Finite Group Databasebeta

← #29583380

Subgroups — #29583380

Order 15616.

708 conjugacy classes of subgroups.

The subgroup lattice has 512 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21450761C211yesmaximal, characteristic
2#21446624C211yesmaximal, characteristic, complemented
3#21445816C211yesmaximal, characteristic, complemented
4C2×#16839505C211yesmaximal, characteristic, complemented
5C2×#16839489C211yesmaximal, characteristic, complemented
6#21443660C211yesmaximal, characteristic, complemented
7C61×#1948C211yesmaximal, characteristic, complemented
8C2×#14519774—21no—
9C2×#14519774C2211yescharacteristic
10C2×#14519752—21no—
11C2×#14519752—21no—
12C2×C4×D244C2211yescharacteristic
13C2×C4⋊#92418C2211yescharacteristic
14C2×#14519697—21no—
15C2×#14519697—22no—
16C2×C4×#92418C2211yescharacteristic
17#16839672—22no—
18#16839664—21no—
19#16839524—21no—
20#16839505—22no—
21#16839489—22no—
22C2×#106×C61—21no—
23C2×C4⋊C8×C61C2211yescharacteristic
24C61×#384C2211yescharacteristic
25C4×C4⋊C4×C61C2211yescharacteristic
26C61×#340—21no—
27C22×D244—21no—
28C22×D244—21no—
29C22×D244—22no—
30C22×D244—22no—
31C22×D244D411yescharacteristic
32C22×D244D412yes—
33C22×C4×D61—21no—
34C22×#92418—21no—
35C22×#92418—21no—
36#14519774—21no—
37#14519774—21no—
38#14519774—21no—
39#14519774—21no—
40#14519774—42no—
41#14519774—42no—
42#14519752—42no—
43#14519752—42no—
44#14519752—42no—
45#14519752—42no—
46C4×D244—21no—
47C4×D244—21no—
48C4×D244—21no—
49C4×D244—21no—
50C2×C4⋊Dic61D411yescharacteristic
51C2×#11758198—22no—
52C2×#11758198—22no—
53C2×#11758198—21no—
54C4⋊#92418—21no—
55C4⋊#92418—21no—
56#14519697—44no—
57#14519697—42no—
58C4×#92418—21no—
59C4×#92418—21no—
60C22×C8×C61—21no—
61C2×C4⋊C4×C61—21no—
62C2×C4⋊C4×C61—21no—
63C2×C4⋊C4×C61—21no—
64C2×C4⋊C4×C61D411yescharacteristic
65C2×C4⋊C4×C61D411yescharacteristic
66C2×C42×C61—21no—
67C2×C42×C61C2311yescharacteristic
68#106×C61—42no—
69C4⋊C8×C61—21no—
70C4⋊C8×C61D412yescomplemented
71#95×C61—21no—
72C23×D61—21no—
73C23×D61—22no—
74C22×C4×C61—21no—
75C22×C4×C61—21no—
76C22×C4×C61—41no—
77C22×C4×C61C2×D411yescharacteristic
78C22×C4×C61C2×D411yescharacteristic
79C22×C4×C61C2×D411yescharacteristic
80C22×Dic61—21no—
81C2×D244—21no—
82C2×D244—21no—
83C2×D244—21no—
84C2×D244—21no—
85C2×D244—22no—
86C2×D244—21no—
87C2×D244—22no—
88C2×D244—42no—
89C2×D244—42no—
90C2×D244—44no—
91C2×D244—44no—
92C2×D244—44no—
93C2×D244—44no—
94C2×D244—41no—
95C2×D244—41no—
96C2×D244—41no—
97C2×D244—41no—
98C2×D244—41no—
99C2×D244—41no—
100C2×D244—41no—
101C2×D244—41no—
102C2×D244—41no—
103C2×D244—41no—
104C2×D244—41no—
105C2×D244—41no—
106C2×D244—82no—
107C2×D244—82no—
108C2×D244SD1612yes—
109C2×C4×D61—41no—
110C2×C4×D61—41no—
111C2×C4×D61—41no—
112C2×C4×D61—41no—
113C2×C4×D61—41no—
114C2×C4×D61—41no—
115C2×C8×C61—22no—
116C2×C8×C61—41no—
117C2×C8×C61—41no—
118C4⋊C4×C61—21no—
119C4⋊C4×C61—21no—
120C4⋊C4×C61—42no—
121C4⋊C4×C61—41no—
122C4⋊C4×C61—41no—
123C4⋊C4×C61—41no—
124C4⋊C4×C61—41no—
125C4⋊C4×C61D812yes—
126C4⋊C4×C61SD1612yes—
127C42×C61—41no—
128C42×C61—41no—
129C42×C61C2×D411yescharacteristic
130C42×C61#4111yescharacteristic
131C42×C61#4111yescharacteristic
132C42×C61#4111yescharacteristic
133#11758198—44no—
134#11758198—44no—
135#11758198—41no—
136#11758198—41no—
137C4⋊Dic61—21no—
138C4⋊Dic61—21no—
139C2×#92418—22no—
140C2×#92418—41no—
141C2×#92418—41no—
142C2×#92418—41no—
143C2×#92418—41no—
144C2×#92418—41no—
145C23×C61#12011yescharacteristic
146C22×D61—22no—
147C22×D61—41no—
148C22×D61—41no—
149C22×D61—41no—
150C22×D61—41no—
151C22×D61—41no—
152C22×D61—41no—
153C22×D61—42no—
154C22×D61—42no—
155C22×D61—42no—
156C22×D61—42no—
157C22×D61—42no—
158C22×D61—42no—
159C22×D61—42no—
160C2×C4×C61—21no—
161C2×C4×C61—21no—
162C2×C4×C61—22no—
163C2×C4×C61—22no—
164C2×C4×C61—41no—
165C2×C4×C61—41no—
166C2×C4×C61—41no—
167C2×C4×C61—41no—
168C2×C4×C61—81no—
169C2×C4×C61—81no—
170C2×C4×C61—81no—
171C2×C4×C61#12111yescharacteristic
172C2×C4×C61#12111yescharacteristic
173C2×C4×C61#12111yescharacteristic
174C2×C4×C61#12311yescharacteristic
175C2×C4×C61#12311yescharacteristic
176C2×C4×C61#12411yescharacteristic
177C2×C4×C61C2×D811yescharacteristic
178C2×C4×C61C2×SD1611yescharacteristic
179C2×C4×C61C2×SD1611yescharacteristic
180C2×C4×C61#13511yescharacteristic
181C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
182C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
183C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
184C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
185C2×Dic61—41no—
186C2×Dic61—41no—
187C2×Dic61—41no—
188D244—22no—
189D244—22no—
190D244—44no—
191D244—41no—
192D244—41no—
193D244—82no—
194D244—88no—
195D244—88no—
196D244—81no—
197D244—81no—
198D244—81no—
199D244—81no—
200D244—81no—
201D244—81no—
202D244—81no—
203D244—81no—
204C4×D61—81no—
205C4×D61—81no—
206C4×D61—81no—
207C4×D61—81no—
208C8×C61—42no—
209#92418—42no—
210#92418—81no—
211#10409—611nomaximal, Sylow
212C22×C61#39411yescharacteristic
213C22×C61#44711yescharacteristic
214C22×C61#44911yescharacteristic
215C22×C61#45011yescharacteristic
216C22×C61#45011yescharacteristic
217C22×C61#45311yescharacteristic
218C22×C61#45511yescharacteristic
219C2×D61—42no—
220C2×D61—42no—
221C2×D61—42no—
222C2×D61—81no—
223C2×D61—81no—
224C2×D61—81no—
225C2×D61—81no—
226C2×D61—82no—
227C2×D61—82no—
228C2×D61—82no—
229C2×D61—82no—
230C2×D61—82no—
231C2×D61—82no—
232C2×D61—82no—
233C4×C61—21no—
234C4×C61—21no—
235C4×C61—42no—
236C4×C61—42no—
237C4×C61—161no—
238C4×C61#45911yescharacteristic
239C4×C61#46011yescharacteristic
240C4×C61#46511yescharacteristic
241C4×C61#46911yescharacteristic
242C4×C61#48111yescharacteristic
243C4×C61#48211yescharacteristic
244C4×C61#48611yescharacteristic
245C4×C61#49011yescharacteristic
246Dic61—81no—
247#2541—611no—
248#1957—611no—
249#1948D6111yescharacteristic, complemented
250#1802—611no—
251C2×#331—611no—
252C2×D4⋊C8—611no—
253#1279—611no—
254C2×C61#162111yescharacteristic
255C2×C61#162911yescharacteristic
256C2×C61#163911yescharacteristic
257C2×C61#164211yescharacteristic
258C2×C61#203411yescharacteristic
259C2×C61#203711yescharacteristic
260C2×C61#204111yescharacteristic
261D61—82no—
262D61—162no—
263C2×#127—611no—
264C2×#127—1221no—
265C2×#121—1221no—
266C2×#121—1221no—
267C2×C4×D4—611no—
268C2×#106—21no—
269C2×C4⋊C8—611no—
270C2×C4⋊C8C2×D6111yescharacteristic
271C2×#102—1221no—
272C2×#102—1222no—
273C2×C4×C8—611no—
274#392—1222no—
275#390—1221no—
276#384C2×D6111yescharacteristic
277C4×C4⋊C4C2×D6111yescharacteristic
278#340—21no—
279#340—1221no—
280#331—1222no—
281D4⋊C8—1222no—
282C61#1040911yescharacteristic, complemented, Sylow
283C22×D4—611no—
284C22×D4—612no—
285C22×D4—1222no—
286C22×D4—1222no—
287C22×D4—1221no—
288C22×D4—1221no—
289C23×C4—1221no—
290C22×C8—21no—
291C22×C8—1221no—
292C22×C8—1221no—
293#127—1221no—
294#127—1221no—
295#127—1221no—
296#127—1221no—
297#127—2442no—
298#127—2442no—
299#121—2442no—
300#121—2442no—
301#121—2442no—
302#121—2442no—
303C4×D4—1221no—
304C4×D4—1221no—
305C4×D4—1221no—
306C4×D4—1221no—
307C2×C4⋊C4—21no—
308C2×C4⋊C4—21no—
309C2×C4⋊C4—21no—
310C2×C4⋊C4—611no—
311C2×C4⋊C4C22⋊D6111yescharacteristic
312C2×C4⋊C4C22⋊D6111yescharacteristic
313C2×C22⋊C4—1222no—
314C2×C22⋊C4—1222no—
315C2×C22⋊C4—1221no—
316C2×C42—21no—
317C2×C42C22×D6111yescharacteristic
318#106—42no—
319C4⋊C8—21no—
320C4⋊C8—1221no—
321C4⋊C8—1221no—
322C4⋊C8D24412yescomplemented
323#102—2444no—
324#102—2442no—
325C4×C8—1221no—
326C4×C8—1221no—
327#95—21no—
328C24—1221no—
329C24—1222no—
330C2×D4—612no—
331C2×D4—1221no—
332C2×D4—1222no—
333C2×D4—1221no—
334C2×D4—1222no—
335C2×D4—1221no—
336C2×D4—1221no—
337C2×D4—1221no—
338C2×D4—4882no—
339C2×D4—4882no—
340C2×D4—2444no—
341C2×D4—2444no—
342C2×D4—2442no—
343C2×D4—2442no—
344C2×D4—2444no—
345C2×D4—2444no—
346C2×D4—2441no—
347C2×D4—2441no—
348C2×D4—2441no—
349C2×D4—2441no—
350C2×D4—2441no—
351C2×D4—2441no—
352C2×D4—2441no—
353C2×D4—2441no—
354C2×D4—2441no—
355C2×D4—2441no—
356C2×D4—2441no—
357C2×D4—2441no—
358C22×C4—21no—
359C22×C4—21no—
360C22×C4—41no—
361C22×C4—1221no—
362C22×C4—2441no—
363C22×C4—2441no—
364C22×C4—2441no—
365C22×C4—2441no—
366C22×C4—2441no—
367C22×C4—2441no—
368C22×C4D4×D6111yescharacteristic
369C22×C4D4×D6111yescharacteristic
370C22×C4C2×C22⋊D6111yescharacteristic
371C2×C8—22no—
372C2×C8—41no—
373C2×C8—41no—
374C2×C8—1222no—
375C2×C8—2441no—
376C2×C8—2441no—
377C2×C8—2441no—
378C2×C8—2441no—
379C2×C8—2441no—
380C4⋊C4—21no—
381C4⋊C4—21no—
382C4⋊C4—42no—
383C4⋊C4—41no—
384C4⋊C4—41no—
385C4⋊C4—41no—
386C4⋊C4—41no—
387C4⋊C4—1221no—
388C4⋊C4—1221no—
389C4⋊C4#1175819912yes—
390C4⋊C4#1175820112yes—
391C22⋊C4—2444no—
392C22⋊C4—2444no—
393C22⋊C4—2441no—
394C22⋊C4—2441no—
395C42—41no—
396C42—41no—
397C42C2×D24411yescharacteristic
398C42#1175822211yescharacteristic
399C42#1175822611yescharacteristic
400C42#1175822611yescharacteristic
401C23—1222no—
402C23—2442no—
403C23—2442no—
404C23—2442no—
405C23—2442no—
406C23—2442no—
407C23—2442no—
408C23—2442no—
409C23—2441no—
410C23—2441no—
411C23—2441no—
412C23—2441no—
413C23—2441no—
414C23—2441no—
415C23#1451974511yescharacteristic
416D4—1222no—
417D4—1222no—
418D4—4882no—
419D4—4888no—
420D4—4888no—
421D4—4881no—
422D4—4881no—
423D4—4881no—
424D4—4881no—
425D4—4881no—
426D4—4881no—
427D4—4881no—
428D4—4881no—
429D4—2444no—
430D4—2441no—
431D4—2441no—
432C2×C4—21no—
433C2×C4—21no—
434C2×C4—22no—
435C2×C4—22no—
436C2×C4—41no—
437C2×C4—41no—
438C2×C4—41no—
439C2×C4—41no—
440C2×C4—81no—
441C2×C4—81no—
442C2×C4—81no—
443C2×C4—4881no—
444C2×C4—4881no—
445C2×C4—4881no—
446C2×C4—4881no—
447C2×C4—2441no—
448C2×C4—2441no—
449C2×C4—2441no—
450C2×C4#1451975111yescharacteristic
451C2×C4#1451975211yescharacteristic
452C2×C4#1451975211yescharacteristic
453C2×C4#1451976211yescharacteristic
454C2×C4#1451976211yescharacteristic
455C2×C4#1451976611yescharacteristic
456C2×C4C2×#1175819911yescharacteristic
457C2×C4SD16×D6111yescharacteristic
458C2×C4C2×#1175820111yescharacteristic
459C2×C4#1451979811yescharacteristic
460C2×C4#1451980211yescharacteristic
461C2×C4#1451980211yescharacteristic
462C2×C4#1451980411yescharacteristic
463C2×C4#1451980411yescharacteristic
464C8—42no—
465C8—4881no—
466C8—2442no—
467C22—4882no—
468C22—4882no—
469C22—4882no—
470C22—4882no—
471C22—4882no—
472C22—4882no—
473C22—4882no—
474C22—4881no—
475C22—4881no—
476C22—4881no—
477C22—4881no—
478C22—2442no—
479C22—2442no—
480C22—2442no—
481C22#1683967911yescharacteristic
482C22#1683989511yescharacteristic
483C22#1683990611yescharacteristic
484C22#1683991111yescharacteristic
485C22#1683991211yescharacteristic
486C22#1683992811yescharacteristic
487C22#1683993811yescharacteristic
488C4—21no—
489C4—21no—
490C4—42no—
491C4—42no—
492C4—161no—
493C4—4881no—
494C4#1683995711yescharacteristic
495C4#1683996211yescharacteristic
496C4#1683999211yescharacteristic
497C4#1684001611yescharacteristic
498C4#1684008211yescharacteristic
499C4#1684008811yescharacteristic
500C4#1684011011yescharacteristic
501C4#1684012811yescharacteristic
502C2—9762no—
503C2—4882no—
504C2#2144488211yescharacteristic
505C2#2144493411yescharacteristic
506C2#2144499611yescharacteristic
507C2#2144501811yescharacteristic
508C2#2144701011yescharacteristic
509C2#2144703111yescharacteristic
510C2#2144705311yescharacteristic
subgroupG/H
centerC23#14519745
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC61×#1948C2
socleC23×C61#120
prime radical#21450761C2
hypercenter#1948D61
hypocenterC61#10409
LCSG ▷ C2×C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1948

Complements

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

NH ≅ G/Ntype
2. #21446624C2semidirect
3. #21445816C2semidirect
4. C2×#16839505C2semidirect
5. C2×#16839489C2semidirect
6. #21443660C2semidirect
7. C61×#1948C2semidirect
70. C4⋊C8×C61D4semidirect
249. #1948D61semidirect
282. C61#10409semidirect
322. C4⋊C8D244semidirect

Maximal subgroups

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

subgroupindex
#214507612
#214466242
#214458162
C2×#168395052
C2×#168394892
#214436602
C61×#19482
#1040961