Finite Group Databasebeta

← C3×#73751 #11800904

Subgroups — C3×#73751 #11800904

Order 1152.

1657 conjugacy classes of subgroups.

The subgroup lattice has 442 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#893C212yesmaximal
2C2×C3×C4×D12C211yesmaximal, characteristic
3C32×C4×C4⋊C4C211yesmaximal, characteristic, complemented
4C3×Dic3×C4⋊C4C212yesmaximal, complemented
5C3×C4×(C2×D3)⋊C4C214yesmaximal, complemented
6C3×#4932C211yesmaximal, characteristic, complemented
7C3×#4666C212yesmaximal, complemented
8C3×D3×#95C212yesmaximal, complemented
9C3×#2275—31nomaximal
10#73751C311yesmaximal, characteristic, direct product factor
11C22×C3×D12C2211yescharacteristic
12C22×C3×C4×D3C2214yes—
13C22×C3×C4×D3C2212yes—
14C2×C32×C4⋊C4C2212yes—
15C2×C32×C42C2212yes—
16C2×C32×C42C2211yescharacteristic
17C2×C3×(C2×D3)⋊C4C2214yes—
18C2×C3×(C2×D3)⋊C4C2212yes—
19C2×C3×C4⋊Dic3C2211yescharacteristic
20C2×C3×C4×Dic3C2214yes—
21C2×C3×C4×Dic3C2212yes—
22C3×#893C4116yescomplemented
23C3×C4×D12C418yescomplemented
24C32×#95C2212yes—
25C3×C3⋊#95C2211yescharacteristic
26C3×C3⋊#95C2214yes—
27C3×C3⋊#95C2211yescharacteristic
28C3×C3⋊#95C2212yes—
29C2×C3×C4×D4—32no—
30C2×C3×C4×D4—31no—
31C2×#893C2×C312yes—
32C2×C4×D12C2×C311yescharacteristic
33C3×C4×C4⋊C4—21no—
34C3×C4×C4⋊C4—32no—
35C3×C4×C4⋊C4D311yescharacteristic, complemented
36C3×C4×C4⋊C4C2×C311yescharacteristic, complemented
37C3×C4×C22⋊C4—34no—
38C3×C4×C22⋊C4—32no—
39C3×#376—31no—
40C2×C3×#95—32no—
41Dic3×C4⋊C4C2×C312yescomplemented
42C4×(C2×D3)⋊C4C2×C314yescomplemented
43#4932C2×C311yescharacteristic, complemented
44#4666C2×C312yescomplemented
45D3×#95C2×C312yescomplemented
46C23×C3×D3C2312yes—
47C22×C32×C4C2314yes—
48C22×C32×C4C2311yescharacteristic
49C22×C32×C4C2311yescharacteristic
50C22×C32×C4C2311yescharacteristic
51C22×C3×Dic3C2312yes—
52C22×C3×Dic3C2312yes—
53C22×C3×Dic3C2312yes—
54C2×C3×D12C2×C418yes—
55C2×C3×D12C2×C414yes—
56C2×C3×C4×D3—44no—
57C2×C3×C4×D3—44no—
58C2×C3×C4×D3—44no—
59C2×C3×C4×D3C2×C4116yescomplemented
60C2×C3×C4×D3C2×C418yescomplemented
61C32×C4⋊C4C2×C418yescomplemented
62C32×C42—42no—
63C32×C42C2×C414yescomplemented
64C3×(C2×D3)⋊C4C2×C4116yescomplemented
65C3×(C2×D3)⋊C4C2×C418yescomplemented
66C3×C4⋊Dic3C2×C414yescomplemented
67C3×C4×Dic3—44no—
68C3×C4×Dic3C2×C418yescomplemented
69#2275—31noSylow
70C22×C3×D4—31no—
71C23×C3×C4—34no—
72C23×C3×C4—32no—
73C22×D12C22×C311yescharacteristic
74C22×C4×D3C22×C312yes—
75C22×C4×D3C22×C314yes—
76C3×C4×D4—316no—
77C3×C4×D4—38no—
78C2×C3×C4⋊C4—22no—
79C2×C3×C4⋊C4—31no—
80C2×C3×C4⋊C4C2×D312yes—
81C2×C3×C4⋊C4C22×C312yes—
82C2×C3×C22⋊C4—34no—
83C2×C3×C22⋊C4—32no—
84C2×C3×C42—21no—
85C2×C3×C42—22no—
86C2×C3×C42—32no—
87C2×C3×C42—34no—
88C2×C3×C42C2×D312yes—
89C2×C3×C42C2×D311yescharacteristic
90C2×C3×C42C22×C312yes—
91C2×C3×C42C22×C311yescharacteristic
92C2×(C2×D3)⋊C4C22×C314yes—
93C2×(C2×D3)⋊C4C22×C312yes—
94C2×C4⋊Dic3C22×C311yescharacteristic
95C2×C4×Dic3C22×C314yes—
96C2×C4×Dic3C22×C312yes—
97#893C3×C4116yescomplemented
98C4×D12C3×C418yescomplemented
99C3×#95—22no—
100C3×#95—31no—
101C3×#95—34no—
102C3×#95—32no—
103C3×#95—31no—
104C3×#95C2×D312yes—
105C3×#95C22×C312yes—
106C3⋊#95C22×C311yescharacteristic
107C3⋊#95C22×C314yes—
108C3⋊#95C22×C311yescharacteristic
109C3⋊#95C22×C312yes—
110C23×C32C2411yescharacteristic
111C22×C3×D3—22no—
112C22×C3×D3—24no—
113C22×C3×D3—22no—
114C22×C3×D3C22×C418yes—
115C22×C3×D3C22×C414yes—
116C2×C32×C4—21no—
117C2×C32×C4—21no—
118C2×C32×C4—24no—
119C2×C32×C4—24no—
120C2×C32×C4—22no—
121C2×C32×C4C22×C412yes—
122C2×C32×C4C22×C418yes—
123C2×C32×C4C22×C412yes—
124C2×C32×C4C22×C414yes—
125C2×C32×C4C22×C412yes—
126C2×C3×Dic3—22no—
127C2×C3×Dic3—24no—
128C2×C3×Dic3—22no—
129C2×C3×Dic3—22no—
130C2×C3×Dic3—22no—
131C2×C3×Dic3C22×C414yes—
132C2×C3×Dic3C22×C414yes—
133C2×C3×Dic3C22×C414yes—
134C3×D12C42116yescomplemented
135C3×C4×D3—416no—
136C3×C4×D3—48no—
137C2×C4×D4—32no—
138C2×C4×D4—31no—
139C4×C4⋊C4—32no—
140C4×C4⋊C4C3×D311yescharacteristic, complemented
141C4×C22⋊C4—34no—
142C4×C22⋊C4—32no—
143#376—31no—
144C2×#95—32no—
145C24×C3—32no—
146C23×D3C23×C312yes—
147C2×C3×D4—38no—
148C2×C3×D4—34no—
149C22×C3×C4—21no—
150C22×C3×C4—21no—
151C22×C3×C4—21no—
152C22×C3×C4—24no—
153C22×C3×C4—32no—
154C22×C3×C4—32no—
155C22×C3×C4—32no—
156C22×C3×C4—316no—
157C22×C3×C4—38no—
158C22×C3×C4—124no—
159C22×C3×C4—124no—
160C22×C3×C4—124no—
161C22×C3×C4C22×D311yescharacteristic
162C22×C3×C4C22×D311yescharacteristic
163C22×C3×C4C22×D314yes—
164C22×C3×C4C22×D311yescharacteristic
165C22×C3×C4C23×C311yescharacteristic
166C22×C3×C4C23×C311yescharacteristic
167C22×C3×C4C23×C314yes—
168C22×C3×C4C23×C311yescharacteristic
169C22×Dic3C23×C312yes—
170C22×Dic3C23×C312yes—
171C22×Dic3C23×C312yes—
172C2×D12C2×C3×C414yes—
173C2×D12C2×C3×C418yes—
174C2×C4×D3—44no—
175C2×C4×D3—44no—
176C2×C4×D3—44no—
177C2×C4×D3C2×C3×C418yescomplemented
178C2×C4×D3C2×C3×C4116yescomplemented
179C3×C4⋊C4—28no—
180C3×C4⋊C4—34no—
181C3×C4⋊C4C4×D318yescomplemented
182C3×C4⋊C4C2×C3×C418yescomplemented
183C3×C22⋊C4—316no—
184C3×C22⋊C4—38no—
185C3×C42—24no—
186C3×C42—38no—
187C3×C42—42no—
188C3×C42—42no—
189C3×C42—44no—
190C3×C42—124no—
191C3×C42C4×D314yescomplemented
192C3×C42C2×C3×C414yescomplemented
193(C2×D3)⋊C4C2×C3×C418yescomplemented
194(C2×D3)⋊C4C2×C3×C4116yescomplemented
195C4⋊Dic3C2×C3×C414yescomplemented
196C4×Dic3—44no—
197C4×Dic3C2×C3×C418yescomplemented
198C22×C32C23×C411yescharacteristic
199C22×C32C23×C412yes—
200C22×C32H(5,𝔽2)11yescharacteristic
201C22×C32H(5,𝔽2)12yes—
202C22×C322−1+411yescharacteristic
203C2×C3×D3—24no—
204C2×C3×D3—28no—
205C2×C3×D3—24no—
206C2×C3×D3—28no—
207C2×C3×D3C2×C4218yes—
208C32×C4—22no—
209C32×C4—22no—
210C32×C4—28no—
211C32×C4C2×C4214yes—
212C3×Dic3—24no—
213C3×Dic3—24no—
214C3×Dic3—24no—
215C22×D4—31no—
216C23×C4—34no—
217C23×C4—32no—
218C4×D4—316no—
219C4×D4—38no—
220C2×C4⋊C4—31no—
221C2×C4⋊C4C2×C3×D312yes—
222C2×C22⋊C4—34no—
223C2×C22⋊C4—32no—
224C2×C42—32no—
225C2×C42—34no—
226C2×C42C2×C3×D312yes—
227C2×C42C2×C3×D311yescharacteristic
228#95—31no—
229#95—34no—
230#95—32no—
231#95—31no—
232#95C2×C3×D312yes—
233C23×C3—21no—
234C23×C3—34no—
235C23×C3—38no—
236C23×C3—62no—
237C23×C3—62no—
238C23×C3—64no—
239C23×C3C23×D311yescharacteristic
240C23×C3C24×C311yescharacteristic
241C22×D3—22no—
242C22×D3—24no—
243C22×D3—22no—
244C22×D3C22×C3×C414yes—
245C22×D3C22×C3×C418yes—
246C3×D4—316no—
247C2×C3×C4—22no—
248C2×C3×C4—22no—
249C2×C3×C4—21no—
250C2×C3×C4—24no—
251C2×C3×C4—21no—
252C2×C3×C4—24no—
253C2×C3×C4—22no—
254C2×C3×C4—24no—
255C2×C3×C4—21no—
256C2×C3×C4—24no—
257C2×C3×C4—22no—
258C2×C3×C4—21no—
259C2×C3×C4—22no—
260C2×C3×C4—22no—
261C2×C3×C4—24no—
262C2×C3×C4—22no—
263C2×C3×C4—28no—
264C2×C3×C4—34no—
265C2×C3×C4—34no—
266C2×C3×C4—34no—
267C2×C3×C4—44no—
268C2×C3×C4—44no—
269C2×C3×C4—42no—
270C2×C3×C4—62no—
271C2×C3×C4—62no—
272C2×C3×C4—62no—
273C2×C3×C4—64no—
274C2×C3×C4—62no—
275C2×C3×C4—128no—
276C2×C3×C4—1216no—
277C2×C3×C4C2×C4×D312yes—
278C2×C3×C4C2×C4×D312yes—
279C2×C3×C4C2×C4×D318yes—
280C2×C3×C4C2×C4×D314yes—
281C2×C3×C4C2×C4×D312yes—
282C2×C3×C4C22×C3×C412yes—
283C2×C3×C4C22×C3×C418yes—
284C2×C3×C4C22×C3×C412yes—
285C2×C3×C4C22×C3×C414yes—
286C2×C3×C4C22×C3×C412yes—
287C2×Dic3—22no—
288C2×Dic3—24no—
289C2×Dic3—22no—
290C2×Dic3—22no—
291C2×Dic3—22no—
292C2×Dic3C22×C3×C414yes—
293C2×Dic3C22×C3×C414yes—
294C2×Dic3C22×C3×C414yes—
295D12C3×C42116yescomplemented
296C4×D3—416no—
297C4×D3—48no—
298C2×C32C22×C4211yescharacteristic
299C2×C32#51811yescharacteristic
300C2×C32#51812yes—
301C2×C32#52011yescharacteristic
302C2×C32#52012yes—
303C3×D3—28no—
304C24—32no—
305C2×D4—38no—
306C2×D4—34no—
307C22×C4—32no—
308C22×C4—32no—
309C22×C4—32no—
310C22×C4—316no—
311C22×C4—38no—
312C22×C4—124no—
313C22×C4—124no—
314C22×C4—124no—
315C22×C4C22×C3×D311yescharacteristic
316C22×C4C22×C3×D311yescharacteristic
317C22×C4C22×C3×D314yes—
318C22×C4C22×C3×D311yescharacteristic
319C4⋊C4—34no—
320C4⋊C4C3×C4×D318yescomplemented
321C22⋊C4—316no—
322C22⋊C4—38no—
323C42—38no—
324C42—42no—
325C42—124no—
326C42C3×C4×D314yescomplemented
327C22×C3—21no—
328C22×C3—22no—
329C22×C3—21no—
330C22×C3—21no—
331C22×C3—22no—
332C22×C3—38no—
333C22×C3—64no—
334C22×C3—64no—
335C22×C3—68no—
336C22×C3—68no—
337C22×C3C22×C4×D311yescharacteristic
338C22×C3C22×C4×D312yes—
339C22×C3#100411yescharacteristic
340C22×C3#100711yescharacteristic
341C22×C3#100912yes—
342C22×C3C23×C3×C411yescharacteristic
343C22×C3C23×C3×C412yes—
344C22×C3C3×H(5,𝔽2)11yescharacteristic
345C22×C3C3×H(5,𝔽2)12yes—
346C22×C3C3×2−1+411yescharacteristic
347C2×D3—24no—
348C2×D3—28no—
349C2×D3—24no—
350C2×D3—28no—
351C2×D3C2×C3×C4218yes—
352C3×C4—24no—
353C3×C4—22no—
354C3×C4—22no—
355C3×C4—28no—
356C3×C4—22no—
357C3×C4—28no—
358C3×C4—22no—
359C3×C4—24no—
360C3×C4—42no—
361C3×C4—48no—
362C3×C4—64no—
363C3×C4—64no—
364C3×C4—64no—
365C3×C4C42×D314yes—
366C3×C4C2×C3×C4214yes—
367Dic3—24no—
368Dic3—24no—
369Dic3—24no—
370C32#227511yescharacteristic, complemented, Sylow
371C23—34no—
372C23—38no—
373C23—62no—
374C23—62no—
375C23—64no—
376C23C23×C3×D311yescharacteristic
377D4—316no—
378C2×C4—21no—
379C2×C4—24no—
380C2×C4—21no—
381C2×C4—24no—
382C2×C4—22no—
383C2×C4—34no—
384C2×C4—34no—
385C2×C4—34no—
386C2×C4—62no—
387C2×C4—62no—
388C2×C4—62no—
389C2×C4—64no—
390C2×C4—62no—
391C2×C4—128no—
392C2×C4—1216no—
393C2×C4C2×C3×C4×D312yes—
394C2×C4C2×C3×C4×D312yes—
395C2×C4C2×C3×C4×D318yes—
396C2×C4C2×C3×C4×D314yes—
397C2×C4C2×C3×C4×D312yes—
398C2×C3—21no—
399C2×C3—21no—
400C2×C3—22no—
401C2×C3—22no—
402C2×C3—21no—
403C2×C3—68no—
404C2×C3C2×C42×D311yescharacteristic
405C2×C3#550411yescharacteristic
406C2×C3#552111yescharacteristic
407C2×C3#554512yes—
408C2×C3#557412yes—
409C2×C3C22×C3×C4211yescharacteristic
410C2×C3C3×#51811yescharacteristic
411C2×C3C3×#51812yes—
412C2×C3C3×#52011yescharacteristic
413C2×C3C3×#52012yes—
414D3—28no—
415C22—38no—
416C22—64no—
417C22—64no—
418C22—68no—
419C22—68no—
420C22C22×C3×C4×D311yescharacteristic
421C22C22×C3×C4×D312yes—
422C22C3×#100411yescharacteristic
423C22C3×#100711yescharacteristic
424C22C3×#100912yes—
425C4—22no—
426C4—22no—
427C4—28no—
428C4—64no—
429C4—64no—
430C4—64no—
431C4C3×C42×D314yes—
432C3—21no—
433C3#7375111yescharacteristic, direct product factor
434C3C3×#227511yescharacteristic, complemented
435C2—68no—
436C2C2×C3×C42×D311yescharacteristic
437C2C3×#550411yescharacteristic
438C2C3×#552111yescharacteristic
439C2C3×#554512yes—
440C2C3×#557412yes—
subgroupG/H
centerC23×C3C23×D3
commutatorC2×C3C22×C3×C42
FrattiniC23C23×C3×D3
FittingC32×C4×C4⋊C4C2
socleC23×C32C24
prime radicalC22×C3×D12C22
cosocleC23×C3C24×C3
hypercenterC3×C4×C4⋊C4D3
hypocenterC3C3×#2275
LCSG ▷ C2×C3 ▷ C3
UCSC1 ◁ C23×C3 ◁ C3×C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
3. C32×C4×C4⋊C4C2semidirect
4. C3×Dic3×C4⋊C4C2semidirect
5. C3×C4×(C2×D3)⋊C4C2semidirect
6. C3×#4932C2semidirect
7. C3×#4666C2semidirect
8. C3×D3×#95C2semidirect
10. #73751C3direct (N × H)
22. C3×#893C4semidirect
23. C3×C4×D12C4semidirect
35. C3×C4×C4⋊C4D3semidirect
36. C3×C4×C4⋊C4C2×C3semidirect
41. Dic3×C4⋊C4C2×C3semidirect
42. C4×(C2×D3)⋊C4C2×C3semidirect
43. #4932C2×C3semidirect
44. #4666C2×C3semidirect
45. D3×#95C2×C3semidirect
59. C2×C3×C4×D3C2×C4semidirect
60. C2×C3×C4×D3C2×C4semidirect
61. C32×C4⋊C4C2×C4semidirect
63. C32×C42C2×C4semidirect
64. C3×(C2×D3)⋊C4C2×C4semidirect
65. C3×(C2×D3)⋊C4C2×C4semidirect
66. C3×C4⋊Dic3C2×C4semidirect
68. C3×C4×Dic3C2×C4semidirect
97. #893C3×C4semidirect
98. C4×D12C3×C4semidirect
134. C3×D12C42semidirect
140. C4×C4⋊C4C3×D3semidirect
177. C2×C4×D3C2×C3×C4semidirect
178. C2×C4×D3C2×C3×C4semidirect
181. C3×C4⋊C4C4×D3semidirect
182. C3×C4⋊C4C2×C3×C4semidirect
191. C3×C42C4×D3semidirect
192. C3×C42C2×C3×C4semidirect
193. (C2×D3)⋊C4C2×C3×C4semidirect
194. (C2×D3)⋊C4C2×C3×C4semidirect
195. C4⋊Dic3C2×C3×C4semidirect
197. C4×Dic3C2×C3×C4semidirect
295. D12C3×C42semidirect
320. C4⋊C4C3×C4×D3semidirect
326. C42C3×C4×D3semidirect
370. C32#2275semidirect
433. C3#73751direct (N × H)
434. C3C3×#2275semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#8932
C2×C3×C4×D122
C32×C4×C4⋊C42
C3×Dic3×C4⋊C42
C3×C4×(C2×D3)⋊C42
C3×#49322
C3×#46662
C3×D3×#952
C3×#22753
#737513