Finite Group Databasebeta

← #11803216

Subgroups — #11803216

Order 1152.

977 conjugacy classes of subgroups.

The subgroup lattice has 328 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#627C211yesmaximal, characteristic
2#10592347C211yesmaximal, characteristic
3C3×#4650C212yesmaximal
4#10591396C212yesmaximal
5#10591337C212yesmaximal
6#10591257C211yesmaximal, characteristic
7#10591254C214yesmaximal
8#10591223C212yesmaximal
9#74151—32nomaximal
10C22×#627C2211yescharacteristic
11C2×C4×C3⋊Dic3C2212yes—
12C2×C4×C3⋊Dic3C2211yescharacteristic
13C2×C3×Dic3⋊C4C2214yes—
14C2×C3×C4×Dic3C2212yes—
15C2×#3724C2212yes—
16C2×#3724C2211yescharacteristic
17C2×Dic3⋊Dic3C2212yes—
18C2×Dic32C2212yes—
19C4×#627C418yescomplemented
20C32×#95C2211yescharacteristic
21#63658C2212yes—
22#63658C2211yescharacteristic
23C3×C3⋊#95C2214yes—
24C3×C3⋊#95C2212yes—
25#63579C2214yes—
26#63579C2214yes—
27C2×C4×Dic6—32no—
28C3×#382—32no—
29#4978—34no—
30#4976—34no—
31#4937—32no—
32#4654—34no—
33#4651—32no—
34#4650D312yes—
35#4649—32no—
36#4648—32no—
37#4648—61no—
38#4646—34no—
39C22×C32×C4C2312yes—
40C22×C32×C4C2311yescharacteristic
41C22×C3⋊Dic3C2312yes—
42C22×C3⋊Dic3C2311yescharacteristic
43C22×C3⋊Dic3C2311yescharacteristic
44C22×C3×Dic3C2314yes—
45C22×C3×Dic3C2312yes—
46C22×C3×Dic3C2312yes—
47C2×#627—24no—
48C2×#627C2×C414yes—
49C4×C3⋊Dic3—24no—
50C4×C3⋊Dic3C2×C414yes—
51C3×Dic3⋊C4—44no—
52C3×C4×Dic3C2×C418yes—
53#3724—24no—
54#3724C2×C414yes—
55Dic3⋊Dic3C2×C418yes—
56Dic32—42no—
57#2320—91noSylow
58C22×Dic6—32no—
59C2×C3×C4⋊C4—34no—
60C2×C3×C42—32no—
61C2×C4⋊Dic3—32no—
62C2×Dic3⋊C4—32no—
63C2×Dic3⋊C4—32no—
64C2×Dic3⋊C4—34no—
65C2×Dic3⋊C4C2×D314yes—
66C2×C4×Dic3—32no—
67C2×C4×Dic3—34no—
68C2×C4×Dic3—34no—
69C2×C4×Dic3—61no—
70C2×C4×Dic3—62no—
71C2×C4×Dic3C2×D312yes—
72C4×Dic6—316no—
73C3×#95—21no—
74C3×#95—34no—
75C3×#95—32no—
76C3×#95C2×D312yes—
77C3⋊#95—32no—
78C3⋊#95—34no—
79C3⋊#95—34no—
80C3⋊#95—34no—
81C3⋊#95—34no—
82C3⋊#95—34no—
83C3⋊#95—61no—
84C3⋊#95—62no—
85C3⋊#95C2×D314yes—
86C3⋊#95C2×D312yes—
87C23×C32C2411yescharacteristic
88C2×C32×C4—22no—
89C2×C32×C4—22no—
90C2×C32×C4—22no—
91C2×C32×C4—22no—
92C2×C32×C4C22×C412yes—
93C2×C3⋊Dic3—22no—
94C2×C3⋊Dic3—21no—
95C2×C3⋊Dic3—21no—
96C2×C3⋊Dic3—22no—
97C2×C3⋊Dic3—22no—
98C2×C3⋊Dic3C22×C412yes—
99C2×C3⋊Dic3C22×C412yes—
100C2×C3⋊Dic3#4114yes—
101C2×C3×Dic3—24no—
102C2×C3×Dic3—22no—
103C2×C3×Dic3—22no—
104C2×C3×Dic3—24no—
105C2×C3×Dic3—24no—
106C2×C3×Dic3—24no—
107C2×C3×Dic3C22×C414yes—
108C2×C3×Dic3C22×C414yes—
109#627—28no—
110C2×C4×Q8—91no—
111#391—92no—
112#389—92no—
113#387—94no—
114#383—92no—
115#382—32no—
116C4×C4⋊C4—91no—
117#376—91no—
118C22×C3×C4—22no—
119C22×C3×C4—21no—
120C22×C3×C4—32no—
121C22×C3×C4—32no—
122C22×C3×C4—34no—
123C22×C3×C4C22×D314yes—
124C22×C3×C4C22×D312yes—
125C22×Dic3—32no—
126C22×Dic3—32no—
127C22×Dic3—34no—
128C22×Dic3—61no—
129C22×Dic3—61no—
130C22×Dic3—62no—
131C22×Dic3C22×D314yes—
132C22×Dic3C22×D312yes—
133C22×Dic3C22×D312yes—
134C2×Dic6—38no—
135C2×Dic6—68no—
136C3×C4⋊C4—124no—
137C3×C42—38no—
138C4⋊Dic3—38no—
139Dic3⋊C4—38no—
140Dic3⋊C4—38no—
141Dic3⋊C4—44no—
142Dic3⋊C4—68no—
143C4×Dic3—38no—
144C4×Dic3—64no—
145C4×Dic3—68no—
146C4×Dic3—68no—
147C4×Dic3—124no—
148C4×Dic3C4×D318yes—
149C22×C32C23×C411yescharacteristic
150C22×C32C2×#4112yes—
151C22×C32H(5,𝔽2)11yescharacteristic
152C22×C322−1+411yescharacteristic
153C22×C322−1+412yes—
154C32×C4—22no—
155C32×C4—42no—
156C3⋊Dic3—22no—
157C3⋊Dic3—42no—
158C3⋊Dic3#11714yes—
159C3×Dic3—24no—
160C3×Dic3—24no—
161C3×Dic3—44no—
162C22×Q8—91no—
163C4×Q8—98no—
164C2×C4⋊C4—34no—
165C2×C4⋊C4—92no—
166C2×C4⋊C4—91no—
167C2×C4⋊C4—92no—
168C2×C42—32no—
169C2×C42—91no—
170C2×C42—92no—
171C2×C42—92no—
172#95—32no—
173#95—34no—
174#95—94no—
175#95—94no—
176#95—91no—
177#95—92no—
178#95D3211yescharacteristic
179C23×C3—21no—
180C23×C3C23×D312yes—
181C2×C3×C4—24no—
182C2×C3×C4—24no—
183C2×C3×C4—24no—
184C2×C3×C4—24no—
185C2×C3×C4—24no—
186C2×C3×C4—22no—
187C2×C3×C4—34no—
188C2×C3×C4—34no—
189C2×C3×C4—42no—
190C2×C3×C4—42no—
191C2×C3×C4—42no—
192C2×C3×C4—62no—
193C2×C3×C4—62no—
194C2×C3×C4—64no—
195C2×C3×C4—64no—
196C2×C3×C4—64no—
197C2×C3×C4—64no—
198C2×C3×C4C2×C4×D314yes—
199C2×Dic3—22no—
200C2×Dic3—22no—
201C2×Dic3—24no—
202C2×Dic3—24no—
203C2×Dic3—24no—
204C2×Dic3—24no—
205C2×Dic3—34no—
206C2×Dic3—38no—
207C2×Dic3—34no—
208C2×Dic3—62no—
209C2×Dic3—64no—
210C2×Dic3—62no—
211C2×Dic3—62no—
212C2×Dic3—62no—
213C2×Dic3—64no—
214C2×Dic3—64no—
215C2×Dic3—64no—
216C2×Dic3—64no—
217C2×Dic3—121no—
218C2×Dic3—121no—
219C2×Dic3—122no—
220C2×Dic3—122no—
221C2×Dic3C2×C4×D314yes—
222C2×Dic3C2×C4×D314yes—
223Dic6—616no—
224C2×C32C2×#11711yescharacteristic
225C2×C32#51911yescharacteristic
226C2×C32#52011yescharacteristic
227C2×C32#54112yes—
228C2×C32#54212yes—
229C2×Q8—94no—
230C2×Q8—184no—
231C22×C4—32no—
232C22×C4—32no—
233C22×C4—34no—
234C22×C4—91no—
235C22×C4—91no—
236C22×C4—92no—
237C22×C4C2×D3212yes—
238C22×C4C2×D3211yescharacteristic
239C4⋊C4—94no—
240C4⋊C4—98no—
241C4⋊C4—124no—
242C4⋊C4—184no—
243C42—38no—
244C42—94no—
245C42—184no—
246C42—362no—
247C22×C3—21no—
248C22×C3—22no—
249C22×C3—22no—
250C22×C3—21no—
251C22×C3—21no—
252C22×C3C22×C4×D312yes—
253C22×C3#100412yes—
254C22×C3#100712yes—
255C22×C3D3×#4114yes—
256C22×C3#101014yes—
257C3×C4—24no—
258C3×C4—42no—
259C3×C4—44no—
260C3×C4—44no—
261C3×C4—64no—
262C3×C4—64no—
263C3×C4—124no—
264Dic3—24no—
265Dic3—24no—
266Dic3—38no—
267Dic3—44no—
268Dic3—64no—
269Dic3—64no—
270Dic3—122no—
271Dic3—124no—
272Dic3—124no—
273C32#232011yescharacteristic, complemented, Sylow
274C23C22×D3211yescharacteristic
275Q8—188no—
276C2×C4—22no—
277C2×C4—22no—
278C2×C4—22no—
279C2×C4—22no—
280C2×C4—34no—
281C2×C4—34no—
282C2×C4—64no—
283C2×C4—62no—
284C2×C4—62no—
285C2×C4—64no—
286C2×C4—64no—
287C2×C4—64no—
288C2×C4—92no—
289C2×C4—94no—
290C2×C4—92no—
291C2×C4—181no—
292C2×C4—181no—
293C2×C4—182no—
294C2×C4—182no—
295C2×C4—182no—
296C2×C4C4×D3212yes—
297C2×C3—22no—
298C2×C3—22no—
299C2×C3—21no—
300C2×C3—21no—
301C2×C3—21no—
302C2×C3#550412yes—
303C2×C3#551612yes—
304C2×C3D3×#11712yes—
305C2×C3#566914yes—
306C2×C3#569614yes—
307C22C2×C4×D3211yescharacteristic
308C22#6430612yes—
309C22#6430912yes—
310C22#6431311yescharacteristic
311C22#6431611yescharacteristic
312C4—22no—
313C4—42no—
314C4—64no—
315C4—64no—
316C4—94no—
317C4—124no—
318C4—182no—
319C4—362no—
320C3—21no—
321C3#7415112yescomplemented
322C2#1059399211yescharacteristic
323C2#1059422412yes—
324C2#1059424511yescharacteristic
325C2#1059450911yescharacteristic
326C2#1059459912yes—
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC32×#95C22
socle, prime radical, cosocleC23×C32C24
hypercenter#95D32
hypocenterC32#2320
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ #95

Complements

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

NH ≅ G/Ntype
19. C4×#627C4semidirect
273. C32#2320semidirect
321. C3#74151semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#6272
#105923472
C3×#46502
#105913962
#105913372
#105912572
#105912542
#105912232
#741513