Finite Group Databasebeta

← #13125366

Subgroups — #13125366

Order 1664.

340 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 340 conjugacy classes of subgroups — too many to draw. Only its 149 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#11719224C211yesmaximal, characteristic
2#11719205C211yesmaximal, characteristic
3C13×#428C211yesmaximal, characteristic
4#11718783C211yesmaximal, characteristic
5#11718782C211yesmaximal, characteristic
6#11718659C211yesmaximal, characteristic
7C2×#88048C211yesmaximal, characteristic
8#11718539C212yesmaximal, complemented
9#11718537C212yesmaximal, complemented
10#11718517C212yesmaximal, complemented
11#11718516C212yesmaximal, complemented
12C2×C13×M16C2211yescharacteristic
13C13×#117C2211yescharacteristic
14C2×C13×C4⋊C4C2211yescharacteristic
15#88180C2211yescharacteristic
16#88180C2211yescharacteristic
17C2×C4⋊Dic13C2211yescharacteristic
18#88178—22no—
19C22×#1055C2211yescharacteristic
20#88144—21no—
21#88144C2212yes—
22#88144C2212yes—
23#88142—21no—
24#88142C2212yes—
25#88142C2212yes—
26#88132—22no—
27#88124—21no—
28#88123—21no—
29C13×#107C2212yes—
30C13×#106C2212yes—
31#88058C2212yes—
32#88057C2212yes—
33#88055C2212yes—
34C8×Dic13C2212yes—
35#88048C2211yescharacteristic
36#88048C2211yescharacteristic
37#88048C2212yes—
38#88048C2212yes—
39#88047C2211yescharacteristic
40#88047C2211yescharacteristic
41C22×C4×C13—21no—
42C22×C4×C13C2311yescharacteristic
43C22×Dic13—21no—
44C2×Dic26—22no—
45C2×Dic26—22no—
46C13×M16Q814yescomplemented
47C2×C8×C13C2312yes—
48C13×C4⋊C4—21no—
49C13×C4⋊C4C2311yescharacteristic
50C13×C4⋊C4C2312yes—
51C13×C4⋊C4C2311yescharacteristic
52C13×C22⋊C4—21no—
53C42×C13—21no—
54C22⋊Dic13—21no—
55C22⋊Dic13D412yes—
56C4⋊Dic13—21no—
57C4⋊Dic13—22no—
58C4⋊Dic13—22no—
59C4⋊Dic13D411yescharacteristic
60C4⋊Dic13D411yescharacteristic
61C4⋊Dic13C2311yescharacteristic
62C4⋊Dic13C2312yes—
63C4⋊Dic13C2311yescharacteristic
64#6101—22no—
65#6101—22no—
66#6101—22no—
67#6101—22no—
68C4×Dic13—21no—
69C4×Dic13C2312yes—
70C2×#1055Q814yescomplemented
71C2×#1055C2311yescharacteristic
72C2×#1055C2311yescharacteristic
73#3163—131nomaximal, Sylow
74C23×C13C2×D411yescharacteristic
75C2×C4×C13—21no—
76C2×C4×C13—22no—
77C2×C4×C13—21no—
78C2×C4×C13—81no—
79C2×C4×C13C2×D411yescharacteristic
80C2×C4×C13C2×Q812yes—
81C2×C4×C13C2×Q812yes—
82C2×C4×C13C2411yescharacteristic
83C2×Dic13—21no—
84C2×Dic13—21no—
85C2×Dic13—22no—
86C2×Dic13—81no—
87C2×Dic13C2×D412yes—
88C2×Dic13C2×D412yes—
89Dic26—82no—
90Dic26—82no—
91C8×C13C2×Q814yes—
92#1055C2×Q812yes—
93#1055C2×Q812yes—
94#544—131no—
95#544—131no—
96#501—132no—
97#501—132no—
98#499—132no—
99#498—132no—
100#428—131no—
101#428D1311yescharacteristic
102#427—131no—
103C2×#106—131no—
104#405—131no—
105C22×C13—21no—
106C22×C13—21no—
107C22×C13C4⋊Q812yes—
108C22×C13C22×D411yescharacteristic
109C4×C13—41no—
110C4×C13—42no—
111C4×C13—41no—
112C4×C13C4⋊Q812yes—
113C4×C13C22×Q811yescharacteristic
114C4×C13C22×Q811yescharacteristic
115Dic13—22no—
116Dic13—22no—
117Dic13—41no—
118Dic13—42no—
119Dic13—41no—
120C2×M16C2×D1311yescharacteristic
121C22×C8—131no—
122C4⋊Q8—132no—
123C4⋊Q8—132no—
124C4⋊Q8—261no—
125C4⋊Q8—261no—
126#125—132no—
127#125—132no—
128#125—261no—
129#125—261no—
130C22⋊Q8—262no—
131C22⋊Q8—262no—
132#117—131no—
133#117—131no—
134#117C2×D1311yescharacteristic
135C2×C4⋊C4—131no—
136C2×C4⋊C4C2×D1311yescharacteristic
137#107—132no—
138#107—131no—
139#107—131no—
140#107C2×D1312yes—
141#106—132no—
142#106—132no—
143#106—132no—
144#106—131no—
145#106—131no—
146#106C2×D1312yes—
147#97—132no—
148C4×C8—132no—
149C2×C13—22no—
150C2×C13C2×C4⋊Q811yescharacteristic
151C2×C13#57711yescharacteristic
152C2×C13#57711yescharacteristic
153C2×Q8—262no—
154C2×Q8—262no—
155C22×C4—21no—
156C22×C4—261no—
157C22×C4C22×D1311yescharacteristic
158M16Dic2614yescomplemented
159C2×C8—134no—
160C2×C8—131no—
161C2×C8—131no—
162C2×C8C22×D1312yes—
163C4⋊C4—21no—
164C4⋊C4—131no—
165C4⋊C4—131no—
166C4⋊C4—132no—
167C4⋊C4—131no—
168C4⋊C4—131no—
169C4⋊C4—262no—
170C4⋊C4—262no—
171C4⋊C4—262no—
172C4⋊C4—262no—
173C4⋊C4—262no—
174C4⋊C4—262no—
175C4⋊C4—261no—
176C4⋊C4C22×D1312yes—
177C4⋊C4C22×D1311yescharacteristic
178C4⋊C4C22×D1311yescharacteristic
179C22⋊C4—21no—
180C22⋊C4—132no—
181C22⋊C4—261no—
182C42—21no—
183C42—132no—
184C42—261no—
185C13#316311yescharacteristic, complemented, Sylow
186C23D4×D1311yescharacteristic
187Q8—1042no—
188Q8—1042no—
189C2×C4—21no—
190C2×C4—21no—
191C2×C4—22no—
192C2×C4—81no—
193C2×C4—132no—
194C2×C4—132no—
195C2×C4—261no—
196C2×C4—261no—
197C2×C4—262no—
198C2×C4—1041no—
199C2×C4C2×Dic2612yes—
200C2×C4D4×D1311yescharacteristic
201C2×C4Q8×D1312yes—
202C2×C4C23×D1311yescharacteristic
203C8—132no—
204C8—132no—
205C8C2×Dic2614yes—
206C22—21no—
207C22—21no—
208C22#8814212yes—
209C22C2×D4×D1311yescharacteristic
210C4—41no—
211C4—42no—
212C4—41no—
213C4—262no—
214C4—262no—
215C4—521no—
216C4—521no—
217C4—522no—
218C4#8814212yes—
219C4C22×Dic2611yescharacteristic
220C4C2×Q8×D1311yescharacteristic
221C2—22no—
222C2C2×#8814211yescharacteristic
223C2#1171948011yescharacteristic
224C2#1171948311yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#428C2
socleC22×C13C22×D4
prime radicalC23×C13C2×D4
hypercenter#428D13
hypocenterC13#3163
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ #428

Complements

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

NH ≅ G/Ntype
8. #11718539C2semidirect
9. #11718537C2semidirect
10. #11718517C2semidirect
11. #11718516C2semidirect
46. C13×M16Q8semidirect
70. C2×#1055Q8semidirect
158. M16Dic26semidirect
185. C13#3163semidirect

Maximal subgroups

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

subgroupindex
#117192242
#117192052
C13×#4282
#117187832
#117187822
#117186592
C2×#880482
#117185392
#117185372
#117185172
#117185162
#316313