Finite Group Databasebeta

← D3×#6399 #13053611

Subgroups — D3×#6399 #13053611

Order 1344.

340 conjugacy classes of subgroups; only the 82 normal subgroups are shown.

normal subgroups only

This group has 340 conjugacy classes of subgroups — too many to draw. Only its 82 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×#1157C211yesmaximal, characteristic
2D3×C7×M16C211yesmaximal, characteristic, complemented
3C4×D3×Dic7C211yesmaximal, characteristic, complemented
4#10620664C211yesmaximal, characteristic, complemented
5C3×#6399C211yesmaximal, characteristic, complemented
6#10620516C211yesmaximal, characteristic, complemented
7#10620511C211yesmaximal, characteristic, complemented
8C2×#6399—31nomaximal, Hall
9#66728C2211yescharacteristic
10C2×C4×D3×C7C2211yescharacteristic
11C3×#1157C2211yescharacteristic
12D3×C22⋊D7—21no—
13C2×D3×Dic7—21no—
14#66683—21no—
15D3×D28C411yescharacteristic, complemented
16C4×D3×D7—21no—
17#66675—21no—
18#66673C411yescharacteristic, complemented
19D3×Dic14C411yescharacteristic, complemented
20#66669C411yescharacteristic, complemented
21C3×C7×M16C2211yescharacteristic, complemented
22C4×Dic21C2211yescharacteristic, complemented
23C7×#208C2211yescharacteristic, complemented
24C7×ΓL(1,𝔽25)—21no—
25D3×C7×C8—21no—
26C3×C4×Dic7C2211yescharacteristic, complemented
27Dic3×Dic7—21no—
28C2×#1157—31no—
29C2×C7×M16—31no—
30C2×C4×Dic7—31no—
31#6399—31no—
32#6399—31no—
33#6399—31no—
34#6399D311yescharacteristic, direct product factor
35D3×#104—71nomaximal, Hall
36C22×D3×C7D411yescharacteristic
37C2×D3×D7—21no—
38C2×C3×C4×C7C2311yescharacteristic
39#4268—21no—
40C2×Dic21—21no—
41D84C2×C411yescharacteristic, complemented
42C4×D21—21no—
43Dic42C2×C411yescharacteristic, complemented
44C2×C7×Dic3D411yescharacteristic
45C4×D3×C7C2×C411yescharacteristic
46C4×D3×C7C2×C411yescharacteristic
47C4×D3×C7D411yescharacteristic
48C4×D3×C7D411yescharacteristic
49C3×C22⋊D7—21no—
50C2×C3×Dic7—21no—
51C3×D28C2×C411yescharacteristic, complemented
52C3×C4×D7—21no—
53C3×Dic14C2×C411yescharacteristic, complemented
54#4248—21no—
55#4247—21no—
56#4246—21no—
57#4245—21no—
58D21⋊C4—21no—
59D3×Dic7—24no—
60D3×Dic7—21no—
61Dic3×D7—21no—
62C3×C7×C8—21no—
63C7×C3⋊C8—21no—
64C22×C4×C7—31no—
65C2×C22⋊D7—61no—
66C22×Dic7—61no—
67#1157—31no—
68#1157—31no—
69#1157—31no—
70#1157—61no—
71#1157—61no—
72#1157C2×D311yescharacteristic
73C2×D28—31no—
74C2×C4×D7—61no—
75C2×Dic14—31no—
76C7×M16—31no—
77C7×M16—61no—
78C7×M16C2×D311yescharacteristic, complemented
79C2×C7×C8—61no—
80C4×Dic7—31no—
81C4×Dic7—61no—
82C4×Dic7C2×D311yescharacteristic, complemented
83D3×#41—71no—
84D3×M16D711yescharacteristic, complemented
85C42×D3—71no—
86C3×#104—71no—
87#837—71no—
88#825—71no—
89#805—71no—
90C22×C3×C7C2×D411yescharacteristic
91C2×D21—21no—
92C2×D3×C7—22no—
93C2×D3×C7C22⋊C411yescharacteristic
94C2×D3×C7C22⋊C411yescharacteristic
95C2×C3×D7—21no—
96D3×D7—42no—
97C3×C4×C7C22×C411yescharacteristic
98C3×C4×C7C2×D411yescharacteristic
99Dic21—22no—
100Dic21—21no—
101C3×Dic7—22no—
102C3×Dic7—21no—
103C7×Dic3C22⋊C411yescharacteristic
104C7×Dic3C22⋊C411yescharacteristic
105C2×#104—211noSylow
106C23×C7—31no—
107C22×D7—61no—
108C2×C4×C7—31no—
109C2×C4×C7—31no—
110C2×C4×C7—31no—
111C2×C4×C7—31no—
112C2×C4×C7—31no—
113C2×C4×C7C22×D311yescharacteristic
114C22⋊D7—21no—
115C22⋊D7—61no—
116C22⋊D7—61no—
117C22⋊D7—61no—
118C2×Dic7—21no—
119C2×Dic7—61no—
120C2×Dic7—64no—
121C2×Dic7—61no—
122D28—31no—
123D28—61no—
124D28C4×D311yescharacteristic, complemented
125C4×D7—21no—
126C4×D7—61no—
127C4×D7—61no—
128C4×D7—61no—
129Dic14—31no—
130Dic14—61no—
131Dic14C4×D311yescharacteristic, complemented
132C7×C8—21no—
133C7×C8—61no—
134C3×#41—71no—
135#239—71no—
136D3×Q8—71no—
137#237—71no—
138#237—141no—
139D3×D4—71no—
140D3×D4—141no—
141#235—71no—
142#235—141no—
143C2×C4×D3—141no—
144C2×C4×D3—141no—
145C2×C4×D3C2×D711yescharacteristic
146C3×M16C2×D711yescharacteristic, complemented
147C3×C42—71no—
148C4×Dic3—71no—
149C4×Dic3—141no—
150#208C2×D711yescharacteristic, complemented
151ΓL(1,𝔽25)—21no—
152D3×C8—21no—
153C2×C3×C7—21no—
154C2×C3×C7C2×C22⋊C411yescharacteristic
155D21—41no—
156C3×D7—41no—
157D3×C7—21no—
158D3×C7#10412yescomplemented
159C2×#41—211no—
160C2×M16—31no—
161C2×C42—211no—
162#104—71no—
163#104—211no—
164#104—211no—
165#104—211no—
166C22×C7—31no—
167C22×C7—31no—
168C22×C7—62no—
169C22×C7D3×D411yescharacteristic
170C2×D7—21no—
171C2×D7—61no—
172C2×D7—122no—
173C4×C7—31no—
174C4×C7—31no—
175C4×C7C2×C4×D311yescharacteristic
176C4×C7D3×D411yescharacteristic
177Dic7—22no—
178Dic7—21no—
179Dic7—62no—
180Dic7—61no—
181C22×D3—141no—
182C22×D3D2811yescharacteristic
183C3×Q8—71no—
184C3×D4—71no—
185C3×D4—141no—
186C2×C3×C4—141no—
187C2×C3×C4—141no—
188C2×C3×C4C22×D711yescharacteristic
189#67—141no—
190#67—141no—
191#67—141no—
192C2×Dic3—141no—
193C2×Dic3—141no—
194C2×Dic3D2811yescharacteristic
195D12—71no—
196D12—141no—
197C4×D3—144no—
198C4×D3—141no—
199C4×D3—141no—
200C4×D3—141no—
201C4×D3C4×D711yescharacteristic
202C4×D3C4×D711yescharacteristic
203C4×D3C22⋊D711yescharacteristic
204C4×D3C22⋊D711yescharacteristic
205Dic6—71no—
206Dic6—141no—
207C3×C8—21no—
208C3⋊C8—21no—
209C3×C7C2×#10411yescharacteristic, complemented, Hall
210#41—71no—
211#41—211no—
212#41—211no—
213#41—211no—
214#41—421no—
215#41—421no—
216C2×Q8—211no—
217C2×D4—211no—
218C2×D4—421no—
219C22×C4—31no—
220C22×C4—421no—
221C22×C4—421no—
222M16—31no—
223M16—61no—
224M16D3×D711yescharacteristic, complemented
225C2×C8—61no—
226C42—71no—
227C42—211no—
228C42—421no—
229C2×C7—21no—
230C2×C7—32no—
231C2×C7—61no—
232C2×C7D3×C22⋊C411yescharacteristic
233D7—41no—
234D7—121no—
235C22×C3—141no—
236C22×C3C2×D2811yescharacteristic
237C2×D3—22no—
238C2×D3—141no—
239C2×D3—282no—
240C2×D3(C2×D7)⋊C411yescharacteristic
241C2×D3(C2×D7)⋊C411yescharacteristic
242C3×C4—142no—
243C3×C4—141no—
244C3×C4C2×C4×D711yescharacteristic
245C3×C4C2×C22⋊D711yescharacteristic
246Dic3—142no—
247Dic3—141no—
248Dic3(C2×D7)⋊C411yescharacteristic
249Dic3(C2×D7)⋊C411yescharacteristic
250C23—31no—
251C23—421no—
252Q8—71no—
253Q8—211no—
254Q8—421no—
255D4—71no—
256D4—141no—
257D4—211no—
258D4—421no—
259D4—421no—
260D4—421no—
261D4—421no—
262C2×C4—31no—
263C2×C4—31no—
264C2×C4—31no—
265C2×C4—31no—
266C2×C4—31no—
267C2×C4—141no—
268C2×C4—141no—
269C2×C4—421no—
270C2×C4—421no—
271C2×C4—421no—
272C2×C4—424no—
273C2×C4—421no—
274C2×C4—421no—
275C2×C4C2×D3×D711yescharacteristic
276C8—21no—
277C8—61no—
278C7D3×#10411yescharacteristic, complemented, Sylow
279C2×C3—21no—
280C2×C3—281no—
281C2×C3C2×(C2×D7)⋊C411yescharacteristic
282D3—21no—
283D3—281no—
284D3#639912yesdirect product factor
285C22—31no—
286C22—31no—
287C22—62no—
288C22—141no—
289C22—421no—
290C22—842no—
291C22D3×D2811yescharacteristic
292C4—31no—
293C4—31no—
294C4—142no—
295C4—141no—
296C4—422no—
297C4—421no—
298C4C4×D3×D711yescharacteristic
299C4D3×C22⋊D711yescharacteristic
300C3C2×#639911yescharacteristic, complemented, Sylow
301C2—21no—
302C2—32no—
303C2—61no—
304C2—281no—
305C2—841no—
306C2D3×(C2×D7)⋊C411yescharacteristic
subgroupG/H
centerC4D3×C22⋊D7
commutatorC3×C4×C7C22×C4
FrattiniC2×C4C2×D3×D7
FittingC3×C7×M16C22
socleC2×C3×C7C2×C22⋊C4
prime radicalD3×#1157C2
cosocleC2×C3×C4×C7C23
hypercenterM16D3×D7
hypocenterC3×C7C2×#104
LCSG ▷ C3×C4×C7 ▷ C2×C3×C7 ▷ C3×C7
UCSC1 ◁ C4 ◁ C2×C4 ◁ M16

Complements

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

NH ≅ G/Ntype
2. D3×C7×M16C2semidirect
3. C4×D3×Dic7C2semidirect
4. #10620664C2semidirect
5. C3×#6399C2semidirect
6. #10620516C2semidirect
7. #10620511C2semidirect
15. D3×D28C4semidirect
18. #66673C4semidirect
19. D3×Dic14C4semidirect
20. #66669C4semidirect
21. C3×C7×M16C22semidirect
22. C4×Dic21C22semidirect
23. C7×#208C22semidirect
26. C3×C4×Dic7C22semidirect
34. #6399D3direct (N × H)
41. D84C2×C4semidirect
43. Dic42C2×C4semidirect
51. C3×D28C2×C4semidirect
53. C3×Dic14C2×C4semidirect
78. C7×M16C2×D3semidirect
82. C4×Dic7C2×D3semidirect
84. D3×M16D7semidirect
124. D28C4×D3semidirect
131. Dic14C4×D3semidirect
146. C3×M16C2×D7semidirect
150. #208C2×D7semidirect
158. D3×C7#104semidirect
209. C3×C7C2×#104semidirect
224. M16D3×D7semidirect
278. C7D3×#104semidirect
284. D3#6399direct (N × H)
300. C3C2×#6399semidirect

Maximal subgroups

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

subgroupindex
D3×#11572
D3×C7×M162
C4×D3×Dic72
#106206642
C3×#63992
#106205162
#106205112
C2×#63993
D3×#1047