Finite Group Databasebeta

← D3×#6442 #13058136

Subgroups — D3×#6442 #13058136

Order 1344.

492 conjugacy classes of subgroups.

The subgroup lattice has 420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10621362C211yesmaximal, characteristic, complemented
2D3×C7×C22⋊C4C211yesmaximal, characteristic
3C3×#6442C211yesmaximal, characteristic, complemented
4D3×C22⋊Dic7C211yesmaximal, characteristic
5D3×C22⋊Dic7C211yesmaximal, characteristic
6#10621093C211yesmaximal, characteristic, complemented
7#10621092C211yesmaximal, characteristic, complemented
8D3×C4⋊Dic7C211yesmaximal, characteristic, complemented
9D3×Dic7⋊C4C211yesmaximal, characteristic, complemented
10D3×Dic7⋊C4C211yesmaximal, characteristic, complemented
11C4×D3×Dic7C211yesmaximal, characteristic, complemented
12#10620934C211yesmaximal, characteristic, complemented
13#10620929C211yesmaximal, characteristic, complemented
14#10620904C211yesmaximal, characteristic, complemented
15#10620903C211yesmaximal, characteristic, complemented
16C2×#6442—31nomaximal, Hall
17C23×D3×C7C2211yescharacteristic
18C2×C4×D3×C7C2211yescharacteristic
19C2×C4×D3×C7C2211yescharacteristic
20C2×D3×Dic7C2211yescharacteristic
21C2×D3×Dic7C2211yescharacteristic
22C2×D3×Dic7C2211yescharacteristic
23C2×D3×Dic7C2211yescharacteristic
24C3×C7×C22⋊C4C2211yescharacteristic
25#66636C2211yescharacteristic
26#66636C2211yescharacteristic
27C4⋊Dic21C2211yescharacteristic, complemented
28#66629C2211yescharacteristic, complemented
29#66629C2211yescharacteristic, complemented
30C4×Dic21C2211yescharacteristic, complemented
31C7×#217C2211yescharacteristic
32C7×(C2×D3)⋊C4C2211yescharacteristic
33C7×(C2×D3)⋊C4C2211yescharacteristic
34C3×C22⋊Dic7C2211yescharacteristic
35C3×C22⋊Dic7C2211yescharacteristic
36C3×C4⋊Dic7C2211yescharacteristic, complemented
37C3×Dic7⋊C4C2211yescharacteristic, complemented
38C3×Dic7⋊C4C2211yescharacteristic, complemented
39C3×C4×Dic7C2211yescharacteristic, complemented
40Dic3⋊Dic7C2211yescharacteristic, complemented
41Dic3⋊Dic7C2211yescharacteristic, complemented
42#66577C2211yescharacteristic, complemented
43#66577C2211yescharacteristic, complemented
44Dic7⋊Dic3C2211yescharacteristic, complemented
45Dic7⋊Dic3C2211yescharacteristic, complemented
46(C2×D3)⋊Dic7C2211yescharacteristic
47(C2×D3)⋊Dic7C2211yescharacteristic
48(C2×D3)⋊Dic7C2211yescharacteristic
49(C2×D3)⋊Dic7C2211yescharacteristic
50Dic3×Dic7C2211yescharacteristic, complemented
51Dic3×Dic7C2211yescharacteristic, complemented
52C2×C7×C22⋊C4—31no—
53C2×C22⋊Dic7—31no—
54C2×C22⋊Dic7—31no—
55C2×C4⋊Dic7—31no—
56C2×Dic7⋊C4—31no—
57C2×Dic7⋊C4—31no—
58C2×C4×Dic7—31no—
59#6442—31no—
60#6442—31no—
61#6442—31no—
62#6442—31no—
63#6442—31no—
64#6442—31no—
65#6442—31no—
66#6442D311yescharacteristic, direct product factor
67D3×#126—71nomaximal, Hall
68C23×C3×C7C2311yescharacteristic
69C22×D3×C7—22no—
70C22×D3×C7—22no—
71C22×D3×C7—22no—
72C22×D3×C7C2311yescharacteristic
73C22×D3×C7C2311yescharacteristic
74C2×C3×C4×C7C2311yescharacteristic
75C2×C3×C4×C7C2311yescharacteristic
76C2×Dic21C2311yescharacteristic
77C2×Dic21C2311yescharacteristic
78C2×Dic21C2311yescharacteristic
79C2×Dic21C2311yescharacteristic
80C2×C7×Dic3C2311yescharacteristic
81C2×C7×Dic3C2311yescharacteristic
82C4×D3×C7—22no—
83C4×D3×C7—22no—
84C2×C3×Dic7C2311yescharacteristic
85C2×C3×Dic7C2311yescharacteristic
86C2×C3×Dic7C2311yescharacteristic
87C2×C3×Dic7C2311yescharacteristic
88D3×Dic7—22no—
89D3×Dic7—22no—
90D3×Dic7—22no—
91D3×Dic7—22no—
92C24×C7—31no—
93C22×C4×C7—31no—
94C22×C4×C7—31no—
95C22×Dic7—31no—
96C22×Dic7—31no—
97C22×Dic7—31no—
98C22×Dic7—31no—
99C7×C22⋊C4—31no—
100C7×C22⋊C4—31no—
101C7×C22⋊C4—31no—
102C7×C22⋊C4C2×D311yescharacteristic
103C22⋊Dic7—31no—
104C22⋊Dic7—31no—
105C22⋊Dic7—31no—
106C22⋊Dic7—31no—
107C22⋊Dic7—31no—
108C22⋊Dic7—31no—
109C22⋊Dic7C2×D311yescharacteristic
110C22⋊Dic7C2×D311yescharacteristic
111C4⋊Dic7—31no—
112C4⋊Dic7—31no—
113C4⋊Dic7—31no—
114C4⋊Dic7C2×D311yescharacteristic, complemented
115Dic7⋊C4—31no—
116Dic7⋊C4—31no—
117Dic7⋊C4—31no—
118Dic7⋊C4—31no—
119Dic7⋊C4—31no—
120Dic7⋊C4—31no—
121Dic7⋊C4C2×D311yescharacteristic, complemented
122Dic7⋊C4C2×D311yescharacteristic, complemented
123C4×Dic7—31no—
124C4×Dic7—31no—
125C4×Dic7—31no—
126C4×Dic7C2×D311yescharacteristic, complemented
127C3×#126—71no—
128#898—71no—
129#898—71no—
130#898—71no—
131D3×C4⋊C4—71no—
132D3×C4⋊C4—71no—
133D3×C4⋊C4—71no—
134D3×C22⋊C4—71no—
135D3×C22⋊C4—71no—
136D3×C22⋊C4D711yescharacteristic
137#879—71no—
138#879—71no—
139#879—71no—
140#876—71no—
141C42×D3—71no—
142C22×C3×C7—21no—
143C22×C3×C7—21no—
144C22×C3×C7—21no—
145C22×C3×C7C2411yescharacteristic
146C2×D3×C7—21no—
147C2×D3×C7—21no—
148C2×D3×C7—21no—
149C2×D3×C7—44no—
150C2×D3×C7#4112yes—
151C2×D3×C7#4112yes—
152C2×D3×C7#4112yes—
153C3×C4×C7—21no—
154C3×C4×C7—21no—
155Dic21—21no—
156Dic21—21no—
157Dic21—21no—
158Dic21—21no—
159C3×Dic7—21no—
160C3×Dic7—21no—
161C3×Dic7—21no—
162C3×Dic7—21no—
163C7×Dic3—21no—
164C7×Dic3—21no—
165C2×#126—211noSylow
166C23×C7—31no—
167C23×C7—31no—
168C23×C7—62no—
169C23×C7—62no—
170C23×C7—62no—
171C23×C7C22×D311yescharacteristic
172C2×C4×C7—31no—
173C2×C4×C7—31no—
174C2×C4×C7—62no—
175C2×C4×C7—62no—
176C2×C4×C7C22×D311yescharacteristic
177C2×C4×C7C22×D311yescharacteristic
178C2×Dic7—31no—
179C2×Dic7—31no—
180C2×Dic7—31no—
181C2×Dic7—31no—
182C2×Dic7—62no—
183C2×Dic7—62no—
184C2×Dic7—62no—
185C2×Dic7—62no—
186C2×Dic7C22×D311yescharacteristic
187C2×Dic7C22×D311yescharacteristic
188C2×Dic7C22×D311yescharacteristic
189C2×Dic7C22×D311yescharacteristic
190C23×D3C2×D711yescharacteristic
191C2×C4×D3—71no—
192C2×C4×D3—71no—
193C2×C4×D3—71no—
194C2×C4×D3—71no—
195C2×C4×D3C2×D711yescharacteristic
196C2×C4×D3C2×D711yescharacteristic
197C3×C4⋊C4—71no—
198C3×C4⋊C4—71no—
199C3×C4⋊C4—71no—
200C3×C22⋊C4—71no—
201C3×C22⋊C4—71no—
202C3×C22⋊C4C2×D711yescharacteristic
203C3×C42—71no—
204#217—71no—
205#217—71no—
206#217C2×D711yescharacteristic
207(C2×D3)⋊C4—71no—
208(C2×D3)⋊C4—71no—
209(C2×D3)⋊C4—71no—
210(C2×D3)⋊C4—71no—
211(C2×D3)⋊C4C2×D711yescharacteristic
212(C2×D3)⋊C4C2×D711yescharacteristic
213C4⋊Dic3—71no—
214C4⋊Dic3—71no—
215C4⋊Dic3—71no—
216Dic3⋊C4—71no—
217Dic3⋊C4—71no—
218Dic3⋊C4—71no—
219Dic3⋊C4—71no—
220Dic3⋊C4—71no—
221Dic3⋊C4—71no—
222C4×Dic3—71no—
223C4×Dic3—71no—
224C4×Dic3—71no—
225C2×C3×C7—41no—
226C2×C3×C7C2×#4111yescharacteristic
227C2×C3×C7C2×#4111yescharacteristic
228C2×C3×C7C2×#4111yescharacteristic
229D3×C7—41no—
230D3×C7#12614yescomplemented
231#126—71no—
232#126—211no—
233#126—211no—
234#126—211no—
235#126—211no—
236#126—211no—
237#126—211no—
238#126—211no—
239C2×C4⋊C4—211no—
240C2×C4⋊C4—211no—
241C2×C4⋊C4—211no—
242C2×C22⋊C4—31no—
243C2×C22⋊C4—211no—
244C2×C22⋊C4—211no—
245C2×C42—211no—
246C22×C7—21no—
247C22×C7—21no—
248C22×C7—21no—
249C22×C7—32no—
250C22×C7—32no—
251C22×C7—32no—
252C22×C7—61no—
253C22×C7—61no—
254C22×C7—61no—
255C22×C7—124no—
256C22×C7C23×D311yescharacteristic
257C4×C7—21no—
258C4×C7—21no—
259C4×C7—61no—
260C4×C7—61no—
261Dic7—21no—
262Dic7—21no—
263Dic7—21no—
264Dic7—21no—
265Dic7—61no—
266Dic7—61no—
267Dic7—61no—
268Dic7—61no—
269C23×C3C22×D711yescharacteristic
270C22×D3—22no—
271C22×D3—22no—
272C22×D3—22no—
273C22×D3C22×D711yescharacteristic
274C22×D3C22×D711yescharacteristic
275C2×C3×C4—71no—
276C2×C3×C4—71no—
277C2×C3×C4—71no—
278C2×C3×C4—71no—
279C2×C3×C4C22×D711yescharacteristic
280C2×C3×C4C22×D711yescharacteristic
281C2×Dic3—71no—
282C2×Dic3—71no—
283C2×Dic3—71no—
284C2×Dic3—71no—
285C2×Dic3C22×D711yescharacteristic
286C2×Dic3C22×D711yescharacteristic
287C4×D3—22no—
288C4×D3—22no—
289C4×D3—142no—
290C4×D3—142no—
291C4×D3—142no—
292C4×D3—142no—
293C3×C7C2×#12611yescharacteristic, complemented, Hall
294C24—31no—
295C22×C4—31no—
296C22×C4—31no—
297C22×C4—211no—
298C22×C4—211no—
299C22×C4—211no—
300C22×C4—211no—
301C4⋊C4—71no—
302C4⋊C4—71no—
303C4⋊C4—71no—
304C4⋊C4—211no—
305C4⋊C4—211no—
306C4⋊C4—211no—
307C4⋊C4—211no—
308C4⋊C4—211no—
309C4⋊C4—211no—
310C4⋊C4—211no—
311C4⋊C4—211no—
312C4⋊C4—211no—
313C22⋊C4—31no—
314C22⋊C4—31no—
315C22⋊C4—31no—
316C22⋊C4—71no—
317C22⋊C4—71no—
318C22⋊C4—211no—
319C22⋊C4—211no—
320C22⋊C4—211no—
321C22⋊C4—211no—
322C22⋊C4—211no—
323C22⋊C4—211no—
324C22⋊C4D3×D711yescharacteristic
325C42—71no—
326C42—211no—
327C42—211no—
328C42—211no—
329C2×C7—34no—
330C2×C7—41no—
331C2×C7—121no—
332C2×C7D3×#4111yescharacteristic
333C2×C7D3×#4111yescharacteristic
334C2×C7D3×#4111yescharacteristic
335C22×C3—21no—
336C22×C3—21no—
337C22×C3—21no—
338C22×C3C23×D711yescharacteristic
339C2×D3—21no—
340C2×D3—21no—
341C2×D3—21no—
342C2×D3—44no—
343C2×D3#115712yes—
344C2×D3#115912yes—
345C2×D3#115912yes—
346C3×C4—21no—
347C3×C4—21no—
348C3×C4—141no—
349C3×C4—141no—
350C3×C4—141no—
351C3×C4—141no—
352Dic3—21no—
353Dic3—21no—
354Dic3—141no—
355Dic3—141no—
356Dic3—141no—
357Dic3—141no—
358C23—31no—
359C23—31no—
360C23—62no—
361C23—62no—
362C23—62no—
363C23C2×D3×D711yescharacteristic
364C2×C4—31no—
365C2×C4—31no—
366C2×C4—62no—
367C2×C4—62no—
368C2×C4—71no—
369C2×C4—71no—
370C2×C4—71no—
371C2×C4—71no—
372C2×C4—211no—
373C2×C4—211no—
374C2×C4—211no—
375C2×C4—211no—
376C2×C4—422no—
377C2×C4—422no—
378C2×C4—422no—
379C2×C4—422no—
380C2×C4C2×D3×D711yescharacteristic
381C2×C4C2×D3×D711yescharacteristic
382C7D3×#12611yescharacteristic, complemented, Sylow
383C2×C3—41no—
384C2×C3C2×#115711yescharacteristic
385C2×C3C2×#115911yescharacteristic
386C2×C3C2×#115911yescharacteristic
387D3—41no—
388D3#644214yesdirect product factor
389C22—21no—
390C22—21no—
391C22—21no—
392C22—32no—
393C22—32no—
394C22—32no—
395C22—61no—
396C22—61no—
397C22—61no—
398C22—124no—
399C22C22×D3×D711yescharacteristic
400C4—21no—
401C4—21no—
402C4—61no—
403C4—61no—
404C4—141no—
405C4—141no—
406C4—141no—
407C4—141no—
408C4—421no—
409C4—421no—
410C4—421no—
411C4—421no—
412C3C2×#644211yescharacteristic, complemented, Sylow
413C2—34no—
414C2—41no—
415C2—121no—
416C2D3×#115711yescharacteristic
417C2D3×#115911yescharacteristic
418C2D3×#115911yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×D7
commutator, socle, cosocleC22×C3×C7C24
FittingC3×C7×C22⋊C4C22
prime radicalC23×D3×C7C22
hypercenterC22⋊C4D3×D7
hypocenterC3×C7C2×#126
LCSG ▷ C22×C3×C7 ▷ C3×C7
UCSC1 ◁ C22 ◁ C22⋊C4

Complements

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

NH ≅ G/Ntype
1. #10621362C2semidirect
3. C3×#6442C2semidirect
6. #10621093C2semidirect
7. #10621092C2semidirect
8. D3×C4⋊Dic7C2semidirect
9. D3×Dic7⋊C4C2semidirect
10. D3×Dic7⋊C4C2semidirect
11. C4×D3×Dic7C2semidirect
12. #10620934C2semidirect
13. #10620929C2semidirect
14. #10620904C2semidirect
15. #10620903C2semidirect
27. C4⋊Dic21C22semidirect
28. #66629C22semidirect
29. #66629C22semidirect
30. C4×Dic21C22semidirect
36. C3×C4⋊Dic7C22semidirect
37. C3×Dic7⋊C4C22semidirect
38. C3×Dic7⋊C4C22semidirect
39. C3×C4×Dic7C22semidirect
40. Dic3⋊Dic7C22semidirect
41. Dic3⋊Dic7C22semidirect
42. #66577C22semidirect
43. #66577C22semidirect
44. Dic7⋊Dic3C22semidirect
45. Dic7⋊Dic3C22semidirect
50. Dic3×Dic7C22semidirect
51. Dic3×Dic7C22semidirect
66. #6442D3direct (N × H)
114. C4⋊Dic7C2×D3semidirect
121. Dic7⋊C4C2×D3semidirect
122. Dic7⋊C4C2×D3semidirect
126. C4×Dic7C2×D3semidirect
230. D3×C7#126semidirect
293. C3×C7C2×#126semidirect
382. C7D3×#126semidirect
388. D3#6442direct (N × H)
412. C3C2×#6442semidirect

Maximal subgroups

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

subgroupindex
#106213622
D3×C7×C22⋊C42
C3×#64422
D3×C22⋊Dic72
#106210932
#106210922
D3×C4⋊Dic72
D3×Dic7⋊C42
C4×D3×Dic72
#106209342
#106209292
#106209042
#106209032
C2×#64423
D3×#1267