Finite Group Databasebeta

← #15775382

Subgroups — #15775382

Order 3328.

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

normal subgroups only

This group has 354 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#13116769C212yesmaximal
2#13116159C211yesmaximal, characteristic
3#13112848C212yesmaximal
4#13112776C211yesmaximal, characteristic
5C13×#3249C211yesmaximal, characteristic
6C13×#533—21no—
7C22×Dic52C2211yescharacteristic
8C13×#477—22no—
9C13×#467—21no—
10C13×#467C2212yes—
11C13×#462—22no—
12C2×C13×C4⋊C8C2211yescharacteristic
13C2×#88069—22no—
14C2×#88056—21no—
15#11718590—21no—
16#11718143C2211yescharacteristic
17C22⋊#6090C2212yes—
18#11718084—22no—
19C22×Dic26—21no—
20C2×C13×Q16—21no—
21C2×C13×Q16D412yes—
22C22×C8×C13D411yescharacteristic
23C22×C8×C13C2311yescharacteristic
24C13×C4⋊Q8—21no—
25C13×C4⋊Q8—21no—
26C13×#125—41no—
27C13×C22⋊Q8—22no—
28C13×C22⋊Q8—41no—
29C4×Q8×C13—22no—
30C4×Q8×C13—41no—
31C13×#117—41no—
32C2×C42×C13D411yescharacteristic
33C2×C4⋊Dic13—21no—
34C2×Dic52—22no—
35C2×Dic52—42no—
36C13×#107—21no—
37C13×#107D412yes—
38C13×C4⋊C8—22no—
39C13×#103—22no—
40C13×#103—22no—
41#88071—41no—
42#88071—41no—
43#88069—44no—
44#88056—42no—
45C2×#6090—22no—
46#12162—131nomaximal, Sylow
47C2×Q8×C13—22no—
48C2×Q8×C13—41no—
49C22×C4×C13D811yescharacteristic
50C22×C4×C13D811yescharacteristic
51C22×C4×C13C2×D411yescharacteristic
52C22×Dic13—41no—
53C22×Dic13—41no—
54C2×Dic26—22no—
55C2×Dic26—41no—
56C2×Dic26—41no—
57C2×Dic26—41no—
58C2×Dic26—41no—
59C2×Dic26—41no—
60C13×Q16—42no—
61C13×Q16—81no—
62C2×C8×C13—21no—
63C2×C8×C13—41no—
64C2×C8×C13—41no—
65C2×C8×C13C2×D412yes—
66C13×C4⋊C4—22no—
67C13×C4⋊C4—41no—
68C13×C4⋊C4—41no—
69C13×C4⋊C4—42no—
70C13×C4⋊C4—41no—
71C13×C4⋊C4—42no—
72C13×C22⋊C4—42no—
73C42×C13—21no—
74C42×C13—21no—
75C42×C13—42no—
76C4⋊Dic13—41no—
77C4⋊Dic13—41no—
78Dic52—24no—
79Dic52—42no—
80#6090—42no—
81#3249D1311yescharacteristic
82#2188—132no—
83#2056—131no—
84#1348—132no—
85#1322—131no—
86C23×C13C2×D811yescharacteristic
87Q8×C13—42no—
88Q8×C13—42no—
89Q8×C13—82no—
90C2×C4×C13—21no—
91C2×C4×C13—21no—
92C2×C4×C13—21no—
93C2×C4×C13—21no—
94C2×C4×C13—21no—
95C2×C4×C13—41no—
96C2×C4×C13—42no—
97C2×C4×C13—42no—
98C2×C4×C13Q3212yescomplemented
99C2×C4×C13#12011yescharacteristic
100C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
101C2×Dic13—42no—
102C2×Dic13—81no—
103C2×Dic13—81no—
104C2×Dic13—81no—
105C2×Dic13—81no—
106C2×Dic13—81no—
107Dic26—42no—
108Dic26—42no—
109Dic26—81no—
110Dic26—81no—
111C8×C13—22no—
112C8×C13—41no—
113C22×Q16—131no—
114#533—21no—
115C2×Q32—262no—
116#477—22no—
117#467—21no—
118#467C2×D1312yes—
119#462—22no—
120C2×C4⋊C8C2×D1311yescharacteristic
121C2×#103—261no—
122#391—261no—
123#358—262no—
124C22⋊C16—132no—
125#340—131no—
126C22×C13—21no—
127C22×C13—21no—
128C22×C13#44711yescharacteristic
129C22×C13C2×Q3211yescharacteristic
130C22×C13#51011yescharacteristic
131C4×C13—21no—
132C4×C13—22no—
133C4×C13—41no—
134C4×C13—82no—
135C4×C13—82no—
136C4×C13#45411yescharacteristic
137C4×C13B(4,𝔽2)11yescharacteristic
138Dic13—82no—
139Dic13—161no—
140C22×Q8—261no—
141C2×Q16—21no—
142C2×Q16—262no—
143C2×Q16—522no—
144C2×Q16C22⋊D1312yes—
145C22×C8C22⋊D1311yescharacteristic
146C22×C8C22×D1311yescharacteristic
147C4⋊Q8—21no—
148C4⋊Q8—21no—
149#125—41no—
150C22⋊Q8—22no—
151C22⋊Q8—41no—
152C4×Q8—22no—
153C4×Q8—41no—
154#117—41no—
155C2×C4⋊C4—261no—
156C2×C42C22⋊D1311yescharacteristic
157Q32—524no—
158C2×C16—262no—
159#107—21no—
160#107C22⋊D1312yes—
161C4⋊C8—22no—
162#103—22no—
163#103—22no—
164#103—522no—
165#95—521no—
166#95—521no—
167C2×C13—21no—
168C2×C13—21no—
169C2×C13#159811yescharacteristic
170C2×C13#218811yescharacteristic
171C2×C13#219111yescharacteristic
172C2×Q8—22no—
173C2×Q8—41no—
174C2×Q8—262no—
175C2×Q8—521no—
176C2×Q8—521no—
177C2×Q8—521no—
178C2×Q8—521no—
179C2×Q8—521no—
180C22×C4—521no—
181C22×C4—521no—
182C22×C4#610411yescharacteristic
183C22×C4#610411yescharacteristic
184C22×C4C2×C22⋊D1311yescharacteristic
185Q16—42no—
186Q16—81no—
187Q16—264no—
188Q16—522no—
189C2×C8—21no—
190C2×C8—41no—
191C2×C8—41no—
192C2×C8C2×C22⋊D1312yes—
193C4⋊C4—22no—
194C4⋊C4—41no—
195C4⋊C4—41no—
196C4⋊C4—42no—
197C4⋊C4—41no—
198C4⋊C4—42no—
199C4⋊C4—521no—
200C4⋊C4—521no—
201C22⋊C4—42no—
202C42—21no—
203C42—21no—
204C42—42no—
205C16—522no—
206C13#1216211yescharacteristic, complemented, Sylow
207C23C2×#610411yescharacteristic
208Q8—42no—
209Q8—42no—
210Q8—82no—
211Q8—522no—
212Q8—522no—
213Q8—1041no—
214Q8—1041no—
215C2×C4—21no—
216C2×C4—21no—
217C2×C4—21no—
218C2×C4—21no—
219C2×C4—21no—
220C2×C4—41no—
221C2×C4—42no—
222C2×C4—42no—
223C2×C4—522no—
224C2×C4—1041no—
225C2×C4—1041no—
226C2×C4—1041no—
227C2×C4—1041no—
228C2×C4—1041no—
229C2×C4#8806912yescomplemented
230C2×C4#8818611yescharacteristic
231C2×C4#8820711yescharacteristic
232C8—22no—
233C8—41no—
234C22—21no—
235C22—21no—
236C22#1171884011yescharacteristic
237C22C2×#8806911yescharacteristic
238C22#1171887811yescharacteristic
239C4—22no—
240C4—21no—
241C4—41no—
242C4—82no—
243C4—82no—
244C4—1042no—
245C4—2081no—
246C4#1171890511yescharacteristic
247C4#1171890611yescharacteristic
248C2—21no—
249C2—21no—
250C2#1311377111yescharacteristic
251C2#1311677011yescharacteristic
252C2#1311678711yescharacteristic
subgroupG/H
centerC22#11718878
commutator, cosocleC22×C8×C13C23
FrattiniC22×C8C22×D13
FittingC13×#3249C2
socleC22×C13#447
prime radicalC23×C13C2×D8
hypercenter#3249D13
hypocenterC13#12162
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
98. C2×C4×C13Q32semidirect
206. C13#12162semidirect
229. C2×C4#88069semidirect

Maximal subgroups

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

subgroupindex
#131167692
#131161592
#131128482
#131127762
C13×#32492
#1216213