Finite Group Databasebeta

← #29601958

Subgroups — #29601958

Order 15616.

1846 conjugacy classes of subgroups.

The subgroup lattice has 822 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839653C212yesmaximal
2C2×#16839631C211yesmaximal, characteristic, complemented
3C2×#16839619C211yesmaximal, characteristic
4C2×#16839619C211yesmaximal, characteristic
5C2×C4×#11758198C211yesmaximal, characteristic
6#21444074C212yesmaximal, complemented
7#21444063C212yesmaximal
8#21444052C212yesmaximal, complemented
9#21444049C211yesmaximal, characteristic, complemented
10#21444048C211yesmaximal, characteristic, complemented
11C2×C4×C4⋊C4×C61C211yesmaximal, characteristic, complemented
12C23×C4×D61C2211yescharacteristic
13C22×C4⋊Dic61C2211yescharacteristic
14C22×C4⋊Dic61C2211yescharacteristic
15C22×#11758196C2212yes—
16C22×#11758196C2212yes—
17C22×#11758198C2212yes—
18C22×#11758198C2212yes—
19C22×#11758198C2211yescharacteristic
20C22×#11758198C2211yescharacteristic
21C22×C4×Dic61C2211yescharacteristic
22#16839653—28no—
23#16839631—24no—
24#16839619—24no—
25#16839619—24no—
26C4×#11758198C418yescomplemented
27C2×#14519684C2212yes—
28C2×#14519684C2212yes—
29C2×#14519684C2212yes—
30C2×#14519684C2212yes—
31C2×#14519684C2212yes—
32C2×#14519684C2212yes—
33C2×#14519684C2211yescharacteristic
34C2×#14519684C2211yescharacteristic
35C22×C4⋊C4×C61C2211yescharacteristic
36C22×C4⋊C4×C61C2211yescharacteristic
37C22×C42×C61C2212yes—
38C22×C42×C61C2211yescharacteristic
39C4×C4⋊C4×C61—24no—
40C2×#95×C61C2212yes—
41C24×D61C2311yescharacteristic
42C23×Dic61C2312yes—
43C23×Dic61C2312yes—
44C23×Dic61C2311yescharacteristic
45C23×Dic61C2311yescharacteristic
46C23×Dic61C2311yescharacteristic
47C22×C4×D61—22no—
48C22×C4×D61—22no—
49C22×C4×D61—22no—
50C22×C4×D61—22no—
51C22×C4×D61—22no—
52C22×C4×D61—22no—
53C22×C4×D61C2×C414yes—
54C2×C4⋊Dic61—22no—
55C2×C4⋊Dic61—22no—
56C2×C4⋊Dic61—22no—
57C2×C4⋊Dic61—22no—
58C2×C4⋊Dic61—22no—
59C2×C4⋊Dic61—22no—
60C2×#11758196—24no—
61C2×#11758196—24no—
62C2×#11758196—24no—
63C2×#11758196—24no—
64C2×#11758196—42no—
65C2×#11758196—42no—
66C2×#11758198—22no—
67C2×#11758198—22no—
68C2×#11758198—24no—
69C2×#11758198—24no—
70C2×#11758198—24no—
71C2×#11758198—24no—
72C2×#11758198—42no—
73C2×#11758198—42no—
74C2×#11758198C2×C414yes—
75C2×#11758198C2×C414yes—
76C2×#11758198D414yes—
77C2×#11758198Q814yes—
78C2×C4×Dic61—22no—
79C2×C4×Dic61—22no—
80C2×C4×Dic61C2×C414yes—
81#14519684—24no—
82#14519684—24no—
83#14519684—24no—
84#14519684—24no—
85#14519684—24no—
86#14519684—42no—
87#14519684C2×C414yes—
88#14519684C2×C414yes—
89C23×C4×C61C2311yescharacteristic
90C23×C4×C61C2312yes—
91C23×C4×C61C2312yes—
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×C61D414yes—
99C2×C4⋊C4×C61D414yes—
100C2×C42×C61—22no—
101C2×C42×C61—22no—
102C2×C42×C61—24no—
103C2×C42×C61—24no—
104C2×C42×C61—42no—
105C2×C42×C61C2×C414yes—
106#95×C61—24no—
107C24×C61C2411yescharacteristic
108C23×D61—21no—
109C23×D61—21no—
110C23×D61—21no—
111C23×D61—21no—
112C23×D61—21no—
113C23×D61—21no—
114C23×D61—21no—
115C23×D61—21no—
116C23×D61—21no—
117C23×D61—21no—
118C23×D61—21no—
119C23×D61—21no—
120C23×D61C22×C412yes—
121C23×D61C2×D412yes—
122C23×D61C2×Q812yes—
123C22×C4×C61—21no—
124C22×C4×C61—21no—
125C22×C4×C61—21no—
126C22×C4×C61—21no—
127C22×C4×C61—21no—
128C22×C4×C61—22no—
129C22×C4×C61—22no—
130C22×C4×C61—22no—
131C22×C4×C61—21no—
132C22×C4×C61—22no—
133C22×C4×C61—22no—
134C22×C4×C61—22no—
135C22×C4×C61—22no—
136C22×C4×C61—21no—
137C22×C4×C61—21no—
138C22×C4×C61—22no—
139C22×C4×C61—22no—
140C22×C4×C61—22no—
141C22×C4×C61—21no—
142C22×C4×C61—22no—
143C22×C4×C61—21no—
144C22×C4×C61—22no—
145C22×C4×C61C22×C412yes—
146C22×C4×C61C22×C412yes—
147C22×C4×C61C22×C412yes—
148C22×C4×C61C2×D414yes—
149C22×C4×C61C2×D414yes—
150C22×C4×C61C2×D412yes—
151C22×C4×C61C2×D412yes—
152C22×C4×C61C2×D412yes—
153C22×C4×C61C2×Q812yes—
154C22×C4×C61#4112yes—
155C22×C4×C61#4112yes—
156C22×C4×C61#4112yes—
157C22×C4×C61#4112yes—
158C22×Dic61—21no—
159C22×Dic61—21no—
160C22×Dic61—21no—
161C22×Dic61—21no—
162C22×Dic61—21no—
163C22×Dic61—21no—
164C22×Dic61—21no—
165C22×Dic61—21no—
166C22×Dic61—21no—
167C22×Dic61—21no—
168C22×Dic61—21no—
169C22×Dic61—21no—
170C22×Dic61—21no—
171C22×Dic61—21no—
172C22×Dic61—22no—
173C22×Dic61—22no—
174C22×Dic61—22no—
175C22×Dic61—22no—
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×Dic61C22×C412yes—
187C22×Dic61C22×C412yes—
188C22×Dic61C22×C412yes—
189C22×Dic61C2×D412yes—
190C22×Dic61C2×Q812yes—
191C22×Dic61#4112yes—
192C22×Dic61#4112yes—
193C2×C4×D61—28no—
194C2×C4×D61—28no—
195C2×C4×D61—28no—
196C2×C4×D61—44no—
197C2×C4×D61—44no—
198C2×C4×D61—44no—
199C2×C4×D61—44no—
200C4⋊C4×C61—28no—
201C4⋊C4×C61—28no—
202C42×C61—28no—
203C42×C61—48no—
204#11758198—28no—
205#11758198—48no—
206#11758198—48no—
207#11758198C4⋊C4116yescomplemented
208C4⋊Dic61—44no—
209C4⋊Dic61—44no—
210#11758196—48no—
211#11758196—48no—
212C4×Dic61—28no—
213C23×C61C23×C411yescharacteristic
214C23×C61C22×D411yescharacteristic
215C23×C61C22×D411yescharacteristic
216C23×C61C22×D411yescharacteristic
217C23×C61C22×Q811yescharacteristic
218C23×C61C2×#4111yescharacteristic
219C23×C61C2×#4111yescharacteristic
220C23×C61C2×#4111yescharacteristic
221C23×C61C2×#4111yescharacteristic
222C23×C61C2×#4111yescharacteristic
223C23×C61C2×#4111yescharacteristic
224C23×C61H(5,𝔽2)11yescharacteristic
225C23×C61H(5,𝔽2)11yescharacteristic
226C23×C612−1+411yescharacteristic
227C23×C612−1+411yescharacteristic
228C22×D61—22no—
229C22×D61—22no—
230C22×D61—22no—
231C22×D61—22no—
232C22×D61—22no—
233C22×D61—22no—
234C22×D61—22no—
235C22×D61—22no—
236C22×D61—22no—
237C22×D61—22no—
238C22×D61—22no—
239C22×D61—22no—
240C22×D61—22no—
241C22×D61—22no—
242C22×D61—22no—
243C22×D61—22no—
244C22×D61—22no—
245C22×D61—22no—
246C22×D61—41no—
247C22×D61—41no—
248C22×D61—41no—
249C22×D61—41no—
250C22×D61—41no—
251C22×D61—41no—
252C22×D61—41no—
253C22×D61—41no—
254C22×D61—41no—
255C22×D61—41no—
256C22×D61—41no—
257C22×D61—41no—
258C22×D61—41no—
259C22×D61—41no—
260C22×D61—41no—
261C22×D61—41no—
262C22×D61C2×C4⋊C414yes—
263C2×C4×C61—22no—
264C2×C4×C61—22no—
265C2×C4×C61—22no—
266C2×C4×C61—22no—
267C2×C4×C61—22no—
268C2×C4×C61—22no—
269C2×C4×C61—22no—
270C2×C4×C61—22no—
271C2×C4×C61—22no—
272C2×C4×C61—24no—
273C2×C4×C61—24no—
274C2×C4×C61—24no—
275C2×C4×C61—24no—
276C2×C4×C61—24no—
277C2×C4×C61—24no—
278C2×C4×C61—42no—
279C2×C4×C61—42no—
280C2×C4×C61—42no—
281C2×C4×C61—42no—
282C2×C4×C61—42no—
283C2×C4×C61—41no—
284C2×C4×C61—42no—
285C2×C4×C61—41no—
286C2×C4×C61—42no—
287C2×C4×C61—42no—
288C2×C4×C61—41no—
289C2×C4×C61—41no—
290C2×C4×C61C2×C4⋊C414yes—
291C2×C4×C61#11714yes—
292C2×C4×C61C4×D414yes—
293C2×C4×C61C4×D414yes—
294C2×C4×C61#12114yes—
295C2×C4×C61#12314yes—
296C2×C4×C61#12414yes—
297C2×C4×C61#12614yes—
298C2×Dic61—22no—
299C2×Dic61—22no—
300C2×Dic61—22no—
301C2×Dic61—22no—
302C2×Dic61—22no—
303C2×Dic61—22no—
304C2×Dic61—22no—
305C2×Dic61—22no—
306C2×Dic61—22no—
307C2×Dic61—22no—
308C2×Dic61—22no—
309C2×Dic61—22no—
310C2×Dic61—22no—
311C2×Dic61—22no—
312C2×Dic61—22no—
313C2×Dic61—41no—
314C2×Dic61—41no—
315C2×Dic61—41no—
316C2×Dic61—41no—
317C2×Dic61—42no—
318C2×Dic61—42no—
319C2×Dic61—42no—
320C2×Dic61—42no—
321C2×Dic61—42no—
322C2×Dic61—42no—
323C2×Dic61—42no—
324C2×Dic61—42no—
325C2×Dic61—42no—
326C2×Dic61—42no—
327C2×Dic61—42no—
328C2×Dic61—42no—
329C2×Dic61—42no—
330C2×Dic61—42no—
331C2×Dic61C2×C4⋊C414yes—
332C2×Dic61#11714yes—
333C4×D61—416no—
334#13876—611nomaximal, Sylow
335C22×C61C22×C4⋊C411yescharacteristic
336C22×C61C2×#11711yescharacteristic
337C22×C61C2×#11711yescharacteristic
338C22×C61C2×C4×D411yescharacteristic
339C22×C61C2×C4×D411yescharacteristic
340C22×C61#52011yescharacteristic
341C22×C61#52011yescharacteristic
342C22×C61C2×#12111yescharacteristic
343C22×C61C2×#12311yescharacteristic
344C22×C61C2×#12411yescharacteristic
345C22×C61C2×#12611yescharacteristic
346C22×C61#53211yescharacteristic
347C22×C61#53211yescharacteristic
348C22×C61#53311yescharacteristic
349C22×C61#53311yescharacteristic
350C22×C61#54011yescharacteristic
351C22×C61#54111yescharacteristic
352C22×C61#54211yescharacteristic
353C22×C61#54211yescharacteristic
354C22×C61D4211yescharacteristic
355C22×C61D4211yescharacteristic
356C22×C61#54611yescharacteristic
357C22×C61#54711yescharacteristic
358C22×C61#54711yescharacteristic
359C22×C61#54711yescharacteristic
360C22×C61#54811yescharacteristic
361C22×C61D4×Q811yescharacteristic
362C22×C61D4×Q811yescharacteristic
363C22×C61#55011yescharacteristic
364C22×C61#55211yescharacteristic
365C22×C61#55311yescharacteristic
366C22×C61#55411yescharacteristic
367C22×C61#55411yescharacteristic
368C22×C61#55511yescharacteristic
369C22×C61#55611yescharacteristic
370C2×D61—24no—
371C2×D61—24no—
372C2×D61—24no—
373C2×D61—42no—
374C2×D61—42no—
375C2×D61—42no—
376C2×D61—42no—
377C2×D61—42no—
378C2×D61—42no—
379C2×D61—42no—
380C2×D61—42no—
381C2×D61—42no—
382C2×D61—42no—
383C2×D61—42no—
384C2×D61—42no—
385C4×C61—24no—
386C4×C61—42no—
387C4×C61—44no—
388C4×C61—44no—
389C4×C61#38818yescomplemented
390Dic61—24no—
391Dic61—24no—
392Dic61—42no—
393Dic61—82no—
394Dic61—82no—
395C2×#388—612no—
396C2×#384—611no—
397C2×#380—611no—
398C2×#380—611no—
399C2×C4×C4⋊C4D6111yescharacteristic, complemented
400C2×C4×C22⋊C4—611no—
401#1442—612no—
402#1439—612no—
403#1436—612no—
404C4⋊#95—611no—
405C4⋊#95—611no—
406C2×C61#228511yescharacteristic
407C2×C61C2×#38811yescharacteristic
408C2×C61#231411yescharacteristic
409C2×C61D4×C4⋊C411yescharacteristic
410C2×C61D4×C4⋊C411yescharacteristic
411C2×C61#235211yescharacteristic
412C2×C61#235411yescharacteristic
413C2×C61#242211yescharacteristic
414C2×C61#242311yescharacteristic
415C2×C61#242811yescharacteristic
416C2×C61#242911yescharacteristic
417C2×C61#249111yescharacteristic
418C2×C61#249211yescharacteristic
419C2×C61#249611yescharacteristic
420C2×C61#249711yescharacteristic
421D61—44no—
422C24×C4—611no—
423C22×C4⋊C4—611no—
424C22×C4⋊C4—611no—
425C22×C4⋊C4—612no—
426C22×C4⋊C4—612no—
427C22×C4⋊C4C2×D6111yescharacteristic
428C22×C4⋊C4C2×D6111yescharacteristic
429C22×C22⋊C4—611no—
430C22×C22⋊C4—611no—
431C22×C22⋊C4—612no—
432C22×C22⋊C4—612no—
433C22×C42—611no—
434C22×C42C2×D6112yes—
435C22×C42C2×D6111yescharacteristic
436#388—1228no—
437#384—1224no—
438#380—1224no—
439#380—1224no—
440C4×C4⋊C4—24no—
441C4×C22⋊C4—618no—
442C2×#95—611no—
443C2×#95—611no—
444C2×#95—612no—
445C2×#95—612no—
446C2×#95—612no—
447C2×#95—612no—
448C2×#95—612no—
449C2×#95—612no—
450C2×#95C2×D6112yes—
451C61#1387611yescharacteristic, complemented, Sylow
452C25—611no—
453C23×C4—611no—
454C23×C4—611no—
455C23×C4—611no—
456C23×C4—614no—
457C23×C4—612no—
458C23×C4—612no—
459C23×C4—1222no—
460C23×C4—1222no—
461C23×C4—1222no—
462C23×C4—1222no—
463C23×C4—1222no—
464C23×C4—1222no—
465C23×C4C22×D6111yescharacteristic
466C23×C4C22×D6112yes—
467C23×C4C22×D6112yes—
468C23×C4C22×D6111yescharacteristic
469C23×C4C22×D6111yescharacteristic
470C2×C4⋊C4—22no—
471C2×C4⋊C4—22no—
472C2×C4⋊C4—22no—
473C2×C4⋊C4—22no—
474C2×C4⋊C4—1224no—
475C2×C4⋊C4—1224no—
476C2×C4⋊C4—1222no—
477C2×C4⋊C4—1224no—
478C2×C4⋊C4—1224no—
479C2×C4⋊C4—1222no—
480C2×C4⋊C4—1222no—
481C2×C4⋊C4—1222no—
482C2×C4⋊C4—1222no—
483C2×C4⋊C4—1222no—
484C2×C4⋊C4—2442no—
485C2×C4⋊C4—2442no—
486C2×C4⋊C4D24414yes—
487C2×C4⋊C4C22⋊D6114yes—
488C2×C22⋊C4—614no—
489C2×C22⋊C4—614no—
490C2×C22⋊C4—614no—
491C2×C22⋊C4—614no—
492C2×C22⋊C4—1222no—
493C2×C22⋊C4—1222no—
494C2×C22⋊C4—1224no—
495C2×C22⋊C4—1224no—
496C2×C22⋊C4—1224no—
497C2×C22⋊C4—1224no—
498C2×C22⋊C4—2442no—
499C2×C22⋊C4—2442no—
500C2×C42—22no—
501C2×C42—22no—
502C2×C42—24no—
503C2×C42—24no—
504C2×C42—42no—
505C2×C42—614no—
506C2×C42—1222no—
507C2×C42—1222no—
508C2×C42C4×D6114yes—
509#95—24no—
510#95—614no—
511#95—614no—
512#95—1224no—
513#95—1224no—
514#95—1224no—
515#95—1224no—
516#95—1224no—
517#95—2442no—
518C24—612no—
519C24—612no—
520C24—612no—
521C24—1221no—
522C24—1221no—
523C24—1221no—
524C24—1221no—
525C24—1221no—
526C24—1221no—
527C24—1221no—
528C24—1221no—
529C24—1221no—
530C24—1221no—
531C24—1221no—
532C24—1221no—
533C24C23×D6111yescharacteristic
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—21no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—22no—
546C22×C4—21no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—21no—
553C22×C4—22no—
554C22×C4—21no—
555C22×C4—22no—
556C22×C4—612no—
557C22×C4—612no—
558C22×C4—612no—
559C22×C4—612no—
560C22×C4—612no—
561C22×C4—612no—
562C22×C4—612no—
563C22×C4—1221no—
564C22×C4—1221no—
565C22×C4—1221no—
566C22×C4—1221no—
567C22×C4—1221no—
568C22×C4—1221no—
569C22×C4—1221no—
570C22×C4—1221no—
571C22×C4—1221no—
572C22×C4—1221no—
573C22×C4—1221no—
574C22×C4—1221no—
575C22×C4—1221no—
576C22×C4—1221no—
577C22×C4—1228no—
578C22×C4—1228no—
579C22×C4—1228no—
580C22×C4—1222no—
581C22×C4—1222no—
582C22×C4—1222no—
583C22×C4—1222no—
584C22×C4—1222no—
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—2444no—
595C22×C4—2444no—
596C22×C4—2444no—
597C22×C4—2444no—
598C22×C4C2×C4×D6112yes—
599C22×C4C2×C4×D6112yes—
600C22×C4C2×C4×D6112yes—
601C22×C4C2×D24414yes—
602C22×C4C2×D24412yes—
603C22×C4#1175822212yes—
604C22×C4#1175822212yes—
605C22×C4#1175822212yes—
606C22×C4#1175822212yes—
607C22×C4D4×D6112yes—
608C22×C4Q8×D6112yes—
609C22×C4C2×C22⋊D6114yes—
610C22×C4C2×C22⋊D6112yes—
611C4⋊C4—28no—
612C4⋊C4—28no—
613C4⋊C4—2448no—
614C4⋊C4—2448no—
615C4⋊C4—2444no—
616C4⋊C4—2444no—
617C22⋊C4—6116no—
618C22⋊C4—1228no—
619C22⋊C4—2448no—
620C22⋊C4—2448no—
621C42—28no—
622C42—48no—
623C42—1228no—
624C23—614no—
625C23—1222no—
626C23—1222no—
627C23—1222no—
628C23—1222no—
629C23—1222no—
630C23—1222no—
631C23—1222no—
632C23—1222no—
633C23—1222no—
634C23—1222no—
635C23—1222no—
636C23—1222no—
637C23—1222no—
638C23—1222no—
639C23—1222no—
640C23—1222no—
641C23—1222no—
642C23—1222no—
643C23—2441no—
644C23—2441no—
645C23—2441no—
646C23—2441no—
647C23—2441no—
648C23—2441no—
649C23—2441no—
650C23—2441no—
651C23—2441no—
652C23—2441no—
653C23—2441no—
654C23—2441no—
655C23—2441no—
656C23—2441no—
657C23—2441no—
658C23—2441no—
659C23C22×C4×D6111yescharacteristic
660C23C2×D4×D6111yescharacteristic
661C23C22×C22⋊D6111yescharacteristic
662C23C22×D24411yescharacteristic
663C23C2×Q8×D6111yescharacteristic
664C23#41×D6111yescharacteristic
665C23#41×D6111yescharacteristic
666C23C2×#1175822211yescharacteristic
667C23C2×#1175822211yescharacteristic
668C23C2×#1175822211yescharacteristic
669C23C2×#1175822211yescharacteristic
670C23#1451982211yescharacteristic
671C23#1451982311yescharacteristic
672C23#1451982411yescharacteristic
673C23#1451982511yescharacteristic
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—24no—
684C2×C4—24no—
685C2×C4—24no—
686C2×C4—24no—
687C2×C4—24no—
688C2×C4—24no—
689C2×C4—42no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—42no—
693C2×C4—42no—
694C2×C4—42no—
695C2×C4—42no—
696C2×C4—42no—
697C2×C4—41no—
698C2×C4—42no—
699C2×C4—41no—
700C2×C4—42no—
701C2×C4—614no—
702C2×C4—614no—
703C2×C4—1222no—
704C2×C4—1222no—
705C2×C4—1222no—
706C2×C4—1222no—
707C2×C4—1222no—
708C2×C4—1222no—
709C2×C4—1222no—
710C2×C4—1222no—
711C2×C4—1222no—
712C2×C4—1222no—
713C2×C4—1222no—
714C2×C4—1222no—
715C2×C4—1222no—
716C2×C4—1222no—
717C2×C4—1222no—
718C2×C4—2442no—
719C2×C4—2442no—
720C2×C4—2442no—
721C2×C4—2442no—
722C2×C4—2442no—
723C2×C4—2442no—
724C2×C4—2442no—
725C2×C4—2442no—
726C2×C4—2442no—
727C2×C4—2442no—
728C2×C4—2442no—
729C2×C4—2442no—
730C2×C4—2442no—
731C2×C4—2442no—
732C2×C4—2441no—
733C2×C4—2441no—
734C2×C4—2441no—
735C2×C4—2441no—
736C2×C4—24416no—
737C2×C4C4⋊C4×D6114yes—
738C2×C4#1451973414yes—
739C2×C4C4×C22⋊D6114yes—
740C2×C4C4×D24414yes—
741C2×C4#1451975114yes—
742C2×C4#1451976014yes—
743C2×C4#1451976514yes—
744C2×C4#1451977114yes—
745C22—1224no—
746C22—1224no—
747C22—1224no—
748C22—2442no—
749C22—2442no—
750C22—2442no—
751C22—2442no—
752C22—2442no—
753C22—2442no—
754C22—2442no—
755C22—2442no—
756C22—2442no—
757C22—2442no—
758C22—2442no—
759C22—2442no—
760C22C2×C4⋊C4×D6111yescharacteristic
761C22#117×D6111yescharacteristic
762C22C2×#1451973411yescharacteristic
763C22C2×C4×C22⋊D6111yescharacteristic
764C22C2×C4×D24411yescharacteristic
765C22#1684024211yescharacteristic
766C22#1684024311yescharacteristic
767C22C2×#1451975111yescharacteristic
768C22C2×#1451976011yescharacteristic
769C22C2×#1451976511yescharacteristic
770C22C2×#1451977111yescharacteristic
771C22#1684030911yescharacteristic
772C22#1684030911yescharacteristic
773C22#1684031611yescharacteristic
774C22#1684031611yescharacteristic
775C22#1684036311yescharacteristic
776C22#1684037011yescharacteristic
777C22#1684037711yescharacteristic
778C22#1684038411yescharacteristic
779C22D4×C22⋊D6111yescharacteristic
780C22D4×D24411yescharacteristic
781C22#1684040711yescharacteristic
782C22#1684041111yescharacteristic
783C22#1684041311yescharacteristic
784C22#1684041711yescharacteristic
785C22#1684042411yescharacteristic
786C22Q8×C22⋊D6111yescharacteristic
787C22Q8×D24411yescharacteristic
788C22#1684043111yescharacteristic
789C22#1684045311yescharacteristic
790C22#1684046211yescharacteristic
791C22#1684046711yescharacteristic
792C22#1684047211yescharacteristic
793C22#1684047511yescharacteristic
794C22#1684048011yescharacteristic
795C4—24no—
796C4—42no—
797C4—44no—
798C4—44no—
799C4—1224no—
800C4—1224no—
801C4—4882no—
802C4—4882no—
803C4—2442no—
804C4#1683965318yescomplemented
805C2—2444no—
806C2#2144822311yescharacteristic
807C2C2×#1683965311yescharacteristic
808C2#2144842411yescharacteristic
809C2C4⋊C4×C22⋊D6111yescharacteristic
810C2C4⋊C4×D24411yescharacteristic
811C2#2144875111yescharacteristic
812C2#2144876911yescharacteristic
813C2#2144932711yescharacteristic
814C2#2144933811yescharacteristic
815C2#2144940111yescharacteristic
816C2#2144941211yescharacteristic
817C2#2145017611yescharacteristic
818C2#2145018711yescharacteristic
819C2#2145023511yescharacteristic
820C2#2145024611yescharacteristic
subgroupG/H
center, FrattiniC24C23×D61
commutatorC23×C61C23×C4
FittingC2×C4×C4⋊C4×C61C2
socle, cosocleC24×C61C24
prime radicalC24×D61C23
hypercenterC2×C4×C4⋊C4D61
hypocenterC61#13876
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C24 ◁ C2×C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×#16839631C2semidirect
6. #21444074C2semidirect
8. #21444052C2semidirect
9. #21444049C2semidirect
10. #21444048C2semidirect
11. C2×C4×C4⋊C4×C61C2semidirect
26. C4×#11758198C4semidirect
207. #11758198C4⋊C4semidirect
389. C4×C61#388semidirect
399. C2×C4×C4⋊C4D61semidirect
451. C61#13876semidirect
804. C4#16839653semidirect

Maximal subgroups

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

subgroupindex
C2×#168396532
C2×#168396312
C2×#168396192
C2×C4×#117581982
#214440742
#214440632
#214440522
#214440492
#214440482
C2×C4×C4⋊C4×C612
#1387661