Finite Group Databasebeta

← #15776959

Subgroups — #15776959

Order 3328.

276 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 276 conjugacy classes of subgroups — too many to draw. Only its 67 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#13127729C211yesmaximal, characteristic
2#13117109C211yesmaximal, characteristic
3#13116979C211yesmaximal, characteristic
4#13114231C211yesmaximal, characteristic
5#13112814C211yesmaximal, characteristic
6#13112799C211yesmaximal, characteristic
7C13×#1364C211yesmaximal, characteristic
8#11719426—21no—
9C13×#500C2211yescharacteristic
10#11718755—21no—
11#11718539—21no—
12#11718538—22no—
13#11718534—21no—
14#11718510—21no—
15C4×Dic52C2211yescharacteristic
16#11718343C2211yescharacteristic
17C8×Dic26C2211yescharacteristic
18C13×C4⋊C16C2211yescharacteristic
19C13×#335C2211yescharacteristic
20#11718097—21no—
21#11718095—21no—
22#11718081—22no—
23#11718074—21no—
24C4×#6090C2211yescharacteristic
25C13×C4⋊Q8—21no—
26Q8×Dic13—41no—
27#88198—41no—
28C2×Dic52—41no—
29C2×Dic52D411yescharacteristic
30#88144—22no—
31#88143—42no—
32#88141—22no—
33#88123—21no—
34C4×Dic26—21no—
35C4×Dic26D411yescharacteristic
36C2×C13×C16—21no—
37C13×#107—21no—
38C13×#107D412yes—
39C13×C4⋊C8—21no—
40C4×C8×C13C2311yescharacteristic
41#88058—21no—
42#88058—21no—
43#88058D411yescharacteristic
44#88056—21no—
45#88056—41no—
46#88054—21no—
47C8×Dic13—21no—
48C2×#6090—21no—
49#88050—22no—
50#88048—22no—
51C4⋊#1055D411yescharacteristic
52#12405—131nomaximal, Sylow
53C2×Q8×C13—41no—
54C2×Dic26—21no—
55C2×Dic26—41no—
56C2×Dic26D811yescharacteristic
57C2×C8×C13—41no—
58C2×C8×C13C2×D411yescharacteristic
59C2×C8×C13C2×D411yescharacteristic
60C13×C4⋊C4—22no—
61C13×C4⋊C4—41no—
62C42×C13C2×D411yescharacteristic
63C4⋊Dic13—21no—
64C4⋊Dic13—42no—
65C4⋊Dic13—41no—
66C4⋊Dic13—41no—
67C4⋊Dic13D811yescharacteristic
68#6101—21no—
69#6101—42no—
70#6101—42no—
71#6101—41no—
72C4×Dic13—21no—
73C4×Dic13—42no—
74C4×Dic13—41no—
75C2×#1055—21no—
76Dic52—21no—
77Dic52—82no—
78Dic52Q1612yescomplemented
79C13×C16—41no—
80#6090—22no—
81#3383—131no—
82#2252—131no—
83#2225—131no—
84#1674—131no—
85#1364D1311yescharacteristic
86Q8⋊C16—131no—
87#1332—131no—
88Q8×C13—81no—
89Q8×C13—81no—
90C2×C4×C13—42no—
91C2×C4×C13#12011yescharacteristic
92C2×C4×C13C2×D811yescharacteristic
93C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
94C2×Dic13—21no—
95C2×Dic13—21no—
96C2×Dic13—41no—
97C2×Dic13—41no—
98C2×Dic13—81no—
99Dic26—22no—
100Dic26—21no—
101Dic26—21no—
102Dic26—41no—
103Dic26—81no—
104Dic26—81no—
105C8×C13—21no—
106C8×C13—81no—
107C8×C13C2×Q1611yescharacteristic
108C8×C13#13711yescharacteristic
109#1055—41no—
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—131no—
119C4×Q16—261no—
120#367—261no—
121#366—262no—
122C4⋊C16C2×D1311yescharacteristic
123#358—261no—
124C4×C16—131no—
125#335C2×D1311yescharacteristic
126#332—261no—
127C22×C13#44711yescharacteristic
128C4×C13—21no—
129C4×C13—82no—
130C4×C13#45111yescharacteristic
131C4×C13#45611yescharacteristic
132C4×C13#50811yescharacteristic
133C4×C13#50911yescharacteristic
134Dic13—42no—
135Dic13—41no—
136Dic13—41no—
137Dic13—81no—
138Dic13—161no—
139C2×Q16—131no—
140C2×Q16—521no—
141C4⋊Q8—21no—
142C4⋊Q8—261no—
143C4⋊Q8—521no—
144#125—262no—
145#125—522no—
146C4×Q8—131no—
147C4×Q8—262no—
148C4×Q8—261no—
149C4×Q8—521no—
150C2×C16—21no—
151C2×C16—261no—
152#107—21no—
153#107—131no—
154#107—261no—
155#107—261no—
156#107D5212yes—
157#106—262no—
158C4⋊C8—21no—
159C4⋊C8—131no—
160C4⋊C8—261no—
161#103—262no—
162#103—261no—
163#103—521no—
164C4×C8—261no—
165C4×C8C22×D1311yescharacteristic
166C2×C13#164911yescharacteristic
167C2×C13#218611yescharacteristic
168C2×C13#219511yescharacteristic
169C2×Q8—41no—
170C2×Q8—131no—
171C2×Q8—261no—
172C2×Q8—521no—
173Q16—132no—
174Q16—261no—
175Q16—1042no—
176C2×C8—41no—
177C2×C8—261no—
178C2×C8C2×D5211yescharacteristic
179C2×C8D4×D1311yescharacteristic
180C4⋊C4—22no—
181C4⋊C4—41no—
182C4⋊C4—131no—
183C4⋊C4—261no—
184C4⋊C4—261no—
185C4⋊C4—522no—
186C4⋊C4—522no—
187C4⋊C4—522no—
188C4⋊C4—521no—
189C4⋊C4—521no—
190C4⋊C4—521no—
191C42—261no—
192C42—522no—
193C42—521no—
194C42D4×D1311yescharacteristic
195C16—41no—
196C16—262no—
197C13#1240511yescharacteristic, complemented, Sylow
198Q8—81no—
199Q8—81no—
200Q8—262no—
201Q8—261no—
202Q8—261no—
203Q8—521no—
204Q8—1041no—
205Q8—1041no—
206C2×C4—42no—
207C2×C4—261no—
208C2×C4—261no—
209C2×C4—521no—
210C2×C4—521no—
211C2×C4—1041no—
212C2×C4#8813611yescharacteristic
213C2×C4D8×D1311yescharacteristic
214C2×C4#8816811yescharacteristic
215C8—21no—
216C8—81no—
217C8—521no—
218C8#8816911yescharacteristic
219C8Q16×D1311yescharacteristic
220C22#1171843411yescharacteristic
221C4—21no—
222C4—82no—
223C4—521no—
224C4—521no—
225C4—522no—
226C4—1041no—
227C4—2081no—
228C4#1171841311yescharacteristic
229C4#1171846911yescharacteristic
230C4#1171857211yescharacteristic
231C4#1171857711yescharacteristic
232C2#1311408611yescharacteristic
233C2#1311676011yescharacteristic
234C2#1311681711yescharacteristic
subgroupG/H
centerC22#11718434
commutator, cosocleC4×C8×C13C23
FrattiniC4×C8C22×D13
FittingC13×#1364C2
socle, prime radicalC22×C13#447
hypercenter#1364D13
hypocenterC13#12405
LCSG ▷ C4×C8×C13 ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #1364

Complements

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

NH ≅ G/Ntype
78. Dic52Q16semidirect
197. C13#12405semidirect

Maximal subgroups

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

subgroupindex
#131277292
#131171092
#131169792
#131142312
#131128142
#131127992
C13×#13642
#1240513