Finite Group Databasebeta

← #11785467

Subgroups — #11785467

Order 1152.

693 conjugacy classes of subgroups; only the 156 normal subgroups are shown.

normal subgroups only

This group has 693 conjugacy classes of subgroups — too many to draw. Only its 156 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
1C22×#3743C211yesmaximal, characteristic
2C2×C3×#819C212yesmaximal, complemented
3#10591074C212yesmaximal
4#10589165C212yesmaximal, complemented
5#70712—32nomaximal
6C22×C4×C3⋊D3C2211yescharacteristic
7C22×C32×C8C2211yescharacteristic
8C22×C3⋊(C3⋊C8)C2211yescharacteristic
9C2×#3743—24no—
10C2×#3743C414yes—
11C2×C3×#208C2214yes—
12C3×#819—24no—
13#63557—24no—
14C22×ΓL(1,𝔽25)—32no—
15C22×ΓL(1,𝔽25)—61no—
16C2×C3×#108—32no—
17#5126—34no—
18C2×#819D312yescomplemented
19#4558—34no—
20C23×C3⋊D3Q811yescharacteristic
21C22×C32×C4C2311yescharacteristic
22C22×C3⋊Dic3Q811yescharacteristic
23C2×C4×C3⋊D3—22no—
24C2×C4×C3⋊D3—22no—
25C2×C4×C3⋊D3C2×C412yes—
26C2×C4×C3⋊D3D412yes—
27C2×C32×C8C2×C412yes—
28C2×C32×C8D414yes—
29C2×C3⋊(C3⋊C8)—22no—
30C2×C3⋊(C3⋊C8)C2×C412yes—
31#3743—28no—
32C3×#208—24no—
33C3×#208—24no—
34C2×C3×C3⋊C8—24no—
35#1811—91noSylow
36C22×C4×D3—32no—
37C22×C4×D3—61no—
38C2×C3×M16—34no—
39C22×C3×C8—21no—
40C22×C3×C8C2×D312yes—
41C2×#208C2×D314yes—
42C22×C3⋊C8—32no—
43C22×C3⋊C8—61no—
44C2×ΓL(1,𝔽25)—38no—
45C2×ΓL(1,𝔽25)—64no—
46C2×ΓL(1,𝔽25)—68no—
47C2×ΓL(1,𝔽25)—64no—
48C2×ΓL(1,𝔽25)—64no—
49C3×#108—64no—
50(C2×D3)⋊C8—68no—
51#819—24no—
52C23×C32C2×Q811yescharacteristic
53C22×C3⋊D3—22no—
54C22×C3⋊D3—42no—
55C22×C3⋊D3C4⋊C412yes—
56C2×C32×C4C22×C411yescharacteristic
57C2×C32×C4C2×D412yes—
58C2×C32×C4C2×D411yescharacteristic
59C2×C32×C4#4112yes—
60C2×C3⋊Dic3—22no—
61C2×C3⋊Dic3C4⋊C412yes—
62C4×C3⋊D3—22no—
63C4×C3⋊D3—22no—
64C4×C3⋊D3—24no—
65C32×C8C22⋊C414yes—
66C3⋊(C3⋊C8)—22no—
67C3×C3⋊C8—44no—
68C22×M16—91no—
69C2×#108—32no—
70#407—92no—
71#341—92no—
72C23×D3—32no—
73C23×D3—61no—
74C22×C3×C4—21no—
75C22×C3×C4C22×D312yes—
76C22×Dic3—32no—
77C22×Dic3—61no—
78C2×C4×D3—34no—
79C2×C4×D3—34no—
80C2×C4×D3—62no—
81C2×C4×D3—62no—
82C2×C4×D3—64no—
83C2×C4×D3—64no—
84C2×C4×D3—62no—
85C2×C4×D3—62no—
86C2×C4×D3—62no—
87C2×C4×D3—62no—
88C3×M16—64no—
89C3×M16—64no—
90C2×C3×C8—22no—
91C2×C3×C8—24no—
92C2×C3×C8—64no—
93C2×C3×C8C4×D314yes—
94C2×C3×C8D1214yes—
95C2×C3×C8#6714yes—
96#208—24no—
97#208—24no—
98C2×C3⋊C8—24no—
99C2×C3⋊C8—34no—
100C2×C3⋊C8—62no—
101C2×C3⋊C8—64no—
102C2×C3⋊C8—62no—
103C2×C3⋊C8—62no—
104ΓL(1,𝔽25)—616no—
105ΓL(1,𝔽25)—616no—
106C22×C32—22no—
107C22×C32C2×C4⋊C411yescharacteristic
108C22×C32C22⋊Q812yes—
109C2×C3⋊D3—22no—
110C2×C3⋊D3—24no—
111C2×C3⋊D3—44no—
112C32×C4C2×C22⋊C411yescharacteristic
113C32×C4#11711yescharacteristic
114C32×C4#12112yes—
115C3⋊Dic3—22no—
116C23×C4—91no—
117C2×M16—34no—
118C2×M16—94no—
119C2×M16—184no—
120C22×C8—91no—
121C22×C8D3211yescharacteristic
122#108—64no—
123C22⋊C8—184no—
124C23×C3—21no—
125C23×C3D3×Q812yes—
126C22×D3—34no—
127C22×D3—62no—
128C22×D3—64no—
129C22×D3—62no—
130C22×D3—62no—
131C22×D3—124no—
132C22×D3—124no—
133C2×C3×C4—22no—
134C2×C3×C4—21no—
135C2×C3×C4—21no—
136C2×C3×C4—22no—
137C2×C3×C4C2×C4×D312yes—
138C2×C3×C4C2×D1212yes—
139C2×C3×C4D3×D412yes—
140C2×C3×C4#23712yes—
141C2×C3×C4#23912yes—
142C2×C3×C4C2×#6712yes—
143C2×Dic3—34no—
144C2×Dic3—62no—
145C2×Dic3—64no—
146C2×Dic3—62no—
147C2×Dic3—62no—
148C4×D3—64no—
149C4×D3—64no—
150C4×D3—68no—
151C4×D3—64no—
152C4×D3—64no—
153C4×D3—64no—
154C4×D3—64no—
155C3×C8—24no—
156C3×C8—124no—
157C3×C8(C2×D3)⋊C418yes—
158C3⋊C8—44no—
159C3⋊C8—64no—
160C3⋊C8—64no—
161C2×C32—22no—
162C2×C32#38011yescharacteristic
163C2×C32#43012yes—
164C3⋊D3—42no—
165C24—91no—
166C22×C4—91no—
167C22×C4—92no—
168C22×C4—92no—
169C22×C4—182no—
170C22×C4—182no—
171C22×C4C2×D3211yescharacteristic
172M16—64no—
173M16—64no—
174M16—188no—
175C2×C8—64no—
176C2×C8—92no—
177C2×C8—182no—
178C2×C8#62412yes—
179C2×C8#62614yes—
180C22×C3—24no—
181C22×C3—24no—
182C22×C3—22no—
183C22×C3—21no—
184C22×C3D3×C4⋊C412yes—
185C22×C3#89712yes—
186C22×C3#94612yes—
187C2×D3—64no—
188C2×D3—68no—
189C2×D3—64no—
190C2×D3—124no—
191C2×D3—128no—
192C2×D3—124no—
193C2×D3—124no—
194C3×C4—21no—
195C3×C4—22no—
196C3×C4—21no—
197C3×C4#89212yes—
198C3×C4#89512yes—
199C3×C4C2×(C2×D3)⋊C412yes—
200C3×C4#93812yes—
201Dic3—64no—
202Dic3—64no—
203C32#181111yescharacteristic, complemented, Sylow
204C23—92no—
205C23—182no—
206C23—362no—
207C23#379711yescharacteristic
208C2×C4—92no—
209C2×C4—182no—
210C2×C4—182no—
211C2×C4—184no—
212C2×C4—182no—
213C2×C4#379612yes—
214C2×C4#380211yescharacteristic
215C2×C4C2×#62411yescharacteristic
216C2×C4C2×#62612yes—
217C8—124no—
218C8—182no—
219C8#372214yes—
220C2×C3—24no—
221C2×C3—22no—
222C2×C3—22no—
223C2×C3—21no—
224C2×C3—22no—
225C2×C3#489314yes—
226C2×C3#498712yes—
227D3—124no—
228D3—124no—
229C22—22no—
230C22—182no—
231C22—184no—
232C22—364no—
233C22#6387112yes—
234C22#6390011yescharacteristic
235C4—182no—
236C4#6384911yescharacteristic
237C4#6391612yes—
238C4C2×#372211yescharacteristic
239C3—21no—
240C3#7071212yescomplemented
241C2—22no—
242C2—362no—
243C2#1059091412yes—
244C2#1059132511yescharacteristic
subgroupG/H
centerC2×C4#3802
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC22×C32×C8C22
socleC22×C32C2×C4⋊C4
prime radicalC23×C3⋊D3Q8
cosocleC22×C32×C4C23
hypercenterC22×C8D32
hypocenterC32#1811
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
2. C2×C3×#819C2semidirect
4. #10589165C2semidirect
18. C2×#819D3semidirect
203. C32#1811semidirect
240. C3#70712semidirect

Maximal subgroups

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

subgroupindex
C22×#37432
C2×C3×#8192
#105910742
#105891652
#707123