Finite Group Databasebeta

← D13⋊C3×#64425 #37524959

Subgroups — D13⋊C3×#64425 #37524959

Order 22932.

280 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 280 conjugacy classes of subgroups — too many to draw. Only its 49 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
1D13⋊C3×#3862C211yesmaximal, characteristic, complemented
2C13⋊C3×#64425C211yesmaximal, characteristic, complemented
3(C13⋊C3)⋊#64425C211yesmaximal, characteristic, complemented
4D13⋊C3×C7⋊D7C311yesmaximal, characteristic, complemented
5D13×#64425C311yesmaximal, characteristic, complemented
6D13⋊#64425C311yesmaximal, characteristic, complemented
7D13⋊#64425C311yesmaximal, characteristic, complemented
8C13⋊C3×#3862C2211yescharacteristic, complemented, Hall
9C13⋊C3×C7⋊D7C2×C311yescharacteristic, complemented
10(C13⋊C3)⋊(C7⋊D7)C2×C311yescharacteristic, complemented
11D13×#3862C2×C311yescharacteristic, complemented
12D13⋊#3862C2×C311yescharacteristic, complemented
13D13⋊#3862C2×C311yescharacteristic, complemented
14#16838454C2×C311yescharacteristic, complemented
15#16838453C2×C311yescharacteristic, complemented
16#16838453C2×C311yescharacteristic, complemented
17#16838452C2×C311yescharacteristic, complemented
18#16838452C2×C311yescharacteristic, complemented
19C13×#64425C2×C311yescharacteristic, complemented
20C72×D13⋊C3C2×C311yescharacteristic, complemented
21AGL(1,𝔽7)×D13⋊C3—71nomaximal
22AGL(1,𝔽7)×D13⋊C3—71nomaximal
23D13×C7⋊D7C3211yescharacteristic, complemented, Hall
24C13⋊#3862C22×C311yescharacteristic, complemented
25C13⋊#3862C22×C311yescharacteristic, complemented
26C13×#3862C22×C311yescharacteristic, complemented
27C72×C13⋊C3C22×C311yescharacteristic, complemented
28C2×C3×#64425—131nomaximal, Hall
29ΓL(1,𝔽8)⋊(D13⋊C3)—71no—
30ΓL(1,𝔽8)⋊(D13⋊C3)—71no—
31C13⋊C3×AGL(1,𝔽7)—71no—
32C13⋊C3×AGL(1,𝔽7)—71no—
33ΓL(1,𝔽8)×D13⋊C3—71no—
34ΓL(1,𝔽8)×D13⋊C3—71no—
35C7⋊D91C2×C3211yescharacteristic, complemented
36C13×C7⋊D7C2×C3211yescharacteristic, complemented
37C72×D13C2×C3211yescharacteristic, complemented
38#10587716⋊C2—71no—
39#10587716⋊C2—71no—
40#10587717⋊C2—71no—
41#10587717⋊C2—71no—
42D13×AGL(1,𝔽7)—71no—
43D13×AGL(1,𝔽7)—71no—
44D7×D13⋊C3—71no—
45D7×D13⋊C3—212no—
46D7×D13⋊C3—211no—
47C2×C3×#3862—131no—
48C3×#64425—131no—
49C3×#64425—131no—
50ΓL(1,𝔽8)×C13⋊C3—71no—
51ΓL(1,𝔽8)×C13⋊C3—71no—
52C72×C13C22×C3211yescharacteristic, complemented, Hall
53C2×C3×C7⋊D7—131no—
54C2×#64425—131no—
55C2×#64425—131no—
56C2×#64425—391no—
57#10587723—71no—
58#10587723—71no—
59#10587722—71no—
60#10587722—71no—
61#10587721—71no—
62#10587721—71no—
63#10587720—71no—
64#10587720—71no—
65ΓL(1,𝔽8)⋊D13—71no—
66ΓL(1,𝔽8)⋊D13—71no—
67C13×AGL(1,𝔽7)—71no—
68C13×AGL(1,𝔽7)—71no—
69#10587717—71no—
70#10587717—71no—
71#10587716—71no—
72#10587716—71no—
73ΓL(1,𝔽8)×D13—71no—
74ΓL(1,𝔽8)×D13—71no—
75(C13⋊C3)⋊D7—212no—
76(C13⋊C3)⋊D7—211no—
77(C13⋊C3)⋊D7—211no—
78D7×C13⋊C3—71no—
79D7×C13⋊C3—212no—
80D7×C13⋊C3—211no—
81C7×D13⋊C3—32no—
82C7×D13⋊C3AGL(1,𝔽7)11yescharacteristic, complemented
83C7×D13⋊C3AGL(1,𝔽7)11yescharacteristic, complemented
84C2×C3×D13⋊C3—491noHall
85C3×#3862—131noHall
86D7×D13—71no—
87D7×D13—212no—
88D7×D13—211no—
89C2×C3×C72—131no—
90C3×C7⋊D7—131no—
91C3×C7⋊D7—131no—
92C2×#3862—131no—
93C2×#3862—131no—
94C2×#3862—391no—
95#64425—131no—
96#64425—131no—
97#64425—131no—
98#64425—131no—
99#64425—391no—
100#64425D13⋊C311yescharacteristic, direct product factor
101#63271—71no—
102#63271—71no—
103#63270—71no—
104#63270—71no—
105C7×C13⋊C3—32no—
106C7×C13⋊C3C2×AGL(1,𝔽7)11yescharacteristic, complemented
107C7×C13⋊C3C2×AGL(1,𝔽7)11yescharacteristic, complemented
108C13×ΓL(1,𝔽8)—71no—
109C13×ΓL(1,𝔽8)—71no—
110C2×C3×AGL(1,𝔽7)—911no—
111C2×C3×AGL(1,𝔽7)—911no—
112C2×C3×C13⋊C3—491no—
113C3×D13⋊C3—491no—
114C3×D13⋊C3—491no—
115C2×C7⋊D7—391noHall
116D91—212no—
117D91—211no—
118D91—211no—
119C7×D13—32no—
120C7×D13C3×AGL(1,𝔽7)11yescharacteristic, complemented
121C7×D13C3×AGL(1,𝔽7)11yescharacteristic, complemented
122C13×D7—71no—
123C13×D7—212no—
124C13×D7—211no—
125C2×C3×D13—491no—
126C2×D13⋊C3—491no—
127C2×D13⋊C3—491no—
128C2×D13⋊C3—1471no—
129C3×C72—131no—
130#3862—131no—
131#3862—131no—
132#3862C2×D13⋊C311yescharacteristic, complemented
133C2×C3×ΓL(1,𝔽8)—911no—
134C2×C3×ΓL(1,𝔽8)—911no—
135C3×AGL(1,𝔽7)—911no—
136C3×AGL(1,𝔽7)—911no—
137C3×AGL(1,𝔽7)—911no—
138C3×AGL(1,𝔽7)—911no—
139C3×C13⋊C3—491noHall
140C2×C72—391no—
141C7⋊D7—391no—
142C7⋊D7C3×D13⋊C311yescharacteristic, complemented
143C7×C13—32no—
144C7×C13C2×C3×AGL(1,𝔽7)11yescharacteristic, complemented
145C7×C13C2×C3×AGL(1,𝔽7)11yescharacteristic, complemented
146C2×C3×D7—2731no—
147C2×C3×D7—2731no—
148C2×C3×D7—2732no—
149C2×AGL(1,𝔽7)—2731no—
150C2×AGL(1,𝔽7)—2731no—
151C2×AGL(1,𝔽7)—911no—
152C2×AGL(1,𝔽7)—911no—
153C2×AGL(1,𝔽7)—911no—
154C2×AGL(1,𝔽7)—911no—
155C2×C3×C13—491no—
156C3×D13—491no—
157C3×D13—491no—
158C2×C13⋊C3—491no—
159C2×C13⋊C3—491no—
160C2×C13⋊C3—1471no—
161D13⋊C3—491no—
162D13⋊C3—491no—
163D13⋊C3—491no—
164D13⋊C3—491no—
165D13⋊C3—1471no—
166D13⋊C3#6442511yescharacteristic, direct product factor
167C3×ΓL(1,𝔽8)—911no—
168C3×ΓL(1,𝔽8)—911no—
169C2×D13—1471noHall
170C72C2×C3×D13⋊C311yescharacteristic, complemented, Sylow
171C2×C3×C7—131no—
172C2×C3×C7—131no—
173C2×C3×C7—392no—
174C3×D7—2731no—
175C3×D7—2731no—
176C3×D7—2731no—
177C3×D7—2732no—
178C3×D7—2731no—
179C3×D7—2732no—
180C2×ΓL(1,𝔽8)—2731no—
181C2×ΓL(1,𝔽8)—911no—
182C2×ΓL(1,𝔽8)—911no—
183C2×ΓL(1,𝔽8)—911no—
184C2×ΓL(1,𝔽8)—911no—
185C2×ΓL(1,𝔽8)—911no—
186AGL(1,𝔽7)—71no—
187AGL(1,𝔽7)—71no—
188AGL(1,𝔽7)—2731no—
189AGL(1,𝔽7)—2731no—
190AGL(1,𝔽7)—911no—
191AGL(1,𝔽7)—911no—
192AGL(1,𝔽7)—911no—
193AGL(1,𝔽7)—911no—
194AGL(1,𝔽7)—911no—
195AGL(1,𝔽7)—911no—
196AGL(1,𝔽7)—911no—
197AGL(1,𝔽7)—911no—
198C3×C13—491no—
199C13⋊C3—491no—
200C13⋊C3—491no—
201C13⋊C3C2×#6442511yescharacteristic, complemented
202C22×C32—6371noHall
203C2×D7—2731no—
204C2×D7—8191no—
205C2×D7—8192no—
206C2×C13—1471no—
207D13—1471no—
208D13C3×#6442511yescharacteristic, complemented
209C3×C7—131no—
210C3×C7—131no—
211C3×C7—392no—
212ΓL(1,𝔽8)—71no—
213ΓL(1,𝔽8)—71no—
214ΓL(1,𝔽8)—911no—
215ΓL(1,𝔽8)—911no—
216ΓL(1,𝔽8)—911no—
217ΓL(1,𝔽8)—911no—
218C2×C32—6371no—
219C2×C32—6371no—
220C2×C32—6371no—
221C2×C7—131no—
222C2×C7—391no—
223C2×C7—1172no—
224D7—2731no—
225D7—212no—
226D7—211no—
227D7—211no—
228D7—8192no—
229D7—8191no—
230C13C2×C3×#6442511yescharacteristic, complemented, Sylow
231C22×C3—19111no—
232C22×C3—19111no—
233C22×C3—6371no—
234C22×C3—6371no—
235C32—6371noSylow
236C7—32no—
237C7AGL(1,𝔽7)×D13⋊C311yescharacteristic, complemented
238C7AGL(1,𝔽7)×D13⋊C311yescharacteristic, complemented
239C2×C3—131no—
240C2×C3—491no—
241C2×C3—19111no—
242C2×C3—19111no—
243C2×C3—19111no—
244C2×C3—6371no—
245C2×C3—6371no—
246C2×C3—6371no—
247C2×C3—6371no—
248C2×C3—6371no—
249C2×C3—6371no—
250C2×C3—6371no—
251C22—57331noSylow
252C3—131no—
253C3—491no—
254C3—6371no—
255C3—6371no—
256C2—131no—
257C2—57331no—
258C2—1471no—
subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC72×C13C22×C32
LCSG ▷ C72×C13
UCSC1

Complements

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

NH ≅ G/Ntype
1. D13⋊C3×#3862C2semidirect
2. C13⋊C3×#64425C2semidirect
3. (C13⋊C3)⋊#64425C2semidirect
4. D13⋊C3×C7⋊D7C3semidirect
5. D13×#64425C3semidirect
6. D13⋊#64425C3semidirect
7. D13⋊#64425C3semidirect
8. C13⋊C3×#3862C22semidirect
9. C13⋊C3×C7⋊D7C2×C3semidirect
10. (C13⋊C3)⋊(C7⋊D7)C2×C3semidirect
11. D13×#3862C2×C3semidirect
12. D13⋊#3862C2×C3semidirect
13. D13⋊#3862C2×C3semidirect
14. #16838454C2×C3semidirect
15. #16838453C2×C3semidirect
16. #16838453C2×C3semidirect
17. #16838452C2×C3semidirect
18. #16838452C2×C3semidirect
19. C13×#64425C2×C3semidirect
20. C72×D13⋊C3C2×C3semidirect
23. D13×C7⋊D7C32semidirect
24. C13⋊#3862C22×C3semidirect
25. C13⋊#3862C22×C3semidirect
26. C13×#3862C22×C3semidirect
27. C72×C13⋊C3C22×C3semidirect
35. C7⋊D91C2×C32semidirect
36. C13×C7⋊D7C2×C32semidirect
37. C72×D13C2×C32semidirect
52. C72×C13C22×C32semidirect
82. C7×D13⋊C3AGL(1,𝔽7)semidirect
83. C7×D13⋊C3AGL(1,𝔽7)semidirect
100. #64425D13⋊C3direct (N × H)
106. C7×C13⋊C3C2×AGL(1,𝔽7)semidirect
107. C7×C13⋊C3C2×AGL(1,𝔽7)semidirect
120. C7×D13C3×AGL(1,𝔽7)semidirect
121. C7×D13C3×AGL(1,𝔽7)semidirect
132. #3862C2×D13⋊C3semidirect
142. C7⋊D7C3×D13⋊C3semidirect
144. C7×C13C2×C3×AGL(1,𝔽7)semidirect
145. C7×C13C2×C3×AGL(1,𝔽7)semidirect
166. D13⋊C3#64425direct (N × H)
170. C72C2×C3×D13⋊C3semidirect
201. C13⋊C3C2×#64425semidirect
208. D13C3×#64425semidirect
230. C13C2×C3×#64425semidirect
237. C7AGL(1,𝔽7)×D13⋊C3semidirect
238. C7AGL(1,𝔽7)×D13⋊C3semidirect

Maximal subgroups

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

subgroupindex
D13⋊C3×#38622
C13⋊C3×#644252
(C13⋊C3)⋊#644252
D13⋊C3×C7⋊D73
D13×#644253
D13⋊#644253
AGL(1,𝔽7)×D13⋊C37
C2×C3×#6442513