Finite Group Databasebeta

← #11807946

Subgroups — #11807946

Order 1152.

1272 conjugacy classes of subgroups.

The subgroup lattice has 312 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64153C211yesmaximal, characteristic
2C32×#391C211yesmaximal, characteristic
3#10592928C211yesmaximal, characteristic
4#10592677C212yesmaximal
5#10592632C212yesmaximal
6#10592354C212yesmaximal
7#10592351C212yesmaximal
8#10592350C212yesmaximal
9#10592345C212yesmaximal
10#76497—34nomaximal
11C22×C32×Q8C2211yescharacteristic
12C22×#634C2211yescharacteristic
13C2×C32×C4⋊C4C2211yescharacteristic
14C2×C32×C42C2211yescharacteristic
15#64153C418yescomplemented
16C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
17C2×#3750C2212yes—
18C2×#3750C2212yes—
19C2×#3750C2212yes—
20C2×C4×C3⋊Dic3C2212yes—
21C2×C4×C3⋊Dic3C2211yescharacteristic
22C2×C4×C3⋊Dic3C2211yescharacteristic
23C32×#95C2212yes—
24C32×#95C2212yes—
25#63658C2212yes—
26#63658C2212yes—
27#63658C2212yes—
28#63658C2212yes—
29#63658C2212yes—
30#63658C2212yes—
31#63658C2212yes—
32#63658C2212yes—
33C2×#944—34no—
34C3×#391D314yes—
35#5229—34no—
36#4978—38no—
37#4933—38no—
38#4655—38no—
39#4652—38no—
40#4651—38no—
41#4646—38no—
42C2×C32×Q8—41no—
43C2×C32×Q8—41no—
44C2×C32×Q8C2×C414yes—
45C22×C32×C4C2312yes—
46C22×C32×C4C2312yes—
47C22×C32×C4C2311yescharacteristic
48C22×C32×C4C2311yescharacteristic
49C22×C32×C4C2311yescharacteristic
50C22×C3⋊Dic3C2312yes—
51C22×C3⋊Dic3C2312yes—
52C22×C3⋊Dic3C2312yes—
53C22×C3⋊Dic3C2312yes—
54C2×#634—41no—
55C2×#634—41no—
56C2×#634C2×C414yes—
57C32×C4⋊C4—41no—
58C32×C42—41no—
59C4⋊(C3⋊Dic3)—41no—
60#3750—42no—
61#3750C2×C418yes—
62#3750C2×C418yes—
63C4×C3⋊Dic3—42no—
64C4×C3⋊Dic3—41no—
65C4×C3⋊Dic3C2×C414yes—
66#2381—91noSylow
67C22×C3×Q8C2×D314yes—
68C22×Dic6—34no—
69C2×C3×C4⋊C4C2×D314yes—
70C2×C3×C42C2×D314yes—
71#944—332no—
72C2×C4⋊Dic3—34no—
73C2×Dic3⋊C4—38no—
74C2×Dic3⋊C4—38no—
75C2×Dic3⋊C4—38no—
76C2×C4×Dic3—34no—
77C2×C4×Dic3—38no—
78C2×C4×Dic3—34no—
79C3×#95C2×D318yes—
80C3×#95C2×D318yes—
81C3⋊#95—38no—
82C3⋊#95—38no—
83C3⋊#95—38no—
84C3⋊#95—38no—
85C3⋊#95—38no—
86C3⋊#95—38no—
87C3⋊#95—38no—
88C3⋊#95—38no—
89C23×C32C2411yescharacteristic
90C32×Q8—44no—
91C2×C32×C4—21no—
92C2×C32×C4—21no—
93C2×C32×C4—21no—
94C2×C32×C4—21no—
95C2×C32×C4—21no—
96C2×C32×C4—21no—
97C2×C32×C4—22no—
98C2×C32×C4—22no—
99C2×C32×C4—22no—
100C2×C32×C4—24no—
101C2×C32×C4—22no—
102C2×C32×C4C22×C412yes—
103C2×C32×C4C22×C412yes—
104C2×C32×C4C22×C412yes—
105C2×C3⋊Dic3—22no—
106C2×C3⋊Dic3—22no—
107C2×C3⋊Dic3—22no—
108C2×C3⋊Dic3—22no—
109C2×C3⋊Dic3—22no—
110C2×C3⋊Dic3—22no—
111C2×C3⋊Dic3—22no—
112C2×C3⋊Dic3—24no—
113C2×C3⋊Dic3—22no—
114C2×C3⋊Dic3C22×C414yes—
115C2×C3⋊Dic3C22×C414yes—
116#634—44no—
117C2×C4⋊Q8—91no—
118#391—91no—
119#391—92no—
120#391C3⋊D311yescharacteristic
121#387—92no—
122#387—92no—
123#387—92no—
124#387—92no—
125#383—92no—
126C2×C3×Q8—44no—
127C2×C3×Q8—44no—
128C2×C3×Q8C4×D3116yes—
129C22×C3×C4C22×D318yes—
130C22×C3×C4C22×D318yes—
131C22×C3×C4C22×D314yes—
132C22×C3×C4C22×D314yes—
133C22×C3×C4C22×D314yes—
134C22×Dic3—38no—
135C22×Dic3—38no—
136C22×Dic3—38no—
137C22×Dic3—38no—
138C2×Dic6—316no—
139C2×Dic6—124no—
140C2×Dic6—124no—
141C3×C4⋊C4—44no—
142C3×C42—44no—
143C4⋊Dic3—124no—
144Dic3⋊C4—332no—
145Dic3⋊C4—332no—
146Dic3⋊C4—128no—
147C4×Dic3—316no—
148C4×Dic3—128no—
149C4×Dic3—124no—
150C22×C32C23×C411yescharacteristic
151C22×C32H(5,𝔽2)11yescharacteristic
152C22×C32H(5,𝔽2)11yescharacteristic
153C22×C322−1+412yes—
154C22×C322−1+412yes—
155C32×C4—22no—
156C32×C4—22no—
157C32×C4—22no—
158C32×C4—42no—
159C32×C4—42no—
160C3⋊Dic3—24no—
161C3⋊Dic3—24no—
162C3⋊Dic3—42no—
163C3⋊Dic3—42no—
164C22×Q8—91no—
165C22×Q8C2×C3⋊D311yescharacteristic
166C4⋊Q8—98no—
167C2×C4⋊C4—92no—
168C2×C4⋊C4—92no—
169C2×C4⋊C4—92no—
170C2×C4⋊C4—91no—
171C2×C4⋊C4C2×C3⋊D311yescharacteristic
172C2×C42—91no—
173C2×C42—92no—
174C2×C42—91no—
175C2×C42C2×C3⋊D311yescharacteristic
176#95—92no—
177#95—92no—
178#95—92no—
179#95—92no—
180#95—92no—
181#95—92no—
182#95—92no—
183#95—92no—
184#95C2×C3⋊D312yes—
185#95C2×C3⋊D312yes—
186C23×C3C23×D314yes—
187C3×Q8—416no—
188C2×C3×C4—24no—
189C2×C3×C4—24no—
190C2×C3×C4—24no—
191C2×C3×C4—24no—
192C2×C3×C4—24no—
193C2×C3×C4—24no—
194C2×C3×C4—28no—
195C2×C3×C4—28no—
196C2×C3×C4—28no—
197C2×C3×C4—28no—
198C2×C3×C4—216no—
199C2×C3×C4C2×C4×D318yes—
200C2×C3×C4C2×C4×D318yes—
201C2×C3×C4C2×C4×D318yes—
202C2×Dic3—316no—
203C2×Dic3—316no—
204C2×Dic3—68no—
205C2×Dic3—68no—
206C2×Dic3—68no—
207C2×Dic3—68no—
208C2×Dic3—68no—
209C2×Dic3—68no—
210C2×Dic3—68no—
211C2×Dic3—616no—
212C2×Dic3—68no—
213Dic6—1216no—
214C2×C32#51811yescharacteristic
215C2×C32#51912yes—
216C2×C32#56312yes—
217C2×C32#56311yescharacteristic
218C2×C32#56311yescharacteristic
219C2×Q8—41no—
220C2×Q8—41no—
221C2×Q8—94no—
222C2×Q8—361no—
223C2×Q8—361no—
224C2×Q8C4×C3⋊D314yes—
225C22×C4—92no—
226C22×C4—92no—
227C22×C4—92no—
228C22×C4—92no—
229C22×C4C22×C3⋊D312yes—
230C22×C4C22×C3⋊D312yes—
231C22×C4C22×C3⋊D311yescharacteristic
232C22×C4C22×C3⋊D311yescharacteristic
233C22×C4C22×C3⋊D311yescharacteristic
234C4⋊C4—41no—
235C4⋊C4—98no—
236C4⋊C4—98no—
237C4⋊C4—362no—
238C4⋊C4—361no—
239C42—41no—
240C42—94no—
241C42—361no—
242C42—362no—
243C22×C3C22×C4×D314yes—
244C22×C3#100414yes—
245C22×C3#100414yes—
246C22×C3#100718yes—
247C22×C3#101018yes—
248C3×C4—28no—
249C3×C4—28no—
250C3×C4—28no—
251C3×C4—48no—
252C3×C4—48no—
253Dic3—616no—
254Dic3—616no—
255Dic3—128no—
256Dic3—128no—
257C32#238111yescharacteristic, complemented, Sylow
258C23C23×C3⋊D311yescharacteristic
259Q8—44no—
260Q8—364no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—22no—
268C2×C4—22no—
269C2×C4—22no—
270C2×C4—22no—
271C2×C4—24no—
272C2×C4—94no—
273C2×C4—94no—
274C2×C4—182no—
275C2×C4—182no—
276C2×C4—182no—
277C2×C4—182no—
278C2×C4—182no—
279C2×C4—182no—
280C2×C4—182no—
281C2×C4—184no—
282C2×C4—182no—
283C2×C4C2×C4×C3⋊D312yes—
284C2×C4C2×C4×C3⋊D312yes—
285C2×C4C2×C4×C3⋊D312yes—
286C2×C3#548614yes—
287C2×C3#557218yes—
288C2×C3#564618yes—
289C2×C3#567214yes—
290C2×C3#573514yes—
291C22C22×C4×C3⋊D311yescharacteristic
292C22#6436111yescharacteristic
293C22#6436111yescharacteristic
294C22#6436412yes—
295C22#6436712yes—
296C4—22no—
297C4—22no—
298C4—22no—
299C4—42no—
300C4—42no—
301C4—184no—
302C4—184no—
303C4—362no—
304C4—362no—
305C3#7649714yescomplemented
306C2#1059595711yescharacteristic
307C2#1059604312yes—
308C2#1059611712yes—
309C2#1059614311yescharacteristic
310C2#1059620611yescharacteristic
subgroupG/H
center, FrattiniC23C23×C3⋊D3
commutatorC22×C32C23×C4
FittingC32×#391C2
socle, prime radical, cosocleC23×C32C24
hypercenter#391C3⋊D3
hypocenterC32#2381
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ #391

Complements

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

NH ≅ G/Ntype
15. #64153C4semidirect
257. C32#2381semidirect
305. C3#76497semidirect

Maximal subgroups

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

subgroupindex
C2×#641532
C32×#3912
#105929282
#105926772
#105926322
#105923542
#105923512
#105923502
#105923452
#764973