Finite Group Databasebeta

← C61×#25139 #29528572

Subgroups — C61×#25139 #29528572

Order 15616.

1194 conjugacy classes of subgroups.

The subgroup lattice has 844 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C61×#468C211yesmaximal, characteristic, complemented
2C2×C61×#449C211yesmaximal, characteristic, complemented
3C2×C61×#436C211yesmaximal, characteristic, complemented
4C2×C61×#417C211yesmaximal, characteristic, complemented
5C61×#2416C211yesmaximal, characteristic, complemented
6C61×#2407C211yesmaximal, characteristic, complemented
7C61×#2067C211yesmaximal, characteristic, complemented
8C61×#2055C211yesmaximal, characteristic, complemented
9C61×#2036C211yesmaximal, characteristic, complemented
10C61×#1999C211yesmaximal, characteristic, complemented
11C61×#1970C211yesmaximal, characteristic, complemented
12C61×#1933C211yesmaximal, characteristic, complemented
13C61×#1895C211yesmaximal, characteristic, complemented
14C61×#1895C211yesmaximal, characteristic, complemented
15C61×#1852C211yesmaximal, characteristic, complemented
16C22×#41×C61C2211yescharacteristic
17C22×SD16×C61C2211yescharacteristic
18C22×D8×C61C2211yescharacteristic
19C22×M16×C61C2211yescharacteristic
20C22×M16×C61C2211yescharacteristic
21C2×C22⋊Q8×C61C2211yescharacteristic
22C2×#121×C61—21no—
23C2×#121×C61C2211yescharacteristic
24C2×#121×C61C2211yescharacteristic
25C2×#121×C61C2211yescharacteristic
26C2×C4×D4×C61C2211yescharacteristic
27C22×C4⋊C4×C61C2211yescharacteristic
28C61×#468—24no—
29C61×#449—24no—
30C61×#436—24no—
31C2×#107×C61C2211yescharacteristic
32C2×#107×C61C2211yescharacteristic
33C2×C4⋊C8×C61C2211yescharacteristic
34C61×#417—24no—
35C2×#103×C61C2211yescharacteristic
36C2×#103×C61C2211yescharacteristic
37C2×#103×C61C2211yescharacteristic
38C2×#102×C61C2211yescharacteristic
39C2×#102×C61C2211yescharacteristic
40C2×#102×C61C2211yescharacteristic
41C2×#102×C61C2211yescharacteristic
42C2×#102×C61C2211yescharacteristic
43C2×C22⋊C8×C61C2211yescharacteristic
44C2×C22⋊C8×C61C2211yescharacteristic
45C2×C4×C8×C61C2211yescharacteristic
46C61×#396—21no—
47C61×#394—21no—
48C61×#394—21no—
49C61×#392—21no—
50C61×#391C2211yescharacteristic
51C61×#390C2211yescharacteristic
52C61×#390C2211yescharacteristic
53C61×#389C2211yescharacteristic
54C61×#386—21no—
55C61×#386—21no—
56C61×#385—21no—
57C61×#380C2211yescharacteristic
58C61×#380C2211yescharacteristic
59C61×#340C2211yescharacteristic
60C61×#340C2211yescharacteristic
61C61×#340C2211yescharacteristic
62C61×#340C2211yescharacteristic
63C2×#41×C61—22no—
64C2×#41×C61—22no—
65C2×#41×C61—22no—
66C2×#41×C61—22no—
67C2×#41×C61—41no—
68C2×#41×C61—41no—
69C22×Q8×C61C2311yescharacteristic
70C22×D4×C61—21no—
71C22×D4×C61—21no—
72C22×D4×C61—21no—
73C22×D4×C61—21no—
74C22×D4×C61D411yescharacteristic
75C22×D4×C61C2311yescharacteristic
76C22×D4×C61C2311yescharacteristic
77C23×C4×C61—21no—
78C23×C4×C61—21no—
79C23×C4×C61C2311yescharacteristic
80C23×C4×C61C2311yescharacteristic
81C2×SD16×C61—22no—
82C2×SD16×C61—22no—
83C2×SD16×C61—41no—
84C2×D8×C61—22no—
85C2×D8×C61—22no—
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
97C22⋊Q8×C61—22no—
98C22⋊Q8×C61—41no—
99#121×C61—22no—
100#121×C61—22no—
101#121×C61—22no—
102#121×C61—22no—
103#121×C61—41no—
104#121×C61—41no—
105#121×C61—44no—
106C4×D4×C61—22no—
107C4×D4×C61—22no—
108C2×C4⋊C4×C61—22no—
109C2×C4⋊C4×C61—21no—
110C2×C4⋊C4×C61—21no—
111C2×C4⋊C4×C61—21no—
112C2×C4⋊C4×C61—41no—
113C2×C4⋊C4×C61D411yescharacteristic
114C2×C4⋊C4×C61C2311yescharacteristic
115C2×C4⋊C4×C61C2311yescharacteristic
116C2×C4⋊C4×C61C2311yescharacteristic
117C2×C4⋊C4×C61C2311yescharacteristic
118C2×C4⋊C4×C61C2311yescharacteristic
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×C61D411yescharacteristic
130C2×C22⋊C4×C61D411yescharacteristic
131C2×C42×C61C2311yescharacteristic
132#107×C61—22no—
133#107×C61—41no—
134C4⋊C8×C61—22no—
135#103×C61—22no—
136#103×C61—22no—
137#103×C61D414yescomplemented
138#102×C61—22no—
139#102×C61—22no—
140#102×C61—22no—
141#102×C61—22no—
142#102×C61—41no—
143C22⋊C8×C61—22no—
144C22⋊C8×C61D414yescomplemented
145C4×C8×C61—22no—
146#95×C61—21no—
147#95×C61—21no—
148#95×C61—21no—
149#95×C61—21no—
150#95×C61—21no—
151C24×C61—21no—
152C24×C61—21no—
153C24×C61C2×D411yescharacteristic
154C24×C61C2×D411yescharacteristic
155#41×C61—28no—
156#41×C61—44no—
157#41×C61—44no—
158#41×C61—44no—
159C2×Q8×C61—21no—
160C2×Q8×C61—21no—
161C2×Q8×C61—21no—
162C2×Q8×C61—21no—
163C2×Q8×C61—21no—
164C2×Q8×C61C2×D412yes—
165C2×D4×C61—22no—
166C2×D4×C61—22no—
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—41no—
179C2×D4×C61—42no—
180C2×D4×C61—42no—
181C2×D4×C61—42no—
182C2×D4×C61—42no—
183C2×D4×C61—42no—
184C2×D4×C61—42no—
185C2×D4×C61—42no—
186C2×D4×C61—42no—
187C2×D4×C61—42no—
188C2×D4×C61—42no—
189C2×D4×C61—81no—
190C2×D4×C61—81no—
191C2×D4×C61#4112yes—
192C22×C4×C61—21no—
193C22×C4×C61—21no—
194C22×C4×C61—21no—
195C22×C4×C61—21no—
196C22×C4×C61—21no—
197C22×C4×C61—21no—
198C22×C4×C61—21no—
199C22×C4×C61—21no—
200C22×C4×C61—21no—
201C22×C4×C61—21no—
202C22×C4×C61—21no—
203C22×C4×C61—21no—
204C22×C4×C61—21no—
205C22×C4×C61—21no—
206C22×C4×C61—21no—
207C22×C4×C61—21no—
208C22×C4×C61—42no—
209C22×C4×C61—42no—
210C22×C4×C61—42no—
211C22×C4×C61—42no—
212C22×C4×C61—42no—
213C22×C4×C61—81no—
214C22×C4×C61C2×D411yescharacteristic
215C22×C4×C61C2×D411yescharacteristic
216C22×C4×C61C2×D411yescharacteristic
217C22×C4×C61C2×D412yes—
218C22×C4×C61C2×D411yescharacteristic
219C22×C4×C61#4112yes—
220C22×C4×C61C2411yescharacteristic
221SD16×C61—44no—
222D8×C61—44no—
223M16×C61—44no—
224M16×C61—44no—
225C2×C8×C61—21no—
226C2×C8×C61—21no—
227C2×C8×C61—21no—
228C2×C8×C61—21no—
229C2×C8×C61—21no—
230C2×C8×C61—21no—
231C2×C8×C61—21no—
232C2×C8×C61—21no—
233C2×C8×C61—21no—
234C2×C8×C61C2×D412yes—
235C2×C8×C61C2×D412yes—
236C2×C8×C61C2×D412yes—
237C4⋊C4×C61—22no—
238C4⋊C4×C61—21no—
239C4⋊C4×C61—21no—
240C4⋊C4×C61—21no—
241C4⋊C4×C61—21no—
242C4⋊C4×C61—21no—
243C4⋊C4×C61—21no—
244C4⋊C4×C61—21no—
245C4⋊C4×C61—21no—
246C4⋊C4×C61—21no—
247C4⋊C4×C61—42no—
248C4⋊C4×C61—42no—
249C4⋊C4×C61—42no—
250C4⋊C4×C61C2×D412yes—
251C22⋊C4×C61—22no—
252C22⋊C4×C61—22no—
253C22⋊C4×C61—42no—
254C22⋊C4×C61—42no—
255C22⋊C4×C61—42no—
256C22⋊C4×C61—42no—
257C22⋊C4×C61—42no—
258C22⋊C4×C61—42no—
259C22⋊C4×C61—42no—
260C22⋊C4×C61—81no—
261C22⋊C4×C61—81no—
262C22⋊C4×C61—81no—
263C42×C61—21no—
264C42×C61—21no—
265C23×C61—21no—
266C23×C61—21no—
267C23×C61—21no—
268C23×C61—21no—
269C23×C61—21no—
270C23×C61—21no—
271C23×C61—21no—
272C23×C61—21no—
273C23×C61—22no—
274C23×C61—21no—
275C23×C61—21no—
276C23×C61—21no—
277C23×C61—21no—
278C23×C61—21no—
279C23×C61—41no—
280C23×C61—41no—
281C23×C61—41no—
282C23×C61—41no—
283C23×C61—41no—
284C23×C61—41no—
285C23×C61—41no—
286C23×C61—41no—
287C23×C61—41no—
288C23×C61—41no—
289C23×C61—41no—
290C23×C61—41no—
291C23×C61—41no—
292C23×C61#12112yes—
293C23×C61C22×D411yescharacteristic
294Q8×C61—22no—
295Q8×C61—22no—
296Q8×C61—41no—
297Q8×C61—41no—
298D4×C61—22no—
299D4×C61—22no—
300D4×C61—44no—
301D4×C61—48no—
302D4×C61—41no—
303D4×C61—41no—
304D4×C61—41no—
305D4×C61—41no—
306D4×C61—41no—
307D4×C61—41no—
308D4×C61—84no—
309D4×C61—84no—
310D4×C61—84no—
311C2×C4×C61—21no—
312C2×C4×C61—21no—
313C2×C4×C61—21no—
314C2×C4×C61—21no—
315C2×C4×C61—22no—
316C2×C4×C61—22no—
317C2×C4×C61—22no—
318C2×C4×C61—22no—
319C2×C4×C61—21no—
320C2×C4×C61—21no—
321C2×C4×C61—21no—
322C2×C4×C61—22no—
323C2×C4×C61—22no—
324C2×C4×C61—21no—
325C2×C4×C61—21no—
326C2×C4×C61—21no—
327C2×C4×C61—48no—
328C2×C4×C61—41no—
329C2×C4×C61—41no—
330C2×C4×C61—41no—
331C2×C4×C61—41no—
332C2×C4×C61—41no—
333C2×C4×C61—41no—
334C2×C4×C61—41no—
335C2×C4×C61—41no—
336C2×C4×C61—41no—
337C2×C4×C61—41no—
338C2×C4×C61—41no—
339C2×C4×C61—41no—
340C2×C4×C61—41no—
341C2×C4×C61—41no—
342C2×C4×C61—41no—
343C2×C4×C61—41no—
344C2×C4×C61—41no—
345C2×C4×C61—41no—
346C2×C4×C61—41no—
347C2×C4×C61—41no—
348C2×C4×C61—84no—
349C2×C4×C61#12112yes—
350C2×C4×C61AGL(1,ℤ/8)12yes—
351C2×C4×C61C22×D411yescharacteristic
352C2×C4×C61C22×D411yescharacteristic
353C2×C4×C61C2×#4111yescharacteristic
354C2×C4×C61C2×#4111yescharacteristic
355C2×C4×C61H(5,𝔽2)11yescharacteristic
356C2×C4×C61H(5,𝔽2)11yescharacteristic
357C8×C61—22no—
358C8×C61—22no—
359C8×C61—22no—
360C8×C61—41no—
361#25139C6111yesmaximal, characteristic, direct product factor, Sylow
362C22×C61—22no—
363C22×C61—22no—
364C22×C61—22no—
365C22×C61—41no—
366C22×C61—41no—
367C22×C61—41no—
368C22×C61—41no—
369C22×C61—41no—
370C22×C61—42no—
371C22×C61—42no—
372C22×C61—41no—
373C22×C61—41no—
374C22×C61—41no—
375C22×C61—41no—
376C22×C61—41no—
377C22×C61—41no—
378C22×C61—42no—
379C22×C61—81no—
380C22×C61—81no—
381C22×C61—81no—
382C22×C61—81no—
383C22×C61—81no—
384C22×C61—81no—
385C22×C61—81no—
386C22×C61—81no—
387C22×C61—81no—
388C22×C61—81no—
389C22×C61—81no—
390C22×C61C2×#12111yescharacteristic
391C22×C61D4211yescharacteristic
392C22×C61#54611yescharacteristic
393C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
394C22×C61#57511yescharacteristic
395C22×C61#57611yescharacteristic
396C22×C61#57811yescharacteristic
397C4×C61—22no—
398C4×C61—22no—
399C4×C61—41no—
400C4×C61—42no—
401C4×C61—42no—
402C4×C61—41no—
403C4×C61—81no—
404C4×C61—81no—
405C4×C61—81no—
406C4×C61—81no—
407C4×C61#52511yescharacteristic
408C4×C61#53811yescharacteristic
409C4×C61D4211yescharacteristic
410C4×C61#54611yescharacteristic
411C2×#468C2×C6111yescharacteristic, complemented
412C2×#449C2×C6111yescharacteristic, complemented
413C2×#436C2×C6111yescharacteristic, complemented
414C2×#417C2×C6111yescharacteristic, complemented
415#2416C2×C6111yescharacteristic, complemented
416#2407C2×C6111yescharacteristic, complemented
417#2067C2×C6111yescharacteristic, complemented
418#2055C2×C6111yescharacteristic, complemented
419#2036C2×C6111yescharacteristic, complemented
420#1999C2×C6111yescharacteristic, complemented
421#1970C2×C6111yescharacteristic, complemented
422#1933C2×C6111yescharacteristic, complemented
423#1895C2×C6111yescharacteristic, complemented
424#1895C2×C6111yescharacteristic, complemented
425#1852C2×C6111yescharacteristic, complemented
426C2×C61—42no—
427C2×C61—81no—
428C2×C61—82no—
429C2×C61—161no—
430C2×C61#242411yescharacteristic
431C2×C61#305511yescharacteristic
432C2×C61#306111yescharacteristic
433C2×C61#327411yescharacteristic
434C2×C61#327711yescharacteristic
435C2×C61#332211yescharacteristic
436C2×C61#333011yescharacteristic
437C22×#41C22×C6111yescharacteristic
438C22×SD16C22×C6111yescharacteristic
439C22×D8C22×C6111yescharacteristic
440C22×M16C22×C6111yescharacteristic
441C22×M16C22×C6111yescharacteristic
442C2×C22⋊Q8C22×C6111yescharacteristic
443C2×#121—21no—
444C2×#121C22×C6111yescharacteristic
445C2×#121C22×C6111yescharacteristic
446C2×#121C22×C6111yescharacteristic
447C2×C4×D4C22×C6111yescharacteristic
448C22×C4⋊C4C22×C6111yescharacteristic
449#468—24no—
450#449—24no—
451#436—24no—
452C2×#107C22×C6111yescharacteristic
453C2×#107C22×C6111yescharacteristic
454C2×C4⋊C8C22×C6111yescharacteristic
455#417—24no—
456C2×#103C22×C6111yescharacteristic
457C2×#103C22×C6111yescharacteristic
458C2×#103C22×C6111yescharacteristic
459C2×#102C22×C6111yescharacteristic
460C2×#102C22×C6111yescharacteristic
461C2×#102C22×C6111yescharacteristic
462C2×#102C22×C6111yescharacteristic
463C2×#102C22×C6111yescharacteristic
464C2×C22⋊C8C22×C6111yescharacteristic
465C2×C22⋊C8C22×C6111yescharacteristic
466C2×C4×C8C22×C6111yescharacteristic
467#396—21no—
468#394—21no—
469#394—21no—
470#392—21no—
471#391C22×C6111yescharacteristic
472#390C22×C6111yescharacteristic
473#390C22×C6111yescharacteristic
474#389C22×C6111yescharacteristic
475#386—21no—
476#386—21no—
477#385—21no—
478#380C22×C6111yescharacteristic
479#380C22×C6111yescharacteristic
480#340C22×C6111yescharacteristic
481#340C22×C6111yescharacteristic
482#340C22×C6111yescharacteristic
483#340C22×C6111yescharacteristic
484C61#2513911yescharacteristic, direct product factor, Sylow
485C2×#41—22no—
486C2×#41—22no—
487C2×#41—22no—
488C2×#41—22no—
489C2×#41—41no—
490C2×#41—41no—
491C22×Q8C23×C6111yescharacteristic
492C22×D4—21no—
493C22×D4—21no—
494C22×D4—21no—
495C22×D4—21no—
496C22×D4D4×C6111yescharacteristic
497C22×D4C23×C6111yescharacteristic
498C22×D4C23×C6111yescharacteristic
499C23×C4—21no—
500C23×C4—21no—
501C23×C4C23×C6111yescharacteristic
502C23×C4C23×C6111yescharacteristic
503C2×SD16—22no—
504C2×SD16—22no—
505C2×SD16—41no—
506C2×D8—22no—
507C2×D8—22no—
508C2×D8—41no—
509C2×M16—22no—
510C2×M16—22no—
511C2×M16—22no—
512C2×M16—22no—
513C2×M16—41no—
514C2×M16—41no—
515C22×C8C23×C6111yescharacteristic
516C22×C8C23×C6111yescharacteristic
517C22×C8C23×C6111yescharacteristic
518C22×C8C23×C6111yescharacteristic
519C22⋊Q8—22no—
520C22⋊Q8—41no—
521#121—22no—
522#121—22no—
523#121—22no—
524#121—22no—
525#121—41no—
526#121—41no—
527#121—44no—
528C4×D4—22no—
529C4×D4—22no—
530C2×C4⋊C4—22no—
531C2×C4⋊C4—21no—
532C2×C4⋊C4—21no—
533C2×C4⋊C4—21no—
534C2×C4⋊C4—41no—
535C2×C4⋊C4D4×C6111yescharacteristic
536C2×C4⋊C4C23×C6111yescharacteristic
537C2×C4⋊C4C23×C6111yescharacteristic
538C2×C4⋊C4C23×C6111yescharacteristic
539C2×C4⋊C4C23×C6111yescharacteristic
540C2×C4⋊C4C23×C6111yescharacteristic
541C2×C22⋊C4—21no—
542C2×C22⋊C4—21no—
543C2×C22⋊C4—21no—
544C2×C22⋊C4—21no—
545C2×C22⋊C4—21no—
546C2×C22⋊C4—21no—
547C2×C22⋊C4—21no—
548C2×C22⋊C4—21no—
549C2×C22⋊C4—21no—
550C2×C22⋊C4—21no—
551C2×C22⋊C4D4×C6111yescharacteristic
552C2×C22⋊C4D4×C6111yescharacteristic
553C2×C42C23×C6111yescharacteristic
554#107—22no—
555#107—41no—
556C4⋊C8—22no—
557#103—22no—
558#103—22no—
559#103D4×C6114yescomplemented
560#102—22no—
561#102—22no—
562#102—22no—
563#102—22no—
564#102—41no—
565C22⋊C8—22no—
566C22⋊C8D4×C6114yescomplemented
567C4×C8—22no—
568#95—21no—
569#95—21no—
570#95—21no—
571#95—21no—
572#95—21no—
573C24—21no—
574C24—21no—
575C24C2×D4×C6111yescharacteristic
576C24C2×D4×C6111yescharacteristic
577#41—28no—
578#41—44no—
579#41—44no—
580#41—44no—
581C2×Q8—21no—
582C2×Q8—21no—
583C2×Q8—21no—
584C2×Q8—21no—
585C2×Q8—21no—
586C2×Q8C2×D4×C6112yes—
587C2×D4—22no—
588C2×D4—22no—
589C2×D4—21no—
590C2×D4—21no—
591C2×D4—21no—
592C2×D4—21no—
593C2×D4—21no—
594C2×D4—21no—
595C2×D4—21no—
596C2×D4—21no—
597C2×D4—21no—
598C2×D4—21no—
599C2×D4—21no—
600C2×D4—41no—
601C2×D4—42no—
602C2×D4—42no—
603C2×D4—42no—
604C2×D4—42no—
605C2×D4—42no—
606C2×D4—42no—
607C2×D4—42no—
608C2×D4—42no—
609C2×D4—42no—
610C2×D4—42no—
611C2×D4—81no—
612C2×D4—81no—
613C2×D4#41×C6112yes—
614C22×C4—21no—
615C22×C4—21no—
616C22×C4—21no—
617C22×C4—21no—
618C22×C4—21no—
619C22×C4—21no—
620C22×C4—21no—
621C22×C4—21no—
622C22×C4—21no—
623C22×C4—21no—
624C22×C4—21no—
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—21no—
628C22×C4—21no—
629C22×C4—21no—
630C22×C4—42no—
631C22×C4—42no—
632C22×C4—42no—
633C22×C4—42no—
634C22×C4—42no—
635C22×C4—81no—
636C22×C4C2×D4×C6111yescharacteristic
637C22×C4C2×D4×C6111yescharacteristic
638C22×C4C2×D4×C6111yescharacteristic
639C22×C4C2×D4×C6112yes—
640C22×C4C2×D4×C6111yescharacteristic
641C22×C4#41×C6112yes—
642C22×C4C24×C6111yescharacteristic
643SD16—44no—
644D8—44no—
645M16—44no—
646M16—44no—
647C2×C8—21no—
648C2×C8—21no—
649C2×C8—21no—
650C2×C8—21no—
651C2×C8—21no—
652C2×C8—21no—
653C2×C8—21no—
654C2×C8—21no—
655C2×C8—21no—
656C2×C8C2×D4×C6112yes—
657C2×C8C2×D4×C6112yes—
658C2×C8C2×D4×C6112yes—
659C4⋊C4—22no—
660C4⋊C4—21no—
661C4⋊C4—21no—
662C4⋊C4—21no—
663C4⋊C4—21no—
664C4⋊C4—21no—
665C4⋊C4—21no—
666C4⋊C4—21no—
667C4⋊C4—21no—
668C4⋊C4—21no—
669C4⋊C4—42no—
670C4⋊C4—42no—
671C4⋊C4—42no—
672C4⋊C4C2×D4×C6112yes—
673C22⋊C4—22no—
674C22⋊C4—22no—
675C22⋊C4—42no—
676C22⋊C4—42no—
677C22⋊C4—42no—
678C22⋊C4—42no—
679C22⋊C4—42no—
680C22⋊C4—42no—
681C22⋊C4—42no—
682C22⋊C4—81no—
683C22⋊C4—81no—
684C22⋊C4—81no—
685C42—21no—
686C42—21no—
687C23—21no—
688C23—21no—
689C23—21no—
690C23—21no—
691C23—21no—
692C23—21no—
693C23—21no—
694C23—22no—
695C23—21no—
696C23—21no—
697C23—21no—
698C23—21no—
699C23—21no—
700C23—21no—
701C23—41no—
702C23—41no—
703C23—41no—
704C23—41no—
705C23—41no—
706C23—41no—
707C23—41no—
708C23—41no—
709C23—41no—
710C23—41no—
711C23—41no—
712C23—41no—
713C23—41no—
714C23#121×C6112yes—
715C23C22×D4×C6111yescharacteristic
716Q8—22no—
717Q8—22no—
718Q8—41no—
719Q8—41no—
720D4—22no—
721D4—22no—
722D4—44no—
723D4—48no—
724D4—41no—
725D4—41no—
726D4—41no—
727D4—41no—
728D4—41no—
729D4—41no—
730D4—84no—
731D4—84no—
732D4—84no—
733C2×C4—21no—
734C2×C4—21no—
735C2×C4—21no—
736C2×C4—21no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—21no—
742C2×C4—22no—
743C2×C4—22no—
744C2×C4—21no—
745C2×C4—21no—
746C2×C4—21no—
747C2×C4—21no—
748C2×C4—21no—
749C2×C4—48no—
750C2×C4—41no—
751C2×C4—41no—
752C2×C4—41no—
753C2×C4—41no—
754C2×C4—41no—
755C2×C4—41no—
756C2×C4—41no—
757C2×C4—41no—
758C2×C4—41no—
759C2×C4—41no—
760C2×C4—41no—
761C2×C4—41no—
762C2×C4—41no—
763C2×C4—41no—
764C2×C4—41no—
765C2×C4—41no—
766C2×C4—41no—
767C2×C4—41no—
768C2×C4—41no—
769C2×C4—41no—
770C2×C4—84no—
771C2×C4#121×C6112yes—
772C2×C4AGL(1,ℤ/8)×C6112yes—
773C2×C4C22×D4×C6111yescharacteristic
774C2×C4C22×D4×C6111yescharacteristic
775C2×C4C2×#41×C6111yescharacteristic
776C2×C4C2×#41×C6111yescharacteristic
777C2×C4H(5,𝔽2)×C6111yescharacteristic
778C2×C4H(5,𝔽2)×C6111yescharacteristic
779C8—22no—
780C8—22no—
781C8—22no—
782C8—41no—
783C22—22no—
784C22—22no—
785C22—22no—
786C22—41no—
787C22—41no—
788C22—41no—
789C22—41no—
790C22—41no—
791C22—41no—
792C22—41no—
793C22—42no—
794C22—41no—
795C22—42no—
796C22—42no—
797C22—41no—
798C22—41no—
799C22—41no—
800C22—81no—
801C22—81no—
802C22—81no—
803C22—81no—
804C22—81no—
805C22—81no—
806C22—81no—
807C22—81no—
808C22—81no—
809C22—81no—
810C22—81no—
811C22C2×#121×C6111yescharacteristic
812C22D42×C6111yescharacteristic
813C22C61×#54611yescharacteristic
814C22C2×AGL(1,ℤ/8)×C6111yescharacteristic
815C22C61×#57511yescharacteristic
816C22C61×#57611yescharacteristic
817C22C61×#57811yescharacteristic
818C4—22no—
819C4—22no—
820C4—41no—
821C4—41no—
822C4—42no—
823C4—42no—
824C4—81no—
825C4—81no—
826C4—81no—
827C4—81no—
828C4C61×#52511yescharacteristic
829C4C61×#53811yescharacteristic
830C4D42×C6111yescharacteristic
831C4C61×#54611yescharacteristic
832C2—42no—
833C2—81no—
834C2—82no—
835C2—161no—
836C2C61×#242411yescharacteristic
837C2C61×#305511yescharacteristic
838C2C61×#306111yescharacteristic
839C2C61×#327411yescharacteristic
840C2C61×#327711yescharacteristic
841C2C61×#332211yescharacteristic
842C2C61×#333011yescharacteristic
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×#468C2semidirect
2. C2×C61×#449C2semidirect
3. C2×C61×#436C2semidirect
4. C2×C61×#417C2semidirect
5. C61×#2416C2semidirect
6. C61×#2407C2semidirect
7. C61×#2067C2semidirect
8. C61×#2055C2semidirect
9. C61×#2036C2semidirect
10. C61×#1999C2semidirect
11. C61×#1970C2semidirect
12. C61×#1933C2semidirect
13. C61×#1895C2semidirect
14. C61×#1895C2semidirect
15. C61×#1852C2semidirect
137. #103×C61D4semidirect
144. C22⋊C8×C61D4semidirect
361. #25139C61direct (N × H)
411. C2×#468C2×C61semidirect
412. C2×#449C2×C61semidirect
413. C2×#436C2×C61semidirect
414. C2×#417C2×C61semidirect
415. #2416C2×C61semidirect
416. #2407C2×C61semidirect
417. #2067C2×C61semidirect
418. #2055C2×C61semidirect
419. #2036C2×C61semidirect
420. #1999C2×C61semidirect
421. #1970C2×C61semidirect
422. #1933C2×C61semidirect
423. #1895C2×C61semidirect
424. #1895C2×C61semidirect
425. #1852C2×C61semidirect
484. C61#25139direct (N × H)
559. #103D4×C61semidirect
566. 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×#4682
C2×C61×#4492
C2×C61×#4362
C2×C61×#4172
C61×#24162
C61×#24072
C61×#20672
C61×#20552
C61×#20362
C61×#19992
C61×#19702
C61×#19332
C61×#18952
C61×#18522
#2513961