Finite Group Databasebeta

← #11790093

Subgroups — #11790093

Order 1152.

744 conjugacy classes of subgroups.

The subgroup lattice has 297 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C8×C3⋊Dic3C211yesmaximal, characteristic
2#10592683C211yesmaximal, characteristic
3#10592671C211yesmaximal, characteristic
4C2×#63635C211yesmaximal, characteristic
5C2×#63635C211yesmaximal, characteristic
6C32×#340C211yesmaximal, characteristic
7#10589417C211yesmaximal, characteristic
8#68858—34nomaximal
9C22×C32×C8C2211yescharacteristic
10C2×C32×C4⋊C4C2211yescharacteristic
11C2×C32×C4⋊C4C2211yescharacteristic
12C2×C4⋊(C3⋊Dic3)—21no—
13C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
14C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
15C2×#3750—21no—
16C2×C4×C3⋊Dic3C2211yescharacteristic
17C22×C3⋊(C3⋊C8)C2211yescharacteristic
18#63658—21no—
19#63658—21no—
20C8×C3⋊Dic3—22no—
21#63635—22no—
22#63635C414yescomplemented
23C2×C8×Dic3—34no—
24#4984—34no—
25#4972—34no—
26C2×#808—34no—
27C2×#808—34no—
28C3×#340D314yes—
29#4551—34no—
30C22×C32×C4—21no—
31C22×C32×C4—21no—
32C22×C32×C4C2311yescharacteristic
33C22×C3⋊Dic3—21no—
34C22×C3⋊Dic3—21no—
35C22×C3⋊Dic3D411yescharacteristic
36C22×C3⋊Dic3D411yescharacteristic
37C2×C32×C8—21no—
38C2×C32×C8—21no—
39C2×C32×C8Q812yes—
40C32×C4⋊C4—21no—
41C32×C4⋊C4—21no—
42C32×C4⋊C4—21no—
43C32×C4⋊C4C2×C412yes—
44C4⋊(C3⋊Dic3)—21no—
45C4⋊(C3⋊Dic3)—21no—
46C4⋊(C3⋊Dic3)—21no—
47C4⋊(C3⋊Dic3)—42no—
48C4⋊(C3⋊Dic3)C2×C412yes—
49#3750—42no—
50C4×C3⋊Dic3—21no—
51C4×C3⋊Dic3—21no—
52C2×C3⋊(C3⋊C8)C2×C412yes—
53C2×C3⋊(C3⋊C8)D412yes—
54C2×C3⋊(C3⋊C8)Q812yes—
55#1941—91noSylow
56C22×C3×C8C2×D314yes—
57C2×C3×C4⋊C4C2×D314yes—
58C2×C3×C4⋊C4C2×D314yes—
59C2×C4⋊Dic3—34no—
60C2×C4⋊Dic3—34no—
61C2×C4⋊Dic3—64no—
62C2×Dic3⋊C4—64no—
63C2×C4×Dic3—34no—
64C22×C3⋊C8—34no—
65C3⋊#95—64no—
66C3⋊#95—64no—
67C8×Dic3—68no—
68#808—316no—
69#808—68no—
70C23×C32C2×D411yescharacteristic
71C2×C32×C4—22no—
72C2×C32×C4—41no—
73C2×C32×C4—41no—
74C2×C32×C4—41no—
75C2×C32×C4—41no—
76C2×C32×C4—41no—
77C2×C32×C4C22×C411yescharacteristic
78C2×C32×C4C2×D411yescharacteristic
79C2×C32×C4C2×Q811yescharacteristic
80C2×C32×C4C2×Q811yescharacteristic
81C2×C32×C4#4111yescharacteristic
82C2×C32×C4#4111yescharacteristic
83C2×C3⋊Dic3—21no—
84C2×C3⋊Dic3—21no—
85C2×C3⋊Dic3—21no—
86C2×C3⋊Dic3—21no—
87C2×C3⋊Dic3—22no—
88C2×C3⋊Dic3—41no—
89C2×C3⋊Dic3—41no—
90C2×C3⋊Dic3—41no—
91C2×C3⋊Dic3—41no—
92C2×C3⋊Dic3—41no—
93C2×C3⋊Dic3SD1612yes—
94C2×C3⋊Dic3SD1612yes—
95C32×C8—22no—
96C3⋊(C3⋊C8)C4⋊C414yescomplemented
97C2×#106—91no—
98C2×#106—91no—
99C2×C4×C8—91no—
100#389—91no—
101#389—91no—
102#340—91no—
103#340C3⋊D311yescharacteristic
104C22×C3×C4—24no—
105C22×C3×C4—24no—
106C22×C3×C4C22×D314yes—
107C22×Dic3—34no—
108C22×Dic3—34no—
109C22×Dic3—64no—
110C22×Dic3—64no—
111C2×C3×C8—24no—
112C2×C3×C8—24no—
113C2×C3×C8Dic618yes—
114C3×C4⋊C4—24no—
115C3×C4⋊C4—24no—
116C3×C4⋊C4—24no—
117C3×C4⋊C4C4×D318yes—
118C4⋊Dic3—38no—
119C4⋊Dic3—64no—
120C4⋊Dic3—64no—
121C4⋊Dic3—64no—
122C4⋊Dic3—128no—
123Dic3⋊C4—128no—
124C4×Dic3—64no—
125C4×Dic3—64no—
126C2×C3⋊C8—38no—
127C2×C3⋊C8—38no—
128C2×C3⋊C8—38no—
129C22×C32C4×D411yescharacteristic
130C22×C32#12111yescharacteristic
131C22×C32C4⋊Q811yescharacteristic
132C22×C32C2×SD1611yescharacteristic
133C22×C32C2×SD1611yescharacteristic
134C22×C32#13511yescharacteristic
135C22×C32#13511yescharacteristic
136C32×C4—42no—
137C32×C4—81no—
138C32×C4C2×C4⋊C411yescharacteristic
139C32×C4C4×Q811yescharacteristic
140C32×C4C22⋊Q811yescharacteristic
141C32×C4#12511yescharacteristic
142C3⋊Dic3—22no—
143C3⋊Dic3—22no—
144C3⋊Dic3—42no—
145C3⋊Dic3—81no—
146C22×C8—91no—
147C22×C8C2×C3⋊D311yescharacteristic
148C2×C4⋊C4—91no—
149C2×C4⋊C4—91no—
150C2×C4⋊C4—181no—
151C2×C4⋊C4—181no—
152C2×C4⋊C4C2×C3⋊D311yescharacteristic
153C2×C4⋊C4C2×C3⋊D311yescharacteristic
154C2×C42—91no—
155#106—94no—
156#106—182no—
157C4×C8—182no—
158#95—181no—
159#95—181no—
160C23×C3D3×D414yes—
161C2×C3×C4—28no—
162C2×C3×C4—44no—
163C2×C3×C4—44no—
164C2×C3×C4—44no—
165C2×C3×C4—44no—
166C2×C3×C4—44no—
167C2×C3×C4C2×Dic614yes—
168C2×C3×C4C2×C4×D314yes—
169C2×C3×C4#23514yes—
170C2×C3×C4D3×D414yes—
171C2×C3×C4#23714yes—
172C2×C3×C4D3×Q814yes—
173C2×Dic3—38no—
174C2×Dic3—38no—
175C2×Dic3—64no—
176C2×Dic3—64no—
177C2×Dic3—64no—
178C2×Dic3—64no—
179C2×Dic3—68no—
180C2×Dic3—124no—
181C2×Dic3—124no—
182C2×Dic3—124no—
183C2×Dic3—124no—
184C2×Dic3—124no—
185C3×C8—28no—
186C3⋊C8—316no—
187C2×C32#38911yescharacteristic
188C2×C32C4×SD1611yescharacteristic
189C2×C32C4×SD1611yescharacteristic
190C2×C32#46511yescharacteristic
191C2×C32#46511yescharacteristic
192C2×C32#49811yescharacteristic
193C2×C32#49911yescharacteristic
194C22×C4—21no—
195C22×C4—21no—
196C22×C4—91no—
197C22×C4—91no—
198C22×C4—181no—
199C22×C4—181no—
200C22×C4C22×C3⋊D311yescharacteristic
201C2×C8—21no—
202C2×C8—21no—
203C2×C8—92no—
204C2×C8—92no—
205C2×C8—92no—
206C2×C8#63412yes—
207C4⋊C4—21no—
208C4⋊C4—21no—
209C4⋊C4—21no—
210C4⋊C4—92no—
211C4⋊C4—181no—
212C4⋊C4—181no—
213C4⋊C4—181no—
214C4⋊C4—362no—
215C4⋊C4—362no—
216C4⋊C4C4×C3⋊D312yes—
217C42—181no—
218C42—181no—
219C22×C3#67⋊C414yes—
220C22×C3#88414yes—
221C22×C3#88814yes—
222C22×C3#91214yes—
223C22×C3D3×SD1614yes—
224C22×C3D3×SD1614yes—
225C22×C3#91914yes—
226C3×C4—48no—
227C3×C4—84no—
228C3×C4C4×Dic614yes—
229C3×C4#87814yes—
230C3×C4#88914yes—
231C3×C4D3×C4⋊C414yes—
232Dic3—68no—
233Dic3—68no—
234Dic3—128no—
235Dic3—244no—
236C32#194111yescharacteristic, complemented, Sylow
237C23D4×C3⋊D311yescharacteristic
238C2×C4—22no—
239C2×C4—41no—
240C2×C4—41no—
241C2×C4—41no—
242C2×C4—41no—
243C2×C4—41no—
244C2×C4—92no—
245C2×C4—92no—
246C2×C4—181no—
247C2×C4—181no—
248C2×C4—181no—
249C2×C4—181no—
250C2×C4—182no—
251C2×C4—361no—
252C2×C4—361no—
253C2×C4—361no—
254C2×C4—361no—
255C2×C4—361no—
256C2×C4C2×#63411yescharacteristic
257C2×C4C2×C4×C3⋊D311yescharacteristic
258C2×C4#382811yescharacteristic
259C2×C4D4×C3⋊D311yescharacteristic
260C2×C4#383011yescharacteristic
261C2×C4Q8×C3⋊D311yescharacteristic
262C8—22no—
263C8—94no—
264C2×C3#464714yes—
265C2×C3#475814yes—
266C2×C3#477814yes—
267C2×C3#478814yes—
268C2×C3#480714yes—
269C2×C3#485514yes—
270C2×C3#487814yes—
271C22#6409011yescharacteristic
272C22#6409311yescharacteristic
273C22#6409711yescharacteristic
274C22#6412111yescharacteristic
275C22SD16×C3⋊D311yescharacteristic
276C22SD16×C3⋊D311yescharacteristic
277C22#6412811yescharacteristic
278C4—42no—
279C4—81no—
280C4—182no—
281C4—182no—
282C4—362no—
283C4—721no—
284C4C4×#63411yescharacteristic
285C4#6408711yescharacteristic
286C4#6409811yescharacteristic
287C4C4⋊C4×C3⋊D311yescharacteristic
288C3#6885814yescomplemented
289C2#1059234611yescharacteristic
290C2#1059245711yescharacteristic
291C2#1059247711yescharacteristic
292C2#1059248711yescharacteristic
293C2#1059250611yescharacteristic
294C2#1059255411yescharacteristic
295C2#1059257711yescharacteristic
subgroupG/H
centerC23D4×C3⋊D3
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C22×C3⋊D3
FittingC32×#340C2
socle, prime radicalC23×C32C2×D4
cosocleC22×C32×C4C23
hypercenter#340C3⋊D3
hypocenterC32#1941
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ #340

Complements

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

NH ≅ G/Ntype
22. #63635C4semidirect
96. C3⋊(C3⋊C8)C4⋊C4semidirect
236. C32#1941semidirect
288. C3#68858semidirect

Maximal subgroups

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

subgroupindex
C2×C8×C3⋊Dic32
#105926832
#105926712
C2×#636352
C32×#3402
#105894172
#688583