Finite Group Databasebeta

← #13126555

Subgroups — #13126555

Order 1664.

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

normal subgroups only

This group has 484 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
1C2×#88173C211yesmaximal, characteristic, complemented
2C2×#88158C211yesmaximal, characteristic, complemented
3#11719336C212yesmaximal, complemented
4C13×#467C211yesmaximal, characteristic, complemented
5#11718842C211yesmaximal, characteristic, complemented
6C8×C22⋊D13C211yesmaximal, characteristic, complemented
7#11718708C212yesmaximal, complemented
8#11718548C211yesmaximal, characteristic, complemented
9#11718533C211yesmaximal, characteristic, complemented
10#11718479C212yesmaximal, complemented
11#11718471C212yesmaximal, complemented
12C2×#6131C2212yes—
13C2×#6127C2212yes—
14C2×C13×Q16C2211yescharacteristic
15C22×C8×C13C2211yescharacteristic
16C13×C22⋊Q8C2212yes—
17#88198C2212yes—
18C2×#6107C2212yes—
19C2×#6106C2212yes—
20C4×C22⋊D13C2211yescharacteristic
21#88173—24no—
22C2×Dic52C2211yescharacteristic
23#88158—24no—
24C2×D104C2211yescharacteristic
25C2×#6095C2212yes—
26C2×C8×D13C2211yescharacteristic
27#88151C2212yes—
28#88148—22no—
29#88147C2212yes—
30C4⋊C4×D13—22no—
31#88138—22no—
32#88137—22no—
33C13×#107C2211yescharacteristic
34C13×#103C2212yes—
35C22⋊#1055C2211yescharacteristic
36#88060C2211yescharacteristic
37#88054C2211yescharacteristic
38C8×Dic13C2211yescharacteristic
39#88050C2212yes—
40#88049C2212yes—
41C2×Q8×C13C2312yes—
42C22×C4×C13C2311yescharacteristic
43C2×C22⋊D13—22no—
44C2×C22⋊D13D411yescharacteristic
45#6131—24no—
46#6131—42no—
47#6127—24no—
48#6127—42no—
49C2×D52—22no—
50C2×D52C2312yes—
51C2×C4×D13—22no—
52C2×C4×D13—22no—
53C2×C4×D13—22no—
54C2×C4×D13C2311yescharacteristic
55C2×Dic26C2312yes—
56C13×Q16—22no—
57C2×C8×C13—22no—
58C2×C8×C13C2311yescharacteristic
59C2×C8×C13C2311yescharacteristic
60C13×C4⋊C4—22no—
61C13×C4⋊C4C2312yes—
62C13×C22⋊C4—22no—
63C22⋊Dic13D411yescharacteristic
64#6107—42no—
65#6106—24no—
66#6103—22no—
67#6103—22no—
68#6103D411yescharacteristic
69C4⋊Dic13—22no—
70#6101—22no—
71#6101—22no—
72#6101D411yescharacteristic
73C4×Dic13C2311yescharacteristic
74C2×#1055C2311yescharacteristic
75C2×#1055C2311yescharacteristic
76Dic52—22no—
77D104D414yescomplemented
78#6095—24no—
79C8×D13—22no—
80#3283—131nomaximal, Sylow
81C23×C13C2×D411yescharacteristic
82C22×D13—22no—
83C22×D13C2×D411yescharacteristic
84Q8×C13—22no—
85Q8×C13—22no—
86C2×C4×C13—21no—
87C2×C4×C13—21no—
88C2×C4×C13—22no—
89C2×C4×C13—22no—
90C2×C4×C13C2×D411yescharacteristic
91C2×C4×C13C2411yescharacteristic
92C22⋊D13—22no—
93C22⋊D13—44no—
94C2×Dic13—22no—
95C2×Dic13C2×D411yescharacteristic
96C2×Dic13C2×D411yescharacteristic
97C2×Dic13C2×D411yescharacteristic
98D52—22no—
99D52—44no—
100D52C2×D414yes—
101C4×D13—21no—
102C4×D13—21no—
103C4×D13—44no—
104C4×D13—44no—
105C4×D13—44no—
106Dic26—22no—
107Dic26—22no—
108C8×C13—21no—
109C8×C13C2×D412yes—
110#1055—21no—
111#1055—21no—
112C2×#135—131no—
113C2×#135—131no—
114#547—132no—
115#494—131no—
116#467—131no—
117#467D1311yescharacteristic, complemented
118#461—132no—
119#452—132no—
120#452—132no—
121C4×D8—131no—
122C8×D4—131no—
123C22×C13—21no—
124C22×C13—21no—
125C22×C13—21no—
126C22×C13C22×D411yescharacteristic
127C2×D13—21no—
128C2×D13—24no—
129C2×D13—21no—
130C2×D13—21no—
131C2×D13—42no—
132C2×D13—42no—
133C4×C13—21no—
134C4×C13—42no—
135C4×C13—42no—
136C4×C13C22×D411yescharacteristic
137C4×C13H(5,𝔽2)11yescharacteristic
138Dic13—21no—
139Dic13—21no—
140Dic13—42no—
141Dic13#13512yescomplemented
142C2×#41—132no—
143C2×#41—132no—
144#135—264no—
145#135—264no—
146C2×Q16—132no—
147C2×Q16—131no—
148C2×Q16C2×D1311yescharacteristic
149C2×SD16—132no—
150C2×SD16—132no—
151C2×D8—131no—
152C22×C8—131no—
153C22×C8C2×D1311yescharacteristic
154C4⋊Q8—132no—
155#123—262no—
156#123—262no—
157C22⋊Q8—132no—
158C22⋊Q8C2×D1312yes—
159#121—262no—
160C4×D4—131no—
161C4×D4—132no—
162C2×C4⋊C4—262no—
163#107C2×D1311yescharacteristic
164C4⋊C8—131no—
165#103—132no—
166#103C2×D1312yes—
167#102—132no—
168C22⋊C8—131no—
169C22⋊C8—131no—
170C4×C8—131no—
171C2×C13—41no—
172C2×C13D4211yescharacteristic
173C2×C13C2×#13511yescharacteristic
174C2×C13#57811yescharacteristic
175D13—41no—
176D13—44no—
177#41—264no—
178#41—264no—
179#41—522no—
180#41—522no—
181C2×Q8—132no—
182C2×Q8C22×D1312yes—
183C2×D4—131no—
184C2×D4—132no—
185C2×D4—262no—
186C2×D4—262no—
187C22×C4—131no—
188C22×C4—262no—
189C22×C4—262no—
190C22×C4—262no—
191C22×C4C22×D1311yescharacteristic
192Q16—22no—
193Q16—262no—
194Q16—522no—
195SD16—264no—
196SD16—264no—
197D8—134no—
198C2×C8—22no—
199C2×C8—131no—
200C2×C8—131no—
201C2×C8—262no—
202C2×C8C22×D1311yescharacteristic
203C2×C8C22×D1311yescharacteristic
204C4⋊C4—22no—
205C4⋊C4—131no—
206C4⋊C4—262no—
207C4⋊C4—262no—
208C4⋊C4—262no—
209C4⋊C4C22×D1312yes—
210C22⋊C4—22no—
211C22⋊C4—131no—
212C22⋊C4—131no—
213C22⋊C4—262no—
214C22⋊C4—262no—
215C42—131no—
216C13#328311yescharacteristic, complemented, Sylow
217C23—131no—
218C23—262no—
219C23D4×D1311yescharacteristic
220Q8—22no—
221Q8—22no—
222Q8—262no—
223Q8—262no—
224D4—134no—
225D4—262no—
226D4—262no—
227D4—524no—
228D4—524no—
229C2×C4—21no—
230C2×C4—21no—
231C2×C4—22no—
232C2×C4—22no—
233C2×C4—131no—
234C2×C4—131no—
235C2×C4—131no—
236C2×C4—261no—
237C2×C4—261no—
238C2×C4—262no—
239C2×C4—524no—
240C2×C4—524no—
241C2×C4—524no—
242C2×C4D4×D1311yescharacteristic
243C2×C4C23×D1311yescharacteristic
244C8—21no—
245C8—261no—
246C8—261no—
247C8D4×D1312yes—
248C22—21no—
249C22—21no—
250C22—21no—
251C22—261no—
252C22—261no—
253C22—261no—
254C22—264no—
255C22—522no—
256C22—522no—
257C22C2×D4×D1311yescharacteristic
258C4—21no—
259C4—42no—
260C4—42no—
261C4—132no—
262C4—261no—
263C4—261no—
264C4—522no—
265C4C2×D4×D1311yescharacteristic
266C4#8825611yescharacteristic
267C2—41no—
268C2—521no—
269C2—524no—
270C2#1171931411yescharacteristic
271C2#1171947111yescharacteristic
272C2D13×#13511yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#467C2
socleC22×C13C22×D4
hypercenter#467D13
hypocenterC13#3283
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ #467

Complements

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

NH ≅ G/Ntype
1. C2×#88173C2semidirect
2. C2×#88158C2semidirect
3. #11719336C2semidirect
4. C13×#467C2semidirect
5. #11718842C2semidirect
6. C8×C22⋊D13C2semidirect
7. #11718708C2semidirect
8. #11718548C2semidirect
9. #11718533C2semidirect
10. #11718479C2semidirect
11. #11718471C2semidirect
77. D104D4semidirect
117. #467D13semidirect
141. Dic13#135semidirect
216. C13#3283semidirect

Maximal subgroups

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

subgroupindex
C2×#881732
C2×#881582
#117193362
C13×#4672
#117188422
C8×C22⋊D132
#117187082
#117185482
#117185332
#117184792
#117184712
#328313