Finite Group Databasebeta

← C4×#1010⋊C3 #11923200

Subgroups — C4×#1010⋊C3 #11923200

Order 1152.

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

normal subgroups only

This group has 767 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×#1010⋊C3C211yesmaximal, characteristic
2C3×C4×#41⋊C3C211yesmaximal, characteristic, complemented
3#5827⋊C3C211yesmaximal, characteristic, complemented
4#5572⋊C3C212yesmaximal, complemented
5C4×D3×SL(2,𝔽3)C212yesmaximal, complemented
6C4×#1010C311yesmaximal, characteristic, complemented
7C4×2−1+4⋊C3—31nomaximal
8C2×C3×#41⋊C3C2211yescharacteristic
9#1010⋊C3C414yesdirect product factor
10C2×D3×SL(2,𝔽3)C2212yes—
11C3×C4×D12—41nomaximal
12C3×C4×SL(2,𝔽3)C2211yescharacteristic
13C3×C4×SL(2,𝔽3)C2211yescharacteristic
14Dic3×SL(2,𝔽3)C2212yes—
15C2×#1010C2×C311yescharacteristic
16C2×2−1+4⋊C3—31no—
17C3×C4×#41C2×C311yescharacteristic, complemented
18#5827C2×C311yescharacteristic, complemented
19#5572C2×C312yescomplemented
20C4×D3×Q8C2×C312yescomplemented
21#5546—32no—
22C4×#237—32no—
23#5523—31no—
24#5516—31no—
25C4×#235—31no—
26C2×C4×Dic6—31no—
27#520⋊C3—31no—
28#519⋊C3—32no—
29C4×#41⋊C3—21no—
30C4×#41⋊C3D311yescharacteristic, complemented
31C2×C4×SL(2,𝔽3)—32no—
32C2×C3×D12—41no—
33C2×C3×C4×D3—42no—
34C3×#41⋊C3C2×C412yescomplemented
35C2×C3×SL(2,𝔽3)C2311yescharacteristic
36D3×SL(2,𝔽3)C2×C414yescomplemented
37C32×C42—41no—
38C3×(C2×D3)⋊C4—42no—
39C3×C4⋊Dic3—41no—
40C4×2−1+4—31noSylow
41C2×C3×#41C22×C311yescharacteristic
42#1010—34no—
43#1010C3×C414yescomplemented
44C2×D3×Q8C22×C312yes—
45C2×#237—32no—
46C2×#235—31no—
47C22×Dic6—31no—
482−1+4⋊C3—34no—
49C2×#41⋊C3—21no—
50C2×#41⋊C3C2×D311yescharacteristic
51C22×SL(2,𝔽3)—32no—
52C3×C4×Q8C22×C311yescharacteristic
53C3×C4×Q8C22×C311yescharacteristic
54C3×C4×D4—31no—
55C3×C4×D4—31no—
56C3×C4×D4—121no—
57C3×#117—31no—
58C2×C3×C42—31no—
59Q8×Dic3C22×C312yes—
60D4×Dic3—32no—
61C4×#67—32no—
62C4×#67—32no—
63#926—31no—
64C2×C4⋊Dic3—31no—
65C2×Dic3⋊C4—32no—
66C2×C4×Dic3—32no—
67#892—32no—
68D3×C4⋊C4—32no—
69#887—32no—
70#887—32no—
71#67⋊C4—34no—
72#877—34no—
73C4×D12—31no—
74C4×D12A411yescharacteristic
75#872—32no—
76C42×D3—32no—
77C4×Dic6—32no—
78C4×Dic6—31no—
79C4×Dic6—31no—
80C4×Dic6—32no—
81C4×Dic6—32no—
82C4×SL(2,𝔽3)—21no—
83C4×SL(2,𝔽3)—21no—
84C4×SL(2,𝔽3)—32no—
85C4×SL(2,𝔽3)C2×D311yescharacteristic
86C4×SL(2,𝔽3)C2×D311yescharacteristic
87C22×C3×D3—42no—
88C2×C32×C4—41no—
89C2×C32×C4—41no—
90C2×C32×C4—41no—
91C2×C3×Dic3—42no—
92C3×D12—44no—
93C3×C4×D3—84no—
94C3×SL(2,𝔽3)C22×C411yescharacteristic
95C2×2−1+4—31no—
96#520—31no—
97#520—91no—
98#520—92no—
99#519—32no—
100#519—91no—
101C4×#41—91no—
102C4×#41—92no—
103C4×#41C3×D311yescharacteristic, complemented
104C2×C4×Q8—32no—
105C2×C4×Q8—91no—
106C3×#41—32no—
107C3×#41C2×C3×C412yescomplemented
108C2×C3×Q8C23×C311yescharacteristic
109C2×C3×D4—31no—
110C2×C3×D4—121no—
111C22×C3×C4—31no—
112C22×C3×C4—31no—
113C22×C3×C4—31no—
114C22×C3×C4—122no—
115C2×#67—32no—
116C22×Dic3—32no—
117C22×Dic3—32no—
118D3×Q8—34no—
119D3×Q8C2×C3×C414yescomplemented
120#237—38no—
121#237—38no—
122#235—34no—
123#235—34no—
124C2×D12C2×A411yescharacteristic
125C2×C4×D3—32no—
126C2×C4×D3—32no—
127C2×C4×D3C2×A412yes—
128C2×Dic6—34no—
129C2×Dic6—31no—
130C2×Dic6—32no—
131C2×Dic6—34no—
132#41⋊C3—22no—
133#41⋊C3C4×D312yescomplemented
134C2×SL(2,𝔽3)—21no—
135C2×SL(2,𝔽3)—34no—
136C2×SL(2,𝔽3)C22×D311yescharacteristic
137C3×C4⋊C4—31no—
138C3×C4⋊C4—31no—
139C3×C4⋊C4—121no—
140C3×C22⋊C4—32no—
141C3×C22⋊C4—122no—
142C3×C42—31no—
143C3×C42—31no—
144C3×C42—31no—
145C3×C42—41no—
146C3×C42—81no—
147C3×C42C2×A411yescharacteristic
148#217—32no—
149(C2×D3)⋊C4—32no—
150(C2×D3)⋊C4C2×A412yes—
151C4⋊Dic3—31no—
152C4⋊Dic3—32no—
153C4⋊Dic3C2×A411yescharacteristic
154Dic3⋊C4—34no—
155Dic3⋊C4—32no—
156Dic3⋊C4—32no—
157C4×Dic3—34no—
158C4×Dic3—32no—
159C4×Dic3—32no—
160C4×Dic3—32no—
161C22×C32—41no—
162C2×C3×D3—44no—
163C2×C3×D3—82no—
164C2×C3×D3—82no—
165C32×C4—42no—
166C32×C4—42no—
167C32×C4—81no—
168C3×Dic3—82no—
1692−1+4—34no—
1702−1+4—94no—
171C2×#41—91no—
172C2×#41—92no—
173C2×#41C2×C3×D311yescharacteristic
174C22×Q8—32no—
175C22×Q8—91no—
176C4×Q8—32no—
177C4×Q8—91no—
178C4×Q8—92no—
179C4×Q8—92no—
180C4×Q8—92no—
181C4×Q8—92no—
182C4×Q8—91no—
183C4×Q8—92no—
184C4×Q8C2×C3×D311yescharacteristic
185C4×Q8C2×C3×D311yescharacteristic
186C4×D4—31no—
187C4×D4—31no—
188C4×D4—31no—
189C4×D4—91no—
190C4×D4—92no—
191C4×D4—94no—
192C4×D4—92no—
193C4×D4—92no—
194#117—31no—
195#117—92no—
196#117—94no—
197#117—91no—
198#117—92no—
199C2×C4⋊C4—92no—
200C2×C4⋊C4—92no—
201C2×C4⋊C4—91no—
202C2×C42—31no—
203C2×C42—92no—
204C2×C42—92no—
205C23×C3—31no—
206C23×C3—122no—
207C22×D3C22×A412yes—
208C3×Q8—31no—
209C3×Q8C22×C3×C411yescharacteristic
210C3×D4—32no—
211C3×D4—32no—
212C3×D4—124no—
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—121no—
227C2×C3×C4—244no—
228C2×C3×C4C22×A411yescharacteristic
229C2×C3×C4C22×A411yescharacteristic
230C2×C3×C4C22×A411yescharacteristic
231#67—38no—
232C2×Dic3—38no—
233C2×Dic3—32no—
234C2×Dic3—32no—
235C2×Dic3—122no—
236C2×Dic3C22×A412yes—
237D12C4×A414yes—
238C4×D3—24no—
239C4×D3—34no—
240C4×D3—34no—
241C4×D3—122no—
242Dic6—34no—
243Dic6—34no—
244Dic6—34no—
245SL(2,𝔽3)—21no—
246SL(2,𝔽3)C2×C4×D311yescharacteristic
247C2×C32—41no—
248C2×C32—41no—
249C2×C32—41no—
250C3×D3—84no—
251#41—32no—
252#41—94no—
253#41—94no—
254#41—98no—
255#41—98no—
256#41C3×C4×D312yescomplemented
257C2×Q8—34no—
258C2×Q8—94no—
259C2×Q8—94no—
260C2×Q8—92no—
261C2×Q8—91no—
262C2×Q8—94no—
263C2×Q8C22×C3×D311yescharacteristic
264C2×D4—31no—
265C2×D4—31no—
266C2×D4—92no—
267C22×C4—31no—
268C22×C4—31no—
269C22×C4—32no—
270C22×C4—31no—
271C22×C4—92no—
272C22×C4—92no—
273C22×C4—92no—
274C22×C4—92no—
275C4⋊C4—31no—
276C4⋊C4—31no—
277C4⋊C4—31no—
278C4⋊C4—92no—
279C4⋊C4—92no—
280C4⋊C4—94no—
281C4⋊C4—92no—
282C4⋊C4—91no—
283C22⋊C4—32no—
284C22⋊C4—32no—
285C22⋊C4—92no—
286C22⋊C4—92no—
287C42—31no—
288C42—31no—
289C42—31no—
290C42—92no—
291C42—92no—
292C42—94no—
293C42—92no—
294C42D3×A411yescharacteristic
295C22×C3—32no—
296C22×C3—41no—
297C22×C3—61no—
298C22×C3—61no—
299C22×C3—81no—
300C22×C3—124no—
301C22×C3—242no—
302C22×C3—242no—
303C22×C3C23×A411yescharacteristic
304C2×D3—22no—
305C2×D3—22no—
306C2×D3C2×C4×A414yes—
307C3×C4—21no—
308C3×C4—31no—
309C3×C4—31no—
310C3×C4—42no—
311C3×C4—42no—
312C3×C4—61no—
313C3×C4—61no—
314C3×C4—81no—
315C3×C4—82no—
316C3×C4—82no—
317C3×C4—82no—
318C3×C4—242no—
319C3×C4C2×C4×A412yes—
320C3×C42−1+4⋊C312yescomplemented
321Dic3—22no—
322Dic3—34no—
323Dic3—62no—
324C32—41noSylow
325C23—31no—
326C23—32no—
327Q8—31no—
328Q8—94no—
329Q8—94no—
330Q8—94no—
331Q8C2×C3×C4×D311yescharacteristic
332D4—32no—
333D4—32no—
334D4—34no—
335D4—98no—
336C2×C4—31no—
337C2×C4—32no—
338C2×C4—32no—
339C2×C4—31no—
340C2×C4—31no—
341C2×C4—32no—
342C2×C4—64no—
343C2×C4—62no—
344C2×C4—94no—
345C2×C4—94no—
346C2×C4—98no—
347C2×C4—92no—
348C2×C4—92no—
349C2×C4—121no—
350C2×C4—362no—
351C2×C4—362no—
352C2×C4C2×D3×A411yescharacteristic
353C2×C4C2×D3×A411yescharacteristic
354C2×C4C2×D3×A411yescharacteristic
355C2×C3—41no—
356C2×C3—41no—
357C2×C3—41no—
358C2×C3—62no—
359C2×C3—81no—
360C2×C3—81no—
361C2×C3—81no—
362C2×C3—244no—
363C2×C3C22×C4×A411yescharacteristic
364C2×C3C2×2−1+4⋊C311yescharacteristic
365C2×C3#594511yescharacteristic
366D3—24no—
367C22—32no—
368C22—34no—
369C22—62no—
370C22—61no—
371C22—61no—
372C22—62no—
373C22C22×D3×A411yescharacteristic
374C4—21no—
375C4—31no—
376C4—31no—
377C4—62no—
378C4—61no—
379C4—61no—
380C4—94no—
381C4—182no—
382C4C4×D3×A412yes—
383C4#1010⋊C312yesdirect product factor
384C3—41no—
385C3—81no—
386C3C4×2−1+4⋊C311yescharacteristic, complemented
387C2—64no—
388C2—62no—
389C2C2×C4×D3×A411yescharacteristic
390C2C2×#1010⋊C311yescharacteristic
391C2#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×#1010⋊C3C2
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. #5572⋊C3C2semidirect
5. C4×D3×SL(2,𝔽3)C2semidirect
6. C4×#1010C3semidirect
9. #1010⋊C3C4direct (N × H)
17. C3×C4×#41C2×C3semidirect
18. #5827C2×C3semidirect
19. #5572C2×C3semidirect
20. C4×D3×Q8C2×C3semidirect
30. C4×#41⋊C3D3semidirect
34. C3×#41⋊C3C2×C4semidirect
36. D3×SL(2,𝔽3)C2×C4semidirect
43. #1010C3×C4semidirect
103. C4×#41C3×D3semidirect
107. C3×#41C2×C3×C4semidirect
119. D3×Q8C2×C3×C4semidirect
133. #41⋊C3C4×D3semidirect
256. #41C3×C4×D3semidirect
320. C3×C42−1+4⋊C3semidirect
383. C4#1010⋊C3direct (N × H)
386. C3C4×2−1+4⋊C3semidirect

Maximal subgroups

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

subgroupindex
C2×#1010⋊C32
C3×C4×#41⋊C32
#5827⋊C32
#5572⋊C32
C4×D3×SL(2,𝔽3)2
C4×#10103
C4×2−1+4⋊C33
C3×C4×D124