Finite Group Databasebeta

← #13126482

Subgroups — #13126482

Order 1664.

472 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 472 conjugacy classes of subgroups — too many to draw. Only its 133 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
2C2×#88196C212yesmaximal, complemented
3#11719256C211yesmaximal, characteristic
4#11718889C212yesmaximal, complemented
5#11718753C211yesmaximal, characteristic, complemented
6#11718744C211yesmaximal, characteristic, complemented
7#11718713C212yesmaximal, complemented
8#11718708C212yesmaximal, complemented
9#11718692C211yesmaximal, characteristic, complemented
10C4×#6106C211yesmaximal, characteristic, complemented
11#11718673C211yesmaximal, characteristic, complemented
12C22×Q8×C13C2212yes—
13C2×#6127C2212yes—
14C13×C4⋊Q8—21no—
15C13×C4⋊Q8C2211yescharacteristic
16C13×C22⋊Q8—22no—
17C13×C22⋊Q8C2212yes—
18C4×Q8×C13C2211yescharacteristic
19C4×D4×C13—21no—
20C4×D4×C13C2211yescharacteristic
21C2×#6107C2212yes—
22C2×#6107C2212yes—
23C2×#6107C2212yes—
24#88196—28no—
25C2×#6106C2212yes—
26C2×#6106C2211yescharacteristic
27#88192—21no—
28#88178C2212yes—
29C2×#6099C2212yes—
30C4⋊C4×D13—21no—
31#88137—22no—
32C4×D52C2211yescharacteristic
33#88123C2211yescharacteristic
34#88075C2211yescharacteristic
35#88075C2212yes—
36C22⋊#1055C2212yes—
37#88050C2212yes—
38#88049C2211yescharacteristic
39#88048C2211yescharacteristic
40C4⋊#1055C2211yescharacteristic
41C4×#1055C2211yescharacteristic
42C2×Q8×C13—22no—
43C2×Q8×C13—24no—
44C2×Q8×C13—42no—
45C2×Q8×C13C2312yes—
46C2×Q8×C13C2311yescharacteristic
47C2×D4×C13D411yescharacteristic
48C22×C4×C13—22no—
49C22×C4×C13C2312yes—
50C2×C22⋊D13—22no—
51#6127—24no—
52#6127—42no—
53C2×D52C2311yescharacteristic
54C2×C4×D13—21no—
55C2×C4×D13—22no—
56C2×Dic26C2312yes—
57C13×C4⋊C4—21no—
58C13×C4⋊C4—21no—
59C13×C4⋊C4—21no—
60C13×C4⋊C4—22no—
61C13×C4⋊C4D411yescharacteristic
62C13×C4⋊C4C2311yescharacteristic
63C13×C22⋊C4—22no—
64C13×C22⋊C4D412yes—
65C42×C13—21no—
66C42×C13C2311yescharacteristic
67C22⋊Dic13—22no—
68#6107—24no—
69#6107—24no—
70#6107—42no—
71#6106—24no—
72#6106D414yescomplemented
73#6103—21no—
74C4⋊Dic13—21no—
75C4⋊Dic13—21no—
76C4⋊Dic13C2311yescharacteristic
77#6101—22no—
78#6099—24no—
79C2×#1055C2311yescharacteristic
80C2×#1055C2312yes—
81C2×#1055C2311yescharacteristic
82#3276—131nomaximal, Sylow
83C23×C13C2×D412yes—
84C22×D13—21no—
85Q8×C13—21no—
86Q8×C13—22no—
87Q8×C13—22no—
88Q8×C13—44no—
89Q8×C13C2×D412yes—
90D4×C13—22no—
91C2×C4×C13—21no—
92C2×C4×C13—22no—
93C2×C4×C13—22no—
94C2×C4×C13—21no—
95C2×C4×C13—22no—
96C2×C4×C13—44no—
97C2×C4×C13C2×D412yes—
98C2×C4×C13C2×D411yescharacteristic
99C2×C4×C13C2×D411yescharacteristic
100C2×C4×C13C2411yescharacteristic
101C22⋊D13—44no—
102C2×Dic13—21no—
103C2×Dic13—22no—
104D52—21no—
105D52C2×D412yes—
106C4×D13—44no—
107C4×D13—42no—
108Dic26—22no—
109Dic26—22no—
110#1055—22no—
111#1055—21no—
112#1055C2×D412yes—
113C2×#137—132no—
114D4×Q8D1311yescharacteristic, complemented
115#547—131no—
116#494—131no—
117#470—132no—
118#462—131no—
119#461—131no—
120#452—132no—
121#451—132no—
122C4×SD16—131no—
123#436—131no—
124C22×C13—22no—
125C22×C13—22no—
126C22×C13—22no—
127C22×C13C22×D411yescharacteristic
128C2×D13—22no—
129C2×D13—41no—
130C2×D13—41no—
131C4×C13—22no—
132C4×C13—22no—
133C4×C13—21no—
134C4×C13—42no—
135C4×C13—41no—
136C4×C13#13712yescomplemented
137C4×C13C22×D411yescharacteristic
138C4×C13H(5,𝔽2)11yescharacteristic
139Dic13—42no—
140Dic13—41no—
141C2×#41—132no—
142C22×Q8C2×D1312yes—
143#137—268no—
144C2×Q16—132no—
145C2×Q16—132no—
146C2×Q16—132no—
147C2×SD16—131no—
148C2×SD16—132no—
149C2×M16—132no—
150C4⋊Q8—21no—
151C4⋊Q8—131no—
152C4⋊Q8C2×D1311yescharacteristic
153#123—262no—
154C22⋊Q8—22no—
155C22⋊Q8—132no—
156C22⋊Q8C2×D1312yes—
157#121—261no—
158C4×Q8C2×D1311yescharacteristic
159C4×D4—21no—
160C4×D4—131no—
161C4×D4C2×D1311yescharacteristic
162C2×C4⋊C4—261no—
163#106—131no—
164C4⋊C8—131no—
165#103—131no—
166#103—132no—
167#103—132no—
168#102—131no—
169C22⋊C8—132no—
170C4×C8—131no—
171C2×C13—42no—
172C2×C13D4211yescharacteristic
173C2×C13C2×#13711yescharacteristic
174C2×C13#57811yescharacteristic
175D13—42no—
176#41—264no—
177#41—522no—
178C2×Q8—22no—
179C2×Q8—24no—
180C2×Q8—42no—
181C2×Q8—132no—
182C2×Q8C22×D1312yes—
183C2×Q8C22×D1311yescharacteristic
184C2×D4—131no—
185C2×D4—262no—
186C2×D4C22⋊D1311yescharacteristic
187C22×C4—22no—
188C22×C4—261no—
189C22×C4—262no—
190C22×C4C22×D1312yes—
191Q16—264no—
192Q16—264no—
193Q16—522no—
194SD16—134no—
195SD16—264no—
196M16—264no—
197C2×C8—131no—
198C2×C8—131no—
199C2×C8—132no—
200C4⋊C4—21no—
201C4⋊C4—21no—
202C4⋊C4—21no—
203C4⋊C4—22no—
204C4⋊C4—131no—
205C4⋊C4—261no—
206C4⋊C4—262no—
207C4⋊C4—261no—
208C4⋊C4C22⋊D1311yescharacteristic
209C4⋊C4C22×D1311yescharacteristic
210C22⋊C4—22no—
211C22⋊C4—262no—
212C22⋊C4—261no—
213C22⋊C4C22⋊D1312yes—
214C42—21no—
215C42C22×D1311yescharacteristic
216C13#327611yescharacteristic, complemented, Sylow
217C23—261no—
218C23C2×C22⋊D1312yes—
219Q8—21no—
220Q8—22no—
221Q8—22no—
222Q8—44no—
223Q8—262no—
224Q8—262no—
225Q8D4×D1312yes—
226D4—22no—
227D4—132no—
228D4—261no—
229D4—524no—
230C2×C4—21no—
231C2×C4—22no—
232C2×C4—22no—
233C2×C4—21no—
234C2×C4—22no—
235C2×C4—44no—
236C2×C4—261no—
237C2×C4—262no—
238C2×C4—524no—
239C2×C4—522no—
240C2×C4C2×C22⋊D1311yescharacteristic
241C2×C4C2×C22⋊D1312yes—
242C2×C4C2×C22⋊D1311yescharacteristic
243C2×C4C23×D1311yescharacteristic
244C8—132no—
245C8—262no—
246C8—261no—
247C22—22no—
248C22—22no—
249C22—22no—
250C22—262no—
251C22—521no—
252C22—521no—
253C22C22×C22⋊D1311yescharacteristic
254C4—22no—
255C4—22no—
256C4—21no—
257C4—42no—
258C4—41no—
259C4—522no—
260C4—521no—
261C4#8819612yescomplemented
262C4C2×D4×D1311yescharacteristic
263C4#8825111yescharacteristic
264C2—42no—
265C2—522no—
266C2D4×C22⋊D1311yescharacteristic
267C2C2×#8819611yescharacteristic
268C2#1171954311yescharacteristic
subgroupG/H
centerC22C22×C22⋊D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingD4×Q8×C13C2
socleC22×C13C22×D4
prime radical#11719256C2
hypercenterD4×Q8D13
hypocenterC13#3276
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
2. C2×#88196C2semidirect
4. #11718889C2semidirect
5. #11718753C2semidirect
6. #11718744C2semidirect
7. #11718713C2semidirect
8. #11718708C2semidirect
9. #11718692C2semidirect
10. C4×#6106C2semidirect
11. #11718673C2semidirect
72. #6106D4semidirect
114. D4×Q8D13semidirect
136. C4×C13#137semidirect
216. C13#3276semidirect
261. C4#88196semidirect

Maximal subgroups

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

subgroupindex
D4×Q8×C132
C2×#881962
#117192562
#117188892
#117187532
#117187442
#117187132
#117187082
#117186922
C4×#61062
#117186732
#327613