Finite Group Databasebeta

← #29603454

Subgroups — #29603454

Order 15616.

1954 conjugacy classes of subgroups.

The subgroup lattice has 834 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839664C211yesmaximal, characteristic
2C2×#16839664C211yesmaximal, characteristic
3C2×#16839664C211yesmaximal, characteristic
4C2×#16839652C212yesmaximal, complemented
5C2×C4×C4⋊Dic61C211yesmaximal, characteristic, complemented
6#21444067C212yesmaximal, complemented
7#21444061C212yesmaximal, complemented
8#21444055C212yesmaximal, complemented
9#21444049C211yesmaximal, characteristic, complemented
10#21444049C211yesmaximal, characteristic, complemented
11C2×C4×C4⋊C4×C61C211yesmaximal, characteristic, complemented
12C23×D244C2211yescharacteristic
13C22×C4⋊Dic61C2211yescharacteristic
14C22×C4⋊Dic61C2211yescharacteristic
15C22×C4⋊Dic61C2211yescharacteristic
16C22×#11758198C2212yes—
17C22×#11758198C2212yes—
18C22×#11758198C2212yes—
19C22×#11758198C2212yes—
20C22×#11758198C2212yes—
21C22×#11758198C2212yes—
22C22×C4×Dic61C2212yes—
23#16839664—24no—
24#16839664—24no—
25#16839664C418yescomplemented
26#16839652—28no—
27C4×C4⋊Dic61—24no—
28C2×#14519684C2212yes—
29C2×#14519684C2212yes—
30C2×#14519684C2212yes—
31C2×#14519684C2212yes—
32C2×#14519684C2212yes—
33C22×C4⋊C4×C61C2211yescharacteristic
34C22×C4⋊C4×C61C2211yescharacteristic
35C22×C42×C61C2211yescharacteristic
36C22×C42×C61C2211yescharacteristic
37C22×C42×C61C2211yescharacteristic
38C4×C4⋊C4×C61—24no—
39C2×#95×C61C2211yescharacteristic
40C2×#95×C61C2211yescharacteristic
41C24×D61C2312yes—
42C22×D244—22no—
43C22×D244—22no—
44C22×D244—22no—
45C22×D244—22no—
46C22×D244—22no—
47C22×D244—22no—
48C22×D244C2×C414yes—
49C23×Dic61C2312yes—
50C23×Dic61C2312yes—
51C23×Dic61C2312yes—
52C2×C4⋊Dic61—22no—
53C2×C4⋊Dic61—22no—
54C2×C4⋊Dic61—22no—
55C2×C4⋊Dic61—22no—
56C2×C4⋊Dic61—22no—
57C2×C4⋊Dic61—22no—
58C2×C4⋊Dic61—22no—
59C2×C4⋊Dic61C2×C414yes—
60C2×C4⋊Dic61D414yes—
61C2×#11758198—24no—
62C2×#11758198—24no—
63C2×#11758198—24no—
64C2×#11758198—24no—
65C2×#11758198—24no—
66C2×#11758198—24no—
67C2×#11758198—24no—
68C2×#11758198—24no—
69C2×#11758198—24no—
70C2×#11758198—24no—
71C2×#11758198—42no—
72C2×#11758198—42no—
73C2×#11758198—42no—
74C2×#11758198—42no—
75C2×#11758198—42no—
76C2×#11758198—42no—
77C2×#11758198C2×C418yes—
78C2×#11758198C2×C418yes—
79C2×C4×Dic61—24no—
80C2×C4×Dic61—24no—
81C2×C4×Dic61—42no—
82#14519684—24no—
83#14519684—24no—
84#14519684—24no—
85#14519684—42no—
86#14519684—42no—
87C23×C4×C61C2311yescharacteristic
88C23×C4×C61C2311yescharacteristic
89C23×C4×C61C2311yescharacteristic
90C23×C4×C61C2311yescharacteristic
91C23×C4×C61C2311yescharacteristic
92C23×C4×C61C2311yescharacteristic
93C23×C4×C61C2311yescharacteristic
94C2×C4⋊C4×C61—22no—
95C2×C4⋊C4×C61—22no—
96C2×C4⋊C4×C61—22no—
97C2×C4⋊C4×C61—22no—
98C2×C4⋊C4×C61—22no—
99C2×C4⋊C4×C61D414yescomplemented
100C2×C42×C61—22no—
101C2×C42×C61—22no—
102C2×C42×C61—22no—
103C2×C42×C61—22no—
104C2×C42×C61—22no—
105C2×C42×C61—22no—
106C2×C42×C61—22no—
107C2×C42×C61C2×C414yes—
108C2×C42×C61D414yes—
109#95×C61—22no—
110#95×C61—22no—
111C24×C61C2411yescharacteristic
112C23×D61—22no—
113C23×D61—22no—
114C23×D61—22no—
115C23×D61—22no—
116C23×D61—22no—
117C23×D61—22no—
118C23×D61—22no—
119C23×D61—22no—
120C23×D61—22no—
121C23×D61—22no—
122C23×D61—22no—
123C23×D61—22no—
124C23×D61—22no—
125C23×D61—22no—
126C23×D61C22×C414yes—
127C22×C4×C61—21no—
128C22×C4×C61—21no—
129C22×C4×C61—21no—
130C22×C4×C61—21no—
131C22×C4×C61—21no—
132C22×C4×C61—21no—
133C22×C4×C61—21no—
134C22×C4×C61—21no—
135C22×C4×C61—21no—
136C22×C4×C61—21no—
137C22×C4×C61—21no—
138C22×C4×C61—21no—
139C22×C4×C61—21no—
140C22×C4×C61—21no—
141C22×C4×C61—21no—
142C22×C4×C61—21no—
143C22×C4×C61—21no—
144C22×C4×C61—21no—
145C22×C4×C61—21no—
146C22×C4×C61—21no—
147C22×C4×C61—21no—
148C22×C4×C61—21no—
149C22×C4×C61—21no—
150C22×C4×C61—21no—
151C22×C4×C61—21no—
152C22×C4×C61—21no—
153C22×C4×C61—21no—
154C22×C4×C61—21no—
155C22×C4×C61—21no—
156C22×C4×C61—21no—
157C22×C4×C61—21no—
158C22×C4×C61—21no—
159C22×C4×C61C22×C412yes—
160C22×C4×C61C22×C412yes—
161C22×C4×C61C22×C412yes—
162C22×C4×C61C2×D412yes—
163C22×C4×C61C2×D412yes—
164C22×C4×C61C2×D412yes—
165C22×C4×C61C2×D412yes—
166C22×C4×C61C2×D412yes—
167C22×C4×C61C2×D412yes—
168C22×C4×C61C2×D412yes—
169C22×C4×C61#4112yes—
170C22×C4×C61#4112yes—
171C22×C4×C61#4112yes—
172C22×C4×C61#4112yes—
173C22×C4×C61#4112yes—
174C22×C4×C61#4112yes—
175C22×C4×C61#4112yes—
176C22×Dic61—22no—
177C22×Dic61—22no—
178C22×Dic61—22no—
179C22×Dic61—22no—
180C22×Dic61—22no—
181C22×Dic61—22no—
182C22×Dic61—22no—
183C22×Dic61—22no—
184C22×Dic61—22no—
185C22×Dic61—22no—
186C22×Dic61—22no—
187C22×Dic61—22no—
188C22×Dic61—22no—
189C22×Dic61—22no—
190C22×Dic61—22no—
191C22×Dic61—22no—
192C22×Dic61—22no—
193C22×Dic61—22no—
194C22×Dic61—22no—
195C22×Dic61C22×C414yes—
196C22×Dic61C2×D414yes—
197C2×D244—28no—
198C2×D244—28no—
199C2×D244—28no—
200C2×D244—44no—
201C2×D244—44no—
202C2×D244—44no—
203C2×D244—44no—
204C4⋊C4×C61—28no—
205C4⋊C4×C61—28no—
206C42×C61—28no—
207C42×C61—28no—
208C42×C61—44no—
209#11758198—216no—
210#11758198—48no—
211#11758198—48no—
212#11758198—48no—
213#11758198—48no—
214#11758198—48no—
215C4⋊Dic61—28no—
216C4⋊Dic61—28no—
217C4⋊Dic61—44no—
218C4×Dic61—48no—
219C23×C61C23×C411yescharacteristic
220C23×C61C22×D411yescharacteristic
221C23×C61C22×D411yescharacteristic
222C23×C61C22×D411yescharacteristic
223C23×C61C2×#4111yescharacteristic
224C23×C61C2×#4111yescharacteristic
225C23×C61C2×#4111yescharacteristic
226C23×C61C2×#4111yescharacteristic
227C23×C61C2×#4111yescharacteristic
228C23×C61C2×#4111yescharacteristic
229C23×C61C2×#4111yescharacteristic
230C23×C61H(5,𝔽2)11yescharacteristic
231C23×C61H(5,𝔽2)11yescharacteristic
232C23×C61H(5,𝔽2)11yescharacteristic
233C23×C612−1+411yescharacteristic
234C22×D61—24no—
235C22×D61—24no—
236C22×D61—24no—
237C22×D61—24no—
238C22×D61—24no—
239C22×D61—24no—
240C22×D61—24no—
241C22×D61—42no—
242C22×D61—42no—
243C22×D61—42no—
244C22×D61—42no—
245C22×D61—42no—
246C22×D61—42no—
247C22×D61—42no—
248C22×D61—42no—
249C22×D61—42no—
250C22×D61—42no—
251C22×D61—42no—
252C22×D61—42no—
253C22×D61—42no—
254C22×D61—42no—
255C22×D61—42no—
256C22×D61—42no—
257C22×D61—42no—
258C22×D61—42no—
259C22×D61—42no—
260C22×D61—42no—
261C22×D61—42no—
262C22×D61—42no—
263C22×D61—42no—
264C22×D61—42no—
265C22×D61—42no—
266C22×D61—42no—
267C22×D61—42no—
268C22×D61—42no—
269C2×C4×C61—22no—
270C2×C4×C61—22no—
271C2×C4×C61—22no—
272C2×C4×C61—22no—
273C2×C4×C61—22no—
274C2×C4×C61—22no—
275C2×C4×C61—22no—
276C2×C4×C61—22no—
277C2×C4×C61—22no—
278C2×C4×C61—22no—
279C2×C4×C61—22no—
280C2×C4×C61—22no—
281C2×C4×C61—22no—
282C2×C4×C61—22no—
283C2×C4×C61—22no—
284C2×C4×C61—22no—
285C2×C4×C61—22no—
286C2×C4×C61—22no—
287C2×C4×C61—22no—
288C2×C4×C61—22no—
289C2×C4×C61—22no—
290C2×C4×C61—22no—
291C2×C4×C61—22no—
292C2×C4×C61—22no—
293C2×C4×C61—41no—
294C2×C4×C61—41no—
295C2×C4×C61—41no—
296C2×C4×C61—41no—
297C2×C4×C61—41no—
298C2×C4×C61—41no—
299C2×C4×C61—41no—
300C2×C4×C61—41no—
301C2×C4×C61—41no—
302C2×C4×C61—41no—
303C2×C4×C61—41no—
304C2×C4×C61—41no—
305C2×C4×C61—41no—
306C2×C4×C61—41no—
307C2×C4×C61—41no—
308C2×C4×C61—41no—
309C2×C4×C61#11714yes—
310C2×C4×C61C4×D414yes—
311C2×C4×C61C4×D414yes—
312C2×C4×C61C4×D414yes—
313C2×C4×C61#12114yes—
314C2×C4×C61#12114yes—
315C2×C4×C61#12314yes—
316C2×C4×C61#12414yes—
317C2×C4×C61#12614yes—
318C2×Dic61—24no—
319C2×Dic61—24no—
320C2×Dic61—24no—
321C2×Dic61—24no—
322C2×Dic61—24no—
323C2×Dic61—24no—
324C2×Dic61—42no—
325C2×Dic61—42no—
326C2×Dic61—42no—
327C2×Dic61—42no—
328C2×Dic61—42no—
329C2×Dic61—42no—
330C2×Dic61—42no—
331C2×Dic61—42no—
332C2×Dic61—42no—
333C2×Dic61—42no—
334C2×Dic61—42no—
335C2×Dic61—42no—
336C2×Dic61—42no—
337C2×Dic61—42no—
338C2×Dic61—42no—
339D244—416no—
340#14022—611nomaximal, Sylow
341C22×C61C2×#11711yescharacteristic
342C22×C61C2×C4×D411yescharacteristic
343C22×C61C2×C4×D411yescharacteristic
344C22×C61C2×C4×D411yescharacteristic
345C22×C61C4×#4111yescharacteristic
346C22×C61#51811yescharacteristic
347C22×C61#52011yescharacteristic
348C22×C61C2×#12111yescharacteristic
349C22×C61C2×#12111yescharacteristic
350C22×C61C2×#12311yescharacteristic
351C22×C61#52511yescharacteristic
352C22×C61C2×#12411yescharacteristic
353C22×C61C2×#12611yescharacteristic
354C22×C61#52911yescharacteristic
355C22×C61#53211yescharacteristic
356C22×C61#53511yescharacteristic
357C22×C61#53711yescharacteristic
358C22×C61#54011yescharacteristic
359C22×C61#54211yescharacteristic
360C22×C61D4211yescharacteristic
361C22×C61#54611yescharacteristic
362C22×C61#54711yescharacteristic
363C22×C61#54811yescharacteristic
364C22×C61#55011yescharacteristic
365C22×C61#55011yescharacteristic
366C22×C61#55011yescharacteristic
367C22×C61#55311yescharacteristic
368C22×C61#55311yescharacteristic
369C22×C61#55511yescharacteristic
370C22×C61#55611yescharacteristic
371C22×C61#55611yescharacteristic
372C22×C61#55911yescharacteristic
373C22×C61#55911yescharacteristic
374C22×C61#55911yescharacteristic
375C22×C61#55911yescharacteristic
376C2×D61—44no—
377C2×D61—44no—
378C2×D61—44no—
379C2×D61—44no—
380C2×D61—44no—
381C2×D61—44no—
382C2×D61—44no—
383C2×D61—82no—
384C2×D61—82no—
385C2×D61—82no—
386C2×D61—82no—
387C2×D61—82no—
388C2×D61—82no—
389C2×D61—82no—
390C2×D61—82no—
391C4×C61—24no—
392C4×C61—24no—
393C4×C61—42no—
394C4×C61—42no—
395C4×C61—42no—
396C4×C61—42no—
397C4×C61#38818yescomplemented
398Dic61—44no—
399Dic61—44no—
400Dic61—82no—
401C2×#390—611no—
402C2×#390—611no—
403C2×#390—611no—
404C2×#388—612no—
405C2×C4×C4⋊C4—611no—
406C2×C4×C4⋊C4D6111yescharacteristic, complemented
407#1440—612no—
408#1439—612no—
409#1437—612no—
410C4⋊#95—611no—
411C4⋊#95—611no—
412C2×C61C2×#38811yescharacteristic
413C2×C61C4×#12111yescharacteristic
414C2×C61#232411yescharacteristic
415C2×C61#235411yescharacteristic
416C2×C61#235711yescharacteristic
417C2×C61#236611yescharacteristic
418C2×C61#236711yescharacteristic
419C2×C61#241411yescharacteristic
420C2×C61#241611yescharacteristic
421C2×C61#244511yescharacteristic
422C2×C61#244811yescharacteristic
423C2×C61#251211yescharacteristic
424C2×C61#251311yescharacteristic
425C2×C61#254811yescharacteristic
426C2×C61#259211yescharacteristic
427D61—84no—
428C23×D4—611no—
429C22×C4⋊C4—611no—
430C22×C4⋊C4—611no—
431C22×C4⋊C4—611no—
432C22×C4⋊C4C2×D6111yescharacteristic
433C22×C4⋊C4C2×D6111yescharacteristic
434C22×C22⋊C4—612no—
435C22×C22⋊C4—612no—
436C22×C22⋊C4—612no—
437C22×C22⋊C4—612no—
438C22×C22⋊C4—612no—
439C22×C22⋊C4—612no—
440C22×C42—612no—
441C22×C42C2×D6111yescharacteristic
442C22×C42C2×D6111yescharacteristic
443C22×C42C2×D6111yescharacteristic
444#390—618no—
445#390—1224no—
446#390—1224no—
447#388—1228no—
448C4×C4⋊C4—24no—
449C4×C4⋊C4—1224no—
450C2×#95—612no—
451C2×#95—612no—
452C2×#95—612no—
453C2×#95—612no—
454C2×#95—612no—
455C2×#95C2×D6111yescharacteristic
456C2×#95C2×D6111yescharacteristic
457C61#1402211yescharacteristic, complemented, Sylow
458C25—612no—
459C22×D4—614no—
460C22×D4—1222no—
461C22×D4—1222no—
462C22×D4—1222no—
463C22×D4—1222no—
464C22×D4—1222no—
465C22×D4—1222no—
466C23×C4—612no—
467C23×C4—612no—
468C23×C4—612no—
469C23×C4C22×D6111yescharacteristic
470C23×C4C22×D6111yescharacteristic
471C23×C4C22×D6111yescharacteristic
472C23×C4C22×D6111yescharacteristic
473C23×C4C22×D6111yescharacteristic
474C23×C4C22×D6111yescharacteristic
475C23×C4C22×D6111yescharacteristic
476C2×C4⋊C4—22no—
477C2×C4⋊C4—22no—
478C2×C4⋊C4—22no—
479C2×C4⋊C4—22no—
480C2×C4⋊C4—22no—
481C2×C4⋊C4—614no—
482C2×C4⋊C4—614no—
483C2×C4⋊C4—1222no—
484C2×C4⋊C4—1222no—
485C2×C4⋊C4—1222no—
486C2×C4⋊C4—1222no—
487C2×C4⋊C4—1222no—
488C2×C4⋊C4—1222no—
489C2×C4⋊C4—1222no—
490C2×C4⋊C4D24414yescomplemented
491C2×C22⋊C4—618no—
492C2×C22⋊C4—618no—
493C2×C22⋊C4—1224no—
494C2×C22⋊C4—1224no—
495C2×C22⋊C4—1224no—
496C2×C22⋊C4—1224no—
497C2×C22⋊C4—1224no—
498C2×C22⋊C4—1224no—
499C2×C22⋊C4—1224no—
500C2×C22⋊C4—1224no—
501C2×C22⋊C4—1224no—
502C2×C22⋊C4—1224no—
503C2×C22⋊C4—2442no—
504C2×C22⋊C4—2442no—
505C2×C22⋊C4—2442no—
506C2×C22⋊C4—2442no—
507C2×C22⋊C4—2442no—
508C2×C22⋊C4—2442no—
509C2×C42—22no—
510C2×C42—22no—
511C2×C42—22no—
512C2×C42—22no—
513C2×C42—22no—
514C2×C42—22no—
515C2×C42—22no—
516C2×C42—1224no—
517C2×C42—1224no—
518C2×C42—2442no—
519C2×C42C4×D6114yes—
520C2×C42C22⋊D6114yes—
521#95—22no—
522#95—22no—
523#95—1224no—
524#95—1224no—
525#95—1224no—
526#95—2442no—
527#95—2442no—
528C24—614no—
529C24—1222no—
530C24—1222no—
531C24—1222no—
532C24—1222no—
533C24—1222no—
534C24—1222no—
535C24—1222no—
536C24—1222no—
537C24—1222no—
538C24—1222no—
539C24—1222no—
540C24—1222no—
541C24—1222no—
542C24—1222no—
543C24C23×D6111yescharacteristic
544C2×D4—1228no—
545C2×D4—1228no—
546C2×D4—1228no—
547C2×D4—2444no—
548C2×D4—2444no—
549C2×D4—2444no—
550C2×D4—2444no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—614no—
584C22×C4—614no—
585C22×C4—1222no—
586C22×C4—1222no—
587C22×C4—1222no—
588C22×C4—1222no—
589C22×C4—1222no—
590C22×C4—1222no—
591C22×C4—1222no—
592C22×C4—1222no—
593C22×C4—1222no—
594C22×C4—1222no—
595C22×C4—1222no—
596C22×C4—1222no—
597C22×C4—1222no—
598C22×C4—1222no—
599C22×C4—1222no—
600C22×C4—1222no—
601C22×C4—1222no—
602C22×C4—1222no—
603C22×C4—1222no—
604C22×C4C2×C4×D6112yes—
605C22×C4C2×C4×D6112yes—
606C22×C4C2×C4×D6112yes—
607C22×C4C2×D24412yes—
608C22×C4C2×D24412yes—
609C22×C4C2×D24412yes—
610C22×C4#1175822212yes—
611C22×C4#1175822212yes—
612C22×C4#1175822212yes—
613C22×C4#1175822212yes—
614C22×C4D4×D6112yes—
615C22×C4#1175822412yes—
616C22×C4#1175822612yes—
617C22×C4#1175822612yes—
618C22×C4C2×C22⋊D6112yes—
619C22×C4C2×C22⋊D6112yes—
620C22×C4C2×C22⋊D6112yes—
621C4⋊C4—28no—
622C4⋊C4—28no—
623C4⋊C4—1228no—
624C4⋊C4—1228no—
625C4⋊C4—2444no—
626C22⋊C4—12216no—
627C22⋊C4—2448no—
628C22⋊C4—2448no—
629C22⋊C4—2448no—
630C22⋊C4—2448no—
631C22⋊C4—2448no—
632C42—28no—
633C42—28no—
634C42—44no—
635C42—2448no—
636C23—1224no—
637C23—1224no—
638C23—1224no—
639C23—1224no—
640C23—1224no—
641C23—1224no—
642C23—1224no—
643C23—2442no—
644C23—2442no—
645C23—2442no—
646C23—2442no—
647C23—2442no—
648C23—2442no—
649C23—2442no—
650C23—2442no—
651C23—2442no—
652C23—2442no—
653C23—2442no—
654C23—2442no—
655C23—2442no—
656C23—2442no—
657C23—2442no—
658C23—2442no—
659C23—2442no—
660C23—2442no—
661C23—2442no—
662C23—2442no—
663C23—2442no—
664C23—2442no—
665C23—2442no—
666C23—2442no—
667C23—2442no—
668C23—2442no—
669C23—2442no—
670C23—2442no—
671C23C22×C4×D6111yescharacteristic
672C23C2×D4×D6111yescharacteristic
673C23C22×C22⋊D6111yescharacteristic
674C23C22×D24411yescharacteristic
675C23C2×#1175822411yescharacteristic
676C23C2×#1175822211yescharacteristic
677C23C2×#1175822211yescharacteristic
678C23C2×#1175822211yescharacteristic
679C23C2×#1175822211yescharacteristic
680C23C2×#1175822611yescharacteristic
681C23C2×#1175822611yescharacteristic
682C23#1451982311yescharacteristic
683C23#1451982311yescharacteristic
684C23#1451982311yescharacteristic
685C23#1451982411yescharacteristic
686D4—24416no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—41no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—1224no—
728C2×C4—1224no—
729C2×C4—1224no—
730C2×C4—1224no—
731C2×C4—1224no—
732C2×C4—1224no—
733C2×C4—2442no—
734C2×C4—2442no—
735C2×C4—2442no—
736C2×C4—2442no—
737C2×C4—2442no—
738C2×C4—2442no—
739C2×C4—2442no—
740C2×C4—2442no—
741C2×C4—2442no—
742C2×C4—2442no—
743C2×C4—2442no—
744C2×C4—2442no—
745C2×C4—2442no—
746C2×C4—2442no—
747C2×C4—2442no—
748C2×C4#1451973514yes—
749C2×C4C4×C22⋊D6114yes—
750C2×C4#1451973914yes—
751C2×C4C4×D24414yes—
752C2×C4#1451974914yes—
753C2×C4#1451975114yes—
754C2×C4#1451976214yes—
755C2×C4#1451976614yes—
756C2×C4#1451977214yes—
757C22—4882no—
758C22—4882no—
759C22—4882no—
760C22—4882no—
761C22—4882no—
762C22—4882no—
763C22—4882no—
764C22—4882no—
765C22—2444no—
766C22—2444no—
767C22—2444no—
768C22—2444no—
769C22—2444no—
770C22—2444no—
771C22—2444no—
772C22C2×#1451973511yescharacteristic
773C22C2×C4×C22⋊D6111yescharacteristic
774C22C2×#1451973911yescharacteristic
775C22C2×C4×D24411yescharacteristic
776C22C4×#1175822211yescharacteristic
777C22#1684023611yescharacteristic
778C22#1684024211yescharacteristic
779C22C2×#1451974911yescharacteristic
780C22C2×#1451975111yescharacteristic
781C22C2×#1451976211yescharacteristic
782C22#1684027311yescharacteristic
783C22C2×#1451976611yescharacteristic
784C22C2×#1451977211yescharacteristic
785C22#1684029611yescharacteristic
786C22#1684031211yescharacteristic
787C22#1684032611yescharacteristic
788C22#1684034011yescharacteristic
789C22#1684036711yescharacteristic
790C22#1684038311yescharacteristic
791C22D4×D24411yescharacteristic
792C22#1684040811yescharacteristic
793C22#1684041611yescharacteristic
794C22#1684042111yescharacteristic
795C22#1684043311yescharacteristic
796C22#1684043411yescharacteristic
797C22#1684043411yescharacteristic
798C22#1684045811yescharacteristic
799C22#1684045811yescharacteristic
800C22#1684047711yescharacteristic
801C22#1684048511yescharacteristic
802C22#1684048511yescharacteristic
803C22#1684049711yescharacteristic
804C22#1684049711yescharacteristic
805C22#1684049711yescharacteristic
806C22#1684049711yescharacteristic
807C4—24no—
808C4—24no—
809C4—42no—
810C4—42no—
811C4—42no—
812C4—42no—
813C4—4882no—
814C4—2444no—
815C4—2444no—
816C4#1683965218yescomplemented
817C2—4884no—
818C2C2×#1683965211yescharacteristic
819C2C4×#1451975111yescharacteristic
820C2#2144851211yescharacteristic
821C2#2144876611yescharacteristic
822C2#2144879011yescharacteristic
823C2#2144888311yescharacteristic
824C2#2144888811yescharacteristic
825C2#2144923711yescharacteristic
826C2#2144925911yescharacteristic
827C2#2144958411yescharacteristic
828C2#2144961711yescharacteristic
829C2#2145040511yescharacteristic
830C2#2145041611yescharacteristic
831C2#2145081811yescharacteristic
832C2#2145130711yescharacteristic
subgroupG/H
center, FrattiniC24C23×D61
commutatorC23×C61C23×C4
FittingC2×C4×C4⋊C4×C61C2
socle, cosocleC24×C61C24
prime radicalC23×D244C22
hypercenterC2×C4×C4⋊C4D61
hypocenterC61#14022
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C24 ◁ C2×C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
4. C2×#16839652C2semidirect
5. C2×C4×C4⋊Dic61C2semidirect
6. #21444067C2semidirect
7. #21444061C2semidirect
8. #21444055C2semidirect
9. #21444049C2semidirect
10. #21444049C2semidirect
11. C2×C4×C4⋊C4×C61C2semidirect
25. #16839664C4semidirect
99. C2×C4⋊C4×C61D4semidirect
397. C4×C61#388semidirect
406. C2×C4×C4⋊C4D61semidirect
457. C61#14022semidirect
490. C2×C4⋊C4D244semidirect
816. C4#16839652semidirect

Maximal subgroups

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

subgroupindex
C2×#168396642
C2×#168396522
C2×C4×C4⋊Dic612
#214440672
#214440612
#214440552
#214440492
C2×C4×C4⋊C4×C612
#1402261