Finite Group Databasebeta

← C3×#2803 #84667

Subgroups — C3×#2803 #84667

Order 384.

470 conjugacy classes of subgroups.

The subgroup lattice has 422 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#397C211yesmaximal, characteristic, complemented
2C3×#394C211yesmaximal, characteristic, complemented
3C3×#394C211yesmaximal, characteristic, complemented
4C3×#394C211yesmaximal, characteristic, complemented
5C3×#394C211yesmaximal, characteristic, complemented
6C3×#392C211yesmaximal, characteristic
7C3×#390C211yesmaximal, characteristic, complemented
8C3×#390C211yesmaximal, characteristic, complemented
9C3×#389C211yesmaximal, characteristic, complemented
10C3×#388C211yesmaximal, characteristic, complemented
11C3×#388C211yesmaximal, characteristic, complemented
12C3×#388C211yesmaximal, characteristic, complemented
13C3×#388C211yesmaximal, characteristic, complemented
14C3×#388C211yesmaximal, characteristic, complemented
15C3×#387C211yesmaximal, characteristic, complemented
16#2803C311yesmaximal, characteristic, direct product factor, Sylow
17C22×C3×D4C2211yescharacteristic
18C22×C3×D4C2211yescharacteristic
19C22×C3×D4C2211yescharacteristic
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×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×C22⋊C4C2211yescharacteristic
38C2×C3×C22⋊C4C2211yescharacteristic
39C2×C3×C22⋊C4C2211yescharacteristic
40C2×C3×C22⋊C4C2211yescharacteristic
41C2×C3×C42C2211yescharacteristic
42C2×C3×C42C2211yescharacteristic
43C2×C3×C42C2211yescharacteristic
44C3×#95C2211yescharacteristic
45C3×#95C2211yescharacteristic
46C3×#95C2211yescharacteristic
47C3×#95C2211yescharacteristic
48C3×#95C2211yescharacteristic
49C3×#95C2211yescharacteristic
50C3×#95C2211yescharacteristic
51C3×#95C2211yescharacteristic
52#397C2×C311yescharacteristic, complemented
53#394C2×C311yescharacteristic, complemented
54#394C2×C311yescharacteristic, complemented
55#394C2×C311yescharacteristic, complemented
56#394C2×C311yescharacteristic, complemented
57#392C2×C311yescharacteristic
58#390C2×C311yescharacteristic, complemented
59#390C2×C311yescharacteristic, complemented
60#389C2×C311yescharacteristic, complemented
61#388C2×C311yescharacteristic, complemented
62#388C2×C311yescharacteristic, complemented
63#388C2×C311yescharacteristic, complemented
64#388C2×C311yescharacteristic, complemented
65#388C2×C311yescharacteristic, complemented
66#387C2×C311yescharacteristic, complemented
67C24×C3C2311yescharacteristic
68C24×C3C2311yescharacteristic
69C24×C3C2311yescharacteristic
70C2×C3×D4—22no—
71C2×C3×D4—22no—
72C2×C3×D4—41no—
73C2×C3×D4—41no—
74C2×C3×D4—41no—
75C2×C3×D4—41no—
76C2×C3×D4—41no—
77C2×C3×D4—41no—
78C2×C3×D4—41no—
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—41no—
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×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×C22⋊C4—41no—
109C3×C22⋊C4—41no—
110C3×C22⋊C4—41no—
111C3×C22⋊C4—41no—
112C3×C42—41no—
113C3×C42—41no—
114C3×C42—41no—
115C22×D4C22×C311yescharacteristic
116C22×D4C22×C311yescharacteristic
117C22×D4C22×C311yescharacteristic
118C2×C4⋊C4C22×C311yescharacteristic
119C2×C4⋊C4C22×C311yescharacteristic
120C2×C4⋊C4C22×C311yescharacteristic
121C2×C4⋊C4C22×C311yescharacteristic
122C2×C4⋊C4C22×C311yescharacteristic
123C2×C4⋊C4C22×C311yescharacteristic
124C2×C22⋊C4C22×C311yescharacteristic
125C2×C22⋊C4C22×C311yescharacteristic
126C2×C22⋊C4C22×C311yescharacteristic
127C2×C22⋊C4C22×C311yescharacteristic
128C2×C22⋊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×C42C22×C311yescharacteristic
140C2×C42C22×C311yescharacteristic
141C2×C42C22×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
150C23×C3—21no—
151C23×C3—21no—
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—21no—
166C23×C3—21no—
167C23×C3—21no—
168C23×C3—21no—
169C23×C3—21no—
170C23×C3—21no—
171C23×C3C2411yescharacteristic
172C3×D4—44no—
173C3×D4—44no—
174C3×D4—44no—
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—21no—
205C2×C3×C4—21no—
206C2×C3×C4—21no—
207C2×C3×C4—21no—
208C2×C3×C4#4112yes—
209C2×C3×C4#4112yes—
210C2×C3×C4#4112yes—
211C24C23×C311yescharacteristic
212C24C23×C311yescharacteristic
213C24C23×C311yescharacteristic
214C2×D4—22no—
215C2×D4—22no—
216C2×D4—41no—
217C2×D4—41no—
218C2×D4—41no—
219C2×D4—41no—
220C2×D4—41no—
221C2×D4—41no—
222C2×D4—41no—
223C22×C4C23×C311yescharacteristic
224C22×C4C23×C311yescharacteristic
225C22×C4C23×C311yescharacteristic
226C22×C4C23×C311yescharacteristic
227C22×C4C23×C311yescharacteristic
228C22×C4C23×C311yescharacteristic
229C22×C4C23×C311yescharacteristic
230C22×C4C23×C311yescharacteristic
231C22×C4C23×C311yescharacteristic
232C22×C4C23×C311yescharacteristic
233C22×C4C23×C311yescharacteristic
234C22×C4C23×C311yescharacteristic
235C4⋊C4—22no—
236C4⋊C4—22no—
237C4⋊C4—41no—
238C4⋊C4—41no—
239C4⋊C4—41no—
240C4⋊C4—41no—
241C22⋊C4—22no—
242C22⋊C4—22no—
243C22⋊C4—22no—
244C22⋊C4—22no—
245C22⋊C4—22no—
246C22⋊C4—41no—
247C22⋊C4—41no—
248C22⋊C4—41no—
249C22⋊C4—41no—
250C22⋊C4—41no—
251C22⋊C4—41no—
252C22⋊C4—41no—
253C22⋊C4—41no—
254C22⋊C4—41no—
255C22⋊C4—41no—
256C42—41no—
257C42—41no—
258C42—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×C3—41no—
269C22×C3—41no—
270C22×C3—41no—
271C22×C3—41no—
272C22×C3—41no—
273C22×C3—41no—
274C22×C3—41no—
275C22×C3—41no—
276C22×C3—41no—
277C22×C3—41no—
278C22×C3—41no—
279C22×C3—41no—
280C22×C3C2×#4111yescharacteristic
281C22×C3C2×#4111yescharacteristic
282C22×C3C2×#4111yescharacteristic
283C22×C3H(5,𝔽2)11yescharacteristic
284C22×C3H(5,𝔽2)11yescharacteristic
285C22×C3H(5,𝔽2)11yescharacteristic
286C22×C3H(5,𝔽2)11yescharacteristic
287C3×C4—22no—
288C3×C4—22no—
289C3×C4—22no—
290C3×C4—41no—
291C3×C4—41no—
292C3×C4—41no—
293C3×C4—41no—
294C3×C4—41no—
295C3×C4—41no—
296C3×C4—41no—
297C3×C4—41no—
298C3×C4—41no—
299C23—21no—
300C23—21no—
301C23—21no—
302C23—21no—
303C23—21no—
304C23—21no—
305C23—21no—
306C23—21no—
307C23—21no—
308C23—21no—
309C23—21no—
310C23—21no—
311C23—21no—
312C23—21no—
313C23—21no—
314C23—21no—
315C23—21no—
316C23—21no—
317C23—21no—
318C23—21no—
319C23—21no—
320C23C24×C311yescharacteristic
321D4—44no—
322D4—44no—
323D4—44no—
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—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×C4C3×#4112yes—
358C2×C4C3×#4112yes—
359C2×C4C3×#4112yes—
360C2×C3—81no—
361C2×C3—81no—
362C2×C3—81no—
363C2×C3#53811yescharacteristic
364C2×C3#53811yescharacteristic
365C2×C3#54011yescharacteristic
366C2×C3#55311yescharacteristic
367C2×C3#55511yescharacteristic
368C2×C3#55911yescharacteristic
369C2×C3#56011yescharacteristic
370C22—41no—
371C22—41no—
372C22—41no—
373C22—41no—
374C22—41no—
375C22—41no—
376C22—41no—
377C22—41no—
378C22—41no—
379C22—41no—
380C22—41no—
381C22—41no—
382C22—41no—
383C22—41no—
384C22—41no—
385C22—41no—
386C22—41no—
387C22—41no—
388C22—41no—
389C22—41no—
390C22—41no—
391C22C2×C3×#4111yescharacteristic
392C22C2×C3×#4111yescharacteristic
393C22C2×C3×#4111yescharacteristic
394C22C3×H(5,𝔽2)11yescharacteristic
395C22C3×H(5,𝔽2)11yescharacteristic
396C22C3×H(5,𝔽2)11yescharacteristic
397C22C3×H(5,𝔽2)11yescharacteristic
398C4—22no—
399C4—22no—
400C4—22no—
401C4—41no—
402C4—41no—
403C4—41no—
404C4—41no—
405C4—41no—
406C4—41no—
407C4—41no—
408C4—41no—
409C4—41no—
410C3#280311yescharacteristic, direct product factor, Sylow
411C2—81no—
412C2—81no—
413C2—81no—
414C2C3×#53811yescharacteristic
415C2C3×#53811yescharacteristic
416C2C3×#54011yescharacteristic
417C2C3×#55311yescharacteristic
418C2C3×#55511yescharacteristic
419C2C3×#55911yescharacteristic
420C2C3×#56011yescharacteristic
subgroupG/H
center, socleC23×C3C24
commutator, Frattini, cosocleC23C24×C3
prime radicalC3×#392C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23×C3 ◁ G

Complements

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

NH ≅ G/Ntype
1. C3×#397C2semidirect
2. C3×#394C2semidirect
3. C3×#394C2semidirect
4. C3×#394C2semidirect
5. C3×#394C2semidirect
7. C3×#390C2semidirect
8. C3×#390C2semidirect
9. C3×#389C2semidirect
10. C3×#388C2semidirect
11. C3×#388C2semidirect
12. C3×#388C2semidirect
13. C3×#388C2semidirect
14. C3×#388C2semidirect
15. C3×#387C2semidirect
16. #2803C3direct (N × H)
52. #397C2×C3semidirect
53. #394C2×C3semidirect
54. #394C2×C3semidirect
55. #394C2×C3semidirect
56. #394C2×C3semidirect
58. #390C2×C3semidirect
59. #390C2×C3semidirect
60. #389C2×C3semidirect
61. #388C2×C3semidirect
62. #388C2×C3semidirect
63. #388C2×C3semidirect
64. #388C2×C3semidirect
65. #388C2×C3semidirect
66. #387C2×C3semidirect
410. C3#2803direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#3972
C3×#3942
C3×#3922
C3×#3902
C3×#3892
C3×#3882
C3×#3872
#28033