Finite Group Databasebeta

← C3×#2449 #84313

Subgroups — C3×#2449 #84313

Order 384.

648 conjugacy classes of subgroups.

The subgroup lattice has 426 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C22⋊Q8C211yesmaximal, characteristic, complemented
2C2×C3×C22⋊Q8C211yesmaximal, characteristic, complemented
3C2×C3×C4×D4C211yesmaximal, characteristic
4C22×C3×C4⋊C4C211yesmaximal, characteristic, complemented
5C3×#399C211yesmaximal, characteristic, complemented
6C3×#398C211yesmaximal, characteristic, complemented
7C3×#396C211yesmaximal, characteristic, complemented
8C3×#395C211yesmaximal, characteristic, complemented
9C3×#389C211yesmaximal, characteristic, complemented
10C3×#387C211yesmaximal, characteristic, complemented
11C3×#386C211yesmaximal, characteristic
12C3×#386C211yesmaximal, characteristic
13C3×#385C211yesmaximal, characteristic, complemented
14C3×#385C211yesmaximal, characteristic, complemented
15C3×#385C211yesmaximal, characteristic, complemented
16#2449C311yesmaximal, characteristic, direct product factor, Sylow
17C22×C3×Q8C2211yescharacteristic
18C22×C3×D4C2211yescharacteristic
19C23×C3×C4C2211yescharacteristic
20C23×C3×C4C2211yescharacteristic
21C23×C3×C4C2211yescharacteristic
22C23×C3×C4C2211yescharacteristic
23C3×C22⋊Q8—24no—
24C3×C22⋊Q8—24no—
25C3×C4×D4—24no—
26C2×C3×C4⋊C4—24no—
27C2×C3×C4⋊C4C2211yescharacteristic
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×C4⋊C4C2211yescharacteristic
37C2×C3×C4⋊C4C2211yescharacteristic
38C2×C3×C4⋊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×C22⋊Q8C2×C311yescharacteristic, complemented
57C2×C22⋊Q8C2×C311yescharacteristic, complemented
58C2×C4×D4C2×C311yescharacteristic
59C22×C4⋊C4C2×C311yescharacteristic, complemented
60#399C2×C311yescharacteristic, complemented
61#398C2×C311yescharacteristic, complemented
62#396C2×C311yescharacteristic, complemented
63#395C2×C311yescharacteristic, complemented
64#389C2×C311yescharacteristic, complemented
65#387C2×C311yescharacteristic, complemented
66#386C2×C311yescharacteristic
67#386C2×C311yescharacteristic
68#385C2×C311yescharacteristic, complemented
69#385C2×C311yescharacteristic, complemented
70#385C2×C311yescharacteristic, complemented
71C24×C3C2311yescharacteristic
72C24×C3C2311yescharacteristic
73C2×C3×Q8—22no—
74C2×C3×Q8—22no—
75C2×C3×Q8—41no—
76C2×C3×D4—22no—
77C2×C3×D4—22no—
78C2×C3×D4Q814yescomplemented
79C22×C3×C4—22no—
80C22×C3×C4—22no—
81C22×C3×C4—22no—
82C22×C3×C4—22no—
83C22×C3×C4—22no—
84C22×C3×C4—22no—
85C22×C3×C4—22no—
86C22×C3×C4—22no—
87C22×C3×C4—22no—
88C22×C3×C4—41no—
89C22×C3×C4—41no—
90C22×C3×C4—41no—
91C22×C3×C4C2311yescharacteristic
92C22×C3×C4C2311yescharacteristic
93C22×C3×C4C2311yescharacteristic
94C22×C3×C4C2311yescharacteristic
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
104C3×C4⋊C4—22no—
105C3×C4⋊C4—22no—
106C3×C4⋊C4—22no—
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×C4⋊C4D414yescomplemented
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—41no—
123C3×C22⋊C4D414yes—
124C3×C42—22no—
125C22×Q8C22×C311yescharacteristic
126C22×D4C22×C311yescharacteristic
127C23×C4C22×C311yescharacteristic
128C23×C4C22×C311yescharacteristic
129C23×C4C22×C311yescharacteristic
130C23×C4C22×C311yescharacteristic
131C22⋊Q8—24no—
132C22⋊Q8—24no—
133C4×D4—24no—
134C2×C4⋊C4—24no—
135C2×C4⋊C4C22×C311yescharacteristic
136C2×C4⋊C4C22×C311yescharacteristic
137C2×C4⋊C4C22×C311yescharacteristic
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×C4⋊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×C42C22×C311yescharacteristic
156#95C22×C311yescharacteristic
157#95C22×C311yescharacteristic
158#95C22×C311yescharacteristic
159#95C22×C311yescharacteristic
160#95C22×C311yescharacteristic
161#95C22×C311yescharacteristic
162#95C22×C311yescharacteristic
163#95C22×C311yescharacteristic
164C23×C3—21no—
165C23×C3—21no—
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×C3C2×D412yes—
175C23×C3C2×Q812yes—
176C23×C3C2×Q812yes—
177C23×C3#4112yes—
178C23×C3C2411yescharacteristic
179C3×Q8—44no—
180C3×D4—28no—
181C2×C3×C4—28no—
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—21no—
209C2×C3×C4—21no—
210C2×C3×C4—21no—
211C2×C3×C4—21no—
212C2×C3×C4—21no—
213C2×C3×C4—21no—
214C2×C3×C4—44no—
215C2×C3×C4—44no—
216C2×C3×C4—44no—
217C2×C3×C4C2×D412yes—
218C2×C3×C4C2×D412yes—
219C2×C3×C4C2×D412yes—
220C2×C3×C4C2×D412yes—
221C2×C3×C4C2×D412yes—
222C2×C3×C4C2×Q812yes—
223C2×C3×C4#4112yes—
224C24C23×C311yescharacteristic
225C24C23×C311yescharacteristic
226C2×Q8—22no—
227C2×Q8—22no—
228C2×Q8—41no—
229C2×D4—22no—
230C2×D4—22no—
231C2×D4C3×Q814yescomplemented
232C22×C4—22no—
233C22×C4—22no—
234C22×C4—22no—
235C22×C4—22no—
236C22×C4—22no—
237C22×C4—22no—
238C22×C4—22no—
239C22×C4—22no—
240C22×C4—22no—
241C22×C4—41no—
242C22×C4—41no—
243C22×C4—41no—
244C22×C4C23×C311yescharacteristic
245C22×C4C23×C311yescharacteristic
246C22×C4C23×C311yescharacteristic
247C22×C4C23×C311yescharacteristic
248C22×C4C23×C311yescharacteristic
249C22×C4C23×C311yescharacteristic
250C22×C4C23×C311yescharacteristic
251C22×C4C23×C311yescharacteristic
252C22×C4C23×C311yescharacteristic
253C22×C4C23×C311yescharacteristic
254C22×C4C23×C311yescharacteristic
255C22×C4C23×C311yescharacteristic
256C22×C4C23×C311yescharacteristic
257C4⋊C4—22no—
258C4⋊C4—22no—
259C4⋊C4—22no—
260C4⋊C4—22no—
261C4⋊C4—22no—
262C4⋊C4—22no—
263C4⋊C4—22no—
264C4⋊C4—22no—
265C4⋊C4—22no—
266C4⋊C4—22no—
267C4⋊C4—41no—
268C4⋊C4C3×D414yescomplemented
269C22⋊C4—22no—
270C22⋊C4—22no—
271C22⋊C4—22no—
272C22⋊C4—22no—
273C22⋊C4—22no—
274C22⋊C4—22no—
275C22⋊C4—41no—
276C22⋊C4C3×D414yes—
277C42—22no—
278C22×C3—22no—
279C22×C3—22no—
280C22×C3—22no—
281C22×C3—22no—
282C22×C3—22no—
283C22×C3—22no—
284C22×C3—22no—
285C22×C3—22no—
286C22×C3—22no—
287C22×C3—41no—
288C22×C3—41no—
289C22×C3—41no—
290C22×C3—41no—
291C22×C3C22⋊Q814yescomplemented
292C22×C3C22×D411yescharacteristic
293C22×C3C22×D411yescharacteristic
294C22×C3C22×Q811yescharacteristic
295C22×C3C2×#4111yescharacteristic
296C22×C3C2×#4111yescharacteristic
297C22×C3H(5,𝔽2)11yescharacteristic
298C22×C32−1+411yescharacteristic
299C3×C4—22no—
300C3×C4—22no—
301C3×C4—22no—
302C3×C4—22no—
303C3×C4—22no—
304C3×C4—22no—
305C3×C4—22no—
306C3×C4—41no—
307C3×C4—41no—
308C3×C4—41no—
309C3×C4—41no—
310C3×C4—41no—
311C3×C4—41no—
312C23—21no—
313C23—21no—
314C23—21no—
315C23—21no—
316C23—21no—
317C23—21no—
318C23—21no—
319C23—21no—
320C23—21no—
321C23—21no—
322C23C2×C3×D412yes—
323C23C2×C3×Q812yes—
324C23C2×C3×Q812yes—
325C23C3×#4112yes—
326C23C24×C311yescharacteristic
327Q8—44no—
328D4—28no—
329C2×C4—28no—
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×C4—21no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—44no—
363C2×C4—44no—
364C2×C4—44no—
365C2×C4C2×C3×D412yes—
366C2×C4C2×C3×D412yes—
367C2×C4C2×C3×D412yes—
368C2×C4C2×C3×D412yes—
369C2×C4C2×C3×D412yes—
370C2×C4C2×C3×Q812yes—
371C2×C4C3×#4112yes—
372C2×C3—24no—
373C2×C3—42no—
374C2×C3C2×C22⋊Q811yescharacteristic
375C2×C3#52511yescharacteristic
376C2×C3#53911yescharacteristic
377C2×C3D4211yescharacteristic
378C2×C3#54711yescharacteristic
379C2×C3D4×Q811yescharacteristic
380C2×C3#55411yescharacteristic
381C22—22no—
382C22—22no—
383C22—22no—
384C22—22no—
385C22—22no—
386C22—22no—
387C22—22no—
388C22—22no—
389C22—22no—
390C22—41no—
391C22—41no—
392C22—41no—
393C22—41no—
394C22C3×C22⋊Q814yescomplemented
395C22C22×C3×D411yescharacteristic
396C22C22×C3×D411yescharacteristic
397C22C22×C3×Q811yescharacteristic
398C22C2×C3×#4111yescharacteristic
399C22C2×C3×#4111yescharacteristic
400C22C3×H(5,𝔽2)11yescharacteristic
401C22C3×2−1+411yescharacteristic
402C4—22no—
403C4—22no—
404C4—22no—
405C4—22no—
406C4—22no—
407C4—22no—
408C4—22no—
409C4—41no—
410C4—41no—
411C4—41no—
412C4—41no—
413C4—41no—
414C4—41no—
415C3#244911yescharacteristic, direct product factor, Sylow
416C2—24no—
417C2—42no—
418C2C2×C3×C22⋊Q811yescharacteristic
419C2C3×#52511yescharacteristic
420C2C3×#53911yescharacteristic
421C2C3×D4211yescharacteristic
422C2C3×#54711yescharacteristic
423C2C3×D4×Q811yescharacteristic
424C2C3×#55411yescharacteristic
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. C2×C3×C22⋊Q8C2semidirect
2. C2×C3×C22⋊Q8C2semidirect
4. C22×C3×C4⋊C4C2semidirect
5. C3×#399C2semidirect
6. C3×#398C2semidirect
7. C3×#396C2semidirect
8. C3×#395C2semidirect
9. C3×#389C2semidirect
10. C3×#387C2semidirect
13. C3×#385C2semidirect
14. C3×#385C2semidirect
15. C3×#385C2semidirect
16. #2449C3direct (N × H)
56. C2×C22⋊Q8C2×C3semidirect
57. C2×C22⋊Q8C2×C3semidirect
59. C22×C4⋊C4C2×C3semidirect
60. #399C2×C3semidirect
61. #398C2×C3semidirect
62. #396C2×C3semidirect
63. #395C2×C3semidirect
64. #389C2×C3semidirect
65. #387C2×C3semidirect
68. #385C2×C3semidirect
69. #385C2×C3semidirect
70. #385C2×C3semidirect
78. C2×C3×D4Q8semidirect
115. C3×C4⋊C4D4semidirect
231. C2×D4C3×Q8semidirect
268. C4⋊C4C3×D4semidirect
291. C22×C3C22⋊Q8semidirect
394. C22C3×C22⋊Q8semidirect
415. C3#2449direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×C22⋊Q82
C2×C3×C4×D42
C22×C3×C4⋊C42
C3×#3992
C3×#3982
C3×#3962
C3×#3952
C3×#3892
C3×#3872
C3×#3862
C3×#3852
#24493