Finite Group Databasebeta

← #13127130

Subgroups — #13127130

Order 1664.

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

normal subgroups only

This group has 386 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
1D4×Q8×C13C211yesmaximal, characteristic, complemented
2#11719268C211yesmaximal, characteristic
3#11718888C212yesmaximal, complemented
4#11718886C212yesmaximal, complemented
5#11718744C211yesmaximal, characteristic, complemented
6#11718742C211yesmaximal, characteristic, complemented
7#11718710C212yesmaximal, complemented
8#11718706C212yesmaximal, complemented
9C4×#6106C211yesmaximal, characteristic, complemented
10#11718682C211yesmaximal, characteristic, complemented
11#11718673C211yesmaximal, characteristic, complemented
12C22×Q8×C13C2212yes—
13C13×C4⋊Q8—21no—
14C13×C4⋊Q8C2211yescharacteristic
15C13×C22⋊Q8—22no—
16C13×C22⋊Q8C2212yes—
17C4×Q8×C13C2211yescharacteristic
18C4×D4×C13—21no—
19C4×D4×C13C2211yescharacteristic
20C2×#6106C2211yescharacteristic
21C2×#6106C2212yes—
22#88192—21no—
23#88184C2212yes—
24#88180C2212yes—
25C2×#6099C2212yes—
26#88146—21no—
27#88139—22no—
28C4×D52C2211yescharacteristic
29#88123C2211yescharacteristic
30#88075C2212yes—
31#88075C2211yescharacteristic
32#88075C2212yes—
33#88075C2212yes—
34#88075C2212yes—
35C22⋊#1055C2212yes—
36#88049C2211yescharacteristic
37#88048C2211yescharacteristic
38#88047C2212yes—
39C4⋊#1055C2211yescharacteristic
40C4×#1055C2211yescharacteristic
41C2×Q8×C13—22no—
42C2×Q8×C13—24no—
43C2×Q8×C13—42no—
44C2×Q8×C13C2312yes—
45C2×Q8×C13C2311yescharacteristic
46C2×D4×C13D411yescharacteristic
47C22×C4×C13—22no—
48C22×C4×C13C2312yes—
49C2×C22⋊D13—22no—
50C2×D52C2311yescharacteristic
51C2×C4×D13—21no—
52C2×Dic26—21no—
53C13×C4⋊C4—21no—
54C13×C4⋊C4—21no—
55C13×C4⋊C4—21no—
56C13×C4⋊C4—22no—
57C13×C4⋊C4D411yescharacteristic
58C13×C4⋊C4C2311yescharacteristic
59C13×C22⋊C4—22no—
60C13×C22⋊C4D412yes—
61C42×C13—21no—
62C42×C13C2311yescharacteristic
63C22⋊Dic13—22no—
64#6106—22no—
65#6106—42no—
66#6103—21no—
67#6103—22no—
68C4⋊Dic13—21no—
69C4⋊Dic13C2312yes—
70C4⋊Dic13C2311yescharacteristic
71C4×Dic13—22no—
72#6099—42no—
73C2×#1055C2311yescharacteristic
74C2×#1055C2312yes—
75C2×#1055C2311yescharacteristic
76#3329—131nomaximal, Sylow
77C23×C13C2×D412yes—
78C22×D13—21no—
79Q8×C13—21no—
80Q8×C13—22no—
81Q8×C13—22no—
82Q8×C13—44no—
83Q8×C13#4112yes—
84D4×C13—22no—
85C2×C4×C13—21no—
86C2×C4×C13—22no—
87C2×C4×C13—22no—
88C2×C4×C13—21no—
89C2×C4×C13—22no—
90C2×C4×C13—44no—
91C2×C4×C13C2×D412yes—
92C2×C4×C13C2×D411yescharacteristic
93C2×C4×C13C2×D411yescharacteristic
94C2×C4×C13C2411yescharacteristic
95C22⋊D13—82no—
96C2×Dic13—21no—
97C2×Dic13—22no—
98D52—21no—
99D52—21no—
100C4×D13—42no—
101Dic26—81no—
102#1055—21no—
103#1055—21no—
104#1055—22no—
105#555—131no—
106D4×Q8D1311yescharacteristic, complemented
107#487—131no—
108#485—132no—
109#477—131no—
110#468—132no—
111#461—131no—
112#448—132no—
113C4×SD16—131no—
114#436—131no—
115#419—132no—
116C22×C13—22no—
117C22×C13—22no—
118C22×C13—22no—
119C22×C13C22×D411yescharacteristic
120C2×D13—41no—
121C2×D13—41no—
122C2×D13—41no—
123C4×C13—22no—
124C4×C13—22no—
125C4×C13—21no—
126C4×C13—42no—
127C4×C13—41no—
128C4×C13#13712yes—
129C4×C13C2×#4111yescharacteristic
130C4×C13H(5,𝔽2)11yescharacteristic
131Dic13—41no—
132Dic13—42no—
133C22×Q8C2×D1312yes—
134C2×SD16—131no—
135C2×SD16—132no—
136C2×M16—132no—
137C4⋊Q8—21no—
138C4⋊Q8—131no—
139C4⋊Q8C2×D1311yescharacteristic
140#124—262no—
141C22⋊Q8—22no—
142C22⋊Q8C2×D1312yes—
143#121—132no—
144#121—261no—
145C4×Q8C2×D1311yescharacteristic
146C4×D4—21no—
147C4×D4—131no—
148C4×D4C2×D1311yescharacteristic
149#117—132no—
150#117—261no—
151#107—132no—
152#106—131no—
153C4⋊C8—131no—
154#103—131no—
155#103—132no—
156#103—132no—
157#103—132no—
158#103—132no—
159#102—131no—
160C22⋊C8—132no—
161C4×C8—131no—
162C2×C13—42no—
163C2×C13#54611yescharacteristic
164C2×C13C2×#13711yescharacteristic
165C2×C13#57711yescharacteristic
166D13—81no—
167C2×Q8—22no—
168C2×Q8—24no—
169C2×Q8—42no—
170C2×Q8—261no—
171C2×Q8C22×D1312yes—
172C2×Q8C22×D1311yescharacteristic
173C2×D4—131no—
174C2×D4—262no—
175C2×D4C22⋊D1311yescharacteristic
176C22×C4—22no—
177C22×C4—261no—
178C22×C4C22×D1312yes—
179SD16—262no—
180SD16—522no—
181M16—522no—
182C2×C8—131no—
183C2×C8—131no—
184C2×C8—132no—
185C4⋊C4—21no—
186C4⋊C4—21no—
187C4⋊C4—21no—
188C4⋊C4—22no—
189C4⋊C4—131no—
190C4⋊C4—132no—
191C4⋊C4—261no—
192C4⋊C4C22⋊D1311yescharacteristic
193C4⋊C4C22×D1311yescharacteristic
194C22⋊C4—22no—
195C22⋊C4—262no—
196C22⋊C4—262no—
197C22⋊C4—261no—
198C22⋊C4C22⋊D1312yes—
199C42—21no—
200C42—262no—
201C42C22×D1311yescharacteristic
202C13#332911yescharacteristic, complemented, Sylow
203C23—261no—
204C23C2×C22⋊D1312yes—
205Q8—21no—
206Q8—22no—
207Q8—22no—
208Q8—44no—
209Q8—1041no—
210Q8#612912yes—
211D4—22no—
212D4—261no—
213D4—261no—
214D4—1042no—
215C2×C4—21no—
216C2×C4—22no—
217C2×C4—22no—
218C2×C4—21no—
219C2×C4—22no—
220C2×C4—44no—
221C2×C4—261no—
222C2×C4—262no—
223C2×C4—522no—
224C2×C4C2×C22⋊D1312yes—
225C2×C4C2×C22⋊D1311yescharacteristic
226C2×C4C2×C22⋊D1311yescharacteristic
227C2×C4C23×D1311yescharacteristic
228C8—261no—
229C8—261no—
230C8—262no—
231C22—22no—
232C22—22no—
233C22—22no—
234C22—521no—
235C22—521no—
236C22—521no—
237C22C22×C22⋊D1311yescharacteristic
238C4—22no—
239C4—22no—
240C4—21no—
241C4—42no—
242C4—41no—
243C4—521no—
244C4—522no—
245C4#8819612yes—
246C4C2×#612911yescharacteristic
247C4#8825111yescharacteristic
248C2—42no—
249C2—1041no—
250C2#1171951111yescharacteristic
251C2C2×#8819611yescharacteristic
252C2#1171954211yescharacteristic
subgroupG/H
centerC22C22×C22⋊D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingD4×Q8×C13C2
socleC22×C13C22×D4
prime radical#11719268C2
hypercenterD4×Q8D13
hypocenterC13#3329
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C4×D4 ◁ D4×Q8

Complements

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

NH ≅ G/Ntype
1. D4×Q8×C13C2semidirect
3. #11718888C2semidirect
4. #11718886C2semidirect
5. #11718744C2semidirect
6. #11718742C2semidirect
7. #11718710C2semidirect
8. #11718706C2semidirect
9. C4×#6106C2semidirect
10. #11718682C2semidirect
11. #11718673C2semidirect
106. D4×Q8D13semidirect
202. C13#3329semidirect

Maximal subgroups

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

subgroupindex
D4×Q8×C132
#117192682
#117188882
#117188862
#117187442
#117187422
#117187102
#117187062
C4×#61062
#117186822
#117186732
#332913