Finite Group Databasebeta

← C3×#71014 #11779203

Subgroups — C3×#71014 #11779203

Order 1152.

570 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
1C3×D4×Dic6C211yesmaximal, characteristic, complemented
2C32×#459C211yesmaximal, characteristic
3C3×#5075C211yesmaximal, characteristic, complemented
4C3×#5070C211yesmaximal, characteristic, complemented
5C3×D4⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
6C3×#4486C211yesmaximal, characteristic, complemented
7C3×#4484C211yesmaximal, characteristic, complemented
8C3×#1627—31nomaximal
9#71014C311yesmaximal, characteristic, direct product factor
10C22×C3×Dic6—21no—
11C2×C32×D8—21no—
12C32×#127C2211yescharacteristic
13C32×C4×D4C2211yescharacteristic
14C3×D4×Dic3—21no—
15C2×C3×#214—21no—
16C3×#924—21no—
17C3×#888—21no—
18C3×#878—22no—
19C3×#869C2211yescharacteristic
20C3×C4×Dic6C2211yescharacteristic
21C32×C4⋊C8C2211yescharacteristic
22C32×#102—21no—
23C3×#832—22no—
24C3×#832—21no—
25C3×C4⋊(C3⋊C8)C2211yescharacteristic
26C3×C4×C3⋊C8C2211yescharacteristic
27C3×D4×Q8—31no—
28D4×Dic6C2×C311yescharacteristic, complemented
29C3×#486—31no—
30C3×#460—31no—
31C3×#459—21no—
32C3×#459D311yescharacteristic
33C3×#459C2×C311yescharacteristic
34#5075C2×C311yescharacteristic, complemented
35#5070C2×C311yescharacteristic, complemented
36C3×#332—31no—
37C3×Q8⋊C8—31no—
38C3×D4⋊C8—31no—
39D4⋊(C3⋊C8)C2×C311yescharacteristic, complemented
40#4486C2×C311yescharacteristic, complemented
41#4484C2×C311yescharacteristic, complemented
42C2×C32×D4—21no—
43C2×C32×D4—21no—
44C2×C32×D4—21no—
45C2×C32×D4D411yescharacteristic
46C22×C32×C4—21no—
47C22×C3×Dic3—22no—
48C2×C3×Dic6—22no—
49C2×C3×Dic6—21no—
50C2×C3×Dic6—42no—
51C2×C3×Dic6—42no—
52C2×C3×Dic6D411yescharacteristic
53C32×D8—42no—
54C2×C32×C8—21no—
55C32×C4⋊C4D411yescharacteristic
56C32×C22⋊C4—21no—
57C32×C42C2311yescharacteristic
58C3×#217—22no—
59C3×#214—42no—
60C3×C4⋊Dic3—21no—
61C3×C4⋊Dic3D412yes—
62C3×C4⋊Dic3D411yescharacteristic
63C3×Dic3⋊C4—22no—
64C3×Dic3⋊C4—21no—
65C3×C4×Dic3—21no—
66C2×C3×C3⋊C8—21no—
67C2×C3×C3⋊C8—21no—
68#1627—31noSylow
69C22×C3×Q8—61no—
70C22×Dic6—21no—
71C2×C3×SD16—61no—
72C2×C3×D8—22no—
73C2×C3×D8—21no—
74C2×C3×D8—21no—
75C3×C4⋊Q8—31no—
76C3×C4⋊Q8—61no—
77C3×#127—21no—
78C3×#127C2×D311yescharacteristic
79C3×#127C22×C311yescharacteristic
80C3×C22⋊Q8—62no—
81C3×C22⋊Q8—61no—
82C3×C4×Q8—31no—
83C3×C4×D4—21no—
84C3×C4×D4—61no—
85C3×C4×D4C2×D311yescharacteristic
86C3×C4×D4C22×C311yescharacteristic
87D4×Dic3—21no—
88C2×#214—21no—
89#924—21no—
90#888—21no—
91#878—22no—
92#869C22×C311yescharacteristic
93C4×Dic6C22×C311yescharacteristic
94C3×C4⋊C8—21no—
95C3×C4⋊C8—31no—
96C3×C4⋊C8C2×D311yescharacteristic
97C3×C4⋊C8C22×C311yescharacteristic
98C3×#102—22no—
99C3×#102—21no—
100C3×#102—21no—
101C3×#102—61no—
102C3×#102—62no—
103C3×C4×C8—31no—
104#832—22no—
105#832—21no—
106C4⋊(C3⋊C8)C22×C311yescharacteristic
107C4×C3⋊C8C22×C311yescharacteristic
108C23×C32—21no—
109C23×C32—41no—
110C32×D4—21no—
111C32×D4—41no—
112C32×D4—41no—
113C32×D4—42no—
114C32×D4—41no—
115C32×D4—41no—
116C32×D4SD1612yescomplemented
117C2×C32×C4—21no—
118C2×C32×C4—41no—
119C2×C32×C4—41no—
120C2×C32×C4C2×D411yescharacteristic
121C2×C32×C4C2×D411yescharacteristic
122C2×C32×C4C2×D411yescharacteristic
123C2×C3×Dic3—21no—
124C2×C3×Dic3—21no—
125C2×C3×Dic3—22no—
126C2×C3×Dic3—44no—
127C3×Dic6—21no—
128C3×Dic6—44no—
129C3×Dic6—41no—
130C3×Dic6—41no—
131C3×Dic6D812yescomplemented
132C32×C8—41no—
133C3×C3⋊C8—41no—
134C3×C3⋊C8—41no—
135D4×Q8—31no—
136#486—31no—
137#460—31no—
138#459C3×D311yescharacteristic
139#332—31no—
140Q8⋊C8—31no—
141D4⋊C8—31no—
142C2×C3×Q8—31no—
143C2×C3×Q8—62no—
144C2×C3×Q8—61no—
145C2×C3×Q8—122no—
146C2×C3×Q8—122no—
147C2×C3×D4—22no—
148C2×C3×D4—21no—
149C2×C3×D4—21no—
150C2×C3×D4—21no—
151C2×C3×D4—21no—
152C2×C3×D4—21no—
153C2×C3×D4—21no—
154C2×C3×D4—21no—
155C2×C3×D4—41no—
156C2×C3×D4—41no—
157C2×C3×D4#6711yescharacteristic
158C2×C3×D4C3×D411yescharacteristic
159C22×C3×C4—21no—
160C22×C3×C4—21no—
161C22×C3×C4—41no—
162C22×C3×C4—62no—
163C22×Dic3—22no—
164C2×Dic6—22no—
165C2×Dic6—21no—
166C2×Dic6—42no—
167C2×Dic6—42no—
168C2×Dic6C3×D411yescharacteristic
169C3×SD16—122no—
170C3×D8—44no—
171C3×D8—42no—
172C3×D8—42no—
173C2×C3×C8—22no—
174C2×C3×C8—21no—
175C2×C3×C8—21no—
176C2×C3×C8—61no—
177C2×C3×C8—61no—
178C3×C4⋊C4—21no—
179C3×C4⋊C4—31no—
180C3×C4⋊C4—32no—
181C3×C4⋊C4—62no—
182C3×C4⋊C4—61no—
183C3×C4⋊C4—61no—
184C3×C4⋊C4#6711yescharacteristic
185C3×C4⋊C4C3×D411yescharacteristic
186C3×C22⋊C4—21no—
187C3×C22⋊C4—21no—
188C3×C22⋊C4—41no—
189C3×C22⋊C4—62no—
190C3×C42—21no—
191C3×C42—61no—
192C3×C42C22×D311yescharacteristic
193C3×C42C23×C311yescharacteristic
194#217—22no—
195#214—42no—
196C4⋊Dic3—21no—
197C4⋊Dic3C3×D411yescharacteristic
198C4⋊Dic3C3×D412yes—
199Dic3⋊C4—22no—
200Dic3⋊C4—21no—
201C4×Dic3—21no—
202C2×C3⋊C8—21no—
203C2×C3⋊C8—21no—
204C22×C32—22no—
205C22×C32—41no—
206C22×C32—41no—
207C22×C32—81no—
208C22×C32—81no—
209C22×C32—81no—
210C22×C32#12011yescharacteristic
211C32×C4—21no—
212C32×C4—41no—
213C32×C4C2×D811yescharacteristic
214C32×C4C2×SD1611yescharacteristic
215C32×C4AGL(1,ℤ/8)11yescharacteristic
216C32×C4#13711yescharacteristic
217C3×Dic3—22no—
218C3×Dic3—42no—
219C3×Dic3—41no—
220C22×Q8—61no—
221C2×SD16—61no—
222C2×D8—21no—
223C4⋊Q8—31no—
224C4⋊Q8—61no—
225#127C2×C3×D311yescharacteristic
226C22⋊Q8—62no—
227C22⋊Q8—61no—
228C4×Q8—31no—
229C4×D4—61no—
230C4×D4C2×C3×D311yescharacteristic
231C4⋊C8—31no—
232C4⋊C8C2×C3×D311yescharacteristic
233#102—21no—
234#102—61no—
235#102—62no—
236C4×C8—31no—
237C23×C3—21no—
238C23×C3—21no—
239C23×C3—41no—
240C23×C3—42no—
241C23×C3—41no—
242C23×C3—41no—
243C3×Q8—32no—
244C3×Q8—61no—
245C3×Q8—124no—
246C3×Q8—121no—
247C3×Q8—121no—
248C3×D4—21no—
249C3×D4—21no—
250C3×D4—22no—
251C3×D4—41no—
252C3×D4—42no—
253C3×D4—42no—
254C3×D4—42no—
255C3×D4—42no—
256C3×D4—41no—
257C3×D4—41no—
258C3×D4—41no—
259C3×D4—41no—
260C3×D4—41no—
261C3×D4—41no—
262C3×D4—41no—
263C3×D4—41no—
264C3×D4—81no—
265C3×D4—81no—
266C3×D4—82no—
267C3×D4#21412yescomplemented
268C3×D4C3×SD1612yescomplemented
269C2×C3×C4—21no—
270C2×C3×C4—21no—
271C2×C3×C4—21no—
272C2×C3×C4—21no—
273C2×C3×C4—21no—
274C2×C3×C4—41no—
275C2×C3×C4—41no—
276C2×C3×C4—41no—
277C2×C3×C4—41no—
278C2×C3×C4—41no—
279C2×C3×C4—61no—
280C2×C3×C4—61no—
281C2×C3×C4—62no—
282C2×C3×C4—81no—
283C2×C3×C4—81no—
284C2×C3×C4—124no—
285C2×C3×C4D3×D411yescharacteristic
286C2×C3×C4D3×D411yescharacteristic
287C2×C3×C4C2×#6711yescharacteristic
288C2×C3×C4C2×C3×D411yescharacteristic
289C2×C3×C4C2×C3×D411yescharacteristic
290C2×C3×C4C2×C3×D411yescharacteristic
291C2×Dic3—21no—
292C2×Dic3—21no—
293C2×Dic3—22no—
294C2×Dic3—44no—
295Dic6—21no—
296Dic6—44no—
297Dic6—41no—
298Dic6—41no—
299Dic6C3×D812yescomplemented
300C3×C8—42no—
301C3×C8—41no—
302C3×C8—41no—
303C3×C8—121no—
304C3×C8—121no—
305C3⋊C8—41no—
306C3⋊C8—41no—
307C2×C32—42no—
308C2×C32—161no—
309C2×C32#44711yescharacteristic
310C2×C32#44811yescharacteristic
311C2×C32#45411yescharacteristic
312C2×Q8—31no—
313C2×Q8—62no—
314C2×Q8—61no—
315C2×Q8—122no—
316C2×Q8—122no—
317C2×D4—21no—
318C2×D4—21no—
319C2×D4—21no—
320C2×D4C3×#6711yescharacteristic
321C22×C4—21no—
322C22×C4—62no—
323SD16—122no—
324D8—42no—
325C2×C8—21no—
326C2×C8—61no—
327C2×C8—61no—
328C4⋊C4—31no—
329C4⋊C4—32no—
330C4⋊C4—62no—
331C4⋊C4—61no—
332C4⋊C4—61no—
333C4⋊C4C3×#6711yescharacteristic
334C22⋊C4—21no—
335C22⋊C4—62no—
336C42—61no—
337C42C22×C3×D311yescharacteristic
338C22×C3—22no—
339C22×C3—22no—
340C22×C3—21no—
341C22×C3—42no—
342C22×C3—41no—
343C22×C3—41no—
344C22×C3—41no—
345C22×C3—41no—
346C22×C3—81no—
347C22×C3—81no—
348C22×C3—82no—
349C22×C3—82no—
350C22×C3—82no—
351C22×C3—81no—
352C22×C3—81no—
353C22×C3—81no—
354C22×C3—81no—
355C22×C3—81no—
356C22×C3—81no—
357C22×C3#93711yescharacteristic
358C22×C3C3×#12011yescharacteristic
359C3×C4—21no—
360C3×C4—21no—
361C3×C4—21no—
362C3×C4—21no—
363C3×C4—21no—
364C3×C4—21no—
365C3×C4—41no—
366C3×C4—41no—
367C3×C4—41no—
368C3×C4—62no—
369C3×C4—81no—
370C3×C4—122no—
371C3×C4—121no—
372C3×C4D3×D811yescharacteristic
373C3×C4#91111yescharacteristic
374C3×C4C2×#21411yescharacteristic
375C3×C4#95111yescharacteristic
376C3×C4C2×C3×D811yescharacteristic
377C3×C4C2×C3×SD1611yescharacteristic
378C3×C4C3×AGL(1,ℤ/8)11yescharacteristic
379C3×C4C3×#13711yescharacteristic
380Dic3—22no—
381Dic3—42no—
382Dic3—41no—
383C32#162711yescharacteristic, complemented, Sylow
384C23—21no—
385C23—41no—
386Q8—32no—
387Q8—61no—
388Q8—124no—
389Q8—121no—
390Q8—121no—
391D4—21no—
392D4—42no—
393D4—41no—
394D4—41no—
395D4—41no—
396D4—41no—
397D4C3×#21412yescomplemented
398C2×C4—21no—
399C2×C4—41no—
400C2×C4—41no—
401C2×C4—61no—
402C2×C4—61no—
403C2×C4—62no—
404C2×C4—124no—
405C2×C4C3×D3×D411yescharacteristic
406C2×C4C3×D3×D411yescharacteristic
407C2×C4C2×C3×#6711yescharacteristic
408C8—41no—
409C8—121no—
410C8—121no—
411C2×C3—21no—
412C2×C3—21no—
413C2×C3—21no—
414C2×C3—42no—
415C2×C3—42no—
416C2×C3—82no—
417C2×C3—162no—
418C2×C3—161no—
419C2×C3—161no—
420C2×C3#504011yescharacteristic
421C2×C3#515611yescharacteristic
422C2×C3#520111yescharacteristic
423C2×C3C3×#44711yescharacteristic
424C2×C3C3×#44811yescharacteristic
425C2×C3C3×#45411yescharacteristic
426C22—22no—
427C22—41no—
428C22—41no—
429C22—81no—
430C22—81no—
431C22—81no—
432C22C3×#93711yescharacteristic
433C4—21no—
434C4—41no—
435C4—62no—
436C4—121no—
437C4—122no—
438C4C3×D3×D811yescharacteristic
439C4C3×#91111yescharacteristic
440C4C2×C3×#21411yescharacteristic
441C4C3×#95111yescharacteristic
442C3—21no—
443C3#7101411yescharacteristic, direct product factor
444C3C3×#162711yescharacteristic, complemented
445C2—42no—
446C2—161no—
447C2C3×#504011yescharacteristic
448C2C3×#515611yescharacteristic
449C2C3×#520111yescharacteristic
subgroupG/H
centerC22×C3#937
commutator, cosocleC3×C42C23×C3
FrattiniC42C22×C3×D3
Fitting, prime radicalC32×#459C2
socleC22×C32#120
hypercenterC3×#459D3
hypocenterC3C3×#1627
LCSG ▷ C3×C42 ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#459

Complements

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

NH ≅ G/Ntype
1. C3×D4×Dic6C2semidirect
3. C3×#5075C2semidirect
4. C3×#5070C2semidirect
5. C3×D4⋊(C3⋊C8)C2semidirect
6. C3×#4486C2semidirect
7. C3×#4484C2semidirect
9. #71014C3direct (N × H)
28. D4×Dic6C2×C3semidirect
34. #5075C2×C3semidirect
35. #5070C2×C3semidirect
39. D4⋊(C3⋊C8)C2×C3semidirect
40. #4486C2×C3semidirect
41. #4484C2×C3semidirect
116. C32×D4SD16semidirect
131. C3×Dic6D8semidirect
267. C3×D4#214semidirect
268. C3×D4C3×SD16semidirect
299. Dic6C3×D8semidirect
383. C32#1627semidirect
397. D4C3×#214semidirect
443. C3#71014direct (N × H)
444. C3C3×#1627semidirect

Maximal subgroups

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

subgroupindex
C3×D4×Dic62
C32×#4592
C3×#50752
C3×#50702
C3×D4⋊(C3⋊C8)2
C3×#44862
C3×#44842
C3×#16273
#710143