Finite Group Databasebeta

← #29607373

Subgroups — #29607373

Order 15616.

2494 conjugacy classes of subgroups.

The subgroup lattice has 1344 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519748C211yesmaximal, characteristic
2C2×#16839662C211yesmaximal, characteristic, complemented
3C2×#16839641C211yesmaximal, characteristic, complemented
4C2×#16839624C211yesmaximal, characteristic, complemented
5#21444071C211yesmaximal, characteristic, complemented
6#21444066C211yesmaximal, characteristic, complemented
7#21444062C211yesmaximal, characteristic, complemented
8#21444060C211yesmaximal, characteristic, complemented
9#21444058C211yesmaximal, characteristic, complemented
10#21444058C211yesmaximal, characteristic, complemented
11#21444056C211yesmaximal, characteristic, complemented
12#21444053C211yesmaximal, characteristic, complemented
13#21444042C211yesmaximal, characteristic, complemented
14#21444040C211yesmaximal, characteristic, complemented
15C2×C61×#386C211yesmaximal, characteristic, complemented
16C23×C22⋊D61C2211yescharacteristic
17C23×C22⋊D61C2211yescharacteristic
18C23×C4×D61C2211yescharacteristic
19C2×#14519748—24no—
20C2×#14519748—24no—
21C2×#14519748C418yescomplemented
22C22×C4⋊Dic61C2211yescharacteristic
23C22×#11758196C2211yescharacteristic
24C22×C22⋊Dic61C2211yescharacteristic
25C22×C22⋊Dic61C2211yescharacteristic
26C22×C22⋊Dic61C2211yescharacteristic
27C22×C22⋊Dic61C2211yescharacteristic
28C22×C22⋊Dic61C2211yescharacteristic
29C22×C22⋊Dic61C2211yescharacteristic
30C22×#11758198C2211yescharacteristic
31C22×#11758198C2211yescharacteristic
32C22×#11758198C2211yescharacteristic
33C22×#11758198C2211yescharacteristic
34C22×C4×Dic61C2211yescharacteristic
35#16839662—24no—
36#16839641—24no—
37#16839624—24no—
38C2×#14519684C2211yescharacteristic
39C2×#14519684C2211yescharacteristic
40C2×#14519684C2211yescharacteristic
41C2×#14519684C2211yescharacteristic
42C2×#14519684C2211yescharacteristic
43C2×#14519684C2211yescharacteristic
44C2×#14519684C2211yescharacteristic
45C2×#14519684C2211yescharacteristic
46C2×#14519684C2211yescharacteristic
47C2×#14519684C2211yescharacteristic
48C2×#14519684C2211yescharacteristic
49C2×#14519684C2211yescharacteristic
50C23×D4×C61C2211yescharacteristic
51C24×C4×C61C2211yescharacteristic
52C22×C22⋊C4×C61C2211yescharacteristic
53C22×C22⋊C4×C61C2211yescharacteristic
54C22×C22⋊C4×C61C2211yescharacteristic
55C61×#386—24no—
56C2×#95×C61C2211yescharacteristic
57C2×#95×C61C2211yescharacteristic
58C24×D61C2311yescharacteristic
59C22×C22⋊D61—22no—
60C22×C22⋊D61—22no—
61C22×C22⋊D61—41no—
62C22×C22⋊D61—41no—
63C22×C22⋊D61—41no—
64C22×C22⋊D61—41no—
65C22×C22⋊D61—41no—
66C22×C22⋊D61—41no—
67C22×C22⋊D61—41no—
68C22×C22⋊D61—41no—
69C22×C22⋊D61C2×C414yes—
70C22×C22⋊D61C2×C414yescomplemented
71C22×C22⋊D61D414yes—
72C22×C22⋊D61D414yes—
73C23×Dic61C2311yescharacteristic
74C23×Dic61C2311yescharacteristic
75C23×Dic61C2311yescharacteristic
76C23×Dic61C2311yescharacteristic
77C23×Dic61C2311yescharacteristic
78C23×Dic61C2311yescharacteristic
79C23×Dic61C2311yescharacteristic
80C22×C4×D61—22no—
81C22×C4×D61—22no—
82C22×C4×D61—22no—
83C22×C4×D61—22no—
84C22×C4×D61—41no—
85C22×C4×D61—41no—
86C22×C4×D61C2×C414yescomplemented
87#14519748—232no—
88C2×C4⋊Dic61—22no—
89C2×C4⋊Dic61—22no—
90C2×C4⋊Dic61C2×C414yescomplemented
91C2×#11758196—22no—
92C2×#11758196—41no—
93C2×#11758196—41no—
94C2×C22⋊Dic61—22no—
95C2×C22⋊Dic61—22no—
96C2×C22⋊Dic61—22no—
97C2×C22⋊Dic61—22no—
98C2×C22⋊Dic61—22no—
99C2×C22⋊Dic61—22no—
100C2×C22⋊Dic61—22no—
101C2×C22⋊Dic61—22no—
102C2×C22⋊Dic61—41no—
103C2×C22⋊Dic61—41no—
104C2×C22⋊Dic61—41no—
105C2×C22⋊Dic61—41no—
106C2×C22⋊Dic61—41no—
107C2×C22⋊Dic61—41no—
108C2×C22⋊Dic61—41no—
109C2×C22⋊Dic61—41no—
110C2×C22⋊Dic61C2×C414yes—
111C2×C22⋊Dic61C2×C414yescomplemented
112C2×#11758198—22no—
113C2×#11758198—22no—
114C2×#11758198—22no—
115C2×#11758198—22no—
116C2×#11758198—22no—
117C2×#11758198—22no—
118C2×#11758198—22no—
119C2×#11758198—22no—
120C2×#11758198—41no—
121C2×#11758198—41no—
122C2×#11758198—41no—
123C2×#11758198—41no—
124C2×C4×Dic61—22no—
125C2×C4×Dic61—41no—
126C2×C4×Dic61—41no—
127#14519684—22no—
128#14519684—22no—
129#14519684—22no—
130#14519684—22no—
131#14519684—22no—
132#14519684—22no—
133#14519684—41no—
134#14519684—41no—
135#14519684—41no—
136#14519684—41no—
137#14519684—41no—
138#14519684—41no—
139C25×C61C2311yescharacteristic
140C25×C61C2311yescharacteristic
141C22×D4×C61—22no—
142C22×D4×C61—22no—
143C22×D4×C61—22no—
144C22×D4×C61—22no—
145C22×D4×C61—41no—
146C22×D4×C61—41no—
147C22×D4×C61C2×C414yes—
148C23×C4×C61—22no—
149C23×C4×C61—22no—
150C23×C4×C61—22no—
151C23×C4×C61—41no—
152C23×C4×C61—41no—
153C23×C4×C61—41no—
154C23×C4×C61—41no—
155C23×C4×C61C2311yescharacteristic
156C23×C4×C61C2311yescharacteristic
157C23×C4×C61C2311yescharacteristic
158C23×C4×C61C2311yescharacteristic
159C23×C4×C61C2311yescharacteristic
160C2×C22⋊C4×C61—22no—
161C2×C22⋊C4×C61—22no—
162C2×C22⋊C4×C61—22no—
163C2×C22⋊C4×C61—22no—
164C2×C22⋊C4×C61—22no—
165C2×C22⋊C4×C61—41no—
166C2×C22⋊C4×C61—41no—
167C2×C22⋊C4×C61—41no—
168C2×C22⋊C4×C61—41no—
169#95×C61—22no—
170#95×C61D414yescomplemented
171C24×C61—21no—
172C24×C61—21no—
173C24×C61—21no—
174C24×C61—21no—
175C24×C61—21no—
176C24×C61—21no—
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×C61—21no—
190C24×C61—21no—
191C24×C61—21no—
192C24×C61—21no—
193C24×C61—21no—
194C24×C61—21no—
195C24×C61—21no—
196C24×C61—21no—
197C24×C61C22×C412yes—
198C24×C61C22×C412yes—
199C24×C61C2×D412yes—
200C24×C61C2×D412yes—
201C24×C61C2411yescharacteristic
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×D61C22×C412yes—
215C23×D61C2×D412yes—
216C23×D61C2×D412yes—
217C2×D4×C61—28no—
218C2×D4×C61—28no—
219C2×D4×C61—44no—
220C2×D4×C61—44no—
221C2×D4×C61—44no—
222C2×D4×C61—44no—
223C2×D4×C61—44no—
224C22×C4×C61—21no—
225C22×C4×C61—21no—
226C22×C4×C61—21no—
227C22×C4×C61—21no—
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—44no—
254C22×C4×C61—44no—
255C22×C4×C61—44no—
256C22×C4×C61—44no—
257C22×C4×C61—44no—
258C22×C4×C61—44no—
259C22×C4×C61—44no—
260C22×C4×C61C22×C412yes—
261C22×C4×C61C2×D412yes—
262C22×C4×C61C2×D412yes—
263C22×C4×C61C2×D412yes—
264C22×C4×C61#4112yes—
265C22×C4×C61#4112yes—
266C2×C22⋊D61—28no—
267C2×C22⋊D61—44no—
268C2×C22⋊D61—44no—
269C2×C22⋊D61—44no—
270C2×C22⋊D61—44no—
271C2×C22⋊D61—44no—
272C2×C22⋊D61—44no—
273C2×C22⋊D61—44no—
274C2×C22⋊D61—44no—
275C2×C22⋊D61—44no—
276C2×C22⋊D61—44no—
277C2×C22⋊D61—44no—
278C2×C22⋊D61—44no—
279C2×C22⋊D61C22⋊C4116yescomplemented
280C22×Dic61—21no—
281C22×Dic61—21no—
282C22×Dic61—21no—
283C22×Dic61—21no—
284C22×Dic61—21no—
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—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×Dic61C22×C412yes—
324C22×Dic61C22×C412yes—
325C22×Dic61C22×C412yes—
326C22×Dic61C2×D412yes—
327C22×Dic61C2×D412yes—
328C22×Dic61#4112yes—
329C2×C4×D61—28no—
330C2×C4×D61—28no—
331C2×C4×D61—44no—
332C2×C4×D61—44no—
333C2×C4×D61—44no—
334C2×C4×D61—44no—
335C2×C4×D61—44no—
336C22⋊C4×C61—44no—
337C22⋊C4×C61—44no—
338C22⋊C4×C61—44no—
339C22⋊Dic61—28no—
340C22⋊Dic61—28no—
341C22⋊Dic61—44no—
342C22⋊Dic61—44no—
343C22⋊Dic61—44no—
344C22⋊Dic61—44no—
345#11758198—44no—
346#11758198—44no—
347#11758198—44no—
348#11758198—44no—
349C4⋊Dic61—28no—
350#11758196—44no—
351C4×Dic61—44no—
352C23×C61—22no—
353C23×C61—22no—
354C23×C61—22no—
355C23×C61—22no—
356C23×C61—22no—
357C23×C61—22no—
358C23×C61—22no—
359C23×C61—22no—
360C23×C61—22no—
361C23×C61—22no—
362C23×C61—22no—
363C23×C61—22no—
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—41no—
378C23×C61—41no—
379C23×C61—41no—
380C23×C61—41no—
381C23×C61—41no—
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×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×C61C2×C22⋊C414yes—
422C23×C61C23×C411yescharacteristic
423C23×C61C22×D411yescharacteristic
424C23×C61C22×D411yescharacteristic
425C23×C61C22×D411yescharacteristic
426C23×C61C2×#4111yescharacteristic
427C23×C61C2×#4111yescharacteristic
428C23×C61C2×#4111yescharacteristic
429C23×C61H(5,𝔽2)11yescharacteristic
430C23×C61H(5,𝔽2)11yescharacteristic
431C23×C61H(5,𝔽2)11yescharacteristic
432C23×C61H(5,𝔽2)11yescharacteristic
433C23×C61H(5,𝔽2)11yescharacteristic
434C23×C61H(5,𝔽2)11yescharacteristic
435C23×C61H(5,𝔽2)11yescharacteristic
436C23×C612−1+411yescharacteristic
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—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×D61C2×C22⋊C414yes—
472D4×C61—416no—
473C2×C4×C61—22no—
474C2×C4×C61—22no—
475C2×C4×C61—22no—
476C2×C4×C61—22no—
477C2×C4×C61—22no—
478C2×C4×C61—22no—
479C2×C4×C61—22no—
480C2×C4×C61—22no—
481C2×C4×C61—22no—
482C2×C4×C61—22no—
483C2×C4×C61—22no—
484C2×C4×C61—22no—
485C2×C4×C61—22no—
486C2×C4×C61—22no—
487C2×C4×C61—22no—
488C2×C4×C61—416no—
489C2×C4×C61—41no—
490C2×C4×C61—41no—
491C2×C4×C61—41no—
492C2×C4×C61—41no—
493C2×C4×C61—41no—
494C2×C4×C61—41no—
495C2×C4×C61—41no—
496C2×C4×C61—41no—
497C2×C4×C61—41no—
498C2×C4×C61—41no—
499C2×C4×C61—41no—
500C2×C4×C61—41no—
501C2×C4×C61—41no—
502C2×C4×C61—41no—
503C2×C4×C61—41no—
504C2×C4×C61—41no—
505C2×C4×C61—41no—
506C2×C4×C61—41no—
507C2×C4×C61—41no—
508C2×C4×C61C4×D414yes—
509C22⋊D61—416no—
510C22⋊D61—416no—
511C2×Dic61—22no—
512C2×Dic61—22no—
513C2×Dic61—22no—
514C2×Dic61—22no—
515C2×Dic61—22no—
516C2×Dic61—22no—
517C2×Dic61—22no—
518C2×Dic61—22no—
519C2×Dic61—22no—
520C2×Dic61—22no—
521C2×Dic61—22no—
522C2×Dic61—22no—
523C2×Dic61—22no—
524C2×Dic61—22no—
525C2×Dic61—22no—
526C2×Dic61—41no—
527C2×Dic61—41no—
528C2×Dic61—41no—
529C2×Dic61—41no—
530C2×Dic61—41no—
531C2×Dic61—41no—
532C2×Dic61—41no—
533C2×Dic61—41no—
534C2×Dic61—41no—
535C2×Dic61—41no—
536C2×Dic61—41no—
537C2×Dic61—41no—
538C2×Dic61—41no—
539C2×Dic61—41no—
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—41no—
557C2×Dic61—41no—
558C2×Dic61—41no—
559C2×Dic61C2×C22⋊C414yes—
560C4×D61—416no—
561#14363—611nomaximal, Sylow
562C22×C61—24no—
563C22×C61—24no—
564C22×C61—24no—
565C22×C61—42no—
566C22×C61—42no—
567C22×C61—42no—
568C22×C61—42no—
569C22×C61—42no—
570C22×C61—42no—
571C22×C61—42no—
572C22×C61—42no—
573C22×C61—42no—
574C22×C61—42no—
575C22×C61—42no—
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—81no—
585C22×C61—81no—
586C22×C61—81no—
587C22×C61—81no—
588C22×C61—81no—
589C22×C61—81no—
590C22×C61—81no—
591C22×C61—81no—
592C22×C61C22×C22⋊C411yescharacteristic
593C22×C61C2×C4×D411yescharacteristic
594C22×C61C4×#4111yescharacteristic
595C22×C61#51811yescharacteristic
596C22×C61#51811yescharacteristic
597C22×C61#51811yescharacteristic
598C22×C61#52011yescharacteristic
599C22×C61#53411yescharacteristic
600C22×C61#53411yescharacteristic
601C22×C61#53411yescharacteristic
602C22×C61#53411yescharacteristic
603C22×C61#53511yescharacteristic
604C22×C61#53711yescharacteristic
605C22×C61#53811yescharacteristic
606C22×C61#53811yescharacteristic
607C22×C61#54011yescharacteristic
608C22×C61#54011yescharacteristic
609C22×C61#54011yescharacteristic
610C22×C61#54211yescharacteristic
611C22×C61D4211yescharacteristic
612C22×C61D4211yescharacteristic
613C22×C61#54611yescharacteristic
614C22×C61#54611yescharacteristic
615C22×C61#54611yescharacteristic
616C22×C61#54611yescharacteristic
617C22×C61#54611yescharacteristic
618C22×C61#54711yescharacteristic
619C22×C61#54711yescharacteristic
620C22×C61#55011yescharacteristic
621C22×C61#55311yescharacteristic
622C22×C61#55511yescharacteristic
623C22×C61#56011yescharacteristic
624C22×C61#56011yescharacteristic
625C22×C61#56211yescharacteristic
626C22×C61#56211yescharacteristic
627C2×D61—24no—
628C2×D61—24no—
629C2×D61—24no—
630C2×D61—42no—
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—
642C4×C61—24no—
643C4×C61—42no—
644C4×C61—42no—
645C4×C61—42no—
646C4×C61—81no—
647Dic61—24no—
648Dic61—42no—
649Dic61—42no—
650Dic61—42no—
651Dic61—81no—
652Dic61—81no—
653Dic61—81no—
654C22×#121—611no—
655C2×#390—611no—
656C2×#386—611no—
657C2×#386D6111yescharacteristic, complemented
658C2×#381—611no—
659#1441—611no—
660#1440—611no—
661#1439—611no—
662#1438—611no—
663#1438—611no—
664#1438—611no—
665#1437—611no—
666#1436—611no—
667C22⋊#95—611no—
668C22⋊#95—611no—
669C2×C61—44no—
670C2×C61—82no—
671C2×C61#230811yescharacteristic
672C2×C61#232411yescharacteristic
673C2×C61#233311yescharacteristic
674C2×C61D4×C22⋊C411yescharacteristic
675C2×C61#233911yescharacteristic
676C2×C61#236311yescharacteristic
677C2×C61#237711yescharacteristic
678C2×C61#267111yescharacteristic
679C2×C61#267311yescharacteristic
680C2×C61#267811yescharacteristic
681C2×C61#268211yescharacteristic
682C2×C61#268611yescharacteristic
683C2×C61#268811yescharacteristic
684C2×C61#269911yescharacteristic
685C2×C61#270111yescharacteristic
686D61—44no—
687C23×D4—611no—
688C23×D4—611no—
689C23×D4C2×D6111yescharacteristic
690C24×C4—611no—
691C24×C4C2×D6111yescharacteristic
692C2×#121—618no—
693C2×#121—1224no—
694C2×#121—1224no—
695C22×C4⋊C4—611no—
696C22×C4⋊C4—611no—
697C22×C22⋊C4—611no—
698C22×C22⋊C4—611no—
699C22×C22⋊C4—611no—
700C22×C22⋊C4—611no—
701C22×C22⋊C4—611no—
702C22×C22⋊C4—611no—
703C22×C22⋊C4—611no—
704C22×C22⋊C4—611no—
705C22×C22⋊C4—611no—
706C22×C22⋊C4—611no—
707C22×C22⋊C4C2×D6111yescharacteristic
708C22×C22⋊C4C2×D6111yescharacteristic
709C22×C22⋊C4C2×D6111yescharacteristic
710C22×C42—611no—
711#390—1224no—
712#386—24no—
713#386—1224no—
714#381—1224no—
715C2×#95—611no—
716C2×#95—611no—
717C2×#95—611no—
718C2×#95—611no—
719C2×#95—611no—
720C2×#95—611no—
721C2×#95—611no—
722C2×#95—611no—
723C2×#95—611no—
724C2×#95—611no—
725C2×#95—611no—
726C2×#95—611no—
727C2×#95C2×D6111yescharacteristic
728C2×#95C2×D6111yescharacteristic
729C61#1436311yescharacteristic, complemented, Sylow
730C25—611no—
731C25C22×D6111yescharacteristic
732C25C22×D6111yescharacteristic
733C22×D4—22no—
734C22×D4—22no—
735C22×D4—22no—
736C22×D4—22no—
737C22×D4—41no—
738C22×D4—41no—
739C22×D4—614no—
740C22×D4—614no—
741C22×D4—614no—
742C22×D4—614no—
743C22×D4—1222no—
744C22×D4—1222no—
745C22×D4—2441no—
746C22×D4—2441no—
747C22×D4—2441no—
748C22×D4—2441no—
749C22×D4—2441no—
750C22×D4—2441no—
751C22×D4—2441no—
752C22×D4—2441no—
753C22×D4C4×D6114yes—
754C23×C4—22no—
755C23×C4—22no—
756C23×C4—22no—
757C23×C4—41no—
758C23×C4—41no—
759C23×C4—41no—
760C23×C4—41no—
761C23×C4—611no—
762C23×C4—611no—
763C23×C4—611no—
764C23×C4—611no—
765C23×C4—614no—
766C23×C4—611no—
767C23×C4—611no—
768C23×C4—611no—
769C23×C4—1222no—
770C23×C4—1222no—
771C23×C4—1222no—
772C23×C4—1222no—
773C23×C4—2441no—
774C23×C4—2441no—
775C23×C4C22×D6111yescharacteristic
776C23×C4C22×D6111yescharacteristic
777C23×C4C22×D6111yescharacteristic
778C23×C4C22×D6111yescharacteristic
779C23×C4C22×D6111yescharacteristic
780#121—12232no—
781C2×C4⋊C4—614no—
782C2×C4⋊C4—1222no—
783C2×C4⋊C4—1222no—
784C2×C4⋊C4—1222no—
785C2×C4⋊C4—2441no—
786C2×C4⋊C4—2441no—
787C2×C22⋊C4—22no—
788C2×C22⋊C4—22no—
789C2×C22⋊C4—22no—
790C2×C22⋊C4—22no—
791C2×C22⋊C4—22no—
792C2×C22⋊C4—41no—
793C2×C22⋊C4—41no—
794C2×C22⋊C4—41no—
795C2×C22⋊C4—41no—
796C2×C22⋊C4—614no—
797C2×C22⋊C4—614no—
798C2×C22⋊C4—1222no—
799C2×C22⋊C4—1222no—
800C2×C22⋊C4—1222no—
801C2×C22⋊C4—1222no—
802C2×C22⋊C4—1222no—
803C2×C22⋊C4—1222no—
804C2×C22⋊C4—1222no—
805C2×C22⋊C4—1222no—
806C2×C22⋊C4—1222no—
807C2×C22⋊C4—1222no—
808C2×C22⋊C4—1222no—
809C2×C22⋊C4—1222no—
810C2×C22⋊C4—1222no—
811C2×C22⋊C4—1222no—
812C2×C22⋊C4—1222no—
813C2×C22⋊C4—1222no—
814C2×C22⋊C4—2441no—
815C2×C22⋊C4—2441no—
816C2×C22⋊C4—2441no—
817C2×C22⋊C4—2441no—
818C2×C22⋊C4—2441no—
819C2×C22⋊C4—2441no—
820C2×C22⋊C4—2441no—
821C2×C22⋊C4—2441no—
822C2×C22⋊C4—2441no—
823C2×C22⋊C4—2441no—
824C2×C22⋊C4—2441no—
825C2×C22⋊C4—2441no—
826C2×C42—1222no—
827C2×C42—2441no—
828C2×C42—2441no—
829#95—22no—
830#95—1222no—
831#95—1222no—
832#95—1222no—
833#95—1222no—
834#95—1222no—
835#95—1222no—
836#95—2441no—
837#95—2441no—
838#95—2441no—
839#95—2441no—
840#95—2441no—
841#95—2441no—
842#95C22⋊D6114yescomplemented
843C24—21no—
844C24—21no—
845C24—21no—
846C24—21no—
847C24—21no—
848C24—21no—
849C24—21no—
850C24—21no—
851C24—21no—
852C24—21no—
853C24—21no—
854C24—21no—
855C24—21no—
856C24—21no—
857C24—21no—
858C24—21no—
859C24—21no—
860C24—21no—
861C24—21no—
862C24—21no—
863C24—21no—
864C24—21no—
865C24—21no—
866C24—21no—
867C24—21no—
868C24—21no—
869C24—612no—
870C24—612no—
871C24—612no—
872C24—1221no—
873C24—1221no—
874C24—1221no—
875C24—1221no—
876C24—1221no—
877C24—1221no—
878C24—1221no—
879C24—1221no—
880C24—1221no—
881C24—1221no—
882C24—1221no—
883C24—1221no—
884C24C2×C4×D6112yes—
885C24C2×C4×D6112yes—
886C24D4×D6112yes—
887C24D4×D6112yes—
888C24C23×D6111yescharacteristic
889C2×D4—28no—
890C2×D4—28no—
891C2×D4—44no—
892C2×D4—44no—
893C2×D4—44no—
894C2×D4—44no—
895C2×D4—44no—
896C2×D4—6116no—
897C2×D4—1228no—
898C2×D4—2444no—
899C2×D4—2444no—
900C2×D4—2444no—
901C2×D4—2444no—
902C2×D4—2444no—
903C2×D4—2444no—
904C2×D4—2444no—
905C2×D4—2444no—
906C2×D4—2444no—
907C2×D4—2444no—
908C2×D4—2444no—
909C2×D4—2444no—
910C22×C4—21no—
911C22×C4—21no—
912C22×C4—21no—
913C22×C4—21no—
914C22×C4—21no—
915C22×C4—21no—
916C22×C4—21no—
917C22×C4—21no—
918C22×C4—21no—
919C22×C4—21no—
920C22×C4—21no—
921C22×C4—21no—
922C22×C4—21no—
923C22×C4—21no—
924C22×C4—21no—
925C22×C4—21no—
926C22×C4—21no—
927C22×C4—21no—
928C22×C4—21no—
929C22×C4—21no—
930C22×C4—21no—
931C22×C4—21no—
932C22×C4—21no—
933C22×C4—21no—
934C22×C4—21no—
935C22×C4—21no—
936C22×C4—21no—
937C22×C4—21no—
938C22×C4—21no—
939C22×C4—44no—
940C22×C4—44no—
941C22×C4—44no—
942C22×C4—44no—
943C22×C4—44no—
944C22×C4—44no—
945C22×C4—44no—
946C22×C4—612no—
947C22×C4—612no—
948C22×C4—612no—
949C22×C4—612no—
950C22×C4—612no—
951C22×C4—612no—
952C22×C4—1228no—
953C22×C4—1221no—
954C22×C4—1221no—
955C22×C4—1221no—
956C22×C4—1221no—
957C22×C4—1221no—
958C22×C4—1221no—
959C22×C4—1221no—
960C22×C4—1221no—
961C22×C4—1221no—
962C22×C4—1221no—
963C22×C4—1221no—
964C22×C4—1221no—
965C22×C4—1221no—
966C22×C4—1221no—
967C22×C4—1221no—
968C22×C4—1221no—
969C22×C4—1221no—
970C22×C4—1221no—
971C22×C4—1221no—
972C22×C4—1221no—
973C22×C4—1221no—
974C22×C4—1221no—
975C22×C4—1228no—
976C22×C4—1221no—
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—2444no—
998C22×C4—2444no—
999C22×C4—2444no—
1000C22×C4—2444no—
1001C22×C4—2444no—
1002C22×C4C2×C4×D6112yes—
1003C22×C4#1175822212yes—
1004C22×C4#1175822412yes—
1005C22×C4C2×C22⋊D6112yes—
1006C22×C4C2×C22⋊D6112yes—
1007C22×C4C2×C22⋊D6112yes—
1008C4⋊C4—1228no—
1009C4⋊C4—2444no—
1010C22⋊C4—44no—
1011C22⋊C4—44no—
1012C22⋊C4—44no—
1013C22⋊C4—1228no—
1014C22⋊C4—1228no—
1015C22⋊C4—2444no—
1016C22⋊C4—2444no—
1017C22⋊C4—2444no—
1018C22⋊C4—2444no—
1019C22⋊C4—2444no—
1020C22⋊C4—2444no—
1021C22⋊C4—2444no—
1022C22⋊C4—2444no—
1023C42—2444no—
1024C23—22no—
1025C23—22no—
1026C23—22no—
1027C23—22no—
1028C23—22no—
1029C23—22no—
1030C23—22no—
1031C23—22no—
1032C23—22no—
1033C23—22no—
1034C23—22no—
1035C23—22no—
1036C23—22no—
1037C23—22no—
1038C23—22no—
1039C23—22no—
1040C23—22no—
1041C23—22no—
1042C23—22no—
1043C23—22no—
1044C23—22no—
1045C23—22no—
1046C23—22no—
1047C23—22no—
1048C23—22no—
1049C23—41no—
1050C23—41no—
1051C23—41no—
1052C23—41no—
1053C23—41no—
1054C23—41no—
1055C23—41no—
1056C23—41no—
1057C23—41no—
1058C23—41no—
1059C23—41no—
1060C23—41no—
1061C23—41no—
1062C23—41no—
1063C23—41no—
1064C23—41no—
1065C23—41no—
1066C23—41no—
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—41no—
1084C23—41no—
1085C23—41no—
1086C23—41no—
1087C23—41no—
1088C23—41no—
1089C23—41no—
1090C23—41no—
1091C23—41no—
1092C23—41no—
1093C23—614no—
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—2441no—
1113C23—2441no—
1114C23—2441no—
1115C23—2441no—
1116C23—2441no—
1117C23—2441no—
1118C23—2441no—
1119C23—2441no—
1120C23—2441no—
1121C23—2441no—
1122C23—2441no—
1123C23—2441no—
1124C23—2441no—
1125C23—2441no—
1126C23—2441no—
1127C23—2441no—
1128C23C22⋊C4×D6114yes—
1129C23C22×C4×D6111yescharacteristic
1130C23C2×D4×D6111yescharacteristic
1131C23C2×D4×D6111yescharacteristic
1132C23C22×C22⋊D6111yescharacteristic
1133C23#41×D6111yescharacteristic
1134C23C2×#1175822411yescharacteristic
1135C23C2×#1175822211yescharacteristic
1136C23#1451982211yescharacteristic
1137C23#1451982211yescharacteristic
1138C23#1451982211yescharacteristic
1139C23#1451982211yescharacteristic
1140C23#1451982211yescharacteristic
1141C23#1451982311yescharacteristic
1142C23#1451982311yescharacteristic
1143C23#1451982411yescharacteristic
1144D4—416no—
1145D4—24416no—
1146D4—24416no—
1147C2×C4—22no—
1148C2×C4—22no—
1149C2×C4—22no—
1150C2×C4—22no—
1151C2×C4—22no—
1152C2×C4—22no—
1153C2×C4—22no—
1154C2×C4—22no—
1155C2×C4—22no—
1156C2×C4—22no—
1157C2×C4—22no—
1158C2×C4—22no—
1159C2×C4—22no—
1160C2×C4—22no—
1161C2×C4—22no—
1162C2×C4—416no—
1163C2×C4—41no—
1164C2×C4—41no—
1165C2×C4—41no—
1166C2×C4—41no—
1167C2×C4—41no—
1168C2×C4—41no—
1169C2×C4—41no—
1170C2×C4—41no—
1171C2×C4—41no—
1172C2×C4—41no—
1173C2×C4—41no—
1174C2×C4—41no—
1175C2×C4—41no—
1176C2×C4—41no—
1177C2×C4—41no—
1178C2×C4—41no—
1179C2×C4—41no—
1180C2×C4—41no—
1181C2×C4—41no—
1182C2×C4—614no—
1183C2×C4—1222no—
1184C2×C4—1222no—
1185C2×C4—1222no—
1186C2×C4—1222no—
1187C2×C4—1222no—
1188C2×C4—1222no—
1189C2×C4—1222no—
1190C2×C4—1222no—
1191C2×C4—1222no—
1192C2×C4—1222no—
1193C2×C4—1222no—
1194C2×C4—1222no—
1195C2×C4—1222no—
1196C2×C4—1222no—
1197C2×C4—1222no—
1198C2×C4—24416no—
1199C2×C4—2441no—
1200C2×C4—2441no—
1201C2×C4—2441no—
1202C2×C4—2441no—
1203C2×C4—2441no—
1204C2×C4—2441no—
1205C2×C4—2441no—
1206C2×C4—2441no—
1207C2×C4—2441no—
1208C2×C4—2441no—
1209C2×C4—2441no—
1210C2×C4—2441no—
1211C2×C4—2441no—
1212C2×C4—2441no—
1213C2×C4—2441no—
1214C2×C4—2441no—
1215C2×C4—2441no—
1216C2×C4—2441no—
1217C2×C4—2441no—
1218C2×C4—2441no—
1219C2×C4—2441no—
1220C2×C4—2441no—
1221C2×C4—2441no—
1222C2×C4—2441no—
1223C2×C4—2441no—
1224C2×C4—2441no—
1225C2×C4—2441no—
1226C2×C4—2441no—
1227C2×C4—2441no—
1228C2×C4—2441no—
1229C2×C4—2441no—
1230C2×C4—2441no—
1231C2×C4—2441no—
1232C2×C4C4×C22⋊D6114yes—
1233C22—24no—
1234C22—24no—
1235C22—24no—
1236C22—42no—
1237C22—42no—
1238C22—42no—
1239C22—42no—
1240C22—42no—
1241C22—42no—
1242C22—42no—
1243C22—42no—
1244C22—42no—
1245C22—42no—
1246C22—42no—
1247C22—42no—
1248C22—42no—
1249C22—42no—
1250C22—42no—
1251C22—42no—
1252C22—42no—
1253C22—42no—
1254C22—42no—
1255C22—81no—
1256C22—81no—
1257C22—81no—
1258C22—81no—
1259C22—81no—
1260C22—81no—
1261C22—81no—
1262C22—81no—
1263C22—1224no—
1264C22—1224no—
1265C22—1224no—
1266C22—2442no—
1267C22—2442no—
1268C22—2442no—
1269C22—2442no—
1270C22—2442no—
1271C22—2442no—
1272C22—2442no—
1273C22—2442no—
1274C22—2442no—
1275C22—2442no—
1276C22—2442no—
1277C22—2442no—
1278C22C2×C22⋊C4×D6111yescharacteristic
1279C22C2×C4×C22⋊D6111yescharacteristic
1280C22C4×#1175822411yescharacteristic
1281C22#1684023411yescharacteristic
1282C22#1684023411yescharacteristic
1283C22#1684023511yescharacteristic
1284C22#1684024111yescharacteristic
1285C22#1684032011yescharacteristic
1286C22#1684032011yescharacteristic
1287C22#1684032211yescharacteristic
1288C22#1684032311yescharacteristic
1289C22#1684032911yescharacteristic
1290C22#1684034011yescharacteristic
1291C22#1684034711yescharacteristic
1292C22#1684034811yescharacteristic
1293C22#1684036211yescharacteristic
1294C22#1684036311yescharacteristic
1295C22#1684036511yescharacteristic
1296C22#1684037711yescharacteristic
1297C22D4×C22⋊D6111yescharacteristic
1298C22D4×C22⋊D6111yescharacteristic
1299C22#1684039911yescharacteristic
1300C22#1684040111yescharacteristic
1301C22#1684040211yescharacteristic
1302C22#1684040211yescharacteristic
1303C22#1684040611yescharacteristic
1304C22#1684041011yescharacteristic
1305C22#1684041211yescharacteristic
1306C22#1684043111yescharacteristic
1307C22#1684046211yescharacteristic
1308C22#1684047711yescharacteristic
1309C22#1684050011yescharacteristic
1310C22#1684050111yescharacteristic
1311C22#1684050711yescharacteristic
1312C22#1684050911yescharacteristic
1313C4—24no—
1314C4—42no—
1315C4—42no—
1316C4—42no—
1317C4—81no—
1318C4—1224no—
1319C4—4881no—
1320C4—4881no—
1321C4—4881no—
1322C4—2442no—
1323C4—2442no—
1324C4—2442no—
1325C2—44no—
1326C2—82no—
1327C2—2444no—
1328C2#2144839311yescharacteristic
1329C2#2144850611yescharacteristic
1330C2#2144858011yescharacteristic
1331C2C22⋊C4×C22⋊D6111yescharacteristic
1332C2#2144864511yescharacteristic
1333C2#2144885311yescharacteristic
1334C2#2144897111yescharacteristic
1335C2#2145205011yescharacteristic
1336C2#2145208011yescharacteristic
1337C2#2145214011yescharacteristic
1338C2#2145218411yescharacteristic
1339C2#2145222011yescharacteristic
1340C2#2145225011yescharacteristic
1341C2#2145240811yescharacteristic
1342C2#2145243511yescharacteristic
subgroupG/H
center, FrattiniC24C23×D61
commutatorC23×C61C23×C4
FittingC2×C61×#386C2
socle, cosocleC24×C61C24
prime radicalC22×#14519748C2
hypercenterC2×#386D61
hypocenterC61#14363
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C24 ◁ C2×#386

Complements

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

NH ≅ G/Ntype
2. C2×#16839662C2semidirect
3. C2×#16839641C2semidirect
4. C2×#16839624C2semidirect
5. #21444071C2semidirect
6. #21444066C2semidirect
7. #21444062C2semidirect
8. #21444060C2semidirect
9. #21444058C2semidirect
10. #21444058C2semidirect
11. #21444056C2semidirect
12. #21444053C2semidirect
13. #21444042C2semidirect
14. #21444040C2semidirect
15. C2×C61×#386C2semidirect
21. C2×#14519748C4semidirect
70. C22×C22⋊D61C2×C4semidirect
86. C22×C4×D61C2×C4semidirect
90. C2×C4⋊Dic61C2×C4semidirect
111. C2×C22⋊Dic61C2×C4semidirect
170. #95×C61D4semidirect
279. C2×C22⋊D61C22⋊C4semidirect
657. C2×#386D61semidirect
729. C61#14363semidirect
842. #95C22⋊D61semidirect

Maximal subgroups

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

subgroupindex
C22×#145197482
C2×#168396622
C2×#168396412
C2×#168396242
#214440712
#214440662
#214440622
#214440602
#214440582
#214440562
#214440532
#214440422
#214440402
C2×C61×#3862
#1436361