Finite Group Databasebeta

← #29601928

Subgroups — #29601928

Order 15616.

3526 conjugacy classes of subgroups.

The subgroup lattice has 1418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C22⋊C4×D61C211yesmaximal, characteristic
2C2×#16839655C211yesmaximal, characteristic, complemented
3C2×#16839619C211yesmaximal, characteristic, complemented
4C2×#16839617C211yesmaximal, characteristic
5C2×#16839617C211yesmaximal, characteristic
6C2×C4×#11758198C211yesmaximal, characteristic, complemented
7#21444066C211yesmaximal, characteristic, complemented
8#21444066C211yesmaximal, characteristic, complemented
9#21444065C211yesmaximal, characteristic, complemented
10#21444061C211yesmaximal, characteristic, complemented
11#21444057C211yesmaximal, characteristic, complemented
12#21444055C211yesmaximal, characteristic, complemented
13#21444040C211yesmaximal, characteristic, complemented
14#21444040C211yesmaximal, characteristic, complemented
15C2×C61×#388C211yesmaximal, characteristic, complemented
16C25×D61C2211yescharacteristic
17C23×C4×D61C2211yescharacteristic
18C23×C4×D61C2211yescharacteristic
19C22×C4⋊Dic61C2211yescharacteristic, complemented
20C22×C22⋊Dic61C2211yescharacteristic
21C22×C22⋊Dic61C2211yescharacteristic
22C22×C22⋊Dic61C2211yescharacteristic
23C22×#11758198C2211yescharacteristic
24C22×#11758198C2211yescharacteristic
25C22×#11758198C2211yescharacteristic
26C22×#11758198C2211yescharacteristic
27C22×#11758198C2211yescharacteristic
28C22×#11758198C2211yescharacteristic
29C22×#11758198C2211yescharacteristic
30C22×#11758198C2211yescharacteristic
31C22×#11758198C2211yescharacteristic
32C22×#11758198C2211yescharacteristic
33C2×C22⋊C4×D61—24no—
34C2×C22⋊C4×D61—24no—
35C2×C22⋊C4×D61C418yescomplemented
36C22×C4×Dic61C2211yescharacteristic, complemented
37#16839655—24no—
38#16839619—24no—
39#16839617—24no—
40#16839617—24no—
41C4×#11758198—24no—
42C2×#14519684C2211yescharacteristic, complemented
43C2×#14519684C2211yescharacteristic, complemented
44C2×#14519684C2211yescharacteristic, complemented
45C2×#14519684C2211yescharacteristic, complemented
46C2×#14519684C2211yescharacteristic, complemented
47C2×#14519684C2211yescharacteristic, complemented
48C2×#14519684C2211yescharacteristic, complemented
49C2×#14519684C2211yescharacteristic, complemented
50C2×#14519684C2211yescharacteristic, complemented
51C2×#14519684C2211yescharacteristic, complemented
52C22×C4⋊C4×C61C2211yescharacteristic, complemented
53C22×C22⋊C4×C61C2211yescharacteristic
54C22×C22⋊C4×C61C2211yescharacteristic
55C22×C22⋊C4×C61C2211yescharacteristic
56C22×C42×C61C2211yescharacteristic, complemented
57C61×#388—24no—
58C2×#95×C61C2211yescharacteristic, complemented
59C2×#95×C61C2211yescharacteristic, complemented
60C24×D61—22no—
61C24×D61—22no—
62C24×D61—22no—
63C24×D61—22no—
64C24×D61—22no—
65C24×D61—22no—
66C24×D61—22no—
67C24×D61—22no—
68C24×D61—22no—
69C24×D61—22no—
70C24×D61—41no—
71C24×D61—41no—
72C24×D61—41no—
73C24×D61—41no—
74C24×D61C2×C414yes—
75C24×D61C2311yescharacteristic
76C24×D61C2311yescharacteristic
77C23×Dic61C2311yescharacteristic
78C23×Dic61C2311yescharacteristic
79C23×Dic61C2311yescharacteristic
80C23×Dic61C2311yescharacteristic
81C23×Dic61C2311yescharacteristic
82C23×Dic61C2311yescharacteristic
83C22×C4×D61—22no—
84C22×C4×D61—22no—
85C22×C4×D61—22no—
86C22×C4×D61—22no—
87C22×C4×D61—22no—
88C22×C4×D61—22no—
89C22×C4×D61—22no—
90C22×C4×D61—22no—
91C22×C4×D61—41no—
92C22×C4×D61—41no—
93C22×C4×D61—41no—
94C22×C4×D61—41no—
95C22×C4×D61C2×C414yes—
96C22×C4×D61C2×C414yes—
97C2×C4⋊Dic61—22no—
98C2×C4⋊Dic61—22no—
99C2×C4⋊Dic61—41no—
100C2×C22⋊Dic61—22no—
101C2×C22⋊Dic61—22no—
102C2×C22⋊Dic61—22no—
103C2×C22⋊Dic61—22no—
104C2×C22⋊Dic61—22no—
105C2×C22⋊Dic61—22no—
106C2×C22⋊Dic61—41no—
107C2×C22⋊Dic61—41no—
108C2×C22⋊Dic61C2×C414yes—
109C2×#11758198—22no—
110C2×#11758198—22no—
111C2×#11758198—22no—
112C2×#11758198—22no—
113C2×#11758198—22no—
114C2×#11758198—22no—
115C2×#11758198—22no—
116C2×#11758198—22no—
117C2×#11758198—22no—
118C2×#11758198—22no—
119C2×#11758198—22no—
120C2×#11758198—22no—
121C2×#11758198—22no—
122C2×#11758198—22no—
123C2×#11758198—22no—
124C2×#11758198—22no—
125C2×#11758198—22no—
126C2×#11758198—22no—
127C2×#11758198—22no—
128C2×#11758198—22no—
129C2×#11758198—22no—
130C2×#11758198—22no—
131C2×#11758198—41no—
132C2×#11758198—41no—
133C2×#11758198—41no—
134C2×#11758198—41no—
135C2×#11758198C2×C414yes—
136C2×#11758198C2×C414yes—
137C2×#11758198D414yes—
138C2×#11758198D414yes—
139C22⋊C4×D61—232no—
140C2×C4×Dic61—22no—
141C2×C4×Dic61—22no—
142C2×C4×Dic61—41no—
143#14519684—22no—
144#14519684—22no—
145#14519684—22no—
146#14519684—22no—
147#14519684—22no—
148#14519684—22no—
149#14519684—41no—
150#14519684—41no—
151#14519684—41no—
152#14519684—41no—
153C25×C61C2311yescharacteristic
154C23×C4×C61C2311yescharacteristic
155C23×C4×C61C2311yescharacteristic
156C23×C4×C61C2311yescharacteristic
157C23×C4×C61C2311yescharacteristic
158C23×C4×C61C2311yescharacteristic
159C23×C4×C61C2311yescharacteristic
160C2×C4⋊C4×C61—22no—
161C2×C4⋊C4×C61—22no—
162C2×C4⋊C4×C61—41no—
163C2×C22⋊C4×C61—22no—
164C2×C22⋊C4×C61—22no—
165C2×C22⋊C4×C61—22no—
166C2×C22⋊C4×C61—22no—
167C2×C22⋊C4×C61—41no—
168C2×C22⋊C4×C61—41no—
169C2×C22⋊C4×C61C2×C414yes—
170C2×C22⋊C4×C61D414yes—
171C2×C22⋊C4×C61D414yes—
172C2×C42×C61—22no—
173C2×C42×C61—22no—
174C2×C42×C61—41no—
175#95×C61—22no—
176#95×C61—22no—
177C24×C61—21no—
178C24×C61—21no—
179C24×C61—21no—
180C24×C61—21no—
181C24×C61—21no—
182C24×C61—21no—
183C24×C61—21no—
184C24×C61—21no—
185C24×C61—21no—
186C24×C61—21no—
187C24×C61—21no—
188C24×C61—21no—
189C24×C61C22×C412yes—
190C24×C61C2×D412yes—
191C24×C61C2×D412yes—
192C24×C61C2411yescharacteristic
193C23×D61—21no—
194C23×D61—21no—
195C23×D61—21no—
196C23×D61—21no—
197C23×D61—21no—
198C23×D61—21no—
199C23×D61—21no—
200C23×D61—21no—
201C23×D61—28no—
202C23×D61—28no—
203C23×D61—28no—
204C23×D61—28no—
205C23×D61—28no—
206C23×D61—21no—
207C23×D61—21no—
208C23×D61—21no—
209C23×D61—21no—
210C23×D61—21no—
211C23×D61—21no—
212C23×D61—21no—
213C23×D61—21no—
214C23×D61—21no—
215C23×D61—21no—
216C23×D61—21no—
217C23×D61—21no—
218C23×D61—28no—
219C23×D61—28no—
220C23×D61—28no—
221C23×D61—28no—
222C23×D61—44no—
223C23×D61—44no—
224C23×D61—44no—
225C23×D61—44no—
226C23×D61—44no—
227C23×D61—44no—
228C23×D61—44no—
229C23×D61—44no—
230C23×D61—44no—
231C23×D61—44no—
232C23×D61—44no—
233C23×D61—44no—
234C23×D61—44no—
235C23×D61—44no—
236C23×D61—44no—
237C23×D61—44no—
238C23×D61—44no—
239C23×D61—44no—
240C23×D61—44no—
241C23×D61—44no—
242C23×D61—44no—
243C23×D61—44no—
244C23×D61—44no—
245C23×D61—44no—
246C23×D61—44no—
247C23×D61—44no—
248C23×D61C22×C412yes—
249C23×D61C22×C412yes—
250C23×D61C2×D412yes—
251C23×D61C2×D412yes—
252C23×D61#4112yes—
253C23×D61#4112yes—
254C23×D61#4112yes—
255C23×D61#4112yes—
256C23×D61#4112yes—
257C23×D61#4112yes—
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—21no—
268C22×C4×C61—21no—
269C22×C4×C61—21no—
270C22×C4×C61—21no—
271C22×C4×C61—21no—
272C22×C4×C61—21no—
273C22×C4×C61—21no—
274C22×C4×C61—21no—
275C22×C4×C61—21no—
276C22×C4×C61—21no—
277C22×C4×C61—21no—
278C22×C4×C61—21no—
279C22×C4×C61—21no—
280C22×C4×C61—21no—
281C22×C4×C61—21no—
282C22×C4×C61—21no—
283C22×C4×C61—21no—
284C22×C4×C61—21no—
285C22×C4×C61—21no—
286C22×C4×C61—21no—
287C22×C4×C61—21no—
288C22×C4×C61—21no—
289C22×C4×C61—21no—
290C22×C4×C61—21no—
291C22×C4×C61—21no—
292C22×C4×C61C22×C412yes—
293C22×C4×C61C22×C412yes—
294C22×C4×C61C2×D412yes—
295C22×C4×C61C2×D412yes—
296C22×C4×C61C2×D412yes—
297C22×C4×C61C2×D412yes—
298C22×C4×C61C2×D412yes—
299C22×C4×C61C2×D412yes—
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—21no—
324C22×Dic61—21no—
325C22×Dic61—21no—
326C22×Dic61—21no—
327C22×Dic61—21no—
328C22×Dic61—21no—
329C22×Dic61—21no—
330C22×Dic61—21no—
331C22×Dic61—21no—
332C22×Dic61—21no—
333C22×Dic61—21no—
334C22×Dic61—21no—
335C22×Dic61—21no—
336C22×Dic61—21no—
337C22×Dic61—21no—
338C22×Dic61C22×C412yes—
339C22×Dic61C22×C412yes—
340C22×Dic61C2×D412yes—
341C22×Dic61C2×D412yes—
342C2×C4×D61—28no—
343C2×C4×D61—28no—
344C2×C4×D61—28no—
345C2×C4×D61—28no—
346C2×C4×D61—44no—
347C2×C4×D61—44no—
348C2×C4×D61—44no—
349C2×C4×D61—44no—
350C2×C4×D61—44no—
351C2×C4×D61—44no—
352C2×C4×D61—44no—
353C2×C4×D61—44no—
354C2×C4×D61—44no—
355C2×C4×D61—44no—
356C4⋊C4×C61—44no—
357C22⋊C4×C61—44no—
358C22⋊C4×C61—44no—
359C22⋊C4×C61C22⋊C4116yescomplemented
360C42×C61—44no—
361C22⋊Dic61—28no—
362C22⋊Dic61—44no—
363C22⋊Dic61—44no—
364#11758198—28no—
365#11758198—28no—
366#11758198—28no—
367#11758198—28no—
368#11758198—44no—
369#11758198—44no—
370#11758198—44no—
371#11758198—44no—
372#11758198—44no—
373#11758198—44no—
374C4⋊Dic61—44no—
375C4×Dic61—44no—
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—41no—
395C23×C61—41no—
396C23×C61—41no—
397C23×C61—41no—
398C23×C61—41no—
399C23×C61—41no—
400C23×C61—41no—
401C23×C61—41no—
402C23×C61—41no—
403C23×C61—41no—
404C23×C61—41no—
405C23×C61—41no—
406C23×C61—41no—
407C23×C61—41no—
408C23×C61—41no—
409C23×C61—41no—
410C23×C61C2×C22⋊C414yes—
411C23×C61C23×C411yescharacteristic
412C23×C61C22×D411yescharacteristic
413C23×C61C22×D411yescharacteristic
414C23×C61C22×D411yescharacteristic
415C23×C61C22×D411yescharacteristic
416C23×C61C2×#4111yescharacteristic
417C23×C61C2×#4111yescharacteristic
418C23×C61C2×#4111yescharacteristic
419C23×C61C2×#4111yescharacteristic
420C23×C61C2×#4111yescharacteristic
421C23×C61C2×#4111yescharacteristic
422C23×C61H(5,𝔽2)11yescharacteristic
423C23×C61H(5,𝔽2)11yescharacteristic
424C23×C61H(5,𝔽2)11yescharacteristic
425C23×C61H(5,𝔽2)11yescharacteristic
426C22×D61—22no—
427C22×D61—22no—
428C22×D61—22no—
429C22×D61—22no—
430C22×D61—22no—
431C22×D61—22no—
432C22×D61—22no—
433C22×D61—22no—
434C22×D61—22no—
435C22×D61—22no—
436C22×D61—22no—
437C22×D61—22no—
438C22×D61—22no—
439C22×D61—22no—
440C22×D61—22no—
441C22×D61—22no—
442C22×D61—22no—
443C22×D61—22no—
444C22×D61—22no—
445C22×D61—22no—
446C22×D61—22no—
447C22×D61—22no—
448C22×D61—22no—
449C22×D61—22no—
450C22×D61—22no—
451C22×D61—22no—
452C22×D61—22no—
453C22×D61—22no—
454C22×D61—232no—
455C22×D61—22no—
456C22×D61—22no—
457C22×D61—22no—
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—416no—
474C22×D61—416no—
475C22×D61—416no—
476C22×D61—416no—
477C22×D61—416no—
478C22×D61—416no—
479C22×D61—416no—
480C22×D61—416no—
481C22×D61—416no—
482C22×D61—416no—
483C22×D61—416no—
484C22×D61—416no—
485C22×D61—416no—
486C22×D61—41no—
487C22×D61—41no—
488C22×D61—41no—
489C22×D61—41no—
490C22×D61—41no—
491C22×D61—41no—
492C22×D61—41no—
493C22×D61—41no—
494C22×D61—41no—
495C22×D61—41no—
496C22×D61—41no—
497C22×D61—41no—
498C22×D61—41no—
499C22×D61—41no—
500C22×D61—41no—
501C22×D61—41no—
502C22×D61—416no—
503C22×D61#11714yes—
504C22×D61#11714yes—
505C22×D61C4×D414yes—
506C22×D61C4×D414yes—
507C22×D61#12114yes—
508C22×D61#12314yes—
509C22×D61#12414yes—
510C22×D61#12614yes—
511C2×C4×C61—22no—
512C2×C4×C61—22no—
513C2×C4×C61—22no—
514C2×C4×C61—22no—
515C2×C4×C61—22no—
516C2×C4×C61—22no—
517C2×C4×C61—22no—
518C2×C4×C61—22no—
519C2×C4×C61—22no—
520C2×C4×C61—22no—
521C2×C4×C61—22no—
522C2×C4×C61—22no—
523C2×C4×C61—22no—
524C2×C4×C61—22no—
525C2×C4×C61—22no—
526C2×C4×C61—22no—
527C2×C4×C61—22no—
528C2×C4×C61—22no—
529C2×C4×C61—41no—
530C2×C4×C61—41no—
531C2×C4×C61—41no—
532C2×C4×C61—41no—
533C2×C4×C61—41no—
534C2×C4×C61—41no—
535C2×C4×C61—41no—
536C2×C4×C61—41no—
537C2×C4×C61—41no—
538C2×C4×C61—41no—
539C2×C4×C61—41no—
540C2×C4×C61—41no—
541C2×C4×C61—41no—
542C2×C4×C61—41no—
543C2×C4×C61—41no—
544C2×C4×C61—41no—
545C2×C4×C61—41no—
546C2×C4×C61—41no—
547C2×C4×C61—41no—
548C2×C4×C61—41no—
549C2×C4×C61—41no—
550C2×C4×C61—41no—
551C2×C4×C61C2×C22⋊C414yes—
552C2×C4×C61C2×C22⋊C414yes—
553C2×Dic61—22no—
554C2×Dic61—22no—
555C2×Dic61—22no—
556C2×Dic61—22no—
557C2×Dic61—22no—
558C2×Dic61—22no—
559C2×Dic61—22no—
560C2×Dic61—22no—
561C2×Dic61—22no—
562C2×Dic61—22no—
563C2×Dic61—22no—
564C2×Dic61—22no—
565C2×Dic61—41no—
566C2×Dic61—41no—
567C2×Dic61—41no—
568C2×Dic61—41no—
569C2×Dic61—41no—
570C2×Dic61—41no—
571C2×Dic61—41no—
572C2×Dic61—41no—
573C2×Dic61—41no—
574C2×Dic61—41no—
575C2×Dic61—41no—
576C2×Dic61—41no—
577C2×Dic61—41no—
578C2×Dic61—41no—
579C2×Dic61—41no—
580C2×Dic61—41no—
581C2×Dic61—41no—
582C2×Dic61—41no—
583C2×Dic61—41no—
584C2×Dic61—41no—
585C2×Dic61—41no—
586C2×Dic61—41no—
587C2×Dic61—41no—
588C2×Dic61—41no—
589C2×Dic61—41no—
590C2×Dic61—41no—
591C2×Dic61—41no—
592C2×Dic61—41no—
593C2×Dic61—41no—
594C2×Dic61—41no—
595C4×D61—416no—
596C4×D61—416no—
597#13873—611nomaximal, Sylow
598C22×C61—24no—
599C22×C61—24no—
600C22×C61—24no—
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×C61C22×C22⋊C411yescharacteristic
614C22×C61C2×#11711yescharacteristic
615C22×C61C2×#11711yescharacteristic
616C22×C61C2×C4×D411yescharacteristic
617C22×C61C2×C4×D411yescharacteristic
618C22×C61#51811yescharacteristic
619C22×C61#51811yescharacteristic
620C22×C61C2×#12111yescharacteristic
621C22×C61C2×#12311yescharacteristic
622C22×C61#52511yescharacteristic
623C22×C61#52511yescharacteristic
624C22×C61#52511yescharacteristic
625C22×C61#52511yescharacteristic
626C22×C61C2×#12411yescharacteristic
627C22×C61C2×#12611yescharacteristic
628C22×C61#53811yescharacteristic
629C22×C61#53811yescharacteristic
630C22×C61#53811yescharacteristic
631C22×C61#53811yescharacteristic
632C22×C61D4211yescharacteristic
633C22×C61D4211yescharacteristic
634C22×C61D4211yescharacteristic
635C22×C61D4211yescharacteristic
636C22×C61#54611yescharacteristic
637C22×C61#54611yescharacteristic
638C22×C61#54611yescharacteristic
639C22×C61#54611yescharacteristic
640C22×C61#54611yescharacteristic
641C22×C61#54611yescharacteristic
642C22×C61#54611yescharacteristic
643C22×C61#54611yescharacteristic
644C22×C61#55111yescharacteristic
645C22×C61#55111yescharacteristic
646C22×C61#55111yescharacteristic
647C22×C61#55111yescharacteristic
648C2×D61—24no—
649C2×D61—24no—
650C2×D61—24no—
651C2×D61—24no—
652C2×D61—24no—
653C2×D61—24no—
654C2×D61—24no—
655C2×D61—24no—
656C2×D61—24no—
657C2×D61—24no—
658C2×D61—24no—
659C2×D61—24no—
660C2×D61—24no—
661C2×D61—24no—
662C2×D61—24no—
663C2×D61—24no—
664C2×D61—24no—
665C2×D61—464no—
666C2×D61—42no—
667C2×D61—42no—
668C2×D61—42no—
669C2×D61—42no—
670C2×D61—42no—
671C2×D61—42no—
672C2×D61—42no—
673C2×D61—42no—
674C2×D61—42no—
675C2×D61—42no—
676C2×D61—42no—
677C2×D61—42no—
678C2×D61#38818yescomplemented
679C4×C61—24no—
680C4×C61—24no—
681C4×C61—42no—
682C4×C61—42no—
683C4×C61—81no—
684C4×C61—81no—
685Dic61—42no—
686Dic61—42no—
687Dic61—42no—
688Dic61—42no—
689Dic61—81no—
690Dic61—81no—
691C23×C22⋊C4—611no—
692C2×#388—611no—
693C2×#388D6111yescharacteristic, complemented
694C2×#380—611no—
695C2×#379—611no—
696C2×#379—611no—
697C2×C4×C22⋊C4—611no—
698#1440—611no—
699#1440—611no—
700#1439—611no—
701#1439—611no—
702#1437—611no—
703#1437—611no—
704C22⋊#95—611no—
705C22⋊#95—611no—
706C2×C61—44no—
707C2×C61#228011yescharacteristic
708C2×C61C2×#38811yescharacteristic
709C2×C61#231211yescharacteristic
710C2×C61D4×C22⋊C411yescharacteristic
711C2×C61D4×C22⋊C411yescharacteristic
712C2×C61#234211yescharacteristic
713C2×C61#234211yescharacteristic
714C2×C61#241811yescharacteristic
715C2×C61#241811yescharacteristic
716C2×C61#242411yescharacteristic
717C2×C61#242411yescharacteristic
718C2×C61#247211yescharacteristic
719C2×C61#247211yescharacteristic
720C2×C61#248011yescharacteristic
721C2×C61#248011yescharacteristic
722D61—28no—
723D61—44no—
724C26—611no—
725C24×C4—611no—
726C24×C4—611no—
727C22×C4⋊C4—611no—
728C22×C4⋊C4C2×D6111yescharacteristic, complemented
729C22×C22⋊C4—611no—
730C22×C22⋊C4—611no—
731C22×C22⋊C4—611no—
732C22×C22⋊C4—611no—
733C22×C22⋊C4—611no—
734C22×C22⋊C4—618no—
735C22×C22⋊C4—611no—
736C22×C22⋊C4—611no—
737C22×C22⋊C4—611no—
738C22×C22⋊C4—611no—
739C22×C22⋊C4—611no—
740C22×C22⋊C4—611no—
741C22×C22⋊C4—611no—
742C22×C22⋊C4—611no—
743C22×C22⋊C4—1224no—
744C22×C22⋊C4—1224no—
745C22×C22⋊C4C2×D6111yescharacteristic
746C22×C22⋊C4C2×D6111yescharacteristic
747C22×C22⋊C4C2×D6111yescharacteristic
748C22×C42—611no—
749C22×C42C2×D6111yescharacteristic, complemented
750#388—24no—
751#388—1224no—
752#380—1224no—
753#379—1224no—
754#379—1224no—
755C4×C22⋊C4—1224no—
756C2×#95—611no—
757C2×#95—611no—
758C2×#95—611no—
759C2×#95—611no—
760C2×#95—611no—
761C2×#95—611no—
762C2×#95—611no—
763C2×#95—611no—
764C2×#95—611no—
765C2×#95—611no—
766C2×#95C2×D6111yescharacteristic, complemented
767C2×#95C2×D6111yescharacteristic, complemented
768C61#1387311yescharacteristic, complemented, Sylow
769C25—611no—
770C25—611no—
771C25—614no—
772C25—1222no—
773C25—1222no—
774C25—1222no—
775C25—1222no—
776C25—1222no—
777C25—1222no—
778C25—1222no—
779C25—1222no—
780C25—1222no—
781C25—1222no—
782C25—2441no—
783C25—2441no—
784C25—2441no—
785C25—2441no—
786C25C22×D6111yescharacteristic
787C23×C4—611no—
788C23×C4—611no—
789C23×C4—611no—
790C23×C4—611no—
791C23×C4—614no—
792C23×C4—614no—
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—2441no—
804C23×C4—2441no—
805C23×C4—2441no—
806C23×C4—2441no—
807C23×C4C22×D6111yescharacteristic
808C23×C4C22×D6111yescharacteristic
809C23×C4C22×D6111yescharacteristic
810C23×C4C22×D6111yescharacteristic
811C23×C4C22×D6111yescharacteristic
812C23×C4C22×D6111yescharacteristic
813C2×C4⋊C4—22no—
814C2×C4⋊C4—22no—
815C2×C4⋊C4—41no—
816C2×C4⋊C4—1222no—
817C2×C4⋊C4—1222no—
818C2×C4⋊C4—2441no—
819C2×C22⋊C4—22no—
820C2×C22⋊C4—22no—
821C2×C22⋊C4—22no—
822C2×C22⋊C4—22no—
823C2×C22⋊C4—41no—
824C2×C22⋊C4—41no—
825C2×C22⋊C4—614no—
826C2×C22⋊C4—614no—
827C2×C22⋊C4—614no—
828C2×C22⋊C4—614no—
829C2×C22⋊C4—614no—
830C2×C22⋊C4—1222no—
831C2×C22⋊C4—1222no—
832C2×C22⋊C4—1222no—
833C2×C22⋊C4—1222no—
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—12232no—
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—1222no—
856C2×C22⋊C4—1222no—
857C2×C22⋊C4—1222no—
858C2×C22⋊C4—1222no—
859C2×C22⋊C4—2441no—
860C2×C22⋊C4—2441no—
861C2×C22⋊C4—2441no—
862C2×C22⋊C4—2441no—
863C2×C22⋊C4—2441no—
864C2×C22⋊C4—2441no—
865C2×C22⋊C4C4×D6114yes—
866C2×C22⋊C4D24414yes—
867C2×C22⋊C4C22⋊D6114yes—
868C2×C42—22no—
869C2×C42—22no—
870C2×C42—41no—
871C2×C42—1222no—
872C2×C42—1222no—
873C2×C42—2441no—
874#95—22no—
875#95—22no—
876#95—1222no—
877#95—1222no—
878#95—1222no—
879#95—1222no—
880#95—1222no—
881#95—1222no—
882#95—2441no—
883#95—2441no—
884#95—2441no—
885#95—2441no—
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—612no—
899C24—612no—
900C24—612no—
901C24—612no—
902C24—612no—
903C24—612no—
904C24—612no—
905C24—612no—
906C24—612no—
907C24—612no—
908C24—1228no—
909C24—1228no—
910C24—1228no—
911C24—1228no—
912C24—1228no—
913C24—1228no—
914C24—1228no—
915C24—1228no—
916C24—1221no—
917C24—1221no—
918C24—1221no—
919C24—1221no—
920C24—1221no—
921C24—1221no—
922C24—1221no—
923C24—1221no—
924C24—1221no—
925C24—1221no—
926C24—1221no—
927C24—1221no—
928C24—1221no—
929C24—1221no—
930C24—1221no—
931C24—1221no—
932C24—1221no—
933C24—1221no—
934C24—1221no—
935C24—1221no—
936C24—1228no—
937C24—2444no—
938C24—2444no—
939C24—2444no—
940C24—2444no—
941C24—2444no—
942C24—2444no—
943C24—2444no—
944C24—2444no—
945C24—2444no—
946C24—2444no—
947C24—2444no—
948C24—2444no—
949C24—2444no—
950C24—2444no—
951C24—2444no—
952C24—2444no—
953C24—2444no—
954C24—2444no—
955C24—2444no—
956C24—2444no—
957C24—2444no—
958C24—2444no—
959C24—2444no—
960C24—2444no—
961C24—2444no—
962C24—2444no—
963C24C2×C4×D6112yes—
964C24C2×D24412yes—
965C24C2×C22⋊D6112yes—
966C24C23×D6111yescharacteristic
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—21no—
976C22×C4—21no—
977C22×C4—21no—
978C22×C4—21no—
979C22×C4—21no—
980C22×C4—21no—
981C22×C4—21no—
982C22×C4—21no—
983C22×C4—21no—
984C22×C4—21no—
985C22×C4—21no—
986C22×C4—21no—
987C22×C4—21no—
988C22×C4—21no—
989C22×C4—21no—
990C22×C4—21no—
991C22×C4—21no—
992C22×C4—21no—
993C22×C4—21no—
994C22×C4—21no—
995C22×C4—21no—
996C22×C4—21no—
997C22×C4—21no—
998C22×C4—21no—
999C22×C4—21no—
1000C22×C4—21no—
1001C22×C4—612no—
1002C22×C4—612no—
1003C22×C4—612no—
1004C22×C4—612no—
1005C22×C4—1228no—
1006C22×C4—1228no—
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—1228no—
1032C22×C4—1228no—
1033C22×C4—1221no—
1034C22×C4—1221no—
1035C22×C4—1221no—
1036C22×C4—1221no—
1037C22×C4—1221no—
1038C22×C4—1221no—
1039C22×C4—1221no—
1040C22×C4—1221no—
1041C22×C4—1221no—
1042C22×C4—1221no—
1043C22×C4—1221no—
1044C22×C4—1221no—
1045C22×C4—1221no—
1046C22×C4—1221no—
1047C22×C4—2444no—
1048C22×C4—2444no—
1049C22×C4—2444no—
1050C22×C4—2444no—
1051C22×C4—2444no—
1052C22×C4—2444no—
1053C22×C4—2444no—
1054C22×C4—2444no—
1055C22×C4—2444no—
1056C22×C4—2444no—
1057C22×C4C2×C4×D6112yes—
1058C22×C4C2×C4×D6112yes—
1059C22×C4C2×D24412yes—
1060C22×C4C2×D24412yes—
1061C22×C4D4×D6112yes—
1062C22×C4D4×D6112yes—
1063C22×C4C2×C22⋊D6112yes—
1064C22×C4C2×C22⋊D6112yes—
1065C4⋊C4—44no—
1066C4⋊C4—2444no—
1067C22⋊C4—44no—
1068C22⋊C4—44no—
1069C22⋊C4—1228no—
1070C22⋊C4—1228no—
1071C22⋊C4—1228no—
1072C22⋊C4—1228no—
1073C22⋊C4—1228no—
1074C22⋊C4—2444no—
1075C22⋊C4—2444no—
1076C22⋊C4—2444no—
1077C22⋊C4—2444no—
1078C22⋊C4—2444no—
1079C22⋊C4—2444no—
1080C22⋊C4—2444no—
1081C22⋊C4—2444no—
1082C22⋊C4#11758198116yescomplemented
1083C42—44no—
1084C42—2444no—
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—614no—
1120C23—614no—
1121C23—614no—
1122C23—614no—
1123C23—614no—
1124C23—614no—
1125C23—614no—
1126C23—614no—
1127C23—12232no—
1128C23—1222no—
1129C23—1222no—
1130C23—1222no—
1131C23—1222no—
1132C23—1222no—
1133C23—1222no—
1134C23—1222no—
1135C23—1222no—
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—1222no—
1155C23—1222no—
1156C23—1222no—
1157C23—1222no—
1158C23—1222no—
1159C23—1222no—
1160C23—1222no—
1161C23—1222no—
1162C23—1222no—
1163C23—1222no—
1164C23—1222no—
1165C23—1222no—
1166C23—1222no—
1167C23—1222no—
1168C23—1222no—
1169C23—1222no—
1170C23—1222no—
1171C23—1222no—
1172C23—1222no—
1173C23—1222no—
1174C23—24416no—
1175C23—24416no—
1176C23—24416no—
1177C23—24416no—
1178C23—24416no—
1179C23—24416no—
1180C23—24416no—
1181C23—24416no—
1182C23—24416no—
1183C23—24416no—
1184C23—24416no—
1185C23—24416no—
1186C23—24416no—
1187C23—24416no—
1188C23—2441no—
1189C23—2441no—
1190C23—2441no—
1191C23—2441no—
1192C23—2441no—
1193C23—2441no—
1194C23—2441no—
1195C23—2441no—
1196C23—2441no—
1197C23—2441no—
1198C23—2441no—
1199C23—2441no—
1200C23—2441no—
1201C23—2441no—
1202C23—2441no—
1203C23—2441no—
1204C23C2×#1175819814yes—
1205C23C22×C4×D6111yescharacteristic
1206C23C2×D4×D6111yescharacteristic
1207C23C2×D4×D6111yescharacteristic
1208C23C22×C22⋊D6111yescharacteristic
1209C23C22×D24411yescharacteristic
1210C23#41×D6111yescharacteristic
1211C23#41×D6111yescharacteristic
1212C23#41×D6111yescharacteristic
1213C23#41×D6111yescharacteristic
1214C23#41×D6111yescharacteristic
1215C23#41×D6111yescharacteristic
1216C23#1451982211yescharacteristic
1217C23#1451982211yescharacteristic
1218C23#1451982311yescharacteristic
1219C23#1451982311yescharacteristic
1220C2×C4—22no—
1221C2×C4—22no—
1222C2×C4—22no—
1223C2×C4—22no—
1224C2×C4—22no—
1225C2×C4—22no—
1226C2×C4—22no—
1227C2×C4—22no—
1228C2×C4—22no—
1229C2×C4—22no—
1230C2×C4—22no—
1231C2×C4—22no—
1232C2×C4—22no—
1233C2×C4—22no—
1234C2×C4—22no—
1235C2×C4—22no—
1236C2×C4—22no—
1237C2×C4—22no—
1238C2×C4—41no—
1239C2×C4—41no—
1240C2×C4—41no—
1241C2×C4—41no—
1242C2×C4—41no—
1243C2×C4—41no—
1244C2×C4—41no—
1245C2×C4—41no—
1246C2×C4—41no—
1247C2×C4—41no—
1248C2×C4—41no—
1249C2×C4—41no—
1250C2×C4—41no—
1251C2×C4—41no—
1252C2×C4—41no—
1253C2×C4—41no—
1254C2×C4—41no—
1255C2×C4—41no—
1256C2×C4—41no—
1257C2×C4—41no—
1258C2×C4—41no—
1259C2×C4—41no—
1260C2×C4—1222no—
1261C2×C4—1222no—
1262C2×C4—1222no—
1263C2×C4—1222no—
1264C2×C4—1222no—
1265C2×C4—1222no—
1266C2×C4—1222no—
1267C2×C4—1222no—
1268C2×C4—1222no—
1269C2×C4—1222no—
1270C2×C4—1222no—
1271C2×C4—1222no—
1272C2×C4—24416no—
1273C2×C4—24416no—
1274C2×C4—2441no—
1275C2×C4—2441no—
1276C2×C4—2441no—
1277C2×C4—2441no—
1278C2×C4—2441no—
1279C2×C4—2441no—
1280C2×C4—2441no—
1281C2×C4—2441no—
1282C2×C4—2441no—
1283C2×C4—2441no—
1284C2×C4—2441no—
1285C2×C4—2441no—
1286C2×C4—2441no—
1287C2×C4—2441no—
1288C2×C4—2441no—
1289C2×C4—2441no—
1290C2×C4—2441no—
1291C2×C4—2441no—
1292C2×C4—2441no—
1293C2×C4—2441no—
1294C2×C4—2441no—
1295C2×C4—2441no—
1296C2×C4—2441no—
1297C2×C4—2441no—
1298C2×C4—2441no—
1299C2×C4—2441no—
1300C2×C4—2441no—
1301C2×C4—2441no—
1302C2×C4—2441no—
1303C2×C4—2441no—
1304C2×C4C2×#1175819814yes—
1305C2×C4C2×#1175819814yes—
1306C22—24no—
1307C22—24no—
1308C22—24no—
1309C22—42no—
1310C22—42no—
1311C22—42no—
1312C22—42no—
1313C22—42no—
1314C22—42no—
1315C22—42no—
1316C22—42no—
1317C22—42no—
1318C22—42no—
1319C22—42no—
1320C22—42no—
1321C22—618no—
1322C22—1224no—
1323C22—1224no—
1324C22—1224no—
1325C22—1224no—
1326C22—1224no—
1327C22—1224no—
1328C22—1224no—
1329C22—1224no—
1330C22—1224no—
1331C22—1224no—
1332C22—1224no—
1333C22—1224no—
1334C22—1224no—
1335C22—1224no—
1336C22—1224no—
1337C22—1224no—
1338C22—1224no—
1339C22—24464no—
1340C22—2442no—
1341C22—2442no—
1342C22—2442no—
1343C22—2442no—
1344C22—2442no—
1345C22—2442no—
1346C22—2442no—
1347C22—2442no—
1348C22—2442no—
1349C22—2442no—
1350C22—2442no—
1351C22—2442no—
1352C22C22×#1175819811yescharacteristic
1353C22#117×D6111yescharacteristic
1354C22#117×D6111yescharacteristic
1355C22C4×D4×D6111yescharacteristic
1356C22C4×D4×D6111yescharacteristic
1357C22#1684023411yescharacteristic
1358C22#1684023411yescharacteristic
1359C22#121×D6111yescharacteristic
1360C22#123×D6111yescharacteristic
1361C22#1684026911yescharacteristic
1362C22#1684026911yescharacteristic
1363C22#1684027411yescharacteristic
1364C22#1684027411yescharacteristic
1365C22#124×D6111yescharacteristic
1366C22#126×D6111yescharacteristic
1367C22#1684034411yescharacteristic
1368C22#1684034611yescharacteristic
1369C22#1684034811yescharacteristic
1370C22#1684035111yescharacteristic
1371C22D4×C22⋊D6111yescharacteristic
1372C22D4×C22⋊D6111yescharacteristic
1373C22D4×D24411yescharacteristic
1374C22D4×D24411yescharacteristic
1375C22#1684040011yescharacteristic
1376C22#1684040011yescharacteristic
1377C22#1684040111yescharacteristic
1378C22#1684040411yescharacteristic
1379C22#1684040511yescharacteristic
1380C22#1684040711yescharacteristic
1381C22#1684040711yescharacteristic
1382C22#1684040911yescharacteristic
1383C22#1684043711yescharacteristic
1384C22#1684043711yescharacteristic
1385C22#1684044011yescharacteristic
1386C22#1684044211yescharacteristic
1387C4—24no—
1388C4—24no—
1389C4—42no—
1390C4—42no—
1391C4—81no—
1392C4—81no—
1393C4—4881no—
1394C4—4881no—
1395C4—2442no—
1396C4—2442no—
1397C4—2442no—
1398C4—2442no—
1399C2—44no—
1400C2—1228no—
1401C2—2444no—
1402C2#2144819811yescharacteristic
1403C2#388×D6111yescharacteristic
1404C2#2144841311yescharacteristic
1405C2D4×#1175819811yescharacteristic
1406C2D4×#1175819811yescharacteristic
1407C2#2144866311yescharacteristic
1408C2#2144866711yescharacteristic
1409C2#2144927811yescharacteristic
1410C2#2144928611yescharacteristic
1411C2#2144935211yescharacteristic
1412C2#2144936011yescharacteristic
1413C2#2144994111yescharacteristic
1414C2#2144994311yescharacteristic
1415C2#2145006111yescharacteristic
1416C2#2145006311yescharacteristic
subgroupG/H
center, FrattiniC24C23×D61
commutatorC23×C61C23×C4
FittingC2×C61×#388C2
socle, cosocleC24×C61C24
prime radicalC25×D61C22
hypercenterC2×#388D61
hypocenterC61#13873
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C24 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
2. C2×#16839655C2semidirect
3. C2×#16839619C2semidirect
6. C2×C4×#11758198C2semidirect
7. #21444066C2semidirect
8. #21444066C2semidirect
9. #21444065C2semidirect
10. #21444061C2semidirect
11. #21444057C2semidirect
12. #21444055C2semidirect
13. #21444040C2semidirect
14. #21444040C2semidirect
15. C2×C61×#388C2semidirect
19. C22×C4⋊Dic61C22semidirect
35. C2×C22⋊C4×D61C4semidirect
36. C22×C4×Dic61C22semidirect
42. C2×#14519684C22semidirect
43. C2×#14519684C22semidirect
44. C2×#14519684C22semidirect
45. C2×#14519684C22semidirect
46. C2×#14519684C22semidirect
47. C2×#14519684C22semidirect
48. C2×#14519684C22semidirect
49. C2×#14519684C22semidirect
50. C2×#14519684C22semidirect
51. C2×#14519684C22semidirect
52. C22×C4⋊C4×C61C22semidirect
56. C22×C42×C61C22semidirect
58. C2×#95×C61C22semidirect
59. C2×#95×C61C22semidirect
359. C22⋊C4×C61C22⋊C4semidirect
678. C2×D61#388semidirect
693. C2×#388D61semidirect
728. C22×C4⋊C4C2×D61semidirect
749. C22×C42C2×D61semidirect
766. C2×#95C2×D61semidirect
767. C2×#95C2×D61semidirect
768. C61#13873semidirect
1082. C22⋊C4#11758198semidirect

Maximal subgroups

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

subgroupindex
C22×C22⋊C4×D612
C2×#168396552
C2×#168396192
C2×#168396172
C2×C4×#117581982
#214440662
#214440652
#214440612
#214440572
#214440552
#214440402
C2×C61×#3882
#1387361