Finite Group Databasebeta

← #29581068

Subgroups — #29581068

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
2C2×#16839954C211yesmaximal, characteristic, complemented
3#21450761C211yesmaximal, characteristic, complemented
4C2×#16839505C211yesmaximal, characteristic, complemented
5C2×#16839489C211yesmaximal, characteristic, complemented
6#21443660C211yesmaximal, characteristic, complemented
7C61×#1982C211yesmaximal, characteristic, complemented
8C22×#11758199—22no—
9C22×#11758199—21no—
10C2×#14519774—21no—
11C2×#14519774C2211yescharacteristic
12C2×#14519752—22no—
13C2×C4×D244C2211yescharacteristic
14#16840138—22no—
15#16840138—22no—
16#16839954—22no—
17#16839954—22no—
18C2×C4⋊#92418C2211yescharacteristic
19C2×#14519698—21no—
20C2×C4×#92418C2211yescharacteristic
21#16839672—22no—
22#16839664—21no—
23#16839505—22no—
24#16839489—22no—
25C2×#127×C61C2211yescharacteristic
26C2×C4⋊C8×C61C2211yescharacteristic
27C2×#102×C61—22no—
28C4×C4⋊C4×C61C2211yescharacteristic
29C22×D244—21no—
30C22×D244—21no—
31C22×D244—24no—
32C22×D244D411yescharacteristic
33C22×D244D412yes—
34C22×C4×D61—21no—
35C2×#11758199—24no—
36C2×#11758199—28no—
37C2×#11758199—48no—
38C2×#11758199—42no—
39C2×#11758199—42no—
40C22×#92418—21no—
41C22×#92418—21no—
42#14519774—21no—
43#14519774—21no—
44#14519774—21no—
45#14519774—21no—
46#14519774—42no—
47#14519774—42no—
48#14519752—44no—
49#14519752—44no—
50C4×D244—21no—
51C4×D244—21no—
52C4×D244—21no—
53C4×D244—21no—
54C2×C4⋊Dic61D411yescharacteristic
55C2×#11758198—24no—
56C2×#11758198—21no—
57C4⋊#92418—21no—
58C4⋊#92418D412yescomplemented
59#14519698—24no—
60C4×#92418—21no—
61C4×#92418D412yescomplemented
62C22×D4×C61—21no—
63C22×D4×C61—21no—
64C22×D4×C61—21no—
65C22×C8×C61—21no—
66#127×C61—21no—
67#127×C61—21no—
68#127×C61—21no—
69#127×C61D412yescomplemented
70C2×C4⋊C4×C61D412yes—
71C2×C42×C61—21no—
72C2×C42×C61C2311yescharacteristic
73C4⋊C8×C61—21no—
74C4⋊C8×C61—21no—
75#102×C61—44no—
76#95×C61—21no—
77C24×C61—41no—
78C23×D61—21no—
79C23×D61—22no—
80C2×D4×C61—22no—
81C2×D4×C61—22no—
82C2×D4×C61—22no—
83C2×D4×C61—44no—
84C2×D4×C61—41no—
85C2×D4×C61—41no—
86C2×D4×C61—41no—
87C2×D4×C61—42no—
88C2×D4×C61—41no—
89C2×D4×C61—41no—
90C2×D4×C61—41no—
91C2×D4×C61—42no—
92C2×D4×C61—41no—
93C22×C4×C61—22no—
94C22×C4×C61C2×D411yescharacteristic
95C22×C4×C61C2×D411yescharacteristic
96C22×C4×C61C2×D411yescharacteristic
97C22×Dic61—21no—
98C2×D244—21no—
99C2×D244—21no—
100C2×D244—21no—
101C2×D244—21no—
102C2×D244—22no—
103C2×D244—21no—
104C2×D244—22no—
105C2×D244—44no—
106C2×D244—48no—
107C2×D244—48no—
108C2×D244—41no—
109C2×D244—41no—
110C2×D244—41no—
111C2×D244—41no—
112C2×D244—42no—
113C2×D244—41no—
114C2×D244—41no—
115C2×D244—41no—
116C2×D244—42no—
117C2×D244—41no—
118C2×D244—84no—
119C2×D244D812yescomplemented
120C2×C4×D61—41no—
121C2×C4×D61—41no—
122C2×C4×D61—42no—
123C2×C4×D61—42no—
124C2×C8×C61—41no—
125C2×C8×C61—42no—
126C4⋊C4×C61—22no—
127C4⋊C4×C61D814yescomplemented
128C42×C61—41no—
129C42×C61—41no—
130C42×C61C2×D411yescharacteristic
131C42×C61C2×D411yescharacteristic
132C42×C61C2×D411yescharacteristic
133C42×C61#4111yescharacteristic
134#11758199—416no—
135#11758199—48no—
136#11758198—48no—
137#11758198—41no—
138#11758198—41no—
139C4⋊Dic61—21no—
140C4⋊Dic61—21no—
141C2×#92418—24no—
142C2×#92418—22no—
143C2×#92418—22no—
144C2×#92418—41no—
145C2×#92418—41no—
146C23×C61—42no—
147C23×C61—81no—
148C23×C61—82no—
149C23×C61—81no—
150C23×C61—82no—
151C23×C61#12011yescharacteristic
152C22×D61—22no—
153C22×D61—41no—
154C22×D61—42no—
155C22×D61—41no—
156C22×D61—42no—
157C22×D61—42no—
158C22×D61—44no—
159C22×D61—42no—
160C22×D61—42no—
161C22×D61—44no—
162D4×C61—44no—
163D4×C61—42no—
164D4×C61—42no—
165D4×C61—44no—
166D4×C61—82no—
167D4×C61—81no—
168D4×C61—81no—
169D4×C61—81no—
170D4×C61—81no—
171C2×C4×C61—22no—
172C2×C4×C61—24no—
173C2×C4×C61—42no—
174C2×C4×C61—42no—
175C2×C4×C61#12011yescharacteristic
176C2×C4×C61#12011yescharacteristic
177C2×C4×C61#12111yescharacteristic
178C2×C4×C61#12111yescharacteristic
179C2×C4×C61#12111yescharacteristic
180C2×C4×C61#12711yescharacteristic
181C2×C4×C61C2×D811yescharacteristic
182C2×C4×C61C2×D812yes—
183C2×C4×C61#13511yescharacteristic
184C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
185C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
186C2×C4×C61AGL(1,ℤ/8)12yes—
187C2×Dic61—41no—
188C2×Dic61—42no—
189D244—22no—
190D244—22no—
191D244—44no—
192D244—41no—
193D244—41no—
194D244—82no—
195D244—816no—
196D244—81no—
197D244—81no—
198D244—82no—
199D244—81no—
200D244—81no—
201D244—81no—
202D244—81no—
203C4×D61—82no—
204C4×D61—81no—
205C4×D61—81no—
206C8×C61—81no—
207#92418—24no—
208#92418—42no—
209#10046—611nomaximal, Sylow
210C22×C61—82no—
211C22×C61—82no—
212C22×C61—82no—
213C22×C61—162no—
214C22×C61—162no—
215C22×C61#39211yescharacteristic
216C22×C61#44711yescharacteristic
217C22×C61#44712yes—
218C22×C61#44911yescharacteristic
219C22×C61#45312yes—
220C2×D61—44no—
221C2×D61—42no—
222C2×D61—82no—
223C2×D61—81no—
224C2×D61—81no—
225C2×D61—84no—
226C2×D61—84no—
227C2×D61—82no—
228C2×D61—82no—
229C2×D61—82no—
230C4×C61—21no—
231C4×C61—21no—
232C4×C61—44no—
233C4×C61#44711yescharacteristic
234C4×C61#44911yescharacteristic
235C4×C61#45912yes—
236C4×C61#46611yescharacteristic
237C4×C61#46911yescharacteristic
238C4×C61#49311yescharacteristic
239C4×C61#49611yescharacteristic
240Dic61—81no—
241C2×#493—611no—
242C2×#459—611no—
243#2541—611no—
244#1982D6111yescharacteristic, complemented
245C2×#331—611no—
246C2×D4⋊C8—611no—
247#1279—611no—
248C2×C61—162no—
249C2×C61#161912yes—
250C2×C61#162112yes—
251C2×C61#199911yescharacteristic
252C2×C61#200211yescharacteristic
253C2×C61#201111yescharacteristic
254D61—82no—
255D61—162no—
256C22×D8—1222no—
257C22×D8—1221no—
258C2×#127—611no—
259C2×#127—1221no—
260C2×#127C2×D6111yescharacteristic
261C2×#121—1222no—
262C2×C4×D4—611no—
263#493—1222no—
264#493—1222no—
265#459—1222no—
266#459—1222no—
267C2×C4⋊C8—611no—
268C2×C4⋊C8C2×D6111yescharacteristic
269C2×#102—22no—
270C2×#102—1221no—
271C2×C4×C8—611no—
272#392—1222no—
273#390—1221no—
274C4×C4⋊C4C2×D6111yescharacteristic
275#331—1222no—
276D4⋊C8—1222no—
277C61#1004611yescharacteristic, complemented, Sylow
278C22×D4—21no—
279C22×D4—21no—
280C22×D4—21no—
281C22×D4—611no—
282C22×D4—612no—
283C22×D4—1224no—
284C22×D4—1221no—
285C22×D4—1221no—
286C23×C4—1221no—
287C2×D8—1224no—
288C2×D8—1228no—
289C2×D8—2448no—
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—1221no—
299#127—1221no—
300#127—1221no—
301#127—1221no—
302#127—2442no—
303#127—2442no—
304#127D24412yescomplemented
305#121—2444no—
306#121—2444no—
307C4×D4—1221no—
308C4×D4—1221no—
309C4×D4—1221no—
310C4×D4—1221no—
311C2×C4⋊C4—611no—
312C2×C4⋊C4C22⋊D6112yes—
313C2×C22⋊C4—1224no—
314C2×C22⋊C4—1221no—
315C2×C42—21no—
316C2×C42C22×D6111yescharacteristic
317C4⋊C8—21no—
318C4⋊C8—21no—
319C4⋊C8—612no—
320C4⋊C8—1221no—
321#102—44no—
322#102—1224no—
323C4×C8—612no—
324C4×C8—1221no—
325#95—21no—
326C24—41no—
327C24—1221no—
328C24—1222no—
329C2×D4—22no—
330C2×D4—22no—
331C2×D4—22no—
332C2×D4—44no—
333C2×D4—41no—
334C2×D4—41no—
335C2×D4—41no—
336C2×D4—41no—
337C2×D4—42no—
338C2×D4—41no—
339C2×D4—41no—
340C2×D4—42no—
341C2×D4—41no—
342C2×D4—612no—
343C2×D4—1221no—
344C2×D4—1222no—
345C2×D4—1221no—
346C2×D4—1222no—
347C2×D4—1221no—
348C2×D4—1221no—
349C2×D4—1221no—
350C2×D4—4884no—
351C2×D4—2448no—
352C2×D4—2444no—
353C2×D4—2448no—
354C2×D4—2441no—
355C2×D4—2441no—
356C2×D4—2441no—
357C2×D4—2441no—
358C2×D4—2441no—
359C2×D4—2442no—
360C2×D4—2441no—
361C2×D4—2441no—
362C2×D4—2442no—
363C2×D4—2441no—
364C22×C4—22no—
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—24416no—
374D8—2448no—
375C2×C8—41no—
376C2×C8—42no—
377C2×C8—1224no—
378C2×C8—1222no—
379C2×C8—1222no—
380C2×C8—2441no—
381C2×C8—2441no—
382C4⋊C4—22no—
383C4⋊C4—1221no—
384C4⋊C4—1221no—
385C4⋊C4#1175819914yescomplemented
386C22⋊C4—2448no—
387C22⋊C4—2441no—
388C22⋊C4—2441no—
389C42—41no—
390C42—41no—
391C42C2×D24411yescharacteristic
392C42#1175822211yescharacteristic
393C42D4×D6111yescharacteristic
394C42D4×D6111yescharacteristic
395C23—42no—
396C23—81no—
397C23—82no—
398C23—81no—
399C23—82no—
400C23—1222no—
401C23—2442no—
402C23—2444no—
403C23—2442no—
404C23—2442no—
405C23—2444no—
406C23—2442no—
407C23—2441no—
408C23—2441no—
409C23—2442no—
410C23#1451974511yescharacteristic
411D4—44no—
412D4—44no—
413D4—42no—
414D4—42no—
415D4—82no—
416D4—81no—
417D4—81no—
418D4—81no—
419D4—81no—
420D4—1222no—
421D4—1222no—
422D4—4882no—
423D4—48816no—
424D4—4882no—
425D4—4881no—
426D4—4881no—
427D4—4881no—
428D4—4881no—
429D4—4881no—
430D4—4881no—
431D4—2444no—
432D4—2441no—
433D4—2441no—
434C2×C4—22no—
435C2×C4—24no—
436C2×C4—42no—
437C2×C4—42no—
438C2×C4—4882no—
439C2×C4—4881no—
440C2×C4—4881no—
441C2×C4—2442no—
442C2×C4—2441no—
443C2×C4#1451974711yescharacteristic
444C2×C4#1451974711yescharacteristic
445C2×C4#1451975011yescharacteristic
446C2×C4#1451975011yescharacteristic
447C2×C4#1451975111yescharacteristic
448C2×C4#1451977311yescharacteristic
449C2×C4D8×D6111yescharacteristic
450C2×C4C2×#1175819912yes—
451C2×C4#1451979811yescharacteristic
452C2×C4#1451980111yescharacteristic
453C2×C4#1451980212yes—
454C2×C4#1451980411yescharacteristic
455C8—81no—
456C8—1224no—
457C8—2442no—
458C22—82no—
459C22—82no—
460C22—82no—
461C22—162no—
462C22—162no—
463C22—4884no—
464C22—4884no—
465C22—4882no—
466C22—4882no—
467C22—4882no—
468C22—4882no—
469C22—4881no—
470C22—4881no—
471C22—2444no—
472C22—2442no—
473C22#1683967111yescharacteristic
474C22#1683989411yescharacteristic
475C22#1683989512yes—
476C22#1683990611yescharacteristic
477C22#1683992812yes—
478C4—21no—
479C4—21no—
480C4—44no—
481C4—4881no—
482C4#1683989711yescharacteristic
483C4#1683990811yescharacteristic
484C4#1683995712yes—
485C4#1683999711yescharacteristic
486C4#1684001411yescharacteristic
487C4#1684013811yescharacteristic
488C4#1684015211yescharacteristic
489C2—162no—
490C2—9762no—
491C2—4882no—
492C2#2144487212yes—
493C2#2144488212yes—
494C2#2144681611yescharacteristic
495C2#2144683511yescharacteristic
496C2#2144688911yescharacteristic
subgroupG/H
centerC23#14519745
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC61×#1982C2
socleC23×C61#120
hypercenter#1982D61
hypocenterC61#10046
LCSG ▷ C2×C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1982

Complements

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

NH ≅ G/Ntype
1. C2×#16840138C2semidirect
2. C2×#16839954C2semidirect
3. #21450761C2semidirect
4. C2×#16839505C2semidirect
5. C2×#16839489C2semidirect
6. #21443660C2semidirect
7. C61×#1982C2semidirect
58. C4⋊#92418D4semidirect
61. C4×#92418D4semidirect
69. #127×C61D4semidirect
119. C2×D244D8semidirect
127. C4⋊C4×C61D8semidirect
244. #1982D61semidirect
277. C61#10046semidirect
304. #127D244semidirect
385. C4⋊C4#11758199semidirect

Maximal subgroups

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

subgroupindex
C2×#168401382
C2×#168399542
#214507612
C2×#168395052
C2×#168394892
#214436602
C61×#19822
#1004661