Finite Group Databasebeta

← #11860764

Subgroups — #11860764

Order 1152.

1153 conjugacy classes of subgroups.

The subgroup lattice has 467 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595992C211yesmaximal, characteristic
2C3×#5516C211yesmaximal, characteristic, complemented
3C22×#3717C211yesmaximal, characteristic
4C3×#4997C211yesmaximal, characteristic, complemented
5#10591122C211yesmaximal, characteristic, complemented
6#10591100C211yesmaximal, characteristic, complemented
7#10591096C211yesmaximal, characteristic
8#10590362C214yesmaximal, complemented
9C4×#3717C214yesmaximal, complemented
10#82548—31nomaximal
11#78572—31nomaximal
12C22×C4⋊(C3⋊D3)C2211yescharacteristic
13C22×C3×Dic6C2211yescharacteristic
14C32×#117C2211yescharacteristic
15#64135C2211yescharacteristic
16#64102—22no—
17C22⋊C4×C3⋊D3—22no—
18C4×C4⋊(C3⋊D3)C2214yes—
19C3×#926C2211yescharacteristic
20C2×C3×#208C2211yescharacteristic
21C22×C3×C3⋊C8C2211yescharacteristic
22C3×#887—22no—
23C3×#877—22no—
24C3×C4×Dic6C2214yescomplemented
25C2×#3717C418yescomplemented
26C2×#3717C2212yes—
27C2×#3717C2212yes—
28C3×#803C2212yescomplemented
29C3×C4×C3⋊C8C2212yescomplemented
30#63575C2212yescomplemented
31#63573C2212yescomplemented
32#63566C2214yescomplemented
33#63564C2214yes—
34C3×#519—31no—
35C22×#215—31no—
36C22×#204—31no—
37#5521—31no—
38#5521—31no—
39#5521—61no—
40#5516D311yescharacteristic, complemented
41C3×#405—31no—
42#5225—31no—
43#5131—31no—
44#5120—31no—
45#5106—31no—
46#5026—34no—
47C4×#215—34no—
48#5001—31no—
49#4998—31no—
50#4997D311yescharacteristic, complemented
51#4710—34no—
52C4×#204—34no—
53C23×C3⋊D3—21no—
54C22×C32×C4C2311yescharacteristic
55C2×C4⋊(C3⋊D3)—21no—
56C2×C4⋊(C3⋊D3)—22no—
57C2×C4⋊(C3⋊D3)C2×C414yes—
58C2×C4⋊(C3⋊D3)C2312yes—
59C2×C4×C3⋊D3—24no—
60C22×C3×Dic3—21no—
61C2×C3×Dic6—21no—
62C2×C3×Dic6—22no—
63C2×C3×Dic6C2×C414yescomplemented
64C2×C3×Dic6C2312yes—
65C32×C4⋊C4D412yes—
66C32×C22⋊C4D412yes—
67C32×C42C2312yes—
68#3757—21no—
69#3752—24no—
70C4⋊(C3⋊Dic3)C2312yes—
71C4×C3⋊Dic3—21no—
72C3×#217—21no—
73C3×C4⋊Dic3C2312yes—
74C3×Dic3⋊C4—24no—
75C3×C4×Dic3—24no—
76C3×C4×Dic3—21no—
77C3×#208—22no—
78C2×C3×C3⋊C8C2×C414yescomplemented
79C2×C3×C3⋊C8C2312yes—
80C2×C3×C3⋊C8C2311yescharacteristic
81C2×C3×C3⋊C8C2311yescharacteristic
82#3717C2×C418yescomplemented
83#3717C2×C418yescomplemented
84#2949—91noSylow
85C22×C3×Q8—31no—
86C22×D12—31no—
87C22×D12—31no—
88C22×D12—61no—
89C22×Dic6C2×D311yescharacteristic
90C2×C3×M16—31no—
91C22×C3×C8—31no—
92C3×C4×Q8—34no—
93C3×C4×Q8—62no—
94C3×#117—21no—
95C3×#117—31no—
96C3×#117—62no—
97C3×#117C2×D311yescharacteristic
98C3×#117C2×D311yescharacteristic
99C2×#215—38no—
100C2×#215—32no—
101C2×#215—32no—
102#926—31no—
103#926—31no—
104#926—61no—
105#926C2×D311yescharacteristic
106C2×#208C2×D311yescharacteristic
107C22×C3⋊C8C2×D311yescharacteristic
108C2×#204—38no—
109C2×#204—32no—
110C2×#204—32no—
111#893—64no—
112#893—62no—
113#893—62no—
114#887—22no—
115D3×C22⋊C4—64no—
116D3×C22⋊C4—62no—
117D3×C22⋊C4—62no—
118#877—22no—
119C4×D12—34no—
120C4×D12—34no—
121C4×D12—64no—
122C4×Dic6C2×D314yescomplemented
123C3×#97—32no—
124C3×C4×C8—32no—
125#835—34no—
126#821—34no—
127#818—32no—
128#817—32no—
129#816—34no—
130#809—34no—
131#808—32no—
132#807—32no—
133#803C2×D312yescomplemented
134C4×C3⋊C8C2×D312yescomplemented
135C23×C32C2×D411yescharacteristic
136C22×C3⋊D3—22no—
137C22×C3⋊D3—24no—
138C22×C3⋊D3—82no—
139C2×C32×C4C22×C412yes—
140C2×C32×C4C2×D414yes—
141C2×C32×C4C2×D411yescharacteristic
142C2×C32×C4#4112yes—
143C2×C32×C4C2411yescharacteristic
144C2×C3⋊Dic3—22no—
145C4⋊(C3⋊D3)—24no—
146C4⋊(C3⋊D3)—22no—
147C4⋊(C3⋊D3)C22×C414yes—
148C4×C3⋊D3—84no—
149C2×C3×Dic3—24no—
150C2×C3×Dic3—22no—
151C2×C3×Dic3—22no—
152C3×Dic6—24no—
153C3×Dic6—22no—
154C3×Dic6C22×C414yes—
155C3×C3⋊C8—22no—
156C3×C3⋊C8C22×C412yes—
157C3×C3⋊C8C22×C412yes—
158C22×SD16—91no—
159#519—31no—
160#518—91no—
161#440—94no—
162C4×SD16—94no—
163#427—91no—
164#419—91no—
165#418—91no—
166#405—31no—
167C23×D3—62no—
168C23×D3—61no—
169C23×D3—61no—
170C2×C3×Q8—34no—
171C2×C3×Q8—32no—
172C2×C3×Q8—61no—
173C2×C3×Q8—62no—
174C22×C3×C4—21no—
175C22×C3×C4—61no—
176C22×C3×C4C22×D311yescharacteristic
177C22×C3×C4C22×D311yescharacteristic
178C22×Dic3—21no—
179C2×D12—34no—
180C2×D12—34no—
181C2×D12—32no—
182C2×D12—32no—
183C2×D12—62no—
184C2×D12—64no—
185C2×D12—62no—
186C2×D12—64no—
187C2×D12—61no—
188C2×D12—62no—
189C2×D12—62no—
190C2×D12—61no—
191C2×C4×D3—68no—
192C2×C4×D3—64no—
193C2×C4×D3—64no—
194C2×Dic6—22no—
195C2×Dic6—21no—
196C2×Dic6C4×D314yescomplemented
197C2×Dic6C22×D312yes—
198C3×M16—62no—
199C2×C3×C8—34no—
200C2×C3×C8—31no—
201C2×C3×C8—31no—
202C2×C3×C8—32no—
203C3×C4⋊C4—22no—
204C3×C4⋊C4—32no—
205C3×C4⋊C4—64no—
206C3×C4⋊C4D1212yes—
207C3×C4⋊C4#6712yes—
208C3×C22⋊C4—22no—
209C3×C22⋊C4—61no—
210C3×C22⋊C4D1212yes—
211C3×C22⋊C4#6712yes—
212C3×C42—22no—
213C3×C42—61no—
214C3×C42—64no—
215C3×C42C22×D312yes—
216C3×C42C22×D312yes—
217#217—21no—
218#217—62no—
219#217—61no—
220#217—61no—
221#215—38no—
222#215—38no—
223(C2×D3)⋊C4—68no—
224(C2×D3)⋊C4—64no—
225(C2×D3)⋊C4—64no—
226C4⋊Dic3—32no—
227C4⋊Dic3—32no—
228C4⋊Dic3—62no—
229C4⋊Dic3C22×D312yes—
230Dic3⋊C4—24no—
231C4×Dic3—24no—
232C4×Dic3—21no—
233C4×Dic3—62no—
234C4×Dic3—61no—
235C4×Dic3—61no—
236#208—22no—
237C2×C3⋊C8C4×D314yescomplemented
238C2×C3⋊C8C22×D312yes—
239C2×C3⋊C8C22×D311yescharacteristic
240C2×C3⋊C8C22×D311yescharacteristic
241#204—38no—
242#204—38no—
243C22×C32—22no—
244C22×C32C4×D412yes—
245C22×C32C22×D411yescharacteristic
246C2×C3⋊D3—24no—
247C2×C3⋊D3—44no—
248C2×C3⋊D3—84no—
249C32×C4—24no—
250C32×C4C4×D412yes—
251C32×C4C23×C411yescharacteristic
252C32×C4C2×#4111yescharacteristic
253C3⋊Dic3—42no—
254C3×Dic3—24no—
255C3×Dic3—42no—
256C22×Q8—31no—
257C22×D4—91no—
258C2×SD16—98no—
259C2×SD16—92no—
260C2×SD16—92no—
261C2×M16—31no—
262C22×C8—31no—
263C4×Q8—34no—
264C4×Q8—62no—
265C4×D4—94no—
266C4×D4—182no—
267#117—31no—
268#117—62no—
269#117—91no—
270#117D3211yescharacteristic
271C2×C22⋊C4—182no—
272#107—92no—
273#106—92no—
274#103—94no—
275#102—94no—
276#97—32no—
277C4×C8—32no—
278C23×C3—21no—
279C23×C3C2×D1211yescharacteristic
280C23×C3C2×#6711yescharacteristic
281C22×D3—64no—
282C22×D3—62no—
283C22×D3—62no—
284C22×D3—68no—
285C22×D3—64no—
286C22×D3—64no—
287C22×D3—242no—
288C22×D3—242no—
289C22×D3—244no—
290C3×Q8—34no—
291C3×Q8—64no—
292C3×Q8—62no—
293C2×C3×C4—21no—
294C2×C3×C4—22no—
295C2×C3×C4—22no—
296C2×C3×C4—21no—
297C2×C3×C4—24no—
298C2×C3×C4—64no—
299C2×C3×C4—62no—
300C2×C3×C4—62no—
301C2×C3×C4C2×C4×D312yes—
302C2×C3×C4C2×C4×D312yes—
303C2×C3×C4C2×D1214yes—
304C2×C3×C4C2×D1211yescharacteristic
305C2×C3×C4#23512yes—
306C2×C3×C4#23512yes—
307C2×C3×C4C2×#6714yes—
308C2×C3×C4C2×#6711yescharacteristic
309C2×C3×C4C23×D311yescharacteristic
310C2×C3×C4C23×D311yescharacteristic
311C2×Dic3—24no—
312C2×Dic3—22no—
313C2×Dic3—22no—
314C2×Dic3—64no—
315C2×Dic3—62no—
316C2×Dic3—62no—
317D12—34no—
318D12—34no—
319D12—64no—
320D12—64no—
321D12—68no—
322D12—64no—
323D12—64no—
324D12—62no—
325D12—62no—
326C4×D3—244no—
327C4×D3—244no—
328C4×D3—248no—
329Dic6—24no—
330Dic6—22no—
331Dic6C2×C4×D314yes—
332C3×C8—32no—
333C3×C8—32no—
334C3×C8—62no—
335C3⋊C8—22no—
336C3⋊C8C2×C4×D312yes—
337C3⋊C8C2×C4×D312yes—
338C2×C32—22no—
339C2×C32C2×C4×D411yescharacteristic
340C2×C32#57712yes—
341C3⋊D3—44no—
342C24—181no—
343C2×Q8—32no—
344C2×Q8—34no—
345C2×Q8—62no—
346C2×Q8—61no—
347C2×D4—92no—
348C2×D4—94no—
349C2×D4—182no—
350C2×D4—181no—
351C22×C4—61no—
352C22×C4—184no—
353C22×C4C2×D3211yescharacteristic
354SD16—98no—
355SD16—98no—
356M16—62no—
357C2×C8—31no—
358C2×C8—31no—
359C2×C8—34no—
360C2×C8—32no—
361C4⋊C4—32no—
362C4⋊C4—64no—
363C4⋊C4—92no—
364C4⋊C4#62612yes—
365C22⋊C4—61no—
366C22⋊C4—181no—
367C22⋊C4—184no—
368C22⋊C4#62612yes—
369C42—61no—
370C42—64no—
371C42—181no—
372C42C2×D3212yes—
373C22×C3—22no—
374C22×C3—22no—
375C22×C3—21no—
376C22×C3—22no—
377C22×C3—42no—
378C22×C3C4×D1212yes—
379C22×C3C4×#6712yes—
380C22×C3C22×D1211yescharacteristic
381C22×C3C22×#6711yescharacteristic
382C2×D3—68no—
383C2×D3—64no—
384C2×D3—64no—
385C2×D3—128no—
386C2×D3—124no—
387C2×D3—124no—
388C2×D3—244no—
389C2×D3—244no—
390C2×D3—248no—
391C3×C4—24no—
392C3×C4—24no—
393C3×C4—21no—
394C3×C4—21no—
395C3×C4—22no—
396C3×C4—44no—
397C3×C4—64no—
398C3×C4—122no—
399C3×C4C4×D1212yes—
400C3×C4C4×#6712yes—
401C3×C4C22×C4×D311yescharacteristic
402C3×C4C22×C4×D311yescharacteristic
403C3×C4C2×#23511yescharacteristic
404C3×C4C2×#23511yescharacteristic
405Dic3—24no—
406Dic3—42no—
407Dic3—124no—
408Dic3—122no—
409Dic3—122no—
410C32#294911yescharacteristic, complemented, Sylow
411C23—182no—
412C23—184no—
413C23—722no—
414C23C2×#62611yescharacteristic
415Q8—34no—
416Q8—62no—
417Q8—64no—
418D4—94no—
419D4—182no—
420D4—184no—
421C2×C4—62no—
422C2×C4—64no—
423C2×C4—62no—
424C2×C4—182no—
425C2×C4—724no—
426C2×C4#379812yes—
427C2×C4C4×D3212yes—
428C2×C4C2×#62614yes—
429C2×C4C2×#62611yescharacteristic
430C2×C4C22×D3211yescharacteristic
431C8—32no—
432C8—32no—
433C8—62no—
434C2×C3—22no—
435C2×C3—22no—
436C2×C3—22no—
437C2×C3—21no—
438C2×C3—42no—
439C2×C3C2×C4×D1211yescharacteristic
440C2×C3#575112yes—
441C2×C3C2×C4×#6711yescharacteristic
442C2×C3#583712yes—
443D3—128no—
444D3—124no—
445D3—124no—
446C22—22no—
447C22—184no—
448C22—364no—
449C22—724no—
450C22C4×#62612yes—
451C22C22×#62611yescharacteristic
452C4—24no—
453C4—64no—
454C4—122no—
455C4—362no—
456C4C4×#62612yes—
457C4C2×#379811yescharacteristic
458C4C2×C4×D3211yescharacteristic
459C3—21no—
460C3#7857211yescharacteristic, complemented
461C3#8254811yescharacteristic, complemented
462C2—22no—
463C2—364no—
464C2C2×C4×#62611yescharacteristic
465C2#1059544812yes—
subgroupG/H
centerC22C22×#626
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC32×#117C22
socleC22×C32C22×D4
prime radicalC22×C4⋊(C3⋊D3)C22
cosocleC2×C32×C4C24
hypercenter#117D32
hypocenterC32#2949
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ #117

Complements

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

NH ≅ G/Ntype
2. C3×#5516C2semidirect
4. C3×#4997C2semidirect
5. #10591122C2semidirect
6. #10591100C2semidirect
8. #10590362C2semidirect
9. C4×#3717C2semidirect
24. C3×C4×Dic6C22semidirect
25. C2×#3717C4semidirect
28. C3×#803C22semidirect
29. C3×C4×C3⋊C8C22semidirect
30. #63575C22semidirect
31. #63573C22semidirect
32. #63566C22semidirect
40. #5516D3semidirect
50. #4997D3semidirect
63. C2×C3×Dic6C2×C4semidirect
78. C2×C3×C3⋊C8C2×C4semidirect
82. #3717C2×C4semidirect
83. #3717C2×C4semidirect
122. C4×Dic6C2×D3semidirect
133. #803C2×D3semidirect
134. C4×C3⋊C8C2×D3semidirect
196. C2×Dic6C4×D3semidirect
237. C2×C3⋊C8C4×D3semidirect
410. C32#2949semidirect
460. C3#78572semidirect
461. C3#82548semidirect

Maximal subgroups

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

subgroupindex
#105959922
C3×#55162
C22×#37172
C3×#49972
#105911222
#105911002
#105910962
#105903622
C4×#37172
#825483
#785723