Finite Group Databasebeta

← #11661704

Subgroups — #11661704

Order 768.

4810 conjugacy classes of subgroups.

The subgroup lattice has 1202 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5964C211yesmaximal, characteristic, complemented
2C2×#5773C212yesmaximal, complemented
3C2×#5608C211yesmaximal, characteristic, complemented
4C3×#3006C211yesmaximal, characteristic, complemented
5#84084C211yesmaximal, characteristic, complemented
6#83946C212yesmaximal, complemented
7#82624C211yesmaximal, characteristic, complemented
8#80088C214yesmaximal, complemented
9#80087C214yesmaximal, complemented
10#80042C214yesmaximal, complemented
11#80005C214yesmaximal, complemented
12#78885C212yesmaximal, complemented
13D3×#417C212yesmaximal, complemented
14#78640C211yesmaximal, characteristic, complemented
15#78630C211yesmaximal, characteristic, complemented
16#60371—31nomaximal, Sylow
17C22×C3×#41C2211yescharacteristic
18#5964—216no—
19C2×#1010—21no—
20C2×#1010C2212yescomplemented
21C2×#1009—21no—
22C2×#1009C2212yescomplemented
23C2×D3×#41—22no—
24C2×D3×#41C2212yes—
25C2×D3×#41C2212yes—
26C2×#1007C2212yescomplemented
27C2×#1004—21no—
28C2×#1004—21no—
29C2×#1004C2212yescomplemented
30C22×#237C2211yescharacteristic, complemented
31C22×#235—22no—
32C22×#235C2211yescharacteristic
33C22×#235C2211yescharacteristic
34C2×C3×AGL(1,ℤ/8)C2212yescomplemented
35C2×C3×#121C2211yescharacteristic, complemented
36C2×#951C2212yescomplemented
37C2×#939—21no—
38C2×#938—21no—
39C2×#938C2211yescharacteristic, complemented
40C2×#932C2212yescomplemented
41C2×#924C2211yescharacteristic, complemented
42#5773—216no—
43C2×#916C2214yescomplemented
44C2×#915C2214yescomplemented
45C2×#912C2214yescomplemented
46C2×#911C2214yescomplemented
47C2×#909C2212yescomplemented
48C2×D3×M16C2212yescomplemented
49#5608—22no—
50#5608—22no—
51#5608C2214yescomplemented
52#5608C2214yescomplemented
53C2×#897C2211yescharacteristic, complemented
54C2×D3×C4⋊C4C2211yescharacteristic, complemented
55C2×#884—21no—
56C2×#878—21no—
57C3×#449C2214yescomplemented
58C3×#448C2212yescomplemented
59C3×#447C2212yescomplemented
60C3×#417C2212yescomplemented
61C3×#407C2211yescharacteristic, complemented
62#5239C2214yescomplemented
63#5232C2212yescomplemented
64#5228C2212yescomplemented
65#5218C2212yescomplemented
66#5207C2211yescharacteristic, complemented
67#5172C2214yescomplemented
68#5170C2214yescomplemented
69#5158C2214yescomplemented
70#5156C2214yescomplemented
71#5133C2212yescomplemented
72#5126C2212yescomplemented
73#5040C2212yescomplemented
74#5037C2214yescomplemented
75#5036C2212yescomplemented
76#4966C2212yescomplemented
77#4809C2214yescomplemented
78#4808C2214yescomplemented
79#4803C2214yescomplemented
80D3×#103C2214yescomplemented
81#4783C2214yescomplemented
82#4776C2214yescomplemented
83#4771C2214yescomplemented
84D3×#102C2214yescomplemented
85#4739C2212yescomplemented
86#4733C2214yescomplemented
87#4731C2212yescomplemented
88#4727C2214yescomplemented
89#4727C2214yescomplemented
90C2×#585—31no—
91C2×#575—32no—
92C2×#537—31no—
93#3013—34no—
94#3013—34no—
95#3012—34no—
96#3012—34no—
97#3007—32no—
98#3007—31no—
99#3007—31no—
100#3006—32no—
101#3006—31no—
102#3006D311yescharacteristic, complemented
103C2×#417—32no—
104#2879—31no—
105C2×C3×#41—28no—
106C2×C3×#41—21no—
107C2×C3×#41—21no—
108C2×C3×#41C2312yes—
109C2×C3×#41C2312yes—
110C22×C3×Q8C2311yescharacteristic
111C22×C3×D4—21no—
112C22×C3×D4—21no—
113C22×C3×D4C2311yescharacteristic
114C22×C3×D4C2311yescharacteristic
115C23×C3×C4—21no—
116C23×C3×C4C2311yescharacteristic
117C22×#67—21no—
118C22×#67—22no—
119C22×#67—22no—
120C22×#67—21no—
121C22×#67—21no—
122C22×#67D411yescharacteristic
123C22×#67D411yescharacteristic
124C23×Dic3—21no—
125#1010—216no—
126#1010—28no—
127#1010—28no—
128#1009—216no—
129#1009—28no—
130#1009—28no—
131D3×#41—232no—
132D3×#41—28no—
133D3×#41—28no—
134D3×#41—28no—
135D3×#41D4116yescomplemented
136#1007—28no—
137#1007—28no—
138C2×#239—22no—
139C2×#239C2312yes—
140C2×#239C2312yes—
141C2×D3×Q8—22no—
142C2×D3×Q8C2312yes—
143C2×D3×Q8C2312yes—
144#1004—216no—
145#1004—216no—
146#1004—28no—
147#1004—28no—
148C2×#237—22no—
149C2×#237—22no—
150C2×#237—22no—
151C2×#237—22no—
152C2×#237—28no—
153C2×#237—22no—
154C2×#237—22no—
155C2×#237C2312yes—
156C2×#237C2314yes—
157C2×#237C2312yes—
158C2×D3×D4—22no—
159C2×D3×D4—22no—
160C2×D3×D4—22no—
161C2×D3×D4—22no—
162C2×D3×D4—22no—
163C2×D3×D4C2312yes—
164C2×D3×D4C2312yes—
165C2×#235—232no—
166C2×#235—21no—
167C2×#235—21no—
168C2×#235—22no—
169C2×#235—22no—
170C2×#235—28no—
171C2×#235—22no—
172C2×#235—22no—
173C2×#235—22no—
174C2×#235—28no—
175C2×#235—22no—
176C2×#235D412yes—
177C2×#235D412yes—
178C2×#235C2312yes—
179C2×#235C2312yes—
180C2×#235C2312yes—
181C2×#235C2312yes—
182C22×D12—22no—
183C22×D12D411yescharacteristic
184C22×D12C2311yescharacteristic
185C22×C4×D3—21no—
186C22×C4×D3—22no—
187C22×C4×D3—22no—
188C22×C4×D3—21no—
189C22×C4×D3C2311yescharacteristic
190C22×C4×D3C2311yescharacteristic
191C22×Dic6—22no—
192C22×Dic6D411yescharacteristic
193C22×Dic6C2311yescharacteristic
194C22×Dic6C2311yescharacteristic
195C3×AGL(1,ℤ/8)—28no—
196C2×C3×SD16C2314yes—
197C2×C3×D8C2314yes—
198C2×C3×M16C2312yes—
199C3×#121—21no—
200C3×#121—21no—
201C3×#121C2312yes—
202C3×#121C2312yes—
203C2×C3×C4⋊C4C2311yescharacteristic
204C2×C3×C22⋊C4—21no—
205C2×#217—21no—
206C2×#217—21no—
207#951—28no—
208C2×#216C2314yes—
209#939—24no—
210#939—24no—
211#938—24no—
212#938—24no—
213#938—22no—
214#938C2314yes—
215C2×#214C2314yes—
216C2×#214C2314yes—
217#932—28no—
218C2×#213C2314yes—
219C2×(C2×D3)⋊C4—21no—
220C2×C4⋊Dic3—21no—
221C2×C4⋊Dic3C2311yescharacteristic
222#924—21no—
223#924—21no—
224#924C2312yes—
225#924C2312yes—
226C2×Dic3⋊C4—21no—
227C2×Dic3⋊C4—21no—
228C2×#208C2312yes—
229#916—216no—
230#915—216no—
231#912—216no—
232#911—216no—
233#909—28no—
234D3×M16—28no—
235C2×Dic12C2314yes—
236C2×#204C2314yes—
237C2×ΓL(1,𝔽25)C2314yes—
238C2×D3×C8C2314yes—
239#897—22no—
240#897C2314yes—
241D3×C4⋊C4—22no—
242D3×C4⋊C4C2314yes—
243#884—24no—
244#884—24no—
245#878—24no—
246#878—24no—
247C3×#103C2314yes—
248C3×#102C2314yes—
249C3×C22⋊C8C2312yes—
250C3×C22⋊C8C2312yes—
251#835C2314yes—
252#832C2314yes—
253#830C2312yes—
254#830C2312yes—
255#821C2314yes—
256(C2×D3)⋊C8C2314yes—
257(C2×D3)⋊C8C2314yes—
258#816C2314yes—
259#810C2314yes—
260#809C2314yes—
261#585—616no—
262C2×2−1+4—32no—
263C2×2−1+4—32no—
264C2×2−1+4—61no—
265C2×H(5,𝔽2)—32no—
266C2×H(5,𝔽2)—32no—
267C2×H(5,𝔽2)—61no—
268C2×H(5,𝔽2)—61no—
269C2×H(5,𝔽2)—61no—
270C22×#41—31no—
271C22×#41—32no—
272C22×#41—32no—
273C22×#41—31no—
274C22×#41—31no—
275C22×#41—62no—
276C22×#41—62no—
277C22×#41C2×D311yescharacteristic
278#575—616no—
279C2×#137—32no—
280C2×#137—34no—
281C2×#137—32no—
282C2×AGL(1,ℤ/8)—32no—
283C2×AGL(1,ℤ/8)—34no—
284C2×AGL(1,ℤ/8)C2×D312yescomplemented
285C2×#135—34no—
286C2×#135—34no—
287C22×M16—32no—
288#537—34no—
289#537—34no—
290#537—62no—
291#537—62no—
292C2×C22⋊Q8—31no—
293C2×C22⋊Q8—31no—
294C2×C22⋊Q8—61no—
295C2×#121—31no—
296C2×#121—61no—
297C2×#121—61no—
298C2×#121—61no—
299C2×#121C2×D311yescharacteristic, complemented
300C22×C4⋊C4—31no—
301#452—34no—
302#452—34no—
303#452—34no—
304#452—34no—
305#451—32no—
306#451—34no—
307#451—32no—
308#450—32no—
309#450—34no—
310#450—32no—
311#449—34no—
312#449—34no—
313#449—34no—
314#449C2×D314yescomplemented
315#448—34no—
316#448—32no—
317#448C2×D312yescomplemented
318#447—34no—
319#447—32no—
320#447C2×D312yescomplemented
321#417—32no—
322#417—32no—
323#417—32no—
324#417—34no—
325#417—34no—
326#417C2×D312yescomplemented
327C2×#103—34no—
328C2×#102—34no—
329#408—34no—
330#408—34no—
331#407—31no—
332#407—32no—
333#407C2×D311yescharacteristic, complemented
334C24×C3—21no—
335C24×C3—21no—
336C24×C3C2×D411yescharacteristic
337C23×D3—21no—
338C23×D3—22no—
339C23×D3—22no—
340C23×D3C2×D411yescharacteristic
341C23×D3C2×D411yescharacteristic
342C3×#41—28no—
343C3×#41—28no—
344C3×#41—24no—
345C3×#41—24no—
346C3×#41—24no—
347C3×#41C2×D418yes—
348C2×C3×Q8—24no—
349C2×C3×Q8—21no—
350C2×C3×Q8C2412yes—
351C2×C3×D4—28no—
352C2×C3×D4—22no—
353C2×C3×D4—22no—
354C2×C3×D4—24no—
355C2×C3×D4—22no—
356C2×C3×D4—22no—
357C2×C3×D4—21no—
358C2×C3×D4—24no—
359C2×C3×D4—21no—
360C2×C3×D4—82no—
361C2×C3×D4C2412yes—
362C2×C3×D4C2412yes—
363C22×C3×C4—28no—
364C22×C3×C4—21no—
365C22×C3×C4—22no—
366C22×C3×C4—22no—
367C22×C3×C4—24no—
368C22×C3×C4—21no—
369C22×C3×C4C2×D411yescharacteristic
370C22×C3×C4C2×D411yescharacteristic
371C22×C3×C4C2×D411yescharacteristic
372C22×C3×C4C2411yescharacteristic
373C22×C3×C4C2411yescharacteristic
374C22×C3×C4C2411yescharacteristic
375C2×#67—28no—
376C2×#67—216no—
377C2×#67—216no—
378C2×#67—22no—
379C2×#67—22no—
380C2×#67—24no—
381C2×#67—22no—
382C2×#67—22no—
383C2×#67—24no—
384C2×#67—24no—
385C2×#67—24no—
386C2×#67—22no—
387C2×#67—22no—
388C2×#67—44no—
389C2×#67—82no—
390C2×#67C2×D412yes—
391C2×#67C2×D412yes—
392C2×#67C2×D412yes—
393C2×#67C2×D412yes—
394C22×Dic3—21no—
395C22×Dic3—22no—
396C22×Dic3—22no—
397C22×Dic3—21no—
398C22×Dic3—21no—
399C22×Dic3—24no—
400C22×Dic3—44no—
401C22×Dic3C2×D411yescharacteristic
402C22×Dic3C2×D411yescharacteristic
403#239—216no—
404#239—24no—
405#239—24no—
406#239—24no—
407#239C2×D418yescomplemented
408D3×Q8—216no—
409D3×Q8—24no—
410D3×Q8—24no—
411D3×Q8—24no—
412D3×Q8C2×D418yescomplemented
413#237—216no—
414#237—216no—
415#237—216no—
416#237—216no—
417#237—24no—
418#237—216no—
419#237—24no—
420#237—28no—
421#237—28no—
422#237—24no—
423#237—48no—
424#237C2×D418yescomplemented
425D3×D4—216no—
426D3×D4—216no—
427D3×D4—216no—
428D3×D4—216no—
429D3×D4—216no—
430D3×D4—24no—
431D3×D4—24no—
432D3×D4—24no—
433D3×D4C2×D418yescomplemented
434#235—28no—
435#235—216no—
436#235—216no—
437#235—216no—
438#235—28no—
439#235—216no—
440#235—216no—
441#235—24no—
442#235—24no—
443#235—28no—
444#235—216no—
445#235—28no—
446#235—24no—
447#235—24no—
448#235—24no—
449#235—24no—
450#235—24no—
451#235C2×D418yes—
452C2×D12—216no—
453C2×D12—24no—
454C2×D12—22no—
455C2×D12—22no—
456C2×D12—21no—
457C2×D12—24no—
458C2×D12C2×D412yes—
459C2×D12C2×D412yes—
460C2×D12C2412yes—
461C2×C4×D3—28no—
462C2×C4×D3—216no—
463C2×C4×D3—22no—
464C2×C4×D3—22no—
465C2×C4×D3—22no—
466C2×C4×D3—22no—
467C2×C4×D3—24no—
468C2×C4×D3—22no—
469C2×C4×D3—22no—
470C2×C4×D3—216no—
471C2×C4×D3—24no—
472C2×C4×D3—82no—
473C2×C4×D3C2×D412yes—
474C2×C4×D3C2×D412yes—
475C2×C4×D3C2×D418yes—
476C2×C4×D3C2412yes—
477C2×C4×D3C2412yes—
478C2×Dic6—216no—
479C2×Dic6—21no—
480C2×Dic6—24no—
481C2×Dic6—22no—
482C2×Dic6—22no—
483C2×Dic6—24no—
484C2×Dic6—24no—
485C2×Dic6—21no—
486C2×Dic6C2×D412yes—
487C2×Dic6C2×D412yes—
488C2×Dic6C2412yes—
489C2×Dic6C2412yes—
490C3×SD16—28no—
491C3×D8—28no—
492C3×M16—24no—
493C2×C3×C8C2414yes—
494C3×C4⋊C4—21no—
495C3×C4⋊C4C2412yes—
496C3×C22⋊C4—22no—
497C3×C22⋊C4—22no—
498#217—22no—
499#217—22no—
500#217—24no—
501#216—28no—
502#214—28no—
503#214—28no—
504#213—28no—
505(C2×D3)⋊C4—24no—
506C4⋊Dic3—21no—
507C4⋊Dic3—24no—
508C4⋊Dic3C2412yes—
509Dic3⋊C4—22no—
510Dic3⋊C4—22no—
511Dic3⋊C4—24no—
512#208—24no—
513C2×C3⋊C8C2414yes—
514Dic12—28no—
515#204—28no—
516ΓL(1,𝔽25)—28no—
517D3×C8—28no—
5182−1+4—68no—
5192−1+4—68no—
5202−1+4—68no—
5212−1+4—68no—
5222−1+4—616no—
523H(5,𝔽2)—68no—
524H(5,𝔽2)—68no—
525H(5,𝔽2)—616no—
526H(5,𝔽2)—616no—
527H(5,𝔽2)—68no—
528H(5,𝔽2)—68no—
529H(5,𝔽2)—616no—
530C2×#41—28no—
531C2×#41—21no—
532C2×#41—21no—
533C2×#41—32no—
534C2×#41—32no—
535C2×#41—32no—
536C2×#41—32no—
537C2×#41—316no—
538C2×#41—32no—
539C2×#41—32no—
540C2×#41—32no—
541C2×#41—34no—
542C2×#41—32no—
543C2×#41—32no—
544C2×#41—32no—
545C2×#41—62no—
546C2×#41—62no—
547C2×#41—68no—
548C2×#41—62no—
549C2×#41—62no—
550C2×#41—62no—
551C2×#41—62no—
552C2×#41—68no—
553C2×#41—632no—
554C2×#41—62no—
555C2×#41—62no—
556C2×#41—62no—
557C2×#41—68no—
558C2×#41—68no—
559C2×#41—62no—
560C2×#41—62no—
561C2×#41—62no—
562C2×#41—62no—
563C2×#41—68no—
564C2×#41—632no—
565C2×#41—68no—
566C2×#41—61no—
567C2×#41—61no—
568C2×#41C22×D312yes—
569C2×#41C22×D312yes—
570C22×Q8—31no—
571C22×Q8—32no—
572C22×Q8—32no—
573C22×Q8—31no—
574C22×Q8—31no—
575C22×Q8—62no—
576C22×Q8—62no—
577C22×Q8C22×D311yescharacteristic
578C22×D4—21no—
579C22×D4—21no—
580C22×D4—32no—
581C22×D4—31no—
582C22×D4—31no—
583C22×D4—32no—
584C22×D4—31no—
585C22×D4—31no—
586C22×D4—62no—
587C22×D4—62no—
588C22×D4—62no—
589C22×D4—62no—
590C22×D4—62no—
591C22×D4—62no—
592C22×D4—62no—
593C22×D4—62no—
594C22×D4—61no—
595C22×D4—61no—
596C22×D4—61no—
597C22×D4C22×D311yescharacteristic
598C22×D4C22×D311yescharacteristic
599C23×C4—21no—
600C23×C4—31no—
601C23×C4—31no—
602C23×C4—62no—
603C23×C4—62no—
604C23×C4—61no—
605C23×C4—61no—
606C23×C4—61no—
607C23×C4C22×D311yescharacteristic
608#137—68no—
609#137—616no—
610#137—68no—
611AGL(1,ℤ/8)—28no—
612AGL(1,ℤ/8)—616no—
613AGL(1,ℤ/8)—68no—
614#135—616no—
615#135—616no—
616C2×Q16—34no—
617C2×Q16—34no—
618C2×SD16—34no—
619C2×SD16—34no—
620C2×SD16—34no—
621C2×SD16C22×D314yes—
622C2×D8—34no—
623C2×D8C22×D314yes—
624C2×M16—32no—
625C2×M16—34no—
626C2×M16—68no—
627C2×M16C22×D312yes—
628C22×C8—34no—
629C22⋊Q8—32no—
630C22⋊Q8—32no—
631C22⋊Q8—34no—
632C22⋊Q8—64no—
633C22⋊Q8—64no—
634C22⋊Q8—62no—
635C22⋊Q8—61no—
636C22⋊Q8—61no—
637#121—21no—
638#121—21no—
639#121—34no—
640#121—64no—
641#121—64no—
642#121—62no—
643#121—64no—
644#121—64no—
645#121—64no—
646#121—64no—
647#121C22×D312yes—
648#121C22×D312yes—
649C2×C4⋊C4—31no—
650C2×C4⋊C4—34no—
651C2×C4⋊C4—62no—
652C2×C4⋊C4—61no—
653C2×C4⋊C4—61no—
654C2×C4⋊C4—61no—
655C2×C4⋊C4C22×D311yescharacteristic
656C2×C22⋊C4—21no—
657C2×C22⋊C4—61no—
658C2×C22⋊C4—61no—
659C2×C22⋊C4—61no—
660#103—34no—
661#103—34no—
662#103—34no—
663#103C22×D314yes—
664#102—34no—
665#102—34no—
666#102—34no—
667#102C22×D314yes—
668C22⋊C8—32no—
669C22⋊C8—32no—
670C22⋊C8—34no—
671C22⋊C8—34no—
672C22⋊C8C22×D312yes—
673C22⋊C8C22×D312yes—
674C23×C3—24no—
675C23×C3—22no—
676C23×C3—22no—
677C23×C3—22no—
678C23×C3—41no—
679C23×C3—41no—
680C23×C3—42no—
681C23×C3—42no—
682C23×C3—42no—
683C23×C3—81no—
684C23×C3—81no—
685C23×C3C22×D411yescharacteristic
686C23×C3C22×D411yescharacteristic
687C23×C3C22×D411yescharacteristic
688C22×D3—22no—
689C22×D3—28no—
690C22×D3—24no—
691C22×D3—22no—
692C22×D3—28no—
693C22×D3—41no—
694C22×D3—41no—
695C22×D3—41no—
696C22×D3—41no—
697C22×D3—82no—
698C22×D3—82no—
699C22×D3—82no—
700C22×D3—82no—
701C22×D3—81no—
702C22×D3—81no—
703C22×D3#12014yes—
704C22×D3C22×D412yes—
705C22×D3C22×D412yes—
706C3×Q8—24no—
707C3×Q8—22no—
708C3×Q8C22×D414yes—
709C3×D4—28no—
710C3×D4—24no—
711C3×D4—28no—
712C3×D4—22no—
713C3×D4—24no—
714C3×D4—42no—
715C3×D4—82no—
716C3×D4—82no—
717C3×D4C22×D414yes—
718C2×C3×C4—28no—
719C2×C3×C4—24no—
720C2×C3×C4—22no—
721C2×C3×C4—22no—
722C2×C3×C4—28no—
723C2×C3×C4—22no—
724C2×C3×C4—22no—
725C2×C3×C4—22no—
726C2×C3×C4—22no—
727C2×C3×C4—22no—
728C2×C3×C4—42no—
729C2×C3×C4C22×D411yescharacteristic
730C2×C3×C4C22×D411yescharacteristic
731C2×C3×C4C22×D411yescharacteristic
732C2×C3×C4C22×D414yes—
733C2×C3×C4C2511yescharacteristic
734#67—28no—
735#67—28no—
736#67—28no—
737#67—28no—
738#67—24no—
739#67—24no—
740#67—28no—
741#67—24no—
742#67—24no—
743#67—28no—
744#67—48no—
745#67—84no—
746C2×Dic3—28no—
747C2×Dic3—24no—
748C2×Dic3—22no—
749C2×Dic3—22no—
750C2×Dic3—28no—
751C2×Dic3—22no—
752C2×Dic3—22no—
753C2×Dic3—42no—
754C2×Dic3—42no—
755C2×Dic3—48no—
756C2×Dic3#12014yes—
757C2×Dic3C22×D412yes—
758C2×Dic3C22×D412yes—
759D12—24no—
760D12—28no—
761D12—24no—
762D12—28no—
763D12—24no—
764D12—22no—
765D12C22×D414yes—
766C4×D3—28no—
767C4×D3—28no—
768C4×D3—28no—
769C4×D3—28no—
770C4×D3—28no—
771C4×D3—24no—
772C4×D3—22no—
773C4×D3—22no—
774C4×D3—28no—
775C4×D3—84no—
776C4×D3#12018yes—
777C4×D3C22×D414yes—
778C4×D3C22×D414yes—
779Dic6—24no—
780Dic6—28no—
781Dic6—22no—
782Dic6—24no—
783Dic6—28no—
784Dic6—24no—
785Dic6—24no—
786Dic6—42no—
787Dic6C22×D414yes—
788C3×C8—24no—
789C3⋊C8—24no—
790C24—21no—
791C24—21no—
792C24—31no—
793C24—31no—
794C24—62no—
795C24—62no—
796C24—61no—
797C24D3×D411yescharacteristic
798#41—28no—
799#41—28no—
800#41—24no—
801#41—24no—
802#41—24no—
803#41—38no—
804#41—38no—
805#41—38no—
806#41—68no—
807#41—616no—
808#41—68no—
809#41—64no—
810#41—64no—
811#41—64no—
812#41—64no—
813#41—64no—
814#41—64no—
815#41—68no—
816#41—616no—
817#41—616no—
818#41—616no—
819#41—616no—
820#41—616no—
821#41—68no—
822#41—616no—
823#41—64no—
824#41—64no—
825#41—68no—
826#41—68no—
827#41—64no—
828#41—616no—
829#41—616no—
830#41—616no—
831#41—616no—
832#41—64no—
833#41—616no—
834#41—64no—
835#41—64no—
836#41—64no—
837#41—128no—
838#41D3×D418yes—
839C2×Q8—24no—
840C2×Q8—21no—
841C2×Q8—32no—
842C2×Q8—32no—
843C2×Q8—38no—
844C2×Q8—32no—
845C2×Q8—32no—
846C2×Q8—62no—
847C2×Q8—62no—
848C2×Q8—64no—
849C2×Q8—64no—
850C2×Q8—616no—
851C2×Q8—64no—
852C2×Q8—64no—
853C2×Q8—616no—
854C2×Q8—64no—
855C2×Q8—61no—
856C2×Q8—61no—
857C2×Q8—64no—
858C2×Q8C23×D312yes—
859C2×D4—28no—
860C2×D4—22no—
861C2×D4—22no—
862C2×D4—24no—
863C2×D4—22no—
864C2×D4—22no—
865C2×D4—21no—
866C2×D4—24no—
867C2×D4—21no—
868C2×D4—38no—
869C2×D4—32no—
870C2×D4—32no—
871C2×D4—32no—
872C2×D4—32no—
873C2×D4—32no—
874C2×D4—32no—
875C2×D4—32no—
876C2×D4—64no—
877C2×D4—64no—
878C2×D4—62no—
879C2×D4—62no—
880C2×D4—616no—
881C2×D4—64no—
882C2×D4—62no—
883C2×D4—62no—
884C2×D4—64no—
885C2×D4—64no—
886C2×D4—616no—
887C2×D4—616no—
888C2×D4—616no—
889C2×D4—616no—
890C2×D4—616no—
891C2×D4—64no—
892C2×D4—62no—
893C2×D4—62no—
894C2×D4—616no—
895C2×D4—616no—
896C2×D4—68no—
897C2×D4—62no—
898C2×D4—62no—
899C2×D4—64no—
900C2×D4—64no—
901C2×D4—64no—
902C2×D4—61no—
903C2×D4—82no—
904C2×D4—124no—
905C2×D4—242no—
906C2×D4C23×D312yes—
907C2×D4C23×D312yes—
908C22×C4—28no—
909C22×C4—21no—
910C22×C4—22no—
911C22×C4—22no—
912C22×C4—24no—
913C22×C4—21no—
914C22×C4—31no—
915C22×C4—32no—
916C22×C4—38no—
917C22×C4—32no—
918C22×C4—31no—
919C22×C4—32no—
920C22×C4—32no—
921C22×C4—62no—
922C22×C4—62no—
923C22×C4—616no—
924C22×C4—62no—
925C22×C4—62no—
926C22×C4—616no—
927C22×C4—68no—
928C22×C4—64no—
929C22×C4—62no—
930C22×C4—62no—
931C22×C4—64no—
932C22×C4—61no—
933C22×C4—64no—
934C22×C4—62no—
935C22×C4—62no—
936C22×C4—61no—
937C22×C4—61no—
938C22×C4—124no—
939C22×C4—242no—
940C22×C4D3×D411yescharacteristic
941C22×C4D3×D411yescharacteristic
942C22×C4D3×D411yescharacteristic
943C22×C4C23×D311yescharacteristic
944C22×C4C23×D311yescharacteristic
945C22×C4C23×D311yescharacteristic
946Q16—68no—
947Q16—68no—
948SD16—28no—
949SD16—68no—
950SD16—68no—
951SD16—68no—
952D8—28no—
953D8—68no—
954M16—24no—
955M16—68no—
956M16—64no—
957C2×C8—34no—
958C2×C8—68no—
959C2×C8C23×D314yes—
960C4⋊C4—21no—
961C4⋊C4—32no—
962C4⋊C4—64no—
963C4⋊C4—64no—
964C4⋊C4—61no—
965C4⋊C4—62no—
966C4⋊C4—62no—
967C4⋊C4C23×D312yes—
968C22⋊C4—22no—
969C22⋊C4—22no—
970C22⋊C4—64no—
971C22⋊C4—64no—
972C22⋊C4—62no—
973C22⋊C4—62no—
974C22×C3—21no—
975C22×C3—21no—
976C22×C3—21no—
977C22×C3—21no—
978C22×C3—21no—
979C22×C3—21no—
980C22×C3—21no—
981C22×C3—24no—
982C22×C3—21no—
983C22×C3—42no—
984C22×C3—42no—
985C22×C3—42no—
986C22×C3—42no—
987C22×C3—42no—
988C22×C3—82no—
989C22×C3—84no—
990C22×C3—84no—
991C22×C3C2×#12012yes—
992C22×C3C23×D411yescharacteristic
993C2×D3—22no—
994C2×D3—22no—
995C2×D3—22no—
996C2×D3—22no—
997C2×D3—22no—
998C2×D3—24no—
999C2×D3—44no—
1000C2×D3—42no—
1001C2×D3—42no—
1002C2×D3—88no—
1003C2×D3—82no—
1004C2×D3—88no—
1005C2×D3—84no—
1006C2×D3C2×#12014yes—
1007C3×C4—21no—
1008C3×C4—24no—
1009C3×C4—21no—
1010C3×C4—42no—
1011C3×C4C2×#12012yes—
1012C3×C4C23×D412yes—
1013Dic3—22no—
1014Dic3—24no—
1015Dic3—42no—
1016Dic3—42no—
1017Dic3C2×#12014yes—
1018C23—24no—
1019C23—22no—
1020C23—22no—
1021C23—22no—
1022C23—32no—
1023C23—34no—
1024C23—32no—
1025C23—41no—
1026C23—41no—
1027C23—42no—
1028C23—42no—
1029C23—42no—
1030C23—68no—
1031C23—64no—
1032C23—68no—
1033C23—62no—
1034C23—62no—
1035C23—81no—
1036C23—81no—
1037C23—121no—
1038C23—121no—
1039C23—121no—
1040C23—121no—
1041C23—241no—
1042C23—241no—
1043C23—242no—
1044C23—242no—
1045C23—242no—
1046C23—242no—
1047C23C2×D3×D411yescharacteristic
1048C23C2×D3×D411yescharacteristic
1049C23C2×D3×D411yescharacteristic
1050Q8—24no—
1051Q8—22no—
1052Q8—34no—
1053Q8—64no—
1054Q8—68no—
1055Q8—64no—
1056Q8—64no—
1057Q8—68no—
1058Q8—62no—
1059Q8—64no—
1060Q8—122no—
1061Q8C2×D3×D414yes—
1062D4—28no—
1063D4—24no—
1064D4—28no—
1065D4—22no—
1066D4—24no—
1067D4—34no—
1068D4—42no—
1069D4—64no—
1070D4—64no—
1071D4—68no—
1072D4—64no—
1073D4—68no—
1074D4—64no—
1075D4—64no—
1076D4—68no—
1077D4—64no—
1078D4—64no—
1079D4—68no—
1080D4—68no—
1081D4—68no—
1082D4—68no—
1083D4—68no—
1084D4—62no—
1085D4—82no—
1086D4—82no—
1087D4—128no—
1088D4—244no—
1089D4C2×D3×D414yes—
1090C2×C4—24no—
1091C2×C4—28no—
1092C2×C4—22no—
1093C2×C4—22no—
1094C2×C4—22no—
1095C2×C4—22no—
1096C2×C4—22no—
1097C2×C4—28no—
1098C2×C4—22no—
1099C2×C4—22no—
1100C2×C4—32no—
1101C2×C4—34no—
1102C2×C4—34no—
1103C2×C4—34no—
1104C2×C4—38no—
1105C2×C4—32no—
1106C2×C4—42no—
1107C2×C4—68no—
1108C2×C4—68no—
1109C2×C4—68no—
1110C2×C4—68no—
1111C2×C4—68no—
1112C2×C4—68no—
1113C2×C4—68no—
1114C2×C4—64no—
1115C2×C4—62no—
1116C2×C4—62no—
1117C2×C4—62no—
1118C2×C4—62no—
1119C2×C4—64no—
1120C2×C4—68no—
1121C2×C4—62no—
1122C2×C4—62no—
1123C2×C4—128no—
1124C2×C4—122no—
1125C2×C4—122no—
1126C2×C4—244no—
1127C2×C4C2×D3×D411yescharacteristic
1128C2×C4C2×D3×D411yescharacteristic
1129C2×C4C2×D3×D414yes—
1130C2×C4C2×D3×D411yescharacteristic
1131C2×C4C24×D311yescharacteristic
1132C8—24no—
1133C8—64no—
1134C2×C3—22no—
1135C2×C3—41no—
1136C2×C3—44no—
1137C2×C3—41no—
1138C2×C3—82no—
1139C2×C3C22×#12011yescharacteristic
1140C2×C3#358511yescharacteristic
1141C2×C3#358611yescharacteristic
1142D3—24no—
1143D3—42no—
1144D3—44no—
1145C22—21no—
1146C22—21no—
1147C22—21no—
1148C22—21no—
1149C22—21no—
1150C22—21no—
1151C22—24no—
1152C22—21no—
1153C22—21no—
1154C22—34no—
1155C22—42no—
1156C22—42no—
1157C22—42no—
1158C22—42no—
1159C22—42no—
1160C22—62no—
1161C22—62no—
1162C22—62no—
1163C22—64no—
1164C22—62no—
1165C22—62no—
1166C22—82no—
1167C22—84no—
1168C22—84no—
1169C22—124no—
1170C22—122no—
1171C22—122no—
1172C22—242no—
1173C22—248no—
1174C22—244no—
1175C22—248no—
1176C22D3×#12012yes—
1177C22C22×D3×D411yescharacteristic
1178C4—21no—
1179C4—24no—
1180C4—21no—
1181C4—34no—
1182C4—42no—
1183C4—62no—
1184C4—64no—
1185C4—122no—
1186C4—122no—
1187C4D3×#12012yes—
1188C4C22×D3×D412yes—
1189C3#6037111yescharacteristic, complemented, Sylow
1190C2—22no—
1191C2—41no—
1192C2—41no—
1193C2—44no—
1194C2—64no—
1195C2—82no—
1196C2—122no—
1197C2—124no—
1198C2C2×D3×#12011yescharacteristic
1199C2#8719211yescharacteristic
1200C2#8720111yescharacteristic
subgroupG/H
centerC22C22×D3×D4
commutator, cosocleC2×C3×C4C25
FrattiniC2×C4C24×D3
FittingC3×#3006C2
socleC22×C3C23×D4
hypercenter#3006D3
hypocenterC3#60371
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. C2×#5964C2semidirect
2. C2×#5773C2semidirect
3. C2×#5608C2semidirect
4. C3×#3006C2semidirect
5. #84084C2semidirect
6. #83946C2semidirect
7. #82624C2semidirect
8. #80088C2semidirect
9. #80087C2semidirect
10. #80042C2semidirect
11. #80005C2semidirect
12. #78885C2semidirect
13. D3×#417C2semidirect
14. #78640C2semidirect
15. #78630C2semidirect
20. C2×#1010C22semidirect
22. C2×#1009C22semidirect
26. C2×#1007C22semidirect
29. C2×#1004C22semidirect
30. C22×#237C22semidirect
34. C2×C3×AGL(1,ℤ/8)C22semidirect
35. C2×C3×#121C22semidirect
36. C2×#951C22semidirect
39. C2×#938C22semidirect
40. C2×#932C22semidirect
41. C2×#924C22semidirect
43. C2×#916C22semidirect
44. C2×#915C22semidirect
45. C2×#912C22semidirect
46. C2×#911C22semidirect
47. C2×#909C22semidirect
48. C2×D3×M16C22semidirect
51. #5608C22semidirect
52. #5608C22semidirect
53. C2×#897C22semidirect
54. C2×D3×C4⋊C4C22semidirect
57. C3×#449C22semidirect
58. C3×#448C22semidirect
59. C3×#447C22semidirect
60. C3×#417C22semidirect
61. C3×#407C22semidirect
62. #5239C22semidirect
63. #5232C22semidirect
64. #5228C22semidirect
65. #5218C22semidirect
66. #5207C22semidirect
67. #5172C22semidirect
68. #5170C22semidirect
69. #5158C22semidirect
70. #5156C22semidirect
71. #5133C22semidirect
72. #5126C22semidirect
73. #5040C22semidirect
74. #5037C22semidirect
75. #5036C22semidirect
76. #4966C22semidirect
77. #4809C22semidirect
78. #4808C22semidirect
79. #4803C22semidirect
80. D3×#103C22semidirect
81. #4783C22semidirect
82. #4776C22semidirect
83. #4771C22semidirect
84. D3×#102C22semidirect
85. #4739C22semidirect
86. #4733C22semidirect
87. #4731C22semidirect
88. #4727C22semidirect
89. #4727C22semidirect
102. #3006D3semidirect
135. D3×#41D4semidirect
284. C2×AGL(1,ℤ/8)C2×D3semidirect
299. C2×#121C2×D3semidirect
314. #449C2×D3semidirect
317. #448C2×D3semidirect
320. #447C2×D3semidirect
326. #417C2×D3semidirect
333. #407C2×D3semidirect
407. #239C2×D4semidirect
412. D3×Q8C2×D4semidirect
424. #237C2×D4semidirect
433. D3×D4C2×D4semidirect
1189. C3#60371semidirect

Maximal subgroups

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

subgroupindex
C2×#59642
C2×#57732
C2×#56082
C3×#30062
#840842
#839462
#826242
#800882
#800872
#800422
#800052
#788852
D3×#4172
#786402
#786302
#603713