Finite Group Databasebeta

← C4×D3×#41⋊C3 #11923198

Subgroups — C4×D3×#41⋊C3 #11923198

Order 1152.

869 conjugacy classes of subgroups; only the 139 normal subgroups are shown.

normal subgroups only

This group has 869 conjugacy classes of subgroups — too many to draw. Only its 139 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
1C2×D3×#41⋊C3C211yesmaximal, characteristic
2C3×C4×#41⋊C3C211yesmaximal, characteristic, complemented
3Dic3×#41⋊C3C211yesmaximal, characteristic, complemented
4C4×D3×SL(2,𝔽3)C212yesmaximal, complemented
5C4×C3⋊(#41⋊C3)C212yesmaximal, complemented
6C4×D3×#41C311yesmaximal, characteristic, complemented
7C2×C4×#41⋊C3—31nomaximal
8C2×C3×#41⋊C3C2211yescharacteristic
9D3×#41⋊C3C414yesdirect product factor
10C2×D3×SL(2,𝔽3)C2211yescharacteristic
11C2×C3⋊(#41⋊C3)C2211yescharacteristic
12C3×C42×D3—41nomaximal
13C3×C4×SL(2,𝔽3)C2212yescomplemented
14Dic3×SL(2,𝔽3)C2212yescomplemented
15C2×D3×#41C2×C311yescharacteristic
16C22×#41⋊C3—31no—
17C3×C4×#41C2×C311yescharacteristic, complemented
18Dic3×#41C2×C311yescharacteristic, complemented
19C4×#239C2×C312yescomplemented
20C4×D3×Q8C2×C312yes—
21C4×D3×D4—32no—
22C4×#237—32no—
23#5522—31no—
24D3×#117—31no—
25C4×#235—31no—
26C2×C42×D3—31no—
27C4×#41⋊C3—21no—
28C4×#41⋊C3—31no—
29C4×#41⋊C3—32no—
30C4×#41⋊C3D311yescharacteristic, direct product factor
31C2×C4×SL(2,𝔽3)—32no—
32C2×C3×C4×D3—41no—
33C2×C3×C4×D3—42no—
34C3×#41⋊C3C2×C412yescomplemented
35C2×C3×SL(2,𝔽3)C2311yescharacteristic
36D3×SL(2,𝔽3)C2×C412yescomplemented
37C3⋊(#41⋊C3)C2×C412yescomplemented
38C32×C42—41no—
39C3×C4×Dic3—42no—
40C3×C4×Dic3—41no—
41C2×C4×#41—31noSylow
42C2×C3×#41C22×C311yescharacteristic
43D3×#41—34no—
44D3×#41C3×C414yescomplemented
45C2×#239C22×C311yescharacteristic
46C2×D3×Q8C22×C311yescharacteristic
47C2×#237—31no—
48C2×D3×D4—31no—
49C2×#235—31no—
50C22×C4×D3—31no—
51C22×C4×D3—32no—
52C2×#41⋊C3—21no—
53C2×#41⋊C3—34no—
54C2×#41⋊C3—31no—
55C2×#41⋊C3C2×D311yescharacteristic
56C22×SL(2,𝔽3)—31no—
57C3×C4×Q8C22×C312yes—
58C3×C4×D4—32no—
59C3×#117—31no—
60C2×C3×C42—31no—
61C2×C3×C42—121no—
62Q8×Dic3C22×C312yes—
63D4×Dic3—32no—
64C4×#67—34no—
65#926—31no—
66C2×C4×Dic3—31no—
67C2×C4×Dic3—32no—
68#893—32no—
69#892—32no—
70D3×C4⋊C4—32no—
71#887—32no—
72#67⋊C4—34no—
73D3×C22⋊C4—32no—
74#877—32no—
75C4×D12—32no—
76#872—32no—
77C42×D3—31no—
78C42×D3—32no—
79C42×D3—31no—
80C42×D3—31no—
81C42×D3—32no—
82C42×D3A411yescharacteristic
83C4×Dic6—32no—
84C4×SL(2,𝔽3)—22no—
85C4×SL(2,𝔽3)—32no—
86C4×SL(2,𝔽3)C2×D312yescomplemented
87C22×C3×D3—41no—
88C2×C32×C4—41no—
89C2×C32×C4—42no—
90C2×C3×Dic3—42no—
91C2×C3×Dic3—41no—
92C3×C4×D3—44no—
93C3×C4×D3—48no—
94C3×SL(2,𝔽3)C22×C411yescharacteristic, complemented
95C22×#41—31no—
96C4×#41—31no—
97C4×#41—32no—
98C4×#41—91no—
99C4×#41—91no—
100C4×#41—92no—
101C4×#41C3×D311yescharacteristic, complemented
102C2×C4×Q8—32no—
103C2×C4×D4—92no—
104C2×#117—91no—
105C22×C42—91no—
106C23×D3—31no—
107C3×#41—32no—
108C3×#41C2×C3×C412yescomplemented
109C2×C3×Q8C23×C311yescharacteristic
110C2×C3×D4—31no—
111C22×C3×C4—31no—
112C22×C3×C4—32no—
113C22×C3×C4—121no—
114C22×C3×C4—122no—
115C2×#67—32no—
116C22×Dic3—31no—
117C22×Dic3—32no—
118#239—32no—
119#239C2×C3×C412yescomplemented
120D3×Q8—32no—
121D3×Q8C2×C3×C412yes—
122#237—34no—
123#237—34no—
124D3×D4—34no—
125D3×D4—34no—
126#235—34no—
127#235—34no—
128C2×D12—31no—
129C2×C4×D3—31no—
130C2×C4×D3—31no—
131C2×C4×D3—31no—
132C2×C4×D3—34no—
133C2×C4×D3—34no—
134C2×C4×D3—32no—
135C2×C4×D3—32no—
136C2×C4×D3—32no—
137C2×C4×D3—68no—
138C2×C4×D3C2×A411yescharacteristic
139C2×C4×D3C2×A412yes—
140C2×Dic6—31no—
141#41⋊C3—22no—
142#41⋊C3—32no—
143#41⋊C3C4×D312yesdirect product factor
144C2×SL(2,𝔽3)—21no—
145C2×SL(2,𝔽3)—32no—
146C2×SL(2,𝔽3)C22×D311yescharacteristic
147C3×C4⋊C4—32no—
148C3×C22⋊C4—32no—
149C3×C42—32no—
150C3×C42—31no—
151C3×C42—41no—
152C3×C42—81no—
153C3×C42—122no—
154C3×C42—121no—
155C3×C42C2×A411yescharacteristic
156#217—32no—
157(C2×D3)⋊C4—34no—
158C4⋊Dic3—32no—
159Dic3⋊C4—34no—
160C4×Dic3—32no—
161C4×Dic3—31no—
162C4×Dic3—32no—
163C4×Dic3—32no—
164C4×Dic3—32no—
165C4×Dic3C2×A412yes—
166C4×Dic3C2×A411yescharacteristic
167C22×C32—41no—
168C2×C3×D3—42no—
169C2×C3×D3—44no—
170C32×C4—42no—
171C32×C4—44no—
172C3×Dic3—42no—
173C3×Dic3—44no—
174C2×#41—34no—
175C2×#41—31no—
176C2×#41—91no—
177C2×#41—91no—
178C2×#41—94no—
179C2×#41C2×C3×D311yescharacteristic
180C22×Q8—31no—
181C22×D4—91no—
182C23×C4—91no—
183C23×C4—92no—
184C4×Q8—32no—
185C4×Q8—92no—
186C4×Q8—92no—
187C4×Q8C2×C3×D312yes—
188C4×D4—32no—
189C4×D4—92no—
190C4×D4—94no—
191C4×D4—92no—
192C4×D4—94no—
193C4×D4—92no—
194#117—31no—
195#117—92no—
196#117—92no—
197#117—92no—
198#117—91no—
199C2×C4⋊C4—92no—
200C2×C22⋊C4—92no—
201C2×C42—31no—
202C2×C42—31no—
203C2×C42—92no—
204C2×C42—91no—
205C2×C42—91no—
206C2×C42—92no—
207C2×C42—91no—
208C2×C42—92no—
209C2×C42—91no—
210C23×C3—31no—
211C23×C3—121no—
212C22×D3—31no—
213C22×D3—34no—
214C22×D3—64no—
215C22×D3C22×A411yescharacteristic
216C3×Q8—31no—
217C3×Q8C22×C3×C411yescharacteristic
218C3×D4—32no—
219C3×D4—32no—
220C2×C3×C4—31no—
221C2×C3×C4—32no—
222C2×C3×C4—32no—
223C2×C3×C4—32no—
224C2×C3×C4—42no—
225C2×C3×C4—41no—
226C2×C3×C4—64no—
227C2×C3×C4—82no—
228C2×C3×C4—81no—
229C2×C3×C4—124no—
230C2×C3×C4—128no—
231C2×C3×C4—122no—
232C2×C3×C4—121no—
233C2×C3×C4C22×A411yescharacteristic
234C2×C3×C4C22×A412yes—
235#67—38no—
236C2×Dic3—31no—
237C2×Dic3—34no—
238C2×Dic3—32no—
239C2×Dic3—64no—
240C2×Dic3C22×A411yescharacteristic
241C2×Dic3C22×A412yes—
242D12—32no—
243D12—32no—
244C4×D3—32no—
245C4×D3—32no—
246C4×D3—34no—
247C4×D3—32no—
248C4×D3—32no—
249C4×D3—64no—
250C4×D3—64no—
251C4×D3—64no—
252C4×D3C4×A414yes—
253C4×D3#41⋊C318yesdirect product factor
254Dic6—32no—
255Dic6—32no—
256SL(2,𝔽3)—21no—
257SL(2,𝔽3)C2×C4×D311yescharacteristic, complemented
258C2×C32—41no—
259C2×C32—42no—
260C3×D3—44no—
261C24—91no—
262#41—32no—
263#41—32no—
264#41—94no—
265#41—94no—
266#41—94no—
267#41—94no—
268#41—92no—
269#41C3×C4×D312yescomplemented
270C2×Q8—32no—
271C2×Q8—91no—
272C2×Q8—92no—
273C2×Q8C22×C3×D311yescharacteristic
274C2×D4—31no—
275C2×D4—91no—
276C2×D4—94no—
277C2×D4—94no—
278C2×D4—92no—
279C22×C4—31no—
280C22×C4—31no—
281C22×C4—32no—
282C22×C4—32no—
283C22×C4—91no—
284C22×C4—94no—
285C22×C4—94no—
286C22×C4—92no—
287C22×C4—91no—
288C22×C4—91no—
289C22×C4—92no—
290C22×C4—92no—
291C22×C4—91no—
292C22×C4—92no—
293C22×C4—188no—
294C4⋊C4—32no—
295C4⋊C4—92no—
296C4⋊C4—94no—
297C22⋊C4—32no—
298C22⋊C4—94no—
299C22⋊C4—92no—
300C42—31no—
301C42—32no—
302C42—31no—
303C42—32no—
304C42—92no—
305C42—92no—
306C42—92no—
307C42—91no—
308C42—92no—
309C42D3×A411yescharacteristic
310C22×C3—32no—
311C22×C3—41no—
312C22×C3—62no—
313C22×C3—81no—
314C22×C3—124no—
315C22×C3—122no—
316C22×C3C23×A411yescharacteristic
317C2×D3—32no—
318C2×D3—62no—
319C2×D3—68no—
320C2×D3C2×C4×A412yes—
321C2×D3C2×#41⋊C314yes—
322C3×C4—31no—
323C3×C4—31no—
324C3×C4—42no—
325C3×C4—44no—
326C3×C4—62no—
327C3×C4—82no—
328C3×C4—84no—
329C3×C4—124no—
330C3×C4—122no—
331C3×C4C2×C4×A412yes—
332C3×C4C2×#41⋊C314yescomplemented
333Dic3—32no—
334Dic3—62no—
335Dic3C2×C4×A412yes—
336Dic3C2×#41⋊C314yescomplemented
337C32—41noSylow
338C23—31no—
339C23—31no—
340C23—94no—
341C23—91no—
342C23—184no—
343Q8—31no—
344Q8—92no—
345Q8—92no—
346Q8C2×C3×C4×D311yescharacteristic
347D4—32no—
348D4—32no—
349D4—92no—
350D4—92no—
351D4—98no—
352C2×C4—31no—
353C2×C4—31no—
354C2×C4—32no—
355C2×C4—32no—
356C2×C4—32no—
357C2×C4—34no—
358C2×C4—38no—
359C2×C4—32no—
360C2×C4—64no—
361C2×C4—92no—
362C2×C4—92no—
363C2×C4—92no—
364C2×C4—92no—
365C2×C4—94no—
366C2×C4—91no—
367C2×C4—94no—
368C2×C4—92no—
369C2×C4—184no—
370C2×C4—184no—
371C2×C4—184no—
372C2×C4—184no—
373C2×C4C2×D3×A411yescharacteristic
374C2×C4C2×D3×A412yes—
375C2×C3—41no—
376C2×C3—42no—
377C2×C3—62no—
378C2×C3—81no—
379C2×C3—82no—
380C2×C3—124no—
381C2×C3C22×C4×A411yescharacteristic
382C2×C3C22×#41⋊C312yes—
383D3—62no—
384D3C4×#41⋊C314yesdirect product factor
385C22—32no—
386C22—34no—
387C22—32no—
388C22—62no—
389C22—92no—
390C22—188no—
391C22—182no—
392C22C22×D3×A411yescharacteristic
393C4—31no—
394C4—31no—
395C4—32no—
396C4—34no—
397C4—62no—
398C4—92no—
399C4—182no—
400C4C4×D3×A412yes—
401C4D3×#41⋊C314yesdirect product factor
402C3—41no—
403C3—81no—
404C3C2×C4×#41⋊C311yescharacteristic, complemented
405C2—34no—
406C2—62no—
407C2—182no—
408C2C2×C4×D3×A411yescharacteristic
409C2C2×D3×#41⋊C312yes—
subgroupG/H
center, hypercenterC42D3×A4
commutator, hypocenterC3×Q8C22×C3×C4
FrattiniC22C22×D3×A4
FittingC3×C4×#41C2×C3
socleC22×C3C23×A4
prime radicalC2×D3×#41⋊C3C2
cosocleC2×C3×Q8C23×C3
LCSG ▷ C3×Q8
UCSC1 ◁ C42

Complements

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

NH ≅ G/Ntype
2. C3×C4×#41⋊C3C2semidirect
3. Dic3×#41⋊C3C2semidirect
4. C4×D3×SL(2,𝔽3)C2semidirect
5. C4×C3⋊(#41⋊C3)C2semidirect
6. C4×D3×#41C3semidirect
9. D3×#41⋊C3C4direct (N × H)
13. C3×C4×SL(2,𝔽3)C22semidirect
14. Dic3×SL(2,𝔽3)C22semidirect
17. C3×C4×#41C2×C3semidirect
18. Dic3×#41C2×C3semidirect
19. C4×#239C2×C3semidirect
30. C4×#41⋊C3D3direct (N × H)
34. C3×#41⋊C3C2×C4semidirect
36. D3×SL(2,𝔽3)C2×C4semidirect
37. C3⋊(#41⋊C3)C2×C4semidirect
44. D3×#41C3×C4semidirect
86. C4×SL(2,𝔽3)C2×D3semidirect
94. C3×SL(2,𝔽3)C22×C4semidirect
101. C4×#41C3×D3semidirect
108. C3×#41C2×C3×C4semidirect
119. #239C2×C3×C4semidirect
143. #41⋊C3C4×D3direct (N × H)
253. C4×D3#41⋊C3direct (N × H)
257. SL(2,𝔽3)C2×C4×D3semidirect
269. #41C3×C4×D3semidirect
332. C3×C4C2×#41⋊C3semidirect
336. Dic3C2×#41⋊C3semidirect
384. D3C4×#41⋊C3direct (N × H)
401. C4D3×#41⋊C3direct (N × H)
404. C3C2×C4×#41⋊C3semidirect

Maximal subgroups

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

subgroupindex
C2×D3×#41⋊C32
C3×C4×#41⋊C32
Dic3×#41⋊C32
C4×D3×SL(2,𝔽3)2
C4×C3⋊(#41⋊C3)2
C4×D3×#413
C2×C4×#41⋊C33
C3×C42×D34