Finite Group Databasebeta

← #11771508

Subgroups — #11771508

Order 1152.

221 conjugacy classes of subgroups; only the 62 normal subgroups are shown.

normal subgroups only

This group has 221 conjugacy classes of subgroups — too many to draw. Only its 62 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×#5118C211yesmaximal, characteristic
2#10589419C211yesmaximal, characteristic
3C3×#4553C211yesmaximal, characteristic
4#67717—31nomaximal
5#67532—31nomaximal
6C2×C32×M16C2211yescharacteristic
7C2×C3×C4×Dic3C411yescharacteristic
8C2×C3×#208C411yescharacteristic
9#63639—21no—
10C3×Dic3⋊C8—21no—
11C3×Dic3⋊C8—21no—
12C3×#812—21no—
13C3×#423—31no—
14#5118D311yescharacteristic
15C3×#349—31no—
16#4553—31no—
17#4553—31no—
18#4553—61no—
19#4553D311yescharacteristic
20C22×C32×C4C2×C411yescharacteristic
21C22×C3×Dic3—21no—
22C32×M16—41no—
23C2×C32×C8D411yescharacteristic
24C2×C32×C8D411yescharacteristic
25C3×C4×Dic3—21no—
26C3×C4×Dic3C811yescharacteristic
27C3×C4×Dic3C811yescharacteristic
28C3×#208—41no—
29C2×C3×C3⋊C8—21no—
30C3⋊(C3⋊C16)—41no—
31C3×C3⋊C16—41no—
32#1327—91noSylow
33C2×C3×M16—21no—
34C2×C3×M16—31no—
35C2×C3×M16C2×D311yescharacteristic
36C2×C3×M16C2×D311yescharacteristic
37C2×C3×C42—31no—
38C2×C4×Dic3Dic311yescharacteristic
39C2×#208Dic311yescharacteristic
40C3×M32—61no—
41C3×C4⋊C8—61no—
42C3×C4⋊C8—61no—
43Dic3⋊C8—21no—
44Dic3⋊C8—21no—
45#812—21no—
46#812—62no—
47#812—61no—
48#812—61no—
49C23×C32M1611yescharacteristic
50C2×C32×C4—21no—
51C2×C32×C4—21no—
52C2×C32×C4C22⋊C411yescharacteristic
53C2×C32×C4C2×C811yescharacteristic
54C2×C3×Dic3—21no—
55C2×C3×Dic3—21no—
56C2×C3×Dic3—42no—
57C32×C8—21no—
58C32×C8—21no—
59C3×C3⋊C8—41no—
60#423—31no—
61#349—31no—
62#349—91no—
63C22×C3×C4—21no—
64C22×C3×C4—61no—
65C22×C3×C4C4×D311yescharacteristic
66C22×C3×C4C2×Dic311yescharacteristic
67C22×Dic3—21no—
68C3×M16—41no—
69C3×M16—41no—
70C3×M16—42no—
71C3×M16—121no—
72C2×C3×C8—21no—
73C2×C3×C8—21no—
74C2×C3×C8—61no—
75C2×C3×C8D1211yescharacteristic
76C2×C3×C8#6711yescharacteristic
77C2×C3×C8#6711yescharacteristic
78C2×C3×C8#6711yescharacteristic
79C3×C42—31no—
80C3×C42—31no—
81C3×C42—61no—
82C4×Dic3—21no—
83C4×Dic3C3⋊C811yescharacteristic
84C4×Dic3C3⋊C811yescharacteristic
85#208—41no—
86C2×C3⋊C8—21no—
87C3×C16—121no—
88C3⋊C16—41no—
89C3⋊C16—122no—
90C3⋊C16—121no—
91C3⋊C16—121no—
92C22×C32—21no—
93C22×C32—41no—
94C22×C32C22⋊C811yescharacteristic
95C32×C4—21no—
96C32×C4#9911yescharacteristic
97C32×C4#10111yescharacteristic
98C3×Dic3—22no—
99C3×Dic3—41no—
100C2×M16—31no—
101C2×M16D3211yescharacteristic
102C2×C42—31no—
103M32—61no—
104M32—181no—
105C4⋊C8—61no—
106C4⋊C8—61no—
107C23×C3—21no—
108C23×C3ΓL(1,𝔽25)11yescharacteristic
109C23×C3#20811yescharacteristic
110C2×C3×C4—21no—
111C2×C3×C4—21no—
112C2×C3×C4—21no—
113C2×C3×C4—21no—
114C2×C3×C4—21no—
115C2×C3×C4—21no—
116C2×C3×C4—41no—
117C2×C3×C4—41no—
118C2×C3×C4—61no—
119C2×C3×C4—61no—
120C2×C3×C4—122no—
121C2×C3×C4D3×C811yescharacteristic
122C2×C3×C4C2×C3⋊C811yescharacteristic
123C2×C3×C4(C2×D3)⋊C411yescharacteristic
124C2×C3×C4#21711yescharacteristic
125C2×Dic3—21no—
126C2×Dic3—21no—
127C2×Dic3—42no—
128C3×C8—22no—
129C3×C8—21no—
130C3×C8—21no—
131C3×C8—21no—
132C3×C8—21no—
133C3×C8—41no—
134C3×C8—121no—
135C3⋊C8—41no—
136C2×C32—21no—
137C2×C32—41no—
138C2×C32#32411yescharacteristic
139C22×C4—61no—
140C22×C4D3×Dic311yescharacteristic
141M16—41no—
142M16—121no—
143C2×C8—61no—
144C2×C8#62511yescharacteristic
145C2×C8#62611yescharacteristic
146C42—31no—
147C42—31no—
148C42—61no—
149C16—121no—
150C16—361no—
151C22×C3—21no—
152C22×C3—21no—
153C22×C3—21no—
154C22×C3—41no—
155C22×C3—41no—
156C22×C3—41no—
157C22×C3—81no—
158C22×C3(C2×D3)⋊C811yescharacteristic
159C22×C3#83011yescharacteristic
160C3×C4—21no—
161C3×C4—21no—
162C3×C4—21no—
163C3×C4—21no—
164C3×C4—41no—
165C3×C4—62no—
166C3×C4—121no—
167C3×C4#80611yescharacteristic
168C3×C4#82411yescharacteristic
169C3×C4#83411yescharacteristic
170C3×C4#83611yescharacteristic
171Dic3—22no—
172Dic3—41no—
173C32#132711yescharacteristic, complemented, Sylow
174C23#371111yescharacteristic
175C2×C4—21no—
176C2×C4—21no—
177C2×C4—61no—
178C2×C4—61no—
179C2×C4—122no—
180C2×C4D3×C3⋊C811yescharacteristic
181C2×C4(C2×D3)⋊Dic311yescharacteristic
182C8—21no—
183C8—21no—
184C8—121no—
185C2×C3—21no—
186C2×C3—21no—
187C2×C3—21no—
188C2×C3—41no—
189C2×C3—41no—
190C2×C3—41no—
191C2×C3—81no—
192C2×C3#446911yescharacteristic
193C2×C3#452811yescharacteristic
194C22—21no—
195C22—41no—
196C22(C2×D3)⋊(C3⋊C8)11yescharacteristic
197C4—21no—
198C4—62no—
199C4—121no—
200C4#6356011yescharacteristic
201C4#6358011yescharacteristic
202C3—21no—
203C3#6753211yescharacteristic, complemented
204C3#6771711yescharacteristic, complemented
205C2—21no—
206C2—41no—
207C2#1058914711yescharacteristic
subgroupG/H
centerC4#63580
commutatorC2×C32×C4C2×C8
Frattini, hypercenterC2×M16D32
Fitting, cosocleC2×C32×M16C22
socleC2×C32#324
prime radicalC23×C32M16
hypocenterC32#1327
LCSG ▷ C2×C32×C4 ▷ C22×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C4 ◁ C2×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
173. C32#1327semidirect
203. C3#67532semidirect
204. C3#67717semidirect

Maximal subgroups

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

subgroupindex
C3×#51182
#105894192
C3×#45532
#677173
#675323