Finite Group Databasebeta

← #11785748

Subgroups — #11785748

Order 1152.

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

normal subgroups only

This group has 709 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×#64101C211yesmaximal, characteristic
2#10591074C212yesmaximal
3C3×#4530C212yesmaximal, complemented
4#10589168C212yesmaximal, complemented
5#68991—32nomaximal
6C22×C4×C3⋊D3C2211yescharacteristic
7C2×C32×C4⋊C4C2211yescharacteristic
8C2×#3752C412yes—
9C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
10C2×C4×C3⋊Dic3C412yes—
11#64101—24no—
12C2×C3×#208C2214yes—
13#63557—24no—
14C2×#892—32no—
15C2×#892—61no—
16#5126—34no—
17C3×#343—32no—
18#4554—34no—
19#4530D312yescomplemented
20C23×C3⋊D3C2×C411yescharacteristic
21C22×C32×C4C2×C412yes—
22C22×C32×C4C2311yescharacteristic
23C22×C3⋊Dic3C2×C411yescharacteristic
24C22×C3⋊Dic3C2×C412yes—
25C2×C4×C3⋊D3—22no—
26C2×C4×C3⋊D3—22no—
27C2×C4×C3⋊D3D414yes—
28C32×C4⋊C4—22no—
29#3752—24no—
30C4⋊(C3⋊Dic3)—22no—
31C4×C3⋊Dic3—24no—
32C3×#208—24no—
33C3×#208—24no—
34C2×C3×C3⋊C8—24no—
35#1822—91noSylow
36C22×C4×D3—32no—
37C22×C4×D3—61no—
38C2×C3×M16—34no—
39C2×C3×C4⋊C4—21no—
40C2×C3×C4⋊C4C2×D312yes—
41C2×(C2×D3)⋊C4—34no—
42C2×(C2×D3)⋊C4—62no—
43C2×C4⋊Dic3—32no—
44C2×C4⋊Dic3—61no—
45C2×C4×Dic3—34no—
46C2×C4×Dic3—62no—
47C2×#208C2×D314yes—
48#892—68no—
49#892—68no—
50(C2×D3)⋊C8—68no—
51C23×C32C22×C411yescharacteristic
52C22×C3⋊D3—21no—
53C22×C3⋊D3—21no—
54C22×C3⋊D3—41no—
55C22×C3⋊D3—41no—
56C22×C3⋊D3C22⋊C412yes—
57C2×C32×C4—22no—
58C2×C32×C4—42no—
59C2×C32×C4C2×D412yes—
60C2×C32×C4#4112yes—
61C2×C32×C4#4112yes—
62C2×C3⋊Dic3—21no—
63C2×C3⋊Dic3—21no—
64C2×C3⋊Dic3—22no—
65C2×C3⋊Dic3—42no—
66C2×C3⋊Dic3C22⋊C412yes—
67C4×C3⋊D3—28no—
68C3×C3⋊C8—44no—
69C2×#117—91no—
70#407—92no—
71#343—32no—
72#343—92no—
73C23×D3—32no—
74C23×D3—61no—
75C22×C3×C4—22no—
76C22×C3×C4—21no—
77C22×C3×C4C4×D314yes—
78C22×C3×C4C22×D312yes—
79C22×Dic3—32no—
80C22×Dic3—34no—
81C22×Dic3—61no—
82C22×Dic3—62no—
83C2×C4×D3—38no—
84C2×C4×D3—64no—
85C2×C4×D3—64no—
86C2×C4×D3—64no—
87C2×C4×D3—64no—
88C2×C4×D3—62no—
89C2×C4×D3—62no—
90C3×M16—64no—
91C3×M16—64no—
92C2×C3×C8—64no—
93C3×C4⋊C4—24no—
94C3×C4⋊C4—24no—
95(C2×D3)⋊C4—68no—
96(C2×D3)⋊C4—68no—
97C4⋊Dic3—64no—
98C4⋊Dic3—64no—
99C4×Dic3—68no—
100C4×Dic3—68no—
101#208—24no—
102#208—24no—
103C2×C3⋊C8—24no—
104C22×C32—21no—
105C22×C32—21no—
106C22×C32C2×C22⋊C411yescharacteristic
107C22×C32#11711yescharacteristic
108C22×C32#11711yescharacteristic
109C2×C3⋊D3—22no—
110C2×C3⋊D3—22no—
111C2×C3⋊D3—22no—
112C2×C3⋊D3—42no—
113C2×C3⋊D3—42no—
114C32×C4—42no—
115C32×C4#12314yes—
116C3⋊Dic3—22no—
117C3⋊Dic3—42no—
118C23×C4—91no—
119C2×M16—34no—
120#117—184no—
121C2×C4⋊C4—91no—
122C2×C4⋊C4D3211yescharacteristic
123C2×C22⋊C4—92no—
124C2×C42—92no—
125C22⋊C8—184no—
126C23×C3—21no—
127C23×C3C2×C4×D312yes—
128C22×D3—34no—
129C22×D3—62no—
130C22×D3—62no—
131C22×D3—62no—
132C22×D3—62no—
133C22×D3—62no—
134C22×D3—122no—
135C22×D3—122no—
136C22×D3—122no—
137C22×D3—122no—
138C2×C3×C4—24no—
139C2×C3×C4—24no—
140C2×C3×C4—22no—
141C2×C3×C4—22no—
142C2×C3×C4—22no—
143C2×C3×C4—44no—
144C2×C3×C4—44no—
145C2×C3×C4#23514yes—
146C2×C3×C4D3×D414yes—
147C2×C3×C4#23712yes—
148C2×C3×C4#23912yes—
149C2×Dic3—34no—
150C2×Dic3—62no—
151C2×Dic3—62no—
152C2×Dic3—62no—
153C2×Dic3—62no—
154C2×Dic3—62no—
155C2×Dic3—64no—
156C2×Dic3—64no—
157C2×Dic3—124no—
158C2×Dic3—124no—
159C4×D3—616no—
160C4×D3—68no—
161C4×D3—68no—
162C3×C8—124no—
163C3⋊C8—44no—
164C2×C32—21no—
165C2×C32—21no—
166C2×C32#38111yescharacteristic
167C2×C32#41311yescharacteristic
168C2×C32#41311yescharacteristic
169C3⋊D3—42no—
170C24—91no—
171C22×C4—91no—
172C22×C4—94no—
173C22×C4—92no—
174C22×C4—182no—
175C22×C4—182no—
176C22×C4#62412yes—
177C22×C4C2×D3211yescharacteristic
178M16—64no—
179M16—64no—
180C2×C8—64no—
181C4⋊C4—22no—
182C4⋊C4—182no—
183C22⋊C4—184no—
184C42—184no—
185C22×C3—22no—
186C22×C3—22no—
187C22×C3—22no—
188C22×C3—22no—
189C22×C3—21no—
190C22×C3—21no—
191C22×C3—21no—
192C22×C3#87212yes—
193C22×C3D3×C22⋊C412yes—
194C22×C3#89212yes—
195C2×D3—64no—
196C2×D3—64no—
197C2×D3—64no—
198C2×D3—64no—
199C2×D3—122no—
200C2×D3—122no—
201C2×D3—124no—
202C2×D3—124no—
203C2×D3—124no—
204C2×D3—124no—
205C3×C4—24no—
206C3×C4—44no—
207C3×C4—44no—
208C3×C4#88314yes—
209C3×C4#89414yes—
210Dic3—64no—
211Dic3—64no—
212Dic3—124no—
213Dic3—124no—
214C32#182211yescharacteristic, complemented, Sylow
215C23—92no—
216C23—181no—
217C23—181no—
218C23—361no—
219C23—361no—
220C23C2×#62411yescharacteristic
221C2×C4—22no—
222C2×C4—42no—
223C2×C4—92no—
224C2×C4—181no—
225C2×C4—181no—
226C2×C4—188no—
227C2×C4—182no—
228C2×C4—362no—
229C2×C4#379612yes—
230C2×C4#379812yes—
231C2×C4#381112yes—
232C8—124no—
233C2×C3—22no—
234C2×C3—22no—
235C2×C3—22no—
236C2×C3—22no—
237C2×C3—21no—
238C2×C3—21no—
239C2×C3—21no—
240C2×C3#466412yes—
241C2×C3#474512yes—
242C2×C3#475112yes—
243D3—124no—
244D3—124no—
245C22—21no—
246C22—21no—
247C22—182no—
248C22—182no—
249C22—182no—
250C22—362no—
251C22—362no—
252C22#6384911yescharacteristic
253C22#6387411yescharacteristic
254C22#6397411yescharacteristic
255C4—42no—
256C4—182no—
257C4—362no—
258C4#6385314yes—
259C3—21no—
260C3#6899112yescomplemented
261C2—21no—
262C2—21no—
263C2—362no—
264C2#1059121911yescharacteristic
265C2#1059150411yescharacteristic
266C2#1059164011yescharacteristic
subgroupG/H
centerC22#63974
commutatorC23×C32C22×C4
FrattiniC22×C4C2×D32
FittingC2×C32×C4⋊C4C22
socleC22×C32C2×C22⋊C4
prime radicalC23×C3⋊D3C2×C4
cosocleC22×C32×C4C23
hypercenterC2×C4⋊C4D32
hypocenterC32#1822
LCSG ▷ C23×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
3. C3×#4530C2semidirect
4. #10589168C2semidirect
19. #4530D3semidirect
214. C32#1822semidirect
260. C3#68991semidirect

Maximal subgroups

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

subgroupindex
C2×#641012
#105910742
C3×#45302
#105891682
#689913