Finite Group Databasebeta

← C13⋊C3×#64423⋊C2 #37524951

Subgroups — C13⋊C3×#64423⋊C2 #37524951

Order 22932.

312 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 312 conjugacy classes of subgroups — too many to draw. Only its 55 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
1C13⋊C3×#64423C211yesmaximal, characteristic, complemented
2C13⋊C3×#64423C211yesmaximal, characteristic, complemented
3C13⋊C3×#64424C211yesmaximal, characteristic, complemented
4D72×C13⋊C3C311yesmaximal, characteristic, complemented
5#21439613C311yesmaximal, characteristic, complemented
6#21439612C311yesmaximal, characteristic, complemented
7C13×#64423⋊C2C311yesmaximal, characteristic, complemented
8C13⋊C3×#3861C2211yescharacteristic, complemented, Hall
9C13⋊C3×C7⋊D7C2×C311yescharacteristic, complemented
10#16838459C2×C311yescharacteristic, complemented
11#16838459C2×C311yescharacteristic, complemented
12#16838458C2×C311yescharacteristic, complemented
13#16838458C2×C311yescharacteristic, complemented
14C13×#64423C2×C311yescharacteristic, complemented
15C13×#64423C2×C311yescharacteristic, complemented
16#16838449C2×C311yescharacteristic, complemented
17#16838448C2×C311yescharacteristic, complemented
18C13×#64424C2×C311yescharacteristic, complemented
19C7×D7×C13⋊C3C2×C311yescharacteristic, complemented
20C7×D7×C13⋊C3C2×C311yescharacteristic, complemented
21C2×C13⋊C3×AGL(1,𝔽7)—71nomaximal
22C2×C13⋊C3×AGL(1,𝔽7)—71nomaximal
23C13×D72C3211yescharacteristic, complemented, Hall
24#14274263C22×C311yescharacteristic, complemented
25#14274262C22×C311yescharacteristic, complemented
26C13×#3861C22×C311yescharacteristic, complemented
27C72×C13⋊C3C22×C311yescharacteristic, complemented
28C3×#64423⋊C2—131nomaximal, Hall
29C2×ΓL(1,𝔽8)×C13⋊C3—71no—
30C2×ΓL(1,𝔽8)×C13⋊C3—71no—
31C13⋊C3×AGL(1,𝔽7)—71no—
32C13⋊C3×AGL(1,𝔽7)—71no—
33C13⋊C3×AGL(1,𝔽7)—71no—
34C13⋊C3×AGL(1,𝔽7)—71no—
35C13⋊C3×AGL(1,𝔽7)—141no—
36C13⋊C3×AGL(1,𝔽7)—141no—
37C13⋊C3×AGL(1,𝔽7)—141no—
38C13×C7⋊D7C2×C3211yescharacteristic, complemented
39C7×C13×D7C2×C3211yescharacteristic, complemented
40C7×C13×D7C2×C3211yescharacteristic, complemented
41C2×#10587721—71no—
42C2×#10587721—71no—
43C2×#10587720—71no—
44C2×#10587720—71no—
45C2×C13×AGL(1,𝔽7)—71no—
46C2×C13×AGL(1,𝔽7)—71no—
47C2×D7×C13⋊C3—211no—
48C2×D7×C13⋊C3—211no—
49C3×#64424—131no—
50C3×#64423—131no—
51C3×#64423—131no—
52ΓL(1,𝔽8)×C13⋊C3—71no—
53ΓL(1,𝔽8)×C13⋊C3—71no—
54ΓL(1,𝔽8)×C13⋊C3—141no—
55ΓL(1,𝔽8)×C13⋊C3—141no—
56ΓL(1,𝔽8)×C13⋊C3—141no—
57C72×C13C22×C3211yescharacteristic, complemented, Hall
58C3×D72—131no—
59#64423⋊C2—131no—
60#64423⋊C2—131no—
61#64423⋊C2C13⋊C311yescharacteristic, direct product factor
62C2×#63271—71no—
63C2×#63271—71no—
64C2×#63270—71no—
65C2×#63270—71no—
66C2×C13×ΓL(1,𝔽8)—71no—
67C2×C13×ΓL(1,𝔽8)—71no—
68C2×C7×C13⋊C3—211no—
69C2×C7×C13⋊C3—211no—
70#10587721—71no—
71#10587721—71no—
72#10587721—71no—
73#10587721—71no—
74#10587721—141no—
75#10587721—141no—
76#10587721—141no—
77#10587720—71no—
78#10587720—71no—
79#10587720—71no—
80#10587720—71no—
81#10587720—141no—
82#10587720—141no—
83#10587720—141no—
84C13×AGL(1,𝔽7)—71no—
85C13×AGL(1,𝔽7)—71no—
86C13×AGL(1,𝔽7)—71no—
87C13×AGL(1,𝔽7)—71no—
88C13×AGL(1,𝔽7)—141no—
89C13×AGL(1,𝔽7)—141no—
90C13×AGL(1,𝔽7)—141no—
91D7×C13⋊C3—71no—
92D7×C13⋊C3—141no—
93D7×C13⋊C3—211no—
94D7×C13⋊C3—421no—
95D7×C13⋊C3—421no—
96D7×C13⋊C3AGL(1,𝔽7)11yescharacteristic, complemented
97D7×C13⋊C3AGL(1,𝔽7)11yescharacteristic, complemented
98C22×C3×C13⋊C3—491noHall
99C3×#3861—131noHall
100C2×C13×D7—211no—
101C2×C13×D7—211no—
102C3×C7⋊D7—131no—
103C3×C7×D7—131no—
104C3×C7×D7—131no—
105#64424—131no—
106#64424—131no—
107#64424C2×C13⋊C311yescharacteristic, complemented
108#64423—131no—
109#64423—131no—
110#64423—131no—
111#64423—131no—
112#64423C2×C13⋊C311yescharacteristic, complemented
113#64423C2×C13⋊C311yescharacteristic, complemented
114#63271—71no—
115#63271—71no—
116#63271—141no—
117#63271—141no—
118#63271—141no—
119#63270—71no—
120#63270—71no—
121#63270—141no—
122#63270—141no—
123#63270—141no—
124C7×C13⋊C3—21no—
125C7×C13⋊C3—21no—
126C7×C13⋊C3—21no—
127C7×C13⋊C3C2×AGL(1,𝔽7)11yescharacteristic, complemented
128C7×C13⋊C3C2×AGL(1,𝔽7)11yescharacteristic, complemented
129C13×ΓL(1,𝔽8)—71no—
130C13×ΓL(1,𝔽8)—71no—
131C13×ΓL(1,𝔽8)—141no—
132C13×ΓL(1,𝔽8)—141no—
133C13×ΓL(1,𝔽8)—141no—
134C2×C3×AGL(1,𝔽7)—911no—
135C2×C3×AGL(1,𝔽7)—911no—
136C2×C3×C13⋊C3—491no—
137C2×C3×C13⋊C3—491no—
138C2×C3×C13⋊C3—491no—
139D72C3×C13⋊C311yescharacteristic, complemented, Hall
140C2×C7×C13—211no—
141C2×C7×C13—211no—
142C13×D7—71no—
143C13×D7—141no—
144C13×D7—211no—
145C13×D7—421no—
146C13×D7—421no—
147C13×D7C3×AGL(1,𝔽7)11yescharacteristic, complemented
148C13×D7C3×AGL(1,𝔽7)11yescharacteristic, complemented
149C22×C3×C13—491no—
150C22×C13⋊C3—491no—
151C22×C13⋊C3—491no—
152C22×C13⋊C3—1471no—
153C3×C72—131no—
154#3861—131no—
155#3861—131no—
156#3861C22×C13⋊C311yescharacteristic, complemented
157C2×C3×ΓL(1,𝔽8)—911no—
158C2×C3×ΓL(1,𝔽8)—911no—
159C3×AGL(1,𝔽7)—911no—
160C3×AGL(1,𝔽7)—911no—
161C3×AGL(1,𝔽7)—911no—
162C3×AGL(1,𝔽7)—911no—
163C3×AGL(1,𝔽7)—1821no—
164C3×AGL(1,𝔽7)—1821no—
165C3×AGL(1,𝔽7)—1821no—
166C3×C13⋊C3—491noHall
167C7⋊D7C2×C3×C13⋊C311yescharacteristic, complemented
168C7×D7C2×C3×C13⋊C311yescharacteristic, complemented
169C7×D7C2×C3×C13⋊C311yescharacteristic, complemented
170C7×C13—21no—
171C7×C13—21no—
172C7×C13—21no—
173C7×C13C2×C3×AGL(1,𝔽7)11yescharacteristic, complemented
174C7×C13C2×C3×AGL(1,𝔽7)11yescharacteristic, complemented
175C2×C3×D7—2731no—
176C2×C3×D7—2731no—
177C2×AGL(1,𝔽7)—71no—
178C2×AGL(1,𝔽7)—71no—
179C2×AGL(1,𝔽7)—911no—
180C2×AGL(1,𝔽7)—911no—
181C2×AGL(1,𝔽7)—911no—
182C2×AGL(1,𝔽7)—911no—
183C2×C3×C13—491no—
184C2×C3×C13—491no—
185C2×C3×C13—491no—
186C2×C13⋊C3—71no—
187C2×C13⋊C3—211no—
188C2×C13⋊C3—491no—
189C2×C13⋊C3—491no—
190C2×C13⋊C3—491no—
191C2×C13⋊C3—491no—
192C2×C13⋊C3—491no—
193C2×C13⋊C3—491no—
194C2×C13⋊C3—1471no—
195C3×ΓL(1,𝔽8)—911no—
196C3×ΓL(1,𝔽8)—911no—
197C3×ΓL(1,𝔽8)—1821no—
198C3×ΓL(1,𝔽8)—1821no—
199C3×ΓL(1,𝔽8)—1821no—
200C22×C13—1471noHall
201C72C22×C3×C13⋊C311yescharacteristic, complemented, Sylow
202C2×C3×C7—2731no—
203C2×C3×C7—2731no—
204C3×D7—131no—
205C3×D7—131no—
206C3×D7—2731no—
207C3×D7—5461no—
208C3×D7—911no—
209C3×D7—1821no—
210C3×D7—1821no—
211C2×ΓL(1,𝔽8)—71no—
212C2×ΓL(1,𝔽8)—71no—
213C2×ΓL(1,𝔽8)—911no—
214C2×ΓL(1,𝔽8)—911no—
215C2×ΓL(1,𝔽8)—911no—
216C2×ΓL(1,𝔽8)—911no—
217AGL(1,𝔽7)—71no—
218AGL(1,𝔽7)—71no—
219AGL(1,𝔽7)—71no—
220AGL(1,𝔽7)—71no—
221AGL(1,𝔽7)—141no—
222AGL(1,𝔽7)—141no—
223AGL(1,𝔽7)—141no—
224AGL(1,𝔽7)—911no—
225AGL(1,𝔽7)—911no—
226AGL(1,𝔽7)—911no—
227AGL(1,𝔽7)—911no—
228AGL(1,𝔽7)—911no—
229AGL(1,𝔽7)—911no—
230AGL(1,𝔽7)—911no—
231AGL(1,𝔽7)—911no—
232AGL(1,𝔽7)—1821no—
233AGL(1,𝔽7)—1821no—
234AGL(1,𝔽7)—1821no—
235AGL(1,𝔽7)—1821no—
236AGL(1,𝔽7)—1821no—
237AGL(1,𝔽7)—1821no—
238C3×C13—491no—
239C13⋊C3—491no—
240C13⋊C3—491no—
241C13⋊C3#64423⋊C211yescharacteristic, direct product factor
242C22×C32—6371noHall
243C2×D7—211no—
244C2×D7—211no—
245C2×C13—71no—
246C2×C13—211no—
247C2×C13—1471no—
248C3×C7—131no—
249C3×C7—131no—
250C3×C7—261no—
251C3×C7—261no—
252C3×C7—261no—
253ΓL(1,𝔽8)—71no—
254ΓL(1,𝔽8)—71no—
255ΓL(1,𝔽8)—141no—
256ΓL(1,𝔽8)—141no—
257ΓL(1,𝔽8)—141no—
258ΓL(1,𝔽8)—911no—
259ΓL(1,𝔽8)—911no—
260ΓL(1,𝔽8)—911no—
261ΓL(1,𝔽8)—911no—
262ΓL(1,𝔽8)—1821no—
263ΓL(1,𝔽8)—1821no—
264ΓL(1,𝔽8)—1821no—
265ΓL(1,𝔽8)—1821no—
266ΓL(1,𝔽8)—1821no—
267ΓL(1,𝔽8)—1821no—
268C2×C32—6371no—
269C2×C32—6371no—
270C2×C32—6371no—
271C2×C7—211no—
272C2×C7—211no—
273D7—71no—
274D7—141no—
275D7—141no—
276D7—211no—
277D7—421no—
278D7C13⋊C3×AGL(1,𝔽7)11yescharacteristic, complemented
279D7C13⋊C3×AGL(1,𝔽7)11yescharacteristic, complemented
280C13C3×#64423⋊C211yescharacteristic, complemented, Sylow
281C22×C3—491no—
282C22×C3—19111no—
283C22×C3—6371no—
284C22×C3—6371no—
285C32—6371noSylow
286C7—21no—
287C7—21no—
288C7—21no—
289C7C2×C13⋊C3×AGL(1,𝔽7)11yescharacteristic, complemented
290C7C2×C13⋊C3×AGL(1,𝔽7)11yescharacteristic, complemented
291C2×C3—2731no—
292C2×C3—2731no—
293C2×C3—491no—
294C2×C3—491no—
295C2×C3—491no—
296C2×C3—19111no—
297C2×C3—6371no—
298C2×C3—6371no—
299C2×C3—6371no—
300C2×C3—6371no—
301C2×C3—6371no—
302C2×C3—6371no—
303C22—1471noSylow
304C3—131no—
305C3—491no—
306C3—6371no—
307C3—6371no—
308C2—211no—
309C2—211no—
310C2—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. C13⋊C3×#64423C2semidirect
2. C13⋊C3×#64423C2semidirect
3. C13⋊C3×#64424C2semidirect
4. D72×C13⋊C3C3semidirect
5. #21439613C3semidirect
6. #21439612C3semidirect
7. C13×#64423⋊C2C3semidirect
8. C13⋊C3×#3861C22semidirect
9. C13⋊C3×C7⋊D7C2×C3semidirect
10. #16838459C2×C3semidirect
11. #16838459C2×C3semidirect
12. #16838458C2×C3semidirect
13. #16838458C2×C3semidirect
14. C13×#64423C2×C3semidirect
15. C13×#64423C2×C3semidirect
16. #16838449C2×C3semidirect
17. #16838448C2×C3semidirect
18. C13×#64424C2×C3semidirect
19. C7×D7×C13⋊C3C2×C3semidirect
20. C7×D7×C13⋊C3C2×C3semidirect
23. C13×D72C32semidirect
24. #14274263C22×C3semidirect
25. #14274262C22×C3semidirect
26. C13×#3861C22×C3semidirect
27. C72×C13⋊C3C22×C3semidirect
38. C13×C7⋊D7C2×C32semidirect
39. C7×C13×D7C2×C32semidirect
40. C7×C13×D7C2×C32semidirect
57. C72×C13C22×C32semidirect
61. #64423⋊C2C13⋊C3direct (N × H)
96. D7×C13⋊C3AGL(1,𝔽7)semidirect
97. D7×C13⋊C3AGL(1,𝔽7)semidirect
107. #64424C2×C13⋊C3semidirect
112. #64423C2×C13⋊C3semidirect
113. #64423C2×C13⋊C3semidirect
127. C7×C13⋊C3C2×AGL(1,𝔽7)semidirect
128. C7×C13⋊C3C2×AGL(1,𝔽7)semidirect
139. D72C3×C13⋊C3semidirect
147. C13×D7C3×AGL(1,𝔽7)semidirect
148. C13×D7C3×AGL(1,𝔽7)semidirect
156. #3861C22×C13⋊C3semidirect
167. C7⋊D7C2×C3×C13⋊C3semidirect
168. C7×D7C2×C3×C13⋊C3semidirect
169. C7×D7C2×C3×C13⋊C3semidirect
173. C7×C13C2×C3×AGL(1,𝔽7)semidirect
174. C7×C13C2×C3×AGL(1,𝔽7)semidirect
201. C72C22×C3×C13⋊C3semidirect
241. C13⋊C3#64423⋊C2direct (N × H)
278. D7C13⋊C3×AGL(1,𝔽7)semidirect
279. D7C13⋊C3×AGL(1,𝔽7)semidirect
280. C13C3×#64423⋊C2semidirect
289. C7C2×C13⋊C3×AGL(1,𝔽7)semidirect
290. C7C2×C13⋊C3×AGL(1,𝔽7)semidirect

Maximal subgroups

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

subgroupindex
C13⋊C3×#644232
C13⋊C3×#644242
D72×C13⋊C33
#214396133
#214396123
C13×#64423⋊C23
C2×C13⋊C3×AGL(1,𝔽7)7
C3×#64423⋊C213