Finite Group Databasebeta

← #29581066

Subgroups — #29581066

Order 15616.

938 conjugacy classes of subgroups.

The subgroup lattice has 498 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839954C211yesmaximal, characteristic, complemented
2#21450766C211yesmaximal, characteristic, complemented
3#21446747C211yesmaximal, characteristic, complemented
4C2×#16839506C211yesmaximal, characteristic, complemented
5C2×#16839491C211yesmaximal, characteristic, complemented
6#21443659C211yesmaximal, characteristic, complemented
7C2×C61×#493C211yesmaximal, characteristic, complemented
8C22×#11758199—21no—
9C2×#14519773—21no—
10C2×#14519748—22no—
11C2×C4×D244C2211yescharacteristic
12#16839954—22no—
13#16839954—22no—
14C2×C4⋊#92418C2211yescharacteristic
15C2×C4⋊#92418C2211yescharacteristic
16C2×#14519698—21no—
17C2×#14519698—22no—
18#16839670—22no—
19#16839665—21no—
20C4×C4⋊Dic61C2211yescharacteristic
21#16839506—22no—
22#16839491—22no—
23C22×D8×C61—22no—
24C2×#127×C61C2211yescharacteristic
25C2×#127×C61C2211yescharacteristic
26C61×#493—22no—
27C61×#493—22no—
28C2×C4×C8×C61C2211yescharacteristic
29C22×D244D411yescharacteristic
30C22×C22⋊D61—24no—
31C22×C4×D61—21no—
32C2×#11758199—24no—
33C2×#11758199—42no—
34C2×#11758199—42no—
35C22×#92418—21no—
36C22×#92418—21no—
37#14519773—42no—
38#14519773—42no—
39#14519748—44no—
40#14519748—44no—
41C4×D244—21no—
42C4×D244—21no—
43C4×D244—21no—
44C4×D244—21no—
45C2×C4⋊Dic61D411yescharacteristic
46C2×C4⋊Dic61D412yes—
47C2×C22⋊Dic61—24no—
48C2×#11758198—21no—
49C2×C4×Dic61—21no—
50C4⋊#92418—21no—
51C4⋊#92418—21no—
52C4⋊#92418—21no—
53C4⋊#92418D412yescomplemented
54#14519698—24no—
55#14519698—44no—
56#14519684—21no—
57C22×D4×C61—21no—
58C22×D4×C61—21no—
59C22×D4×C61—21no—
60C22×D4×C61—21no—
61C22×D4×C61—21no—
62C22×D4×C61D412yes—
63C2×D8×C61—28no—
64C2×D8×C61—48no—
65C22×C8×C61—21no—
66#127×C61—21no—
67#127×C61—21no—
68#127×C61—21no—
69#127×C61—21no—
70#127×C61—21no—
71#127×C61—21no—
72#127×C61—21no—
73#127×C61D412yescomplemented
74C2×C42×C61C2311yescharacteristic
75C4×C8×C61—21no—
76C4×C8×C61D412yescomplemented
77C24×C61—22no—
78C24×C61—41no—
79C23×D61—21no—
80C2×D4×C61—22no—
81C2×D4×C61—22no—
82C2×D4×C61—22no—
83C2×D4×C61—22no—
84C2×D4×C61—22no—
85C2×D4×C61—44no—
86C2×D4×C61—44no—
87C2×D4×C61—41no—
88C2×D4×C61—41no—
89C2×D4×C61—41no—
90C2×D4×C61—41no—
91C2×D4×C61—41no—
92C2×D4×C61—41no—
93C2×D4×C61—41no—
94C2×D4×C61—42no—
95C2×D4×C61—41no—
96C2×D4×C61—42no—
97C2×D4×C61—41no—
98C2×D4×C61—41no—
99C2×D4×C61—41no—
100C2×D4×C61—41no—
101C2×D4×C61—42no—
102C2×D4×C61—41no—
103C2×D4×C61—41no—
104C2×D4×C61—42no—
105C2×D4×C61—41no—
106C22×C4×C61C2×D411yescharacteristic
107C22×C4×C61C2×D411yescharacteristic
108C22×C4×C61C2×D411yescharacteristic
109C2×C22⋊D61—48no—
110C2×C22⋊D61—48no—
111C2×C22⋊D61—84no—
112C22×Dic61—22no—
113C22×Dic61—21no—
114C2×D244—21no—
115C2×D244—21no—
116C2×D244—21no—
117C2×D244—21no—
118C2×D244—21no—
119C2×D244D812yescomplemented
120C2×C4×D61—41no—
121C2×C4×D61—41no—
122C2×C4×D61—42no—
123C2×C4×D61—42no—
124D8×C61—416no—
125C2×C8×C61—24no—
126C2×C8×C61—22no—
127C42×C61C2×D411yescharacteristic
128C42×C61C2×D411yescharacteristic
129C42×C61C2×D411yescharacteristic
130C42×C61#4111yescharacteristic
131C22⋊Dic61—48no—
132#11758199—48no—
133#11758198—41no—
134#11758198—41no—
135C4⋊Dic61—22no—
136C4⋊Dic61—21no—
137C4⋊Dic61—21no—
138C4⋊Dic61D814yescomplemented
139C4×Dic61—41no—
140C4×Dic61—41no—
141C2×#92418—22no—
142C2×#92418—41no—
143C2×#92418—41no—
144C2×#92418—41no—
145C2×#92418—42no—
146C23×C61—42no—
147C23×C61—42no—
148C23×C61—44no—
149C23×C61—42no—
150C23×C61—42no—
151C23×C61—44no—
152C23×C61—81no—
153C23×C61—82no—
154C23×C61—81no—
155C23×C61—82no—
156C23×C61#12011yescharacteristic
157C22×D61—22no—
158C22×D61—41no—
159C22×D61—42no—
160C22×D61—41no—
161C22×D61—42no—
162D4×C61—44no—
163D4×C61—44no—
164D4×C61—42no—
165D4×C61—42no—
166D4×C61—44no—
167D4×C61—82no—
168D4×C61—82no—
169D4×C61—81no—
170D4×C61—81no—
171D4×C61—82no—
172D4×C61—81no—
173D4×C61—81no—
174D4×C61—81no—
175D4×C61—81no—
176D4×C61—81no—
177D4×C61—81no—
178D4×C61—81no—
179D4×C61—81no—
180C2×C4×C61—22no—
181C2×C4×C61#12011yescharacteristic
182C2×C4×C61#12011yescharacteristic
183C2×C4×C61#12111yescharacteristic
184C2×C4×C61#12111yescharacteristic
185C2×C4×C61#12111yescharacteristic
186C2×C4×C61#12711yescharacteristic
187C2×C4×C61C2×D811yescharacteristic
188C2×C4×C61C2×D812yes—
189C2×C4×C61#13511yescharacteristic
190C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
191C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
192C2×C4×C61AGL(1,ℤ/8)12yes—
193C22⋊D61—816no—
194C2×Dic61—24no—
195C2×Dic61—42no—
196C2×Dic61—42no—
197C2×Dic61—41no—
198C2×Dic61—42no—
199D244—22no—
200D244—22no—
201D244—41no—
202D244—41no—
203C4×D61—82no—
204C4×D61—81no—
205C4×D61—81no—
206C8×C61—24no—
207#92418—42no—
208#92418—81no—
209#10046—611nomaximal, Sylow
210C22×C61—84no—
211C22×C61—84no—
212C22×C61—82no—
213C22×C61—82no—
214C22×C61—82no—
215C22×C61—82no—
216C22×C61—82no—
217C22×C61—82no—
218C22×C61—162no—
219C22×C61—162no—
220C22×C61#39211yescharacteristic
221C22×C61#44711yescharacteristic
222C22×C61#44712yes—
223C22×C61#44911yescharacteristic
224C22×C61#45312yes—
225C2×D61—44no—
226C2×D61—42no—
227C2×D61—82no—
228C2×D61—81no—
229C2×D61—81no—
230C4×C61—21no—
231C4×C61—21no—
232C4×C61#44711yescharacteristic
233C4×C61#44911yescharacteristic
234C4×C61#45912yes—
235C4×C61#46611yescharacteristic
236C4×C61#46911yescharacteristic
237C4×C61#49311yescharacteristic
238C4×C61#49611yescharacteristic
239Dic61—44no—
240Dic61—81no—
241C2×#493D6111yescharacteristic, complemented
242C2×#459—611no—
243#2541—611no—
244#1982—611no—
245C2×#331—611no—
246C2×D4⋊C8—611no—
247#1279—611no—
248C2×C61—162no—
249C2×C61—162no—
250C2×C61#161912yes—
251C2×C61#162112yes—
252C2×C61#199911yescharacteristic
253C2×C61#200211yescharacteristic
254C2×C61#201111yescharacteristic
255D61—82no—
256C22×D8—22no—
257C22×D8—1221no—
258C2×#127—1221no—
259C2×#127C2×D6111yescharacteristic
260C2×#127C2×D6111yescharacteristic
261C2×#121—1222no—
262C2×C4×D4—611no—
263#493—22no—
264#493—22no—
265#459—1222no—
266#459—1222no—
267C2×C4⋊C8—611no—
268C2×C4⋊C8—611no—
269C2×#102—1221no—
270C2×#102—1222no—
271C2×C4×C8C2×D6111yescharacteristic
272#392—1222no—
273#390—1221no—
274C4×C4⋊C4—611no—
275#331—1222no—
276D4⋊C8—1222no—
277C61#1004611yescharacteristic, complemented, Sylow
278C22×D4—21no—
279C22×D4—21no—
280C22×D4—21no—
281C22×D4—21no—
282C22×D4—21no—
283C22×D4—611no—
284C22×D4—1224no—
285C22×D4C22⋊D6112yes—
286C23×C4—1221no—
287C2×D8—28no—
288C2×D8—48no—
289C2×D8—1224no—
290C2×D8—2442no—
291C2×D8—2442no—
292C22×C8—21no—
293C22×C8—1221no—
294C22×C8—1221no—
295#127—21no—
296#127—21no—
297#127—21no—
298#127—21no—
299#127—21no—
300#127—21no—
301#127—21no—
302#127—2442no—
303#127—2442no—
304#127C22⋊D6112yescomplemented
305#121—2444no—
306#121—2444no—
307C4×D4—1221no—
308C4×D4—1221no—
309C4×D4—1221no—
310C4×D4—1221no—
311C2×C4⋊C4—612no—
312C2×C4⋊C4—611no—
313C2×C22⋊C4—1224no—
314C2×C22⋊C4—1221no—
315C2×C42—1221no—
316C2×C42C22×D6111yescharacteristic
317C4⋊C8—612no—
318C4⋊C8—1221no—
319C4⋊C8—1221no—
320C4⋊C8—1221no—
321#102—1224no—
322#102—2444no—
323C4×C8—21no—
324C4×C8C22⋊D6112yescomplemented
325#95—1221no—
326C24—22no—
327C24—41no—
328C24—1221no—
329C2×D4—22no—
330C2×D4—22no—
331C2×D4—22no—
332C2×D4—22no—
333C2×D4—22no—
334C2×D4—44no—
335C2×D4—44no—
336C2×D4—41no—
337C2×D4—41no—
338C2×D4—41no—
339C2×D4—41no—
340C2×D4—41no—
341C2×D4—41no—
342C2×D4—41no—
343C2×D4—42no—
344C2×D4—41no—
345C2×D4—42no—
346C2×D4—41no—
347C2×D4—41no—
348C2×D4—41no—
349C2×D4—41no—
350C2×D4—42no—
351C2×D4—41no—
352C2×D4—42no—
353C2×D4—41no—
354C2×D4—41no—
355C2×D4—612no—
356C2×D4—1221no—
357C2×D4—1221no—
358C2×D4—1221no—
359C2×D4—1221no—
360C2×D4—1221no—
361C2×D4—4884no—
362C2×D4—2448no—
363C2×D4—2448no—
364C22×C4—1222no—
365C22×C4—1221no—
366C22×C4—2441no—
367C22×C4—2441no—
368C22×C4—2442no—
369C22×C4—2442no—
370C22×C4D4×D6111yescharacteristic
371C22×C4D4×D6111yescharacteristic
372C22×C4C2×C22⋊D6111yescharacteristic
373D8—416no—
374D8—2448no—
375C2×C8—24no—
376C2×C8—22no—
377C2×C8—1222no—
378C2×C8—2441no—
379C2×C8—2442no—
380C2×C8—2441no—
381C2×C8—2441no—
382C4⋊C4—614no—
383C4⋊C4—1222no—
384C4⋊C4—1221no—
385C4⋊C4—1221no—
386C22⋊C4—2448no—
387C22⋊C4—2441no—
388C22⋊C4—2441no—
389C42—2441no—
390C42—2441no—
391C42D4×D6111yescharacteristic
392C42#1175822411yescharacteristic
393C42C2×C22⋊D6111yescharacteristic
394C42C2×C22⋊D6111yescharacteristic
395C23—44no—
396C23—42no—
397C23—42no—
398C23—42no—
399C23—42no—
400C23—44no—
401C23—81no—
402C23—82no—
403C23—81no—
404C23—82no—
405C23—1222no—
406C23—2442no—
407C23—2441no—
408C23—2441no—
409C23—2442no—
410C23#1451974511yescharacteristic
411D4—44no—
412D4—44no—
413D4—44no—
414D4—42no—
415D4—42no—
416D4—82no—
417D4—82no—
418D4—82no—
419D4—81no—
420D4—81no—
421D4—81no—
422D4—81no—
423D4—81no—
424D4—81no—
425D4—81no—
426D4—81no—
427D4—81no—
428D4—81no—
429D4—1222no—
430D4—1222no—
431D4—48816no—
432D4—2441no—
433D4—2441no—
434C2×C4—22no—
435C2×C4—1224no—
436C2×C4—4882no—
437C2×C4—4881no—
438C2×C4—4881no—
439C2×C4—2442no—
440C2×C4—2441no—
441C2×C4—2442no—
442C2×C4—2442no—
443C2×C4#1451974511yescharacteristic
444C2×C4#1451974611yescharacteristic
445C2×C4#1451974811yescharacteristic
446C2×C4#1451974911yescharacteristic
447C2×C4#1451974911yescharacteristic
448C2×C4#1451977311yescharacteristic
449C2×C4D8×D6112yes—
450C2×C4D8×D6111yescharacteristic
451C2×C4#1451979611yescharacteristic
452C2×C4#1451980112yes—
453C2×C4#1451980111yescharacteristic
454C2×C4#1451980111yescharacteristic
455C8—24no—
456C8—4881no—
457C8—2442no—
458C22—84no—
459C22—84no—
460C22—82no—
461C22—82no—
462C22—82no—
463C22—82no—
464C22—82no—
465C22—82no—
466C22—162no—
467C22—162no—
468C22—4882no—
469C22—4881no—
470C22—4881no—
471C22—2444no—
472C22—2442no—
473C22#1683967011yescharacteristic
474C22#1683989411yescharacteristic
475C22#1683989412yes—
476C22#1683990411yescharacteristic
477C22#1683992912yes—
478C4—21no—
479C4—21no—
480C4—4881no—
481C4—2444no—
482C4#1683989411yescharacteristic
483C4#1683990411yescharacteristic
484C4#1683995512yes—
485C4#1683999511yescharacteristic
486C4#1684001211yescharacteristic
487C4#1684013711yescharacteristic
488C4#1684015011yescharacteristic
489C2—162no—
490C2—162no—
491C2—4882no—
492C2#2144487112yes—
493C2#2144488112yes—
494C2#2144681411yescharacteristic
495C2#2144683411yescharacteristic
496C2#2144688811yescharacteristic
subgroupG/H
centerC23#14519745
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC2×C61×#493C2
socleC23×C61#120
hypercenterC2×#493D61
hypocenterC61#10046
LCSG ▷ C2×C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#493

Complements

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

NH ≅ G/Ntype
1. C2×#16839954C2semidirect
2. #21450766C2semidirect
3. #21446747C2semidirect
4. C2×#16839506C2semidirect
5. C2×#16839491C2semidirect
6. #21443659C2semidirect
7. C2×C61×#493C2semidirect
53. C4⋊#92418D4semidirect
73. #127×C61D4semidirect
76. C4×C8×C61D4semidirect
119. C2×D244D8semidirect
138. C4⋊Dic61D8semidirect
241. C2×#493D61semidirect
277. C61#10046semidirect
304. #127C22⋊D61semidirect
324. C4×C8C22⋊D61semidirect

Maximal subgroups

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

subgroupindex
C2×#168399542
#214507662
#214467472
C2×#168395062
C2×#168394912
#214436592
C2×C61×#4932
#1004661