Finite Group Databasebeta

← #11772591

Subgroups — #11772591

Order 1152.

395 conjugacy classes of subgroups; only the 96 normal subgroups are shown.

normal subgroups only

This group has 395 conjugacy classes of subgroups — too many to draw. Only its 96 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#10592933C211yesmaximal, characteristic
2C3×#5237C212yesmaximal
3#67700—32nomaximal
4C2×C32×#41C2211yescharacteristic
5C2×#3748C411yescharacteristic
6C22×C3⋊(C3⋊C8)C411yescharacteristic
7C2×C3×#208—22no—
8#63657—22no—
9C3×#836—22no—
10C3×#833C414yes—
11C3×#413—32no—
12#5237D312yes—
13#5234—32no—
14#5234—61no—
15C32×#41—41no—
16C32×#41—41no—
17C2×C32×Q8D411yescharacteristic
18C2×C32×D4C2×C412yes—
19C2×C32×D4Q811yescharacteristic
20C22×C32×C4C2×C411yescharacteristic
21C22×C32×C4D412yes—
22#3748—41no—
23C2×C3⋊(C3⋊C8)—21no—
24C2×C3⋊(C3⋊C8)—21no—
25C2×C3⋊(C3⋊C8)—41no—
26C3×#208—24no—
27C3×#208—42no—
28C2×C3×C3⋊C8—42no—
29#1392—91noSylow
30C2×C3×#41—21no—
31C2×C3×#41C2×D312yes—
32C2×C3×M16—62no—
33C2×#208—22no—
34C2×#208—32no—
35C2×#208—61no—
36C22×C3⋊C8—32no—
37C22×C3⋊C8—61no—
38C3×#101—62no—
39C3×#100—34no—
40#836—22no—
41#833Dic314yes—
42#830—64no—
43#830—62no—
44#830—62no—
45C23×C32C4211yescharacteristic
46C23×C32C4⋊C412yes—
47C32×Q8—41no—
48C32×D4—42no—
49C32×D4—41no—
50C2×C32×C4—21no—
51C2×C32×C4—21no—
52C2×C32×C4—22no—
53C2×C32×C4—22no—
54C2×C32×C4C22⋊C411yescharacteristic
55C2×C32×C4C22⋊C412yes—
56C2×C32×C4C4⋊C411yescharacteristic
57C3⋊(C3⋊C8)—41no—
58C3⋊(C3⋊C8)—41no—
59C3×C3⋊C8—44no—
60#413—32no—
61#408—91no—
62C3×#41—42no—
63C3×#41—42no—
64C3×#41—42no—
65C3×#41—42no—
66C2×C3×Q8—21no—
67C2×C3×Q8#6712yes—
68C2×C3×D4—22no—
69C2×C3×D4—21no—
70C2×C3×D4Dic612yes—
71C2×C3×D4C4×D312yes—
72C2×C3×D4C2×Dic312yes—
73C22×C3×C4—21no—
74C22×C3×C4—22no—
75C22×C3×C4C4×D312yes—
76C22×C3×C4D1212yes—
77C22×C3×C4#6712yes—
78C3×M16—64no—
79C3×M16—122no—
80C2×C3×C8—122no—
81#208—24no—
82#208—42no—
83#208—122no—
84#208—122no—
85C2×C3⋊C8—42no—
86C2×C3⋊C8—62no—
87C2×C3⋊C8—62no—
88C2×C3⋊C8—62no—
89C2×C3⋊C8—62no—
90C2×C3⋊C8—122no—
91C2×C3⋊C8—122no—
92C22×C32—21no—
93C22×C32—22no—
94C22×C32—41no—
95C22×C32—42no—
96C22×C32#9511yescharacteristic
97C32×C4—21no—
98C32×C4—22no—
99C32×C4#9911yescharacteristic
100C32×C4#9911yescharacteristic
101C2×#41D3211yescharacteristic
102C2×M16—62no—
103C2×M16—91no—
104C22×C8—91no—
105#101—62no—
106#100—34no—
107C22⋊C8—182no—
108C23×C3—21no—
109C23×C3—22no—
110C23×C3C4×Dic312yes—
111C23×C3Dic3⋊C412yes—
112C23×C3C4⋊Dic312yes—
113C3×Q8—42no—
114C3×Q8—42no—
115C3×D4—42no—
116C3×D4—42no—
117C3×D4—42no—
118C3×D4—42no—
119C3×D4—44no—
120C2×C3×C4—22no—
121C2×C3×C4—22no—
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—21no—
130C2×C3×C4—21no—
131C2×C3×C4—42no—
132C2×C3×C4—42no—
133C2×C3×C4Dic3⋊C412yes—
134C2×C3×C4(C2×D3)⋊C412yes—
135C2×C3×C4(C2×D3)⋊C412yes—
136C2×C3×C4#21712yes—
137C3×C8—124no—
138C3⋊C8—44no—
139C3⋊C8—122no—
140C3⋊C8—122no—
141C3⋊C8—122no—
142C3⋊C8—122no—
143C2×C32—21no—
144C2×C32—41no—
145C2×C32—42no—
146C2×C32#34211yescharacteristic
147#41—41no—
148#41—41no—
149C2×Q8#62511yescharacteristic
150C2×D4D3×Dic312yes—
151C2×D4#62711yescharacteristic
152C22×C4#62411yescharacteristic
153C22×C4#62612yes—
154M16—64no—
155M16—122no—
156M16—361no—
157C2×C8—122no—
158C2×C8—181no—
159C2×C8—181no—
160C2×C8—361no—
161C22×C3—22no—
162C22×C3—22no—
163C22×C3—22no—
164C22×C3—22no—
165C22×C3—21no—
166C22×C3—42no—
167C22×C3—42no—
168C22×C3—42no—
169C22×C3—42no—
170C22×C3—42no—
171C22×C3—44no—
172C22×C3C3⋊#9512yes—
173C3×C4—22no—
174C3×C4—22no—
175C3×C4—22no—
176C3×C4—22no—
177C3×C4—21no—
178C3×C4—21no—
179C3×C4—42no—
180C3×C4#80612yes—
181C3×C4#80612yes—
182C32#139211yescharacteristic, complemented, Sylow
183C23Dic3211yescharacteristic
184C23Dic3⋊Dic312yes—
185Q8—41no—
186D4—42no—
187D4—41no—
188C2×C4—22no—
189C2×C4—21no—
190C2×C4—22no—
191C2×C4—21no—
192C2×C4(C2×D3)⋊Dic312yes—
193C2×C4#372211yescharacteristic
194C2×C4#372411yescharacteristic
195C8—124no—
196C8—361no—
197C8—361no—
198C2×C3—22no—
199C2×C3—22no—
200C2×C3—21no—
201C2×C3—42no—
202C2×C3—42no—
203C2×C3—42no—
204C2×C3—42no—
205C2×C3—82no—
206C2×C3#452712yes—
207C22—21no—
208C22—22no—
209C22—41no—
210C22—42no—
211C22#6357911yescharacteristic
212C4—22no—
213C4—21no—
214C4#6358111yescharacteristic
215C4#6358111yescharacteristic
216C3—21no—
217C3#6770012yescomplemented
218C2—21no—
219C2—41no—
220C2—42no—
221C2#1058918711yescharacteristic
subgroupG/H
centerC4#63581
commutatorC23×C32C42
Frattini, hypercenterC2×#41D32
Fitting, prime radical, cosocleC2×C32×#41C22
socleC2×C32#342
hypocenterC32#1392
LCSG ▷ C23×C32 ▷ C22×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C4 ◁ C2×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
182. C32#1392semidirect
217. C3#67700semidirect

Maximal subgroups

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

subgroupindex
#105929332
C3×#52372
#677003