Finite Group Databasebeta

← #11801786

Subgroups — #11801786

Order 1152.

1129 conjugacy classes of subgroups.

The subgroup lattice has 337 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#627C211yesmaximal, characteristic
2C42×C3⋊Dic3C211yesmaximal, characteristic
3C3×#4932C212yesmaximal
4#10591396C212yesmaximal
5C4×#3724C211yesmaximal, characteristic
6#10591335C214yesmaximal
7C4×Dic3⋊Dic3C212yesmaximal
8#10591328C212yesmaximal
9#73384—32nomaximal
10C22×#627C2211yescharacteristic
11C2×C32×C42C2211yescharacteristic
12C2×C4×C3⋊Dic3C2212yes—
13C2×C4×C3⋊Dic3C2211yescharacteristic
14C2×C4×C3⋊Dic3C2212yes—
15C2×C4×C3⋊Dic3C2211yescharacteristic
16C2×C3×C4×Dic3C2212yes—
17C2×C3×C4×Dic3C2212yes—
18C2×#3724C2212yes—
19C2×#3724C2211yescharacteristic
20C2×Dic3⋊Dic3C2214yes—
21C2×Dic3⋊Dic3C2212yes—
22C4×#627C418yescomplemented
23C3×C3⋊#95C2214yes—
24C3×C3⋊#95C2214yes—
25#63579C2214yes—
26#63579C2212yes—
27C2×C4×Dic6—32no—
28C3×#376—32no—
29C4×C4⋊Dic3—32no—
30#4932D312yes—
31C4×Dic3⋊C4—32no—
32C4×Dic3⋊C4—32no—
33C42×Dic3—32no—
34C42×Dic3—61no—
35#4655—34no—
36#4654—34no—
37#4647—34no—
38#4646—34no—
39C22×C32×C4C2312yes—
40C22×C32×C4C2311yescharacteristic
41C22×C3⋊Dic3C2311yescharacteristic
42C22×C3⋊Dic3C2312yes—
43C22×C3⋊Dic3C2311yescharacteristic
44C22×C3×Dic3C2314yes—
45C22×C3×Dic3C2312yes—
46C22×C3×Dic3C2312yes—
47C2×#627—24no—
48C2×#627C2×C414yes—
49C32×C42Q814yescomplemented
50C4×C3⋊Dic3—22no—
51C4×C3⋊Dic3—24no—
52C4×C3⋊Dic3—24no—
53C4×C3⋊Dic3C2×C414yes—
54C3×C4×Dic3—24no—
55C3×C4×Dic3C2×C418yes—
56#3724—24no—
57#3724C2×C414yes—
58Dic3⋊Dic3—28no—
59Dic3⋊Dic3C2×C418yes—
60#2295—91noSylow
61C22×Dic6—32no—
62C2×C3×C42—21no—
63C2×C3×C42—32no—
64C2×C3×C42—32no—
65C2×C3×C42C2×D312yes—
66C2×C4⋊Dic3—32no—
67C2×C4⋊Dic3—34no—
68C2×Dic3⋊C4—32no—
69C2×Dic3⋊C4—32no—
70C2×Dic3⋊C4—34no—
71C2×Dic3⋊C4—34no—
72C2×C4×Dic3—32no—
73C2×C4×Dic3—34no—
74C2×C4×Dic3—34no—
75C2×C4×Dic3—32no—
76C2×C4×Dic3—61no—
77C2×C4×Dic3—62no—
78C2×C4×Dic3—62no—
79C2×C4×Dic3—61no—
80C2×C4×Dic3C2×D312yes—
81C2×C4×Dic3C2×D312yes—
82C4×Dic6—316no—
83C3×#95—34no—
84C3×#95—34no—
85C3⋊#95—34no—
86C3⋊#95—34no—
87C3⋊#95—34no—
88C3⋊#95C2×D314yes—
89C3⋊#95C2×D314yes—
90C23×C32C2411yescharacteristic
91C2×C32×C4—22no—
92C2×C32×C4—22no—
93C2×C32×C4C22×C412yes—
94C2×C32×C4C2×Q814yes—
95C2×C32×C4C2×Q812yes—
96C2×C32×C4#4112yes—
97C2×C3⋊Dic3—22no—
98C2×C3⋊Dic3—22no—
99C2×C3⋊Dic3—22no—
100C2×C3⋊Dic3C22×C412yes—
101C2×C3⋊Dic3C22×C412yes—
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×C414yes—
110C2×C3×Dic3C22×C414yes—
111#627—28no—
112C2×C4×Q8—91no—
113#391—92no—
114#389—92no—
115#387—94no—
116C4×C4⋊C4—91no—
117C4×C4⋊C4—92no—
118#376—32no—
119C43—91no—
120C22×C3×C4—22no—
121C22×C3×C4—21no—
122C22×C3×C4—32no—
123C22×C3×C4—32no—
124C22×C3×C4—34no—
125C22×C3×C4C22×D314yes—
126C22×C3×C4C22×D312yes—
127C22×Dic3—32no—
128C22×Dic3—32no—
129C22×Dic3—34no—
130C22×Dic3—61no—
131C22×Dic3—61no—
132C22×Dic3—62no—
133C22×Dic3C22×D314yes—
134C22×Dic3C22×D312yes—
135C22×Dic3C22×D312yes—
136C2×Dic6—38no—
137C2×Dic6—68no—
138C3×C42—24no—
139C3×C42—38no—
140C3×C42—64no—
141C3×C42Dic618yescomplemented
142C4⋊Dic3—38no—
143C4⋊Dic3—68no—
144Dic3⋊C4—38no—
145Dic3⋊C4—38no—
146Dic3⋊C4—68no—
147Dic3⋊C4—68no—
148C4×Dic3—24no—
149C4×Dic3—38no—
150C4×Dic3—64no—
151C4×Dic3—68no—
152C4×Dic3—68no—
153C4×Dic3—68no—
154C4×Dic3—68no—
155C4×Dic3—64no—
156C4×Dic3—64no—
157C4×Dic3C4×D318yes—
158C22×C32C23×C411yescharacteristic
159C22×C32C22×Q811yescharacteristic
160C22×C32C2×#4111yescharacteristic
161C22×C32C2×#4112yes—
162C22×C32C2×#4112yes—
163C32×C4—24no—
164C32×C4C4×Q814yes—
165C3⋊Dic3—22no—
166C3⋊Dic3—24no—
167C3⋊Dic3#11714yes—
168C3×Dic3—24no—
169C3×Dic3—24no—
170C3×Dic3—44no—
171C22×Q8—91no—
172C4×Q8—98no—
173C2×C4⋊C4—92no—
174C2×C4⋊C4—91no—
175C2×C4⋊C4—94no—
176C2×C4⋊C4—92no—
177C2×C42—32no—
178C2×C42—32no—
179C2×C42—91no—
180C2×C42—92no—
181C2×C42—92no—
182C2×C42—91no—
183C2×C42D3211yescharacteristic
184#95—34no—
185#95—34no—
186#95—92no—
187#95—94no—
188C23×C3—21no—
189C23×C3C23×D312yes—
190C2×C3×C4—24no—
191C2×C3×C4—24no—
192C2×C3×C4—24no—
193C2×C3×C4—24no—
194C2×C3×C4—22no—
195C2×C3×C4—22no—
196C2×C3×C4—24no—
197C2×C3×C4—22no—
198C2×C3×C4—34no—
199C2×C3×C4—34no—
200C2×C3×C4—64no—
201C2×C3×C4—64no—
202C2×C3×C4—64no—
203C2×C3×C4—64no—
204C2×C3×C4—64no—
205C2×C3×C4C2×Dic618yes—
206C2×C3×C4C2×Dic614yes—
207C2×C3×C4C2×C4×D314yes—
208C2×C3×C4#23514yes—
209C2×Dic3—24no—
210C2×Dic3—24no—
211C2×Dic3—24no—
212C2×Dic3—24no—
213C2×Dic3—24no—
214C2×Dic3—34no—
215C2×Dic3—38no—
216C2×Dic3—34no—
217C2×Dic3—38no—
218C2×Dic3—62no—
219C2×Dic3—62no—
220C2×Dic3—64no—
221C2×Dic3—64no—
222C2×Dic3—64no—
223C2×Dic3—64no—
224C2×Dic3—64no—
225C2×Dic3—64no—
226C2×Dic3—64no—
227C2×Dic3—64no—
228C2×Dic3C2×C4×D314yes—
229C2×Dic3C2×C4×D314yes—
230Dic6—616no—
231C2×C32C2×#11711yescharacteristic
232C2×C32C2×C4×Q811yescharacteristic
233C2×C32C4×#4111yescharacteristic
234C2×C32#52912yes—
235C2×C32#53312yes—
236C2×Q8—94no—
237C2×Q8—184no—
238C22×C4—32no—
239C22×C4—32no—
240C22×C4—34no—
241C22×C4—91no—
242C22×C4—91no—
243C22×C4—92no—
244C22×C4C2×D3212yes—
245C22×C4C2×D3211yescharacteristic
246C4⋊C4—94no—
247C4⋊C4—98no—
248C4⋊C4—184no—
249C4⋊C4—188no—
250C42—38no—
251C42—64no—
252C42—94no—
253C42—184no—
254C42—184no—
255C42—182no—
256C42#62714yescomplemented
257C22×C3—21no—
258C22×C3—21no—
259C22×C3—22no—
260C22×C3—22no—
261C22×C3—21no—
262C22×C3C22×Dic612yes—
263C22×C3C22×C4×D312yes—
264C22×C3C2×#23512yes—
265C22×C3D3×#4114yes—
266C22×C3D3×#4114yes—
267C3×C4—28no—
268C3×C4—28no—
269C3×C4—24no—
270C3×C4—64no—
271C3×C4—64no—
272C3×C4—124no—
273C3×C4C4×Dic618yes—
274Dic3—24no—
275Dic3—24no—
276Dic3—38no—
277Dic3—44no—
278Dic3—64no—
279Dic3—64no—
280Dic3—68no—
281Dic3—64no—
282Dic3—68no—
283C32#229511yescharacteristic, complemented, Sylow
284C23C22×D3211yescharacteristic
285Q8—188no—
286C2×C4—22no—
287C2×C4—22no—
288C2×C4—34no—
289C2×C4—34no—
290C2×C4—64no—
291C2×C4—64no—
292C2×C4—64no—
293C2×C4—64no—
294C2×C4—64no—
295C2×C4—92no—
296C2×C4—94no—
297C2×C4—92no—
298C2×C4—94no—
299C2×C4—182no—
300C2×C4—182no—
301C2×C4—182no—
302C2×C4#379812yes—
303C2×C4C4×D3212yes—
304C2×C4C2×#62714yes—
305C2×C4C2×#62712yes—
306C2×C3—21no—
307C2×C3—22no—
308C2×C3—21no—
309C2×C3—21no—
310C2×C3—22no—
311C2×C3C2×C4×Dic612yes—
312C2×C3#551714yes—
313C2×C3D3×#11712yes—
314C2×C3#552212yes—
315C2×C3#552814yes—
316C22C2×#379811yescharacteristic
317C22C2×C4×D3211yescharacteristic
318C22#6430612yes—
319C22#6430612yes—
320C22C22×#62711yescharacteristic
321C4—24no—
322C4—64no—
323C4—64no—
324C4—94no—
325C4—124no—
326C4—182no—
327C4—184no—
328C4C4×#62714yes—
329C3—21no—
330C3#7338412yescomplemented
331C2#1059396611yescharacteristic
332C2#1059398012yes—
333C2#1059399211yescharacteristic
334C2C2×C4×#62711yescharacteristic
335C2#1059505012yes—
subgroupG/H
centerC22×C4C2×D32
commutatorC22×C32C23×C4
FrattiniC23C22×D32
FittingC2×C32×C42C22
socle, prime radical, cosocleC23×C32C24
hypercenterC2×C42D32
hypocenterC32#2295
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22×C4 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
22. C4×#627C4semidirect
49. C32×C42Q8semidirect
141. C3×C42Dic6semidirect
256. C42#627semidirect
283. C32#2295semidirect
330. C3#73384semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#6272
C42×C3⋊Dic32
C3×#49322
#105913962
C4×#37242
#105913352
C4×Dic3⋊Dic32
#105913282
#733843