Finite Group Databasebeta

← #15759618

Subgroups — #15759618

Order 3328.

594 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13125777C211yesmaximal, characteristic
2#13115817C211yesmaximal, characteristic, complemented
3#13113504C211yesmaximal, characteristic
4#13113399C211yesmaximal, characteristic, complemented
5#13112694C211yesmaximal, characteristic, complemented
6#13112665C211yesmaximal, characteristic, complemented
7C13×#2328C211yesmaximal, characteristic
8C2×C13×#127C2211yescharacteristic
9C2×C4×D4×C13—21no—
10#11719175C2211yescharacteristic
11C13×#390—21no—
12C13×#386—22no—
13C13×#386—22no—
14C13×#382C2211yescharacteristic
15C13×#376C2211yescharacteristic
16#11718879—22no—
17#11718737C412yescomplemented
18#11718736—22no—
19#11718731C412yescomplemented
20#11718586C2211yescharacteristic
21#11718586C2211yescharacteristic
22#11718585C2211yescharacteristic
23#11718136—22no—
24#11718115—21no—
25#11718115—21no—
26#11718044—22no—
27C22×D4×C13—21no—
28C22×D4×C13—21no—
29C22×D4×C13D412yes—
30C23×C4×C13—22no—
31C13×#127—21no—
32C13×#127—21no—
33C13×#127C2×C412yes—
34C13×#127D412yes—
35C4×D4×C13—42no—
36C4×D4×C13—42no—
37C2×C13×C4⋊C4—21no—
38C2×C13×C22⋊C4—22no—
39C2×C13×C22⋊C4—22no—
40C2×C13×C22⋊C4—22no—
41C2×C42×C13D411yescharacteristic
42C2×C42×C13D411yescharacteristic
43C2×C42×C13C2311yescharacteristic
44C2×#6105—24no—
45#88180—21no—
46#88178—21no—
47#88178—21no—
48C2×#6099—21no—
49#88124—21no—
50#88123C2×C411yescharacteristic, complemented
51#88123C2×C411yescharacteristic, complemented
52C4×Dic26—21no—
53C4×Dic26—21no—
54C13×#95—21no—
55C13×#95—21no—
56C13×#95—21no—
57C13×#95D412yes—
58#88072—24no—
59C22⋊#1055—21no—
60C22⋊#1055—21no—
61C4⋊#1055—21no—
62C4⋊#1055—21no—
63C4⋊#1055—21no—
64C4⋊#1055—21no—
65C4×#1055—21no—
66C4×#1055C2×C412yescomplemented
67#9295—131nomaximal, Sylow
68C24×C13—22no—
69C2×D4×C13—22no—
70C2×D4×C13—22no—
71C2×D4×C13—22no—
72C2×D4×C13—22no—
73C2×D4×C13—22no—
74C2×D4×C13—41no—
75C2×D4×C13—41no—
76C2×D4×C13—41no—
77C2×D4×C13—41no—
78C2×D4×C13—82no—
79C2×D4×C13—82no—
80C2×D4×C13C22⋊C414yes—
81C22×C4×C13—21no—
82C22×C4×C13—21no—
83C22×C4×C13—22no—
84C22×C4×C13—44no—
85C22×C4×C13—82no—
86C22×C4×C13—82no—
87C22×C4×C13C2×D411yescharacteristic
88C22×C4×C13C2×D411yescharacteristic
89C22×C4×C13C2×D411yescharacteristic
90C2×Dic26—21no—
91C2×Dic26—21no—
92C13×C4⋊C4—41no—
93C13×C4⋊C4—41no—
94C13×C22⋊C4—44no—
95C13×C22⋊C4—82no—
96C13×C22⋊C4—82no—
97C42×C13—21no—
98C42×C13—21no—
99C42×C13—21no—
100C42×C13SD1612yescomplemented
101C42×C13C22×C411yescharacteristic
102C42×C13C2×D411yescharacteristic
103C42×C13#4111yescharacteristic
104C42×C13#4111yescharacteristic
105C22⋊Dic13—41no—
106#6105—84no—
107C4⋊Dic13—21no—
108C4⋊Dic13—21no—
109C4⋊Dic13—21no—
110C4⋊Dic13—21no—
111#6101—41no—
112#6101—41no—
113C4×Dic13—41no—
114#6099—41no—
115#6099—41no—
116C2×#1055—22no—
117C2×#1055—41no—
118C2×#1055—41no—
119#3208—131no—
120#2328D1311yescharacteristic
121#1995—131no—
122#1545—131no—
123#1518—131no—
124#1286—131no—
125#1274—131no—
126C23×C13—24no—
127C23×C13—42no—
128C23×C13—42no—
129C23×C13—42no—
130C23×C13—42no—
131C23×C13—42no—
132C23×C13—42no—
133C23×C13#12011yescharacteristic
134D4×C13—44no—
135D4×C13—42no—
136D4×C13—42no—
137D4×C13—42no—
138D4×C13—42no—
139D4×C13—82no—
140D4×C13—82no—
141D4×C13—82no—
142C2×C4×C13—22no—
143C2×C4×C13—41no—
144C2×C4×C13—41no—
145C2×C4×C13—41no—
146C2×C4×C13—41no—
147C2×C4×C13—41no—
148C2×C4×C13—41no—
149C2×C4×C13—42no—
150C2×C4×C13—42no—
151C2×C4×C13—42no—
152C2×C4×C13—41no—
153C2×C4×C13—88no—
154C2×C4×C13C2×C22⋊C411yescharacteristic
155C2×C4×C13C4×D411yescharacteristic
156C2×C4×C13C4×D411yescharacteristic
157C2×C4×C13#12111yescharacteristic
158C2×C4×C13#12111yescharacteristic
159C2×C4×C13#12311yescharacteristic
160C2×C4×C13C2×SD1611yescharacteristic
161C2×C4×C13#13511yescharacteristic
162C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
163C2×C4×C13#13711yescharacteristic
164C2×Dic13—41no—
165C2×Dic13—41no—
166Dic26—42no—
167Dic26—81no—
168#1055—42no—
169#1055—81no—
170#1055—81no—
171#533—131no—
172C2×#127C2×D1311yescharacteristic
173C2×C4×D4—21no—
174#492—132no—
175#486—132no—
176#460—262no—
177#450—262no—
178#431—131no—
179#431—131no—
180#423—131no—
181#390—21no—
182#386—22no—
183#386—22no—
184#382C2×D1311yescharacteristic
185#376C2×D1311yescharacteristic
186#339—261no—
187#339—261no—
188#331—262no—
189#328—262no—
190C22×C13—21no—
191C22×C13—21no—
192C22×C13—44no—
193C22×C13—44no—
194C22×C13—44no—
195C22×C13—82no—
196C22×C13—82no—
197C22×C13—82no—
198C22×C13—82no—
199C22×C13#38611yescharacteristic
200C22×C13#45011yescharacteristic
201C22×C13#45211yescharacteristic
202C4×C13—21no—
203C4×C13—21no—
204C4×C13—21no—
205C4×C13—21no—
206C4×C13—42no—
207C4×C13—81no—
208C4×C13—82no—
209C4×C13C4×SD1611yescharacteristic
210C4×C13#44011yescharacteristic
211C4×C13#46111yescharacteristic
212C4×C13#46311yescharacteristic
213Dic13—81no—
214Dic13—81no—
215C22×D4—21no—
216C22×D4—21no—
217C22×D4C22⋊D1312yes—
218C23×C4—22no—
219C2×SD16—264no—
220C2×M16—261no—
221C4⋊Q8—131no—
222C4⋊Q8—131no—
223#127—21no—
224#127—21no—
225#127C4×D1312yes—
226#127D5212yes—
227#125—261no—
228C22⋊Q8—261no—
229C22⋊Q8—261no—
230C4×Q8—261no—
231C4×Q8—261no—
232C4×D4—42no—
233C4×D4—42no—
234#117—261no—
235C2×C4⋊C4—21no—
236C2×C22⋊C4—22no—
237C2×C22⋊C4—22no—
238C2×C22⋊C4—22no—
239C2×C42C22⋊D1311yescharacteristic
240C2×C42C22⋊D1311yescharacteristic
241C2×C42C22×D1311yescharacteristic
242C4⋊C8—261no—
243C4⋊C8—261no—
244C4⋊C8—261no—
245C4⋊C8—261no—
246#102—264no—
247C22⋊C8—261no—
248C22⋊C8—261no—
249C4×C8—132no—
250C4×C8—261no—
251#95—21no—
252#95—21no—
253#95—21no—
254#95C22⋊D1312yes—
255C2×C13—21no—
256C2×C13—21no—
257C2×C13—84no—
258C2×C13#187711yescharacteristic
259C2×C13#190411yescharacteristic
260C2×C13#191111yescharacteristic
261C24—22no—
262C2×Q8—261no—
263C2×Q8—261no—
264C2×D4—22no—
265C2×D4—22no—
266C2×D4—22no—
267C2×D4—22no—
268C2×D4—22no—
269C2×D4—41no—
270C2×D4—41no—
271C2×D4—41no—
272C2×D4—41no—
273C2×D4—82no—
274C2×D4—82no—
275C2×D4#610314yes—
276C22×C4—21no—
277C22×C4—21no—
278C22×C4—22no—
279C22×C4—44no—
280C22×C4—82no—
281C22×C4—82no—
282C22×C4C2×C22⋊D1311yescharacteristic
283C22×C4C2×C22⋊D1311yescharacteristic
284C22×C4C2×C22⋊D1311yescharacteristic
285SD16—1044no—
286M16—521no—
287M16—521no—
288C2×C8—262no—
289C2×C8—521no—
290C2×C8—521no—
291C4⋊C4—41no—
292C4⋊C4—41no—
293C4⋊C4—261no—
294C4⋊C4—261no—
295C4⋊C4—261no—
296C4⋊C4—261no—
297C4⋊C4—521no—
298C4⋊C4—521no—
299C22⋊C4—44no—
300C22⋊C4—82no—
301C22⋊C4—82no—
302C22⋊C4—521no—
303C42—21no—
304C42—21no—
305C42—21no—
306C42—521no—
307C42#610512yescomplemented
308C42C2×C4×D1311yescharacteristic
309C42C2×D5211yescharacteristic
310C42#612711yescharacteristic
311C42#612711yescharacteristic
312C13#929511yescharacteristic, complemented, Sylow
313C23—24no—
314C23—42no—
315C23—42no—
316C23—42no—
317C23—42no—
318C23—42no—
319C23—42no—
320C23#8820711yescharacteristic
321Q8—522no—
322Q8—1041no—
323D4—44no—
324D4—42no—
325D4—42no—
326D4—42no—
327D4—42no—
328D4—82no—
329D4—82no—
330D4—82no—
331C2×C4—22no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—41no—
338C2×C4—42no—
339C2×C4—42no—
340C2×C4—42no—
341C2×C4—41no—
342C2×C4—88no—
343C2×C4—521no—
344C2×C4—521no—
345C2×C4C2×#610311yescharacteristic
346C2×C4C4×C22⋊D1311yescharacteristic
347C2×C4C4×C22⋊D1311yescharacteristic
348C2×C4#8818311yescharacteristic
349C2×C4#8818411yescharacteristic
350C2×C4#8818411yescharacteristic
351C2×C4#8818611yescharacteristic
352C2×C4C2×#610511yescharacteristic
353C2×C4#8820411yescharacteristic
354C2×C4#8820511yescharacteristic
355C8—522no—
356C8—1041no—
357C8—1041no—
358C22—21no—
359C22—21no—
360C22—44no—
361C22—44no—
362C22—44no—
363C22—82no—
364C22—82no—
365C22—82no—
366C22—82no—
367C22#1171887411yescharacteristic
368C22#1171887911yescharacteristic
369C22#1171890011yescharacteristic
370C4—21no—
371C4—21no—
372C4—21no—
373C4—21no—
374C4—42no—
375C4—81no—
376C4—82no—
377C4—1041no—
378C4—1041no—
379C4#1171867711yescharacteristic
380C4C4×#610511yescharacteristic
381C4#1171867911yescharacteristic
382C4#1171868011yescharacteristic
383C2—21no—
384C2—21no—
385C2—84no—
386C2#1311517011yescharacteristic
387C2#1311532311yescharacteristic
388C2#1311536811yescharacteristic
subgroupG/H
centerC22#11718874
commutatorC42×C13C22×C4
FrattiniC2×C42C22×D13
FittingC13×#2328C2
socleC22×C13#386
prime radicalC2×C13×#127C22
cosocleC2×C42×C13C23
hypercenter#2328D13
hypocenterC13#9295
LCSG ▷ C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2328

Complements

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

NH ≅ G/Ntype
2. #13115817C2semidirect
4. #13113399C2semidirect
5. #13112694C2semidirect
6. #13112665C2semidirect
17. #11718737C4semidirect
19. #11718731C4semidirect
50. #88123C2×C4semidirect
51. #88123C2×C4semidirect
66. C4×#1055C2×C4semidirect
100. C42×C13SD16semidirect
307. C42#6105semidirect
312. C13#9295semidirect

Maximal subgroups

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

subgroupindex
#131257772
#131158172
#131135042
#131133992
#131126942
#131126652
C13×#23282
#929513