Finite Group Databasebeta

← C3×#33040 #10651647

Subgroups — C3×#33040 #10651647

Order 768.

876 conjugacy classes of subgroups.

The subgroup lattice has 444 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#478C211yesmaximal, characteristic
2C2×C3×#461C211yesmaximal, characteristic
3C3×#2642C211yesmaximal, characteristic, complemented
4C3×#2275C211yesmaximal, characteristic
5C3×#1989C211yesmaximal, characteristic, complemented
6C3×#1981C211yesmaximal, characteristic, complemented
7C3×#1928C212yesmaximal, complemented
8C3×#1927C212yesmaximal, complemented
9C3×#1877C212yesmaximal
10C3×#1877C212yesmaximal
11C3×#1832C211yesmaximal, characteristic, complemented
12#33040C311yesmaximal, characteristic, direct product factor, Sylow
13C22×C3×SD16C2212yes—
14C2×C3×C4⋊Q8C2211yescharacteristic
15C2×C3×#125C2211yescharacteristic
16C2×C3×C4×D4C2212yes—
17C2×C3×C4×D4C2211yescharacteristic
18C3×#478—24no—
19C3×#461—24no—
20C2×C3×#107C2211yescharacteristic
21C2×C3×#106C2211yescharacteristic
22C2×C3×C4⋊C8C2211yescharacteristic
23C2×C3×C4⋊C8C2211yescharacteristic
24C2×C3×#103C2212yes—
25C2×C3×#103C2212yes—
26C2×C3×#103C2212yes—
27C2×C3×#102C2211yescharacteristic
28C2×C3×#102C2211yescharacteristic
29C3×#400—21no—
30C3×#400—22no—
31C3×#400—21no—
32C3×#391C2212yes—
33C3×#391C2212yes—
34C3×C4×C4⋊C4C2211yescharacteristic
35C3×C4×C4⋊C4C2212yes—
36C3×C4×C22⋊C4—22no—
37C3×C4×C22⋊C4—21no—
38C3×#376C2211yescharacteristic
39C2×C3×#95—21no—
40C3×#340C2212yes—
41C3×#340C2212yes—
42C3×#336C2212yes—
43C3×#336C2212yes—
44C2×#478C2×C311yescharacteristic
45C2×#461C2×C311yescharacteristic
46#2642C2×C311yescharacteristic, complemented
47#2275C2×C311yescharacteristic
48#1989C2×C311yescharacteristic, complemented
49#1981C2×C311yescharacteristic, complemented
50#1928C2×C312yescomplemented
51#1927C2×C312yescomplemented
52#1877C2×C312yes—
53#1877C2×C312yes—
54#1832C2×C311yescharacteristic, complemented
55C22×C3×Q8C2312yes—
56C22×C3×D4C2311yescharacteristic
57C23×C3×C4—22no—
58C23×C3×C4—21no—
59C2×C3×SD16—24no—
60C2×C3×SD16—24no—
61C2×C3×SD16—24no—
62C22×C3×C8C2312yes—
63C22×C3×C8C2311yescharacteristic
64C22×C3×C8C2311yescharacteristic
65C3×C4⋊Q8—22no—
66C3×C4⋊Q8—22no—
67C3×#125—22no—
68C3×#125—22no—
69C3×C4×D4—24no—
70C3×C4×D4—24no—
71C3×C4×D4—22no—
72C3×C4×D4D414yes—
73C2×C3×C4⋊C4—21no—
74C2×C3×C4⋊C4—21no—
75C2×C3×C4⋊C4—21no—
76C2×C3×C4⋊C4—21no—
77C2×C3×C4⋊C4C2311yescharacteristic
78C2×C3×C4⋊C4C2311yescharacteristic
79C2×C3×C4⋊C4C2311yescharacteristic
80C2×C3×C4⋊C4C2312yes—
81C2×C3×C22⋊C4—22no—
82C2×C3×C22⋊C4—21no—
83C2×C3×C42—22no—
84C2×C3×C42—21no—
85C2×C3×C42C2312yes—
86C2×C3×C42C2311yescharacteristic
87C3×#107—22no—
88C3×#106—22no—
89C3×C4⋊C8—22no—
90C3×C4⋊C8—22no—
91C3×#103—24no—
92C3×#103—24no—
93C3×#103—24no—
94C3×#102—22no—
95C3×#102—22no—
96C3×#95—22no—
97C3×#95—21no—
98C3×#95—22no—
99C3×#95—22no—
100C3×#95—22no—
101C3×#95—22no—
102C3×#95D411yescharacteristic
103C3×#95D412yes—
104C3×#95D411yescharacteristic
105C22×SD16C22×C312yes—
106C2×C4⋊Q8C22×C311yescharacteristic
107C2×#125C22×C311yescharacteristic
108C2×C4×D4C22×C312yes—
109C2×C4×D4C22×C311yescharacteristic
110#478—24no—
111#461—24no—
112C2×#107C22×C311yescharacteristic
113C2×#106C22×C311yescharacteristic
114C2×C4⋊C8C22×C311yescharacteristic
115C2×C4⋊C8C22×C311yescharacteristic
116C2×#103C22×C312yes—
117C2×#103C22×C312yes—
118C2×#103C22×C312yes—
119C2×#102C22×C311yescharacteristic
120C2×#102C22×C311yescharacteristic
121#400—21no—
122#400—22no—
123#400—21no—
124#391C22×C312yes—
125#391C22×C312yes—
126C4×C4⋊C4C22×C312yes—
127C4×C4⋊C4C22×C311yescharacteristic
128C4×C22⋊C4—22no—
129C4×C22⋊C4—21no—
130#376C22×C311yescharacteristic
131C2×#95—21no—
132#340C22×C312yes—
133#340C22×C312yes—
134#336C22×C312yes—
135#336C22×C312yes—
136C24×C3—21no—
137C2×C3×Q8—22no—
138C2×C3×Q8—22no—
139C2×C3×Q8—22no—
140C2×C3×Q8—22no—
141C2×C3×Q8—22no—
142C2×C3×Q8—22no—
143C2×C3×D4—21no—
144C2×C3×D4—22no—
145C2×C3×D4C2×D412yes—
146C2×C3×D4#4114yes—
147C22×C3×C4—21no—
148C22×C3×C4—22no—
149C22×C3×C4—28no—
150C22×C3×C4—24no—
151C22×C3×C4—21no—
152C22×C3×C4—21no—
153C22×C3×C4—22no—
154C22×C3×C4—82no—
155C22×C3×C4—82no—
156C22×C3×C4—82no—
157C22×C3×C4C2×D412yes—
158C22×C3×C4C2×D412yes—
159C22×C3×C4C2×D411yescharacteristic
160C22×C3×C4C2×D411yescharacteristic
161C22×C3×C4C2411yescharacteristic
162C3×SD16—48no—
163C2×C3×C8—21no—
164C2×C3×C8—21no—
165C2×C3×C8—22no—
166C2×C3×C8—22no—
167C2×C3×C8—22no—
168C2×C3×C8—22no—
169C2×C3×C8—22no—
170C3×C4⋊C4—21no—
171C3×C4⋊C4—22no—
172C3×C4⋊C4—21no—
173C3×C4⋊C4—21no—
174C3×C4⋊C4—21no—
175C3×C4⋊C4—21no—
176C3×C4⋊C4—42no—
177C3×C4⋊C4—42no—
178C3×C4⋊C4—42no—
179C3×C4⋊C4—42no—
180C3×C4⋊C4C2×D412yes—
181C3×C4⋊C4#4114yes—
182C3×C22⋊C4—28no—
183C3×C22⋊C4—24no—
184C3×C42—22no—
185C3×C42—22no—
186C3×C42—81no—
187C3×C42—82no—
188C3×C42C2×D412yes—
189C3×C42#4112yes—
190C22×Q8C23×C312yes—
191C22×D4C23×C311yescharacteristic
192C23×C4—22no—
193C23×C4—21no—
194C2×SD16—24no—
195C2×SD16—24no—
196C2×SD16—24no—
197C22×C8C23×C312yes—
198C22×C8C23×C311yescharacteristic
199C22×C8C23×C311yescharacteristic
200C4⋊Q8—22no—
201C4⋊Q8—22no—
202#125—22no—
203#125—22no—
204C4×D4—24no—
205C4×D4—24no—
206C4×D4—22no—
207C4×D4C3×D414yes—
208C2×C4⋊C4—21no—
209C2×C4⋊C4—21no—
210C2×C4⋊C4—21no—
211C2×C4⋊C4—21no—
212C2×C4⋊C4C23×C311yescharacteristic
213C2×C4⋊C4C23×C311yescharacteristic
214C2×C4⋊C4C23×C311yescharacteristic
215C2×C4⋊C4C23×C312yes—
216C2×C22⋊C4—22no—
217C2×C22⋊C4—21no—
218C2×C42—22no—
219C2×C42—21no—
220C2×C42C23×C312yes—
221C2×C42C23×C311yescharacteristic
222#107—22no—
223#106—22no—
224C4⋊C8—22no—
225C4⋊C8—22no—
226#103—24no—
227#103—24no—
228#103—24no—
229#102—22no—
230#102—22no—
231#95—22no—
232#95—21no—
233#95—22no—
234#95—22no—
235#95—22no—
236#95—22no—
237#95C3×D411yescharacteristic
238#95C3×D412yes—
239#95C3×D411yescharacteristic
240C23×C3—22no—
241C23×C3—24no—
242C23×C3—42no—
243C23×C3—41no—
244C23×C3—41no—
245C23×C3C22×D411yescharacteristic
246C3×Q8—42no—
247C3×Q8—42no—
248C3×Q8—42no—
249C3×Q8—42no—
250C3×D4—24no—
251C3×D4—22no—
252C3×D4#12414yes—
253C2×C3×C4—21no—
254C2×C3×C4—22no—
255C2×C3×C4—21no—
256C2×C3×C4—22no—
257C2×C3×C4—22no—
258C2×C3×C4—22no—
259C2×C3×C4—24no—
260C2×C3×C4—22no—
261C2×C3×C4—22no—
262C2×C3×C4—22no—
263C2×C3×C4—22no—
264C2×C3×C4—42no—
265C2×C3×C4—42no—
266C2×C3×C4—42no—
267C2×C3×C4—41no—
268C2×C3×C4—41no—
269C2×C3×C4—42no—
270C2×C3×C4—42no—
271C2×C3×C4—42no—
272C2×C3×C4—42no—
273C2×C3×C4—41no—
274C2×C3×C4—41no—
275C2×C3×C4—84no—
276C2×C3×C4—88no—
277C2×C3×C4#12112yes—
278C2×C3×C4#12112yes—
279C2×C3×C4C22×D411yescharacteristic
280C2×C3×C4C2×#4112yes—
281C2×C3×C4C2×#4111yescharacteristic
282C2×C3×C4C2×#4112yes—
283C3×C8—42no—
284C3×C8—41no—
285C3×C8—41no—
286C24—21no—
287C2×Q8—22no—
288C2×Q8—22no—
289C2×Q8—22no—
290C2×Q8—22no—
291C2×Q8—22no—
292C2×Q8—22no—
293C2×D4—21no—
294C2×D4—22no—
295C2×D4C2×C3×D412yes—
296C2×D4C3×#4114yes—
297C22×C4—21no—
298C22×C4—22no—
299C22×C4—28no—
300C22×C4—24no—
301C22×C4—21no—
302C22×C4—21no—
303C22×C4—22no—
304C22×C4—82no—
305C22×C4—82no—
306C22×C4—82no—
307C22×C4C2×C3×D412yes—
308C22×C4C2×C3×D412yes—
309C22×C4C2×C3×D411yescharacteristic
310C22×C4C2×C3×D411yescharacteristic
311C22×C4C24×C311yescharacteristic
312SD16—48no—
313C2×C8—21no—
314C2×C8—21no—
315C2×C8—22no—
316C2×C8—22no—
317C2×C8—22no—
318C2×C8—22no—
319C2×C8—22no—
320C4⋊C4—21no—
321C4⋊C4—22no—
322C4⋊C4—21no—
323C4⋊C4—21no—
324C4⋊C4—21no—
325C4⋊C4—21no—
326C4⋊C4—42no—
327C4⋊C4—42no—
328C4⋊C4—42no—
329C4⋊C4—42no—
330C4⋊C4C2×C3×D412yes—
331C4⋊C4C3×#4114yes—
332C22⋊C4—28no—
333C22⋊C4—24no—
334C42—22no—
335C42—22no—
336C42—81no—
337C42—82no—
338C42C2×C3×D412yes—
339C42C3×#4112yes—
340C22×C3—24no—
341C22×C3—44no—
342C22×C3—44no—
343C22×C3—42no—
344C22×C3—42no—
345C22×C3C2×#12111yescharacteristic
346C22×C3#52512yes—
347C22×C3#57712yes—
348C22×C3#57711yescharacteristic
349C22×C3#57811yescharacteristic
350C3×C4—22no—
351C3×C4—22no—
352C3×C4—42no—
353C3×C4—42no—
354C3×C4—44no—
355C3×C4—42no—
356C3×C4—82no—
357C3×C4—81no—
358C3×C4—81no—
359C3×C4C2×#12411yescharacteristic
360C3×C4#52912yes—
361C3×C4#53211yescharacteristic
362C23—22no—
363C23—24no—
364C23—42no—
365C23—41no—
366C23—41no—
367C23C22×C3×D411yescharacteristic
368Q8—42no—
369Q8—42no—
370Q8—42no—
371Q8—42no—
372D4—24no—
373D4—22no—
374D4C3×#12414yes—
375C2×C4—21no—
376C2×C4—22no—
377C2×C4—21no—
378C2×C4—22no—
379C2×C4—22no—
380C2×C4—22no—
381C2×C4—22no—
382C2×C4—22no—
383C2×C4—22no—
384C2×C4—22no—
385C2×C4—24no—
386C2×C4—42no—
387C2×C4—42no—
388C2×C4—42no—
389C2×C4—42no—
390C2×C4—41no—
391C2×C4—41no—
392C2×C4—41no—
393C2×C4—41no—
394C2×C4—42no—
395C2×C4—42no—
396C2×C4—42no—
397C2×C4—84no—
398C2×C4—88no—
399C2×C4C3×#12112yes—
400C2×C4C3×#12112yes—
401C2×C4C22×C3×D411yescharacteristic
402C2×C4C2×C3×#4112yes—
403C2×C4C2×C3×#4111yescharacteristic
404C2×C4C2×C3×#4112yes—
405C8—42no—
406C8—41no—
407C8—41no—
408C2×C3—44no—
409C2×C3#285011yescharacteristic
410C2×C3#304211yescharacteristic
411C2×C3#304611yescharacteristic
412C2×C3#312012yes—
413C2×C3#312312yes—
414C22—24no—
415C22—42no—
416C22—42no—
417C22—44no—
418C22—44no—
419C22C2×C3×#12111yescharacteristic
420C22C3×#52512yes—
421C22C3×#57712yes—
422C22C3×#57711yescharacteristic
423C22C3×#57811yescharacteristic
424C4—22no—
425C4—22no—
426C4—42no—
427C4—42no—
428C4—42no—
429C4—44no—
430C4—81no—
431C4—81no—
432C4—82no—
433C4C2×C3×#12411yescharacteristic
434C4C3×#52912yes—
435C4C3×#53211yescharacteristic
436C3#3304011yescharacteristic, direct product factor, Sylow
437C2—44no—
438C2C3×#285011yescharacteristic
439C2C3×#304211yescharacteristic
440C2C3×#304611yescharacteristic
441C2C3×#312012yes—
442C2C3×#312312yes—
subgroupG/H
center, socleC23×C3C22×D4
commutator, Frattini, cosocleC22×C4C24×C3
prime radicalC22×C3×D4C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C3 ◁ C3×#376 ◁ G

Complements

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

NH ≅ G/Ntype
3. C3×#2642C2semidirect
5. C3×#1989C2semidirect
6. C3×#1981C2semidirect
7. C3×#1928C2semidirect
8. C3×#1927C2semidirect
11. C3×#1832C2semidirect
12. #33040C3direct (N × H)
46. #2642C2×C3semidirect
48. #1989C2×C3semidirect
49. #1981C2×C3semidirect
50. #1928C2×C3semidirect
51. #1927C2×C3semidirect
54. #1832C2×C3semidirect
436. C3#33040direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#4782
C2×C3×#4612
C3×#26422
C3×#22752
C3×#19892
C3×#19812
C3×#19282
C3×#19272
C3×#18772
C3×#18322
#330403