Finite Group Databasebeta

← #11860765

Subgroups — #11860765

Order 1152.

1117 conjugacy classes of subgroups.

The subgroup lattice has 462 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595987C211yesmaximal, characteristic, complemented
2C3×#5521C211yesmaximal, characteristic
3C22×#3716C211yesmaximal, characteristic
4C3×#4997C211yesmaximal, characteristic, complemented
5#10591122C211yesmaximal, characteristic, complemented
6#10591107C211yesmaximal, characteristic, complemented
7#10591086C211yesmaximal, characteristic
8#10590360C214yesmaximal, complemented
9C4×#3716C214yesmaximal, complemented
10#82543—31nomaximal
11#78572—31nomaximal
12C22×#634C2211yescharacteristic
13C22×C3×D12C2211yescharacteristic
14C32×#117C2211yescharacteristic
15#64135C2211yescharacteristic
16#64096—22no—
17#64086—22no—
18C4×#634C2214yescomplemented
19C3×#926C2211yescharacteristic
20C2×C3×#208C2211yescharacteristic
21C22×C3×C3⋊C8C2211yescharacteristic
22C3×#893—22no—
23C3×D3×C22⋊C4—22no—
24C3×C4×D12C2214yes—
25C2×#3716C418yescomplemented
26C2×#3716C2212yes—
27C2×#3716C2212yes—
28C3×#803C2212yescomplemented
29C3×C4×C3⋊C8C2212yescomplemented
30#63575C2212yescomplemented
31#63573C2212yescomplemented
32#63567C2214yescomplemented
33#63563C2214yes—
34C3×#518—31no—
35C22×#214—31no—
36C22×#204—31no—
37#5521D311yescharacteristic
38#5516—31no—
39#5516—31no—
40#5516—61no—
41C3×#405—31no—
42#5215—31no—
43#5131—31no—
44#5120—31no—
45#5106—31no—
46#5018—34no—
47C4×#214—34no—
48#5004—31no—
49#4998—31no—
50#4997D311yescharacteristic, complemented
51#4710—34no—
52C4×#204—34no—
53C23×C3×D3—21no—
54C22×C32×C4C2311yescharacteristic
55C22×C3⋊Dic3—21no—
56C2×#634—21no—
57C2×#634—22no—
58C2×#634C2×C414yescomplemented
59C2×#634C2312yes—
60C2×C3×D12—21no—
61C2×C3×D12—22no—
62C2×C3×D12C2×C414yes—
63C2×C3×D12C2312yes—
64C2×C3×C4×D3—24no—
65C32×C4⋊C4D412yes—
66C32×C22⋊C4D412yes—
67C32×C42C2312yes—
68#3757—21no—
69C4⋊(C3⋊Dic3)C2312yes—
70#3750—24no—
71C4×C3⋊Dic3—24no—
72C4×C3⋊Dic3—21no—
73C3×#217—21no—
74C3×(C2×D3)⋊C4—24no—
75C3×C4⋊Dic3C2312yes—
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#3716C2×C418yescomplemented
83#3716C2×C418yescomplemented
84#2949—91noSylow
85C22×C3×D4—31no—
86C22×D12C2×D311yescharacteristic
87C22×Dic6—31no—
88C22×Dic6—31no—
89C22×Dic6—61no—
90C2×C3×M16—31no—
91C22×C3×C8—31no—
92C3×C4×D4—34no—
93C3×C4×D4—62no—
94C3×#117—21no—
95C3×#117—31no—
96C3×#117C2×D311yescharacteristic
97C3×#117C2×D311yescharacteristic
98C2×C3×C22⋊C4—62no—
99C2×#214—38no—
100C2×#214—32no—
101C2×#214—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—22no—
112#887—64no—
113#887—62no—
114#887—62no—
115D3×C22⋊C4—22no—
116#877—64no—
117#877—62no—
118#877—62no—
119C4×D12C2×D314yes—
120C4×Dic6—34no—
121C4×Dic6—34no—
122C4×Dic6—64no—
123C3×#97—32no—
124C3×C4×C8—32no—
125#832—34no—
126#821—34no—
127#818—32no—
128#817—32no—
129#816—34no—
130#810—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—24no—
145C2×C3⋊Dic3—22no—
146C2×C3⋊Dic3—22no—
147#634—24no—
148#634—22no—
149#634C22×C414yes—
150C2×C3×Dic3—22no—
151C3×D12—24no—
152C3×D12—22no—
153C3×D12C22×C414yes—
154C3×C4×D3—84no—
155C3×C3⋊C8—22no—
156C3×C3⋊C8C22×C412yes—
157C3×C3⋊C8C22×C412yes—
158C22×SD16—91no—
159#519—91no—
160#518—31no—
161#440—94no—
162C4×SD16—94no—
163#427—91no—
164#419—91no—
165#418—91no—
166#405—31no—
167C24×C3—61no—
168C23×D3—21no—
169C2×C3×D4—34no—
170C2×C3×D4—32no—
171C2×C3×D4—61no—
172C2×C3×D4—62no—
173C22×C3×C4—21no—
174C22×C3×C4—64no—
175C22×C3×C4C22×D311yescharacteristic
176C22×C3×C4C22×D311yescharacteristic
177C22×Dic3—62no—
178C22×Dic3—61no—
179C22×Dic3—61no—
180C2×D12—22no—
181C2×D12—21no—
182C2×D12C4×D314yes—
183C2×D12C22×D312yes—
184C2×C4×D3—24no—
185C2×Dic6—34no—
186C2×Dic6—34no—
187C2×Dic6—32no—
188C2×Dic6—32no—
189C2×Dic6—62no—
190C2×Dic6—64no—
191C2×Dic6—62no—
192C2×Dic6—64no—
193C2×Dic6—61no—
194C2×Dic6—62no—
195C2×Dic6—62no—
196C2×Dic6—61no—
197C3×M16—62no—
198C2×C3×C8—34no—
199C2×C3×C8—31no—
200C2×C3×C8—31no—
201C2×C3×C8—32no—
202C3×C4⋊C4—22no—
203C3×C4⋊C4—32no—
204C3×C4⋊C4D1212yes—
205C3×C4⋊C4#6712yes—
206C3×C22⋊C4—22no—
207C3×C22⋊C4—61no—
208C3×C22⋊C4—64no—
209C3×C22⋊C4D1212yes—
210C3×C22⋊C4#6712yes—
211C3×C42—22no—
212C3×C42—61no—
213C3×C42C22×D312yes—
214C3×C42C22×D312yes—
215#217—21no—
216#217—62no—
217#217—61no—
218#217—61no—
219#214—38no—
220#214—38no—
221(C2×D3)⋊C4—24no—
222C4⋊Dic3—32no—
223C4⋊Dic3—32no—
224C4⋊Dic3—62no—
225C4⋊Dic3C22×D312yes—
226Dic3⋊C4—68no—
227Dic3⋊C4—64no—
228Dic3⋊C4—64no—
229C4×Dic3—21no—
230C4×Dic3—68no—
231C4×Dic3—62no—
232C4×Dic3—64no—
233C4×Dic3—61no—
234C4×Dic3—64no—
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—24no—
254C3⋊Dic3—42no—
255C3×Dic3—42no—
256C22×Q8—91no—
257C22×D4—31no—
258C2×SD16—98no—
259C2×SD16—92no—
260C2×SD16—92no—
261C2×M16—31no—
262C22×C8—31no—
263C4×Q8—94no—
264C4×Q8—182no—
265C4×D4—34no—
266C4×D4—62no—
267#117—31no—
268#117—91no—
269#117—182no—
270#117D3211yescharacteristic
271C2×C22⋊C4—62no—
272#107—92no—
273#106—92no—
274#103—94no—
275#102—94no—
276#97—32no—
277C4×C8—32no—
278C23×C3—21no—
279C23×C3—62no—
280C23×C3—64no—
281C23×C3—242no—
282C23×C3C2×D1211yescharacteristic
283C23×C3C2×#6711yescharacteristic
284C22×D3—22no—
285C22×D3—24no—
286C22×D3—82no—
287C3×D4—34no—
288C3×D4—64no—
289C3×D4—62no—
290C2×C3×C4—21no—
291C2×C3×C4—22no—
292C2×C3×C4—22no—
293C2×C3×C4—21no—
294C2×C3×C4—24no—
295C2×C3×C4—62no—
296C2×C3×C4—244no—
297C2×C3×C4C2×C4×D312yes—
298C2×C3×C4C2×C4×D312yes—
299C2×C3×C4C2×D1214yes—
300C2×C3×C4C2×D1211yescharacteristic
301C2×C3×C4#23512yes—
302C2×C3×C4#23512yes—
303C2×C3×C4C2×#6714yes—
304C2×C3×C4C2×#6711yescharacteristic
305C2×C3×C4C23×D311yescharacteristic
306C2×C3×C4C23×D311yescharacteristic
307C2×Dic3—22no—
308C2×Dic3—64no—
309C2×Dic3—68no—
310C2×Dic3—64no—
311C2×Dic3—64no—
312C2×Dic3—62no—
313C2×Dic3—62no—
314C2×Dic3—64no—
315C2×Dic3—62no—
316C2×Dic3—62no—
317D12—24no—
318D12—22no—
319D12C2×C4×D314yes—
320C4×D3—84no—
321Dic6—34no—
322Dic6—34no—
323Dic6—64no—
324Dic6—64no—
325Dic6—68no—
326Dic6—64no—
327Dic6—64no—
328Dic6—62no—
329Dic6—62no—
330C3×C8—32no—
331C3×C8—32no—
332C3×C8—62no—
333C3⋊C8—22no—
334C3⋊C8C2×C4×D312yes—
335C3⋊C8C2×C4×D312yes—
336C2×C32—22no—
337C2×C32C2×C4×D411yescharacteristic
338C2×C32#57712yes—
339C3×D3—44no—
340C24—61no—
341C2×Q8—92no—
342C2×Q8—94no—
343C2×Q8—182no—
344C2×Q8—181no—
345C2×D4—32no—
346C2×D4—34no—
347C2×D4—62no—
348C2×D4—61no—
349C22×C4—64no—
350C22×C4—181no—
351C22×C4C2×D3211yescharacteristic
352SD16—98no—
353SD16—98no—
354M16—62no—
355C2×C8—31no—
356C2×C8—31no—
357C2×C8—34no—
358C2×C8—32no—
359C4⋊C4—32no—
360C4⋊C4—92no—
361C4⋊C4—184no—
362C4⋊C4#62612yes—
363C22⋊C4—61no—
364C22⋊C4—64no—
365C22⋊C4—181no—
366C22⋊C4#62612yes—
367C42—61no—
368C42—181no—
369C42—184no—
370C42C2×D3212yes—
371C22×C3—22no—
372C22×C3—22no—
373C22×C3—21no—
374C22×C3—22no—
375C22×C3—42no—
376C22×C3—64no—
377C22×C3—124no—
378C22×C3—244no—
379C22×C3C4×D1212yes—
380C22×C3C4×#6712yes—
381C22×C3C22×D1211yescharacteristic
382C22×C3C22×#6711yescharacteristic
383C2×D3—24no—
384C2×D3—44no—
385C2×D3—84no—
386C3×C4—24no—
387C3×C4—24no—
388C3×C4—21no—
389C3×C4—21no—
390C3×C4—22no—
391C3×C4—44no—
392C3×C4—122no—
393C3×C4C4×D1212yes—
394C3×C4C4×#6712yes—
395C3×C4C22×C4×D311yescharacteristic
396C3×C4C22×C4×D311yescharacteristic
397C3×C4C2×#23511yescharacteristic
398C3×C4C2×#23511yescharacteristic
399Dic3—42no—
400Dic3—68no—
401Dic3—64no—
402Dic3—64no—
403Dic3—124no—
404Dic3—122no—
405Dic3—122no—
406C32#294911yescharacteristic, complemented, Sylow
407C23—62no—
408C23—64no—
409C23—242no—
410C23C2×#62611yescharacteristic
411Q8—94no—
412Q8—182no—
413Q8—184no—
414D4—34no—
415D4—62no—
416D4—64no—
417C2×C4—62no—
418C2×C4—182no—
419C2×C4—184no—
420C2×C4—182no—
421C2×C4—244no—
422C2×C4#379812yes—
423C2×C4C4×D3212yes—
424C2×C4C2×#62614yes—
425C2×C4C2×#62611yescharacteristic
426C2×C4C22×D3211yescharacteristic
427C8—32no—
428C8—32no—
429C8—62no—
430C2×C3—22no—
431C2×C3—22no—
432C2×C3—22no—
433C2×C3—21no—
434C2×C3—42no—
435C2×C3—124no—
436C2×C3C2×C4×D1211yescharacteristic
437C2×C3#575112yes—
438C2×C3C2×C4×#6711yescharacteristic
439C2×C3#583612yes—
440D3—44no—
441C22—22no—
442C22—64no—
443C22—124no—
444C22—244no—
445C22C4×#62612yes—
446C22C22×#62611yescharacteristic
447C4—24no—
448C4—122no—
449C4—184no—
450C4—362no—
451C4C4×#62612yes—
452C4C2×#379811yescharacteristic
453C4C2×C4×D3211yescharacteristic
454C3—21no—
455C3#7857211yescharacteristic, complemented
456C3#8254311yescharacteristic, complemented
457C2—22no—
458C2—124no—
459C2C2×C4×#62611yescharacteristic
460C2#1059544712yes—
subgroupG/H
centerC22C22×#626
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC32×#117C22
socleC22×C32C22×D4
prime radicalC22×C3×D12C22
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
1. #10595987C2semidirect
4. C3×#4997C2semidirect
5. #10591122C2semidirect
6. #10591107C2semidirect
8. #10590360C2semidirect
9. C4×#3716C2semidirect
18. C4×#634C22semidirect
25. C2×#3716C4semidirect
28. C3×#803C22semidirect
29. C3×C4×C3⋊C8C22semidirect
30. #63575C22semidirect
31. #63573C22semidirect
32. #63567C22semidirect
50. #4997D3semidirect
58. C2×#634C2×C4semidirect
78. C2×C3×C3⋊C8C2×C4semidirect
82. #3716C2×C4semidirect
83. #3716C2×C4semidirect
133. #803C2×D3semidirect
134. C4×C3⋊C8C2×D3semidirect
237. C2×C3⋊C8C4×D3semidirect
406. C32#2949semidirect
455. C3#78572semidirect
456. C3#82543semidirect

Maximal subgroups

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

subgroupindex
#105959872
C3×#55212
C22×#37162
C3×#49972
#105911222
#105911072
#105910862
#105903602
C4×#37162
#825433
#785723