Finite Group Databasebeta

← #15774245

Subgroups — #15774245

Order 3328.

354 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 354 conjugacy classes of subgroups — too many to draw. Only its 115 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#13125415C211yesmaximal, characteristic
2#13116635C211yesmaximal, characteristic, complemented
3#13112892C212yesmaximal, complemented
4#13112881C212yesmaximal, complemented
5C2×C13×#335C211yesmaximal, characteristic, complemented
6#11719182—21no—
7C2×C13×C4⋊C8—21no—
8C2×C4×C8×C13C2211yescharacteristic
9#11718776—21no—
10#11718776C412yes—
11#11718356C2211yescharacteristic
12#11718355—21no—
13C4×D104—21no—
14C4×D104C412yes—
15#11718343C2211yescharacteristic
16C13×#335—21no—
17C13×#335C2212yes—
18C22⋊#6090—21no—
19C4⋊#6090C2212yes—
20C4×#6090—21no—
21C2×#6127—41no—
22C22×C8×C13—41no—
23C22×C8×C13C2×C411yescharacteristic
24C22×C8×C13D411yescharacteristic
25C2×C42×C13D411yescharacteristic
26#88184—22no—
27#88184—41no—
28C2×D104—21no—
29C2×D104C2×C412yes—
30#88129—41no—
31#88128—21no—
32C4×D52—22no—
33C4×D52—41no—
34#88123—21no—
35C13×C4⋊C8—22no—
36C13×C4⋊C8—41no—
37C4×C8×C13C2×C411yescharacteristic
38C4×C8×C13D411yescharacteristic
39C4×C8×C13D411yescharacteristic
40C4×C8×C13C2311yescharacteristic
41#88061—22no—
42#88061—22no—
43#88058—21no—
44#88058C2×C412yes—
45C2×#6090—22no—
46#11947—131nomaximal, Sylow
47C22×C4×C13C22⋊C411yescharacteristic
48C22×C4×C13D811yescharacteristic
49C22×C4×C13SD1611yescharacteristic
50C2×C22⋊D13—42no—
51#6127—82no—
52#6127—82no—
53C2×D52—22no—
54C2×D52—41no—
55C2×D52—41no—
56C2×C4×D13—42no—
57C2×Dic26—41no—
58C2×C8×C13—22no—
59C2×C8×C13—41no—
60C2×C8×C13—42no—
61C2×C8×C13—82no—
62C2×C8×C13C22⋊C411yescharacteristic
63C2×C8×C13C22⋊C411yescharacteristic
64C2×C8×C13C22×C411yescharacteristic
65C2×C8×C13C2×D411yescharacteristic
66C42×C13C22⋊C411yescharacteristic
67C42×C13D811yescharacteristic
68C42×C13SD1611yescharacteristic
69C42×C13C2×D411yescharacteristic
70#6103—42no—
71#6103—42no—
72C4⋊Dic13—22no—
73C4⋊Dic13—41no—
74D104—42no—
75D104—42no—
76#6090—42no—
77#3169—131no—
78#2162—131no—
79C2×#335D1311yescharacteristic, complemented
80#1364—132no—
81#1361—132no—
82C23×C13#10211yescharacteristic
83C22×D13—42no—
84C2×C4×C13—21no—
85C2×C4×C13—21no—
86C2×C4×C13—41no—
87C2×C4×C13#10211yescharacteristic
88C2×C4×C13#10211yescharacteristic
89C2×C4×C13#10211yescharacteristic
90C2×C4×C13D1612yes—
91C2×C4×C13SD3212yes—
92C2×C4×C13C2×C22⋊C411yescharacteristic
93C2×C4×C13C2×D811yescharacteristic
94C2×C4×C13C2×SD1611yescharacteristic
95C22⋊D13—84no—
96C2×Dic13—42no—
97D52—42no—
98D52—42no—
99D52—82no—
100D52—81no—
101D52—81no—
102C4×D13—84no—
103Dic26—81no—
104Dic26—81no—
105C8×C13—21no—
106C8×C13—21no—
107C8×C13—21no—
108C8×C13—82no—
109C8×C13#13512yes—
110#532—261no—
111#500—131no—
112#493—131no—
113#486—261no—
114#466—132no—
115#466—261no—
116C4×D8—132no—
117C4×D8—261no—
118C2×C4⋊C8—21no—
119C2×C4×C8C2×D1311yescharacteristic
120C4⋊C16—132no—
121C22⋊C16—261no—
122C4×C16—261no—
123#335—21no—
124#335C2×D1312yes—
125C22×C13—21no—
126C22×C13—21no—
127C22×C13#35712yes—
128C22×C13C2×#10211yescharacteristic
129C2×D13—82no—
130C2×D13—82no—
131C2×D13—82no—
132C4×C13—21no—
133C4×C13—21no—
134C4×C13—21no—
135C4×C13#35712yes—
136C4×C13#41311yescharacteristic
137C4×C13#41611yescharacteristic
138C4×C13C2×D1611yescharacteristic
139C4×C13C2×SD3211yescharacteristic
140Dic13—82no—
141C2×#41—521no—
142C2×D8—132no—
143C2×D8—261no—
144C22×C8—41no—
145C22×C8C4×D1311yescharacteristic
146C22×C8D5211yescharacteristic
147C4⋊Q8—261no—
148#127—261no—
149#124—521no—
150#121—262no—
151#121—521no—
152C4×D4—262no—
153C4×D4—521no—
154C2×C42C22⋊D1311yescharacteristic
155C2×C16—262no—
156#107—132no—
157#107—261no—
158C4⋊C8—22no—
159C4⋊C8—41no—
160#102—262no—
161#102—262no—
162C4×C8C4×D1311yescharacteristic
163C4×C8D5211yescharacteristic
164C4×C8C22⋊D1311yescharacteristic
165C4×C8C22×D1311yescharacteristic
166C2×C13—22no—
167C2×C13#154011yescharacteristic
168C2×C13C2×#35711yescharacteristic
169C2×C13#214811yescharacteristic
170D13—162no—
171#41—1042no—
172#41—1042no—
173C2×Q8—521no—
174C2×D4—262no—
175C2×D4—522no—
176C2×D4—521no—
177C2×D4—521no—
178C22×C4—522no—
179C22×C4#610311yescharacteristic
180C22×C4#610411yescharacteristic
181C22×C4#610611yescharacteristic
182D8—522no—
183D8—522no—
184C2×C8—22no—
185C2×C8—41no—
186C2×C8—42no—
187C2×C8—82no—
188C2×C8#610311yescharacteristic
189C2×C8#610311yescharacteristic
190C2×C8C2×C4×D1311yescharacteristic
191C2×C8C2×D5211yescharacteristic
192C4⋊C4—262no—
193C4⋊C4—521no—
194C22⋊C4—522no—
195C22⋊C4—522no—
196C42#610311yescharacteristic
197C42#610411yescharacteristic
198C42#610611yescharacteristic
199C42C2×C22⋊D1311yescharacteristic
200C16—522no—
201C13#1194711yescharacteristic, complemented, Sylow
202C23—522no—
203C23#8804911yescharacteristic
204Q8—1041no—
205Q8—1041no—
206D4—522no—
207D4—522no—
208D4—1042no—
209D4—1044no—
210D4—1041no—
211D4—1041no—
212C2×C4—21no—
213C2×C4—21no—
214C2×C4—41no—
215C2×C4—522no—
216C2×C4—1044no—
217C2×C4#8804911yescharacteristic
218C2×C4#8804911yescharacteristic
219C2×C4#8804911yescharacteristic
220C2×C4#8806612yes—
221C2×C4#8806812yes—
222C2×C4C2×#610311yescharacteristic
223C2×C4C2×#610411yescharacteristic
224C2×C4C2×#610611yescharacteristic
225C8—21no—
226C8—21no—
227C8—21no—
228C8—82no—
229C8#8815812yes—
230C22—21no—
231C22—21no—
232C22—1042no—
233C22—1042no—
234C22—1042no—
235C22#1171808312yes—
236C22C2×#8804911yescharacteristic
237C4—21no—
238C4—21no—
239C4—21no—
240C4—1042no—
241C4#1171808312yes—
242C4#1171877411yescharacteristic
243C4#1171879311yescharacteristic
244C4C2×#8806611yescharacteristic
245C4C2×#8806811yescharacteristic
246C2—22no—
247C2—2082no—
248C2#1311348611yescharacteristic
249C2C2×#1171808311yescharacteristic
250C2#1311658311yescharacteristic
subgroupG/H
centerC2×C4#88049
commutatorC2×C8×C13C22×C4
FrattiniC4×C8C22×D13
FittingC2×C13×#335C2
socleC22×C13C2×#102
prime radical#13125415C2
cosocleC4×C8×C13C23
hypercenterC2×#335D13
hypocenterC13#11947
LCSG ▷ C2×C8×C13 ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C2×C4×C8 ◁ C2×#335

Complements

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

NH ≅ G/Ntype
2. #13116635C2semidirect
3. #13112892C2semidirect
4. #13112881C2semidirect
5. C2×C13×#335C2semidirect
79. C2×#335D13semidirect
201. C13#11947semidirect

Maximal subgroups

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

subgroupindex
#131254152
#131166352
#131128922
#131128812
C2×C13×#3352
#1194713