Finite Group Databasebeta

← #10690921

Subgroups — #10690921

Order 768.

1348 conjugacy classes of subgroups.

The subgroup lattice has 564 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#74048C211yesmaximal, characteristic
2C2×D3×#95C211yesmaximal, characteristic, complemented
3#69955C211yesmaximal, characteristic, complemented
4C2×#4470C211yesmaximal, characteristic, complemented
5C2×#4451C211yesmaximal, characteristic, complemented
6C3×#1294C211yesmaximal, characteristic, complemented
7#67624C211yesmaximal, characteristic, complemented
8#9147—31nomaximal, Sylow
9C23×C4×D3—21no—
10C23×C4×D3C2211yescharacteristic
11C2×#930C2211yescharacteristic
12C2×#895C412yescomplemented
13C2×#882—21no—
14C2×C3×C22⋊C8C2211yescharacteristic
15C3×#380C2211yescharacteristic
16C2×C3×#95C2211yescharacteristic
17C2×C3⋊#95—21no—
18C2×C3⋊#95C2211yescharacteristic
19C2×#830C2211yescharacteristic
20C2×(C2×D3)⋊C8—22no—
21#4987C412yescomplemented
22#4958—21no—
23#4665—22no—
24D3×#95—22no—
25D3×#95—22no—
26#4470—22no—
27#4451—22no—
28#2847—31no—
29C22×#95—31no—
30#1779—31no—
31C2×#327—31no—
32C2×#327—31no—
33#1294—31no—
34#1294D311yescharacteristic, complemented
35C24×D3D411yescharacteristic
36C23×C3×C4—21no—
37C23×C3×C4C2311yescharacteristic
38C22×#67—21no—
39C23×Dic3—21no—
40C23×Dic3D411yescharacteristic
41C22×D12—22no—
42C22×D12C2×C411yescharacteristic, complemented
43C22×C4×D3—24no—
44C22×C4×D3—28no—
45C22×C4×D3—21no—
46C22×C4×D3—21no—
47C22×C4×D3—21no—
48C22×C4×D3—21no—
49C22×C4×D3—44no—
50C22×C4×D3—44no—
51C22×C4×D3—42no—
52C22×C4×D3—42no—
53C22×C4×D3C2×C412yes—
54C22×C4×D3D412yes—
55C22×C3×C8—21no—
56C2×C3×C4⋊C4C2×C412yescomplemented
57C2×C3×C22⋊C4—21no—
58#930—21no—
59#930—21no—
60#930—21no—
61#930—21no—
62C2×(C2×D3)⋊C4—22no—
63C2×(C2×D3)⋊C4—21no—
64C2×(C2×D3)⋊C4—22no—
65C2×C4⋊Dic3C2×C411yescharacteristic, complemented
66C22×C3⋊C8—21no—
67#895—44no—
68#882—42no—
69#882—42no—
70C3×C22⋊C8—21no—
71C3×C22⋊C8—21no—
72C3×#95—21no—
73C3×#95—21no—
74C3×#95D412yescomplemented
75C3⋊#95—24no—
76C3⋊#95—21no—
77C3⋊#95—22no—
78C3⋊#95D412yescomplemented
79#830—21no—
80#830—21no—
81(C2×D3)⋊C8—44no—
82C24×C4—31no—
83C24×C4—61no—
84C2×#121—31no—
85C2×#121—32no—
86C2×#120—61no—
87C2×C22⋊C8—31no—
88C2×C22⋊C8—62no—
89C2×C22⋊C8C2×D311yescharacteristic
90#386—62no—
91#386—61no—
92#380—32no—
93#380C2×D311yescharacteristic
94C2×#95—31no—
95C2×#95—62no—
96C2×#95—61no—
97C2×#95—62no—
98C2×#95C2×D311yescharacteristic
99#327—62no—
100#327—62no—
101C24×C3C2×D411yescharacteristic
102C23×D3—21no—
103C23×D3—21no—
104C23×D3—21no—
105C23×D3—21no—
106C23×D3—24no—
107C23×D3—24no—
108C23×D3—21no—
109C23×D3C22⋊C412yes—
110C23×D3D812yes—
111C23×D3SD1612yes—
112C22×C3×C4—24no—
113C22×C3×C4—22no—
114C22×C3×C4—22no—
115C22×C3×C4—42no—
116C22×C3×C4—42no—
117C22×C3×C4—41no—
118C22×C3×C4—41no—
119C22×C3×C4C22×C411yescharacteristic
120C22×C3×C4C2×D411yescharacteristic
121C22×C3×C4C2×D411yescharacteristic
122C22×C3×C4C2×D411yescharacteristic
123C22×C3×C4#4111yescharacteristic
124C22×C3×C4#4111yescharacteristic
125C2×#67—41no—
126C2×#67—41no—
127C2×#67—41no—
128C2×#67—41no—
129C2×#67—41no—
130C2×#67—41no—
131C22×Dic3—24no—
132C22×Dic3—21no—
133C22×Dic3—22no—
134C22×Dic3—21no—
135C22×Dic3—21no—
136C22×Dic3—42no—
137C22×Dic3—42no—
138C22×Dic3—41no—
139C22×Dic3—41no—
140C22×Dic3C22⋊C412yes—
141C2×D12—21no—
142C2×D12—21no—
143C2×D12—42no—
144C2×D12—44no—
145C2×D12—44no—
146C2×D12—44no—
147C2×C4×D3—216no—
148C2×C4×D3—24no—
149C2×C4×D3—24no—
150C2×C4×D3—22no—
151C2×C4×D3—22no—
152C2×C4×D3—22no—
153C2×C4×D3—22no—
154C2×C4×D3—42no—
155C2×C4×D3—42no—
156C2×C4×D3—44no—
157C2×C4×D3—44no—
158C2×C4×D3—44no—
159C2×C4×D3—44no—
160C2×C4×D3—48no—
161C2×C4×D3—416no—
162C2×C4×D3—416no—
163C2×C4×D3—48no—
164C2×C3×C8—42no—
165C2×C3×C8—41no—
166C3×C4⋊C4—42no—
167C3×C22⋊C4—41no—
168C3×C22⋊C4—41no—
169(C2×D3)⋊C4—44no—
170(C2×D3)⋊C4—44no—
171(C2×D3)⋊C4—41no—
172(C2×D3)⋊C4—41no—
173C4⋊Dic3—21no—
174C4⋊Dic3—21no—
175C2×C3⋊C8—42no—
176C2×C3⋊C8—41no—
177C25—31no—
178C22×D4—31no—
179C22×D4—62no—
180C22×D4—61no—
181C23×C4—21no—
182C23×C4—31no—
183C23×C4—32no—
184C23×C4—32no—
185C23×C4—64no—
186C23×C4—68no—
187C23×C4—61no—
188C23×C4—61no—
189C23×C4—61no—
190C23×C4—61no—
191C23×C4—61no—
192C23×C4—124no—
193C23×C4—122no—
194C23×C4—124no—
195C23×C4—122no—
196C23×C4C22×D311yescharacteristic
197C22×C8—21no—
198C22×C8—61no—
199#121—61no—
200#121—61no—
201#121—61no—
202#121—61no—
203#121—124no—
204#120—122no—
205#120—122no—
206C2×C4⋊C4—31no—
207C2×C4⋊C4C4×D312yescomplemented
208C2×C22⋊C4—21no—
209C2×C22⋊C4—62no—
210C2×C22⋊C4—62no—
211C2×C22⋊C4—61no—
212C22⋊C8—21no—
213C22⋊C8—21no—
214C22⋊C8—61no—
215C22⋊C8—61no—
216C22⋊C8—124no—
217#95—21no—
218#95—21no—
219#95—32no—
220#95—62no—
221#95—64no—
222#95—61no—
223#95D1212yescomplemented
224C23×C3—22no—
225C23×C3—22no—
226C23×C3C2×C22⋊C411yescharacteristic
227C23×C3#12011yescharacteristic
228C23×C3#12311yescharacteristic
229C23×C3C2×D811yescharacteristic
230C23×C3C2×SD1611yescharacteristic
231C23×C3AGL(1,ℤ/8)11yescharacteristic
232C23×C3#13711yescharacteristic
233C22×D3—24no—
234C22×D3—24no—
235C22×D3—28no—
236C22×D3—24no—
237C22×D3—24no—
238C22×D3—28no—
239C22×D3—22no—
240C22×D3—22no—
241C22×D3—22no—
242C22×D3—22no—
243C22×D3—22no—
244C22×D3—22no—
245C22×D3—22no—
246C22×D3—22no—
247C22×D3—28no—
248C22×D3—28no—
249C22×D3—41no—
250C22×D3—42no—
251C22×D3—41no—
252C22×D3—41no—
253C22×D3—42no—
254C22×D3#9914yes—
255C22×D3#10214yes—
256C22×D3#10414yes—
257C2×C3×C4—22no—
258C2×C3×C4—22no—
259C2×C3×C4—24no—
260C2×C3×C4—41no—
261C2×C3×C4—41no—
262C2×C3×C4—41no—
263C2×C3×C4—41no—
264C2×C3×C4—42no—
265C2×C3×C4—44no—
266C2×C3×C4—44no—
267C2×C3×C4—42no—
268C2×C3×C4—42no—
269C2×C3×C4—42no—
270C2×C3×C4—42no—
271C2×C3×C4C4×D411yescharacteristic
272C2×C3×C4C4×D411yescharacteristic
273C2×C3×C4#12111yescharacteristic
274C2×C3×C4#12111yescharacteristic
275#67—81no—
276#67—81no—
277#67—81no—
278#67—81no—
279C2×Dic3—24no—
280C2×Dic3—22no—
281C2×Dic3—22no—
282C2×Dic3—22no—
283C2×Dic3—42no—
284C2×Dic3—44no—
285C2×Dic3—44no—
286C2×Dic3—42no—
287C2×Dic3—42no—
288C2×Dic3—42no—
289C2×Dic3—41no—
290C2×Dic3—41no—
291C2×Dic3—41no—
292D12—81no—
293D12—81no—
294D12—88no—
295C4×D3—44no—
296C4×D3—44no—
297C4×D3—44no—
298C4×D3—44no—
299C4×D3—432no—
300C3×C8—81no—
301C3⋊C8—81no—
302C24—32no—
303C24—32no—
304C24—32no—
305C24—64no—
306C24—64no—
307C24—61no—
308C24—61no—
309C24—61no—
310C24—61no—
311C24—61no—
312C24D3×D411yescharacteristic
313C2×D4—61no—
314C2×D4—61no—
315C2×D4—122no—
316C2×D4—124no—
317C2×D4—124no—
318C2×D4—124no—
319C2×D4—121no—
320C2×D4—121no—
321C2×D4—121no—
322C2×D4—121no—
323C2×D4—121no—
324C2×D4—121no—
325C22×C4—24no—
326C22×C4—22no—
327C22×C4—22no—
328C22×C4—32no—
329C22×C4—42no—
330C22×C4—42no—
331C22×C4—41no—
332C22×C4—41no—
333C22×C4—64no—
334C22×C4—64no—
335C22×C4—616no—
336C22×C4—64no—
337C22×C4—62no—
338C22×C4—61no—
339C22×C4—61no—
340C22×C4—62no—
341C22×C4—62no—
342C22×C4—62no—
343C22×C4—62no—
344C22×C4—61no—
345C22×C4—122no—
346C22×C4—122no—
347C22×C4—124no—
348C22×C4—124no—
349C22×C4—124no—
350C22×C4—124no—
351C22×C4—1216no—
352C22×C4—128no—
353C22×C4—1216no—
354C22×C4—128no—
355C22×C4—122no—
356C22×C4—122no—
357C22×C4—121no—
358C22×C4—121no—
359C22×C4C2×C4×D311yescharacteristic
360C22×C4C2×D1211yescharacteristic
361C22×C4#23511yescharacteristic
362C22×C4D3×D411yescharacteristic
363C22×C4D3×D411yescharacteristic
364C22×C4#23911yescharacteristic
365C2×C8—42no—
366C2×C8—41no—
367C2×C8—122no—
368C2×C8—121no—
369C4⋊C4—42no—
370C4⋊C4—61no—
371C4⋊C4—61no—
372C22⋊C4—41no—
373C22⋊C4—41no—
374C22⋊C4—124no—
375C22⋊C4—124no—
376C22⋊C4—121no—
377C22⋊C4—121no—
378C22×C3—21no—
379C22×C3—21no—
380C22×C3—21no—
381C22×C3—21no—
382C22×C3—22no—
383C22×C3—22no—
384C22×C3—22no—
385C22×C3—22no—
386C22×C3#38611yescharacteristic
387C22×C3C2×#9912yes—
388C22×C3C2×#10211yescharacteristic
389C22×C3#41711yescharacteristic
390C22×C3C2×#10412yes—
391C22×C3#44711yescharacteristic
392C22×C3#44811yescharacteristic
393C22×C3#48011yescharacteristic
394C22×C3#48111yescharacteristic
395C2×D3—28no—
396C2×D3—28no—
397C2×D3—28no—
398C2×D3—28no—
399C2×D3—24no—
400C2×D3—24no—
401C2×D3—24no—
402C2×D3—24no—
403C2×D3—24no—
404C2×D3—24no—
405C2×D3—81no—
406C2×D3—81no—
407C2×D3—81no—
408C2×D3—82no—
409C2×D3—82no—
410C2×D3#32718yescomplemented
411C3×C4—21no—
412C3×C4—21no—
413C3×C4—21no—
414C3×C4—21no—
415C3×C4—44no—
416C3×C4—82no—
417Dic3—44no—
418Dic3—42no—
419Dic3—81no—
420C23—22no—
421C23—22no—
422C23—34no—
423C23—34no—
424C23—34no—
425C23—68no—
426C23—68no—
427C23—64no—
428C23—64no—
429C23—64no—
430C23—68no—
431C23—64no—
432C23—68no—
433C23—62no—
434C23—62no—
435C23—62no—
436C23—62no—
437C23—62no—
438C23—62no—
439C23—62no—
440C23—62no—
441C23—121no—
442C23—122no—
443C23—121no—
444C23—121no—
445C23—122no—
446C23D3×C22⋊C411yescharacteristic
447C23#88211yescharacteristic
448C23#89411yescharacteristic
449C23D3×D811yescharacteristic
450C23D3×SD1611yescharacteristic
451C23#91411yescharacteristic
452C23#91811yescharacteristic
453D4—241no—
454D4—241no—
455D4—248no—
456D4—241no—
457D4—241no—
458D4—241no—
459D4—241no—
460C2×C4—22no—
461C2×C4—22no—
462C2×C4—24no—
463C2×C4—41no—
464C2×C4—41no—
465C2×C4—41no—
466C2×C4—41no—
467C2×C4—42no—
468C2×C4—44no—
469C2×C4—44no—
470C2×C4—42no—
471C2×C4—42no—
472C2×C4—42no—
473C2×C4—42no—
474C2×C4—64no—
475C2×C4—62no—
476C2×C4—62no—
477C2×C4—62no—
478C2×C4—124no—
479C2×C4—124no—
480C2×C4—124no—
481C2×C4—124no—
482C2×C4—1232no—
483C2×C4—122no—
484C2×C4—124no—
485C2×C4—124no—
486C2×C4—122no—
487C2×C4—122no—
488C2×C4—122no—
489C2×C4—121no—
490C2×C4—121no—
491C2×C4—121no—
492C2×C4C4×D1211yescharacteristic
493C2×C4#88411yescharacteristic
494C2×C4#89311yescharacteristic
495C2×C4#89511yescharacteristic
496C8—81no—
497C8—241no—
498C2×C3—21no—
499C2×C3—21no—
500C2×C3—21no—
501C2×C3—21no—
502C2×C3C2×#32712yes—
503C2×C3#150412yes—
504C2×C3#187411yescharacteristic
505C2×C3#189611yescharacteristic
506C2×C3#189811yescharacteristic
507D3—28no—
508D3—161no—
509C22—21no—
510C22—21no—
511C22—21no—
512C22—21no—
513C22—22no—
514C22—22no—
515C22—22no—
516C22—22no—
517C22—38no—
518C22—68no—
519C22—68no—
520C22—68no—
521C22—68no—
522C22—64no—
523C22—64no—
524C22—64no—
525C22—64no—
526C22—64no—
527C22—64no—
528C22—241no—
529C22—241no—
530C22—241no—
531C22—242no—
532C22—242no—
533C22#466511yescharacteristic
534C22D3×#9912yes—
535C22D3×#10211yescharacteristic
536C22#477311yescharacteristic
537C22#480311yescharacteristic
538C22#480611yescharacteristic
539C22D3×#10412yes—
540C22#486311yescharacteristic
541C22#488211yescharacteristic
542C4—21no—
543C4—21no—
544C4—21no—
545C4—21no—
546C4—44no—
547C4—82no—
548C4—124no—
549C4—122no—
550C4—241no—
551C3#914711yescharacteristic, complemented, Sylow
552C2—21no—
553C2—21no—
554C2—21no—
555C2—21no—
556C2—68no—
557C2—481no—
558C2D3×#32712yes—
559C2#6833412yes—
560C2#6875611yescharacteristic
561C2#6888011yescharacteristic
562C2#6897011yescharacteristic
subgroupG/H
centerC23D3×C22⋊C4
commutatorC22×C3×C4C22×C4
FrattiniC23×C4C22×D3
FittingC3×#1294C2
socleC23×C3C2×C22⋊C4
prime radical#74048C2
cosocleC23×C3×C4C23
hypercenter#1294D3
hypocenterC3#9147
LCSG ▷ C22×C3×C4 ▷ C22×C3 ▷ C3
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1294

Complements

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

NH ≅ G/Ntype
2. C2×D3×#95C2semidirect
3. #69955C2semidirect
4. C2×#4470C2semidirect
5. C2×#4451C2semidirect
6. C3×#1294C2semidirect
7. #67624C2semidirect
12. C2×#895C4semidirect
21. #4987C4semidirect
34. #1294D3semidirect
42. C22×D12C2×C4semidirect
56. C2×C3×C4⋊C4C2×C4semidirect
65. C2×C4⋊Dic3C2×C4semidirect
74. C3×#95D4semidirect
78. C3⋊#95D4semidirect
207. C2×C4⋊C4C4×D3semidirect
223. #95D12semidirect
410. C2×D3#327semidirect
551. C3#9147semidirect

Maximal subgroups

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

subgroupindex
#740482
C2×D3×#952
#699552
C2×#44702
C2×#44512
C3×#12942
#676242
#91473