Finite Group Databasebeta

← C61×#33938 #29537371

Subgroups — C61×#33938 #29537371

Order 15616.

480 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×#3396C211yesmaximal, characteristic
2C61×#3383C211yesmaximal, characteristic, complemented
3C61×#2244C211yesmaximal, characteristic
4C61×#2243C211yesmaximal, characteristic, complemented
5C61×#2242C211yesmaximal, characteristic, complemented
6C61×#2229C211yesmaximal, characteristic, complemented
7C61×#2228C211yesmaximal, characteristic, complemented
8C61×#2226C211yesmaximal, characteristic, complemented
9C61×#2211C211yesmaximal, characteristic, complemented
10C61×#2211C211yesmaximal, characteristic, complemented
11C61×#2207C211yesmaximal, characteristic
12C61×#2183C211yesmaximal, characteristic, complemented
13C61×#2176C211yesmaximal, characteristic, complemented
14C61×#2175C211yesmaximal, characteristic, complemented
15C4×SD32×C61C211yesmaximal, characteristic, complemented
16C61×#559—21no—
17C61×#557—21no—
18C2×Q32×C61C2211yescharacteristic
19C2×SD32×C61C2211yescharacteristic
20C2×SD32×C61C2211yescharacteristic
21C61×#500C2211yescharacteristic
22C61×#499C2211yescharacteristic
23C61×#499C2211yescharacteristic
24C61×#495C2211yescharacteristic
25C61×#495C2211yescharacteristic
26C61×#493C2211yescharacteristic
27C61×#479—21no—
28C61×#479—21no—
29C61×#475—21no—
30C61×#463—21no—
31C61×#463—21no—
32C61×#460—21no—
33C8×Q8×C61C2211yescharacteristic
34C4×Q16×C61C2211yescharacteristic
35C4×Q16×C61C2211yescharacteristic
36C4×Q16×C61C2211yescharacteristic
37C4×Q16×C61C2211yescharacteristic
38C4×D8×C61C2211yescharacteristic
39C4×D8×C61C2211yescharacteristic
40C61×#367C2211yescharacteristic
41C61×#367C2211yescharacteristic
42C61×#366C2211yescharacteristic
43C61×C4⋊C16C2211yescharacteristic
44C61×C4⋊C16C2211yescharacteristic
45C61×C4⋊C16C2211yescharacteristic
46C61×#358C2211yescharacteristic
47C61×#358C2211yescharacteristic
48C61×#358C2211yescharacteristic
49C61×#358C2211yescharacteristic
50C61×#357C2211yescharacteristic
51C61×#357C2211yescharacteristic
52C61×#357C2211yescharacteristic
53C61×#357C2211yescharacteristic
54C61×#357C2211yescharacteristic
55C61×#357C2211yescharacteristic
56C61×#346C2211yescharacteristic
57C61×#346C2211yescharacteristic
58C4×C16×C61C2211yescharacteristic
59C2×Q16×C61C2311yescharacteristic
60C2×Q16×C61C2311yescharacteristic
61C2×SD16×C61—21no—
62C2×SD16×C61—21no—
63C2×D8×C61—21no—
64C2×D8×C61C2311yescharacteristic
65C2×D8×C61C2311yescharacteristic
66C4⋊Q8×C61—21no—
67C4⋊Q8×C61—41no—
68#127×C61—21no—
69#125×C61—21no—
70#125×C61—21no—
71#125×C61—41no—
72#125×C61—41no—
73#124×C61—21no—
74#124×C61—21no—
75#124×C61—41no—
76#123×C61—41no—
77#123×C61—41no—
78C4×Q8×C61—21no—
79C4×Q8×C61—21no—
80C4×Q8×C61—21no—
81C4×Q8×C61—21no—
82C4×Q8×C61—41no—
83C4×Q8×C61D411yescharacteristic
84C4×D4×C61—21no—
85C4×D4×C61—21no—
86C4×D4×C61—41no—
87Q32×C61—22no—
88SD32×C61—22no—
89SD32×C61—22no—
90C2×C16×C61C2311yescharacteristic
91C2×C16×C61C2311yescharacteristic
92C2×C16×C61C2311yescharacteristic
93C2×C16×C61C2311yescharacteristic
94#107×C61—21no—
95#107×C61C2311yescharacteristic
96#107×C61C2311yescharacteristic
97#107×C61C2311yescharacteristic
98#107×C61C2311yescharacteristic
99#106×C61—21no—
100#106×C61—21no—
101C4⋊C8×C61D411yescharacteristic
102C4⋊C8×C61D411yescharacteristic
103C4⋊C8×C61D411yescharacteristic
104#103×C61—21no—
105#103×C61—21no—
106#103×C61—21no—
107#103×C61—21no—
108#102×C61—21no—
109#102×C61—21no—
110C4×C8×C61C2311yescharacteristic
111C4×C8×C61C2311yescharacteristic
112C4×C8×C61C2311yescharacteristic
113C2×Q8×C61—21no—
114C2×Q8×C61—21no—
115C2×Q8×C61—41no—
116C2×Q8×C61D811yescharacteristic
117C2×D4×C61—21no—
118C2×D4×C61—21no—
119C2×D4×C61—41no—
120C2×D4×C61—41no—
121C22×C4×C61—41no—
122C22×C4×C61—41no—
123Q16×C61—21no—
124Q16×C61—21no—
125Q16×C61—21no—
126Q16×C61#4112yes—
127SD16×C61—81no—
128SD16×C61—81no—
129D8×C61—21no—
130D8×C61—21no—
131D8×C61—21no—
132D8×C61—21no—
133D8×C61—81no—
134C2×C8×C61C2×D411yescharacteristic
135C2×C8×C61C2×D411yescharacteristic
136C2×C8×C61C2×D411yescharacteristic
137C2×C8×C61C2411yescharacteristic
138C4⋊C4×C61—21no—
139C4⋊C4×C61—21no—
140C4⋊C4×C61—21no—
141C4⋊C4×C61—21no—
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×C61—41no—
149C4⋊C4×C61—41no—
150C4⋊C4×C61—41no—
151C4⋊C4×C61D811yescharacteristic
152C4⋊C4×C61D811yescharacteristic
153C4⋊C4×C61D811yescharacteristic
154C22⋊C4×C61—41no—
155C22⋊C4×C61—41no—
156C22⋊C4×C61—41no—
157C22⋊C4×C61—41no—
158C22⋊C4×C61—41no—
159C22⋊C4×C61—41no—
160C42×C61—41no—
161C42×C61—41no—
162C42×C61—41no—
163C42×C61—41no—
164C42×C61C2×D411yescharacteristic
165C42×C61C2×D411yescharacteristic
166C42×C61C2×D411yescharacteristic
167C16×C61—21no—
168C16×C61—21no—
169C16×C61—21no—
170C16×C61—21no—
171C23×C61—41no—
172C23×C61—41no—
173Q8×C61—22no—
174Q8×C61—41no—
175Q8×C61—41no—
176Q8×C61—41no—
177Q8×C61—41no—
178Q8×C61—82no—
179D4×C61—41no—
180D4×C61—41no—
181D4×C61—41no—
182D4×C61—41no—
183D4×C61—82no—
184D4×C61—161no—
185C2×C4×C61—41no—
186C2×C4×C61—41no—
187C2×C4×C61—41no—
188C2×C4×C61—41no—
189C2×C4×C61—41no—
190C2×C4×C61—41no—
191C2×C4×C61—161no—
192C2×C4×C61—161no—
193C2×C4×C61C2×D811yescharacteristic
194C2×C4×C61C2×D811yescharacteristic
195C2×C4×C61C2×D811yescharacteristic
196C2×C4×C61C2×D811yescharacteristic
197C2×C4×C61C2×D811yescharacteristic
198C2×C4×C61C2×D811yescharacteristic
199C2×C4×C61C22×D411yescharacteristic
200C8×C61—21no—
201C8×C61—21no—
202C8×C61—21no—
203C8×C61C2×#4111yescharacteristic
204C8×C612−1+411yescharacteristic
205#33938C6111yesmaximal, characteristic, direct product factor, Sylow
206C22×C61—81no—
207C22×C61—81no—
208C22×C61—81no—
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—21no—
218C4×C61—21no—
219C4×C61—42no—
220C4×C61—81no—
221C4×C61—81no—
222C4×C61—81no—
223C4×C61—81no—
224C4×C61—81no—
225C4×C61#54811yescharacteristic
226C4×C61#57711yescharacteristic
227#3396C2×C6111yescharacteristic
228#3383C2×C6111yescharacteristic, complemented
229#2244C2×C6111yescharacteristic
230#2243C2×C6111yescharacteristic, complemented
231#2242C2×C6111yescharacteristic, complemented
232#2229C2×C6111yescharacteristic, complemented
233#2228C2×C6111yescharacteristic, complemented
234#2226C2×C6111yescharacteristic, complemented
235#2211C2×C6111yescharacteristic, complemented
236#2211C2×C6111yescharacteristic, complemented
237#2207C2×C6111yescharacteristic
238#2183C2×C6111yescharacteristic, complemented
239#2176C2×C6111yescharacteristic, complemented
240#2175C2×C6111yescharacteristic, complemented
241C4×SD32C2×C6111yescharacteristic, complemented
242C2×C61—161no—
243C2×C61—161no—
244C2×C61#335811yescharacteristic
245C2×C61#341411yescharacteristic
246C2×C61#341611yescharacteristic
247#559—21no—
248#557—21no—
249C2×Q32C22×C6111yescharacteristic
250C2×SD32C22×C6111yescharacteristic
251C2×SD32C22×C6111yescharacteristic
252#500C22×C6111yescharacteristic
253#499C22×C6111yescharacteristic
254#499C22×C6111yescharacteristic
255#495C22×C6111yescharacteristic
256#495C22×C6111yescharacteristic
257#493C22×C6111yescharacteristic
258#479—21no—
259#479—21no—
260#475—21no—
261#463—21no—
262#463—21no—
263#460—21no—
264C8×Q8C22×C6111yescharacteristic
265C4×Q16C22×C6111yescharacteristic
266C4×Q16C22×C6111yescharacteristic
267C4×Q16C22×C6111yescharacteristic
268C4×Q16C22×C6111yescharacteristic
269C4×D8C22×C6111yescharacteristic
270C4×D8C22×C6111yescharacteristic
271#367C22×C6111yescharacteristic
272#367C22×C6111yescharacteristic
273#366C22×C6111yescharacteristic
274C4⋊C16C22×C6111yescharacteristic
275C4⋊C16C22×C6111yescharacteristic
276C4⋊C16C22×C6111yescharacteristic
277#358C22×C6111yescharacteristic
278#358C22×C6111yescharacteristic
279#358C22×C6111yescharacteristic
280#358C22×C6111yescharacteristic
281#357C22×C6111yescharacteristic
282#357C22×C6111yescharacteristic
283#357C22×C6111yescharacteristic
284#357C22×C6111yescharacteristic
285#357C22×C6111yescharacteristic
286#357C22×C6111yescharacteristic
287#346C22×C6111yescharacteristic
288#346C22×C6111yescharacteristic
289C4×C16C22×C6111yescharacteristic
290C61#3393811yescharacteristic, direct product factor, Sylow
291C2×Q16C23×C6111yescharacteristic
292C2×Q16C23×C6111yescharacteristic
293C2×SD16—21no—
294C2×SD16—21no—
295C2×D8—21no—
296C2×D8C23×C6111yescharacteristic
297C2×D8C23×C6111yescharacteristic
298C4⋊Q8—21no—
299C4⋊Q8—41no—
300#127—21no—
301#125—21no—
302#125—21no—
303#125—41no—
304#125—41no—
305#124—21no—
306#124—21no—
307#124—41no—
308#123—41no—
309#123—41no—
310C4×Q8—21no—
311C4×Q8—21no—
312C4×Q8—21no—
313C4×Q8—21no—
314C4×Q8—41no—
315C4×Q8D4×C6111yescharacteristic
316C4×D4—21no—
317C4×D4—21no—
318C4×D4—41no—
319Q32—22no—
320SD32—22no—
321SD32—22no—
322C2×C16C23×C6111yescharacteristic
323C2×C16C23×C6111yescharacteristic
324C2×C16C23×C6111yescharacteristic
325C2×C16C23×C6111yescharacteristic
326#107—21no—
327#107C23×C6111yescharacteristic
328#107C23×C6111yescharacteristic
329#107C23×C6111yescharacteristic
330#107C23×C6111yescharacteristic
331#106—21no—
332#106—21no—
333C4⋊C8D4×C6111yescharacteristic
334C4⋊C8D4×C6111yescharacteristic
335C4⋊C8D4×C6111yescharacteristic
336#103—21no—
337#103—21no—
338#103—21no—
339#103—21no—
340#102—21no—
341#102—21no—
342C4×C8C23×C6111yescharacteristic
343C4×C8C23×C6111yescharacteristic
344C4×C8C23×C6111yescharacteristic
345C2×Q8—21no—
346C2×Q8—21no—
347C2×Q8—41no—
348C2×Q8D8×C6111yescharacteristic
349C2×D4—21no—
350C2×D4—21no—
351C2×D4—41no—
352C2×D4—41no—
353C22×C4—41no—
354C22×C4—41no—
355Q16—21no—
356Q16—21no—
357Q16—21no—
358Q16#41×C6112yes—
359SD16—81no—
360SD16—81no—
361D8—21no—
362D8—21no—
363D8—21no—
364D8—21no—
365D8—81no—
366C2×C8C2×D4×C6111yescharacteristic
367C2×C8C2×D4×C6111yescharacteristic
368C2×C8C2×D4×C6111yescharacteristic
369C2×C8C24×C6111yescharacteristic
370C4⋊C4—21no—
371C4⋊C4—21no—
372C4⋊C4—21no—
373C4⋊C4—21no—
374C4⋊C4—41no—
375C4⋊C4—41no—
376C4⋊C4—41no—
377C4⋊C4—41no—
378C4⋊C4—41no—
379C4⋊C4—41no—
380C4⋊C4—41no—
381C4⋊C4—41no—
382C4⋊C4—41no—
383C4⋊C4D8×C6111yescharacteristic
384C4⋊C4D8×C6111yescharacteristic
385C4⋊C4D8×C6111yescharacteristic
386C22⋊C4—41no—
387C22⋊C4—41no—
388C22⋊C4—41no—
389C22⋊C4—41no—
390C22⋊C4—41no—
391C22⋊C4—41no—
392C42—41no—
393C42—41no—
394C42—41no—
395C42—41no—
396C42C2×D4×C6111yescharacteristic
397C42C2×D4×C6111yescharacteristic
398C42C2×D4×C6111yescharacteristic
399C16—21no—
400C16—21no—
401C16—21no—
402C16—21no—
403C23—41no—
404C23—41no—
405Q8—22no—
406Q8—41no—
407Q8—41no—
408Q8—41no—
409Q8—41no—
410Q8—82no—
411D4—41no—
412D4—41no—
413D4—41no—
414D4—41no—
415D4—82no—
416D4—161no—
417C2×C4—41no—
418C2×C4—41no—
419C2×C4—41no—
420C2×C4—41no—
421C2×C4—41no—
422C2×C4—41no—
423C2×C4—161no—
424C2×C4—161no—
425C2×C4C2×D8×C6111yescharacteristic
426C2×C4C2×D8×C6111yescharacteristic
427C2×C4C2×D8×C6111yescharacteristic
428C2×C4C2×D8×C6111yescharacteristic
429C2×C4C2×D8×C6111yescharacteristic
430C2×C4C2×D8×C6111yescharacteristic
431C2×C4C22×D4×C6111yescharacteristic
432C8—21no—
433C8—21no—
434C8—21no—
435C8C2×#41×C6111yescharacteristic
436C82−1+4×C6111yescharacteristic
437C22—81no—
438C22—81no—
439C22—81no—
440C22—81no—
441C22—81no—
442C22—81no—
443C22C22×D8×C6111yescharacteristic
444C4—21no—
445C4—21no—
446C4—21no—
447C4—21no—
448C4—21no—
449C4—21no—
450C4—42no—
451C4—81no—
452C4—81no—
453C4—81no—
454C4—81no—
455C4—81no—
456C4C61×#54811yescharacteristic
457C4C61×#57711yescharacteristic
458C2—161no—
459C2—161no—
460C2C61×#335811yescharacteristic
461C2C61×#341411yescharacteristic
462C2C61×#341611yescharacteristic
subgroupG/H
center, socleC22×C61C22×D8
commutator, Frattini, cosocleC2×C8C24×C61
prime radicalC61×#493C22
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C61 ◁ C4×Q8×C61 ◁ C8×Q8×C61 ◁ G

Complements

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

NH ≅ G/Ntype
2. C61×#3383C2semidirect
4. C61×#2243C2semidirect
5. C61×#2242C2semidirect
6. C61×#2229C2semidirect
7. C61×#2228C2semidirect
8. C61×#2226C2semidirect
9. C61×#2211C2semidirect
10. C61×#2211C2semidirect
12. C61×#2183C2semidirect
13. C61×#2176C2semidirect
14. C61×#2175C2semidirect
15. C4×SD32×C61C2semidirect
205. #33938C61direct (N × H)
228. #3383C2×C61semidirect
230. #2243C2×C61semidirect
231. #2242C2×C61semidirect
232. #2229C2×C61semidirect
233. #2228C2×C61semidirect
234. #2226C2×C61semidirect
235. #2211C2×C61semidirect
236. #2211C2×C61semidirect
238. #2183C2×C61semidirect
239. #2176C2×C61semidirect
240. #2175C2×C61semidirect
241. C4×SD32C2×C61semidirect
290. C61#33938direct (N × H)

Maximal subgroups

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

subgroupindex
C61×#33962
C61×#33832
C61×#22442
C61×#22432
C61×#22422
C61×#22292
C61×#22282
C61×#22262
C61×#22112
C61×#22072
C61×#21832
C61×#21762
C61×#21752
C4×SD32×C612
#3393861