Finite Group Databasebeta

← C61×#36978 #29540411

Subgroups — C61×#36978 #29540411

Order 15616.

1726 conjugacy classes of subgroups.

The subgroup lattice has 494 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C61×#2854C212yesmaximal, complemented
2C61×#2777C214yesmaximal, complemented
3C61×#2756C214yesmaximal, complemented
4C61×#2749C214yesmaximal, complemented
5C61×#2738C214yesmaximal, complemented
6C61×#2656C211yesmaximal, characteristic
7C61×#2646C211yesmaximal, characteristic, complemented
8C61×#2444C214yesmaximal, complemented
9C61×#2425C214yesmaximal, complemented
10C61×#2325C212yesmaximal, complemented
11C2×C61×#383C211yesmaximal, characteristic, complemented
12C2×#123×C61C2214yes—
13C2×#121×C61C2212yes—
14C2×#121×C61C2214yes—
15C2×C4×D4×C61C2214yes—
16C22×C42×C61C2211yescharacteristic
17C61×#400C2214yes—
18C61×#400C2214yes—
19C61×#399C2214yes—
20C61×#398C2214yes—
21C61×#398C2214yes—
22C61×#397C2214yes—
23C61×#397C2214yes—
24C61×#397C2214yes—
25C61×#396C2214yes—
26C61×#394C2214yes—
27C61×#394C2214yes—
28C61×#392C2214yes—
29C61×#390C2212yes—
30C61×#390C2212yes—
31C61×#389C2212yes—
32C61×#389C2214yes—
33C61×#389C2212yes—
34C61×#388C2214yes—
35C61×#388C2214yes—
36C61×#388C2214yes—
37C61×#388C2214yes—
38C61×#388C2214yes—
39C61×#387C2214yes—
40C61×#387C2214yes—
41C61×#386C2214yes—
42C61×#386C2214yes—
43C61×#386C2214yes—
44C61×#386C2214yes—
45C61×#386C2214yes—
46C61×#385C2214yes—
47C61×#385C2214yes—
48C61×#383C2214yes—
49C61×#383C2214yes—
50C61×#381C2214yes—
51C61×#380C2212yes—
52C61×#380C2214yes—
53C2×#95×C61C2211yescharacteristic
54C2×#95×C61C2211yescharacteristic
55C2×#95×C61C2212yes—
56C2×#95×C61C2212yes—
57C22×D4×C61C2314yes—
58C22×D4×C61C2312yes—
59C22×D4×C61C2314yes—
60C23×C4×C61C2311yescharacteristic
61C23×C4×C61C2312yes—
62C23×C4×C61C2312yes—
63C23×C4×C61C2311yescharacteristic
64C23×C4×C61C2314yes—
65C23×C4×C61C2311yescharacteristic
66#123×C61—48no—
67#121×C61—28no—
68#121×C61—48no—
69C4×D4×C61—48no—
70C2×C4⋊C4×C61C2312yes—
71C2×C4⋊C4×C61C2312yes—
72C2×C4⋊C4×C61C2314yes—
73C2×C4⋊C4×C61C2312yes—
74C2×C4⋊C4×C61C2314yes—
75C2×C4⋊C4×C61C2314yes—
76C2×C4⋊C4×C61C2314yes—
77C2×C4⋊C4×C61C2314yes—
78C2×C4⋊C4×C61C2314yes—
79C2×C22⋊C4×C61C2314yes—
80C2×C22⋊C4×C61C2314yes—
81C2×C22⋊C4×C61C2314yes—
82C2×C22⋊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×C42×C61—24no—
91C2×C42×C61C2312yes—
92C2×C42×C61C2312yes—
93C2×C42×C61C2314yes—
94#95×C61C2314yes—
95#95×C61C2314yes—
96#95×C61C2314yes—
97#95×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—
107C24×C61C2414yes—
108C24×C61C2411yescharacteristic
109C2×D4×C61—28no—
110C2×D4×C61—28no—
111C2×D4×C61—28no—
112C2×D4×C61—24no—
113C2×D4×C61—44no—
114C2×D4×C61—42no—
115C2×D4×C61—42no—
116C2×D4×C61—44no—
117C2×D4×C61—44no—
118C22×C4×C61—22no—
119C22×C4×C61—22no—
120C22×C4×C61—24no—
121C22×C4×C61—24no—
122C22×C4×C61—24no—
123C22×C4×C61—42no—
124C22×C4×C61—41no—
125C22×C4×C61—41no—
126C22×C4×C61—44no—
127C22×C4×C61—44no—
128C22×C4×C61—42no—
129C22×C4×C61—42no—
130C22×C4×C61—44no—
131C22×C4×C61—42no—
132C22×C4×C61—42no—
133C22×C4×C61#4114yes—
134C22×C4×C61C2412yes—
135C22×C4×C61C2414yes—
136C22×C4×C61C2414yes—
137C22×C4×C61C2414yes—
138C22×C4×C61C2411yescharacteristic
139C22×C4×C61C2411yescharacteristic
140C22×C4×C61C2414yes—
141C22×C4×C61C2414yes—
142C22×C4×C61C2412yes—
143C4⋊C4×C61—24no—
144C4⋊C4×C61—42no—
145C4⋊C4×C61—42no—
146C4⋊C4×C61—44no—
147C4⋊C4×C61—44no—
148C4⋊C4×C61—44no—
149C4⋊C4×C61—44no—
150C4⋊C4×C61—44no—
151C4⋊C4×C61—44no—
152C22⋊C4×C61—28no—
153C22⋊C4×C61—28no—
154C22⋊C4×C61—44no—
155C22⋊C4×C61—44no—
156C22⋊C4×C61—44no—
157C22⋊C4×C61—44no—
158C22⋊C4×C61—44no—
159C22⋊C4×C61—44no—
160C22⋊C4×C61—44no—
161C22⋊C4×C61—44no—
162C22⋊C4×C61—44no—
163C42×C61—24no—
164C42×C61—24no—
165C42×C61—44no—
166C23×C61—22no—
167C23×C61—21no—
168C23×C61—21no—
169C23×C61—24no—
170C23×C61—24no—
171C23×C61—24no—
172C23×C61—24no—
173C23×C61—24no—
174C23×C61—24no—
175C23×C61—24no—
176C23×C61C2×#4112yes—
177C23×C61H(5,𝔽2)14yes—
178C23×C61C2511yescharacteristic
179D4×C61—416no—
180D4×C61—84no—
181D4×C61—88no—
182C2×C4×C61—22no—
183C2×C4×C61—22no—
184C2×C4×C61—21no—
185C2×C4×C61—21no—
186C2×C4×C61—22no—
187C2×C4×C61—24no—
188C2×C4×C61—24no—
189C2×C4×C61—24no—
190C2×C4×C61—24no—
191C2×C4×C61—24no—
192C2×C4×C61—22no—
193C2×C4×C61—22no—
194C2×C4×C61—24no—
195C2×C4×C61—24no—
196C2×C4×C61—22no—
197C2×C4×C61—22no—
198C2×C4×C61—24no—
199C2×C4×C61—24no—
200C2×C4×C61—24no—
201C2×C4×C61—24no—
202C2×C4×C61—24no—
203C2×C4×C61—24no—
204C2×C4×C61—24no—
205C2×C4×C61—24no—
206C2×C4×C61—44no—
207C2×C4×C61—44no—
208C2×C4×C61—44no—
209C2×C4×C61—84no—
210C2×C4×C61—84no—
211C2×C4×C61—88no—
212C2×C4×C61C2×#4114yes—
213#36978C6111yesmaximal, characteristic, direct product factor, Sylow
214C22×C61—22no—
215C22×C61—22no—
216C22×C61—24no—
217C22×C61—24no—
218C22×C61—44no—
219C22×C61—44no—
220C22×C61—44no—
221C22×C61—44no—
222C22×C61—44no—
223C22×C61—44no—
224C22×C61—44no—
225C22×C61#54014yes—
226C22×C61C22×#4111yescharacteristic
227C22×C61C2×H(5,𝔽2)12yes—
228C22×C61#58512yes—
229C22×C61#58511yescharacteristic
230C22×C61#58511yescharacteristic
231C4×C61—24no—
232C4×C61—41no—
233C4×C61—41no—
234C4×C61—44no—
235C4×C61—42no—
236C4×C61—44no—
237C4×C61—44no—
238C4×C61—44no—
239C4×C61—44no—
240#2854C2×C6112yescomplemented
241#2777C2×C6114yescomplemented
242#2756C2×C6114yescomplemented
243#2749C2×C6114yescomplemented
244#2738C2×C6114yescomplemented
245#2656C2×C6111yescharacteristic
246#2646C2×C6111yescharacteristic, complemented
247#2444C2×C6114yescomplemented
248#2425C2×C6114yescomplemented
249#2325C2×C6112yescomplemented
250C2×#383C2×C6111yescharacteristic, complemented
251C2×C61—24no—
252C2×C61—84no—
253C2×C61C2×#54011yescharacteristic
254C2×C61#349111yescharacteristic
255C2×C61#349311yescharacteristic
256C2×C61#356012yes—
257C2×C61#356012yes—
258C2×#123C22×C6114yes—
259C2×#121C22×C6112yes—
260C2×#121C22×C6114yes—
261C2×C4×D4C22×C6114yes—
262C22×C42C22×C6111yescharacteristic
263#400C22×C6114yes—
264#400C22×C6114yes—
265#399C22×C6114yes—
266#398C22×C6114yes—
267#398C22×C6114yes—
268#397C22×C6114yes—
269#397C22×C6114yes—
270#397C22×C6114yes—
271#396C22×C6114yes—
272#394C22×C6114yes—
273#394C22×C6114yes—
274#392C22×C6114yes—
275#390C22×C6112yes—
276#390C22×C6112yes—
277#389C22×C6112yes—
278#389C22×C6112yes—
279#389C22×C6114yes—
280#388C22×C6114yes—
281#388C22×C6114yes—
282#388C22×C6114yes—
283#388C22×C6114yes—
284#388C22×C6114yes—
285#387C22×C6114yes—
286#387C22×C6114yes—
287#386C22×C6114yes—
288#386C22×C6114yes—
289#386C22×C6114yes—
290#386C22×C6114yes—
291#386C22×C6114yes—
292#385C22×C6114yes—
293#385C22×C6114yes—
294#383C22×C6114yes—
295#383C22×C6114yes—
296#381C22×C6114yes—
297#380C22×C6112yes—
298#380C22×C6114yes—
299C2×#95C22×C6111yescharacteristic
300C2×#95C22×C6111yescharacteristic
301C2×#95C22×C6112yes—
302C2×#95C22×C6112yes—
303C61#3697811yescharacteristic, direct product factor, Sylow
304C22×D4C23×C6114yes—
305C22×D4C23×C6112yes—
306C22×D4C23×C6114yes—
307C23×C4C23×C6111yescharacteristic
308C23×C4C23×C6112yes—
309C23×C4C23×C6112yes—
310C23×C4C23×C6111yescharacteristic
311C23×C4C23×C6114yes—
312C23×C4C23×C6111yescharacteristic
313#123—48no—
314#121—28no—
315#121—48no—
316C4×D4—48no—
317C2×C4⋊C4C23×C6112yes—
318C2×C4⋊C4C23×C6114yes—
319C2×C4⋊C4C23×C6114yes—
320C2×C4⋊C4C23×C6114yes—
321C2×C4⋊C4C23×C6114yes—
322C2×C4⋊C4C23×C6112yes—
323C2×C4⋊C4C23×C6114yes—
324C2×C4⋊C4C23×C6112yes—
325C2×C4⋊C4C23×C6114yes—
326C2×C22⋊C4C23×C6114yes—
327C2×C22⋊C4C23×C6114yes—
328C2×C22⋊C4C23×C6114yes—
329C2×C22⋊C4C23×C6114yes—
330C2×C22⋊C4C23×C6114yes—
331C2×C22⋊C4C23×C6114yes—
332C2×C22⋊C4C23×C6114yes—
333C2×C22⋊C4C23×C6114yes—
334C2×C22⋊C4C23×C6114yes—
335C2×C22⋊C4C23×C6114yes—
336C2×C22⋊C4C23×C6114yes—
337C2×C42—24no—
338C2×C42C23×C6112yes—
339C2×C42C23×C6112yes—
340C2×C42C23×C6114yes—
341#95C23×C6114yes—
342#95C23×C6114yes—
343#95C23×C6114yes—
344#95C23×C6114yes—
345#95C23×C6114yes—
346#95C23×C6114yes—
347#95C23×C6114yes—
348#95C23×C6114yes—
349#95C23×C6114yes—
350#95C23×C6114yes—
351#95C23×C6114yes—
352#95C23×C6114yes—
353#95C23×C6114yes—
354C24C24×C6114yes—
355C24C24×C6111yescharacteristic
356C2×D4—28no—
357C2×D4—28no—
358C2×D4—28no—
359C2×D4—24no—
360C2×D4—44no—
361C2×D4—42no—
362C2×D4—42no—
363C2×D4—44no—
364C2×D4—44no—
365C22×C4—22no—
366C22×C4—22no—
367C22×C4—24no—
368C22×C4—24no—
369C22×C4—24no—
370C22×C4—42no—
371C22×C4—41no—
372C22×C4—41no—
373C22×C4—44no—
374C22×C4—44no—
375C22×C4—42no—
376C22×C4—42no—
377C22×C4—44no—
378C22×C4—42no—
379C22×C4—42no—
380C22×C4#41×C6114yes—
381C22×C4C24×C6112yes—
382C22×C4C24×C6114yes—
383C22×C4C24×C6114yes—
384C22×C4C24×C6114yes—
385C22×C4C24×C6111yescharacteristic
386C22×C4C24×C6111yescharacteristic
387C22×C4C24×C6114yes—
388C22×C4C24×C6114yes—
389C22×C4C24×C6112yes—
390C4⋊C4—24no—
391C4⋊C4—44no—
392C4⋊C4—44no—
393C4⋊C4—44no—
394C4⋊C4—44no—
395C4⋊C4—42no—
396C4⋊C4—42no—
397C4⋊C4—44no—
398C4⋊C4—44no—
399C22⋊C4—28no—
400C22⋊C4—28no—
401C22⋊C4—44no—
402C22⋊C4—44no—
403C22⋊C4—44no—
404C22⋊C4—44no—
405C22⋊C4—44no—
406C22⋊C4—44no—
407C22⋊C4—44no—
408C22⋊C4—44no—
409C22⋊C4—44no—
410C42—24no—
411C42—24no—
412C42—44no—
413C23—22no—
414C23—21no—
415C23—21no—
416C23—24no—
417C23—24no—
418C23—24no—
419C23—24no—
420C23—24no—
421C23—24no—
422C23—24no—
423C23C2×#41×C6112yes—
424C23H(5,𝔽2)×C6114yes—
425C23C25×C6111yescharacteristic
426D4—416no—
427D4—84no—
428D4—88no—
429C2×C4—22no—
430C2×C4—22no—
431C2×C4—21no—
432C2×C4—21no—
433C2×C4—22no—
434C2×C4—24no—
435C2×C4—24no—
436C2×C4—24no—
437C2×C4—24no—
438C2×C4—24no—
439C2×C4—22no—
440C2×C4—22no—
441C2×C4—24no—
442C2×C4—24no—
443C2×C4—24no—
444C2×C4—22no—
445C2×C4—22no—
446C2×C4—24no—
447C2×C4—24no—
448C2×C4—24no—
449C2×C4—24no—
450C2×C4—24no—
451C2×C4—24no—
452C2×C4—24no—
453C2×C4—44no—
454C2×C4—44no—
455C2×C4—44no—
456C2×C4—84no—
457C2×C4—84no—
458C2×C4—88no—
459C2×C4C2×#41×C6114yes—
460C22—24no—
461C22—24no—
462C22—22no—
463C22—22no—
464C22—44no—
465C22—44no—
466C22—44no—
467C22—44no—
468C22—44no—
469C22—44no—
470C22—44no—
471C22C61×#54014yes—
472C22C22×#41×C6111yescharacteristic
473C22C2×H(5,𝔽2)×C6112yes—
474C22C61×#58512yes—
475C22C61×#58511yescharacteristic
476C22C61×#58511yescharacteristic
477C4—24no—
478C4—44no—
479C4—44no—
480C4—44no—
481C4—44no—
482C4—41no—
483C4—41no—
484C4—44no—
485C4—42no—
486C2—24no—
487C2—84no—
488C2C2×C61×#54011yescharacteristic
489C2C61×#349111yescharacteristic
490C2C61×#349311yescharacteristic
491C2C61×#356012yes—
492C2C61×#356012yes—
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×#2777C2semidirect
3. C61×#2756C2semidirect
4. C61×#2749C2semidirect
5. C61×#2738C2semidirect
7. C61×#2646C2semidirect
8. C61×#2444C2semidirect
9. C61×#2425C2semidirect
10. C61×#2325C2semidirect
11. C2×C61×#383C2semidirect
213. #36978C61direct (N × H)
240. #2854C2×C61semidirect
241. #2777C2×C61semidirect
242. #2756C2×C61semidirect
243. #2749C2×C61semidirect
244. #2738C2×C61semidirect
246. #2646C2×C61semidirect
247. #2444C2×C61semidirect
248. #2425C2×C61semidirect
249. #2325C2×C61semidirect
250. C2×#383C2×C61semidirect
303. C61#36978direct (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×#27772
C61×#27562
C61×#27492
C61×#27382
C61×#26562
C61×#26462
C61×#24442
C61×#24252
C61×#23252
C2×C61×#3832
#3697861