—216no—
751C2×Dic3—28no—
752C2×Dic3—28no—
753C2×Dic3—24no—
754C2×Dic3—24no—
755C2×Dic3—216no—
756C2×Dic3—21no—
757C2×Dic3—21no—
758C2×Dic3—21no—
759C2×Dic3—44no—
760C2×Dic3C22×D412yes—
761C2×Dic3C22×D412yes—
762D12—24no—
763D12—22no—
764D12—22no—
765D12—82no—
766D12#12014yes—
767C4×D3—216no—
768C4×D3—216no—
769C4×D3—24no—
770C4×D3—24no—
771C4×D3—24no—
772C4×D3—42no—
773C4×D3—82no—
774C4×D3C22×D418yes—
775Dic6—28no—
776Dic6—216no—
777Dic6—28no—
778Dic6—22no—
779Dic6—28no—
780Dic6—24no—
781Dic6—24no—
782Dic6—216no—
783Dic6—22no—
784Dic6#12014yes—
785Dic6C22×D418yes—
786C3×C8—24no—
787C3⋊C8—22no—
788C3⋊C8—22no—
789C24—21no—
790C24—21no—
791C24—32no—
792C24—62no—
793C24D3×D411yescharacteristic
794#41—28no—
795#41—28no—
796#41—24no—
797#41—24no—
798#41—24no—
799#41—38no—
800#41—316no—
801#41—68no—
802#41—68no—
803#41—64no—
804#41—616no—
805#41—64no—
806#41—632no—
807#41—616no—
808#41—68no—
809#41—68no—
810#41—632no—
811#41—68no—
812#41—616no—
813#41—616no—
814#41—632no—
815#41—632no—
816#41—632no—
817#41—68no—
818#41—64no—
819#41—64no—
820#41—124no—
821#41D3×D418yescomplemented
822C2×Q8—24no—
823C2×Q8—21no—
824C2×Q8—31no—
825C2×Q8—32no—
826C2×Q8—31no—
827C2×Q8—316no—
828C2×Q8—38no—
829C2×Q8—34no—
830C2×Q8—31no—
831C2×Q8—64no—
832C2×Q8—64no—
833C2×Q8—68no—
834C2×Q8—64no—
835C2×Q8—68no—
836C2×Q8—616no—
837C2×Q8—616no—
838C2×Q8—68no—
839C2×Q8—632no—
840C2×Q8—68no—
841C2×Q8—616no—
842C2×Q8—68no—
843C2×Q8—68no—
844C2×Q8—68no—
845C2×Q8—616no—
846C2×Q8—616no—
847C2×Q8—68no—
848C2×Q8—62no—
849C2×Q8—62no—
850C2×Q8—62no—
851C2×Q8—64no—
852C2×Q8C23×D312yes—
853C2×D4—28no—
854C2×D4—22no—
855C2×D4—22no—
856C2×D4—24no—
857C2×D4—22no—
858C2×D4—22no—
859C2×D4—21no—
860C2×D4—24no—
861C2×D4—21no—
862C2×D4—32no—
863C2×D4—32no—
864C2×D4—32no—
865C2×D4—32no—
866C2×D4—31no—
867C2×D4—32no—
868C2×D4—31no—
869C2×D4—31no—
870C2×D4—64no—
871C2×D4—62no—
872C2×D4—68no—
873C2×D4—62no—
874C2×D4—68no—
875C2×D4—64no—
876C2×D4—64no—
877C2×D4—616no—
878C2×D4—62no—
879C2×D4—61no—
880C2×D4—61no—
881C2×D4—62no—
882C2×D4—62no—
883C2×D4—61no—
884C2×D4—82no—
885C2×D4—124no—
886C2×D4—128no—
887C2×D4—244no—
888C2×D4C23×D312yes—
889C2×D4C23×D312yes—
890C22×C4—28no—
891C22×C4—21no—
892C22×C4—22no—
893C22×C4—22no—
894C22×C4—24no—
895C22×C4—21no—
896C22×C4—32no—
897C22×C4—32no—
898C22×C4—32no—
899C22×C4—32no—
900C22×C4—32no—
901C22×C4—68no—
902C22×C4—64no—
903C22×C4—64no—
904C22×C4—616no—
905C22×C4—62no—
906C22×C4—64no—
907C22×C4—64no—
908C22×C4—62no—
909C22×C4—616no—
910C22×C4—68no—
911C22×C4—62no—
912C22×C4—62no—
913C22×C4—62no—
914C22×C4—61no—
915C22×C4D3×D411yescharacteristic
916C22×C4D3×D411yescharacteristic
917C22×C4D3×D411yescharacteristic
918C22×C4C23×D311yescharacteristic
919C22×C4C23×D311yescharacteristic
920C22×C4C23×D311yescharacteristic
921Q16—68no—
922Q16—64no—
923SD16—28no—
924SD16—68no—
925SD16—68no—
926SD16—68no—
927SD16—64no—
928SD16—64no—
929D8—28no—
930D8—64no—
931M16—24no—
932M16—68no—
933C2×C8—32no—
934C2×C8—32no—
935C2×C8—68no—
936C2×C8—64no—
937C2×C8C23×D314yes—
938C4⋊C4—21no—
939C4⋊C4—31no—
940C4⋊C4—31no—
941C4⋊C4—62no—
942C4⋊C4—62no—
943C4⋊C4—61no—
944C4⋊C4—61no—
945C4⋊C4C23×D312yes—
946C22⋊C4—22no—
947C22⋊C4—22no—
948C22⋊C4—62no—
949C22⋊C4—62no—
950C22⋊C4—62no—
951C22⋊C4—62no—
952C22⋊C4—62no—
953C22⋊C4—61no—
954C22⋊C4—61no—
955C22⋊C4—61no—
956C22⋊C4—61no—
957C22⋊C4—61no—
958C42—62no—
959C42—61no—
960C22×C3—21no—
961C22×C3—21no—
962C22×C3—21no—
963C22×C3—21no—
964C22×C3—21no—
965C22×C3—21no—
966C22×C3—24no—
967C22×C3—21no—
968C22×C3—44no—
969C22×C3—48no—
970C22×C3—42no—
971C22×C3—42no—
972C22×C3—42no—
973C22×C3—42no—
974C22×C3—42no—
975C22×C3—162no—
976C22×C3C2×#12012yes—
977C22×C3#57712yescomplemented
978C22×C3C23×D411yescharacteristic
979C2×D3—22no—
980C2×D3—22no—
981C2×D3—22no—
982C2×D3—22no—
983C2×D3—22no—
984C2×D3—48no—
985C2×D3—41no—
986C2×D3—41no—
987C2×D3—41no—
988C2×D3—164no—
989C2×D3C2×#12014yes—
990C3×C4—21no—
991C3×C4—24no—
992C3×C4—21no—
993C3×C4—42no—
994C3×C4C2×#12012yes—
995C3×C4C23×D412yes—
996Dic3—22no—
997Dic3—28no—
998Dic3—41no—
999Dic3—41no—
1000Dic3—41no—
1001Dic3C2×#12014yes—
1002C23—24no—
1003C23—22no—
1004C23—22no—
1005C23—22no—
1006C23—22no—
1007C23—32no—
1008C23—32no—
1009C23—41no—
1010C23—42no—
1011C23—42no—
1012C23—42no—
1013C23—64no—
1014C23—64no—
1015C23—61no—
1016C23—81no—
1017C23—81no—
1018C23—122no—
1019C23—124no—
1020C23—242no—
1021C23—242no—
1022C23C2×D3×D411yescharacteristic
1023C23C2×D3×D411yescharacteristic
1024C23C2×D3×D411yescharacteristic
1025Q8—24no—
1026Q8—22no—
1027Q8—34no—
1028Q8—38no—
1029Q8—64no—
1030Q8—616no—
1031Q8—68no—
1032Q8—616no—
1033Q8—68no—
1034Q8—64no—
1035Q8—62no—
1036Q8—68no—
1037Q8—62no—
1038Q8C2×D3×D414yes—
1039D4—28no—
1040D4—24no—
1041D4—28no—
1042D4—22no—
1043D4—24no—
1044D4—38no—
1045D4—34no—
1046D4—44no—
1047D4—42no—
1048D4—64no—
1049D4—64no—
1050D4—64no—
1051D4—616no—
1052D4—616no—
1053D4—64no—
1054D4—62no—
1055D4—62no—
1056D4—82no—
1057D4—124no—
1058D4—124no—
1059D4—122no—
1060D4—122no—
1061D4—242no—
1062D4—241no—
1063D4—242no—
1064D4—242no—
1065D4C2×D3×D414yes—
1066C2×C4—24no—
1067C2×C4—28no—
1068C2×C4—22no—
1069C2×C4—22no—
1070C2×C4—22no—
1071C2×C4—22no—
1072C2×C4—22no—
1073C2×C4—28no—
1074C2×C4—22no—
1075C2×C4—22no—
1076C2×C4—32no—
1077C2×C4—38no—
1078C2×C4—32no—
1079C2×C4—64no—
1080C2×C4—64no—
1081C2×C4—616no—
1082C2×C4—616no—
1083C2×C4—64no—
1084C2×C4—616no—
1085C2×C4—68no—
1086C2×C4—616no—
1087C2×C4—68no—
1088C2×C4—64no—
1089C2×C4—68no—
1090C2×C4—64no—
1091C2×C4—61no—
1092C2×C4—61no—
1093C2×C4—61no—
1094C2×C4—81no—
1095C2×C4—124no—
1096C2×C4—122no—
1097C2×C4—242no—
1098C2×C4C2×D3×D411yescharacteristic
1099C2×C4C2×D3×D411yescharacteristic
1100C2×C4C2×D3×D414yes—
1101C2×C4C2×D3×D411yescharacteristic
1102C2×C4C24×D311yescharacteristic
1103C8—24no—
1104C8—62no—
1105C8—62no—
1106C2×C3—22no—
1107C2×C3—22no—
1108C2×C3—41no—
1109C2×C3—44no—
1110C2×C3—82no—
1111C2×C3C22×#12011yescharacteristic
1112C2×C3C2×#57711yescharacteristic
1113C2×C3#358611yescharacteristic
1114D3—24no—
1115D3—42no—
1116D3—81no—
1117C22—21no—
1118C22—21no—
1119C22—21no—
1120C22—21no—
1121C22—21no—
1122C22—21no—
1123C22—24no—
1124C22—21no—
1125C22—34no—
1126C22—44no—
1127C22—48no—
1128C22—42no—
1129C22—42no—
1130C22—42no—
1131C22—42no—
1132C22—42no—
1133C22—62no—
1134C22—62no—
1135C22—62no—
1136C22—62no—
1137C22—62no—
1138C22—128no—
1139C22—121no—
1140C22—121no—
1141C22—121no—
1142C22—162no—
1143C22—484no—
1144C22D3×#12012yes—
1145C22#577512yescomplemented
1146C22C22×D3×D411yescharacteristic
1147C4—21no—
1148C4—24no—
1149C4—21no—
1150C4—34no—
1151C4—42no—
1152C4—62no—
1153C4—68no—
1154C4—121no—
1155C4—121no—
1156C4—121no—
1157C4D3×#12012yes—
1158C4C22×D3×D412yes—
1159C3#6037411yescharacteristic, complemented, Sylow
1160C2—22no—
1161C2—22no—
1162C2—41no—
1163C2—44no—
1164C2—64no—
1165C2—82no—
1166C2—122no—
1167C2—241no—
1168C2C2×D3×#12011yescharacteristic
1169C2C2×#577511yescharacteristic
1170C2#8720111yescharacteristic
subgroupG/H
centerC22C22×D3×D4
commutator, cosocleC2×C3×C4C25
FrattiniC2×C4C24×D3
FittingC3×#3006C2
socleC22×C3C23×D4
hypercenter#3006D3
hypocenterC3#60374
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C23×C4 ◁ #3006

Complements

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

NH ≅ G/Ntype
1. C22×#1010C2semidirect
2. C2×#5775C2semidirect
3. #85949C2semidirect
4. C3×#3006C2semidirect
5. #84080C2semidirect
6. #83948C2semidirect
7. C2×#5040C2semidirect
8. #80088C2semidirect
9. #80086C2semidirect
10. #80039C2semidirect
11. D3×#448C2semidirect
12. #80003C2semidirect
13. #80001C2semidirect
14. #78887C2semidirect
15. #78883C2semidirect
16. #78645C2semidirect
17. #78631C2semidirect
19. C22×C3×#41C22semidirect
25. C2×#1010C22semidirect
26. C2×#1010C22semidirect
27. C22×D3×Q8C22semidirect
28. C2×#1004C22semidirect
30. C22×#237C22semidirect
34. C23×Dic6C22semidirect
35. C2×C3×AGL(1,ℤ/8)C22semidirect
37. C2×#950C22semidirect
38. #5805C22semidirect
40. C22×#214C22semidirect
43. C2×#915C22semidirect
44. C2×D3×SD16C22semidirect
45. C2×#912C22semidirect
46. C2×#911C22semidirect
47. C2×#909C22semidirect
48. C2×#907C22semidirect
51. #5608C22semidirect
52. #5607C22semidirect
57. #5510C22semidirect
58. #5504C22semidirect
60. C3×#449C22semidirect
61. C3×#448C22semidirect
62. C3×#447C22semidirect
63. C3×#417C22semidirect
64. C3×#407C22semidirect
65. #5239C22semidirect
66. #5238C22semidirect
67. #5233C22semidirect
68. #5228C22semidirect
69. #5227C22semidirect
70. #5218C22semidirect
71. #5217C22semidirect
72. C2×#830C22semidirect
73. #5170C22semidirect
74. #5170C22semidirect
75. #5158C22semidirect
76. #5158C22semidirect
77. #5129C22semidirect
78. #5120C22semidirect
79. #5040C22semidirect
80. #5040C22semidirect
81. #5040C22semidirect
82. C2×#810C22semidirect
83. #4809C22semidirect
84. #4806C22semidirect
85. #4802C22semidirect
86. D3×#103C22semidirect
87. #4783C22semidirect
88. #4781C22semidirect
89. #4772C22semidirect
90. #4771C22semidirect
91. #4739C22semidirect
92. #4739C22semidirect
93. #4738C22semidirect
94. #4738C22semidirect
95. #4727C22semidirect
96. #4726C22semidirect
97. D3×C22⋊C8C22semidirect
106. #3006D3semidirect
140. #1010D4semidirect
287. C22×#41C2×D3semidirect
295. C2×AGL(1,ℤ/8)C2×D3semidirect
327. #449C2×D3semidirect
337. #448C2×D3semidirect
339. #447C2×D3semidirect
343. #417C2×D3semidirect
351. #407C2×D3semidirect
364. C3×#41C2×D4semidirect
422. D3×Q8C2×D4semidirect
434. #237C2×D4semidirect
483. C2×Dic6C2×D4semidirect
821. #41D3×D4semidirect
977. C22×C3#577semidirect
1145. C22#5775semidirect
1159. C3#60374semidirect

Maximal subgroups

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

subgroupindex
C22×#10102
C2×#57752
#859492
C3×#30062
#840802
#839482
C2×#50402
#800882
#800862
#800392
D3×#4482
#800032
#800012
#788872
#788832
#786452
#786312
#603743