Finite Group Databasebeta

← #15761196

Subgroups — #15761196

Order 3328.

450 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13115630C211yesmaximal, characteristic
2C4×#88049C211yesmaximal, characteristic
3C2×#11718075C211yesmaximal, characteristic
4C2×#11718046C211yesmaximal, characteristic, complemented
5#13112677C211yesmaximal, characteristic, complemented
6#13112670C211yesmaximal, characteristic, complemented
7C13×#1939C211yesmaximal, characteristic, complemented
8C2×C4×D52C2211yescharacteristic
9C2×C13×C4⋊C8—21no—
10C2×C13×C4⋊C8C2211yescharacteristic
11C2×C4×C8×C13C2211yescharacteristic
12C4×C13×C4⋊C4C2211yescharacteristic
13C2×#88060—21no—
14C2×#88060—21no—
15C2×#88049C411yescharacteristic
16C2×#88049C411yescharacteristic
17C2×C4⋊#1055C2211yescharacteristic
18C2×C4×#1055C2211yescharacteristic
19C2×C4×#1055C2211yescharacteristic
20C13×#336—21no—
21#11718121C411yescharacteristic
22#11718121C411yescharacteristic
23#11718075—22no—
24#11718046—22no—
25C22×D52C2×C411yescharacteristic
26C22×C4×D13—21no—
27C22×C8×C13—21no—
28C22×C8×C13D411yescharacteristic
29C22×C8×C13D411yescharacteristic
30C2×C13×C4⋊C4C2×C411yescharacteristic
31C2×C13×C4⋊C4C2×C411yescharacteristic
32C2×C42×C13—21no—
33C2×C42×C13C2311yescharacteristic
34C2×#6103—21no—
35C2×C4⋊Dic13C2×C411yescharacteristic
36C22×#1055—21no—
37C22×#1055—21no—
38C22×#1055C2×C411yescharacteristic
39C22×#1055C2×C411yescharacteristic
40C4×D52—21no—
41C4×D52—21no—
42C4×D52—21no—
43C4×D52—21no—
44C13×C4⋊C8—21no—
45C13×C4⋊C8—21no—
46C13×C4⋊C8—42no—
47C4×C8×C13—21no—
48C4×C8×C13—21no—
49C13×#95—21no—
50#88060—42no—
51#88060—42no—
52#88049—22no—
53#88049C814yescomplemented
54C4⋊#1055—21no—
55C4⋊#1055—21no—
56C4×#1055—21no—
57C4×#1055—21no—
58C4×#1055—21no—
59C4×#1055D412yes—
60#9556—131nomaximal, Sylow
61C23×D13—21no—
62C22×C4×C13—21no—
63C22×C4×C13—21no—
64C22×C4×C13C22×C411yescharacteristic
65C22×C4×C13C2×D411yescharacteristic
66C22×C4×C13#4111yescharacteristic
67C22×Dic13—21no—
68C2×D52—21no—
69C2×D52—21no—
70C2×D52—21no—
71C2×D52—21no—
72C2×D52—21no—
73C2×D52C2×C812yes—
74C2×C4×D13—41no—
75C2×C4×D13—41no—
76C2×C4×D13—41no—
77C2×C4×D13—41no—
78C2×C4×D13—41no—
79C2×C4×D13—41no—
80C2×C8×C13—21no—
81C2×C8×C13—21no—
82C2×C8×C13—21no—
83C2×C8×C13—21no—
84C2×C8×C13—21no—
85C2×C8×C13—21no—
86C2×C8×C13—41no—
87C2×C8×C13—41no—
88C2×C8×C13—41no—
89C13×C4⋊C4—21no—
90C13×C4⋊C4—21no—
91C13×C4⋊C4—21no—
92C13×C4⋊C4C2×C812yes—
93C42×C13—41no—
94C42×C13—41no—
95C42×C13C2×D411yescharacteristic
96C42×C13#4111yescharacteristic
97C42×C13#4111yescharacteristic
98C42×C13#4111yescharacteristic
99#6103—41no—
100#6103—41no—
101C4⋊Dic13—21no—
102C4⋊Dic13—21no—
103C2×#1055—21no—
104C2×#1055—21no—
105C2×#1055—21no—
106C2×#1055—21no—
107C2×#1055—22no—
108C2×#1055—41no—
109C2×#1055—41no—
110C2×#1055—41no—
111C2×#1055—41no—
112C2×#1055—41no—
113C2×#1055C2×C812yes—
114C2×#1055M1612yes—
115#1954—131no—
116#1939D1311yescharacteristic, complemented
117C4×#102—131no—
118C2×D4⋊C8—131no—
119C2×#322—131no—
120#1279—131no—
121#1277—131no—
122C23×C13C4×D411yescharacteristic
123C22×D13—22no—
124C22×D13—41no—
125C22×D13—41no—
126C22×D13—41no—
127C22×D13—41no—
128C22×D13—41no—
129C22×D13—41no—
130C2×C4×C13—21no—
131C2×C4×C13—21no—
132C2×C4×C13—22no—
133C2×C4×C13—41no—
134C2×C4×C13—41no—
135C2×C4×C13—41no—
136C2×C4×C13—41no—
137C2×C4×C13—41no—
138C2×C4×C13#11711yescharacteristic
139C2×C4×C13C4×D411yescharacteristic
140C2×C4×C13#12111yescharacteristic
141C2×C4×C13#12311yescharacteristic
142C2×C4×C13#12411yescharacteristic
143C2×C4×C13#12611yescharacteristic
144C2×C4×C13C22×C811yescharacteristic
145C2×C4×C13C2×M1611yescharacteristic
146C2×C4×C13#13111yescharacteristic
147C2×C4×C13#13111yescharacteristic
148C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
149C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
150C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
151C2×C4×C13#13711yescharacteristic
152C2×Dic13—41no—
153C2×Dic13—41no—
154C2×Dic13—41no—
155D52—22no—
156D52—22no—
157D52—41no—
158D52—41no—
159C4×D13—81no—
160C4×D13—81no—
161C4×D13—81no—
162C4×D13—81no—
163C8×C13—41no—
164C8×C13—41no—
165C8×C13—81no—
166#1055—22no—
167#1055—22no—
168#1055—42no—
169#1055—81no—
170C2×C4×D4—131no—
171C2×C4⋊C8—21no—
172C2×C4⋊C8—131no—
173C2×C4⋊C8C2×D1311yescharacteristic
174C2×#102—131no—
175C2×#102—131no—
176C2×C22⋊C8—261no—
177C2×C22⋊C8—261no—
178C2×C4×C8—131no—
179C2×C4×C8—131no—
180C2×C4×C8C2×D1311yescharacteristic
181C4×C4⋊C4C2×D1311yescharacteristic
182#340—131no—
183#340—131no—
184#336—21no—
185D4⋊C8—262no—
186#322—262no—
187C22×C13#38811yescharacteristic
188C22×C13C8×D411yescharacteristic
189C22×C13#43611yescharacteristic
190C22×C13#44011yescharacteristic
191C22×C13#44211yescharacteristic
192C22×C13#44411yescharacteristic
193C22×C13#44411yescharacteristic
194C2×D13—42no—
195C2×D13—42no—
196C2×D13—42no—
197C2×D13—81no—
198C2×D13—81no—
199C2×D13—81no—
200C2×D13—81no—
201C4×C13—21no—
202C4×C13—21no—
203C4×C13—42no—
204C4×C13—81no—
205C4×C13#43111yescharacteristic
206C4×C13#43311yescharacteristic
207C4×C13C8×D411yescharacteristic
208C4×C13#43511yescharacteristic
209C4×C13#46811yescharacteristic
210C4×C13#46911yescharacteristic
211C4×C13#48911yescharacteristic
212C4×C13#49011yescharacteristic
213Dic13—81no—
214C22×D4—131no—
215C23×C4—261no—
216C22×C8—21no—
217C22×C8—131no—
218C22×C8—131no—
219C22×C8—261no—
220C22×C8—261no—
221C22×C8C22⋊D1311yescharacteristic
222C22×C8C22⋊D1311yescharacteristic
223C4×D4—261no—
224C4×D4—261no—
225C4×D4—261no—
226C4×D4—261no—
227C2×C4⋊C4—131no—
228C2×C4⋊C4C4×D1311yescharacteristic
229C2×C4⋊C4C4×D1311yescharacteristic
230C2×C22⋊C4—261no—
231C2×C42—21no—
232C2×C42C22×D1311yescharacteristic
233C4⋊C8—21no—
234C4⋊C8—21no—
235C4⋊C8—42no—
236C4⋊C8—261no—
237C4⋊C8—261no—
238#102—134no—
239#102—262no—
240C22⋊C8—522no—
241C22⋊C8—522no—
242C4×C8—21no—
243C4×C8—21no—
244C4×C8—132no—
245C4×C8—261no—
246C4×C8—261no—
247C4×C8—261no—
248#95—21no—
249C2×C13SD16⋊C811yescharacteristic
250C2×C13#158011yescharacteristic
251C2×C13#159211yescharacteristic
252C2×C13#159411yescharacteristic
253C2×C13#192311yescharacteristic
254C2×C13#193611yescharacteristic
255C2×C13#193811yescharacteristic
256D13—82no—
257C24—261no—
258C2×D4—132no—
259C2×D4—261no—
260C2×D4—261no—
261C2×D4—261no—
262C2×D4—261no—
263C2×D4—261no—
264C22×C4—21no—
265C22×C4—21no—
266C22×C4—261no—
267C22×C4—521no—
268C22×C4—521no—
269C22×C4—521no—
270C22×C4—521no—
271C22×C4—521no—
272C22×C4—521no—
273C22×C4C2×C4×D1311yescharacteristic
274C22×C4#612711yescharacteristic
275C22×C4C2×C22⋊D1311yescharacteristic
276C2×C8—21no—
277C2×C8—21no—
278C2×C8—21no—
279C2×C8—21no—
280C2×C8—21no—
281C2×C8—21no—
282C2×C8—41no—
283C2×C8—41no—
284C2×C8—41no—
285C2×C8—132no—
286C2×C8—132no—
287C2×C8—261no—
288C2×C8—261no—
289C2×C8—261no—
290C2×C8—261no—
291C2×C8—262no—
292C2×C8—521no—
293C2×C8—521no—
294C2×C8—521no—
295C2×C8—521no—
296C2×C8—521no—
297C4⋊C4—21no—
298C4⋊C4—21no—
299C4⋊C4—21no—
300C4⋊C4—261no—
301C4⋊C4—261no—
302C4⋊C4C8×D1312yes—
303C22⋊C4—521no—
304C22⋊C4—521no—
305C42—41no—
306C42—41no—
307C42D4×D1311yescharacteristic
308C42#612911yescharacteristic
309C42#613111yescharacteristic
310C42#613111yescharacteristic
311C13#955611yescharacteristic, complemented, Sylow
312C23—262no—
313C23—521no—
314C23—521no—
315C23—521no—
316C23—521no—
317C23—521no—
318C23—521no—
319C23C4×C22⋊D1311yescharacteristic
320D4—262no—
321D4—262no—
322D4—521no—
323D4—521no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—22no—
327C2×C4—41no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—521no—
333C2×C4—521no—
334C2×C4—521no—
335C2×C4—1041no—
336C2×C4—1041no—
337C2×C4—1041no—
338C2×C4—1041no—
339C2×C4#8814611yescharacteristic
340C2×C4#8814711yescharacteristic
341C2×C4#8814811yescharacteristic
342C2×C4#8815211yescharacteristic
343C2×C4C2×C8×D1311yescharacteristic
344C2×C4#8815511yescharacteristic
345C2×C4M16×D1311yescharacteristic
346C2×C4#8816111yescharacteristic
347C2×C4#8818611yescharacteristic
348C2×C4#8819311yescharacteristic
349C2×C4#8819611yescharacteristic
350C2×C4#8820111yescharacteristic
351C2×C4#8820311yescharacteristic
352C2×C4#8820311yescharacteristic
353C8—41no—
354C8—41no—
355C8—81no—
356C8—262no—
357C8—262no—
358C8—522no—
359C8—1041no—
360C22—522no—
361C22—522no—
362C22—522no—
363C22—1041no—
364C22—1041no—
365C22—1041no—
366C22—1041no—
367C22#1171865111yescharacteristic
368C22#1171867511yescharacteristic
369C22#1171868711yescharacteristic
370C22C8×C22⋊D1311yescharacteristic
371C22#1171878911yescharacteristic
372C22#1171880611yescharacteristic
373C22#1171880611yescharacteristic
374C4—21no—
375C4—21no—
376C4—42no—
377C4—81no—
378C4—1041no—
379C4#1171849411yescharacteristic
380C4#1171849511yescharacteristic
381C4#1171849711yescharacteristic
382C4#1171850111yescharacteristic
383C4#1171870011yescharacteristic
384C4#1171871011yescharacteristic
385C4#1171872811yescharacteristic
386C4#1171875011yescharacteristic
387C2—1042no—
388C2#1311364611yescharacteristic
389C2#1311365811yescharacteristic
390C2#1311373611yescharacteristic
391C2#1311374811yescharacteristic
392C2#1311544111yescharacteristic
393C2#1311553211yescharacteristic
394C2#1311554611yescharacteristic
subgroupG/H
centerC22×C4C2×C22⋊D13
commutatorC2×C4×C13C22×C8
FrattiniC2×C42C22×D13
FittingC13×#1939C2
socleC23×C13C4×D4
prime radicalC22×D52C2×C4
cosocleC2×C42×C13C23
hypercenter#1939D13
hypocenterC13#9556
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22×C4 ◁ C2×C4×C8 ◁ #1939

Complements

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

NH ≅ G/Ntype
4. C2×#11718046C2semidirect
5. #13112677C2semidirect
6. #13112670C2semidirect
7. C13×#1939C2semidirect
53. #88049C8semidirect
116. #1939D13semidirect
311. C13#9556semidirect

Maximal subgroups

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

subgroupindex
#131156302
C4×#880492
C2×#117180752
C2×#117180462
#131126772
#131126702
C13×#19392
#955613