Finite Group Databasebeta

← #15783584

Subgroups — #15783584

Order 3328.

288 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 288 conjugacy classes of subgroups — too many to draw. Only its 63 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
1C2×#11718565C211yesmaximal, characteristic
2C2×#11718114C211yesmaximal, characteristic, complemented
3C2×#11718113C211yesmaximal, characteristic, complemented
4#13113016C211yesmaximal, characteristic, complemented
5#13113013C211yesmaximal, characteristic, complemented
6C22⋊#88034C211yesmaximal, characteristic, complemented
7C13×#2216C211yesmaximal, characteristic, complemented
8C2×#88158—21no—
9C2×C13×Q32C2211yescharacteristic
10C22×C13×C16C2211yescharacteristic
11C13×#467—21no—
12C2×Dic104C2211yescharacteristic
13#11718565—22no—
14#11718565—22no—
15C2×#88040—21no—
16C2×D208C2211yescharacteristic
17C13×#366C2211yescharacteristic
18C13×#358—21no—
19#11718114—22no—
20#11718113—22no—
21C2×#88034C2211yescharacteristic
22C2×#88034C2211yescharacteristic
23C2×#6127—41no—
24C2×C13×Q16—21no—
25C22×C8×C13D411yescharacteristic
26C13×C22⋊Q8—41no—
27C2×Dic52—21no—
28#88158—24no—
29#88158—42no—
30C2×D104—21no—
31C2×#6095—41no—
32C13×Q32—21no—
33C13×Q32—21no—
34C2×C13×C16—21no—
35C2×C13×C16—21no—
36C2×C13×C16D411yescharacteristic
37C2×C13×C16C2311yescharacteristic
38C13×#107—21no—
39C13×#103—41no—
40Dic104—21no—
41Dic104D412yes—
42#88040—24no—
43D208—21no—
44D208D412yes—
45#88034—21no—
46#88034—21no—
47#13666—131nomaximal, Sylow
48C2×Q8×C13—41no—
49C22×C4×C13D811yescharacteristic
50C2×C22⋊D13—81no—
51#6127—44no—
52#6127—82no—
53C2×D52—41no—
54C2×C4×D13—81no—
55C2×Dic26—41no—
56C13×Q16—41no—
57C13×Q16—41no—
58C2×C8×C13—21no—
59C2×C8×C13—21no—
60C2×C8×C13D811yescharacteristic
61C2×C8×C13C2×D411yescharacteristic
62C13×C4⋊C4—41no—
63C13×C4⋊C4—81no—
64C13×C22⋊C4—81no—
65Dic52—22no—
66Dic52—41no—
67D104—22no—
68D104—41no—
69#6095—44no—
70C13×C16—21no—
71C13×C16C2×D411yescharacteristic
72C13×C16C2×D411yescharacteristic
73C2×#508—131no—
74C2×Q64—131no—
75C2×SD64—131no—
76#2216D1311yescharacteristic, complemented
77#1416—131no—
78#1415—131no—
79C22⋊C32—131no—
80C23×C13D1611yescharacteristic
81C22×D13—81no—
82Q8×C13—81no—
83Q8×C13—81no—
84C2×C4×C13—21no—
85C2×C4×C13—21no—
86C2×C4×C13—81no—
87C2×C4×C13—81no—
88C2×C4×C13D1611yescharacteristic
89C2×C4×C13C2×D811yescharacteristic
90C22⋊D13—84no—
91C2×Dic13—81no—
92D52—42no—
93D52—81no—
94C4×D13—84no—
95Dic26—42no—
96Dic26—81no—
97C8×C13—21no—
98C8×C13#12011yescharacteristic
99C8×C13AGL(1,ℤ/8)11yescharacteristic
100C2×#135—261no—
101#508—262no—
102#508—262no—
103C2×Q32—131no—
104C2×Q32C2×D1311yescharacteristic
105C2×SD32—261no—
106C2×D16—131no—
107C22×C16C2×D1311yescharacteristic
108#467—21no—
109Q64—262no—
110SD64—262no—
111C2×C32—131no—
112C2×C32—131no—
113#366C2×D1311yescharacteristic
114#358—21no—
115C22×C13—21no—
116C22×C13—21no—
117C22×C13—21no—
118C22×C13C2×D1611yescharacteristic
119C2×D13—82no—
120C2×D13—161no—
121C2×D13—161no—
122C4×C13—21no—
123C4×C13—161no—
124C4×C13—161no—
125C4×C13#44711yescharacteristic
126C4×C13#50911yescharacteristic
127Dic13—82no—
128C2×#41—521no—
129#135—264no—
130#135—522no—
131C2×Q16—21no—
132C2×Q16—261no—
133C2×SD16—521no—
134C2×D8—261no—
135C22×C8C22⋊D1311yescharacteristic
136C22⋊Q8—41no—
137Q32—21no—
138Q32—21no—
139Q32—132no—
140Q32—261no—
141SD32—264no—
142D16—132no—
143D16—261no—
144C2×C16—21no—
145C2×C16—21no—
146C2×C16C22⋊D1311yescharacteristic
147C2×C16C22×D1311yescharacteristic
148#107—21no—
149#103—41no—
150C32—261no—
151C32—261no—
152C2×C13—41no—
153C2×C13#218411yescharacteristic
154C2×C13#226211yescharacteristic
155C2×C13#226411yescharacteristic
156D13—162no—
157#41—524no—
158#41—1042no—
159C2×Q8—41no—
160C2×Q8—521no—
161C2×D4—521no—
162C2×D4—1041no—
163C22×C4—1041no—
164C22×C4#610411yescharacteristic
165Q16—41no—
166Q16—41no—
167Q16—262no—
168Q16—521no—
169SD16—524no—
170D8—262no—
171D8—521no—
172C2×C8—21no—
173C2×C8—21no—
174C2×C8#610411yescharacteristic
175C2×C8C2×C22⋊D1311yescharacteristic
176C4⋊C4—41no—
177C4⋊C4—81no—
178C22⋊C4—81no—
179C16—21no—
180C16D4×D1311yescharacteristic
181C16D4×D1311yescharacteristic
182C13#1366611yescharacteristic, complemented, Sylow
183C23—1041no—
184C23#8806611yescharacteristic
185Q8—81no—
186Q8—81no—
187Q8—522no—
188Q8—1041no—
189D4—522no—
190D4—1044no—
191D4—1041no—
192C2×C4—21no—
193C2×C4—21no—
194C2×C4—81no—
195C2×C4—81no—
196C2×C4—1044no—
197C2×C4—1041no—
198C2×C4#8806611yescharacteristic
199C2×C4C2×#610411yescharacteristic
200C8—21no—
201C8#8819111yescharacteristic
202C8#8820311yescharacteristic
203C22—21no—
204C22—21no—
205C22—21no—
206C22—1042no—
207C22—2081no—
208C22—2081no—
209C22C2×#8806611yescharacteristic
210C4—21no—
211C4—161no—
212C4—161no—
213C4—1042no—
214C4#1171869711yescharacteristic
215C4#1171885411yescharacteristic
216C2—41no—
217C2—2082no—
218C2#1311674711yescharacteristic
219C2#1311714311yescharacteristic
220C2#1311715411yescharacteristic
subgroupG/H
centerC22C2×#88066
commutator, cosocleC2×C13×C16C23
FrattiniC2×C16C22×D13
FittingC13×#2216C2
socleC22×C13C2×D16
prime radicalC2×#11718565C2
hypercenter#2216D13
hypocenterC13#13666
LCSG ▷ C2×C13×C16 ▷ C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ C22×C16 ◁ #2216

Complements

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

NH ≅ G/Ntype
2. C2×#11718114C2semidirect
3. C2×#11718113C2semidirect
4. #13113016C2semidirect
5. #13113013C2semidirect
6. C22⋊#88034C2semidirect
7. C13×#2216C2semidirect
76. #2216D13semidirect
182. C13#13666semidirect

Maximal subgroups

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

subgroupindex
C2×#117185652
C2×#117181142
C2×#117181132
#131130162
#131130132
C22⋊#880342
C13×#22162
#1366613