Finite Group Databasebeta

← C3×#2493 #84357

Subgroups — C3×#2493 #84357

Order 384.

440 conjugacy classes of subgroups.

The subgroup lattice has 354 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#401C211yesmaximal, characteristic, complemented
2C3×#400C211yesmaximal, characteristic, complemented
3C3×#400C211yesmaximal, characteristic, complemented
4C3×#400C211yesmaximal, characteristic, complemented
5C3×#387C211yesmaximal, characteristic, complemented
6C3×#387C211yesmaximal, characteristic, complemented
7C3×#387C211yesmaximal, characteristic, complemented
8C3×#385C211yesmaximal, characteristic
9C3×#385C211yesmaximal, characteristic
10C3×#383C211yesmaximal, characteristic, complemented
11C3×#381C211yesmaximal, characteristic
12C3×#381C211yesmaximal, characteristic
13C3×#380C211yesmaximal, characteristic
14C3×C4×C22⋊C4C211yesmaximal, characteristic
15C2×C3×#95C211yesmaximal, characteristic
16#2493C311yesmaximal, characteristic, direct product factor, Sylow
17C23×C3×C4C2211yescharacteristic
18C23×C3×C4C2211yescharacteristic
19C23×C3×C4C2211yescharacteristic
20C2×C3×C4⋊C4C2211yescharacteristic
21C2×C3×C4⋊C4C2211yescharacteristic
22C2×C3×C4⋊C4C2211yescharacteristic
23C2×C3×C4⋊C4C2211yescharacteristic
24C2×C3×C4⋊C4C2211yescharacteristic
25C2×C3×C4⋊C4C2211yescharacteristic
26C2×C3×C22⋊C4C2211yescharacteristic
27C2×C3×C22⋊C4C2211yescharacteristic
28C2×C3×C22⋊C4C2211yescharacteristic
29C2×C3×C22⋊C4C2211yescharacteristic
30C2×C3×C42C2211yescharacteristic
31C2×C3×C42C2211yescharacteristic
32C3×#95C2211yescharacteristic
33C3×#95C2211yescharacteristic
34C3×#95C2211yescharacteristic
35C3×#95C2211yescharacteristic
36C3×#95C2211yescharacteristic
37C3×#95C2211yescharacteristic
38C3×#95C2211yescharacteristic
39C3×#95C2211yescharacteristic
40C3×#95C2211yescharacteristic
41C3×#95C2211yescharacteristic
42C3×#95C2211yescharacteristic
43C3×#95C2211yescharacteristic
44C3×#95C2211yescharacteristic
45C3×#95C2211yescharacteristic
46C3×#95C2211yescharacteristic
47C3×#95C2211yescharacteristic
48C3×#95C2211yescharacteristic
49C3×#95C2211yescharacteristic
50C3×#95C2211yescharacteristic
51C3×#95C2211yescharacteristic
52#401C2×C311yescharacteristic, complemented
53#400C2×C311yescharacteristic, complemented
54#400C2×C311yescharacteristic, complemented
55#400C2×C311yescharacteristic, complemented
56#387C2×C311yescharacteristic, complemented
57#387C2×C311yescharacteristic, complemented
58#387C2×C311yescharacteristic, complemented
59#385C2×C311yescharacteristic
60#385C2×C311yescharacteristic
61#383C2×C311yescharacteristic, complemented
62#381C2×C311yescharacteristic
63#381C2×C311yescharacteristic
64#380C2×C311yescharacteristic
65C4×C22⋊C4C2×C311yescharacteristic
66C2×#95C2×C311yescharacteristic
67C24×C3C2311yescharacteristic
68C22×C3×C4—22no—
69C22×C3×C4—22no—
70C22×C3×C4—22no—
71C22×C3×C4—22no—
72C22×C3×C4—22no—
73C22×C3×C4—22no—
74C22×C3×C4—22no—
75C22×C3×C4—41no—
76C22×C3×C4—41no—
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
90C22×C3×C4C2311yescharacteristic
91C3×C4⋊C4—22no—
92C3×C4⋊C4—22no—
93C3×C4⋊C4—22no—
94C3×C4⋊C4—41no—
95C3×C4⋊C4—41no—
96C3×C4⋊C4—41no—
97C3×C22⋊C4—22no—
98C3×C22⋊C4—22no—
99C3×C22⋊C4—22no—
100C3×C22⋊C4—22no—
101C3×C42—22no—
102C3×C42—41no—
103C23×C4C22×C311yescharacteristic
104C23×C4C22×C311yescharacteristic
105C23×C4C22×C311yescharacteristic
106C2×C4⋊C4C22×C311yescharacteristic
107C2×C4⋊C4C22×C311yescharacteristic
108C2×C4⋊C4C22×C311yescharacteristic
109C2×C4⋊C4C22×C311yescharacteristic
110C2×C4⋊C4C22×C311yescharacteristic
111C2×C4⋊C4C22×C311yescharacteristic
112C2×C22⋊C4C22×C311yescharacteristic
113C2×C22⋊C4C22×C311yescharacteristic
114C2×C22⋊C4C22×C311yescharacteristic
115C2×C22⋊C4C22×C311yescharacteristic
116C2×C42C22×C311yescharacteristic
117C2×C42C22×C311yescharacteristic
118#95C22×C311yescharacteristic
119#95C22×C311yescharacteristic
120#95C22×C311yescharacteristic
121#95C22×C311yescharacteristic
122#95C22×C311yescharacteristic
123#95C22×C311yescharacteristic
124#95C22×C311yescharacteristic
125#95C22×C311yescharacteristic
126#95C22×C311yescharacteristic
127#95C22×C311yescharacteristic
128#95C22×C311yescharacteristic
129#95C22×C311yescharacteristic
130#95C22×C311yescharacteristic
131#95C22×C311yescharacteristic
132#95C22×C311yescharacteristic
133#95C22×C311yescharacteristic
134#95C22×C311yescharacteristic
135#95C22×C311yescharacteristic
136#95C22×C311yescharacteristic
137#95C22×C311yescharacteristic
138C23×C3—21no—
139C23×C3—21no—
140C23×C3—21no—
141C23×C3—21no—
142C23×C3#4112yes—
143C23×C3#4112yes—
144C23×C3#4112yes—
145C23×C3C2411yescharacteristic
146C2×C3×C4—21no—
147C2×C3×C4—21no—
148C2×C3×C4—21no—
149C2×C3×C4—21no—
150C2×C3×C4—21no—
151C2×C3×C4—21no—
152C2×C3×C4—21no—
153C2×C3×C4—21no—
154C2×C3×C4—21no—
155C2×C3×C4—21no—
156C2×C3×C4—21no—
157C2×C3×C4—21no—
158C2×C3×C4—21no—
159C2×C3×C4—21no—
160C2×C3×C4—21no—
161C2×C3×C4—21no—
162C2×C3×C4—21no—
163C2×C3×C4—21no—
164C2×C3×C4—21no—
165C2×C3×C4—21no—
166C2×C3×C4—21no—
167C2×C3×C4—21no—
168C2×C3×C4—21no—
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—44no—
187C2×C3×C4—44no—
188C2×C3×C4—44no—
189C2×C3×C4#4112yes—
190C2×C3×C4#4112yes—
191C24C23×C311yescharacteristic
192C22×C4—22no—
193C22×C4—22no—
194C22×C4—22no—
195C22×C4—22no—
196C22×C4—22no—
197C22×C4—22no—
198C22×C4—22no—
199C22×C4—41no—
200C22×C4—41no—
201C22×C4C23×C311yescharacteristic
202C22×C4C23×C311yescharacteristic
203C22×C4C23×C311yescharacteristic
204C22×C4C23×C311yescharacteristic
205C22×C4C23×C311yescharacteristic
206C22×C4C23×C311yescharacteristic
207C22×C4C23×C311yescharacteristic
208C22×C4C23×C311yescharacteristic
209C22×C4C23×C311yescharacteristic
210C22×C4C23×C311yescharacteristic
211C22×C4C23×C311yescharacteristic
212C22×C4C23×C311yescharacteristic
213C22×C4C23×C311yescharacteristic
214C22×C4C23×C311yescharacteristic
215C4⋊C4—22no—
216C4⋊C4—22no—
217C4⋊C4—22no—
218C4⋊C4—41no—
219C4⋊C4—41no—
220C4⋊C4—41no—
221C22⋊C4—22no—
222C22⋊C4—22no—
223C22⋊C4—22no—
224C22⋊C4—22no—
225C42—22no—
226C42—41no—
227C22×C3—22no—
228C22×C3—22no—
229C22×C3—22no—
230C22×C3—22no—
231C22×C3—22no—
232C22×C3—22no—
233C22×C3#12614yes—
234C22×C3C2×#4111yescharacteristic
235C22×C3C2×#4111yescharacteristic
236C22×C3C2×#4111yescharacteristic
237C22×C3C2×#4111yescharacteristic
238C22×C3C2×#4111yescharacteristic
239C22×C3H(5,𝔽2)11yescharacteristic
240C22×C32−1+411yescharacteristic
241C3×C4—22no—
242C3×C4—22no—
243C3×C4—41no—
244C3×C4—41no—
245C3×C4—41no—
246C3×C4—41no—
247C3×C4—41no—
248C3×C4—41no—
249C3×C4—41no—
250C3×C4—41no—
251C3×C4—41no—
252C3×C4—41no—
253C3×C4—41no—
254C3×C4—41no—
255C23—21no—
256C23—21no—
257C23—21no—
258C23—21no—
259C23C3×#4112yes—
260C23C3×#4112yes—
261C23C3×#4112yes—
262C23C24×C311yescharacteristic
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—44no—
304C2×C4—44no—
305C2×C4—44no—
306C2×C4C3×#4112yes—
307C2×C4C3×#4112yes—
308C2×C3—24no—
309C2×C3C2×#12611yescharacteristic
310C2×C3#52911yescharacteristic
311C2×C3#53911yescharacteristic
312C2×C3#55111yescharacteristic
313C2×C3#55111yescharacteristic
314C2×C3#55211yescharacteristic
315C2×C3#55211yescharacteristic
316C22—22no—
317C22—22no—
318C22—22no—
319C22—22no—
320C22—22no—
321C22—22no—
322C22C3×#12614yes—
323C22C2×C3×#4111yescharacteristic
324C22C2×C3×#4111yescharacteristic
325C22C2×C3×#4111yescharacteristic
326C22C2×C3×#4111yescharacteristic
327C22C2×C3×#4111yescharacteristic
328C22C3×H(5,𝔽2)11yescharacteristic
329C22C3×2−1+411yescharacteristic
330C4—22no—
331C4—22no—
332C4—41no—
333C4—41no—
334C4—41no—
335C4—41no—
336C4—41no—
337C4—41no—
338C4—41no—
339C4—41no—
340C4—41no—
341C4—41no—
342C4—41no—
343C4—41no—
344C3#249311yescharacteristic, direct product factor, Sylow
345C2—24no—
346C2C2×C3×#12611yescharacteristic
347C2C3×#52911yescharacteristic
348C2C3×#53911yescharacteristic
349C2C3×#55111yescharacteristic
350C2C3×#55111yescharacteristic
351C2C3×#55211yescharacteristic
352C2C3×#55211yescharacteristic
subgroupG/H
center, socleC23×C3C24
commutator, Frattini, cosocleC23C24×C3
prime radicalC24×C3C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23×C3 ◁ G

Complements

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

NH ≅ G/Ntype
1. C3×#401C2semidirect
2. C3×#400C2semidirect
3. C3×#400C2semidirect
4. C3×#400C2semidirect
5. C3×#387C2semidirect
6. C3×#387C2semidirect
7. C3×#387C2semidirect
10. C3×#383C2semidirect
16. #2493C3direct (N × H)
52. #401C2×C3semidirect
53. #400C2×C3semidirect
54. #400C2×C3semidirect
55. #400C2×C3semidirect
56. #387C2×C3semidirect
57. #387C2×C3semidirect
58. #387C2×C3semidirect
61. #383C2×C3semidirect
344. C3#2493direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#4012
C3×#4002
C3×#3872
C3×#3852
C3×#3832
C3×#3812
C3×#3802
C3×C4×C22⋊C42
C2×C3×#952
#24933