Finite Group Databasebeta

← C4×C3⋊#994 #11923191

Subgroups — C4×C3⋊#994 #11923191

Order 1152.

783 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 783 conjugacy classes of subgroups — too many to draw. Only its 115 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×C3⋊#994C211yesmaximal, characteristic
2C3×C4×#41⋊C3C211yesmaximal, characteristic, complemented
3#5827⋊C3C211yesmaximal, characteristic, complemented
4#5574⋊C3C212yesmaximal, complemented
5C4×C3⋊(#41⋊C3)C212yesmaximal, complemented
6C4×#1009C311yesmaximal, characteristic, complemented
7C4×#994—31nomaximal
8C2×C3×#41⋊C3C2211yescharacteristic
9C3⋊#994C414yesdirect product factor
10C2×C3⋊(#41⋊C3)C2212yes—
11C3×C4×Dic6—41nomaximal
12C3×C4×SL(2,𝔽3)C2211yescharacteristic, complemented
13C3×C4×SL(2,𝔽3)C2211yescharacteristic, complemented
14Dic3×SL(2,𝔽3)C2212yescomplemented
15C2×#1009C2×C311yescharacteristic
16C2×#994—31no—
17C3×C4×#41C2×C311yescharacteristic
18#5827C2×C311yescharacteristic
19#5574C2×C312yes—
20C4×#239C2×C312yes—
21#5545—32no—
22C4×D3×D4—32no—
23#5523—31no—
24#5521—31no—
25C4×#235—31no—
26C2×C4×D12—31no—
27#520⋊C3—31no—
28#520⋊C3—32no—
29C4×#41⋊C3—21no—
30C4×#41⋊C3—32no—
31C4×#41⋊C3D311yescharacteristic, complemented
32C2×C3×Dic6—41no—
33C3×#41⋊C3C2×C412yescomplemented
34C2×C3×SL(2,𝔽3)C2311yescharacteristic
35C3⋊(#41⋊C3)C2×C414yescomplemented
36C32×C42—41no—
37C3×C4⋊Dic3—41no—
38C3×Dic3⋊C4—42no—
39C3×C4×Dic3—42no—
40C4×H(5,𝔽2)—31noSylow
41C2×C3×#41C22×C311yescharacteristic
42#1009—34no—
43#1009C3×C414yescomplemented
44C2×#239C22×C312yes—
45C2×D3×D4—32no—
46C2×#235—31no—
47C22×D12—31no—
48C22×C4×D3—32no—
49#994—34no—
50C2×#41⋊C3—21no—
51C2×#41⋊C3—32no—
52C2×#41⋊C3C2×D311yescharacteristic
53C3×C4×Q8—121no—
54C3×C4×Q8C22×C311yescharacteristic
55C3×C4×Q8C22×C311yescharacteristic
56C3×C4×D4—31no—
57C3×C4×D4—31no—
58C3×#117—31no—
59C2×C3×C42—31no—
60Q8×Dic3C22×C312yes—
61D4×Dic3—32no—
62C4×#67—32no—
63C4×#67—32no—
64C2×(C2×D3)⋊C4—32no—
65#926—31no—
66C2×C4⋊Dic3—31no—
67#893—32no—
68#893—32no—
69#892—32no—
70D3×C4⋊C4—32no—
71#67⋊C4—34no—
72D3×C22⋊C4—34no—
73C4×D12—32no—
74C4×D12—32no—
75C4×D12—31no—
76C4×D12—32no—
77C4×D12—31no—
78#872—32no—
79C42×D3—32no—
80C4×Dic6—31no—
81C4×Dic6A411yescharacteristic
82C4×SL(2,𝔽3)—21no—
83C4×SL(2,𝔽3)—21no—
84C4×SL(2,𝔽3)—32no—
85C4×SL(2,𝔽3)C2×D311yescharacteristic, complemented
86C4×SL(2,𝔽3)C2×D311yescharacteristic, complemented
87C2×C32×C4—41no—
88C2×C32×C4—41no—
89C2×C32×C4—41no—
90C2×C3×Dic3—42no—
91C2×C3×Dic3—42no—
92C3×Dic6—44no—
93C3×SL(2,𝔽3)C22×C411yescharacteristic, complemented
94C2×H(5,𝔽2)—31no—
95#520—31no—
96#520—32no—
97#520—91no—
98#518—91no—
99#518—92no—
100C4×#41—32no—
101C4×#41—91no—
102C4×#41C3×D311yescharacteristic
103C2×C4×D4—91no—
104C2×C4×D4—92no—
105C23×D3—32no—
106C3×#41—32no—
107C3×#41C2×C3×C412yes—
108C2×C3×Q8—121no—
109C2×C3×Q8C23×C311yescharacteristic
110C2×C3×D4—31no—
111C22×C3×C4—31no—
112C22×C3×C4—31no—
113C22×C3×C4—31no—
114C2×#67—32no—
115C22×Dic3—32no—
116#239—34no—
117#239C2×C3×C414yes—
118D3×D4—38no—
119D3×D4—38no—
120#235—34no—
121#235—34no—
122C2×D12—32no—
123C2×D12—34no—
124C2×D12—31no—
125C2×D12—34no—
126C2×C4×D3—32no—
127C2×C4×D3—32no—
128C2×C4×D3—34no—
129C2×C4×D3—32no—
130C2×C4×D3—124no—
131C2×Dic6C2×A411yescharacteristic
132#41⋊C3—22no—
133#41⋊C3—34no—
134#41⋊C3C4×D312yescomplemented
135C2×SL(2,𝔽3)—21no—
136C2×SL(2,𝔽3)C22×D311yescharacteristic
137C3×C4⋊C4—31no—
138C3×C4⋊C4—31no—
139C3×C4⋊C4—122no—
140C3×C4⋊C4—121no—
141C3×C22⋊C4—32no—
142C3×C42—31no—
143C3×C42—31no—
144C3×C42—31no—
145C3×C42—41no—
146C3×C42—81no—
147C3×C42—122no—
148C3×C42C2×A411yescharacteristic
149#217—32no—
150(C2×D3)⋊C4—34no—
151(C2×D3)⋊C4—32no—
152(C2×D3)⋊C4—32no—
153C4⋊Dic3—31no—
154C4⋊Dic3—32no—
155C4⋊Dic3C2×A411yescharacteristic
156Dic3⋊C4—32no—
157Dic3⋊C4C2×A412yes—
158C4×Dic3—32no—
159C4×Dic3—32no—
160C4×Dic3C2×A412yes—
161C22×C32—41no—
162C32×C4—42no—
163C32×C4—42no—
164C32×C4—81no—
165C3×Dic3—44no—
166C3×Dic3—82no—
167H(5,𝔽2)—34no—
168H(5,𝔽2)—94no—
169C2×#41—32no—
170C2×#41—91no—
171C2×#41C2×C3×D311yescharacteristic
172C22×D4—91no—
173C22×D4—92no—
174C23×C4—92no—
175C4×Q8—31no—
176C4×Q8—32no—
177C4×Q8—91no—
178C4×Q8C2×C3×D311yescharacteristic
179C4×Q8C2×C3×D311yescharacteristic
180C4×D4—31no—
181C4×D4—31no—
182C4×D4—91no—
183C4×D4—92no—
184C4×D4—92no—
185C4×D4—92no—
186C4×D4—92no—
187C4×D4—94no—
188C4×D4—92no—
189C4×D4—92no—
190C4×D4—92no—
191C4×D4—92no—
192C4×D4—91no—
193#117—31no—
194#117—92no—
195#117—91no—
196#117—92no—
197C2×C4⋊C4—92no—
198C2×C4⋊C4—91no—
199C2×C22⋊C4—94no—
200C2×C22⋊C4—92no—
201C2×C42—31no—
202C2×C42—92no—
203C23×C3—31no—
204C22×D3—32no—
205C22×D3—38no—
206C22×D3—122no—
207C22×D3—122no—
208C3×Q8—31no—
209C3×Q8—124no—
210C3×Q8C22×C3×C411yescharacteristic
211C3×D4—32no—
212C3×D4—32no—
213C2×C3×C4—31no—
214C2×C3×C4—32no—
215C2×C3×C4—32no—
216C2×C3×C4—31no—
217C2×C3×C4—31no—
218C2×C3×C4—41no—
219C2×C3×C4—41no—
220C2×C3×C4—41no—
221C2×C3×C4—62no—
222C2×C3×C4—81no—
223C2×C3×C4—81no—
224C2×C3×C4—81no—
225C2×C3×C4—122no—
226C2×C3×C4—122no—
227C2×C3×C4—121no—
228C2×C3×C4C22×A411yescharacteristic
229C2×C3×C4C22×A411yescharacteristic
230C2×C3×C4C22×A411yescharacteristic
231#67—38no—
232C2×Dic3—32no—
233C2×Dic3—122no—
234C2×Dic3C22×A412yes—
235C2×Dic3C22×A412yes—
236D12—34no—
237D12—34no—
238D12—34no—
239C4×D3—34no—
240C4×D3—34no—
241C4×D3—64no—
242C4×D3—122no—
243C4×D3—124no—
244Dic6C4×A414yes—
245SL(2,𝔽3)—21no—
246SL(2,𝔽3)C2×C4×D311yescharacteristic, complemented
247C2×C32—41no—
248C2×C32—41no—
249C2×C32—41no—
250C24—92no—
251#41—32no—
252#41—34no—
253#41—94no—
254#41—94no—
255#41—94no—
256#41C3×C4×D312yes—
257C2×Q8—31no—
258C2×Q8C22×C3×D311yescharacteristic
259C2×D4—31no—
260C2×D4—92no—
261C2×D4—92no—
262C2×D4—94no—
263C2×D4—94no—
264C2×D4—98no—
265C2×D4—98no—
266C2×D4—91no—
267C22×C4—31no—
268C22×C4—31no—
269C22×C4—31no—
270C22×C4—92no—
271C22×C4—92no—
272C22×C4—94no—
273C22×C4—92no—
274C22×C4—92no—
275C22×C4—364no—
276C4⋊C4—31no—
277C4⋊C4—31no—
278C4⋊C4—32no—
279C4⋊C4—31no—
280C4⋊C4—92no—
281C4⋊C4—92no—
282C4⋊C4—91no—
283C22⋊C4—32no—
284C22⋊C4—92no—
285C22⋊C4—92no—
286C22⋊C4—94no—
287C22⋊C4—92no—
288C42—31no—
289C42—31no—
290C42—31no—
291C42—32no—
292C42—92no—
293C42—92no—
294C42D3×A411yescharacteristic
295C22×C3—32no—
296C22×C3—41no—
297C22×C3—61no—
298C22×C3—61no—
299C22×C3—81no—
300C22×C3C23×A411yescharacteristic
301C2×D3—34no—
302C2×D3—62no—
303C2×D3—62no—
304C2×D3—128no—
305C3×C4—21no—
306C3×C4—31no—
307C3×C4—31no—
308C3×C4—42no—
309C3×C4—42no—
310C3×C4—61no—
311C3×C4—61no—
312C3×C4—81no—
313C3×C4—82no—
314C3×C4—82no—
315C3×C4—82no—
316C3×C4—124no—
317C3×C4—242no—
318C3×C4C2×C4×A412yes—
319C3×C4#99412yescomplemented
320Dic3—22no—
321Dic3—62no—
322Dic3C2×C4×A414yes—
323C32—41noSylow
324C23—31no—
325C23—98no—
326C23—92no—
327C23—362no—
328C23—362no—
329Q8—31no—
330Q8—34no—
331Q8C2×C3×C4×D311yescharacteristic
332D4—32no—
333D4—32no—
334D4—98no—
335D4—94no—
336D4—94no—
337D4—94no—
338C2×C4—31no—
339C2×C4—32no—
340C2×C4—32no—
341C2×C4—32no—
342C2×C4—31no—
343C2×C4—31no—
344C2×C4—32no—
345C2×C4—62no—
346C2×C4—94no—
347C2×C4—94no—
348C2×C4—92no—
349C2×C4—121no—
350C2×C4—184no—
351C2×C4—362no—
352C2×C4—364no—
353C2×C4—362no—
354C2×C4C2×D3×A411yescharacteristic
355C2×C4C2×D3×A411yescharacteristic
356C2×C4C2×D3×A411yescharacteristic
357C2×C3—41no—
358C2×C3—41no—
359C2×C3—41no—
360C2×C3—62no—
361C2×C3—81no—
362C2×C3—81no—
363C2×C3—81no—
364C2×C3C22×C4×A411yescharacteristic
365C2×C3C2×#99411yescharacteristic
366C2×C3#594511yescharacteristic
367D3—64no—
368C22—32no—
369C22—61no—
370C22—61no—
371C22—94no—
372C22—182no—
373C22—182no—
374C22—368no—
375C22C22×D3×A411yescharacteristic
376C4—21no—
377C4—31no—
378C4—31no—
379C4—34no—
380C4—61no—
381C4—61no—
382C4—62no—
383C4—182no—
384C4C4×D3×A412yes—
385C4C3⋊#99412yesdirect product factor
386C3—41no—
387C3—81no—
388C3C4×#99411yescharacteristic, complemented
389C2—62no—
390C2—184no—
391C2C2×C4×D3×A411yescharacteristic
392C2C2×C3⋊#99411yescharacteristic
393C2#5964⋊C311yescharacteristic
subgroupG/H
centerC2×C4C2×D3×A4
commutator, hypocenterC3×Q8C22×C3×C4
FrattiniC22C22×D3×A4
FittingC3×C4×#41C2×C3
socleC22×C3C23×A4
prime radicalC2×C3⋊#994C2
cosocleC2×C3×Q8C23×C3
hypercenterC42D3×A4
LCSG ▷ C3×Q8
UCSC1 ◁ C2×C4 ◁ C42

Complements

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

NH ≅ G/Ntype
2. C3×C4×#41⋊C3C2semidirect
3. #5827⋊C3C2semidirect
4. #5574⋊C3C2semidirect
5. C4×C3⋊(#41⋊C3)C2semidirect
6. C4×#1009C3semidirect
9. C3⋊#994C4direct (N × H)
12. C3×C4×SL(2,𝔽3)C22semidirect
13. C3×C4×SL(2,𝔽3)C22semidirect
14. Dic3×SL(2,𝔽3)C22semidirect
31. C4×#41⋊C3D3semidirect
33. C3×#41⋊C3C2×C4semidirect
35. C3⋊(#41⋊C3)C2×C4semidirect
43. #1009C3×C4semidirect
85. C4×SL(2,𝔽3)C2×D3semidirect
86. C4×SL(2,𝔽3)C2×D3semidirect
93. C3×SL(2,𝔽3)C22×C4semidirect
134. #41⋊C3C4×D3semidirect
246. SL(2,𝔽3)C2×C4×D3semidirect
319. C3×C4#994semidirect
385. C4C3⋊#994direct (N × H)
388. C3C4×#994semidirect

Maximal subgroups

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

subgroupindex
C2×C3⋊#9942
C3×C4×#41⋊C32
#5827⋊C32
#5574⋊C32
C4×C3⋊(#41⋊C3)2
C4×#10093
C4×#9943
C3×C4×Dic64