Finite Group Databasebeta

← #13120458

Subgroups — #13120458

Order 1664.

582 conjugacy classes of subgroups; only the 137 normal subgroups are shown.

normal subgroups only

This group has 582 conjugacy classes of subgroups — too many to draw. Only its 137 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×D4×Dic13C211yesmaximal, characteristic, complemented
2C2×#88152C211yesmaximal, characteristic, complemented
3C13×#394C211yesmaximal, characteristic, complemented
4#11718884C211yesmaximal, characteristic
5#11718644C211yesmaximal, characteristic, complemented
6#11718619C212yesmaximal, complemented
7#11718618C212yesmaximal, complemented
8#11718612C212yesmaximal, complemented
9#11718607C212yesmaximal, complemented
10#11718335C211yesmaximal, characteristic, complemented
11#11718309C211yesmaximal, characteristic, complemented
12C22×D4×C13C2211yescharacteristic
13C22×C22⋊D13C2212yes—
14C23×Dic13C2212yes—
15C2×C13×C4⋊C4C2211yescharacteristic
16C2×C13×C22⋊C4C2212yes—
17C2×C13×C22⋊C4C2212yes—
18C2×C22⋊Dic13C2212yes—
19C2×C22⋊Dic13C2212yes—
20D4×Dic13—24no—
21C2×#6103C2211yescharacteristic
22C2×#6103C2211yescharacteristic
23C2×#6103C2211yescharacteristic
24C2×#6103C2212yes—
25C2×C4⋊Dic13C2211yescharacteristic
26C2×C4⋊Dic13C2211yescharacteristic
27C2×#6101C2211yescharacteristic
28C2×#6101C2212yes—
29C2×C4×Dic13C2212yes—
30C2×C4×Dic13C2211yescharacteristic
31#88152—24no—
32C13×#95C2211yescharacteristic
33#88071C2212yes—
34#88071C2211yescharacteristic
35#88071C2212yes—
36#88071C2212yes—
37C24×C13C2312yes—
38C23×D13C2311yescharacteristic
39C2×D4×C13—24no—
40C2×D4×C13—22no—
41C22×C4×C13C2312yes—
42C22×C4×C13C2311yescharacteristic
43C22×C4×C13C2311yescharacteristic
44C22×C4×C13C2311yescharacteristic
45C2×C22⋊D13—24no—
46C2×C22⋊D13—24no—
47C2×C22⋊D13—42no—
48C22×Dic13—24no—
49C22×Dic13—42no—
50C22×Dic13—42no—
51C22×Dic13C2311yescharacteristic
52C22×Dic13C2312yes—
53C22×Dic13C2311yescharacteristic
54C22×Dic13C2311yescharacteristic
55C22×Dic13C2312yes—
56C13×C4⋊C4—22no—
57C13×C22⋊C4—24no—
58C13×C22⋊C4—42no—
59C22⋊Dic13—24no—
60C22⋊Dic13—24no—
61#6103—22no—
62#6103—22no—
63#6103—22no—
64#6103—42no—
65C4⋊Dic13—22no—
66C4⋊Dic13—22no—
67#6101—22no—
68#6101—42no—
69C4×Dic13—24no—
70C4×Dic13D414yescomplemented
71#2603—131nomaximal, Sylow
72C23×C13—22no—
73C23×C13—22no—
74C23×C13—22no—
75C23×C13—22no—
76C23×C13—22no—
77C23×C13—22no—
78C23×C13#4114yes—
79C23×C13C2411yescharacteristic
80C22×D13—21no—
81C22×D13—22no—
82C22×D13—22no—
83C22×D13—21no—
84C22×D13—21no—
85D4×C13—28no—
86C2×C4×C13—22no—
87C2×C4×C13—21no—
88C2×C4×C13—21no—
89C2×C4×C13—22no—
90C2×C4×C13—22no—
91C2×C4×C13—22no—
92C2×C4×C13—21no—
93C2×C4×C13—22no—
94C2×C4×C13—21no—
95C2×C4×C13C2×D412yes—
96C22⋊D13—48no—
97C2×Dic13—22no—
98C2×Dic13—22no—
99C2×Dic13—22no—
100C2×Dic13—21no—
101C2×Dic13—21no—
102C2×Dic13—21no—
103C2×Dic13—22no—
104C2×Dic13—22no—
105C2×Dic13—22no—
106C2×Dic13—22no—
107C2×Dic13—48no—
108C2×Dic13C2×D412yes—
109C2×Dic13C2×D412yes—
110C2×Dic13#4114yes—
111C2×#126—131no—
112C2×C4×D4—131no—
113#398—131no—
114#397—131no—
115#394D1311yescharacteristic, complemented
116#392—131no—
117#390—132no—
118#388—132no—
119#386—132no—
120#385—132no—
121#376—131no—
122C22×C13—24no—
123C22×C13—24no—
124C22×C13—24no—
125C22×C13—42no—
126C22×C13—42no—
127C22×C13—42no—
128C22×C13—42no—
129C22×C13C22×D411yescharacteristic
130C22×C13C2×#4112yes—
131C22×C13C2×#4112yes—
132C22×C13H(5,𝔽2)11yescharacteristic
133C22×C13H(5,𝔽2)11yescharacteristic
134C2×D13—41no—
135C2×D13—41no—
136C2×D13—41no—
137C2×D13—42no—
138C2×D13—42no—
139C4×C13—22no—
140C4×C13—41no—
141C4×C13—41no—
142C4×C13—42no—
143Dic13—22no—
144Dic13—22no—
145Dic13—24no—
146Dic13—41no—
147Dic13—42no—
148C22×D4—132no—
149C22×D4C2×D1311yescharacteristic
150C23×C4—132no—
151#126—264no—
152C4×D4—264no—
153C2×C4⋊C4—131no—
154C2×C4⋊C4—131no—
155C2×C4⋊C4—131no—
156C2×C4⋊C4—132no—
157C2×C4⋊C4C2×D1311yescharacteristic
158C2×C22⋊C4—132no—
159C2×C22⋊C4—132no—
160C2×C22⋊C4—131no—
161C2×C22⋊C4—131no—
162C2×C22⋊C4—131no—
163C2×C22⋊C4—132no—
164C2×C22⋊C4C2×D1312yes—
165C2×C22⋊C4C2×D1312yes—
166C2×C42—131no—
167C2×C42—132no—
168#95—132no—
169#95—131no—
170#95—132no—
171#95—132no—
172#95C2×D1311yescharacteristic
173C2×C13—44no—
174C2×C13#52511yescharacteristic
175C2×C13#53211yescharacteristic
176C2×C13#53511yescharacteristic
177C2×C13#55112yes—
178C2×C13#55312yes—
179D13—81no—
180C24—131no—
181C24C22×D1312yes—
182C2×D4—24no—
183C2×D4—22no—
184C2×D4—264no—
185C2×D4—264no—
186C2×D4—522no—
187C22×C4—132no—
188C22×C4—131no—
189C22×C4—131no—
190C22×C4—131no—
191C22×C4—132no—
192C22×C4—264no—
193C22×C4—522no—
194C22×C4—522no—
195C22×C4C22×D1312yes—
196C22×C4C22×D1311yescharacteristic
197C22×C4C22×D1311yescharacteristic
198C22×C4C22×D1311yescharacteristic
199C4⋊C4—22no—
200C4⋊C4—262no—
201C4⋊C4—262no—
202C4⋊C4—262no—
203C4⋊C4—522no—
204C22⋊C4—24no—
205C22⋊C4—42no—
206C22⋊C4—262no—
207C22⋊C4—262no—
208C22⋊C4—264no—
209C22⋊C4—264no—
210C22⋊C4—262no—
211C22⋊C4—522no—
212C42—134no—
213C42—264no—
214C13#260311yescharacteristic, complemented, Sylow
215C23—22no—
216C23—22no—
217C23—22no—
218C23—22no—
219C23—22no—
220C23—22no—
221C23—261no—
222C23—262no—
223C23—261no—
224C23—262no—
225C23—261no—
226C23#612914yes—
227C23C23×D1311yescharacteristic
228D4—28no—
229D4—528no—
230C2×C4—22no—
231C2×C4—21no—
232C2×C4—21no—
233C2×C4—22no—
234C2×C4—22no—
235C2×C4—21no—
236C2×C4—22no—
237C2×C4—22no—
238C2×C4—21no—
239C2×C4—132no—
240C2×C4—132no—
241C2×C4—134no—
242C2×C4—262no—
243C2×C4—261no—
244C2×C4—262no—
245C2×C4—262no—
246C2×C4—261no—
247C2×C4—261no—
248C2×C4—262no—
249C2×C4—262no—
250C2×C4—262no—
251C2×C4—262no—
252C2×C4—528no—
253C2×C4D4×D1312yes—
254C22—24no—
255C22—24no—
256C22—24no—
257C22—42no—
258C22—42no—
259C22—42no—
260C22—42no—
261C22—521no—
262C22—522no—
263C22—521no—
264C22—522no—
265C22—521no—
266C22C2×D4×D1311yescharacteristic
267C22C2×#612912yes—
268C22#8825111yescharacteristic
269C22#41×D1312yes—
270C22#8825611yescharacteristic
271C4—22no—
272C4—41no—
273C4—42no—
274C4—41no—
275C4—262no—
276C4—264no—
277C4—262no—
278C4—522no—
279C4—521no—
280C2—44no—
281C2—1041no—
282C2#1171929111yescharacteristic
283C2#1171930612yes—
284C2#1171931211yescharacteristic
285C2#1171936312yes—
286C2#1171937311yescharacteristic
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, cosocleC23×C13C24
FittingC13×#394C2
prime radical#11718884C2
hypercenter#394D13
hypocenterC13#2603
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ #394

Complements

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

NH ≅ G/Ntype
1. C2×D4×Dic13C2semidirect
2. C2×#88152C2semidirect
3. C13×#394C2semidirect
5. #11718644C2semidirect
6. #11718619C2semidirect
7. #11718618C2semidirect
8. #11718612C2semidirect
9. #11718607C2semidirect
10. #11718335C2semidirect
11. #11718309C2semidirect
70. C4×Dic13D4semidirect
115. #394D13semidirect
214. C13#2603semidirect

Maximal subgroups

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

subgroupindex
C2×D4×Dic132
C2×#881522
C13×#3942
#117188842
#117186442
#117186192
#117186182
#117186122
#117186072
#117183352
#117183092
#260313