Finite Group Databasebeta

← #10697482

Subgroups — #10697482

Order 768.

828 conjugacy classes of subgroups.

The subgroup lattice has 590 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#459C211yesmaximal, characteristic, complemented
2C2×#5072C211yesmaximal, characteristic, complemented
3#82417C211yesmaximal, characteristic, complemented
4#71764C211yesmaximal, characteristic, complemented
5C2×D4⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
6C2×#4483C211yesmaximal, characteristic, complemented
7#67702C211yesmaximal, characteristic, complemented
8#10228—31nomaximal, Sylow
9C22×C3×D8—21no—
10C2×C3×#127C2211yescharacteristic
11C2×C3×C4×D4C2211yescharacteristic
12C2×#938—21no—
13C22×#213—21no—
14C2×#930—21no—
15C2×C4×D12C2211yescharacteristic
16C3×#459—22no—
17C3×#459—22no—
18C2×C3×C4⋊C8C2211yescharacteristic
19C2×C3×#102—21no—
20C2×#832—21no—
21C2×#832—22no—
22#5212—21no—
23#5072—22no—
24#5072—22no—
25#4987—21no—
26#4961—22no—
27#4935C2211yescharacteristic
28C2×C4⋊(C3⋊C8)C2211yescharacteristic
29C2×C4×C3⋊C8C2211yescharacteristic
30D4⋊(C3⋊C8)—22no—
31#4483—22no—
32C2×#459—31no—
33C2×#459D311yescharacteristic, complemented
34#2537—31no—
35#1957—31no—
36C2×D4⋊C8—31no—
37C2×D4⋊C8—31no—
38#1296—31no—
39C22×C3×D4—21no—
40C22×C3×D4—21no—
41C22×C3×D4—21no—
42C22×C3×D4D411yescharacteristic
43C23×C3×C4—21no—
44C22×#67—22no—
45C22×D12D411yescharacteristic
46C22×C4×D3—21no—
47C2×C3×D8—24no—
48C2×C3×D8—42no—
49C2×C3×D8—42no—
50C22×C3×C8—21no—
51C3×#127—21no—
52C3×#127—21no—
53C3×#127—21no—
54C3×#127D412yescomplemented
55C3×C4×D4—21no—
56C3×C4×D4—21no—
57C3×C4×D4—21no—
58C3×C4×D4—21no—
59C2×C3×C4⋊C4D411yescharacteristic
60C2×C3×C22⋊C4—21no—
61C2×C3×C42C2311yescharacteristic
62C2×#217—22no—
63#938—42no—
64#938—42no—
65C2×#213—24no—
66C2×#213—42no—
67C2×#213—42no—
68#930—42no—
69#930—42no—
70C2×(C2×D3)⋊C4—22no—
71C2×(C2×D3)⋊C4—21no—
72C2×C4⋊Dic3—21no—
73C2×C4⋊Dic3—21no—
74C2×C4⋊Dic3D411yescharacteristic
75C2×C4⋊Dic3D412yes—
76C22×C3⋊C8—21no—
77C22×C3⋊C8—21no—
78C4×D12—21no—
79C4×D12—21no—
80C4×D12—21no—
81C4×D12—21no—
82C3×C4⋊C8—21no—
83C3×C4⋊C8D412yescomplemented
84C3×#102—24no—
85#832—24no—
86#832—44no—
87C3⋊#95—22no—
88C4⋊(C3⋊C8)—21no—
89C4⋊(C3⋊C8)D412yescomplemented
90C4×C3⋊C8—21no—
91C4×C3⋊C8—21no—
92C22×D8—21no—
93C22×D8—61no—
94C2×#127C2×D311yescharacteristic
95C2×#121—61no—
96C2×#121—61no—
97C2×C4×D4—31no—
98C2×C4×D4C2×D311yescharacteristic
99#459—22no—
100#459—22no—
101#459—62no—
102#459—62no—
103C2×C4⋊C8—31no—
104C2×C4⋊C8C2×D311yescharacteristic
105C2×#102—21no—
106C2×#102—61no—
107C2×#102—62no—
108C2×C4×C8—31no—
109#394—62no—
110#384—31no—
111#380—61no—
112#380—61no—
113D4⋊C8—62no—
114D4⋊C8—62no—
115C24×C3—21no—
116C24×C3—41no—
117C23×D3—21no—
118C2×C3×D4—21no—
119C2×C3×D4—22no—
120C2×C3×D4—22no—
121C2×C3×D4—21no—
122C2×C3×D4—22no—
123C2×C3×D4—21no—
124C2×C3×D4—21no—
125C2×C3×D4—21no—
126C2×C3×D4—42no—
127C2×C3×D4—42no—
128C2×C3×D4—41no—
129C2×C3×D4—41no—
130C2×C3×D4—41no—
131C2×C3×D4—41no—
132C2×C3×D4—41no—
133C2×C3×D4—41no—
134C2×C3×D4—41no—
135C2×C3×D4—41no—
136C2×C3×D4—41no—
137C2×C3×D4—41no—
138C2×C3×D4—41no—
139C2×C3×D4D812yescomplemented
140C22×C3×C4—21no—
141C22×C3×C4—41no—
142C22×C3×C4—41no—
143C22×C3×C4—41no—
144C22×C3×C4—41no—
145C22×C3×C4—41no—
146C22×C3×C4—41no—
147C22×C3×C4C2×D411yescharacteristic
148C22×C3×C4C2×D411yescharacteristic
149C22×C3×C4C2×D411yescharacteristic
150C2×#67—44no—
151C2×#67—44no—
152C2×#67—82no—
153C22×Dic3—21no—
154C22×Dic3—22no—
155C2×D12—21no—
156C2×D12—21no—
157C2×D12—21no—
158C2×D12—21no—
159C2×D12—21no—
160C2×D12D812yescomplemented
161C2×C4×D3—41no—
162C2×C4×D3—41no—
163C2×C4×D3—41no—
164C2×C4×D3—41no—
165C2×C4×D3—41no—
166C2×C4×D3—41no—
167C3×D8—48no—
168C2×C3×C8—22no—
169C2×C3×C8—41no—
170C2×C3×C8—41no—
171C3×C4⋊C4—21no—
172C3×C4⋊C4—21no—
173C3×C22⋊C4—41no—
174C3×C22⋊C4—41no—
175C3×C42C2×D411yescharacteristic
176C3×C42C2×D411yescharacteristic
177C3×C42C2×D411yescharacteristic
178C3×C42#4111yescharacteristic
179#217—44no—
180#213—48no—
181(C2×D3)⋊C4—44no—
182(C2×D3)⋊C4—41no—
183(C2×D3)⋊C4—41no—
184C4⋊Dic3—21no—
185C4⋊Dic3—21no—
186C4⋊Dic3—41no—
187C4⋊Dic3—41no—
188C4⋊Dic3—41no—
189C4⋊Dic3—41no—
190C4⋊Dic3—42no—
191C2×C3⋊C8—22no—
192C2×C3⋊C8—22no—
193C2×C3⋊C8—41no—
194C2×C3⋊C8—41no—
195C2×C3⋊C8—41no—
196C2×C3⋊C8—41no—
197C22×D4—21no—
198C22×D4—21no—
199C22×D4—21no—
200C22×D4—31no—
201C22×D4—62no—
202C22×D4#6711yescharacteristic
203C23×C4—21no—
204C23×C4—61no—
205C2×D8—24no—
206C2×D8—42no—
207C2×D8—42no—
208C2×D8—64no—
209C2×D8—122no—
210C2×D8—122no—
211C22×C8—21no—
212C22×C8—61no—
213C22×C8—61no—
214#127—21no—
215#127—21no—
216#127—21no—
217#127#6712yescomplemented
218#121—122no—
219#121—122no—
220#121—122no—
221#121—122no—
222C4×D4—21no—
223C4×D4—21no—
224C4×D4—21no—
225C4×D4—21no—
226C4×D4—61no—
227C4×D4—61no—
228C4×D4—61no—
229C4×D4—61no—
230C2×C4⋊C4—31no—
231C2×C4⋊C4—32no—
232C2×C4⋊C4—61no—
233C2×C4⋊C4—61no—
234C2×C4⋊C4#6711yescharacteristic
235C2×C22⋊C4—21no—
236C2×C22⋊C4—62no—
237C2×C22⋊C4—62no—
238C2×C22⋊C4—61no—
239C2×C42C22×D311yescharacteristic
240C4⋊C8—21no—
241C4⋊C8—32no—
242C4⋊C8—61no—
243C4⋊C8#6712yescomplemented
244#102—24no—
245#102—64no—
246#102—124no—
247C4×C8—61no—
248C4×C8—61no—
249#95—62no—
250C23×C3—22no—
251C23×C3—41no—
252C23×C3—41no—
253C23×C3—41no—
254C23×C3—41no—
255C23×C3—41no—
256C23×C3—41no—
257C23×C3—42no—
258C23×C3—81no—
259C23×C3—81no—
260C23×C3—81no—
261C23×C3—81no—
262C23×C3—81no—
263C23×C3—81no—
264C23×C3#12011yescharacteristic
265C22×D3—22no—
266C22×D3—41no—
267C22×D3—41no—
268C22×D3—41no—
269C22×D3—41no—
270C22×D3—41no—
271C22×D3—41no—
272C3×D4—22no—
273C3×D4—22no—
274C3×D4—44no—
275C3×D4—42no—
276C3×D4—42no—
277C3×D4—41no—
278C3×D4—42no—
279C3×D4—42no—
280C3×D4—41no—
281C3×D4—82no—
282C3×D4—81no—
283C3×D4—81no—
284C3×D4—81no—
285C3×D4—81no—
286C2×C3×C4—21no—
287C2×C3×C4—21no—
288C2×C3×C4—41no—
289C2×C3×C4—41no—
290C2×C3×C4—41no—
291C2×C3×C4—81no—
292C2×C3×C4—81no—
293C2×C3×C4—81no—
294C2×C3×C4—81no—
295C2×C3×C4#12011yescharacteristic
296C2×C3×C4#12011yescharacteristic
297C2×C3×C4#12111yescharacteristic
298C2×C3×C4#12111yescharacteristic
299C2×C3×C4#12111yescharacteristic
300C2×C3×C4#12711yescharacteristic
301C2×C3×C4C2×D811yescharacteristic
302C2×C3×C4C2×D811yescharacteristic
303C2×C3×C4#13511yescharacteristic
304C2×C3×C4#13511yescharacteristic
305C2×C3×C4AGL(1,ℤ/8)11yescharacteristic
306C2×C3×C4AGL(1,ℤ/8)11yescharacteristic
307C2×C3×C4AGL(1,ℤ/8)11yescharacteristic
308C2×C3×C4AGL(1,ℤ/8)11yescharacteristic
309#67—88no—
310C2×Dic3—41no—
311C2×Dic3—42no—
312C2×Dic3—42no—
313C2×Dic3—41no—
314C2×Dic3—41no—
315C2×Dic3—42no—
316D12—22no—
317D12—22no—
318D12—41no—
319D12—41no—
320C4×D3—81no—
321C4×D3—81no—
322C4×D3—81no—
323C4×D3—81no—
324C3×C8—42no—
325C3⋊C8—42no—
326C3⋊C8—42no—
327C24—21no—
328C24—41no—
329C24—61no—
330C2×D4—21no—
331C2×D4—22no—
332C2×D4—21no—
333C2×D4—22no—
334C2×D4—21no—
335C2×D4—21no—
336C2×D4—21no—
337C2×D4—22no—
338C2×D4—32no—
339C2×D4—42no—
340C2×D4—42no—
341C2×D4—41no—
342C2×D4—41no—
343C2×D4—41no—
344C2×D4—41no—
345C2×D4—41no—
346C2×D4—41no—
347C2×D4—41no—
348C2×D4—41no—
349C2×D4—41no—
350C2×D4—41no—
351C2×D4—41no—
352C2×D4—61no—
353C2×D4—61no—
354C2×D4—61no—
355C2×D4—61no—
356C2×D4—61no—
357C2×D4—124no—
358C2×D4—124no—
359C2×D4—242no—
360C2×D4#21312yescomplemented
361C22×C4—21no—
362C22×C4—41no—
363C22×C4—41no—
364C22×C4—41no—
365C22×C4—41no—
366C22×C4—41no—
367C22×C4—41no—
368C22×C4—61no—
369C22×C4—62no—
370C22×C4—121no—
371C22×C4—121no—
372C22×C4—121no—
373C22×C4—121no—
374C22×C4—121no—
375C22×C4—121no—
376C22×C4D3×D411yescharacteristic
377C22×C4D3×D411yescharacteristic
378C22×C4C2×#6711yescharacteristic
379D8—48no—
380D8—128no—
381C2×C8—22no—
382C2×C8—41no—
383C2×C8—41no—
384C2×C8—62no—
385C2×C8—62no—
386C2×C8—121no—
387C2×C8—121no—
388C2×C8—121no—
389C2×C8—121no—
390C4⋊C4—21no—
391C4⋊C4—21no—
392C4⋊C4—61no—
393C4⋊C4—61no—
394C4⋊C4—122no—
395C4⋊C4—121no—
396C4⋊C4—121no—
397C4⋊C4—121no—
398C4⋊C4—121no—
399C22⋊C4—41no—
400C22⋊C4—41no—
401C22⋊C4—124no—
402C22⋊C4—124no—
403C22⋊C4—121no—
404C22⋊C4—121no—
405C42D3×D411yescharacteristic
406C42#23711yescharacteristic
407C42C2×#6711yescharacteristic
408C42C2×#6711yescharacteristic
409C22×C3—42no—
410C22×C3—42no—
411C22×C3—42no—
412C22×C3—81no—
413C22×C3—81no—
414C22×C3—81no—
415C22×C3—81no—
416C22×C3—82no—
417C22×C3—82no—
418C22×C3—82no—
419C22×C3—161no—
420C22×C3—161no—
421C22×C3—161no—
422C22×C3—161no—
423C22×C3#39211yescharacteristic
424C22×C3#44711yescharacteristic
425C22×C3#44711yescharacteristic
426C22×C3#44911yescharacteristic
427C22×C3#44911yescharacteristic
428C22×C3#45311yescharacteristic
429C22×C3#45411yescharacteristic
430C2×D3—42no—
431C2×D3—42no—
432C2×D3—42no—
433C2×D3—81no—
434C2×D3—81no—
435C2×D3—81no—
436C2×D3—81no—
437C3×C4—21no—
438C3×C4—21no—
439C3×C4—81no—
440C3×C4#44711yescharacteristic
441C3×C4#44711yescharacteristic
442C3×C4#44911yescharacteristic
443C3×C4#44911yescharacteristic
444C3×C4#46611yescharacteristic
445C3×C4#46611yescharacteristic
446C3×C4#46911yescharacteristic
447C3×C4#46911yescharacteristic
448Dic3—82no—
449Dic3—81no—
450C23—22no—
451C23—41no—
452C23—41no—
453C23—41no—
454C23—41no—
455C23—41no—
456C23—41no—
457C23—42no—
458C23—62no—
459C23—81no—
460C23—81no—
461C23—81no—
462C23—81no—
463C23—81no—
464C23—81no—
465C23—121no—
466C23—121no—
467C23—121no—
468C23—121no—
469C23—121no—
470C23—121no—
471C23#93711yescharacteristic
472D4—22no—
473D4—22no—
474D4—44no—
475D4—42no—
476D4—42no—
477D4—42no—
478D4—41no—
479D4—42no—
480D4—41no—
481D4—62no—
482D4—62no—
483D4—82no—
484D4—81no—
485D4—81no—
486D4—81no—
487D4—81no—
488D4—121no—
489D4—121no—
490D4—248no—
491C2×C4—21no—
492C2×C4—21no—
493C2×C4—41no—
494C2×C4—41no—
495C2×C4—41no—
496C2×C4—81no—
497C2×C4—81no—
498C2×C4—81no—
499C2×C4—81no—
500C2×C4—122no—
501C2×C4—122no—
502C2×C4—121no—
503C2×C4—121no—
504C2×C4—122no—
505C2×C4—121no—
506C2×C4—241no—
507C2×C4—241no—
508C2×C4—241no—
509C2×C4—241no—
510C2×C4D3×D811yescharacteristic
511C2×C4#91111yescharacteristic
512C2×C4#91111yescharacteristic
513C2×C4#91211yescharacteristic
514C2×C4C2×#21311yescharacteristic
515C2×C4#93211yescharacteristic
516C2×C4#93711yescharacteristic
517C2×C4#93811yescharacteristic
518C2×C4#93911yescharacteristic
519C2×C4#93911yescharacteristic
520C2×C4#94011yescharacteristic
521C2×C4#94911yescharacteristic
522C2×C4#95011yescharacteristic
523C2×C4#95311yescharacteristic
524C8—42no—
525C8—122no—
526C8—122no—
527C2×C3—82no—
528C2×C3—162no—
529C2×C3#161911yescharacteristic
530C2×C3#162411yescharacteristic
531C2×C3#162511yescharacteristic
532C2×C3#162511yescharacteristic
533C2×C3#199911yescharacteristic
534C2×C3#199911yescharacteristic
535C2×C3#200611yescharacteristic
536D3—82no—
537C22—42no—
538C22—42no—
539C22—42no—
540C22—81no—
541C22—81no—
542C22—81no—
543C22—81no—
544C22—82no—
545C22—82no—
546C22—82no—
547C22—122no—
548C22—122no—
549C22—122no—
550C22—161no—
551C22—161no—
552C22—161no—
553C22—161no—
554C22—241no—
555C22—241no—
556C22—241no—
557C22—241no—
558C22#503611yescharacteristic
559C22#503711yescharacteristic
560C22#515611yescharacteristic
561C22#515811yescharacteristic
562C22#519811yescharacteristic
563C22#520111yescharacteristic
564C22#522311yescharacteristic
565C4—21no—
566C4—21no—
567C4—81no—
568C4—241no—
569C4—242no—
570C4#503811yescharacteristic
571C4#503911yescharacteristic
572C4#515611yescharacteristic
573C4#515711yescharacteristic
574C4#515811yescharacteristic
575C4#515911yescharacteristic
576C4#521711yescharacteristic
577C4#523811yescharacteristic
578C3#1022811yescharacteristic, complemented, Sylow
579C2—82no—
580C2—162no—
581C2—242no—
582C2#7101211yescharacteristic
583C2#7101511yescharacteristic
584C2#7101711yescharacteristic
585C2#7101811yescharacteristic
586C2#7168411yescharacteristic
587C2#7204311yescharacteristic
588C2#7209811yescharacteristic
subgroupG/H
centerC23#937
commutator, cosocleC2×C3×C42C23
FrattiniC2×C42C22×D3
FittingC2×C3×#459C2
socleC23×C3#120
hypercenterC2×#459D3
hypocenterC3#10228
LCSG ▷ C2×C3×C42 ▷ C22×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#459

Complements

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

NH ≅ G/Ntype
1. C2×C3×#459C2semidirect
2. C2×#5072C2semidirect
3. #82417C2semidirect
4. #71764C2semidirect
5. C2×D4⋊(C3⋊C8)C2semidirect
6. C2×#4483C2semidirect
7. #67702C2semidirect
33. C2×#459D3semidirect
54. C3×#127D4semidirect
83. C3×C4⋊C8D4semidirect
89. C4⋊(C3⋊C8)D4semidirect
139. C2×C3×D4D8semidirect
160. C2×D12D8semidirect
217. #127#67semidirect
243. C4⋊C8#67semidirect
360. C2×D4#213semidirect
578. C3#10228semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#4592
C2×#50722
#824172
#717642
C2×D4⋊(C3⋊C8)2
C2×#44832
#677022
#102283