Finite Group Databasebeta

← #11661735

Subgroups — #11661735

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×#5770C212yesmaximal, complemented
3#86041C211yesmaximal, characteristic, complemented
4C3×#3002C211yesmaximal, characteristic, complemented
5#84082C211yesmaximal, characteristic, complemented
6#83913C212yesmaximal, complemented
7#82933C211yesmaximal, characteristic, complemented
8#80232C214yesmaximal, complemented
9#80183C212yesmaximal, complemented
10#80145C212yesmaximal, complemented
11#80086C214yesmaximal, complemented
12D3×#448C212yesmaximal, complemented
13#80003C212yesmaximal, complemented
14#78836C212yesmaximal, complemented
15#78832C212yesmaximal, complemented
16C2×#4738C211yesmaximal, characteristic, complemented
17#78600C211yesmaximal, 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×#1010C2214yescomplemented
26C2×#1010C2212yescomplemented
27C2×#1009C2211yescharacteristic, complemented
28C22×D3×Q8C2212yescomplemented
29C22×#237—22no—
30C22×#237C2212yescomplemented
31C22×#235—21no—
32C22×#235C2211yescharacteristic
33C23×Dic6—21no—
34C23×Dic6C2211yescharacteristic, complemented
35C2×C3×#135C2212yescomplemented
36C3×#525C2211yescharacteristic
37#5833C2211yescharacteristic, complemented
38C2×#951C2212yescomplemented
39C2×#949C2212yescomplemented
40C2×#930C2211yescharacteristic
41#5770—216no—
42C2×#918C2214yescomplemented
43C2×#916C2214yescomplemented
44C2×D3×SD16C2214yescomplemented
45C2×#911C2214yescomplemented
46C22×#204C2212yescomplemented
47C2×#901C2212yescomplemented
48#5654—22no—
49#5629C2212yescomplemented
50#5627C2212yes—
51#5607C2212yescomplemented
52D3×#121C2212yes—
53#5590—22no—
54#5553—21no—
55#5552—21no—
56#5550—21no—
57D4×D12—21no—
58#5525C2211yescharacteristic, complemented
59#5523C2211yescharacteristic, complemented
60C3×#452C2212yescomplemented
61C3×#451C2211yescharacteristic, complemented
62C3×#450C2211yescharacteristic, complemented
63C3×#449C2212yescomplemented
64C3×#448C2211yescharacteristic, complemented
65C3×#447C2211yescharacteristic, complemented
66C3×#416C2212yescomplemented
67C2×C3×C22⋊C8C2211yescharacteristic, complemented
68#5238C2214yescomplemented
69#5232C2212yescomplemented
70#5227C2212yescomplemented
71#5217C2212yescomplemented
72#5207C2211yescharacteristic, complemented
73#5186C2214yescomplemented
74#5173C2214yescomplemented
75#5170C2214yescomplemented
76#5158C2214yescomplemented
77#5110C2212yescomplemented
78C2×#816C2212yescomplemented
79#5050C2212yescomplemented
80#5050C2212yescomplemented
81#5040C2212yescomplemented
82#5040C2212yescomplemented
83#5004C2212yescomplemented
84#4806C2214yescomplemented
85#4806C2214yescomplemented
86#4802C2214yescomplemented
87D3×#103C2214yescomplemented
88#4781C2214yescomplemented
89#4781C2214yescomplemented
90#4772C2214yescomplemented
91#4771C2214yescomplemented
92#4738C2212yescomplemented
93#4738C2212yescomplemented
94#4738C2214yescomplemented
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#3006—31no—
107#3004—32no—
108#3004—31no—
109#3002—32no—
110#3002D311yescharacteristic, complemented
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×#41C2311yescharacteristic
119C2×C3×#41C2312yes—
120C2×C3×#41C2312yes—
121C22×C3×Q8C2311yescharacteristic
122C22×C3×D4—21no—
123C22×C3×D4C2311yescharacteristic
124C23×C3×C4—21no—
125C23×C3×C4C2311yescharacteristic
126C22×#67—22no—
127C22×#67—21no—
128C22×#67D412yes—
129C23×Dic3—21no—
130C23×Dic3—22no—
131#1010—232no—
132#1010—216no—
133#1010—216no—
134#1010—28no—
135#1010—216no—
136#1010—216no—
137#1010—28no—
138#1010—28no—
139#1010D4116yescomplemented
140#1009—28no—
141C2×#239C2312yes—
142C2×D3×Q8—216no—
143C2×D3×Q8—22no—
144C2×D3×Q8—22no—
145C2×D3×Q8C2314yes—
146C2×D3×Q8C2314yes—
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×#237C2314yes—
156C2×#237C2314yes—
157C2×D3×D4—22no—
158C2×D3×D4—22no—
159C2×D3×D4C2312yes—
160C2×#235—216no—
161C2×#235—28no—
162C2×#235—22no—
163C2×#235—22no—
164C2×#235—24no—
165C2×#235—21no—
166C2×#235D412yes—
167C2×#235D411yescharacteristic
168C2×#235D411yescharacteristic
169C2×#235C2312yes—
170C2×#235C2311yescharacteristic
171C2×#235C2311yescharacteristic
172C22×D12—21no—
173C22×D12D411yescharacteristic
174C22×D12C2311yescharacteristic
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—22no—
184C22×Dic6—24no—
185C22×Dic6—28no—
186C22×Dic6D411yescharacteristic
187C22×Dic6C2312yes—
188C22×Dic6C2312yes—
189C22×Dic6C2312yes—
190C3×#135—28no—
191C2×C3×Q16C2312yes—
192C2×C3×SD16C2312yes—
193C2×C3×SD16C2312yes—
194C2×C3×D8C2312yes—
195C22×C3×C8C2312yes—
196C3×#123—21no—
197C3×C22⋊Q8C2311yescharacteristic
198C3×C22⋊Q8C2311yescharacteristic
199C3×#121C2311yescharacteristic
200C3×#121C2311yescharacteristic
201C3×#120—21no—
202C3×C4×D4—21no—
203C3×C4×D4—21no—
204C3×#117C2311yescharacteristic
205#951—28no—
206#949—28no—
207#946C2312yes—
208C2×#216C2314yes—
209C2×#215C2314yes—
210#940—22no—
211#939—22no—
212#939—22no—
213#938C2312yes—
214#937—22no—
215C2×#214C2314yes—
216C2×#213C2314yes—
217#930—21no—
218#930—21no—
219#930—21no—
220#930C2312yes—
221#930C2312yes—
222C2×(C2×D3)⋊C4—21no—
223C2×C4⋊Dic3C2311yescharacteristic
224#924—21no—
225C2×#208C2312yes—
226#918—216no—
227#916—216no—
228D3×SD16—216no—
229#911—216no—
230C2×#204—28no—
231C2×#204C2314yes—
232C2×#204C2314yes—
233#901—28no—
234C2×ΓL(1,𝔽25)C2314yes—
235C2×D3×C8C2314yes—
236#896—22no—
237#895—22no—
238#895C2312yes—
239#895C2312yes—
240#894—22no—
241#893—22no—
242#892C2312yes—
243D3×C4⋊C4C2312yes—
244#885—22no—
245#884—22no—
246#884—22no—
247#884—22no—
248#882—22no—
249#882—22no—
250#882—22no—
251#67⋊C4—22no—
252#67⋊C4—22no—
253D3×C22⋊C4—22no—
254#875—21no—
255#874—21no—
256C4×D12—21no—
257C4×Dic6—21no—
258C3×#103C2312yes—
259C3×#103C2312yes—
260C3×#102C2312yes—
261C3×#102C2312yes—
262C3×C22⋊C8C2311yescharacteristic
263C3×C22⋊C8C2311yescharacteristic
264C3×C22⋊C8C2312yes—
265#835C2314yes—
266#832C2314yes—
267#830C2312yes—
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—32no—
293C2×#137—34no—
294C2×AGL(1,ℤ/8)—32no—
295C2×AGL(1,ℤ/8)—34no—
296C2×#135—34no—
297C2×#135C2×D312yescomplemented
298C22×SD16—34no—
299C22×SD16—32no—
300C2×#131—32no—
301#550—61no—
302#548—61no—
303#546—61no—
304#546—62no—
305D42—61no—
306D42—62no—
307#537—31no—
308#537—32no—
309#535—32no—
310#535—31no—
311#525—32no—
312#525C2×D311yescharacteristic
313C2×#121—31no—
314C2×#121—32no—
315#520—31no—
316#452—34no—
317#452C2×D312yescomplemented
318#451—34no—
319#451—32no—
320#451—32no—
321#451C2×D311yescharacteristic, complemented
322#450C2×D311yescharacteristic, complemented
323#449—34no—
324#449—34no—
325#449—34no—
326#449—34no—
327#449C2×D312yescomplemented
328#448—32no—
329#448—34no—
330#448—32no—
331#448—32no—
332#448—34no—
333#448—34no—
334#448—32no—
335#448—32no—
336#448—34no—
337#448C2×D311yescharacteristic, complemented
338#447—32no—
339#447C2×D311yescharacteristic, complemented
340#419—32no—
341#419—34no—
342#417—32no—
343#417—34no—
344#416—34no—
345#416C2×D312yescomplemented
346C2×#103—32no—
347C2×#103—34no—
348#408—32no—
349#408—34no—
350#407—31no—
351#407—32no—
352C2×C22⋊C8—32no—
353C2×C22⋊C8C2×D311yescharacteristic, complemented
354C24×C3—21no—
355C24×C3C2×D411yescharacteristic
356C23×D3—21no—
357C23×D3—22no—
358C23×D3C2×D412yes—
359C3×#41—28no—
360C3×#41—28no—
361C3×#41—24no—
362C3×#41—24no—
363C3×#41—24no—
364C3×#41—24no—
365C3×#41C2×D418yescomplemented
366C2×C3×Q8—24no—
367C2×C3×Q8—21no—
368C2×C3×Q8C2411yescharacteristic
369C2×C3×Q8C2412yes—
370C2×C3×D4—28no—
371C2×C3×D4—22no—
372C2×C3×D4—22no—
373C2×C3×D4—24no—
374C2×C3×D4—21no—
375C2×C3×D4—21no—
376C2×C3×D4—21no—
377C2×C3×D4—21no—
378C2×C3×D4C2411yescharacteristic
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—22no—
397C2×#67—22no—
398C2×#67—22no—
399C2×#67—22no—
400C2×#67—82no—
401C2×#67C2×D412yes—
402C2×#67C2×D412yes—
403C2×#67C2×D412yes—
404C2×#67C2×D412yes—
405C22×Dic3—28no—
406C22×Dic3—216no—
407C22×Dic3—22no—
408C22×Dic3—22no—
409C22×Dic3—22no—
410C22×Dic3—24no—
411C22×Dic3—24no—
412C22×Dic3—21no—
413C22×Dic3C2×D412yes—
414#239—28no—
415D3×Q8—216no—
416D3×Q8—216no—
417D3×Q8—28no—
418D3×Q8—28no—
419D3×Q8—28no—
420D3×Q8C2×D4116yescomplemented
421#237—232no—
422#237—232no—
423#237—216no—
424#237—216no—
425#237—232no—
426#237—28no—
427#237—232no—
428#237—28no—
429#237—28no—
430#237C2×D4116yescomplemented
431D3×D4—28no—
432D3×D4—48no—
433D3×D4—84no—
434#235—232no—
435#235—216no—
436#235—24no—
437#235—28no—
438#235—216no—
439#235—24no—
440#235—28no—
441#235—24no—
442#235—44no—
443#235C2×D418yes—
444C2×D12—24no—
445C2×D12—24no—
446C2×D12—22no—
447C2×D12—21no—
448C2×D12—22no—
449C2×D12—22no—
450C2×D12—44no—
451C2×D12C2×D411yescharacteristic
452C2×D12C2×D412yes—
453C2×D12C2×D411yescharacteristic
454C2×D12C2412yes—
455C2×C4×D3—216no—
456C2×C4×D3—24no—
457C2×C4×D3—24no—
458C2×C4×D3—28no—
459C2×C4×D3—22no—
460C2×C4×D3—22no—
461C2×C4×D3C2×D412yes—
462C2×C4×D3C2×D412yes—
463C2×C4×D3C2412yes—
464C2×C4×D3C2412yes—
465C2×Dic6—28no—
466C2×Dic6—216no—
467C2×Dic6—28no—
468C2×Dic6—232no—
469C2×Dic6—216no—
470C2×Dic6—28no—
471C2×Dic6—22no—
472C2×Dic6—22no—
473C2×Dic6—22no—
474C2×Dic6—24no—
475C2×Dic6—24no—
476C2×Dic6—24no—
477C2×Dic6—24no—
478C2×Dic6—216no—
479C2×Dic6—28no—
480C2×Dic6—28no—
481C2×Dic6C2×D411yescharacteristic
482C2×Dic6C2×D412yes—
483C2×Dic6C2×D411yescharacteristic
484C2×Dic6C2×D418yescomplemented
485C2×Dic6C2414yes—
486C3×Q16—24no—
487C3×SD16—24no—
488C3×SD16—24no—
489C3×D8—24no—
490C2×C3×C8—24no—
491C2×C3×C8C2412yes—
492C2×C3×C8C2412yes—
493C3×C4⋊C4—21no—
494C3×C4⋊C4—21no—
495C3×C4⋊C4C2411yescharacteristic
496C3×C4⋊C4C2411yescharacteristic
497C3×C22⋊C4—21no—
498C3×C22⋊C4—21no—
499C3×C22⋊C4—21no—
500C3×C22⋊C4—21no—
501C3×C22⋊C4—21no—
502C3×C42—21no—
503#217—22no—
504#216—28no—
505#215—28no—
506#214—28no—
507#213—28no—
508(C2×D3)⋊C4—22no—
509(C2×D3)⋊C4—22no—
510(C2×D3)⋊C4—22no—
511(C2×D3)⋊C4—22no—
512(C2×D3)⋊C4—22no—
513(C2×D3)⋊C4—22no—
514C4⋊Dic3—21no—
515C4⋊Dic3C2412yes—
516Dic3⋊C4—22no—
517Dic3⋊C4—22no—
518C4×Dic3—22no—
519#208—24no—
520C2×C3⋊C8C2414yes—
521#204—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—32no—
545C2×#41—34no—
546C2×#41—34no—
547C2×#41—62no—
548C2×#41—64no—
549C2×#41—62no—
550C2×#41—61no—
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—616no—
560C2×#41—632no—
561C2×#41C22×D311yescharacteristic
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—32no—
585C22×D4—32no—
586C22×D4—31no—
587C22×D4—31no—
588C22×D4—61no—
589C22×D4—62no—
590C22×D4—62no—
591C22×D4—62no—
592C22×D4—61no—
593C22×D4C22×D311yescharacteristic
594C23×C4—21no—
595C23×C4—32no—
596C23×C4—62no—
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—28no—
605#135—616no—
606C2×Q16—34no—
607C2×Q16C22×D312yes—
608C2×SD16—34no—
609C2×SD16—34no—
610C2×SD16—34no—
611C2×SD16—34no—
612C2×SD16—68no—
613C2×SD16—616no—
614C2×SD16C22×D312yes—
615C2×SD16C22×D312yes—
616C2×D8—34no—
617C2×D8C22×D312yes—
618#131—68no—
619C2×M16—32no—
620C2×M16—34no—
621C22×C8—34no—
622C22×C8C22×D312yes—
623#127—61no—
624#127—62no—
625#124—61no—
626#124—62no—
627#123—21no—
628#123—62no—
629C22⋊Q8—32no—
630C22⋊Q8—62no—
631C22⋊Q8—61no—
632C22⋊Q8C22×D311yescharacteristic
633C22⋊Q8C22×D311yescharacteristic
634#121—32no—
635#121—32no—
636#121—32no—
637#121—32no—
638#121—32no—
639#121—62no—
640#121—62no—
641#121—62no—
642#121—62no—
643#121—61no—
644#121—62no—
645#121—62no—
646#121—61no—
647#121—61no—
648#121C22×D311yescharacteristic
649#121C22×D311yescharacteristic
650#120—21no—
651#120—62no—
652#120—62no—
653#120—62no—
654#120—62no—
655C4×Q8—61no—
656C4×D4—21no—
657C4×D4—21no—
658C4×D4—61no—
659C4×D4—62no—
660C4×D4—62no—
661C4×D4—62no—
662#117—32no—
663#117C22×D311yescharacteristic
664C2×C4⋊C4—31no—
665C2×C4⋊C4—32no—
666C2×C22⋊C4—62no—
667C2×C22⋊C4—61no—
668#103—34no—
669#103—34no—
670#103—34no—
671#103—34no—
672#103—34no—
673#103C22×D312yes—
674#103C22×D312yes—
675#102—34no—
676#102C22×D312yes—
677#102C22×D312yes—
678C22⋊C8—32no—
679C22⋊C8—32no—
680C22⋊C8—34no—
681C22⋊C8—34no—
682C22⋊C8C22×D311yescharacteristic
683C22⋊C8C22×D311yescharacteristic
684C22⋊C8C22×D312yes—
685C23×C3—24no—
686C23×C3—22no—
687C23×C3—22no—
688C23×C3—22no—
689C23×C3—21no—
690C23×C3—41no—
691C23×C3—42no—
692C23×C3—42no—
693C23×C3C22×D411yescharacteristic
694C23×C3C22×D411yescharacteristic
695C23×C3C22×D411yescharacteristic
696C22×D3—24no—
697C22×D3—24no—
698C22×D3—22no—
699C22×D3—42no—
700C22×D3—42no—
701C22×D3—44no—
702C22×D3—82no—
703C22×D3—82no—
704C22×D3—81no—
705C22×D3—81no—
706C22×D3C22×D412yes—
707C22×D3C22×D412yes—
708C3×Q8—24no—
709C3×Q8—22no—
710C3×Q8—22no—
711C3×Q8C22×D414yes—
712C3×D4—28no—
713C3×D4—24no—
714C3×D4—28no—
715C3×D4—22no—
716C3×D4—22no—
717C3×D4—42no—
718C3×D4—42no—
719C3×D4—81no—
720C3×D4C22×D414yes—
721C2×C3×C4—24no—
722C2×C3×C4—28no—
723C2×C3×C4—22no—
724C2×C3×C4—22no—
725C2×C3×C4—22no—
726C2×C3×C4—28no—
727C2×C3×C4—22no—
728C2×C3×C4—22no—
729C2×C3×C4—22no—
730C2×C3×C4—21no—
731C2×C3×C4—21no—
732C2×C3×C4—21no—
733C2×C3×C4—42no—
734C2×C3×C4C22×D411yescharacteristic
735C2×C3×C4C22×D411yescharacteristic
736C2×C3×C4C22×D411yescharacteristic
737C2×C3×C4C22×D414yes—
738C2×C3×C4C2511yescharacteristic
739#67—216no—
740#67—24no—
741#67—24no—
742#67—216no—
743#67—24no—
744#67—44no—
745#67—44no—
746#67—82no—
747#67—82no—
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—22no—
757C2×Dic3—81no—
758C2×Dic3C22×D412yes—
759C2×Dic3C22×D412yes—
760D12—24no—
761D12—22no—
762D12—24no—
763D12—44no—
764D12—42no—
765D12—82no—
766D12—82no—
767D12#12014yes—
768C4×D3—216no—
769C4×D3—216no—
770C4×D3—24no—
771C4×D3—24no—
772C4×D3—24no—
773C4×D3—44no—
774C4×D3—82no—
775C4×D3C22×D418yes—
776Dic6—28no—
777Dic6—216no—
778Dic6—28no—
779Dic6—22no—
780Dic6—28no—
781Dic6—24no—
782Dic6—24no—
783Dic6—216no—
784Dic6#12014yes—
785Dic6C22×D418yes—
786C3×C8—22no—
787C3×C8—22no—
788C3⋊C8—24no—
789C24—21no—
790C24—32no—
791C24—62no—
792C24—61no—
793C24D3×D411yescharacteristic
794#41—28no—
795#41—28no—
796#41—24no—
797#41—24no—
798#41—24no—
799#41—24no—
800#41—38no—
801#41—316no—
802#41—68no—
803#41—68no—
804#41—64no—
805#41—616no—
806#41—64no—
807#41—632no—
808#41—616no—
809#41—68no—
810#41—68no—
811#41—632no—
812#41—68no—
813#41—616no—
814#41—616no—
815#41—632no—
816#41—632no—
817#41—632no—
818#41—68no—
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—64no—
831C2×Q8—64no—
832C2×Q8—68no—
833C2×Q8—64no—
834C2×Q8—68no—
835C2×Q8—616no—
836C2×Q8—616no—
837C2×Q8—68no—
838C2×Q8—632no—
839C2×Q8—68no—
840C2×Q8—616no—
841C2×Q8—68no—
842C2×Q8—68no—
843C2×Q8—68no—
844C2×Q8—616no—
845C2×Q8—616no—
846C2×Q8—68no—
847C2×Q8—62no—
848C2×Q8—62no—
849C2×Q8—62no—
850C2×Q8—64no—
851C2×Q8C23×D311yescharacteristic
852C2×Q8C23×D312yes—
853C2×D4—28no—
854C2×D4—22no—
855C2×D4—22no—
856C2×D4—24no—
857C2×D4—21no—
858C2×D4—21no—
859C2×D4—21no—
860C2×D4—21no—
861C2×D4—32no—
862C2×D4—32no—
863C2×D4—32no—
864C2×D4—32no—
865C2×D4—31no—
866C2×D4—32no—
867C2×D4—31no—
868C2×D4—32no—
869C2×D4—64no—
870C2×D4—62no—
871C2×D4—62no—
872C2×D4—62no—
873C2×D4—68no—
874C2×D4—62no—
875C2×D4—68no—
876C2×D4—64no—
877C2×D4—64no—
878C2×D4—616no—
879C2×D4—62no—
880C2×D4—62no—
881C2×D4—62no—
882C2×D4—64no—
883C2×D4—61no—
884C2×D4—124no—
885C2×D4—128no—
886C2×D4—244no—
887C2×D4—242no—
888C2×D4C23×D311yescharacteristic
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—62no—
903C22×C4—64no—
904C22×C4—64no—
905C22×C4—616no—
906C22×C4—62no—
907C22×C4—64no—
908C22×C4—64no—
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—24no—
922Q16—68no—
923SD16—24no—
924SD16—24no—
925SD16—68no—
926SD16—68no—
927SD16—68no—
928SD16—68no—
929D8—24no—
930D8—68no—
931M16—68no—
932M16—64no—
933C2×C8—24no—
934C2×C8—34no—
935C2×C8—68no—
936C2×C8C23×D312yes—
937C2×C8C23×D312yes—
938C4⋊C4—21no—
939C4⋊C4—21no—
940C4⋊C4—32no—
941C4⋊C4—62no—
942C4⋊C4—62no—
943C4⋊C4—61no—
944C4⋊C4C23×D311yescharacteristic
945C4⋊C4C23×D311yescharacteristic
946C22⋊C4—21no—
947C22⋊C4—21no—
948C22⋊C4—21no—
949C22⋊C4—21no—
950C22⋊C4—21no—
951C22⋊C4—62no—
952C22⋊C4—62no—
953C22⋊C4—62no—
954C22⋊C4—62no—
955C22⋊C4—62no—
956C22⋊C4—62no—
957C22⋊C4—62no—
958C42—21no—
959C42—62no—
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—41no—
973C22×C3—41no—
974C22×C3—41no—
975C22×C3C2×#12012yes—
976C22×C3#57712yescomplemented
977C22×C3C23×D411yescharacteristic
978C2×D3—22no—
979C2×D3—22no—
980C2×D3—22no—
981C2×D3—22no—
982C2×D3—22no—
983C2×D3—48no—
984C2×D3—42no—
985C2×D3—42no—
986C2×D3—42no—
987C2×D3—164no—
988C2×D3—162no—
989C2×D3C2×#12014yes—
990C3×C4—21no—
991C3×C4—24no—
992C3×C4—21no—
993C3×C4—41no—
994C3×C4—41no—
995C3×C4—41no—
996C3×C4C2×#12012yes—
997C3×C4C23×D412yes—
998Dic3—22no—
999Dic3—28no—
1000Dic3—42no—
1001Dic3C2×#12014yes—
1002C23—24no—
1003C23—22no—
1004C23—22no—
1005C23—22no—
1006C23—21no—
1007C23—32no—
1008C23—32no—
1009C23—41no—
1010C23—42no—
1011C23—42no—
1012C23—64no—
1013C23—64no—
1014C23—62no—
1015C23—122no—
1016C23—124no—
1017C23—122no—
1018C23—241no—
1019C23—241no—
1020C23—242no—
1021C23—242no—
1022C23C2×D3×D411yescharacteristic
1023C23C2×D3×D411yescharacteristic
1024C23C2×D3×D411yescharacteristic
1025Q8—24no—
1026Q8—22no—
1027Q8—22no—
1028Q8—34no—
1029Q8—38no—
1030Q8—64no—
1031Q8—616no—
1032Q8—68no—
1033Q8—616no—
1034Q8—68no—
1035Q8—64no—
1036Q8—62no—
1037Q8—68no—
1038Q8C2×D3×D414yes—
1039D4—28no—
1040D4—24no—
1041D4—28no—
1042D4—22no—
1043D4—22no—
1044D4—38no—
1045D4—34no—
1046D4—42no—
1047D4—42no—
1048D4—64no—
1049D4—64no—
1050D4—64no—
1051D4—616no—
1052D4—616no—
1053D4—64no—
1054D4—64no—
1055D4—62no—
1056D4—81no—
1057D4—124no—
1058D4—124no—
1059D4—124no—
1060D4—122no—
1061D4—242no—
1062D4—242no—
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—21no—
1076C2×C4—21no—
1077C2×C4—21no—
1078C2×C4—32no—
1079C2×C4—38no—
1080C2×C4—32no—
1081C2×C4—42no—
1082C2×C4—64no—
1083C2×C4—64no—
1084C2×C4—616no—
1085C2×C4—616no—
1086C2×C4—64no—
1087C2×C4—616no—
1088C2×C4—68no—
1089C2×C4—616no—
1090C2×C4—68no—
1091C2×C4—64no—
1092C2×C4—68no—
1093C2×C4—64no—
1094C2×C4—62no—
1095C2×C4—124no—
1096C2×C4—242no—
1097C2×C4—241no—
1098C2×C4C2×D3×D411yescharacteristic
1099C2×C4C2×D3×D411yescharacteristic
1100C2×C4C2×D3×D414yes—
1101C2×C4C2×D3×D411yescharacteristic
1102C2×C4C24×D311yescharacteristic
1103C8—22no—
1104C8—22no—
1105C8—64no—
1106C2×C3—22no—
1107C2×C3—22no—
1108C2×C3—41no—
1109C2×C3—44no—
1110C2×C3—81no—
1111C2×C3C22×#12011yescharacteristic
1112C2×C3C2×#57711yescharacteristic
1113C2×C3#358611yescharacteristic
1114D3—24no—
1115D3—42no—
1116D3—82no—
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—41no—
1131C22—41no—
1132C22—41no—
1133C22—62no—
1134C22—62no—
1135C22—62no—
1136C22—62no—
1137C22—62no—
1138C22—128no—
1139C22—122no—
1140C22—122no—
1141C22—122no—
1142C22—482no—
1143C22—484no—
1144C22D3×#12012yes—
1145C22#577012yescomplemented
1146C22C22×D3×D411yescharacteristic
1147C4—21no—
1148C4—24no—
1149C4—21no—
1150C4—34no—
1151C4—41no—
1152C4—41no—
1153C4—41no—
1154C4—62no—
1155C4—68no—
1156C4—122no—
1157C4D3×#12012yes—
1158C4C22×D3×D412yes—
1159C3#6037411yescharacteristic, complemented, Sylow
1160C2—22no—
1161C2—22no—
1162C2—41no—
1163C2—44no—
1164C2—64no—
1165C2—81no—
1166C2—122no—
1167C2—242no—
1168C2C2×D3×#12011yescharacteristic
1169C2C2×#577011yescharacteristic
1170C2#8720111yescharacteristic
subgroupG/H
centerC22C22×D3×D4
commutator, cosocleC2×C3×C4C25
FrattiniC2×C4C24×D3
FittingC3×#3002C2
socleC22×C3C23×D4
hypercenter#3002D3
hypocenterC3#60374
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C23×C4 ◁ #3002

Complements

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

NH ≅ G/Ntype
1. C22×#1010C2semidirect
2. C2×#5770C2semidirect
3. #86041C2semidirect
4. C3×#3002C2semidirect
5. #84082C2semidirect
6. #83913C2semidirect
7. #82933C2semidirect
8. #80232C2semidirect
9. #80183C2semidirect
10. #80145C2semidirect
11. #80086C2semidirect
12. D3×#448C2semidirect
13. #80003C2semidirect
14. #78836C2semidirect
15. #78832C2semidirect
16. C2×#4738C2semidirect
17. #78600C2semidirect
19. C22×C3×#41C22semidirect
25. C2×#1010C22semidirect
26. C2×#1010C22semidirect
27. C2×#1009C22semidirect
28. C22×D3×Q8C22semidirect
30. C22×#237C22semidirect
34. C23×Dic6C22semidirect
35. C2×C3×#135C22semidirect
37. #5833C22semidirect
38. C2×#951C22semidirect
39. C2×#949C22semidirect
42. C2×#918C22semidirect
43. C2×#916C22semidirect
44. C2×D3×SD16C22semidirect
45. C2×#911C22semidirect
46. C22×#204C22semidirect
47. C2×#901C22semidirect
49. #5629C22semidirect
51. #5607C22semidirect
58. #5525C22semidirect
59. #5523C22semidirect
60. C3×#452C22semidirect
61. C3×#451C22semidirect
62. C3×#450C22semidirect
63. C3×#449C22semidirect
64. C3×#448C22semidirect
65. C3×#447C22semidirect
66. C3×#416C22semidirect
67. C2×C3×C22⋊C8C22semidirect
68. #5238C22semidirect
69. #5232C22semidirect
70. #5227C22semidirect
71. #5217C22semidirect
72. #5207C22semidirect
73. #5186C22semidirect
74. #5173C22semidirect
75. #5170C22semidirect
76. #5158C22semidirect
77. #5110C22semidirect
78. C2×#816C22semidirect
79. #5050C22semidirect
80. #5050C22semidirect
81. #5040C22semidirect
82. #5040C22semidirect
83. #5004C22semidirect
84. #4806C22semidirect
85. #4806C22semidirect
86. #4802C22semidirect
87. D3×#103C22semidirect
88. #4781C22semidirect
89. #4781C22semidirect
90. #4772C22semidirect
91. #4771C22semidirect
92. #4738C22semidirect
93. #4738C22semidirect
94. #4738C22semidirect
95. #4727C22semidirect
96. #4726C22semidirect
97. D3×C22⋊C8C22semidirect
110. #3002D3semidirect
139. #1010D4semidirect
287. C22×#41C2×D3semidirect
297. C2×#135C2×D3semidirect
317. #452C2×D3semidirect
321. #451C2×D3semidirect
322. #450C2×D3semidirect
327. #449C2×D3semidirect
337. #448C2×D3semidirect
339. #447C2×D3semidirect
345. #416C2×D3semidirect
353. C2×C22⋊C8C2×D3semidirect
365. C3×#41C2×D4semidirect
420. D3×Q8C2×D4semidirect
430. #237C2×D4semidirect
484. C2×Dic6C2×D4semidirect
821. #41D3×D4semidirect
976. C22×C3#577semidirect
1145. C22#5770semidirect
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×#57702
#860412
C3×#30022
#840822
#839132
#829332
#802322
#801832
#801452
#800862
D3×#4482
#800032
#788362
#788322
C2×#47382
#786002
#603743