Finite Group Databasebeta

← Dic3×#984 #11922281

Subgroups — Dic3×#984 #11922281

Order 1152.

541 conjugacy classes of subgroups; only the 77 normal subgroups are shown.

normal subgroups only

This group has 541 conjugacy classes of subgroups — too many to draw. Only its 77 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×#984C211yesmaximal, characteristic
2Dic3×#41⋊C3C211yesmaximal, characteristic
3#10593660C211yesmaximal, characteristic
4#10593198C212yesmaximal, complemented
5Dic3×#226C212yesmaximal, complemented
6C4×#984—31nomaximal
7Dic3×#137—31nomaximal
8C2×C3×#41⋊C3C2211yescharacteristic
9C3×#984C414yescomplemented
10C2×C3×#226C2212yes—
11Dic3×Dic6—41nomaximal
12Dic3×SL(2,𝔽3)C2211yescharacteristic
13Dic3×SL(2,𝔽3)C2211yescharacteristic
14C3⋊#859C2212yes—
15C2×#984D311yescharacteristic
16C2×C3×#137—31no—
17Dic3×#41D311yescharacteristic
18C2×Q8×Dic3—31no—
19C4×#41⋊C3—31no—
20#5426—31no—
21#5426—61no—
22#5388—32no—
23C4×#226—32no—
24#5232—31no—
25#5225—31no—
26#5184—32no—
27Dic3×Q16—32no—
28#5164—32no—
29Dic3×SD16—32no—
30#5121—31no—
31Dic3×M16—31no—
32C2×C3×Dic6—41no—
33C3×#41⋊C3C2×C412yes—
34C2×C3×SL(2,𝔽3)C2311yescharacteristic
35C3×#226C2×C414yescomplemented
36C4⋊(C3⋊Dic3)—41no—
37C3×C4×Dic3—41no—
38Dic3⋊Dic3—42no—
39Dic32—42no—
40C4×#137—91noSylow
41C2×C3×#41C2×D311yescharacteristic
42C22×C3×Q8—31no—
43C2×#41⋊C3—21no—
44C2×#41⋊C3C2×D311yescharacteristic
45#984Dic314yesdirect product factor
46C2×#226C2×D312yes—
47C3×#137—34no—
48C3×#137—34no—
49C2×C3×Q16—32no—
50C2×C3×SD16—32no—
51C2×C3×M16—31no—
52Q8×Dic3—32no—
53Q8×Dic3—32no—
54Q8×Dic3—61no—
55Q8×Dic3—61no—
56Q8×Dic3C2×D311yescharacteristic
57Q8×Dic3C2×D311yescharacteristic
58D4×Dic3—31no—
59D4×Dic3—31no—
60#926—31no—
61C2×C4⋊Dic3—31no—
62C2×C4⋊Dic3—61no—
63C2×C4×Dic3—31no—
64C2×C4×Dic3—61no—
65C2×#208—31no—
66C4×Dic6—121no—
67C4×SL(2,𝔽3)—31no—
68C4×SL(2,𝔽3)—31no—
69#859—32no—
70#859—62no—
71#835—32no—
72#835—32no—
73#835—32no—
74#832—32no—
75#818—32no—
76#817—32no—
77#815—32no—
78C8×Dic3—32no—
79C2×C32×C4—41no—
80C2×C3⋊Dic3—42no—
81C2×C3×Dic3—42no—
82C2×C3×Dic3—41no—
83C2×C3×Dic3—41no—
84C3×Dic6—44no—
85C3×SL(2,𝔽3)C22×C411yescharacteristic
86C2×#137—31no—
87C4×#41—31no—
88C2×C4×Q8—91no—
89#441—92no—
90#440—92no—
91C4×Q16—92no—
92C4×SD16—92no—
93#428—91no—
94#419—91no—
95#417—91no—
96C4×M16—91no—
97C3×#41—32no—
98C3×#41C4×D312yes—
99C2×C3×Q8—32no—
100C2×C3×Q8—34no—
101C2×C3×Q8—62no—
102C2×C3×Q8—61no—
103C2×C3×Q8C22×D311yescharacteristic
104C2×C3×D4—31no—
105C22×C3×C4—31no—
106C22×C3×C4—61no—
107C22×Dic3—31no—
108C22×Dic3—31no—
109C22×Dic3—61no—
110C2×Dic6—41no—
111#41⋊C3—22no—
112#41⋊C3C2×Dic312yes—
113C2×SL(2,𝔽3)—21no—
114C2×SL(2,𝔽3)C22×D311yescharacteristic
115#226C2×Dic314yescomplemented
116C3×Q16—34no—
117C3×Q16—34no—
118C3×SD16—38no—
119C3×M16—34no—
120C2×C3×C8—32no—
121C3×C42—121no—
122#217—61no—
123C4⋊Dic3—31no—
124C4⋊Dic3—31no—
125C4⋊Dic3—32no—
126C4⋊Dic3—62no—
127C4⋊Dic3—61no—
128C4⋊Dic3—62no—
129C4⋊Dic3—121no—
130C4⋊Dic3—241no—
131Dic3⋊C4—122no—
132C4×Dic3—31no—
133C4×Dic3—31no—
134C4×Dic3—31no—
135C4×Dic3—62no—
136C4×Dic3—62no—
137C4×Dic3—122no—
138C4×Dic3S411yescharacteristic
139#208—62no—
140C2×C3⋊C8—32no—
141C22×C32—41no—
142C32×C4—42no—
143C3⋊Dic3—82no—
144C3×Dic3—44no—
145C3×Dic3—42no—
146C3×Dic3—81no—
147C2×#41D3211yescharacteristic
148C22×Q8—31no—
149#137—34no—
150#137—34no—
151C2×Q16—32no—
152C2×SD16—32no—
153C2×M16—31no—
154C2×M16—91no—
155C4×Q8—31no—
156C4×Q8—31no—
157C4×Q8—92no—
158C4×Q8—92no—
159C4×Q8—181no—
160C4×Q8—181no—
161C4×D4—91no—
162C4×D4—91no—
163#117—91no—
164C2×C4⋊C4—91no—
165C2×C4⋊C4—181no—
166C2×C42—91no—
167C2×C42—181no—
168#107—92no—
169#106—92no—
170#103—92no—
171#103—92no—
172#103—92no—
173#102—92no—
174#97—92no—
175C4×C8—92no—
176C23×C3—31no—
177C3×Q8—31no—
178C3×Q8—34no—
179C3×Q8—62no—
180C3×Q8—64no—
181C3×Q8C2×C4×D311yescharacteristic
182C3×D4—32no—
183C3×D4—61no—
184C2×C3×C4—31no—
185C2×C3×C4—32no—
186C2×C3×C4—32no—
187C2×C3×C4—41no—
188C2×C3×C4—64no—
189C2×C3×C4—62no—
190C2×C3×C4—81no—
191C2×C3×C4—121no—
192C2×C3×C4—121no—
193C2×C3×C4C2×S411yescharacteristic
194C2×Dic3—31no—
195C2×Dic3—31no—
196C2×Dic3—42no—
197C2×Dic3—62no—
198C2×Dic3—62no—
199C2×Dic3—122no—
200C2×Dic3—121no—
201C2×Dic3—122no—
202C2×Dic3—242no—
203C2×Dic3C2×S411yescharacteristic
204C2×Dic3C2×S411yescharacteristic
205Dic6—44no—
206SL(2,𝔽3)—21no—
207SL(2,𝔽3)C22×Dic311yescharacteristic
208C3×C8—34no—
209C3⋊C8—62no—
210C2×C32—41no—
211C2×C32—41no—
212C2×C32—41no—
213#41—32no—
214#41D3×Dic312yes—
215C2×Q8—32no—
216C2×Q8—34no—
217C2×Q8—62no—
218C2×Q8—61no—
219C2×Q8C2×D3211yescharacteristic
220C2×D4—31no—
221C22×C4—31no—
222C22×C4—61no—
223C22×C4—91no—
224C22×C4—91no—
225C22×C4—181no—
226Q16—34no—
227Q16—34no—
228SD16—38no—
229M16—34no—
230M16—182no—
231C2×C8—32no—
232C2×C8—92no—
233C4⋊C4—91no—
234C4⋊C4—91no—
235C4⋊C4—92no—
236C4⋊C4—182no—
237C4⋊C4—182no—
238C4⋊C4—181no—
239C22⋊C4—181no—
240C42—31no—
241C42—91no—
242C42—91no—
243C42—91no—
244C42—182no—
245C42—182no—
246C22×C3—32no—
247C22×C3—41no—
248C22×C3—61no—
249C22×C3—61no—
250C22×C3—81no—
251C22×C3C22×S411yescharacteristic
252C3×C4—31no—
253C3×C4—31no—
254C3×C4—42no—
255C3×C4—64no—
256C3×C4—82no—
257C3×C4—122no—
258C3×C4—241no—
259C3×C4C4×S412yes—
260Dic3—21no—
261Dic3—44no—
262Dic3—61no—
263Dic3—61no—
264Dic3—122no—
265Dic3—242no—
266Dic3—482no—
267Dic3#98412yesdirect product factor
268C32—41noSylow
269C23—31no—
270Q8—31no—
271Q8—34no—
272Q8—62no—
273Q8—64no—
274Q8C2×D3×Dic311yescharacteristic
275D4—32no—
276D4—61no—
277C2×C4—31no—
278C2×C4—31no—
279C2×C4—32no—
280C2×C4—32no—
281C2×C4—31no—
282C2×C4—64no—
283C2×C4—62no—
284C2×C4—91no—
285C2×C4—91no—
286C2×C4—182no—
287C2×C4—182no—
288C2×C4—361no—
289C2×C4—362no—
290C2×C4D3×S411yescharacteristic
291C8—34no—
292C8—182no—
293C2×C3—41no—
294C2×C3—41no—
295C2×C3—41no—
296C2×C3—62no—
297C2×C3—81no—
298C2×C3—81no—
299C2×C3—81no—
300C2×C3C2×C4×S411yescharacteristic
301C2×C3C2×#98411yescharacteristic
302C2×C3#592311yescharacteristic
303C22—32no—
304C22—61no—
305C22—61no—
306C22C2×D3×S411yescharacteristic
307C4—32no—
308C4—31no—
309C4—31no—
310C4—61no—
311C4—64no—
312C4—181no—
313C4—181no—
314C4—362no—
315C4Dic3×S412yes—
316C3—41no—
317C3—81no—
318C3C4×#98411yescharacteristic, complemented
319C2—62no—
320C2D3×#98411yescharacteristic
321C2#1059645611yescharacteristic
322C2C2×Dic3×S411yescharacteristic
subgroupG/H
center, FrattiniC22C2×D3×S4
commutator, hypocenterC3×SL(2,𝔽3)C22×C4
FittingC2×C3×#41C2×D3
socleC22×C3C22×S4
prime radicalC2×C3×#41⋊C3C22
cosocleC2×C3×SL(2,𝔽3)C23
hypercenterC2×C4D3×S4
LCSG ▷ C3×SL(2,𝔽3)
UCSC1 ◁ C22 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
4. #10593198C2semidirect
5. Dic3×#226C2semidirect
9. C3×#984C4semidirect
35. C3×#226C2×C4semidirect
45. #984Dic3direct (N × H)
115. #226C2×Dic3semidirect
267. Dic3#984direct (N × H)
318. C3C4×#984semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9842
Dic3×#41⋊C32
#105936602
#105931982
Dic3×#2262
C4×#9843
Dic3×#1373
Dic3×Dic64