Finite Group Databasebeta

← #29837629

Subgroups — #29837629

Order 15616.

488 conjugacy classes of subgroups.

The subgroup lattice has 476 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21458217C211yesmaximal, characteristic, complemented
2#21458216C211yesmaximal, characteristic, complemented
3#21448096C211yesmaximal, characteristic, complemented
4#21448011C211yesmaximal, characteristic, complemented
5#21448008C211yesmaximal, characteristic, complemented
6#21448001C211yesmaximal, characteristic, complemented
7#21447979C211yesmaximal, characteristic, complemented
8#21447978C211yesmaximal, characteristic, complemented
9#21447921C211yesmaximal, characteristic, complemented
10#21447920C211yesmaximal, characteristic, complemented
11#21447663C211yesmaximal, characteristic, complemented
12#21447648C211yesmaximal, characteristic, complemented
13#21447605C211yesmaximal, characteristic, complemented
14#21447604C211yesmaximal, characteristic, complemented
15C61×#2232C211yesmaximal, characteristic, complemented
16#16840460—21no—
17#16840459—21no—
18C2×#14519718C2211yescharacteristic
19C2×#14519717C2211yescharacteristic
20C2×#14519716C2211yescharacteristic
21#16840163C2211yescharacteristic
22#16840163C2211yescharacteristic
23#16840089—21no—
24#16840083—21no—
25#16840080—21no—
26#16840079—21no—
27#16840065—21no—
28#16840064—21no—
29#16839999C2211yescharacteristic
30#16839998C2211yescharacteristic
31#16839995C2211yescharacteristic
32D8×Dic61C2211yescharacteristic
33#16839844C2211yescharacteristic
34C8×C22⋊D61C2211yescharacteristic
35#16839800C2211yescharacteristic
36#16839799C2211yescharacteristic
37#107×D61C2211yescharacteristic
38#16839590C2211yescharacteristic
39#16839589C2211yescharacteristic
40#16839589C2211yescharacteristic
41#16839589C2211yescharacteristic
42#16839588C2211yescharacteristic
43#16839587C2211yescharacteristic
44#16839587C2211yescharacteristic
45#16839580C2211yescharacteristic
46#16839564C2211yescharacteristic
47#16839564C2211yescharacteristic
48#16839563C2211yescharacteristic
49#16839562C2211yescharacteristic
50#16839541C2211yescharacteristic
51C16×Dic61C2211yescharacteristic
52C61×#466C2211yescharacteristic
53C2×#107×C61C2211yescharacteristic
54C61×#366C2211yescharacteristic
55C61×#366C2211yescharacteristic
56C61×#357C2211yescharacteristic
57C61×#357C2211yescharacteristic
58C61×C22⋊C16C2211yescharacteristic
59C2×D488C2311yescharacteristic
60C2×C8×D61C2311yescharacteristic
61#14519772—41no—
62#14519770—41no—
63#14519768—21no—
64#14519768—21no—
65#14519762—41no—
66#14519758—41no—
67#14519752—21no—
68#14519751—21no—
69#14519751—41no—
70#14519748—21no—
71#14519748—41no—
72D4×Dic61—21no—
73#14519739—21no—
74C4×C22⋊D61—41no—
75C4×C22⋊D61D411yescharacteristic
76#14519737—41no—
77#14519736—21no—
78#14519735—21no—
79C4⋊C4×D61—21no—
80#14519718—22no—
81#14519717—22no—
82#14519716—22no—
83C2×#11758185C2311yescharacteristic
84C2×#11758185C2311yescharacteristic
85#14519711C2311yescharacteristic
86#14519711C2311yescharacteristic
87#14519711C2311yescharacteristic
88#14519710—21no—
89#14519709—21no—
90#14519708—21no—
91#14519708—21no—
92#14519708—21no—
93#14519706D411yescharacteristic
94#14519699—21no—
95#14519698—21no—
96#14519698—21no—
97#14519697—21no—
98#14519697—21no—
99C22⋊#92418D411yescharacteristic
100#14519689D411yescharacteristic
101C8×Dic61C2311yescharacteristic
102C2×D8×C61C2311yescharacteristic
103C22×C8×C61C2311yescharacteristic
104#121×C61—21no—
105C2×C4⋊C4×C61—21no—
106C2×C16×C61C2311yescharacteristic
107C2×C16×C61C2311yescharacteristic
108#107×C61—21no—
109#107×C61C2311yescharacteristic
110#107×C61C2311yescharacteristic
111#107×C61C2311yescharacteristic
112#102×C61—21no—
113C2×D4×C61—21no—
114C2×D4×C61—41no—
115C22×C4×C61—41no—
116C22×C4×C61C2×D411yescharacteristic
117C2×C22⋊D61—41no—
118C2×C22⋊D61—41no—
119C2×C22⋊D61D811yescharacteristic
120C22×Dic61—41no—
121C2×D244—21no—
122C2×D244—41no—
123C2×C4×D61—41no—
124C2×C4×D61—41no—
125C2×C4×D61C2×D411yescharacteristic
126D8×C61—21no—
127D8×C61—21no—
128C2×C8×C61—21no—
129C2×C8×C61—21no—
130C2×C8×C61C2×D411yescharacteristic
131C2×C8×C61C2411yescharacteristic
132C4⋊C4×C61—21no—
133C4⋊C4×C61—21no—
134C4⋊C4×C61—21no—
135C4⋊C4×C61—41no—
136C22⋊C4×C61—41no—
137C22⋊Dic61—41no—
138C22⋊Dic61—41no—
139C22⋊Dic61—41no—
140C22⋊Dic61D811yescharacteristic
141#11758198—41no—
142#11758198—41no—
143#11758198—41no—
144#11758198—41no—
145#11758198D811yescharacteristic
146C4⋊Dic61—21no—
147C4⋊Dic61—21no—
148C4⋊Dic61—21no—
149C4⋊Dic61—41no—
150C4⋊Dic61—41no—
151#11758196—41no—
152#11758196—41no—
153#11758196—41no—
154#11758196D811yescharacteristic
155C4×Dic61—41no—
156C4×Dic61—41no—
157C4×Dic61C2×D411yescharacteristic
158C2×#92418C2×D411yescharacteristic
159C2×#92418C2×D411yescharacteristic
160D488—21no—
161D488—21no—
162C8×D61—21no—
163C8×D61—21no—
164C16×C61—21no—
165C16×C61—21no—
166#11758185—21no—
167#11758185#4112yes—
168C23×C61—41no—
169C23×C61C2×D811yescharacteristic
170C22×D61—41no—
171C22×D61C2×D811yescharacteristic
172D4×C61—41no—
173D4×C61—41no—
174D4×C61—161no—
175C2×C4×C61—21no—
176C2×C4×C61—21no—
177C2×C4×C61—41no—
178C2×C4×C61—41no—
179C2×C4×C61—41no—
180C2×C4×C61—161no—
181C2×C4×C61C2×D811yescharacteristic
182C2×C4×C61C22×D411yescharacteristic
183C22⋊D61—41no—
184C22⋊D61—82no—
185C22⋊D61—82no—
186C2×Dic61—41no—
187C2×Dic61—41no—
188C2×Dic61—41no—
189C2×Dic61—161no—
190C2×Dic61C2×D811yescharacteristic
191C2×Dic61C2×D811yescharacteristic
192C2×Dic61C2×D811yescharacteristic
193D244—41no—
194D244—41no—
195D244—161no—
196C4×D61—21no—
197C4×D61—21no—
198C4×D61—161no—
199C4×D61—161no—
200C8×C61—21no—
201C8×C61C2×#4111yescharacteristic
202C8×C612−1+411yescharacteristic
203#92418—21no—
204#92418—21no—
205#33922—611nomaximal, Sylow
206C22×C61—21no—
207C22×C61—21no—
208C22×C61—21no—
209C22×C61—81no—
210C22×C61—81no—
211C22×C61—81no—
212C22×C61C22×D811yescharacteristic
213C2×D61—21no—
214C2×D61—21no—
215C2×D61—21no—
216C2×D61—81no—
217C2×D61—81no—
218C2×D61—81no—
219C4×C61—21no—
220C4×C61—81no—
221C4×C61—81no—
222C4×C61—81no—
223C4×C61#54711yescharacteristic
224C4×C61#57811yescharacteristic
225Dic61—21no—
226Dic61—21no—
227Dic61—21no—
228Dic61—81no—
229Dic61—81no—
230Dic61—81no—
231#3339—611no—
232#3339—611no—
233#2253—611no—
234#2234—611no—
235#2234—611no—
236#2232—611no—
237#2232D6111yescharacteristic, complemented
238#2228—611no—
239#2228—611no—
240#2218—611no—
241#2218—611no—
242C4×D16—611no—
243#2169—611no—
244#2159—611no—
245#2159—611no—
246C2×C61—41no—
247C2×C61—161no—
248C2×C61#333411yescharacteristic
249C2×C61#341411yescharacteristic
250C2×C61#341511yescharacteristic
251D61—41no—
252D61—161no—
253#553—1221no—
254#553—1221no—
255C2×D16—611no—
256C2×M32—611no—
257C2×M32—611no—
258#499—611no—
259#499—611no—
260#482—1221no—
261#482—1221no—
262#481—1221no—
263#481—1221no—
264#478—1221no—
265#478—1221no—
266#466—611no—
267#466—611no—
268#466—611no—
269#466C2×D6111yescharacteristic
270C4×D8—611no—
271C4×D8—611no—
272C8×D4—611no—
273#427—611no—
274#427—611no—
275C2×#107—611no—
276C2×#107C2×D6111yescharacteristic
277#367—611no—
278#367—611no—
279#367—611no—
280#367—611no—
281#366—611no—
282#366—611no—
283#366—611no—
284#366C2×D6111yescharacteristic
285#366C2×D6111yescharacteristic
286C4⋊C16—611no—
287#357—611no—
288#357—611no—
289#357—611no—
290#357—611no—
291#357C2×D6111yescharacteristic
292#357C2×D6111yescharacteristic
293C22⋊C16—611no—
294C22⋊C16C2×D6111yescharacteristic
295C4×C16—611no—
296C61#3392211yescharacteristic, complemented, Sylow
297C2×D8—611no—
298C2×D8C22×D6111yescharacteristic
299C22×C8—611no—
300C22×C8C22×D6111yescharacteristic
301#126—2441no—
302#126—2441no—
303#125—1221no—
304#125—1221no—
305#123—2441no—
306#123—2441no—
307#121—21no—
308#121—1221no—
309#121—1221no—
310#121—1221no—
311#121—2441no—
312#121—2441no—
313C4×D4—611no—
314C4×D4—1221no—
315C4×D4—1221no—
316C4×D4—2441no—
317C4×D4—2441no—
318#117—1221no—
319#117—1221no—
320C2×C4⋊C4—21no—
321C2×C4⋊C4—1221no—
322D16—1222no—
323M32—1222no—
324M32—1222no—
325C2×C16—611no—
326C2×C16—611no—
327C2×C16C22×D6111yescharacteristic
328C2×C16C22×D6111yescharacteristic
329#107—21no—
330#107—611no—
331#107—611no—
332#107—611no—
333#107—1221no—
334#107C22×D6111yescharacteristic
335#107C22×D6111yescharacteristic
336#107C22×D6111yescharacteristic
337#106—1221no—
338#106—1221no—
339#106—1221no—
340#106—1221no—
341C4⋊C8—611no—
342#102—21no—
343#102—1221no—
344#102—1221no—
345#102—1221no—
346#102—1221no—
347#102—1221no—
348C22⋊C8—611no—
349C22⋊C8—611no—
350C4×C8—611no—
351C2×D4—21no—
352C2×D4—41no—
353C2×D4—611no—
354C2×D4—1221no—
355C2×D4—2441no—
356C2×D4—2441no—
357C2×D4—2441no—
358C22×C4—41no—
359C22×C4—611no—
360C22×C4—2441no—
361C22×C4—2441no—
362C22×C4—2441no—
363C22×C4D4×D6111yescharacteristic
364D8—21no—
365D8—21no—
366D8—1221no—
367D8—1221no—
368C2×C8—21no—
369C2×C8—21no—
370C2×C8—611no—
371C2×C8—611no—
372C2×C8—1221no—
373C2×C8—1221no—
374C2×C8D4×D6111yescharacteristic
375C2×C8C23×D6111yescharacteristic
376C4⋊C4—21no—
377C4⋊C4—21no—
378C4⋊C4—21no—
379C4⋊C4—41no—
380C4⋊C4—611no—
381C4⋊C4—1221no—
382C4⋊C4—1221no—
383C4⋊C4—1221no—
384C4⋊C4—2441no—
385C4⋊C4—2441no—
386C4⋊C4—2441no—
387C4⋊C4—2441no—
388C4⋊C4—2441no—
389C22⋊C4—41no—
390C22⋊C4—611no—
391C22⋊C4—611no—
392C22⋊C4—2441no—
393C22⋊C4—2441no—
394C22⋊C4—2441no—
395C22⋊C4—2441no—
396C22⋊C4—2441no—
397C22⋊C4—2441no—
398C22⋊C4—2441no—
399C42—611no—
400C42—2441no—
401C42—2441no—
402C16—21no—
403C16—21no—
404C16—612no—
405C16—1221no—
406C23—41no—
407C23—611no—
408C23—2441no—
409C23D8×D6111yescharacteristic
410D4—41no—
411D4—41no—
412D4—161no—
413D4—9761no—
414D4—4882no—
415D4—4882no—
416D4—2441no—
417D4—2441no—
418D4—2441no—
419C2×C4—21no—
420C2×C4—21no—
421C2×C4—41no—
422C2×C4—41no—
423C2×C4—41no—
424C2×C4—161no—
425C2×C4—611no—
426C2×C4—611no—
427C2×C4—611no—
428C2×C4—1221no—
429C2×C4—1221no—
430C2×C4—9761no—
431C2×C4—9761no—
432C2×C4—9761no—
433C2×C4—2441no—
434C2×C4—2441no—
435C2×C4—2441no—
436C2×C4D8×D6111yescharacteristic
437C2×C4C2×D4×D6111yescharacteristic
438C8—21no—
439C8—1221no—
440C8—1221no—
441C8#41×D6111yescharacteristic
442C8#1451982411yescharacteristic
443C22—21no—
444C22—21no—
445C22—21no—
446C22—81no—
447C22—81no—
448C22—81no—
449C22—1221no—
450C22—1221no—
451C22—1221no—
452C22—4881no—
453C22—4881no—
454C22—4881no—
455C22C2×D8×D6111yescharacteristic
456C4—21no—
457C4—81no—
458C4—81no—
459C4—81no—
460C4—1221no—
461C4—1221no—
462C4—1221no—
463C4—4881no—
464C4—4881no—
465C4—4881no—
466C4#1684041011yescharacteristic
467C4#1684057811yescharacteristic
468C2—41no—
469C2—161no—
470C2—9761no—
471C2—2441no—
472C2#2145816111yescharacteristic
473C2#2145895411yescharacteristic
474C2#2145895611yescharacteristic
subgroupG/H
centerC22C2×D8×D61
commutator, cosocleC2×C8×C61C24
FrattiniC2×C8C23×D61
FittingC61×#2232C2
socleC22×C61C22×D8
hypercenter#2232D61
hypocenterC61#33922
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2232

Complements

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

NH ≅ G/Ntype
1. #21458217C2semidirect
2. #21458216C2semidirect
3. #21448096C2semidirect
4. #21448011C2semidirect
5. #21448008C2semidirect
6. #21448001C2semidirect
7. #21447979C2semidirect
8. #21447978C2semidirect
9. #21447921C2semidirect
10. #21447920C2semidirect
11. #21447663C2semidirect
12. #21447648C2semidirect
13. #21447605C2semidirect
14. #21447604C2semidirect
15. C61×#2232C2semidirect
237. #2232D61semidirect
296. C61#33922semidirect

Maximal subgroups

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

subgroupindex
#214582172
#214582162
#214480962
#214480112
#214480082
#214480012
#214479792
#214479782
#214479212
#214479202
#214476632
#214476482
#214476052
#214476042
C61×#22322
#3392261