Finite Group Databasebeta

← C3×#19076 #10637683

Subgroups — C3×#19076 #10637683

Order 768.

1000 conjugacy classes of subgroups.

The subgroup lattice has 486 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#3548C211yesmaximal, characteristic
2C3×#3165C211yesmaximal, characteristic, complemented
3C3×#3152C211yesmaximal, characteristic, complemented
4C3×#3141C211yesmaximal, characteristic, complemented
5C3×#1661C218yesmaximal, complemented
6C3×#1526C211yesmaximal, characteristic, complemented
7C3×#1525C211yesmaximal, characteristic, complemented
8C3×#1525C211yesmaximal, characteristic, complemented
9#19076C311yesmaximal, characteristic, direct product factor, Sylow
10C2×C3×#137—22no—
11C3×#562C2214yes—
12C3×#554—21no—
13C3×#554—21no—
14C3×#550—21no—
15C3×#550—21no—
16C3×#547—21no—
17C3×#547—21no—
18C3×#540—22no—
19C3×#537—22no—
20C3×#537—22no—
21C3×#533C2211yescharacteristic
22C3×#532C2211yescharacteristic
23C3×#532C2211yescharacteristic
24C2×C3×C4⋊Q8C2211yescharacteristic
25C3×#501C2214yes—
26C3×#500—21no—
27C3×#498—21no—
28C3×#497C2214yes—
29C3×#494—21no—
30C3×#492—21no—
31C3×#489C2214yes—
32C3×#487—21no—
33C3×#486—21no—
34C3×#428—22no—
35C3×#417—22no—
36C3×C4×M16C2211yescharacteristic
37C3×C4×M16C2211yescharacteristic
38C3×C4×M16C2211yescharacteristic
39C3×#330C2214yes—
40C3×#329C2214yes—
41C3×#329C2214yes—
42#3548C2×C311yescharacteristic
43#3165C2×C311yescharacteristic, complemented
44#3152C2×C311yescharacteristic, complemented
45#3141C2×C311yescharacteristic, complemented
46#1661C2×C318yescomplemented
47#1526C2×C311yescharacteristic, complemented
48#1525C2×C311yescharacteristic, complemented
49#1525C2×C311yescharacteristic, complemented
50C2×C3×#41—22no—
51C2×C3×#41—22no—
52C2×C3×#41D412yes—
53C2×C3×#41D412yes—
54C22×C3×Q8—21no—
55C3×#137—48no—
56C2×C3×Q16—24no—
57C2×C3×SD16—24no—
58C2×C3×M16—21no—
59C2×C3×M16—21no—
60C2×C3×M16—21no—
61C3×C4⋊Q8—21no—
62C3×C4⋊Q8—21no—
63C3×C4⋊Q8—21no—
64C3×C4⋊Q8D411yescharacteristic
65C3×C4⋊Q8D411yescharacteristic
66C3×C4⋊Q8D411yescharacteristic
67C3×C4⋊Q8D411yescharacteristic
68C3×C4⋊Q8C2312yes—
69C3×#127—22no—
70C3×#127D411yescharacteristic
71C3×#127D411yescharacteristic
72C3×#125—22no—
73C3×#125C2312yes—
74C3×#124C2312yes—
75C3×#124C2312yes—
76C3×#123—24no—
77C3×#123—24no—
78C3×C22⋊Q8—22no—
79C3×C22⋊Q8—22no—
80C3×C22⋊Q8—24no—
81C3×C22⋊Q8—24no—
82C3×C22⋊Q8—21no—
83C3×C22⋊Q8—21no—
84C3×#121—24no—
85C3×#121—24no—
86C3×#121—22no—
87C3×#121—22no—
88C3×#121—24no—
89C3×#121—24no—
90C3×#121—21no—
91C3×#121—21no—
92C3×#121—21no—
93C3×#121—21no—
94C3×C4×Q8—21no—
95C3×C4×Q8—21no—
96C3×C4×D4—22no—
97C3×C4×D4—22no—
98C3×C4×D4—21no—
99C3×C4×D4—21no—
100C3×C4×D4—21no—
101C3×C4×D4—21no—
102C3×#117D412yes—
103C2×C3×C4⋊C4—22no—
104C2×C3×C4⋊C4—22no—
105C2×C3×C4⋊C4—21no—
106C2×C3×C4⋊C4—21no—
107C2×C3×C42C2311yescharacteristic
108C3×#107—24no—
109C3×#106—24no—
110C3×#103—24no—
111C3×#102—24no—
112C3×#97C2312yes—
113C3×#97C2312yes—
114C3×#97C2312yes—
115C3×C4×C8—21no—
116C3×C4×C8—21no—
117C3×C4×C8—21no—
118C2×#137—22no—
119#562C22×C314yes—
120#554—21no—
121#554—21no—
122#550—21no—
123#550—21no—
124#547—21no—
125#547—21no—
126#540—22no—
127#537—22no—
128#537—22no—
129#533C22×C311yescharacteristic
130#532C22×C311yescharacteristic
131#532C22×C311yescharacteristic
132C2×C4⋊Q8C22×C311yescharacteristic
133#501C22×C314yes—
134#500—21no—
135#498—21no—
136#497C22×C314yes—
137#494—21no—
138#492—21no—
139#489C22×C314yes—
140#487—21no—
141#486—21no—
142#428—22no—
143#417—22no—
144C4×M16C22×C311yescharacteristic
145C4×M16C22×C311yescharacteristic
146C4×M16C22×C311yescharacteristic
147#330C22×C314yes—
148#329C22×C314yes—
149#329C22×C314yes—
150C3×#41—44no—
151C3×#41—44no—
152C3×#41—84no—
153C3×#41—84no—
154C2×C3×Q8—21no—
155C2×C3×Q8—21no—
156C2×C3×Q8—22no—
157C2×C3×Q8—44no—
158C2×C3×Q8—41no—
159C2×C3×Q8C2×D412yes—
160C2×C3×Q8C2×D412yes—
161C2×C3×D4—24no—
162C2×C3×D4—24no—
163C2×C3×D4—22no—
164C2×C3×D4—22no—
165C2×C3×D4—21no—
166C2×C3×D4—21no—
167C2×C3×D4—21no—
168C2×C3×D4—21no—
169C2×C3×D4C2×D412yes—
170C2×C3×D4C2×D412yes—
171C22×C3×C4—24no—
172C22×C3×C4—24no—
173C22×C3×C4—22no—
174C22×C3×C4—22no—
175C22×C3×C4—41no—
176C22×C3×C4C2×D411yescharacteristic
177C22×C3×C4C2×D411yescharacteristic
178C22×C3×C4C2×D411yescharacteristic
179C3×Q16—48no—
180C3×SD16—48no—
181C3×M16—24no—
182C3×M16—24no—
183C3×M16—42no—
184C2×C3×C8—22no—
185C2×C3×C8—22no—
186C2×C3×C8—22no—
187C3×C4⋊C4—24no—
188C3×C4⋊C4—24no—
189C3×C4⋊C4—21no—
190C3×C4⋊C4—21no—
191C3×C4⋊C4—21no—
192C3×C4⋊C4—21no—
193C3×C4⋊C4—21no—
194C3×C4⋊C4—21no—
195C3×C4⋊C4—22no—
196C3×C4⋊C4—22no—
197C3×C4⋊C4—22no—
198C3×C4⋊C4—22no—
199C3×C4⋊C4—41no—
200C3×C4⋊C4—41no—
201C3×C4⋊C4C2×D412yes—
202C3×C4⋊C4C2×D412yes—
203C3×C22⋊C4—24no—
204C3×C22⋊C4—24no—
205C3×C22⋊C4—22no—
206C3×C22⋊C4—22no—
207C3×C22⋊C4—22no—
208C3×C22⋊C4—22no—
209C3×C22⋊C4—22no—
210C3×C42—22no—
211C3×C42C2×D411yescharacteristic
212C3×C42C2×D411yescharacteristic
213C3×C42C2×D411yescharacteristic
214C3×C42C2411yescharacteristic
215C2×#41—22no—
216C2×#41—22no—
217C2×#41C3×D412yes—
218C2×#41C3×D412yes—
219C22×Q8—21no—
220#137—48no—
221C2×Q16—24no—
222C2×SD16—24no—
223C2×M16—21no—
224C2×M16—21no—
225C2×M16—21no—
226C4⋊Q8—21no—
227C4⋊Q8—21no—
228C4⋊Q8—21no—
229C4⋊Q8C3×D411yescharacteristic
230C4⋊Q8C3×D411yescharacteristic
231C4⋊Q8C3×D411yescharacteristic
232C4⋊Q8C3×D411yescharacteristic
233C4⋊Q8C23×C312yes—
234#127—22no—
235#127C3×D411yescharacteristic
236#127C3×D411yescharacteristic
237#125—22no—
238#125C23×C312yes—
239#124C23×C312yes—
240#124C23×C312yes—
241#123—24no—
242#123—24no—
243C22⋊Q8—22no—
244C22⋊Q8—22no—
245C22⋊Q8—24no—
246C22⋊Q8—24no—
247C22⋊Q8—21no—
248C22⋊Q8—21no—
249#121—24no—
250#121—24no—
251#121—22no—
252#121—22no—
253#121—24no—
254#121—24no—
255#121—21no—
256#121—21no—
257#121—21no—
258#121—21no—
259C4×Q8—21no—
260C4×Q8—21no—
261C4×D4—22no—
262C4×D4—22no—
263C4×D4—21no—
264C4×D4—21no—
265C4×D4—21no—
266C4×D4—21no—
267#117C3×D412yes—
268C2×C4⋊C4—22no—
269C2×C4⋊C4—22no—
270C2×C4⋊C4—21no—
271C2×C4⋊C4—21no—
272C2×C42C23×C311yescharacteristic
273#107—24no—
274#106—24no—
275#103—24no—
276#102—24no—
277#97C23×C312yes—
278#97C23×C312yes—
279#97C23×C312yes—
280C4×C8—21no—
281C4×C8—21no—
282C4×C8—21no—
283C23×C3—22no—
284C23×C3—22no—
285C23×C3#12011yescharacteristic
286C3×Q8—42no—
287C3×Q8—42no—
288C3×Q8—44no—
289C3×Q8—42no—
290C3×Q8—42no—
291C3×Q8—82no—
292C3×D4—42no—
293C3×D4—42no—
294C3×D4—42no—
295C3×D4—42no—
296C3×D4—42no—
297C3×D4—42no—
298C3×D4—82no—
299C3×D4—82no—
300C3×D4—84no—
301C3×D4—84no—
302C2×C3×C4—22no—
303C2×C3×C4—22no—
304C2×C3×C4—22no—
305C2×C3×C4—22no—
306C2×C3×C4—22no—
307C2×C3×C4—22no—
308C2×C3×C4—22no—
309C2×C3×C4—44no—
310C2×C3×C4—44no—
311C2×C3×C4—42no—
312C2×C3×C4—84no—
313C2×C3×C4—84no—
314C2×C3×C4—82no—
315C2×C3×C4#12011yescharacteristic
316C2×C3×C4#12011yescharacteristic
317C2×C3×C4#12011yescharacteristic
318C2×C3×C4C22×D411yescharacteristic
319C2×C3×C4C22×D411yescharacteristic
320C2×C3×C4C22×D411yescharacteristic
321C3×C8—24no—
322C3×C8—24no—
323C3×C8—42no—
324#41—44no—
325#41—44no—
326#41—84no—
327#41—84no—
328C2×Q8—21no—
329C2×Q8—21no—
330C2×Q8—22no—
331C2×Q8—44no—
332C2×Q8—41no—
333C2×Q8C2×C3×D412yes—
334C2×Q8C2×C3×D412yes—
335C2×D4—24no—
336C2×D4—24no—
337C2×D4—22no—
338C2×D4—22no—
339C2×D4—21no—
340C2×D4—21no—
341C2×D4—21no—
342C2×D4—21no—
343C2×D4C2×C3×D412yes—
344C2×D4C2×C3×D412yes—
345C22×C4—24no—
346C22×C4—24no—
347C22×C4—22no—
348C22×C4—22no—
349C22×C4—41no—
350C22×C4C2×C3×D411yescharacteristic
351C22×C4C2×C3×D411yescharacteristic
352C22×C4C2×C3×D411yescharacteristic
353Q16—48no—
354SD16—48no—
355M16—24no—
356M16—24no—
357M16—42no—
358C2×C8—22no—
359C2×C8—22no—
360C2×C8—22no—
361C4⋊C4—24no—
362C4⋊C4—24no—
363C4⋊C4—21no—
364C4⋊C4—21no—
365C4⋊C4—21no—
366C4⋊C4—21no—
367C4⋊C4—21no—
368C4⋊C4—21no—
369C4⋊C4—22no—
370C4⋊C4—22no—
371C4⋊C4—22no—
372C4⋊C4—22no—
373C4⋊C4—41no—
374C4⋊C4—41no—
375C4⋊C4C2×C3×D412yes—
376C4⋊C4C2×C3×D412yes—
377C22⋊C4—24no—
378C22⋊C4—24no—
379C22⋊C4—22no—
380C22⋊C4—22no—
381C22⋊C4—22no—
382C22⋊C4—22no—
383C22⋊C4—22no—
384C42—22no—
385C42C2×C3×D411yescharacteristic
386C42C2×C3×D411yescharacteristic
387C42C2×C3×D411yescharacteristic
388C42C24×C311yescharacteristic
389C22×C3—21no—
390C22×C3—21no—
391C22×C3—21no—
392C22×C3—42no—
393C22×C3—42no—
394C22×C3—42no—
395C22×C3—42no—
396C22×C3—42no—
397C22×C3—42no—
398C22×C3C2×#12011yescharacteristic
399C3×C4—21no—
400C3×C4—21no—
401C3×C4—21no—
402C3×C4—42no—
403C3×C4—42no—
404C3×C4—42no—
405C3×C4—42no—
406C3×C4—82no—
407C3×C4#45312yes—
408C3×C4#45512yes—
409C3×C4#45612yes—
410C23—22no—
411C23—22no—
412C23C3×#12011yescharacteristic
413Q8—42no—
414Q8—42no—
415Q8—44no—
416Q8—42no—
417Q8—42no—
418Q8—82no—
419D4—42no—
420D4—42no—
421D4—42no—
422D4—42no—
423D4—42no—
424D4—42no—
425D4—82no—
426D4—82no—
427D4—84no—
428D4—84no—
429C2×C4—22no—
430C2×C4—22no—
431C2×C4—22no—
432C2×C4—22no—
433C2×C4—22no—
434C2×C4—22no—
435C2×C4—22no—
436C2×C4—44no—
437C2×C4—44no—
438C2×C4—42no—
439C2×C4—84no—
440C2×C4—84no—
441C2×C4—82no—
442C2×C4C3×#12011yescharacteristic
443C2×C4C3×#12011yescharacteristic
444C2×C4C3×#12011yescharacteristic
445C2×C4C22×C3×D411yescharacteristic
446C2×C4C22×C3×D411yescharacteristic
447C2×C4C22×C3×D411yescharacteristic
448C8—24no—
449C8—24no—
450C8—42no—
451C2×C3—41no—
452C2×C3—82no—
453C2×C3—82no—
454C2×C3C2×#45311yescharacteristic
455C2×C3C2×#45511yescharacteristic
456C2×C3C2×#45611yescharacteristic
457C22—21no—
458C22—21no—
459C22—21no—
460C22—42no—
461C22—42no—
462C22—42no—
463C22—42no—
464C22—42no—
465C22—42no—
466C22C2×C3×#12011yescharacteristic
467C4—21no—
468C4—21no—
469C4—21no—
470C4—42no—
471C4—42no—
472C4—42no—
473C4—42no—
474C4—82no—
475C4C3×#45312yes—
476C4C3×#45512yes—
477C4C3×#45612yes—
478C3#1907611yescharacteristic, direct product factor, Sylow
479C2—41no—
480C2—82no—
481C2—82no—
482C2C2×C3×#45311yescharacteristic
483C2C2×C3×#45511yescharacteristic
484C2C2×C3×#45611yescharacteristic
subgroupG/H
center, socleC22×C3C2×#120
commutator, Frattini, cosocleC42C24×C3
prime radicalC3×#3548C2
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
2. C3×#3165C2semidirect
3. C3×#3152C2semidirect
4. C3×#3141C2semidirect
5. C3×#1661C2semidirect
6. C3×#1526C2semidirect
7. C3×#1525C2semidirect
8. C3×#1525C2semidirect
9. #19076C3direct (N × H)
43. #3165C2×C3semidirect
44. #3152C2×C3semidirect
45. #3141C2×C3semidirect
46. #1661C2×C3semidirect
47. #1526C2×C3semidirect
48. #1525C2×C3semidirect
49. #1525C2×C3semidirect
478. C3#19076direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#35482
C3×#31652
C3×#31522
C3×#31412
C3×#16612
C3×#15262
C3×#15252
#190763