Finite Group Databasebeta

← #13126277

Subgroups — #13126277

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
1C13×#541C211yesmaximal, characteristic, complemented
2#11719240C211yesmaximal, characteristic
3#11718744C212yesmaximal, complemented
4#11718727C212yesmaximal, complemented
5#11718710C212yesmaximal, complemented
6#11718709C212yesmaximal, complemented
7#11718688C212yesmaximal, complemented
8#11718683C212yesmaximal, complemented
9#11718660C211yesmaximal, characteristic, complemented
10C13×C4⋊Q8C2211yescharacteristic
11C13×#126—22no—
12C13×#125—22no—
13C13×#125C2211yescharacteristic
14C13×C22⋊Q8C2212yes—
15C4×Q8×C13C2212yes—
16C13×#117C2211yescharacteristic
17C2×#6106C2212yes—
18C2×#6106C2212yes—
19#88184C2212yes—
20C2×#6099C2211yescharacteristic
21C22×#1055C2211yescharacteristic
22#88148—22no—
23#88138—22no—
24#88128C2211yescharacteristic
25C4×D52C2212yes—
26#88124C2211yescharacteristic
27#88075C2212yes—
28#88075C2212yes—
29#88049C2212yes—
30#88049C2212yes—
31#88048C2212yes—
32#88047C2212yes—
33C4⋊#1055C2212yes—
34C4⋊#1055C2212yes—
35C2×Q8×C13C2312yes—
36C22×C4×C13C2311yescharacteristic
37C2×C22⋊D13—22no—
38C2×D52—22no—
39C2×D52C2312yes—
40C2×C4×D13—22no—
41C13×C4⋊C4—22no—
42C13×C4⋊C4—22no—
43C13×C4⋊C4—22no—
44C13×C4⋊C4—22no—
45C13×C4⋊C4D412yes—
46C13×C4⋊C4C2312yes—
47C13×C22⋊C4—22no—
48C13×C22⋊C4D412yes—
49C42×C13—22no—
50C42×C13C2311yescharacteristic
51C42×C13C2311yescharacteristic
52#6106—42no—
53#6106—42no—
54#6103—22no—
55#6103—22no—
56C4⋊Dic13C2312yes—
57#6101—22no—
58#6099—41no—
59C2×#1055—41no—
60C2×#1055C2312yes—
61C2×#1055C2312yes—
62#3260—131nomaximal, Sylow
63C23×C13C2×D411yescharacteristic
64C22×D13—22no—
65Q8×C13—22no—
66Q8×C13—22no—
67C2×C4×C13—21no—
68C2×C4×C13—21no—
69C2×C4×C13—22no—
70C2×C4×C13—22no—
71C2×C4×C13C2×D412yes—
72C2×C4×C13C2×D411yescharacteristic
73C2×C4×C13C2×D412yes—
74C2×C4×C13C2411yescharacteristic
75C22⋊D13—82no—
76C2×Dic13—22no—
77D52—22no—
78D52—22no—
79D52—82no—
80C4×D13—82no—
81#1055—22no—
82#1055—22no—
83#541D1311yescharacteristic, complemented
84#540—131no—
85#479—132no—
86#478—132no—
87#468—132no—
88#465—132no—
89#461—132no—
90#460—132no—
91#424—131no—
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×C13—42no—
102C4×C13—42no—
103C4×C13H(5,𝔽2)11yescharacteristic
104C4×C132−1+411yescharacteristic
105Dic13—42no—
106C2×SD16—132no—
107C2×SD16—132no—
108C2×M16—131no—
109C22×C8—131no—
110C4⋊Q8C2×D1311yescharacteristic
111#127—131no—
112#126—22no—
113#125—22no—
114#125—131no—
115#125C2×D1311yescharacteristic
116#123—262no—
117C22⋊Q8C2×D1312yes—
118#121—132no—
119#121—262no—
120C4×Q8C2×D1312yes—
121C4×D4—132no—
122#117C2×D1311yescharacteristic
123#107—132no—
124#106—132no—
125C4⋊C8—132no—
126C4⋊C8—132no—
127#103—132no—
128#103—132no—
129#102—132no—
130#102—132no—
131C2×C13—41no—
132C2×C13#53711yescharacteristic
133C2×C13#57712yes—
134D13—82no—
135C2×Q8C22×D1312yes—
136C2×D4—132no—
137C2×D4—262no—
138C2×D4—262no—
139C22×C4—262no—
140C22×C4C22×D1311yescharacteristic
141SD16—522no—
142SD16—522no—
143M16—521no—
144C2×C8—132no—
145C2×C8—132no—
146C2×C8—521no—
147C4⋊C4—22no—
148C4⋊C4—22no—
149C4⋊C4—22no—
150C4⋊C4—22no—
151C4⋊C4—132no—
152C4⋊C4—262no—
153C4⋊C4C22⋊D1312yes—
154C4⋊C4C22×D1312yes—
155C22⋊C4—22no—
156C22⋊C4—262no—
157C22⋊C4—262no—
158C22⋊C4C22⋊D1312yes—
159C42—22no—
160C42C22×D1311yescharacteristic
161C42C22×D1311yescharacteristic
162C13#326011yescharacteristic, complemented, Sylow
163C23—262no—
164C23C2×C22⋊D1311yescharacteristic
165Q8—22no—
166Q8—22no—
167D4—262no—
168D4—262no—
169D4—1042no—
170D4—1042no—
171C2×C4—21no—
172C2×C4—21no—
173C2×C4—22no—
174C2×C4—22no—
175C2×C4—262no—
176C2×C4—1042no—
177C2×C4C2×C22⋊D1312yes—
178C2×C4C2×C22⋊D1312yes—
179C2×C4C2×C22⋊D1311yescharacteristic
180C2×C4C23×D1311yescharacteristic
181C8—262no—
182C8—262no—
183C22—21no—
184C22—22no—
185C22—522no—
186C22—522no—
187C22—522no—
188C22C22×C22⋊D1311yescharacteristic
189C4—21no—
190C4—22no—
191C4—22no—
192C4—42no—
193C4—42no—
194C4—522no—
195C4#8825611yescharacteristic
196C4#8825711yescharacteristic
197C2—41no—
198C2—1042no—
199C2#1171953811yescharacteristic
200C2#1171954212yes—
subgroupG/H
centerC22C22×C22⋊D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#541C2
socleC22×C13C22×D4
prime radical#11719240C2
hypercenter#541D13
hypocenterC13#3260
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ #117 ◁ #541

Complements

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

NH ≅ G/Ntype
1. C13×#541C2semidirect
3. #11718744C2semidirect
4. #11718727C2semidirect
5. #11718710C2semidirect
6. #11718709C2semidirect
7. #11718688C2semidirect
8. #11718683C2semidirect
9. #11718660C2semidirect
83. #541D13semidirect
162. C13#3260semidirect

Maximal subgroups

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

subgroupindex
C13×#5412
#117192402
#117187442
#117187272
#117187102
#117187092
#117186882
#117186832
#117186602
#326013