Finite Group Databasebeta

← #13126023

Subgroups — #13126023

Order 1664.

368 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 368 conjugacy classes of subgroups — too many to draw. Only its 113 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
1#11719301C211yesmaximal, characteristic
2C2×#88144C211yesmaximal, characteristic, complemented
3C13×#480C211yesmaximal, characteristic, complemented
4#11718695C211yesmaximal, characteristic, complemented
5#11718628C211yesmaximal, characteristic, complemented
6#11718552C212yesmaximal, complemented
7#11718537C212yesmaximal, complemented
8#11718425C212yesmaximal, complemented
9#11718424C212yesmaximal, complemented
10#11718396C211yesmaximal, characteristic, complemented
11#11718380C211yesmaximal, characteristic, complemented
12C2×#6129—21no—
13C13×#121C2211yescharacteristic
14C2×C13×C4⋊C4C2211yescharacteristic
15#88194C2211yescharacteristic
16#88193—21no—
17D4×Dic13C2211yescharacteristic
18#88184C2211yescharacteristic
19C2×C4⋊Dic13—21no—
20C2×C4⋊Dic13C2211yescharacteristic
21C2×#6101—21no—
22C2×C4×Dic13C2211yescharacteristic
23#88147C2211yescharacteristic
24#88144—21no—
25#88144—21no—
26#88144C2212yes—
27#88144C2212yes—
28#88142C2211yescharacteristic
29#88139—21no—
30#88135—21no—
31C13×#107C2212yes—
32C13×#102C2212yes—
33C13×C22⋊C8C2211yescharacteristic
34#88072C2212yes—
35C22⋊#1055C2211yescharacteristic
36#88061C2212yes—
37#88057C2212yes—
38#88055C2212yes—
39#88054C2212yes—
40#88049C2212yes—
41#88048C2212yes—
42#88047C2212yes—
43C2×D4×C13—21no—
44C2×D4×C13C2311yescharacteristic
45C22×C4×C13—21no—
46C22×C4×C13C2311yescharacteristic
47C2×C22⋊D13—21no—
48C2×C22⋊D13—21no—
49C2×C22⋊D13—21no—
50C22×Dic13—21no—
51C22×Dic13—21no—
52C22×Dic13D411yescharacteristic
53C22×Dic13D411yescharacteristic
54#6129—44no—
55C2×D52C2311yescharacteristic
56C2×C4×D13—21no—
57C2×Dic26—21no—
58C2×C8×C13C2312yes—
59C13×C4⋊C4—21no—
60C13×C4⋊C4C2312yes—
61C13×C4⋊C4C2311yescharacteristic
62C13×C22⋊C4—21no—
63C22⋊Dic13—21no—
64#6103—21no—
65#6103—21no—
66C4⋊Dic13—21no—
67C4⋊Dic13—22no—
68C4⋊Dic13—22no—
69C4⋊Dic13C2312yes—
70C4⋊Dic13C2311yescharacteristic
71#6101—21no—
72#6101—22no—
73#6101—22no—
74C4×Dic13D411yescharacteristic
75C4×Dic13D411yescharacteristic
76C4×Dic13C2311yescharacteristic
77C4×Dic13C2311yescharacteristic
78C2×#1055C2312yes—
79#3234—131nomaximal, Sylow
80C23×C13—21no—
81C23×C13C2×D411yescharacteristic
82C22×D13—21no—
83D4×C13—22no—
84D4×C13—42no—
85C2×C4×C13—22no—
86C2×C4×C13—22no—
87C2×C4×C13—21no—
88C2×C4×C13—42no—
89C2×C4×C13C2×D411yescharacteristic
90C2×C4×C13C2411yescharacteristic
91C22⋊D13—42no—
92C22⋊D13—42no—
93C22⋊D13—42no—
94C2×Dic13—22no—
95C2×Dic13—22no—
96C2×Dic13—21no—
97C2×Dic13—41no—
98C2×Dic13—42no—
99C2×Dic13—42no—
100C2×Dic13C2×D411yescharacteristic
101C2×Dic13C2×D411yescharacteristic
102C2×Dic13C2×D411yescharacteristic
103C2×Dic13C2×D411yescharacteristic
104D52—22no—
105C4×D13—42no—
106Dic26—42no—
107C8×C13—22no—
108#1055—22no—
109#532—131no—
110C2×#125—131no—
111#501—132no—
112#490—132no—
113#481—131no—
114#481—131no—
115#480—131no—
116#480D1311yescharacteristic, complemented
117#478—132no—
118#478—132no—
119#432—131no—
120C22×C13—21no—
121C22×C13—21no—
122C22×C13—41no—
123C22×C13—41no—
124C22×C13—41no—
125C22×C13AGL(1,ℤ/8)12yes—
126C22×C13C22×D411yescharacteristic
127C2×D13—41no—
128C2×D13—41no—
129C2×D13—41no—
130C4×C13—21no—
131C4×C13—41no—
132C4×C13—42no—
133C4×C132−1+412yes—
134Dic13—21no—
135Dic13—21no—
136Dic13—21no—
137Dic13—21no—
138Dic13—41no—
139Dic13—42no—
140C2×#41—261no—
141C4⋊Q8—131no—
142#127—131no—
143#125—132no—
144#125—132no—
145#125—261no—
146#125—261no—
147#124—261no—
148#121—131no—
149#121—261no—
150#121C2×D1311yescharacteristic
151C4×D4—131no—
152C4×D4—131no—
153C4×D4—261no—
154C2×C4⋊C4—131no—
155C2×C4⋊C4—261no—
156C2×C4⋊C4—261no—
157C2×C4⋊C4C2×D1311yescharacteristic
158C2×C42—131no—
159#107—132no—
160#107C2×D1312yes—
161#106—132no—
162#106—132no—
163C4⋊C8—132no—
164#102—132no—
165#102—132no—
166#102—132no—
167#102C2×D1312yes—
168C22⋊C8—131no—
169C22⋊C8C2×D1311yescharacteristic
170#97—132no—
171C2×C13—22no—
172C2×C13—81no—
173C2×C13#53611yescharacteristic
174C2×C13C2×AGL(1,ℤ/8)11yescharacteristic
175C2×C13#57511yescharacteristic
176D13—81no—
177#41—524no—
178C2×Q8—261no—
179C2×D4—21no—
180C2×D4—131no—
181C2×D4—261no—
182C2×D4—261no—
183C2×D4—261no—
184C2×D4C22×D1311yescharacteristic
185C22×C4—21no—
186C22×C4—131no—
187C22×C4—131no—
188C22×C4—261no—
189C22×C4—261no—
190C22×C4—261no—
191C22×C4C22×D1311yescharacteristic
192C2×C8—132no—
193C2×C8C22×D1312yes—
194C4⋊C4—21no—
195C4⋊C4—132no—
196C4⋊C4—131no—
197C4⋊C4—262no—
198C4⋊C4—262no—
199C4⋊C4—262no—
200C4⋊C4—262no—
201C4⋊C4—261no—
202C4⋊C4—261no—
203C4⋊C4C22×D1312yes—
204C4⋊C4C22×D1311yescharacteristic
205C22⋊C4—21no—
206C22⋊C4—261no—
207C22⋊C4—261no—
208C22⋊C4—261no—
209C42—131no—
210C42—131no—
211C42—131no—
212C42—131no—
213C13#323411yescharacteristic, complemented, Sylow
214C23—21no—
215C23—261no—
216C23D4×D1311yescharacteristic
217Q8—522no—
218D4—22no—
219D4—42no—
220D4—262no—
221D4—522no—
222D4—522no—
223D4—522no—
224C2×C4—22no—
225C2×C4—21no—
226C2×C4—22no—
227C2×C4—42no—
228C2×C4—131no—
229C2×C4—131no—
230C2×C4—131no—
231C2×C4—131no—
232C2×C4—262no—
233C2×C4—261no—
234C2×C4—262no—
235C2×C4—522no—
236C2×C4—521no—
237C2×C4—522no—
238C2×C4—522no—
239C2×C4D4×D1311yescharacteristic
240C2×C4C23×D1311yescharacteristic
241C8—22no—
242C8—262no—
243C22—21no—
244C22—21no—
245C22—41no—
246C22—41no—
247C22—41no—
248C22—521no—
249C22—521no—
250C22—521no—
251C22#8816512yes—
252C22C2×D4×D1311yescharacteristic
253C4—21no—
254C4—42no—
255C4—41no—
256C4—261no—
257C4—261no—
258C4—261no—
259C4—261no—
260C4—521no—
261C4—522no—
262C4#8825712yes—
263C2—22no—
264C2—81no—
265C2—1041no—
266C2#1171935311yescharacteristic
267C2C2×#8816511yescharacteristic
268C2#1171948211yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#480C2
socleC22×C13C22×D4
prime radical#11719301C2
hypercenter#480D13
hypocenterC13#3234
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ #480

Complements

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

NH ≅ G/Ntype
2. C2×#88144C2semidirect
3. C13×#480C2semidirect
4. #11718695C2semidirect
5. #11718628C2semidirect
6. #11718552C2semidirect
7. #11718537C2semidirect
8. #11718425C2semidirect
9. #11718424C2semidirect
10. #11718396C2semidirect
11. #11718380C2semidirect
116. #480D13semidirect
213. C13#3234semidirect

Maximal subgroups

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

subgroupindex
#117193012
C2×#881442
C13×#4802
#117186952
#117186282
#117185522
#117185372
#117184252
#117184242
#117183962
#117183802
#323413