Finite Group Databasebeta

← C61×#25132 #29528565

Subgroups — C61×#25132 #29528565

Order 15616.

1314 conjugacy classes of subgroups.

The subgroup lattice has 892 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C61×#469C211yesmaximal, characteristic, complemented
2C2×C61×#447C211yesmaximal, characteristic, complemented
3C2×C61×#436C211yesmaximal, characteristic, complemented
4C2×C61×#418C211yesmaximal, characteristic, complemented
5C61×#2414C211yesmaximal, characteristic, complemented
6C61×#2408C211yesmaximal, characteristic, complemented
7C61×#2065C211yesmaximal, characteristic, complemented
8C61×#2054C211yesmaximal, characteristic, complemented
9C61×#2033C211yesmaximal, characteristic, complemented
10C61×#1999C211yesmaximal, characteristic, complemented
11C61×#1970C211yesmaximal, characteristic, complemented
12C61×#1934C211yesmaximal, characteristic, complemented
13C61×#1895C211yesmaximal, characteristic, complemented
14C61×#1895C211yesmaximal, characteristic, complemented
15C61×#1854C211yesmaximal, characteristic, complemented
16C23×D4×C61C2211yescharacteristic
17C22×D8×C61C2211yescharacteristic
18C22×D8×C61C2211yescharacteristic
19C22×M16×C61C2211yescharacteristic
20C22×M16×C61C2211yescharacteristic, complemented
21C2×#121×C61C2211yescharacteristic
22C2×#121×C61C2211yescharacteristic
23C2×#121×C61C2211yescharacteristic
24C2×#121×C61C2211yescharacteristic, complemented
25C2×#120×C61—21no—
26C2×C4×D4×C61C2211yescharacteristic
27C2×#117×C61C2211yescharacteristic
28C61×#469—24no—
29C61×#447—24no—
30C61×#436—24no—
31C2×#107×C61C2211yescharacteristic, complemented
32C2×#106×C61C2211yescharacteristic, complemented
33C2×C4⋊C8×C61C2211yescharacteristic, complemented
34C61×#418—24no—
35C2×#102×C61C2211yescharacteristic
36C2×#102×C61C2211yescharacteristic
37C2×#102×C61C2211yescharacteristic
38C2×#102×C61C2211yescharacteristic
39C2×#102×C61C2211yescharacteristic
40C2×#102×C61C2211yescharacteristic
41C2×#102×C61C2211yescharacteristic, complemented
42C2×#102×C61C2211yescharacteristic, complemented
43C2×C22⋊C8×C61C2211yescharacteristic
44C2×C22⋊C8×C61C2211yescharacteristic, complemented
45C2×C4×C8×C61C2211yescharacteristic, complemented
46C61×#394—21no—
47C61×#394—21no—
48C61×#392—21no—
49C61×#392—21no—
50C61×#390—21no—
51C61×#390C2211yescharacteristic
52C61×#390C2211yescharacteristic
53C61×#390C2211yescharacteristic, complemented
54C61×#389C2211yescharacteristic, complemented
55C61×#388—21no—
56C61×#380C2211yescharacteristic
57C61×#380C2211yescharacteristic, complemented
58C61×#379—21no—
59C61×#340C2211yescharacteristic, complemented
60C61×#340C2211yescharacteristic, complemented
61C61×#340C2211yescharacteristic, complemented
62C61×#340C2211yescharacteristic, complemented
63C25×C61—21no—
64C22×D4×C61—22no—
65C22×D4×C61—22no—
66C22×D4×C61—21no—
67C22×D4×C61—21no—
68C22×D4×C61—21no—
69C22×D4×C61—21no—
70C22×D4×C61—22no—
71C22×D4×C61—21no—
72C22×D4×C61—22no—
73C22×D4×C61—41no—
74C22×D4×C61—41no—
75C22×D4×C61D411yescharacteristic
76C22×D4×C61C2311yescharacteristic
77C22×D4×C61C2311yescharacteristic
78C22×D4×C61C2311yescharacteristic
79C23×C4×C61C2311yescharacteristic
80C23×C4×C61C2311yescharacteristic
81C2×D8×C61—22no—
82C2×D8×C61—22no—
83C2×D8×C61—22no—
84C2×D8×C61—22no—
85C2×D8×C61—41no—
86C2×D8×C61—41no—
87C2×M16×C61—22no—
88C2×M16×C61—22no—
89C2×M16×C61—22no—
90C2×M16×C61—22no—
91C2×M16×C61—41no—
92C2×M16×C61—41no—
93C22×C8×C61C2311yescharacteristic
94C22×C8×C61C2311yescharacteristic
95C22×C8×C61C2311yescharacteristic
96C22×C8×C61C2311yescharacteristic
97#121×C61—22no—
98#121×C61—22no—
99#121×C61—22no—
100#121×C61—22no—
101#121×C61—22no—
102#121×C61—41no—
103#121×C61—41no—
104#121×C61—41no—
105#120×C61—44no—
106C4×D4×C61—22no—
107C4×D4×C61—22no—
108#117×C61—22no—
109#117×C61—41no—
110C2×C4⋊C4×C61—21no—
111C2×C4⋊C4×C61D411yescharacteristic
112C2×C4⋊C4×C61C2311yescharacteristic
113C2×C4⋊C4×C61C2311yescharacteristic
114C2×C4⋊C4×C61C2311yescharacteristic
115C2×C4⋊C4×C61C2311yescharacteristic
116C2×C4⋊C4×C61C2311yescharacteristic
117C2×C22⋊C4×C61—21no—
118C2×C22⋊C4×C61—21no—
119C2×C22⋊C4×C61—21no—
120C2×C22⋊C4×C61—21no—
121C2×C22⋊C4×C61—21no—
122C2×C22⋊C4×C61—21no—
123C2×C22⋊C4×C61—21no—
124C2×C22⋊C4×C61—21no—
125C2×C22⋊C4×C61—21no—
126C2×C22⋊C4×C61—21no—
127C2×C22⋊C4×C61—21no—
128C2×C22⋊C4×C61—21no—
129C2×C22⋊C4×C61—21no—
130C2×C22⋊C4×C61D411yescharacteristic
131C2×C22⋊C4×C61D411yescharacteristic
132C2×C42×C61—21no—
133C2×C42×C61C2311yescharacteristic
134#107×C61—41no—
135#106×C61—22no—
136C4⋊C8×C61—22no—
137#102×C61—22no—
138#102×C61—22no—
139#102×C61—22no—
140#102×C61—22no—
141#102×C61—22no—
142#102×C61—22no—
143#102×C61—41no—
144#102×C61D414yescomplemented
145C22⋊C8×C61—22no—
146C22⋊C8×C61D414yescomplemented
147C4×C8×C61—22no—
148#95×C61—21no—
149#95×C61—21no—
150#95×C61—21no—
151C24×C61—21no—
152C24×C61—21no—
153C24×C61—21no—
154C24×C61—42no—
155C24×C61—42no—
156C24×C61—42no—
157C24×C61—42no—
158C24×C61—42no—
159C24×C61—81no—
160C24×C61—81no—
161C24×C61C2×D411yescharacteristic
162C24×C61C2×D411yescharacteristic
163C2×D4×C61—28no—
164C2×D4×C61—22no—
165C2×D4×C61—22no—
166C2×D4×C61—21no—
167C2×D4×C61—21no—
168C2×D4×C61—21no—
169C2×D4×C61—21no—
170C2×D4×C61—21no—
171C2×D4×C61—21no—
172C2×D4×C61—21no—
173C2×D4×C61—21no—
174C2×D4×C61—21no—
175C2×D4×C61—21no—
176C2×D4×C61—21no—
177C2×D4×C61—21no—
178C2×D4×C61—21no—
179C2×D4×C61—21no—
180C2×D4×C61—21no—
181C2×D4×C61—21no—
182C2×D4×C61—44no—
183C2×D4×C61—44no—
184C2×D4×C61—41no—
185C2×D4×C61—42no—
186C2×D4×C61—42no—
187C2×D4×C61—44no—
188C2×D4×C61—42no—
189C2×D4×C61—42no—
190C2×D4×C61—42no—
191C2×D4×C61—42no—
192C2×D4×C61—42no—
193C2×D4×C61—42no—
194C2×D4×C61—42no—
195C2×D4×C61—42no—
196C2×D4×C61—81no—
197C2×D4×C61—81no—
198C2×D4×C61—81no—
199C2×D4×C61—81no—
200C2×D4×C61—81no—
201C2×D4×C61C2×D412yes—
202C2×D4×C61#4112yes—
203C22×C4×C61—21no—
204C22×C4×C61—21no—
205C22×C4×C61—21no—
206C22×C4×C61—21no—
207C22×C4×C61—21no—
208C22×C4×C61—21no—
209C22×C4×C61—21no—
210C22×C4×C61—21no—
211C22×C4×C61—21no—
212C22×C4×C61—21no—
213C22×C4×C61—21no—
214C22×C4×C61—21no—
215C22×C4×C61—21no—
216C22×C4×C61—21no—
217C22×C4×C61—21no—
218C22×C4×C61C2×D411yescharacteristic
219C22×C4×C61C2×D411yescharacteristic
220C22×C4×C61C2×D411yescharacteristic
221C22×C4×C61C2×D412yes—
222C22×C4×C61C2×D411yescharacteristic
223C22×C4×C61#4112yes—
224C22×C4×C61C2411yescharacteristic
225D8×C61—44no—
226D8×C61—44no—
227M16×C61—44no—
228M16×C61—44no—
229C2×C8×C61—21no—
230C2×C8×C61—21no—
231C2×C8×C61—21no—
232C2×C8×C61—21no—
233C2×C8×C61—21no—
234C2×C8×C61—21no—
235C2×C8×C61—21no—
236C2×C8×C61—21no—
237C2×C8×C61—21no—
238C2×C8×C61C2×D412yes—
239C2×C8×C61C2×D412yes—
240C2×C8×C61C2×D412yes—
241C4⋊C4×C61—22no—
242C4⋊C4×C61—21no—
243C4⋊C4×C61—21no—
244C4⋊C4×C61—21no—
245C4⋊C4×C61—21no—
246C4⋊C4×C61—21no—
247C4⋊C4×C61—21no—
248C4⋊C4×C61—21no—
249C4⋊C4×C61—21no—
250C4⋊C4×C61—21no—
251C4⋊C4×C61—81no—
252C4⋊C4×C61C2×D412yes—
253C22⋊C4×C61—22no—
254C22⋊C4×C61—22no—
255C22⋊C4×C61—42no—
256C22⋊C4×C61—42no—
257C22⋊C4×C61—42no—
258C22⋊C4×C61—42no—
259C22⋊C4×C61—42no—
260C22⋊C4×C61—42no—
261C22⋊C4×C61—42no—
262C22⋊C4×C61—42no—
263C22⋊C4×C61—42no—
264C22⋊C4×C61—81no—
265C22⋊C4×C61—81no—
266C22⋊C4×C61—81no—
267C22⋊C4×C61—81no—
268C42×C61—21no—
269C42×C61—21no—
270C42×C61—42no—
271C23×C61—21no—
272C23×C61—21no—
273C23×C61—21no—
274C23×C61—21no—
275C23×C61—21no—
276C23×C61—21no—
277C23×C61—21no—
278C23×C61—22no—
279C23×C61—21no—
280C23×C61—22no—
281C23×C61—21no—
282C23×C61—21no—
283C23×C61—21no—
284C23×C61—21no—
285C23×C61—21no—
286C23×C61—48no—
287C23×C61—41no—
288C23×C61—41no—
289C23×C61—41no—
290C23×C61—41no—
291C23×C61—41no—
292C23×C61—41no—
293C23×C61—41no—
294C23×C61—41no—
295C23×C61—41no—
296C23×C61—41no—
297C23×C61—41no—
298C23×C61—41no—
299C23×C61—41no—
300C23×C61—41no—
301C23×C61—41no—
302C23×C61—41no—
303C23×C61—41no—
304C23×C61—41no—
305C23×C61—41no—
306C23×C61—84no—
307C23×C61—84no—
308C23×C61—84no—
309C23×C61—84no—
310C23×C61—84no—
311C23×C61—84no—
312C23×C61#12112yes—
313C23×C61C22×D411yescharacteristic
314D4×C61—22no—
315D4×C61—22no—
316D4×C61—22no—
317D4×C61—22no—
318D4×C61—44no—
319D4×C61—48no—
320D4×C61—41no—
321D4×C61—41no—
322D4×C61—41no—
323D4×C61—41no—
324D4×C61—41no—
325D4×C61—41no—
326D4×C61—41no—
327D4×C61—41no—
328D4×C61—84no—
329D4×C61—84no—
330D4×C61—84no—
331D4×C61—84no—
332C2×C4×C61—21no—
333C2×C4×C61—21no—
334C2×C4×C61—21no—
335C2×C4×C61—21no—
336C2×C4×C61—22no—
337C2×C4×C61—22no—
338C2×C4×C61—22no—
339C2×C4×C61—22no—
340C2×C4×C61—21no—
341C2×C4×C61—21no—
342C2×C4×C61—22no—
343C2×C4×C61—21no—
344C2×C4×C61—21no—
345C2×C4×C61—21no—
346C2×C4×C61—21no—
347C2×C4×C61—41no—
348C2×C4×C61—41no—
349C2×C4×C61—41no—
350C2×C4×C61—41no—
351C2×C4×C61—41no—
352C2×C4×C61—41no—
353C2×C4×C61—41no—
354C2×C4×C61—41no—
355C2×C4×C61—41no—
356C2×C4×C61—41no—
357C2×C4×C61—41no—
358C2×C4×C61—41no—
359C2×C4×C61—41no—
360C2×C4×C61—41no—
361C2×C4×C61—41no—
362C2×C4×C61—41no—
363C2×C4×C61—41no—
364C2×C4×C61—41no—
365C2×C4×C61#12112yes—
366C2×C4×C61AGL(1,ℤ/8)12yes—
367C2×C4×C61C22×D411yescharacteristic
368C2×C4×C61C22×D411yescharacteristic
369C2×C4×C61C2×#4111yescharacteristic
370C2×C4×C61C2×#4111yescharacteristic
371C2×C4×C61H(5,𝔽2)11yescharacteristic
372C2×C4×C61H(5,𝔽2)11yescharacteristic
373C8×C61—22no—
374C8×C61—22no—
375C8×C61—22no—
376C8×C61—41no—
377#25132C6111yesmaximal, characteristic, direct product factor, Sylow
378C22×C61—22no—
379C22×C61—22no—
380C22×C61—22no—
381C22×C61—41no—
382C22×C61—41no—
383C22×C61—41no—
384C22×C61—41no—
385C22×C61—41no—
386C22×C61—42no—
387C22×C61—42no—
388C22×C61—41no—
389C22×C61—42no—
390C22×C61—41no—
391C22×C61—42no—
392C22×C61—41no—
393C22×C61—41no—
394C22×C61—41no—
395C22×C61—42no—
396C22×C61—41no—
397C22×C61—42no—
398C22×C61—816no—
399C22×C61—81no—
400C22×C61—81no—
401C22×C61—81no—
402C22×C61—81no—
403C22×C61—81no—
404C22×C61—81no—
405C22×C61—81no—
406C22×C61—81no—
407C22×C61—81no—
408C22×C61—81no—
409C22×C61—81no—
410C22×C61—81no—
411C22×C61—81no—
412C22×C61—81no—
413C22×C61—81no—
414C22×C61C2×#12111yescharacteristic
415C22×C61D4211yescharacteristic
416C22×C61#54611yescharacteristic
417C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
418C22×C61#57511yescharacteristic
419C22×C61#57611yescharacteristic
420C22×C61#57611yescharacteristic
421C4×C61—22no—
422C4×C61—22no—
423C4×C61—41no—
424C4×C61—42no—
425C4×C61—41no—
426C4×C61—81no—
427C4×C61—81no—
428C4×C61—81no—
429C4×C61—81no—
430C4×C61#52511yescharacteristic
431C4×C61#53811yescharacteristic
432C4×C61D4211yescharacteristic
433C4×C61#54611yescharacteristic
434C2×#469C2×C6111yescharacteristic, complemented
435C2×#447C2×C6111yescharacteristic, complemented
436C2×#436C2×C6111yescharacteristic, complemented
437C2×#418C2×C6111yescharacteristic, complemented
438#2414C2×C6111yescharacteristic, complemented
439#2408C2×C6111yescharacteristic, complemented
440#2065C2×C6111yescharacteristic, complemented
441#2054C2×C6111yescharacteristic, complemented
442#2033C2×C6111yescharacteristic, complemented
443#1999C2×C6111yescharacteristic, complemented
444#1970C2×C6111yescharacteristic, complemented
445#1934C2×C6111yescharacteristic, complemented
446#1895C2×C6111yescharacteristic, complemented
447#1895C2×C6111yescharacteristic, complemented
448#1854C2×C6111yescharacteristic, complemented
449C2×C61—42no—
450C2×C61—81no—
451C2×C61—82no—
452C2×C61—82no—
453C2×C61—161no—
454C2×C61#242411yescharacteristic
455C2×C61#305511yescharacteristic
456C2×C61#305811yescharacteristic
457C2×C61#327311yescharacteristic
458C2×C61#327411yescharacteristic
459C2×C61#332211yescharacteristic
460C2×C61#332511yescharacteristic
461C23×D4C22×C6111yescharacteristic
462C22×D8C22×C6111yescharacteristic
463C22×D8C22×C6111yescharacteristic
464C22×M16C22×C6111yescharacteristic
465C22×M16C22×C6111yescharacteristic, complemented
466C2×#121C22×C6111yescharacteristic
467C2×#121C22×C6111yescharacteristic
468C2×#121C22×C6111yescharacteristic
469C2×#121C22×C6111yescharacteristic, complemented
470C2×#120—21no—
471C2×C4×D4C22×C6111yescharacteristic
472C2×#117C22×C6111yescharacteristic
473#469—24no—
474#447—24no—
475#436—24no—
476C2×#107C22×C6111yescharacteristic, complemented
477C2×#106C22×C6111yescharacteristic, complemented
478C2×C4⋊C8C22×C6111yescharacteristic, complemented
479#418—24no—
480C2×#102C22×C6111yescharacteristic
481C2×#102C22×C6111yescharacteristic
482C2×#102C22×C6111yescharacteristic
483C2×#102C22×C6111yescharacteristic
484C2×#102C22×C6111yescharacteristic
485C2×#102C22×C6111yescharacteristic
486C2×#102C22×C6111yescharacteristic, complemented
487C2×#102C22×C6111yescharacteristic, complemented
488C2×C22⋊C8C22×C6111yescharacteristic
489C2×C22⋊C8C22×C6111yescharacteristic, complemented
490C2×C4×C8C22×C6111yescharacteristic, complemented
491#394—21no—
492#394—21no—
493#392—21no—
494#392—21no—
495#390—21no—
496#390C22×C6111yescharacteristic
497#390C22×C6111yescharacteristic
498#390C22×C6111yescharacteristic, complemented
499#389C22×C6111yescharacteristic, complemented
500#388—21no—
501#380C22×C6111yescharacteristic
502#380C22×C6111yescharacteristic, complemented
503#379—21no—
504#340C22×C6111yescharacteristic, complemented
505#340C22×C6111yescharacteristic, complemented
506#340C22×C6111yescharacteristic, complemented
507#340C22×C6111yescharacteristic, complemented
508C61#2513211yescharacteristic, direct product factor, Sylow
509C25—21no—
510C22×D4—22no—
511C22×D4—22no—
512C22×D4—21no—
513C22×D4—21no—
514C22×D4—21no—
515C22×D4—21no—
516C22×D4—22no—
517C22×D4—21no—
518C22×D4—22no—
519C22×D4—41no—
520C22×D4—41no—
521C22×D4D4×C6111yescharacteristic
522C22×D4C23×C6111yescharacteristic
523C22×D4C23×C6111yescharacteristic
524C22×D4C23×C6111yescharacteristic
525C23×C4C23×C6111yescharacteristic
526C23×C4C23×C6111yescharacteristic
527C2×D8—22no—
528C2×D8—22no—
529C2×D8—22no—
530C2×D8—22no—
531C2×D8—41no—
532C2×D8—41no—
533C2×M16—22no—
534C2×M16—22no—
535C2×M16—22no—
536C2×M16—22no—
537C2×M16—41no—
538C2×M16—41no—
539C22×C8C23×C6111yescharacteristic
540C22×C8C23×C6111yescharacteristic
541C22×C8C23×C6111yescharacteristic
542C22×C8C23×C6111yescharacteristic
543#121—22no—
544#121—22no—
545#121—22no—
546#121—22no—
547#121—22no—
548#121—41no—
549#121—41no—
550#121—41no—
551#120—44no—
552C4×D4—22no—
553C4×D4—22no—
554#117—22no—
555#117—41no—
556C2×C4⋊C4—21no—
557C2×C4⋊C4D4×C6111yescharacteristic
558C2×C4⋊C4C23×C6111yescharacteristic
559C2×C4⋊C4C23×C6111yescharacteristic
560C2×C4⋊C4C23×C6111yescharacteristic
561C2×C4⋊C4C23×C6111yescharacteristic
562C2×C4⋊C4C23×C6111yescharacteristic
563C2×C22⋊C4—21no—
564C2×C22⋊C4—21no—
565C2×C22⋊C4—21no—
566C2×C22⋊C4—21no—
567C2×C22⋊C4—21no—
568C2×C22⋊C4—21no—
569C2×C22⋊C4—21no—
570C2×C22⋊C4—21no—
571C2×C22⋊C4—21no—
572C2×C22⋊C4—21no—
573C2×C22⋊C4—21no—
574C2×C22⋊C4—21no—
575C2×C22⋊C4—21no—
576C2×C22⋊C4D4×C6111yescharacteristic
577C2×C22⋊C4D4×C6111yescharacteristic
578C2×C42—21no—
579C2×C42C23×C6111yescharacteristic
580#107—41no—
581#106—22no—
582C4⋊C8—22no—
583#102—22no—
584#102—22no—
585#102—22no—
586#102—22no—
587#102—22no—
588#102—22no—
589#102—41no—
590#102D4×C6114yescomplemented
591C22⋊C8—22no—
592C22⋊C8D4×C6114yescomplemented
593C4×C8—22no—
594#95—21no—
595#95—21no—
596#95—21no—
597C24—21no—
598C24—21no—
599C24—21no—
600C24—42no—
601C24—42no—
602C24—42no—
603C24—42no—
604C24—42no—
605C24—81no—
606C24—81no—
607C24C2×D4×C6111yescharacteristic
608C24C2×D4×C6111yescharacteristic
609C2×D4—28no—
610C2×D4—22no—
611C2×D4—22no—
612C2×D4—21no—
613C2×D4—21no—
614C2×D4—21no—
615C2×D4—21no—
616C2×D4—21no—
617C2×D4—21no—
618C2×D4—21no—
619C2×D4—21no—
620C2×D4—21no—
621C2×D4—21no—
622C2×D4—21no—
623C2×D4—21no—
624C2×D4—21no—
625C2×D4—21no—
626C2×D4—21no—
627C2×D4—21no—
628C2×D4—44no—
629C2×D4—44no—
630C2×D4—41no—
631C2×D4—42no—
632C2×D4—42no—
633C2×D4—44no—
634C2×D4—42no—
635C2×D4—42no—
636C2×D4—42no—
637C2×D4—42no—
638C2×D4—42no—
639C2×D4—42no—
640C2×D4—42no—
641C2×D4—42no—
642C2×D4—81no—
643C2×D4—81no—
644C2×D4—81no—
645C2×D4—81no—
646C2×D4—81no—
647C2×D4C2×D4×C6112yes—
648C2×D4#41×C6112yes—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—21no—
664C22×C4C2×D4×C6111yescharacteristic
665C22×C4C2×D4×C6111yescharacteristic
666C22×C4C2×D4×C6111yescharacteristic
667C22×C4C2×D4×C6112yes—
668C22×C4C2×D4×C6111yescharacteristic
669C22×C4#41×C6112yes—
670C22×C4C24×C6111yescharacteristic
671D8—44no—
672D8—44no—
673M16—44no—
674M16—44no—
675C2×C8—21no—
676C2×C8—21no—
677C2×C8—21no—
678C2×C8—21no—
679C2×C8—21no—
680C2×C8—21no—
681C2×C8—21no—
682C2×C8—21no—
683C2×C8—21no—
684C2×C8C2×D4×C6112yes—
685C2×C8C2×D4×C6112yes—
686C2×C8C2×D4×C6112yes—
687C4⋊C4—22no—
688C4⋊C4—21no—
689C4⋊C4—21no—
690C4⋊C4—21no—
691C4⋊C4—21no—
692C4⋊C4—21no—
693C4⋊C4—21no—
694C4⋊C4—21no—
695C4⋊C4—21no—
696C4⋊C4—21no—
697C4⋊C4—81no—
698C4⋊C4C2×D4×C6112yes—
699C22⋊C4—22no—
700C22⋊C4—22no—
701C22⋊C4—42no—
702C22⋊C4—42no—
703C22⋊C4—42no—
704C22⋊C4—42no—
705C22⋊C4—42no—
706C22⋊C4—42no—
707C22⋊C4—42no—
708C22⋊C4—42no—
709C22⋊C4—42no—
710C22⋊C4—81no—
711C22⋊C4—81no—
712C22⋊C4—81no—
713C22⋊C4—81no—
714C42—21no—
715C42—21no—
716C42—42no—
717C23—21no—
718C23—21no—
719C23—21no—
720C23—21no—
721C23—21no—
722C23—21no—
723C23—22no—
724C23—21no—
725C23—22no—
726C23—21no—
727C23—21no—
728C23—21no—
729C23—21no—
730C23—21no—
731C23—21no—
732C23—48no—
733C23—41no—
734C23—41no—
735C23—41no—
736C23—41no—
737C23—41no—
738C23—41no—
739C23—41no—
740C23—41no—
741C23—41no—
742C23—41no—
743C23—41no—
744C23—41no—
745C23—41no—
746C23—41no—
747C23—41no—
748C23—41no—
749C23—41no—
750C23—41no—
751C23—41no—
752C23—84no—
753C23—84no—
754C23—84no—
755C23—84no—
756C23—84no—
757C23—84no—
758C23#121×C6112yes—
759C23C22×D4×C6111yescharacteristic
760D4—22no—
761D4—22no—
762D4—22no—
763D4—22no—
764D4—44no—
765D4—48no—
766D4—41no—
767D4—41no—
768D4—41no—
769D4—41no—
770D4—41no—
771D4—41no—
772D4—41no—
773D4—41no—
774D4—84no—
775D4—84no—
776D4—84no—
777D4—84no—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—21no—
782C2×C4—22no—
783C2×C4—22no—
784C2×C4—22no—
785C2×C4—22no—
786C2×C4—22no—
787C2×C4—21no—
788C2×C4—21no—
789C2×C4—21no—
790C2×C4—21no—
791C2×C4—21no—
792C2×C4—21no—
793C2×C4—41no—
794C2×C4—41no—
795C2×C4—41no—
796C2×C4—41no—
797C2×C4—41no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—41no—
801C2×C4—41no—
802C2×C4—41no—
803C2×C4—41no—
804C2×C4—41no—
805C2×C4—41no—
806C2×C4—41no—
807C2×C4—41no—
808C2×C4—41no—
809C2×C4—41no—
810C2×C4—41no—
811C2×C4#121×C6112yes—
812C2×C4AGL(1,ℤ/8)×C6112yes—
813C2×C4C22×D4×C6111yescharacteristic
814C2×C4C22×D4×C6111yescharacteristic
815C2×C4C2×#41×C6111yescharacteristic
816C2×C4C2×#41×C6111yescharacteristic
817C2×C4H(5,𝔽2)×C6111yescharacteristic
818C2×C4H(5,𝔽2)×C6111yescharacteristic
819C8—22no—
820C8—22no—
821C8—22no—
822C8—41no—
823C22—22no—
824C22—22no—
825C22—22no—
826C22—41no—
827C22—41no—
828C22—41no—
829C22—41no—
830C22—41no—
831C22—41no—
832C22—41no—
833C22—42no—
834C22—41no—
835C22—42no—
836C22—41no—
837C22—42no—
838C22—42no—
839C22—41no—
840C22—42no—
841C22—41no—
842C22—42no—
843C22—816no—
844C22—81no—
845C22—81no—
846C22—81no—
847C22—81no—
848C22—81no—
849C22—81no—
850C22—81no—
851C22—81no—
852C22—81no—
853C22—81no—
854C22—81no—
855C22—81no—
856C22—81no—
857C22—81no—
858C22—81no—
859C22C2×#121×C6111yescharacteristic
860C22D42×C6111yescharacteristic
861C22C61×#54611yescharacteristic
862C22C2×AGL(1,ℤ/8)×C6111yescharacteristic
863C22C61×#57511yescharacteristic
864C22C61×#57611yescharacteristic
865C22C61×#57611yescharacteristic
866C4—22no—
867C4—22no—
868C4—41no—
869C4—41no—
870C4—42no—
871C4—81no—
872C4—81no—
873C4—81no—
874C4—81no—
875C4C61×#52511yescharacteristic
876C4C61×#53811yescharacteristic
877C4D42×C6111yescharacteristic
878C4C61×#54611yescharacteristic
879C2—42no—
880C2—81no—
881C2—82no—
882C2—82no—
883C2—161no—
884C2C61×#242411yescharacteristic
885C2C61×#305511yescharacteristic
886C2C61×#305811yescharacteristic
887C2C61×#327311yescharacteristic
888C2C61×#327411yescharacteristic
889C2C61×#332211yescharacteristic
890C2C61×#332511yescharacteristic
subgroupG/H
center, socleC23×C61C22×D4
commutator, Frattini, cosocleC22×C4C24×C61
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C61 ◁ C2×C4×D4×C61 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C61×#469C2semidirect
2. C2×C61×#447C2semidirect
3. C2×C61×#436C2semidirect
4. C2×C61×#418C2semidirect
5. C61×#2414C2semidirect
6. C61×#2408C2semidirect
7. C61×#2065C2semidirect
8. C61×#2054C2semidirect
9. C61×#2033C2semidirect
10. C61×#1999C2semidirect
11. C61×#1970C2semidirect
12. C61×#1934C2semidirect
13. C61×#1895C2semidirect
14. C61×#1895C2semidirect
15. C61×#1854C2semidirect
20. C22×M16×C61C22semidirect
24. C2×#121×C61C22semidirect
31. C2×#107×C61C22semidirect
32. C2×#106×C61C22semidirect
33. C2×C4⋊C8×C61C22semidirect
41. C2×#102×C61C22semidirect
42. C2×#102×C61C22semidirect
44. C2×C22⋊C8×C61C22semidirect
45. C2×C4×C8×C61C22semidirect
53. C61×#390C22semidirect
54. C61×#389C22semidirect
57. C61×#380C22semidirect
59. C61×#340C22semidirect
60. C61×#340C22semidirect
61. C61×#340C22semidirect
62. C61×#340C22semidirect
144. #102×C61D4semidirect
146. C22⋊C8×C61D4semidirect
377. #25132C61direct (N × H)
434. C2×#469C2×C61semidirect
435. C2×#447C2×C61semidirect
436. C2×#436C2×C61semidirect
437. C2×#418C2×C61semidirect
438. #2414C2×C61semidirect
439. #2408C2×C61semidirect
440. #2065C2×C61semidirect
441. #2054C2×C61semidirect
442. #2033C2×C61semidirect
443. #1999C2×C61semidirect
444. #1970C2×C61semidirect
445. #1934C2×C61semidirect
446. #1895C2×C61semidirect
447. #1895C2×C61semidirect
448. #1854C2×C61semidirect
465. C22×M16C22×C61semidirect
469. C2×#121C22×C61semidirect
476. C2×#107C22×C61semidirect
477. C2×#106C22×C61semidirect
478. C2×C4⋊C8C22×C61semidirect
486. C2×#102C22×C61semidirect
487. C2×#102C22×C61semidirect
489. C2×C22⋊C8C22×C61semidirect
490. C2×C4×C8C22×C61semidirect
498. #390C22×C61semidirect
499. #389C22×C61semidirect
502. #380C22×C61semidirect
504. #340C22×C61semidirect
505. #340C22×C61semidirect
506. #340C22×C61semidirect
507. #340C22×C61semidirect
508. C61#25132direct (N × H)
590. #102D4×C61semidirect
592. 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×#4692
C2×C61×#4472
C2×C61×#4362
C2×C61×#4182
C61×#24142
C61×#24082
C61×#20652
C61×#20542
C61×#20332
C61×#19992
C61×#19702
C61×#19342
C61×#18952
C61×#18542
#2513261