Finite Group Databasebeta

← #15766716

Subgroups — #15766716

Order 3328.

574 conjugacy classes of subgroups.

The subgroup lattice has 470 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718676C211yesmaximal, characteristic
2#13115641C211yesmaximal, characteristic, complemented
3#13115631C211yesmaximal, characteristic, complemented
4C2×#11718072C211yesmaximal, characteristic, complemented
5C2×#11718077C211yesmaximal, characteristic, complemented
6#13112719C211yesmaximal, characteristic, complemented
7C13×#1802C211yesmaximal, characteristic, complemented
8C2×C4×D4×C13C2211yescharacteristic
9C22×#6104—21no—
10C2×#88128C2211yescharacteristic
11C2×C13×C4⋊C8C2211yescharacteristic
12C2×C13×#102—21no—
13C13×#384C2211yescharacteristic
14C2×C22⋊#1055—21no—
15C2×C22⋊#1055—21no—
16#11718676—22no—
17#11718676—22no—
18C2×#88049—21no—
19C2×#88049—21no—
20C2×#88049—21no—
21C2×C4⋊#1055C2211yescharacteristic
22C2×C4⋊#1055C2211yescharacteristic
23C2×C4×#1055C2211yescharacteristic
24C13×#340—21no—
25#11718077—22no—
26#11718072—22no—
27C22×D4×C13D411yescharacteristic
28C23×C4×C13—21no—
29C22×D52—21no—
30C22×D52—21no—
31C22×D52—21no—
32C22×C8×C13—21no—
33C4×D4×C13—21no—
34C4×D4×C13—21no—
35C4×D4×C13—21no—
36C4×D4×C13—21no—
37C2×C13×C4⋊C4—21no—
38C2×C13×C4⋊C4—21no—
39C2×C13×C4⋊C4—21no—
40C2×C13×C4⋊C4D411yescharacteristic
41C2×C13×C22⋊C4—21no—
42C2×C42×C13C2311yescharacteristic
43C2×#6104—24no—
44C2×#6104—42no—
45C2×#6104—42no—
46C22×#1055—21no—
47C22×#1055—21no—
48C22×#1055D411yescharacteristic
49C22×#1055D411yescharacteristic
50#88128—21no—
51#88128—21no—
52#88128—21no—
53#88128D412yes—
54C13×C4⋊C8—21no—
55C13×C4⋊C8—21no—
56C13×#102—42no—
57C22⋊#1055—42no—
58C22⋊#1055—42no—
59#88049—24no—
60#88049—42no—
61#88049—42no—
62C4⋊#1055—21no—
63C4⋊#1055—21no—
64C4⋊#1055—21no—
65C4⋊#1055D412yes—
66C4×#1055—21no—
67C4×#1055—21no—
68#10473—131nomaximal, Sylow
69C24×C13—21no—
70C23×D13—41no—
71C2×D4×C13—21no—
72C2×D4×C13—21no—
73C2×D4×C13—21no—
74C2×D4×C13—21no—
75C2×D4×C13—21no—
76C2×D4×C13SD1612yes—
77C22×C4×C13—21no—
78C22×C4×C13—41no—
79C22×C4×C13—41no—
80C22×C4×C13—41no—
81C22×C4×C13—41no—
82C22×C4×C13—41no—
83C22×C4×C13—41no—
84C22×C4×C13—41no—
85C22×C4×C13C2×D411yescharacteristic
86C22×C4×C13C2×D411yescharacteristic
87C22×C4×C13#4111yescharacteristic
88C2×D52—22no—
89C2×D52—22no—
90C2×D52—22no—
91C2×D52—41no—
92C2×D52—41no—
93C2×D52—41no—
94C2×D52—41no—
95C2×D52—41no—
96C2×D52—41no—
97C2×D52—41no—
98C2×D52—41no—
99C2×D52—41no—
100C2×D52—41no—
101C2×D52—41no—
102C2×D52—81no—
103C2×D52—81no—
104C2×C8×C13—41no—
105C2×C8×C13—41no—
106C2×C8×C13—41no—
107C13×C4⋊C4—21no—
108C13×C4⋊C4—21no—
109C13×C4⋊C4—41no—
110C13×C4⋊C4—41no—
111C13×C4⋊C4—41no—
112C13×C4⋊C4—41no—
113C13×C4⋊C4—81no—
114C13×C22⋊C4—41no—
115C13×C22⋊C4—41no—
116C42×C13C2×D411yescharacteristic
117C42×C13C2×D411yescharacteristic
118C42×C13#4111yescharacteristic
119C42×C13#4111yescharacteristic
120#6104—48no—
121C2×#1055—21no—
122C2×#1055—21no—
123C2×#1055—22no—
124C2×#1055—21no—
125C2×#1055—21no—
126C2×#1055—21no—
127C2×#1055—41no—
128C2×#1055—41no—
129C2×#1055—41no—
130C2×#1055—41no—
131C2×#1055—41no—
132C2×#1055D812yescomplemented
133C2×#459—131no—
134#1957—131no—
135#1954—131no—
136#1802D1311yescharacteristic, complemented
137C2×#334—131no—
138C2×#331—131no—
139#1296—131no—
140C23×C13—22no—
141C23×C13—41no—
142C23×C13—41no—
143C23×C13—41no—
144C23×C13—41no—
145C23×C13—41no—
146C23×C13—41no—
147C23×C13#12111yescharacteristic
148C22×D13—42no—
149C22×D13—81no—
150C22×D13—81no—
151C22×D13—81no—
152C22×D13—81no—
153C22×D13—81no—
154C22×D13—81no—
155D4×C13—22no—
156D4×C13—22no—
157D4×C13—41no—
158D4×C13—41no—
159C2×C4×C13—21no—
160C2×C4×C13—21no—
161C2×C4×C13—41no—
162C2×C4×C13—41no—
163C2×C4×C13—41no—
164C2×C4×C13—81no—
165C2×C4×C13—81no—
166C2×C4×C13—81no—
167C2×C4×C13—81no—
168C2×C4×C13—81no—
169C2×C4×C13—81no—
170C2×C4×C13—81no—
171C2×C4×C13#12011yescharacteristic
172C2×C4×C13#12111yescharacteristic
173C2×C4×C13#12111yescharacteristic
174C2×C4×C13#12311yescharacteristic
175C2×C4×C13#12311yescharacteristic
176C2×C4×C13#12411yescharacteristic
177C2×C4×C13C2×D811yescharacteristic
178C2×C4×C13C2×SD1611yescharacteristic
179C2×C4×C13#13511yescharacteristic
180C2×C4×C13#13511yescharacteristic
181C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
182C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
183C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
184C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
185D52—42no—
186D52—42no—
187D52—42no—
188D52—42no—
189D52—82no—
190D52—82no—
191D52—81no—
192D52—81no—
193D52—81no—
194D52—81no—
195C8×C13—81no—
196#1055—22no—
197#1055—42no—
198#1055—41no—
199#1055—81no—
200C22×D8—261no—
201C2×#127—131no—
202C2×C4×D4C2×D1311yescharacteristic
203#459—262no—
204#459—262no—
205C2×C4⋊C8—131no—
206C2×C4⋊C8—131no—
207C2×C4⋊C8C2×D1311yescharacteristic
208C2×#102—21no—
209C2×#102—261no—
210C2×#102—261no—
211C2×#102—261no—
212C2×C22⋊C8—261no—
213C2×C22⋊C8—261no—
214C2×C4×C8—131no—
215#384C2×D1311yescharacteristic
216#340—21no—
217#334—262no—
218#331—262no—
219C22×C13—42no—
220C22×C13—42no—
221C22×C13—42no—
222C22×C13—81no—
223C22×C13—81no—
224C22×C13—81no—
225C22×C13—81no—
226C22×C13#39411yescharacteristic
227C22×C13#45911yescharacteristic
228C22×C13#46311yescharacteristic
229C22×C13#46511yescharacteristic
230C22×C13#46911yescharacteristic
231C22×C13#47111yescharacteristic
232C22×C13#47211yescharacteristic
233C2×D13—82no—
234C2×D13—82no—
235C2×D13—82no—
236C2×D13—161no—
237C2×D13—161no—
238C2×D13—161no—
239C2×D13—161no—
240C4×C13—21no—
241C4×C13—21no—
242C4×C13—81no—
243C4×C13—161no—
244C4×C13#44911yescharacteristic
245C4×C13#45011yescharacteristic
246C4×C13#45911yescharacteristic
247C4×C13#46311yescharacteristic
248C4×C13#46611yescharacteristic
249C4×C13#46911yescharacteristic
250C4×C13#48111yescharacteristic
251C4×C13#48211yescharacteristic
252C22×D4—261no—
253C22×D4—261no—
254C22×D4—261no—
255C22×D4C22⋊D1311yescharacteristic
256C23×C4—21no—
257C2×D8—264no—
258C2×D8—522no—
259C2×D8—522no—
260C22×C8—21no—
261C22×C8—131no—
262C22×C8—131no—
263C22×C8—261no—
264C22×C8—261no—
265#127—132no—
266#127—261no—
267#127—261no—
268#127—261no—
269C4×D4—21no—
270C4×D4—21no—
271C4×D4—21no—
272C4×D4—21no—
273C2×C4⋊C4—21no—
274C2×C4⋊C4—21no—
275C2×C4⋊C4—21no—
276C2×C4⋊C4C22⋊D1311yescharacteristic
277C2×C22⋊C4—21no—
278C2×C42C22×D1311yescharacteristic
279C4⋊C8—21no—
280C4⋊C8—21no—
281C4⋊C8—132no—
282C4⋊C8—261no—
283C4⋊C8—261no—
284C4⋊C8—261no—
285#102—42no—
286#102—264no—
287#102—522no—
288#102—522no—
289C22⋊C8—522no—
290C22⋊C8—522no—
291C4×C8—261no—
292C4×C8—261no—
293C2×C13—82no—
294C2×C13#166511yescharacteristic
295C2×C13#167711yescharacteristic
296C2×C13#168711yescharacteristic
297C2×C13#170111yescharacteristic
298C2×C13#203411yescharacteristic
299C2×C13#205111yescharacteristic
300C2×C13#205411yescharacteristic
301D13—162no—
302C24—21no—
303C24—521no—
304C2×D4—21no—
305C2×D4—21no—
306C2×D4—21no—
307C2×D4—21no—
308C2×D4—21no—
309C2×D4—262no—
310C2×D4—262no—
311C2×D4—262no—
312C2×D4—521no—
313C2×D4—521no—
314C2×D4—521no—
315C2×D4—521no—
316C2×D4—521no—
317C2×D4—521no—
318C2×D4—521no—
319C2×D4—521no—
320C2×D4—521no—
321C2×D4—521no—
322C2×D4—521no—
323C2×D4—1041no—
324C2×D4—1041no—
325C2×D4#610612yes—
326C22×C4—21no—
327C22×C4—41no—
328C22×C4—41no—
329C22×C4—41no—
330C22×C4—41no—
331C22×C4—41no—
332C22×C4—41no—
333C22×C4—41no—
334C22×C4D4×D1311yescharacteristic
335C22×C4#612911yescharacteristic
336C22×C4C2×C22⋊D1311yescharacteristic
337D8—528no—
338C2×C8—41no—
339C2×C8—41no—
340C2×C8—41no—
341C2×C8—132no—
342C2×C8—261no—
343C2×C8—261no—
344C2×C8—261no—
345C2×C8—261no—
346C2×C8—261no—
347C2×C8—262no—
348C2×C8—521no—
349C2×C8—521no—
350C2×C8—521no—
351C2×C8—521no—
352C2×C8—521no—
353C4⋊C4—21no—
354C4⋊C4—21no—
355C4⋊C4—41no—
356C4⋊C4—41no—
357C4⋊C4—41no—
358C4⋊C4—41no—
359C4⋊C4—81no—
360C22⋊C4—41no—
361C22⋊C4—41no—
362C42#612711yescharacteristic
363C42#612711yescharacteristic
364C42D4×D1311yescharacteristic
365C42D4×D1311yescharacteristic
366C13#1047311yescharacteristic, complemented, Sylow
367C23—22no—
368C23—41no—
369C23—41no—
370C23—41no—
371C23—41no—
372C23—41no—
373C23—41no—
374C23—522no—
375C23—1041no—
376C23—1041no—
377C23—1041no—
378C23—1041no—
379C23—1041no—
380C23—1041no—
381C23#8819311yescharacteristic
382D4—22no—
383D4—22no—
384D4—41no—
385D4—41no—
386D4—522no—
387D4—522no—
388D4—522no—
389D4—522no—
390D4—1042no—
391D4—1042no—
392D4—1041no—
393D4—1041no—
394D4—1041no—
395D4—1041no—
396C2×C4—21no—
397C2×C4—21no—
398C2×C4—41no—
399C2×C4—41no—
400C2×C4—41no—
401C2×C4—81no—
402C2×C4—81no—
403C2×C4—81no—
404C2×C4—81no—
405C2×C4—81no—
406C2×C4—81no—
407C2×C4—81no—
408C2×C4#8813711yescharacteristic
409C2×C4#8813811yescharacteristic
410C2×C4#8813811yescharacteristic
411C2×C4#8813911yescharacteristic
412C2×C4D8×D1311yescharacteristic
413C2×C4#8816511yescharacteristic
414C2×C4#8816811yescharacteristic
415C2×C4#8817011yescharacteristic
416C2×C4#8818311yescharacteristic
417C2×C4#8818611yescharacteristic
418C2×C4#8819111yescharacteristic
419C2×C4C2×#610611yescharacteristic
420C2×C4#8820311yescharacteristic
421C2×C4#8820411yescharacteristic
422C8—81no—
423C8—262no—
424C8—521no—
425C8—522no—
426C8—1041no—
427C22—42no—
428C22—42no—
429C22—42no—
430C22—81no—
431C22—81no—
432C22—81no—
433C22—81no—
434C22—1042no—
435C22—1042no—
436C22—1042no—
437C22—2081no—
438C22—2081no—
439C22—2081no—
440C22—2081no—
441C22#1171862011yescharacteristic
442C22#1171870011yescharacteristic
443C22#1171870911yescharacteristic
444C22#1171881111yescharacteristic
445C22#1171882611yescharacteristic
446C22#1171886011yescharacteristic
447C22#1171886411yescharacteristic
448C4—21no—
449C4—21no—
450C4—81no—
451C4—161no—
452C4#1171843611yescharacteristic
453C4#1171844311yescharacteristic
454C4#1171844711yescharacteristic
455C4#1171844811yescharacteristic
456C4#1171862911yescharacteristic
457C4#1171866411yescharacteristic
458C4#1171869811yescharacteristic
459C4#1171870711yescharacteristic
460C2—82no—
461C2—2082no—
462C2#1311417911yescharacteristic
463C2#1311424711yescharacteristic
464C2#1311431311yescharacteristic
465C2#1311439911yescharacteristic
466C2#1311602511yescharacteristic
467C2#1311612611yescharacteristic
468C2#1311614511yescharacteristic
subgroupG/H
centerC23#88193
commutator, cosocleC2×C42×C13C23
FrattiniC2×C42C22×D13
FittingC13×#1802C2
socleC23×C13#121
prime radicalC2×#11718676C2
hypercenter#1802D13
hypocenterC13#10473
LCSG ▷ C2×C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1802

Complements

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

NH ≅ G/Ntype
2. #13115641C2semidirect
3. #13115631C2semidirect
4. C2×#11718072C2semidirect
5. C2×#11718077C2semidirect
6. #13112719C2semidirect
7. C13×#1802C2semidirect
132. C2×#1055D8semidirect
136. #1802D13semidirect
366. C13#10473semidirect

Maximal subgroups

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

subgroupindex
C2×#117186762
#131156412
#131156312
C2×#117180722
C2×#117180772
#131127192
C13×#18022
#1047313