Finite Group Databasebeta

← #11807984

Subgroups — #11807984

Order 1152.

1224 conjugacy classes of subgroups.

The subgroup lattice has 318 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64079C211yesmaximal, characteristic
2C32×#382C211yesmaximal, characteristic
3#10592677C212yesmaximal
4#10592675C212yesmaximal
5#10592635C211yesmaximal, characteristic
6#10592354C212yesmaximal
7#10592353C212yesmaximal
8#10592352C212yesmaximal
9#10592346C212yesmaximal
10#74161—34nomaximal
11C2×C32×C4⋊C4C2211yescharacteristic
12C2×C32×C4⋊C4C2211yescharacteristic
13C2×C32×C42C2211yescharacteristic
14C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
15C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
16C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
17C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
18C2×#3750C2212yes—
19C2×#3750C2212yes—
20C2×#3750C2212yes—
21C2×#3750C2212yes—
22C2×C4×C3⋊Dic3C2212yes—
23C2×C4×C3⋊Dic3C2212yes—
24#64079C418yescomplemented
25C32×#95C2212yes—
26C32×#95C2212yes—
27#63658C2212yes—
28#63658C2212yes—
29#63658C2212yes—
30#63658C2212yes—
31#63658C2212yes—
32#63658C2212yes—
33C2×#870—34no—
34C3×#382D314yes—
35#4978—38no—
36#4976—38no—
37#4936—34no—
38#4655—38no—
39#4654—38no—
40#4653—38no—
41#4647—38no—
42C22×C32×C4C2312yes—
43C22×C32×C4C2312yes—
44C22×C32×C4C2311yescharacteristic
45C22×C32×C4C2311yescharacteristic
46C22×C32×C4C2311yescharacteristic
47C22×C3⋊Dic3C2312yes—
48C22×C3⋊Dic3C2312yes—
49C22×C3⋊Dic3C2312yes—
50C22×C3⋊Dic3C2312yes—
51C32×C4⋊C4—41no—
52C32×C4⋊C4—41no—
53C32×C42C2×C414yes—
54C4⋊(C3⋊Dic3)—41no—
55C4⋊(C3⋊Dic3)—41no—
56C4⋊(C3⋊Dic3)C2×C414yes—
57C4⋊(C3⋊Dic3)C2×C414yes—
58#3750—42no—
59#3750—42no—
60#3750C2×C418yes—
61#3750C2×C418yes—
62C4×C3⋊Dic3—42no—
63C4×C3⋊Dic3—42no—
64#2382—91noSylow
65C2×C3×C4⋊C4C2×D314yes—
66C2×C3×C4⋊C4C2×D314yes—
67C2×C3×C42C2×D314yes—
68C2×C4⋊Dic3—34no—
69C2×C4⋊Dic3—34no—
70C2×C4⋊Dic3—34no—
71C2×C4⋊Dic3—34no—
72C2×Dic3⋊C4—38no—
73C2×Dic3⋊C4—38no—
74C2×Dic3⋊C4—38no—
75C2×Dic3⋊C4—38no—
76C2×C4×Dic3—38no—
77C2×C4×Dic3—38no—
78#870—332no—
79C3×#95C2×D318yes—
80C3×#95C2×D318yes—
81C3⋊#95—38no—
82C3⋊#95—38no—
83C3⋊#95—38no—
84C3⋊#95—38no—
85C3⋊#95—38no—
86C3⋊#95—38no—
87C23×C32C2411yescharacteristic
88C2×C32×C4—21no—
89C2×C32×C4—21no—
90C2×C32×C4—21no—
91C2×C32×C4—21no—
92C2×C32×C4—21no—
93C2×C32×C4—21no—
94C2×C32×C4—22no—
95C2×C32×C4—22no—
96C2×C32×C4—22no—
97C2×C32×C4—22no—
98C2×C32×C4—22no—
99C2×C32×C4—22no—
100C2×C32×C4C22×C412yes—
101C2×C32×C4C22×C412yes—
102C2×C32×C4C22×C412yes—
103C2×C3⋊Dic3—22no—
104C2×C3⋊Dic3—22no—
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—22no—
113C2×C3⋊Dic3C22×C414yes—
114C2×C3⋊Dic3C22×C414yes—
115C2×#125—91no—
116#389—92no—
117#389—92no—
118#387—92no—
119#387—92no—
120#387—92no—
121#387—92no—
122#382—91no—
123#382C3⋊D311yescharacteristic
124C22×C3×C4C22×D318yes—
125C22×C3×C4C22×D318yes—
126C22×C3×C4C22×D314yes—
127C22×C3×C4C22×D314yes—
128C22×C3×C4C22×D314yes—
129C22×Dic3—38no—
130C22×Dic3—38no—
131C22×Dic3—38no—
132C22×Dic3—38no—
133C3×C4⋊C4—44no—
134C3×C4⋊C4—44no—
135C3×C42C4×D3116yes—
136C4⋊Dic3—316no—
137C4⋊Dic3—316no—
138C4⋊Dic3—124no—
139C4⋊Dic3—124no—
140Dic3⋊C4—332no—
141Dic3⋊C4—332no—
142Dic3⋊C4—128no—
143Dic3⋊C4—128no—
144C4×Dic3—128no—
145C4×Dic3—128no—
146C22×C32C23×C411yescharacteristic
147C22×C32H(5,𝔽2)11yescharacteristic
148C22×C32H(5,𝔽2)11yescharacteristic
149C22×C322−1+411yescharacteristic
150C22×C322−1+411yescharacteristic
151C22×C322−1+411yescharacteristic
152C22×C322−1+411yescharacteristic
153C32×C4—22no—
154C32×C4—22no—
155C32×C4—22no—
156C32×C4—42no—
157C32×C4—42no—
158C3⋊Dic3—24no—
159C3⋊Dic3—24no—
160C3⋊Dic3—42no—
161C3⋊Dic3—42no—
162#125—98no—
163C2×C4⋊C4—91no—
164C2×C4⋊C4—91no—
165C2×C4⋊C4—92no—
166C2×C4⋊C4—92no—
167C2×C4⋊C4—91no—
168C2×C4⋊C4—91no—
169C2×C4⋊C4—92no—
170C2×C4⋊C4—92no—
171C2×C4⋊C4C2×C3⋊D311yescharacteristic
172C2×C4⋊C4C2×C3⋊D311yescharacteristic
173C2×C42—92no—
174C2×C42—92no—
175C2×C42C2×C3⋊D311yescharacteristic
176#95—92no—
177#95—92no—
178#95—92no—
179#95—92no—
180#95—92no—
181#95—92no—
182#95C2×C3⋊D312yes—
183#95C2×C3⋊D312yes—
184C23×C3C23×D314yes—
185C2×C3×C4—24no—
186C2×C3×C4—24no—
187C2×C3×C4—24no—
188C2×C3×C4—24no—
189C2×C3×C4—24no—
190C2×C3×C4—24no—
191C2×C3×C4—28no—
192C2×C3×C4—28no—
193C2×C3×C4—28no—
194C2×C3×C4—28no—
195C2×C3×C4—28no—
196C2×C3×C4—28no—
197C2×C3×C4C2×C4×D318yes—
198C2×C3×C4C2×C4×D318yes—
199C2×C3×C4C2×C4×D318yes—
200C2×Dic3—316no—
201C2×Dic3—316no—
202C2×Dic3—68no—
203C2×Dic3—68no—
204C2×Dic3—68no—
205C2×Dic3—68no—
206C2×Dic3—68no—
207C2×Dic3—68no—
208C2×Dic3—68no—
209C2×Dic3—68no—
210C2×Dic3—68no—
211C2×Dic3—68no—
212C2×C32#51911yescharacteristic
213C2×C32#52011yescharacteristic
214C2×C32#52011yescharacteristic
215C2×C32#56211yescharacteristic
216C2×C32#56311yescharacteristic
217C2×C32#56311yescharacteristic
218C2×C32#56411yescharacteristic
219C22×C4—92no—
220C22×C4—92no—
221C22×C4—92no—
222C22×C4—92no—
223C22×C4C22×C3⋊D312yes—
224C22×C4C22×C3⋊D312yes—
225C22×C4C22×C3⋊D311yescharacteristic
226C22×C4C22×C3⋊D311yescharacteristic
227C22×C4C22×C3⋊D311yescharacteristic
228C4⋊C4—41no—
229C4⋊C4—41no—
230C4⋊C4—98no—
231C4⋊C4—98no—
232C4⋊C4—94no—
233C4⋊C4—94no—
234C4⋊C4—362no—
235C4⋊C4—362no—
236C4⋊C4—361no—
237C4⋊C4—361no—
238C42—362no—
239C42—362no—
240C42C4×C3⋊D314yes—
241C22×C3C22×C4×D314yes—
242C22×C3#100414yes—
243C22×C3#100714yes—
244C22×C3#100914yes—
245C22×C3#101014yes—
246C22×C3#101014yes—
247C22×C3#101014yes—
248C3×C4—28no—
249C3×C4—28no—
250C3×C4—28no—
251C3×C4—48no—
252C3×C4—48no—
253Dic3—616no—
254Dic3—616no—
255Dic3—128no—
256Dic3—128no—
257C32#238211yescharacteristic, complemented, Sylow
258C23C23×C3⋊D311yescharacteristic
259C2×C4—21no—
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—22no—
266C2×C4—22no—
267C2×C4—22no—
268C2×C4—22no—
269C2×C4—22no—
270C2×C4—22no—
271C2×C4—94no—
272C2×C4—94no—
273C2×C4—182no—
274C2×C4—182no—
275C2×C4—182no—
276C2×C4—182no—
277C2×C4—182no—
278C2×C4—182no—
279C2×C4—182no—
280C2×C4—182no—
281C2×C4—182no—
282C2×C4—182no—
283C2×C4C2×C4×C3⋊D312yes—
284C2×C4C2×C4×C3⋊D312yes—
285C2×C4C2×C4×C3⋊D312yes—
286C2×C3#550414yes—
287C2×C3#551614yes—
288C2×C3#552314yes—
289C2×C3#567214yes—
290C2×C3#568414yes—
291C2×C3C3⋊#56414yes—
292C2×C3#569914yes—
293C22C22×C4×C3⋊D311yescharacteristic
294C22#6436111yescharacteristic
295C22#6436411yescharacteristic
296C22#6436611yescharacteristic
297C22#6436711yescharacteristic
298C22#6436711yescharacteristic
299C22#6436711yescharacteristic
300C4—22no—
301C4—22no—
302C4—22no—
303C4—42no—
304C4—42no—
305C4—184no—
306C4—184no—
307C4—362no—
308C4—362no—
309C3#7416114yescomplemented
310C2#1059597511yescharacteristic
311C2#1059598711yescharacteristic
312C2#1059599411yescharacteristic
313C2#1059614311yescharacteristic
314C2#1059615511yescharacteristic
315C2#1059615711yescharacteristic
316C2#1059617011yescharacteristic
subgroupG/H
center, FrattiniC23C23×C3⋊D3
commutatorC22×C32C23×C4
FittingC32×#382C2
socle, prime radical, cosocleC23×C32C24
hypercenter#382C3⋊D3
hypocenterC32#2382
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ #382

Complements

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

NH ≅ G/Ntype
24. #64079C4semidirect
257. C32#2382semidirect
309. C3#74161semidirect

Maximal subgroups

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

subgroupindex
C2×#640792
C32×#3822
#105926772
#105926752
#105926352
#105923542
#105923532
#105923522
#105923462
#741613