Finite Group Databasebeta

← #11860696

Subgroups — #11860696

Order 1152.

1113 conjugacy classes of subgroups.

The subgroup lattice has 473 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5521C211yesmaximal, characteristic, complemented
2#10594982C211yesmaximal, characteristic, complemented
3C22×#3713C211yesmaximal, characteristic
4#10592697C211yesmaximal, characteristic, complemented
5C3×#5001C211yesmaximal, characteristic, complemented
6#10591086C211yesmaximal, characteristic, complemented
7#10591057C211yesmaximal, characteristic, complemented
8#10590455C214yesmaximal, complemented
9#10590452C214yesmaximal, complemented
10#82538—31nomaximal
11#78915—31nomaximal
12C22×C3×D12C2211yescharacteristic
13C22×C3×D12C2211yescharacteristic
14C32×#117C2211yescharacteristic
15#64135C2211yescharacteristic
16C22×C3⋊(C3⋊C8)C2211yescharacteristic
17C3×#926C2211yescharacteristic
18C2×C3×#208C2211yescharacteristic
19C3×#893C2214yescomplemented
20C3×D3×C22⋊C4—22no—
21C3×C4×D12—22no—
22D3×#217—22no—
23#63898—22no—
24Dic3×D12C2214yescomplemented
25C2×#3713C418yescomplemented
26C2×#3713C2212yes—
27C2×#3713C2212yes—
28#63635C2212yescomplemented
29#63634C2212yescomplemented
30C3×#809C2214yescomplemented
31#63563C2214yescomplemented
32#63554C2212yescomplemented
33Dic3×C3⋊C8C2212yescomplemented
34C3×#518—31no—
35#5798—31no—
36C22×#213—31no—
37C22×#213—31no—
38#5521—31no—
39#5521D311yescharacteristic, complemented
40C3×#418—31no—
41#5215—31no—
42#5131—31no—
43#5122—31no—
44#5014—34no—
45C4×#213—34no—
46#5001D311yescharacteristic, complemented
47#4998—31no—
48#4998—31no—
49#4998—61no—
50#4997—31no—
51#4785—34no—
52#4756—34no—
53C23×C3×D3—21no—
54C23×C3×D3—21no—
55C22×C32×C4C2311yescharacteristic
56C2×C3×D12—21no—
57C2×C3×D12—21no—
58C2×C3×D12—22no—
59C2×C3×D12—22no—
60C2×C3×D12C2×C414yescomplemented
61C2×C3×D12C2×C414yescomplemented
62C2×C3×D12C2312yes—
63C2×C3×D12C2312yes—
64C2×C3×C4×D3—24no—
65C2×D3×Dic3—24no—
66C32×C4⋊C4C2312yes—
67C32×C22⋊C4—21no—
68C32×C42—21no—
69#3757—21no—
70C4⋊(C3⋊Dic3)C2312yes—
71C4×C3⋊Dic3—21no—
72C2×C3⋊(C3⋊C8)C2×C414yescomplemented
73C2×C3⋊(C3⋊C8)C2311yescharacteristic
74C2×C3⋊(C3⋊C8)C2311yescharacteristic
75C3×#217D412yes—
76C3×(C2×D3)⋊C4—24no—
77C3×C4⋊Dic3D412yes—
78C3×C4×Dic3C2312yes—
79C3×#208—22no—
80C2×C3×C3⋊C8C2312yes—
81(C2×D3)⋊Dic3—24no—
82#3713C2×C418yescomplemented
83#3713C2×C418yescomplemented
84#2948—91noSylow
85C22×C3×D4—31no—
86C22×C3×D4—31no—
87C22×D12C2×D311yescharacteristic
88C22×D12C2×D311yescharacteristic
89C2×C3×M16—31no—
90C3×C4×D4—34no—
91C3×C4×D4—62no—
92C3×#117—21no—
93C3×#117—31no—
94C3×#117C2×D311yescharacteristic
95C3×#117C2×D311yescharacteristic
96C2×C3×C22⋊C4—62no—
97C2×#217—62no—
98D4×Dic3—34no—
99D4×Dic3—62no—
100C2×#213—38no—
101C2×#213—38no—
102C2×#213—32no—
103C2×#213—32no—
104C2×#213—32no—
105C2×#213—32no—
106#926—31no—
107#926—31no—
108#926—61no—
109#926C2×D311yescharacteristic
110C2×#208C2×D311yescharacteristic
111C22×C3⋊C8—31no—
112C22×C3⋊C8—31no—
113C22×C3⋊C8—61no—
114#893—62no—
115#893C2×D314yescomplemented
116D3×C22⋊C4—22no—
117D3×C22⋊C4—62no—
118C4×D12—22no—
119C4×D12—34no—
120C3×#102—34no—
121#832—34no—
122#821—34no—
123#815—32no—
124C8×Dic3—32no—
125#809C2×D314yescomplemented
126#808—32no—
127#808—32no—
128#808—62no—
129#807—32no—
130#807—32no—
131#807—62no—
132#803—32no—
133C4×C3⋊C8—32no—
134C23×C32C2×D411yescharacteristic
135C22×C3×D3—22no—
136C22×C3×D3—22no—
137C22×C3×D3—24no—
138C22×C3×D3—24no—
139C22×C3×D3—82no—
140C22×C3×D3—82no—
141C2×C32×C4—22no—
142C2×C32×C4C22×C412yes—
143C2×C32×C4C2×D411yescharacteristic
144C2×C32×C4#4112yes—
145C2×C32×C4C2411yescharacteristic
146C2×C3⋊Dic3—22no—
147C2×C3×Dic3C2×D414yes—
148C3×D12—24no—
149C3×D12—24no—
150C3×D12—22no—
151C3×D12—22no—
152C3×D12C22×C414yes—
153C3×D12C22×C414yes—
154C3×C4×D3—84no—
155D3×Dic3—84no—
156C3⋊(C3⋊C8)C22×C412yes—
157C3⋊(C3⋊C8)C22×C412yes—
158C3×C3⋊C8—22no—
159C22×D8—91no—
160#518—31no—
161#518—91no—
162#442—94no—
163C4×D8—94no—
164#427—91no—
165#418—31no—
166#418—91no—
167#405—91no—
168C24×C3—61no—
169C24×C3—61no—
170C23×D3—21no—
171C23×D3—21no—
172C2×C3×D4—34no—
173C2×C3×D4—34no—
174C2×C3×D4—32no—
175C2×C3×D4—32no—
176C2×C3×D4—62no—
177C2×C3×D4—61no—
178C2×C3×D4—62no—
179C2×C3×D4—61no—
180C22×C3×C4—21no—
181C22×C3×C4—64no—
182C22×C3×C4C22×D311yescharacteristic
183C22×C3×C4C22×D311yescharacteristic
184C22×Dic3—64no—
185C2×D12—22no—
186C2×D12—21no—
187C2×D12—22no—
188C2×D12—21no—
189C2×D12C4×D314yescomplemented
190C2×D12C4×D314yescomplemented
191C2×D12C22×D312yes—
192C2×D12C22×D312yes—
193C2×C4×D3—24no—
194C2×C4×D3—64no—
195C3×M16—62no—
196C2×C3×C8—32no—
197C3×C4⋊C4—22no—
198C3×C4⋊C4—32no—
199C3×C4⋊C4C22×D312yes—
200C3×C4⋊C4C22×D312yes—
201C3×C22⋊C4—21no—
202C3×C22⋊C4—21no—
203C3×C22⋊C4—32no—
204C3×C22⋊C4—41no—
205C3×C22⋊C4—64no—
206C3×C42—21no—
207C3×C42—21no—
208C3×C42—32no—
209C3×C42—41no—
210#217—61no—
211#217—61no—
212#217—64no—
213#217—121no—
214#217#6712yes—
215#213—38no—
216#213—38no—
217#213—38no—
218#213—38no—
219(C2×D3)⋊C4—24no—
220(C2×D3)⋊C4—64no—
221C4⋊Dic3—32no—
222C4⋊Dic3—32no—
223C4⋊Dic3—62no—
224C4⋊Dic3#6712yes—
225C4×Dic3—61no—
226C4×Dic3—61no—
227C4×Dic3—121no—
228C4×Dic3C22×D312yes—
229#208—22no—
230C2×C3⋊C8—34no—
231C2×C3⋊C8—34no—
232C2×C3⋊C8—31no—
233C2×C3⋊C8—31no—
234C2×C3⋊C8—31no—
235C2×C3⋊C8—31no—
236C2×C3⋊C8—61no—
237C2×C3⋊C8—61no—
238C2×C3⋊C8—64no—
239C2×C3⋊C8C22×D312yes—
240C22×C32—22no—
241C22×C32C4×D412yes—
242C22×C32C22×D411yescharacteristic
243C2×C3×D3—24no—
244C2×C3×D3—24no—
245C2×C3×D3—44no—
246C2×C3×D3—44no—
247C2×C3×D3—84no—
248C2×C3×D3—84no—
249C32×C4—42no—
250C32×C4C4×D412yes—
251C32×C4C23×C411yescharacteristic
252C32×C4C2×#4111yescharacteristic
253C3⋊Dic3—42no—
254C3×Dic3—24no—
255C22×D4—31no—
256C22×D4—31no—
257C2×D8—98no—
258C2×D8—92no—
259C2×D8—92no—
260C2×M16—31no—
261C22×C8—91no—
262C4×D4—34no—
263C4×D4—62no—
264C4×D4—94no—
265C4×D4—182no—
266#117—31no—
267#117—91no—
268#117D3211yescharacteristic
269C2×C22⋊C4—62no—
270C2×C22⋊C4—182no—
271#107—92no—
272#106—92no—
273#102—34no—
274#102—94no—
275#97—92no—
276C4×C8—92no—
277C23×C3—21no—
278C23×C3—62no—
279C23×C3—62no—
280C23×C3—64no—
281C23×C3—64no—
282C23×C3—242no—
283C23×C3—242no—
284C23×C3D3×D411yescharacteristic
285C23×C3C2×#6711yescharacteristic
286C22×D3—22no—
287C22×D3—22no—
288C22×D3—24no—
289C22×D3—24no—
290C22×D3—82no—
291C22×D3—82no—
292C3×D4—34no—
293C3×D4—34no—
294C3×D4—64no—
295C3×D4—64no—
296C3×D4—62no—
297C3×D4—62no—
298C2×C3×C4—22no—
299C2×C3×C4—22no—
300C2×C3×C4—21no—
301C2×C3×C4—22no—
302C2×C3×C4—22no—
303C2×C3×C4—21no—
304C2×C3×C4—34no—
305C2×C3×C4—42no—
306C2×C3×C4—244no—
307C2×C3×C4C2×C4×D312yes—
308C2×C3×C4C2×C4×D312yes—
309C2×C3×C4#23512yes—
310C2×C3×C4D3×D411yescharacteristic
311C2×C3×C4#23712yes—
312C2×C3×C4C2×#6711yescharacteristic
313C2×C3×C4C23×D311yescharacteristic
314C2×C3×C4C23×D311yescharacteristic
315C2×Dic3—62no—
316C2×Dic3—62no—
317C2×Dic3—122no—
318C2×Dic3—244no—
319C2×Dic3C2×#6714yes—
320D12—24no—
321D12—24no—
322D12—22no—
323D12—22no—
324D12C2×C4×D314yes—
325D12C2×C4×D314yes—
326C4×D3—84no—
327C4×D3—244no—
328C3×C8—62no—
329C3⋊C8—22no—
330C3⋊C8—32no—
331C3⋊C8—32no—
332C3⋊C8—32no—
333C3⋊C8—32no—
334C3⋊C8—62no—
335C3⋊C8—62no—
336C2×C32—22no—
337C2×C32C2×C4×D411yescharacteristic
338C2×C32#57612yes—
339C3×D3—44no—
340C3×D3—44no—
341C24—61no—
342C24—61no—
343C2×D4—32no—
344C2×D4—32no—
345C2×D4—34no—
346C2×D4—34no—
347C2×D4—62no—
348C2×D4—62no—
349C2×D4—61no—
350C2×D4—61no—
351C22×C4—64no—
352C22×C4—184no—
353C22×C4C2×D3211yescharacteristic
354D8—98no—
355D8—98no—
356M16—62no—
357C2×C8—32no—
358C2×C8—91no—
359C2×C8—91no—
360C2×C8—94no—
361C4⋊C4—32no—
362C4⋊C4—92no—
363C4⋊C4C2×D3212yes—
364C22⋊C4—21no—
365C22⋊C4—32no—
366C22⋊C4—64no—
367C22⋊C4—184no—
368C22⋊C4—181no—
369C42—21no—
370C42—32no—
371C42—181no—
372C22×C3—22no—
373C22×C3—22no—
374C22×C3—21no—
375C22×C3—22no—
376C22×C3—42no—
377C22×C3—64no—
378C22×C3—64no—
379C22×C3—124no—
380C22×C3—124no—
381C22×C3—244no—
382C22×C3—244no—
383C22×C3#67⋊C412yes—
384C22×C3C4×#6712yes—
385C22×C3C2×D3×D411yescharacteristic
386C22×C3C22×#6711yescharacteristic
387C2×D3—24no—
388C2×D3—24no—
389C2×D3—44no—
390C2×D3—44no—
391C2×D3—84no—
392C2×D3—84no—
393C3×C4—21no—
394C3×C4—21no—
395C3×C4—22no—
396C3×C4—42no—
397C3×C4—42no—
398C3×C4—64no—
399C3×C4—82no—
400C3×C4#67⋊C412yes—
401C3×C4C4×#6712yes—
402C3×C4C22×C4×D311yescharacteristic
403C3×C4C22×C4×D311yescharacteristic
404C3×C4C2×#23511yescharacteristic
405C3×C4C2×#23711yescharacteristic
406Dic3—24no—
407Dic3—122no—
408Dic3—122no—
409Dic3—242no—
410C32#294811yescharacteristic, complemented, Sylow
411C23—62no—
412C23—62no—
413C23—64no—
414C23—64no—
415C23—242no—
416C23—242no—
417C23D3×#6711yescharacteristic
418D4—34no—
419D4—34no—
420D4—62no—
421D4—62no—
422D4—64no—
423D4—64no—
424C2×C4—22no—
425C2×C4—34no—
426C2×C4—182no—
427C2×C4—244no—
428C2×C4—724no—
429C2×C4#379512yes—
430C2×C4C4×D3212yes—
431C2×C4D3×#6711yescharacteristic
432C2×C4C22×D3211yescharacteristic
433C8—62no—
434C8—92no—
435C8—92no—
436C2×C3—22no—
437C2×C3—22no—
438C2×C3—21no—
439C2×C3—22no—
440C2×C3—42no—
441C2×C3—124no—
442C2×C3—124no—
443C2×C3C2×#67⋊C411yescharacteristic
444C2×C3#577412yes—
445C2×C3C2×C4×#6711yescharacteristic
446C2×C3#583512yes—
447D3—44no—
448D3—44no—
449C22—22no—
450C22—64no—
451C22—64no—
452C22—124no—
453C22—124no—
454C22—244no—
455C22—244no—
456C22#6387912yes—
457C22C2×D3×#6711yescharacteristic
458C4—42no—
459C4—64no—
460C4—362no—
461C4#6387912yes—
462C4C2×#379511yescharacteristic
463C4C2×C4×D3211yescharacteristic
464C3—21no—
465C3#7891511yescharacteristic, complemented
466C3#8253811yescharacteristic, complemented
467C2—22no—
468C2—124no—
469C2—124no—
470C2C2×#6387911yescharacteristic
471C2#1059545412yes—
subgroupG/H
centerC22C2×D3×#67
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC32×#117C22
socleC22×C32C22×D4
prime radicalC22×#3713C2
cosocleC2×C32×C4C24
hypercenter#117D32
hypocenterC32#2948
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #117

Complements

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

NH ≅ G/Ntype
1. C3×#5521C2semidirect
2. #10594982C2semidirect
4. #10592697C2semidirect
5. C3×#5001C2semidirect
6. #10591086C2semidirect
7. #10591057C2semidirect
8. #10590455C2semidirect
9. #10590452C2semidirect
19. C3×#893C22semidirect
24. Dic3×D12C22semidirect
25. C2×#3713C4semidirect
28. #63635C22semidirect
29. #63634C22semidirect
30. C3×#809C22semidirect
31. #63563C22semidirect
32. #63554C22semidirect
33. Dic3×C3⋊C8C22semidirect
39. #5521D3semidirect
46. #5001D3semidirect
60. C2×C3×D12C2×C4semidirect
61. C2×C3×D12C2×C4semidirect
72. C2×C3⋊(C3⋊C8)C2×C4semidirect
82. #3713C2×C4semidirect
83. #3713C2×C4semidirect
115. #893C2×D3semidirect
125. #809C2×D3semidirect
189. C2×D12C4×D3semidirect
190. C2×D12C4×D3semidirect
410. C32#2948semidirect
465. C3#78915semidirect
466. C3#82538semidirect

Maximal subgroups

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

subgroupindex
C3×#55212
#105949822
C22×#37132
#105926972
C3×#50012
#105910862
#105910572
#105904552
#105904522
#825383
#789153