Finite Group Databasebeta

← #13127484

Subgroups — #13127484

Order 1664.

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

normal subgroups only

This group has 350 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#11719435C211yesmaximal, characteristic, complemented
2#11719247C211yesmaximal, characteristic, complemented
3C13×#476C211yesmaximal, characteristic, complemented
4#11718754C211yesmaximal, characteristic, complemented
5C4×#6104C211yesmaximal, characteristic
6#11718518C212yesmaximal, complemented
7#11718513C212yesmaximal, complemented
8#11718502C211yesmaximal, characteristic, complemented
9#11718491C211yesmaximal, characteristic, complemented
10#11718448C212yesmaximal
11#11718429C212yesmaximal, complemented
12C13×C4⋊Q8C2211yescharacteristic
13C4×D4×C13C2211yescharacteristic
14#88200—22no—
15#88190C2212yes—
16C2×#6104C2211yescharacteristic
17#88180—21no—
18#88178—21no—
19C2×#6095C2212yes—
20#88151—21no—
21#88147C2212yes—
22C4⋊C4×D13—21no—
23#88144C2212yes—
24#88141C2212yes—
25#88133—22no—
26C4×D52C2211yescharacteristic
27#88123C2211yescharacteristic
28C4×Dic26C2211yescharacteristic
29C13×#106C2212yes—
30C13×C4⋊C8C2211yescharacteristic
31C13×#102C2212yes—
32#88072C2211yescharacteristic
33#88056C2212yes—
34#88054C2212yes—
35C8×Dic13C2212yes—
36#88050C2212yes—
37#88050C2212yes—
38#88049C2211yescharacteristic
39#88047C2211yescharacteristic
40C4×#1055C2211yescharacteristic
41C2×Q8×C13—21no—
42C2×D4×C13C2311yescharacteristic
43C22×C4×C13—21no—
44C2×D52C2311yescharacteristic
45C2×C4×D13—21no—
46C2×C4×D13—22no—
47C2×Dic26D411yescharacteristic
48C2×Dic26C2312yes—
49C2×C8×C13C2312yes—
50C13×C4⋊C4—21no—
51C13×C4⋊C4C2312yes—
52C13×C4⋊C4C2311yescharacteristic
53C13×C22⋊C4—21no—
54C42×C13C2311yescharacteristic
55C22⋊Dic13—22no—
56C22⋊Dic13—22no—
57#6104—22no—
58#6103—21no—
59#6103—22no—
60C4⋊Dic13—21no—
61C4⋊Dic13—21no—
62C4⋊Dic13—22no—
63C4⋊Dic13D411yescharacteristic
64C4⋊Dic13C2311yescharacteristic
65#6101—22no—
66#6101—22no—
67#6101D412yes—
68C4×Dic13—22no—
69C4×Dic13C2312yes—
70C2×#1055C2311yescharacteristic
71C2×#1055C2311yescharacteristic
72#6095—24no—
73#3360—131nomaximal, Sylow
74C23×C13—21no—
75C22×D13—21no—
76Q8×C13—81no—
77D4×C13—21no—
78D4×C13—21no—
79C2×C4×C13—21no—
80C2×C4×C13—22no—
81C2×C4×C13—42no—
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—82no—
93Dic26—22no—
94Dic26—22no—
95Dic26—22no—
96C8×C13—22no—
97#1055—21no—
98#1055—21no—
99#556—131no—
100#554—131no—
101#488—132no—
102#487—131no—
103#479—132no—
104#476D1311yescharacteristic, complemented
105#463—132no—
106#461—131no—
107C8×Q8—131no—
108C4×SD16—132no—
109C4×D8—131no—
110C22×C13—41no—
111C22×C13—41no—
112C22×C13—41no—
113C22×C13C22×D411yescharacteristic
114C2×D13—22no—
115C2×D13—41no—
116C2×D13—41no—
117C4×C13—21no—
118C4×C13—41no—
119C4×C13—42no—
120C4×C13#13512yes—
121C4×C13C2×#4111yescharacteristic
122C4×C132−1+411yescharacteristic
123Dic13—22no—
124Dic13—22no—
125Dic13—42no—
126Dic13—41no—
127C2×SD16—132no—
128C2×D8—131no—
129C4⋊Q8—131no—
130C4⋊Q8C2×D1311yescharacteristic
131#126—262no—
132#125—132no—
133#124—132no—
134C22⋊Q8—261no—
135C22⋊Q8—262no—
136C22⋊Q8—261no—
137C4×Q8—131no—
138C4×Q8—132no—
139C4×D4—132no—
140C4×D4—131no—
141C4×D4C2×D1311yescharacteristic
142#117—261no—
143C2×C4⋊C4—261no—
144#107—131no—
145#106C2×D1312yes—
146C4⋊C8—132no—
147C4⋊C8C2×D1311yescharacteristic
148#103—132no—
149#103—132no—
150#103—132no—
151#102—131no—
152#102—131no—
153#102C2×D1312yes—
154C4×C8—132no—
155C4×C8—131no—
156C2×C13—81no—
157C2×C13#54811yescharacteristic
158C2×C13C2×#13511yescharacteristic
159C2×C13#57711yescharacteristic
160D13—42no—
161C2×Q8—21no—
162C2×Q8—131no—
163C2×Q8—132no—
164C2×D4—131no—
165C2×D4C22×D1311yescharacteristic
166C22×C4—21no—
167C22×C4—262no—
168C22×C4—261no—
169SD16—264no—
170D8—262no—
171C2×C8—131no—
172C2×C8—131no—
173C2×C8C22×D1312yes—
174C4⋊C4—21no—
175C4⋊C4—131no—
176C4⋊C4—132no—
177C4⋊C4—131no—
178C4⋊C4—262no—
179C4⋊C4—262no—
180C4⋊C4—262no—
181C4⋊C4—261no—
182C4⋊C4—261no—
183C4⋊C4C22×D1311yescharacteristic
184C4⋊C4C22×D1312yes—
185C22⋊C4—21no—
186C22⋊C4—262no—
187C22⋊C4—262no—
188C22⋊C4—262no—
189C22⋊C4—261no—
190C42—132no—
191C42—262no—
192C42C22×D1311yescharacteristic
193C13#336011yescharacteristic, complemented, Sylow
194C23—21no—
195C23—261no—
196Q8—81no—
197Q8—262no—
198Q8—262no—
199Q8—262no—
200D4—21no—
201D4—21no—
202D4—132no—
203D4—261no—
204C2×C4—21no—
205C2×C4—22no—
206C2×C4—42no—
207C2×C4—132no—
208C2×C4—132no—
209C2×C4—262no—
210C2×C4—261no—
211C2×C4—522no—
212C2×C4—1042no—
213C2×C4D4×D1311yescharacteristic
214C2×C4D4×D1311yescharacteristic
215C2×C4C23×D1311yescharacteristic
216C8—22no—
217C8—261no—
218C8—261no—
219C22—41no—
220C22—41no—
221C22—41no—
222C22—262no—
223C22—521no—
224C22—521no—
225C22C2×D4×D1311yescharacteristic
226C4—21no—
227C4—41no—
228C4—42no—
229C4—262no—
230C4—262no—
231C4—521no—
232C4—522no—
233C4#8817012yes—
234C4#8825411yescharacteristic
235C4#41×D1311yescharacteristic
236C2—81no—
237C2—522no—
238C2#1171933811yescharacteristic
239C2C2×#8817011yescharacteristic
240C2#1171948011yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#476C2
socleC22×C13C22×D4
prime radicalC2×#6104C22
hypercenter#476D13
hypocenterC13#3360
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ #476

Complements

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

NH ≅ G/Ntype
1. #11719435C2semidirect
2. #11719247C2semidirect
3. C13×#476C2semidirect
4. #11718754C2semidirect
6. #11718518C2semidirect
7. #11718513C2semidirect
8. #11718502C2semidirect
9. #11718491C2semidirect
11. #11718429C2semidirect
104. #476D13semidirect
193. C13#3360semidirect

Maximal subgroups

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

subgroupindex
#117194352
#117192472
C13×#4762
#117187542
C4×#61042
#117185182
#117185132
#117185022
#117184912
#117184482
#117184292
#336013