Finite Group Databasebeta

← #13123183

Subgroups — #13123183

Order 1664.

644 conjugacy classes of subgroups; only the 209 normal subgroups are shown.

normal subgroups only

This group has 644 conjugacy classes of subgroups — too many to draw. Only its 209 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×C13×C4⋊Q8C211yesmaximal, characteristic, complemented
2C2×#88200C212yesmaximal
3C2×C42×D13C211yesmaximal, characteristic
4#11718891C212yesmaximal, complemented
5#11718648C214yesmaximal
6#11718634C214yesmaximal, complemented
7#11718596C211yesmaximal, characteristic, complemented
8C22×Q8×C13C2212yes—
9C22×C4×D13C2211yescharacteristic
10C22×C4×D13C2212yes—
11C13×C4⋊Q8—24no—
12C2×C13×C4⋊C4C2214yes—
13C2×C42×C13C2211yescharacteristic
14#88200—28no—
15C2×#6103C2214yes—
16C2×C4⋊Dic13C2212yes—
17C2×C4⋊Dic13C2214yes—
18C2×#6101C2214yes—
19C2×C4×Dic13C2212yes—
20C2×C4×Dic13C2211yescharacteristic
21C42×D13—24no—
22#88071C2218yes—
23C23×D13C2311yescharacteristic
24C2×Q8×C13—24no—
25C2×Q8×C13—24no—
26C2×Q8×C13—24no—
27C22×C4×C13C2314yes—
28C22×C4×C13C2311yescharacteristic
29C22×C4×C13C2312yes—
30C22×Dic13C2314yes—
31C22×Dic13C2311yescharacteristic
32C22×Dic13C2312yes—
33C2×C4×D13—22no—
34C2×C4×D13—24no—
35C2×C4×D13—22no—
36C2×C4×D13—24no—
37C2×C4×D13D414yes—
38C2×C4×D13Q818yescomplemented
39C13×C4⋊C4—28no—
40C42×C13D414yes—
41#6103—28no—
42C4⋊Dic13—24no—
43C4⋊Dic13—28no—
44#6101—28no—
45C4×Dic13—22no—
46C4×Dic13—24no—
47#2857—131nomaximal, Sylow
48C23×C13C2411yescharacteristic
49C22×D13—21no—
50C22×D13—21no—
51C22×D13—22no—
52C22×D13C2×D412yes—
53C22×D13C2×Q814yes—
54Q8×C13—48no—
55C2×C4×C13—24no—
56C2×C4×C13—24no—
57C2×C4×C13—24no—
58C2×C4×C13C2×D412yes—
59C2×C4×C13C2×D412yes—
60C2×C4×C13C2×D414yes—
61C2×C4×C13C2×Q814yes—
62C2×C4×C13#4112yes—
63C2×C4×C13#4114yes—
64C2×Dic13—21no—
65C2×Dic13—22no—
66C2×Dic13—21no—
67C2×Dic13—22no—
68C2×Dic13—24no—
69C2×Dic13—28no—
70C2×Dic13C2×D412yes—
71C2×Dic13C2×Q814yes—
72C4×D13—28no—
73C4×D13—216no—
74C2×C4⋊Q8D1311yescharacteristic, complemented
75C2×C22⋊Q8—132no—
76C22×C42—131no—
77#391—132no—
78#389—134no—
79#384—131no—
80#380—134no—
81C22×C13C22×D411yescharacteristic
82C22×C13C22×D411yescharacteristic
83C22×C13C22×Q812yes—
84C22×C13C2×#4111yescharacteristic
85C22×C13C2×#4112yes—
86C2×D13—22no—
87C2×D13—24no—
88C2×D13—22no—
89C2×D13—24no—
90C2×D13C4⋊Q814yescomplemented
91C4×C13—44no—
92C4×C13#12114yes—
93C4×C13C22⋊Q818yescomplemented
94Dic13—22no—
95Dic13—24no—
96Dic13—44no—
97C22×Q8C2×D1312yes—
98C23×C4—131no—
99C23×C4—132no—
100C4⋊Q8—24no—
101C22⋊Q8—268no—
102C2×C4⋊C4—134no—
103C2×C4⋊C4—132no—
104C2×C4⋊C4—134no—
105C2×C4⋊C4C2×D1314yes—
106C2×C22⋊C4—134no—
107C2×C42—132no—
108C2×C42—131no—
109C2×C42—264no—
110C2×C42C2×D1311yescharacteristic
111#95—138no—
112C2×C13C2×#12111yescharacteristic
113C2×C13C2×C22⋊Q812yes—
114C2×C13C2×C4⋊Q811yescharacteristic
115C2×C13#53211yescharacteristic
116C2×C13#53312yes—
117D13—24no—
118C24—131no—
119C2×Q8—24no—
120C2×Q8—24no—
121C2×Q8—24no—
122C22×C4—132no—
123C22×C4—131no—
124C22×C4—134no—
125C22×C4—138no—
126C22×C4—134no—
127C22×C4—262no—
128C22×C4—264no—
129C22×C4—262no—
130C22×C4—264no—
131C22×C4C22×D1314yes—
132C22×C4C22×D1311yescharacteristic
133C22×C4C22×D1312yes—
134C4⋊C4—28no—
135C4⋊C4—268no—
136C4⋊C4—264no—
137C4⋊C4—268no—
138C22⋊C4—268no—
139C42—262no—
140C42—264no—
141C42C22⋊D1314yes—
142C13#285711yescharacteristic, complemented, Sylow
143C23—132no—
144C23—134no—
145C23—261no—
146C23—262no—
147C23—261no—
148C23C23×D1311yescharacteristic
149Q8—48no—
150C2×C4—24no—
151C2×C4—24no—
152C2×C4—24no—
153C2×C4—132no—
154C2×C4—134no—
155C2×C4—261no—
156C2×C4—262no—
157C2×C4—261no—
158C2×C4—262no—
159C2×C4—268no—
160C2×C4—2616no—
161C2×C4—264no—
162C2×C4—268no—
163C2×C4D4×D1312yes—
164C2×C4#612912yes—
165C2×C4Q8×D1314yes—
166C2×C4#613114yes—
167C2×C4C2×C22⋊D1312yes—
168C2×C4C2×C22⋊D1314yes—
169C22—134no—
170C22—262no—
171C22—264no—
172C22—262no—
173C22—264no—
174C22C2×D4×D1311yescharacteristic
175C22C2×#612911yescharacteristic
176C22C2×Q8×D1312yes—
177C22C2×#613112yes—
178C22C22×C22⋊D1311yescharacteristic
179C4—44no—
180C4—262no—
181C4—264no—
182C4—524no—
183C4#8819214yes—
184C4#8820018yescomplemented
185C2—264no—
186C2D13×C4⋊Q811yescharacteristic
187C2#1171943011yescharacteristic
188C2#1171943312yes—
189C2C2×#8819211yescharacteristic
190C2C2×#8820012yes—
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, cosocleC23×C13C24
FittingC2×C13×C4⋊Q8C2
prime radicalC23×D13C23
hypercenterC2×C4⋊Q8D13
hypocenterC13#2857
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C4⋊Q8

Complements

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

NH ≅ G/Ntype
1. C2×C13×C4⋊Q8C2semidirect
4. #11718891C2semidirect
6. #11718634C2semidirect
7. #11718596C2semidirect
38. C2×C4×D13Q8semidirect
74. C2×C4⋊Q8D13semidirect
90. C2×D13C4⋊Q8semidirect
93. C4×C13C22⋊Q8semidirect
142. C13#2857semidirect
184. C4#88200semidirect

Maximal subgroups

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

subgroupindex
C2×C13×C4⋊Q82
C2×#882002
C2×C42×D132
#117188912
#117186482
#117186342
#117185962
#285713