Finite Group Databasebeta

← C3×#71721 #11791485

Subgroups — C3×#71721 #11791485

Order 1152.

853 conjugacy classes of subgroups.

The subgroup lattice has 451 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C32×#124C211yesmaximal, characteristic
2C2×C3×#835C212yesmaximal, complemented
3C2×C3×#832C212yesmaximal
4C3×C4×C4⋊Dic3C211yesmaximal, characteristic, complemented
5C2×C3×C4⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
6C3×#1983—31nomaximal
7#71721C311yesmaximal, characteristic, direct product factor
8C22×C32×Q8C2211yescharacteristic
9C22×C32×D4C2211yescharacteristic
10C32×#124—22no—
11C32×#124C414yescomplemented
12C2×C32×C22⋊C4—21no—
13C2×C32×C22⋊C4—21no—
14C2×C32×C42C2211yescharacteristic
15C2×C3×C4⋊Dic3C2212yes—
16C2×C3×C4×Dic3—21no—
17C22×C3×C3⋊C8C2212yes—
18C3×#835—24no—
19C3×#832—24no—
20C3×C3⋊#95—21no—
21C3×C4⋊(C3⋊C8)—22no—
22C2×C3×#124—21no—
23C2×C3×#124D311yescharacteristic
24C2×C3×#124C2×C311yescharacteristic
25C2×C3×C4⋊C8—31no—
26C2×C3×#103—32no—
27C2×C3×#102—32no—
28C3×C4×C4⋊C4—31no—
29C2×#835C2×C312yescomplemented
30C2×#832C2×C312yes—
31C4×C4⋊Dic3C2×C311yescharacteristic, complemented
32C2×C4⋊(C3⋊C8)C2×C311yescharacteristic, complemented
33C24×C32—21no—
34C2×C32×Q8—21no—
35C2×C32×Q8—22no—
36C2×C32×Q8—22no—
37C2×C32×Q8C2×C412yes—
38C2×C32×D4—22no—
39C2×C32×D4—21no—
40C2×C32×D4—22no—
41C2×C32×D4C2×C412yes—
42C22×C32×C4—21no—
43C22×C32×C4D411yescharacteristic
44C22×C32×C4D411yescharacteristic
45C22×C32×C4C2311yescharacteristic
46C22×C3×Dic3—22no—
47C32×C22⋊C4—24no—
48C32×C22⋊C4—24no—
49C32×C42C2×C412yes—
50C32×C42D412yes—
51C3×C4⋊Dic3—22no—
52C3×C4⋊Dic3D414yes—
53C3×C4×Dic3—42no—
54C2×C3×C3⋊C8—22no—
55C2×C3×C3⋊C8—22no—
56C2×C3×C3⋊C8—22no—
57#1983—31noSylow
58C22×C3×Q8—21no—
59C22×C3×Q8C2×D311yescharacteristic
60C22×C3×Q8C22×C311yescharacteristic
61C22×C3×D4—21no—
62C22×C3×D4C2×D311yescharacteristic
63C22×C3×D4C22×C311yescharacteristic
64C22×C3×C8—32no—
65C3×#124—24no—
66C3×#124—22no—
67C3×#124—22no—
68C3×#124—24no—
69C3×#124Dic314yescomplemented
70C3×#124C3×C414yescomplemented
71C2×C3×C4⋊C4—32no—
72C2×C3×C22⋊C4—22no—
73C2×C3×C22⋊C4—22no—
74C2×C3×C22⋊C4—21no—
75C2×C3×C22⋊C4—21no—
76C2×C3×C22⋊C4—21no—
77C2×C3×C22⋊C4—21no—
78C2×C3×C42—21no—
79C2×C3×C42—61no—
80C2×C3×C42C2×D311yescharacteristic
81C2×C3×C42C22×C311yescharacteristic
82C2×C4⋊Dic3C22×C312yes—
83C2×C4×Dic3—21no—
84C22×C3⋊C8C22×C312yes—
85C3×C4⋊C8—62no—
86C3×#103—64no—
87C3×#102—64no—
88C3×#95—61no—
89#835—24no—
90#832—24no—
91C3⋊#95—21no—
92C4⋊(C3⋊C8)—22no—
93C23×C32—22no—
94C23×C32—42no—
95C23×C32—42no—
96C23×C32—41no—
97C23×C32—41no—
98C23×C32C2×D411yescharacteristic
99C32×Q8—24no—
100C32×Q8—41no—
101C32×Q8—41no—
102C32×D4—24no—
103C32×D4—41no—
104C32×D4—41no—
105C2×C32×C4—22no—
106C2×C32×C4—22no—
107C2×C32×C4—21no—
108C2×C32×C4—21no—
109C2×C32×C4—42no—
110C2×C32×C4C22⋊C412yes—
111C2×C32×C4C22⋊C412yes—
112C2×C32×C4C22×C411yescharacteristic
113C2×C32×C4C2×D412yes—
114C2×C32×C4C2×D411yescharacteristic
115C2×C32×C4#4112yes—
116C2×C3×Dic3—24no—
117C2×C3×Dic3—42no—
118C2×C3×Dic3—42no—
119C3×C3⋊C8—42no—
120C2×#124C3×D311yescharacteristic
121C2×C4⋊C8—31no—
122C2×#103—32no—
123C2×#102—32no—
124C4×C4⋊C4—31no—
125C24×C3—22no—
126C24×C3—21no—
127C24×C3—21no—
128C2×C3×Q8—22no—
129C2×C3×Q8—21no—
130C2×C3×Q8—21no—
131C2×C3×Q8—22no—
132C2×C3×Q8—22no—
133C2×C3×Q8—22no—
134C2×C3×Q8—22no—
135C2×C3×Q8—22no—
136C2×C3×Q8—42no—
137C2×C3×Q8—42no—
138C2×C3×Q8C2×Dic312yes—
139C2×C3×Q8C2×C3×C412yes—
140C2×C3×D4—22no—
141C2×C3×D4—22no—
142C2×C3×D4—22no—
143C2×C3×D4—21no—
144C2×C3×D4—22no—
145C2×C3×D4—21no—
146C2×C3×D4—22no—
147C2×C3×D4—22no—
148C2×C3×D4—42no—
149C2×C3×D4—42no—
150C2×C3×D4C2×Dic312yes—
151C2×C3×D4C2×C3×C412yes—
152C22×C3×C4—22no—
153C22×C3×C4—21no—
154C22×C3×C4—21no—
155C22×C3×C4—21no—
156C22×C3×C4—21no—
157C22×C3×C4—21no—
158C22×C3×C4—62no—
159C22×C3×C4#6711yescharacteristic
160C22×C3×C4#6711yescharacteristic
161C22×C3×C4C3×D411yescharacteristic
162C22×C3×C4C3×D411yescharacteristic
163C22×C3×C4C22×D311yescharacteristic
164C22×C3×C4C23×C311yescharacteristic
165C22×Dic3—22no—
166C2×C3×C8—62no—
167C2×C3×C8—62no—
168C2×C3×C8—62no—
169C3×C4⋊C4—34no—
170C3×C4⋊C4—62no—
171C3×C22⋊C4—28no—
172C3×C22⋊C4—28no—
173C3×C22⋊C4—24no—
174C3×C22⋊C4—24no—
175C3×C22⋊C4—24no—
176C3×C22⋊C4—24no—
177C3×C42—22no—
178C3×C42—22no—
179C3×C42—122no—
180C3×C42C2×Dic312yes—
181C3×C42#6712yes—
182C3×C42C2×C3×C412yes—
183C3×C42C3×D412yes—
184C4⋊Dic3—22no—
185C4⋊Dic3C3×D414yes—
186C4×Dic3—42no—
187C2×C3⋊C8—22no—
188C2×C3⋊C8—22no—
189C2×C3⋊C8—22no—
190C22×C32—42no—
191C22×C32—42no—
192C22×C32—42no—
193C22×C32—82no—
194C22×C32—82no—
195C22×C32C2×C22⋊C411yescharacteristic
196C22×C32#12112yes—
197C22×C32#13512yes—
198C22×C32AGL(1,ℤ/8)11yescharacteristic
199C22×C32#13711yescharacteristic
200C32×C4—22no—
201C32×C4—22no—
202C32×C4—42no—
203C32×C4C4×D412yes—
204C32×C4#12411yescharacteristic
205C32×C4#12711yescharacteristic
206C3×Dic3—44no—
207C22×Q8C2×C3×D311yescharacteristic
208C22×D4C2×C3×D311yescharacteristic
209C22×C8—32no—
210#124—22no—
211#124C3×Dic314yescomplemented
212C2×C4⋊C4—32no—
213C2×C22⋊C4—21no—
214C2×C22⋊C4—21no—
215C2×C42—61no—
216C2×C42C2×C3×D311yescharacteristic
217C4⋊C8—62no—
218#103—64no—
219#102—64no—
220#95—61no—
221C23×C3—24no—
222C23×C3—22no—
223C23×C3—22no—
224C23×C3—21no—
225C23×C3—44no—
226C23×C3—42no—
227C23×C3—44no—
228C23×C3—42no—
229C23×C3—42no—
230C23×C3—41no—
231C23×C3—42no—
232C23×C3—41no—
233C23×C3—42no—
234C23×C3—42no—
235C23×C3—41no—
236C23×C3—41no—
237C23×C3C2×#6711yescharacteristic
238C23×C3C2×C3×D411yescharacteristic
239C3×Q8—24no—
240C3×Q8—24no—
241C3×Q8—44no—
242C3×Q8—42no—
243C3×Q8—42no—
244C3×Q8—41no—
245C3×Q8—41no—
246C3×Q8—41no—
247C3×Q8—41no—
248C3×D4—24no—
249C3×D4—24no—
250C3×D4—44no—
251C3×D4—42no—
252C3×D4—42no—
253C3×D4—41no—
254C3×D4—41no—
255C3×D4—41no—
256C3×D4—41no—
257C2×C3×C4—21no—
258C2×C3×C4—22no—
259C2×C3×C4—21no—
260C2×C3×C4—22no—
261C2×C3×C4—21no—
262C2×C3×C4—21no—
263C2×C3×C4—24no—
264C2×C3×C4—22no—
265C2×C3×C4—22no—
266C2×C3×C4—22no—
267C2×C3×C4—22no—
268C2×C3×C4—22no—
269C2×C3×C4—22no—
270C2×C3×C4—21no—
271C2×C3×C4—21no—
272C2×C3×C4—41no—
273C2×C3×C4—42no—
274C2×C3×C4—41no—
275C2×C3×C4—44no—
276C2×C3×C4—42no—
277C2×C3×C4—42no—
278C2×C3×C4—64no—
279C2×C3×C4—122no—
280C2×C3×C4—122no—
281C2×C3×C4#21712yes—
282C2×C3×C4#21712yes—
283C2×C3×C4C3×C22⋊C412yes—
284C2×C3×C4C3×C22⋊C412yes—
285C2×C3×C4D3×D412yes—
286C2×C3×C4#23712yes—
287C2×C3×C4C22×Dic311yescharacteristic
288C2×C3×C4C2×#6711yescharacteristic
289C2×C3×C4C22×C3×C411yescharacteristic
290C2×C3×C4C2×C3×D412yes—
291C2×C3×C4C2×C3×D411yescharacteristic
292C2×C3×C4C3×#4112yes—
293C2×Dic3—24no—
294C2×Dic3—42no—
295C2×Dic3—42no—
296C3×C8—122no—
297C3⋊C8—42no—
298C2×C32—82no—
299C2×C32#39011yescharacteristic
300C2×C32#41611yescharacteristic
301C2×C32#41711yescharacteristic
302C2×C32#46312yes—
303C2×C32#46412yes—
304C24—21no—
305C2×Q8—21no—
306C2×Q8—22no—
307C2×Q8—22no—
308C2×Q8C2×C3×Dic312yes—
309C2×D4—22no—
310C2×D4—22no—
311C2×D4—21no—
312C2×D4C2×C3×Dic312yes—
313C22×C4—21no—
314C22×C4—62no—
315C22×C4C3×#6711yescharacteristic
316C22×C4C3×#6711yescharacteristic
317C22×C4C22×C3×D311yescharacteristic
318C2×C8—62no—
319C2×C8—62no—
320C2×C8—62no—
321C4⋊C4—34no—
322C4⋊C4—62no—
323C22⋊C4—24no—
324C22⋊C4—24no—
325C42—122no—
326C42C2×C3×Dic312yes—
327C42C3×#6712yes—
328C22×C3—22no—
329C22×C3—21no—
330C22×C3—22no—
331C22×C3—21no—
332C22×C3—21no—
333C22×C3—44no—
334C22×C3—44no—
335C22×C3—44no—
336C22×C3—42no—
337C22×C3—42no—
338C22×C3—42no—
339C22×C3—42no—
340C22×C3—42no—
341C22×C3—42no—
342C22×C3—84no—
343C22×C3—84no—
344C22×C3—82no—
345C22×C3—82no—
346C22×C3—82no—
347C22×C3—82no—
348C22×C3#93812yes—
349C22×C3#94911yescharacteristic
350C22×C3#95012yes—
351C22×C3#95111yescharacteristic
352C22×C3C2×#21711yescharacteristic
353C22×C3C2×C3×C22⋊C411yescharacteristic
354C22×C3C3×#12112yes—
355C22×C3C3×#13512yes—
356C22×C3C3×AGL(1,ℤ/8)11yescharacteristic
357C22×C3C3×#13711yescharacteristic
358C3×C4—22no—
359C3×C4—22no—
360C3×C4—22no—
361C3×C4—22no—
362C3×C4—22no—
363C3×C4—21no—
364C3×C4—21no—
365C3×C4—42no—
366C3×C4—42no—
367C3×C4—44no—
368C3×C4—42no—
369C3×C4—42no—
370C3×C4—124no—
371C3×C4D4×Dic312yes—
372C3×C4#93611yescharacteristic
373C3×C4#94011yescharacteristic
374C3×C4C3×C4×D412yes—
375C3×C4C3×#12411yescharacteristic
376C3×C4C3×#12711yescharacteristic
377Dic3—44no—
378C32#198311yescharacteristic, complemented, Sylow
379C23—22no—
380C23—42no—
381C23—41no—
382C23—42no—
383C23—41no—
384C23C2×C3×#6711yescharacteristic
385Q8—24no—
386Q8—41no—
387Q8—41no—
388D4—24no—
389D4—41no—
390D4—41no—
391C2×C4—21no—
392C2×C4—22no—
393C2×C4—21no—
394C2×C4—22no—
395C2×C4—42no—
396C2×C4—64no—
397C2×C4—122no—
398C2×C4—122no—
399C2×C4C3×#21712yes—
400C2×C4C3×#21712yes—
401C2×C4C3×D3×D412yes—
402C2×C4C3×#23712yes—
403C2×C4C22×C3×Dic311yescharacteristic
404C2×C4C2×C3×#6711yescharacteristic
405C8—122no—
406C2×C3—21no—
407C2×C3—21no—
408C2×C3—21no—
409C2×C3—22no—
410C2×C3—22no—
411C2×C3—84no—
412C2×C3—82no—
413C2×C3—82no—
414C2×C3#505412yes—
415C2×C3#505712yes—
416C2×C3#522111yescharacteristic
417C2×C3#523211yescharacteristic
418C2×C3#523311yescharacteristic
419C2×C3C3×#39011yescharacteristic
420C2×C3C3×#41611yescharacteristic
421C2×C3C3×#41711yescharacteristic
422C2×C3C3×#46312yes—
423C2×C3C3×#46412yes—
424C22—42no—
425C22—42no—
426C22—42no—
427C22—82no—
428C22—82no—
429C22C3×#93812yes—
430C22C3×#94911yescharacteristic
431C22C3×#95012yes—
432C22C3×#95111yescharacteristic
433C22C2×C3×#21711yescharacteristic
434C4—22no—
435C4—22no—
436C4—42no—
437C4—124no—
438C4C3×D4×Dic312yes—
439C4C3×#93611yescharacteristic
440C4C3×#94011yescharacteristic
441C3—21no—
442C3#7172111yescharacteristic, direct product factor
443C3C3×#198311yescharacteristic, complemented
444C2—82no—
445C2C3×#505412yes—
446C2C3×#505712yes—
447C2C3×#522111yescharacteristic
448C2C3×#523211yescharacteristic
449C2C3×#523311yescharacteristic
subgroupG/H
centerC23×C3C2×#67
commutatorC2×C3×C4C22×C3×C4
FrattiniC22×C4C22×C3×D3
FittingC2×C32×#124C2
socleC23×C32C2×D4
prime radicalC22×C32×D4C22
cosocleC22×C3×C4C23×C3
hypercenterC2×C3×#124D3
hypocenterC3C3×#1983
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23×C3 ◁ C2×C3×C42 ◁ C2×C3×#124

Complements

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

NH ≅ G/Ntype
2. C2×C3×#835C2semidirect
4. C3×C4×C4⋊Dic3C2semidirect
5. C2×C3×C4⋊(C3⋊C8)C2semidirect
7. #71721C3direct (N × H)
11. C32×#124C4semidirect
29. C2×#835C2×C3semidirect
31. C4×C4⋊Dic3C2×C3semidirect
32. C2×C4⋊(C3⋊C8)C2×C3semidirect
69. C3×#124Dic3semidirect
70. C3×#124C3×C4semidirect
211. #124C3×Dic3semidirect
378. C32#1983semidirect
442. C3#71721direct (N × H)
443. C3C3×#1983semidirect

Maximal subgroups

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

subgroupindex
C2×C32×#1242
C2×C3×#8352
C2×C3×#8322
C3×C4×C4⋊Dic32
C2×C3×C4⋊(C3⋊C8)2
C3×#19833
#717213