Finite Group Databasebeta

← #11771775

Subgroups — #11771775

Order 1152.

229 conjugacy classes of subgroups; only the 58 normal subgroups are shown.

normal subgroups only

This group has 229 conjugacy classes of subgroups — too many to draw. Only its 58 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
1C3×#5137C211yesmaximal, characteristic
2#10589419C211yesmaximal, characteristic
3C3×C3⋊#338C211yesmaximal, characteristic
4#67781—31nomaximal
5#67484—31nomaximal
6C2×C32×M16C2211yescharacteristic
7C3×#924—21no—
8C2×C3×#208—21no—
9C2×C3×Dic12C411yescharacteristic
10#63639—21no—
11C3×#817C411yescharacteristic
12C3×#816—21no—
13C3×#470—31no—
14#5137D311yescharacteristic
15C3×#338—31no—
16C3⋊#338D311yescharacteristic
17#4553—31no—
18#4553—31no—
19#4553—61no—
20C22×C32×C4D411yescharacteristic
21C2×C3×Dic6—21no—
22C32×M16—41no—
23C2×C32×C8C2×C411yescharacteristic
24C2×C32×C8D411yescharacteristic
25C3×#217—41no—
26C3×C4⋊Dic3—21no—
27C3×Dic3⋊C4—41no—
28C3×#208—41no—
29C3×#208—41no—
30C2×C3×C3⋊C8—22no—
31C3×Dic12—41no—
32C3⋊(C3⋊C16)—41no—
33#1342—91noSylow
34C2×C3×Q16—31no—
35C2×C3×M16—21no—
36C2×C3×M16—61no—
37C2×C3×M16C2×D311yescharacteristic
38C2×C3×M16C2×D311yescharacteristic
39C3×C22⋊Q8—61no—
40#924—21no—
41C2×#208—21no—
42C2×Dic12Dic311yescharacteristic
43C3×#106—31no—
44C3×#103—61no—
45#817Dic311yescharacteristic
46#816—21no—
47#812—62no—
48#812—61no—
49#812—61no—
50C23×C32SD1611yescharacteristic
51C2×C32×C4—21no—
52C2×C32×C4—21no—
53C2×C32×C4C22⋊C411yescharacteristic
54C2×C32×C4D811yescharacteristic
55C2×C3×Dic3—41no—
56C2×C3×Dic3—41no—
57C3×Dic6—41no—
58C3×Dic6—41no—
59C32×C8—21no—
60C32×C8—21no—
61C3×C3⋊C8—42no—
62#470—31no—
63#349—91no—
64#338—31no—
65C2×C3×Q8—61no—
66C22×C3×C4—21no—
67C22×C3×C4#6711yescharacteristic
68C22×C3×C4#6711yescharacteristic
69C2×Dic6—21no—
70C3×Q16—121no—
71C3×M16—41no—
72C3×M16—41no—
73C3×M16—42no—
74C3×M16—121no—
75C3×M16—121no—
76C2×C3×C8—21no—
77C2×C3×C8—21no—
78C2×C3×C8—62no—
79C2×C3×C8C4×D311yescharacteristic
80C2×C3×C8D1211yescharacteristic
81C2×C3×C8C2×Dic311yescharacteristic
82C2×C3×C8#6711yescharacteristic
83C3×C4⋊C4—61no—
84C3×C4⋊C4—121no—
85C3×C22⋊C4—121no—
86#217—41no—
87C4⋊Dic3—21no—
88Dic3⋊C4—41no—
89#208—41no—
90#208—41no—
91C2×C3⋊C8—22no—
92Dic12—41no—
93C3⋊C16—122no—
94C3⋊C16—121no—
95C3⋊C16—121no—
96C22×C32—21no—
97C22×C32—41no—
98C22×C32#10211yescharacteristic
99C32×C4—21no—
100C32×C4#9911yescharacteristic
101C32×C4#10411yescharacteristic
102C3×Dic3—81no—
103C3×Dic3—81no—
104C2×Q16—31no—
105C2×M16—61no—
106C2×M16D3211yescharacteristic
107C22⋊Q8—61no—
108M32—181no—
109#106—31no—
110#103—61no—
111C23×C3—21no—
112C23×C3#21411yescharacteristic
113C23×C3#21511yescharacteristic
114C3×Q8—121no—
115C3×Q8—121no—
116C2×C3×C4—21no—
117C2×C3×C4—21no—
118C2×C3×C4—21no—
119C2×C3×C4—21no—
120C2×C3×C4—21no—
121C2×C3×C4—21no—
122C2×C3×C4—41no—
123C2×C3×C4—41no—
124C2×C3×C4—121no—
125C2×C3×C4—121no—
126C2×C3×C4(C2×D3)⋊C411yescharacteristic
127C2×C3×C4#21311yescharacteristic
128C2×C3×C4#21311yescharacteristic
129C2×C3×C4#21711yescharacteristic
130C2×Dic3—41no—
131C2×Dic3—41no—
132Dic6—41no—
133Dic6—41no—
134C3×C8—22no—
135C3×C8—21no—
136C3×C8—21no—
137C3×C8—21no—
138C3×C8—21no—
139C3×C8—41no—
140C3×C8—122no—
141C3⋊C8—42no—
142C2×C32—21no—
143C2×C32—41no—
144C2×C32#32711yescharacteristic
145C2×Q8—61no—
146C22×C4#62511yescharacteristic
147Q16—121no—
148M16—41no—
149M16—121no—
150M16—121no—
151C2×C8—62no—
152C2×C8D3×Dic311yescharacteristic
153C2×C8#62611yescharacteristic
154C4⋊C4—61no—
155C4⋊C4—121no—
156C22⋊C4—121no—
157C16—361no—
158C22×C3—21no—
159C22×C3—21no—
160C22×C3—21no—
161C22×C3—41no—
162C22×C3—41no—
163C22×C3—41no—
164C22×C3—81no—
165C22×C3#80911yescharacteristic
166C22×C3#83211yescharacteristic
167C3×C4—21no—
168C3×C4—21no—
169C3×C4—21no—
170C3×C4—21no—
171C3×C4—41no—
172C3×C4—241no—
173C3×C4—241no—
174C3×C4#80511yescharacteristic
175C3×C4#80611yescharacteristic
176C3×C4#83411yescharacteristic
177C3×C4#83711yescharacteristic
178Dic3—81no—
179Dic3—81no—
180C32#134211yescharacteristic, complemented, Sylow
181C23#371511yescharacteristic
182Q8—121no—
183Q8—121no—
184C2×C4—21no—
185C2×C4—21no—
186C2×C4—121no—
187C2×C4—121no—
188C2×C4#371311yescharacteristic
189C2×C4(C2×D3)⋊Dic311yescharacteristic
190C8—21no—
191C8—21no—
192C8—122no—
193C2×C3—21no—
194C2×C3—21no—
195C2×C3—21no—
196C2×C3—41no—
197C2×C3—41no—
198C2×C3—41no—
199C2×C3—81no—
200C2×C3#445111yescharacteristic
201C2×C3#453711yescharacteristic
202C22—21no—
203C22—41no—
204C22#6356211yescharacteristic
205C4—21no—
206C4—241no—
207C4—241no—
208C4#6356911yescharacteristic
209C4#6358011yescharacteristic
210C3—21no—
211C3#6748411yescharacteristic, complemented
212C3#6778111yescharacteristic, complemented
213C2—21no—
214C2—41no—
215C2#1058914911yescharacteristic
subgroupG/H
centerC2#10589149
commutatorC2×C32×C8C2×C4
Frattini, hypercenterC2×M16D32
Fitting, cosocleC2×C32×M16C22
socleC2×C32#327
prime radicalC23×C32SD16
hypocenterC32#1342
LCSG ▷ C2×C32×C8 ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
180. C32#1342semidirect
211. C3#67484semidirect
212. C3#67781semidirect

Maximal subgroups

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

subgroupindex
C3×#51372
#105894192
C3×C3⋊#3382
#677813
#674843