Finite Group Databasebeta

← C61×#13873 #29517306

Subgroups — C61×#13873 #29517306

Order 15616.

3526 conjugacy classes of subgroups.

The subgroup lattice has 938 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C22⋊C4×C61C211yesmaximal, characteristic
2C2×C61×#388C212yesmaximal, complemented
3C2×C61×#380C211yesmaximal, characteristic, complemented
4C2×C61×#379C211yesmaximal, characteristic
5C2×C61×#379C211yesmaximal, characteristic
6C2×C4×C22⋊C4×C61C211yesmaximal, characteristic, complemented
7C61×#1440C212yesmaximal, complemented
8C61×#1439C212yesmaximal, complemented
9C61×#1437C212yesmaximal, complemented
10C61×C22⋊#95C211yesmaximal, characteristic, complemented
11C61×C22⋊#95C211yesmaximal, characteristic, complemented
12C26×C61C2211yescharacteristic
13C24×C4×C61C2211yescharacteristic
14C24×C4×C61C2211yescharacteristic
15C22×C4⋊C4×C61C2212yescomplemented
16C22×C22⋊C4×C61—28no—
17C22×C22⋊C4×C61C418yescomplemented
18C22×C22⋊C4×C61C2211yescharacteristic
19C22×C22⋊C4×C61C2211yescharacteristic
20C22×C22⋊C4×C61C2212yes—
21C22×C22⋊C4×C61C2212yes—
22C22×C22⋊C4×C61C2212yes—
23C22×C22⋊C4×C61C2212yes—
24C22×C22⋊C4×C61C2211yescharacteristic
25C22×C22⋊C4×C61C2211yescharacteristic
26C22×C22⋊C4×C61C2211yescharacteristic
27C22×C22⋊C4×C61C2211yescharacteristic
28C22×C22⋊C4×C61C2211yescharacteristic
29C22×C22⋊C4×C61C2211yescharacteristic
30C22×C42×C61C2212yescomplemented
31C61×#388—28no—
32C61×#380—24no—
33C61×#379—24no—
34C61×#379—24no—
35C4×C22⋊C4×C61—24no—
36C2×#95×C61C2212yescomplemented
37C2×#95×C61C2212yescomplemented
38C2×#95×C61C2212yescomplemented
39C2×#95×C61C2212yescomplemented
40C2×#95×C61C2212yescomplemented
41C2×#95×C61C2212yescomplemented
42C25×C61—24no—
43C25×C61—24no—
44C25×C61—22no—
45C25×C61—22no—
46C25×C61—22no—
47C25×C61—22no—
48C25×C61—22no—
49C25×C61—22no—
50C25×C61—42no—
51C25×C61—42no—
52C25×C61C2×C414yes—
53C25×C61C2311yescharacteristic
54C25×C61C2311yescharacteristic
55C25×C61C2311yescharacteristic
56C23×C4×C61—22no—
57C23×C4×C61—22no—
58C23×C4×C61—22no—
59C23×C4×C61—22no—
60C23×C4×C61—24no—
61C23×C4×C61—24no—
62C23×C4×C61—42no—
63C23×C4×C61—42no—
64C23×C4×C61C2×C414yes—
65C23×C4×C61C2×C414yes—
66C23×C4×C61C2312yes—
67C23×C4×C61C2312yes—
68C23×C4×C61C2311yescharacteristic
69C23×C4×C61C2311yescharacteristic
70C23×C4×C61C2312yes—
71C23×C4×C61C2312yes—
72C23×C4×C61C2311yescharacteristic
73C23×C4×C61C2311yescharacteristic
74C2×C4⋊C4×C61—24no—
75C2×C4⋊C4×C61—24no—
76C2×C4⋊C4×C61—42no—
77C2×C22⋊C4×C61—22no—
78C2×C22⋊C4×C61—24no—
79C2×C22⋊C4×C61—22no—
80C2×C22⋊C4×C61—22no—
81C2×C22⋊C4×C61—22no—
82C2×C22⋊C4×C61—24no—
83C2×C22⋊C4×C61—24no—
84C2×C22⋊C4×C61—232no—
85C2×C22⋊C4×C61—22no—
86C2×C22⋊C4×C61—22no—
87C2×C22⋊C4×C61—22no—
88C2×C22⋊C4×C61—24no—
89C2×C22⋊C4×C61—24no—
90C2×C22⋊C4×C61—24no—
91C2×C22⋊C4×C61—24no—
92C2×C22⋊C4×C61—22no—
93C2×C22⋊C4×C61—22no—
94C2×C22⋊C4×C61—22no—
95C2×C22⋊C4×C61—24no—
96C2×C22⋊C4×C61—24no—
97C2×C22⋊C4×C61—24no—
98C2×C22⋊C4×C61—24no—
99C2×C22⋊C4×C61—42no—
100C2×C22⋊C4×C61—42no—
101C2×C22⋊C4×C61—42no—
102C2×C22⋊C4×C61—42no—
103C2×C22⋊C4×C61C2×C414yes—
104C2×C22⋊C4×C61C2×C414yes—
105C2×C22⋊C4×C61C2×C414yes—
106C2×C22⋊C4×C61C2×C414yes—
107C2×C22⋊C4×C61D414yes—
108C2×C22⋊C4×C61D414yes—
109C2×C22⋊C4×C61D418yes—
110C2×C42×C61—24no—
111C2×C42×C61—24no—
112C2×C42×C61—42no—
113#95×C61—24no—
114#95×C61—24no—
115#95×C61—24no—
116#95×C61—24no—
117#95×C61—42no—
118#95×C61—42no—
119C24×C61—22no—
120C24×C61—22no—
121C24×C61—22no—
122C24×C61—22no—
123C24×C61—216no—
124C24×C61—216no—
125C24×C61—28no—
126C24×C61—28no—
127C24×C61—28no—
128C24×C61—22no—
129C24×C61—21no—
130C24×C61—21no—
131C24×C61—21no—
132C24×C61—21no—
133C24×C61—21no—
134C24×C61—21no—
135C24×C61—22no—
136C24×C61—21no—
137C24×C61—21no—
138C24×C61—21no—
139C24×C61—21no—
140C24×C61—21no—
141C24×C61—21no—
142C24×C61—22no—
143C24×C61—22no—
144C24×C61—22no—
145C24×C61—22no—
146C24×C61—28no—
147C24×C61—28no—
148C24×C61—44no—
149C24×C61—44no—
150C24×C61—48no—
151C24×C61—48no—
152C24×C61—48no—
153C24×C61—48no—
154C24×C61—48no—
155C24×C61—48no—
156C24×C61—48no—
157C24×C61—48no—
158C24×C61—48no—
159C24×C61—48no—
160C24×C61—44no—
161C24×C61—44no—
162C24×C61—44no—
163C24×C61—44no—
164C24×C61C22×C412yes—
165C24×C61C22×C412yes—
166C24×C61C22×C412yes—
167C24×C61C2×D414yes—
168C24×C61C2×D412yes—
169C24×C61C2×D412yes—
170C24×C61#4114yes—
171C24×C61#4112yes—
172C24×C61#4112yes—
173C24×C61#4112yes—
174C24×C61#4112yes—
175C24×C61C2411yescharacteristic
176C22×C4×C61—21no—
177C22×C4×C61—21no—
178C22×C4×C61—21no—
179C22×C4×C61—21no—
180C22×C4×C61—22no—
181C22×C4×C61—22no—
182C22×C4×C61—28no—
183C22×C4×C61—28no—
184C22×C4×C61—21no—
185C22×C4×C61—21no—
186C22×C4×C61—22no—
187C22×C4×C61—22no—
188C22×C4×C61—22no—
189C22×C4×C61—22no—
190C22×C4×C61—22no—
191C22×C4×C61—22no—
192C22×C4×C61—22no—
193C22×C4×C61—22no—
194C22×C4×C61—22no—
195C22×C4×C61—22no—
196C22×C4×C61—21no—
197C22×C4×C61—21no—
198C22×C4×C61—22no—
199C22×C4×C61—22no—
200C22×C4×C61—22no—
201C22×C4×C61—22no—
202C22×C4×C61—22no—
203C22×C4×C61—22no—
204C22×C4×C61—28no—
205C22×C4×C61—28no—
206C22×C4×C61—22no—
207C22×C4×C61—22no—
208C22×C4×C61—22no—
209C22×C4×C61—22no—
210C22×C4×C61—22no—
211C22×C4×C61—22no—
212C22×C4×C61—22no—
213C22×C4×C61—22no—
214C22×C4×C61—22no—
215C22×C4×C61—22no—
216C22×C4×C61—22no—
217C22×C4×C61—22no—
218C22×C4×C61—22no—
219C22×C4×C61—22no—
220C22×C4×C61—44no—
221C22×C4×C61—44no—
222C22×C4×C61—48no—
223C22×C4×C61—48no—
224C22×C4×C61—48no—
225C22×C4×C61—48no—
226C22×C4×C61C22×C412yes—
227C22×C4×C61C22×C412yes—
228C22×C4×C61C22×C412yes—
229C22×C4×C61C22×C412yes—
230C22×C4×C61C2×D414yes—
231C22×C4×C61C2×D414yes—
232C22×C4×C61C2×D414yes—
233C22×C4×C61C2×D414yes—
234C4⋊C4×C61—48no—
235C22⋊C4×C61—28no—
236C22⋊C4×C61—28no—
237C22⋊C4×C61—28no—
238C22⋊C4×C61—28no—
239C22⋊C4×C61—28no—
240C22⋊C4×C61—48no—
241C22⋊C4×C61—48no—
242C22⋊C4×C61—48no—
243C22⋊C4×C61—48no—
244C22⋊C4×C61—44no—
245C22⋊C4×C61—44no—
246C22⋊C4×C61C22⋊C4116yescomplemented
247C42×C61—48no—
248C23×C61—22no—
249C23×C61—22no—
250C23×C61—22no—
251C23×C61—22no—
252C23×C61—24no—
253C23×C61—24no—
254C23×C61—24no—
255C23×C61—24no—
256C23×C61—24no—
257C23×C61—24no—
258C23×C61—24no—
259C23×C61—24no—
260C23×C61—24no—
261C23×C61—24no—
262C23×C61—24no—
263C23×C61—24no—
264C23×C61—232no—
265C23×C61—22no—
266C23×C61—22no—
267C23×C61—22no—
268C23×C61—22no—
269C23×C61—22no—
270C23×C61—22no—
271C23×C61—22no—
272C23×C61—22no—
273C23×C61—22no—
274C23×C61—22no—
275C23×C61—22no—
276C23×C61—22no—
277C23×C61—24no—
278C23×C61—24no—
279C23×C61—24no—
280C23×C61—24no—
281C23×C61—24no—
282C23×C61—24no—
283C23×C61—24no—
284C23×C61—24no—
285C23×C61—24no—
286C23×C61—24no—
287C23×C61—24no—
288C23×C61—24no—
289C23×C61—416no—
290C23×C61—416no—
291C23×C61—416no—
292C23×C61—416no—
293C23×C61—416no—
294C23×C61—432no—
295C23×C61—432no—
296C23×C61—432no—
297C23×C61—432no—
298C23×C61—41no—
299C23×C61—41no—
300C23×C61—41no—
301C23×C61—41no—
302C23×C61—41no—
303C23×C61—41no—
304C23×C61—41no—
305C23×C61—41no—
306C23×C61—42no—
307C23×C61—42no—
308C23×C61—42no—
309C23×C61—42no—
310C23×C61—42no—
311C23×C61—42no—
312C23×C61—42no—
313C23×C61—42no—
314C23×C61—42no—
315C23×C61—42no—
316C23×C61—42no—
317C23×C61—42no—
318C23×C61—416no—
319C23×C61C2×C22⋊C414yes—
320C23×C61#11714yes—
321C23×C61#11714yes—
322C23×C61C4×D414yes—
323C23×C61C4×D414yes—
324C23×C61#12114yes—
325C23×C61#12314yes—
326C23×C61#12414yes—
327C23×C61#12614yes—
328C23×C61C23×C411yescharacteristic
329C23×C61C22×D412yes—
330C23×C61C22×D411yescharacteristic
331C23×C61C22×D411yescharacteristic
332C23×C61C2×#4111yescharacteristic
333C23×C61C2×#4111yescharacteristic
334C23×C61C2×#4112yes—
335C23×C61C2×#4111yescharacteristic
336C23×C61C2×#4111yescharacteristic
337C23×C61H(5,𝔽2)12yes—
338C23×C61H(5,𝔽2)12yes—
339C2×C4×C61—22no—
340C2×C4×C61—22no—
341C2×C4×C61—22no—
342C2×C4×C61—22no—
343C2×C4×C61—24no—
344C2×C4×C61—24no—
345C2×C4×C61—24no—
346C2×C4×C61—24no—
347C2×C4×C61—22no—
348C2×C4×C61—22no—
349C2×C4×C61—22no—
350C2×C4×C61—22no—
351C2×C4×C61—22no—
352C2×C4×C61—22no—
353C2×C4×C61—24no—
354C2×C4×C61—24no—
355C2×C4×C61—24no—
356C2×C4×C61—24no—
357C2×C4×C61—24no—
358C2×C4×C61—24no—
359C2×C4×C61—416no—
360C2×C4×C61—416no—
361C2×C4×C61—42no—
362C2×C4×C61—42no—
363C2×C4×C61—42no—
364C2×C4×C61—42no—
365C2×C4×C61—42no—
366C2×C4×C61—42no—
367C2×C4×C61—42no—
368C2×C4×C61—42no—
369C2×C4×C61—42no—
370C2×C4×C61—42no—
371C2×C4×C61—42no—
372C2×C4×C61—42no—
373C2×C4×C61—42no—
374C2×C4×C61—42no—
375C2×C4×C61—42no—
376C2×C4×C61—42no—
377C2×C4×C61—42no—
378C2×C4×C61—42no—
379C2×C4×C61—42no—
380C2×C4×C61—42no—
381C2×C4×C61—42no—
382C2×C4×C61—42no—
383C2×C4×C61—42no—
384C2×C4×C61—42no—
385C2×C4×C61—42no—
386C2×C4×C61—42no—
387C2×C4×C61C2×C22⋊C414yes—
388C2×C4×C61C2×C22⋊C414yes—
389#13873C6111yesmaximal, characteristic, direct product factor, Sylow
390C22×C61—24no—
391C22×C61—24no—
392C22×C61—24no—
393C22×C61—24no—
394C22×C61—24no—
395C22×C61—28no—
396C22×C61—28no—
397C22×C61—28no—
398C22×C61—28no—
399C22×C61—24no—
400C22×C61—24no—
401C22×C61—24no—
402C22×C61—24no—
403C22×C61—24no—
404C22×C61—24no—
405C22×C61—24no—
406C22×C61—464no—
407C22×C61—42no—
408C22×C61—42no—
409C22×C61—42no—
410C22×C61—42no—
411C22×C61—42no—
412C22×C61—42no—
413C22×C61—44no—
414C22×C61—44no—
415C22×C61—44no—
416C22×C61—44no—
417C22×C61—44no—
418C22×C61—44no—
419C22×C61—44no—
420C22×C61—44no—
421C22×C61—42no—
422C22×C61—42no—
423C22×C61#38818yescomplemented
424C22×C61C22×C22⋊C411yescharacteristic
425C22×C61C2×#11711yescharacteristic
426C22×C61C2×#11711yescharacteristic
427C22×C61C2×C4×D411yescharacteristic
428C22×C61C2×C4×D411yescharacteristic
429C22×C61#51811yescharacteristic
430C22×C61#51811yescharacteristic
431C22×C61C2×#12111yescharacteristic
432C22×C61C2×#12311yescharacteristic
433C22×C61#52512yes—
434C22×C61#52512yes—
435C22×C61C2×#12411yescharacteristic
436C22×C61C2×#12611yescharacteristic
437C22×C61#53812yes—
438C22×C61#53812yes—
439C22×C61D4212yes—
440C22×C61D4212yes—
441C22×C61#54612yes—
442C22×C61#54612yes—
443C22×C61#54612yes—
444C22×C61#54612yes—
445C22×C61#55112yes—
446C22×C61#55112yes—
447C4×C61—24no—
448C4×C61—24no—
449C4×C61—42no—
450C4×C61—42no—
451C4×C61—44no—
452C4×C61—44no—
453C4×C61—82no—
454C4×C61—82no—
455C23×C22⋊C4C2×C6111yescharacteristic
456C2×#388C2×C6112yescomplemented
457C2×#380C2×C6111yescharacteristic, complemented
458C2×#379C2×C6111yescharacteristic
459C2×#379C2×C6111yescharacteristic
460C2×C4×C22⋊C4C2×C6111yescharacteristic, complemented
461#1440C2×C6112yescomplemented
462#1439C2×C6112yescomplemented
463#1437C2×C6112yescomplemented
464C22⋊#95C2×C6111yescharacteristic, complemented
465C22⋊#95C2×C6111yescharacteristic, complemented
466C2×C61—28no—
467C2×C61—44no—
468C2×C61—44no—
469C2×C61#228011yescharacteristic
470C2×C61C2×#38811yescharacteristic
471C2×C61#231211yescharacteristic
472C2×C61D4×C22⋊C411yescharacteristic
473C2×C61D4×C22⋊C411yescharacteristic
474C2×C61#234211yescharacteristic
475C2×C61#234211yescharacteristic
476C2×C61#241812yes—
477C2×C61#242412yes—
478C2×C61#247212yes—
479C2×C61#248012yes—
480C26C22×C6111yescharacteristic
481C24×C4C22×C6111yescharacteristic
482C24×C4C22×C6111yescharacteristic
483C22×C4⋊C4C22×C6112yescomplemented
484C22×C22⋊C4—28no—
485C22×C22⋊C4C4×C6118yescomplemented
486C22×C22⋊C4C22×C6111yescharacteristic
487C22×C22⋊C4C22×C6111yescharacteristic
488C22×C22⋊C4C22×C6112yes—
489C22×C22⋊C4C22×C6112yes—
490C22×C22⋊C4C22×C6112yes—
491C22×C22⋊C4C22×C6112yes—
492C22×C22⋊C4C22×C6111yescharacteristic
493C22×C22⋊C4C22×C6111yescharacteristic
494C22×C22⋊C4C22×C6111yescharacteristic
495C22×C22⋊C4C22×C6111yescharacteristic
496C22×C22⋊C4C22×C6111yescharacteristic
497C22×C22⋊C4C22×C6111yescharacteristic
498C22×C42C22×C6112yescomplemented
499#388—28no—
500#380—24no—
501#379—24no—
502#379—24no—
503C4×C22⋊C4—24no—
504C2×#95C22×C6112yescomplemented
505C2×#95C22×C6112yescomplemented
506C2×#95C22×C6112yescomplemented
507C2×#95C22×C6112yescomplemented
508C2×#95C22×C6112yescomplemented
509C2×#95C22×C6112yescomplemented
510C61#1387311yescharacteristic, direct product factor, Sylow
511C25—24no—
512C25—24no—
513C25—22no—
514C25—22no—
515C25—22no—
516C25—22no—
517C25—22no—
518C25—22no—
519C25—42no—
520C25—42no—
521C25C2×C4×C6114yes—
522C25C23×C6111yescharacteristic
523C25C23×C6111yescharacteristic
524C25C23×C6111yescharacteristic
525C23×C4—22no—
526C23×C4—22no—
527C23×C4—22no—
528C23×C4—22no—
529C23×C4—24no—
530C23×C4—24no—
531C23×C4—42no—
532C23×C4—42no—
533C23×C4C2×C4×C6114yes—
534C23×C4C2×C4×C6114yes—
535C23×C4C23×C6112yes—
536C23×C4C23×C6112yes—
537C23×C4C23×C6111yescharacteristic
538C23×C4C23×C6111yescharacteristic
539C23×C4C23×C6112yes—
540C23×C4C23×C6112yes—
541C23×C4C23×C6111yescharacteristic
542C23×C4C23×C6111yescharacteristic
543C2×C4⋊C4—24no—
544C2×C4⋊C4—24no—
545C2×C4⋊C4—42no—
546C2×C22⋊C4—24no—
547C2×C22⋊C4—22no—
548C2×C22⋊C4—22no—
549C2×C22⋊C4—22no—
550C2×C22⋊C4—22no—
551C2×C22⋊C4—24no—
552C2×C22⋊C4—24no—
553C2×C22⋊C4—232no—
554C2×C22⋊C4—22no—
555C2×C22⋊C4—22no—
556C2×C22⋊C4—22no—
557C2×C22⋊C4—24no—
558C2×C22⋊C4—24no—
559C2×C22⋊C4—24no—
560C2×C22⋊C4—24no—
561C2×C22⋊C4—22no—
562C2×C22⋊C4—22no—
563C2×C22⋊C4—22no—
564C2×C22⋊C4—24no—
565C2×C22⋊C4—24no—
566C2×C22⋊C4—24no—
567C2×C22⋊C4—24no—
568C2×C22⋊C4—42no—
569C2×C22⋊C4—42no—
570C2×C22⋊C4—42no—
571C2×C22⋊C4—42no—
572C2×C22⋊C4C2×C4×C6114yes—
573C2×C22⋊C4C2×C4×C6114yes—
574C2×C22⋊C4C2×C4×C6114yes—
575C2×C22⋊C4C2×C4×C6114yes—
576C2×C22⋊C4D4×C6114yes—
577C2×C22⋊C4D4×C6114yes—
578C2×C22⋊C4D4×C6118yes—
579C2×C42—24no—
580C2×C42—24no—
581C2×C42—42no—
582#95—24no—
583#95—24no—
584#95—24no—
585#95—24no—
586#95—42no—
587#95—42no—
588C24—22no—
589C24—22no—
590C24—22no—
591C24—22no—
592C24—216no—
593C24—216no—
594C24—28no—
595C24—28no—
596C24—28no—
597C24—21no—
598C24—21no—
599C24—21no—
600C24—21no—
601C24—22no—
602C24—21no—
603C24—21no—
604C24—21no—
605C24—21no—
606C24—21no—
607C24—21no—
608C24—22no—
609C24—21no—
610C24—21no—
611C24—22no—
612C24—22no—
613C24—22no—
614C24—22no—
615C24—28no—
616C24—28no—
617C24—44no—
618C24—44no—
619C24—48no—
620C24—48no—
621C24—48no—
622C24—48no—
623C24—48no—
624C24—48no—
625C24—48no—
626C24—48no—
627C24—48no—
628C24—48no—
629C24—44no—
630C24—44no—
631C24—44no—
632C24—44no—
633C24C22×C4×C6112yes—
634C24C22×C4×C6112yes—
635C24C22×C4×C6112yes—
636C24C2×D4×C6114yes—
637C24C2×D4×C6112yes—
638C24C2×D4×C6112yes—
639C24#41×C6114yes—
640C24#41×C6112yes—
641C24#41×C6112yes—
642C24#41×C6112yes—
643C24#41×C6112yes—
644C24C24×C6111yescharacteristic
645C22×C4—21no—
646C22×C4—21no—
647C22×C4—21no—
648C22×C4—21no—
649C22×C4—22no—
650C22×C4—22no—
651C22×C4—28no—
652C22×C4—28no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—22no—
656C22×C4—22no—
657C22×C4—22no—
658C22×C4—22no—
659C22×C4—22no—
660C22×C4—22no—
661C22×C4—22no—
662C22×C4—22no—
663C22×C4—22no—
664C22×C4—22no—
665C22×C4—21no—
666C22×C4—21no—
667C22×C4—22no—
668C22×C4—22no—
669C22×C4—22no—
670C22×C4—22no—
671C22×C4—22no—
672C22×C4—22no—
673C22×C4—28no—
674C22×C4—28no—
675C22×C4—22no—
676C22×C4—22no—
677C22×C4—22no—
678C22×C4—22no—
679C22×C4—22no—
680C22×C4—22no—
681C22×C4—22no—
682C22×C4—22no—
683C22×C4—22no—
684C22×C4—22no—
685C22×C4—22no—
686C22×C4—22no—
687C22×C4—22no—
688C22×C4—22no—
689C22×C4—44no—
690C22×C4—44no—
691C22×C4—48no—
692C22×C4—48no—
693C22×C4—48no—
694C22×C4—48no—
695C22×C4C22×C4×C6112yes—
696C22×C4C22×C4×C6112yes—
697C22×C4C22×C4×C6112yes—
698C22×C4C22×C4×C6112yes—
699C22×C4C2×D4×C6114yes—
700C22×C4C2×D4×C6114yes—
701C22×C4C2×D4×C6114yes—
702C22×C4C2×D4×C6114yes—
703C4⋊C4—48no—
704C22⋊C4—28no—
705C22⋊C4—28no—
706C22⋊C4—28no—
707C22⋊C4—28no—
708C22⋊C4—28no—
709C22⋊C4—48no—
710C22⋊C4—48no—
711C22⋊C4—48no—
712C22⋊C4—48no—
713C22⋊C4—44no—
714C22⋊C4—44no—
715C22⋊C4C22⋊C4×C61116yescomplemented
716C42—48no—
717C23—24no—
718C23—24no—
719C23—24no—
720C23—24no—
721C23—24no—
722C23—24no—
723C23—24no—
724C23—24no—
725C23—24no—
726C23—24no—
727C23—22no—
728C23—22no—
729C23—22no—
730C23—22no—
731C23—24no—
732C23—24no—
733C23—232no—
734C23—24no—
735C23—24no—
736C23—24no—
737C23—24no—
738C23—24no—
739C23—24no—
740C23—24no—
741C23—24no—
742C23—22no—
743C23—22no—
744C23—22no—
745C23—22no—
746C23—22no—
747C23—22no—
748C23—22no—
749C23—22no—
750C23—22no—
751C23—22no—
752C23—22no—
753C23—22no—
754C23—24no—
755C23—24no—
756C23—24no—
757C23—24no—
758C23—416no—
759C23—416no—
760C23—416no—
761C23—416no—
762C23—416no—
763C23—432no—
764C23—432no—
765C23—432no—
766C23—432no—
767C23—42no—
768C23—42no—
769C23—42no—
770C23—42no—
771C23—42no—
772C23—42no—
773C23—42no—
774C23—42no—
775C23—42no—
776C23—42no—
777C23—42no—
778C23—42no—
779C23—416no—
780C23—41no—
781C23—41no—
782C23—41no—
783C23—41no—
784C23—41no—
785C23—41no—
786C23—41no—
787C23—41no—
788C23C2×C22⋊C4×C6114yes—
789C23#117×C6114yes—
790C23#117×C6114yes—
791C23C4×D4×C6114yes—
792C23C4×D4×C6114yes—
793C23#121×C6114yes—
794C23#123×C6114yes—
795C23#124×C6114yes—
796C23#126×C6114yes—
797C23C23×C4×C6111yescharacteristic
798C23C22×D4×C6112yes—
799C23C22×D4×C6111yescharacteristic
800C23C22×D4×C6111yescharacteristic
801C23C2×#41×C6111yescharacteristic
802C23C2×#41×C6111yescharacteristic
803C23C2×#41×C6112yes—
804C23C2×#41×C6111yescharacteristic
805C23C2×#41×C6111yescharacteristic
806C23H(5,𝔽2)×C6112yes—
807C23H(5,𝔽2)×C6112yes—
808C2×C4—24no—
809C2×C4—24no—
810C2×C4—24no—
811C2×C4—24no—
812C2×C4—22no—
813C2×C4—22no—
814C2×C4—22no—
815C2×C4—22no—
816C2×C4—24no—
817C2×C4—24no—
818C2×C4—24no—
819C2×C4—24no—
820C2×C4—22no—
821C2×C4—22no—
822C2×C4—22no—
823C2×C4—22no—
824C2×C4—22no—
825C2×C4—22no—
826C2×C4—24no—
827C2×C4—24no—
828C2×C4—416no—
829C2×C4—416no—
830C2×C4—42no—
831C2×C4—42no—
832C2×C4—42no—
833C2×C4—42no—
834C2×C4—42no—
835C2×C4—42no—
836C2×C4—42no—
837C2×C4—42no—
838C2×C4—42no—
839C2×C4—42no—
840C2×C4—42no—
841C2×C4—42no—
842C2×C4—42no—
843C2×C4—42no—
844C2×C4—42no—
845C2×C4—42no—
846C2×C4—42no—
847C2×C4—42no—
848C2×C4—42no—
849C2×C4—42no—
850C2×C4—42no—
851C2×C4—42no—
852C2×C4—42no—
853C2×C4—42no—
854C2×C4—42no—
855C2×C4—42no—
856C2×C4C2×C22⋊C4×C6114yes—
857C2×C4C2×C22⋊C4×C6114yes—
858C22—24no—
859C22—24no—
860C22—24no—
861C22—24no—
862C22—24no—
863C22—24no—
864C22—28no—
865C22—28no—
866C22—28no—
867C22—28no—
868C22—24no—
869C22—24no—
870C22—24no—
871C22—24no—
872C22—24no—
873C22—24no—
874C22—464no—
875C22—42no—
876C22—42no—
877C22—42no—
878C22—42no—
879C22—42no—
880C22—42no—
881C22—42no—
882C22—42no—
883C22—44no—
884C22—44no—
885C22—44no—
886C22—44no—
887C22—44no—
888C22—44no—
889C22—44no—
890C22—44no—
891C22C61×#38818yescomplemented
892C22C22×C22⋊C4×C6111yescharacteristic
893C22C2×#117×C6111yescharacteristic
894C22C2×#117×C6111yescharacteristic
895C22C2×C4×D4×C6111yescharacteristic
896C22C2×C4×D4×C6111yescharacteristic
897C22C61×#51811yescharacteristic
898C22C61×#51811yescharacteristic
899C22C2×#121×C6111yescharacteristic
900C22C2×#123×C6111yescharacteristic
901C22C61×#52512yes—
902C22C61×#52512yes—
903C22C2×#124×C6111yescharacteristic
904C22C2×#126×C6111yescharacteristic
905C22C61×#53812yes—
906C22C61×#53812yes—
907C22D42×C6112yes—
908C22D42×C6112yes—
909C22C61×#54612yes—
910C22C61×#54612yes—
911C22C61×#54612yes—
912C22C61×#54612yes—
913C22C61×#55112yes—
914C22C61×#55112yes—
915C4—24no—
916C4—24no—
917C4—42no—
918C4—42no—
919C4—44no—
920C4—44no—
921C4—82no—
922C4—82no—
923C2—28no—
924C2—44no—
925C2—44no—
926C2C61×#228011yescharacteristic
927C2C2×C61×#38811yescharacteristic
928C2C61×#231211yescharacteristic
929C2D4×C22⋊C4×C6111yescharacteristic
930C2D4×C22⋊C4×C6111yescharacteristic
931C2C61×#234211yescharacteristic
932C2C61×#234211yescharacteristic
933C2C61×#241812yes—
934C2C61×#242412yes—
935C2C61×#247212yes—
936C2C61×#248012yes—
subgroupG/H
center, socleC24×C61C24
commutatorC23C23×C4×C61
Frattini, cosocleC24C24×C61
prime radicalC26×C61C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C61 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C61×#388C2semidirect
3. C2×C61×#380C2semidirect
6. C2×C4×C22⋊C4×C61C2semidirect
7. C61×#1440C2semidirect
8. C61×#1439C2semidirect
9. C61×#1437C2semidirect
10. C61×C22⋊#95C2semidirect
11. C61×C22⋊#95C2semidirect
15. C22×C4⋊C4×C61C22semidirect
17. C22×C22⋊C4×C61C4semidirect
30. C22×C42×C61C22semidirect
36. C2×#95×C61C22semidirect
37. C2×#95×C61C22semidirect
38. C2×#95×C61C22semidirect
39. C2×#95×C61C22semidirect
40. C2×#95×C61C22semidirect
41. C2×#95×C61C22semidirect
246. C22⋊C4×C61C22⋊C4semidirect
389. #13873C61direct (N × H)
423. C22×C61#388semidirect
456. C2×#388C2×C61semidirect
457. C2×#380C2×C61semidirect
460. C2×C4×C22⋊C4C2×C61semidirect
461. #1440C2×C61semidirect
462. #1439C2×C61semidirect
463. #1437C2×C61semidirect
464. C22⋊#95C2×C61semidirect
465. C22⋊#95C2×C61semidirect
483. C22×C4⋊C4C22×C61semidirect
485. C22×C22⋊C4C4×C61semidirect
498. C22×C42C22×C61semidirect
504. C2×#95C22×C61semidirect
505. C2×#95C22×C61semidirect
506. C2×#95C22×C61semidirect
507. C2×#95C22×C61semidirect
508. C2×#95C22×C61semidirect
509. C2×#95C22×C61semidirect
510. C61#13873direct (N × H)
715. C22⋊C4C22⋊C4×C61semidirect
891. C22C61×#388semidirect

Maximal subgroups

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

subgroupindex
C23×C22⋊C4×C612
C2×C61×#3882
C2×C61×#3802
C2×C61×#3792
C2×C4×C22⋊C4×C612
C61×#14402
C61×#14392
C61×#14372
C61×C22⋊#952
#1387361