Finite Group Databasebeta

← #11786079

Subgroups — #11786079

Order 1152.

541 conjugacy classes of subgroups; only the 154 normal subgroups are shown.

normal subgroups only

This group has 541 conjugacy classes of subgroups — too many to draw. Only its 154 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#10592674C211yesmaximal, characteristic
2#10591230C211yesmaximal, characteristic
3C2×#63555C211yesmaximal, characteristic
4C3×#4529C212yesmaximal
5#10589164C212yesmaximal
6#68849—32nomaximal
7C2×C32×C4⋊C4C2211yescharacteristic
8C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
9C2×#3750—22no—
10C2×C4×C3⋊Dic3C2211yescharacteristic
11C2×C3×C4⋊Dic3C2212yes—
12C22×C3×C3⋊C8C2212yes—
13#63579—22no—
14#63555C414yescomplemented
15C2×#815—32no—
16#4977—32no—
17#4975—32no—
18#4975—61no—
19C3×#340—32no—
20#4551—32no—
21#4529—32no—
22#4529D312yes—
23C22×C32×C4—21no—
24C22×C32×C4C2311yescharacteristic
25C22×C3⋊Dic3—21no—
26C22×C3⋊Dic3D412yes—
27C22×C3×Dic3—22no—
28C32×C4⋊C4—22no—
29C4⋊(C3⋊Dic3)—22no—
30#3750—44no—
31C4×C3⋊Dic3C2×C412yes—
32C4×C3⋊Dic3Q812yes—
33C3×C4⋊Dic3—22no—
34C3×C4⋊Dic3—22no—
35C2×C3×C3⋊C8—22no—
36C2×C3×C3⋊C8—22no—
37C2×C3×C3⋊C8C2×C414yes—
38#1836—91noSylow
39C22×C3×C8—32no—
40C2×C3×C4⋊C4—21no—
41C2×C3×C4⋊C4—32no—
42C2×C3×C4⋊C4C2×D312yes—
43C2×C4⋊Dic3—32no—
44C2×C4⋊Dic3—61no—
45C2×C4⋊Dic3C2×D312yes—
46C2×Dic3⋊C4—62no—
47C2×Dic3⋊C4—62no—
48C2×Dic3⋊C4—64no—
49C2×C4×Dic3—32no—
50C2×C4×Dic3—61no—
51C22×C3⋊C8C2×D312yes—
52C3⋊#95—62no—
53C3⋊#95—62no—
54#815—38no—
55C23×C32C2×D411yescharacteristic
56C2×C32×C4—41no—
57C2×C32×C4—42no—
58C2×C32×C4C22×C411yescharacteristic
59C2×C32×C4C2×Q811yescharacteristic
60C2×C32×C4#4112yes—
61C2×C32×C4#4112yes—
62C2×C3⋊Dic3—22no—
63C2×C3⋊Dic3—22no—
64C2×C3⋊Dic3—41no—
65C2×C3⋊Dic3—42no—
66C2×C3⋊Dic3C4⋊C414yes—
67C2×C3×Dic3—42no—
68C2×C3×Dic3—42no—
69C2×C3×Dic3—42no—
70C3×C3⋊C8—24no—
71C2×#97—91no—
72#384—91no—
73#382—91no—
74#340—32no—
75#340—92no—
76C22×C3×C4—22no—
77C22×C3×C4—22no—
78C22×C3×C4—21no—
79C22×C3×C4—62no—
80C22×C3×C4C22×D312yes—
81C22×Dic3—22no—
82C22×Dic3—32no—
83C22×Dic3—32no—
84C22×Dic3—62no—
85C22×Dic3—62no—
86C22×Dic3—62no—
87C2×C3×C8—34no—
88C2×C3×C8—62no—
89C2×C3×C8—62no—
90C3×C4⋊C4—22no—
91C3×C4⋊C4—22no—
92C3×C4⋊C4—42no—
93C3×C4⋊C4—62no—
94C3×C4⋊C4—62no—
95C4⋊Dic3—22no—
96C4⋊Dic3—22no—
97C4⋊Dic3—62no—
98C4⋊Dic3—62no—
99C4⋊Dic3—122no—
100Dic3⋊C4—128no—
101Dic3⋊C4—124no—
102Dic3⋊C4—124no—
103C4×Dic3—34no—
104C4×Dic3—34no—
105C4×Dic3—62no—
106C4×Dic3—62no—
107C2×C3⋊C8—22no—
108C2×C3⋊C8—22no—
109C2×C3⋊C8C4×D314yes—
110C22×C32C2×C4⋊C411yescharacteristic
111C22×C32#12411yescharacteristic
112C22×C32#12411yescharacteristic
113C22×C32AGL(1,ℤ/8)12yes—
114C22×C32#13712yes—
115C32×C4—81no—
116C32×C4#11712yes—
117C32×C4#12512yes—
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#97—94no—
128#95—182no—
129C23×C3—21no—
130C23×C3D3×D412yes—
131C2×C3×C4—22no—
132C2×C3×C4—21no—
133C2×C3×C4—21no—
134C2×C3×C4—22no—
135C2×C3×C4—44no—
136C2×C3×C4—42no—
137C2×C3×C4—42no—
138C2×C3×C4—42no—
139C2×C3×C4—42no—
140C2×C3×C4—122no—
141C2×C3×C4—122no—
142C2×C3×C4—122no—
143C2×C3×C4C2×C4×D312yes—
144C2×C3×C4#23512yes—
145C2×C3×C4#23512yes—
146C2×C3×C4#23712yes—
147C2×C3×C4#23712yes—
148C2×C3×C4D3×Q812yes—
149C2×Dic3—34no—
150C2×Dic3—34no—
151C2×Dic3—42no—
152C2×Dic3—42no—
153C2×Dic3—42no—
154C2×Dic3—64no—
155C2×Dic3—64no—
156C2×Dic3—64no—
157C2×Dic3—62no—
158C2×Dic3—62no—
159C2×Dic3—62no—
160C2×Dic3—62no—
161C2×Dic3—124no—
162C2×Dic3—122no—
163C2×Dic3—122no—
164C2×Dic3—122no—
165C2×Dic3—122no—
166C3×C8—64no—
167C3⋊C8—24no—
168C2×C32#38211yescharacteristic
169C2×C32#42812yes—
170C2×C32#48912yes—
171C2×C32#49011yescharacteristic
172C2×C32#49111yescharacteristic
173C22×C4—21no—
174C22×C4—62no—
175C22×C4—92no—
176C22×C4—181no—
177C22×C4C2×D3211yescharacteristic
178C2×C8—34no—
179C2×C8—62no—
180C2×C8—62no—
181C4⋊C4—22no—
182C4⋊C4—62no—
183C4⋊C4—62no—
184C4⋊C4—182no—
185C4⋊C4—364no—
186C42—92no—
187C42—92no—
188C22×C3—21no—
189C22×C3—21no—
190C22×C3—22no—
191C22×C3—22no—
192C22×C3—21no—
193C22×C3#88512yes—
194C22×C3#88512yes—
195C22×C3D3×C4⋊C412yes—
196C22×C3#91112yes—
197C22×C3#91412yes—
198C22×C3#91512yes—
199C22×C3#91812yes—
200C3×C4—22no—
201C3×C4—22no—
202C3×C4—82no—
203C3×C4—82no—
204C3×C4—242no—
205C3×C4#87212yes—
206C3×C4#87712yes—
207C3×C4#88912yes—
208C3×C4#88912yes—
209Dic3—68no—
210Dic3—64no—
211Dic3—64no—
212Dic3—82no—
213Dic3—242no—
214Dic3—242no—
215C32#183611yescharacteristic, complemented, Sylow
216C23#381111yescharacteristic
217C2×C4—42no—
218C2×C4—41no—
219C2×C4—94no—
220C2×C4—122no—
221C2×C4—122no—
222C2×C4—122no—
223C2×C4—182no—
224C2×C4—182no—
225C2×C4—362no—
226C2×C4—361no—
227C2×C4#379512yes—
228C2×C4#379711yescharacteristic
229C2×C4C4×D3211yescharacteristic
230C2×C4#380412yes—
231C8—64no—
232C2×C3—21no—
233C2×C3—22no—
234C2×C3—22no—
235C2×C3—21no—
236C2×C3—21no—
237C2×C3#465012yes—
238C2×C3#476412yes—
239C2×C3#476512yes—
240C2×C3#479412yes—
241C2×C3#479712yes—
242C2×C3#486112yes—
243C2×C3#488112yes—
244C22#6388311yescharacteristic
245C22#6391311yescharacteristic
246C22#6393712yes—
247C22#6395112yes—
248C22#6395311yescharacteristic
249C4—81no—
250C4—184no—
251C4—242no—
252C4—721no—
253C4#6384712yes—
254C4#6387712yes—
255C3—21no—
256C3#6884912yescomplemented
257C2#1059054112yes—
258C2#1059058312yes—
259C2#1059124711yescharacteristic
260C2#1059148011yescharacteristic
261C2#1059161611yescharacteristic
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#1836
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
14. #63555C4semidirect
215. C32#1836semidirect
256. C3#68849semidirect

Maximal subgroups

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

subgroupindex
#105926742
#105912302
C2×#635552
C3×#45292
#105891642
#688493