Finite Group Databasebeta

← #13126283

Subgroups — #13126283

Order 1664.

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

normal subgroups only

This group has 346 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
1#11719240C211yesmaximal, characteristic
2#11719223C211yesmaximal, characteristic, complemented
3C13×#424C211yesmaximal, characteristic, complemented
4#11718795C212yesmaximal, complemented
5#11718775C212yesmaximal, complemented
6#11718509C212yesmaximal, complemented
7#11718508C212yesmaximal, complemented
8#11718502C212yesmaximal, complemented
9#11718490C212yesmaximal, complemented
10C2×C13×M16C2211yescharacteristic
11C22×C8×C13C2211yescharacteristic
12C13×#117C2211yescharacteristic
13#88184C2212yes—
14#88178C2212yes—
15C2×#6095C2212yes—
16C2×#6095C2212yes—
17#88148—22no—
18#88143—22no—
19#88138—22no—
20#88133—22no—
21#88128C2211yescharacteristic
22C4×D52C2212yes—
23#88124C2211yescharacteristic
24#88124C2211yescharacteristic
25#88123C2211yescharacteristic
26C4×Dic26C2212yes—
27C13×C4⋊C8C2212yes—
28C13×C4⋊C8C2212yes—
29#88061C2212yes—
30#88061C2212yes—
31#88058C2212yes—
32#88057C2212yes—
33#88056C2212yes—
34#88056C2212yes—
35C22×C4×C13C2311yescharacteristic
36C2×C22⋊D13—22no—
37C2×D52—22no—
38C2×D52C2312yes—
39C2×C4×D13—22no—
40C2×Dic26C2312yes—
41C13×M16—41no—
42C2×C8×C13—41no—
43C2×C8×C13C2312yes—
44C2×C8×C13C2312yes—
45C13×C4⋊C4D412yes—
46C13×C22⋊C4D412yes—
47C42×C13C2311yescharacteristic
48C42×C13C2311yescharacteristic
49C22⋊Dic13—22no—
50#6103—22no—
51#6103—22no—
52C4⋊Dic13—22no—
53C4⋊Dic13C2312yes—
54C4⋊Dic13C2312yes—
55#6101—22no—
56#6101—22no—
57#6101—22no—
58#6101—22no—
59C4×Dic13—22no—
60#6095—42no—
61#6095—42no—
62#3260—131nomaximal, Sylow
63C23×C13C2×D411yescharacteristic
64C22×D13—22no—
65C2×C4×C13—21no—
66C2×C4×C13—21no—
67C2×C4×C13C2×D412yes—
68C2×C4×C13C2×D411yescharacteristic
69C2×C4×C13C2×D412yes—
70C2×C4×C13C2411yescharacteristic
71C22⋊D13—82no—
72C2×Dic13—22no—
73C2×Dic13—22no—
74C2×Dic13—22no—
75D52—22no—
76D52—22no—
77D52—82no—
78C4×D13—82no—
79Dic26—22no—
80Dic26—22no—
81C8×C13—22no—
82C8×C13—22no—
83#541—131no—
84#540—131no—
85#479—132no—
86#478—132no—
87#468—132no—
88#465—132no—
89#461—132no—
90#460—132no—
91#424D1311yescharacteristic, complemented
92C22×C13—21no—
93C22×C13—22no—
94C22×C13C22×D411yescharacteristic
95C2×D13—42no—
96C2×D13—42no—
97C2×D13—42no—
98C4×C13—21no—
99C4×C13—22no—
100C4×C13—22no—
101C4×C13H(5,𝔽2)11yescharacteristic
102C4×C132−1+411yescharacteristic
103Dic13—42no—
104Dic13—42no—
105Dic13—42no—
106C2×SD16—132no—
107C2×SD16—132no—
108C2×M16C2×D1311yescharacteristic
109C22×C8C2×D1311yescharacteristic
110C4⋊Q8—131no—
111#127—131no—
112#126—262no—
113#125—131no—
114#125—131no—
115#125—262no—
116#123—262no—
117C22⋊Q8—132no—
118#121—132no—
119#121—262no—
120C4×Q8—132no—
121C4×D4—132no—
122#117C2×D1311yescharacteristic
123#107—132no—
124#106—132no—
125C4⋊C8C2×D1312yes—
126C4⋊C8C2×D1312yes—
127#103—132no—
128#103—132no—
129#102—132no—
130#102—132no—
131C2×C13—41no—
132C2×C13#53711yescharacteristic
133C2×C13#57712yes—
134D13—82no—
135C2×Q8—132no—
136C2×D4—132no—
137C2×D4—262no—
138C2×D4—262no—
139C22×C4—262no—
140C22×C4C22×D1311yescharacteristic
141SD16—522no—
142SD16—522no—
143M16—41no—
144C2×C8—41no—
145C2×C8C22×D1312yes—
146C2×C8C22×D1312yes—
147C4⋊C4—132no—
148C4⋊C4—132no—
149C4⋊C4—262no—
150C4⋊C4—262no—
151C4⋊C4—262no—
152C4⋊C4—262no—
153C4⋊C4—262no—
154C4⋊C4D5212yes—
155C22⋊C4—262no—
156C22⋊C4—262no—
157C22⋊C4—262no—
158C22⋊C4D5212yes—
159C42—262no—
160C42C22×D1311yescharacteristic
161C42C22×D1311yescharacteristic
162C13#326011yescharacteristic, complemented, Sylow
163C23—262no—
164C23C2×D5211yescharacteristic
165Q8—262no—
166Q8—262no—
167D4—262no—
168D4—262no—
169D4—1042no—
170D4—1042no—
171C2×C4—21no—
172C2×C4—21no—
173C2×C4—262no—
174C2×C4—262no—
175C2×C4—262no—
176C2×C4—1042no—
177C2×C4C2×D5212yes—
178C2×C4C2×D5212yes—
179C2×C4C2×D5211yescharacteristic
180C2×C4C23×D1311yescharacteristic
181C8—22no—
182C8—22no—
183C22—22no—
184C22—21no—
185C22—522no—
186C22—522no—
187C22—522no—
188C22C22×D5211yescharacteristic
189C4—22no—
190C4—22no—
191C4—21no—
192C4—522no—
193C4—522no—
194C4—522no—
195C4#8825111yescharacteristic
196C4#8825411yescharacteristic
197C2—41no—
198C2—1042no—
199C2#1171921511yescharacteristic
200C2#1171945612yes—
subgroupG/H
centerC22C22×D52
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#424C2
socleC22×C13C22×D4
prime radical#11719240C2
hypercenter#424D13
hypocenterC13#3260
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ #117 ◁ #424

Complements

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

NH ≅ G/Ntype
2. #11719223C2semidirect
3. C13×#424C2semidirect
4. #11718795C2semidirect
5. #11718775C2semidirect
6. #11718509C2semidirect
7. #11718508C2semidirect
8. #11718502C2semidirect
9. #11718490C2semidirect
91. #424D13semidirect
162. C13#3260semidirect

Maximal subgroups

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

subgroupindex
#117192402
#117192232
C13×#4242
#117187952
#117187752
#117185092
#117185082
#117185022
#117184902
#326013