Finite Group Databasebeta

← #13118245

Subgroups — #13118245

Order 1664.

610 conjugacy classes of subgroups; only the 153 normal subgroups are shown.

normal subgroups only

This group has 610 conjugacy classes of subgroups — too many to draw. Only its 153 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×#88183C211yesmaximal, characteristic
2C22×#6101C211yesmaximal, characteristic, complemented
3C2×#88140C211yesmaximal, characteristic
4C2×#88131C211yesmaximal, characteristic, complemented
5C13×#381C211yesmaximal, characteristic, complemented
6#11718619C211yesmaximal, characteristic
7#11718607C211yesmaximal, characteristic, complemented
8#11718337C212yesmaximal, complemented
9#11718330C212yesmaximal, complemented
10#11718318C212yesmaximal, complemented
11#11718308C212yesmaximal, complemented
12C23×C4×C13C2211yescharacteristic
13C22×C22⋊D13C2211yescharacteristic
14C23×Dic13C2211yescharacteristic
15C23×Dic13C2211yescharacteristic
16C2×C13×C22⋊C4C2211yescharacteristic
17C2×C13×C22⋊C4C2211yescharacteristic
18C2×C22⋊Dic13C2211yescharacteristic
19#88183—24no—
20C2×#6103C2211yescharacteristic
21C2×#6103C2211yescharacteristic
22C2×#6103C2212yes—
23C2×#6103C2212yes—
24C2×C4⋊Dic13C2211yescharacteristic
25C2×C4⋊Dic13C2211yescharacteristic
26C2×#6101—24no—
27C2×#6101C2212yes—
28C2×#6101C2212yes—
29C2×#6101C2212yes—
30C2×#6101C2212yes—
31C2×#6101C2212yes—
32C2×C4×Dic13C2212yes—
33#88140—24no—
34#88131—24no—
35C13×#95C2212yes—
36C13×#95C2212yes—
37#88071C2212yes—
38#88071C2212yes—
39C24×C13C2311yescharacteristic
40C23×D13C2311yescharacteristic
41C22×C4×C13—22no—
42C22×C4×C13—22no—
43C22×C4×C13—22no—
44C22×C4×C13C2311yescharacteristic
45C22×C4×C13C2312yes—
46C22×C4×C13C2312yes—
47C22×C4×C13C2311yescharacteristic
48C2×C22⋊D13—22no—
49C2×C22⋊D13—22no—
50C2×C22⋊D13—22no—
51C22×Dic13—22no—
52C22×Dic13—22no—
53C22×Dic13—22no—
54C22×Dic13—24no—
55C22×Dic13D414yes—
56C22×Dic13C2311yescharacteristic
57C22×Dic13C2312yes—
58C22×Dic13C2311yescharacteristic
59C22×Dic13C2311yescharacteristic
60C22×Dic13C2312yes—
61C13×C22⋊C4—22no—
62C13×C22⋊C4—22no—
63C22⋊Dic13D414yes—
64#6103—22no—
65#6103—22no—
66#6103—24no—
67#6103—24no—
68C4⋊Dic13—22no—
69C4⋊Dic13—22no—
70#6101—24no—
71#6101—24no—
72#6101—24no—
73#6101—24no—
74#6101—24no—
75C4×Dic13—24no—
76#2413—131nomaximal, Sylow
77C23×C13—22no—
78C23×C13—22no—
79C23×C13C2×D412yes—
80C23×C13C2×D412yes—
81C23×C13#4112yes—
82C23×C13C2411yescharacteristic
83C22×D13—21no—
84C22×D13—21no—
85C22×D13—22no—
86C22×D13—21no—
87C22×D13—22no—
88C2×C4×C13—22no—
89C2×C4×C13—22no—
90C2×C4×C13—22no—
91C2×C4×C13—21no—
92C2×C4×C13—21no—
93C2×C4×C13—22no—
94C2×C4×C13—22no—
95C2×C4×C13—22no—
96C2×C4×C13—22no—
97C2×C4×C13—22no—
98C2×C4×C13—44no—
99C22⋊D13—44no—
100C2×Dic13—28no—
101C2×Dic13—28no—
102C2×Dic13—21no—
103C2×Dic13—21no—
104C2×Dic13—22no—
105C2×Dic13—22no—
106C2×Dic13—21no—
107C2×Dic13—21no—
108C2×Dic13—22no—
109C2×Dic13—22no—
110C2×Dic13—21no—
111C2×Dic13—21no—
112C2×Dic13—21no—
113C2×Dic13C2×D414yes—
114C2×Dic13C2×D412yes—
115C2×Dic13C2×D412yes—
116C2×Dic13#4114yes—
117C2×#123—131no—
118C2×#123—131no—
119C2×#117—131no—
120C22×C4⋊C4—131no—
121#398—132no—
122#396—132no—
123#389—132no—
124#388—132no—
125#386—131no—
126#385—131no—
127#381D1311yescharacteristic, complemented
128C22×C13—22no—
129C22×C13—22no—
130C22×C13—24no—
131C22×C13—24no—
132C22×C13#12114yes—
133C22×C13C22×D411yescharacteristic
134C22×C13C22×D411yescharacteristic
135C22×C13C2×#4111yescharacteristic
136C22×C13C2×#4112yes—
137C22×C132−1+412yes—
138C2×D13—41no—
139C2×D13—41no—
140C2×D13—41no—
141C2×D13—42no—
142C2×D13—42no—
143C4×C13—42no—
144C4×C13—41no—
145C4×C13—41no—
146C4×C13—42no—
147Dic13—22no—
148Dic13—22no—
149Dic13—24no—
150Dic13—24no—
151Dic13—41no—
152C22×D4—131no—
153C23×C4—131no—
154C23×C4—131no—
155C23×C4C2×D1311yescharacteristic
156#123—264no—
157#123—264no—
158#117—264no—
159C2×C4⋊C4—132no—
160C2×C4⋊C4—132no—
161C2×C4⋊C4—132no—
162C2×C4⋊C4—132no—
163C2×C4⋊C4—131no—
164C2×C4⋊C4—131no—
165C2×C4⋊C4—132no—
166C2×C4⋊C4—264no—
167C2×C22⋊C4—131no—
168C2×C22⋊C4—131no—
169C2×C22⋊C4—132no—
170C2×C22⋊C4—131no—
171C2×C22⋊C4—132no—
172C2×C22⋊C4C2×D1311yescharacteristic
173C2×C22⋊C4C2×D1311yescharacteristic
174C2×C42—132no—
175#95—132no—
176#95—132no—
177#95C2×D1312yes—
178#95C2×D1312yes—
179C2×C13—24no—
180C2×C13C2×#12111yescharacteristic
181C2×C13#52511yescharacteristic
182C2×C13#53611yescharacteristic
183C2×C13#54712yes—
184C2×C13#55212yes—
185D13—81no—
186C24—131no—
187C24C22×D1311yescharacteristic
188C2×D4—262no—
189C2×D4—262no—
190C2×D4—262no—
191C22×C4—22no—
192C22×C4—22no—
193C22×C4—22no—
194C22×C4—134no—
195C22×C4—132no—
196C22×C4—132no—
197C22×C4—131no—
198C22×C4—131no—
199C22×C4—131no—
200C22×C4—264no—
201C22×C4—262no—
202C22×C4—262no—
203C22×C4—262no—
204C22×C4C22×D1311yescharacteristic
205C22×C4C22×D1312yes—
206C22×C4C22×D1311yescharacteristic
207C22×C4C22×D1312yes—
208C4⋊C4—264no—
209C4⋊C4—264no—
210C4⋊C4—264no—
211C4⋊C4—264no—
212C4⋊C4—262no—
213C4⋊C4—262no—
214C4⋊C4—264no—
215C22⋊C4—22no—
216C22⋊C4—22no—
217C22⋊C4—134no—
218C22⋊C4—262no—
219C22⋊C4—262no—
220C22⋊C4—264no—
221C22⋊C4—264no—
222C42—264no—
223C13#241311yescharacteristic, complemented, Sylow
224C23—22no—
225C23—22no—
226C23—261no—
227C23—261no—
228C23—261no—
229C23—262no—
230C23—262no—
231C23#612712yes—
232C23D4×D1312yes—
233C23D4×D1312yes—
234C23C23×D1311yescharacteristic
235D4—524no—
236C2×C4—22no—
237C2×C4—22no—
238C2×C4—21no—
239C2×C4—21no—
240C2×C4—22no—
241C2×C4—22no—
242C2×C4—22no—
243C2×C4—22no—
244C2×C4—22no—
245C2×C4—22no—
246C2×C4—44no—
247C2×C4—134no—
248C2×C4—132no—
249C2×C4—132no—
250C2×C4—134no—
251C2×C4—268no—
252C2×C4—268no—
253C2×C4—261no—
254C2×C4—261no—
255C2×C4—261no—
256C2×C4—261no—
257C2×C4—262no—
258C2×C4—262no—
259C2×C4—262no—
260C2×C4—262no—
261C2×C4—261no—
262C2×C4—261no—
263C2×C4—261no—
264C22—24no—
265C22—22no—
266C22—24no—
267C22—22no—
268C22—521no—
269C22—522no—
270C22—521no—
271C22—522no—
272C22—521no—
273C22#8813814yes—
274C22C2×#612711yescharacteristic
275C22C2×D4×D1311yescharacteristic
276C22C2×D4×D1311yescharacteristic
277C22#41×D1312yes—
278C22#8825712yes—
279C4—42no—
280C4—41no—
281C4—42no—
282C4—41no—
283C4—262no—
284C4—262no—
285C4—264no—
286C4—264no—
287C4—521no—
288C2—24no—
289C2—1041no—
290C2C2×#8813811yescharacteristic
291C2#1171923612yes—
292C2#1171935311yescharacteristic
293C2#1171936012yes—
294C2#1171936111yescharacteristic
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, cosocleC23×C13C24
FittingC13×#381C2
prime radicalC22×C22⋊D13C22
hypercenter#381D13
hypocenterC13#2413
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ #381

Complements

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

NH ≅ G/Ntype
2. C22×#6101C2semidirect
4. C2×#88131C2semidirect
5. C13×#381C2semidirect
7. #11718607C2semidirect
8. #11718337C2semidirect
9. #11718330C2semidirect
10. #11718318C2semidirect
11. #11718308C2semidirect
127. #381D13semidirect
223. C13#2413semidirect

Maximal subgroups

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

subgroupindex
C2×#881832
C22×#61012
C2×#881402
C2×#881312
C13×#3812
#117186192
#117186072
#117183372
#117183302
#117183182
#117183082
#241313