Finite Group Databasebeta

← #29606396

Subgroups — #29606396

Order 15616.

2098 conjugacy classes of subgroups.

The subgroup lattice has 1178 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839640C211yesmaximal, characteristic
2C2×#16839640C211yesmaximal, characteristic
3C2×#16839640C211yesmaximal, characteristic
4C2×#16839633C211yesmaximal, characteristic, complemented
5C2×#95×D61C211yesmaximal, characteristic, complemented
6#21444081C211yesmaximal, characteristic, complemented
7#21444079C211yesmaximal, characteristic, complemented
8#21444074C211yesmaximal, characteristic, complemented
9#21444067C211yesmaximal, characteristic, complemented
10#21444067C211yesmaximal, characteristic, complemented
11#21444063C211yesmaximal, characteristic, complemented
12#21444061C211yesmaximal, characteristic, complemented
13#21444040C211yesmaximal, characteristic, complemented
14#21444040C211yesmaximal, characteristic, complemented
15C61×#1442C211yesmaximal, characteristic, complemented
16C23×D244C2211yescharacteristic
17C23×C4×D61C2211yescharacteristic
18C23×C4×D61C2211yescharacteristic
19C23×C4×D61C2211yescharacteristic
20C22×#11758196C2211yescharacteristic
21C22×#11758198C2211yescharacteristic
22C22×#11758198C2211yescharacteristic
23C22×#11758198C2211yescharacteristic
24C22×#11758198C2211yescharacteristic
25C22×#11758198C2211yescharacteristic
26C22×#11758198C2211yescharacteristic
27C22×#11758198C2211yescharacteristic
28C22×#11758198C2211yescharacteristic
29C22×#11758198C2211yescharacteristic
30#16839640—24no—
31#16839640—24no—
32#16839640C418yescomplemented
33#16839633—24no—
34C2×#14519684C2211yescharacteristic
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
48#95×D61—24no—
49C22×C4⋊C4×C61C2211yescharacteristic
50C2×#95×C61C2211yescharacteristic
51C2×#95×C61C2211yescharacteristic
52C2×#95×C61C2211yescharacteristic
53C2×#95×C61C2211yescharacteristic
54C2×#95×C61C2211yescharacteristic
55C2×#95×C61C2211yescharacteristic
56C24×D61C2311yescharacteristic
57C24×D61C2311yescharacteristic
58C22×D244—22no—
59C22×D244—22no—
60C22×D244—22no—
61C22×D244—22no—
62C22×D244—22no—
63C22×D244—22no—
64C22×D244C2×C414yes—
65C23×Dic61C2311yescharacteristic
66C23×Dic61C2311yescharacteristic
67C23×Dic61C2311yescharacteristic
68C23×Dic61C2311yescharacteristic
69C23×Dic61C2311yescharacteristic
70C23×Dic61C2311yescharacteristic
71C22×C4×D61—22no—
72C22×C4×D61—22no—
73C22×C4×D61—22no—
74C22×C4×D61—22no—
75C22×C4×D61—22no—
76C22×C4×D61—22no—
77C22×C4×D61—41no—
78C22×C4×D61—41no—
79C22×C4×D61—41no—
80C22×C4×D61—41no—
81C22×C4×D61—41no—
82C22×C4×D61—41no—
83C22×C4×D61—41no—
84C22×C4×D61—41no—
85C22×C4×D61—41no—
86C22×C4×D61—41no—
87C22×C4×D61—41no—
88C22×C4×D61—41no—
89C22×C4×D61C2×C414yes—
90C22×C4×D61D414yes—
91C22×C4×D61D414yes—
92C2×#11758196—22no—
93C2×#11758196—41no—
94C2×#11758196—41no—
95C2×#11758198—22no—
96C2×#11758198—22no—
97C2×#11758198—22no—
98C2×#11758198—22no—
99C2×#11758198—22no—
100C2×#11758198—22no—
101C2×#11758198—22no—
102C2×#11758198—22no—
103C2×#11758198—22no—
104C2×#11758198—22no—
105C2×#11758198—22no—
106C2×#11758198—22no—
107C2×#11758198—41no—
108C2×#11758198—41no—
109C2×#11758198—41no—
110C2×#11758198—41no—
111C2×#11758198—41no—
112C2×#11758198—41no—
113C2×#11758198—41no—
114C2×#11758198—41no—
115C2×#11758198—41no—
116C2×#11758198—41no—
117C2×#11758198—41no—
118C2×#11758198—41no—
119C2×#11758198C2×C414yes—
120C2×#11758198C2×C414yescomplemented
121C2×#11758198C2×C414yescomplemented
122#14519684—22no—
123#14519684—22no—
124#14519684—22no—
125#14519684—22no—
126#14519684—22no—
127#14519684—22no—
128#14519684—22no—
129#14519684—41no—
130#14519684—41no—
131#14519684—41no—
132#14519684—41no—
133#14519684—41no—
134#14519684—41no—
135#14519684C2×C414yescomplemented
136C23×C4×C61C2311yescharacteristic
137C23×C4×C61C2311yescharacteristic
138C23×C4×C61C2311yescharacteristic
139C23×C4×C61C2311yescharacteristic
140C23×C4×C61C2311yescharacteristic
141C23×C4×C61C2311yescharacteristic
142C23×C4×C61C2311yescharacteristic
143C2×C4⋊C4×C61—22no—
144C2×C4⋊C4×C61—41no—
145C2×C4⋊C4×C61—41no—
146#95×C61—22no—
147#95×C61—22no—
148#95×C61—22no—
149#95×C61—41no—
150#95×C61—41no—
151#95×C61C2×C414yescomplemented
152C24×C61C2411yescharacteristic
153C23×D61—21no—
154C23×D61—21no—
155C23×D61—21no—
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×D61—21no—
165C23×D61—21no—
166C23×D61—21no—
167C23×D61—21no—
168C23×D61—21no—
169C23×D61—21no—
170C23×D61—21no—
171C23×D61—21no—
172C23×D61—21no—
173C23×D61—21no—
174C23×D61—21no—
175C23×D61C22×C412yes—
176C23×D61C22×C412yes—
177C23×D61C2×D412yes—
178C23×D61C2×D412yes—
179C23×D61#4112yes—
180C23×D61#4112yes—
181C23×D61#4112yes—
182C23×D61#4112yes—
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×C61—21no—
213C22×C4×C61—21no—
214C22×C4×C61—21no—
215C22×C4×C61—21no—
216C22×C4×C61—21no—
217C22×C4×C61—21no—
218C22×C4×C61—21no—
219C22×C4×C61—21no—
220C22×C4×C61—21no—
221C22×C4×C61—21no—
222C22×C4×C61—21no—
223C22×C4×C61—21no—
224C22×C4×C61—21no—
225C22×C4×C61—21no—
226C22×C4×C61—21no—
227C22×C4×C61C22×C412yes—
228C22×C4×C61C22×C412yes—
229C22×C4×C61C22×C412yes—
230C22×C4×C61C2×D412yes—
231C22×C4×C61C2×D412yes—
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×Dic61—21no—
258C22×Dic61—21no—
259C22×Dic61—21no—
260C22×Dic61—21no—
261C22×Dic61—21no—
262C22×Dic61—21no—
263C22×Dic61—21no—
264C22×Dic61—21no—
265C22×Dic61—21no—
266C22×Dic61—21no—
267C22×Dic61—21no—
268C22×Dic61—21no—
269C22×Dic61—21no—
270C22×Dic61C22×C412yes—
271C22×Dic61C22×C412yes—
272C22×Dic61C2×D412yes—
273C22×Dic61C2×D412yes—
274C2×D244—28no—
275C2×D244—28no—
276C2×D244—28no—
277C2×D244—44no—
278C2×D244—44no—
279C2×D244—44no—
280C2×D244—44no—
281C2×C4×D61—28no—
282C2×C4×D61—28no—
283C2×C4×D61—28no—
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×C4×D61—44no—
291C2×C4×D61—44no—
292C2×C4×D61—44no—
293C2×C4×D61—44no—
294C2×C4×D61—44no—
295C2×C4×D61—44no—
296C2×C4×D61—44no—
297C2×C4×D61—44no—
298C2×C4×D61—44no—
299C2×C4×D61—44no—
300C2×C4×D61—44no—
301C2×C4×D61—44no—
302C4⋊C4×C61—44no—
303#11758198—28no—
304#11758198—44no—
305#11758198—44no—
306#11758198—44no—
307#11758198—44no—
308#11758198—44no—
309#11758198—44no—
310#11758198—44no—
311#11758198—44no—
312#11758196—44no—
313C23×C61C23×C411yescharacteristic
314C23×C61C22×D411yescharacteristic
315C23×C61C22×D411yescharacteristic
316C23×C61C2×#4111yescharacteristic
317C23×C61C2×#4111yescharacteristic
318C23×C61C2×#4111yescharacteristic
319C23×C61C2×#4111yescharacteristic
320C23×C61H(5,𝔽2)11yescharacteristic
321C23×C61H(5,𝔽2)11yescharacteristic
322C23×C61H(5,𝔽2)11yescharacteristic
323C23×C61H(5,𝔽2)11yescharacteristic
324C23×C61H(5,𝔽2)11yescharacteristic
325C23×C61H(5,𝔽2)11yescharacteristic
326C23×C612−1+411yescharacteristic
327C23×C612−1+411yescharacteristic
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×D61—22no—
352C22×D61—22no—
353C22×D61—22no—
354C22×D61—22no—
355C22×D61—22no—
356C22×D61—22no—
357C22×D61—22no—
358C22×D61—22no—
359C22×D61—22no—
360C22×D61—22no—
361C22×D61—22no—
362C22×D61—22no—
363C22×D61—41no—
364C22×D61—41no—
365C22×D61—41no—
366C22×D61—41no—
367C22×D61—41no—
368C22×D61—41no—
369C22×D61—41no—
370C22×D61—41no—
371C22×D61—41no—
372C22×D61—41no—
373C22×D61—41no—
374C22×D61—41no—
375C22×D61—41no—
376C22×D61—41no—
377C22×D61—41no—
378C22×D61—41no—
379C22×D61—41no—
380C22×D61—41no—
381C22×D61—41no—
382C22×D61—41no—
383C22×D61—41no—
384C22×D61—41no—
385C22×D61—41no—
386C22×D61—41no—
387C22×D61—41no—
388C22×D61—41no—
389C22×D61—41no—
390C22×D61—41no—
391C22×D61#11714yes—
392C22×D61C4×D414yes—
393C22×D61C4×D414yes—
394C22×D61#12114yes—
395C22×D61#12314yes—
396C22×D61#12414yes—
397C22×D61#12614yes—
398C2×C4×C61—22no—
399C2×C4×C61—22no—
400C2×C4×C61—22no—
401C2×C4×C61—22no—
402C2×C4×C61—22no—
403C2×C4×C61—22no—
404C2×C4×C61—22no—
405C2×C4×C61—22no—
406C2×C4×C61—22no—
407C2×C4×C61—22no—
408C2×C4×C61—22no—
409C2×C4×C61—22no—
410C2×C4×C61—22no—
411C2×C4×C61—22no—
412C2×C4×C61—22no—
413C2×C4×C61—41no—
414C2×C4×C61—41no—
415C2×C4×C61—41no—
416C2×C4×C61—41no—
417C2×C4×C61—41no—
418C2×C4×C61—41no—
419C2×C4×C61—41no—
420C2×C4×C61—41no—
421C2×C4×C61—41no—
422C2×C4×C61—41no—
423C2×C4×C61—41no—
424C2×C4×C61—41no—
425C2×C4×C61—41no—
426C2×C4×C61—41no—
427C2×C4×C61—41no—
428C2×C4×C61—41no—
429C2×C4×C61—41no—
430C2×C4×C61—41no—
431C2×C4×C61—41no—
432C2×C4×C61—41no—
433C2×C4×C61—41no—
434C2×C4×C61—41no—
435C2×C4×C61—41no—
436C2×C4×C61—41no—
437C2×C4×C61—41no—
438C2×C4×C61—41no—
439C2×C4×C61—41no—
440C2×C4×C61—41no—
441C2×C4×C61—41no—
442C2×C4×C61—41no—
443C2×C4×C61—41no—
444C2×C4×C61—41no—
445C2×C4×C61—41no—
446C2×C4×C61—41no—
447C2×Dic61—22no—
448C2×Dic61—22no—
449C2×Dic61—22no—
450C2×Dic61—22no—
451C2×Dic61—22no—
452C2×Dic61—22no—
453C2×Dic61—22no—
454C2×Dic61—22no—
455C2×Dic61—22no—
456C2×Dic61—22no—
457C2×Dic61—22no—
458C2×Dic61—22no—
459C2×Dic61—41no—
460C2×Dic61—41no—
461C2×Dic61—41no—
462C2×Dic61—41no—
463C2×Dic61—41no—
464C2×Dic61—41no—
465C2×Dic61—41no—
466C2×Dic61—41no—
467C2×Dic61—41no—
468C2×Dic61—41no—
469C2×Dic61—41no—
470C2×Dic61—41no—
471C2×Dic61—41no—
472C2×Dic61—41no—
473C2×Dic61—41no—
474C2×Dic61—41no—
475C2×Dic61—41no—
476C2×Dic61—41no—
477C2×Dic61—41no—
478C2×Dic61—41no—
479C2×Dic61—41no—
480C2×Dic61—41no—
481C2×Dic61—41no—
482C2×Dic61—41no—
483C2×Dic61—41no—
484C2×Dic61—41no—
485C2×Dic61—41no—
486C2×Dic61—41no—
487C2×Dic61—41no—
488C2×Dic61—41no—
489D244—416no—
490C4×D61—416no—
491C4×D61—416no—
492C4×D61—416no—
493#14259—611nomaximal, Sylow
494C22×C61C2×#11711yescharacteristic
495C22×C61C2×C4×D411yescharacteristic
496C22×C61C2×C4×D411yescharacteristic
497C22×C61#51811yescharacteristic
498C22×C61#51811yescharacteristic
499C22×C61#52011yescharacteristic
500C22×C61#52011yescharacteristic
501C22×C61C2×#12111yescharacteristic
502C22×C61C2×#12311yescharacteristic
503C22×C61C2×#12411yescharacteristic
504C22×C61C2×#12611yescharacteristic
505C22×C61#53411yescharacteristic
506C22×C61#53411yescharacteristic
507C22×C61#53411yescharacteristic
508C22×C61#53411yescharacteristic
509C22×C61#53511yescharacteristic
510C22×C61#53611yescharacteristic
511C22×C61#53711yescharacteristic
512C22×C61#53711yescharacteristic
513C22×C61#53811yescharacteristic
514C22×C61#53811yescharacteristic
515C22×C61#53811yescharacteristic
516C22×C61#53811yescharacteristic
517C22×C61#53811yescharacteristic
518C22×C61#53811yescharacteristic
519C22×C61#53811yescharacteristic
520C22×C61#53811yescharacteristic
521C22×C61#53911yescharacteristic
522C22×C61#53911yescharacteristic
523C22×C61#53911yescharacteristic
524C22×C61#53911yescharacteristic
525C22×C61#53911yescharacteristic
526C22×C61#53911yescharacteristic
527C22×C61#53911yescharacteristic
528C22×C61#53911yescharacteristic
529C2×D61—24no—
530C2×D61—24no—
531C2×D61—24no—
532C2×D61—24no—
533C2×D61—24no—
534C2×D61—24no—
535C2×D61—24no—
536C2×D61—24no—
537C2×D61—24no—
538C2×D61—24no—
539C2×D61—24no—
540C2×D61—24no—
541C2×D61—24no—
542C2×D61—24no—
543C2×D61—42no—
544C2×D61—42no—
545C2×D61—42no—
546C2×D61—42no—
547C2×D61—42no—
548C2×D61—42no—
549C2×D61—42no—
550C2×D61—81no—
551C2×D61—81no—
552C2×D61—81no—
553C2×D61—81no—
554C2×D61—81no—
555C2×D61—81no—
556C2×D61—81no—
557C2×D61—81no—
558C2×D61#38818yes—
559C4×C61—42no—
560C4×C61—42no—
561C4×C61—42no—
562C4×C61—42no—
563C4×C61—42no—
564C4×C61—81no—
565C4×C61—81no—
566Dic61—42no—
567Dic61—42no—
568Dic61—42no—
569Dic61—42no—
570Dic61—81no—
571Dic61—81no—
572C2×#386—611no—
573C2×#386—611no—
574C2×#386—611no—
575C2×#385—611no—
576C22×#95—611no—
577#1443—611no—
578#1443—611no—
579#1442—611no—
580#1442D6111yescharacteristic, complemented
581#1440—611no—
582#1440—611no—
583#1439—611no—
584#1439—611no—
585C22⋊#95—611no—
586C22⋊#95—611no—
587C2×C61C2×#38811yescharacteristic
588C2×C61#231811yescharacteristic
589C2×C61#231811yescharacteristic
590C2×C61#232111yescharacteristic
591C2×C61#232211yescharacteristic
592C2×C61#232511yescharacteristic
593C2×C61#232511yescharacteristic
594C2×C61#261711yescharacteristic
595C2×C61#261811yescharacteristic
596C2×C61#262211yescharacteristic
597C2×C61#262311yescharacteristic
598C2×C61#263911yescharacteristic
599C2×C61#263911yescharacteristic
600C2×C61#264311yescharacteristic
601C2×C61#264311yescharacteristic
602D61—28no—
603D61—82no—
604C23×D4—611no—
605C24×C4—611no—
606C24×C4—611no—
607C24×C4—611no—
608C22×C4⋊C4—611no—
609C22×C4⋊C4C2×D6111yescharacteristic
610C22×C22⋊C4—611no—
611C22×C22⋊C4—611no—
612C22×C22⋊C4—611no—
613C22×C22⋊C4—611no—
614C22×C22⋊C4—611no—
615C22×C22⋊C4—611no—
616C22×C22⋊C4—611no—
617C22×C22⋊C4—611no—
618C22×C22⋊C4—611no—
619#386—618no—
620#386—1224no—
621#386—1224no—
622#385—1224no—
623C2×#95—611no—
624C2×#95—611no—
625C2×#95—611no—
626C2×#95—611no—
627C2×#95—611no—
628C2×#95—611no—
629C2×#95—611no—
630C2×#95—611no—
631C2×#95—611no—
632C2×#95—611no—
633C2×#95—611no—
634C2×#95—611no—
635C2×#95—611no—
636C2×#95—611no—
637C2×#95—1224no—
638C2×#95C2×D6111yescharacteristic
639C2×#95C2×D6111yescharacteristic
640C2×#95C2×D6111yescharacteristic
641C2×#95C2×D6111yescharacteristic
642C2×#95C2×D6111yescharacteristic
643C2×#95C2×D6111yescharacteristic
644C61#1425911yescharacteristic, complemented, Sylow
645C25—611no—
646C25—611no—
647C22×D4—614no—
648C22×D4—1222no—
649C22×D4—1222no—
650C22×D4—1222no—
651C22×D4—1222no—
652C22×D4—1222no—
653C22×D4—1222no—
654C23×C4—611no—
655C23×C4—611no—
656C23×C4—611no—
657C23×C4—611no—
658C23×C4—614no—
659C23×C4—614no—
660C23×C4—614no—
661C23×C4—611no—
662C23×C4—611no—
663C23×C4—1222no—
664C23×C4—1222no—
665C23×C4—1222no—
666C23×C4—1222no—
667C23×C4—1222no—
668C23×C4—1222no—
669C23×C4—2441no—
670C23×C4—2441no—
671C23×C4—2441no—
672C23×C4—2441no—
673C23×C4—2441no—
674C23×C4—2441no—
675C23×C4—2441no—
676C23×C4—2441no—
677C23×C4—2441no—
678C23×C4—2441no—
679C23×C4—2441no—
680C23×C4—2441no—
681C23×C4C22×D6111yescharacteristic
682C23×C4C22×D6111yescharacteristic
683C23×C4C22×D6111yescharacteristic
684C23×C4C22×D6111yescharacteristic
685C23×C4C22×D6111yescharacteristic
686C23×C4C22×D6111yescharacteristic
687C23×C4C22×D6111yescharacteristic
688C2×C4⋊C4—22no—
689C2×C4⋊C4—41no—
690C2×C4⋊C4—41no—
691C2×C4⋊C4—1222no—
692C2×C4⋊C4—2441no—
693C2×C4⋊C4—2441no—
694C2×C22⋊C4—614no—
695C2×C22⋊C4—614no—
696C2×C22⋊C4—614no—
697C2×C22⋊C4—1222no—
698C2×C22⋊C4—1222no—
699C2×C22⋊C4—1222no—
700C2×C22⋊C4—1222no—
701C2×C22⋊C4—1222no—
702C2×C22⋊C4—1222no—
703C2×C22⋊C4—1222no—
704C2×C22⋊C4—1222no—
705C2×C22⋊C4—1222no—
706C2×C22⋊C4—1222no—
707C2×C22⋊C4—1222no—
708C2×C22⋊C4—1222no—
709C2×C22⋊C4—2441no—
710C2×C22⋊C4—2441no—
711C2×C22⋊C4—2441no—
712C2×C22⋊C4—2441no—
713C2×C22⋊C4—2441no—
714C2×C22⋊C4—2441no—
715C2×C22⋊C4—2441no—
716C2×C22⋊C4—2441no—
717C2×C22⋊C4—2441no—
718C2×C22⋊C4—2441no—
719C2×C22⋊C4—2441no—
720C2×C22⋊C4—2441no—
721#95—22no—
722#95—22no—
723#95—22no—
724#95—41no—
725#95—41no—
726#95—614no—
727#95—1222no—
728#95—1222no—
729#95—1222no—
730#95—1222no—
731#95—1222no—
732#95—1222no—
733#95—1222no—
734#95—2441no—
735#95—2441no—
736#95—2441no—
737#95—2441no—
738#95—2441no—
739#95—2441no—
740#95C4×D6114yescomplemented
741C24—612no—
742C24—612no—
743C24—612no—
744C24—612no—
745C24—612no—
746C24—612no—
747C24—612no—
748C24—612no—
749C24—1221no—
750C24—1221no—
751C24—1221no—
752C24—1221no—
753C24—1221no—
754C24—1221no—
755C24—1221no—
756C24—1221no—
757C24—1221no—
758C24—1221no—
759C24—1221no—
760C24—1221no—
761C24—1221no—
762C24—1221no—
763C24—1221no—
764C24—1221no—
765C24—1221no—
766C24—1221no—
767C24—1221no—
768C24—1221no—
769C24—1221no—
770C24—1221no—
771C24C23×D6111yescharacteristic
772C2×D4—1228no—
773C2×D4—1228no—
774C2×D4—1228no—
775C2×D4—2444no—
776C2×D4—2444no—
777C2×D4—2444no—
778C2×D4—2444no—
779C22×C4—21no—
780C22×C4—21no—
781C22×C4—21no—
782C22×C4—21no—
783C22×C4—21no—
784C22×C4—21no—
785C22×C4—21no—
786C22×C4—21no—
787C22×C4—21no—
788C22×C4—21no—
789C22×C4—21no—
790C22×C4—21no—
791C22×C4—21no—
792C22×C4—21no—
793C22×C4—21no—
794C22×C4—21no—
795C22×C4—21no—
796C22×C4—21no—
797C22×C4—21no—
798C22×C4—21no—
799C22×C4—21no—
800C22×C4—21no—
801C22×C4—21no—
802C22×C4—21no—
803C22×C4—21no—
804C22×C4—21no—
805C22×C4—21no—
806C22×C4—21no—
807C22×C4—21no—
808C22×C4—21no—
809C22×C4—21no—
810C22×C4—21no—
811C22×C4—21no—
812C22×C4—21no—
813C22×C4—21no—
814C22×C4—21no—
815C22×C4—21no—
816C22×C4—21no—
817C22×C4—21no—
818C22×C4—21no—
819C22×C4—21no—
820C22×C4—21no—
821C22×C4—21no—
822C22×C4—21no—
823C22×C4—612no—
824C22×C4—612no—
825C22×C4—612no—
826C22×C4—612no—
827C22×C4—1228no—
828C22×C4—1228no—
829C22×C4—1228no—
830C22×C4—1221no—
831C22×C4—1221no—
832C22×C4—1221no—
833C22×C4—1221no—
834C22×C4—1221no—
835C22×C4—1221no—
836C22×C4—1221no—
837C22×C4—1221no—
838C22×C4—1221no—
839C22×C4—1221no—
840C22×C4—1221no—
841C22×C4—1221no—
842C22×C4—1221no—
843C22×C4—1221no—
844C22×C4—1221no—
845C22×C4—1221no—
846C22×C4—1221no—
847C22×C4—1221no—
848C22×C4—1221no—
849C22×C4—1221no—
850C22×C4—1221no—
851C22×C4—1221no—
852C22×C4—1221no—
853C22×C4—1221no—
854C22×C4—1221no—
855C22×C4—1221no—
856C22×C4—1221no—
857C22×C4—1221no—
858C22×C4—1221no—
859C22×C4—1221no—
860C22×C4—1221no—
861C22×C4—1221no—
862C22×C4—1221no—
863C22×C4—1221no—
864C22×C4—1221no—
865C22×C4—1221no—
866C22×C4—1221no—
867C22×C4—1221no—
868C22×C4—2444no—
869C22×C4—2444no—
870C22×C4—2444no—
871C22×C4—2444no—
872C22×C4—2444no—
873C22×C4—2444no—
874C22×C4—2444no—
875C22×C4—2444no—
876C22×C4—2444no—
877C22×C4—2444no—
878C22×C4—2444no—
879C22×C4—2444no—
880C22×C4—2444no—
881C22×C4—2444no—
882C22×C4—2444no—
883C22×C4—2444no—
884C22×C4—2444no—
885C22×C4—2444no—
886C22×C4C2×C4×D6112yes—
887C22×C4C2×C4×D6112yes—
888C22×C4C2×C4×D6112yes—
889C22×C4D4×D6112yes—
890C22×C4D4×D6112yes—
891C4⋊C4—44no—
892C4⋊C4—2444no—
893C22⋊C4—1228no—
894C22⋊C4—2444no—
895C22⋊C4—2444no—
896C22⋊C4—2444no—
897C22⋊C4—2444no—
898C22⋊C4—2444no—
899C22⋊C4—2444no—
900C22⋊C4—2444no—
901C22⋊C4—2444no—
902C23—614no—
903C23—614no—
904C23—614no—
905C23—614no—
906C23—614no—
907C23—614no—
908C23—614no—
909C23—1222no—
910C23—1222no—
911C23—1222no—
912C23—1222no—
913C23—1222no—
914C23—1222no—
915C23—1222no—
916C23—1222no—
917C23—1222no—
918C23—1222no—
919C23—1222no—
920C23—1222no—
921C23—1222no—
922C23—1222no—
923C23—1222no—
924C23—1222no—
925C23—1222no—
926C23—1222no—
927C23—1222no—
928C23—1222no—
929C23—1222no—
930C23—1222no—
931C23—1222no—
932C23—1222no—
933C23—1222no—
934C23—1222no—
935C23—1222no—
936C23—1222no—
937C23—1222no—
938C23—1222no—
939C23—1222no—
940C23—1222no—
941C23—1222no—
942C23—1222no—
943C23—1222no—
944C23—2441no—
945C23—2441no—
946C23—2441no—
947C23—2441no—
948C23—2441no—
949C23—2441no—
950C23—2441no—
951C23—2441no—
952C23—2441no—
953C23—2441no—
954C23—2441no—
955C23—2441no—
956C23—2441no—
957C23—2441no—
958C23—2441no—
959C23—2441no—
960C23—2441no—
961C23—2441no—
962C23—2441no—
963C23—2441no—
964C23—2441no—
965C23—2441no—
966C23—2441no—
967C23—2441no—
968C23—2441no—
969C23—2441no—
970C23—2441no—
971C23—2441no—
972C23C22×C4×D6111yescharacteristic
973C23C2×D4×D6111yescharacteristic
974C23C2×D4×D6111yescharacteristic
975C23#41×D6111yescharacteristic
976C23#41×D6111yescharacteristic
977C23#41×D6111yescharacteristic
978C23#41×D6111yescharacteristic
979C23#1451982211yescharacteristic
980C23#1451982211yescharacteristic
981C23#1451982311yescharacteristic
982C23#1451982311yescharacteristic
983C23#1451982311yescharacteristic
984C23#1451982311yescharacteristic
985C23#1451982511yescharacteristic
986C23#1451982511yescharacteristic
987D4—24416no—
988C2×C4—22no—
989C2×C4—22no—
990C2×C4—22no—
991C2×C4—22no—
992C2×C4—22no—
993C2×C4—22no—
994C2×C4—22no—
995C2×C4—22no—
996C2×C4—22no—
997C2×C4—22no—
998C2×C4—22no—
999C2×C4—22no—
1000C2×C4—22no—
1001C2×C4—22no—
1002C2×C4—22no—
1003C2×C4—41no—
1004C2×C4—41no—
1005C2×C4—41no—
1006C2×C4—41no—
1007C2×C4—41no—
1008C2×C4—41no—
1009C2×C4—41no—
1010C2×C4—41no—
1011C2×C4—41no—
1012C2×C4—41no—
1013C2×C4—41no—
1014C2×C4—41no—
1015C2×C4—41no—
1016C2×C4—41no—
1017C2×C4—41no—
1018C2×C4—41no—
1019C2×C4—41no—
1020C2×C4—41no—
1021C2×C4—41no—
1022C2×C4—41no—
1023C2×C4—41no—
1024C2×C4—41no—
1025C2×C4—41no—
1026C2×C4—41no—
1027C2×C4—41no—
1028C2×C4—41no—
1029C2×C4—41no—
1030C2×C4—41no—
1031C2×C4—41no—
1032C2×C4—41no—
1033C2×C4—41no—
1034C2×C4—41no—
1035C2×C4—41no—
1036C2×C4—41no—
1037C2×C4—1222no—
1038C2×C4—1222no—
1039C2×C4—1222no—
1040C2×C4—1222no—
1041C2×C4—1222no—
1042C2×C4—1222no—
1043C2×C4—1222no—
1044C2×C4—1222no—
1045C2×C4—1222no—
1046C2×C4—1222no—
1047C2×C4—1222no—
1048C2×C4—1222no—
1049C2×C4—24416no—
1050C2×C4—24416no—
1051C2×C4—24416no—
1052C2×C4—2441no—
1053C2×C4—2441no—
1054C2×C4—2441no—
1055C2×C4—2441no—
1056C2×C4—2441no—
1057C2×C4—2441no—
1058C2×C4—2441no—
1059C2×C4—2441no—
1060C2×C4—2441no—
1061C2×C4—2441no—
1062C2×C4—2441no—
1063C2×C4—2441no—
1064C2×C4—2441no—
1065C2×C4—2441no—
1066C2×C4—2441no—
1067C2×C4—2441no—
1068C2×C4—2441no—
1069C2×C4—2441no—
1070C2×C4—2441no—
1071C2×C4—2441no—
1072C2×C4—2441no—
1073C2×C4—2441no—
1074C2×C4—2441no—
1075C2×C4—2441no—
1076C2×C4—2441no—
1077C2×C4—2441no—
1078C2×C4—2441no—
1079C2×C4—2441no—
1080C2×C4—2441no—
1081C2×C4—2441no—
1082C22—618no—
1083C22—1224no—
1084C22—1224no—
1085C22—1224no—
1086C22—1224no—
1087C22—1224no—
1088C22—1224no—
1089C22—1224no—
1090C22—1224no—
1091C22—1224no—
1092C22—1224no—
1093C22—1224no—
1094C22—1224no—
1095C22—1224no—
1096C22—1224no—
1097C22—4881no—
1098C22—4881no—
1099C22—4881no—
1100C22—4881no—
1101C22—4881no—
1102C22—4881no—
1103C22—4881no—
1104C22—4881no—
1105C22—2442no—
1106C22—2442no—
1107C22—2442no—
1108C22—2442no—
1109C22—2442no—
1110C22—2442no—
1111C22—2442no—
1112C22#117×D6111yescharacteristic
1113C22C4×D4×D6111yescharacteristic
1114C22C4×D4×D6111yescharacteristic
1115C22#1684023411yescharacteristic
1116C22#1684023611yescharacteristic
1117C22#1684024311yescharacteristic
1118C22#1684024411yescharacteristic
1119C22#121×D6111yescharacteristic
1120C22#123×D6111yescharacteristic
1121C22#124×D6111yescharacteristic
1122C22#126×D6111yescharacteristic
1123C22#1684032011yescharacteristic
1124C22#1684032211yescharacteristic
1125C22#1684032311yescharacteristic
1126C22#1684032311yescharacteristic
1127C22#1684032811yescharacteristic
1128C22#1684033711yescharacteristic
1129C22#1684034211yescharacteristic
1130C22#1684034211yescharacteristic
1131C22#1684034611yescharacteristic
1132C22#1684034611yescharacteristic
1133C22#1684034611yescharacteristic
1134C22#1684034811yescharacteristic
1135C22#1684034811yescharacteristic
1136C22#1684035111yescharacteristic
1137C22#1684035111yescharacteristic
1138C22#1684035111yescharacteristic
1139C22#1684035811yescharacteristic
1140C22#1684035811yescharacteristic
1141C22#1684035811yescharacteristic
1142C22#1684036011yescharacteristic
1143C22#1684036011yescharacteristic
1144C22#1684036011yescharacteristic
1145C22#1684036011yescharacteristic
1146C22#1684036011yescharacteristic
1147C4—42no—
1148C4—42no—
1149C4—42no—
1150C4—42no—
1151C4—42no—
1152C4—81no—
1153C4—81no—
1154C4—4881no—
1155C4—4881no—
1156C4—2442no—
1157C4—2442no—
1158C4—2442no—
1159C4—2442no—
1160C2—1228no—
1161C2—4882no—
1162C2#388×D6111yescharacteristic
1163C2#2144845111yescharacteristic
1164C2#2144845511yescharacteristic
1165C2#2144848111yescharacteristic
1166C2#2144848311yescharacteristic
1167C2#2144851611yescharacteristic
1168C2#2144851811yescharacteristic
1169C2#2145155811yescharacteristic
1170C2#2145156211yescharacteristic
1171C2#2145159311yescharacteristic
1172C2#2145160011yescharacteristic
1173C2#2145174811yescharacteristic
1174C2#2145175111yescharacteristic
1175C2#2145177311yescharacteristic
1176C2#2145177311yescharacteristic
subgroupG/H
center, FrattiniC24C23×D61
commutatorC23×C61C23×C4
FittingC61×#1442C2
socle, cosocleC24×C61C24
prime radicalC23×D244C22
hypercenter#1442D61
hypocenterC61#14259
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C24 ◁ #1442

Complements

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

NH ≅ G/Ntype
4. C2×#16839633C2semidirect
5. C2×#95×D61C2semidirect
6. #21444081C2semidirect
7. #21444079C2semidirect
8. #21444074C2semidirect
9. #21444067C2semidirect
10. #21444067C2semidirect
11. #21444063C2semidirect
12. #21444061C2semidirect
13. #21444040C2semidirect
14. #21444040C2semidirect
15. C61×#1442C2semidirect
32. #16839640C4semidirect
120. C2×#11758198C2×C4semidirect
121. C2×#11758198C2×C4semidirect
135. #14519684C2×C4semidirect
151. #95×C61C2×C4semidirect
580. #1442D61semidirect
644. C61#14259semidirect
740. #95C4×D61semidirect

Maximal subgroups

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

subgroupindex
C2×#168396402
C2×#168396332
C2×#95×D612
#214440812
#214440792
#214440742
#214440672
#214440632
#214440612
#214440402
C61×#14422
#1425961