Finite Group Databasebeta

← #16788641

Subgroups — #16788641

Order 3328.

360 conjugacy classes of subgroups; only the 64 normal subgroups are shown.

normal subgroups only

This group has 360 conjugacy classes of subgroups — too many to draw. Only its 64 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#13131205C212yesmaximal, complemented
2#13129846C212yesmaximal, complemented
3#13129845C212yesmaximal, complemented
4#13125296C211yesmaximal, characteristic
5C13×#532C411yescharacteristic
6C2×#88205—22no—
7C2×#88123C411yescharacteristic
8#11718753C411yescharacteristic
9#11718753C2211yescharacteristic
10#11718737C411yescharacteristic
11#11718737C2211yescharacteristic
12#11718721—22no—
13C4×#6099C2211yescharacteristic
14#11718284—22no—
15#11718233C2214yes—
16#11718232—22no—
17C2×C13×#41—21no—
18C22×Dic26—21no—
19C13×C4⋊Q8C2×C411yescharacteristic
20C13×#127C2×C411yescharacteristic
21C13×#124—21no—
22C13×#121—41no—
23C4×D4×C13—41no—
24C2×C42×C13C2×C411yescharacteristic
25#88205—48no—
26C2×#6107—22no—
27C2×#6107—22no—
28C2×#6105—22no—
29C2×#6105—22no—
30C2×C4⋊Dic13—41no—
31C2×#6099D412yes—
32#88123—21no—
33#88123—41no—
34#88123C2×C411yescharacteristic
35#88123C2×C411yescharacteristic
36#88106—24no—
37#88043D412yes—
38C4×#1055C2×C411yescharacteristic
39C4×#1055C2311yescharacteristic
40#11993—131nomaximal, Sylow
41C13×#41—44no—
42C2×Q8×C13—21no—
43C2×D4×C13—21no—
44C2×D4×C13—41no—
45C2×D4×C13—41no—
46C22×C4×C13—21no—
47C22×C4×C13—41no—
48C22×C4×C13C22⋊C411yescharacteristic
49C22×Dic13—41no—
50C2×Dic26—21no—
51C2×Dic26—21no—
52C2×Dic26—44no—
53C2×Dic26—41no—
54C13×C4⋊C4—41no—
55C13×C22⋊C4—42no—
56C42×C13—21no—
57C42×C13C22⋊C411yescharacteristic
58C42×C13C22×C411yescharacteristic
59#6107—44no—
60#6107—44no—
61#6105—44no—
62#6105—44no—
63C4⋊Dic13—42no—
64C4⋊Dic13—41no—
65C4⋊Dic13—41no—
66#6099—24no—
67C2×#1055C22⋊C412yes—
68C2×#1055C2×D412yes—
69#6092—44no—
70#3152—131no—
71#2165—132no—
72#1359—132no—
73#1358—132no—
74C23×C13—41no—
75C23×C13#10011yescharacteristic
76Q8×C13—42no—
77D4×C13—42no—
78D4×C13—82no—
79D4×C13—82no—
80C2×C4×C13—21no—
81C2×C4×C13—22no—
82C2×C4×C13—21no—
83C2×C4×C13—42no—
84C2×C4×C13—41no—
85C2×C4×C13—82no—
86C2×C4×C13#10011yescharacteristic
87C2×C4×C13C2×C22⋊C411yescharacteristic
88C2×Dic13—41no—
89C2×Dic13—41no—
90C2×Dic13—82no—
91Dic26—42no—
92Dic26—42no—
93Dic26—82no—
94#1055—22no—
95#1055AGL(1,ℤ/8)14yes—
96C2×#137—262no—
97#532#26111yescharacteristic
98C2×C4⋊Q8—131no—
99#497—262no—
100#494—131no—
101#494—131no—
102#492—131no—
103#492—131no—
104C4×M16—131no—
105#364—134no—
106#349—262no—
107#347—262no—
108C22×C13—21no—
109C22×C13—41no—
110C22×C13—82no—
111C22×C13—81no—
112C22×C13C2×#10011yescharacteristic
113C4×C13—22no—
114C4×C13—21no—
115C4×C13—41no—
116C4×C13—81no—
117C4×C13#41812yes—
118Dic13—81no—
119Dic13—81no—
120C2×#41—21no—
121C22×Q8—261no—
122#137—528no—
123C2×Q16—262no—
124C2×Q16—262no—
125C2×SD16—262no—
126C2×SD16—262no—
127C2×M16—132no—
128C4⋊Q8—131no—
129C4⋊Q8—131no—
130C4⋊Q8—261no—
131C4⋊Q8—521no—
132C4⋊Q8C2×#26111yescharacteristic
133#127C2×#26111yescharacteristic
134#124—21no—
135#121—41no—
136C4×D4—41no—
137C2×C4⋊C4—521no—
138C2×C42C2×#26111yescharacteristic
139M32—264no—
140#97—132no—
141C4×C8—131no—
142C4×C8—131no—
143C2×C13—21no—
144C2×C13—41no—
145C2×C13—161no—
146C2×C13#155511yescharacteristic
147#41—44no—
148C2×Q8—21no—
149C2×Q8—261no—
150C2×Q8—261no—
151C2×Q8—524no—
152C2×Q8—521no—
153C2×D4—21no—
154C2×D4—41no—
155C2×D4—41no—
156C22×C4—21no—
157C22×C4—41no—
158C22×C4—521no—
159C22×C4C22⋊#26111yescharacteristic
160Q16—524no—
161Q16—524no—
162SD16—524no—
163SD16—524no—
164M16—264no—
165C2×C8—132no—
166C2×C8—132no—
167C4⋊C4—41no—
168C4⋊C4—521no—
169C4⋊C4—521no—
170C4⋊C4—522no—
171C22⋊C4—42no—
172C42—21no—
173C42C22⋊#26111yescharacteristic
174C42C22×#26111yescharacteristic
175C16—524no—
176C13#1199311yescharacteristic, complemented, Sylow
177C23—41no—
178C23#8812111yescharacteristic
179Q8—42no—
180Q8—522no—
181Q8—522no—
182Q8—1042no—
183D4—42no—
184D4—82no—
185D4—82no—
186C2×C4—21no—
187C2×C4—22no—
188C2×C4—21no—
189C2×C4—42no—
190C2×C4—41no—
191C2×C4—82no—
192C2×C4—521no—
193C2×C4—521no—
194C2×C4—1042no—
195C2×C4#8812111yescharacteristic
196C2×C4C2×C22⋊#26111yescharacteristic
197C8—134no—
198C8—262no—
199C22—21no—
200C22—41no—
201C22—82no—
202C22—81no—
203C22C2×#8812111yescharacteristic
204C4—22no—
205C4—21no—
206C4—41no—
207C4—81no—
208C4—1041no—
209C4—1041no—
210C4#1171913812yes—
211C2—21no—
212C2—41no—
213C2—161no—
214C2#1313036311yescharacteristic
subgroupG/H
centerC2#13130363
commutatorC42×C13C22×C4
FrattiniC42C22×#261
Fitting, prime radicalC13×#532C4
socleC2×C13#1555
cosocleC4×#1055C23
hypercenter#532#261
hypocenterC13#11993
LCSG ▷ C42×C13 ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C42 ◁ #532

Complements

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

NH ≅ G/Ntype
1. #13131205C2semidirect
2. #13129846C2semidirect
3. #13129845C2semidirect
176. C13#11993semidirect

Maximal subgroups

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

subgroupindex
#131312052
#131298462
#131298452
#131252962
#1199313