Finite Group Databasebeta

← #29836404

Subgroups — #29836404

Order 15616.

500 conjugacy classes of subgroups.

The subgroup lattice has 496 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21456469C211yesmaximal, characteristic, complemented
2#21456458C211yesmaximal, characteristic, complemented
3#21447984C211yesmaximal, characteristic, complemented
4#21447977C211yesmaximal, characteristic, complemented
5#21447967C211yesmaximal, characteristic, complemented
6#21447957C211yesmaximal, characteristic, complemented
7#21447932C211yesmaximal, characteristic, complemented
8#21447922C211yesmaximal, characteristic, complemented
9#21447915C211yesmaximal, characteristic, complemented
10#21447905C211yesmaximal, characteristic, complemented
11#21447875C211yesmaximal, characteristic, complemented
12#21447875C211yesmaximal, characteristic, complemented
13#21447860C211yesmaximal, characteristic, complemented
14#21447855C211yesmaximal, characteristic, complemented
15C61×#2151C211yesmaximal, characteristic, complemented
16#16840383—21no—
17#16840367—21no—
18C2×#14519722C2211yescharacteristic
19C2×#14519722C2211yescharacteristic
20C2×D976C2211yescharacteristic
21C2×D976C2211yescharacteristic
22#16840167C2211yescharacteristic
23#16840164C2211yescharacteristic
24#16840146C2211yescharacteristic
25#16840139C2211yescharacteristic
26#16840127—21no—
27#16840122—21no—
28#16840015—21no—
29#16840008—21no—
30#16840003C2211yescharacteristic
31#16839998C2211yescharacteristic
32#16839998C2211yescharacteristic
33#16839998C2211yescharacteristic
34#16839875—21no—
35#16839864—21no—
36C4×Dic244C2211yescharacteristic
37C4×D488C2211yescharacteristic
38C4×D488C2211yescharacteristic
39C4×D488C2211yescharacteristic
40#16839590C2211yescharacteristic
41#16839590C2211yescharacteristic
42#16839588C2211yescharacteristic
43#16839588C2211yescharacteristic
44#16839567C2211yescharacteristic
45#16839567C2211yescharacteristic
46#16839564C2211yescharacteristic
47#16839564C2211yescharacteristic
48#16839564C2211yescharacteristic
49#16839564C2211yescharacteristic
50#16839564C2211yescharacteristic
51#16839564C2211yescharacteristic
52C2×M32×C61C2211yescharacteristic
53C22×C16×C61C2211yescharacteristic
54C61×#405C2211yescharacteristic
55C61×C4⋊C16C2211yescharacteristic
56C61×C4⋊C16C2211yescharacteristic
57C61×C4⋊C16C2211yescharacteristic
58C61×C4⋊C16C2211yescharacteristic
59C2×Dic244C2311yescharacteristic
60C2×#11758190—21no—
61C2×D488—21no—
62C2×D488C2311yescharacteristic
63C2×D488C2311yescharacteristic
64C2×D488C2311yescharacteristic
65#14519777—21no—
66#14519774—21no—
67#14519772—41no—
68#14519769—21no—
69#14519765—21no—
70#14519763—41no—
71#14519762—41no—
72#14519762—41no—
73#14519759—41no—
74#14519756—21no—
75#14519755—41no—
76#14519751—21no—
77#14519751—21no—
78#14519751—21no—
79#14519750—41no—
80#14519750—41no—
81C4×Dic122—21no—
82C4×D244—21no—
83C4×D244—21no—
84C4×D244—21no—
85#14519722—41no—
86#14519722—41no—
87D976—41no—
88D976—41no—
89#14519711—21no—
90#14519711C2311yescharacteristic
91#14519711C2311yescharacteristic
92#14519711C2311yescharacteristic
93#14519711C2311yescharacteristic
94#14519709—21no—
95#14519702—21no—
96#14519702—21no—
97#14519699—21no—
98#14519699—21no—
99#14519699—21no—
100#14519699—21no—
101#14519699—21no—
102#14519699—21no—
103C2×M16×C61D411yescharacteristic
104C22×C8×C61C2311yescharacteristic
105#117×C61D411yescharacteristic
106M32×C61—41no—
107C2×C16×C61—41no—
108C2×C16×C61C2311yescharacteristic
109C2×C16×C61C2311yescharacteristic
110C2×C16×C61C2311yescharacteristic
111C2×C16×C61C2311yescharacteristic
112#97×C61D411yescharacteristic
113#97×C61D411yescharacteristic
114C4×C8×C61C2311yescharacteristic
115C4×C8×C61C2311yescharacteristic
116C22×C4×C61C2×D411yescharacteristic
117C2×C22⋊D61—41no—
118C2×C22⋊D61—41no—
119C2×C22⋊D61—41no—
120C2×D244—21no—
121C2×D244—21no—
122C2×D244—21no—
123C2×D244—41no—
124C2×D244—41no—
125C2×C4×D61—41no—
126C2×C4×D61—41no—
127C2×C4×D61—41no—
128C2×Dic122—21no—
129C2×Dic122—41no—
130M16×C61—41no—
131C2×C8×C61—21no—
132C2×C8×C61—21no—
133C2×C8×C61C2×D411yescharacteristic
134C2×C8×C61C2×D411yescharacteristic
135C2×C8×C61C2×D411yescharacteristic
136C2×C8×C61C2411yescharacteristic
137C4⋊C4×C61D811yescharacteristic
138C4⋊C4×C61D811yescharacteristic
139C22⋊C4×C61D811yescharacteristic
140C22⋊C4×C61D811yescharacteristic
141C42×C61C2×D411yescharacteristic
142C42×C61C2×D411yescharacteristic
143C22⋊Dic61—41no—
144#11758198—41no—
145#11758198—41no—
146#11758198—41no—
147#11758198—41no—
148#11758198—41no—
149#11758198—41no—
150#11758198—41no—
151#11758198—41no—
152C4⋊Dic61—21no—
153C4⋊Dic61—21no—
154C4⋊Dic61—21no—
155C4⋊Dic61—21no—
156C4⋊Dic61—41no—
157#11758196—41no—
158#11758196—41no—
159#11758196—41no—
160#11758196—41no—
161C4×Dic61—41no—
162Dic244—21no—
163Dic244—21no—
164D488—21no—
165D488—21no—
166D488—21no—
167D488—21no—
168D488—21no—
169D488—21no—
170D488—42no—
171#11758190—42no—
172C16×C61—21no—
173C16×C61—21no—
174C16×C61—21no—
175C16×C61—21no—
176C23×C61C2×D811yescharacteristic
177C22×D61—41no—
178C22×D61—41no—
179C22×D61—41no—
180C2×C4×C61—21no—
181C2×C4×C61—21no—
182C2×C4×C61C2×D811yescharacteristic
183C2×C4×C61C2×D811yescharacteristic
184C2×C4×C61C2×D811yescharacteristic
185C2×C4×C61C2×D811yescharacteristic
186C2×C4×C61C2×D811yescharacteristic
187C2×C4×C61C22×D411yescharacteristic
188C22⋊D61—161no—
189C22⋊D61—161no—
190C22⋊D61—161no—
191C2×Dic61—41no—
192C2×Dic61—41no—
193C2×Dic61—41no—
194C2×Dic61—41no—
195C2×Dic61—41no—
196D244—41no—
197D244—41no—
198D244—41no—
199D244—41no—
200D244—41no—
201D244—41no—
202D244—161no—
203D244—161no—
204C4×D61—161no—
205C4×D61—161no—
206C4×D61—161no—
207Dic122—41no—
208Dic122—41no—
209Dic122—161no—
210C8×C61—21no—
211C8×C61—21no—
212C8×C61—21no—
213C8×C61H(5,𝔽2)11yescharacteristic
214C8×C612−1+411yescharacteristic
215#33823—611nomaximal, Sylow
216C22×C61—21no—
217C22×C61—21no—
218C22×C61—21no—
219C22×C61C22×D811yescharacteristic
220C2×D61—81no—
221C2×D61—81no—
222C2×D61—81no—
223C2×D61—81no—
224C2×D61—81no—
225C2×D61—81no—
226C2×D61—81no—
227C2×D61—81no—
228C2×D61—81no—
229C4×C61—21no—
230C4×C61—21no—
231C4×C61—21no—
232C4×C61—21no—
233C4×C61—21no—
234C4×C61#53711yescharacteristic
235C4×C61#57511yescharacteristic
236Dic61—81no—
237Dic61—81no—
238Dic61—81no—
239Dic61—81no—
240Dic61—81no—
241#3176—611no—
242#3175—611no—
243#2229—611no—
244#2228—611no—
245#2226—611no—
246#2224—611no—
247#2220—611no—
248#2218—611no—
249#2217—611no—
250#2215—611no—
251#2210—611no—
252#2210—611no—
253#2207—611no—
254#2206—611no—
255#2151D6111yescharacteristic, complemented
256C2×C61—41no—
257C2×C61#324511yescharacteristic
258C2×C61#341511yescharacteristic
259C2×C61#341611yescharacteristic
260D61—161no—
261D61—161no—
262D61—161no—
263#542—1221no—
264#540—1221no—
265C2×SD32—611no—
266C2×SD32—611no—
267C2×D16—611no—
268C2×D16—611no—
269C2×M32C2×D6111yescharacteristic
270C22×C16C2×D6111yescharacteristic
271#500—611no—
272#499—611no—
273#495—611no—
274#493—611no—
275#490—1221no—
276#489—1221no—
277#469—1221no—
278#468—1221no—
279#467—611no—
280#466—611no—
281#466—611no—
282#466—611no—
283#442—1221no—
284#440—1221no—
285C4×Q16—611no—
286C4×D8—611no—
287C4×D8—611no—
288C4×D8—611no—
289#405C2×D6111yescharacteristic
290#367—611no—
291#367—611no—
292#366—611no—
293#366—611no—
294C4⋊C16C2×D6111yescharacteristic
295C4⋊C16C2×D6111yescharacteristic
296C4⋊C16C2×D6111yescharacteristic
297C4⋊C16C2×D6111yescharacteristic
298#358—611no—
299#358—611no—
300#357—611no—
301#357—611no—
302#357—611no—
303#357—611no—
304#357—611no—
305#357—611no—
306C61#3382311yescharacteristic, complemented, Sylow
307C2×Q16—611no—
308C2×SD16—1221no—
309C2×D8—611no—
310C2×D8—611no—
311C2×D8—611no—
312C2×D8—1221no—
313C2×M16D24411yescharacteristic
314C22×C8C22×D6111yescharacteristic
315C4⋊Q8—1221no—
316#127—1221no—
317#126—2441no—
318#125—1221no—
319#124—1221no—
320#124—2441no—
321#123—2441no—
322#123—2441no—
323#123—2441no—
324C22⋊Q8—1221no—
325C22⋊Q8—2441no—
326#121—1221no—
327#121—1221no—
328#121—1221no—
329#121—2441no—
330#121—2441no—
331C4×Q8—1221no—
332C4×D4—1221no—
333C4×D4—1221no—
334C4×D4—1221no—
335#117D24411yescharacteristic
336SD32—2441no—
337SD32—2441no—
338D16—2441no—
339D16—2441no—
340M32—41no—
341C2×C16—41no—
342C2×C16C22×D6111yescharacteristic
343C2×C16C22×D6111yescharacteristic
344C2×C16C22×D6111yescharacteristic
345C2×C16C22×D6111yescharacteristic
346#107—611no—
347#107—611no—
348#107—611no—
349#107—611no—
350#107—1221no—
351#106—1221no—
352#103—1221no—
353#103—1221no—
354#102—1221no—
355#102—1221no—
356#102—1221no—
357#102—1221no—
358#102—1221no—
359#102—1221no—
360#97D24411yescharacteristic
361#97D24411yescharacteristic
362C4×C8C22×D6111yescharacteristic
363C4×C8C22×D6111yescharacteristic
364C2×Q8—1221no—
365C2×Q8—2441no—
366C2×D4—1221no—
367C2×D4—1221no—
368C2×D4—1221no—
369C2×D4—2441no—
370C2×D4—2441no—
371C2×D4—2441no—
372C2×D4—2441no—
373C2×D4—2441no—
374C22×C4—2441no—
375C22×C4—2441no—
376C22×C4—2441no—
377C22×C4C2×D24411yescharacteristic
378Q16—1221no—
379Q16—1221no—
380SD16—2442no—
381D8—1221no—
382D8—1221no—
383D8—1221no—
384D8—1221no—
385D8—1221no—
386D8—1221no—
387D8—2442no—
388M16—41no—
389C2×C8—21no—
390C2×C8—21no—
391C2×C8C2×D24411yescharacteristic
392C2×C8C2×D24411yescharacteristic
393C2×C8C2×D24411yescharacteristic
394C2×C8C23×D6111yescharacteristic
395C4⋊C4—1221no—
396C4⋊C4—1221no—
397C4⋊C4—1221no—
398C4⋊C4—1221no—
399C4⋊C4—2441no—
400C4⋊C4—2441no—
401C4⋊C4—2441no—
402C4⋊C4—2441no—
403C4⋊C4—2441no—
404C4⋊C4D48811yescharacteristic
405C4⋊C4D48811yescharacteristic
406C22⋊C4—2441no—
407C22⋊C4—2441no—
408C22⋊C4—2441no—
409C22⋊C4—2441no—
410C22⋊C4—2441no—
411C22⋊C4—2441no—
412C22⋊C4—2441no—
413C22⋊C4—2441no—
414C22⋊C4—2441no—
415C22⋊C4D48811yescharacteristic
416C22⋊C4D48811yescharacteristic
417C42—2441no—
418C42C2×D24411yescharacteristic
419C42C2×D24411yescharacteristic
420C16—21no—
421C16—21no—
422C16—21no—
423C16—21no—
424C23—2441no—
425C23—2441no—
426C23—2441no—
427C23C2×D48811yescharacteristic
428Q8—9761no—
429Q8—2441no—
430Q8—2441no—
431D4—9761no—
432D4—9761no—
433D4—9761no—
434D4—9761no—
435D4—9761no—
436D4—2441no—
437D4—2441no—
438D4—2441no—
439D4—2441no—
440D4—2441no—
441D4—2441no—
442C2×C4—21no—
443C2×C4—21no—
444C2×C4—9761no—
445C2×C4—9761no—
446C2×C4—9761no—
447C2×C4—2441no—
448C2×C4—2441no—
449C2×C4—2441no—
450C2×C4—2441no—
451C2×C4—2441no—
452C2×C4C2×D48811yescharacteristic
453C2×C4C2×D48811yescharacteristic
454C2×C4C2×D48811yescharacteristic
455C2×C4C2×D48811yescharacteristic
456C2×C4C2×D48811yescharacteristic
457C2×C4C22×D24411yescharacteristic
458C8—21no—
459C8—21no—
460C8—21no—
461C8#1451982211yescharacteristic
462C8#1451982511yescharacteristic
463C22—21no—
464C22—21no—
465C22—21no—
466C22—4881no—
467C22—4881no—
468C22—4881no—
469C22—4881no—
470C22—4881no—
471C22—4881no—
472C22—4881no—
473C22—4881no—
474C22—4881no—
475C22C22×D48811yescharacteristic
476C4—21no—
477C4—21no—
478C4—21no—
479C4—21no—
480C4—21no—
481C4—4881no—
482C4—4881no—
483C4—4881no—
484C4—4881no—
485C4—4881no—
486C4#1684034311yescharacteristic
487C4#1684056211yescharacteristic
488C2—41no—
489C2—9761no—
490C2—9761no—
491C2—9761no—
492C2#2145712911yescharacteristic
493C2#2145896011yescharacteristic
494C2#2145896711yescharacteristic
subgroupG/H
centerC22C22×D488
commutator, cosocleC2×C8×C61C24
FrattiniC2×C8C23×D61
FittingC61×#2151C2
socleC22×C61C22×D8
hypercenter#2151D61
hypocenterC61#33823
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ #117 ◁ #405 ◁ #2151

Complements

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

NH ≅ G/Ntype
1. #21456469C2semidirect
2. #21456458C2semidirect
3. #21447984C2semidirect
4. #21447977C2semidirect
5. #21447967C2semidirect
6. #21447957C2semidirect
7. #21447932C2semidirect
8. #21447922C2semidirect
9. #21447915C2semidirect
10. #21447905C2semidirect
11. #21447875C2semidirect
12. #21447875C2semidirect
13. #21447860C2semidirect
14. #21447855C2semidirect
15. C61×#2151C2semidirect
255. #2151D61semidirect
306. C61#33823semidirect

Maximal subgroups

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

subgroupindex
#214564692
#214564582
#214479842
#214479772
#214479672
#214479572
#214479322
#214479222
#214479152
#214479052
#214478752
#214478602
#214478552
C61×#21512
#3382361