Finite Group Databasebeta

← C3×#2746 #84610

Subgroups — C3×#2746 #84610

Order 384.

448 conjugacy classes of subgroups.

The subgroup lattice has 388 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×#399C211yesmaximal, characteristic, complemented
4C3×#398C211yesmaximal, characteristic, complemented
5C3×#397C211yesmaximal, characteristic, complemented
6C3×#394C211yesmaximal, characteristic
7C3×#388C211yesmaximal, characteristic, complemented
8C3×#388C211yesmaximal, characteristic, complemented
9C3×#387C211yesmaximal, characteristic, complemented
10C3×#386C211yesmaximal, characteristic
11C3×#386C211yesmaximal, characteristic
12C3×#385C211yesmaximal, characteristic, complemented
13C3×#385C211yesmaximal, characteristic, complemented
14C3×#381C211yesmaximal, characteristic, complemented
15C3×#380C211yesmaximal, characteristic, complemented
16#2746C311yesmaximal, characteristic, direct product factor, Sylow
17C22×C3×D4C2211yescharacteristic
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×C4⋊C4C2211yescharacteristic
27C2×C3×C22⋊C4C2211yescharacteristic
28C2×C3×C22⋊C4C2211yescharacteristic
29C2×C3×C22⋊C4C2211yescharacteristic
30C2×C3×C22⋊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×C42C2211yescharacteristic
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#399C2×C311yescharacteristic, complemented
55#398C2×C311yescharacteristic, complemented
56#397C2×C311yescharacteristic, complemented
57#394C2×C311yescharacteristic
58#388C2×C311yescharacteristic, complemented
59#388C2×C311yescharacteristic, complemented
60#387C2×C311yescharacteristic, complemented
61#386C2×C311yescharacteristic
62#386C2×C311yescharacteristic
63#385C2×C311yescharacteristic, complemented
64#385C2×C311yescharacteristic, complemented
65#381C2×C311yescharacteristic, complemented
66#380C2×C311yescharacteristic, complemented
67C24×C3C2311yescharacteristic
68C24×C3C2311yescharacteristic
69C2×C3×D4—22no—
70C2×C3×D4—22no—
71C2×C3×D4—41no—
72C22×C3×C4—22no—
73C22×C3×C4—22no—
74C22×C3×C4—41no—
75C22×C3×C4—41no—
76C22×C3×C4—41no—
77C22×C3×C4—41no—
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—41no—
93C3×C4⋊C4—41no—
94C3×C4⋊C4—41no—
95C3×C4⋊C4—41no—
96C3×C4⋊C4—41no—
97C3×C4⋊C4—41no—
98C3×C22⋊C4—22no—
99C3×C22⋊C4—22no—
100C3×C22⋊C4—22no—
101C3×C22⋊C4—22no—
102C3×C22⋊C4—41no—
103C3×C22⋊C4—41no—
104C3×C22⋊C4—41no—
105C3×C22⋊C4—41no—
106C3×C22⋊C4—41no—
107C3×C22⋊C4—41no—
108C3×C42—41no—
109C22×D4C22×C311yescharacteristic
110C23×C4C22×C311yescharacteristic
111C23×C4C22×C311yescharacteristic
112C2×C4⋊C4C22×C311yescharacteristic
113C2×C4⋊C4C22×C311yescharacteristic
114C2×C4⋊C4C22×C311yescharacteristic
115C2×C4⋊C4C22×C311yescharacteristic
116C2×C4⋊C4C22×C311yescharacteristic
117C2×C4⋊C4C22×C311yescharacteristic
118C2×C4⋊C4C22×C311yescharacteristic
119C2×C22⋊C4C22×C311yescharacteristic
120C2×C22⋊C4C22×C311yescharacteristic
121C2×C22⋊C4C22×C311yescharacteristic
122C2×C22⋊C4C22×C311yescharacteristic
123C2×C22⋊C4C22×C311yescharacteristic
124C2×C22⋊C4C22×C311yescharacteristic
125C2×C22⋊C4C22×C311yescharacteristic
126C2×C22⋊C4C22×C311yescharacteristic
127C2×C22⋊C4C22×C311yescharacteristic
128C2×C22⋊C4C22×C311yescharacteristic
129C2×C42C22×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
138#95C22×C311yescharacteristic
139#95C22×C311yescharacteristic
140#95C22×C311yescharacteristic
141#95C22×C311yescharacteristic
142#95C22×C311yescharacteristic
143#95C22×C311yescharacteristic
144C23×C3—21no—
145C23×C3—21no—
146C23×C3—21no—
147C23×C3—21no—
148C23×C3—21no—
149C23×C3—21no—
150C23×C3—21no—
151C23×C3—21no—
152C23×C3—21no—
153C23×C3—21no—
154C23×C3—21no—
155C23×C3—21no—
156C23×C3#4112yes—
157C23×C3#4112yes—
158C23×C3C2411yescharacteristic
159C3×D4—44no—
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—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—44no—
199C2×C3×C4—44no—
200C2×C3×C4#4112yes—
201C24C23×C311yescharacteristic
202C24C23×C311yescharacteristic
203C2×D4—22no—
204C2×D4—22no—
205C2×D4—41no—
206C22×C4—22no—
207C22×C4—22no—
208C22×C4—41no—
209C22×C4—41no—
210C22×C4—41no—
211C22×C4—41no—
212C22×C4C23×C311yescharacteristic
213C22×C4C23×C311yescharacteristic
214C22×C4C23×C311yescharacteristic
215C22×C4C23×C311yescharacteristic
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
225C4⋊C4—22no—
226C4⋊C4—41no—
227C4⋊C4—41no—
228C4⋊C4—41no—
229C4⋊C4—41no—
230C4⋊C4—41no—
231C4⋊C4—41no—
232C22⋊C4—22no—
233C22⋊C4—22no—
234C22⋊C4—22no—
235C22⋊C4—22no—
236C22⋊C4—41no—
237C22⋊C4—41no—
238C22⋊C4—41no—
239C22⋊C4—41no—
240C22⋊C4—41no—
241C22⋊C4—41no—
242C42—41no—
243C22×C3—22no—
244C22×C3—22no—
245C22×C3—22no—
246C22×C3—22no—
247C22×C3—22no—
248C22×C3—22no—
249C22×C3—41no—
250C22×C3—41no—
251C22×C3—41no—
252C22×C3—41no—
253C22×C3—41no—
254C22×C3—41no—
255C22×C3—41no—
256C22×C3—41no—
257C22×C3C2×#4111yescharacteristic
258C22×C3C2×#4111yescharacteristic
259C22×C3C2×#4111yescharacteristic
260C22×C3H(5,𝔽2)11yescharacteristic
261C22×C3H(5,𝔽2)11yescharacteristic
262C22×C3H(5,𝔽2)11yescharacteristic
263C22×C32−1+411yescharacteristic
264C3×C4—22no—
265C3×C4—41no—
266C3×C4—41no—
267C3×C4—41no—
268C3×C4—41no—
269C3×C4—41no—
270C3×C4—41no—
271C3×C4—41no—
272C3×C4—41no—
273C3×C4—41no—
274C3×C4—41no—
275C3×C4—41no—
276C3×C4—41no—
277C23—21no—
278C23—21no—
279C23—21no—
280C23—21no—
281C23—21no—
282C23—21no—
283C23—21no—
284C23—21no—
285C23—21no—
286C23—21no—
287C23—21no—
288C23—21no—
289C23C3×#4112yes—
290C23C3×#4112yes—
291C23C24×C311yescharacteristic
292D4—44no—
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—21no—
304C2×C4—21no—
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—44no—
332C2×C4—44no—
333C2×C4C3×#4112yes—
334C2×C3—42no—
335C2×C3—42no—
336C2×C3#53911yescharacteristic
337C2×C3#53911yescharacteristic
338C2×C3#54211yescharacteristic
339C2×C3#55111yescharacteristic
340C2×C3#55111yescharacteristic
341C2×C3#55311yescharacteristic
342C2×C3#56011yescharacteristic
343C22—22no—
344C22—22no—
345C22—22no—
346C22—22no—
347C22—22no—
348C22—22no—
349C22—41no—
350C22—41no—
351C22—41no—
352C22—41no—
353C22—41no—
354C22—41no—
355C22—41no—
356C22—41no—
357C22C2×C3×#4111yescharacteristic
358C22C2×C3×#4111yescharacteristic
359C22C2×C3×#4111yescharacteristic
360C22C3×H(5,𝔽2)11yescharacteristic
361C22C3×H(5,𝔽2)11yescharacteristic
362C22C3×H(5,𝔽2)11yescharacteristic
363C22C3×2−1+411yescharacteristic
364C4—22no—
365C4—41no—
366C4—41no—
367C4—41no—
368C4—41no—
369C4—41no—
370C4—41no—
371C4—41no—
372C4—41no—
373C4—41no—
374C4—41no—
375C4—41no—
376C4—41no—
377C3#274611yescharacteristic, direct product factor, Sylow
378C2—42no—
379C2—42no—
380C2C3×#53911yescharacteristic
381C2C3×#53911yescharacteristic
382C2C3×#54211yescharacteristic
383C2C3×#55111yescharacteristic
384C2C3×#55111yescharacteristic
385C2C3×#55311yescharacteristic
386C2C3×#56011yescharacteristic
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. C3×#401C2semidirect
2. C3×#400C2semidirect
3. C3×#399C2semidirect
4. C3×#398C2semidirect
5. C3×#397C2semidirect
7. C3×#388C2semidirect
8. C3×#388C2semidirect
9. C3×#387C2semidirect
12. C3×#385C2semidirect
13. C3×#385C2semidirect
14. C3×#381C2semidirect
15. C3×#380C2semidirect
16. #2746C3direct (N × H)
52. #401C2×C3semidirect
53. #400C2×C3semidirect
54. #399C2×C3semidirect
55. #398C2×C3semidirect
56. #397C2×C3semidirect
58. #388C2×C3semidirect
59. #388C2×C3semidirect
60. #387C2×C3semidirect
63. #385C2×C3semidirect
64. #385C2×C3semidirect
65. #381C2×C3semidirect
66. #380C2×C3semidirect
377. C3#2746direct (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×#3992
C3×#3982
C3×#3972
C3×#3942
C3×#3882
C3×#3872
C3×#3862
C3×#3852
C3×#3812
C3×#3802
#27463