Finite Group Databasebeta

← #13119134

Subgroups — #13119134

Order 1664.

540 conjugacy classes of subgroups.

The subgroup lattice has 314 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×C22⋊D13C211yesmaximal, characteristic
2C2×#88180C211yesmaximal, characteristic, complemented
3C13×#380C211yesmaximal, characteristic, complemented
4#11718648C211yesmaximal, characteristic, complemented
5#11718648C211yesmaximal, characteristic, complemented
6#11718646C211yesmaximal, characteristic, complemented
7#11718646C211yesmaximal, characteristic, complemented
8#11718622C212yesmaximal
9#11718614C212yesmaximal, complemented
10#11718331C212yesmaximal, complemented
11#11718314C212yesmaximal, complemented
12C23×C4×C13C2211yescharacteristic
13C22×C22⋊D13C2211yescharacteristic
14C22×C4×D13C2211yescharacteristic
15C2×C13×C4⋊C4C2211yescharacteristic
16C2×C13×C4⋊C4C2211yescharacteristic
17C2×C13×C22⋊C4C2212yes—
18C2×C22⋊Dic13C2212yes—
19C2×C22⋊Dic13C2211yescharacteristic
20C4×C22⋊D13—24no—
21C2×#6103C2211yescharacteristic
22C2×#6103C2212yes—
23C2×#6103C2212yes—
24#88180—24no—
25C2×C4⋊Dic13C2211yescharacteristic
26C2×C4⋊Dic13C2211yescharacteristic
27C2×C4⋊Dic13C2212yes—
28C2×C4⋊Dic13C2212yes—
29C2×#6101C2211yescharacteristic
30C2×C4×Dic13C2212yes—
31C2×C4×Dic13C2211yescharacteristic
32C13×#95C2212yes—
33#88071C2212yes—
34#88071C2212yes—
35#88071C2212yes—
36#88071C2212yes—
37C24×C13C2311yescharacteristic
38C23×D13C2311yescharacteristic
39C22×C4×C13—22no—
40C22×C4×C13—22no—
41C22×C4×C13D414yes—
42C22×C4×C13C2312yes—
43C22×C4×C13C2312yes—
44C22×C4×C13C2311yescharacteristic
45C22×C4×C13C2311yescharacteristic
46C2×C22⋊D13—22no—
47C2×C22⋊D13—22no—
48C2×C22⋊D13—22no—
49C22×Dic13C2311yescharacteristic
50C22×Dic13C2312yes—
51C22×Dic13C2312yes—
52C22×Dic13C2311yescharacteristic
53C22×Dic13C2311yescharacteristic
54C2×C4×D13—22no—
55C2×C4×D13—22no—
56C2×C4×D13—22no—
57C13×C4⋊C4—22no—
58C13×C4⋊C4—22no—
59C13×C22⋊C4—42no—
60C22⋊Dic13—24no—
61C22⋊Dic13—22no—
62#6103—24no—
63#6103—22no—
64#6103—42no—
65C4⋊Dic13—22no—
66C4⋊Dic13—22no—
67C4⋊Dic13—24no—
68C4⋊Dic13—42no—
69#6101—22no—
70C4×Dic13—24no—
71C4×Dic13—22no—
72#2485—131nomaximal, Sylow
73C23×C13—21no—
74C23×C13—21no—
75C23×C13—21no—
76C23×C13—21no—
77C23×C13—21no—
78C23×C13—21no—
79C23×C13C2×D412yes—
80C23×C13C2411yescharacteristic
81C22×D13—21no—
82C22×D13—21no—
83C22×D13—21no—
84C22×D13—21no—
85C22×D13—21no—
86C22×D13—21no—
87C22×D13#4112yes—
88C2×C4×C13—21no—
89C2×C4×C13—21no—
90C2×C4×C13—28no—
91C2×C4×C13—22no—
92C2×C4×C13—22no—
93C2×C4×C13—22no—
94C2×C4×C13—22no—
95C2×C4×C13—22no—
96C2×C4×C13—22no—
97C2×C4×C13C2×D412yes—
98C2×C4×C13C2×D412yes—
99C2×C4×C13#4112yes—
100C2×C4×C13#4112yes—
101C22⋊D13—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×Dic13—22no—
114C2×Dic13—22no—
115C2×Dic13—21no—
116C2×Dic13#4112yes—
117C4×D13—44no—
118C2×C4×D4—131no—
119C2×#117—131no—
120#397—132no—
121#394—132no—
122#389—131no—
123#389—131no—
124#388—132no—
125#387—132no—
126#380—131no—
127#380—131no—
128#380D1311yescharacteristic, complemented
129C22×C13—22no—
130C22×C13—22no—
131C22×C13—22no—
132C22×C13—41no—
133C22×C13—41no—
134C22×C13—41no—
135C22×C13—41no—
136C22×C13C22×D411yescharacteristic
137C22×C13C2×#4111yescharacteristic
138C22×C13C2×#4111yescharacteristic
139C22×C13C2×#4111yescharacteristic
140C22×C13C2×#4111yescharacteristic
141C22×C13H(5,𝔽2)11yescharacteristic
142C22×C132−1+411yescharacteristic
143C2×D13—22no—
144C2×D13—22no—
145C2×D13—22no—
146C2×D13—41no—
147C2×D13—41no—
148C2×D13—41no—
149C2×D13—41no—
150C4×C13—22no—
151C4×C13—42no—
152C4×C13—42no—
153C4×C13#12314yes—
154Dic13—22no—
155Dic13—41no—
156Dic13—42no—
157Dic13—42no—
158Dic13—41no—
159C22×D4—131no—
160C23×C4—131no—
161C23×C4C2×D1311yescharacteristic
162C4×D4—264no—
163#117—264no—
164C2×C4⋊C4—131no—
165C2×C4⋊C4—131no—
166C2×C4⋊C4—131no—
167C2×C4⋊C4—132no—
168C2×C4⋊C4—132no—
169C2×C4⋊C4C2×D1311yescharacteristic
170C2×C4⋊C4C2×D1311yescharacteristic
171C2×C22⋊C4—132no—
172C2×C22⋊C4—131no—
173C2×C22⋊C4—131no—
174C2×C22⋊C4—132no—
175C2×C22⋊C4—132no—
176C2×C22⋊C4C2×D1312yes—
177C2×C42—132no—
178C2×C42—131no—
179#95—132no—
180#95—132no—
181#95—132no—
182#95—132no—
183#95C2×D1312yes—
184C2×C13—42no—
185C2×C13C2×#12311yescharacteristic
186C2×C13#52511yescharacteristic
187C2×C13#53711yescharacteristic
188C2×C13#55211yescharacteristic
189C2×C13#55311yescharacteristic
190C2×C13#55511yescharacteristic
191C2×C13#55611yescharacteristic
192D13—42no—
193C24—131no—
194C24C22×D1311yescharacteristic
195C2×D4—262no—
196C2×D4—262no—
197C2×D4—262no—
198C22×C4—22no—
199C22×C4—22no—
200C22×C4—131no—
201C22×C4—131no—
202C22×C4—131no—
203C22×C4—132no—
204C22×C4—132no—
205C22×C4—262no—
206C22×C4—262no—
207C22×C4—262no—
208C22×C4D5214yes—
209C22×C4C22×D1312yes—
210C22×C4C22×D1312yes—
211C22×C4C22×D1311yescharacteristic
212C22×C4C22×D1311yescharacteristic
213C4⋊C4—22no—
214C4⋊C4—22no—
215C4⋊C4—264no—
216C4⋊C4—262no—
217C4⋊C4—262no—
218C4⋊C4—262no—
219C4⋊C4—522no—
220C22⋊C4—42no—
221C22⋊C4—264no—
222C22⋊C4—264no—
223C22⋊C4—262no—
224C22⋊C4—262no—
225C22⋊C4—522no—
226C42—264no—
227C42—262no—
228C13#248511yescharacteristic, complemented, Sylow
229C23—21no—
230C23—21no—
231C23—21no—
232C23—21no—
233C23—21no—
234C23—21no—
235C23—132no—
236C23—261no—
237C23—261no—
238C23—261no—
239C23—261no—
240C23—261no—
241C23—261no—
242C23C2×D5212yes—
243C23C23×D1311yescharacteristic
244D4—268no—
245C2×C4—21no—
246C2×C4—21no—
247C2×C4—28no—
248C2×C4—22no—
249C2×C4—22no—
250C2×C4—22no—
251C2×C4—22no—
252C2×C4—22no—
253C2×C4—22no—
254C2×C4—132no—
255C2×C4—261no—
256C2×C4—261no—
257C2×C4—261no—
258C2×C4—262no—
259C2×C4—262no—
260C2×C4—261no—
261C2×C4—261no—
262C2×C4—261no—
263C2×C4—262no—
264C2×C4—261no—
265C2×C4—261no—
266C2×C4—262no—
267C2×C4—262no—
268C2×C4—262no—
269C2×C4—524no—
270C2×C4C2×D5212yes—
271C2×C4C2×D5212yes—
272C2×C4#612912yes—
273C2×C4#612912yes—
274C22—22no—
275C22—22no—
276C22—22no—
277C22—41no—
278C22—41no—
279C22—41no—
280C22—41no—
281C22—262no—
282C22—262no—
283C22—262no—
284C22—521no—
285C22—521no—
286C22—521no—
287C22—521no—
288C22C22×D5211yescharacteristic
289C22C2×#612911yescharacteristic
290C22C2×#612911yescharacteristic
291C22#8825111yescharacteristic
292C22#8825411yescharacteristic
293C22#41×D1311yescharacteristic
294C22#41×D1311yescharacteristic
295C4—22no—
296C4—42no—
297C4—42no—
298C4—262no—
299C4—521no—
300C4—521no—
301C4—522no—
302C4—522no—
303C4#8814014yes—
304C2—42no—
305C2—522no—
306C2C2×#8814011yescharacteristic
307C2#1171921511yescharacteristic
308C2#1171922911yescharacteristic
309C2#1171931911yescharacteristic
310C2#1171932111yescharacteristic
311C2#1171934411yescharacteristic
312C2#1171934611yescharacteristic
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, cosocleC23×C13C24
FittingC13×#380C2
prime radicalC22×C22⋊D13C22
hypercenter#380D13
hypocenterC13#2485
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ #380

Complements

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

NH ≅ G/Ntype
2. C2×#88180C2semidirect
3. C13×#380C2semidirect
4. #11718648C2semidirect
5. #11718648C2semidirect
6. #11718646C2semidirect
7. #11718646C2semidirect
9. #11718614C2semidirect
10. #11718331C2semidirect
11. #11718314C2semidirect
128. #380D13semidirect
228. C13#2485semidirect

Maximal subgroups

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

subgroupindex
C2×C4×C22⋊D132
C2×#881802
C13×#3802
#117186482
#117186462
#117186222
#117186142
#117183312
#117183142
#248513