Finite Group Databasebeta

← C61×#8423 #29511856

Subgroups — C61×#8423 #29511856

Order 15616.

772 conjugacy classes of subgroups.

The subgroup lattice has 514 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C61×#3511C211yesmaximal, characteristic
2C61×#1981C211yesmaximal, characteristic, complemented
3C61×#1806C211yesmaximal, characteristic, complemented
4C61×#1548C211yesmaximal, characteristic, complemented
5C61×#1547C211yesmaximal, characteristic, complemented
6C61×#1502C211yesmaximal, characteristic, complemented
7C61×#1477C211yesmaximal, characteristic, complemented
8C61×#556—21no—
9C61×#555C412yescomplemented
10C61×#554C412yescomplemented
11C61×#553—22no—
12C61×#548—22no—
13C61×#547—21no—
14C61×#542—22no—
15C61×#537—21no—
16C61×#533—21no—
17C61×#532—21no—
18C61×#532C2211yescharacteristic
19C2×C4⋊Q8×C61C2211yescharacteristic
20C61×#520—21no—
21C4×#41×C61C2211yescharacteristic
22C61×#431C2211yescharacteristic
23C61×#423C2211yescharacteristic
24C2×C4⋊C8×C61C2211yescharacteristic
25C2×#104×C61—21no—
26C2×#103×C61—22no—
27C4×C4⋊C4×C61C2211yescharacteristic
28C61×#339—21no—
29C61×#333—22no—
30C61×#332—21no—
31C61×#331—21no—
32C61×#327—22no—
33C61×Q8⋊C8—21no—
34C61×D4⋊C8—21no—
35C2×#41×C61—22no—
36C2×#41×C61—21no—
37C2×#41×C61D411yescharacteristic
38C22×Q8×C61D412yes—
39C2×M16×C61—21no—
40C22×C8×C61—21no—
41C4⋊Q8×C61—21no—
42C4⋊Q8×C61—21no—
43C4⋊Q8×C61C2×C412yes—
44C4⋊Q8×C61D412yes—
45C4⋊Q8×C61D411yescharacteristic
46#127×C61D411yescharacteristic
47#126×C61—24no—
48#125×C61—22no—
49#124×C61—22no—
50#124×C61—24no—
51#124×C61—21no—
52#123×C61—24no—
53C22⋊Q8×C61—22no—
54C22⋊Q8×C61—22no—
55C22⋊Q8×C61—22no—
56C22⋊Q8×C61—24no—
57#121×C61—22no—
58#121×C61—24no—
59#121×C61—22no—
60#121×C61—22no—
61#121×C61—21no—
62#121×C61D412yes—
63C4×Q8×C61—22no—
64C4×Q8×C61—22no—
65C4×Q8×C61C2×C411yescharacteristic
66C4×Q8×C61D411yescharacteristic
67C4×D4×C61—22no—
68C4×D4×C61—24no—
69C4×D4×C61—22no—
70C4×D4×C61—21no—
71C4×D4×C61—21no—
72C4×D4×C61—21no—
73C4×D4×C61C2×C412yes—
74C4×D4×C61C2×C411yescharacteristic
75C4×D4×C61D411yescharacteristic
76#117×C61—22no—
77#117×C61—22no—
78#117×C61—21no—
79#117×C61D411yescharacteristic
80C2×C4⋊C4×C61—21no—
81C2×C4⋊C4×C61—21no—
82C2×C4⋊C4×C61—22no—
83C2×C4⋊C4×C61—21no—
84C2×C42×C61—21no—
85C2×C42×C61—21no—
86C2×C42×C61C2311yescharacteristic
87C4⋊C8×C61—21no—
88C4⋊C8×C61—21no—
89C4⋊C8×C61—21no—
90C4⋊C8×C61—21no—
91C4⋊C8×C61—21no—
92#104×C61—42no—
93#103×C61—44no—
94C22⋊C8×C61—21no—
95C4×C8×C61—21no—
96#95×C61—21no—
97#41×C61—21no—
98#41×C61—21no—
99#41×C61—21no—
100#41×C61—21no—
101#41×C61—41no—
102#41×C61—41no—
103#41×C61—41no—
104#41×C61—41no—
105#41×C61—82no—
106#41×C61—82no—
107C2×Q8×C61—21no—
108C2×Q8×C61—22no—
109C2×Q8×C61—42no—
110C2×Q8×C61—42no—
111C2×Q8×C61C22⋊C411yescharacteristic
112C2×Q8×C61C22⋊C414yes—
113C2×D4×C61—21no—
114C2×D4×C61—22no—
115C2×D4×C61—24no—
116C2×D4×C61—21no—
117C2×D4×C61—21no—
118C2×D4×C61C22⋊C411yescharacteristic
119C2×D4×C61C22⋊C412yes—
120C22×C4×C61—24no—
121C22×C4×C61—22no—
122C22×C4×C61—21no—
123C22×C4×C61—22no—
124C22×C4×C61—21no—
125C22×C4×C61—21no—
126C22×C4×C61—41no—
127C22×C4×C61C2×D411yescharacteristic
128C22×C4×C61C2×D411yescharacteristic
129C22×C4×C61C2×D411yescharacteristic
130M16×C61—41no—
131M16×C61—41no—
132C2×C8×C61—42no—
133C2×C8×C61—41no—
134C2×C8×C61—41no—
135C2×C8×C61—41no—
136C4⋊C4×C61—24no—
137C4⋊C4×C61—24no—
138C4⋊C4×C61—22no—
139C4⋊C4×C61—22no—
140C4⋊C4×C61—21no—
141C4⋊C4×C61—22no—
142C4⋊C4×C61—22no—
143C4⋊C4×C61—21no—
144C4⋊C4×C61—21no—
145C4⋊C4×C61—22no—
146C4⋊C4×C61—41no—
147C4⋊C4×C61C22⋊C411yescharacteristic
148C4⋊C4×C61C22⋊C411yescharacteristic
149C4⋊C4×C61C22⋊C412yes—
150C22⋊C4×C61—24no—
151C22⋊C4×C61—24no—
152C22⋊C4×C61—24no—
153C22⋊C4×C61—21no—
154C22⋊C4×C61—21no—
155C22⋊C4×C61—22no—
156C22⋊C4×C61—21no—
157C22⋊C4×C61—22no—
158C42×C61—24no—
159C42×C61—21no—
160C42×C61—21no—
161C42×C61—21no—
162C42×C61—41no—
163C42×C61—41no—
164C42×C61C22×C411yescharacteristic
165C42×C61C2×D411yescharacteristic
166C42×C61C2×D411yescharacteristic
167C42×C61C2×D411yescharacteristic
168C23×C61—21no—
169C23×C61—22no—
170C23×C61#12011yescharacteristic
171Q8×C61—21no—
172Q8×C61—21no—
173Q8×C61—44no—
174Q8×C61—41no—
175Q8×C61—41no—
176Q8×C61—42no—
177Q8×C61—42no—
178D4×C61—21no—
179D4×C61—21no—
180D4×C61—42no—
181D4×C61—41no—
182D4×C61—42no—
183D4×C61—41no—
184D4×C61—42no—
185D4×C61—41no—
186D4×C61—41no—
187D4×C61—41no—
188D4×C61—41no—
189D4×C61—84no—
190C2×C4×C61—21no—
191C2×C4×C61—21no—
192C2×C4×C61—21no—
193C2×C4×C61—21no—
194C2×C4×C61—22no—
195C2×C4×C61—21no—
196C2×C4×C61—24no—
197C2×C4×C61—41no—
198C2×C4×C61—42no—
199C2×C4×C61—42no—
200C2×C4×C61—42no—
201C2×C4×C61—41no—
202C2×C4×C61—41no—
203C2×C4×C61—41no—
204C2×C4×C61—41no—
205C2×C4×C61—42no—
206C2×C4×C61—82no—
207C2×C4×C61—84no—
208C2×C4×C61—81no—
209C2×C4×C61—81no—
210C2×C4×C61C2×C22⋊C411yescharacteristic
211C2×C4×C61C2×C22⋊C411yescharacteristic
212C2×C4×C61C2×C22⋊C411yescharacteristic
213C2×C4×C61#12011yescharacteristic
214C2×C4×C61#12011yescharacteristic
215C2×C4×C61#12011yescharacteristic
216C2×C4×C61#13511yescharacteristic
217C2×C4×C61#13511yescharacteristic
218C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
219C2×C4×C61#13711yescharacteristic
220C8×C61—81no—
221C8×C61—81no—
222C8×C61—81no—
223#8423C6111yesmaximal, characteristic, direct product factor, Sylow
224C22×C61—21no—
225C22×C61—21no—
226C22×C61—41no—
227C22×C61—42no—
228C22×C61—41no—
229C22×C61—42no—
230C22×C61—41no—
231C22×C61—42no—
232C22×C61#37911yescharacteristic
233C22×C61#44911yescharacteristic
234C22×C61#45211yescharacteristic
235C4×C61—21no—
236C4×C61—21no—
237C4×C61—21no—
238C4×C61—41no—
239C4×C61—44no—
240C4×C61—41no—
241C4×C61—41no—
242C4×C61—42no—
243C4×C61—82no—
244C4×C61#41611yescharacteristic
245C4×C61#41711yescharacteristic
246C4×C61#44911yescharacteristic
247C4×C61#45211yescharacteristic
248C4×C61#45311yescharacteristic
249C4×C61#45511yescharacteristic
250#3511C2×C6111yescharacteristic
251#1981C2×C6111yescharacteristic, complemented
252#1806C2×C6111yescharacteristic, complemented
253#1548C2×C6111yescharacteristic, complemented
254#1547C2×C6111yescharacteristic, complemented
255#1502C2×C6111yescharacteristic, complemented
256#1477C2×C6111yescharacteristic, complemented
257C2×C61—21no—
258C2×C61—21no—
259C2×C61—81no—
260C2×C61—82no—
261C2×C61#178811yescharacteristic
262C2×C61#179211yescharacteristic
263C2×C61#179611yescharacteristic
264#556—21no—
265#555C4×C6112yescomplemented
266#554C4×C6112yescomplemented
267#553—22no—
268#548—22no—
269#547—21no—
270#542—22no—
271#537—21no—
272#533—21no—
273#532—21no—
274#532C22×C6111yescharacteristic
275C2×C4⋊Q8C22×C6111yescharacteristic
276#520—21no—
277C4×#41C22×C6111yescharacteristic
278#431C22×C6111yescharacteristic
279#423C22×C6111yescharacteristic
280C2×C4⋊C8C22×C6111yescharacteristic
281C2×#104—21no—
282C2×#103—22no—
283C4×C4⋊C4C22×C6111yescharacteristic
284#339—21no—
285#333—22no—
286#332—21no—
287#331—21no—
288#327—22no—
289Q8⋊C8—21no—
290D4⋊C8—21no—
291C61#842311yescharacteristic, direct product factor, Sylow
292C2×#41—22no—
293C2×#41—21no—
294C2×#41D4×C6111yescharacteristic
295C22×Q8D4×C6112yes—
296C2×M16—21no—
297C22×C8—21no—
298C4⋊Q8—21no—
299C4⋊Q8—21no—
300C4⋊Q8C2×C4×C6112yes—
301C4⋊Q8D4×C6112yes—
302C4⋊Q8D4×C6111yescharacteristic
303#127D4×C6111yescharacteristic
304#126—24no—
305#125—22no—
306#124—22no—
307#124—24no—
308#124—21no—
309#123—24no—
310C22⋊Q8—22no—
311C22⋊Q8—22no—
312C22⋊Q8—22no—
313C22⋊Q8—24no—
314#121—22no—
315#121—24no—
316#121—22no—
317#121—22no—
318#121—21no—
319#121D4×C6112yes—
320C4×Q8—22no—
321C4×Q8—22no—
322C4×Q8C2×C4×C6111yescharacteristic
323C4×Q8D4×C6111yescharacteristic
324C4×D4—22no—
325C4×D4—24no—
326C4×D4—22no—
327C4×D4—21no—
328C4×D4—21no—
329C4×D4—21no—
330C4×D4C2×C4×C6111yescharacteristic
331C4×D4C2×C4×C6112yes—
332C4×D4D4×C6111yescharacteristic
333#117—22no—
334#117—22no—
335#117—21no—
336#117D4×C6111yescharacteristic
337C2×C4⋊C4—21no—
338C2×C4⋊C4—21no—
339C2×C4⋊C4—22no—
340C2×C4⋊C4—21no—
341C2×C42—21no—
342C2×C42—21no—
343C2×C42C23×C6111yescharacteristic
344C4⋊C8—21no—
345C4⋊C8—21no—
346C4⋊C8—21no—
347C4⋊C8—21no—
348C4⋊C8—21no—
349#104—42no—
350#103—44no—
351C22⋊C8—21no—
352C4×C8—21no—
353#95—21no—
354#41—21no—
355#41—21no—
356#41—21no—
357#41—21no—
358#41—41no—
359#41—41no—
360#41—41no—
361#41—41no—
362#41—82no—
363#41—82no—
364C2×Q8—21no—
365C2×Q8—22no—
366C2×Q8—42no—
367C2×Q8—42no—
368C2×Q8C22⋊C4×C6111yescharacteristic
369C2×Q8C22⋊C4×C6114yes—
370C2×D4—21no—
371C2×D4—22no—
372C2×D4—24no—
373C2×D4—21no—
374C2×D4—21no—
375C2×D4C22⋊C4×C6111yescharacteristic
376C2×D4C22⋊C4×C6112yes—
377C22×C4—24no—
378C22×C4—22no—
379C22×C4—21no—
380C22×C4—22no—
381C22×C4—21no—
382C22×C4—21no—
383C22×C4—41no—
384C22×C4C2×D4×C6111yescharacteristic
385C22×C4C2×D4×C6111yescharacteristic
386C22×C4C2×D4×C6111yescharacteristic
387M16—41no—
388M16—41no—
389C2×C8—42no—
390C2×C8—41no—
391C2×C8—41no—
392C2×C8—41no—
393C4⋊C4—24no—
394C4⋊C4—24no—
395C4⋊C4—22no—
396C4⋊C4—22no—
397C4⋊C4—21no—
398C4⋊C4—22no—
399C4⋊C4—22no—
400C4⋊C4—21no—
401C4⋊C4—21no—
402C4⋊C4—22no—
403C4⋊C4—41no—
404C4⋊C4C22⋊C4×C6111yescharacteristic
405C4⋊C4C22⋊C4×C6111yescharacteristic
406C4⋊C4C22⋊C4×C6112yes—
407C22⋊C4—24no—
408C22⋊C4—24no—
409C22⋊C4—24no—
410C22⋊C4—21no—
411C22⋊C4—21no—
412C22⋊C4—22no—
413C22⋊C4—21no—
414C22⋊C4—22no—
415C42—24no—
416C42—21no—
417C42—21no—
418C42—21no—
419C42—41no—
420C42—41no—
421C42C22×C4×C6111yescharacteristic
422C42C2×D4×C6111yescharacteristic
423C42C2×D4×C6111yescharacteristic
424C42C2×D4×C6111yescharacteristic
425C23—21no—
426C23—22no—
427C23#120×C6111yescharacteristic
428Q8—21no—
429Q8—21no—
430Q8—44no—
431Q8—41no—
432Q8—41no—
433Q8—42no—
434Q8—42no—
435D4—21no—
436D4—21no—
437D4—42no—
438D4—41no—
439D4—42no—
440D4—41no—
441D4—42no—
442D4—41no—
443D4—41no—
444D4—41no—
445D4—41no—
446D4—84no—
447C2×C4—21no—
448C2×C4—21no—
449C2×C4—21no—
450C2×C4—21no—
451C2×C4—22no—
452C2×C4—21no—
453C2×C4—24no—
454C2×C4—41no—
455C2×C4—42no—
456C2×C4—42no—
457C2×C4—42no—
458C2×C4—41no—
459C2×C4—41no—
460C2×C4—41no—
461C2×C4—41no—
462C2×C4—42no—
463C2×C4—82no—
464C2×C4—84no—
465C2×C4—81no—
466C2×C4—81no—
467C2×C4C2×C22⋊C4×C6111yescharacteristic
468C2×C4C2×C22⋊C4×C6111yescharacteristic
469C2×C4C2×C22⋊C4×C6111yescharacteristic
470C2×C4#120×C6111yescharacteristic
471C2×C4#120×C6111yescharacteristic
472C2×C4#120×C6111yescharacteristic
473C2×C4#135×C6111yescharacteristic
474C2×C4#135×C6111yescharacteristic
475C2×C4AGL(1,ℤ/8)×C6111yescharacteristic
476C2×C4#137×C6111yescharacteristic
477C8—81no—
478C8—81no—
479C8—81no—
480C22—21no—
481C22—21no—
482C22—41no—
483C22—42no—
484C22—41no—
485C22—42no—
486C22—41no—
487C22—42no—
488C22C61×#37911yescharacteristic
489C22C61×#44911yescharacteristic
490C22C61×#45211yescharacteristic
491C4—21no—
492C4—21no—
493C4—21no—
494C4—41no—
495C4—42no—
496C4—41no—
497C4—44no—
498C4—41no—
499C4—82no—
500C4C61×#41611yescharacteristic
501C4C61×#41711yescharacteristic
502C4C61×#44911yescharacteristic
503C4C61×#45211yescharacteristic
504C4C61×#45311yescharacteristic
505C4C61×#45511yescharacteristic
506C2—21no—
507C2—21no—
508C2—81no—
509C2—82no—
510C2C61×#178811yescharacteristic
511C2C61×#179211yescharacteristic
512C2C61×#179611yescharacteristic
subgroupG/H
center, socleC22×C61#379
commutatorC42C22×C4×C61
Frattini, cosocleC2×C42C23×C61
prime radicalC61×#3511C2
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×#1981C2semidirect
3. C61×#1806C2semidirect
4. C61×#1548C2semidirect
5. C61×#1547C2semidirect
6. C61×#1502C2semidirect
7. C61×#1477C2semidirect
9. C61×#555C4semidirect
10. C61×#554C4semidirect
223. #8423C61direct (N × H)
251. #1981C2×C61semidirect
252. #1806C2×C61semidirect
253. #1548C2×C61semidirect
254. #1547C2×C61semidirect
255. #1502C2×C61semidirect
256. #1477C2×C61semidirect
265. #555C4×C61semidirect
266. #554C4×C61semidirect
291. C61#8423direct (N × H)

Maximal subgroups

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

subgroupindex
C61×#35112
C61×#19812
C61×#18062
C61×#15482
C61×#15472
C61×#15022
C61×#14772
#842361