Finite Group Databasebeta

← #13118285

Subgroups — #13118285

Order 1664.

648 conjugacy classes of subgroups.

The subgroup lattice has 332 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#88151C211yesmaximal, characteristic, complemented
2C2×#88151C211yesmaximal, characteristic, complemented
3C2×C4⋊C4×D13C211yesmaximal, characteristic, complemented
4C2×C4×D52C211yesmaximal, characteristic
5C13×#389C211yesmaximal, characteristic, complemented
6#11718655C212yesmaximal, complemented
7#11718648C211yesmaximal, characteristic, complemented
8#11718648C212yesmaximal, complemented
9#11718590C211yesmaximal, characteristic, complemented
10#11718326C212yesmaximal
11#11718322C212yesmaximal, complemented
12C22×D52C2211yescharacteristic
13C22×C4×D13C2211yescharacteristic
14C22×C4×D13C2212yes—
15C22×C4×D13C2211yescharacteristic
16C22×Dic26C2211yescharacteristic
17C2×C13×C4⋊C4C2211yescharacteristic
18C2×C13×C4⋊C4C2212yes—
19C2×C13×C4⋊C4C2211yescharacteristic
20C2×C42×C13C2211yescharacteristic
21C2×#6103C2211yescharacteristic
22C2×#6103C2211yescharacteristic
23C2×#6103C2212yes—
24C2×#6103C2212yes—
25C2×#6103C2212yes—
26C2×C4⋊Dic13C2211yescharacteristic
27C2×C4⋊Dic13C2211yescharacteristic
28C2×C4⋊Dic13C2212yes—
29C2×C4⋊Dic13C2212yes—
30C2×#6101C2212yes—
31#88151—24no—
32#88151—24no—
33C4⋊C4×D13—24no—
34C4×D52—24no—
35C13×#95C2212yes—
36#88071C2212yes—
37#88071C2212yes—
38#88071C2212yes—
39C23×D13C2311yescharacteristic
40C23×D13C2311yescharacteristic
41C22×C4×C13C2311yescharacteristic
42C22×C4×C13C2312yes—
43C22×C4×C13C2312yes—
44C22×C4×C13C2311yescharacteristic
45C22×C4×C13C2311yescharacteristic
46C22×Dic13C2312yes—
47C22×Dic13C2311yescharacteristic
48C22×Dic13C2312yes—
49C22×Dic13C2311yescharacteristic
50C2×D52—22no—
51C2×D52—22no—
52C2×D52Q814yescomplemented
53C2×C4×D13—22no—
54C2×C4×D13—22no—
55C2×C4×D13—24no—
56C2×C4×D13—22no—
57C2×C4×D13—24no—
58C2×C4×D13—22no—
59C2×C4×D13—22no—
60C2×C4×D13—42no—
61C2×C4×D13D414yes—
62C2×Dic26—22no—
63C2×Dic26—22no—
64C2×Dic26—22no—
65C13×C4⋊C4—22no—
66C13×C4⋊C4—42no—
67C13×C4⋊C4D414yescomplemented
68C42×C13—22no—
69#6103—22no—
70#6103—24no—
71#6103—24no—
72#6103—22no—
73#6103—42no—
74C4⋊Dic13—22no—
75C4⋊Dic13—24no—
76C4⋊Dic13—22no—
77C4⋊Dic13—24no—
78#6101—24no—
79#2417—131nomaximal, Sylow
80C23×C13C2411yescharacteristic
81C22×D13—21no—
82C22×D13—21no—
83C22×D13—21no—
84C22×D13—21no—
85C22×D13—21no—
86C22×D13—21no—
87C22×D13—21no—
88C22×D13—21no—
89C22×D13—21no—
90C22×D13—21no—
91C22×D13C2×D412yes—
92C22×D13C2×Q812yes—
93C22×D13C2×Q812yes—
94C22×D13#4112yes—
95C2×C4×C13—21no—
96C2×C4×C13—22no—
97C2×C4×C13—21no—
98C2×C4×C13—22no—
99C2×C4×C13—22no—
100C2×C4×C13—21no—
101C2×C4×C13—22no—
102C2×C4×C13—21no—
103C2×C4×C13—21no—
104C2×C4×C13—22no—
105C2×C4×C13C2×D414yes—
106C2×C4×C13C2×D412yes—
107C2×C4×C13C2×D412yes—
108C2×C4×C13C2×Q812yes—
109C2×C4×C13#4112yes—
110C2×Dic13—21no—
111C2×Dic13—21no—
112C2×Dic13—22no—
113C2×Dic13—21no—
114C2×Dic13—22no—
115C2×Dic13—22no—
116C2×Dic13—21no—
117C2×Dic13—22no—
118C2×Dic13—21no—
119C2×Dic13—22no—
120C2×Dic13—22no—
121C2×Dic13C2×D412yes—
122D52—28no—
123C4×D13—28no—
124C4×D13—48no—
125C4×D13—44no—
126Dic26—44no—
127C2×C22⋊Q8—131no—
128C2×C22⋊Q8—131no—
129C2×C4×D4—131no—
130C22×C4⋊C4—131no—
131#398—132no—
132#396—132no—
133#391—131no—
134#389D1311yescharacteristic, complemented
135#386—132no—
136#380—131no—
137#380—132no—
138C22×C13C22×D411yescharacteristic
139C22×C13C22×D411yescharacteristic
140C22×C13C22×Q811yescharacteristic
141C22×C13C2×#4111yescharacteristic
142C22×C13C2×#4111yescharacteristic
143C22×C13H(5,𝔽2)11yescharacteristic
144C22×C132−1+411yescharacteristic
145C2×D13—22no—
146C2×D13—22no—
147C2×D13—22no—
148C2×D13—22no—
149C2×D13—22no—
150C2×D13—22no—
151C2×D13—22no—
152C2×D13—22no—
153C2×D13—22no—
154C2×D13—41no—
155C2×D13—41no—
156C2×D13—41no—
157C2×D13—41no—
158C2×D13C22⋊Q814yescomplemented
159C4×C13—22no—
160C4×C13—24no—
161C4×C13—42no—
162C4×C13—41no—
163C4×C13#12114yes—
164Dic13—22no—
165Dic13—42no—
166Dic13—41no—
167Dic13—42no—
168C22×Q8—131no—
169C22×D4—131no—
170C23×C4—131no—
171C23×C4—131no—
172C23×C4—132no—
173C22⋊Q8—264no—
174C22⋊Q8—264no—
175C4×D4—264no—
176C2×C4⋊C4—132no—
177C2×C4⋊C4—131no—
178C2×C4⋊C4—131no—
179C2×C4⋊C4—132no—
180C2×C4⋊C4—132no—
181C2×C4⋊C4—264no—
182C2×C4⋊C4C2×D1311yescharacteristic
183C2×C4⋊C4C2×D1312yes—
184C2×C4⋊C4C2×D1311yescharacteristic
185C2×C22⋊C4—131no—
186C2×C22⋊C4—131no—
187C2×C22⋊C4—132no—
188C2×C22⋊C4—132no—
189C2×C22⋊C4—132no—
190C2×C42C2×D1311yescharacteristic
191#95—132no—
192#95—132no—
193#95—132no—
194#95C2×D1312yes—
195C2×C13C2×#12111yescharacteristic
196C2×C13C2×C22⋊Q811yescharacteristic
197C2×C13#53711yescharacteristic
198C2×C13#54611yescharacteristic
199C2×C13D4×Q811yescharacteristic
200C2×C13#55211yescharacteristic
201C2×C13#55411yescharacteristic
202D13—24no—
203D13—42no—
204C24—131no—
205C24—131no—
206C2×Q8—262no—
207C2×Q8—262no—
208C2×Q8—262no—
209C2×D4—134no—
210C2×D4—262no—
211C2×D4—262no—
212C22×C4—131no—
213C22×C4—134no—
214C22×C4—132no—
215C22×C4—132no—
216C22×C4—131no—
217C22×C4—264no—
218C22×C4—262no—
219C22×C4—262no—
220C22×C4—264no—
221C22×C4—262no—
222C22×C4—262no—
223C22×C4—262no—
224C22×C4—522no—
225C22×C4C22×D1311yescharacteristic
226C22×C4C22×D1312yes—
227C22×C4C22×D1312yes—
228C22×C4C22×D1311yescharacteristic
229C22×C4C22×D1311yescharacteristic
230C4⋊C4—22no—
231C4⋊C4—42no—
232C4⋊C4—262no—
233C4⋊C4—264no—
234C4⋊C4—264no—
235C4⋊C4—262no—
236C4⋊C4—264no—
237C4⋊C4D5214yescomplemented
238C22⋊C4—262no—
239C22⋊C4—262no—
240C22⋊C4—264no—
241C22⋊C4—264no—
242C22⋊C4—522no—
243C42—22no—
244C13#241711yescharacteristic, complemented, Sylow
245C23—132no—
246C23—132no—
247C23—132no—
248C23—132no—
249C23—261no—
250C23—261no—
251C23—261no—
252C23—261no—
253C23—261no—
254C23—261no—
255C23—261no—
256C23—261no—
257C23—261no—
258C23—261no—
259C23C23×D1311yescharacteristic
260Q8—524no—
261D4—268no—
262C2×C4—21no—
263C2×C4—22no—
264C2×C4—22no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—22no—
268C2×C4—22no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—22no—
272C2×C4—132no—
273C2×C4—261no—
274C2×C4—261no—
275C2×C4—268no—
276C2×C4—262no—
277C2×C4—261no—
278C2×C4—262no—
279C2×C4—261no—
280C2×C4—262no—
281C2×C4—262no—
282C2×C4—261no—
283C2×C4—262no—
284C2×C4—262no—
285C2×C4—528no—
286C2×C4—524no—
287C2×C4C2×D5214yes—
288C2×C4C2×D5212yes—
289C2×C4D4×D1312yes—
290C2×C4Q8×D1312yes—
291C2×C4#613112yes—
292C22—134no—
293C22—262no—
294C22—262no—
295C22—262no—
296C22—262no—
297C22—262no—
298C22—262no—
299C22—262no—
300C22—262no—
301C22—262no—
302C22—521no—
303C22—521no—
304C22—521no—
305C22—521no—
306C22C22×D5211yescharacteristic
307C22C2×D4×D1311yescharacteristic
308C22#8825111yescharacteristic
309C22C2×Q8×D1311yescharacteristic
310C22C2×#613111yescharacteristic
311C22#41×D1311yescharacteristic
312C22#8825711yescharacteristic
313C4—24no—
314C4—22no—
315C4—41no—
316C4—42no—
317C4—262no—
318C4—521no—
319C4—522no—
320C4—522no—
321C4#8814914yes—
322C2—264no—
323C2—522no—
324C2C2×#8814911yescharacteristic
325C2#1171925911yescharacteristic
326C2Q8×D5211yescharacteristic
327C2#1171931311yescharacteristic
328C2D13×C22⋊Q811yescharacteristic
329C2#1171939911yescharacteristic
330C2#1171943511yescharacteristic
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, cosocleC23×C13C24
FittingC13×#389C2
prime radicalC22×D52C22
hypercenter#389D13
hypocenterC13#2417
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ #389

Complements

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

NH ≅ G/Ntype
1. C2×#88151C2semidirect
2. C2×#88151C2semidirect
3. C2×C4⋊C4×D13C2semidirect
5. C13×#389C2semidirect
6. #11718655C2semidirect
7. #11718648C2semidirect
8. #11718648C2semidirect
9. #11718590C2semidirect
11. #11718322C2semidirect
52. C2×D52Q8semidirect
67. C13×C4⋊C4D4semidirect
134. #389D13semidirect
158. C2×D13C22⋊Q8semidirect
237. C4⋊C4D52semidirect
244. C13#2417semidirect

Maximal subgroups

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

subgroupindex
C2×#881512
C2×C4⋊C4×D132
C2×C4×D522
C13×#3892
#117186552
#117186482
#117185902
#117183262
#117183222
#241713