Finite Group Databasebeta

← #16777856

Subgroups — #16777856

Order 3328.

252 conjugacy classes of subgroups; only the 36 normal subgroups are shown.

normal subgroups only

This group has 252 conjugacy classes of subgroups — too many to draw. Only its 36 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#13129933C211yesmaximal, characteristic
2#13129767C211yesmaximal, characteristic
3#13115936C211yesmaximal, characteristic
4C2×C13×C4⋊Q8C411yescharacteristic
5C22×#6107—21no—
6C2×#88113—21no—
7C2×#88075—21no—
8#11718590C2211yescharacteristic
9#11718285—21no—
10#11718116C411yescharacteristic
11C22×Q8×C13—21no—
12C22×Dic26D411yescharacteristic
13C2×#6122—41no—
14C13×C4⋊Q8—42no—
15C2×C13×C4⋊C4—41no—
16C2×C42×C13C2×C411yescharacteristic
17C2×#6107—42no—
18C2×#6107—42no—
19C2×#6107—41no—
20C2×#6107—41no—
21C2×C4⋊Dic13D411yescharacteristic
22C22×#1055—21no—
23C22⋊#1057—41no—
24#88113—22no—
25#88113—41no—
26#88075—42no—
27#88071—41no—
28#7405—131nomaximal, Sylow
29C2×Q8×C13—22no—
30C2×Q8×C13—41no—
31C2×Q8×C13—41no—
32C2×Q8×C13—41no—
33C2×Q8×C13—41no—
34C2×Q8×C13—41no—
35C22×C4×C13—21no—
36C22×C4×C13—41no—
37C22×C4×C13C22⋊C411yescharacteristic
38C22×Dic13—21no—
39C22×Dic13—21no—
40C2×Dic26—21no—
41C2×Dic26—41no—
42C2×Dic26—41no—
43C2×Dic26D811yescharacteristic
44C2×Dic26SD1611yescharacteristic
45#6122—42no—
46#6122—81no—
47C2×#1057—81no—
48C2×#1057—81no—
49C13×C4⋊C4—42no—
50C13×C4⋊C4—42no—
51C42×C13—41no—
52#6107—44no—
53#6107—44no—
54C4⋊Dic13—41no—
55C2×#1055—22no—
56C2×#1055—41no—
57C2×#1055—41no—
58#2016—131no—
59#1394—131no—
60#1319—131no—
61C23×C13#9911yescharacteristic
62Q8×C13—42no—
63Q8×C13—42no—
64Q8×C13—81no—
65Q8×C13—81no—
66C2×C4×C13—21no—
67C2×C4×C13—21no—
68C2×C4×C13—22no—
69C2×C4×C13—41no—
70C2×C4×C13—41no—
71C2×C4×C13—42no—
72C2×C4×C13—81no—
73C2×C4×C13—81no—
74C2×C4×C13#10211yescharacteristic
75C2×C4×C13#10411yescharacteristic
76C2×Dic13—21no—
77C2×Dic13—21no—
78C2×Dic13—41no—
79C2×Dic13—41no—
80C2×Dic13—41no—
81C2×Dic13—81no—
82Dic26—41no—
83Dic26—41no—
84Dic26—81no—
85#1057—82no—
86#1057—161no—
87#1055—42no—
88C22×Q16—261no—
89C2×C4⋊Q8#26111yescharacteristic
90C2×#103—261no—
91C2×#101—261no—
92#391—131no—
93#336—131no—
94#324—261no—
95C22×C13—21no—
96C22×C13—21no—
97C22×C13#32711yescharacteristic
98C22×C13AΣL(1,𝔽16)11yescharacteristic
99C22×C13#35311yescharacteristic
100C4×C13—21no—
101C4×C13—21no—
102C4×C13—42no—
103C4×C13—82no—
104Dic13—41no—
105Dic13—41no—
106Dic13—81no—
107C22×Q8—21no—
108C22×Q8—131no—
109C2×Q16—522no—
110C2×Q16—522no—
111C2×Q16—521no—
112C2×Q16—521no—
113C2×M16—521no—
114C22×C8—261no—
115C4⋊Q8—42no—
116C2×C4⋊C4—41no—
117C2×C4⋊C4—131no—
118C2×C42C2×#26111yescharacteristic
119#103—522no—
120#101—262no—
121#101—521no—
122C22⋊C8—521no—
123#95—521no—
124C2×C13—21no—
125C2×C13—21no—
126C2×C13#134311yescharacteristic
127C2×C13#140711yescharacteristic
128C2×C13#141111yescharacteristic
129C2×Q8—22no—
130C2×Q8—41no—
131C2×Q8—41no—
132C2×Q8—41no—
133C2×Q8—41no—
134C2×Q8—41no—
135C2×Q8—131no—
136C2×Q8—131no—
137C2×Q8—261no—
138C2×Q8—521no—
139C2×Q8—521no—
140C22×C4—21no—
141C22×C4—41no—
142C22×C4—261no—
143C22×C4—261no—
144C22×C4C22⋊#26111yescharacteristic
145Q16—524no—
146Q16—524no—
147M16—522no—
148M16—1041no—
149C2×C8—262no—
150C2×C8—521no—
151C2×C8—521no—
152C2×C8—1041no—
153C2×C8—1041no—
154C4⋊C4—42no—
155C4⋊C4—42no—
156C4⋊C4—521no—
157C42—41no—
158C13#740511yescharacteristic, complemented, Sylow
159C23#8811911yescharacteristic
160Q8—42no—
161Q8—42no—
162Q8—81no—
163Q8—81no—
164Q8—521no—
165Q8—521no—
166Q8—1041no—
167C2×C4—21no—
168C2×C4—21no—
169C2×C4—22no—
170C2×C4—41no—
171C2×C4—41no—
172C2×C4—42no—
173C2×C4—81no—
174C2×C4—81no—
175C2×C4—261no—
176C2×C4—261no—
177C2×C4—521no—
178C2×C4—521no—
179C2×C4—521no—
180C2×C4—1041no—
181C2×C4#8811511yescharacteristic
182C2×C4#8811611yescharacteristic
183C8—522no—
184C8—1042no—
185C8—2081no—
186C22—21no—
187C22—21no—
188C22#1171829211yescharacteristic
189C22#1171829411yescharacteristic
190C22#1171830611yescharacteristic
191C4—21no—
192C4—21no—
193C4—42no—
194C4—82no—
195C4—521no—
196C4—521no—
197C4—1041no—
198C2—21no—
199C2—21no—
200C2#1312981411yescharacteristic
201C2#1312996511yescharacteristic
202C2#1312997311yescharacteristic
subgroupG/H
centerC22#11718294
commutatorC2×C42×C13C2×C4
FrattiniC2×C42C2×#261
FittingC2×C13×C4⋊Q8C4
socleC22×C13#353
prime radicalC23×C13#99
cosocle#11718590C22
hypercenterC2×C4⋊Q8#261
hypocenterC13#7405
LCSG ▷ C2×C42×C13 ▷ C22×C4×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23 ◁ C22×C4 ◁ C2×C42 ◁ C2×C4⋊Q8

Complements

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

NH ≅ G/Ntype
158. C13#7405semidirect

Maximal subgroups

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

subgroupindex
#131299332
#131297672
#131159362
#740513