Finite Group Databasebeta

← #29602815

Subgroups — #29602815

Order 15616.

3058 conjugacy classes of subgroups.

The subgroup lattice has 1388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519749C211yesmaximal, characteristic
2C22×C4×C22⋊D61C211yesmaximal, characteristic, complemented
3C2×#16839662C211yesmaximal, characteristic, complemented
4C2×#16839638C211yesmaximal, characteristic, complemented
5C2×#16839620C211yesmaximal, characteristic, complemented
6C2×C22⋊C4×Dic61C211yesmaximal, characteristic, complemented
7#21444067C211yesmaximal, characteristic, complemented
8#21444066C211yesmaximal, characteristic, complemented
9#21444060C211yesmaximal, characteristic, complemented
10#21444058C211yesmaximal, characteristic, complemented
11#21444047C211yesmaximal, characteristic, complemented
12#21444047C211yesmaximal, characteristic, complemented
13#21444042C211yesmaximal, characteristic, complemented
14#21444040C211yesmaximal, characteristic, complemented
15C2×C61×#386C211yesmaximal, characteristic, complemented
16C23×C22⋊D61C2211yescharacteristic
17C23×C22⋊D61C2211yescharacteristic
18C24×Dic61C2211yescharacteristic
19C23×C4×D61C2211yescharacteristic
20C2×#14519749—24no—
21C2×#14519749—24no—
22C2×#14519749C418yescomplemented
23C2×C4×C22⋊D61—24no—
24C2×C4×C22⋊D61—24no—
25C2×C4×C22⋊D61—24no—
26C22×#11758196C2211yescharacteristic
27C22×#11758196C2211yescharacteristic
28C22×#11758196C2211yescharacteristic
29C22×C22⋊Dic61C2211yescharacteristic
30C22×C22⋊Dic61C2211yescharacteristic
31C22×C22⋊Dic61C2211yescharacteristic
32C22×C22⋊Dic61C2211yescharacteristic
33C22×C22⋊Dic61C2211yescharacteristic
34C22×#11758198C2211yescharacteristic
35C22×#11758198C2211yescharacteristic
36C22×#11758198C2211yescharacteristic
37C22×#11758198C2211yescharacteristic
38C22×C4×Dic61C2211yescharacteristic
39C22×C4×Dic61C2211yescharacteristic
40#16839662—24no—
41#16839638—24no—
42#16839620—24no—
43C22⋊C4×Dic61—24no—
44C2×#14519684C2211yescharacteristic
45C2×#14519684C2211yescharacteristic
46C2×#14519684C2211yescharacteristic
47C2×#14519684C2211yescharacteristic
48C2×#14519684C2211yescharacteristic
49C2×#14519684C2211yescharacteristic
50C2×#14519684C2211yescharacteristic
51C2×#14519684C2211yescharacteristic
52C2×#14519684C2211yescharacteristic
53C2×#14519684C2211yescharacteristic
54C23×D4×C61C2211yescharacteristic
55C24×C4×C61C2211yescharacteristic
56C22×C22⋊C4×C61C2211yescharacteristic
57C22×C22⋊C4×C61C2211yescharacteristic
58C22×C22⋊C4×C61C2211yescharacteristic
59C61×#386—24no—
60C2×#95×C61C2211yescharacteristic
61C2×#95×C61C2211yescharacteristic
62C24×D61C2311yescharacteristic
63C22×C22⋊D61—22no—
64C22×C22⋊D61—22no—
65C22×C22⋊D61—22no—
66C22×C22⋊D61—22no—
67C22×C22⋊D61—22no—
68C22×C22⋊D61—22no—
69C22×C22⋊D61—22no—
70C22×C22⋊D61—22no—
71C22×C22⋊D61—41no—
72C22×C22⋊D61—41no—
73C22×C22⋊D61C2×C414yes—
74C22×C22⋊D61C2×C414yescomplemented
75C22×C22⋊D61D414yes—
76C22×C22⋊D61D414yes—
77C23×Dic61—22no—
78C23×Dic61—22no—
79C23×Dic61—22no—
80C23×Dic61—22no—
81C23×Dic61—22no—
82C23×Dic61—22no—
83C23×Dic61C2×C414yescomplemented
84C23×Dic61C2311yescharacteristic
85C23×Dic61C2311yescharacteristic
86C23×Dic61C2311yescharacteristic
87C23×Dic61C2311yescharacteristic
88C23×Dic61C2311yescharacteristic
89C23×Dic61C2311yescharacteristic
90C23×Dic61C2311yescharacteristic
91C22×C4×D61—22no—
92C22×C4×D61—22no—
93C22×C4×D61—22no—
94C22×C4×D61—22no—
95C22×C4×D61—22no—
96C22×C4×D61—41no—
97C22×C4×D61—41no—
98#14519749—232no—
99C4×C22⋊D61—232no—
100C2×#11758196—22no—
101C2×#11758196—22no—
102C2×#11758196—22no—
103C2×#11758196—22no—
104C2×#11758196—22no—
105C2×#11758196—22no—
106C2×#11758196—22no—
107C2×#11758196C2×C414yescomplemented
108C2×#11758196D414yescomplemented
109C2×C22⋊Dic61—22no—
110C2×C22⋊Dic61—22no—
111C2×C22⋊Dic61—22no—
112C2×C22⋊Dic61—22no—
113C2×C22⋊Dic61—22no—
114C2×C22⋊Dic61—22no—
115C2×C22⋊Dic61—22no—
116C2×C22⋊Dic61—22no—
117C2×C22⋊Dic61—22no—
118C2×C22⋊Dic61—22no—
119C2×C22⋊Dic61—22no—
120C2×C22⋊Dic61—22no—
121C2×C22⋊Dic61—41no—
122C2×C22⋊Dic61—41no—
123C2×C22⋊Dic61C2×C414yescomplemented
124C2×#11758198—22no—
125C2×#11758198—22no—
126C2×#11758198—22no—
127C2×#11758198—22no—
128C2×#11758198—22no—
129C2×#11758198—22no—
130C2×#11758198—22no—
131C2×#11758198—22no—
132C2×#11758198—22no—
133C2×#11758198—41no—
134C2×#11758198—41no—
135C2×#11758198C2×C414yescomplemented
136C2×C4×Dic61—22no—
137C2×C4×Dic61—22no—
138C2×C4×Dic61—22no—
139C2×C4×Dic61—22no—
140C2×C4×Dic61—22no—
141C2×C4×Dic61D414yescomplemented
142#14519684—22no—
143#14519684—22no—
144#14519684—22no—
145#14519684—22no—
146#14519684—22no—
147#14519684—22no—
148#14519684—41no—
149#14519684—41no—
150#14519684—41no—
151#14519684—41no—
152C25×C61C2311yescharacteristic
153C25×C61C2311yescharacteristic
154C22×D4×C61—22no—
155C22×D4×C61—22no—
156C22×D4×C61—22no—
157C22×D4×C61—22no—
158C22×D4×C61—41no—
159C22×D4×C61—41no—
160C22×D4×C61C2×C414yescomplemented
161C23×C4×C61—22no—
162C23×C4×C61—22no—
163C23×C4×C61—22no—
164C23×C4×C61—22no—
165C23×C4×C61—22no—
166C23×C4×C61—41no—
167C23×C4×C61—41no—
168C23×C4×C61C2311yescharacteristic
169C23×C4×C61C2311yescharacteristic
170C23×C4×C61C2311yescharacteristic
171C23×C4×C61C2311yescharacteristic
172C23×C4×C61C2311yescharacteristic
173C2×C22⋊C4×C61—22no—
174C2×C22⋊C4×C61—22no—
175C2×C22⋊C4×C61—22no—
176C2×C22⋊C4×C61—22no—
177C2×C22⋊C4×C61—22no—
178C2×C22⋊C4×C61—22no—
179C2×C22⋊C4×C61—41no—
180C2×C22⋊C4×C61—41no—
181C2×C22⋊C4×C61D414yescomplemented
182#95×C61—22no—
183#95×C61—22no—
184C24×C61—21no—
185C24×C61—21no—
186C24×C61—21no—
187C24×C61—21no—
188C24×C61—21no—
189C24×C61—21no—
190C24×C61—21no—
191C24×C61—21no—
192C24×C61—21no—
193C24×C61—21no—
194C24×C61—21no—
195C24×C61—21no—
196C24×C61—21no—
197C24×C61—21no—
198C24×C61—21no—
199C24×C61—21no—
200C24×C61—21no—
201C24×C61—21no—
202C24×C61—21no—
203C24×C61—21no—
204C24×C61—21no—
205C24×C61—21no—
206C24×C61—21no—
207C24×C61—21no—
208C24×C61C22×C412yes—
209C24×C61C22×C412yes—
210C24×C61C2×D412yes—
211C24×C61C2×D412yes—
212C24×C61C2×D412yes—
213C24×C61#4112yes—
214C24×C61C2411yescharacteristic
215C23×D61—21no—
216C23×D61—21no—
217C23×D61—21no—
218C23×D61—21no—
219C23×D61—21no—
220C23×D61—21no—
221C23×D61—21no—
222C23×D61—21no—
223C23×D61—21no—
224C23×D61—21no—
225C23×D61—21no—
226C23×D61—21no—
227C23×D61C22×C412yes—
228C23×D61C2×D412yes—
229C23×D61C2×D412yes—
230C2×D4×C61—28no—
231C2×D4×C61—28no—
232C2×D4×C61—44no—
233C2×D4×C61—44no—
234C2×D4×C61—44no—
235C2×D4×C61—44no—
236C2×D4×C61—44no—
237C22×C4×C61—21no—
238C22×C4×C61—21no—
239C22×C4×C61—21no—
240C22×C4×C61—21no—
241C22×C4×C61—28no—
242C22×C4×C61—21no—
243C22×C4×C61—21no—
244C22×C4×C61—21no—
245C22×C4×C61—21no—
246C22×C4×C61—21no—
247C22×C4×C61—21no—
248C22×C4×C61—21no—
249C22×C4×C61—21no—
250C22×C4×C61—21no—
251C22×C4×C61—21no—
252C22×C4×C61—21no—
253C22×C4×C61—21no—
254C22×C4×C61—21no—
255C22×C4×C61—21no—
256C22×C4×C61—21no—
257C22×C4×C61—21no—
258C22×C4×C61—21no—
259C22×C4×C61—21no—
260C22×C4×C61—21no—
261C22×C4×C61—21no—
262C22×C4×C61—21no—
263C22×C4×C61—21no—
264C22×C4×C61—21no—
265C22×C4×C61—21no—
266C22×C4×C61—21no—
267C22×C4×C61—44no—
268C22×C4×C61—44no—
269C22×C4×C61—44no—
270C22×C4×C61—44no—
271C22×C4×C61—44no—
272C22×C4×C61—44no—
273C22×C4×C61C22×C412yes—
274C22×C4×C61C2×D412yes—
275C22×C4×C61C2×D412yes—
276C22×C4×C61C2×D412yes—
277C22×C4×C61C2×D412yes—
278C22×C4×C61#4112yes—
279C2×C22⋊D61—28no—
280C2×C22⋊D61—28no—
281C2×C22⋊D61—28no—
282C2×C22⋊D61—28no—
283C2×C22⋊D61—28no—
284C2×C22⋊D61—28no—
285C2×C22⋊D61—28no—
286C2×C22⋊D61—28no—
287C2×C22⋊D61—44no—
288C2×C22⋊D61—44no—
289C2×C22⋊D61—44no—
290C2×C22⋊D61—44no—
291C2×C22⋊D61—44no—
292C2×C22⋊D61C22⋊C4116yescomplemented
293C22×Dic61—21no—
294C22×Dic61—21no—
295C22×Dic61—21no—
296C22×Dic61—21no—
297C22×Dic61—21no—
298C22×Dic61—21no—
299C22×Dic61—21no—
300C22×Dic61—21no—
301C22×Dic61—21no—
302C22×Dic61—21no—
303C22×Dic61—21no—
304C22×Dic61—21no—
305C22×Dic61—21no—
306C22×Dic61—21no—
307C22×Dic61—21no—
308C22×Dic61—21no—
309C22×Dic61—21no—
310C22×Dic61—21no—
311C22×Dic61—21no—
312C22×Dic61—21no—
313C22×Dic61—21no—
314C22×Dic61—21no—
315C22×Dic61—21no—
316C22×Dic61—21no—
317C22×Dic61—21no—
318C22×Dic61—21no—
319C22×Dic61—21no—
320C22×Dic61—21no—
321C22×Dic61—21no—
322C22×Dic61—21no—
323C22×Dic61—28no—
324C22×Dic61—28no—
325C22×Dic61—28no—
326C22×Dic61—21no—
327C22×Dic61—21no—
328C22×Dic61—21no—
329C22×Dic61—21no—
330C22×Dic61—21no—
331C22×Dic61—21no—
332C22×Dic61—21no—
333C22×Dic61—44no—
334C22×Dic61—44no—
335C22×Dic61—44no—
336C22×Dic61—44no—
337C22×Dic61C22×C412yes—
338C22×Dic61C22×C412yes—
339C22×Dic61C22×C412yes—
340C22×Dic61C2×D412yes—
341C22×Dic61C2×D412yes—
342C22×Dic61C2×D412yes—
343C22×Dic61C2×D412yes—
344C22×Dic61C2×D412yes—
345C22×Dic61C2×D412yes—
346C22×Dic61#4112yes—
347C22×Dic61#4112yes—
348C22×Dic61#4112yes—
349C2×C4×D61—28no—
350C2×C4×D61—44no—
351C2×C4×D61—44no—
352C2×C4×D61—44no—
353C2×C4×D61—44no—
354C2×C4×D61—44no—
355C2×C4×D61—44no—
356C22⋊C4×C61—28no—
357C22⋊C4×C61—44no—
358C22⋊C4×C61—44no—
359C22⋊Dic61—28no—
360C22⋊Dic61—28no—
361C22⋊Dic61—28no—
362C22⋊Dic61—44no—
363C22⋊Dic61—44no—
364#11758198—28no—
365#11758198—28no—
366#11758198—44no—
367#11758198—44no—
368#11758196—28no—
369#11758196—28no—
370#11758196—44no—
371C4×Dic61—28no—
372C4×Dic61—44no—
373C23×C61—22no—
374C23×C61—22no—
375C23×C61—22no—
376C23×C61—22no—
377C23×C61—22no—
378C23×C61—22no—
379C23×C61—22no—
380C23×C61—22no—
381C23×C61—22no—
382C23×C61—22no—
383C23×C61—22no—
384C23×C61—22no—
385C23×C61—22no—
386C23×C61—22no—
387C23×C61—22no—
388C23×C61—22no—
389C23×C61—22no—
390C23×C61—22no—
391C23×C61—22no—
392C23×C61—22no—
393C23×C61—22no—
394C23×C61—22no—
395C23×C61—22no—
396C23×C61—22no—
397C23×C61—22no—
398C23×C61—22no—
399C23×C61—22no—
400C23×C61—22no—
401C23×C61—22no—
402C23×C61—22no—
403C23×C61—22no—
404C23×C61—22no—
405C23×C61—22no—
406C23×C61—22no—
407C23×C61—22no—
408C23×C61—22no—
409C23×C61—41no—
410C23×C61—41no—
411C23×C61—41no—
412C23×C61—41no—
413C23×C61—41no—
414C23×C61—41no—
415C23×C61—41no—
416C23×C61—41no—
417C23×C61—41no—
418C23×C61—41no—
419C23×C61—41no—
420C23×C61—41no—
421C23×C61—41no—
422C23×C61—41no—
423C23×C61—41no—
424C23×C61—41no—
425C23×C61—41no—
426C23×C61—41no—
427C23×C61—41no—
428C23×C61—41no—
429C23×C61—41no—
430C23×C61—41no—
431C23×C61—41no—
432C23×C61—41no—
433C23×C61—41no—
434C23×C61—41no—
435C23×C61—41no—
436C23×C61—41no—
437C23×C61—41no—
438C23×C61—41no—
439C23×C61—41no—
440C23×C61—41no—
441C23×C61C2×C22⋊C414yes—
442C23×C61C4×D414yescomplemented
443C23×C61C23×C411yescharacteristic
444C23×C61C22×D411yescharacteristic
445C23×C61C22×D411yescharacteristic
446C23×C61C22×D411yescharacteristic
447C23×C61C22×D411yescharacteristic
448C23×C61C22×D411yescharacteristic
449C23×C61C2×#4111yescharacteristic
450C23×C61C2×#4111yescharacteristic
451C23×C61C2×#4111yescharacteristic
452C23×C61C2×#4111yescharacteristic
453C23×C61C2×#4111yescharacteristic
454C23×C61H(5,𝔽2)11yescharacteristic
455C23×C61H(5,𝔽2)11yescharacteristic
456C23×C61H(5,𝔽2)11yescharacteristic
457C23×C612−1+411yescharacteristic
458C22×D61—22no—
459C22×D61—22no—
460C22×D61—22no—
461C22×D61—22no—
462C22×D61—22no—
463C22×D61—22no—
464C22×D61—22no—
465C22×D61—22no—
466C22×D61—22no—
467C22×D61—22no—
468C22×D61—22no—
469C22×D61—22no—
470C22×D61—22no—
471C22×D61—22no—
472C22×D61—22no—
473C22×D61—22no—
474C22×D61—22no—
475C22×D61—22no—
476C22×D61—41no—
477C22×D61—41no—
478C22×D61—41no—
479C22×D61—41no—
480C22×D61—41no—
481C22×D61—41no—
482C22×D61—41no—
483C22×D61—41no—
484C22×D61—41no—
485C22×D61—41no—
486C22×D61—41no—
487C22×D61—41no—
488C22×D61—41no—
489C22×D61—41no—
490C22×D61—41no—
491C22×D61—41no—
492C22×D61C2×C22⋊C414yes—
493D4×C61—416no—
494C2×C4×C61—22no—
495C2×C4×C61—22no—
496C2×C4×C61—22no—
497C2×C4×C61—22no—
498C2×C4×C61—22no—
499C2×C4×C61—22no—
500C2×C4×C61—22no—
501C2×C4×C61—22no—
502C2×C4×C61—22no—
503C2×C4×C61—22no—
504C2×C4×C61—22no—
505C2×C4×C61—22no—
506C2×C4×C61—22no—
507C2×C4×C61—22no—
508C2×C4×C61—22no—
509C2×C4×C61—416no—
510C2×C4×C61—41no—
511C2×C4×C61—41no—
512C2×C4×C61—41no—
513C2×C4×C61—41no—
514C2×C4×C61—41no—
515C2×C4×C61—41no—
516C2×C4×C61—41no—
517C2×C4×C61—41no—
518C2×C4×C61—41no—
519C2×C4×C61—41no—
520C2×C4×C61—41no—
521C2×C4×C61—41no—
522C2×C4×C61—41no—
523C2×C4×C61—41no—
524C2×C4×C61—41no—
525C2×C4×C61—41no—
526C2×C4×C61—41no—
527C2×C4×C61—41no—
528C2×C4×C61—41no—
529C2×C4×C61#12114yescomplemented
530C22⋊D61—232no—
531C22⋊D61—416no—
532C2×Dic61—22no—
533C2×Dic61—22no—
534C2×Dic61—22no—
535C2×Dic61—22no—
536C2×Dic61—22no—
537C2×Dic61—22no—
538C2×Dic61—22no—
539C2×Dic61—22no—
540C2×Dic61—22no—
541C2×Dic61—22no—
542C2×Dic61—22no—
543C2×Dic61—22no—
544C2×Dic61—22no—
545C2×Dic61—22no—
546C2×Dic61—22no—
547C2×Dic61—41no—
548C2×Dic61—41no—
549C2×Dic61—41no—
550C2×Dic61—41no—
551C2×Dic61—41no—
552C2×Dic61—41no—
553C2×Dic61—41no—
554C2×Dic61—41no—
555C2×Dic61—41no—
556C2×Dic61—41no—
557C2×Dic61—41no—
558C2×Dic61—41no—
559C2×Dic61—41no—
560C2×Dic61—41no—
561C2×Dic61—41no—
562C2×Dic61—41no—
563C2×Dic61—41no—
564C2×Dic61—41no—
565C2×Dic61—41no—
566C2×Dic61—41no—
567C2×Dic61—416no—
568C2×Dic61—41no—
569C2×Dic61—41no—
570C2×Dic61—41no—
571C2×Dic61—41no—
572C2×Dic61—41no—
573C2×Dic61—41no—
574C2×Dic61—41no—
575C2×Dic61C2×C22⋊C414yes—
576C2×Dic61C4×D414yes—
577C2×Dic61C4×D414yes—
578C2×Dic61#12014yes—
579C2×Dic61#12114yes—
580C2×Dic61#12114yes—
581C2×Dic61#12314yes—
582C4×D61—416no—
583#13970—611nomaximal, Sylow
584C22×C61—24no—
585C22×C61—24no—
586C22×C61—24no—
587C22×C61—24no—
588C22×C61—24no—
589C22×C61—24no—
590C22×C61—42no—
591C22×C61—42no—
592C22×C61—42no—
593C22×C61—42no—
594C22×C61—42no—
595C22×C61—42no—
596C22×C61—42no—
597C22×C61—42no—
598C22×C61—42no—
599C22×C61—42no—
600C22×C61—42no—
601C22×C61—42no—
602C22×C61—42no—
603C22×C61—42no—
604C22×C61—42no—
605C22×C61—42no—
606C22×C61—42no—
607C22×C61—42no—
608C22×C61—42no—
609C22×C61—42no—
610C22×C61—42no—
611C22×C61—42no—
612C22×C61—42no—
613C22×C61—42no—
614C22×C61C22×C22⋊C411yescharacteristic
615C22×C61C2×C4×D411yescharacteristic
616C22×C61C2×C4×D411yescharacteristic
617C22×C61C2×C4×D411yescharacteristic
618C22×C61C4×#4111yescharacteristic
619C22×C61#51811yescharacteristic
620C22×C61#52011yescharacteristic
621C22×C61C2×#12011yescharacteristic
622C22×C61C2×#12111yescharacteristic
623C22×C61C2×#12111yescharacteristic
624C22×C61C2×#12111yescharacteristic
625C22×C61C2×#12311yescharacteristic
626C22×C61#52511yescharacteristic
627C22×C61#52911yescharacteristic
628C22×C61#53211yescharacteristic
629C22×C61#53511yescharacteristic
630C22×C61#53711yescharacteristic
631C22×C61#54011yescharacteristic
632C22×C61#54211yescharacteristic
633C22×C61D4211yescharacteristic
634C22×C61D4211yescharacteristic
635C22×C61D4211yescharacteristic
636C22×C61#54611yescharacteristic
637C22×C61#54611yescharacteristic
638C22×C61#54611yescharacteristic
639C22×C61#54611yescharacteristic
640C22×C61#54611yescharacteristic
641C22×C61#54711yescharacteristic
642C22×C61#54711yescharacteristic
643C22×C61#54711yescharacteristic
644C22×C61#54811yescharacteristic
645C22×C61#55011yescharacteristic
646C22×C61#55311yescharacteristic
647C22×C61#55311yescharacteristic
648C22×C61#55511yescharacteristic
649C2×D61—24no—
650C2×D61—24no—
651C2×D61—24no—
652C2×D61—42no—
653C2×D61—42no—
654C2×D61—42no—
655C2×D61—42no—
656C2×D61—42no—
657C2×D61—42no—
658C2×D61—42no—
659C2×D61—42no—
660C2×D61—42no—
661C2×D61—42no—
662C2×D61—42no—
663C2×D61—42no—
664C4×C61—24no—
665C4×C61—42no—
666C4×C61—42no—
667C4×C61—42no—
668C4×C61—81no—
669Dic61—42no—
670Dic61—42no—
671Dic61—42no—
672Dic61—42no—
673Dic61—42no—
674Dic61—81no—
675Dic61#38618yescomplemented
676C22×#121—611no—
677C22×C4×D4—611no—
678C2×#390—611no—
679C2×#386—611no—
680C2×#386D6111yescharacteristic, complemented
681C2×#380—611no—
682C2×C4×C22⋊C4—611no—
683#1440—611no—
684#1440—611no—
685#1438—611no—
686#1438—611no—
687C4⋊#95—611no—
688C4⋊#95—611no—
689C22⋊#95—611no—
690C22⋊#95—611no—
691C2×C61—44no—
692C2×C61—44no—
693C2×C61C2×#38611yescharacteristic
694C2×C61C4×#12111yescharacteristic
695C2×C61#232411yescharacteristic
696C2×C61D4×C22⋊C411yescharacteristic
697C2×C61#233911yescharacteristic
698C2×C61#236111yescharacteristic
699C2×C61#236311yescharacteristic
700C2×C61#240711yescharacteristic
701C2×C61#240811yescharacteristic
702C2×C61#242011yescharacteristic
703C2×C61#242211yescharacteristic
704C2×C61#242711yescharacteristic
705C2×C61#242811yescharacteristic
706C2×C61#253511yescharacteristic
707C2×C61#253711yescharacteristic
708D61—44no—
709C23×D4—611no—
710C23×D4—611no—
711C23×D4C2×D6111yescharacteristic
712C24×C4—611no—
713C24×C4—611no—
714C24×C4C2×D6111yescharacteristic
715C2×#121—618no—
716C2×#121—1224no—
717C2×#121—1224no—
718C2×C4×D4—1224no—
719C2×C4×D4—1224no—
720C2×C4×D4—1224no—
721C22×C4⋊C4—611no—
722C22×C4⋊C4—611no—
723C22×C4⋊C4—611no—
724C22×C22⋊C4—611no—
725C22×C22⋊C4—611no—
726C22×C22⋊C4—611no—
727C22×C22⋊C4—611no—
728C22×C22⋊C4—611no—
729C22×C22⋊C4—611no—
730C22×C22⋊C4—611no—
731C22×C22⋊C4—611no—
732C22×C22⋊C4—611no—
733C22×C22⋊C4C2×D6111yescharacteristic
734C22×C22⋊C4C2×D6111yescharacteristic
735C22×C22⋊C4C2×D6111yescharacteristic
736C22×C42—611no—
737C22×C42—611no—
738#390—1224no—
739#386—24no—
740#386—1224no—
741#380—1224no—
742C4×C22⋊C4—1224no—
743C2×#95—611no—
744C2×#95—611no—
745C2×#95—611no—
746C2×#95—611no—
747C2×#95—611no—
748C2×#95—611no—
749C2×#95—611no—
750C2×#95—611no—
751C2×#95—611no—
752C2×#95—611no—
753C2×#95C2×D6111yescharacteristic
754C2×#95C2×D6111yescharacteristic
755C61#1397011yescharacteristic, complemented, Sylow
756C25—611no—
757C25C22×D6111yescharacteristic
758C25C22×D6111yescharacteristic
759C22×D4—22no—
760C22×D4—22no—
761C22×D4—22no—
762C22×D4—22no—
763C22×D4—41no—
764C22×D4—41no—
765C22×D4—614no—
766C22×D4—614no—
767C22×D4—614no—
768C22×D4—614no—
769C22×D4—1222no—
770C22×D4—1222no—
771C22×D4—1222no—
772C22×D4—1222no—
773C22×D4—1222no—
774C22×D4—1222no—
775C22×D4—1222no—
776C22×D4—1222no—
777C22×D4—2441no—
778C22×D4—2441no—
779C22×D4C4×D6114yescomplemented
780C23×C4—22no—
781C23×C4—22no—
782C23×C4—22no—
783C23×C4—22no—
784C23×C4—22no—
785C23×C4—41no—
786C23×C4—41no—
787C23×C4—611no—
788C23×C4—614no—
789C23×C4—611no—
790C23×C4—611no—
791C23×C4—611no—
792C23×C4—611no—
793C23×C4—611no—
794C23×C4—611no—
795C23×C4—1222no—
796C23×C4—1222no—
797C23×C4—1222no—
798C23×C4—1222no—
799C23×C4—1222no—
800C23×C4—1222no—
801C23×C4—1222no—
802C23×C4—1222no—
803C23×C4—1222no—
804C23×C4—1222no—
805C23×C4—1222no—
806C23×C4—2441no—
807C23×C4—2441no—
808C23×C4C22×D6111yescharacteristic
809C23×C4C22×D6111yescharacteristic
810C23×C4C22×D6111yescharacteristic
811C23×C4C22×D6111yescharacteristic
812C23×C4C22×D6111yescharacteristic
813#121—12232no—
814C4×D4—12232no—
815C2×C4⋊C4—614no—
816C2×C4⋊C4—614no—
817C2×C4⋊C4—1222no—
818C2×C4⋊C4—1222no—
819C2×C4⋊C4—1222no—
820C2×C4⋊C4—1222no—
821C2×C4⋊C4—1222no—
822C2×C4⋊C4—1222no—
823C2×C4⋊C4—1222no—
824C2×C22⋊C4—22no—
825C2×C22⋊C4—22no—
826C2×C22⋊C4—22no—
827C2×C22⋊C4—22no—
828C2×C22⋊C4—22no—
829C2×C22⋊C4—22no—
830C2×C22⋊C4—41no—
831C2×C22⋊C4—41no—
832C2×C22⋊C4—614no—
833C2×C22⋊C4—614no—
834C2×C22⋊C4—1222no—
835C2×C22⋊C4—1222no—
836C2×C22⋊C4—1222no—
837C2×C22⋊C4—1222no—
838C2×C22⋊C4—1222no—
839C2×C22⋊C4—1222no—
840C2×C22⋊C4—1222no—
841C2×C22⋊C4—1222no—
842C2×C22⋊C4—1222no—
843C2×C22⋊C4—1222no—
844C2×C22⋊C4—1222no—
845C2×C22⋊C4—1222no—
846C2×C22⋊C4—1222no—
847C2×C22⋊C4—1222no—
848C2×C22⋊C4—1222no—
849C2×C22⋊C4—1222no—
850C2×C22⋊C4—1222no—
851C2×C22⋊C4—1222no—
852C2×C22⋊C4—1222no—
853C2×C22⋊C4—1222no—
854C2×C22⋊C4—1222no—
855C2×C22⋊C4—2441no—
856C2×C22⋊C4—2441no—
857C2×C22⋊C4—2441no—
858C2×C22⋊C4—2441no—
859C2×C22⋊C4C22⋊D6114yescomplemented
860C2×C42—614no—
861C2×C42—1222no—
862C2×C42—1222no—
863C2×C42—1222no—
864C2×C42—1222no—
865C2×C42—1222no—
866#95—22no—
867#95—22no—
868#95—1222no—
869#95—1222no—
870#95—1222no—
871#95—1222no—
872#95—1222no—
873#95—1222no—
874#95—2441no—
875#95—2441no—
876#95—2441no—
877#95—2441no—
878C24—21no—
879C24—21no—
880C24—21no—
881C24—21no—
882C24—21no—
883C24—21no—
884C24—21no—
885C24—21no—
886C24—21no—
887C24—21no—
888C24—21no—
889C24—21no—
890C24—21no—
891C24—21no—
892C24—21no—
893C24—21no—
894C24—21no—
895C24—21no—
896C24—21no—
897C24—21no—
898C24—21no—
899C24—21no—
900C24—21no—
901C24—21no—
902C24—612no—
903C24—612no—
904C24—612no—
905C24—1221no—
906C24—1221no—
907C24—1221no—
908C24—1221no—
909C24—1221no—
910C24—1221no—
911C24—1221no—
912C24—1221no—
913C24—1221no—
914C24—1221no—
915C24—1221no—
916C24—1221no—
917C24C2×C4×D6112yes—
918C24C2×C4×D6112yes—
919C24#1175822212yes—
920C24D4×D6112yes—
921C24D4×D6112yes—
922C24C2×C22⋊D6112yes—
923C24C23×D6111yescharacteristic
924C2×D4—28no—
925C2×D4—28no—
926C2×D4—44no—
927C2×D4—44no—
928C2×D4—44no—
929C2×D4—44no—
930C2×D4—44no—
931C2×D4—6116no—
932C2×D4—1228no—
933C2×D4—1228no—
934C2×D4—1228no—
935C2×D4—1228no—
936C2×D4—1228no—
937C2×D4—1228no—
938C2×D4—1228no—
939C2×D4—1228no—
940C2×D4—2444no—
941C2×D4—2444no—
942C2×D4—2444no—
943C2×D4—2444no—
944C2×D4—2444no—
945C22×C4—21no—
946C22×C4—21no—
947C22×C4—21no—
948C22×C4—21no—
949C22×C4—28no—
950C22×C4—21no—
951C22×C4—21no—
952C22×C4—21no—
953C22×C4—21no—
954C22×C4—21no—
955C22×C4—21no—
956C22×C4—21no—
957C22×C4—21no—
958C22×C4—21no—
959C22×C4—21no—
960C22×C4—21no—
961C22×C4—21no—
962C22×C4—21no—
963C22×C4—21no—
964C22×C4—21no—
965C22×C4—21no—
966C22×C4—21no—
967C22×C4—21no—
968C22×C4—21no—
969C22×C4—21no—
970C22×C4—21no—
971C22×C4—21no—
972C22×C4—21no—
973C22×C4—21no—
974C22×C4—21no—
975C22×C4—44no—
976C22×C4—44no—
977C22×C4—44no—
978C22×C4—44no—
979C22×C4—44no—
980C22×C4—44no—
981C22×C4—612no—
982C22×C4—612no—
983C22×C4—612no—
984C22×C4—612no—
985C22×C4—612no—
986C22×C4—612no—
987C22×C4—612no—
988C22×C4—612no—
989C22×C4—612no—
990C22×C4—612no—
991C22×C4—612no—
992C22×C4—612no—
993C22×C4—1228no—
994C22×C4—1228no—
995C22×C4—1228no—
996C22×C4—1228no—
997C22×C4—1221no—
998C22×C4—1221no—
999C22×C4—1221no—
1000C22×C4—1221no—
1001C22×C4—1221no—
1002C22×C4—1221no—
1003C22×C4—1221no—
1004C22×C4—1221no—
1005C22×C4—1221no—
1006C22×C4—1221no—
1007C22×C4—1221no—
1008C22×C4—1221no—
1009C22×C4—1221no—
1010C22×C4—1221no—
1011C22×C4—1221no—
1012C22×C4—1221no—
1013C22×C4—1221no—
1014C22×C4—1221no—
1015C22×C4—1221no—
1016C22×C4—1221no—
1017C22×C4—1221no—
1018C22×C4—1221no—
1019C22×C4—1221no—
1020C22×C4—1221no—
1021C22×C4—1221no—
1022C22×C4—1221no—
1023C22×C4—1221no—
1024C22×C4—1221no—
1025C22×C4—1221no—
1026C22×C4—1221no—
1027C22×C4—1221no—
1028C22×C4—1221no—
1029C22×C4—1221no—
1030C22×C4—1221no—
1031C22×C4—1221no—
1032C22×C4—1221no—
1033C22×C4—1221no—
1034C22×C4—2444no—
1035C22×C4—2444no—
1036C22×C4—2444no—
1037C22×C4—2444no—
1038C22×C4—2444no—
1039C22×C4—2444no—
1040C22×C4—2444no—
1041C22×C4—2444no—
1042C22×C4—2444no—
1043C22×C4—2444no—
1044C22×C4C2×C4×D6112yes—
1045C22×C4D4×D6112yes—
1046C22×C4D4×D6112yes—
1047C22×C4#1175822412yes—
1048C22×C4C2×C22⋊D6112yes—
1049C22×C4C2×C22⋊D6112yes—
1050C4⋊C4—1228no—
1051C4⋊C4—1228no—
1052C4⋊C4—2444no—
1053C22⋊C4—28no—
1054C22⋊C4—44no—
1055C22⋊C4—44no—
1056C22⋊C4—1228no—
1057C22⋊C4—1228no—
1058C22⋊C4—1228no—
1059C22⋊C4—1228no—
1060C22⋊C4—1228no—
1061C22⋊C4—2444no—
1062C22⋊C4—2444no—
1063C22⋊C4—2444no—
1064C22⋊C4—2444no—
1065C42—1228no—
1066C42—2444no—
1067C23—22no—
1068C23—22no—
1069C23—22no—
1070C23—22no—
1071C23—22no—
1072C23—22no—
1073C23—22no—
1074C23—22no—
1075C23—22no—
1076C23—22no—
1077C23—22no—
1078C23—22no—
1079C23—22no—
1080C23—22no—
1081C23—22no—
1082C23—22no—
1083C23—22no—
1084C23—22no—
1085C23—22no—
1086C23—22no—
1087C23—22no—
1088C23—22no—
1089C23—22no—
1090C23—22no—
1091C23—22no—
1092C23—22no—
1093C23—22no—
1094C23—22no—
1095C23—22no—
1096C23—22no—
1097C23—22no—
1098C23—22no—
1099C23—22no—
1100C23—22no—
1101C23—22no—
1102C23—22no—
1103C23—41no—
1104C23—41no—
1105C23—41no—
1106C23—41no—
1107C23—41no—
1108C23—41no—
1109C23—41no—
1110C23—41no—
1111C23—41no—
1112C23—41no—
1113C23—41no—
1114C23—41no—
1115C23—41no—
1116C23—41no—
1117C23—41no—
1118C23—41no—
1119C23—41no—
1120C23—41no—
1121C23—41no—
1122C23—41no—
1123C23—41no—
1124C23—41no—
1125C23—41no—
1126C23—41no—
1127C23—41no—
1128C23—41no—
1129C23—41no—
1130C23—41no—
1131C23—41no—
1132C23—41no—
1133C23—41no—
1134C23—41no—
1135C23—614no—
1136C23—1222no—
1137C23—1222no—
1138C23—1222no—
1139C23—1222no—
1140C23—1222no—
1141C23—1222no—
1142C23—1222no—
1143C23—1222no—
1144C23—1222no—
1145C23—1222no—
1146C23—1222no—
1147C23—1222no—
1148C23—1222no—
1149C23—1222no—
1150C23—1222no—
1151C23—1222no—
1152C23—1222no—
1153C23—1222no—
1154C23—2441no—
1155C23—2441no—
1156C23—2441no—
1157C23—2441no—
1158C23—2441no—
1159C23—2441no—
1160C23—2441no—
1161C23—2441no—
1162C23—2441no—
1163C23—2441no—
1164C23—2441no—
1165C23—2441no—
1166C23—2441no—
1167C23—2441no—
1168C23—2441no—
1169C23—2441no—
1170C23C22⋊C4×D6114yes—
1171C23C4×C22⋊D6114yescomplemented
1172C23C22×C4×D6111yescharacteristic
1173C23C2×D4×D6111yescharacteristic
1174C23C2×D4×D6111yescharacteristic
1175C23C2×D4×D6111yescharacteristic
1176C23C2×D4×D6111yescharacteristic
1177C23C22×C22⋊D6111yescharacteristic
1178C23#41×D6111yescharacteristic
1179C23#41×D6111yescharacteristic
1180C23#41×D6111yescharacteristic
1181C23C2×#1175822411yescharacteristic
1182C23C2×#1175822211yescharacteristic
1183C23#1451982211yescharacteristic
1184C23#1451982211yescharacteristic
1185C23#1451982211yescharacteristic
1186C23#1451982411yescharacteristic
1187D4—416no—
1188D4—12232no—
1189D4—24416no—
1190C2×C4—22no—
1191C2×C4—22no—
1192C2×C4—22no—
1193C2×C4—22no—
1194C2×C4—22no—
1195C2×C4—22no—
1196C2×C4—22no—
1197C2×C4—22no—
1198C2×C4—22no—
1199C2×C4—22no—
1200C2×C4—22no—
1201C2×C4—22no—
1202C2×C4—22no—
1203C2×C4—22no—
1204C2×C4—22no—
1205C2×C4—416no—
1206C2×C4—41no—
1207C2×C4—41no—
1208C2×C4—41no—
1209C2×C4—41no—
1210C2×C4—41no—
1211C2×C4—41no—
1212C2×C4—41no—
1213C2×C4—41no—
1214C2×C4—41no—
1215C2×C4—41no—
1216C2×C4—41no—
1217C2×C4—41no—
1218C2×C4—41no—
1219C2×C4—41no—
1220C2×C4—41no—
1221C2×C4—41no—
1222C2×C4—41no—
1223C2×C4—41no—
1224C2×C4—41no—
1225C2×C4—614no—
1226C2×C4—614no—
1227C2×C4—614no—
1228C2×C4—614no—
1229C2×C4—614no—
1230C2×C4—614no—
1231C2×C4—614no—
1232C2×C4—1222no—
1233C2×C4—1222no—
1234C2×C4—1222no—
1235C2×C4—1222no—
1236C2×C4—1222no—
1237C2×C4—1222no—
1238C2×C4—1222no—
1239C2×C4—1222no—
1240C2×C4—1222no—
1241C2×C4—1222no—
1242C2×C4—1222no—
1243C2×C4—1222no—
1244C2×C4—1222no—
1245C2×C4—1222no—
1246C2×C4—1222no—
1247C2×C4—24416no—
1248C2×C4—24416no—
1249C2×C4—2441no—
1250C2×C4—2441no—
1251C2×C4—2441no—
1252C2×C4—2441no—
1253C2×C4—2441no—
1254C2×C4—2441no—
1255C2×C4—2441no—
1256C2×C4—2441no—
1257C2×C4—2441no—
1258C2×C4—2441no—
1259C2×C4—2441no—
1260C2×C4—2441no—
1261C2×C4—2441no—
1262C2×C4—2441no—
1263C2×C4—2441no—
1264C2×C4—2441no—
1265C2×C4—2441no—
1266C2×C4—2441no—
1267C2×C4—2441no—
1268C2×C4—2441no—
1269C2×C4—2441no—
1270C2×C4—2441no—
1271C2×C4—2441no—
1272C2×C4—2441no—
1273C2×C4—2441no—
1274C2×C4—2441no—
1275C2×C4—2441no—
1276C2×C4#1451974914yescomplemented
1277C22—24no—
1278C22—24no—
1279C22—24no—
1280C22—24no—
1281C22—24no—
1282C22—24no—
1283C22—42no—
1284C22—42no—
1285C22—42no—
1286C22—42no—
1287C22—42no—
1288C22—42no—
1289C22—42no—
1290C22—42no—
1291C22—42no—
1292C22—42no—
1293C22—42no—
1294C22—42no—
1295C22—42no—
1296C22—42no—
1297C22—42no—
1298C22—42no—
1299C22—42no—
1300C22—42no—
1301C22—42no—
1302C22—42no—
1303C22—42no—
1304C22—42no—
1305C22—42no—
1306C22—42no—
1307C22—1224no—
1308C22—1224no—
1309C22—1224no—
1310C22—2442no—
1311C22—2442no—
1312C22—2442no—
1313C22—2442no—
1314C22—2442no—
1315C22—2442no—
1316C22—2442no—
1317C22—2442no—
1318C22—2442no—
1319C22—2442no—
1320C22—2442no—
1321C22—2442no—
1322C22C2×C22⋊C4×D6111yescharacteristic
1323C22C4×D4×D6111yescharacteristic
1324C22C4×D4×D6111yescharacteristic
1325C22C2×C4×C22⋊D6111yescharacteristic
1326C22C4×#1175822411yescharacteristic
1327C22#1684023511yescharacteristic
1328C22#1684024111yescharacteristic
1329C22#120×D6111yescharacteristic
1330C22#121×D6111yescharacteristic
1331C22#121×D6111yescharacteristic
1332C22C2×#1451974911yescharacteristic
1333C22#123×D6111yescharacteristic
1334C22#1684027111yescharacteristic
1335C22#1684029211yescharacteristic
1336C22#1684030811yescharacteristic
1337C22#1684032711yescharacteristic
1338C22#1684034111yescharacteristic
1339C22#1684036211yescharacteristic
1340C22#1684038011yescharacteristic
1341C22D4×C22⋊D6111yescharacteristic
1342C22D4×C22⋊D6111yescharacteristic
1343C22D4×C22⋊D6111yescharacteristic
1344C22#1684039911yescharacteristic
1345C22#1684039911yescharacteristic
1346C22#1684040111yescharacteristic
1347C22#1684040211yescharacteristic
1348C22#1684040211yescharacteristic
1349C22#1684041011yescharacteristic
1350C22#1684041111yescharacteristic
1351C22#1684041211yescharacteristic
1352C22#1684042111yescharacteristic
1353C22#1684043011yescharacteristic
1354C22#1684045711yescharacteristic
1355C22#1684046111yescharacteristic
1356C22#1684047611yescharacteristic
1357C4—24no—
1358C4—42no—
1359C4—42no—
1360C4—42no—
1361C4—81no—
1362C4—618no—
1363C4—4881no—
1364C4—2442no—
1365C4—2442no—
1366C4—2442no—
1367C4—2442no—
1368C4—2442no—
1369C2—44no—
1370C2—44no—
1371C2—2444no—
1372C2#386×D6111yescharacteristic
1373C2C4×#1451974911yescharacteristic
1374C2#2144850911yescharacteristic
1375C2C22⋊C4×C22⋊D6111yescharacteristic
1376C2#2144864511yescharacteristic
1377C2#2144883611yescharacteristic
1378C2#2144886011yescharacteristic
1379C2#2144916111yescharacteristic
1380C2#2144917211yescharacteristic
1381C2#2144930811yescharacteristic
1382C2#2144933011yescharacteristic
1383C2#2144939311yescharacteristic
1384C2#2144940411yescharacteristic
1385C2#2145071911yescharacteristic
1386C2#2145073311yescharacteristic
subgroupG/H
center, FrattiniC24C23×D61
commutatorC23×C61C23×C4
FittingC2×C61×#386C2
socle, cosocleC24×C61C24
prime radicalC22×#14519749C2
hypercenterC2×#386D61
hypocenterC61#13970
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C24 ◁ C2×#386

Complements

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

NH ≅ G/Ntype
2. C22×C4×C22⋊D61C2semidirect
3. C2×#16839662C2semidirect
4. C2×#16839638C2semidirect
5. C2×#16839620C2semidirect
6. C2×C22⋊C4×Dic61C2semidirect
7. #21444067C2semidirect
8. #21444066C2semidirect
9. #21444060C2semidirect
10. #21444058C2semidirect
11. #21444047C2semidirect
12. #21444047C2semidirect
13. #21444042C2semidirect
14. #21444040C2semidirect
15. C2×C61×#386C2semidirect
22. C2×#14519749C4semidirect
74. C22×C22⋊D61C2×C4semidirect
83. C23×Dic61C2×C4semidirect
107. C2×#11758196C2×C4semidirect
108. C2×#11758196D4semidirect
123. C2×C22⋊Dic61C2×C4semidirect
135. C2×#11758198C2×C4semidirect
141. C2×C4×Dic61D4semidirect
160. C22×D4×C61C2×C4semidirect
181. C2×C22⋊C4×C61D4semidirect
292. C2×C22⋊D61C22⋊C4semidirect
442. C23×C61C4×D4semidirect
529. C2×C4×C61#121semidirect
675. Dic61#386semidirect
680. C2×#386D61semidirect
755. C61#13970semidirect
779. C22×D4C4×D61semidirect
859. C2×C22⋊C4C22⋊D61semidirect
1171. C23C4×C22⋊D61semidirect
1276. C2×C4#14519749semidirect

Maximal subgroups

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

subgroupindex
C22×#145197492
C22×C4×C22⋊D612
C2×#168396622
C2×#168396382
C2×#168396202
C2×C22⋊C4×Dic612
#214440672
#214440662
#214440602
#214440582
#214440472
#214440422
#214440402
C2×C61×#3862
#1397061