Finite Group Databasebeta

← #13127638

Subgroups — #13127638

Order 1664.

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

normal subgroups only

This group has 326 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
1#11719426C211yesmaximal, characteristic
2#11719272C211yesmaximal, characteristic
3C13×#475C211yesmaximal, characteristic
4#11718754C211yesmaximal, characteristic
5C4×#6107C211yesmaximal, characteristic
6#11718518C212yesmaximal
7#11718514C212yesmaximal
8#11718510C211yesmaximal, characteristic
9#11718492C211yesmaximal, characteristic
10#11718458C212yesmaximal
11#11718454C212yesmaximal
12C13×C4⋊Q8C2211yescharacteristic
13C4×Q8×C13C2211yescharacteristic
14Q8×Dic13—21no—
15#88198—21no—
16#88198C2212yes—
17C2×#6107C2211yescharacteristic
18C2×Dic52C2212yes—
19#88144C2212yes—
20#88143—22no—
21#88143—22no—
22#88141C2212yes—
23#88141C2212yes—
24#88124—21no—
25#88123C2211yescharacteristic
26C4×Dic26—21no—
27C4×Dic26C2211yescharacteristic
28C4×Dic26C2211yescharacteristic
29C13×#106C2212yes—
30C13×C4⋊C8C2211yescharacteristic
31C13×#103C2212yes—
32#88075C2211yescharacteristic
33#88056C2212yes—
34#88055C2212yes—
35#88054C2212yes—
36#88050C2211yescharacteristic
37#88050C2212yes—
38#88050C2212yes—
39#88047C2211yescharacteristic
40C4×#1055C2211yescharacteristic
41C2×Q8×C13—21no—
42C2×Q8×C13C2311yescharacteristic
43C2×Dic26D411yescharacteristic
44C2×Dic26C2312yes—
45C2×Dic26C2311yescharacteristic
46C2×C8×C13C2312yes—
47C13×C4⋊C4—21no—
48C13×C4⋊C4—21no—
49C13×C4⋊C4C2312yes—
50C13×C4⋊C4C2311yescharacteristic
51C42×C13—21no—
52C42×C13C2311yescharacteristic
53#6107—22no—
54C4⋊Dic13—21no—
55C4⋊Dic13—21no—
56C4⋊Dic13—22no—
57C4⋊Dic13D411yescharacteristic
58C4⋊Dic13C2311yescharacteristic
59#6101—21no—
60#6101—22no—
61#6101—22no—
62#6101—22no—
63#6101—22no—
64#6101—22no—
65#6101D412yes—
66C4×Dic13—21no—
67C4×Dic13—22no—
68C4×Dic13—22no—
69C4×Dic13C2312yes—
70C2×#1055C2311yescharacteristic
71C2×#1055C2311yescharacteristic
72Dic52—24no—
73#3374—131nomaximal, Sylow
74Q8×C13—21no—
75Q8×C13—21no—
76Q8×C13—42no—
77C2×C4×C13—21no—
78C2×C4×C13—22no—
79C2×C4×C13—21no—
80C2×C4×C13C2×D411yescharacteristic
81C2×C4×C13C2×D411yescharacteristic
82C2×C4×C13C2411yescharacteristic
83C2×Dic13—21no—
84C2×Dic13—21no—
85C2×Dic13—22no—
86C2×Dic13C2×D412yes—
87C2×Dic13C2×D412yes—
88Dic26—22no—
89Dic26—21no—
90Dic26—22no—
91Dic26—22no—
92Dic26#4112yes—
93C8×C13—22no—
94#1055—21no—
95#1055—21no—
96#557—131no—
97#557—131no—
98#491—132no—
99#487—131no—
100#479—132no—
101#475D1311yescharacteristic
102#462—131no—
103#462—132no—
104#446—131no—
105#441—132no—
106C4×Q16—131no—
107C22×C13C22×D411yescharacteristic
108C4×C13—21no—
109C4×C13—41no—
110C4×C13—42no—
111C4×C13—41no—
112C4×C13#13712yes—
113C4×C13C2×#4111yescharacteristic
114C4×C132−1+411yescharacteristic
115Dic13—22no—
116Dic13—22no—
117Dic13—22no—
118Dic13—42no—
119Dic13—41no—
120C2×Q16—131no—
121C2×Q16—132no—
122C4⋊Q8—132no—
123C4⋊Q8—131no—
124C4⋊Q8—261no—
125C4⋊Q8C2×D1311yescharacteristic
126#125—132no—
127#125—261no—
128#125—262no—
129#125—262no—
130C4×Q8—131no—
131C4×Q8—132no—
132C4×Q8—132no—
133C4×Q8—131no—
134C4×Q8—261no—
135C4×Q8—261no—
136C4×Q8C2×D1311yescharacteristic
137#107—131no—
138#106C2×D1312yes—
139C4⋊C8—132no—
140C4⋊C8C2×D1311yescharacteristic
141#103—131no—
142#103—132no—
143#103—131no—
144#103—132no—
145#103—132no—
146#103C2×D1312yes—
147#97—132no—
148C4×C8—131no—
149C2×C13#54811yescharacteristic
150C2×C13C2×#13711yescharacteristic
151C2×C13#57811yescharacteristic
152C2×Q8—21no—
153C2×Q8—131no—
154C2×Q8—131no—
155C2×Q8—132no—
156C2×Q8C22×D1311yescharacteristic
157Q16—264no—
158Q16—262no—
159C2×C8—131no—
160C2×C8—131no—
161C2×C8C22×D1312yes—
162C4⋊C4—21no—
163C4⋊C4—21no—
164C4⋊C4—131no—
165C4⋊C4—132no—
166C4⋊C4—131no—
167C4⋊C4—262no—
168C4⋊C4—262no—
169C4⋊C4—262no—
170C4⋊C4—262no—
171C4⋊C4—262no—
172C4⋊C4—262no—
173C4⋊C4—261no—
174C4⋊C4—261no—
175C4⋊C4—261no—
176C4⋊C4C22×D1312yes—
177C4⋊C4C22×D1311yescharacteristic
178C42—21no—
179C42—132no—
180C42—262no—
181C42—262no—
182C42—261no—
183C42C22×D1311yescharacteristic
184C13#337411yescharacteristic, complemented, Sylow
185Q8—21no—
186Q8—21no—
187Q8—42no—
188Q8—132no—
189Q8—262no—
190Q8—261no—
191Q8—262no—
192Q8—262no—
193C2×C4—21no—
194C2×C4—21no—
195C2×C4—22no—
196C2×C4—132no—
197C2×C4—132no—
198C2×C4—261no—
199C2×C4—261no—
200C2×C4—262no—
201C2×C4D4×D1311yescharacteristic
202C2×C4D4×D1311yescharacteristic
203C2×C4C23×D1311yescharacteristic
204C8—22no—
205C8—261no—
206C8—261no—
207C22C2×D4×D1311yescharacteristic
208C4—21no—
209C4—42no—
210C4—41no—
211C4—41no—
212C4—262no—
213C4—262no—
214C4—262no—
215C4—521no—
216C4—522no—
217C4#8816912yes—
218C4#8825411yescharacteristic
219C4#41×D1311yescharacteristic
220C2#1171933811yescharacteristic
221C2C2×#8816911yescharacteristic
222C2#1171948411yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#475C2
socle, prime radicalC22×C13C22×D4
hypercenter#475D13
hypocenterC13#3374
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
184. C13#3374semidirect

Maximal subgroups

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

subgroupindex
#117194262
#117192722
C13×#4752
#117187542
C4×#61072
#117185182
#117185142
#117185102
#117184922
#117184582
#117184542
#337413