Finite Group Databasebeta

← #11786295

Subgroups — #11786295

Order 1152.

589 conjugacy classes of subgroups; only the 186 normal subgroups are shown.

normal subgroups only

This group has 589 conjugacy classes of subgroups — too many to draw. Only its 186 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
1#10592676C211yesmaximal, characteristic
2C2×C3×#808C212yesmaximal
3#10591359C211yesmaximal, characteristic
4C2×#63575C212yesmaximal
5C2×#63555C211yesmaximal, characteristic
6#70556—32nomaximal
7C2×C32×C4⋊C4C2211yescharacteristic
8C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
9C2×C4×C3⋊Dic3C2211yescharacteristic
10C2×C3×C4⋊Dic3C2212yes—
11C22×C3×C3⋊C8C2212yes—
12C2×#3724—22no—
13#63658—22no—
14C3×#808—24no—
15#63575—24no—
16#63555C414yescomplemented
17C2×C3×#106—32no—
18C2×#818—32no—
19C2×#815—32no—
20#4977—32no—
21#4977—61no—
22#4975—32no—
23C2×#808D312yes—
24C2×#807—32no—
25C22×C32×C4—21no—
26C22×C32×C4C2311yescharacteristic
27C22×C3⋊Dic3—21no—
28C22×C3⋊Dic3D412yes—
29C22×C3×Dic3—22no—
30C32×C4⋊C4—22no—
31C4⋊(C3⋊Dic3)—22no—
32C4×C3⋊Dic3C2×C412yes—
33C4×C3⋊Dic3Q812yes—
34C3×C4⋊Dic3—22no—
35C3×C4⋊Dic3—22no—
36C2×C3×C3⋊C8C2×C414yes—
37C2×C3×C3⋊C8D414yes—
38C2×C3×C3⋊C8Q814yes—
39#3724—44no—
40#1847—91noSylow
41C22×C3×C8—32no—
42C2×C3×C4⋊C4—21no—
43C2×C3×C4⋊C4—32no—
44C2×C3×C4⋊C4C2×D312yes—
45C2×C4⋊Dic3—32no—
46C2×C4⋊Dic3—61no—
47C2×C4⋊Dic3C2×D312yes—
48C2×Dic3⋊C4—64no—
49C2×C4×Dic3—32no—
50C2×C4×Dic3—61no—
51C22×C3⋊C8C2×D312yes—
52C3×#106—64no—
53C3⋊#95—64no—
54C3⋊#95—64no—
55#818—64no—
56#815—38no—
57#808—24no—
58#807—64no—
59C23×C32C2×D411yescharacteristic
60C2×C32×C4—41no—
61C2×C32×C4—42no—
62C2×C32×C4C22×C411yescharacteristic
63C2×C32×C4C2×D412yes—
64C2×C32×C4C2×Q812yes—
65C2×C32×C4C2×Q811yescharacteristic
66C2×C3⋊Dic3—22no—
67C2×C3⋊Dic3—22no—
68C2×C3⋊Dic3—41no—
69C2×C3⋊Dic3—42no—
70C2×C3⋊Dic3C4⋊C414yes—
71C2×C3×Dic3—42no—
72C2×C3×Dic3—44no—
73C3×C3⋊C8C4⋊C418yescomplemented
74C2×#107—92no—
75C2×#106—32no—
76C2×#97—91no—
77#384—91no—
78#382—91no—
79C22×C3×C4—22no—
80C22×C3×C4—22no—
81C22×C3×C4—21no—
82C22×C3×C4—62no—
83C22×C3×C4C22×D312yes—
84C22×Dic3—22no—
85C22×Dic3—34no—
86C22×Dic3—62no—
87C22×Dic3—62no—
88C22×Dic3—62no—
89C2×C3×C8—34no—
90C2×C3×C8—34no—
91C2×C3×C8—34no—
92C3×C4⋊C4—22no—
93C3×C4⋊C4—22no—
94C3×C4⋊C4—42no—
95C3×C4⋊C4—62no—
96C3×C4⋊C4—62no—
97C4⋊Dic3—22no—
98C4⋊Dic3—22no—
99C4⋊Dic3—62no—
100C4⋊Dic3—62no—
101C4⋊Dic3—122no—
102Dic3⋊C4—128no—
103C4×Dic3—34no—
104C4×Dic3—34no—
105C4×Dic3—62no—
106C4×Dic3—62no—
107C2×C3⋊C8Dic614yes—
108C2×C3⋊C8C4×D314yes—
109C2×C3⋊C8#6714yes—
110C22×C32C2×C4⋊C411yescharacteristic
111C22×C32#12711yescharacteristic
112C22×C32C4⋊Q811yescharacteristic
113C22×C32AGL(1,ℤ/8)12yes—
114C22×C32#13712yes—
115C32×C4—81no—
116C32×C4C2×C4⋊C412yes—
117C32×C4C4⋊Q812yes—
118C3⋊Dic3—24no—
119C3⋊Dic3—81no—
120C3×Dic3—82no—
121C22×C8—32no—
122C2×C4⋊C4—32no—
123C2×C4⋊C4—91no—
124C2×C4⋊C4—182no—
125C2×C4⋊C4D3211yescharacteristic
126C2×C42—91no—
127#107—184no—
128#106—64no—
129#97—94no—
130#95—182no—
131C23×C3—21no—
132C23×C3D3×D412yes—
133C2×C3×C4—22no—
134C2×C3×C4—21no—
135C2×C3×C4—21no—
136C2×C3×C4—22no—
137C2×C3×C4—42no—
138C2×C3×C4—44no—
139C2×C3×C4—44no—
140C2×C3×C4—42no—
141C2×C3×C4—124no—
142C2×C3×C4—122no—
143C2×C3×C4C2×Dic612yes—
144C2×C3×C4C2×C4×D312yes—
145C2×C3×C4D3×D412yes—
146C2×C3×C4D3×Q812yes—
147C2×C3×C4D3×Q812yes—
148C2×C3×C4C2×#6712yes—
149C2×Dic3—38no—
150C2×Dic3—44no—
151C2×Dic3—42no—
152C2×Dic3—64no—
153C2×Dic3—64no—
154C2×Dic3—64no—
155C2×Dic3—122no—
156C2×Dic3—122no—
157C2×Dic3—122no—
158C2×Dic3—124no—
159C2×Dic3—124no—
160C2×Dic3—122no—
161C3×C8—38no—
162C3⋊C8Dic3⋊C418yescomplemented
163C2×C32#38411yescharacteristic
164C2×C32#42812yes—
165C2×C32#49611yescharacteristic
166C2×C32#49711yescharacteristic
167C2×C32#50112yes—
168C22×C4—21no—
169C22×C4—62no—
170C22×C4—92no—
171C22×C4—181no—
172C22×C4C2×D3211yescharacteristic
173C2×C8—34no—
174C2×C8—34no—
175C2×C8—34no—
176C4⋊C4—22no—
177C4⋊C4—62no—
178C4⋊C4—62no—
179C4⋊C4—182no—
180C4⋊C4—364no—
181C42—92no—
182C42—92no—
183C22×C3—21no—
184C22×C3—21no—
185C22×C3—22no—
186C22×C3—22no—
187C22×C3—21no—
188C22×C3#88812yes—
189C22×C3D3×C4⋊C412yes—
190C22×C3#91414yes—
191C22×C3#91514yes—
192C22×C3#94012yes—
193C3×C4—22no—
194C3×C4—22no—
195C3×C4—82no—
196C3×C4—82no—
197C3×C4—242no—
198C3×C4#88812yes—
199C3×C4D3×C4⋊C412yes—
200C3×C4C2×Dic3⋊C412yes—
201C3×C4#94412yes—
202Dic3—68no—
203Dic3—82no—
204Dic3—124no—
205Dic3—242no—
206Dic3—242no—
207C32#184711yescharacteristic, complemented, Sylow
208C23#381111yescharacteristic
209C2×C4—42no—
210C2×C4—41no—
211C2×C4—94no—
212C2×C4—124no—
213C2×C4—122no—
214C2×C4—182no—
215C2×C4—182no—
216C2×C4—362no—
217C2×C4—361no—
218C2×C4D3×Dic612yes—
219C2×C4#379711yescharacteristic
220C2×C4C4×D3211yescharacteristic
221C2×C4D3×#6712yes—
222C8—38no—
223C2×C3—21no—
224C2×C3—21no—
225C2×C3—22no—
226C2×C3—22no—
227C2×C3—21no—
228C2×C3#485614yes—
229C2×C3#486114yes—
230C2×C3#497512yes—
231C2×C3#516712yes—
232C2×C3#517612yes—
233C22#6384011yescharacteristic
234C22#6388311yescharacteristic
235C22#6393112yes—
236C22#6394112yes—
237C22#6397911yescharacteristic
238C4—81no—
239C4—184no—
240C4—242no—
241C4—721no—
242C4#6383912yes—
243C4D3×Dic3⋊C412yes—
244C3—21no—
245C3#7055612yescomplemented
246C2#1059056412yes—
247C2#1059058412yes—
248C2#1059124411yescharacteristic
249C2#1059149311yescharacteristic
250C2#1059162111yescharacteristic
subgroupG/H
centerC23#3811
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC2×C32×C4⋊C4C22
socle, prime radicalC23×C32C2×D4
cosocleC22×C32×C4C23
hypercenterC2×C4⋊C4D32
hypocenterC32#1847
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
16. #63555C4semidirect
73. C3×C3⋊C8C4⋊C4semidirect
162. C3⋊C8Dic3⋊C4semidirect
207. C32#1847semidirect
245. C3#70556semidirect

Maximal subgroups

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

subgroupindex
#105926762
C2×C3×#8082
#105913592
C2×#635752
C2×#635552
#705563