Finite Group Databasebeta

← C61×#25087 #29528520

Subgroups — C61×#25087 #29528520

Order 15616.

1192 conjugacy classes of subgroups.

The subgroup lattice has 840 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C61×#466C211yesmaximal, characteristic, complemented
2C2×C61×#463C211yesmaximal, characteristic, complemented
3C2×C61×#449C211yesmaximal, characteristic, complemented
4C2×C61×#416C211yesmaximal, characteristic, complemented
5C61×#2431C211yesmaximal, characteristic, complemented
6C61×#2363C211yesmaximal, characteristic, complemented
7C61×#2067C211yesmaximal, characteristic, complemented
8C61×#2055C211yesmaximal, characteristic, complemented
9C61×#2042C211yesmaximal, characteristic, complemented
10C61×#2011C211yesmaximal, characteristic, complemented
11C61×#1982C211yesmaximal, characteristic, complemented
12C61×#1928C211yesmaximal, characteristic, complemented
13C61×#1879C211yesmaximal, characteristic, complemented
14C61×#1875C211yesmaximal, characteristic, complemented
15C61×#1850C211yesmaximal, characteristic, complemented
16C22×#41×C61C2211yescharacteristic
17C22×SD16×C61C2211yescharacteristic
18C22×D8×C61C2211yescharacteristic
19C22×D8×C61C2211yescharacteristic
20C23×C8×C61C2211yescharacteristic
21C2×#127×C61C2211yescharacteristic
22C2×#124×C61C2211yescharacteristic
23C2×#121×C61C2211yescharacteristic
24C2×#121×C61C2211yescharacteristic
25C2×C4×D4×C61C2211yescharacteristic
26C2×#117×C61C2211yescharacteristic
27C61×#466—24no—
28C61×#463—24no—
29C61×#449—24no—
30C2×#107×C61C2211yescharacteristic
31C2×C4⋊C8×C61C2211yescharacteristic
32C2×C4⋊C8×C61C2211yescharacteristic
33C61×#416—24no—
34C2×#103×C61C2211yescharacteristic
35C2×#103×C61C2211yescharacteristic
36C2×#103×C61C2211yescharacteristic
37C2×#102×C61C2211yescharacteristic
38C2×#102×C61C2211yescharacteristic
39C2×#102×C61C2211yescharacteristic
40C2×#102×C61C2211yescharacteristic
41C2×#102×C61C2211yescharacteristic
42C2×#102×C61C2211yescharacteristic
43C2×#102×C61C2211yescharacteristic
44C2×C22⋊C8×C61C2211yescharacteristic
45C61×#392—21no—
46C61×#392—21no—
47C61×#391C2211yescharacteristic
48C61×#390—21no—
49C61×#390C2211yescharacteristic
50C61×#390C2211yescharacteristic
51C61×#389C2211yescharacteristic
52C61×#388—21no—
53C61×#386—21no—
54C61×#386—21no—
55C61×#386—21no—
56C4×C4⋊C4×C61C2211yescharacteristic
57C4×C22⋊C4×C61—21no—
58C4×C22⋊C4×C61C2211yescharacteristic
59C61×#340C2211yescharacteristic
60C61×#340C2211yescharacteristic
61C61×#336C2211yescharacteristic
62C61×#336C2211yescharacteristic
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×C61—21no—
75C22×D4×C61C2311yescharacteristic
76C22×D4×C61C2311yescharacteristic
77C22×D4×C61C2311yescharacteristic
78C23×C4×C61—21no—
79C23×C4×C61—21no—
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—22no—
87C2×D8×C61—22no—
88C2×D8×C61—41no—
89C2×D8×C61—41no—
90C22×C8×C61—22no—
91C22×C8×C61—22no—
92C22×C8×C61—41no—
93C22×C8×C61C2311yescharacteristic
94C22×C8×C61C2311yescharacteristic
95C22×C8×C61C2311yescharacteristic
96C22×C8×C61C2311yescharacteristic
97#127×C61—22no—
98#127×C61—41no—
99#124×C61—22no—
100#124×C61—41no—
101#121×C61—22no—
102#121×C61—22no—
103#121×C61—22no—
104#121×C61D414yescomplemented
105C4×D4×C61—22no—
106C4×D4×C61—41no—
107#117×C61—22no—
108#117×C61—41no—
109C2×C4⋊C4×C61—21no—
110C2×C4⋊C4×C61C2311yescharacteristic
111C2×C4⋊C4×C61C2311yescharacteristic
112C2×C4⋊C4×C61C2311yescharacteristic
113C2×C4⋊C4×C61C2311yescharacteristic
114C2×C22⋊C4×C61—21no—
115C2×C22⋊C4×C61—21no—
116C2×C22⋊C4×C61—21no—
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×C61D411yescharacteristic
125C2×C22⋊C4×C61D411yescharacteristic
126C2×C42×C61—21no—
127C2×C42×C61—21no—
128C2×C42×C61C2311yescharacteristic
129C2×C42×C61C2311yescharacteristic
130#107×C61—22no—
131C4⋊C8×C61—22no—
132C4⋊C8×C61—41no—
133#103×C61—22no—
134#103×C61—22no—
135#103×C61D414yescomplemented
136#102×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—41no—
143C22⋊C8×C61—22no—
144#95×C61—21no—
145#95×C61—21no—
146#95×C61—21no—
147#95×C61—21no—
148#95×C61D411yescharacteristic
149#95×C61D411yescharacteristic
150C24×C61—21no—
151C24×C61—21no—
152C24×C61—21no—
153C24×C61C2×D411yescharacteristic
154#41×C61—28no—
155#41×C61—44no—
156#41×C61—44no—
157#41×C61—44no—
158C2×Q8×C61—21no—
159C2×Q8×C61—21no—
160C2×Q8×C61—21no—
161C2×Q8×C61—21no—
162C2×Q8×C61—21no—
163C2×Q8×C61C2×D412yes—
164C2×D4×C61—24no—
165C2×D4×C61—21no—
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—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—81no—
192C2×D4×C61—81no—
193C2×D4×C61—81no—
194C2×D4×C61—81no—
195C2×D4×C61C2×D412yes—
196C2×D4×C61#4112yes—
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—42no—
207C22×C4×C61—42no—
208C22×C4×C61—42no—
209C22×C4×C61—42no—
210C22×C4×C61—42no—
211C22×C4×C61—81no—
212C22×C4×C61C2×D411yescharacteristic
213C22×C4×C61C2×D411yescharacteristic
214C22×C4×C61C2×D411yescharacteristic
215C22×C4×C61C2×D411yescharacteristic
216C22×C4×C61C2×D412yes—
217C22×C4×C61C2×D411yescharacteristic
218C22×C4×C61#4112yes—
219C22×C4×C61C2411yescharacteristic
220SD16×C61—44no—
221D8×C61—44no—
222D8×C61—44no—
223C2×C8×C61—21no—
224C2×C8×C61—21no—
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×C61—44no—
235C2×C8×C61C2×D412yes—
236C4⋊C4×C61—21no—
237C4⋊C4×C61—21no—
238C4⋊C4×C61—21no—
239C4⋊C4×C61—21no—
240C4⋊C4×C61—21no—
241C4⋊C4×C61—21no—
242C4⋊C4×C61—81no—
243C4⋊C4×C61C2×D412yes—
244C4⋊C4×C61C2×D412yes—
245C22⋊C4×C61—24no—
246C22⋊C4×C61—22no—
247C22⋊C4×C61—41no—
248C22⋊C4×C61—42no—
249C22⋊C4×C61—42no—
250C22⋊C4×C61—42no—
251C22⋊C4×C61—42no—
252C22⋊C4×C61—42no—
253C22⋊C4×C61—42no—
254C22⋊C4×C61—81no—
255C22⋊C4×C61—81no—
256C22⋊C4×C61—81no—
257C42×C61—21no—
258C42×C61—21no—
259C42×C61—21no—
260C42×C61—21no—
261C42×C61—42no—
262C42×C61—81no—
263C23×C61—21no—
264C23×C61—21no—
265C23×C61—21no—
266C23×C61—21no—
267C23×C61—21no—
268C23×C61—21no—
269C23×C61—22no—
270C23×C61—22no—
271C23×C61—41no—
272C23×C61—41no—
273C23×C61—41no—
274C23×C61—41no—
275C23×C61—41no—
276C23×C61—41no—
277C23×C61—41no—
278C23×C61—41no—
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#12112yes—
291C23×C61C22×D411yescharacteristic
292Q8×C61—22no—
293Q8×C61—22no—
294Q8×C61—41no—
295Q8×C61—41no—
296D4×C61—22no—
297D4×C61—22no—
298D4×C61—22no—
299D4×C61—22no—
300D4×C61—48no—
301D4×C61—41no—
302D4×C61—41no—
303D4×C61—41no—
304D4×C61—41no—
305D4×C61—41no—
306D4×C61—41no—
307D4×C61—41no—
308D4×C61—41no—
309D4×C61—84no—
310D4×C61—84no—
311D4×C61—84no—
312D4×C61—84no—
313C2×C4×C61—21no—
314C2×C4×C61—21no—
315C2×C4×C61—21no—
316C2×C4×C61—21no—
317C2×C4×C61—22no—
318C2×C4×C61—22no—
319C2×C4×C61—22no—
320C2×C4×C61—22no—
321C2×C4×C61—22no—
322C2×C4×C61—21no—
323C2×C4×C61—21no—
324C2×C4×C61—22no—
325C2×C4×C61—22no—
326C2×C4×C61—21no—
327C2×C4×C61—21no—
328C2×C4×C61—21no—
329C2×C4×C61—21no—
330C2×C4×C61—21no—
331C2×C4×C61—21no—
332C2×C4×C61—21no—
333C2×C4×C61—48no—
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—84no—
347C2×C4×C61#12112yes—
348C2×C4×C61#13512yes—
349C2×C4×C61C22×D411yescharacteristic
350C2×C4×C61C22×D411yescharacteristic
351C2×C4×C61C2×#4111yescharacteristic
352C2×C4×C61C2×#4111yescharacteristic
353C2×C4×C61H(5,𝔽2)11yescharacteristic
354C2×C4×C61H(5,𝔽2)11yescharacteristic
355C8×C61—22no—
356C8×C61—41no—
357C8×C61—41no—
358C8×C61—41no—
359#25087C6111yesmaximal, characteristic, direct product factor, Sylow
360C22×C61—22no—
361C22×C61—22no—
362C22×C61—22no—
363C22×C61—41no—
364C22×C61—41no—
365C22×C61—41no—
366C22×C61—41no—
367C22×C61—42no—
368C22×C61—42no—
369C22×C61—42no—
370C22×C61—42no—
371C22×C61—42no—
372C22×C61—42no—
373C22×C61—81no—
374C22×C61—81no—
375C22×C61—81no—
376C22×C61—81no—
377C22×C61—81no—
378C22×C61—81no—
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×C61C2×#12111yescharacteristic
389C22×C61D4211yescharacteristic
390C22×C61#54611yescharacteristic
391C22×C61C2×#13511yescharacteristic
392C22×C61#57511yescharacteristic
393C22×C61#57611yescharacteristic
394C22×C61#57611yescharacteristic
395C4×C61—22no—
396C4×C61—22no—
397C4×C61—42no—
398C4×C61—41no—
399C4×C61—42no—
400C4×C61—41no—
401C4×C61—42no—
402C4×C61—41no—
403C4×C61—81no—
404C4×C61—81no—
405C4×C61#52511yescharacteristic
406C4×C61#53811yescharacteristic
407C4×C61D4211yescharacteristic
408C4×C61#54611yescharacteristic
409C2×#466C2×C6111yescharacteristic, complemented
410C2×#463C2×C6111yescharacteristic, complemented
411C2×#449C2×C6111yescharacteristic, complemented
412C2×#416C2×C6111yescharacteristic, complemented
413#2431C2×C6111yescharacteristic, complemented
414#2363C2×C6111yescharacteristic, complemented
415#2067C2×C6111yescharacteristic, complemented
416#2055C2×C6111yescharacteristic, complemented
417#2042C2×C6111yescharacteristic, complemented
418#2011C2×C6111yescharacteristic, complemented
419#1982C2×C6111yescharacteristic, complemented
420#1928C2×C6111yescharacteristic, complemented
421#1879C2×C6111yescharacteristic, complemented
422#1875C2×C6111yescharacteristic, complemented
423#1850C2×C6111yescharacteristic, complemented
424C2×C61—42no—
425C2×C61—82no—
426C2×C61—82no—
427C2×C61—161no—
428C2×C61#242411yescharacteristic
429C2×C61#303511yescharacteristic
430C2×C61#304111yescharacteristic
431C2×C61#326811yescharacteristic
432C2×C61#328711yescharacteristic
433C2×C61#329711yescharacteristic
434C2×C61#331911yescharacteristic
435C22×#41C22×C6111yescharacteristic
436C22×SD16C22×C6111yescharacteristic
437C22×D8C22×C6111yescharacteristic
438C22×D8C22×C6111yescharacteristic
439C23×C8C22×C6111yescharacteristic
440C2×#127C22×C6111yescharacteristic
441C2×#124C22×C6111yescharacteristic
442C2×#121C22×C6111yescharacteristic
443C2×#121C22×C6111yescharacteristic
444C2×C4×D4C22×C6111yescharacteristic
445C2×#117C22×C6111yescharacteristic
446#466—24no—
447#463—24no—
448#449—24no—
449C2×#107C22×C6111yescharacteristic
450C2×C4⋊C8C22×C6111yescharacteristic
451C2×C4⋊C8C22×C6111yescharacteristic
452#416—24no—
453C2×#103C22×C6111yescharacteristic
454C2×#103C22×C6111yescharacteristic
455C2×#103C22×C6111yescharacteristic
456C2×#102C22×C6111yescharacteristic
457C2×#102C22×C6111yescharacteristic
458C2×#102C22×C6111yescharacteristic
459C2×#102C22×C6111yescharacteristic
460C2×#102C22×C6111yescharacteristic
461C2×#102C22×C6111yescharacteristic
462C2×#102C22×C6111yescharacteristic
463C2×C22⋊C8C22×C6111yescharacteristic
464#392—21no—
465#392—21no—
466#391C22×C6111yescharacteristic
467#390—21no—
468#390C22×C6111yescharacteristic
469#390C22×C6111yescharacteristic
470#389C22×C6111yescharacteristic
471#388—21no—
472#386—21no—
473#386—21no—
474#386—21no—
475C4×C4⋊C4C22×C6111yescharacteristic
476C4×C22⋊C4—21no—
477C4×C22⋊C4C22×C6111yescharacteristic
478#340C22×C6111yescharacteristic
479#340C22×C6111yescharacteristic
480#336C22×C6111yescharacteristic
481#336C22×C6111yescharacteristic
482C61#2508711yescharacteristic, direct product factor, Sylow
483C2×#41—22no—
484C2×#41—22no—
485C2×#41—22no—
486C2×#41—22no—
487C2×#41—41no—
488C2×#41—41no—
489C22×Q8C23×C6111yescharacteristic
490C22×D4—21no—
491C22×D4—21no—
492C22×D4—21no—
493C22×D4—21no—
494C22×D4—21no—
495C22×D4C23×C6111yescharacteristic
496C22×D4C23×C6111yescharacteristic
497C22×D4C23×C6111yescharacteristic
498C23×C4—21no—
499C23×C4—21no—
500C23×C4C23×C6111yescharacteristic
501C2×SD16—22no—
502C2×SD16—22no—
503C2×SD16—41no—
504C2×D8—22no—
505C2×D8—22no—
506C2×D8—22no—
507C2×D8—22no—
508C2×D8—41no—
509C2×D8—41no—
510C22×C8—22no—
511C22×C8—22no—
512C22×C8—41no—
513C22×C8C23×C6111yescharacteristic
514C22×C8C23×C6111yescharacteristic
515C22×C8C23×C6111yescharacteristic
516C22×C8C23×C6111yescharacteristic
517#127—22no—
518#127—41no—
519#124—22no—
520#124—41no—
521#121—22no—
522#121—22no—
523#121—22no—
524#121D4×C6114yescomplemented
525C4×D4—22no—
526C4×D4—41no—
527#117—22no—
528#117—41no—
529C2×C4⋊C4—21no—
530C2×C4⋊C4C23×C6111yescharacteristic
531C2×C4⋊C4C23×C6111yescharacteristic
532C2×C4⋊C4C23×C6111yescharacteristic
533C2×C4⋊C4C23×C6111yescharacteristic
534C2×C22⋊C4—21no—
535C2×C22⋊C4—21no—
536C2×C22⋊C4—21no—
537C2×C22⋊C4—21no—
538C2×C22⋊C4—21no—
539C2×C22⋊C4—21no—
540C2×C22⋊C4—21no—
541C2×C22⋊C4—21no—
542C2×C22⋊C4—21no—
543C2×C22⋊C4—21no—
544C2×C22⋊C4D4×C6111yescharacteristic
545C2×C22⋊C4D4×C6111yescharacteristic
546C2×C42—21no—
547C2×C42—21no—
548C2×C42C23×C6111yescharacteristic
549C2×C42C23×C6111yescharacteristic
550#107—22no—
551C4⋊C8—22no—
552C4⋊C8—41no—
553#103—22no—
554#103—22no—
555#103D4×C6114yescomplemented
556#102—22no—
557#102—22no—
558#102—22no—
559#102—22no—
560#102—22no—
561#102—22no—
562#102—41no—
563C22⋊C8—22no—
564#95—21no—
565#95—21no—
566#95—21no—
567#95—21no—
568#95D4×C6111yescharacteristic
569#95D4×C6111yescharacteristic
570C24—21no—
571C24—21no—
572C24—21no—
573C24C2×D4×C6111yescharacteristic
574#41—28no—
575#41—44no—
576#41—44no—
577#41—44no—
578C2×Q8—21no—
579C2×Q8—21no—
580C2×Q8—21no—
581C2×Q8—21no—
582C2×Q8—21no—
583C2×Q8C2×D4×C6112yes—
584C2×D4—24no—
585C2×D4—21no—
586C2×D4—21no—
587C2×D4—21no—
588C2×D4—21no—
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—21no—
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—81no—
610C2×D4—81no—
611C2×D4—81no—
612C2×D4—81no—
613C2×D4—81no—
614C2×D4—81no—
615C2×D4C2×D4×C6112yes—
616C2×D4#41×C6112yes—
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—42no—
627C22×C4—42no—
628C22×C4—42no—
629C22×C4—42no—
630C22×C4—42no—
631C22×C4—81no—
632C22×C4C2×D4×C6111yescharacteristic
633C22×C4C2×D4×C6111yescharacteristic
634C22×C4C2×D4×C6111yescharacteristic
635C22×C4C2×D4×C6111yescharacteristic
636C22×C4C2×D4×C6112yes—
637C22×C4C2×D4×C6111yescharacteristic
638C22×C4#41×C6112yes—
639C22×C4C24×C6111yescharacteristic
640SD16—44no—
641D8—44no—
642D8—44no—
643C2×C8—21no—
644C2×C8—21no—
645C2×C8—21no—
646C2×C8—21no—
647C2×C8—21no—
648C2×C8—21no—
649C2×C8—21no—
650C2×C8—21no—
651C2×C8—21no—
652C2×C8—21no—
653C2×C8—21no—
654C2×C8—44no—
655C2×C8C2×D4×C6112yes—
656C4⋊C4—21no—
657C4⋊C4—21no—
658C4⋊C4—21no—
659C4⋊C4—21no—
660C4⋊C4—21no—
661C4⋊C4—21no—
662C4⋊C4—81no—
663C4⋊C4C2×D4×C6112yes—
664C4⋊C4C2×D4×C6112yes—
665C22⋊C4—24no—
666C22⋊C4—22no—
667C22⋊C4—41no—
668C22⋊C4—42no—
669C22⋊C4—42no—
670C22⋊C4—42no—
671C22⋊C4—42no—
672C22⋊C4—42no—
673C22⋊C4—42no—
674C22⋊C4—81no—
675C22⋊C4—81no—
676C22⋊C4—81no—
677C42—21no—
678C42—21no—
679C42—21no—
680C42—21no—
681C42—42no—
682C42—81no—
683C23—21no—
684C23—21no—
685C23—21no—
686C23—21no—
687C23—21no—
688C23—21no—
689C23—22no—
690C23—22no—
691C23—41no—
692C23—41no—
693C23—41no—
694C23—41no—
695C23—41no—
696C23—41no—
697C23—41no—
698C23—41no—
699C23—41no—
700C23—41no—
701C23—41no—
702C23—41no—
703C23—41no—
704C23—41no—
705C23—41no—
706C23—41no—
707C23—41no—
708C23—41no—
709C23—41no—
710C23#121×C6112yes—
711C23C22×D4×C6111yescharacteristic
712Q8—22no—
713Q8—22no—
714Q8—41no—
715Q8—41no—
716D4—22no—
717D4—22no—
718D4—22no—
719D4—22no—
720D4—48no—
721D4—41no—
722D4—41no—
723D4—41no—
724D4—41no—
725D4—41no—
726D4—41no—
727D4—41no—
728D4—41no—
729D4—84no—
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—21no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—21no—
746C2×C4—21no—
747C2×C4—21no—
748C2×C4—21no—
749C2×C4—21no—
750C2×C4—21no—
751C2×C4—21no—
752C2×C4—22no—
753C2×C4—48no—
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—84no—
767C2×C4#121×C6112yes—
768C2×C4#135×C6112yes—
769C2×C4C22×D4×C6111yescharacteristic
770C2×C4C22×D4×C6111yescharacteristic
771C2×C4C2×#41×C6111yescharacteristic
772C2×C4C2×#41×C6111yescharacteristic
773C2×C4H(5,𝔽2)×C6111yescharacteristic
774C2×C4H(5,𝔽2)×C6111yescharacteristic
775C8—22no—
776C8—41no—
777C8—41no—
778C8—41no—
779C22—22no—
780C22—22no—
781C22—22no—
782C22—41no—
783C22—41no—
784C22—41no—
785C22—41no—
786C22—42no—
787C22—42no—
788C22—42no—
789C22—42no—
790C22—42no—
791C22—42no—
792C22—81no—
793C22—81no—
794C22—81no—
795C22—81no—
796C22—81no—
797C22—81no—
798C22—81no—
799C22—81no—
800C22—81no—
801C22—81no—
802C22—81no—
803C22—81no—
804C22—81no—
805C22—81no—
806C22—81no—
807C22C2×#121×C6111yescharacteristic
808C22D42×C6111yescharacteristic
809C22C61×#54611yescharacteristic
810C22C2×#135×C6111yescharacteristic
811C22C61×#57511yescharacteristic
812C22C61×#57611yescharacteristic
813C22C61×#57611yescharacteristic
814C4—22no—
815C4—22no—
816C4—41no—
817C4—42no—
818C4—41no—
819C4—42no—
820C4—41no—
821C4—42no—
822C4—81no—
823C4—81no—
824C4C61×#52511yescharacteristic
825C4C61×#53811yescharacteristic
826C4D42×C6111yescharacteristic
827C4C61×#54611yescharacteristic
828C2—42no—
829C2—82no—
830C2—82no—
831C2—161no—
832C2C61×#242411yescharacteristic
833C2C61×#303511yescharacteristic
834C2C61×#304111yescharacteristic
835C2C61×#326811yescharacteristic
836C2C61×#328711yescharacteristic
837C2C61×#329711yescharacteristic
838C2C61×#331911yescharacteristic
subgroupG/H
center, socleC23×C61C22×D4
commutator, Frattini, cosocleC22×C4C24×C61
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C61 ◁ C4×C22⋊C4×C61 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C61×#466C2semidirect
2. C2×C61×#463C2semidirect
3. C2×C61×#449C2semidirect
4. C2×C61×#416C2semidirect
5. C61×#2431C2semidirect
6. C61×#2363C2semidirect
7. C61×#2067C2semidirect
8. C61×#2055C2semidirect
9. C61×#2042C2semidirect
10. C61×#2011C2semidirect
11. C61×#1982C2semidirect
12. C61×#1928C2semidirect
13. C61×#1879C2semidirect
14. C61×#1875C2semidirect
15. C61×#1850C2semidirect
104. #121×C61D4semidirect
135. #103×C61D4semidirect
359. #25087C61direct (N × H)
409. C2×#466C2×C61semidirect
410. C2×#463C2×C61semidirect
411. C2×#449C2×C61semidirect
412. C2×#416C2×C61semidirect
413. #2431C2×C61semidirect
414. #2363C2×C61semidirect
415. #2067C2×C61semidirect
416. #2055C2×C61semidirect
417. #2042C2×C61semidirect
418. #2011C2×C61semidirect
419. #1982C2×C61semidirect
420. #1928C2×C61semidirect
421. #1879C2×C61semidirect
422. #1875C2×C61semidirect
423. #1850C2×C61semidirect
482. C61#25087direct (N × H)
524. #121D4×C61semidirect
555. #103D4×C61semidirect

Maximal subgroups

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

subgroupindex
C2×C61×#4662
C2×C61×#4632
C2×C61×#4492
C2×C61×#4162
C61×#24312
C61×#23632
C61×#20672
C61×#20552
C61×#20422
C61×#20112
C61×#19822
C61×#19282
C61×#18792
C61×#18752
C61×#18502
#2508761