Finite Group Databasebeta

← #10596874⋊(C13⋊C3) #37524640

Subgroups — #10596874⋊(C13⋊C3) #37524640

Order 22932.

168 conjugacy classes of subgroups; only the 40 normal subgroups are shown.

normal subgroups only

This group has 168 conjugacy classes of subgroups — too many to draw. Only its 40 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
1C2×#3861⋊(C13⋊C3)C211yesmaximal, characteristic
2#21439547C311yesmaximal, characteristic, complemented
3#21439546C311yesmaximal, characteristic, complemented
4#21439529C311yesmaximal, characteristic, complemented
5C13×#10596874C311yesmaximal, characteristic, complemented
6#3861⋊(C13⋊C3)C411yescharacteristic, complemented, Hall
7C2×C13⋊#3862C2×C311yescharacteristic
8C2×C13×#3861C2×C311yescharacteristic
9C2×C7×#63271C2×C311yescharacteristic
10C2×C7×#63270C2×C311yescharacteristic
11C13⋊C3×ΓL(1,𝔽8)⋊C4—71nomaximal
12C13⋊C3×ΓL(1,𝔽8)⋊C4—71nomaximal
13C13×C7⋊Dic7C3211yescharacteristic, complemented, Hall
14C13⋊#3862C3×C411yescharacteristic, complemented
15C13×#3861C3×C411yescharacteristic, complemented
16C7×#63270C3×C411yescharacteristic, complemented
17C7×#63271C3×C411yescharacteristic, complemented
18ΓL(1,𝔽8)⋊(ΓL(1,𝔽8)⋊C4)—131nomaximal, Hall
19C2×ΓL(1,𝔽8)×C13⋊C3—71no—
20C2×ΓL(1,𝔽8)×C13⋊C3—71no—
21C2×C72×C13C2×C3211yescharacteristic
22#11763962—71no—
23#11763962—211no—
24#11763961—71no—
25#11763961—211no—
26C13×ΓL(1,𝔽8)⋊C4—71no—
27C13×ΓL(1,𝔽8)⋊C4—71no—
28C13×ΓL(1,𝔽8)⋊C4—212no—
29Dic7×C13⋊C3—71no—
30Dic7×C13⋊C3—71no—
31C2×ΓL(1,𝔽8)2—131no—
32ΓL(1,𝔽8)×C13⋊C3—71no—
33ΓL(1,𝔽8)×C13⋊C3—71no—
34C72×C13C32×C411yescharacteristic, complemented, Hall
35#10596875—131no—
36#10596874C13⋊C311yescharacteristic, complemented
37ΓL(1,𝔽8)⋊Dic7—131no—
38ΓL(1,𝔽8)⋊Dic7—131no—
39C2×#63271—71no—
40C2×#63271AGL(1,𝔽7)11yescharacteristic
41C2×#63270—71no—
42C2×#63270AGL(1,𝔽7)11yescharacteristic
43C2×C13×ΓL(1,𝔽8)—71no—
44C2×C13×ΓL(1,𝔽8)—71no—
45C2×C13×ΓL(1,𝔽8)—212no—
46C2×C7×C13⋊C3—71no—
47C2×C7×C13⋊C3—71no—
48C3×C4×C13⋊C3—491noHall
49ΓL(1,𝔽8)2—131noHall
50C13×Dic7—211no—
51C13×Dic7—211no—
52C13×Dic7—632no—
53C2×#3862—131no—
54C2×#3861C2×C13⋊C311yescharacteristic
55C2×C7×ΓL(1,𝔽8)—131no—
56C2×C7×ΓL(1,𝔽8)—131no—
57#63271—71no—
58#63271ΓL(1,𝔽8)⋊C411yescharacteristic, complemented
59#63270—71no—
60#63270ΓL(1,𝔽8)⋊C411yescharacteristic, complemented
61C7×C13⋊C3—71no—
62C7×C13⋊C3—71no—
63C13×ΓL(1,𝔽8)—71no—
64C13×ΓL(1,𝔽8)—71no—
65C13×ΓL(1,𝔽8)—212no—
66C3×ΓL(1,𝔽8)⋊C4—911no—
67C3×ΓL(1,𝔽8)⋊C4—911no—
68C2×C3×C13⋊C3—491no—
69C7⋊Dic7C3×C13⋊C311yescharacteristic, complemented, Hall
70C2×C7×C13—32no—
71C2×C7×C13C3×AGL(1,𝔽7)11yescharacteristic
72C2×C7×C13C3×AGL(1,𝔽7)11yescharacteristic
73C3×C4×C13—491no—
74C4×C13⋊C3—491no—
75C4×C13⋊C3—1471no—
76C4×C13⋊C3—1471no—
77#3862—131no—
78#3861C4×C13⋊C311yescharacteristic, complemented
79C7×ΓL(1,𝔽8)—131no—
80C7×ΓL(1,𝔽8)—131no—
81C2×C3×ΓL(1,𝔽8)—911no—
82C2×C3×ΓL(1,𝔽8)—911no—
83C3×C13⋊C3—491noHall
84C2×C72C2×C3×C13⋊C311yescharacteristic
85C7×C13—32no—
86C7×C13C3×ΓL(1,𝔽8)⋊C411yescharacteristic, complemented
87C7×C13C3×ΓL(1,𝔽8)⋊C411yescharacteristic, complemented
88C3×Dic7—911no—
89C3×Dic7—911no—
90ΓL(1,𝔽8)⋊C4—71no—
91ΓL(1,𝔽8)⋊C4—71no—
92ΓL(1,𝔽8)⋊C4—2731no—
93ΓL(1,𝔽8)⋊C4—2731no—
94ΓL(1,𝔽8)⋊C4—212no—
95ΓL(1,𝔽8)⋊C4—911no—
96ΓL(1,𝔽8)⋊C4—911no—
97C2×C3×C13—491no—
98C2×C13⋊C3—71no—
99C2×C13⋊C3—71no—
100C2×C13⋊C3—491no—
101C3×ΓL(1,𝔽8)—911no—
102C3×ΓL(1,𝔽8)—911no—
103C4×C13—4411noHall
104C72C3×C4×C13⋊C311yescharacteristic, complemented, Sylow
105C2×C3×C7—911no—
106C2×C3×C7—911no—
107C2×ΓL(1,𝔽8)—71no—
108C2×ΓL(1,𝔽8)—71no—
109C2×ΓL(1,𝔽8)—131no—
110C2×ΓL(1,𝔽8)—131no—
111C2×ΓL(1,𝔽8)—212no—
112C2×ΓL(1,𝔽8)—911no—
113C2×ΓL(1,𝔽8)—911no—
114C3×C13—491no—
115C13⋊C3—71no—
116C13⋊C3—71no—
117C13⋊C3—491no—
118C32×C4—6371noHall
119Dic7—211no—
120Dic7—211no—
121Dic7—632no—
122C2×C13ΓL(1,𝔽8)⋊AGL(1,𝔽7)11yescharacteristic
123C3×C7—911no—
124C3×C7—911no—
125ΓL(1,𝔽8)—71no—
126ΓL(1,𝔽8)—71no—
127ΓL(1,𝔽8)—131no—
128ΓL(1,𝔽8)—131no—
129ΓL(1,𝔽8)—212no—
130ΓL(1,𝔽8)—911no—
131ΓL(1,𝔽8)—911no—
132C2×C32—6371no—
133C2×C7—32no—
134C2×C7C13⋊C3×AGL(1,𝔽7)11yescharacteristic
135C2×C7C13⋊C3×AGL(1,𝔽7)11yescharacteristic
136C13ΓL(1,𝔽8)⋊(ΓL(1,𝔽8)⋊C4)11yescharacteristic, complemented, Sylow
137C3×C4—491no—
138C3×C4—19111no—
139C3×C4—19111no—
140C3×C4—6371no—
141C32—6371noSylow
142C7—32no—
143C7C13⋊C3×ΓL(1,𝔽8)⋊C411yescharacteristic, complemented
144C7C13⋊C3×ΓL(1,𝔽8)⋊C411yescharacteristic, complemented
145C2×C3—491no—
146C2×C3—911no—
147C2×C3—911no—
148C2×C3—6371no—
149C4—4411noSylow
150C3—491no—
151C3—911no—
152C3—911no—
153C3—6371no—
154C2#64424⋊(C13⋊C3)11yescharacteristic
subgroupG/H
center, Frattini, hypercenterC2#64424⋊(C13⋊C3)
commutator, hypocenterC72×C13C32×C4
Fitting, socle, cosocleC2×C72×C13C2×C32
prime radicalC2×#3861⋊(C13⋊C3)C2
LCSG ▷ C72×C13
UCSC1 ◁ C2

Complements

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

NH ≅ G/Ntype
2. #21439547C3semidirect
3. #21439546C3semidirect
4. #21439529C3semidirect
5. C13×#10596874C3semidirect
6. #3861⋊(C13⋊C3)C4semidirect
13. C13×C7⋊Dic7C32semidirect
14. C13⋊#3862C3×C4semidirect
15. C13×#3861C3×C4semidirect
16. C7×#63270C3×C4semidirect
17. C7×#63271C3×C4semidirect
34. C72×C13C32×C4semidirect
36. #10596874C13⋊C3semidirect
58. #63271ΓL(1,𝔽8)⋊C4semidirect
60. #63270ΓL(1,𝔽8)⋊C4semidirect
69. C7⋊Dic7C3×C13⋊C3semidirect
78. #3861C4×C13⋊C3semidirect
86. C7×C13C3×ΓL(1,𝔽8)⋊C4semidirect
87. C7×C13C3×ΓL(1,𝔽8)⋊C4semidirect
104. C72C3×C4×C13⋊C3semidirect
136. C13ΓL(1,𝔽8)⋊(ΓL(1,𝔽8)⋊C4)semidirect
143. C7C13⋊C3×ΓL(1,𝔽8)⋊C4semidirect
144. C7C13⋊C3×ΓL(1,𝔽8)⋊C4semidirect

Maximal subgroups

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

subgroupindex
C2×#3861⋊(C13⋊C3)2
#214395473
#214395463
#214395293
C13×#105968743
C13⋊C3×ΓL(1,𝔽8)⋊C47
ΓL(1,𝔽8)⋊(ΓL(1,𝔽8)⋊C4)13