Finite Group Databasebeta

← #11661709

Subgroups — #11661709

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×#5777C212yesmaximal, complemented
3C2×#5629C211yesmaximal, characteristic, complemented
4C3×#3007C211yesmaximal, characteristic, complemented
5#84082C211yesmaximal, characteristic, complemented
6#83981C212yesmaximal, complemented
7#82735C211yesmaximal, characteristic, complemented
8#80232C214yesmaximal, complemented
9#80231C214yesmaximal, complemented
10#80186C214yesmaximal, complemented
11#80149C214yesmaximal, complemented
12#78884C212yesmaximal, complemented
13D3×#417C212yesmaximal, complemented
14#78639C211yesmaximal, 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
27C22×#239C2211yescharacteristic, complemented
28C2×#1004—21no—
29C2×#1004—21no—
30C2×#1004C2212yescomplemented
31C22×#235—22no—
32C22×#235C2211yescharacteristic
33C22×#235C2211yescharacteristic
34C2×C3×#137C2212yescomplemented
35C2×C3×C22⋊Q8C2211yescharacteristic, complemented
36C2×#949C2212yescomplemented
37C2×#946C2211yescharacteristic, complemented
38C2×#942C2212yescomplemented
39C2×#930C2211yescharacteristic, complemented
40#5777—216no—
41C2×#919C2214yescomplemented
42C2×#918C2214yescomplemented
43C2×#916C2214yescomplemented
44C2×#914C2214yescomplemented
45C2×#908C2212yescomplemented
46C2×D3×M16C2212yescomplemented
47#5629—22no—
48#5629—22no—
49#5629C2214yescomplemented
50#5629C2214yescomplemented
51C2×#896—21no—
52C2×#895—21no—
53C2×#895C2211yescharacteristic, complemented
54C2×D3×C4⋊C4C2211yescharacteristic, complemented
55C2×#884—21no—
56C2×#884—21no—
57C3×#452C2214yescomplemented
58C3×#451C2212yescomplemented
59C3×#450C2212yescomplemented
60C3×#417C2212yescomplemented
61C3×#407C2211yescharacteristic, complemented
62#5238C2214yescomplemented
63#5232C2212yescomplemented
64#5227C2212yescomplemented
65#5217C2212yescomplemented
66#5207C2211yescharacteristic, complemented
67#5187C2214yescomplemented
68#5186C2214yescomplemented
69#5173C2214yescomplemented
70#5169C2214yescomplemented
71#5133C2212yescomplemented
72#5126C2212yescomplemented
73#5050C2212yescomplemented
74#5047C2214yescomplemented
75#5046C2212yescomplemented
76#4966C2212yescomplemented
77#4810C2214yescomplemented
78#4806C2214yescomplemented
79#4803C2214yescomplemented
80D3×#103C2214yescomplemented
81#4781C2214yescomplemented
82#4773C2214yescomplemented
83#4771C2214yescomplemented
84D3×#102C2214yescomplemented
85#4738C2212yescomplemented
86#4734C2214yescomplemented
87#4732C2212yescomplemented
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#3007D311yescharacteristic, complemented
100#3006—32no—
101#3006—31no—
102#3006—31no—
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×Q8C2311yescharacteristic
112C22×C3×D4—21no—
113C22×C3×D4C2311yescharacteristic
114C23×C3×C4—21no—
115C23×C3×C4C2311yescharacteristic
116C22×#67—21no—
117C22×#67—22no—
118C22×#67—22no—
119C22×#67—21no—
120C22×#67D411yescharacteristic
121C22×#67D411yescharacteristic
122#1010—216no—
123#1010—28no—
124#1010—28no—
125#1009—216no—
126#1009—28no—
127#1009—28no—
128D3×#41—232no—
129D3×#41—28no—
130D3×#41—28no—
131D3×#41—28no—
132D3×#41D4116yescomplemented
133#1007—28no—
134#1007—28no—
135C2×#239—22no—
136C2×#239—22no—
137C2×#239—28no—
138C2×#239C2312yes—
139C2×#239C2314yes—
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—22no—
153C2×#237C2312yes—
154C2×#237C2312yes—
155C2×D3×D4—22no—
156C2×D3×D4—22no—
157C2×D3×D4—22no—
158C2×D3×D4—22no—
159C2×D3×D4—22no—
160C2×D3×D4C2312yes—
161C2×D3×D4C2312yes—
162C2×#235—232no—
163C2×#235—21no—
164C2×#235—21no—
165C2×#235—22no—
166C2×#235—22no—
167C2×#235—28no—
168C2×#235—22no—
169C2×#235—22no—
170C2×#235—22no—
171C2×#235—28no—
172C2×#235—22no—
173C2×#235D412yes—
174C2×#235D412yes—
175C2×#235C2312yes—
176C2×#235C2312yes—
177C2×#235C2312yes—
178C2×#235C2312yes—
179C22×D12—22no—
180C22×D12—21no—
181C22×D12—21no—
182C22×D12D411yescharacteristic
183C22×D12C2311yescharacteristic
184C22×D12C2311yescharacteristic
185C22×C4×D3—21no—
186C22×C4×D3—22no—
187C22×C4×D3—22no—
188C22×C4×D3—21no—
189C22×C4×D3—21no—
190C22×C4×D3C2311yescharacteristic
191C22×C4×D3C2311yescharacteristic
192C22×Dic6—22no—
193C22×Dic6D411yescharacteristic
194C22×Dic6C2311yescharacteristic
195C3×#137—28no—
196C2×C3×Q16C2314yes—
197C2×C3×SD16C2314yes—
198C2×C3×M16C2312yes—
199C3×C22⋊Q8—21no—
200C3×C22⋊Q8—21no—
201C3×C22⋊Q8C2312yes—
202C3×C22⋊Q8C2312yes—
203C2×C3×C4⋊C4—21no—
204C2×C3×C4⋊C4C2311yescharacteristic
205C2×C3×C22⋊C4—21no—
206#949—28no—
207#946—22no—
208#946C2314yes—
209C2×#216C2314yes—
210#942—28no—
211C2×#215C2314yes—
212C2×#215C2314yes—
213C2×#213C2314yes—
214#930—21no—
215#930—21no—
216#930C2312yes—
217#930C2312yes—
218C2×(C2×D3)⋊C4—21no—
219C2×(C2×D3)⋊C4—21no—
220C2×(C2×D3)⋊C4—21no—
221C2×C4⋊Dic3C2311yescharacteristic
222C2×Dic3⋊C4—21no—
223C2×Dic3⋊C4—21no—
224C2×#208C2312yes—
225#919—216no—
226#918—216no—
227#916—216no—
228#914—216no—
229#908—28no—
230D3×M16—28no—
231C2×D24C2314yes—
232C2×#204C2314yes—
233C2×ΓL(1,𝔽25)C2314yes—
234C2×D3×C8C2314yes—
235#896—24no—
236#896—24no—
237#895—24no—
238#895—24no—
239#895—22no—
240#895C2314yes—
241D3×C4⋊C4—22no—
242D3×C4⋊C4C2314yes—
243#884—24no—
244#884—24no—
245#884—24no—
246#884—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×#137C2×D312yescomplemented
282C2×AGL(1,ℤ/8)—32no—
283C2×AGL(1,ℤ/8)—34no—
284C2×AGL(1,ℤ/8)—32no—
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—61no—
294C2×C22⋊Q8C2×D311yescharacteristic, complemented
295C2×#121—31no—
296C2×#121—31no—
297C2×#121—61no—
298C2×#121—61no—
299C2×#121—61no—
300C22×C4⋊C4—31no—
301#452—34no—
302#452—34no—
303#452—34no—
304#452C2×D314yescomplemented
305#451—34no—
306#451—32no—
307#451C2×D312yescomplemented
308#450—34no—
309#450—32no—
310#450C2×D312yescomplemented
311#449—34no—
312#449—34no—
313#449—34no—
314#449—34no—
315#448—32no—
316#448—34no—
317#448—32no—
318#447—32no—
319#447—34no—
320#447—32no—
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×C3C2×D411yescharacteristic
336C23×D3—21no—
337C23×D3—22no—
338C23×D3—22no—
339C23×D3—21no—
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×Q8—21no—
351C2×C3×Q8—24no—
352C2×C3×Q8C2412yes—
353C2×C3×Q8C2412yes—
354C2×C3×D4—28no—
355C2×C3×D4—22no—
356C2×C3×D4—22no—
357C2×C3×D4—24no—
358C2×C3×D4—21no—
359C2×C3×D4C2412yes—
360C22×C3×C4—28no—
361C22×C3×C4—21no—
362C22×C3×C4—22no—
363C22×C3×C4—22no—
364C22×C3×C4—24no—
365C22×C3×C4—21no—
366C22×C3×C4—21no—
367C22×C3×C4C2×D411yescharacteristic
368C22×C3×C4C2×D411yescharacteristic
369C22×C3×C4C2×D411yescharacteristic
370C22×C3×C4C2411yescharacteristic
371C22×C3×C4C2411yescharacteristic
372C22×C3×C4C2411yescharacteristic
373C2×#67—28no—
374C2×#67—216no—
375C2×#67—216no—
376C2×#67—22no—
377C2×#67—22no—
378C2×#67—24no—
379C2×#67—22no—
380C2×#67—22no—
381C2×#67—22no—
382C2×#67—22no—
383C2×#67—24no—
384C2×#67—22no—
385C2×#67—22no—
386C2×#67—82no—
387C2×#67C2×D412yes—
388C2×#67C2×D412yes—
389C2×#67C2×D412yes—
390C2×#67C2×D412yes—
391C22×Dic3—21no—
392C22×Dic3—22no—
393C22×Dic3—22no—
394C22×Dic3—21no—
395C22×Dic3C2×D411yescharacteristic
396C22×Dic3C2×D411yescharacteristic
397#239—216no—
398#239—24no—
399#239—24no—
400#239—24no—
401#239—28no—
402#239—28no—
403#239—48no—
404#239C2×D418yescomplemented
405D3×Q8—216no—
406D3×Q8—24no—
407D3×Q8—24no—
408D3×Q8—24no—
409D3×Q8C2×D418yescomplemented
410#237—216no—
411#237—216no—
412#237—216no—
413#237—216no—
414#237—24no—
415#237—216no—
416#237—24no—
417#237—24no—
418#237C2×D418yescomplemented
419D3×D4—216no—
420D3×D4—216no—
421D3×D4—216no—
422D3×D4—216no—
423D3×D4—216no—
424D3×D4—24no—
425D3×D4—24no—
426D3×D4—24no—
427D3×D4C2×D418yescomplemented
428#235—28no—
429#235—216no—
430#235—216no—
431#235—216no—
432#235—28no—
433#235—216no—
434#235—216no—
435#235—24no—
436#235—24no—
437#235—28no—
438#235—216no—
439#235—28no—
440#235—24no—
441#235—24no—
442#235—24no—
443#235—24no—
444#235—24no—
445#235C2×D418yes—
446C2×D12—216no—
447C2×D12—24no—
448C2×D12—22no—
449C2×D12—22no—
450C2×D12—21no—
451C2×D12—24no—
452C2×D12—24no—
453C2×D12—24no—
454C2×D12—21no—
455C2×D12—24no—
456C2×D12—44no—
457C2×D12—82no—
458C2×D12C2×D412yes—
459C2×D12C2×D412yes—
460C2×D12C2412yes—
461C2×D12C2412yes—
462C2×C4×D3—28no—
463C2×C4×D3—216no—
464C2×C4×D3—22no—
465C2×C4×D3—22no—
466C2×C4×D3—22no—
467C2×C4×D3—22no—
468C2×C4×D3—24no—
469C2×C4×D3—22no—
470C2×C4×D3—22no—
471C2×C4×D3—216no—
472C2×C4×D3—24no—
473C2×C4×D3—24no—
474C2×C4×D3—44no—
475C2×C4×D3—82no—
476C2×C4×D3C2×D412yes—
477C2×C4×D3C2×D412yes—
478C2×C4×D3C2×D418yes—
479C2×C4×D3C2412yes—
480C2×C4×D3C2412yes—
481C2×Dic6—216no—
482C2×Dic6—21no—
483C2×Dic6—24no—
484C2×Dic6—22no—
485C2×Dic6—22no—
486C2×Dic6—24no—
487C2×Dic6C2×D412yes—
488C2×Dic6C2×D412yes—
489C2×Dic6C2412yes—
490C3×Q16—28no—
491C3×SD16—28no—
492C3×M16—24no—
493C2×C3×C8C2414yes—
494C3×C4⋊C4—21no—
495C3×C4⋊C4—22no—
496C3×C4⋊C4—22no—
497C3×C4⋊C4C2412yes—
498C3×C22⋊C4—22no—
499C3×C22⋊C4—22no—
500#216—28no—
501#215—28no—
502#215—28no—
503#213—28no—
504(C2×D3)⋊C4—24no—
505(C2×D3)⋊C4—22no—
506(C2×D3)⋊C4—22no—
507(C2×D3)⋊C4—24no—
508C4⋊Dic3—21no—
509C4⋊Dic3C2412yes—
510Dic3⋊C4—24no—
511Dic3⋊C4—24no—
512#208—24no—
513C2×C3⋊C8C2414yes—
514D24—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—34no—
540C2×#41—32no—
541C2×#41—32no—
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—62no—
575C22×Q8—62no—
576C22×Q8C22×D311yescharacteristic
577C22×Q8C22×D311yescharacteristic
578C22×D4—21no—
579C22×D4—32no—
580C22×D4—31no—
581C22×D4—31no—
582C22×D4—32no—
583C22×D4—31no—
584C22×D4—31no—
585C22×D4—31no—
586C22×D4—62no—
587C22×D4—61no—
588C22×D4—61no—
589C22×D4—62no—
590C22×D4—62no—
591C22×D4—62no—
592C22×D4—62no—
593C22×D4—62no—
594C22×D4—62no—
595C22×D4—62no—
596C22×D4—61no—
597C22×D4—61no—
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—28no—
609#137—616no—
610#137—68no—
611AGL(1,ℤ/8)—68no—
612AGL(1,ℤ/8)—616no—
613AGL(1,ℤ/8)—68no—
614#135—616no—
615#135—616no—
616C2×Q16—34no—
617C2×Q16C22×D314yes—
618C2×SD16—34no—
619C2×SD16—34no—
620C2×SD16—34no—
621C2×SD16C22×D314yes—
622C2×D8—34no—
623C2×D8—34no—
624C2×M16—32no—
625C2×M16—34no—
626C2×M16—68no—
627C2×M16C22×D312yes—
628C22×C8—34no—
629C22⋊Q8—21no—
630C22⋊Q8—21no—
631C22⋊Q8—34no—
632C22⋊Q8—64no—
633C22⋊Q8—64no—
634C22⋊Q8—62no—
635C22⋊Q8C22×D312yes—
636C22⋊Q8C22×D312yes—
637#121—32no—
638#121—32no—
639#121—34no—
640#121—64no—
641#121—64no—
642#121—64no—
643#121—64no—
644#121—62no—
645#121—64no—
646#121—64no—
647#121—61no—
648#121—61no—
649C2×C4⋊C4—21no—
650C2×C4⋊C4—31no—
651C2×C4⋊C4—34no—
652C2×C4⋊C4—62no—
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—41no—
678C23×C3—41no—
679C23×C3—81no—
680C23×C3—81no—
681C23×C3C22×D411yescharacteristic
682C23×C3C22×D411yescharacteristic
683C23×C3C22×D411yescharacteristic
684C22×D3—22no—
685C22×D3—28no—
686C22×D3—24no—
687C22×D3—22no—
688C22×D3—28no—
689C22×D3—22no—
690C22×D3—41no—
691C22×D3—41no—
692C22×D3—41no—
693C22×D3—41no—
694C22×D3—42no—
695C22×D3—42no—
696C22×D3—42no—
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×Q8—24no—
709C3×Q8—42no—
710C3×Q8C22×D414yes—
711C3×D4—28no—
712C3×D4—24no—
713C3×D4—28no—
714C3×D4—22no—
715C3×D4C22×D414yes—
716C2×C3×C4—28no—
717C2×C3×C4—24no—
718C2×C3×C4—22no—
719C2×C3×C4—22no—
720C2×C3×C4—28no—
721C2×C3×C4—22no—
722C2×C3×C4—22no—
723C2×C3×C4—22no—
724C2×C3×C4—22no—
725C2×C3×C4—22no—
726C2×C3×C4—22no—
727C2×C3×C4—42no—
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—82no—
745#67—82no—
746C2×Dic3—28no—
747C2×Dic3—24no—
748C2×Dic3—22no—
749C2×Dic3—22no—
750C2×Dic3—28no—
751C2×Dic3—22no—
752C2×Dic3—42no—
753C2×Dic3#12014yes—
754C2×Dic3C22×D412yes—
755C2×Dic3C22×D412yes—
756D12—24no—
757D12—28no—
758D12—24no—
759D12—28no—
760D12—24no—
761D12—22no—
762D12—24no—
763D12—48no—
764D12—42no—
765D12—84no—
766D12C22×D414yes—
767C4×D3—28no—
768C4×D3—28no—
769C4×D3—28no—
770C4×D3—28no—
771C4×D3—28no—
772C4×D3—24no—
773C4×D3—22no—
774C4×D3—22no—
775C4×D3—28no—
776C4×D3—48no—
777C4×D3—84no—
778C4×D3#12018yes—
779C4×D3C22×D414yes—
780C4×D3C22×D414yes—
781Dic6—24no—
782Dic6—28no—
783Dic6—22no—
784Dic6—24no—
785Dic6—28no—
786Dic6—24no—
787Dic6C22×D414yes—
788C3×C8—24no—
789C3⋊C8—24no—
790C24—21no—
791C24—31no—
792C24—31no—
793C24—62no—
794C24—62no—
795C24—61no—
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—21no—
842C2×Q8—24no—
843C2×Q8—32no—
844C2×Q8—32no—
845C2×Q8—38no—
846C2×Q8—32no—
847C2×Q8—62no—
848C2×Q8—62no—
849C2×Q8—64no—
850C2×Q8—64no—
851C2×Q8—616no—
852C2×Q8—64no—
853C2×Q8—64no—
854C2×Q8—616no—
855C2×Q8—64no—
856C2×Q8—61no—
857C2×Q8C23×D312yes—
858C2×Q8C23×D312yes—
859C2×D4—28no—
860C2×D4—22no—
861C2×D4—22no—
862C2×D4—24no—
863C2×D4—21no—
864C2×D4—38no—
865C2×D4—32no—
866C2×D4—32no—
867C2×D4—32no—
868C2×D4—32no—
869C2×D4—32no—
870C2×D4—32no—
871C2×D4—32no—
872C2×D4—32no—
873C2×D4—64no—
874C2×D4—64no—
875C2×D4—62no—
876C2×D4—62no—
877C2×D4—616no—
878C2×D4—64no—
879C2×D4—64no—
880C2×D4—64no—
881C2×D4—62no—
882C2×D4—62no—
883C2×D4—64no—
884C2×D4—64no—
885C2×D4—616no—
886C2×D4—616no—
887C2×D4—616no—
888C2×D4—616no—
889C2×D4—616no—
890C2×D4—64no—
891C2×D4—62no—
892C2×D4—62no—
893C2×D4—616no—
894C2×D4—616no—
895C2×D4—68no—
896C2×D4—62no—
897C2×D4—62no—
898C2×D4—64no—
899C2×D4—62no—
900C2×D4—62no—
901C2×D4—61no—
902C2×D4—64no—
903C2×D4—61no—
904C2×D4—124no—
905C2×D4—242no—
906C2×D4—242no—
907C2×D4C23×D312yes—
908C22×C4—28no—
909C22×C4—21no—
910C22×C4—22no—
911C22×C4—22no—
912C22×C4—24no—
913C22×C4—21no—
914C22×C4—21no—
915C22×C4—31no—
916C22×C4—32no—
917C22×C4—38no—
918C22×C4—32no—
919C22×C4—31no—
920C22×C4—32no—
921C22×C4—32no—
922C22×C4—62no—
923C22×C4—62no—
924C22×C4—616no—
925C22×C4—64no—
926C22×C4—62no—
927C22×C4—62no—
928C22×C4—616no—
929C22×C4—68no—
930C22×C4—64no—
931C22×C4—62no—
932C22×C4—62no—
933C22×C4—61no—
934C22×C4—64no—
935C22×C4—62no—
936C22×C4—62no—
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—28no—
947Q16—68no—
948SD16—28no—
949SD16—68no—
950SD16—68no—
951SD16—68no—
952D8—68no—
953D8—68no—
954M16—24no—
955M16—68no—
956M16—64no—
957C2×C8—34no—
958C2×C8—68no—
959C2×C8C23×D314yes—
960C4⋊C4—22no—
961C4⋊C4—22no—
962C4⋊C4—21no—
963C4⋊C4—32no—
964C4⋊C4—64no—
965C4⋊C4—64no—
966C4⋊C4—61no—
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—82no—
986C22×C3—84no—
987C22×C3C2×#12012yes—
988C22×C3C23×D411yescharacteristic
989C2×D3—22no—
990C2×D3—22no—
991C2×D3—22no—
992C2×D3—22no—
993C2×D3—22no—
994C2×D3—24no—
995C2×D3—44no—
996C2×D3—42no—
997C2×D3—42no—
998C2×D3—42no—
999C2×D3—42no—
1000C2×D3—42no—
1001C2×D3—88no—
1002C2×D3—82no—
1003C2×D3—88no—
1004C2×D3—84no—
1005C2×D3—84no—
1006C2×D3C2×#12014yes—
1007C3×C4—21no—
1008C3×C4—24no—
1009C3×C4—21no—
1010C3×C4—42no—
1011C3×C4—42no—
1012C3×C4C2×#12012yes—
1013C3×C4C23×D412yes—
1014Dic3—22no—
1015Dic3—24no—
1016Dic3—42no—
1017Dic3C2×#12014yes—
1018C23—24no—
1019C23—22no—
1020C23—22no—
1021C23—32no—
1022C23—34no—
1023C23—32no—
1024C23—41no—
1025C23—41no—
1026C23—68no—
1027C23—64no—
1028C23—68no—
1029C23—62no—
1030C23—62no—
1031C23—62no—
1032C23—81no—
1033C23—81no—
1034C23—121no—
1035C23—121no—
1036C23—121no—
1037C23—121no—
1038C23—122no—
1039C23—122no—
1040C23—122no—
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—24no—
1053Q8—34no—
1054Q8—42no—
1055Q8—64no—
1056Q8—68no—
1057Q8—64no—
1058Q8—64no—
1059Q8—68no—
1060Q8—62no—
1061Q8C2×D3×D414yes—
1062D4—28no—
1063D4—24no—
1064D4—28no—
1065D4—22no—
1066D4—34no—
1067D4—64no—
1068D4—64no—
1069D4—68no—
1070D4—64no—
1071D4—68no—
1072D4—64no—
1073D4—64no—
1074D4—68no—
1075D4—64no—
1076D4—64no—
1077D4—68no—
1078D4—68no—
1079D4—68no—
1080D4—68no—
1081D4—68no—
1082D4—62no—
1083D4—64no—
1084D4—128no—
1085D4—122no—
1086D4—244no—
1087D4—242no—
1088D4—242no—
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—22no—
1101C2×C4—32no—
1102C2×C4—34no—
1103C2×C4—34no—
1104C2×C4—34no—
1105C2×C4—38no—
1106C2×C4—32no—
1107C2×C4—42no—
1108C2×C4—42no—
1109C2×C4—68no—
1110C2×C4—68no—
1111C2×C4—68no—
1112C2×C4—68no—
1113C2×C4—68no—
1114C2×C4—68no—
1115C2×C4—68no—
1116C2×C4—64no—
1117C2×C4—62no—
1118C2×C4—62no—
1119C2×C4—62no—
1120C2×C4—62no—
1121C2×C4—64no—
1122C2×C4—68no—
1123C2×C4—62no—
1124C2×C4—128no—
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×C3C22×#12011yescharacteristic
1139C2×C3#358511yescharacteristic
1140C2×C3#358611yescharacteristic
1141D3—24no—
1142D3—42no—
1143D3—44no—
1144D3—82no—
1145C22—21no—
1146C22—21no—
1147C22—21no—
1148C22—21no—
1149C22—24no—
1150C22—21no—
1151C22—21no—
1152C22—21no—
1153C22—21no—
1154C22—34no—
1155C22—42no—
1156C22—42no—
1157C22—62no—
1158C22—62no—
1159C22—64no—
1160C22—62no—
1161C22—62no—
1162C22—62no—
1163C22—82no—
1164C22—84no—
1165C22—124no—
1166C22—122no—
1167C22—122no—
1168C22—122no—
1169C22—122no—
1170C22—122no—
1171C22—242no—
1172C22—244no—
1173C22—248no—
1174C22—244no—
1175C22—248no—
1176C22D3×#12012yes—
1177C22C22×D3×D411yescharacteristic
1178C4—21no—
1179C4—24no—
1180C4—21no—
1181C4—34no—
1182C4—42no—
1183C4—42no—
1184C4—62no—
1185C4—64no—
1186C4—122no—
1187C4D3×#12012yes—
1188C4C22×D3×D412yes—
1189C3#6037111yescharacteristic, complemented, Sylow
1190C2—22no—
1191C2—41no—
1192C2—41no—
1193C2—44no—
1194C2—64no—
1195C2—122no—
1196C2—124no—
1197C2—242no—
1198C2C2×D3×#12011yescharacteristic
1199C2#8719711yescharacteristic
1200C2#8720011yescharacteristic
subgroupG/H
centerC22C22×D3×D4
commutator, cosocleC2×C3×C4C25
FrattiniC2×C4C24×D3
FittingC3×#3007C2
socleC22×C3C23×D4
hypercenter#3007D3
hypocenterC3#60371
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C23×C4 ◁ #3007

Complements

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

NH ≅ G/Ntype
1. C2×#5964C2semidirect
2. C2×#5777C2semidirect
3. C2×#5629C2semidirect
4. C3×#3007C2semidirect
5. #84082C2semidirect
6. #83981C2semidirect
7. #82735C2semidirect
8. #80232C2semidirect
9. #80231C2semidirect
10. #80186C2semidirect
11. #80149C2semidirect
12. #78884C2semidirect
13. D3×#417C2semidirect
14. #78639C2semidirect
15. #78630C2semidirect
20. C2×#1010C22semidirect
22. C2×#1009C22semidirect
26. C2×#1007C22semidirect
27. C22×#239C22semidirect
30. C2×#1004C22semidirect
34. C2×C3×#137C22semidirect
35. C2×C3×C22⋊Q8C22semidirect
36. C2×#949C22semidirect
37. C2×#946C22semidirect
38. C2×#942C22semidirect
39. C2×#930C22semidirect
41. C2×#919C22semidirect
42. C2×#918C22semidirect
43. C2×#916C22semidirect
44. C2×#914C22semidirect
45. C2×#908C22semidirect
46. C2×D3×M16C22semidirect
49. #5629C22semidirect
50. #5629C22semidirect
53. C2×#895C22semidirect
54. C2×D3×C4⋊C4C22semidirect
57. C3×#452C22semidirect
58. C3×#451C22semidirect
59. C3×#450C22semidirect
60. C3×#417C22semidirect
61. C3×#407C22semidirect
62. #5238C22semidirect
63. #5232C22semidirect
64. #5227C22semidirect
65. #5217C22semidirect
66. #5207C22semidirect
67. #5187C22semidirect
68. #5186C22semidirect
69. #5173C22semidirect
70. #5169C22semidirect
71. #5133C22semidirect
72. #5126C22semidirect
73. #5050C22semidirect
74. #5047C22semidirect
75. #5046C22semidirect
76. #4966C22semidirect
77. #4810C22semidirect
78. #4806C22semidirect
79. #4803C22semidirect
80. D3×#103C22semidirect
81. #4781C22semidirect
82. #4773C22semidirect
83. #4771C22semidirect
84. D3×#102C22semidirect
85. #4738C22semidirect
86. #4734C22semidirect
87. #4732C22semidirect
88. #4727C22semidirect
89. #4727C22semidirect
99. #3007D3semidirect
132. D3×#41D4semidirect
281. C2×#137C2×D3semidirect
294. C2×C22⋊Q8C2×D3semidirect
304. #452C2×D3semidirect
307. #451C2×D3semidirect
310. #450C2×D3semidirect
326. #417C2×D3semidirect
333. #407C2×D3semidirect
404. #239C2×D4semidirect
409. D3×Q8C2×D4semidirect
418. #237C2×D4semidirect
427. 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×#57772
C2×#56292
C3×#30072
#840822
#839812
#827352
#802322
#802312
#801862
#801492
#788842
D3×#4172
#786392
#786302
#603713