Finite Group Databasebeta

← #29602813

Subgroups — #29602813

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×#14519750C211yesmaximal, characteristic
2C22×#14519737C211yesmaximal, characteristic, complemented
3C2×#16839662C211yesmaximal, characteristic, complemented
4C2×#16839640C211yesmaximal, characteristic, complemented
5C2×#16839639C211yesmaximal, characteristic, complemented
6C2×#16839621C211yesmaximal, characteristic, complemented
7C2×#16839609C211yesmaximal, characteristic, complemented
8#21444067C211yesmaximal, characteristic, complemented
9#21444059C211yesmaximal, characteristic, complemented
10#21444058C211yesmaximal, characteristic, complemented
11#21444047C211yesmaximal, characteristic, complemented
12#21444047C211yesmaximal, characteristic, complemented
13#21444041C211yesmaximal, characteristic, complemented
14#21444040C211yesmaximal, characteristic, complemented
15C61×#1440C211yesmaximal, characteristic, complemented
16C23×D244C2211yescharacteristic
17C23×C22⋊D61C2211yescharacteristic
18C23×C22⋊D61C2211yescharacteristic
19C24×Dic61C2211yescharacteristic
20C23×C4×D61C2211yescharacteristic
21C23×C4×D61C2211yescharacteristic
22C2×#14519750—24no—
23C2×#14519750—24no—
24C2×#14519750C418yescomplemented
25C2×#14519737—24no—
26C2×#14519737—24no—
27C2×#14519737—24no—
28C22×#11758196C2211yescharacteristic
29C22×#11758196C2211yescharacteristic
30C22×#11758196C2211yescharacteristic
31C22×C22⋊Dic61C2211yescharacteristic
32C22×#11758198C2211yescharacteristic
33C22×#11758198C2211yescharacteristic
34C22×#11758198C2211yescharacteristic
35C22×#11758198C2211yescharacteristic
36C22×#11758198C2211yescharacteristic
37C22×#11758198C2211yescharacteristic
38C22×#11758198C2211yescharacteristic
39C22×#11758198C2211yescharacteristic
40C22×C4×Dic61C2211yescharacteristic
41C22×C4×Dic61C2211yescharacteristic
42#16839662—24no—
43#16839640—24no—
44#16839639—24no—
45#16839621—24no—
46#16839609—24no—
47C2×#14519684C2211yescharacteristic
48C2×#14519684C2211yescharacteristic
49C2×#14519684C2211yescharacteristic
50C2×#14519684C2211yescharacteristic
51C2×#14519684C2211yescharacteristic
52C2×#14519684C2211yescharacteristic
53C2×#14519684C2211yescharacteristic
54C2×#14519684C2211yescharacteristic
55C22×C22⋊C4×C61C2211yescharacteristic
56C22×C22⋊C4×C61C2211yescharacteristic
57C22×C22⋊C4×C61C2211yescharacteristic
58C2×#95×C61C2211yescharacteristic
59C2×#95×C61C2211yescharacteristic
60C2×#95×C61C2211yescharacteristic
61C2×#95×C61C2211yescharacteristic
62C24×D61C2311yescharacteristic
63C24×D61C2311yescharacteristic
64C22×D244—22no—
65C22×D244—22no—
66C22×D244—22no—
67C22×D244—22no—
68C22×D244—41no—
69C22×D244—41no—
70C22×D244C2×C414yescomplemented
71C22×C22⋊D61—22no—
72C22×C22⋊D61—22no—
73C22×C22⋊D61—22no—
74C22×C22⋊D61—22no—
75C22×C22⋊D61—22no—
76C22×C22⋊D61—22no—
77C22×C22⋊D61—22no—
78C22×C22⋊D61—22no—
79C22×C22⋊D61—41no—
80C22×C22⋊D61—41no—
81C22×C22⋊D61C2×C414yes—
82C22×C22⋊D61C2×C414yescomplemented
83C22×C22⋊D61D414yes—
84C22×C22⋊D61D414yes—
85C23×Dic61—22no—
86C23×Dic61—22no—
87C23×Dic61—22no—
88C23×Dic61—22no—
89C23×Dic61—22no—
90C23×Dic61—41no—
91C23×Dic61—41no—
92C23×Dic61C2311yescharacteristic
93C23×Dic61C2311yescharacteristic
94C23×Dic61C2311yescharacteristic
95C23×Dic61C2311yescharacteristic
96C23×Dic61C2311yescharacteristic
97C23×Dic61C2311yescharacteristic
98C22×C4×D61—22no—
99C22×C4×D61—22no—
100C22×C4×D61—22no—
101C22×C4×D61—22no—
102C22×C4×D61—22no—
103C22×C4×D61—22no—
104C22×C4×D61—22no—
105C22×C4×D61—22no—
106C22×C4×D61—22no—
107C22×C4×D61—22no—
108C22×C4×D61—22no—
109C22×C4×D61—41no—
110C22×C4×D61—41no—
111C22×C4×D61C2×C414yescomplemented
112#14519750—232no—
113#14519737—232no—
114C2×#11758196—22no—
115C2×#11758196—22no—
116C2×#11758196—22no—
117C2×#11758196—22no—
118C2×#11758196—22no—
119C2×#11758196—22no—
120C2×#11758196—22no—
121C2×#11758196C2×C414yescomplemented
122C2×#11758196D414yescomplemented
123C2×C22⋊Dic61—22no—
124C2×C22⋊Dic61—22no—
125C2×C22⋊Dic61—41no—
126C2×#11758198—22no—
127C2×#11758198—22no—
128C2×#11758198—22no—
129C2×#11758198—22no—
130C2×#11758198—22no—
131C2×#11758198—22no—
132C2×#11758198—22no—
133C2×#11758198—22no—
134C2×#11758198—22no—
135C2×#11758198—22no—
136C2×#11758198—22no—
137C2×#11758198—22no—
138C2×#11758198—22no—
139C2×#11758198—22no—
140C2×#11758198—22no—
141C2×#11758198—22no—
142C2×#11758198—22no—
143C2×#11758198—22no—
144C2×#11758198—41no—
145C2×#11758198—41no—
146C2×#11758198—41no—
147C2×#11758198—41no—
148C2×#11758198C2×C414yescomplemented
149C2×#11758198D414yescomplemented
150C2×C4×Dic61—22no—
151C2×C4×Dic61—22no—
152C2×C4×Dic61—22no—
153C2×C4×Dic61—22no—
154C2×C4×Dic61—22no—
155C2×C4×Dic61D414yescomplemented
156#14519684—22no—
157#14519684—22no—
158#14519684—22no—
159#14519684—22no—
160#14519684—22no—
161#14519684—41no—
162#14519684—41no—
163#14519684—41no—
164C25×C61C2311yescharacteristic
165C23×C4×C61C2311yescharacteristic
166C23×C4×C61C2311yescharacteristic
167C23×C4×C61C2311yescharacteristic
168C23×C4×C61C2311yescharacteristic
169C23×C4×C61C2311yescharacteristic
170C23×C4×C61C2311yescharacteristic
171C2×C22⋊C4×C61—22no—
172C2×C22⋊C4×C61—22no—
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—41no—
179C2×C22⋊C4×C61C2×C414yescomplemented
180#95×C61—22no—
181#95×C61—22no—
182#95×C61—22no—
183#95×C61—41no—
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×C61C22×C412yes—
197C24×C61C2×D412yes—
198C24×C61C2×D412yes—
199C24×C61C2411yescharacteristic
200C23×D61—21no—
201C23×D61—21no—
202C23×D61—21no—
203C23×D61—21no—
204C23×D61—21no—
205C23×D61—21no—
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—21no—
219C23×D61—21no—
220C23×D61—21no—
221C23×D61—21no—
222C23×D61—21no—
223C23×D61—21no—
224C23×D61C22×C412yes—
225C23×D61C22×C412yes—
226C23×D61C2×D412yes—
227C23×D61C2×D412yes—
228C23×D61C2×D412yes—
229C23×D61#4112yes—
230C22×C4×C61—21no—
231C22×C4×C61—21no—
232C22×C4×C61—21no—
233C22×C4×C61—21no—
234C22×C4×C61—21no—
235C22×C4×C61—21no—
236C22×C4×C61—21no—
237C22×C4×C61—21no—
238C22×C4×C61—21no—
239C22×C4×C61—21no—
240C22×C4×C61—21no—
241C22×C4×C61—21no—
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×C61C22×C412yes—
268C22×C4×C61C22×C412yes—
269C22×C4×C61C2×D412yes—
270C22×C4×C61C2×D412yes—
271C22×C4×C61C2×D412yes—
272C2×C22⋊D61—28no—
273C2×C22⋊D61—28no—
274C2×C22⋊D61—28no—
275C2×C22⋊D61—28no—
276C2×C22⋊D61—28no—
277C2×C22⋊D61—28no—
278C2×C22⋊D61—28no—
279C2×C22⋊D61—28no—
280C2×C22⋊D61—44no—
281C2×C22⋊D61—44no—
282C2×C22⋊D61—44no—
283C2×C22⋊D61—44no—
284C2×C22⋊D61—44no—
285C2×C22⋊D61C22⋊C4116yescomplemented
286C22×Dic61—21no—
287C22×Dic61—21no—
288C22×Dic61—21no—
289C22×Dic61—21no—
290C22×Dic61—28no—
291C22×Dic61—21no—
292C22×Dic61—21no—
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—44no—
317C22×Dic61—44no—
318C22×Dic61—44no—
319C22×Dic61—44no—
320C22×Dic61—44no—
321C22×Dic61—44no—
322C22×Dic61C22×C412yes—
323C22×Dic61C22×C412yes—
324C22×Dic61C2×D412yes—
325C22×Dic61C2×D412yes—
326C22×Dic61C2×D412yes—
327C22×Dic61C2×D412yes—
328C22×Dic61C2×D412yes—
329C22×Dic61C2×D412yes—
330C22×Dic61C2×D412yes—
331C22×Dic61#4112yes—
332C22×Dic61#4112yes—
333C22×Dic61#4112yes—
334C22×Dic61#4112yes—
335C2×D244—28no—
336C2×D244—28no—
337C2×D244—44no—
338C2×D244—44no—
339C2×D244—44no—
340C2×D244—44no—
341C2×D244—44no—
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—
356C22⋊C4×C61—28no—
357C22⋊C4×C61—28no—
358C22⋊C4×C61—44no—
359C22⋊Dic61—44no—
360#11758198—28no—
361#11758198—28no—
362#11758198—28no—
363#11758198—28no—
364#11758198—44no—
365#11758198—44no—
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—41no—
392C23×C61—41no—
393C23×C61—41no—
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×C61C2×C22⋊C414yes—
408C23×C61C23×C411yescharacteristic
409C23×C61C22×D411yescharacteristic
410C23×C61C22×D411yescharacteristic
411C23×C61C22×D411yescharacteristic
412C23×C61C22×D411yescharacteristic
413C23×C61C22×D411yescharacteristic
414C23×C61C2×#4111yescharacteristic
415C23×C61C2×#4111yescharacteristic
416C23×C61C2×#4111yescharacteristic
417C23×C61C2×#4111yescharacteristic
418C23×C61C2×#4111yescharacteristic
419C23×C61H(5,𝔽2)11yescharacteristic
420C23×C61H(5,𝔽2)11yescharacteristic
421C23×C61H(5,𝔽2)11yescharacteristic
422C23×C612−1+411yescharacteristic
423C22×D61—22no—
424C22×D61—22no—
425C22×D61—22no—
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—22no—
455C22×D61—22no—
456C22×D61—22no—
457C22×D61—22no—
458C22×D61—22no—
459C22×D61—41no—
460C22×D61—41no—
461C22×D61—41no—
462C22×D61—41no—
463C22×D61—41no—
464C22×D61—41no—
465C22×D61—41no—
466C22×D61—41no—
467C22×D61—41no—
468C22×D61—41no—
469C22×D61—41no—
470C22×D61—41no—
471C22×D61—41no—
472C22×D61—41no—
473C22×D61—41no—
474C22×D61—41no—
475C22×D61—41no—
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×D61C2×C22⋊C414yes—
492C22×D61C4×D414yescomplemented
493C2×C4×C61—22no—
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—41no—
509C2×C4×C61—41no—
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—41no—
530C2×C4×C61—41no—
531C2×C4×C61—41no—
532C2×C4×C61—41no—
533C2×C4×C61—41no—
534C2×C4×C61—41no—
535C22⋊D61—232no—
536C22⋊D61—416no—
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—22no—
548C2×Dic61—22no—
549C2×Dic61—22no—
550C2×Dic61—22no—
551C2×Dic61—22no—
552C2×Dic61—416no—
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—41no—
568C2×Dic61—41no—
569C2×Dic61—41no—
570C2×Dic61—41no—
571C2×Dic61—41no—
572C2×Dic61C2×C22⋊C414yes—
573C2×Dic61C4×D414yes—
574C2×Dic61C4×D414yes—
575C2×Dic61#12014yes—
576C2×Dic61#12114yes—
577C2×Dic61#12114yes—
578C2×Dic61#12114yescomplemented
579C2×Dic61#12314yes—
580D244—416no—
581C4×D61—416no—
582C4×D61—416no—
583#13970—611nomaximal, Sylow
584C22×C61—24no—
585C22×C61—24no—
586C22×C61—24no—
587C22×C61—42no—
588C22×C61—42no—
589C22×C61—42no—
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×C61C22×C22⋊C411yescharacteristic
600C22×C61C2×C4×D411yescharacteristic
601C22×C61C2×C4×D411yescharacteristic
602C22×C61C2×C4×D411yescharacteristic
603C22×C61C4×#4111yescharacteristic
604C22×C61#51811yescharacteristic
605C22×C61#52011yescharacteristic
606C22×C61C2×#12011yescharacteristic
607C22×C61C2×#12111yescharacteristic
608C22×C61C2×#12111yescharacteristic
609C22×C61C2×#12111yescharacteristic
610C22×C61C2×#12311yescharacteristic
611C22×C61#52511yescharacteristic
612C22×C61#52911yescharacteristic
613C22×C61#53211yescharacteristic
614C22×C61#53511yescharacteristic
615C22×C61#53711yescharacteristic
616C22×C61#54011yescharacteristic
617C22×C61#54211yescharacteristic
618C22×C61D4211yescharacteristic
619C22×C61D4211yescharacteristic
620C22×C61D4211yescharacteristic
621C22×C61#54611yescharacteristic
622C22×C61#54611yescharacteristic
623C22×C61#54611yescharacteristic
624C22×C61#54611yescharacteristic
625C22×C61#54611yescharacteristic
626C22×C61#54711yescharacteristic
627C22×C61#54711yescharacteristic
628C22×C61#54711yescharacteristic
629C22×C61#54811yescharacteristic
630C22×C61#55011yescharacteristic
631C22×C61#55311yescharacteristic
632C22×C61#55311yescharacteristic
633C22×C61#55511yescharacteristic
634C2×D61—24no—
635C2×D61—24no—
636C2×D61—24no—
637C2×D61—24no—
638C2×D61—24no—
639C2×D61—24no—
640C2×D61—42no—
641C2×D61—42no—
642C2×D61—42no—
643C2×D61—42no—
644C2×D61—42no—
645C2×D61—42no—
646C2×D61—42no—
647C2×D61—42no—
648C2×D61—42no—
649C2×D61—42no—
650C2×D61—42no—
651C2×D61—42no—
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—42no—
665C4×C61—42no—
666C4×C61—42no—
667C4×C61—42no—
668C4×C61—42no—
669C4×C61—81no—
670Dic61—24no—
671Dic61—42no—
672Dic61—42no—
673Dic61—42no—
674Dic61—81no—
675Dic61#38618yescomplemented
676C22×#121—611no—
677C22×C4×D4—611no—
678C2×#390—611no—
679C2×#386—611no—
680C2×#386—611no—
681C2×#380—611no—
682C2×C4×C22⋊C4—611no—
683#1440—611no—
684#1440D6111yescharacteristic, complemented
685#1438—611no—
686#1438—611no—
687C4⋊#95—611no—
688C4⋊#95—611no—
689C22⋊#95—611no—
690C22⋊#95—611no—
691C2×C61—44no—
692C2×C61C2×#38611yescharacteristic
693C2×C61C4×#12111yescharacteristic
694C2×C61#232411yescharacteristic
695C2×C61D4×C22⋊C411yescharacteristic
696C2×C61#233911yescharacteristic
697C2×C61#236111yescharacteristic
698C2×C61#236311yescharacteristic
699C2×C61#240711yescharacteristic
700C2×C61#240811yescharacteristic
701C2×C61#242011yescharacteristic
702C2×C61#242211yescharacteristic
703C2×C61#242711yescharacteristic
704C2×C61#242811yescharacteristic
705C2×C61#253511yescharacteristic
706C2×C61#253711yescharacteristic
707D61—44no—
708D61—44no—
709C23×D4—611no—
710C23×D4—611no—
711C23×D4—611no—
712C24×C4—611no—
713C24×C4—611no—
714C24×C4—611no—
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—1224no—
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×#95C2×D6111yescharacteristic
752C2×#95C2×D6111yescharacteristic
753C2×#95C2×D6111yescharacteristic
754C2×#95C2×D6111yescharacteristic
755C61#1397011yescharacteristic, complemented, Sylow
756C25—611no—
757C25—611no—
758C25C22×D6111yescharacteristic
759C22×D4—614no—
760C22×D4—614no—
761C22×D4—614no—
762C22×D4—614no—
763C22×D4—614no—
764C22×D4—1222no—
765C22×D4—1222no—
766C22×D4—1222no—
767C22×D4—1222no—
768C22×D4—1222no—
769C22×D4—1222no—
770C22×D4—1222no—
771C22×D4—1222no—
772C22×D4—1222no—
773C22×D4—1222no—
774C22×D4—1222no—
775C22×D4—1222no—
776C22×D4—2441no—
777C22×D4—2441no—
778C22×D4—2441no—
779C22×D4—2441no—
780C23×C4—611no—
781C23×C4—611no—
782C23×C4—611no—
783C23×C4—611no—
784C23×C4—611no—
785C23×C4—614no—
786C23×C4—611no—
787C23×C4—1222no—
788C23×C4—1222no—
789C23×C4—1222no—
790C23×C4—1222no—
791C23×C4—1222no—
792C23×C4—1222no—
793C23×C4—1222no—
794C23×C4—1222no—
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
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—22no—
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—2441no—
855C2×C22⋊C4—2441no—
856C2×C22⋊C4—2441no—
857C2×C22⋊C4—2441no—
858C2×C22⋊C4—2441no—
859C2×C22⋊C4C4×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—22no—
869#95—41no—
870#95—1222no—
871#95—1222no—
872#95—1222no—
873#95—1222no—
874#95—1222no—
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—612no—
891C24—612no—
892C24—612no—
893C24—612no—
894C24—612no—
895C24—612no—
896C24—1221no—
897C24—1221no—
898C24—1221no—
899C24—1221no—
900C24—1221no—
901C24—1221no—
902C24—1221no—
903C24—1221no—
904C24—1221no—
905C24—1221no—
906C24—1221no—
907C24—1221no—
908C24—1221no—
909C24—1221no—
910C24—1221no—
911C24—1221no—
912C24—1221no—
913C24—1221no—
914C24—1221no—
915C24—1221no—
916C24—1221no—
917C24—1221no—
918C24—1221no—
919C24—1221no—
920C24C2×C4×D6112yes—
921C24D4×D6112yes—
922C24D4×D6112yes—
923C24C23×D6111yescharacteristic
924C2×D4—6116no—
925C2×D4—1228no—
926C2×D4—1228no—
927C2×D4—1228no—
928C2×D4—1228no—
929C2×D4—1228no—
930C2×D4—1228no—
931C2×D4—1228no—
932C2×D4—1228no—
933C2×D4—1228no—
934C2×D4—1228no—
935C2×D4—2444no—
936C2×D4—2444no—
937C2×D4—2444no—
938C2×D4—2444no—
939C2×D4—2444no—
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—21no—
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—21no—
976C22×C4—21no—
977C22×C4—21no—
978C22×C4—21no—
979C22×C4—21no—
980C22×C4—21no—
981C22×C4—21no—
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—612no—
994C22×C4—612no—
995C22×C4—1228no—
996C22×C4—1228no—
997C22×C4—1228no—
998C22×C4—1228no—
999C22×C4—1221no—
1000C22×C4—1221no—
1001C22×C4—1221no—
1002C22×C4—1221no—
1003C22×C4—1228no—
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—2444no—
1030C22×C4—2444no—
1031C22×C4—2444no—
1032C22×C4—2444no—
1033C22×C4—2444no—
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×C4—2444no—
1045C22×C4C2×C4×D6112yes—
1046C22×C4C2×C4×D6112yes—
1047C22×C4D4×D6112yes—
1048C22×C4D4×D6112yes—
1049C22×C4D4×D6112yes—
1050C4⋊C4—1228no—
1051C4⋊C4—1228no—
1052C4⋊C4—2444no—
1053C22⋊C4—28no—
1054C22⋊C4—28no—
1055C22⋊C4—44no—
1056C22⋊C4—1228no—
1057C22⋊C4—1228no—
1058C22⋊C4—1228no—
1059C22⋊C4—1228no—
1060C22⋊C4—2444no—
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—41no—
1086C23—41no—
1087C23—41no—
1088C23—41no—
1089C23—41no—
1090C23—41no—
1091C23—41no—
1092C23—41no—
1093C23—41no—
1094C23—41no—
1095C23—41no—
1096C23—41no—
1097C23—41no—
1098C23—41no—
1099C23—41no—
1100C23—41no—
1101C23—614no—
1102C23—614no—
1103C23—1222no—
1104C23—1222no—
1105C23—1222no—
1106C23—1222no—
1107C23—1222no—
1108C23—1222no—
1109C23—1222no—
1110C23—1222no—
1111C23—1222no—
1112C23—1222no—
1113C23—1222no—
1114C23—1222no—
1115C23—1222no—
1116C23—1222no—
1117C23—1222no—
1118C23—1222no—
1119C23—1222no—
1120C23—1222no—
1121C23—1222no—
1122C23—1222no—
1123C23—1222no—
1124C23—1222no—
1125C23—1222no—
1126C23—1222no—
1127C23—1222no—
1128C23—1222no—
1129C23—1222no—
1130C23—1222no—
1131C23—1222no—
1132C23—1222no—
1133C23—1222no—
1134C23—1222no—
1135C23—1222no—
1136C23—1222no—
1137C23—1222no—
1138C23—1222no—
1139C23—2441no—
1140C23—2441no—
1141C23—2441no—
1142C23—2441no—
1143C23—2441no—
1144C23—2441no—
1145C23—2441no—
1146C23—2441no—
1147C23—2441no—
1148C23—2441no—
1149C23—2441no—
1150C23—2441no—
1151C23—2441no—
1152C23—2441no—
1153C23—2441no—
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—
1170C23—2441no—
1171C23C22⋊C4×D6114yes—
1172C23C22×C4×D6111yescharacteristic
1173C23C2×D4×D6111yescharacteristic
1174C23C2×D4×D6111yescharacteristic
1175C23C2×D4×D6111yescharacteristic
1176C23C2×D4×D6111yescharacteristic
1177C23C2×D4×D6111yescharacteristic
1178C23#41×D6111yescharacteristic
1179C23#41×D6111yescharacteristic
1180C23#41×D6111yescharacteristic
1181C23#41×D6111yescharacteristic
1182C23#41×D6111yescharacteristic
1183C23#1451982211yescharacteristic
1184C23#1451982311yescharacteristic
1185C23#1451982311yescharacteristic
1186C23#1451982411yescharacteristic
1187D4—12232no—
1188D4—24416no—
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—41no—
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—41no—
1226C2×C4—41no—
1227C2×C4—41no—
1228C2×C4—41no—
1229C2×C4—41no—
1230C2×C4—41no—
1231C2×C4—41no—
1232C2×C4—614no—
1233C2×C4—614no—
1234C2×C4—614no—
1235C2×C4—614no—
1236C2×C4—614no—
1237C2×C4—614no—
1238C2×C4—614no—
1239C2×C4—614no—
1240C2×C4—1222no—
1241C2×C4—1222no—
1242C2×C4—1222no—
1243C2×C4—1222no—
1244C2×C4—1222no—
1245C2×C4—1222no—
1246C2×C4—1222no—
1247C2×C4—1222no—
1248C2×C4—1222no—
1249C2×C4—1222no—
1250C2×C4—1222no—
1251C2×C4—1222no—
1252C2×C4—1222no—
1253C2×C4—1222no—
1254C2×C4—1222no—
1255C2×C4—24416no—
1256C2×C4—24416no—
1257C2×C4—24416no—
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—2441no—
1277C22—24no—
1278C22—24no—
1279C22—24no—
1280C22—42no—
1281C22—42no—
1282C22—42no—
1283C22—42no—
1284C22—42no—
1285C22—42no—
1286C22—42no—
1287C22—42no—
1288C22—42no—
1289C22—42no—
1290C22—42no—
1291C22—42no—
1292C22—1224no—
1293C22—1224no—
1294C22—1224no—
1295C22—1224no—
1296C22—1224no—
1297C22—1224no—
1298C22—2442no—
1299C22—2442no—
1300C22—2442no—
1301C22—2442no—
1302C22—2442no—
1303C22—2442no—
1304C22—2442no—
1305C22—2442no—
1306C22—2442no—
1307C22—2442no—
1308C22—2442no—
1309C22—2442no—
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
1325C22C4×D4×D6111yescharacteristic
1326C22#1684023011yescharacteristic
1327C22#1684023411yescharacteristic
1328C22#1684024211yescharacteristic
1329C22#120×D6111yescharacteristic
1330C22#121×D6111yescharacteristic
1331C22#121×D6111yescharacteristic
1332C22#121×D6111yescharacteristic
1333C22#123×D6111yescharacteristic
1334C22#1684027011yescharacteristic
1335C22#1684029511yescharacteristic
1336C22#1684031111yescharacteristic
1337C22#1684033011yescharacteristic
1338C22#1684033911yescharacteristic
1339C22#1684036411yescharacteristic
1340C22#1684037811yescharacteristic
1341C22#1684039411yescharacteristic
1342C22#1684039611yescharacteristic
1343C22#1684039611yescharacteristic
1344C22#1684040111yescharacteristic
1345C22#1684040411yescharacteristic
1346C22#1684040411yescharacteristic
1347C22#1684040411yescharacteristic
1348C22#1684040411yescharacteristic
1349C22#1684041011yescharacteristic
1350C22#1684041011yescharacteristic
1351C22#1684041011yescharacteristic
1352C22#1684042011yescharacteristic
1353C22#1684043011yescharacteristic
1354C22#1684046311yescharacteristic
1355C22#1684046311yescharacteristic
1356C22#1684047411yescharacteristic
1357C4—42no—
1358C4—42no—
1359C4—42no—
1360C4—42no—
1361C4—42no—
1362C4—81no—
1363C4—618no—
1364C4—1224no—
1365C4—4881no—
1366C4—2442no—
1367C4—2442no—
1368C4—2442no—
1369C2—44no—
1370C2—2444no—
1371C2—2444no—
1372C2#386×D6111yescharacteristic
1373C2#2144833111yescharacteristic
1374C2#2144850711yescharacteristic
1375C2#2144863711yescharacteristic
1376C2#2144864311yescharacteristic
1377C2#2144883211yescharacteristic
1378C2#2144885211yescharacteristic
1379C2#2144915911yescharacteristic
1380C2#2144917011yescharacteristic
1381C2#2144930611yescharacteristic
1382C2#2144932811yescharacteristic
1383C2#2144939111yescharacteristic
1384C2#2144940211yescharacteristic
1385C2#2145071711yescharacteristic
1386C2#2145073111yescharacteristic
subgroupG/H
center, FrattiniC24C23×D61
commutatorC23×C61C23×C4
FittingC61×#1440C2
socle, cosocleC24×C61C24
prime radicalC22×#14519750C2
hypercenter#1440D61
hypocenterC61#13970
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C24 ◁ #1440

Complements

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

NH ≅ G/Ntype
2. C22×#14519737C2semidirect
3. C2×#16839662C2semidirect
4. C2×#16839640C2semidirect
5. C2×#16839639C2semidirect
6. C2×#16839621C2semidirect
7. C2×#16839609C2semidirect
8. #21444067C2semidirect
9. #21444059C2semidirect
10. #21444058C2semidirect
11. #21444047C2semidirect
12. #21444047C2semidirect
13. #21444041C2semidirect
14. #21444040C2semidirect
15. C61×#1440C2semidirect
24. C2×#14519750C4semidirect
70. C22×D244C2×C4semidirect
82. C22×C22⋊D61C2×C4semidirect
111. C22×C4×D61C2×C4semidirect
121. C2×#11758196C2×C4semidirect
122. C2×#11758196D4semidirect
148. C2×#11758198C2×C4semidirect
149. C2×#11758198D4semidirect
155. C2×C4×Dic61D4semidirect
179. C2×C22⋊C4×C61C2×C4semidirect
285. C2×C22⋊D61C22⋊C4semidirect
492. C22×D61C4×D4semidirect
578. C2×Dic61#121semidirect
675. Dic61#386semidirect
684. #1440D61semidirect
755. C61#13970semidirect
859. C2×C22⋊C4C4×D61semidirect

Maximal subgroups

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

subgroupindex
C22×#145197502
C22×#145197372
C2×#168396622
C2×#168396402
C2×#168396392
C2×#168396212
C2×#168396092
#214440672
#214440592
#214440582
#214440472
#214440412
#214440402
C61×#14402
#1397061