Finite Group Databasebeta

← #15772155

Subgroups — #15772155

Order 3328.

398 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 398 conjugacy classes of subgroups — too many to draw. Only its 91 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#13123529C211yesmaximal, characteristic
2D13×C22⋊C16C212yesmaximal, complemented
3#13112778C211yesmaximal, characteristic, complemented
4#13112761C212yesmaximal, complemented
5C13×#1323C211yesmaximal, characteristic, complemented
6C2×#88161C411yescharacteristic
7C22×C8×D13C2211yescharacteristic
8#11719229C411yescharacteristic
9C13×#424C2211yescharacteristic
10#11718787C411yescharacteristic
11#11718771C2211yescharacteristic
12#11718658C411yescharacteristic
13C2×C16×D13—22no—
14#11718497—22no—
15#11718495—22no—
16C13×C22⋊C16C2212yes—
17C22⋊#6090C2212yes—
18#11718099—22no—
19C2×#6127C2×C411yescharacteristic
20C22×C4×D13C2×C411yescharacteristic
21C2×C13×M16C2×C411yescharacteristic
22C22×C8×C13C2311yescharacteristic
23C13×#117C2×C411yescharacteristic
24C2×#6099C2×C411yescharacteristic
25C22×#1055C2×C411yescharacteristic
26#88161—42no—
27C2×#6094—21no—
28C2×C8×D13—21no—
29C2×C8×D13—42no—
30C2×C8×D13D412yes—
31C2×C8×D13D412yes—
32#88151C812yes—
33#88149C812yes—
34#88140—21no—
35#88136—21no—
36C4×D52—22no—
37C2×C13×C16—22no—
38C13×C4⋊C8—22no—
39#88060—22no—
40#88060—22no—
41C2×#6090—22no—
42#88043—21no—
43C4×#1055—21no—
44C16×D13—44no—
45#11468—131nomaximal, Sylow
46C23×D13M1611yescharacteristic
47C22×C4×C13C22×C411yescharacteristic
48C2×C22⋊D13—21no—
49C22×Dic13M1611yescharacteristic
50#6127—41no—
51#6127—41no—
52C2×D52—22no—
53C2×D52C2×C811yescharacteristic
54C2×C4×D13—21no—
55C2×C4×D13—41no—
56C2×C4×D13—41no—
57C2×C4×D13C22⋊C412yes—
58C2×C4×D13C2×C812yes—
59C2×Dic26C2×C811yescharacteristic
60C13×M16—41no—
61C2×C8×C13—21no—
62C2×C8×C13—41no—
63C2×C8×C13C2×D412yes—
64C13×C4⋊C4C2×C812yes—
65C13×C22⋊C4—21no—
66C42×C13—21no—
67#6103—22no—
68#6103—22no—
69C4⋊Dic13—22no—
70#6099—41no—
71C2×#1055—22no—
72C2×#1055—21no—
73C2×#1055C22⋊C411yescharacteristic
74C2×#1055C22⋊C411yescharacteristic
75#6094—42no—
76C8×D13—24no—
77C8×D13—42no—
78C8×D13—42no—
79C13×C16—42no—
80#6090—42no—
81#2929—131no—
82C2×C22⋊C16—132no—
83#1323—131no—
84#1323D1311yescharacteristic, complemented
85#1315—132no—
86C23×C13C2×M1611yescharacteristic
87C22×D13—24no—
88C22×D13—21no—
89C22×D13—41no—
90C22×D13C22⋊C812yes—
91C2×C4×C13—21no—
92C2×C4×C13—21no—
93C2×C4×C13—22no—
94C2×C4×C13C2×C22⋊C411yescharacteristic
95C2×C4×C13C22×C811yescharacteristic
96C22⋊D13—42no—
97C2×Dic13—21no—
98C2×Dic13—41no—
99C2×Dic13C22⋊C812yes—
100D52—41no—
101D52—44no—
102C4×D13—22no—
103C4×D13—22no—
104C4×D13—42no—
105C4×D13—41no—
106C4×D13—41no—
107Dic26—41no—
108C8×C13—22no—
109C8×C13—41no—
110#1055—21no—
111#1055—41no—
112#1055#9912yes—
113C2×#131—131no—
114C23×C8—131no—
115#525—131no—
116C22×C16—262no—
117#435—262no—
118C8×D4—262no—
119#424C2×D1311yescharacteristic
120#408—131no—
121#407—131no—
122#405—131no—
123C22⋊C16—132no—
124C22⋊C16—262no—
125C22⋊C16C2×D1312yes—
126C22×C13—22no—
127C22×C13—21no—
128C22×C13C2×C22⋊C811yescharacteristic
129C2×D13—22no—
130C2×D13—22no—
131C2×D13—44no—
132C2×D13—42no—
133C2×D13—41no—
134C2×D13#35014yes—
135C4×C13—21no—
136C4×C13—42no—
137C4×C13C2×#9911yescharacteristic
138C4×C13#41311yescharacteristic
139Dic13—22no—
140Dic13—41no—
141C2×#41—131no—
142C23×C4—131no—
143#131—522no—
144C2×M16—131no—
145C2×M16—261no—
146C2×M16C4×D1311yescharacteristic
147C22×C8—131no—
148C22×C8—132no—
149C22×C8—132no—
150C22×C8—261no—
151C22×C8—522no—
152C22×C8C22×D1311yescharacteristic
153#123—261no—
154C22⋊Q8—132no—
155#121—132no—
156#120—261no—
157C4×D4—262no—
158#117C4×D1311yescharacteristic
159C2×C16—22no—
160C2×C16—262no—
161C2×C16—524no—
162C4⋊C8—22no—
163C22⋊C8—262no—
164C22⋊C8—262no—
165#97—261no—
166C4×C8—261no—
167C2×C13—41no—
168C2×C13#145911yescharacteristic
169C2×C13C2×#35012yes—
170D13—24no—
171D13—81no—
172C24—131no—
173#41—521no—
174#41—521no—
175C2×Q8—131no—
176C2×D4—131no—
177C2×D4—262no—
178C2×D4—261no—
179C22×C4—131no—
180C22×C4—132no—
181C22×C4—132no—
182C22×C4—261no—
183C22×C4—521no—
184C22×C4—521no—
185C22×C4C2×C4×D1311yescharacteristic
186M16—41no—
187M16—522no—
188M16—521no—
189C2×C8—21no—
190C2×C8—41no—
191C2×C8—131no—
192C2×C8—131no—
193C2×C8—264no—
194C2×C8—262no—
195C2×C8—261no—
196C2×C8—522no—
197C2×C8—522no—
198C2×C8D4×D1312yes—
199C4⋊C4—262no—
200C4⋊C4C8×D1312yes—
201C22⋊C4—21no—
202C22⋊C4—262no—
203C22⋊C4—262no—
204C42—21no—
205C16—42no—
206C16—522no—
207C13#1146811yescharacteristic, complemented, Sylow
208C23—132no—
209C23—264no—
210C23—261no—
211C23—521no—
212C23M16×D1311yescharacteristic
213Q8—521no—
214D4—521no—
215D4—524no—
216D4—522no—
217C2×C4—21no—
218C2×C4—21no—
219C2×C4—22no—
220C2×C4—132no—
221C2×C4—262no—
222C2×C4—262no—
223C2×C4—261no—
224C2×C4—522no—
225C2×C4—521no—
226C2×C4—521no—
227C2×C4—521no—
228C2×C4C22⋊C4×D1311yescharacteristic
229C2×C4C2×C8×D1311yescharacteristic
230C8—22no—
231C8—41no—
232C8—132no—
233C8—261no—
234C8—521no—
235C22—22no—
236C22—21no—
237C22—134no—
238C22—262no—
239C22—262no—
240C22—524no—
241C22—522no—
242C22—521no—
243C22D13×C22⋊C811yescharacteristic
244C4—21no—
245C4—42no—
246C4—262no—
247C4—521no—
248C4D13×#9911yescharacteristic
249C4#1171841211yescharacteristic
250C2—41no—
251C2—264no—
252C2—1041no—
253C2#1311315311yescharacteristic
254C2D13×#35012yes—
subgroupG/H
centerC2×C4C22⋊C4×D13
commutatorC2×C4×C13C22×C8
FrattiniC22×C8C22×D13
FittingC13×#1323C2
socleC22×C13C2×C22⋊C8
prime radical#11719229C4
cosocleC22×C8×C13C23
hypercenter#1323D13
hypocenterC13#11468
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ #1323

Complements

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

NH ≅ G/Ntype
2. D13×C22⋊C16C2semidirect
3. #13112778C2semidirect
4. #13112761C2semidirect
5. C13×#1323C2semidirect
84. #1323D13semidirect
207. C13#11468semidirect

Maximal subgroups

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

subgroupindex
#131235292
D13×C22⋊C162
#131127782
#131127612
C13×#13232
#1146813