Finite Group Databasebeta

← #16786940

Subgroups — #16786940

Order 3328.

364 conjugacy classes of subgroups; only the 82 normal subgroups are shown.

normal subgroups only

This group has 364 conjugacy classes of subgroups — too many to draw. Only its 82 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#13131073C212yesmaximal, complemented
2#13129782C212yesmaximal, complemented
3#13129771C212yesmaximal, complemented
4#13123555C211yesmaximal, characteristic
5C2×#88155C411yescharacteristic
6C2×#88155C2211yescharacteristic
7#11719182C411yescharacteristic
8D13⋊M32—22no—
9C2×C13×#97C411yescharacteristic
10#11718771C411yescharacteristic
11#11718771C2211yescharacteristic
12#11718585C2211yescharacteristic
13#11718367—22no—
14#11718367—22no—
15#11718284C2214yes—
16#11718263—22no—
17C2×#6127C2×C411yescharacteristic
18C2×#6127C2×C411yescharacteristic
19C22×C8×C13C2×C411yescharacteristic
20C22×C8×C13C2×C411yescharacteristic
21C2×C42×C13C2×C411yescharacteristic
22#88184—22no—
23C2×#6099C2×C411yescharacteristic
24C2×#6099C2311yescharacteristic
25#88155—42no—
26#88155—42no—
27C2×#6094—21no—
28C2×#6094D412yes—
29C2×C8×D13—21no—
30C2×C8×D13D412yes—
31#88129C811yescharacteristic
32#88129C811yescharacteristic
33#88128C811yescharacteristic
34C4×D52—22no—
35#88123C811yescharacteristic
36#88106—24no—
37#88098—42no—
38D13⋊C16—42no—
39C13×#97—21no—
40C13×#97—21no—
41#88060—22no—
42#88060—22no—
43C4⋊#1055—22no—
44#11486—131nomaximal, Sylow
45C22×C4×C13—21no—
46C22×C4×C13C22×C411yescharacteristic
47C2×C22⋊D13—21no—
48C2×C22⋊D13M1612yes—
49#6127—41no—
50#6127—41no—
51#6127—41no—
52#6127—41no—
53C2×D52—22no—
54C2×D52C2×C811yescharacteristic
55C2×D52C2×C811yescharacteristic
56C2×C4×D13—21no—
57C2×C4×D13C22⋊C412yes—
58C2×Dic26C2×C811yescharacteristic
59C2×Dic26C2×C811yescharacteristic
60C2×C8×C13—22no—
61C2×C8×C13—21no—
62C2×C8×C13—41no—
63C2×C8×C13C22⋊C411yescharacteristic
64C2×C8×C13C22⋊C411yescharacteristic
65C42×C13—21no—
66C42×C13C2×C811yescharacteristic
67C42×C13C2×C811yescharacteristic
68#6103—22no—
69#6103—22no—
70C4⋊Dic13—22no—
71#6099—41no—
72#6099—41no—
73C2×#1055—21no—
74C2×#1055C2×D412yes—
75#6094—42no—
76#6094—42no—
77C8×D13—22no—
78C8×D13—22no—
79C8×D13—42no—
80#6092—44no—
81#2932—131no—
82#2115—132no—
83#1327—132no—
84#1321—132no—
85C23×C13C2×M1611yescharacteristic
86C22×D13—21no—
87C22×D13C22⋊C812yes—
88C2×C4×C13—21no—
89C2×C4×C13—21no—
90C2×C4×C13—21no—
91C2×C4×C13—21no—
92C2×C4×C13—81no—
93C2×C4×C13C2×C22⋊C411yescharacteristic
94C2×C4×C13C22×C811yescharacteristic
95C22⋊D13—42no—
96C22⋊D13—42no—
97C2×Dic13—21no—
98C2×Dic13C22⋊C812yes—
99D52—41no—
100D52—41no—
101D52—82no—
102C4×D13—22no—
103C4×D13—22no—
104C4×D13—41no—
105C4×D13—41no—
106Dic26—41no—
107Dic26—41no—
108C8×C13—21no—
109C8×C13—41no—
110C8×C13#9912yes—
111#1055—22no—
112#1055—41no—
113C2×#131—131no—
114C2×#131—131no—
115#532—131no—
116C2×M32—262no—
117#435—262no—
118#435—262no—
119#423—131no—
120#408—131no—
121#408—131no—
122C2×#97#26111yescharacteristic
123#349—134no—
124#349—262no—
125C22×C13—21no—
126C22×C13—41no—
127C22×C13C2×C22⋊C811yescharacteristic
128C2×D13—22no—
129C2×D13—42no—
130C2×D13—42no—
131C2×D13—41no—
132C4×C13—21no—
133C4×C13—41no—
134C4×C13—41no—
135C4×C13C2×#9911yescharacteristic
136C4×C13#41311yescharacteristic
137Dic13—22no—
138Dic13—41no—
139C2×#41—131no—
140C2×#41—131no—
141#131—522no—
142#131—522no—
143C2×M16—131no—
144C2×M16—132no—
145C2×M16—131no—
146C2×M16—261no—
147C22×C8—132no—
148C22×C8—261no—
149C22×C8C2×#26111yescharacteristic
150C22×C8C2×#26111yescharacteristic
151C4⋊Q8—131no—
152#127—131no—
153#124—131no—
154#124—131no—
155#121—262no—
156C4×D4—262no—
157C2×C42C2×#26111yescharacteristic
158M32—264no—
159M32—522no—
160C2×C16—522no—
161C4⋊C8—262no—
162C22⋊C8—262no—
163C22⋊C8—262no—
164#97—21no—
165#97—21no—
166C2×C13—21no—
167C2×C13—41no—
168C2×C13#145911yescharacteristic
169D13—42no—
170D13—81no—
171#41—521no—
172#41—521no—
173#41—521no—
174#41—521no—
175C2×Q8—131no—
176C2×Q8—131no—
177C2×D4—132no—
178C2×D4—131no—
179C2×D4—131no—
180C2×D4—262no—
181C2×D4—261no—
182C22×C4—21no—
183C22×C4—132no—
184C22×C4—261no—
185C22×C4C22×#26111yescharacteristic
186M16—522no—
187M16—521no—
188M16—522no—
189M16—521no—
190C2×C8—22no—
191C2×C8—21no—
192C2×C8—41no—
193C2×C8—132no—
194C2×C8—262no—
195C2×C8—262no—
196C2×C8—261no—
197C2×C8—522no—
198C2×C8C22⋊#26111yescharacteristic
199C2×C8C22⋊#26111yescharacteristic
200C4⋊C4—262no—
201C22⋊C4—262no—
202C22⋊C4—262no—
203C42—21no—
204C42D13⋊C811yescharacteristic
205C42D13⋊C811yescharacteristic
206C16—524no—
207C13#1148611yescharacteristic, complemented, Sylow
208C23—132no—
209C23—261no—
210C23D13⋊M1611yescharacteristic
211Q8—521no—
212Q8—521no—
213D4—521no—
214D4—521no—
215D4—522no—
216D4—522no—
217D4—1042no—
218C2×C4—21no—
219C2×C4—21no—
220C2×C4—21no—
221C2×C4—21no—
222C2×C4—81no—
223C2×C4—132no—
224C2×C4—262no—
225C2×C4—262no—
226C2×C4—261no—
227C2×C4—521no—
228C2×C4—521no—
229C2×C4C2×D13⋊C811yescharacteristic
230C2×C4C2×C22⋊#26111yescharacteristic
231C8—21no—
232C8—41no—
233C8—262no—
234C8—521no—
235C8#8810712yes—
236C22—21no—
237C22—41no—
238C22—262no—
239C22—522no—
240C22—522no—
241C22—521no—
242C22D13⋊(C22⋊C8)11yescharacteristic
243C4—21no—
244C4—41no—
245C4—41no—
246C4—262no—
247C4—521no—
248C4C2×#8810711yescharacteristic
249C4#1171913211yescharacteristic
250C2—21no—
251C2—41no—
252C2—522no—
253C2—1041no—
254C2#1313007311yescharacteristic
subgroupG/H
centerC4C2×#88107
commutatorC2×C4×C13C22×C8
FrattiniC22×C4C22×#261
FittingC2×C13×#97C4
socleC2×C13#1459
prime radical#11719182C4
cosocleC2×#6099C23
hypercenterC2×#97#261
hypocenterC13#11486
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C4 ◁ C2×C8 ◁ C22×C8 ◁ C2×#97

Complements

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

NH ≅ G/Ntype
1. #13131073C2semidirect
2. #13129782C2semidirect
3. #13129771C2semidirect
207. C13#11486semidirect

Maximal subgroups

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

subgroupindex
#131310732
#131297822
#131297712
#131235552
#1148613