Finite Group Databasebeta

← #10690463

Subgroups — #10690463

Order 768.

822 conjugacy classes of subgroups.

The subgroup lattice has 520 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#4695C211yesmaximal, characteristic
2#73653C211yesmaximal, characteristic, complemented
3#70457C211yesmaximal, characteristic, complemented
4C2×#4485C211yesmaximal, characteristic, complemented
5#69487C211yesmaximal, characteristic, complemented
6C3×#1279C211yesmaximal, characteristic, complemented
7#67655C211yesmaximal, characteristic, complemented
8#9061—31nomaximal, Sylow
9C22×D24—22no—
10C2×#893—21no—
11C2×#874C2211yescharacteristic
12C2×#874C2211yescharacteristic
13C2×C4×D12—21no—
14C2×C3×C4⋊C8C2211yescharacteristic
15C2×C3×C4×C8C2211yescharacteristic
16C3×C4×C4⋊C4C2211yescharacteristic
17C2×#821—21no—
18C2×#821—21no—
19#4988—21no—
20C2×#809—21no—
21C2×#809—21no—
22#4939—21no—
23C4×C4⋊Dic3C2211yescharacteristic
24C2×C4⋊(C3⋊C8)C2211yescharacteristic
25#4695—22no—
26#4695C414yescomplemented
27#4665—22no—
28#4485—22no—
29C2×#493—31no—
30#2366—31no—
31#1982—31no—
32#1982—31no—
33C2×#331—31no—
34#1279—31no—
35#1279D311yescharacteristic, complemented
36C22×D12—21no—
37C22×D12—21no—
38C22×D12—21no—
39C22×D12—21no—
40C22×D12—21no—
41C22×D12D412yes—
42C22×C4×D3—22no—
43C22×C3×C8—21no—
44C22×C3×C8—21no—
45C2×C3×C4⋊C4D411yescharacteristic
46C2×C3×C4⋊C4D411yescharacteristic
47C2×C3×C42—21no—
48C2×C3×C42C2311yescharacteristic
49C2×(C2×D3)⋊C4—22no—
50C2×(C2×D3)⋊C4—22no—
51C2×(C2×D3)⋊C4—22no—
52C2×C4⋊Dic3D411yescharacteristic
53C2×C4⋊Dic3D411yescharacteristic
54C2×C4×Dic3—21no—
55C22×C3⋊C8—21no—
56C2×D24—28no—
57C2×D24—44no—
58C2×D24—44no—
59#893—42no—
60#893—42no—
61#874—21no—
62#874—21no—
63#874—21no—
64#874—21no—
65#874—21no—
66#874C2×C412yes—
67#874C2×C412yescomplemented
68#874D412yes—
69C4×D12—42no—
70C4×D12—42no—
71C3×C4⋊C8—21no—
72C3×C4⋊C8—21no—
73C3×C4×C8—21no—
74C3×C4×C8C2×C412yescomplemented
75C3×#95—21no—
76C3⋊#95—21no—
77#821—42no—
78#821—42no—
79#809—42no—
80#809—42no—
81C4⋊(C3⋊C8)—21no—
82C4⋊(C3⋊C8)—21no—
83C22×D8—62no—
84C2×#127—31no—
85C2×#127—31no—
86C2×C4×D4—61no—
87C2×C4×D4—61no—
88#493—34no—
89#493—62no—
90C2×C4⋊C8—31no—
91C2×C4⋊C8C2×D311yescharacteristic
92C2×#102—61no—
93C2×#102—61no—
94C2×#102—61no—
95C2×#102—61no—
96C2×C4×C8C2×D311yescharacteristic
97#390—61no—
98#390—61no—
99#386—62no—
100C4×C4⋊C4—31no—
101C4×C4⋊C4C2×D311yescharacteristic
102#331—62no—
103C23×D3—22no—
104C23×D3—41no—
105C22×C3×C4—21no—
106C22×C3×C4—21no—
107C22×C3×C4C2×D411yescharacteristic
108C22×C3×C4C2×D411yescharacteristic
109C22×C3×C4C2×D411yescharacteristic
110C22×Dic3—21no—
111C22×Dic3—21no—
112C2×D12—22no—
113C2×D12—22no—
114C2×D12—22no—
115C2×D12—22no—
116C2×D12—22no—
117C2×D12—22no—
118C2×D12—22no—
119C2×D12—22no—
120C2×D12—41no—
121C2×D12—41no—
122C2×D12—41no—
123C2×D12—41no—
124C2×D12—41no—
125C2×D12—41no—
126C2×D12—41no—
127C2×D12—41no—
128C2×D12—42no—
129C2×D12—42no—
130C2×D12—42no—
131C2×D12—42no—
132C2×D12—41no—
133C2×D12—41no—
134C2×D12—41no—
135C2×D12—41no—
136C2×D12—41no—
137C2×D12—41no—
138C2×D12—41no—
139C2×D12—41no—
140C2×D12—41no—
141C2×D12—41no—
142C2×D12—41no—
143C2×D12C22⋊C414yes—
144C2×C4×D3—44no—
145C2×C4×D3—44no—
146C2×C4×D3—82no—
147C2×C3×C8—22no—
148C2×C3×C8—22no—
149C2×C3×C8—22no—
150C2×C3×C8—41no—
151C2×C3×C8—41no—
152C2×C3×C8—41no—
153C3×C4⋊C4—21no—
154C3×C4⋊C4—21no—
155C3×C4⋊C4—21no—
156C3×C4⋊C4D812yescomplemented
157C3×C42—41no—
158C3×C42—41no—
159C3×C42C22×C411yescharacteristic
160C3×C42C2×D411yescharacteristic
161C3×C42#4111yescharacteristic
162C3×C42#4111yescharacteristic
163(C2×D3)⋊C4—44no—
164(C2×D3)⋊C4—44no—
165(C2×D3)⋊C4—82no—
166C4⋊Dic3—21no—
167C4⋊Dic3—21no—
168C4⋊Dic3—21no—
169C4⋊Dic3D812yescomplemented
170C4×Dic3—41no—
171C4×Dic3—41no—
172C2×C3⋊C8—41no—
173C2×C3⋊C8—41no—
174C2×C3⋊C8—41no—
175D24—416no—
176C22×D4—32no—
177C22×D4—61no—
178C22×D4—61no—
179C22×D4—61no—
180C22×D4—61no—
181C22×D4—61no—
182C23×C4—62no—
183C2×D8—68no—
184C2×D8—124no—
185C2×D8—124no—
186C22×C8—21no—
187C22×C8—21no—
188C22×C8—61no—
189#127—32no—
190#127—32no—
191#127—32no—
192#127—61no—
193#127—61no—
194#127—61no—
195#127—61no—
196#127—61no—
197C4×D4—122no—
198C4×D4—122no—
199C4×D4—122no—
200C4×D4—122no—
201C2×C4⋊C4—31no—
202C2×C4⋊C4—31no—
203C2×C4⋊C4D1211yescharacteristic
204C2×C4⋊C4D1211yescharacteristic
205C2×C22⋊C4—62no—
206C2×C22⋊C4—62no—
207C2×C22⋊C4—62no—
208C2×C42—21no—
209C2×C42—61no—
210C2×C42C22×D311yescharacteristic
211C4⋊C8—21no—
212C4⋊C8—21no—
213C4⋊C8—61no—
214C4⋊C8—61no—
215#102—122no—
216#102—122no—
217#102—122no—
218#102—122no—
219C4×C8—21no—
220C4×C8C4×D312yescomplemented
221#95—21no—
222#95—61no—
223C23×C3#12011yescharacteristic
224C22×D3—24no—
225C22×D3—42no—
226C22×D3—42no—
227C22×D3—42no—
228C22×D3—42no—
229C22×D3—42no—
230C22×D3—42no—
231C22×D3—42no—
232C22×D3—81no—
233C22×D3—81no—
234C22×D3—81no—
235C22×D3—81no—
236C22×D3—81no—
237C22×D3—81no—
238C2×C3×C4—21no—
239C2×C3×C4—21no—
240C2×C3×C4—22no—
241C2×C3×C4—41no—
242C2×C3×C4—41no—
243C2×C3×C4—41no—
244C2×C3×C4—41no—
245C2×C3×C4—41no—
246C2×C3×C4C2×C22⋊C411yescharacteristic
247C2×C3×C4C4×D411yescharacteristic
248C2×C3×C4C4×D411yescharacteristic
249C2×C3×C4#12111yescharacteristic
250C2×C3×C4#12111yescharacteristic
251C2×C3×C4#12311yescharacteristic
252C2×C3×C4C2×D811yescharacteristic
253C2×C3×C4C2×D811yescharacteristic
254C2×C3×C4#13511yescharacteristic
255C2×C3×C4#13511yescharacteristic
256C2×C3×C4AGL(1,ℤ/8)11yescharacteristic
257C2×C3×C4AGL(1,ℤ/8)11yescharacteristic
258C2×C3×C4AGL(1,ℤ/8)11yescharacteristic
259C2×C3×C4AGL(1,ℤ/8)11yescharacteristic
260C2×Dic3—22no—
261C2×Dic3—41no—
262C2×Dic3—41no—
263C2×Dic3—41no—
264C2×Dic3—41no—
265C2×Dic3—41no—
266D12—44no—
267D12—44no—
268D12—42no—
269D12—42no—
270D12—42no—
271D12—42no—
272D12—42no—
273D12—42no—
274D12—42no—
275D12—42no—
276D12—42no—
277D12—42no—
278D12—42no—
279D12—42no—
280D12—82no—
281D12—82no—
282D12—81no—
283D12—81no—
284D12—81no—
285D12—81no—
286C4×D3—88no—
287C3×C8—24no—
288C3×C8—81no—
289C3⋊C8—81no—
290C24—62no—
291C24—121no—
292C2×D4—34no—
293C2×D4—62no—
294C2×D4—62no—
295C2×D4—62no—
296C2×D4—62no—
297C2×D4—62no—
298C2×D4—62no—
299C2×D4—62no—
300C2×D4—62no—
301C2×D4—122no—
302C2×D4—122no—
303C2×D4—122no—
304C2×D4—122no—
305C2×D4—121no—
306C2×D4—121no—
307C2×D4—121no—
308C2×D4—121no—
309C2×D4—121no—
310C2×D4—121no—
311C2×D4—121no—
312C2×D4—121no—
313C2×D4—121no—
314C2×D4—121no—
315C2×D4—121no—
316C2×D4—121no—
317C2×D4—121no—
318C2×D4—121no—
319C2×D4—121no—
320C2×D4—121no—
321C2×D4—121no—
322C2×D4—121no—
323C2×D4—121no—
324C22×C4—21no—
325C22×C4—21no—
326C22×C4—61no—
327C22×C4—61no—
328C22×C4—124no—
329C22×C4—124no—
330C22×C4—242no—
331C22×C4C2×D1211yescharacteristic
332C22×C4D3×D411yescharacteristic
333C22×C4D3×D411yescharacteristic
334D8—1216no—
335C2×C8—22no—
336C2×C8—22no—
337C2×C8—22no—
338C2×C8—41no—
339C2×C8—41no—
340C2×C8—41no—
341C2×C8—121no—
342C2×C8—121no—
343C2×C8—121no—
344C4⋊C4—21no—
345C4⋊C4—21no—
346C4⋊C4—21no—
347C4⋊C4—32no—
348C4⋊C4—61no—
349C4⋊C4—61no—
350C4⋊C4—61no—
351C4⋊C4D2412yescomplemented
352C22⋊C4—124no—
353C22⋊C4—124no—
354C22⋊C4—242no—
355C42—41no—
356C42—41no—
357C42—121no—
358C42—121no—
359C42C2×C4×D311yescharacteristic
360C42#23511yescharacteristic
361C42D3×D411yescharacteristic
362C42#23911yescharacteristic
363C22×C3#38611yescharacteristic
364C22×C3#44711yescharacteristic
365C22×C3#44711yescharacteristic
366C22×C3#44911yescharacteristic
367C22×C3#44911yescharacteristic
368C22×C3#45311yescharacteristic
369C22×C3#45311yescharacteristic
370C2×D3—44no—
371C2×D3—44no—
372C2×D3—44no—
373C2×D3—82no—
374C2×D3—82no—
375C2×D3—82no—
376C2×D3—82no—
377C2×D3—82no—
378C2×D3—82no—
379C2×D3—82no—
380C2×D3—161no—
381C2×D3—161no—
382C2×D3—161no—
383C2×D3—161no—
384C3×C4—21no—
385C3×C4—21no—
386C3×C4—42no—
387C3×C4—81no—
388C3×C4C4×D811yescharacteristic
389C3×C4C4×D811yescharacteristic
390C3×C4#44211yescharacteristic
391C3×C4#44211yescharacteristic
392C3×C4#45911yescharacteristic
393C3×C4#45911yescharacteristic
394C3×C4#46311yescharacteristic
395C3×C4#46311yescharacteristic
396Dic3—42no—
397Dic3—81no—
398C23—64no—
399C23—122no—
400C23—122no—
401C23—122no—
402C23—122no—
403C23—122no—
404C23—122no—
405C23—122no—
406C23—241no—
407C23—241no—
408C23—241no—
409C23—241no—
410C23—241no—
411C23—241no—
412C23#88211yescharacteristic
413D4—124no—
414D4—124no—
415D4—122no—
416D4—122no—
417D4—122no—
418D4—122no—
419D4—122no—
420D4—122no—
421D4—122no—
422D4—122no—
423D4—122no—
424D4—122no—
425D4—122no—
426D4—122no—
427D4—242no—
428D4—242no—
429D4—241no—
430D4—241no—
431D4—241no—
432D4—241no—
433C2×C4—21no—
434C2×C4—21no—
435C2×C4—22no—
436C2×C4—41no—
437C2×C4—41no—
438C2×C4—41no—
439C2×C4—41no—
440C2×C4—41no—
441C2×C4—62no—
442C2×C4—121no—
443C2×C4—121no—
444C2×C4—121no—
445C2×C4—121no—
446C2×C4—121no—
447C2×C4—248no—
448C2×C4C4×D1211yescharacteristic
449C2×C4D3×C22⋊C411yescharacteristic
450C2×C4#88411yescharacteristic
451C2×C4#89311yescharacteristic
452C2×C4#89411yescharacteristic
453C2×C4#89511yescharacteristic
454C2×C4C2×D2411yescharacteristic
455C2×C4#90411yescharacteristic
456C2×C4#90811yescharacteristic
457C2×C4#90811yescharacteristic
458C2×C4D3×D811yescharacteristic
459C2×C4#91411yescharacteristic
460C2×C4#91411yescharacteristic
461C2×C4#91911yescharacteristic
462C8—24no—
463C8—81no—
464C8—241no—
465C2×C3#161911yescharacteristic
466C2×C3#162011yescharacteristic
467C2×C3#162111yescharacteristic
468C2×C3#162111yescharacteristic
469C2×C3#187911yescharacteristic
470C2×C3#187911yescharacteristic
471C2×C3#188711yescharacteristic
472D3—84no—
473D3—162no—
474C22—124no—
475C22—124no—
476C22—124no—
477C22—242no—
478C22—242no—
479C22—242no—
480C22—242no—
481C22—242no—
482C22—242no—
483C22—242no—
484C22—481no—
485C22—481no—
486C22—481no—
487C22—481no—
488C22#466511yescharacteristic
489C22#473211yescharacteristic
490C22#473411yescharacteristic
491C22#477311yescharacteristic
492C22#481011yescharacteristic
493C22#482211yescharacteristic
494C22#482211yescharacteristic
495C4—21no—
496C4—21no—
497C4—42no—
498C4—81no—
499C4—122no—
500C4—241no—
501C4C4×D2411yescharacteristic
502C4#471111yescharacteristic
503C4#478611yescharacteristic
504C4#481911yescharacteristic
505C4#484311yescharacteristic
506C4#484411yescharacteristic
507C4#486911yescharacteristic
508C4#487211yescharacteristic
509C3#906111yescharacteristic, complemented, Sylow
510C2—244no—
511C2—482no—
512C2#6818611yescharacteristic
513C2#6819411yescharacteristic
514C2#6825811yescharacteristic
515C2#6825911yescharacteristic
516C2#6867311yescharacteristic
517C2#6876011yescharacteristic
518C2#6889711yescharacteristic
subgroupG/H
centerC23#882
commutatorC3×C42C22×C4
FrattiniC2×C42C22×D3
FittingC3×#1279C2
socleC23×C3#120
prime radicalC2×#4695C2
cosocleC2×C3×C42C23
hypercenter#1279D3
hypocenterC3#9061
LCSG ▷ C3×C42 ▷ C22×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1279

Complements

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

NH ≅ G/Ntype
2. #73653C2semidirect
3. #70457C2semidirect
4. C2×#4485C2semidirect
5. #69487C2semidirect
6. C3×#1279C2semidirect
7. #67655C2semidirect
26. #4695C4semidirect
35. #1279D3semidirect
67. #874C2×C4semidirect
74. C3×C4×C8C2×C4semidirect
156. C3×C4⋊C4D8semidirect
169. C4⋊Dic3D8semidirect
220. C4×C8C4×D3semidirect
351. C4⋊C4D24semidirect
509. C3#9061semidirect

Maximal subgroups

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

subgroupindex
C2×#46952
#736532
#704572
C2×#44852
#694872
C3×#12792
#676552
#90613