Finite Group Databasebeta

← #29603464

Subgroups — #29603464

Order 15616.

3166 conjugacy classes of subgroups.

The subgroup lattice has 1398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519750C211yesmaximal, characteristic
2C22×C4×C22⋊D61C211yesmaximal, characteristic, complemented
3C2×#16839641C211yesmaximal, characteristic, complemented
4C2×#16839640C211yesmaximal, characteristic, complemented
5C2×#16839640C211yesmaximal, characteristic, complemented
6C2×#16839638C211yesmaximal, characteristic, complemented
7C2×#95×D61C211yesmaximal, characteristic, complemented
8#21444070C211yesmaximal, characteristic, complemented
9#21444068C211yesmaximal, characteristic, complemented
10#21444063C211yesmaximal, characteristic, complemented
11#21444058C211yesmaximal, characteristic, complemented
12#21444055C211yesmaximal, characteristic, complemented
13#21444050C211yesmaximal, characteristic, complemented
14#21444040C211yesmaximal, characteristic, complemented
15C61×C22⋊#95C211yesmaximal, characteristic, complemented
16C23×D244C2211yescharacteristic
17C23×C22⋊D61C2211yescharacteristic
18C23×C22⋊D61C2211yescharacteristic
19C23×C4×D61C2211yescharacteristic
20C23×C4×D61C2211yescharacteristic
21C23×C4×D61C2211yescharacteristic
22C2×#14519750—24no—
23C2×#14519750—24no—
24C2×#14519750C418yescomplemented
25C2×C4×C22⋊D61—24no—
26C2×C4×C22⋊D61—24no—
27C2×C4×C22⋊D61—24no—
28C22×#11758196C2211yescharacteristic
29C22×#11758196C2211yescharacteristic
30C22×C22⋊Dic61C2211yescharacteristic
31C22×C22⋊Dic61C2211yescharacteristic
32C22×#11758198C2211yescharacteristic
33C22×#11758198C2211yescharacteristic
34C22×#11758198C2211yescharacteristic
35C22×#11758198C2211yescharacteristic
36C22×#11758198C2211yescharacteristic
37C22×#11758198C2211yescharacteristic
38C22×#11758198C2211yescharacteristic
39C22×C4×Dic61C2211yescharacteristic
40#16839641—24no—
41#16839640—24no—
42#16839640—24no—
43#16839638—24no—
44C2×#14519684C2211yescharacteristic
45C2×#14519684C2211yescharacteristic
46C2×#14519684C2211yescharacteristic
47C2×#14519684C2211yescharacteristic
48C2×#14519684C2211yescharacteristic
49C2×#14519684C2211yescharacteristic
50C2×#14519684C2211yescharacteristic
51C2×#14519684C2211yescharacteristic
52C2×#14519684C2211yescharacteristic
53C2×#14519684C2211yescharacteristic
54#95×D61—24no—
55C24×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—22no—
69C22×D244—22no—
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×Dic61C2311yescharacteristic
86C23×Dic61C2311yescharacteristic
87C23×Dic61C2311yescharacteristic
88C23×Dic61C2311yescharacteristic
89C23×Dic61C2311yescharacteristic
90C23×Dic61C2311yescharacteristic
91C22×C4×D61—22no—
92C22×C4×D61—22no—
93C22×C4×D61—22no—
94C22×C4×D61—22no—
95C22×C4×D61—22no—
96C22×C4×D61—22no—
97C22×C4×D61—22no—
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—41no—
105C22×C4×D61—41no—
106C22×C4×D61—41no—
107C22×C4×D61—41no—
108C22×C4×D61—41no—
109C22×C4×D61—41no—
110C22×C4×D61C2×C414yescomplemented
111C22×C4×D61D414yescomplemented
112#14519750—232no—
113C4×C22⋊D61—232no—
114C2×#11758196—22no—
115C2×#11758196—22no—
116C2×#11758196—22no—
117C2×#11758196—22no—
118C2×#11758196—22no—
119C2×#11758196C2×C414yescomplemented
120C2×C22⋊Dic61—22no—
121C2×C22⋊Dic61—22no—
122C2×C22⋊Dic61—22no—
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—41no—
142C2×#11758198—41no—
143C2×#11758198—41no—
144C2×#11758198—41no—
145C2×#11758198C2×C414yescomplemented
146C2×#11758198D414yescomplemented
147C2×C4×Dic61—22no—
148C2×C4×Dic61—22no—
149C2×C4×Dic61—22no—
150#14519684—22no—
151#14519684—22no—
152#14519684—22no—
153#14519684—22no—
154#14519684—22no—
155#14519684—22no—
156#14519684—22no—
157#14519684—22no—
158#14519684—41no—
159#14519684D414yescomplemented
160C25×C61C2311yescharacteristic
161C23×C4×C61—22no—
162C23×C4×C61—22no—
163C23×C4×C61—22no—
164C23×C4×C61—22no—
165C23×C4×C61—22no—
166C23×C4×C61—41no—
167C23×C4×C61—41no—
168C23×C4×C61C2311yescharacteristic
169C23×C4×C61C2311yescharacteristic
170C23×C4×C61C2311yescharacteristic
171C23×C4×C61C2311yescharacteristic
172C23×C4×C61C2311yescharacteristic
173C23×C4×C61C2311yescharacteristic
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×D61C22×C412yes—
223C23×D61C22×C412yes—
224C23×D61C2×D412yes—
225C23×D61C2×D412yes—
226C23×D61C2×D412yes—
227C23×D61C2×D412yes—
228C23×D61#4112yes—
229C23×D61#4112yes—
230C22×C4×C61—21no—
231C22×C4×C61—21no—
232C22×C4×C61—21no—
233C22×C4×C61—21no—
234C22×C4×C61—28no—
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—44no—
267C22×C4×C61—44no—
268C22×C4×C61—44no—
269C22×C4×C61—44no—
270C22×C4×C61—44no—
271C22×C4×C61—44no—
272C22×C4×C61C22×C412yes—
273C22×C4×C61C22×C412yes—
274C22×C4×C61C2×D412yes—
275C22×C4×C61C2×D412yes—
276C22×C4×C61C2×D412yes—
277C22×C4×C61#4112yes—
278C22×C4×C61#4112yes—
279C2×C22⋊D61—28no—
280C2×C22⋊D61—28no—
281C2×C22⋊D61—28no—
282C2×C22⋊D61—28no—
283C2×C22⋊D61—28no—
284C2×C22⋊D61—28no—
285C2×C22⋊D61—28no—
286C2×C22⋊D61—28no—
287C2×C22⋊D61—44no—
288C2×C22⋊D61—44no—
289C2×C22⋊D61—44no—
290C2×C22⋊D61—44no—
291C2×C22⋊D61—44no—
292C2×C22⋊D61C22⋊C4116yescomplemented
293C22×Dic61—21no—
294C22×Dic61—21no—
295C22×Dic61—21no—
296C22×Dic61—21no—
297C22×Dic61—21no—
298C22×Dic61—21no—
299C22×Dic61—21no—
300C22×Dic61—21no—
301C22×Dic61—21no—
302C22×Dic61—21no—
303C22×Dic61—21no—
304C22×Dic61—21no—
305C22×Dic61—21no—
306C22×Dic61—21no—
307C22×Dic61—21no—
308C22×Dic61—21no—
309C22×Dic61—21no—
310C22×Dic61—21no—
311C22×Dic61—21no—
312C22×Dic61—21no—
313C22×Dic61—21no—
314C22×Dic61—21no—
315C22×Dic61—21no—
316C22×Dic61—21no—
317C22×Dic61—21no—
318C22×Dic61—21no—
319C22×Dic61—21no—
320C22×Dic61—21no—
321C22×Dic61—21no—
322C22×Dic61—21no—
323C22×Dic61—21no—
324C22×Dic61—21no—
325C22×Dic61—21no—
326C22×Dic61C22×C412yes—
327C22×Dic61C22×C412yes—
328C22×Dic61C2×D412yes—
329C22×Dic61C2×D412yes—
330C22×Dic61C2×D412yes—
331C22×Dic61C2×D412yes—
332C22×Dic61C2×D412yes—
333C22×Dic61C2×D412yes—
334C22×Dic61#4112yes—
335C2×D244—28no—
336C2×D244—28no—
337C2×D244—28no—
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—28no—
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—
356C2×C4×D61—44no—
357C2×C4×D61—44no—
358C2×C4×D61—44no—
359C2×C4×D61—44no—
360C2×C4×D61—44no—
361C2×C4×D61—44no—
362C2×C4×D61—44no—
363C22⋊C4×C61—28no—
364C22⋊C4×C61—44no—
365C22⋊Dic61—28no—
366C22⋊Dic61—44no—
367#11758198—28no—
368#11758198—28no—
369#11758198—44no—
370#11758198—44no—
371#11758198—44no—
372#11758198—44no—
373#11758198—44no—
374#11758196—28no—
375#11758196—28no—
376C4×Dic61—28no—
377C23×C61—22no—
378C23×C61—22no—
379C23×C61—22no—
380C23×C61—22no—
381C23×C61—22no—
382C23×C61—22no—
383C23×C61—22no—
384C23×C61—22no—
385C23×C61—22no—
386C23×C61—22no—
387C23×C61—22no—
388C23×C61—22no—
389C23×C61—22no—
390C23×C61—22no—
391C23×C61—22no—
392C23×C61—22no—
393C23×C61—22no—
394C23×C61—22no—
395C23×C61—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×C61C2×C22⋊C414yes—
412C23×C61C23×C411yescharacteristic
413C23×C61C22×D411yescharacteristic
414C23×C61C22×D411yescharacteristic
415C23×C61C22×D411yescharacteristic
416C23×C61C22×D411yescharacteristic
417C23×C61C22×D411yescharacteristic
418C23×C61C2×#4111yescharacteristic
419C23×C61C2×#4111yescharacteristic
420C23×C61C2×#4111yescharacteristic
421C23×C61C2×#4111yescharacteristic
422C23×C61C2×#4111yescharacteristic
423C23×C61H(5,𝔽2)11yescharacteristic
424C23×C61H(5,𝔽2)11yescharacteristic
425C23×C61H(5,𝔽2)11yescharacteristic
426C23×C612−1+411yescharacteristic
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—22no—
460C22×D61—22no—
461C22×D61—22no—
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×D61C2×C22⋊C414yes—
491C22×D61C4×D414yes—
492C22×D61C4×D414yes—
493C22×D61#12014yes—
494C22×D61#12114yes—
495C22×D61#12114yes—
496C22×D61#12314yes—
497C2×C4×C61—22no—
498C2×C4×C61—22no—
499C2×C4×C61—22no—
500C2×C4×C61—22no—
501C2×C4×C61—22no—
502C2×C4×C61—22no—
503C2×C4×C61—22no—
504C2×C4×C61—22no—
505C2×C4×C61—22no—
506C2×C4×C61—22no—
507C2×C4×C61—22no—
508C2×C4×C61—22no—
509C2×C4×C61—22no—
510C2×C4×C61—22no—
511C2×C4×C61—22no—
512C2×C4×C61—22no—
513C2×C4×C61—22no—
514C2×C4×C61—22no—
515C2×C4×C61—416no—
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—
535C2×C4×C61—41no—
536C2×C4×C61—41no—
537C2×C4×C61—41no—
538C2×C4×C61—41no—
539C2×C4×C61#12114yescomplemented
540C22⋊D61—232no—
541C22⋊D61—416no—
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—22no—
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—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×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×Dic61C2×C22⋊C414yes—
583C2×Dic61C4×D414yescomplemented
584D244—416no—
585C4×D61—416no—
586C4×D61—416no—
587C4×D61—416no—
588#14023—611nomaximal, Sylow
589C22×C61—24no—
590C22×C61—24no—
591C22×C61—24no—
592C22×C61—42no—
593C22×C61—42no—
594C22×C61—42no—
595C22×C61—42no—
596C22×C61—42no—
597C22×C61—42no—
598C22×C61—42no—
599C22×C61—42no—
600C22×C61—42no—
601C22×C61—42no—
602C22×C61—42no—
603C22×C61—42no—
604C22×C61C22×C22⋊C411yescharacteristic
605C22×C61C2×C4×D411yescharacteristic
606C22×C61C2×C4×D411yescharacteristic
607C22×C61C2×C4×D411yescharacteristic
608C22×C61C4×#4111yescharacteristic
609C22×C61#51811yescharacteristic
610C22×C61#52011yescharacteristic
611C22×C61C2×#12011yescharacteristic
612C22×C61C2×#12111yescharacteristic
613C22×C61C2×#12111yescharacteristic
614C22×C61C2×#12111yescharacteristic
615C22×C61C2×#12311yescharacteristic
616C22×C61#52511yescharacteristic
617C22×C61#52911yescharacteristic
618C22×C61#53211yescharacteristic
619C22×C61#53411yescharacteristic
620C22×C61#53711yescharacteristic
621C22×C61#53811yescharacteristic
622C22×C61#53911yescharacteristic
623C22×C61D4211yescharacteristic
624C22×C61D4211yescharacteristic
625C22×C61D4211yescharacteristic
626C22×C61#54611yescharacteristic
627C22×C61#54611yescharacteristic
628C22×C61#54611yescharacteristic
629C22×C61#54611yescharacteristic
630C22×C61#54611yescharacteristic
631C22×C61#54611yescharacteristic
632C22×C61#54711yescharacteristic
633C22×C61#54711yescharacteristic
634C22×C61#54711yescharacteristic
635C22×C61#54811yescharacteristic
636C22×C61#55311yescharacteristic
637C22×C61#55311yescharacteristic
638C22×C61#55311yescharacteristic
639C2×D61—24no—
640C2×D61—24no—
641C2×D61—24no—
642C2×D61—24no—
643C2×D61—24no—
644C2×D61—24no—
645C2×D61—24no—
646C2×D61—24no—
647C2×D61—24no—
648C2×D61—24no—
649C2×D61—24no—
650C2×D61—24no—
651C2×D61—24no—
652C2×D61—24no—
653C2×D61—42no—
654C2×D61—42no—
655C2×D61—42no—
656C2×D61—42no—
657C2×D61—42no—
658C2×D61—42no—
659C2×D61—42no—
660C2×D61—81no—
661C2×D61—81no—
662C2×D61—81no—
663C2×D61—81no—
664C2×D61—81no—
665C2×D61—81no—
666C2×D61—81no—
667C2×D61—81no—
668C2×D61#38618yescomplemented
669C4×C61—24no—
670C4×C61—42no—
671C4×C61—42no—
672C4×C61—42no—
673C4×C61—42no—
674C4×C61—81no—
675Dic61—24no—
676Dic61—24no—
677Dic61—42no—
678Dic61—42no—
679Dic61—42no—
680Dic61—81no—
681C22×#121—611no—
682C22×C4×D4—611no—
683C2×#386—611no—
684C2×#386—611no—
685C2×#386—611no—
686C2×#386—611no—
687C22×#95—611no—
688#1441—611no—
689#1440—611no—
690#1439—611no—
691#1438—611no—
692#1437—611no—
693#1436—611no—
694C22⋊#95—611no—
695C22⋊#95D6111yescharacteristic, complemented
696C2×C61—44no—
697C2×C61C2×#38611yescharacteristic
698C2×C61C4×#12111yescharacteristic
699C2×C61#232511yescharacteristic
700C2×C61D4×C22⋊C411yescharacteristic
701C2×C61#233911yescharacteristic
702C2×C61#236111yescharacteristic
703C2×C61#236411yescharacteristic
704C2×C61#241011yescharacteristic
705C2×C61#241611yescharacteristic
706C2×C61#242411yescharacteristic
707C2×C61#242511yescharacteristic
708C2×C61#243011yescharacteristic
709C2×C61#244311yescharacteristic
710C2×C61#244411yescharacteristic
711C2×C61#254311yescharacteristic
712D61—28no—
713D61—82no—
714C23×D4—611no—
715C23×D4—611no—
716C23×D4—611no—
717C24×C4—611no—
718C24×C4—611no—
719C24×C4—611no—
720C24×C4C2×D6111yescharacteristic
721C2×#121—618no—
722C2×#121—1224no—
723C2×#121—1224no—
724C2×C4×D4—1224no—
725C2×C4×D4—1224no—
726C2×C4×D4—1224no—
727C22×C4⋊C4—611no—
728C22×C4⋊C4—611no—
729C22×C22⋊C4—611no—
730C22×C22⋊C4—611no—
731C22×C22⋊C4—611no—
732C22×C22⋊C4—611no—
733C22×C22⋊C4—611no—
734C22×C22⋊C4—611no—
735C22×C22⋊C4—611no—
736C22×C22⋊C4—611no—
737C22×C22⋊C4—611no—
738C22×C22⋊C4C2×D6111yescharacteristic
739C22×C22⋊C4C2×D6111yescharacteristic
740C22×C42—611no—
741#386—1224no—
742#386—1224no—
743#386—1224no—
744#386—1224no—
745C2×#95—611no—
746C2×#95—611no—
747C2×#95—611no—
748C2×#95—611no—
749C2×#95—611no—
750C2×#95—611no—
751C2×#95—611no—
752C2×#95—611no—
753C2×#95—611no—
754C2×#95—611no—
755C2×#95—1224no—
756C2×#95C2×D6111yescharacteristic
757C2×#95C2×D6111yescharacteristic
758C2×#95C2×D6111yescharacteristic
759C2×#95C2×D6111yescharacteristic
760C61#1402311yescharacteristic, complemented, Sylow
761C25—611no—
762C25—611no—
763C25C22×D6111yescharacteristic
764C22×D4—614no—
765C22×D4—614no—
766C22×D4—614no—
767C22×D4—614no—
768C22×D4—614no—
769C22×D4—1222no—
770C22×D4—1222no—
771C22×D4—1222no—
772C22×D4—1222no—
773C22×D4—1222no—
774C22×D4—1222no—
775C22×D4—1222no—
776C22×D4—1222no—
777C22×D4—1222no—
778C22×D4—1222no—
779C22×D4—1222no—
780C22×D4—1222no—
781C22×D4—1222no—
782C22×D4—1222no—
783C22×D4—2441no—
784C22×D4—2441no—
785C23×C4—22no—
786C23×C4—22no—
787C23×C4—22no—
788C23×C4—22no—
789C23×C4—22no—
790C23×C4—41no—
791C23×C4—41no—
792C23×C4—611no—
793C23×C4—611no—
794C23×C4—611no—
795C23×C4—611no—
796C23×C4—611no—
797C23×C4—614no—
798C23×C4—614no—
799C23×C4—611no—
800C23×C4—1222no—
801C23×C4—1222no—
802C23×C4—1222no—
803C23×C4—1222no—
804C23×C4—1222no—
805C23×C4—1222no—
806C23×C4—1222no—
807C23×C4—1222no—
808C23×C4—1222no—
809C23×C4—1222no—
810C23×C4—1222no—
811C23×C4—1222no—
812C23×C4—1222no—
813C23×C4—2441no—
814C23×C4—2441no—
815C23×C4—2441no—
816C23×C4—2441no—
817C23×C4—2441no—
818C23×C4—2441no—
819C23×C4C22×D6111yescharacteristic
820C23×C4C22×D6111yescharacteristic
821C23×C4C22×D6111yescharacteristic
822C23×C4C22×D6111yescharacteristic
823C23×C4C22×D6111yescharacteristic
824C23×C4C22×D6111yescharacteristic
825#121—12232no—
826C4×D4—12232no—
827C2×C4⋊C4—614no—
828C2×C4⋊C4—1222no—
829C2×C4⋊C4—1222no—
830C2×C4⋊C4—1222no—
831C2×C4⋊C4—1222no—
832C2×C4⋊C4—1222no—
833C2×C22⋊C4—22no—
834C2×C22⋊C4—22no—
835C2×C22⋊C4—22no—
836C2×C22⋊C4—22no—
837C2×C22⋊C4—41no—
838C2×C22⋊C4—614no—
839C2×C22⋊C4—614no—
840C2×C22⋊C4—1222no—
841C2×C22⋊C4—1222no—
842C2×C22⋊C4—1222no—
843C2×C22⋊C4—1222no—
844C2×C22⋊C4—1222no—
845C2×C22⋊C4—1222no—
846C2×C22⋊C4—1222no—
847C2×C22⋊C4—1222no—
848C2×C22⋊C4—1222no—
849C2×C22⋊C4—1222no—
850C2×C22⋊C4—1222no—
851C2×C22⋊C4—1222no—
852C2×C22⋊C4—1222no—
853C2×C22⋊C4—1222no—
854C2×C22⋊C4—1222no—
855C2×C22⋊C4—1222no—
856C2×C22⋊C4—1222no—
857C2×C22⋊C4—1222no—
858C2×C22⋊C4—1222no—
859C2×C22⋊C4—1222no—
860C2×C22⋊C4—2441no—
861C2×C22⋊C4—2441no—
862C2×C22⋊C4—2441no—
863C2×C22⋊C4—2441no—
864C2×C22⋊C4—2441no—
865C2×C22⋊C4C4×D6114yescomplemented
866C2×C42—1222no—
867C2×C42—1222no—
868C2×C42—1222no—
869#95—22no—
870#95—22no—
871#95—22no—
872#95—41no—
873#95—614no—
874#95—1222no—
875#95—1222no—
876#95—1222no—
877#95—1222no—
878#95—1222no—
879#95—1222no—
880#95—1222no—
881#95—1222no—
882#95—2441no—
883C24—21no—
884C24—21no—
885C24—21no—
886C24—21no—
887C24—21no—
888C24—21no—
889C24—21no—
890C24—21no—
891C24—21no—
892C24—21no—
893C24—21no—
894C24—21no—
895C24—612no—
896C24—612no—
897C24—612no—
898C24—612no—
899C24—612no—
900C24—612no—
901C24—612no—
902C24—612no—
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—
920C24—1221no—
921C24—1221no—
922C24—1221no—
923C24—1221no—
924C24—1221no—
925C24C2×C4×D6112yes—
926C24D4×D6112yes—
927C24D4×D6112yes—
928C24C23×D6111yescharacteristic
929C2×D4—6116no—
930C2×D4—1228no—
931C2×D4—1228no—
932C2×D4—1228no—
933C2×D4—1228no—
934C2×D4—1228no—
935C2×D4—1228no—
936C2×D4—1228no—
937C2×D4—1228no—
938C2×D4—1228no—
939C2×D4—1228no—
940C2×D4—1228no—
941C2×D4—2444no—
942C2×D4—2444no—
943C2×D4—2444no—
944C2×D4—2444no—
945C2×D4—2444no—
946C2×D4—2444no—
947C2×D4—2444no—
948C2×D4—2444no—
949C2×D4—2444no—
950C22×C4—21no—
951C22×C4—21no—
952C22×C4—21no—
953C22×C4—21no—
954C22×C4—28no—
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—21no—
983C22×C4—21no—
984C22×C4—21no—
985C22×C4—21no—
986C22×C4—44no—
987C22×C4—44no—
988C22×C4—44no—
989C22×C4—44no—
990C22×C4—44no—
991C22×C4—44no—
992C22×C4—612no—
993C22×C4—612no—
994C22×C4—612no—
995C22×C4—612no—
996C22×C4—612no—
997C22×C4—612no—
998C22×C4—612no—
999C22×C4—612no—
1000C22×C4—612no—
1001C22×C4—1228no—
1002C22×C4—1228no—
1003C22×C4—1228no—
1004C22×C4—1228no—
1005C22×C4—1221no—
1006C22×C4—1221no—
1007C22×C4—1221no—
1008C22×C4—1221no—
1009C22×C4—1221no—
1010C22×C4—1221no—
1011C22×C4—1221no—
1012C22×C4—1221no—
1013C22×C4—1221no—
1014C22×C4—1221no—
1015C22×C4—1221no—
1016C22×C4—1221no—
1017C22×C4—1221no—
1018C22×C4—1221no—
1019C22×C4—1221no—
1020C22×C4—1221no—
1021C22×C4—1221no—
1022C22×C4—1221no—
1023C22×C4—1221no—
1024C22×C4—1221no—
1025C22×C4—1221no—
1026C22×C4—1221no—
1027C22×C4—1221no—
1028C22×C4—1221no—
1029C22×C4—1221no—
1030C22×C4—1221no—
1031C22×C4—1228no—
1032C22×C4—1221no—
1033C22×C4—1221no—
1034C22×C4—1221no—
1035C22×C4—1221no—
1036C22×C4—1221no—
1037C22×C4—1221no—
1038C22×C4—1221no—
1039C22×C4—2444no—
1040C22×C4—2444no—
1041C22×C4—2444no—
1042C22×C4—2444no—
1043C22×C4—2444no—
1044C22×C4—2444no—
1045C22×C4—2444no—
1046C22×C4—2444no—
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×C4C2×C4×D6112yes—
1056C22×C4C2×C4×D6112yes—
1057C22×C4#1175822212yes—
1058C22×C4#1175822212yes—
1059C22×C4D4×D6112yes—
1060C22×C4D4×D6112yes—
1061C22×C4D4×D6112yes—
1062C4⋊C4—1228no—
1063C4⋊C4—1228no—
1064C22⋊C4—28no—
1065C22⋊C4—44no—
1066C22⋊C4—1228no—
1067C22⋊C4—1228no—
1068C22⋊C4—1228no—
1069C22⋊C4—2444no—
1070C22⋊C4—2444no—
1071C22⋊C4—2444no—
1072C22⋊C4—2444no—
1073C22⋊C4—2444no—
1074C22⋊C4—2444no—
1075C42—1228no—
1076C23—22no—
1077C23—22no—
1078C23—22no—
1079C23—22no—
1080C23—22no—
1081C23—22no—
1082C23—22no—
1083C23—22no—
1084C23—22no—
1085C23—22no—
1086C23—22no—
1087C23—22no—
1088C23—22no—
1089C23—22no—
1090C23—22no—
1091C23—22no—
1092C23—22no—
1093C23—22no—
1094C23—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—614no—
1111C23—614no—
1112C23—614no—
1113C23—614no—
1114C23—614no—
1115C23—614no—
1116C23—614no—
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—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—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—
1171C23—2441no—
1172C23—2441no—
1173C23—2441no—
1174C23—2441no—
1175C23—2441no—
1176C23—2441no—
1177C23—2441no—
1178C23—2441no—
1179C23—2441no—
1180C23C22⋊C4×D6114yes—
1181C23C22×C4×D6111yescharacteristic
1182C23C2×D4×D6111yescharacteristic
1183C23C2×D4×D6111yescharacteristic
1184C23C2×D4×D6111yescharacteristic
1185C23C2×D4×D6111yescharacteristic
1186C23C2×D4×D6111yescharacteristic
1187C23#41×D6111yescharacteristic
1188C23#41×D6111yescharacteristic
1189C23#41×D6111yescharacteristic
1190C23C2×#1175822211yescharacteristic
1191C23C2×#1175822211yescharacteristic
1192C23#1451982211yescharacteristic
1193C23#1451982211yescharacteristic
1194C23#1451982311yescharacteristic
1195C23#1451982511yescharacteristic
1196D4—12232no—
1197D4—24416no—
1198D4—24416no—
1199C2×C4—22no—
1200C2×C4—22no—
1201C2×C4—22no—
1202C2×C4—22no—
1203C2×C4—22no—
1204C2×C4—22no—
1205C2×C4—22no—
1206C2×C4—22no—
1207C2×C4—22no—
1208C2×C4—22no—
1209C2×C4—22no—
1210C2×C4—22no—
1211C2×C4—22no—
1212C2×C4—22no—
1213C2×C4—22no—
1214C2×C4—22no—
1215C2×C4—22no—
1216C2×C4—22no—
1217C2×C4—416no—
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—41no—
1233C2×C4—41no—
1234C2×C4—41no—
1235C2×C4—41no—
1236C2×C4—41no—
1237C2×C4—41no—
1238C2×C4—41no—
1239C2×C4—41no—
1240C2×C4—41no—
1241C2×C4—614no—
1242C2×C4—614no—
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—1222no—
1256C2×C4—1222no—
1257C2×C4—1222no—
1258C2×C4—1222no—
1259C2×C4—1222no—
1260C2×C4—1222no—
1261C2×C4—1222no—
1262C2×C4—1222no—
1263C2×C4—1222no—
1264C2×C4—24416no—
1265C2×C4—24416no—
1266C2×C4—24416no—
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—
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#1451975014yescomplemented
1287C22—24no—
1288C22—24no—
1289C22—24no—
1290C22—42no—
1291C22—42no—
1292C22—42no—
1293C22—42no—
1294C22—42no—
1295C22—42no—
1296C22—42no—
1297C22—42no—
1298C22—42no—
1299C22—42no—
1300C22—42no—
1301C22—42no—
1302C22—618no—
1303C22—1224no—
1304C22—1224no—
1305C22—1224no—
1306C22—1224no—
1307C22—1224no—
1308C22—1224no—
1309C22—1224no—
1310C22—1224no—
1311C22—1224no—
1312C22—1224no—
1313C22—1224no—
1314C22—1224no—
1315C22—1224no—
1316C22—1224no—
1317C22—4881no—
1318C22—4881no—
1319C22—4881no—
1320C22—4881no—
1321C22—4881no—
1322C22—4881no—
1323C22—4881no—
1324C22—4881no—
1325C22—2442no—
1326C22—2442no—
1327C22—2442no—
1328C22—2442no—
1329C22—2442no—
1330C22—2442no—
1331C22—2442no—
1332C22C2×C22⋊C4×D6111yescharacteristic
1333C22C4×D4×D6111yescharacteristic
1334C22C4×D4×D6111yescharacteristic
1335C22C4×D4×D6111yescharacteristic
1336C22C4×#1175822211yescharacteristic
1337C22#1684023411yescharacteristic
1338C22#1684024311yescharacteristic
1339C22#120×D6111yescharacteristic
1340C22#121×D6111yescharacteristic
1341C22#121×D6111yescharacteristic
1342C22C2×#1451975011yescharacteristic
1343C22#123×D6111yescharacteristic
1344C22#1684027111yescharacteristic
1345C22#1684029011yescharacteristic
1346C22#1684030911yescharacteristic
1347C22#1684032211yescharacteristic
1348C22#1684034211yescharacteristic
1349C22#1684034811yescharacteristic
1350C22#1684035811yescharacteristic
1351C22#1684039411yescharacteristic
1352C22#1684039411yescharacteristic
1353C22#1684039611yescharacteristic
1354C22#1684040111yescharacteristic
1355C22#1684040211yescharacteristic
1356C22#1684040211yescharacteristic
1357C22#1684040211yescharacteristic
1358C22#1684040411yescharacteristic
1359C22#1684040811yescharacteristic
1360C22#1684041311yescharacteristic
1361C22#1684041311yescharacteristic
1362C22#1684041411yescharacteristic
1363C22#1684042211yescharacteristic
1364C22#1684045611yescharacteristic
1365C22#1684045711yescharacteristic
1366C22#1684046211yescharacteristic
1367C4—24no—
1368C4—42no—
1369C4—42no—
1370C4—42no—
1371C4—42no—
1372C4—81no—
1373C4—1224no—
1374C4—1224no—
1375C4—4881no—
1376C4—2442no—
1377C4—2442no—
1378C4—2442no—
1379C2—44no—
1380C2—1228no—
1381C2—4882no—
1382C2#386×D6111yescharacteristic
1383C2C4×#1451975011yescharacteristic
1384C2#2144851611yescharacteristic
1385C2#2144863711yescharacteristic
1386C2#2144864611yescharacteristic
1387C2#2144883811yescharacteristic
1388C2#2144887011yescharacteristic
1389C2#2144919511yescharacteristic
1390C2#2144926111yescharacteristic
1391C2#2144935411yescharacteristic
1392C2#2144936711yescharacteristic
1393C2#2144942811yescharacteristic
1394C2#2144955311yescharacteristic
1395C2#2144956811yescharacteristic
1396C2#2145077811yescharacteristic
subgroupG/H
center, FrattiniC24C23×D61
commutatorC23×C61C23×C4
FittingC61×C22⋊#95C2
socle, cosocleC24×C61C24
prime radicalC22×#14519750C2
hypercenterC22⋊#95D61
hypocenterC61#14023
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C24 ◁ C22⋊#95

Complements

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

NH ≅ G/Ntype
2. C22×C4×C22⋊D61C2semidirect
3. C2×#16839641C2semidirect
4. C2×#16839640C2semidirect
5. C2×#16839640C2semidirect
6. C2×#16839638C2semidirect
7. C2×#95×D61C2semidirect
8. #21444070C2semidirect
9. #21444068C2semidirect
10. #21444063C2semidirect
11. #21444058C2semidirect
12. #21444055C2semidirect
13. #21444050C2semidirect
14. #21444040C2semidirect
15. C61×C22⋊#95C2semidirect
24. C2×#14519750C4semidirect
70. C22×D244C2×C4semidirect
82. C22×C22⋊D61C2×C4semidirect
110. C22×C4×D61C2×C4semidirect
111. C22×C4×D61D4semidirect
119. C2×#11758196C2×C4semidirect
145. C2×#11758198C2×C4semidirect
146. C2×#11758198D4semidirect
159. #14519684D4semidirect
179. C2×C22⋊C4×C61C2×C4semidirect
292. C2×C22⋊D61C22⋊C4semidirect
539. C2×C4×C61#121semidirect
583. C2×Dic61C4×D4semidirect
668. C2×D61#386semidirect
695. C22⋊#95D61semidirect
760. C61#14023semidirect
865. C2×C22⋊C4C4×D61semidirect
1286. C2×C4#14519750semidirect

Maximal subgroups

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

subgroupindex
C22×#145197502
C22×C4×C22⋊D612
C2×#168396412
C2×#168396402
C2×#168396382
C2×#95×D612
#214440702
#214440682
#214440632
#214440582
#214440552
#214440502
#214440402
C61×C22⋊#952
#1402361