Finite Group Databasebeta

← C61×#14044 #29517477

Subgroups — C61×#14044 #29517477

Order 15616.

2006 conjugacy classes of subgroups.

The subgroup lattice has 696 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C61×#385C211yesmaximal, characteristic
2C2×C61×#385C211yesmaximal, characteristic
3C2×C61×#385C211yesmaximal, characteristic
4C2×C4×C22⋊C4×C61C211yesmaximal, characteristic
5C22×#95×C61C211yesmaximal, characteristic
6C61×#1442C212yesmaximal, complemented
7C61×#1441C212yesmaximal, complemented
8C61×#1436C212yesmaximal, complemented
9C61×C4⋊#95C212yesmaximal, complemented
10C61×C22⋊#95C211yesmaximal, characteristic
11C61×C22⋊#95C211yesmaximal, characteristic
12C24×C4×C61C2211yescharacteristic
13C24×C4×C61C2211yescharacteristic
14C24×C4×C61C2211yescharacteristic
15C22×C4⋊C4×C61C2211yescharacteristic
16C22×C4⋊C4×C61C2212yes—
17C22×C4⋊C4×C61C2211yescharacteristic
18C22×C4⋊C4×C61C2212yes—
19C22×C22⋊C4×C61C2211yescharacteristic
20C22×C22⋊C4×C61C2211yescharacteristic
21C22×C22⋊C4×C61C2211yescharacteristic
22C22×C22⋊C4×C61C2211yescharacteristic
23C22×C42×C61C2212yes—
24C61×#385—24no—
25C61×#385—24no—
26C61×#385C418yescomplemented
27C4×C22⋊C4×C61—24no—
28C2×#95×C61—24no—
29C2×#95×C61C2212yes—
30C2×#95×C61C2212yes—
31C2×#95×C61C2212yes—
32C2×#95×C61C2211yescharacteristic
33C2×#95×C61C2212yes—
34C2×#95×C61C2211yescharacteristic
35C2×#95×C61C2212yes—
36C2×#95×C61C2212yes—
37C2×#95×C61C2212yes—
38C2×#95×C61C2212yes—
39C2×#95×C61C2212yes—
40C25×C61C2311yescharacteristic
41C23×C4×C61—22no—
42C23×C4×C61—22no—
43C23×C4×C61—22no—
44C23×C4×C61—22no—
45C23×C4×C61—22no—
46C23×C4×C61—24no—
47C23×C4×C61—24no—
48C23×C4×C61—22no—
49C23×C4×C61—22no—
50C23×C4×C61—42no—
51C23×C4×C61—42no—
52C23×C4×C61—42no—
53C23×C4×C61—42no—
54C23×C4×C61C2×C414yes—
55C23×C4×C61D414yes—
56C23×C4×C61C2311yescharacteristic
57C23×C4×C61C2311yescharacteristic
58C23×C4×C61C2312yes—
59C23×C4×C61C2311yescharacteristic
60C23×C4×C61C2311yescharacteristic
61C23×C4×C61C2311yescharacteristic
62C23×C4×C61C2312yes—
63C23×C4×C61C2312yes—
64C23×C4×C61C2312yes—
65C23×C4×C61C2311yescharacteristic
66C2×C4⋊C4×C61—24no—
67C2×C4⋊C4×C61—22no—
68C2×C4⋊C4×C61—22no—
69C2×C4⋊C4×C61—24no—
70C2×C4⋊C4×C61—24no—
71C2×C4⋊C4×C61—42no—
72C2×C4⋊C4×C61—42no—
73C2×C4⋊C4×C61—42no—
74C2×C4⋊C4×C61—42no—
75C2×C4⋊C4×C61C2×C418yescomplemented
76C2×C22⋊C4×C61—22no—
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×C61C2×C414yes—
84C2×C22⋊C4×C61C2×C414yes—
85C2×C22⋊C4×C61D414yes—
86C2×C22⋊C4×C61Q814yes—
87C2×C22⋊C4×C61Q814yes—
88C2×C42×C61—24no—
89C2×C42×C61—24no—
90C2×C42×C61—42no—
91#95×C61—24no—
92#95×C61—24no—
93#95×C61—24no—
94#95×C61—22no—
95#95×C61—22no—
96#95×C61—24no—
97#95×C61—24no—
98#95×C61—42no—
99#95×C61—42no—
100#95×C61—42no—
101#95×C61C2×C418yescomplemented
102C24×C61—22no—
103C24×C61—22no—
104C24×C61—22no—
105C24×C61—22no—
106C24×C61C22×C412yes—
107C24×C61C2×D412yes—
108C24×C61C2×D412yes—
109C24×C61C2×Q812yes—
110C24×C61C2×Q812yes—
111C24×C61#4112yes—
112C24×C61#4112yes—
113C24×C61C2411yescharacteristic
114C22×C4×C61—21no—
115C22×C4×C61—22no—
116C22×C4×C61—22no—
117C22×C4×C61—21no—
118C22×C4×C61—22no—
119C22×C4×C61—22no—
120C22×C4×C61—22no—
121C22×C4×C61—28no—
122C22×C4×C61—28no—
123C22×C4×C61—28no—
124C22×C4×C61—22no—
125C22×C4×C61—21no—
126C22×C4×C61—22no—
127C22×C4×C61—22no—
128C22×C4×C61—21no—
129C22×C4×C61—21no—
130C22×C4×C61—22no—
131C22×C4×C61—22no—
132C22×C4×C61—22no—
133C22×C4×C61—22no—
134C22×C4×C61—21no—
135C22×C4×C61—21no—
136C22×C4×C61—22no—
137C22×C4×C61—22no—
138C22×C4×C61—22no—
139C22×C4×C61—21no—
140C22×C4×C61—22no—
141C22×C4×C61—22no—
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—22no—
149C22×C4×C61—22no—
150C22×C4×C61—22no—
151C22×C4×C61—22no—
152C22×C4×C61—22no—
153C22×C4×C61—22no—
154C22×C4×C61—28no—
155C22×C4×C61—21no—
156C22×C4×C61—21no—
157C22×C4×C61—21no—
158C22×C4×C61—21no—
159C22×C4×C61—21no—
160C22×C4×C61—21no—
161C22×C4×C61—22no—
162C22×C4×C61—22no—
163C22×C4×C61—22no—
164C22×C4×C61—22no—
165C22×C4×C61—48no—
166C22×C4×C61—44no—
167C22×C4×C61—48no—
168C22×C4×C61—48no—
169C22×C4×C61—48no—
170C22×C4×C61—48no—
171C22×C4×C61—44no—
172C22×C4×C61—44no—
173C22×C4×C61—44no—
174C22×C4×C61—48no—
175C22×C4×C61—44no—
176C22×C4×C61C22×C412yes—
177C22×C4×C61C22×C414yes—
178C22×C4×C61C22×C412yes—
179C22×C4×C61C22×C414yes—
180C22×C4×C61C2×D412yes—
181C22×C4×C61C2×D414yes—
182C22×C4×C61C2×D412yes—
183C22×C4×C61C2×Q814yes—
184C22×C4×C61C2×Q814yes—
185C22×C4×C61#4114yes—
186C22×C4×C61#4114yes—
187C4⋊C4×C61—48no—
188C4⋊C4×C61—48no—
189C4⋊C4×C61—44no—
190C4⋊C4×C61—44no—
191C22⋊C4×C61—28no—
192C22⋊C4×C61—28no—
193C22⋊C4×C61—44no—
194C22⋊C4×C61C4⋊C4116yescomplemented
195C42×C61—48no—
196C23×C61—24no—
197C23×C61—24no—
198C23×C61—22no—
199C23×C61—22no—
200C23×C61—24no—
201C23×C61—22no—
202C23×C61—22no—
203C23×C61—24no—
204C23×C61—24no—
205C23×C61—24no—
206C23×C61—24no—
207C23×C61—24no—
208C23×C61—24no—
209C23×C61—24no—
210C23×C61—24no—
211C23×C61—24no—
212C23×C61C2×C4⋊C414yes—
213C23×C61C4×D414yes—
214C23×C61C4×Q814yes—
215C23×C61#12114yes—
216C23×C61C22⋊Q814yes—
217C23×C61#12514yes—
218C23×C61C4⋊Q814yes—
219C23×C61C23×C411yescharacteristic
220C23×C61C22×D411yescharacteristic
221C23×C61C22×D411yescharacteristic
222C23×C61C22×Q811yescharacteristic
223C23×C61C22×Q811yescharacteristic
224C23×C61C2×#4111yescharacteristic
225C23×C61C2×#4111yescharacteristic
226C23×C61C2×#4112yes—
227C23×C61C2×#4112yes—
228C23×C61H(5,𝔽2)12yes—
229C23×C61H(5,𝔽2)12yes—
230C2×C4×C61—24no—
231C2×C4×C61—24no—
232C2×C4×C61—22no—
233C2×C4×C61—22no—
234C2×C4×C61—24no—
235C2×C4×C61—24no—
236C2×C4×C61—24no—
237C2×C4×C61—24no—
238C2×C4×C61—24no—
239C2×C4×C61—24no—
240C2×C4×C61—22no—
241C2×C4×C61—22no—
242C2×C4×C61—24no—
243C2×C4×C61—24no—
244C2×C4×C61—24no—
245C2×C4×C61—24no—
246C2×C4×C61—24no—
247C2×C4×C61—22no—
248C2×C4×C61—24no—
249C2×C4×C61—22no—
250C2×C4×C61—24no—
251C2×C4×C61—22no—
252C2×C4×C61—24no—
253C2×C4×C61—24no—
254C2×C4×C61—24no—
255C2×C4×C61—24no—
256C2×C4×C61—416no—
257C2×C4×C61—416no—
258C2×C4×C61—416no—
259C2×C4×C61—42no—
260C2×C4×C61—41no—
261C2×C4×C61—41no—
262C2×C4×C61—42no—
263C2×C4×C61—42no—
264C2×C4×C61—41no—
265C2×C4×C61—42no—
266C2×C4×C61—41no—
267C2×C4×C61—42no—
268C2×C4×C61—42no—
269C2×C4×C61—42no—
270C2×C4×C61—42no—
271C2×C4×C61—42no—
272C2×C4×C61—42no—
273C2×C4×C61—42no—
274C2×C4×C61—42no—
275C2×C4×C61—42no—
276C2×C4×C61—42no—
277C2×C4×C61—42no—
278C2×C4×C61—42no—
279C2×C4×C61—41no—
280C2×C4×C61—41no—
281C2×C4×C61—41no—
282C2×C4×C61—41no—
283C2×C4×C61—41no—
284C2×C4×C61—41no—
285C2×C4×C61—42no—
286C2×C4×C61—42no—
287C2×C4×C61—42no—
288C2×C4×C61—42no—
289C2×C4×C61C2×C4⋊C418yes—
290C2×C4×C61#12314yes—
291#14044C6111yesmaximal, characteristic, direct product factor, Sylow
292C22×C61—24no—
293C22×C61—24no—
294C22×C61—28no—
295C22×C61—28no—
296C22×C61—24no—
297C22×C61—24no—
298C22×C61—28no—
299C22×C61—24no—
300C22×C61—28no—
301C22×C61—24no—
302C22×C61#38918yes—
303C22×C61C22×C4⋊C411yescharacteristic
304C22×C61C2×C4×D411yescharacteristic
305C22×C61C2×C4×Q811yescharacteristic
306C22×C61C4×#4112yes—
307C22×C61#51812yes—
308C22×C61C2×#12111yescharacteristic
309C22×C61C2×C22⋊Q811yescharacteristic
310C22×C61C2×#12311yescharacteristic
311C22×C61#52511yescharacteristic
312C22×C61C2×#12511yescharacteristic
313C22×C61#52912yes—
314C22×C61C2×C4⋊Q811yescharacteristic
315C22×C61#53411yescharacteristic
316C22×C61#53511yescharacteristic
317C22×C61#53812yes—
318C22×C61#54612yes—
319C22×C61#54612yes—
320C22×C61#55112yes—
321C22×C61#55112yes—
322C22×C61#55412yes—
323C22×C61#55412yes—
324C22×C61#55412yes—
325C22×C61#55412yes—
326C4×C61—28no—
327C4×C61—24no—
328C4×C61—42no—
329C4×C61—44no—
330C4×C61—44no—
331C4×C61—42no—
332C4×C61—44no—
333C4×C61—42no—
334C4×C61—81no—
335C4×C61—81no—
336C2×#385C2×C6111yescharacteristic
337C2×#385C2×C6111yescharacteristic
338C2×#385C2×C6111yescharacteristic
339C2×C4×C22⋊C4C2×C6111yescharacteristic
340C22×#95C2×C6111yescharacteristic
341#1442C2×C6112yescomplemented
342#1441C2×C6112yescomplemented
343#1436C2×C6112yescomplemented
344C4⋊#95C2×C6112yescomplemented
345C22⋊#95C2×C6111yescharacteristic
346C22⋊#95C2×C6111yescharacteristic
347C2×C61—28no—
348C2×C61C2×#38911yescharacteristic
349C2×C61C4×#12311yescharacteristic
350C2×C61#232111yescharacteristic
351C2×C61#234912yes—
352C2×C61#236812yes—
353C2×C61#241111yescharacteristic
354C2×C61#241211yescharacteristic
355C2×C61#245012yes—
356C2×C61#250211yescharacteristic
357C2×C61#250512yes—
358C2×C61#258311yescharacteristic
359C24×C4C22×C6111yescharacteristic
360C24×C4C22×C6111yescharacteristic
361C24×C4C22×C6111yescharacteristic
362C22×C4⋊C4C22×C6111yescharacteristic
363C22×C4⋊C4C22×C6112yes—
364C22×C4⋊C4C22×C6111yescharacteristic
365C22×C4⋊C4C22×C6112yes—
366C22×C22⋊C4C22×C6111yescharacteristic
367C22×C22⋊C4C22×C6111yescharacteristic
368C22×C22⋊C4C22×C6111yescharacteristic
369C22×C22⋊C4C22×C6111yescharacteristic
370C22×C42C22×C6112yes—
371#385—24no—
372#385—24no—
373#385C4×C6118yescomplemented
374C4×C22⋊C4—24no—
375C2×#95—24no—
376C2×#95C22×C6112yes—
377C2×#95C22×C6111yescharacteristic
378C2×#95C22×C6112yes—
379C2×#95C22×C6112yes—
380C2×#95C22×C6112yes—
381C2×#95C22×C6112yes—
382C2×#95C22×C6111yescharacteristic
383C2×#95C22×C6112yes—
384C2×#95C22×C6112yes—
385C2×#95C22×C6112yes—
386C2×#95C22×C6112yes—
387C61#1404411yescharacteristic, direct product factor, Sylow
388C25C23×C6111yescharacteristic
389C23×C4—22no—
390C23×C4—22no—
391C23×C4—22no—
392C23×C4—22no—
393C23×C4—22no—
394C23×C4—24no—
395C23×C4—24no—
396C23×C4—22no—
397C23×C4—22no—
398C23×C4—42no—
399C23×C4—42no—
400C23×C4—42no—
401C23×C4—42no—
402C23×C4C2×C4×C6114yes—
403C23×C4D4×C6114yes—
404C23×C4C23×C6111yescharacteristic
405C23×C4C23×C6111yescharacteristic
406C23×C4C23×C6111yescharacteristic
407C23×C4C23×C6111yescharacteristic
408C23×C4C23×C6112yes—
409C23×C4C23×C6111yescharacteristic
410C23×C4C23×C6112yes—
411C23×C4C23×C6112yes—
412C23×C4C23×C6112yes—
413C23×C4C23×C6111yescharacteristic
414C2×C4⋊C4—24no—
415C2×C4⋊C4—22no—
416C2×C4⋊C4—22no—
417C2×C4⋊C4—24no—
418C2×C4⋊C4—24no—
419C2×C4⋊C4—42no—
420C2×C4⋊C4—42no—
421C2×C4⋊C4—42no—
422C2×C4⋊C4—42no—
423C2×C4⋊C4C2×C4×C6118yescomplemented
424C2×C22⋊C4—22no—
425C2×C22⋊C4—22no—
426C2×C22⋊C4—22no—
427C2×C22⋊C4—22no—
428C2×C22⋊C4—22no—
429C2×C22⋊C4—22no—
430C2×C22⋊C4—22no—
431C2×C22⋊C4C2×C4×C6114yes—
432C2×C22⋊C4C2×C4×C6114yes—
433C2×C22⋊C4D4×C6114yes—
434C2×C22⋊C4Q8×C6114yes—
435C2×C22⋊C4Q8×C6114yes—
436C2×C42—24no—
437C2×C42—24no—
438C2×C42—42no—
439#95—24no—
440#95—24no—
441#95—24no—
442#95—22no—
443#95—22no—
444#95—24no—
445#95—24no—
446#95—42no—
447#95—42no—
448#95—42no—
449#95C2×C4×C6118yescomplemented
450C24—22no—
451C24—22no—
452C24—22no—
453C24—22no—
454C24C22×C4×C6112yes—
455C24C2×D4×C6112yes—
456C24C2×D4×C6112yes—
457C24C2×Q8×C6112yes—
458C24C2×Q8×C6112yes—
459C24#41×C6112yes—
460C24#41×C6112yes—
461C24C24×C6111yescharacteristic
462C22×C4—21no—
463C22×C4—22no—
464C22×C4—22no—
465C22×C4—21no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—28no—
470C22×C4—28no—
471C22×C4—28no—
472C22×C4—22no—
473C22×C4—21no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—21no—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—28no—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—21no—
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—48no—
514C22×C4—44no—
515C22×C4—48no—
516C22×C4—48no—
517C22×C4—48no—
518C22×C4—48no—
519C22×C4—44no—
520C22×C4—44no—
521C22×C4—44no—
522C22×C4—48no—
523C22×C4—44no—
524C22×C4C22×C4×C6112yes—
525C22×C4C22×C4×C6114yes—
526C22×C4C22×C4×C6112yes—
527C22×C4C22×C4×C6114yes—
528C22×C4C2×D4×C6112yes—
529C22×C4C2×D4×C6114yes—
530C22×C4C2×D4×C6112yes—
531C22×C4C2×Q8×C6114yes—
532C22×C4C2×Q8×C6114yes—
533C22×C4#41×C6114yes—
534C22×C4#41×C6114yes—
535C4⋊C4—48no—
536C4⋊C4—48no—
537C4⋊C4—44no—
538C4⋊C4—44no—
539C22⋊C4—28no—
540C22⋊C4—28no—
541C22⋊C4—44no—
542C22⋊C4C4⋊C4×C61116yescomplemented
543C42—48no—
544C23—22no—
545C23—22no—
546C23—24no—
547C23—24no—
548C23—24no—
549C23—24no—
550C23—24no—
551C23—24no—
552C23—24no—
553C23—24no—
554C23—24no—
555C23—24no—
556C23—24no—
557C23—22no—
558C23—22no—
559C23—24no—
560C23C2×C4⋊C4×C6114yes—
561C23C4×D4×C6114yes—
562C23C4×Q8×C6114yes—
563C23#121×C6114yes—
564C23C22⋊Q8×C6114yes—
565C23#125×C6114yes—
566C23C4⋊Q8×C6114yes—
567C23C23×C4×C6111yescharacteristic
568C23C22×D4×C6111yescharacteristic
569C23C22×D4×C6111yescharacteristic
570C23C22×Q8×C6111yescharacteristic
571C23C22×Q8×C6111yescharacteristic
572C23C2×#41×C6111yescharacteristic
573C23C2×#41×C6112yes—
574C23C2×#41×C6112yes—
575C23C2×#41×C6111yescharacteristic
576C23H(5,𝔽2)×C6112yes—
577C23H(5,𝔽2)×C6112yes—
578C2×C4—22no—
579C2×C4—24no—
580C2×C4—24no—
581C2×C4—24no—
582C2×C4—24no—
583C2×C4—24no—
584C2×C4—24no—
585C2×C4—24no—
586C2×C4—24no—
587C2×C4—22no—
588C2×C4—22no—
589C2×C4—24no—
590C2×C4—24no—
591C2×C4—24no—
592C2×C4—24no—
593C2×C4—22no—
594C2×C4—22no—
595C2×C4—24no—
596C2×C4—24no—
597C2×C4—24no—
598C2×C4—24no—
599C2×C4—24no—
600C2×C4—22no—
601C2×C4—24no—
602C2×C4—22no—
603C2×C4—24no—
604C2×C4—416no—
605C2×C4—416no—
606C2×C4—416no—
607C2×C4—41no—
608C2×C4—42no—
609C2×C4—41no—
610C2×C4—42no—
611C2×C4—42no—
612C2×C4—42no—
613C2×C4—42no—
614C2×C4—42no—
615C2×C4—42no—
616C2×C4—42no—
617C2×C4—42no—
618C2×C4—42no—
619C2×C4—42no—
620C2×C4—42no—
621C2×C4—42no—
622C2×C4—42no—
623C2×C4—41no—
624C2×C4—41no—
625C2×C4—42no—
626C2×C4—42no—
627C2×C4—41no—
628C2×C4—41no—
629C2×C4—42no—
630C2×C4—42no—
631C2×C4—42no—
632C2×C4—42no—
633C2×C4—41no—
634C2×C4—41no—
635C2×C4—41no—
636C2×C4—41no—
637C2×C4C2×C4⋊C4×C6118yes—
638C2×C4#123×C6114yes—
639C22—24no—
640C22—24no—
641C22—24no—
642C22—28no—
643C22—28no—
644C22—24no—
645C22—24no—
646C22—28no—
647C22—24no—
648C22—28no—
649C22C61×#38918yes—
650C22C22×C4⋊C4×C6111yescharacteristic
651C22C2×C4×D4×C6111yescharacteristic
652C22C2×C4×Q8×C6111yescharacteristic
653C22C4×#41×C6112yes—
654C22C61×#51812yes—
655C22C2×#121×C6111yescharacteristic
656C22C2×C22⋊Q8×C6111yescharacteristic
657C22C2×#123×C6111yescharacteristic
658C22C61×#52511yescharacteristic
659C22C2×#125×C6111yescharacteristic
660C22C61×#52912yes—
661C22C2×C4⋊Q8×C6111yescharacteristic
662C22C61×#53411yescharacteristic
663C22C61×#53511yescharacteristic
664C22C61×#53812yes—
665C22C61×#54612yes—
666C22C61×#54612yes—
667C22C61×#55112yes—
668C22C61×#55112yes—
669C22C61×#55412yes—
670C22C61×#55412yes—
671C22C61×#55412yes—
672C22C61×#55412yes—
673C4—28no—
674C4—24no—
675C4—42no—
676C4—42no—
677C4—44no—
678C4—44no—
679C4—42no—
680C4—44no—
681C4—81no—
682C4—81no—
683C2—28no—
684C2C2×C61×#38911yescharacteristic
685C2C4×#123×C6111yescharacteristic
686C2C61×#232111yescharacteristic
687C2C61×#234912yes—
688C2C61×#236812yes—
689C2C61×#241111yescharacteristic
690C2C61×#241211yescharacteristic
691C2C61×#245012yes—
692C2C61×#250211yescharacteristic
693C2C61×#250512yes—
694C2C61×#258311yescharacteristic
subgroupG/H
center, socleC24×C61C24
commutatorC23C23×C4×C61
Frattini, cosocleC24C24×C61
prime radicalC25×C61C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C61 ◁ G

Complements

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

NH ≅ G/Ntype
6. C61×#1442C2semidirect
7. C61×#1441C2semidirect
8. C61×#1436C2semidirect
9. C61×C4⋊#95C2semidirect
26. C61×#385C4semidirect
75. C2×C4⋊C4×C61C2×C4semidirect
101. #95×C61C2×C4semidirect
194. C22⋊C4×C61C4⋊C4semidirect
291. #14044C61direct (N × H)
341. #1442C2×C61semidirect
342. #1441C2×C61semidirect
343. #1436C2×C61semidirect
344. C4⋊#95C2×C61semidirect
373. #385C4×C61semidirect
387. C61#14044direct (N × H)
423. C2×C4⋊C4C2×C4×C61semidirect
449. #95C2×C4×C61semidirect
542. C22⋊C4C4⋊C4×C61semidirect

Maximal subgroups

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

subgroupindex
C2×C61×#3852
C2×C4×C22⋊C4×C612
C22×#95×C612
C61×#14422
C61×#14412
C61×#14362
C61×C4⋊#952
C61×C22⋊#952
#1404461