Finite Group Databasebeta

← C61×#18647 #29522080

Subgroups — C61×#18647 #29522080

Order 15616.

928 conjugacy classes of subgroups.

The subgroup lattice has 516 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C61×#3511C211yesmaximal, characteristic
2C61×#3227C211yesmaximal, characteristic, complemented
3C2×C61×#487C211yesmaximal, characteristic, complemented
4C61×#3079C211yesmaximal, characteristic, complemented
5C61×#1638C214yesmaximal, complemented
6C61×#1635C214yesmaximal, complemented
7C61×#1549C211yesmaximal, characteristic, complemented
8C61×#1492C211yesmaximal, characteristic, complemented
9C61×#1476C211yesmaximal, characteristic, complemented
10C61×#556C2212yes—
11C61×#555—21no—
12C61×#554—21no—
13C61×#553—22no—
14C61×#548—22no—
15C61×#547C2212yes—
16C61×#542—22no—
17C61×#537—21no—
18C61×#533—21no—
19C61×#532—21no—
20C61×#532C2211yescharacteristic
21C2×C4⋊Q8×C61C2211yescharacteristic
22C2×C4⋊Q8×C61C2211yescharacteristic
23C61×#520—21no—
24C4×#41×C61C2211yescharacteristic
25C61×#498—21no—
26C61×#487—22no—
27C61×#487C2214yes—
28C61×#486—21no—
29C61×#481—22no—
30C61×#477C2212yes—
31C61×#476C2212yes—
32C61×#476C2214yes—
33C61×#475—21no—
34C61×#474—21no—
35C61×#431C2211yescharacteristic
36C61×#428—21no—
37C61×#423C2211yescharacteristic
38C61×#417—21no—
39C2×#103×C61—22no—
40C2×C4×C8×C61C2211yescharacteristic
41C61×#332C2214yes—
42C61×Q8⋊C8C2212yes—
43C61×D4⋊C8C2212yes—
44C61×D4⋊C8C2214yes—
45C2×#41×C61—22no—
46C2×#41×C61—21no—
47C2×#41×C61D411yescharacteristic
48C22×Q8×C61—21no—
49C22×Q8×C61—21no—
50C2×M16×C61—21no—
51C22×C8×C61—21no—
52C4⋊Q8×C61—21no—
53C4⋊Q8×C61—21no—
54C4⋊Q8×C61—21no—
55C4⋊Q8×C61—21no—
56C4⋊Q8×C61—21no—
57C4⋊Q8×C61D412yes—
58C4⋊Q8×C61D411yescharacteristic
59C4⋊Q8×C61C2312yes—
60C4⋊Q8×C61C2312yes—
61#127×C61D411yescharacteristic
62#126×C61—24no—
63#125×C61—22no—
64#124×C61—24no—
65#124×C61—22no—
66#124×C61—21no—
67#123×C61—24no—
68C22⋊Q8×C61—22no—
69C22⋊Q8×C61—24no—
70C22⋊Q8×C61—22no—
71C22⋊Q8×C61—22no—
72#121×C61—22no—
73#121×C61—22no—
74#121×C61—24no—
75#121×C61—22no—
76#121×C61—21no—
77#121×C61D412yes—
78C4×Q8×C61—22no—
79C4×Q8×C61—22no—
80C4×Q8×C61D411yescharacteristic
81C4×Q8×C61C2311yescharacteristic
82C4×D4×C61—22no—
83C4×D4×C61—22no—
84C4×D4×C61—24no—
85C4×D4×C61—21no—
86C4×D4×C61—21no—
87C4×D4×C61—21no—
88C4×D4×C61D411yescharacteristic
89C4×D4×C61C2312yes—
90C4×D4×C61C2311yescharacteristic
91#117×C61—22no—
92#117×C61—22no—
93#117×C61—21no—
94#117×C61D411yescharacteristic
95C2×C4⋊C4×C61—21no—
96C2×C4⋊C4×C61—22no—
97C2×C4⋊C4×C61—21no—
98C2×C4⋊C4×C61—21no—
99C2×C4⋊C4×C61D412yes—
100C2×C42×C61—21no—
101C2×C42×C61C2311yescharacteristic
102#107×C61—22no—
103#106×C61—22no—
104#106×C61—24no—
105C4⋊C8×C61—21no—
106C4⋊C8×C61C2312yes—
107C4⋊C8×C61C2312yes—
108#103×C61—22no—
109#103×C61—28no—
110#102×C61—22no—
111#102×C61—24no—
112C22⋊C8×C61—21no—
113C4×C8×C61—21no—
114C4×C8×C61—21no—
115C4×C8×C61C2312yes—
116#41×C61—22no—
117#41×C61—22no—
118#41×C61—42no—
119#41×C61—42no—
120#41×C61—84no—
121C2×Q8×C61—21no—
122C2×Q8×C61—22no—
123C2×Q8×C61—22no—
124C2×Q8×C61—22no—
125C2×Q8×C61—44no—
126C2×Q8×C61—41no—
127C2×Q8×C61—82no—
128C2×Q8×C61C2×D411yescharacteristic
129C2×D4×C61—21no—
130C2×D4×C61—22no—
131C2×D4×C61—24no—
132C2×D4×C61—21no—
133C2×D4×C61—21no—
134C2×D4×C61C2×D411yescharacteristic
135C2×D4×C61C2×D412yes—
136C22×C4×C61—24no—
137C22×C4×C61—22no—
138C22×C4×C61—21no—
139C22×C4×C61—21no—
140C22×C4×C61—21no—
141C22×C4×C61—22no—
142C22×C4×C61—41no—
143C22×C4×C61C2×D411yescharacteristic
144C22×C4×C61C2×D411yescharacteristic
145C22×C4×C61C2×D411yescharacteristic
146M16×C61—42no—
147C2×C8×C61—22no—
148C2×C8×C61—22no—
149C2×C8×C61—22no—
150C2×C8×C61—42no—
151C4⋊C4×C61—24no—
152C4⋊C4×C61—24no—
153C4⋊C4×C61—22no—
154C4⋊C4×C61—22no—
155C4⋊C4×C61—21no—
156C4⋊C4×C61—21no—
157C4⋊C4×C61—22no—
158C4⋊C4×C61—21no—
159C4⋊C4×C61—22no—
160C4⋊C4×C61—22no—
161C4⋊C4×C61—41no—
162C4⋊C4×C61—41no—
163C4⋊C4×C61C2×D414yes—
164C4⋊C4×C61C2×D411yescharacteristic
165C4⋊C4×C61C2×D412yes—
166C4⋊C4×C61C2×D411yescharacteristic
167C22⋊C4×C61—24no—
168C22⋊C4×C61—24no—
169C22⋊C4×C61—24no—
170C22⋊C4×C61—21no—
171C22⋊C4×C61—21no—
172C22⋊C4×C61—22no—
173C22⋊C4×C61—21no—
174C22⋊C4×C61—22no—
175C42×C61—24no—
176C42×C61—21no—
177C42×C61—21no—
178C42×C61—21no—
179C42×C61C2×D411yescharacteristic
180C42×C61C2×D411yescharacteristic
181C42×C61C2×D411yescharacteristic
182C42×C61C2411yescharacteristic
183C23×C61—21no—
184C23×C61—22no—
185C23×C61#12011yescharacteristic
186Q8×C61—21no—
187Q8×C61—21no—
188Q8×C61—44no—
189Q8×C61—44no—
190Q8×C61—42no—
191Q8×C61—82no—
192Q8×C61—82no—
193D4×C61—21no—
194D4×C61—21no—
195D4×C61—24no—
196D4×C61—42no—
197D4×C61—44no—
198D4×C61—42no—
199D4×C61—42no—
200D4×C61—84no—
201C2×C4×C61—22no—
202C2×C4×C61—22no—
203C2×C4×C61—21no—
204C2×C4×C61—21no—
205C2×C4×C61—22no—
206C2×C4×C61—21no—
207C2×C4×C61—24no—
208C2×C4×C61—42no—
209C2×C4×C61—42no—
210C2×C4×C61—42no—
211C2×C4×C61—42no—
212C2×C4×C61—42no—
213C2×C4×C61—42no—
214C2×C4×C61—82no—
215C2×C4×C61—84no—
216C2×C4×C61—82no—
217C2×C4×C61#12011yescharacteristic
218C2×C4×C61#12011yescharacteristic
219C2×C4×C61#12011yescharacteristic
220C2×C4×C61#13512yes—
221C2×C4×C61#13712yes—
222C2×C4×C61C22×D411yescharacteristic
223C2×C4×C61C22×D411yescharacteristic
224C2×C4×C61C22×D411yescharacteristic
225C8×C61—42no—
226C8×C61—42no—
227C8×C61—42no—
228#18647C6111yesmaximal, characteristic, direct product factor, Sylow
229C22×C61—21no—
230C22×C61—21no—
231C22×C61—41no—
232C22×C61—42no—
233C22×C61—41no—
234C22×C61—42no—
235C22×C61—41no—
236C22×C61—42no—
237C22×C61#45212yes—
238C22×C61C2×#12011yescharacteristic
239C4×C61—21no—
240C4×C61—21no—
241C4×C61—41no—
242C4×C61—42no—
243C4×C61—41no—
244C4×C61—44no—
245C4×C61—41no—
246C4×C61—82no—
247C4×C61#45212yes—
248C4×C61#45412yes—
249C4×C61C2×#13511yescharacteristic
250C4×C61C2×#13711yescharacteristic
251C4×C61#57712yes—
252#3511C2×C6111yescharacteristic
253#3227C2×C6111yescharacteristic, complemented
254C2×#487C2×C6111yescharacteristic, complemented
255#3079C2×C6111yescharacteristic, complemented
256#1638C2×C6114yescomplemented
257#1635C2×C6114yescomplemented
258#1549C2×C6111yescharacteristic, complemented
259#1492C2×C6111yescharacteristic, complemented
260#1476C2×C6111yescharacteristic, complemented
261C2×C61—22no—
262C2×C61—81no—
263C2×C61—82no—
264C2×C61C2×#45211yescharacteristic
265C2×C61#300911yescharacteristic
266C2×C61C2×#45411yescharacteristic
267#556C22×C6112yes—
268#555—21no—
269#554—21no—
270#553—22no—
271#548—22no—
272#547C22×C6112yes—
273#542—22no—
274#537—21no—
275#533—21no—
276#532—21no—
277#532C22×C6111yescharacteristic
278C2×C4⋊Q8C22×C6111yescharacteristic
279C2×C4⋊Q8C22×C6111yescharacteristic
280#520—21no—
281C4×#41C22×C6111yescharacteristic
282#498—21no—
283#487—22no—
284#487C22×C6114yes—
285#486—21no—
286#481—22no—
287#477C22×C6112yes—
288#476C22×C6112yes—
289#476C22×C6114yes—
290#475—21no—
291#474—21no—
292#431C22×C6111yescharacteristic
293#428—21no—
294#423C22×C6111yescharacteristic
295#417—21no—
296C2×#103—22no—
297C2×C4×C8C22×C6111yescharacteristic
298#332C22×C6114yes—
299Q8⋊C8C22×C6112yes—
300D4⋊C8C22×C6112yes—
301D4⋊C8C22×C6114yes—
302C61#1864711yescharacteristic, direct product factor, Sylow
303C2×#41—22no—
304C2×#41—21no—
305C2×#41D4×C6111yescharacteristic
306C22×Q8—21no—
307C22×Q8—21no—
308C2×M16—21no—
309C22×C8—21no—
310C4⋊Q8—21no—
311C4⋊Q8—21no—
312C4⋊Q8—21no—
313C4⋊Q8—21no—
314C4⋊Q8—21no—
315C4⋊Q8D4×C6112yes—
316C4⋊Q8D4×C6111yescharacteristic
317C4⋊Q8C23×C6112yes—
318C4⋊Q8C23×C6112yes—
319#127D4×C6111yescharacteristic
320#126—24no—
321#125—22no—
322#124—24no—
323#124—22no—
324#124—21no—
325#123—24no—
326C22⋊Q8—22no—
327C22⋊Q8—24no—
328C22⋊Q8—22no—
329C22⋊Q8—22no—
330#121—22no—
331#121—22no—
332#121—24no—
333#121—22no—
334#121—21no—
335#121D4×C6112yes—
336C4×Q8—22no—
337C4×Q8—22no—
338C4×Q8D4×C6111yescharacteristic
339C4×Q8C23×C6111yescharacteristic
340C4×D4—22no—
341C4×D4—24no—
342C4×D4—22no—
343C4×D4—21no—
344C4×D4—21no—
345C4×D4—21no—
346C4×D4D4×C6111yescharacteristic
347C4×D4C23×C6111yescharacteristic
348C4×D4C23×C6112yes—
349#117—22no—
350#117—22no—
351#117—21no—
352#117D4×C6111yescharacteristic
353C2×C4⋊C4—21no—
354C2×C4⋊C4—22no—
355C2×C4⋊C4—21no—
356C2×C4⋊C4—21no—
357C2×C4⋊C4D4×C6112yes—
358C2×C42—21no—
359C2×C42C23×C6111yescharacteristic
360#107—22no—
361#106—22no—
362#106—24no—
363C4⋊C8—21no—
364C4⋊C8C23×C6112yes—
365C4⋊C8C23×C6112yes—
366#103—22no—
367#103—28no—
368#102—22no—
369#102—24no—
370C22⋊C8—21no—
371C4×C8—21no—
372C4×C8—21no—
373C4×C8C23×C6112yes—
374#41—22no—
375#41—22no—
376#41—42no—
377#41—42no—
378#41—84no—
379C2×Q8—21no—
380C2×Q8—22no—
381C2×Q8—22no—
382C2×Q8—22no—
383C2×Q8—44no—
384C2×Q8—41no—
385C2×Q8—82no—
386C2×Q8C2×D4×C6111yescharacteristic
387C2×D4—21no—
388C2×D4—22no—
389C2×D4—24no—
390C2×D4—21no—
391C2×D4—21no—
392C2×D4C2×D4×C6111yescharacteristic
393C2×D4C2×D4×C6112yes—
394C22×C4—24no—
395C22×C4—22no—
396C22×C4—21no—
397C22×C4—21no—
398C22×C4—21no—
399C22×C4—22no—
400C22×C4—41no—
401C22×C4C2×D4×C6111yescharacteristic
402C22×C4C2×D4×C6111yescharacteristic
403C22×C4C2×D4×C6111yescharacteristic
404M16—42no—
405C2×C8—22no—
406C2×C8—22no—
407C2×C8—22no—
408C2×C8—42no—
409C4⋊C4—24no—
410C4⋊C4—24no—
411C4⋊C4—22no—
412C4⋊C4—22no—
413C4⋊C4—21no—
414C4⋊C4—21no—
415C4⋊C4—22no—
416C4⋊C4—21no—
417C4⋊C4—22no—
418C4⋊C4—22no—
419C4⋊C4—41no—
420C4⋊C4—41no—
421C4⋊C4C2×D4×C6114yes—
422C4⋊C4C2×D4×C6111yescharacteristic
423C4⋊C4C2×D4×C6112yes—
424C4⋊C4C2×D4×C6111yescharacteristic
425C22⋊C4—24no—
426C22⋊C4—24no—
427C22⋊C4—24no—
428C22⋊C4—21no—
429C22⋊C4—21no—
430C22⋊C4—22no—
431C22⋊C4—21no—
432C22⋊C4—22no—
433C42—24no—
434C42—21no—
435C42—21no—
436C42—21no—
437C42C2×D4×C6111yescharacteristic
438C42C2×D4×C6111yescharacteristic
439C42C2×D4×C6111yescharacteristic
440C42C24×C6111yescharacteristic
441C23—21no—
442C23—22no—
443C23#120×C6111yescharacteristic
444Q8—21no—
445Q8—21no—
446Q8—44no—
447Q8—44no—
448Q8—42no—
449Q8—82no—
450Q8—82no—
451D4—21no—
452D4—21no—
453D4—24no—
454D4—42no—
455D4—44no—
456D4—42no—
457D4—42no—
458D4—84no—
459C2×C4—22no—
460C2×C4—22no—
461C2×C4—21no—
462C2×C4—21no—
463C2×C4—22no—
464C2×C4—21no—
465C2×C4—24no—
466C2×C4—42no—
467C2×C4—42no—
468C2×C4—42no—
469C2×C4—42no—
470C2×C4—42no—
471C2×C4—42no—
472C2×C4—82no—
473C2×C4—84no—
474C2×C4—82no—
475C2×C4#120×C6111yescharacteristic
476C2×C4#120×C6111yescharacteristic
477C2×C4#120×C6111yescharacteristic
478C2×C4#135×C6112yes—
479C2×C4#137×C6112yes—
480C2×C4C22×D4×C6111yescharacteristic
481C2×C4C22×D4×C6111yescharacteristic
482C2×C4C22×D4×C6111yescharacteristic
483C8—42no—
484C8—42no—
485C8—42no—
486C22—21no—
487C22—21no—
488C22—41no—
489C22—42no—
490C22—41no—
491C22—42no—
492C22—41no—
493C22—42no—
494C22C61×#45212yes—
495C22C2×#120×C6111yescharacteristic
496C4—21no—
497C4—21no—
498C4—41no—
499C4—42no—
500C4—41no—
501C4—44no—
502C4—41no—
503C4—82no—
504C4C61×#45212yes—
505C4C61×#45412yes—
506C4C2×#135×C6111yescharacteristic
507C4C2×#137×C6111yescharacteristic
508C4C61×#57712yes—
509C2—22no—
510C2—81no—
511C2—82no—
512C2C2×C61×#45211yescharacteristic
513C2C61×#300911yescharacteristic
514C2C2×C61×#45411yescharacteristic
subgroupG/H
center, socleC22×C61C2×#120
commutator, Frattini, cosocleC42C24×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×#3227C2semidirect
3. C2×C61×#487C2semidirect
4. C61×#3079C2semidirect
5. C61×#1638C2semidirect
6. C61×#1635C2semidirect
7. C61×#1549C2semidirect
8. C61×#1492C2semidirect
9. C61×#1476C2semidirect
228. #18647C61direct (N × H)
253. #3227C2×C61semidirect
254. C2×#487C2×C61semidirect
255. #3079C2×C61semidirect
256. #1638C2×C61semidirect
257. #1635C2×C61semidirect
258. #1549C2×C61semidirect
259. #1492C2×C61semidirect
260. #1476C2×C61semidirect
302. C61#18647direct (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×#32272
C2×C61×#4872
C61×#30792
C61×#16382
C61×#16352
C61×#15492
C61×#14922
C61×#14762
#1864761