Finite Group Databasebeta

← #13127141

Subgroups — #13127141

Order 1664.

420 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 420 conjugacy classes of subgroups — too many to draw. Only its 125 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×#547C211yesmaximal, characteristic, complemented
2#11719260C211yesmaximal, characteristic, complemented
3#11718899C212yesmaximal, complemented
4#11718893C212yesmaximal, complemented
5#11718744C211yesmaximal, characteristic, complemented
6#11718742C211yesmaximal, characteristic, complemented
7#11718710C212yesmaximal, complemented
8#11718705C212yesmaximal, complemented
9C4×#6104C211yesmaximal, characteristic, complemented
10#11718673C211yesmaximal, characteristic, complemented
11#11718668C211yesmaximal, characteristic, complemented
12C2×C13×#41C2212yes—
13C2×#6129—21no—
14C13×C4⋊Q8C2211yescharacteristic
15C13×#123—22no—
16C13×C22⋊Q8C2212yes—
17C13×#121—21no—
18C4×D4×C13C2211yescharacteristic
19C4×D4×C13C2211yescharacteristic
20C2×C13×C4⋊C4—21no—
21C2×#6106C2212yes—
22C2×#6104C2211yescharacteristic
23#88184C2212yes—
24C2×C4⋊Dic13C2212yes—
25C2×#6099C2212yes—
26#88151—21no—
27#88140—22no—
28C4×D52C2211yescharacteristic
29#88123C2211yescharacteristic
30#88075C2212yes—
31#88075C2212yes—
32#88075C2212yes—
33#88072C2212yes—
34#88072C2211yescharacteristic
35C22⋊#1055C2212yes—
36#88049C2211yescharacteristic
37#88047C2212yes—
38#88047C2211yescharacteristic
39C4⋊#1055C2211yescharacteristic
40C4×#1055C2211yescharacteristic
41C13×#41—24no—
42C13×#41—42no—
43C2×Q8×C13C2312yes—
44C2×D4×C13—22no—
45C2×D4×C13D411yescharacteristic
46C2×D4×C13C2311yescharacteristic
47C22×C4×C13—21no—
48C22×C4×C13—22no—
49C22×C4×C13C2312yes—
50C2×C22⋊D13—22no—
51C22×Dic13—22no—
52#6129—44no—
53C2×D52C2311yescharacteristic
54C2×C4×D13—21no—
55C2×Dic26—21no—
56C13×C4⋊C4—21no—
57C13×C4⋊C4—22no—
58C13×C4⋊C4—21no—
59C13×C4⋊C4D411yescharacteristic
60C13×C4⋊C4C2311yescharacteristic
61C13×C22⋊C4—22no—
62C13×C22⋊C4—21no—
63C13×C22⋊C4D412yes—
64C42×C13C2311yescharacteristic
65#6106—42no—
66#6104—22no—
67#6103—21no—
68#6103—22no—
69C4⋊Dic13—21no—
70C4⋊Dic13—22no—
71C4⋊Dic13C2312yes—
72C4⋊Dic13C2311yescharacteristic
73#6099—42no—
74C2×#1055C2311yescharacteristic
75C2×#1055C2312yes—
76C2×#1055C2311yescharacteristic
77#3330—131nomaximal, Sylow
78C23×C13—21no—
79C23×C13C2×D412yes—
80C22×D13—21no—
81Q8×C13—22no—
82Q8×C13—22no—
83D4×C13—22no—
84D4×C13—21no—
85D4×C13—44no—
86D4×C13#4112yescomplemented
87C2×C4×C13—22no—
88C2×C4×C13—22no—
89C2×C4×C13—21no—
90C2×C4×C13—22no—
91C2×C4×C13—44no—
92C2×C4×C13—42no—
93C2×C4×C13C2×D411yescharacteristic
94C2×C4×C13C2×D412yes—
95C2×C4×C13C2×D411yescharacteristic
96C2×C4×C13C2411yescharacteristic
97C22⋊D13—44no—
98C2×Dic13—22no—
99C2×Dic13—21no—
100C2×Dic13—44no—
101D52—21no—
102D52—21no—
103C4×D13—42no—
104Dic26—42no—
105#1055—21no—
106#1055—21no—
107#1055—22no—
108#547—131no—
109#547D1311yescharacteristic, complemented
110#487—131no—
111#484—132no—
112#474—131no—
113#468—132no—
114#461—131no—
115#449—132no—
116C4×D8—131no—
117#436—131no—
118#417—132no—
119C22×C13—22no—
120C22×C13—22no—
121C22×C13—22no—
122C22×C13—22no—
123C22×C13—41no—
124C22×C13—41no—
125C22×C13C22×D411yescharacteristic
126C2×D13—41no—
127C2×D13—41no—
128C2×D13—41no—
129C4×C13—22no—
130C4×C13—21no—
131C4×C13—42no—
132C4×C13—41no—
133C4×C13AGL(1,ℤ/8)12yes—
134C4×C13C2×#4111yescharacteristic
135C4×C13H(5,𝔽2)11yescharacteristic
136Dic13—42no—
137Dic13—41no—
138C2×#41—261no—
139C2×#41C2×D1312yes—
140C2×SD16—132no—
141C2×D8—131no—
142C2×M16—132no—
143C4⋊Q8—131no—
144C4⋊Q8C2×D1311yescharacteristic
145#123—22no—
146#123—262no—
147C22⋊Q8—261no—
148C22⋊Q8C2×D1312yes—
149#121—21no—
150#121—132no—
151C4×D4—131no—
152C4×D4C2×D1311yescharacteristic
153C4×D4C2×D1311yescharacteristic
154C2×C4⋊C4—21no—
155C2×C4⋊C4—132no—
156#107—131no—
157#107—132no—
158C4⋊C8—131no—
159#103—132no—
160#103—132no—
161#103—132no—
162#102—131no—
163#102—132no—
164#102—131no—
165C22⋊C8—132no—
166C4×C8—131no—
167C2×C13—42no—
168C2×C13—42no—
169C2×C13#54611yescharacteristic
170C2×C13C2×AGL(1,ℤ/8)11yescharacteristic
171C2×C13#57811yescharacteristic
172D13—81no—
173#41—24no—
174#41—42no—
175#41—524no—
176C2×Q8—261no—
177C2×Q8C22×D1312yes—
178C2×D4—22no—
179C2×D4—131no—
180C2×D4—262no—
181C2×D4C22⋊D1311yescharacteristic
182C2×D4C22×D1311yescharacteristic
183C22×C4—21no—
184C22×C4—22no—
185C22×C4—262no—
186C22×C4—261no—
187C22×C4C22×D1312yes—
188SD16—522no—
189D8—262no—
190M16—522no—
191C2×C8—131no—
192C2×C8—131no—
193C2×C8—132no—
194C4⋊C4—21no—
195C4⋊C4—22no—
196C4⋊C4—21no—
197C4⋊C4—131no—
198C4⋊C4—132no—
199C4⋊C4—262no—
200C4⋊C4—261no—
201C4⋊C4C22⋊D1311yescharacteristic
202C4⋊C4C22×D1311yescharacteristic
203C22⋊C4—22no—
204C22⋊C4—21no—
205C22⋊C4—261no—
206C22⋊C4—262no—
207C22⋊C4C22⋊D1312yes—
208C42C22×D1311yescharacteristic
209C13#333011yescharacteristic, complemented, Sylow
210C23—21no—
211C23—261no—
212C23C2×C22⋊D1312yes—
213Q8—22no—
214Q8—22no—
215Q8—522no—
216D4—22no—
217D4—21no—
218D4—44no—
219D4—261no—
220D4—261no—
221D4—524no—
222D4#612912yescomplemented
223C2×C4—22no—
224C2×C4—22no—
225C2×C4—21no—
226C2×C4—22no—
227C2×C4—44no—
228C2×C4—42no—
229C2×C4—261no—
230C2×C4—262no—
231C2×C4—524no—
232C2×C4—522no—
233C2×C4C2×C22⋊D1311yescharacteristic
234C2×C4C2×C22⋊D1312yes—
235C2×C4C2×C22⋊D1311yescharacteristic
236C2×C4C23×D1311yescharacteristic
237C8—261no—
238C8—261no—
239C8—262no—
240C22—22no—
241C22—22no—
242C22—22no—
243C22—22no—
244C22—41no—
245C22—41no—
246C22—521no—
247C22—521no—
248C22—521no—
249C22C22×C22⋊D1311yescharacteristic
250C4—22no—
251C4—21no—
252C4—42no—
253C4—41no—
254C4—521no—
255C4—522no—
256C4#8820312yes—
257C4C2×#612911yescharacteristic
258C4#8825111yescharacteristic
259C2—42no—
260C2—42no—
261C2—1041no—
262C2#1171951111yescharacteristic
263C2C2×#8820311yescharacteristic
264C2#1171954311yescharacteristic
subgroupG/H
centerC22C22×C22⋊D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#547C2
socleC22×C13C22×D4
hypercenter#547D13
hypocenterC13#3330
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C4×D4 ◁ #547

Complements

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

NH ≅ G/Ntype
1. C13×#547C2semidirect
2. #11719260C2semidirect
3. #11718899C2semidirect
4. #11718893C2semidirect
5. #11718744C2semidirect
6. #11718742C2semidirect
7. #11718710C2semidirect
8. #11718705C2semidirect
9. C4×#6104C2semidirect
10. #11718673C2semidirect
11. #11718668C2semidirect
86. D4×C13#41semidirect
109. #547D13semidirect
209. C13#3330semidirect
222. D4#6129semidirect

Maximal subgroups

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

subgroupindex
C13×#5472
#117192602
#117188992
#117188932
#117187442
#117187422
#117187102
#117187052
C4×#61042
#117186732
#117186682
#333013