Finite Group Databasebeta

← #16788646

Subgroups — #16788646

Order 3328.

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

normal subgroups only

This group has 258 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#13131205C211yesmaximal, characteristic
2#13131205C211yesmaximal, characteristic
3#13129857C212yesmaximal, complemented
4#13129856C212yesmaximal, complemented
5#13125389C211yesmaximal, characteristic
6C13×#533C411yescharacteristic
7C2×#88124C411yescharacteristic
8#11718741—21no—
9#11718741—21no—
10#11718725C411yescharacteristic
11#11718725C411yescharacteristic
12#11718725C2211yescharacteristic
13#11718725C2211yescharacteristic
14#11718656—21no—
15#11718656—21no—
16C4×#6099C2211yescharacteristic
17#11718284—21no—
18#11718284—21no—
19#11718233C2212yes—
20#11718233C2212yes—
21#11718232—21no—
22#11718232—21no—
23C13×C4⋊Q8—21no—
24C13×#125C2×C411yescharacteristic
25C13×#125C2×C411yescharacteristic
26C13×C22⋊Q8—41no—
27C4×Q8×C13—41no—
28C13×#117—21no—
29C2×C42×C13C2×C411yescharacteristic
30C2×C4⋊Dic13—21no—
31C2×#6101—41no—
32C2×#6099D411yescharacteristic
33C2×#6099D411yescharacteristic
34#88124—21no—
35#88124—41no—
36#88124C2×C411yescharacteristic
37#88124C2×C411yescharacteristic
38#88106—22no—
39#88106—22no—
40#88048—21no—
41#88048—21no—
42#88048—21no—
43#88048—21no—
44#88047—21no—
45#88047—21no—
46#88047—21no—
47#88047—21no—
48#88043D411yescharacteristic
49#88043D411yescharacteristic
50C4×#1055C2×C411yescharacteristic
51C4×#1055C2311yescharacteristic
52#11994—131nomaximal, Sylow
53C2×Q8×C13—41no—
54C22×C4×C13—21no—
55C22×C4×C13C22⋊C411yescharacteristic
56C22×Dic13—41no—
57C13×C4⋊C4—21no—
58C13×C4⋊C4—21no—
59C13×C4⋊C4—41no—
60C13×C4⋊C4—41no—
61C13×C4⋊C4—41no—
62C13×C22⋊C4—41no—
63C42×C13—21no—
64C42×C13—41no—
65C42×C13C22⋊C411yescharacteristic
66C42×C13C22×C411yescharacteristic
67C4⋊Dic13—21no—
68C4⋊Dic13—21no—
69C4⋊Dic13—41no—
70#6101—42no—
71#6101—41no—
72#6101—41no—
73#6099—22no—
74#6099—22no—
75C2×#1055C22⋊C411yescharacteristic
76C2×#1055C22⋊C411yescharacteristic
77C2×#1055C2×D411yescharacteristic
78C2×#1055C2×D411yescharacteristic
79#6092—42no—
80#6092—42no—
81#3166—131no—
82#2165—131no—
83#2165—131no—
84#1366—132no—
85#1366—132no—
86C23×C13#10011yescharacteristic
87Q8×C13—82no—
88C2×C4×C13—21no—
89C2×C4×C13—21no—
90C2×C4×C13—21no—
91C2×C4×C13—21no—
92C2×C4×C13—41no—
93C2×C4×C13—41no—
94C2×C4×C13—81no—
95C2×C4×C13#10011yescharacteristic
96C2×C4×C13C2×C22⋊C411yescharacteristic
97C2×Dic13—41no—
98C2×Dic13—41no—
99C2×Dic13—82no—
100#1055—21no—
101#1055—21no—
102#1055#13712yes—
103#1055#13712yes—
104#533#26111yescharacteristic
105C2×#125—131no—
106#501—261no—
107#501—261no—
108#499—131no—
109#499—131no—
110#499—131no—
111#499—131no—
112#428—261no—
113#428—261no—
114C4×M16—131no—
115#364—132no—
116#364—132no—
117#349—261no—
118#349—261no—
119#347—261no—
120#347—261no—
121C22×C13—21no—
122C22×C13—41no—
123C22×C13C2×#10011yescharacteristic
124C4×C13—21no—
125C4×C13—41no—
126C4×C13—41no—
127C4×C13—81no—
128C4×C13—81no—
129C4×C13#41911yescharacteristic
130C4×C13#41911yescharacteristic
131Dic13—81no—
132Dic13—81no—
133C2×M16—131no—
134C2×M16—131no—
135C4⋊Q8—21no—
136#125—131no—
137#125—131no—
138#125—261no—
139#125—521no—
140#125C2×#26111yescharacteristic
141#125C2×#26111yescharacteristic
142C22⋊Q8—41no—
143C4×Q8—41no—
144#117—21no—
145C2×C4⋊C4—261no—
146C2×C4⋊C4—521no—
147C2×C42C2×#26111yescharacteristic
148M32—262no—
149M32—262no—
150#107—261no—
151#107—261no—
152#107—261no—
153#107—261no—
154#106—261no—
155#106—261no—
156#106—261no—
157#106—261no—
158#97—131no—
159#97—131no—
160C4×C8—131no—
161C4×C8—131no—
162C2×C13—21no—
163C2×C13—41no—
164C2×C13#155811yescharacteristic
165C2×Q8—41no—
166C22×C4—21no—
167C22×C4—521no—
168C22×C4C22⋊#26111yescharacteristic
169M16—262no—
170M16—262no—
171C2×C8—131no—
172C2×C8—131no—
173C2×C8—131no—
174C2×C8—131no—
175C4⋊C4—21no—
176C4⋊C4—21no—
177C4⋊C4—41no—
178C4⋊C4—41no—
179C4⋊C4—41no—
180C4⋊C4—261no—
181C4⋊C4—261no—
182C4⋊C4—521no—
183C4⋊C4—521no—
184C4⋊C4—522no—
185C4⋊C4—521no—
186C22⋊C4—41no—
187C42—21no—
188C42—41no—
189C42C22⋊#26111yescharacteristic
190C42C22×#26111yescharacteristic
191C16—522no—
192C16—522no—
193C13#1199411yescharacteristic, complemented, Sylow
194C23#8812111yescharacteristic
195Q8—82no—
196C2×C4—21no—
197C2×C4—21no—
198C2×C4—21no—
199C2×C4—21no—
200C2×C4—41no—
201C2×C4—41no—
202C2×C4—81no—
203C2×C4—521no—
204C2×C4—521no—
205C2×C4—1042no—
206C2×C4#8812111yescharacteristic
207C2×C4C2×C22⋊#26111yescharacteristic
208C8—132no—
209C8—132no—
210C8—261no—
211C8—261no—
212C22—21no—
213C22—41no—
214C22C2×#8812111yescharacteristic
215C4—21no—
216C4—41no—
217C4—41no—
218C4—81no—
219C4—81no—
220C4—1041no—
221C4—1041no—
222C4#1171915311yescharacteristic
223C4#1171915311yescharacteristic
224C2—21no—
225C2—41no—
226C2#1313036911yescharacteristic
subgroupG/H
centerC2#13130369
commutatorC42×C13C22×C4
FrattiniC42C22×#261
FittingC13×#533C4
socleC2×C13#1558
prime radicalC23×C13#100
cosocleC4×#1055C23
hypercenter#533#261
hypocenterC13#11994
LCSG ▷ C42×C13 ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C42 ◁ #533

Complements

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

NH ≅ G/Ntype
3. #13129857C2semidirect
4. #13129856C2semidirect
193. C13#11994semidirect

Maximal subgroups

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

subgroupindex
#131312052
#131298572
#131298562
#131253892
#1199413