Finite Group Databasebeta

← C3×#83447 #11872786

Subgroups — C3×#83447 #11872786

Order 1152.

884 conjugacy classes of subgroups.

The subgroup lattice has 456 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×#541C211yesmaximal, characteristic, complemented
2C3×#5521C211yesmaximal, characteristic
3C3×#5083C212yesmaximal, complemented
4C3×#5066C212yesmaximal, complemented
5C3×#5046C212yesmaximal
6C3×#5045C212yesmaximal, complemented
7C3×#5026C212yesmaximal, complemented
8C3×C4×#215C212yesmaximal, complemented
9C3×#5000C211yesmaximal, characteristic, complemented
10C3×#3123—31nomaximal
11#83447C311yesmaximal, characteristic, direct product factor
12C22×C3×D12C2211yescharacteristic
13C32×C4⋊Q8C2211yescharacteristic, complemented
14C32×#126—22no—
15C32×#125—22no—
16C32×#125C2211yescharacteristic, complemented
17C32×C22⋊Q8C2212yes—
18C32×C4×Q8C2212yescomplemented
19C32×#117C2211yescharacteristic
20C2×C3×#215C2212yes—
21C2×C3×#215C2212yes—
22C3×#926C2211yescharacteristic
23C3×#893—22no—
24C3×D3×C22⋊C4—22no—
25C3×C4×D12C2212yes—
26C3×C4×D12C2212yes—
27C3×#835C2212yescomplemented
28C3×#835C2212yescomplemented
29C3×#830C2212yes—
30C3×#809C2212yes—
31C3×#809C2212yes—
32C3×#808C2212yescomplemented
33C3×#807C2212yescomplemented
34C3×C4⋊(C3⋊C8)C2212yescomplemented
35C3×#803C2211yescharacteristic, complemented
36C3×C4×C3⋊C8C2211yescharacteristic, complemented
37C3×#541—21no—
38C3×#541D311yescharacteristic, complemented
39C3×#541C2×C311yescharacteristic, complemented
40C3×#518—31no—
41#5521C2×C311yescharacteristic
42C3×#485—32no—
43C3×#478—32no—
44C3×#461—32no—
45C3×#450—32no—
46C3×#440—32no—
47C3×C4×SD16—32no—
48C3×#433—31no—
49#5083C2×C312yescomplemented
50#5066C2×C312yescomplemented
51#5046C2×C312yes—
52#5045C2×C312yescomplemented
53#5026C2×C312yescomplemented
54C4×#215C2×C312yescomplemented
55#5000C2×C311yescharacteristic, complemented
56C23×C3×D3—21no—
57C2×C32×Q8C2312yes—
58C22×C32×C4C2311yescharacteristic
59C2×C3×D12—21no—
60C2×C3×D12—24no—
61C2×C3×D12C2312yes—
62C2×C3×C4×D3—22no—
63C2×C3×C4×D3—22no—
64C32×C4⋊C4—22no—
65C32×C4⋊C4—22no—
66C32×C4⋊C4—22no—
67C32×C4⋊C4—22no—
68C32×C4⋊C4D412yes—
69C32×C4⋊C4C2312yes—
70C32×C22⋊C4—22no—
71C32×C22⋊C4D412yes—
72C32×C42—22no—
73C32×C42C2311yescharacteristic
74C32×C42C2311yescharacteristic
75C3×#217—21no—
76C3×#215—24no—
77C3×#215—24no—
78C3×(C2×D3)⋊C4—22no—
79C3×(C2×D3)⋊C4—22no—
80C3×C4⋊Dic3C2312yes—
81C3×C4×Dic3—21no—
82C2×C3×C3⋊C8C2312yes—
83C2×C3×C3⋊C8C2312yes—
84#3123—31noSylow
85C22×C3×D4—31no—
86C22×D12C22×C311yescharacteristic
87C2×C3×SD16—32no—
88C2×C3×SD16—32no—
89C3×C4⋊Q8—21no—
90C3×C4⋊Q8C2×D311yescharacteristic, complemented
91C3×C4⋊Q8C22×C311yescharacteristic, complemented
92C3×#126—24no—
93C3×#126—22no—
94C3×#126—22no—
95C3×#125—24no—
96C3×#125—22no—
97C3×#125—22no—
98C3×#125—21no—
99C3×#125C2×D311yescharacteristic, complemented
100C3×#125C22×C311yescharacteristic, complemented
101C3×C22⋊Q8—22no—
102C3×C22⋊Q8C2×D312yes—
103C3×C22⋊Q8C22×C312yes—
104C3×C4×Q8—22no—
105C3×C4×Q8C2×D312yescomplemented
106C3×C4×Q8C22×C312yescomplemented
107C3×C4×D4—32no—
108C3×C4×D4—32no—
109C3×C4×D4—62no—
110C3×#117—21no—
111C3×#117—31no—
112C3×#117C2×D311yescharacteristic
113C3×#117C22×C311yescharacteristic
114C2×C3×C22⋊C4—62no—
115C2×#215C22×C312yes—
116C2×#215C22×C312yes—
117#926C22×C311yescharacteristic
118#893—22no—
119D3×C22⋊C4—22no—
120C4×D12C22×C312yes—
121C4×D12C22×C312yes—
122C3×#107—32no—
123C3×#106—32no—
124C3×C4⋊C8—32no—
125C3×#103—32no—
126C3×#103—32no—
127C3×#102—32no—
128C3×#102—32no—
129C3×C22⋊C8—32no—
130C3×#97—31no—
131C3×C4×C8—31no—
132#835C22×C312yescomplemented
133#835C22×C312yescomplemented
134#830C22×C312yes—
135#809C22×C312yes—
136#809C22×C312yes—
137#808C22×C312yescomplemented
138#807C22×C312yescomplemented
139C4⋊(C3⋊C8)C22×C312yescomplemented
140#803C22×C311yescharacteristic, complemented
141C4×C3⋊C8C22×C311yescharacteristic, complemented
142C23×C32C2×D411yescharacteristic
143C22×C3×D3—22no—
144C22×C3×D3—24no—
145C22×C3×D3—82no—
146C32×Q8—22no—
147C32×Q8—22no—
148C2×C32×C4—22no—
149C2×C32×C4—22no—
150C2×C32×C4—22no—
151C2×C32×C4C2×D411yescharacteristic
152C2×C32×C4C2×D412yes—
153C2×C32×C4C2×D412yes—
154C2×C32×C4C2411yescharacteristic
155C2×C3×Dic3—22no—
156C3×D12—24no—
157C3×D12—22no—
158C3×D12#4114yes—
159C3×C4×D3—82no—
160C3×C4×D3—82no—
161C3×C3⋊C8—22no—
162C3×C3⋊C8—22no—
163#541C3×D311yescharacteristic, complemented
164#518—31no—
165#485—32no—
166#478—32no—
167#461—32no—
168#450—32no—
169#440—32no—
170C4×SD16—32no—
171#433—31no—
172C24×C3—61no—
173C23×D3—21no—
174C2×C3×Q8—22no—
175C2×C3×Q8C22×D312yes—
176C2×C3×Q8C23×C312yes—
177C2×C3×D4—32no—
178C2×C3×D4—64no—
179C2×C3×D4—61no—
180C22×C3×C4—21no—
181C22×C3×C4—62no—
182C22×C3×C4—62no—
183C22×C3×C4C22×D311yescharacteristic
184C22×C3×C4C23×C311yescharacteristic
185C2×D12—21no—
186C2×D12—24no—
187C2×D12C23×C312yes—
188C2×C4×D3—22no—
189C2×C4×D3—22no—
190C3×SD16—64no—
191C3×SD16—64no—
192C2×C3×C8—32no—
193C2×C3×C8—32no—
194C3×C4⋊C4—24no—
195C3×C4⋊C4—24no—
196C3×C4⋊C4—24no—
197C3×C4⋊C4—24no—
198C3×C4⋊C4—22no—
199C3×C4⋊C4—22no—
200C3×C4⋊C4—22no—
201C3×C4⋊C4—22no—
202C3×C4⋊C4—22no—
203C3×C4⋊C4—22no—
204C3×C4⋊C4—22no—
205C3×C4⋊C4—22no—
206C3×C4⋊C4—22no—
207C3×C4⋊C4—22no—
208C3×C4⋊C4—32no—
209C3×C4⋊C4#6712yes—
210C3×C4⋊C4C3×D412yes—
211C3×C4⋊C4C22×D312yes—
212C3×C4⋊C4C23×C312yes—
213C3×C22⋊C4—24no—
214C3×C22⋊C4—22no—
215C3×C22⋊C4—22no—
216C3×C22⋊C4—22no—
217C3×C22⋊C4—61no—
218C3×C22⋊C4—62no—
219C3×C22⋊C4—62no—
220C3×C22⋊C4#6712yes—
221C3×C22⋊C4C3×D412yes—
222C3×C42—24no—
223C3×C42—22no—
224C3×C42—22no—
225C3×C42—21no—
226C3×C42—21no—
227C3×C42—61no—
228C3×C42C22×D311yescharacteristic
229C3×C42C22×D311yescharacteristic
230C3×C42C23×C311yescharacteristic
231C3×C42C23×C311yescharacteristic
232#217—21no—
233#215—24no—
234#215—24no—
235(C2×D3)⋊C4—22no—
236(C2×D3)⋊C4—22no—
237C4⋊Dic3C23×C312yes—
238C4×Dic3—21no—
239C2×C3⋊C8C23×C312yes—
240C2×C3⋊C8C23×C312yes—
241C22×C32—21no—
242C22×C32—22no—
243C22×C32C22×D411yescharacteristic
244C2×C3×D3—24no—
245C2×C3×D3—42no—
246C2×C3×D3—42no—
247C2×C3×D3—84no—
248C32×C4—21no—
249C32×C4—22no—
250C32×C4—22no—
251C32×C4—42no—
252C32×C4—42no—
253C32×C4C2×#4112yes—
254C3×Dic3—42no—
255C22×D4—31no—
256C2×SD16—32no—
257C2×SD16—32no—
258C4⋊Q8C2×C3×D311yescharacteristic, complemented
259#126—22no—
260#125—22no—
261#125C2×C3×D311yescharacteristic, complemented
262C22⋊Q8C2×C3×D312yes—
263C4×Q8C2×C3×D312yescomplemented
264C4×D4—32no—
265C4×D4—32no—
266C4×D4—62no—
267#117—31no—
268#117C2×C3×D311yescharacteristic
269C2×C22⋊C4—62no—
270#107—32no—
271#106—32no—
272C4⋊C8—32no—
273#103—32no—
274#103—32no—
275#102—32no—
276#102—32no—
277C22⋊C8—32no—
278#97—31no—
279C4×C8—31no—
280C23×C3—21no—
281C23×C3—64no—
282C23×C3—62no—
283C23×C3—242no—
284C23×C3C2×#6711yescharacteristic
285C23×C3C2×C3×D411yescharacteristic
286C22×D3—22no—
287C22×D3—24no—
288C22×D3—82no—
289C3×Q8—22no—
290C3×Q8—22no—
291C3×Q8—22no—
292C3×Q8—22no—
293C3×Q8—42no—
294C3×Q8—42no—
295C3×D4—34no—
296C3×D4—64no—
297C3×D4—62no—
298C2×C3×C4—22no—
299C2×C3×C4—22no—
300C2×C3×C4—24no—
301C2×C3×C4—24no—
302C2×C3×C4—22no—
303C2×C3×C4—22no—
304C2×C3×C4—22no—
305C2×C3×C4—22no—
306C2×C3×C4—21no—
307C2×C3×C4—22no—
308C2×C3×C4—22no—
309C2×C3×C4—21no—
310C2×C3×C4—42no—
311C2×C3×C4—62no—
312C2×C3×C4—242no—
313C2×C3×C4—242no—
314C2×C3×C4C2×#6712yes—
315C2×C3×C4C2×#6711yescharacteristic
316C2×C3×C4C2×#6712yes—
317C2×C3×C4C2×C3×D411yescharacteristic
318C2×C3×C4C2×C3×D412yes—
319C2×C3×C4C2×C3×D412yes—
320C2×C3×C4C23×D311yescharacteristic
321C2×C3×C4C24×C311yescharacteristic
322C2×Dic3—22no—
323D12—24no—
324D12—22no—
325D12C3×#4114yes—
326C4×D3—82no—
327C4×D3—82no—
328C3×C8—62no—
329C3×C8—62no—
330C3⋊C8—22no—
331C3⋊C8—22no—
332C2×C32—41no—
333C2×C32#52511yescharacteristic
334C2×C32#57712yes—
335C3×D3—44no—
336C24—61no—
337C2×Q8C22×C3×D312yes—
338C2×D4—32no—
339C2×D4—64no—
340C2×D4—61no—
341C22×C4—62no—
342C22×C4—62no—
343C22×C4C22×C3×D311yescharacteristic
344SD16—64no—
345SD16—64no—
346C2×C8—32no—
347C2×C8—32no—
348C4⋊C4—22no—
349C4⋊C4—22no—
350C4⋊C4—22no—
351C4⋊C4—22no—
352C4⋊C4—32no—
353C4⋊C4C3×#6712yes—
354C4⋊C4C22×C3×D312yes—
355C22⋊C4—22no—
356C22⋊C4—61no—
357C22⋊C4—62no—
358C22⋊C4—62no—
359C22⋊C4C3×#6712yes—
360C42—22no—
361C42—61no—
362C42C22×C3×D311yescharacteristic
363C42C22×C3×D311yescharacteristic
364C22×C3—22no—
365C22×C3—21no—
366C22×C3—22no—
367C22×C3—21no—
368C22×C3—21no—
369C22×C3—41no—
370C22×C3—42no—
371C22×C3—64no—
372C22×C3—122no—
373C22×C3—122no—
374C22×C3—244no—
375C22×C3C22×#6711yescharacteristic
376C22×C3C22×C3×D411yescharacteristic
377C2×D3—24no—
378C2×D3—42no—
379C2×D3—42no—
380C2×D3—84no—
381C3×C4—22no—
382C3×C4—22no—
383C3×C4—21no—
384C3×C4—22no—
385C3×C4—22no—
386C3×C4—21no—
387C3×C4—22no—
388C3×C4—41no—
389C3×C4—42no—
390C3×C4—42no—
391C3×C4—44no—
392C3×C4—44no—
393C3×C4—42no—
394C3×C4—42no—
395C3×C4—42no—
396C3×C4—42no—
397C3×C4—122no—
398C3×C4D3×#4112yes—
399C3×C4C2×C3×#4112yes—
400Dic3—42no—
401C32#312311yescharacteristic, complemented, Sylow
402C23—64no—
403C23—62no—
404C23—242no—
405C23C2×C3×#6711yescharacteristic
406Q8—22no—
407Q8—22no—
408D4—34no—
409D4—64no—
410D4—62no—
411C2×C4—22no—
412C2×C4—22no—
413C2×C4—22no—
414C2×C4—62no—
415C2×C4—242no—
416C2×C4—242no—
417C2×C4C2×C3×#6712yes—
418C2×C4C2×C3×#6711yescharacteristic
419C2×C4C2×C3×#6712yes—
420C2×C4C23×C3×D311yescharacteristic
421C8—62no—
422C8—62no—
423C2×C3—21no—
424C2×C3—22no—
425C2×C3—41no—
426C2×C3—41no—
427C2×C3—81no—
428C2×C3—124no—
429C2×C3#582811yescharacteristic
430C2×C3#583712yes—
431C2×C3C3×#52511yescharacteristic
432C2×C3C3×#57712yes—
433D3—44no—
434C22—21no—
435C22—22no—
436C22—64no—
437C22—122no—
438C22—122no—
439C22—244no—
440C22C22×C3×#6711yescharacteristic
441C4—21no—
442C4—22no—
443C4—22no—
444C4—42no—
445C4—42no—
446C4—122no—
447C4C3×D3×#4112yes—
448C3—21no—
449C3#8344711yescharacteristic, direct product factor
450C3C3×#312311yescharacteristic, complemented
451C2—41no—
452C2—124no—
453C2C3×#582811yescharacteristic
454C2C3×#583712yes—
subgroupG/H
centerC22×C3C22×#67
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#541C2
socleC22×C32C22×D4
prime radicalC22×C3×D12C22
hypercenterC3×#541D3
hypocenterC3C3×#3123
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×#117 ◁ C3×#541

Complements

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

NH ≅ G/Ntype
1. C32×#541C2semidirect
3. C3×#5083C2semidirect
4. C3×#5066C2semidirect
6. C3×#5045C2semidirect
7. C3×#5026C2semidirect
8. C3×C4×#215C2semidirect
9. C3×#5000C2semidirect
11. #83447C3direct (N × H)
13. C32×C4⋊Q8C22semidirect
16. C32×#125C22semidirect
18. C32×C4×Q8C22semidirect
27. C3×#835C22semidirect
28. C3×#835C22semidirect
32. C3×#808C22semidirect
33. C3×#807C22semidirect
34. C3×C4⋊(C3⋊C8)C22semidirect
35. C3×#803C22semidirect
36. C3×C4×C3⋊C8C22semidirect
38. C3×#541D3semidirect
39. C3×#541C2×C3semidirect
49. #5083C2×C3semidirect
50. #5066C2×C3semidirect
52. #5045C2×C3semidirect
53. #5026C2×C3semidirect
54. C4×#215C2×C3semidirect
55. #5000C2×C3semidirect
90. C3×C4⋊Q8C2×D3semidirect
91. C3×C4⋊Q8C22×C3semidirect
99. C3×#125C2×D3semidirect
100. C3×#125C22×C3semidirect
105. C3×C4×Q8C2×D3semidirect
106. C3×C4×Q8C22×C3semidirect
132. #835C22×C3semidirect
133. #835C22×C3semidirect
137. #808C22×C3semidirect
138. #807C22×C3semidirect
139. C4⋊(C3⋊C8)C22×C3semidirect
140. #803C22×C3semidirect
141. C4×C3⋊C8C22×C3semidirect
163. #541C3×D3semidirect
258. C4⋊Q8C2×C3×D3semidirect
261. #125C2×C3×D3semidirect
263. C4×Q8C2×C3×D3semidirect
401. C32#3123semidirect
449. C3#83447direct (N × H)
450. C3C3×#3123semidirect

Maximal subgroups

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

subgroupindex
C32×#5412
C3×#55212
C3×#50832
C3×#50662
C3×#50462
C3×#50452
C3×#50262
C3×C4×#2152
C3×#50002
C3×#31233
#834473