Finite Group Databasebeta

← #15759170

Subgroups — #15759170

Order 3328.

686 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13124844C211yesmaximal, characteristic
2#13115813C211yesmaximal, characteristic, complemented
3#13113334C211yesmaximal, characteristic, complemented
4#13113261C211yesmaximal, characteristic
5#13112739C211yesmaximal, characteristic, complemented
6#13112669C211yesmaximal, characteristic, complemented
7C42×D4×C13C211yesmaximal, characteristic
8C2×C4×D4×C13—21no—
9C2×C4×D4×C13C2211yescharacteristic
10C22×C42×C13—21no—
11#11719175C2211yescharacteristic
12C4×C13×C4⋊C4—21no—
13C4×C13×C4⋊C4C2211yescharacteristic
14C4×C13×C22⋊C4—21no—
15C4×C13×C22⋊C4—22no—
16C43×C13C2211yescharacteristic
17#11718879—21no—
18#11718680C412yescomplemented
19C4×#6105—22no—
20#11718669C412yescomplemented
21#11718632—21no—
22#11718586C2211yescharacteristic
23#11718586C2211yescharacteristic
24#11718585C2211yescharacteristic
25D4⋊#1055—22no—
26#11718115—21no—
27#11718115—21no—
28#11718044—22no—
29C22×D4×C13D411yescharacteristic
30C23×C4×C13—22no—
31C23×C4×C13—21no—
32C4×D4×C13—28no—
33C4×D4×C13—21no—
34C4×D4×C13—21no—
35C4×D4×C13C2×C412yes—
36C4×D4×C13D412yes—
37C2×C13×C4⋊C4—21no—
38C2×C13×C4⋊C4D411yescharacteristic
39C2×C13×C22⋊C4—22no—
40C2×C13×C22⋊C4—21no—
41C2×C42×C13—21no—
42C2×C42×C13—22no—
43C2×C42×C13—21no—
44C2×C42×C13—21no—
45C2×C42×C13—42no—
46C2×C42×C13—42no—
47C2×C42×C13D411yescharacteristic
48C2×C42×C13D411yescharacteristic
49C2×C42×C13C2311yescharacteristic
50C2×#6105—22no—
51#88180—21no—
52#88178—21no—
53#88178—21no—
54C2×#6099—21no—
55#88124—21no—
56#88123C2×C411yescharacteristic, complemented
57#88123C2×C411yescharacteristic, complemented
58C4×Dic26—21no—
59C4×Dic26—21no—
60C13×#95—22no—
61C13×#95D412yes—
62#88072—22no—
63C22⋊#1055—21no—
64C22⋊#1055—21no—
65#88050—22no—
66#88048—22no—
67C4⋊#1055—21no—
68C4⋊#1055—21no—
69C4⋊#1055—21no—
70C4⋊#1055C2×C412yescomplemented
71C4×#1055—21no—
72C4×#1055—21no—
73#9231—131nomaximal, Sylow
74C24×C13—21no—
75C2×D4×C13—24no—
76C2×D4×C13—21no—
77C2×D4×C13C22⋊C412yes—
78C22×C4×C13—21no—
79C22×C4×C13—28no—
80C22×C4×C13—21no—
81C22×C4×C13—21no—
82C22×C4×C13—22no—
83C22×C4×C13—22no—
84C22×C4×C13—22no—
85C22×C4×C13—44no—
86C22×C4×C13—44no—
87C22×C4×C13—41no—
88C22×C4×C13—41no—
89C22×C4×C13—41no—
90C22×C4×C13—41no—
91C22×C4×C13C2×D411yescharacteristic
92C22×C4×C13C2×D411yescharacteristic
93C22×C4×C13C2×D411yescharacteristic
94C2×Dic26—21no—
95C2×Dic26—21no—
96C13×C4⋊C4—24no—
97C13×C4⋊C4—21no—
98C13×C4⋊C4C22⋊C412yes—
99C13×C22⋊C4—28no—
100C13×C22⋊C4—22no—
101C13×C22⋊C4—22no—
102C42×C13—24no—
103C42×C13—21no—
104C42×C13—21no—
105C42×C13—21no—
106C42×C13—42no—
107C42×C13—44no—
108C42×C13—41no—
109C42×C13—41no—
110C42×C13SD1612yescomplemented
111C42×C13C22×C411yescharacteristic
112C42×C13C2×D411yescharacteristic
113C42×C13#4111yescharacteristic
114C42×C13#4111yescharacteristic
115C22⋊Dic13—41no—
116#6105—44no—
117C4⋊Dic13—21no—
118C4⋊Dic13—21no—
119C4⋊Dic13—21no—
120C4⋊Dic13—21no—
121#6101—41no—
122#6101—41no—
123C4×Dic13—41no—
124#6099—41no—
125#6099—41no—
126C2×#1055—22no—
127C2×#1055—41no—
128C2×#1055—41no—
129#3101—131no—
130C42×D4D1311yescharacteristic
131#1994—131no—
132#1503—131no—
133#1486—131no—
134#1303—131no—
135#1276—131no—
136C23×C13—24no—
137C23×C13—22no—
138C23×C13—42no—
139C23×C13—41no—
140C23×C13—41no—
141C23×C13#12011yescharacteristic
142D4×C13—24no—
143D4×C13—22no—
144D4×C13#10414yes—
145C2×C4×C13—22no—
146C2×C4×C13—22no—
147C2×C4×C13—22no—
148C2×C4×C13—22no—
149C2×C4×C13—22no—
150C2×C4×C13—24no—
151C2×C4×C13—22no—
152C2×C4×C13—41no—
153C2×C4×C13—416no—
154C2×C4×C13—41no—
155C2×C4×C13—42no—
156C2×C4×C13—42no—
157C2×C4×C13—41no—
158C2×C4×C13—41no—
159C2×C4×C13—41no—
160C2×C4×C13—42no—
161C2×C4×C13—42no—
162C2×C4×C13—42no—
163C2×C4×C13—42no—
164C2×C4×C13C2×C22⋊C411yescharacteristic
165C2×C4×C13C4×D411yescharacteristic
166C2×C4×C13C4×D411yescharacteristic
167C2×C4×C13#12111yescharacteristic
168C2×C4×C13#12111yescharacteristic
169C2×C4×C13#12311yescharacteristic
170C2×C4×C13C2×SD1611yescharacteristic
171C2×C4×C13#13511yescharacteristic
172C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
173C2×C4×C13#13711yescharacteristic
174C2×Dic13—41no—
175C2×Dic13—41no—
176Dic26—42no—
177Dic26—81no—
178#1055—42no—
179#1055—81no—
180#1055—81no—
181#533—131no—
182C2×C4×D4—21no—
183C2×C4×D4C2×D1311yescharacteristic
184C22×C42—21no—
185#483—261no—
186#476—132no—
187#461—132no—
188#450—261no—
189C4×SD16—262no—
190#431—131no—
191#431—131no—
192#423—131no—
193C4×C4⋊C4—21no—
194C4×C4⋊C4C2×D1311yescharacteristic
195C4×C22⋊C4—21no—
196C4×C22⋊C4—22no—
197C43C2×D1311yescharacteristic
198#339—261no—
199#339—261no—
200#328—262no—
201D4⋊C8—262no—
202C22×C13—21no—
203C22×C13—21no—
204C22×C13—24no—
205C22×C13—44no—
206C22×C13—44no—
207C22×C13—42no—
208C22×C13—42no—
209C22×C13#38611yescharacteristic
210C22×C13#45011yescharacteristic
211C22×C13#45211yescharacteristic
212C4×C13—24no—
213C4×C13—21no—
214C4×C13—21no—
215C4×C13—21no—
216C4×C13—42no—
217C4×C13—44no—
218C4×C13—42no—
219C4×C13C2×#10412yes—
220C4×C13C4×SD1611yescharacteristic
221C4×C13#44011yescharacteristic
222C4×C13#46111yescharacteristic
223C4×C13#46311yescharacteristic
224Dic13—81no—
225Dic13—81no—
226C22×D4C22⋊D1311yescharacteristic
227C23×C4—22no—
228C23×C4—21no—
229C2×SD16—262no—
230C2×M16—261no—
231C4⋊Q8—131no—
232C4⋊Q8—131no—
233#125—261no—
234C22⋊Q8—261no—
235C22⋊Q8—261no—
236C4×Q8—261no—
237C4×Q8—261no—
238C4×D4—28no—
239C4×D4—21no—
240C4×D4—21no—
241C4×D4C4×D1312yes—
242C4×D4D5212yes—
243#117—261no—
244C2×C4⋊C4—21no—
245C2×C4⋊C4C22⋊D1311yescharacteristic
246C2×C22⋊C4—22no—
247C2×C22⋊C4—21no—
248C2×C42—21no—
249C2×C42—22no—
250C2×C42—21no—
251C2×C42—21no—
252C2×C42—42no—
253C2×C42—42no—
254C2×C42C22⋊D1311yescharacteristic
255C2×C42C22⋊D1311yescharacteristic
256C2×C42C22×D1311yescharacteristic
257#106—262no—
258C4⋊C8—132no—
259C4⋊C8—261no—
260C4⋊C8—261no—
261C4⋊C8—261no—
262#103—262no—
263#102—262no—
264C22⋊C8—261no—
265C22⋊C8—261no—
266C4×C8—261no—
267C4×C8—261no—
268#95—22no—
269#95C22⋊D1312yes—
270C2×C13—21no—
271C2×C13—21no—
272C2×C13—44no—
273C2×C13#187711yescharacteristic
274C2×C13#189611yescharacteristic
275C2×C13#190611yescharacteristic
276C24—21no—
277C2×Q8—261no—
278C2×Q8—261no—
279C2×D4—24no—
280C2×D4—21no—
281C2×D4#610312yes—
282C22×C4—21no—
283C22×C4—28no—
284C22×C4—21no—
285C22×C4—21no—
286C22×C4—22no—
287C22×C4—22no—
288C22×C4—22no—
289C22×C4—44no—
290C22×C4—44no—
291C22×C4—41no—
292C22×C4—41no—
293C22×C4—41no—
294C22×C4—41no—
295C22×C4C2×C22⋊D1311yescharacteristic
296C22×C4C2×C22⋊D1311yescharacteristic
297C22×C4C2×C22⋊D1311yescharacteristic
298SD16—524no—
299M16—521no—
300M16—521no—
301C2×C8—262no—
302C2×C8—521no—
303C2×C8—521no—
304C4⋊C4—24no—
305C4⋊C4—21no—
306C4⋊C4—261no—
307C4⋊C4—261no—
308C4⋊C4—261no—
309C4⋊C4—261no—
310C4⋊C4—521no—
311C4⋊C4—521no—
312C4⋊C4#610312yes—
313C22⋊C4—28no—
314C22⋊C4—22no—
315C22⋊C4—22no—
316C22⋊C4—521no—
317C42—24no—
318C42—21no—
319C42—21no—
320C42—21no—
321C42—44no—
322C42—42no—
323C42—41no—
324C42—41no—
325C42—521no—
326C42#610512yescomplemented
327C42C2×C4×D1311yescharacteristic
328C42C2×D5211yescharacteristic
329C42#612711yescharacteristic
330C42#612711yescharacteristic
331C13#923111yescharacteristic, complemented, Sylow
332C23—24no—
333C23—22no—
334C23—42no—
335C23—41no—
336C23—41no—
337C23#8820711yescharacteristic
338Q8—522no—
339Q8—1041no—
340D4—24no—
341D4—22no—
342D4#8804514yes—
343C2×C4—22no—
344C2×C4—22no—
345C2×C4—22no—
346C2×C4—22no—
347C2×C4—22no—
348C2×C4—24no—
349C2×C4—22no—
350C2×C4—41no—
351C2×C4—416no—
352C2×C4—41no—
353C2×C4—42no—
354C2×C4—42no—
355C2×C4—41no—
356C2×C4—41no—
357C2×C4—41no—
358C2×C4—42no—
359C2×C4—42no—
360C2×C4—42no—
361C2×C4—42no—
362C2×C4—521no—
363C2×C4—521no—
364C2×C4C2×#610311yescharacteristic
365C2×C4C4×C22⋊D1311yescharacteristic
366C2×C4C4×C22⋊D1311yescharacteristic
367C2×C4#8818311yescharacteristic
368C2×C4#8818411yescharacteristic
369C2×C4#8818411yescharacteristic
370C2×C4#8818611yescharacteristic
371C2×C4C2×#610511yescharacteristic
372C2×C4#8820411yescharacteristic
373C2×C4#8820511yescharacteristic
374C8—522no—
375C8—1041no—
376C8—1041no—
377C22—21no—
378C22—21no—
379C22—24no—
380C22—44no—
381C22—44no—
382C22—42no—
383C22—42no—
384C22#1171887411yescharacteristic
385C22#1171887911yescharacteristic
386C22#1171890011yescharacteristic
387C4—24no—
388C4—21no—
389C4—21no—
390C4—21no—
391C4—42no—
392C4—44no—
393C4—42no—
394C4—1041no—
395C4—1041no—
396C4C2×#8804512yes—
397C4#1171867711yescharacteristic
398C4C4×#610511yescharacteristic
399C4#1171867911yescharacteristic
400C4#1171868011yescharacteristic
401C2—21no—
402C2—21no—
403C2—44no—
404C2#1311517011yescharacteristic
405C2#1311527911yescharacteristic
406C2#1311533711yescharacteristic
subgroupG/H
centerC2×C4#88184
commutatorC42×C13C22×C4
FrattiniC2×C42C22×D13
FittingC42×D4×C13C2
socleC22×C13#386
prime radicalC22×D4×C13D4
cosocleC2×C42×C13C23
hypercenterC42×D4D13
hypocenterC13#9231
LCSG ▷ C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C42×D4

Complements

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

NH ≅ G/Ntype
2. #13115813C2semidirect
3. #13113334C2semidirect
5. #13112739C2semidirect
6. #13112669C2semidirect
18. #11718680C4semidirect
20. #11718669C4semidirect
56. #88123C2×C4semidirect
57. #88123C2×C4semidirect
70. C4⋊#1055C2×C4semidirect
110. C42×C13SD16semidirect
326. C42#6105semidirect
331. C13#9231semidirect

Maximal subgroups

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

subgroupindex
#131248442
#131158132
#131133342
#131132612
#131127392
#131126692
C42×D4×C132
#923113