Finite Group Databasebeta

← #15784397

Subgroups — #15784397

Order 3328.

2154 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#6103C213yesmaximal
2C2×#11718309C211yesmaximal, characteristic, complemented
3C2×D13×#95C211yesmaximal, characteristic
4#13113063C213yesmaximal, complemented
5#13113060C213yesmaximal, complemented
6#13113057C213yesmaximal
7C4×C13×#95C211yesmaximal, characteristic, complemented
8C23×C4×D13C2213yes—
9C22×C42×C13C2213yes—
10C22×#6103C2213yes—
11C22×#6103C2211yescharacteristic
12C22×C4×Dic13C2213yes—
13C2×C13×#95C2213yes—
14C2×C13×#95C2211yescharacteristic
15C2×#88071C2213yes—
16C2×#88071C2213yes—
17C2×#88071C2216yes—
18C2×#88071C2213yes—
19C2×#88071C2213yes—
20C4×#6103C4124yescomplemented
21D13×#95—24no—
22#11718309—24no—
23C24×D13C2311yescharacteristic
24C23×C4×C13C2313yes—
25C23×C4×C13C2311yescharacteristic
26C23×C4×C13C2313yes—
27C23×Dic13C2313yes—
28C23×Dic13C2313yes—
29C23×Dic13C2311yescharacteristic
30C22×C4×D13—212no—
31C22×C4×D13—26no—
32C22×C4×D13—26no—
33C22×C4×D13—46no—
34C22×C4×D13C2×C4112yes—
35C2×C42×C13—46no—
36C2×C42×C13C2×C4112yescomplemented
37C2×#6103—26no—
38C2×#6103—26no—
39C2×#6103C2×C4112yes—
40C2×#6103C2×C4112yes—
41C2×C4×Dic13—26no—
42C2×C4×Dic13—26no—
43C2×C4×Dic13C2×C4112yescomplemented
44C13×#95—26no—
45C13×#95D414yes—
46#88071—26no—
47#88071—26no—
48#88071—46no—
49#88071C2×C4112yescomplemented
50#88071C2×C4112yescomplemented
51#13809—131nomaximal, Sylow
52C24×C13C2411yescharacteristic
53C23×D13—21no—
54C23×D13—23no—
55C23×D13—23no—
56C23×D13—21no—
57C23×D13C22×C416yes—
58C23×D13#4112yes—
59C23×D13#4116yes—
60C22×C4×C13—26no—
61C22×C4×C13—23no—
62C22×C4×C13—26no—
63C22×C4×C13—21no—
64C22×C4×C13—26no—
65C22×C4×C13—23no—
66C22×C4×C13—23no—
67C22×C4×C13—26no—
68C22×C4×C13C22×C416yes—
69C22×C4×C13C22×C416yes—
70C22×C4×C13C22×C416yes—
71C22×C4×C13C2×D416yes—
72C22×C4×C13#4116yes—
73C22×Dic13—21no—
74C22×Dic13—23no—
75C22×Dic13—23no—
76C22×Dic13—23no—
77C22×Dic13—23no—
78C22×Dic13—23no—
79C22×Dic13—23no—
80C22×Dic13—26no—
81C22×Dic13—23no—
82C22×Dic13—23no—
83C22×Dic13—26no—
84C22×Dic13—23no—
85C22×Dic13C22×C416yes—
86C22×Dic13C22×C416yes—
87C22×Dic13C22×C416yes—
88C2×C4×D13—224no—
89C2×C4×D13—224no—
90C2×C4×D13—412no—
91C2×C4×D13—424no—
92C2×C4×D13—424no—
93C42×C13—412no—
94#6103—224no—
95#6103C42116yes—
96C4×Dic13—224no—
97C2×C4×C22⋊C4—133no—
98C2×#376—131no—
99C22×#95—131no—
100#1434—133no—
101#1434—133no—
102C22⋊#95—133no—
103C4×#95D1311yescharacteristic, complemented
104C23×C13C23×C413yes—
105C23×C13C22×D411yescharacteristic
106C23×C13C2×#4113yes—
107C23×C13C2×#4111yescharacteristic
108C23×C13C2×#4113yes—
109C23×C13H(5,𝔽2)13yes—
110C23×C132−1+411yescharacteristic
111C22×D13—26no—
112C22×D13—26no—
113C22×D13—26no—
114C22×D13—26no—
115C22×D13—26no—
116C22×D13—22no—
117C22×D13—212no—
118C22×D13—26no—
119C22×D13—26no—
120C22×D13C2×C4214yes—
121C22×D13#117112yes—
122C22×D13#117112yes—
123C2×C4×C13—26no—
124C2×C4×C13—26no—
125C2×C4×C13—26no—
126C2×C4×C13—26no—
127C2×C4×C13—212no—
128C2×C4×C13—212no—
129C2×C4×C13—26no—
130C2×C4×C13—26no—
131C2×C4×C13—26no—
132C2×C4×C13—46no—
133C2×C4×C13—46no—
134C2×C4×C13C2×C4214yes—
135C2×C4×C13C4×D4112yes—
136C2×Dic13—26no—
137C2×Dic13—26no—
138C2×Dic13—26no—
139C2×Dic13—26no—
140C2×Dic13—26no—
141C2×Dic13—26no—
142C2×Dic13—26no—
143C2×Dic13—26no—
144C2×Dic13—46no—
145C2×Dic13—43no—
146C2×Dic13—43no—
147C2×Dic13—46no—
148C2×Dic13—43no—
149C2×Dic13—43no—
150C2×Dic13C2×C4214yes—
151C4×D13—448no—
152C24×C4—133no—
153C22×C22⋊C4—131no—
154C22×C22⋊C4—133no—
155C22×C42—133no—
156C22×C42C2×D1313yes—
157C4×C22⋊C4—1324no—
158#376—264no—
159C2×#95—133no—
160C2×#95—133no—
161C2×#95—133no—
162C2×#95—133no—
163C2×#95—136no—
164C2×#95—264no—
165C2×#95C2×D1313yes—
166C2×#95C2×D1311yescharacteristic
167C22×C13C22×C4211yescharacteristic
168C22×C13C2×#11713yes—
169C22×C13C2×#11713yes—
170C22×C13C2×C4×D413yes—
171C22×C13C4×#4113yes—
172C22×C13#51813yes—
173C22×C13#52013yes—
174C22×C13#54613yes—
175C22×C13#54811yescharacteristic
176C22×C13#55116yes—
177C22×C13#55213yes—
178C22×C13#55313yes—
179C2×D13—212no—
180C2×D13—212no—
181C2×D13—212no—
182C2×D13—212no—
183C2×D13—24no—
184C2×D13—24no—
185C2×D13#37618yescomplemented
186C4×C13—212no—
187C4×C13—24no—
188C4×C13—46no—
189Dic13—24no—
190Dic13—46no—
191Dic13—46no—
192C25—131no—
193C23×C4—131no—
194C23×C4—133no—
195C23×C4—133no—
196C23×C4—1312no—
197C23×C4—2612no—
198C23×C4—266no—
199C23×C4—266no—
200C23×C4—526no—
201C23×C4C22×D1313yes—
202C23×C4C22×D1311yescharacteristic
203C23×C4C22×D1313yes—
204C2×C22⋊C4—1312no—
205C2×C22⋊C4—1312no—
206C2×C22⋊C4—266no—
207C2×C22⋊C4—266no—
208C2×C42—46no—
209C2×C42—1312no—
210C2×C42—266no—
211C2×C42—266no—
212C2×C42C4×D13112yescomplemented
213#95—26no—
214#95—1312no—
215#95—1312no—
216#95—266no—
217#95—266no—
218#95—526no—
219#95D5214yes—
220C2×C13C2×#37611yescharacteristic
221C2×C13C42×D411yescharacteristic
222C2×C13#227511yescharacteristic
223C2×C13#234213yes—
224C2×C13#234313yes—
225C2×C13#235213yes—
226C2×C13#235313yes—
227D13—28no—
228C24—136no—
229C24—132no—
230C24—136no—
231C24—261no—
232C24—263no—
233C24—263no—
234C24—261no—
235C24C23×D1311yescharacteristic
236C22×C4—23no—
237C22×C4—26no—
238C22×C4—21no—
239C22×C4—26no—
240C22×C4—26no—
241C22×C4—26no—
242C22×C4—23no—
243C22×C4—23no—
244C22×C4—136no—
245C22×C4—136no—
246C22×C4—136no—
247C22×C4—2624no—
248C22×C4—261no—
249C22×C4—263no—
250C22×C4—263no—
251C22×C4—263no—
252C22×C4—263no—
253C22×C4—263no—
254C22×C4—263no—
255C22×C4—266no—
256C22×C4—263no—
257C22×C4—263no—
258C22×C4—263no—
259C22×C4—266no—
260C22×C4—2624no—
261C22×C4—5212no—
262C22×C4—5224no—
263C22×C4—5224no—
264C22×C4C2×C4×D1316yes—
265C22×C4C2×C4×D1316yes—
266C22×C4C2×C4×D1316yes—
267C22×C4C2×D5216yes—
268C22×C4#612716yes—
269C22⋊C4—1316no—
270C22⋊C4—2624no—
271C42—412no—
272C42—2624no—
273C13#1380911yescharacteristic, complemented, Sylow
274C23—134no—
275C23—1312no—
276C23—1312no—
277C23—266no—
278C23—266no—
279C23—266no—
280C23—266no—
281C23—266no—
282C23—2612no—
283C23—266no—
284C23—262no—
285C23—266no—
286C23C22×C4×D1313yes—
287C23C22×D5211yescharacteristic
288C23C2×#612713yes—
289C23#8825113yes—
290C23#8825411yescharacteristic
291C23#41×D1313yes—
292C23#41×D1311yescharacteristic
293C2×C4—26no—
294C2×C4—26no—
295C2×C4—26no—
296C2×C4—26no—
297C2×C4—212no—
298C2×C4—212no—
299C2×C4—26no—
300C2×C4—26no—
301C2×C4—26no—
302C2×C4—46no—
303C2×C4—46no—
304C2×C4—134no—
305C2×C4—266no—
306C2×C4—266no—
307C2×C4—266no—
308C2×C4—266no—
309C2×C4—266no—
310C2×C4—266no—
311C2×C4—266no—
312C2×C4—266no—
313C2×C4—5248no—
314C2×C4—523no—
315C2×C4—526no—
316C2×C4—526no—
317C2×C4—523no—
318C2×C4—523no—
319C2×C4—523no—
320C2×C4C42×D1314yes—
321C2×C4C4×D52112yes—
322C22—138no—
323C22—264no—
324C22—2612no—
325C22—264no—
326C22—2612no—
327C22—2612no—
328C22—2612no—
329C22C2×C42×D1311yescharacteristic
330C22C2×C4×D5213yes—
331C22C4×#612713yes—
332C22#1171919113yes—
333C22#1171920913yes—
334C22D13×#11713yes—
335C22D13×#11713yes—
336C22#1171925913yes—
337C22#1171926116yes—
338C22#1171926313yes—
339C22#1171928111yescharacteristic
340C22#1171928613yes—
341C4—24no—
342C4—212no—
343C4—46no—
344C4—264no—
345C4—526no—
346C4—526no—
347C2—268no—
348C2D13×#37611yescharacteristic
349C2C42×D5211yescharacteristic
350C2#1311719411yescharacteristic
351C2#1311768813yes—
352C2#1311769913yes—
353C2#1311776813yes—
354C2#1311777913yes—
subgroupG/H
center, FrattiniC24C23×D13
commutatorC22×C13C22×C42
FittingC4×C13×#95C2
socle, cosocleC24×C13C24
prime radicalC24×D13C23
hypercenterC4×#95D13
hypocenterC13#13809
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C24 ◁ C4×#95

Complements

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

NH ≅ G/Ntype
2. C2×#11718309C2semidirect
4. #13113063C2semidirect
5. #13113060C2semidirect
7. C4×C13×#95C2semidirect
20. C4×#6103C4semidirect
36. C2×C42×C13C2×C4semidirect
43. C2×C4×Dic13C2×C4semidirect
49. #88071C2×C4semidirect
50. #88071C2×C4semidirect
103. C4×#95D13semidirect
185. C2×D13#376semidirect
212. C2×C42C4×D13semidirect
273. C13#13809semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#61032
C2×#117183092
C2×D13×#952
#131130632
#131130602
#131130572
C4×C13×#952
#1380913