Finite Group Databasebeta

← C61×#36976 #29540409

Subgroups — C61×#36976 #29540409

Order 15616.

1810 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
1C61×#2854C212yesmaximal, complemented
2C61×#2773C214yesmaximal, complemented
3C61×#2768C214yesmaximal, complemented
4C61×#2753C214yesmaximal, complemented
5C61×#2706C214yesmaximal, complemented
6C61×#2656C211yesmaximal, characteristic
7C61×#2646C211yesmaximal, characteristic, complemented
8C61×#2443C214yesmaximal, complemented
9C61×#2425C214yesmaximal, complemented
10C61×#2325C212yesmaximal, complemented
11C2×C61×#382C211yesmaximal, characteristic, complemented
12C2×#123×C61C2214yes—
13C2×#123×C61C2214yes—
14C2×#121×C61C2212yes—
15C2×#121×C61C2214yes—
16C2×C4×D4×C61C2214yes—
17C22×C4⋊C4×C61C2212yes—
18C22×C42×C61C2211yescharacteristic
19C61×#400C2214yes—
20C61×#399C2214yes—
21C61×#399C2214yes—
22C61×#398C2214yes—
23C61×#398C2214yes—
24C61×#398C2214yes—
25C61×#397C2214yes—
26C61×#397C2214yes—
27C61×#396C2214yes—
28C61×#394C2214yes—
29C61×#394C2214yes—
30C61×#392C2214yes—
31C61×#390C2212yes—
32C61×#390C2212yes—
33C61×#389C2212yes—
34C61×#389C2212yes—
35C61×#389C2214yes—
36C61×#388C2214yes—
37C61×#388C2214yes—
38C61×#388C2214yes—
39C61×#388C2214yes—
40C61×#388C2214yes—
41C61×#387C2214yes—
42C61×#387C2214yes—
43C61×#386C2214yes—
44C61×#386C2214yes—
45C61×#386C2214yes—
46C61×#386C2214yes—
47C61×#385C2214yes—
48C61×#385C2214yes—
49C61×#385C2214yes—
50C61×#382C2214yes—
51C61×#382C2214yes—
52C61×#380C2212yes—
53C61×#380C2214yes—
54C2×#95×C61C2211yescharacteristic
55C2×#95×C61C2211yescharacteristic
56C2×#95×C61C2212yes—
57C22×D4×C61C2314yes—
58C22×D4×C61C2312yes—
59C22×D4×C61C2314yes—
60C23×C4×C61C2311yescharacteristic
61C23×C4×C61C2311yescharacteristic
62C23×C4×C61C2312yes—
63C23×C4×C61C2312yes—
64C23×C4×C61C2314yes—
65C23×C4×C61C2311yescharacteristic
66#123×C61—48no—
67#123×C61—48no—
68#121×C61—28no—
69#121×C61—48no—
70C4×D4×C61—48no—
71C2×C4⋊C4×C61—44no—
72C2×C4⋊C4×C61C2314yes—
73C2×C4⋊C4×C61C2312yes—
74C2×C4⋊C4×C61C2312yes—
75C2×C4⋊C4×C61C2314yes—
76C2×C4⋊C4×C61C2312yes—
77C2×C4⋊C4×C61C2314yes—
78C2×C4⋊C4×C61C2314yes—
79C2×C4⋊C4×C61C2314yes—
80C2×C4⋊C4×C61C2314yes—
81C2×C4⋊C4×C61C2314yes—
82C2×C4⋊C4×C61C2314yes—
83C2×C22⋊C4×C61C2314yes—
84C2×C22⋊C4×C61C2314yes—
85C2×C22⋊C4×C61C2314yes—
86C2×C22⋊C4×C61C2314yes—
87C2×C22⋊C4×C61C2314yes—
88C2×C22⋊C4×C61C2314yes—
89C2×C22⋊C4×C61C2314yes—
90C2×C22⋊C4×C61C2314yes—
91C2×C22⋊C4×C61C2314yes—
92C2×C22⋊C4×C61C2314yes—
93C2×C22⋊C4×C61C2314yes—
94C2×C42×C61—24no—
95C2×C42×C61C2312yes—
96C2×C42×C61C2312yes—
97C2×C42×C61C2314yes—
98#95×C61C2314yes—
99#95×C61C2314yes—
100#95×C61C2314yes—
101#95×C61C2314yes—
102#95×C61C2314yes—
103#95×C61C2314yes—
104#95×C61C2314yes—
105#95×C61C2314yes—
106#95×C61C2314yes—
107#95×C61C2314yes—
108#95×C61C2314yes—
109C24×C61C2414yes—
110C24×C61C2411yescharacteristic
111C2×D4×C61—28no—
112C2×D4×C61—28no—
113C2×D4×C61—28no—
114C2×D4×C61—24no—
115C2×D4×C61—44no—
116C2×D4×C61—44no—
117C2×D4×C61—42no—
118C2×D4×C61—42no—
119C2×D4×C61—44no—
120C22×C4×C61—22no—
121C22×C4×C61—22no—
122C22×C4×C61—22no—
123C22×C4×C61—22no—
124C22×C4×C61—24no—
125C22×C4×C61—24no—
126C22×C4×C61—24no—
127C22×C4×C61—42no—
128C22×C4×C61—42no—
129C22×C4×C61—42no—
130C22×C4×C61—44no—
131C22×C4×C61—44no—
132C22×C4×C61—42no—
133C22×C4×C61—44no—
134C22×C4×C61—42no—
135C22×C4×C61#4114yes—
136C22×C4×C61C2414yes—
137C22×C4×C61C2414yes—
138C22×C4×C61C2414yes—
139C22×C4×C61C2412yes—
140C22×C4×C61C2414yes—
141C22×C4×C61C2414yes—
142C22×C4×C61C2412yes—
143C22×C4×C61C2411yescharacteristic
144C22×C4×C61C2411yescharacteristic
145C4⋊C4×C61—24no—
146C4⋊C4×C61—28no—
147C4⋊C4×C61—44no—
148C4⋊C4×C61—42no—
149C4⋊C4×C61—42no—
150C4⋊C4×C61—44no—
151C4⋊C4×C61—44no—
152C4⋊C4×C61—44no—
153C4⋊C4×C61—44no—
154C4⋊C4×C61—44no—
155C4⋊C4×C61—44no—
156C22⋊C4×C61—28no—
157C22⋊C4×C61—28no—
158C22⋊C4×C61—28no—
159C22⋊C4×C61—28no—
160C22⋊C4×C61—44no—
161C22⋊C4×C61—44no—
162C22⋊C4×C61—44no—
163C22⋊C4×C61—44no—
164C22⋊C4×C61—44no—
165C22⋊C4×C61—44no—
166C22⋊C4×C61—44no—
167C42×C61—24no—
168C42×C61—24no—
169C42×C61—44no—
170C23×C61—21no—
171C23×C61—21no—
172C23×C61—22no—
173C23×C61—24no—
174C23×C61—24no—
175C23×C61—24no—
176C23×C61—24no—
177C23×C61—24no—
178C23×C61—24no—
179C23×C61—24no—
180C23×C61C2×#4112yes—
181C23×C61H(5,𝔽2)14yes—
182C23×C61C2511yescharacteristic
183D4×C61—416no—
184D4×C61—84no—
185D4×C61—88no—
186C2×C4×C61—28no—
187C2×C4×C61—21no—
188C2×C4×C61—21no—
189C2×C4×C61—21no—
190C2×C4×C61—21no—
191C2×C4×C61—22no—
192C2×C4×C61—22no—
193C2×C4×C61—22no—
194C2×C4×C61—24no—
195C2×C4×C61—24no—
196C2×C4×C61—24no—
197C2×C4×C61—24no—
198C2×C4×C61—24no—
199C2×C4×C61—24no—
200C2×C4×C61—22no—
201C2×C4×C61—22no—
202C2×C4×C61—24no—
203C2×C4×C61—24no—
204C2×C4×C61—24no—
205C2×C4×C61—24no—
206C2×C4×C61—24no—
207C2×C4×C61—24no—
208C2×C4×C61—24no—
209C2×C4×C61—24no—
210C2×C4×C61—24no—
211C2×C4×C61—44no—
212C2×C4×C61—44no—
213C2×C4×C61—84no—
214C2×C4×C61—84no—
215C2×C4×C61—88no—
216C2×C4×C61C2×#4114yes—
217C2×C4×C61H(5,𝔽2)12yes—
218C2×C4×C612−1+412yes—
219#36976C6111yesmaximal, characteristic, direct product factor, Sylow
220C22×C61—22no—
221C22×C61—22no—
222C22×C61—24no—
223C22×C61—24no—
224C22×C61—44no—
225C22×C61—44no—
226C22×C61—44no—
227C22×C61—44no—
228C22×C61—44no—
229C22×C61—44no—
230C22×C61—44no—
231C22×C61#54014yes—
232C22×C61C22×#4111yescharacteristic
233C22×C61C2×H(5,𝔽2)12yes—
234C22×C61C2×H(5,𝔽2)11yescharacteristic
235C22×C61C2×2−1+411yescharacteristic
236C22×C61#58512yes—
237C4×C61—24no—
238C4×C61—22no—
239C4×C61—22no—
240C4×C61—42no—
241C4×C61—44no—
242C4×C61—44no—
243C4×C61—44no—
244C4×C61—44no—
245C4×C61—44no—
246#2854C2×C6112yescomplemented
247#2773C2×C6114yescomplemented
248#2768C2×C6114yescomplemented
249#2753C2×C6114yescomplemented
250#2706C2×C6114yescomplemented
251#2656C2×C6111yescharacteristic
252#2646C2×C6111yescharacteristic, complemented
253#2443C2×C6114yescomplemented
254#2425C2×C6114yescomplemented
255#2325C2×C6112yescomplemented
256C2×#382C2×C6111yescharacteristic, complemented
257C2×C61—24no—
258C2×C61—84no—
259C2×C61C2×#54011yescharacteristic
260C2×C61#349111yescharacteristic
261C2×C61#349211yescharacteristic
262C2×C61#355812yes—
263C2×C61#355912yes—
264C2×#123C22×C6114yes—
265C2×#123C22×C6114yes—
266C2×#121C22×C6112yes—
267C2×#121C22×C6114yes—
268C2×C4×D4C22×C6114yes—
269C22×C4⋊C4C22×C6112yes—
270C22×C42C22×C6111yescharacteristic
271#400C22×C6114yes—
272#399C22×C6114yes—
273#399C22×C6114yes—
274#398C22×C6114yes—
275#398C22×C6114yes—
276#398C22×C6114yes—
277#397C22×C6114yes—
278#397C22×C6114yes—
279#396C22×C6114yes—
280#394C22×C6114yes—
281#394C22×C6114yes—
282#392C22×C6114yes—
283#390C22×C6112yes—
284#390C22×C6112yes—
285#389C22×C6112yes—
286#389C22×C6112yes—
287#389C22×C6114yes—
288#388C22×C6114yes—
289#388C22×C6114yes—
290#388C22×C6114yes—
291#388C22×C6114yes—
292#388C22×C6114yes—
293#387C22×C6114yes—
294#387C22×C6114yes—
295#386C22×C6114yes—
296#386C22×C6114yes—
297#386C22×C6114yes—
298#386C22×C6114yes—
299#385C22×C6114yes—
300#385C22×C6114yes—
301#385C22×C6114yes—
302#382C22×C6114yes—
303#382C22×C6114yes—
304#380C22×C6112yes—
305#380C22×C6114yes—
306C2×#95C22×C6111yescharacteristic
307C2×#95C22×C6111yescharacteristic
308C2×#95C22×C6112yes—
309C61#3697611yescharacteristic, direct product factor, Sylow
310C22×D4C23×C6114yes—
311C22×D4C23×C6112yes—
312C22×D4C23×C6114yes—
313C23×C4C23×C6111yescharacteristic
314C23×C4C23×C6111yescharacteristic
315C23×C4C23×C6112yes—
316C23×C4C23×C6112yes—
317C23×C4C23×C6114yes—
318C23×C4C23×C6111yescharacteristic
319#123—48no—
320#123—48no—
321#121—28no—
322#121—48no—
323C4×D4—48no—
324C2×C4⋊C4—44no—
325C2×C4⋊C4C23×C6114yes—
326C2×C4⋊C4C23×C6112yes—
327C2×C4⋊C4C23×C6114yes—
328C2×C4⋊C4C23×C6114yes—
329C2×C4⋊C4C23×C6114yes—
330C2×C4⋊C4C23×C6114yes—
331C2×C4⋊C4C23×C6114yes—
332C2×C4⋊C4C23×C6114yes—
333C2×C4⋊C4C23×C6112yes—
334C2×C4⋊C4C23×C6112yes—
335C2×C4⋊C4C23×C6114yes—
336C2×C22⋊C4C23×C6114yes—
337C2×C22⋊C4C23×C6114yes—
338C2×C22⋊C4C23×C6114yes—
339C2×C22⋊C4C23×C6114yes—
340C2×C22⋊C4C23×C6114yes—
341C2×C22⋊C4C23×C6114yes—
342C2×C22⋊C4C23×C6114yes—
343C2×C22⋊C4C23×C6114yes—
344C2×C22⋊C4C23×C6114yes—
345C2×C22⋊C4C23×C6114yes—
346C2×C22⋊C4C23×C6114yes—
347C2×C42—24no—
348C2×C42C23×C6112yes—
349C2×C42C23×C6112yes—
350C2×C42C23×C6114yes—
351#95C23×C6114yes—
352#95C23×C6114yes—
353#95C23×C6114yes—
354#95C23×C6114yes—
355#95C23×C6114yes—
356#95C23×C6114yes—
357#95C23×C6114yes—
358#95C23×C6114yes—
359#95C23×C6114yes—
360#95C23×C6114yes—
361#95C23×C6114yes—
362C24C24×C6114yes—
363C24C24×C6111yescharacteristic
364C2×D4—28no—
365C2×D4—28no—
366C2×D4—28no—
367C2×D4—24no—
368C2×D4—44no—
369C2×D4—44no—
370C2×D4—42no—
371C2×D4—42no—
372C2×D4—44no—
373C22×C4—22no—
374C22×C4—22no—
375C22×C4—22no—
376C22×C4—22no—
377C22×C4—24no—
378C22×C4—24no—
379C22×C4—24no—
380C22×C4—42no—
381C22×C4—42no—
382C22×C4—42no—
383C22×C4—44no—
384C22×C4—44no—
385C22×C4—42no—
386C22×C4—44no—
387C22×C4—42no—
388C22×C4#41×C6114yes—
389C22×C4C24×C6114yes—
390C22×C4C24×C6114yes—
391C22×C4C24×C6114yes—
392C22×C4C24×C6112yes—
393C22×C4C24×C6114yes—
394C22×C4C24×C6114yes—
395C22×C4C24×C6112yes—
396C22×C4C24×C6111yescharacteristic
397C22×C4C24×C6111yescharacteristic
398C4⋊C4—24no—
399C4⋊C4—28no—
400C4⋊C4—44no—
401C4⋊C4—44no—
402C4⋊C4—44no—
403C4⋊C4—44no—
404C4⋊C4—44no—
405C4⋊C4—44no—
406C4⋊C4—42no—
407C4⋊C4—42no—
408C4⋊C4—44no—
409C22⋊C4—28no—
410C22⋊C4—28no—
411C22⋊C4—28no—
412C22⋊C4—28no—
413C22⋊C4—44no—
414C22⋊C4—44no—
415C22⋊C4—44no—
416C22⋊C4—44no—
417C22⋊C4—44no—
418C22⋊C4—44no—
419C22⋊C4—44no—
420C42—24no—
421C42—24no—
422C42—44no—
423C23—21no—
424C23—21no—
425C23—22no—
426C23—24no—
427C23—24no—
428C23—24no—
429C23—24no—
430C23—24no—
431C23—24no—
432C23—24no—
433C23C2×#41×C6112yes—
434C23H(5,𝔽2)×C6114yes—
435C23C25×C6111yescharacteristic
436D4—416no—
437D4—84no—
438D4—88no—
439C2×C4—28no—
440C2×C4—21no—
441C2×C4—21no—
442C2×C4—21no—
443C2×C4—21no—
444C2×C4—22no—
445C2×C4—22no—
446C2×C4—22no—
447C2×C4—24no—
448C2×C4—24no—
449C2×C4—24no—
450C2×C4—24no—
451C2×C4—24no—
452C2×C4—24no—
453C2×C4—22no—
454C2×C4—22no—
455C2×C4—24no—
456C2×C4—24no—
457C2×C4—24no—
458C2×C4—24no—
459C2×C4—24no—
460C2×C4—24no—
461C2×C4—24no—
462C2×C4—24no—
463C2×C4—24no—
464C2×C4—44no—
465C2×C4—44no—
466C2×C4—84no—
467C2×C4—84no—
468C2×C4—88no—
469C2×C4C2×#41×C6114yes—
470C2×C4H(5,𝔽2)×C6112yes—
471C2×C42−1+4×C6112yes—
472C22—24no—
473C22—24no—
474C22—22no—
475C22—22no—
476C22—44no—
477C22—44no—
478C22—44no—
479C22—44no—
480C22—44no—
481C22—44no—
482C22—44no—
483C22C61×#54014yes—
484C22C22×#41×C6111yescharacteristic
485C22C2×H(5,𝔽2)×C6111yescharacteristic
486C22C2×H(5,𝔽2)×C6112yes—
487C22C2×2−1+4×C6111yescharacteristic
488C22C61×#58512yes—
489C4—24no—
490C4—22no—
491C4—22no—
492C4—44no—
493C4—44no—
494C4—44no—
495C4—44no—
496C4—42no—
497C4—44no—
498C2—24no—
499C2—84no—
500C2C2×C61×#54011yescharacteristic
501C2C61×#349111yescharacteristic
502C2C61×#349211yescharacteristic
503C2C61×#355812yes—
504C2C61×#355912yes—
subgroupG/H
center, socleC23×C61C25
commutator, Frattini, cosocleC23C25×C61
prime radicalC61×#2656C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23×C61 ◁ G

Complements

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

NH ≅ G/Ntype
1. C61×#2854C2semidirect
2. C61×#2773C2semidirect
3. C61×#2768C2semidirect
4. C61×#2753C2semidirect
5. C61×#2706C2semidirect
7. C61×#2646C2semidirect
8. C61×#2443C2semidirect
9. C61×#2425C2semidirect
10. C61×#2325C2semidirect
11. C2×C61×#382C2semidirect
219. #36976C61direct (N × H)
246. #2854C2×C61semidirect
247. #2773C2×C61semidirect
248. #2768C2×C61semidirect
249. #2753C2×C61semidirect
250. #2706C2×C61semidirect
252. #2646C2×C61semidirect
253. #2443C2×C61semidirect
254. #2425C2×C61semidirect
255. #2325C2×C61semidirect
256. C2×#382C2×C61semidirect
309. C61#36976direct (N × H)

Maximal subgroups

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

subgroupindex
C61×#28542
C61×#27732
C61×#27682
C61×#27532
C61×#27062
C61×#26562
C61×#26462
C61×#24432
C61×#24252
C61×#23252
C2×C61×#3822
#3697661