Finite Group Databasebeta

← C61×#33745 #29537178

Subgroups — C61×#33745 #29537178

Order 15616.

496 conjugacy classes of subgroups.

The subgroup lattice has 472 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C61×#3177C211yesmaximal, characteristic, complemented
2C61×#3175C211yesmaximal, characteristic
3C61×#2255C211yesmaximal, characteristic, complemented
4C61×#2251C211yesmaximal, characteristic, complemented
5C61×#2242C211yesmaximal, characteristic, complemented
6C61×#2241C211yesmaximal, characteristic, complemented
7C61×#2220C211yesmaximal, characteristic
8C61×#2219C211yesmaximal, characteristic, complemented
9C61×#2217C211yesmaximal, characteristic
10C61×#2216C211yesmaximal, characteristic, complemented
11C61×#2176C211yesmaximal, characteristic, complemented
12C61×#2175C211yesmaximal, characteristic, complemented
13C4×Q32×C61C211yesmaximal, characteristic, complemented
14C4×SD32×C61C211yesmaximal, characteristic, complemented
15C61×#2108C211yesmaximal, characteristic, complemented
16C61×#542—21no—
17C61×#541—21no—
18C2×Q32×C61C2211yescharacteristic
19C2×Q32×C61C2211yescharacteristic
20C2×SD32×C61C2211yescharacteristic
21C2×SD32×C61C2211yescharacteristic
22C2×M32×C61C2211yescharacteristic
23C22×C16×C61C2211yescharacteristic
24C61×#500C2211yescharacteristic
25C61×#499C2211yescharacteristic
26C61×#495C2211yescharacteristic
27C61×#494C2211yescharacteristic
28C61×#491—21no—
29C61×#489—21no—
30C61×#470—21no—
31C61×#468—21no—
32C61×#467C2211yescharacteristic
33C61×#467C2211yescharacteristic
34C61×#467C2211yescharacteristic
35C61×#466C2211yescharacteristic
36C61×#441—21no—
37C61×#440—21no—
38C4×Q16×C61C2211yescharacteristic
39C4×Q16×C61C2211yescharacteristic
40C4×Q16×C61C2211yescharacteristic
41C4×D8×C61C2211yescharacteristic
42C61×#405C2211yescharacteristic
43C61×#367C2211yescharacteristic
44C61×#367C2211yescharacteristic
45C61×#366C2211yescharacteristic
46C61×#366C2211yescharacteristic
47C61×#358C2211yescharacteristic
48C61×#358C2211yescharacteristic
49C61×#358C2211yescharacteristic
50C61×#358C2211yescharacteristic
51C61×#358C2211yescharacteristic
52C61×#358C2211yescharacteristic
53C61×#357C2211yescharacteristic
54C61×#357C2211yescharacteristic
55C61×#346C2211yescharacteristic
56C61×#346C2211yescharacteristic
57C4×C16×C61C2211yescharacteristic
58C4×C16×C61C2211yescharacteristic
59C2×Q16×C61—21no—
60C2×Q16×C61C2311yescharacteristic
61C2×Q16×C61C2311yescharacteristic
62C2×Q16×C61C2311yescharacteristic
63C2×SD16×C61—21no—
64C2×D8×C61C2311yescharacteristic
65C2×M16×C61D411yescharacteristic
66C22×C8×C61C2311yescharacteristic
67C4⋊Q8×C61—21no—
68C4⋊Q8×C61—21no—
69#126×C61—41no—
70#126×C61—41no—
71#126×C61—41no—
72#125×C61—21no—
73#125×C61—41no—
74#125×C61—41no—
75#124×C61—21no—
76#124×C61—41no—
77#123×C61—41no—
78C22⋊Q8×C61—21no—
79C22⋊Q8×C61—21no—
80C22⋊Q8×C61—21no—
81C22⋊Q8×C61—41no—
82#121×C61—21no—
83C4×Q8×C61—21no—
84C4×Q8×C61—21no—
85C4×Q8×C61—21no—
86C4×D4×C61—21no—
87#117×C61D411yescharacteristic
88Q32×C61—22no—
89Q32×C61—22no—
90SD32×C61—22no—
91SD32×C61—22no—
92M32×C61—22no—
93C2×C16×C61—22no—
94C2×C16×C61C2311yescharacteristic
95C2×C16×C61C2311yescharacteristic
96C2×C16×C61C2311yescharacteristic
97C2×C16×C61C2311yescharacteristic
98#107×C61—21no—
99#107×C61C2311yescharacteristic
100#107×C61C2311yescharacteristic
101#107×C61C2311yescharacteristic
102#107×C61C2311yescharacteristic
103#106×C61—21no—
104#103×C61—21no—
105#103×C61—21no—
106#103×C61—21no—
107#103×C61—21no—
108#103×C61—21no—
109#103×C61—21no—
110#102×C61—21no—
111#102×C61—21no—
112#97×C61D411yescharacteristic
113#97×C61D411yescharacteristic
114C4×C8×C61C2311yescharacteristic
115C4×C8×C61C2311yescharacteristic
116C2×Q8×C61—21no—
117C2×Q8×C61—21no—
118C2×Q8×C61—21no—
119C2×Q8×C61—41no—
120C2×D4×C61—21no—
121C2×D4×C61—41no—
122C22×C4×C61—41no—
123C22×C4×C61C2×D411yescharacteristic
124Q16×C61—21no—
125Q16×C61—21no—
126Q16×C61—21no—
127Q16×C61—21no—
128Q16×C61—21no—
129Q16×C61—21no—
130Q16×C61—42no—
131SD16×C61—42no—
132D8×C61—21no—
133D8×C61—21no—
134M16×C61—22no—
135C2×C8×C61—21no—
136C2×C8×C61—21no—
137C2×C8×C61C2×D411yescharacteristic
138C2×C8×C61C2×D411yescharacteristic
139C2×C8×C61C2×D411yescharacteristic
140C2×C8×C61C2411yescharacteristic
141C4⋊C4×C61—21no—
142C4⋊C4×C61—21no—
143C4⋊C4×C61—21no—
144C4⋊C4×C61—21no—
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×C61—41no—
152C4⋊C4×C61—41no—
153C4⋊C4×C61—41no—
154C4⋊C4×C61—41no—
155C4⋊C4×C61—41no—
156C4⋊C4×C61D811yescharacteristic
157C4⋊C4×C61D811yescharacteristic
158C22⋊C4×C61—41no—
159C22⋊C4×C61—41no—
160C22⋊C4×C61—41no—
161C22⋊C4×C61—41no—
162C22⋊C4×C61—41no—
163C22⋊C4×C61—41no—
164C22⋊C4×C61—41no—
165C22⋊C4×C61D811yescharacteristic
166C22⋊C4×C61D811yescharacteristic
167C42×C61—41no—
168C42×C61—41no—
169C42×C61—41no—
170C42×C61C2×D411yescharacteristic
171C42×C61C2×D411yescharacteristic
172C16×C61—21no—
173C16×C61—21no—
174C16×C61#4112yes—
175C16×C61#4112yes—
176C23×C61—41no—
177C23×C61C2×D811yescharacteristic
178Q8×C61—41no—
179Q8×C61—41no—
180Q8×C61—41no—
181Q8×C61—41no—
182Q8×C61—41no—
183Q8×C61—41no—
184Q8×C61—161no—
185D4×C61—41no—
186D4×C61—41no—
187D4×C61—161no—
188C2×C4×C61—21no—
189C2×C4×C61—21no—
190C2×C4×C61—41no—
191C2×C4×C61—41no—
192C2×C4×C61—41no—
193C2×C4×C61—41no—
194C2×C4×C61—41no—
195C2×C4×C61—41no—
196C2×C4×C61—41no—
197C2×C4×C61—161no—
198C2×C4×C61C2×D811yescharacteristic
199C2×C4×C61C2×D811yescharacteristic
200C2×C4×C61C2×D811yescharacteristic
201C2×C4×C61C2×D811yescharacteristic
202C2×C4×C61C2×D811yescharacteristic
203C2×C4×C61C22×D411yescharacteristic
204C8×C61—21no—
205C8×C61—21no—
206C8×C61#13512yes—
207C8×C61C2×#4111yescharacteristic
208C8×C61C2×#4111yescharacteristic
209#33745C6111yesmaximal, characteristic, direct product factor, Sylow
210C22×C61—21no—
211C22×C61—21no—
212C22×C61—21no—
213C22×C61—81no—
214C22×C61—81no—
215C22×C61—81no—
216C22×C61C22×D811yescharacteristic
217C4×C61—21no—
218C4×C61—21no—
219C4×C61—21no—
220C4×C61—21no—
221C4×C61—21no—
222C4×C61—81no—
223C4×C61—81no—
224C4×C61—81no—
225C4×C61—81no—
226C4×C61—81no—
227C4×C61—81no—
228C4×C61—81no—
229C4×C61#53211yescharacteristic
230C4×C61C2×#13511yescharacteristic
231#3177C2×C6111yescharacteristic, complemented
232#3175C2×C6111yescharacteristic
233#2255C2×C6111yescharacteristic, complemented
234#2251C2×C6111yescharacteristic, complemented
235#2242C2×C6111yescharacteristic, complemented
236#2241C2×C6111yescharacteristic, complemented
237#2220C2×C6111yescharacteristic
238#2219C2×C6111yescharacteristic, complemented
239#2217C2×C6111yescharacteristic
240#2216C2×C6111yescharacteristic, complemented
241#2176C2×C6111yescharacteristic, complemented
242#2175C2×C6111yescharacteristic, complemented
243C4×Q32C2×C6111yescharacteristic, complemented
244C4×SD32C2×C6111yescharacteristic, complemented
245#2108C2×C6111yescharacteristic, complemented
246C2×C61—41no—
247C2×C61—161no—
248C2×C61#316911yescharacteristic
249C2×C61#341611yescharacteristic
250C2×C61#341711yescharacteristic
251#542—21no—
252#541—21no—
253C2×Q32C22×C6111yescharacteristic
254C2×Q32C22×C6111yescharacteristic
255C2×SD32C22×C6111yescharacteristic
256C2×SD32C22×C6111yescharacteristic
257C2×M32C22×C6111yescharacteristic
258C22×C16C22×C6111yescharacteristic
259#500C22×C6111yescharacteristic
260#499C22×C6111yescharacteristic
261#495C22×C6111yescharacteristic
262#494C22×C6111yescharacteristic
263#491—21no—
264#489—21no—
265#470—21no—
266#468—21no—
267#467C22×C6111yescharacteristic
268#467C22×C6111yescharacteristic
269#467C22×C6111yescharacteristic
270#466C22×C6111yescharacteristic
271#441—21no—
272#440—21no—
273C4×Q16C22×C6111yescharacteristic
274C4×Q16C22×C6111yescharacteristic
275C4×Q16C22×C6111yescharacteristic
276C4×D8C22×C6111yescharacteristic
277#405C22×C6111yescharacteristic
278#367C22×C6111yescharacteristic
279#367C22×C6111yescharacteristic
280#366C22×C6111yescharacteristic
281#366C22×C6111yescharacteristic
282#358C22×C6111yescharacteristic
283#358C22×C6111yescharacteristic
284#358C22×C6111yescharacteristic
285#358C22×C6111yescharacteristic
286#358C22×C6111yescharacteristic
287#358C22×C6111yescharacteristic
288#357C22×C6111yescharacteristic
289#357C22×C6111yescharacteristic
290#346C22×C6111yescharacteristic
291#346C22×C6111yescharacteristic
292C4×C16C22×C6111yescharacteristic
293C4×C16C22×C6111yescharacteristic
294C61#3374511yescharacteristic, direct product factor, Sylow
295C2×Q16—21no—
296C2×Q16C23×C6111yescharacteristic
297C2×Q16C23×C6111yescharacteristic
298C2×Q16C23×C6111yescharacteristic
299C2×SD16—21no—
300C2×D8C23×C6111yescharacteristic
301C2×M16D4×C6111yescharacteristic
302C22×C8C23×C6111yescharacteristic
303C4⋊Q8—21no—
304C4⋊Q8—21no—
305#126—41no—
306#126—41no—
307#126—41no—
308#125—21no—
309#125—41no—
310#125—41no—
311#124—21no—
312#124—41no—
313#123—41no—
314C22⋊Q8—21no—
315C22⋊Q8—21no—
316C22⋊Q8—21no—
317C22⋊Q8—41no—
318#121—21no—
319C4×Q8—21no—
320C4×Q8—21no—
321C4×Q8—21no—
322C4×D4—21no—
323#117D4×C6111yescharacteristic
324Q32—22no—
325Q32—22no—
326SD32—22no—
327SD32—22no—
328M32—22no—
329C2×C16—22no—
330C2×C16C23×C6111yescharacteristic
331C2×C16C23×C6111yescharacteristic
332C2×C16C23×C6111yescharacteristic
333C2×C16C23×C6111yescharacteristic
334#107—21no—
335#107C23×C6111yescharacteristic
336#107C23×C6111yescharacteristic
337#107C23×C6111yescharacteristic
338#107C23×C6111yescharacteristic
339#106—21no—
340#103—21no—
341#103—21no—
342#103—21no—
343#103—21no—
344#103—21no—
345#103—21no—
346#102—21no—
347#102—21no—
348#97D4×C6111yescharacteristic
349#97D4×C6111yescharacteristic
350C4×C8C23×C6111yescharacteristic
351C4×C8C23×C6111yescharacteristic
352C2×Q8—21no—
353C2×Q8—21no—
354C2×Q8—21no—
355C2×Q8—41no—
356C2×D4—21no—
357C2×D4—41no—
358C22×C4—41no—
359C22×C4C2×D4×C6111yescharacteristic
360Q16—21no—
361Q16—21no—
362Q16—21no—
363Q16—21no—
364Q16—21no—
365Q16—21no—
366Q16—42no—
367SD16—42no—
368D8—21no—
369D8—21no—
370M16—22no—
371C2×C8—21no—
372C2×C8—21no—
373C2×C8C2×D4×C6111yescharacteristic
374C2×C8C2×D4×C6111yescharacteristic
375C2×C8C2×D4×C6111yescharacteristic
376C2×C8C24×C6111yescharacteristic
377C4⋊C4—21no—
378C4⋊C4—21no—
379C4⋊C4—21no—
380C4⋊C4—21no—
381C4⋊C4—41no—
382C4⋊C4—41no—
383C4⋊C4—41no—
384C4⋊C4—41no—
385C4⋊C4—41no—
386C4⋊C4—41no—
387C4⋊C4—41no—
388C4⋊C4—41no—
389C4⋊C4—41no—
390C4⋊C4—41no—
391C4⋊C4—41no—
392C4⋊C4D8×C6111yescharacteristic
393C4⋊C4D8×C6111yescharacteristic
394C22⋊C4—41no—
395C22⋊C4—41no—
396C22⋊C4—41no—
397C22⋊C4—41no—
398C22⋊C4—41no—
399C22⋊C4—41no—
400C22⋊C4—41no—
401C22⋊C4D8×C6111yescharacteristic
402C22⋊C4D8×C6111yescharacteristic
403C42—41no—
404C42—41no—
405C42—41no—
406C42C2×D4×C6111yescharacteristic
407C42C2×D4×C6111yescharacteristic
408C16—21no—
409C16—21no—
410C16#41×C6112yes—
411C16#41×C6112yes—
412C23—41no—
413C23C2×D8×C6111yescharacteristic
414Q8—41no—
415Q8—41no—
416Q8—41no—
417Q8—41no—
418Q8—41no—
419Q8—41no—
420Q8—161no—
421D4—41no—
422D4—41no—
423D4—161no—
424C2×C4—21no—
425C2×C4—21no—
426C2×C4—41no—
427C2×C4—41no—
428C2×C4—41no—
429C2×C4—41no—
430C2×C4—41no—
431C2×C4—41no—
432C2×C4—41no—
433C2×C4—161no—
434C2×C4C2×D8×C6111yescharacteristic
435C2×C4C2×D8×C6111yescharacteristic
436C2×C4C2×D8×C6111yescharacteristic
437C2×C4C2×D8×C6111yescharacteristic
438C2×C4C2×D8×C6111yescharacteristic
439C2×C4C22×D4×C6111yescharacteristic
440C8—21no—
441C8—21no—
442C8#135×C6112yes—
443C8C2×#41×C6111yescharacteristic
444C8C2×#41×C6111yescharacteristic
445C22—21no—
446C22—21no—
447C22—21no—
448C22—81no—
449C22—81no—
450C22—81no—
451C22C22×D8×C6111yescharacteristic
452C4—21no—
453C4—21no—
454C4—21no—
455C4—21no—
456C4—21no—
457C4—81no—
458C4—81no—
459C4—81no—
460C4—81no—
461C4—81no—
462C4—81no—
463C4—81no—
464C4C61×#53211yescharacteristic
465C4C2×#135×C6111yescharacteristic
466C2—41no—
467C2—161no—
468C2C61×#316911yescharacteristic
469C2C61×#341611yescharacteristic
470C2C61×#341711yescharacteristic
subgroupG/H
center, socleC22×C61C22×D8
commutator, Frattini, cosocleC2×C8C24×C61
prime radicalC61×#466C22
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C61 ◁ #117×C61 ◁ C61×#405 ◁ G

Complements

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

NH ≅ G/Ntype
1. C61×#3177C2semidirect
3. C61×#2255C2semidirect
4. C61×#2251C2semidirect
5. C61×#2242C2semidirect
6. C61×#2241C2semidirect
8. C61×#2219C2semidirect
10. C61×#2216C2semidirect
11. C61×#2176C2semidirect
12. C61×#2175C2semidirect
13. C4×Q32×C61C2semidirect
14. C4×SD32×C61C2semidirect
15. C61×#2108C2semidirect
209. #33745C61direct (N × H)
231. #3177C2×C61semidirect
233. #2255C2×C61semidirect
234. #2251C2×C61semidirect
235. #2242C2×C61semidirect
236. #2241C2×C61semidirect
238. #2219C2×C61semidirect
240. #2216C2×C61semidirect
241. #2176C2×C61semidirect
242. #2175C2×C61semidirect
243. C4×Q32C2×C61semidirect
244. C4×SD32C2×C61semidirect
245. #2108C2×C61semidirect
294. C61#33745direct (N × H)

Maximal subgroups

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

subgroupindex
C61×#31772
C61×#31752
C61×#22552
C61×#22512
C61×#22422
C61×#22412
C61×#22202
C61×#22192
C61×#22172
C61×#22162
C61×#21762
C61×#21752
C4×Q32×C612
C4×SD32×C612
C61×#21082
#3374561