Finite Group Databasebeta

← #11794674

Subgroups — #11794674

Order 1152.

714 conjugacy classes of subgroups; only the 235 normal subgroups are shown.

normal subgroups only

This group has 714 conjugacy classes of subgroups — too many to draw. Only its 235 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
1C32×#384C211yesmaximal, characteristic
2C2×#63637C212yesmaximal
3#10592628C211yesmaximal, characteristic
4#10589395C212yesmaximal
5#10589390C211yesmaximal, characteristic
6#69589—34nomaximal
7C22×#634C2211yescharacteristic
8C2×C32×C4⋊C4—21no—
9C2×C32×C4⋊C4—21no—
10C2×C32×C4⋊C4C2212yes—
11C2×C32×C42C2211yescharacteristic
12C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
13C22×C3⋊(C3⋊C8)C2212yes—
14#63658—21no—
15#63658—21no—
16#63637—24no—
17C3×#384D314yes—
18C2×#810—38no—
19#4929—34no—
20#4529—38no—
21#4524—34no—
22C22×C32×C4—22no—
23C22×C32×C4D411yescharacteristic
24C22×C32×C4D411yescharacteristic
25C22×C32×C4C2311yescharacteristic
26C22×C3⋊Dic3—21no—
27C22×C3⋊Dic3—21no—
28C2×#634—22no—
29C2×#634—22no—
30C2×#634—21no—
31C2×#634D412yes—
32C32×C4⋊C4—22no—
33C32×C4⋊C4—22no—
34C32×C4⋊C4—42no—
35C32×C4⋊C4—42no—
36C32×C42—22no—
37C4⋊(C3⋊Dic3)—22no—
38C2×C3⋊(C3⋊C8)—22no—
39C2×C3⋊(C3⋊C8)—22no—
40C2×C3⋊(C3⋊C8)—22no—
41#2072—91noSylow
42C22×Dic6—34no—
43C2×C3×C4⋊C4—24no—
44C2×C3×C4⋊C4—24no—
45C2×C3×C4⋊C4C2×D318yes—
46C2×C3×C42C2×D314yes—
47C2×C4⋊Dic3—34no—
48C22×C3⋊C8—38no—
49C3⋊#95—64no—
50C3⋊#95—64no—
51#810—616no—
52C23×C32C2×D411yescharacteristic
53C2×C32×C4—21no—
54C2×C32×C4—21no—
55C2×C32×C4—21no—
56C2×C32×C4—21no—
57C2×C32×C4—42no—
58C2×C32×C4—42no—
59C2×C32×C4—42no—
60C2×C32×C4SD1612yes—
61C2×C32×C4Q1612yes—
62C2×C32×C4C2×D411yescharacteristic
63C2×C32×C4#4112yes—
64C2×C32×C4#4111yescharacteristic
65C2×C32×C4#4112yes—
66C2×C3⋊Dic3—22no—
67C2×C3⋊Dic3—41no—
68C2×C3⋊Dic3—41no—
69C2×C3⋊Dic3—41no—
70C2×C3⋊Dic3—41no—
71C2×C3⋊Dic3—41no—
72#634—24no—
73#634—42no—
74C3⋊(C3⋊C8)—42no—
75C2×#103—92no—
76#391—91no—
77#384C3⋊D311yescharacteristic
78#340—92no—
79#336—91no—
80C22×C3×C4—28no—
81C22×C3×C4#6714yes—
82C22×C3×C4#6714yes—
83C22×C3×C4C22×D314yes—
84C22×Dic3—64no—
85C22×Dic3—64no—
86C2×Dic6—38no—
87C2×Dic6—68no—
88C2×Dic6—68no—
89C2×Dic6—64no—
90C3×C4⋊C4—28no—
91C3×C4⋊C4—28no—
92C3×C4⋊C4—48no—
93C3×C4⋊C4—48no—
94C3×C42—28no—
95C4⋊Dic3—68no—
96C2×C3⋊C8—68no—
97C2×C3⋊C8—68no—
98C2×C3⋊C8—68no—
99C22×C32#12111yescharacteristic
100C22×C32#12311yescharacteristic
101C22×C32#12411yescharacteristic
102C22×C32C2×SD1611yescharacteristic
103C22×C32C2×Q1611yescharacteristic
104C22×C32AGL(1,ℤ/8)11yescharacteristic
105C22×C32#13711yescharacteristic
106C32×C4—22no—
107C32×C4—22no—
108C32×C4—82no—
109C32×C4#12312yes—
110C32×C4#12612yes—
111C3⋊Dic3—42no—
112C3⋊Dic3—81no—
113C22×Q8—91no—
114C22×C8—92no—
115C2×C4⋊C4—21no—
116C2×C4⋊C4—21no—
117C2×C4⋊C4—91no—
118C2×C4⋊C4C2×C3⋊D312yes—
119C2×C42C2×C3⋊D311yescharacteristic
120#103—184no—
121#95—181no—
122#95—181no—
123C23×C3C2×#6714yes—
124C2×C3×C4—24no—
125C2×C3×C4—24no—
126C2×C3×C4—24no—
127C2×C3×C4—24no—
128C2×C3×C4—48no—
129C2×C3×C4—48no—
130C2×C3×C4—48no—
131C2×C3×C4#21418yes—
132C2×C3×C4#21618yes—
133C2×C3×C4#23518yes—
134C2×C3×C4D3×D414yes—
135C2×C3×C4#23714yes—
136C2×C3×C4#23918yes—
137C2×Dic3—68no—
138C2×Dic3—124no—
139C2×Dic3—124no—
140C2×Dic3—124no—
141C2×Dic3—124no—
142C2×Dic3—124no—
143Dic6—616no—
144Dic6—128no—
145C3⋊C8—128no—
146C2×C32#39711yescharacteristic
147C2×C32#46011yescharacteristic
148C2×C32#46211yescharacteristic
149C2×C32#48311yescharacteristic
150C2×C32#48411yescharacteristic
151C2×C32#48711yescharacteristic
152C2×C32#48911yescharacteristic
153C2×Q8—92no—
154C2×Q8—181no—
155C2×Q8—182no—
156C2×Q8—182no—
157C22×C4—22no—
158C22×C4—181no—
159C22×C4—181no—
160C22×C4#63811yescharacteristic
161C22×C4#63811yescharacteristic
162C22×C4C22×C3⋊D311yescharacteristic
163C2×C8—182no—
164C2×C8—182no—
165C2×C8—182no—
166C4⋊C4—22no—
167C4⋊C4—22no—
168C4⋊C4—42no—
169C4⋊C4—42no—
170C4⋊C4—182no—
171C42—22no—
172C22×C3#92914yes—
173C22×C3#93214yes—
174C22×C3C2×#21414yes—
175C22×C3#93814yes—
176C22×C3#94214yes—
177C22×C3C2×#21614yes—
178C22×C3#94714yes—
179C3×C4—28no—
180C3×C4—28no—
181C3×C4—88no—
182C3×C4#89418yes—
183C3×C4#89818yes—
184Dic3—128no—
185Dic3—244no—
186C32#207211yescharacteristic, complemented, Sylow
187C23C2×#63811yescharacteristic
188Q8—184no—
189Q8—362no—
190C2×C4—21no—
191C2×C4—21no—
192C2×C4—21no—
193C2×C4—21no—
194C2×C4—42no—
195C2×C4—42no—
196C2×C4—42no—
197C2×C4—182no—
198C2×C4—361no—
199C2×C4—361no—
200C2×C4—361no—
201C2×C4—361no—
202C2×C4—361no—
203C2×C4#375412yes—
204C2×C4#375612yes—
205C2×C4#382812yes—
206C2×C4D4×C3⋊D311yescharacteristic
207C2×C4#383011yescharacteristic
208C2×C4#383212yes—
209C8—362no—
210C2×C3#497014yes—
211C2×C3#497114yes—
212C2×C3#499214yes—
213C2×C3#507514yes—
214C2×C3#508914yes—
215C2×C3#509014yes—
216C2×C3#509314yes—
217C22#6413811yescharacteristic
218C22#6414111yescharacteristic
219C22C2×#375411yescharacteristic
220C22#6414711yescharacteristic
221C22#6415111yescharacteristic
222C22C2×#375611yescharacteristic
223C22#6415611yescharacteristic
224C4—22no—
225C4—22no—
226C4—82no—
227C4—362no—
228C4—721no—
229C4#6410312yes—
230C4#6410712yes—
231C3#6958914yescomplemented
232C2#1059266911yescharacteristic
233C2#1059267011yescharacteristic
234C2#1059269111yescharacteristic
235C2#1059277411yescharacteristic
236C2#1059278811yescharacteristic
237C2#1059278911yescharacteristic
238C2#1059279211yescharacteristic
subgroupG/H
centerC23C2×#638
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C22×C3⋊D3
FittingC32×#384C2
socle, prime radicalC23×C32C2×D4
hypercenter#384C3⋊D3
hypocenterC32#2072
LCSG ▷ C22×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C42 ◁ #384

Complements

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

NH ≅ G/Ntype
186. C32#2072semidirect
231. C3#69589semidirect

Maximal subgroups

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

subgroupindex
C32×#3842
C2×#636372
#105926282
#105893952
#105893902
#695893