Finite Group Databasebeta

← #15777080

Subgroups — #15777080

Order 3328.

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

normal subgroups only

This group has 234 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
1#13116970C211yesmaximal, characteristic
2#13116882C211yesmaximal, characteristic
3#13114434C211yesmaximal, characteristic, complemented
4#13113630C211yesmaximal, characteristic
5#13112899C211yesmaximal, characteristic, complemented
6#13112884C211yesmaximal, characteristic, complemented
7C13×#1364C211yesmaximal, characteristic, complemented
8C13×#500C2211yescharacteristic
9#11718742—21no—
10#11718740—21no—
11C2×#88040—21no—
12#11718495—21no—
13#11718360C2211yescharacteristic
14C4×D104C2211yescharacteristic
15C13×C4⋊C16C2211yescharacteristic
16C13×#335C2211yescharacteristic
17#11718095—21no—
18#11718083—21no—
19#11718081—21no—
20#11718075—21no—
21C4⋊#6090C2211yescharacteristic
22C8×#1055C2211yescharacteristic
23C13×C4⋊Q8—21no—
24C2×Dic52—21no—
25C2×Dic52—21no—
26C2×D104D411yescharacteristic
27C2×C8×D13—41no—
28C4×D52—21no—
29#88123—21no—
30C2×C13×C16—21no—
31C13×#107—21no—
32C13×#107—21no—
33C13×C4⋊C8—21no—
34C4×C8×C13C2311yescharacteristic
35#88075—41no—
36#88075—41no—
37#88061—21no—
38#88060—41no—
39#88058D411yescharacteristic
40C2×#6090—21no—
41#88048—42no—
42C4×#1055D411yescharacteristic
43C4×#1055D411yescharacteristic
44#88040—42no—
45#12422—131nomaximal, Sylow
46C2×Q8×C13—41no—
47C2×D52—21no—
48C2×C4×D13—41no—
49C2×Dic26—41no—
50C2×C8×C13—41no—
51C2×C8×C13C2×D411yescharacteristic
52C2×C8×C13#4111yescharacteristic
53C13×C4⋊C4—41no—
54C13×C4⋊C4—41no—
55C42×C13C2×D411yescharacteristic
56#6103—41no—
57C4⋊Dic13—21no—
58C4⋊Dic13—41no—
59C4⋊Dic13—41no—
60C2×#1055—21no—
61C2×#1055D811yescharacteristic
62C2×#1055D811yescharacteristic
63Dic52—41no—
64Dic52—41no—
65Dic52—81no—
66D104—21no—
67D104SD1612yes—
68C8×D13—82no—
69C13×C16—41no—
70#6090—41no—
71#2224—131no—
72#2208—131no—
73#1707—131no—
74C8×D8—131no—
75#1367—131no—
76#1364D1311yescharacteristic, complemented
77#1362—131no—
78C22×D13—41no—
79Q8×C13—81no—
80Q8×C13—81no—
81C2×C4×C13—81no—
82C2×C4×C13#12111yescharacteristic
83C2×C4×C13C2×D811yescharacteristic
84C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
85C2×Dic13—41no—
86C2×Dic13—81no—
87D52—22no—
88D52—41no—
89C4×D13—81no—
90C4×D13—81no—
91Dic26—81no—
92Dic26—81no—
93C8×C13—21no—
94C8×C13—81no—
95C8×C13C2×SD1611yescharacteristic
96C8×C13#13511yescharacteristic
97#1055—22no—
98#1055—21no—
99#1055—21no—
100C2×SD32—261no—
101#500C2×D1311yescharacteristic
102#498—261no—
103#494—131no—
104#487—261no—
105C4×D8—131no—
106C8×D4—261no—
107#366—261no—
108C4⋊C16—131no—
109C4⋊C16C2×D1311yescharacteristic
110#358—261no—
111#357—261no—
112#335C2×D1311yescharacteristic
113D4⋊C8—261no—
114C82—131no—
115C22×C13#45911yescharacteristic
116C2×D13—42no—
117C2×D13—81no—
118C2×D13—81no—
119C4×C13—21no—
120C4×C13—161no—
121C4×C13#46511yescharacteristic
122C4×C13#47111yescharacteristic
123C4×C13#50811yescharacteristic
124C4×C13#50911yescharacteristic
125Dic13—81no—
126Dic13—161no—
127C2×Q16—261no—
128C2×Q16—261no—
129C2×D8—131no—
130C22×C8—521no—
131C4⋊Q8—21no—
132C4⋊Q8—261no—
133C4×D4—261no—
134SD32—522no—
135C2×C16—21no—
136C2×C16—261no—
137#107—21no—
138#107—21no—
139#107—131no—
140#106—522no—
141C4⋊C8—21no—
142#103—521no—
143#103—521no—
144#102—261no—
145C22⋊C8—521no—
146C4×C8—131no—
147C4×C8—131no—
148C4×C8C22×D1311yescharacteristic
149C2×C13#166511yescharacteristic
150C2×C13#221011yescharacteristic
151C2×C13#221411yescharacteristic
152D13—82no—
153C2×Q8—41no—
154C2×Q8—521no—
155C2×D4—261no—
156C22×C4—521no—
157Q16—521no—
158Q16—521no—
159Q16—1041no—
160D8—132no—
161D8—261no—
162C2×C8—41no—
163C2×C8—131no—
164C2×C8—131no—
165C2×C8—261no—
166C2×C8—1042no—
167C2×C8#612711yescharacteristic
168C2×C8D4×D1311yescharacteristic
169C4⋊C4—41no—
170C4⋊C4—41no—
171C4⋊C4—261no—
172C4⋊C4—521no—
173C4⋊C4—521no—
174C22⋊C4—521no—
175C42D4×D1311yescharacteristic
176C16—41no—
177C16—521no—
178C13#1242211yescharacteristic, complemented, Sylow
179C23—521no—
180Q8—81no—
181Q8—81no—
182Q8—1041no—
183Q8—1041no—
184D4—262no—
185D4—521no—
186C2×C4—81no—
187C2×C4—521no—
188C2×C4—1041no—
189C2×C4—1041no—
190C2×C4—1041no—
191C2×C4#8813811yescharacteristic
192C2×C4D8×D1311yescharacteristic
193C2×C4#8816811yescharacteristic
194C8—21no—
195C8—81no—
196C8—262no—
197C8—261no—
198C8—261no—
199C8SD16×D1311yescharacteristic
200C8#8817311yescharacteristic
201C22—522no—
202C22—1041no—
203C22—1041no—
204C22#1171844711yescharacteristic
205C4—21no—
206C4—161no—
207C4—1041no—
208C4—2081no—
209C4#1171841511yescharacteristic
210C4#1171846811yescharacteristic
211C4#1171857211yescharacteristic
212C4#1171857711yescharacteristic
213C2—1042no—
214C2#1311418011yescharacteristic
215C2#1311689011yescharacteristic
216C2#1311691611yescharacteristic
subgroupG/H
centerC22#11718447
commutator, cosocleC4×C8×C13C23
FrattiniC4×C8C22×D13
FittingC13×#1364C2
socleC22×C13#459
prime radicalC2×D104D4
hypercenter#1364D13
hypocenterC13#12422
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
3. #13114434C2semidirect
5. #13112899C2semidirect
6. #13112884C2semidirect
7. C13×#1364C2semidirect
76. #1364D13semidirect
178. C13#12422semidirect

Maximal subgroups

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

subgroupindex
#131169702
#131168822
#131144342
#131136302
#131128992
#131128842
C13×#13642
#1242213