Finite Group Databasebeta

← C61×#24394 #29527827

Subgroups — C61×#24394 #29527827

Order 15616.

1578 conjugacy classes of subgroups.

The subgroup lattice has 964 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C61×#535C211yesmaximal, characteristic
2C2×C61×#468C211yesmaximal, characteristic, complemented
3C2×C61×#465C211yesmaximal, characteristic, complemented
4C2×C61×#450C211yesmaximal, characteristic, complemented
5C2×C61×#408C211yesmaximal, characteristic, complemented
6C61×#2616C211yesmaximal, characteristic, complemented
7C61×#2034C211yesmaximal, characteristic, complemented
8C61×#2033C211yesmaximal, characteristic, complemented
9C61×#2000C211yesmaximal, characteristic, complemented
10C61×#2000C211yesmaximal, characteristic, complemented
11C61×#1895C211yesmaximal, characteristic, complemented
12C61×#1893C211yesmaximal, characteristic, complemented
13C61×#1873C211yesmaximal, characteristic, complemented
14C61×#1854C211yesmaximal, characteristic, complemented
15C61×#1786C211yesmaximal, characteristic, complemented
16C22×#41×C61C2211yescharacteristic
17C23×D4×C61C2211yescharacteristic
18C22×SD16×C61C2211yescharacteristic
19C22×SD16×C61C2211yescharacteristic
20C22×M16×C61C2211yescharacteristic, complemented
21C23×C8×C61C2211yescharacteristic, complemented
22C61×#535—24no—
23C61×#535—24no—
24C2×#127×C61—21no—
25C2×#124×C61—21no—
26C2×C22⋊Q8×C61C2211yescharacteristic
27C2×C22⋊Q8×C61C2211yescharacteristic, complemented
28C2×C22⋊Q8×C61C2211yescharacteristic, complemented
29C2×#121×C61C2211yescharacteristic
30C2×#121×C61C2211yescharacteristic
31C2×#121×C61C2211yescharacteristic
32C2×#121×C61C2211yescharacteristic
33C2×#120×C61—21no—
34C2×#120×C61—21no—
35C2×#117×C61C2211yescharacteristic
36C61×#468—24no—
37C61×#465—24no—
38C61×#450—24no—
39C2×#107×C61C2211yescharacteristic, complemented
40C2×#106×C61C2211yescharacteristic, complemented
41C2×#103×C61C2211yescharacteristic, complemented
42C2×#103×C61C2211yescharacteristic, complemented
43C2×#102×C61C2211yescharacteristic
44C2×#102×C61C2211yescharacteristic
45C2×#102×C61C2211yescharacteristic
46C2×#102×C61C2211yescharacteristic
47C2×#102×C61C2211yescharacteristic
48C2×#102×C61C2211yescharacteristic
49C61×#408—24no—
50C2×C22⋊C8×C61C2211yescharacteristic
51C2×C22⋊C8×C61C2211yescharacteristic
52C2×C22⋊C8×C61C2211yescharacteristic, complemented
53C2×C22⋊C8×C61C2211yescharacteristic, complemented
54C61×#395—21no—
55C61×#394—21no—
56C61×#394—21no—
57C61×#394—21no—
58C61×#380C2211yescharacteristic
59C61×#380C2211yescharacteristic, complemented
60C61×#380C2211yescharacteristic, complemented
61C61×#340C2211yescharacteristic, complemented
62C61×#340C2211yescharacteristic, complemented
63C61×#340C2211yescharacteristic, complemented
64C61×#340C2211yescharacteristic, complemented
65C25×C61—21no—
66C2×#41×C61—22no—
67C2×#41×C61—22no—
68C2×#41×C61—22no—
69C2×#41×C61—22no—
70C2×#41×C61—41no—
71C2×#41×C61—41no—
72C22×Q8×C61D411yescharacteristic
73C22×Q8×C61C2311yescharacteristic
74C22×D4×C61—21no—
75C22×D4×C61—21no—
76C22×D4×C61—21no—
77C22×D4×C61—21no—
78C22×D4×C61—22no—
79C22×D4×C61—22no—
80C22×D4×C61—21no—
81C22×D4×C61—22no—
82C22×D4×C61—22no—
83C22×D4×C61—41no—
84C22×D4×C61—41no—
85C22×D4×C61D411yescharacteristic
86C22×D4×C61D411yescharacteristic
87C22×D4×C61D411yescharacteristic
88C22×D4×C61C2311yescharacteristic
89C22×D4×C61C2311yescharacteristic
90C23×C4×C61C2311yescharacteristic
91C23×C4×C61C2311yescharacteristic
92C23×C4×C61C2311yescharacteristic
93C2×SD16×C61—22no—
94C2×SD16×C61—22no—
95C2×SD16×C61—22no—
96C2×SD16×C61—22no—
97C2×SD16×C61—41no—
98C2×SD16×C61—41no—
99C2×M16×C61—22no—
100C2×M16×C61—22no—
101C2×M16×C61—41no—
102C22×C8×C61—22no—
103C22×C8×C61—22no—
104C22×C8×C61—41no—
105C22×C8×C61C2311yescharacteristic
106C22×C8×C61C2311yescharacteristic
107C22×C8×C61C2311yescharacteristic
108C22×C8×C61C2311yescharacteristic
109#127×C61—28no—
110#124×C61—28no—
111C22⋊Q8×C61—22no—
112C22⋊Q8×C61—22no—
113C22⋊Q8×C61—22no—
114C22⋊Q8×C61—22no—
115C22⋊Q8×C61—41no—
116C22⋊Q8×C61—41no—
117#121×C61—22no—
118#121×C61—22no—
119#121×C61—22no—
120#121×C61—22no—
121#121×C61—22no—
122#121×C61—22no—
123#121×C61D414yes—
124#121×C61D414yes—
125#120×C61—28no—
126#120×C61—28no—
127#117×C61—22no—
128#117×C61—22no—
129C2×C4⋊C4×C61—21no—
130C2×C4⋊C4×C61—21no—
131C2×C4⋊C4×C61—21no—
132C2×C4⋊C4×C61C2311yescharacteristic
133C2×C4⋊C4×C61C2311yescharacteristic
134C2×C4⋊C4×C61C2311yescharacteristic
135C2×C4⋊C4×C61C2311yescharacteristic
136C2×C4⋊C4×C61C2311yescharacteristic
137C2×C22⋊C4×C61—21no—
138C2×C22⋊C4×C61—21no—
139C2×C22⋊C4×C61—21no—
140C2×C22⋊C4×C61—21no—
141C2×C22⋊C4×C61—21no—
142C2×C22⋊C4×C61—21no—
143C2×C22⋊C4×C61—21no—
144C2×C22⋊C4×C61—21no—
145C2×C22⋊C4×C61—21no—
146C2×C22⋊C4×C61—21no—
147C2×C22⋊C4×C61—21no—
148C2×C42×C61—21no—
149#107×C61—22no—
150#106×C61—22no—
151#103×C61—22no—
152#103×C61—22no—
153#102×C61—22no—
154#102×C61—22no—
155#102×C61—22no—
156#102×C61—22no—
157#102×C61—41no—
158#102×C61—41no—
159C22⋊C8×C61—22no—
160C22⋊C8×C61—22no—
161C22⋊C8×C61—22no—
162C22⋊C8×C61D414yescomplemented
163#95×C61—21no—
164#95×C61—21no—
165#95×C61—21no—
166C24×C61—24no—
167C24×C61—21no—
168C24×C61—21no—
169C24×C61—42no—
170C24×C61—42no—
171C24×C61—81no—
172C24×C61—81no—
173C24×C61—81no—
174C24×C61—81no—
175C24×C61C2×D411yescharacteristic
176C24×C61C2×D411yescharacteristic
177C24×C61C2×D411yescharacteristic
178#41×C61—44no—
179#41×C61—44no—
180#41×C61—44no—
181#41×C61—44no—
182C2×Q8×C61—22no—
183C2×Q8×C61—22no—
184C2×Q8×C61—21no—
185C2×Q8×C61—21no—
186C2×Q8×C61—21no—
187C2×Q8×C61—21no—
188C2×Q8×C61—21no—
189C2×Q8×C61—21no—
190C2×Q8×C61—41no—
191C2×D4×C61—24no—
192C2×D4×C61—22no—
193C2×D4×C61—22no—
194C2×D4×C61—22no—
195C2×D4×C61—22no—
196C2×D4×C61—24no—
197C2×D4×C61—24no—
198C2×D4×C61—24no—
199C2×D4×C61—24no—
200C2×D4×C61—22no—
201C2×D4×C61—22no—
202C2×D4×C61—21no—
203C2×D4×C61—21no—
204C2×D4×C61—21no—
205C2×D4×C61—21no—
206C2×D4×C61—21no—
207C2×D4×C61—21no—
208C2×D4×C61—21no—
209C2×D4×C61—21no—
210C2×D4×C61—21no—
211C2×D4×C61—21no—
212C2×D4×C61—44no—
213C2×D4×C61—44no—
214C2×D4×C61—44no—
215C2×D4×C61—44no—
216C2×D4×C61—41no—
217C2×D4×C61—41no—
218C2×D4×C61—41no—
219C2×D4×C61—42no—
220C2×D4×C61—42no—
221C2×D4×C61—81no—
222C2×D4×C61—81no—
223C2×D4×C61—81no—
224C2×D4×C61—81no—
225C2×D4×C61—81no—
226C2×D4×C61—81no—
227C2×D4×C61—81no—
228C2×D4×C61—81no—
229C2×D4×C61C2×D412yes—
230C2×D4×C61C2×D412yes—
231C22×C4×C61—21no—
232C22×C4×C61—21no—
233C22×C4×C61—21no—
234C22×C4×C61—21no—
235C22×C4×C61—21no—
236C22×C4×C61—21no—
237C22×C4×C61—21no—
238C22×C4×C61—21no—
239C22×C4×C61—21no—
240C22×C4×C61—21no—
241C22×C4×C61—21no—
242C22×C4×C61—21no—
243C22×C4×C61—21no—
244C22×C4×C61—21no—
245C22×C4×C61—21no—
246C22×C4×C61—21no—
247C22×C4×C61—21no—
248C22×C4×C61—21no—
249C22×C4×C61—21no—
250C22×C4×C61—21no—
251C22×C4×C61C2×D411yescharacteristic
252C22×C4×C61C2×D411yescharacteristic
253C22×C4×C61C2×D412yes—
254C22×C4×C61C2×D412yes—
255C22×C4×C61C2×D411yescharacteristic
256C22×C4×C61C2×D412yes—
257C22×C4×C61#4112yes—
258C22×C4×C61C2411yescharacteristic
259SD16×C61—44no—
260SD16×C61—44no—
261M16×C61—44no—
262C2×C8×C61—21no—
263C2×C8×C61—21no—
264C2×C8×C61—21no—
265C2×C8×C61—21no—
266C2×C8×C61—21no—
267C2×C8×C61—21no—
268C2×C8×C61—21no—
269C2×C8×C61—21no—
270C2×C8×C61—21no—
271C2×C8×C61—21no—
272C2×C8×C61—44no—
273C2×C8×C61C2×D412yes—
274C2×C8×C61C2×D412yes—
275C4⋊C4×C61—21no—
276C4⋊C4×C61—21no—
277C4⋊C4×C61—21no—
278C4⋊C4×C61—21no—
279C4⋊C4×C61—21no—
280C4⋊C4×C61—21no—
281C4⋊C4×C61—21no—
282C4⋊C4×C61—21no—
283C4⋊C4×C61—42no—
284C4⋊C4×C61—42no—
285C4⋊C4×C61—42no—
286C4⋊C4×C61C2×D412yes—
287C4⋊C4×C61C2×D412yes—
288C22⋊C4×C61—24no—
289C22⋊C4×C61—24no—
290C22⋊C4×C61—24no—
291C22⋊C4×C61—24no—
292C22⋊C4×C61—24no—
293C22⋊C4×C61—42no—
294C22⋊C4×C61—42no—
295C22⋊C4×C61—42no—
296C22⋊C4×C61—81no—
297C22⋊C4×C61—81no—
298C22⋊C4×C61—81no—
299C42×C61—24no—
300C23×C61—21no—
301C23×C61—21no—
302C23×C61—21no—
303C23×C61—21no—
304C23×C61—21no—
305C23×C61—21no—
306C23×C61—21no—
307C23×C61—21no—
308C23×C61—21no—
309C23×C61—21no—
310C23×C61—21no—
311C23×C61—21no—
312C23×C61—22no—
313C23×C61—22no—
314C23×C61—21no—
315C23×C61—21no—
316C23×C61—21no—
317C23×C61—21no—
318C23×C61—21no—
319C23×C61—21no—
320C23×C61—21no—
321C23×C61—48no—
322C23×C61—41no—
323C23×C61—41no—
324C23×C61—41no—
325C23×C61—41no—
326C23×C61—41no—
327C23×C61—41no—
328C23×C61—41no—
329C23×C61—41no—
330C23×C61—41no—
331C23×C61—41no—
332C23×C61—41no—
333C23×C61—41no—
334C23×C61—84no—
335C23×C61—84no—
336C23×C61—84no—
337C23×C61—84no—
338C23×C61—84no—
339C23×C61—84no—
340C23×C61#12012yes—
341C23×C61#12112yes—
342C23×C61C22×D411yescharacteristic
343Q8×C61—44no—
344Q8×C61—41no—
345Q8×C61—41no—
346Q8×C61—41no—
347Q8×C61—41no—
348D4×C61—22no—
349D4×C61—22no—
350D4×C61—22no—
351D4×C61—22no—
352D4×C61—44no—
353D4×C61—44no—
354D4×C61—48no—
355D4×C61—44no—
356D4×C61—41no—
357D4×C61—41no—
358D4×C61—41no—
359D4×C61—41no—
360D4×C61—84no—
361D4×C61—84no—
362D4×C61—84no—
363D4×C61—84no—
364C2×C4×C61—21no—
365C2×C4×C61—21no—
366C2×C4×C61—21no—
367C2×C4×C61—21no—
368C2×C4×C61—22no—
369C2×C4×C61—22no—
370C2×C4×C61—22no—
371C2×C4×C61—22no—
372C2×C4×C61—22no—
373C2×C4×C61—22no—
374C2×C4×C61—22no—
375C2×C4×C61—22no—
376C2×C4×C61—22no—
377C2×C4×C61—22no—
378C2×C4×C61—21no—
379C2×C4×C61—21no—
380C2×C4×C61—21no—
381C2×C4×C61—41no—
382C2×C4×C61—41no—
383C2×C4×C61—41no—
384C2×C4×C61—41no—
385C2×C4×C61—41no—
386C2×C4×C61—41no—
387C2×C4×C61—41no—
388C2×C4×C61—41no—
389C2×C4×C61—41no—
390C2×C4×C61—41no—
391C2×C4×C61—41no—
392C2×C4×C61—41no—
393C2×C4×C61—41no—
394C2×C4×C61—41no—
395C2×C4×C61—41no—
396C2×C4×C61—41no—
397C2×C4×C61—41no—
398C2×C4×C61—41no—
399C2×C4×C61—41no—
400C2×C4×C61—41no—
401C2×C4×C61#12012yes—
402C2×C4×C61#12112yes—
403C2×C4×C61C22×D411yescharacteristic
404C2×C4×C61C22×D411yescharacteristic
405C2×C4×C61C22×D411yescharacteristic
406C2×C4×C61C2×#4111yescharacteristic
407C2×C4×C61H(5,𝔽2)11yescharacteristic
408C2×C4×C61H(5,𝔽2)11yescharacteristic
409C8×C61—22no—
410C8×C61—22no—
411C8×C61—41no—
412C8×C61—41no—
413#24394C6111yesmaximal, characteristic, direct product factor, Sylow
414C22×C61—22no—
415C22×C61—22no—
416C22×C61—22no—
417C22×C61—22no—
418C22×C61—22no—
419C22×C61—22no—
420C22×C61—41no—
421C22×C61—41no—
422C22×C61—41no—
423C22×C61—41no—
424C22×C61—41no—
425C22×C61—41no—
426C22×C61—41no—
427C22×C61—41no—
428C22×C61—41no—
429C22×C61—42no—
430C22×C61—42no—
431C22×C61—41no—
432C22×C61—41no—
433C22×C61—41no—
434C22×C61—42no—
435C22×C61—42no—
436C22×C61—41no—
437C22×C61—42no—
438C22×C61—42no—
439C22×C61—41no—
440C22×C61—41no—
441C22×C61—816no—
442C22×C61—81no—
443C22×C61—81no—
444C22×C61—81no—
445C22×C61—81no—
446C22×C61—81no—
447C22×C61—81no—
448C22×C61—81no—
449C22×C61—81no—
450C22×C61C2×#12011yescharacteristic
451C22×C61C2×#12111yescharacteristic
452C22×C61#53411yescharacteristic
453C22×C61#57611yescharacteristic
454C22×C61#57711yescharacteristic
455C22×C61#57711yescharacteristic
456C22×C61#57711yescharacteristic
457C4×C61—22no—
458C4×C61—22no—
459C4×C61—41no—
460C4×C61—42no—
461C4×C61—42no—
462C4×C61—81no—
463C4×C61—81no—
464C4×C61—81no—
465C4×C61—81no—
466C4×C61D4211yescharacteristic
467C4×C61D4211yescharacteristic
468C4×C61#54611yescharacteristic
469C4×C61#54611yescharacteristic
470C2×#535C2×C6111yescharacteristic
471C2×#468C2×C6111yescharacteristic, complemented
472C2×#465C2×C6111yescharacteristic, complemented
473C2×#450C2×C6111yescharacteristic, complemented
474C2×#408C2×C6111yescharacteristic, complemented
475#2616C2×C6111yescharacteristic, complemented
476#2034C2×C6111yescharacteristic, complemented
477#2033C2×C6111yescharacteristic, complemented
478#2000C2×C6111yescharacteristic, complemented
479#2000C2×C6111yescharacteristic, complemented
480#1895C2×C6111yescharacteristic, complemented
481#1893C2×C6111yescharacteristic, complemented
482#1873C2×C6111yescharacteristic, complemented
483#1854C2×C6111yescharacteristic, complemented
484#1786C2×C6111yescharacteristic, complemented
485C2×C61—42no—
486C2×C61—42no—
487C2×C61—81no—
488C2×C61—82no—
489C2×C61—82no—
490C2×C61#241011yescharacteristic
491C2×C61#300911yescharacteristic
492C2×C61#301211yescharacteristic
493C2×C61#305711yescharacteristic
494C2×C61#306211yescharacteristic
495C2×C61#319811yescharacteristic
496C2×C61#320011yescharacteristic
497C22×#41C22×C6111yescharacteristic
498C23×D4C22×C6111yescharacteristic
499C22×SD16C22×C6111yescharacteristic
500C22×SD16C22×C6111yescharacteristic
501C22×M16C22×C6111yescharacteristic, complemented
502C23×C8C22×C6111yescharacteristic, complemented
503#535—24no—
504#535—24no—
505C2×#127—21no—
506C2×#124—21no—
507C2×C22⋊Q8C22×C6111yescharacteristic
508C2×C22⋊Q8C22×C6111yescharacteristic, complemented
509C2×C22⋊Q8C22×C6111yescharacteristic, complemented
510C2×#121C22×C6111yescharacteristic
511C2×#121C22×C6111yescharacteristic
512C2×#121C22×C6111yescharacteristic
513C2×#121C22×C6111yescharacteristic
514C2×#120—21no—
515C2×#120—21no—
516C2×#117C22×C6111yescharacteristic
517#468—24no—
518#465—24no—
519#450—24no—
520C2×#107C22×C6111yescharacteristic, complemented
521C2×#106C22×C6111yescharacteristic, complemented
522C2×#103C22×C6111yescharacteristic, complemented
523C2×#103C22×C6111yescharacteristic, complemented
524C2×#102C22×C6111yescharacteristic
525C2×#102C22×C6111yescharacteristic
526C2×#102C22×C6111yescharacteristic
527C2×#102C22×C6111yescharacteristic
528C2×#102C22×C6111yescharacteristic
529C2×#102C22×C6111yescharacteristic
530#408—24no—
531C2×C22⋊C8C22×C6111yescharacteristic
532C2×C22⋊C8C22×C6111yescharacteristic
533C2×C22⋊C8C22×C6111yescharacteristic, complemented
534C2×C22⋊C8C22×C6111yescharacteristic, complemented
535#395—21no—
536#394—21no—
537#394—21no—
538#394—21no—
539#380C22×C6111yescharacteristic
540#380C22×C6111yescharacteristic, complemented
541#380C22×C6111yescharacteristic, complemented
542#340C22×C6111yescharacteristic, complemented
543#340C22×C6111yescharacteristic, complemented
544#340C22×C6111yescharacteristic, complemented
545#340C22×C6111yescharacteristic, complemented
546C61#2439411yescharacteristic, direct product factor, Sylow
547C25—21no—
548C2×#41—22no—
549C2×#41—22no—
550C2×#41—22no—
551C2×#41—22no—
552C2×#41—41no—
553C2×#41—41no—
554C22×Q8D4×C6111yescharacteristic
555C22×Q8C23×C6111yescharacteristic
556C22×D4—21no—
557C22×D4—21no—
558C22×D4—21no—
559C22×D4—21no—
560C22×D4—22no—
561C22×D4—22no—
562C22×D4—21no—
563C22×D4—22no—
564C22×D4—22no—
565C22×D4—41no—
566C22×D4—41no—
567C22×D4D4×C6111yescharacteristic
568C22×D4D4×C6111yescharacteristic
569C22×D4D4×C6111yescharacteristic
570C22×D4C23×C6111yescharacteristic
571C22×D4C23×C6111yescharacteristic
572C23×C4C23×C6111yescharacteristic
573C23×C4C23×C6111yescharacteristic
574C23×C4C23×C6111yescharacteristic
575C2×SD16—22no—
576C2×SD16—22no—
577C2×SD16—22no—
578C2×SD16—22no—
579C2×SD16—41no—
580C2×SD16—41no—
581C2×M16—22no—
582C2×M16—22no—
583C2×M16—41no—
584C22×C8—22no—
585C22×C8—22no—
586C22×C8—41no—
587C22×C8C23×C6111yescharacteristic
588C22×C8C23×C6111yescharacteristic
589C22×C8C23×C6111yescharacteristic
590C22×C8C23×C6111yescharacteristic
591#127—28no—
592#124—28no—
593C22⋊Q8—22no—
594C22⋊Q8—22no—
595C22⋊Q8—22no—
596C22⋊Q8—22no—
597C22⋊Q8—41no—
598C22⋊Q8—41no—
599#121—22no—
600#121—22no—
601#121—22no—
602#121—22no—
603#121—22no—
604#121—22no—
605#121D4×C6114yes—
606#121D4×C6114yes—
607#120—28no—
608#120—28no—
609#117—22no—
610#117—22no—
611C2×C4⋊C4—21no—
612C2×C4⋊C4—21no—
613C2×C4⋊C4—21no—
614C2×C4⋊C4C23×C6111yescharacteristic
615C2×C4⋊C4C23×C6111yescharacteristic
616C2×C4⋊C4C23×C6111yescharacteristic
617C2×C4⋊C4C23×C6111yescharacteristic
618C2×C4⋊C4C23×C6111yescharacteristic
619C2×C22⋊C4—21no—
620C2×C22⋊C4—21no—
621C2×C22⋊C4—21no—
622C2×C22⋊C4—21no—
623C2×C22⋊C4—21no—
624C2×C22⋊C4—21no—
625C2×C22⋊C4—21no—
626C2×C22⋊C4—21no—
627C2×C22⋊C4—21no—
628C2×C22⋊C4—21no—
629C2×C22⋊C4—21no—
630C2×C42—21no—
631#107—22no—
632#106—22no—
633#103—22no—
634#103—22no—
635#102—22no—
636#102—22no—
637#102—22no—
638#102—22no—
639#102—41no—
640#102—41no—
641C22⋊C8—22no—
642C22⋊C8—22no—
643C22⋊C8—22no—
644C22⋊C8D4×C6114yescomplemented
645#95—21no—
646#95—21no—
647#95—21no—
648C24—24no—
649C24—21no—
650C24—21no—
651C24—42no—
652C24—42no—
653C24—81no—
654C24—81no—
655C24—81no—
656C24—81no—
657C24C2×D4×C6111yescharacteristic
658C24C2×D4×C6111yescharacteristic
659C24C2×D4×C6111yescharacteristic
660#41—44no—
661#41—44no—
662#41—44no—
663#41—44no—
664C2×Q8—22no—
665C2×Q8—22no—
666C2×Q8—21no—
667C2×Q8—21no—
668C2×Q8—21no—
669C2×Q8—21no—
670C2×Q8—21no—
671C2×Q8—21no—
672C2×Q8—41no—
673C2×D4—24no—
674C2×D4—22no—
675C2×D4—22no—
676C2×D4—22no—
677C2×D4—22no—
678C2×D4—24no—
679C2×D4—24no—
680C2×D4—24no—
681C2×D4—24no—
682C2×D4—22no—
683C2×D4—22no—
684C2×D4—21no—
685C2×D4—21no—
686C2×D4—21no—
687C2×D4—21no—
688C2×D4—21no—
689C2×D4—21no—
690C2×D4—21no—
691C2×D4—21no—
692C2×D4—21no—
693C2×D4—21no—
694C2×D4—44no—
695C2×D4—44no—
696C2×D4—44no—
697C2×D4—44no—
698C2×D4—41no—
699C2×D4—41no—
700C2×D4—41no—
701C2×D4—42no—
702C2×D4—42no—
703C2×D4—81no—
704C2×D4—81no—
705C2×D4—81no—
706C2×D4—81no—
707C2×D4—81no—
708C2×D4—81no—
709C2×D4—81no—
710C2×D4—81no—
711C2×D4C2×D4×C6112yes—
712C2×D4C2×D4×C6112yes—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—21no—
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—21no—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—21no—
733C22×C4C2×D4×C6111yescharacteristic
734C22×C4C2×D4×C6111yescharacteristic
735C22×C4C2×D4×C6112yes—
736C22×C4C2×D4×C6112yes—
737C22×C4C2×D4×C6111yescharacteristic
738C22×C4C2×D4×C6112yes—
739C22×C4#41×C6112yes—
740C22×C4C24×C6111yescharacteristic
741SD16—44no—
742SD16—44no—
743M16—44no—
744C2×C8—21no—
745C2×C8—21no—
746C2×C8—21no—
747C2×C8—21no—
748C2×C8—21no—
749C2×C8—21no—
750C2×C8—21no—
751C2×C8—21no—
752C2×C8—21no—
753C2×C8—21no—
754C2×C8—44no—
755C2×C8C2×D4×C6112yes—
756C2×C8C2×D4×C6112yes—
757C4⋊C4—21no—
758C4⋊C4—21no—
759C4⋊C4—21no—
760C4⋊C4—21no—
761C4⋊C4—21no—
762C4⋊C4—21no—
763C4⋊C4—21no—
764C4⋊C4—21no—
765C4⋊C4—42no—
766C4⋊C4—42no—
767C4⋊C4—42no—
768C4⋊C4C2×D4×C6112yes—
769C4⋊C4C2×D4×C6112yes—
770C22⋊C4—24no—
771C22⋊C4—24no—
772C22⋊C4—24no—
773C22⋊C4—24no—
774C22⋊C4—24no—
775C22⋊C4—42no—
776C22⋊C4—42no—
777C22⋊C4—42no—
778C22⋊C4—81no—
779C22⋊C4—81no—
780C22⋊C4—81no—
781C42—24no—
782C23—21no—
783C23—21no—
784C23—21no—
785C23—21no—
786C23—21no—
787C23—21no—
788C23—21no—
789C23—21no—
790C23—21no—
791C23—21no—
792C23—21no—
793C23—21no—
794C23—21no—
795C23—21no—
796C23—21no—
797C23—21no—
798C23—21no—
799C23—22no—
800C23—22no—
801C23—21no—
802C23—21no—
803C23—48no—
804C23—41no—
805C23—41no—
806C23—41no—
807C23—41no—
808C23—41no—
809C23—41no—
810C23—41no—
811C23—41no—
812C23—41no—
813C23—41no—
814C23—41no—
815C23—41no—
816C23—84no—
817C23—84no—
818C23—84no—
819C23—84no—
820C23—84no—
821C23—84no—
822C23#120×C6112yes—
823C23#121×C6112yes—
824C23C22×D4×C6111yescharacteristic
825Q8—44no—
826Q8—41no—
827Q8—41no—
828Q8—41no—
829Q8—41no—
830D4—22no—
831D4—22no—
832D4—22no—
833D4—22no—
834D4—44no—
835D4—44no—
836D4—48no—
837D4—44no—
838D4—41no—
839D4—41no—
840D4—41no—
841D4—41no—
842D4—84no—
843D4—84no—
844D4—84no—
845D4—84no—
846C2×C4—21no—
847C2×C4—21no—
848C2×C4—21no—
849C2×C4—21no—
850C2×C4—22no—
851C2×C4—22no—
852C2×C4—22no—
853C2×C4—22no—
854C2×C4—22no—
855C2×C4—22no—
856C2×C4—22no—
857C2×C4—22no—
858C2×C4—21no—
859C2×C4—22no—
860C2×C4—22no—
861C2×C4—21no—
862C2×C4—21no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—41no—
869C2×C4—41no—
870C2×C4—41no—
871C2×C4—41no—
872C2×C4—41no—
873C2×C4—41no—
874C2×C4—41no—
875C2×C4—41no—
876C2×C4—41no—
877C2×C4—41no—
878C2×C4—41no—
879C2×C4—41no—
880C2×C4—41no—
881C2×C4—41no—
882C2×C4—41no—
883C2×C4#120×C6112yes—
884C2×C4#121×C6112yes—
885C2×C4C22×D4×C6111yescharacteristic
886C2×C4C22×D4×C6111yescharacteristic
887C2×C4C22×D4×C6111yescharacteristic
888C2×C4C2×#41×C6111yescharacteristic
889C2×C4H(5,𝔽2)×C6111yescharacteristic
890C2×C4H(5,𝔽2)×C6111yescharacteristic
891C8—22no—
892C8—22no—
893C8—41no—
894C8—41no—
895C22—22no—
896C22—22no—
897C22—22no—
898C22—22no—
899C22—22no—
900C22—22no—
901C22—41no—
902C22—41no—
903C22—41no—
904C22—41no—
905C22—41no—
906C22—41no—
907C22—41no—
908C22—41no—
909C22—41no—
910C22—41no—
911C22—41no—
912C22—42no—
913C22—42no—
914C22—41no—
915C22—41no—
916C22—41no—
917C22—42no—
918C22—42no—
919C22—41no—
920C22—42no—
921C22—42no—
922C22—816no—
923C22—81no—
924C22—81no—
925C22—81no—
926C22—81no—
927C22—81no—
928C22—81no—
929C22—81no—
930C22—81no—
931C22C2×#120×C6111yescharacteristic
932C22C2×#121×C6111yescharacteristic
933C22C61×#53411yescharacteristic
934C22C61×#57611yescharacteristic
935C22C61×#57711yescharacteristic
936C22C61×#57711yescharacteristic
937C22C61×#57711yescharacteristic
938C4—22no—
939C4—22no—
940C4—41no—
941C4—42no—
942C4—42no—
943C4—81no—
944C4—81no—
945C4—81no—
946C4—81no—
947C4D42×C6111yescharacteristic
948C4D42×C6111yescharacteristic
949C4C61×#54611yescharacteristic
950C4C61×#54611yescharacteristic
951C2—42no—
952C2—42no—
953C2—81no—
954C2—82no—
955C2—82no—
956C2C61×#241011yescharacteristic
957C2C61×#300911yescharacteristic
958C2C61×#301211yescharacteristic
959C2C61×#305711yescharacteristic
960C2C61×#306211yescharacteristic
961C2C61×#319811yescharacteristic
962C2C61×#320011yescharacteristic
subgroupG/H
center, socleC23×C61C22×D4
commutator, Frattini, cosocleC22×C4C24×C61
prime radicalC2×C61×#535C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C61 ◁ C22×#41×C61 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C61×#468C2semidirect
3. C2×C61×#465C2semidirect
4. C2×C61×#450C2semidirect
5. C2×C61×#408C2semidirect
6. C61×#2616C2semidirect
7. C61×#2034C2semidirect
8. C61×#2033C2semidirect
9. C61×#2000C2semidirect
10. C61×#2000C2semidirect
11. C61×#1895C2semidirect
12. C61×#1893C2semidirect
13. C61×#1873C2semidirect
14. C61×#1854C2semidirect
15. C61×#1786C2semidirect
20. C22×M16×C61C22semidirect
21. C23×C8×C61C22semidirect
27. C2×C22⋊Q8×C61C22semidirect
28. C2×C22⋊Q8×C61C22semidirect
39. C2×#107×C61C22semidirect
40. C2×#106×C61C22semidirect
41. C2×#103×C61C22semidirect
42. C2×#103×C61C22semidirect
52. C2×C22⋊C8×C61C22semidirect
53. C2×C22⋊C8×C61C22semidirect
59. C61×#380C22semidirect
60. C61×#380C22semidirect
61. C61×#340C22semidirect
62. C61×#340C22semidirect
63. C61×#340C22semidirect
64. C61×#340C22semidirect
162. C22⋊C8×C61D4semidirect
413. #24394C61direct (N × H)
471. C2×#468C2×C61semidirect
472. C2×#465C2×C61semidirect
473. C2×#450C2×C61semidirect
474. C2×#408C2×C61semidirect
475. #2616C2×C61semidirect
476. #2034C2×C61semidirect
477. #2033C2×C61semidirect
478. #2000C2×C61semidirect
479. #2000C2×C61semidirect
480. #1895C2×C61semidirect
481. #1893C2×C61semidirect
482. #1873C2×C61semidirect
483. #1854C2×C61semidirect
484. #1786C2×C61semidirect
501. C22×M16C22×C61semidirect
502. C23×C8C22×C61semidirect
508. C2×C22⋊Q8C22×C61semidirect
509. C2×C22⋊Q8C22×C61semidirect
520. C2×#107C22×C61semidirect
521. C2×#106C22×C61semidirect
522. C2×#103C22×C61semidirect
523. C2×#103C22×C61semidirect
533. C2×C22⋊C8C22×C61semidirect
534. C2×C22⋊C8C22×C61semidirect
540. #380C22×C61semidirect
541. #380C22×C61semidirect
542. #340C22×C61semidirect
543. #340C22×C61semidirect
544. #340C22×C61semidirect
545. #340C22×C61semidirect
546. C61#24394direct (N × H)
644. C22⋊C8D4×C61semidirect

Maximal subgroups

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

subgroupindex
C2×C61×#5352
C2×C61×#4682
C2×C61×#4652
C2×C61×#4502
C2×C61×#4082
C61×#26162
C61×#20342
C61×#20332
C61×#20002
C61×#18952
C61×#18932
C61×#18732
C61×#18542
C61×#17862
#2439461