Finite Group Databasebeta

← #13121613

Subgroups — #13121613

Order 1664.

432 conjugacy classes of subgroups.

The subgroup lattice has 338 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C13×#125C211yesmaximal, characteristic
2C2×#88142C211yesmaximal, characteristic
3#11718647C211yesmaximal, characteristic
4#11718645C211yesmaximal, characteristic
5#11718644C211yesmaximal, characteristic
6#11718643C211yesmaximal, characteristic
7#11718642C211yesmaximal, characteristic
8#11718640C211yesmaximal, characteristic
9#11718640C211yesmaximal, characteristic
10#11718639C211yesmaximal, characteristic
11#11718639C211yesmaximal, characteristic
12#11718635C211yesmaximal, characteristic
13#11718633C211yesmaximal, characteristic
14#11718594C211yesmaximal, characteristic
15#11718590C211yesmaximal, characteristic
16C22×Dic26C2211yescharacteristic
17C22×Dic26C2211yescharacteristic
18C13×#125—24no—
19C2×C13×C4⋊C4C2211yescharacteristic
20C2×C13×C4⋊C4C2211yescharacteristic
21C2×C13×C4⋊C4C2211yescharacteristic
22C2×C13×C4⋊C4C2211yescharacteristic
23C2×C13×C4⋊C4C2211yescharacteristic
24C2×C13×C4⋊C4C2211yescharacteristic
25C2×C42×C13C2211yescharacteristic
26C2×C4⋊Dic13C2211yescharacteristic
27C2×C4⋊Dic13C2211yescharacteristic
28C2×#6101C2211yescharacteristic
29C2×#6101C2211yescharacteristic
30C2×#6101C2211yescharacteristic
31C2×#6101C2211yescharacteristic
32C2×#6101C2211yescharacteristic
33C2×#6101C2211yescharacteristic
34C2×C4×Dic13C2211yescharacteristic
35C2×C4×Dic13C2211yescharacteristic
36#88142—24no—
37#88071C2211yescharacteristic
38#88071C2211yescharacteristic
39#88071C2211yescharacteristic
40#88071C2211yescharacteristic
41#88071C2211yescharacteristic
42#88071C2211yescharacteristic
43#88071C2211yescharacteristic
44#88071C2211yescharacteristic
45#88071C2211yescharacteristic
46#88071C2211yescharacteristic
47#88071C2211yescharacteristic
48#88071C2211yescharacteristic
49#88071C2211yescharacteristic
50#88071C2211yescharacteristic
51#88071C2211yescharacteristic
52#88071C2211yescharacteristic
53C22×C4×C13C2311yescharacteristic
54C22×C4×C13C2311yescharacteristic
55C22×C4×C13C2311yescharacteristic
56C22×C4×C13C2311yescharacteristic
57C22×C4×C13C2311yescharacteristic
58C22×C4×C13C2311yescharacteristic
59C22×C4×C13C2311yescharacteristic
60C22×Dic13C2311yescharacteristic
61C22×Dic13C2311yescharacteristic
62C22×Dic13C2311yescharacteristic
63C22×Dic13C2311yescharacteristic
64C22×Dic13C2311yescharacteristic
65C22×Dic13C2311yescharacteristic
66C22×Dic13C2311yescharacteristic
67C22×Dic13C2311yescharacteristic
68C2×Dic26—22no—
69C2×Dic26—22no—
70C2×Dic26—22no—
71C2×Dic26—22no—
72C2×Dic26—41no—
73C2×Dic26—41no—
74C13×C4⋊C4—22no—
75C13×C4⋊C4—22no—
76C13×C4⋊C4—22no—
77C13×C4⋊C4—22no—
78C13×C4⋊C4—22no—
79C13×C4⋊C4D414yes—
80C42×C13—22no—
81C4⋊Dic13—22no—
82C4⋊Dic13—41no—
83#6101—22no—
84#6101—22no—
85#6101—22no—
86#6101—41no—
87#6101—41no—
88#6101Q814yescomplemented
89C4×Dic13—22no—
90C4×Dic13—41no—
91#2713—131nomaximal, Sylow
92C23×C13C2411yescharacteristic
93C2×C4×C13—21no—
94C2×C4×C13—21no—
95C2×C4×C13—21no—
96C2×C4×C13—21no—
97C2×C4×C13—21no—
98C2×C4×C13—21no—
99C2×C4×C13—21no—
100C2×C4×C13—21no—
101C2×C4×C13—21no—
102C2×C4×C13—21no—
103C2×C4×C13—21no—
104C2×C4×C13—21no—
105C2×C4×C13—21no—
106C2×C4×C13—21no—
107C2×C4×C13—21no—
108C2×C4×C13—21no—
109C2×C4×C13—21no—
110C2×C4×C13C2×D412yes—
111C2×C4×C13C2×D412yes—
112C2×C4×C13C2×D412yes—
113C2×C4×C13C2×Q812yes—
114C2×Dic13—21no—
115C2×Dic13—21no—
116C2×Dic13—21no—
117C2×Dic13—21no—
118C2×Dic13—21no—
119C2×Dic13—21no—
120C2×Dic13—21no—
121C2×Dic13—21no—
122C2×Dic13—21no—
123C2×Dic13—21no—
124C2×Dic13—21no—
125C2×Dic13—21no—
126C2×Dic13—21no—
127C2×Dic13—21no—
128C2×Dic13—21no—
129C2×Dic13—21no—
130C2×Dic13—21no—
131C2×Dic13—21no—
132C2×Dic13—21no—
133C2×Dic13—21no—
134C2×Dic13—21no—
135C2×Dic13C2×Q812yes—
136C2×Dic13C2×Q812yes—
137C2×Dic13#4112yes—
138Dic26—44no—
139Dic26—44no—
140C2×C4⋊Q8—131no—
141C2×#125D1311yescharacteristic
142#400—131no—
143#400—131no—
144#398—131no—
145#398—131no—
146#395—131no—
147#395—131no—
148#391—131no—
149#391—131no—
150#389—131no—
151#387—131no—
152#387—131no—
153#387—131no—
154#387—131no—
155C22×C13C22×D411yescharacteristic
156C22×C13C22×Q811yescharacteristic
157C22×C13C2×#4111yescharacteristic
158C22×C13H(5,𝔽2)11yescharacteristic
159C22×C132−1+411yescharacteristic
160C22×C132−1+411yescharacteristic
161C22×C132−1+411yescharacteristic
162C4×C13—22no—
163C4×C13—22no—
164C4×C13—22no—
165C4×C13—22no—
166C4×C13—41no—
167C4×C13—41no—
168C4×C13—41no—
169Dic13—22no—
170Dic13—22no—
171Dic13—22no—
172Dic13—41no—
173Dic13—41no—
174Dic13—41no—
175Dic13—41no—
176Dic13—41no—
177C22×Q8—131no—
178C22×Q8—131no—
179C4⋊Q8—264no—
180#125—24no—
181C2×C4⋊C4—131no—
182C2×C4⋊C4—131no—
183C2×C4⋊C4—131no—
184C2×C4⋊C4—131no—
185C2×C4⋊C4—131no—
186C2×C4⋊C4—131no—
187C2×C4⋊C4—131no—
188C2×C4⋊C4—131no—
189C2×C4⋊C4C2×D1311yescharacteristic
190C2×C4⋊C4C2×D1311yescharacteristic
191C2×C4⋊C4C2×D1311yescharacteristic
192C2×C4⋊C4C2×D1311yescharacteristic
193C2×C4⋊C4C2×D1311yescharacteristic
194C2×C4⋊C4C2×D1311yescharacteristic
195C2×C42—131no—
196C2×C42—131no—
197C2×C42C2×D1311yescharacteristic
198#95—131no—
199#95—131no—
200#95—131no—
201#95—131no—
202#95—131no—
203#95—131no—
204#95—131no—
205#95—131no—
206#95—131no—
207#95—131no—
208#95—131no—
209#95—131no—
210#95—131no—
211#95—131no—
212#95—131no—
213#95—131no—
214C2×C13#53611yescharacteristic
215C2×C13#54111yescharacteristic
216C2×C13#54411yescharacteristic
217C2×C13#54611yescharacteristic
218C2×C13D4×Q811yescharacteristic
219C2×C13#55711yescharacteristic
220C2×C13#56311yescharacteristic
221C2×Q8—262no—
222C2×Q8—262no—
223C2×Q8—262no—
224C2×Q8—262no—
225C2×Q8—521no—
226C2×Q8—521no—
227C22×C4—131no—
228C22×C4—131no—
229C22×C4—131no—
230C22×C4—131no—
231C22×C4—131no—
232C22×C4—131no—
233C22×C4—131no—
234C22×C4—131no—
235C22×C4C22×D1311yescharacteristic
236C22×C4C22×D1311yescharacteristic
237C22×C4C22×D1311yescharacteristic
238C22×C4C22×D1311yescharacteristic
239C22×C4C22×D1311yescharacteristic
240C22×C4C22×D1311yescharacteristic
241C22×C4C22×D1311yescharacteristic
242C4⋊C4—22no—
243C4⋊C4—22no—
244C4⋊C4—22no—
245C4⋊C4—22no—
246C4⋊C4—22no—
247C4⋊C4—134no—
248C4⋊C4—262no—
249C4⋊C4—262no—
250C4⋊C4—262no—
251C4⋊C4—262no—
252C4⋊C4—521no—
253C4⋊C4—521no—
254C4⋊C4—521no—
255C4⋊C4C22⋊D1314yes—
256C42—22no—
257C42—262no—
258C42—521no—
259C13#271311yescharacteristic, complemented, Sylow
260C23C23×D1311yescharacteristic
261Q8—524no—
262Q8—524no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—132no—
281C2×C4—132no—
282C2×C4—132no—
283C2×C4—261no—
284C2×C4—261no—
285C2×C4—261no—
286C2×C4—261no—
287C2×C4—261no—
288C2×C4—261no—
289C2×C4—261no—
290C2×C4—261no—
291C2×C4—261no—
292C2×C4—261no—
293C2×C4—261no—
294C2×C4—261no—
295C2×C4—261no—
296C2×C4—261no—
297C2×C4—261no—
298C2×C4—261no—
299C2×C4—261no—
300C2×C4—261no—
301C2×C4—261no—
302C2×C4—261no—
303C2×C4—261no—
304C2×C4Q8×D1312yes—
305C2×C4C2×C22⋊D1312yes—
306C2×C4C2×C22⋊D1312yes—
307C2×C4C2×C22⋊D1312yes—
308C22C2×Q8×D1311yescharacteristic
309C22#8825411yescharacteristic
310C22#41×D1311yescharacteristic
311C22#8825611yescharacteristic
312C22#8825711yescharacteristic
313C22#8825711yescharacteristic
314C22C22×C22⋊D1311yescharacteristic
315C4—22no—
316C4—22no—
317C4—22no—
318C4—22no—
319C4—41no—
320C4—41no—
321C4—41no—
322C4—262no—
323C4—262no—
324C4—262no—
325C4—521no—
326C4—521no—
327C4—521no—
328C4—521no—
329C4—521no—
330C2#1171939011yescharacteristic
331C2#1171939411yescharacteristic
332C2#1171940111yescharacteristic
333C2#1171940411yescharacteristic
334C2Q8×C22⋊D1311yescharacteristic
335C2#1171953011yescharacteristic
336C2#1171953411yescharacteristic
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, prime radical, cosocleC23×C13C24
FittingC2×C13×#125C2
hypercenterC2×#125D13
hypocenterC13#2713
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×#125

Complements

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

NH ≅ G/Ntype
88. #6101Q8semidirect
259. C13#2713semidirect

Maximal subgroups

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

subgroupindex
C2×C13×#1252
C2×#881422
#117186472
#117186452
#117186442
#117186432
#117186422
#117186402
#117186392
#117186352
#117186332
#117185942
#117185902
#271313