Finite Group Databasebeta

← C3⋊D3×#462 #11865618

Subgroups — C3⋊D3×#462 #11865618

Order 1152.

1440 conjugacy classes of subgroups.

The subgroup lattice has 426 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×Q16×C3⋊D3C212yesmaximal
2C3⋊D3×C4⋊Q8C211yesmaximal, characteristic
3C4×Q8×C3⋊D3C211yesmaximal, characteristic
4C32×#462C211yesmaximal, characteristic, complemented
5#10592881C212yesmaximal, complemented
6#10592789C211yesmaximal, characteristic, complemented
7#10592730C211yesmaximal, characteristic, complemented
8#10592548C211yesmaximal, characteristic, complemented
9C3⋊D3×C4⋊C8C211yesmaximal, characteristic
10C3⋊D3×#103C212yesmaximal
11#10592494C212yesmaximal, complemented
12D3×#462—34nomaximal
13C2×Q8×C3⋊D3C2212yes—
14C2×Q8×C3⋊D3C2211yescharacteristic
15C2×C32×Q16C2212yes—
16C32×C4⋊Q8C2211yescharacteristic
17C32×C4×Q8C2211yescharacteristic
18Q8×C3⋊Dic3C2211yescharacteristic
19#64153C2212yes—
20C2×#3756C2212yes—
21C2×#3756C2212yes—
22Q16×C3⋊D3—28no—
23C2×#3746C2212yes—
24C2×C8×C3⋊D3C2212yes—
25C4⋊C4×C3⋊D3—21no—
26C4⋊C4×C3⋊D3—21no—
27C4⋊C4×C3⋊D3—21no—
28C4⋊C4×C3⋊D3C2211yescharacteristic
29#64097—21no—
30#64097—21no—
31#64096—21no—
32#64096C2211yescharacteristic
33C42×C3⋊D3—21no—
34C42×C3⋊D3C2211yescharacteristic
35#64078C2211yescharacteristic
36C4×#634—21no—
37C4×#634C2211yescharacteristic
38C32×C4⋊C8C2211yescharacteristic
39C32×#103C2212yes—
40#63662C2212yes—
41#63643C2212yes—
42#63641C2212yes—
43#63637C2212yes—
44C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
45C2×D3×Q16—38no—
46D3×C4⋊Q8—34no—
47C4×D3×Q8—34no—
48C3×#462D314yescomplemented
49#5182—38no—
50#5090—34no—
51#5031—34no—
52#4849—34no—
53D3×C4⋊C8—34no—
54D3×#103—38no—
55#4795—38no—
56C2×C32×Q8C2312yes—
57C2×C32×Q8C2311yescharacteristic
58Q8×C3⋊D3—22no—
59Q8×C3⋊D3—24no—
60Q8×C3⋊D3—24no—
61Q8×C3⋊D3D414yes—
62C2×C4×C3⋊D3—21no—
63C2×C4×C3⋊D3—21no—
64C2×C4×C3⋊D3—22no—
65C2×C4×C3⋊D3D411yescharacteristic
66C2×C4×C3⋊D3D411yescharacteristic
67C2×C4×C3⋊D3C2311yescharacteristic
68C2×#634—21no—
69C2×#634—22no—
70C2×#634C2312yes—
71C2×#634C2311yescharacteristic
72C32×Q16—24no—
73C2×C32×C8C2312yes—
74C32×C4⋊C4—21no—
75C32×C4⋊C4—21no—
76C32×C4⋊C4—21no—
77C32×C4⋊C4C2311yescharacteristic
78C32×C42—21no—
79C32×C42C2311yescharacteristic
80#3756—24no—
81#3756—24no—
82C4⋊(C3⋊Dic3)—21no—
83C4⋊(C3⋊Dic3)—21no—
84C4⋊(C3⋊Dic3)—21no—
85C4⋊(C3⋊Dic3)C2311yescharacteristic
86#3750—21no—
87#3750—21no—
88#3750—21no—
89#3750—22no—
90#3750—22no—
91C4×C3⋊Dic3—21no—
92C4×C3⋊Dic3—21no—
93C4×C3⋊Dic3—21no—
94C4×C3⋊Dic3D411yescharacteristic
95C4×C3⋊Dic3D411yescharacteristic
96C4×C3⋊Dic3C2311yescharacteristic
97C2×C3⋊(C3⋊C8)C2312yes—
98#3746—24no—
99C8×C3⋊D3—24no—
100C2×#462—91noSylow
101C2×D3×Q8—34no—
102C2×D3×Q8—38no—
103C2×C3×Q16C2×D318yes—
104C3×C4⋊Q8C2×D314yes—
105C3×C4×Q8C2×D314yes—
106Q8×Dic3—34no—
107#944—38no—
108C2×#216—38no—
109C2×#216—38no—
110D3×Q16—632no—
111C2×Dic12—38no—
112C2×D3×C8—38no—
113D3×C4⋊C4—34no—
114D3×C4⋊C4—64no—
115D3×C4⋊C4—64no—
116D3×C4⋊C4—64no—
117#888—64no—
118#888—64no—
119#887—34no—
120#887—64no—
121C42×D3—34no—
122C42×D3—64no—
123#869—34no—
124C4×Dic6—34no—
125C4×Dic6—64no—
126C3×C4⋊C8C2×D314yes—
127C3×#103C2×D318yes—
128#835—38no—
129#816—38no—
130Dic3⋊C8—38no—
131#810—38no—
132C4⋊(C3⋊C8)—34no—
133C22×C3⋊D3C2×D411yescharacteristic
134C32×Q8—21no—
135C32×Q8—22no—
136C32×Q8—22no—
137C32×Q8C2×D412yes—
138C2×C32×C4—21no—
139C2×C32×C4—21no—
140C2×C32×C4—22no—
141C2×C32×C4C2×D411yescharacteristic
142C2×C32×C4C2×D411yescharacteristic
143C2×C32×C4C2411yescharacteristic
144C2×C3⋊Dic3—21no—
145C2×C3⋊Dic3—21no—
146C2×C3⋊Dic3—22no—
147C2×C3⋊Dic3C2×D411yescharacteristic
148C2×C3⋊Dic3C2×D411yescharacteristic
149C2×C3⋊Dic3C2×D411yescharacteristic
150C4×C3⋊D3—24no—
151C4×C3⋊D3—22no—
152C4×C3⋊D3—44no—
153C4×C3⋊D3—42no—
154C4×C3⋊D3Q1614yescomplemented
155C4×C3⋊D3C2×D412yes—
156C4×C3⋊D3#4112yes—
157#634—21no—
158#634—24no—
159#634—22no—
160#634—22no—
161#634—44no—
162#634C2×D412yes—
163C32×C8—22no—
164C3⋊(C3⋊C8)—22no—
165C22×Q16—92no—
166C2×C4⋊Q8—91no—
167C2×C4×Q8—91no—
168#462—92no—
169#462—91no—
170#462—91no—
171#462—91no—
172#462—92no—
173#462C3⋊D311yescharacteristic, direct product factor
174C2×C4⋊C8—91no—
175C2×#103—92no—
176C2×C3×Q8C22×D318yes—
177C2×C3×Q8C22×D314yes—
178D3×Q8—316no—
179D3×Q8—68no—
180D3×Q8—616no—
181D3×Q8—616no—
182C2×C4×D3—34no—
183C2×C4×D3—34no—
184C2×C4×D3—34no—
185C2×C4×D3—64no—
186C2×C4×D3—64no—
187C2×C4×D3—68no—
188C2×Dic6—34no—
189C2×Dic6—38no—
190C2×Dic6—64no—
191C2×Dic6—68no—
192C3×Q16—216no—
193C2×C3×C8C22×D318yes—
194C3×C4⋊C4—24no—
195C3×C4⋊C4—24no—
196C3×C4⋊C4—24no—
197C3×C4⋊C4C22×D314yes—
198C3×C42—24no—
199C3×C42C22×D314yes—
200#216—616no—
201#216—616no—
202C4⋊Dic3—34no—
203C4⋊Dic3—64no—
204C4⋊Dic3—64no—
205C4⋊Dic3—64no—
206Dic3⋊C4—64no—
207Dic3⋊C4—64no—
208Dic3⋊C4—68no—
209Dic3⋊C4—68no—
210Dic3⋊C4—64no—
211C4×Dic3—34no—
212C4×Dic3—34no—
213C4×Dic3—34no—
214C4×Dic3—64no—
215C4×Dic3—64no—
216C4×Dic3—64no—
217C2×C3⋊C8—38no—
218Dic12—616no—
219D3×C8—616no—
220C22×C32C22×D411yescharacteristic
221C2×C3⋊D3#12112yes—
222C2×C3⋊D3C2×Q1612yes—
223C2×C3⋊D3#13712yes—
224C32×C4—22no—
225C32×C4—21no—
226C32×C4—42no—
227C32×C4—41no—
228C32×C4C2×Q1612yescomplemented
229C32×C4C22×D411yescharacteristic
230C32×C4C2×#4111yescharacteristic
231C3⋊Dic3—22no—
232C3⋊Dic3—21no—
233C3⋊Dic3—42no—
234C3⋊Dic3—41no—
235C3⋊Dic3#12112yes—
236C3⋊Dic3C2×Q1612yescomplemented
237C22×Q8—91no—
238C22×Q8—92no—
239C2×Q16—92no—
240C2×Q16—92no—
241C2×Q16—92no—
242C2×Q16—188no—
243C2×Q16C2×C3⋊D312yes—
244C22×C8—92no—
245C4⋊Q8—92no—
246C4⋊Q8—91no—
247C4⋊Q8—181no—
248C4⋊Q8—181no—
249C4⋊Q8C2×C3⋊D311yescharacteristic
250C4×Q8—91no—
251C4×Q8—91no—
252C4×Q8—91no—
253C4×Q8—181no—
254C4×Q8—181no—
255C4×Q8C2×C3⋊D311yescharacteristic
256C2×C4⋊C4—91no—
257C2×C4⋊C4—181no—
258C2×C4⋊C4—181no—
259C2×C4⋊C4—181no—
260C2×C42—91no—
261C2×C42—181no—
262C4⋊C8—92no—
263C4⋊C8—91no—
264C4⋊C8C2×C3⋊D311yescharacteristic
265#103—92no—
266#103—92no—
267#103—92no—
268#103C2×C3⋊D312yes—
269C22×D3—34no—
270C3×Q8—24no—
271C3×Q8—28no—
272C3×Q8—28no—
273C3×Q8D3×D418yes—
274C2×C3×C4—24no—
275C2×C3×C4—24no—
276C2×C3×C4—28no—
277C2×C3×C4D3×D414yes—
278C2×C3×C4D3×D414yes—
279C2×C3×C4C23×D314yes—
280C2×Dic3—34no—
281C2×Dic3—34no—
282C2×Dic3—34no—
283C2×Dic3—64no—
284C2×Dic3—64no—
285C2×Dic3—68no—
286C4×D3—316no—
287C4×D3—38no—
288C4×D3—38no—
289C4×D3—68no—
290C4×D3—616no—
291C4×D3—128no—
292C4×D3—1216no—
293Dic6—38no—
294Dic6—616no—
295Dic6—64no—
296Dic6—68no—
297Dic6—68no—
298Dic6—1216no—
299C3×C8—28no—
300C3⋊C8—68no—
301C2×C32C2×#12111yescharacteristic
302C2×C32C22×Q1611yescharacteristic
303C2×C32C2×#13711yescharacteristic
304C3⋊D3#46214yesdirect product factor
305C2×Q8—94no—
306C2×Q8—91no—
307C2×Q8—92no—
308C2×Q8—181no—
309C2×Q8—182no—
310C2×Q8—182no—
311C2×Q8—184no—
312C2×Q8—184no—
313C2×Q8C22×C3⋊D312yes—
314C2×Q8C22×C3⋊D311yescharacteristic
315C22×C4—91no—
316C22×C4—91no—
317C22×C4—91no—
318C22×C4—181no—
319C22×C4—181no—
320C22×C4—182no—
321Q16—24no—
322Q16—184no—
323Q16—184no—
324Q16—184no—
325C2×C8—92no—
326C2×C8—184no—
327C2×C8C22×C3⋊D312yes—
328C4⋊C4—21no—
329C4⋊C4—21no—
330C4⋊C4—21no—
331C4⋊C4—91no—
332C4⋊C4—181no—
333C4⋊C4—181no—
334C4⋊C4—181no—
335C4⋊C4—182no—
336C4⋊C4—182no—
337C4⋊C4—181no—
338C4⋊C4—181no—
339C4⋊C4—181no—
340C4⋊C4C22×C3⋊D311yescharacteristic
341C42—21no—
342C42—91no—
343C42—91no—
344C42—91no—
345C42—181no—
346C42—181no—
347C42—181no—
348C42C22×C3⋊D311yescharacteristic
349C22×C3C2×D3×D414yes—
350C2×D3—38no—
351C2×D3—38no—
352C2×D3—38no—
353C3×C4—24no—
354C3×C4—28no—
355C3×C4—44no—
356C3×C4—48no—
357C3×C4D3×Q1618yescomplemented
358C3×C4C2×D3×D414yes—
359C3×C4D3×#4114yes—
360Dic3—38no—
361Dic3—38no—
362Dic3—64no—
363Dic3—68no—
364Dic3—124no—
365Dic3—128no—
366C32C2×#46211yescharacteristic, complemented, Sylow
367C23—91no—
368Q8—21no—
369Q8—22no—
370Q8—22no—
371Q8—92no—
372Q8—184no—
373Q8—181no—
374Q8—182no—
375Q8—182no—
376Q8—364no—
377Q8D4×C3⋊D312yes—
378C2×C4—21no—
379C2×C4—21no—
380C2×C4—22no—
381C2×C4—91no—
382C2×C4—91no—
383C2×C4—92no—
384C2×C4—92no—
385C2×C4—94no—
386C2×C4—91no—
387C2×C4—182no—
388C2×C4—184no—
389C2×C4—181no—
390C2×C4—181no—
391C2×C4—182no—
392C2×C4—364no—
393C2×C4—362no—
394C2×C4D4×C3⋊D311yescharacteristic
395C2×C4D4×C3⋊D311yescharacteristic
396C2×C4C23×C3⋊D311yescharacteristic
397C8—22no—
398C8—182no—
399C2×C3D3×#12114yes—
400C2×C3C2×D3×Q1614yes—
401C2×C3D3×#13714yes—
402D3—316no—
403C22—92no—
404C22—92no—
405C22—92no—
406C22C2×D4×C3⋊D311yescharacteristic
407C4—21no—
408C4—22no—
409C4—41no—
410C4—42no—
411C4—92no—
412C4—92no—
413C4—181no—
414C4—182no—
415C4—361no—
416C4—362no—
417C4Q16×C3⋊D312yescomplemented
418C4C2×D4×C3⋊D311yescharacteristic
419C4#41×C3⋊D311yescharacteristic
420C3D3×#46214yescomplemented
421C2—94no—
422C2C3⋊D3×#12111yescharacteristic
423C2C2×Q16×C3⋊D311yescharacteristic
424C2C3⋊D3×#13711yescharacteristic
subgroupG/H
centerC22C2×D4×C3⋊D3
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC32×#462C2
socleC22×C32C22×D4
prime radicalC22×C3⋊D3C2×D4
hypercenter#462C3⋊D3
hypocenterC32C2×#462
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #462

Complements

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

NH ≅ G/Ntype
4. C32×#462C2semidirect
5. #10592881C2semidirect
6. #10592789C2semidirect
7. #10592730C2semidirect
8. #10592548C2semidirect
11. #10592494C2semidirect
48. C3×#462D3semidirect
154. C4×C3⋊D3Q16semidirect
173. #462C3⋊D3direct (N × H)
228. C32×C4C2×Q16semidirect
236. C3⋊Dic3C2×Q16semidirect
304. C3⋊D3#462direct (N × H)
357. C3×C4D3×Q16semidirect
366. C32C2×#462semidirect
417. C4Q16×C3⋊D3semidirect
420. C3D3×#462semidirect

Maximal subgroups

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

subgroupindex
C2×Q16×C3⋊D32
C3⋊D3×C4⋊Q82
C4×Q8×C3⋊D32
C32×#4622
#105928812
#105927892
#105927302
#105925482
C3⋊D3×C4⋊C82
C3⋊D3×#1032
#105924942
D3×#4623