Finite Group Databasebeta

← #16025639

Subgroups — #16025639

Order 3328.

1800 conjugacy classes of subgroups.

The subgroup lattice has 406 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C13⋊#564C211yesmaximal, characteristic
2#13118021C212yesmaximal
3#13118020C214yesmaximal
4#13118019C214yesmaximal
5#13118018C214yesmaximal
6#125×Dic13C211yesmaximal, characteristic
7#13117395C214yesmaximal
8#13117393C214yesmaximal
9#13117393C214yesmaximal
10#13117391C212yesmaximal
11C13×#2382C211yesmaximal, characteristic
12C2×C13×#125C2211yescharacteristic
13C13⋊#564C4116yescomplemented
14C2×#88144C2214yes—
15C2×#88143C2214yes—
16C2×#88143C2214yes—
17C2×#88124C2212yes—
18C13×#389C2214yes—
19C13×#387C2214yes—
20C13×#387C2214yes—
21C13×#382C2212yes—
22#11718646C2212yes—
23#11718642C2214yes—
24#11718639C2214yes—
25#11718639C2214yes—
26#11718638C2214yes—
27C4⋊C4×Dic13C2212yes—
28C4⋊C4×Dic13C2212yes—
29C4⋊C4×Dic13C2212yes—
30C4⋊C4×Dic13C2214yes—
31C4⋊C4×Dic13C2214yes—
32#11718634C2212yes—
33#11718634C2212yes—
34#11718633C2214yes—
35#11718633C2214yes—
36#11718597C2211yescharacteristic
37#11718594C2214yes—
38#11718594C2214yes—
39C42×Dic13C2211yescharacteristic
40C42×Dic13C2214yes—
41#11718589C2214yes—
42#11718316C2214yes—
43#11718316C2214yes—
44#11718315C2214yes—
45#11718315C2214yes—
46#11718314C2214yes—
47#11718314C2214yes—
48#11718313C2214yes—
49#11718313C2214yes—
50#11718311C2214yes—
51#11718311C2214yes—
52#11718310C2214yes—
53#11718310C2214yes—
54#11718310C2214yes—
55#11718310C2214yes—
56#11718308C2214yes—
57#11718308C2214yes—
58C13×#125C2×C418yes—
59C2×C13×C4⋊C4C2312yes—
60C2×C13×C4⋊C4C2312yes—
61C2×C13×C4⋊C4C2314yes—
62C2×C13×C4⋊C4C2312yes—
63C2×C13×C4⋊C4C2314yes—
64C2×C42×C13C2314yes—
65C2×C42×C13C2311yescharacteristic
66C2×C4⋊Dic13C2312yes—
67C2×C4⋊Dic13C2314yes—
68C2×C4⋊Dic13C2312yes—
69C2×C4⋊Dic13C2312yes—
70C2×C4⋊Dic13C2314yes—
71C2×#6101C2314yes—
72C2×#6101C2314yes—
73C2×#6101C2314yes—
74C2×#6101C2314yes—
75C2×#6101C2314yes—
76C2×#6101C2314yes—
77C2×#6101C2314yes—
78C2×#6101C2314yes—
79C2×C4×Dic13C2314yes—
80C2×C4×Dic13C2311yescharacteristic
81C2×C4×Dic13C2314yes—
82C2×C4×Dic13C2312yes—
83C2×C4×Dic13C2314yes—
84C2×C4×Dic13C2314yes—
85C2×C4×Dic13C2314yes—
86C2×C4×Dic13C2311yescharacteristic
87C2×C4×Dic13C2312yes—
88C2×C4×Dic13C2314yes—
89#88144C2×C4132yes—
90#88143C2×C4132yes—
91#88143C2×C4132yes—
92#88124C2×C4116yes—
93C13×#95C2314yes—
94C13×#95C2314yes—
95C13×#95C2314yes—
96C13×#95C2314yes—
97#88071C2314yes—
98#88071C2314yes—
99#88071C2314yes—
100#88071C2314yes—
101#88071C2314yes—
102#88071C2314yes—
103#88071C2314yes—
104#88071C2314yes—
105#88071C2314yes—
106#88071C2314yes—
107#88071C2314yes—
108C4×#564—131nomaximal, Sylow
109C22×C4×C13C2414yes—
110C22×C4×C13C2414yes—
111C22×C4×C13C2412yes—
112C22×C4×C13C2414yes—
113C22×C4×C13C2411yescharacteristic
114C22×Dic13C2411yescharacteristic
115C22×Dic13C2412yes—
116C22×Dic13C2414yes—
117C22×Dic13C2414yes—
118C22×Dic13C2414yes—
119C22×Dic13C2411yescharacteristic
120C13×C4⋊C4—42no—
121C13×C4⋊C4—42no—
122C13×C4⋊C4—44no—
123C13×C4⋊C4C22×C418yes—
124C13×C4⋊C4C22×C4116yes—
125C42×C13—44no—
126C42×C13C22×C414yes—
127C4⋊Dic13—42no—
128C4⋊Dic13—44no—
129C4⋊Dic13C22×C418yes—
130C4⋊Dic13C22×C418yes—
131C4⋊Dic13C22×C4116yes—
132#6101—44no—
133#6101—44no—
134#6101—44no—
135#6101—44no—
136#6101C22×C4116yes—
137#6101C22×C4116yes—
138#6101C22×C4116yes—
139#6101C22×C4116yes—
140C4×Dic13—28no—
141C4×Dic13—28no—
142C4×Dic13—22no—
143C4×Dic13—24no—
144C4×Dic13—28no—
145C4×Dic13—44no—
146C4×Dic13—44no—
147C4×Dic13—41no—
148C4×Dic13—42no—
149C4×Dic13C22×C4116yes—
150C2×#564—131no—
151#2382—134no—
152#2382—134no—
153#2382—134no—
154#2382—132no—
155#2382D1311yescharacteristic
156C4×#125—134no—
157C4×#125—134no—
158C4×#125—134no—
159C4×#125—132no—
160C4×#125—131no—
161C23×C13C2511yescharacteristic
162C2×C4×C13—22no—
163C2×C4×C13—24no—
164C2×C4×C13—21no—
165C2×C4×C13—21no—
166C2×C4×C13—22no—
167C2×C4×C13—24no—
168C2×C4×C13—24no—
169C2×C4×C13—24no—
170C2×C4×C13—24no—
171C2×C4×C13—24no—
172C2×C4×C13—24no—
173C2×C4×C13—24no—
174C2×C4×C13C23×C418yes—
175C2×C4×C13C23×C412yes—
176C2×C4×C13C23×C414yes—
177C2×Dic13—24no—
178C2×Dic13—24no—
179C2×Dic13—24no—
180C2×Dic13—24no—
181C2×Dic13—21no—
182C2×Dic13—22no—
183C2×Dic13—24no—
184C2×Dic13—22no—
185C2×Dic13—22no—
186C2×Dic13—24no—
187C2×Dic13—24no—
188C2×Dic13—22no—
189C2×Dic13C23×C418yes—
190C2×Dic13C23×C418yes—
191C2×Dic132−1+412yes—
192C2×Dic132−1+414yes—
193#564—1316no—
194C2×#125—134no—
195C2×#125—134no—
196C2×#125—134no—
197C2×#125—132no—
198C2×#125C2×D1311yescharacteristic
199#389—134no—
200#389—134no—
201#389—132no—
202#389—132no—
203#389—132no—
204#389—134no—
205#389—134no—
206#389—134no—
207#389C2×D1314yes—
208#387—134no—
209#387—134no—
210#387—134no—
211#387—134no—
212#387—134no—
213#387—134no—
214#387—134no—
215#387—134no—
216#387—134no—
217#387—134no—
218#387—134no—
219#387—134no—
220#387—134no—
221#387C2×D1314yes—
222#387C2×D1314yes—
223#382—134no—
224#382—131no—
225#382—134no—
226#382—134no—
227#382C2×D1312yes—
228C4×C4⋊C4—134no—
229C4×C4⋊C4—132no—
230C4×C4⋊C4—132no—
231C4×C4⋊C4—134no—
232C4×C4⋊C4—132no—
233C4×C4⋊C4—134no—
234C4×C4⋊C4—134no—
235C4×C4⋊C4—134no—
236C4×C4⋊C4—134no—
237C43—134no—
238C43—131no—
239C22×C13C24×C411yescharacteristic
240C22×C13C2×2−1+411yescharacteristic
241C22×C13C2×2−1+412yes—
242C22×C13#58512yes—
243C22×C13#58511yescharacteristic
244C4×C13—22no—
245C4×C13—24no—
246C4×C13—28no—
247C4×C13—44no—
248C4×C13—44no—
249Dic13—28no—
250Dic13—28no—
251Dic13—41no—
252Dic13—42no—
253Dic13—44no—
254Dic13#56414yescomplemented
255#125—1332no—
256#125—1332no—
257#125—1332no—
258#125—1316no—
259#125C4×D1318yes—
260C2×C4⋊C4—134no—
261C2×C4⋊C4—134no—
262C2×C4⋊C4—134no—
263C2×C4⋊C4—134no—
264C2×C4⋊C4—132no—
265C2×C4⋊C4—134no—
266C2×C4⋊C4—132no—
267C2×C4⋊C4—134no—
268C2×C4⋊C4—134no—
269C2×C4⋊C4—134no—
270C2×C4⋊C4—134no—
271C2×C4⋊C4—134no—
272C2×C4⋊C4—132no—
273C2×C4⋊C4C22×D1314yes—
274C2×C4⋊C4C22×D1312yes—
275C2×C4⋊C4C22×D1312yes—
276C2×C4⋊C4C22×D1314yes—
277C2×C4⋊C4C22×D1312yes—
278C2×C42—134no—
279C2×C42—134no—
280C2×C42—134no—
281C2×C42—134no—
282C2×C42—132no—
283C2×C42—131no—
284C2×C42—134no—
285C2×C42—134no—
286C2×C42—132no—
287C2×C42—131no—
288C2×C42C22×D1314yes—
289C2×C42C22×D1311yescharacteristic
290#95—134no—
291#95—134no—
292#95—134no—
293#95—134no—
294#95—134no—
295#95—134no—
296#95—134no—
297#95—134no—
298#95—134no—
299#95—134no—
300#95—134no—
301#95C22×D1314yes—
302#95C22×D1314yes—
303#95C22×D1314yes—
304#95C22×D1314yes—
305C2×C13C4×2−1+411yescharacteristic
306C2×C13C4×2−1+412yes—
307C2×C13C2×#56411yescharacteristic
308C2×C13#353111yescharacteristic
309C2×C13#353112yes—
310C22×C4—131no—
311C22×C4—134no—
312C22×C4—134no—
313C22×C4—131no—
314C22×C4—134no—
315C22×C4—132no—
316C22×C4C23×D1314yes—
317C22×C4C23×D1314yes—
318C22×C4C23×D1314yes—
319C22×C4C23×D1312yes—
320C22×C4C23×D1311yescharacteristic
321C4⋊C4—44no—
322C4⋊C4—42no—
323C4⋊C4—42no—
324C4⋊C4—1316no—
325C4⋊C4—1316no—
326C4⋊C4—1316no—
327C4⋊C4—1316no—
328C4⋊C4—1316no—
329C4⋊C4—138no—
330C4⋊C4—138no—
331C4⋊C4—524no—
332C4⋊C4—524no—
333C4⋊C4—524no—
334C4⋊C4—524no—
335C4⋊C4—524no—
336C4⋊C4—522no—
337C4⋊C4C2×C4×D13116yes—
338C4⋊C4C2×C4×D1318yes—
339C42—44no—
340C42—1316no—
341C42—262no—
342C42—268no—
343C42—264no—
344C42—268no—
345C42—268no—
346C42—522no—
347C42—521no—
348C42—524no—
349C42—524no—
350C42C2×C4×D1314yes—
351C13C4×#56411yescharacteristic, complemented, Sylow
352C23C24×D1311yescharacteristic
353C2×C4—24no—
354C2×C4—22no—
355C2×C4—21no—
356C2×C4—24no—
357C2×C4—22no—
358C2×C4—21no—
359C2×C4—24no—
360C2×C4—24no—
361C2×C4—24no—
362C2×C4—24no—
363C2×C4—24no—
364C2×C4—24no—
365C2×C4—132no—
366C2×C4—134no—
367C2×C4—138no—
368C2×C4—138no—
369C2×C4—264no—
370C2×C4—264no—
371C2×C4—264no—
372C2×C4—264no—
373C2×C4—262no—
374C2×C4—264no—
375C2×C4—262no—
376C2×C4—261no—
377C2×C4—262no—
378C2×C4—264no—
379C2×C4—262no—
380C2×C4—264no—
381C2×C4C22×C4×D1318yes—
382C2×C4C22×C4×D1312yes—
383C2×C4C22×C4×D1314yes—
384C22C23×C4×D1311yescharacteristic
385C22#1171965012yes—
386C22D13×2−1+411yescharacteristic
387C22D13×2−1+412yes—
388C22#1171965211yescharacteristic
389C4—22no—
390C4—28no—
391C4—24no—
392C4—44no—
393C4—44no—
394C4—134no—
395C4—268no—
396C4—268no—
397C4—521no—
398C4—522no—
399C4—524no—
400C2#1312804511yescharacteristic
401C2#1312804712yes—
402C2D13×#56411yescharacteristic
403C2#1312898011yescharacteristic
404C2#1312898212yes—
subgroupG/H
center, FrattiniC23C24×D13
commutatorC22×C13C24×C4
FittingC13×#2382C2
socle, prime radical, cosocleC23×C13C25
hypercenter#2382D13
hypocenterC13C4×#564
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ #2382

Complements

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

NH ≅ G/Ntype
13. C13⋊#564C4semidirect
254. Dic13#564semidirect
351. C13C4×#564semidirect

Maximal subgroups

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

subgroupindex
C2×C13⋊#5642
#131180212
#131180202
#131180192
#131180182
#125×Dic132
#131173952
#131173932
#131173912
C13×#23822
C4×#56413