Finite Group Databasebeta

← C4×#63872 #11802496

Subgroups — C4×#63872 #11802496

Order 1152.

1097 conjugacy classes of subgroups.

The subgroup lattice has 324 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63872C211yesmaximal, characteristic
2C42×C3⋊Dic3C211yesmaximal, characteristic
3C3×C4×C4⋊Dic3C212yesmaximal
4#10591357C212yesmaximal
5#10591335C214yesmaximal
6C4×Dic3⋊Dic3C214yesmaximal
7#10591230C211yesmaximal, characteristic
8C4×#890—32nomaximal
9C2×C32×C42C2211yescharacteristic
10C2×C4×C3⋊Dic3C2212yes—
11C2×C4×C3⋊Dic3C2212yes—
12C2×C4×C3⋊Dic3C2211yescharacteristic
13C2×C4×C3⋊Dic3C2211yescharacteristic
14C2×C3×C4⋊Dic3C2212yes—
15C2×C3×C4⋊Dic3C2212yes—
16C2×C3×C4×Dic3C2214yes—
17C2×Dic3⋊Dic3C2214yes—
18C2×Dic3⋊Dic3C2214yes—
19#63872C418yesdirect product factor
20C3×C3⋊#95C2214yes—
21#63579C2214yes—
22#63579C2214yes—
23C2×#890—32no—
24C3×C4×C4⋊C4—32no—
25#4984—32no—
26#4977—32no—
27#4972—32no—
28C4×C4⋊Dic3—34no—
29C4×C4⋊Dic3D312yes—
30C4×Dic3⋊C4—34no—
31C42×Dic3—32no—
32C42×Dic3—61no—
33#4655—34no—
34#4654—34no—
35C22×C32×C4C2311yescharacteristic
36C22×C32×C4C2311yescharacteristic
37C22×C32×C4C2311yescharacteristic
38C22×C3⋊Dic3C2312yes—
39C22×C3⋊Dic3C2312yes—
40C22×C3×Dic3C2314yes—
41C22×C3×Dic3C2314yes—
42C32×C42Q814yes—
43C4×C3⋊Dic3—22no—
44C4×C3⋊Dic3—24no—
45C4×C3⋊Dic3—24no—
46C4×C3⋊Dic3C2×C414yes—
47C3×C4⋊Dic3—24no—
48C3×C4⋊Dic3C2×C418yes—
49C3×C4×Dic3—28no—
50Dic3⋊Dic3—28no—
51Dic3⋊Dic3C2×C4116yes—
52C4×#125—91noSylow
53C2×C3×C4⋊C4—32no—
54C2×C3×C4⋊C4—32no—
55C2×C3×C42—21no—
56C2×C3×C42—34no—
57C2×C3×C42C2×D312yes—
58C2×C4⋊Dic3—34no—
59C2×C4⋊Dic3—34no—
60C2×C4⋊Dic3C2×D312yes—
61C2×C4⋊Dic3C2×D312yes—
62C2×Dic3⋊C4—34no—
63C2×Dic3⋊C4—34no—
64C2×C4×Dic3—32no—
65C2×C4×Dic3—32no—
66C2×C4×Dic3—32no—
67C2×C4×Dic3—32no—
68C2×C4×Dic3—32no—
69C2×C4×Dic3—32no—
70C2×C4×Dic3—61no—
71C2×C4×Dic3—62no—
72C2×C4×Dic3—61no—
73C2×C4×Dic3—62no—
74C2×C4×Dic3C2×D314yes—
75#890—316no—
76C3×#95—34no—
77C3⋊#95—34no—
78C3⋊#95—34no—
79C3⋊#95—34no—
80C3⋊#95—34no—
81C3⋊#95C2×D314yes—
82C23×C32C2411yescharacteristic
83C2×C32×C4—22no—
84C2×C32×C4C22×C412yes—
85C2×C32×C4C2×Q812yes—
86C2×C32×C4C2×Q812yes—
87C2×C32×C4C2×Q812yes—
88C2×C32×C4#4112yes—
89C2×C32×C4#4114yes—
90C2×C3⋊Dic3—22no—
91C2×C3⋊Dic3—22no—
92C2×C3⋊Dic3—22no—
93C2×C3⋊Dic3—22no—
94C2×C3⋊Dic3C22×C414yes—
95C2×C3⋊Dic3#4114yes—
96C2×C3×Dic3—24no—
97C2×C3×Dic3—24no—
98C2×C3×Dic3—24no—
99C2×C3×Dic3—24no—
100C2×C3×Dic3—24no—
101C2×C3×Dic3C22×C418yes—
102C2×#125—91no—
103#389—92no—
104#387—94no—
105#382—91no—
106C4×C4⋊C4—32no—
107C4×C4⋊C4—94no—
108C43—91no—
109C22×C3×C4—21no—
110C22×C3×C4—21no—
111C22×C3×C4—21no—
112C22×C3×C4—34no—
113C22×C3×C4—34no—
114C22×C3×C4C22×D312yes—
115C22×C3×C4C22×D312yes—
116C22×C3×C4C22×D312yes—
117C22×Dic3—32no—
118C22×Dic3—32no—
119C22×Dic3—32no—
120C22×Dic3—32no—
121C22×Dic3—62no—
122C22×Dic3—62no—
123C22×Dic3C22×D314yes—
124C22×Dic3C22×D314yes—
125C3×C4⋊C4—38no—
126C3×C4⋊C4—64no—
127C3×C42—24no—
128C3×C42—68no—
129C3×C42Dic618yes—
130C4⋊Dic3—24no—
131C4⋊Dic3—316no—
132C4⋊Dic3—68no—
133C4⋊Dic3C4×D318yes—
134Dic3⋊C4—316no—
135Dic3⋊C4—68no—
136C4×Dic3—28no—
137C4×Dic3—38no—
138C4×Dic3—64no—
139C4×Dic3—64no—
140C4×Dic3—64no—
141C4×Dic3—68no—
142C4×Dic3—68no—
143C4×Dic3—64no—
144C4×Dic3—64no—
145C4×Dic3—64no—
146C4×Dic3—64no—
147C22×C32C23×C411yescharacteristic
148C22×C32C22×Q811yescharacteristic
149C22×C32C2×#4111yescharacteristic
150C22×C32C2×#4112yes—
151C22×C32C2×#4112yes—
152C32×C4—22no—
153C32×C4C4×Q814yes—
154C32×C4#12514yescomplemented
155C3⋊Dic3—24no—
156C3⋊Dic3—24no—
157C3×Dic3—28no—
158C3×Dic3—44no—
159#125—98no—
160C2×C4⋊C4—32no—
161C2×C4⋊C4—32no—
162C2×C4⋊C4—94no—
163C2×C4⋊C4—94no—
164C2×C42—34no—
165C2×C42—91no—
166C2×C42—92no—
167C2×C42—91no—
168C2×C42—92no—
169C2×C42D3211yescharacteristic
170#95—34no—
171#95—94no—
172#95—94no—
173C23×C3—21no—
174C23×C3C23×D312yes—
175C2×C3×C4—24no—
176C2×C3×C4—22no—
177C2×C3×C4—22no—
178C2×C3×C4—24no—
179C2×C3×C4—22no—
180C2×C3×C4—22no—
181C2×C3×C4—22no—
182C2×C3×C4—22no—
183C2×C3×C4—22no—
184C2×C3×C4—38no—
185C2×C3×C4—64no—
186C2×C3×C4—64no—
187C2×C3×C4—64no—
188C2×C3×C4—64no—
189C2×C3×C4—64no—
190C2×C3×C4C2×Dic614yes—
191C2×C3×C4C2×Dic614yes—
192C2×C3×C4C2×Dic614yes—
193C2×C3×C4C2×C4×D314yes—
194C2×C3×C4#23514yes—
195C2×C3×C4#23714yes—
196C2×C3×C4#23914yes—
197C2×Dic3—24no—
198C2×Dic3—24no—
199C2×Dic3—24no—
200C2×Dic3—24no—
201C2×Dic3—24no—
202C2×Dic3—34no—
203C2×Dic3—34no—
204C2×Dic3—34no—
205C2×Dic3—34no—
206C2×Dic3—64no—
207C2×Dic3—64no—
208C2×Dic3—64no—
209C2×Dic3—64no—
210C2×Dic3—64no—
211C2×Dic3—64no—
212C2×Dic3—62no—
213C2×Dic3—62no—
214C2×Dic3—62no—
215C2×Dic3—62no—
216C2×Dic3—62no—
217C2×Dic3—62no—
218C2×Dic3—62no—
219C2×Dic3—62no—
220C2×Dic3C2×C4×D318yes—
221C2×C32C2×C4×Q811yescharacteristic
222C2×C32C4×#4112yes—
223C2×C32C2×#12511yescharacteristic
224C2×C32#52912yes—
225C2×C32#53311yescharacteristic
226C22×C4—34no—
227C22×C4—34no—
228C22×C4—92no—
229C22×C4—92no—
230C22×C4C2×D3211yescharacteristic
231C22×C4C2×D3211yescharacteristic
232C22×C4C2×D3211yescharacteristic
233C4⋊C4—38no—
234C4⋊C4—64no—
235C4⋊C4—916no—
236C4⋊C4—188no—
237C42—68no—
238C42—94no—
239C42—184no—
240C42—184no—
241C42—182no—
242C42#62714yes—
243C22×C3—22no—
244C22×C3—21no—
245C22×C3—21no—
246C22×C3—22no—
247C22×C3—21no—
248C22×C3C22×Dic612yes—
249C22×C3C22×C4×D312yes—
250C22×C3C2×#23512yes—
251C22×C3C2×#23712yes—
252C22×C3C2×#23912yes—
253C22×C3D3×#4112yes—
254C22×C3D3×#4112yes—
255C3×C4—24no—
256C3×C4—24no—
257C3×C4—24no—
258C3×C4—24no—
259C3×C4—68no—
260C3×C4—124no—
261C3×C4C4×Dic618yes—
262C3×C4#89018yescomplemented
263Dic3—28no—
264Dic3—44no—
265Dic3—68no—
266Dic3—68no—
267Dic3—64no—
268Dic3—64no—
269Dic3—64no—
270Dic3—64no—
271C32C4×#12511yescharacteristic, complemented, Sylow
272C23C22×D3211yescharacteristic
273C2×C4—22no—
274C2×C4—38no—
275C2×C4—64no—
276C2×C4—64no—
277C2×C4—64no—
278C2×C4—64no—
279C2×C4—64no—
280C2×C4—94no—
281C2×C4—94no—
282C2×C4—182no—
283C2×C4—182no—
284C2×C4—182no—
285C2×C4—182no—
286C2×C4#379614yes—
287C2×C4#379812yes—
288C2×C4C4×D3212yes—
289C2×C4C2×#62712yes—
290C2×C4C2×#62712yes—
291C2×C4C2×#62712yes—
292C2×C3—21no—
293C2×C3—22no—
294C2×C3—22no—
295C2×C3—21no—
296C2×C3—21no—
297C2×C3C2×C4×Dic612yes—
298C2×C3C2×#89012yes—
299C2×C3#551712yes—
300C2×C3C4×#23712yes—
301C2×C3#555712yes—
302C2×C3C4×#23912yes—
303C2×C3#558012yes—
304C22C2×#379612yes—
305C22C2×#379811yescharacteristic
306C22C2×C4×D3211yescharacteristic
307C22#6430612yes—
308C22C22×#62711yescharacteristic
309C4—22no—
310C4—68no—
311C4—124no—
312C4—184no—
313C4—184no—
314C4#6387214yesdirect product factor
315C4C4×#62714yes—
316C3—21no—
317C3C4×#89012yescomplemented
318C2#1059387512yes—
319C2C4×#379612yes—
320C2C2×#6387211yescharacteristic
321C2C2×C4×#62711yescharacteristic
322C2#1059505011yescharacteristic
subgroupG/H
centerC22×C4C2×D32
commutatorC22×C32C23×C4
FrattiniC23C22×D32
FittingC2×C32×C42C22
socle, prime radical, cosocleC23×C32C24
hypercenterC2×C42D32
hypocenterC32C4×#125
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22×C4 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
19. #63872C4direct (N × H)
154. C32×C4#125semidirect
262. C3×C4#890semidirect
271. C32C4×#125semidirect
314. C4#63872direct (N × H)
317. C3C4×#890semidirect

Maximal subgroups

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

subgroupindex
C2×#638722
C42×C3⋊Dic32
C3×C4×C4⋊Dic32
#105913572
#105913352
C4×Dic3⋊Dic32
#105912302
C4×#8903