Finite Group Databasebeta

← #29603155

Subgroups — #29603155

Order 15616.

2682 conjugacy classes of subgroups.

The subgroup lattice has 1366 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519749C211yesmaximal, characteristic
2C2×#16839662C211yesmaximal, characteristic, complemented
3C2×#16839662C211yesmaximal, characteristic, complemented
4C2×#16839662C211yesmaximal, characteristic, complemented
5C2×#16839657C211yesmaximal, characteristic, complemented
6C2×#16839620C211yesmaximal, characteristic, complemented
7C2×C4×#11758196C211yesmaximal, characteristic, complemented
8C2×C22⋊C4×Dic61C211yesmaximal, characteristic, complemented
9#21444062C211yesmaximal, characteristic, complemented
10#21444061C211yesmaximal, characteristic, complemented
11#21444060C211yesmaximal, characteristic, complemented
12#21444058C211yesmaximal, characteristic, complemented
13#21444057C211yesmaximal, characteristic, complemented
14#21444056C211yesmaximal, characteristic, complemented
15C2×C61×#390C211yesmaximal, characteristic, complemented
16C23×C22⋊D61C2211yescharacteristic
17C23×C22⋊D61C2211yescharacteristic
18C24×Dic61C2211yescharacteristic
19C2×#14519749—24no—
20C2×#14519749—24no—
21C2×#14519749C418yescomplemented
22C22×#11758196C2211yescharacteristic
23C22×#11758196C2211yescharacteristic
24C22×#11758196C2211yescharacteristic
25C22×#11758196C2211yescharacteristic
26C22×C22⋊Dic61C2211yescharacteristic
27C22×C22⋊Dic61C2211yescharacteristic
28C22×C22⋊Dic61C2211yescharacteristic
29C22×C22⋊Dic61C2211yescharacteristic
30C22×C22⋊Dic61C2211yescharacteristic
31C22×#11758198C2211yescharacteristic
32C22×#11758198C2211yescharacteristic
33C22×#11758198C2211yescharacteristic
34C22×#11758198C2211yescharacteristic
35C22×#11758198C2211yescharacteristic
36C22×C4×Dic61C2211yescharacteristic
37C22×C4×Dic61C2211yescharacteristic
38C22×C4×Dic61C2211yescharacteristic
39#16839662—24no—
40#16839662—24no—
41#16839662—24no—
42#16839657—24no—
43#16839620—24no—
44C4×#11758196—24no—
45C22⋊C4×Dic61—24no—
46C2×#14519684C2211yescharacteristic
47C2×#14519684C2211yescharacteristic
48C2×#14519684C2211yescharacteristic
49C2×#14519684C2211yescharacteristic
50C2×#14519684C2211yescharacteristic
51C2×#14519684C2211yescharacteristic
52C2×#14519684C2211yescharacteristic
53C2×#14519684C2211yescharacteristic
54C23×D4×C61C2211yescharacteristic
55C22×C4⋊C4×C61C2211yescharacteristic
56C22×C22⋊C4×C61C2211yescharacteristic
57C22×C22⋊C4×C61C2211yescharacteristic
58C22×C22⋊C4×C61C2211yescharacteristic
59C22×C22⋊C4×C61C2211yescharacteristic
60C22×C42×C61C2211yescharacteristic
61C61×#390—24no—
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—22no—
72C22×C22⋊D61—22no—
73C22×C22⋊D61—41no—
74C22×C22⋊D61—41no—
75C22×C22⋊D61C2×C414yes—
76C22×C22⋊D61C2×C414yes—
77C23×Dic61—22no—
78C23×Dic61—22no—
79C23×Dic61—22no—
80C23×Dic61—22no—
81C23×Dic61—22no—
82C23×Dic61—22no—
83C23×Dic61C2×C414yes—
84C23×Dic61C2311yescharacteristic
85C23×Dic61C2311yescharacteristic
86C23×Dic61C2311yescharacteristic
87C23×Dic61C2311yescharacteristic
88C23×Dic61C2311yescharacteristic
89C23×Dic61C2311yescharacteristic
90C23×Dic61C2311yescharacteristic
91#14519749—232no—
92C2×#11758196—22no—
93C2×#11758196—22no—
94C2×#11758196—22no—
95C2×#11758196—22no—
96C2×#11758196—22no—
97C2×#11758196—22no—
98C2×#11758196—22no—
99C2×#11758196—41no—
100C2×#11758196C2×C414yes—
101C2×#11758196D414yes—
102C2×#11758196D414yes—
103C2×#11758196D414yescomplemented
104C2×C22⋊Dic61—22no—
105C2×C22⋊Dic61—22no—
106C2×C22⋊Dic61—22no—
107C2×C22⋊Dic61—22no—
108C2×C22⋊Dic61—22no—
109C2×C22⋊Dic61—22no—
110C2×C22⋊Dic61—22no—
111C2×C22⋊Dic61—22no—
112C2×C22⋊Dic61—22no—
113C2×C22⋊Dic61—22no—
114C2×C22⋊Dic61—41no—
115C2×C22⋊Dic61—41no—
116C2×C22⋊Dic61—41no—
117C2×C22⋊Dic61—41no—
118C2×C22⋊Dic61C2×C414yes—
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—41no—
130C2×#11758198—41no—
131C2×#11758198—41no—
132C2×#11758198—41no—
133C2×#11758198C2×C414yes—
134C2×C4×Dic61—22no—
135C2×C4×Dic61—22no—
136C2×C4×Dic61—22no—
137C2×C4×Dic61—22no—
138C2×C4×Dic61—22no—
139C2×C4×Dic61—22no—
140C2×C4×Dic61—22no—
141C2×C4×Dic61—41no—
142C2×C4×Dic61D414yescomplemented
143#14519684—22no—
144#14519684—22no—
145#14519684—22no—
146#14519684—22no—
147#14519684—22no—
148#14519684—22no—
149#14519684—22no—
150#14519684—22no—
151C25×C61C2311yescharacteristic
152C25×C61C2311yescharacteristic
153C22×D4×C61—22no—
154C22×D4×C61—22no—
155C22×D4×C61—22no—
156C22×D4×C61—22no—
157C22×D4×C61—41no—
158C22×D4×C61—41no—
159C22×D4×C61C2×C414yes—
160C23×C4×C61C2311yescharacteristic
161C23×C4×C61C2311yescharacteristic
162C23×C4×C61C2311yescharacteristic
163C23×C4×C61C2311yescharacteristic
164C23×C4×C61C2311yescharacteristic
165C2×C4⋊C4×C61—22no—
166C2×C4⋊C4×C61—22no—
167C2×C4⋊C4×C61—41no—
168C2×C22⋊C4×C61—22no—
169C2×C22⋊C4×C61—22no—
170C2×C22⋊C4×C61—22no—
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—41no—
178C2×C22⋊C4×C61—41no—
179C2×C22⋊C4×C61D414yescomplemented
180C2×C42×C61—22no—
181C2×C42×C61—22no—
182C2×C42×C61—41no—
183C24×C61—21no—
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×C61—21no—
209C24×C61C22×C412yes—
210C24×C61C22×C412yes—
211C24×C61C2×D412yes—
212C24×C61#4112yes—
213C24×C61C2411yescharacteristic
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×D61—21no—
225C23×D61—21no—
226C23×D61—21no—
227C23×D61—21no—
228C23×D61C22×C412yes—
229C2×D4×C61—28no—
230C2×D4×C61—28no—
231C2×D4×C61—44no—
232C2×D4×C61—44no—
233C2×D4×C61—44no—
234C2×D4×C61—44no—
235C2×D4×C61—44no—
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×C61C22×C412yes—
264C22×C4×C61C2×D412yes—
265C22×C4×C61C2×D412yes—
266C22×C4×C61C2×D412yes—
267C22×C4×C61C2×D412yes—
268C22×C4×C61C2×D412yes—
269C22×C4×C61C2×D412yes—
270C22×C4×C61#4112yes—
271C2×C22⋊D61—28no—
272C2×C22⋊D61—28no—
273C2×C22⋊D61—28no—
274C2×C22⋊D61—28no—
275C2×C22⋊D61—28no—
276C2×C22⋊D61—44no—
277C2×C22⋊D61—44no—
278C2×C22⋊D61—44no—
279C2×C22⋊D61—44no—
280C2×C22⋊D61—44no—
281C2×C22⋊D61—44no—
282C2×C22⋊D61—44no—
283C2×C22⋊D61—44no—
284C2×C22⋊D61—44no—
285C22×Dic61—21no—
286C22×Dic61—21no—
287C22×Dic61—21no—
288C22×Dic61—21no—
289C22×Dic61—21no—
290C22×Dic61—21no—
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—28no—
314C22×Dic61—28no—
315C22×Dic61—28no—
316C22×Dic61—21no—
317C22×Dic61—21no—
318C22×Dic61—21no—
319C22×Dic61—21no—
320C22×Dic61—21no—
321C22×Dic61—21no—
322C22×Dic61—21no—
323C22×Dic61—44no—
324C22×Dic61—44no—
325C22×Dic61—44no—
326C22×Dic61—44no—
327C22×Dic61C22×C412yes—
328C22×Dic61C22×C412yes—
329C22×Dic61C22×C412yes—
330C22×Dic61C2×D412yes—
331C22×Dic61C2×D412yes—
332C22×Dic61C2×D412yes—
333C22×Dic61C2×D412yes—
334C22×Dic61C2×D412yes—
335C22×Dic61C2×D412yes—
336C22×Dic61C2×D412yes—
337C22×Dic61C2×D412yes—
338C22×Dic61#4112yes—
339C22×Dic61#4112yes—
340C22×Dic61#4112yes—
341C4⋊C4×C61—44no—
342C22⋊C4×C61—28no—
343C22⋊C4×C61—44no—
344C22⋊C4×C61—44no—
345C22⋊C4×C61—44no—
346C42×C61—44no—
347C22⋊Dic61—28no—
348C22⋊Dic61—28no—
349C22⋊Dic61—44no—
350C22⋊Dic61—44no—
351C22⋊Dic61—44no—
352#11758198—28no—
353#11758198—44no—
354#11758198—44no—
355#11758198—44no—
356#11758198—44no—
357#11758196—28no—
358#11758196—44no—
359#11758196—44no—
360#11758196C22⋊C4116yescomplemented
361C4×Dic61—28no—
362C4×Dic61—44no—
363C4×Dic61—44no—
364C23×C61—22no—
365C23×C61—22no—
366C23×C61—22no—
367C23×C61—22no—
368C23×C61—22no—
369C23×C61—22no—
370C23×C61—22no—
371C23×C61—22no—
372C23×C61—22no—
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—41no—
390C23×C61—41no—
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×C61—41no—
408C23×C61—41no—
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×C61C4×D414yes—
434C23×C61C23×C411yescharacteristic
435C23×C61C22×D411yescharacteristic
436C23×C61C22×D411yescharacteristic
437C23×C61C22×D411yescharacteristic
438C23×C61C22×D411yescharacteristic
439C23×C61C22×D411yescharacteristic
440C23×C61C2×#4111yescharacteristic
441C23×C61C2×#4111yescharacteristic
442C23×C61C2×#4111yescharacteristic
443C23×C61C2×#4111yescharacteristic
444C23×C61C2×#4111yescharacteristic
445C23×C61H(5,𝔽2)11yescharacteristic
446C23×C61H(5,𝔽2)11yescharacteristic
447C23×C61H(5,𝔽2)11yescharacteristic
448C23×C612−1+411yescharacteristic
449C22×D61—22no—
450C22×D61—22no—
451C22×D61—22no—
452C22×D61—22no—
453C22×D61—22no—
454C22×D61—22no—
455C22×D61—22no—
456C22×D61—41no—
457C22×D61—41no—
458C22×D61—41no—
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—
484D4×C61—416no—
485C2×C4×C61—22no—
486C2×C4×C61—22no—
487C2×C4×C61—22no—
488C2×C4×C61—22no—
489C2×C4×C61—22no—
490C2×C4×C61—22no—
491C2×C4×C61—22no—
492C2×C4×C61—22no—
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—41no—
504C2×C4×C61—41no—
505C2×C4×C61—41no—
506C2×C4×C61—41no—
507C2×C4×C61—41no—
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×C61C2×C22⋊C414yes—
519C2×C4×C61#12114yescomplemented
520C22⋊D61—416no—
521C22⋊D61—416no—
522C2×Dic61—22no—
523C2×Dic61—22no—
524C2×Dic61—22no—
525C2×Dic61—22no—
526C2×Dic61—22no—
527C2×Dic61—22no—
528C2×Dic61—22no—
529C2×Dic61—22no—
530C2×Dic61—22no—
531C2×Dic61—22no—
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—41no—
541C2×Dic61—41no—
542C2×Dic61—41no—
543C2×Dic61—41no—
544C2×Dic61—41no—
545C2×Dic61—41no—
546C2×Dic61—41no—
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—416no—
557C2×Dic61—41no—
558C2×Dic61—41no—
559C2×Dic61—41no—
560C2×Dic61—41no—
561C2×Dic61—41no—
562C2×Dic61—41no—
563C2×Dic61—41no—
564C2×Dic61C2×C22⋊C414yes—
565C2×Dic61C2×C22⋊C414yes—
566C2×Dic61C4×D414yes—
567C2×Dic61C4×D414yes—
568C2×Dic61#12114yes—
569C2×Dic61#12114yes—
570C2×Dic61#12414yes—
571C2×Dic61#12714yes—
572#13998—611nomaximal, Sylow
573C22×C61—24no—
574C22×C61—24no—
575C22×C61—24no—
576C22×C61—42no—
577C22×C61—42no—
578C22×C61—42no—
579C22×C61—42no—
580C22×C61—42no—
581C22×C61—42no—
582C22×C61—42no—
583C22×C61—42no—
584C22×C61—42no—
585C22×C61—42no—
586C22×C61—42no—
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—81no—
596C22×C61—81no—
597C22×C61—81no—
598C22×C61—81no—
599C22×C61—81no—
600C22×C61—81no—
601C22×C61—81no—
602C22×C61—81no—
603C22×C61C22×C22⋊C411yescharacteristic
604C22×C61C2×C4×D411yescharacteristic
605C22×C61C2×C4×D411yescharacteristic
606C22×C61C2×C4×D411yescharacteristic
607C22×C61C4×#4111yescharacteristic
608C22×C61#51811yescharacteristic
609C22×C61#52011yescharacteristic
610C22×C61C2×#12111yescharacteristic
611C22×C61C2×#12111yescharacteristic
612C22×C61C2×#12111yescharacteristic
613C22×C61#52511yescharacteristic
614C22×C61C2×#12411yescharacteristic
615C22×C61#52911yescharacteristic
616C22×C61C2×#12711yescharacteristic
617C22×C61#53211yescharacteristic
618C22×C61#53511yescharacteristic
619C22×C61#53711yescharacteristic
620C22×C61#54011yescharacteristic
621C22×C61#54211yescharacteristic
622C22×C61D4211yescharacteristic
623C22×C61D4211yescharacteristic
624C22×C61D4211yescharacteristic
625C22×C61#54611yescharacteristic
626C22×C61#54611yescharacteristic
627C22×C61#54611yescharacteristic
628C22×C61#54711yescharacteristic
629C22×C61#54811yescharacteristic
630C22×C61#54811yescharacteristic
631C22×C61#54811yescharacteristic
632C22×C61#55011yescharacteristic
633C22×C61#55011yescharacteristic
634C22×C61#55011yescharacteristic
635C22×C61#55311yescharacteristic
636C22×C61#55311yescharacteristic
637C22×C61#55511yescharacteristic
638C2×D61—42no—
639C2×D61—42no—
640C2×D61—42no—
641C2×D61—42no—
642C2×D61—42no—
643C2×D61—42no—
644C2×D61—42no—
645C2×D61—81no—
646C2×D61—81no—
647C2×D61—81no—
648C2×D61—81no—
649C2×D61—81no—
650C2×D61—81no—
651C2×D61—81no—
652C2×D61—81no—
653C4×C61—24no—
654C4×C61—24no—
655C4×C61—42no—
656C4×C61—42no—
657C4×C61—81no—
658Dic61—24no—
659Dic61—42no—
660Dic61—42no—
661Dic61—42no—
662Dic61—42no—
663Dic61—81no—
664Dic61#39018yescomplemented
665C22×#121—611no—
666C2×#390—611no—
667C2×#390—611no—
668C2×#390—611no—
669C2×#390D6111yescharacteristic, complemented
670C2×#389—611no—
671C2×#380—611no—
672C2×C4×C4⋊C4—611no—
673C2×C4×C22⋊C4—611no—
674#1439—611no—
675#1439—611no—
676#1438—611no—
677#1438—611no—
678#1437—611no—
679#1437—611no—
680C2×C61—44no—
681C2×C61—82no—
682C2×C61C2×#39011yescharacteristic
683C2×C61C4×#12111yescharacteristic
684C2×C61#232411yescharacteristic
685C2×C61D4×C22⋊C411yescharacteristic
686C2×C61#234111yescharacteristic
687C2×C61#236111yescharacteristic
688C2×C61#236311yescharacteristic
689C2×C61#241411yescharacteristic
690C2×C61#241611yescharacteristic
691C2×C61#242611yescharacteristic
692C2×C61#242811yescharacteristic
693C2×C61#249011yescharacteristic
694C2×C61#249111yescharacteristic
695C2×C61#254011yescharacteristic
696C2×C61#254111yescharacteristic
697D61—82no—
698C23×D4—611no—
699C23×D4—611no—
700C23×D4C2×D6111yescharacteristic
701C24×C4—611no—
702C2×#121—618no—
703C2×#121—1224no—
704C2×#121—1224no—
705C22×C4⋊C4—611no—
706C22×C4⋊C4—611no—
707C22×C4⋊C4—611no—
708C22×C4⋊C4—611no—
709C22×C4⋊C4C2×D6111yescharacteristic
710C22×C22⋊C4—611no—
711C22×C22⋊C4—611no—
712C22×C22⋊C4—611no—
713C22×C22⋊C4—611no—
714C22×C22⋊C4—611no—
715C22×C22⋊C4—611no—
716C22×C22⋊C4—611no—
717C22×C22⋊C4—611no—
718C22×C22⋊C4—611no—
719C22×C22⋊C4—611no—
720C22×C22⋊C4C2×D6111yescharacteristic
721C22×C22⋊C4C2×D6111yescharacteristic
722C22×C22⋊C4C2×D6111yescharacteristic
723C22×C22⋊C4C2×D6111yescharacteristic
724C22×C42—611no—
725C22×C42—611no—
726C22×C42—611no—
727C22×C42C2×D6111yescharacteristic
728#390—24no—
729#390—1224no—
730#390—1224no—
731#390—1224no—
732#389—1224no—
733#380—1224no—
734C4×C4⋊C4—1224no—
735C4×C22⋊C4—1224no—
736C2×#95—611no—
737C2×#95—611no—
738C2×#95—611no—
739C2×#95—611no—
740C2×#95—611no—
741C2×#95—611no—
742C2×#95—611no—
743C2×#95—611no—
744C61#1399811yescharacteristic, complemented, Sylow
745C25—611no—
746C25C22×D6111yescharacteristic
747C25C22×D6111yescharacteristic
748C22×D4—22no—
749C22×D4—22no—
750C22×D4—22no—
751C22×D4—22no—
752C22×D4—41no—
753C22×D4—41no—
754C22×D4—614no—
755C22×D4—614no—
756C22×D4—1222no—
757C22×D4—1222no—
758C22×D4—1222no—
759C22×D4—1222no—
760C22×D4—1222no—
761C22×D4—1222no—
762C22×D4—1222no—
763C22×D4—1222no—
764C22×D4—1222no—
765C22×D4—1222no—
766C22×D4—2441no—
767C22×D4—2441no—
768C22×D4C4×D6114yes—
769C23×C4—611no—
770C23×C4—611no—
771C23×C4—614no—
772C23×C4—611no—
773C23×C4—611no—
774C23×C4—611no—
775C23×C4—611no—
776C23×C4—611no—
777C23×C4—1222no—
778C23×C4—1222no—
779C23×C4—1222no—
780C23×C4—1222no—
781C23×C4—1222no—
782C23×C4—1222no—
783C23×C4C22×D6111yescharacteristic
784C23×C4C22×D6111yescharacteristic
785C23×C4C22×D6111yescharacteristic
786C23×C4C22×D6111yescharacteristic
787C23×C4C22×D6111yescharacteristic
788#121—12232no—
789C2×C4⋊C4—22no—
790C2×C4⋊C4—22no—
791C2×C4⋊C4—41no—
792C2×C4⋊C4—614no—
793C2×C4⋊C4—614no—
794C2×C4⋊C4—614no—
795C2×C4⋊C4—614no—
796C2×C4⋊C4—1222no—
797C2×C4⋊C4—1222no—
798C2×C4⋊C4—1222no—
799C2×C4⋊C4—1222no—
800C2×C4⋊C4—1222no—
801C2×C4⋊C4—1222no—
802C2×C4⋊C4—1222no—
803C2×C4⋊C4—2441no—
804C2×C22⋊C4—22no—
805C2×C22⋊C4—22no—
806C2×C22⋊C4—22no—
807C2×C22⋊C4—22no—
808C2×C22⋊C4—22no—
809C2×C22⋊C4—22no—
810C2×C22⋊C4—22no—
811C2×C22⋊C4—22no—
812C2×C22⋊C4—22no—
813C2×C22⋊C4—41no—
814C2×C22⋊C4—41no—
815C2×C22⋊C4—614no—
816C2×C22⋊C4—614no—
817C2×C22⋊C4—1222no—
818C2×C22⋊C4—1222no—
819C2×C22⋊C4—1222no—
820C2×C22⋊C4—1222no—
821C2×C22⋊C4—1222no—
822C2×C22⋊C4—1222no—
823C2×C22⋊C4—1222no—
824C2×C22⋊C4—1222no—
825C2×C22⋊C4—1222no—
826C2×C22⋊C4—1222no—
827C2×C22⋊C4—1222no—
828C2×C22⋊C4—1222no—
829C2×C22⋊C4—1222no—
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—2441no—
838C2×C22⋊C4—2441no—
839C2×C22⋊C4—2441no—
840C2×C22⋊C4—2441no—
841C2×C22⋊C4—2441no—
842C2×C22⋊C4—2441no—
843C2×C22⋊C4—2441no—
844C2×C22⋊C4—2441no—
845C2×C22⋊C4C22⋊D6114yescomplemented
846C2×C42—22no—
847C2×C42—22no—
848C2×C42—41no—
849C2×C42—614no—
850C2×C42—1222no—
851C2×C42—1222no—
852C2×C42—1222no—
853C2×C42—1222no—
854C2×C42—1222no—
855C2×C42—1222no—
856C2×C42—1222no—
857C2×C42—2441no—
858#95—1222no—
859#95—1222no—
860#95—1222no—
861#95—1222no—
862#95—1222no—
863#95—1222no—
864#95—1222no—
865#95—1222no—
866C24—21no—
867C24—21no—
868C24—21no—
869C24—21no—
870C24—21no—
871C24—21no—
872C24—21no—
873C24—21no—
874C24—21no—
875C24—21no—
876C24—21no—
877C24—21no—
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—612no—
893C24—1221no—
894C24—1221no—
895C24—1221no—
896C24—1221no—
897C24—1221no—
898C24—1221no—
899C24—1221no—
900C24—1221no—
901C24—1221no—
902C24—1221no—
903C24—1221no—
904C24—1221no—
905C24—1221no—
906C24—1221no—
907C24C2×C4×D6112yes—
908C24C2×C4×D6112yes—
909C24#1175822212yes—
910C24C2×C22⋊D6112yes—
911C24C23×D6111yescharacteristic
912C2×D4—28no—
913C2×D4—28no—
914C2×D4—44no—
915C2×D4—44no—
916C2×D4—44no—
917C2×D4—44no—
918C2×D4—44no—
919C2×D4—1228no—
920C2×D4—1228no—
921C2×D4—1228no—
922C2×D4—1228no—
923C2×D4—1228no—
924C2×D4—2444no—
925C2×D4—2444no—
926C2×D4—2444no—
927C2×D4—2444no—
928C2×D4—2444no—
929C2×D4—2444no—
930C2×D4—2444no—
931C2×D4—2444no—
932C2×D4—2444no—
933C22×C4—21no—
934C22×C4—21no—
935C22×C4—21no—
936C22×C4—21no—
937C22×C4—21no—
938C22×C4—21no—
939C22×C4—21no—
940C22×C4—21no—
941C22×C4—21no—
942C22×C4—21no—
943C22×C4—21no—
944C22×C4—21no—
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—612no—
961C22×C4—612no—
962C22×C4—612no—
963C22×C4—612no—
964C22×C4—612no—
965C22×C4—612no—
966C22×C4—612no—
967C22×C4—612no—
968C22×C4—612no—
969C22×C4—612no—
970C22×C4—612no—
971C22×C4—612no—
972C22×C4—612no—
973C22×C4—612no—
974C22×C4—1228no—
975C22×C4—1228no—
976C22×C4—1228no—
977C22×C4—1221no—
978C22×C4—1221no—
979C22×C4—1221no—
980C22×C4—1221no—
981C22×C4—1221no—
982C22×C4—1221no—
983C22×C4—1221no—
984C22×C4—1221no—
985C22×C4—1221no—
986C22×C4—1221no—
987C22×C4—1221no—
988C22×C4—1221no—
989C22×C4—1221no—
990C22×C4—1221no—
991C22×C4—1221no—
992C22×C4—1221no—
993C22×C4—1221no—
994C22×C4—1221no—
995C22×C4—1221no—
996C22×C4—1221no—
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—2444no—
1013C22×C4—2444no—
1014C22×C4—2444no—
1015C22×C4—2444no—
1016C22×C4C2×C4×D6112yes—
1017C22×C4D4×D6112yes—
1018C22×C4D4×D6112yes—
1019C22×C4D4×D6112yes—
1020C22×C4D4×D6112yes—
1021C22×C4#1175822412yes—
1022C22×C4C2×C22⋊D6112yes—
1023C22×C4C2×C22⋊D6112yes—
1024C4⋊C4—44no—
1025C4⋊C4—6116no—
1026C4⋊C4—1228no—
1027C4⋊C4—2444no—
1028C4⋊C4—2444no—
1029C22⋊C4—28no—
1030C22⋊C4—44no—
1031C22⋊C4—44no—
1032C22⋊C4—44no—
1033C22⋊C4—1228no—
1034C22⋊C4—1228no—
1035C22⋊C4—1228no—
1036C22⋊C4—2444no—
1037C22⋊C4—2444no—
1038C22⋊C4—2444no—
1039C22⋊C4—2444no—
1040C22⋊C4—2444no—
1041C22⋊C4—2444no—
1042C22⋊C4—2444no—
1043C42—44no—
1044C42—1228no—
1045C42—2444no—
1046C42—2444no—
1047C23—22no—
1048C23—22no—
1049C23—22no—
1050C23—22no—
1051C23—22no—
1052C23—22no—
1053C23—22no—
1054C23—22no—
1055C23—22no—
1056C23—22no—
1057C23—22no—
1058C23—22no—
1059C23—22no—
1060C23—22no—
1061C23—22no—
1062C23—22no—
1063C23—22no—
1064C23—22no—
1065C23—22no—
1066C23—22no—
1067C23—22no—
1068C23—22no—
1069C23—22no—
1070C23—22no—
1071C23—22no—
1072C23—41no—
1073C23—41no—
1074C23—41no—
1075C23—41no—
1076C23—41no—
1077C23—41no—
1078C23—41no—
1079C23—41no—
1080C23—41no—
1081C23—41no—
1082C23—41no—
1083C23—41no—
1084C23—41no—
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—41no—
1102C23—41no—
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—1222no—
1117C23—1222no—
1118C23—1222no—
1119C23—1222no—
1120C23—1222no—
1121C23—1222no—
1122C23—1222no—
1123C23—2441no—
1124C23—2441no—
1125C23—2441no—
1126C23—2441no—
1127C23—2441no—
1128C23—2441no—
1129C23—2441no—
1130C23—2441no—
1131C23—2441no—
1132C23—2441no—
1133C23—2441no—
1134C23—2441no—
1135C23—2441no—
1136C23—2441no—
1137C23—2441no—
1138C23—2441no—
1139C23—2441no—
1140C23—2441no—
1141C23—2441no—
1142C23—2441no—
1143C23—2441no—
1144C23—2441no—
1145C23—2441no—
1146C23—2441no—
1147C23—2441no—
1148C23—2441no—
1149C23—2441no—
1150C23—2441no—
1151C23C4×C22⋊D6114yes—
1152C23C22×C4×D6111yescharacteristic
1153C23C2×D4×D6111yescharacteristic
1154C23C2×D4×D6111yescharacteristic
1155C23C2×D4×D6111yescharacteristic
1156C23C2×D4×D6111yescharacteristic
1157C23C22×C22⋊D6111yescharacteristic
1158C23#41×D6111yescharacteristic
1159C23#41×D6111yescharacteristic
1160C23#41×D6111yescharacteristic
1161C23C2×#1175822411yescharacteristic
1162C23C2×#1175822211yescharacteristic
1163C23#1451982211yescharacteristic
1164C23#1451982211yescharacteristic
1165C23#1451982211yescharacteristic
1166C23#1451982411yescharacteristic
1167D4—416no—
1168D4—24416no—
1169D4—24416no—
1170C2×C4—22no—
1171C2×C4—22no—
1172C2×C4—22no—
1173C2×C4—22no—
1174C2×C4—22no—
1175C2×C4—22no—
1176C2×C4—22no—
1177C2×C4—22no—
1178C2×C4—22no—
1179C2×C4—22no—
1180C2×C4—22no—
1181C2×C4—22no—
1182C2×C4—22no—
1183C2×C4—22no—
1184C2×C4—22no—
1185C2×C4—22no—
1186C2×C4—22no—
1187C2×C4—22no—
1188C2×C4—41no—
1189C2×C4—41no—
1190C2×C4—41no—
1191C2×C4—41no—
1192C2×C4—41no—
1193C2×C4—41no—
1194C2×C4—41no—
1195C2×C4—41no—
1196C2×C4—41no—
1197C2×C4—41no—
1198C2×C4—41no—
1199C2×C4—41no—
1200C2×C4—41no—
1201C2×C4—41no—
1202C2×C4—41no—
1203C2×C4—614no—
1204C2×C4—614no—
1205C2×C4—614no—
1206C2×C4—614no—
1207C2×C4—614no—
1208C2×C4—614no—
1209C2×C4—614no—
1210C2×C4—614no—
1211C2×C4—1222no—
1212C2×C4—1222no—
1213C2×C4—1222no—
1214C2×C4—1222no—
1215C2×C4—1222no—
1216C2×C4—1222no—
1217C2×C4—1222no—
1218C2×C4—1222no—
1219C2×C4—1222no—
1220C2×C4—1222no—
1221C2×C4—1222no—
1222C2×C4—1222no—
1223C2×C4—1222no—
1224C2×C4—1222no—
1225C2×C4—1222no—
1226C2×C4—1222no—
1227C2×C4—1222no—
1228C2×C4—1222no—
1229C2×C4—24416no—
1230C2×C4—2441no—
1231C2×C4—2441no—
1232C2×C4—2441no—
1233C2×C4—2441no—
1234C2×C4—2441no—
1235C2×C4—2441no—
1236C2×C4—2441no—
1237C2×C4—2441no—
1238C2×C4—2441no—
1239C2×C4—2441no—
1240C2×C4—2441no—
1241C2×C4—2441no—
1242C2×C4—2441no—
1243C2×C4—2441no—
1244C2×C4—2441no—
1245C2×C4—2441no—
1246C2×C4—2441no—
1247C2×C4—2441no—
1248C2×C4—2441no—
1249C2×C4—2441no—
1250C2×C4—2441no—
1251C2×C4—2441no—
1252C2×C4—2441no—
1253C2×C4C22⋊C4×D6114yes—
1254C2×C4#1451974914yescomplemented
1255C22—24no—
1256C22—24no—
1257C22—24no—
1258C22—42no—
1259C22—42no—
1260C22—42no—
1261C22—42no—
1262C22—42no—
1263C22—42no—
1264C22—42no—
1265C22—42no—
1266C22—42no—
1267C22—42no—
1268C22—42no—
1269C22—42no—
1270C22—42no—
1271C22—42no—
1272C22—42no—
1273C22—42no—
1274C22—42no—
1275C22—42no—
1276C22—42no—
1277C22—81no—
1278C22—81no—
1279C22—81no—
1280C22—81no—
1281C22—81no—
1282C22—81no—
1283C22—81no—
1284C22—81no—
1285C22—4881no—
1286C22—4881no—
1287C22—4881no—
1288C22—4881no—
1289C22—4881no—
1290C22—4881no—
1291C22—4881no—
1292C22—4881no—
1293C22—2442no—
1294C22—2442no—
1295C22—2442no—
1296C22—2442no—
1297C22—2442no—
1298C22—2442no—
1299C22—2442no—
1300C22C2×C22⋊C4×D6111yescharacteristic
1301C22C4×D4×D6111yescharacteristic
1302C22C4×D4×D6111yescharacteristic
1303C22C2×C4×C22⋊D6111yescharacteristic
1304C22C4×#1175822411yescharacteristic
1305C22#1684023511yescharacteristic
1306C22#1684024111yescharacteristic
1307C22#121×D6111yescharacteristic
1308C22#121×D6111yescharacteristic
1309C22C2×#1451974911yescharacteristic
1310C22#1684027111yescharacteristic
1311C22#124×D6111yescharacteristic
1312C22#1684029211yescharacteristic
1313C22#127×D6111yescharacteristic
1314C22#1684030811yescharacteristic
1315C22#1684032511yescharacteristic
1316C22#1684033911yescharacteristic
1317C22#1684036211yescharacteristic
1318C22#1684037611yescharacteristic
1319C22D4×C22⋊D6111yescharacteristic
1320C22D4×C22⋊D6111yescharacteristic
1321C22D4×C22⋊D6111yescharacteristic
1322C22#1684040111yescharacteristic
1323C22#1684040211yescharacteristic
1324C22#1684040211yescharacteristic
1325C22#1684041111yescharacteristic
1326C22#1684041811yescharacteristic
1327C22#1684042011yescharacteristic
1328C22#1684042111yescharacteristic
1329C22#1684043011yescharacteristic
1330C22#1684043211yescharacteristic
1331C22#1684043211yescharacteristic
1332C22#1684045511yescharacteristic
1333C22#1684046111yescharacteristic
1334C22#1684047411yescharacteristic
1335C4—24no—
1336C4—24no—
1337C4—42no—
1338C4—42no—
1339C4—81no—
1340C4—618no—
1341C4—1224no—
1342C4—4881no—
1343C4—2442no—
1344C4—2442no—
1345C4—2442no—
1346C4—2442no—
1347C2—44no—
1348C2—82no—
1349C2—4882no—
1350C2#390×D6111yescharacteristic
1351C2C4×#1451974911yescharacteristic
1352C2#2144850511yescharacteristic
1353C2C22⋊C4×C22⋊D6111yescharacteristic
1354C2#2144865811yescharacteristic
1355C2#2144883611yescharacteristic
1356C2#2144885411yescharacteristic
1357C2#2144923411yescharacteristic
1358C2#2144925611yescharacteristic
1359C2#2144938211yescharacteristic
1360C2#2144940411yescharacteristic
1361C2#2145016811yescharacteristic
1362C2#2145017911yescharacteristic
1363C2#2145075611yescharacteristic
1364C2#2145076311yescharacteristic
subgroupG/H
center, FrattiniC24C23×D61
commutatorC23×C61C23×C4
FittingC2×C61×#390C2
socle, cosocleC24×C61C24
prime radicalC22×#14519749C2
hypercenterC2×#390D61
hypocenterC61#13998
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C24 ◁ C2×#390

Complements

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

NH ≅ G/Ntype
2. C2×#16839662C2semidirect
3. C2×#16839662C2semidirect
4. C2×#16839662C2semidirect
5. C2×#16839657C2semidirect
6. C2×#16839620C2semidirect
7. C2×C4×#11758196C2semidirect
8. C2×C22⋊C4×Dic61C2semidirect
9. #21444062C2semidirect
10. #21444061C2semidirect
11. #21444060C2semidirect
12. #21444058C2semidirect
13. #21444057C2semidirect
14. #21444056C2semidirect
15. C2×C61×#390C2semidirect
21. C2×#14519749C4semidirect
103. C2×#11758196D4semidirect
142. C2×C4×Dic61D4semidirect
179. C2×C22⋊C4×C61D4semidirect
360. #11758196C22⋊C4semidirect
519. C2×C4×C61#121semidirect
664. Dic61#390semidirect
669. C2×#390D61semidirect
744. C61#13998semidirect
845. C2×C22⋊C4C22⋊D61semidirect
1254. 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
C2×#168396622
C2×#168396572
C2×#168396202
C2×C4×#117581962
C2×C22⋊C4×Dic612
#214440622
#214440612
#214440602
#214440582
#214440572
#214440562
C2×C61×#3902
#1399861