Finite Group Databasebeta

← Dic3×#983 #11922150

Subgroups — Dic3×#983 #11922150

Order 1152.

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

normal subgroups only

This group has 581 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×#983C211yesmaximal, characteristic
2C2×Dic3×SL(2,𝔽3)C211yesmaximal, characteristic, complemented
3#10593654C211yesmaximal, characteristic, complemented
4Dic3×GL(2,𝔽3)C211yesmaximal, characteristic, complemented
5#10593204C211yesmaximal, characteristic, complemented
6#10593198C211yesmaximal, characteristic, complemented
7Dic3×#226C211yesmaximal, characteristic, complemented
8C4×#983—31nomaximal
9Dic3×#137—31nomaximal
10C22×C3×SL(2,𝔽3)C2211yescharacteristic
11C3×#983C414yescomplemented
12C2×C3×GL(2,𝔽3)C2211yescharacteristic
13C2×C3×#226C2211yescharacteristic
14Dic3×#67—41nomaximal
15Dic3×SL(2,𝔽3)C2211yescharacteristic
16Dic3×SL(2,𝔽3)C2211yescharacteristic
17C3⋊#859C2211yescharacteristic
18C3⋊#859C2211yescharacteristic
19C2×#983D311yescharacteristic
20C2×C3×#137—31no—
21Dic3×#41—31no—
22C2×Q8×Dic3D311yescharacteristic, complemented
23C2×C4×SL(2,𝔽3)—31no—
24#5420—31no—
25#5420—61no—
26#5394—31no—
27C4×GL(2,𝔽3)—31no—
28#5388—31no—
29C4×#226—31no—
30#5232—31no—
31#5225—31no—
32#5184—31no—
33#5184—31no—
34Dic3×Q16—31no—
35Dic3×Q16—31no—
36#5164—31no—
37#5164—31no—
38Dic3×SD16—31no—
39Dic3×SD16—31no—
40#5121—31no—
41Dic3×M16—31no—
42C2×C3×#67—41no—
43C22×C3×Dic3—41no—
44C2×C3×SL(2,𝔽3)C2×C412yescomplemented
45C2×C3×SL(2,𝔽3)C2311yescharacteristic
46C2×D3×Dic3—41no—
47C3×GL(2,𝔽3)C2×C412yescomplemented
48C3×#226C2×C412yescomplemented
49#3757—41no—
50Dic3⋊Dic3—41no—
51(C2×D3)⋊Dic3—41no—
52Dic32—41no—
53C4×#137—91noSylow
54C2×C3×#41—31no—
55C22×C3×Q8C2×D311yescharacteristic
56C22×SL(2,𝔽3)—21no—
57C22×SL(2,𝔽3)C2×D311yescharacteristic
58#983Dic314yesdirect product factor
59C2×GL(2,𝔽3)C2×D311yescharacteristic
60C2×#226C2×D311yescharacteristic
61C3×#137—34no—
62C3×#137—34no—
63C2×C3×Q16—31no—
64C2×C3×Q16—31no—
65C2×C3×SD16—31no—
66C2×C3×SD16—31no—
67C2×C3×M16—31no—
68Q8×Dic3—31no—
69Q8×Dic3—31no—
70Q8×Dic3—31no—
71Q8×Dic3—31no—
72Q8×Dic3C2×D311yescharacteristic
73Q8×Dic3C2×D311yescharacteristic
74D4×Dic3—31no—
75D4×Dic3—31no—
76D4×Dic3—61no—
77D4×Dic3—61no—
78C4×#67—121no—
79#926—31no—
80#926—61no—
81C2×C4⋊Dic3—31no—
82C2×C4×Dic3—31no—
83C2×C4×Dic3—61no—
84C2×#208—31no—
85C4×SL(2,𝔽3)—31no—
86C4×SL(2,𝔽3)—31no—
87#859—31no—
88#859—31no—
89#859—61no—
90#859—61no—
91#835—31no—
92#835—31no—
93#835—31no—
94#835—31no—
95#835—31no—
96#835—31no—
97#832—31no—
98#832—31no—
99#818—31no—
100#818—31no—
101#817—31no—
102#817—31no—
103#815—31no—
104#815—31no—
105C8×Dic3—31no—
106C8×Dic3—31no—
107C23×C32—41no—
108C22×C3×D3—41no—
109C2×C3⋊Dic3—41no—
110C2×C3⋊Dic3—41no—
111C3×#67—44no—
112C2×C3×Dic3—41no—
113C2×C3×Dic3—41no—
114C2×C3×Dic3—41no—
115C2×C3×Dic3—82no—
116C3×SL(2,𝔽3)C22×C411yescharacteristic
117D3×Dic3—82no—
118C2×#137—31no—
119C4×#41—91no—
120C2×C4×Q8—31no—
121#441—91no—
122#441—91no—
123#440—91no—
124#440—91no—
125C4×Q16—91no—
126C4×Q16—91no—
127C4×SD16—91no—
128C4×SD16—91no—
129#428—91no—
130#419—91no—
131#417—91no—
132C4×M16—91no—
133C3×#41—34no—
134C3×#41—62no—
135C2×C3×Q8—31no—
136C2×C3×Q8—32no—
137C2×C3×Q8—31no—
138C2×C3×Q8C4×D312yescomplemented
139C2×C3×Q8C22×D311yescharacteristic
140C2×C3×D4—31no—
141C2×C3×D4—61no—
142C22×C3×C4—31no—
143C22×C3×C4—61no—
144C22×C3×C4—121no—
145C2×#67—41no—
146C22×Dic3—31no—
147C22×Dic3—61no—
148C22×Dic3—61no—
149C22×Dic3S411yescharacteristic
150C2×C4×D3—121no—
151C2×SL(2,𝔽3)—22no—
152C2×SL(2,𝔽3)—21no—
153C2×SL(2,𝔽3)C2×Dic312yescomplemented
154C2×SL(2,𝔽3)C22×D311yescharacteristic
155GL(2,𝔽3)C2×Dic312yescomplemented
156#226C2×Dic312yescomplemented
157C3×Q16—34no—
158C3×Q16—32no—
159C3×Q16—32no—
160C3×SD16—34no—
161C3×SD16—32no—
162C3×SD16—32no—
163C3×M16—34no—
164C2×C3×C8—31no—
165C2×C3×C8—31no—
166#217—61no—
167#217—61no—
168#217—61no—
169#217—121no—
170#217—241no—
171(C2×D3)⋊C4—121no—
172C4⋊Dic3—31no—
173C4⋊Dic3—31no—
174C4⋊Dic3—31no—
175C4⋊Dic3—31no—
176C4⋊Dic3—61no—
177C4⋊Dic3—61no—
178C4⋊Dic3—61no—
179Dic3⋊C4—121no—
180C4×Dic3—31no—
181C4×Dic3—31no—
182C4×Dic3—31no—
183C4×Dic3—31no—
184C4×Dic3—61no—
185C4×Dic3—61no—
186C4×Dic3—61no—
187C4×Dic3—121no—
188#208—62no—
189C2×C3⋊C8—31no—
190C2×C3⋊C8—31no—
191C22×C32—42no—
192C22×C32—41no—
193C22×C32—81no—
194C22×C32—81no—
195C2×C3×D3—42no—
196C2×C3×D3—81no—
197C2×C3×D3—81no—
198C3⋊Dic3—81no—
199C3⋊Dic3—81no—
200C3×Dic3—42no—
201C3×Dic3—42no—
202C3×Dic3—81no—
203C2×#41—31no—
204C22×Q8D3211yescharacteristic
205#137—34no—
206#137—34no—
207C2×Q16—31no—
208C2×Q16—31no—
209C2×SD16—31no—
210C2×SD16—31no—
211C2×M16—31no—
212C2×M16—91no—
213C4×Q8—31no—
214C4×Q8—31no—
215C4×Q8—91no—
216C4×Q8—91no—
217C4×Q8—91no—
218C4×Q8—91no—
219C4×D4—91no—
220C4×D4—91no—
221C4×D4—181no—
222C4×D4—181no—
223#117—91no—
224#117—181no—
225C2×C4⋊C4—91no—
226C2×C42—91no—
227C2×C42—181no—
228#107—91no—
229#107—91no—
230#106—91no—
231#106—91no—
232#103—91no—
233#103—91no—
234#103—91no—
235#103—91no—
236#103—91no—
237#103—91no—
238#102—91no—
239#102—91no—
240#97—91no—
241#97—91no—
242C4×C8—91no—
243C4×C8—91no—
244C23×C3—41no—
245C23×C3—61no—
246C23×C3—81no—
247C23×C3C2×S411yescharacteristic
248C22×D3—41no—
249C3×Q8—32no—
250C3×Q8—31no—
251C3×Q8—32no—
252C3×Q8—61no—
253C3×Q8—61no—
254C3×Q8C2×C4×D311yescharacteristic
255C3×D4—32no—
256C3×D4—61no—
257C3×D4—64no—
258C2×C3×C4—32no—
259C2×C3×C4—32no—
260C2×C3×C4—31no—
261C2×C3×C4—31no—
262C2×C3×C4—64no—
263C2×C3×C4—61no—
264C2×C3×C4—121no—
265C2×C3×C4—121no—
266C2×C3×C4—242no—
267#67—44no—
268C2×Dic3—22no—
269C2×Dic3—31no—
270C2×Dic3—31no—
271C2×Dic3—41no—
272C2×Dic3—61no—
273C2×Dic3—61no—
274C2×Dic3—121no—
275C2×Dic3—121no—
276C2×Dic3—121no—
277C2×Dic3—122no—
278C2×Dic3—122no—
279C2×Dic3—241no—
280C2×Dic3—241no—
281C2×Dic3C2×S411yescharacteristic
282C2×Dic3C2×S411yescharacteristic
283C4×D3—242no—
284SL(2,𝔽3)—21no—
285SL(2,𝔽3)C22×Dic311yescharacteristic
286C3×C8—32no—
287C3×C8—32no—
288C3⋊C8—61no—
289C3⋊C8—61no—
290C2×C32—41no—
291C2×C32—41no—
292C2×C32—41no—
293C2×C32—82no—
294C3×D3—82no—
295#41—34no—
296#41—62no—
297C2×Q8—31no—
298C2×Q8—32no—
299C2×Q8—31no—
300C2×Q8D3×Dic312yescomplemented
301C2×Q8C2×D3211yescharacteristic
302C2×D4—31no—
303C2×D4—61no—
304C22×C4—31no—
305C22×C4—31no—
306C22×C4—61no—
307C22×C4—91no—
308C22×C4—181no—
309C22×C4—181no—
310Q16—34no—
311Q16—32no—
312Q16—32no—
313SD16—34no—
314SD16—32no—
315SD16—32no—
316M16—34no—
317M16—182no—
318C2×C8—31no—
319C2×C8—31no—
320C2×C8—91no—
321C2×C8—91no—
322C4⋊C4—91no—
323C4⋊C4—91no—
324C4⋊C4—91no—
325C4⋊C4—91no—
326C4⋊C4—181no—
327C4⋊C4—181no—
328C4⋊C4—181no—
329C22⋊C4—181no—
330C22⋊C4—181no—
331C22⋊C4—181no—
332C42—91no—
333C42—91no—
334C42—91no—
335C42—91no—
336C42—181no—
337C42—181no—
338C42—181no—
339C22×C3—21no—
340C22×C3—21no—
341C22×C3—41no—
342C22×C3—42no—
343C22×C3—62no—
344C22×C3—81no—
345C22×C3—81no—
346C22×C3—81no—
347C22×C3—82no—
348C22×C3—121no—
349C22×C3—121no—
350C22×C3—161no—
351C22×C3—161no—
352C22×C3C4×S412yes—
353C22×C3C22×S411yescharacteristic
354C2×D3—42no—
355C2×D3—81no—
356C2×D3—81no—
357C3×C4—31no—
358C3×C4—31no—
359C3×C4—32no—
360C3×C4—62no—
361C3×C4—122no—
362C3×C4—241no—
363Dic3—21no—
364Dic3—42no—
365Dic3—61no—
366Dic3—61no—
367Dic3—121no—
368Dic3—121no—
369Dic3—241no—
370Dic3—241no—
371Dic3—481no—
372Dic3—481no—
373Dic3#98312yesdirect product factor
374C32—41noSylow
375C23—61no—
376C23D3×S411yescharacteristic
377Q8—32no—
378Q8—31no—
379Q8—32no—
380Q8—61no—
381Q8—61no—
382Q8C2×D3×Dic311yescharacteristic
383D4—32no—
384D4—61no—
385D4—64no—
386C2×C4—31no—
387C2×C4—31no—
388C2×C4—31no—
389C2×C4—32no—
390C2×C4—32no—
391C2×C4—31no—
392C2×C4—62no—
393C2×C4—64no—
394C2×C4—61no—
395C2×C4—91no—
396C2×C4—91no—
397C2×C4—181no—
398C2×C4—181no—
399C2×C4—362no—
400C2×C4—361no—
401C2×C4—362no—
402C8—32no—
403C8—32no—
404C8—181no—
405C8—181no—
406C2×C3—22no—
407C2×C3—41no—
408C2×C3—41no—
409C2×C3—41no—
410C2×C3—82no—
411C2×C3—81no—
412C2×C3—81no—
413C2×C3—81no—
414C2×C3—122no—
415C2×C3—162no—
416C2×C3C2×C4×S411yescharacteristic
417C2×C3C2×#98311yescharacteristic
418C2×C3#592311yescharacteristic
419D3—82no—
420C22—21no—
421C22—21no—
422C22—62no—
423C22—121no—
424C22—121no—
425C22Dic3×S412yes—
426C22C2×D3×S411yescharacteristic
427C4—32no—
428C4—31no—
429C4—31no—
430C4—32no—
431C4—61no—
432C4—62no—
433C4—181no—
434C4—181no—
435C4—361no—
436C4—361no—
437C3—41no—
438C3—81no—
439C3C4×#98311yescharacteristic, complemented
440C2—22no—
441C2—122no—
442C2#1059643511yescharacteristic
443C2D3×#98311yescharacteristic
444C2C2×Dic3×S411yescharacteristic
subgroupG/H
center, FrattiniC22C2×D3×S4
commutator, hypocenterC3×SL(2,𝔽3)C22×C4
FittingC22×C3×Q8C2×D3
socleC22×C3C22×S4
prime radicalC2×C3×#983C2
cosocleC2×C3×SL(2,𝔽3)C23
hypercenterC23D3×S4
LCSG ▷ C3×SL(2,𝔽3)
UCSC1 ◁ C22 ◁ C23

Complements

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

NH ≅ G/Ntype
2. C2×Dic3×SL(2,𝔽3)C2semidirect
3. #10593654C2semidirect
4. Dic3×GL(2,𝔽3)C2semidirect
5. #10593204C2semidirect
6. #10593198C2semidirect
7. Dic3×#226C2semidirect
11. C3×#983C4semidirect
22. C2×Q8×Dic3D3semidirect
44. C2×C3×SL(2,𝔽3)C2×C4semidirect
47. C3×GL(2,𝔽3)C2×C4semidirect
48. C3×#226C2×C4semidirect
58. #983Dic3direct (N × H)
138. C2×C3×Q8C4×D3semidirect
153. C2×SL(2,𝔽3)C2×Dic3semidirect
155. GL(2,𝔽3)C2×Dic3semidirect
156. #226C2×Dic3semidirect
300. C2×Q8D3×Dic3semidirect
373. Dic3#983direct (N × H)
439. C3C4×#983semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9832
C2×Dic3×SL(2,𝔽3)2
#105936542
Dic3×GL(2,𝔽3)2
#105932042
#105931982
Dic3×#2262
C4×#9833
Dic3×#1373
Dic3×#674