Finite Group Databasebeta

← C61×#19260 #29522693

Subgroups — C61×#19260 #29522693

Order 15616.

656 conjugacy classes of subgroups.

The subgroup lattice has 470 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C61×#3167C211yesmaximal, characteristic
2C61×#3078C211yesmaximal, characteristic, complemented
3C61×#3037C211yesmaximal, characteristic
4C2×C8×Q8×C61C211yesmaximal, characteristic, complemented
5C61×#1680C212yesmaximal, complemented
6C61×#1678C212yesmaximal, complemented
7C61×#1672C212yesmaximal, complemented
8C61×#1666C212yesmaximal, complemented
9C61×#1566C211yesmaximal, characteristic, complemented
10C61×#1550C211yesmaximal, characteristic, complemented
11C61×#1547C211yesmaximal, characteristic
12C2×#137×C61—21no—
13C61×#533C2211yescharacteristic
14C61×#532C2211yescharacteristic
15C2×C4×Q8×C61C2211yescharacteristic
16C61×#498C2211yescharacteristic
17C61×#492C2211yescharacteristic
18C61×#487C2211yescharacteristic
19C61×#486C2211yescharacteristic
20C61×#479—22no—
21C61×#477C2212yes—
22C61×#475C2212yes—
23C61×#465—21no—
24C61×#465—21no—
25C61×#464—22no—
26C61×#462C2212yes—
27C61×#460C2212yes—
28C8×Q8×C61—21no—
29C8×Q8×C61—21no—
30C8×Q8×C61C2212yes—
31C8×Q8×C61C2212yes—
32C4×SD16×C61—21no—
33C4×SD16×C61—21no—
34C61×#428—21no—
35C61×#423C2211yescharacteristic
36C61×#423C2211yescharacteristic
37C2×C4⋊C8×C61—21no—
38C2×C4⋊C8×C61C2211yescharacteristic
39C61×#419—21no—
40C61×#417—21no—
41C2×C4×C8×C61—21no—
42C2×C4×C8×C61C2211yescharacteristic
43C61×#334C2212yes—
44C61×#334C2212yes—
45C61×#333C2212yes—
46C61×#332C2212yes—
47C61×#332C2212yes—
48C61×#331C2212yes—
49C2×#41×C61—21no—
50C22×Q8×C61D411yescharacteristic
51#137×C61—44no—
52C2×Q16×C61—22no—
53C2×SD16×C61—22no—
54C2×SD16×C61—21no—
55C2×SD16×C61—21no—
56C2×M16×C61—21no—
57C2×M16×C61—21no—
58C22×C8×C61—21no—
59C22×C8×C61D411yescharacteristic
60C22×C8×C61D411yescharacteristic
61C4⋊Q8×C61C2311yescharacteristic
62C4⋊Q8×C61C2311yescharacteristic
63C4⋊Q8×C61C2311yescharacteristic
64#127×C61C2311yescharacteristic
65#125×C61—21no—
66#124×C61—21no—
67C22⋊Q8×C61—21no—
68C22⋊Q8×C61—21no—
69#121×C61—21no—
70#121×C61—21no—
71C4×Q8×C61—21no—
72C4×Q8×C61—21no—
73C4×Q8×C61—21no—
74C4×Q8×C61—21no—
75C4×Q8×C61D412yes—
76C4×Q8×C61C2312yes—
77C4×D4×C61—21no—
78C4×D4×C61—21no—
79#117×C61—21no—
80C2×C4⋊C4×C61—21no—
81C2×C4⋊C4×C61D411yescharacteristic
82C2×C42×C61—21no—
83C2×C42×C61C2311yescharacteristic
84#107×C61—22no—
85#106×C61—21no—
86#106×C61—21no—
87#106×C61—22no—
88C4⋊C8×C61—22no—
89C4⋊C8×C61—22no—
90C4⋊C8×C61—21no—
91C4⋊C8×C61—21no—
92C4⋊C8×C61—21no—
93C4⋊C8×C61C2312yes—
94C4⋊C8×C61C2312yes—
95C4⋊C8×C61C2312yes—
96#103×C61—22no—
97#103×C61—22no—
98#103×C61—21no—
99#103×C61—21no—
100#103×C61—22no—
101#102×C61—21no—
102#102×C61—21no—
103#102×C61—22no—
104C4×C8×C61—22no—
105C4×C8×C61—22no—
106C4×C8×C61D411yescharacteristic
107C4×C8×C61D411yescharacteristic
108C4×C8×C61C2311yescharacteristic
109C4×C8×C61C2311yescharacteristic
110#41×C61—42no—
111#41×C61—42no—
112C2×Q8×C61—21no—
113C2×Q8×C61—22no—
114C2×Q8×C61—21no—
115C2×Q8×C61—21no—
116C2×Q8×C61—21no—
117C2×Q8×C61SD1614yescomplemented
118C2×Q8×C61C2×D412yes—
119C2×D4×C61—21no—
120C2×D4×C61—21no—
121C2×D4×C61—21no—
122C2×D4×C61—41no—
123C22×C4×C61—21no—
124C22×C4×C61—21no—
125C22×C4×C61—41no—
126C22×C4×C61C2×D411yescharacteristic
127C22×C4×C61C2×D411yescharacteristic
128C22×C4×C61#4111yescharacteristic
129Q16×C61—44no—
130SD16×C61—42no—
131SD16×C61—44no—
132SD16×C61—42no—
133M16×C61—42no—
134M16×C61—42no—
135C2×C8×C61—22no—
136C2×C8×C61—22no—
137C2×C8×C61—22no—
138C2×C8×C61—22no—
139C2×C8×C61—41no—
140C2×C8×C61—42no—
141C2×C8×C61C2×D411yescharacteristic
142C2×C8×C61C2×D411yescharacteristic
143C2×C8×C61C2×D411yescharacteristic
144C2×C8×C61C2×D411yescharacteristic
145C4⋊C4×C61—22no—
146C4⋊C4×C61—21no—
147C4⋊C4×C61—22no—
148C4⋊C4×C61—21no—
149C4⋊C4×C61—21no—
150C4⋊C4×C61—21no—
151C4⋊C4×C61—21no—
152C4⋊C4×C61—21no—
153C4⋊C4×C61—21no—
154C4⋊C4×C61—41no—
155C4⋊C4×C61—41no—
156C4⋊C4×C61C2×D412yes—
157C22⋊C4×C61—41no—
158C22⋊C4×C61—41no—
159C22⋊C4×C61—41no—
160C42×C61—22no—
161C42×C61—22no—
162C42×C61—41no—
163C42×C61C2×D411yescharacteristic
164C42×C61C2×D411yescharacteristic
165C42×C61#4111yescharacteristic
166C42×C61C2411yescharacteristic
167C23×C61—41no—
168C23×C61#12111yescharacteristic
169Q8×C61—22no—
170Q8×C61—24no—
171Q8×C61—41no—
172Q8×C61—41no—
173Q8×C61—41no—
174Q8×C61—41no—
175Q8×C61—81no—
176Q8×C61C2×SD1614yes—
177D4×C61—41no—
178D4×C61—41no—
179D4×C61—41no—
180D4×C61—41no—
181D4×C61—81no—
182D4×C61—82no—
183C2×C4×C61—22no—
184C2×C4×C61—24no—
185C2×C4×C61—21no—
186C2×C4×C61—21no—
187C2×C4×C61—22no—
188C2×C4×C61—41no—
189C2×C4×C61—42no—
190C2×C4×C61—41no—
191C2×C4×C61—41no—
192C2×C4×C61—41no—
193C2×C4×C61—82no—
194C2×C4×C61#12111yescharacteristic
195C2×C4×C61#12111yescharacteristic
196C2×C4×C61#12111yescharacteristic
197C2×C4×C61C2×SD1612yes—
198C2×C4×C61#13512yes—
199C2×C4×C61C22×D411yescharacteristic
200C2×C4×C61C22×D411yescharacteristic
201C2×C4×C61C2×#4111yescharacteristic
202C8×C61—21no—
203C8×C61—21no—
204C8×C61—21no—
205C8×C61—42no—
206C8×C61—42no—
207C8×C61—42no—
208C8×C61#13712yescomplemented
209#19260C6111yesmaximal, characteristic, direct product factor, Sylow
210C22×C61—21no—
211C22×C61—21no—
212C22×C61—81no—
213C22×C61—81no—
214C22×C61—81no—
215C22×C61#46512yes—
216C22×C61C2×#12111yescharacteristic
217C4×C61—21no—
218C4×C61—24no—
219C4×C61—21no—
220C4×C61—21no—
221C4×C61—42no—
222C4×C61—81no—
223C4×C61—81no—
224C4×C61—81no—
225C4×C61#46512yes—
226C4×C61C22×SD1611yescharacteristic
227C4×C61C2×#13511yescharacteristic
228C4×C61C2×#13711yescharacteristic
229C4×C61#57511yescharacteristic
230#3167C2×C6111yescharacteristic
231#3078C2×C6111yescharacteristic, complemented
232#3037C2×C6111yescharacteristic
233C2×C8×Q8C2×C6111yescharacteristic, complemented
234#1680C2×C6112yescomplemented
235#1678C2×C6112yescomplemented
236#1672C2×C6112yescomplemented
237#1666C2×C6112yescomplemented
238#1566C2×C6111yescharacteristic, complemented
239#1550C2×C6111yescharacteristic, complemented
240#1547C2×C6111yescharacteristic
241C2×C61—22no—
242C2×C61—161no—
243C2×C61#303711yescharacteristic
244C2×C61C2×#46511yescharacteristic
245C2×C61#306711yescharacteristic
246C2×#137—21no—
247#533C22×C6111yescharacteristic
248#532C22×C6111yescharacteristic
249C2×C4×Q8C22×C6111yescharacteristic
250#498C22×C6111yescharacteristic
251#492C22×C6111yescharacteristic
252#487C22×C6111yescharacteristic
253#486C22×C6111yescharacteristic
254#479—22no—
255#477C22×C6112yes—
256#475C22×C6112yes—
257#465—21no—
258#465—21no—
259#464—22no—
260#462C22×C6112yes—
261#460C22×C6112yes—
262C8×Q8—21no—
263C8×Q8—21no—
264C8×Q8C22×C6112yes—
265C8×Q8C22×C6112yes—
266C4×SD16—21no—
267C4×SD16—21no—
268#428—21no—
269#423C22×C6111yescharacteristic
270#423C22×C6111yescharacteristic
271C2×C4⋊C8—21no—
272C2×C4⋊C8C22×C6111yescharacteristic
273#419—21no—
274#417—21no—
275C2×C4×C8—21no—
276C2×C4×C8C22×C6111yescharacteristic
277#334C22×C6112yes—
278#334C22×C6112yes—
279#333C22×C6112yes—
280#332C22×C6112yes—
281#332C22×C6112yes—
282#331C22×C6112yes—
283C61#1926011yescharacteristic, direct product factor, Sylow
284C2×#41—21no—
285C22×Q8D4×C6111yescharacteristic
286#137—44no—
287C2×Q16—22no—
288C2×SD16—22no—
289C2×SD16—21no—
290C2×SD16—21no—
291C2×M16—21no—
292C2×M16—21no—
293C22×C8—21no—
294C22×C8D4×C6111yescharacteristic
295C22×C8D4×C6111yescharacteristic
296C4⋊Q8C23×C6111yescharacteristic
297C4⋊Q8C23×C6111yescharacteristic
298C4⋊Q8C23×C6111yescharacteristic
299#127C23×C6111yescharacteristic
300#125—21no—
301#124—21no—
302C22⋊Q8—21no—
303C22⋊Q8—21no—
304#121—21no—
305#121—21no—
306C4×Q8—21no—
307C4×Q8—21no—
308C4×Q8—21no—
309C4×Q8—21no—
310C4×Q8D4×C6112yes—
311C4×Q8C23×C6112yes—
312C4×D4—21no—
313C4×D4—21no—
314#117—21no—
315C2×C4⋊C4—21no—
316C2×C4⋊C4D4×C6111yescharacteristic
317C2×C42—21no—
318C2×C42C23×C6111yescharacteristic
319#107—22no—
320#106—21no—
321#106—21no—
322#106—22no—
323C4⋊C8—22no—
324C4⋊C8—22no—
325C4⋊C8—21no—
326C4⋊C8—21no—
327C4⋊C8—21no—
328C4⋊C8C23×C6112yes—
329C4⋊C8C23×C6112yes—
330C4⋊C8C23×C6112yes—
331#103—22no—
332#103—22no—
333#103—21no—
334#103—21no—
335#103—22no—
336#102—21no—
337#102—21no—
338#102—22no—
339C4×C8—22no—
340C4×C8—22no—
341C4×C8D4×C6111yescharacteristic
342C4×C8D4×C6111yescharacteristic
343C4×C8C23×C6111yescharacteristic
344C4×C8C23×C6111yescharacteristic
345#41—42no—
346#41—42no—
347C2×Q8—21no—
348C2×Q8—22no—
349C2×Q8—21no—
350C2×Q8—21no—
351C2×Q8—21no—
352C2×Q8SD16×C6114yescomplemented
353C2×Q8C2×D4×C6112yes—
354C2×D4—21no—
355C2×D4—21no—
356C2×D4—21no—
357C2×D4—41no—
358C22×C4—21no—
359C22×C4—21no—
360C22×C4—41no—
361C22×C4C2×D4×C6111yescharacteristic
362C22×C4C2×D4×C6111yescharacteristic
363C22×C4#41×C6111yescharacteristic
364Q16—44no—
365SD16—42no—
366SD16—44no—
367SD16—42no—
368M16—42no—
369M16—42no—
370C2×C8—22no—
371C2×C8—22no—
372C2×C8—22no—
373C2×C8—22no—
374C2×C8—41no—
375C2×C8—42no—
376C2×C8C2×D4×C6111yescharacteristic
377C2×C8C2×D4×C6111yescharacteristic
378C2×C8C2×D4×C6111yescharacteristic
379C2×C8C2×D4×C6111yescharacteristic
380C4⋊C4—22no—
381C4⋊C4—21no—
382C4⋊C4—22no—
383C4⋊C4—21no—
384C4⋊C4—21no—
385C4⋊C4—21no—
386C4⋊C4—21no—
387C4⋊C4—21no—
388C4⋊C4—21no—
389C4⋊C4—41no—
390C4⋊C4—41no—
391C4⋊C4C2×D4×C6112yes—
392C22⋊C4—41no—
393C22⋊C4—41no—
394C22⋊C4—41no—
395C42—22no—
396C42—22no—
397C42—41no—
398C42C2×D4×C6111yescharacteristic
399C42C2×D4×C6111yescharacteristic
400C42#41×C6111yescharacteristic
401C42C24×C6111yescharacteristic
402C23—41no—
403C23#121×C6111yescharacteristic
404Q8—22no—
405Q8—24no—
406Q8—41no—
407Q8—41no—
408Q8—41no—
409Q8—41no—
410Q8—81no—
411Q8C2×SD16×C6114yes—
412D4—41no—
413D4—41no—
414D4—41no—
415D4—41no—
416D4—81no—
417D4—82no—
418C2×C4—24no—
419C2×C4—22no—
420C2×C4—21no—
421C2×C4—21no—
422C2×C4—22no—
423C2×C4—41no—
424C2×C4—42no—
425C2×C4—41no—
426C2×C4—41no—
427C2×C4—41no—
428C2×C4—82no—
429C2×C4#121×C6111yescharacteristic
430C2×C4#121×C6111yescharacteristic
431C2×C4#121×C6111yescharacteristic
432C2×C4C2×SD16×C6112yes—
433C2×C4#135×C6112yes—
434C2×C4C22×D4×C6111yescharacteristic
435C2×C4C22×D4×C6111yescharacteristic
436C2×C4C2×#41×C6111yescharacteristic
437C8—21no—
438C8—21no—
439C8—21no—
440C8—42no—
441C8—42no—
442C8—42no—
443C8#137×C6112yescomplemented
444C22—21no—
445C22—21no—
446C22—81no—
447C22—81no—
448C22—81no—
449C22C61×#46512yes—
450C22C2×#121×C6111yescharacteristic
451C4—21no—
452C4—24no—
453C4—21no—
454C4—21no—
455C4—42no—
456C4—81no—
457C4—81no—
458C4—81no—
459C4C61×#46512yes—
460C4C22×SD16×C6111yescharacteristic
461C4C2×#135×C6111yescharacteristic
462C4C2×#137×C6111yescharacteristic
463C4C61×#57511yescharacteristic
464C2—22no—
465C2—161no—
466C2C61×#303711yescharacteristic
467C2C2×C61×#46511yescharacteristic
468C2C61×#306711yescharacteristic
subgroupG/H
center, socleC22×C61C2×#121
commutator, Frattini, cosocleC42C24×C61
prime radicalC61×#532C22
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C61 ◁ C2×C42×C61 ◁ G

Complements

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

NH ≅ G/Ntype
2. C61×#3078C2semidirect
4. C2×C8×Q8×C61C2semidirect
5. C61×#1680C2semidirect
6. C61×#1678C2semidirect
7. C61×#1672C2semidirect
8. C61×#1666C2semidirect
9. C61×#1566C2semidirect
10. C61×#1550C2semidirect
117. C2×Q8×C61SD16semidirect
208. C8×C61#137semidirect
209. #19260C61direct (N × H)
231. #3078C2×C61semidirect
233. C2×C8×Q8C2×C61semidirect
234. #1680C2×C61semidirect
235. #1678C2×C61semidirect
236. #1672C2×C61semidirect
237. #1666C2×C61semidirect
238. #1566C2×C61semidirect
239. #1550C2×C61semidirect
283. C61#19260direct (N × H)
352. C2×Q8SD16×C61semidirect
443. C8#137×C61semidirect

Maximal subgroups

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

subgroupindex
C61×#31672
C61×#30782
C61×#30372
C2×C8×Q8×C612
C61×#16802
C61×#16782
C61×#16722
C61×#16662
C61×#15662
C61×#15502
C61×#15472
#1926061