Finite Group Databasebeta

← C3×#10062 #10628669

Subgroups — C3×#10062 #10628669

Order 768.

806 conjugacy classes of subgroups.

The subgroup lattice has 462 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#486C211yesmaximal, characteristic, complemented
2C2×C3×#461C211yesmaximal, characteristic, complemented
3C3×#2541C211yesmaximal, characteristic
4C3×#1988C211yesmaximal, characteristic, complemented
5C2×C3×#331C211yesmaximal, characteristic, complemented
6C2×C3×D4⋊C8C211yesmaximal, characteristic, complemented
7C3×#1279C211yesmaximal, characteristic, complemented
8#10062C311yesmaximal, characteristic, direct product factor, Sylow
9C22×C3×SD16—21no—
10C2×C3×C4⋊Q8C2211yescharacteristic
11C2×C3×#127—21no—
12C2×C3×#127C2211yescharacteristic
13C2×C3×#121—22no—
14C2×C3×C4×D4C2211yescharacteristic
15C3×#486—22no—
16C3×#486—22no—
17C3×#461—22no—
18C3×#461—22no—
19C2×C3×C4⋊C8C2211yescharacteristic
20C2×C3×C4⋊C8C2211yescharacteristic
21C2×C3×#103—21no—
22C2×C3×#102—22no—
23C2×C3×C4×C8C2211yescharacteristic
24C3×#392—22no—
25C3×#390—21no—
26C3×C4×C4⋊C4C2211yescharacteristic
27C3×#340—22no—
28C3×#331—22no—
29C3×D4⋊C8—22no—
30C2×#486C2×C311yescharacteristic, complemented
31C2×#461C2×C311yescharacteristic, complemented
32#2541C2×C311yescharacteristic
33#1988C2×C311yescharacteristic, complemented
34C2×#331C2×C311yescharacteristic, complemented
35C2×D4⋊C8C2×C311yescharacteristic, complemented
36#1279C2×C311yescharacteristic, complemented
37C22×C3×Q8—21no—
38C22×C3×D4—24no—
39C22×C3×D4—21no—
40C22×C3×D4—21no—
41C22×C3×D4D411yescharacteristic
42C22×C3×D4D412yes—
43C23×C3×C4—21no—
44C2×C3×SD16—24no—
45C2×C3×SD16—42no—
46C2×C3×SD16—42no—
47C22×C3×C8—21no—
48C22×C3×C8—21no—
49C22×C3×C8—21no—
50C3×C4⋊Q8—21no—
51C3×C4⋊Q8—21no—
52C3×C4⋊Q8—21no—
53C3×C4⋊Q8D412yescomplemented
54C3×#127—21no—
55C3×#127—21no—
56C3×#127—21no—
57C3×#127—21no—
58C3×#127—42no—
59C3×#127—42no—
60C3×#121—44no—
61C3×#121—44no—
62C3×C4×D4—21no—
63C3×C4×D4—21no—
64C3×C4×D4—21no—
65C3×C4×D4—21no—
66C2×C3×C4⋊C4—21no—
67C2×C3×C4⋊C4—21no—
68C2×C3×C4⋊C4D411yescharacteristic
69C2×C3×C4⋊C4D412yes—
70C2×C3×C22⋊C4—24no—
71C2×C3×C22⋊C4—21no—
72C2×C3×C42—21no—
73C2×C3×C42C2311yescharacteristic
74C3×C4⋊C8—21no—
75C3×C4⋊C8—21no—
76C3×C4⋊C8—21no—
77C3×C4⋊C8D412yescomplemented
78C3×#103—24no—
79C3×#102—28no—
80C3×C4×C8—21no—
81C3×C4×C8D412yescomplemented
82C3×#95—21no—
83C22×SD16—21no—
84C2×C4⋊Q8C22×C311yescharacteristic
85C2×#127—21no—
86C2×#127C22×C311yescharacteristic
87C2×#121—22no—
88C2×C4×D4C22×C311yescharacteristic
89#486—22no—
90#486—22no—
91#461—22no—
92#461—22no—
93C2×C4⋊C8C22×C311yescharacteristic
94C2×C4⋊C8C22×C311yescharacteristic
95C2×#103—21no—
96C2×#102—22no—
97C2×C4×C8C22×C311yescharacteristic
98#392—22no—
99#390—21no—
100C4×C4⋊C4C22×C311yescharacteristic
101#340—22no—
102#331—22no—
103D4⋊C8—22no—
104C24×C3—21no—
105C24×C3—22no—
106C2×C3×Q8—22no—
107C2×C3×Q8—41no—
108C2×C3×Q8—41no—
109C2×C3×Q8—41no—
110C2×C3×Q8—41no—
111C2×C3×Q8—41no—
112C2×C3×D4—21no—
113C2×C3×D4—22no—
114C2×C3×D4—21no—
115C2×C3×D4—22no—
116C2×C3×D4—21no—
117C2×C3×D4—21no—
118C2×C3×D4—21no—
119C2×C3×D4—44no—
120C2×C3×D4—48no—
121C2×C3×D4—48no—
122C2×C3×D4—41no—
123C2×C3×D4—41no—
124C2×C3×D4—41no—
125C2×C3×D4—41no—
126C2×C3×D4—41no—
127C2×C3×D4—42no—
128C2×C3×D4—41no—
129C2×C3×D4—42no—
130C2×C3×D4—41no—
131C2×C3×D4—41no—
132C2×C3×D4—84no—
133C2×C3×D4D812yes—
134C22×C3×C4—22no—
135C22×C3×C4—21no—
136C22×C3×C4—41no—
137C22×C3×C4—41no—
138C22×C3×C4—41no—
139C22×C3×C4—42no—
140C22×C3×C4—42no—
141C22×C3×C4C2×D411yescharacteristic
142C22×C3×C4C2×D411yescharacteristic
143C22×C3×C4C2×D411yescharacteristic
144C3×SD16—48no—
145C2×C3×C8—22no—
146C2×C3×C8—22no—
147C2×C3×C8—42no—
148C2×C3×C8—41no—
149C2×C3×C8—41no—
150C2×C3×C8—41no—
151C2×C3×C8—42no—
152C3×C4⋊C4—22no—
153C3×C4⋊C4—22no—
154C3×C4⋊C4—21no—
155C3×C4⋊C4—22no—
156C3×C4⋊C4—21no—
157C3×C4⋊C4—41no—
158C3×C4⋊C4—41no—
159C3×C4⋊C4SD1614yescomplemented
160C3×C22⋊C4—48no—
161C3×C22⋊C4—41no—
162C3×C22⋊C4—41no—
163C3×C42—41no—
164C3×C42—41no—
165C3×C42C2×D411yescharacteristic
166C3×C42C2×D411yescharacteristic
167C3×C42C2×D411yescharacteristic
168C3×C42#4111yescharacteristic
169C22×Q8—21no—
170C22×D4—24no—
171C22×D4—21no—
172C22×D4—21no—
173C22×D4C3×D411yescharacteristic
174C22×D4C3×D412yes—
175C23×C4—21no—
176C2×SD16—24no—
177C2×SD16—42no—
178C2×SD16—42no—
179C22×C8—21no—
180C22×C8—21no—
181C22×C8—21no—
182C4⋊Q8—21no—
183C4⋊Q8—21no—
184C4⋊Q8—21no—
185C4⋊Q8C3×D412yescomplemented
186#127—21no—
187#127—21no—
188#127—21no—
189#127—21no—
190#127—42no—
191#127—42no—
192#121—44no—
193#121—44no—
194C4×D4—21no—
195C4×D4—21no—
196C4×D4—21no—
197C4×D4—21no—
198C2×C4⋊C4—21no—
199C2×C4⋊C4—21no—
200C2×C4⋊C4C3×D411yescharacteristic
201C2×C4⋊C4C3×D412yes—
202C2×C22⋊C4—24no—
203C2×C22⋊C4—21no—
204C2×C42—21no—
205C2×C42C23×C311yescharacteristic
206C4⋊C8—21no—
207C4⋊C8—21no—
208C4⋊C8—21no—
209C4⋊C8C3×D412yescomplemented
210#103—24no—
211#102—28no—
212C4×C8—21no—
213C4×C8C3×D412yescomplemented
214#95—21no—
215C23×C3—22no—
216C23×C3—41no—
217C23×C3—41no—
218C23×C3—42no—
219C23×C3—42no—
220C23×C3—42no—
221C23×C3—42no—
222C23×C3—42no—
223C23×C3—44no—
224C23×C3—44no—
225C23×C3#12011yescharacteristic
226C3×Q8—42no—
227C3×Q8—42no—
228C3×Q8—81no—
229C3×Q8—81no—
230C3×D4—22no—
231C3×D4—22no—
232C3×D4—44no—
233C3×D4—41no—
234C3×D4—41no—
235C3×D4—82no—
236C3×D4—816no—
237C3×D4—81no—
238C3×D4—81no—
239C3×D4—82no—
240C3×D4—81no—
241C3×D4—81no—
242C3×D4—81no—
243C3×D4—81no—
244C2×C3×C4—22no—
245C2×C3×C4—24no—
246C2×C3×C4—42no—
247C2×C3×C4—42no—
248C2×C3×C4—41no—
249C2×C3×C4—42no—
250C2×C3×C4—42no—
251C2×C3×C4—81no—
252C2×C3×C4—81no—
253C2×C3×C4—82no—
254C2×C3×C4—81no—
255C2×C3×C4—81no—
256C2×C3×C4#12011yescharacteristic
257C2×C3×C4#12011yescharacteristic
258C2×C3×C4#12111yescharacteristic
259C2×C3×C4#12111yescharacteristic
260C2×C3×C4#12111yescharacteristic
261C2×C3×C4#12711yescharacteristic
262C2×C3×C4C2×D811yescharacteristic
263C2×C3×C4C2×SD1612yes—
264C2×C3×C4#13511yescharacteristic
265C2×C3×C4AGL(1,ℤ/8)11yescharacteristic
266C2×C3×C4AGL(1,ℤ/8)11yescharacteristic
267C2×C3×C4AGL(1,ℤ/8)12yes—
268C3×C8—42no—
269C3×C8—42no—
270C3×C8—81no—
271C24—21no—
272C24—22no—
273C2×Q8—22no—
274C2×Q8—41no—
275C2×Q8—41no—
276C2×Q8—41no—
277C2×Q8—41no—
278C2×Q8—41no—
279C2×D4—21no—
280C2×D4—22no—
281C2×D4—21no—
282C2×D4—22no—
283C2×D4—21no—
284C2×D4—21no—
285C2×D4—21no—
286C2×D4—44no—
287C2×D4—48no—
288C2×D4—48no—
289C2×D4—41no—
290C2×D4—41no—
291C2×D4—41no—
292C2×D4—41no—
293C2×D4—41no—
294C2×D4—42no—
295C2×D4—41no—
296C2×D4—42no—
297C2×D4—41no—
298C2×D4—41no—
299C2×D4—84no—
300C2×D4C3×D812yes—
301C22×C4—22no—
302C22×C4—21no—
303C22×C4—41no—
304C22×C4—41no—
305C22×C4—41no—
306C22×C4—42no—
307C22×C4—42no—
308C22×C4C2×C3×D411yescharacteristic
309C22×C4C2×C3×D411yescharacteristic
310C22×C4C2×C3×D411yescharacteristic
311SD16—48no—
312C2×C8—22no—
313C2×C8—22no—
314C2×C8—42no—
315C2×C8—41no—
316C2×C8—41no—
317C2×C8—41no—
318C2×C8—42no—
319C4⋊C4—22no—
320C4⋊C4—22no—
321C4⋊C4—21no—
322C4⋊C4—22no—
323C4⋊C4—21no—
324C4⋊C4—41no—
325C4⋊C4—41no—
326C4⋊C4C3×SD1614yescomplemented
327C22⋊C4—48no—
328C22⋊C4—41no—
329C22⋊C4—41no—
330C42—41no—
331C42—41no—
332C42C2×C3×D411yescharacteristic
333C42C2×C3×D411yescharacteristic
334C42C2×C3×D411yescharacteristic
335C42C3×#4111yescharacteristic
336C22×C3—44no—
337C22×C3—42no—
338C22×C3—82no—
339C22×C3—81no—
340C22×C3—81no—
341C22×C3—84no—
342C22×C3—84no—
343C22×C3—82no—
344C22×C3—82no—
345C22×C3—82no—
346C22×C3#39211yescharacteristic
347C22×C3#44711yescharacteristic
348C22×C3#44911yescharacteristic
349C22×C3#45012yes—
350C22×C3#45512yes—
351C3×C4—21no—
352C3×C4—21no—
353C3×C4—44no—
354C3×C4—82no—
355C3×C4—81no—
356C3×C4#44711yescharacteristic
357C3×C4#44911yescharacteristic
358C3×C4#46012yes—
359C3×C4#46611yescharacteristic
360C3×C4#46911yescharacteristic
361C3×C4#49211yescharacteristic
362C3×C4#49611yescharacteristic
363C23—22no—
364C23—41no—
365C23—41no—
366C23—42no—
367C23—42no—
368C23—42no—
369C23—42no—
370C23—42no—
371C23—44no—
372C23—44no—
373C23C3×#12011yescharacteristic
374Q8—42no—
375Q8—42no—
376Q8—81no—
377Q8—81no—
378D4—22no—
379D4—22no—
380D4—44no—
381D4—41no—
382D4—41no—
383D4—82no—
384D4—816no—
385D4—81no—
386D4—81no—
387D4—82no—
388D4—81no—
389D4—81no—
390D4—81no—
391D4—81no—
392C2×C4—22no—
393C2×C4—24no—
394C2×C4—42no—
395C2×C4—42no—
396C2×C4—41no—
397C2×C4—42no—
398C2×C4—42no—
399C2×C4—81no—
400C2×C4—81no—
401C2×C4—82no—
402C2×C4—81no—
403C2×C4—81no—
404C2×C4C3×#12011yescharacteristic
405C2×C4C3×#12011yescharacteristic
406C2×C4C3×#12111yescharacteristic
407C2×C4C3×#12111yescharacteristic
408C2×C4C3×#12111yescharacteristic
409C2×C4C3×#12711yescharacteristic
410C2×C4C2×C3×D811yescharacteristic
411C2×C4C2×C3×SD1612yes—
412C2×C4C3×#13511yescharacteristic
413C2×C4C3×AGL(1,ℤ/8)11yescharacteristic
414C2×C4C3×AGL(1,ℤ/8)11yescharacteristic
415C2×C4C3×AGL(1,ℤ/8)12yes—
416C8—42no—
417C8—42no—
418C8—81no—
419C2×C3—82no—
420C2×C3—162no—
421C2×C3#163912yes—
422C2×C3#164212yes—
423C2×C3#199911yescharacteristic
424C2×C3#200411yescharacteristic
425C2×C3#201411yescharacteristic
426C22—42no—
427C22—44no—
428C22—81no—
429C22—81no—
430C22—82no—
431C22—82no—
432C22—82no—
433C22—82no—
434C22—84no—
435C22—84no—
436C22C3×#39211yescharacteristic
437C22C3×#44711yescharacteristic
438C22C3×#44911yescharacteristic
439C22C3×#45012yes—
440C22C3×#45512yes—
441C4—21no—
442C4—21no—
443C4—44no—
444C4—82no—
445C4—81no—
446C4C3×#44711yescharacteristic
447C4C3×#44911yescharacteristic
448C4C3×#46012yes—
449C4C3×#46611yescharacteristic
450C4C3×#46911yescharacteristic
451C4C3×#49211yescharacteristic
452C4C3×#49611yescharacteristic
453C3#1006211yescharacteristic, direct product factor, Sylow
454C2—82no—
455C2—162no—
456C2C3×#163912yes—
457C2C3×#164212yes—
458C2C3×#199911yescharacteristic
459C2C3×#200411yescharacteristic
460C2C3×#201411yescharacteristic
subgroupG/H
center, socleC23×C3#120
commutator, Frattini, cosocleC2×C42C23×C3
prime radicalC3×#2541C2
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C23×C3 ◁ C2×C3×C42 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C3×#486C2semidirect
2. C2×C3×#461C2semidirect
4. C3×#1988C2semidirect
5. C2×C3×#331C2semidirect
6. C2×C3×D4⋊C8C2semidirect
7. C3×#1279C2semidirect
8. #10062C3direct (N × H)
30. C2×#486C2×C3semidirect
31. C2×#461C2×C3semidirect
33. #1988C2×C3semidirect
34. C2×#331C2×C3semidirect
35. C2×D4⋊C8C2×C3semidirect
36. #1279C2×C3semidirect
53. C3×C4⋊Q8D4semidirect
77. C3×C4⋊C8D4semidirect
81. C3×C4×C8D4semidirect
159. C3×C4⋊C4SD16semidirect
185. C4⋊Q8C3×D4semidirect
209. C4⋊C8C3×D4semidirect
213. C4×C8C3×D4semidirect
326. C4⋊C4C3×SD16semidirect
453. C3#10062direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#4862
C2×C3×#4612
C3×#25412
C3×#19882
C2×C3×#3312
C2×C3×D4⋊C82
C3×#12792
#100623