Finite Group Databasebeta

← Dic3×2−1+4⋊C3 #11923395

Subgroups — Dic3×2−1+4⋊C3 #11923395

Order 1152.

787 conjugacy classes of subgroups; only the 137 normal subgroups are shown.

normal subgroups only

This group has 787 conjugacy classes of subgroups — too many to draw. Only its 137 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×C3×2−1+4⋊C3C211yesmaximal, characteristic
2#5827⋊C3C211yesmaximal, characteristic, complemented
3Dic3×#41⋊C3C211yesmaximal, characteristic, complemented
4#5812⋊C3C212yesmaximal, complemented
5C2×Dic3×SL(2,𝔽3)C212yesmaximal, complemented
6Dic3×2−1+4C311yesmaximal, characteristic, complemented
7C4×2−1+4⋊C3—31nomaximal
8C3×2−1+4⋊C3C414yescomplemented
9C2×C3×#41⋊C3C2211yescharacteristic
10C22×C3×SL(2,𝔽3)C2212yes—
11C3×D4×Dic3—41nomaximal
12Dic3×SL(2,𝔽3)C2211yescharacteristic
13Dic3×SL(2,𝔽3)C2212yes—
14Dic3×SL(2,𝔽3)C2211yescharacteristic
15C2×C3×2−1+4C2×C311yescharacteristic
16C2×2−1+4⋊C3—21no—
17C2×2−1+4⋊C3D311yescharacteristic
18#5827—32no—
19#5827—31no—
20#5827C2×C311yescharacteristic, complemented
21Dic3×#41—31no—
22Dic3×#41—32no—
23Dic3×#41C2×C311yescharacteristic, complemented
24#5812—31no—
25#5812C2×C312yescomplemented
26C2×Q8×Dic3—31no—
27C2×Q8×Dic3C2×C312yescomplemented
28#520⋊C3—31no—
29#519⋊C3—32no—
30C4×#41⋊C3—31no—
31C2×C4×SL(2,𝔽3)—32no—
32C2×C32×D4—41no—
33C22×C3×Dic3—42no—
34C3×#41⋊C3C2×C412yescomplemented
35C2×C3×SL(2,𝔽3)C2×C414yescomplemented
36C2×C3×SL(2,𝔽3)C2311yescharacteristic
37C3×#217—42no—
38C3×C4⋊Dic3—41no—
39C3×C4×Dic3—41no—
40C4×2−1+4—31noSylow
41C3×2−1+4—34no—
42C3×2−1+4C3×C414yescomplemented
43C2×C3×#41—31no—
44C2×C3×#41—32no—
45C2×C3×#41C22×C311yescharacteristic
46C22×C3×Q8—31no—
47C22×C3×Q8C22×C312yes—
482−1+4⋊C3—24no—
492−1+4⋊C3Dic314yesdirect product factor
50C2×#41⋊C3—21no—
51C2×#41⋊C3C2×D311yescharacteristic
52C22×SL(2,𝔽3)—22no—
53C22×SL(2,𝔽3)C2×D312yes—
54C3×C4×D4—121no—
55Q8×Dic3—32no—
56Q8×Dic3—31no—
57Q8×Dic3—32no—
58Q8×Dic3—32no—
59Q8×Dic3—31no—
60Q8×Dic3—32no—
61Q8×Dic3—32no—
62Q8×Dic3C22×C311yescharacteristic
63Q8×Dic3C22×C312yes—
64Q8×Dic3C22×C311yescharacteristic
65D4×Dic3—34no—
66D4×Dic3—31no—
67D4×Dic3—32no—
68D4×Dic3—31no—
69D4×Dic3—31no—
70D4×Dic3—32no—
71D4×Dic3—32no—
72D4×Dic3A411yescharacteristic
73#926—34no—
74#926—32no—
75#926—32no—
76#926—31no—
77#926—31no—
78C2×C4⋊Dic3—32no—
79C2×C4⋊Dic3—32no—
80C2×C4⋊Dic3—31no—
81C2×C4×Dic3—32no—
82C2×C4×Dic3—32no—
83C2×C4×Dic3—31no—
84C4×SL(2,𝔽3)—31no—
85C4×SL(2,𝔽3)—32no—
86C4×SL(2,𝔽3)—31no—
87C23×C32—42no—
88C32×D4—44no—
89C2×C32×C4—41no—
90C2×C3×Dic3—41no—
91C2×C3×Dic3—41no—
92C2×C3×Dic3—42no—
93C2×C3×Dic3—84no—
94C3×SL(2,𝔽3)C22×C411yescharacteristic
95C2×2−1+4C3×D311yescharacteristic
96#520—31no—
97#520—91no—
98#520—92no—
99#519—32no—
100#519—91no—
101C4×#41—31no—
102C4×#41—91no—
103C4×#41—92no—
104C2×C4×Q8—32no—
105C2×C4×Q8—91no—
106C3×#41—38no—
107C3×#41—34no—
108C3×#41—34no—
109C3×#41—38no—
110C3×#41—32no—
111C3×#41C2×C3×C412yescomplemented
112C2×C3×Q8—34no—
113C2×C3×Q8—34no—
114C2×C3×Q8—31no—
115C2×C3×Q8—32no—
116C2×C3×Q8—34no—
117C2×C3×Q8C2×C3×C414yescomplemented
118C2×C3×Q8C23×C311yescharacteristic
119C2×C3×D4—31no—
120C2×C3×D4—32no—
121C2×C3×D4—41no—
122C2×C3×D4—81no—
123C2×C3×D4C2×A411yescharacteristic
124C22×C3×C4—32no—
125C22×C3×C4—32no—
126C22×C3×C4—31no—
127C22×C3×C4—122no—
128C22×Dic3—32no—
129C22×Dic3—32no—
130C22×Dic3—31no—
131C22×Dic3—31no—
132C22×Dic3C2×A412yes—
133#41⋊C3—22no—
134#41⋊C3C2×Dic312yescomplemented
135C2×SL(2,𝔽3)—24no—
136C2×SL(2,𝔽3)—21no—
137C2×SL(2,𝔽3)C2×Dic314yescomplemented
138C2×SL(2,𝔽3)C22×D311yescharacteristic
139C3×C4⋊C4—121no—
140C3×C22⋊C4—122no—
141C3×C42—121no—
142#217—32no—
143#217—32no—
144#217—32no—
145#217C2×A412yes—
146C4⋊Dic3—34no—
147C4⋊Dic3—31no—
148C4⋊Dic3—32no—
149C4⋊Dic3—32no—
150C4⋊Dic3—31no—
151C4⋊Dic3—32no—
152C4⋊Dic3—31no—
153C4⋊Dic3C2×A411yescharacteristic
154C4×Dic3—34no—
155C4×Dic3—31no—
156C4×Dic3—32no—
157C4×Dic3—31no—
158C4×Dic3—32no—
159C4×Dic3—31no—
160C4×Dic3—32no—
161C4×Dic3C2×A411yescharacteristic
162C22×C32—44no—
163C22×C32—41no—
164C22×C32—82no—
165C22×C32—82no—
166C32×C4—42no—
167C3×Dic3—42no—
168C3×Dic3—81no—
169C3×Dic3—82no—
1702−1+4—34no—
1712−1+4C3×Dic314yescomplemented
172C2×#41—31no—
173C2×#41—32no—
174C2×#41C2×C3×D311yescharacteristic
175C22×Q8—31no—
176C22×Q8C2×C3×D312yes—
177C4×Q8—31no—
178C4×Q8—32no—
179C4×Q8—31no—
180C4×Q8—91no—
181C4×Q8—91no—
182C4×Q8—92no—
183C4×Q8—92no—
184C4×Q8—92no—
185C4×Q8—92no—
186C4×Q8—92no—
187C4×D4—31no—
188C4×D4—92no—
189C4×D4—92no—
190C4×D4—94no—
191C4×D4—91no—
192C4×D4—91no—
193C4×D4—91no—
194C4×D4—92no—
195#117—92no—
196#117—91no—
197#117—94no—
198#117—92no—
199#117—91no—
200C2×C4⋊C4—92no—
201C2×C4⋊C4—92no—
202C2×C4⋊C4—91no—
203C2×C42—91no—
204C2×C42—92no—
205C2×C42—92no—
206C23×C3—31no—
207C23×C3—42no—
208C23×C3—82no—
209C23×C3C22×A412yes—
210C3×Q8—34no—
211C3×Q8—31no—
212C3×Q8—34no—
213C3×Q8—34no—
214C3×Q8C22×C3×C411yescharacteristic
215C3×D4—32no—
216C3×D4—32no—
217C3×D4—38no—
218C3×D4—44no—
219C3×D4—84no—
220C3×D4C4×A414yes—
221C2×C3×C4—38no—
222C2×C3×C4—34no—
223C2×C3×C4—34no—
224C2×C3×C4—32no—
225C2×C3×C4—31no—
226C2×C3×C4—32no—
227C2×C3×C4—32no—
228C2×C3×C4—41no—
229C2×C3×C4—81no—
230C2×C3×C4—121no—
231C2×C3×C4—121no—
232C2×C3×C4—122no—
233C2×C3×C4—244no—
234C2×C3×C4C22×A411yescharacteristic
235C2×Dic3—24no—
236C2×Dic3—31no—
237C2×Dic3—32no—
238C2×Dic3—31no—
239C2×Dic3—62no—
240C2×Dic3—121no—
241C2×Dic3—122no—
242C2×Dic3—122no—
243C2×Dic3C22×A412yes—
244C2×Dic3C22×A411yescharacteristic
245C2×Dic3C22×A411yescharacteristic
246SL(2,𝔽3)—21no—
247SL(2,𝔽3)C22×Dic311yescharacteristic
248C2×C32—41no—
249C2×C32—41no—
250C2×C32—41no—
251C2×C32—84no—
252#41—38no—
253#41—34no—
254#41—34no—
255#41—38no—
256#41—32no—
257#41C2×C3×Dic312yescomplemented
258C2×Q8—34no—
259C2×Q8—34no—
260C2×Q8—31no—
261C2×Q8—32no—
262C2×Q8—34no—
263C2×Q8C2×C3×Dic314yescomplemented
264C2×Q8C22×C3×D311yescharacteristic
265C2×D4—31no—
266C2×D4—32no—
267C2×D4D3×A411yescharacteristic
268C22×C4—32no—
269C22×C4—32no—
270C22×C4—31no—
271C22×C4—32no—
272C22×C4—91no—
273C22×C4—91no—
274C22×C4—92no—
275C22×C4—92no—
276C4⋊C4—31no—
277C4⋊C4—92no—
278C4⋊C4—92no—
279C4⋊C4—91no—
280C4⋊C4—92no—
281C4⋊C4—91no—
282C4⋊C4—94no—
283C4⋊C4—91no—
284C22⋊C4—32no—
285C22⋊C4—92no—
286C22⋊C4—92no—
287C22⋊C4—92no—
288C42—31no—
289C42—91no—
290C42—92no—
291C42—91no—
292C42—92no—
293C42—92no—
294C42—94no—
295C42—91no—
296C22×C3—22no—
297C22×C3—22no—
298C22×C3—32no—
299C22×C3—44no—
300C22×C3—41no—
301C22×C3—61no—
302C22×C3—61no—
303C22×C3—82no—
304C22×C3—82no—
305C22×C3—84no—
306C22×C3—81no—
307C22×C3—162no—
308C22×C3—162no—
309C22×C3C2×C4×A414yes—
310C22×C3C23×A411yescharacteristic
311C3×C4—34no—
312C3×C4—31no—
313C3×C4—31no—
314C3×C4—42no—
315C3×C4—82no—
316C3×C4—122no—
317C3×C4—242no—
318C3×C4—241no—
319C3×C4C2×C4×A412yes—
320Dic3—22no—
321Dic3—21no—
322Dic3—61no—
323Dic3—61no—
324Dic3—62no—
325Dic32−1+4⋊C312yesdirect product factor
326C32—41noSylow
327C23—31no—
328C23C2×D3×A412yes—
329Q8—34no—
330Q8—31no—
331Q8—34no—
332Q8—34no—
333Q8C22×C3×Dic311yescharacteristic
334D4—32no—
335D4—32no—
336D4—38no—
337D4Dic3×A414yes—
338C2×C4—38no—
339C2×C4—34no—
340C2×C4—34no—
341C2×C4—31no—
342C2×C4—31no—
343C2×C4—32no—
344C2×C4—32no—
345C2×C4—32no—
346C2×C4—31no—
347C2×C4—32no—
348C2×C4—64no—
349C2×C4—91no—
350C2×C4—91no—
351C2×C4—92no—
352C2×C4—182no—
353C2×C4—361no—
354C2×C4—362no—
355C2×C4—362no—
356C2×C4C2×D3×A411yescharacteristic
357C2×C3—24no—
358C2×C3—41no—
359C2×C3—41no—
360C2×C3—41no—
361C2×C3—62no—
362C2×C3—84no—
363C2×C3—81no—
364C2×C3—81no—
365C2×C3—81no—
366C2×C3—164no—
367C2×C3C22×C4×A411yescharacteristic
368C2×C3C2×2−1+4⋊C311yescharacteristic
369C2×C3#594511yescharacteristic
370C22—22no—
371C22—22no—
372C22—32no—
373C22—61no—
374C22—61no—
375C22C2×Dic3×A414yes—
376C22C22×D3×A411yescharacteristic
377C4—32no—
378C4—31no—
379C4—34no—
380C4—31no—
381C4—62no—
382C4—61no—
383C4—181no—
384C4—181no—
385C4—182no—
386C4C2×Dic3×A412yes—
387C3—41no—
388C3—81no—
389C3C4×2−1+4⋊C311yescharacteristic, complemented
390C2—24no—
391C2—62no—
392C2D3×2−1+4⋊C311yescharacteristic
393C2#5968⋊C311yescharacteristic
394C2C22×Dic3×A411yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×A4
commutator, hypocenterC3×Q8C22×C3×C4
FittingC2×C3×2−1+4C2×C3
socleC22×C3C23×A4
prime radicalC2×C3×2−1+4⋊C3C2
cosocleC2×C3×Q8C23×C3
hypercenterC2×D4D3×A4
LCSG ▷ C3×Q8
UCSC1 ◁ C22 ◁ C2×D4

Complements

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

NH ≅ G/Ntype
2. #5827⋊C3C2semidirect
3. Dic3×#41⋊C3C2semidirect
4. #5812⋊C3C2semidirect
5. C2×Dic3×SL(2,𝔽3)C2semidirect
6. Dic3×2−1+4C3semidirect
8. C3×2−1+4⋊C3C4semidirect
20. #5827C2×C3semidirect
23. Dic3×#41C2×C3semidirect
25. #5812C2×C3semidirect
27. C2×Q8×Dic3C2×C3semidirect
34. C3×#41⋊C3C2×C4semidirect
35. C2×C3×SL(2,𝔽3)C2×C4semidirect
42. C3×2−1+4C3×C4semidirect
49. 2−1+4⋊C3Dic3direct (N × H)
111. C3×#41C2×C3×C4semidirect
117. C2×C3×Q8C2×C3×C4semidirect
134. #41⋊C3C2×Dic3semidirect
137. C2×SL(2,𝔽3)C2×Dic3semidirect
171. 2−1+4C3×Dic3semidirect
257. #41C2×C3×Dic3semidirect
263. C2×Q8C2×C3×Dic3semidirect
325. Dic32−1+4⋊C3direct (N × H)
389. 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×C3×2−1+4⋊C32
#5827⋊C32
Dic3×#41⋊C32
#5812⋊C32
C2×Dic3×SL(2,𝔽3)2
Dic3×2−1+43
C4×2−1+4⋊C33
C3×D4×Dic34