Finite Group Databasebeta

← #487×D103 #27205452

Subgroups — #487×D103 #27205452

Order 13184.

424 conjugacy classes of subgroups; only the 145 normal subgroups are shown.

normal subgroups only

This group has 424 conjugacy classes of subgroups — too many to draw. Only its 145 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
1C4⋊Q8×D103C211yesmaximal, characteristic
2C4⋊Q8×D103C211yesmaximal, characteristic
3#20268143C211yesmaximal, characteristic, complemented
4#20268142C211yesmaximal, characteristic, complemented
5#20268141C211yesmaximal, characteristic, complemented
6#20268140C214yesmaximal, complemented
7#103×D103C214yesmaximal
8C4×C8×D103C211yesmaximal, characteristic
9#487×C103C211yesmaximal, characteristic, complemented
10C2×Q8×D103—21no—
11C2×Q8×D103C2212yes—
12C2×C8×D103C2212yes—
13#15693021C2211yescharacteristic
14#15693021C2211yescharacteristic
15#15693020—21no—
16#15693020—21no—
17#15693020—21no—
18#15693020C2212yes—
19#15693019—21no—
20#15693019C2212yes—
21C4⋊C4×D103—21no—
22C4⋊C4×D103—21no—
23C4⋊C4×D103—21no—
24C4⋊C4×D103C2212yes—
25C42×D103C2211yescharacteristic
26#15692946C2214yes—
27#15692945C2214yes—
28#15692944C2214yes—
29C4×C103⋊C8C2211yescharacteristic
30C8×Dic103C2212yes—
31C4⋊Q8×C103C2211yescharacteristic
32C4⋊Q8×C103C2211yescharacteristic
33#103×C103C2214yes—
34C4×C8×C103C2211yescharacteristic
35C2×Dic206—21no—
36C2×Dic206—22no—
37C2×Dic206—22no—
38C2×Dic206C2312yes—
39Q8×D103—28no—
40Q8×D103—44no—
41C2×C4×D103—22no—
42C2×C4×D103—22no—
43C2×C4×D103D411yescharacteristic
44C2×C4×D103D411yescharacteristic
45C2×C4×D103C2311yescharacteristic
46C2×C103⋊C8C2312yes—
47C8×D103—24no—
48C4⋊Dic103—21no—
49C4⋊Dic103—21no—
50C4⋊Dic103—21no—
51C4⋊Dic103C2312yes—
52Dic103⋊C4—22no—
53Dic103⋊C4—22no—
54Dic103⋊C4—22no—
55Dic103⋊C4—22no—
56C4×Dic103D411yescharacteristic
57C4×Dic103D411yescharacteristic
58C4×Dic103C2311yescharacteristic
59C2×Q8×C103—21no—
60C2×Q8×C103C2312yes—
61C2×C8×C103C2312yes—
62C4⋊C4×C103—21no—
63C4⋊C4×C103—21no—
64C4⋊C4×C103—21no—
65C4⋊C4×C103C2312yes—
66C42×C103C2311yescharacteristic
67C22×D103C2×D411yescharacteristic
68Q8×C103—24no—
69Q8×C103—42no—
70C2×C4×C103—22no—
71C2×C4×C103—22no—
72C2×C4×C103C2×D411yescharacteristic
73C2×C4×C103C2×D411yescharacteristic
74C2×C4×C103C2411yescharacteristic
75C2×Dic103—22no—
76C2×Dic103—22no—
77C2×Dic103C2×D411yescharacteristic
78C2×Dic103C2×D411yescharacteristic
79C2×Dic103C2×D411yescharacteristic
80C4×D103—44no—
81C4×D103—44no—
82C4×D103SD1614yes—
83C4×D103Q1614yes—
84C4×D103#4114yes—
85Dic206—24no—
86Dic206—42no—
87Dic206—44no—
88Dic206—44no—
89C8×C103—22no—
90C103⋊C8—22no—
91C22×C103C22×D411yescharacteristic
92C2×D103#12412yes—
93C2×D103C2×SD1612yes—
94C2×D103C2×Q1612yes—
95C4×C103—42no—
96C4×C103—42no—
97C4×C103C2×SD1612yes—
98C4×C103C2×Q1612yes—
99C4×C103C2×#4112yes—
100Dic103—42no—
101Dic103—42no—
102Dic103#12412yes—
103Dic103C2×SD1612yes—
104Dic103C2×Q1612yes—
105C2×C103C2×#12411yescharacteristic
106C2×C103C22×SD1611yescharacteristic
107C2×C103C22×Q1611yescharacteristic
108D103#48714yesdirect product factor
109C2×#487—1031nomaximal, Sylow
110C103C2×#48711yescharacteristic, complemented, Sylow
111C2×C4⋊Q8—1031no—
112C2×C4⋊Q8—1031no—
113#487—1031no—
114#487—1031no—
115#487—1034no—
116#487—1031no—
117#487D10311yescharacteristic, direct product factor
118C2×#103—1034no—
119C2×C4×C8—1031no—
120C22×Q8—1032no—
121C22×Q8—2061no—
122C22×C8—1032no—
123C4⋊Q8—1032no—
124C4⋊Q8—1032no—
125C4⋊Q8—1031no—
126C4⋊Q8—1031no—
127C4⋊Q8—2061no—
128C4⋊Q8—2061no—
129C4⋊Q8—2061no—
130C4⋊Q8—2061no—
131C4⋊Q8C2×D10311yescharacteristic
132C4⋊Q8C2×D10311yescharacteristic
133C2×C4⋊C4—1032no—
134C2×C4⋊C4—2061no—
135C2×C4⋊C4—2061no—
136C2×C4⋊C4—2061no—
137C2×C42—1031no—
138#103—1034no—
139#103—1034no—
140#103—1034no—
141#103C2×D10314yes—
142C4×C8—1032no—
143C4×C8—1031no—
144C4×C8C2×D10311yescharacteristic
145C2×Q8—21no—
146C2×Q8—1032no—
147C2×Q8—4124no—
148C2×Q8—2062no—
149C2×Q8—2062no—
150C2×Q8—2068no—
151C2×Q8—2061no—
152C2×Q8C22×D10312yes—
153C22×C4—1031no—
154C22×C4—1031no—
155C22×C4—1031no—
156C22×C4—2062no—
157C22×C4—2062no—
158C2×C8—1032no—
159C2×C8—2064no—
160C2×C8C22×D10312yes—
161C4⋊C4—21no—
162C4⋊C4—21no—
163C4⋊C4—21no—
164C4⋊C4—1032no—
165C4⋊C4—2062no—
166C4⋊C4—2062no—
167C4⋊C4—2062no—
168C4⋊C4—2062no—
169C4⋊C4—2061no—
170C4⋊C4—2061no—
171C4⋊C4—2061no—
172C4⋊C4C22×D10312yes—
173C42—1031no—
174C42—1031no—
175C42—1031no—
176C42C22×D10311yescharacteristic
177C23—1031no—
178Q8—24no—
179Q8—42no—
180Q8—4124no—
181Q8—4124no—
182Q8—4122no—
183Q8—2064no—
184C2×C4—22no—
185C2×C4—22no—
186C2×C4—1031no—
187C2×C4—1031no—
188C2×C4—1031no—
189C2×C4—1034no—
190C2×C4—1034no—
191C2×C4—1034no—
192C2×C4—4124no—
193C2×C4—4124no—
194C2×C4—2062no—
195C2×C4—2062no—
196C2×C4D4×D10311yescharacteristic
197C2×C4D4×D10311yescharacteristic
198C2×C4C23×D10311yescharacteristic
199C8—22no—
200C8—2062no—
201C22—1032no—
202C22—1032no—
203C22—1032no—
204C22C2×D4×D10311yescharacteristic
205C4—42no—
206C4—42no—
207C4—1032no—
208C4—1032no—
209C4—1032no—
210C4—4122no—
211C4—4122no—
212C4SD16×D10312yes—
213C4Q16×D10312yes—
214C4#41×D10312yes—
215C2—1034no—
216C2#124×D10311yescharacteristic
217C2C2×SD16×D10311yescharacteristic
218C2C2×Q16×D10311yescharacteristic
subgroupG/H
centerC22C2×D4×D103
commutator, cosocleC2×C4×C103C24
FrattiniC2×C4C23×D103
Fitting#487×C103C2
socleC22×C103C22×D4
prime radicalC22×D103C2×D4
hypercenter#487D103
hypocenterC103C2×#487
LCSG ▷ C2×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C22 ◁ C42 ◁ #487

Complements

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

NH ≅ G/Ntype
3. #20268143C2semidirect
4. #20268142C2semidirect
5. #20268141C2semidirect
6. #20268140C2semidirect
9. #487×C103C2semidirect
108. D103#487direct (N × H)
110. C103C2×#487semidirect
117. #487D103direct (N × H)

Maximal subgroups

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

subgroupindex
C4⋊Q8×D1032
#202681432
#202681422
#202681412
#202681402
#103×D1032
C4×C8×D1032
#487×C1032
C2×#487103