Finite Group Databasebeta

← #13120579

Subgroups — #13120579

Order 1664.

632 conjugacy classes of subgroups; only the 143 normal subgroups are shown.

normal subgroups only

This group has 632 conjugacy classes of subgroups — too many to draw. Only its 143 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×#88149C211yesmaximal, characteristic
2C2×#88148C212yesmaximal, complemented
3C2×C4⋊C4×D13C211yesmaximal, characteristic, complemented
4C13×#398C211yesmaximal, characteristic, complemented
5#11718655C212yesmaximal, complemented
6#11718652C211yesmaximal, characteristic, complemented
7#11718641C211yesmaximal, characteristic, complemented
8#11718337C212yesmaximal, complemented
9#11718333C211yesmaximal, characteristic, complemented
10#11718328C211yesmaximal, characteristic, complemented
11#11718326C212yesmaximal, complemented
12C22×D52C2212yes—
13C22×D52C2211yescharacteristic
14C22×C4×D13C2211yescharacteristic
15C22×C4×D13C2211yescharacteristic
16C22×C4×D13C2211yescharacteristic
17C2×C13×C4⋊C4C2211yescharacteristic
18C2×C13×C4⋊C4C2212yes—
19C2×C13×C4⋊C4C2211yescharacteristic
20C2×#6103C2212yes—
21C2×#6103C2212yes—
22C2×#6103C2212yes—
23C2×#6103C2212yes—
24C2×#6103C2212yes—
25C2×#6103C2212yes—
26C2×C4⋊Dic13C2211yescharacteristic
27C2×#6101C2211yescharacteristic
28C2×#6101C2211yescharacteristic
29C2×#6101C2212yes—
30C2×#6101C2212yes—
31#88149—24no—
32#88148—28no—
33C4⋊C4×D13—24no—
34C13×#95C2212yes—
35C13×#95C2211yescharacteristic
36#88071C2212yes—
37#88071C2211yescharacteristic
38C23×D13C2312yes—
39C23×D13C2311yescharacteristic
40C22×C4×C13C2312yes—
41C22×C4×C13C2312yes—
42C22×C4×C13C2311yescharacteristic
43C22×C4×C13C2311yescharacteristic
44C22×C4×C13C2311yescharacteristic
45C22×Dic13C2312yes—
46C22×Dic13C2311yescharacteristic
47C22×Dic13C2311yescharacteristic
48C22×Dic13C2311yescharacteristic
49C2×D52—24no—
50C2×D52—24no—
51C2×D52—24no—
52C2×D52—22no—
53C2×D52—42no—
54C2×C4×D13—22no—
55C2×C4×D13—22no—
56C2×C4×D13—22no—
57C2×C4×D13—42no—
58C2×C4×D13—42no—
59C2×C4×D13D414yes—
60C2×C4×D13D414yescomplemented
61C13×C4⋊C4—22no—
62C13×C4⋊C4—24no—
63C13×C4⋊C4—22no—
64#6103—24no—
65#6103—24no—
66#6103—24no—
67#6103—24no—
68#6103—42no—
69#6103—42no—
70C4⋊Dic13—22no—
71#6101—22no—
72#6101—22no—
73#6101—24no—
74#6101—42no—
75#2618—131nomaximal, Sylow
76C23×C13C2411yescharacteristic
77C22×D13—22no—
78C22×D13—22no—
79C22×D13—22no—
80C22×D13—22no—
81C22×D13—22no—
82C22×D13—22no—
83C22×D13—22no—
84C22×D13—22no—
85C22×D13—22no—
86C22×D13C2×D412yes—
87C22×D13C2×D412yes—
88C22×D13#4112yes—
89C2×C4×C13—21no—
90C2×C4×C13—21no—
91C2×C4×C13—22no—
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—22no—
99C2×C4×C13—22no—
100C2×C4×C13C2×D412yes—
101C2×C4×C13C2×D412yes—
102C2×Dic13—21no—
103C2×Dic13—21no—
104C2×Dic13—22no—
105C2×Dic13—21no—
106C2×Dic13—22no—
107C2×Dic13—22no—
108C2×Dic13—22no—
109C2×Dic13—22no—
110C2×Dic13C2×D412yes—
111C2×Dic13C2×D412yes—
112D52—44no—
113D52—48no—
114C4×D13—28no—
115C4×D13—44no—
116C4×D13—44no—
117C2×#123—132no—
118C2×#121—131no—
119C22×C4⋊C4—131no—
120#398—131no—
121#398D1311yescharacteristic, complemented
122#396—132no—
123#396—132no—
124#394—131no—
125#394—131no—
126#386—132no—
127#380—131no—
128C22×C13C22×D411yescharacteristic
129C22×C13C22×D411yescharacteristic
130C22×C13C2×#4111yescharacteristic
131C22×C13H(5,𝔽2)12yes—
132C22×C132−1+412yes—
133C2×D13—22no—
134C2×D13—22no—
135C2×D13—24no—
136C2×D13—24no—
137C2×D13—42no—
138C2×D13—42no—
139C2×D13—42no—
140C2×D13—42no—
141C2×D13—42no—
142C2×D13—42no—
143C2×D13—42no—
144C2×D13#12114yes—
145C4×C13—22no—
146C4×C13—22no—
147C4×C13—42no—
148C4×C13—41no—
149C4×C13—42no—
150Dic13—22no—
151Dic13—22no—
152Dic13—41no—
153Dic13—42no—
154C22×D4—132no—
155C22×D4—131no—
156C23×C4—131no—
157C23×C4—131no—
158C23×C4—131no—
159#123—268no—
160#121—264no—
161C2×C4⋊C4—131no—
162C2×C4⋊C4—131no—
163C2×C4⋊C4—131no—
164C2×C4⋊C4—132no—
165C2×C4⋊C4—132no—
166C2×C4⋊C4—264no—
167C2×C4⋊C4C2×D1311yescharacteristic
168C2×C4⋊C4C2×D1311yescharacteristic
169C2×C4⋊C4C2×D1312yes—
170C2×C22⋊C4—132no—
171C2×C22⋊C4—132no—
172C2×C22⋊C4—132no—
173C2×C22⋊C4—132no—
174C2×C22⋊C4—132no—
175C2×C22⋊C4—132no—
176#95—131no—
177#95—132no—
178#95C2×D1311yescharacteristic
179#95C2×D1312yes—
180C2×C13C2×#12111yescharacteristic
181C2×C13#53411yescharacteristic
182C2×C13#53611yescharacteristic
183C2×C13#53712yes—
184C2×C13#53912yes—
185D13—24no—
186D13—82no—
187C24—131no—
188C24—132no—
189C2×D4—264no—
190C2×D4—264no—
191C2×D4—264no—
192C2×D4—262no—
193C2×D4—522no—
194C22×C4—131no—
195C22×C4—131no—
196C22×C4—134no—
197C22×C4—134no—
198C22×C4—132no—
199C22×C4—131no—
200C22×C4—262no—
201C22×C4—262no—
202C22×C4—262no—
203C22×C4—522no—
204C22×C4—522no—
205C22×C4C22×D1312yes—
206C22×C4C22×D1312yes—
207C22×C4C22×D1311yescharacteristic
208C22×C4C22×D1311yescharacteristic
209C22×C4C22×D1311yescharacteristic
210C4⋊C4—22no—
211C4⋊C4—22no—
212C4⋊C4—24no—
213C4⋊C4—262no—
214C4⋊C4—262no—
215C4⋊C4—264no—
216C4⋊C4—262no—
217C4⋊C4—522no—
218C22⋊C4—264no—
219C22⋊C4—264no—
220C22⋊C4—264no—
221C22⋊C4—264no—
222C22⋊C4—522no—
223C22⋊C4—522no—
224C13#261811yescharacteristic, complemented, Sylow
225C23—132no—
226C23—132no—
227C23—132no—
228C23—262no—
229C23—262no—
230C23—262no—
231C23—262no—
232C23—262no—
233C23—262no—
234C23—262no—
235C23—262no—
236C23—262no—
237C23C23×D1311yescharacteristic
238D4—524no—
239D4—528no—
240C2×C4—21no—
241C2×C4—21no—
242C2×C4—22no—
243C2×C4—22no—
244C2×C4—22no—
245C2×C4—21no—
246C2×C4—22no—
247C2×C4—22no—
248C2×C4—22no—
249C2×C4—22no—
250C2×C4—22no—
251C2×C4—132no—
252C2×C4—132no—
253C2×C4—268no—
254C2×C4—261no—
255C2×C4—261no—
256C2×C4—262no—
257C2×C4—262no—
258C2×C4—261no—
259C2×C4—262no—
260C2×C4—262no—
261C2×C4—262no—
262C2×C4—524no—
263C2×C4—524no—
264C2×C4D4×D1312yes—
265C2×C4D4×D1312yes—
266C22—134no—
267C22—262no—
268C22—264no—
269C22—262no—
270C22—264no—
271C22—522no—
272C22—522no—
273C22—522no—
274C22—522no—
275C22—522no—
276C22—522no—
277C22—522no—
278C22C2×D4×D1311yescharacteristic
279C22C2×D4×D1311yescharacteristic
280C22#8825412yes—
281C22#41×D1311yescharacteristic
282C22#8825612yes—
283C4—22no—
284C4—22no—
285C4—42no—
286C4—42no—
287C4—41no—
288C4—262no—
289C4—262no—
290C4—522no—
291C4—521no—
292C2—264no—
293C2—1042no—
294C2D13×#12111yescharacteristic
295C2#1171933412yes—
296C2#1171935811yescharacteristic
297C2#1171939712yes—
298C2#1171942911yescharacteristic
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, cosocleC23×C13C24
FittingC13×#398C2
prime radicalC2×#88149C2
hypercenter#398D13
hypocenterC13#2618
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ #398

Complements

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

NH ≅ G/Ntype
2. C2×#88148C2semidirect
3. C2×C4⋊C4×D13C2semidirect
4. C13×#398C2semidirect
5. #11718655C2semidirect
6. #11718652C2semidirect
7. #11718641C2semidirect
8. #11718337C2semidirect
9. #11718333C2semidirect
10. #11718328C2semidirect
11. #11718326C2semidirect
60. C2×C4×D13D4semidirect
121. #398D13semidirect
224. C13#2618semidirect

Maximal subgroups

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

subgroupindex
C2×#881492
C2×#881482
C2×C4⋊C4×D132
C13×#3982
#117186552
#117186522
#117186412
#117183372
#117183332
#117183282
#117183262
#261813