Finite Group Databasebeta

← #11790627

Subgroups — #11790627

Order 1152.

494 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 494 conjugacy classes of subgroups — too many to draw. Only its 89 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×#64222C211yesmaximal, characteristic
2C2×C8×#157C211yesmaximal, characteristic
3#10593413C211yesmaximal, characteristic
4#10593375C212yesmaximal
5#10590672C212yesmaximal
6C2×#3797C2212yes—
7C2×C4×#157C2211yescharacteristic
8C2×#3787C2211yescharacteristic
9C2×#3773—22no—
10C2×#3773—22no—
11#64222—22no—
12#64222C414yescomplemented
13C2×C8×C3⋊D3C2211yescharacteristic
14#63900C2212yes—
15C8×#157—22no—
16#63740—24no—
17C3×#816—22no—
18#63565—22no—
19D3×#103—62no—
20C22×#157D412yes—
21C2×C4×C3⋊D3C2311yescharacteristic
22C2×C3×Dic6—22no—
23C2×#627—22no—
24C2×#624—22no—
25C2×#624—22no—
26#3797—22no—
27#3797—22no—
28#3797—22no—
29#3797C2×C414yes—
30C2×#622D412yes—
31C4×#157C2×C412yes—
32C4×#157D412yes—
33#3787—21no—
34#3787—21no—
35#3773—28no—
36#3773—44no—
37C2×C32×C8D411yescharacteristic
38C2×C3⋊(C3⋊C8)D411yescharacteristic
39C8×C3⋊D3—21no—
40C8×C3⋊D3—21no—
41C3×C4⋊Dic3—22no—
42#3724—22no—
43#1956—91nomaximal, Sylow
44C2×D3×Q8—62no—
45C2×D3×C8—62no—
46D3×C4⋊C4—62no—
47C3×#103—62no—
48#835—62no—
49#816—22no—
50#810—62no—
51C22×C3⋊D3C2×D411yescharacteristic
52C2×#157C22⋊C414yes—
53C2×#157SD1614yes—
54C2×#157Q1614yes—
55C2×C32×C4C2×D411yescharacteristic
56C2×C3⋊Dic3C2×D411yescharacteristic
57C4×C3⋊D3C22×C411yescharacteristic
58C4×C3⋊D3C2×D411yescharacteristic
59C4×C3⋊D3#4111yescharacteristic
60C4×C3⋊D3#4111yescharacteristic
61C2×C3×Dic3—42no—
62C2×C3×Dic3—42no—
63C3×Dic6—24no—
64C3×Dic6—42no—
65#627—24no—
66#627—42no—
67#624—24no—
68#624—42no—
69#624—44no—
70#622—22no—
71C32×C8—21no—
72C3⋊(C3⋊C8)—21no—
73C2×C4⋊Q8—91no—
74C2×#103—92no—
75C2×#103—92no—
76C2×C4×C8—91no—
77#384—91no—
78C2×C3×Q8—62no—
79D3×Q8—64no—
80D3×Q8—64no—
81D3×Q8—122no—
82D3×Q8—122no—
83C2×C4×D3—62no—
84C2×C4×D3—122no—
85C2×C4×D3—122no—
86C2×Dic6—22no—
87C2×Dic6—122no—
88C2×C3×C8—22no—
89C3×C4⋊C4—62no—
90C4⋊Dic3—22no—
91Dic3⋊C4—122no—
92C2×C3⋊C8—62no—
93D3×C8—122no—
94D3×C8—122no—
95C22×C32#12711yescharacteristic
96C2×C3⋊D3C2×C22⋊C411yescharacteristic
97C2×C3⋊D3#12411yescharacteristic
98C2×C3⋊D3C2×SD1612yes—
99C2×C3⋊D3C2×Q1612yes—
100#157#10318yescomplemented
101C32×C4C4×D411yescharacteristic
102C32×C4#12111yescharacteristic
103C3⋊Dic3C4×D411yescharacteristic
104C3⋊Dic3#12111yescharacteristic
105C3×Dic3—44no—
106C3×Dic3—82no—
107C22×Q8—92no—
108C22×C8—91no—
109C22×C8—91no—
110C4⋊Q8—94no—
111C4⋊Q8—182no—
112C2×C4⋊C4—92no—
113C2×C4⋊C4—182no—
114C2×C4⋊C4—182no—
115C2×C42—91no—
116#103—62no—
117#103—182no—
118#103—184no—
119C4×C8—182no—
120C22×D3—62no—
121C3×Q8—64no—
122C3×Q8—122no—
123C2×C3×C4—22no—
124C2×C3×C4—122no—
125C2×C3×C4—122no—
126C2×Dic3—42no—
127C2×Dic3—42no—
128C2×Dic3—62no—
129C4×D3—62no—
130C4×D3—62no—
131C4×D3—62no—
132C4×D3—62no—
133C4×D3—124no—
134C4×D3—124no—
135C4×D3—244no—
136Dic6—24no—
137Dic6—42no—
138Dic6—124no—
139Dic6—124no—
140C3×C8—42no—
141C3⋊C8—122no—
142C2×C32#39011yescharacteristic
143C2×C32#49211yescharacteristic
144C2×C32#49411yescharacteristic
145C3⋊D3C2×#10312yes—
146C3⋊D3#48712yes—
147C2×Q8—62no—
148C2×Q8—94no—
149C2×Q8—182no—
150C2×Q8—182no—
151C2×Q8—182no—
152C2×Q8—182no—
153C22×C4—92no—
154C22×C4—91no—
155C22×C4—182no—
156C22×C4—182no—
157C2×C8—92no—
158C2×C8—91no—
159C2×C8—181no—
160C2×C8—181no—
161C2×C8—181no—
162C2×C8—181no—
163C2×C8GO+(4,𝔽2)11yescharacteristic
164C4⋊C4—62no—
165C4⋊C4—182no—
166C4⋊C4—188no—
167C4⋊C4—364no—
168C42—92no—
169C42—92no—
170C22×C3—22no—
171C2×D3—62no—
172C2×D3—62no—
173C2×D3—64no—
174C2×D3—64no—
175C3×C4—22no—
176C3×C4—22no—
177C3×C4—124no—
178C3×C4—242no—
179Dic3—44no—
180Dic3—62no—
181Dic3—62no—
182Dic3—82no—
183C32#195611yescharacteristic, complemented, Sylow
184C23—91no—
185Q8—64no—
186Q8—122no—
187Q8—184no—
188Q8—362no—
189C2×C4—94no—
190C2×C4—94no—
191C2×C4—94no—
192C2×C4—91no—
193C2×C4—91no—
194C2×C4—91no—
195C2×C4—91no—
196C2×C4—91no—
197C2×C4—122no—
198C2×C4—122no—
199C2×C4—184no—
200C2×C4—362no—
201C2×C4—364no—
202C2×C4C2×GO+(4,𝔽2)11yescharacteristic
203C8—21no—
204C8—182no—
205C8—181no—
206C2×C3—22no—
207C2×C3—22no—
208C2×C3—22no—
209D3—64no—
210D3—64no—
211C22—92no—
212C22—92no—
213C22—91no—
214C22—91no—
215C22#6423111yescharacteristic
216C4—98no—
217C4—91no—
218C4—91no—
219C4—124no—
220C4—242no—
221C4C4×GO+(4,𝔽2)11yescharacteristic
222C4#6424211yescharacteristic
223C3—22no—
224C2—92no—
225C2—92no—
226C2#1059329211yescharacteristic
227C2#1059329511yescharacteristic
228C2#1059345411yescharacteristic
subgroupG/H
centerC22#64231
commutatorC4×C3⋊D3C22×C4
FrattiniC2×C4C2×GO+(4,𝔽2)
FittingC2×C32×C8D4
socleC22×C32#127
prime radicalC22×C3⋊D3C2×D4
cosocleC2×C4×C3⋊D3C23
hypercenterC2×C8GO+(4,𝔽2)
hypocenterC32#1956
LCSG ▷ C4×C3⋊D3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8

Complements

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

NH ≅ G/Ntype
12. #64222C4semidirect
100. #157#103semidirect
183. C32#1956semidirect

Maximal subgroups

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

subgroupindex
C2×#642222
C2×C8×#1572
#105934132
#105933752
#105906722
#19569