Finite Group Databasebeta

← D61×#2237 #29834787

Subgroups — D61×#2237 #29834787

Order 15616.

586 conjugacy classes of subgroups.

The subgroup lattice has 506 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#467×D61C211yesmaximal, characteristic
2#427×D61C211yesmaximal, characteristic
3#21448030C211yesmaximal, characteristic, complemented
4#21448029C211yesmaximal, characteristic, complemented
5#21448028C211yesmaximal, characteristic, complemented
6#21448027C211yesmaximal, characteristic, complemented
7#21448026C211yesmaximal, characteristic, complemented
8#21448025C211yesmaximal, characteristic, complemented
9#21448024C211yesmaximal, characteristic, complemented
10#367×D61C211yesmaximal, characteristic, complemented
11#366×D61C211yesmaximal, characteristic, complemented
12#358×D61C211yesmaximal, characteristic, complemented
13#358×D61C211yesmaximal, characteristic, complemented
14C22⋊C16×D61C211yesmaximal, characteristic
15C61×#2237C211yesmaximal, characteristic, complemented
16C2×Q16×D61C2211yescharacteristic
17C22×C8×D61C2211yescharacteristic
18C22⋊Q8×D61—21no—
19#117×D61—21no—
20C2×C16×D61C2211yescharacteristic
21C2×C16×D61C2211yescharacteristic
22#16840004C2211yescharacteristic
23#16840003C2211yescharacteristic
24#16840002—21no—
25#16840001—21no—
26#16840000C2211yescharacteristic
27#16839800C2211yescharacteristic
28#16839799C2211yescharacteristic
29#16839799C2211yescharacteristic
30#16839798—21no—
31#16839797—21no—
32#107×D61C2211yescharacteristic
33#107×D61C2211yescharacteristic
34#107×D61C2211yescharacteristic
35#106×D61—21no—
36#103×D61—21no—
37#16839590C2211yescharacteristic, complemented
38#16839589C2211yescharacteristic, complemented
39#16839589C2211yescharacteristic, complemented
40#16839588C2211yescharacteristic, complemented
41#16839587C2211yescharacteristic, complemented
42#16839587C2211yescharacteristic, complemented
43#16839567C2211yescharacteristic, complemented
44#16839567C2211yescharacteristic, complemented
45#16839566C2211yescharacteristic, complemented
46#16839566C2211yescharacteristic, complemented
47#16839565C2211yescharacteristic, complemented
48#16839565C2211yescharacteristic, complemented
49C22⋊#11758185C2211yescharacteristic
50#16839541C2211yescharacteristic
51#16839541C2211yescharacteristic
52C61×#467C2211yescharacteristic
53C61×#427C2211yescharacteristic
54C61×#367C2211yescharacteristic, complemented
55C61×#366C2211yescharacteristic, complemented
56C61×#358C2211yescharacteristic, complemented
57C61×#358C2211yescharacteristic, complemented
58C61×C22⋊C16C2211yescharacteristic
59C2×Q8×D61—21no—
60C22×C4×D61D411yescharacteristic
61C2×Dic244C2311yescharacteristic
62C2×#11758202—21no—
63Q16×D61—22no—
64Q16×D61—22no—
65C22×#92418D411yescharacteristic
66C2×C8×D61—22no—
67C2×C8×D61—22no—
68C2×C8×D61D411yescharacteristic
69C2×C8×D61D411yescharacteristic
70C2×C8×D61C2311yescharacteristic
71C2×C8×D61C2311yescharacteristic
72#14519757—21no—
73#14519756—21no—
74#14519755—41no—
75#14519754—41no—
76#14519753—21no—
77#14519736—21no—
78#14519735—21no—
79#14519735—21no—
80#14519734—41no—
81#14519733—41no—
82C4⋊C4×D61—21no—
83C4⋊C4×D61—21no—
84C4⋊C4×D61—21no—
85C4⋊C4×D61—41no—
86C22⋊C4×D61—41no—
87C22⋊C4×D61—41no—
88C42×D61—41no—
89C2×#11758185C2311yescharacteristic
90C2×#11758185C2311yescharacteristic
91C16×D61—22no—
92C16×D61—22no—
93#14519711C2311yescharacteristic
94#14519711C2311yescharacteristic
95#14519711C2311yescharacteristic
96#14519710—21no—
97#14519710—21no—
98#14519710—21no—
99#14519709—21no—
100#14519708—21no—
101#14519708—21no—
102#14519702—21no—
103#14519701—21no—
104#14519700—21no—
105C2×Q16×C61C2311yescharacteristic
106C22×C8×C61C2311yescharacteristic
107C22⋊Q8×C61—21no—
108#117×C61—21no—
109C2×C16×C61C2311yescharacteristic
110C2×C16×C61C2311yescharacteristic
111#107×C61C2311yescharacteristic
112#107×C61C2311yescharacteristic
113#107×C61C2311yescharacteristic
114#106×C61—21no—
115#103×C61—21no—
116C23×D61D811yescharacteristic
117C2×Q8×C61—21no—
118C22×C4×C61C2×D411yescharacteristic
119C22×Dic61D811yescharacteristic
120Q8×D61—42no—
121Q8×D61—42no—
122C2×C4×D61—22no—
123C2×C4×D61—22no—
124C2×C4×D61—41no—
125C2×C4×D61—41no—
126C2×C4×D61—41no—
127C2×C4×D61—41no—
128C2×C4×D61D811yescharacteristic
129C2×C4×D61D811yescharacteristic
130C2×C4×D61C2×D411yescharacteristic
131C2×C4×D61C2×D411yescharacteristic
132C2×Dic122—21no—
133C2×Dic122—41no—
134Q16×C61—21no—
135Q16×C61—21no—
136C2×C8×C61—21no—
137C2×C8×C61—21no—
138C2×C8×C61C2×D411yescharacteristic
139C2×C8×C61C2411yescharacteristic
140C4⋊C4×C61—21no—
141C4⋊C4×C61—21no—
142C4⋊C4×C61—21no—
143C4⋊C4×C61—41no—
144C22⋊C4×C61—41no—
145C22⋊C4×C61—41no—
146C42×C61—41no—
147C22⋊Dic61—41no—
148C22⋊Dic61—41no—
149#11758202—42no—
150#11758198—41no—
151#11758198—41no—
152#11758198—41no—
153#11758198—41no—
154C4⋊Dic61—21no—
155C4⋊Dic61—21no—
156C4⋊Dic61—21no—
157C4⋊Dic61—41no—
158#11758196—41no—
159#11758196—41no—
160#11758196—41no—
161#11758196—41no—
162#11758196—41no—
163C4×Dic61—41no—
164C4×Dic61—41no—
165C4×Dic61—41no—
166C2×#92418—22no—
167C2×#92418C2×D411yescharacteristic
168C2×#92418C2×D411yescharacteristic
169Dic244—21no—
170Dic244—21no—
171C8×D61—22no—
172C8×D61—21no—
173C8×D61—21no—
174C8×D61—22no—
175C8×D61#4112yes—
176C8×D61#4112yes—
177C16×C61—21no—
178C16×C61—21no—
179#11758185—21no—
180#11758185—21no—
181C23×C61C2×D811yescharacteristic
182C22×D61—22no—
183C22×D61—22no—
184C22×D61—22no—
185C22×D61C2×D811yescharacteristic
186C22×D61C2×D811yescharacteristic
187Q8×C61—41no—
188Q8×C61—41no—
189C2×C4×C61—21no—
190C2×C4×C61—21no—
191C2×C4×C61—41no—
192C2×C4×C61—41no—
193C2×C4×C61—41no—
194C2×C4×C61—41no—
195C2×C4×C61C2×D811yescharacteristic
196C2×C4×C61C22×D411yescharacteristic
197C2×Dic61—22no—
198C2×Dic61—41no—
199C2×Dic61—41no—
200C2×Dic61—41no—
201C2×Dic61—41no—
202C2×Dic61C2×D811yescharacteristic
203C2×Dic61C2×D811yescharacteristic
204C4×D61—22no—
205C4×D61—21no—
206C4×D61—21no—
207C4×D61—22no—
208C4×D61—82no—
209C4×D61—82no—
210C4×D61—82no—
211C4×D61—82no—
212C4×D61#12312yes—
213C4×D61#13712yes—
214Dic122—41no—
215Dic122—41no—
216Dic122—82no—
217C8×C61—21no—
218C8×C61C2×#4111yescharacteristic
219C8×C61C2×#4111yescharacteristic
220#92418—21no—
221#92418#12312yes—
222C2×#2237—611nomaximal, Sylow
223C22×C61—21no—
224C22×C61—21no—
225C22×C61—21no—
226C22×C61C22×D811yescharacteristic
227C2×D61—21no—
228C2×D61—21no—
229C2×D61—21no—
230C2×D61—44no—
231C2×D61#48012yes—
232C2×D61#50812yes—
233C2×D61#51012yes—
234C4×C61—21no—
235C4×C61—81no—
236C4×C61—81no—
237C4×C61—81no—
238C4×C61—81no—
239C4×C61C2×#12311yescharacteristic
240C4×C61C2×#13711yescharacteristic
241Dic61—21no—
242Dic61—81no—
243Dic61—81no—
244Dic61—81no—
245Dic61—81no—
246Dic61#48012yes—
247C2×#467—611no—
248C2×#427—611no—
249#2237—611no—
250#2237—611no—
251#2237—611no—
252#2237—611no—
253#2237—611no—
254#2237—611no—
255#2237—611no—
256#2237D6111yescharacteristic, direct product factor
257C2×#367—611no—
258C2×#366—611no—
259C2×#358—611no—
260C2×#358—611no—
261C2×C22⋊C16—611no—
262C2×C61—41no—
263C2×C61C2×#48011yescharacteristic
264C2×C61C2×#50811yescharacteristic
265C2×C61C2×#51011yescharacteristic
266D61—41no—
267D61#223714yesdirect product factor
268C22×Q16—611no—
269C23×C8—611no—
270C2×C22⋊Q8—1221no—
271C2×#117—1221no—
272C22×C16—611no—
273C22×C16—611no—
274#467—611no—
275#467—611no—
276#467—611no—
277#467—1221no—
278#467—1221no—
279#467C2×D6111yescharacteristic
280#427—611no—
281#427—611no—
282#427—611no—
283#427—1221no—
284#427—1221no—
285#427C2×D6111yescharacteristic
286C2×#107—611no—
287C2×#107—611no—
288C2×#107—611no—
289C2×#106—1221no—
290C2×#103—1221no—
291#367—611no—
292#367—611no—
293#367—611no—
294#367C2×D6111yescharacteristic, complemented
295#366—611no—
296#366—611no—
297#366—611no—
298#366C2×D6111yescharacteristic, complemented
299#358—611no—
300#358—611no—
301#358—611no—
302#358—611no—
303#358—611no—
304#358—611no—
305#358C2×D6111yescharacteristic, complemented
306#358C2×D6111yescharacteristic, complemented
307C22⋊C16—611no—
308C22⋊C16—611no—
309C22⋊C16—611no—
310C22⋊C16C2×D6111yescharacteristic
311C61C2×#223711yescharacteristic, complemented, Sylow
312C22×Q8—1221no—
313C23×C4—611no—
314C2×Q16—611no—
315C2×Q16—1222no—
316C2×Q16—1222no—
317C2×Q16—1221no—
318C2×Q16C22×D6111yescharacteristic
319C22×C8—611no—
320C22×C8—611no—
321C22×C8—611no—
322C22×C8—611no—
323C22×C8—611no—
324C22×C8—1222no—
325C22×C8—1222no—
326C22×C8C22×D6111yescharacteristic
327C22⋊Q8—21no—
328C22⋊Q8—1221no—
329C22⋊Q8—1221no—
330C22⋊Q8—1221no—
331C22⋊Q8—2441no—
332C22⋊Q8—2441no—
333#117—21no—
334#117—1221no—
335#117—1221no—
336#117—1221no—
337#117—2441no—
338#117—2441no—
339C2×C4⋊C4—1221no—
340C2×C4⋊C4—1221no—
341C2×C4⋊C4—1221no—
342C2×C4⋊C4—2441no—
343C2×C22⋊C4—2441no—
344C2×C22⋊C4—2441no—
345C2×C42—2441no—
346C2×C16—611no—
347C2×C16—611no—
348C2×C16—1222no—
349C2×C16—1222no—
350C2×C16C22×D6111yescharacteristic
351C2×C16C22×D6111yescharacteristic
352#107—611no—
353#107—611no—
354#107—611no—
355#107—1221no—
356#107—1221no—
357#107—1221no—
358#107C22×D6111yescharacteristic
359#107C22×D6111yescharacteristic
360#107C22×D6111yescharacteristic
361#106—21no—
362#106—1221no—
363#106—1221no—
364#106—1221no—
365#103—21no—
366#103—1221no—
367#103—1221no—
368#103—1221no—
369C24—611no—
370C2×Q8—21no—
371C2×Q8—1221no—
372C2×Q8—2441no—
373C2×Q8—2442no—
374C2×Q8—2442no—
375C22×C4—611no—
376C22×C4—611no—
377C22×C4—611no—
378C22×C4—611no—
379C22×C4—611no—
380C22×C4—1222no—
381C22×C4—1222no—
382C22×C4—2441no—
383C22×C4—2441no—
384C22×C4—2441no—
385C22×C4—2441no—
386C22×C4D4×D6111yescharacteristic
387Q16—21no—
388Q16—21no—
389Q16—1221no—
390Q16—1221no—
391Q16—2442no—
392C2×C8—21no—
393C2×C8—21no—
394C2×C8—611no—
395C2×C8—612no—
396C2×C8—612no—
397C2×C8—611no—
398C2×C8—1222no—
399C2×C8—1222no—
400C2×C8—1222no—
401C2×C8—1221no—
402C2×C8—1221no—
403C2×C8D4×D6111yescharacteristic
404C2×C8C23×D6111yescharacteristic
405C4⋊C4—21no—
406C4⋊C4—21no—
407C4⋊C4—21no—
408C4⋊C4—41no—
409C4⋊C4—1221no—
410C4⋊C4—1221no—
411C4⋊C4—1221no—
412C4⋊C4—2441no—
413C4⋊C4—2441no—
414C4⋊C4—2441no—
415C4⋊C4—2441no—
416C4⋊C4—2441no—
417C4⋊C4—2441no—
418C22⋊C4—41no—
419C22⋊C4—41no—
420C22⋊C4—2441no—
421C22⋊C4—2441no—
422C22⋊C4—2441no—
423C22⋊C4—2441no—
424C22⋊C4—2441no—
425C22⋊C4—2441no—
426C42—41no—
427C42—2441no—
428C42—2441no—
429C42—2441no—
430C16—21no—
431C16—21no—
432C16—1221no—
433C16—1221no—
434C23—611no—
435C23—611no—
436C23—1222no—
437C23—1222no—
438C23—1222no—
439C23D8×D6111yescharacteristic
440Q8—41no—
441Q8—41no—
442Q8—4882no—
443Q8—2441no—
444Q8—2441no—
445C2×C4—21no—
446C2×C4—21no—
447C2×C4—41no—
448C2×C4—41no—
449C2×C4—41no—
450C2×C4—41no—
451C2×C4—611no—
452C2×C4—612no—
453C2×C4—612no—
454C2×C4—611no—
455C2×C4—1222no—
456C2×C4—1222no—
457C2×C4—1222no—
458C2×C4—1221no—
459C2×C4—1221no—
460C2×C4—4882no—
461C2×C4—4882no—
462C2×C4—4882no—
463C2×C4—4882no—
464C2×C4—2441no—
465C2×C4—2441no—
466C2×C4—2441no—
467C2×C4—2441no—
468C2×C4D8×D6111yescharacteristic
469C2×C4C2×D4×D6111yescharacteristic
470C8—21no—
471C8—612no—
472C8—1221no—
473C8#41×D6111yescharacteristic
474C8#41×D6111yescharacteristic
475C22—21no—
476C22—21no—
477C22—21no—
478C22—612no—
479C22—612no—
480C22—612no—
481C22—1221no—
482C22—1221no—
483C22—1221no—
484C22—2444no—
485C22C2×D8×D6111yescharacteristic
486C4—21no—
487C4—81no—
488C4—81no—
489C4—81no—
490C4—81no—
491C4—612no—
492C4—1221no—
493C4—4881no—
494C4—4881no—
495C4—4881no—
496C4—4881no—
497C4#123×D6111yescharacteristic
498C4#137×D6111yescharacteristic
499C2—41no—
500C2—614no—
501C2—2441no—
502C2#480×D6111yescharacteristic
503C2#508×D6111yescharacteristic
504C2#510×D6111yescharacteristic
subgroupG/H
centerC22C2×D8×D61
commutator, cosocleC2×C8×C61C24
FrattiniC2×C8C23×D61
FittingC61×#2237C2
socleC22×C61C22×D8
prime radicalC23×D61D8
hypercenter#2237D61
hypocenterC61C2×#2237
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2237

Complements

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

NH ≅ G/Ntype
3. #21448030C2semidirect
4. #21448029C2semidirect
5. #21448028C2semidirect
6. #21448027C2semidirect
7. #21448026C2semidirect
8. #21448025C2semidirect
9. #21448024C2semidirect
10. #367×D61C2semidirect
11. #366×D61C2semidirect
12. #358×D61C2semidirect
13. #358×D61C2semidirect
15. C61×#2237C2semidirect
37. #16839590C22semidirect
38. #16839589C22semidirect
39. #16839589C22semidirect
40. #16839588C22semidirect
41. #16839587C22semidirect
42. #16839587C22semidirect
43. #16839567C22semidirect
44. #16839567C22semidirect
45. #16839566C22semidirect
46. #16839566C22semidirect
47. #16839565C22semidirect
48. #16839565C22semidirect
54. C61×#367C22semidirect
55. C61×#366C22semidirect
56. C61×#358C22semidirect
57. C61×#358C22semidirect
256. #2237D61direct (N × H)
267. D61#2237direct (N × H)
294. #367C2×D61semidirect
298. #366C2×D61semidirect
305. #358C2×D61semidirect
306. #358C2×D61semidirect
311. C61C2×#2237semidirect

Maximal subgroups

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

subgroupindex
#467×D612
#427×D612
#214480302
#214480292
#214480282
#214480272
#214480262
#214480252
#214480242
#367×D612
#366×D612
#358×D612
C22⋊C16×D612
C61×#22372
C2×#223761