Finite Group Databasebeta

← #11800788

Subgroups — #11800788

Order 1152.

1633 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#872C211yesmaximal, characteristic
2C2×C4×D3×Dic3C211yesmaximal, characteristic
3C2×#63855C211yesmaximal, characteristic
4C42×C3⋊Dic3C211yesmaximal, characteristic, complemented
5C3×#4932C211yesmaximal, characteristic, complemented
6#10591368C214yesmaximal
7#10591241C214yesmaximal, complemented
8C4×Dic32C211yesmaximal, characteristic, complemented
9#10591222C211yesmaximal, characteristic, complemented
10Dic3×#117—31nomaximal
11#73382—31nomaximal
12C22×C3×C4×D3C2211yescharacteristic
13C22×D3×Dic3C2212yes—
14C2×C32×C42C2211yescharacteristic
15C2×C4×C3⋊Dic3C2214yes—
16C2×C4×C3⋊Dic3C2211yescharacteristic
17C2×C4×C3⋊Dic3C2211yescharacteristic
18C2×C3×(C2×D3)⋊C4C2212yes—
19C2×C3×Dic3⋊C4C2212yes—
20C2×C3×C4×Dic3C2211yescharacteristic
21C2×C3×C4×Dic3C2211yescharacteristic
22C2×C3×C4×Dic3C2211yescharacteristic
23C3×#872C418yescomplemented
24C2×Dic3⋊Dic3C2212yes—
25C2×(C2×D3)⋊Dic3C2212yes—
26C2×Dic32C2214yes—
27C2×Dic32C2212yes—
28C4×D3×Dic3C418yescomplemented
29#63855C418yescomplemented
30C3×C3⋊#95C2214yes—
31#63579C2214yes—
32C2×C3×#117—31no—
33C2×#926—31no—
34C22×C4×Dic3—31no—
35C2×#872—31no—
36C2×#872D311yescharacteristic
37C2×C42×D3—31no—
38C3×#376—31no—
39Dic3×C4⋊C4—34no—
40Dic3×C22⋊C4—34no—
41#4932—31no—
42#4932—31no—
43#4932D311yescharacteristic, complemented
44C42×Dic3—31no—
45C42×Dic3—31no—
46C42×Dic3—31no—
47C42×Dic3—31no—
48C42×Dic3—61no—
49#4666—34no—
50#4649—34no—
51C23×C3×D3C2311yescharacteristic
52C22×C32×C4C2312yes—
53C22×C32×C4C2311yescharacteristic
54C22×C3⋊Dic3C2312yes—
55C22×C3⋊Dic3C2312yes—
56C22×C3×Dic3C2312yes—
57C22×C3×Dic3C2312yes—
58C22×C3×Dic3C2312yes—
59C22×C3×Dic3C2311yescharacteristic
60C2×C3×C4×D3C2×C414yes—
61C2×C3×C4×D3C2×C414yes—
62C2×C3×C4×D3C2×C414yes—
63C2×D3×Dic3—28no—
64C2×D3×Dic3C2×C418yes—
65C32×C42C2×C414yescomplemented
66C4×C3⋊Dic3—28no—
67C4×C3⋊Dic3C2×C414yes—
68C4×C3⋊Dic3C2×C414yescomplemented
69C3×(C2×D3)⋊C4C2×C418yes—
70C3×Dic3⋊C4C2×C418yescomplemented
71C3×C4×Dic3C2×C414yes—
72C3×C4×Dic3C2×C414yescomplemented
73C3×C4×Dic3C2×C414yescomplemented
74Dic3⋊Dic3C2×C418yescomplemented
75(C2×D3)⋊Dic3C2×C418yes—
76Dic32—28no—
77Dic32C2×C418yes—
78C4×#117—91noSylow
79C23×C3×C4—31no—
80C23×Dic3—32no—
81C22×C4×D3—32no—
82C22×C4×D3C2×D311yescharacteristic
83C3×#117—38no—
84C2×C3×C4⋊C4—32no—
85C2×C3×C22⋊C4—32no—
86C2×C3×C42—21no—
87C2×C3×C42—31no—
88C2×C3×C42—31no—
89C2×C3×C42—31no—
90C2×C3×C42C2×D311yescharacteristic
91C2×C3×C42C2×D311yescharacteristic
92C2×#217—32no—
93C2×(C2×D3)⋊C4—32no—
94C2×(C2×D3)⋊C4C2×D312yes—
95#926—38no—
96C2×C4⋊Dic3—32no—
97C2×Dic3⋊C4—32no—
98C2×Dic3⋊C4C2×D312yes—
99C2×C4×Dic3—31no—
100C2×C4×Dic3—31no—
101C2×C4×Dic3—31no—
102C2×C4×Dic3—31no—
103C2×C4×Dic3—32no—
104C2×C4×Dic3—32no—
105C2×C4×Dic3—38no—
106C2×C4×Dic3—34no—
107C2×C4×Dic3—34no—
108C2×C4×Dic3—34no—
109C2×C4×Dic3—34no—
110C2×C4×Dic3—61no—
111C2×C4×Dic3—61no—
112C2×C4×Dic3—64no—
113C2×C4×Dic3C2×D311yescharacteristic
114C2×C4×Dic3C2×D311yescharacteristic
115C2×C4×Dic3C2×D311yescharacteristic
116#872—38no—
117#872Dic318yescomplemented
118C42×D3—38no—
119C3×#95—34no—
120C3⋊#95—34no—
121C3⋊#95—34no—
122C3⋊#95C2×D314yes—
123C23×C32C2411yescharacteristic
124C22×C3×D3—24no—
125C22×C3×D3C22×C412yes—
126C22×C3×D3C22×C412yes—
127C22×C3×D3C22×C412yes—
128C2×C32×C4—24no—
129C2×C32×C4C22×C412yes—
130C2×C32×C4C22×C412yes—
131C2×C32×C4C22×C414yes—
132C2×C32×C4C22×C412yes—
133C2×C3⋊Dic3—24no—
134C2×C3⋊Dic3C22×C414yes—
135C2×C3⋊Dic3C22×C414yes—
136C2×C3⋊Dic3#4118yes—
137C2×C3×Dic3—24no—
138C2×C3×Dic3—24no—
139C2×C3×Dic3—24no—
140C2×C3×Dic3C22×C414yes—
141C2×C3×Dic3C22×C414yes—
142C2×C3×Dic3C22×C412yes—
143C2×C3×Dic3C22×C412yes—
144C2×C3×Dic3C22×C414yes—
145C2×C3×Dic3C22×C412yes—
146C3×C4×D3C42116yescomplemented
147D3×Dic3—216no—
148C2×#117—31no—
149C2×#117—91no—
150C22×C42—91no—
151C4×C4⋊C4—94no—
152C4×C22⋊C4—94no—
153#376—31no—
154#376—91no—
155C43—91no—
156C43—91no—
157C24×C3—31no—
158C23×D3C22×D311yescharacteristic
159C22×C3×C4—22no—
160C22×C3×C4—21no—
161C22×C3×C4—31no—
162C22×C3×C4—34no—
163C22×C3×C4—34no—
164C22×C3×C4—34no—
165C22×C3×C4—32no—
166C22×C3×C4—32no—
167C22×C3×C4—32no—
168C22×C3×C4C22×D312yes—
169C22×C3×C4C22×D312yes—
170C22×C3×C4C22×D311yescharacteristic
171C22×C3×C4C22×D311yescharacteristic
172C22×Dic3—32no—
173C22×Dic3—32no—
174C22×Dic3—32no—
175C22×Dic3—32no—
176C22×Dic3—38no—
177C22×Dic3—62no—
178C22×Dic3—62no—
179C22×Dic3—68no—
180C22×Dic3C22×D312yes—
181C22×Dic3C22×D312yes—
182C22×Dic3C22×D312yes—
183C22×Dic3C22×D311yescharacteristic
184C2×C4×D3—38no—
185C2×C4×D3—68no—
186C2×C4×D3C4×D314yes—
187C2×C4×D3C4×D314yes—
188C2×C4×D3C2×Dic314yes—
189C3×C4⋊C4—38no—
190C3×C22⋊C4—38no—
191C3×C42—24no—
192C3×C42—34no—
193C3×C42—34no—
194C3×C42—34no—
195C3×C42C4×D314yescomplemented
196C3×C42C2×Dic314yescomplemented
197#217—38no—
198(C2×D3)⋊C4—38no—
199(C2×D3)⋊C4C2×Dic318yes—
200C4⋊Dic3—38no—
201Dic3⋊C4—38no—
202Dic3⋊C4C2×Dic318yescomplemented
203C4×Dic3—34no—
204C4×Dic3—34no—
205C4×Dic3—34no—
206C4×Dic3—34no—
207C4×Dic3—38no—
208C4×Dic3—38no—
209C4×Dic3—64no—
210C4×Dic3—64no—
211C4×Dic3—68no—
212C4×Dic3—68no—
213C4×Dic3—68no—
214C4×Dic3—68no—
215C4×Dic3—616no—
216C4×Dic3C4×D314yes—
217C4×Dic3C4×D314yescomplemented
218C4×Dic3C2×Dic314yescomplemented
219C22×C32C23×C411yescharacteristic
220C22×C32C23×C411yescharacteristic
221C22×C32C23×C411yescharacteristic
222C22×C32C2×#4114yes—
223C2×C3×D3—24no—
224C2×C3×D3—24no—
225C2×C3×D3—24no—
226C2×C3×D3C2×C4214yes—
227C32×C4—24no—
228C32×C4C2×C4214yes—
229C3⋊Dic3—24no—
230C3⋊Dic3#11718yescomplemented
231C3×Dic3—24no—
232C3×Dic3—24no—
233C3×Dic3—24no—
234C3×Dic3C2×C4214yes—
235C23×C4—31no—
236C23×C4—92no—
237#117—38no—
238#117—98no—
239C2×C4⋊C4—32no—
240C2×C4⋊C4—92no—
241C2×C22⋊C4—32no—
242C2×C22⋊C4—92no—
243C2×C42—31no—
244C2×C42—31no—
245C2×C42—31no—
246C2×C42—98no—
247C2×C42—92no—
248C2×C42—91no—
249C2×C42—91no—
250C2×C42—94no—
251C2×C42—94no—
252C2×C42D3211yescharacteristic
253#95—34no—
254#95—94no—
255C23×C3—21no—
256C23×C3—32no—
257C23×C3—32no—
258C23×C3—32no—
259C23×C3—64no—
260C23×C3C23×D311yescharacteristic
261C23×C3C23×D311yescharacteristic
262C22×D3—24no—
263C22×D3C2×C4×D312yes—
264C22×D3C2×C4×D312yes—
265C22×D3C22×Dic312yes—
266C2×C3×C4—28no—
267C2×C3×C4—24no—
268C2×C3×C4—24no—
269C2×C3×C4—22no—
270C2×C3×C4—22no—
271C2×C3×C4—24no—
272C2×C3×C4—22no—
273C2×C3×C4—32no—
274C2×C3×C4—32no—
275C2×C3×C4—32no—
276C2×C3×C4—316no—
277C2×C3×C4—34no—
278C2×C3×C4—34no—
279C2×C3×C4—34no—
280C2×C3×C4—64no—
281C2×C3×C4—64no—
282C2×C3×C4—64no—
283C2×C3×C4C2×C4×D312yes—
284C2×C3×C4C2×C4×D312yes—
285C2×C3×C4C2×C4×D312yes—
286C2×C3×C4C2×C4×D312yes—
287C2×C3×C4C2×C4×D314yes—
288C2×C3×C4C2×C4×D312yes—
289C2×C3×C4C22×Dic314yes—
290C2×C3×C4C22×Dic312yes—
291C2×Dic3—24no—
292C2×Dic3—24no—
293C2×Dic3—24no—
294C2×Dic3—34no—
295C2×Dic3—34no—
296C2×Dic3—38no—
297C2×Dic3—38no—
298C2×Dic3—34no—
299C2×Dic3—34no—
300C2×Dic3—64no—
301C2×Dic3—64no—
302C2×Dic3—68no—
303C2×Dic3—616no—
304C2×Dic3—68no—
305C2×Dic3—64no—
306C2×Dic3—64no—
307C2×Dic3C2×C4×D314yes—
308C2×Dic3C2×C4×D314yes—
309C2×Dic3C2×C4×D312yes—
310C2×Dic3C2×C4×D312yes—
311C2×Dic3C22×Dic314yes—
312C2×Dic3C22×Dic312yes—
313C4×D3—616no—
314C4×D3C4×Dic3116yescomplemented
315C2×C32C22×C4211yescharacteristic
316C2×C32C2×#11712yes—
317C2×C32C4×#4112yes—
318C2×C32C4×#4112yes—
319C3×D3—24no—
320C24—31no—
321C22×C4—31no—
322C22×C4—34no—
323C22×C4—34no—
324C22×C4—34no—
325C22×C4—32no—
326C22×C4—32no—
327C22×C4—32no—
328C22×C4—98no—
329C22×C4—92no—
330C22×C4—92no—
331C22×C4—188no—
332C22×C4C2×D3212yes—
333C22×C4C2×D3211yescharacteristic
334C4⋊C4—38no—
335C4⋊C4—98no—
336C22⋊C4—38no—
337C22⋊C4—98no—
338C42—34no—
339C42—34no—
340C42—34no—
341C42—98no—
342C42—94no—
343C42—94no—
344C42—188no—
345C42—188no—
346C42D3×Dic314yescomplemented
347C22×C3—21no—
348C22×C3—21no—
349C22×C3—24no—
350C22×C3—21no—
351C22×C3—34no—
352C22×C3—64no—
353C22×C3—64no—
354C22×C3—64no—
355C22×C3C22×C4×D311yescharacteristic
356C22×C3C22×C4×D311yescharacteristic
357C22×C3C22×C4×D311yescharacteristic
358C22×C3C22×C4×D311yescharacteristic
359C22×C3C22×C4×D311yescharacteristic
360C22×C3D3×#4114yes—
361C22×C3D3×#4114yes—
362C22×C3C23×Dic311yescharacteristic
363C2×D3—24no—
364C2×D3—24no—
365C2×D3—24no—
366C2×D3C2×C4×Dic314yes—
367C3×C4—28no—
368C3×C4—24no—
369C3×C4—24no—
370C3×C4—24no—
371C3×C4—34no—
372C3×C4—64no—
373C3×C4—64no—
374C3×C4—64no—
375C3×C4C42×D314yes—
376C3×C4C2×C4×Dic314yes—
377Dic3—24no—
378Dic3—24no—
379Dic3—24no—
380Dic3—38no—
381Dic3—38no—
382Dic3—68no—
383Dic3—68no—
384Dic3—64no—
385Dic3—64no—
386Dic3C2×C4×Dic314yes—
387C32C4×#11711yescharacteristic, complemented, Sylow
388C23—32no—
389C23—32no—
390C23—32no—
391C23—64no—
392C23C22×D3211yescharacteristic
393C2×C4—24no—
394C2×C4—32no—
395C2×C4—32no—
396C2×C4—32no—
397C2×C4—316no—
398C2×C4—34no—
399C2×C4—34no—
400C2×C4—34no—
401C2×C4—64no—
402C2×C4—64no—
403C2×C4—64no—
404C2×C4—94no—
405C2×C4—98no—
406C2×C4—94no—
407C2×C4—1816no—
408C2×C4—184no—
409C2×C4C4×D3212yes—
410C2×C4C4×D3212yes—
411C2×C4C2×D3×Dic314yes—
412C2×C4C2×D3×Dic312yes—
413C2×C3—21no—
414C2×C3—22no—
415C2×C3—22no—
416C2×C3—22no—
417C2×C3—64no—
418C2×C3C2×C42×D311yescharacteristic
419C2×C3D3×#11712yes—
420C2×C3D3×#11712yes—
421C2×C3#552212yes—
422C2×C3#552212yes—
423C2×C3#552212yes—
424C2×C3C22×C4×Dic311yescharacteristic
425C2×C3Dic3×#4112yes—
426D3—24no—
427C22—34no—
428C22—64no—
429C22—64no—
430C22—64no—
431C22C2×C4×D3211yescharacteristic
432C22C2×C4×D3211yescharacteristic
433C22#6430614yes—
434C22C22×D3×Dic311yescharacteristic
435C4—24no—
436C4—34no—
437C4—64no—
438C4—64no—
439C4—64no—
440C4—98no—
441C4—184no—
442C4C4×D3×Dic314yes—
443C3—21no—
444C3#7338211yescharacteristic, complemented
445C3Dic3×#11711yescharacteristic, complemented
446C2—64no—
447C2#1059396612yes—
448C2#1059399212yes—
449C2C2×C4×D3×Dic311yescharacteristic
450C2#1059495812yes—
subgroupG/H
centerC22×C4C2×D32
commutatorC2×C32C22×C42
FrattiniC23C22×D32
FittingC2×C32×C42C22
socle, cosocleC23×C32C24
prime radicalC23×C3×D3C23
hypercenterC2×C42D32
hypocenterC32C4×#117
LCSG ▷ C2×C32 ▷ C32
UCSC1 ◁ C22×C4 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
4. C42×C3⋊Dic3C2semidirect
5. C3×#4932C2semidirect
7. #10591241C2semidirect
8. C4×Dic32C2semidirect
9. #10591222C2semidirect
23. C3×#872C4semidirect
28. C4×D3×Dic3C4semidirect
29. #63855C4semidirect
43. #4932D3semidirect
65. C32×C42C2×C4semidirect
68. C4×C3⋊Dic3C2×C4semidirect
70. C3×Dic3⋊C4C2×C4semidirect
72. C3×C4×Dic3C2×C4semidirect
73. C3×C4×Dic3C2×C4semidirect
74. Dic3⋊Dic3C2×C4semidirect
117. #872Dic3semidirect
146. C3×C4×D3C42semidirect
195. C3×C42C4×D3semidirect
196. C3×C42C2×Dic3semidirect
202. Dic3⋊C4C2×Dic3semidirect
217. C4×Dic3C4×D3semidirect
218. C4×Dic3C2×Dic3semidirect
230. C3⋊Dic3#117semidirect
314. C4×D3C4×Dic3semidirect
346. C42D3×Dic3semidirect
387. C32C4×#117semidirect
444. C3#73382semidirect
445. C3Dic3×#117semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#8722
C2×C4×D3×Dic32
C2×#638552
C42×C3⋊Dic32
C3×#49322
#105913682
#105912412
C4×Dic322
#105912222
Dic3×#1173
#733823