Finite Group Databasebeta

← C3×#2419 #84283

Subgroups — C3×#2419 #84283

Order 384.

560 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#123C211yesmaximal, characteristic
2C2×C3×C4×D4C211yesmaximal, characteristic
3C3×#400C211yesmaximal, characteristic, complemented
4C3×#398C211yesmaximal, characteristic, complemented
5C3×#397C211yesmaximal, characteristic, complemented
6C3×#397C211yesmaximal, characteristic, complemented
7C3×#387C211yesmaximal, characteristic, complemented
8C3×#387C211yesmaximal, characteristic, complemented
9C3×#386C211yesmaximal, characteristic
10C3×#385C211yesmaximal, characteristic, complemented
11C3×#385C211yesmaximal, characteristic, complemented
12C3×#381C211yesmaximal, characteristic, complemented
13C3×#381C211yesmaximal, characteristic, complemented
14C3×#380C211yesmaximal, characteristic, complemented
15C2×C3×#95C211yesmaximal, characteristic, complemented
16#2419C311yesmaximal, characteristic, direct product factor, Sylow
17C22×C3×D4C2211yescharacteristic
18C23×C3×C4C2211yescharacteristic
19C23×C3×C4C2211yescharacteristic
20C23×C3×C4C2211yescharacteristic
21C23×C3×C4C2211yescharacteristic
22C3×#123—24no—
23C3×C4×D4—24no—
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×C42C2211yescharacteristic
40C3×#95C2211yescharacteristic
41C3×#95C2211yescharacteristic
42C3×#95C2211yescharacteristic
43C3×#95C2211yescharacteristic
44C3×#95C2211yescharacteristic
45C3×#95C2211yescharacteristic
46C3×#95C2211yescharacteristic
47C3×#95C2211yescharacteristic
48C3×#95C2211yescharacteristic
49C3×#95C2211yescharacteristic
50C3×#95C2211yescharacteristic
51C3×#95C2211yescharacteristic
52C3×#95C2211yescharacteristic
53C3×#95C2211yescharacteristic
54C2×#123C2×C311yescharacteristic
55C2×C4×D4C2×C311yescharacteristic
56#400C2×C311yescharacteristic, complemented
57#398C2×C311yescharacteristic, complemented
58#397C2×C311yescharacteristic, complemented
59#397C2×C311yescharacteristic, complemented
60#387C2×C311yescharacteristic, complemented
61#387C2×C311yescharacteristic, complemented
62#386C2×C311yescharacteristic
63#385C2×C311yescharacteristic, complemented
64#385C2×C311yescharacteristic, complemented
65#381C2×C311yescharacteristic, complemented
66#381C2×C311yescharacteristic, complemented
67#380C2×C311yescharacteristic, complemented
68C2×#95C2×C311yescharacteristic, complemented
69C24×C3C2311yescharacteristic
70C24×C3C2311yescharacteristic
71C2×C3×D4—22no—
72C2×C3×D4—22no—
73C2×C3×D4D414yes—
74C22×C3×C4—22no—
75C22×C3×C4—22no—
76C22×C3×C4—22no—
77C22×C3×C4—22no—
78C22×C3×C4—22no—
79C22×C3×C4—22no—
80C22×C3×C4—22no—
81C22×C3×C4—22no—
82C22×C3×C4—22no—
83C22×C3×C4—41no—
84C22×C3×C4—41no—
85C22×C3×C4—41no—
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
96C22×C3×C4C2311yescharacteristic
97C22×C3×C4C2311yescharacteristic
98C22×C3×C4C2311yescharacteristic
99C3×C4⋊C4—22no—
100C3×C4⋊C4—22no—
101C3×C4⋊C4—22no—
102C3×C4⋊C4—22no—
103C3×C4⋊C4—22no—
104C3×C4⋊C4—41no—
105C3×C4⋊C4—41no—
106C3×C22⋊C4—22no—
107C3×C22⋊C4—22no—
108C3×C22⋊C4—22no—
109C3×C22⋊C4—22no—
110C3×C22⋊C4—22no—
111C3×C22⋊C4—22no—
112C3×C22⋊C4—22no—
113C3×C22⋊C4—41no—
114C3×C42—22no—
115C22×D4C22×C311yescharacteristic
116C23×C4C22×C311yescharacteristic
117C23×C4C22×C311yescharacteristic
118C23×C4C22×C311yescharacteristic
119C23×C4C22×C311yescharacteristic
120#123—24no—
121C4×D4—24no—
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×C42C22×C311yescharacteristic
138#95C22×C311yescharacteristic
139#95C22×C311yescharacteristic
140#95C22×C311yescharacteristic
141#95C22×C311yescharacteristic
142#95C22×C311yescharacteristic
143#95C22×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×C3C2×D412yes—
163C23×C3C2×D412yes—
164C23×C3#4112yes—
165C23×C3#4112yes—
166C23×C3C2411yescharacteristic
167C3×D4—28no—
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—21no—
199C2×C3×C4—21no—
200C2×C3×C4—21no—
201C2×C3×C4—21no—
202C2×C3×C4—21no—
203C2×C3×C4—21no—
204C2×C3×C4—44no—
205C2×C3×C4—44no—
206C2×C3×C4—44no—
207C2×C3×C4—44no—
208C2×C3×C4C2×D412yes—
209C2×C3×C4#4112yes—
210C2×C3×C4#4112yes—
211C24C23×C311yescharacteristic
212C24C23×C311yescharacteristic
213C2×D4—22no—
214C2×D4—22no—
215C2×D4C3×D414yes—
216C22×C4—22no—
217C22×C4—22no—
218C22×C4—22no—
219C22×C4—22no—
220C22×C4—22no—
221C22×C4—22no—
222C22×C4—22no—
223C22×C4—22no—
224C22×C4—22no—
225C22×C4—41no—
226C22×C4—41no—
227C22×C4—41no—
228C22×C4C23×C311yescharacteristic
229C22×C4C23×C311yescharacteristic
230C22×C4C23×C311yescharacteristic
231C22×C4C23×C311yescharacteristic
232C22×C4C23×C311yescharacteristic
233C22×C4C23×C311yescharacteristic
234C22×C4C23×C311yescharacteristic
235C22×C4C23×C311yescharacteristic
236C22×C4C23×C311yescharacteristic
237C22×C4C23×C311yescharacteristic
238C22×C4C23×C311yescharacteristic
239C22×C4C23×C311yescharacteristic
240C22×C4C23×C311yescharacteristic
241C4⋊C4—22no—
242C4⋊C4—22no—
243C4⋊C4—22no—
244C4⋊C4—22no—
245C4⋊C4—22no—
246C4⋊C4—41no—
247C4⋊C4—41no—
248C22⋊C4—22no—
249C22⋊C4—22no—
250C22⋊C4—22no—
251C22⋊C4—22no—
252C22⋊C4—22no—
253C22⋊C4—22no—
254C22⋊C4—22no—
255C22⋊C4—41no—
256C42—22no—
257C22×C3—22no—
258C22×C3—22no—
259C22×C3—22no—
260C22×C3—22no—
261C22×C3—22no—
262C22×C3—22no—
263C22×C3—22no—
264C22×C3—22no—
265C22×C3—22no—
266C22×C3—41no—
267C22×C3—41no—
268C22×C3—41no—
269C22×C3—41no—
270C22×C3#12314yes—
271C22×C3C22×D411yescharacteristic
272C22×C3C2×#4111yescharacteristic
273C22×C3C2×#4111yescharacteristic
274C22×C3C2×#4111yescharacteristic
275C22×C3C2×#4111yescharacteristic
276C22×C3H(5,𝔽2)11yescharacteristic
277C22×C32−1+411yescharacteristic
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—
288C3×C4—41no—
289C3×C4—41no—
290C3×C4—41no—
291C23—21no—
292C23—21no—
293C23—21no—
294C23—21no—
295C23—21no—
296C23—21no—
297C23—21no—
298C23—21no—
299C23—21no—
300C23—21no—
301C23C2×C3×D412yes—
302C23C2×C3×D412yes—
303C23C3×#4112yes—
304C23C3×#4112yes—
305C23C24×C311yescharacteristic
306D4—28no—
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×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—44no—
344C2×C4—44no—
345C2×C4—44no—
346C2×C4—44no—
347C2×C4C2×C3×D412yes—
348C2×C4C3×#4112yes—
349C2×C4C3×#4112yes—
350C2×C3—24no—
351C2×C3—42no—
352C2×C3C2×#12311yescharacteristic
353C2×C3#52911yescharacteristic
354C2×C3#53911yescharacteristic
355C2×C3#54611yescharacteristic
356C2×C3#54711yescharacteristic
357C2×C3#55111yescharacteristic
358C2×C3#55211yescharacteristic
359C22—22no—
360C22—22no—
361C22—22no—
362C22—22no—
363C22—22no—
364C22—22no—
365C22—22no—
366C22—22no—
367C22—22no—
368C22—41no—
369C22—41no—
370C22—41no—
371C22—41no—
372C22C3×#12314yes—
373C22C22×C3×D411yescharacteristic
374C22C2×C3×#4111yescharacteristic
375C22C2×C3×#4111yescharacteristic
376C22C2×C3×#4111yescharacteristic
377C22C2×C3×#4111yescharacteristic
378C22C3×H(5,𝔽2)11yescharacteristic
379C22C3×2−1+411yescharacteristic
380C4—22no—
381C4—22no—
382C4—22no—
383C4—41no—
384C4—41no—
385C4—41no—
386C4—41no—
387C4—41no—
388C4—41no—
389C4—41no—
390C4—41no—
391C4—41no—
392C4—41no—
393C3#241911yescharacteristic, direct product factor, Sylow
394C2—24no—
395C2—42no—
396C2C2×C3×#12311yescharacteristic
397C2C3×#52911yescharacteristic
398C2C3×#53911yescharacteristic
399C2C3×#54611yescharacteristic
400C2C3×#54711yescharacteristic
401C2C3×#55111yescharacteristic
402C2C3×#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
3. C3×#400C2semidirect
4. C3×#398C2semidirect
5. C3×#397C2semidirect
6. C3×#397C2semidirect
7. C3×#387C2semidirect
8. C3×#387C2semidirect
10. C3×#385C2semidirect
11. C3×#385C2semidirect
12. C3×#381C2semidirect
13. C3×#381C2semidirect
14. C3×#380C2semidirect
15. C2×C3×#95C2semidirect
16. #2419C3direct (N × H)
56. #400C2×C3semidirect
57. #398C2×C3semidirect
58. #397C2×C3semidirect
59. #397C2×C3semidirect
60. #387C2×C3semidirect
61. #387C2×C3semidirect
63. #385C2×C3semidirect
64. #385C2×C3semidirect
65. #381C2×C3semidirect
66. #381C2×C3semidirect
67. #380C2×C3semidirect
68. C2×#95C2×C3semidirect
393. C3#2419direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#1232
C2×C3×C4×D42
C3×#4002
C3×#3982
C3×#3972
C3×#3872
C3×#3862
C3×#3852
C3×#3812
C3×#3802
C2×C3×#952
#24193