Finite Group Databasebeta

← C61×#33917 #29537350

Subgroups — C61×#33917 #29537350

Order 15616.

476 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C61×#3342C211yesmaximal, characteristic, complemented
2C61×#3339C211yesmaximal, characteristic
3C61×#2255C211yesmaximal, characteristic, complemented
4C61×#2237C211yesmaximal, characteristic, complemented
5C61×#2235C211yesmaximal, characteristic, complemented
6C61×#2234C211yesmaximal, characteristic, complemented
7C61×#2234C211yesmaximal, characteristic, complemented
8C61×#2229C211yesmaximal, characteristic, complemented
9C61×#2226C211yesmaximal, characteristic, complemented
10C61×#2220C211yesmaximal, characteristic, complemented
11C61×#2217C211yesmaximal, characteristic, complemented
12C61×#2175C211yesmaximal, characteristic, complemented
13C61×#2168C211yesmaximal, characteristic, complemented
14C61×#2159C211yesmaximal, characteristic, complemented
15C61×#2158C211yesmaximal, characteristic, complemented
16C61×#556—21no—
17C61×#553—21no—
18C2×SD32×C61C2211yescharacteristic
19C2×M32×C61C2211yescharacteristic
20C22×C16×C61C2211yescharacteristic
21C61×#500C2211yescharacteristic
22C61×#499C2211yescharacteristic
23C61×#485—21no—
24C61×#485—21no—
25C61×#482—21no—
26C61×#481—21no—
27C61×#478—21no—
28C61×#475—21no—
29C61×#467C2211yescharacteristic
30C61×#467C2211yescharacteristic
31C61×#466C2211yescharacteristic
32C61×#466C2211yescharacteristic
33C4×Q16×C61C2211yescharacteristic
34C4×D8×C61C2211yescharacteristic
35C8×D4×C61C2211yescharacteristic
36C61×#427C2211yescharacteristic
37C61×#427C2211yescharacteristic
38C61×#427C2211yescharacteristic
39C2×#107×C61C2211yescharacteristic
40C61×#367C2211yescharacteristic
41C61×#367C2211yescharacteristic
42C61×#367C2211yescharacteristic
43C61×#367C2211yescharacteristic
44C61×#367C2211yescharacteristic
45C61×#366C2211yescharacteristic
46C61×#366C2211yescharacteristic
47C61×#366C2211yescharacteristic
48C61×#366C2211yescharacteristic
49C61×C4⋊C16C2211yescharacteristic
50C61×#358C2211yescharacteristic
51C61×#358C2211yescharacteristic
52C61×#358C2211yescharacteristic
53C61×#357C2211yescharacteristic
54C61×#357C2211yescharacteristic
55C61×#357C2211yescharacteristic
56C61×C22⋊C16C2211yescharacteristic
57C61×C22⋊C16C2211yescharacteristic
58C61×#346C2211yescharacteristic
59C2×Q16×C61C2311yescharacteristic
60C2×D8×C61C2311yescharacteristic
61C22×C8×C61C2311yescharacteristic
62C22×C8×C61C2311yescharacteristic
63C4⋊Q8×C61—21no—
64#126×C61—41no—
65#126×C61—41no—
66#126×C61—41no—
67#125×C61—21no—
68#124×C61—41no—
69#123×C61—41no—
70C22⋊Q8×C61—21no—
71C22⋊Q8×C61—21no—
72#121×C61—21no—
73#121×C61—21no—
74#121×C61—41no—
75C4×Q8×C61—21no—
76C4×Q8×C61—41no—
77C4×D4×C61—21no—
78C4×D4×C61—41no—
79C4×D4×C61D411yescharacteristic
80#117×C61—21no—
81#117×C61—21no—
82#117×C61—21no—
83C2×C4⋊C4×C61—21no—
84SD32×C61—22no—
85M32×C61—22no—
86C2×C16×C61—22no—
87C2×C16×C61C2311yescharacteristic
88C2×C16×C61C2311yescharacteristic
89C2×C16×C61C2311yescharacteristic
90C2×C16×C61C2311yescharacteristic
91#107×C61—21no—
92#107×C61—21no—
93#107×C61C2311yescharacteristic
94#107×C61C2311yescharacteristic
95#107×C61C2311yescharacteristic
96#107×C61C2311yescharacteristic
97#107×C61C2311yescharacteristic
98#107×C61C2311yescharacteristic
99#106×C61—21no—
100#106×C61—21no—
101#106×C61—21no—
102#106×C61—21no—
103C4⋊C8×C61D411yescharacteristic
104#103×C61—21no—
105#103×C61—21no—
106#103×C61—21no—
107#102×C61—21no—
108#102×C61—21no—
109#102×C61—21no—
110C22⋊C8×C61D411yescharacteristic
111C22⋊C8×C61D411yescharacteristic
112C4×C8×C61C2311yescharacteristic
113C2×Q8×C61—21no—
114C2×Q8×C61—41no—
115C2×D4×C61—21no—
116C2×D4×C61—41no—
117C2×D4×C61—41no—
118C2×D4×C61D811yescharacteristic
119C22×C4×C61—41no—
120C22×C4×C61—41no—
121C22×C4×C61C2×D411yescharacteristic
122C22×C4×C61C2×D411yescharacteristic
123Q16×C61—21no—
124Q16×C61—21no—
125D8×C61—21no—
126D8×C61—21no—
127C2×C8×C61—21no—
128C2×C8×C61—21no—
129C2×C8×C61—21no—
130C2×C8×C61—21no—
131C2×C8×C61C2×D411yescharacteristic
132C2×C8×C61C2×D411yescharacteristic
133C2×C8×C61C2×D411yescharacteristic
134C2×C8×C61C2411yescharacteristic
135C4⋊C4×C61—21no—
136C4⋊C4×C61—21no—
137C4⋊C4×C61—21no—
138C4⋊C4×C61—21no—
139C4⋊C4×C61—21no—
140C4⋊C4×C61—21no—
141C4⋊C4×C61—41no—
142C4⋊C4×C61—41no—
143C4⋊C4×C61—41no—
144C4⋊C4×C61—41no—
145C4⋊C4×C61—41no—
146C4⋊C4×C61—41no—
147C4⋊C4×C61—41no—
148C4⋊C4×C61D811yescharacteristic
149C22⋊C4×C61—41no—
150C22⋊C4×C61—41no—
151C22⋊C4×C61—41no—
152C22⋊C4×C61—41no—
153C22⋊C4×C61—41no—
154C22⋊C4×C61—41no—
155C22⋊C4×C61—41no—
156C22⋊C4×C61—41no—
157C22⋊C4×C61D811yescharacteristic
158C22⋊C4×C61D811yescharacteristic
159C42×C61—41no—
160C42×C61—41no—
161C42×C61—41no—
162C42×C61—41no—
163C42×C61C2×D411yescharacteristic
164C16×C61—21no—
165C16×C61—21no—
166C16×C61—21no—
167C16×C61#4112yes—
168C23×C61—41no—
169C23×C61C2×D811yescharacteristic
170C23×C61C2×D811yescharacteristic
171Q8×C61—41no—
172Q8×C61—41no—
173Q8×C61—82no—
174D4×C61—41no—
175D4×C61—41no—
176D4×C61—41no—
177D4×C61—82no—
178D4×C61—161no—
179C2×C4×C61—21no—
180C2×C4×C61—21no—
181C2×C4×C61—21no—
182C2×C4×C61—21no—
183C2×C4×C61—41no—
184C2×C4×C61—41no—
185C2×C4×C61—41no—
186C2×C4×C61—41no—
187C2×C4×C61—41no—
188C2×C4×C61—41no—
189C2×C4×C61—41no—
190C2×C4×C61—161no—
191C2×C4×C61—161no—
192C2×C4×C61C2×D811yescharacteristic
193C2×C4×C61C2×D811yescharacteristic
194C2×C4×C61C2×D811yescharacteristic
195C2×C4×C61C2×D811yescharacteristic
196C2×C4×C61C22×D411yescharacteristic
197C8×C61—21no—
198C8×C61—21no—
199C8×C61—21no—
200C8×C61C2×#4111yescharacteristic
201C8×C612−1+411yescharacteristic
202#33917C6111yesmaximal, characteristic, direct product factor, Sylow
203C22×C61—21no—
204C22×C61—21no—
205C22×C61—21no—
206C22×C61—21no—
207C22×C61—21no—
208C22×C61—21no—
209C22×C61—81no—
210C22×C61—81no—
211C22×C61—81no—
212C22×C61C22×D811yescharacteristic
213C4×C61—21no—
214C4×C61—21no—
215C4×C61—21no—
216C4×C61—21no—
217C4×C61—81no—
218C4×C61—81no—
219C4×C61—81no—
220C4×C61—81no—
221C4×C61—81no—
222C4×C61—81no—
223C4×C61—81no—
224C4×C61#54711yescharacteristic
225C4×C61#57811yescharacteristic
226#3342C2×C6111yescharacteristic, complemented
227#3339C2×C6111yescharacteristic
228#2255C2×C6111yescharacteristic, complemented
229#2237C2×C6111yescharacteristic, complemented
230#2235C2×C6111yescharacteristic, complemented
231#2234C2×C6111yescharacteristic, complemented
232#2234C2×C6111yescharacteristic, complemented
233#2229C2×C6111yescharacteristic, complemented
234#2226C2×C6111yescharacteristic, complemented
235#2220C2×C6111yescharacteristic, complemented
236#2217C2×C6111yescharacteristic, complemented
237#2175C2×C6111yescharacteristic, complemented
238#2168C2×C6111yescharacteristic, complemented
239#2159C2×C6111yescharacteristic, complemented
240#2158C2×C6111yescharacteristic, complemented
241C2×C61—41no—
242C2×C61—41no—
243C2×C61—161no—
244C2×C61#333411yescharacteristic
245C2×C61#341411yescharacteristic
246C2×C61#341611yescharacteristic
247#556—21no—
248#553—21no—
249C2×SD32C22×C6111yescharacteristic
250C2×M32C22×C6111yescharacteristic
251C22×C16C22×C6111yescharacteristic
252#500C22×C6111yescharacteristic
253#499C22×C6111yescharacteristic
254#485—21no—
255#485—21no—
256#482—21no—
257#481—21no—
258#478—21no—
259#475—21no—
260#467C22×C6111yescharacteristic
261#467C22×C6111yescharacteristic
262#466C22×C6111yescharacteristic
263#466C22×C6111yescharacteristic
264C4×Q16C22×C6111yescharacteristic
265C4×D8C22×C6111yescharacteristic
266C8×D4C22×C6111yescharacteristic
267#427C22×C6111yescharacteristic
268#427C22×C6111yescharacteristic
269#427C22×C6111yescharacteristic
270C2×#107C22×C6111yescharacteristic
271#367C22×C6111yescharacteristic
272#367C22×C6111yescharacteristic
273#367C22×C6111yescharacteristic
274#367C22×C6111yescharacteristic
275#367C22×C6111yescharacteristic
276#366C22×C6111yescharacteristic
277#366C22×C6111yescharacteristic
278#366C22×C6111yescharacteristic
279#366C22×C6111yescharacteristic
280C4⋊C16C22×C6111yescharacteristic
281#358C22×C6111yescharacteristic
282#358C22×C6111yescharacteristic
283#358C22×C6111yescharacteristic
284#357C22×C6111yescharacteristic
285#357C22×C6111yescharacteristic
286#357C22×C6111yescharacteristic
287C22⋊C16C22×C6111yescharacteristic
288C22⋊C16C22×C6111yescharacteristic
289#346C22×C6111yescharacteristic
290C61#3391711yescharacteristic, direct product factor, Sylow
291C2×Q16C23×C6111yescharacteristic
292C2×D8C23×C6111yescharacteristic
293C22×C8C23×C6111yescharacteristic
294C22×C8C23×C6111yescharacteristic
295C4⋊Q8—21no—
296#126—41no—
297#126—41no—
298#126—41no—
299#125—21no—
300#124—41no—
301#123—41no—
302C22⋊Q8—21no—
303C22⋊Q8—21no—
304#121—21no—
305#121—21no—
306#121—41no—
307C4×Q8—21no—
308C4×Q8—41no—
309C4×D4—21no—
310C4×D4—41no—
311C4×D4D4×C6111yescharacteristic
312#117—21no—
313#117—21no—
314#117—21no—
315C2×C4⋊C4—21no—
316SD32—22no—
317M32—22no—
318C2×C16—22no—
319C2×C16C23×C6111yescharacteristic
320C2×C16C23×C6111yescharacteristic
321C2×C16C23×C6111yescharacteristic
322C2×C16C23×C6111yescharacteristic
323#107—21no—
324#107—21no—
325#107C23×C6111yescharacteristic
326#107C23×C6111yescharacteristic
327#107C23×C6111yescharacteristic
328#107C23×C6111yescharacteristic
329#107C23×C6111yescharacteristic
330#107C23×C6111yescharacteristic
331#106—21no—
332#106—21no—
333#106—21no—
334#106—21no—
335C4⋊C8D4×C6111yescharacteristic
336#103—21no—
337#103—21no—
338#103—21no—
339#102—21no—
340#102—21no—
341#102—21no—
342C22⋊C8D4×C6111yescharacteristic
343C22⋊C8D4×C6111yescharacteristic
344C4×C8C23×C6111yescharacteristic
345C2×Q8—21no—
346C2×Q8—41no—
347C2×D4—21no—
348C2×D4—41no—
349C2×D4—41no—
350C2×D4D8×C6111yescharacteristic
351C22×C4—41no—
352C22×C4—41no—
353C22×C4C2×D4×C6111yescharacteristic
354C22×C4C2×D4×C6111yescharacteristic
355Q16—21no—
356Q16—21no—
357D8—21no—
358D8—21no—
359C2×C8—21no—
360C2×C8—21no—
361C2×C8—21no—
362C2×C8—21no—
363C2×C8C2×D4×C6111yescharacteristic
364C2×C8C2×D4×C6111yescharacteristic
365C2×C8C2×D4×C6111yescharacteristic
366C2×C8C24×C6111yescharacteristic
367C4⋊C4—21no—
368C4⋊C4—21no—
369C4⋊C4—21no—
370C4⋊C4—21no—
371C4⋊C4—21no—
372C4⋊C4—21no—
373C4⋊C4—41no—
374C4⋊C4—41no—
375C4⋊C4—41no—
376C4⋊C4—41no—
377C4⋊C4—41no—
378C4⋊C4—41no—
379C4⋊C4—41no—
380C4⋊C4D8×C6111yescharacteristic
381C22⋊C4—41no—
382C22⋊C4—41no—
383C22⋊C4—41no—
384C22⋊C4—41no—
385C22⋊C4—41no—
386C22⋊C4—41no—
387C22⋊C4—41no—
388C22⋊C4—41no—
389C22⋊C4D8×C6111yescharacteristic
390C22⋊C4D8×C6111yescharacteristic
391C42—41no—
392C42—41no—
393C42—41no—
394C42—41no—
395C42C2×D4×C6111yescharacteristic
396C16—21no—
397C16—21no—
398C16—21no—
399C16#41×C6112yes—
400C23—41no—
401C23C2×D8×C6111yescharacteristic
402C23C2×D8×C6111yescharacteristic
403Q8—41no—
404Q8—41no—
405Q8—82no—
406D4—41no—
407D4—41no—
408D4—41no—
409D4—82no—
410D4—161no—
411C2×C4—21no—
412C2×C4—21no—
413C2×C4—21no—
414C2×C4—21no—
415C2×C4—41no—
416C2×C4—41no—
417C2×C4—41no—
418C2×C4—41no—
419C2×C4—41no—
420C2×C4—41no—
421C2×C4—41no—
422C2×C4—161no—
423C2×C4—161no—
424C2×C4C2×D8×C6111yescharacteristic
425C2×C4C2×D8×C6111yescharacteristic
426C2×C4C2×D8×C6111yescharacteristic
427C2×C4C2×D8×C6111yescharacteristic
428C2×C4C22×D4×C6111yescharacteristic
429C8—21no—
430C8—21no—
431C8—21no—
432C8C2×#41×C6111yescharacteristic
433C82−1+4×C6111yescharacteristic
434C22—21no—
435C22—21no—
436C22—21no—
437C22—21no—
438C22—21no—
439C22—21no—
440C22—81no—
441C22—81no—
442C22—81no—
443C22C22×D8×C6111yescharacteristic
444C4—21no—
445C4—21no—
446C4—21no—
447C4—21no—
448C4—81no—
449C4—81no—
450C4—81no—
451C4—81no—
452C4—81no—
453C4—81no—
454C4—81no—
455C4C61×#54711yescharacteristic
456C4C61×#57811yescharacteristic
457C2—41no—
458C2—41no—
459C2—161no—
460C2C61×#333411yescharacteristic
461C2C61×#341411yescharacteristic
462C2C61×#341611yescharacteristic
subgroupG/H
center, socleC22×C61C22×D8
commutator, Frattini, cosocleC2×C8C24×C61
prime radicalC61×#3339C2
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C61 ◁ C4×D4×C61 ◁ C8×D4×C61 ◁ G

Complements

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

NH ≅ G/Ntype
1. C61×#3342C2semidirect
3. C61×#2255C2semidirect
4. C61×#2237C2semidirect
5. C61×#2235C2semidirect
6. C61×#2234C2semidirect
7. C61×#2234C2semidirect
8. C61×#2229C2semidirect
9. C61×#2226C2semidirect
10. C61×#2220C2semidirect
11. C61×#2217C2semidirect
12. C61×#2175C2semidirect
13. C61×#2168C2semidirect
14. C61×#2159C2semidirect
15. C61×#2158C2semidirect
202. #33917C61direct (N × H)
226. #3342C2×C61semidirect
228. #2255C2×C61semidirect
229. #2237C2×C61semidirect
230. #2235C2×C61semidirect
231. #2234C2×C61semidirect
232. #2234C2×C61semidirect
233. #2229C2×C61semidirect
234. #2226C2×C61semidirect
235. #2220C2×C61semidirect
236. #2217C2×C61semidirect
237. #2175C2×C61semidirect
238. #2168C2×C61semidirect
239. #2159C2×C61semidirect
240. #2158C2×C61semidirect
290. C61#33917direct (N × H)

Maximal subgroups

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

subgroupindex
C61×#33422
C61×#33392
C61×#22552
C61×#22372
C61×#22352
C61×#22342
C61×#22292
C61×#22262
C61×#22202
C61×#22172
C61×#21752
C61×#21682
C61×#21592
C61×#21582
#3391761