Finite Group Databasebeta

← #11774066

Subgroups — #11774066

Order 1152.

376 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 376 conjugacy classes of subgroups — too many to draw. Only its 57 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#10593948C211yesmaximal, characteristic
2#10593730C211yesmaximal, characteristic
3#10590297C211yesmaximal, characteristic
4#10590028C214yesmaximal
5C42×C3⋊D3C2211yescharacteristic
6C3×#870—21no—
7#63900C411yescharacteristic
8#63900C411yescharacteristic
9#63883C412yes—
10#63883C2212yes—
11#63872—21no—
12#63870—21no—
13#63870—21no—
14#63778C2212yes—
15#63777—21no—
16C4⋊#622—21no—
17C3×C4×C3⋊C8—21no—
18#63572—21no—
19#63557C2212yes—
20D3×#125—61no—
21#4685—61no—
22C2×C4×C3⋊D3C2×C411yescharacteristic
23C2×C4×C3⋊D3C2×C411yescharacteristic
24C2×C4×C3⋊D3C2311yescharacteristic
25C2×#624C2×C412yes—
26C2×#624C2×C412yes—
27C2×#622—22no—
28C32×C42D411yescharacteristic
29C4×C3⋊Dic3D411yescharacteristic
30C4×C3⋊Dic3D411yescharacteristic
31C4×C3⋊Dic3D411yescharacteristic
32C3×C4⋊Dic3—21no—
33C3×C4⋊Dic3—21no—
34C3×Dic3⋊C4—22no—
35C3×Dic3⋊C4—22no—
36C2×C3×C3⋊C8—22no—
37#3724—21no—
38#3724—21no—
39Dic3⋊Dic3—22no—
40Dic3⋊Dic3—22no—
41#1470—91nomaximal, Sylow
42C3×#125—61no—
43D3×C4⋊C4—62no—
44D3×C4⋊C4—62no—
45D3×C4⋊C4—61no—
46D3×C4⋊C4—61no—
47#890—61no—
48#890—61no—
49#889—62no—
50#889—62no—
51C42×D3—61no—
52C42×D3—61no—
53#870—21no—
54C3×C4×C8—61no—
55(C2×D3)⋊C8—62no—
56Dic3⋊C8—62no—
57C4×C3⋊C8—21no—
58C22×C3⋊D3C22×C411yescharacteristic
59C2×C32×C4C22⋊C411yescharacteristic
60C2×C32×C4C22⋊C411yescharacteristic
61C2×C32×C4C2×D411yescharacteristic
62C2×C3⋊Dic3C22⋊C411yescharacteristic
63C2×C3⋊Dic3C22⋊C411yescharacteristic
64C2×C3⋊Dic3C2×D411yescharacteristic
65C4×C3⋊D3—22no—
66C4×C3⋊D3—22no—
67C4×C3⋊D3—41no—
68C2×C3×Dic3—22no—
69C2×C3×Dic3—22no—
70#624—24no—
71#624—42no—
72#622—42no—
73C3×C3⋊C8—42no—
74C2×#125—91no—
75#432—91no—
76#431—91no—
77#324—94no—
78C2×C4×D3—61no—
79C2×C4×D3—61no—
80C2×C4×D3—62no—
81C2×C4×D3—62no—
82C2×C4×D3—61no—
83C2×C4×D3—61no—
84C2×C4×D3—61no—
85C2×C4×D3—61no—
86C2×C3×C8—62no—
87C3×C4⋊C4—62no—
88C3×C4⋊C4—62no—
89C3×C4⋊C4—61no—
90C3×C4⋊C4—61no—
91C3×C42—21no—
92C3×C42—21no—
93C4⋊Dic3—21no—
94C4⋊Dic3—21no—
95C4⋊Dic3—62no—
96C4⋊Dic3—62no—
97Dic3⋊C4—22no—
98Dic3⋊C4—22no—
99Dic3⋊C4—62no—
100Dic3⋊C4—62no—
101Dic3⋊C4—62no—
102Dic3⋊C4—62no—
103C4×Dic3—61no—
104C4×Dic3—61no—
105C4×Dic3—61no—
106C4×Dic3—61no—
107C4×Dic3—61no—
108C4×Dic3—61no—
109C2×C3⋊C8—22no—
110C22×C32C2×C22⋊C411yescharacteristic
111C2×C3⋊D3—21no—
112C2×C3⋊D3—21no—
113C2×C3⋊D3#13112yes—
114C32×C4—21no—
115C32×C4—21no—
116C32×C4#10112yes—
117C3⋊Dic3—21no—
118C3⋊Dic3—21no—
119C3⋊Dic3—21no—
120C3×Dic3—42no—
121C3×Dic3—42no—
122#125—61no—
123#125—181no—
124#125—181no—
125#125—181no—
126C2×C4⋊C4—92no—
127C2×C4⋊C4—92no—
128C2×C4⋊C4—91no—
129C2×C4⋊C4—91no—
130C2×C42—91no—
131C4⋊C8—181no—
132C4⋊C8—181no—
133C22⋊C8—92no—
134C22⋊C8—92no—
135#97—181no—
136C4×C8—61no—
137C22×D3—61no—
138C22×D3—61no—
139C2×C3×C4—21no—
140C2×C3×C4—21no—
141C2×C3×C4—21no—
142C2×C3×C4—21no—
143C2×C3×C4—21no—
144C2×C3×C4—21no—
145C2×C3×C4—62no—
146C2×C3×C4—62no—
147C2×Dic3—22no—
148C2×Dic3—22no—
149C2×Dic3—61no—
150C2×Dic3—61no—
151C2×Dic3—61no—
152C2×Dic3—61no—
153C2×Dic3—61no—
154C2×Dic3—61no—
155C4×D3—64no—
156C4×D3—64no—
157C4×D3—124no—
158C4×D3—122no—
159C4×D3—122no—
160C4×D3—124no—
161C4×D3—122no—
162C4×D3—122no—
163C3×C8—122no—
164C3⋊C8—42no—
165C2×C32#40811yescharacteristic
166C2×C32#41011yescharacteristic
167C2×C32C2×#10111yescharacteristic
168C3⋊D3—22no—
169C22×C4—92no—
170C22×C4—92no—
171C22×C4—91no—
172C22×C4—91no—
173C22×C4—91no—
174C2×C8—62no—
175C2×C8—182no—
176C4⋊C4—62no—
177C4⋊C4—62no—
178C4⋊C4—61no—
179C4⋊C4—61no—
180C4⋊C4—181no—
181C4⋊C4—181no—
182C4⋊C4—182no—
183C4⋊C4—182no—
184C42—91no—
185C42—91no—
186C42—91no—
187C42GO+(4,𝔽2)11yescharacteristic
188C22×C3—21no—
189C22×C3—21no—
190C2×D3—62no—
191C2×D3—62no—
192C2×D3—62no—
193C2×D3—62no—
194C2×D3—121no—
195C2×D3—121no—
196C3×C4—22no—
197C3×C4—22no—
198C3×C4—22no—
199C3×C4—22no—
200C3×C4—41no—
201C3×C4—41no—
202C3×C4—122no—
203C3×C4—122no—
204Dic3—42no—
205Dic3—42no—
206Dic3—62no—
207Dic3—62no—
208Dic3—121no—
209Dic3—121no—
210Dic3—121no—
211Dic3—121no—
212C32#147011yescharacteristic, complemented, Sylow
213C23—91no—
214C2×C4—62no—
215C2×C4—62no—
216C2×C4—91no—
217C2×C4—91no—
218C2×C4—91no—
219C2×C4—182no—
220C2×C4—184no—
221C2×C4—182no—
222C2×C4—361no—
223C2×C4—362no—
224C2×C4D32⋊C411yescharacteristic
225C2×C4D32⋊C411yescharacteristic
226C2×C4C2×GO+(4,𝔽2)11yescharacteristic
227C8—122no—
228C8—362no—
229C2×C3—21no—
230C2×C3—21no—
231C2×C3—21no—
232C2×C3—21no—
233C2×C3—21no—
234C2×C3—21no—
235D3—64no—
236D3—122no—
237C22—92no—
238C22—181no—
239C22—181no—
240C22C2×D32⋊C411yescharacteristic
241C4—21no—
242C4—21no—
243C4—122no—
244C4—122no—
245C4—181no—
246C4—181no—
247C4—181no—
248C4#6372812yes—
249C3—21no—
250C3—21no—
251C2—182no—
252C2#1059330811yescharacteristic
253C2C2×#6372811yescharacteristic
254C2#1059334511yescharacteristic
subgroupG/H
centerC22C2×D32⋊C4
commutator, prime radicalC22×C3⋊D3C22×C4
FrattiniC2×C4C2×GO+(4,𝔽2)
FittingC32×C42D4
socleC22×C32C2×C22⋊C4
cosocleC2×C4×C3⋊D3C23
hypercenterC42GO+(4,𝔽2)
hypocenterC32#1470
LCSG ▷ C22×C3⋊D3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42

Complements

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

NH ≅ G/Ntype
212. C32#1470semidirect

Maximal subgroups

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

subgroupindex
#105939482
#105937302
#105902972
#105900282
#14709