Finite Group Databasebeta

← #16788578

Subgroups — #16788578

Order 3328.

284 conjugacy classes of subgroups; only the 76 normal subgroups are shown.

normal subgroups only

This group has 284 conjugacy classes of subgroups — too many to draw. Only its 76 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#13131199C211yesmaximal, characteristic
2#13130399C211yesmaximal, characteristic
3#13129853C214yesmaximal, complemented
4#13125347C211yesmaximal, characteristic
5#11719433—21no—
6#11719054—21no—
7C13×#500C411yescharacteristic
8#11718740—21no—
9#11718541—21no—
10#11718541C412yes—
11#11718539—21no—
12#11718539C2212yes—
13C4×C8×D13C2211yescharacteristic
14#11718343C411yescharacteristic
15#11718260C2212yes—
16#11718259—21no—
17#11718256—21no—
18#11718255C2212yes—
19#11718231—21no—
20C13×C4⋊Q8—21no—
21#88200—41no—
22Q8×Dic13—41no—
23C2×C8×D13C2×C411yescharacteristic
24C2×C8×D13D411yescharacteristic
25#88151—41no—
26#88146—22no—
27#88144—22no—
28#88141—41no—
29C42×D13D411yescharacteristic
30#88123—21no—
31#88111—41no—
32#88110—41no—
33C4⋊#1057—22no—
34C2×#6092—22no—
35C13×#107—21no—
36C13×#107C2×C412yes—
37C4×C8×C13C2×C411yescharacteristic
38#88058—21no—
39#88058C2×C412yes—
40C8×Dic13D411yescharacteristic
41C8×Dic13C2311yescharacteristic
42#88048—22no—
43#88048—22no—
44C4×#1055D411yescharacteristic
45#11970—131nomaximal, Sylow
46C2×Q8×C13—41no—
47C2×C4×D13C22⋊C411yescharacteristic
48C2×C4×D13D811yescharacteristic
49C2×C4×D13SD1611yescharacteristic
50C2×Dic26—41no—
51C2×#1057—42no—
52C2×C8×C13C22⋊C411yescharacteristic
53C2×C8×C13C22×C411yescharacteristic
54C13×C4⋊C4—22no—
55C13×C4⋊C4—41no—
56C42×C13C22⋊C411yescharacteristic
57#6103—42no—
58C4⋊Dic13—22no—
59C4⋊Dic13—41no—
60C4⋊Dic13—42no—
61#6101—42no—
62C4×Dic13—42no—
63C4×Dic13D811yescharacteristic
64C4×Dic13SD1611yescharacteristic
65C4×Dic13C2×D411yescharacteristic
66C2×#1055C22⋊C411yescharacteristic
67C2×#1055C2×D411yescharacteristic
68C8×D13—22no—
69C8×D13—22no—
70#6092—42no—
71#3160—131no—
72#2163—131no—
73#1568—131no—
74#1363—134no—
75C22×D13#10211yescharacteristic
76Q8×C13—82no—
77C2×C4×C13—42no—
78C2×C4×C13#10211yescharacteristic
79C2×C4×C13#10211yescharacteristic
80C2×C4×C13C2×C22⋊C411yescharacteristic
81C2×Dic13—42no—
82C2×Dic13#10211yescharacteristic
83C2×Dic13C2×D811yescharacteristic
84C2×Dic13C2×SD1611yescharacteristic
85C4×D13—21no—
86C4×D13—21no—
87C4×D13—41no—
88C4×D13—41no—
89Dic26—82no—
90#1057—82no—
91C8×C13—21no—
92C8×C13—21no—
93#1055#10112yes—
94#1055#13712yes—
95#533—261no—
96#500—131no—
97#500#26111yescharacteristic
98#499—132no—
99#499—261no—
100#498—261no—
101#432—261no—
102#427—132no—
103#427—261no—
104C2×C4×C8—131no—
105C4⋊C16—132no—
106C22⋊C16—261no—
107#346—261no—
108#335—261no—
109#334—132no—
110C22×C13C2×#10211yescharacteristic
111C2×D13—21no—
112C2×D13—21no—
113C2×D13—21no—
114C4×C13—21no—
115C4×C13—21no—
116C4×C13—82no—
117C4×C13C2×#10111yescharacteristic
118C4×C13#41911yescharacteristic
119Dic13—21no—
120Dic13—21no—
121Dic13—21no—
122Dic13—82no—
123C22×C8—131no—
124C22×C8—131no—
125C4⋊Q8—21no—
126C4⋊Q8—261no—
127#125—262no—
128C22⋊Q8—521no—
129C22⋊Q8—521no—
130C4×Q8—521no—
131C4×Q8—521no—
132#117—262no—
133C2×C42—131no—
134C2×C16—262no—
135#107—21no—
136#107—132no—
137#107—261no—
138#107C2×#26112yes—
139#106—262no—
140#106—262no—
141C4⋊C8—262no—
142C22⋊C8—521no—
143#97—521no—
144C4×C8—131no—
145C4×C8—131no—
146C4×C8—131no—
147C4×C8C2×#26111yescharacteristic
148C2×C13#154611yescharacteristic
149C2×C13#214311yescharacteristic
150C2×C13#214511yescharacteristic
151D13—41no—
152C2×Q8—41no—
153C2×Q8—521no—
154C22×C4—131no—
155C22×C4—131no—
156C22×C4—131no—
157C2×C8—131no—
158C2×C8—131no—
159C2×C8—262no—
160C2×C8—262no—
161C2×C8—522no—
162C2×C8C22⋊#26111yescharacteristic
163C2×C8C22×#26111yescharacteristic
164C4⋊C4—22no—
165C4⋊C4—41no—
166C4⋊C4—262no—
167C4⋊C4—522no—
168C4⋊C4—522no—
169C4⋊C4—521no—
170C22⋊C4—522no—
171C42—131no—
172C42—131no—
173C42—131no—
174C42—522no—
175C42C22⋊#26111yescharacteristic
176C16—522no—
177C13#1197011yescharacteristic, complemented, Sylow
178C23—131no—
179Q8—82no—
180Q8—1042no—
181C2×C4—42no—
182C2×C4—131no—
183C2×C4—131no—
184C2×C4—131no—
185C2×C4—261no—
186C2×C4—261no—
187C2×C4—521no—
188C2×C4—521no—
189C2×C4—522no—
190C2×C4#8811511yescharacteristic
191C2×C4#8811511yescharacteristic
192C2×C4C2×C22⋊#26111yescharacteristic
193C8—21no—
194C8—21no—
195C8—132no—
196C8—132no—
197C8—1042no—
198C22—261no—
199C22—261no—
200C22—261no—
201C22C2×#8811511yescharacteristic
202C4—21no—
203C4—21no—
204C4—82no—
205C4—261no—
206C4—261no—
207C4—261no—
208C4—1042no—
209C4#1171915311yescharacteristic
210C4D13⋊#10111yescharacteristic
211C2—521no—
212C2#1313034611yescharacteristic
213C2#1313115211yescharacteristic
214C2#1313115711yescharacteristic
subgroupG/H
centerC22C2×#88115
commutatorC2×C8×C13C22×C4
FrattiniC2×C8C22×#261
FittingC13×#500C4
socleC22×C13C2×#102
prime radicalC22×D13#102
cosocleC8×Dic13C23
hypercenter#500#261
hypocenterC13#11970
LCSG ▷ C2×C8×C13 ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #500

Complements

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

NH ≅ G/Ntype
3. #13129853C2semidirect
177. C13#11970semidirect

Maximal subgroups

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

subgroupindex
#131311992
#131303992
#131298532
#131253472
#1197013