Finite Group Databasebeta

← C3×D4×#41⋊C3 #11919720

Subgroups — C3×D4×#41⋊C3 #11919720

Order 1152.

944 conjugacy classes of subgroups; only the 178 normal subgroups are shown.

normal subgroups only

This group has 944 conjugacy classes of subgroups — too many to draw. Only its 178 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#41⋊C3C212yesmaximal, complemented
2C3×C4⋊(#41⋊C3)C211yesmaximal, characteristic, complemented
3C3×D4×SL(2,𝔽3)C211yesmaximal, characteristic, complemented
4C3×#548⋊C3C212yesmaximal, complemented
5C3×C4×#41⋊C3C211yesmaximal, characteristic, complemented
6C3×D4×#41C311yesmaximal, characteristic, complemented
7D4×#41⋊C3C313yesmaximal, direct product factor
8C2×C3×#41⋊C3—24no—
9C2×C3×#41⋊C3C2211yescharacteristic
10C2×C3×#41⋊C3C2212yescomplemented
11C22×C3×SL(2,𝔽3)C2212yescomplemented
12C32×C4×D4—41nomaximal
13C3×C4×SL(2,𝔽3)C2211yescharacteristic, complemented
14C3×C4×SL(2,𝔽3)C2211yescharacteristic, complemented
15C22×C3×#41C2×C312yescomplemented
16C22×#41⋊C3C2×C316yescomplemented
17C3×#550C2×C311yescharacteristic, complemented
18C3×D4×Q8C2×C311yescharacteristic
19C3×#548C2×C312yescomplemented
20C3×#547—31no—
21C3×#546—32no—
22C3×D42—31no—
23C3×#532—31no—
24C3×#525—32no—
25C3×C4×#41C2×C311yescharacteristic, complemented
26C2×C3×C4×D4—31no—
27C4⋊(#41⋊C3)C2×C313yescomplemented
28D4×SL(2,𝔽3)C2×C313yescomplemented
29#548⋊C3C2×C316yescomplemented
30C4×#41⋊C3C2×C313yescomplemented
31C2×C32×D4—41no—
32C22×C32×C4—42no—
33C3×#41⋊C3—22no—
34C3×#41⋊C3D412yesdirect product factor
35C2×C3×SL(2,𝔽3)—22no—
36C2×C3×SL(2,𝔽3)C2311yescharacteristic
37C32×C4⋊C4—41no—
38C32×C22⋊C4—42no—
39C32×C42—41no—
40D4×#41C3211yescharacteristic, complemented, Sylow
41C2×C3×#41—24no—
42C2×C3×#41—32no—
43C2×C3×#41—32no—
44C2×C3×#41—64no—
45C2×C3×#41C22×C312yes—
46C2×C3×#41C22×C311yescharacteristic
47C22×C3×Q8C22×C312yes—
48C22×C3×D4—32no—
49C22×C3×D4—31no—
50C23×C3×C4—32no—
51C2×#41⋊C3—212no—
52C2×#41⋊C3C22×C313yes—
53C2×#41⋊C3C22×C316yescomplemented
54C22×SL(2,𝔽3)C22×C316yescomplemented
55C3×C4⋊Q8—31no—
56C3×#127—31no—
57C3×#124—32no—
58C3×#123—34no—
59C3×C22⋊Q8—32no—
60C3×C22⋊Q8—32no—
61C3×#121—32no—
62C3×#121—32no—
63C3×#121—32no—
64C3×#121—32no—
65C3×#120—34no—
66C3×C4×Q8C22×C311yescharacteristic
67C3×C4×Q8C22×C311yescharacteristic
68C3×C4×D4—32no—
69C3×C4×D4—31no—
70C3×C4×D4—32no—
71C3×C4×D4—31no—
72C3×C4×D4—31no—
73C3×C4×D4—31no—
74C3×C4×D4—32no—
75C3×C4×D4—31no—
76C3×C4×D4—43no—
77C3×C4×D4A411yescharacteristic
78C3×#117—31no—
79C2×C3×C4⋊C4—31no—
80C2×C3×C22⋊C4—32no—
81C2×C3×C42—31no—
82C4×SL(2,𝔽3)C22×C313yescomplemented
83C4×SL(2,𝔽3)C22×C313yescomplemented
84C23×C32—42no—
85C32×D4—44no—
86C2×C32×C4—41no—
87C2×C32×C4—42no—
88C2×C32×C4—41no—
89C2×C32×C4—41no—
90C2×C32×C4—84no—
91C3×SL(2,𝔽3)C2×D411yescharacteristic, complemented
92C22×#41C2×C3212yescomplemented
93#550C2×C3211yescharacteristic, complemented
94D4×Q8C2×C3211yescharacteristic
95#548C2×C3212yescomplemented
96#547—31no—
97#546—32no—
98D42—31no—
99#532—31no—
100#525—32no—
101C4×#41C2×C3211yescharacteristic, complemented
102C2×C4×D4—31no—
103C24×C3—32no—
104C3×#41—22no—
105C3×#41—32no—
106C3×#41—64no—
107C3×#41—64no—
108C3×#41—64no—
109C3×#41—64no—
110C3×#41—62no—
111C3×#41C3×D412yescomplemented
112C2×C3×Q8—22no—
113C2×C3×Q8—32no—
114C2×C3×Q8—62no—
115C2×C3×Q8C23×C311yescharacteristic
116C2×C3×D4—31no—
117C2×C3×D4—32no—
118C2×C3×D4—34no—
119C2×C3×D4—32no—
120C2×C3×D4—32no—
121C2×C3×D4—31no—
122C2×C3×D4—43no—
123C2×C3×D4—64no—
124C2×C3×D4—64no—
125C2×C3×D4—64no—
126C2×C3×D4C2×A411yescharacteristic
127C22×C3×C4—31no—
128C22×C3×C4—32no—
129C22×C3×C4—31no—
130C22×C3×C4—32no—
131C22×C3×C4—32no—
132C22×C3×C4—32no—
133C22×C3×C4—31no—
134C22×C3×C4—46no—
135C22×C3×C4—64no—
136C22×C3×C4—64no—
137C22×C3×C4C2×A412yes—
138#41⋊C3—26no—
139#41⋊C3C3×D416yesdirect product factor
140C2×SL(2,𝔽3)—26no—
141C2×SL(2,𝔽3)C23×C313yes—
142C3×C4⋊C4—31no—
143C3×C4⋊C4—31no—
144C3×C4⋊C4—32no—
145C3×C4⋊C4—31no—
146C3×C4⋊C4—32no—
147C3×C4⋊C4—43no—
148C3×C4⋊C4C2×A411yescharacteristic
149C3×C22⋊C4—32no—
150C3×C22⋊C4—34no—
151C3×C22⋊C4—32no—
152C3×C22⋊C4—32no—
153C3×C22⋊C4—32no—
154C3×C22⋊C4—46no—
155C3×C22⋊C4C2×A412yes—
156C3×C42—31no—
157C3×C42—31no—
158C3×C42—31no—
159C3×C42—43no—
160C3×C42C2×A411yescharacteristic
161C22×C32—44no—
162C22×C32—41no—
163C22×C32—82no—
164C22×C32—82no—
165C32×C4—42no—
166C32×C4—42no—
167C32×C4—81no—
168C32×C4—82no—
169C2×#41—24no—
170C2×#41—32no—
171C2×#41—32no—
172C2×#41—64no—
173C2×#41C22×C3212yes—
174C2×#41C22×C3211yescharacteristic
175C22×Q8C22×C3212yes—
176C22×D4—32no—
177C22×D4—31no—
178C23×C4—32no—
179C4⋊Q8—31no—
180#127—31no—
181#124—32no—
182#123—34no—
183C22⋊Q8—32no—
184C22⋊Q8—32no—
185#121—32no—
186#121—32no—
187#121—32no—
188#121—32no—
189#120—34no—
190C4×Q8C22×C3211yescharacteristic
191C4×Q8C22×C3211yescharacteristic
192C4×D4—32no—
193C4×D4—31no—
194C4×D4—32no—
195C4×D4—31no—
196C4×D4—31no—
197C4×D4—31no—
198C4×D4—32no—
199C4×D4—31no—
200C4×D4C3×A411yescharacteristic
201#117—31no—
202C2×C4⋊C4—31no—
203C2×C22⋊C4—32no—
204C2×C42—31no—
205C23×C3—31no—
206C23×C3—32no—
207C23×C3—46no—
208C23×C3—64no—
209C23×C3—64no—
210C23×C3—122no—
211C23×C3C22×A412yes—
212C3×Q8—31no—
213C3×Q8—62no—
214C3×Q8—62no—
215C3×Q8C2×C3×D411yescharacteristic
216C3×D4—32no—
217C3×D4—32no—
218C3×D4—412no—
219C3×D4—62no—
220C3×D4—62no—
221C3×D4—68no—
222C3×D4—64no—
223C3×D4—62no—
224C3×D4—122no—
225C3×D4#41⋊C314yesdirect product factor
226C2×C3×C4—24no—
227C2×C3×C4—31no—
228C2×C3×C4—32no—
229C2×C3×C4—32no—
230C2×C3×C4—31no—
231C2×C3×C4—31no—
232C2×C3×C4—32no—
233C2×C3×C4—43no—
234C2×C3×C4—43no—
235C2×C3×C4—43no—
236C2×C3×C4—46no—
237C2×C3×C4—62no—
238C2×C3×C4—62no—
239C2×C3×C4—64no—
240C2×C3×C4—62no—
241C2×C3×C4—62no—
242C2×C3×C4—64no—
243C2×C3×C4—62no—
244C2×C3×C4—812no—
245C2×C3×C4—121no—
246C2×C3×C4C22×A411yescharacteristic
247C2×C3×C4C22×A412yes—
248C2×C3×C4C22×A411yescharacteristic
249C2×C3×C4C22×A411yescharacteristic
250SL(2,𝔽3)C2×C3×D413yescomplemented
251C2×C32—41no—
252C2×C32—41no—
253C2×C32—41no—
254C2×C32—84no—
255C24—32no—
256#41—22no—
257#41—32no—
258#41—64no—
259#41—64no—
260#41—64no—
261#41—64no—
262#41—62no—
263#41C32×D412yescomplemented
264C2×Q8—22no—
265C2×Q8—32no—
266C2×Q8—62no—
267C2×Q8C23×C3211yescharacteristic
268C2×D4—31no—
269C2×D4—32no—
270C2×D4—34no—
271C2×D4—32no—
272C2×D4—32no—
273C2×D4—31no—
274C2×D4—64no—
275C2×D4—64no—
276C2×D4—64no—
277C2×D4C2×C3×A411yescharacteristic
278C22×C4—31no—
279C22×C4—32no—
280C22×C4—31no—
281C22×C4—32no—
282C22×C4—32no—
283C22×C4—32no—
284C22×C4—31no—
285C22×C4—64no—
286C22×C4—64no—
287C22×C4C2×C3×A412yes—
288C4⋊C4—31no—
289C4⋊C4—31no—
290C4⋊C4—32no—
291C4⋊C4—31no—
292C4⋊C4—32no—
293C4⋊C4C2×C3×A411yescharacteristic
294C22⋊C4—32no—
295C22⋊C4—34no—
296C22⋊C4—32no—
297C22⋊C4—32no—
298C22⋊C4—32no—
299C22⋊C4C2×C3×A412yes—
300C42—31no—
301C42—31no—
302C42—31no—
303C42C2×C3×A411yescharacteristic
304C22×C3—22no—
305C22×C3—22no—
306C22×C3—32no—
307C22×C3—412no—
308C22×C3—43no—
309C22×C3—61no—
310C22×C3—61no—
311C22×C3—62no—
312C22×C3—62no—
313C22×C3—62no—
314C22×C3—86no—
315C22×C3—86no—
316C22×C3—128no—
317C22×C3C2×#41⋊C314yescomplemented
318C22×C3C23×A411yescharacteristic
319C3×C4—22no—
320C3×C4—21no—
321C3×C4—31no—
322C3×C4—31no—
323C3×C4—46no—
324C3×C4—46no—
325C3×C4—62no—
326C3×C4—61no—
327C3×C4—61no—
328C3×C4—86no—
329C3×C4—83no—
330C3×C4D4×A412yes—
331C3×C4C2×#41⋊C312yescomplemented
332C32—41noSylow
333C23—31no—
334C23—32no—
335C23—64no—
336C23—64no—
337C23—122no—
338C23C22×C3×A412yes—
339Q8—31no—
340Q8—62no—
341Q8—62no—
342Q8C2×C32×D411yescharacteristic
343D4—32no—
344D4—32no—
345D4—62no—
346D4—62no—
347D4—68no—
348D4—64no—
349D4—62no—
350D4—122no—
351D4C3×#41⋊C314yesdirect product factor
352C2×C4—24no—
353C2×C4—31no—
354C2×C4—32no—
355C2×C4—32no—
356C2×C4—31no—
357C2×C4—31no—
358C2×C4—32no—
359C2×C4—62no—
360C2×C4—62no—
361C2×C4—64no—
362C2×C4—62no—
363C2×C4—62no—
364C2×C4—64no—
365C2×C4—62no—
366C2×C4—121no—
367C2×C4C22×C3×A411yescharacteristic
368C2×C4C22×C3×A412yes—
369C2×C4C22×C3×A411yescharacteristic
370C2×C4C22×C3×A411yescharacteristic
371C2×C3—24no—
372C2×C3—43no—
373C2×C3—43no—
374C2×C3—43no—
375C2×C3—62no—
376C2×C3—812no—
377C2×C3—122no—
378C2×C3C2×D4×A411yescharacteristic
379C2×C3C22×#41⋊C311yescharacteristic
380C2×C3#594511yescharacteristic
381C22—22no—
382C22—22no—
383C22—32no—
384C22—61no—
385C22—61no—
386C22—62no—
387C22—62no—
388C22—62no—
389C22—128no—
390C22C2×C3×#41⋊C314yescomplemented
391C22C23×C3×A411yescharacteristic
392C4—22no—
393C4—21no—
394C4—31no—
395C4—31no—
396C4—62no—
397C4—61no—
398C4—61no—
399C4C3×D4×A412yes—
400C4C2×C3×#41⋊C312yescomplemented
401C3—43no—
402C3D4×#41⋊C311yescharacteristic, direct product factor
403C2—24no—
404C2—62no—
405C2—122no—
406C2C2×C3×D4×A411yescharacteristic
407C2C22×C3×#41⋊C311yescharacteristic
408C2C3×#594511yescharacteristic
subgroupG/H
centerC2×C3×C4C22×A4
commutator, cosocleC2×Q8C23×C32
FrattiniC22C23×C3×A4
FittingC3×D4×#41C3
socleC22×C3C23×A4
hypercenterC3×C4×D4A4
hypocenterQ8C2×C32×D4
LCSG ▷ C2×Q8 ▷ Q8
UCSC1 ◁ C2×C3×C4 ◁ C3×C4×D4

Complements

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

NH ≅ G/Ntype
1. C22×C3×#41⋊C3C2semidirect
2. C3×C4⋊(#41⋊C3)C2semidirect
3. C3×D4×SL(2,𝔽3)C2semidirect
4. C3×#548⋊C3C2semidirect
5. C3×C4×#41⋊C3C2semidirect
6. C3×D4×#41C3semidirect
7. D4×#41⋊C3C3direct (N × H)
10. C2×C3×#41⋊C3C22semidirect
11. C22×C3×SL(2,𝔽3)C22semidirect
13. C3×C4×SL(2,𝔽3)C22semidirect
14. C3×C4×SL(2,𝔽3)C22semidirect
15. C22×C3×#41C2×C3semidirect
16. C22×#41⋊C3C2×C3semidirect
17. C3×#550C2×C3semidirect
19. C3×#548C2×C3semidirect
25. C3×C4×#41C2×C3semidirect
27. C4⋊(#41⋊C3)C2×C3semidirect
28. D4×SL(2,𝔽3)C2×C3semidirect
29. #548⋊C3C2×C3semidirect
30. C4×#41⋊C3C2×C3semidirect
34. C3×#41⋊C3D4direct (N × H)
40. D4×#41C32semidirect
53. C2×#41⋊C3C22×C3semidirect
54. C22×SL(2,𝔽3)C22×C3semidirect
82. C4×SL(2,𝔽3)C22×C3semidirect
83. C4×SL(2,𝔽3)C22×C3semidirect
91. C3×SL(2,𝔽3)C2×D4semidirect
92. C22×#41C2×C32semidirect
93. #550C2×C32semidirect
95. #548C2×C32semidirect
101. C4×#41C2×C32semidirect
111. C3×#41C3×D4semidirect
139. #41⋊C3C3×D4direct (N × H)
225. C3×D4#41⋊C3direct (N × H)
250. SL(2,𝔽3)C2×C3×D4semidirect
263. #41C32×D4semidirect
317. C22×C3C2×#41⋊C3semidirect
331. C3×C4C2×#41⋊C3semidirect
351. D4C3×#41⋊C3direct (N × H)
390. C22C2×C3×#41⋊C3semidirect
400. C4C2×C3×#41⋊C3semidirect
402. C3D4×#41⋊C3direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×#41⋊C32
C3×C4⋊(#41⋊C3)2
C3×D4×SL(2,𝔽3)2
C3×#548⋊C32
C3×C4×#41⋊C32
C3×D4×#413
D4×#41⋊C33
C32×C4×D44