Finite Group Databasebeta

← C3×#2479 #84343

Subgroups — C3×#2479 #84343

Order 384.

518 conjugacy classes of subgroups.

The subgroup lattice has 398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#126C211yesmaximal, characteristic, complemented
2C2×C3×#117C211yesmaximal, characteristic, complemented
3C3×#399C211yesmaximal, characteristic, complemented
4C3×#399C211yesmaximal, characteristic, complemented
5C3×#398C211yesmaximal, characteristic, complemented
6C3×#394C211yesmaximal, characteristic
7C3×#390C211yesmaximal, characteristic
8C3×#389C211yesmaximal, characteristic, complemented
9C3×#388C211yesmaximal, characteristic, complemented
10C3×#388C211yesmaximal, characteristic, complemented
11C3×#388C211yesmaximal, characteristic, complemented
12C3×#387C211yesmaximal, characteristic, complemented
13C3×#386C211yesmaximal, characteristic
14C3×#385C211yesmaximal, characteristic, complemented
15C3×C4×C4⋊C4C211yesmaximal, characteristic, complemented
16#2479C311yesmaximal, characteristic, direct product factor, Sylow
17C22×C3×D4C2211yescharacteristic
18C23×C3×C4C2211yescharacteristic
19C3×#126—24no—
20C3×#117—24no—
21C2×C3×C4⋊C4C2211yescharacteristic
22C2×C3×C4⋊C4C2211yescharacteristic
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×C22⋊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×C42C2211yescharacteristic
43C2×C3×C42C2211yescharacteristic
44C2×C3×C42C2211yescharacteristic
45C2×C3×C42C2211yescharacteristic
46C3×#95C2211yescharacteristic
47C3×#95C2211yescharacteristic
48C3×#95C2211yescharacteristic
49C3×#95C2211yescharacteristic
50C3×#95C2211yescharacteristic
51C3×#95C2211yescharacteristic
52C3×#95C2211yescharacteristic
53C3×#95C2211yescharacteristic
54C2×#126C2×C311yescharacteristic, complemented
55C2×#117C2×C311yescharacteristic, complemented
56#399C2×C311yescharacteristic, complemented
57#399C2×C311yescharacteristic, complemented
58#398C2×C311yescharacteristic, complemented
59#394C2×C311yescharacteristic
60#390C2×C311yescharacteristic
61#389C2×C311yescharacteristic, complemented
62#388C2×C311yescharacteristic, complemented
63#388C2×C311yescharacteristic, complemented
64#388C2×C311yescharacteristic, complemented
65#387C2×C311yescharacteristic, complemented
66#386C2×C311yescharacteristic
67#385C2×C311yescharacteristic, complemented
68C4×C4⋊C4C2×C311yescharacteristic, complemented
69C24×C3C2311yescharacteristic
70C24×C3C2311yescharacteristic
71C2×C3×D4—22no—
72C2×C3×D4—22no—
73C2×C3×D4—41no—
74C22×C3×C4—22no—
75C22×C3×C4—22no—
76C22×C3×C4—22no—
77C22×C3×C4C2311yescharacteristic
78C22×C3×C4C2311yescharacteristic
79C22×C3×C4C2311yescharacteristic
80C22×C3×C4C2311yescharacteristic
81C22×C3×C4C2311yescharacteristic
82C22×C3×C4C2311yescharacteristic
83C22×C3×C4C2311yescharacteristic
84C22×C3×C4C2311yescharacteristic
85C22×C3×C4C2311yescharacteristic
86C22×C3×C4C2311yescharacteristic
87C22×C3×C4C2311yescharacteristic
88C22×C3×C4C2311yescharacteristic
89C22×C3×C4C2311yescharacteristic
90C3×C4⋊C4—22no—
91C3×C4⋊C4—22no—
92C3×C4⋊C4—22no—
93C3×C4⋊C4—22no—
94C3×C4⋊C4—22no—
95C3×C4⋊C4—22no—
96C3×C4⋊C4—41no—
97C3×C4⋊C4—41no—
98C3×C4⋊C4—41no—
99C3×C4⋊C4D414yescomplemented
100C3×C22⋊C4—22no—
101C3×C22⋊C4—22no—
102C3×C22⋊C4—22no—
103C3×C22⋊C4—22no—
104C3×C22⋊C4—22no—
105C3×C22⋊C4—22no—
106C3×C22⋊C4—22no—
107C3×C22⋊C4—22no—
108C3×C22⋊C4—22no—
109C3×C22⋊C4—41no—
110C3×C22⋊C4—41no—
111C3×C42—22no—
112C3×C42—22no—
113C3×C42—22no—
114C3×C42—22no—
115C22×D4C22×C311yescharacteristic
116C23×C4C22×C311yescharacteristic
117#126—24no—
118#117—24no—
119C2×C4⋊C4C22×C311yescharacteristic
120C2×C4⋊C4C22×C311yescharacteristic
121C2×C4⋊C4C22×C311yescharacteristic
122C2×C4⋊C4C22×C311yescharacteristic
123C2×C4⋊C4C22×C311yescharacteristic
124C2×C4⋊C4C22×C311yescharacteristic
125C2×C4⋊C4C22×C311yescharacteristic
126C2×C4⋊C4C22×C311yescharacteristic
127C2×C4⋊C4C22×C311yescharacteristic
128C2×C4⋊C4C22×C311yescharacteristic
129C2×C22⋊C4C22×C311yescharacteristic
130C2×C22⋊C4C22×C311yescharacteristic
131C2×C22⋊C4C22×C311yescharacteristic
132C2×C22⋊C4C22×C311yescharacteristic
133C2×C22⋊C4C22×C311yescharacteristic
134C2×C22⋊C4C22×C311yescharacteristic
135C2×C22⋊C4C22×C311yescharacteristic
136C2×C22⋊C4C22×C311yescharacteristic
137C2×C22⋊C4C22×C311yescharacteristic
138C2×C22⋊C4C22×C311yescharacteristic
139C2×C22⋊C4C22×C311yescharacteristic
140C2×C42C22×C311yescharacteristic
141C2×C42C22×C311yescharacteristic
142C2×C42C22×C311yescharacteristic
143C2×C42C22×C311yescharacteristic
144#95C22×C311yescharacteristic
145#95C22×C311yescharacteristic
146#95C22×C311yescharacteristic
147#95C22×C311yescharacteristic
148#95C22×C311yescharacteristic
149#95C22×C311yescharacteristic
150#95C22×C311yescharacteristic
151#95C22×C311yescharacteristic
152C23×C3—21no—
153C23×C3—21no—
154C23×C3—21no—
155C23×C3—21no—
156C23×C3—21no—
157C23×C3—21no—
158C23×C3—21no—
159C23×C3—21no—
160C23×C3—21no—
161C23×C3—21no—
162C23×C3—21no—
163C23×C3—21no—
164C23×C3—21no—
165C23×C3#4112yes—
166C23×C3C2411yescharacteristic
167C3×D4—44no—
168C2×C3×C4—28no—
169C2×C3×C4—21no—
170C2×C3×C4—21no—
171C2×C3×C4—21no—
172C2×C3×C4—21no—
173C2×C3×C4—21no—
174C2×C3×C4—21no—
175C2×C3×C4—21no—
176C2×C3×C4—21no—
177C2×C3×C4—21no—
178C2×C3×C4—21no—
179C2×C3×C4—21no—
180C2×C3×C4—21no—
181C2×C3×C4—21no—
182C2×C3×C4—21no—
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×C4C2×D412yes—
203C2×C3×C4C2×D412yes—
204C2×C3×C4C2×D412yes—
205C2×C3×C4#4112yes—
206C2×C3×C4#4112yes—
207C2×C3×C4#4112yes—
208C24C23×C311yescharacteristic
209C24C23×C311yescharacteristic
210C2×D4—22no—
211C2×D4—22no—
212C2×D4—41no—
213C22×C4—22no—
214C22×C4—22no—
215C22×C4—22no—
216C22×C4C23×C311yescharacteristic
217C22×C4C23×C311yescharacteristic
218C22×C4C23×C311yescharacteristic
219C22×C4C23×C311yescharacteristic
220C22×C4C23×C311yescharacteristic
221C22×C4C23×C311yescharacteristic
222C22×C4C23×C311yescharacteristic
223C22×C4C23×C311yescharacteristic
224C22×C4C23×C311yescharacteristic
225C22×C4C23×C311yescharacteristic
226C22×C4C23×C311yescharacteristic
227C22×C4C23×C311yescharacteristic
228C22×C4C23×C311yescharacteristic
229C4⋊C4—22no—
230C4⋊C4—22no—
231C4⋊C4—22no—
232C4⋊C4—22no—
233C4⋊C4—22no—
234C4⋊C4—22no—
235C4⋊C4—41no—
236C4⋊C4—41no—
237C4⋊C4—41no—
238C4⋊C4C3×D414yescomplemented
239C22⋊C4—22no—
240C22⋊C4—22no—
241C22⋊C4—22no—
242C22⋊C4—22no—
243C22⋊C4—22no—
244C22⋊C4—22no—
245C22⋊C4—22no—
246C22⋊C4—22no—
247C22⋊C4—22no—
248C22⋊C4—41no—
249C22⋊C4—41no—
250C42—22no—
251C42—22no—
252C42—22no—
253C42—22no—
254C22×C3—22no—
255C22×C3—22no—
256C22×C3—22no—
257C22×C3—41no—
258C22×C3—41no—
259C22×C3—41no—
260C22×C3—41no—
261C22×C3—41no—
262C22×C3—41no—
263C22×C3—41no—
264C22×C3—41no—
265C22×C3—41no—
266C22×C3—41no—
267C22×C3—41no—
268C22×C3C22×D411yescharacteristic
269C22×C3C2×#4111yescharacteristic
270C22×C3C2×#4111yescharacteristic
271C22×C3C2×#4111yescharacteristic
272C22×C3C2×#4111yescharacteristic
273C22×C3H(5,𝔽2)11yescharacteristic
274C22×C32−1+411yescharacteristic
275C3×C4—22no—
276C3×C4—22no—
277C3×C4—22no—
278C3×C4—22no—
279C3×C4—22no—
280C3×C4—22no—
281C3×C4—41no—
282C3×C4—41no—
283C3×C4—41no—
284C3×C4—41no—
285C3×C4—41no—
286C3×C4—41no—
287C3×C4—41no—
288C23—21no—
289C23—21no—
290C23—21no—
291C23—21no—
292C23—21no—
293C23—21no—
294C23—21no—
295C23—21no—
296C23—21no—
297C23—21no—
298C23—21no—
299C23—21no—
300C23—21no—
301C23C3×#4112yes—
302C23C24×C311yescharacteristic
303D4—44no—
304C2×C4—28no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4C2×C3×D412yes—
339C2×C4C2×C3×D412yes—
340C2×C4C2×C3×D412yes—
341C2×C4C3×#4112yes—
342C2×C4C3×#4112yes—
343C2×C4C3×#4112yes—
344C2×C3—42no—
345C2×C3—81no—
346C2×C3#52511yescharacteristic
347C2×C3#52911yescharacteristic
348C2×C3#54211yescharacteristic
349C2×C3#54711yescharacteristic
350C2×C3#55011yescharacteristic
351C2×C3#55111yescharacteristic
352C2×C3#55211yescharacteristic
353C22—22no—
354C22—22no—
355C22—22no—
356C22—41no—
357C22—41no—
358C22—41no—
359C22—41no—
360C22—41no—
361C22—41no—
362C22—41no—
363C22—41no—
364C22—41no—
365C22—41no—
366C22—41no—
367C22C22×C3×D411yescharacteristic
368C22C2×C3×#4111yescharacteristic
369C22C2×C3×#4111yescharacteristic
370C22C2×C3×#4111yescharacteristic
371C22C2×C3×#4111yescharacteristic
372C22C3×H(5,𝔽2)11yescharacteristic
373C22C3×2−1+411yescharacteristic
374C4—22no—
375C4—22no—
376C4—22no—
377C4—22no—
378C4—22no—
379C4—22no—
380C4—41no—
381C4—41no—
382C4—41no—
383C4—41no—
384C4—41no—
385C4—41no—
386C4—41no—
387C3#247911yescharacteristic, direct product factor, Sylow
388C2—42no—
389C2—81no—
390C2C3×#52511yescharacteristic
391C2C3×#52911yescharacteristic
392C2C3×#54211yescharacteristic
393C2C3×#54711yescharacteristic
394C2C3×#55011yescharacteristic
395C2C3×#55111yescharacteristic
396C2C3×#55211yescharacteristic
subgroupG/H
center, socleC23×C3C24
commutator, Frattini, cosocleC23C24×C3
prime radicalC22×C3×D4C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23×C3 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C3×#126C2semidirect
2. C2×C3×#117C2semidirect
3. C3×#399C2semidirect
4. C3×#399C2semidirect
5. C3×#398C2semidirect
8. C3×#389C2semidirect
9. C3×#388C2semidirect
10. C3×#388C2semidirect
11. C3×#388C2semidirect
12. C3×#387C2semidirect
14. C3×#385C2semidirect
15. C3×C4×C4⋊C4C2semidirect
16. #2479C3direct (N × H)
54. C2×#126C2×C3semidirect
55. C2×#117C2×C3semidirect
56. #399C2×C3semidirect
57. #399C2×C3semidirect
58. #398C2×C3semidirect
61. #389C2×C3semidirect
62. #388C2×C3semidirect
63. #388C2×C3semidirect
64. #388C2×C3semidirect
65. #387C2×C3semidirect
67. #385C2×C3semidirect
68. C4×C4⋊C4C2×C3semidirect
99. C3×C4⋊C4D4semidirect
238. C4⋊C4C3×D4semidirect
387. C3#2479direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#1262
C2×C3×#1172
C3×#3992
C3×#3982
C3×#3942
C3×#3902
C3×#3892
C3×#3882
C3×#3872
C3×#3862
C3×#3852
C3×C4×C4⋊C42
#24793