Finite Group Databasebeta

← #16787115

Subgroups — #16787115

Order 3328.

348 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 348 conjugacy classes of subgroups — too many to draw. Only its 70 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#13131209C212yesmaximal, complemented
2#13129770C212yesmaximal, complemented
3#13129768C212yesmaximal, complemented
4#13123531C211yesmaximal, characteristic
5C13×#525C411yescharacteristic
6C2×#88202C411yescharacteristic
7C23×#1055C411yescharacteristic
8#11718895C2211yescharacteristic
9#11718868C2211yescharacteristic
10#11718672—22no—
11D4×#1055—22no—
12#11718660C411yescharacteristic
13#11718658C2211yescharacteristic
14#11718284C2214yes—
15#11718233—22no—
16#11718232—22no—
17C2×C13×#41C2×C411yescharacteristic
18C23×C4×C13C2×C411yescharacteristic
19C13×#123—21no—
20C13×C22⋊Q8—21no—
21C13×#121—21no—
22C13×#120—21no—
23C4×D4×C13—22no—
24C13×#117C2×C411yescharacteristic
25#88202—42no—
26C2×#6099—21no—
27C2×#6099C2×C411yescharacteristic
28C2×#6099C2311yescharacteristic
29C22×#1055—21no—
30C22×#1055—21no—
31C22×#1055—21no—
32C22×#1055—42no—
33C22×#1055C2×C411yescharacteristic
34C22×#1055C2×C411yescharacteristic
35#88106—24no—
36C22⋊#1055—22no—
37C22⋊#1055—22no—
38C4⋊#1055—22no—
39#88043D412yes—
40C4×#1055D412yes—
41#11537—131nomaximal, Sylow
42C24×C13M1611yescharacteristic
43C13×#41—41no—
44C13×#41—41no—
45C2×Q8×C13M1611yescharacteristic
46C2×D4×C13—22no—
47C2×D4×C13—21no—
48C2×D4×C13M1611yescharacteristic
49C22×C4×C13—21no—
50C22×C4×C13—21no—
51C22×C4×C13—21no—
52C22×C4×C13—41no—
53C22×C4×C13—41no—
54C22×C4×C13M1611yescharacteristic
55C22×C4×C13C22×C411yescharacteristic
56C13×C4⋊C4—22no—
57C13×C4⋊C4—21no—
58C13×C22⋊C4—22no—
59C13×C22⋊C4—22no—
60C13×C22⋊C4—21no—
61C42×C13C22⋊C412yes—
62#6099—41no—
63#6099—42no—
64#6099—41no—
65C2×#1055—22no—
66C2×#1055—21no—
67C2×#1055—21no—
68C2×#1055—42no—
69C2×#1055—42no—
70C2×#1055—42no—
71C2×#1055—41no—
72C2×#1055C22⋊C411yescharacteristic
73C2×#1055C22⋊C411yescharacteristic
74C2×#1055C2×D412yes—
75#6092—44no—
76#2929—131no—
77#2166—132no—
78#1321—132no—
79#1320—132no—
80C23×C13—21no—
81C23×C13—21no—
82C23×C13—41no—
83C23×C13—42no—
84C23×C13C2×M1611yescharacteristic
85Q8×C13—41no—
86D4×C13—41no—
87D4×C13—44no—
88D4×C13—42no—
89C2×C4×C13—21no—
90C2×C4×C13—21no—
91C2×C4×C13—22no—
92C2×C4×C13—21no—
93C2×C4×C13—21no—
94C2×C4×C13—42no—
95C2×C4×C13—41no—
96C2×C4×C13—41no—
97C2×C4×C13—41no—
98C2×C4×C13—41no—
99C2×C4×C13—41no—
100C2×C4×C13C2×C22⋊C411yescharacteristic
101C2×C4×C13C2×M1611yescharacteristic
102#1055—22no—
103#1055—21no—
104#1055—41no—
105#1055—41no—
106#1055#10012yes—
107C2×#131—131no—
108C23×C8—131no—
109#525#26111yescharacteristic
110#435—262no—
111C8×D4—262no—
112#424—131no—
113#408—131no—
114#407—131no—
115#405—131no—
116#364—262no—
117#349—134no—
118#347—262no—
119C22×C13—22no—
120C22×C13—21no—
121C22×C13—41no—
122C22×C13—41no—
123C22×C13—42no—
124C22×C13—42no—
125C22×C13—42no—
126C22×C13—41no—
127C22×C13—41no—
128C22×C13#40711yescharacteristic
129C4×C13—21no—
130C4×C13—42no—
131C4×C13—41no—
132C4×C13—41no—
133C4×C13#41011yescharacteristic
134C4×C13C2×#10011yescharacteristic
135C2×#41C2×#26111yescharacteristic
136C23×C4C2×#26111yescharacteristic
137#131—522no—
138C2×M16—131no—
139C2×M16—131no—
140C2×M16—261no—
141C22×C8—131no—
142C22×C8—131no—
143C22×C8—261no—
144C22×C8—261no—
145C22×C8—261no—
146C22×C8—522no—
147#123—21no—
148C22⋊Q8—21no—
149#121—21no—
150#120—21no—
151C4×D4—22no—
152#117C2×#26111yescharacteristic
153M32—264no—
154C4⋊C8—262no—
155C22⋊C8—262no—
156C22⋊C8—262no—
157#97—132no—
158C4×C8—132no—
159C2×C13—21no—
160C2×C13—42no—
161C2×C13—41no—
162C2×C13—81no—
163C2×C13#146611yescharacteristic
164C24#612211yescharacteristic
165#41—41no—
166#41—41no—
167C2×Q8#612211yescharacteristic
168C2×D4—22no—
169C2×D4—21no—
170C2×D4#612211yescharacteristic
171C22×C4—21no—
172C22×C4—21no—
173C22×C4—21no—
174C22×C4—41no—
175C22×C4—41no—
176C22×C4#612211yescharacteristic
177C22×C4C22×#26111yescharacteristic
178M16—521no—
179M16—522no—
180M16—521no—
181C2×C8—131no—
182C2×C8—132no—
183C2×C8—131no—
184C2×C8—262no—
185C2×C8—261no—
186C2×C8—261no—
187C2×C8—522no—
188C2×C8—522no—
189C2×C8—522no—
190C2×C8—521no—
191C4⋊C4—22no—
192C4⋊C4—21no—
193C22⋊C4—22no—
194C22⋊C4—22no—
195C22⋊C4—21no—
196C42C22⋊#26112yes—
197C16—524no—
198C13#1153711yescharacteristic, complemented, Sylow
199C23—21no—
200C23—21no—
201C23—41no—
202C23—42no—
203C23C2×#612211yescharacteristic
204Q8—41no—
205D4—41no—
206D4—44no—
207D4—42no—
208C2×C4—21no—
209C2×C4—21no—
210C2×C4—22no—
211C2×C4—21no—
212C2×C4—21no—
213C2×C4—42no—
214C2×C4—41no—
215C2×C4—41no—
216C2×C4—41no—
217C2×C4—41no—
218C2×C4—41no—
219C2×C4C2×#612211yescharacteristic
220C2×C4C2×C22⋊#26111yescharacteristic
221C8—132no—
222C8—262no—
223C8—261no—
224C8—521no—
225C8—521no—
226C22—22no—
227C22—21no—
228C22—41no—
229C22—41no—
230C22—42no—
231C22—42no—
232C22—42no—
233C22—41no—
234C22—41no—
235C22#1171916911yescharacteristic
236C4—21no—
237C4—42no—
238C4—41no—
239C4—41no—
240C4#1171914211yescharacteristic
241C4D13⋊#10011yescharacteristic
242C2—21no—
243C2—42no—
244C2—41no—
245C2—81no—
246C2#1313009611yescharacteristic
subgroupG/H
centerC4#11719142
commutatorC22×C4×C13C22×C4
FrattiniC22×C4C22×#261
Fitting, prime radicalC13×#525C4
socleC2×C13#1466
cosocleC2×#6099C23
hypercenter#525#261
hypocenterC13#11537
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C4 ◁ C2×C4 ◁ #117 ◁ #525

Complements

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

NH ≅ G/Ntype
1. #13131209C2semidirect
2. #13129770C2semidirect
3. #13129768C2semidirect
198. C13#11537semidirect

Maximal subgroups

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

subgroupindex
#131312092
#131297702
#131297682
#131235312
#1153713