Finite Group Databasebeta

← C32×#1781 #11768830

Subgroups — C32×#1781 #11768830

Order 1152.

2640 conjugacy classes of subgroups; only the 432 normal subgroups are shown.

normal subgroups only

This group has 2640 conjugacy classes of subgroups — too many to draw. Only its 432 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
1C23×C32×D4C211yesmaximal, characteristic
2C2×C32×#99C214yesmaximal, complemented
3C32×#379C212yesmaximal, complemented
4C3×#1781C314yesmaximal, direct product factor
5C25×C32C411yescharacteristic, complemented
6C25×C32C2211yescharacteristic
7C22×C32×D4—28no—
8C22×C32×D4—24no—
9C22×C32×D4C412yescomplemented
10C22×C32×D4C2212yes—
11C23×C32×C4C411yescharacteristic, complemented
12C2×C32×C22⋊C4—24no—
13C2×C32×C22⋊C4C2214yescomplemented
14C32×#99—28no—
15C23×C3×D4C2×C314yes—
16C2×C3×#99C2×C3116yescomplemented
17C3×#379C2×C318yescomplemented
18C24×C32—22no—
19C24×C32—24no—
20C24×C32—24no—
21C24×C32—44no—
22C24×C32—44no—
23C24×C32C2×C411yescharacteristic
24C24×C32C2×C411yescharacteristic
25C24×C32C2×C412yes—
26C24×C32D414yes—
27C24×C32C2311yescharacteristic
28C2×C32×D4—232no—
29C2×C32×D4—24no—
30C2×C32×D4—24no—
31C2×C32×D4—24no—
32C2×C32×D4—24no—
33C2×C32×D4—24no—
34C2×C32×D4D418yes—
35C22×C32×C4—22no—
36C22×C32×C4—24no—
37C22×C32×C4—24no—
38C22×C32×C4C2×C412yes—
39C32×C22⋊C4—28no—
40C32×C22⋊C4—48no—
41#1781C3211yescharacteristic, direct product factor, Sylow
42C25×C3C3×C414yescomplemented
43C25×C3C22×C314yes—
44C22×C3×D4—216no—
45C22×C3×D4—232no—
46C22×C3×D4C3×C418yescomplemented
47C22×C3×D4C22×C318yes—
48C23×C3×C4C3×C414yescomplemented
49C2×C3×C22⋊C4—216no—
50C2×C3×C22⋊C4C22×C3116yescomplemented
51C3×#99—232no—
52C23×C32—24no—
53C23×C32—22no—
54C23×C32—28no—
55C23×C32—28no—
56C23×C32—22no—
57C23×C32—22no—
58C23×C32—22no—
59C23×C32—28no—
60C23×C32—42no—
61C23×C32—44no—
62C23×C32—42no—
63C23×C32—44no—
64C23×C32—416no—
65C23×C32—416no—
66C23×C32—44no—
67C23×C32—44no—
68C23×C32C22⋊C412yes—
69C23×C32C22⋊C412yes—
70C23×C32C22⋊C414yescomplemented
71C23×C32C22×C411yescharacteristic
72C23×C32C2×D412yes—
73C23×C32C2×D414yes—
74C32×D4—216no—
75C32×D4—216no—
76C2×C32×C4—28no—
77C2×C32×C4—22no—
78C2×C32×C4—22no—
79C2×C32×C4—48no—
80C2×C32×C4—44no—
81C2×C32×C4C22⋊C414yescomplemented
82C23×D4C2×C3211yescharacteristic
83C2×#99C2×C3214yescomplemented
84#379C2×C3212yescomplemented
85C24×C3—28no—
86C24×C3—216no—
87C24×C3—216no—
88C24×C3—416no—
89C24×C3—416no—
90C24×C3C2×C3×C414yes—
91C24×C3C2×C3×C414yes—
92C24×C3C2×C3×C418yes—
93C24×C3C3×D4116yes—
94C24×C3C23×C314yes—
95C2×C3×D4—2128no—
96C2×C3×D4—216no—
97C2×C3×D4—216no—
98C2×C3×D4—216no—
99C2×C3×D4—216no—
100C2×C3×D4—216no—
101C2×C3×D4C3×D4132yes—
102C22×C3×C4—28no—
103C22×C3×C4—216no—
104C22×C3×C4—216no—
105C22×C3×C4C2×C3×C418yes—
106C3×C22⋊C4—232no—
107C3×C22⋊C4—432no—
108C22×C32—28no—
109C22×C32—22no—
110C22×C32—24no—
111C22×C32—22no—
112C22×C32—22no—
113C22×C32—22no—
114C22×C32—24no—
115C22×C32—24no—
116C22×C32—44no—
117C22×C32—416no—
118C22×C32—44no—
119C22×C32—416no—
120C22×C32—44no—
121C22×C32—44no—
122C22×C32—44no—
123C22×C32#9914yescomplemented
124C22×C32C2×C22⋊C412yes—
125C22×C32C2×C22⋊C411yescharacteristic
126C22×C32#12014yes—
127C32×C4—24no—
128C32×C4—84no—
129C25C32×C411yescharacteristic, complemented
130C25C22×C3211yescharacteristic
131C22×D4—24no—
132C22×D4—28no—
133C22×D4C32×C412yescomplemented
134C22×D4C22×C3212yes—
135C23×C4C32×C411yescharacteristic, complemented
136C2×C22⋊C4—24no—
137C2×C22⋊C4C22×C3214yescomplemented
138#99—28no—
139C23×C3—216no—
140C23×C3—28no—
141C23×C3—232no—
142C23×C3—232no—
143C23×C3—28no—
144C23×C3—28no—
145C23×C3—28no—
146C23×C3—232no—
147C23×C3—48no—
148C23×C3—416no—
149C23×C3—48no—
150C23×C3—416no—
151C23×C3—464no—
152C23×C3—464no—
153C23×C3—416no—
154C23×C3—416no—
155C23×C3C3×C22⋊C418yes—
156C23×C3C3×C22⋊C418yes—
157C23×C3C3×C22⋊C4116yescomplemented
158C23×C3C22×C3×C414yes—
159C23×C3C2×C3×D418yes—
160C23×C3C2×C3×D4116yes—
161C3×D4—264no—
162C3×D4—264no—
163C2×C3×C4—232no—
164C2×C3×C4—28no—
165C2×C3×C4—28no—
166C2×C3×C4—432no—
167C2×C3×C4—416no—
168C2×C3×C4C3×C22⋊C4116yescomplemented
169C2×C32—24no—
170C2×C32—24no—
171C2×C32—22no—
172C2×C32—42no—
173C2×C32—44no—
174C2×C32#37911yescharacteristic
175C2×C32C2×#9912yes—
176C24—22no—
177C24—24no—
178C24—24no—
179C24—44no—
180C24—44no—
181C24C2×C32×C411yescharacteristic
182C24C2×C32×C411yescharacteristic
183C24C2×C32×C412yes—
184C24C32×D414yes—
185C24C23×C3211yescharacteristic
186C2×D4—232no—
187C2×D4—24no—
188C2×D4—24no—
189C2×D4—24no—
190C2×D4—24no—
191C2×D4—24no—
192C2×D4C32×D418yes—
193C22×C4—22no—
194C22×C4—24no—
195C22×C4—24no—
196C22×C4C2×C32×C412yes—
197C22⋊C4—28no—
198C22⋊C4—48no—
199C22×C3—232no—
200C22×C3—28no—
201C22×C3—216no—
202C22×C3—28no—
203C22×C3—28no—
204C22×C3—28no—
205C22×C3—216no—
206C22×C3—216no—
207C22×C3—416no—
208C22×C3—464no—
209C22×C3—416no—
210C22×C3—464no—
211C22×C3—416no—
212C22×C3—416no—
213C22×C3—416no—
214C22×C3C3×#99116yescomplemented
215C22×C3C2×C3×C22⋊C418yes—
216C22×C3C2×C3×C22⋊C414yes—
217C22×C3C3×#120116yes—
218C3×C4—216no—
219C3×C4—816no—
220C32#178111yescharacteristic, direct product factor, Sylow
221C23—22no—
222C23—24no—
223C23—28no—
224C23—22no—
225C23—22no—
226C23—22no—
227C23—28no—
228C23—28no—
229C23—42no—
230C23—44no—
231C23—42no—
232C23—44no—
233C23—416no—
234C23—416no—
235C23—44no—
236C23—44no—
237C23C32×C22⋊C412yes—
238C23C32×C22⋊C412yes—
239C23C32×C22⋊C414yescomplemented
240C23C22×C32×C411yescharacteristic
241C23C2×C32×D412yes—
242C23C2×C32×D414yes—
243D4—216no—
244D4—216no—
245C2×C4—28no—
246C2×C4—22no—
247C2×C4—22no—
248C2×C4—48no—
249C2×C4—44no—
250C2×C4C32×C22⋊C414yescomplemented
251C2×C3—216no—
252C2×C3—216no—
253C2×C3—28no—
254C2×C3—48no—
255C2×C3—416no—
256C2×C3C3×#37914yes—
257C2×C3C2×C3×#9918yes—
258C22—28no—
259C22—22no—
260C22—24no—
261C22—22no—
262C22—22no—
263C22—22no—
264C22—24no—
265C22—24no—
266C22—44no—
267C22—416no—
268C22—44no—
269C22—44no—
270C22—44no—
271C22—416no—
272C22—44no—
273C22C32×#9914yescomplemented
274C22C2×C32×C22⋊C412yes—
275C22C2×C32×C22⋊C411yescharacteristic
276C22C32×#12014yes—
277C4—24no—
278C4—84no—
279C3C3×#178114yesdirect product factor
280C2—24no—
281C2—22no—
282C2—24no—
283C2—42no—
284C2—44no—
285C2C32×#37911yescharacteristic
286C2C2×C32×#9912yes—
subgroupG/H
center, socleC22×C32C2×C22⋊C4
commutatorC23C22×C32×C4
Frattini, cosocleC24C23×C32
prime radicalC23×C32×D4C2
LCSG ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C32 ◁ C25×C32 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C32×#99C2semidirect
3. C32×#379C2semidirect
4. C3×#1781C3direct (N × H)
5. C25×C32C4semidirect
9. C22×C32×D4C4semidirect
11. C23×C32×C4C4semidirect
13. C2×C32×C22⋊C4C22semidirect
16. C2×C3×#99C2×C3semidirect
17. C3×#379C2×C3semidirect
41. #1781C32direct (N × H)
42. C25×C3C3×C4semidirect
46. C22×C3×D4C3×C4semidirect
48. C23×C3×C4C3×C4semidirect
50. C2×C3×C22⋊C4C22×C3semidirect
70. C23×C32C22⋊C4semidirect
81. C2×C32×C4C22⋊C4semidirect
83. C2×#99C2×C32semidirect
84. #379C2×C32semidirect
123. C22×C32#99semidirect
129. C25C32×C4semidirect
133. C22×D4C32×C4semidirect
135. C23×C4C32×C4semidirect
137. C2×C22⋊C4C22×C32semidirect
157. C23×C3C3×C22⋊C4semidirect
168. C2×C3×C4C3×C22⋊C4semidirect
214. C22×C3C3×#99semidirect
220. C32#1781direct (N × H)
239. C23C32×C22⋊C4semidirect
250. C2×C4C32×C22⋊C4semidirect
273. C22C32×#99semidirect
279. C3C3×#1781direct (N × H)

Maximal subgroups

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

subgroupindex
C23×C32×D42
C2×C32×#992
C32×#3792
C3×#17813