Finite Group Databasebeta

← #16787119

Subgroups — #16787119

Order 3328.

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

normal subgroups only

This group has 334 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#13123540C211yesmaximal, characteristic
5C13×#525C411yescharacteristic
6C2×#88202C411yescharacteristic
7C22×#6099C411yescharacteristic
8#11718895C2211yescharacteristic
9#11718868C2211yescharacteristic
10#11718673—22no—
11#11718672—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×#6099—21no—
28C2×#6099—21no—
29C2×#6099—42no—
30C2×#6099C2×C411yescharacteristic
31C2×#6099C2311yescharacteristic
32C22×#1055—21no—
33C22×#1055C2×C411yescharacteristic
34C22×#1055C2×C411yescharacteristic
35#88106—24no—
36C22⋊#1055—22no—
37C22⋊#1055—22no—
38C4⋊#1055—22no—
39#88043D412yes—
40C4×#1055D412yes—
41#11538—131nomaximal, Sylow
42C24×C13M1611yescharacteristic
43C13×#41—41no—
44C13×#41—41no—
45C2×Q8×C13M1611yescharacteristic
46C2×D4×C13—21no—
47C2×D4×C13—22no—
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—42no—
65#6099—42no—
66#6099—41no—
67C2×#1055—22no—
68C2×#1055—21no—
69C2×#1055—21no—
70C2×#1055—42no—
71C2×#1055—41no—
72C2×#1055C22⋊C411yescharacteristic
73C2×#1055C22⋊C411yescharacteristic
74C2×#1055C2×D412yes—
75#6092—44no—
76#2930—131no—
77#2166—132no—
78#1321—132no—
79#1320—132no—
80C23×C13—21no—
81C23×C13—21no—
82C23×C13—41no—
83C23×C13—81no—
84C23×C13C2×M1611yescharacteristic
85Q8×C13—41no—
86D4×C13—41no—
87D4×C13—42no—
88D4×C13—82no—
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—
108C22×M16—131no—
109#525#26111yescharacteristic
110#436—262no—
111#435—262no—
112#424—131no—
113#408—131no—
114#407—131no—
115#405—131no—
116#364—262no—
117#349—134no—
118#347—262no—
119C22×C13—21no—
120C22×C13—41no—
121C22×C13—41no—
122C22×C13—42no—
123C22×C13—41no—
124C22×C13—41no—
125C22×C13—41no—
126C22×C13—82no—
127C22×C13#40711yescharacteristic
128C4×C13—21no—
129C4×C13—42no—
130C4×C13—41no—
131C4×C13—41no—
132C4×C13#41011yescharacteristic
133C4×C13C2×#10011yescharacteristic
134C2×#41C2×#26111yescharacteristic
135C23×C4C2×#26111yescharacteristic
136#131—522no—
137C2×M16—131no—
138C2×M16—131no—
139C2×M16—261no—
140C2×M16—261no—
141C2×M16—261no—
142C2×M16—522no—
143C22×C8—131no—
144C22×C8—131no—
145C22×C8—261no—
146#123—21no—
147C22⋊Q8—21no—
148#121—21no—
149#120—21no—
150C4×D4—22no—
151#117C2×#26111yescharacteristic
152M32—264no—
153C4⋊C8—262no—
154C22⋊C8—262no—
155C22⋊C8—262no—
156#97—132no—
157C4×C8—132no—
158C2×C13—21no—
159C2×C13—41no—
160C2×C13—81no—
161C2×C13—81no—
162C2×C13#146611yescharacteristic
163C24#612211yescharacteristic
164#41—41no—
165#41—41no—
166C2×Q8#612211yescharacteristic
167C2×D4—21no—
168C2×D4—22no—
169C2×D4#612211yescharacteristic
170C22×C4—21no—
171C22×C4—21no—
172C22×C4—21no—
173C22×C4—41no—
174C22×C4—41no—
175C22×C4#612211yescharacteristic
176C22×C4C22×#26111yescharacteristic
177M16—522no—
178M16—522no—
179M16—521no—
180M16—522no—
181M16—521no—
182C2×C8—131no—
183C2×C8—132no—
184C2×C8—131no—
185C2×C8—262no—
186C2×C8—261no—
187C2×C8—261no—
188C2×C8—522no—
189C2×C8—521no—
190C4⋊C4—22no—
191C4⋊C4—21no—
192C22⋊C4—22no—
193C22⋊C4—22no—
194C22⋊C4—21no—
195C42C22⋊#26112yes—
196C16—524no—
197C13#1153811yescharacteristic, complemented, Sylow
198C23—21no—
199C23—21no—
200C23—41no—
201C23—81no—
202C23C2×#612211yescharacteristic
203Q8—41no—
204D4—41no—
205D4—42no—
206D4—82no—
207C2×C4—21no—
208C2×C4—21no—
209C2×C4—22no—
210C2×C4—21no—
211C2×C4—21no—
212C2×C4—42no—
213C2×C4—41no—
214C2×C4—41no—
215C2×C4—41no—
216C2×C4—41no—
217C2×C4—41no—
218C2×C4C2×#612211yescharacteristic
219C2×C4C2×C22⋊#26111yescharacteristic
220C8—132no—
221C8—262no—
222C8—261no—
223C8—521no—
224C8—521no—
225C22—21no—
226C22—41no—
227C22—41no—
228C22—42no—
229C22—41no—
230C22—41no—
231C22—41no—
232C22—82no—
233C22#1171916911yescharacteristic
234C4—21no—
235C4—42no—
236C4—41no—
237C4—41no—
238C4#1171914211yescharacteristic
239C4D13⋊#10011yescharacteristic
240C2—21no—
241C2—41no—
242C2—81no—
243C2—81no—
244C2#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#11538
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
197. C13#11538semidirect

Maximal subgroups

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

subgroupindex
#131312092
#131297702
#131297682
#131235402
#1153813