Finite Group Databasebeta

← #15758674

Subgroups — #15758674

Order 3328.

946 conjugacy classes of subgroups.

The subgroup lattice has 414 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13123123C211yesmaximal, characteristic
2#13114746C211yesmaximal, characteristic
3C2×#11718044C212yesmaximal, complemented
4#13112715C212yesmaximal, complemented
5C2×C13×#380C211yesmaximal, characteristic
6C24×C4×C13C2211yescharacteristic
7C22×C13×C4⋊C4—21no—
8C22×C13×C22⋊C4—21no—
9C2×#88178C412yescomplemented
10C2×#88178C2211yescharacteristic
11C13×#380—24no—
12C2×C13×#95C2212yes—
13#11718908—21no—
14#11718873C412yescomplemented
15#11718873C2211yescharacteristic
16#11718871—21no—
17#11718871—22no—
18C2×C22⋊#1055—22no—
19C2×C22⋊#1055C2212yes—
20#11718044—24no—
21C25×C13D411yescharacteristic
22C23×C4×C13—22no—
23C23×C4×C13—22no—
24C23×C4×C13—22no—
25C23×C4×C13—44no—
26C23×C4×C13C2×C412yes—
27C23×C4×C13D412yes—
28C23×C4×C13D411yescharacteristic
29C23×C4×C13C2311yescharacteristic
30C22×Dic26C2×C411yescharacteristic
31C2×C13×C4⋊C4—24no—
32C2×C13×C4⋊C4—44no—
33C2×C13×C22⋊C4—24no—
34C2×C13×C22⋊C4—42no—
35C2×C13×C22⋊C4—42no—
36C2×C22⋊Dic13—22no—
37C2×C22⋊Dic13—22no—
38C2×C22⋊Dic13—21no—
39C2×C22⋊Dic13—21no—
40C2×C4⋊Dic13C2×C411yescharacteristic
41C2×C4⋊Dic13C2×C412yes—
42#88178—22no—
43#88178—22no—
44#88178—44no—
45C2×#6101—22no—
46C2×#6101—21no—
47C22×#1055—22no—
48C13×#95—22no—
49C13×#95D414yes—
50#88071—22no—
51#88071—21no—
52C22⋊#1055—22no—
53C22⋊#1055—22no—
54C22⋊#1055—44no—
55#9151—131nomaximal, Sylow
56C24×C13—21no—
57C24×C13—21no—
58C24×C13—21no—
59C24×C13—21no—
60C24×C13—42no—
61C24×C13—42no—
62C24×C13C22⋊C412yes—
63C24×C13SD1612yes—
64C24×C13Q1612yes—
65C24×C13C2×D411yescharacteristic
66C22×C4×C13—21no—
67C22×C4×C13—21no—
68C22×C4×C13—24no—
69C22×C4×C13—24no—
70C22×C4×C13—24no—
71C22×C4×C13—24no—
72C22×C4×C13—24no—
73C22×C4×C13—24no—
74C22×C4×C13—42no—
75C22×C4×C13—42no—
76C22×C4×C13—42no—
77C22×C4×C13—48no—
78C22×C4×C13—48no—
79C22×C4×C13—44no—
80C22×C4×C13—44no—
81C22×C4×C13—42no—
82C22×C4×C13—42no—
83C22×C4×C13C22⋊C412yes—
84C22×C4×C13C22×C411yescharacteristic
85C22×C4×C13C2×D411yescharacteristic
86C22×C4×C13C2×D412yes—
87C22×C4×C13#4112yes—
88C22×Dic13—21no—
89C22×Dic13—22no—
90C22×Dic13—21no—
91C2×Dic26—22no—
92C2×Dic26—42no—
93C13×C4⋊C4—48no—
94C13×C22⋊C4—48no—
95C22⋊Dic13—44no—
96C22⋊Dic13—44no—
97C22⋊Dic13—41no—
98C22⋊Dic13—41no—
99C22⋊Dic13—41no—
100C22⋊Dic13—41no—
101C4⋊Dic13—22no—
102C4⋊Dic13—42no—
103#6101—44no—
104#6101—42no—
105C2×#1055—44no—
106C2×#1055—42no—
107#2848—131no—
108C2×#380D1311yescharacteristic
109#1779—131no—
110C2×#328—132no—
111#1294—132no—
112C23×C13—22no—
113C23×C13—22no—
114C23×C13—22no—
115C23×C13—22no—
116C23×C13—22no—
117C23×C13—22no—
118C23×C13—22no—
119C23×C13—22no—
120C23×C13—22no—
121C23×C13—22no—
122C23×C13—22no—
123C23×C13—22no—
124C23×C13—44no—
125C23×C13—44no—
126C23×C13—42no—
127C23×C13—42no—
128C23×C13—42no—
129C23×C13—42no—
130C23×C13—44no—
131C23×C13—44no—
132C23×C13#10314yes—
133C23×C13C2×C22⋊C411yescharacteristic
134C23×C13#12011yescharacteristic
135C23×C13#12311yescharacteristic
136C23×C13C2×SD1611yescharacteristic
137C23×C13C2×Q1611yescharacteristic
138C23×C13AGL(1,ℤ/8)11yescharacteristic
139C23×C13#13711yescharacteristic
140C2×C4×C13—24no—
141C2×C4×C13—24no—
142C2×C4×C13—22no—
143C2×C4×C13—22no—
144C2×C4×C13—22no—
145C2×C4×C13—22no—
146C2×C4×C13—42no—
147C2×C4×C13—42no—
148C2×C4×C13—48no—
149C2×C4×C13—48no—
150C2×C4×C13—44no—
151C2×C4×C13—44no—
152C2×C4×C13—44no—
153C2×C4×C13—84no—
154C2×C4×C13—84no—
155C2×C4×C13#9914yes—
156C2×C4×C13C4×D412yes—
157C2×C4×C13#12112yes—
158C2×Dic13—41no—
159C2×Dic13—41no—
160C2×Dic13—42no—
161C2×Dic13—42no—
162C2×Dic13—42no—
163C2×Dic13—42no—
164C2×Dic13—42no—
165Dic26—82no—
166#1055—82no—
167C24×C4C2×D1311yescharacteristic
168C2×C22⋊Q8—131no—
169C2×C22⋊Q8—132no—
170C22×C4⋊C4—21no—
171C22×C22⋊C4—21no—
172C2×C22⋊C8—132no—
173C2×C22⋊C8—262no—
174#385—262no—
175#385—261no—
176#380—24no—
177#380—132no—
178#380—131no—
179#379—261no—
180C2×#95C2×D1312yes—
181#328—264no—
182C22×C13—21no—
183C22×C13—21no—
184C22×C13—21no—
185C22×C13—21no—
186C22×C13—22no—
187C22×C13—22no—
188C22×C13—22no—
189C22×C13—22no—
190C22×C13—24no—
191C22×C13—24no—
192C22×C13—24no—
193C22×C13—44no—
194C22×C13—44no—
195C22×C13—44no—
196C22×C13—44no—
197C22×C13—42no—
198C22×C13—42no—
199C22×C13—42no—
200C22×C13—42no—
201C22×C13#38611yescharacteristic
202C22×C13C2×#9912yes—
203C22×C13C2×#10311yescharacteristic
204C22×C13#41711yescharacteristic
205C22×C13#42112yes—
206C22×C13#45011yescharacteristic
207C22×C13#45111yescharacteristic
208C22×C13#48311yescharacteristic
209C22×C13#48411yescharacteristic
210C4×C13—22no—
211C4×C13—22no—
212C4×C13—24no—
213C4×C13—84no—
214Dic13—81no—
215Dic13—81no—
216Dic13—82no—
217C25C22⋊D1311yescharacteristic
218C22×Q8—131no—
219C23×C4—22no—
220C23×C4—22no—
221C23×C4—22no—
222C23×C4—44no—
223C23×C4C4×D1312yes—
224C23×C4D5212yes—
225C23×C4C22⋊D1311yescharacteristic
226C23×C4C22×D1311yescharacteristic
227C22×C8—262no—
228C22⋊Q8—262no—
229C22⋊Q8—262no—
230C22⋊Q8—524no—
231C2×C4⋊C4—24no—
232C2×C4⋊C4—44no—
233C2×C4⋊C4—131no—
234C2×C4⋊C4—132no—
235C2×C4⋊C4—262no—
236C2×C4⋊C4—261no—
237C2×C22⋊C4—24no—
238C2×C22⋊C4—42no—
239C2×C22⋊C4—42no—
240C2×C22⋊C4—262no—
241C2×C22⋊C4—262no—
242C2×C22⋊C4—261no—
243C2×C22⋊C4—261no—
244C22⋊C8—262no—
245C22⋊C8—262no—
246C22⋊C8—524no—
247#95—22no—
248#95—262no—
249#95—261no—
250#95C22⋊D1314yes—
251C2×C13—21no—
252C2×C13—21no—
253C2×C13—21no—
254C2×C13—21no—
255C2×C13—44no—
256C2×C13#151312yes—
257C2×C13#152012yes—
258C2×C13#187211yescharacteristic
259C2×C13#189711yescharacteristic
260C2×C13#189811yescharacteristic
261C24—21no—
262C24—21no—
263C24—21no—
264C24—21no—
265C24—42no—
266C24—42no—
267C24#610312yes—
268C24#610512yes—
269C24#610712yes—
270C24C2×C22⋊D1311yescharacteristic
271C2×Q8—262no—
272C2×Q8—522no—
273C22×C4—21no—
274C22×C4—21no—
275C22×C4—24no—
276C22×C4—24no—
277C22×C4—24no—
278C22×C4—24no—
279C22×C4—24no—
280C22×C4—24no—
281C22×C4—42no—
282C22×C4—42no—
283C22×C4—42no—
284C22×C4—48no—
285C22×C4—48no—
286C22×C4—44no—
287C22×C4—44no—
288C22×C4—42no—
289C22×C4—42no—
290C22×C4—261no—
291C22×C4—262no—
292C22×C4—261no—
293C22×C4#610312yes—
294C22×C4C2×C4×D1311yescharacteristic
295C22×C4C2×D5211yescharacteristic
296C22×C4#612712yes—
297C22×C4C2×C22⋊D1312yes—
298C2×C8—524no—
299C2×C8—522no—
300C4⋊C4—48no—
301C4⋊C4—262no—
302C4⋊C4—522no—
303C4⋊C4—522no—
304C4⋊C4—524no—
305C22⋊C4—48no—
306C22⋊C4—524no—
307C22⋊C4—524no—
308C22⋊C4—521no—
309C22⋊C4—521no—
310C22⋊C4—521no—
311C22⋊C4—521no—
312C13#915111yescharacteristic, complemented, Sylow
313C23—22no—
314C23—22no—
315C23—22no—
316C23—22no—
317C23—22no—
318C23—22no—
319C23—22no—
320C23—22no—
321C23—22no—
322C23—22no—
323C23—22no—
324C23—22no—
325C23—44no—
326C23—44no—
327C23—42no—
328C23—42no—
329C23—44no—
330C23—44no—
331C23—42no—
332C23—42no—
333C23#8805014yes—
334C23C2×#610311yescharacteristic
335C23#8818311yescharacteristic
336C23#8818611yescharacteristic
337C23C2×#610511yescharacteristic
338C23#8819611yescharacteristic
339C23C2×#610711yescharacteristic
340C23#8820711yescharacteristic
341Q8—1042no—
342C2×C4—24no—
343C2×C4—24no—
344C2×C4—22no—
345C2×C4—22no—
346C2×C4—22no—
347C2×C4—22no—
348C2×C4—42no—
349C2×C4—42no—
350C2×C4—48no—
351C2×C4—48no—
352C2×C4—44no—
353C2×C4—44no—
354C2×C4—44no—
355C2×C4—84no—
356C2×C4—84no—
357C2×C4—522no—
358C2×C4—522no—
359C2×C4—522no—
360C2×C4—522no—
361C2×C4—521no—
362C2×C4—521no—
363C2×C4—522no—
364C2×C4#8804614yes—
365C2×C4C4×C22⋊D1312yes—
366C2×C4#8818412yes—
367C8—1042no—
368C22—22no—
369C22—22no—
370C22—22no—
371C22—22no—
372C22—21no—
373C22—21no—
374C22—21no—
375C22—21no—
376C22—24no—
377C22—24no—
378C22—24no—
379C22—44no—
380C22—44no—
381C22—44no—
382C22—44no—
383C22—42no—
384C22—42no—
385C22—42no—
386C22—42no—
387C22C2×#8804612yes—
388C22#1171862711yescharacteristic
389C22C2×#8805011yescharacteristic
390C22#1171863111yescharacteristic
391C22#1171863211yescharacteristic
392C22#1171866612yes—
393C22#1171887411yescharacteristic
394C22#1171887911yescharacteristic
395C22#1171888911yescharacteristic
396C4—22no—
397C4—24no—
398C4—22no—
399C4—84no—
400C4—1042no—
401C4—1041no—
402C4—1041no—
403C2—21no—
404C2—21no—
405C2—21no—
406C2—21no—
407C2—44no—
408C2#1311337712yes—
409C2#1311340712yes—
410C2#1311514311yescharacteristic
411C2#1311528411yescharacteristic
412C2#1311528911yescharacteristic
subgroupG/H
centerC23C2×#6103
commutatorC22×C4×C13C22×C4
FrattiniC23×C4C22×D13
FittingC2×C13×#380C2
socleC23×C13C2×C22⋊C4
prime radicalC25×C13D4
cosocleC23×C4×C13C23
hypercenterC2×#380D13
hypocenterC13#9151
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C24×C4 ◁ C2×#380

Complements

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

NH ≅ G/Ntype
3. C2×#11718044C2semidirect
4. #13112715C2semidirect
9. C2×#88178C4semidirect
14. #11718873C4semidirect
312. C13#9151semidirect

Maximal subgroups

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

subgroupindex
#131231232
#131147462
C2×#117180442
#131127152
C2×C13×#3802
#915113