Finite Group Databasebeta

← #11808516

Subgroups — #11808516

Order 1152.

1417 conjugacy classes of subgroups.

The subgroup lattice has 424 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4⋊C4×C3⋊D3C211yesmaximal, characteristic
2C2×#63900C211yesmaximal, characteristic
3C3×#4986C212yesmaximal, complemented
4#10591370C212yesmaximal
5#10591370C212yesmaximal
6#10591370C211yesmaximal, characteristic
7#10591227C212yesmaximal, complemented
8#10591218C212yesmaximal, complemented
9#10591217C212yesmaximal, complemented
10D3×#400—32nomaximal
11C22×C4×C3⋊D3C2211yescharacteristic
12C22×C4×C3⋊D3C2211yescharacteristic
13C22×C4×C3⋊D3C2211yescharacteristic
14C22×#624C2212yes—
15C22×#624C2212yes—
16C2×C32×C4⋊C4C2211yescharacteristic
17C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
18C2×#3750C2211yescharacteristic
19C2×#3750C2211yescharacteristic
20C4⋊C4×C3⋊D3—24no—
21C2×C3×C4⋊Dic3C2212yes—
22C2×#3724C2212yes—
23#63900—24no—
24C3×C3⋊#95C2214yes—
25C3×C3⋊#95C2214yes—
26C3×C3⋊#95C2212yes—
27#63579C2212yes—
28#63579C2214yes—
29#63579C2214yes—
30C2×D3×C4⋊C4—32no—
31C2×D3×C4⋊C4—32no—
32C2×D3×C4⋊C4—61no—
33C3×#400—32no—
34#4986D312yescomplemented
35#4985—32no—
36D3×#95—34no—
37D3×#95—32no—
38D3×#95—34no—
39#4660—34no—
40#4659—32no—
41#4658—34no—
42C23×C3⋊D3C2311yescharacteristic
43C22×C32×C4C2311yescharacteristic
44C22×C32×C4C2311yescharacteristic
45C22×C32×C4C2311yescharacteristic
46C22×C3⋊Dic3C2311yescharacteristic
47C22×C3⋊Dic3C2311yescharacteristic
48C22×C3⋊Dic3C2311yescharacteristic
49C2×C4×C3⋊D3—22no—
50C2×C4×C3⋊D3—22no—
51C2×C4×C3⋊D3—24no—
52C2×C4×C3⋊D3—22no—
53C2×C4×C3⋊D3—24no—
54C2×C4×C3⋊D3D414yes—
55C2×C4×C3⋊D3Q814yes—
56C22×C3×Dic3C2314yes—
57C22×C3×Dic3C2314yes—
58C2×#624—24no—
59C2×#624—28no—
60C2×#624—24no—
61C2×#624—24no—
62C2×#624—24no—
63C32×C4⋊C4—22no—
64C4⋊(C3⋊Dic3)—22no—
65#3750—22no—
66#3750—22no—
67C3×C4⋊Dic3—24no—
68#3724—24no—
69C2×#400—91noSylow
70C22×C4×D3—32no—
71C22×C4×D3—32no—
72C22×C4×D3—32no—
73C22×C4×D3—34no—
74C22×C4×D3—34no—
75C22×C4×D3—61no—
76C22×C4×D3—61no—
77C22×C4×D3—61no—
78C2×C3×C4⋊C4—21no—
79C2×C3×C4⋊C4—32no—
80C2×C3×C4⋊C4C2×D312yes—
81C2×C4⋊Dic3—32no—
82C2×C4⋊Dic3—61no—
83C2×C4⋊Dic3C2×D312yes—
84C2×Dic3⋊C4—32no—
85C2×Dic3⋊C4—32no—
86C2×Dic3⋊C4—34no—
87C2×Dic3⋊C4—61no—
88C2×Dic3⋊C4—61no—
89D3×C4⋊C4—68no—
90D3×C4⋊C4—68no—
91D3×C4⋊C4—68no—
92C3×#95—34no—
93C3×#95—32no—
94C3×#95—34no—
95C3⋊#95—34no—
96C3⋊#95—34no—
97C3⋊#95—34no—
98C3⋊#95—34no—
99C3⋊#95—34no—
100C3⋊#95C2×D314yes—
101C3⋊#95C2×D314yes—
102C3⋊#95C2×D312yes—
103C23×C32C2411yescharacteristic
104C22×C3⋊D3C2×D412yes—
105C22×C3⋊D3C2×Q812yes—
106C22×C3⋊D3#4112yes—
107C22×C3⋊D3#4114yes—
108C22×C3⋊D3#4114yes—
109C2×C32×C4—21no—
110C2×C32×C4—21no—
111C2×C32×C4—21no—
112C2×C32×C4—22no—
113C2×C32×C4—22no—
114C2×C32×C4C2×D412yes—
115C2×C32×C4C2×Q812yes—
116C2×C3⋊Dic3—21no—
117C2×C3⋊Dic3—21no—
118C2×C3⋊Dic3—21no—
119C2×C3⋊Dic3—22no—
120C2×C3⋊Dic3—22no—
121C2×C3⋊Dic3C2×D412yes—
122C2×C3⋊Dic3C2×Q812yes—
123C4×C3⋊D3—28no—
124C4×C3⋊D3—28no—
125C4×C3⋊D3—44no—
126C2×C3×Dic3—24no—
127C2×C3×Dic3—28no—
128C2×C3×Dic3—24no—
129C2×C3×Dic3—24no—
130C2×C3×Dic3—24no—
131#624—48no—
132#624—48no—
133C22×C4⋊C4—91no—
134C22×C4⋊C4—91no—
135#400—32no—
136#400—92no—
137#400—92no—
138#400—92no—
139C2×#95—92no—
140C2×#95—92no—
141C2×#95—91no—
142C23×D3—32no—
143C23×D3—61no—
144C22×C3×C4—21no—
145C22×C3×C4—21no—
146C22×C3×C4—21no—
147C22×C3×C4—34no—
148C22×C3×C4—34no—
149C22×C3×C4C22×D312yes—
150C22×C3×C4C22×D312yes—
151C22×C3×C4C22×D312yes—
152C22×Dic3—32no—
153C22×Dic3—32no—
154C22×Dic3—32no—
155C22×Dic3—61no—
156C22×Dic3—61no—
157C22×Dic3—61no—
158C22×Dic3C22×D314yes—
159C22×Dic3C22×D314yes—
160C2×C4×D3—38no—
161C2×C4×D3—38no—
162C2×C4×D3—64no—
163C2×C4×D3—64no—
164C2×C4×D3—64no—
165C2×C4×D3—64no—
166C2×C4×D3—68no—
167C2×C4×D3—64no—
168C2×C4×D3—64no—
169C2×C4×D3—68no—
170C2×C4×D3—68no—
171C2×C4×D3—68no—
172C2×C4×D3—68no—
173C2×C4×D3—616no—
174C2×C4×D3—64no—
175C2×C4×D3—68no—
176C2×C4×D3—64no—
177C2×C4×D3—124no—
178C2×C4×D3—124no—
179C3×C4⋊C4—24no—
180C3×C4⋊C4—24no—
181C3×C4⋊C4—64no—
182C4⋊Dic3—24no—
183C4⋊Dic3—64no—
184C4⋊Dic3—64no—
185Dic3⋊C4—68no—
186Dic3⋊C4—64no—
187Dic3⋊C4—64no—
188Dic3⋊C4—64no—
189Dic3⋊C4—64no—
190C22×C32C22×D411yescharacteristic
191C22×C32C22×Q811yescharacteristic
192C22×C32C2×#4111yescharacteristic
193C22×C32C2×#4112yes—
194C22×C32C2×#4112yes—
195C2×C3⋊D3C22⋊Q814yes—
196C2×C3⋊D3#12314yes—
197C2×C3⋊D3#12414yes—
198C2×C3⋊D3#12518yes—
199C2×C3⋊D3#12618yes—
200C32×C4—22no—
201C32×C4—22no—
202C32×C4—41no—
203C3⋊Dic3—22no—
204C3⋊Dic3—22no—
205C3⋊Dic3—41no—
206C3×Dic3—44no—
207C3×Dic3—44no—
208C23×C4—92no—
209C23×C4—92no—
210C23×C4—91no—
211C23×C4—91no—
212C23×C4—91no—
213C2×C4⋊C4—32no—
214C2×C4⋊C4—92no—
215C2×C4⋊C4—91no—
216C2×C4⋊C4—91no—
217C2×C4⋊C4—91no—
218C2×C4⋊C4—184no—
219C2×C4⋊C4—184no—
220C2×C4⋊C4D3211yescharacteristic
221#95—32no—
222#95—34no—
223#95—34no—
224#95—92no—
225#95—94no—
226#95—94no—
227C23×C3—21no—
228C23×C3C23×D312yes—
229C22×D3—34no—
230C22×D3—34no—
231C22×D3—34no—
232C22×D3—38no—
233C22×D3—38no—
234C22×D3—62no—
235C22×D3—62no—
236C22×D3—62no—
237C22×D3—64no—
238C22×D3—64no—
239C2×C3×C4—22no—
240C2×C3×C4—22no—
241C2×C3×C4—22no—
242C2×C3×C4—22no—
243C2×C3×C4—24no—
244C2×C3×C4—22no—
245C2×C3×C4—22no—
246C2×C3×C4—24no—
247C2×C3×C4—22no—
248C2×C3×C4—22no—
249C2×C3×C4—42no—
250C2×C3×C4—42no—
251C2×C3×C4—64no—
252C2×C3×C4—64no—
253C2×C3×C4—64no—
254C2×C3×C4—68no—
255C2×C3×C4—64no—
256C2×C3×C4D3×D414yes—
257C2×C3×C4D3×Q814yes—
258C2×Dic3—24no—
259C2×Dic3—24no—
260C2×Dic3—24no—
261C2×Dic3—28no—
262C2×Dic3—24no—
263C2×Dic3—34no—
264C2×Dic3—34no—
265C2×Dic3—62no—
266C2×Dic3—62no—
267C2×Dic3—62no—
268C2×Dic3—62no—
269C2×Dic3—62no—
270C2×Dic3—62no—
271C2×Dic3—64no—
272C2×Dic3—62no—
273C2×Dic3—62no—
274C2×Dic3—64no—
275C2×Dic3—122no—
276C2×Dic3—122no—
277C4×D3—616no—
278C4×D3—616no—
279C4×D3—616no—
280C4×D3—128no—
281C4×D3—1216no—
282C4×D3—1216no—
283C4×D3—128no—
284C4×D3—128no—
285C2×C32C2×C22⋊Q811yescharacteristic
286C2×C32C2×#12311yescharacteristic
287C2×C32C2×#12411yescharacteristic
288C2×C32C2×#12512yes—
289C2×C32C2×#12612yes—
290C3⋊D3#40018yescomplemented
291C24—91no—
292C22×C4—34no—
293C22×C4—34no—
294C22×C4—91no—
295C22×C4—91no—
296C22×C4—94no—
297C22×C4—94no—
298C22×C4—91no—
299C22×C4—182no—
300C22×C4—182no—
301C22×C4—184no—
302C22×C4—182no—
303C22×C4—184no—
304C22×C4—184no—
305C22×C4—184no—
306C22×C4—184no—
307C22×C4—188no—
308C22×C4—184no—
309C22×C4C2×D3211yescharacteristic
310C22×C4C2×D3211yescharacteristic
311C22×C4C2×D3211yescharacteristic
312C4⋊C4—22no—
313C4⋊C4—64no—
314C4⋊C4—182no—
315C4⋊C4—182no—
316C4⋊C4—184no—
317C4⋊C4—182no—
318C22×C3—21no—
319C22×C3—21no—
320C22×C3—22no—
321C22×C3—22no—
322C22×C3—21no—
323C22×C3C2×D3×D412yes—
324C22×C3C2×D3×Q812yes—
325C22×C3D3×#4112yes—
326C22×C3D3×#4114yes—
327C22×C3D3×#4114yes—
328C2×D3—38no—
329C2×D3—38no—
330C2×D3—316no—
331C2×D3—316no—
332C2×D3—38no—
333C2×D3—64no—
334C2×D3—64no—
335C2×D3—64no—
336C2×D3—68no—
337C2×D3—68no—
338C3×C4—24no—
339C3×C4—24no—
340C3×C4—24no—
341C3×C4—42no—
342C3×C4—42no—
343C3×C4—42no—
344C3×C4—124no—
345C3×C4—124no—
346Dic3—44no—
347Dic3—44no—
348Dic3—64no—
349Dic3—64no—
350Dic3—64no—
351Dic3—122no—
352Dic3—122no—
353Dic3—122no—
354C32C2×#40011yescharacteristic, complemented, Sylow
355C23—92no—
356C23—92no—
357C23—94no—
358C23—94no—
359C23—92no—
360C23C22×D3211yescharacteristic
361C2×C4—21no—
362C2×C4—22no—
363C2×C4—21no—
364C2×C4—22no—
365C2×C4—21no—
366C2×C4—64no—
367C2×C4—64no—
368C2×C4—64no—
369C2×C4—68no—
370C2×C4—64no—
371C2×C4—92no—
372C2×C4—92no—
373C2×C4—188no—
374C2×C4—188no—
375C2×C4—181no—
376C2×C4—182no—
377C2×C4—181no—
378C2×C4—182no—
379C2×C4—181no—
380C2×C4—364no—
381C2×C4—368no—
382C2×C4—368no—
383C2×C4#379712yes—
384C2×C4#381112yes—
385C2×C3—22no—
386C2×C3—21no—
387C2×C3—21no—
388C2×C3—21no—
389C2×C3—22no—
390C2×C3D3×C22⋊Q812yes—
391C2×C3D3×#12312yes—
392C2×C3D3×#12412yes—
393C2×C3D3×#12514yes—
394C2×C3D3×#12614yes—
395D3—316no—
396D3—68no—
397C22—98no—
398C22—94no—
399C22—94no—
400C22—94no—
401C22—98no—
402C22C2×#379711yescharacteristic
403C22#6430611yescharacteristic
404C22#6431212yes—
405C22#6431912yes—
406C22C2×#381111yescharacteristic
407C4—22no—
408C4—22no—
409C4—41no—
410C4—124no—
411C4—124no—
412C4—182no—
413C4—182no—
414C4—361no—
415C3—21no—
416C3D3×#40012yescomplemented
417C2—98no—
418C2#1059448212yes—
419C2#1059465612yes—
420C2#1059492511yescharacteristic
421C2#1059516911yescharacteristic
422C2#1059543211yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutator, socle, cosocleC23×C32C24
FittingC2×C32×C4⋊C4C22
prime radicalC23×C3⋊D3C23
hypercenterC2×C4⋊C4D32
hypocenterC32C2×#400
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
3. C3×#4986C2semidirect
7. #10591227C2semidirect
8. #10591218C2semidirect
9. #10591217C2semidirect
34. #4986D3semidirect
290. C3⋊D3#400semidirect
354. C32C2×#400semidirect
416. C3D3×#400semidirect

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×#639002
C3×#49862
#105913702
#105912272
#105912182
#105912172
D3×#4003