Finite Group Databasebeta

← C3×#19082 #10637689

Subgroups — C3×#19082 #10637689

Order 768.

864 conjugacy classes of subgroups.

The subgroup lattice has 474 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#3553C211yesmaximal, characteristic, complemented
2C3×#3180C212yesmaximal, complemented
3C3×#3142C211yesmaximal, characteristic, complemented
4C3×#1664C212yesmaximal, complemented
5C3×#1663C211yesmaximal, characteristic, complemented
6C3×#1662C211yesmaximal, characteristic, complemented
7C3×#1658C211yesmaximal, characteristic, complemented
8C3×#1657C212yesmaximal, complemented
9C3×#1656C211yesmaximal, characteristic, complemented
10C3×#1524C212yesmaximal, complemented
11C2×C3×#330C211yesmaximal, characteristic, complemented
12#19082C311yesmaximal, characteristic, direct product factor, Sylow
13C3×#564C2211yescharacteristic
14C3×#563C2212yes—
15C3×#562C2211yescharacteristic
16C3×#554—22no—
17C3×#553—22no—
18C3×#552—22no—
19C3×#541—22no—
20C3×#539—22no—
21C3×#539—22no—
22C3×#532C2211yescharacteristic
23C3×#529C2212yes—
24C2×C3×#125C2211yescharacteristic
25C3×#501C2212yes—
26C3×#496C2212yes—
27C3×#491C2211yescharacteristic
28C3×#491C2211yescharacteristic
29C3×#490C2211yescharacteristic
30C3×#490C2211yescharacteristic
31C3×#490C2212yes—
32C3×#489C2212yes—
33C3×#488—22no—
34C3×#466—22no—
35C3×#465—22no—
36C3×#442—22no—
37C3×#440—22no—
38C3×#417—22no—
39C3×C4×M16C2211yescharacteristic
40C2×C3×#97C2212yes—
41C3×#330C2211yescharacteristic
42C3×#330C2212yes—
43C3×#330C2211yescharacteristic
44C3×#330C2212yes—
45C3×#330C2212yes—
46C3×#329C2212yes—
47C3×#329C2212yes—
48#3553C2×C311yescharacteristic, complemented
49#3180C2×C312yescomplemented
50#3142C2×C311yescharacteristic, complemented
51#1664C2×C312yescomplemented
52#1663C2×C311yescharacteristic, complemented
53#1662C2×C311yescharacteristic, complemented
54#1658C2×C311yescharacteristic, complemented
55#1657C2×C312yescomplemented
56#1656C2×C311yescharacteristic, complemented
57#1524C2×C312yescomplemented
58C2×#330C2×C311yescharacteristic, complemented
59C2×C3×#41—21no—
60C2×C3×SD16—22no—
61C2×C3×D8—22no—
62C2×C3×M16—21no—
63C22×C3×C8—22no—
64C3×C4⋊Q8—22no—
65C3×C4⋊Q8C2311yescharacteristic
66C3×#127C2311yescharacteristic
67C3×#126—22no—
68C3×#126—22no—
69C3×#126—22no—
70C3×#126—22no—
71C3×#126—22no—
72C3×#125—22no—
73C3×#125—22no—
74C3×#125—22no—
75C3×#125—22no—
76C3×#125—22no—
77C3×#125—22no—
78C3×#125D412yes—
79C3×#125C2311yescharacteristic
80C3×#125C2311yescharacteristic
81C3×#125C2312yes—
82C3×#124—21no—
83C3×#124C2312yes—
84C3×#123—22no—
85C3×#123—22no—
86C3×#123—22no—
87C3×#123—22no—
88C3×#123—22no—
89C3×C22⋊Q8—22no—
90C3×C22⋊Q8—22no—
91C3×C22⋊Q8—22no—
92C3×C22⋊Q8—22no—
93C3×C22⋊Q8—22no—
94C3×C22⋊Q8—22no—
95C3×C22⋊Q8D412yes—
96C3×#121—22no—
97C3×#121—22no—
98C3×#121—22no—
99C3×#121D412yes—
100C3×C4×Q8—22no—
101C3×C4×Q8D412yes—
102C3×C4×D4—22no—
103C3×C4×D4—22no—
104C3×C4×D4—22no—
105C3×C4×D4—22no—
106C3×C4×D4—22no—
107C3×C4×D4D412yes—
108C3×#117—22no—
109C3×#117—22no—
110C2×C3×C4⋊C4—22no—
111C2×C3×C4⋊C4—22no—
112C2×C3×C4⋊C4D412yes—
113C2×C3×C42C2311yescharacteristic
114C3×#107—22no—
115C3×#106—22no—
116C3×#103—22no—
117C3×#103—22no—
118C3×#103—22no—
119C3×#102—22no—
120C3×#102—22no—
121C3×#102—22no—
122C3×#102—22no—
123C3×#102—22no—
124C3×#97—22no—
125C3×#97C2312yes—
126C3×#97C2312yes—
127C3×#97C2311yescharacteristic
128C3×#97C2311yescharacteristic
129C3×C4×C8—21no—
130#564C22×C311yescharacteristic
131#563C22×C312yes—
132#562C22×C311yescharacteristic
133#554—22no—
134#553—22no—
135#552—22no—
136#541—22no—
137#539—22no—
138#539—22no—
139#532C22×C311yescharacteristic
140#529C22×C312yes—
141C2×#125C22×C311yescharacteristic
142#501C22×C312yes—
143#496C22×C312yes—
144#491C22×C311yescharacteristic
145#491C22×C311yescharacteristic
146#490C22×C311yescharacteristic
147#490C22×C311yescharacteristic
148#490C22×C312yes—
149#489C22×C312yes—
150#488—22no—
151#466—22no—
152#465—22no—
153#442—22no—
154#440—22no—
155#417—22no—
156C4×M16C22×C311yescharacteristic
157C2×#97C22×C312yes—
158#330C22×C311yescharacteristic
159#330C22×C312yes—
160#330C22×C312yes—
161#330C22×C311yescharacteristic
162#330C22×C312yes—
163#329C22×C312yes—
164#329C22×C312yes—
165C3×#41—44no—
166C2×C3×Q8—22no—
167C2×C3×Q8—21no—
168C2×C3×Q8C2×D412yes—
169C2×C3×D4—22no—
170C2×C3×D4—22no—
171C2×C3×D4—21no—
172C2×C3×D4—22no—
173C2×C3×D4—41no—
174C2×C3×D4C2×D412yes—
175C22×C3×C4—22no—
176C22×C3×C4—22no—
177C22×C3×C4—22no—
178C22×C3×C4—22no—
179C22×C3×C4—41no—
180C22×C3×C4C2×D411yescharacteristic
181C22×C3×C4C2×D412yes—
182C3×SD16—44no—
183C3×D8—44no—
184C3×M16—42no—
185C2×C3×C8—22no—
186C2×C3×C8—21no—
187C2×C3×C8—21no—
188C2×C3×C8—22no—
189C2×C3×C8—44no—
190C3×C4⋊C4—22no—
191C3×C4⋊C4—22no—
192C3×C4⋊C4—22no—
193C3×C4⋊C4—22no—
194C3×C4⋊C4—22no—
195C3×C4⋊C4—22no—
196C3×C4⋊C4—22no—
197C3×C4⋊C4—22no—
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⋊C4C2×D412yes—
207C3×C4⋊C4C2×D412yes—
208C3×C4⋊C4C2×D412yes—
209C3×C4⋊C4C2×D412yes—
210C3×C22⋊C4—22no—
211C3×C22⋊C4—22no—
212C3×C22⋊C4—22no—
213C3×C22⋊C4—22no—
214C3×C22⋊C4—22no—
215C3×C22⋊C4—22no—
216C3×C22⋊C4—22no—
217C3×C22⋊C4—22no—
218C3×C22⋊C4—22no—
219C3×C22⋊C4—42no—
220C3×C42—22no—
221C3×C42—22no—
222C3×C42—22no—
223C3×C42C2×D411yescharacteristic
224C3×C42C2×D412yes—
225C3×C42C2411yescharacteristic
226C2×#41—21no—
227C2×SD16—22no—
228C2×D8—22no—
229C2×M16—21no—
230C22×C8—22no—
231C4⋊Q8—22no—
232C4⋊Q8C23×C311yescharacteristic
233#127C23×C311yescharacteristic
234#126—22no—
235#126—22no—
236#126—22no—
237#126—22no—
238#126—22no—
239#125—22no—
240#125—22no—
241#125—22no—
242#125—22no—
243#125—22no—
244#125—22no—
245#125C3×D412yes—
246#125C23×C311yescharacteristic
247#125C23×C311yescharacteristic
248#125C23×C312yes—
249#124—21no—
250#124C23×C312yes—
251#123—22no—
252#123—22no—
253#123—22no—
254#123—22no—
255#123—22no—
256C22⋊Q8—22no—
257C22⋊Q8—22no—
258C22⋊Q8—22no—
259C22⋊Q8—22no—
260C22⋊Q8—22no—
261C22⋊Q8—22no—
262C22⋊Q8C3×D412yes—
263#121—22no—
264#121—22no—
265#121—22no—
266#121C3×D412yes—
267C4×Q8—22no—
268C4×Q8C3×D412yes—
269C4×D4—22no—
270C4×D4—22no—
271C4×D4—22no—
272C4×D4—22no—
273C4×D4—22no—
274C4×D4C3×D412yes—
275#117—22no—
276#117—22no—
277C2×C4⋊C4—22no—
278C2×C4⋊C4—22no—
279C2×C4⋊C4C3×D412yes—
280C2×C42C23×C311yescharacteristic
281#107—22no—
282#106—22no—
283#103—22no—
284#103—22no—
285#103—22no—
286#102—22no—
287#102—22no—
288#102—22no—
289#102—22no—
290#102—22no—
291#97—22no—
292#97C23×C311yescharacteristic
293#97C23×C311yescharacteristic
294#97C23×C312yes—
295#97C23×C312yes—
296C4×C8—21no—
297C23×C3—22no—
298C23×C3—41no—
299C23×C3#12011yescharacteristic
300C3×Q8—42no—
301C3×Q8—42no—
302C3×Q8—82no—
303C3×D4—42no—
304C3×D4—42no—
305C3×D4—42no—
306C3×D4—42no—
307C3×D4—44no—
308C3×D4—82no—
309C3×D4—82no—
310C2×C3×C4—22no—
311C2×C3×C4—22no—
312C2×C3×C4—22no—
313C2×C3×C4—22no—
314C2×C3×C4—22no—
315C2×C3×C4—22no—
316C2×C3×C4—42no—
317C2×C3×C4—41no—
318C2×C3×C4—82no—
319C2×C3×C4—82no—
320C2×C3×C4—82no—
321C2×C3×C4—82no—
322C2×C3×C4—82no—
323C2×C3×C4#12012yes—
324C2×C3×C4#12011yescharacteristic
325C2×C3×C4C22×D411yescharacteristic
326C2×C3×C4C22×D412yes—
327C3×C8—24no—
328C3×C8—42no—
329C3×C8—41no—
330C3×C8—41no—
331#41—44no—
332C2×Q8—22no—
333C2×Q8—21no—
334C2×Q8C2×C3×D412yes—
335C2×D4—22no—
336C2×D4—22no—
337C2×D4—21no—
338C2×D4—22no—
339C2×D4—41no—
340C2×D4C2×C3×D412yes—
341C22×C4—22no—
342C22×C4—22no—
343C22×C4—22no—
344C22×C4—22no—
345C22×C4—41no—
346C22×C4C2×C3×D411yescharacteristic
347C22×C4C2×C3×D412yes—
348SD16—44no—
349D8—44no—
350M16—42no—
351C2×C8—22no—
352C2×C8—21no—
353C2×C8—21no—
354C2×C8—22no—
355C2×C8—44no—
356C4⋊C4—22no—
357C4⋊C4—22no—
358C4⋊C4—22no—
359C4⋊C4—22no—
360C4⋊C4—22no—
361C4⋊C4—22no—
362C4⋊C4—22no—
363C4⋊C4—22no—
364C4⋊C4—22no—
365C4⋊C4—22no—
366C4⋊C4—22no—
367C4⋊C4—22no—
368C4⋊C4—22no—
369C4⋊C4—22no—
370C4⋊C4—22no—
371C4⋊C4—22no—
372C4⋊C4C2×C3×D412yes—
373C4⋊C4C2×C3×D412yes—
374C4⋊C4C2×C3×D412yes—
375C4⋊C4C2×C3×D412yes—
376C22⋊C4—22no—
377C22⋊C4—22no—
378C22⋊C4—22no—
379C22⋊C4—22no—
380C22⋊C4—22no—
381C22⋊C4—22no—
382C22⋊C4—22no—
383C22⋊C4—22no—
384C22⋊C4—22no—
385C22⋊C4—42no—
386C42—22no—
387C42—22no—
388C42—22no—
389C42C2×C3×D411yescharacteristic
390C42C2×C3×D412yes—
391C42C24×C311yescharacteristic
392C22×C3—22no—
393C22×C3—42no—
394C22×C3—42no—
395C22×C3—42no—
396C22×C3—81no—
397C22×C3—82no—
398C22×C3#45412yes—
399C22×C3C2×#12011yescharacteristic
400C3×C4—21no—
401C3×C4—21no—
402C3×C4—22no—
403C3×C4—22no—
404C3×C4—42no—
405C3×C4—42no—
406C3×C4—42no—
407C3×C4—42no—
408C3×C4—42no—
409C3×C4—81no—
410C23—22no—
411C23—41no—
412C23C3×#12011yescharacteristic
413Q8—42no—
414Q8—42no—
415Q8—82no—
416D4—42no—
417D4—42no—
418D4—42no—
419D4—42no—
420D4—44no—
421D4—82no—
422D4—82no—
423C2×C4—22no—
424C2×C4—22no—
425C2×C4—22no—
426C2×C4—22no—
427C2×C4—22no—
428C2×C4—22no—
429C2×C4—42no—
430C2×C4—41no—
431C2×C4—82no—
432C2×C4—82no—
433C2×C4—82no—
434C2×C4—82no—
435C2×C4—82no—
436C2×C4C3×#12012yes—
437C2×C4C3×#12011yescharacteristic
438C2×C4C22×C3×D411yescharacteristic
439C2×C4C22×C3×D412yes—
440C8—24no—
441C8—42no—
442C8—41no—
443C8—41no—
444C2×C3—22no—
445C2×C3—82no—
446C2×C3—161no—
447C2×C3C2×#45411yescharacteristic
448C2×C3#301812yes—
449C22—22no—
450C22—42no—
451C22—42no—
452C22—42no—
453C22—81no—
454C22—82no—
455C22C3×#45412yes—
456C22C2×C3×#12011yescharacteristic
457C4—21no—
458C4—21no—
459C4—22no—
460C4—22no—
461C4—42no—
462C4—42no—
463C4—42no—
464C4—42no—
465C4—42no—
466C4—81no—
467C3#1908211yescharacteristic, direct product factor, Sylow
468C2—22no—
469C2—82no—
470C2—161no—
471C2C2×C3×#45411yescharacteristic
472C2C3×#301812yes—
subgroupG/H
center, socleC22×C3C2×#120
commutator, Frattini, cosocleC42C24×C3
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C3 ◁ C2×C3×C42 ◁ G

Complements

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

NH ≅ G/Ntype
1. C3×#3553C2semidirect
2. C3×#3180C2semidirect
3. C3×#3142C2semidirect
4. C3×#1664C2semidirect
5. C3×#1663C2semidirect
6. C3×#1662C2semidirect
7. C3×#1658C2semidirect
8. C3×#1657C2semidirect
9. C3×#1656C2semidirect
10. C3×#1524C2semidirect
11. C2×C3×#330C2semidirect
12. #19082C3direct (N × H)
48. #3553C2×C3semidirect
49. #3180C2×C3semidirect
50. #3142C2×C3semidirect
51. #1664C2×C3semidirect
52. #1663C2×C3semidirect
53. #1662C2×C3semidirect
54. #1658C2×C3semidirect
55. #1657C2×C3semidirect
56. #1656C2×C3semidirect
57. #1524C2×C3semidirect
58. C2×#330C2×C3semidirect
467. C3#19082direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#35532
C3×#31802
C3×#31422
C3×#16642
C3×#16632
C3×#16622
C3×#16582
C3×#16572
C3×#16562
C3×#15242
C2×C3×#3302
#190823