Finite Group Databasebeta

← C32×#1390 #11768439

Subgroups — C32×#1390 #11768439

Order 1152.

702 conjugacy classes of subgroups; only the 192 normal subgroups are shown.

normal subgroups only

This group has 702 conjugacy classes of subgroups — too many to draw. Only its 192 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×C32×#100C211yesmaximal, characteristic
2C2×C32×#99C211yesmaximal, characteristic
3C32×#386C211yesmaximal, characteristic
4C3×#1390C314yesmaximal, direct product factor
5C22×C32×D4C2211yescharacteristic
6C23×C32×C4C411yescharacteristic, complemented
7C2×C32×M16—21no—
8C2×C32×C22⋊C4—21no—
9C2×C32×C22⋊C4—21no—
10C2×C32×C22⋊C4C411yescharacteristic, complemented
11C32×#100—21no—
12C32×#100C412yescomplemented
13C32×#99—21no—
14C32×#99C412yescomplemented
15C32×#95—21no—
16C2×C3×#100C2×C314yes—
17C2×C3×#99C2×C314yes—
18C3×#386C2×C314yes—
19C24×C32C2×C411yescharacteristic
20C24×C32D411yescharacteristic
21C2×C32×D4—41no—
22C2×C32×D4—41no—
23C2×C32×D4C2×C411yescharacteristic
24C2×C32×D4C2×C411yescharacteristic
25C2×C32×D4D411yescharacteristic
26C2×C32×D4Q811yescharacteristic
27C22×C32×C4—21no—
28C22×C32×C4—21no—
29C22×C32×C4—42no—
30C22×C32×C4—41no—
31C22×C32×C4—41no—
32C22×C32×C4D411yescharacteristic
33C32×M16—22no—
34C32×M16—41no—
35C2×C32×C8—41no—
36C32×C22⋊C4—22no—
37C32×C22⋊C4—42no—
38C32×C22⋊C4—41no—
39C32×C22⋊C4—41no—
40#1390C3211yescharacteristic, direct product factor, Sylow
41C22×C3×D4C22×C314yes—
42C23×C3×C4C3×C414yescomplemented
43C2×C3×M16—24no—
44C2×C3×C22⋊C4—24no—
45C2×C3×C22⋊C4—24no—
46C2×C3×C22⋊C4C3×C414yescomplemented
47C3×#100—24no—
48C3×#100C3×C418yescomplemented
49C3×#99—24no—
50C3×#99C3×C418yescomplemented
51C3×#95—24no—
52C23×C32—21no—
53C23×C32—21no—
54C23×C32—21no—
55C23×C32—21no—
56C23×C32—41no—
57C23×C32—41no—
58C23×C32—41no—
59C23×C32—41no—
60C23×C32C4211yescharacteristic
61C23×C32C22⋊C411yescharacteristic
62C23×C32C22⋊C411yescharacteristic
63C23×C32C4⋊C411yescharacteristic
64C23×C32C4⋊C411yescharacteristic
65C32×D4—41no—
66C32×D4—41no—
67C32×D4—41no—
68C32×D4—41no—
69C2×C32×C4—21no—
70C2×C32×C4—21no—
71C2×C32×C4—22no—
72C2×C32×C4—41no—
73C2×C32×C4—42no—
74C2×C32×C4—41no—
75C2×C32×C4—42no—
76C2×C32×C4—42no—
77C2×C32×C4—41no—
78C2×C32×C4—41no—
79C2×C32×C4—41no—
80C2×C32×C4—81no—
81C2×C32×C4—81no—
82C2×C32×C4C22⋊C411yescharacteristic
83C2×C32×C4C4⋊C411yescharacteristic
84C32×C8—42no—
85C2×#100C2×C3211yescharacteristic
86C2×#99C2×C3211yescharacteristic
87#386C2×C3211yescharacteristic
88C24×C3C2×C3×C414yes—
89C24×C3C3×D414yes—
90C2×C3×D4—44no—
91C2×C3×D4—44no—
92C2×C3×D4C2×C3×C414yes—
93C2×C3×D4C2×C3×C414yes—
94C2×C3×D4C3×D414yes—
95C2×C3×D4C3×Q814yes—
96C22×C3×C4—24no—
97C22×C3×C4—24no—
98C22×C3×C4—48no—
99C22×C3×C4—44no—
100C22×C3×C4—44no—
101C22×C3×C4C3×D414yes—
102C3×M16—28no—
103C3×M16—44no—
104C2×C3×C8—44no—
105C3×C22⋊C4—28no—
106C3×C22⋊C4—48no—
107C3×C22⋊C4—44no—
108C3×C22⋊C4—44no—
109C22×C32—21no—
110C22×C32—21no—
111C22×C32—21no—
112C22×C32—21no—
113C22×C32—21no—
114C22×C32—21no—
115C22×C32—41no—
116C22×C32—41no—
117C22×C32—41no—
118C22×C32—41no—
119C22×C32—42no—
120C22×C32—41no—
121C22×C32—41no—
122C22×C32—41no—
123C22×C32—41no—
124C22×C32—81no—
125C22×C32#9511yescharacteristic
126C22×C32#9911yescharacteristic
127C22×C32#9911yescharacteristic
128C32×C4—21no—
129C32×C4—21no—
130C32×C4—42no—
131C32×C4—81no—
132C32×C4—82no—
133C22×D4C22×C3211yescharacteristic
134C23×C4C32×C411yescharacteristic, complemented
135C2×M16—21no—
136C2×C22⋊C4—21no—
137C2×C22⋊C4—21no—
138C2×C22⋊C4C32×C411yescharacteristic, complemented
139#100—21no—
140#100C32×C412yescomplemented
141#99—21no—
142#99C32×C412yescomplemented
143#95—21no—
144C23×C3—24no—
145C23×C3—24no—
146C23×C3—24no—
147C23×C3—24no—
148C23×C3—44no—
149C23×C3—44no—
150C23×C3—44no—
151C23×C3—44no—
152C23×C3C3×C4214yes—
153C23×C3C3×C22⋊C414yes—
154C23×C3C3×C22⋊C414yes—
155C23×C3C3×C4⋊C414yes—
156C23×C3C3×C4⋊C414yes—
157C3×D4—44no—
158C3×D4—44no—
159C3×D4—44no—
160C3×D4—44no—
161C2×C3×C4—24no—
162C2×C3×C4—24no—
163C2×C3×C4—28no—
164C2×C3×C4—44no—
165C2×C3×C4—48no—
166C2×C3×C4—44no—
167C2×C3×C4—48no—
168C2×C3×C4—48no—
169C2×C3×C4—44no—
170C2×C3×C4—44no—
171C2×C3×C4—44no—
172C2×C3×C4—84no—
173C2×C3×C4—84no—
174C2×C3×C4C3×C22⋊C414yes—
175C2×C3×C4C3×C4⋊C414yes—
176C3×C8—48no—
177C2×C32—21no—
178C2×C32—21no—
179C2×C32—41no—
180C2×C32—41no—
181C2×C32—41no—
182C2×C32—41no—
183C2×C32#34211yescharacteristic
184C2×C32AΣL(1,𝔽16)11yescharacteristic
185C2×C32#35211yescharacteristic
186C24C2×C32×C411yescharacteristic
187C24C32×D411yescharacteristic
188C2×D4—41no—
189C2×D4—41no—
190C2×D4C2×C32×C411yescharacteristic
191C2×D4C2×C32×C411yescharacteristic
192C2×D4C32×D411yescharacteristic
193C2×D4C32×Q811yescharacteristic
194C22×C4—21no—
195C22×C4—21no—
196C22×C4—42no—
197C22×C4—41no—
198C22×C4—41no—
199C22×C4C32×D411yescharacteristic
200M16—22no—
201M16—41no—
202C2×C8—41no—
203C22⋊C4—22no—
204C22⋊C4—42no—
205C22⋊C4—41no—
206C22⋊C4—41no—
207C22×C3—24no—
208C22×C3—24no—
209C22×C3—24no—
210C22×C3—24no—
211C22×C3—24no—
212C22×C3—24no—
213C22×C3—44no—
214C22×C3—44no—
215C22×C3—44no—
216C22×C3—44no—
217C22×C3—48no—
218C22×C3—44no—
219C22×C3—44no—
220C22×C3—44no—
221C22×C3—44no—
222C22×C3—84no—
223C22×C3C3×#9514yes—
224C22×C3C3×#9914yes—
225C22×C3C3×#9914yes—
226C3×C4—24no—
227C3×C4—24no—
228C3×C4—48no—
229C3×C4—84no—
230C3×C4—88no—
231C32#139011yescharacteristic, direct product factor, Sylow
232C23—21no—
233C23—21no—
234C23—21no—
235C23—21no—
236C23—41no—
237C23—41no—
238C23—41no—
239C23—41no—
240C23C32×C4211yescharacteristic
241C23C32×C22⋊C411yescharacteristic
242C23C32×C22⋊C411yescharacteristic
243C23C32×C4⋊C411yescharacteristic
244C23C32×C4⋊C411yescharacteristic
245D4—41no—
246D4—41no—
247D4—41no—
248D4—41no—
249C2×C4—21no—
250C2×C4—21no—
251C2×C4—22no—
252C2×C4—41no—
253C2×C4—42no—
254C2×C4—41no—
255C2×C4—42no—
256C2×C4—42no—
257C2×C4—41no—
258C2×C4—41no—
259C2×C4—41no—
260C2×C4—81no—
261C2×C4—81no—
262C2×C4C32×C22⋊C411yescharacteristic
263C2×C4C32×C4⋊C411yescharacteristic
264C8—42no—
265C2×C3—24no—
266C2×C3—24no—
267C2×C3—44no—
268C2×C3—44no—
269C2×C3—44no—
270C2×C3—44no—
271C2×C3C3×#34214yes—
272C2×C3C3×AΣL(1,𝔽16)14yes—
273C2×C3C3×#35214yes—
274C22—21no—
275C22—21no—
276C22—21no—
277C22—21no—
278C22—21no—
279C22—21no—
280C22—41no—
281C22—41no—
282C22—41no—
283C22—41no—
284C22—42no—
285C22—41no—
286C22—41no—
287C22—41no—
288C22—41no—
289C22—81no—
290C22C32×#9511yescharacteristic
291C22C32×#9911yescharacteristic
292C22C32×#9911yescharacteristic
293C4—21no—
294C4—21no—
295C4—42no—
296C4—81no—
297C4—82no—
298C3C3×#139014yesdirect product factor
299C2—21no—
300C2—21no—
301C2—41no—
302C2—41no—
303C2—41no—
304C2—41no—
305C2C32×#34211yescharacteristic
306C2C32×AΣL(1,𝔽16)11yescharacteristic
307C2C32×#35211yescharacteristic
subgroupG/H
center, socleC22×C32#99
commutatorC23C32×C42
Frattini, cosocleC22×D4C22×C32
prime radicalC22×C32×D4C22
LCSG ▷ C23 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C32 ◁ C23×C32 ◁ C22×C32×D4 ◁ G

Complements

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

NH ≅ G/Ntype
4. C3×#1390C3direct (N × H)
6. C23×C32×C4C4semidirect
10. C2×C32×C22⋊C4C4semidirect
12. C32×#100C4semidirect
14. C32×#99C4semidirect
40. #1390C32direct (N × H)
42. C23×C3×C4C3×C4semidirect
46. C2×C3×C22⋊C4C3×C4semidirect
48. C3×#100C3×C4semidirect
50. C3×#99C3×C4semidirect
134. C23×C4C32×C4semidirect
138. C2×C22⋊C4C32×C4semidirect
140. #100C32×C4semidirect
142. #99C32×C4semidirect
231. C32#1390direct (N × H)
298. C3C3×#1390direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C32×#1002
C2×C32×#992
C32×#3862
C3×#13903