Finite Group Databasebeta

← #11772619

Subgroups — #11772619

Order 1152.

437 conjugacy classes of subgroups; only the 104 normal subgroups are shown.

normal subgroups only

This group has 437 conjugacy classes of subgroups — too many to draw. Only its 104 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10592928C211yesmaximal, characteristic
2C2×C3×#836C212yesmaximal
3#67699—32nomaximal
4C22×C32×Q8C2211yescharacteristic
5C2×C4⋊(C3⋊Dic3)C411yescharacteristic
6C2×C4×C3⋊Dic3C411yescharacteristic
7C2×C3×#208—22no—
8#63658—22no—
9C3×#836—22no—
10C3×#836C414yescomplemented
11C2×C3×#101—32no—
12#5229—32no—
13#5229—61no—
14C2×#836D312yes—
15C2×C32×Q8—41no—
16C2×C32×Q8—41no—
17C2×C32×Q8C2×C412yes—
18C2×C32×Q8D411yescharacteristic
19C2×C32×Q8Q811yescharacteristic
20C22×C32×C4C2×C411yescharacteristic
21C22×C32×C4D412yes—
22C22×C3⋊Dic3—21no—
23C22×C3⋊Dic3—21no—
24C4⋊(C3⋊Dic3)—41no—
25C4×C3⋊Dic3—41no—
26C3×#208—24no—
27C3×#208—42no—
28C2×C3×C3⋊C8—42no—
29#1394—91noSylow
30C22×C3×Q8—21no—
31C22×C3×Q8C2×D312yes—
32C2×C3×M16—62no—
33C2×C4⋊Dic3—32no—
34C2×C4⋊Dic3—61no—
35C2×C4×Dic3—32no—
36C2×C4×Dic3—61no—
37C2×#208—22no—
38C3×#101—34no—
39C3×#101—62no—
40#836—22no—
41#836Dic314yescomplemented
42C3⋊#95—64no—
43C3⋊#95—62no—
44C3⋊#95—62no—
45C23×C32C22⋊C411yescharacteristic
46C32×Q8—42no—
47C32×Q8—41no—
48C32×Q8—41no—
49C2×C32×C4—21no—
50C2×C32×C4—21no—
51C2×C32×C4—22no—
52C2×C32×C4—22no—
53C2×C32×C4C4211yescharacteristic
54C2×C32×C4C22⋊C412yes—
55C2×C32×C4C4⋊C411yescharacteristic
56C2×C32×C4C4⋊C412yes—
57C2×C3⋊Dic3—22no—
58C2×C3⋊Dic3—41no—
59C2×C3⋊Dic3—41no—
60C2×C3⋊Dic3—42no—
61C2×C3⋊Dic3—41no—
62C3×C3⋊C8—44no—
63C2×#101—32no—
64#391—91no—
65C2×C3×Q8—22no—
66C2×C3×Q8—21no—
67C2×C3×Q8—21no—
68C2×C3×Q8—42no—
69C2×C3×Q8—42no—
70C2×C3×Q8—42no—
71C2×C3×Q8—42no—
72C2×C3×Q8Dic612yes—
73C2×C3×Q8C4×D312yes—
74C2×C3×Q8C2×Dic312yes—
75C2×C3×Q8#6712yes—
76C22×C3×C4—21no—
77C22×C3×C4—22no—
78C22×C3×C4C4×D312yes—
79C22×C3×C4D1212yes—
80C22×C3×C4#6712yes—
81C22×Dic3—62no—
82C22×Dic3—62no—
83C22×Dic3—62no—
84C22×Dic3—62no—
85C3×M16—64no—
86C3×M16—122no—
87C2×C3×C8—122no—
88C4⋊Dic3—122no—
89C4⋊Dic3—122no—
90C4×Dic3—122no—
91C4×Dic3—122no—
92#208—24no—
93#208—42no—
94C2×C3⋊C8—42no—
95C22×C32—21no—
96C22×C32—21no—
97C22×C32#9511yescharacteristic
98C22×C32#9911yescharacteristic
99C22×C32#9911yescharacteristic
100C32×C4—21no—
101C32×C4—21no—
102C32×C4—22no—
103C32×C4—22no—
104C3⋊Dic3—42no—
105C3⋊Dic3—81no—
106C22×Q8D3211yescharacteristic
107C2×M16—62no—
108C2×C4⋊C4—91no—
109C2×C42—91no—
110#101—34no—
111#101—62no—
112#95—182no—
113C23×C3—21no—
114C23×C3(C2×D3)⋊C412yes—
115C3×Q8—42no—
116C3×Q8—42no—
117C3×Q8—42no—
118C3×Q8—42no—
119C3×Q8—44no—
120C3×Q8—42no—
121C3×Q8—42no—
122C2×C3×C4—22no—
123C2×C3×C4—22no—
124C2×C3×C4—22no—
125C2×C3×C4—22no—
126C2×C3×C4—22no—
127C2×C3×C4—22no—
128C2×C3×C4—22no—
129C2×C3×C4—22no—
130C2×C3×C4—21no—
131C2×C3×C4—22no—
132C2×C3×C4—22no—
133C2×C3×C4—21no—
134C2×C3×C4—42no—
135C2×C3×C4—42no—
136C2×C3×C4C4×Dic312yes—
137C2×C3×C4Dic3⋊C412yes—
138C2×C3×C4Dic3⋊C412yes—
139C2×C3×C4C4⋊Dic312yes—
140C2×C3×C4(C2×D3)⋊C412yes—
141C2×C3×C4#21712yes—
142C2×Dic3—64no—
143C2×Dic3—64no—
144C2×Dic3—122no—
145C2×Dic3—122no—
146C2×Dic3—122no—
147C2×Dic3—122no—
148C2×Dic3—122no—
149C2×Dic3—124no—
150C2×Dic3—124no—
151C2×Dic3—122no—
152C3×C8—124no—
153C3⋊C8—44no—
154C2×C32—21no—
155C2×C32—21no—
156C2×C32#34211yescharacteristic
157C2×C32#35511yescharacteristic
158C2×C32#35611yescharacteristic
159C2×Q8—41no—
160C2×Q8—41no—
161C2×Q8D3×Dic312yes—
162C2×Q8#62511yescharacteristic
163C2×Q8#62711yescharacteristic
164C22×C4—181no—
165C22×C4—181no—
166C22×C4#62411yescharacteristic
167C22×C4#62612yes—
168M16—64no—
169M16—122no—
170C2×C8—122no—
171C4⋊C4—361no—
172C42—361no—
173C22×C3—22no—
174C22×C3—22no—
175C22×C3—22no—
176C22×C3—22no—
177C22×C3—21no—
178C22×C3—21no—
179C22×C3—21no—
180C22×C3#80612yes—
181C22×C3#80612yes—
182C22×C3C3⋊#9512yes—
183C3×C4—22no—
184C3×C4—22no—
185C3×C4—22no—
186C3×C4—22no—
187C3×C4—22no—
188C3×C4—22no—
189C3×C4—22no—
190C3×C4—22no—
191C3×C4—42no—
192C3×C4—42no—
193Dic3—124no—
194Dic3—124no—
195Dic3—242no—
196Dic3—242no—
197C32#139411yescharacteristic, complemented, Sylow
198C23#372211yescharacteristic
199Q8—42no—
200Q8—41no—
201Q8—41no—
202C2×C4—21no—
203C2×C4—22no—
204C2×C4—21no—
205C2×C4—22no—
206C2×C4—182no—
207C2×C4—361no—
208C2×C4—361no—
209C2×C4—362no—
210C2×C4—361no—
211C2×C4Dic3211yescharacteristic
212C2×C4(C2×D3)⋊Dic312yes—
213C2×C4Dic3⋊Dic312yes—
214C2×C4#372411yescharacteristic
215C8—124no—
216C2×C3—22no—
217C2×C3—22no—
218C2×C3—22no—
219C2×C3—22no—
220C2×C3—21no—
221C2×C3—21no—
222C2×C3—21no—
223C2×C3#447712yes—
224C2×C3#447812yes—
225C2×C3#452712yes—
226C22—21no—
227C22—21no—
228C22#6357911yescharacteristic
229C22#6358111yescharacteristic
230C22#6358111yescharacteristic
231C4—22no—
232C4—21no—
233C4—22no—
234C4—21no—
235C4—362no—
236C4—721no—
237C3—21no—
238C3#6769912yescomplemented
239C2—21no—
240C2—21no—
241C2#1058918311yescharacteristic
242C2#1058918511yescharacteristic
243C2#1058918711yescharacteristic
subgroupG/H
centerC22#63581
commutatorC2×C32×C4C42
Frattini, hypercenterC22×Q8D32
Fitting, cosocleC22×C32×Q8C22
socleC22×C32#99
prime radicalC23×C32C22⋊C4
hypocenterC32#1394
LCSG ▷ C2×C32×C4 ▷ C22×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C23 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
10. C3×#836C4semidirect
41. #836Dic3semidirect
197. C32#1394semidirect
238. C3#67699semidirect

Maximal subgroups

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

subgroupindex
#105929282
C2×C3×#8362
#676993