Finite Group Databasebeta

← #13127477

Subgroups — #13127477

Order 1664.

370 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

normal subgroups only

This group has 370 conjugacy classes of subgroups — too many to draw. Only its 123 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#11719432C211yesmaximal, characteristic
2#11719272C211yesmaximal, characteristic, complemented
3C13×#475C211yesmaximal, characteristic, complemented
4#11718754C211yesmaximal, characteristic, complemented
5C4×#6106C211yesmaximal, characteristic
6#11718515C212yesmaximal, complemented
7#11718513C212yesmaximal
8#11718502C211yesmaximal, characteristic
9#11718491C211yesmaximal, characteristic, complemented
10#11718479C212yesmaximal
11#11718453C212yesmaximal, complemented
12C2×Q8×D13—21no—
13C13×C4⋊Q8C2211yescharacteristic
14C4×Q8×C13C2211yescharacteristic
15#88200—21no—
16#88198C2212yes—
17C2×#6106C2211yescharacteristic
18C2×#6095C2212yes—
19#88150—22no—
20#88147C2212yes—
21#88143—22no—
22#88142C2212yes—
23#88141C2212yes—
24C4×D52C2211yescharacteristic
25#88124—21no—
26#88123C2211yescharacteristic
27C4×Dic26—21no—
28C4×Dic26C2211yescharacteristic
29C13×#106C2212yes—
30C13×C4⋊C8C2211yescharacteristic
31C13×#103C2212yes—
32#88075C2211yescharacteristic
33#88056C2212yes—
34#88054C2212yes—
35C8×Dic13C2212yes—
36#88050C2212yes—
37#88050C2212yes—
38#88049C2211yescharacteristic
39#88048C2211yescharacteristic
40C4×#1055C2211yescharacteristic
41C2×Q8×C13—21no—
42C2×Q8×C13C2311yescharacteristic
43Q8×D13—44no—
44C2×D52C2311yescharacteristic
45C2×C4×D13—21no—
46C2×C4×D13—22no—
47C2×Dic26—22no—
48C2×Dic26D411yescharacteristic
49C2×Dic26C2312yes—
50C2×C8×C13C2312yes—
51C13×C4⋊C4—21no—
52C13×C4⋊C4—21no—
53C13×C4⋊C4C2312yes—
54C13×C4⋊C4C2311yescharacteristic
55C42×C13—21no—
56C42×C13C2311yescharacteristic
57#6106—22no—
58#6103—21no—
59#6103—22no—
60C4⋊Dic13—21no—
61C4⋊Dic13—21no—
62C4⋊Dic13D411yescharacteristic
63C4⋊Dic13C2311yescharacteristic
64#6101—22no—
65#6101—22no—
66#6101—22no—
67#6101—22no—
68#6101D412yes—
69C4×Dic13—22no—
70C4×Dic13C2312yes—
71C2×#1055C2311yescharacteristic
72C2×#1055C2311yescharacteristic
73#6095—24no—
74#3359—131nomaximal, Sylow
75C22×D13—21no—
76Q8×C13—21no—
77Q8×C13—21no—
78Q8×C13—42no—
79C2×C4×C13—21no—
80C2×C4×C13—21no—
81C2×C4×C13—22no—
82C2×C4×C13C2×D411yescharacteristic
83C2×C4×C13C2×D411yescharacteristic
84C2×C4×C13C2411yescharacteristic
85C2×Dic13—22no—
86C2×Dic13—21no—
87C2×Dic13C2×D412yes—
88C2×Dic13C2×D412yes—
89D52—21no—
90D52#4112yes—
91C4×D13—42no—
92C4×D13—44no—
93Dic26—22no—
94Dic26—22no—
95Dic26—44no—
96Dic26SD1614yescomplemented
97C8×C13—22no—
98#1055—21no—
99#1055—21no—
100#557—131no—
101D4×Q8—131no—
102#487—131no—
103#487—132no—
104#475—132no—
105#475D1311yescharacteristic, complemented
106#461—131no—
107#461—132no—
108C8×Q8—131no—
109C4×SD16—131no—
110C4×SD16—132no—
111C22×C13C22×D411yescharacteristic
112C2×D13—22no—
113C2×D13—41no—
114C2×D13—41no—
115C4×C13—21no—
116C4×C13—41no—
117C4×C13—42no—
118C4×C13—41no—
119C4×C13C2×SD1612yes—
120C4×C13C2×#4111yescharacteristic
121C4×C132−1+411yescharacteristic
122Dic13—22no—
123Dic13—42no—
124Dic13—41no—
125Dic13C2×SD1614yes—
126C22×Q8—261no—
127C2×SD16—131no—
128C2×SD16—132no—
129C4⋊Q8—132no—
130C4⋊Q8—132no—
131C4⋊Q8—131no—
132C4⋊Q8C2×D1311yescharacteristic
133#125—261no—
134#125—262no—
135C22⋊Q8—262no—
136C22⋊Q8—261no—
137C4×Q8—131no—
138C4×Q8—132no—
139C4×Q8—261no—
140C4×Q8C2×D1311yescharacteristic
141C4×D4—132no—
142C4×D4—131no—
143#106—131no—
144#106C2×D1312yes—
145C4⋊C8—132no—
146C4⋊C8C2×D1311yescharacteristic
147#103—131no—
148#103—132no—
149#103—132no—
150#103—132no—
151#103C2×D1312yes—
152#102—131no—
153C4×C8—132no—
154C4×C8—131no—
155C2×C13#54811yescharacteristic
156C2×C13C22×SD1611yescharacteristic
157C2×C13#57811yescharacteristic
158D13—42no—
159C2×Q8—21no—
160C2×Q8—131no—
161C2×Q8—132no—
162C2×Q8—262no—
163C2×Q8—524no—
164C2×Q8C22×D1311yescharacteristic
165C2×D4—131no—
166C22×C4—262no—
167C22×C4—261no—
168SD16—264no—
169SD16—262no—
170C2×C8—131no—
171C2×C8—131no—
172C2×C8C22×D1312yes—
173C4⋊C4—21no—
174C4⋊C4—21no—
175C4⋊C4—132no—
176C4⋊C4—131no—
177C4⋊C4—131no—
178C4⋊C4—262no—
179C4⋊C4—262no—
180C4⋊C4—262no—
181C4⋊C4—262no—
182C4⋊C4—261no—
183C4⋊C4—261no—
184C4⋊C4C22×D1311yescharacteristic
185C4⋊C4C22×D1312yes—
186C22⋊C4—262no—
187C22⋊C4—261no—
188C42—21no—
189C42—132no—
190C42—262no—
191C42C22×D1311yescharacteristic
192C13#335911yescharacteristic, complemented, Sylow
193C23—261no—
194Q8—21no—
195Q8—21no—
196Q8—42no—
197Q8—134no—
198Q8—262no—
199Q8—262no—
200Q8—524no—
201D4—132no—
202D4—261no—
203C2×C4—21no—
204C2×C4—21no—
205C2×C4—22no—
206C2×C4—132no—
207C2×C4—132no—
208C2×C4—262no—
209C2×C4—261no—
210C2×C4—524no—
211C2×C4—522no—
212C2×C4D4×D1311yescharacteristic
213C2×C4D4×D1311yescharacteristic
214C2×C4C23×D1311yescharacteristic
215C8—22no—
216C8—261no—
217C8—261no—
218C22—262no—
219C22—521no—
220C22—521no—
221C22C2×D4×D1311yescharacteristic
222C4—21no—
223C4—42no—
224C4—41no—
225C4—41no—
226C4—134no—
227C4—262no—
228C4—521no—
229C4—522no—
230C4SD16×D1312yes—
231C4#8825411yescharacteristic
232C4#41×D1311yescharacteristic
233C2—522no—
234C2#1171933811yescharacteristic
235C2C2×SD16×D1311yescharacteristic
236C2#1171948411yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#475C2
socleC22×C13C22×D4
prime radicalC2×D52C23
hypercenter#475D13
hypocenterC13#3359
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ #475

Complements

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

NH ≅ G/Ntype
2. #11719272C2semidirect
3. C13×#475C2semidirect
4. #11718754C2semidirect
6. #11718515C2semidirect
9. #11718491C2semidirect
11. #11718453C2semidirect
96. Dic26SD16semidirect
105. #475D13semidirect
192. C13#3359semidirect

Maximal subgroups

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

subgroupindex
#117194322
#117192722
C13×#4752
#117187542
C4×#61062
#117185152
#117185132
#117185022
#117184912
#117184792
#117184532
#335913