Finite Group Databasebeta

← C61×#24183 #29527616

Subgroups — C61×#24183 #29527616

Order 15616.

1002 conjugacy classes of subgroups.

The subgroup lattice has 606 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C61×#3507C211yesmaximal, characteristic
2C61×#3078C211yesmaximal, characteristic, complemented
3C61×#3037C211yesmaximal, characteristic
4C61×#2327C211yesmaximal, characteristic, complemented
5C61×#2038C212yesmaximal, complemented
6C61×#2005C212yesmaximal, complemented
7C61×#1995C211yesmaximal, characteristic, complemented
8C61×#1963C211yesmaximal, characteristic
9C61×#1882C212yesmaximal, complemented
10C61×#1860C212yesmaximal, complemented
11C61×#1801C211yesmaximal, characteristic, complemented
12C2×#137×C61C2212yes—
13C61×#559—21no—
14C61×#557—21no—
15C61×#556—21no—
16C61×#556—22no—
17C61×#554—21no—
18C61×#552—22no—
19C61×#539—22no—
20C61×#536C2212yes—
21C61×#533C2211yescharacteristic
22C61×#532C2211yescharacteristic
23C2×C4⋊Q8×C61C2211yescharacteristic
24C61×#529—22no—
25C61×#520C2212yes—
26C2×C4×Q8×C61C2211yescharacteristic
27C2×C4×Q8×C61C2211yescharacteristic
28C61×#479—22no—
29C61×#477—21no—
30C61×#475—21no—
31C61×#464—22no—
32C61×#462—21no—
33C61×#460—21no—
34C61×#428C2212yes—
35C61×#423C2211yescharacteristic
36C61×#423C2211yescharacteristic
37C2×#104×C61C2212yes—
38C2×#104×C61C2212yes—
39C61×#419C2212yes—
40C61×#417C2212yes—
41C2×#101×C61C2212yes—
42C61×#391C2211yescharacteristic
43C61×#391C2211yescharacteristic
44C61×#387—22no—
45C61×#387—22no—
46C61×#382C2211yescharacteristic
47C61×#376C2211yescharacteristic
48C61×#343C2212yes—
49C61×#339C2212yes—
50C61×#339C2212yes—
51C2×#41×C61C2312yes—
52C22×Q8×C61C2311yescharacteristic
53C22×Q8×C61C2311yescharacteristic
54#137×C61—24no—
55#137×C61—42no—
56C2×Q16×C61—22no—
57C2×SD16×C61—22no—
58C2×M16×C61C2312yes—
59C2×M16×C61C2312yes—
60C4⋊Q8×C61—22no—
61C4⋊Q8×C61—22no—
62C4⋊Q8×C61—22no—
63C4⋊Q8×C61D411yescharacteristic
64C4⋊Q8×C61D411yescharacteristic
65C4⋊Q8×C61D411yescharacteristic
66#127×C61D411yescharacteristic
67#126×C61—24no—
68#126×C61—24no—
69#125×C61—24no—
70#125×C61—22no—
71#125×C61D412yes—
72#124×C61—22no—
73#124×C61—22no—
74#124×C61D412yes—
75#123×C61—24no—
76#123×C61—24no—
77C22⋊Q8×C61—24no—
78C22⋊Q8×C61—21no—
79C22⋊Q8×C61—21no—
80C22⋊Q8×C61—22no—
81C22⋊Q8×C61—22no—
82#121×C61—21no—
83#121×C61—21no—
84C4×Q8×C61—22no—
85C4×Q8×C61—22no—
86C4×Q8×C61—21no—
87C4×Q8×C61—21no—
88C4×Q8×C61—21no—
89C4×Q8×C61—21no—
90C4×Q8×C61—21no—
91C4×Q8×C61—21no—
92C4×Q8×C61—21no—
93C4×Q8×C61—21no—
94C4×Q8×C61—21no—
95C4×Q8×C61—21no—
96C4×D4×C61—22no—
97C4×D4×C61—22no—
98C4×D4×C61—24no—
99C4×D4×C61—21no—
100C4×D4×C61—21no—
101#117×C61—24no—
102#117×C61—22no—
103#117×C61C2312yes—
104C2×C4⋊C4×C61—22no—
105C2×C4⋊C4×C61—22no—
106C2×C4⋊C4×C61—21no—
107C2×C4⋊C4×C61D412yes—
108C2×C4⋊C4×C61C2311yescharacteristic
109C2×C4⋊C4×C61C2311yescharacteristic
110C2×C42×C61—21no—
111C2×C42×C61D412yes—
112C2×C42×C61C2311yescharacteristic
113C2×C42×C61C2311yescharacteristic
114C2×C42×C61C2311yescharacteristic
115#107×C61—22no—
116#106×C61—22no—
117C4⋊C8×C61—21no—
118C4⋊C8×C61—21no—
119C4⋊C8×C61—21no—
120C4⋊C8×C61—21no—
121#104×C61—24no—
122#104×C61—42no—
123#103×C61—22no—
124#103×C61—22no—
125#103×C61—22no—
126#102×C61—22no—
127#101×C61—42no—
128#95×C61—21no—
129#95×C61—21no—
130#95×C61—22no—
131#95×C61—22no—
132#95×C61—22no—
133#41×C61—22no—
134#41×C61—22no—
135#41×C61—22no—
136#41×C61—22no—
137C2×Q8×C61—21no—
138C2×Q8×C61—21no—
139C2×Q8×C61—21no—
140C2×Q8×C61—21no—
141C2×Q8×C61—21no—
142C2×Q8×C61—21no—
143C2×Q8×C61—21no—
144C2×Q8×C61—21no—
145C2×Q8×C61—21no—
146C2×Q8×C61—21no—
147C2×Q8×C61—21no—
148C2×Q8×C61—21no—
149C2×Q8×C61—21no—
150C2×Q8×C61C2×D412yes—
151C2×Q8×C61#4112yes—
152C2×D4×C61—22no—
153C2×D4×C61—21no—
154C2×D4×C61—21no—
155C2×D4×C61C2×D412yes—
156C22×C4×C61—21no—
157C22×C4×C61—21no—
158C22×C4×C61—24no—
159C22×C4×C61—22no—
160C22×C4×C61—21no—
161C22×C4×C61—21no—
162C22×C4×C61C2×D412yes—
163C22×C4×C61C2×D412yes—
164C22×C4×C61C2×D411yescharacteristic
165C22×C4×C61C2×D411yescharacteristic
166C22×C4×C61C2411yescharacteristic
167Q16×C61—44no—
168SD16×C61—44no—
169M16×C61—22no—
170M16×C61—22no—
171M16×C61—22no—
172M16×C61—22no—
173C2×C8×C61—22no—
174C2×C8×C61—22no—
175C4⋊C4×C61—24no—
176C4⋊C4×C61—28no—
177C4⋊C4×C61—24no—
178C4⋊C4×C61—24no—
179C4⋊C4×C61—22no—
180C4⋊C4×C61—22no—
181C4⋊C4×C61—22no—
182C4⋊C4×C61—21no—
183C4⋊C4×C61—21no—
184C4⋊C4×C61—21no—
185C4⋊C4×C61—22no—
186C4⋊C4×C61—21no—
187C4⋊C4×C61—21no—
188C4⋊C4×C61—21no—
189C4⋊C4×C61—21no—
190C4⋊C4×C61—21no—
191C4⋊C4×C61—41no—
192C4⋊C4×C61—41no—
193C4⋊C4×C61C2×D412yes—
194C4⋊C4×C61C2×D412yes—
195C22⋊C4×C61—24no—
196C22⋊C4×C61—24no—
197C22⋊C4×C61—24no—
198C22⋊C4×C61—22no—
199C22⋊C4×C61—22no—
200C22⋊C4×C61—22no—
201C42×C61—24no—
202C42×C61—22no—
203C42×C61—22no—
204C42×C61—22no—
205C42×C61—21no—
206C42×C61—21no—
207C42×C61—21no—
208C42×C61—41no—
209C42×C61—41no—
210C42×C61C2×D411yescharacteristic
211C42×C61C2×D411yescharacteristic
212C42×C61C2×D411yescharacteristic
213C42×C61C2×D411yescharacteristic
214C42×C61#4112yes—
215C23×C61—22no—
216C23×C61C22×D411yescharacteristic
217Q8×C61—22no—
218Q8×C61—22no—
219Q8×C61—22no—
220Q8×C61—22no—
221Q8×C61—42no—
222Q8×C61—41no—
223Q8×C61—41no—
224Q8×C61—41no—
225Q8×C61—41no—
226Q8×C61—41no—
227Q8×C61—41no—
228Q8×C61—81no—
229D4×C61—22no—
230D4×C61—22no—
231D4×C61—42no—
232D4×C61—42no—
233D4×C61—42no—
234D4×C61—81no—
235C2×C4×C61—22no—
236C2×C4×C61—22no—
237C2×C4×C61—22no—
238C2×C4×C61—22no—
239C2×C4×C61—22no—
240C2×C4×C61—22no—
241C2×C4×C61—22no—
242C2×C4×C61—22no—
243C2×C4×C61—22no—
244C2×C4×C61—41no—
245C2×C4×C61—41no—
246C2×C4×C61—41no—
247C2×C4×C61—41no—
248C2×C4×C61—41no—
249C2×C4×C61—41no—
250C2×C4×C61—42no—
251C2×C4×C61—42no—
252C2×C4×C61—42no—
253C2×C4×C61—41no—
254C2×C4×C61—41no—
255C2×C4×C61—42no—
256C2×C4×C61—41no—
257C2×C4×C61—41no—
258C2×C4×C61—84no—
259C2×C4×C61#12011yescharacteristic
260C2×C4×C61#12011yescharacteristic
261C2×C4×C61#12011yescharacteristic
262C2×C4×C61#12011yescharacteristic
263C2×C4×C61C22×D411yescharacteristic
264C2×C4×C61C22×D411yescharacteristic
265C2×C4×C61C2×#4111yescharacteristic
266C2×C4×C61C2×#4111yescharacteristic
267C2×C4×C61H(5,𝔽2)11yescharacteristic
268C2×C4×C612−1+411yescharacteristic
269C8×C61—42no—
270C8×C61—42no—
271#24183C6111yesmaximal, characteristic, direct product factor, Sylow
272C22×C61—21no—
273C22×C61—21no—
274C22×C61—42no—
275C22×C61—42no—
276C22×C61—42no—
277C22×C61C2×#12011yescharacteristic
278C22×C61#52511yescharacteristic
279C22×C61#53711yescharacteristic
280C4×C61—21no—
281C4×C61—21no—
282C4×C61—21no—
283C4×C61—21no—
284C4×C61—42no—
285C4×C61—42no—
286C4×C61—42no—
287C4×C61—42no—
288C4×C61—42no—
289C4×C61—42no—
290C4×C61—42no—
291C4×C61—81no—
292C4×C61—81no—
293C4×C61#54611yescharacteristic
294C4×C61#54711yescharacteristic
295C4×C61#54811yescharacteristic
296C4×C61#55011yescharacteristic
297#3507C2×C6111yescharacteristic
298#3078C2×C6111yescharacteristic, complemented
299#3037C2×C6111yescharacteristic
300#2327C2×C6111yescharacteristic, complemented
301#2038C2×C6112yescomplemented
302#2005C2×C6112yescomplemented
303#1995C2×C6111yescharacteristic, complemented
304#1963C2×C6111yescharacteristic
305#1882C2×C6112yescomplemented
306#1860C2×C6112yescomplemented
307#1801C2×C6111yescharacteristic, complemented
308C2×C61—21no—
309C2×C61—21no—
310C2×C61—82no—
311C2×C61#240711yescharacteristic
312C2×C61#302011yescharacteristic
313C2×C61#302211yescharacteristic
314C2×#137C22×C6112yes—
315#559—21no—
316#557—21no—
317#556—21no—
318#556—22no—
319#554—21no—
320#552—22no—
321#539—22no—
322#536C22×C6112yes—
323#533C22×C6111yescharacteristic
324#532C22×C6111yescharacteristic
325C2×C4⋊Q8C22×C6111yescharacteristic
326#529—22no—
327#520C22×C6112yes—
328C2×C4×Q8C22×C6111yescharacteristic
329C2×C4×Q8C22×C6111yescharacteristic
330#479—22no—
331#477—21no—
332#475—21no—
333#464—22no—
334#462—21no—
335#460—21no—
336#428C22×C6112yes—
337#423C22×C6111yescharacteristic
338#423C22×C6111yescharacteristic
339C2×#104C22×C6112yes—
340C2×#104C22×C6112yes—
341#419C22×C6112yes—
342#417C22×C6112yes—
343C2×#101C22×C6112yes—
344#391C22×C6111yescharacteristic
345#391C22×C6111yescharacteristic
346#387—22no—
347#387—22no—
348#382C22×C6111yescharacteristic
349#376C22×C6111yescharacteristic
350#343C22×C6112yes—
351#339C22×C6112yes—
352#339C22×C6112yes—
353C61#2418311yescharacteristic, direct product factor, Sylow
354C2×#41C23×C6112yes—
355C22×Q8C23×C6111yescharacteristic
356C22×Q8C23×C6111yescharacteristic
357#137—24no—
358#137—42no—
359C2×Q16—22no—
360C2×SD16—22no—
361C2×M16C23×C6112yes—
362C2×M16C23×C6112yes—
363C4⋊Q8—22no—
364C4⋊Q8—22no—
365C4⋊Q8—22no—
366C4⋊Q8D4×C6111yescharacteristic
367C4⋊Q8D4×C6111yescharacteristic
368C4⋊Q8D4×C6111yescharacteristic
369#127D4×C6111yescharacteristic
370#126—24no—
371#126—24no—
372#125—22no—
373#125—24no—
374#125D4×C6112yes—
375#124—22no—
376#124—22no—
377#124D4×C6112yes—
378#123—24no—
379#123—24no—
380C22⋊Q8—24no—
381C22⋊Q8—21no—
382C22⋊Q8—21no—
383C22⋊Q8—22no—
384C22⋊Q8—22no—
385#121—21no—
386#121—21no—
387C4×Q8—22no—
388C4×Q8—22no—
389C4×Q8—21no—
390C4×Q8—21no—
391C4×Q8—21no—
392C4×Q8—21no—
393C4×Q8—21no—
394C4×Q8—21no—
395C4×Q8—21no—
396C4×Q8—21no—
397C4×Q8—21no—
398C4×Q8—21no—
399C4×D4—22no—
400C4×D4—22no—
401C4×D4—24no—
402C4×D4—21no—
403C4×D4—21no—
404#117—24no—
405#117—22no—
406#117C23×C6112yes—
407C2×C4⋊C4—22no—
408C2×C4⋊C4—22no—
409C2×C4⋊C4—21no—
410C2×C4⋊C4D4×C6112yes—
411C2×C4⋊C4C23×C6111yescharacteristic
412C2×C4⋊C4C23×C6111yescharacteristic
413C2×C42—21no—
414C2×C42D4×C6112yes—
415C2×C42C23×C6111yescharacteristic
416C2×C42C23×C6111yescharacteristic
417C2×C42C23×C6111yescharacteristic
418#107—22no—
419#106—22no—
420C4⋊C8—21no—
421C4⋊C8—21no—
422C4⋊C8—21no—
423C4⋊C8—21no—
424#104—24no—
425#104—42no—
426#103—22no—
427#103—22no—
428#103—22no—
429#102—22no—
430#101—42no—
431#95—21no—
432#95—21no—
433#95—22no—
434#95—22no—
435#95—22no—
436#41—22no—
437#41—22no—
438#41—22no—
439#41—22no—
440C2×Q8—21no—
441C2×Q8—21no—
442C2×Q8—21no—
443C2×Q8—21no—
444C2×Q8—21no—
445C2×Q8—21no—
446C2×Q8—21no—
447C2×Q8—21no—
448C2×Q8—21no—
449C2×Q8—21no—
450C2×Q8—21no—
451C2×Q8—21no—
452C2×Q8—21no—
453C2×Q8C2×D4×C6112yes—
454C2×Q8#41×C6112yes—
455C2×D4—22no—
456C2×D4—21no—
457C2×D4—21no—
458C2×D4C2×D4×C6112yes—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—24no—
462C22×C4—22no—
463C22×C4—21no—
464C22×C4—21no—
465C22×C4C2×D4×C6112yes—
466C22×C4C2×D4×C6112yes—
467C22×C4C2×D4×C6111yescharacteristic
468C22×C4C2×D4×C6111yescharacteristic
469C22×C4C24×C6111yescharacteristic
470Q16—44no—
471SD16—44no—
472M16—22no—
473M16—22no—
474M16—22no—
475M16—22no—
476C2×C8—22no—
477C2×C8—22no—
478C4⋊C4—24no—
479C4⋊C4—28no—
480C4⋊C4—24no—
481C4⋊C4—24no—
482C4⋊C4—22no—
483C4⋊C4—22no—
484C4⋊C4—22no—
485C4⋊C4—21no—
486C4⋊C4—21no—
487C4⋊C4—21no—
488C4⋊C4—22no—
489C4⋊C4—21no—
490C4⋊C4—21no—
491C4⋊C4—21no—
492C4⋊C4—21no—
493C4⋊C4—21no—
494C4⋊C4—41no—
495C4⋊C4—41no—
496C4⋊C4C2×D4×C6112yes—
497C4⋊C4C2×D4×C6112yes—
498C22⋊C4—24no—
499C22⋊C4—24no—
500C22⋊C4—24no—
501C22⋊C4—22no—
502C22⋊C4—22no—
503C22⋊C4—22no—
504C42—24no—
505C42—22no—
506C42—22no—
507C42—22no—
508C42—21no—
509C42—21no—
510C42—21no—
511C42—41no—
512C42—41no—
513C42C2×D4×C6111yescharacteristic
514C42C2×D4×C6111yescharacteristic
515C42C2×D4×C6111yescharacteristic
516C42C2×D4×C6111yescharacteristic
517C42#41×C6112yes—
518C23—22no—
519C23C22×D4×C6111yescharacteristic
520Q8—22no—
521Q8—22no—
522Q8—22no—
523Q8—22no—
524Q8—42no—
525Q8—41no—
526Q8—41no—
527Q8—41no—
528Q8—41no—
529Q8—41no—
530Q8—41no—
531Q8—81no—
532D4—22no—
533D4—22no—
534D4—42no—
535D4—42no—
536D4—42no—
537D4—81no—
538C2×C4—22no—
539C2×C4—22no—
540C2×C4—22no—
541C2×C4—22no—
542C2×C4—22no—
543C2×C4—22no—
544C2×C4—22no—
545C2×C4—22no—
546C2×C4—22no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—42no—
554C2×C4—42no—
555C2×C4—42no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—42no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4—84no—
562C2×C4#120×C6111yescharacteristic
563C2×C4#120×C6111yescharacteristic
564C2×C4#120×C6111yescharacteristic
565C2×C4#120×C6111yescharacteristic
566C2×C4C22×D4×C6111yescharacteristic
567C2×C4C22×D4×C6111yescharacteristic
568C2×C4C2×#41×C6111yescharacteristic
569C2×C4C2×#41×C6111yescharacteristic
570C2×C4H(5,𝔽2)×C6111yescharacteristic
571C2×C42−1+4×C6111yescharacteristic
572C8—42no—
573C8—42no—
574C22—21no—
575C22—21no—
576C22—42no—
577C22—42no—
578C22—42no—
579C22C2×#120×C6111yescharacteristic
580C22C61×#52511yescharacteristic
581C22C61×#53711yescharacteristic
582C4—21no—
583C4—21no—
584C4—21no—
585C4—21no—
586C4—42no—
587C4—42no—
588C4—42no—
589C4—42no—
590C4—42no—
591C4—42no—
592C4—42no—
593C4—81no—
594C4—81no—
595C4C61×#54611yescharacteristic
596C4C61×#54711yescharacteristic
597C4C61×#54811yescharacteristic
598C4C61×#55011yescharacteristic
599C2—21no—
600C2—21no—
601C2—82no—
602C2C61×#240711yescharacteristic
603C2C61×#302011yescharacteristic
604C2C61×#302211yescharacteristic
subgroupG/H
center, socleC22×C61C2×#120
commutator, Frattini, cosocleC22×C4C24×C61
prime radicalC61×#532C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C61 ◁ C2×C42×C61 ◁ G

Complements

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

NH ≅ G/Ntype
2. C61×#3078C2semidirect
4. C61×#2327C2semidirect
5. C61×#2038C2semidirect
6. C61×#2005C2semidirect
7. C61×#1995C2semidirect
9. C61×#1882C2semidirect
10. C61×#1860C2semidirect
11. C61×#1801C2semidirect
271. #24183C61direct (N × H)
298. #3078C2×C61semidirect
300. #2327C2×C61semidirect
301. #2038C2×C61semidirect
302. #2005C2×C61semidirect
303. #1995C2×C61semidirect
305. #1882C2×C61semidirect
306. #1860C2×C61semidirect
307. #1801C2×C61semidirect
353. C61#24183direct (N × H)

Maximal subgroups

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

subgroupindex
C61×#35072
C61×#30782
C61×#30372
C61×#23272
C61×#20382
C61×#20052
C61×#19952
C61×#19632
C61×#18822
C61×#18602
C61×#18012
#2418361