Finite Group Databasebeta

← C3×#2711 #84575

Subgroups — C3×#2711 #84575

Order 384.

540 conjugacy classes of subgroups.

The subgroup lattice has 436 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#125C211yesmaximal, characteristic, complemented
2C2×C3×#121C211yesmaximal, characteristic
3C3×#399C211yesmaximal, characteristic, complemented
4C3×#396C211yesmaximal, characteristic, complemented
5C3×#394C211yesmaximal, characteristic, complemented
6C3×#394C211yesmaximal, characteristic, complemented
7C3×#394C211yesmaximal, characteristic, complemented
8C3×#394C211yesmaximal, characteristic, complemented
9C3×#390C211yesmaximal, characteristic, complemented
10C3×#390C211yesmaximal, characteristic, complemented
11C3×#388C211yesmaximal, characteristic, complemented
12C3×#388C211yesmaximal, characteristic, complemented
13C3×#387C211yesmaximal, characteristic, complemented
14C3×#385C211yesmaximal, characteristic, complemented
15C3×#385C211yesmaximal, characteristic, complemented
16#2711C311yesmaximal, characteristic, direct product factor, Sylow
17C22×C3×D4C2211yescharacteristic
18C22×C3×D4C2211yescharacteristic
19C22×C3×D4C2211yescharacteristic
20C23×C3×C4C2211yescharacteristic
21C3×#125—24no—
22C3×#121—24no—
23C2×C3×C4⋊C4C2211yescharacteristic
24C2×C3×C4⋊C4C2211yescharacteristic
25C2×C3×C4⋊C4C2211yescharacteristic
26C2×C3×C4⋊C4C2211yescharacteristic
27C2×C3×C4⋊C4C2211yescharacteristic
28C2×C3×C4⋊C4C2211yescharacteristic
29C2×C3×C4⋊C4C2211yescharacteristic
30C2×C3×C4⋊C4C2211yescharacteristic
31C2×C3×C4⋊C4C2211yescharacteristic
32C2×C3×C22⋊C4C2211yescharacteristic
33C2×C3×C22⋊C4C2211yescharacteristic
34C2×C3×C22⋊C4C2211yescharacteristic
35C2×C3×C22⋊C4C2211yescharacteristic
36C2×C3×C22⋊C4C2211yescharacteristic
37C2×C3×C22⋊C4C2211yescharacteristic
38C2×C3×C22⋊C4C2211yescharacteristic
39C2×C3×C22⋊C4C2211yescharacteristic
40C2×C3×C22⋊C4C2211yescharacteristic
41C2×C3×C22⋊C4C2211yescharacteristic
42C2×C3×C22⋊C4C2211yescharacteristic
43C2×C3×C22⋊C4C2211yescharacteristic
44C2×C3×C22⋊C4C2211yescharacteristic
45C2×C3×C22⋊C4C2211yescharacteristic
46C2×C3×C42C2211yescharacteristic
47C2×C3×C42C2211yescharacteristic
48C3×#95C2211yescharacteristic
49C3×#95C2211yescharacteristic
50C3×#95C2211yescharacteristic
51C3×#95C2211yescharacteristic
52C3×#95C2211yescharacteristic
53C3×#95C2211yescharacteristic
54C2×#125C2×C311yescharacteristic, complemented
55C2×#121C2×C311yescharacteristic
56#399C2×C311yescharacteristic, complemented
57#396C2×C311yescharacteristic, complemented
58#394C2×C311yescharacteristic, complemented
59#394C2×C311yescharacteristic, complemented
60#394C2×C311yescharacteristic, complemented
61#394C2×C311yescharacteristic, complemented
62#390C2×C311yescharacteristic, complemented
63#390C2×C311yescharacteristic, complemented
64#388C2×C311yescharacteristic, complemented
65#388C2×C311yescharacteristic, complemented
66#387C2×C311yescharacteristic, complemented
67#385C2×C311yescharacteristic, complemented
68#385C2×C311yescharacteristic, complemented
69C24×C3C2311yescharacteristic
70C24×C3C2311yescharacteristic
71C24×C3C2311yescharacteristic
72C2×C3×D4—22no—
73C2×C3×D4—22no—
74C2×C3×D4—22no—
75C2×C3×D4—22no—
76C2×C3×D4—22no—
77C2×C3×D4—41no—
78C2×C3×D4—41no—
79C2×C3×D4—41no—
80C2×C3×D4—41no—
81C22×C3×C4—22no—
82C22×C3×C4—41no—
83C22×C3×C4—41no—
84C22×C3×C4C2311yescharacteristic
85C22×C3×C4C2311yescharacteristic
86C22×C3×C4C2311yescharacteristic
87C22×C3×C4C2311yescharacteristic
88C22×C3×C4C2311yescharacteristic
89C22×C3×C4C2311yescharacteristic
90C22×C3×C4C2311yescharacteristic
91C22×C3×C4C2311yescharacteristic
92C22×C3×C4C2311yescharacteristic
93C22×C3×C4C2311yescharacteristic
94C22×C3×C4C2311yescharacteristic
95C22×C3×C4C2311yescharacteristic
96C3×C4⋊C4—22no—
97C3×C4⋊C4—22no—
98C3×C4⋊C4—22no—
99C3×C4⋊C4—22no—
100C3×C4⋊C4—22no—
101C3×C4⋊C4—41no—
102C3×C4⋊C4—41no—
103C3×C4⋊C4—41no—
104C3×C4⋊C4D414yes—
105C3×C22⋊C4—22no—
106C3×C22⋊C4—22no—
107C3×C22⋊C4—22no—
108C3×C22⋊C4—22no—
109C3×C22⋊C4—22no—
110C3×C22⋊C4—22no—
111C3×C22⋊C4—41no—
112C3×C22⋊C4—41no—
113C3×C22⋊C4—41no—
114C3×C22⋊C4—41no—
115C3×C22⋊C4—41no—
116C3×C22⋊C4—41no—
117C3×C22⋊C4—41no—
118C3×C22⋊C4—41no—
119C3×C42—22no—
120C3×C42—41no—
121C22×D4C22×C311yescharacteristic
122C22×D4C22×C311yescharacteristic
123C22×D4C22×C311yescharacteristic
124C23×C4C22×C311yescharacteristic
125#125—24no—
126#121—24no—
127C2×C4⋊C4C22×C311yescharacteristic
128C2×C4⋊C4C22×C311yescharacteristic
129C2×C4⋊C4C22×C311yescharacteristic
130C2×C4⋊C4C22×C311yescharacteristic
131C2×C4⋊C4C22×C311yescharacteristic
132C2×C4⋊C4C22×C311yescharacteristic
133C2×C4⋊C4C22×C311yescharacteristic
134C2×C4⋊C4C22×C311yescharacteristic
135C2×C4⋊C4C22×C311yescharacteristic
136C2×C22⋊C4C22×C311yescharacteristic
137C2×C22⋊C4C22×C311yescharacteristic
138C2×C22⋊C4C22×C311yescharacteristic
139C2×C22⋊C4C22×C311yescharacteristic
140C2×C22⋊C4C22×C311yescharacteristic
141C2×C22⋊C4C22×C311yescharacteristic
142C2×C22⋊C4C22×C311yescharacteristic
143C2×C22⋊C4C22×C311yescharacteristic
144C2×C22⋊C4C22×C311yescharacteristic
145C2×C22⋊C4C22×C311yescharacteristic
146C2×C22⋊C4C22×C311yescharacteristic
147C2×C22⋊C4C22×C311yescharacteristic
148C2×C22⋊C4C22×C311yescharacteristic
149C2×C22⋊C4C22×C311yescharacteristic
150C2×C42C22×C311yescharacteristic
151C2×C42C22×C311yescharacteristic
152#95C22×C311yescharacteristic
153#95C22×C311yescharacteristic
154#95C22×C311yescharacteristic
155#95C22×C311yescharacteristic
156#95C22×C311yescharacteristic
157#95C22×C311yescharacteristic
158C23×C3—21no—
159C23×C3—21no—
160C23×C3—21no—
161C23×C3—21no—
162C23×C3—21no—
163C23×C3—21no—
164C23×C3—21no—
165C23×C3—21no—
166C23×C3—21no—
167C23×C3—21no—
168C23×C3—21no—
169C23×C3—21no—
170C23×C3—21no—
171C23×C3—21no—
172C23×C3—21no—
173C23×C3—21no—
174C23×C3—21no—
175C23×C3—21no—
176C23×C3—21no—
177C23×C3—21no—
178C23×C3#4112yes—
179C23×C3C2411yescharacteristic
180C3×D4—44no—
181C3×D4—44no—
182C3×D4—44no—
183C2×C3×C4—21no—
184C2×C3×C4—21no—
185C2×C3×C4—21no—
186C2×C3×C4—21no—
187C2×C3×C4—21no—
188C2×C3×C4—21no—
189C2×C3×C4—21no—
190C2×C3×C4—21no—
191C2×C3×C4—21no—
192C2×C3×C4—21no—
193C2×C3×C4—21no—
194C2×C3×C4—21no—
195C2×C3×C4—21no—
196C2×C3×C4—21no—
197C2×C3×C4—21no—
198C2×C3×C4—21no—
199C2×C3×C4—21no—
200C2×C3×C4—21no—
201C2×C3×C4—21no—
202C2×C3×C4—21no—
203C2×C3×C4—21no—
204C2×C3×C4—21no—
205C2×C3×C4—21no—
206C2×C3×C4—21no—
207C2×C3×C4—21no—
208C2×C3×C4—21no—
209C2×C3×C4—21no—
210C2×C3×C4—21no—
211C2×C3×C4—21no—
212C2×C3×C4—21no—
213C2×C3×C4—21no—
214C2×C3×C4—21no—
215C2×C3×C4—44no—
216C2×C3×C4C2×D412yes—
217C2×C3×C4C2×D412yes—
218C2×C3×C4C2×D412yes—
219C2×C3×C4#4112yes—
220C24C23×C311yescharacteristic
221C24C23×C311yescharacteristic
222C24C23×C311yescharacteristic
223C2×D4—22no—
224C2×D4—22no—
225C2×D4—22no—
226C2×D4—22no—
227C2×D4—22no—
228C2×D4—41no—
229C2×D4—41no—
230C2×D4—41no—
231C2×D4—41no—
232C22×C4—22no—
233C22×C4—41no—
234C22×C4—41no—
235C22×C4C23×C311yescharacteristic
236C22×C4C23×C311yescharacteristic
237C22×C4C23×C311yescharacteristic
238C22×C4C23×C311yescharacteristic
239C22×C4C23×C311yescharacteristic
240C22×C4C23×C311yescharacteristic
241C22×C4C23×C311yescharacteristic
242C22×C4C23×C311yescharacteristic
243C22×C4C23×C311yescharacteristic
244C22×C4C23×C311yescharacteristic
245C22×C4C23×C311yescharacteristic
246C22×C4C23×C311yescharacteristic
247C4⋊C4—22no—
248C4⋊C4—22no—
249C4⋊C4—22no—
250C4⋊C4—22no—
251C4⋊C4—22no—
252C4⋊C4—41no—
253C4⋊C4—41no—
254C4⋊C4—41no—
255C4⋊C4C3×D414yes—
256C22⋊C4—22no—
257C22⋊C4—22no—
258C22⋊C4—22no—
259C22⋊C4—22no—
260C22⋊C4—22no—
261C22⋊C4—22no—
262C22⋊C4—41no—
263C22⋊C4—41no—
264C22⋊C4—41no—
265C22⋊C4—41no—
266C22⋊C4—41no—
267C22⋊C4—41no—
268C22⋊C4—41no—
269C22⋊C4—41no—
270C42—22no—
271C42—41no—
272C22×C3—22no—
273C22×C3—22no—
274C22×C3—22no—
275C22×C3—41no—
276C22×C3—41no—
277C22×C3—41no—
278C22×C3—41no—
279C22×C3—41no—
280C22×C3—41no—
281C22×C3—41no—
282C22×C3—41no—
283C22×C3—41no—
284C22×C3—41no—
285C22×C3—41no—
286C22×C3—41no—
287C22×C3—41no—
288C22×C3—41no—
289C22×C3—41no—
290C22×C3—41no—
291C22×C3—41no—
292C22×C3—41no—
293C22×C3C22×D411yescharacteristic
294C22×C3C2×#4111yescharacteristic
295C22×C3C2×#4111yescharacteristic
296C22×C3H(5,𝔽2)11yescharacteristic
297C22×C3H(5,𝔽2)11yescharacteristic
298C22×C3H(5,𝔽2)11yescharacteristic
299C22×C32−1+411yescharacteristic
300C3×C4—22no—
301C3×C4—22no—
302C3×C4—22no—
303C3×C4—22no—
304C3×C4—41no—
305C3×C4—41no—
306C3×C4—41no—
307C3×C4—41no—
308C3×C4—41no—
309C3×C4—41no—
310C3×C4—41no—
311C3×C4—41no—
312C23—21no—
313C23—21no—
314C23—21no—
315C23—21no—
316C23—21no—
317C23—21no—
318C23—21no—
319C23—21no—
320C23—21no—
321C23—21no—
322C23—21no—
323C23—21no—
324C23—21no—
325C23—21no—
326C23—21no—
327C23—21no—
328C23—21no—
329C23—21no—
330C23—21no—
331C23—21no—
332C23C3×#4112yes—
333C23C24×C311yescharacteristic
334D4—44no—
335D4—44no—
336D4—44no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—21no—
346C2×C4—21no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—21no—
365C2×C4—21no—
366C2×C4—21no—
367C2×C4—21no—
368C2×C4—21no—
369C2×C4—44no—
370C2×C4C2×C3×D412yes—
371C2×C4C2×C3×D412yes—
372C2×C4C2×C3×D412yes—
373C2×C4C3×#4112yes—
374C2×C3—42no—
375C2×C3—81no—
376C2×C3—81no—
377C2×C3#53511yescharacteristic
378C2×C3#53911yescharacteristic
379C2×C3#54011yescharacteristic
380C2×C3#54611yescharacteristic
381C2×C3#54811yescharacteristic
382C2×C3#55311yescharacteristic
383C2×C3#56211yescharacteristic
384C22—22no—
385C22—22no—
386C22—22no—
387C22—41no—
388C22—41no—
389C22—41no—
390C22—41no—
391C22—41no—
392C22—41no—
393C22—41no—
394C22—41no—
395C22—41no—
396C22—41no—
397C22—41no—
398C22—41no—
399C22—41no—
400C22—41no—
401C22—41no—
402C22—41no—
403C22—41no—
404C22—41no—
405C22C22×C3×D411yescharacteristic
406C22C2×C3×#4111yescharacteristic
407C22C2×C3×#4111yescharacteristic
408C22C3×H(5,𝔽2)11yescharacteristic
409C22C3×H(5,𝔽2)11yescharacteristic
410C22C3×H(5,𝔽2)11yescharacteristic
411C22C3×2−1+411yescharacteristic
412C4—22no—
413C4—22no—
414C4—22no—
415C4—22no—
416C4—41no—
417C4—41no—
418C4—41no—
419C4—41no—
420C4—41no—
421C4—41no—
422C4—41no—
423C4—41no—
424C3#271111yescharacteristic, direct product factor, Sylow
425C2—42no—
426C2—81no—
427C2—81no—
428C2C3×#53511yescharacteristic
429C2C3×#53911yescharacteristic
430C2C3×#54011yescharacteristic
431C2C3×#54611yescharacteristic
432C2C3×#54811yescharacteristic
433C2C3×#55311yescharacteristic
434C2C3×#56211yescharacteristic
subgroupG/H
center, socleC23×C3C24
commutator, Frattini, cosocleC23C24×C3
prime radicalC2×C3×#121C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23×C3 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C3×#125C2semidirect
3. C3×#399C2semidirect
4. C3×#396C2semidirect
5. C3×#394C2semidirect
6. C3×#394C2semidirect
7. C3×#394C2semidirect
8. C3×#394C2semidirect
9. C3×#390C2semidirect
10. C3×#390C2semidirect
11. C3×#388C2semidirect
12. C3×#388C2semidirect
13. C3×#387C2semidirect
14. C3×#385C2semidirect
15. C3×#385C2semidirect
16. #2711C3direct (N × H)
54. C2×#125C2×C3semidirect
56. #399C2×C3semidirect
57. #396C2×C3semidirect
58. #394C2×C3semidirect
59. #394C2×C3semidirect
60. #394C2×C3semidirect
61. #394C2×C3semidirect
62. #390C2×C3semidirect
63. #390C2×C3semidirect
64. #388C2×C3semidirect
65. #388C2×C3semidirect
66. #387C2×C3semidirect
67. #385C2×C3semidirect
68. #385C2×C3semidirect
424. C3#2711direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#1252
C2×C3×#1212
C3×#3992
C3×#3962
C3×#3942
C3×#3902
C3×#3882
C3×#3872
C3×#3852
#27113