Finite Group Databasebeta

← #13127639

Subgroups — #13127639

Order 1664.

326 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 326 conjugacy classes of subgroups — too many to draw. Only its 125 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
1C13×#557C211yesmaximal, characteristic
2#11719275C211yesmaximal, characteristic
3#11718755C211yesmaximal, characteristic
4#11718754C211yesmaximal, characteristic
5#11718730C212yesmaximal
6#11718724C212yesmaximal
7#11718692C212yesmaximal
8#11718692C211yesmaximal, characteristic
9#11718691C212yesmaximal
10C4×#6107C211yesmaximal, characteristic
11#11718685C211yesmaximal, characteristic
12C13×C4⋊Q8—21no—
13C13×C4⋊Q8C2211yescharacteristic
14C13×#125—22no—
15C13×#125C2212yes—
16C4×Q8×C13—21no—
17C4×Q8×C13C2211yescharacteristic
18C4×Q8×C13C2212yes—
19C4×Q8×C13C2211yescharacteristic
20Q8×Dic13—21no—
21C2×#6107C2211yescharacteristic
22C2×#6107C2212yes—
23#88144—21no—
24#88144—22no—
25#88123C2212yes—
26#88123C2211yescharacteristic
27C4×Dic26C2211yescharacteristic
28C4×Dic26C2212yes—
29#88075C2211yescharacteristic
30#88050C2211yescharacteristic
31#88050C2212yes—
32#88050C2212yes—
33#88050C2212yes—
34#88050C2212yes—
35#88048C2212yes—
36#88047C2211yescharacteristic
37C4⋊#1055C2212yes—
38C4⋊#1055C2211yescharacteristic
39#88043C2212yes—
40C4×#1055C2211yescharacteristic
41C2×Q8×C13—21no—
42C2×Q8×C13D411yescharacteristic
43C2×Q8×C13C2311yescharacteristic
44C2×Dic26C2311yescharacteristic
45C2×Dic26C2312yes—
46C13×C4⋊C4—22no—
47C13×C4⋊C4—21no—
48C13×C4⋊C4—22no—
49C13×C4⋊C4—21no—
50C13×C4⋊C4—22no—
51C13×C4⋊C4D411yescharacteristic
52C13×C4⋊C4D412yes—
53C13×C4⋊C4C2311yescharacteristic
54C13×C4⋊C4C2312yes—
55C42×C13—22no—
56C42×C13—21no—
57C42×C13C2312yes—
58C42×C13C2311yescharacteristic
59#6107—22no—
60#6107—24no—
61C4⋊Dic13—22no—
62C4⋊Dic13—21no—
63C4⋊Dic13—22no—
64C4⋊Dic13—21no—
65C4⋊Dic13C2311yescharacteristic
66#6101—22no—
67#6101—21no—
68C4×Dic13—22no—
69C4×Dic13—21no—
70C2×#1055C2311yescharacteristic
71C2×#1055C2311yescharacteristic
72C2×#1055C2312yes—
73#3374—131nomaximal, Sylow
74Q8×C13—22no—
75Q8×C13—21no—
76Q8×C13—42no—
77Q8×C13#4112yes—
78C2×C4×C13—21no—
79C2×C4×C13—21no—
80C2×C4×C13—22no—
81C2×C4×C13C2×D412yes—
82C2×C4×C13C2×D412yes—
83C2×C4×C13C2×D411yescharacteristic
84C2×C4×C13C2×D411yescharacteristic
85C2×C4×C13C2411yescharacteristic
86C2×Dic13—21no—
87C2×Dic13—22no—
88C2×Dic13—21no—
89Dic26—21no—
90Dic26—22no—
91Dic26—21no—
92Dic26—22no—
93#1055—21no—
94#1055—22no—
95#1055—21no—
96#557—131no—
97#557D1311yescharacteristic
98#491—132no—
99#487—131no—
100#479—132no—
101#475—131no—
102#462—132no—
103#462—131no—
104#446—131no—
105#441—132no—
106C4×Q16—131no—
107C22×C13C22×D411yescharacteristic
108C4×C13—22no—
109C4×C13—22no—
110C4×C13—22no—
111C4×C13—21no—
112C4×C13—42no—
113C4×C13—41no—
114C4×C13#13712yes—
115C4×C13C2×#4111yescharacteristic
116C4×C132−1+411yescharacteristic
117Dic13—41no—
118Dic13—42no—
119Dic13—41no—
120C2×Q16—131no—
121C2×Q16—132no—
122C4⋊Q8—21no—
123C4⋊Q8—131no—
124C4⋊Q8—132no—
125C4⋊Q8C2×D1311yescharacteristic
126#125—22no—
127#125—261no—
128#125—262no—
129#125C2×D1312yes—
130C4×Q8—21no—
131C4×Q8—131no—
132C4×Q8—132no—
133C4×Q8—261no—
134C4×Q8C2×D1311yescharacteristic
135C4×Q8C2×D1312yes—
136C4×Q8C2×D1311yescharacteristic
137#107—131no—
138#106—132no—
139C4⋊C8—131no—
140C4⋊C8—132no—
141#103—131no—
142#103—131no—
143#103—132no—
144#103—132no—
145#103—132no—
146#103—132no—
147#97—132no—
148C4×C8—131no—
149C2×C13#54811yescharacteristic
150C2×C13C2×#13711yescharacteristic
151C2×C13#57811yescharacteristic
152C2×Q8—21no—
153C2×Q8—131no—
154C2×Q8—132no—
155C2×Q8C22⋊D1311yescharacteristic
156C2×Q8C22×D1311yescharacteristic
157Q16—262no—
158Q16—264no—
159C2×C8—131no—
160C2×C8—131no—
161C2×C8—132no—
162C4⋊C4—22no—
163C4⋊C4—21no—
164C4⋊C4—22no—
165C4⋊C4—21no—
166C4⋊C4—22no—
167C4⋊C4—131no—
168C4⋊C4—262no—
169C4⋊C4—261no—
170C4⋊C4—262no—
171C4⋊C4—261no—
172C4⋊C4—262no—
173C4⋊C4—261no—
174C4⋊C4C22⋊D1311yescharacteristic
175C4⋊C4C22⋊D1312yes—
176C4⋊C4C22×D1312yes—
177C4⋊C4C22×D1311yescharacteristic
178C42—22no—
179C42—21no—
180C42—262no—
181C42—261no—
182C42C22×D1311yescharacteristic
183C42C22×D1312yes—
184C13#337411yescharacteristic, complemented, Sylow
185Q8—22no—
186Q8—21no—
187Q8—42no—
188Q8—261no—
189Q8—262no—
190Q8—261no—
191Q8—262no—
192Q8#613112yes—
193C2×C4—21no—
194C2×C4—21no—
195C2×C4—22no—
196C2×C4—261no—
197C2×C4—262no—
198C2×C4—261no—
199C2×C4C2×C22⋊D1312yes—
200C2×C4C2×C22⋊D1312yes—
201C2×C4C2×C22⋊D1311yescharacteristic
202C2×C4C2×C22⋊D1311yescharacteristic
203C2×C4C23×D1311yescharacteristic
204C8—261no—
205C8—262no—
206C8—261no—
207C22C22×C22⋊D1311yescharacteristic
208C4—22no—
209C4—22no—
210C4—22no—
211C4—21no—
212C4—42no—
213C4—41no—
214C4—522no—
215C4—521no—
216C4—521no—
217C4#8820512yes—
218C4C2×#613111yescharacteristic
219C4#8825411yescharacteristic
220C2#1171952211yescharacteristic
221C2C2×#8820511yescharacteristic
222C2#1171954311yescharacteristic
subgroupG/H
centerC22C22×C22⋊D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#557C2
socle, prime radicalC22×C13C22×D4
hypercenter#557D13
hypocenterC13#3374
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C4×Q8 ◁ #557

Complements

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

NH ≅ G/Ntype
184. C13#3374semidirect

Maximal subgroups

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

subgroupindex
C13×#5572
#117192752
#117187552
#117187542
#117187302
#117187242
#117186922
#117186912
C4×#61072
#117186852
#337413