Finite Group Databasebeta

← C32×#1603 #11768652

Subgroups — C32×#1603 #11768652

Order 1152.

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

normal subgroups only

This group has 732 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
1C32×#539C211yesmaximal, characteristic
2C32×#451C211yesmaximal, characteristic, complemented
3C32×#448C211yesmaximal, characteristic
4C32×#395C211yesmaximal, characteristic, complemented
5C32×#328C211yesmaximal, characteristic, complemented
6C32×#327C211yesmaximal, characteristic
7C32×#324C211yesmaximal, characteristic, complemented
8C3×#1603C314yesmaximal, direct product factor
9C22×C32×Q8C2211yescharacteristic
10C2×C32×Q16—21no—
11C2×C32×SD16—21no—
12C32×#126—21no—
13C32×#125—21no—
14C32×#123—21no—
15C32×#123—21no—
16C32×C22⋊Q8—21no—
17C32×C22⋊Q8C2211yescharacteristic
18C32×#121C2211yescharacteristic
19C32×C4×D4—21no—
20C2×C32×C4⋊C4—21no—
21C2×C32×C4⋊C4C2211yescharacteristic
22C32×#103—21no—
23C32×#103—21no—
24C32×C22⋊C8C2211yescharacteristic
25C32×C22⋊C8C2211yescharacteristic
26C32×#95—21no—
27C32×#95C2211yescharacteristic
28C3×#539C2×C314yes—
29C3×#451C2×C314yescomplemented
30C3×#448C2×C314yes—
31C3×#395C2×C314yescomplemented
32C3×#328C2×C314yescomplemented
33C3×#327C2×C314yes—
34C3×#324C2×C314yescomplemented
35C2×C32×Q8—21no—
36C2×C32×Q8—21no—
37C2×C32×Q8—42no—
38C2×C32×Q8D411yescharacteristic
39C2×C32×D4—21no—
40C2×C32×D4D411yescharacteristic
41C22×C32×C4—21no—
42C22×C32×C4—21no—
43C22×C32×C4—21no—
44C22×C32×C4D411yescharacteristic
45C22×C32×C4D411yescharacteristic
46C22×C32×C4C2311yescharacteristic
47C32×Q16—42no—
48C32×SD16—42no—
49C2×C32×C8—21no—
50C2×C32×C8—21no—
51C32×C4⋊C4—21no—
52C32×C4⋊C4—21no—
53C32×C4⋊C4—21no—
54C32×C4⋊C4—21no—
55C32×C4⋊C4—21no—
56C32×C4⋊C4—21no—
57C32×C4⋊C4—42no—
58C32×C4⋊C4D411yescharacteristic
59C32×C4⋊C4D411yescharacteristic
60C32×C22⋊C4—21no—
61C32×C22⋊C4—21no—
62C32×C22⋊C4—21no—
63C32×C22⋊C4—21no—
64C32×C22⋊C4—21no—
65C32×C42—21no—
66#1603C3211yescharacteristic, direct product factor, Sylow
67C22×C3×Q8C22×C314yes—
68C2×C3×Q16—24no—
69C2×C3×SD16—24no—
70C3×#126—24no—
71C3×#125—24no—
72C3×#123—24no—
73C3×#123—24no—
74C3×C22⋊Q8—24no—
75C3×C22⋊Q8C22×C314yes—
76C3×#121C22×C314yes—
77C3×C4×D4—24no—
78C2×C3×C4⋊C4—24no—
79C2×C3×C4⋊C4C22×C314yes—
80C3×#103—24no—
81C3×#103—24no—
82C3×C22⋊C8C22×C314yes—
83C3×C22⋊C8C22×C314yes—
84C3×#95—24no—
85C3×#95C22×C314yes—
86C23×C32—21no—
87C23×C32C2×D411yescharacteristic
88C32×Q8—22no—
89C32×Q8—22no—
90C32×Q8—41no—
91C32×Q8—41no—
92C32×Q8—41no—
93C32×D4—41no—
94C32×D4—41no—
95C32×D4—41no—
96C2×C32×C4—22no—
97C2×C32×C4—22no—
98C2×C32×C4—21no—
99C2×C32×C4—21no—
100C2×C32×C4—21no—
101C2×C32×C4—21no—
102C2×C32×C4—21no—
103C2×C32×C4—21no—
104C2×C32×C4—21no—
105C2×C32×C4—41no—
106C2×C32×C4—41no—
107C2×C32×C4—41no—
108C2×C32×C4—41no—
109C2×C32×C4—41no—
110C2×C32×C4—41no—
111C2×C32×C4—81no—
112C2×C32×C4C2×D411yescharacteristic
113C2×C32×C4C2×D411yescharacteristic
114C32×C8—41no—
115C32×C8—41no—
116#539C2×C3211yescharacteristic
117#451C2×C3211yescharacteristic, complemented
118#448C2×C3211yescharacteristic
119#395C2×C3211yescharacteristic, complemented
120#328C2×C3211yescharacteristic, complemented
121#327C2×C3211yescharacteristic
122#324C2×C3211yescharacteristic, complemented
123C2×C3×Q8—24no—
124C2×C3×Q8—24no—
125C2×C3×Q8—48no—
126C2×C3×Q8C3×D414yes—
127C2×C3×D4—24no—
128C2×C3×D4C3×D414yes—
129C22×C3×C4—24no—
130C22×C3×C4—24no—
131C22×C3×C4—24no—
132C22×C3×C4C3×D414yes—
133C22×C3×C4C3×D414yes—
134C22×C3×C4C23×C314yes—
135C3×Q16—48no—
136C3×SD16—48no—
137C2×C3×C8—24no—
138C2×C3×C8—24no—
139C3×C4⋊C4—24no—
140C3×C4⋊C4—24no—
141C3×C4⋊C4—24no—
142C3×C4⋊C4—24no—
143C3×C4⋊C4—24no—
144C3×C4⋊C4—24no—
145C3×C4⋊C4—48no—
146C3×C4⋊C4C3×D414yes—
147C3×C4⋊C4C3×D414yes—
148C3×C22⋊C4—24no—
149C3×C22⋊C4—24no—
150C3×C22⋊C4—24no—
151C3×C22⋊C4—24no—
152C3×C22⋊C4—24no—
153C3×C42—24no—
154C22×C32—21no—
155C22×C32—21no—
156C22×C32—41no—
157C22×C32—41no—
158C22×C32—41no—
159C22×C32#12011yescharacteristic
160C22×C32#13511yescharacteristic
161C22×C32#13711yescharacteristic
162C32×C4—21no—
163C32×C4—21no—
164C32×C4—42no—
165C32×C4—41no—
166C32×C4—41no—
167C32×C4—41no—
168C32×C4—42no—
169C32×C4—41no—
170C32×C4—41no—
171C22×Q8C22×C3211yescharacteristic
172C2×Q16—21no—
173C2×SD16—21no—
174#126—21no—
175#125—21no—
176#123—21no—
177#123—21no—
178C22⋊Q8—21no—
179C22⋊Q8C22×C3211yescharacteristic
180#121C22×C3211yescharacteristic
181C4×D4—21no—
182C2×C4⋊C4—21no—
183C2×C4⋊C4C22×C3211yescharacteristic
184#103—21no—
185#103—21no—
186C22⋊C8C22×C3211yescharacteristic
187C22⋊C8C22×C3211yescharacteristic
188#95—21no—
189#95C22×C3211yescharacteristic
190C23×C3—24no—
191C23×C3C2×C3×D414yes—
192C3×Q8—28no—
193C3×Q8—28no—
194C3×Q8—44no—
195C3×Q8—44no—
196C3×Q8—44no—
197C3×D4—44no—
198C3×D4—44no—
199C3×D4—44no—
200C2×C3×C4—28no—
201C2×C3×C4—28no—
202C2×C3×C4—24no—
203C2×C3×C4—24no—
204C2×C3×C4—24no—
205C2×C3×C4—24no—
206C2×C3×C4—24no—
207C2×C3×C4—24no—
208C2×C3×C4—24no—
209C2×C3×C4—44no—
210C2×C3×C4—44no—
211C2×C3×C4—44no—
212C2×C3×C4—44no—
213C2×C3×C4—44no—
214C2×C3×C4—44no—
215C2×C3×C4—84no—
216C2×C3×C4C2×C3×D414yes—
217C2×C3×C4C2×C3×D414yes—
218C3×C8—44no—
219C3×C8—44no—
220C2×C32—21no—
221C2×C32—21no—
222C2×C32—81no—
223C2×C32#45211yescharacteristic
224C2×C32#45611yescharacteristic
225C2×C32B(4,𝔽2)11yescharacteristic
226C2×Q8—21no—
227C2×Q8—21no—
228C2×Q8—42no—
229C2×Q8C32×D411yescharacteristic
230C2×D4—21no—
231C2×D4C32×D411yescharacteristic
232C22×C4—21no—
233C22×C4—21no—
234C22×C4—21no—
235C22×C4C32×D411yescharacteristic
236C22×C4C32×D411yescharacteristic
237C22×C4C23×C3211yescharacteristic
238Q16—42no—
239SD16—42no—
240C2×C8—21no—
241C2×C8—21no—
242C4⋊C4—21no—
243C4⋊C4—21no—
244C4⋊C4—21no—
245C4⋊C4—21no—
246C4⋊C4—21no—
247C4⋊C4—21no—
248C4⋊C4—42no—
249C4⋊C4C32×D411yescharacteristic
250C4⋊C4C32×D411yescharacteristic
251C22⋊C4—21no—
252C22⋊C4—21no—
253C22⋊C4—21no—
254C22⋊C4—21no—
255C22⋊C4—21no—
256C42—21no—
257C22×C3—24no—
258C22×C3—24no—
259C22×C3—44no—
260C22×C3—44no—
261C22×C3—44no—
262C22×C3C3×#12014yes—
263C22×C3C3×#13514yes—
264C22×C3C3×#13714yes—
265C3×C4—24no—
266C3×C4—24no—
267C3×C4—48no—
268C3×C4—44no—
269C3×C4—44no—
270C3×C4—44no—
271C3×C4—48no—
272C3×C4—44no—
273C3×C4—44no—
274C32#160311yescharacteristic, direct product factor, Sylow
275C23—21no—
276C23C2×C32×D411yescharacteristic
277Q8—22no—
278Q8—22no—
279Q8—41no—
280Q8—41no—
281Q8—41no—
282D4—41no—
283D4—41no—
284D4—41no—
285C2×C4—22no—
286C2×C4—22no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—41no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—81no—
301C2×C4C2×C32×D411yescharacteristic
302C2×C4C2×C32×D411yescharacteristic
303C8—41no—
304C8—41no—
305C2×C3—24no—
306C2×C3—24no—
307C2×C3—84no—
308C2×C3C3×#45214yes—
309C2×C3C3×#45614yes—
310C2×C3C3×B(4,𝔽2)14yes—
311C22—21no—
312C22—21no—
313C22—41no—
314C22—41no—
315C22—41no—
316C22C32×#12011yescharacteristic
317C22C32×#13511yescharacteristic
318C22C32×#13711yescharacteristic
319C4—21no—
320C4—21no—
321C4—42no—
322C4—41no—
323C4—41no—
324C4—41no—
325C4—42no—
326C4—41no—
327C4—41no—
328C3C3×#160314yesdirect product factor
329C2—21no—
330C2—21no—
331C2—81no—
332C2C32×#45211yescharacteristic
333C2C32×#45611yescharacteristic
334C2C32×B(4,𝔽2)11yescharacteristic
subgroupG/H
center, socleC22×C32#120
commutator, Frattini, cosocleC22×C4C23×C32
prime radicalC32×#121C22
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C32 ◁ C22×C32×C4 ◁ G

Complements

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

NH ≅ G/Ntype
2. C32×#451C2semidirect
4. C32×#395C2semidirect
5. C32×#328C2semidirect
7. C32×#324C2semidirect
8. C3×#1603C3direct (N × H)
29. C3×#451C2×C3semidirect
31. C3×#395C2×C3semidirect
32. C3×#328C2×C3semidirect
34. C3×#324C2×C3semidirect
66. #1603C32direct (N × H)
117. #451C2×C32semidirect
119. #395C2×C32semidirect
120. #328C2×C32semidirect
122. #324C2×C32semidirect
274. C32#1603direct (N × H)
328. C3C3×#1603direct (N × H)

Maximal subgroups

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

subgroupindex
C32×#5392
C32×#4512
C32×#4482
C32×#3952
C32×#3282
C32×#3272
C32×#3242
C3×#16033