Finite Group Databasebeta

← #11808533

Subgroups — #11808533

Order 1152.

1373 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63900C211yesmaximal, characteristic
2C2×#63883C211yesmaximal, characteristic
3C3⋊D3×#95C211yesmaximal, characteristic
4C3×#4659C212yesmaximal, complemented
5#10591370C212yesmaximal
6#10591370C212yesmaximal
7#10591225C212yesmaximal, complemented
8#10591211C214yesmaximal, complemented
9D3×#400—32nomaximal
10C22×C4×C3⋊D3C2212yes—
11C22×C4×C3⋊D3C2211yescharacteristic
12C22×#624C2211yescharacteristic
13C22×#624C2212yes—
14C22×#624C2211yescharacteristic
15C2×C3×C4⋊Dic3C2212yes—
16C2×C3×Dic3⋊C4C2212yes—
17C2×#3724C2212yes—
18C2×Dic3⋊Dic3C2212yes—
19#63900—24no—
20#63883—24no—
21C32×#95C2211yescharacteristic
22#63658C2212yes—
23#63658C2211yescharacteristic
24C3×C3⋊#95C2214yes—
25C3×C3⋊#95C2214yes—
26#63579C2214yes—
27#63579C2214yes—
28C2×D3×C4⋊C4—32no—
29C2×D3×C4⋊C4—32no—
30C3×#400—32no—
31#4986—32no—
32#4985—32no—
33D3×#95—32no—
34D3×#95—34no—
35D3×#95—34no—
36D3×#95—61no—
37#4660—34no—
38#4659D312yescomplemented
39#4658—34no—
40C23×C3⋊D3C2311yescharacteristic
41C22×C32×C4C2312yes—
42C22×C32×C4C2311yescharacteristic
43C22×C3⋊Dic3C2312yes—
44C22×C3⋊Dic3C2311yescharacteristic
45C2×C4×C3⋊D3—24no—
46C2×C4×C3⋊D3—24no—
47C2×C4×C3⋊D3—24no—
48C2×C4×C3⋊D3—24no—
49C2×C4×C3⋊D3D414yes—
50C22×C3×Dic3C2312yes—
51C22×C3×Dic3C2314yes—
52C22×C3×Dic3C2312yes—
53C2×#624—22no—
54C2×#624—22no—
55C2×#624—22no—
56C2×#624—24no—
57C2×#624—24no—
58C2×#624—28no—
59C2×#624Q814yes—
60C3×C4⋊Dic3—24no—
61C3×Dic3⋊C4—24no—
62#3724—24no—
63Dic3⋊Dic3—24no—
64C2×#400—91noSylow
65C22×C4×D3—32no—
66C22×C4×D3—32no—
67C22×C4×D3—34no—
68C22×C4×D3—34no—
69C22×C4×D3—32no—
70C22×C4×D3—61no—
71C22×C4×D3—62no—
72C2×C3×C4⋊C4—32no—
73C2×C3×C4⋊C4—32no—
74C2×C4⋊Dic3—32no—
75C2×C4⋊Dic3C2×D312yes—
76C2×Dic3⋊C4—32no—
77C2×Dic3⋊C4—34no—
78C2×Dic3⋊C4C2×D312yes—
79D3×C4⋊C4—68no—
80D3×C4⋊C4—68no—
81C3×#95—21no—
82C3×#95—34no—
83C3×#95—34no—
84C3×#95C2×D312yes—
85C3⋊#95—34no—
86C3⋊#95—32no—
87C3⋊#95—34no—
88C3⋊#95—34no—
89C3⋊#95—34no—
90C3⋊#95—34no—
91C3⋊#95—62no—
92C3⋊#95—61no—
93C3⋊#95C2×D314yes—
94C3⋊#95C2×D314yes—
95C23×C32C2411yescharacteristic
96C22×C3⋊D3C2×D412yes—
97C22×C3⋊D3C2×Q812yes—
98C22×C3⋊D3#4112yes—
99C22×C3⋊D3#4114yes—
100C22×C3⋊D3#4114yes—
101C2×C32×C4—22no—
102C2×C32×C4—22no—
103C2×C32×C4—22no—
104C2×C32×C4—22no—
105C2×C32×C4C2×D412yes—
106C2×C3⋊Dic3—22no—
107C2×C3⋊Dic3—22no—
108C2×C3⋊Dic3—22no—
109C2×C3⋊Dic3—22no—
110C2×C3⋊Dic3C2×D412yes—
111C4×C3⋊D3—28no—
112C4×C3⋊D3—48no—
113C2×C3×Dic3—22no—
114C2×C3×Dic3—22no—
115C2×C3×Dic3—22no—
116C2×C3×Dic3—24no—
117C2×C3×Dic3—24no—
118C2×C3×Dic3—28no—
119C2×C3×Dic3C2×Q814yes—
120#624—28no—
121#624—44no—
122#624—48no—
123C22×C4⋊C4—91no—
124C22×C4⋊C4—91no—
125#400—32no—
126#400—94no—
127#400—92no—
128C2×#95—92no—
129C2×#95—92no—
130C2×#95—91no—
131C23×D3—32no—
132C23×D3—61no—
133C22×C3×C4—22no—
134C22×C3×C4—21no—
135C22×C3×C4—32no—
136C22×C3×C4—34no—
137C22×C3×C4—32no—
138C22×C3×C4C22×D314yes—
139C22×C3×C4C22×D312yes—
140C22×Dic3—32no—
141C22×Dic3—34no—
142C22×Dic3—61no—
143C22×Dic3—62no—
144C22×Dic3C22×D314yes—
145C22×Dic3C22×D312yes—
146C22×Dic3C22×D312yes—
147C2×C4×D3—38no—
148C2×C4×D3—38no—
149C2×C4×D3—64no—
150C2×C4×D3—64no—
151C2×C4×D3—64no—
152C2×C4×D3—68no—
153C2×C4×D3—64no—
154C2×C4×D3—68no—
155C2×C4×D3—616no—
156C2×C4×D3—68no—
157C2×C4×D3—68no—
158C2×C4×D3—68no—
159C2×C4×D3—68no—
160C2×C4×D3—68no—
161C2×C4×D3—124no—
162C2×C4×D3—124no—
163C2×C4×D3—124no—
164C3×C4⋊C4—64no—
165C3×C4⋊C4—64no—
166C4⋊Dic3—24no—
167C4⋊Dic3—64no—
168Dic3⋊C4—24no—
169Dic3⋊C4—64no—
170Dic3⋊C4—68no—
171C22×C32C22×D411yescharacteristic
172C22×C32C22×Q811yescharacteristic
173C22×C32C2×#4111yescharacteristic
174C22×C32C2×#4112yes—
175C22×C32C2×#4112yes—
176C2×C3⋊D3C22⋊Q814yes—
177C2×C3⋊D3#12314yes—
178C2×C3⋊D3#12414yes—
179C2×C3⋊D3#12518yes—
180C2×C3⋊D3#12618yes—
181C32×C4—22no—
182C32×C4—42no—
183C3⋊Dic3—22no—
184C3⋊Dic3—42no—
185C3×Dic3—24no—
186C3×Dic3—42no—
187C3×Dic3—44no—
188C23×C4—91no—
189C23×C4—92no—
190C23×C4—91no—
191C23×C4—91no—
192C23×C4—92no—
193C2×C4⋊C4—32no—
194C2×C4⋊C4—32no—
195C2×C4⋊C4—92no—
196C2×C4⋊C4—92no—
197C2×C4⋊C4—184no—
198C2×C4⋊C4—184no—
199#95—34no—
200#95—34no—
201#95—94no—
202#95—94no—
203#95—92no—
204#95—91no—
205#95D3211yescharacteristic
206C23×C3—21no—
207C23×C3C23×D312yes—
208C22×D3—34no—
209C22×D3—34no—
210C22×D3—38no—
211C22×D3—38no—
212C22×D3—34no—
213C22×D3—62no—
214C22×D3—62no—
215C22×D3—64no—
216C22×D3—64no—
217C22×D3—62no—
218C2×C3×C4—24no—
219C2×C3×C4—24no—
220C2×C3×C4—24no—
221C2×C3×C4—24no—
222C2×C3×C4—24no—
223C2×C3×C4—22no—
224C2×C3×C4—34no—
225C2×C3×C4—42no—
226C2×C3×C4—42no—
227C2×C3×C4—42no—
228C2×C3×C4—62no—
229C2×C3×C4—62no—
230C2×C3×C4—62no—
231C2×C3×C4—64no—
232C2×C3×C4—68no—
233C2×C3×C4—64no—
234C2×C3×C4D3×D414yes—
235C2×Dic3—22no—
236C2×Dic3—22no—
237C2×Dic3—22no—
238C2×Dic3—24no—
239C2×Dic3—28no—
240C2×Dic3—24no—
241C2×Dic3—34no—
242C2×Dic3—62no—
243C2×Dic3—64no—
244C2×Dic3—64no—
245C2×Dic3—64no—
246C2×Dic3—64no—
247C2×Dic3—64no—
248C2×Dic3—122no—
249C2×Dic3—122no—
250C2×Dic3—122no—
251C2×Dic3D3×Q814yes—
252C4×D3—616no—
253C4×D3—616no—
254C4×D3—128no—
255C4×D3—128no—
256C4×D3—1216no—
257C4×D3—1216no—
258C4×D3—1216no—
259C2×C32C2×C22⋊Q811yescharacteristic
260C2×C32C2×#12311yescharacteristic
261C2×C32C2×#12411yescharacteristic
262C2×C32C2×#12512yes—
263C2×C32C2×#12612yes—
264C3⋊D3#40018yescomplemented
265C24—91no—
266C22×C4—32no—
267C22×C4—34no—
268C22×C4—32no—
269C22×C4—94no—
270C22×C4—91no—
271C22×C4—94no—
272C22×C4—92no—
273C22×C4—184no—
274C22×C4—184no—
275C22×C4—184no—
276C22×C4—184no—
277C22×C4—182no—
278C22×C4—182no—
279C22×C4—184no—
280C22×C4—182no—
281C22×C4—188no—
282C22×C4—184no—
283C22×C4C2×D3212yes—
284C22×C4C2×D3211yescharacteristic
285C4⋊C4—64no—
286C4⋊C4—64no—
287C4⋊C4—184no—
288C4⋊C4—184no—
289C22×C3—21no—
290C22×C3—22no—
291C22×C3—21no—
292C22×C3—22no—
293C22×C3—21no—
294C22×C3C2×D3×D412yes—
295C22×C3C2×D3×Q812yes—
296C22×C3D3×#4114yes—
297C22×C3D3×#4114yes—
298C22×C3D3×#4112yes—
299C2×D3—38no—
300C2×D3—38no—
301C2×D3—316no—
302C2×D3—316no—
303C2×D3—38no—
304C2×D3—64no—
305C2×D3—68no—
306C2×D3—64no—
307C2×D3—64no—
308C2×D3—68no—
309C3×C4—24no—
310C3×C4—42no—
311C3×C4—44no—
312C3×C4—44no—
313C3×C4—64no—
314C3×C4—122no—
315C3×C4—124no—
316Dic3—24no—
317Dic3—42no—
318Dic3—44no—
319Dic3—64no—
320Dic3—122no—
321Dic3—124no—
322Dic3—124no—
323C32C2×#40011yescharacteristic, complemented, Sylow
324C23—92no—
325C23—94no—
326C23—92no—
327C23—94no—
328C23—92no—
329C23C22×D3211yescharacteristic
330C2×C4—22no—
331C2×C4—22no—
332C2×C4—22no—
333C2×C4—22no—
334C2×C4—34no—
335C2×C4—62no—
336C2×C4—62no—
337C2×C4—64no—
338C2×C4—62no—
339C2×C4—68no—
340C2×C4—64no—
341C2×C4—92no—
342C2×C4—188no—
343C2×C4—188no—
344C2×C4—182no—
345C2×C4—182no—
346C2×C4—182no—
347C2×C4—182no—
348C2×C4—368no—
349C2×C4—368no—
350C2×C4—364no—
351C2×C4#380212yes—
352C2×C3—21no—
353C2×C3—22no—
354C2×C3—22no—
355C2×C3—21no—
356C2×C3—21no—
357C2×C3D3×C22⋊Q812yes—
358C2×C3D3×#12312yes—
359C2×C3D3×#12412yes—
360C2×C3D3×#12514yes—
361C2×C3D3×#12614yes—
362D3—316no—
363D3—68no—
364C22—94no—
365C22—98no—
366C22—98no—
367C22—94no—
368C22—94no—
369C22C2×#380211yescharacteristic
370C22#6430612yes—
371C22#6431211yescharacteristic
372C22#6431212yes—
373C22D32×Q811yescharacteristic
374C4—22no—
375C4—42no—
376C4—64no—
377C4—124no—
378C4—122no—
379C4—182no—
380C4—362no—
381C3—21no—
382C3D3×#40012yescomplemented
383C2—98no—
384C2#1059400911yescharacteristic
385C2#1059415412yes—
386C2#1059429511yescharacteristic
387C2#1059439912yes—
388C2#1059463111yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutator, socle, cosocleC23×C32C24
FittingC32×#95C22
prime radicalC23×C3⋊D3C23
hypercenter#95D32
hypocenterC32C2×#400
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ #95

Complements

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

NH ≅ G/Ntype
4. C3×#4659C2semidirect
7. #10591225C2semidirect
8. #10591211C2semidirect
38. #4659D3semidirect
264. C3⋊D3#400semidirect
323. C32C2×#400semidirect
382. C3D3×#400semidirect

Maximal subgroups

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

subgroupindex
C2×#639002
C2×#638832
C3⋊D3×#952
C3×#46592
#105913702
#105912252
#105912112
D3×#4003