Finite Group Databasebeta

← #11783608

Subgroups — #11783608

Order 1152.

666 conjugacy classes of subgroups; only the 108 normal subgroups are shown.

normal subgroups only

This group has 666 conjugacy classes of subgroups — too many to draw. Only its 108 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
2C2×#63778C212yesmaximal
3C2×#63777C211yesmaximal, characteristic, complemented
4C2×C4×#622C211yesmaximal, characteristic, complemented
5#10590207C212yesmaximal, complemented
6C22×C4×C3⋊D3C2211yescharacteristic
7C22×#622C2212yes—
8C22×#622C2212yes—
9C2×C32×C4⋊C4C411yescharacteristic
10C2×#3752C411yescharacteristic
11C2×#3752C411yescharacteristic
12C2×C4⋊(C3⋊Dic3)C411yescharacteristic
13C2×C4×C3⋊Dic3C2211yescharacteristic
14C2×C4×C3⋊Dic3C2211yescharacteristic
15#64101—22no—
16#64101—22no—
17#63778C418yescomplemented
18#63777—22no—
19C4×#622—22no—
20C2×#892—62no—
21C23×C3⋊D3C2×C411yescharacteristic
22C22×C32×C4C2×C411yescharacteristic
23C22×C32×C4C2×C411yescharacteristic
24C22×C32×C4C2×C411yescharacteristic
25C22×C3⋊Dic3C2×C411yescharacteristic
26C22×C3⋊Dic3C2×C411yescharacteristic
27C22×C3⋊Dic3C2311yescharacteristic
28C2×C4×C3⋊D3—21no—
29C2×C4×C3⋊D3—21no—
30C2×C4×C3⋊D3—22no—
31C2×C4×C3⋊D3C2×C414yes—
32C2×#622—22no—
33C2×#622—22no—
34C2×#622—22no—
35C2×#622—22no—
36C2×#622C2×C414yes—
37C2×#622C2×C414yes—
38C32×C4⋊C4—22no—
39#3752—22no—
40#3752—22no—
41C4⋊(C3⋊Dic3)—22no—
42C4×C3⋊Dic3—21no—
43C4×C3⋊Dic3—21no—
44C4×C3⋊Dic3D412yes—
45C4×C3⋊Dic3D412yes—
46#1750—91nomaximal, Sylow
47C22×C4×D3—62no—
48C2×C3×C4⋊C4—22no—
49C2×(C2×D3)⋊C4—62no—
50C2×(C2×D3)⋊C4—62no—
51C2×C4⋊Dic3—62no—
52C2×C4×Dic3—62no—
53C2×C4×Dic3—62no—
54#892—68no—
55#892—68no—
56C23×C32C22×C411yescharacteristic
57C22×C3⋊D3—21no—
58C22×C3⋊D3—21no—
59C22×C3⋊D3—22no—
60C22×C3⋊D3—22no—
61C22×C3⋊D3C4212yes—
62C2×C32×C4—21no—
63C2×C32×C4—21no—
64C2×C32×C4—21no—
65C2×C32×C4—22no—
66C2×C32×C4—22no—
67C2×C32×C4C4212yes—
68C2×C32×C4C22⋊C412yes—
69C2×C3⋊Dic3—21no—
70C2×C3⋊Dic3—22no—
71C2×C3⋊Dic3—22no—
72C2×C3⋊Dic3C22⋊C412yes—
73C2×C3⋊Dic3C22×C412yes—
74C2×C3⋊Dic3C2×D411yescharacteristic
75C2×C3⋊Dic3C2×D411yescharacteristic
76C2×C3⋊Dic3#4112yes—
77C4×C3⋊D3—24no—
78C4×C3⋊D3—24no—
79#622—24no—
80#622—24no—
81C2×#117—91no—
82C2×C22⋊C8—92no—
83C2×#97—91no—
84C2×C4×C8—91no—
85#336—92no—
86C23×D3—62no—
87C22×C3×C4—22no—
88C22×C3×C4—22no—
89C22×C3×C4—22no—
90C22×Dic3—62no—
91C22×Dic3—62no—
92C22×Dic3—62no—
93C2×C4×D3—68no—
94C2×C4×D3—64no—
95C2×C4×D3—64no—
96C2×C4×D3—68no—
97C3×C4⋊C4—28no—
98(C2×D3)⋊C4—68no—
99(C2×D3)⋊C4—68no—
100C4⋊Dic3—68no—
101C4×Dic3—64no—
102C4×Dic3—64no—
103C4×Dic3—64no—
104C4×Dic3—64no—
105C22×C32C2×C4211yescharacteristic
106C22×C32C2×C22⋊C411yescharacteristic
107C22×C32#11711yescharacteristic
108C22×C32#13112yes—
109C22×C32#13112yes—
110C2×C3⋊D3—22no—
111C2×C3⋊D3—24no—
112C2×C3⋊D3—41no—
113C2×C3⋊D3—41no—
114C2×C3⋊D3—42no—
115C32×C4—22no—
116C32×C4—22no—
117C32×C4—41no—
118C3⋊Dic3—22no—
119C3⋊Dic3—41no—
120C3⋊Dic3C4×D412yes—
121C3⋊Dic3C4×D412yes—
122C23×C4—91no—
123C22×C8—92no—
124C22×C8—92no—
125#117—182no—
126#117—182no—
127C2×C4⋊C4—91no—
128C2×C4⋊C4#15711yescharacteristic
129C2×C22⋊C4—91no—
130C2×C22⋊C4—91no—
131C2×C42—91no—
132C2×C42—91no—
133C22⋊C8—98no—
134#97—182no—
135C4×C8—182no—
136C23×C3—22no—
137C22×D3—64no—
138C22×D3—64no—
139C22×D3—64no—
140C22×D3—124no—
141C22×D3—124no—
142C2×C3×C4—24no—
143C2×C3×C4—24no—
144C2×C3×C4—24no—
145C2×C3×C4—24no—
146C2×C3×C4—24no—
147C2×C3×C4—44no—
148C2×C3×C4—44no—
149C2×Dic3—64no—
150C2×Dic3—62no—
151C2×Dic3—62no—
152C2×Dic3—64no—
153C2×Dic3—64no—
154C2×Dic3—64no—
155C2×Dic3—124no—
156C2×Dic3—124no—
157C4×D3—616no—
158C4×D3—616no—
159C2×C32C4×C22⋊C411yescharacteristic
160C2×C32#40512yes—
161C2×C32#40811yescharacteristic
162C2×C32#40811yescharacteristic
163C2×C32#43312yes—
164C3⋊D3—42no—
165C24—91no—
166C22×C4—91no—
167C22×C4—91no—
168C22×C4—94no—
169C22×C4—91no—
170C22×C4—181no—
171C22×C4—181no—
172C22×C4—182no—
173C22×C4C2×#15711yescharacteristic
174C22×C4C2×#15711yescharacteristic
175C22×C4C2×#15711yescharacteristic
176C2×C8—94no—
177C2×C8—94no—
178C2×C8—182no—
179C2×C8—182no—
180C2×C8—182no—
181C2×C8—182no—
182C4⋊C4—22no—
183C4⋊C4—182no—
184C22⋊C4—182no—
185C22⋊C4—182no—
186C42—92no—
187C42—92no—
188C42—181no—
189C42—181no—
190C22×C3—22no—
191C22×C3—22no—
192C22×C3—24no—
193C22×C3—24no—
194C22×C3—22no—
195C2×D3—68no—
196C2×D3—128no—
197C2×D3—124no—
198C2×D3—124no—
199C2×D3—128no—
200C3×C4—28no—
201C3×C4—44no—
202C3×C4—44no—
203Dic3—64no—
204Dic3—64no—
205Dic3—124no—
206Dic3—124no—
207C32#175011yescharacteristic, complemented, Sylow
208C23—92no—
209C23—181no—
210C23—182no—
211C23—182no—
212C23—181no—
213C23C22×#15711yescharacteristic
214C2×C4—21no—
215C2×C4—22no—
216C2×C4—21no—
217C2×C4—22no—
218C2×C4—21no—
219C2×C4—92no—
220C2×C4—92no—
221C2×C4—91no—
222C2×C4—91no—
223C2×C4—92no—
224C2×C4—184no—
225C2×C4—184no—
226C2×C4—182no—
227C2×C4—182no—
228C2×C4—181no—
229C2×C4C4×#15712yes—
230C2×C4C22⋊#15712yes—
231C8—184no—
232C8—184no—
233C2×C3—22no—
234C2×C3—22no—
235C2×C3—22no—
236C2×C3—24no—
237C2×C3—24no—
238D3—128no—
239C22—182no—
240C22—184no—
241C22—361no—
242C22—361no—
243C22—362no—
244C22C2×C4×#15711yescharacteristic
245C22#6428611yescharacteristic
246C22#6428712yes—
247C22#6428912yes—
248C22C2×C22⋊#15711yescharacteristic
249C4—22no—
250C4—22no—
251C4—41no—
252C4—92no—
253C4—92no—
254C4—182no—
255C4—361no—
256C3—22no—
257C2—362no—
258C2#1059374812yes—
259C2#1059375312yes—
260C2C4×C22⋊#15711yescharacteristic
261C2#1059382211yescharacteristic
262C2#1059383411yescharacteristic
subgroupG/H
center, FrattiniC23C22×#157
commutatorC22×C32C2×C42
FittingC2×C32×C4⋊C4C4
socleC23×C32C22×C4
prime radicalC23×C3⋊D3C2×C4
cosocleC22×C3⋊Dic3C23
hypercenterC2×C4⋊C4#157
hypocenterC32#1750
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
3. C2×#63777C2semidirect
4. C2×C4×#622C2semidirect
5. #10590207C2semidirect
17. #63778C4semidirect
207. C32#1750semidirect

Maximal subgroups

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

subgroupindex
C2×#641012
C2×#637782
C2×#637772
C2×C4×#6222
#105902072
#17509