Finite Group Databasebeta

← #15783255

Subgroups — #15783255

Order 3328.

398 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 398 conjugacy classes of subgroups — too many to draw. Only its 79 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×#11718140C212yesmaximal, complemented
2#13113005C212yesmaximal, complemented
3#13113003C212yesmaximal, complemented
4C13×#3152C211yesmaximal, characteristic
5C2×C13×#137—22no—
6C13×#532C411yescharacteristic
7C2×C13×C4⋊Q8C2211yescharacteristic
8C13×#497—22no—
9C13×#494C411yescharacteristic
10C13×#494C2211yescharacteristic
11C13×#492C411yescharacteristic
12C13×#492C2211yescharacteristic
13C4×C13×M16C411yescharacteristic
14C2×#88076—22no—
15#11718140—22no—
16#11718140C2214yes—
17C2×C13×#41—21no—
18C22×Q8×C13D412yes—
19C13×#137—44no—
20C13×#137—44no—
21C2×C13×Q16—22no—
22C2×C13×Q16—22no—
23C2×C13×SD16—22no—
24C2×C13×SD16—22no—
25C2×C13×M16—21no—
26C13×C4⋊Q8—41no—
27C13×C4⋊Q8C2×C411yescharacteristic
28C13×C4⋊Q8C2×C411yescharacteristic
29C13×C4⋊Q8D412yes—
30C13×C4⋊Q8C2311yescharacteristic
31C13×#127C2×C411yescharacteristic
32C13×#124—21no—
33C13×#121—41no—
34C4×D4×C13—41no—
35C2×C13×C4⋊C4—41no—
36C2×C42×C13C2×C411yescharacteristic
37C2×#6099—42no—
38C13×#97—21no—
39C4×C8×C13C2×C411yescharacteristic
40C4×C8×C13C2×C411yescharacteristic
41#88076—24no—
42#88076—42no—
43#13590—131nomaximal, Sylow
44C13×#41—42no—
45C13×#41—42no—
46C2×Q8×C13—22no—
47C2×Q8×C13—21no—
48C2×Q8×C13—42no—
49C2×Q8×C13—42no—
50C2×Q8×C13C22⋊C412yes—
51C2×Q8×C13C2×D412yes—
52C2×D4×C13—21no—
53C2×D4×C13—41no—
54C2×D4×C13—41no—
55C22×C4×C13—22no—
56C22×C4×C13—21no—
57C22×C4×C13—41no—
58C22×C4×C13C22⋊C411yescharacteristic
59C13×Q16—44no—
60C13×Q16—44no—
61C13×SD16—44no—
62C13×SD16—44no—
63C13×M16—24no—
64C2×C8×C13—21no—
65C2×C8×C13—21no—
66C13×C4⋊C4—41no—
67C13×C4⋊C4—42no—
68C13×C4⋊C4—41no—
69C13×C4⋊C4—41no—
70C13×C22⋊C4—42no—
71C42×C13—21no—
72C42×C13C22⋊C411yescharacteristic
73C42×C13C22×C411yescharacteristic
74#6099—44no—
75#6099—82no—
76C2×#1055—82no—
77#3152D1311yescharacteristic
78C2×#356—132no—
79#1411—132no—
80#1410—132no—
81C23×C13—41no—
82C23×C13#9911yescharacteristic
83Q8×C13—42no—
84Q8×C13—42no—
85Q8×C13—42no—
86Q8×C13—82no—
87D4×C13—42no—
88D4×C13—82no—
89D4×C13—82no—
90C2×C4×C13—22no—
91C2×C4×C13—21no—
92C2×C4×C13—22no—
93C2×C4×C13—21no—
94C2×C4×C13—22no—
95C2×C4×C13—42no—
96C2×C4×C13—42no—
97C2×C4×C13—42no—
98C2×C4×C13—41no—
99C2×C4×C13—81no—
100C2×C4×C13—81no—
101C2×C4×C13#9911yescharacteristic
102C2×C4×C13C2×C22⋊C411yescharacteristic
103C8×C13—22no—
104C8×C13—22no—
105#1055—84no—
106C2×#137—22no—
107#532Dic1311yescharacteristic
108C2×C4⋊Q8C2×D1311yescharacteristic
109#497—22no—
110#494Dic1311yescharacteristic
111#494C2×D1311yescharacteristic
112#492Dic1311yescharacteristic
113#492C2×D1311yescharacteristic
114C2×#101—262no—
115C4×M16Dic1311yescharacteristic
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—42no—
128C4×C13—42no—
129C4×C13—81no—
130C2×#41—21no—
131C22×Q8C22⋊D1312yes—
132#137—44no—
133#137—44no—
134C2×Q16—22no—
135C2×Q16—22no—
136C2×SD16—22no—
137C2×SD16—22no—
138C2×M16—21no—
139C2×M16—522no—
140C4⋊Q8—41no—
141C4⋊Q8C2×Dic1311yescharacteristic
142C4⋊Q8C2×Dic1311yescharacteristic
143C4⋊Q8C22⋊D1312yes—
144C4⋊Q8C22×D1311yescharacteristic
145#127C2×Dic1311yescharacteristic
146#124—21no—
147#121—41no—
148C4×D4—41no—
149C2×C4⋊C4—41no—
150C2×C42C2×Dic1311yescharacteristic
151#101—264no—
152#101—522no—
153#97—21no—
154C4×C8C2×Dic1311yescharacteristic
155C4×C8C2×Dic1311yescharacteristic
156C2×C13—21no—
157C2×C13—22no—
158C2×C13—161no—
159C2×C13C2×#35311yescharacteristic
160#41—42no—
161#41—42no—
162C2×Q8—22no—
163C2×Q8—21no—
164C2×Q8—42no—
165C2×Q8—42no—
166C2×Q8C22⋊Dic1312yes—
167C2×Q8C2×C22⋊D1312yes—
168C2×D4—21no—
169C2×D4—41no—
170C2×D4—41no—
171C22×C4—21no—
172C22×C4—22no—
173C22×C4—41no—
174C22×C4C22⋊Dic1311yescharacteristic
175Q16—44no—
176Q16—44no—
177SD16—44no—
178SD16—44no—
179M16—24no—
180M16—524no—
181M16—1042no—
182C2×C8—21no—
183C2×C8—21no—
184C2×C8—1042no—
185C4⋊C4—41no—
186C4⋊C4—42no—
187C4⋊C4—41no—
188C4⋊C4—41no—
189C22⋊C4—42no—
190C42—21no—
191C42C22⋊Dic1311yescharacteristic
192C42C22×Dic1311yescharacteristic
193C13#1359011yescharacteristic, complemented, Sylow
194C23—41no—
195C23#8807411yescharacteristic
196Q8—42no—
197Q8—42no—
198Q8—42no—
199Q8—82no—
200D4—42no—
201D4—82no—
202D4—82no—
203C2×C4—21no—
204C2×C4—22no—
205C2×C4—21no—
206C2×C4—22no—
207C2×C4—22no—
208C2×C4—42no—
209C2×C4—42no—
210C2×C4—42no—
211C2×C4—41no—
212C2×C4—81no—
213C2×C4—81no—
214C2×C4#8807411yescharacteristic
215C2×C4C2×C22⋊Dic1311yescharacteristic
216C8—22no—
217C8—22no—
218C8—1044no—
219C22—41no—
220C22—82no—
221C22—81no—
222C22#1171813712yes—
223C22C2×#8807411yescharacteristic
224C4—22no—
225C4—21no—
226C4—21no—
227C4—41no—
228C4—42no—
229C4—42no—
230C4—81no—
231C2—21no—
232C2—22no—
233C2—161no—
234C2C2×#1171813711yescharacteristic
subgroupG/H
centerC2C2×#11718137
commutatorC42×C13C22×C4
FrattiniC4⋊Q8C22×D13
FittingC13×#3152C2
socleC2×C13C2×#353
prime radicalC13×#532C4
cosocleC13×C4⋊Q8C23
hypercenter#3152D13
hypocenterC13#13590
LCSG ▷ C42×C13 ▷ C2×C4×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2 ◁ C23 ◁ C22×C4 ◁ C2×C4⋊Q8 ◁ #3152

Complements

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

NH ≅ G/Ntype
1. C2×#11718140C2semidirect
2. #13113005C2semidirect
3. #13113003C2semidirect
193. C13#13590semidirect

Maximal subgroups

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

subgroupindex
C2×#117181402
#131130052
#131130032
C13×#31522
#1359013