Finite Group Databasebeta

← #15784061

Subgroups — #15784061

Order 3328.

2294 conjugacy classes of subgroups.

The subgroup lattice has 378 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#88126C211yesmaximal, characteristic
2C2×C4×#6103C212yesmaximal
3C2×#11718593C211yesmaximal, characteristic, complemented
4#13113074C214yesmaximal
5#13113069C214yesmaximal, complemented
6C4×#88071C212yesmaximal, complemented
7C2×C43×C13C211yesmaximal, characteristic, complemented
8C23×C4×D13C2211yescharacteristic
9C22×C42×C13C2214yes—
10C22×C42×C13C2212yes—
11C22×C42×C13C2211yescharacteristic
12C22×#6103C2212yes—
13C22×#6103C2214yes—
14C22×#6101C2212yes—
15C22×C4×Dic13C2211yescharacteristic
16C22×C4×Dic13C2212yes—
17C2×#88126—24no—
18C2×#88126—24no—
19C2×#88126C418yescomplemented
20C43×C13—24no—
21C2×#88071C2218yes—
22C2×#88071C2214yes—
23C2×#88071C2214yes—
24C4×#6103C4116yescomplemented
25#11718593—24no—
26C24×D13C2311yescharacteristic
27C23×C4×C13C2312yes—
28C23×C4×C13C2314yes—
29C23×C4×C13C2311yescharacteristic
30C23×Dic13C2312yes—
31C23×Dic13C2314yes—
32C23×Dic13C2311yescharacteristic
33C22×C4×D13—22no—
34C22×C4×D13—22no—
35C22×C4×D13—24no—
36C22×C4×D13C2×C414yes—
37C22×C4×D13C2×C418yes—
38C2×C42×C13—28no—
39C2×C42×C13—24no—
40C2×C42×C13—216no—
41C2×C42×C13—24no—
42C2×C42×C13C2×C418yes—
43C2×C42×C13C2×C414yes—
44C2×C42×C13D414yes—
45C2×C42×C13D414yes—
46C2×#6103—24no—
47C2×#6103—24no—
48C2×#6103—216no—
49C2×#6103C2×C418yes—
50C2×#6103C2×C4116yes—
51C2×#6101—24no—
52C2×#6101—24no—
53C2×#6101C2×C418yes—
54C2×C4×Dic13—22no—
55C2×C4×Dic13—22no—
56C2×C4×Dic13—24no—
57C2×C4×Dic13—24no—
58C2×C4×Dic13C2×C414yes—
59C2×C4×Dic13C2×C418yes—
60#88126—232no—
61#88071—28no—
62#88071—216no—
63#88071C2×C4116yes—
64#13761—131nomaximal, Sylow
65C24×C13C2411yescharacteristic
66C23×D13—21no—
67C23×D13—21no—
68C23×D13—28no—
69C23×D13—22no—
70C23×D13C22×C412yes—
71C23×D13C22×C414yes—
72C22×C4×C13—24no—
73C22×C4×C13—24no—
74C22×C4×C13—28no—
75C22×C4×C13—28no—
76C22×C4×C13C22×C414yes—
77C22×C4×C13C22×C418yes—
78C22×C4×C13C22×C412yes—
79C22×C4×C13C22×C414yes—
80C22×C4×C13C2×D414yes—
81C22×C4×C13C2×D412yes—
82C22×C4×C13C2×D414yes—
83C22×C4×C13C2×D412yes—
84C22×C4×C13#41116yes—
85C22×C4×C13#4114yes—
86C22×Dic13—21no—
87C22×Dic13—21no—
88C22×Dic13—22no—
89C22×Dic13—24no—
90C22×Dic13—22no—
91C22×Dic13—22no—
92C22×Dic13—28no—
93C22×Dic13—28no—
94C22×Dic13—24no—
95C22×Dic13—28no—
96C22×Dic13C22×C418yes—
97C22×Dic13C22×C414yes—
98C22×Dic13C22×C414yes—
99C22×Dic13C22×C412yes—
100C2×C4×D13—28no—
101C2×C4×D13—28no—
102C2×C4×D13—216no—
103C2×C4×D13—216no—
104C2×C4×D13C42116yescomplemented
105C42×C13—232no—
106C42×C13—216no—
107C42×C13C22⋊C4116yescomplemented
108#6103—216no—
109#6103—232no—
110#6101—216no—
111C4×Dic13—28no—
112C4×Dic13—216no—
113C22×#117—131no—
114C2×C4×C22⋊C4—132no—
115C2×#376—131no—
116C2×C43D1311yescharacteristic, complemented
117#1437—134no—
118#1436—134no—
119C4×#95—132no—
120C23×C13C23×C411yescharacteristic
121C23×C13C23×C412yes—
122C23×C13C22×D411yescharacteristic
123C23×C13C22×D411yescharacteristic
124C23×C13C2×#4112yes—
125C23×C13C2×#4118yes—
126C22×D13—22no—
127C22×D13—28no—
128C22×D13—22no—
129C22×D13—24no—
130C22×D13—24no—
131C22×D13—28no—
132C22×D13—28no—
133C22×D13—44no—
134C22×D13—48no—
135C22×D13—44no—
136C22×D13C2×C4214yes—
137C2×C4×C13—28no—
138C2×C4×C13—28no—
139C2×C4×C13—28no—
140C2×C4×C13—28no—
141C2×C4×C13—216no—
142C2×C4×C13—216no—
143C2×C4×C13—28no—
144C2×C4×C13C2×C4214yes—
145C2×C4×C13C2×C22⋊C418yes—
146C2×C4×C13C2×C22⋊C414yes—
147C2×C4×C13#11714yes—
148C2×C4×C13#117116yescomplemented
149C2×C4×C13C4×D418yes—
150C2×C4×C13C4×D418yes—
151C2×Dic13—22no—
152C2×Dic13—22no—
153C2×Dic13—24no—
154C2×Dic13—24no—
155C2×Dic13—24no—
156C2×Dic13—28no—
157C2×Dic13—28no—
158C2×Dic13—28no—
159C2×Dic13—28no—
160C2×Dic13—44no—
161C2×Dic13—48no—
162C2×Dic13—48no—
163C2×Dic13—44no—
164C2×Dic13C2×C4214yes—
165C4×D13—232no—
166C24×C4—131no—
167C2×#117—138no—
168C2×#117—264no—
169C2×#117—264no—
170C22×C4⋊C4—132no—
171C22×C22⋊C4—132no—
172C22×C22⋊C4—134no—
173C22×C42—131no—
174C22×C42—132no—
175C22×C42C2×D1314yes—
176C22×C42C2×D1312yes—
177C22×C42C2×D1311yescharacteristic
178C4×C22⋊C4—1316no—
179#376—264no—
180C2×#95—134no—
181C2×#95—138no—
182C2×#95—134no—
183C43—24no—
184C22×C13C22×C4211yescharacteristic
185C22×C13C22×C22⋊C411yescharacteristic
186C22×C13C2×#11711yescharacteristic
187C22×C13C2×#11714yes—
188C22×C13C2×C4×D412yes—
189C22×C13C2×C4×D412yes—
190C22×C13C4×#4114yes—
191C22×C13C4×#4114yes—
192C22×C13#52514yes—
193C22×C13#52918yes—
194C22×C13#53214yes—
195C2×D13—24no—
196C2×D13—28no—
197C2×D13—48no—
198C2×D13—48no—
199C2×D13—44no—
200C2×D13—44no—
201C4×C13—216no—
202C4×C13—28no—
203C4×C13C4×C22⋊C418yes—
204Dic13—24no—
205Dic13—48no—
206Dic13—44no—
207C25—131no—
208C23×C4—131no—
209C23×C4—134no—
210C23×C4—138no—
211C23×C4—132no—
212C23×C4—134no—
213C23×C4—262no—
214C23×C4—264no—
215C23×C4—262no—
216C23×C4C22×D1312yes—
217C23×C4C22×D1314yes—
218C23×C4C22×D1311yescharacteristic
219#117—2632no—
220C2×C4⋊C4—138no—
221C2×C4⋊C4—264no—
222C2×C4⋊C4—264no—
223C2×C22⋊C4—138no—
224C2×C22⋊C4—1316no—
225C2×C22⋊C4—264no—
226C2×C22⋊C4—2616no—
227C2×C22⋊C4—264no—
228C2×C42—216no—
229C2×C42—24no—
230C2×C42—28no—
231C2×C42—24no—
232C2×C42—134no—
233C2×C42—138no—
234C2×C42—262no—
235C2×C42—264no—
236C2×C42—264no—
237C2×C42—262no—
238C2×C42C4×D1318yes—
239C2×C42C4×D1314yes—
240C2×C42D5214yes—
241C2×C42C22⋊D1314yes—
242#95—1316no—
243#95—268no—
244#95—2616no—
245C2×C13C2×C4×C22⋊C411yescharacteristic
246C2×C13C4×#11712yes—
247C2×C13#229014yes—
248C2×C13#229314yes—
249C2×C13#229712yes—
250C2×C13#229812yes—
251D13—44no—
252C24—134no—
253C24—132no—
254C24—261no—
255C24—268no—
256C24—262no—
257C24—261no—
258C24C23×D1311yescharacteristic
259C22×C4—28no—
260C22×C4—28no—
261C22×C4—24no—
262C22×C4—24no—
263C22×C4—134no—
264C22×C4—132no—
265C22×C4—1316no—
266C22×C4—138no—
267C22×C4—134no—
268C22×C4—261no—
269C22×C4—262no—
270C22×C4—261no—
271C22×C4—268no—
272C22×C4—2616no—
273C22×C4—268no—
274C22×C4—2616no—
275C22×C4—264no—
276C22×C4—262no—
277C22×C4—268no—
278C22×C4—268no—
279C22×C4—264no—
280C22×C4—268no—
281C22×C4—262no—
282C22×C4C2×C4×D1318yes—
283C22×C4C2×C4×D1314yes—
284C22×C4C2×C4×D1312yes—
285C22×C4C2×C4×D1314yes—
286C22×C4C2×D5214yes—
287C22×C4C2×D5212yes—
288C22×C4#6127116yes—
289C22×C4#612714yes—
290C22×C4C2×C22⋊D1314yes—
291C22×C4C2×C22⋊D1312yes—
292C4⋊C4—2616no—
293C22⋊C4—2632no—
294C22⋊C4—2616no—
295C42—232no—
296C42—216no—
297C42—2616no—
298C42—268no—
299C42#6103116yescomplemented
300C13#1376111yescharacteristic, complemented, Sylow
301C23—134no—
302C23—268no—
303C23—262no—
304C23—264no—
305C23—268no—
306C23—268no—
307C23—262no—
308C23—264no—
309C23—524no—
310C23—528no—
311C23—524no—
312C23C22×C4×D1312yes—
313C23C22×C4×D1311yescharacteristic
314C23C22×D5211yescharacteristic
315C23C2×#612712yes—
316C23C2×#612718yes—
317C23C22×C22⋊D1311yescharacteristic
318C2×C4—28no—
319C2×C4—28no—
320C2×C4—28no—
321C2×C4—216no—
322C2×C4—28no—
323C2×C4—216no—
324C2×C4—28no—
325C2×C4—134no—
326C2×C4—262no—
327C2×C4—264no—
328C2×C4—262no—
329C2×C4—264no—
330C2×C4—2632no—
331C2×C4—268no—
332C2×C4—268no—
333C2×C4—268no—
334C2×C4—268no—
335C2×C4—264no—
336C2×C4—528no—
337C2×C4—524no—
338C2×C4—528no—
339C2×C4—524no—
340C2×C4C42×D1314yes—
341C2×C4#8812614yes—
342C2×C4#88126116yescomplemented
343C2×C4C4×D5218yes—
344C2×C4C2×#610318yes—
345C2×C4C2×#610314yes—
346C2×C4C4×C22⋊D1318yes—
347C22—264no—
348C22—268no—
349C22—528no—
350C22—528no—
351C22—524no—
352C22—524no—
353C22C2×C42×D1311yescharacteristic
354C22C2×#8812614yes—
355C22C2×#8812611yescharacteristic
356C22C2×C4×D5212yes—
357C22C4×#612714yes—
358C22C4×#612714yes—
359C22#1171918214yes—
360C22#1171918418yes—
361C22C22×#610311yescharacteristic
362C22C2×C4×C22⋊D1312yes—
363C22#1171949614yes—
364C4—216no—
365C4—28no—
366C4—264no—
367C4—528no—
368C4—524no—
369C4C4×#610318yes—
370C2—524no—
371C2C2×C4×#610311yescharacteristic
372C2C4×#8812612yes—
373C2#1311727914yes—
374C2#1311730014yes—
375C2#1311732612yes—
376C2#1311733312yes—
subgroupG/H
centerC23×C4C22×D13
commutatorC22×C13C22×C42
FrattiniC24C23×D13
FittingC2×C43×C13C2
socle, cosocleC24×C13C24
prime radicalC24×D13C23
hypercenterC2×C43D13
hypocenterC13#13761
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C23×C4 ◁ C2×C43

Complements

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

NH ≅ G/Ntype
3. C2×#11718593C2semidirect
5. #13113069C2semidirect
6. C4×#88071C2semidirect
7. C2×C43×C13C2semidirect
19. C2×#88126C4semidirect
24. C4×#6103C4semidirect
104. C2×C4×D13C42semidirect
107. C42×C13C22⋊C4semidirect
116. C2×C43D13semidirect
148. C2×C4×C13#117semidirect
299. C42#6103semidirect
300. C13#13761semidirect
342. C2×C4#88126semidirect

Maximal subgroups

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

subgroupindex
C22×#881262
C2×C4×#61032
C2×#117185932
#131130742
#131130692
C4×#880712
C2×C43×C132
#1376113