Finite Group Databasebeta

← #15760299

Subgroups — #15760299

Order 3328.

470 conjugacy classes of subgroups; only the 135 normal subgroups are shown.

normal subgroups only

This group has 470 conjugacy classes of subgroups — too many to draw. Only its 135 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#13120048C211yesmaximal, characteristic
2#13114832C211yesmaximal, characteristic
3#13113520C212yesmaximal
4#13112738C212yesmaximal
5C13×#2982C211yesmaximal, characteristic
6C2×C4×Q8×C13C2211yescharacteristic
7C2×#88123C2211yescharacteristic
8C8×Q8×C13—24no—
9C13×#431—22no—
10C13×#431C2212yes—
11#11718891—21no—
12C2×#88076—21no—
13#11718647C414yes—
14#11718638—21no—
15C4×C4⋊Dic13C2211yescharacteristic
16#11718590—22no—
17#11718585C2212yes—
18#11718122—21no—
19#11718074—24no—
20C22×Q8×C13D411yescharacteristic
21C22×Dic26—21no—
22C4×Q8×C13—22no—
23C4×Q8×C13—22no—
24C2×C13×C4⋊C4C2×C412yes—
25C2×C13×C4⋊C4D411yescharacteristic
26C2×C42×C13D412yes—
27C2×C42×C13C2311yescharacteristic
28C2×C4⋊Dic13—21no—
29C2×C4⋊Dic13—21no—
30C2×C4⋊Dic13C2×C412yes—
31C2×C4×Dic13—21no—
32C2×#6099—22no—
33#88123—22no—
34#88123—22no—
35C13×C4⋊C8—24no—
36C13×C4⋊C8D414yes—
37C13×C22⋊C8—22no—
38C4×C8×C13—24no—
39C4×C8×C13—22no—
40#88076—42no—
41#88071—24no—
42#88071—24no—
43#88071C2×C412yes—
44C4⋊#1055—22no—
45C4⋊#1055—22no—
46#9396—131nomaximal, Sylow
47C2×Q8×C13—22no—
48C2×Q8×C13—22no—
49C2×Q8×C13SD1612yes—
50C2×Q8×C13Q1612yes—
51C22×C4×C13C22⋊C412yes—
52C22×C4×C13C22⋊C412yes—
53C22×C4×C13C22×C411yescharacteristic
54C22×C4×C13C2×D411yescharacteristic
55C22×C4×C13C2×D411yescharacteristic
56C22×Dic13—22no—
57C22×Dic13—22no—
58C2×Dic26—44no—
59C2×Dic26—41no—
60C2×Dic26—41no—
61C2×C8×C13—24no—
62C13×C4⋊C4—24no—
63C13×C4⋊C4—22no—
64C42×C13—22no—
65C42×C13—22no—
66C42×C13C2×D412yes—
67C42×C13#4112yes—
68C4⋊Dic13—24no—
69C4⋊Dic13—42no—
70C4⋊Dic13—42no—
71C4×Dic13—42no—
72#6099—42no—
73#6099—42no—
74C2×#1055—42no—
75#2982D1311yescharacteristic
76#2568—131no—
77#1801—131no—
78#1549—132no—
79#1303—132no—
80C23×C13C2×C22⋊C411yescharacteristic
81Q8×C13—24no—
82Q8×C13—24no—
83C2×C4×C13—22no—
84C2×C4×C13—22no—
85C2×C4×C13—22no—
86C2×C4×C13—22no—
87C2×C4×C13—41no—
88C2×C4×C13—42no—
89C2×C4×C13#10314yes—
90C2×C4×C13C4×D412yes—
91C2×C4×C13#12011yescharacteristic
92C2×C4×C13#12112yes—
93C2×C4×C13#12311yescharacteristic
94C2×C4×C13C2×SD1611yescharacteristic
95C2×C4×C13C2×Q1611yescharacteristic
96C2×C4×C13#13512yes—
97C2×Dic13—42no—
98C2×Dic13—44no—
99C2×Dic13—42no—
100C2×Dic13—42no—
101C2×Dic13—42no—
102Dic26—82no—
103Dic26—82no—
104C8×C13—44no—
105#1055—82no—
106C2×C4⋊Q8—131no—
107C2×C4×Q8C2×D1311yescharacteristic
108C8×Q8—24no—
109#431—22no—
110#431C2×D1312yes—
111#423—132no—
112C2×#101—261no—
113#400—134no—
114#391—261no—
115#391—262no—
116#382—261no—
117C4×C4⋊C4—131no—
118#343—261no—
119#332—264no—
120C22×C13—21no—
121C22×C13—21no—
122C22×C13#38611yescharacteristic
123C22×C13C2×#10311yescharacteristic
124C22×C13#41611yescharacteristic
125C4×C13—21no—
126C4×C13—24no—
127C4×C13—22no—
128C4×C13—42no—
129C4×C13#45412yes—
130C4×C13#46512yes—
131C4×C13#46712yes—
132Dic13—82no—
133Dic13—82no—
134C22×Q8—261no—
135C22×Q8D5211yescharacteristic
136C2×M16—262no—
137C4⋊Q8—262no—
138C4⋊Q8—262no—
139C4×Q8—22no—
140C4×Q8—22no—
141C2×C4⋊C4—132no—
142C2×C4⋊C4—261no—
143C2×C4⋊C4—261no—
144C2×C4⋊C4C4×D1312yes—
145C2×C4⋊C4D5211yescharacteristic
146C2×C42—261no—
147C2×C42C22⋊D1312yes—
148C2×C42C22×D1311yescharacteristic
149C4⋊C8—24no—
150C4⋊C8—262no—
151C4⋊C8—262no—
152C4⋊C8C22⋊D1314yes—
153#101—522no—
154C22⋊C8—22no—
155C4×C8—24no—
156C4×C8—22no—
157#95—132no—
158#95—264no—
159#95—264no—
160C2×C13—21no—
161C2×C13—21no—
162C2×C13#188811yescharacteristic
163C2×C13#189211yescharacteristic
164C2×C13#191511yescharacteristic
165C2×Q8—22no—
166C2×Q8—22no—
167C2×Q8—524no—
168C2×Q8—521no—
169C2×Q8—521no—
170C2×Q8#609512yes—
171C2×Q8Dic5212yes—
172C22×C4—262no—
173C22×C4—262no—
174C22×C4#610312yes—
175C22×C4#610312yes—
176C22×C4C2×C4×D1311yescharacteristic
177C22×C4C2×D5211yescharacteristic
178C22×C4C2×C22⋊D1311yescharacteristic
179M16—522no—
180M16—522no—
181C2×C8—24no—
182C2×C8—522no—
183C4⋊C4—24no—
184C4⋊C4—22no—
185C4⋊C4—264no—
186C4⋊C4—522no—
187C4⋊C4—522no—
188C42—22no—
189C42—22no—
190C42—522no—
191C42#612712yes—
192C42C2×C22⋊D1312yes—
193C13#939611yescharacteristic, complemented, Sylow
194C23C2×#610311yescharacteristic
195Q8—24no—
196Q8—24no—
197Q8—1042no—
198Q8—1042no—
199C2×C4—22no—
200C2×C4—22no—
201C2×C4—22no—
202C2×C4—22no—
203C2×C4—41no—
204C2×C4—42no—
205C2×C4—522no—
206C2×C4—522no—
207C2×C4—524no—
208C2×C4—522no—
209C2×C4—522no—
210C2×C4#8805614yes—
211C2×C4C2×#609511yescharacteristic
212C2×C4#8815812yes—
213C2×C4C2×Dic5211yescharacteristic
214C2×C4C4×C22⋊D1312yes—
215C2×C4#8818311yescharacteristic
216C2×C4#8818412yes—
217C2×C4#8820711yescharacteristic
218C8—44no—
219C8—1042no—
220C22—21no—
221C22—21no—
222C22C2×#8805611yescharacteristic
223C22#1171877411yescharacteristic
224C22#1171887411yescharacteristic
225C4—21no—
226C4—24no—
227C4—22no—
228C4—42no—
229C4—1042no—
230C4—1042no—
231C4#1171877512yes—
232C4#1171877712yes—
233C4#1171890612yes—
234C2—21no—
235C2—21no—
236C2#1311523911yescharacteristic
237C2#1311525911yescharacteristic
238C2#1311538811yescharacteristic
subgroupG/H
centerC22#11718874
commutatorC22×C4×C13C22×C4
FrattiniC2×C42C22×D13
FittingC13×#2982C2
socleC22×C13#386
prime radicalC23×C13C2×C22⋊C4
cosocleC2×C42×C13C23
hypercenter#2982D13
hypocenterC13#9396
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2982

Complements

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

NH ≅ G/Ntype
193. C13#9396semidirect

Maximal subgroups

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

subgroupindex
#131200482
#131148322
#131135202
#131127382
C13×#29822
#939613