Finite Group Databasebeta

← #29836428

Subgroups — #29836428

Order 15616.

512 conjugacy classes of subgroups.

The subgroup lattice has 508 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21456466C211yesmaximal, characteristic, complemented
2#21456465C211yesmaximal, characteristic, complemented
3#21447978C211yesmaximal, characteristic, complemented
4#21447977C211yesmaximal, characteristic, complemented
5#21447976C211yesmaximal, characteristic, complemented
6#21447974C211yesmaximal, characteristic, complemented
7#21447921C211yesmaximal, characteristic, complemented
8#21447919C211yesmaximal, characteristic, complemented
9#21447904C211yesmaximal, characteristic, complemented
10#21447902C211yesmaximal, characteristic, complemented
11#21447852C211yesmaximal, characteristic, complemented
12#21447852C211yesmaximal, characteristic, complemented
13#21447851C211yesmaximal, characteristic, complemented
14#21447576C211yesmaximal, characteristic, complemented
15C61×#2206C211yesmaximal, characteristic, complemented
16#16840366—21no—
17#16840363—21no—
18C2×#14519718C2211yescharacteristic
19C2×#14519718C2211yescharacteristic
20C2×#14519716C2211yescharacteristic
21C2×C16×D61C2211yescharacteristic
22#16840164C2211yescharacteristic
23#16840163C2211yescharacteristic
24#16840137C2211yescharacteristic
25#16840126—21no—
26#16840125—21no—
27#16840014—21no—
28#16840012—21no—
29#16839999C2211yescharacteristic
30#16839995C2211yescharacteristic
31#16839995C2211yescharacteristic
32#16839995C2211yescharacteristic
33#16839874—21no—
34#16839872—21no—
35C4×D488C2211yescharacteristic
36D8×Dic61C2211yescharacteristic
37D8×Dic61C2211yescharacteristic
38#16839716C2211yescharacteristic
39#16839590C2211yescharacteristic
40#16839589C2211yescharacteristic
41#16839588C2211yescharacteristic
42#16839587C2211yescharacteristic
43C4⋊#11758185C2211yescharacteristic
44#16839580C2211yescharacteristic
45#16839580C2211yescharacteristic
46#16839564C2211yescharacteristic
47#16839564C2211yescharacteristic
48#16839563C2211yescharacteristic
49#16839563C2211yescharacteristic
50#16839563C2211yescharacteristic
51#16839563C2211yescharacteristic
52C2×D16×C61C2211yescharacteristic
53C2×D16×C61C2211yescharacteristic
54C61×#493C2211yescharacteristic
55C4×D8×C61C2211yescharacteristic
56C61×C4⋊C16C2211yescharacteristic
57C61×#357C2211yescharacteristic
58C61×#357C2211yescharacteristic
59C2×D488C2311yescharacteristic
60C2×#11758199—21no—
61C2×#11758189D411yescharacteristic
62C2×C8×D61C2311yescharacteristic
63#14519773—21no—
64#14519769—21no—
65#14519768—21no—
66#14519760—41no—
67#14519759—41no—
68#14519758—41no—
69#14519758—41no—
70#14519752—21no—
71#14519751—41no—
72#14519750—41no—
73#14519749—41no—
74#14519749—41no—
75#14519748—21no—
76#14519748—21no—
77#14519748—21no—
78C4×D244—21no—
79D4×Dic61—21no—
80D4×Dic61—21no—
81#14519734D411yescharacteristic
82#14519718—41no—
83#14519718—41no—
84#14519716—41no—
85C2×#11758185C2311yescharacteristic
86C2×#11758185C2311yescharacteristic
87C16×D61—41no—
88#14519711C2311yescharacteristic
89#14519711C2311yescharacteristic
90#14519711C2311yescharacteristic
91#14519709—21no—
92#14519708—21no—
93#14519699—21no—
94#14519698—21no—
95#14519698—21no—
96#14519698—21no—
97#14519698—21no—
98#14519698—21no—
99#14519697—21no—
100#14519688D411yescharacteristic
101#14519687D411yescharacteristic
102C8×Dic61C2311yescharacteristic
103C2×D8×C61—21no—
104C2×D8×C61C2311yescharacteristic
105C2×D8×C61C2311yescharacteristic
106C2×D8×C61C2311yescharacteristic
107#127×C61—21no—
108C4×D4×C61—21no—
109D16×C61—41no—
110D16×C61—41no—
111C2×C16×C61C2311yescharacteristic
112C2×C16×C61C2311yescharacteristic
113#107×C61C2311yescharacteristic
114#102×C61—21no—
115C4×C8×C61C2311yescharacteristic
116C2×D4×C61—21no—
117C2×D4×C61—21no—
118C2×D4×C61—21no—
119C2×D4×C61—41no—
120C2×D4×C61—41no—
121C22×C4×C61—41no—
122C2×C22⋊D61—41no—
123C2×C22⋊D61—41no—
124C2×C22⋊D61—41no—
125C2×C22⋊D61—41no—
126C2×C22⋊D61—41no—
127C22×Dic61—41no—
128C22×Dic61—41no—
129C2×D244—21no—
130C2×D244—41no—
131C2×C4×D61—41no—
132C2×C4×D61C2×D411yescharacteristic
133D8×C61—21no—
134D8×C61—21no—
135D8×C61—21no—
136D8×C61—21no—
137D8×C61—21no—
138D8×C61—21no—
139D8×C61—42no—
140C2×C8×C61C2×D411yescharacteristic
141C2×C8×C61C2411yescharacteristic
142C4⋊C4×C61—21no—
143C22⋊C4×C61—41no—
144C42×C61C2×D411yescharacteristic
145C22⋊Dic61—41no—
146C22⋊Dic61—41no—
147C22⋊Dic61—41no—
148C22⋊Dic61—41no—
149C22⋊Dic61—41no—
150#11758199—42no—
151#11758198—41no—
152#11758198—41no—
153#11758198D811yescharacteristic
154#11758198D811yescharacteristic
155C4⋊Dic61—21no—
156C4⋊Dic61—21no—
157C4⋊Dic61—21no—
158C4⋊Dic61—41no—
159#11758196—41no—
160#11758196—41no—
161#11758196—41no—
162#11758196D811yescharacteristic
163#11758196D811yescharacteristic
164C4×Dic61C2×D411yescharacteristic
165C2×#92418C2×D411yescharacteristic
166C2×#92418C2×D411yescharacteristic
167D488—21no—
168D488—21no—
169#11758189—41no—
170C8×D61—21no—
171C8×D61—21no—
172C16×C61—21no—
173C16×C61—21no—
174#11758185—21no—
175#11758185—21no—
176C23×C61—41no—
177C23×C61—41no—
178C23×C61—41no—
179C22×D61—41no—
180C22×D61C2×D811yescharacteristic
181D4×C61—41no—
182D4×C61—41no—
183D4×C61—41no—
184D4×C61—41no—
185D4×C61—41no—
186D4×C61—41no—
187D4×C61—161no—
188D4×C61—161no—
189C2×C4×C61—41no—
190C2×C4×C61—161no—
191C2×C4×C61C2×D811yescharacteristic
192C2×C4×C61C2×D811yescharacteristic
193C2×C4×C61C22×D411yescharacteristic
194C22⋊D61—161no—
195C22⋊D61—161no—
196C22⋊D61—161no—
197C22⋊D61—161no—
198C22⋊D61—161no—
199C2×Dic61—41no—
200C2×Dic61—41no—
201C2×Dic61—41no—
202C2×Dic61—161no—
203C2×Dic61—161no—
204C2×Dic61C2×D811yescharacteristic
205C2×Dic61C2×D811yescharacteristic
206C2×Dic61C2×D811yescharacteristic
207D244—41no—
208D244—41no—
209D244—161no—
210C4×D61—21no—
211C4×D61—21no—
212C4×D61—161no—
213C8×C61—21no—
214C8×C61H(5,𝔽2)11yescharacteristic
215C8×C612−1+411yescharacteristic
216#92418—21no—
217#92418—21no—
218#33825—611nomaximal, Sylow
219C22×C61—81no—
220C22×C61—81no—
221C22×C61—81no—
222C22×C61—81no—
223C22×C61—81no—
224C22×C61—81no—
225C22×C61—81no—
226C22×C61—81no—
227C22×C61—81no—
228C22×C61C22×D811yescharacteristic
229C2×D61—21no—
230C2×D61—21no—
231C2×D61—21no—
232C2×D61—81no—
233C2×D61—81no—
234C2×D61—81no—
235C4×C61—21no—
236C4×C61—21no—
237C4×C61—81no—
238C4×C61#53711yescharacteristic
239C4×C61#57511yescharacteristic
240Dic61—21no—
241Dic61—21no—
242Dic61—21no—
243Dic61—81no—
244Dic61—81no—
245Dic61—81no—
246#3176—611no—
247#3176—611no—
248#2228—611no—
249#2228—611no—
250#2228—611no—
251#2228—611no—
252#2218—611no—
253#2218—611no—
254#2215—611no—
255#2215—611no—
256#2206—611no—
257#2206—611no—
258#2206—611no—
259#2206D6111yescharacteristic, complemented
260#2151—611no—
261C2×C61—161no—
262C2×C61—161no—
263C2×C61—161no—
264C2×C61#324511yescharacteristic
265C2×C61#341511yescharacteristic
266C2×C61#341511yescharacteristic
267D61—41no—
268D61—161no—
269#540—1221no—
270#540—1221no—
271C2×D16—611no—
272C2×D16—611no—
273C2×D16C2×D6111yescharacteristic
274C2×D16C2×D6111yescharacteristic
275C2×M32—611no—
276C22×C16—611no—
277#499—611no—
278#499—611no—
279#493—611no—
280#493C2×D6111yescharacteristic
281#490—1221no—
282#490—1221no—
283#469—1221no—
284#469—1221no—
285#466—611no—
286#466—611no—
287#466—611no—
288#466—611no—
289#442—1221no—
290#442—1221no—
291C4×D8—611no—
292C4×D8—611no—
293C4×D8—611no—
294C4×D8C2×D6111yescharacteristic
295#405—611no—
296#367—611no—
297#367—611no—
298#366—611no—
299#366—611no—
300C4⋊C16—611no—
301C4⋊C16—611no—
302C4⋊C16—611no—
303C4⋊C16C2×D6111yescharacteristic
304#357—611no—
305#357—611no—
306#357—611no—
307#357—611no—
308#357—611no—
309#357—611no—
310#357C2×D6111yescharacteristic
311#357C2×D6111yescharacteristic
312C61#3382511yescharacteristic, complemented, Sylow
313C2×D8—21no—
314C2×D8—611no—
315C2×D8—1221no—
316C2×D8C22×D6111yescharacteristic
317C2×D8C22×D6111yescharacteristic
318C2×D8C22×D6111yescharacteristic
319C2×M16—611no—
320C22×C8—611no—
321#127—21no—
322#127—1221no—
323#125—1221no—
324#125—1221no—
325#123—2441no—
326#123—2441no—
327#123—2441no—
328#123—2441no—
329#121—1221no—
330#121—1221no—
331#121—1221no—
332#121—1221no—
333#121—2441no—
334#121—2441no—
335#121—2441no—
336#121—2441no—
337C4×D4—21no—
338C4×D4—1221no—
339C4×D4—1221no—
340C4×D4—1221no—
341#117—611no—
342D16—41no—
343D16—41no—
344D16—2441no—
345D16—2441no—
346M32—2441no—
347C2×C16—611no—
348C2×C16—611no—
349C2×C16—2441no—
350C2×C16C22×D6111yescharacteristic
351C2×C16C22×D6111yescharacteristic
352#107—611no—
353#107—611no—
354#107—611no—
355#107C22×D6111yescharacteristic
356#106—1221no—
357#106—1221no—
358#102—21no—
359#102—1221no—
360#102—1221no—
361#102—1221no—
362#102—1221no—
363#102—1221no—
364#102—1221no—
365#102—1221no—
366#97—611no—
367#97—611no—
368C4×C8—611no—
369C4×C8C22×D6111yescharacteristic
370C2×D4—21no—
371C2×D4—21no—
372C2×D4—21no—
373C2×D4—41no—
374C2×D4—41no—
375C2×D4—1221no—
376C2×D4—2441no—
377C2×D4—2441no—
378C2×D4—2441no—
379C2×D4—2441no—
380C2×D4—2441no—
381C2×D4—2441no—
382C22×C4—41no—
383C22×C4—611no—
384C22×C4—2441no—
385C22×C4—2441no—
386C22×C4—2441no—
387D8—21no—
388D8—21no—
389D8—21no—
390D8—21no—
391D8—21no—
392D8—21no—
393D8—42no—
394D8—1221no—
395D8—1221no—
396D8—2442no—
397M16—2441no—
398C2×C8—611no—
399C2×C8—611no—
400C2×C8—1221no—
401C2×C8—1221no—
402C2×C8D4×D6111yescharacteristic
403C2×C8C23×D6111yescharacteristic
404C4⋊C4—21no—
405C4⋊C4—611no—
406C4⋊C4—611no—
407C4⋊C4—1221no—
408C4⋊C4—1221no—
409C4⋊C4—1221no—
410C4⋊C4—2441no—
411C4⋊C4—2441no—
412C4⋊C4—2441no—
413C4⋊C4—2441no—
414C22⋊C4—41no—
415C22⋊C4—611no—
416C22⋊C4—611no—
417C22⋊C4—2441no—
418C22⋊C4—2441no—
419C22⋊C4—2441no—
420C22⋊C4—2441no—
421C22⋊C4—2441no—
422C22⋊C4—2441no—
423C22⋊C4—2441no—
424C42—611no—
425C42D4×D6111yescharacteristic
426C16—21no—
427C16—21no—
428C16—1221no—
429C16—1221no—
430C23—41no—
431C23—41no—
432C23—41no—
433C23—611no—
434C23—2441no—
435D4—41no—
436D4—41no—
437D4—41no—
438D4—41no—
439D4—41no—
440D4—41no—
441D4—161no—
442D4—161no—
443D4—9761no—
444D4—9761no—
445D4—9761no—
446D4—9761no—
447D4—9761no—
448D4—9761no—
449D4—2441no—
450D4—2441no—
451C2×C4—41no—
452C2×C4—161no—
453C2×C4—611no—
454C2×C4—611no—
455C2×C4—611no—
456C2×C4—1221no—
457C2×C4—1221no—
458C2×C4—9761no—
459C2×C4—9761no—
460C2×C4—9761no—
461C2×C4—2441no—
462C2×C4—2441no—
463C2×C4—2441no—
464C2×C4D8×D6111yescharacteristic
465C2×C4D8×D6111yescharacteristic
466C2×C4C2×D4×D6111yescharacteristic
467C8—21no—
468C8—1221no—
469C8—1221no—
470C8#1451982211yescharacteristic
471C8#1451982411yescharacteristic
472C22—81no—
473C22—81no—
474C22—81no—
475C22—81no—
476C22—81no—
477C22—81no—
478C22—81no—
479C22—81no—
480C22—81no—
481C22—1221no—
482C22—1221no—
483C22—1221no—
484C22—4881no—
485C22—4881no—
486C22—4881no—
487C22C2×D8×D6111yescharacteristic
488C4—21no—
489C4—21no—
490C4—81no—
491C4—1221no—
492C4—1221no—
493C4—1221no—
494C4—4881no—
495C4—4881no—
496C4—4881no—
497C4#1684034111yescharacteristic
498C4#1684055811yescharacteristic
499C2—161no—
500C2—161no—
501C2—161no—
502C2—9761no—
503C2—2441no—
504C2#2145712711yescharacteristic
505C2#2145895611yescharacteristic
506C2#2145895911yescharacteristic
subgroupG/H
centerC22C2×D8×D61
commutator, cosocleC2×C8×C61C24
FrattiniC2×C8C23×D61
FittingC61×#2206C2
socleC22×C61C22×D8
hypercenter#2206D61
hypocenterC61#33825
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2206

Complements

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

NH ≅ G/Ntype
1. #21456466C2semidirect
2. #21456465C2semidirect
3. #21447978C2semidirect
4. #21447977C2semidirect
5. #21447976C2semidirect
6. #21447974C2semidirect
7. #21447921C2semidirect
8. #21447919C2semidirect
9. #21447904C2semidirect
10. #21447902C2semidirect
11. #21447852C2semidirect
12. #21447852C2semidirect
13. #21447851C2semidirect
14. #21447576C2semidirect
15. C61×#2206C2semidirect
259. #2206D61semidirect
312. C61#33825semidirect

Maximal subgroups

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

subgroupindex
#214564662
#214564652
#214479782
#214479772
#214479762
#214479742
#214479212
#214479192
#214479042
#214479022
#214478522
#214478512
#214475762
C61×#22062
#3382561