Finite Group Databasebeta

← C61×#9938 #29513371

Subgroups — C61×#9938 #29513371

Order 15616.

1008 conjugacy classes of subgroups; only the 102 normal subgroups are shown.

normal subgroups only

This group has 1008 conjugacy classes of subgroups — too many to draw. Only its 102 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C61×#3006C211yesmaximal, characteristic, complemented
2C61×#2539C211yesmaximal, characteristic, complemented
3C61×#2404C211yesmaximal, characteristic, complemented
4C61×#1789C211yesmaximal, characteristic, complemented
5C61×#1510C211yesmaximal, characteristic, complemented
6C61×#1462C211yesmaximal, characteristic, complemented
7C61×#1284C211yesmaximal, characteristic, complemented
8C22×#41×C61C2211yescharacteristic
9C2×AGL(1,ℤ/8)×C61—21no—
10C2×#123×C61—21no—
11C2×#121×C61C2211yescharacteristic
12C2×#120×C61—21no—
13C2×#120×C61—21no—
14C22×C22⋊C4×C61C2211yescharacteristic
15C61×#449—22no—
16C61×#448—21no—
17C61×#447—21no—
18C2×#104×C61—22no—
19C61×#417—21no—
20C61×#407C2211yescharacteristic
21C61×#407C2211yescharacteristic
22C61×#399—21no—
23C61×#393—21no—
24C61×#392—21no—
25C61×#392—21no—
26C61×#390—22no—
27C61×#386—21no—
28C61×#386—22no—
29C61×#381C2211yescharacteristic
30C4×C22⋊C4×C61C2211yescharacteristic
31C61×#327—22no—
32C61×#323—22no—
33C25×C61D411yescharacteristic
34C2×#41×C61—21no—
35C2×#41×C61—21no—
36C2×#41×C61—21no—
37C2×#41×C61—21no—
38C2×#41×C61—44no—
39C22×Q8×C61D411yescharacteristic, complemented
40C22×D4×C61—21no—
41C22×D4×C61—21no—
42C22×D4×C61—22no—
43C22×D4×C61—22no—
44C22×D4×C61D411yescharacteristic, complemented
45C22×D4×C61D411yescharacteristic, complemented
46C23×C4×C61—21no—
47C23×C4×C61D411yescharacteristic
48C23×C4×C61C2311yescharacteristic
49AGL(1,ℤ/8)×C61—44no—
50C2×SD16×C61—22no—
51C2×D8×C61—22no—
52C2×M16×C61—21no—
53C2×M16×C61—21no—
54#123×C61—44no—
55#121×C61—21no—
56#121×C61—21no—
57#121×C61—21no—
58#121×C61—21no—
59#120×C61—44no—
60#120×C61—44no—
61C2×C4⋊C4×C61—22no—
62C2×C4⋊C4×C61D411yescharacteristic, complemented
63C2×C22⋊C4×C61—21no—
64C2×C22⋊C4×C61—22no—
65C2×C22⋊C4×C61—22no—
66C2×C22⋊C4×C61—22no—
67C2×C22⋊C4×C61—21no—
68C2×C22⋊C4×C61—21no—
69C2×C22⋊C4×C61—21no—
70C2×C22⋊C4×C61—21no—
71C2×C22⋊C4×C61—21no—
72C2×C22⋊C4×C61—21no—
73C2×C22⋊C4×C61—21no—
74C2×C22⋊C4×C61—21no—
75C2×C22⋊C4×C61—22no—
76C2×C42×C61D412yescomplemented
77#104×C61—44no—
78#103×C61—22no—
79#102×C61—22no—
80C22⋊C8×C61—21no—
81C22⋊C8×C61—21no—
82C22⋊C8×C61—21no—
83C22⋊C8×C61D412yescomplemented
84#95×C61—22no—
85#95×C61—21no—
86#95×C61—21no—
87#95×C61D412yescomplemented
88C24×C61—21no—
89C24×C61—21no—
90C24×C61—21no—
91C24×C61—21no—
92C24×C61—21no—
93C24×C61—42no—
94C24×C61—42no—
95C24×C61—42no—
96C24×C61C2×D411yescharacteristic
97#41×C61—24no—
98#41×C61—24no—
99#41×C61—42no—
100#41×C61—42no—
101#41×C61—42no—
102#41×C61—42no—
103#41×C61—42no—
104#41×C61—42no—
105C2×Q8×C61—21no—
106C2×Q8×C61—21no—
107C2×Q8×C61—42no—
108C2×D4×C61—24no—
109C2×D4×C61—21no—
110C2×D4×C61—21no—
111C2×D4×C61—21no—
112C2×D4×C61—21no—
113C2×D4×C61—42no—
114C2×D4×C61—44no—
115C2×D4×C61—42no—
116C2×D4×C61—42no—
117C2×D4×C61—41no—
118C2×D4×C61—41no—
119C2×D4×C61—42no—
120C2×D4×C61—44no—
121C2×D4×C61—42no—
122C2×D4×C61—44no—
123C2×D4×C61—44no—
124C2×D4×C61—41no—
125C2×D4×C61—41no—
126C2×D4×C61—82no—
127C2×D4×C61—82no—
128C22×C4×C61—21no—
129C22×C4×C61—22no—
130C22×C4×C61—22no—
131C22×C4×C61—21no—
132C22×C4×C61—21no—
133C22×C4×C61—21no—
134C22×C4×C61—21no—
135C22×C4×C61—42no—
136C22×C4×C61—42no—
137C22×C4×C61—42no—
138C22×C4×C61—41no—
139C22×C4×C61—41no—
140C22×C4×C61—42no—
141C22×C4×C61C2×D411yescharacteristic
142C22×C4×C61C2×D411yescharacteristic
143C22×C4×C61C2×D411yescharacteristic
144C22×C4×C61C2×D411yescharacteristic
145C22×C4×C61C2×D411yescharacteristic
146C22×C4×C61#4111yescharacteristic
147SD16×C61—44no—
148D8×C61—44no—
149M16×C61—42no—
150M16×C61—42no—
151C2×C8×C61—22no—
152C2×C8×C61—41no—
153C4⋊C4×C61—21no—
154C4⋊C4×C61—21no—
155C4⋊C4×C61—44no—
156C22⋊C4×C61—24no—
157C22⋊C4×C61—44no—
158C22⋊C4×C61—44no—
159C22⋊C4×C61—44no—
160C22⋊C4×C61—42no—
161C22⋊C4×C61—41no—
162C22⋊C4×C61—41no—
163C22⋊C4×C61—41no—
164C22⋊C4×C61—41no—
165C22⋊C4×C61—41no—
166C22⋊C4×C61—41no—
167C22⋊C4×C61—82no—
168C42×C61—42no—
169C23×C61—22no—
170C23×C61—22no—
171C23×C61—22no—
172C23×C61—22no—
173C23×C61—22no—
174C23×C61—22no—
175C23×C61—41no—
176C23×C61—42no—
177C23×C61—42no—
178C23×C61—41no—
179C23×C61—42no—
180C23×C61—41no—
181C23×C61—41no—
182C23×C61—41no—
183C23×C61—41no—
184C23×C61—41no—
185C23×C61—42no—
186C23×C61—41no—
187C23×C61—41no—
188C23×C61—42no—
189C23×C61—42no—
190C23×C61—42no—
191C23×C61—41no—
192C23×C61—42no—
193C23×C61—81no—
194C23×C61—81no—
195C23×C61—88no—
196C23×C61#12011yescharacteristic
197C23×C61#12011yescharacteristic
198C23×C61#12111yescharacteristic
199Q8×C61—22no—
200Q8×C61—22no—
201Q8×C61—41no—
202Q8×C61—41no—
203D4×C61—22no—
204D4×C61—22no—
205D4×C61—41no—
206D4×C61—41no—
207D4×C61—42no—
208D4×C61—44no—
209D4×C61—44no—
210D4×C61—81no—
211D4×C61—88no—
212D4×C61—82no—
213D4×C61—88no—
214D4×C61—82no—
215C2×C4×C61—22no—
216C2×C4×C61—22no—
217C2×C4×C61—24no—
218C2×C4×C61—22no—
219C2×C4×C61—41no—
220C2×C4×C61—41no—
221C2×C4×C61—41no—
222C2×C4×C61—41no—
223C2×C4×C61—44no—
224C2×C4×C61—44no—
225C2×C4×C61—41no—
226C2×C4×C61—42no—
227C2×C4×C61—41no—
228C2×C4×C61—42no—
229C2×C4×C61—42no—
230C2×C4×C61—41no—
231C2×C4×C61—42no—
232C2×C4×C61—41no—
233C2×C4×C61—42no—
234C2×C4×C61—41no—
235C2×C4×C61—41no—
236C2×C4×C61—42no—
237C2×C4×C61—42no—
238C2×C4×C61—81no—
239C2×C4×C61#12011yescharacteristic
240C2×C4×C61#12111yescharacteristic
241C2×C4×C61#12111yescharacteristic
242C2×C4×C61#12711yescharacteristic
243C8×C61—42no—
244C8×C61—81no—
245#9938C6111yesmaximal, characteristic, direct product factor, Sylow
246C22×C61—21no—
247C22×C61—21no—
248C22×C61—21no—
249C22×C61—21no—
250C22×C61—21no—
251C22×C61—21no—
252C22×C61—21no—
253C22×C61—44no—
254C22×C61—44no—
255C22×C61—44no—
256C22×C61—44no—
257C22×C61—42no—
258C22×C61—42no—
259C22×C61—82no—
260C22×C61—82no—
261C22×C61—82no—
262C22×C61—82no—
263C22×C61—82no—
264C22×C61—82no—
265C22×C61—82no—
266C22×C61—81no—
267C22×C61—81no—
268C22×C61—81no—
269C22×C61—81no—
270C22×C61—81no—
271C22×C61—81no—
272C22×C61—81no—
273C22×C61#39211yescharacteristic
274C22×C61#45312yes—
275C22×C61B(4,𝔽2)12yes—
276C4×C61—21no—
277C4×C61—21no—
278C4×C61—21no—
279C4×C61—21no—
280C4×C61—44no—
281C4×C61—42no—
282C4×C61—82no—
283C4×C61—81no—
284C4×C61—81no—
285#3006C2×C6111yescharacteristic, complemented
286#2539C2×C6111yescharacteristic, complemented
287#2404C2×C6111yescharacteristic, complemented
288#1789C2×C6111yescharacteristic, complemented
289#1510C2×C6111yescharacteristic, complemented
290#1462C2×C6111yescharacteristic, complemented
291#1284C2×C6111yescharacteristic, complemented
292C2×C61—22no—
293C2×C61—22no—
294C2×C61—41no—
295C2×C61—82no—
296C2×C61—82no—
297C2×C61—161no—
298C2×C61#200211yescharacteristic
299C2×C61#201011yescharacteristic
300C2×C61#202111yescharacteristic
301C22×#41C22×C6111yescharacteristic
302C2×AGL(1,ℤ/8)—21no—
303C2×#123—21no—
304C2×#121C22×C6111yescharacteristic
305C2×#120—21no—
306C2×#120—21no—
307C22×C22⋊C4C22×C6111yescharacteristic
308#449—22no—
309#448—21no—
310#447—21no—
311C2×#104—22no—
312#417—21no—
313#407C22×C6111yescharacteristic
314#407C22×C6111yescharacteristic
315#399—21no—
316#393—21no—
317#392—21no—
318#392—21no—
319#390—22no—
320#386—21no—
321#386—22no—
322#381C22×C6111yescharacteristic
323C4×C22⋊C4C22×C6111yescharacteristic
324#327—22no—
325#323—22no—
326C61#993811yescharacteristic, direct product factor, Sylow
327C25D4×C6111yescharacteristic
328C2×#41—21no—
329C2×#41—21no—
330C2×#41—21no—
331C2×#41—21no—
332C2×#41—44no—
333C22×Q8D4×C6111yescharacteristic, complemented
334C22×D4—21no—
335C22×D4—21no—
336C22×D4—22no—
337C22×D4—22no—
338C22×D4D4×C6111yescharacteristic, complemented
339C22×D4D4×C6111yescharacteristic, complemented
340C23×C4—21no—
341C23×C4D4×C6111yescharacteristic
342C23×C4C23×C6111yescharacteristic
343AGL(1,ℤ/8)—44no—
344C2×SD16—22no—
345C2×D8—22no—
346C2×M16—21no—
347C2×M16—21no—
348#123—44no—
349#121—21no—
350#121—21no—
351#121—21no—
352#121—21no—
353#120—44no—
354#120—44no—
355C2×C4⋊C4—22no—
356C2×C4⋊C4D4×C6111yescharacteristic, complemented
357C2×C22⋊C4—21no—
358C2×C22⋊C4—22no—
359C2×C22⋊C4—22no—
360C2×C22⋊C4—22no—
361C2×C22⋊C4—21no—
362C2×C22⋊C4—21no—
363C2×C22⋊C4—21no—
364C2×C22⋊C4—21no—
365C2×C22⋊C4—21no—
366C2×C22⋊C4—21no—
367C2×C22⋊C4—21no—
368C2×C22⋊C4—21no—
369C2×C22⋊C4—22no—
370C2×C42D4×C6112yescomplemented
371#104—44no—
372#103—22no—
373#102—22no—
374C22⋊C8—21no—
375C22⋊C8—21no—
376C22⋊C8—21no—
377C22⋊C8D4×C6112yescomplemented
378#95—22no—
379#95—21no—
380#95—21no—
381#95D4×C6112yescomplemented
382C24—21no—
383C24—21no—
384C24—21no—
385C24—21no—
386C24—21no—
387C24—42no—
388C24—42no—
389C24—42no—
390C24C2×D4×C6111yescharacteristic
391#41—24no—
392#41—24no—
393#41—42no—
394#41—42no—
395#41—42no—
396#41—42no—
397#41—42no—
398#41—42no—
399C2×Q8—21no—
400C2×Q8—21no—
401C2×Q8—42no—
402C2×D4—24no—
403C2×D4—21no—
404C2×D4—21no—
405C2×D4—21no—
406C2×D4—21no—
407C2×D4—42no—
408C2×D4—44no—
409C2×D4—42no—
410C2×D4—42no—
411C2×D4—41no—
412C2×D4—41no—
413C2×D4—42no—
414C2×D4—44no—
415C2×D4—42no—
416C2×D4—44no—
417C2×D4—44no—
418C2×D4—41no—
419C2×D4—41no—
420C2×D4—82no—
421C2×D4—82no—
422C22×C4—21no—
423C22×C4—22no—
424C22×C4—22no—
425C22×C4—21no—
426C22×C4—21no—
427C22×C4—21no—
428C22×C4—21no—
429C22×C4—42no—
430C22×C4—42no—
431C22×C4—42no—
432C22×C4—41no—
433C22×C4—41no—
434C22×C4—42no—
435C22×C4C2×D4×C6111yescharacteristic
436C22×C4C2×D4×C6111yescharacteristic
437C22×C4C2×D4×C6111yescharacteristic
438C22×C4C2×D4×C6111yescharacteristic
439C22×C4C2×D4×C6111yescharacteristic
440C22×C4#41×C6111yescharacteristic
441SD16—44no—
442D8—44no—
443M16—42no—
444M16—42no—
445C2×C8—22no—
446C2×C8—41no—
447C4⋊C4—21no—
448C4⋊C4—21no—
449C4⋊C4—44no—
450C22⋊C4—24no—
451C22⋊C4—44no—
452C22⋊C4—44no—
453C22⋊C4—44no—
454C22⋊C4—42no—
455C22⋊C4—41no—
456C22⋊C4—41no—
457C22⋊C4—41no—
458C22⋊C4—41no—
459C22⋊C4—41no—
460C22⋊C4—41no—
461C22⋊C4—82no—
462C42—42no—
463C23—22no—
464C23—22no—
465C23—22no—
466C23—22no—
467C23—22no—
468C23—22no—
469C23—41no—
470C23—42no—
471C23—42no—
472C23—41no—
473C23—42no—
474C23—41no—
475C23—41no—
476C23—41no—
477C23—41no—
478C23—41no—
479C23—42no—
480C23—41no—
481C23—41no—
482C23—42no—
483C23—42no—
484C23—42no—
485C23—41no—
486C23—42no—
487C23—81no—
488C23—81no—
489C23—88no—
490C23#120×C6111yescharacteristic
491C23#120×C6111yescharacteristic
492C23#121×C6111yescharacteristic
493Q8—22no—
494Q8—22no—
495Q8—41no—
496Q8—41no—
497D4—22no—
498D4—22no—
499D4—41no—
500D4—41no—
501D4—42no—
502D4—44no—
503D4—44no—
504D4—81no—
505D4—88no—
506D4—82no—
507D4—88no—
508D4—82no—
509C2×C4—22no—
510C2×C4—22no—
511C2×C4—24no—
512C2×C4—22no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—44no—
518C2×C4—44no—
519C2×C4—41no—
520C2×C4—42no—
521C2×C4—41no—
522C2×C4—42no—
523C2×C4—42no—
524C2×C4—41no—
525C2×C4—42no—
526C2×C4—41no—
527C2×C4—42no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—42no—
531C2×C4—42no—
532C2×C4—81no—
533C2×C4#120×C6111yescharacteristic
534C2×C4#121×C6111yescharacteristic
535C2×C4#121×C6111yescharacteristic
536C2×C4#127×C6111yescharacteristic
537C8—42no—
538C8—81no—
539C22—21no—
540C22—21no—
541C22—21no—
542C22—21no—
543C22—21no—
544C22—21no—
545C22—21no—
546C22—44no—
547C22—44no—
548C22—44no—
549C22—44no—
550C22—42no—
551C22—42no—
552C22—82no—
553C22—82no—
554C22—82no—
555C22—82no—
556C22—82no—
557C22—82no—
558C22—82no—
559C22—81no—
560C22—81no—
561C22—81no—
562C22—81no—
563C22—81no—
564C22—81no—
565C22—81no—
566C22C61×#39211yescharacteristic
567C22C61×#45312yes—
568C22C61×B(4,𝔽2)12yes—
569C4—21no—
570C4—21no—
571C4—21no—
572C4—21no—
573C4—44no—
574C4—42no—
575C4—82no—
576C4—81no—
577C4—81no—
578C2—22no—
579C2—22no—
580C2—41no—
581C2—82no—
582C2—82no—
583C2—161no—
584C2C61×#200211yescharacteristic
585C2C61×#201011yescharacteristic
586C2C61×#202111yescharacteristic
subgroupG/H
center, socleC22×C61#392
commutator, Frattini, cosocleC23×C4C23×C61
LCSG ▷ C23×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C61 ◁ C23×C4×C61 ◁ G

Complements

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

NH ≅ G/Ntype
1. C61×#3006C2semidirect
2. C61×#2539C2semidirect
3. C61×#2404C2semidirect
4. C61×#1789C2semidirect
5. C61×#1510C2semidirect
6. C61×#1462C2semidirect
7. C61×#1284C2semidirect
39. C22×Q8×C61D4semidirect
44. C22×D4×C61D4semidirect
45. C22×D4×C61D4semidirect
62. C2×C4⋊C4×C61D4semidirect
76. C2×C42×C61D4semidirect
83. C22⋊C8×C61D4semidirect
87. #95×C61D4semidirect
245. #9938C61direct (N × H)
285. #3006C2×C61semidirect
286. #2539C2×C61semidirect
287. #2404C2×C61semidirect
288. #1789C2×C61semidirect
289. #1510C2×C61semidirect
290. #1462C2×C61semidirect
291. #1284C2×C61semidirect
326. C61#9938direct (N × H)
333. C22×Q8D4×C61semidirect
338. C22×D4D4×C61semidirect
339. C22×D4D4×C61semidirect
356. C2×C4⋊C4D4×C61semidirect
370. C2×C42D4×C61semidirect
377. C22⋊C8D4×C61semidirect
381. #95D4×C61semidirect

Maximal subgroups

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

subgroupindex
C61×#30062
C61×#25392
C61×#24042
C61×#17892
C61×#15102
C61×#14622
C61×#12842
#993861