Finite Group Databasebeta

← #29605350

Subgroups — #29605350

Order 15616.

2854 conjugacy classes of subgroups.

The subgroup lattice has 1370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×C22⋊D61C211yesmaximal, characteristic, complemented
2C2×#16839671C211yesmaximal, characteristic
3C2×#16839641C211yesmaximal, characteristic, complemented
4C2×#16839640C211yesmaximal, characteristic, complemented
5C2×#16839640C211yesmaximal, characteristic, complemented
6C2×#16839638C211yesmaximal, characteristic, complemented
7C2×#16839609C211yesmaximal, characteristic, complemented
8#21444077C211yesmaximal, characteristic, complemented
9#21444063C211yesmaximal, characteristic, complemented
10#21444058C211yesmaximal, characteristic, complemented
11#21444056C211yesmaximal, characteristic, complemented
12#21444055C211yesmaximal, characteristic, complemented
13#21444045C211yesmaximal, 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
21C2×C4×C22⋊D61—24no—
22C2×C4×C22⋊D61—24no—
23C2×C4×C22⋊D61—24no—
24C22×#11758196C2211yescharacteristic
25C22×C22⋊Dic61C2211yescharacteristic
26C22×C22⋊Dic61C2211yescharacteristic
27C22×#11758198C2211yescharacteristic
28C22×#11758198C2211yescharacteristic
29C22×#11758198C2211yescharacteristic
30C22×#11758198C2211yescharacteristic
31C22×#11758198C2211yescharacteristic
32C22×#11758198C2211yescharacteristic
33C22×#11758198C2211yescharacteristic
34C22×#11758198C2211yescharacteristic
35C22×C4×Dic61C2211yescharacteristic
36C22×C4×Dic61C2211yescharacteristic
37#16839671C418yescomplemented
38#16839641—24no—
39#16839640—24no—
40#16839640—24no—
41#16839638—24no—
42#16839609—24no—
43C2×#14519684C2211yescharacteristic
44C2×#14519684C2211yescharacteristic
45C2×#14519684C2211yescharacteristic
46C2×#14519684C2211yescharacteristic
47C2×#14519684C2211yescharacteristic
48C2×#14519684C2211yescharacteristic
49C2×#14519684C2211yescharacteristic
50C2×#14519684C2211yescharacteristic
51C2×#14519684C2211yescharacteristic
52C2×#14519684C2211yescharacteristic
53C24×C4×C61C2211yescharacteristic
54C22×C22⋊C4×C61C2211yescharacteristic
55C22×C22⋊C4×C61C2211yescharacteristic
56C2×#95×C61C2211yescharacteristic
57C2×#95×C61C2211yescharacteristic
58C2×#95×C61C2211yescharacteristic
59C2×#95×C61C2211yescharacteristic
60C24×D61C2311yescharacteristic
61C24×D61C2311yescharacteristic
62C22×D244—22no—
63C22×D244—22no—
64C22×D244—22no—
65C22×D244—22no—
66C22×D244—41no—
67C22×D244—41no—
68C22×D244C2×C414yescomplemented
69C22×C22⋊D61—22no—
70C22×C22⋊D61—22no—
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×C414yescomplemented
82C22×C22⋊D61C2×C414yescomplemented
83C23×Dic61C2311yescharacteristic
84C23×Dic61C2311yescharacteristic
85C23×Dic61C2311yescharacteristic
86C23×Dic61C2311yescharacteristic
87C23×Dic61C2311yescharacteristic
88C23×Dic61C2311yescharacteristic
89C22×C4×D61—22no—
90C22×C4×D61—22no—
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—41no—
100C22×C4×D61—41no—
101C22×C4×D61—41no—
102C22×C4×D61—41no—
103C4×C22⋊D61—232no—
104C2×#11758196—22no—
105C2×#11758196—22no—
106C2×#11758196—22no—
107C2×C22⋊Dic61—22no—
108C2×C22⋊Dic61—22no—
109C2×C22⋊Dic61—22no—
110C2×C22⋊Dic61—22no—
111C2×C22⋊Dic61—41no—
112C2×C22⋊Dic61D414yescomplemented
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—41no—
128C2×#11758198—41no—
129C2×#11758198—41no—
130C2×#11758198—41no—
131C2×#11758198—41no—
132C2×#11758198—41no—
133C2×#11758198C2×C414yescomplemented
134C2×#11758198C2×C414yescomplemented
135C2×#11758198D414yescomplemented
136C2×#11758198D414yescomplemented
137C2×C4×Dic61—22no—
138C2×C4×Dic61—22no—
139C2×C4×Dic61—22no—
140C2×C4×Dic61—41no—
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—
151#14519684—41no—
152#14519684C2×C414yescomplemented
153C25×C61C2311yescharacteristic
154C23×C4×C61—22no—
155C23×C4×C61—22no—
156C23×C4×C61—22no—
157C23×C4×C61—22no—
158C23×C4×C61—22no—
159C23×C4×C61—41no—
160C23×C4×C61—41no—
161C23×C4×C61C2311yescharacteristic
162C23×C4×C61C2311yescharacteristic
163C23×C4×C61C2311yescharacteristic
164C23×C4×C61C2311yescharacteristic
165C23×C4×C61C2311yescharacteristic
166C23×C4×C61C2311yescharacteristic
167C2×C22⋊C4×C61—22no—
168C2×C22⋊C4×C61—22no—
169C2×C22⋊C4×C61—41no—
170C2×C22⋊C4×C61—41no—
171C2×C22⋊C4×C61—41no—
172C2×C22⋊C4×C61C2×C414yescomplemented
173#95×C61—22no—
174#95×C61—22no—
175#95×C61—22no—
176#95×C61—41no—
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×C61#4112yes—
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—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×D61C22×C412yes—
218C23×D61C22×C412yes—
219C23×D61C2×D412yes—
220C23×D61C2×D412yes—
221C23×D61#4112yes—
222C23×D61#4112yes—
223C22×C4×C61—21no—
224C22×C4×C61—21no—
225C22×C4×C61—21no—
226C22×C4×C61—21no—
227C22×C4×C61—28no—
228C22×C4×C61—21no—
229C22×C4×C61—21no—
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—44no—
260C22×C4×C61—44no—
261C22×C4×C61—44no—
262C22×C4×C61—44no—
263C22×C4×C61—44no—
264C22×C4×C61—44no—
265C22×C4×C61C22×C412yes—
266C22×C4×C61C22×C412yes—
267C22×C4×C61C2×D412yes—
268C22×C4×C61C2×D412yes—
269C22×C4×C61C2×D412yes—
270C22×C4×C61#4112yes—
271C22×C4×C61#4112yes—
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—28no—
281C2×C22⋊D61—44no—
282C2×C22⋊D61—44no—
283C2×C22⋊D61—44no—
284C2×C22⋊D61—44no—
285C2×C22⋊D61—44no—
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—21no—
314C22×Dic61—21no—
315C22×Dic61—21no—
316C22×Dic61—21no—
317C22×Dic61—21no—
318C22×Dic61—21no—
319C22×Dic61C22×C412yes—
320C22×Dic61C22×C412yes—
321C22×Dic61C2×D412yes—
322C22×Dic61C2×D412yes—
323C22×Dic61C2×D412yes—
324C22×Dic61C2×D412yes—
325C22×Dic61C2×D412yes—
326C22×Dic61C2×D412yes—
327C22×Dic61#4112yes—
328C2×D244—28no—
329C2×D244—28no—
330C2×D244—44no—
331C2×D244—44no—
332C2×D244—44no—
333C2×D244—44no—
334C2×D244—44no—
335C2×C4×D61—28no—
336C2×C4×D61—28no—
337C2×C4×D61—44no—
338C2×C4×D61—44no—
339C2×C4×D61—44no—
340C2×C4×D61—44no—
341C2×C4×D61—44no—
342C2×C4×D61—44no—
343C2×C4×D61—44no—
344C2×C4×D61—44no—
345C2×C4×D61—44no—
346C2×C4×D61—44no—
347C2×C4×D61—44no—
348C2×C4×D61—44no—
349C22⋊C4×C61—44no—
350C22⋊C4×C61—44no—
351C22⋊Dic61—28no—
352C22⋊Dic61—44no—
353#11758198—28no—
354#11758198—28no—
355#11758198—28no—
356#11758198—44no—
357#11758198—44no—
358#11758198—44no—
359#11758198—44no—
360#11758198—44no—
361#11758196—28no—
362C4×Dic61—28no—
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—41no—
383C23×C61—41no—
384C23×C61—41no—
385C23×C61—41no—
386C23×C61—41no—
387C23×C61—41no—
388C23×C61—41no—
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×C61C4×D414yes—
399C23×C61C23×C411yescharacteristic
400C23×C61C22×D411yescharacteristic
401C23×C61C22×D411yescharacteristic
402C23×C61C22×D411yescharacteristic
403C23×C61C22×D411yescharacteristic
404C23×C61C2×#4111yescharacteristic
405C23×C61C2×#4111yescharacteristic
406C23×C61C2×#4111yescharacteristic
407C23×C61C2×#4111yescharacteristic
408C23×C61C2×#4111yescharacteristic
409C23×C61C2×#4111yescharacteristic
410C23×C61H(5,𝔽2)11yescharacteristic
411C23×C61H(5,𝔽2)11yescharacteristic
412C23×C61H(5,𝔽2)11yescharacteristic
413C23×C61H(5,𝔽2)11yescharacteristic
414C22×D61—22no—
415C22×D61—22no—
416C22×D61—22no—
417C22×D61—22no—
418C22×D61—22no—
419C22×D61—22no—
420C22×D61—22no—
421C22×D61—22no—
422C22×D61—22no—
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—41no—
451C22×D61—41no—
452C22×D61—41no—
453C22×D61—41no—
454C22×D61—41no—
455C22×D61—41no—
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×D61C4×D414yes—
483C22×D61C4×D414yescomplemented
484C2×C4×C61—22no—
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—416no—
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×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#12114yes—
527C22⋊D61—232no—
528C22⋊D61—416no—
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—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—41no—
551C2×Dic61—41no—
552C2×Dic61—41no—
553C2×Dic61—41no—
554C2×Dic61—41no—
555C2×Dic61—41no—
556C2×Dic61—41no—
557C2×Dic61—41no—
558C2×Dic61—41no—
559C2×Dic61—41no—
560C2×Dic61—41no—
561C2×Dic61—41no—
562C2×Dic61—41no—
563C2×Dic61—41no—
564C2×Dic61—41no—
565C2×Dic61—41no—
566C2×Dic61—41no—
567C2×Dic61—41no—
568C2×Dic61—41no—
569C2×Dic61C4×D414yes—
570C2×Dic61#12014yes—
571D244—416no—
572C4×D61—416no—
573C4×D61—416no—
574#14175—611nomaximal, Sylow
575C22×C61—24no—
576C22×C61—24no—
577C22×C61—24no—
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×C61C2×C4×D411yescharacteristic
591C22×C61C2×C4×D411yescharacteristic
592C22×C61C2×C4×D411yescharacteristic
593C22×C61C2×C4×D411yescharacteristic
594C22×C61C4×#4111yescharacteristic
595C22×C61#51811yescharacteristic
596C22×C61#51811yescharacteristic
597C22×C61C2×#12011yescharacteristic
598C22×C61C2×#12111yescharacteristic
599C22×C61#52511yescharacteristic
600C22×C61#52511yescharacteristic
601C22×C61#52511yescharacteristic
602C22×C61#52511yescharacteristic
603C22×C61#52911yescharacteristic
604C22×C61#53211yescharacteristic
605C22×C61#53511yescharacteristic
606C22×C61#53511yescharacteristic
607C22×C61#54011yescharacteristic
608C22×C61#54011yescharacteristic
609C22×C61D4211yescharacteristic
610C22×C61D4211yescharacteristic
611C22×C61#54611yescharacteristic
612C22×C61#54611yescharacteristic
613C22×C61#54611yescharacteristic
614C22×C61#54611yescharacteristic
615C22×C61#54611yescharacteristic
616C22×C61#54611yescharacteristic
617C22×C61#54611yescharacteristic
618C22×C61#54611yescharacteristic
619C22×C61#55111yescharacteristic
620C22×C61#55111yescharacteristic
621C22×C61#55311yescharacteristic
622C22×C61#55311yescharacteristic
623C22×C61#55311yescharacteristic
624C22×C61#55311yescharacteristic
625C2×D61—24no—
626C2×D61—24no—
627C2×D61—24no—
628C2×D61—24no—
629C2×D61—24no—
630C2×D61—24no—
631C2×D61—42no—
632C2×D61—42no—
633C2×D61—42no—
634C2×D61—42no—
635C2×D61—42no—
636C2×D61—42no—
637C2×D61—42no—
638C2×D61—42no—
639C2×D61—42no—
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—
655C4×C61—24no—
656C4×C61—42no—
657C4×C61—42no—
658C4×C61—42no—
659C4×C61—42no—
660C4×C61—81no—
661Dic61—24no—
662Dic61—24no—
663Dic61—42no—
664Dic61—42no—
665Dic61—42no—
666Dic61—81no—
667C22×C4×D4—611no—
668C2×#392—611no—
669C2×#386—611no—
670C2×#386—611no—
671C2×#386—611no—
672C2×#386—611no—
673C2×C4×C22⋊C4—611no—
674#1442—611no—
675#1439—611no—
676#1438—611no—
677#1437—611no—
678#1437—611no—
679#1434—611no—
680C22⋊#95—611no—
681C22⋊#95D6111yescharacteristic, complemented
682C2×C61—44no—
683C2×C61C4×#12011yescharacteristic
684C2×C61C4×#12111yescharacteristic
685C2×C61#232811yescharacteristic
686C2×C61#235811yescharacteristic
687C2×C61#235811yescharacteristic
688C2×C61#236411yescharacteristic
689C2×C61#236411yescharacteristic
690C2×C61#240411yescharacteristic
691C2×C61#240811yescharacteristic
692C2×C61#245711yescharacteristic
693C2×C61#245711yescharacteristic
694C2×C61#246411yescharacteristic
695C2×C61#246411yescharacteristic
696C2×C61#253511yescharacteristic
697C2×C61#259811yescharacteristic
698D61—44no—
699D61—44no—
700C23×D4—611no—
701C23×D4—611no—
702C23×D4—611no—
703C24×C4—611no—
704C24×C4—611no—
705C24×C4C2×D6111yescharacteristic
706C2×C4×D4—1224no—
707C2×C4×D4—1224no—
708C2×C4×D4—1224no—
709C22×C4⋊C4—611no—
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×C42—611no—
723C22×C42—611no—
724#392—618no—
725#386—1224no—
726#386—1224no—
727#386—1224no—
728#386—1224no—
729C4×C22⋊C4—1224no—
730C2×#95—611no—
731C2×#95—611no—
732C2×#95—611no—
733C2×#95—611no—
734C2×#95—611no—
735C2×#95—611no—
736C2×#95—611no—
737C2×#95—611no—
738C2×#95—611no—
739C2×#95—611no—
740C2×#95C2×D6111yescharacteristic
741C2×#95C2×D6111yescharacteristic
742C2×#95C2×D6111yescharacteristic
743C2×#95C2×D6111yescharacteristic
744C61#1417511yescharacteristic, complemented, Sylow
745C25—611no—
746C25—611no—
747C25C22×D6111yescharacteristic
748C22×D4—614no—
749C22×D4—614no—
750C22×D4—614no—
751C22×D4—1222no—
752C22×D4—1222no—
753C22×D4—1222no—
754C22×D4—1222no—
755C22×D4—1222no—
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—2441no—
766C22×D4—2441no—
767C22×D4—2441no—
768C22×D4—2441no—
769C23×C4—22no—
770C23×C4—22no—
771C23×C4—22no—
772C23×C4—22no—
773C23×C4—22no—
774C23×C4—41no—
775C23×C4—41no—
776C23×C4—611no—
777C23×C4—611no—
778C23×C4—611no—
779C23×C4—611no—
780C23×C4—611no—
781C23×C4—611no—
782C23×C4—1222no—
783C23×C4—1222no—
784C23×C4—1222no—
785C23×C4—1222no—
786C23×C4—1222no—
787C23×C4—1222no—
788C23×C4—1222no—
789C23×C4—1222no—
790C23×C4—1222no—
791C23×C4—1222no—
792C23×C4—2441no—
793C23×C4—2441no—
794C23×C4—2441no—
795C23×C4—2441no—
796C23×C4C22×D6111yescharacteristic
797C23×C4C22×D6111yescharacteristic
798C23×C4C22×D6111yescharacteristic
799C23×C4C22×D6111yescharacteristic
800C23×C4C22×D6111yescharacteristic
801C23×C4C22×D6111yescharacteristic
802C4×D4—12232no—
803C2×C4⋊C4—1222no—
804C2×C4⋊C4—1222no—
805C2×C4⋊C4—1222no—
806C2×C22⋊C4—22no—
807C2×C22⋊C4—22no—
808C2×C22⋊C4—41no—
809C2×C22⋊C4—41no—
810C2×C22⋊C4—41no—
811C2×C22⋊C4—614no—
812C2×C22⋊C4—614no—
813C2×C22⋊C4—614no—
814C2×C22⋊C4—614no—
815C2×C22⋊C4—614no—
816C2×C22⋊C4—1222no—
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—2441no—
835C2×C22⋊C4—2441no—
836C2×C22⋊C4—2441no—
837C2×C22⋊C4—2441no—
838C2×C22⋊C4—2441no—
839C2×C22⋊C4—2441no—
840C2×C22⋊C4—2441no—
841C2×C22⋊C4C4×D6114yescomplemented
842C2×C42—614no—
843C2×C42—1222no—
844C2×C42—1222no—
845C2×C42—1222no—
846C2×C42—2441no—
847C2×C42—2441no—
848#95—22no—
849#95—22no—
850#95—22no—
851#95—41no—
852#95—614no—
853#95—1222no—
854#95—1222no—
855#95—1222no—
856#95—1222no—
857#95—1222no—
858#95—1222no—
859#95—1222no—
860#95—1222no—
861#95—2441no—
862C24—21no—
863C24—21no—
864C24—21no—
865C24—21no—
866C24—21no—
867C24—21no—
868C24—21no—
869C24—21no—
870C24—21no—
871C24—21no—
872C24—21no—
873C24—21no—
874C24—612no—
875C24—612no—
876C24—612no—
877C24—612no—
878C24—612no—
879C24—612no—
880C24—1221no—
881C24—1221no—
882C24—1221no—
883C24—1221no—
884C24—1221no—
885C24—1221no—
886C24—1221no—
887C24—1221no—
888C24—1221no—
889C24—1221no—
890C24—1221no—
891C24—1221no—
892C24—1221no—
893C24—1221no—
894C24—1221no—
895C24—1221no—
896C24—1221no—
897C24—1221no—
898C24—1221no—
899C24—1221no—
900C24—1221no—
901C24—1221no—
902C24—1221no—
903C24—1221no—
904C24C2×C4×D6112yes—
905C24D4×D6112yes—
906C24#1175822612yes—
907C24C23×D6111yescharacteristic
908C2×D4—1228no—
909C2×D4—1228no—
910C2×D4—1228no—
911C2×D4—1228no—
912C2×D4—1228no—
913C2×D4—1228no—
914C2×D4—1228no—
915C2×D4—1228no—
916C2×D4—1228no—
917C2×D4—1228no—
918C2×D4—1228no—
919C2×D4—2444no—
920C2×D4—2444no—
921C2×D4—2444no—
922C2×D4—2444no—
923C2×D4—2444no—
924C2×D4—2444no—
925C2×D4—2444no—
926C2×D4—2444no—
927C2×D4—2444no—
928C2×D4—2444no—
929C22×C4—21no—
930C22×C4—21no—
931C22×C4—21no—
932C22×C4—21no—
933C22×C4—28no—
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—21no—
961C22×C4—21no—
962C22×C4—21no—
963C22×C4—21no—
964C22×C4—21no—
965C22×C4—44no—
966C22×C4—44no—
967C22×C4—44no—
968C22×C4—44no—
969C22×C4—44no—
970C22×C4—44no—
971C22×C4—612no—
972C22×C4—612no—
973C22×C4—612no—
974C22×C4—612no—
975C22×C4—612no—
976C22×C4—612no—
977C22×C4—612no—
978C22×C4—612no—
979C22×C4—612no—
980C22×C4—1228no—
981C22×C4—1228no—
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—1221no—
1013C22×C4—1221no—
1014C22×C4—1221no—
1015C22×C4—2444no—
1016C22×C4—2444no—
1017C22×C4—2444no—
1018C22×C4—2444no—
1019C22×C4—2444no—
1020C22×C4—2444no—
1021C22×C4—2444no—
1022C22×C4—2444no—
1023C22×C4—2444no—
1024C22×C4—2444no—
1025C22×C4—2444no—
1026C22×C4—2444no—
1027C22×C4C2×C4×D6112yes—
1028C22×C4C2×C4×D6112yes—
1029C22×C4#1175822212yes—
1030C22×C4#1175822212yes—
1031C22×C4D4×D6112yes—
1032C22×C4D4×D6112yes—
1033C22×C4D4×D6112yes—
1034C4⋊C4—1228no—
1035C22⋊C4—44no—
1036C22⋊C4—44no—
1037C22⋊C4—1228no—
1038C22⋊C4—1228no—
1039C22⋊C4—1228no—
1040C22⋊C4—1228no—
1041C22⋊C4—2444no—
1042C22⋊C4—2444no—
1043C22⋊C4—2444no—
1044C22⋊C4—2444no—
1045C22⋊C4—2444no—
1046C22⋊C4—2444no—
1047C42—1228no—
1048C42—2444no—
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—41no—
1068C23—41no—
1069C23—41no—
1070C23—41no—
1071C23—41no—
1072C23—41no—
1073C23—41no—
1074C23—41no—
1075C23—41no—
1076C23—41no—
1077C23—41no—
1078C23—41no—
1079C23—41no—
1080C23—41no—
1081C23—41no—
1082C23—41no—
1083C23—614no—
1084C23—614no—
1085C23—1222no—
1086C23—1222no—
1087C23—1222no—
1088C23—1222no—
1089C23—1222no—
1090C23—1222no—
1091C23—1222no—
1092C23—1222no—
1093C23—1222no—
1094C23—1222no—
1095C23—1222no—
1096C23—1222no—
1097C23—1222no—
1098C23—1222no—
1099C23—1222no—
1100C23—1222no—
1101C23—1222no—
1102C23—1222no—
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—2441no—
1122C23—2441no—
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—
1151C23—2441no—
1152C23—2441no—
1153C23#1451973914yes—
1154C23C22×C4×D6111yescharacteristic
1155C23C2×D4×D6111yescharacteristic
1156C23C2×D4×D6111yescharacteristic
1157C23C2×D4×D6111yescharacteristic
1158C23C2×D4×D6111yescharacteristic
1159C23#41×D6111yescharacteristic
1160C23#41×D6111yescharacteristic
1161C23#41×D6111yescharacteristic
1162C23C2×#1175822211yescharacteristic
1163C23C2×#1175822211yescharacteristic
1164C23C2×#1175822611yescharacteristic
1165C23#1451982211yescharacteristic
1166C23#1451982211yescharacteristic
1167C23#1451982211yescharacteristic
1168C23#1451982311yescharacteristic
1169D4—12232no—
1170D4—24416no—
1171D4—24416no—
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—22no—
1189C2×C4—22no—
1190C2×C4—416no—
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—41no—
1204C2×C4—41no—
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—614no—
1215C2×C4—614no—
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—1222no—
1230C2×C4—1222no—
1231C2×C4—1222no—
1232C2×C4—1222no—
1233C2×C4—1222no—
1234C2×C4—1222no—
1235C2×C4—1222no—
1236C2×C4—1222no—
1237C2×C4—24416no—
1238C2×C4—24416no—
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×C4—2441no—
1254C2×C4—2441no—
1255C2×C4—2441no—
1256C2×C4—2441no—
1257C2×C4—2441no—
1258C2×C4#1451975014yes—
1259C22—24no—
1260C22—24no—
1261C22—24no—
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—1224no—
1275C22—1224no—
1276C22—1224no—
1277C22—1224no—
1278C22—1224no—
1279C22—1224no—
1280C22—2442no—
1281C22—2442no—
1282C22—2442no—
1283C22—2442no—
1284C22—2442no—
1285C22—2442no—
1286C22—2442no—
1287C22—2442no—
1288C22—2442no—
1289C22—2442no—
1290C22—2442no—
1291C22—2442no—
1292C22—2442no—
1293C22—2442no—
1294C22—2442no—
1295C22—2442no—
1296C22—2442no—
1297C22—2442no—
1298C22—2442no—
1299C22—2442no—
1300C22—2442no—
1301C22—2442no—
1302C22—2442no—
1303C22—2442no—
1304C22C4×D4×D6111yescharacteristic
1305C22C4×D4×D6111yescharacteristic
1306C22C4×D4×D6111yescharacteristic
1307C22C2×#1451973911yescharacteristic
1308C22C4×#1175822211yescharacteristic
1309C22#1684023411yescharacteristic
1310C22#1684023511yescharacteristic
1311C22#120×D6111yescharacteristic
1312C22C2×#1451975011yescharacteristic
1313C22#1684027011yescharacteristic
1314C22#1684027111yescharacteristic
1315C22#1684027511yescharacteristic
1316C22#1684027511yescharacteristic
1317C22#1684029011yescharacteristic
1318C22#1684030911yescharacteristic
1319C22#1684032711yescharacteristic
1320C22#1684032811yescharacteristic
1321C22#1684036211yescharacteristic
1322C22#1684036411yescharacteristic
1323C22#1684039411yescharacteristic
1324C22#1684039411yescharacteristic
1325C22#1684040211yescharacteristic
1326C22#1684040211yescharacteristic
1327C22#1684040211yescharacteristic
1328C22#1684040311yescharacteristic
1329C22#1684040411yescharacteristic
1330C22#1684040811yescharacteristic
1331C22#1684040911yescharacteristic
1332C22#1684040911yescharacteristic
1333C22#1684043911yescharacteristic
1334C22#1684044011yescharacteristic
1335C22#1684045611yescharacteristic
1336C22#1684046011yescharacteristic
1337C22#1684046011yescharacteristic
1338C22#1684046211yescharacteristic
1339C4—24no—
1340C4—42no—
1341C4—42no—
1342C4—42no—
1343C4—42no—
1344C4—81no—
1345C4—1224no—
1346C4—1224no—
1347C4—4881no—
1348C4—2442no—
1349C4—2442no—
1350C4—2442no—
1351C2—44no—
1352C2—2444no—
1353C2—2444no—
1354C2#2144832011yescharacteristic
1355C2C4×#1451975011yescharacteristic
1356C2#2144854011yescharacteristic
1357C2#2144879511yescharacteristic
1358C2#2144880211yescharacteristic
1359C2#2144886611yescharacteristic
1360C2#2144887011yescharacteristic
1361C2#2144913611yescharacteristic
1362C2#2144917411yescharacteristic
1363C2#2144972511yescharacteristic
1364C2#2144973311yescharacteristic
1365C2#2144982411yescharacteristic
1366C2#2144983211yescharacteristic
1367C2#2145072211yescharacteristic
1368C2#2145138411yescharacteristic
subgroupG/H
center, FrattiniC24C23×D61
commutatorC23×C61C23×C4
FittingC61×C22⋊#95C2
socle, cosocleC24×C61C24
prime radicalC2×#16839671C2
hypercenterC22⋊#95D61
hypocenterC61#14175
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C24 ◁ C22⋊#95

Complements

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

NH ≅ G/Ntype
1. C22×C4×C22⋊D61C2semidirect
3. C2×#16839641C2semidirect
4. C2×#16839640C2semidirect
5. C2×#16839640C2semidirect
6. C2×#16839638C2semidirect
7. C2×#16839609C2semidirect
8. #21444077C2semidirect
9. #21444063C2semidirect
10. #21444058C2semidirect
11. #21444056C2semidirect
12. #21444055C2semidirect
13. #21444045C2semidirect
14. #21444040C2semidirect
15. C61×C22⋊#95C2semidirect
37. #16839671C4semidirect
68. C22×D244C2×C4semidirect
81. C22×C22⋊D61C2×C4semidirect
82. C22×C22⋊D61C2×C4semidirect
112. C2×C22⋊Dic61D4semidirect
133. C2×#11758198C2×C4semidirect
134. C2×#11758198C2×C4semidirect
135. C2×#11758198D4semidirect
136. C2×#11758198D4semidirect
142. C2×C4×Dic61D4semidirect
152. #14519684C2×C4semidirect
172. C2×C22⋊C4×C61C2×C4semidirect
483. C22×D61C4×D4semidirect
681. C22⋊#95D61semidirect
744. C61#14175semidirect
841. 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×C4×C22⋊D612
C2×#168396712
C2×#168396412
C2×#168396402
C2×#168396382
C2×#168396092
#214440772
#214440632
#214440582
#214440562
#214440552
#214440452
#214440402
C61×C22⋊#952
#1417561