Finite Group Databasebeta

← C61×#24034 #29527467

Subgroups — C61×#24034 #29527467

Order 15616.

1380 conjugacy classes of subgroups.

The subgroup lattice has 864 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C61×#550C211yesmaximal, characteristic
2C2×C61×#482C211yesmaximal, characteristic, complemented
3C2×C61×#416C211yesmaximal, characteristic, complemented
4C61×#2485C211yesmaximal, characteristic, complemented
5C61×#2041C211yesmaximal, characteristic, complemented
6C61×#2041C211yesmaximal, characteristic, complemented
7C61×#2034C211yesmaximal, characteristic, complemented
8C61×#2033C211yesmaximal, characteristic, complemented
9C61×#1893C211yesmaximal, characteristic, complemented
10C61×#1869C211yesmaximal, characteristic, complemented
11C61×#1865C211yesmaximal, characteristic, complemented
12C61×#1863C211yesmaximal, characteristic, complemented
13C61×#1788C211yesmaximal, characteristic, complemented
14C61×#1788C211yesmaximal, characteristic, complemented
15C61×#1788C211yesmaximal, characteristic, complemented
16C22×#41×C61C2211yescharacteristic
17C22×#41×C61C2211yescharacteristic
18C23×C8×C61C2211yescharacteristic
19C61×#550—24no—
20C61×#550—24no—
21C2×#127×C61—21no—
22C2×#127×C61C2211yescharacteristic
23C2×#121×C61—21no—
24C2×#121×C61—21no—
25C2×#121×C61C2211yescharacteristic
26C2×#121×C61C2211yescharacteristic
27C2×C4×Q8×C61C2211yescharacteristic
28C2×C4×D4×C61—21no—
29C2×C4×D4×C61C2211yescharacteristic
30C2×#117×C61C2211yescharacteristic
31C61×#482—24no—
32C2×#107×C61C2211yescharacteristic
33C2×#106×C61C2211yescharacteristic
34C61×#416—24no—
35C2×#103×C61C2211yescharacteristic
36C2×#103×C61C2211yescharacteristic
37C2×#103×C61C2211yescharacteristic
38C2×#103×C61C2211yescharacteristic
39C2×#102×C61C2211yescharacteristic
40C2×#102×C61C2211yescharacteristic
41C2×#102×C61C2211yescharacteristic
42C2×#102×C61C2211yescharacteristic
43C2×#102×C61C2211yescharacteristic
44C2×#102×C61C2211yescharacteristic
45C2×#102×C61C2211yescharacteristic
46C2×#102×C61C2211yescharacteristic
47C2×C22⋊C8×C61C2211yescharacteristic
48C2×C22⋊C8×C61C2211yescharacteristic
49C2×C22⋊C8×C61C2211yescharacteristic
50C61×#397—21no—
51C61×#394—21no—
52C61×#389C2211yescharacteristic
53C61×#389C2211yescharacteristic
54C61×#388—21no—
55C61×#387—21no—
56C61×#380C2211yescharacteristic
57C61×#380C2211yescharacteristic
58C61×#380C2211yescharacteristic
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—22no—
68C2×#41×C61—22no—
69C2×#41×C61—22no—
70C2×#41×C61—41no—
71C2×#41×C61—41no—
72C2×#41×C61—41no—
73C2×#41×C61—41no—
74C2×#41×C61D414yes—
75C22×Q8×C61C2311yescharacteristic
76C22×D4×C61—21no—
77C22×D4×C61—21no—
78C22×D4×C61—21no—
79C22×D4×C61—21no—
80C22×D4×C61—21no—
81C22×D4×C61—21no—
82C22×D4×C61D411yescharacteristic
83C22×D4×C61C2311yescharacteristic
84C22×D4×C61C2311yescharacteristic
85C23×C4×C61—21no—
86C23×C4×C61—21no—
87C23×C4×C61C2311yescharacteristic
88C23×C4×C61C2311yescharacteristic
89C22×C8×C61—22no—
90C22×C8×C61—41no—
91C22×C8×C61—41no—
92C22×C8×C61C2311yescharacteristic
93C22×C8×C61C2311yescharacteristic
94C22×C8×C61C2311yescharacteristic
95C22×C8×C61C2311yescharacteristic
96#127×C61—28no—
97#127×C61—22no—
98#127×C61—22no—
99#121×C61—28no—
100#121×C61—28no—
101#121×C61—22no—
102#121×C61—22no—
103#121×C61—22no—
104#121×C61D414yes—
105C4×Q8×C61—22no—
106C4×Q8×C61—22no—
107C4×D4×C61—28no—
108C4×D4×C61—22no—
109C4×D4×C61—22no—
110#117×C61—22no—
111#117×C61—22no—
112C2×C4⋊C4×C61—21no—
113C2×C4⋊C4×C61—21no—
114C2×C4⋊C4×C61—21no—
115C2×C4⋊C4×C61D411yescharacteristic
116C2×C4⋊C4×C61C2311yescharacteristic
117C2×C4⋊C4×C61C2311yescharacteristic
118C2×C4⋊C4×C61C2311yescharacteristic
119C2×C4⋊C4×C61C2311yescharacteristic
120C2×C4⋊C4×C61C2311yescharacteristic
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×C61D411yescharacteristic
128C2×C22⋊C4×C61D411yescharacteristic
129C2×C42×C61—21no—
130C2×C42×C61—21no—
131C2×C42×C61C2311yescharacteristic
132#107×C61—22no—
133#106×C61—22no—
134#103×C61—22no—
135#103×C61—22no—
136#103×C61—22no—
137#103×C61—22no—
138#102×C61—22no—
139#102×C61—22no—
140#102×C61—22no—
141#102×C61—22no—
142#102×C61—41no—
143#102×C61—41no—
144#102×C61—41no—
145#102×C61—41no—
146C22⋊C8×C61—22no—
147C22⋊C8×C61—41no—
148C22⋊C8×C61—41no—
149#95×C61—21no—
150#95×C61—21no—
151#95×C61—21no—
152#95×C61—21no—
153#95×C61—21no—
154C24×C61—21no—
155C24×C61—21no—
156C24×C61C2×D411yescharacteristic
157C24×C61C2×D411yescharacteristic
158#41×C61—28no—
159#41×C61—44no—
160#41×C61—44no—
161#41×C61—44no—
162#41×C61—44no—
163#41×C61—44no—
164#41×C61—44no—
165#41×C61—44no—
166C2×Q8×C61—21no—
167C2×Q8×C61—21no—
168C2×Q8×C61—21no—
169C2×Q8×C61C2×D412yes—
170C2×Q8×C61#4112yes—
171C2×Q8×C61#4112yes—
172C2×D4×C61—24no—
173C2×D4×C61—24no—
174C2×D4×C61—22no—
175C2×D4×C61—24no—
176C2×D4×C61—24no—
177C2×D4×C61—24no—
178C2×D4×C61—24no—
179C2×D4×C61—22no—
180C2×D4×C61—21no—
181C2×D4×C61—21no—
182C2×D4×C61—21no—
183C2×D4×C61—21no—
184C2×D4×C61—21no—
185C2×D4×C61—21no—
186C2×D4×C61—21no—
187C2×D4×C61—21no—
188C2×D4×C61—21no—
189C2×D4×C61—21no—
190C2×D4×C61—41no—
191C2×D4×C61—42no—
192C2×D4×C61—42no—
193C2×D4×C61—42no—
194C2×D4×C61—42no—
195C2×D4×C61—42no—
196C2×D4×C61—42no—
197C2×D4×C61—81no—
198C2×D4×C61—81no—
199C2×D4×C61—81no—
200C2×D4×C61—81no—
201C2×D4×C61—81no—
202C2×D4×C61—81no—
203C2×D4×C61C2×D412yes—
204C2×D4×C61C2×D412yes—
205C22×C4×C61—21no—
206C22×C4×C61—21no—
207C22×C4×C61—21no—
208C22×C4×C61—21no—
209C22×C4×C61—21no—
210C22×C4×C61—24no—
211C22×C4×C61—21no—
212C22×C4×C61—24no—
213C22×C4×C61—21no—
214C22×C4×C61—21no—
215C22×C4×C61—21no—
216C22×C4×C61—21no—
217C22×C4×C61—21no—
218C22×C4×C61—21no—
219C22×C4×C61—21no—
220C22×C4×C61—21no—
221C22×C4×C61—21no—
222C22×C4×C61—21no—
223C22×C4×C61—42no—
224C22×C4×C61—42no—
225C22×C4×C61—42no—
226C22×C4×C61—42no—
227C22×C4×C61C2×D411yescharacteristic
228C22×C4×C61C2×D411yescharacteristic
229C22×C4×C61C2×D411yescharacteristic
230C22×C4×C61C2×D412yes—
231C22×C4×C61C2×D412yes—
232C22×C4×C61C2×D411yescharacteristic
233C22×C4×C61C2411yescharacteristic
234C2×C8×C61—21no—
235C2×C8×C61—21no—
236C2×C8×C61—21no—
237C2×C8×C61—21no—
238C2×C8×C61—21no—
239C2×C8×C61—21no—
240C2×C8×C61—21no—
241C2×C8×C61—21no—
242C2×C8×C61—21no—
243C2×C8×C61—21no—
244C2×C8×C61—21no—
245C2×C8×C61—21no—
246C2×C8×C61—44no—
247C4⋊C4×C61—24no—
248C4⋊C4×C61—22no—
249C4⋊C4×C61—21no—
250C4⋊C4×C61—21no—
251C4⋊C4×C61—21no—
252C4⋊C4×C61—21no—
253C4⋊C4×C61—21no—
254C4⋊C4×C61—21no—
255C4⋊C4×C61—21no—
256C4⋊C4×C61—21no—
257C4⋊C4×C61—21no—
258C4⋊C4×C61—42no—
259C4⋊C4×C61—81no—
260C4⋊C4×C61C2×D412yes—
261C22⋊C4×C61—24no—
262C22⋊C4×C61—22no—
263C22⋊C4×C61—24no—
264C22⋊C4×C61—22no—
265C22⋊C4×C61—42no—
266C22⋊C4×C61—42no—
267C22⋊C4×C61—81no—
268C22⋊C4×C61—81no—
269C42×C61—24no—
270C42×C61—21no—
271C42×C61—21no—
272C42×C61—42no—
273C23×C61—21no—
274C23×C61—21no—
275C23×C61—21no—
276C23×C61—21no—
277C23×C61—21no—
278C23×C61—21no—
279C23×C61—21no—
280C23×C61—22no—
281C23×C61—22no—
282C23×C61—21no—
283C23×C61—21no—
284C23×C61—21no—
285C23×C61—21no—
286C23×C61—21no—
287C23×C61—21no—
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#12012yes—
301C23×C61C22×D411yescharacteristic
302Q8×C61—22no—
303Q8×C61—22no—
304Q8×C61—22no—
305Q8×C61#12314yes—
306D4×C61—22no—
307D4×C61—22no—
308D4×C61—22no—
309D4×C61—22no—
310D4×C61—44no—
311D4×C61—48no—
312D4×C61—48no—
313D4×C61—48no—
314D4×C61—41no—
315D4×C61—41no—
316D4×C61—41no—
317D4×C61—41no—
318D4×C61—84no—
319D4×C61—84no—
320D4×C61—84no—
321C2×C4×C61—21no—
322C2×C4×C61—22no—
323C2×C4×C61—21no—
324C2×C4×C61—21no—
325C2×C4×C61—22no—
326C2×C4×C61—22no—
327C2×C4×C61—21no—
328C2×C4×C61—22no—
329C2×C4×C61—22no—
330C2×C4×C61—22no—
331C2×C4×C61—22no—
332C2×C4×C61—21no—
333C2×C4×C61—22no—
334C2×C4×C61—21no—
335C2×C4×C61—21no—
336C2×C4×C61—21no—
337C2×C4×C61—21no—
338C2×C4×C61—21no—
339C2×C4×C61—48no—
340C2×C4×C61—48no—
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—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#12012yes—
360C2×C4×C61#13512yes—
361C2×C4×C61C22×D411yescharacteristic
362C2×C4×C61C22×D411yescharacteristic
363C2×C4×C61C2×#4111yescharacteristic
364C2×C4×C61C2×#4111yescharacteristic
365C2×C4×C61H(5,𝔽2)11yescharacteristic
366C2×C4×C61H(5,𝔽2)11yescharacteristic
367C8×C61—41no—
368C8×C61—41no—
369C8×C61—41no—
370C8×C61—41no—
371#24034C6111yesmaximal, characteristic, direct product factor, Sylow
372C22×C61—22no—
373C22×C61—22no—
374C22×C61—22no—
375C22×C61—41no—
376C22×C61—41no—
377C22×C61—41no—
378C22×C61—41no—
379C22×C61—42no—
380C22×C61—42no—
381C22×C61—41no—
382C22×C61—41no—
383C22×C61—42no—
384C22×C61—42no—
385C22×C61—41no—
386C22×C61—42no—
387C22×C61—42no—
388C22×C61—41no—
389C22×C61—41no—
390C22×C61—41no—
391C22×C61—41no—
392C22×C61—81no—
393C22×C61—81no—
394C22×C61—81no—
395C22×C61—81no—
396C22×C61—81no—
397C22×C61—81no—
398C22×C61—81no—
399C22×C61—81no—
400C22×C61C2×#12011yescharacteristic
401C22×C61#54611yescharacteristic
402C22×C61#54611yescharacteristic
403C22×C61C2×#13511yescharacteristic
404C22×C61#57511yescharacteristic
405C22×C61#57611yescharacteristic
406C22×C61#57711yescharacteristic
407C4×C61—22no—
408C4×C61—24no—
409C4×C61—22no—
410C4×C61—41no—
411C4×C61—41no—
412C4×C61—42no—
413C4×C61—81no—
414C4×C61—81no—
415C4×C61—81no—
416C4×C61—81no—
417C4×C61C2×#12311yescharacteristic
418C4×C61#53411yescharacteristic
419C4×C61#54611yescharacteristic
420C4×C61#54611yescharacteristic
421C2×#550C2×C6111yescharacteristic
422C2×#482C2×C6111yescharacteristic, complemented
423C2×#416C2×C6111yescharacteristic, complemented
424#2485C2×C6111yescharacteristic, complemented
425#2041C2×C6111yescharacteristic, complemented
426#2041C2×C6111yescharacteristic, complemented
427#2034C2×C6111yescharacteristic, complemented
428#2033C2×C6111yescharacteristic, complemented
429#1893C2×C6111yescharacteristic, complemented
430#1869C2×C6111yescharacteristic, complemented
431#1865C2×C6111yescharacteristic, complemented
432#1863C2×C6111yescharacteristic, complemented
433#1788C2×C6111yescharacteristic, complemented
434#1788C2×C6111yescharacteristic, complemented
435#1788C2×C6111yescharacteristic, complemented
436C2×C61—42no—
437C2×C61—81no—
438C2×C61—82no—
439C2×C61—82no—
440C2×C61#240511yescharacteristic
441C2×C61#300211yescharacteristic
442C2×C61#301211yescharacteristic
443C2×C61#330411yescharacteristic
444C2×C61#330511yescharacteristic
445C2×C61#330911yescharacteristic
446C2×C61#331711yescharacteristic
447C22×#41C22×C6111yescharacteristic
448C22×#41C22×C6111yescharacteristic
449C23×C8C22×C6111yescharacteristic
450#550—24no—
451#550—24no—
452C2×#127—21no—
453C2×#127C22×C6111yescharacteristic
454C2×#121—21no—
455C2×#121—21no—
456C2×#121C22×C6111yescharacteristic
457C2×#121C22×C6111yescharacteristic
458C2×C4×Q8C22×C6111yescharacteristic
459C2×C4×D4—21no—
460C2×C4×D4C22×C6111yescharacteristic
461C2×#117C22×C6111yescharacteristic
462#482—24no—
463C2×#107C22×C6111yescharacteristic
464C2×#106C22×C6111yescharacteristic
465#416—24no—
466C2×#103C22×C6111yescharacteristic
467C2×#103C22×C6111yescharacteristic
468C2×#103C22×C6111yescharacteristic
469C2×#103C22×C6111yescharacteristic
470C2×#102C22×C6111yescharacteristic
471C2×#102C22×C6111yescharacteristic
472C2×#102C22×C6111yescharacteristic
473C2×#102C22×C6111yescharacteristic
474C2×#102C22×C6111yescharacteristic
475C2×#102C22×C6111yescharacteristic
476C2×#102C22×C6111yescharacteristic
477C2×#102C22×C6111yescharacteristic
478C2×C22⋊C8C22×C6111yescharacteristic
479C2×C22⋊C8C22×C6111yescharacteristic
480C2×C22⋊C8C22×C6111yescharacteristic
481#397—21no—
482#394—21no—
483#389C22×C6111yescharacteristic
484#389C22×C6111yescharacteristic
485#388—21no—
486#387—21no—
487#380C22×C6111yescharacteristic
488#380C22×C6111yescharacteristic
489#380C22×C6111yescharacteristic
490#340C22×C6111yescharacteristic
491#340C22×C6111yescharacteristic
492#336C22×C6111yescharacteristic
493#336C22×C6111yescharacteristic
494C61#2403411yescharacteristic, direct product factor, Sylow
495C2×#41—22no—
496C2×#41—22no—
497C2×#41—22no—
498C2×#41—22no—
499C2×#41—22no—
500C2×#41—22no—
501C2×#41—22no—
502C2×#41—41no—
503C2×#41—41no—
504C2×#41—41no—
505C2×#41—41no—
506C2×#41D4×C6114yes—
507C22×Q8C23×C6111yescharacteristic
508C22×D4—21no—
509C22×D4—21no—
510C22×D4—21no—
511C22×D4—21no—
512C22×D4—21no—
513C22×D4—21no—
514C22×D4D4×C6111yescharacteristic
515C22×D4C23×C6111yescharacteristic
516C22×D4C23×C6111yescharacteristic
517C23×C4—21no—
518C23×C4—21no—
519C23×C4C23×C6111yescharacteristic
520C23×C4C23×C6111yescharacteristic
521C22×C8—22no—
522C22×C8—41no—
523C22×C8—41no—
524C22×C8C23×C6111yescharacteristic
525C22×C8C23×C6111yescharacteristic
526C22×C8C23×C6111yescharacteristic
527C22×C8C23×C6111yescharacteristic
528#127—28no—
529#127—22no—
530#127—22no—
531#121—28no—
532#121—28no—
533#121—22no—
534#121—22no—
535#121—22no—
536#121D4×C6114yes—
537C4×Q8—22no—
538C4×Q8—22no—
539C4×D4—28no—
540C4×D4—22no—
541C4×D4—22no—
542#117—22no—
543#117—22no—
544C2×C4⋊C4—21no—
545C2×C4⋊C4—21no—
546C2×C4⋊C4—21no—
547C2×C4⋊C4D4×C6111yescharacteristic
548C2×C4⋊C4C23×C6111yescharacteristic
549C2×C4⋊C4C23×C6111yescharacteristic
550C2×C4⋊C4C23×C6111yescharacteristic
551C2×C4⋊C4C23×C6111yescharacteristic
552C2×C4⋊C4C23×C6111yescharacteristic
553C2×C22⋊C4—21no—
554C2×C22⋊C4—21no—
555C2×C22⋊C4—21no—
556C2×C22⋊C4—21no—
557C2×C22⋊C4—21no—
558C2×C22⋊C4—21no—
559C2×C22⋊C4D4×C6111yescharacteristic
560C2×C22⋊C4D4×C6111yescharacteristic
561C2×C42—21no—
562C2×C42—21no—
563C2×C42C23×C6111yescharacteristic
564#107—22no—
565#106—22no—
566#103—22no—
567#103—22no—
568#103—22no—
569#103—22no—
570#102—22no—
571#102—22no—
572#102—22no—
573#102—22no—
574#102—41no—
575#102—41no—
576#102—41no—
577#102—41no—
578C22⋊C8—22no—
579C22⋊C8—41no—
580C22⋊C8—41no—
581#95—21no—
582#95—21no—
583#95—21no—
584#95—21no—
585#95—21no—
586C24—21no—
587C24—21no—
588C24C2×D4×C6111yescharacteristic
589C24C2×D4×C6111yescharacteristic
590#41—28no—
591#41—44no—
592#41—44no—
593#41—44no—
594#41—44no—
595#41—44no—
596#41—44no—
597#41—44no—
598C2×Q8—21no—
599C2×Q8—21no—
600C2×Q8—21no—
601C2×Q8C2×D4×C6112yes—
602C2×Q8#41×C6112yes—
603C2×Q8#41×C6112yes—
604C2×D4—24no—
605C2×D4—24no—
606C2×D4—22no—
607C2×D4—24no—
608C2×D4—24no—
609C2×D4—24no—
610C2×D4—24no—
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—41no—
623C2×D4—42no—
624C2×D4—42no—
625C2×D4—42no—
626C2×D4—42no—
627C2×D4—42no—
628C2×D4—42no—
629C2×D4—81no—
630C2×D4—81no—
631C2×D4—81no—
632C2×D4—81no—
633C2×D4—81no—
634C2×D4—81no—
635C2×D4C2×D4×C6112yes—
636C2×D4C2×D4×C6112yes—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—24no—
643C22×C4—21no—
644C22×C4—24no—
645C22×C4—21no—
646C22×C4—21no—
647C22×C4—21no—
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—42no—
656C22×C4—42no—
657C22×C4—42no—
658C22×C4—42no—
659C22×C4C2×D4×C6111yescharacteristic
660C22×C4C2×D4×C6111yescharacteristic
661C22×C4C2×D4×C6111yescharacteristic
662C22×C4C2×D4×C6112yes—
663C22×C4C2×D4×C6112yes—
664C22×C4C2×D4×C6111yescharacteristic
665C22×C4C24×C6111yescharacteristic
666C2×C8—21no—
667C2×C8—21no—
668C2×C8—21no—
669C2×C8—21no—
670C2×C8—21no—
671C2×C8—21no—
672C2×C8—21no—
673C2×C8—21no—
674C2×C8—21no—
675C2×C8—21no—
676C2×C8—21no—
677C2×C8—21no—
678C2×C8—44no—
679C4⋊C4—24no—
680C4⋊C4—22no—
681C4⋊C4—21no—
682C4⋊C4—21no—
683C4⋊C4—21no—
684C4⋊C4—21no—
685C4⋊C4—21no—
686C4⋊C4—21no—
687C4⋊C4—21no—
688C4⋊C4—21no—
689C4⋊C4—21no—
690C4⋊C4—42no—
691C4⋊C4—81no—
692C4⋊C4C2×D4×C6112yes—
693C22⋊C4—24no—
694C22⋊C4—22no—
695C22⋊C4—24no—
696C22⋊C4—22no—
697C22⋊C4—42no—
698C22⋊C4—42no—
699C22⋊C4—81no—
700C22⋊C4—81no—
701C42—24no—
702C42—21no—
703C42—21no—
704C42—42no—
705C23—21no—
706C23—21no—
707C23—21no—
708C23—21no—
709C23—21no—
710C23—21no—
711C23—21no—
712C23—21no—
713C23—21no—
714C23—21no—
715C23—21no—
716C23—21no—
717C23—21no—
718C23—22no—
719C23—22no—
720C23—41no—
721C23—41no—
722C23—41no—
723C23—41no—
724C23—41no—
725C23—41no—
726C23—41no—
727C23—41no—
728C23—41no—
729C23—41no—
730C23—41no—
731C23—41no—
732C23#120×C6112yes—
733C23C22×D4×C6111yescharacteristic
734Q8—22no—
735Q8—22no—
736Q8—22no—
737Q8#123×C6114yes—
738D4—22no—
739D4—22no—
740D4—22no—
741D4—22no—
742D4—44no—
743D4—48no—
744D4—48no—
745D4—48no—
746D4—41no—
747D4—41no—
748D4—41no—
749D4—41no—
750D4—84no—
751D4—84no—
752D4—84no—
753C2×C4—21no—
754C2×C4—21no—
755C2×C4—22no—
756C2×C4—22no—
757C2×C4—21no—
758C2×C4—21no—
759C2×C4—22no—
760C2×C4—22no—
761C2×C4—22no—
762C2×C4—22no—
763C2×C4—22no—
764C2×C4—21no—
765C2×C4—21no—
766C2×C4—21no—
767C2×C4—21no—
768C2×C4—21no—
769C2×C4—22no—
770C2×C4—21no—
771C2×C4—48no—
772C2×C4—48no—
773C2×C4—41no—
774C2×C4—41no—
775C2×C4—41no—
776C2×C4—41no—
777C2×C4—41no—
778C2×C4—41no—
779C2×C4—41no—
780C2×C4—41no—
781C2×C4—41no—
782C2×C4—41no—
783C2×C4—41no—
784C2×C4—41no—
785C2×C4—41no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—41no—
791C2×C4#120×C6112yes—
792C2×C4#135×C6112yes—
793C2×C4C22×D4×C6111yescharacteristic
794C2×C4C22×D4×C6111yescharacteristic
795C2×C4C2×#41×C6111yescharacteristic
796C2×C4C2×#41×C6111yescharacteristic
797C2×C4H(5,𝔽2)×C6111yescharacteristic
798C2×C4H(5,𝔽2)×C6111yescharacteristic
799C8—41no—
800C8—41no—
801C8—41no—
802C8—41no—
803C22—22no—
804C22—22no—
805C22—22no—
806C22—41no—
807C22—41no—
808C22—41no—
809C22—41no—
810C22—41no—
811C22—41no—
812C22—41no—
813C22—41no—
814C22—42no—
815C22—42no—
816C22—41no—
817C22—41no—
818C22—42no—
819C22—42no—
820C22—41no—
821C22—42no—
822C22—42no—
823C22—81no—
824C22—81no—
825C22—81no—
826C22—81no—
827C22—81no—
828C22—81no—
829C22—81no—
830C22—81no—
831C22C2×#120×C6111yescharacteristic
832C22C61×#54611yescharacteristic
833C22C61×#54611yescharacteristic
834C22C2×#135×C6111yescharacteristic
835C22C61×#57511yescharacteristic
836C22C61×#57611yescharacteristic
837C22C61×#57711yescharacteristic
838C4—22no—
839C4—24no—
840C4—22no—
841C4—41no—
842C4—41no—
843C4—42no—
844C4—81no—
845C4—81no—
846C4—81no—
847C4—81no—
848C4C2×#123×C6111yescharacteristic
849C4C61×#53411yescharacteristic
850C4C61×#54611yescharacteristic
851C4C61×#54611yescharacteristic
852C2—42no—
853C2—81no—
854C2—82no—
855C2—82no—
856C2C61×#240511yescharacteristic
857C2C61×#300211yescharacteristic
858C2C61×#301211yescharacteristic
859C2C61×#330411yescharacteristic
860C2C61×#330511yescharacteristic
861C2C61×#330911yescharacteristic
862C2C61×#331711yescharacteristic
subgroupG/H
center, socleC23×C61C22×D4
commutator, Frattini, cosocleC22×C4C24×C61
prime radicalC2×C61×#550C2
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
2. C2×C61×#482C2semidirect
3. C2×C61×#416C2semidirect
4. C61×#2485C2semidirect
5. C61×#2041C2semidirect
6. C61×#2041C2semidirect
7. C61×#2034C2semidirect
8. C61×#2033C2semidirect
9. C61×#1893C2semidirect
10. C61×#1869C2semidirect
11. C61×#1865C2semidirect
12. C61×#1863C2semidirect
13. C61×#1788C2semidirect
14. C61×#1788C2semidirect
15. C61×#1788C2semidirect
371. #24034C61direct (N × H)
422. C2×#482C2×C61semidirect
423. C2×#416C2×C61semidirect
424. #2485C2×C61semidirect
425. #2041C2×C61semidirect
426. #2041C2×C61semidirect
427. #2034C2×C61semidirect
428. #2033C2×C61semidirect
429. #1893C2×C61semidirect
430. #1869C2×C61semidirect
431. #1865C2×C61semidirect
432. #1863C2×C61semidirect
433. #1788C2×C61semidirect
434. #1788C2×C61semidirect
435. #1788C2×C61semidirect
494. C61#24034direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C61×#5502
C2×C61×#4822
C2×C61×#4162
C61×#24852
C61×#20412
C61×#20342
C61×#20332
C61×#18932
C61×#18692
C61×#18652
C61×#18632
C61×#17882
#2403461