Finite Group Databasebeta

← #16791280

Subgroups — #16791280

Order 3328.

398 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 398 conjugacy classes of subgroups — too many to draw. Only its 60 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×#11718227C212yesmaximal, complemented
2#13129973C212yesmaximal, complemented
3#13129971C212yesmaximal, complemented
4#13125296C211yesmaximal, characteristic
5C13×#532C411yescharacteristic
6C2×#88205—22no—
7C2×#88123C2211yescharacteristic
8C2×#88113—22no—
9#11718753C411yescharacteristic
10#11718753C2211yescharacteristic
11#11718737C411yescharacteristic
12#11718737C2211yescharacteristic
13#11718721—22no—
14C4×#6099C411yescharacteristic
15#11718227—22no—
16#11718227C2214yes—
17C2×C13×#41—21no—
18C22×Dic26D412yes—
19C2×#6122—42no—
20C13×C4⋊Q8C2×C411yescharacteristic
21C13×#127C2×C411yescharacteristic
22C13×#124—21no—
23C13×#121—41no—
24C4×D4×C13—41no—
25C2×C42×C13C2×C411yescharacteristic
26#88205—44no—
27#88205—44no—
28C2×#6107—22no—
29C2×#6107—22no—
30C2×#6105—22no—
31C2×#6105—22no—
32C2×C4⋊Dic13—41no—
33C2×#6099—21no—
34#88123—41no—
35#88123C2×C411yescharacteristic
36#88123D412yes—
37#88123C2311yescharacteristic
38#88113—24no—
39#88113—42no—
40#88043—21no—
41C4×#1055C2×C411yescharacteristic
42C4×#1055C2×C411yescharacteristic
43#13590—131nomaximal, Sylow
44C13×#41—42no—
45C13×#41—42no—
46C2×Q8×C13—21no—
47C2×D4×C13—21no—
48C2×D4×C13—41no—
49C2×D4×C13—41no—
50C22×C4×C13—21no—
51C22×C4×C13—41no—
52C22×C4×C13C22⋊C411yescharacteristic
53C22×Dic13—22no—
54C2×Dic26—22no—
55C2×Dic26—42no—
56C2×Dic26—42no—
57C2×Dic26C22⋊C412yes—
58C2×Dic26C2×D412yes—
59#6122—44no—
60#6122—82no—
61C2×#1057—82no—
62C13×C4⋊C4—41no—
63C13×C22⋊C4—42no—
64C42×C13—21no—
65C42×C13C22⋊C411yescharacteristic
66C42×C13C22×C411yescharacteristic
67#6107—44no—
68#6107—44no—
69#6105—44no—
70#6105—44no—
71C4⋊Dic13—41no—
72C4⋊Dic13—42no—
73C4⋊Dic13—41no—
74#6099—24no—
75C2×#1055—21no—
76C2×#1055—21no—
77#3152—131no—
78C2×#356—132no—
79#1411—132no—
80#1410—132no—
81C23×C13—41no—
82C23×C13#9911yescharacteristic
83Q8×C13—42no—
84D4×C13—42no—
85D4×C13—82no—
86D4×C13—82no—
87C2×C4×C13—22no—
88C2×C4×C13—21no—
89C2×C4×C13—21no—
90C2×C4×C13—42no—
91C2×C4×C13—41no—
92C2×C4×C13—81no—
93C2×C4×C13—81no—
94C2×C4×C13#9911yescharacteristic
95C2×C4×C13C2×C22⋊C411yescharacteristic
96C2×Dic13—22no—
97C2×Dic13—22no—
98C2×Dic13—42no—
99C2×Dic13—42no—
100Dic26—42no—
101Dic26—42no—
102Dic26—82no—
103#1057—84no—
104#1055—22no—
105#1055—22no—
106C2×#137—262no—
107#532#26111yescharacteristic
108C2×C4⋊Q8—131no—
109#497—262no—
110#494—131no—
111#494—131no—
112#492—131no—
113#492—131no—
114C2×#101—262no—
115C4×M16—131no—
116#356—134no—
117#356—262no—
118C22×C13—41no—
119C22×C13—82no—
120C22×C13—81no—
121C22×C13#35312yes—
122C22×C13C2×#9911yescharacteristic
123C4×C13—22no—
124C4×C13—21no—
125C4×C13—21no—
126C4×C13—41no—
127C4×C13—81no—
128Dic13—42no—
129Dic13—42no—
130C2×#41—21no—
131C22×Q8—132no—
132#137—524no—
133#137—524no—
134C2×Q16—262no—
135C2×Q16—262no—
136C2×SD16—262no—
137C2×SD16—262no—
138C2×M16—261no—
139C2×M16—522no—
140C4⋊Q8—132no—
141C4⋊Q8—131no—
142C4⋊Q8—131no—
143C4⋊Q8—521no—
144C4⋊Q8C2×#26111yescharacteristic
145#127C2×#26111yescharacteristic
146#124—21no—
147#121—41no—
148C4×D4—41no—
149C2×C4⋊C4—521no—
150C2×C42C2×#26111yescharacteristic
151#101—264no—
152#101—522no—
153#97—261no—
154C4×C8—131no—
155C4×C8—131no—
156C2×C13—21no—
157C2×C13—22no—
158C2×C13—161no—
159C2×C13C2×#35311yescharacteristic
160#41—42no—
161#41—42no—
162C2×Q8—21no—
163C2×Q8—132no—
164C2×Q8—132no—
165C2×Q8—262no—
166C2×Q8—522no—
167C2×Q8—522no—
168C2×D4—21no—
169C2×D4—41no—
170C2×D4—41no—
171C22×C4—21no—
172C22×C4—41no—
173C22×C4—262no—
174C22×C4C22⋊#26111yescharacteristic
175Q16—524no—
176Q16—524no—
177SD16—524no—
178SD16—524no—
179M16—264no—
180M16—524no—
181M16—1042no—
182C2×C8—261no—
183C2×C8—261no—
184C2×C8—1042no—
185C4⋊C4—41no—
186C4⋊C4—521no—
187C4⋊C4—521no—
188C4⋊C4—522no—
189C22⋊C4—42no—
190C42—21no—
191C42C22⋊#26111yescharacteristic
192C42C22×#26111yescharacteristic
193C13#1359011yescharacteristic, complemented, Sylow
194C23—41no—
195C23#8811911yescharacteristic
196Q8—42no—
197Q8—522no—
198Q8—522no—
199Q8—1042no—
200D4—42no—
201D4—82no—
202D4—82no—
203C2×C4—22no—
204C2×C4—21no—
205C2×C4—21no—
206C2×C4—42no—
207C2×C4—41no—
208C2×C4—81no—
209C2×C4—81no—
210C2×C4—262no—
211C2×C4—262no—
212C2×C4—522no—
213C2×C4—522no—
214C2×C4#8811911yescharacteristic
215C2×C4C2×C22⋊#26111yescharacteristic
216C8—262no—
217C8—262no—
218C8—1044no—
219C22—41no—
220C22—82no—
221C22—81no—
222C22#1171829412yes—
223C22C2×#8811911yescharacteristic
224C4—22no—
225C4—21no—
226C4—21no—
227C4—41no—
228C4—81no—
229C4—522no—
230C4—522no—
231C2—21no—
232C2—22no—
233C2—161no—
234C2C2×#1171829411yescharacteristic
subgroupG/H
centerC2C2×#11718294
commutatorC42×C13C22×C4
FrattiniC42C22×#261
Fitting, prime radicalC13×#532C4
socleC2×C13C2×#353
cosocle#88123C23
hypercenter#532#261
hypocenterC13#13590
LCSG ▷ C42×C13 ▷ C2×C4×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2 ◁ C23 ◁ C22×C4 ◁ C2×C42 ◁ #532

Complements

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

NH ≅ G/Ntype
1. C2×#11718227C2semidirect
2. #13129973C2semidirect
3. #13129971C2semidirect
193. C13#13590semidirect

Maximal subgroups

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

subgroupindex
C2×#117182272
#131299732
#131299712
#131252962
#1359013