Finite Group Databasebeta

← #11773924

Subgroups — #11773924

Order 1152.

742 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 742 conjugacy classes of subgroups — too many to draw. Only its 68 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×C4×C4⋊(C3⋊D3)C211yesmaximal, characteristic
2#10593803C212yesmaximal, complemented
3#10590204C212yesmaximal, complemented
4#10590202C212yesmaximal, complemented
5C22×C4⋊(C3⋊D3)C411yescharacteristic
6C22×C4×C3⋊D3C411yescharacteristic
7C22×C4×C3⋊D3C2211yescharacteristic
8C2×#3788—22no—
9C2×C32×C42C411yescharacteristic
10C2×#3752C411yescharacteristic
11C2×#3752C2211yescharacteristic
12C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
13C4×C4⋊(C3⋊D3)—22no—
14C4×C4⋊(C3⋊D3)—22no—
15C22⋊#622C2214yes—
16#63778—22no—
17C2×C4×D12—62no—
18C23×C3⋊D3C2×C411yescharacteristic
19C23×C3⋊D3C2×C411yescharacteristic
20C22×C32×C4C2×C411yescharacteristic
21C22×C32×C4C2×C411yescharacteristic
22C22×C32×C4C2×C411yescharacteristic
23C22×C3⋊Dic3C2×C411yescharacteristic
24C22×C3⋊Dic3C2311yescharacteristic
25C2×C4⋊(C3⋊D3)—22no—
26C2×C4⋊(C3⋊D3)—22no—
27C2×C4⋊(C3⋊D3)—22no—
28C2×C4×C3⋊D3—21no—
29C2×C4×C3⋊D3—21no—
30C2×C4×C3⋊D3—42no—
31C2×C4×C3⋊D3—42no—
32C2×C4×C3⋊D3D412yes—
33C2×C4×C3⋊D3D412yes—
34C2×#622—24no—
35#3788—44no—
36C32×C42—21no—
37C32×C42—21no—
38#3752—22no—
39#3752—22no—
40C4⋊(C3⋊Dic3)—22no—
41#1465—91nomaximal, Sylow
42C22×D12—62no—
43C22×C4×D3—62no—
44C22×C4×D3—62no—
45C2×C3×C42—22no—
46C2×(C2×D3)⋊C4—62no—
47C2×(C2×D3)⋊C4—62no—
48C2×C4⋊Dic3—62no—
49C4×D12—68no—
50C4×D12—68no—
51C23×C32C22×C411yescharacteristic
52C22×C3⋊D3—21no—
53C22×C3⋊D3—21no—
54C22×C3⋊D3—21no—
55C22×C3⋊D3—21no—
56C22×C3⋊D3—41no—
57C22×C3⋊D3—41no—
58C22×C3⋊D3—41no—
59C22×C3⋊D3—41no—
60C22×C3⋊D3C22⋊C412yes—
61C22×C3⋊D3M1612yescomplemented
62C2×C32×C4—21no—
63C2×C32×C4—21no—
64C2×C32×C4—22no—
65C2×C32×C4—21no—
66C2×C32×C4—41no—
67C2×C32×C4C22⋊C411yescharacteristic
68C2×C32×C4C22⋊C411yescharacteristic
69C2×C32×C4M1612yescomplemented
70C2×C3⋊Dic3—21no—
71C2×C3⋊Dic3—41no—
72C2×C3⋊Dic3—41no—
73C2×C3⋊Dic3C2×D412yes—
74C4⋊(C3⋊D3)—28no—
75C4×C3⋊D3—24no—
76C4×C3⋊D3—42no—
77C4×C3⋊D3—42no—
78C4×C3⋊D3—42no—
79#622—44no—
80C2×C4×D4—91no—
81#407—92no—
82#324—92no—
83#323—92no—
84C23×D3—62no—
85C23×D3—62no—
86C22×C3×C4—22no—
87C22×C3×C4—22no—
88C22×C3×C4—22no—
89C22×Dic3—62no—
90C22×Dic3—62no—
91C2×D12—68no—
92C2×D12—68no—
93C2×D12—68no—
94C2×C4×D3—64no—
95C2×C4×D3—64no—
96C2×C4×D3—64no—
97C2×C4×D3—64no—
98C2×C4×D3—128no—
99C2×C4×D3—128no—
100C3×C42—24no—
101C3×C42—24no—
102(C2×D3)⋊C4—68no—
103(C2×D3)⋊C4—68no—
104C4⋊Dic3—68no—
105C22×C32—21no—
106C22×C32—21no—
107C22×C32C2×C22⋊C411yescharacteristic
108C22×C32C2×M1611yescharacteristic
109C22×C32C2×M1611yescharacteristic
110C2×C3⋊D3—22no—
111C2×C3⋊D3—22no—
112C2×C3⋊D3—22no—
113C2×C3⋊D3—22no—
114C2×C3⋊D3—42no—
115C2×C3⋊D3—42no—
116C2×C3⋊D3—42no—
117C2×C3⋊D3—41no—
118C2×C3⋊D3—41no—
119C2×C3⋊D3—42no—
120C32×C4—22no—
121C32×C4—21no—
122C32×C4—41no—
123C32×C4#9912yes—
124C3⋊Dic3—22no—
125C3⋊Dic3—41no—
126C22×D4—91no—
127C23×C4—91no—
128C23×C4—91no—
129C2×M16—182no—
130C4×D4—182no—
131C4×D4—182no—
132C2×C4⋊C4—91no—
133C2×C22⋊C4—91no—
134C2×C22⋊C4—91no—
135C2×C42#15711yescharacteristic
136C22⋊C8—94no—
137C22⋊C8—182no—
138C23×C3—22no—
139C22×D3—64no—
140C22×D3—64no—
141C22×D3—64no—
142C22×D3—64no—
143C22×D3—64no—
144C22×D3—64no—
145C22×D3—124no—
146C22×D3—124no—
147C22×D3—124no—
148C22×D3—124no—
149C2×C3×C4—24no—
150C2×C3×C4—28no—
151C2×C3×C4—24no—
152C2×C3×C4—24no—
153C2×C3×C4—24no—
154C2×C3×C4—22no—
155C2×C3×C4—22no—
156C2×C3×C4—44no—
157C2×Dic3—64no—
158C2×Dic3—64no—
159C2×Dic3—124no—
160C2×Dic3—124no—
161D12—632no—
162C4×D3—128no—
163C4×D3—128no—
164C4×D3—128no—
165C4×D3—128no—
166C2×C32—21no—
167C2×C32—21no—
168C2×C32#40711yescharacteristic
169C2×C32C2×#9911yescharacteristic
170C2×C32#41311yescharacteristic
171C3⋊D3—42no—
172C3⋊D3—42no—
173C24—91no—
174C24—91no—
175C2×D4—182no—
176C2×D4—182no—
177C2×D4—182no—
178C22×C4—91no—
179C22×C4—92no—
180C22×C4—92no—
181C22×C4—91no—
182C22×C4—181no—
183C22×C4—181no—
184C22×C4—362no—
185C22×C4—362no—
186C22×C4C2×#15711yescharacteristic
187C22×C4C2×#15711yescharacteristic
188C22×C4C2×#15711yescharacteristic
189M16—364no—
190C2×C8—184no—
191C4⋊C4—182no—
192C22⋊C4—182no—
193C22⋊C4—182no—
194C42—21no—
195C42—21no—
196C22×C3—24no—
197C22×C3—24no—
198C22×C3—22no—
199C22×C3—22no—
200C22×C3—22no—
201C2×D3—68no—
202C2×D3—68no—
203C2×D3—124no—
204C2×D3—124no—
205C2×D3—124no—
206C2×D3—128no—
207C2×D3—128no—
208C2×D3—128no—
209C2×D3—128no—
210C2×D3—124no—
211C3×C4—24no—
212C3×C4—28no—
213C3×C4—24no—
214C3×C4—44no—
215Dic3—124no—
216Dic3—124no—
217C32#146511yescharacteristic, complemented, Sylow
218C23—92no—
219C23—92no—
220C23—181no—
221C23—181no—
222C23—181no—
223C23—181no—
224C23—361no—
225C23—361no—
226C23—361no—
227C23—361no—
228C23C22×#15711yescharacteristic
229D4—188no—
230C2×C4—21no—
231C2×C4—21no—
232C2×C4—22no—
233C2×C4—21no—
234C2×C4—41no—
235C2×C4—92no—
236C2×C4—184no—
237C2×C4—181no—
238C2×C4—362no—
239C2×C4—362no—
240C2×C4—361no—
241C2×C4—362no—
242C2×C4—361no—
243C2×C4#378812yescomplemented
244C2×C4C22⋊#15711yescharacteristic
245C2×C4C22⋊#15711yescharacteristic
246C8—364no—
247C2×C3—24no—
248C2×C3—24no—
249C2×C3—22no—
250C2×C3—22no—
251C2×C3—22no—
252D3—128no—
253D3—128no—
254C22—21no—
255C22—21no—
256C22—182no—
257C22—182no—
258C22—182no—
259C22—182no—
260C22—362no—
261C22—362no—
262C22—362no—
263C22—362no—
264C22—361no—
265C22—361no—
266C22C2×#378811yescharacteristic
267C22#6428311yescharacteristic
268C22C2×C22⋊#15711yescharacteristic
269C4—22no—
270C4—21no—
271C4—41no—
272C4—182no—
273C4—361no—
274C4#6377412yes—
275C3—22no—
276C2—21no—
277C2—21no—
278C2—362no—
279C2—362no—
280C2C2×#6377411yescharacteristic
281C2#1059380311yescharacteristic
282C2#1059380811yescharacteristic
subgroupG/H
centerC22C2×C22⋊#157
commutatorC23×C32C22×C4
FrattiniC23C22×#157
FittingC2×C32×C42C4
socleC22×C32C2×C22⋊C4
prime radicalC22×C4⋊(C3⋊D3)C4
cosocleC22×C3⋊Dic3C23
hypercenterC2×C42#157
hypocenterC32#1465
LCSG ▷ C23×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
2. #10593803C2semidirect
3. #10590204C2semidirect
4. #10590202C2semidirect
61. C22×C3⋊D3M16semidirect
69. C2×C32×C4M16semidirect
217. C32#1465semidirect
243. C2×C4#3788semidirect

Maximal subgroups

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

subgroupindex
C2×C4×C4⋊(C3⋊D3)2
#105938032
#105902042
#105902022
#14659