Finite Group Databasebeta

← #11802486

Subgroups — #11802486

Order 1152.

1097 conjugacy classes of subgroups.

The subgroup lattice has 354 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#870C211yesmaximal, characteristic
2C42×C3⋊Dic3C211yesmaximal, characteristic
3C3×#4936C211yesmaximal, characteristic
4#10591357C212yesmaximal
5#10591274C212yesmaximal
6#10591241C214yesmaximal
7#10591192C214yesmaximal
8Dic3×#125—31nomaximal
9#74150—31nomaximal
10C2×C32×C42C2211yescharacteristic
11C2×C4×C3⋊Dic3C2212yes—
12C2×C4×C3⋊Dic3C2211yescharacteristic
13C2×C4×C3⋊Dic3C2212yes—
14C2×C4×C3⋊Dic3C2211yescharacteristic
15C2×C3×C4⋊Dic3C2212yes—
16C2×C3×C4⋊Dic3C2212yes—
17C2×C3×Dic3⋊C4C2214yes—
18C3×#870C418yescomplemented
19C2×Dic3⋊Dic3C2214yes—
20C2×Dic32C2214yes—
21C3×C3⋊#95C2214yes—
22#63579C2214yes—
23#63579C2214yes—
24C2×C3×#125—31no—
25C2×#870D311yescharacteristic
26C3×#382—31no—
27#4984—32no—
28#4980—34no—
29Dic3×C4⋊C4—32no—
30Dic3×C4⋊C4—32no—
31Dic3×C4⋊C4—34no—
32#4972—32no—
33#4936D311yescharacteristic
34C42×Dic3—31no—
35C42×Dic3—31no—
36C42×Dic3—61no—
37#4652—34no—
38#4649—34no—
39C22×C32×C4C2312yes—
40C22×C32×C4C2311yescharacteristic
41C22×C3⋊Dic3C2311yescharacteristic
42C22×C3⋊Dic3C2312yes—
43C22×C3⋊Dic3C2311yescharacteristic
44C22×C3×Dic3C2314yes—
45C22×C3×Dic3C2314yes—
46C32×C42C2×C414yes—
47C4×C3⋊Dic3—22no—
48C4×C3⋊Dic3—24no—
49C4×C3⋊Dic3—24no—
50C4×C3⋊Dic3Q814yes—
51C3×C4⋊Dic3—24no—
52C3×C4⋊Dic3C2×C418yes—
53C3×Dic3⋊C4C2×C4116yes—
54Dic3⋊Dic3—28no—
55Dic32—28no—
56C4×#125—91noSylow
57C3×#125—38no—
58C2×C3×C4⋊C4—34no—
59C2×C3×C4⋊C4—32no—
60C2×C3×C4⋊C4—32no—
61C2×C3×C42—21no—
62C2×C3×C42C2×D311yescharacteristic
63C2×C3×C42C2×D311yescharacteristic
64C2×C4⋊Dic3—34no—
65C2×C4⋊Dic3C2×D312yes—
66C2×C4⋊Dic3C2×D312yes—
67C2×Dic3⋊C4—34no—
68C2×Dic3⋊C4C2×D314yes—
69C2×C4×Dic3—31no—
70C2×C4×Dic3—31no—
71C2×C4×Dic3—32no—
72C2×C4×Dic3—32no—
73C2×C4×Dic3—31no—
74C2×C4×Dic3—32no—
75C2×C4×Dic3—32no—
76C2×C4×Dic3—31no—
77C2×C4×Dic3—34no—
78C2×C4×Dic3—34no—
79C2×C4×Dic3—61no—
80C2×C4×Dic3—62no—
81C2×C4×Dic3—62no—
82C2×C4×Dic3—61no—
83#870Dic318yescomplemented
84C3×#95—34no—
85C3⋊#95—34no—
86C3⋊#95—34no—
87C3⋊#95—34no—
88C3⋊#95—34no—
89C3⋊#95C2×D314yes—
90C23×C32C2411yescharacteristic
91C2×C32×C4—22no—
92C2×C32×C4—22no—
93C2×C32×C4C22×C414yes—
94C2×C32×C4C22×C412yes—
95C2×C32×C4C2×Q812yes—
96C2×C32×C4#4112yes—
97C2×C3⋊Dic3—22no—
98C2×C3⋊Dic3—22no—
99C2×C3⋊Dic3—22no—
100C2×C3⋊Dic3C2×Q812yes—
101C2×C3⋊Dic3C2×Q812yes—
102C2×C3⋊Dic3#4114yes—
103C2×C3⋊Dic3#4114yes—
104C2×C3×Dic3—24no—
105C2×C3×Dic3—24no—
106C2×C3×Dic3—24no—
107C2×C3×Dic3—24no—
108C2×C3×Dic3—24no—
109C2×C3×Dic3C22×C418yes—
110C2×#125—31no—
111#389—92no—
112#387—94no—
113#382—31no—
114C4×C4⋊C4—94no—
115C4×C4⋊C4—92no—
116C43—91no—
117C22×C3×C4—22no—
118C22×C3×C4—21no—
119C22×C3×C4—34no—
120C22×C3×C4—34no—
121C22×C3×C4C22×D312yes—
122C22×C3×C4C22×D312yes—
123C22×C3×C4C22×D311yescharacteristic
124C22×C3×C4C22×D311yescharacteristic
125C22×Dic3—31no—
126C22×Dic3—31no—
127C22×Dic3—31no—
128C22×Dic3—31no—
129C22×Dic3—32no—
130C22×Dic3—32no—
131C22×Dic3—61no—
132C22×Dic3—61no—
133C22×Dic3—62no—
134C22×Dic3C22×D314yes—
135C22×Dic3C22×D314yes—
136C3×C4⋊C4—316no—
137C3×C4⋊C4—38no—
138C3×C4⋊C4—64no—
139C3×C42—24no—
140C3×C42C4×D314yes—
141C3×C42C2×Dic314yes—
142C4⋊Dic3—24no—
143C4⋊Dic3—68no—
144C4⋊Dic3C2×Dic318yes—
145Dic3⋊C4—68no—
146Dic3⋊C4C2×Dic3116yes—
147C4×Dic3—34no—
148C4×Dic3—34no—
149C4×Dic3—64no—
150C4×Dic3—68no—
151C4×Dic3—68no—
152C4×Dic3—64no—
153C4×Dic3—64no—
154C4×Dic3—64no—
155C4×Dic3—64no—
156C4×Dic3—68no—
157C4×Dic3—68no—
158C4×Dic3—64no—
159C4×Dic3—62no—
160C4×Dic3—62no—
161C22×C32C23×C411yescharacteristic
162C22×C32C22×Q811yescharacteristic
163C22×C32C2×#4111yescharacteristic
164C22×C32C2×#4112yes—
165C22×C32C2×#4112yes—
166C32×C4—24no—
167C32×C4C4×Q814yes—
168C3⋊Dic3—24no—
169C3⋊Dic3—22no—
170C3⋊Dic3#12514yescomplemented
171C3×Dic3—28no—
172C3×Dic3—44no—
173#125—38no—
174C2×C4⋊C4—34no—
175C2×C4⋊C4—32no—
176C2×C4⋊C4—32no—
177C2×C4⋊C4—94no—
178C2×C42—91no—
179C2×C42—94no—
180C2×C42—92no—
181C2×C42—92no—
182C2×C42—91no—
183C2×C42D3211yescharacteristic
184#95—34no—
185#95—94no—
186#95—94no—
187C23×C3—21no—
188C23×C3C23×D311yescharacteristic
189C23×C3C23×D311yescharacteristic
190C2×C3×C4—24no—
191C2×C3×C4—24no—
192C2×C3×C4—22no—
193C2×C3×C4—22no—
194C2×C3×C4—22no—
195C2×C3×C4—22no—
196C2×C3×C4—22no—
197C2×C3×C4—22no—
198C2×C3×C4—24no—
199C2×C3×C4—22no—
200C2×C3×C4—38no—
201C2×C3×C4—64no—
202C2×C3×C4—64no—
203C2×C3×C4—64no—
204C2×C3×C4—64no—
205C2×C3×C4—64no—
206C2×C3×C4C2×C4×D314yes—
207C2×C3×C4C2×C4×D312yes—
208C2×C3×C4#23712yes—
209C2×C3×C4D3×Q812yes—
210C2×C3×C4D3×Q812yes—
211C2×C3×C4#23912yes—
212C2×C3×C4C22×Dic314yes—
213C2×C3×C4C22×Dic312yes—
214C2×Dic3—24no—
215C2×Dic3—24no—
216C2×Dic3—24no—
217C2×Dic3—24no—
218C2×Dic3—24no—
219C2×Dic3—32no—
220C2×Dic3—32no—
221C2×Dic3—34no—
222C2×Dic3—34no—
223C2×Dic3—32no—
224C2×Dic3—32no—
225C2×Dic3—34no—
226C2×Dic3—34no—
227C2×Dic3—62no—
228C2×Dic3—62no—
229C2×Dic3—64no—
230C2×Dic3—64no—
231C2×Dic3—64no—
232C2×Dic3—64no—
233C2×Dic3—64no—
234C2×Dic3—62no—
235C2×Dic3—62no—
236C2×Dic3—62no—
237C2×Dic3—62no—
238C2×Dic3—62no—
239C2×Dic3—62no—
240C2×Dic3C22×Dic318yes—
241C2×C32C2×C4×Q811yescharacteristic
242C2×C32C4×#4112yes—
243C2×C32C2×#12511yescharacteristic
244C2×C32#52912yes—
245C2×C32#53311yescharacteristic
246C22×C4—34no—
247C22×C4—34no—
248C22×C4—91no—
249C22×C4—91no—
250C22×C4—92no—
251C22×C4C2×D3212yes—
252C22×C4C2×D3211yescharacteristic
253C4⋊C4—316no—
254C4⋊C4—38no—
255C4⋊C4—64no—
256C4⋊C4—188no—
257C42—94no—
258C42—184no—
259C42—184no—
260C42—188no—
261C42—182no—
262C42D3×Dic314yes—
263C22×C3—21no—
264C22×C3—21no—
265C22×C3—22no—
266C22×C3—22no—
267C22×C3—21no—
268C22×C3C22×C4×D311yescharacteristic
269C22×C3C2×#23711yescharacteristic
270C22×C3C2×D3×Q811yescharacteristic
271C22×C3C2×D3×Q811yescharacteristic
272C22×C3C2×#23911yescharacteristic
273C22×C3D3×#4112yes—
274C22×C3D3×#4112yes—
275C22×C3D3×#4112yes—
276C22×C3D3×#4112yes—
277C22×C3C23×Dic311yescharacteristic
278C3×C4—28no—
279C3×C4—24no—
280C3×C4—24no—
281C3×C4—24no—
282C3×C4—68no—
283C3×C4—124no—
284C3×C4#88714yes—
285C3×C4Q8×Dic314yes—
286Dic3—28no—
287Dic3—34no—
288Dic3—34no—
289Dic3—44no—
290Dic3—64no—
291Dic3—64no—
292Dic3—68no—
293Dic3—64no—
294Dic3—62no—
295Dic3—62no—
296Dic3—64no—
297C32C4×#12511yescharacteristic, complemented, Sylow
298C23C22×D3211yescharacteristic
299C2×C4—22no—
300C2×C4—22no—
301C2×C4—38no—
302C2×C4—64no—
303C2×C4—64no—
304C2×C4—64no—
305C2×C4—64no—
306C2×C4—64no—
307C2×C4—92no—
308C2×C4—94no—
309C2×C4—92no—
310C2×C4—94no—
311C2×C4—182no—
312C2×C4—182no—
313C2×C4—182no—
314C2×C4#379612yes—
315C2×C4#379712yes—
316C2×C4C2×D3×Dic314yes—
317C2×C4C2×D3×Dic312yes—
318C2×C3—21no—
319C2×C3—21no—
320C2×C3—22no—
321C2×C3—22no—
322C2×C3—21no—
323C2×C3C2×#88711yescharacteristic
324C2×C3#552212yes—
325C2×C3#568012yes—
326C2×C3D3×#12511yescharacteristic
327C2×C3D3×#12511yescharacteristic
328C2×C3#568811yescharacteristic
329C2×C3#568811yescharacteristic
330C2×C3#569112yes—
331C2×C3C2×Q8×Dic311yescharacteristic
332C2×C3Dic3×#4112yes—
333C22C2×#379611yescharacteristic
334C22C2×#379711yescharacteristic
335C22#6430612yes—
336C22#6430612yes—
337C22C22×D3×Dic311yescharacteristic
338C4—24no—
339C4—68no—
340C4—94no—
341C4—124no—
342C4—182no—
343C4—184no—
344C4#6384314yes—
345C3—21no—
346C3#7415011yescharacteristic, complemented
347C3Dic3×#12511yescharacteristic, complemented
348C2#1059385411yescharacteristic
349C2#1059394312yes—
350C2#1059394811yescharacteristic
351C2C2×#6384311yescharacteristic
352C2#1059495812yes—
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC2×C32×C42C22
socle, prime radical, cosocleC23×C32C24
hypercenterC2×C42D32
hypocenterC32C4×#125
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
18. C3×#870C4semidirect
83. #870Dic3semidirect
170. C3⋊Dic3#125semidirect
297. C32C4×#125semidirect
346. C3#74150semidirect
347. C3Dic3×#125semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#8702
C42×C3⋊Dic32
C3×#49362
#105913572
#105912742
#105912412
#105911922
Dic3×#1253
#741503