Finite Group Databasebeta

← D3×#6482 #13059331

Subgroups — D3×#6482 #13059331

Order 1344.

532 conjugacy classes of subgroups; only the 130 normal subgroups are shown.

normal subgroups only

This group has 532 conjugacy classes of subgroups — too many to draw. Only its 130 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
1D3×#1161C212yesmaximal, complemented
2#10621402C211yesmaximal, characteristic, complemented
3D3×C7×Q16C211yesmaximal, characteristic, complemented
4C3×#6482C211yesmaximal, characteristic, complemented
5#10621083C212yesmaximal, complemented
6#10621078C212yesmaximal, complemented
7D3×#1143C212yesmaximal, complemented
8#10620839C211yesmaximal, characteristic, complemented
9#10620833C211yesmaximal, characteristic, complemented
10D3×D56C211yesmaximal, characteristic, complemented
11D3×C8×D7C211yesmaximal, characteristic, complemented
12C2×#6482—31nomaximal, Hall
13#66732C2212yescomplemented
14D3×C7×Q8C2212yes—
15C3×#1161C2212yescomplemented
16D3×D28—22no—
17D3×D28C2212yes—
18C4×D3×D7—22no—
19C4×D3×D7C2211yescharacteristic
20#66677—22no—
21#66677C2212yescomplemented
22#66670—22no—
23#66670C2212yescomplemented
24C3×C7×Q16C2211yescharacteristic, complemented
25#66634C2212yescomplemented
26D168C2211yescharacteristic, complemented
27C8×D21C2211yescharacteristic, complemented
28C7×#216C2212yescomplemented
29C7×Dic12C2211yescharacteristic, complemented
30D3×C7×C8C2211yescharacteristic
31C3×#1143C2212yescomplemented
32C3×D56C2211yescharacteristic, complemented
33C3×C8×D7C2211yescharacteristic, complemented
34#66568C2212yescomplemented
35#66563C2212yescomplemented
36#66561C2212yescomplemented
37D21⋊C8C2211yescharacteristic, complemented
38D3×C7⋊C8C2211yescharacteristic
39D7×C3⋊C8C2211yescharacteristic, complemented
40C2×#1161—32no—
41C2×C7×Q16—31no—
42C2×#1143—32no—
43#6482—32no—
44#6482—31no—
45#6482—32no—
46#6482—31no—
47#6482—31no—
48#6482D311yescharacteristic, direct product factor
49C2×D56—31no—
50C2×C8×D7—31no—
51D3×#135—71nomaximal, Hall
52C2×D3×D7—22no—
53C2×D3×D7D411yescharacteristic
54C3×C7×Q8C2312yes—
55D84—22no—
56D84C2312yes—
57C4×D21—22no—
58C4×D21C2311yescharacteristic
59C4×D3×C7—22no—
60C4×D3×C7C2311yescharacteristic
61C7×Dic6—22no—
62C7×Dic6C2312yes—
63C3×D28—22no—
64C3×D28C2312yes—
65C3×C4×D7—22no—
66C3×C4×D7C2311yescharacteristic
67#4246—22no—
68#4246—22no—
69#4246—22no—
70D21⋊C4—22no—
71D21⋊C4D411yescharacteristic
72D3×Dic7D411yescharacteristic
73Dic3×D7—22no—
74Dic3×D7D411yescharacteristic
75C3×C7×C8C2311yescharacteristic
76C3⋊(C7⋊C8)C2311yescharacteristic
77C3×C7⋊C8C2311yescharacteristic
78C7×C3⋊C8C2311yescharacteristic
79C2×C7×Q8—32no—
80#1161—32no—
81#1161—32no—
82#1161—32no—
83#1161—62no—
84#1161—62no—
85#1161C2×D312yescomplemented
86C2×D28—32no—
87C2×D28—62no—
88C2×C4×D7—31no—
89C2×C4×D7—62no—
90C7×Q16—32no—
91C7×Q16—31no—
92C7×Q16C2×D311yescharacteristic, complemented
93C2×C7×C8—31no—
94#1143—32no—
95#1143—32no—
96#1143—32no—
97#1143C2×D312yescomplemented
98C2×C7⋊C8—31no—
99D56—32no—
100D56—31no—
101D56C2×D311yescharacteristic, complemented
102C8×D7—31no—
103C8×D7—31no—
104C8×D7—31no—
105C8×D7C2×D311yescharacteristic, complemented
106D3×#41—72no—
107C3×#135—71no—
108#950—72no—
109#919—71no—
110D3×Q16D711yescharacteristic, complemented
111#916—72no—
112D3×SD16—72no—
113#912—71no—
114D3×D8—71no—
115#904—71no—
116C2×D3×C8—71no—
117C2×D21—22no—
118C2×D21C2×D411yescharacteristic
119C2×D3×C7C2×D411yescharacteristic
120C2×C3×D7—22no—
121C2×C3×D7C2×D411yescharacteristic
122D3×D7—22no—
123D3×D7—44no—
124C3×C4×C7—22no—
125C3×C4×C7C2411yescharacteristic
126Dic21C2×D411yescharacteristic
127C3×Dic7C2×D411yescharacteristic
128C7×Dic3—22no—
129C7×Dic3C2×D411yescharacteristic
130C2×#135—211noSylow
131C22×D7—31no—
132C22×D7—62no—
133C7×Q8—32no—
134C7×Q8—62no—
135C7×Q8C22×D312yes—
136C2×C4×C7—31no—
137C2×C4×C7—62no—
138C2×Dic7—31no—
139D28—22no—
140D28—32no—
141D28—62no—
142D28—62no—
143D28—62no—
144D28—62no—
145D28C22×D312yes—
146C4×D7—22no—
147C4×D7—31no—
148C4×D7—31no—
149C4×D7—31no—
150C4×D7—62no—
151C4×D7—62no—
152C4×D7—62no—
153C4×D7C22×D311yescharacteristic
154C7×C8—31no—
155C7×C8C22×D311yescharacteristic
156C7⋊C8—31no—
157C7⋊C8C22×D311yescharacteristic
158C3×#41—72no—
159#239—72no—
160D3×Q8C2×D712yes—
161#237—72no—
162#237—142no—
163D3×D4—72no—
164D3×D4—142no—
165#235—72no—
166#235—142no—
167C2×C4×D3—71no—
168C2×C4×D3—142no—
169C3×Q16C2×D711yescharacteristic, complemented
170C3×SD16—72no—
171C3×D8—71no—
172C2×C3×C8—71no—
173#216C2×D712yescomplemented
174#215—72no—
175#214—72no—
176#213—72no—
177C2×C3⋊C8—71no—
178Dic12C2×D711yescharacteristic, complemented
179D24—71no—
180#204—72no—
181D3×C8—71no—
182D3×C8—71no—
183D3×C8—71no—
184D3×C8C2×D711yescharacteristic
185C2×C3×C7C22×D411yescharacteristic
186D21—21no—
187D21—42no—
188C3×D7—21no—
189C3×D7—42no—
190D3×C7#13512yescomplemented
191C2×#41—212no—
192#135—71no—
193#135—211no—
194#135—211no—
195#135—212no—
196#135—212no—
197#135—211no—
198C2×Q16—31no—
199C2×SD16—212no—
200C2×D8—211no—
201C22×C8—211no—
202C22×C7—31no—
203C2×D7—22no—
204C2×D7—31no—
205C2×D7—62no—
206C2×D7—62no—
207C2×D7—124no—
208C2×D7D3×D411yescharacteristic
209C4×C7—22no—
210C4×C7—31no—
211C4×C7—62no—
212C4×C7C23×D311yescharacteristic
213Dic7—31no—
214Dic7D3×D411yescharacteristic
215C22×D3—71no—
216C22×D3—142no—
217C3×Q8C22×D712yes—
218C3×D4—72no—
219C3×D4—142no—
220C2×C3×C4—71no—
221C2×C3×C4—142no—
222#67—142no—
223#67—142no—
224#67—142no—
225C2×Dic3—71no—
226C2×Dic3—142no—
227D12—72no—
228D12—142no—
229C4×D3—22no—
230C4×D3—71no—
231C4×D3—71no—
232C4×D3—71no—
233C4×D3—142no—
234C4×D3—142no—
235C4×D3C22×D711yescharacteristic
236Dic6—22no—
237Dic6C22×D712yes—
238C3×C8—71no—
239C3×C8C22×D711yescharacteristic
240C3⋊C8—71no—
241C3⋊C8C22×D711yescharacteristic
242C3×C7C2×#13511yescharacteristic, complemented, Hall
243#41—72no—
244#41—212no—
245#41—212no—
246#41—212no—
247#41—422no—
248#41—422no—
249C2×Q8—32no—
250C2×D4—212no—
251C2×D4—422no—
252C22×C4—211no—
253C22×C4—422no—
254Q16—32no—
255Q16—31no—
256Q16D3×D711yescharacteristic, complemented
257SD16—72no—
258SD16—212no—
259SD16—212no—
260SD16—212no—
261D8—71no—
262D8—212no—
263D8—211no—
264C2×C8—31no—
265C2×C8—71no—
266C2×C8—211no—
267C2×C8—211no—
268C2×C8—211no—
269C2×C8—211no—
270C2×C7—32no—
271C2×C7C2×D3×D411yescharacteristic
272D7—21no—
273D7—42no—
274D7—61no—
275D7—122no—
276C22×C3—71no—
277C22×C3—142no—
278C2×D3—71no—
279C2×D3—142no—
280C2×D3—142no—
281C2×D3—284no—
282C2×D3D4×D711yescharacteristic
283C3×C4—22no—
284C3×C4—71no—
285C3×C4C23×D711yescharacteristic
286Dic3—22no—
287Dic3—71no—
288Dic3D4×D711yescharacteristic
289C23—211no—
290C23—422no—
291Q8—32no—
292Q8—62no—
293Q8C2×D3×D712yes—
294D4—72no—
295D4—142no—
296D4—212no—
297D4—422no—
298D4—422no—
299D4—422no—
300D4—422no—
301C2×C4—31no—
302C2×C4—62no—
303C2×C4—71no—
304C2×C4—142no—
305C2×C4—211no—
306C2×C4—211no—
307C2×C4—211no—
308C2×C4—211no—
309C2×C4—422no—
310C2×C4—422no—
311C2×C4—422no—
312C8—31no—
313C8—71no—
314C8—211no—
315C8C2×D3×D711yescharacteristic
316C7D3×#13511yescharacteristic, complemented, Sylow
317C2×C3—141no—
318C2×C3—282no—
319C2×C3C2×D4×D711yescharacteristic
320D3—141no—
321D3—282no—
322D3#648212yesdirect product factor
323C22—31no—
324C22—71no—
325C22—142no—
326C22—211no—
327C22—422no—
328C22—422no—
329C22—844no—
330C4—22no—
331C4—31no—
332C4—62no—
333C4—71no—
334C4—211no—
335C4C22×D3×D711yescharacteristic
336C3C2×#648211yescharacteristic, complemented, Sylow
337C2—32no—
338C2—141no—
339C2—282no—
340C2—421no—
341C2—842no—
342C2D3×D4×D711yescharacteristic
subgroupG/H
centerC2D3×D4×D7
commutator, cosocleC3×C4×C7C24
FrattiniC4C22×D3×D7
FittingC3×C7×Q16C22
socleC2×C3×C7C22×D4
hypercenterQ16D3×D7
hypocenterC3×C7C2×#135
LCSG ▷ C3×C4×C7 ▷ C2×C3×C7 ▷ C3×C7
UCSC1 ◁ C2 ◁ C4 ◁ Q16

Complements

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

NH ≅ G/Ntype
1. D3×#1161C2semidirect
2. #10621402C2semidirect
3. D3×C7×Q16C2semidirect
4. C3×#6482C2semidirect
5. #10621083C2semidirect
6. #10621078C2semidirect
7. D3×#1143C2semidirect
8. #10620839C2semidirect
9. #10620833C2semidirect
10. D3×D56C2semidirect
11. D3×C8×D7C2semidirect
13. #66732C22semidirect
15. C3×#1161C22semidirect
21. #66677C22semidirect
23. #66670C22semidirect
24. C3×C7×Q16C22semidirect
25. #66634C22semidirect
26. D168C22semidirect
27. C8×D21C22semidirect
28. C7×#216C22semidirect
29. C7×Dic12C22semidirect
31. C3×#1143C22semidirect
32. C3×D56C22semidirect
33. C3×C8×D7C22semidirect
34. #66568C22semidirect
35. #66563C22semidirect
36. #66561C22semidirect
37. D21⋊C8C22semidirect
39. D7×C3⋊C8C22semidirect
48. #6482D3direct (N × H)
85. #1161C2×D3semidirect
92. C7×Q16C2×D3semidirect
97. #1143C2×D3semidirect
101. D56C2×D3semidirect
105. C8×D7C2×D3semidirect
110. D3×Q16D7semidirect
169. C3×Q16C2×D7semidirect
173. #216C2×D7semidirect
178. Dic12C2×D7semidirect
190. D3×C7#135semidirect
242. C3×C7C2×#135semidirect
256. Q16D3×D7semidirect
316. C7D3×#135semidirect
322. D3#6482direct (N × H)
336. C3C2×#6482semidirect

Maximal subgroups

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

subgroupindex
D3×#11612
#106214022
D3×C7×Q162
C3×#64822
#106210832
#106210782
D3×#11432
#106208392
#106208332
D3×D562
D3×C8×D72
C2×#64823
D3×#1357