Finite Group Databasebeta

← #15774862

Subgroups — #15774862

Order 3328.

210 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 210 conjugacy classes of subgroups — too many to draw. Only its 73 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
1C4×Dic104C211yesmaximal, characteristic
2#13113732C211yesmaximal, characteristic
3#13113642C211yesmaximal, characteristic
4#13112799C211yesmaximal, characteristic
5#13112799C211yesmaximal, characteristic
6#13112755C211yesmaximal, characteristic
7C13×#1372C211yesmaximal, characteristic
8C2×Dic104C411yescharacteristic
9#11718492—21no—
10#11718491—21no—
11C4×Dic52C2211yescharacteristic
12C4×Dic52C2211yescharacteristic
13C4×C13×C16C2211yescharacteristic
14C13×#335C2211yescharacteristic
15C13×#335C2211yescharacteristic
16#11718096C411yescharacteristic
17#11718095C411yescharacteristic
18#11718095C411yescharacteristic
19#11718076—21no—
20#11718076—21no—
21C4×#6090C2211yescharacteristic
22C8×#1055C2211yescharacteristic
23C2×Dic52C2×C411yescharacteristic
24C2×Dic52C2×C411yescharacteristic
25C4×Dic26—21no—
26C4×Dic26—21no—
27C2×C13×C16C2×C411yescharacteristic
28C2×C13×C16C2×C411yescharacteristic
29C13×C4⋊C8—21no—
30C13×C4⋊C8—21no—
31C4×C8×C13C2311yescharacteristic
32#88058C2×C411yescharacteristic
33#88058C2×C411yescharacteristic
34#88056—21no—
35#88056—21no—
36#88055—41no—
37#88054—41no—
38#88054—41no—
39C8×Dic13—41no—
40C2×#6090—21no—
41C4×#1055D411yescharacteristic
42C4×#1055D411yescharacteristic
43Dic104—22no—
44#12076—131nomaximal, Sylow
45C2×Dic26—21no—
46C2×Dic26—21no—
47C2×C8×C13—41no—
48C2×C8×C13—41no—
49C2×C8×C13C22×C411yescharacteristic
50C2×C8×C13#4111yescharacteristic
51C42×C13C2×D411yescharacteristic
52C4⋊Dic13—21no—
53C4⋊Dic13—21no—
54#6101—41no—
55#6101—41no—
56C4×Dic13—41no—
57C4×Dic13—41no—
58C2×#1055—21no—
59C2×#1055D811yescharacteristic
60C2×#1055D811yescharacteristic
61Dic52—21no—
62Dic52—21no—
63Dic52—21no—
64Dic52M1612yes—
65C13×C16—21no—
66C13×C16—21no—
67#6090—41no—
68C4×Q32—131no—
69#1591—131no—
70C8×Q16—131no—
71#1372D1311yescharacteristic
72#1332—131no—
73#1332—131no—
74#1312—131no—
75C2×C4×C13C4×D411yescharacteristic
76C2×C4×C13C2×D811yescharacteristic
77C2×C4×C13#13511yescharacteristic
78C2×Dic13—41no—
79C2×Dic13—41no—
80C2×Dic13—41no—
81C2×Dic13—41no—
82Dic26—22no—
83Dic26—41no—
84Dic26—41no—
85Dic26—41no—
86C8×C13—21no—
87C8×C13—81no—
88C8×C13—81no—
89C8×C13C2×M1611yescharacteristic
90C8×C13#13111yescharacteristic
91#1055—22no—
92#1055—21no—
93#1055—21no—
94C2×Q32—131no—
95#446—261no—
96C8×Q8—261no—
97C4×Q16—131no—
98C4×Q16—131no—
99#366—131no—
100#358—131no—
101#358—131no—
102C4×C16—131no—
103C4×C16C2×D1311yescharacteristic
104#335C2×D1311yescharacteristic
105#335C2×D1311yescharacteristic
106Q8⋊C8—261no—
107Q8⋊C8—261no—
108C82—131no—
109C22×C13C4×D811yescharacteristic
110C4×C13—21no—
111C4×C13#43511yescharacteristic
112C4×C13#44411yescharacteristic
113C4×C13#51011yescharacteristic
114C4×C13#51011yescharacteristic
115Dic13—42no—
116Dic13—81no—
117Dic13—81no—
118Dic13—81no—
119C2×Q16—131no—
120C2×Q16—131no—
121C4×Q8—261no—
122C4×Q8—261no—
123Q32—262no—
124C2×C16—261no—
125C2×C16C4×D1311yescharacteristic
126C2×C16C4×D1311yescharacteristic
127#107—131no—
128#107—131no—
129C4⋊C8—21no—
130C4⋊C8—21no—
131C4⋊C8—521no—
132C4⋊C8—521no—
133#103—261no—
134#103—261no—
135#97—521no—
136C4×C8—131no—
137C4×C8—131no—
138C4×C8—521no—
139C4×C8C22×D1311yescharacteristic
140C2×C13#158111yescharacteristic
141C2×C13#217611yescharacteristic
142C2×C13#217811yescharacteristic
143C2×Q8—261no—
144C2×Q8—261no—
145Q16—132no—
146Q16—261no—
147Q16—261no—
148Q16—261no—
149C2×C8—41no—
150C2×C8—41no—
151C2×C8—131no—
152C2×C8—131no—
153C2×C8—261no—
154C2×C8C2×C4×D1311yescharacteristic
155C2×C8#613111yescharacteristic
156C4⋊C4—261no—
157C4⋊C4—261no—
158C4⋊C4—521no—
159C4⋊C4—521no—
160C42—521no—
161C42—521no—
162C42D4×D1311yescharacteristic
163C16—21no—
164C16—21no—
165C16—521no—
166C13#1207611yescharacteristic, complemented, Sylow
167Q8—262no—
168Q8—521no—
169Q8—521no—
170Q8—521no—
171C2×C4—521no—
172C2×C4—521no—
173C2×C4—521no—
174C2×C4—521no—
175C2×C4#8814711yescharacteristic
176C2×C4D8×D1311yescharacteristic
177C2×C4#8817311yescharacteristic
178C8—21no—
179C8—81no—
180C8—81no—
181C8—262no—
182C8—261no—
183C8—261no—
184C8#8815511yescharacteristic
185C8M16×D1311yescharacteristic
186C22#1171853311yescharacteristic
187C4—21no—
188C4—522no—
189C4—1041no—
190C4—1041no—
191C4—1041no—
192C4#1171849711yescharacteristic
193C4#1171855511yescharacteristic
194C4#1171857611yescharacteristic
195C4#1171857611yescharacteristic
196C2#1311366411yescharacteristic
197C2#1311670611yescharacteristic
198C2#1311671611yescharacteristic
subgroupG/H
centerC2×C4D8×D13
commutatorC2×C8×C13C22×C4
FrattiniC4×C8C22×D13
FittingC13×#1372C2
socle, prime radicalC22×C13C4×D8
cosocleC4×C8×C13C23
hypercenter#1372D13
hypocenterC13#12076
LCSG ▷ C2×C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×C8 ◁ #1372

Complements

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

NH ≅ G/Ntype
166. C13#12076semidirect

Maximal subgroups

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

subgroupindex
C4×Dic1042
#131137322
#131136422
#131127992
#131127552
C13×#13722
#1207613