Finite Group Databasebeta

← #27195159

Subgroups — #27195159

Order 13184.

292 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 292 conjugacy classes of subgroups — too many to draw. Only its 125 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×C4⋊(C103⋊C8)C211yesmaximal, characteristic
2C2×#15692945C212yesmaximal
3#20267657C211yesmaximal, characteristic
4#20267553C212yesmaximal
5C2×C4×Q8×C103C211yesmaximal, characteristic
6C22×C103⋊C8C2212yes—
7C2×C4⋊Dic103C2212yes—
8C4⋊(C103⋊C8)—22no—
9#15692945—24no—
10C103⋊#95—21no—
11C103⋊#95—21no—
12C22×Q8×C103C2211yescharacteristic
13C4×Q8×C103—22no—
14C4×Q8×C103C414yescomplemented
15C2×C4⋊C4×C103—21no—
16C2×C4⋊C4×C103C2211yescharacteristic
17C2×C42×C103—21no—
18C2×C42×C103C2211yescharacteristic
19C22×Dic103—22no—
20C2×C103⋊C8—22no—
21C2×C103⋊C8—22no—
22C2×C103⋊C8—22no—
23C4⋊Dic103—22no—
24C4⋊Dic103—22no—
25C2×Q8×C103—21no—
26C2×Q8×C103—21no—
27C2×Q8×C103—21no—
28C2×Q8×C103C2×C412yes—
29C2×Q8×C103D412yes—
30C2×Q8×C103Q812yes—
31C22×C4×C103—21no—
32C22×C4×C103—21no—
33C22×C4×C103D411yescharacteristic
34C22×C4×C103D411yescharacteristic
35C22×C4×C103C2311yescharacteristic
36C4⋊C4×C103—24no—
37C4⋊C4×C103—21no—
38C4⋊C4×C103C2×C412yes—
39C42×C103—24no—
40C42×C103C2×C412yes—
41C42×C103D412yes—
42C23×C103C2×D411yescharacteristic
43Q8×C103—22no—
44Q8×C103—22no—
45Q8×C103—22no—
46Q8×C103C4⋊C414yes—
47C2×C4×C103—22no—
48C2×C4×C103—22no—
49C2×C4×C103—22no—
50C2×C4×C103—22no—
51C2×C4×C103—22no—
52C2×C4×C103—22no—
53C2×C4×C103—42no—
54C2×C4×C103C22⋊C412yes—
55C2×C4×C103C22⋊C412yes—
56C2×C4×C103C22×C411yescharacteristic
57C2×C4×C103C2×D411yescharacteristic
58C2×C4×C103C2×D411yescharacteristic
59C2×C4×C103C2×Q811yescharacteristic
60C2×C4×C103#4111yescharacteristic
61C2×C4×C103#4111yescharacteristic
62C2×Dic103—42no—
63C2×Dic103—42no—
64C2×Dic103—42no—
65C103⋊C8—42no—
66C22×C103C2×C22⋊C411yescharacteristic
67C22×C103#12111yescharacteristic
68C22×C103C22⋊Q811yescharacteristic
69C22×C103#13512yes—
70C22×C103#13712yes—
71C4×C103—24no—
72C4×C103—22no—
73C4×C103—22no—
74C4×C103—42no—
75C4×C103C2×C4⋊C411yescharacteristic
76C4×C103#11711yescharacteristic
77C4×C103#12111yescharacteristic
78C4×C103C22⋊Q811yescharacteristic
79Dic103—82no—
80C2×C103#38011yescharacteristic
81C2×C103#41611yescharacteristic
82C2×C103#41911yescharacteristic
83C2×C103#46412yes—
84C2×C103#47912yes—
85#1805—1031nomaximal, Sylow
86C103#180511yescharacteristic, complemented, Sylow
87C2×C4×Q8D10311yescharacteristic
88C2×C4⋊C8—1031no—
89C2×#103—1032no—
90#382—1031no—
91#340—1032no—
92C22×Q8C2×D10311yescharacteristic
93C22×C8—1032no—
94C4×Q8—22no—
95C4×Q8Dic10314yescomplemented
96C2×C4⋊C4—21no—
97C2×C4⋊C4—1032no—
98C2×C4⋊C4C2×D10311yescharacteristic
99C2×C42—21no—
100C2×C42C2×D10311yescharacteristic
101C4⋊C8—2062no—
102#103—2064no—
103#95—2061no—
104#95—2061no—
105C2×Q8—21no—
106C2×Q8—21no—
107C2×Q8—21no—
108C2×Q8Dic20612yes—
109C2×Q8D41212yes—
110C2×Q8C2×Dic10312yes—
111C22×C4—21no—
112C22×C4—21no—
113C22×C4—2062no—
114C22×C4C22⋊D10311yescharacteristic
115C22×C4C22⋊D10311yescharacteristic
116C22×C4C22×D10311yescharacteristic
117C2×C8—2062no—
118C2×C8—2062no—
119C2×C8—2062no—
120C4⋊C4—24no—
121C4⋊C4—21no—
122C4⋊C4—2062no—
123C4⋊C4—2062no—
124C4⋊C4C2×Dic10312yes—
125C42—24no—
126C42C2×Dic10312yes—
127C42C22⋊D10312yes—
128C23C2×C22⋊D10311yescharacteristic
129Q8—22no—
130Q8—22no—
131Q8—22no—
132Q8C4⋊Dic10314yes—
133C2×C4—22no—
134C2×C4—22no—
135C2×C4—22no—
136C2×C4—22no—
137C2×C4—22no—
138C2×C4—22no—
139C2×C4—42no—
140C2×C4—4122no—
141C2×C4—4122no—
142C2×C4—4122no—
143C2×C4C22⋊Dic10312yes—
144C2×C4C22⋊Dic10312yes—
145C2×C4C22×Dic10311yescharacteristic
146C2×C4C2×C22⋊D10311yescharacteristic
147C2×C4C2×D41211yescharacteristic
148C2×C4C2×Dic20611yescharacteristic
149C2×C4#1311010511yescharacteristic
150C2×C4#1311010511yescharacteristic
151C8—4122no—
152C22C2×C22⋊Dic10311yescharacteristic
153C22#1569299511yescharacteristic
154C22#1569300011yescharacteristic
155C22#1569304112yes—
156C22#1569305212yes—
157C4—22no—
158C4—22no—
159C4—24no—
160C4—42no—
161C4—8242no—
162C4C2×C4⋊Dic10311yescharacteristic
163C4#1569298011yescharacteristic
164C4#1569299511yescharacteristic
165C4#1569300011yescharacteristic
166C2#2026765111yescharacteristic
167C2#2026778711yescharacteristic
168C2#2026780011yescharacteristic
169C2#2026801312yes—
170C2#2026809812yes—
subgroupG/H
centerC23C2×C22⋊D103
commutatorC2×C4×C103C22×C4
FrattiniC22×C4C22×D103
FittingC2×C4×Q8×C103C2
socle, prime radicalC23×C103C2×D4
cosocleC22×C4×C103C23
hypercenterC2×C4×Q8D103
hypocenterC103#1805
LCSG ▷ C2×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×Q8

Complements

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

NH ≅ G/Ntype
14. C4×Q8×C103C4semidirect
86. C103#1805semidirect
95. C4×Q8Dic103semidirect

Maximal subgroups

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

subgroupindex
C2×C4⋊(C103⋊C8)2
C2×#156929452
#202676572
#202675532
C2×C4×Q8×C1032
#1805103