Finite Group Databasebeta

← #15776957

Subgroups — #15776957

Order 3328.

276 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 276 conjugacy classes of subgroups — too many to draw. Only its 69 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#13127725C211yesmaximal, characteristic
2#13117109C211yesmaximal, characteristic
3#13114227C211yesmaximal, characteristic
4#13112890C211yesmaximal, characteristic
5#13112814C211yesmaximal, characteristic
6#13112800C211yesmaximal, characteristic
7C13×#2225C211yesmaximal, characteristic
8#11719275—21no—
9C13×#500C2211yescharacteristic
10C4×C13×Q16C2211yescharacteristic
11Q16×Dic13—21no—
12#11718751—21no—
13#11718681—21no—
14#11718539—21no—
15#11718457—22no—
16#11718343C2211yescharacteristic
17C8×Dic26C2211yescharacteristic
18C13×#367—21no—
19C13×C4⋊C16C2211yescharacteristic
20C13×#358—21no—
21#11718139—21no—
22#11718081—22no—
23C4×#6090C2211yescharacteristic
24#11718050C2211yescharacteristic
25C2×C13×Q16D411yescharacteristic
26C13×C4⋊Q8—21no—
27C4×Q8×C13—21no—
28Q8×Dic13—22no—
29C2×#6107—41no—
30#88144—22no—
31#88144—42no—
32#88123—21no—
33#88123—41no—
34C4×Dic26—41no—
35C4×Dic26D411yescharacteristic
36C2×C13×C16—21no—
37C13×#107—21no—
38C13×#107—21no—
39C13×#107D411yescharacteristic
40C13×#103—21no—
41C4×C8×C13C2311yescharacteristic
42#88075—22no—
43#88075—41no—
44#88058—21no—
45#88058D412yes—
46#88054—21no—
47C8×Dic13—21no—
48C2×#6090—21no—
49#88048—22no—
50C4⋊#1055—21no—
51C4⋊#1055D411yescharacteristic
52#12405—131nomaximal, Sylow
53C2×Q8×C13—21no—
54C2×Q8×C13—41no—
55C2×Dic26—41no—
56C2×Dic26D811yescharacteristic
57C13×Q16—21no—
58C13×Q16Q1612yescomplemented
59C2×C8×C13C2×D411yescharacteristic
60C2×C8×C13C2×D411yescharacteristic
61C13×C4⋊C4—21no—
62C13×C4⋊C4—41no—
63C13×C4⋊C4—41no—
64C13×C4⋊C4—41no—
65C42×C13—41no—
66C42×C13C2×D411yescharacteristic
67#6107—82no—
68C4⋊Dic13—22no—
69C4⋊Dic13—42no—
70C4⋊Dic13—42no—
71C4⋊Dic13—41no—
72C4⋊Dic13D811yescharacteristic
73#6101—21no—
74#6101—42no—
75C4×Dic13—21no—
76C4×Dic13—42no—
77C2×#1055—21no—
78C2×#1055—41no—
79C13×C16—41no—
80#6090—22no—
81#3383—131no—
82#2252—131no—
83#2225D1311yescharacteristic
84#1674—131no—
85#1364—131no—
86Q8⋊C16—131no—
87#1332—131no—
88Q8×C13—22no—
89Q8×C13—41no—
90Q8×C13—81no—
91Q8×C13—81no—
92C2×C4×C13—41no—
93C2×C4×C13—41no—
94C2×C4×C13—81no—
95C2×C4×C13#12011yescharacteristic
96C2×C4×C13C2×D811yescharacteristic
97C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
98C2×Dic13—21no—
99C2×Dic13—21no—
100C2×Dic13—42no—
101Dic26—21no—
102Dic26—21no—
103Dic26—81no—
104Dic26—81no—
105C8×C13—21no—
106C8×C13C2×Q1611yescharacteristic
107C8×C13#13711yescharacteristic
108#1055—41no—
109#1055—81no—
110#557—261no—
111#500—131no—
112#500C2×D1311yescharacteristic
113#499—261no—
114#479—262no—
115#475—261no—
116#462—261no—
117C8×Q8—131no—
118C4×Q16—261no—
119C4×Q16C2×D1311yescharacteristic
120#367—21no—
121#366—262no—
122C4⋊C16C2×D1311yescharacteristic
123#358—21no—
124C4×C16—131no—
125#335—131no—
126#332—261no—
127C22×C13#44711yescharacteristic
128C4×C13—21no—
129C4×C13—42no—
130C4×C13—81no—
131C4×C13—161no—
132C4×C13#45111yescharacteristic
133C4×C13#45611yescharacteristic
134C4×C13#50811yescharacteristic
135C4×C13#50911yescharacteristic
136Dic13—41no—
137Dic13—41no—
138Dic13—82no—
139C2×Q16—521no—
140C2×Q16C22⋊D1311yescharacteristic
141C4⋊Q8—21no—
142C4⋊Q8—261no—
143C4⋊Q8—521no—
144#125—262no—
145#125—522no—
146C4×Q8—21no—
147C4×Q8—131no—
148C4×Q8—262no—
149C4×Q8—521no—
150C2×C16—21no—
151C2×C16—261no—
152#107—21no—
153#107—21no—
154#107—132no—
155#107—261no—
156#107C22⋊D1311yescharacteristic
157#106—262no—
158C4⋊C8—131no—
159C4⋊C8—261no—
160C4⋊C8—261no—
161#103—21no—
162#103—262no—
163#103—521no—
164C4×C8—261no—
165C4×C8C22×D1311yescharacteristic
166C2×C13#164911yescharacteristic
167C2×C13#218611yescharacteristic
168C2×C13#219511yescharacteristic
169C2×Q8—21no—
170C2×Q8—41no—
171C2×Q8—131no—
172C2×Q8—521no—
173Q16—21no—
174Q16—1042no—
175Q16#610712yescomplemented
176C2×C8—261no—
177C2×C8—521no—
178C2×C8D4×D1311yescharacteristic
179C2×C8C2×C22⋊D1311yescharacteristic
180C4⋊C4—21no—
181C4⋊C4—41no—
182C4⋊C4—41no—
183C4⋊C4—41no—
184C4⋊C4—131no—
185C4⋊C4—261no—
186C4⋊C4—262no—
187C4⋊C4—522no—
188C4⋊C4—522no—
189C4⋊C4—522no—
190C4⋊C4—521no—
191C42—41no—
192C42—261no—
193C42—522no—
194C42D4×D1311yescharacteristic
195C16—41no—
196C16—262no—
197C13#1240511yescharacteristic, complemented, Sylow
198Q8—22no—
199Q8—41no—
200Q8—81no—
201Q8—81no—
202Q8—261no—
203Q8—261no—
204Q8—1041no—
205Q8—1041no—
206C2×C4—41no—
207C2×C4—41no—
208C2×C4—81no—
209C2×C4—261no—
210C2×C4—261no—
211C2×C4—522no—
212C2×C4D8×D1311yescharacteristic
213C2×C4#8816511yescharacteristic
214C2×C4#8819111yescharacteristic
215C8—21no—
216C8—521no—
217C8—1041no—
218C8C2×#610711yescharacteristic
219C8#8820511yescharacteristic
220C22#1171881711yescharacteristic
221C4—21no—
222C4—42no—
223C4—81no—
224C4—161no—
225C4—521no—
226C4—521no—
227C4—1042no—
228C4#1171857511yescharacteristic
229C4#1171857711yescharacteristic
230C4#1171871111yescharacteristic
231C4#1171886611yescharacteristic
232C2#1311408411yescharacteristic
233C2#1311675811yescharacteristic
234C2#1311681111yescharacteristic
subgroupG/H
centerC22#11718817
commutator, cosocleC4×C8×C13C23
FrattiniC4×C8C22×D13
FittingC13×#2225C2
socle, prime radicalC22×C13#447
hypercenter#2225D13
hypocenterC13#12405
LCSG ▷ C4×C8×C13 ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2225

Complements

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

NH ≅ G/Ntype
58. C13×Q16Q16semidirect
175. Q16#6107semidirect
197. C13#12405semidirect

Maximal subgroups

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

subgroupindex
#131277252
#131171092
#131142272
#131128902
#131128142
#131128002
C13×#22252
#1240513