Finite Group Databasebeta

← #15756916

Subgroups — #15756916

Order 3328.

612 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#13117454C211yesmaximal, characteristic
2#13115029C212yesmaximal
3C2×#11718120C211yesmaximal, characteristic
4#13112715C212yesmaximal
5C13×#1441C211yesmaximal, characteristic
6C22×C13×C4⋊C4C2211yescharacteristic
7C22×C13×C4⋊C4C2211yescharacteristic
8C2×#88180—21no—
9C2×C13×#95—21no—
10C2×C13×#95—21no—
11C2×C13×#95C2211yescharacteristic
12#11718873—21no—
13#11718873C2212yes—
14C2×C22⋊#1055C2212yes—
15#11718646—22no—
16#11718646—22no—
17C2×#88048—22no—
18#11718121—22no—
19#11718120C414yescomplemented
20C23×C4×C13—21no—
21C23×C4×C13—21no—
22C23×C4×C13D411yescharacteristic
23C23×C4×C13D411yescharacteristic
24C23×C4×C13C2311yescharacteristic
25C2×C13×C4⋊C4—22no—
26C2×C13×C4⋊C4—22no—
27C2×C13×C4⋊C4—22no—
28C2×C13×C4⋊C4—42no—
29C2×C13×C4⋊C4C2×C412yes—
30C2×C13×C4⋊C4Q812yes—
31C2×C22⋊Dic13—22no—
32#88180—42no—
33#88180—42no—
34C2×C4⋊Dic13—21no—
35C2×C4⋊Dic13—21no—
36C2×C4⋊Dic13—21no—
37C2×C4⋊Dic13—21no—
38C2×C4⋊Dic13D412yes—
39C2×C4⋊Dic13D412yes—
40C2×C4×Dic13—22no—
41C22×#1055—22no—
42C13×#95—22no—
43C13×#95—42no—
44C13×#95—42no—
45#88071—22no—
46#88071—22no—
47C22⋊#1055—22no—
48C22⋊#1055C2×C414yes—
49#88048—44no—
50#8857—131nomaximal, Sylow
51C24×C13C2×D411yescharacteristic
52C22×C4×C13—21no—
53C22×C4×C13—21no—
54C22×C4×C13—21no—
55C22×C4×C13—21no—
56C22×C4×C13—21no—
57C22×C4×C13—21no—
58C22×C4×C13—22no—
59C22×C4×C13—22no—
60C22×C4×C13—41no—
61C22×C4×C13—41no—
62C22×C4×C13—41no—
63C22×C4×C13—41no—
64C22×C4×C13—41no—
65C22×C4×C13—41no—
66C22×C4×C13—41no—
67C22×C4×C13—41no—
68C22×C4×C13—41no—
69C22×C4×C13—41no—
70C22×C4×C13—41no—
71C22×C4×C13—41no—
72C22×C4×C13—41no—
73C22×C4×C13—41no—
74C22×C4×C13—41no—
75C22×C4×C13—41no—
76C22×C4×C13C4⋊C412yes—
77C22×C4×C13C4⋊C412yes—
78C22×C4×C13SD1612yes—
79C22×C4×C13SD1612yes—
80C22×C4×C13C22×C411yescharacteristic
81C22×C4×C13C2×D412yes—
82C22×C4×C13C2×Q811yescharacteristic
83C22×C4×C13#4112yes—
84C22×Dic13—22no—
85C22×Dic13—22no—
86C13×C4⋊C4—24no—
87C13×C4⋊C4—24no—
88C13×C4⋊C4—24no—
89C13×C4⋊C4—42no—
90C22⋊Dic13—42no—
91C22⋊Dic13—42no—
92C4⋊Dic13—42no—
93C4⋊Dic13—42no—
94C4⋊Dic13—42no—
95C4⋊Dic13—42no—
96C4⋊Dic13—81no—
97C4⋊Dic13—81no—
98C4×Dic13—44no—
99C2×#1055—24no—
100C2×#1055—42no—
101C2×#1055—42no—
102#2316—131no—
103#1853—132no—
104C2×#324—131no—
105#1441D1311yescharacteristic
106#1294—132no—
107C23×C13—21no—
108C23×C13—21no—
109C23×C13—21no—
110C23×C13—21no—
111C23×C13C2×C4⋊C411yescharacteristic
112C23×C13#12011yescharacteristic
113C23×C13#12311yescharacteristic
114C23×C13C2×SD1611yescharacteristic
115C23×C13C2×SD1611yescharacteristic
116C23×C13AGL(1,ℤ/8)11yescharacteristic
117C23×C13#13711yescharacteristic
118C2×C4×C13—22no—
119C2×C4×C13—22no—
120C2×C4×C13—22no—
121C2×C4×C13—22no—
122C2×C4×C13—22no—
123C2×C4×C13—22no—
124C2×C4×C13—22no—
125C2×C4×C13—22no—
126C2×C4×C13—22no—
127C2×C4×C13—41no—
128C2×C4×C13—41no—
129C2×C4×C13—42no—
130C2×C4×C13—41no—
131C2×C4×C13—41no—
132C2×C4×C13—42no—
133C2×C4×C13—42no—
134C2×C4×C13—42no—
135C2×C4×C13—42no—
136C2×C4×C13—42no—
137C2×C4×C13—42no—
138C2×C4×C13—42no—
139C2×C4×C13—81no—
140C2×C4×C13—81no—
141C2×C4×C13—81no—
142C2×C4×C13—81no—
143C2×C4×C13—81no—
144C2×C4×C13—81no—
145C2×C4×C13—81no—
146C2×C4×C13—81no—
147C2×C4×C13—81no—
148C2×C4×C13#10614yescomplemented
149C2×C4×C13C4×D412yes—
150C2×C4×C13C22⋊Q812yes—
151C2×Dic13—42no—
152C2×Dic13—42no—
153C2×Dic13—42no—
154C2×Dic13—42no—
155C2×Dic13—42no—
156C2×Dic13—42no—
157#1055—44no—
158C2×#117—261no—
159C22×C4⋊C4C2×D1311yescharacteristic
160C22×C4⋊C4C2×D1311yescharacteristic
161C2×#106—262no—
162C2×C22⋊C8—132no—
163#389—262no—
164#389—262no—
165#380—132no—
166#380—261no—
167C2×#95—21no—
168C2×#95—21no—
169C2×#95C2×D1311yescharacteristic
170#340—262no—
171#324—134no—
172C22×C13—21no—
173C22×C13—21no—
174C22×C13—21no—
175C22×C13—21no—
176C22×C13—21no—
177C22×C13—21no—
178C22×C13—21no—
179C22×C13—21no—
180C22×C13—21no—
181C22×C13—21no—
182C22×C13—21no—
183C22×C13—21no—
184C22×C13#38511yescharacteristic
185C22×C13C2×#10611yescharacteristic
186C22×C13#42811yescharacteristic
187C22×C13#44811yescharacteristic
188C22×C13#45011yescharacteristic
189C22×C13#45411yescharacteristic
190C22×C13#45611yescharacteristic
191C22×C13B(4,𝔽2)11yescharacteristic
192C22×C13#45811yescharacteristic
193C22×C13#48111yescharacteristic
194C22×C13#48311yescharacteristic
195C4×C13—24no—
196C4×C13—22no—
197C4×C13—22no—
198C4×C13—42no—
199C4×C13—82no—
200C4×C13—82no—
201Dic13—82no—
202Dic13—82no—
203C23×C4—21no—
204C23×C4—21no—
205C23×C4C22⋊D1311yescharacteristic
206C23×C4C22⋊D1311yescharacteristic
207C23×C4C22×D1311yescharacteristic
208C22×C8—262no—
209#117—522no—
210#117—522no—
211C2×C4⋊C4—22no—
212C2×C4⋊C4—22no—
213C2×C4⋊C4—22no—
214C2×C4⋊C4—42no—
215C2×C4⋊C4—132no—
216C2×C4⋊C4—132no—
217C2×C4⋊C4—261no—
218C2×C4⋊C4—261no—
219C2×C4⋊C4—261no—
220C2×C4⋊C4—261no—
221C2×C4⋊C4Dic2612yes—
222C2×C4⋊C4C4×D1312yes—
223C2×C22⋊C4—262no—
224C2×C42—262no—
225#106—524no—
226C22⋊C8—134no—
227C22⋊C8—262no—
228#95—22no—
229#95—42no—
230#95—42no—
231#95—262no—
232#95—262no—
233C2×C13—21no—
234C2×C13—21no—
235C2×C13—21no—
236C2×C13—21no—
237C2×C13#159911yescharacteristic
238C2×C13#160411yescharacteristic
239C2×C13#161111yescharacteristic
240C2×C13#161611yescharacteristic
241C2×C13#185311yescharacteristic
242C2×C13#185711yescharacteristic
243C2×C13#186711yescharacteristic
244C24C2×C22⋊D1311yescharacteristic
245C22×C4—21no—
246C22×C4—21no—
247C22×C4—21no—
248C22×C4—21no—
249C22×C4—21no—
250C22×C4—21no—
251C22×C4—22no—
252C22×C4—22no—
253C22×C4—41no—
254C22×C4—41no—
255C22×C4—41no—
256C22×C4—41no—
257C22×C4—41no—
258C22×C4—41no—
259C22×C4—41no—
260C22×C4—41no—
261C22×C4—41no—
262C22×C4—41no—
263C22×C4—41no—
264C22×C4—41no—
265C22×C4—41no—
266C22×C4—41no—
267C22×C4—41no—
268C22×C4—41no—
269C22×C4—262no—
270C22×C4—262no—
271C22×C4#610112yes—
272C22×C4#610112yes—
273C22×C4#610512yes—
274C22×C4#610612yes—
275C22×C4C2×Dic2611yescharacteristic
276C22×C4C2×C4×D1311yescharacteristic
277C22×C4D4×D1312yes—
278C22×C4#612912yes—
279C2×C8—264no—
280C2×C8—522no—
281C2×C8—522no—
282C4⋊C4—24no—
283C4⋊C4—24no—
284C4⋊C4—24no—
285C4⋊C4—42no—
286C4⋊C4—522no—
287C4⋊C4—522no—
288C4⋊C4—522no—
289C4⋊C4—522no—
290C4⋊C4—1041no—
291C4⋊C4—1041no—
292C22⋊C4—522no—
293C22⋊C4—522no—
294C42—524no—
295C13#885711yescharacteristic, complemented, Sylow
296C23—21no—
297C23—21no—
298C23—21no—
299C23—21no—
300C23C2×#610111yescharacteristic
301C23C2×#610511yescharacteristic
302C23#8818911yescharacteristic
303C23#8819111yescharacteristic
304C23C2×#610611yescharacteristic
305C23#8820311yescharacteristic
306C23#8820511yescharacteristic
307C2×C4—22no—
308C2×C4—22no—
309C2×C4—22no—
310C2×C4—22no—
311C2×C4—22no—
312C2×C4—22no—
313C2×C4—22no—
314C2×C4—22no—
315C2×C4—22no—
316C2×C4—41no—
317C2×C4—41no—
318C2×C4—42no—
319C2×C4—41no—
320C2×C4—41no—
321C2×C4—42no—
322C2×C4—42no—
323C2×C4—42no—
324C2×C4—42no—
325C2×C4—42no—
326C2×C4—42no—
327C2×C4—42no—
328C2×C4—81no—
329C2×C4—81no—
330C2×C4—81no—
331C2×C4—81no—
332C2×C4—81no—
333C2×C4—81no—
334C2×C4—81no—
335C2×C4—81no—
336C2×C4—81no—
337C2×C4—522no—
338C2×C4—522no—
339C2×C4—522no—
340C2×C4—522no—
341C2×C4—522no—
342C2×C4—522no—
343C2×C4#8804814yescomplemented
344C2×C4#8813212yes—
345C2×C4#8813512yes—
346C8—524no—
347C22—21no—
348C22—21no—
349C22—21no—
350C22—21no—
351C22—21no—
352C22—21no—
353C22—21no—
354C22—21no—
355C22—21no—
356C22—21no—
357C22—21no—
358C22—21no—
359C22#1171860711yescharacteristic
360C22C2×#8804811yescharacteristic
361C22#1171865611yescharacteristic
362C22#1171869311yescharacteristic
363C22#1171869511yescharacteristic
364C22#1171870111yescharacteristic
365C22#1171870411yescharacteristic
366C22#1171870711yescharacteristic
367C22#1171871411yescharacteristic
368C22#1171872311yescharacteristic
369C22#1171875611yescharacteristic
370C4—24no—
371C4—22no—
372C4—22no—
373C4—42no—
374C4—82no—
375C4—82no—
376C4—1042no—
377C4—1042no—
378C2—21no—
379C2—21no—
380C2—21no—
381C2—21no—
382C2#1311377511yescharacteristic
383C2#1311380411yescharacteristic
384C2#1311384311yescharacteristic
385C2#1311387211yescharacteristic
386C2#1311502811yescharacteristic
387C2#1311505011yescharacteristic
388C2#1311511611yescharacteristic
subgroupG/H
centerC23#88191
commutatorC22×C4×C13C22×C4
FrattiniC23×C4C22×D13
FittingC13×#1441C2
socleC23×C13#120
prime radicalC24×C13C2×D4
cosocleC23×C4×C13C23
hypercenter#1441D13
hypocenterC13#8857
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1441

Complements

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

NH ≅ G/Ntype
19. #11718120C4semidirect
148. C2×C4×C13#106semidirect
295. C13#8857semidirect
343. C2×C4#88048semidirect

Maximal subgroups

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

subgroupindex
#131174542
#131150292
C2×#117181202
#131127152
C13×#14412
#885713