Finite Group Databasebeta

← #27195259

Subgroups — #27195259

Order 13184.

260 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 260 conjugacy classes of subgroups — too many to draw. Only its 117 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×Dic103⋊C8C212yesmaximal
2C42×Dic103C211yesmaximal, characteristic
3#20267546C211yesmaximal, characteristic
4#20267545C212yesmaximal
5#336×C103C211yesmaximal, characteristic
6C22×C103⋊C8C2212yes—
7C2×C4×Dic103C411yescharacteristic
8C2×C4×Dic103C411yescharacteristic
9C2×C4×Dic103C411yescharacteristic
10C2×C4×Dic103C411yescharacteristic
11C2×C4×Dic103C2211yescharacteristic
12C2×C4×Dic103C2211yescharacteristic
13Dic103⋊C8—24no—
14C22×C8×C103C2212yes—
15C2×C42×C103C2211yescharacteristic
16C22×Dic103C2×C411yescharacteristic
17C22×Dic103C2×C411yescharacteristic
18C22×Dic103C2×C411yescharacteristic
19C22×Dic103C2×C411yescharacteristic
20C2×C103⋊C8—22no—
21C2×C103⋊C8—22no—
22C2×C103⋊C8—22no—
23C4×Dic103—22no—
24C4×Dic103—22no—
25C4×Dic103—22no—
26C4×Dic103—22no—
27C4×Dic103C814yescomplemented
28C4×Dic103D412yes—
29C4×Dic103Q812yes—
30C22×C4×C103C2×C411yescharacteristic
31C22×C4×C103C2×C411yescharacteristic
32C22×C4×C103C2311yescharacteristic
33C2×C8×C103—22no—
34C2×C8×C103—22no—
35C2×C8×C103—22no—
36C42×C103—22no—
37C23×C103C22×C411yescharacteristic
38C2×C4×C103—21no—
39C2×C4×C103—21no—
40C2×C4×C103—21no—
41C2×C4×C103—21no—
42C2×C4×C103C2×C812yes—
43C2×C4×C103M1612yes—
44C2×C4×C103C2×D411yescharacteristic
45C2×C4×C103C2×Q811yescharacteristic
46C2×C4×C103#4112yes—
47C2×C4×C103#4112yes—
48C2×Dic103—21no—
49C2×Dic103—21no—
50C2×Dic103—21no—
51C2×Dic103—21no—
52C2×Dic103—21no—
53C2×Dic103—21no—
54C2×Dic103C4⋊C412yes—
55C2×Dic103C4⋊C412yes—
56C2×Dic103C2×C812yes—
57C2×Dic103C2×C812yes—
58C2×Dic103M1612yes—
59C2×Dic103M1612yes—
60C8×C103—42no—
61C103⋊C8—42no—
62C22×C103C2×C4⋊C411yescharacteristic
63C22×C103#11711yescharacteristic
64C22×C103#11711yescharacteristic
65C22×C103C22×C811yescharacteristic
66C22×C103C2×M1611yescharacteristic
67C22×C103C2×M1611yescharacteristic
68C22×C103C2×M1611yescharacteristic
69C4×C103—22no—
70C4×C103—22no—
71C4×C103#12412yes—
72C4×C103#12512yes—
73Dic103—22no—
74Dic103—22no—
75Dic103—22no—
76Dic103C4⋊C814yes—
77C2×C103#38211yescharacteristic
78C2×C103C2×C4⋊C811yescharacteristic
79C2×C103#42311yescharacteristic
80C2×C103#43111yescharacteristic
81C2×C103#43111yescharacteristic
82C2×C103#43211yescharacteristic
83C2×C103#43211yescharacteristic
84#1831—1031nomaximal, Sylow
85C103#183111yescharacteristic, complemented, Sylow
86C2×C4⋊C8—1032no—
87C43—1031no—
88#336—1032no—
89#336—1031no—
90#336D10311yescharacteristic
91C22×C8—1032no—
92C22×C8C2×D10312yes—
93C2×C42—1031no—
94C2×C42—1031no—
95C2×C42—1031no—
96C2×C42—1031no—
97C2×C42—1031no—
98C2×C42—1031no—
99C2×C42C2×D10311yescharacteristic
100C4⋊C8—2064no—
101C22×C4—1031no—
102C22×C4—1031no—
103C22×C4—1031no—
104C22×C4—1031no—
105C22×C4C4×D10311yescharacteristic
106C22×C4C4×D10311yescharacteristic
107C22×C4C22×D10311yescharacteristic
108C2×C8—22no—
109C2×C8—22no—
110C2×C8—22no—
111C2×C8—2062no—
112C2×C8—2062no—
113C2×C8—2062no—
114C42—22no—
115C42—1034no—
116C42—1032no—
117C42—1032no—
118C42—2062no—
119C42—2062no—
120C42—2062no—
121C42—2062no—
122C23C2×C4×D10311yescharacteristic
123C2×C4—21no—
124C2×C4—21no—
125C2×C4—21no—
126C2×C4—21no—
127C2×C4—1032no—
128C2×C4—1032no—
129C2×C4—1032no—
130C2×C4—1032no—
131C2×C4—1032no—
132C2×C4—1032no—
133C2×C4—2061no—
134C2×C4—2061no—
135C2×C4—2061no—
136C2×C4—2061no—
137C2×C4—2061no—
138C2×C4—2061no—
139C2×C4C8×D10312yes—
140C2×C4#1311008812yes—
141C2×C4D4×D10311yescharacteristic
142C2×C4Q8×D10311yescharacteristic
143C2×C4#1311010412yes—
144C2×C4#1311010512yes—
145C8—42no—
146C8—4122no—
147C22C4⋊C4×D10311yescharacteristic
148C22#1569297711yescharacteristic
149C22#1569297811yescharacteristic
150C22C2×C8×D10311yescharacteristic
151C22M16×D10311yescharacteristic
152C22M16×D10311yescharacteristic
153C22C2×#1311008811yescharacteristic
154C4—22no—
155C4—22no—
156C4—1034no—
157C4—2062no—
158C4—2062no—
159C4—2062no—
160C4#1569300712yes—
161C4#1569301112yes—
162C2#2026765511yescharacteristic
163C2C4⋊C8×D10311yescharacteristic
164C2#2026781311yescharacteristic
165C2#2026784111yescharacteristic
166C2#2026784211yescharacteristic
167C2#2026784511yescharacteristic
168C2#2026784611yescharacteristic
subgroupG/H
center, FrattiniC22×C4C22×D103
commutatorC22×C103C22×C8
Fitting#336×C103C2
socle, prime radicalC23×C103C22×C4
cosocleC22×C4×C103C23
hypercenter#336D103
hypocenterC103#1831
LCSG ▷ C22×C103 ▷ C103
UCSC1 ◁ C22×C4 ◁ #336

Complements

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

NH ≅ G/Ntype
27. C4×Dic103C8semidirect
85. C103#1831semidirect

Maximal subgroups

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

subgroupindex
C2×Dic103⋊C82
C42×Dic1032
#202675462
#202675452
#336×C1032
#1831103