Finite Group Databasebeta

← #13116041

Subgroups — #13116041

Order 1664.

316 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 316 conjugacy classes of subgroups — too many to draw. Only its 87 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×#88151C211yesmaximal, characteristic
2C2×C13×#107C211yesmaximal, characteristic, complemented
3C2×#88060C211yesmaximal, characteristic
4C2×#88056C211yesmaximal, characteristic, complemented
5#11718648C211yesmaximal, characteristic
6C2×#88050C211yesmaximal, characteristic, complemented
7#11718121C211yesmaximal, characteristic, complemented
8C22×C4×D13C2211yescharacteristic
9C22×Dic26C2211yescharacteristic
10C22×C8×C13C2211yescharacteristic
11C2×C13×C4⋊C4C2211yescharacteristic
12C2×C13×C4⋊C4C2211yescharacteristic
13C2×#6103—21no—
14C2×#6103—21no—
15C2×C4⋊Dic13—21no—
16C2×C4⋊Dic13C2211yescharacteristic
17C22×#1055C2211yescharacteristic
18#88151—22no—
19#88151—22no—
20C13×#107—22no—
21#88071—21no—
22#88060—22no—
23#88056—22no—
24#88050—22no—
25C23×D13D411yescharacteristic
26C22×C4×C13—21no—
27C22×C4×C13—21no—
28C22×C4×C13C2311yescharacteristic
29C22×Dic13—21no—
30C22×Dic13—21no—
31C22×Dic13D411yescharacteristic
32C2×C4×D13—21no—
33C2×C4×D13—21no—
34C2×C4×D13—21no—
35C2×C4×D13—21no—
36C2×C4×D13—21no—
37C2×C4×D13—21no—
38C2×Dic26—21no—
39C2×Dic26—21no—
40C2×Dic26—21no—
41C2×Dic26—21no—
42C2×Dic26—21no—
43C2×Dic26D412yes—
44C2×C8×C13—21no—
45C2×C8×C13—21no—
46C2×C8×C13D412yes—
47C13×C4⋊C4—21no—
48C13×C4⋊C4—21no—
49C13×C4⋊C4—21no—
50C13×C4⋊C4D412yes—
51#6103—24no—
52#6103—42no—
53C4⋊Dic13—24no—
54C4⋊Dic13—21no—
55C4⋊Dic13—21no—
56C2×#1055—21no—
57C2×#1055—21no—
58C2×#1055—21no—
59#2036—131nomaximal, Sylow
60C23×C13C2×D411yescharacteristic
61C22×D13—21no—
62C22×D13—21no—
63C22×D13—21no—
64C22×D13—21no—
65C22×D13—21no—
66C22×D13—21no—
67C22×D13Q1612yes—
68C2×C4×C13—22no—
69C2×C4×C13—41no—
70C2×C4×C13—41no—
71C2×C4×C13—41no—
72C2×C4×C13—41no—
73C2×C4×C13—41no—
74C2×C4×C13C2×D411yescharacteristic
75C2×C4×C13C2×D411yescharacteristic
76C2×C4×C13C2×D411yescharacteristic
77C2×C4×C13#4111yescharacteristic
78C2×C4×C13#4111yescharacteristic
79C2×C4×C13#4111yescharacteristic
80C2×Dic13—21no—
81C2×Dic13—22no—
82C2×Dic13—21no—
83C2×Dic13—21no—
84C2×Dic13—41no—
85C2×Dic13—41no—
86C2×Dic13—41no—
87C2×Dic13—41no—
88C2×Dic13—41no—
89C4×D13—41no—
90C4×D13—41no—
91C4×D13—41no—
92C4×D13—41no—
93Dic26—22no—
94Dic26—22no—
95Dic26—41no—
96Dic26—41no—
97C8×C13—22no—
98#1055—41no—
99C2×C22⋊Q8—131no—
100C2×#107D1311yescharacteristic, complemented
101C2×#103—131no—
102C2×#103—131no—
103C2×C22⋊C8—131no—
104#380—131no—
105#340—131no—
106C22×C13#12011yescharacteristic
107C22×C13#12111yescharacteristic
108C22×C13#12311yescharacteristic
109C22×C13C2×Q1611yescharacteristic
110C22×C13#13511yescharacteristic
111C22×C13AGL(1,ℤ/8)11yescharacteristic
112C22×C13#13711yescharacteristic
113C2×D13—22no—
114C2×D13—22no—
115C2×D13—22no—
116C2×D13—41no—
117C2×D13—41no—
118C2×D13—41no—
119C2×D13—41no—
120C4×C13—42no—
121C4×C13—81no—
122C4×C13#12111yescharacteristic
123C4×C13#12111yescharacteristic
124C4×C13#12311yescharacteristic
125C4×C13#12411yescharacteristic
126Dic13—42no—
127Dic13—41no—
128Dic13—81no—
129C22×Q8—131no—
130C23×C4—131no—
131C22×C8—131no—
132C22×C8C2×D1311yescharacteristic
133C22⋊Q8—262no—
134C22⋊Q8—262no—
135C2×C4⋊C4—131no—
136C2×C4⋊C4—261no—
137C2×C4⋊C4C2×D1311yescharacteristic
138C2×C4⋊C4C2×D1311yescharacteristic
139C2×C22⋊C4—261no—
140C2×C22⋊C4—261no—
141#107—22no—
142#103—262no—
143#103—262no—
144C22⋊C8—262no—
145#95—261no—
146C2×C13#39411yescharacteristic
147C2×C13#44911yescharacteristic
148C2×C13#45111yescharacteristic
149C2×C13#46711yescharacteristic
150C2×C13#46811yescharacteristic
151C2×C13#48411yescharacteristic
152C2×C13#48511yescharacteristic
153D13—42no—
154C24—131no—
155C2×Q8—132no—
156C2×Q8—261no—
157C2×Q8—261no—
158C2×Q8—261no—
159C2×Q8—261no—
160C2×Q8—261no—
161C22×C4—21no—
162C22×C4—21no—
163C22×C4—131no—
164C22×C4—261no—
165C22×C4—261no—
166C22×C4—261no—
167C22×C4—261no—
168C22×C4—261no—
169C22×C4—261no—
170C22×C4—261no—
171C22×C4—261no—
172C22×C4C22×D1311yescharacteristic
173C2×C8—21no—
174C2×C8—21no—
175C2×C8—261no—
176C2×C8—261no—
177C2×C8—261no—
178C2×C8D5212yes—
179C4⋊C4—21no—
180C4⋊C4—21no—
181C4⋊C4—21no—
182C4⋊C4—264no—
183C4⋊C4—261no—
184C4⋊C4—261no—
185C4⋊C4C22⋊D1312yes—
186C22⋊C4—264no—
187C22⋊C4—522no—
188C13#203611yescharacteristic, complemented, Sylow
189C23—132no—
190C23—261no—
191C23—261no—
192C23—261no—
193C23—261no—
194C23—261no—
195C23—261no—
196C23D4×D1311yescharacteristic
197Q8—262no—
198Q8—262no—
199Q8—521no—
200Q8—521no—
201C2×C4—22no—
202C2×C4—41no—
203C2×C4—41no—
204C2×C4—41no—
205C2×C4—41no—
206C2×C4—41no—
207C2×C4—261no—
208C2×C4—261no—
209C2×C4—262no—
210C2×C4—261no—
211C2×C4—521no—
212C2×C4—521no—
213C2×C4—521no—
214C2×C4—521no—
215C2×C4—521no—
216C2×C4—521no—
217C2×C4—521no—
218C2×C4—521no—
219C2×C4—521no—
220C2×C4C2×D5211yescharacteristic
221C2×C4#612711yescharacteristic
222C2×C4D4×D1311yescharacteristic
223C2×C4#613111yescharacteristic
224C2×C4#613111yescharacteristic
225C2×C4C2×C22⋊D1311yescharacteristic
226C8—22no—
227C8—521no—
228C22—262no—
229C22—262no—
230C22—262no—
231C22—521no—
232C22—521no—
233C22—521no—
234C22—521no—
235C22#8814811yescharacteristic
236C22#8814911yescharacteristic
237C22#8816511yescharacteristic
238C22#8816611yescharacteristic
239C22Q16×D1311yescharacteristic
240C22#8817211yescharacteristic
241C22#8819111yescharacteristic
242C4—42no—
243C4—81no—
244C4—521no—
245C4—522no—
246C4—1041no—
247C4#8814811yescharacteristic
248C4#8814911yescharacteristic
249C4#8818411yescharacteristic
250C4#8820111yescharacteristic
251C2—522no—
252C2#1171854511yescharacteristic
253C2#1171854711yescharacteristic
254C2#1171854811yescharacteristic
255C2#1171854911yescharacteristic
256C2#1171865211yescharacteristic
257C2#1171881911yescharacteristic
258C2#1171884711yescharacteristic
subgroupG/H
centerC23D4×D13
commutator, cosocleC22×C4×C13C23
FrattiniC22×C4C22×D13
FittingC2×C13×#107C2
socleC23×C13C2×D4
prime radicalC23×D13D4
hypercenterC2×#107D13
hypocenterC13#2036
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#107

Complements

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

NH ≅ G/Ntype
2. C2×C13×#107C2semidirect
4. C2×#88056C2semidirect
6. C2×#88050C2semidirect
7. #11718121C2semidirect
100. C2×#107D13semidirect
188. C13#2036semidirect

Maximal subgroups

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

subgroupindex
C2×#881512
C2×C13×#1072
C2×#880602
C2×#880562
#117186482
C2×#880502
#117181212
#203613