Finite Group Databasebeta

← #15772232

Subgroups — #15772232

Order 3328.

364 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 364 conjugacy classes of subgroups — too many to draw. Only its 83 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#13123553C211yesmaximal, characteristic
2#13116455C212yesmaximal, complemented
3#13112787C211yesmaximal, characteristic, complemented
4#13112773C212yesmaximal, complemented
5C13×#1327C211yesmaximal, characteristic, complemented
6C2×#88161C411yescharacteristic
7C2×#88161C2211yescharacteristic
8#11719182C411yescharacteristic
9C13×#423C2211yescharacteristic
10#11718790C411yescharacteristic
11#11718790C2211yescharacteristic
12C2×#88043C411yescharacteristic
13D13×M32—22no—
14#11718497—22no—
15#11718497—22no—
16C13×#349C2212yes—
17#11718145C2212yes—
18#11718106—22no—
19C2×#6127C2×C411yescharacteristic
20C2×#6127C2×C411yescharacteristic
21C2×C13×M16C2×C411yescharacteristic
22C2×C13×M16C2311yescharacteristic
23C2×C42×C13C2×C411yescharacteristic
24#88184—22no—
25C22×#1055C2×C411yescharacteristic
26C22×#1055C2×C411yescharacteristic
27#88161—42no—
28#88161—42no—
29C2×#6094—21no—
30C2×#6094D412yes—
31C2×C8×D13—21no—
32C2×C8×D13D412yes—
33#88129C811yescharacteristic
34#88129C811yescharacteristic
35#88128C811yescharacteristic
36C4×D52—22no—
37#88123C811yescharacteristic
38C13×M32—22no—
39C13×C4⋊C8—22no—
40#88060—22no—
41#88060—22no—
42#88052—22no—
43#88043—21no—
44#88043—21no—
45#88038—42no—
46C16×D13—42no—
47#11486—131nomaximal, Sylow
48C22×C4×C13—21no—
49C22×C4×C13C22×C411yescharacteristic
50C2×C22⋊D13—21no—
51C2×C22⋊D13M1612yes—
52#6127—41no—
53#6127—41no—
54#6127—41no—
55#6127—41no—
56C2×D52—22no—
57C2×D52C2×C811yescharacteristic
58C2×D52C2×C811yescharacteristic
59C2×C4×D13—21no—
60C2×C4×D13C22⋊C412yes—
61C2×Dic26C2×C811yescharacteristic
62C2×Dic26C2×C811yescharacteristic
63C13×M16—41no—
64C13×M16—41no—
65C2×C8×C13—21no—
66C2×C8×C13C2×D412yes—
67C42×C13—21no—
68C42×C13C2×C811yescharacteristic
69C42×C13C2×C811yescharacteristic
70#6103—22no—
71#6103—22no—
72C4⋊Dic13—22no—
73C2×#1055—22no—
74C2×#1055—21no—
75C2×#1055—41no—
76C2×#1055C22⋊C411yescharacteristic
77C2×#1055C22⋊C411yescharacteristic
78#6094—42no—
79#6094—42no—
80C8×D13—22no—
81C8×D13—22no—
82C8×D13—42no—
83C13×C16—42no—
84#6090—42no—
85#2932—131no—
86#2115—132no—
87#1327—131no—
88#1327D1311yescharacteristic, complemented
89#1321—132no—
90C23×C13C2×M1611yescharacteristic
91C22×D13—21no—
92C22×D13C22⋊C812yes—
93C2×C4×C13—21no—
94C2×C4×C13—21no—
95C2×C4×C13—21no—
96C2×C4×C13—21no—
97C2×C4×C13—81no—
98C2×C4×C13C2×C22⋊C411yescharacteristic
99C2×C4×C13C22×C811yescharacteristic
100C22⋊D13—42no—
101C22⋊D13—42no—
102C2×Dic13—21no—
103C2×Dic13C22⋊C812yes—
104D52—41no—
105D52—41no—
106D52—82no—
107C4×D13—22no—
108C4×D13—22no—
109C4×D13—41no—
110C4×D13—41no—
111Dic26—41no—
112Dic26—41no—
113C8×C13—22no—
114C8×C13—41no—
115#1055—21no—
116#1055—41no—
117#1055#9912yes—
118C2×#131—131no—
119C2×#131—131no—
120#532—131no—
121C2×M32—262no—
122#435—262no—
123#435—262no—
124#423C2×D1311yescharacteristic
125#408—131no—
126#408—131no—
127C2×#97—131no—
128#349—132no—
129#349—262no—
130#349C2×D1312yes—
131C22×C13—21no—
132C22×C13—41no—
133C22×C13C2×C22⋊C811yescharacteristic
134C2×D13—22no—
135C2×D13—42no—
136C2×D13—42no—
137C2×D13—41no—
138C4×C13—21no—
139C4×C13—41no—
140C4×C13—41no—
141C4×C13C2×#9911yescharacteristic
142C4×C13#41311yescharacteristic
143Dic13—22no—
144Dic13—41no—
145C2×#41—131no—
146C2×#41—131no—
147#131—522no—
148#131—522no—
149C2×M16—132no—
150C2×M16—261no—
151C2×M16C4×D1311yescharacteristic
152C2×M16C22×D1311yescharacteristic
153C22×C8—131no—
154C22×C8—132no—
155C22×C8—131no—
156C22×C8—261no—
157C4⋊Q8—131no—
158#127—131no—
159#124—131no—
160#124—131no—
161#121—262no—
162C4×D4—262no—
163C2×C42C4×D1311yescharacteristic
164M32—22no—
165M32—262no—
166M32—522no—
167C2×C16—522no—
168C4⋊C8—22no—
169C22⋊C8—262no—
170C22⋊C8—262no—
171#97—261no—
172#97—261no—
173C2×C13—21no—
174C2×C13—41no—
175C2×C13#145911yescharacteristic
176D13—42no—
177D13—81no—
178#41—521no—
179#41—521no—
180#41—521no—
181#41—521no—
182C2×Q8—131no—
183C2×Q8—131no—
184C2×D4—132no—
185C2×D4—131no—
186C2×D4—131no—
187C2×D4—262no—
188C2×D4—261no—
189C22×C4—21no—
190C22×C4—132no—
191C22×C4—261no—
192C22×C4C2×C4×D1311yescharacteristic
193M16—41no—
194M16—41no—
195M16—522no—
196M16—522no—
197C2×C8—21no—
198C2×C8—131no—
199C2×C8—131no—
200C2×C8—262no—
201C2×C8—262no—
202C2×C8—262no—
203C2×C8—261no—
204C2×C8—522no—
205C2×C8—521no—
206C2×C8D4×D1312yes—
207C4⋊C4—262no—
208C22⋊C4—262no—
209C22⋊C4—262no—
210C42—21no—
211C42C8×D1311yescharacteristic
212C42C8×D1311yescharacteristic
213C16—42no—
214C16—522no—
215C13#1148611yescharacteristic, complemented, Sylow
216C23—132no—
217C23—261no—
218C23M16×D1311yescharacteristic
219Q8—521no—
220Q8—521no—
221D4—521no—
222D4—521no—
223D4—522no—
224D4—522no—
225D4—1042no—
226C2×C4—21no—
227C2×C4—21no—
228C2×C4—21no—
229C2×C4—21no—
230C2×C4—81no—
231C2×C4—132no—
232C2×C4—262no—
233C2×C4—262no—
234C2×C4—261no—
235C2×C4—521no—
236C2×C4—521no—
237C2×C4C22⋊C4×D1311yescharacteristic
238C2×C4C2×C8×D1311yescharacteristic
239C8—22no—
240C8—41no—
241C8—132no—
242C8—261no—
243C8—521no—
244C22—21no—
245C22—41no—
246C22—262no—
247C22—522no—
248C22—522no—
249C22—521no—
250C22D13×C22⋊C811yescharacteristic
251C4—21no—
252C4—41no—
253C4—41no—
254C4—262no—
255C4—521no—
256C4D13×#9911yescharacteristic
257C4#1171841211yescharacteristic
258C2—21no—
259C2—41no—
260C2—522no—
261C2—1041no—
262C2#1311315311yescharacteristic
subgroupG/H
centerC4D13×#99
commutatorC2×C4×C13C22×C8
FrattiniC2×M16C22×D13
FittingC13×#1327C2
socleC2×C13#1459
prime radical#11719182C4
cosocleC2×C13×M16C23
hypercenter#1327D13
hypocenterC13#11486
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C4 ◁ C2×C4 ◁ C2×M16 ◁ #1327

Complements

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

NH ≅ G/Ntype
2. #13116455C2semidirect
3. #13112787C2semidirect
4. #13112773C2semidirect
5. C13×#1327C2semidirect
88. #1327D13semidirect
215. C13#11486semidirect

Maximal subgroups

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

subgroupindex
#131235532
#131164552
#131127872
#131127732
C13×#13272
#1148613