Finite Group Databasebeta

← #13124116

Subgroups — #13124116

Order 1664.

752 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 752 conjugacy classes of subgroups — too many to draw. Only its 149 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
1C2×#88256C211yesmaximal, characteristic
2C2×#88205C211yesmaximal, characteristic, complemented
3C22×#6095C211yesmaximal, characteristic, complemented
4#11719231C211yesmaximal, characteristic, complemented
5C13×#416C211yesmaximal, characteristic, complemented
6#11718771C211yesmaximal, characteristic, complemented
7#11718662C211yesmaximal, characteristic, complemented
8#11718471C214yesmaximal, complemented
9#11718437C214yesmaximal, complemented
10C2×C13×#41C2211yescharacteristic
11#88256—24no—
12#88256—24no—
13C2×#6131C2212yes—
14C2×D4×D13—22no—
15C2×D4×D13C2212yes—
16C2×#6127—21no—
17C2×#6127C2211yescharacteristic
18C22×D52—21no—
19C22×D52C2211yescharacteristic
20C22×Dic26C2211yescharacteristic, complemented
21C22×C8×C13C2211yescharacteristic, complemented
22C13×#117C2211yescharacteristic, complemented
23#88205—24no—
24C2×#6107C2212yescomplemented
25C2×#6105C2212yescomplemented
26C2×#6099C2211yescharacteristic, complemented
27C2×#6095—24no—
28C2×#6095C2214yescomplemented
29#88151C2214yescomplemented
30#88140—22no—
31#88129—21no—
32#88123—21no—
33C13×#103C2212yescomplemented
34C13×#102C2212yescomplemented
35#88060C2214yescomplemented
36#88049C2214yescomplemented
37C23×D13—21no—
38C23×D13—22no—
39C13×#41—22no—
40C13×#41D414yes—
41C2×Q8×C13C2311yescharacteristic
42C2×D4×C13—21no—
43C2×D4×C13C2311yescharacteristic
44C22×C4×C13—21no—
45C22×C4×C13C2311yescharacteristic
46C2×C22⋊D13—22no—
47C2×C22⋊D13D412yes—
48C22×Dic13—21no—
49#6131—24no—
50#6131—24no—
51D4×D13—216no—
52D4×D13—24no—
53D4×D13—24no—
54#6127—28no—
55#6127—22no—
56#6127—22no—
57C2×D52—28no—
58C2×D52—22no—
59C2×D52—21no—
60C2×D52—22no—
61C2×D52D411yescharacteristic
62C2×D52D414yes—
63C2×D52C2312yes—
64C2×C4×D13—22no—
65C2×C4×D13C2312yes—
66C2×Dic26—22no—
67C2×Dic26—22no—
68C2×Dic26—21no—
69C2×Dic26D411yescharacteristic
70C2×Dic26C2312yes—
71C2×C8×C13—22no—
72C2×C8×C13C2312yes—
73C13×C4⋊C4C2312yes—
74C13×C22⋊C4—21no—
75C42×C13—21no—
76#6107—24no—
77#6105—24no—
78#6103—24no—
79C4⋊Dic13—24no—
80#6099—22no—
81C2×#1055C2312yes—
82#6095—28no—
83#3009—131nomaximal, Sylow
84C23×C13—21no—
85C23×C13C2×D411yescharacteristic
86C22×D13—22no—
87C22×D13—28no—
88C22×D13—24no—
89C22×D13—84no—
90C22×D13—82no—
91C22×D13C2×D412yes—
92Q8×C13—21no—
93Q8×C13C2×D412yes—
94D4×C13—24no—
95D4×C13—21no—
96D4×C13C2×D412yes—
97C2×C4×C13—21no—
98C2×C4×C13—24no—
99C2×C4×C13—22no—
100C2×C4×C13C2×D411yescharacteristic
101C2×C4×C13C2×D412yes—
102C2×C4×C13C2×D412yes—
103C2×C4×C13C2411yescharacteristic
104C22⋊D13—28no—
105C22⋊D13—24no—
106C2×Dic13—22no—
107C2×Dic13—42no—
108C2×Dic13C2×D412yes—
109D52—28no—
110D52—22no—
111D52—24no—
112D52—22no—
113D52C2×D414yes—
114C4×D13—28no—
115C4×D13—22no—
116C4×D13—22no—
117Dic26—22no—
118Dic26—22no—
119Dic26—22no—
120Dic26—42no—
121C8×C13—22no—
122#1055—22no—
123C2×H(5,𝔽2)—131no—
124C2×#137—131no—
125C22×SD16—131no—
126#536—131no—
127#452—134no—
128#450—134no—
129#418—131no—
130#416D1311yescharacteristic, complemented
131#408—131no—
132C22×C13—22no—
133C22×C13—22no—
134C22×C13—42no—
135C22×C13#12012yes—
136C22×C13C22×D411yescharacteristic
137C2×D13—22no—
138C2×D13—24no—
139C2×D13—24no—
140C2×D13—44no—
141C2×D13—84no—
142C2×D13—88no—
143C4×C13—22no—
144C4×C13—42no—
145C4×C13#12012yes—
146C4×C13C22×D411yescharacteristic
147C4×C13C22×D411yescharacteristic
148Dic13—22no—
149Dic13—42no—
150H(5,𝔽2)—264no—
151H(5,𝔽2)—264no—
152C2×#41—131no—
153C2×#41—132no—
154C2×#41—261no—
155C2×#41C2×D1311yescharacteristic
156C22×Q8—131no—
157C22×D4—132no—
158C22×D4—131no—
159C22×D4—261no—
160C22×D4—262no—
161#137—264no—
162C2×Q16—132no—
163C2×SD16—132no—
164C2×SD16—134no—
165C2×SD16—264no—
166C2×M16—131no—
167C22×C8C2×D1311yescharacteristic, complemented
168C4⋊Q8—261no—
169#124—261no—
170#123—262no—
171C22⋊Q8—134no—
172#117C2×D1311yescharacteristic, complemented
173#103C2×D1312yescomplemented
174#102—134no—
175#102C2×D1312yescomplemented
176C22⋊C8—134no—
177C2×C13—22no—
178C2×C13—42no—
179C2×C13C2×#12011yescharacteristic
180C2×C13#57712yes—
181D13—42no—
182D13—44no—
183C24—262no—
184C24—261no—
185#41—22no—
186#41—268no—
187#41—264no—
188#41—264no—
189#41—262no—
190#41—262no—
191#41D5214yes—
192C2×Q8—131no—
193C2×Q8—132no—
194C2×Q8—261no—
195C2×Q8—262no—
196C2×Q8—262no—
197C2×Q8C22×D1311yescharacteristic
198C2×D4—21no—
199C2×D4—132no—
200C2×D4—134no—
201C2×D4—131no—
202C2×D4—132no—
203C2×D4—262no—
204C2×D4—268no—
205C2×D4—262no—
206C2×D4—264no—
207C2×D4—2616no—
208C2×D4—264no—
209C2×D4—262no—
210C2×D4—261no—
211C2×D4C22×D1311yescharacteristic
212C22×C4—21no—
213C22×C4—132no—
214C22×C4—262no—
215C22×C4—261no—
216C22×C4C22×D1311yescharacteristic
217Q16—264no—
218SD16—268no—
219SD16—264no—
220M16—262no—
221C2×C8—22no—
222C2×C8—132no—
223C2×C8C22×D1312yes—
224C4⋊C4—264no—
225C4⋊C4C22×D1312yes—
226C22⋊C4—21no—
227C22⋊C4—264no—
228C42—21no—
229C13#300911yescharacteristic, complemented, Sylow
230C23—21no—
231C23—132no—
232C23—268no—
233C23—262no—
234C23—264no—
235C23—1042no—
236C23—1044no—
237C23D4×D1311yescharacteristic
238Q8—21no—
239Q8—262no—
240Q8—262no—
241Q8—262no—
242Q8—522no—
243Q8C2×D5212yes—
244D4—24no—
245D4—21no—
246D4—134no—
247D4—268no—
248D4—268no—
249D4—264no—
250D4—264no—
251D4—262no—
252D4—262no—
253D4C2×D5212yes—
254C2×C4—21no—
255C2×C4—24no—
256C2×C4—22no—
257C2×C4—132no—
258C2×C4—268no—
259C2×C4—262no—
260C2×C4—262no—
261C2×C4—262no—
262C2×C4—522no—
263C2×C4C2×D5212yes—
264C2×C4D4×D1311yescharacteristic
265C2×C4D4×D1312yes—
266C2×C4C23×D1311yescharacteristic
267C8—22no—
268C8—262no—
269C22—22no—
270C22—22no—
271C22—42no—
272C22—264no—
273C22—262no—
274C22—264no—
275C22—524no—
276C22—1044no—
277C22—1048no—
278C22#8813612yes—
279C22C2×D4×D1311yescharacteristic
280C4—22no—
281C4—42no—
282C4—262no—
283C4—522no—
284C4#8813612yes—
285C4C22×D5211yescharacteristic
286C4C2×D4×D1311yescharacteristic
287C2—22no—
288C2—42no—
289C2—522no—
290C2—524no—
291C2C2×#8813611yescharacteristic
292C2#1171947512yes—
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#416C2
socleC22×C13C22×D4
prime radicalC2×#88256C2
hypercenter#416D13
hypocenterC13#3009
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ #416

Complements

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

NH ≅ G/Ntype
2. C2×#88205C2semidirect
3. C22×#6095C2semidirect
4. #11719231C2semidirect
5. C13×#416C2semidirect
6. #11718771C2semidirect
7. #11718662C2semidirect
8. #11718471C2semidirect
9. #11718437C2semidirect
20. C22×Dic26C22semidirect
21. C22×C8×C13C22semidirect
22. C13×#117C22semidirect
24. C2×#6107C22semidirect
25. C2×#6105C22semidirect
26. C2×#6099C22semidirect
28. C2×#6095C22semidirect
29. #88151C22semidirect
33. C13×#103C22semidirect
34. C13×#102C22semidirect
35. #88060C22semidirect
36. #88049C22semidirect
130. #416D13semidirect
167. C22×C8C2×D13semidirect
172. #117C2×D13semidirect
173. #103C2×D13semidirect
175. #102C2×D13semidirect
229. C13#3009semidirect

Maximal subgroups

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

subgroupindex
C2×#882562
C2×#882052
C22×#60952
#117192312
C13×#4162
#117187712
#117186622
#117184712
#117184372
#300913