Finite Group Databasebeta

← #15776204

Subgroups — #15776204

Order 3328.

310 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 310 conjugacy classes of subgroups — too many to draw. Only its 71 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#13117036C212yesmaximal
2#13116329C211yesmaximal, characteristic
3#13112848C212yesmaximal
4#13112776C211yesmaximal, characteristic
5C13×#3249C211yesmaximal, characteristic
6C13×#533—21no—
7C13×#477—22no—
8C13×#467—21no—
9C13×#467C2212yes—
10C13×#462—22no—
11C2×C13×C4⋊C8C2211yescharacteristic
12C2×#88058C2211yescharacteristic
13#11718589—21no—
14#11718156—22no—
15#11718143—21no—
16#11718143C2211yescharacteristic
17C22⋊#6090C2212yes—
18#11718081—22no—
19C2×C13×Q16—21no—
20C2×C13×Q16D412yes—
21C22×C8×C13D411yescharacteristic
22C22×C8×C13C2311yescharacteristic
23C13×C4⋊Q8—21no—
24C13×C4⋊Q8—21no—
25C13×#125—41no—
26C13×C22⋊Q8—22no—
27C13×C22⋊Q8—41no—
28C4×Q8×C13—22no—
29C4×Q8×C13—41no—
30C13×#117—41no—
31C2×C42×C13D411yescharacteristic
32C2×C4⋊Dic13—21no—
33C2×C4⋊Dic13—21no—
34C2×#6101—41no—
35C13×#107—21no—
36C13×#107D412yes—
37C13×C4⋊C8—22no—
38C13×#103—22no—
39C13×#103—22no—
40#88071—41no—
41#88058—22no—
42C2×#6090—22no—
43#12292—131nomaximal, Sylow
44C2×Q8×C13—22no—
45C2×Q8×C13—41no—
46C22×C4×C13D811yescharacteristic
47C22×C4×C13D811yescharacteristic
48C22×C4×C13C2×D411yescharacteristic
49C22×Dic13—41no—
50C22×Dic13—41no—
51C13×Q16—42no—
52C13×Q16—81no—
53C2×C8×C13—21no—
54C2×C8×C13—41no—
55C2×C8×C13—41no—
56C2×C8×C13C2×D412yes—
57C13×C4⋊C4—22no—
58C13×C4⋊C4—41no—
59C13×C4⋊C4—41no—
60C13×C4⋊C4—42no—
61C13×C4⋊C4—41no—
62C13×C4⋊C4—42no—
63C13×C22⋊C4—42no—
64C42×C13—21no—
65C42×C13—21no—
66C42×C13—42no—
67C4⋊Dic13—22no—
68C4⋊Dic13—41no—
69C4⋊Dic13—41no—
70C4⋊Dic13—41no—
71#6101—82no—
72#6090—42no—
73#3249D1311yescharacteristic
74#2236—132no—
75#2087—131no—
76#1348—132no—
77#1322—131no—
78C23×C13C2×D811yescharacteristic
79Q8×C13—42no—
80Q8×C13—42no—
81Q8×C13—82no—
82C2×C4×C13—21no—
83C2×C4×C13—21no—
84C2×C4×C13—21no—
85C2×C4×C13—21no—
86C2×C4×C13—21no—
87C2×C4×C13—41no—
88C2×C4×C13—42no—
89C2×C4×C13—42no—
90C2×C4×C13Q3212yes—
91C2×C4×C13#12011yescharacteristic
92C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
93C2×Dic13—42no—
94C2×Dic13—81no—
95C2×Dic13—81no—
96C2×Dic13—81no—
97C2×Dic13—81no—
98C2×Dic13—81no—
99C8×C13—22no—
100C8×C13—41no—
101#533—21no—
102#477—22no—
103#467—21no—
104#467C2×D1312yes—
105#462—22no—
106C2×#107—131no—
107C2×C4⋊C8C2×D1311yescharacteristic
108#389—261no—
109#366—262no—
110#358—262no—
111C22⋊C16—132no—
112#340—131no—
113#340—261no—
114C22×C13—21no—
115C22×C13—21no—
116C22×C13#44711yescharacteristic
117C22×C13C2×Q3211yescharacteristic
118C22×C13#51011yescharacteristic
119C4×C13—21no—
120C4×C13—22no—
121C4×C13—41no—
122C4×C13—82no—
123C4×C13—82no—
124C4×C13#45611yescharacteristic
125C4×C13#45811yescharacteristic
126Dic13—82no—
127Dic13—161no—
128C2×Q16—21no—
129C2×Q16C22⋊D1312yes—
130C22×C8C22⋊D1311yescharacteristic
131C22×C8C22×D1311yescharacteristic
132C4⋊Q8—21no—
133C4⋊Q8—21no—
134#125—41no—
135C22⋊Q8—22no—
136C22⋊Q8—41no—
137C4×Q8—22no—
138C4×Q8—41no—
139#117—41no—
140C2×C4⋊C4—261no—
141C2×C4⋊C4—261no—
142C2×C4⋊C4—521no—
143C2×C42C22⋊D1311yescharacteristic
144C2×C16—262no—
145#107—21no—
146#107—262no—
147#107C22⋊D1312yes—
148C4⋊C8—22no—
149#103—22no—
150#103—22no—
151#95—521no—
152C2×C13—21no—
153C2×C13—21no—
154C2×C13#161011yescharacteristic
155C2×C13#218811yescharacteristic
156C2×C13#219011yescharacteristic
157C2×Q8—22no—
158C2×Q8—41no—
159C22×C4—521no—
160C22×C4—521no—
161C22×C4#610411yescharacteristic
162C22×C4#610411yescharacteristic
163C22×C4C2×C22⋊D1311yescharacteristic
164Q16—42no—
165Q16—81no—
166C2×C8—21no—
167C2×C8—41no—
168C2×C8—41no—
169C2×C8C2×C22⋊D1312yes—
170C4⋊C4—22no—
171C4⋊C4—41no—
172C4⋊C4—41no—
173C4⋊C4—42no—
174C4⋊C4—41no—
175C4⋊C4—42no—
176C4⋊C4—262no—
177C4⋊C4—521no—
178C4⋊C4—521no—
179C4⋊C4—521no—
180C4⋊C4—1042no—
181C22⋊C4—42no—
182C42—21no—
183C42—21no—
184C42—42no—
185C16—522no—
186C13#1229211yescharacteristic, complemented, Sylow
187C23C2×#610411yescharacteristic
188Q8—42no—
189Q8—42no—
190Q8—82no—
191C2×C4—21no—
192C2×C4—21no—
193C2×C4—21no—
194C2×C4—21no—
195C2×C4—21no—
196C2×C4—41no—
197C2×C4—42no—
198C2×C4—42no—
199C2×C4—522no—
200C2×C4—1041no—
201C2×C4—1041no—
202C2×C4—1041no—
203C2×C4—1041no—
204C2×C4—1041no—
205C2×C4#8806912yes—
206C2×C4#8818611yescharacteristic
207C2×C4#8820711yescharacteristic
208C8—22no—
209C8—41no—
210C22—21no—
211C22—21no—
212C22#1171884011yescharacteristic
213C22C2×#8806911yescharacteristic
214C22#1171887811yescharacteristic
215C4—22no—
216C4—21no—
217C4—41no—
218C4—82no—
219C4—82no—
220C4—1042no—
221C4—2081no—
222C4#1171890411yescharacteristic
223C4#1171890711yescharacteristic
224C2—21no—
225C2—21no—
226C2#1311383911yescharacteristic
227C2#1311677011yescharacteristic
228C2#1311678211yescharacteristic
subgroupG/H
centerC22#11718878
commutator, cosocleC22×C8×C13C23
FrattiniC22×C8C22×D13
FittingC13×#3249C2
socleC22×C13#447
prime radicalC23×C13C2×D8
hypercenter#3249D13
hypocenterC13#12292
LCSG ▷ C22×C8×C13 ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C8 ◁ #3249

Complements

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

NH ≅ G/Ntype
186. C13#12292semidirect

Maximal subgroups

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

subgroupindex
#131170362
#131163292
#131128482
#131127762
C13×#32492
#1229213