Finite Group Databasebeta

← #13120397

Subgroups — #13120397

Order 1664.

604 conjugacy classes of subgroups; only the 139 normal subgroups are shown.

normal subgroups only

This group has 604 conjugacy classes of subgroups — too many to draw. Only its 139 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×#88146C211yesmaximal, characteristic, complemented
3C13×#394C211yesmaximal, characteristic, complemented
4#11718884C211yesmaximal, characteristic
5#11718647C211yesmaximal, characteristic, complemented
6#11718619C212yesmaximal, complemented
7#11718617C212yesmaximal, complemented
8#11718612C212yesmaximal, complemented
9#11718611C212yesmaximal, complemented
10#11718338C211yesmaximal, characteristic, complemented
11#11718312C211yesmaximal, characteristic, complemented
12C22×D4×C13C2211yescharacteristic
13C22×C22⋊D13C2212yes—
14C23×Dic13C2212yes—
15C22×C4×D13C2211yescharacteristic
16C2×C13×C4⋊C4C2211yescharacteristic
17C2×C13×C22⋊C4C2212yes—
18C2×C13×C22⋊C4C2212yes—
19C2×C22⋊Dic13C2212yes—
20C2×C22⋊Dic13C2212yes—
21D4×Dic13—24no—
22C2×#6103C2211yescharacteristic
23C2×#6103C2211yescharacteristic
24C2×#6103C2212yes—
25C2×C4⋊Dic13C2211yescharacteristic
26C2×C4⋊Dic13C2211yescharacteristic
27C2×C4⋊Dic13C2212yes—
28C2×C4×Dic13C2211yescharacteristic
29C2×C4×Dic13C2211yescharacteristic
30#88146—24no—
31C13×#95C2211yescharacteristic
32#88071C2212yes—
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×Dic13C2312yes—
52C22×Dic13C2312yes—
53C22×Dic13C2311yescharacteristic
54C22×Dic13C2311yescharacteristic
55C22×Dic13C2311yescharacteristic
56C2×C4×D13—22no—
57C2×C4×D13—22no—
58C2×C4×D13—22no—
59C13×C4⋊C4—22no—
60C13×C22⋊C4—24no—
61C13×C22⋊C4—24no—
62C22⋊Dic13—24no—
63C22⋊Dic13—42no—
64#6103—22no—
65#6103—22no—
66#6103—42no—
67C4⋊Dic13—22no—
68C4⋊Dic13—22no—
69C4⋊Dic13—42no—
70C4×Dic13—22no—
71C4×Dic13D414yescomplemented
72#2598—131nomaximal, Sylow
73C23×C13—22no—
74C23×C13—22no—
75C23×C13—22no—
76C23×C13—22no—
77C23×C13—22no—
78C23×C13—22no—
79C23×C13#4114yes—
80C23×C13C2411yescharacteristic
81C22×D13—21no—
82C22×D13—21no—
83C22×D13—22no—
84C22×D13—22no—
85C22×D13#4112yes—
86D4×C13—28no—
87C2×C4×C13—21no—
88C2×C4×C13—21no—
89C2×C4×C13—22no—
90C2×C4×C13—21no—
91C2×C4×C13—22no—
92C2×C4×C13—22no—
93C2×C4×C13—22no—
94C2×C4×C13—22no—
95C2×C4×C13C2×D412yes—
96C2×C4×C13#4112yes—
97C22⋊D13—48no—
98C2×Dic13—21no—
99C2×Dic13—21no—
100C2×Dic13—22no—
101C2×Dic13—21no—
102C2×Dic13—22no—
103C2×Dic13—22no—
104C2×Dic13—22no—
105C2×Dic13—22no—
106C2×Dic13—22no—
107C2×Dic13—22no—
108C2×Dic13—22no—
109C2×Dic13—48no—
110C2×Dic13C2×D412yes—
111C2×Dic13C2×D412yes—
112C4×D13—28no—
113C2×C4×D4—131no—
114C2×#117—131no—
115#400—131no—
116#399—131no—
117#394D1311yescharacteristic, complemented
118#392—131no—
119#388—132no—
120#386—132no—
121#386—132no—
122#385—132no—
123#383—131no—
124C22×C13—24no—
125C22×C13—24no—
126C22×C13—24no—
127C22×C13—42no—
128C22×C13—42no—
129C22×C13—42no—
130C22×C13—42no—
131C22×C13C22×D411yescharacteristic
132C22×C13C2×#4112yes—
133C22×C13C2×#4111yescharacteristic
134C22×C13C2×#4111yescharacteristic
135C22×C13H(5,𝔽2)12yes—
136C2×D13—22no—
137C2×D13—24no—
138C2×D13—41no—
139C2×D13—41no—
140C2×D13—42no—
141C4×C13—22no—
142C4×C13—22no—
143C4×C13—41no—
144C4×C13—42no—
145Dic13—22no—
146Dic13—22no—
147Dic13—41no—
148Dic13—42no—
149Dic13—42no—
150C22×D4—132no—
151C22×D4C2×D1311yescharacteristic
152C23×C4—132no—
153C23×C4—131no—
154C4×D4—264no—
155#117—264no—
156C2×C4⋊C4—131no—
157C2×C4⋊C4—131no—
158C2×C4⋊C4—132no—
159C2×C4⋊C4C2×D1311yescharacteristic
160C2×C22⋊C4—132no—
161C2×C22⋊C4—131no—
162C2×C22⋊C4—131no—
163C2×C22⋊C4—132no—
164C2×C22⋊C4—132no—
165C2×C22⋊C4C2×D1312yes—
166C2×C22⋊C4C2×D1312yes—
167C2×C42—131no—
168C2×C42—131no—
169#95—132no—
170#95—132no—
171#95—131no—
172#95—132no—
173#95—132no—
174#95C2×D1311yescharacteristic
175C2×C13—44no—
176C2×C13#52511yescharacteristic
177C2×C13#52511yescharacteristic
178C2×C13#53511yescharacteristic
179C2×C13#55112yes—
180C2×C13#55312yes—
181D13—42no—
182C24—131no—
183C24C22×D1312yes—
184C2×D4—24no—
185C2×D4—22no—
186C2×D4—264no—
187C2×D4—264no—
188C2×D4—522no—
189C22×C4—131no—
190C22×C4—131no—
191C22×C4—132no—
192C22×C4—132no—
193C22×C4—131no—
194C22×C4—262no—
195C22×C4—262no—
196C22×C4—264no—
197C22×C4—262no—
198C22×C4—522no—
199C22×C4—522no—
200C22×C4C22×D1312yes—
201C22×C4C22×D1311yescharacteristic
202C22×C4C22×D1311yescharacteristic
203C22×C4C22×D1311yescharacteristic
204C4⋊C4—22no—
205C4⋊C4—262no—
206C4⋊C4—262no—
207C4⋊C4—522no—
208C22⋊C4—24no—
209C22⋊C4—24no—
210C22⋊C4—262no—
211C22⋊C4—264no—
212C22⋊C4—262no—
213C22⋊C4—522no—
214C22⋊C4—522no—
215C42—134no—
216C42—262no—
217C13#259811yescharacteristic, complemented, Sylow
218C23—22no—
219C23—22no—
220C23—22no—
221C23—22no—
222C23—22no—
223C23—22no—
224C23—132no—
225C23—261no—
226C23—261no—
227C23—262no—
228C23—262no—
229C23#612914yes—
230C23C23×D1311yescharacteristic
231D4—28no—
232D4—528no—
233C2×C4—21no—
234C2×C4—22no—
235C2×C4—21no—
236C2×C4—21no—
237C2×C4—22no—
238C2×C4—22no—
239C2×C4—22no—
240C2×C4—22no—
241C2×C4—132no—
242C2×C4—132no—
243C2×C4—268no—
244C2×C4—261no—
245C2×C4—261no—
246C2×C4—262no—
247C2×C4—261no—
248C2×C4—262no—
249C2×C4—262no—
250C2×C4—262no—
251C2×C4—262no—
252C2×C4—262no—
253C2×C4—262no—
254C2×C4—262no—
255C2×C4—528no—
256C2×C4D4×D1312yes—
257C2×C4#612912yes—
258C22—24no—
259C22—24no—
260C22—24no—
261C22—42no—
262C22—42no—
263C22—42no—
264C22—42no—
265C22—262no—
266C22—264no—
267C22—521no—
268C22—522no—
269C22—521no—
270C22C2×D4×D1311yescharacteristic
271C22C2×#612912yes—
272C22C2×#612911yescharacteristic
273C22#41×D1311yescharacteristic
274C22#8825612yes—
275C4—22no—
276C4—22no—
277C4—41no—
278C4—42no—
279C4—262no—
280C4—262no—
281C4—522no—
282C4—521no—
283C4—522no—
284C2—44no—
285C2—522no—
286C2#1171929111yescharacteristic
287C2#1171931111yescharacteristic
288C2#1171932312yes—
289C2#1171936312yes—
290C2#1171937911yescharacteristic
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, cosocleC23×C13C24
FittingC13×#394C2
prime radical#11718884C2
hypercenter#394D13
hypocenterC13#2598
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×#88146C2semidirect
3. C13×#394C2semidirect
5. #11718647C2semidirect
6. #11718619C2semidirect
7. #11718617C2semidirect
8. #11718612C2semidirect
9. #11718611C2semidirect
10. #11718338C2semidirect
11. #11718312C2semidirect
71. C4×Dic13D4semidirect
117. #394D13semidirect
217. C13#2598semidirect

Maximal subgroups

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

subgroupindex
C2×D4×Dic132
C2×#881462
C13×#3942
#117188842
#117186472
#117186192
#117186172
#117186122
#117186112
#117183382
#117183122
#259813