Finite Group Databasebeta

← #11808303

Subgroups — #11808303

Order 1152.

1849 conjugacy classes of subgroups.

The subgroup lattice has 463 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4⋊C4×C3⋊D3C211yesmaximal, characteristic, complemented
2C2×#63921C212yesmaximal
3C2×#63921C211yesmaximal, characteristic
4C3×#4992C212yesmaximal, complemented
5#10591370C211yesmaximal, characteristic, complemented
6#10591370C212yesmaximal, complemented
7#10591315C212yesmaximal, complemented
8#10591298C214yesmaximal, complemented
9D3×#397—32nomaximal
10C23×D32C2211yescharacteristic
11C22×C4×C3⋊D3C2212yes—
12C22×C4×C3⋊D3C2211yescharacteristic
13C22×#624C2212yes—
14C22×#624C2211yescharacteristic
15C2×C32×C4⋊C4C2211yescharacteristic, complemented
16C2×C4⋊(C3⋊Dic3)C2211yescharacteristic, complemented
17C2×#3750C2212yescomplemented
18C4⋊C4×C3⋊D3—24no—
19C2×C3×(C2×D3)⋊C4C2214yes—
20C2×C3×(C2×D3)⋊C4C2212yes—
21C2×(C2×D3)⋊Dic3C2212yes—
22C2×(C2×D3)⋊Dic3C2214yes—
23#63921—24no—
24#63921—28no—
25C3×C3⋊#95C2214yescomplemented
26C3×C3⋊#95C2212yescomplemented
27#63579C2212yescomplemented
28#63579C2214yescomplemented
29C2×D3×C4⋊C4—32no—
30C2×D3×C4⋊C4—61no—
31C2×D3×C22⋊C4—32no—
32C2×D3×C22⋊C4—34no—
33C3×#397—32no—
34#4992D312yescomplemented
35#4953—32no—
36#4952—34no—
37#4675—34no—
38#4674—32no—
39D3×#95—34no—
40D3×#95—32no—
41C23×C3⋊D3C2311yescharacteristic
42C23×C3×D3C2312yes—
43C22×D32—22no—
44C22×D32—22no—
45C22×D32—24no—
46C22×D32—24no—
47C22×D32D414yes—
48C22×C32×C4C2312yes—
49C22×C32×C4C2311yescharacteristic
50C22×C3⋊Dic3C2312yes—
51C22×C3⋊Dic3C2311yescharacteristic
52C2×C4×C3⋊D3—24no—
53C2×C4×C3⋊D3—24no—
54C2×C4×C3⋊D3—24no—
55C2×C4×C3⋊D3—24no—
56C2×C4×C3⋊D3D414yes—
57C22×C3×Dic3C2314yes—
58C22×C3×Dic3C2312yes—
59C2×#624—24no—
60C2×#624—22no—
61C2×#624—24no—
62C2×#624—24no—
63C2×#624—24no—
64C32×C4⋊C4—22no—
65C4⋊(C3⋊Dic3)—22no—
66#3750—24no—
67C3×(C2×D3)⋊C4—28no—
68C3×(C2×D3)⋊C4—24no—
69(C2×D3)⋊Dic3—28no—
70(C2×D3)⋊Dic3—24no—
71C2×#397—91noSylow
72C24×D3—32no—
73C22×C4×D3—32no—
74C22×C4×D3—34no—
75C22×C4×D3—32no—
76C22×C4×D3—34no—
77C22×C4×D3—61no—
78C22×C4×D3—62no—
79C2×C3×C4⋊C4—21no—
80C2×C3×C4⋊C4C2×D312yescomplemented
81C2×C3×C22⋊C4—34no—
82C2×C3×C22⋊C4—32no—
83C2×#217—32no—
84C2×#217—34no—
85C2×(C2×D3)⋊C4—34no—
86C2×(C2×D3)⋊C4—32no—
87C2×(C2×D3)⋊C4C2×D312yes—
88C2×(C2×D3)⋊C4C2×D314yes—
89C2×C4⋊Dic3—32no—
90C2×C4⋊Dic3—61no—
91C2×Dic3⋊C4—34no—
92C2×Dic3⋊C4—62no—
93D3×C4⋊C4—68no—
94D3×C4⋊C4—68no—
95D3×C22⋊C4—68no—
96D3×C22⋊C4—616no—
97C3×#95—32no—
98C3×#95—34no—
99C3⋊#95—34no—
100C3⋊#95—34no—
101C3⋊#95—34no—
102C3⋊#95C2×D314yescomplemented
103C3⋊#95C2×D312yescomplemented
104C23×C32C2411yescharacteristic
105C22×C3⋊D3C2×D412yes—
106C22×C3⋊D3C2×D412yes—
107C22×C3⋊D3#4112yes—
108C22×C3⋊D3#4114yes—
109C22×C3⋊D3#4114yes—
110C22×C3×D3—22no—
111C22×C3×D3—22no—
112C22×C3×D3—24no—
113C22×C3×D3—24no—
114C22×C3×D3C2×D414yes—
115C2×D32—28no—
116C2×D32—216no—
117C2×D32—44no—
118C2×D32—44no—
119C2×D32—48no—
120C2×C32×C4—22no—
121C2×C32×C4—22no—
122C2×C32×C4—22no—
123C2×C32×C4—22no—
124C2×C32×C4C2×D412yes—
125C2×C3⋊Dic3—22no—
126C2×C3⋊Dic3—22no—
127C2×C3⋊Dic3—22no—
128C2×C3⋊Dic3—22no—
129C2×C3⋊Dic3C2×D412yes—
130C4×C3⋊D3—28no—
131C4×C3⋊D3—48no—
132C2×C3×Dic3—24no—
133C2×C3×Dic3—22no—
134C2×C3×Dic3—24no—
135C2×C3×Dic3—24no—
136C2×C3×Dic3—24no—
137#624—48no—
138#624—44no—
139C22×C4⋊C4—91no—
140C22×C22⋊C4—91no—
141C22×C22⋊C4—92no—
142#397—32no—
143#397—92no—
144#397—94no—
145C2×#95—91no—
146C2×#95—92no—
147C24×C3—32no—
148C23×D3—32no—
149C23×D3—38no—
150C23×D3—61no—
151C23×D3—64no—
152C23×D3—68no—
153C23×D3—64no—
154C23×D3—68no—
155C23×D3C22×D312yes—
156C22×C3×C4—21no—
157C22×C3×C4—22no—
158C22×C3×C4—34no—
159C22×C3×C4—32no—
160C22×C3×C4C22×D314yes—
161C22×C3×C4C22×D312yes—
162C22×Dic3—32no—
163C22×Dic3—34no—
164C22×Dic3—61no—
165C22×Dic3—62no—
166C22×Dic3C22×D312yes—
167C22×Dic3C22×D314yes—
168C2×C4×D3—38no—
169C2×C4×D3—64no—
170C2×C4×D3—68no—
171C2×C4×D3—68no—
172C2×C4×D3—64no—
173C2×C4×D3—68no—
174C2×C4×D3—68no—
175C2×C4×D3—68no—
176C2×C4×D3—68no—
177C2×C4×D3—68no—
178C2×C4×D3—68no—
179C2×C4×D3—68no—
180C2×C4×D3—68no—
181C2×C4×D3—124no—
182C2×C4×D3—124no—
183C3×C4⋊C4—24no—
184C3×C4⋊C4—24no—
185C3×C22⋊C4—68no—
186C3×C22⋊C4—64no—
187#217—64no—
188#217—68no—
189(C2×D3)⋊C4—28no—
190(C2×D3)⋊C4—24no—
191(C2×D3)⋊C4—64no—
192(C2×D3)⋊C4—68no—
193C4⋊Dic3—64no—
194C4⋊Dic3—64no—
195Dic3⋊C4—68no—
196Dic3⋊C4—68no—
197C22×C32C22×D411yescharacteristic
198C22×C32C22×D411yescharacteristic
199C22×C32C2×#4111yescharacteristic
200C22×C32C2×#4112yes—
201C22×C32C2×#4112yes—
202C2×C3⋊D3#12114yes—
203C2×C3⋊D3#12318yes—
204C2×C3⋊D3#12314yes—
205C2×C3⋊D3#12414yes—
206C2×C3⋊D3#12618yes—
207C2×C3×D3—24no—
208C2×C3×D3—28no—
209C2×C3×D3—42no—
210C2×C3×D3—42no—
211C2×C3×D3—44no—
212D32—416no—
213C32×C4—22no—
214C32×C4—42no—
215C3⋊Dic3—22no—
216C3⋊Dic3—42no—
217C3×Dic3—44no—
218C3×Dic3—42no—
219C25—91no—
220C23×C4—92no—
221C23×C4—91no—
222C23×C4—91no—
223C23×C4—92no—
224C2×C4⋊C4—92no—
225C2×C4⋊C4—91no—
226C2×C4⋊C4—184no—
227C2×C4⋊C4D3211yescharacteristic, complemented
228C2×C22⋊C4—34no—
229C2×C22⋊C4—32no—
230C2×C22⋊C4—92no—
231C2×C22⋊C4—94no—
232C2×C22⋊C4—184no—
233C2×C22⋊C4—188no—
234#95—34no—
235#95—32no—
236#95—92no—
237#95—94no—
238C23×C3—21no—
239C23×C3—34no—
240C23×C3—62no—
241C23×C3—64no—
242C23×C3—62no—
243C23×C3—64no—
244C23×C3C23×D312yes—
245C22×D3—22no—
246C22×D3—24no—
247C22×D3—22no—
248C22×D3—24no—
249C22×D3—34no—
250C22×D3—34no—
251C22×D3—38no—
252C22×D3—34no—
253C22×D3—38no—
254C22×D3—62no—
255C22×D3—62no—
256C22×D3—64no—
257C22×D3—62no—
258C22×D3—64no—
259C22×D3—632no—
260C22×D3—616no—
261C22×D3—128no—
262C22×D3—128no—
263C22×D3—1216no—
264C22×D3D3×D414yes—
265C2×C3×C4—24no—
266C2×C3×C4—24no—
267C2×C3×C4—24no—
268C2×C3×C4—24no—
269C2×C3×C4—24no—
270C2×C3×C4—24no—
271C2×C3×C4—22no—
272C2×C3×C4—42no—
273C2×C3×C4—42no—
274C2×C3×C4—64no—
275C2×C3×C4—62no—
276C2×C3×C4—64no—
277C2×C3×C4—64no—
278C2×C3×C4—64no—
279C2×C3×C4D3×D414yes—
280C2×Dic3—24no—
281C2×Dic3—22no—
282C2×Dic3—24no—
283C2×Dic3—24no—
284C2×Dic3—24no—
285C2×Dic3—34no—
286C2×Dic3—62no—
287C2×Dic3—64no—
288C2×Dic3—64no—
289C2×Dic3—64no—
290C2×Dic3—64no—
291C2×Dic3—64no—
292C2×Dic3—64no—
293C2×Dic3—122no—
294C2×Dic3—122no—
295C4×D3—616no—
296C4×D3—616no—
297C4×D3—1216no—
298C4×D3—128no—
299C4×D3—1216no—
300C4×D3—1216no—
301C2×C32C2×#12111yescharacteristic
302C2×C32C2×#12312yes—
303C2×C32C2×#12311yescharacteristic
304C2×C32C2×#12411yescharacteristic
305C2×C32C2×#12612yes—
306C3⋊D3#39718yescomplemented
307C3×D3—44no—
308C24—32no—
309C24—94no—
310C24—91no—
311C24—182no—
312C24—184no—
313C24—182no—
314C24—184no—
315C22×C4—34no—
316C22×C4—32no—
317C22×C4—91no—
318C22×C4—94no—
319C22×C4—92no—
320C22×C4—184no—
321C22×C4—184no—
322C22×C4—184no—
323C22×C4—184no—
324C22×C4—184no—
325C22×C4—182no—
326C22×C4—184no—
327C22×C4—184no—
328C22×C4—184no—
329C22×C4C2×D3212yes—
330C22×C4C2×D3211yescharacteristic
331C4⋊C4—22no—
332C4⋊C4—184no—
333C4⋊C4—182no—
334C22⋊C4—68no—
335C22⋊C4—64no—
336C22⋊C4—184no—
337C22⋊C4—188no—
338C22×C3—22no—
339C22×C3—21no—
340C22×C3—21no—
341C22×C3—22no—
342C22×C3—21no—
343C22×C3—68no—
344C22×C3—64no—
345C22×C3—122no—
346C22×C3—122no—
347C22×C3—124no—
348C22×C3C2×D3×D412yes—
349C22×C3C2×D3×D412yes—
350C22×C3D3×#4114yes—
351C22×C3D3×#4112yes—
352C22×C3D3×#4114yes—
353C2×D3—28no—
354C2×D3—24no—
355C2×D3—38no—
356C2×D3—316no—
357C2×D3—38no—
358C2×D3—316no—
359C2×D3—38no—
360C2×D3—42no—
361C2×D3—42no—
362C2×D3—44no—
363C2×D3—64no—
364C2×D3—64no—
365C2×D3—68no—
366C2×D3—64no—
367C2×D3—68no—
368C2×D3—1232no—
369C3×C4—24no—
370C3×C4—24no—
371C3×C4—44no—
372C3×C4—44no—
373C3×C4—124no—
374C3×C4—122no—
375Dic3—44no—
376Dic3—42no—
377Dic3—64no—
378Dic3—64no—
379Dic3—124no—
380Dic3—124no—
381C32C2×#39711yescharacteristic, complemented, Sylow
382C23—34no—
383C23—64no—
384C23—62no—
385C23—64no—
386C23—62no—
387C23—94no—
388C23—92no—
389C23—92no—
390C23—94no—
391C23—92no—
392C23—1816no—
393C23—188no—
394C23—364no—
395C23—368no—
396C23—364no—
397C23C22×D3211yescharacteristic
398C2×C4—22no—
399C2×C4—22no—
400C2×C4—22no—
401C2×C4—22no—
402C2×C4—64no—
403C2×C4—64no—
404C2×C4—64no—
405C2×C4—64no—
406C2×C4—62no—
407C2×C4—92no—
408C2×C4—188no—
409C2×C4—182no—
410C2×C4—182no—
411C2×C4—182no—
412C2×C4—182no—
413C2×C4—368no—
414C2×C4—368no—
415C2×C4—364no—
416C2×C4#381112yes—
417C2×C3—21no—
418C2×C3—22no—
419C2×C3—22no—
420C2×C3—21no—
421C2×C3—21no—
422C2×C3—124no—
423C2×C3D3×#12112yes—
424C2×C3D3×#12312yes—
425C2×C3D3×#12314yes—
426C2×C3D3×#12412yes—
427C2×C3D3×#12614yes—
428D3—316no—
429D3—44no—
430D3—68no—
431C22—68no—
432C22—64no—
433C22—94no—
434C22—98no—
435C22—98no—
436C22—94no—
437C22—94no—
438C22—122no—
439C22—124no—
440C22—122no—
441C22—3616no—
442C22#6430612yes—
443C22D32×D411yescharacteristic
444C22#6431211yescharacteristic
445C22#6431912yes—
446C22C2×#381111yescharacteristic
447C4—22no—
448C4—42no—
449C4—124no—
450C4—122no—
451C4—182no—
452C4—362no—
453C3—21no—
454C3D3×#39712yescomplemented
455C2—98no—
456C2—124no—
457C2#1059460812yes—
458C2#1059465612yes—
459C2#1059507911yescharacteristic
460C2#1059528211yescharacteristic
461C2#1059543211yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutator, socle, cosocleC23×C32C24
FittingC2×C32×C4⋊C4C22
prime radicalC23×D32C22
hypercenterC2×C4⋊C4D32
hypocenterC32C2×#397
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×C4⋊C4×C3⋊D3C2semidirect
4. C3×#4992C2semidirect
5. #10591370C2semidirect
6. #10591370C2semidirect
7. #10591315C2semidirect
8. #10591298C2semidirect
15. C2×C32×C4⋊C4C22semidirect
16. C2×C4⋊(C3⋊Dic3)C22semidirect
17. C2×#3750C22semidirect
25. C3×C3⋊#95C22semidirect
26. C3×C3⋊#95C22semidirect
27. #63579C22semidirect
28. #63579C22semidirect
34. #4992D3semidirect
80. C2×C3×C4⋊C4C2×D3semidirect
102. C3⋊#95C2×D3semidirect
103. C3⋊#95C2×D3semidirect
227. C2×C4⋊C4D32semidirect
306. C3⋊D3#397semidirect
381. C32C2×#397semidirect
454. C3D3×#397semidirect

Maximal subgroups

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

subgroupindex
C2×C4⋊C4×C3⋊D32
C2×#639212
C3×#49922
#105913702
#105913152
#105912982
D3×#3973