Finite Group Databasebeta

← #15767688

Subgroups — #15767688

Order 3328.

330 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 330 conjugacy classes of subgroups — too many to draw. Only its 93 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#13115668C211yesmaximal, characteristic
2#13113486C212yesmaximal
3#13112733C212yesmaximal, complemented
4#13112665C211yesmaximal, characteristic, complemented
5C13×#1843C211yesmaximal, characteristic, complemented
6#11719182C2211yescharacteristic
7C2×C13×C4⋊C8—21no—
8C2×C13×C4⋊C8—21no—
9C2×C13×C4⋊C8C2212yes—
10C13×#376C2211yescharacteristic
11C2×#88045—21no—
12C2×#88045—21no—
13#11718586C2212yes—
14#11718585C2211yescharacteristic
15#11718077—22no—
16#11718074—22no—
17C2×#6127—21no—
18C22×C8×C13—22no—
19C2×C42×C13D411yescharacteristic
20C2×C42×C13D411yescharacteristic
21C2×C42×C13C2311yescharacteristic
22#88184—22no—
23C2×#6099—21no—
24#88129—21no—
25#88128D411yescharacteristic
26C4×D52—22no—
27#88123D411yescharacteristic
28C13×C4⋊C8—22no—
29C13×C4⋊C8—22no—
30C13×C4⋊C8—42no—
31C13×C4⋊C8—42no—
32C13×#95—22no—
33C22⋊#1055—22no—
34#88045—42no—
35#88045—42no—
36C4⋊#1055—22no—
37C4⋊#1055—22no—
38C4×#1055—22no—
39#10627—131nomaximal, Sylow
40C22×C4×C13—21no—
41C22×C4×C13—21no—
42C22×C4×C13C2×D411yescharacteristic
43C22×C4×C13#4112yes—
44C2×C22⋊D13—41no—
45#6127—41no—
46#6127—41no—
47#6127—41no—
48#6127—41no—
49C2×D52—21no—
50C2×D52—22no—
51C2×C4×D13—41no—
52C2×Dic26—21no—
53C2×C8×C13—42no—
54C2×C8×C13—42no—
55C2×C8×C13—42no—
56C42×C13—21no—
57C42×C13—21no—
58C42×C13D812yes—
59C42×C13SD1612yes—
60C42×C13C2×D411yescharacteristic
61C42×C13#4111yescharacteristic
62C42×C13#4112yes—
63#6103—42no—
64C4⋊Dic13—22no—
65#6099—41no—
66#6099—41no—
67C2×#1055—42no—
68C2×#1055—41no—
69#1963—131no—
70#1843D1311yescharacteristic, complemented
71#1540—132no—
72#1301—132no—
73#1274—131no—
74C23×C13#12311yescharacteristic
75C22×D13—41no—
76C2×C4×C13—22no—
77C2×C4×C13—22no—
78C2×C4×C13—42no—
79C2×C4×C13—42no—
80C2×C4×C13—42no—
81C2×C4×C13#12111yescharacteristic
82C2×C4×C13#12312yes—
83C2×C4×C13#12411yescharacteristic
84C2×C4×C13#12612yes—
85C2×C4×C13C2×D811yescharacteristic
86C2×C4×C13C2×SD1611yescharacteristic
87C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
88C2×C4×C13#13711yescharacteristic
89C22⋊D13—81no—
90C22⋊D13—81no—
91C2×Dic13—41no—
92D52—41no—
93D52—41no—
94D52—82no—
95C4×D13—81no—
96C4×D13—81no—
97Dic26—41no—
98Dic26—41no—
99C8×C13—82no—
100#1055—82no—
101#1055—81no—
102#532—131no—
103#431—132no—
104#423—131no—
105C2×C4⋊C8—21no—
106C2×C4⋊C8—21no—
107C2×C4⋊C8C2×D1312yes—
108C2×#104—261no—
109C2×#104—261no—
110#376C2×D1311yescharacteristic
111#332—262no—
112#331—262no—
113C22×C13—22no—
114C22×C13#39711yescharacteristic
115C22×C13#48011yescharacteristic
116C22×C13#48111yescharacteristic
117C2×D13—81no—
118C2×D13—82no—
119C4×C13—22no—
120C4×C13—22no—
121C4×C13—42no—
122C4×C13—42no—
123C4×C13#45911yescharacteristic
124C4×C13#46111yescharacteristic
125C4×C13#48611yescharacteristic
126C4×C13#48911yescharacteristic
127Dic13—81no—
128C2×#41—261no—
129C2×M16—261no—
130C22×C8—22no—
131C4⋊Q8—131no—
132#127—131no—
133#124—261no—
134#121—262no—
135C4×D4—262no—
136C2×C42C22⋊D1311yescharacteristic
137C2×C42C22⋊D1311yescharacteristic
138C2×C42C22×D1311yescharacteristic
139C4⋊C8—22no—
140C4⋊C8—22no—
141C4⋊C8—42no—
142C4⋊C8—42no—
143C4⋊C8—262no—
144C4⋊C8—262no—
145#104—522no—
146#104—522no—
147C22⋊C8—262no—
148C4×C8—262no—
149#95—22no—
150C2×C13—21no—
151C2×C13—21no—
152C2×C13#207111yescharacteristic
153C2×C13#208012yes—
154D13—161no—
155#41—521no—
156#41—521no—
157#41—521no—
158#41—521no—
159C2×Q8—261no—
160C2×D4—262no—
161C2×D4—261no—
162C2×D4—521no—
163C22×C4—21no—
164C22×C4—21no—
165C22×C4—521no—
166C22×C4#612712yes—
167C22×C4C2×C22⋊D1311yescharacteristic
168M16—521no—
169M16—521no—
170C2×C8—42no—
171C2×C8—42no—
172C2×C8—42no—
173C2×C8—522no—
174C2×C8—521no—
175C4⋊C4—262no—
176C22⋊C4—522no—
177C42—21no—
178C42—21no—
179C42#610412yes—
180C42#610612yes—
181C42D4×D1311yescharacteristic
182C42#612911yescharacteristic
183C42#613112yes—
184C13#1062711yescharacteristic, complemented, Sylow
185C23—521no—
186C23#8818311yescharacteristic
187Q8—521no—
188Q8—521no—
189D4—521no—
190D4—521no—
191D4—1042no—
192D4—1041no—
193D4—1041no—
194C2×C4—22no—
195C2×C4—22no—
196C2×C4—42no—
197C2×C4—42no—
198C2×C4—42no—
199C2×C4—521no—
200C2×C4—1041no—
201C2×C4—1041no—
202C2×C4#8814812yes—
203C2×C4#8815212yes—
204C2×C4C2×#610411yescharacteristic
205C2×C4#8818611yescharacteristic
206C2×C4#8819211yescharacteristic
207C2×C4C2×#610611yescharacteristic
208C2×C4#8819611yescharacteristic
209C2×C4#8820111yescharacteristic
210C8—82no—
211C8—1042no—
212C8—1041no—
213C22—22no—
214C22—1041no—
215C22—1042no—
216C22#1171862811yescharacteristic
217C22#1171862911yescharacteristic
218C22#1171865411yescharacteristic
219C4—22no—
220C4—22no—
221C4—42no—
222C4—42no—
223C4—1041no—
224C4#1171873311yescharacteristic
225C4#1171874411yescharacteristic
226C4#1171874911yescharacteristic
227C4#1171875011yescharacteristic
228C2—21no—
229C2—21no—
230C2—2081no—
231C2#1311624011yescharacteristic
232C2#1311628712yes—
subgroupG/H
centerC2×C4#88201
commutator, cosocleC2×C42×C13C23
FrattiniC2×C42C22×D13
FittingC13×#1843C2
socleC22×C13#397
prime radical#11719182C22
hypercenter#1843D13
hypocenterC13#10627
LCSG ▷ C2×C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1843

Complements

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

NH ≅ G/Ntype
3. #13112733C2semidirect
4. #13112665C2semidirect
5. C13×#1843C2semidirect
70. #1843D13semidirect
184. C13#10627semidirect

Maximal subgroups

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

subgroupindex
#131156682
#131134862
#131127332
#131126652
C13×#18432
#1062713