Finite Group Databasebeta

← #29581067

Subgroups — #29581067

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×#16840138C211yesmaximal, characteristic, complemented
2#21450765C211yesmaximal, characteristic, complemented
3#21446747C211yesmaximal, characteristic, complemented
4C2×#16839505C211yesmaximal, characteristic, complemented
5C2×D4⋊#92418C211yesmaximal, characteristic, complemented
6#21443658C211yesmaximal, characteristic, complemented
7C2×C61×#459C211yesmaximal, characteristic, complemented
8C22×#11758199—22no—
9C2×#14519774C2211yescharacteristic
10C2×#14519773—21no—
11C2×#14519751—22no—
12#16840138—22no—
13#16840138—22no—
14C2×C4⋊#92418C2211yescharacteristic
15C2×#14519698—22no—
16C2×C4×#92418C2211yescharacteristic
17#16839671—22no—
18#16839663—21no—
19C4×C4⋊Dic61C2211yescharacteristic
20#16839505—22no—
21D4⋊#92418—22no—
22C22×D8×C61—21no—
23C2×#127×C61C2211yescharacteristic
24C2×C4×D4×C61C2211yescharacteristic
25C61×#459—22no—
26C61×#459—22no—
27C2×C4⋊C8×C61C2211yescharacteristic
28C2×#102×C61—21no—
29C22×D244—21no—
30C22×D244—21no—
31C22×D244D412yes—
32C22×C22⋊D61—24no—
33C2×#11758199—28no—
34C2×#11758199—48no—
35C22×#92418—21no—
36C22×#92418—21no—
37#14519774—21no—
38#14519774—21no—
39#14519774—21no—
40#14519774—21no—
41#14519773—42no—
42#14519773—42no—
43#14519751—44no—
44#14519751—44no—
45C2×C4⋊Dic61D412yes—
46C2×#11758198—24no—
47C2×C4×Dic61—21no—
48C4⋊#92418—21no—
49C4⋊#92418—21no—
50#14519698—44no—
51C4×#92418—21no—
52C4×#92418D412yescomplemented
53#14519684—21no—
54C22×D4×C61—21no—
55C22×D4×C61—21no—
56C22×D4×C61—21no—
57C22×D4×C61D411yescharacteristic
58C23×C4×C61—21no—
59C2×D8×C61—24no—
60C2×D8×C61—42no—
61C2×D8×C61—42no—
62C22×C8×C61—21no—
63#127×C61—21no—
64#127×C61—21no—
65#127×C61—21no—
66#127×C61D412yescomplemented
67C4×D4×C61—21no—
68C4×D4×C61—21no—
69C4×D4×C61—21no—
70C4×D4×C61—21no—
71C2×C4⋊C4×C61D411yescharacteristic
72C2×C22⋊C4×C61—21no—
73C2×C42×C61C2311yescharacteristic
74C4⋊C8×C61—21no—
75C4⋊C8×C61D412yescomplemented
76#102×C61—24no—
77C24×C61—21no—
78C24×C61—41no—
79C23×D61—22no—
80C2×D4×C61—21no—
81C2×D4×C61—22no—
82C2×D4×C61—22no—
83C2×D4×C61—21no—
84C2×D4×C61—22no—
85C2×D4×C61—21no—
86C2×D4×C61—21no—
87C2×D4×C61—21no—
88C2×D4×C61—44no—
89C2×D4×C61—41no—
90C2×D4×C61—41no—
91C2×D4×C61—41no—
92C2×D4×C61—41no—
93C2×D4×C61—42no—
94C2×D4×C61—41no—
95C2×D4×C61—41no—
96C2×D4×C61—41no—
97C2×D4×C61—42no—
98C2×D4×C61D812yescomplemented
99C22×C4×C61—21no—
100C22×C4×C61—41no—
101C22×C4×C61—41no—
102C22×C4×C61—42no—
103C22×C4×C61—42no—
104C22×C4×C61C2×D411yescharacteristic
105C22×C4×C61C2×D411yescharacteristic
106C22×C4×C61C2×D411yescharacteristic
107C2×C22⋊D61—48no—
108C2×C22⋊D61—48no—
109C2×C22⋊D61—84no—
110C22×Dic61—22no—
111C2×D244—22no—
112C2×D244—22no—
113C2×D244—44no—
114C2×D244—41no—
115C2×D244—41no—
116C2×D244—41no—
117C2×D244—41no—
118C2×D244—42no—
119C2×D244—41no—
120C2×D244—41no—
121C2×D244—41no—
122C2×D244—42no—
123C2×D244—41no—
124D8×C61—48no—
125C2×C8×C61—22no—
126C2×C8×C61—41no—
127C2×C8×C61—41no—
128C4⋊C4×C61—21no—
129C4⋊C4×C61—21no—
130C22⋊C4×C61—41no—
131C22⋊C4×C61—41no—
132C42×C61C2×D411yescharacteristic
133C42×C61C2×D411yescharacteristic
134C42×C61C2×D411yescharacteristic
135C42×C61#4111yescharacteristic
136#11758199—416no—
137#11758198—48no—
138C4⋊Dic61—22no—
139C4⋊Dic61D814yescomplemented
140C4×Dic61—41no—
141C4×Dic61—41no—
142C2×#92418—24no—
143C2×#92418—22no—
144C2×#92418—41no—
145C2×#92418—42no—
146C23×C61—22no—
147C23×C61—41no—
148C23×C61—42no—
149C23×C61—41no—
150C23×C61—42no—
151C23×C61—42no—
152C23×C61—81no—
153C23×C61—82no—
154C23×C61—81no—
155C23×C61—82no—
156C23×C61#12011yescharacteristic
157C22×D61—42no—
158C22×D61—44no—
159C22×D61—42no—
160C22×D61—42no—
161C22×D61—44no—
162D4×C61—22no—
163D4×C61—22no—
164D4×C61—44no—
165D4×C61—42no—
166D4×C61—41no—
167D4×C61—42no—
168D4×C61—44no—
169D4×C61—41no—
170D4×C61—82no—
171D4×C61—81no—
172D4×C61—81no—
173D4×C61—81no—
174D4×C61—81no—
175C2×C4×C61—22no—
176C2×C4×C61—41no—
177C2×C4×C61—42no—
178C2×C4×C61—82no—
179C2×C4×C61—81no—
180C2×C4×C61—81no—
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—
197D244—44no—
198D244—82no—
199D244—81no—
200D244—81no—
201D244—82no—
202D244—81no—
203D244—81no—
204D244—81no—
205D244—81no—
206C8×C61—42no—
207#92418—24no—
208#92418—81no—
209#10046—611nomaximal, Sylow
210C22×C61—44no—
211C22×C61—42no—
212C22×C61—82no—
213C22×C61—81no—
214C22×C61—81no—
215C22×C61—82no—
216C22×C61—82no—
217C22×C61—82no—
218C22×C61—162no—
219C22×C61—162no—
220C22×C61#39211yescharacteristic
221C22×C61#44712yes—
222C22×C61#44711yescharacteristic
223C22×C61#44911yescharacteristic
224C22×C61#45312yes—
225C2×D61—84no—
226C2×D61—84no—
227C2×D61—82no—
228C2×D61—82no—
229C2×D61—82no—
230C4×C61—21no—
231C4×C61—21no—
232C4×C61—81no—
233C4×C61#44711yescharacteristic
234C4×C61#44911yescharacteristic
235C4×C61#45912yes—
236C4×C61#46611yescharacteristic
237C4×C61#46911yescharacteristic
238C4×C61#49311yescharacteristic
239C4×C61#49611yescharacteristic
240Dic61—44no—
241C2×#493—611no—
242C2×#459D6111yescharacteristic, complemented
243#2541—611no—
244#1982—611no—
245C2×#331—611no—
246C2×D4⋊C8—611no—
247#1279—611no—
248C2×C61—82no—
249C2×C61—162no—
250C2×C61#161912yes—
251C2×C61#162112yes—
252C2×C61#199911yescharacteristic
253C2×C61#200211yescharacteristic
254C2×C61#201111yescharacteristic
255D61—162no—
256C22×D8—21no—
257C22×D8—1222no—
258C2×#127—611no—
259C2×#127—1221no—
260C2×#127C2×D6111yescharacteristic
261C2×#121—1222no—
262C2×C4×D4C2×D6111yescharacteristic
263#493—1222no—
264#493—1222no—
265#459—22no—
266#459—22no—
267C2×C4⋊C8—611no—
268C2×C4⋊C8C2×D6111yescharacteristic
269C2×#102—21no—
270C2×#102—1222no—
271C2×C4×C8—611no—
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—612no—
282C22×D4—1224no—
283C22×D4—1221no—
284C22×D4—1221no—
285C22×D4C22⋊D6111yescharacteristic
286C23×C4—21no—
287C2×D8—24no—
288C2×D8—42no—
289C2×D8—42no—
290C2×D8—1228no—
291C2×D8—2448no—
292C22×C8—21no—
293C22×C8—1221no—
294C22×C8—1221no—
295#127—21no—
296#127—21no—
297#127—21no—
298#127—1221no—
299#127—1221no—
300#127—1221no—
301#127—1221no—
302#127—2442no—
303#127—2442no—
304#127C22⋊D6112yescomplemented
305#121—2444no—
306#121—2444no—
307C4×D4—21no—
308C4×D4—21no—
309C4×D4—21no—
310C4×D4—21no—
311C2×C4⋊C4—612no—
312C2×C4⋊C4C22⋊D6111yescharacteristic
313C2×C22⋊C4—21no—
314C2×C22⋊C4—1224no—
315C2×C42—1221no—
316C2×C42C22×D6111yescharacteristic
317C4⋊C8—21no—
318C4⋊C8—1221no—
319C4⋊C8—1221no—
320C4⋊C8C22⋊D6112yescomplemented
321#102—24no—
322#102—2444no—
323C4×C8—612no—
324C4×C8—1221no—
325#95—1221no—
326C24—21no—
327C24—41no—
328C24—1222no—
329C2×D4—22no—
330C2×D4—21no—
331C2×D4—22no—
332C2×D4—21no—
333C2×D4—22no—
334C2×D4—21no—
335C2×D4—21no—
336C2×D4—21no—
337C2×D4—44no—
338C2×D4—41no—
339C2×D4—41no—
340C2×D4—41no—
341C2×D4—42no—
342C2×D4—41no—
343C2×D4—41no—
344C2×D4—42no—
345C2×D4—41no—
346C2×D4—41no—
347C2×D4—1222no—
348C2×D4—1222no—
349C2×D4—4884no—
350C2×D4—2444no—
351C2×D4—2448no—
352C2×D4—2448no—
353C2×D4—2441no—
354C2×D4—2441no—
355C2×D4—2441no—
356C2×D4—2441no—
357C2×D4—2442no—
358C2×D4—2441no—
359C2×D4—2441no—
360C2×D4—2442no—
361C2×D4—2441no—
362C2×D4—2441no—
363C2×D4#1175819912yescomplemented
364C22×C4—21no—
365C22×C4—41no—
366C22×C4—41no—
367C22×C4—42no—
368C22×C4—42no—
369C22×C4—1222no—
370C22×C4D4×D6111yescharacteristic
371C22×C4D4×D6111yescharacteristic
372C22×C4C2×C22⋊D6111yescharacteristic
373D8—48no—
374D8—24416no—
375C2×C8—22no—
376C2×C8—41no—
377C2×C8—41no—
378C2×C8—1224no—
379C2×C8—1222no—
380C2×C8—2441no—
381C2×C8—2442no—
382C4⋊C4—21no—
383C4⋊C4—21no—
384C4⋊C4—614no—
385C4⋊C4—1222no—
386C22⋊C4—41no—
387C22⋊C4—41no—
388C22⋊C4—2448no—
389C42—2441no—
390C42—2441no—
391C42D4×D6111yescharacteristic
392C42#1175822411yescharacteristic
393C42C2×C22⋊D6111yescharacteristic
394C42C2×C22⋊D6111yescharacteristic
395C23—22no—
396C23—42no—
397C23—41no—
398C23—41no—
399C23—42no—
400C23—42no—
401C23—82no—
402C23—81no—
403C23—81no—
404C23—82no—
405C23—2444no—
406C23—2442no—
407C23—2442no—
408C23—2442no—
409C23—2444no—
410C23#1451974511yescharacteristic
411D4—22no—
412D4—22no—
413D4—44no—
414D4—44no—
415D4—41no—
416D4—42no—
417D4—41no—
418D4—42no—
419D4—82no—
420D4—81no—
421D4—81no—
422D4—81no—
423D4—81no—
424D4—4882no—
425D4—48816no—
426D4—4882no—
427D4—4881no—
428D4—4881no—
429D4—4881no—
430D4—4881no—
431D4—4881no—
432D4—4881no—
433D4—2444no—
434C2×C4—22no—
435C2×C4—42no—
436C2×C4—41no—
437C2×C4—82no—
438C2×C4—81no—
439C2×C4—81no—
440C2×C4—1224no—
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×C4C2×#1175819911yescharacteristic
451C2×C4#1451979711yescharacteristic
452C2×C4#1451980112yes—
453C2×C4#1451980211yescharacteristic
454C2×C4#1451980311yescharacteristic
455C8—42no—
456C8—1224no—
457C8—4881no—
458C22—44no—
459C22—42no—
460C22—82no—
461C22—81no—
462C22—81no—
463C22—82no—
464C22—82no—
465C22—82no—
466C22—162no—
467C22—162no—
468C22—4884no—
469C22—4884no—
470C22—4882no—
471C22—4882no—
472C22—4882no—
473C22#1683967011yescharacteristic
474C22#1683989412yes—
475C22#1683989511yescharacteristic
476C22#1683990511yescharacteristic
477C22#1683992812yes—
478C4—21no—
479C4—21no—
480C4—81no—
481C4—2444no—
482C4#1683989611yescharacteristic
483C4#1683990711yescharacteristic
484C4#1683995512yes—
485C4#1683999611yescharacteristic
486C4#1684001311yescharacteristic
487C4#1684013711yescharacteristic
488C4#1684015011yescharacteristic
489C2—82no—
490C2—162no—
491C2—9762no—
492C2#2144487212yes—
493C2#2144488312yes—
494C2#2144681511yescharacteristic
495C2#2144683111yescharacteristic
496C2#2144688811yescharacteristic
subgroupG/H
centerC23#14519745
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC2×C61×#459C2
socleC23×C61#120
hypercenterC2×#459D61
hypocenterC61#10046
LCSG ▷ C2×C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#459

Complements

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

NH ≅ G/Ntype
1. C2×#16840138C2semidirect
2. #21450765C2semidirect
3. #21446747C2semidirect
4. C2×#16839505C2semidirect
5. C2×D4⋊#92418C2semidirect
6. #21443658C2semidirect
7. C2×C61×#459C2semidirect
52. C4×#92418D4semidirect
66. #127×C61D4semidirect
75. C4⋊C8×C61D4semidirect
98. C2×D4×C61D8semidirect
139. C4⋊Dic61D8semidirect
242. C2×#459D61semidirect
277. C61#10046semidirect
304. #127C22⋊D61semidirect
320. C4⋊C8C22⋊D61semidirect
363. C2×D4#11758199semidirect

Maximal subgroups

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

subgroupindex
C2×#168401382
#214507652
#214467472
C2×#168395052
C2×D4⋊#924182
#214436582
C2×C61×#4592
#1004661