Finite Group Databasebeta

← #29608192

Subgroups — #29608192

Order 15616.

2126 conjugacy classes of subgroups.

The subgroup lattice has 1186 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519766C211yesmaximal, characteristic
2C2×#16839669C211yesmaximal, characteristic, complemented
3C2×#16839651C211yesmaximal, characteristic, complemented
4C2×#16839640C211yesmaximal, characteristic
5C2×#16839636C211yesmaximal, characteristic, complemented
6#21444067C211yesmaximal, characteristic, complemented
7#21444065C211yesmaximal, characteristic, complemented
8#21444063C211yesmaximal, characteristic, complemented
9#21444063C211yesmaximal, characteristic, complemented
10#21444059C211yesmaximal, characteristic
11#21444055C211yesmaximal, characteristic, complemented
12#21444047C211yesmaximal, characteristic, complemented
13#21444044C211yesmaximal, characteristic, complemented
14#21444040C211yesmaximal, characteristic, complemented
15C61×#1446C211yesmaximal, characteristic, complemented
16C23×D244C2211yescharacteristic
17C23×C4×D61C2211yescharacteristic
18C2×#14519766—24no—
19C2×#14519766—24no—
20C2×#14519766C418yescomplemented
21C22×C4⋊Dic61C2211yescharacteristic
22C22×#11758196C2211yescharacteristic
23C22×#11758196C2211yescharacteristic
24C22×#11758198C2211yescharacteristic
25C22×#11758198C2211yescharacteristic
26C22×#11758198C2211yescharacteristic
27C22×#11758198C2211yescharacteristic
28C22×#11758198C2211yescharacteristic
29C22×#11758198C2211yescharacteristic
30C22×#11758198C2211yescharacteristic
31C22×#11758198C2211yescharacteristic
32C22×#11758198C2211yescharacteristic
33C22×#11758198C2211yescharacteristic
34C22×#11758198C2211yescharacteristic
35C22×C4×Dic61C2211yescharacteristic
36C22×C4×Dic61C2211yescharacteristic
37#16839669—24no—
38#16839651—24no—
39#16839640—24no—
40#16839636—24no—
41C2×#14519684C2211yescharacteristic
42C2×#14519684C2211yescharacteristic
43C2×#14519684C2211yescharacteristic
44C2×#14519684C2211yescharacteristic
45C2×#14519684C2211yescharacteristic
46C2×#14519684C2211yescharacteristic
47C2×#14519684C2211yescharacteristic
48C2×#14519684C2211yescharacteristic
49C2×#14519684C2211yescharacteristic
50C2×#14519684C2211yescharacteristic
51C23×Q8×C61C2211yescharacteristic
52C2×#95×C61C2211yescharacteristic
53C2×#95×C61C2211yescharacteristic
54C2×#95×C61C2211yescharacteristic
55C2×#95×C61C2211yescharacteristic
56C2×#95×C61C2211yescharacteristic
57C2×#95×C61C2211yescharacteristic
58C24×D61C2311yescharacteristic
59C24×D61C2311yescharacteristic
60C22×D244—22no—
61C22×D244—22no—
62C22×D244—22no—
63C22×D244—22no—
64C22×D244—41no—
65C22×D244—41no—
66C22×D244C2×C414yes—
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—41no—
77C22×C4×D61—41no—
78C22×C4×D61—41no—
79C22×C4×D61—41no—
80#14519766—232no—
81C2×C4⋊Dic61—22no—
82C2×C4⋊Dic61—22no—
83C2×C4⋊Dic61—41no—
84C2×#11758196—22no—
85C2×#11758196—22no—
86C2×#11758196—22no—
87C2×#11758196—22no—
88C2×#11758196—41no—
89C2×#11758196—41no—
90C2×#11758198—22no—
91C2×#11758198—22no—
92C2×#11758198—22no—
93C2×#11758198—22no—
94C2×#11758198—22no—
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—41no—
106C2×#11758198—41no—
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×#11758198C2×C414yes—
118C2×#11758198C2×C414yes—
119C2×#11758198C2×C414yescomplemented
120C2×#11758198C2×C414yescomplemented
121C2×#11758198D414yes—
122C2×#11758198D414yes—
123C2×C4×Dic61—22no—
124C2×C4×Dic61—22no—
125C2×C4×Dic61—22no—
126C2×C4×Dic61—22no—
127C2×C4×Dic61—41no—
128C2×C4×Dic61C2×C414yescomplemented
129#14519684—22no—
130#14519684—22no—
131#14519684—22no—
132#14519684—22no—
133#14519684—22no—
134#14519684—41no—
135#14519684—41no—
136#14519684—41no—
137#14519684—41no—
138#14519684D414yes—
139C22×Q8×C61—22no—
140C22×Q8×C61—22no—
141C22×Q8×C61—22no—
142C22×Q8×C61—22no—
143C22×Q8×C61—41no—
144C22×Q8×C61—41no—
145C22×Q8×C61C2×C414yescomplemented
146C23×C4×C61C2311yescharacteristic
147C23×C4×C61C2311yescharacteristic
148C23×C4×C61C2311yescharacteristic
149C23×C4×C61C2311yescharacteristic
150C23×C4×C61C2311yescharacteristic
151C23×C4×C61C2311yescharacteristic
152C23×C4×C61C2311yescharacteristic
153#95×C61—22no—
154#95×C61—22no—
155#95×C61—22no—
156#95×C61—22no—
157#95×C61—41no—
158#95×C61—41no—
159C24×C61C2411yescharacteristic
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×D61—21no—
176C23×D61—21no—
177C23×D61—21no—
178C23×D61—21no—
179C23×D61—21no—
180C23×D61—21no—
181C23×D61—21no—
182C23×D61—21no—
183C23×D61—21no—
184C23×D61—21no—
185C23×D61—21no—
186C23×D61C22×C412yes—
187C23×D61C22×C412yes—
188C23×D61C2×D412yes—
189C23×D61C2×D412yes—
190C2×Q8×C61—28no—
191C2×Q8×C61—28no—
192C2×Q8×C61—44no—
193C2×Q8×C61—44no—
194C2×Q8×C61—44no—
195C2×Q8×C61—44no—
196C2×Q8×C61—44no—
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×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×C61C22×C412yes—
239C22×C4×C61C22×C412yes—
240C22×C4×C61C22×C412yes—
241C22×C4×C61C2×D412yes—
242C22×C4×C61C2×D412yes—
243C22×C4×C61C2×D412yes—
244C22×C4×C61#4112yes—
245C22×C4×C61#4112yes—
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×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×Dic61C22×C412yes—
282C22×Dic61C22×C412yes—
283C22×Dic61C2×D412yes—
284C22×Dic61C2×D412yes—
285C22×Dic61C2×D412yes—
286C22×Dic61C2×D412yes—
287C22×Dic61#4112yes—
288C2×D244—28no—
289C2×D244—28no—
290C2×D244—44no—
291C2×D244—44no—
292C2×D244—44no—
293C2×D244—44no—
294C2×D244—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—
302#11758198—28no—
303#11758198—28no—
304#11758198—28no—
305#11758198—44no—
306#11758198—44no—
307#11758198—44no—
308#11758198—44no—
309#11758198—44no—
310#11758198—44no—
311#11758198—44no—
312#11758198C22⋊C4116yescomplemented
313C4⋊Dic61—44no—
314#11758196—44no—
315#11758196—44no—
316C4×Dic61—28no—
317C4×Dic61—44no—
318C23×C61C23×C411yescharacteristic
319C23×C61C22×D411yescharacteristic
320C23×C61C22×D411yescharacteristic
321C23×C61C22×D411yescharacteristic
322C23×C61C2×#4111yescharacteristic
323C23×C61C2×#4111yescharacteristic
324C23×C61C2×#4111yescharacteristic
325C23×C61H(5,𝔽2)11yescharacteristic
326C23×C61H(5,𝔽2)11yescharacteristic
327C23×C61H(5,𝔽2)11yescharacteristic
328C23×C61H(5,𝔽2)11yescharacteristic
329C23×C61H(5,𝔽2)11yescharacteristic
330C23×C612−1+411yescharacteristic
331C23×C612−1+411yescharacteristic
332C23×C612−1+411yescharacteristic
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—41no—
359C22×D61—41no—
360C22×D61—41no—
361C22×D61—41no—
362C22×D61—41no—
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—41no—
392C22×D61—41no—
393C22×D61—41no—
394C22×D61—41no—
395C22×D61—41no—
396C22×D61—41no—
397C22×D61—41no—
398C22×D61—41no—
399C22×D61—41no—
400C22×D61—41no—
401C22×D61—41no—
402C22×D61C2×C22⋊C414yes—
403Q8×C61—416no—
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—22no—
414C2×C4×C61—22no—
415C2×C4×C61—22no—
416C2×C4×C61—22no—
417C2×C4×C61—22no—
418C2×C4×C61—22no—
419C2×C4×C61—22no—
420C2×C4×C61—22no—
421C2×C4×C61—22no—
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×C4×C61—41no—
448C2×C4×C61—41no—
449C2×C4×C61—41no—
450C2×C4×C61—41no—
451C2×C4×C61C2×C22⋊C414yes—
452C2×C4×C61C4×D414yes—
453C2×Dic61—22no—
454C2×Dic61—22no—
455C2×Dic61—22no—
456C2×Dic61—22no—
457C2×Dic61—22no—
458C2×Dic61—22no—
459C2×Dic61—22no—
460C2×Dic61—22no—
461C2×Dic61—22no—
462C2×Dic61—22no—
463C2×Dic61—22no—
464C2×Dic61—22no—
465C2×Dic61—22no—
466C2×Dic61—22no—
467C2×Dic61—22no—
468C2×Dic61—22no—
469C2×Dic61—22no—
470C2×Dic61—22no—
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—
489C2×Dic61—41no—
490C2×Dic61—41no—
491C2×Dic61—41no—
492C2×Dic61—41no—
493C2×Dic61—41no—
494C2×Dic61C2×C22⋊C414yes—
495D244—416no—
496C4×D61—416no—
497#14421—611nomaximal, Sylow
498C22×C61C22×C22⋊C411yescharacteristic
499C22×C61C2×C4×D411yescharacteristic
500C22×C61C4×#4111yescharacteristic
501C22×C61#51811yescharacteristic
502C22×C61#52011yescharacteristic
503C22×C61#52011yescharacteristic
504C22×C61#52011yescharacteristic
505C22×C61#53511yescharacteristic
506C22×C61#53511yescharacteristic
507C22×C61#53611yescharacteristic
508C22×C61#53611yescharacteristic
509C22×C61#53711yescharacteristic
510C22×C61#53711yescharacteristic
511C22×C61#53811yescharacteristic
512C22×C61#53811yescharacteristic
513C22×C61#54211yescharacteristic
514C22×C61#54211yescharacteristic
515C22×C61#54211yescharacteristic
516C22×C61#54211yescharacteristic
517C22×C61D4211yescharacteristic
518C22×C61D4211yescharacteristic
519C22×C61#54611yescharacteristic
520C22×C61#54611yescharacteristic
521C22×C61#54611yescharacteristic
522C22×C61#54611yescharacteristic
523C22×C61#54611yescharacteristic
524C22×C61#54711yescharacteristic
525C22×C61#54711yescharacteristic
526C22×C61#54811yescharacteristic
527C22×C61#55611yescharacteristic
528C22×C61#55911yescharacteristic
529C22×C61H(3,𝔽4)11yescharacteristic
530C22×C61#56211yescharacteristic
531C22×C61#56211yescharacteristic
532C22×C61#56311yescharacteristic
533C2×D61—24no—
534C2×D61—24no—
535C2×D61—24no—
536C2×D61—42no—
537C2×D61—42no—
538C2×D61—42no—
539C2×D61—42no—
540C2×D61—42no—
541C2×D61—42no—
542C2×D61—42no—
543C2×D61—42no—
544C2×D61—42no—
545C2×D61—42no—
546C2×D61—42no—
547C2×D61—42no—
548C2×D61—42no—
549C2×D61—42no—
550C2×D61—42no—
551C2×D61—42no—
552C2×D61—42no—
553C2×D61—42no—
554C2×D61—42no—
555C2×D61—81no—
556C2×D61—81no—
557C2×D61—81no—
558C2×D61—81no—
559C2×D61—81no—
560C2×D61—81no—
561C2×D61—81no—
562C2×D61—81no—
563C4×C61—24no—
564C4×C61—24no—
565C4×C61—42no—
566C4×C61—42no—
567C4×C61—81no—
568C4×C61—81no—
569C4×C61—81no—
570Dic61—24no—
571Dic61—42no—
572Dic61—42no—
573Dic61—42no—
574Dic61—42no—
575Dic61—81no—
576C22×#124—611no—
577C2×#391—611no—
578C2×#388—611no—
579C2×#386—611no—
580C2×#385—611no—
581#1446D6111yescharacteristic, complemented
582#1440—611no—
583#1439—611no—
584#1439—611no—
585#1439—611no—
586#1438—611no—
587#1437—611no—
588C4⋊#95—611no—
589#1434—611no—
590C22⋊#95—611no—
591C2×C61#231111yescharacteristic
592C2×C61#232611yescharacteristic
593C2×C61#233711yescharacteristic
594C2×C61D4×C22⋊C411yescharacteristic
595C2×C61#233911yescharacteristic
596C2×C61#236711yescharacteristic
597C2×C61#237911yescharacteristic
598C2×C61#267011yescharacteristic
599C2×C61#267211yescharacteristic
600C2×C61#267411yescharacteristic
601C2×C61#267611yescharacteristic
602C2×C61#270011yescharacteristic
603C2×C61#271011yescharacteristic
604C2×C61#271211yescharacteristic
605C2×C61#271511yescharacteristic
606D61—44no—
607D61—82no—
608C23×Q8C2×D6111yescharacteristic
609C23×D4—611no—
610C24×C4—611no—
611C2×#124—618no—
612C2×#124—1224no—
613C2×#124—1224no—
614C22×C4⋊C4—611no—
615C22×C4⋊C4—611no—
616C22×C4⋊C4—611no—
617C22×C22⋊C4—611no—
618C22×C22⋊C4—611no—
619C22×C22⋊C4—611no—
620C22×C22⋊C4—611no—
621C22×C22⋊C4—611no—
622C22×C22⋊C4—611no—
623C22×C22⋊C4—611no—
624C22×C22⋊C4—611no—
625C22×C22⋊C4—611no—
626C22×C22⋊C4—611no—
627C22×C22⋊C4—611no—
628C22×C42—611no—
629C22×C42—611no—
630#391—1224no—
631#388—1224no—
632#386—1224no—
633#385—1224no—
634C2×#95—611no—
635C2×#95—611no—
636C2×#95—611no—
637C2×#95—611no—
638C2×#95—611no—
639C2×#95—611no—
640C2×#95—611no—
641C2×#95—611no—
642C2×#95—611no—
643C2×#95—611no—
644C2×#95C2×D6111yescharacteristic
645C2×#95C2×D6111yescharacteristic
646C2×#95C2×D6111yescharacteristic
647C2×#95C2×D6111yescharacteristic
648C2×#95C2×D6111yescharacteristic
649C2×#95C2×D6111yescharacteristic
650C61#1442111yescharacteristic, complemented, Sylow
651C25—611no—
652C25—611no—
653C22×Q8—22no—
654C22×Q8—22no—
655C22×Q8—22no—
656C22×Q8—22no—
657C22×Q8—41no—
658C22×Q8—41no—
659C22×Q8C4×D6114yescomplemented
660C22×D4—614no—
661C22×D4—1222no—
662C22×D4—1222no—
663C22×D4—1222no—
664C22×D4—1222no—
665C22×D4—2441no—
666C22×D4—2441no—
667C23×C4—611no—
668C23×C4—611no—
669C23×C4—611no—
670C23×C4—611no—
671C23×C4—611no—
672C23×C4—611no—
673C23×C4—1222no—
674C23×C4—1222no—
675C23×C4—1222no—
676C23×C4—2441no—
677C23×C4—2441no—
678C23×C4—2441no—
679C23×C4—2441no—
680C23×C4C22×D6111yescharacteristic
681C23×C4C22×D6111yescharacteristic
682C23×C4C22×D6111yescharacteristic
683C23×C4C22×D6111yescharacteristic
684C23×C4C22×D6111yescharacteristic
685C23×C4C22×D6111yescharacteristic
686C23×C4C22×D6111yescharacteristic
687#124—12232no—
688C2×C4⋊C4—1222no—
689C2×C4⋊C4—1222no—
690C2×C4⋊C4—1222no—
691C2×C4⋊C4—1222no—
692C2×C4⋊C4—1222no—
693C2×C4⋊C4—1222no—
694C2×C4⋊C4—2441no—
695C2×C4⋊C4—2441no—
696C2×C4⋊C4—2441no—
697C2×C22⋊C4—614no—
698C2×C22⋊C4—614no—
699C2×C22⋊C4—614no—
700C2×C22⋊C4—614no—
701C2×C22⋊C4—614no—
702C2×C22⋊C4—614no—
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—1222no—
710C2×C22⋊C4—1222no—
711C2×C22⋊C4—1222no—
712C2×C22⋊C4—1222no—
713C2×C22⋊C4—1222no—
714C2×C22⋊C4—1222no—
715C2×C22⋊C4—1222no—
716C2×C22⋊C4—1222no—
717C2×C22⋊C4—1222no—
718C2×C22⋊C4—2441no—
719C2×C22⋊C4—2441no—
720C2×C22⋊C4—2441no—
721C2×C22⋊C4—2441no—
722C2×C22⋊C4—2441no—
723C2×C22⋊C4—2441no—
724C2×C22⋊C4—2441no—
725C2×C22⋊C4—2441no—
726C2×C22⋊C4—2441no—
727C2×C22⋊C4—2441no—
728C2×C22⋊C4—2441no—
729C2×C22⋊C4—2441no—
730C2×C42—614no—
731C2×C42—1222no—
732C2×C42—1222no—
733C2×C42—1222no—
734C2×C42—1222no—
735C2×C42—2441no—
736#95—22no—
737#95—22no—
738#95—22no—
739#95—22no—
740#95—41no—
741#95—41no—
742#95—614no—
743#95—1222no—
744#95—1222no—
745#95—1222no—
746#95—1222no—
747#95—1222no—
748#95—2441no—
749#95—2441no—
750#95—2441no—
751#95—2441no—
752C24—612no—
753C24—612no—
754C24—612no—
755C24—612no—
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—
771C24—1221no—
772C24—1221no—
773C24—1221no—
774C24—1221no—
775C24—1221no—
776C24—1221no—
777C24—1221no—
778C24—1221no—
779C24—1221no—
780C24—1221no—
781C24—1221no—
782C24C23×D6111yescharacteristic
783C2×Q8—28no—
784C2×Q8—28no—
785C2×Q8—44no—
786C2×Q8—44no—
787C2×Q8—44no—
788C2×Q8—44no—
789C2×Q8—44no—
790C2×D4—1228no—
791C2×D4—1228no—
792C2×D4—2444no—
793C2×D4—2444no—
794C2×D4—2444no—
795C2×D4—2444no—
796C2×D4—2444no—
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—21no—
824C22×C4—21no—
825C22×C4—21no—
826C22×C4—21no—
827C22×C4—21no—
828C22×C4—21no—
829C22×C4—21no—
830C22×C4—21no—
831C22×C4—21no—
832C22×C4—21no—
833C22×C4—21no—
834C22×C4—21no—
835C22×C4—21no—
836C22×C4—21no—
837C22×C4—21no—
838C22×C4—612no—
839C22×C4—612no—
840C22×C4—612no—
841C22×C4—612no—
842C22×C4—612no—
843C22×C4—612no—
844C22×C4—612no—
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—1221no—
869C22×C4—1221no—
870C22×C4—1221no—
871C22×C4—1221no—
872C22×C4—1221no—
873C22×C4—1221no—
874C22×C4—1221no—
875C22×C4—1221no—
876C22×C4—1221no—
877C22×C4—1221no—
878C22×C4—1221no—
879C22×C4—1221no—
880C22×C4—2444no—
881C22×C4—2444no—
882C22×C4—2444no—
883C22×C4—2444no—
884C22×C4—2444no—
885C22×C4—2444no—
886C22×C4—2444no—
887C22×C4C2×C4×D6112yes—
888C22×C4C2×C4×D6112yes—
889C22×C4C2×C4×D6112yes—
890C22×C4D4×D6112yes—
891C22×C4D4×D6112yes—
892C22×C4D4×D6112yes—
893C22×C4#1175822412yes—
894C22×C4#1175822612yes—
895C4⋊C4—2444no—
896C4⋊C4—2444no—
897C4⋊C4—2444no—
898C22⋊C4—6116no—
899C22⋊C4—1228no—
900C22⋊C4—1228no—
901C22⋊C4—1228no—
902C22⋊C4—2444no—
903C22⋊C4—2444no—
904C22⋊C4—2444no—
905C22⋊C4—2444no—
906C22⋊C4—2444no—
907C22⋊C4—2444no—
908C22⋊C4—2444no—
909C42—1228no—
910C42—2444no—
911C23—614no—
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—2441no—
938C23—2441no—
939C23—2441no—
940C23—2441no—
941C23—2441no—
942C23—2441no—
943C23—2441no—
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—
972C23—2441no—
973C23—2441no—
974C23—2441no—
975C23—2441no—
976C23—2441no—
977C23—2441no—
978C23—2441no—
979C23—2441no—
980C23—2441no—
981C23C22×C4×D6111yescharacteristic
982C23C2×D4×D6111yescharacteristic
983C23C2×D4×D6111yescharacteristic
984C23C2×D4×D6111yescharacteristic
985C23#41×D6111yescharacteristic
986C23C2×#1175822411yescharacteristic
987C23C2×#1175822611yescharacteristic
988C23#1451982211yescharacteristic
989C23#1451982211yescharacteristic
990C23#1451982311yescharacteristic
991C23#1451982311yescharacteristic
992C23#1451982311yescharacteristic
993C23#1451982511yescharacteristic
994C23#1451982511yescharacteristic
995C23#1451982511yescharacteristic
996Q8—416no—
997D4—24416no—
998C2×C4—22no—
999C2×C4—22no—
1000C2×C4—22no—
1001C2×C4—22no—
1002C2×C4—22no—
1003C2×C4—22no—
1004C2×C4—22no—
1005C2×C4—22no—
1006C2×C4—22no—
1007C2×C4—22no—
1008C2×C4—22no—
1009C2×C4—22no—
1010C2×C4—22no—
1011C2×C4—22no—
1012C2×C4—22no—
1013C2×C4—22no—
1014C2×C4—22no—
1015C2×C4—22no—
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—41no—
1038C2×C4—41no—
1039C2×C4—41no—
1040C2×C4—41no—
1041C2×C4—41no—
1042C2×C4—41no—
1043C2×C4—41no—
1044C2×C4—41no—
1045C2×C4—614no—
1046C2×C4—1222no—
1047C2×C4—1222no—
1048C2×C4—1222no—
1049C2×C4—1222no—
1050C2×C4—1222no—
1051C2×C4—1222no—
1052C2×C4—1222no—
1053C2×C4—1222no—
1054C2×C4—1222no—
1055C2×C4—1222no—
1056C2×C4—1222no—
1057C2×C4—1222no—
1058C2×C4—1222no—
1059C2×C4—1222no—
1060C2×C4—1222no—
1061C2×C4—1222no—
1062C2×C4—1222no—
1063C2×C4—1222no—
1064C2×C4—24416no—
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—
1082C2×C4—2441no—
1083C2×C4—2441no—
1084C2×C4—2441no—
1085C2×C4—2441no—
1086C2×C4—2441no—
1087C2×C4—2441no—
1088C2×C4C22⋊C4×D6114yes—
1089C2×C4#1451973714yes—
1090C22—1224no—
1091C22—1224no—
1092C22—1224no—
1093C22—4881no—
1094C22—4881no—
1095C22—4881no—
1096C22—4881no—
1097C22—4881no—
1098C22—4881no—
1099C22—4881no—
1100C22—4881no—
1101C22—2442no—
1102C22—2442no—
1103C22—2442no—
1104C22—2442no—
1105C22—2442no—
1106C22—2442no—
1107C22—2442no—
1108C22—2442no—
1109C22—2442no—
1110C22—2442no—
1111C22—2442no—
1112C22—2442no—
1113C22—2442no—
1114C22—2442no—
1115C22—2442no—
1116C22—2442no—
1117C22—2442no—
1118C22—2442no—
1119C22—2442no—
1120C22C2×C22⋊C4×D6111yescharacteristic
1121C22C2×#1451973711yescharacteristic
1122C22C4×#1175822611yescharacteristic
1123C22#1684023511yescharacteristic
1124C22#1684024411yescharacteristic
1125C22#1684024411yescharacteristic
1126C22#1684024411yescharacteristic
1127C22#1684033011yescharacteristic
1128C22#1684033011yescharacteristic
1129C22#1684033711yescharacteristic
1130C22#1684033711yescharacteristic
1131C22#1684034211yescharacteristic
1132C22#1684034211yescharacteristic
1133C22#1684034611yescharacteristic
1134C22#1684035211yescharacteristic
1135C22#1684038211yescharacteristic
1136C22#1684038511yescharacteristic
1137C22#1684038511yescharacteristic
1138C22#1684038611yescharacteristic
1139C22#1684039411yescharacteristic
1140C22#1684039411yescharacteristic
1141C22#1684039911yescharacteristic
1142C22#1684039911yescharacteristic
1143C22#1684040311yescharacteristic
1144C22#1684040311yescharacteristic
1145C22#1684040511yescharacteristic
1146C22#1684041411yescharacteristic
1147C22#1684041511yescharacteristic
1148C22#1684042211yescharacteristic
1149C22#1684048611yescharacteristic
1150C22#1684049411yescharacteristic
1151C22#1684050411yescharacteristic
1152C22#1684050811yescharacteristic
1153C22#1684050811yescharacteristic
1154C22#1684051111yescharacteristic
1155C4—24no—
1156C4—24no—
1157C4—42no—
1158C4—42no—
1159C4—81no—
1160C4—81no—
1161C4—81no—
1162C4—1224no—
1163C4—4881no—
1164C4—2442no—
1165C4—2442no—
1166C4—2442no—
1167C4—2442no—
1168C2—4882no—
1169C2—2444no—
1170C2#2144841011yescharacteristic
1171C2#2144853311yescharacteristic
1172C2#2144863111yescharacteristic
1173C2#2144863511yescharacteristic
1174C2#2144864811yescharacteristic
1175C2#2144889511yescharacteristic
1176C2#2144899111yescharacteristic
1177C2#2145203911yescharacteristic
1178C2#2145206911yescharacteristic
1179C2#2145209311yescharacteristic
1180C2#2145211911yescharacteristic
1181C2#2145241611yescharacteristic
1182C2#2145255411yescharacteristic
1183C2#2145259011yescharacteristic
1184C2#2145263211yescharacteristic
subgroupG/H
center, FrattiniC24C23×D61
commutatorC23×C61C23×C4
FittingC61×#1446C2
socle, cosocleC24×C61C24
prime radicalC23×D244C22
hypercenter#1446D61
hypocenterC61#14421
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C24 ◁ #1446

Complements

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

NH ≅ G/Ntype
2. C2×#16839669C2semidirect
3. C2×#16839651C2semidirect
5. C2×#16839636C2semidirect
6. #21444067C2semidirect
7. #21444065C2semidirect
8. #21444063C2semidirect
9. #21444063C2semidirect
11. #21444055C2semidirect
12. #21444047C2semidirect
13. #21444044C2semidirect
14. #21444040C2semidirect
15. C61×#1446C2semidirect
20. C2×#14519766C4semidirect
119. C2×#11758198C2×C4semidirect
120. C2×#11758198C2×C4semidirect
128. C2×C4×Dic61C2×C4semidirect
145. C22×Q8×C61C2×C4semidirect
312. #11758198C22⋊C4semidirect
581. #1446D61semidirect
650. C61#14421semidirect
659. C22×Q8C4×D61semidirect

Maximal subgroups

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

subgroupindex
C22×#145197662
C2×#168396692
C2×#168396512
C2×#168396402
C2×#168396362
#214440672
#214440652
#214440632
#214440592
#214440552
#214440472
#214440442
#214440402
C61×#14462
#1442161