Finite Group Databasebeta

← #11788792

Subgroups — #11788792

Order 1152.

801 conjugacy classes of subgroups.

The subgroup lattice has 525 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5830C211yesmaximal, characteristic
2#10594982C211yesmaximal, characteristic, complemented
3#10592935C211yesmaximal, characteristic, complemented
4C3×#5236C211yesmaximal, characteristic, complemented
5C2×#63558C211yesmaximal, characteristic, complemented
6#10589158C211yesmaximal, characteristic, complemented
7#10589157C211yesmaximal, characteristic, complemented
8#71853—31nomaximal
9#70408—31nomaximal
10C2×C32×#41C2211yescharacteristic
11C22×C3×D12C2211yescharacteristic
12#64135C2211yescharacteristic
13C2×#3748C2211yescharacteristic
14C3×#947C412yescomplemented
15C3×#940C412yescomplemented
16C3×#937—22no—
17C3×#930—22no—
18C3×#926C2211yescharacteristic
19C3×#926C2211yescharacteristic
20C2×C3×#208C2211yescharacteristic
21D3×#217—22no—
22#63898—22no—
23Dic3×D12—22no—
24#63664—22no—
25C3×#837—22no—
26#63558—22no—
27C3×#535—31no—
28#5830D311yescharacteristic
29#5798—31no—
30#5521—31no—
31C3×#421—31no—
32#5236—31no—
33#5236—31no—
34#5236—61no—
35#5236D311yescharacteristic, complemented
36C2×#833—31no—
37C2×#823—31no—
38#4557—31no—
39#4531—31no—
40#4531—31no—
41#4531—31no—
42C23×C3×D3D412yes—
43C32×#41—21no—
44C32×#41—21no—
45C32×#41—21no—
46C32×#41—21no—
47C2×C32×Q8C2×C411yescharacteristic, complemented
48C2×C32×D4—21no—
49C2×C32×D4C2×C411yescharacteristic, complemented
50C22×C32×C4—21no—
51C22×C32×C4C2311yescharacteristic
52C2×C3×#67—24no—
53C2×C3×D12—21no—
54C2×C3×D12—21no—
55C2×C3×D12—21no—
56C2×C3×D12—21no—
57C2×C3×D12C2×C412yes—
58C2×C3×D12D412yes—
59C2×D3×Dic3—24no—
60#3757—21no—
61C4⋊(C3⋊Dic3)—21no—
62C4×C3⋊Dic3D412yescomplemented
63#3748—21no—
64#3748—21no—
65C2×C3⋊(C3⋊C8)—21no—
66C3×#217—21no—
67C3×#217—21no—
68C3×(C2×D3)⋊C4—24no—
69C3×C4⋊Dic3—21no—
70C3×C4⋊Dic3—21no—
71C3×C4×Dic3C2×C412yescomplemented
72C3×C4×Dic3D412yescomplemented
73C3×#208—21no—
74C3×#208—21no—
75C2×C3×C3⋊C8—21no—
76(C2×D3)⋊Dic3—24no—
77#1911—91noSylow
78C2×C3×#41—21no—
79C2×C3×#41C2×D311yescharacteristic
80C2×C3×#41C2×D311yescharacteristic
81C22×C3×D4—31no—
82C22×D12C2×D311yescharacteristic
83C2×C3×M16—31no—
84C3×#127—32no—
85C3×#124—32no—
86C3×#121—62no—
87C3×#120—62no—
88C3×#117—31no—
89C3×#117—31no—
90C2×#217—62no—
91#947Dic312yescomplemented
92#940Dic312yescomplemented
93#937—22no—
94D4×Dic3—62no—
95D4×Dic3—62no—
96#930—22no—
97#926—31no—
98#926—31no—
99#926—61no—
100#926C2×D311yescharacteristic
101#926C2×D311yescharacteristic
102C2×#208—31no—
103C2×#208—31no—
104C2×#208—61no—
105C2×#208C2×D311yescharacteristic
106#893—62no—
107D3×C22⋊C4—62no—
108C4×D12—62no—
109C3×#104—62no—
110#837—22no—
111#837—62no—
112#837—62no—
113#837—64no—
114#833—62no—
115#823—62no—
116C23×C32—21no—
117C23×C32C2×D411yescharacteristic
118C22×C3×D3—22no—
119C22×C3×D3—22no—
120C22×C3×D3—82no—
121C22×C3×D3C22⋊C414yes—
122C32×Q8—21no—
123C32×Q8—21no—
124C32×D4—21no—
125C32×D4—21no—
126C32×D4—41no—
127C32×D4—41no—
128C2×C32×C4—21no—
129C2×C32×C4—41no—
130C2×C32×C4—41no—
131C2×C32×C4C22×C411yescharacteristic
132C2×C32×C4C2×D411yescharacteristic
133C2×C32×C4C2×D411yescharacteristic
134C2×C32×C4C2×D411yescharacteristic
135C2×C32×C4#4111yescharacteristic
136C2×C32×C4#4111yescharacteristic
137C2×C3⋊Dic3—22no—
138C3×#67—84no—
139C2×C3×Dic3—22no—
140C2×C3×Dic3—22no—
141C3×D12—22no—
142C3×D12—22no—
143C3×D12—22no—
144C3×D12—22no—
145D3×Dic3—84no—
146C3⋊(C3⋊C8)—41no—
147C3×C3⋊C8—41no—
148#535—31no—
149#518—91no—
150#421—31no—
151#421—91no—
152C2×#100—91no—
153H(3,ℤ/4)—91no—
154H(3,ℤ/4)—91no—
155C24×C3—32no—
156C23×D3#6712yes—
157C3×#41—22no—
158C3×#41—22no—
159C3×#41—21no—
160C3×#41—21no—
161C3×#41—21no—
162C3×#41—21no—
163C3×#41—21no—
164C3×#41—21no—
165C3×#41—21no—
166C3×#41—21no—
167C3×#41—41no—
168C3×#41—41no—
169C2×C3×Q8—21no—
170C2×C3×Q8C4×D311yescharacteristic, complemented
171C2×C3×Q8C2×Dic311yescharacteristic, complemented
172C2×C3×D4—21no—
173C2×C3×D4—21no—
174C2×C3×D4—21no—
175C2×C3×D4—32no—
176C2×C3×D4—32no—
177C2×C3×D4—41no—
178C2×C3×D4—64no—
179C2×C3×D4—61no—
180C2×C3×D4—61no—
181C2×C3×D4—61no—
182C2×C3×D4—61no—
183C2×C3×D4C4×D311yescharacteristic, complemented
184C2×C3×D4C2×Dic311yescharacteristic, complemented
185C22×C3×C4—21no—
186C22×C3×C4—21no—
187C22×C3×C4—21no—
188C22×C3×C4—41no—
189C22×C3×C4C22×D311yescharacteristic
190C22×C3×C4C22×D311yescharacteristic
191C2×#67—24no—
192C22×Dic3—64no—
193C2×D12—21no—
194C2×D12—21no—
195C2×D12—21no—
196C2×D12—21no—
197C2×D12C2×Dic312yes—
198C2×D12#6712yes—
199C2×C4×D3—64no—
200C3×M16—61no—
201C3×M16—61no—
202C2×C3×C8—61no—
203C3×C4⋊C4—61no—
204C3×C4⋊C4—61no—
205C3×C22⋊C4—64no—
206C3×C22⋊C4—61no—
207C3×C22⋊C4—61no—
208C3×C42—32no—
209C3×C42—32no—
210#217—21no—
211#217—21no—
212#217—64no—
213#217—61no—
214#217—61no—
215#217—121no—
216(C2×D3)⋊C4—24no—
217(C2×D3)⋊C4—64no—
218C4⋊Dic3—21no—
219C4⋊Dic3—21no—
220C4⋊Dic3—61no—
221C4⋊Dic3—61no—
222C4⋊Dic3—121no—
223C4×Dic3—32no—
224C4×Dic3—32no—
225C4×Dic3—62no—
226C4×Dic3C2×Dic312yescomplemented
227C4×Dic3#6712yescomplemented
228#208—21no—
229#208—21no—
230#208—62no—
231#208—61no—
232#208—61no—
233#208—61no—
234#208—61no—
235#208—121no—
236C2×C3⋊C8—21no—
237C2×C3⋊C8—61no—
238C2×C3⋊C8—61no—
239C2×C3⋊C8—121no—
240C22×C32—41no—
241C22×C32—41no—
242C22×C32—42no—
243C22×C32C2×C22⋊C411yescharacteristic
244C22×C32#12011yescharacteristic
245C22×C32#12311yescharacteristic
246C2×C3×D3—24no—
247C2×C3×D3—44no—
248C2×C3×D3—44no—
249C2×C3×D3—82no—
250C32×C4—41no—
251C32×C4C4×D411yescharacteristic
252C32×C4C4×D411yescharacteristic
253C32×C4#12111yescharacteristic
254C32×C4#12111yescharacteristic
255C3⋊Dic3—42no—
256C3×Dic3—42no—
257C3×Dic3—42no—
258C2×#41D3211yescharacteristic
259C22×D4—31no—
260C2×M16—31no—
261C2×M16—91no—
262#127—32no—
263#124—32no—
264#121—62no—
265#120—62no—
266C4×D4—182no—
267C4×D4—182no—
268#117—31no—
269#117—31no—
270#117—91no—
271C2×C22⋊C4—182no—
272#104—62no—
273#104—182no—
274#100—182no—
275C23×C3—21no—
276C23×C3—21no—
277C23×C3—21no—
278C23×C3—34no—
279C23×C3—41no—
280C23×C3—62no—
281C23×C3—62no—
282C23×C3—242no—
283C23×C3D3×D411yescharacteristic
284C23×C3C2×#6711yescharacteristic
285C22×D3—22no—
286C22×D3—22no—
287C22×D3—82no—
288C22×D3#21714yes—
289C3×Q8—22no—
290C3×Q8—21no—
291C3×Q8—21no—
292C3×Q8—21no—
293C3×Q8—21no—
294C3×Q8—41no—
295C3×D4—22no—
296C3×D4—21no—
297C3×D4—21no—
298C3×D4—21no—
299C3×D4—21no—
300C3×D4—41no—
301C3×D4—42no—
302C3×D4—42no—
303C3×D4—41no—
304C3×D4—41no—
305C3×D4—41no—
306C3×D4—41no—
307C3×D4—62no—
308C3×D4—62no—
309C3×D4—62no—
310C3×D4—62no—
311C3×D4—244no—
312C2×C3×C4—21no—
313C2×C3×C4—21no—
314C2×C3×C4—21no—
315C2×C3×C4—21no—
316C2×C3×C4—21no—
317C2×C3×C4—21no—
318C2×C3×C4—21no—
319C2×C3×C4—21no—
320C2×C3×C4—41no—
321C2×C3×C4—42no—
322C2×C3×C4—42no—
323C2×C3×C4—41no—
324C2×C3×C4—41no—
325C2×C3×C4—41no—
326C2×C3×C4—41no—
327C2×C3×C4—62no—
328C2×C3×C4—62no—
329C2×C3×C4C2×C4×D311yescharacteristic
330C2×C3×C4#23511yescharacteristic
331C2×C3×C4D3×D411yescharacteristic
332C2×C3×C4D3×D411yescharacteristic
333C2×C3×C4D3×D411yescharacteristic
334C2×C3×C4D3×D411yescharacteristic
335C2×C3×C4#23711yescharacteristic
336C2×C3×C4#23711yescharacteristic
337C2×C3×C4#23711yescharacteristic
338C2×C3×C4C22×Dic311yescharacteristic
339C2×C3×C4C2×#6711yescharacteristic
340C2×C3×C4C2×#6711yescharacteristic
341#67—84no—
342C2×Dic3—22no—
343C2×Dic3—22no—
344C2×Dic3—62no—
345C2×Dic3—62no—
346C2×Dic3—122no—
347C2×Dic3—244no—
348D12—22no—
349D12—22no—
350D12—22no—
351D12—22no—
352C4×D3—244no—
353C3×C8—121no—
354C3⋊C8—41no—
355C3⋊C8—122no—
356C3⋊C8—121no—
357C3⋊C8—121no—
358C2×C32—21no—
359C2×C32—21no—
360C2×C32—21no—
361C2×C32—81no—
362C2×C32#38611yescharacteristic
363C3×D3—44no—
364C24—32no—
365#41—21no—
366#41—21no—
367#41—21no—
368#41—21no—
369C2×Q8D3×Dic311yescharacteristic, complemented
370C2×D4—21no—
371C2×D4—32no—
372C2×D4—32no—
373C2×D4—64no—
374C2×D4—61no—
375C2×D4—61no—
376C2×D4—61no—
377C2×D4—61no—
378C2×D4D3×Dic311yescharacteristic, complemented
379C22×C4—21no—
380C22×C4—184no—
381C22×C4C2×D3211yescharacteristic
382M16—61no—
383M16—61no—
384M16—181no—
385M16—181no—
386C2×C8—61no—
387C2×C8—181no—
388C4⋊C4—61no—
389C4⋊C4—61no—
390C4⋊C4—181no—
391C22⋊C4—64no—
392C22⋊C4—61no—
393C22⋊C4—61no—
394C22⋊C4—184no—
395C22⋊C4—181no—
396C42—32no—
397C42—32no—
398C42—92no—
399C22×C3—21no—
400C22×C3—21no—
401C22×C3—21no—
402C22×C3—41no—
403C22×C3—41no—
404C22×C3—42no—
405C22×C3—42no—
406C22×C3—42no—
407C22×C3—41no—
408C22×C3—41no—
409C22×C3—64no—
410C22×C3—81no—
411C22×C3—82no—
412C22×C3—124no—
413C22×C3—124no—
414C22×C3—242no—
415C22×C3D3×C22⋊C411yescharacteristic
416C22×C3#88311yescharacteristic
417C22×C3#93511yescharacteristic
418C22×C3#93711yescharacteristic
419C22×C3#93711yescharacteristic
420C22×C3C2×#21711yescharacteristic
421C2×D3—24no—
422C2×D3—44no—
423C2×D3—44no—
424C2×D3—82no—
425C3×C4—21no—
426C3×C4—21no—
427C3×C4—21no—
428C3×C4—21no—
429C3×C4—42no—
430C3×C4—41no—
431C3×C4—41no—
432C3×C4—122no—
433C3×C4—122no—
434C3×C4#67⋊C411yescharacteristic
435C3×C4#88411yescharacteristic
436C3×C4C4×#6711yescharacteristic
437C3×C4D4×Dic311yescharacteristic
438C3×C4D4×Dic311yescharacteristic
439C3×C4#93811yescharacteristic
440C3×C4#93911yescharacteristic
441C3×C4#93911yescharacteristic
442Dic3—42no—
443Dic3—42no—
444Dic3—122no—
445Dic3—122no—
446Dic3—242no—
447C32#191111yescharacteristic, complemented, Sylow
448C23—21no—
449C23—34no—
450C23—62no—
451C23—62no—
452C23—242no—
453C23D3×#6711yescharacteristic
454Q8—21no—
455Q8—21no—
456D4—21no—
457D4—21no—
458D4—41no—
459D4—41no—
460D4—62no—
461D4—62no—
462D4—62no—
463D4—62no—
464D4—244no—
465C2×C4—21no—
466C2×C4—41no—
467C2×C4—41no—
468C2×C4—62no—
469C2×C4—62no—
470C2×C4—182no—
471C2×C4—724no—
472C2×C4C2×D3×Dic311yescharacteristic
473C2×C4#380411yescharacteristic
474C2×C4#380511yescharacteristic
475C2×C4D3×#6711yescharacteristic
476C2×C4D3×#6711yescharacteristic
477C2×C4#381111yescharacteristic
478C8—121no—
479C8—361no—
480C2×C3—21no—
481C2×C3—21no—
482C2×C3—21no—
483C2×C3—21no—
484C2×C3—21no—
485C2×C3—21no—
486C2×C3—21no—
487C2×C3—41no—
488C2×C3—41no—
489C2×C3—41no—
490C2×C3—82no—
491C2×C3—81no—
492C2×C3—81no—
493C2×C3—124no—
494C2×C3#495611yescharacteristic
495C2×C3#522011yescharacteristic
496D3—44no—
497C22—41no—
498C22—42no—
499C22—41no—
500C22—64no—
501C22—124no—
502C22—124no—
503C22—242no—
504C22D3×#21711yescharacteristic
505C22#6396911yescharacteristic
506C22#6398311yescharacteristic
507C4—41no—
508C4—122no—
509C4—122no—
510C4—362no—
511C4#6397011yescharacteristic
512C4#6397111yescharacteristic
513C4Dic3×#6711yescharacteristic
514C4#67⋊Dic311yescharacteristic
515C3—21no—
516C3#7040811yescharacteristic, complemented
517C3#7185311yescharacteristic, complemented
518C2—21no—
519C2—21no—
520C2—21no—
521C2—81no—
522C2—124no—
523C2#1059172111yescharacteristic
subgroupG/H
centerC2#10591721
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC2×C32×#41C22
socleC2×C32#386
prime radicalC3×#5830C2
cosocleC22×C32×C4C23
hypercenterC2×#41D32
hypocenterC32#1911
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
2. #10594982C2semidirect
3. #10592935C2semidirect
4. C3×#5236C2semidirect
5. C2×#63558C2semidirect
6. #10589158C2semidirect
7. #10589157C2semidirect
14. C3×#947C4semidirect
15. C3×#940C4semidirect
35. #5236D3semidirect
47. C2×C32×Q8C2×C4semidirect
49. C2×C32×D4C2×C4semidirect
62. C4×C3⋊Dic3D4semidirect
71. C3×C4×Dic3C2×C4semidirect
72. C3×C4×Dic3D4semidirect
91. #947Dic3semidirect
92. #940Dic3semidirect
170. C2×C3×Q8C4×D3semidirect
171. C2×C3×Q8C2×Dic3semidirect
183. C2×C3×D4C4×D3semidirect
184. C2×C3×D4C2×Dic3semidirect
226. C4×Dic3C2×Dic3semidirect
227. C4×Dic3#67semidirect
369. C2×Q8D3×Dic3semidirect
378. C2×D4D3×Dic3semidirect
447. C32#1911semidirect
516. C3#70408semidirect
517. C3#71853semidirect

Maximal subgroups

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

subgroupindex
C3×#58302
#105949822
#105929352
C3×#52362
C2×#635582
#105891582
#105891572
#718533
#704083