Finite Group Databasebeta

← C3×#73861 #11856162

Subgroups — C3×#73861 #11856162

Order 1152.

7097 conjugacy classes of subgroups; only the 490 normal subgroups are shown.

normal subgroups only

This group has 7097 conjugacy classes of subgroups — too many to draw. Only its 490 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
1C25×C3×D3C211yesmaximal, characteristic, complemented
2C2×C3×#953C211yesmaximal, characteristic, complemented
3C2×C3×#882C216yesmaximal, complemented
4C32×#379C211yesmaximal, characteristic, complemented
5C3×#4955C216yesmaximal, complemented
6C3×#2846—31nomaximal
7#73861C311yesmaximal, characteristic, direct product factor
8C25×C32C2211yescharacteristic
9C24×C3×D3—24no—
10C24×C3×D3—224no—
11C24×C3×D3C2216yes—
12C22×C3×#67C2213yescomplemented
13C22×C3×D12C2214yescomplemented
14C2×C32×C22⋊C4C2216yescomplemented
15C3×#953—24no—
16C2×C3×#217C2213yescomplemented
17C2×C3×(C2×D3)⋊C4C22112yescomplemented
18C3×#882—224no—
19C26×C3—31no—
20C25×D3C2×C311yescharacteristic, complemented
21C2×C3×#120—36no—
22C2×C3×#120—31no—
23C2×#953C2×C311yescharacteristic, complemented
24C2×#882C2×C316yescomplemented
25C3×#379—21no—
26C3×#379—36no—
27C3×#379D311yescharacteristic, complemented
28C3×#379C2×C311yescharacteristic, complemented
29#4955C2×C316yescomplemented
30C24×C32—212no—
31C24×C32D414yescomplemented
32C24×C32C2313yes—
33C23×C3×D3—296no—
34C23×C3×D3—2128no—
35C23×C3×D3—212no—
36C23×C3×D3—212no—
37C23×C3×D3—248no—
38C23×C3×D3D4124yescomplemented
39C23×C3×D3C2314yes—
40C23×C3×D3C2311yescharacteristic, complemented
41C22×C32×C4C2314yescomplemented
42C2×C3×#67—212no—
43C2×C3×#67—26no—
44C22×C3×Dic3C2313yescomplemented
45C2×C3×D12—224no—
46C32×C22⋊C4—212no—
47C3×#217—26no—
48C3×(C2×D3)⋊C4—224no—
49#2846—31noSylow
50C25×C3—21no—
51C25×C3—36no—
52C25×C3—624no—
53C25×C3—64no—
54C25×C3C2×D311yescharacteristic
55C25×C3C22×C311yescharacteristic
56C24×D3—24no—
57C24×D3—224no—
58C24×D3C22×C316yes—
59C22×C3×D4—33no—
60C22×C3×D4—34no—
61C22×#67C22×C313yescomplemented
62C22×D12C22×C314yescomplemented
63C3×#120—624no—
64C3×#120—64no—
65C2×C3×C22⋊C4—26no—
66C2×C3×C22⋊C4—33no—
67C2×C3×C22⋊C4—312no—
68C2×C3×C22⋊C4C2×D316yescomplemented
69C2×C3×C22⋊C4C22×C316yescomplemented
70#953—24no—
71C2×#217C22×C313yescomplemented
72C2×(C2×D3)⋊C4C22×C3112yescomplemented
73#882—224no—
74C23×C32—232no—
75C23×C32—224no—
76C23×C32—212no—
77C23×C32C2×D416yes—
78C23×C32C2×D4112yes—
79C23×C32C2411yescharacteristic
80C22×C3×D3—2256no—
81C22×C3×D3—296no—
82C22×C3×D3—296no—
83C22×C3×D3—248no—
84C22×C3×D3—24no—
85C22×C3×D3—212no—
86C22×C3×D3—296no—
87C22×C3×D3—26no—
88C22×C3×D3—21no—
89C22×C3×D3C2×D4124yes—
90C2×C32×C4—212no—
91C3×#67—412no—
92C2×C3×Dic3—26no—
93C2×C3×Dic3—23no—
94C3×D12—416no—
95C26—31no—
96C2×#120—31no—
97C2×#120—36no—
98#379—36no—
99#379C3×D311yescharacteristic, complemented
100C24×C3—212no—
101C24×C3—212no—
102C24×C3—24no—
103C24×C3—23no—
104C24×C3—34no—
105C24×C3—324no—
106C24×C3—31no—
107C24×C3—412no—
108C24×C3—648no—
109C24×C3—6128no—
110C24×C3—696no—
111C24×C3—612no—
112C24×C3—612no—
113C24×C3D1214yescomplemented
114C24×C3C3×D414yescomplemented
115C24×C3C22×D313yes—
116C24×C3C23×C313yes—
117C23×D3—296no—
118C23×D3—2128no—
119C23×D3—212no—
120C23×D3—212no—
121C23×D3—248no—
122C23×D3C3×D4124yescomplemented
123C23×D3C23×C314yes—
124C23×D3C23×C311yescharacteristic, complemented
125C2×C3×D4—624no—
126C2×C3×D4—66no—
127C2×C3×D4—612no—
128C22×C3×C4—24no—
129C22×C3×C4—33no—
130C22×C3×C4C22×D314yescomplemented
131C22×C3×C4C23×C314yescomplemented
132C2×#67—212no—
133C2×#67—26no—
134C22×Dic3C23×C313yescomplemented
135C2×D12—224no—
136C3×C22⋊C4—212no—
137C3×C22⋊C4—212no—
138C3×C22⋊C4—412no—
139C3×C22⋊C4—624no—
140C3×C22⋊C4—66no—
141#217—26no—
142(C2×D3)⋊C4—224no—
143C22×C32—232no—
144C22×C32—212no—
145C22×C32—224no—
146C22×C32#120112yescomplemented
147C22×C32C22×D411yescharacteristic
148C22×C32C22×D416yes—
149C2×C3×D3—2192no—
150C2×C3×D3—224no—
151C2×C3×D3—224no—
152C2×C3×D3—44no—
153C2×C3×D3—43no—
154C2×C3×D3#120116yescomplemented
155C32×C4—44no—
156C3×Dic3—43no—
157C25—36no—
158C25—624no—
159C25—64no—
160C25C2×C3×D311yescharacteristic
161C22×D4—33no—
162C22×D4—34no—
163#120—624no—
164#120—64no—
165C2×C22⋊C4—33no—
166C2×C22⋊C4—312no—
167C2×C22⋊C4C2×C3×D316yescomplemented
168C23×C3—232no—
169C23×C3—232no—
170C23×C3—224no—
171C23×C3—224no—
172C23×C3—212no—
173C23×C3—212no—
174C23×C3—21no—
175C23×C3—26no—
176C23×C3—212no—
177C23×C3—324no—
178C23×C3—424no—
179C23×C3—412no—
180C23×C3—432no—
181C23×C3—696no—
182C23×C3—6256no—
183C23×C3—696no—
184C23×C3—696no—
185C23×C3—648no—
186C23×C3—64no—
187C23×C3—612no—
188C23×C3—61no—
189C23×C3—66no—
190C23×C3C2×D1216yes—
191C23×C3D3×D4112yes—
192C23×C3C2×C3×D416yes—
193C23×C3C2×C3×D4112yes—
194C23×C3C23×D311yescharacteristic
195C23×C3C24×C311yescharacteristic
196C22×D3—2256no—
197C22×D3—296no—
198C22×D3—296no—
199C22×D3—248no—
200C22×D3—24no—
201C22×D3—212no—
202C22×D3—296no—
203C22×D3—26no—
204C22×D3—21no—
205C22×D3C2×C3×D4124yes—
206C3×D4—1216no—
207C3×D4—1212no—
208C2×C3×C4—212no—
209C2×C3×C4—212no—
210C2×C3×C4—412no—
211C2×C3×C4—63no—
212C2×C3×C4—66no—
213#67—412no—
214C2×Dic3—26no—
215C2×Dic3—23no—
216D12—416no—
217C2×C32—212no—
218C2×C32C2×#12013yes—
219C2×C32C2×#12014yes—
220C3×D3—216no—
221C3×D3—81no—
222C24—212no—
223C24—34no—
224C24—324no—
225C24—31no—
226C24—648no—
227C24—6128no—
228C24—696no—
229C24—612no—
230C24—612no—
231C24C3×D1214yescomplemented
232C24C22×C3×D313yes—
233C2×D4—624no—
234C2×D4—66no—
235C2×D4—612no—
236C22×C4—33no—
237C22×C4C22×C3×D314yescomplemented
238C22⋊C4—212no—
239C22⋊C4—624no—
240C22⋊C4—66no—
241C22×C3—232no—
242C22×C3—232no—
243C22×C3—212no—
244C22×C3—224no—
245C22×C3—212no—
246C22×C3—224no—
247C22×C3—212no—
248C22×C3—21no—
249C22×C3—26no—
250C22×C3—316no—
251C22×C3—412no—
252C22×C3—424no—
253C22×C3—432no—
254C22×C3—6192no—
255C22×C3—624no—
256C22×C3—624no—
257C22×C3—123no—
258C22×C3—124no—
259C22×C3#882112yescomplemented
260C22×C3C3×#120112yescomplemented
261C22×C3C22×D1211yescharacteristic
262C22×C3C2×D3×D416yes—
263C22×C3C22×C3×D411yescharacteristic
264C22×C3C22×C3×D416yes—
265C2×D3—2192no—
266C2×D3—224no—
267C2×D3—224no—
268C2×D3—44no—
269C2×D3—43no—
270C2×D3C3×#120116yescomplemented
271C3×C4—44no—
272C3×C4—44no—
273C3×C4—84no—
274C3×C4—123no—
275Dic3—43no—
276C32#284611yescharacteristic, complemented, Sylow
277C23—232no—
278C23—224no—
279C23—212no—
280C23—324no—
281C23—696no—
282C23—6256no—
283C23—696no—
284C23—696no—
285C23—648no—
286C23—64no—
287C23—612no—
288C23—61no—
289C23—66no—
290C23C2×C3×D1216yes—
291C23C3×D3×D4112yes—
292C23C23×C3×D311yescharacteristic
293D4—1216no—
294D4—1212no—
295C2×C4—212no—
296C2×C4—63no—
297C2×C4—66no—
298C2×C3—212no—
299C2×C3—212no—
300C2×C3—23no—
301C2×C3—24no—
302C2×C3—412no—
303C2×C3—616no—
304C2×C3—241no—
305C2×C3C2×#88213yes—
306C2×C3D3×#12014yes—
307C2×C3C2×C3×#12013yes—
308C2×C3C2×C3×#12014yes—
309D3—216no—
310D3—81no—
311C22—232no—
312C22—212no—
313C22—224no—
314C22—316no—
315C22—6192no—
316C22—624no—
317C22—624no—
318C22—123no—
319C22—124no—
320C22C3×#882112yescomplemented
321C22C22×C3×D1211yescharacteristic
322C22C2×C3×D3×D416yes—
323C4—44no—
324C4—123no—
325C3—21no—
326C3#7386111yescharacteristic, direct product factor
327C3C3×#284611yescharacteristic, complemented
328C2—212no—
329C2—616no—
330C2—241no—
331C2C2×C3×#88213yes—
332C2C3×D3×#12014yes—
subgroupG/H
centerC23×C3C23×D3
commutator, cosocleC23×C3C24×C3
FrattiniC23C23×C3×D3
FittingC32×#379C2
socleC23×C32C24
hypercenterC3×#379D3
hypocenterC3C3×#2846
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23×C3 ◁ C3×#379

Complements

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

NH ≅ G/Ntype
1. C25×C3×D3C2semidirect
2. C2×C3×#953C2semidirect
3. C2×C3×#882C2semidirect
4. C32×#379C2semidirect
5. C3×#4955C2semidirect
7. #73861C3direct (N × H)
12. C22×C3×#67C22semidirect
13. C22×C3×D12C22semidirect
14. C2×C32×C22⋊C4C22semidirect
16. C2×C3×#217C22semidirect
17. C2×C3×(C2×D3)⋊C4C22semidirect
20. C25×D3C2×C3semidirect
23. C2×#953C2×C3semidirect
24. C2×#882C2×C3semidirect
27. C3×#379D3semidirect
28. C3×#379C2×C3semidirect
29. #4955C2×C3semidirect
31. C24×C32D4semidirect
38. C23×C3×D3D4semidirect
40. C23×C3×D3C23semidirect
41. C22×C32×C4C23semidirect
44. C22×C3×Dic3C23semidirect
61. C22×#67C22×C3semidirect
62. C22×D12C22×C3semidirect
68. C2×C3×C22⋊C4C2×D3semidirect
69. C2×C3×C22⋊C4C22×C3semidirect
71. C2×#217C22×C3semidirect
72. C2×(C2×D3)⋊C4C22×C3semidirect
99. #379C3×D3semidirect
113. C24×C3D12semidirect
114. C24×C3C3×D4semidirect
122. C23×D3C3×D4semidirect
124. C23×D3C23×C3semidirect
130. C22×C3×C4C22×D3semidirect
131. C22×C3×C4C23×C3semidirect
134. C22×Dic3C23×C3semidirect
146. C22×C32#120semidirect
154. C2×C3×D3#120semidirect
167. C2×C22⋊C4C2×C3×D3semidirect
231. C24C3×D12semidirect
237. C22×C4C22×C3×D3semidirect
259. C22×C3#882semidirect
260. C22×C3C3×#120semidirect
270. C2×D3C3×#120semidirect
276. C32#2846semidirect
320. C22C3×#882semidirect
326. C3#73861direct (N × H)
327. C3C3×#2846semidirect

Maximal subgroups

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

subgroupindex
C25×C3×D32
C2×C3×#9532
C2×C3×#8822
C32×#3792
C3×#49552
C3×#28463
#738613