Finite Group Databasebeta

← #13125128

Subgroups — #13125128

Order 1664.

382 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 382 conjugacy classes of subgroups — too many to draw. Only its 121 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
1#11719240C211yesmaximal, characteristic
2#11719221C211yesmaximal, characteristic, complemented
3C13×#433C211yesmaximal, characteristic, complemented
4#11718509C212yesmaximal, complemented
5#11718490C212yesmaximal, complemented
6#11718399C212yesmaximal, complemented
7#11718398C212yesmaximal, complemented
8#11718371C212yesmaximal, complemented
9C4×#6095C212yesmaximal, complemented
10C22×Dic26C2211yescharacteristic
11C13×#117C2211yescharacteristic
12#88184C2212yes—
13#88180C2211yescharacteristic
14C2×#6095C2212yes—
15C2×#6095C2212yes—
16#88148—22no—
17#88141—22no—
18#88138—22no—
19#88131—22no—
20#88128C2211yescharacteristic
21C4×D52C2212yes—
22#88124C2211yescharacteristic
23C4×Dic26C2212yes—
24C4×Dic26C2212yes—
25C13×C4⋊C8C2212yes—
26C13×C22⋊C8C2212yes—
27C13×#97C2211yescharacteristic
28C4×C8×C13C2211yescharacteristic
29#88061C2212yes—
30#88061C2212yes—
31#88058C2212yes—
32#88057C2212yes—
33#88056C2212yes—
34#88056C2212yes—
35C22×C4×C13C2311yescharacteristic
36C2×C22⋊D13—22no—
37C22×Dic13—21no—
38C2×D52—22no—
39C2×D52C2312yes—
40C2×C4×D13—22no—
41C2×Dic26—21no—
42C2×Dic26—24no—
43C2×Dic26C2312yes—
44C2×C8×C13C2312yes—
45C2×C8×C13C2312yes—
46C13×C4⋊C4D412yes—
47C13×C22⋊C4D412yes—
48C42×C13C2311yescharacteristic
49C42×C13C2311yescharacteristic
50C22⋊Dic13—21no—
51#6103—22no—
52#6103—22no—
53C4⋊Dic13C2312yes—
54C4⋊Dic13C2312yes—
55#6101—22no—
56#6101—22no—
57#6101—22no—
58C4×Dic13—22no—
59C4×Dic13—22no—
60C4×Dic13—21no—
61#6095—24no—
62#6095—24no—
63#3126—131nomaximal, Sylow
64C23×C13C2×D411yescharacteristic
65C22×D13—22no—
66C2×C4×C13—22no—
67C2×C4×C13C2×D412yes—
68C2×C4×C13C2×D412yes—
69C2×C4×C13C2×D411yescharacteristic
70C2×C4×C13C2411yescharacteristic
71C22⋊D13—82no—
72C2×Dic13—24no—
73C2×Dic13—22no—
74C2×Dic13—22no—
75C2×Dic13—22no—
76D52—22no—
77D52—22no—
78D52—82no—
79C4×D13—82no—
80Dic26—24no—
81Dic26—22no—
82Dic26#4114yes—
83C8×C13—22no—
84C8×C13—22no—
85#540—131no—
86#519—131no—
87#482—132no—
88#479—132no—
89#460—132no—
90#448—132no—
91#440—132no—
92C4×SD16—132no—
93#433D1311yescharacteristic, complemented
94C22×C13—21no—
95C22×C13—22no—
96C22×C13C22×D411yescharacteristic
97C2×D13—42no—
98C2×D13—42no—
99C2×D13—42no—
100C4×C13—21no—
101C4×C13—22no—
102C4×C13—22no—
103C4×C13C2×#4112yes—
104Dic13—24no—
105Dic13—42no—
106Dic13—42no—
107C22×Q8—131no—
108C2×SD16—132no—
109C2×SD16—132no—
110#127—131no—
111#125—131no—
112#123—262no—
113#121—132no—
114#121—262no—
115C4×Q8—132no—
116C4×Q8—132no—
117C4×Q8—262no—
118C4×D4—132no—
119#117—131no—
120#117—262no—
121#117C2×D1311yescharacteristic
122#107—132no—
123#106—132no—
124C4⋊C8C2×D1312yes—
125#103—132no—
126#103—132no—
127#102—132no—
128#102—132no—
129C22⋊C8C2×D1312yes—
130#97C2×D1311yescharacteristic
131C4×C8C2×D1311yescharacteristic
132C2×C13—41no—
133C2×C13#52511yescharacteristic
134C2×C13#57712yes—
135D13—82no—
136C2×Q8—132no—
137C2×Q8—264no—
138C2×Q8—261no—
139C2×D4—132no—
140C2×D4—262no—
141C2×D4—262no—
142C22×C4—261no—
143C22×C4—262no—
144C22×C4C22×D1311yescharacteristic
145SD16—264no—
146SD16—264no—
147C2×C8C22×D1312yes—
148C2×C8C22×D1312yes—
149C4⋊C4—132no—
150C4⋊C4—132no—
151C4⋊C4—262no—
152C4⋊C4—262no—
153C4⋊C4—262no—
154C4⋊C4D5212yes—
155C22⋊C4—261no—
156C22⋊C4—262no—
157C22⋊C4—262no—
158C22⋊C4D5212yes—
159C42—261no—
160C42—262no—
161C42—262no—
162C42C22×D1311yescharacteristic
163C42C22×D1311yescharacteristic
164C13#312611yescharacteristic, complemented, Sylow
165C23—262no—
166C23C2×D5211yescharacteristic
167Q8—134no—
168Q8—264no—
169Q8—262no—
170D4—262no—
171D4—262no—
172D4—1042no—
173D4—1042no—
174C2×C4—22no—
175C2×C4—264no—
176C2×C4—262no—
177C2×C4—262no—
178C2×C4—262no—
179C2×C4—1042no—
180C2×C4C2×D5212yes—
181C2×C4C2×D5212yes—
182C2×C4C2×D5211yescharacteristic
183C2×C4C23×D1311yescharacteristic
184C8—22no—
185C8—22no—
186C22—22no—
187C22—21no—
188C22—522no—
189C22—522no—
190C22—522no—
191C22C22×D5211yescharacteristic
192C4—22no—
193C4—22no—
194C4—21no—
195C4—264no—
196C4—522no—
197C4—522no—
198C4#41×D1312yes—
199C2—41no—
200C2—1042no—
201C2#1171922911yescharacteristic
202C2#1171945612yes—
subgroupG/H
centerC22C22×D52
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#433C2
socleC22×C13C22×D4
prime radical#11719240C2
hypercenter#433D13
hypocenterC13#3126
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ #117 ◁ #433

Complements

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

NH ≅ G/Ntype
2. #11719221C2semidirect
3. C13×#433C2semidirect
4. #11718509C2semidirect
5. #11718490C2semidirect
6. #11718399C2semidirect
7. #11718398C2semidirect
8. #11718371C2semidirect
9. C4×#6095C2semidirect
93. #433D13semidirect
164. C13#3126semidirect

Maximal subgroups

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

subgroupindex
#117192402
#117192212
C13×#4332
#117185092
#117184902
#117183992
#117183982
#117183712
C4×#60952
#312613