Finite Group Databasebeta

← #11785526

Subgroups — #11785526

Order 1152.

637 conjugacy classes of subgroups; only the 124 normal subgroups are shown.

normal subgroups only

This group has 637 conjugacy classes of subgroups — too many to draw. Only its 124 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
1C2×#64116C211yesmaximal, characteristic
2C2×#63578C212yesmaximal, complemented
3#10591078C212yesmaximal
4C3×C3⋊#338C212yesmaximal, complemented
5#68724—32nomaximal
6C2×#3828C2211yescharacteristic
7C2×C32×M16C2211yescharacteristic
8C22×C3⋊(C3⋊C8)C2211yescharacteristic
9#64116—24no—
10C2×#3743C412yes—
11C2×C8×C3⋊D3C412yes—
12C2×C3×#208C2214yes—
13#63578—24no—
14#63561—22no—
15#63559—22no—
16C2×#907—32no—
17C2×#907—61no—
18#5132—34no—
19C2×#822—34no—
20C3×#338—32no—
21C3⋊#338D312yescomplemented
22C22×C32×C4C2311yescharacteristic
23C2×#638Q812yes—
24#3828—22no—
25#3828—22no—
26C2×C4⋊(C3⋊D3)D411yescharacteristic
27C2×C4×C3⋊D3C2×C412yes—
28C2×#634D411yescharacteristic
29C32×M16—22no—
30C2×C32×C8C2×C412yes—
31C2×C3⋊(C3⋊C8)C2×C411yescharacteristic
32C2×C3⋊(C3⋊C8)C2×C411yescharacteristic
33C2×C3⋊(C3⋊C8)D414yes—
34#3743—24no—
35C8×C3⋊D3—24no—
36C3×#208—24no—
37C3×#208—24no—
38C2×C3×C3⋊C8—24no—
39#1813—91noSylow
40C2×#235—32no—
41C2×#235—61no—
42C2×C3×M16—21no—
43C2×C3×M16—34no—
44C2×C3×M16C2×D312yes—
45C2×#208C2×D314yes—
46C22×C3⋊C8—32no—
47C22×C3⋊C8—61no—
48#907—68no—
49#907—68no—
50C2×ΓL(1,𝔽25)—34no—
51C2×ΓL(1,𝔽25)—62no—
52C2×D3×C8—34no—
53C2×D3×C8—62no—
54#824—64no—
55#823—64no—
56#822—68no—
57C23×C32C2×Q811yescharacteristic
58C22×C3⋊D3C4⋊C412yes—
59C2×C32×C4C22×C411yescharacteristic
60C2×C32×C4C2×D412yes—
61C2×C32×C4C2×D411yescharacteristic
62C2×C32×C4#4112yes—
63#638—24no—
64C2×C3⋊Dic3C4⋊C412yes—
65C4⋊(C3⋊D3)—22no—
66C4×C3⋊D3—22no—
67C4×C3⋊D3—22no—
68#634—22no—
69C32×C8—22no—
70C3⋊(C3⋊C8)C22⋊C412yes—
71C3⋊(C3⋊C8)C22⋊C412yes—
72C3×C3⋊C8—44no—
73C2×#131—91no—
74C2×#108—92no—
75#413—92no—
76#338—32no—
77C22×C3×C4—21no—
78C22×C3×C4C22×D312yes—
79C2×#67—34no—
80C2×#67—62no—
81#235—64no—
82#235—64no—
83#235—64no—
84#235—64no—
85C2×D12—32no—
86C2×D12—61no—
87C2×C4×D3—34no—
88C2×C4×D3—62no—
89C2×Dic6—32no—
90C2×Dic6—61no—
91C3×M16—24no—
92C3×M16—24no—
93C3×M16—64no—
94C3×M16—64no—
95C2×C3×C8—22no—
96C2×C3×C8—64no—
97C2×C3×C8C4×D314yes—
98#208—24no—
99#208—24no—
100C2×C3⋊C8—24no—
101C2×C3⋊C8—32no—
102C2×C3⋊C8—32no—
103C2×C3⋊C8—38no—
104C2×C3⋊C8—61no—
105C2×C3⋊C8—61no—
106C2×C3⋊C8—64no—
107ΓL(1,𝔽25)—68no—
108ΓL(1,𝔽25)—68no—
109D3×C8—68no—
110D3×C8—68no—
111C22×C32—41no—
112C22×C32C2×C4⋊C411yescharacteristic
113C22×C32C22⋊Q812yes—
114C2×C3⋊D3—22no—
115C2×C3⋊D3—42no—
116C32×C4C2×C22⋊C411yescharacteristic
117C32×C4#11711yescharacteristic
118C32×C4#12112yes—
119C3⋊Dic3—22no—
120C2×#41—91no—
121#131—184no—
122C2×M16—34no—
123C2×M16—92no—
124C2×M16D3211yescharacteristic
125C22×C8—91no—
126C22×C8—92no—
127#108—184no—
128#101—182no—
129#100—182no—
130C23×C3—21no—
131C23×C3D3×Q812yes—
132C22×D3—34no—
133C22×D3—62no—
134C2×C3×C4—22no—
135C2×C3×C4—21no—
136C2×C3×C4—21no—
137C2×C3×C4—22no—
138C2×C3×C4C2×C4×D312yes—
139C2×C3×C4#23514yes—
140C2×C3×C4D3×D412yes—
141C2×C3×C4D3×D414yes—
142#67—68no—
143#67—68no—
144C2×Dic3—34no—
145C2×Dic3—62no—
146D12—64no—
147D12—64no—
148C4×D3—64no—
149C4×D3—64no—
150C4×D3—64no—
151C4×D3—64no—
152Dic6—64no—
153Dic6—64no—
154C3×C8—24no—
155C3×C8—24no—
156C3×C8—124no—
157C3⋊C8—34no—
158C3⋊C8—34no—
159C3⋊C8—44no—
160C3⋊C8—62no—
161C3⋊C8—62no—
162C2×C32—21no—
163C2×C32—22no—
164C2×C32#38011yescharacteristic
165C3⋊D3—42no—
166#41—182no—
167#41—182no—
168C2×Q8—91no—
169C2×D4—92no—
170C2×D4—91no—
171C22×C4—92no—
172C22×C4C2×D3211yescharacteristic
173M16—22no—
174M16—64no—
175M16—64no—
176M16—184no—
177C2×C8—64no—
178C2×C8—91no—
179C2×C8—91no—
180C2×C8—94no—
181C2×C8—184no—
182C2×C8#62412yes—
183C22×C3—22no—
184C22×C3—21no—
185C22×C3—42no—
186C22×C3—42no—
187C22×C3D3×C4⋊C412yes—
188C22×C3#89614yes—
189C2×D3—64no—
190C2×D3—64no—
191C2×D3—124no—
192C2×D3—124no—
193C3×C4—21no—
194C3×C4—22no—
195C3×C4—21no—
196C3×C4#87212yes—
197C3×C4D3×C22⋊C412yes—
198C3×C4#88414yes—
199Dic3—64no—
200Dic3—64no—
201C32#181311yescharacteristic, complemented, Sylow
202C23—92no—
203C23#379711yescharacteristic
204Q8—182no—
205D4—184no—
206D4—182no—
207C2×C4—92no—
208C2×C4—182no—
209C2×C4—182no—
210C2×C4#379812yes—
211C2×C4#380211yescharacteristic
212C2×C4C2×#62411yescharacteristic
213C2×C4#381112yes—
214C8—22no—
215C8—92no—
216C8—92no—
217C8—124no—
218C2×C3—22no—
219C2×C3—22no—
220C2×C3—24no—
221C2×C3—21no—
222C2×C3—42no—
223C2×C3#466712yes—
224D3—124no—
225D3—124no—
226C22—41no—
227C22—182no—
228C22—362no—
229C22#6386512yes—
230C22#6390011yescharacteristic
231C4—182no—
232C4#6387411yescharacteristic
233C4#6391212yes—
234C4#6397411yescharacteristic
235C3—21no—
236C3#6872412yescomplemented
237C2—21no—
238C2—22no—
239C2—362no—
240C2#1059135511yescharacteristic
subgroupG/H
centerC4#63874
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC2×C32×M16C22
socleC2×C32#380
prime radicalC2×#3828C22
cosocleC22×C32×C4C23
hypercenterC2×M16D32
hypocenterC32#1813
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
2. C2×#63578C2semidirect
4. C3×C3⋊#338C2semidirect
21. C3⋊#338D3semidirect
201. C32#1813semidirect
236. C3#68724semidirect

Maximal subgroups

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

subgroupindex
C2×#641162
C2×#635782
#105910782
C3×C3⋊#3382
#687243