Finite Group Databasebeta

← C3⋊D3×#501 #11875009

Subgroups — C3⋊D3×#501 #11875009

Order 1152.

1152 conjugacy classes of subgroups.

The subgroup lattice has 375 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3⋊D3×C4⋊Q8C211yesmaximal, characteristic
2C3⋊D3×#125C211yesmaximal, characteristic
3C32×#501C211yesmaximal, characteristic, complemented
4#10592780C211yesmaximal, characteristic, complemented
5#10592763C211yesmaximal, characteristic, complemented
6C3⋊D3×#107C212yesmaximal
7#10592575C212yesmaximal, complemented
8C3⋊D3×#106C212yesmaximal
9#10592555C212yesmaximal, complemented
10C3⋊D3×#97C211yesmaximal, characteristic
11#10592401C211yesmaximal, characteristic, complemented
12D3×#501—34nomaximal
13C2×Q8×C3⋊D3—21no—
14C32×C4⋊Q8C2211yescharacteristic
15C32×#125C2211yescharacteristic
16#64153—21no—
17C2×C8×C3⋊D3C2212yes—
18C4⋊C4×C3⋊D3—21no—
19C4⋊C4×C3⋊D3—21no—
20C4⋊C4×C3⋊D3—21no—
21C4⋊C4×C3⋊D3C2211yescharacteristic
22C4⋊C4×C3⋊D3C2212yes—
23C4⋊C4×C3⋊D3C2211yescharacteristic
24#64099C2211yescharacteristic
25#64099C2211yescharacteristic
26#64098—21no—
27#64098—21no—
28#64097—21no—
29#64097C2212yes—
30C42×C3⋊D3C2211yescharacteristic
31#64079C2211yescharacteristic
32#64078C2211yescharacteristic
33C32×#107C2212yes—
34C32×#106C2212yes—
35C32×#97C2211yescharacteristic
36#63645C2212yes—
37#63644C2212yes—
38#63642C2212yes—
39#63635C2212yes—
40#63635C2212yes—
41#63634C2212yes—
42#63634C2212yes—
43#63630C2211yescharacteristic
44D3×C4⋊Q8—34no—
45D3×#125—34no—
46C3×#501D314yescomplemented
47#5081—34no—
48#5064—34no—
49D3×#107—38no—
50#4876—38no—
51D3×#106—38no—
52#4856—38no—
53D3×#97—34no—
54#4702—34no—
55C2×C32×Q8—21no—
56Q8×C3⋊D3—44no—
57C2×C4×C3⋊D3—21no—
58C2×C4×C3⋊D3—21no—
59C2×C4×C3⋊D3—22no—
60C2×C4×C3⋊D3D411yescharacteristic
61C2×C4×C3⋊D3D411yescharacteristic
62C2×C4×C3⋊D3C2311yescharacteristic
63C2×#634—21no—
64C2×#634—22no—
65C2×C32×C8C2312yes—
66C32×C4⋊C4—21no—
67C32×C4⋊C4—21no—
68C32×C4⋊C4—21no—
69C32×C4⋊C4C2312yes—
70C32×C4⋊C4C2311yescharacteristic
71C32×C4⋊C4C2311yescharacteristic
72C32×C42C2311yescharacteristic
73C4⋊(C3⋊Dic3)—21no—
74C4⋊(C3⋊Dic3)—21no—
75C4⋊(C3⋊Dic3)—21no—
76C4⋊(C3⋊Dic3)C2312yes—
77C4⋊(C3⋊Dic3)C2311yescharacteristic
78C4⋊(C3⋊Dic3)C2311yescharacteristic
79#3750—21no—
80#3750—21no—
81#3750—22no—
82#3750—22no—
83#3750—21no—
84#3750—21no—
85#3750—21no—
86#3750—21no—
87C4×C3⋊Dic3D411yescharacteristic
88C4×C3⋊Dic3D411yescharacteristic
89C4×C3⋊Dic3C2311yescharacteristic
90C2×C3⋊(C3⋊C8)C2312yes—
91C8×C3⋊D3Q818yescomplemented
92C2×#501—91noSylow
93C2×D3×Q8—64no—
94C3×C4⋊Q8C2×D314yes—
95C3×#125C2×D314yes—
96#944—64no—
97C2×D3×C8—38no—
98D3×C4⋊C4—34no—
99D3×C4⋊C4—38no—
100D3×C4⋊C4—34no—
101D3×C4⋊C4—64no—
102D3×C4⋊C4—64no—
103D3×C4⋊C4—64no—
104#890—34no—
105#890—34no—
106#889—64no—
107#889—64no—
108#888—38no—
109#888—64no—
110C42×D3—34no—
111#870—34no—
112#869—34no—
113C3×#107C2×D318yes—
114C3×#106C2×D318yes—
115C3×#97C2×D314yes—
116#818—38no—
117#817—38no—
118#815—38no—
119#808—38no—
120#808—38no—
121#807—38no—
122#807—38no—
123#803—34no—
124C22×C3⋊D3C2×D411yescharacteristic
125C32×Q8—42no—
126C2×C32×C4—21no—
127C2×C32×C4—21no—
128C2×C32×C4—22no—
129C2×C32×C4C2×D411yescharacteristic
130C2×C32×C4C2×D411yescharacteristic
131C2×C32×C4C2411yescharacteristic
132C2×C3⋊Dic3—21no—
133C2×C3⋊Dic3—21no—
134C2×C3⋊Dic3—22no—
135C2×C3⋊Dic3C2×D411yescharacteristic
136C2×C3⋊Dic3C2×D411yescharacteristic
137C2×C3⋊Dic3C2×D411yescharacteristic
138C4×C3⋊D3—22no—
139C4×C3⋊D3—22no—
140C4×C3⋊D3—42no—
141C4×C3⋊D3—44no—
142C4×C3⋊D3—42no—
143C4×C3⋊D3C2×Q814yes—
144#634—44no—
145#634—42no—
146C32×C8C2×Q814yescomplemented
147C3⋊(C3⋊C8)C2×Q814yescomplemented
148C2×C4⋊Q8—91no—
149C2×#125—91no—
150#501—91no—
151#501—91no—
152#501—92no—
153#501—92no—
154#501—91no—
155#501C3⋊D311yescharacteristic, direct product factor
156C2×#107—92no—
157C2×#106—92no—
158C2×#97—91no—
159C2×C3×Q8—24no—
160D3×Q8—1216no—
161C2×C4×D3—34no—
162C2×C4×D3—34no—
163C2×C4×D3—34no—
164C2×C4×D3—64no—
165C2×C4×D3—64no—
166C2×C4×D3—68no—
167C2×Dic6—68no—
168C2×Dic6—64no—
169C2×C3×C8C22×D318yes—
170C3×C4⋊C4—24no—
171C3×C4⋊C4—24no—
172C3×C4⋊C4—24no—
173C3×C4⋊C4C22×D314yes—
174C3×C4⋊C4C22×D318yes—
175C3×C4⋊C4C22×D314yes—
176C3×C42C22×D314yes—
177C4⋊Dic3—34no—
178C4⋊Dic3—38no—
179C4⋊Dic3—34no—
180C4⋊Dic3—64no—
181C4⋊Dic3—64no—
182C4⋊Dic3—64no—
183Dic3⋊C4—68no—
184Dic3⋊C4—68no—
185Dic3⋊C4—64no—
186Dic3⋊C4—64no—
187Dic3⋊C4—64no—
188Dic3⋊C4—64no—
189Dic3⋊C4—64no—
190Dic3⋊C4—64no—
191C4×Dic3—34no—
192C4×Dic3—34no—
193C4×Dic3—34no—
194C2×C3⋊C8—38no—
195D3×C8—332no—
196C22×C32C22×D411yescharacteristic
197C2×C3⋊D3C4⋊Q812yes—
198C2×C3⋊D3AGL(1,ℤ/8)12yes—
199C2×C3⋊D3#13712yes—
200C32×C4—21no—
201C32×C4—21no—
202C32×C4—42no—
203C32×C4—41no—
204C32×C4—41no—
205C32×C4C22×Q812yes—
206C3⋊Dic3—21no—
207C3⋊Dic3—21no—
208C3⋊Dic3—42no—
209C3⋊Dic3—41no—
210C3⋊Dic3—41no—
211C3⋊Dic3C4⋊Q812yes—
212C22×Q8—181no—
213C22×C8—92no—
214C4⋊Q8—92no—
215C4⋊Q8—91no—
216C4⋊Q8—181no—
217C4⋊Q8—181no—
218C4⋊Q8C2×C3⋊D311yescharacteristic
219#125—91no—
220#125—91no—
221#125—91no—
222#125—181no—
223#125—181no—
224#125C2×C3⋊D311yescharacteristic
225C2×C4⋊C4—91no—
226C2×C4⋊C4—91no—
227C2×C4⋊C4—92no—
228C2×C4⋊C4—181no—
229C2×C4⋊C4—181no—
230C2×C4⋊C4—181no—
231C2×C42—91no—
232#107—92no—
233#107—92no—
234#107—92no—
235#107C2×C3⋊D312yes—
236#106—92no—
237#106—92no—
238#106—92no—
239#106C2×C3⋊D312yes—
240#97—92no—
241#97—91no—
242#97C2×C3⋊D311yescharacteristic
243C22×D3—34no—
244C3×Q8—48no—
245C2×C3×C4—24no—
246C2×C3×C4—24no—
247C2×C3×C4—28no—
248C2×C3×C4D3×D414yes—
249C2×C3×C4D3×D414yes—
250C2×C3×C4C23×D314yes—
251C2×Dic3—34no—
252C2×Dic3—34no—
253C2×Dic3—34no—
254C2×Dic3—64no—
255C2×Dic3—64no—
256C2×Dic3—68no—
257C4×D3—316no—
258C4×D3—68no—
259C4×D3—68no—
260C4×D3—128no—
261C4×D3—128no—
262C4×D3—1216no—
263Dic6—1216no—
264Dic6—128no—
265C3×C8D3×Q8116yescomplemented
266C3⋊C8—316no—
267C2×C32C2×C4⋊Q811yescharacteristic
268C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
269C2×C32C2×#13711yescharacteristic
270C3⋊D3#50114yesdirect product factor
271C2×Q8—21no—
272C2×Q8—182no—
273C2×Q8—181no—
274C2×Q8—364no—
275C22×C4—91no—
276C22×C4—91no—
277C22×C4—91no—
278C22×C4—181no—
279C22×C4—181no—
280C22×C4—182no—
281C2×C8—92no—
282C2×C8—98no—
283C2×C8C22×C3⋊D312yes—
284C4⋊C4—21no—
285C4⋊C4—21no—
286C4⋊C4—21no—
287C4⋊C4—91no—
288C4⋊C4—92no—
289C4⋊C4—91no—
290C4⋊C4—181no—
291C4⋊C4—181no—
292C4⋊C4—182no—
293C4⋊C4—181no—
294C4⋊C4—181no—
295C4⋊C4—181no—
296C4⋊C4—181no—
297C4⋊C4—182no—
298C4⋊C4—181no—
299C4⋊C4—181no—
300C4⋊C4—181no—
301C4⋊C4C22×C3⋊D311yescharacteristic
302C4⋊C4C22×C3⋊D312yes—
303C4⋊C4C22×C3⋊D311yescharacteristic
304C42—91no—
305C42—91no—
306C42—91no—
307C42C22×C3⋊D311yescharacteristic
308C22×C3C2×D3×D414yes—
309C2×D3—38no—
310C2×D3—38no—
311C2×D3—38no—
312C3×C4—24no—
313C3×C4—24no—
314C3×C4—48no—
315C3×C4—44no—
316C3×C4—44no—
317C3×C4C2×D3×Q818yes—
318Dic3—38no—
319Dic3—64no—
320Dic3—64no—
321Dic3—128no—
322Dic3—124no—
323Dic3—124no—
324C32C2×#50111yescharacteristic, complemented, Sylow
325C23—91no—
326Q8—42no—
327Q8—362no—
328Q8—364no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—22no—
332C2×C4—91no—
333C2×C4—94no—
334C2×C4—91no—
335C2×C4—91no—
336C2×C4—182no—
337C2×C4—182no—
338C2×C4—181no—
339C2×C4—181no—
340C2×C4—182no—
341C2×C4—364no—
342C2×C4—362no—
343C2×C4—362no—
344C2×C4D4×C3⋊D311yescharacteristic
345C2×C4D4×C3⋊D311yescharacteristic
346C2×C4C23×C3⋊D311yescharacteristic
347C8—94no—
348C8Q8×C3⋊D314yescomplemented
349C2×C3D3×C4⋊Q814yes—
350C2×C3D3×AGL(1,ℤ/8)14yes—
351C2×C3D3×#13714yes—
352D3—316no—
353C22—92no—
354C22—92no—
355C22—92no—
356C22C2×D4×C3⋊D311yescharacteristic
357C4—21no—
358C4—21no—
359C4—42no—
360C4—41no—
361C4—41no—
362C4—92no—
363C4—181no—
364C4—181no—
365C4—362no—
366C4—361no—
367C4—361no—
368C4C2×Q8×C3⋊D312yes—
369C3D3×#50114yescomplemented
370C2—94no—
371C2C3⋊D3×C4⋊Q811yescharacteristic
372C2C3⋊D3×AGL(1,ℤ/8)11yescharacteristic
373C2C3⋊D3×#13711yescharacteristic
subgroupG/H
centerC22C2×D4×C3⋊D3
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC32×#501C2
socleC22×C32C22×D4
prime radicalC22×C3⋊D3C2×D4
hypercenter#501C3⋊D3
hypocenterC32C2×#501
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #501

Complements

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

NH ≅ G/Ntype
3. C32×#501C2semidirect
4. #10592780C2semidirect
5. #10592763C2semidirect
7. #10592575C2semidirect
9. #10592555C2semidirect
11. #10592401C2semidirect
46. C3×#501D3semidirect
91. C8×C3⋊D3Q8semidirect
146. C32×C8C2×Q8semidirect
147. C3⋊(C3⋊C8)C2×Q8semidirect
155. #501C3⋊D3direct (N × H)
265. C3×C8D3×Q8semidirect
270. C3⋊D3#501direct (N × H)
324. C32C2×#501semidirect
348. C8Q8×C3⋊D3semidirect
369. C3D3×#501semidirect

Maximal subgroups

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

subgroupindex
C3⋊D3×C4⋊Q82
C3⋊D3×#1252
C32×#5012
#105927802
#105927632
C3⋊D3×#1072
#105925752
C3⋊D3×#1062
#105925552
C3⋊D3×#972
#105924012
D3×#5013