Finite Group Databasebeta

← #13125759

Subgroups — #13125759

Order 1664.

428 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

normal subgroups only

This group has 428 conjugacy classes of subgroups — too many to draw. Only its 123 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×#88198C211yesmaximal, characteristic, complemented
2#11719301C211yesmaximal, characteristic
3C13×#448C211yesmaximal, characteristic, complemented
4#11718888C211yesmaximal, characteristic, complemented
5#11718836C212yesmaximal, complemented
6#11718823C212yesmaximal, complemented
7#11718701C211yesmaximal, characteristic, complemented
8#11718479C212yesmaximal, complemented
9#11718453C212yesmaximal, complemented
10#11718399C211yesmaximal, characteristic, complemented
11#11718379C211yesmaximal, characteristic, complemented
12C22×Q8×C13C2211yescharacteristic
13C2×#6129—21no—
14C22×Dic26C2211yescharacteristic
15C2×C13×SD16C2212yes—
16C13×#121C2211yescharacteristic
17#88198—21no—
18#88198—21no—
19#88198C2212yes—
20#88198C2212yes—
21C2×#6106C2212yes—
22#88194C2211yescharacteristic
23#88193—21no—
24D4×Dic13C2211yescharacteristic
25C2×#6105C2212yes—
26#88184C2211yescharacteristic
27C2×#6101—21no—
28C2×#6101—21no—
29C2×C4×Dic13C2211yescharacteristic
30C2×#6095C2212yes—
31#88147C2211yescharacteristic
32#88142C2211yescharacteristic
33#88139—21no—
34#88135—21no—
35C13×#103C2212yes—
36C13×C22⋊C8C2211yescharacteristic
37#88075C2212yes—
38C22⋊#1055C2211yescharacteristic
39#88056C2212yes—
40#88054C2212yes—
41C8×Dic13C2212yes—
42#88050C2212yes—
43C2×Q8×C13—21no—
44C2×Q8×C13—42no—
45C2×Q8×C13C2312yes—
46C2×D4×C13—21no—
47C2×D4×C13C2311yescharacteristic
48C22×C4×C13—21no—
49C22×C4×C13C2311yescharacteristic
50C2×C22⋊D13—21no—
51C2×C22⋊D13—21no—
52C2×C22⋊D13—21no—
53C22×Dic13—21no—
54C22×Dic13—21no—
55C22×Dic13D411yescharacteristic
56C22×Dic13D411yescharacteristic
57#6129—44no—
58C2×D52C2311yescharacteristic
59C2×C4×D13—21no—
60C2×Dic26—21no—
61C2×Dic26—21no—
62C2×Dic26—42no—
63C2×Dic26C2312yes—
64C13×SD16—42no—
65C2×C8×C13C2312yes—
66C13×C4⋊C4C2311yescharacteristic
67C13×C22⋊C4—21no—
68C22⋊Dic13—21no—
69#6106—42no—
70#6105—42no—
71#6103—21no—
72#6103—21no—
73C4⋊Dic13C2311yescharacteristic
74#6101—21no—
75#6101—22no—
76#6101—22no—
77#6101—22no—
78#6101—22no—
79C4×Dic13D411yescharacteristic
80C4×Dic13D411yescharacteristic
81C4×Dic13C2311yescharacteristic
82C4×Dic13C2311yescharacteristic
83C2×#1055C2312yes—
84#6095—42no—
85#3206—131nomaximal, Sylow
86C23×C13—21no—
87C23×C13C2×D411yescharacteristic
88C22×D13—21no—
89Q8×C13—22no—
90Q8×C13—22no—
91Q8×C13—42no—
92D4×C13—22no—
93D4×C13—42no—
94C2×C4×C13—22no—
95C2×C4×C13—22no—
96C2×C4×C13—21no—
97C2×C4×C13—42no—
98C2×C4×C13C2×D411yescharacteristic
99C2×C4×C13C2411yescharacteristic
100C22⋊D13—42no—
101C22⋊D13—42no—
102C22⋊D13—42no—
103C2×Dic13—22no—
104C2×Dic13—22no—
105C2×Dic13—21no—
106C2×Dic13—42no—
107C2×Dic13—42no—
108C2×Dic13SD1614yescomplemented
109C2×Dic13C2×D411yescharacteristic
110C2×Dic13C2×D411yescharacteristic
111C2×Dic13C2×D411yescharacteristic
112C2×Dic13C2×D411yescharacteristic
113D52—22no—
114C4×D13—42no—
115Dic26—22no—
116Dic26—22no—
117Dic26—42no—
118Dic26—42no—
119C8×C13—22no—
120#1055—22no—
121#532—131no—
122C2×C4⋊Q8—131no—
123#492—132no—
124#487—132no—
125#461—132no—
126#461—132no—
127#448—131no—
128#448—131no—
129#448—131no—
130#448D1311yescharacteristic, complemented
131#431—131no—
132C22×C13—21no—
133C22×C13—21no—
134C22×C13—41no—
135C22×C13—41no—
136C22×C13—41no—
137C22×C13C2×SD1612yes—
138C22×C13C22×D411yescharacteristic
139C2×D13—41no—
140C2×D13—41no—
141C2×D13—41no—
142C4×C13—21no—
143C4×C13—42no—
144C4×C13—41no—
145C4×C13H(5,𝔽2)12yes—
146Dic13—21no—
147Dic13—42no—
148Dic13—41no—
149Dic13C2×SD1612yes—
150Dic13C2×SD1612yes—
151Dic13#13712yes—
152C2×#41—261no—
153C22×Q8—131no—
154C22×Q8C2×D1311yescharacteristic
155C2×SD16—132no—
156C2×SD16—132no—
157C2×SD16—132no—
158C2×SD16C2×D1312yes—
159C4⋊Q8—131no—
160C4⋊Q8—132no—
161C4⋊Q8—132no—
162C4⋊Q8—261no—
163C4⋊Q8—261no—
164#127—131no—
165#124—261no—
166#121—131no—
167#121—261no—
168#121C2×D1311yescharacteristic
169C4×D4—131no—
170C4×D4—131no—
171C4×D4—261no—
172C2×C4⋊C4—261no—
173C2×C4⋊C4—261no—
174C2×C42—131no—
175C4⋊C8—132no—
176#103—132no—
177#103—132no—
178#103—132no—
179#103C2×D1312yes—
180C22⋊C8—131no—
181C22⋊C8C2×D1311yescharacteristic
182C4×C8—132no—
183C2×C13—22no—
184C2×C13—81no—
185C2×C13#53511yescharacteristic
186C2×C13C22×SD1611yescharacteristic
187C2×C13C2×#13711yescharacteristic
188D13—81no—
189#41—524no—
190C2×Q8—21no—
191C2×Q8—42no—
192C2×Q8—132no—
193C2×Q8—261no—
194C2×Q8—261no—
195C2×Q8—522no—
196C2×Q8C22×D1312yes—
197C2×D4—21no—
198C2×D4—131no—
199C2×D4—261no—
200C2×D4—261no—
201C2×D4—261no—
202C2×D4C22×D1311yescharacteristic
203C22×C4—21no—
204C22×C4—131no—
205C22×C4—131no—
206C22×C4—261no—
207C22×C4—261no—
208C22×C4—261no—
209C22×C4C22×D1311yescharacteristic
210SD16—42no—
211SD16—522no—
212SD16—522no—
213SD16—522no—
214C2×C8—132no—
215C2×C8C22×D1312yes—
216C4⋊C4—131no—
217C4⋊C4—262no—
218C4⋊C4—262no—
219C4⋊C4—262no—
220C4⋊C4—262no—
221C4⋊C4—261no—
222C4⋊C4C22×D1311yescharacteristic
223C22⋊C4—21no—
224C22⋊C4—261no—
225C22⋊C4—261no—
226C22⋊C4—261no—
227C42—131no—
228C42—131no—
229C42—131no—
230C42—131no—
231C13#320611yescharacteristic, complemented, Sylow
232C23—21no—
233C23—261no—
234C23D4×D1311yescharacteristic
235Q8—22no—
236Q8—22no—
237Q8—42no—
238Q8—262no—
239Q8—262no—
240Q8—522no—
241Q8—522no—
242D4—22no—
243D4—42no—
244D4—262no—
245D4—522no—
246D4—522no—
247D4—522no—
248C2×C4—22no—
249C2×C4—21no—
250C2×C4—22no—
251C2×C4—42no—
252C2×C4—134no—
253C2×C4—131no—
254C2×C4—131no—
255C2×C4—131no—
256C2×C4—131no—
257C2×C4—262no—
258C2×C4—261no—
259C2×C4—262no—
260C2×C4—522no—
261C2×C4—522no—
262C2×C4—522no—
263C2×C4D4×D1311yescharacteristic
264C2×C4C23×D1311yescharacteristic
265C8—22no—
266C8—262no—
267C22—21no—
268C22—21no—
269C22—41no—
270C22—41no—
271C22—41no—
272C22—521no—
273C22—521no—
274C22—521no—
275C22SD16×D1312yes—
276C22C2×D4×D1311yescharacteristic
277C4—21no—
278C4—41no—
279C4—42no—
280C4—132no—
281C4—132no—
282C4—132no—
283C4—261no—
284C4—521no—
285C4—522no—
286C4#8825112yes—
287C2—22no—
288C2—81no—
289C2—1041no—
290C2#1171929711yescharacteristic
291C2C2×SD16×D1311yescharacteristic
292C2D13×#13711yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#448C2
socleC22×C13C22×D4
prime radical#11719301C2
hypercenter#448D13
hypocenterC13#3206
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ #448

Complements

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

NH ≅ G/Ntype
1. C2×#88198C2semidirect
3. C13×#448C2semidirect
4. #11718888C2semidirect
5. #11718836C2semidirect
6. #11718823C2semidirect
7. #11718701C2semidirect
8. #11718479C2semidirect
9. #11718453C2semidirect
10. #11718399C2semidirect
11. #11718379C2semidirect
108. C2×Dic13SD16semidirect
130. #448D13semidirect
231. C13#3206semidirect

Maximal subgroups

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

subgroupindex
C2×#881982
#117193012
C13×#4482
#117188882
#117188362
#117188232
#117187012
#117184792
#117184532
#117183992
#117183792
#320613