Finite Group Databasebeta

← #11802989

Subgroups — #11802989

Order 1152.

1277 conjugacy classes of subgroups.

The subgroup lattice has 478 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#872C211yesmaximal, characteristic
2C2×D3×C4⋊Dic3C211yesmaximal, characteristic
3C2×#63841C211yesmaximal, characteristic
4#10592635C211yesmaximal, characteristic, complemented
5C3×#4935C211yesmaximal, characteristic, complemented
6#10591377C214yesmaximal
7#10591349C211yesmaximal, characteristic, complemented
8#10591265C214yesmaximal, complemented
9#10591224C211yesmaximal, characteristic, complemented
10#82233—31nomaximal
11#74359—31nomaximal
12C22×C3×C4×D3C2211yescharacteristic
13C22×D3×Dic3C2212yes—
14C2×C32×C42C2211yescharacteristic
15C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
16C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
17C2×C3×(C2×D3)⋊C4C2212yes—
18C2×C3×C4⋊Dic3C2211yescharacteristic
19C2×C3×C4⋊Dic3C2211yescharacteristic
20C2×C3×C4⋊Dic3C2214yes—
21C2×C3×Dic3⋊C4C2212yes—
22C2×C3×C4×Dic3C2211yescharacteristic
23C3×#872C418yescomplemented
24C2×Dic3⋊Dic3C2212yes—
25C2×Dic3⋊Dic3C2214yes—
26C2×(C2×D3)⋊Dic3C2212yes—
27C2×Dic32C2212yes—
28D3×C4⋊Dic3—24no—
29#63841—24no—
30#63658C2214yes—
31#63579C2214yes—
32C2×C3×#117—31no—
33C2×#926—31no—
34C22×C4⋊Dic3—31no—
35C2×#892—31no—
36C2×D3×C4⋊C4—31no—
37C2×#872D311yescharacteristic
38C3×#384—31no—
39#4989—34no—
40#4984—34no—
41#4977—31no—
42#4976—34no—
43#4975—31no—
44#4950—34no—
45#4936—31no—
46#4936—31no—
47#4936—31no—
48#4936—61no—
49#4935—31no—
50#4935D311yescharacteristic, complemented
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×D3D414yes—
62C2×C3×C4×D3Q814yes—
63C2×D3×Dic3—24no—
64C2×D3×Dic3—44no—
65C32×C42C2×C414yescomplemented
66C4⋊(C3⋊Dic3)—22no—
67C4⋊(C3⋊Dic3)—22no—
68C3×(C2×D3)⋊C4C2×C418yes—
69C3×C4⋊Dic3—22no—
70C3×C4⋊Dic3—22no—
71C3×C4⋊Dic3—44no—
72C3×Dic3⋊C4C2×C418yescomplemented
73C3×C4×Dic3C2×C414yescomplemented
74Dic3⋊Dic3—24no—
75Dic3⋊Dic3—44no—
76(C2×D3)⋊Dic3—24no—
77Dic32—24no—
78#2317—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×C4⋊C4—31no—
86C2×C3×C4⋊C4—31no—
87C2×C3×C4⋊C4—34no—
88C2×C3×C22⋊C4—32no—
89C2×C3×C42—21no—
90C2×C3×C42—31no—
91C2×C3×C42C2×D311yescharacteristic
92C2×C3×C42C2×D311yescharacteristic
93C2×#217—32no—
94C2×(C2×D3)⋊C4—32no—
95C2×(C2×D3)⋊C4C2×D312yes—
96#926—64no—
97C2×C4⋊Dic3—31no—
98C2×C4⋊Dic3—31no—
99C2×C4⋊Dic3—31no—
100C2×C4⋊Dic3—31no—
101C2×C4⋊Dic3—32no—
102C2×C4⋊Dic3—34no—
103C2×C4⋊Dic3—61no—
104C2×C4⋊Dic3—61no—
105C2×C4⋊Dic3—64no—
106C2×C4⋊Dic3C2×D311yescharacteristic
107C2×C4⋊Dic3C2×D311yescharacteristic
108C2×C4⋊Dic3C2×D314yes—
109C2×Dic3⋊C4—32no—
110C2×Dic3⋊C4—34no—
111C2×Dic3⋊C4C2×D312yes—
112C2×C4×Dic3—32no—
113C2×C4×Dic3—32no—
114C2×C4×Dic3C2×D311yescharacteristic
115#892—64no—
116D3×C4⋊C4—64no—
117#872Dic318yescomplemented
118C3⋊#95—34no—
119C3⋊#95—34no—
120C3⋊#95—34no—
121C3⋊#95—34no—
122C3⋊#95—64no—
123C23×C32C2411yescharacteristic
124C22×C3×D3—22no—
125C22×C3×D3—22no—
126C22×C3×D3C22×C412yes—
127C22×C3×D3C2×D412yes—
128C22×C3×D3C2×Q812yes—
129C2×C32×C4—22no—
130C2×C32×C4—22no—
131C2×C32×C4C22×C414yes—
132C2×C32×C4C22×C412yes—
133C2×C32×C4C2×D412yes—
134C2×C32×C4C2×Q812yes—
135C2×C3⋊Dic3—22no—
136C2×C3⋊Dic3—22no—
137C2×C3⋊Dic3—24no—
138C2×C3⋊Dic3—24no—
139C2×C3×Dic3—22no—
140C2×C3×Dic3—22no—
141C2×C3×Dic3—22no—
142C2×C3×Dic3—22no—
143C2×C3×Dic3—24no—
144C2×C3×Dic3—24no—
145C2×C3×Dic3C22×C414yes—
146C2×C3×Dic3C22×C412yes—
147C2×C3×Dic3C2×D412yes—
148C2×C3×Dic3C2×Q812yes—
149C3×C4×D3C4⋊C4116yescomplemented
150D3×Dic3—48no—
151C2×#117—31no—
152C2×#117—91no—
153C22×C4⋊C4—91no—
154#389—94no—
155#385—94no—
156#384—31no—
157#384—91no—
158#382—91no—
159#382—91no—
160C24×C3—31no—
161C23×D3C22×D311yescharacteristic
162C22×C3×C4—21no—
163C22×C3×C4—22no—
164C22×C3×C4—31no—
165C22×C3×C4—34no—
166C22×C3×C4—34no—
167C22×C3×C4—34no—
168C22×C3×C4—32no—
169C22×C3×C4—32no—
170C22×C3×C4—32no—
171C22×C3×C4C22×D312yes—
172C22×C3×C4C22×D312yes—
173C22×C3×C4C22×D311yescharacteristic
174C22×C3×C4C22×D311yescharacteristic
175C22×Dic3—32no—
176C22×Dic3—32no—
177C22×Dic3—32no—
178C22×Dic3—32no—
179C22×Dic3—62no—
180C22×Dic3—62no—
181C22×Dic3—64no—
182C22×Dic3—124no—
183C22×Dic3C22×D312yes—
184C22×Dic3C22×D312yes—
185C22×Dic3C22×D312yes—
186C22×Dic3C22×D311yescharacteristic
187C2×C4×D3—64no—
188C2×C4×D3—124no—
189C2×C4×D3Dic614yes—
190C2×C4×D3D1214yes—
191C2×C4×D3C2×Dic314yes—
192C3×C4⋊C4—38no—
193C3×C4⋊C4—62no—
194C3×C4⋊C4—62no—
195C3×C4⋊C4—124no—
196C3×C22⋊C4—38no—
197C3×C42—24no—
198C3×C42—34no—
199C3×C42C4×D314yescomplemented
200C3×C42C2×Dic314yescomplemented
201#217—64no—
202(C2×D3)⋊C4—64no—
203(C2×D3)⋊C4C2×Dic318yes—
204C4⋊Dic3—22no—
205C4⋊Dic3—22no—
206C4⋊Dic3—44no—
207C4⋊Dic3—64no—
208C4⋊Dic3—62no—
209C4⋊Dic3—62no—
210C4⋊Dic3—62no—
211C4⋊Dic3—62no—
212C4⋊Dic3—122no—
213C4⋊Dic3—122no—
214C4⋊Dic3—124no—
215Dic3⋊C4—64no—
216Dic3⋊C4—124no—
217Dic3⋊C4C2×Dic318yescomplemented
218C4×Dic3—64no—
219C4×Dic3—64no—
220C4×Dic3C2×Dic314yescomplemented
221C22×C32C23×C411yescharacteristic
222C22×C32C22×D411yescharacteristic
223C22×C32C22×Q811yescharacteristic
224C22×C32H(5,𝔽2)12yes—
225C22×C322−1+412yes—
226C2×C3×D3—24no—
227C2×C3×D3—22no—
228C2×C3×D3—22no—
229C2×C3×D3—24no—
230C2×C3×D3C2×C4⋊C414yes—
231C32×C4—24no—
232C32×C4C2×C4⋊C414yes—
233C3⋊Dic3—42no—
234C3⋊Dic3—42no—
235C3×Dic3—24no—
236C3×Dic3—42no—
237C3×Dic3—42no—
238C3×Dic3C2×C4⋊C414yes—
239C23×C4—31no—
240C23×C4—92no—
241#117—38no—
242#117—184no—
243C2×C4⋊C4—32no—
244C2×C4⋊C4—31no—
245C2×C4⋊C4—31no—
246C2×C4⋊C4—34no—
247C2×C4⋊C4—92no—
248C2×C4⋊C4—91no—
249C2×C4⋊C4—91no—
250C2×C4⋊C4—94no—
251C2×C4⋊C4—184no—
252C2×C22⋊C4—32no—
253C2×C22⋊C4—92no—
254C2×C42—31no—
255C2×C42—92no—
256C2×C42D3211yescharacteristic
257#95—94no—
258#95—94no—
259C23×C3—21no—
260C23×C3—32no—
261C23×C3—32no—
262C23×C3—32no—
263C23×C3—62no—
264C23×C3—62no—
265C23×C3C23×D311yescharacteristic
266C23×C3C23×D311yescharacteristic
267C22×D3—22no—
268C22×D3—22no—
269C22×D3C2×Dic612yes—
270C22×D3C2×D1212yes—
271C22×D3C22×Dic312yes—
272C2×C3×C4—22no—
273C2×C3×C4—22no—
274C2×C3×C4—22no—
275C2×C3×C4—22no—
276C2×C3×C4—22no—
277C2×C3×C4—22no—
278C2×C3×C4—22no—
279C2×C3×C4—24no—
280C2×C3×C4—32no—
281C2×C3×C4—32no—
282C2×C3×C4—32no—
283C2×C3×C4—316no—
284C2×C3×C4—34no—
285C2×C3×C4—42no—
286C2×C3×C4—42no—
287C2×C3×C4—62no—
288C2×C3×C4—62no—
289C2×C3×C4—62no—
290C2×C3×C4—62no—
291C2×C3×C4—64no—
292C2×C3×C4—64no—
293C2×C3×C4C2×Dic612yes—
294C2×C3×C4C2×C4×D314yes—
295C2×C3×C4C2×C4×D312yes—
296C2×C3×C4C2×D1212yes—
297C2×C3×C4D3×D412yes—
298C2×C3×C4D3×Q812yes—
299C2×C3×C4C22×Dic314yes—
300C2×C3×C4C22×Dic312yes—
301C2×Dic3—22no—
302C2×Dic3—22no—
303C2×Dic3—22no—
304C2×Dic3—22no—
305C2×Dic3—24no—
306C2×Dic3—24no—
307C2×Dic3—62no—
308C2×Dic3—62no—
309C2×Dic3—62no—
310C2×Dic3—62no—
311C2×Dic3—64no—
312C2×Dic3—64no—
313C2×Dic3—64no—
314C2×Dic3—64no—
315C2×Dic3—122no—
316C2×Dic3—122no—
317C2×Dic3—124no—
318C2×Dic3—124no—
319C2×Dic3—128no—
320C2×Dic3C2×Dic612yes—
321C2×Dic3C2×D1212yes—
322C2×Dic3C22×Dic314yes—
323C2×Dic3C22×Dic312yes—
324C4×D3—128no—
325C4×D3C4⋊Dic3116yescomplemented
326C2×C32C22×C4⋊C411yescharacteristic
327C2×C32#52012yes—
328C2×C32#53511yescharacteristic
329C2×C32#53611yescharacteristic
330C2×C32#54412yes—
331C3×D3—24no—
332C24—31no—
333C22×C4—31no—
334C22×C4—34no—
335C22×C4—34no—
336C22×C4—34no—
337C22×C4—32no—
338C22×C4—32no—
339C22×C4—32no—
340C22×C4—92no—
341C22×C4—92no—
342C22×C4—184no—
343C22×C4—364no—
344C22×C4C2×D3212yes—
345C22×C4C2×D3211yescharacteristic
346C4⋊C4—38no—
347C4⋊C4—62no—
348C4⋊C4—62no—
349C4⋊C4—124no—
350C4⋊C4—184no—
351C4⋊C4—182no—
352C4⋊C4—182no—
353C4⋊C4—364no—
354C22⋊C4—38no—
355C22⋊C4—184no—
356C42—34no—
357C42—184no—
358C42D3×Dic314yescomplemented
359C22×C3—21no—
360C22×C3—22no—
361C22×C3—21no—
362C22×C3—22no—
363C22×C3—21no—
364C22×C3—34no—
365C22×C3—62no—
366C22×C3—62no—
367C22×C3—64no—
368C22×C3—64no—
369C22×C3C22×Dic611yescharacteristic
370C22×C3C22×C4×D311yescharacteristic
371C22×C3C22×D1211yescharacteristic
372C22×C3C2×D3×D411yescharacteristic
373C22×C3#100412yes—
374C22×C3C2×D3×Q811yescharacteristic
375C22×C3#100712yes—
376C22×C3#100912yes—
377C22×C3#101012yes—
378C22×C3C23×Dic311yescharacteristic
379C2×D3—24no—
380C2×D3—22no—
381C2×D3—22no—
382C2×D3—24no—
383C2×D3C2×C4⋊Dic314yes—
384C3×C4—24no—
385C3×C4—24no—
386C3×C4—24no—
387C3×C4—34no—
388C3×C4—44no—
389C3×C4—64no—
390C3×C4—122no—
391C3×C4—122no—
392C3×C4D3×C4⋊C414yes—
393C3×C4C2×C4⋊Dic314yes—
394Dic3—24no—
395Dic3—42no—
396Dic3—42no—
397Dic3—122no—
398Dic3—122no—
399Dic3—122no—
400Dic3—122no—
401Dic3—242no—
402Dic3—242no—
403Dic3C2×C4⋊Dic314yes—
404C32#231711yescharacteristic, complemented, Sylow
405C23—32no—
406C23—32no—
407C23—32no—
408C23—62no—
409C23—62no—
410C23C22×D3211yescharacteristic
411C2×C4—22no—
412C2×C4—22no—
413C2×C4—32no—
414C2×C4—32no—
415C2×C4—32no—
416C2×C4—316no—
417C2×C4—34no—
418C2×C4—62no—
419C2×C4—62no—
420C2×C4—62no—
421C2×C4—62no—
422C2×C4—64no—
423C2×C4—64no—
424C2×C4—184no—
425C2×C4—182no—
426C2×C4—182no—
427C2×C4—184no—
428C2×C4—368no—
429C2×C4D3×Dic612yes—
430C2×C4D3×D1212yes—
431C2×C4C2×D3×Dic314yes—
432C2×C4C2×D3×Dic312yes—
433C2×C3—21no—
434C2×C3—21no—
435C2×C3—22no—
436C2×C3—22no—
437C2×C3—21no—
438C2×C3—64no—
439C2×C3C2×D3×C4⋊C411yescharacteristic
440C2×C3#550412yes—
441C2×C3#551912yes—
442C2×C3#552511yescharacteristic
443C2×C3#552611yescharacteristic
444C2×C3#571511yescharacteristic
445C2×C3#572411yescharacteristic
446C2×C3#572912yes—
447C2×C3C22×C4⋊Dic311yescharacteristic
448C2×C3#582712yes—
449D3—24no—
450C22—34no—
451C22—62no—
452C22—64no—
453C22—64no—
454C22—62no—
455C22C2×D3×Dic611yescharacteristic
456C22#6429712yes—
457C22C2×D3×D1211yescharacteristic
458C22#6430712yes—
459C22C22×D3×Dic311yescharacteristic
460C4—24no—
461C4—34no—
462C4—64no—
463C4—122no—
464C4—122no—
465C4—362no—
466C4—362no—
467C4D3×C4⋊Dic314yes—
468C3—21no—
469C3#7435911yescharacteristic, complemented
470C3#8223311yescharacteristic, complemented
471C2—64no—
472C2#1059389311yescharacteristic
473C2#1059395412yes—
474C2#1059400011yescharacteristic
475C2C2×D3×C4⋊Dic311yescharacteristic
476C2#1059498612yes—
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC2×C32×C42C22
socle, cosocleC23×C32C24
prime radicalC23×C3×D3C23
hypercenterC2×C42D32
hypocenterC32#2317
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
4. #10592635C2semidirect
5. C3×#4935C2semidirect
7. #10591349C2semidirect
8. #10591265C2semidirect
9. #10591224C2semidirect
23. C3×#872C4semidirect
50. #4935D3semidirect
65. C32×C42C2×C4semidirect
72. C3×Dic3⋊C4C2×C4semidirect
73. C3×C4×Dic3C2×C4semidirect
117. #872Dic3semidirect
149. C3×C4×D3C4⋊C4semidirect
199. C3×C42C4×D3semidirect
200. C3×C42C2×Dic3semidirect
217. Dic3⋊C4C2×Dic3semidirect
220. C4×Dic3C2×Dic3semidirect
325. C4×D3C4⋊Dic3semidirect
358. C42D3×Dic3semidirect
404. C32#2317semidirect
469. C3#74359semidirect
470. C3#82233semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#8722
C2×D3×C4⋊Dic32
C2×#638412
#105926352
C3×#49352
#105913772
#105913492
#105912652
#105912242
#822333
#743593