Finite Group Databasebeta

← #13127265

Subgroups — #13127265

Order 1664.

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

normal subgroups only

This group has 340 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#11719437C211yesmaximal, characteristic
2#11719289C211yesmaximal, characteristic
3C13×#475C211yesmaximal, characteristic, complemented
4#11718739C211yesmaximal, characteristic, complemented
5C4×#6107C211yesmaximal, characteristic, complemented
6#11718528C212yesmaximal, complemented
7#11718521C212yesmaximal, complemented
8#11718512C211yesmaximal, characteristic, complemented
9#11718495C211yesmaximal, characteristic
10#11718476C212yesmaximal, complemented
11#11718474C212yesmaximal, complemented
12C13×C4⋊Q8C2211yescharacteristic
13C4×Q8×C13C2211yescharacteristic
14#88201—21no—
15#88200C2212yes—
16Q8×Dic13—21no—
17C2×#6107C2211yescharacteristic
18C2×C8×D13C2212yes—
19#88152—22no—
20#88152—22no—
21#88151C2212yes—
22#88146C2212yes—
23#88146C2212yes—
24#88129—21no—
25C4×D52C2211yescharacteristic
26#88123C2211yescharacteristic
27C4×Dic26—21no—
28C4×Dic26C2211yescharacteristic
29C13×#106C2212yes—
30C13×C4⋊C8C2211yescharacteristic
31C13×#103C2212yes—
32#88075C2211yescharacteristic
33#88060C2212yes—
34#88057C2212yes—
35#88056C2212yes—
36#88050C2211yescharacteristic
37#88047C2211yescharacteristic
38#88047C2212yes—
39#88047C2212yes—
40C4×#1055C2211yescharacteristic
41C2×Q8×C13—21no—
42C2×Q8×C13C2311yescharacteristic
43C2×D52D411yescharacteristic
44C2×C4×D13C2312yes—
45C2×Dic26—21no—
46C2×Dic26C2311yescharacteristic
47C2×C8×C13C2312yes—
48C13×C4⋊C4—21no—
49C13×C4⋊C4—21no—
50C13×C4⋊C4C2312yes—
51C13×C4⋊C4C2311yescharacteristic
52C42×C13—21no—
53C42×C13C2311yescharacteristic
54#6107—22no—
55#6103—22no—
56#6103—22no—
57#6103—22no—
58#6103—22no—
59#6103D412yes—
60C4⋊Dic13—21no—
61C4⋊Dic13—22no—
62C4⋊Dic13D411yescharacteristic
63C4⋊Dic13C2311yescharacteristic
64C4⋊Dic13C2312yes—
65#6101—21no—
66#6101—22no—
67C4×Dic13—21no—
68C4×Dic13—22no—
69C4×Dic13—22no—
70C2×#1055C2311yescharacteristic
71C2×#1055C2311yescharacteristic
72C8×D13—24no—
73#3342—131nomaximal, Sylow
74C22×D13C2×D412yes—
75Q8×C13—21no—
76Q8×C13—21no—
77Q8×C13—42no—
78C2×C4×C13—21no—
79C2×C4×C13—22no—
80C2×C4×C13—21no—
81C2×C4×C13C2×D411yescharacteristic
82C2×C4×C13C2×D411yescharacteristic
83C2×C4×C13C2411yescharacteristic
84C2×Dic13—21no—
85C2×Dic13—21no—
86C2×Dic13—22no—
87C2×Dic13C2×D412yes—
88D52—22no—
89C4×D13—22no—
90C4×D13—22no—
91Dic26—21no—
92Dic26—21no—
93Dic26—42no—
94C8×C13—22no—
95#1055—21no—
96#1055#4112yes—
97#556—131no—
98#556—131no—
99#500—131no—
100#485—132no—
101#485—132no—
102#475—131no—
103#475D1311yescharacteristic, complemented
104#467—132no—
105C4×Q16—131no—
106C8×D4—131no—
107#427—132no—
108C22×C13C22×D411yescharacteristic
109C2×D13—22no—
110C2×D13—22no—
111C2×D13—22no—
112C4×C13—21no—
113C4×C13—41no—
114C4×C13—42no—
115C4×C13—41no—
116C4×C13#13512yes—
117C4×C13C2×#4111yescharacteristic
118C4×C132−1+411yescharacteristic
119Dic13—22no—
120Dic13—41no—
121Dic13—42no—
122Dic13—41no—
123C2×Q16—131no—
124C22×C8—132no—
125C4⋊Q8—131no—
126C4⋊Q8C2×D1311yescharacteristic
127#126—262no—
128#126—262no—
129#124—261no—
130#124—261no—
131C22⋊Q8—132no—
132C22⋊Q8—132no—
133C4×Q8—131no—
134C4×Q8—261no—
135C4×Q8—261no—
136C4×Q8C2×D1311yescharacteristic
137C4×D4—131no—
138#117—132no—
139#117—132no—
140#107—131no—
141#107—132no—
142#107—132no—
143#106—132no—
144#106C2×D1312yes—
145C4⋊C8C2×D1311yescharacteristic
146#103—131no—
147#103—132no—
148#103—131no—
149#103C2×D1312yes—
150C22⋊C8—132no—
151C4×C8—131no—
152C2×C13#54711yescharacteristic
153C2×C13C2×#13511yescharacteristic
154C2×C13#57811yescharacteristic
155D13—42no—
156C2×Q8—21no—
157C2×Q8—131no—
158C2×Q8—261no—
159C2×Q8C22×D1311yescharacteristic
160C2×D4—131no—
161C22×C4—132no—
162Q16—262no—
163C2×C8—131no—
164C2×C8—131no—
165C2×C8—264no—
166C2×C8C22×D1312yes—
167C4⋊C4—21no—
168C4⋊C4—21no—
169C4⋊C4—131no—
170C4⋊C4—131no—
171C4⋊C4—132no—
172C4⋊C4—262no—
173C4⋊C4—262no—
174C4⋊C4—261no—
175C4⋊C4—261no—
176C4⋊C4C22×D1311yescharacteristic
177C4⋊C4C22×D1312yes—
178C22⋊C4—132no—
179C22⋊C4—262no—
180C22⋊C4—262no—
181C22⋊C4—262no—
182C22⋊C4—262no—
183C42—21no—
184C42—262no—
185C42—262no—
186C42—261no—
187C42C22×D1311yescharacteristic
188C13#334211yescharacteristic, complemented, Sylow
189C23—132no—
190Q8—21no—
191Q8—21no—
192Q8—42no—
193Q8—261no—
194Q8—261no—
195Q8—522no—
196D4—262no—
197C2×C4—21no—
198C2×C4—21no—
199C2×C4—22no—
200C2×C4—132no—
201C2×C4—262no—
202C2×C4—262no—
203C2×C4—261no—
204C2×C4—262no—
205C2×C4—261no—
206C2×C4D4×D1311yescharacteristic
207C2×C4D4×D1311yescharacteristic
208C2×C4C23×D1311yescharacteristic
209C8—22no—
210C8—132no—
211C8—261no—
212C22—262no—
213C22—262no—
214C22—262no—
215C22C2×D4×D1311yescharacteristic
216C4—21no—
217C4—42no—
218C4—41no—
219C4—41no—
220C4—262no—
221C4—522no—
222C4—521no—
223C4—521no—
224C4#8817012yes—
225C4#8825411yescharacteristic
226C4#41×D1311yescharacteristic
227C2—522no—
228C2#1171933611yescharacteristic
229C2C2×#8817011yescharacteristic
230C2#1171948411yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#475C2
socleC22×C13C22×D4
prime radicalC2×D52D4
hypercenter#475D13
hypocenterC13#3342
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
3. C13×#475C2semidirect
4. #11718739C2semidirect
5. C4×#6107C2semidirect
6. #11718528C2semidirect
7. #11718521C2semidirect
8. #11718512C2semidirect
10. #11718476C2semidirect
11. #11718474C2semidirect
103. #475D13semidirect
188. C13#3342semidirect

Maximal subgroups

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

subgroupindex
#117194372
#117192892
C13×#4752
#117187392
C4×#61072
#117185282
#117185212
#117185122
#117184952
#117184762
#117184742
#334213