Finite Group Databasebeta

← #15773874

Subgroups — #15773874

Order 3328.

314 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 314 conjugacy classes of subgroups — too many to draw. Only its 95 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#13125422C211yesmaximal, characteristic
2#13114967C211yesmaximal, characteristic
3#13112849C214yesmaximal
4C13×#2163C211yesmaximal, characteristic
5#11719175—21no—
6C2×C4×C8×C13C2211yescharacteristic
7#11718777—21no—
8#11718777C2212yes—
9#11718597—21no—
10#11718360C411yescharacteristic, complemented
11C4×Dic52—21no—
12C4×Dic52C412yescomplemented
13#11718343C411yescharacteristic, complemented
14#11718342—21no—
15C13×C4⋊C16—21no—
16C13×C22⋊C16C2212yes—
17C13×#346—21no—
18#11718143—21no—
19#11718143C2212yes—
20C22×C8×C13D411yescharacteristic
21C22×C8×C13C2311yescharacteristic
22C2×C42×C13D411yescharacteristic
23#88180—41no—
24C2×C4⋊Dic13—22no—
25#88178—22no—
26#88178—41no—
27C2×Dic52—21no—
28C2×Dic52C2×C412yes—
29#88124—41no—
30#88123—21no—
31#88123—21no—
32C4×Dic26—22no—
33C4×Dic26—41no—
34C2×C13×C16—22no—
35C4×C8×C13C2×C411yescharacteristic
36C4×C8×C13C2×C411yescharacteristic
37C4×C8×C13D411yescharacteristic
38C4×C8×C13D411yescharacteristic
39#88071—41no—
40#88071—41no—
41#88058—21no—
42#88058C2×C412yes—
43#88056—22no—
44#88056—22no—
45#11859—131nomaximal, Sylow
46C22×C4×C13D811yescharacteristic
47C22×C4×C13D811yescharacteristic
48C22×C4×C13C2×D411yescharacteristic
49C22×Dic13—42no—
50C2×Dic26—22no—
51C2×Dic26—41no—
52C2×C8×C13—41no—
53C2×C8×C13—41no—
54C2×C8×C13C22⋊C411yescharacteristic
55C2×C8×C13C22⋊C411yescharacteristic
56C2×C8×C13C22×C411yescharacteristic
57C2×C8×C13C2×D411yescharacteristic
58C42×C13C22⋊C411yescharacteristic
59C42×C13C22⋊C411yescharacteristic
60C42×C13SD1611yescharacteristic
61C42×C13SD1611yescharacteristic
62C22⋊Dic13—42no—
63C4⋊Dic13—22no—
64C4⋊Dic13—41no—
65C4⋊Dic13—41no—
66C4⋊Dic13—41no—
67C4⋊Dic13—42no—
68C4⋊Dic13—42no—
69#6101—42no—
70#6101—42no—
71C4×Dic13—42no—
72Dic52—42no—
73Dic52—42no—
74C13×C16—42no—
75#3170—131no—
76#2163D1311yescharacteristic
77#1835—131no—
78#1348—134no—
79C23×C13C2×D811yescharacteristic
80C2×C4×C13—22no—
81C2×C4×C13—21no—
82C2×C4×C13—21no—
83C2×C4×C13—41no—
84C2×C4×C13#10211yescharacteristic
85C2×C4×C13#10211yescharacteristic
86C2×C4×C13#10211yescharacteristic
87C2×C4×C13#10211yescharacteristic
88C2×C4×C13C2×C22⋊C411yescharacteristic
89C2×C4×C13C2×SD1611yescharacteristic
90C2×Dic13—42no—
91C2×Dic13—42no—
92C2×Dic13—82no—
93C2×Dic13—82no—
94C2×Dic13—82no—
95Dic26—42no—
96Dic26—42no—
97Dic26—82no—
98C8×C13—21no—
99C8×C13—21no—
100C8×C13—21no—
101C8×C13—21no—
102#533—261no—
103#500—131no—
104#494—131no—
105#487—261no—
106#467—132no—
107#467—261no—
108C4×Q16—132no—
109C4×Q16—261no—
110C2×C4×C8C2×D1311yescharacteristic
111#382—261no—
112C4⋊C16—21no—
113C22⋊C16C2×D1312yes—
114#346—21no—
115#340—132no—
116#340—261no—
117C22×C13—21no—
118C22×C13—21no—
119C22×C13C2×#10211yescharacteristic
120C22×C13#51012yes—
121C4×C13—21no—
122C4×C13—21no—
123C4×C13—21no—
124C4×C13—21no—
125C4×C13—21no—
126C4×C13#41011yescharacteristic
127C4×C13#42111yescharacteristic
128Dic13—82no—
129Dic13—82no—
130Dic13—162no—
131C2×Q16—132no—
132C2×Q16—261no—
133C22×C8D5211yescharacteristic
134C22×C8C22×D1311yescharacteristic
135C4⋊Q8—261no—
136C4⋊Q8—261no—
137#125—521no—
138C22⋊Q8—262no—
139C22⋊Q8—521no—
140C4×Q8—262no—
141C4×Q8—521no—
142#117—521no—
143C2×C4⋊C4—262no—
144C2×C42D5211yescharacteristic
145C2×C16—22no—
146#107—132no—
147#107—261no—
148#103—262no—
149#103—262no—
150C4×C8C4×D1311yescharacteristic
151C4×C8C4×D1311yescharacteristic
152C4×C8C22⋊D1311yescharacteristic
153C4×C8C22⋊D1311yescharacteristic
154#95—521no—
155#95—521no—
156C2×C13—22no—
157C2×C13#151711yescharacteristic
158C2×C13#214111yescharacteristic
159C2×C13#214511yescharacteristic
160C2×Q8—262no—
161C2×Q8—521no—
162C22×C4—522no—
163C22×C4D10411yescharacteristic
164C22×C4D10411yescharacteristic
165C22×C4C2×D5211yescharacteristic
166Q16—522no—
167Q16—522no—
168C2×C8—41no—
169C2×C8—41no—
170C2×C8#610311yescharacteristic
171C2×C8#610311yescharacteristic
172C2×C8C2×C4×D1311yescharacteristic
173C2×C8C2×C22⋊D1311yescharacteristic
174C4⋊C4—262no—
175C4⋊C4—522no—
176C4⋊C4—522no—
177C4⋊C4—522no—
178C4⋊C4—521no—
179C4⋊C4—521no—
180C4⋊C4—522no—
181C4⋊C4—521no—
182C22⋊C4—522no—
183C42—522no—
184C42#609511yescharacteristic
185C42#609511yescharacteristic
186C42#610311yescharacteristic
187C42#610311yescharacteristic
188C16—42no—
189C13#1185911yescharacteristic, complemented, Sylow
190C23C2×D10411yescharacteristic
191Q8—522no—
192Q8—522no—
193Q8—1042no—
194C2×C4—22no—
195C2×C4—21no—
196C2×C4—21no—
197C2×C4—41no—
198C2×C4—522no—
199C2×C4—522no—
200C2×C4—1042no—
201C2×C4—1042no—
202C2×C4—1042no—
203C2×C4#8806111yescharacteristic
204C2×C4#8806111yescharacteristic
205C2×C4#8806111yescharacteristic
206C2×C4#8806111yescharacteristic
207C2×C4C2×#609511yescharacteristic
208C2×C4C2×#610311yescharacteristic
209C8—21no—
210C8—21no—
211C8—21no—
212C8—21no—
213C22—21no—
214C22—21no—
215C22#1171857012yes—
216C22C2×#8806111yescharacteristic
217C4—21no—
218C4—21no—
219C4—21no—
220C4—21no—
221C4—21no—
222C4—1042no—
223C4—1042no—
224C4—2082no—
225C4#1171866711yescharacteristic
226C4#1171880011yescharacteristic
227C2—22no—
228C2#1311339711yescharacteristic
229C2#1311655711yescharacteristic
230C2#1311657311yescharacteristic
subgroupG/H
centerC22C2×#88061
commutatorC2×C8×C13C22×C4
FrattiniC22×C8C22×D13
FittingC13×#2163C2
socleC22×C13C2×#102
prime radicalC23×C13C2×D8
cosocleC22×C8×C13C23
hypercenter#2163D13
hypocenterC13#11859
LCSG ▷ C2×C8×C13 ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×C4×C8 ◁ #2163

Complements

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

NH ≅ G/Ntype
10. #11718360C4semidirect
12. C4×Dic52C4semidirect
13. #11718343C4semidirect
189. C13#11859semidirect

Maximal subgroups

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

subgroupindex
#131254222
#131149672
#131128492
C13×#21632
#1185913