Finite Group Databasebeta

← #13127481

Subgroups — #13127481

Order 1664.

350 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

normal subgroups only

This group has 350 conjugacy classes of subgroups — too many to draw. Only its 123 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×#556C211yesmaximal, characteristic, complemented
2#11719284C211yesmaximal, characteristic, complemented
3#11718744C211yesmaximal, characteristic, complemented
4#11718742C211yesmaximal, characteristic, complemented
5#11718718C212yesmaximal
6#11718717C212yesmaximal, complemented
7C4×#6106C212yesmaximal, complemented
8Q8×#1055C211yesmaximal, characteristic, complemented
9#11718683C212yesmaximal, complemented
10C4×#6104C211yesmaximal, characteristic
11#11718669C211yesmaximal, characteristic, complemented
12C13×C4⋊Q8C2211yescharacteristic
13C13×#126—22no—
14C13×#124C2212yes—
15C13×C22⋊Q8—21no—
16C4×Q8×C13C2212yes—
17C4×Q8×C13C2211yescharacteristic
18C4×D4×C13C2211yescharacteristic
19C13×#117—21no—
20#88200—21no—
21C2×#6106C2212yes—
22C2×#6104C2211yescharacteristic
23#88150—22no—
24C4⋊C4×D13—21no—
25C4×D52C2211yescharacteristic
26C4×D52C2212yes—
27#88124C2212yes—
28#88123C2211yescharacteristic
29#88075C2212yes—
30#88075C2212yes—
31#88075C2212yes—
32#88072C2212yes—
33#88072C2211yescharacteristic
34#88049C2211yescharacteristic
35#88048C2212yes—
36#88047C2211yescharacteristic
37C4⋊#1055C2211yescharacteristic
38C4⋊#1055C2212yes—
39C4×#1055C2211yescharacteristic
40C4×#1055C2212yes—
41C2×Q8×C13D411yescharacteristic
42C2×Q8×C13C2312yes—
43C2×D4×C13C2311yescharacteristic
44C22×C4×C13—21no—
45C2×D52C2311yescharacteristic
46C2×C4×D13—21no—
47C2×C4×D13—22no—
48C2×Dic26—21no—
49C13×C4⋊C4—21no—
50C13×C4⋊C4—22no—
51C13×C4⋊C4—21no—
52C13×C4⋊C4D411yescharacteristic
53C13×C4⋊C4D412yes—
54C13×C4⋊C4C2311yescharacteristic
55C13×C22⋊C4—22no—
56C13×C22⋊C4—21no—
57C13×C22⋊C4—22no—
58C42×C13—22no—
59C42×C13C2311yescharacteristic
60C42×C13C2312yes—
61#6106—24no—
62#6104—22no—
63#6103—21no—
64#6103—22no—
65C4⋊Dic13—21no—
66C4⋊Dic13C2312yes—
67C4⋊Dic13C2311yescharacteristic
68#6101—22no—
69#6101—22no—
70C2×#1055C2311yescharacteristic
71C2×#1055C2312yes—
72C2×#1055C2311yescharacteristic
73#3360—131nomaximal, Sylow
74C23×C13—21no—
75C22×D13—21no—
76Q8×C13—22no—
77Q8×C13—22no—
78Q8×C13—22no—
79D4×C13—21no—
80D4×C13—21no—
81C2×C4×C13—21no—
82C2×C4×C13—22no—
83C2×C4×C13—42no—
84C2×C4×C13C2×D412yes—
85C2×C4×C13C2×D412yes—
86C2×C4×C13C2×D411yescharacteristic
87C2×C4×C13C2×D411yescharacteristic
88C2×C4×C13C2411yescharacteristic
89C2×Dic13—21no—
90C2×Dic13—22no—
91D52—21no—
92D52#4112yes—
93C4×D13—42no—
94C4×D13—82no—
95Dic26—81no—
96#1055—21no—
97#1055—22no—
98#1055—21no—
99#556D1311yescharacteristic, complemented
100#554—131no—
101#488—132no—
102#487—131no—
103#479—132no—
104#476—131no—
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—22no—
118C4×C13—21no—
119C4×C13—22no—
120C4×C13—42no—
121C4×C13—41no—
122C4×C13#13512yes—
123C4×C13C2×#4111yescharacteristic
124C4×C132−1+411yescharacteristic
125Dic13—41no—
126Dic13—42no—
127C2×SD16—132no—
128C2×D8—131no—
129C4⋊Q8—131no—
130C4⋊Q8C2×D1311yescharacteristic
131#126—22no—
132#125—132no—
133#124C2×D1312yes—
134C22⋊Q8—21no—
135C22⋊Q8—261no—
136C22⋊Q8—262no—
137C4×Q8C2×D1312yes—
138C4×Q8C2×D1311yescharacteristic
139C4×D4—131no—
140C4×D4—132no—
141C4×D4C2×D1311yescharacteristic
142#117—21no—
143C2×C4⋊C4—261no—
144#107—131no—
145#106—132no—
146C4⋊C8—131no—
147C4⋊C8—132no—
148#103—132no—
149#103—132no—
150#103—132no—
151#102—131no—
152#102—132no—
153#102—131no—
154C4×C8—131no—
155C4×C8—132no—
156C2×C13—81no—
157C2×C13#54811yescharacteristic
158C2×C13C2×#13511yescharacteristic
159C2×C13#57711yescharacteristic
160D13—42no—
161C2×Q8—261no—
162C2×Q8C22⋊D1311yescharacteristic
163C2×Q8C22×D1312yes—
164C2×D4—131no—
165C2×D4C22×D1311yescharacteristic
166C22×C4—21no—
167C22×C4—261no—
168C22×C4—262no—
169SD16—264no—
170D8—262no—
171C2×C8—131no—
172C2×C8—132no—
173C2×C8—131no—
174C4⋊C4—21no—
175C4⋊C4—22no—
176C4⋊C4—21no—
177C4⋊C4—132no—
178C4⋊C4—131no—
179C4⋊C4—262no—
180C4⋊C4—261no—
181C4⋊C4—262no—
182C4⋊C4C22⋊D1311yescharacteristic
183C4⋊C4C22⋊D1312yes—
184C4⋊C4C22×D1311yescharacteristic
185C22⋊C4—22no—
186C22⋊C4—21no—
187C22⋊C4—22no—
188C22⋊C4—261no—
189C22⋊C4—262no—
190C42—22no—
191C42C22×D1311yescharacteristic
192C42C22×D1312yes—
193C13#336011yescharacteristic, complemented, Sylow
194C23—21no—
195C23—261no—
196Q8—22no—
197Q8—22no—
198Q8—22no—
199Q8—1041no—
200D4—21no—
201D4—21no—
202D4—132no—
203D4—261no—
204C2×C4—21no—
205C2×C4—22no—
206C2×C4—42no—
207C2×C4—261no—
208C2×C4—262no—
209C2×C4—522no—
210C2×C4—1042no—
211C2×C4C2×C22⋊D1312yes—
212C2×C4C2×C22⋊D1312yes—
213C2×C4C2×C22⋊D1311yescharacteristic
214C2×C4C2×C22⋊D1311yescharacteristic
215C2×C4C23×D1311yescharacteristic
216C8—261no—
217C8—262no—
218C8—261no—
219C22—41no—
220C22—41no—
221C22—41no—
222C22—262no—
223C22—521no—
224C22—521no—
225C22C22×C22⋊D1311yescharacteristic
226C4—22no—
227C4—22no—
228C4—21no—
229C4—41no—
230C4—42no—
231C4—521no—
232C4—522no—
233C4#8820412yes—
234C4#41×D1311yescharacteristic
235C4#8825711yescharacteristic
236C2—81no—
237C2—522no—
238C2C2×#8820411yescharacteristic
239C2#1171953611yescharacteristic
240C2#1171954211yescharacteristic
subgroupG/H
centerC22C22×C22⋊D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#556C2
socleC22×C13C22×D4
prime radicalC2×#6104C22
hypercenter#556D13
hypocenterC13#3360
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C4×Q8 ◁ #556

Complements

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

NH ≅ G/Ntype
1. C13×#556C2semidirect
2. #11719284C2semidirect
3. #11718744C2semidirect
4. #11718742C2semidirect
6. #11718717C2semidirect
7. C4×#6106C2semidirect
8. Q8×#1055C2semidirect
9. #11718683C2semidirect
11. #11718669C2semidirect
99. #556D13semidirect
193. C13#3360semidirect

Maximal subgroups

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

subgroupindex
C13×#5562
#117192842
#117187442
#117187422
#117187182
#117187172
C4×#61062
Q8×#10552
#117186832
C4×#61042
#117186692
#336013