Finite Group Databasebeta

← #13118283

Subgroups — #13118283

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×C13×C22⋊Q8C211yesmaximal, characteristic, complemented
2C2×#88200C211yesmaximal, characteristic, complemented
3C2×C4×C22⋊D13C211yesmaximal, characteristic
4C2×C4⋊C4×D13C211yesmaximal, characteristic, complemented
5#11718891C211yesmaximal, characteristic, complemented
6#11718873C211yesmaximal, characteristic, complemented
7#11718648C212yesmaximal, complemented
8#11718646C211yesmaximal, characteristic, complemented
9#11718641C212yesmaximal, complemented
10#11718617C212yesmaximal
11#11718609C212yesmaximal, complemented
12C22×Q8×C13C2211yescharacteristic
13C23×C4×C13C2211yescharacteristic
14C22×C22⋊D13C2211yescharacteristic
15C22×C4×D13C2212yes—
16C22×C4×D13C2211yescharacteristic
17C13×C22⋊Q8—24no—
18C2×C13×C4⋊C4C2212yes—
19C2×C13×C4⋊C4C2211yescharacteristic
20C2×C13×C22⋊C4C2212yes—
21C2×C22⋊Dic13C2211yescharacteristic
22C2×C22⋊Dic13C2212yes—
23#88200—24no—
24C4×C22⋊D13—24no—
25C2×#6103C2211yescharacteristic
26C2×#6103C2212yes—
27C2×C4⋊Dic13C2211yescharacteristic
28C2×C4⋊Dic13C2211yescharacteristic
29C2×C4⋊Dic13C2212yes—
30C2×#6101C2212yes—
31C2×#6101C2211yescharacteristic
32C2×#6101C2212yes—
33C2×C4×Dic13C2211yescharacteristic
34C4⋊C4×D13—24no—
35#88071C2212yes—
36#88071C2212yes—
37#88071C2212yes—
38#88071C2212yes—
39C24×C13C2311yescharacteristic
40C23×D13C2311yescharacteristic
41C2×Q8×C13—22no—
42C2×Q8×C13—22no—
43C2×Q8×C13—22no—
44C22×C4×C13—22no—
45C22×C4×C13—22no—
46C22×C4×C13—22no—
47C22×C4×C13C2312yes—
48C22×C4×C13C2311yescharacteristic
49C22×C4×C13C2312yes—
50C22×C4×C13C2311yescharacteristic
51C2×C22⋊D13—22no—
52C2×C22⋊D13—22no—
53C2×C22⋊D13Q814yescomplemented
54C22×Dic13C2312yes—
55C22×Dic13C2311yescharacteristic
56C22×Dic13C2312yes—
57C22×Dic13C2311yescharacteristic
58C22×Dic13C2311yescharacteristic
59C2×C4×D13—22no—
60C2×C4×D13—22no—
61C2×C4×D13—24no—
62C2×C4×D13—24no—
63C2×C4×D13—42no—
64C2×C4×D13D414yes—
65C13×C4⋊C4—24no—
66C13×C4⋊C4D414yescomplemented
67C13×C22⋊C4—24no—
68C22⋊Dic13—22no—
69C22⋊Dic13—42no—
70#6103—22no—
71#6103—24no—
72C4⋊Dic13—22no—
73C4⋊Dic13—22no—
74C4⋊Dic13—42no—
75#6101—24no—
76#6101—22no—
77#6101—24no—
78C4×Dic13—22no—
79#2417—131nomaximal, Sylow
80C23×C13—21no—
81C23×C13—21no—
82C23×C13—21no—
83C23×C13—21no—
84C23×C13—21no—
85C23×C13—21no—
86C23×C13C2×Q812yes—
87C23×C13C2411yescharacteristic
88C22×D13—21no—
89C22×D13—21no—
90C22×D13—21no—
91C22×D13—21no—
92C22×D13C2×D412yes—
93C22×D13C2×Q812yes—
94C22×D13#4112yes—
95Q8×C13—44no—
96C2×C4×C13—22no—
97C2×C4×C13—22no—
98C2×C4×C13—21no—
99C2×C4×C13—22no—
100C2×C4×C13—22no—
101C2×C4×C13—21no—
102C2×C4×C13—21no—
103C2×C4×C13—22no—
104C2×C4×C13—44no—
105C2×C4×C13C2×D414yes—
106C2×C4×C13C2×D412yes—
107C2×C4×C13C2×D412yes—
108C2×C4×C13#4112yes—
109C22⋊D13—28no—
110C2×Dic13—21no—
111C2×Dic13—21no—
112C2×Dic13—21no—
113C2×Dic13—21no—
114C2×Dic13—21no—
115C2×Dic13—22no—
116C2×Dic13—22no—
117C2×Dic13—22no—
118C2×Dic13—21no—
119C2×Dic13—22no—
120C2×Dic13—22no—
121C2×Dic13—21no—
122C2×Dic13—22no—
123C2×Dic13C2×D412yes—
124C2×Dic13C2×Q812yes—
125C4×D13—28no—
126C4×D13—48no—
127C2×C22⋊Q8—131no—
128C2×C22⋊Q8D1311yescharacteristic, complemented
129C2×C4×D4—131no—
130C22×C4⋊C4—131no—
131#398—132no—
132#396—132no—
133#391—131no—
134#389—131no—
135#386—132no—
136#380—131no—
137#380—132no—
138C22×C13—22no—
139C22×C13—22no—
140C22×C13—22no—
141C22×C13—41no—
142C22×C13—41no—
143C22×C13—41no—
144C22×C13—41no—
145C22×C13C22×D411yescharacteristic
146C22×C13C22×D411yescharacteristic
147C22×C13C22×Q811yescharacteristic
148C22×C13C2×#4111yescharacteristic
149C22×C13C2×#4111yescharacteristic
150C22×C13H(5,𝔽2)11yescharacteristic
151C22×C132−1+411yescharacteristic
152C2×D13—22no—
153C2×D13—22no—
154C2×D13—22no—
155C2×D13—22no—
156C2×D13—22no—
157C2×D13—22no—
158C2×D13C22⋊Q814yescomplemented
159C4×C13—24no—
160C4×C13—41no—
161C4×C13—42no—
162C4×C13#12114yes—
163Dic13—22no—
164Dic13—22no—
165Dic13—41no—
166Dic13—42no—
167Dic13—42no—
168C22×Q8C2×D1311yescharacteristic
169C22×D4—131no—
170C23×C4—131no—
171C23×C4—132no—
172C23×C4C2×D1311yescharacteristic
173C22⋊Q8—24no—
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—131no—
181C2×C4⋊C4—132no—
182C2×C4⋊C4—264no—
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⋊C4C2×D1312yes—
190C2×C42—131no—
191#95—132no—
192#95—132no—
193#95—132no—
194#95—132no—
195C2×C13—42no—
196C2×C13C2×#12111yescharacteristic
197C2×C13C2×C22⋊Q811yescharacteristic
198C2×C13#53711yescharacteristic
199C2×C13#54611yescharacteristic
200C2×C13D4×Q811yescharacteristic
201C2×C13#55211yescharacteristic
202C2×C13#55411yescharacteristic
203D13—24no—
204C24—131no—
205C24C22×D1311yescharacteristic
206C2×Q8—22no—
207C2×Q8—22no—
208C2×Q8—22no—
209C2×D4—134no—
210C2×D4—262no—
211C2×D4—262no—
212C22×C4—22no—
213C22×C4—22no—
214C22×C4—22no—
215C22×C4—131no—
216C22×C4—131no—
217C22×C4—134no—
218C22×C4—132no—
219C22×C4—131no—
220C22×C4—132no—
221C22×C4—264no—
222C22×C4—262no—
223C22×C4—262no—
224C22×C4—264no—
225C22×C4—522no—
226C22×C4C22×D1312yes—
227C22×C4C22×D1311yescharacteristic
228C22×C4C22×D1312yes—
229C22×C4C22×D1311yescharacteristic
230C4⋊C4—24no—
231C4⋊C4—262no—
232C4⋊C4—264no—
233C4⋊C4—262no—
234C4⋊C4—264no—
235C4⋊C4—262no—
236C4⋊C4—522no—
237C4⋊C4C22⋊D1314yescomplemented
238C22⋊C4—24no—
239C22⋊C4—262no—
240C22⋊C4—264no—
241C22⋊C4—262no—
242C22⋊C4—522no—
243C42—262no—
244C13#241711yescharacteristic, complemented, Sylow
245C23—21no—
246C23—21no—
247C23—21no—
248C23—21no—
249C23—21no—
250C23—21no—
251C23—132no—
252C23—132no—
253C23—132no—
254C23—261no—
255C23—261no—
256C23—261no—
257C23—261no—
258C23Q8×D1312yes—
259C23C23×D1311yescharacteristic
260Q8—44no—
261D4—268no—
262C2×C4—22no—
263C2×C4—22no—
264C2×C4—21no—
265C2×C4—22no—
266C2×C4—21no—
267C2×C4—22no—
268C2×C4—22no—
269C2×C4—21no—
270C2×C4—44no—
271C2×C4—132no—
272C2×C4—132no—
273C2×C4—261no—
274C2×C4—261no—
275C2×C4—261no—
276C2×C4—261no—
277C2×C4—268no—
278C2×C4—261no—
279C2×C4—262no—
280C2×C4—261no—
281C2×C4—262no—
282C2×C4—262no—
283C2×C4—262no—
284C2×C4—262no—
285C2×C4—261no—
286C2×C4—262no—
287C2×C4—528no—
288C2×C4D4×D1312yes—
289C2×C4#612912yes—
290C2×C4C2×C22⋊D1314yes—
291C2×C4C2×C22⋊D1312yes—
292C22—22no—
293C22—22no—
294C22—22no—
295C22—41no—
296C22—41no—
297C22—41no—
298C22—41no—
299C22—134no—
300C22—262no—
301C22—262no—
302C22—262no—
303C22—262no—
304C22—262no—
305C22—262no—
306C22C2×D4×D1311yescharacteristic
307C22C2×#612911yescharacteristic
308C22C2×Q8×D1311yescharacteristic
309C22#8825411yescharacteristic
310C22#41×D1311yescharacteristic
311C22#8825611yescharacteristic
312C22C22×C22⋊D1311yescharacteristic
313C4—24no—
314C4—41no—
315C4—42no—
316C4—262no—
317C4—262no—
318C4—522no—
319C4—521no—
320C4—522no—
321C4#8819214yes—
322C2—42no—
323C2—264no—
324C2D13×C22⋊Q811yescharacteristic
325C2#1171933411yescharacteristic
326C2#1171934011yescharacteristic
327C2#1171934411yescharacteristic
328C2C2×#8819211yescharacteristic
329C2Q8×C22⋊D1311yescharacteristic
330C2#1171953411yescharacteristic
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, cosocleC23×C13C24
FittingC2×C13×C22⋊Q8C2
prime radicalC22×C22⋊D13C22
hypercenterC2×C22⋊Q8D13
hypocenterC13#2417
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. C2×C13×C22⋊Q8C2semidirect
2. C2×#88200C2semidirect
4. C2×C4⋊C4×D13C2semidirect
5. #11718891C2semidirect
6. #11718873C2semidirect
7. #11718648C2semidirect
8. #11718646C2semidirect
9. #11718641C2semidirect
11. #11718609C2semidirect
53. C2×C22⋊D13Q8semidirect
66. C13×C4⋊C4D4semidirect
128. C2×C22⋊Q8D13semidirect
158. C2×D13C22⋊Q8semidirect
237. C4⋊C4C22⋊D13semidirect
244. C13#2417semidirect

Maximal subgroups

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

subgroupindex
C2×C13×C22⋊Q82
C2×#882002
C2×C4×C22⋊D132
C2×C4⋊C4×D132
#117188912
#117188732
#117186482
#117186462
#117186412
#117186172
#117186092
#241713