Finite Group Databasebeta

← #29609348

Subgroups — #29609348

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×#16839670C211yesmaximal, characteristic
2C2×#16839665C211yesmaximal, characteristic, complemented
3C2×#16839641C211yesmaximal, characteristic, complemented
4C2×#16839638C211yesmaximal, characteristic, complemented
5C2×#16839638C211yesmaximal, characteristic, complemented
6C2×#16839636C211yesmaximal, characteristic, complemented
7#21444075C211yesmaximal, characteristic, complemented
8#21444066C211yesmaximal, characteristic, complemented
9#21444062C211yesmaximal, characteristic, complemented
10#21444062C211yesmaximal, characteristic, complemented
11#21444058C211yesmaximal, characteristic, complemented
12#21444055C211yesmaximal, characteristic, complemented
13#21444044C211yesmaximal, characteristic, complemented
14#21444042C211yesmaximal, characteristic, complemented
15C2×C61×#386C211yesmaximal, characteristic, complemented
16C23×C22⋊D61C2211yescharacteristic
17C23×C22⋊D61C2211yescharacteristic
18C23×C4×D61C2211yescharacteristic
19C22×C4⋊Dic61C2211yescharacteristic
20C22×#11758196C2211yescharacteristic
21C22×C22⋊Dic61C2211yescharacteristic
22C22×C22⋊Dic61C2211yescharacteristic
23C22×C22⋊Dic61C2211yescharacteristic
24C22×C22⋊Dic61C2211yescharacteristic
25C22×C22⋊Dic61C2211yescharacteristic
26C22×C22⋊Dic61C2211yescharacteristic
27C22×#11758198C2211yescharacteristic
28C22×#11758198C2211yescharacteristic
29C22×#11758198C2211yescharacteristic
30C22×#11758198C2211yescharacteristic
31C22×C4×Dic61C2211yescharacteristic
32#16839670C418yescomplemented
33#16839665—24no—
34#16839641—24no—
35#16839638—24no—
36#16839638—24no—
37#16839636—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—22no—
62C22×C22⋊D61—22no—
63C22×C22⋊D61—22no—
64C22×C22⋊D61—22no—
65C22×C22⋊D61—41no—
66C22×C22⋊D61—41no—
67C22×C22⋊D61—41no—
68C22×C22⋊D61—41no—
69C22×C22⋊D61—41no—
70C22×C22⋊D61—41no—
71C22×C22⋊D61C2×C414yes—
72C22×C22⋊D61C2×C414yescomplemented
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—41no—
84C22×C4×D61—41no—
85C22×C4×D61—41no—
86C22×C4×D61—41no—
87C2×C4⋊Dic61—22no—
88C2×C4⋊Dic61—22no—
89C2×C4⋊Dic61—41no—
90C2×#11758196—22no—
91C2×#11758196—41no—
92C2×#11758196—41no—
93C2×C22⋊Dic61—22no—
94C2×C22⋊Dic61—22no—
95C2×C22⋊Dic61—22no—
96C2×C22⋊Dic61—22no—
97C2×C22⋊Dic61—22no—
98C2×C22⋊Dic61—41no—
99C2×C22⋊Dic61—41no—
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⋊Dic61C2×C414yescomplemented
109C2×C22⋊Dic61C2×C414yescomplemented
110C2×C22⋊Dic61D414yescomplemented
111C2×#11758198—22no—
112C2×#11758198—22no—
113C2×#11758198—22no—
114C2×#11758198—22no—
115C2×#11758198—22no—
116C2×#11758198—22no—
117C2×#11758198—41no—
118C2×#11758198—41no—
119C2×#11758198—41no—
120C2×#11758198—41no—
121C2×#11758198C2×C414yescomplemented
122C2×#11758198D414yescomplemented
123C2×C4×Dic61—22no—
124C2×C4×Dic61—22no—
125C2×C4×Dic61—41no—
126#14519684—22no—
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#14519684C2×C414yescomplemented
138C25×C61C2311yescharacteristic
139C25×C61C2311yescharacteristic
140C22×D4×C61—22no—
141C22×D4×C61—22no—
142C22×D4×C61—22no—
143C22×D4×C61—22no—
144C22×D4×C61—41no—
145C22×D4×C61—41no—
146C22×D4×C61C2×C414yescomplemented
147C23×C4×C61—22no—
148C23×C4×C61—22no—
149C23×C4×C61—22no—
150C23×C4×C61—41no—
151C23×C4×C61—41no—
152C23×C4×C61—41no—
153C23×C4×C61—41no—
154C23×C4×C61C2311yescharacteristic
155C23×C4×C61C2311yescharacteristic
156C23×C4×C61C2311yescharacteristic
157C23×C4×C61C2311yescharacteristic
158C23×C4×C61C2311yescharacteristic
159C2×C22⋊C4×C61—22no—
160C2×C22⋊C4×C61—22no—
161C2×C22⋊C4×C61—22no—
162C2×C22⋊C4×C61—22no—
163C2×C22⋊C4×C61—22no—
164C2×C22⋊C4×C61—41no—
165C2×C22⋊C4×C61—41no—
166C2×C22⋊C4×C61—41no—
167C2×C22⋊C4×C61—41no—
168#95×C61—22no—
169#95×C61D414yescomplemented
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×C61C22×C412yes—
197C24×C61C22×C412yes—
198C24×C61C2×D412yes—
199C24×C61#4112yes—
200C24×C61C2411yescharacteristic
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×D61C22×C412yes—
214C23×D61C2×D412yes—
215C23×D61#4112yes—
216C2×D4×C61—28no—
217C2×D4×C61—28no—
218C2×D4×C61—44no—
219C2×D4×C61—44no—
220C2×D4×C61—44no—
221C2×D4×C61—44no—
222C2×D4×C61—44no—
223C22×C4×C61—21no—
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—44no—
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×C61C22×C412yes—
260C22×C4×C61C2×D412yes—
261C22×C4×C61C2×D412yes—
262C22×C4×C61C2×D412yes—
263C22×C4×C61C2×D412yes—
264C22×C4×C61#4112yes—
265C2×C22⋊D61—28no—
266C2×C22⋊D61—28no—
267C2×C22⋊D61—28no—
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—
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—21no—
316C22×Dic61—21no—
317C22×Dic61—21no—
318C22×Dic61—21no—
319C22×Dic61—21no—
320C22×Dic61—21no—
321C22×Dic61—21no—
322C22×Dic61C22×C412yes—
323C22×Dic61C22×C412yes—
324C22×Dic61C22×C412yes—
325C22×Dic61C2×D412yes—
326C22×Dic61C2×D412yes—
327C22×Dic61C2×D412yes—
328C2×C4×D61—44no—
329C2×C4×D61—44no—
330C2×C4×D61—44no—
331C2×C4×D61—44no—
332C2×C4×D61—44no—
333C2×C4×D61—44no—
334C2×C4×D61—44no—
335C22⋊C4×C61—44no—
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—
344#11758198—28no—
345#11758198—44no—
346#11758198—44no—
347#11758198—44no—
348C4⋊Dic61—44no—
349#11758196—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—41no—
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×C61C4×D414yes—
421C23×C61C23×C411yescharacteristic
422C23×C61C22×D411yescharacteristic
423C23×C61C22×D411yescharacteristic
424C23×C61C22×D411yescharacteristic
425C23×C61C2×#4111yescharacteristic
426C23×C61C2×#4111yescharacteristic
427C23×C61C2×#4111yescharacteristic
428C23×C61H(5,𝔽2)11yescharacteristic
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×C612−1+411yescharacteristic
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—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×D61C4×D414yes—
471D4×C61—416no—
472C2×C4×C61—22no—
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—416no—
488C2×C4×C61—41no—
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×C61C4×D414yes—
508C22⋊D61—416no—
509C22⋊D61—416no—
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—22no—
521C2×Dic61—22no—
522C2×Dic61—22no—
523C2×Dic61—22no—
524C2×Dic61—22no—
525C2×Dic61—22no—
526C2×Dic61—22no—
527C2×Dic61—22no—
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—
559C4×D61—416no—
560#14519—611nomaximal, Sylow
561C22×C61—24no—
562C22×C61—24no—
563C22×C61—24no—
564C22×C61—42no—
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—81no—
584C22×C61—81no—
585C22×C61—81no—
586C22×C61—81no—
587C22×C61—81no—
588C22×C61—81no—
589C22×C61—81no—
590C22×C61—81no—
591C22×C61C2×C4×D411yescharacteristic
592C22×C61C2×C4×D411yescharacteristic
593C22×C61C2×C4×D411yescharacteristic
594C22×C61#51811yescharacteristic
595C22×C61#51811yescharacteristic
596C22×C61#51811yescharacteristic
597C22×C61#52011yescharacteristic
598C22×C61#53411yescharacteristic
599C22×C61#53411yescharacteristic
600C22×C61#53511yescharacteristic
601C22×C61#53511yescharacteristic
602C22×C61#53511yescharacteristic
603C22×C61#53711yescharacteristic
604C22×C61#53811yescharacteristic
605C22×C61#53811yescharacteristic
606C22×C61#53811yescharacteristic
607C22×C61#53911yescharacteristic
608C22×C61#54011yescharacteristic
609C22×C61#54011yescharacteristic
610C22×C61D4211yescharacteristic
611C22×C61D4211yescharacteristic
612C22×C61D4211yescharacteristic
613C22×C61#54611yescharacteristic
614C22×C61#54611yescharacteristic
615C22×C61#54611yescharacteristic
616C22×C61#54611yescharacteristic
617C22×C61#54711yescharacteristic
618C22×C61#54811yescharacteristic
619C22×C61#55111yescharacteristic
620C22×C61#55111yescharacteristic
621C22×C61#55311yescharacteristic
622C22×C61#56011yescharacteristic
623C22×C61#56011yescharacteristic
624C22×C61#56211yescharacteristic
625C22×C61#56211yescharacteristic
626C2×D61—24no—
627C2×D61—24no—
628C2×D61—24no—
629C2×D61—42no—
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—
641C4×C61—24no—
642C4×C61—42no—
643C4×C61—42no—
644C4×C61—42no—
645C4×C61—81no—
646Dic61—42no—
647Dic61—42no—
648Dic61—42no—
649Dic61—42no—
650Dic61—42no—
651Dic61—42no—
652Dic61—81no—
653C2×#392—611no—
654C2×#390—611no—
655C2×#386—611no—
656C2×#386—611no—
657C2×#386—611no—
658C2×#386D6111yescharacteristic, complemented
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—82no—
670C2×C61#232111yescharacteristic
671C2×C61#232511yescharacteristic
672C2×C61#232811yescharacteristic
673C2×C61#235811yescharacteristic
674C2×C61#235811yescharacteristic
675C2×C61#236111yescharacteristic
676C2×C61#237711yescharacteristic
677C2×C61#266911yescharacteristic
678C2×C61#267111yescharacteristic
679C2×C61#267611yescharacteristic
680C2×C61#267811yescharacteristic
681C2×C61#268811yescharacteristic
682C2×C61#269611yescharacteristic
683C2×C61#270611yescharacteristic
684C2×C61#274911yescharacteristic
685D61—44no—
686C23×D4—611no—
687C23×D4—611no—
688C23×D4C2×D6111yescharacteristic
689C24×C4—611no—
690C24×C4C2×D6111yescharacteristic
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#392—618no—
708#390—1224no—
709#386—24no—
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×#95C2×D6111yescharacteristic
727C2×#95C2×D6111yescharacteristic
728C61#1451911yescharacteristic, complemented, Sylow
729C25—611no—
730C25C22×D6111yescharacteristic
731C25C22×D6111yescharacteristic
732C22×D4—22no—
733C22×D4—22no—
734C22×D4—22no—
735C22×D4—22no—
736C22×D4—41no—
737C22×D4—41no—
738C22×D4—614no—
739C22×D4—614no—
740C22×D4—1222no—
741C22×D4—1222no—
742C22×D4—1222no—
743C22×D4—1222no—
744C22×D4—1222no—
745C22×D4—1222no—
746C22×D4—2441no—
747C22×D4—2441no—
748C22×D4—2441no—
749C22×D4—2441no—
750C22×D4—2441no—
751C22×D4—2441no—
752C22×D4C4×D6114yescomplemented
753C23×C4—22no—
754C23×C4—22no—
755C23×C4—22no—
756C23×C4—41no—
757C23×C4—41no—
758C23×C4—41no—
759C23×C4—41no—
760C23×C4—611no—
761C23×C4—611no—
762C23×C4—611no—
763C23×C4—611no—
764C23×C4—611no—
765C23×C4—611no—
766C23×C4—611no—
767C23×C4—1222no—
768C23×C4—1222no—
769C23×C4—1222no—
770C23×C4—2441no—
771C23×C4—2441no—
772C23×C4—2441no—
773C23×C4—2441no—
774C23×C4C22×D6111yescharacteristic
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—22no—
788C2×C22⋊C4—22no—
789C2×C22⋊C4—22no—
790C2×C22⋊C4—41no—
791C2×C22⋊C4—41no—
792C2×C22⋊C4—41no—
793C2×C22⋊C4—41no—
794C2×C22⋊C4—614no—
795C2×C22⋊C4—614no—
796C2×C22⋊C4—614no—
797C2×C22⋊C4—614no—
798C2×C22⋊C4—614no—
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—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⋊C4—2441no—
822C2×C22⋊C4—2441no—
823C2×C22⋊C4—2441no—
824C2×C42—1222no—
825C2×C42—1222no—
826C2×C42—2441no—
827#95—22no—
828#95—614no—
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#95C22⋊D6114yescomplemented
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—612no—
868C24—612no—
869C24—612no—
870C24—1221no—
871C24—1221no—
872C24—1221no—
873C24—1221no—
874C24—1221no—
875C24—1221no—
876C24—1221no—
877C24—1221no—
878C24—1221no—
879C24—1221no—
880C24—1221no—
881C24—1221no—
882C24C2×C4×D6112yes—
883C24C2×C4×D6112yes—
884C24D4×D6112yes—
885C24#1175822412yes—
886C24C23×D6111yescharacteristic
887C2×D4—28no—
888C2×D4—28no—
889C2×D4—44no—
890C2×D4—44no—
891C2×D4—44no—
892C2×D4—44no—
893C2×D4—44no—
894C2×D4—1228no—
895C2×D4—1228no—
896C2×D4—1228no—
897C2×D4—2444no—
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—
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—21no—
931C22×C4—21no—
932C22×C4—21no—
933C22×C4—21no—
934C22×C4—21no—
935C22×C4—21no—
936C22×C4—21no—
937C22×C4—44no—
938C22×C4—44no—
939C22×C4—44no—
940C22×C4—44no—
941C22×C4—44no—
942C22×C4—44no—
943C22×C4—44no—
944C22×C4—612no—
945C22×C4—612no—
946C22×C4—612no—
947C22×C4—612no—
948C22×C4—612no—
949C22×C4—612no—
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—1221no—
987C22×C4—1221no—
988C22×C4—1221no—
989C22×C4—1221no—
990C22×C4—1221no—
991C22×C4—1221no—
992C22×C4—1221no—
993C22×C4—2444no—
994C22×C4—2444no—
995C22×C4—2444no—
996C22×C4—2444no—
997C22×C4—2444no—
998C22×C4—2444no—
999C22×C4—2444no—
1000C22×C4C2×C4×D6112yes—
1001C22×C4#1175822212yes—
1002C22×C4D4×D6112yes—
1003C22×C4C2×C22⋊D6112yes—
1004C22×C4C2×C22⋊D6112yes—
1005C22×C4C2×C22⋊D6112yes—
1006C4⋊C4—2444no—
1007C4⋊C4—2444no—
1008C22⋊C4—44no—
1009C22⋊C4—44no—
1010C22⋊C4—44no—
1011C22⋊C4—1228no—
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—41no—
1048C23—41no—
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—614no—
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—2441no—
1111C23—2441no—
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#1451973714yes—
1127C23C22×C4×D6111yescharacteristic
1128C23C2×D4×D6111yescharacteristic
1129C23C2×D4×D6111yescharacteristic
1130C23C22×C22⋊D6111yescharacteristic
1131C23#41×D6111yescharacteristic
1132C23C2×#1175822411yescharacteristic
1133C23C2×#1175822211yescharacteristic
1134C23#1451982211yescharacteristic
1135C23#1451982211yescharacteristic
1136C23#1451982211yescharacteristic
1137C23#1451982211yescharacteristic
1138C23#1451982211yescharacteristic
1139C23#1451982311yescharacteristic
1140C23#1451982311yescharacteristic
1141C23#1451982411yescharacteristic
1142D4—416no—
1143D4—24416no—
1144D4—24416no—
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—416no—
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—41no—
1173C2×C4—41no—
1174C2×C4—41no—
1175C2×C4—41no—
1176C2×C4—41no—
1177C2×C4—41no—
1178C2×C4—41no—
1179C2×C4—41no—
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—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×C4C4×C22⋊D6114yes—
1231C22—24no—
1232C22—24no—
1233C22—24no—
1234C22—42no—
1235C22—42no—
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—81no—
1254C22—81no—
1255C22—81no—
1256C22—81no—
1257C22—81no—
1258C22—81no—
1259C22—81no—
1260C22—81no—
1261C22—1224no—
1262C22—1224no—
1263C22—1224no—
1264C22—2442no—
1265C22—2442no—
1266C22—2442no—
1267C22—2442no—
1268C22—2442no—
1269C22—2442no—
1270C22—2442no—
1271C22—2442no—
1272C22—2442no—
1273C22—2442no—
1274C22—2442no—
1275C22—2442no—
1276C22C4×D4×D6111yescharacteristic
1277C22C2×#1451973711yescharacteristic
1278C22C2×C4×C22⋊D6111yescharacteristic
1279C22#1684023411yescharacteristic
1280C22#1684023411yescharacteristic
1281C22#1684023511yescharacteristic
1282C22#1684024111yescharacteristic
1283C22#1684032011yescharacteristic
1284C22#1684032211yescharacteristic
1285C22#1684032611yescharacteristic
1286C22#1684032811yescharacteristic
1287C22#1684032911yescharacteristic
1288C22#1684033911yescharacteristic
1289C22#1684034411yescharacteristic
1290C22#1684034711yescharacteristic
1291C22#1684034811yescharacteristic
1292C22#1684035611yescharacteristic
1293C22#1684036311yescharacteristic
1294C22#1684036311yescharacteristic
1295C22D4×C22⋊D6111yescharacteristic
1296C22D4×C22⋊D6111yescharacteristic
1297C22#1684039611yescharacteristic
1298C22#1684039911yescharacteristic
1299C22#1684040111yescharacteristic
1300C22#1684040211yescharacteristic
1301C22#1684040611yescharacteristic
1302C22#1684041711yescharacteristic
1303C22#1684041911yescharacteristic
1304C22#1684043511yescharacteristic
1305C22#1684043811yescharacteristic
1306C22#1684046211yescharacteristic
1307C22#1684050011yescharacteristic
1308C22#1684050111yescharacteristic
1309C22#1684050711yescharacteristic
1310C22#1684050911yescharacteristic
1311C4—24no—
1312C4—42no—
1313C4—42no—
1314C4—42no—
1315C4—81no—
1316C4—4881no—
1317C4—2442no—
1318C4—2442no—
1319C4—2442no—
1320C4—2442no—
1321C4—2442no—
1322C4—2442no—
1323C2—44no—
1324C2—82no—
1325C2—2444no—
1326C2#2144847511yescharacteristic
1327C2#2144852011yescharacteristic
1328C2#2144854111yescharacteristic
1329C2#2144879811yescharacteristic
1330C2#2144879911yescharacteristic
1331C2#2144883111yescharacteristic
1332C2#2144897711yescharacteristic
1333C2#2145203111yescharacteristic
1334C2#2145205611yescharacteristic
1335C2#2145211411yescharacteristic
1336C2#2145214011yescharacteristic
1337C2#2145225011yescharacteristic
1338C2#2145236511yescharacteristic
1339C2#2145251111yescharacteristic
1340C2#2145304611yescharacteristic
subgroupG/H
center, FrattiniC24C23×D61
commutatorC23×C61C23×C4
FittingC2×C61×#386C2
socle, cosocleC24×C61C24
prime radicalC2×#16839670C2
hypercenterC2×#386D61
hypocenterC61#14519
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C24 ◁ C2×#386

Complements

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

NH ≅ G/Ntype
2. C2×#16839665C2semidirect
3. C2×#16839641C2semidirect
4. C2×#16839638C2semidirect
5. C2×#16839638C2semidirect
6. C2×#16839636C2semidirect
7. #21444075C2semidirect
8. #21444066C2semidirect
9. #21444062C2semidirect
10. #21444062C2semidirect
11. #21444058C2semidirect
12. #21444055C2semidirect
13. #21444044C2semidirect
14. #21444042C2semidirect
15. C2×C61×#386C2semidirect
32. #16839670C4semidirect
72. C22×C22⋊D61C2×C4semidirect
108. C2×C22⋊Dic61C2×C4semidirect
109. C2×C22⋊Dic61C2×C4semidirect
110. C2×C22⋊Dic61D4semidirect
121. C2×#11758198C2×C4semidirect
122. C2×#11758198D4semidirect
137. #14519684C2×C4semidirect
146. C22×D4×C61C2×C4semidirect
169. #95×C61D4semidirect
658. C2×#386D61semidirect
728. C61#14519semidirect
752. C22×D4C4×D61semidirect
840. #95C22⋊D61semidirect

Maximal subgroups

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

subgroupindex
C2×#168396702
C2×#168396652
C2×#168396412
C2×#168396382
C2×#168396362
#214440752
#214440662
#214440622
#214440582
#214440552
#214440442
#214440422
C2×C61×#3862
#1451961