Finite Group Databasebeta

← #11803802

Subgroups — #11803802

Order 1152.

1548 conjugacy classes of subgroups.

The subgroup lattice has 303 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×Q8×C3⋊Dic3C211yesmaximal, characteristic
2C2×#64153C211yesmaximal, characteristic
3C2×#64096C211yesmaximal, characteristic
4C32×#391C211yesmaximal, characteristic
5#10592676C211yesmaximal, characteristic
6#10592631C211yesmaximal, characteristic
7#10592628C211yesmaximal, characteristic
8#10592354C214yesmaximal
9#10592351C214yesmaximal
10#76485—34nomaximal
11C22×C32×Q8C2211yescharacteristic
12C22×#634C2211yescharacteristic
13C2×C32×C4⋊C4C2211yescharacteristic
14C2×C32×C42C2211yescharacteristic
15Q8×C3⋊Dic3—24no—
16#64153C418yescomplemented
17C2×C4⋊(C3⋊Dic3)C2212yes—
18C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
19C2×#3750C2212yes—
20C2×#3750C2214yes—
21C2×C4×C3⋊Dic3C2212yes—
22C2×C4×C3⋊Dic3C2212yes—
23C2×C4×C3⋊Dic3C2211yescharacteristic
24C2×C4×C3⋊Dic3C2211yescharacteristic
25#64096—24no—
26C32×#95C2214yes—
27#63658C2212yes—
28#63658C2214yes—
29#63658C2214yes—
30#63658C2212yes—
31C2×Q8×Dic3—34no—
32C2×#944—34no—
33C2×#887—34no—
34C3×#391D314yes—
35#4977—34no—
36#4932—34no—
37#4929—34no—
38#4655—316no—
39#4652—316no—
40C2×C32×Q8—22no—
41C2×C32×Q8—22no—
42C2×C32×Q8C2×C414yes—
43C22×C32×C4C2312yes—
44C22×C32×C4C2312yes—
45C22×C32×C4C2312yes—
46C22×C32×C4C2311yescharacteristic
47C22×C3⋊Dic3C2312yes—
48C22×C3⋊Dic3C2312yes—
49C22×C3⋊Dic3C2312yes—
50C22×C3⋊Dic3C2311yescharacteristic
51C22×C3⋊Dic3C2311yescharacteristic
52C2×#634—22no—
53C2×#634—22no—
54C2×#634C2×C414yes—
55C32×C4⋊C4—22no—
56C32×C42—22no—
57C4⋊(C3⋊Dic3)—22no—
58C4⋊(C3⋊Dic3)—24no—
59#3750—24no—
60#3750C2×C4116yes—
61C4×C3⋊Dic3—24no—
62C4×C3⋊Dic3—24no—
63C4×C3⋊Dic3C2×C414yes—
64C4×C3⋊Dic3D414yes—
65#2327—91noSylow
66C22×C3×Q8C2×D314yes—
67C22×Dic6—34no—
68C2×C3×C4⋊C4C2×D314yes—
69C2×C3×C42C2×D314yes—
70Q8×Dic3—616no—
71#944—332no—
72C2×C4⋊Dic3—38no—
73C2×C4⋊Dic3—34no—
74C2×Dic3⋊C4—316no—
75C2×Dic3⋊C4—38no—
76C2×C4×Dic3—34no—
77C2×C4×Dic3—34no—
78C2×C4×Dic3—38no—
79C2×C4×Dic3—38no—
80#887—616no—
81C3×#95C2×D3116yes—
82C3⋊#95—38no—
83C3⋊#95—316no—
84C3⋊#95—316no—
85C3⋊#95—38no—
86C23×C32C2411yescharacteristic
87C32×Q8—28no—
88C2×C32×C4—22no—
89C2×C32×C4—22no—
90C2×C32×C4—22no—
91C2×C32×C4—22no—
92C2×C32×C4—22no—
93C2×C32×C4—24no—
94C2×C32×C4—22no—
95C2×C32×C4C22×C414yes—
96C2×C32×C4C22×C412yes—
97C2×C32×C4C2×D412yes—
98C2×C32×C4#4112yes—
99C2×C3⋊Dic3—22no—
100C2×C3⋊Dic3—22no—
101C2×C3⋊Dic3—22no—
102C2×C3⋊Dic3—22no—
103C2×C3⋊Dic3—22no—
104C2×C3⋊Dic3—22no—
105C2×C3⋊Dic3—22no—
106C2×C3⋊Dic3—24no—
107C2×C3⋊Dic3C22×C414yes—
108C2×C3⋊Dic3C22×C414yes—
109C2×C3⋊Dic3C2×D412yes—
110C2×C3⋊Dic3C2×D412yes—
111#634—28no—
112C2×C4⋊Q8—91no—
113C2×C4×Q8—91no—
114C2×C4×Q8—91no—
115#391—91no—
116#391C3⋊D311yescharacteristic
117#387—94no—
118#387—94no—
119#382—91no—
120#376—91no—
121C2×C3×Q8—28no—
122C2×C3×Q8—28no—
123C2×C3×Q8C4×D3116yes—
124C22×C3×C4C22×D318yes—
125C22×C3×C4C22×D318yes—
126C22×C3×C4C22×D318yes—
127C22×C3×C4C22×D314yes—
128C22×Dic3—38no—
129C22×Dic3—34no—
130C22×Dic3—34no—
131C22×Dic3—38no—
132C22×Dic3—38no—
133C2×Dic6—316no—
134C2×Dic6—68no—
135C2×Dic6—68no—
136C3×C4⋊C4—28no—
137C3×C42—28no—
138C4⋊Dic3—616no—
139C4⋊Dic3—68no—
140Dic3⋊C4—364no—
141Dic3⋊C4—616no—
142C4×Dic3—316no—
143C4×Dic3—316no—
144C4×Dic3—616no—
145C4×Dic3—616no—
146C22×C32C23×C411yescharacteristic
147C22×C32C22×D411yescharacteristic
148C22×C32C2×#4111yescharacteristic
149C22×C322−1+412yes—
150C22×C322−1+412yes—
151C32×C4—24no—
152C32×C4—42no—
153C32×C4—42no—
154C32×C4C4×D414yes—
155C3⋊Dic3—24no—
156C3⋊Dic3—24no—
157C3⋊Dic3—22no—
158C3⋊Dic3—22no—
159C3⋊Dic3—42no—
160C22×Q8—91no—
161C22×Q8C2×C3⋊D311yescharacteristic
162C4⋊Q8—98no—
163C4×Q8—184no—
164C4×Q8—184no—
165C2×C4⋊C4—94no—
166C2×C4⋊C4—91no—
167C2×C4⋊C4—92no—
168C2×C4⋊C4—92no—
169C2×C4⋊C4C2×C3⋊D311yescharacteristic
170C2×C42—91no—
171C2×C42—91no—
172C2×C42—92no—
173C2×C42—92no—
174C2×C42C2×C3⋊D311yescharacteristic
175#95—92no—
176#95—92no—
177#95—94no—
178#95—94no—
179#95C2×C3⋊D314yes—
180C23×C3C23×D314yes—
181C3×Q8—232no—
182C2×C3×C4—28no—
183C2×C3×C4—28no—
184C2×C3×C4—28no—
185C2×C3×C4—28no—
186C2×C3×C4—28no—
187C2×C3×C4—216no—
188C2×C3×C4—28no—
189C2×C3×C4C2×C4×D3116yes—
190C2×C3×C4C2×C4×D318yes—
191C2×C3×C4D3×D418yes—
192C2×C3×C4#23718yes—
193C2×Dic3—316no—
194C2×Dic3—316no—
195C2×Dic3—38no—
196C2×Dic3—38no—
197C2×Dic3—68no—
198C2×Dic3—68no—
199C2×Dic3—68no—
200C2×Dic3—68no—
201C2×Dic3—68no—
202C2×Dic3—68no—
203C2×Dic3—68no—
204C2×Dic3—616no—
205Dic6—632no—
206C2×C32C2×C4×D411yescharacteristic
207C2×C32#51912yes—
208C2×C32#53611yescharacteristic
209C2×C32#53611yescharacteristic
210C2×C32#54112yes—
211C2×Q8—22no—
212C2×Q8—22no—
213C2×Q8—94no—
214C2×Q8—182no—
215C2×Q8—182no—
216C2×Q8C4×C3⋊D314yes—
217C22×C4—92no—
218C22×C4—91no—
219C22×C4—91no—
220C22×C4—92no—
221C22×C4—92no—
222C22×C4C22×C3⋊D312yes—
223C22×C4C22×C3⋊D312yes—
224C22×C4C22×C3⋊D312yes—
225C22×C4C22×C3⋊D311yescharacteristic
226C4⋊C4—22no—
227C4⋊C4—916no—
228C4⋊C4—184no—
229C4⋊C4—184no—
230C4⋊C4—182no—
231C42—22no—
232C42—94no—
233C42—94no—
234C42—184no—
235C42—184no—
236C22×C3C22×C4×D314yes—
237C22×C3C2×D3×D414yes—
238C22×C3C2×#23714yes—
239C22×C3#100718yes—
240C22×C3#101018yes—
241C3×C4—216no—
242C3×C4—48no—
243C3×C4—48no—
244C3×C4#67⋊C4116yes—
245Dic3—68no—
246Dic3—68no—
247Dic3—616no—
248Dic3—616no—
249Dic3—128no—
250C32#232711yescharacteristic, complemented, Sylow
251C23C23×C3⋊D311yescharacteristic
252Q8—28no—
253Q8—188no—
254C2×C4—22no—
255C2×C4—22no—
256C2×C4—22no—
257C2×C4—22no—
258C2×C4—22no—
259C2×C4—22no—
260C2×C4—24no—
261C2×C4—94no—
262C2×C4—94no—
263C2×C4—92no—
264C2×C4—92no—
265C2×C4—182no—
266C2×C4—182no—
267C2×C4—182no—
268C2×C4—182no—
269C2×C4—182no—
270C2×C4—182no—
271C2×C4—182no—
272C2×C4—184no—
273C2×C4C2×C4×C3⋊D314yes—
274C2×C4C2×C4×C3⋊D312yes—
275C2×C4D4×C3⋊D312yes—
276C2×C4#383012yes—
277C2×C3C2×#67⋊C414yes—
278C2×C3#557218yes—
279C2×C3#562518yes—
280C2×C3#567514yes—
281C2×C3#572414yes—
282C22C22×C4×C3⋊D311yescharacteristic
283C22C2×D4×C3⋊D311yescharacteristic
284C22C2×#383011yescharacteristic
285C22#6436412yes—
286C22#6436712yes—
287C4—24no—
288C4—42no—
289C4—42no—
290C4—182no—
291C4—182no—
292C4—184no—
293C4—184no—
294C4—362no—
295C4#6409014yes—
296C3#7648514yescomplemented
297C2C2×#6409011yescharacteristic
298C2#1059604312yes—
299C2#1059609612yes—
300C2#1059614611yescharacteristic
301C2#1059619511yescharacteristic
subgroupG/H
center, FrattiniC23C23×C3⋊D3
commutatorC22×C32C23×C4
FittingC32×#391C2
socle, prime radical, cosocleC23×C32C24
hypercenter#391C3⋊D3
hypocenterC32#2327
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ #391

Complements

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

NH ≅ G/Ntype
16. #64153C4semidirect
250. C32#2327semidirect
296. C3#76485semidirect

Maximal subgroups

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

subgroupindex
C2×Q8×C3⋊Dic32
C2×#641532
C2×#640962
C32×#3912
#105926762
#105926312
#105926282
#105923542
#105923512
#764853