Finite Group Databasebeta

← #29603815

Subgroups — #29603815

Order 15616.

2266 conjugacy classes of subgroups.

The subgroup lattice has 1082 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519755C211yesmaximal, characteristic
2C2×#16839667C211yesmaximal, characteristic, complemented
3C2×#16839633C211yesmaximal, characteristic
4C2×#16839609C211yesmaximal, characteristic
5C2×#95×D61C211yesmaximal, characteristic
6#21444089C211yesmaximal, characteristic, complemented
7#21444085C211yesmaximal, characteristic, complemented
8#21444070C211yesmaximal, characteristic, complemented
9#21444051C211yesmaximal, characteristic, complemented
10#21444050C211yesmaximal, characteristic, complemented
11#21444047C211yesmaximal, characteristic, complemented
12#21444040C211yesmaximal, characteristic
13#21444040C211yesmaximal, characteristic
14#21444040C211yesmaximal, characteristic
15C61×#1441C211yesmaximal, characteristic, complemented
16C23×Dic122C2211yescharacteristic
17C23×C4×D61C2211yescharacteristic
18C23×C4×D61C2211yescharacteristic
19C23×C4×D61C2211yescharacteristic
20C2×#14519755—24no—
21C2×#14519755—24no—
22C2×#14519755C418yescomplemented
23C22×#11758196C2211yescharacteristic
24C22×#11758196C2211yescharacteristic
25C22×#11758196C2211yescharacteristic
26C22×#11758198C2211yescharacteristic
27C22×#11758198C2211yescharacteristic
28C22×#11758198C2211yescharacteristic
29C22×#11758198C2211yescharacteristic
30C22×C4×Dic61C2211yescharacteristic
31C22×C4×Dic61C2211yescharacteristic
32#16839667—24no—
33#16839633—24no—
34#16839609—24no—
35C2×#14519684C2211yescharacteristic
36C2×#14519684C2211yescharacteristic
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
50#95×D61—24no—
51C22×C4⋊C4×C61C2211yescharacteristic
52C22×C4⋊C4×C61C2211yescharacteristic
53C2×#95×C61C2211yescharacteristic
54C2×#95×C61C2211yescharacteristic
55C2×#95×C61C2211yescharacteristic
56C2×#95×C61C2211yescharacteristic
57C2×#95×C61C2211yescharacteristic
58C24×D61C2311yescharacteristic
59C22×Dic122—22no—
60C22×Dic122—22no—
61C22×Dic122—22no—
62C22×Dic122—22no—
63C22×Dic122—41no—
64C22×Dic122—41no—
65C22×Dic122C2×C414yescomplemented
66C23×Dic61C2311yescharacteristic
67C23×Dic61C2311yescharacteristic
68C23×Dic61C2311yescharacteristic
69C23×Dic61C2311yescharacteristic
70C23×Dic61C2311yescharacteristic
71C23×Dic61C2311yescharacteristic
72C23×Dic61C2311yescharacteristic
73C22×C4×D61—22no—
74C22×C4×D61—22no—
75C22×C4×D61—22no—
76C22×C4×D61—22no—
77C22×C4×D61—22no—
78C22×C4×D61—22no—
79C22×C4×D61—22no—
80C22×C4×D61—22no—
81C22×C4×D61—22no—
82C22×C4×D61—22no—
83C22×C4×D61—22no—
84C22×C4×D61—22no—
85C22×C4×D61—22no—
86C22×C4×D61—41no—
87C22×C4×D61—41no—
88C22×C4×D61—41no—
89C22×C4×D61—41no—
90C22×C4×D61—41no—
91C22×C4×D61—41no—
92C22×C4×D61C2×C414yes—
93C22×C4×D61Q814yescomplemented
94#14519755—232no—
95C2×#11758196—22no—
96C2×#11758196—22no—
97C2×#11758196—22no—
98C2×#11758196—22no—
99C2×#11758196—22no—
100C2×#11758196—22no—
101C2×#11758196—41no—
102C2×#11758196C2×C414yescomplemented
103C2×#11758196C2×C414yescomplemented
104C2×#11758198—22no—
105C2×#11758198—22no—
106C2×#11758198—22no—
107C2×#11758198—22no—
108C2×#11758198—22no—
109C2×#11758198—22no—
110C2×#11758198—22no—
111C2×#11758198C2×C414yes—
112C2×#11758198C2×C414yes—
113C2×#11758198D414yes—
114C2×#11758198D414yes—
115C2×#11758198Q814yescomplemented
116C2×C4×Dic61—22no—
117C2×C4×Dic61—22no—
118C2×C4×Dic61—22no—
119C2×C4×Dic61—22no—
120C2×C4×Dic61—41no—
121C2×C4×Dic61—41no—
122#14519684—22no—
123#14519684—22no—
124#14519684—22no—
125#14519684—22no—
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#14519684D414yes—
137C23×C4×C61C2311yescharacteristic
138C23×C4×C61C2311yescharacteristic
139C23×C4×C61C2311yescharacteristic
140C23×C4×C61C2311yescharacteristic
141C23×C4×C61C2311yescharacteristic
142C23×C4×C61C2311yescharacteristic
143C23×C4×C61C2311yescharacteristic
144C2×C4⋊C4×C61—22no—
145C2×C4⋊C4×C61—22no—
146C2×C4⋊C4×C61—22no—
147C2×C4⋊C4×C61—22no—
148C2×C4⋊C4×C61—41no—
149C2×C4⋊C4×C61C2×C414yescomplemented
150#95×C61—22no—
151#95×C61—22no—
152#95×C61—41no—
153#95×C61—41no—
154#95×C61—41no—
155C24×C61C2411yescharacteristic
156C23×D61—21no—
157C23×D61—21no—
158C23×D61—21no—
159C23×D61—21no—
160C23×D61—21no—
161C23×D61—21no—
162C23×D61—21no—
163C23×D61—21no—
164C23×D61C22×C412yes—
165C23×D61C2×D412yes—
166C23×D61C2×D412yes—
167C23×D61C2×Q812yes—
168C23×D61C2×Q812yes—
169C23×D61#4112yes—
170C23×D61#4112yes—
171C22×C4×C61—21no—
172C22×C4×C61—21no—
173C22×C4×C61—21no—
174C22×C4×C61—21no—
175C22×C4×C61—21no—
176C22×C4×C61—21no—
177C22×C4×C61—21no—
178C22×C4×C61—21no—
179C22×C4×C61—21no—
180C22×C4×C61—21no—
181C22×C4×C61—21no—
182C22×C4×C61—21no—
183C22×C4×C61—21no—
184C22×C4×C61—21no—
185C22×C4×C61—21no—
186C22×C4×C61—21no—
187C22×C4×C61—21no—
188C22×C4×C61—21no—
189C22×C4×C61—21no—
190C22×C4×C61—21no—
191C22×C4×C61—21no—
192C22×C4×C61—21no—
193C22×C4×C61—21no—
194C22×C4×C61—21no—
195C22×C4×C61—21no—
196C22×C4×C61—21no—
197C22×C4×C61—21no—
198C22×C4×C61—21no—
199C22×C4×C61—21no—
200C22×C4×C61—21no—
201C22×C4×C61—21no—
202C22×C4×C61—21no—
203C22×C4×C61—21no—
204C22×C4×C61—21no—
205C22×C4×C61—21no—
206C22×C4×C61—21no—
207C22×C4×C61—21no—
208C22×C4×C61—21no—
209C22×C4×C61—21no—
210C22×C4×C61—21no—
211C22×C4×C61—21no—
212C22×C4×C61C22×C412yes—
213C22×C4×C61C22×C412yes—
214C22×C4×C61C22×C412yes—
215C22×C4×C61C2×D412yes—
216C22×C4×C61C2×D412yes—
217C22×C4×C61C2×D412yes—
218C22×C4×C61C2×Q812yes—
219C22×C4×C61C2×Q812yes—
220C22×Dic61—21no—
221C22×Dic61—21no—
222C22×Dic61—21no—
223C22×Dic61—21no—
224C22×Dic61—21no—
225C22×Dic61—21no—
226C22×Dic61—21no—
227C22×Dic61—21no—
228C22×Dic61—21no—
229C22×Dic61—21no—
230C22×Dic61—21no—
231C22×Dic61—21no—
232C22×Dic61—21no—
233C22×Dic61—21no—
234C22×Dic61—21no—
235C22×Dic61—21no—
236C22×Dic61—21no—
237C22×Dic61—21no—
238C22×Dic61—21no—
239C22×Dic61—21no—
240C22×Dic61—21no—
241C22×Dic61—21no—
242C22×Dic61—21no—
243C22×Dic61—21no—
244C22×Dic61—21no—
245C22×Dic61—21no—
246C22×Dic61—21no—
247C22×Dic61—21no—
248C22×Dic61—21no—
249C22×Dic61—21no—
250C22×Dic61—21no—
251C22×Dic61—21no—
252C22×Dic61—21no—
253C22×Dic61—21no—
254C22×Dic61—21no—
255C22×Dic61—21no—
256C22×Dic61—21no—
257C22×Dic61C22×C412yes—
258C22×Dic61C22×C412yes—
259C22×Dic61C22×C412yes—
260C22×Dic61C2×D412yes—
261C22×Dic61C2×D412yes—
262C22×Dic61C2×D412yes—
263C22×Dic61C2×D412yes—
264C22×Dic61C2×Q812yes—
265C22×Dic61C2×Q812yes—
266C22×Dic61#4112yes—
267C22×Dic61#4112yes—
268C22×Dic61#4112yes—
269C2×C4×D61—28no—
270C2×C4×D61—28no—
271C2×C4×D61—28no—
272C2×C4×D61—28no—
273C2×C4×D61—28no—
274C2×C4×D61—44no—
275C2×C4×D61—44no—
276C2×C4×D61—44no—
277C2×C4×D61—44no—
278C2×C4×D61—44no—
279C2×C4×D61—44no—
280C2×C4×D61—44no—
281C2×C4×D61—44no—
282C2×C4×D61—44no—
283C2×C4×D61—44no—
284C2×C4×D61—44no—
285C2×C4×D61—44no—
286C2×C4×D61—44no—
287C2×C4×D61—44no—
288C2×C4×D61—44no—
289C2×C4×D61—44no—
290C2×Dic122—28no—
291C2×Dic122—28no—
292C2×Dic122—44no—
293C2×Dic122—44no—
294C2×Dic122—44no—
295C2×Dic122—44no—
296C2×Dic122—44no—
297C4⋊C4×C61—28no—
298C4⋊C4×C61—44no—
299#11758198—28no—
300#11758198—28no—
301#11758198—44no—
302#11758198C22⋊C4116yes—
303#11758196—28no—
304#11758196—28no—
305#11758196—44no—
306C4×Dic61—44no—
307C4×Dic61—44no—
308C23×C61C23×C411yescharacteristic
309C23×C61C22×D411yescharacteristic
310C23×C61C22×D411yescharacteristic
311C23×C61C22×D411yescharacteristic
312C23×C61C22×Q811yescharacteristic
313C23×C61C22×Q811yescharacteristic
314C23×C61C2×#4111yescharacteristic
315C23×C61C2×#4111yescharacteristic
316C23×C61C2×#4111yescharacteristic
317C23×C61C2×#4111yescharacteristic
318C23×C61C2×#4111yescharacteristic
319C23×C61H(5,𝔽2)11yescharacteristic
320C23×C61H(5,𝔽2)11yescharacteristic
321C23×C61H(5,𝔽2)11yescharacteristic
322C23×C612−1+411yescharacteristic
323C22×D61—22no—
324C22×D61—22no—
325C22×D61—22no—
326C22×D61—22no—
327C22×D61—22no—
328C22×D61—22no—
329C22×D61—22no—
330C22×D61—22no—
331C22×D61—22no—
332C22×D61—22no—
333C22×D61—22no—
334C22×D61—22no—
335C22×D61—22no—
336C22×D61—22no—
337C22×D61—22no—
338C22×D61—22no—
339C22×D61—22no—
340C22×D61—22no—
341C22×D61—22no—
342C22×D61—22no—
343C22×D61—22no—
344C22×D61—22no—
345C22×D61—22no—
346C22×D61—22no—
347C22×D61—22no—
348C22×D61—22no—
349C22×D61—22no—
350C22×D61—22no—
351C22×D61C2×C22⋊C414yes—
352C22×D61C4×Q814yes—
353C22×D61C4×Q814yes—
354C22×D61C22⋊Q814yes—
355C22×D61C22⋊Q814yes—
356C22×D61#12414yes—
357C22×D61C4⋊Q814yes—
358C2×C4×C61—22no—
359C2×C4×C61—22no—
360C2×C4×C61—22no—
361C2×C4×C61—22no—
362C2×C4×C61—22no—
363C2×C4×C61—22no—
364C2×C4×C61—22no—
365C2×C4×C61—22no—
366C2×C4×C61—22no—
367C2×C4×C61—22no—
368C2×C4×C61—22no—
369C2×C4×C61—22no—
370C2×C4×C61—22no—
371C2×C4×C61—22no—
372C2×C4×C61—22no—
373C2×C4×C61—22no—
374C2×C4×C61—22no—
375C2×C4×C61—22no—
376C2×C4×C61—22no—
377C2×C4×C61—22no—
378C2×C4×C61—22no—
379C2×C4×C61—41no—
380C2×C4×C61—41no—
381C2×C4×C61—41no—
382C2×C4×C61—41no—
383C2×C4×C61—41no—
384C2×C4×C61—41no—
385C2×C4×C61—41no—
386C2×C4×C61—41no—
387C2×C4×C61—41no—
388C2×C4×C61—41no—
389C2×C4×C61—41no—
390C2×C4×C61—41no—
391C2×C4×C61—41no—
392C2×C4×C61—41no—
393C2×C4×C61—41no—
394C2×C4×C61—41no—
395C2×C4×C61—41no—
396C2×C4×C61—41no—
397C2×C4×C61—41no—
398C2×C4×C61—41no—
399C2×C4×C61—41no—
400C2×C4×C61—41no—
401C2×C4×C61—41no—
402C2×C4×C61—41no—
403C2×C4×C61—41no—
404C2×C4×C61—41no—
405C2×C4×C61—41no—
406C2×C4×C61C2×C22⋊C414yes—
407C2×Dic61—22no—
408C2×Dic61—22no—
409C2×Dic61—22no—
410C2×Dic61—22no—
411C2×Dic61—22no—
412C2×Dic61—22no—
413C2×Dic61—22no—
414C2×Dic61—22no—
415C2×Dic61—22no—
416C2×Dic61—22no—
417C2×Dic61—22no—
418C2×Dic61—22no—
419C2×Dic61—22no—
420C2×Dic61—22no—
421C2×Dic61—22no—
422C2×Dic61—22no—
423C2×Dic61—22no—
424C2×Dic61—22no—
425C2×Dic61—22no—
426C2×Dic61—22no—
427C2×Dic61—22no—
428C2×Dic61—22no—
429C2×Dic61—22no—
430C2×Dic61—22no—
431C2×Dic61—22no—
432C2×Dic61—22no—
433C2×Dic61—22no—
434C2×Dic61—41no—
435C2×Dic61—41no—
436C2×Dic61—41no—
437C2×Dic61—41no—
438C2×Dic61—41no—
439C2×Dic61—41no—
440C2×Dic61—41no—
441C2×Dic61—41no—
442C2×Dic61—41no—
443C2×Dic61—41no—
444C2×Dic61—41no—
445C2×Dic61—41no—
446C2×Dic61—41no—
447C2×Dic61—41no—
448C2×Dic61—41no—
449C2×Dic61—41no—
450C2×Dic61—41no—
451C2×Dic61—41no—
452C2×Dic61—41no—
453C2×Dic61C2×C22⋊C414yes—
454C2×Dic61C4×D414yes—
455C2×Dic61C22⋊Q814yescomplemented
456C4×D61—416no—
457C4×D61—416no—
458C4×D61—416no—
459Dic122—416no—
460#14052—611nomaximal, Sylow
461C22×C61C22×C22⋊C411yescharacteristic
462C22×C61C2×C4×D411yescharacteristic
463C22×C61C2×C4×Q811yescharacteristic
464C22×C61C2×C4×Q811yescharacteristic
465C22×C61C4×#4111yescharacteristic
466C22×C61#51811yescharacteristic
467C22×C61#52011yescharacteristic
468C22×C61C2×C22⋊Q811yescharacteristic
469C22×C61C2×C22⋊Q811yescharacteristic
470C22×C61C2×C22⋊Q811yescharacteristic
471C22×C61#52511yescharacteristic
472C22×C61C2×#12411yescharacteristic
473C22×C61#52911yescharacteristic
474C22×C61C2×C4⋊Q811yescharacteristic
475C22×C61#53311yescharacteristic
476C22×C61#53811yescharacteristic
477C22×C61#53911yescharacteristic
478C22×C61#54311yescharacteristic
479C22×C61#54411yescharacteristic
480C22×C61D4211yescharacteristic
481C22×C61D4211yescharacteristic
482C22×C61#54611yescharacteristic
483C22×C61#54611yescharacteristic
484C22×C61#54611yescharacteristic
485C22×C61#54611yescharacteristic
486C22×C61#54611yescharacteristic
487C22×C61#54711yescharacteristic
488C22×C61#54711yescharacteristic
489C22×C61D4×Q811yescharacteristic
490C22×C61#55111yescharacteristic
491C22×C61#55111yescharacteristic
492C22×C61#55211yescharacteristic
493C22×C61#55411yescharacteristic
494C22×C61#55411yescharacteristic
495C22×C61#55411yescharacteristic
496C2×D61—24no—
497C2×D61—24no—
498C2×D61—24no—
499C2×D61—24no—
500C2×D61—24no—
501C2×D61—24no—
502C2×D61—24no—
503C2×D61—24no—
504C2×D61—24no—
505C2×D61—24no—
506C2×D61—24no—
507C2×D61—24no—
508C2×D61—24no—
509C2×D61—24no—
510C2×D61#39118yescomplemented
511C4×C61—24no—
512C4×C61—42no—
513C4×C61—42no—
514C4×C61—42no—
515C4×C61—42no—
516C4×C61—42no—
517C4×C61—81no—
518Dic61—24no—
519Dic61—24no—
520Dic61—24no—
521Dic61—42no—
522Dic61—42no—
523Dic61—42no—
524Dic61—81no—
525C22×C22⋊Q8—611no—
526C2×#391—611no—
527C2×#385—611no—
528C2×C4×C22⋊C4—611no—
529C22×#95—611no—
530#1446—611no—
531#1445—611no—
532#1441—611no—
533#1441D6111yescharacteristic, complemented
534#1436—611no—
535#1436—611no—
536C4⋊#95—611no—
537C22⋊#95—611no—
538C22⋊#95—611no—
539C22⋊#95—611no—
540C2×C61C2×#39111yescharacteristic
541C2×C61C4×C22⋊Q811yescharacteristic
542C2×C61#232911yescharacteristic
543C2×C61D4×C22⋊C411yescharacteristic
544C2×C61#233911yescharacteristic
545C2×C61#236011yescharacteristic
546C2×C61#236811yescharacteristic
547C2×C61#243711yescharacteristic
548C2×C61#243811yescharacteristic
549C2×C61#244011yescharacteristic
550C2×C61#244911yescharacteristic
551C2×C61#245011yescharacteristic
552C2×C61#247211yescharacteristic
553C2×C61#248811yescharacteristic
554C2×C61#254911yescharacteristic
555D61—28no—
556C23×Q8—611no—
557C24×C4—611no—
558C24×C4—611no—
559C24×C4—611no—
560C2×C22⋊Q8—618no—
561C2×C22⋊Q8—1224no—
562C2×C22⋊Q8—1224no—
563C22×C4⋊C4—611no—
564C22×C4⋊C4—611no—
565C22×C4⋊C4—611no—
566C22×C4⋊C4C2×D6111yescharacteristic
567C22×C4⋊C4C2×D6111yescharacteristic
568C22×C22⋊C4—611no—
569C22×C22⋊C4—611no—
570C22×C22⋊C4—611no—
571C22×C22⋊C4—611no—
572C22×C42—611no—
573C22×C42—611no—
574#391—1224no—
575#385—1224no—
576C4×C22⋊C4—1224no—
577C2×#95—611no—
578C2×#95—611no—
579C2×#95—611no—
580C2×#95—611no—
581C2×#95—611no—
582C2×#95—611no—
583C2×#95—611no—
584C2×#95—611no—
585C2×#95—611no—
586C2×#95—611no—
587C2×#95—611no—
588C2×#95—611no—
589C2×#95—611no—
590C2×#95—611no—
591C2×#95—611no—
592C2×#95—1224no—
593C2×#95C2×D6111yescharacteristic
594C2×#95C2×D6111yescharacteristic
595C2×#95C2×D6111yescharacteristic
596C2×#95C2×D6111yescharacteristic
597C2×#95C2×D6111yescharacteristic
598C61#1405211yescharacteristic, complemented, Sylow
599C25—611no—
600C22×Q8—614no—
601C22×Q8—1222no—
602C22×Q8—1222no—
603C22×Q8—1222no—
604C22×Q8—1222no—
605C22×Q8—2441no—
606C22×Q8—2441no—
607C23×C4—611no—
608C23×C4—611no—
609C23×C4—611no—
610C23×C4—611no—
611C23×C4—611no—
612C23×C4—611no—
613C23×C4—614no—
614C23×C4—614no—
615C23×C4—611no—
616C23×C4—1222no—
617C23×C4—1222no—
618C23×C4—1222no—
619C23×C4—1222no—
620C23×C4—1222no—
621C23×C4—1222no—
622C23×C4—1222no—
623C23×C4—1222no—
624C23×C4—1222no—
625C23×C4—1222no—
626C23×C4—1222no—
627C23×C4—1222no—
628C23×C4—1222no—
629C23×C4—2441no—
630C23×C4—2441no—
631C23×C4—2441no—
632C23×C4—2441no—
633C23×C4—2441no—
634C23×C4—2441no—
635C23×C4C22×D6111yescharacteristic
636C23×C4C22×D6111yescharacteristic
637C23×C4C22×D6111yescharacteristic
638C23×C4C22×D6111yescharacteristic
639C23×C4C22×D6111yescharacteristic
640C23×C4C22×D6111yescharacteristic
641C23×C4C22×D6111yescharacteristic
642C22⋊Q8—12232no—
643C2×C4⋊C4—22no—
644C2×C4⋊C4—22no—
645C2×C4⋊C4—22no—
646C2×C4⋊C4—22no—
647C2×C4⋊C4—41no—
648C2×C4⋊C4—614no—
649C2×C4⋊C4—614no—
650C2×C4⋊C4—1222no—
651C2×C4⋊C4—1222no—
652C2×C4⋊C4—1222no—
653C2×C4⋊C4—1222no—
654C2×C4⋊C4—1222no—
655C2×C4⋊C4—1222no—
656C2×C4⋊C4—2441no—
657C2×C4⋊C4C4×D6114yescomplemented
658C2×C22⋊C4—614no—
659C2×C22⋊C4—614no—
660C2×C22⋊C4—614no—
661C2×C22⋊C4—614no—
662C2×C22⋊C4—614no—
663C2×C22⋊C4—1222no—
664C2×C22⋊C4—1222no—
665C2×C22⋊C4—1222no—
666C2×C22⋊C4—1222no—
667C2×C22⋊C4—1222no—
668C2×C22⋊C4—1222no—
669C2×C22⋊C4—1222no—
670C2×C42—1222no—
671C2×C42—1222no—
672C2×C42—1222no—
673C2×C42—1222no—
674C2×C42—2441no—
675C2×C42—2441no—
676#95—22no—
677#95—22no—
678#95—41no—
679#95—41no—
680#95—41no—
681#95—614no—
682#95—1222no—
683#95—1222no—
684#95—1222no—
685#95—1222no—
686#95—1222no—
687#95—1222no—
688#95—1222no—
689#95—1222no—
690#95—1222no—
691#95—1222no—
692#95—1222no—
693#95—2441no—
694#95—2441no—
695#95—2441no—
696C24—612no—
697C24—612no—
698C24—612no—
699C24—612no—
700C24—612no—
701C24—612no—
702C24—612no—
703C24—1221no—
704C24—1221no—
705C24—1221no—
706C24—1221no—
707C24—1221no—
708C24—1221no—
709C24—1221no—
710C24—1221no—
711C24C23×D6111yescharacteristic
712C2×Q8—1228no—
713C2×Q8—1228no—
714C2×Q8—2444no—
715C2×Q8—2444no—
716C2×Q8—2444no—
717C2×Q8—2444no—
718C2×Q8—2444no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—21no—
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—21no—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—21no—
733C22×C4—21no—
734C22×C4—21no—
735C22×C4—21no—
736C22×C4—21no—
737C22×C4—21no—
738C22×C4—21no—
739C22×C4—21no—
740C22×C4—21no—
741C22×C4—21no—
742C22×C4—21no—
743C22×C4—21no—
744C22×C4—21no—
745C22×C4—21no—
746C22×C4—21no—
747C22×C4—21no—
748C22×C4—21no—
749C22×C4—21no—
750C22×C4—21no—
751C22×C4—21no—
752C22×C4—21no—
753C22×C4—21no—
754C22×C4—21no—
755C22×C4—21no—
756C22×C4—21no—
757C22×C4—21no—
758C22×C4—21no—
759C22×C4—21no—
760C22×C4—612no—
761C22×C4—612no—
762C22×C4—612no—
763C22×C4—612no—
764C22×C4—612no—
765C22×C4—612no—
766C22×C4—612no—
767C22×C4—612no—
768C22×C4—612no—
769C22×C4—612no—
770C22×C4—612no—
771C22×C4—612no—
772C22×C4—1228no—
773C22×C4—1228no—
774C22×C4—1228no—
775C22×C4—1228no—
776C22×C4—1228no—
777C22×C4—1221no—
778C22×C4—1221no—
779C22×C4—1221no—
780C22×C4—1221no—
781C22×C4—1221no—
782C22×C4—1221no—
783C22×C4—1221no—
784C22×C4—1221no—
785C22×C4—1221no—
786C22×C4—1221no—
787C22×C4—1221no—
788C22×C4—1221no—
789C22×C4—1221no—
790C22×C4—1221no—
791C22×C4—1221no—
792C22×C4—1221no—
793C22×C4—1221no—
794C22×C4—1221no—
795C22×C4—1221no—
796C22×C4—1221no—
797C22×C4—1221no—
798C22×C4—1221no—
799C22×C4—1221no—
800C22×C4—1221no—
801C22×C4—1221no—
802C22×C4—1221no—
803C22×C4—1221no—
804C22×C4—1221no—
805C22×C4—1221no—
806C22×C4—1221no—
807C22×C4—1221no—
808C22×C4—1221no—
809C22×C4—1221no—
810C22×C4—1221no—
811C22×C4—1221no—
812C22×C4—1221no—
813C22×C4—1221no—
814C22×C4—2444no—
815C22×C4—2444no—
816C22×C4—2444no—
817C22×C4—2444no—
818C22×C4—2444no—
819C22×C4—2444no—
820C22×C4—2444no—
821C22×C4—2444no—
822C22×C4—2444no—
823C22×C4—2444no—
824C22×C4—2444no—
825C22×C4—2444no—
826C22×C4—2444no—
827C22×C4—2444no—
828C22×C4—2444no—
829C22×C4—2444no—
830C22×C4C2×C4×D6112yes—
831C22×C4C2×C4×D6112yes—
832C22×C4C2×C4×D6112yes—
833C22×C4D4×D6112yes—
834C22×C4D4×D6112yes—
835C22×C4D4×D6112yes—
836C22×C4Q8×D6112yes—
837C22×C4Q8×D6112yes—
838C4⋊C4—28no—
839C4⋊C4—44no—
840C4⋊C4—1228no—
841C4⋊C4—1228no—
842C4⋊C4—2444no—
843C22⋊C4—6116no—
844C22⋊C4—1228no—
845C22⋊C4—1228no—
846C22⋊C4—2444no—
847C42—2444no—
848C42—2444no—
849C23—614no—
850C23—614no—
851C23—614no—
852C23—614no—
853C23—614no—
854C23—614no—
855C23—614no—
856C23—1222no—
857C23—1222no—
858C23—1222no—
859C23—1222no—
860C23—1222no—
861C23—1222no—
862C23—1222no—
863C23—1222no—
864C23—1222no—
865C23—1222no—
866C23—1222no—
867C23—1222no—
868C23—1222no—
869C23—1222no—
870C23—1222no—
871C23—1222no—
872C23—1222no—
873C23—1222no—
874C23—1222no—
875C23—1222no—
876C23—1222no—
877C23—1222no—
878C23—1222no—
879C23—1222no—
880C23—1222no—
881C23—1222no—
882C23—1222no—
883C23—1222no—
884C23C22×C4×D6111yescharacteristic
885C23C2×D4×D6111yescharacteristic
886C23C2×D4×D6111yescharacteristic
887C23C2×D4×D6111yescharacteristic
888C23C2×Q8×D6111yescharacteristic
889C23C2×Q8×D6111yescharacteristic
890C23#41×D6111yescharacteristic
891C23#41×D6111yescharacteristic
892C23#41×D6111yescharacteristic
893C23#41×D6111yescharacteristic
894C23#41×D6111yescharacteristic
895C23#1451982211yescharacteristic
896C23#1451982211yescharacteristic
897C23#1451982311yescharacteristic
898C23#1451982511yescharacteristic
899Q8—24416no—
900C2×C4—22no—
901C2×C4—22no—
902C2×C4—22no—
903C2×C4—22no—
904C2×C4—22no—
905C2×C4—22no—
906C2×C4—22no—
907C2×C4—22no—
908C2×C4—22no—
909C2×C4—22no—
910C2×C4—22no—
911C2×C4—22no—
912C2×C4—22no—
913C2×C4—22no—
914C2×C4—22no—
915C2×C4—22no—
916C2×C4—22no—
917C2×C4—22no—
918C2×C4—22no—
919C2×C4—22no—
920C2×C4—22no—
921C2×C4—41no—
922C2×C4—41no—
923C2×C4—41no—
924C2×C4—41no—
925C2×C4—41no—
926C2×C4—41no—
927C2×C4—41no—
928C2×C4—41no—
929C2×C4—41no—
930C2×C4—41no—
931C2×C4—41no—
932C2×C4—41no—
933C2×C4—41no—
934C2×C4—41no—
935C2×C4—41no—
936C2×C4—41no—
937C2×C4—41no—
938C2×C4—41no—
939C2×C4—41no—
940C2×C4—41no—
941C2×C4—41no—
942C2×C4—41no—
943C2×C4—41no—
944C2×C4—41no—
945C2×C4—41no—
946C2×C4—41no—
947C2×C4—41no—
948C2×C4—614no—
949C2×C4—614no—
950C2×C4—614no—
951C2×C4—1222no—
952C2×C4—1222no—
953C2×C4—1222no—
954C2×C4—1222no—
955C2×C4—1222no—
956C2×C4—1222no—
957C2×C4—1222no—
958C2×C4—1222no—
959C2×C4—1222no—
960C2×C4—1222no—
961C2×C4—1222no—
962C2×C4—1222no—
963C2×C4—1222no—
964C2×C4—1222no—
965C2×C4—1222no—
966C2×C4—1222no—
967C2×C4—1222no—
968C2×C4—1222no—
969C2×C4—1222no—
970C2×C4—1222no—
971C2×C4—1222no—
972C2×C4—1222no—
973C2×C4—1222no—
974C2×C4—1222no—
975C2×C4—1222no—
976C2×C4—1222no—
977C2×C4—1222no—
978C2×C4—24416no—
979C2×C4—24416no—
980C2×C4—24416no—
981C2×C4—2441no—
982C2×C4—2441no—
983C2×C4—2441no—
984C2×C4—2441no—
985C2×C4—2441no—
986C2×C4—2441no—
987C2×C4—2441no—
988C2×C4—2441no—
989C2×C4—2441no—
990C2×C4—2441no—
991C2×C4—2441no—
992C2×C4—2441no—
993C2×C4—2441no—
994C2×C4—2441no—
995C2×C4—2441no—
996C2×C4—2441no—
997C2×C4—2441no—
998C2×C4—2441no—
999C2×C4—2441no—
1000C2×C4C22⋊C4×D6114yes—
1001C22—618no—
1002C22—1224no—
1003C22—1224no—
1004C22—1224no—
1005C22—1224no—
1006C22—1224no—
1007C22—1224no—
1008C22—1224no—
1009C22—1224no—
1010C22—1224no—
1011C22—1224no—
1012C22—1224no—
1013C22—1224no—
1014C22—1224no—
1015C22—1224no—
1016C22C2×C22⋊C4×D6111yescharacteristic
1017C22C4×D4×D6111yescharacteristic
1018C22C4×Q8×D6111yescharacteristic
1019C22C4×Q8×D6111yescharacteristic
1020C22#1684023011yescharacteristic
1021C22#1684023411yescharacteristic
1022C22#1684024311yescharacteristic
1023C22C22⋊Q8×D6111yescharacteristic
1024C22C22⋊Q8×D6111yescharacteristic
1025C22C22⋊Q8×D6111yescharacteristic
1026C22#1684027011yescharacteristic
1027C22#124×D6111yescharacteristic
1028C22#1684029511yescharacteristic
1029C22C4⋊Q8×D6111yescharacteristic
1030C22#1684031811yescharacteristic
1031C22#1684034411yescharacteristic
1032C22#1684036011yescharacteristic
1033C22#1684038711yescharacteristic
1034C22#1684038911yescharacteristic
1035C22#1684039411yescharacteristic
1036C22#1684039611yescharacteristic
1037C22#1684040111yescharacteristic
1038C22#1684040111yescharacteristic
1039C22#1684040411yescharacteristic
1040C22#1684040911yescharacteristic
1041C22#1684040911yescharacteristic
1042C22#1684041411yescharacteristic
1043C22#1684041411yescharacteristic
1044C22#1684042711yescharacteristic
1045C22#1684043711yescharacteristic
1046C22#1684044011yescharacteristic
1047C22#1684044411yescharacteristic
1048C22#1684046611yescharacteristic
1049C22#1684046611yescharacteristic
1050C22#1684046811yescharacteristic
1051C4—24no—
1052C4—42no—
1053C4—42no—
1054C4—42no—
1055C4—42no—
1056C4—42no—
1057C4—81no—
1058C4—1224no—
1059C4—1224no—
1060C4—1224no—
1061C4—4881no—
1062C4—2442no—
1063C4—2442no—
1064C4—2442no—
1065C2—1228no—
1066C2#391×D6111yescharacteristic
1067C2#2144835311yescharacteristic
1068C2#2144855311yescharacteristic
1069C2#2144863711yescharacteristic
1070C2#2144864711yescharacteristic
1071C2#2144882111yescharacteristic
1072C2#2144889611yescharacteristic
1073C2#2144948111yescharacteristic
1074C2#2144949011yescharacteristic
1075C2#2144951411yescharacteristic
1076C2#2144962311yescharacteristic
1077C2#2144963811yescharacteristic
1078C2#2144994011yescharacteristic
1079C2#2145014011yescharacteristic
1080C2#2145082611yescharacteristic
subgroupG/H
center, FrattiniC24C23×D61
commutatorC23×C61C23×C4
FittingC61×#1441C2
socle, cosocleC24×C61C24
prime radicalC24×D61C23
hypercenter#1441D61
hypocenterC61#14052
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C24 ◁ #1441

Complements

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

NH ≅ G/Ntype
2. C2×#16839667C2semidirect
6. #21444089C2semidirect
7. #21444085C2semidirect
8. #21444070C2semidirect
9. #21444051C2semidirect
10. #21444050C2semidirect
11. #21444047C2semidirect
15. C61×#1441C2semidirect
22. C2×#14519755C4semidirect
65. C22×Dic122C2×C4semidirect
93. C22×C4×D61Q8semidirect
102. C2×#11758196C2×C4semidirect
103. C2×#11758196C2×C4semidirect
115. C2×#11758198Q8semidirect
149. C2×C4⋊C4×C61C2×C4semidirect
455. C2×Dic61C22⋊Q8semidirect
510. C2×D61#391semidirect
533. #1441D61semidirect
598. C61#14052semidirect
657. C2×C4⋊C4C4×D61semidirect

Maximal subgroups

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

subgroupindex
C22×#145197552
C2×#168396672
C2×#168396332
C2×#168396092
C2×#95×D612
#214440892
#214440852
#214440702
#214440512
#214440502
#214440472
#214440402
C61×#14412
#1405261