Finite Group Databasebeta

← #15777069

Subgroups — #15777069

Order 3328.

218 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 218 conjugacy classes of subgroups — too many to draw. Only its 65 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#13116989C211yesmaximal, characteristic
2#13116883C211yesmaximal, characteristic
3#13114430C211yesmaximal, characteristic
4#13113642C211yesmaximal, characteristic
5#13112899C211yesmaximal, characteristic
6#13112895C211yesmaximal, characteristic
7C13×#1362C211yesmaximal, characteristic
8C13×#494C2211yescharacteristic
9C2×#88069—21no—
10#11718754—21no—
11#11718740—21no—
12#11718491—21no—
13C4×Dic52C2211yescharacteristic
14#11718343C2211yescharacteristic
15C13×C4⋊C16C2211yescharacteristic
16C13×#335C2211yescharacteristic
17#11718156—21no—
18#11718096—21no—
19#11718095—21no—
20#11718076—21no—
21C4⋊#6090C2211yescharacteristic
22C8×#1055C2211yescharacteristic
23C2×C13×Q16—21no—
24C2×C13×Q16—21no—
25C13×C4⋊Q8—21no—
26C2×Dic52D411yescharacteristic
27#88123—21no—
28C4×Dic26—21no—
29C2×C13×C16—21no—
30C13×C4⋊C8—21no—
31C4×C8×C13C2311yescharacteristic
32#88069—42no—
33#88058—21no—
34#88058—21no—
35#88058D411yescharacteristic
36#88056—21no—
37#88054—41no—
38C8×Dic13—41no—
39C2×#6090—21no—
40#88050—42no—
41#88048—41no—
42#88048—41no—
43C4×#1055D411yescharacteristic
44C4×#1055D411yescharacteristic
45#12421—131nomaximal, Sylow
46C2×Q8×C13—41no—
47C2×Dic26—21no—
48C2×Dic26—41no—
49C13×Q16—41no—
50C13×Q16—41no—
51C13×Q16—81no—
52C2×C8×C13—41no—
53C2×C8×C13C2×D411yescharacteristic
54C2×C8×C13#4111yescharacteristic
55C13×C4⋊C4—41no—
56C13×C4⋊C4—41no—
57C42×C13C2×D411yescharacteristic
58C4⋊Dic13—21no—
59C4⋊Dic13—41no—
60C4⋊Dic13—41no—
61#6101—41no—
62C4×Dic13—41no—
63C2×#1055—21no—
64C2×#1055D811yescharacteristic
65C2×#1055D811yescharacteristic
66Dic52—21no—
67Dic52SD1612yes—
68C13×C16—41no—
69#6090—41no—
70#2227—131no—
71#2209—131no—
72#1707—131no—
73C8×Q16—131no—
74#1367—131no—
75#1365—131no—
76#1362D1311yescharacteristic
77Q8×C13—81no—
78Q8×C13—81no—
79C2×C4×C13—81no—
80C2×C4×C13#12111yescharacteristic
81C2×C4×C13C2×D811yescharacteristic
82C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
83C2×Dic13—41no—
84C2×Dic13—41no—
85C2×Dic13—81no—
86Dic26—22no—
87Dic26—41no—
88Dic26—82no—
89C8×C13—21no—
90C8×C13—81no—
91C8×C13C2×SD1611yescharacteristic
92C8×C13#13511yescharacteristic
93#1055—21no—
94#1055—41no—
95#1055Q3212yescomplemented
96C2×Q32—261no—
97#500—131no—
98#498—261no—
99#494C2×D1311yescharacteristic
100#487—261no—
101C8×Q8—261no—
102C4×Q16—131no—
103#366—261no—
104C4⋊C16—131no—
105C4⋊C16C2×D1311yescharacteristic
106#358—261no—
107#358—261no—
108#335C2×D1311yescharacteristic
109Q8⋊C8—261no—
110C82—131no—
111C22×C13#45911yescharacteristic
112C4×C13—21no—
113C4×C13—161no—
114C4×C13#46511yescharacteristic
115C4×C13#47111yescharacteristic
116C4×C13C2×Q3211yescharacteristic
117C4×C13#51011yescharacteristic
118Dic13—42no—
119Dic13—81no—
120Dic13—161no—
121C2×Q16—21no—
122C2×Q16—21no—
123C2×Q16—131no—
124C4⋊Q8—21no—
125C4⋊Q8—261no—
126C4×Q8—261no—
127Q32—522no—
128C2×C16—21no—
129C2×C16—261no—
130#107—131no—
131#107—261no—
132#107—261no—
133#106—521no—
134#106—521no—
135C4⋊C8—21no—
136C4⋊C8—521no—
137#103—261no—
138#103—522no—
139C4×C8—131no—
140C4×C8—131no—
141C4×C8—521no—
142C4×C8C22×D1311yescharacteristic
143C2×C13#166511yescharacteristic
144C2×C13#220911yescharacteristic
145C2×C13#221211yescharacteristic
146C2×Q8—41no—
147C2×Q8—261no—
148C2×Q8—521no—
149Q16—41no—
150Q16—41no—
151Q16—81no—
152Q16—132no—
153Q16—261no—
154C2×C8—41no—
155C2×C8—131no—
156C2×C8—131no—
157C2×C8—261no—
158C2×C8#612711yescharacteristic
159C2×C8D4×D1311yescharacteristic
160C4⋊C4—41no—
161C4⋊C4—41no—
162C4⋊C4—261no—
163C4⋊C4—521no—
164C4⋊C4—521no—
165C4⋊C4—521no—
166C42—521no—
167C42D4×D1311yescharacteristic
168C16—41no—
169C16—521no—
170C13#1242111yescharacteristic, complemented, Sylow
171Q8—81no—
172Q8—81no—
173Q8—262no—
174Q8—521no—
175Q8—1042no—
176C2×C4—81no—
177C2×C4—521no—
178C2×C4—521no—
179C2×C4—1041no—
180C2×C4#8813811yescharacteristic
181C2×C4D8×D1311yescharacteristic
182C2×C4#8816811yescharacteristic
183C8—21no—
184C8—81no—
185C8—132no—
186C8—261no—
187C8—521no—
188C8#8816611yescharacteristic
189C8SD16×D1311yescharacteristic
190C22#1171844711yescharacteristic
191C4—21no—
192C4—161no—
193C4—522no—
194C4—1041no—
195C4—2081no—
196C4#1171840911yescharacteristic
197C4#1171843911yescharacteristic
198C4#1171857611yescharacteristic
199C4D13×Q3211yescharacteristic
200C2#1311417611yescharacteristic
201C2#1311688511yescharacteristic
202C2#1311690811yescharacteristic
subgroupG/H
centerC22#11718447
commutator, cosocleC4×C8×C13C23
FrattiniC4×C8C22×D13
FittingC13×#1362C2
socle, prime radicalC22×C13#459
hypercenter#1362D13
hypocenterC13#12421
LCSG ▷ C4×C8×C13 ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #1362

Complements

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

NH ≅ G/Ntype
95. #1055Q32semidirect
170. C13#12421semidirect

Maximal subgroups

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

subgroupindex
#131169892
#131168832
#131144302
#131136422
#131128992
#131128952
C13×#13622
#1242113