Finite Group Databasebeta

← #15846785

Subgroups — #15846785

Order 3328.

650 conjugacy classes of subgroups.

The subgroup lattice has 352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13124954C212yesmaximal, complemented
2C2×C8×Dic26C211yesmaximal, characteristic, complemented
3#13114249C214yesmaximal, complemented
4#13114237C212yesmaximal, complemented
5#13114193C212yesmaximal, complemented
6#13113599C211yesmaximal, characteristic, complemented
7#13113531C212yesmaximal, complemented
8C13×#3169C211yesmaximal, characteristic
9C13×#532C2212yes—
10C2×C4×Dic26C2211yescharacteristic
11C13×#500C2211yescharacteristic
12C13×#493C2211yescharacteristic
13C13×#486C2212yes—
14C13×#466—21no—
15C13×#466—21no—
16C4×C13×D8—21no—
17C4×C13×D8—21no—
18C2×C4×C8×C13C2211yescharacteristic
19C2×#88054—21no—
20C2×C8×Dic13—21no—
21#11718752C2214yes—
22#11718736C2214yes—
23#11718701—22no—
24#11718694—22no—
25#11718679—24no—
26#11718587C2212yes—
27C2×C4⋊#1055C2211yescharacteristic
28C8×Dic26—21no—
29C8×Dic26—21no—
30C8×Dic26C2212yes—
31C8×Dic26C2212yes—
32#11718138C2214yes—
33#11718136C2214yes—
34#11718050C2212yes—
35#11718049C2212yes—
36C2×C13×#41—22no—
37C22×Dic26D411yescharacteristic
38C2×C13×D8—21no—
39C2×C13×D8—21no—
40C22×C8×C13D411yescharacteristic
41C22×C8×C13D411yescharacteristic
42C13×C4⋊Q8C2312yes—
43C13×#127C2312yes—
44C13×#124—22no—
45C13×#121—22no—
46C13×#121—22no—
47C4×D4×C13—22no—
48C4×D4×C13—22no—
49C2×C42×C13C2311yescharacteristic
50C2×#6105—24no—
51C2×C4⋊Dic13D411yescharacteristic
52C2×#6101—21no—
53C2×C4×Dic13—21no—
54C22×#1055—21no—
55C4×Dic26—21no—
56C4×Dic26—21no—
57C4×Dic26D412yes—
58C4×Dic26C2312yes—
59C13×#107—21no—
60C13×#107—21no—
61C13×#102—22no—
62C13×#102—22no—
63C4×C8×C13D411yescharacteristic
64C4×C8×C13D411yescharacteristic
65C4×C8×C13C2311yescharacteristic
66C4×C8×C13C2311yescharacteristic
67#88072—24no—
68C22⋊#1055—22no—
69#88054—22no—
70#88054—22no—
71C8×Dic13—22no—
72C8×Dic13—22no—
73#88050—24no—
74#88047—24no—
75C4⋊#1055—21no—
76C4⋊#1055C2314yes—
77C4⋊#1055C2312yes—
78#88043—22no—
79#19264—131nomaximal, Sylow
80C13×#41—84no—
81C2×Q8×C13—22no—
82C2×D4×C13—22no—
83C2×D4×C13—22no—
84C2×D4×C13—22no—
85C2×D4×C13—42no—
86C22×C4×C13—42no—
87C22×C4×C13C2×D411yescharacteristic
88C22×C4×C13C2×D411yescharacteristic
89C22×C4×C13#4111yescharacteristic
90C22×Dic13—21no—
91C22×Dic13—21no—
92C2×Dic26—21no—
93C2×Dic26—24no—
94C2×Dic26C2×D412yes—
95C13×D8—42no—
96C13×D8—42no—
97C2×C8×C13—22no—
98C2×C8×C13—41no—
99C2×C8×C13C2×D411yescharacteristic
100C2×C8×C13C2×D411yescharacteristic
101C2×C8×C13C2×D411yescharacteristic
102C2×C8×C13C2×D411yescharacteristic
103C13×C4⋊C4—22no—
104C13×C4⋊C4—22no—
105C13×C22⋊C4—42no—
106C13×C22⋊C4—42no—
107C42×C13C2×D411yescharacteristic
108C42×C13C2×D411yescharacteristic
109C42×C13#4111yescharacteristic
110C42×C13C2411yescharacteristic
111#6105—48no—
112C4⋊Dic13—21no—
113C4⋊Dic13C2×D412yes—
114#6101—22no—
115#6101—22no—
116C4×Dic13—22no—
117C4×Dic13—22no—
118C2×#1055—24no—
119C2×#1055—22no—
120C2×#1055—42no—
121#3169D1311yescharacteristic
122#3112—132no—
123C2×C8×Q8—131no—
124#1678—134no—
125#1676—132no—
126#1668—132no—
127#1568—131no—
128#1551—132no—
129C23×C13—42no—
130C23×C13#12111yescharacteristic
131Q8×C13—82no—
132D4×C13—44no—
133D4×C13—42no—
134D4×C13—42no—
135D4×C13—82no—
136D4×C13—84no—
137C2×C4×C13—22no—
138C2×C4×C13—22no—
139C2×C4×C13—21no—
140C2×C4×C13—21no—
141C2×C4×C13—42no—
142C2×C4×C13—84no—
143C2×C4×C13#12111yescharacteristic
144C2×C4×C13#12111yescharacteristic
145C2×C4×C13#12111yescharacteristic
146C2×C4×C13C22×D411yescharacteristic
147C2×C4×C13C22×D411yescharacteristic
148C2×C4×C13C2×#4111yescharacteristic
149C2×Dic13—24no—
150C2×Dic13—22no—
151C2×Dic13—22no—
152C2×Dic13—42no—
153Dic26—24no—
154Dic26—22no—
155Dic26#13514yes—
156C8×C13—21no—
157C8×C13—21no—
158C8×C13—21no—
159C8×C13#13712yes—
160#1055—44no—
161#1055—42no—
162#532C2×D1312yes—
163C2×C4×Q8—131no—
164#500C2×D1311yescharacteristic
165#493C2×D1311yescharacteristic
166#486C2×D1312yes—
167#480—262no—
168#477—134no—
169#466—21no—
170#466—21no—
171#460—134no—
172#448—262no—
173C8×Q8—132no—
174C8×Q8—132no—
175C8×Q8—261no—
176C8×Q8—261no—
177#440—264no—
178C4×D8—21no—
179C4×D8—21no—
180#432—132no—
181C2×C4⋊C8—131no—
182C2×C4⋊C8—261no—
183C2×C4×C8—261no—
184C2×C4×C8C2×D1311yescharacteristic
185#335—132no—
186#334—132no—
187#333—134no—
188#331—134no—
189C22×C13—21no—
190C22×C13—21no—
191C22×C13—82no—
192C22×C13—82no—
193C22×C13—82no—
194C22×C13#47212yes—
195C22×C13C2×#12111yescharacteristic
196C4×C13—21no—
197C4×C13—21no—
198C4×C13—21no—
199C4×C13—21no—
200C4×C13—82no—
201C4×C13C2×#13512yes—
202C4×C13C2×#13711yescharacteristic
203C4×C13#57511yescharacteristic
204Dic13—24no—
205Dic13—42no—
206C2×#41—22no—
207C22×Q8—131no—
208C2×SD16—264no—
209C2×D8—21no—
210C2×D8—21no—
211C22×C8—261no—
212C22×C8C22⋊D1311yescharacteristic
213C22×C8C22⋊D1311yescharacteristic
214C4⋊Q8C22×D1312yes—
215#127C22×D1312yes—
216#124—22no—
217#121—22no—
218#121—22no—
219C4×Q8—132no—
220C4×Q8—132no—
221C4×Q8—261no—
222C4×Q8—261no—
223C4×D4—22no—
224C4×D4—22no—
225C2×C4⋊C4—131no—
226C2×C4⋊C4—261no—
227C2×C42—261no—
228C2×C42C22×D1311yescharacteristic
229#107—21no—
230#107—21no—
231#107—264no—
232C4⋊C8—132no—
233C4⋊C8—134no—
234C4⋊C8—262no—
235C4⋊C8—262no—
236C4⋊C8—261no—
237#103—264no—
238#102—22no—
239#102—22no—
240#102—264no—
241C22⋊C8—262no—
242#97—262no—
243C4×C8—262no—
244C4×C8—262no—
245C4×C8C22⋊D1311yescharacteristic
246C4×C8C22⋊D1311yescharacteristic
247C4×C8C22×D1311yescharacteristic
248C4×C8C22×D1311yescharacteristic
249C2×C13—22no—
250C2×C13—162no—
251C2×C13#303711yescharacteristic
252C2×C13#305011yescharacteristic
253C2×C13C2×#47211yescharacteristic
254#41—84no—
255C2×Q8—22no—
256C2×Q8—132no—
257C2×Q8—264no—
258C2×Q8—261no—
259C2×D4—22no—
260C2×D4—22no—
261C2×D4—22no—
262C2×D4—42no—
263C22×C4—42no—
264C22×C4—261no—
265C22×C4—261no—
266C22×C4D4×D1311yescharacteristic
267C22×C4#612911yescharacteristic
268C22×C4C2×C22⋊D1311yescharacteristic
269SD16—528no—
270D8—42no—
271D8—42no—
272C2×C8—22no—
273C2×C8—41no—
274C2×C8—264no—
275C2×C8—262no—
276C2×C8—522no—
277C2×C8C2×C22⋊D1311yescharacteristic
278C2×C8C2×C22⋊D1311yescharacteristic
279C2×C8C2×C22⋊D1311yescharacteristic
280C2×C8C2×C22⋊D1311yescharacteristic
281C4⋊C4—22no—
282C4⋊C4—22no—
283C4⋊C4—132no—
284C4⋊C4—261no—
285C4⋊C4—262no—
286C4⋊C4—262no—
287C22⋊C4—42no—
288C22⋊C4—42no—
289C42—262no—
290C42—262no—
291C42D4×D1311yescharacteristic
292C42#612911yescharacteristic
293C42C2×C22⋊D1311yescharacteristic
294C42C23×D1311yescharacteristic
295C13#1926411yescharacteristic, complemented, Sylow
296C23—42no—
297C23#8819211yescharacteristic
298Q8—82no—
299Q8—134no—
300Q8—264no—
301Q8—262no—
302D4—44no—
303D4—42no—
304D4—42no—
305D4—82no—
306D4—84no—
307C2×C4—22no—
308C2×C4—22no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—42no—
312C2×C4—84no—
313C2×C4—264no—
314C2×C4—262no—
315C2×C4—262no—
316C2×C4—522no—
317C2×C4#8819211yescharacteristic
318C2×C4#8819211yescharacteristic
319C2×C4#8819211yescharacteristic
320C2×C4C2×D4×D1311yescharacteristic
321C2×C4C2×#612911yescharacteristic
322C2×C4C22×C22⋊D1311yescharacteristic
323C8—21no—
324C8—21no—
325C8—21no—
326C8—524no—
327C8—522no—
328C8#8820512yes—
329C22—21no—
330C22—21no—
331C22—82no—
332C22—82no—
333C22—82no—
334C22#1171882112yes—
335C22C2×#8819211yescharacteristic
336C4—21no—
337C4—21no—
338C4—21no—
339C4—21no—
340C4—82no—
341C4—264no—
342C4—522no—
343C4D13×#13512yes—
344C4#1171952711yescharacteristic
345C4C2×#8820511yescharacteristic
346C2—22no—
347C2—162no—
348C2#1312430411yescharacteristic
349C2#1312441311yescharacteristic
350C2C2×#1171882111yescharacteristic
subgroupG/H
centerC22C2×#88192
commutator, cosocleC42×C13C24
FrattiniC42C23×D13
Fitting, prime radicalC13×#3169C2
socleC22×C13C2×#121
hypercenter#3169D13
hypocenterC13#19264
LCSG ▷ C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3169

Complements

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

NH ≅ G/Ntype
1. #13124954C2semidirect
2. C2×C8×Dic26C2semidirect
3. #13114249C2semidirect
4. #13114237C2semidirect
5. #13114193C2semidirect
6. #13113599C2semidirect
7. #13113531C2semidirect
295. C13#19264semidirect

Maximal subgroups

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

subgroupindex
#131249542
C2×C8×Dic262
#131142492
#131142372
#131141932
#131135992
#131135312
C13×#31692
#1926413