Finite Group Databasebeta

← #13124803

Subgroups — #13124803

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
1#11719521C211yesmaximal, characteristic
2#11719228C211yesmaximal, characteristic
3C13×#419C211yesmaximal, characteristic, complemented
4C2×#88075C211yesmaximal, characteristic, complemented
5#11718790C211yesmaximal, characteristic
6#11718782C211yesmaximal, characteristic, complemented
7#11718659C211yesmaximal, characteristic, complemented
8#11718476C212yesmaximal, complemented
9#11718475C212yesmaximal, complemented
10#11718470C212yesmaximal, complemented
11#11718466C212yesmaximal, complemented
12C22×Q8×C13C2211yescharacteristic
13C2×#6127C2211yescharacteristic
14C2×C13×M16C2211yescharacteristic
15C13×#117C2211yescharacteristic
16#88201—21no—
17#88200C2212yes—
18#88200C2212yes—
19#88198—21no—
20#88183—22no—
21#88180C2211yescharacteristic
22C2×C4⋊Dic13C2211yescharacteristic
23C22×#1055C2211yescharacteristic
24#88146C2212yes—
25C4⋊C4×D13C2212yes—
26#88135—22no—
27C4×D52—21no—
28C4×Dic26—21no—
29C13×#103C2212yes—
30C13×#103C2212yes—
31#88075C2212yes—
32#88075C2212yes—
33#88060C2212yes—
34#88060C2212yes—
35#88058C2212yes—
36#88057C2212yes—
37#88048C2211yescharacteristic
38#88048C2211yescharacteristic
39#88047C2211yescharacteristic
40#88047C2211yescharacteristic
41C2×Q8×C13—21no—
42C2×Q8×C13—22no—
43C2×Q8×C13—22no—
44C2×Q8×C13C2312yes—
45C22×C4×C13—21no—
46C22×C4×C13C2311yescharacteristic
47C2×C22⋊D13D412yes—
48C22×Dic13—21no—
49#6127—22no—
50#6127—22no—
51C2×D52D411yescharacteristic
52C2×C4×D13—22no—
53C2×C4×D13C2312yes—
54C2×Dic26D411yescharacteristic
55C13×M16—22no—
56C2×C8×C13C2312yes—
57C13×C4⋊C4C2311yescharacteristic
58C13×C4⋊C4C2311yescharacteristic
59C13×C22⋊C4—21no—
60C42×C13—21no—
61C22⋊Dic13—21no—
62#6103—22no—
63#6103—22no—
64#6103—22no—
65C4⋊Dic13—21no—
66C4⋊Dic13C2312yes—
67C4⋊Dic13C2311yescharacteristic
68C4⋊Dic13C2311yescharacteristic
69#6101—22no—
70#6101—22no—
71#6101—22no—
72C4×Dic13—21no—
73C4×Dic13—22no—
74C2×#1055—22no—
75C2×#1055C2311yescharacteristic
76C2×#1055C2311yescharacteristic
77#3097—131nomaximal, Sylow
78C23×C13C2×D411yescharacteristic
79C22×D13C2×D412yes—
80Q8×C13—22no—
81Q8×C13—22no—
82Q8×C13—42no—
83C2×C4×C13—21no—
84C2×C4×C13—22no—
85C2×C4×C13—21no—
86C2×C4×C13—42no—
87C2×C4×C13C2×D411yescharacteristic
88C2×C4×C13#4112yes—
89C2×C4×C13#4112yes—
90C2×C4×C13C2411yescharacteristic
91C22⋊D13—24no—
92C2×Dic13—21no—
93C2×Dic13—21no—
94C2×Dic13—22no—
95C2×Dic13—81no—
96C2×Dic13C2×D412yes—
97D52—22no—
98C4×D13—22no—
99C4×D13—22no—
100C4×D13—82no—
101Dic26—22no—
102C8×C13—22no—
103#1055—21no—
104#1055—21no—
105#536—131no—
106#520—131no—
107#485—132no—
108#485—132no—
109#484—132no—
110#483—132no—
111#428—131no—
112#427—131no—
113#419D1311yescharacteristic, complemented
114C2×#103—131no—
115#408—131no—
116C22×C13—21no—
117C22×C13—21no—
118C22×C13#12312yes—
119C22×C13C22×D411yescharacteristic
120C2×D13—22no—
121C2×D13—22no—
122C2×D13—22no—
123C4×C13—42no—
124C4×C13—41no—
125C4×C13—41no—
126C4×C13#12312yes—
127C4×C13C2×#4111yescharacteristic
128C4×C13C2×#4111yescharacteristic
129Dic13—22no—
130Dic13—42no—
131Dic13—41no—
132Dic13—41no—
133C2×#41—131no—
134C22×Q8C2×D1311yescharacteristic
135C2×M16C2×D1311yescharacteristic
136C22×C8—131no—
137C4⋊Q8—261no—
138#124—261no—
139#123—262no—
140C22⋊Q8—132no—
141C22⋊Q8—132no—
142C4×Q8—261no—
143C4×D4—261no—
144C4×D4—262no—
145#117—131no—
146#117—132no—
147#117C2×D1311yescharacteristic
148C2×C4⋊C4—131no—
149C2×C4⋊C4—132no—
150#107—132no—
151#107—131no—
152#107—131no—
153#106—132no—
154#106—131no—
155#106—131no—
156#103—132no—
157#103—132no—
158#103C2×D1312yes—
159#103C2×D1312yes—
160C22⋊C8—132no—
161C22⋊C8—132no—
162C2×C13—22no—
163C2×C13C2×#12311yescharacteristic
164C2×C13#57711yescharacteristic
165C2×C13#57811yescharacteristic
166D13—42no—
167#41—262no—
168#41—262no—
169C2×Q8—21no—
170C2×Q8—22no—
171C2×Q8—22no—
172C2×Q8—131no—
173C2×Q8C22×D1312yes—
174C2×D4—132no—
175C2×D4—131no—
176C22×C4—21no—
177C22×C4—132no—
178C22×C4—262no—
179C22×C4—261no—
180C22×C4C22×D1311yescharacteristic
181M16—22no—
182C2×C8—131no—
183C2×C8—131no—
184C2×C8—262no—
185C2×C8C22×D1312yes—
186C4⋊C4—132no—
187C4⋊C4—131no—
188C4⋊C4—131no—
189C4⋊C4—262no—
190C4⋊C4—262no—
191C4⋊C4—262no—
192C4⋊C4—261no—
193C4⋊C4C22×D1311yescharacteristic
194C4⋊C4C22×D1311yescharacteristic
195C22⋊C4—21no—
196C22⋊C4—262no—
197C22⋊C4—262no—
198C22⋊C4—262no—
199C22⋊C4—261no—
200C42—21no—
201C42—262no—
202C42—261no—
203C13#309711yescharacteristic, complemented, Sylow
204C23—132no—
205C23D4×D1311yescharacteristic
206Q8—22no—
207Q8—22no—
208Q8—42no—
209Q8—262no—
210D4—264no—
211D4—262no—
212C2×C4—21no—
213C2×C4—21no—
214C2×C4—22no—
215C2×C4—42no—
216C2×C4—132no—
217C2×C4—262no—
218C2×C4—262no—
219C2×C4—261no—
220C2×C4—261no—
221C2×C4—262no—
222C2×C4—1042no—
223C2×C4—1041no—
224C2×C4#612712yes—
225C2×C4D4×D1311yescharacteristic
226C2×C4#612912yes—
227C2×C4C23×D1311yescharacteristic
228C8—22no—
229C8—261no—
230C8—261no—
231C22—21no—
232C22—21no—
233C22—262no—
234C22—262no—
235C22—262no—
236C22#8813712yes—
237C22C2×D4×D1311yescharacteristic
238C4—42no—
239C4—41no—
240C4—41no—
241C4—262no—
242C4—521no—
243C4—522no—
244C4—521no—
245C4#8813712yes—
246C4C2×#612711yescharacteristic
247C4C2×#612911yescharacteristic
248C2—22no—
249C2—522no—
250C2C2×#8813711yescharacteristic
251C2#1171948311yescharacteristic
252C2#1171948411yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#419C2
socleC22×C13C22×D4
prime radicalC2×#6127C22
hypercenter#419D13
hypocenterC13#3097
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ #419

Complements

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

NH ≅ G/Ntype
3. C13×#419C2semidirect
4. C2×#88075C2semidirect
6. #11718782C2semidirect
7. #11718659C2semidirect
8. #11718476C2semidirect
9. #11718475C2semidirect
10. #11718470C2semidirect
11. #11718466C2semidirect
113. #419D13semidirect
203. C13#3097semidirect

Maximal subgroups

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

subgroupindex
#117195212
#117192282
C13×#4192
C2×#880752
#117187902
#117187822
#117186592
#117184762
#117184752
#117184702
#117184662
#309713