Finite Group Databasebeta

← #29609349

Subgroups — #29609349

Order 15616.

2390 conjugacy classes of subgroups.

The subgroup lattice has 1342 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839665C211yesmaximal, characteristic, complemented
2C2×#16839642C211yesmaximal, characteristic, complemented
3C2×#16839642C211yesmaximal, characteristic, complemented
4C2×#16839642C211yesmaximal, characteristic, complemented
5C2×#16839642C211yesmaximal, characteristic, complemented
6C2×#16839637C211yesmaximal, characteristic, complemented
7#21444076C211yesmaximal, characteristic, complemented
8#21444068C211yesmaximal, characteristic, complemented
9#21444064C211yesmaximal, characteristic, complemented
10#21444064C211yesmaximal, characteristic, complemented
11#21444060C211yesmaximal, characteristic, complemented
12#21444056C211yesmaximal, characteristic, complemented
13#21444044C211yesmaximal, characteristic, complemented
14#21444041C211yesmaximal, characteristic, complemented
15C2×C61×#392C211yesmaximal, characteristic
16C24×Dic61C2211yescharacteristic
17C24×Dic61C2211yescharacteristic
18C22×C4⋊Dic61C2211yescharacteristic
19C22×C4⋊Dic61C2211yescharacteristic
20C22×C22⋊Dic61C2211yescharacteristic
21C22×C22⋊Dic61C2211yescharacteristic
22C22×C22⋊Dic61C2211yescharacteristic
23C22×C22⋊Dic61C2211yescharacteristic
24C22×C22⋊Dic61C2211yescharacteristic
25C22×C22⋊Dic61C2211yescharacteristic
26C22×C22⋊Dic61C2211yescharacteristic
27C22×C22⋊Dic61C2211yescharacteristic
28C22×C22⋊Dic61C2211yescharacteristic
29C22×C22⋊Dic61C2211yescharacteristic
30C22×C4×Dic61C2211yescharacteristic
31#16839665—24no—
32#16839642—24no—
33#16839642—24no—
34#16839642—24no—
35#16839642—24no—
36#16839637—24no—
37C2×#14519684C2211yescharacteristic
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
51C23×D4×C61C2211yescharacteristic
52C23×D4×C61C2211yescharacteristic
53C22×C22⋊C4×C61C2211yescharacteristic
54C22×C22⋊C4×C61C2211yescharacteristic
55C22×C22⋊C4×C61C2211yescharacteristic
56C61×#392C418yescomplemented
57C2×#95×C61C2211yescharacteristic
58C23×Dic61—22no—
59C23×Dic61—22no—
60C23×Dic61—22no—
61C23×Dic61—22no—
62C23×Dic61—22no—
63C23×Dic61—22no—
64C23×Dic61—41no—
65C23×Dic61—41no—
66C23×Dic61—41no—
67C23×Dic61—41no—
68C23×Dic61—41no—
69C23×Dic61—41no—
70C23×Dic61—41no—
71C23×Dic61—41no—
72C23×Dic61C2311yescharacteristic
73C23×Dic61C2311yescharacteristic
74C23×Dic61C2311yescharacteristic
75C23×Dic61C2311yescharacteristic
76C23×Dic61C2311yescharacteristic
77C23×Dic61C2311yescharacteristic
78C23×Dic61C2311yescharacteristic
79C23×Dic61C2311yescharacteristic
80C2×C4⋊Dic61—22no—
81C2×C4⋊Dic61—22no—
82C2×C4⋊Dic61—22no—
83C2×C4⋊Dic61—41no—
84C2×C4⋊Dic61—41no—
85C2×C4⋊Dic61—41no—
86C2×C22⋊Dic61—22no—
87C2×C22⋊Dic61—22no—
88C2×C22⋊Dic61—22no—
89C2×C22⋊Dic61—22no—
90C2×C22⋊Dic61—22no—
91C2×C22⋊Dic61—22no—
92C2×C22⋊Dic61—22no—
93C2×C22⋊Dic61—22no—
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—41no—
101C2×C22⋊Dic61—41no—
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⋊Dic61—41no—
111C2×C22⋊Dic61—41no—
112C2×C22⋊Dic61—41no—
113C2×C22⋊Dic61—41no—
114C2×C22⋊Dic61D414yescomplemented
115C2×C22⋊Dic61D414yescomplemented
116C2×C4×Dic61—22no—
117C2×C4×Dic61—22no—
118C2×C4×Dic61—41no—
119#14519684—22no—
120#14519684—22no—
121#14519684—22no—
122#14519684—22no—
123#14519684—22no—
124#14519684—22no—
125#14519684—22no—
126#14519684—22no—
127#14519684—41no—
128#14519684—41no—
129#14519684—41no—
130#14519684—41no—
131#14519684D414yescomplemented
132C25×C61C2311yescharacteristic
133C25×C61C2311yescharacteristic
134C25×C61C2311yescharacteristic
135C22×D4×C61—22no—
136C22×D4×C61—22no—
137C22×D4×C61—22no—
138C22×D4×C61—22no—
139C22×D4×C61—22no—
140C22×D4×C61—22no—
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×C61—41no—
148C22×D4×C61—41no—
149C22×D4×C61—41no—
150C22×D4×C61—41no—
151C22×D4×C61—41no—
152C22×D4×C61—41no—
153C22×D4×C61C2×C414yes—
154C22×D4×C61C2×C414yescomplemented
155C22×D4×C61C2×C414yescomplemented
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—41no—
163C2×C22⋊C4×C61—41no—
164C2×C22⋊C4×C61—41no—
165C2×C22⋊C4×C61—41no—
166C2×C22⋊C4×C61C2×C414yescomplemented
167C2×C22⋊C4×C61C2×C414yescomplemented
168C2×C22⋊C4×C61C2×C414yescomplemented
169#95×C61C2×C414yescomplemented
170C24×C61—21no—
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×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×C61C22×C412yes—
209C24×C61C22×C412yes—
210C24×C61C22×C412yes—
211C24×C61C2×D412yes—
212C24×C61C2×D412yes—
213C24×C61#4112yes—
214C24×C61#4112yes—
215C24×C61C2411yescharacteristic
216C2×D4×C61—28no—
217C2×D4×C61—28no—
218C2×D4×C61—28no—
219C2×D4×C61—28no—
220C2×D4×C61—28no—
221C2×D4×C61—44no—
222C2×D4×C61—44no—
223C2×D4×C61—44no—
224C2×D4×C61—44no—
225C2×D4×C61—44no—
226C2×D4×C61—44no—
227C2×D4×C61—44no—
228C2×D4×C61—44no—
229C2×D4×C61—44no—
230C2×D4×C61—44no—
231C2×D4×C61—44no—
232C2×D4×C61—44no—
233C2×D4×C61—44no—
234C2×D4×C61—44no—
235C2×D4×C61—44no—
236C2×D4×C61—44no—
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×C61C22×C412yes—
260C22×C4×C61C22×C412yes—
261C22×C4×C61C22×C412yes—
262C22×C4×C61C22×C412yes—
263C22×C4×C61C2×D412yes—
264C22×C4×C61#4112yes—
265C22×Dic61—21no—
266C22×Dic61—21no—
267C22×Dic61—21no—
268C22×Dic61—21no—
269C22×Dic61—21no—
270C22×Dic61—21no—
271C22×Dic61—21no—
272C22×Dic61—21no—
273C22×Dic61—21no—
274C22×Dic61—21no—
275C22×Dic61—21no—
276C22×Dic61—21no—
277C22×Dic61—21no—
278C22×Dic61—21no—
279C22×Dic61—21no—
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—44no—
316C22×Dic61—44no—
317C22×Dic61—44no—
318C22×Dic61—44no—
319C22×Dic61—44no—
320C22×Dic61—44no—
321C22×Dic61—44no—
322C22×Dic61—44no—
323C22×Dic61—44no—
324C22×Dic61—44no—
325C22×Dic61—44no—
326C22×Dic61—44no—
327C22×Dic61—44no—
328C22×Dic61—44no—
329C22×Dic61C2×D412yes—
330C22×Dic61C2×D412yes—
331C22×Dic61C2×D412yes—
332C22×Dic61C2×D412yes—
333C22×Dic61C2×D412yes—
334C22×Dic61C2×D412yes—
335C22⋊C4×C61—28no—
336C22⋊C4×C61—44no—
337C22⋊C4×C61—44no—
338C22⋊Dic61—44no—
339C22⋊Dic61—44no—
340C22⋊Dic61—44no—
341C22⋊Dic61—44no—
342C22⋊Dic61—44no—
343C22⋊Dic61—44no—
344C22⋊Dic61—44no—
345C22⋊Dic61—44no—
346C22⋊Dic61—44no—
347C22⋊Dic61—44no—
348C4⋊Dic61—44no—
349C4⋊Dic61—44no—
350C4×Dic61—44no—
351C23×C61—22no—
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—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—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×C61—41no—
434C23×C61—41no—
435C23×C61—41no—
436C23×C61—41no—
437C23×C61—41no—
438C23×C61—41no—
439C23×C61—41no—
440C23×C61—41no—
441C23×C61—41no—
442C23×C61—41no—
443C23×C61—41no—
444C23×C61—41no—
445C23×C61—41no—
446C23×C61—41no—
447C23×C61—41no—
448C23×C61—41no—
449C23×C61—41no—
450C23×C61—41no—
451C23×C61—41no—
452C23×C61—41no—
453C23×C61—41no—
454C23×C61C4×D414yes—
455C23×C61C4×D414yes—
456C23×C61C23×C411yescharacteristic
457C23×C61C22×D411yescharacteristic
458C23×C61C22×D411yescharacteristic
459C23×C61C22×D411yescharacteristic
460C23×C61C2×#4111yescharacteristic
461C23×C61C2×#4111yescharacteristic
462C23×C61C2×#4111yescharacteristic
463C23×C61H(5,𝔽2)11yescharacteristic
464C23×C61H(5,𝔽2)11yescharacteristic
465C23×C61H(5,𝔽2)11yescharacteristic
466C23×C61H(5,𝔽2)11yescharacteristic
467C23×C61H(5,𝔽2)11yescharacteristic
468C23×C61H(5,𝔽2)11yescharacteristic
469C23×C61H(5,𝔽2)11yescharacteristic
470C23×C612−1+411yescharacteristic
471D4×C61—416no—
472D4×C61—416no—
473D4×C61—416no—
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—22no—
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×C61C4×D414yes—
502C2×Dic61—22no—
503C2×Dic61—22no—
504C2×Dic61—22no—
505C2×Dic61—22no—
506C2×Dic61—22no—
507C2×Dic61—22no—
508C2×Dic61—22no—
509C2×Dic61—22no—
510C2×Dic61—22no—
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—416no—
521C2×Dic61—416no—
522C2×Dic61—41no—
523C2×Dic61—41no—
524C2×Dic61—41no—
525C2×Dic61—41no—
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×Dic61—41no—
560#14519—611nomaximal, Sylow
561C22×C61—24no—
562C22×C61—24no—
563C22×C61—24no—
564C22×C61—24no—
565C22×C61—24no—
566C22×C61—24no—
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—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—42no—
596C22×C61—42no—
597C22×C61—42no—
598C22×C61—81no—
599C22×C61—81no—
600C22×C61—81no—
601C22×C61—81no—
602C22×C61—81no—
603C22×C61—81no—
604C22×C61—81no—
605C22×C61—81no—
606C22×C61C2×C4×D411yescharacteristic
607C22×C61C2×C4×D411yescharacteristic
608C22×C61C2×C4×D411yescharacteristic
609C22×C61#51811yescharacteristic
610C22×C61#51811yescharacteristic
611C22×C61#51811yescharacteristic
612C22×C61#52011yescharacteristic
613C22×C61#53411yescharacteristic
614C22×C61#53411yescharacteristic
615C22×C61#53511yescharacteristic
616C22×C61#53511yescharacteristic
617C22×C61#53511yescharacteristic
618C22×C61#53711yescharacteristic
619C22×C61#53811yescharacteristic
620C22×C61#53811yescharacteristic
621C22×C61#53811yescharacteristic
622C22×C61#53911yescharacteristic
623C22×C61#54011yescharacteristic
624C22×C61#54011yescharacteristic
625C22×C61D4211yescharacteristic
626C22×C61D4211yescharacteristic
627C22×C61D4211yescharacteristic
628C22×C61#54611yescharacteristic
629C22×C61#54611yescharacteristic
630C22×C61#54611yescharacteristic
631C22×C61#54611yescharacteristic
632C22×C61#54711yescharacteristic
633C22×C61#54811yescharacteristic
634C22×C61#55111yescharacteristic
635C22×C61#55111yescharacteristic
636C22×C61#55311yescharacteristic
637C22×C61#56011yescharacteristic
638C22×C61#56011yescharacteristic
639C22×C61#56211yescharacteristic
640C22×C61#56211yescharacteristic
641C4×C61—24no—
642C4×C61—42no—
643C4×C61—42no—
644C4×C61—42no—
645Dic61—42no—
646Dic61—42no—
647Dic61—42no—
648Dic61—42no—
649Dic61—42no—
650Dic61—42no—
651Dic61—81no—
652Dic61—81no—
653C2×#392D6111yescharacteristic
654C2×#390—611no—
655C2×#386—611no—
656C2×#386—611no—
657C2×#386—611no—
658C2×#386—611no—
659C2×#385—611no—
660#1442—611no—
661#1440—611no—
662#1439—611no—
663#1439—611no—
664#1438—611no—
665#1437—611no—
666#1434—611no—
667C22⋊#95—611no—
668C2×C61—44no—
669C2×C61—44no—
670C2×C61—82no—
671C2×C61#232111yescharacteristic
672C2×C61#232511yescharacteristic
673C2×C61#232811yescharacteristic
674C2×C61#235811yescharacteristic
675C2×C61#235811yescharacteristic
676C2×C61#236111yescharacteristic
677C2×C61#237711yescharacteristic
678C2×C61#266911yescharacteristic
679C2×C61#267111yescharacteristic
680C2×C61#267611yescharacteristic
681C2×C61#267811yescharacteristic
682C2×C61#268811yescharacteristic
683C2×C61#269611yescharacteristic
684C2×C61#270611yescharacteristic
685C2×C61#274911yescharacteristic
686C23×D4C2×D6111yescharacteristic
687C23×D4C2×D6111yescharacteristic
688C23×D4C2×D6111yescharacteristic
689C24×C4—611no—
690C24×C4—611no—
691C22×C4⋊C4—611no—
692C22×C4⋊C4—611no—
693C22×C22⋊C4—611no—
694C22×C22⋊C4—611no—
695C22×C22⋊C4—611no—
696C22×C22⋊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⋊C4C2×D6111yescharacteristic
704C22×C22⋊C4C2×D6111yescharacteristic
705C22×C22⋊C4C2×D6111yescharacteristic
706C22×C42—611no—
707#392Dic6118yescomplemented
708#390—1224no—
709#386—1224no—
710#386—1224no—
711#386—1224no—
712#386—1224no—
713#385—1224no—
714C2×#95—611no—
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
728C61#1451911yescharacteristic, complemented, Sylow
729C25C22×D6111yescharacteristic
730C25C22×D6111yescharacteristic
731C25C22×D6111yescharacteristic
732C22×D4—22no—
733C22×D4—22no—
734C22×D4—22no—
735C22×D4—22no—
736C22×D4—22no—
737C22×D4—22no—
738C22×D4—22no—
739C22×D4—22no—
740C22×D4—22no—
741C22×D4—22no—
742C22×D4—41no—
743C22×D4—41no—
744C22×D4—41no—
745C22×D4—41no—
746C22×D4—41no—
747C22×D4—41no—
748C22×D4—41no—
749C22×D4—41no—
750C22×D4C2×Dic6114yes—
751C22×D4C2×Dic6114yescomplemented
752C22×D4C2×Dic6114yescomplemented
753C23×C4—611no—
754C23×C4—611no—
755C23×C4—611no—
756C23×C4—611no—
757C23×C4—611no—
758C23×C4—611no—
759C23×C4—611no—
760C23×C4—611no—
761C23×C4—1222no—
762C23×C4—1222no—
763C23×C4—1222no—
764C23×C4—1222no—
765C23×C4—1222no—
766C23×C4—1222no—
767C23×C4—2441no—
768C23×C4—2441no—
769C23×C4—2441no—
770C23×C4—2441no—
771C23×C4—2441no—
772C23×C4—2441no—
773C23×C4—2441no—
774C23×C4—2441no—
775C23×C4C22×D6111yescharacteristic
776C23×C4C22×D6111yescharacteristic
777C23×C4C22×D6111yescharacteristic
778C23×C4C22×D6111yescharacteristic
779C2×C4⋊C4—1222no—
780C2×C4⋊C4—1222no—
781C2×C4⋊C4—1222no—
782C2×C4⋊C4—2441no—
783C2×C4⋊C4—2441no—
784C2×C4⋊C4—2441no—
785C2×C22⋊C4—22no—
786C2×C22⋊C4—22no—
787C2×C22⋊C4—41no—
788C2×C22⋊C4—41no—
789C2×C22⋊C4—41no—
790C2×C22⋊C4—41no—
791C2×C22⋊C4—614no—
792C2×C22⋊C4—614no—
793C2×C22⋊C4—1222no—
794C2×C22⋊C4—1222no—
795C2×C22⋊C4—1222no—
796C2×C22⋊C4—1222no—
797C2×C22⋊C4—1222no—
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—2441no—
808C2×C22⋊C4—2441no—
809C2×C22⋊C4—2441no—
810C2×C22⋊C4—2441no—
811C2×C22⋊C4—2441no—
812C2×C22⋊C4—2441no—
813C2×C22⋊C4—2441no—
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⋊C4C2×Dic6114yescomplemented
822C2×C22⋊C4C2×Dic6114yescomplemented
823C2×C22⋊C4C2×Dic6114yescomplemented
824C2×C42—1222no—
825C2×C42—1222no—
826C2×C42—2441no—
827#95—614no—
828#95—1222no—
829#95—1222no—
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#95C2×Dic6114yescomplemented
841C24—21no—
842C24—21no—
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—21no—
870C24—21no—
871C24—21no—
872C24—21no—
873C24—21no—
874C24—21no—
875C24—21no—
876C24—21no—
877C24—21no—
878C24—21no—
879C24D4×D6112yes—
880C24D4×D6112yes—
881C24#1175822412yes—
882C24#1175822412yes—
883C24C22×Dic6112yes—
884C24C22×Dic6112yes—
885C24C22×Dic6112yes—
886C24C23×D6111yescharacteristic
887C2×D4—28no—
888C2×D4—28no—
889C2×D4—28no—
890C2×D4—28no—
891C2×D4—28no—
892C2×D4—44no—
893C2×D4—44no—
894C2×D4—44no—
895C2×D4—44no—
896C2×D4—44no—
897C2×D4—44no—
898C2×D4—44no—
899C2×D4—44no—
900C2×D4—44no—
901C2×D4—44no—
902C2×D4—44no—
903C2×D4—44no—
904C2×D4—44no—
905C2×D4—44no—
906C2×D4—44no—
907C2×D4—44no—
908C22×C4—21no—
909C22×C4—21no—
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—612no—
931C22×C4—612no—
932C22×C4—612no—
933C22×C4—612no—
934C22×C4—612no—
935C22×C4—612no—
936C22×C4—1221no—
937C22×C4—1221no—
938C22×C4—1221no—
939C22×C4—1221no—
940C22×C4—1221no—
941C22×C4—1221no—
942C22×C4—1221no—
943C22×C4—1221no—
944C22×C4—1221no—
945C22×C4—1221no—
946C22×C4—1221no—
947C22×C4—1221no—
948C22×C4—1221no—
949C22×C4—1221no—
950C22×C4—1221no—
951C22×C4—1221no—
952C22×C4—1221no—
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—1221no—
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—2444no—
987C22×C4—2444no—
988C22×C4—2444no—
989C22×C4—2444no—
990C22×C4—2444no—
991C22×C4—2444no—
992C22×C4—2444no—
993C22×C4—2444no—
994C22×C4—2444no—
995C22×C4—2444no—
996C22×C4—2444no—
997C22×C4—2444no—
998C22×C4—2444no—
999C22×C4—2444no—
1000C22×C4D4×D6112yes—
1001C22×C4#1175822412yes—
1002C22×C4C22×Dic6112yes—
1003C22×C4C22×Dic6112yes—
1004C22×C4C22×Dic6112yes—
1005C22×C4C22×Dic6112yes—
1006C4⋊C4—2444no—
1007C4⋊C4—2444no—
1008C22⋊C4—28no—
1009C22⋊C4—44no—
1010C22⋊C4—44no—
1011C22⋊C4—2444no—
1012C22⋊C4—2444no—
1013C22⋊C4—2444no—
1014C22⋊C4—2444no—
1015C22⋊C4—2444no—
1016C22⋊C4—2444no—
1017C22⋊C4—2444no—
1018C22⋊C4—2444no—
1019C22⋊C4—2444no—
1020C22⋊C4—2444no—
1021C42—2444no—
1022C23—22no—
1023C23—22no—
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—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—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—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—41no—
1117C23—41no—
1118C23—41no—
1119C23—41no—
1120C23—41no—
1121C23—41no—
1122C23—41no—
1123C23—41no—
1124C23—41no—
1125C23D4×Dic6114yes—
1126C23D4×Dic6114yes—
1127C23C23×Dic6111yescharacteristic
1128C23C2×D4×D6111yescharacteristic
1129C23C2×D4×D6111yescharacteristic
1130C23C2×D4×D6111yescharacteristic
1131C23C2×#1175822411yescharacteristic
1132C23C2×#1175822411yescharacteristic
1133C23C2×#1175822411yescharacteristic
1134C23#1451982211yescharacteristic
1135C23#1451982211yescharacteristic
1136C23#1451982211yescharacteristic
1137C23#1451982211yescharacteristic
1138C23#1451982211yescharacteristic
1139C23#1451982211yescharacteristic
1140C23#1451982311yescharacteristic
1141C23#1451982411yescharacteristic
1142D4—416no—
1143D4—416no—
1144D4—416no—
1145C2×C4—22no—
1146C2×C4—22no—
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—41no—
1161C2×C4—41no—
1162C2×C4—41no—
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—1222no—
1173C2×C4—1222no—
1174C2×C4—1222no—
1175C2×C4—1222no—
1176C2×C4—1222no—
1177C2×C4—1222no—
1178C2×C4—1222no—
1179C2×C4—1222no—
1180C2×C4—1222no—
1181C2×C4—1222no—
1182C2×C4—1222no—
1183C2×C4—1222no—
1184C2×C4—1222no—
1185C2×C4—1222no—
1186C2×C4—1222no—
1187C2×C4—1222no—
1188C2×C4—1222no—
1189C2×C4—1222no—
1190C2×C4—2441no—
1191C2×C4—2441no—
1192C2×C4—2441no—
1193C2×C4—2441no—
1194C2×C4—2441no—
1195C2×C4—2441no—
1196C2×C4—2441no—
1197C2×C4—2441no—
1198C2×C4—2441no—
1199C2×C4—2441no—
1200C2×C4—2441no—
1201C2×C4—2441no—
1202C2×C4—2441no—
1203C2×C4—2441no—
1204C2×C4—24416no—
1205C2×C4—24416no—
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×C4D4×Dic6114yes—
1231C22—24no—
1232C22—24no—
1233C22—24no—
1234C22—24no—
1235C22—24no—
1236C22—24no—
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—42no—
1256C22—42no—
1257C22—42no—
1258C22—42no—
1259C22—42no—
1260C22—42no—
1261C22—42no—
1262C22—42no—
1263C22—42no—
1264C22—42no—
1265C22—42no—
1266C22—42no—
1267C22—42no—
1268C22—81no—
1269C22—81no—
1270C22—81no—
1271C22—81no—
1272C22—81no—
1273C22—81no—
1274C22—81no—
1275C22—81no—
1276C22C2×D4×Dic6111yescharacteristic
1277C22C2×D4×Dic6111yescharacteristic
1278C22C2×D4×Dic6111yescharacteristic
1279C22#1684023711yescharacteristic
1280C22#1684023711yescharacteristic
1281C22#1684023711yescharacteristic
1282C22#1684024511yescharacteristic
1283C22#1684032011yescharacteristic
1284C22#1684032211yescharacteristic
1285C22#1684032511yescharacteristic
1286C22#1684032511yescharacteristic
1287C22#1684032711yescharacteristic
1288C22#1684033911yescharacteristic
1289C22#1684034711yescharacteristic
1290C22#1684034711yescharacteristic
1291C22#1684034911yescharacteristic
1292C22#1684035711yescharacteristic
1293C22#1684036611yescharacteristic
1294C22#1684036611yescharacteristic
1295C22#1684039411yescharacteristic
1296C22#1684039411yescharacteristic
1297C22#1684039611yescharacteristic
1298C22#1684039911yescharacteristic
1299C22#1684039911yescharacteristic
1300C22#1684039911yescharacteristic
1301C22#1684039911yescharacteristic
1302C22#1684041211yescharacteristic
1303C22#1684041811yescharacteristic
1304C22#1684044311yescharacteristic
1305C22#1684044311yescharacteristic
1306C22#1684046411yescharacteristic
1307C22#1684050011yescharacteristic
1308C22#1684050011yescharacteristic
1309C22#1684050711yescharacteristic
1310C22#1684050711yescharacteristic
1311C4—24no—
1312C4—42no—
1313C4—42no—
1314C4—42no—
1315C4—4881no—
1316C4—4881no—
1317C4—2442no—
1318C4—2442no—
1319C4—2442no—
1320C4—2442no—
1321C4—2442no—
1322C4—2442no—
1323C2—44no—
1324C2—44no—
1325C2—82no—
1326C2#2144848011yescharacteristic
1327C2#2144852411yescharacteristic
1328C2#2144854511yescharacteristic
1329C2#2144880311yescharacteristic
1330C2#2144880311yescharacteristic
1331C2#2144883911yescharacteristic
1332C2#2144897611yescharacteristic
1333C2#2145203011yescharacteristic
1334C2#2145205711yescharacteristic
1335C2#2145211311yescharacteristic
1336C2#2145213711yescharacteristic
1337C2#2145225411yescharacteristic
1338C2#2145236811yescharacteristic
1339C2#2145251411yescharacteristic
1340C2#2145304411yescharacteristic
subgroupG/H
center, FrattiniC24C23×D61
commutatorC23×C61C23×C4
Fitting, prime radicalC2×C61×#392C2
socle, cosocleC24×C61C24
hypercenterC2×#392D61
hypocenterC61#14519
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C24 ◁ C2×#392

Complements

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

NH ≅ G/Ntype
1. C2×#16839665C2semidirect
2. C2×#16839642C2semidirect
3. C2×#16839642C2semidirect
4. C2×#16839642C2semidirect
5. C2×#16839642C2semidirect
6. C2×#16839637C2semidirect
7. #21444076C2semidirect
8. #21444068C2semidirect
9. #21444064C2semidirect
10. #21444064C2semidirect
11. #21444060C2semidirect
12. #21444056C2semidirect
13. #21444044C2semidirect
14. #21444041C2semidirect
56. C61×#392C4semidirect
114. C2×C22⋊Dic61D4semidirect
115. C2×C22⋊Dic61D4semidirect
131. #14519684D4semidirect
154. C22×D4×C61C2×C4semidirect
155. C22×D4×C61C2×C4semidirect
166. C2×C22⋊C4×C61C2×C4semidirect
167. C2×C22⋊C4×C61C2×C4semidirect
168. C2×C22⋊C4×C61C2×C4semidirect
169. #95×C61C2×C4semidirect
707. #392Dic61semidirect
728. C61#14519semidirect
751. C22×D4C2×Dic61semidirect
752. C22×D4C2×Dic61semidirect
821. C2×C22⋊C4C2×Dic61semidirect
822. C2×C22⋊C4C2×Dic61semidirect
823. C2×C22⋊C4C2×Dic61semidirect
840. #95C2×Dic61semidirect

Maximal subgroups

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

subgroupindex
C2×#168396652
C2×#168396422
C2×#168396372
#214440762
#214440682
#214440642
#214440602
#214440562
#214440442
#214440412
C2×C61×#3922
#1451961