Finite Group Databasebeta

← #29603174

Subgroups — #29603174

Order 15616.

2278 conjugacy classes of subgroups.

The subgroup lattice has 1194 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839654C211yesmaximal, characteristic, complemented
2C2×#16839640C211yesmaximal, characteristic
3C2×#16839640C211yesmaximal, characteristic
4C2×#16839640C211yesmaximal, characteristic
5C2×#16839619C211yesmaximal, characteristic, complemented
6C2×C4×#11758198C211yesmaximal, characteristic, complemented
7C2×#95×D61C211yesmaximal, characteristic, complemented
8#21444079C211yesmaximal, characteristic, complemented
9#21444076C211yesmaximal, characteristic, complemented
10#21444067C211yesmaximal, characteristic, complemented
11#21444061C211yesmaximal, characteristic, complemented
12#21444057C211yesmaximal, characteristic, complemented
13#21444043C211yesmaximal, characteristic, complemented
14#21444040C211yesmaximal, characteristic, complemented
15C61×#1436C211yesmaximal, characteristic, complemented
16C23×D244C2211yescharacteristic
17C23×C4×D61C2211yescharacteristic
18C23×C4×D61C2211yescharacteristic
19C23×C4×D61C2211yescharacteristic
20C22×C4⋊Dic61C2211yescharacteristic
21C22×#11758198C2211yescharacteristic
22C22×#11758198C2211yescharacteristic
23C22×#11758198C2211yescharacteristic
24C22×#11758198C2211yescharacteristic
25C22×#11758198C2211yescharacteristic
26C22×#11758198C2211yescharacteristic
27C22×#11758198C2211yescharacteristic
28C22×#11758198C2211yescharacteristic
29C22×#11758198C2211yescharacteristic
30C22×C4×Dic61C2211yescharacteristic
31#16839654—24no—
32#16839640—24no—
33#16839640—24no—
34#16839640C418yescomplemented
35#16839619—24no—
36C4×#11758198—24no—
37C2×#14519684C2211yescharacteristic
38C2×#14519684C2211yescharacteristic
39C2×#14519684C2211yescharacteristic
40C2×#14519684C2211yescharacteristic
41C2×#14519684C2211yescharacteristic
42C2×#14519684C2211yescharacteristic
43C2×#14519684C2211yescharacteristic
44C2×#14519684C2211yescharacteristic
45C2×#14519684C2211yescharacteristic
46C2×#14519684C2211yescharacteristic
47C2×#14519684C2211yescharacteristic
48C2×#14519684C2211yescharacteristic
49C2×#14519684C2211yescharacteristic
50#95×D61—24no—
51C22×C4⋊C4×C61C2211yescharacteristic
52C22×C42×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—22no—
65C22×D244—22no—
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—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×D61D414yes—
94C2×C4⋊Dic61—22no—
95C2×C4⋊Dic61—22no—
96C2×C4⋊Dic61—41no—
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—22no—
108C2×#11758198—22no—
109C2×#11758198—22no—
110C2×#11758198—22no—
111C2×#11758198—22no—
112C2×#11758198—22no—
113C2×#11758198—22no—
114C2×#11758198—41no—
115C2×#11758198—41no—
116C2×#11758198—41no—
117C2×#11758198—41no—
118C2×#11758198—41no—
119C2×#11758198—41no—
120C2×#11758198C2×C414yes—
121C2×#11758198C2×C414yescomplemented
122C2×#11758198C2×C414yescomplemented
123C2×#11758198D414yes—
124C2×C4×Dic61—22no—
125C2×C4×Dic61—22no—
126C2×C4×Dic61—22no—
127#14519684—22no—
128#14519684—22no—
129#14519684—22no—
130#14519684—22no—
131#14519684—22no—
132#14519684—22no—
133#14519684—22no—
134#14519684—22no—
135#14519684—22no—
136#14519684—22no—
137#14519684—22no—
138#14519684—41no—
139#14519684C2×C414yescomplemented
140C23×C4×C61C2311yescharacteristic
141C23×C4×C61C2311yescharacteristic
142C23×C4×C61C2311yescharacteristic
143C23×C4×C61C2311yescharacteristic
144C23×C4×C61C2311yescharacteristic
145C23×C4×C61C2311yescharacteristic
146C23×C4×C61C2311yescharacteristic
147C2×C4⋊C4×C61—22no—
148C2×C4⋊C4×C61—22no—
149C2×C4⋊C4×C61—41no—
150C2×C42×C61—22no—
151C2×C42×C61—41no—
152C2×C42×C61—41no—
153#95×C61—22no—
154#95×C61—22no—
155#95×C61—41no—
156#95×C61C2×C414yescomplemented
157#95×C61D414yescomplemented
158C24×C61C2411yescharacteristic
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×D61—21no—
176C23×D61—21no—
177C23×D61—21no—
178C23×D61—21no—
179C23×D61—21no—
180C23×D61—21no—
181C23×D61C22×C412yes—
182C23×D61C22×C412yes—
183C23×D61C2×D412yes—
184C23×D61C2×D412yes—
185C23×D61#4112yes—
186C23×D61#4112yes—
187C23×D61#4112yes—
188C23×D61#4112yes—
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×C61—21no—
228C22×C4×C61C22×C412yes—
229C22×C4×C61C22×C412yes—
230C22×C4×C61C22×C412yes—
231C22×C4×C61C2×D412yes—
232C22×C4×C61C2×D412yes—
233C22×C4×C61C2×D412yes—
234C22×C4×C61C2×D412yes—
235C22×C4×C61C2×D412yes—
236C22×C4×C61#4112yes—
237C22×C4×C61#4112yes—
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×Dic61—21no—
271C22×Dic61—21no—
272C22×Dic61—21no—
273C22×Dic61—21no—
274C22×Dic61—21no—
275C22×Dic61C22×C412yes—
276C22×Dic61C22×C412yes—
277C22×Dic61C2×D412yes—
278C22×Dic61C2×D412yes—
279C22×Dic61#4112yes—
280C2×D244—28no—
281C2×D244—28no—
282C2×D244—28no—
283C2×D244—44no—
284C2×D244—44no—
285C2×D244—44no—
286C2×D244—44no—
287C2×C4×D61—28no—
288C2×C4×D61—28no—
289C2×C4×D61—28no—
290C2×C4×D61—28no—
291C2×C4×D61—28no—
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—
302C2×C4×D61—44no—
303C2×C4×D61—44no—
304C2×C4×D61—44no—
305C2×C4×D61—44no—
306C2×C4×D61—44no—
307C2×C4×D61—44no—
308C4⋊C4×C61—44no—
309C42×C61—44no—
310#11758198—28no—
311#11758198—28no—
312#11758198—28no—
313#11758198—44no—
314#11758198—44no—
315#11758198—44no—
316#11758198—44no—
317#11758198—44no—
318#11758198—44no—
319C4⋊Dic61—44no—
320C4×Dic61—44no—
321C23×C61C23×C411yescharacteristic
322C23×C61C22×D411yescharacteristic
323C23×C61C22×D411yescharacteristic
324C23×C61C22×D411yescharacteristic
325C23×C61C2×#4111yescharacteristic
326C23×C61C2×#4111yescharacteristic
327C23×C61C2×#4111yescharacteristic
328C23×C61C2×#4111yescharacteristic
329C23×C61C2×#4111yescharacteristic
330C23×C61C2×#4111yescharacteristic
331C23×C61C2×#4111yescharacteristic
332C23×C61H(5,𝔽2)11yescharacteristic
333C23×C61H(5,𝔽2)11yescharacteristic
334C23×C61H(5,𝔽2)11yescharacteristic
335C23×C612−1+411yescharacteristic
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—22no—
364C22×D61—22no—
365C22×D61—22no—
366C22×D61—22no—
367C22×D61—22no—
368C22×D61—22no—
369C22×D61—22no—
370C22×D61—22no—
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#11714yes—
400C22×D61C4×D414yes—
401C22×D61C4×D414yes—
402C22×D61#12114yes—
403C22×D61#12314yes—
404C22×D61#12414yes—
405C22×D61#12614yes—
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—22no—
423C2×C4×C61—22no—
424C2×C4×C61—22no—
425C2×C4×C61—22no—
426C2×C4×C61—22no—
427C2×C4×C61—22no—
428C2×C4×C61—22no—
429C2×C4×C61—22no—
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×C61—41no—
452C2×C4×C61—41no—
453C2×C4×C61C4×D414yes—
454C2×C4×C61#12114yes—
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—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—
489C2×Dic61—41no—
490C2×Dic61—41no—
491C2×Dic61—41no—
492C2×Dic61—41no—
493C2×Dic61—41no—
494C2×Dic61—41no—
495C2×Dic61—41no—
496C2×Dic61—41no—
497D244—416no—
498C4×D61—416no—
499C4×D61—416no—
500C4×D61—416no—
501#13999—611nomaximal, Sylow
502C22×C61C2×#11711yescharacteristic
503C22×C61C2×C4×D411yescharacteristic
504C22×C61C2×C4×D411yescharacteristic
505C22×C61C2×C4×D411yescharacteristic
506C22×C61C4×#4111yescharacteristic
507C22×C61#51811yescharacteristic
508C22×C61#52011yescharacteristic
509C22×C61C2×#12111yescharacteristic
510C22×C61C2×#12111yescharacteristic
511C22×C61C2×#12311yescharacteristic
512C22×C61#52511yescharacteristic
513C22×C61C2×#12411yescharacteristic
514C22×C61C2×#12611yescharacteristic
515C22×C61#52911yescharacteristic
516C22×C61#53211yescharacteristic
517C22×C61#53411yescharacteristic
518C22×C61#53711yescharacteristic
519C22×C61#53811yescharacteristic
520C22×C61#53911yescharacteristic
521C22×C61D4211yescharacteristic
522C22×C61#54611yescharacteristic
523C22×C61#54611yescharacteristic
524C22×C61#54611yescharacteristic
525C22×C61#54611yescharacteristic
526C22×C61#54711yescharacteristic
527C22×C61#54811yescharacteristic
528C22×C61#55111yescharacteristic
529C22×C61#55111yescharacteristic
530C22×C61#55111yescharacteristic
531C22×C61#55111yescharacteristic
532C22×C61#55211yescharacteristic
533C22×C61#55211yescharacteristic
534C22×C61#55311yescharacteristic
535C22×C61#55311yescharacteristic
536C22×C61#55311yescharacteristic
537C2×D61—24no—
538C2×D61—24no—
539C2×D61—24no—
540C2×D61—24no—
541C2×D61—24no—
542C2×D61—24no—
543C2×D61—24no—
544C2×D61—24no—
545C2×D61—24no—
546C2×D61—24no—
547C2×D61—24no—
548C2×D61—24no—
549C2×D61—24no—
550C2×D61—24no—
551C2×D61—42no—
552C2×D61—42no—
553C2×D61—42no—
554C2×D61—42no—
555C2×D61—42no—
556C2×D61—42no—
557C2×D61—42no—
558C2×D61—81no—
559C2×D61—81no—
560C2×D61—81no—
561C2×D61—81no—
562C2×D61—81no—
563C2×D61—81no—
564C2×D61—81no—
565C2×D61—81no—
566C2×D61#38818yescomplemented
567C4×C61—24no—
568C4×C61—24no—
569C4×C61—42no—
570C4×C61—42no—
571C4×C61—42no—
572C4×C61—42no—
573C4×C61—81no—
574Dic61—42no—
575Dic61—42no—
576Dic61—42no—
577Dic61—42no—
578Dic61—42no—
579Dic61—81no—
580C2×#388—611no—
581C2×#386—611no—
582C2×#386—611no—
583C2×#386—611no—
584C2×#380—611no—
585C2×C4×C22⋊C4—611no—
586C22×#95—611no—
587#1443—611no—
588#1442—611no—
589#1440—611no—
590#1439—611no—
591#1437—611no—
592#1436D6111yescharacteristic, complemented
593#1434—611no—
594C22⋊#95—611no—
595C2×C61C2×#38811yescharacteristic
596C2×C61C4×#12111yescharacteristic
597C2×C61#232511yescharacteristic
598C2×C61#235211yescharacteristic
599C2×C61#235311yescharacteristic
600C2×C61#235811yescharacteristic
601C2×C61#235911yescharacteristic
602C2×C61#241211yescharacteristic
603C2×C61#241611yescharacteristic
604C2×C61#247211yescharacteristic
605C2×C61#248111yescharacteristic
606C2×C61#248811yescharacteristic
607C2×C61#249811yescharacteristic
608C2×C61#251011yescharacteristic
609C2×C61#254311yescharacteristic
610D61—28no—
611D61—82no—
612C23×D4—611no—
613C24×C4—611no—
614C24×C4—611no—
615C24×C4—611no—
616C22×C4⋊C4—611no—
617C22×C4⋊C4C2×D6111yescharacteristic
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×C42—611no—
628C22×C42C2×D6111yescharacteristic
629#388—1224no—
630#386—618no—
631#386—1224no—
632#386—1224no—
633#380—1224no—
634C4×C22⋊C4—1224no—
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×#95—611no—
645C2×#95—611no—
646C2×#95—611no—
647C2×#95—611no—
648C2×#95—1224no—
649C2×#95C2×D6111yescharacteristic
650C2×#95C2×D6111yescharacteristic
651C2×#95C2×D6111yescharacteristic
652C2×#95C2×D6111yescharacteristic
653C2×#95C2×D6111yescharacteristic
654C61#1399911yescharacteristic, complemented, Sylow
655C25—611no—
656C25—611no—
657C22×D4—614no—
658C22×D4—1222no—
659C22×D4—1222no—
660C22×D4—1222no—
661C22×D4—1222no—
662C22×D4—1222no—
663C22×D4—1222no—
664C23×C4—611no—
665C23×C4—611no—
666C23×C4—611no—
667C23×C4—611no—
668C23×C4—611no—
669C23×C4—614no—
670C23×C4—614no—
671C23×C4—611no—
672C23×C4—1222no—
673C23×C4—1222no—
674C23×C4—1222no—
675C23×C4—1222no—
676C23×C4—1222no—
677C23×C4—1222no—
678C23×C4—1222no—
679C23×C4—1222no—
680C23×C4—1222no—
681C23×C4—1222no—
682C23×C4—1222no—
683C23×C4—1222no—
684C23×C4—1222no—
685C23×C4—2441no—
686C23×C4—2441no—
687C23×C4—2441no—
688C23×C4—2441no—
689C23×C4—2441no—
690C23×C4—2441no—
691C23×C4C22×D6111yescharacteristic
692C23×C4C22×D6111yescharacteristic
693C23×C4C22×D6111yescharacteristic
694C23×C4C22×D6111yescharacteristic
695C23×C4C22×D6111yescharacteristic
696C23×C4C22×D6111yescharacteristic
697C23×C4C22×D6111yescharacteristic
698C2×C4⋊C4—22no—
699C2×C4⋊C4—22no—
700C2×C4⋊C4—41no—
701C2×C4⋊C4—1222no—
702C2×C4⋊C4—1222no—
703C2×C4⋊C4—2441no—
704C2×C22⋊C4—614no—
705C2×C22⋊C4—614no—
706C2×C22⋊C4—614no—
707C2×C22⋊C4—614no—
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—1222no—
719C2×C22⋊C4—1222no—
720C2×C22⋊C4—1222no—
721C2×C22⋊C4—1222no—
722C2×C22⋊C4—1222no—
723C2×C22⋊C4—1222no—
724C2×C22⋊C4—1222no—
725C2×C22⋊C4—2441no—
726C2×C22⋊C4—2441no—
727C2×C22⋊C4—2441no—
728C2×C22⋊C4—2441no—
729C2×C22⋊C4—2441no—
730C2×C22⋊C4—2441no—
731C2×C42—22no—
732C2×C42—41no—
733C2×C42—41no—
734C2×C42—1222no—
735C2×C42—1222no—
736C2×C42—1222no—
737#95—22no—
738#95—22no—
739#95—41no—
740#95—614no—
741#95—1222no—
742#95—1222no—
743#95—1222no—
744#95—1222no—
745#95—1222no—
746#95—1222no—
747#95—1222no—
748#95—1222no—
749#95—1222no—
750#95—1222no—
751#95—1222no—
752#95—2441no—
753#95C4×D6114yescomplemented
754#95D24414yescomplemented
755C24—612no—
756C24—612no—
757C24—612no—
758C24—612no—
759C24—612no—
760C24—612no—
761C24—612no—
762C24—612no—
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—
782C24—1221no—
783C24—1221no—
784C24—1221no—
785C24C23×D6111yescharacteristic
786C2×D4—1228no—
787C2×D4—1228no—
788C2×D4—1228no—
789C2×D4—2444no—
790C2×D4—2444no—
791C2×D4—2444no—
792C2×D4—2444no—
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—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—612no—
833C22×C4—612no—
834C22×C4—612no—
835C22×C4—612no—
836C22×C4—612no—
837C22×C4—1228no—
838C22×C4—1228no—
839C22×C4—1228no—
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—1221no—
869C22×C4—1221no—
870C22×C4—1228no—
871C22×C4—1228no—
872C22×C4—1221no—
873C22×C4—1221no—
874C22×C4—1221no—
875C22×C4—1221no—
876C22×C4—1221no—
877C22×C4—1221no—
878C22×C4—1221no—
879C22×C4—2444no—
880C22×C4—2444no—
881C22×C4—2444no—
882C22×C4—2444no—
883C22×C4—2444no—
884C22×C4—2444no—
885C22×C4—2444no—
886C22×C4—2444no—
887C22×C4—2444no—
888C22×C4—2444no—
889C22×C4—2444no—
890C22×C4—2444no—
891C22×C4—2444no—
892C22×C4—2444no—
893C22×C4—2444no—
894C22×C4—2444no—
895C22×C4C2×C4×D6112yes—
896C22×C4C2×C4×D6112yes—
897C22×C4C2×C4×D6112yes—
898C22×C4C2×D24412yes—
899C22×C4C2×D24412yes—
900C22×C4C2×D24412yes—
901C22×C4#1175822212yes—
902C22×C4D4×D6112yes—
903C22×C4D4×D6112yes—
904C22×C4#1175822612yes—
905C4⋊C4—44no—
906C4⋊C4—2444no—
907C22⋊C4—1228no—
908C22⋊C4—1228no—
909C22⋊C4—1228no—
910C22⋊C4—2444no—
911C22⋊C4—2444no—
912C22⋊C4—2444no—
913C22⋊C4—2444no—
914C22⋊C4—2444no—
915C22⋊C4—2444no—
916C42—44no—
917C42—2444no—
918C23—614no—
919C23—614no—
920C23—614no—
921C23—614no—
922C23—614no—
923C23—614no—
924C23—614no—
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—1222no—
945C23—1222no—
946C23—1222no—
947C23—1222no—
948C23—1222no—
949C23—1222no—
950C23—1222no—
951C23—1222no—
952C23—1222no—
953C23—1222no—
954C23—1222no—
955C23—1222no—
956C23—1222no—
957C23—1222no—
958C23—1222no—
959C23—1222no—
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—
981C23—2441no—
982C23—2441no—
983C23—2441no—
984C23—2441no—
985C23—2441no—
986C23—2441no—
987C23—2441no—
988C23C22×C4×D6111yescharacteristic
989C23C2×D4×D6111yescharacteristic
990C23C2×D4×D6111yescharacteristic
991C23C22×D24411yescharacteristic
992C23#41×D6111yescharacteristic
993C23#41×D6111yescharacteristic
994C23#41×D6111yescharacteristic
995C23#41×D6111yescharacteristic
996C23#41×D6111yescharacteristic
997C23C2×#1175822211yescharacteristic
998C23C2×#1175822611yescharacteristic
999C23#1451982211yescharacteristic
1000C23#1451982211yescharacteristic
1001C23#1451982311yescharacteristic
1002C23#1451982511yescharacteristic
1003D4—24416no—
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—22no—
1017C2×C4—22no—
1018C2×C4—22no—
1019C2×C4—22no—
1020C2×C4—22no—
1021C2×C4—22no—
1022C2×C4—22no—
1023C2×C4—22no—
1024C2×C4—22no—
1025C2×C4—22no—
1026C2×C4—22no—
1027C2×C4—22no—
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—41no—
1046C2×C4—41no—
1047C2×C4—41no—
1048C2×C4—41no—
1049C2×C4—41no—
1050C2×C4—41no—
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—1222no—
1065C2×C4—1222no—
1066C2×C4—24416no—
1067C2×C4—24416no—
1068C2×C4—24416no—
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×C4—2441no—
1089C2×C4—2441no—
1090C2×C4—2441no—
1091C2×C4—2441no—
1092C2×C4—2441no—
1093C2×C4—2441no—
1094C2×C4—2441no—
1095C2×C4—2441no—
1096C2×C4C4×D24414yes—
1097C2×C4#1451975214yes—
1098C22—618no—
1099C22—1224no—
1100C22—1224no—
1101C22—1224no—
1102C22—1224no—
1103C22—1224no—
1104C22—1224no—
1105C22—1224no—
1106C22—1224no—
1107C22—1224no—
1108C22—1224no—
1109C22—1224no—
1110C22—1224no—
1111C22—1224no—
1112C22—1224no—
1113C22—4881no—
1114C22—4881no—
1115C22—4881no—
1116C22—4881no—
1117C22—4881no—
1118C22—4881no—
1119C22—4881no—
1120C22—4881no—
1121C22—2442no—
1122C22—2442no—
1123C22—2442no—
1124C22—2442no—
1125C22—2442no—
1126C22—2442no—
1127C22—2442no—
1128C22#117×D6111yescharacteristic
1129C22C4×D4×D6111yescharacteristic
1130C22C4×D4×D6111yescharacteristic
1131C22C2×C4×D24411yescharacteristic
1132C22C4×#1175822611yescharacteristic
1133C22#1684023411yescharacteristic
1134C22#1684024311yescharacteristic
1135C22#121×D6111yescharacteristic
1136C22C2×#1451975211yescharacteristic
1137C22#123×D6111yescharacteristic
1138C22#1684027411yescharacteristic
1139C22#124×D6111yescharacteristic
1140C22#126×D6111yescharacteristic
1141C22#1684029911yescharacteristic
1142C22#1684030911yescharacteristic
1143C22#1684032211yescharacteristic
1144C22#1684034211yescharacteristic
1145C22#1684034811yescharacteristic
1146C22#1684035811yescharacteristic
1147C22D4×D24411yescharacteristic
1148C22#1684040111yescharacteristic
1149C22#1684040211yescharacteristic
1150C22#1684040711yescharacteristic
1151C22#1684040711yescharacteristic
1152C22#1684041511yescharacteristic
1153C22#1684042411yescharacteristic
1154C22#1684043611yescharacteristic
1155C22#1684043711yescharacteristic
1156C22#1684043911yescharacteristic
1157C22#1684043911yescharacteristic
1158C22#1684044411yescharacteristic
1159C22#1684045311yescharacteristic
1160C22#1684045711yescharacteristic
1161C22#1684046211yescharacteristic
1162C22#1684046511yescharacteristic
1163C4—24no—
1164C4—24no—
1165C4—42no—
1166C4—42no—
1167C4—42no—
1168C4—42no—
1169C4—81no—
1170C4—4881no—
1171C4—2442no—
1172C4—2442no—
1173C4—2442no—
1174C4—2442no—
1175C4—2442no—
1176C2—1228no—
1177C2—4882no—
1178C2#388×D6111yescharacteristic
1179C2C4×#1451975211yescharacteristic
1180C2#2144851611yescharacteristic
1181C2#2144875111yescharacteristic
1182C2#2144875811yescharacteristic
1183C2#2144880111yescharacteristic
1184C2#2144880611yescharacteristic
1185C2#2144921311yescharacteristic
1186C2#2144925711yescharacteristic
1187C2#2144994311yescharacteristic
1188C2#2145007811yescharacteristic
1189C2#2145015211yescharacteristic
1190C2#2145026011yescharacteristic
1191C2#2145037611yescharacteristic
1192C2#2145077811yescharacteristic
subgroupG/H
center, FrattiniC24C23×D61
commutatorC23×C61C23×C4
FittingC61×#1436C2
socle, cosocleC24×C61C24
prime radicalC23×D244C22
hypercenter#1436D61
hypocenterC61#13999
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C24 ◁ #1436

Complements

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

NH ≅ G/Ntype
1. C2×#16839654C2semidirect
5. C2×#16839619C2semidirect
6. C2×C4×#11758198C2semidirect
7. C2×#95×D61C2semidirect
8. #21444079C2semidirect
9. #21444076C2semidirect
10. #21444067C2semidirect
11. #21444061C2semidirect
12. #21444057C2semidirect
13. #21444043C2semidirect
14. #21444040C2semidirect
15. C61×#1436C2semidirect
34. #16839640C4semidirect
121. C2×#11758198C2×C4semidirect
122. C2×#11758198C2×C4semidirect
139. #14519684C2×C4semidirect
156. #95×C61C2×C4semidirect
157. #95×C61D4semidirect
566. C2×D61#388semidirect
592. #1436D61semidirect
654. C61#13999semidirect
753. #95C4×D61semidirect
754. #95D244semidirect

Maximal subgroups

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

subgroupindex
C2×#168396542
C2×#168396402
C2×#168396192
C2×C4×#117581982
C2×#95×D612
#214440792
#214440762
#214440672
#214440612
#214440572
#214440432
#214440402
C61×#14362
#1399961