Finite Group Databasebeta

← C3×#29679 #10648286

Subgroups — C3×#29679 #10648286

Order 768.

1106 conjugacy classes of subgroups.

The subgroup lattice has 482 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#3461C211yesmaximal, characteristic, complemented
2C3×#3038C212yesmaximal, complemented
3C3×#2548C211yesmaximal, characteristic, complemented
4C3×#2027C212yesmaximal, complemented
5C3×#2006C212yesmaximal, complemented
6C3×#2003C214yesmaximal, complemented
7C3×#1806C212yesmaximal, complemented
8C3×#1801C211yesmaximal, characteristic, complemented
9#29679C311yesmaximal, characteristic, direct product factor, Sylow
10C2×C3×AGL(1,ℤ/8)C2214yes—
11C3×#544C2211yescharacteristic
12C3×#542—22no—
13C3×#541—22no—
14C3×#539—22no—
15C3×#537C2211yescharacteristic
16C3×#536C2212yes—
17C3×#533—22no—
18C2×C3×#127C2211yescharacteristic
19C3×#529—22no—
20C3×#529—22no—
21C2×C3×#124C2212yes—
22C3×C4×#41C2212yes—
23C2×C3×C4×Q8C2211yescharacteristic
24C3×#460—22no—
25C3×#460—22no—
26C3×#459—22no—
27C3×#459—22no—
28C3×#423C2212yes—
29C2×C3×#104C2214yes—
30C3×#418C2214yes—
31C2×C3×#101C2212yes—
32C3×#394—22no—
33C3×#390—22no—
34C3×#390C2212yes—
35C3×C4×C4⋊C4C2211yescharacteristic
36C3×#343C2212yes—
37C3×#339C2214yes—
38#3461C2×C311yescharacteristic, complemented
39#3038C2×C312yescomplemented
40#2548C2×C311yescharacteristic, complemented
41#2027C2×C312yescomplemented
42#2006C2×C312yescomplemented
43#2003C2×C314yescomplemented
44#1806C2×C312yescomplemented
45#1801C2×C311yescharacteristic, complemented
46C2×C3×#41C2312yes—
47C22×C3×Q8C2311yescharacteristic
48C22×C3×D4—21no—
49C22×C3×D4—21no—
50C22×C3×D4C2312yes—
51C3×AGL(1,ℤ/8)—44no—
52C3×AGL(1,ℤ/8)—44no—
53C2×C3×SD16—24no—
54C2×C3×D8—24no—
55C2×C3×M16C2314yes—
56C3×C4⋊Q8—22no—
57C3×C4⋊Q8—22no—
58C3×#127—22no—
59C3×#127—22no—
60C3×#126—24no—
61C3×#126—24no—
62C3×#125—22no—
63C3×#125—24no—
64C3×#125—22no—
65C3×#124—22no—
66C3×#124—22no—
67C3×#124—44no—
68C3×#123—24no—
69C3×#123—24no—
70C3×C22⋊Q8—24no—
71C3×C22⋊Q8—22no—
72C3×C22⋊Q8—22no—
73C3×C22⋊Q8—22no—
74C3×C22⋊Q8—22no—
75C3×#121—22no—
76C3×#121—22no—
77C3×C4×Q8—22no—
78C3×C4×Q8—22no—
79C3×C4×Q8—22no—
80C3×C4×Q8D412yes—
81C3×C4×Q8D412yes—
82C3×C4×D4—22no—
83C3×C4×D4—22no—
84C3×C4×D4—22no—
85C3×C4×D4D412yes—
86C3×C4×D4D412yes—
87C3×#117—24no—
88C3×#117—22no—
89C3×#117C2312yes—
90C2×C3×C4⋊C4—21no—
91C2×C3×C4⋊C4D412yes—
92C2×C3×C4⋊C4C2311yescharacteristic
93C2×C3×C22⋊C4—24no—
94C2×C3×C22⋊C4—24no—
95C2×C3×C42—22no—
96C2×C3×C42D412yes—
97C2×C3×C42C2312yes—
98C2×C3×C42C2311yescharacteristic
99C3×C4⋊C8—22no—
100C3×C4⋊C8—22no—
101C3×#104—44no—
102C3×#102—24no—
103C3×#102—24no—
104C3×#101—42no—
105C3×#95—21no—
106C2×AGL(1,ℤ/8)C22×C314yes—
107#544C22×C311yescharacteristic
108#542—22no—
109#541—22no—
110#539—22no—
111#537C22×C311yescharacteristic
112#536C22×C312yes—
113#533—22no—
114C2×#127C22×C311yescharacteristic
115#529—22no—
116#529—22no—
117C2×#124C22×C312yes—
118C4×#41C22×C312yes—
119C2×C4×Q8C22×C311yescharacteristic
120#460—22no—
121#460—22no—
122#459—22no—
123#459—22no—
124#423C22×C312yes—
125C2×#104C22×C314yes—
126#418C22×C314yes—
127C2×#101C22×C312yes—
128#394—22no—
129#390—22no—
130#390C22×C312yes—
131C4×C4⋊C4C22×C311yescharacteristic
132#343C22×C312yes—
133#339C22×C314yes—
134C24×C3—22no—
135C3×#41—22no—
136C3×#41—22no—
137C3×#41—22no—
138C3×#41—22no—
139C2×C3×Q8—22no—
140C2×C3×Q8—22no—
141C2×C3×Q8—21no—
142C2×C3×Q8—22no—
143C2×C3×Q8—21no—
144C2×C3×Q8C2×D412yes—
145C2×C3×D4—22no—
146C2×C3×D4—22no—
147C2×C3×D4—24no—
148C2×C3×D4—24no—
149C2×C3×D4—22no—
150C2×C3×D4—22no—
151C2×C3×D4—44no—
152C2×C3×D4—41no—
153C2×C3×D4—42no—
154C2×C3×D4—41no—
155C2×C3×D4—82no—
156C2×C3×D4C2×D412yes—
157C22×C3×C4—22no—
158C22×C3×C4—22no—
159C22×C3×C4—22no—
160C22×C3×C4—22no—
161C22×C3×C4C2×D412yes—
162C22×C3×C4C2×D411yescharacteristic
163C22×C3×C4C2×D412yes—
164C22×C3×C4C2×D411yescharacteristic
165C22×C3×C4C2411yescharacteristic
166C3×SD16—48no—
167C3×D8—48no—
168C3×M16—24no—
169C3×M16—24no—
170C2×C3×C8—24no—
171C3×C4⋊C4—24no—
172C3×C4⋊C4—24no—
173C3×C4⋊C4—22no—
174C3×C4⋊C4—22no—
175C3×C4⋊C4—24no—
176C3×C4⋊C4—24no—
177C3×C4⋊C4—22no—
178C3×C4⋊C4—22no—
179C3×C4⋊C4—22no—
180C3×C4⋊C4—42no—
181C3×C4⋊C4C2×D412yes—
182C3×C4⋊C4C2×D412yes—
183C3×C22⋊C4—24no—
184C3×C22⋊C4—24no—
185C3×C22⋊C4—24no—
186C3×C22⋊C4—22no—
187C3×C22⋊C4—22no—
188C3×C22⋊C4—22no—
189C3×C22⋊C4—48no—
190C3×C22⋊C4—84no—
191C3×C42—22no—
192C3×C42—22no—
193C3×C42—22no—
194C3×C42—22no—
195C3×C42—22no—
196C3×C42—24no—
197C3×C42C2×D412yes—
198C3×C42C2×D412yes—
199C2×#41C23×C312yes—
200C22×Q8C23×C311yescharacteristic
201C22×D4—21no—
202C22×D4—21no—
203C22×D4C23×C312yes—
204AGL(1,ℤ/8)—44no—
205AGL(1,ℤ/8)—44no—
206C2×SD16—24no—
207C2×D8—24no—
208C2×M16C23×C314yes—
209C4⋊Q8—22no—
210C4⋊Q8—22no—
211#127—22no—
212#127—22no—
213#126—24no—
214#126—24no—
215#125—22no—
216#125—24no—
217#125—22no—
218#124—22no—
219#124—22no—
220#124—44no—
221#123—24no—
222#123—24no—
223C22⋊Q8—24no—
224C22⋊Q8—22no—
225C22⋊Q8—22no—
226C22⋊Q8—22no—
227C22⋊Q8—22no—
228#121—22no—
229#121—22no—
230C4×Q8—22no—
231C4×Q8—22no—
232C4×Q8—22no—
233C4×Q8C3×D412yes—
234C4×Q8C3×D412yes—
235C4×D4—22no—
236C4×D4—22no—
237C4×D4—22no—
238C4×D4C3×D412yes—
239C4×D4C3×D412yes—
240#117—24no—
241#117—22no—
242#117C23×C312yes—
243C2×C4⋊C4—21no—
244C2×C4⋊C4C3×D412yes—
245C2×C4⋊C4C23×C311yescharacteristic
246C2×C22⋊C4—24no—
247C2×C22⋊C4—24no—
248C2×C42—22no—
249C2×C42C3×D412yes—
250C2×C42C23×C312yes—
251C2×C42C23×C311yescharacteristic
252C4⋊C8—22no—
253C4⋊C8—22no—
254#104—44no—
255#102—24no—
256#102—24no—
257#101—42no—
258#95—21no—
259C23×C3—22no—
260C23×C3—44no—
261C23×C3—44no—
262C23×C3—42no—
263C23×C3—42no—
264C23×C3—42no—
265C23×C3C22×D411yescharacteristic
266C3×Q8—22no—
267C3×Q8—22no—
268C3×Q8—42no—
269C3×Q8—42no—
270C3×Q8—82no—
271C3×D4—22no—
272C3×D4—22no—
273C3×D4—42no—
274C3×D4—42no—
275C3×D4—44no—
276C3×D4—44no—
277C3×D4—82no—
278C3×D4—84no—
279C3×D4—82no—
280C3×D4—82no—
281C2×C3×C4—22no—
282C2×C3×C4—22no—
283C2×C3×C4—22no—
284C2×C3×C4—22no—
285C2×C3×C4—22no—
286C2×C3×C4—22no—
287C2×C3×C4—22no—
288C2×C3×C4—22no—
289C2×C3×C4—41no—
290C2×C3×C4—42no—
291C2×C3×C4—42no—
292C2×C3×C4—44no—
293C2×C3×C4—42no—
294C2×C3×C4—42no—
295C2×C3×C4—42no—
296C2×C3×C4—42no—
297C2×C3×C4—82no—
298C2×C3×C4#12011yescharacteristic
299C2×C3×C4#12012yes—
300C2×C3×C4#12011yescharacteristic
301C2×C3×C4C22×D412yes—
302C2×C3×C4H(5,𝔽2)11yescharacteristic
303C2×C3×C4H(5,𝔽2)12yes—
304C2×C3×C42−1+411yescharacteristic
305C3×C8—44no—
306C24—22no—
307#41—22no—
308#41—22no—
309#41—22no—
310#41—22no—
311C2×Q8—22no—
312C2×Q8—22no—
313C2×Q8—21no—
314C2×Q8—22no—
315C2×Q8—21no—
316C2×Q8C2×C3×D412yes—
317C2×D4—22no—
318C2×D4—22no—
319C2×D4—24no—
320C2×D4—24no—
321C2×D4—22no—
322C2×D4—22no—
323C2×D4—44no—
324C2×D4—41no—
325C2×D4—42no—
326C2×D4—41no—
327C2×D4—82no—
328C2×D4C2×C3×D412yes—
329C22×C4—22no—
330C22×C4—22no—
331C22×C4—22no—
332C22×C4—22no—
333C22×C4C2×C3×D412yes—
334C22×C4C2×C3×D411yescharacteristic
335C22×C4C2×C3×D412yes—
336C22×C4C2×C3×D411yescharacteristic
337C22×C4C24×C311yescharacteristic
338SD16—48no—
339D8—48no—
340M16—24no—
341M16—24no—
342C2×C8—24no—
343C4⋊C4—24no—
344C4⋊C4—24no—
345C4⋊C4—22no—
346C4⋊C4—22no—
347C4⋊C4—24no—
348C4⋊C4—24no—
349C4⋊C4—22no—
350C4⋊C4—22no—
351C4⋊C4—22no—
352C4⋊C4—42no—
353C4⋊C4C2×C3×D412yes—
354C4⋊C4C2×C3×D412yes—
355C22⋊C4—24no—
356C22⋊C4—24no—
357C22⋊C4—24no—
358C22⋊C4—22no—
359C22⋊C4—22no—
360C22⋊C4—22no—
361C22⋊C4—48no—
362C22⋊C4—84no—
363C42—22no—
364C42—22no—
365C42—22no—
366C42—22no—
367C42—22no—
368C42—24no—
369C42C2×C3×D412yes—
370C42C2×C3×D412yes—
371C22×C3—21no—
372C22×C3—21no—
373C22×C3—42no—
374C22×C3—42no—
375C22×C3—42no—
376C22×C3—84no—
377C22×C3—84no—
378C22×C3—82no—
379C22×C3—82no—
380C22×C3—82no—
381C22×C3C2×#12011yescharacteristic
382C22×C3#53511yescharacteristic
383C22×C3#53711yescharacteristic
384C3×C4—21no—
385C3×C4—22no—
386C3×C4—42no—
387C3×C4—42no—
388C3×C4—42no—
389C3×C4—42no—
390C3×C4—42no—
391C3×C4—82no—
392C3×C4#45412yes—
393C3×C4#53512yes—
394C3×C4#53712yes—
395C23—22no—
396C23—44no—
397C23—44no—
398C23—42no—
399C23—42no—
400C23—42no—
401C23C22×C3×D411yescharacteristic
402Q8—22no—
403Q8—22no—
404Q8—42no—
405Q8—42no—
406Q8—82no—
407D4—22no—
408D4—22no—
409D4—42no—
410D4—42no—
411D4—44no—
412D4—44no—
413D4—82no—
414D4—84no—
415D4—82no—
416D4—82no—
417C2×C4—22no—
418C2×C4—22no—
419C2×C4—22no—
420C2×C4—22no—
421C2×C4—22no—
422C2×C4—22no—
423C2×C4—22no—
424C2×C4—22no—
425C2×C4—41no—
426C2×C4—44no—
427C2×C4—42no—
428C2×C4—42no—
429C2×C4—42no—
430C2×C4—42no—
431C2×C4—42no—
432C2×C4—42no—
433C2×C4—82no—
434C2×C4C3×#12011yescharacteristic
435C2×C4C3×#12012yes—
436C2×C4C3×#12011yescharacteristic
437C2×C4C22×C3×D412yes—
438C2×C4C3×H(5,𝔽2)11yescharacteristic
439C2×C4C3×H(5,𝔽2)12yes—
440C2×C4C3×2−1+411yescharacteristic
441C8—44no—
442C2×C3—21no—
443C2×C3—21no—
444C2×C3—82no—
445C2×C3—162no—
446C2×C3#261511yescharacteristic
447C2×C3C2×#45411yescharacteristic
448C2×C3#302111yescharacteristic
449C22—21no—
450C22—21no—
451C22—42no—
452C22—42no—
453C22—42no—
454C22—84no—
455C22—84no—
456C22—82no—
457C22—82no—
458C22—82no—
459C22C2×C3×#12011yescharacteristic
460C22C3×#53511yescharacteristic
461C22C3×#53711yescharacteristic
462C4—21no—
463C4—22no—
464C4—42no—
465C4—42no—
466C4—42no—
467C4—42no—
468C4—42no—
469C4—82no—
470C4C3×#45412yes—
471C4C3×#53512yes—
472C4C3×#53712yes—
473C3#2967911yescharacteristic, direct product factor, Sylow
474C2—21no—
475C2—21no—
476C2—82no—
477C2—162no—
478C2C3×#261511yescharacteristic
479C2C2×C3×#45411yescharacteristic
480C2C3×#302111yescharacteristic
subgroupG/H
center, socleC22×C3C2×#120
commutator, Frattini, cosocleC22×C4C24×C3
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C3 ◁ C2×C3×C42 ◁ G

Complements

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

NH ≅ G/Ntype
1. C3×#3461C2semidirect
2. C3×#3038C2semidirect
3. C3×#2548C2semidirect
4. C3×#2027C2semidirect
5. C3×#2006C2semidirect
6. C3×#2003C2semidirect
7. C3×#1806C2semidirect
8. C3×#1801C2semidirect
9. #29679C3direct (N × H)
38. #3461C2×C3semidirect
39. #3038C2×C3semidirect
40. #2548C2×C3semidirect
41. #2027C2×C3semidirect
42. #2006C2×C3semidirect
43. #2003C2×C3semidirect
44. #1806C2×C3semidirect
45. #1801C2×C3semidirect
473. C3#29679direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#34612
C3×#30382
C3×#25482
C3×#20272
C3×#20062
C3×#20032
C3×#18062
C3×#18012
#296793