Finite Group Databasebeta

← C61×#15220 #29518653

Subgroups — C61×#15220 #29518653

Order 15616.

1686 conjugacy classes of subgroups.

The subgroup lattice has 816 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C61×#389C211yesmaximal, characteristic, complemented
2C2×C61×#389C211yesmaximal, characteristic, complemented
3C2×C61×#382C211yesmaximal, characteristic, complemented
4C2×C61×#380C211yesmaximal, characteristic
5C2×C61×#380C211yesmaximal, characteristic
6C2×C4×C22⋊C4×C61C211yesmaximal, characteristic
7C61×#1443C212yesmaximal, complemented
8C61×#1441C212yesmaximal, complemented
9C61×#1439C212yesmaximal
10C61×#1439C212yesmaximal
11C61×C4⋊#95C211yesmaximal, characteristic, complemented
12C24×C4×C61C2211yescharacteristic
13C22×C4⋊C4×C61C2211yescharacteristic
14C22×C4⋊C4×C61C2211yescharacteristic
15C22×C4⋊C4×C61C2212yes—
16C22×C4⋊C4×C61C2211yescharacteristic
17C22×C4⋊C4×C61C2211yescharacteristic
18C22×C4⋊C4×C61C2212yes—
19C22×C22⋊C4×C61C2211yescharacteristic
20C22×C22⋊C4×C61C2211yescharacteristic
21C22×C22⋊C4×C61C2212yes—
22C22×C22⋊C4×C61C2212yes—
23C22×C42×C61C2211yescharacteristic
24C22×C42×C61C2211yescharacteristic
25C61×#389—24no—
26C61×#389—24no—
27C61×#382—24no—
28C61×#380—24no—
29C61×#380—24no—
30C4×C22⋊C4×C61—24no—
31C2×#95×C61C2211yescharacteristic
32C2×#95×C61C2211yescharacteristic
33C2×#95×C61C2212yes—
34C2×#95×C61C2212yes—
35C2×#95×C61C2212yes—
36C2×#95×C61C2212yes—
37C2×#95×C61C2212yes—
38C2×#95×C61C2212yes—
39C2×#95×C61C2212yes—
40C2×#95×C61C2212yes—
41C25×C61C2311yescharacteristic
42C23×C4×C61—22no—
43C23×C4×C61—22no—
44C23×C4×C61—22no—
45C23×C4×C61—22no—
46C23×C4×C61—22no—
47C23×C4×C61—22no—
48C23×C4×C61Q814yes—
49C23×C4×C61C2312yes—
50C23×C4×C61C2312yes—
51C23×C4×C61C2311yescharacteristic
52C23×C4×C61C2312yes—
53C23×C4×C61C2311yescharacteristic
54C23×C4×C61C2312yes—
55C23×C4×C61C2311yescharacteristic
56C23×C4×C61C2311yescharacteristic
57C23×C4×C61C2311yescharacteristic
58C23×C4×C61C2311yescharacteristic
59C2×C4⋊C4×C61—22no—
60C2×C4⋊C4×C61—22no—
61C2×C4⋊C4×C61—22no—
62C2×C4⋊C4×C61—22no—
63C2×C4⋊C4×C61—22no—
64C2×C4⋊C4×C61—22no—
65C2×C4⋊C4×C61—22no—
66C2×C4⋊C4×C61—24no—
67C2×C4⋊C4×C61—24no—
68C2×C4⋊C4×C61—22no—
69C2×C4⋊C4×C61—24no—
70C2×C4⋊C4×C61—22no—
71C2×C4⋊C4×C61—22no—
72C2×C4⋊C4×C61—42no—
73C2×C4⋊C4×C61—42no—
74C2×C4⋊C4×C61—42no—
75C2×C4⋊C4×C61D414yes—
76C2×C4⋊C4×C61D414yes—
77C2×C22⋊C4×C61—22no—
78C2×C22⋊C4×C61—22no—
79C2×C22⋊C4×C61—22no—
80C2×C22⋊C4×C61—22no—
81C2×C22⋊C4×C61—22no—
82C2×C22⋊C4×C61—22no—
83C2×C22⋊C4×C61—24no—
84C2×C22⋊C4×C61—24no—
85C2×C22⋊C4×C61—24no—
86C2×C22⋊C4×C61—24no—
87C2×C22⋊C4×C61—42no—
88C2×C22⋊C4×C61—42no—
89C2×C42×C61—22no—
90C2×C42×C61—22no—
91C2×C42×C61—22no—
92C2×C42×C61—22no—
93C2×C42×C61—22no—
94C2×C42×C61D414yes—
95#95×C61—22no—
96#95×C61—22no—
97#95×C61—24no—
98#95×C61—24no—
99#95×C61—24no—
100#95×C61—24no—
101#95×C61—24no—
102#95×C61—24no—
103#95×C61—24no—
104#95×C61—42no—
105C24×C61—21no—
106C24×C61—21no—
107C24×C61—21no—
108C24×C61—21no—
109C24×C61—21no—
110C24×C61—21no—
111C24×C61—21no—
112C24×C61—21no—
113C24×C61—21no—
114C24×C61—21no—
115C24×C61—21no—
116C24×C61—21no—
117C24×C61C2×Q812yes—
118C24×C61#4112yes—
119C24×C61#4112yes—
120C24×C61C2411yescharacteristic
121C22×C4×C61—21no—
122C22×C4×C61—21no—
123C22×C4×C61—21no—
124C22×C4×C61—21no—
125C22×C4×C61—21no—
126C22×C4×C61—21no—
127C22×C4×C61—21no—
128C22×C4×C61—21no—
129C22×C4×C61—22no—
130C22×C4×C61—22no—
131C22×C4×C61—21no—
132C22×C4×C61—21no—
133C22×C4×C61—21no—
134C22×C4×C61—21no—
135C22×C4×C61—21no—
136C22×C4×C61—21no—
137C22×C4×C61—21no—
138C22×C4×C61—21no—
139C22×C4×C61—21no—
140C22×C4×C61—21no—
141C22×C4×C61—21no—
142C22×C4×C61—22no—
143C22×C4×C61—22no—
144C22×C4×C61—22no—
145C22×C4×C61—22no—
146C22×C4×C61—22no—
147C22×C4×C61—22no—
148C22×C4×C61—21no—
149C22×C4×C61—21no—
150C22×C4×C61—21no—
151C22×C4×C61—21no—
152C22×C4×C61—22no—
153C22×C4×C61—22no—
154C22×C4×C61—21no—
155C22×C4×C61—21no—
156C22×C4×C61—21no—
157C22×C4×C61—22no—
158C22×C4×C61—21no—
159C22×C4×C61—21no—
160C22×C4×C61—22no—
161C22×C4×C61—21no—
162C22×C4×C61—21no—
163C22×C4×C61—28no—
164C22×C4×C61—28no—
165C22×C4×C61—28no—
166C22×C4×C61—22no—
167C22×C4×C61—22no—
168C22×C4×C61—22no—
169C22×C4×C61—22no—
170C22×C4×C61—22no—
171C22×C4×C61—22no—
172C22×C4×C61—22no—
173C22×C4×C61—22no—
174C22×C4×C61—22no—
175C22×C4×C61—22no—
176C22×C4×C61—22no—
177C22×C4×C61—22no—
178C22×C4×C61—22no—
179C22×C4×C61—22no—
180C22×C4×C61—44no—
181C22×C4×C61—44no—
182C22×C4×C61—44no—
183C22×C4×C61—44no—
184C22×C4×C61C2×D412yes—
185C22×C4×C61C2×D414yes—
186C22×C4×C61C2×D414yes—
187C22×C4×C61C2×D412yes—
188C22×C4×C61C2×D412yes—
189C22×C4×C61C2×D412yes—
190C22×C4×C61C2×D412yes—
191C22×C4×C61C2×Q812yes—
192C22×C4×C61C2×Q812yes—
193C22×C4×C61#4112yes—
194C22×C4×C61#4112yes—
195C22×C4×C61#4112yes—
196C22×C4×C61#4112yes—
197C22×C4×C61#4112yes—
198C4⋊C4×C61—28no—
199C4⋊C4×C61—28no—
200C4⋊C4×C61—48no—
201C4⋊C4×C61—48no—
202C4⋊C4×C61—44no—
203C4⋊C4×C61—44no—
204C22⋊C4×C61—28no—
205C22⋊C4×C61—28no—
206C22⋊C4×C61—48no—
207C22⋊C4×C61—48no—
208C42×C61—28no—
209C42×C61—44no—
210C23×C61—22no—
211C23×C61—22no—
212C23×C61—22no—
213C23×C61—22no—
214C23×C61—22no—
215C23×C61—22no—
216C23×C61—22no—
217C23×C61—22no—
218C23×C61—22no—
219C23×C61—22no—
220C23×C61—22no—
221C23×C61—22no—
222C23×C61—22no—
223C23×C61—22no—
224C23×C61—22no—
225C23×C61—22no—
226C23×C61—22no—
227C23×C61—22no—
228C23×C61—41no—
229C23×C61—41no—
230C23×C61—41no—
231C23×C61—41no—
232C23×C61—41no—
233C23×C61—41no—
234C23×C61—41no—
235C23×C61—41no—
236C23×C61—41no—
237C23×C61—41no—
238C23×C61—41no—
239C23×C61—41no—
240C23×C61—41no—
241C23×C61—41no—
242C23×C61—41no—
243C23×C61—41no—
244C23×C61#12514yes—
245C23×C61C22×D411yescharacteristic
246C23×C61C22×D411yescharacteristic
247C23×C61C22×D411yescharacteristic
248C23×C61C22×Q811yescharacteristic
249C23×C61C2×#4111yescharacteristic
250C23×C61C2×#4111yescharacteristic
251C23×C61C2×#4111yescharacteristic
252C23×C61C2×#4111yescharacteristic
253C23×C61C2×#4111yescharacteristic
254C23×C61C2×#4111yescharacteristic
255C23×C61C2×#4111yescharacteristic
256C23×C61H(5,𝔽2)11yescharacteristic
257C23×C61H(5,𝔽2)11yescharacteristic
258C23×C612−1+411yescharacteristic
259C23×C612−1+411yescharacteristic
260C2×C4×C61—22no—
261C2×C4×C61—22no—
262C2×C4×C61—24no—
263C2×C4×C61—24no—
264C2×C4×C61—22no—
265C2×C4×C61—22no—
266C2×C4×C61—22no—
267C2×C4×C61—22no—
268C2×C4×C61—22no—
269C2×C4×C61—22no—
270C2×C4×C61—22no—
271C2×C4×C61—22no—
272C2×C4×C61—22no—
273C2×C4×C61—24no—
274C2×C4×C61—24no—
275C2×C4×C61—22no—
276C2×C4×C61—24no—
277C2×C4×C61—24no—
278C2×C4×C61—22no—
279C2×C4×C61—22no—
280C2×C4×C61—22no—
281C2×C4×C61—41no—
282C2×C4×C61—41no—
283C2×C4×C61—41no—
284C2×C4×C61—41no—
285C2×C4×C61—41no—
286C2×C4×C61—42no—
287C2×C4×C61—41no—
288C2×C4×C61—42no—
289C2×C4×C61—42no—
290C2×C4×C61—41no—
291C2×C4×C61—41no—
292C2×C4×C61—42no—
293C2×C4×C61—42no—
294C2×C4×C61—41no—
295C2×C4×C61—41no—
296C2×C4×C61—41no—
297C2×C4×C61—41no—
298C2×C4×C61—42no—
299C2×C4×C61—41no—
300C2×C4×C61—41no—
301C2×C4×C61—41no—
302C2×C4×C61—41no—
303C2×C4×C61—41no—
304C2×C4×C61—42no—
305C2×C4×C61—41no—
306C2×C4×C61—42no—
307C2×C4×C61—41no—
308C2×C4×C61—41no—
309C2×C4×C61—416no—
310C2×C4×C61—42no—
311C2×C4×C61—42no—
312C2×C4×C61—42no—
313C2×C4×C61—42no—
314C2×C4×C61—42no—
315C2×C4×C61—42no—
316C2×C4×C61—42no—
317C2×C4×C61—42no—
318C2×C4×C61—42no—
319C2×C4×C61—42no—
320C2×C4×C61—42no—
321C2×C4×C61—42no—
322C2×C4×C61—42no—
323C2×C4×C61—42no—
324C2×C4×C61#12114yes—
325C2×C4×C61#12114yes—
326C2×C4×C61#12114yes—
327C2×C4×C61C22⋊Q814yes—
328C2×C4×C61C22⋊Q814yes—
329C2×C4×C61C22⋊Q814yes—
330C2×C4×C61#12614yes—
331#15220C6111yesmaximal, characteristic, direct product factor, Sylow
332C22×C61—24no—
333C22×C61—24no—
334C22×C61—24no—
335C22×C61—42no—
336C22×C61—42no—
337C22×C61—42no—
338C22×C61—42no—
339C22×C61—42no—
340C22×C61—42no—
341C22×C61—42no—
342C22×C61—42no—
343C22×C61—42no—
344C22×C61—42no—
345C22×C61—42no—
346C22×C61—42no—
347C22×C61C2×#12111yescharacteristic
348C22×C61C2×#12111yescharacteristic
349C22×C61C2×#12111yescharacteristic
350C22×C61C2×C22⋊Q811yescharacteristic
351C22×C61C2×C22⋊Q811yescharacteristic
352C22×C61C2×C22⋊Q811yescharacteristic
353C22×C61#52511yescharacteristic
354C22×C61#52511yescharacteristic
355C22×C61C2×#12511yescharacteristic
356C22×C61C2×#12611yescharacteristic
357C22×C61#52911yescharacteristic
358C22×C61#52911yescharacteristic
359C22×C61#53311yescharacteristic
360C22×C61#53511yescharacteristic
361C22×C61#53611yescharacteristic
362C22×C61#54211yescharacteristic
363C22×C61#54211yescharacteristic
364C22×C61#54411yescharacteristic
365C22×C61#54411yescharacteristic
366C22×C61#54611yescharacteristic
367C22×C61#54611yescharacteristic
368C22×C61#54611yescharacteristic
369C22×C61#54711yescharacteristic
370C22×C61#54811yescharacteristic
371C22×C61#54811yescharacteristic
372C22×C61#54811yescharacteristic
373C22×C61#55011yescharacteristic
374C22×C61#55211yescharacteristic
375C22×C61#55211yescharacteristic
376C22×C61#55211yescharacteristic
377C22×C61#55311yescharacteristic
378C22×C61#55311yescharacteristic
379C22×C61#55311yescharacteristic
380C22×C61#55511yescharacteristic
381C22×C61#55611yescharacteristic
382C4×C61—42no—
383C4×C61—42no—
384C4×C61—42no—
385C4×C61—44no—
386C4×C61—44no—
387C4×C61—42no—
388C4×C61—42no—
389C4×C61—82no—
390C4×C61—82no—
391C4×C61#39618yes—
392C2×#389C2×C6111yescharacteristic, complemented
393C2×#389C2×C6111yescharacteristic, complemented
394C2×#382C2×C6111yescharacteristic, complemented
395C2×#380C2×C6111yescharacteristic
396C2×#380C2×C6111yescharacteristic
397C2×C4×C22⋊C4C2×C6111yescharacteristic
398#1443C2×C6112yescomplemented
399#1441C2×C6112yescomplemented
400#1439C2×C6112yes—
401#1439C2×C6112yes—
402C4⋊#95C2×C6111yescharacteristic, complemented
403C2×C61—44no—
404C2×C61C2×#39611yescharacteristic
405C2×C61#241411yescharacteristic
406C2×C61#241511yescharacteristic
407C2×C61#242611yescharacteristic
408C2×C61#242711yescharacteristic
409C2×C61#243911yescharacteristic
410C2×C61#244111yescharacteristic
411C2×C61#244211yescharacteristic
412C2×C61#244211yescharacteristic
413C2×C61#249411yescharacteristic
414C2×C61#249511yescharacteristic
415C2×C61#253511yescharacteristic
416C2×C61#253611yescharacteristic
417C2×C61#262811yescharacteristic
418C2×C61#285111yescharacteristic
419C24×C4C22×C6111yescharacteristic
420C22×C4⋊C4C22×C6111yescharacteristic
421C22×C4⋊C4C22×C6111yescharacteristic
422C22×C4⋊C4C22×C6112yes—
423C22×C4⋊C4C22×C6111yescharacteristic
424C22×C4⋊C4C22×C6111yescharacteristic
425C22×C4⋊C4C22×C6112yes—
426C22×C22⋊C4C22×C6111yescharacteristic
427C22×C22⋊C4C22×C6111yescharacteristic
428C22×C22⋊C4C22×C6112yes—
429C22×C22⋊C4C22×C6112yes—
430C22×C42C22×C6111yescharacteristic
431C22×C42C22×C6111yescharacteristic
432#389—24no—
433#389—24no—
434#382—24no—
435#380—24no—
436#380—24no—
437C4×C22⋊C4—24no—
438C2×#95C22×C6112yes—
439C2×#95C22×C6112yes—
440C2×#95C22×C6112yes—
441C2×#95C22×C6112yes—
442C2×#95C22×C6112yes—
443C2×#95C22×C6111yescharacteristic
444C2×#95C22×C6112yes—
445C2×#95C22×C6112yes—
446C2×#95C22×C6111yescharacteristic
447C2×#95C22×C6112yes—
448C61#1522011yescharacteristic, direct product factor, Sylow
449C25C23×C6111yescharacteristic
450C23×C4—22no—
451C23×C4—22no—
452C23×C4—22no—
453C23×C4—22no—
454C23×C4—22no—
455C23×C4—22no—
456C23×C4Q8×C6114yes—
457C23×C4C23×C6112yes—
458C23×C4C23×C6112yes—
459C23×C4C23×C6112yes—
460C23×C4C23×C6112yes—
461C23×C4C23×C6111yescharacteristic
462C23×C4C23×C6111yescharacteristic
463C23×C4C23×C6111yescharacteristic
464C23×C4C23×C6111yescharacteristic
465C23×C4C23×C6111yescharacteristic
466C23×C4C23×C6111yescharacteristic
467C2×C4⋊C4—22no—
468C2×C4⋊C4—22no—
469C2×C4⋊C4—22no—
470C2×C4⋊C4—22no—
471C2×C4⋊C4—22no—
472C2×C4⋊C4—22no—
473C2×C4⋊C4—22no—
474C2×C4⋊C4—24no—
475C2×C4⋊C4—24no—
476C2×C4⋊C4—22no—
477C2×C4⋊C4—24no—
478C2×C4⋊C4—22no—
479C2×C4⋊C4—22no—
480C2×C4⋊C4—42no—
481C2×C4⋊C4—42no—
482C2×C4⋊C4—42no—
483C2×C4⋊C4D4×C6114yes—
484C2×C4⋊C4D4×C6114yes—
485C2×C22⋊C4—22no—
486C2×C22⋊C4—22no—
487C2×C22⋊C4—22no—
488C2×C22⋊C4—22no—
489C2×C22⋊C4—22no—
490C2×C22⋊C4—22no—
491C2×C22⋊C4—24no—
492C2×C22⋊C4—24no—
493C2×C22⋊C4—24no—
494C2×C22⋊C4—24no—
495C2×C22⋊C4—42no—
496C2×C22⋊C4—42no—
497C2×C42—22no—
498C2×C42—22no—
499C2×C42—22no—
500C2×C42—22no—
501C2×C42—22no—
502C2×C42D4×C6114yes—
503#95—22no—
504#95—22no—
505#95—24no—
506#95—24no—
507#95—24no—
508#95—24no—
509#95—24no—
510#95—24no—
511#95—24no—
512#95—42no—
513C24—21no—
514C24—21no—
515C24—21no—
516C24—21no—
517C24—21no—
518C24—21no—
519C24—21no—
520C24—21no—
521C24—21no—
522C24—21no—
523C24—21no—
524C24—21no—
525C24C2×Q8×C6112yes—
526C24#41×C6112yes—
527C24#41×C6112yes—
528C24C24×C6111yescharacteristic
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—22no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—22no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—28no—
572C22×C4—28no—
573C22×C4—28no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—44no—
589C22×C4—44no—
590C22×C4—44no—
591C22×C4—44no—
592C22×C4C2×D4×C6112yes—
593C22×C4C2×D4×C6114yes—
594C22×C4C2×D4×C6114yes—
595C22×C4C2×D4×C6112yes—
596C22×C4C2×D4×C6112yes—
597C22×C4C2×D4×C6112yes—
598C22×C4C2×D4×C6112yes—
599C22×C4C2×Q8×C6112yes—
600C22×C4C2×Q8×C6112yes—
601C22×C4#41×C6112yes—
602C22×C4#41×C6112yes—
603C22×C4#41×C6112yes—
604C22×C4#41×C6112yes—
605C22×C4#41×C6112yes—
606C4⋊C4—28no—
607C4⋊C4—28no—
608C4⋊C4—48no—
609C4⋊C4—48no—
610C4⋊C4—44no—
611C4⋊C4—44no—
612C22⋊C4—28no—
613C22⋊C4—28no—
614C22⋊C4—48no—
615C22⋊C4—48no—
616C42—28no—
617C42—44no—
618C23—22no—
619C23—22no—
620C23—22no—
621C23—22no—
622C23—22no—
623C23—22no—
624C23—22no—
625C23—22no—
626C23—22no—
627C23—22no—
628C23—22no—
629C23—22no—
630C23—22no—
631C23—22no—
632C23—22no—
633C23—22no—
634C23—22no—
635C23—22no—
636C23—41no—
637C23—41no—
638C23—41no—
639C23—41no—
640C23—41no—
641C23—41no—
642C23—41no—
643C23—41no—
644C23—41no—
645C23—41no—
646C23—41no—
647C23—41no—
648C23—41no—
649C23—41no—
650C23—41no—
651C23—41no—
652C23#125×C6114yes—
653C23C22×D4×C6111yescharacteristic
654C23C22×D4×C6111yescharacteristic
655C23C22×D4×C6111yescharacteristic
656C23C22×Q8×C6111yescharacteristic
657C23C2×#41×C6111yescharacteristic
658C23C2×#41×C6111yescharacteristic
659C23C2×#41×C6111yescharacteristic
660C23C2×#41×C6111yescharacteristic
661C23C2×#41×C6111yescharacteristic
662C23C2×#41×C6111yescharacteristic
663C23C2×#41×C6111yescharacteristic
664C23H(5,𝔽2)×C6111yescharacteristic
665C23H(5,𝔽2)×C6111yescharacteristic
666C232−1+4×C6111yescharacteristic
667C232−1+4×C6111yescharacteristic
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—24no—
671C2×C4—24no—
672C2×C4—22no—
673C2×C4—24no—
674C2×C4—24no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—24no—
681C2×C4—24no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—42no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—42no—
693C2×C4—42no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—42no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—42no—
704C2×C4—41no—
705C2×C4—42no—
706C2×C4—41no—
707C2×C4—41no—
708C2×C4—41no—
709C2×C4—41no—
710C2×C4—41no—
711C2×C4—41no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—42no—
715C2×C4—41no—
716C2×C4—42no—
717C2×C4—416no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—42no—
725C2×C4—42no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—42no—
729C2×C4—42no—
730C2×C4—42no—
731C2×C4—42no—
732C2×C4#121×C6114yes—
733C2×C4#121×C6114yes—
734C2×C4#121×C6114yes—
735C2×C4C22⋊Q8×C6114yes—
736C2×C4C22⋊Q8×C6114yes—
737C2×C4C22⋊Q8×C6114yes—
738C2×C4#126×C6114yes—
739C22—24no—
740C22—24no—
741C22—24no—
742C22—42no—
743C22—42no—
744C22—42no—
745C22—42no—
746C22—42no—
747C22—42no—
748C22—42no—
749C22—42no—
750C22—42no—
751C22—42no—
752C22—42no—
753C22—42no—
754C22C2×#121×C6111yescharacteristic
755C22C2×#121×C6111yescharacteristic
756C22C2×#121×C6111yescharacteristic
757C22C2×C22⋊Q8×C6111yescharacteristic
758C22C2×C22⋊Q8×C6111yescharacteristic
759C22C2×C22⋊Q8×C6111yescharacteristic
760C22C61×#52511yescharacteristic
761C22C61×#52511yescharacteristic
762C22C2×#125×C6111yescharacteristic
763C22C2×#126×C6111yescharacteristic
764C22C61×#52911yescharacteristic
765C22C61×#52911yescharacteristic
766C22C61×#53311yescharacteristic
767C22C61×#53511yescharacteristic
768C22C61×#53611yescharacteristic
769C22C61×#54211yescharacteristic
770C22C61×#54211yescharacteristic
771C22C61×#54411yescharacteristic
772C22C61×#54411yescharacteristic
773C22C61×#54611yescharacteristic
774C22C61×#54611yescharacteristic
775C22C61×#54611yescharacteristic
776C22C61×#54711yescharacteristic
777C22C61×#54811yescharacteristic
778C22C61×#54811yescharacteristic
779C22C61×#54811yescharacteristic
780C22C61×#55011yescharacteristic
781C22C61×#55211yescharacteristic
782C22C61×#55211yescharacteristic
783C22C61×#55211yescharacteristic
784C22C61×#55311yescharacteristic
785C22C61×#55311yescharacteristic
786C22C61×#55311yescharacteristic
787C22C61×#55511yescharacteristic
788C22C61×#55611yescharacteristic
789C4—44no—
790C4—42no—
791C4—42no—
792C4—42no—
793C4—42no—
794C4—42no—
795C4—44no—
796C4—82no—
797C4—82no—
798C4C61×#39618yes—
799C2—44no—
800C2C2×C61×#39611yescharacteristic
801C2C61×#241411yescharacteristic
802C2C61×#241511yescharacteristic
803C2C61×#242611yescharacteristic
804C2C61×#242711yescharacteristic
805C2C61×#243911yescharacteristic
806C2C61×#244111yescharacteristic
807C2C61×#244211yescharacteristic
808C2C61×#244211yescharacteristic
809C2C61×#249411yescharacteristic
810C2C61×#249511yescharacteristic
811C2C61×#253511yescharacteristic
812C2C61×#253611yescharacteristic
813C2C61×#262811yescharacteristic
814C2C61×#285111yescharacteristic
subgroupG/H
center, socleC24×C61C24
commutator, Frattini, cosocleC24C24×C61
prime radicalC25×C61C23
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C61 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C61×#389C2semidirect
2. C2×C61×#389C2semidirect
3. C2×C61×#382C2semidirect
7. C61×#1443C2semidirect
8. C61×#1441C2semidirect
11. C61×C4⋊#95C2semidirect
331. #15220C61direct (N × H)
392. C2×#389C2×C61semidirect
393. C2×#389C2×C61semidirect
394. C2×#382C2×C61semidirect
398. #1443C2×C61semidirect
399. #1441C2×C61semidirect
402. C4⋊#95C2×C61semidirect
448. C61#15220direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C61×#3892
C2×C61×#3822
C2×C61×#3802
C2×C4×C22⋊C4×C612
C61×#14432
C61×#14412
C61×#14392
C61×C4⋊#952
#1522061