Finite Group Databasebeta

← #15767903

Subgroups — #15767903

Order 3328.

372 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 372 conjugacy classes of subgroups — too many to draw. Only its 97 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#13115634C211yesmaximal, characteristic
2#13113608C212yesmaximal, complemented
3#13113260C212yesmaximal
4#13112667C211yesmaximal, characteristic, complemented
5C13×#1849C211yesmaximal, characteristic, complemented
6C2×C4×D52C2211yescharacteristic
7C2×C13×#108—22no—
8C13×#423C2212yes—
9C2×C13×#97C2211yescharacteristic
10C2×#88060—22no—
11#11718586C2212yes—
12C2×C4⋊#1055C2211yescharacteristic
13#11718075—24no—
14#11718072—24no—
15C22×D52Q811yescharacteristic
16C22×C4×D13—21no—
17C2×C13×M16—22no—
18C22×C8×C13D412yes—
19C2×C42×C13C2311yescharacteristic
20C2×#6103—21no—
21C2×C4⋊Dic13Q811yescharacteristic
22C22×#1055—21no—
23C4×D52—22no—
24C4×D52—22no—
25C13×#108—44no—
26C13×C4⋊C8—22no—
27C13×C4⋊C8—22no—
28C13×#97—22no—
29C22⋊#1055—22no—
30#88060—44no—
31C4⋊#1055—22no—
32C4⋊#1055—22no—
33C4×#1055D414yes—
34#10661—131nomaximal, Sylow
35C23×D13—21no—
36C22×C4×C13C2×D411yescharacteristic
37C22×C4×C13C2×Q811yescharacteristic
38C22×C4×C13#4111yescharacteristic
39C22×Dic13—21no—
40C2×D52—22no—
41C2×D52—42no—
42C2×C4×D13—41no—
43C2×C4×D13—41no—
44C2×C4×D13—42no—
45C2×C4×D13—42no—
46C13×M16—44no—
47C2×C8×C13—22no—
48C2×C8×C13—22no—
49C2×C8×C13—42no—
50C2×C8×C13SD1614yes—
51C42×C13C2×D412yes—
52C42×C13#4112yes—
53#6103—42no—
54C4⋊Dic13—22no—
55C2×#1055—24no—
56C2×#1055—41no—
57C2×#1055—42no—
58#1955—131no—
59#1849D1311yescharacteristic, complemented
60#1570—132no—
61#1486—132no—
62#1275—131no—
63C23×C13C22⋊Q811yescharacteristic
64C22×D13—22no—
65C22×D13—41no—
66C22×D13—42no—
67C22×D13—41no—
68C22×D13—42no—
69C2×C4×C13—41no—
70C2×C4×C13—41no—
71C2×C4×C13C22⋊Q812yes—
72C2×C4×C13#12312yes—
73C2×C4×C13#12311yescharacteristic
74C2×C4×C13#12711yescharacteristic
75C2×C4×C13C2×SD1612yes—
76C2×C4×C13AGL(1,ℤ/8)12yes—
77C2×Dic13—41no—
78C2×Dic13—42no—
79D52—24no—
80D52—42no—
81C4×D13—82no—
82C4×D13—81no—
83C4×D13—81no—
84C8×C13—24no—
85C8×C13—82no—
86#1055—44no—
87#1055—81no—
88C2×C4×D4—131no—
89#431—132no—
90C2×#108—22no—
91#423C2×D1312yes—
92C2×C4⋊C8—131no—
93C2×C22⋊C8—262no—
94C2×#97C2×D1311yescharacteristic
95#334—264no—
96D4⋊C8—264no—
97C22×C13—21no—
98C22×C13—21no—
99C22×C13#39911yescharacteristic
100C22×C13#47612yes—
101C2×D13—44no—
102C2×D13—42no—
103C2×D13—82no—
104C2×D13—81no—
105C2×D13—81no—
106C4×C13—22no—
107C4×C13—22no—
108C4×C13#48112yes—
109C4×C13#49211yescharacteristic
110C4×C13#49611yescharacteristic
111Dic13—81no—
112C22×D4—131no—
113C23×C4—261no—
114C2×M16—22no—
115C22×C8—261no—
116C22×C8C22⋊D1312yes—
117C4×D4—262no—
118C4×D4—262no—
119C2×C4⋊C4—131no—
120C2×C22⋊C4—261no—
121C2×C42C22×D1311yescharacteristic
122#108—44no—
123C4⋊C8—22no—
124C4⋊C8—22no—
125C4⋊C8—262no—
126C4⋊C8—262no—
127C22⋊C8—262no—
128C22⋊C8—524no—
129#97—22no—
130C4×C8—134no—
131C2×C13—22no—
132C2×C13#209111yescharacteristic
133C2×C13#209411yescharacteristic
134C2×C13#209811yescharacteristic
135D13—82no—
136C24—261no—
137C2×D4—262no—
138C2×D4—522no—
139C22×C4—261no—
140C22×C4—521no—
141C22×C4—522no—
142C22×C4—521no—
143C22×C4—522no—
144C22×C4Q8×D1311yescharacteristic
145C22×C4#613111yescharacteristic
146C22×C4C2×C22⋊D1311yescharacteristic
147M16—44no—
148C2×C8—22no—
149C2×C8—22no—
150C2×C8—42no—
151C2×C8—264no—
152C2×C8—521no—
153C2×C8—522no—
154C2×C8#610614yes—
155C4⋊C4—262no—
156C22⋊C4—522no—
157C42#612712yes—
158C42D4×D1312yes—
159C13#1066111yescharacteristic, complemented, Sylow
160C23—262no—
161C23—521no—
162C23—522no—
163C23—522no—
164C23—521no—
165C23#8820011yescharacteristic
166D4—264no—
167D4—522no—
168C2×C4—41no—
169C2×C4—41no—
170C2×C4—522no—
171C2×C4—521no—
172C2×C4—1041no—
173C2×C4—1041no—
174C2×C4—1042no—
175C2×C4#8814812yes—
176C2×C4#8815012yes—
177C2×C4#8818311yescharacteristic
178C2×C4#8818612yes—
179C2×C4#8819411yescharacteristic
180C2×C4C2×#610612yes—
181C8—24no—
182C8—82no—
183C8—524no—
184C8—1041no—
185C22—21no—
186C22—21no—
187C22—524no—
188C22—522no—
189C22—1042no—
190C22—1041no—
191C22—1041no—
192C22#1171865311yescharacteristic
193C22#1171874512yes—
194C4—22no—
195C4—22no—
196C4—1041no—
197C4#1171862912yes—
198C4#1171873511yescharacteristic
199C4#1171874611yescharacteristic
200C2—22no—
201C2—1042no—
202C2#1311635111yescharacteristic
203C2#1311637011yescharacteristic
204C2#1311638811yescharacteristic
subgroupG/H
centerC2×C4#88194
commutator, cosocleC2×C42×C13C23
FrattiniC2×C42C22×D13
FittingC13×#1849C2
socleC22×C13#399
prime radicalC22×D52Q8
hypercenter#1849D13
hypocenterC13#10661
LCSG ▷ C2×C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1849

Complements

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

NH ≅ G/Ntype
2. #13113608C2semidirect
4. #13112667C2semidirect
5. C13×#1849C2semidirect
59. #1849D13semidirect
159. C13#10661semidirect

Maximal subgroups

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

subgroupindex
#131156342
#131136082
#131132602
#131126672
C13×#18492
#1066113