Finite Group Databasebeta

← #13124501

Subgroups — #13124501

Order 1664.

484 conjugacy classes of subgroups; only the 127 normal subgroups are shown.

normal subgroups only

This group has 484 conjugacy classes of subgroups — too many to draw. Only its 127 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
1C2×#88166C211yesmaximal, characteristic, complemented
2C2×#88155C211yesmaximal, characteristic, complemented
3#11719313C212yesmaximal, complemented
4C13×#466C211yesmaximal, characteristic, complemented
5#11718818C211yesmaximal, characteristic, complemented
6#11718777C211yesmaximal, characteristic, complemented
7#11718703C212yesmaximal, complemented
8#11718548C211yesmaximal, characteristic, complemented
9D13×#107C211yesmaximal, characteristic, complemented
10#11718441C212yesmaximal, complemented
11#11718432C212yesmaximal, complemented
12C2×#6129C2212yes—
13C2×#6127C2211yescharacteristic
14C2×C13×D8C2211yescharacteristic
15C22×C8×C13C2211yescharacteristic
16C13×#121C2212yes—
17#88193—22no—
18#88192—22no—
19#88192C2212yes—
20C2×#6105C2212yes—
21#88178C2212yes—
22C2×#6099C2211yescharacteristic
23#88166—24no—
24C2×Dic52C2211yescharacteristic
25#88155—24no—
26C2×#6094C2211yescharacteristic
27C2×#6094C2211yescharacteristic
28C2×C8×D13C2211yescharacteristic
29C2×C8×D13C2211yescharacteristic
30#88151C2212yes—
31C4⋊C4×D13C2212yes—
32#88138—22no—
33#88132—22no—
34C13×#107C2211yescharacteristic
35C13×#102C2212yes—
36#88072C2212yes—
37#88058C2211yescharacteristic
38#88056C2212yes—
39#88050C2212yes—
40#88047C2212yes—
41C2×D4×C13—22no—
42C2×D4×C13C2312yes—
43C22×C4×C13C2311yescharacteristic
44C2×C22⋊D13—22no—
45C2×C22⋊D13—22no—
46C2×C22⋊D13D411yescharacteristic
47C2×C22⋊D13D411yescharacteristic
48C22×Dic13—22no—
49#6129—24no—
50#6129—24no—
51#6127—22no—
52#6127—22no—
53C2×D52D411yescharacteristic
54C2×C4×D13—22no—
55C2×C4×D13C2311yescharacteristic
56C2×C4×D13C2311yescharacteristic
57C2×Dic26D411yescharacteristic
58C2×Dic26C2312yes—
59C13×D8—22no—
60C2×C8×C13—22no—
61C2×C8×C13C2311yescharacteristic
62C2×C8×C13C2311yescharacteristic
63C13×C4⋊C4C2312yes—
64C13×C22⋊C4—22no—
65C22⋊Dic13—22no—
66C22⋊Dic13—22no—
67#6105—24no—
68#6103—22no—
69C4⋊Dic13—22no—
70C4⋊Dic13C2312yes—
71#6101—22no—
72#6101—22no—
73#6099—22no—
74C2×#1055C2311yescharacteristic
75C2×#1055C2311yescharacteristic
76Dic52—22no—
77#6094—22no—
78#6094—22no—
79C8×D13—22no—
80C8×D13D414yescomplemented
81#3061—131nomaximal, Sylow
82C23×C13—22no—
83C23×C13C2×D411yescharacteristic
84C22×D13C2×D411yescharacteristic
85C22×D13C2×D411yescharacteristic
86D4×C13—22no—
87D4×C13—22no—
88D4×C13—82no—
89C2×C4×C13—21no—
90C2×C4×C13—21no—
91C2×C4×C13—22no—
92C2×C4×C13C2×D411yescharacteristic
93C2×C4×C13C2411yescharacteristic
94C22⋊D13—22no—
95C22⋊D13—22no—
96C22⋊D13—44no—
97C22⋊D13—82no—
98C2×Dic13—22no—
99C2×Dic13—22no—
100C2×Dic13—44no—
101C2×Dic13C2×D411yescharacteristic
102C2×Dic13C2×D411yescharacteristic
103D52—22no—
104C4×D13—21no—
105C4×D13—21no—
106C4×D13—82no—
107C4×D13C2×D412yes—
108C4×D13#4112yes—
109Dic26—22no—
110Dic26—22no—
111Dic26—22no—
112C8×C13—21no—
113C8×C13C2×D412yes—
114#1055—21no—
115#1055C2×D412yes—
116C2×#135—131no—
117C2×#131—131no—
118#537—132no—
119#468—132no—
120#468—132no—
121#467—131no—
122#467—131no—
123#466—131no—
124#466D1311yescharacteristic, complemented
125C2×#107—131no—
126#417—132no—
127C22×C13—21no—
128C22×C13—21no—
129C22×C13—21no—
130C22×C13—42no—
131C22×C13—42no—
132C22×C13—42no—
133C22×C13C22×D411yescharacteristic
134C2×D13—21no—
135C2×D13—21no—
136C2×D13—21no—
137C2×D13—21no—
138C2×D13—21no—
139C2×D13#12112yes—
140C4×C13—21no—
141C4×C13—42no—
142C4×C13C22×D411yescharacteristic
143C4×C13C2×#4111yescharacteristic
144Dic13—21no—
145Dic13—42no—
146Dic13—42no—
147Dic13#12112yes—
148C2×#41—131no—
149C2×#41—132no—
150#135—264no—
151C2×Q16—131no—
152C2×SD16—132no—
153C2×D8C2×D1311yescharacteristic
154#131—264no—
155C2×M16—131no—
156C2×M16—131no—
157C2×M16—131no—
158C22×C8—131no—
159C22×C8—131no—
160C22×C8C2×D1311yescharacteristic
161C22⋊Q8—132no—
162C22⋊Q8—132no—
163C22⋊Q8—262no—
164#121—132no—
165#121—262no—
166#121—262no—
167#121—262no—
168#121C2×D1312yes—
169C2×C4⋊C4—132no—
170#107—131no—
171#107—132no—
172#107C2×D1311yescharacteristic
173#103—132no—
174#103—132no—
175#102—132no—
176#102C2×D1312yes—
177C2×C13—41no—
178C2×C13—82no—
179C2×C13C2×#12111yescharacteristic
180C2×C13#57611yescharacteristic
181C2×C13#57811yescharacteristic
182D13—22no—
183D13—41no—
184#41—262no—
185#41—262no—
186#41—264no—
187#41—264no—
188C2×Q8—131no—
189C2×Q8—132no—
190C2×D4—22no—
191C2×D4—131no—
192C2×D4—131no—
193C2×D4—131no—
194C2×D4—262no—
195C2×D4—262no—
196C2×D4C22×D1312yes—
197C22×C4—131no—
198C22×C4—131no—
199C22×C4—262no—
200C22×C4—262no—
201C22×C4C22×D1311yescharacteristic
202Q16—262no—
203SD16—264no—
204D8—22no—
205M16—262no—
206M16—262no—
207M16—262no—
208C2×C8—22no—
209C2×C8—131no—
210C2×C8—134no—
211C2×C8—131no—
212C2×C8—262no—
213C2×C8C22×D1311yescharacteristic
214C2×C8C22×D1311yescharacteristic
215C4⋊C4—132no—
216C4⋊C4—262no—
217C4⋊C4—262no—
218C4⋊C4—262no—
219C4⋊C4C22×D1312yes—
220C22⋊C4—22no—
221C22⋊C4—262no—
222C22⋊C4—262no—
223C22⋊C4—262no—
224C13#306111yescharacteristic, complemented, Sylow
225C23—22no—
226C23—131no—
227C23—131no—
228C23D4×D1311yescharacteristic
229Q8—262no—
230Q8—262no—
231Q8—262no—
232D4—22no—
233D4—22no—
234D4—82no—
235D4—262no—
236D4—262no—
237D4—262no—
238D4—524no—
239D4—1042no—
240C2×C4—21no—
241C2×C4—21no—
242C2×C4—22no—
243C2×C4—131no—
244C2×C4—132no—
245C2×C4—132no—
246C2×C4—131no—
247C2×C4—261no—
248C2×C4—261no—
249C2×C4—262no—
250C2×C4—262no—
251C2×C4—524no—
252C2×C4—1042no—
253C2×C4D4×D1311yescharacteristic
254C2×C4C23×D1311yescharacteristic
255C8—21no—
256C8—132no—
257C8—261no—
258C8D4×D1312yes—
259C22—21no—
260C22—21no—
261C22—21no—
262C22—42no—
263C22—42no—
264C22—42no—
265C22—132no—
266C22—261no—
267C22—261no—
268C22—261no—
269C22—261no—
270C22—261no—
271C22C2×D4×D1311yescharacteristic
272C4—21no—
273C4—42no—
274C4—132no—
275C4—261no—
276C4—522no—
277C4—522no—
278C4C2×D4×D1311yescharacteristic
279C4#41×D1311yescharacteristic
280C2—41no—
281C2—82no—
282C2—262no—
283C2—521no—
284C2D13×#12111yescharacteristic
285C2#1171946211yescharacteristic
286C2#1171947611yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#466C2
socleC22×C13C22×D4
hypercenter#466D13
hypocenterC13#3061
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ #466

Complements

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

NH ≅ G/Ntype
1. C2×#88166C2semidirect
2. C2×#88155C2semidirect
3. #11719313C2semidirect
4. C13×#466C2semidirect
5. #11718818C2semidirect
6. #11718777C2semidirect
7. #11718703C2semidirect
8. #11718548C2semidirect
9. D13×#107C2semidirect
10. #11718441C2semidirect
11. #11718432C2semidirect
80. C8×D13D4semidirect
124. #466D13semidirect
224. C13#3061semidirect

Maximal subgroups

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

subgroupindex
C2×#881662
C2×#881552
#117193132
C13×#4662
#117188182
#117187772
#117187032
#117185482
D13×#1072
#117184412
#117184322
#306113