Finite Group Databasebeta

← #11860697

Subgroups — #11860697

Order 1152.

1151 conjugacy classes of subgroups.

The subgroup lattice has 480 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5798C211yesmaximal, characteristic, complemented
2C22×C3×#213C211yesmaximal, characteristic
3#10594982C211yesmaximal, characteristic, complemented
4#10592914C211yesmaximal, characteristic, complemented
5#10591430C214yesmaximal, complemented
6Dic3×#213C214yesmaximal, complemented
7#10591122C211yesmaximal, characteristic, complemented
8#10591085C211yesmaximal, characteristic, complemented
9#10591055C211yesmaximal, characteristic, complemented
10#83823—31nomaximal
11#82538—31nomaximal
12C22×C32×D4C2211yescharacteristic
13C22×C3×D12C2211yescharacteristic
14#64135C2211yescharacteristic
15C2×#3748C2211yescharacteristic
16C2×C3×#217—22no—
17C3×D4×Dic3—22no—
18C3×D4×Dic3C2214yescomplemented
19C2×C3×#213C418yescomplemented
20C2×C3×#213C2212yes—
21C2×C3×#213C2212yes—
22C3×#926C2211yescharacteristic
23C3×#926C2211yescharacteristic
24C22×C3×C3⋊C8C2211yescharacteristic
25D3×#217—22no—
26#63898—22no—
27Dic3×D12C2214yescomplemented
28#63659C2214yescomplemented
29#63575C2212yescomplemented
30#63573C2212yescomplemented
31#63562C2214yescomplemented
32#63554C2212yescomplemented
33Dic3×C3⋊C8C2212yescomplemented
34C22×C3×D8—31no—
35C3×#518—31no—
36#5798—31no—
37#5798D311yescharacteristic, complemented
38C22×#213D311yescharacteristic
39#5521—31no—
40#5215—31no—
41#5215—31no—
42#5215—31no—
43#5215—61no—
44#5152—34no—
45Dic3×D8—34no—
46#5106—31no—
47#5101—31no—
48#5014—34no—
49C4×#213—34no—
50#5001—31no—
51#4998—31no—
52#4997—31no—
53C24×C32—21no—
54C23×C3×D3—21no—
55C2×C32×D4—21no—
56C2×C32×D4—22no—
57C2×C32×D4C2×C414yescomplemented
58C2×C32×D4C2312yes—
59C22×C32×C4C2311yescharacteristic
60C22×C3×Dic3—24no—
61C2×C3×D12—21no—
62C2×C3×D12—22no—
63C2×C3×D12C2×C414yescomplemented
64C2×C3×D12C2312yes—
65C2×D3×Dic3—24no—
66#3757—21no—
67C4⋊(C3⋊Dic3)C2312yes—
68C4×C3⋊Dic3—21no—
69#3748—22no—
70C2×C3⋊(C3⋊C8)C2312yes—
71C3×#217—21no—
72C3×#217—24no—
73C3×#217D412yes—
74C3×#213C2×C418yescomplemented
75C3×#213C2×C418yescomplemented
76C3×C4⋊Dic3D412yes—
77C3×C4⋊Dic3C2312yes—
78C3×C4×Dic3—21no—
79C3×C4×Dic3C2312yes—
80C2×C3×C3⋊C8C2×C414yescomplemented
81C2×C3×C3⋊C8C2311yescharacteristic
82C2×C3×C3⋊C8C2311yescharacteristic
83(C2×D3)⋊Dic3—24no—
84#2948—91noSylow
85C22×C3×D4—21no—
86C22×C3×D4—31no—
87C22×C3×D4C2×D311yescharacteristic
88C22×C3×D4C2×D311yescharacteristic
89C22×D12C2×D311yescharacteristic
90C2×C3×D8—38no—
91C2×C3×D8—32no—
92C2×C3×D8—32no—
93C22×C3×C8—31no—
94C3×C4×D4—34no—
95C3×C4×D4—62no—
96C3×#117—31no—
97C3×#117—31no—
98C2×C3×C22⋊C4—62no—
99C2×#217—22no—
100C2×#217—62no—
101D4×Dic3—22no—
102D4×Dic3—34no—
103D4×Dic3—62no—
104D4×Dic3C2×D314yescomplemented
105C2×#213Dic318yescomplemented
106C2×#213C2×D312yes—
107C2×#213C2×D312yes—
108#926—31no—
109#926—31no—
110#926—61no—
111#926C2×D311yescharacteristic
112#926C2×D311yescharacteristic
113C2×#208—31no—
114C2×#208—31no—
115C2×#208—61no—
116C22×C3⋊C8C2×D311yescharacteristic
117#893—62no—
118D3×C22⋊C4—62no—
119C4×D12—34no—
120#832—34no—
121#832—34no—
122#832—34no—
123#832—64no—
124#818—32no—
125#817—32no—
126#815—32no—
127C8×Dic3—32no—
128#809—34no—
129#808—32no—
130#807—32no—
131#803—32no—
132C4×C3⋊C8—32no—
133C23×C32—22no—
134C23×C32—24no—
135C23×C32—82no—
136C23×C32C2×D411yescharacteristic
137C22×C3×D3—22no—
138C22×C3×D3—24no—
139C22×C3×D3—82no—
140C32×D4—24no—
141C32×D4—22no—
142C32×D4C22×C414yes—
143C2×C32×C4C22×C412yes—
144C2×C32×C4C2×D411yescharacteristic
145C2×C32×C4#4112yes—
146C2×C32×C4C2411yescharacteristic
147C2×C3⋊Dic3—22no—
148C2×C3×Dic3—22no—
149C2×C3×Dic3—84no—
150C2×C3×Dic3C2×D414yes—
151C3×D12—24no—
152C3×D12—22no—
153C3×D12C22×C414yes—
154D3×Dic3—84no—
155C3⋊(C3⋊C8)—22no—
156C3×C3⋊C8C22×C412yes—
157C3×C3⋊C8C22×C412yes—
158C22×D8—31no—
159#518—31no—
160#518—91no—
161#442—94no—
162C4×D8—94no—
163#427—91no—
164#418—91no—
165#418—91no—
166#405—91no—
167C24×C3—21no—
168C24×C3—21no—
169C24×C3—41no—
170C24×C3—61no—
171C23×D3—21no—
172C2×C3×D4—22no—
173C2×C3×D4—21no—
174C2×C3×D4—22no—
175C2×C3×D4—21no—
176C2×C3×D4—24no—
177C2×C3×D4—22no—
178C2×C3×D4—34no—
179C2×C3×D4—32no—
180C2×C3×D4—42no—
181C2×C3×D4—41no—
182C2×C3×D4—62no—
183C2×C3×D4—61no—
184C2×C3×D4C4×D314yescomplemented
185C2×C3×D4C2×Dic314yescomplemented
186C2×C3×D4C22×D312yes—
187C2×C3×D4C22×D312yes—
188C22×C3×C4—21no—
189C22×C3×C4—64no—
190C22×C3×C4C22×D311yescharacteristic
191C22×C3×C4C22×D311yescharacteristic
192C22×Dic3—24no—
193C22×Dic3—64no—
194C2×D12—21no—
195C2×D12—22no—
196C2×D12C2×Dic314yescomplemented
197C2×D12C22×D312yes—
198C2×C4×D3—64no—
199C3×D8—38no—
200C3×D8—38no—
201C2×C3×C8—34no—
202C2×C3×C8—31no—
203C2×C3×C8—31no—
204C3×C4⋊C4—32no—
205C3×C4⋊C4—32no—
206C3×C22⋊C4—32no—
207C3×C22⋊C4—64no—
208C3×C22⋊C4—61no—
209C3×C42—32no—
210C3×C42—61no—
211#217—21no—
212#217—24no—
213#217—61no—
214#217—61no—
215#217—64no—
216#217—121no—
217#217#6712yes—
218#213C2×Dic318yescomplemented
219#213C2×Dic318yescomplemented
220(C2×D3)⋊C4—64no—
221C4⋊Dic3—32no—
222C4⋊Dic3—32no—
223C4⋊Dic3—62no—
224C4⋊Dic3#6712yes—
225C4⋊Dic3C22×D312yes—
226C4×Dic3—21no—
227C4×Dic3—61no—
228C4×Dic3—61no—
229C4×Dic3—121no—
230C4×Dic3C22×D312yes—
231#208—62no—
232#208—62no—
233#208—122no—
234C2×C3⋊C8—32no—
235C2×C3⋊C8—32no—
236C2×C3⋊C8—62no—
237C2×C3⋊C8C2×Dic314yescomplemented
238C2×C3⋊C8C22×D311yescharacteristic
239C2×C3⋊C8C22×D311yescharacteristic
240C22×C32—22no—
241C22×C32—24no—
242C22×C32—44no—
243C22×C32—84no—
244C22×C32C4×D412yes—
245C22×C32C22×D411yescharacteristic
246C2×C3×D3—24no—
247C2×C3×D3—44no—
248C2×C3×D3—84no—
249C32×C4C4×D412yes—
250C32×C4C23×C411yescharacteristic
251C32×C4C2×#4111yescharacteristic
252C3⋊Dic3—42no—
253C3×Dic3—24no—
254C3×Dic3—42no—
255C22×D4—31no—
256C22×D4D3211yescharacteristic
257C2×D8—38no—
258C2×D8—32no—
259C2×D8—32no—
260C2×M16—91no—
261C22×C8—31no—
262C4×D4—34no—
263C4×D4—62no—
264C4×D4—94no—
265C4×D4—182no—
266#117—31no—
267#117—31no—
268#117—91no—
269C2×C22⋊C4—62no—
270C2×C22⋊C4—182no—
271#107—92no—
272#106—92no—
273#102—94no—
274#102—94no—
275#97—92no—
276C4×C8—92no—
277C23×C3—22no—
278C23×C3—22no—
279C23×C3—24no—
280C23×C3—24no—
281C23×C3—21no—
282C23×C3—42no—
283C23×C3—44no—
284C23×C3—62no—
285C23×C3—64no—
286C23×C3—82no—
287C23×C3—82no—
288C23×C3—84no—
289C23×C3—242no—
290C23×C3D3×D411yescharacteristic
291C23×C3C2×#6711yescharacteristic
292C22×D3—22no—
293C22×D3—24no—
294C22×D3—82no—
295C3×D4—24no—
296C3×D4—24no—
297C3×D4—22no—
298C3×D4—22no—
299C3×D4—24no—
300C3×D4—34no—
301C3×D4—42no—
302C3×D4—44no—
303C3×D4—64no—
304C3×D4—62no—
305C3×D4C2×C4×D314yes—
306C3×D4C22×Dic314yes—
307C2×C3×C4—21no—
308C2×C3×C4—22no—
309C2×C3×C4—22no—
310C2×C3×C4—21no—
311C2×C3×C4—34no—
312C2×C3×C4—62no—
313C2×C3×C4—244no—
314C2×C3×C4C2×C4×D312yes—
315C2×C3×C4#23512yes—
316C2×C3×C4D3×D411yescharacteristic
317C2×C3×C4#23712yes—
318C2×C3×C4C22×Dic312yes—
319C2×C3×C4C2×#6711yescharacteristic
320C2×C3×C4C23×D311yescharacteristic
321C2×C3×C4C23×D311yescharacteristic
322C2×Dic3—22no—
323C2×Dic3—62no—
324C2×Dic3—62no—
325C2×Dic3—84no—
326C2×Dic3—122no—
327C2×Dic3—244no—
328C2×Dic3C2×#6714yes—
329D12—24no—
330D12—22no—
331D12C22×Dic314yes—
332C4×D3—244no—
333C3×C8—32no—
334C3×C8—32no—
335C3⋊C8—62no—
336C3⋊C8—62no—
337C3⋊C8—122no—
338C3⋊C8C22×Dic312yes—
339C3⋊C8C22×Dic312yes—
340C2×C32—22no—
341C2×C32—44no—
342C2×C32C2×C4×D411yescharacteristic
343C2×C32#57612yes—
344C3×D3—44no—
345C24—21no—
346C24—61no—
347C2×D4—22no—
348C2×D4—21no—
349C2×D4—32no—
350C2×D4—34no—
351C2×D4—62no—
352C2×D4—61no—
353C2×D4D3×Dic314yescomplemented
354C2×D4C2×D3212yes—
355C22×C4—64no—
356C22×C4—184no—
357C22×C4C2×D3211yescharacteristic
358D8—38no—
359D8—38no—
360M16—182no—
361C2×C8—31no—
362C2×C8—31no—
363C2×C8—34no—
364C2×C8—92no—
365C4⋊C4—32no—
366C4⋊C4—32no—
367C4⋊C4—92no—
368C22⋊C4—32no—
369C22⋊C4—64no—
370C22⋊C4—61no—
371C22⋊C4—184no—
372C22⋊C4—181no—
373C42—32no—
374C42—61no—
375C42—181no—
376C22×C3—22no—
377C22×C3—22no—
378C22×C3—24no—
379C22×C3—24no—
380C22×C3—21no—
381C22×C3—22no—
382C22×C3—42no—
383C22×C3—44no—
384C22×C3—44no—
385C22×C3—44no—
386C22×C3—64no—
387C22×C3—84no—
388C22×C3—84no—
389C22×C3—84no—
390C22×C3—88no—
391C22×C3—124no—
392C22×C3—244no—
393C22×C3C4×#6712yes—
394C22×C3D4×Dic312yes—
395C22×C3C2×D3×D411yescharacteristic
396C22×C3C22×#6711yescharacteristic
397C2×D3—24no—
398C2×D3—44no—
399C2×D3—84no—
400C3×C4—21no—
401C3×C4—21no—
402C3×C4—22no—
403C3×C4—64no—
404C3×C4—122no—
405C3×C4C4×#6712yes—
406C3×C4D4×Dic312yes—
407C3×C4C22×C4×D311yescharacteristic
408C3×C4C2×#23511yescharacteristic
409C3×C4C2×#23711yescharacteristic
410C3×C4C23×Dic311yescharacteristic
411Dic3—24no—
412Dic3—42no—
413Dic3—122no—
414Dic3—122no—
415Dic3—242no—
416C32#294811yescharacteristic, complemented, Sylow
417C23—22no—
418C23—24no—
419C23—62no—
420C23—64no—
421C23—82no—
422C23—242no—
423C23D3×#6711yescharacteristic
424D4—22no—
425D4—24no—
426D4—34no—
427D4—62no—
428D4—64no—
429D4C2×D3×Dic314yes—
430C2×C4—34no—
431C2×C4—62no—
432C2×C4—182no—
433C2×C4—244no—
434C2×C4—724no—
435C2×C4C2×D3×Dic312yes—
436C2×C4#380412yes—
437C2×C4D3×#6711yescharacteristic
438C2×C4C22×D3211yescharacteristic
439C8—32no—
440C8—32no—
441C8—182no—
442C2×C3—22no—
443C2×C3—22no—
444C2×C3—22no—
445C2×C3—21no—
446C2×C3—42no—
447C2×C3—44no—
448C2×C3—44no—
449C2×C3—84no—
450C2×C3—124no—
451C2×C3#575712yes—
452C2×C3C2×C4×#6711yescharacteristic
453C2×C3C2×D4×Dic311yescharacteristic
454C2×C3#583512yes—
455D3—44no—
456C22—22no—
457C22—24no—
458C22—44no—
459C22—64no—
460C22—84no—
461C22—124no—
462C22—244no—
463C22Dic3×#6712yes—
464C22C2×D3×#6711yescharacteristic
465C4—64no—
466C4—122no—
467C4—362no—
468C4Dic3×#6712yes—
469C4C22×D3×Dic311yescharacteristic
470C4C2×#380411yescharacteristic
471C3—21no—
472C3#8253811yescharacteristic, complemented
473C3#8382311yescharacteristic, complemented
474C2—22no—
475C2—44no—
476C2—124no—
477C2#1059509612yes—
478C2C2×Dic3×#6711yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC22×C32×D4C22
socleC22×C32C22×D4
prime radicalC22×C3×#213C2
cosocleC2×C32×C4C24
hypercenterC22×D4D32
hypocenterC32#2948
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. C3×#5798C2semidirect
3. #10594982C2semidirect
4. #10592914C2semidirect
5. #10591430C2semidirect
6. Dic3×#213C2semidirect
7. #10591122C2semidirect
8. #10591085C2semidirect
9. #10591055C2semidirect
18. C3×D4×Dic3C22semidirect
19. C2×C3×#213C4semidirect
27. Dic3×D12C22semidirect
28. #63659C22semidirect
29. #63575C22semidirect
30. #63573C22semidirect
31. #63562C22semidirect
32. #63554C22semidirect
33. Dic3×C3⋊C8C22semidirect
37. #5798D3semidirect
57. C2×C32×D4C2×C4semidirect
63. C2×C3×D12C2×C4semidirect
74. C3×#213C2×C4semidirect
75. C3×#213C2×C4semidirect
80. C2×C3×C3⋊C8C2×C4semidirect
104. D4×Dic3C2×D3semidirect
105. C2×#213Dic3semidirect
184. C2×C3×D4C4×D3semidirect
185. C2×C3×D4C2×Dic3semidirect
196. C2×D12C2×Dic3semidirect
218. #213C2×Dic3semidirect
219. #213C2×Dic3semidirect
237. C2×C3⋊C8C2×Dic3semidirect
353. C2×D4D3×Dic3semidirect
416. C32#2948semidirect
472. C3#82538semidirect
473. C3#83823semidirect

Maximal subgroups

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

subgroupindex
C3×#57982
C22×C3×#2132
#105949822
#105929142
#105914302
Dic3×#2132
#105911222
#105910852
#105910552
#838233
#825383