Finite Group Databasebeta

← #13124799

Subgroups — #13124799

Order 1664.

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

normal subgroups only

This group has 386 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
1C13×#536C211yesmaximal, characteristic
2#11719532C211yesmaximal, characteristic
3#11718895C211yesmaximal, characteristic
4#11718886C211yesmaximal, characteristic, complemented
5C2×#88075C211yesmaximal, characteristic, complemented
6#11718706C212yesmaximal, complemented
7#11718706C212yesmaximal, complemented
8#11718705C212yesmaximal, complemented
9#11718704C212yesmaximal, complemented
10#11718659C211yesmaximal, characteristic, complemented
11#11718656C211yesmaximal, characteristic, complemented
12C2×C13×#41C2211yescharacteristic
13C22×Q8×C13C2211yescharacteristic
14C13×C4⋊Q8—21no—
15C13×#124—21no—
16C13×#123—22no—
17C13×C22⋊Q8C2212yes—
18C13×C22⋊Q8C2212yes—
19C13×#117C2211yescharacteristic
20Q8×Dic13—21no—
21D4×Dic13—22no—
22D4×Dic13—21no—
23#88180C2211yescharacteristic
24#88180C2212yes—
25C2×C4⋊Dic13C2211yescharacteristic
26C2×C4⋊Dic13C2212yes—
27C2×#6099C2211yescharacteristic
28C22×#1055C2211yescharacteristic
29#88075C2212yes—
30#88075C2212yes—
31#88075C2212yes—
32#88075C2212yes—
33C22⋊#1055C2212yes—
34C22⋊#1055C2212yes—
35#88048C2212yes—
36#88048C2211yescharacteristic
37#88048C2211yescharacteristic
38#88047C2212yes—
39#88047C2211yescharacteristic
40#88047C2211yescharacteristic
41C13×#41—22no—
42C13×#41—22no—
43C2×Q8×C13—21no—
44C2×Q8×C13—22no—
45C2×Q8×C13—22no—
46C2×Q8×C13D411yescharacteristic
47C2×Q8×C13C2312yes—
48C2×D4×C13D412yes—
49C2×D4×C13D411yescharacteristic
50C22×C4×C13—21no—
51C22×C4×C13C2312yes—
52C22×C4×C13C2311yescharacteristic
53C22×Dic13—22no—
54C22×Dic13—21no—
55C13×C4⋊C4—22no—
56C13×C4⋊C4—22no—
57C13×C4⋊C4C2311yescharacteristic
58C13×C4⋊C4C2311yescharacteristic
59C13×C22⋊C4—21no—
60C13×C22⋊C4—22no—
61C13×C22⋊C4—22no—
62C42×C13—21no—
63C22⋊Dic13—22no—
64C22⋊Dic13—21no—
65C4⋊Dic13—22no—
66C4⋊Dic13—21no—
67C4⋊Dic13C2311yescharacteristic
68C4⋊Dic13C2312yes—
69C4⋊Dic13C2311yescharacteristic
70C4×Dic13—22no—
71C4×Dic13—21no—
72#6099—22no—
73C2×#1055—22no—
74C2×#1055C2311yescharacteristic
75C2×#1055C2311yescharacteristic
76C2×#1055C2312yes—
77#3097—131nomaximal, Sylow
78C23×C13C2×D412yes—
79C23×C13C2×D411yescharacteristic
80Q8×C13—22no—
81Q8×C13—22no—
82Q8×C13—22no—
83Q8×C13—42no—
84D4×C13—24no—
85D4×C13—22no—
86C2×C4×C13—22no—
87C2×C4×C13—22no—
88C2×C4×C13—21no—
89C2×C4×C13—21no—
90C2×C4×C13—22no—
91C2×C4×C13—42no—
92C2×C4×C13C2×D412yes—
93C2×C4×C13C2×D411yescharacteristic
94C2×C4×C13#4112yes—
95C2×C4×C13#4112yes—
96C2×C4×C13C2411yescharacteristic
97C2×Dic13—21no—
98C2×Dic13—22no—
99C2×Dic13—21no—
100C2×Dic13—81no—
101C2×Dic13—82no—
102#1055—21no—
103#1055—21no—
104#1055—22no—
105#536D1311yescharacteristic
106#520—131no—
107#485—132no—
108#485—132no—
109#484—132no—
110#483—132no—
111#428—131no—
112#427—131no—
113#419—131no—
114C2×#103—131no—
115#408—131no—
116C22×C13—21no—
117C22×C13—21no—
118C22×C13—22no—
119C22×C13—22no—
120C22×C13—22no—
121C22×C13#12312yes—
122C22×C13C22×D411yescharacteristic
123C4×C13—22no—
124C4×C13—42no—
125C4×C13—41no—
126C4×C13—41no—
127C4×C13#12312yes—
128C4×C13C2×#4111yescharacteristic
129C4×C13C2×#4111yescharacteristic
130Dic13—42no—
131Dic13—41no—
132Dic13—41no—
133C2×#41C2×D1311yescharacteristic
134C22×Q8C2×D1311yescharacteristic
135C2×M16—131no—
136C22×C8—131no—
137C4⋊Q8—21no—
138#124—21no—
139#123—22no—
140C22⋊Q8C2×D1312yes—
141C22⋊Q8C2×D1312yes—
142C4×Q8—261no—
143C4×D4—262no—
144C4×D4—261no—
145#117—131no—
146#117—132no—
147#117C2×D1311yescharacteristic
148C2×C4⋊C4—131no—
149C2×C4⋊C4—132no—
150#107—131no—
151#107—131no—
152#107—132no—
153#106—131no—
154#106—131no—
155#106—132no—
156#103—132no—
157#103—132no—
158#103—132no—
159#103—132no—
160C22⋊C8—132no—
161C22⋊C8—132no—
162C2×C13—22no—
163C2×C13—42no—
164C2×C13C2×#12311yescharacteristic
165C2×C13#57711yescharacteristic
166C2×C13#57811yescharacteristic
167#41—22no—
168#41—22no—
169C2×Q8—21no—
170C2×Q8—22no—
171C2×Q8—22no—
172C2×Q8C22⋊D1311yescharacteristic
173C2×Q8C22×D1312yes—
174C2×D4C22⋊D1312yes—
175C2×D4C22⋊D1311yescharacteristic
176C22×C4—21no—
177C22×C4—262no—
178C22×C4—261no—
179C22×C4C22×D1312yes—
180C22×C4C22×D1311yescharacteristic
181M16—262no—
182C2×C8—131no—
183C2×C8—132no—
184C2×C8—131no—
185C2×C8—262no—
186C4⋊C4—22no—
187C4⋊C4—22no—
188C4⋊C4—132no—
189C4⋊C4—131no—
190C4⋊C4—131no—
191C4⋊C4—262no—
192C4⋊C4—261no—
193C4⋊C4C22×D1311yescharacteristic
194C4⋊C4C22×D1311yescharacteristic
195C22⋊C4—21no—
196C22⋊C4—22no—
197C22⋊C4—22no—
198C22⋊C4—262no—
199C22⋊C4—261no—
200C42—21no—
201C42—262no—
202C42—261no—
203C13#309711yescharacteristic, complemented, Sylow
204C23C2×C22⋊D1312yes—
205C23C2×C22⋊D1311yescharacteristic
206Q8—22no—
207Q8—22no—
208Q8—22no—
209Q8—42no—
210D4—24no—
211D4—22no—
212C2×C4—22no—
213C2×C4—22no—
214C2×C4—21no—
215C2×C4—21no—
216C2×C4—22no—
217C2×C4—42no—
218C2×C4—261no—
219C2×C4—262no—
220C2×C4—261no—
221C2×C4—1041no—
222C2×C4—1042no—
223C2×C4#612912yes—
224C2×C4#612912yes—
225C2×C4C2×C22⋊D1312yes—
226C2×C4C2×C22⋊D1311yescharacteristic
227C2×C4C23×D1311yescharacteristic
228C8—261no—
229C8—261no—
230C8—262no—
231C22—21no—
232C22—21no—
233C22—22no—
234C22—22no—
235C22—22no—
236C22#8818912yes—
237C22C22×C22⋊D1311yescharacteristic
238C4—22no—
239C4—42no—
240C4—41no—
241C4—41no—
242C4—522no—
243C4—521no—
244C4—521no—
245C4#8818912yes—
246C4C2×#612911yescharacteristic
247C4C2×#612911yescharacteristic
248C2—22no—
249C2—42no—
250C2C2×#8818911yescharacteristic
251C2#1171954211yescharacteristic
252C2#1171954311yescharacteristic
subgroupG/H
centerC22C22×C22⋊D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#536C2
socleC22×C13C22×D4
prime radicalC2×C13×#41C22
hypercenter#536D13
hypocenterC13#3097
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×#41 ◁ #536

Complements

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

NH ≅ G/Ntype
4. #11718886C2semidirect
5. C2×#88075C2semidirect
6. #11718706C2semidirect
7. #11718706C2semidirect
8. #11718705C2semidirect
9. #11718704C2semidirect
10. #11718659C2semidirect
11. #11718656C2semidirect
203. C13#3097semidirect

Maximal subgroups

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

subgroupindex
C13×#5362
#117195322
#117188952
#117188862
C2×#880752
#117187062
#117187052
#117187042
#117186592
#117186562
#309713