Finite Group Databasebeta

← C61×#18763 #29522196

Subgroups — C61×#18763 #29522196

Order 15616.

910 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
1C2×C61×#556C211yesmaximal, characteristic
2C61×#3230C211yesmaximal, characteristic, complemented
3C61×#3101C211yesmaximal, characteristic
4C61×#3078C211yesmaximal, characteristic, complemented
5C61×#1650C214yesmaximal, complemented
6C61×#1638C214yesmaximal, complemented
7C61×#1549C211yesmaximal, characteristic, complemented
8C61×#1486C211yesmaximal, characteristic
9C61×#1479C211yesmaximal, characteristic, complemented
10C61×#556—22no—
11C61×#556—22no—
12C61×#556—22no—
13C61×#556C2214yes—
14C61×#533C2211yescharacteristic
15C2×C4⋊Q8×C61C2211yescharacteristic
16C2×#126×C61—22no—
17C2×#124×C61—21no—
18C2×C22⋊Q8×C61—21no—
19C2×C4×Q8×C61—21no—
20C2×C4×Q8×C61C2211yescharacteristic
21C2×C4×D4×C61C2211yescharacteristic
22C2×#117×C61—21no—
23C61×#500C2212yescomplemented
24C61×#487C2212yescomplemented
25C61×#484—22no—
26C61×#483—21no—
27C61×#479—22no—
28C61×#477—22no—
29C61×#477C2212yescomplemented
30C61×#476C2212yes—
31C61×#475C2212yescomplemented
32C61×#461C2212yes—
33C61×#450—21no—
34C4×SD16×C61—22no—
35C61×#431C2211yescharacteristic
36C61×#431C2211yescharacteristic
37C61×#428—21no—
38C61×#423C2211yescharacteristic
39C61×#419—21no—
40C61×#332C2214yescomplemented
41C61×Q8⋊C8C2214yescomplemented
42C61×D4⋊C8C2214yes—
43C22×Q8×C61—21no—
44C22×Q8×C61D411yescharacteristic
45C22×D4×C61D411yescharacteristic
46C23×C4×C61—21no—
47C2×SD16×C61—22no—
48C2×M16×C61—21no—
49C4⋊Q8×C61—21no—
50C4⋊Q8×C61—21no—
51C4⋊Q8×C61D412yes—
52C4⋊Q8×C61C2311yescharacteristic
53C4⋊Q8×C61C2311yescharacteristic
54C4⋊Q8×C61C2312yes—
55#126×C61—28no—
56#126×C61—28no—
57#125×C61—21no—
58#124×C61—24no—
59#124×C61—24no—
60C22⋊Q8×C61—24no—
61C22⋊Q8×C61—24no—
62C22⋊Q8×C61—21no—
63C22⋊Q8×C61—21no—
64C4×Q8×C61—24no—
65C4×Q8×C61—24no—
66C4×Q8×C61—21no—
67C4×Q8×C61—21no—
68C4×Q8×C61—21no—
69C4×Q8×C61—21no—
70C4×Q8×C61D412yes—
71C4×Q8×C61C2312yes—
72C4×D4×C61—21no—
73C4×D4×C61—21no—
74C4×D4×C61D412yes—
75C4×D4×C61C2312yes—
76#117×C61—24no—
77#117×C61—24no—
78#117×C61—21no—
79C2×C4⋊C4×C61—22no—
80C2×C4⋊C4×C61—21no—
81C2×C4⋊C4×C61—21no—
82C2×C4⋊C4×C61D412yes—
83C2×C4⋊C4×C61D411yescharacteristic
84C2×C4⋊C4×C61D411yescharacteristic
85C2×C22⋊C4×C61—22no—
86C2×C22⋊C4×C61—22no—
87C2×C22⋊C4×C61—21no—
88C2×C42×C61—22no—
89C2×C42×C61—21no—
90C2×C42×C61C2311yescharacteristic
91#107×C61—22no—
92#107×C61—24no—
93#106×C61—22no—
94#106×C61—22no—
95C4⋊C8×C61—21no—
96C4⋊C8×C61—21no—
97C4⋊C8×C61C2312yes—
98C4⋊C8×C61C2312yes—
99#103×C61—22no—
100#103×C61—22no—
101#103×C61—22no—
102#103×C61—24no—
103#102×C61—22no—
104C22⋊C8×C61—21no—
105C22⋊C8×C61—21no—
106C4×C8×C61—21no—
107C4×C8×C61C2312yes—
108C24×C61—21no—
109C2×Q8×C61—21no—
110C2×Q8×C61—22no—
111C2×Q8×C61—22no—
112C2×Q8×C61—22no—
113C2×Q8×C61—22no—
114C2×Q8×C61—21no—
115C2×Q8×C61—21no—
116C2×Q8×C61—44no—
117C2×Q8×C61C2×D412yes—
118C2×D4×C61—21no—
119C2×D4×C61—42no—
120C2×D4×C61C2×D412yes—
121C22×C4×C61—21no—
122C22×C4×C61—21no—
123C22×C4×C61—21no—
124C22×C4×C61—22no—
125C22×C4×C61—22no—
126C22×C4×C61—22no—
127C22×C4×C61—42no—
128C22×C4×C61—42no—
129C22×C4×C61C2×D411yescharacteristic
130C22×C4×C61C2×D411yescharacteristic
131C22×C4×C61C2×D411yescharacteristic
132SD16×C61—44no—
133M16×C61—42no—
134C2×C8×C61—22no—
135C2×C8×C61—22no—
136C2×C8×C61—22no—
137C4⋊C4×C61—28no—
138C4⋊C4×C61—22no—
139C4⋊C4×C61—22no—
140C4⋊C4×C61—21no—
141C4⋊C4×C61—21no—
142C4⋊C4×C61—22no—
143C4⋊C4×C61—22no—
144C4⋊C4×C61—22no—
145C4⋊C4×C61—21no—
146C4⋊C4×C61—21no—
147C4⋊C4×C61—21no—
148C4⋊C4×C61—21no—
149C4⋊C4×C61—41no—
150C4⋊C4×C61—41no—
151C4⋊C4×C61C2×D412yes—
152C4⋊C4×C61C2×D414yes—
153C4⋊C4×C61C2×D412yes—
154C22⋊C4×C61—28no—
155C22⋊C4×C61—28no—
156C22⋊C4×C61—22no—
157C22⋊C4×C61—22no—
158C22⋊C4×C61—41no—
159C42×C61—28no—
160C42×C61—22no—
161C42×C61—22no—
162C42×C61—41no—
163C42×C61C2×D411yescharacteristic
164C42×C61C2×D411yescharacteristic
165C42×C61C2×D411yescharacteristic
166C42×C61C2411yescharacteristic
167C23×C61—22no—
168C23×C61—42no—
169C23×C61—42no—
170C23×C61—42no—
171C23×C61#12011yescharacteristic
172Q8×C61—22no—
173Q8×C61—22no—
174Q8×C61—44no—
175Q8×C61—42no—
176Q8×C61—44no—
177Q8×C61—42no—
178Q8×C61—42no—
179D4×C61—22no—
180D4×C61—22no—
181D4×C61—42no—
182C2×C4×C61—22no—
183C2×C4×C61—22no—
184C2×C4×C61—22no—
185C2×C4×C61—22no—
186C2×C4×C61—24no—
187C2×C4×C61—41no—
188C2×C4×C61—42no—
189C2×C4×C61—44no—
190C2×C4×C61—42no—
191C2×C4×C61—42no—
192C2×C4×C61—42no—
193C2×C4×C61—42no—
194C2×C4×C61—44no—
195C2×C4×C61—41no—
196C2×C4×C61—41no—
197C2×C4×C61#12011yescharacteristic
198C2×C4×C61#12011yescharacteristic
199C2×C4×C61#12011yescharacteristic
200C2×C4×C61#13512yes—
201C2×C4×C61#13712yes—
202C2×C4×C61C22×D411yescharacteristic
203C2×C4×C61C22×D411yescharacteristic
204C2×C4×C61C22×D411yescharacteristic
205C8×C61—42no—
206C8×C61—42no—
207C8×C61—42no—
208#18763C6111yesmaximal, characteristic, direct product factor, Sylow
209C22×C61—21no—
210C22×C61—21no—
211C22×C61—42no—
212C22×C61—42no—
213C22×C61—42no—
214C22×C61—84no—
215C22×C61#45212yes—
216C22×C61C2×#12011yescharacteristic
217C4×C61—21no—
218C4×C61—21no—
219C4×C61—21no—
220C4×C61—42no—
221C4×C61—42no—
222C4×C61—44no—
223C4×C61—42no—
224C4×C61—81no—
225C4×C61—81no—
226C4×C61#45212yes—
227C4×C61C2×#13511yescharacteristic
228C4×C61C2×#13711yescharacteristic
229C4×C61#57512yes—
230C2×#556C2×C6111yescharacteristic
231#3230C2×C6111yescharacteristic, complemented
232#3101C2×C6111yescharacteristic
233#3078C2×C6111yescharacteristic, complemented
234#1650C2×C6114yescomplemented
235#1638C2×C6114yescomplemented
236#1549C2×C6111yescharacteristic, complemented
237#1486C2×C6111yescharacteristic
238#1479C2×C6111yescharacteristic, complemented
239C2×C61—22no—
240C2×C61—82no—
241C2×C61C2×#45211yescharacteristic
242C2×C61#300511yescharacteristic
243C2×C61#302011yescharacteristic
244#556—22no—
245#556—22no—
246#556—22no—
247#556C22×C6114yes—
248#533C22×C6111yescharacteristic
249C2×C4⋊Q8C22×C6111yescharacteristic
250C2×#126—22no—
251C2×#124—21no—
252C2×C22⋊Q8—21no—
253C2×C4×Q8—21no—
254C2×C4×Q8C22×C6111yescharacteristic
255C2×C4×D4C22×C6111yescharacteristic
256C2×#117—21no—
257#500C22×C6112yescomplemented
258#487C22×C6112yescomplemented
259#484—22no—
260#483—21no—
261#479—22no—
262#477—22no—
263#477C22×C6112yescomplemented
264#476C22×C6112yes—
265#475C22×C6112yescomplemented
266#461C22×C6112yes—
267#450—21no—
268C4×SD16—22no—
269#431C22×C6111yescharacteristic
270#431C22×C6111yescharacteristic
271#428—21no—
272#423C22×C6111yescharacteristic
273#419—21no—
274#332C22×C6114yescomplemented
275Q8⋊C8C22×C6114yescomplemented
276D4⋊C8C22×C6114yes—
277C61#1876311yescharacteristic, direct product factor, Sylow
278C22×Q8—21no—
279C22×Q8D4×C6111yescharacteristic
280C22×D4D4×C6111yescharacteristic
281C23×C4—21no—
282C2×SD16—22no—
283C2×M16—21no—
284C4⋊Q8—21no—
285C4⋊Q8—21no—
286C4⋊Q8D4×C6112yes—
287C4⋊Q8C23×C6111yescharacteristic
288C4⋊Q8C23×C6111yescharacteristic
289C4⋊Q8C23×C6112yes—
290#126—28no—
291#126—28no—
292#125—21no—
293#124—24no—
294#124—24no—
295C22⋊Q8—24no—
296C22⋊Q8—24no—
297C22⋊Q8—21no—
298C22⋊Q8—21no—
299C4×Q8—24no—
300C4×Q8—24no—
301C4×Q8—21no—
302C4×Q8—21no—
303C4×Q8—21no—
304C4×Q8—21no—
305C4×Q8D4×C6112yes—
306C4×Q8C23×C6112yes—
307C4×D4—21no—
308C4×D4—21no—
309C4×D4D4×C6112yes—
310C4×D4C23×C6112yes—
311#117—24no—
312#117—24no—
313#117—21no—
314C2×C4⋊C4—22no—
315C2×C4⋊C4—21no—
316C2×C4⋊C4—21no—
317C2×C4⋊C4D4×C6111yescharacteristic
318C2×C4⋊C4D4×C6111yescharacteristic
319C2×C4⋊C4D4×C6112yes—
320C2×C22⋊C4—22no—
321C2×C22⋊C4—22no—
322C2×C22⋊C4—21no—
323C2×C42—22no—
324C2×C42—21no—
325C2×C42C23×C6111yescharacteristic
326#107—22no—
327#107—24no—
328#106—22no—
329#106—22no—
330C4⋊C8—21no—
331C4⋊C8—21no—
332C4⋊C8C23×C6112yes—
333C4⋊C8C23×C6112yes—
334#103—22no—
335#103—22no—
336#103—22no—
337#103—24no—
338#102—22no—
339C22⋊C8—21no—
340C22⋊C8—21no—
341C4×C8—21no—
342C4×C8C23×C6112yes—
343C24—21no—
344C2×Q8—21no—
345C2×Q8—22no—
346C2×Q8—22no—
347C2×Q8—22no—
348C2×Q8—22no—
349C2×Q8—21no—
350C2×Q8—21no—
351C2×Q8—44no—
352C2×Q8C2×D4×C6112yes—
353C2×D4—21no—
354C2×D4—42no—
355C2×D4C2×D4×C6112yes—
356C22×C4—21no—
357C22×C4—21no—
358C22×C4—21no—
359C22×C4—22no—
360C22×C4—22no—
361C22×C4—22no—
362C22×C4—42no—
363C22×C4—42no—
364C22×C4C2×D4×C6111yescharacteristic
365C22×C4C2×D4×C6111yescharacteristic
366C22×C4C2×D4×C6111yescharacteristic
367SD16—44no—
368M16—42no—
369C2×C8—22no—
370C2×C8—22no—
371C2×C8—22no—
372C4⋊C4—28no—
373C4⋊C4—22no—
374C4⋊C4—22no—
375C4⋊C4—21no—
376C4⋊C4—21no—
377C4⋊C4—22no—
378C4⋊C4—22no—
379C4⋊C4—22no—
380C4⋊C4—21no—
381C4⋊C4—21no—
382C4⋊C4—21no—
383C4⋊C4—21no—
384C4⋊C4—41no—
385C4⋊C4—41no—
386C4⋊C4C2×D4×C6112yes—
387C4⋊C4C2×D4×C6114yes—
388C4⋊C4C2×D4×C6112yes—
389C22⋊C4—28no—
390C22⋊C4—28no—
391C22⋊C4—22no—
392C22⋊C4—22no—
393C22⋊C4—41no—
394C42—28no—
395C42—22no—
396C42—22no—
397C42—41no—
398C42C2×D4×C6111yescharacteristic
399C42C2×D4×C6111yescharacteristic
400C42C2×D4×C6111yescharacteristic
401C42C24×C6111yescharacteristic
402C23—22no—
403C23—42no—
404C23—42no—
405C23—42no—
406C23#120×C6111yescharacteristic
407Q8—22no—
408Q8—22no—
409Q8—44no—
410Q8—42no—
411Q8—44no—
412Q8—42no—
413Q8—42no—
414D4—22no—
415D4—22no—
416D4—42no—
417C2×C4—22no—
418C2×C4—22no—
419C2×C4—22no—
420C2×C4—22no—
421C2×C4—24no—
422C2×C4—41no—
423C2×C4—42no—
424C2×C4—44no—
425C2×C4—42no—
426C2×C4—42no—
427C2×C4—42no—
428C2×C4—42no—
429C2×C4—44no—
430C2×C4—41no—
431C2×C4—41no—
432C2×C4#120×C6111yescharacteristic
433C2×C4#120×C6111yescharacteristic
434C2×C4#120×C6111yescharacteristic
435C2×C4#135×C6112yes—
436C2×C4#137×C6112yes—
437C2×C4C22×D4×C6111yescharacteristic
438C2×C4C22×D4×C6111yescharacteristic
439C2×C4C22×D4×C6111yescharacteristic
440C8—42no—
441C8—42no—
442C8—42no—
443C22—21no—
444C22—21no—
445C22—42no—
446C22—42no—
447C22—42no—
448C22—84no—
449C22C61×#45212yes—
450C22C2×#120×C6111yescharacteristic
451C4—21no—
452C4—21no—
453C4—21no—
454C4—42no—
455C4—42no—
456C4—44no—
457C4—42no—
458C4—81no—
459C4—81no—
460C4C61×#45212yes—
461C4C2×#135×C6111yescharacteristic
462C4C2×#137×C6111yescharacteristic
463C4C61×#57512yes—
464C2—22no—
465C2—82no—
466C2C2×C61×#45211yescharacteristic
467C2C61×#300511yescharacteristic
468C2C61×#302011yescharacteristic
subgroupG/H
center, socleC22×C61C2×#120
commutator, Frattini, cosocleC42C24×C61
prime radicalC22×D4×C61D4
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×#3230C2semidirect
4. C61×#3078C2semidirect
5. C61×#1650C2semidirect
6. C61×#1638C2semidirect
7. C61×#1549C2semidirect
9. C61×#1479C2semidirect
23. C61×#500C22semidirect
24. C61×#487C22semidirect
29. C61×#477C22semidirect
31. C61×#475C22semidirect
40. C61×#332C22semidirect
41. C61×Q8⋊C8C22semidirect
208. #18763C61direct (N × H)
231. #3230C2×C61semidirect
233. #3078C2×C61semidirect
234. #1650C2×C61semidirect
235. #1638C2×C61semidirect
236. #1549C2×C61semidirect
238. #1479C2×C61semidirect
257. #500C22×C61semidirect
258. #487C22×C61semidirect
263. #477C22×C61semidirect
265. #475C22×C61semidirect
274. #332C22×C61semidirect
275. Q8⋊C8C22×C61semidirect
277. C61#18763direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C61×#5562
C61×#32302
C61×#31012
C61×#30782
C61×#16502
C61×#16382
C61×#15492
C61×#14862
C61×#14792
#1876361