Finite Group Databasebeta

← C7×D33⋊D35 #44568896

Subgroups — C7×D33⋊D35 #44568896

Order 32340.

208 conjugacy classes of subgroups; only the 50 normal subgroups are shown.

normal subgroups only

This group has 208 conjugacy classes of subgroups — too many to draw. Only its 50 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
1C3×C7×D385C211yesmaximal, characteristic, complemented
2C5×C72×D33C211yesmaximal, characteristic, complemented
3C7×C11×D105C211yesmaximal, characteristic, complemented
4C7×D11×D35—31nomaximal, Hall
5C3×C5×C72×C11C2211yescharacteristic, complemented, Hall
6C7×D21⋊D11—51nomaximal, Hall
7C7×D385D311yescharacteristic, complemented
8C7×C11×D35—31no—
9C5×C72×D11—31no—
10D33⋊D35C711yesmaximal, characteristic, direct product factor
11C7×D15⋊D11—71nomaximal
12C7×C11×D21—51no—
13C72×D33D511yescharacteristic, complemented
14C3×C7×D77—51no—
15D3×C7×D35—111nomaximal, Hall
16C5×C72×C11C2×D311yescharacteristic, complemented, Hall
17C11×D105C2×C711yescharacteristic, complemented
18C7×C11×D15—71no—
19C5×C7×D33—23no—
20C5×C7×D33D711yescharacteristic, complemented
21C5×C7×D33C2×C711yescharacteristic, complemented
22C3×D385C2×C711yescharacteristic, complemented
23C3×C7×D55—71no—
24C7×D7×D11—151noHall
25C3×C72×C11C2×D511yescharacteristic, complemented, Hall
26D11×D35—31no—
27C7×D5×D11—211no—
28C7×D105D1111yescharacteristic, complemented
29C5×D3×C72—111no—
30C3×C7×D35—111no—
31C3×C5×C7×C11—23no—
32C3×C5×C7×C11C2×D711yescharacteristic, complemented
33C3×C5×C7×C11C22×C711yescharacteristic, complemented
34C7×D77—51no—
35C7×C11×D7—151no—
36C72×D11—31no—
37C2×C7×D35—331noHall
38D21⋊D11—51no—
39D3×C7×D11—351no—
40D385D3×C711yescharacteristic, complemented
41C11×D35—31no—
42C7×D55—71no—
43C7×D5×C11—211no—
44C5×C7×D11—31no—
45C5×C7×D11—31no—
46C5×C7×D11—63no—
47C3×C5×C72C2×D1111yescharacteristic, complemented, Hall
48D15⋊D11—71noHall
49D3×C7×D7—551noHall
50C72×C11D3×D511yescharacteristic, complemented, Hall
51C2×C5×C72—331no—
52C7×D35—31no—
53C7×D35—111no—
54C11×D21—51no—
55C7×D33—23no—
56C7×D33C7×D511yescharacteristic, complemented
57C7×D33D3511yescharacteristic, complemented
58D3×C7×C11—351no—
59C3×D77—51no—
60C3×C7×D11—351no—
61D3×D35—111no—
62D3×C7×D5—771no—
63C5×C7×C11—23no—
64C5×C7×C11D3×D711yescharacteristic, complemented
65C5×C7×C11C2×D3×C711yescharacteristic, complemented
66C11×D15—71no—
67C5×D33C7×D711yescharacteristic, complemented
68C3×D55—71no—
69C2×C7×D11—1051no—
70D7×D11—151no—
71C7×D21—51no—
72D3×C72—111no—
73C3×C7×D7—551no—
74C5×C72D3×D1111yescharacteristic, complemented, Hall
75C3×C7×C11—23no—
76C3×C7×C11C2×C7×D511yescharacteristic, complemented
77C3×C7×C11C2×D3511yescharacteristic, complemented
78D5×D11—211noHall
79D105C7×D1111yescharacteristic, complemented
80C7×D15—71no—
81C5×D3×C7—111no—
82C5×D3×C7—111no—
83C5×D3×C7—223no—
84C3×D35—111no—
85C3×C7×D5—771no—
86C2×C7×D7—1651noHall
87C3×C5×C11C2×C7×D711yescharacteristic, complemented, Hall
88C2×C7×C11—1051no—
89D77—51no—
90C7×D11—31no—
91C7×D11—31no—
92C7×D11—63no—
93C7×D11—351no—
94C11×D7—151no—
95C3×C72D5×D1111yescharacteristic, complemented, Hall
96C2×D35—331no—
97C2×C7×D5—2311no—
98D3×D11—351noHall
99D55—71no—
100C5×D11—31no—
101D5×C11—211no—
102C3×C5×C7—23no—
103C3×C5×C7D7×D1111yescharacteristic, complemented
104C3×C5×C7C2×C7×D1111yescharacteristic, complemented
105C2×C72—331no—
106C7×D7—151no—
107C7×D7—551no—
108C2×D3×C7—3851no—
109D3×D7—551no—
110C7×C11—23no—
111C7×C11D3×C7×D511yescharacteristic, complemented
112C7×C11D3×D3511yescharacteristic, complemented
113C2×C5×C7—331no—
114C2×C5×C7—331no—
115C2×C5×C7—663no—
116D35—31no—
117D35—111no—
118C7×D5—211no—
119C7×D5—771no—
120D33C7×D3511yescharacteristic, complemented
121C3×D11—351no—
122D3×C11—351no—
123D3×D5—771noHall
124C5×C11D3×C7×D711yescharacteristic, complemented, Hall
125C72D15⋊D1111yescharacteristic, complemented, Sylow
126C2×D11—1051noHall
127C2×C3×C7—3851no—
128D21—51no—
129C3×D7—551no—
130D3×C7—111no—
131D3×C7—111no—
132D3×C7—223no—
133D3×C7—351no—
134C5×C7—23no—
135C5×C7D3×C7×D1111yescharacteristic, complemented
136C5×C7D21⋊D1111yescharacteristic, complemented
137C3×C11C2×C7×D3511yescharacteristic, complemented, Hall
138D15—71no—
139C3×D5—771no—
140C5×D3—111no—
141C22×C7—11551no—
142C2×D7—1651no—
143C2×C11—1051no—
144D11—31no—
145D11—351no—
146C3×C7—23no—
147C3×C7C7×D5×D1111yescharacteristic, complemented
148C3×C7D11×D3511yescharacteristic, complemented
149C2×D5—2311noHall
150C3×C5C7×D7×D1111yescharacteristic, complemented, Hall
151C2×C7—331no—
152C2×C7—331no—
153C2×C7—663no—
154C2×C7—1051no—
155C2×C7—3851no—
156D7—151no—
157D7—551no—
158C2×D3—3851noHall
159C11D3×C7×D3511yescharacteristic, complemented, Sylow
160C2×C5—331no—
161D5—211no—
162D5—771no—
163C7—23no—
164C7C7×D15⋊D1111yescharacteristic, complemented
165C7D33⋊D3511yescharacteristic, direct product factor
166C2×C3—3851no—
167D3—111no—
168D3—351no—
169C5C7×D21⋊D1111yescharacteristic, complemented, Sylow
170C22—11551noSylow
171C3C7×D11×D3511yescharacteristic, complemented, Sylow
172C2—331no—
173C2—1051no—
174C2—3851no—
subgroupG/H
center, hypercenterC7D33⋊D35
commutator, cosocle, hypocenterC3×C5×C7×C11C22×C7
FrattiniC1G
Fitting, socleC3×C5×C72×C11C22
LCSG ▷ C3×C5×C7×C11
UCSC1 ◁ C7

Complements

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

NH ≅ G/Ntype
1. C3×C7×D385C2semidirect
2. C5×C72×D33C2semidirect
3. C7×C11×D105C2semidirect
5. C3×C5×C72×C11C22semidirect
7. C7×D385D3semidirect
10. D33⋊D35C7direct (N × H)
13. C72×D33D5semidirect
16. C5×C72×C11C2×D3semidirect
17. C11×D105C2×C7semidirect
20. C5×C7×D33D7semidirect
21. C5×C7×D33C2×C7semidirect
22. C3×D385C2×C7semidirect
25. C3×C72×C11C2×D5semidirect
28. C7×D105D11semidirect
32. C3×C5×C7×C11C2×D7semidirect
33. C3×C5×C7×C11C22×C7semidirect
40. D385D3×C7semidirect
47. C3×C5×C72C2×D11semidirect
50. C72×C11D3×D5semidirect
56. C7×D33C7×D5semidirect
57. C7×D33D35semidirect
64. C5×C7×C11D3×D7semidirect
65. C5×C7×C11C2×D3×C7semidirect
67. C5×D33C7×D7semidirect
74. C5×C72D3×D11semidirect
76. C3×C7×C11C2×C7×D5semidirect
77. C3×C7×C11C2×D35semidirect
79. D105C7×D11semidirect
87. C3×C5×C11C2×C7×D7semidirect
95. C3×C72D5×D11semidirect
103. C3×C5×C7D7×D11semidirect
104. C3×C5×C7C2×C7×D11semidirect
111. C7×C11D3×C7×D5semidirect
112. C7×C11D3×D35semidirect
120. D33C7×D35semidirect
124. C5×C11D3×C7×D7semidirect
125. C72D15⋊D11semidirect
135. C5×C7D3×C7×D11semidirect
136. C5×C7D21⋊D11semidirect
137. C3×C11C2×C7×D35semidirect
147. C3×C7C7×D5×D11semidirect
148. C3×C7D11×D35semidirect
150. C3×C5C7×D7×D11semidirect
159. C11D3×C7×D35semidirect
164. C7C7×D15⋊D11semidirect
165. C7D33⋊D35direct (N × H)
169. C5C7×D21⋊D11semidirect
171. C3C7×D11×D35semidirect

Maximal subgroups

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

subgroupindex
C3×C7×D3852
C5×C72×D332
C7×C11×D1052
C7×D11×D353
C7×D21⋊D115
D33⋊D357
C7×D15⋊D117
D3×C7×D3511