Finite Group Databasebeta

← C3×#73818 #11801970

Subgroups — C3×#73818 #11801970

Order 1152.

2701 conjugacy classes of subgroups.

The subgroup lattice has 424 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C24×C3×Dic3C211yesmaximal, characteristic, complemented
2C2×C3×#953C211yesmaximal, characteristic
3C2×C3×#67⋊C4C213yesmaximal, complemented
4C32×#379C211yesmaximal, characteristic, complemented
5C3×#4958C213yesmaximal, complemented
6C3×#4946C213yesmaximal, complemented
7C3×Dic3×C22⋊C4C213yesmaximal, complemented
8C3×C4×#120—31nomaximal
9#73818C311yesmaximal, characteristic, direct product factor
10C25×C32C2211yescharacteristic
11C22×C3×#67C2213yes—
12C23×C3×Dic3—212no—
13C23×C3×Dic3C2213yes—
14C23×C3×Dic3C2213yes—
15C22×C3×C4×D3C2211yescharacteristic, complemented
16C2×C32×C22⋊C4C2213yes—
17C2×C32×C22⋊C4C2213yes—
18C3×#953C418yescomplemented
19C2×C3×#217C2213yes—
20C2×C3×(C2×D3)⋊C4C2213yescomplemented
21C2×C3×Dic3⋊C4C2213yescomplemented
22C2×C3×C4×Dic3C2213yescomplemented
23C3×#67⋊C4—212no—
24C3×C3⋊#95C2216yescomplemented
25C24×C3×C4—31no—
26C24×Dic3C2×C311yescharacteristic, complemented
27C2×C3×#120—31no—
28C2×C3×C4×D4—33no—
29C2×#953C2×C311yescharacteristic
30C2×#67⋊C4C2×C313yescomplemented
31C3×#386—33no—
32C3×#385—33no—
33C3×#379—21no—
34C3×#379D311yescharacteristic, complemented
35C3×#379C2×C311yescharacteristic, complemented
36C3×C4×C22⋊C4—33no—
37#4958C2×C313yescomplemented
38#4946C2×C313yescomplemented
39Dic3×C22⋊C4C2×C313yescomplemented
40C24×C32—26no—
41C24×C32—26no—
42C24×C32C2×C414yescomplemented
43C24×C32C2313yes—
44C23×C3×D3C2311yescharacteristic
45C22×C32×C4C2313yes—
46C22×C32×C4C2311yescharacteristic
47C2×C3×#67—26no—
48C2×C3×#67—26no—
49C2×C3×#67C2×C4112yescomplemented
50C22×C3×Dic3—232no—
51C22×C3×Dic3—26no—
52C22×C3×Dic3—212no—
53C22×C3×Dic3—212no—
54C22×C3×Dic3D4112yescomplemented
55C22×C3×Dic3C2313yes—
56C22×C3×Dic3C2313yes—
57C22×C3×Dic3C2311yescharacteristic
58C2×C3×C4×D3—26no—
59C32×C22⋊C4—26no—
60C32×C22⋊C4—26no—
61C3×#217C2×C4112yescomplemented
62C3×(C2×D3)⋊C4—26no—
63C3×Dic3⋊C4—26no—
64C3×C4×Dic3—26no—
65C4×#120—31noSylow
66C25×C3—21no—
67C25×C3C2×D311yescharacteristic
68C25×C3C22×C311yescharacteristic
69C22×C3×D4—33no—
70C23×C3×C4—33no—
71C23×C3×C4—33no—
72C23×C3×C4—31no—
73C23×C3×C4—612no—
74C22×#67C22×C313yes—
75C23×Dic3—212no—
76C23×Dic3C22×C313yes—
77C23×Dic3C22×C313yes—
78C22×C4×D3C22×C311yescharacteristic, complemented
79C3×#120—38no—
80C3×C4×D4—612no—
81C2×C3×C4⋊C4—33no—
82C2×C3×C22⋊C4—23no—
83C2×C3×C22⋊C4—23no—
84C2×C3×C22⋊C4—33no—
85C2×C3×C22⋊C4—33no—
86C2×C3×C22⋊C4C2×D313yes—
87C2×C3×C22⋊C4C2×D313yes—
88C2×C3×C22⋊C4C22×C313yes—
89C2×C3×C22⋊C4C22×C313yes—
90C2×C3×C42—33no—
91#953C3×C418yescomplemented
92C2×#217C22×C313yes—
93C2×(C2×D3)⋊C4C22×C313yescomplemented
94C2×Dic3⋊C4C22×C313yescomplemented
95C2×C4×Dic3C22×C313yescomplemented
96#67⋊C4—212no—
97C3×#95—36no—
98C3⋊#95C22×C316yescomplemented
99C23×C32—224no—
100C23×C32—28no—
101C23×C32—224no—
102C23×C32—26no—
103C23×C32—26no—
104C23×C32C22×C416yes—
105C23×C32C2×D416yes—
106C23×C32#4116yes—
107C23×C32C2411yescharacteristic
108C22×C3×D3—23no—
109C22×C3×D3—23no—
110C22×C3×D3C22×C412yescomplemented
111C2×C32×C4—23no—
112C2×C32×C4—23no—
113C2×C32×C4—26no—
114C3×#67—224no—
115C2×C3×Dic3—224no—
116C2×C3×Dic3—23no—
117C2×C3×Dic3—26no—
118C2×C3×Dic3—23no—
119C2×C3×Dic3—224no—
120C2×C3×Dic3C22×C416yescomplemented
121C2×C3×Dic3C2×D416yes—
122C2×C3×Dic3C2×D416yes—
123C3×C4×D3—44no—
124C24×C4—31no—
125C2×#120—31no—
126C2×C4×D4—33no—
127#386—33no—
128#385—33no—
129#379C3×D311yescharacteristic, complemented
130C4×C22⋊C4—33no—
131C24×C3—26no—
132C24×C3—26no—
133C24×C3—26no—
134C24×C3—26no—
135C24×C3—24no—
136C24×C3—23no—
137C24×C3—31no—
138C24×C3—46no—
139C24×C3—46no—
140C24×C3C4×D314yescomplemented
141C24×C3C2×C3×C414yescomplemented
142C24×C3C22×D313yes—
143C24×C3C23×C313yes—
144C23×D3C23×C311yescharacteristic
145C2×C3×D4—312no—
146C2×C3×D4—66no—
147C2×C3×D4—66no—
148C22×C3×C4—23no—
149C22×C3×C4—21no—
150C22×C3×C4—31no—
151C22×C3×C4—312no—
152C22×C3×C4—33no—
153C22×C3×C4—33no—
154C22×C3×C4—66no—
155C22×C3×C4—612no—
156C22×C3×C4—612no—
157C22×C3×C4—632no—
158C22×C3×C4—66no—
159C22×C3×C4C22×D313yes—
160C22×C3×C4C22×D311yescharacteristic
161C22×C3×C4C23×C313yes—
162C22×C3×C4C23×C311yescharacteristic
163C2×#67—26no—
164C2×#67—26no—
165C2×#67C2×C3×C4112yescomplemented
166C22×Dic3—232no—
167C22×Dic3—26no—
168C22×Dic3—212no—
169C22×Dic3—212no—
170C22×Dic3C3×D4112yescomplemented
171C22×Dic3C23×C313yes—
172C22×Dic3C23×C313yes—
173C22×Dic3C23×C311yescharacteristic
174C2×C4×D3—26no—
175C3×C4⋊C4—66no—
176C3×C22⋊C4—26no—
177C3×C22⋊C4—26no—
178C3×C22⋊C4—26no—
179C3×C22⋊C4—26no—
180C3×C22⋊C4—312no—
181C3×C22⋊C4—46no—
182C3×C22⋊C4—46no—
183C3×C22⋊C4—66no—
184C3×C42—66no—
185#217C2×C3×C4112yescomplemented
186(C2×D3)⋊C4—26no—
187Dic3⋊C4—26no—
188C4×Dic3—26no—
189C22×C32—232no—
190C22×C32—212no—
191C22×C32—26no—
192C22×C32—26no—
193C22×C32—212no—
194C22×C32C4×D4112yescomplemented
195C22×C32C23×C411yescharacteristic
196C22×C32C22×D413yes—
197C22×C32C2×#4113yes—
198C2×C3×D3—26no—
199C2×C3×D3—41no—
200C2×C3×D3—43no—
201C32×C4—41no—
202C32×C4—43no—
203C3×Dic3—26no—
204C3×Dic3—26no—
205C3×Dic3#12014yescomplemented
206C25C2×C3×D311yescharacteristic
207C22×D4—33no—
208C23×C4—33no—
209C23×C4—33no—
210C23×C4—31no—
211C23×C4—612no—
212#120—38no—
213C4×D4—612no—
214C2×C4⋊C4—33no—
215C2×C22⋊C4—33no—
216C2×C22⋊C4—33no—
217C2×C22⋊C4C2×C3×D313yes—
218C2×C22⋊C4C2×C3×D313yes—
219C2×C42—33no—
220#95—36no—
221C23×C3—28no—
222C23×C3—28no—
223C23×C3—224no—
224C23×C3—224no—
225C23×C3—224no—
226C23×C3—224no—
227C23×C3—26no—
228C23×C3—26no—
229C23×C3—26no—
230C23×C3—26no—
231C23×C3—21no—
232C23×C3—26no—
233C23×C3—26no—
234C23×C3—26no—
235C23×C3—32no—
236C23×C3—424no—
237C23×C3—46no—
238C23×C3—46no—
239C23×C3—48no—
240C23×C3—424no—
241C23×C3—63no—
242C23×C3—63no—
243C23×C3C2×C4×D316yes—
244C23×C3D3×D416yes—
245C23×C3#23716yes—
246C23×C3C22×C3×C416yes—
247C23×C3C2×C3×D416yes—
248C23×C3C3×#4116yes—
249C23×C3C23×D311yescharacteristic
250C23×C3C24×C311yescharacteristic
251C22×D3—23no—
252C22×D3—23no—
253C22×D3C22×C3×C412yescomplemented
254C3×D4—624no—
255C2×C3×C4—23no—
256C2×C3×C4—23no—
257C2×C3×C4—26no—
258C2×C3×C4—23no—
259C2×C3×C4—23no—
260C2×C3×C4—26no—
261C2×C3×C4—36no—
262C2×C3×C4—36no—
263C2×C3×C4—36no—
264C2×C3×C4—43no—
265C2×C3×C4—43no—
266C2×C3×C4—46no—
267C2×C3×C4—624no—
268C2×C3×C4—624no—
269C2×C3×C4—63no—
270C2×C3×C4—66no—
271C2×C3×C4—63no—
272C2×C3×C4—124no—
273#67—224no—
274C2×Dic3—224no—
275C2×Dic3—23no—
276C2×Dic3—26no—
277C2×Dic3—23no—
278C2×Dic3—224no—
279C2×Dic3C22×C3×C416yescomplemented
280C2×Dic3C2×C3×D416yes—
281C2×Dic3C2×C3×D416yes—
282C4×D3—44no—
283C2×C32—212no—
284C2×C32C2×C4×D413yes—
285C2×C32C2×#12011yescharacteristic
286C2×C32#52513yes—
287C3×D3—42no—
288C24—26no—
289C24—26no—
290C24—31no—
291C24C3×C4×D314yescomplemented
292C24C22×C3×D313yes—
293C2×D4—312no—
294C2×D4—66no—
295C2×D4—66no—
296C22×C4—31no—
297C22×C4—33no—
298C22×C4—33no—
299C22×C4—312no—
300C22×C4—66no—
301C22×C4—612no—
302C22×C4—612no—
303C22×C4—632no—
304C22×C4—66no—
305C22×C4C22×C3×D313yes—
306C22×C4C22×C3×D311yescharacteristic
307C4⋊C4—66no—
308C22⋊C4—26no—
309C22⋊C4—26no—
310C22⋊C4—312no—
311C22⋊C4—66no—
312C42—66no—
313C22×C3—232no—
314C22×C3—232no—
315C22×C3—212no—
316C22×C3—26no—
317C22×C3—212no—
318C22×C3—26no—
319C22×C3—212no—
320C22×C3—26no—
321C22×C3—26no—
322C22×C3—212no—
323C22×C3—212no—
324C22×C3—21no—
325C22×C3—23no—
326C22×C3—23no—
327C22×C3—46no—
328C22×C3—412no—
329C22×C3—46no—
330C22×C3—412no—
331C22×C3—432no—
332C22×C3—66no—
333C22×C3—123no—
334C22×C3—121no—
335C22×C3#67⋊C4112yescomplemented
336C22×C3C3×C4×D4112yescomplemented
337C22×C3C22×C4×D311yescharacteristic
338C22×C3C2×D3×D413yes—
339C22×C3C2×#23713yes—
340C22×C3C23×C3×C411yescharacteristic
341C22×C3C22×C3×D413yes—
342C22×C3C2×C3×#4113yes—
343C2×D3—26no—
344C2×D3—41no—
345C2×D3—43no—
346C3×C4—34no—
347C3×C4—43no—
348C3×C4—41no—
349C3×C4—41no—
350C3×C4—43no—
351C3×C4—66no—
352C3×C4—66no—
353C3×C4—83no—
354C3×C4—81no—
355Dic3—26no—
356Dic3—26no—
357Dic3C3×#12014yescomplemented
358C32C4×#12011yescharacteristic, complemented, Sylow
359C23—28no—
360C23—224no—
361C23—224no—
362C23—26no—
363C23—26no—
364C23—32no—
365C23—63no—
366C23—63no—
367C23C2×C3×C4×D316yes—
368C23C3×D3×D416yes—
369C23C3×#23716yes—
370C23C23×C3×D311yescharacteristic
371D4—624no—
372C2×C4—23no—
373C2×C4—23no—
374C2×C4—26no—
375C2×C4—36no—
376C2×C4—36no—
377C2×C4—36no—
378C2×C4—624no—
379C2×C4—624no—
380C2×C4—63no—
381C2×C4—66no—
382C2×C4—63no—
383C2×C4—124no—
384C2×C3—212no—
385C2×C3—212no—
386C2×C3—23no—
387C2×C3—21no—
388C2×C3—23no—
389C2×C3—412no—
390C2×C3—122no—
391C2×C3C2×#67⋊C413yes—
392C2×C3#558613yes—
393C2×C3D3×#12011yescharacteristic
394C2×C3C2×C3×C4×D413yes—
395C2×C3C2×C3×#12011yescharacteristic
396C2×C3C3×#52513yes—
397D3—42no—
398C22—232no—
399C22—26no—
400C22—212no—
401C22—26no—
402C22—212no—
403C22—66no—
404C22—123no—
405C22—121no—
406C22C3×#67⋊C4112yescomplemented
407C22C22×C3×C4×D311yescharacteristic
408C22C2×C3×D3×D413yes—
409C22C2×C3×#23713yes—
410C4—34no—
411C4—43no—
412C4—41no—
413C4—66no—
414C4—66no—
415C3—21no—
416C3#7381811yescharacteristic, direct product factor
417C3C3×C4×#12011yescharacteristic, complemented
418C2—212no—
419C2—122no—
420C2C2×C3×#67⋊C413yes—
421C2C3×#558613yes—
422C2C3×D3×#12011yescharacteristic
subgroupG/H
centerC23×C3C23×D3
commutatorC22×C3C23×C3×C4
FrattiniC23C23×C3×D3
FittingC32×#379C2
socleC23×C32C24
prime radicalC2×C3×#953C2
cosocleC23×C3C24×C3
hypercenterC3×#379D3
hypocenterC3C3×C4×#120
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C23×C3 ◁ C3×#379

Complements

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

NH ≅ G/Ntype
1. C24×C3×Dic3C2semidirect
3. C2×C3×#67⋊C4C2semidirect
4. C32×#379C2semidirect
5. C3×#4958C2semidirect
6. C3×#4946C2semidirect
7. C3×Dic3×C22⋊C4C2semidirect
9. #73818C3direct (N × H)
15. C22×C3×C4×D3C22semidirect
18. C3×#953C4semidirect
20. C2×C3×(C2×D3)⋊C4C22semidirect
21. C2×C3×Dic3⋊C4C22semidirect
22. C2×C3×C4×Dic3C22semidirect
24. C3×C3⋊#95C22semidirect
26. C24×Dic3C2×C3semidirect
30. C2×#67⋊C4C2×C3semidirect
34. C3×#379D3semidirect
35. C3×#379C2×C3semidirect
37. #4958C2×C3semidirect
38. #4946C2×C3semidirect
39. Dic3×C22⋊C4C2×C3semidirect
42. C24×C32C2×C4semidirect
49. C2×C3×#67C2×C4semidirect
54. C22×C3×Dic3D4semidirect
61. C3×#217C2×C4semidirect
78. C22×C4×D3C22×C3semidirect
91. #953C3×C4semidirect
93. C2×(C2×D3)⋊C4C22×C3semidirect
94. C2×Dic3⋊C4C22×C3semidirect
95. C2×C4×Dic3C22×C3semidirect
98. C3⋊#95C22×C3semidirect
110. C22×C3×D3C22×C4semidirect
120. C2×C3×Dic3C22×C4semidirect
129. #379C3×D3semidirect
140. C24×C3C4×D3semidirect
141. C24×C3C2×C3×C4semidirect
165. C2×#67C2×C3×C4semidirect
170. C22×Dic3C3×D4semidirect
185. #217C2×C3×C4semidirect
194. C22×C32C4×D4semidirect
205. C3×Dic3#120semidirect
253. C22×D3C22×C3×C4semidirect
279. C2×Dic3C22×C3×C4semidirect
291. C24C3×C4×D3semidirect
335. C22×C3#67⋊C4semidirect
336. C22×C3C3×C4×D4semidirect
357. Dic3C3×#120semidirect
358. C32C4×#120semidirect
406. C22C3×#67⋊C4semidirect
416. C3#73818direct (N × H)
417. C3C3×C4×#120semidirect

Maximal subgroups

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

subgroupindex
C24×C3×Dic32
C2×C3×#9532
C2×C3×#67⋊C42
C32×#3792
C3×#49582
C3×#49462
C3×Dic3×C22⋊C42
C3×C4×#1203
#738183