Finite Group Databasebeta

← #37524928

Subgroups — #37524928

Order 22932.

248 conjugacy classes of subgroups; only the 46 normal subgroups are shown.

normal subgroups only

This group has 248 conjugacy classes of subgroups — too many to draw. Only its 46 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
1#26039532C211yesmaximal, characteristic, complemented
2#26039531C211yesmaximal, characteristic, complemented
3#64424⋊(C13⋊C3)C211yesmaximal, characteristic, complemented
4#10587723⋊D7C311yesmaximal, characteristic, complemented
5#10587722⋊D7C311yesmaximal, characteristic, complemented
6#21439619C311yesmaximal, characteristic, complemented
7#64424⋊D13C311yesmaximal, characteristic, complemented
8#3861⋊(C13⋊C3)C2211yescharacteristic, complemented, Hall
9#16838480C2×C311yescharacteristic, complemented
10#16838479C2×C311yescharacteristic, complemented
11#16838471C2×C311yescharacteristic, complemented
12#16838470C2×C311yescharacteristic, complemented
13#16838463C2×C311yescharacteristic, complemented
14#16838462C2×C311yescharacteristic, complemented
15#16838460C2×C311yescharacteristic, complemented
16#16838460C2×C311yescharacteristic, complemented
17#16838453C2×C311yescharacteristic, complemented
18C13×#64424C2×C311yescharacteristic, complemented
19C7×#10587723C2×C311yescharacteristic, complemented
20C7×#10587722C2×C311yescharacteristic, complemented
21AGL(1,𝔽7)×D13⋊C3—71nomaximal
22AGL(1,𝔽7)×D13⋊C3—71nomaximal
23(C7⋊D7)⋊D13C3211yescharacteristic, complemented, Hall
24C13⋊#3862C22×C311yescharacteristic, complemented
25C13×#3861C22×C311yescharacteristic, complemented
26C7×#63270C22×C311yescharacteristic, complemented
27C7×#63271C22×C311yescharacteristic, complemented
28AGL(1,𝔽7)2—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—
35C13×C7⋊D7C2×C3211yescharacteristic, complemented
36C7×D91C2×C3211yescharacteristic, complemented
37C7×D91C2×C3211yescharacteristic, complemented
38#10587716⋊C2—71no—
39#10587716⋊C2—71no—
40#10587717⋊C2—71no—
41#10587717⋊C2—211no—
42D13×AGL(1,𝔽7)—71no—
43D13×AGL(1,𝔽7)—71no—
44D7×D13⋊C3—71no—
45D7×D13⋊C3—71no—
46ΓL(1,𝔽8)⋊AGL(1,𝔽7)—131no—
47ΓL(1,𝔽8)×AGL(1,𝔽7)—131no—
48ΓL(1,𝔽8)×AGL(1,𝔽7)—131no—
49ΓL(1,𝔽8)×C13⋊C3—71no—
50ΓL(1,𝔽8)×C13⋊C3—71no—
51C72×C13C22×C3211yescharacteristic, complemented, Hall
52#64422⋊C2—131no—
53#64423⋊C2—391no—
54D7×AGL(1,𝔽7)—131no—
55D7×AGL(1,𝔽7)—131no—
56#10587723—71no—
57#10587723AGL(1,𝔽7)11yescharacteristic, complemented
58#10587722—71no—
59#10587722AGL(1,𝔽7)11yescharacteristic, complemented
60#10587721—71no—
61#10587721—71no—
62#10587720—71no—
63#10587720—211no—
64ΓL(1,𝔽8)⋊D13—71no—
65ΓL(1,𝔽8)⋊D13—71no—
66C13×AGL(1,𝔽7)—71no—
67C13×AGL(1,𝔽7)—71no—
68C13×AGL(1,𝔽7)—421no—
69#10587717—71no—
70#10587717—211no—
71#10587716—71no—
72#10587716—211no—
73ΓL(1,𝔽8)×D13—71no—
74ΓL(1,𝔽8)×D13—71no—
75(C13⋊C3)⋊D7—71no—
76(C13⋊C3)⋊D7—71no—
77D7×C13⋊C3—71no—
78D7×C13⋊C3—71no—
79C7×D13⋊C3—71no—
80C7×D13⋊C3—71no—
81C2×C3×D13⋊C3—491noHall
82ΓL(1,𝔽8)2—131noHall
83D7×D13—71no—
84D7×D13—211no—
85#64425—131no—
86#64424D13⋊C311yescharacteristic, complemented
87#64423—391no—
88#64423—391no—
89#64422—131no—
90#64422—131no—
91ΓL(1,𝔽8)⋊D7—131no—
92ΓL(1,𝔽8)⋊D7—131no—
93D7×ΓL(1,𝔽8)—131no—
94D7×ΓL(1,𝔽8)—131no—
95C7×AGL(1,𝔽7)—131no—
96C7×AGL(1,𝔽7)—131no—
97#63271—71no—
98#63271C2×AGL(1,𝔽7)11yescharacteristic, complemented
99#63270—71no—
100#63270C2×AGL(1,𝔽7)11yescharacteristic, complemented
101C7×C13⋊C3—71no—
102C7×C13⋊C3—71no—
103C13×ΓL(1,𝔽8)—71no—
104C13×ΓL(1,𝔽8)—71no—
105C13×ΓL(1,𝔽8)—421no—
106C2×C3×AGL(1,𝔽7)—911no—
107C2×C3×AGL(1,𝔽7)—911no—
108C2×C3×C13⋊C3—491no—
109C3×D13⋊C3—491no—
110C3×D13⋊C3—491no—
111D72—391noHall
112D91C3×AGL(1,𝔽7)11yescharacteristic, complemented
113D91C3×AGL(1,𝔽7)11yescharacteristic, complemented
114C7×D13—211no—
115C7×D13—211no—
116C13×D7—71no—
117C13×D7—211no—
118C13×D7—421no—
119C2×C3×D13—491no—
120C2×D13⋊C3—491no—
121C2×D13⋊C3—491no—
122C2×D13⋊C3—491no—
123#3862—131no—
124#3861C2×D13⋊C311yescharacteristic, complemented
125C7×ΓL(1,𝔽8)—131no—
126C7×ΓL(1,𝔽8)—131no—
127C2×C3×ΓL(1,𝔽8)—911no—
128C2×C3×ΓL(1,𝔽8)—911no—
129C3×AGL(1,𝔽7)—911no—
130C3×AGL(1,𝔽7)—911no—
131C3×AGL(1,𝔽7)—911no—
132C3×AGL(1,𝔽7)—911no—
133C3×C13⋊C3—491noHall
134C7⋊D7C3×D13⋊C311yescharacteristic, complemented
135C7×D7—391no—
136C7×D7—391no—
137C7×C13—61no—
138C7×C13C2×C3×AGL(1,𝔽7)11yescharacteristic, complemented
139C7×C13C2×C3×AGL(1,𝔽7)11yescharacteristic, complemented
140C2×C3×D7—911no—
141C2×C3×D7—911no—
142C2×AGL(1,𝔽7)—2731no—
143C2×AGL(1,𝔽7)—2731no—
144C2×AGL(1,𝔽7)—2731no—
145C2×AGL(1,𝔽7)—2731no—
146C2×AGL(1,𝔽7)—911no—
147C2×AGL(1,𝔽7)—911no—
148C2×C3×C13—491no—
149C3×D13—491no—
150C3×D13—491no—
151C2×C13⋊C3—491no—
152C2×C13⋊C3—491no—
153C2×C13⋊C3—491no—
154D13⋊C3—71no—
155D13⋊C3—71no—
156D13⋊C3—491no—
157D13⋊C3—491no—
158D13⋊C3—1471no—
159D13⋊C3—1471no—
160C3×ΓL(1,𝔽8)—911no—
161C3×ΓL(1,𝔽8)—911no—
162C2×D13—4411noHall
163C72C2×C3×D13⋊C311yescharacteristic, complemented, Sylow
164C2×C3×C7—911no—
165C2×C3×C7—911no—
166C3×D7—911no—
167C3×D7—911no—
168C3×D7—911no—
169C3×D7—911no—
170C2×ΓL(1,𝔽8)—2731no—
171C2×ΓL(1,𝔽8)—2731no—
172C2×ΓL(1,𝔽8)—2731no—
173C2×ΓL(1,𝔽8)—911no—
174C2×ΓL(1,𝔽8)—911no—
175C2×ΓL(1,𝔽8)—911no—
176AGL(1,𝔽7)—71no—
177AGL(1,𝔽7)—71no—
178AGL(1,𝔽7)—131no—
179AGL(1,𝔽7)—131no—
180AGL(1,𝔽7)—2731no—
181AGL(1,𝔽7)—2731no—
182AGL(1,𝔽7)—2731no—
183AGL(1,𝔽7)—2731no—
184AGL(1,𝔽7)—421no—
185AGL(1,𝔽7)—911no—
186AGL(1,𝔽7)—911no—
187AGL(1,𝔽7)—911no—
188AGL(1,𝔽7)—911no—
189C3×C13—491no—
190C13⋊C3—71no—
191C13⋊C3—71no—
192C13⋊C3—491no—
193C22×C32—6371noHall
194C2×D7—8191no—
195C2×D7—8191no—
196C2×C13—4411no—
197D13—211no—
198D13—211no—
199C3×C7—911no—
200C3×C7—911no—
201ΓL(1,𝔽8)—71no—
202ΓL(1,𝔽8)—71no—
203ΓL(1,𝔽8)—131no—
204ΓL(1,𝔽8)—131no—
205ΓL(1,𝔽8)—421no—
206ΓL(1,𝔽8)—911no—
207ΓL(1,𝔽8)—911no—
208C2×C32—6371no—
209C2×C32—6371no—
210C2×C32—6371no—
211C2×C7—8191no—
212C2×C7—8191no—
213D7—211no—
214D7—211no—
215D7—391no—
216D7—391no—
217D7—1261no—
218C13AGL(1,𝔽7)211yescharacteristic, complemented, Sylow
219C22×C3—6371no—
220C22×C3—6371no—
221C22×C3—6371no—
222C22×C3—6371no—
223C32—6371noSylow
224C7—61no—
225C7AGL(1,𝔽7)×D13⋊C311yescharacteristic, complemented
226C7AGL(1,𝔽7)×D13⋊C311yescharacteristic, complemented
227C2×C3—491no—
228C2×C3—911no—
229C2×C3—911no—
230C2×C3—19111no—
231C2×C3—19111no—
232C2×C3—19111no—
233C2×C3—19111no—
234C2×C3—19111no—
235C2×C3—19111no—
236C2×C3—6371no—
237C2×C3—6371no—
238C2×C3—6371no—
239C22—57331noSylow
240C3—491no—
241C3—911no—
242C3—911no—
243C3—6371no—
244C2—2731no—
245C2—8191no—
246C2—4411no—
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. #26039532C2semidirect
2. #26039531C2semidirect
3. #64424⋊(C13⋊C3)C2semidirect
4. #10587723⋊D7C3semidirect
5. #10587722⋊D7C3semidirect
6. #21439619C3semidirect
7. #64424⋊D13C3semidirect
8. #3861⋊(C13⋊C3)C22semidirect
9. #16838480C2×C3semidirect
10. #16838479C2×C3semidirect
11. #16838471C2×C3semidirect
12. #16838470C2×C3semidirect
13. #16838463C2×C3semidirect
14. #16838462C2×C3semidirect
15. #16838460C2×C3semidirect
16. #16838460C2×C3semidirect
17. #16838453C2×C3semidirect
18. C13×#64424C2×C3semidirect
19. C7×#10587723C2×C3semidirect
20. C7×#10587722C2×C3semidirect
23. (C7⋊D7)⋊D13C32semidirect
24. C13⋊#3862C22×C3semidirect
25. C13×#3861C22×C3semidirect
26. C7×#63270C22×C3semidirect
27. C7×#63271C22×C3semidirect
35. C13×C7⋊D7C2×C32semidirect
36. C7×D91C2×C32semidirect
37. C7×D91C2×C32semidirect
51. C72×C13C22×C32semidirect
57. #10587723AGL(1,𝔽7)semidirect
59. #10587722AGL(1,𝔽7)semidirect
86. #64424D13⋊C3semidirect
98. #63271C2×AGL(1,𝔽7)semidirect
100. #63270C2×AGL(1,𝔽7)semidirect
112. D91C3×AGL(1,𝔽7)semidirect
113. D91C3×AGL(1,𝔽7)semidirect
124. #3861C2×D13⋊C3semidirect
134. C7⋊D7C3×D13⋊C3semidirect
138. C7×C13C2×C3×AGL(1,𝔽7)semidirect
139. C7×C13C2×C3×AGL(1,𝔽7)semidirect
163. C72C2×C3×D13⋊C3semidirect
218. C13AGL(1,𝔽7)2semidirect
225. C7AGL(1,𝔽7)×D13⋊C3semidirect
226. 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
#260395322
#260395312
#64424⋊(C13⋊C3)2
#10587723⋊D73
#10587722⋊D73
#214396193
#64424⋊D133
AGL(1,𝔽7)×D13⋊C37
AGL(1,𝔽7)213