Finite Group Databasebeta

← C3×#71591 #11788199

Subgroups — C3×#71591 #11788199

Order 1152.

881 conjugacy classes of subgroups.

The subgroup lattice has 449 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C32×#117C211yesmaximal, characteristic, complemented
2C3×#5791C211yesmaximal, characteristic
3C3×#5207C211yesmaximal, characteristic, complemented
4C2×C3×#805C212yesmaximal, complemented
5C3×#4523C212yesmaximal, complemented
6C3×#1897—31nomaximal
7#71591C311yesmaximal, characteristic, direct product factor
8C23×C32×C4C2211yescharacteristic
9C2×C3×#235C2211yescharacteristic
10C32×#117—24no—
11C2×C32×C4⋊C4—21no—
12C2×C32×C22⋊C4—21no—
13C2×C32×C42C2212yes—
14C3×#953—21no—
15C3×#930C412yescomplemented
16C3×#929—21no—
17C3×C4×#67—22no—
18C3×#926C2211yescharacteristic
19C3×#924C412yescomplemented
20C2×C3×#208C2212yes—
21C3×#830—22no—
22C3×#805—24no—
23C3×#525—31no—
24C2×C3×#117—21no—
25C2×C3×#117D311yescharacteristic, complemented
26C2×C3×#117C2×C311yescharacteristic, complemented
27#5791C2×C311yescharacteristic
28C2×C3×#104—32no—
29C3×#407—31no—
30#5207C2×C311yescharacteristic, complemented
31C2×#805C2×C312yescomplemented
32C3×#339—32no—
33#4523C2×C312yescomplemented
34C24×C32D411yescharacteristic
35C22×C32×C4—22no—
36C22×C32×C4—22no—
37C22×C32×C4—22no—
38C22×C32×C4C2×C412yes—
39C22×C32×C4D411yescharacteristic
40C22×C32×C4D412yes—
41C22×C32×C4C2311yescharacteristic
42C2×C3×#67—22no—
43C2×C3×#67—21no—
44C3×#235—22no—
45C3×#235—22no—
46C2×C3×D12C2×C411yescharacteristic
47C2×C3×C4×D3—21no—
48C2×C3×Dic6C2×C411yescharacteristic
49C32×C4⋊C4—24no—
50C32×C22⋊C4—24no—
51C32×C42—22no—
52C32×C42D414yescomplemented
53C3×#217—22no—
54C3×#217—21no—
55C3×(C2×D3)⋊C4—22no—
56C3×C4⋊Dic3C2×C412yes—
57C3×Dic3⋊C4—22no—
58C3×C4×Dic3—21no—
59C3×#208—22no—
60C3×#208—22no—
61C2×C3×C3⋊C8—22no—
62#1897—31noSylow
63C2×C3×#41—31no—
64C23×C3×C4—21no—
65C23×C3×C4C2×D311yescharacteristic
66C23×C3×C4C22×C311yescharacteristic
67C2×#235C22×C311yescharacteristic
68C2×C3×M16—32no—
69C3×#123—61no—
70C3×C22⋊Q8—32no—
71C3×#121—32no—
72C3×#120—61no—
73C3×C4×D4—62no—
74C3×#117—28no—
75C3×#117—24no—
76C3×#117—24no—
77C3×#117—31no—
78C2×C3×C4⋊C4—22no—
79C2×C3×C4⋊C4—21no—
80C2×C3×C4⋊C4—21no—
81C2×C3×C22⋊C4—22no—
82C2×C3×C22⋊C4—21no—
83C2×C3×C22⋊C4—21no—
84C2×C3×C42—22no—
85C2×C3×C42C2×D312yes—
86C2×C3×C42C22×C312yes—
87#953—21no—
88#930C3×C412yescomplemented
89#929—21no—
90C4×#67—22no—
91#926C22×C311yescharacteristic
92#924C3×C412yescomplemented
93C2×#208C22×C312yes—
94C3×#104—64no—
95C3×C22⋊C8—62no—
96#830—22no—
97#805—24no—
98C23×C32—21no—
99C23×C32—21no—
100C23×C32—42no—
101C23×C32C22⋊C412yes—
102C23×C32C2×D411yescharacteristic
103C22×C3×D3—21no—
104C2×C32×C4—21no—
105C2×C32×C4—21no—
106C2×C32×C4—24no—
107C2×C32×C4—24no—
108C2×C32×C4—24no—
109C2×C32×C4—44no—
110C2×C32×C4C22⋊C412yes—
111C2×C32×C4C22×C411yescharacteristic
112C2×C32×C4C2×D411yescharacteristic
113C2×C32×C4C2×D412yes—
114C2×C32×C4#4112yes—
115C3×#67—44no—
116C3×#67—41no—
117C3×#67—41no—
118C2×C3×Dic3—22no—
119C2×C3×Dic3—21no—
120C3×D12—22no—
121C3×C4×D3—42no—
122C3×Dic6—22no—
123C3×C3⋊C8—42no—
124#525—31no—
125C2×#117C3×D311yescharacteristic, complemented
126C2×#104—32no—
127#407—31no—
128#339—32no—
129C24×C3—21no—
130C24×C3#6711yescharacteristic
131C24×C3C3×D411yescharacteristic
132C3×#41—62no—
133C3×#41—62no—
134C2×C3×Q8—31no—
135C2×C3×D4—31no—
136C2×C3×D4—62no—
137C2×C3×D4—61no—
138C22×C3×C4—24no—
139C22×C3×C4—24no—
140C22×C3×C4—22no—
141C22×C3×C4—22no—
142C22×C3×C4—22no—
143C22×C3×C4—22no—
144C22×C3×C4—24no—
145C22×C3×C4—22no—
146C22×C3×C4—22no—
147C22×C3×C4—22no—
148C22×C3×C4—22no—
149C22×C3×C4—21no—
150C22×C3×C4—21no—
151C22×C3×C4—61no—
152C22×C3×C4C4×D312yes—
153C22×C3×C4D1212yes—
154C22×C3×C4#6711yescharacteristic
155C22×C3×C4C2×C3×C412yes—
156C22×C3×C4C3×D412yes—
157C22×C3×C4C3×D411yescharacteristic
158C22×C3×C4C22×D311yescharacteristic
159C22×C3×C4C23×C311yescharacteristic
160C2×#67—22no—
161C2×#67—21no—
162#235—22no—
163#235—22no—
164C2×D12C2×C3×C411yescharacteristic
165C2×C4×D3—21no—
166C2×Dic6C2×C3×C411yescharacteristic
167C3×M16—62no—
168C3×M16—62no—
169C2×C3×C8—62no—
170C3×C4⋊C4—28no—
171C3×C4⋊C4—24no—
172C3×C4⋊C4—24no—
173C3×C4⋊C4—32no—
174C3×C4⋊C4—62no—
175C3×C22⋊C4—28no—
176C3×C22⋊C4—24no—
177C3×C22⋊C4—24no—
178C3×C22⋊C4—62no—
179C3×C22⋊C4—61no—
180C3×C22⋊C4—62no—
181C3×C42—24no—
182C3×C42—22no—
183C3×C42—22no—
184C3×C42—24no—
185C3×C42—61no—
186C3×C42#6714yescomplemented
187C3×C42C3×D414yescomplemented
188#217—22no—
189#217—21no—
190(C2×D3)⋊C4—22no—
191C4⋊Dic3C2×C3×C412yes—
192Dic3⋊C4—22no—
193C4×Dic3—21no—
194#208—22no—
195#208—22no—
196C2×C3⋊C8—22no—
197C22×C32—22no—
198C22×C32—22no—
199C22×C32—22no—
200C22×C32—22no—
201C22×C32—42no—
202C22×C32—42no—
203C22×C32C2×C22⋊C411yescharacteristic
204C22×C32#12011yescharacteristic
205C22×C32#12311yescharacteristic
206C2×C3×D3—41no—
207C2×C3×D3—42no—
208C32×C4—22no—
209C32×C4—44no—
210C32×C4C4×D412yes—
211C32×C4#12112yes—
212C3×Dic3—41no—
213C3×Dic3—42no—
214C2×#41—31no—
215C23×C4C2×C3×D311yescharacteristic
216C2×M16—32no—
217#123—61no—
218C22⋊Q8—32no—
219#121—32no—
220#120—61no—
221C4×D4—62no—
222#117—24no—
223#117—31no—
224C2×C4⋊C4—21no—
225C2×C22⋊C4—21no—
226C2×C42C2×C3×D312yes—
227#104—64no—
228C22⋊C8—62no—
229C23×C3—22no—
230C23×C3—22no—
231C23×C3—21no—
232C23×C3—21no—
233C23×C3—21no—
234C23×C3—21no—
235C23×C3—22no—
236C23×C3—21no—
237C23×C3—42no—
238C23×C3—42no—
239C23×C3—44no—
240C23×C3—61no—
241C23×C3(C2×D3)⋊C412yes—
242C23×C3C3×C22⋊C412yes—
243C23×C3C2×#6711yescharacteristic
244C23×C3C2×C3×D411yescharacteristic
245C22×D3—21no—
246C3×Q8—62no—
247C3×D4—62no—
248C3×D4—124no—
249C3×D4—121no—
250C3×D4—121no—
251C2×C3×C4—22no—
252C2×C3×C4—22no—
253C2×C3×C4—28no—
254C2×C3×C4—28no—
255C2×C3×C4—21no—
256C2×C3×C4—21no—
257C2×C3×C4—21no—
258C2×C3×C4—21no—
259C2×C3×C4—24no—
260C2×C3×C4—24no—
261C2×C3×C4—24no—
262C2×C3×C4—24no—
263C2×C3×C4—28no—
264C2×C3×C4—24no—
265C2×C3×C4—24no—
266C2×C3×C4—22no—
267C2×C3×C4—21no—
268C2×C3×C4—21no—
269C2×C3×C4—22no—
270C2×C3×C4—22no—
271C2×C3×C4—48no—
272C2×C3×C4—44no—
273C2×C3×C4—44no—
274C2×C3×C4—62no—
275C2×C3×C4—61no—
276C2×C3×C4—122no—
277C2×C3×C4(C2×D3)⋊C412yes—
278C2×C3×C4C3×C22⋊C412yes—
279C2×C3×C4C2×C4×D311yescharacteristic
280C2×C3×C4C2×D1211yescharacteristic
281C2×C3×C4#23512yes—
282C2×C3×C4C2×#6712yes—
283C2×C3×C4C22×C3×C411yescharacteristic
284C2×C3×C4C2×C3×D411yescharacteristic
285C2×C3×C4C2×C3×D412yes—
286C2×C3×C4C3×#4112yes—
287#67—44no—
288#67—41no—
289#67—41no—
290C2×Dic3—22no—
291C2×Dic3—21no—
292D12—22no—
293C4×D3—42no—
294Dic6—22no—
295C3×C8—122no—
296C3⋊C8—42no—
297C2×C32—21no—
298C2×C32—21no—
299C2×C32—42no—
300C2×C32#38611yescharacteristic
301C2×C32#42112yes—
302C3×D3—81no—
303C24C3×#6711yescharacteristic
304#41—62no—
305#41—62no—
306C2×Q8—31no—
307C2×D4—31no—
308C2×D4—62no—
309C2×D4—61no—
310C22×C4—22no—
311C22×C4—22no—
312C22×C4—22no—
313C22×C4—61no—
314C22×C4C3×C4×D312yes—
315C22×C4C3×D1212yes—
316C22×C4C3×#6711yescharacteristic
317C22×C4C22×C3×D311yescharacteristic
318M16—62no—
319M16—62no—
320C2×C8—62no—
321C4⋊C4—24no—
322C4⋊C4—32no—
323C4⋊C4—62no—
324C22⋊C4—24no—
325C22⋊C4—62no—
326C22⋊C4—61no—
327C22⋊C4—62no—
328C42—22no—
329C42—61no—
330C42C3×#6714yescomplemented
331C22×C3—24no—
332C22×C3—22no—
333C22×C3—22no—
334C22×C3—24no—
335C22×C3—22no—
336C22×C3—22no—
337C22×C3—22no—
338C22×C3—22no—
339C22×C3—22no—
340C22×C3—22no—
341C22×C3—21no—
342C22×C3—21no—
343C22×C3—21no—
344C22×C3—42no—
345C22×C3—42no—
346C22×C3—44no—
347C22×C3—44no—
348C22×C3—42no—
349C22×C3—42no—
350C22×C3—42no—
351C22×C3—42no—
352C22×C3—121no—
353C22×C3—122no—
354C22×C3C2×(C2×D3)⋊C411yescharacteristic
355C22×C3#92911yescharacteristic
356C22×C3#95311yescharacteristic
357C22×C3C2×C3×C22⋊C411yescharacteristic
358C22×C3C3×#12011yescharacteristic
359C22×C3C3×#12311yescharacteristic
360C2×D3—41no—
361C2×D3—42no—
362C3×C4—24no—
363C3×C4—22no—
364C3×C4—22no—
365C3×C4—22no—
366C3×C4—22no—
367C3×C4—48no—
368C3×C4—44no—
369C3×C4—44no—
370C3×C4—121no—
371C3×C4—122no—
372C3×C4C4×#6712yes—
373C3×C4#93012yes—
374C3×C4C3×C4×D412yes—
375C3×C4C3×#12112yes—
376Dic3—41no—
377Dic3—42no—
378C32#189711yescharacteristic, complemented, Sylow
379C23—21no—
380C23—21no—
381C23—42no—
382C23—61no—
383C23C3×(C2×D3)⋊C412yes—
384C23C2×C3×#6711yescharacteristic
385Q8—62no—
386D4—62no—
387D4—124no—
388D4—121no—
389D4—121no—
390C2×C4—21no—
391C2×C4—21no—
392C2×C4—24no—
393C2×C4—24no—
394C2×C4—24no—
395C2×C4—44no—
396C2×C4—62no—
397C2×C4—61no—
398C2×C4—122no—
399C2×C4C3×(C2×D3)⋊C412yes—
400C2×C4C2×C3×C4×D311yescharacteristic
401C2×C4C2×C3×D1211yescharacteristic
402C2×C4C3×#23512yes—
403C2×C4C2×C3×#6712yes—
404C8—122no—
405C2×C3—22no—
406C2×C3—22no—
407C2×C3—21no—
408C2×C3—21no—
409C2×C3—21no—
410C2×C3—21no—
411C2×C3—21no—
412C2×C3—22no—
413C2×C3—44no—
414C2×C3—42no—
415C2×C3—42no—
416C2×C3—241no—
417C2×C3#500512yes—
418C2×C3#521311yescharacteristic
419C2×C3C3×#38611yescharacteristic
420C2×C3C3×#42112yes—
421D3—81no—
422C22—22no—
423C22—22no—
424C22—22no—
425C22—22no—
426C22—42no—
427C22—42no—
428C22—121no—
429C22—122no—
430C22C2×C3×(C2×D3)⋊C411yescharacteristic
431C22C3×#92911yescharacteristic
432C22C3×#95311yescharacteristic
433C4—22no—
434C4—44no—
435C4—121no—
436C4—122no—
437C4C3×C4×#6712yes—
438C4C3×#93012yes—
439C3—21no—
440C3#7159111yescharacteristic, direct product factor
441C3C3×#189711yescharacteristic, complemented
442C2—21no—
443C2—21no—
444C2—42no—
445C2—241no—
446C2C3×#500512yes—
447C2C3×#521311yescharacteristic
subgroupG/H
centerC2×C3×C4C2×D12
commutatorC2×C3×C4C22×C3×C4
FrattiniC22×C4C22×C3×D3
FittingC2×C32×#117C2
socleC22×C32C2×C22⋊C4
prime radicalC3×#5791C2
cosocleC22×C3×C4C23×C3
hypercenterC2×C3×#117D3
hypocenterC3C3×#1897
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C3×C4 ◁ C23×C3×C4 ◁ C2×C3×#117

Complements

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

NH ≅ G/Ntype
1. C2×C32×#117C2semidirect
3. C3×#5207C2semidirect
4. C2×C3×#805C2semidirect
5. C3×#4523C2semidirect
7. #71591C3direct (N × H)
15. C3×#930C4semidirect
19. C3×#924C4semidirect
25. C2×C3×#117D3semidirect
26. C2×C3×#117C2×C3semidirect
30. #5207C2×C3semidirect
31. C2×#805C2×C3semidirect
33. #4523C2×C3semidirect
52. C32×C42D4semidirect
88. #930C3×C4semidirect
92. #924C3×C4semidirect
125. C2×#117C3×D3semidirect
186. C3×C42#67semidirect
187. C3×C42C3×D4semidirect
330. C42C3×#67semidirect
378. C32#1897semidirect
440. C3#71591direct (N × H)
441. C3C3×#1897semidirect

Maximal subgroups

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

subgroupindex
C2×C32×#1172
C3×#57912
C3×#52072
C2×C3×#8052
C3×#45232
C3×#18973
#715913