Finite Group Databasebeta

← #15757863

Subgroups — #15757863

Order 3328.

458 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 458 conjugacy classes of subgroups — too many to draw. Only its 115 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
1C2×#11718730C211yesmaximal, characteristic
2#13115808C212yesmaximal
3C2×#11718135C211yesmaximal, characteristic
4#13112717C212yesmaximal
5C13×#2382C211yesmaximal, characteristic
6C2×C13×#125C2211yescharacteristic
7C2×#88123C2211yescharacteristic
8C13×#389—22no—
9C13×#387—22no—
10C13×#387—22no—
11C13×#382C2212yes—
12#11718730—22no—
13#11718730C414yescomplemented
14C2×#88050—22no—
15C2×#88043C2212yes—
16C2×#88043C2211yescharacteristic
17#11718135—22no—
18#11718121—22no—
19#11718121—22no—
20C22×Dic26—21no—
21C13×#125—22no—
22C13×#125C2×C412yes—
23C13×#125D412yes—
24C2×C13×C4⋊C4—22no—
25C2×C13×C4⋊C4—22no—
26C2×C13×C4⋊C4D412yes—
27C2×C13×C4⋊C4D412yes—
28C2×C13×C4⋊C4D412yes—
29C2×C42×C13—22no—
30C2×C42×C13C2311yescharacteristic
31C2×C4⋊Dic13—22no—
32C22×#1055—21no—
33C22×#1055—22no—
34#88123—22no—
35#88123—21no—
36#88123C2×C412yes—
37C13×#95—22no—
38C13×#95—22no—
39C13×#95—22no—
40C13×#95—22no—
41#88050—28no—
42#88043—21no—
43#88043—22no—
44#88043—22no—
45#88043C2×C412yes—
46#9004—131nomaximal, Sylow
47C22×C4×C13—22no—
48C22×C4×C13—22no—
49C22×C4×C13—22no—
50C22×C4×C13C2×D411yescharacteristic
51C22×C4×C13C2×D412yes—
52C22×Dic13—41no—
53C2×Dic26—22no—
54C2×Dic26—42no—
55C2×Dic26—42no—
56C2×Dic26—41no—
57C13×C4⋊C4—24no—
58C13×C4⋊C4—24no—
59C13×C4⋊C4—22no—
60C13×C4⋊C4—42no—
61C13×C4⋊C4—42no—
62C13×C4⋊C4—82no—
63C13×C4⋊C4C22⋊C414yes—
64C42×C13—82no—
65C42×C13C22×C411yescharacteristic
66C42×C13C2×D411yescharacteristic
67C42×C13#4112yes—
68C4⋊Dic13—24no—
69C4⋊Dic13—42no—
70C2×#1055—24no—
71C2×#1055—22no—
72C2×#1055—41no—
73C2×#1055—41no—
74C2×#1055—42no—
75C2×#1055—42no—
76C2×#491—131no—
77#2382D1311yescharacteristic
78#1993—132no—
79C2×#330—131no—
80#1295—132no—
81C23×C13#12011yescharacteristic
82C2×C4×C13—21no—
83C2×C4×C13—21no—
84C2×C4×C13—22no—
85C2×C4×C13—22no—
86C2×C4×C13—24no—
87C2×C4×C13—42no—
88C2×C4×C13—42no—
89C2×C4×C13—42no—
90C2×C4×C13—42no—
91C2×C4×C13—42no—
92C2×C4×C13—42no—
93C2×C4×C13—42no—
94C2×C4×C13—42no—
95C2×C4×C13C2×C22⋊C411yescharacteristic
96C2×C4×C13C4×D412yes—
97C2×C4×C13#12112yes—
98C2×C4×C13#12311yescharacteristic
99C2×Dic13—42no—
100C2×Dic13—81no—
101C2×Dic13—81no—
102Dic26—44no—
103Dic26—82no—
104#1055—44no—
105#1055—42no—
106C2×C4⋊Q8—131no—
107C2×#125C2×D1311yescharacteristic
108#491—134no—
109#491—262no—
110C2×#103—262no—
111C2×#97—131no—
112C2×#97—132no—
113#389—22no—
114#387—22no—
115#387—22no—
116#382C2×D1312yes—
117#340—262no—
118#340—262no—
119#330—262no—
120C22×C13#38611yescharacteristic
121C22×C13#45411yescharacteristic
122C22×C13#45411yescharacteristic
123C22×C13#45512yes—
124C22×C13#45612yes—
125C4×C13—22no—
126C4×C13—22no—
127C4×C13—21no—
128C4×C13—21no—
129C4×C13—44no—
130C4×C13—82no—
131C4×C13—82no—
132Dic13—82no—
133C22×Q8—261no—
134C22×C8—262no—
135C22×C8—261no—
136C4⋊Q8—132no—
137C4⋊Q8—261no—
138C4⋊Q8—262no—
139#125—22no—
140#125C4×D1312yes—
141#125D5212yes—
142C2×C4⋊C4—22no—
143C2×C4⋊C4—22no—
144C2×C4⋊C4—262no—
145C2×C4⋊C4C22⋊D1312yes—
146C2×C4⋊C4C22⋊D1312yes—
147C2×C4⋊C4C22⋊D1312yes—
148C2×C42—22no—
149C2×C42C22×D1311yescharacteristic
150#103—268no—
151#97—132no—
152#97—261no—
153#97—262no—
154#97—262no—
155#95—22no—
156#95—22no—
157#95—22no—
158#95—22no—
159C2×C13#166211yescharacteristic
160C2×C13#166311yescharacteristic
161C2×C13#166412yes—
162C2×C13#188212yes—
163C2×C13#188811yescharacteristic
164C2×Q8—262no—
165C2×Q8—522no—
166C2×Q8—522no—
167C2×Q8—521no—
168C22×C4—22no—
169C22×C4—22no—
170C22×C4—22no—
171C22×C4—521no—
172C22×C4C2×C22⋊D1311yescharacteristic
173C22×C4C2×C22⋊D1312yes—
174C2×C8—264no—
175C2×C8—262no—
176C2×C8—522no—
177C2×C8—521no—
178C2×C8—521no—
179C2×C8—522no—
180C4⋊C4—24no—
181C4⋊C4—22no—
182C4⋊C4—24no—
183C4⋊C4—42no—
184C4⋊C4—42no—
185C4⋊C4—82no—
186C4⋊C4—264no—
187C4⋊C4—522no—
188C4⋊C4#610314yes—
189C42—82no—
190C42C2×C4×D1311yescharacteristic
191C42C2×D5211yescharacteristic
192C42#612712yes—
193C13#900411yescharacteristic, complemented, Sylow
194C23#8820711yescharacteristic
195Q8—524no—
196Q8—1042no—
197C2×C4—22no—
198C2×C4—21no—
199C2×C4—21no—
200C2×C4—22no—
201C2×C4—24no—
202C2×C4—42no—
203C2×C4—42no—
204C2×C4—42no—
205C2×C4—42no—
206C2×C4—42no—
207C2×C4—42no—
208C2×C4—42no—
209C2×C4—42no—
210C2×C4—522no—
211C2×C4—1041no—
212C2×C4—1041no—
213C2×C4C2×#610311yescharacteristic
214C2×C4C4×C22⋊D1312yes—
215C2×C4#8818311yescharacteristic
216C2×C4#8818412yes—
217C8—524no—
218C8—522no—
219C22#1171887411yescharacteristic
220C22#1171890312yes—
221C22#1171890611yescharacteristic
222C22#1171890611yescharacteristic
223C22#1171890712yes—
224C4—22no—
225C4—22no—
226C4—21no—
227C4—21no—
228C4—44no—
229C4—82no—
230C4—82no—
231C4—1042no—
232C2#1311415911yescharacteristic
233C2#1311416411yescharacteristic
234C2#1311417012yes—
235C2#1311520512yes—
236C2#1311523911yescharacteristic
subgroupG/H
centerC23#88207
commutatorC42×C13C22×C4
FrattiniC2×C42C22×D13
FittingC13×#2382C2
socle, prime radicalC23×C13#120
cosocleC2×C42×C13C23
hypercenter#2382D13
hypocenterC13#9004
LCSG ▷ C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2382

Complements

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

NH ≅ G/Ntype
13. #11718730C4semidirect
193. C13#9004semidirect

Maximal subgroups

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

subgroupindex
C2×#117187302
#131158082
C2×#117181352
#131127172
C13×#23822
#900413