Finite Group Databasebeta

← C3×#2425 #84289

Subgroups — C3×#2425 #84289

Order 384.

666 conjugacy classes of subgroups.

The subgroup lattice has 454 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#123C211yesmaximal, characteristic, complemented
2C2×C3×#123C211yesmaximal, characteristic, complemented
3C2×C3×#121C211yesmaximal, characteristic
4C2×C3×C4×D4C211yesmaximal, characteristic, complemented
5C3×#398C211yesmaximal, characteristic, complemented
6C3×#397C211yesmaximal, characteristic, complemented
7C3×#396C211yesmaximal, characteristic, complemented
8C3×#394C211yesmaximal, characteristic, complemented
9C3×#389C211yesmaximal, characteristic, complemented
10C3×#388C211yesmaximal, characteristic, complemented
11C3×#386C211yesmaximal, characteristic, complemented
12C3×#386C211yesmaximal, characteristic, complemented
13C3×#385C211yesmaximal, characteristic, complemented
14C3×#380C211yesmaximal, characteristic, complemented
15C2×C3×#95C211yesmaximal, characteristic, complemented
16#2425C311yesmaximal, characteristic, direct product factor, Sylow
17C22×C3×D4C2211yescharacteristic
18C22×C3×D4C2211yescharacteristic
19C22×C3×D4C2211yescharacteristic
20C23×C3×C4C2211yescharacteristic
21C23×C3×C4C2211yescharacteristic
22C23×C3×C4C2211yescharacteristic
23C23×C3×C4C2211yescharacteristic
24C3×#123—24no—
25C3×#123—24no—
26C3×#121—24no—
27C3×C4×D4—24no—
28C2×C3×C4⋊C4C2211yescharacteristic
29C2×C3×C4⋊C4C2211yescharacteristic
30C2×C3×C4⋊C4C2211yescharacteristic
31C2×C3×C4⋊C4C2211yescharacteristic
32C2×C3×C4⋊C4C2211yescharacteristic
33C2×C3×C4⋊C4C2211yescharacteristic
34C2×C3×C4⋊C4C2211yescharacteristic
35C2×C3×C4⋊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×C22⋊C4C2211yescharacteristic
43C2×C3×C22⋊C4C2211yescharacteristic
44C2×C3×C22⋊C4C2211yescharacteristic
45C2×C3×C22⋊C4C2211yescharacteristic
46C2×C3×C22⋊C4C2211yescharacteristic
47C2×C3×C42C2211yescharacteristic
48C3×#95C2211yescharacteristic
49C3×#95C2211yescharacteristic
50C3×#95C2211yescharacteristic
51C3×#95C2211yescharacteristic
52C3×#95C2211yescharacteristic
53C3×#95C2211yescharacteristic
54C3×#95C2211yescharacteristic
55C3×#95C2211yescharacteristic
56C2×#123C2×C311yescharacteristic, complemented
57C2×#123C2×C311yescharacteristic, complemented
58C2×#121C2×C311yescharacteristic
59C2×C4×D4C2×C311yescharacteristic, complemented
60#398C2×C311yescharacteristic, complemented
61#397C2×C311yescharacteristic, complemented
62#396C2×C311yescharacteristic, complemented
63#394C2×C311yescharacteristic, complemented
64#389C2×C311yescharacteristic, complemented
65#388C2×C311yescharacteristic, complemented
66#386C2×C311yescharacteristic, complemented
67#386C2×C311yescharacteristic, complemented
68#385C2×C311yescharacteristic, complemented
69#380C2×C311yescharacteristic, complemented
70C2×#95C2×C311yescharacteristic, complemented
71C24×C3C2311yescharacteristic
72C24×C3C2311yescharacteristic
73C24×C3C2311yescharacteristic
74C2×C3×D4—22no—
75C2×C3×D4—22no—
76C2×C3×D4—22no—
77C2×C3×D4—22no—
78C2×C3×D4—22no—
79C2×C3×D4—22no—
80C2×C3×D4—22no—
81C2×C3×D4—41no—
82C2×C3×D4D414yes—
83C22×C3×C4—22no—
84C22×C3×C4—22no—
85C22×C3×C4—22no—
86C22×C3×C4—22no—
87C22×C3×C4—22no—
88C22×C3×C4—22no—
89C22×C3×C4—22no—
90C22×C3×C4—22no—
91C22×C3×C4—22no—
92C22×C3×C4—41no—
93C22×C3×C4—41no—
94C22×C3×C4—41no—
95C22×C3×C4C2311yescharacteristic
96C22×C3×C4C2311yescharacteristic
97C22×C3×C4C2311yescharacteristic
98C22×C3×C4C2311yescharacteristic
99C22×C3×C4C2311yescharacteristic
100C22×C3×C4C2311yescharacteristic
101C22×C3×C4C2311yescharacteristic
102C22×C3×C4C2311yescharacteristic
103C22×C3×C4C2311yescharacteristic
104C22×C3×C4C2311yescharacteristic
105C22×C3×C4C2311yescharacteristic
106C22×C3×C4C2311yescharacteristic
107C3×C4⋊C4—22no—
108C3×C4⋊C4—22no—
109C3×C4⋊C4—22no—
110C3×C4⋊C4—22no—
111C3×C4⋊C4—22no—
112C3×C4⋊C4—22no—
113C3×C4⋊C4—22no—
114C3×C4⋊C4—41no—
115C3×C22⋊C4—22no—
116C3×C22⋊C4—22no—
117C3×C22⋊C4—22no—
118C3×C22⋊C4—22no—
119C3×C22⋊C4—22no—
120C3×C22⋊C4—22no—
121C3×C22⋊C4—22no—
122C3×C22⋊C4—22no—
123C3×C22⋊C4—22no—
124C3×C22⋊C4—41no—
125C3×C22⋊C4D414yescomplemented
126C3×C42—22no—
127C22×D4C22×C311yescharacteristic
128C22×D4C22×C311yescharacteristic
129C22×D4C22×C311yescharacteristic
130C23×C4C22×C311yescharacteristic
131C23×C4C22×C311yescharacteristic
132C23×C4C22×C311yescharacteristic
133C23×C4C22×C311yescharacteristic
134#123—24no—
135#123—24no—
136#121—24no—
137C4×D4—24no—
138C2×C4⋊C4C22×C311yescharacteristic
139C2×C4⋊C4C22×C311yescharacteristic
140C2×C4⋊C4C22×C311yescharacteristic
141C2×C4⋊C4C22×C311yescharacteristic
142C2×C4⋊C4C22×C311yescharacteristic
143C2×C4⋊C4C22×C311yescharacteristic
144C2×C4⋊C4C22×C311yescharacteristic
145C2×C4⋊C4C22×C311yescharacteristic
146C2×C22⋊C4C22×C311yescharacteristic
147C2×C22⋊C4C22×C311yescharacteristic
148C2×C22⋊C4C22×C311yescharacteristic
149C2×C22⋊C4C22×C311yescharacteristic
150C2×C22⋊C4C22×C311yescharacteristic
151C2×C22⋊C4C22×C311yescharacteristic
152C2×C22⋊C4C22×C311yescharacteristic
153C2×C22⋊C4C22×C311yescharacteristic
154C2×C22⋊C4C22×C311yescharacteristic
155C2×C22⋊C4C22×C311yescharacteristic
156C2×C22⋊C4C22×C311yescharacteristic
157C2×C42C22×C311yescharacteristic
158#95C22×C311yescharacteristic
159#95C22×C311yescharacteristic
160#95C22×C311yescharacteristic
161#95C22×C311yescharacteristic
162#95C22×C311yescharacteristic
163#95C22×C311yescharacteristic
164#95C22×C311yescharacteristic
165#95C22×C311yescharacteristic
166C23×C3—21no—
167C23×C3—21no—
168C23×C3—21no—
169C23×C3—21no—
170C23×C3—21no—
171C23×C3—21no—
172C23×C3—21no—
173C23×C3—21no—
174C23×C3—21no—
175C23×C3—21no—
176C23×C3—21no—
177C23×C3—21no—
178C23×C3—21no—
179C23×C3—21no—
180C23×C3—21no—
181C23×C3—21no—
182C23×C3—21no—
183C23×C3C2×D412yes—
184C23×C3C2×D412yes—
185C23×C3C2×D412yes—
186C23×C3#4112yes—
187C23×C3C2411yescharacteristic
188C3×D4—28no—
189C3×D4—44no—
190C3×D4—44no—
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—21no—
209C2×C3×C4—21no—
210C2×C3×C4—21no—
211C2×C3×C4—21no—
212C2×C3×C4—21no—
213C2×C3×C4—21no—
214C2×C3×C4—21no—
215C2×C3×C4—21no—
216C2×C3×C4—21no—
217C2×C3×C4—21no—
218C2×C3×C4—21no—
219C2×C3×C4—21no—
220C2×C3×C4—21no—
221C2×C3×C4—21no—
222C2×C3×C4—44no—
223C2×C3×C4—44no—
224C2×C3×C4—44no—
225C2×C3×C4—44no—
226C2×C3×C4C2×D412yes—
227C2×C3×C4C2×D412yes—
228C2×C3×C4C2×D412yes—
229C2×C3×C4#4112yes—
230C2×C3×C4#4112yes—
231C24C23×C311yescharacteristic
232C24C23×C311yescharacteristic
233C24C23×C311yescharacteristic
234C2×D4—22no—
235C2×D4—22no—
236C2×D4—22no—
237C2×D4—22no—
238C2×D4—22no—
239C2×D4—22no—
240C2×D4—22no—
241C2×D4—41no—
242C2×D4C3×D414yes—
243C22×C4—22no—
244C22×C4—22no—
245C22×C4—22no—
246C22×C4—22no—
247C22×C4—22no—
248C22×C4—22no—
249C22×C4—22no—
250C22×C4—22no—
251C22×C4—22no—
252C22×C4—41no—
253C22×C4—41no—
254C22×C4—41no—
255C22×C4C23×C311yescharacteristic
256C22×C4C23×C311yescharacteristic
257C22×C4C23×C311yescharacteristic
258C22×C4C23×C311yescharacteristic
259C22×C4C23×C311yescharacteristic
260C22×C4C23×C311yescharacteristic
261C22×C4C23×C311yescharacteristic
262C22×C4C23×C311yescharacteristic
263C22×C4C23×C311yescharacteristic
264C22×C4C23×C311yescharacteristic
265C22×C4C23×C311yescharacteristic
266C22×C4C23×C311yescharacteristic
267C4⋊C4—22no—
268C4⋊C4—22no—
269C4⋊C4—22no—
270C4⋊C4—22no—
271C4⋊C4—22no—
272C4⋊C4—22no—
273C4⋊C4—22no—
274C4⋊C4—41no—
275C22⋊C4—22no—
276C22⋊C4—22no—
277C22⋊C4—22no—
278C22⋊C4—22no—
279C22⋊C4—22no—
280C22⋊C4—22no—
281C22⋊C4—22no—
282C22⋊C4—22no—
283C22⋊C4—22no—
284C22⋊C4—41no—
285C22⋊C4C3×D414yescomplemented
286C42—22no—
287C22×C3—22no—
288C22×C3—22no—
289C22×C3—22no—
290C22×C3—22no—
291C22×C3—22no—
292C22×C3—22no—
293C22×C3—22no—
294C22×C3—22no—
295C22×C3—22no—
296C22×C3—41no—
297C22×C3—41no—
298C22×C3—41no—
299C22×C3—41no—
300C22×C3—41no—
301C22×C3—41no—
302C22×C3—41no—
303C22×C3—41no—
304C22×C3—41no—
305C22×C3—41no—
306C22×C3—41no—
307C22×C3#12114yes—
308C22×C3C22×D411yescharacteristic
309C22×C3C22×D411yescharacteristic
310C22×C3C2×#4111yescharacteristic
311C22×C3C2×#4111yescharacteristic
312C22×C3C2×#4111yescharacteristic
313C22×C3H(5,𝔽2)11yescharacteristic
314C22×C32−1+411yescharacteristic
315C3×C4—22no—
316C3×C4—22no—
317C3×C4—22no—
318C3×C4—22no—
319C3×C4—22no—
320C3×C4—41no—
321C3×C4—41no—
322C3×C4—41no—
323C3×C4—41no—
324C3×C4—41no—
325C3×C4—41no—
326C3×C4—41no—
327C23—21no—
328C23—21no—
329C23—21no—
330C23—21no—
331C23—21no—
332C23—21no—
333C23—21no—
334C23—21no—
335C23—21no—
336C23—21no—
337C23—21no—
338C23—21no—
339C23—21no—
340C23—21no—
341C23—21no—
342C23—21no—
343C23—21no—
344C23C2×C3×D412yes—
345C23C2×C3×D412yes—
346C23C2×C3×D412yes—
347C23C3×#4112yes—
348C23C24×C311yescharacteristic
349D4—28no—
350D4—44no—
351D4—44no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—21no—
365C2×C4—21no—
366C2×C4—21no—
367C2×C4—21no—
368C2×C4—21no—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—21no—
375C2×C4—21no—
376C2×C4—21no—
377C2×C4—21no—
378C2×C4—21no—
379C2×C4—21no—
380C2×C4—21no—
381C2×C4—21no—
382C2×C4—21no—
383C2×C4—44no—
384C2×C4—44no—
385C2×C4—44no—
386C2×C4—44no—
387C2×C4C2×C3×D412yes—
388C2×C4C2×C3×D412yes—
389C2×C4C2×C3×D412yes—
390C2×C4C3×#4112yes—
391C2×C4C3×#4112yes—
392C2×C3—24no—
393C2×C3—42no—
394C2×C3—81no—
395C2×C3C2×#12111yescharacteristic
396C2×C3#52911yescharacteristic
397C2×C3#53911yescharacteristic
398C2×C3#54611yescharacteristic
399C2×C3#54611yescharacteristic
400C2×C3#54711yescharacteristic
401C2×C3#54711yescharacteristic
402C22—22no—
403C22—22no—
404C22—22no—
405C22—22no—
406C22—22no—
407C22—22no—
408C22—22no—
409C22—22no—
410C22—22no—
411C22—41no—
412C22—41no—
413C22—41no—
414C22—41no—
415C22—41no—
416C22—41no—
417C22—41no—
418C22—41no—
419C22—41no—
420C22—41no—
421C22—41no—
422C22C3×#12114yes—
423C22C22×C3×D411yescharacteristic
424C22C22×C3×D411yescharacteristic
425C22C2×C3×#4111yescharacteristic
426C22C2×C3×#4111yescharacteristic
427C22C2×C3×#4111yescharacteristic
428C22C3×H(5,𝔽2)11yescharacteristic
429C22C3×2−1+411yescharacteristic
430C4—22no—
431C4—22no—
432C4—22no—
433C4—22no—
434C4—22no—
435C4—41no—
436C4—41no—
437C4—41no—
438C4—41no—
439C4—41no—
440C4—41no—
441C4—41no—
442C3#242511yescharacteristic, direct product factor, Sylow
443C2—24no—
444C2—42no—
445C2—81no—
446C2C2×C3×#12111yescharacteristic
447C2C3×#52911yescharacteristic
448C2C3×#53911yescharacteristic
449C2C3×#54611yescharacteristic
450C2C3×#54611yescharacteristic
451C2C3×#54711yescharacteristic
452C2C3×#54711yescharacteristic
subgroupG/H
center, socleC23×C3C24
commutator, Frattini, cosocleC23C24×C3
prime radicalC2×C3×#121C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23×C3 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C3×#123C2semidirect
2. C2×C3×#123C2semidirect
4. C2×C3×C4×D4C2semidirect
5. C3×#398C2semidirect
6. C3×#397C2semidirect
7. C3×#396C2semidirect
8. C3×#394C2semidirect
9. C3×#389C2semidirect
10. C3×#388C2semidirect
11. C3×#386C2semidirect
12. C3×#386C2semidirect
13. C3×#385C2semidirect
14. C3×#380C2semidirect
15. C2×C3×#95C2semidirect
16. #2425C3direct (N × H)
56. C2×#123C2×C3semidirect
57. C2×#123C2×C3semidirect
59. C2×C4×D4C2×C3semidirect
60. #398C2×C3semidirect
61. #397C2×C3semidirect
62. #396C2×C3semidirect
63. #394C2×C3semidirect
64. #389C2×C3semidirect
65. #388C2×C3semidirect
66. #386C2×C3semidirect
67. #386C2×C3semidirect
68. #385C2×C3semidirect
69. #380C2×C3semidirect
70. C2×#95C2×C3semidirect
125. C3×C22⋊C4D4semidirect
285. C22⋊C4C3×D4semidirect
442. C3#2425direct (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×#1212
C2×C3×C4×D42
C3×#3982
C3×#3972
C3×#3962
C3×#3942
C3×#3892
C3×#3882
C3×#3862
C3×#3852
C3×#3802
C2×C3×#952
#24253