Finite Group Databasebeta

← #13119143

Subgroups — #13119143

Order 1664.

624 conjugacy classes of subgroups; only the 157 normal subgroups are shown.

normal subgroups only

This group has 624 conjugacy classes of subgroups — too many to draw. Only its 157 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×#88135C211yesmaximal, characteristic
5C13×#381C211yesmaximal, characteristic, complemented
6#11718604C211yesmaximal, characteristic, complemented
7#11718603C211yesmaximal, characteristic, complemented
8#11718336C212yesmaximal, complemented
9#11718328C212yesmaximal, complemented
10#11718318C212yesmaximal, complemented
11#11718308C212yesmaximal, complemented
12C23×C4×C13C2211yescharacteristic
13C22×C22⋊D13C2211yescharacteristic
14C23×Dic13C2211yescharacteristic
15C23×Dic13C2211yescharacteristic
16C22×C4×D13C2211yescharacteristic
17C2×C13×C22⋊C4C2211yescharacteristic
18C2×C13×C22⋊C4C2211yescharacteristic
19C2×C22⋊Dic13C2211yescharacteristic
20#88183—24no—
21C2×#6103C2211yescharacteristic
22C2×#6103C2212yes—
23C2×#6103C2212yes—
24C2×C4⋊Dic13C2212yes—
25C2×#6101—24no—
26C2×#6101C2211yescharacteristic
27C2×#6101C2212yes—
28C2×#6101C2212yes—
29C2×#6101C2212yes—
30C2×#6101C2212yes—
31C2×C4×Dic13C2211yescharacteristic
32#88140—24no—
33#88135—24no—
34C13×#95C2212yes—
35C13×#95C2212yes—
36#88071C2212yes—
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×C13C2311yescharacteristic
46C22×C4×C13C2312yes—
47C22×C4×C13C2312yes—
48C2×C22⋊D13—22no—
49C2×C22⋊D13—22no—
50C2×C22⋊D13D414yes—
51C22×Dic13—24no—
52C22×Dic13—22no—
53C22×Dic13—22no—
54C22×Dic13—22no—
55C22×Dic13D414yes—
56C22×Dic13C2312yes—
57C22×Dic13C2312yes—
58C22×Dic13C2311yescharacteristic
59C22×Dic13C2311yescharacteristic
60C22×Dic13C2311yescharacteristic
61C2×C4×D13—22no—
62C2×C4×D13—24no—
63C13×C22⋊C4—22no—
64C13×C22⋊C4—22no—
65C22⋊Dic13—22no—
66#6103—24no—
67#6103—24no—
68#6103—22no—
69C4⋊Dic13—24no—
70#6101—22no—
71#6101—24no—
72#6101—24no—
73#6101—24no—
74#6101—24no—
75C4×Dic13—22no—
76#2486—131nomaximal, Sylow
77C23×C13—22no—
78C23×C13—22no—
79C23×C13C2×D412yes—
80C23×C13C2×D412yes—
81C23×C13#4112yes—
82C23×C13C2411yescharacteristic
83C22×D13—21no—
84C22×D13—22no—
85C22×D13—21no—
86C22×D13—22no—
87C22×D13C2×D412yes—
88C2×C4×C13—21no—
89C2×C4×C13—22no—
90C2×C4×C13—22no—
91C2×C4×C13—21no—
92C2×C4×C13—22no—
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—28no—
100C2×Dic13—21no—
101C2×Dic13—22no—
102C2×Dic13—21no—
103C2×Dic13—28no—
104C2×Dic13—22no—
105C2×Dic13—22no—
106C2×Dic13—22no—
107C2×Dic13—22no—
108C2×Dic13—22no—
109C2×Dic13—22no—
110C2×Dic13—44no—
111C2×Dic13C2×D412yes—
112C2×Dic13C2×D412yes—
113C2×Dic13C2×D412yes—
114C2×Dic13#4114yes—
115C4×D13—44no—
116C2×#123—131no—
117C2×#123—131no—
118C2×C4×D4—131no—
119C22×C4⋊C4—131no—
120#398—132no—
121#397—132no—
122#389—132no—
123#381—131no—
124#381D1311yescharacteristic, complemented
125#380—131no—
126#380—132no—
127C22×C13—22no—
128C22×C13—22no—
129C22×C13—24no—
130C22×C13—24no—
131C22×C13#12114yes—
132C22×C13C22×D411yescharacteristic
133C22×C13C22×D411yescharacteristic
134C22×C13C2×#4111yescharacteristic
135C22×C13C2×#4112yes—
136C22×C132−1+412yes—
137C2×D13—22no—
138C2×D13—24no—
139C2×D13—41no—
140C2×D13—41no—
141C2×D13—42no—
142C4×C13—42no—
143C4×C13—41no—
144C4×C13—41no—
145C4×C13—42no—
146Dic13—22no—
147Dic13—22no—
148Dic13—42no—
149Dic13—42no—
150Dic13#12314yescomplemented
151C22×D4—131no—
152C23×C4—131no—
153C23×C4—131no—
154C23×C4—131no—
155C23×C4C2×D1311yescharacteristic
156#123—264no—
157#123—264no—
158C4×D4—264no—
159C2×C4⋊C4—132no—
160C2×C4⋊C4—132no—
161C2×C4⋊C4—131no—
162C2×C4⋊C4—132no—
163C2×C4⋊C4—132no—
164C2×C4⋊C4—132no—
165C2×C4⋊C4—264no—
166C2×C22⋊C4—131no—
167C2×C22⋊C4—131no—
168C2×C22⋊C4—132no—
169C2×C22⋊C4—132no—
170C2×C22⋊C4C2×D1311yescharacteristic
171C2×C22⋊C4C2×D1311yescharacteristic
172C2×C42—131no—
173#95—132no—
174#95—132no—
175#95—132no—
176#95C2×D1312yes—
177#95C2×D1312yes—
178C2×C13—24no—
179C2×C13C2×#12111yescharacteristic
180C2×C13C2×#12311yescharacteristic
181C2×C13#53611yescharacteristic
182C2×C13#54712yes—
183C2×C13#55212yes—
184D13—42no—
185C24—131no—
186C24C22×D1311yescharacteristic
187C2×D4—134no—
188C2×D4—262no—
189C2×D4—262no—
190C22×C4—22no—
191C22×C4—22no—
192C22×C4—22no—
193C22×C4—131no—
194C22×C4—134no—
195C22×C4—131no—
196C22×C4—131no—
197C22×C4—132no—
198C22×C4—132no—
199C22×C4—262no—
200C22×C4—264no—
201C22×C4—264no—
202C22×C4—262no—
203C22×C4—262no—
204C22×C4—262no—
205C22×C4C22×D1311yescharacteristic
206C22×C4C22×D1311yescharacteristic
207C22×C4C22×D1312yes—
208C22×C4C22×D1312yes—
209C4⋊C4—264no—
210C4⋊C4—264no—
211C4⋊C4—262no—
212C4⋊C4—264no—
213C4⋊C4—264no—
214C4⋊C4—264no—
215C22⋊C4—22no—
216C22⋊C4—22no—
217C22⋊C4—262no—
218C22⋊C4—264no—
219C22⋊C4—264no—
220C22⋊C4—262no—
221C42—262no—
222C13#248611yescharacteristic, complemented, Sylow
223C23—22no—
224C23—22no—
225C23—132no—
226C23—261no—
227C23—261no—
228C23—262no—
229C23—262no—
230C23#612712yes—
231C23D4×D1312yes—
232C23D4×D1312yes—
233C23C23×D1311yescharacteristic
234D4—268no—
235C2×C4—22no—
236C2×C4—21no—
237C2×C4—22no—
238C2×C4—21no—
239C2×C4—22no—
240C2×C4—22no—
241C2×C4—22no—
242C2×C4—22no—
243C2×C4—22no—
244C2×C4—22no—
245C2×C4—44no—
246C2×C4—132no—
247C2×C4—134no—
248C2×C4—132no—
249C2×C4—132no—
250C2×C4—268no—
251C2×C4—261no—
252C2×C4—261no—
253C2×C4—262no—
254C2×C4—262no—
255C2×C4—262no—
256C2×C4—262no—
257C2×C4—262no—
258C2×C4—262no—
259C2×C4—262no—
260C2×C4—524no—
261C2×C4—524no—
262C22—24no—
263C22—22no—
264C22—22no—
265C22—24no—
266C22—262no—
267C22—264no—
268C22—522no—
269C22—521no—
270C22—521no—
271C22#8813814yes—
272C22C2×#612711yescharacteristic
273C22C2×D4×D1311yescharacteristic
274C22C2×D4×D1311yescharacteristic
275C22#41×D1312yes—
276C22#8825712yes—
277C4—42no—
278C4—41no—
279C4—41no—
280C4—42no—
281C4—134no—
282C4—262no—
283C4—262no—
284C4—522no—
285C4—522no—
286C2—24no—
287C2—522no—
288C2C2×#8813811yescharacteristic
289C2#1171923612yes—
290C2#1171935311yescharacteristic
291C2D13×#12311yescharacteristic
292C2#1171936012yes—
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, cosocleC23×C13C24
FittingC13×#381C2
prime radicalC22×C22⋊D13C22
hypercenter#381D13
hypocenterC13#2486
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ #381

Complements

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

NH ≅ G/Ntype
2. C22×#6101C2semidirect
5. C13×#381C2semidirect
6. #11718604C2semidirect
7. #11718603C2semidirect
8. #11718336C2semidirect
9. #11718328C2semidirect
10. #11718318C2semidirect
11. #11718308C2semidirect
124. #381D13semidirect
150. Dic13#123semidirect
222. C13#2486semidirect

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×#881352
C13×#3812
#117186042
#117186032
#117183362
#117183282
#117183182
#117183082
#248613