Finite Group Databasebeta

← C7×D55⋊D21 #44568892

Subgroups — C7×D55⋊D21 #44568892

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×C72×D55C211yesmaximal, characteristic, complemented
2C5×C7×D231C211yesmaximal, characteristic, complemented
3C7×C11×D105C211yesmaximal, characteristic, complemented
4C7×D35⋊D11—31nomaximal, Hall
5C3×C5×C72×C11C2211yescharacteristic, complemented, Hall
6C7×D11×D21—51nomaximal, Hall
7C7×C11×D35—31no—
8C72×D55D311yescharacteristic, complemented
9C5×C7×D77—31no—
10D55⋊D21C711yesmaximal, characteristic, direct product factor
11C7×D15⋊D11—71nomaximal
12C7×D231D511yescharacteristic, complemented
13C7×C11×D21—51no—
14C3×C72×D11—51no—
15C7×D5×D21—111nomaximal, Hall
16C5×C72×C11C2×D311yescharacteristic, complemented, Hall
17C11×D105C2×C711yescharacteristic, complemented
18C7×C11×D15—71no—
19C5×D231C2×C711yescharacteristic, complemented
20C5×C7×D33—71no—
21C3×C7×D55—23no—
22C3×C7×D55D711yescharacteristic, complemented
23C3×C7×D55C2×C711yescharacteristic, complemented
24C7×D7×D11—151noHall
25C3×C72×C11C2×D511yescharacteristic, complemented, Hall
26D35⋊D11—31no—
27C7×D5×D11—211no—
28C7×D105D1111yescharacteristic, complemented
29C5×C7×D21—111no—
30C3×C72×D5—111no—
31C3×C5×C7×C11—23no—
32C3×C5×C7×C11C2×D711yescharacteristic, complemented
33C3×C5×C7×C11C22×C711yescharacteristic, complemented
34C7×D77—31no—
35C7×C11×D7—151no—
36C72×D11—51no—
37C7×D5×D7—331noHall
38D11×D21—51no—
39D3×C7×D11—351no—
40C11×D35—31no—
41C7×D55—23no—
42C7×D55D3×C711yescharacteristic, complemented
43C7×D55D2111yescharacteristic, complemented
44C7×D5×C11—211no—
45C5×D77—31no—
46C5×C7×D11—211no—
47C3×C5×C72C2×D1111yescharacteristic, complemented, Hall
48D15⋊D11—71noHall
49C2×C7×D21—551noHall
50C72×C11D3×D511yescharacteristic, complemented, Hall
51C7×D35—31no—
52C72×D5—111no—
53C5×C7×D7—331no—
54D231C7×D511yescharacteristic, complemented
55C11×D21—51no—
56C7×D33—71no—
57D3×C7×C11—351no—
58C3×C7×D11—51no—
59C3×C7×D11—51no—
60C3×C7×D11—103no—
61D5×D21—111no—
62D3×C7×D5—771no—
63C5×C7×C11—23no—
64C5×C7×C11C2×D3×C711yescharacteristic, complemented
65C5×C7×C11C2×D2111yescharacteristic, complemented
66C11×D15—71no—
67C5×D33—71no—
68C3×D55C7×D711yescharacteristic, complemented
69C2×C7×D11—1051no—
70D7×D11—151no—
71C2×C3×C72—551no—
72C7×D21—51no—
73C7×D21—111no—
74C5×C72D3×D1111yescharacteristic, complemented, Hall
75C3×C7×C11—23no—
76C3×C7×C11D5×D711yescharacteristic, complemented
77C3×C7×C11C2×C7×D511yescharacteristic, complemented
78D5×D11—211noHall
79D105C7×D1111yescharacteristic, complemented
80C7×D15—71no—
81C5×D21—111no—
82C5×D3×C7—771no—
83C3×C7×D5—111no—
84C3×C7×D5—111no—
85C3×C7×D5—223no—
86C2×C7×D7—1651noHall
87C3×C5×C11C2×C7×D711yescharacteristic, complemented, Hall
88C2×C7×C11—1051no—
89D77—31no—
90C7×D11—51no—
91C7×D11—51no—
92C7×D11—103no—
93C7×D11—211no—
94C11×D7—151no—
95C3×C72D5×D1111yescharacteristic, complemented, Hall
96C2×C7×D5—2311no—
97D5×D7—331no—
98D3×D11—351noHall
99D55C7×D2111yescharacteristic, complemented
100C5×D11—211no—
101D5×C11—211no—
102C3×C5×C7—23no—
103C3×C5×C7D7×D1111yescharacteristic, complemented
104C3×C5×C7C2×C7×D1111yescharacteristic, complemented
105C2×C72—551no—
106C7×D7—151no—
107C7×D7—331no—
108C2×D21—551no—
109C2×D3×C7—3851no—
110C7×C11—23no—
111C7×C11D3×C7×D511yescharacteristic, complemented
112C7×C11D5×D2111yescharacteristic, complemented
113C2×C5×C7—2311no—
114D35—31no—
115C5×D7—331no—
116C7×D5—111no—
117C7×D5—111no—
118C7×D5—211no—
119C7×D5—223no—
120D33—71no—
121C3×D11—51no—
122D3×C11—351no—
123D3×D5—771noHall
124C5×C11C2×C7×D2111yescharacteristic, complemented, Hall
125C72D15⋊D1111yescharacteristic, complemented, Sylow
126C2×D11—1051noHall
127C2×C3×C7—551no—
128C2×C3×C7—551no—
129C2×C3×C7—1103no—
130D21—51no—
131D21—111no—
132D3×C7—351no—
133D3×C7—771no—
134C5×C7—23no—
135C5×C7D3×C7×D1111yescharacteristic, complemented
136C5×C7D11×D2111yescharacteristic, complemented
137C3×C11C7×D5×D711yescharacteristic, complemented, Hall
138D15—71no—
139C3×D5—111no—
140C5×D3—771no—
141C22×C7—11551no—
142C2×D7—1651no—
143C2×C11—1051no—
144D11—51no—
145D11—211no—
146C3×C7—23no—
147C3×C7C7×D5×D1111yescharacteristic, complemented
148C3×C7D35⋊D1111yescharacteristic, complemented
149C2×D5—2311noHall
150C3×C5C7×D7×D1111yescharacteristic, complemented, Hall
151C2×C7—551no—
152C2×C7—551no—
153C2×C7—1051no—
154C2×C7—1103no—
155C2×C7—2311no—
156D7—151no—
157D7—331no—
158C2×D3—3851noHall
159C11C7×D5×D2111yescharacteristic, complemented, Sylow
160C2×C5—2311no—
161D5—111no—
162D5—211no—
163C7—23no—
164C7C7×D15⋊D1111yescharacteristic, complemented
165C7D55⋊D2111yescharacteristic, direct product factor
166C2×C3—551no—
167D3—351no—
168D3—771no—
169C5C7×D11×D2111yescharacteristic, complemented, Sylow
170C22—11551noSylow
171C3C7×D35⋊D1111yescharacteristic, complemented, Sylow
172C2—551no—
173C2—1051no—
174C2—2311no—
subgroupG/H
center, hypercenterC7D55⋊D21
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×C72×D55C2semidirect
2. C5×C7×D231C2semidirect
3. C7×C11×D105C2semidirect
5. C3×C5×C72×C11C22semidirect
8. C72×D55D3semidirect
10. D55⋊D21C7direct (N × H)
12. C7×D231D5semidirect
16. C5×C72×C11C2×D3semidirect
17. C11×D105C2×C7semidirect
19. C5×D231C2×C7semidirect
22. C3×C7×D55D7semidirect
23. C3×C7×D55C2×C7semidirect
25. C3×C72×C11C2×D5semidirect
28. C7×D105D11semidirect
32. C3×C5×C7×C11C2×D7semidirect
33. C3×C5×C7×C11C22×C7semidirect
42. C7×D55D3×C7semidirect
43. C7×D55D21semidirect
47. C3×C5×C72C2×D11semidirect
50. C72×C11D3×D5semidirect
54. D231C7×D5semidirect
64. C5×C7×C11C2×D3×C7semidirect
65. C5×C7×C11C2×D21semidirect
68. C3×D55C7×D7semidirect
74. C5×C72D3×D11semidirect
76. C3×C7×C11D5×D7semidirect
77. C3×C7×C11C2×C7×D5semidirect
79. D105C7×D11semidirect
87. C3×C5×C11C2×C7×D7semidirect
95. C3×C72D5×D11semidirect
99. D55C7×D21semidirect
103. C3×C5×C7D7×D11semidirect
104. C3×C5×C7C2×C7×D11semidirect
111. C7×C11D3×C7×D5semidirect
112. C7×C11D5×D21semidirect
124. C5×C11C2×C7×D21semidirect
125. C72D15⋊D11semidirect
135. C5×C7D3×C7×D11semidirect
136. C5×C7D11×D21semidirect
137. C3×C11C7×D5×D7semidirect
147. C3×C7C7×D5×D11semidirect
148. C3×C7D35⋊D11semidirect
150. C3×C5C7×D7×D11semidirect
159. C11C7×D5×D21semidirect
164. C7C7×D15⋊D11semidirect
165. C7D55⋊D21direct (N × H)
169. C5C7×D11×D21semidirect
171. C3C7×D35⋊D11semidirect

Maximal subgroups

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

subgroupindex
C3×C72×D552
C5×C7×D2312
C7×C11×D1052
C7×D35⋊D113
C7×D11×D215
D55⋊D217
C7×D15⋊D117
C7×D5×D2111