Finite Group Databasebeta

← #15772258

Subgroups — #15772258

Order 3328.

330 conjugacy classes of subgroups; only the 111 normal subgroups are shown.

normal subgroups only

This group has 330 conjugacy classes of subgroups — too many to draw. Only its 111 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
1C2×C8×Dic26C211yesmaximal, characteristic
2#13116639C211yesmaximal, characteristic
3#13112775C214yesmaximal
4C13×#2163C211yesmaximal, characteristic
5C2×C4×Dic26C411yescharacteristic
6C2×C4×C8×C13C2211yescharacteristic
7C2×#88054C2212yes—
8C2×C8×Dic13C412yes—
9C2×C4⋊#1055C411yescharacteristic
10C8×Dic26—21no—
11C8×Dic26—21no—
12C8×Dic26—21no—
13C8×Dic26—21no—
14C13×C4⋊C16—21no—
15C13×C22⋊C16C2212yes—
16C13×#346—21no—
17C22⋊#6090C2212yes—
18C4⋊#6090—21no—
19#11718053—21no—
20C22×Dic26C811yescharacteristic
21C22×C8×C13C2×C411yescharacteristic
22C22×C8×C13C2311yescharacteristic
23C2×C42×C13C2×C411yescharacteristic
24C2×C4⋊Dic13C811yescharacteristic
25C2×#6101C812yes—
26C2×C4×Dic13C2×C412yes—
27C22×#1055C2×C412yes—
28C4×Dic26—21no—
29C4×Dic26—21no—
30C4×Dic26—21no—
31C4×Dic26—21no—
32C2×C13×C16—22no—
33C4×C8×C13D411yescharacteristic
34C4×C8×C13D411yescharacteristic
35C4×C8×C13D411yescharacteristic
36C4×C8×C13D411yescharacteristic
37#88054—22no—
38#88054—22no—
39C8×Dic13—22no—
40C8×Dic13—22no—
41C2×#6090—22no—
42C4⋊#1055—21no—
43C4⋊#1055—21no—
44#11494—131nomaximal, Sylow
45C22×C4×C13C2×C811yescharacteristic
46C22×C4×C13C2×C811yescharacteristic
47C22×C4×C13C22×C411yescharacteristic
48C22×Dic13C2×C812yes—
49C22×Dic13C2×C812yes—
50C2×Dic26—21no—
51C2×Dic26—21no—
52C2×Dic26—24no—
53C2×C8×C13—22no—
54C2×C8×C13—41no—
55C2×C8×C13C22⋊C411yescharacteristic
56C2×C8×C13C22⋊C411yescharacteristic
57C2×C8×C13C2×D411yescharacteristic
58C2×C8×C13C2×D411yescharacteristic
59C42×C13C22⋊C411yescharacteristic
60C42×C13C22⋊C411yescharacteristic
61C42×C13M1611yescharacteristic
62C42×C13M1611yescharacteristic
63C4⋊Dic13—21no—
64C4⋊Dic13—21no—
65#6101—22no—
66#6101—22no—
67C4×Dic13—22no—
68C4×Dic13—22no—
69C2×#1055—22no—
70C2×#1055—42no—
71C13×C16—42no—
72#6090—42no—
73C2×C8×Q8—131no—
74#2163—131no—
75#2163D1311yescharacteristic
76#1322—134no—
77C23×C13C22×C811yescharacteristic
78C2×C4×C13—22no—
79C2×C4×C13—21no—
80C2×C4×C13—21no—
81C2×C4×C13—41no—
82C2×C4×C13C22⋊C811yescharacteristic
83C2×C4×C13C22⋊C811yescharacteristic
84C2×C4×C13C22⋊C811yescharacteristic
85C2×C4×C13C22⋊C811yescharacteristic
86C2×C4×C13C2×C22⋊C411yescharacteristic
87C2×C4×C13C2×M1611yescharacteristic
88C2×Dic13—22no—
89C2×Dic13—22no—
90C2×Dic13—22no—
91C2×Dic13—42no—
92C2×Dic13M3214yes—
93Dic26—24no—
94Dic26—24no—
95C8×C13—21no—
96C8×C13—21no—
97C8×C13—21no—
98C8×C13#10112yes—
99#1055—42no—
100C2×C4×Q8—131no—
101C8×Q8—261no—
102C8×Q8—261no—
103C8×Q8—261no—
104C8×Q8—261no—
105C2×C4⋊C8—132no—
106C2×C4⋊C8—131no—
107C2×C4×C8—132no—
108C2×C4×C8C2×D1311yescharacteristic
109C4⋊C16—21no—
110C4⋊C16—261no—
111C22⋊C16—132no—
112C22⋊C16C2×D1312yes—
113#346—21no—
114#346—261no—
115C22×C13—21no—
116C22×C13—21no—
117C22×C13C2×C22⋊C811yescharacteristic
118C22×C13C2×M3212yes—
119C4×C13—21no—
120C4×C13—21no—
121C4×C13—21no—
122C4×C13—21no—
123C4×C13—21no—
124C4×C13#41011yescharacteristic
125C4×C13C2×#10111yescharacteristic
126Dic13—24no—
127Dic13—42no—
128C22×Q8—131no—
129C22×C8—132no—
130C22×C8C4×D1311yescharacteristic
131C22×C8C22×D1311yescharacteristic
132C4×Q8—261no—
133C4×Q8—261no—
134C4×Q8—261no—
135C4×Q8—261no—
136C2×C4⋊C4—132no—
137C2×C4⋊C4—131no—
138C2×C42—132no—
139C2×C42C4×D1311yescharacteristic
140C2×C16—22no—
141C2×C16—262no—
142C4⋊C8—262no—
143C4⋊C8—262no—
144C4⋊C8—261no—
145C4⋊C8—261no—
146C4×C8—262no—
147C4×C8—262no—
148C4×C8D5211yescharacteristic
149C4×C8D5211yescharacteristic
150C4×C8C22⋊D1311yescharacteristic
151C4×C8C22⋊D1311yescharacteristic
152C2×C13—22no—
153C2×C13#146111yescharacteristic
154C2×C13#211211yescharacteristic
155C2×C13#211511yescharacteristic
156C2×Q8—264no—
157C2×Q8—261no—
158C2×Q8—261no—
159C22×C4—132no—
160C22×C4—132no—
161C22×C4C8×D1311yescharacteristic
162C22×C4C8×D1311yescharacteristic
163C22×C4C2×C4×D1311yescharacteristic
164C2×C8—22no—
165C2×C8—41no—
166C2×C8—262no—
167C2×C8—522no—
168C2×C8#610311yescharacteristic
169C2×C8#610311yescharacteristic
170C2×C8C2×D5211yescharacteristic
171C2×C8C2×C22⋊D1311yescharacteristic
172C4⋊C4—262no—
173C4⋊C4—262no—
174C4⋊C4—261no—
175C4⋊C4—261no—
176C42—262no—
177C42—262no—
178C42#609411yescharacteristic
179C42#609411yescharacteristic
180C42#610311yescharacteristic
181C42#610311yescharacteristic
182C16—42no—
183C16—522no—
184C13#1149411yescharacteristic, complemented, Sylow
185C23C2×C8×D1311yescharacteristic
186Q8—264no—
187Q8—264no—
188C2×C4—22no—
189C2×C4—21no—
190C2×C4—21no—
191C2×C4—41no—
192C2×C4—134no—
193C2×C4—262no—
194C2×C4—262no—
195C2×C4—262no—
196C2×C4—522no—
197C2×C4#8806011yescharacteristic
198C2×C4#8806011yescharacteristic
199C2×C4#8806011yescharacteristic
200C2×C4#8806011yescharacteristic
201C2×C4C2×#609411yescharacteristic
202C2×C4C2×#610311yescharacteristic
203C8—21no—
204C8—21no—
205C8—21no—
206C8—522no—
207C8#8806412yes—
208C22—21no—
209C22—21no—
210C22D13×M3212yes—
211C22C2×#8806011yescharacteristic
212C4—21no—
213C4—21no—
214C4—21no—
215C4—21no—
216C4—21no—
217C4—264no—
218C4—522no—
219C4#1171866711yescharacteristic
220C4C2×#8806411yescharacteristic
221C2—22no—
222C2#1311315911yescharacteristic
223C2#1311644611yescharacteristic
224C2#1311645611yescharacteristic
subgroupG/H
centerC2×C4C2×#6103
commutator, prime radicalC23×C13C22×C8
FrattiniC22×C8C22×D13
FittingC13×#2163C2
socleC22×C13C2×C22⋊C8
cosocleC22×C8×C13C23
hypercenter#2163D13
hypocenterC13#11494
LCSG ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C2×C4×C8 ◁ #2163

Complements

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

NH ≅ G/Ntype
184. C13#11494semidirect

Maximal subgroups

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

subgroupindex
C2×C8×Dic262
#131166392
#131127752
C13×#21632
#1149413