Finite Group Databasebeta

← C3⋊D3×#475 #11868379

Subgroups — C3⋊D3×#475 #11868379

Order 1152.

1248 conjugacy classes of subgroups.

The subgroup lattice has 402 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3⋊D3×C4⋊Q8C211yesmaximal, characteristic
2C4×Q8×C3⋊D3C211yesmaximal, characteristic
3C32×#475C211yesmaximal, characteristic, complemented
4#10592793C211yesmaximal, characteristic, complemented
5#10592719C211yesmaximal, characteristic, complemented
6C3⋊D3×#106C212yesmaximal
7#10592553C212yesmaximal, complemented
8#10592550C211yesmaximal, characteristic, complemented
9C3⋊D3×C4⋊C8C211yesmaximal, characteristic
10C3⋊D3×#103C212yesmaximal
11#10592490C212yesmaximal, complemented
12D3×#475—34nomaximal
13C2×Q8×C3⋊D3—21no—
14C2×Q8×C3⋊D3C2211yescharacteristic
15C32×C4⋊Q8C2211yescharacteristic
16C32×C4×Q8C2211yescharacteristic
17Q8×C3⋊Dic3C2211yescharacteristic
18#64153—21no—
19C2×C8×C3⋊D3C2212yes—
20C4⋊C4×C3⋊D3—21no—
21C4⋊C4×C3⋊D3—21no—
22C4⋊C4×C3⋊D3C2211yescharacteristic
23C4⋊C4×C3⋊D3C2212yes—
24#64097—21no—
25#64097C2212yes—
26#64096—21no—
27#64096C2211yescharacteristic
28C42×C3⋊D3—21no—
29C42×C3⋊D3C2211yescharacteristic
30#64078C2211yescharacteristic
31C4×#634—21no—
32C4×#634C2211yescharacteristic
33C32×#106C2212yes—
34C32×C4⋊C8C2211yescharacteristic
35C32×#103C2212yes—
36#63662C2212yes—
37#63644C2212yes—
38#63643C2212yes—
39#63641C2212yes—
40#63637C2212yes—
41#63635C2212yes—
42#63635C2212yes—
43C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
44D3×C4⋊Q8—34no—
45C4×D3×Q8—34no—
46C3×#475D314yescomplemented
47#5094—34no—
48#5020—34no—
49D3×#106—38no—
50#4854—38no—
51#4851—34no—
52D3×C4⋊C8—34no—
53D3×#103—38no—
54#4791—38no—
55C2×C32×Q8—21no—
56C2×C32×Q8C2311yescharacteristic
57Q8×C3⋊D3—22no—
58Q8×C3⋊D3—44no—
59Q8×C3⋊D3Q814yescomplemented
60C2×C4×C3⋊D3—21no—
61C2×C4×C3⋊D3—21no—
62C2×C4×C3⋊D3—22no—
63C2×C4×C3⋊D3D411yescharacteristic
64C2×C4×C3⋊D3D411yescharacteristic
65C2×C4×C3⋊D3C2311yescharacteristic
66C2×#634—21no—
67C2×#634—21no—
68C2×#634—22no—
69C2×#634C2311yescharacteristic
70C2×C32×C8C2312yes—
71C32×C4⋊C4—21no—
72C32×C4⋊C4—21no—
73C32×C4⋊C4C2311yescharacteristic
74C32×C4⋊C4C2312yes—
75C32×C42—21no—
76C32×C42C2311yescharacteristic
77C4⋊(C3⋊Dic3)—21no—
78C4⋊(C3⋊Dic3)—21no—
79C4⋊(C3⋊Dic3)C2311yescharacteristic
80C4⋊(C3⋊Dic3)C2312yes—
81#3750—21no—
82#3750—21no—
83#3750—21no—
84#3750—22no—
85#3750—22no—
86C4×C3⋊Dic3—21no—
87C4×C3⋊Dic3—21no—
88C4×C3⋊Dic3—21no—
89C4×C3⋊Dic3D411yescharacteristic
90C4×C3⋊Dic3D411yescharacteristic
91C4×C3⋊Dic3C2311yescharacteristic
92C2×C3⋊(C3⋊C8)C2312yes—
93C8×C3⋊D3—24no—
94C2×#475—91noSylow
95C2×D3×Q8—34no—
96C2×D3×Q8—64no—
97C3×C4⋊Q8C2×D314yes—
98C3×C4×Q8C2×D314yes—
99Q8×Dic3—34no—
100#944—64no—
101C2×D3×C8—38no—
102D3×C4⋊C4—38no—
103D3×C4⋊C4—34no—
104D3×C4⋊C4—64no—
105D3×C4⋊C4—64no—
106#888—38no—
107#888—64no—
108#887—34no—
109#887—64no—
110C42×D3—34no—
111C42×D3—64no—
112#869—34no—
113C4×Dic6—34no—
114C4×Dic6—64no—
115C3×#106C2×D318yes—
116C3×C4⋊C8C2×D314yes—
117C3×#103C2×D318yes—
118#835—38no—
119#817—38no—
120#816—38no—
121Dic3⋊C8—38no—
122#810—38no—
123#808—38no—
124#808—38no—
125C4⋊(C3⋊C8)—34no—
126C22×C3⋊D3C2×D411yescharacteristic
127C32×Q8—21no—
128C32×Q8—42no—
129C32×Q8C2×Q812yescomplemented
130C2×C32×C4—21no—
131C2×C32×C4—21no—
132C2×C32×C4—22no—
133C2×C32×C4C2×D411yescharacteristic
134C2×C32×C4C2×D411yescharacteristic
135C2×C32×C4C2411yescharacteristic
136C2×C3⋊Dic3—21no—
137C2×C3⋊Dic3—21no—
138C2×C3⋊Dic3—22no—
139C2×C3⋊Dic3C2×D411yescharacteristic
140C2×C3⋊Dic3C2×D411yescharacteristic
141C2×C3⋊Dic3C2×D411yescharacteristic
142C4×C3⋊D3—24no—
143C4×C3⋊D3—22no—
144C4×C3⋊D3—44no—
145C4×C3⋊D3—42no—
146C4×C3⋊D3SD1614yes—
147C4×C3⋊D3C2×Q812yes—
148C4×C3⋊D3#4112yes—
149#634—21no—
150#634—24no—
151#634—42no—
152#634—44no—
153#634C2×Q812yescomplemented
154C32×C8—22no—
155C3⋊(C3⋊C8)—22no—
156C2×C4⋊Q8—91no—
157C2×C4×Q8—91no—
158#475—91no—
159#475—91no—
160#475—92no—
161#475—91no—
162#475—92no—
163#475C3⋊D311yescharacteristic, direct product factor
164C2×#106—92no—
165C2×C4⋊C8—91no—
166C2×#103—92no—
167C2×C3×Q8—24no—
168C2×C3×Q8C22×D314yes—
169D3×Q8—316no—
170D3×Q8—68no—
171D3×Q8—1216no—
172C2×C4×D3—34no—
173C2×C4×D3—34no—
174C2×C4×D3—34no—
175C2×C4×D3—64no—
176C2×C4×D3—64no—
177C2×C4×D3—68no—
178C2×Dic6—34no—
179C2×Dic6—64no—
180C2×Dic6—68no—
181C2×Dic6—64no—
182C2×C3×C8C22×D318yes—
183C3×C4⋊C4—24no—
184C3×C4⋊C4—24no—
185C3×C4⋊C4C22×D314yes—
186C3×C4⋊C4C22×D318yes—
187C3×C42—24no—
188C3×C42C22×D314yes—
189C4⋊Dic3—34no—
190C4⋊Dic3—38no—
191C4⋊Dic3—64no—
192C4⋊Dic3—64no—
193Dic3⋊C4—64no—
194Dic3⋊C4—64no—
195Dic3⋊C4—68no—
196Dic3⋊C4—68no—
197Dic3⋊C4—64no—
198C4×Dic3—34no—
199C4×Dic3—34no—
200C4×Dic3—34no—
201C4×Dic3—64no—
202C4×Dic3—64no—
203C4×Dic3—64no—
204C2×C3⋊C8—38no—
205D3×C8—616no—
206C22×C32C22×D411yescharacteristic
207C2×C3⋊D3C22⋊Q812yes—
208C2×C3⋊D3C2×SD1612yes—
209C2×C3⋊D3#13712yes—
210C32×C4—22no—
211C32×C4—21no—
212C32×C4—42no—
213C32×C4—41no—
214C32×C4C2×SD1612yes—
215C32×C4C22×Q811yescharacteristic
216C32×C4C2×#4111yescharacteristic
217C3⋊Dic3—22no—
218C3⋊Dic3—21no—
219C3⋊Dic3—42no—
220C3⋊Dic3—41no—
221C3⋊Dic3C22⋊Q812yes—
222C3⋊Dic3C2×SD1612yes—
223C22×Q8—91no—
224C22×Q8—181no—
225C22×C8—92no—
226C4⋊Q8—92no—
227C4⋊Q8—91no—
228C4⋊Q8—181no—
229C4⋊Q8—181no—
230C4⋊Q8C2×C3⋊D311yescharacteristic
231C4×Q8—91no—
232C4×Q8—91no—
233C4×Q8—91no—
234C4×Q8—181no—
235C4×Q8—181no—
236C4×Q8C2×C3⋊D311yescharacteristic
237C2×C4⋊C4—91no—
238C2×C4⋊C4—92no—
239C2×C4⋊C4—181no—
240C2×C4⋊C4—181no—
241C2×C42—91no—
242C2×C42—181no—
243#106—92no—
244#106—92no—
245#106—92no—
246#106C2×C3⋊D312yes—
247C4⋊C8—92no—
248C4⋊C8—91no—
249C4⋊C8C2×C3⋊D311yescharacteristic
250#103—92no—
251#103—92no—
252#103—92no—
253#103C2×C3⋊D312yes—
254C22×D3—34no—
255C3×Q8—24no—
256C3×Q8—48no—
257C3×Q8D3×Q818yescomplemented
258C2×C3×C4—24no—
259C2×C3×C4—24no—
260C2×C3×C4—28no—
261C2×C3×C4D3×D414yes—
262C2×C3×C4D3×D414yes—
263C2×C3×C4C23×D314yes—
264C2×Dic3—34no—
265C2×Dic3—34no—
266C2×Dic3—34no—
267C2×Dic3—64no—
268C2×Dic3—64no—
269C2×Dic3—68no—
270C4×D3—316no—
271C4×D3—38no—
272C4×D3—38no—
273C4×D3—68no—
274C4×D3—616no—
275C4×D3—128no—
276C4×D3—1216no—
277Dic6—38no—
278Dic6—616no—
279Dic6—64no—
280Dic6—1216no—
281Dic6—128no—
282C3×C8—28no—
283C3⋊C8—68no—
284C2×C32C2×C22⋊Q811yescharacteristic
285C2×C32C22×SD1611yescharacteristic
286C2×C32C2×#13711yescharacteristic
287C3⋊D3#47514yesdirect product factor
288C2×Q8—21no—
289C2×Q8—94no—
290C2×Q8—91no—
291C2×Q8—181no—
292C2×Q8—182no—
293C2×Q8—182no—
294C2×Q8—181no—
295C2×Q8—364no—
296C2×Q8C22×C3⋊D311yescharacteristic
297C22×C4—91no—
298C22×C4—91no—
299C22×C4—91no—
300C22×C4—181no—
301C22×C4—181no—
302C22×C4—182no—
303C2×C8—92no—
304C2×C8—184no—
305C2×C8C22×C3⋊D312yes—
306C4⋊C4—21no—
307C4⋊C4—21no—
308C4⋊C4—92no—
309C4⋊C4—91no—
310C4⋊C4—181no—
311C4⋊C4—182no—
312C4⋊C4—181no—
313C4⋊C4—181no—
314C4⋊C4—182no—
315C4⋊C4—181no—
316C4⋊C4—181no—
317C4⋊C4C22×C3⋊D312yes—
318C4⋊C4C22×C3⋊D311yescharacteristic
319C42—21no—
320C42—91no—
321C42—91no—
322C42—91no—
323C42—181no—
324C42—181no—
325C42—181no—
326C42C22×C3⋊D311yescharacteristic
327C22×C3C2×D3×D414yes—
328C2×D3—38no—
329C2×D3—38no—
330C2×D3—38no—
331C3×C4—24no—
332C3×C4—28no—
333C3×C4—48no—
334C3×C4—44no—
335C3×C4D3×SD1618yes—
336C3×C4C2×D3×Q814yes—
337C3×C4D3×#4114yes—
338Dic3—38no—
339Dic3—38no—
340Dic3—64no—
341Dic3—68no—
342Dic3—128no—
343Dic3—124no—
344C32C2×#47511yescharacteristic, complemented, Sylow
345C23—91no—
346Q8—21no—
347Q8—42no—
348Q8—92no—
349Q8—184no—
350Q8—181no—
351Q8—364no—
352Q8—362no—
353Q8Q8×C3⋊D312yescomplemented
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—22no—
357C2×C4—91no—
358C2×C4—91no—
359C2×C4—92no—
360C2×C4—92no—
361C2×C4—94no—
362C2×C4—91no—
363C2×C4—182no—
364C2×C4—184no—
365C2×C4—181no—
366C2×C4—181no—
367C2×C4—182no—
368C2×C4—364no—
369C2×C4—362no—
370C2×C4D4×C3⋊D311yescharacteristic
371C2×C4D4×C3⋊D311yescharacteristic
372C2×C4C23×C3⋊D311yescharacteristic
373C8—22no—
374C8—182no—
375C2×C3D3×C22⋊Q814yes—
376C2×C3C2×D3×SD1614yes—
377C2×C3D3×#13714yes—
378D3—316no—
379C22—92no—
380C22—92no—
381C22—92no—
382C22C2×D4×C3⋊D311yescharacteristic
383C4—22no—
384C4—21no—
385C4—42no—
386C4—41no—
387C4—92no—
388C4—92no—
389C4—182no—
390C4—181no—
391C4—362no—
392C4—361no—
393C4SD16×C3⋊D312yes—
394C4C2×Q8×C3⋊D311yescharacteristic
395C4#41×C3⋊D311yescharacteristic
396C3D3×#47514yescomplemented
397C2—94no—
398C2C3⋊D3×C22⋊Q811yescharacteristic
399C2C2×SD16×C3⋊D311yescharacteristic
400C2C3⋊D3×#13711yescharacteristic
subgroupG/H
centerC22C2×D4×C3⋊D3
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC32×#475C2
socleC22×C32C22×D4
prime radicalC22×C3⋊D3C2×D4
hypercenter#475C3⋊D3
hypocenterC32C2×#475
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #475

Complements

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

NH ≅ G/Ntype
3. C32×#475C2semidirect
4. #10592793C2semidirect
5. #10592719C2semidirect
7. #10592553C2semidirect
8. #10592550C2semidirect
11. #10592490C2semidirect
46. C3×#475D3semidirect
59. Q8×C3⋊D3Q8semidirect
129. C32×Q8C2×Q8semidirect
153. #634C2×Q8semidirect
163. #475C3⋊D3direct (N × H)
257. C3×Q8D3×Q8semidirect
287. C3⋊D3#475direct (N × H)
344. C32C2×#475semidirect
353. Q8Q8×C3⋊D3semidirect
396. C3D3×#475semidirect

Maximal subgroups

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

subgroupindex
C3⋊D3×C4⋊Q82
C4×Q8×C3⋊D32
C32×#4752
#105927932
#105927192
C3⋊D3×#1062
#105925532
#105925502
C3⋊D3×C4⋊C82
C3⋊D3×#1032
#105924902
D3×#4753