Finite Group Databasebeta

← C2×#21455289 #30546850

Subgroups — C2×#21455289 #30546850

Order 15616.

2810 conjugacy classes of subgroups.

The subgroup lattice has 852 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519809C211yesmaximal, characteristic, complemented
2C22×#14519806C211yesmaximal, characteristic, complemented
3C2×#16840311C211yesmaximal, characteristic
4C2×C4×Q8×D61C211yesmaximal, characteristic, complemented
5#21455289C2116yesmaximal, direct product factor
6C2×#16839985C211yesmaximal, characteristic, complemented
7C2×#16839984C211yesmaximal, characteristic, complemented
8C2×#16839981C211yesmaximal, characteristic, complemented
9C2×#16839971C211yesmaximal, characteristic, complemented
10C2×#16839970C211yesmaximal, characteristic, complemented
11C2×#16839961C211yesmaximal, characteristic, complemented
12C2×#16839960C211yesmaximal, characteristic, complemented
13C2×#16839784C211yesmaximal, characteristic, complemented
14C2×#16839762C211yesmaximal, characteristic, complemented
15C2×#16839760C211yesmaximal, characteristic, complemented
16C2×C61×#464C211yesmaximal, characteristic, complemented
17C22×#11758226C2211yescharacteristic
18C22×#11758224C2211yescharacteristic
19C22×Q8×D61C2211yescharacteristic
20C2×#14519809—28no—
21C2×#14519809C2218yescomplemented
22C2×#14519806—28no—
23C2×#14519806C2218yescomplemented
24C22×Dic244C2211yescharacteristic
25C22×#11758202C2211yescharacteristic
26C22×#11758202C2211yescharacteristic
27C22×#11758190C2211yescharacteristic
28C22×#11758200C2211yescharacteristic
29C22×#11758201C2211yescharacteristic
30C22×#11758189C2211yescharacteristic
31C22×#11758189C2211yescharacteristic
32#16840311—24no—
33#16840311C2218yes—
34C2×#14519775C2211yescharacteristic
35C2×#14519773C2211yescharacteristic
36C2×#14519765C2211yescharacteristic
37C2×#14519750—21no—
38C2×#14519750—21no—
39C2×Q8×Dic61C2211yescharacteristic
40C2×C4×Dic122—21no—
41C2×C4×Dic122C2211yescharacteristic
42C2×#14519742—21no—
43C2×#14519742C2211yescharacteristic
44C4×Q8×D61—24no—
45C4×Q8×D61C2218yescomplemented
46C2×#14519737—21no—
47C2×#14519737—21no—
48C2×C4⋊C4×D61—21no—
49C2×C4⋊C4×D61C2211yescharacteristic
50C2×C42×D61—21no—
51C2×C42×D61C2211yescharacteristic
52#16839985C2218yescomplemented
53#16839984C2218yescomplemented
54#16839981C2218yescomplemented
55#16839971C2218yescomplemented
56#16839970C2218yescomplemented
57#16839961C2218yescomplemented
58#16839960C2218yescomplemented
59#16839784C2218yescomplemented
60C2×C4⋊#92418C2211yescharacteristic
61C2×#14519706C2211yescharacteristic
62C2×#14519706C2211yescharacteristic
63#16839762C2218yescomplemented
64#16839760C2218yescomplemented
65C2×#14519702C2211yescharacteristic
66C2×#14519701C2211yescharacteristic
67C2×#14519700C2211yescharacteristic
68C2×#14519699C2211yescharacteristic
69C2×#14519698C2211yescharacteristic
70C2×#14519697C2211yescharacteristic
71C22×Q16×C61C2211yescharacteristic
72C22×SD16×C61C2211yescharacteristic
73C2×#124×C61C2211yescharacteristic
74C2×C4×Q8×C61C2211yescharacteristic
75C61×#464C2218yescomplemented
76C2×C4⋊C8×C61C2211yescharacteristic
77C2×#103×C61C2211yescharacteristic
78C2×#102×C61C2211yescharacteristic
79C2×#11758226—22no—
80C2×#11758226—24no—
81C2×#11758226—24no—
82C2×#11758226C2314yes—
83C2×#11758224—24no—
84C2×#11758224—22no—
85C2×#11758224—24no—
86C2×#11758224C2314yes—
87C22×Dic122—21no—
88C22×Dic122C2311yescharacteristic
89C22×Dic122C2311yescharacteristic
90C2×Q8×D61—22no—
91C2×Q8×D61—24no—
92C2×Q8×D61D418yescomplemented
93C2×Q8×D61C2314yes—
94C22×D244—21no—
95C22×D244C2311yescharacteristic
96C22×C22⋊D61—21no—
97C22×C22⋊D61—21no—
98C22×C22⋊D61—21no—
99C23×Dic61—21no—
100C22×C4×D61—21no—
101C22×C4×D61—21no—
102C22×C4×D61—21no—
103C22×C4×D61D411yescharacteristic
104C22×C4×D61D411yescharacteristic
105C22×C4×D61C2311yescharacteristic
106#14519809—232no—
107#14519806—232no—
108C2×Dic244—24no—
109C2×Dic244C2314yes—
110C2×#11758202—24no—
111C2×#11758202—24no—
112C2×#11758202C2314yes—
113C2×#11758202C2314yes—
114C2×#11758190—24no—
115C2×#11758190C2314yes—
116C2×#11758200—24no—
117C2×#11758200C2314yes—
118C2×#11758201—24no—
119C2×#11758201C2314yes—
120C2×#11758189—24no—
121C2×#11758189—24no—
122C2×#11758189C2314yes—
123C2×#11758189C2314yes—
124C22×#92418C2311yescharacteristic
125C22×#92418C2311yescharacteristic
126#14519775—22no—
127#14519775C2314yes—
128#14519773—22no—
129#14519773C2314yes—
130#14519765—22no—
131#14519765C2314yes—
132#14519750—28no—
133#14519750—28no—
134Q8×Dic61—22no—
135Q8×Dic61C2314yes—
136C4×Dic122—22no—
137C4×Dic122—28no—
138C4×Dic122C2314yes—
139#14519742—22no—
140#14519742—28no—
141#14519742C2314yes—
142#14519737—28no—
143#14519737—28no—
144C2×C4⋊Dic61—21no—
145C2×C4⋊Dic61C2311yescharacteristic
146C2×#11758196—21no—
147C2×#11758196—21no—
148C2×#11758196—21no—
149C2×#11758196—21no—
150C2×#11758196—21no—
151C4⋊C4×D61—28no—
152C4⋊C4×D61—22no—
153C4⋊C4×D61C2314yes—
154C2×#11758198—21no—
155C2×#11758198—21no—
156C2×C4×Dic61—21no—
157C2×C4×Dic61—21no—
158C2×C4×Dic61—21no—
159C2×C4×Dic61D411yescharacteristic
160C2×C4×Dic61D411yescharacteristic
161C2×C4×Dic61C2311yescharacteristic
162C42×D61—28no—
163C42×D61D414yes—
164C42×D61C2314yes—
165C4⋊#92418C2314yes—
166#14519706C2314yes—
167#14519706C2314yes—
168#14519702C2314yes—
169#14519701C2314yes—
170#14519700C2314yes—
171#14519699C2314yes—
172#14519698C2314yes—
173#14519697C2314yes—
174C22×Q8×C61C2311yescharacteristic
175C22×Q8×C61C2311yescharacteristic
176C22×D4×C61C2311yescharacteristic
177C2×Q16×C61—24no—
178C2×Q16×C61C2314yes—
179C2×SD16×C61—24no—
180C2×SD16×C61C2314yes—
181C22×C8×C61C2311yescharacteristic
182C22×C8×C61C2311yescharacteristic
183#124×C61—22no—
184#124×C61C2314yes—
185C4×Q8×C61—22no—
186C4×Q8×C61C2314yes—
187C2×C4⋊C4×C61—21no—
188C2×C4⋊C4×C61C2311yescharacteristic
189C2×C22⋊C4×C61—21no—
190C2×C22⋊C4×C61—21no—
191C2×C42×C61—21no—
192C2×C42×C61C2311yescharacteristic
193C4⋊C8×C61C2314yes—
194#103×C61C2314yes—
195#102×C61C2314yes—
196C24×C61—21no—
197C23×D61—21no—
198C23×D61C2×D411yescharacteristic
199C2×Q8×C61—21no—
200C2×Q8×C61—21no—
201C2×Q8×C61—22no—
202C2×Q8×C61—22no—
203C2×Q8×C61—22no—
204C2×Q8×C61C2×D414yes—
205C2×Q8×C61C2412yes—
206C2×Q8×C61C2412yes—
207C2×D4×C61—22no—
208C2×D4×C61—21no—
209C2×D4×C61—22no—
210C2×D4×C61C2412yes—
211C22×C4×C61—21no—
212C22×C4×C61—21no—
213C22×C4×C61—21no—
214C22×C4×C61C2×D411yescharacteristic
215C22×C4×C61C2×D411yescharacteristic
216C22×C4×C61C2411yescharacteristic
217C2×C22⋊D61—24no—
218C2×C22⋊D61—24no—
219C2×C22⋊D61—24no—
220C2×C22⋊D61—44no—
221C2×C22⋊D61—44no—
222C2×C22⋊D61—44no—
223C22×Dic61—21no—
224C22×Dic61—21no—
225C22×Dic61—21no—
226C22×Dic61—24no—
227C22×Dic61—44no—
228C22×Dic61C2×D411yescharacteristic
229C22×Dic61C2×D411yescharacteristic
230C22×Dic61C2×D411yescharacteristic
231#11758226—28no—
232#11758226—28no—
233#11758226—48no—
234Q8×D61—216no—
235Q8×D61—28no—
236Q8×D61C2×D4116yescomplemented
237#11758224—28no—
238#11758224—28no—
239#11758224—48no—
240C2×D244—22no—
241C2×D244—22no—
242C2×D244—24no—
243C2×D244—21no—
244C2×D244—44no—
245C2×D244C2412yes—
246C2×C4×D61—28no—
247C2×C4×D61—24no—
248C2×C4×D61—24no—
249C2×C4×D61—24no—
250C2×C4×D61—24no—
251C2×C4×D61—42no—
252C2×C4×D61—44no—
253C2×C4×D61—44no—
254C2×C4×D61C2×D414yes—
255C2×C4×D61C2×D414yes—
256C2×C4×D61C2×D412yes—
257C2×C4×D61C2×D414yes—
258C2×C4×D61#4114yes—
259C2×C4×D61C2412yes—
260C2×Dic122—21no—
261C2×Dic122—22no—
262C2×Dic122—28no—
263C2×Dic122—24no—
264C2×Dic122—22no—
265C2×Dic122—22no—
266C2×Dic122—21no—
267C2×Dic122C2×D414yes—
268C2×Dic122C2412yes—
269C2×Dic122C2412yes—
270Q16×C61—28no—
271SD16×C61—28no—
272C2×C8×C61—22no—
273C2×C8×C61—22no—
274C2×C8×C61C2412yes—
275C2×C8×C61C2412yes—
276C4⋊C4×C61—24no—
277C4⋊C4×C61—21no—
278C4⋊C4×C61C2412yes—
279C22⋊C4×C61—24no—
280C22⋊C4×C61—24no—
281C42×C61—24no—
282C42×C61C2×D412yes—
283C42×C61C2412yes—
284#11758202—28no—
285#11758202—28no—
286#11758201—28no—
287#11758200—28no—
288#11758198—24no—
289#11758198—24no—
290C4⋊Dic61—21no—
291C4⋊Dic61—24no—
292C4⋊Dic61C2412yes—
293#11758196—24no—
294#11758196—24no—
295#11758196—24no—
296#11758196—24no—
297#11758196—24no—
298C4×Dic61—24no—
299C4×Dic61—24no—
300C4×Dic61—24no—
301C4×Dic61C2×D412yes—
302C4×Dic61C2×D414yes—
303C4×Dic61C2×D414yes—
304C4×Dic61C2412yes—
305C2×#92418—22no—
306C2×#92418—22no—
307C2×#92418C2412yes—
308C2×#92418C2412yes—
309Dic244—28no—
310#11758190—28no—
311#11758189—28no—
312#11758189—28no—
313C23×C61—22no—
314C23×C61—42no—
315C23×C61—42no—
316C23×C61—42no—
317C23×C61C22×D411yescharacteristic
318C22×D61—22no—
319C22×D61—22no—
320C22×D61—22no—
321C22×D61—42no—
322C22×D61—42no—
323C22×D61—42no—
324C22×D61#12114yes—
325C22×D61C22×D412yes—
326Q8×C61—24no—
327Q8×C61—22no—
328Q8×C61—22no—
329Q8×C61—22no—
330Q8×C61—42no—
331Q8×C61C22×D414yes—
332D4×C61—22no—
333D4×C61—22no—
334D4×C61—42no—
335C2×C4×C61—24no—
336C2×C4×C61—22no—
337C2×C4×C61—22no—
338C2×C4×C61—22no—
339C2×C4×C61—22no—
340C2×C4×C61—22no—
341C2×C4×C61—42no—
342C2×C4×C61—42no—
343C2×C4×C61C22×D412yes—
344C2×C4×C61C22×D412yes—
345C2×C4×C61C22×D411yescharacteristic
346C2×C4×C61C22×D412yes—
347C2×C4×C61C2×#4112yes—
348C2×C4×C61C2511yescharacteristic
349C22⋊D61—48no—
350C22⋊D61—48no—
351C22⋊D61—48no—
352C2×Dic61—24no—
353C2×Dic61—22no—
354C2×Dic61—22no—
355C2×Dic61—22no—
356C2×Dic61—22no—
357C2×Dic61—42no—
358C2×Dic61—42no—
359C2×Dic61—48no—
360C2×Dic61#12114yes—
361C2×Dic61#13714yescomplemented
362C2×Dic61C22×D412yes—
363C2×Dic61C22×D412yes—
364C2×Dic61C22×D412yes—
365D244—22no—
366D244—22no—
367D244—48no—
368D244—42no—
369C4×D61—216no—
370C4×D61—28no—
371C4×D61—44no—
372C4×D61—48no—
373C4×D61—48no—
374C4×D61#12118yes—
375C4×D61C22×D414yes—
376C4×D61C2×#4114yes—
377Dic122—24no—
378Dic122—22no—
379Dic122—216no—
380Dic122—22no—
381Dic122—22no—
382Dic122—42no—
383Dic122C22×D414yes—
384C8×C61—22no—
385C8×C61—22no—
386#92418—22no—
387#92418—22no—
388C2×#3037—611nomaximal, Sylow
389C22×C61—42no—
390C22×C61—42no—
391C22×C61—42no—
392C22×C61—84no—
393C22×C61C2×#12112yes—
394C22×C61C2×#13712yes—
395C22×C61#57512yes—
396C22×C61C23×D411yescharacteristic
397C2×D61—28no—
398C2×D61—22no—
399C2×D61—22no—
400C2×D61—42no—
401C2×D61—42no—
402C2×D61—42no—
403C2×D61—84no—
404C2×D61C2×#12114yes—
405C4×C61—24no—
406C4×C61—22no—
407C4×C61—22no—
408C4×C61—42no—
409C4×C61—42no—
410C4×C61C2×#12112yes—
411C4×C61C23×D411yescharacteristic
412C4×C61C22×#4111yescharacteristic
413Dic61—24no—
414Dic61—22no—
415Dic61—42no—
416Dic61—42no—
417Dic61C2×#12114yes—
418Dic61C2×#13714yescomplemented
419C22×#137—611no—
420C22×#137—611no—
421C2×#532—611no—
422C22×C4×Q8—611no—
423#3037—6116no—
424C2×#464—611no—
425C2×#464—611no—
426C2×#464—611no—
427C2×#464D6111yescharacteristic, complemented
428C2×#462—611no—
429C2×#462—611no—
430C2×#460—611no—
431C2×#460—611no—
432C2×#423—611no—
433C2×#417—611no—
434C2×#417—611no—
435C2×C61—82no—
436C2×C61#303714yescomplemented
437C2×C61C22×#12111yescharacteristic
438C2×C61C22×#13711yescharacteristic
439C2×C61C2×#57511yescharacteristic
440D61—24no—
441D61—82no—
442C22×#41—611no—
443C22×#41—611no—
444C23×Q8—611no—
445C2×#137—618no—
446C2×#137—618no—
447C2×#137—1228no—
448C2×#137—1228no—
449C22×Q16—611no—
450C22×Q16—611no—
451C22×Q16—611no—
452C22×Q16C2×D6111yescharacteristic
453C22×SD16—611no—
454C22×SD16—611no—
455C22×SD16—611no—
456C22×SD16C2×D6111yescharacteristic
457C22×M16—611no—
458C22×M16—611no—
459#532—618no—
460#532—1224no—
461C2×C4⋊Q8—611no—
462C2×#127—611no—
463C2×#124—611no—
464C2×#124C2×D6111yescharacteristic
465C2×#121—1221no—
466C2×#121—1221no—
467C2×C4×Q8—611no—
468C2×C4×Q8—618no—
469C2×C4×Q8—611no—
470C2×C4×Q8—611no—
471C2×C4×Q8—1221no—
472C2×C4×Q8—1221no—
473C2×C4×Q8—1224no—
474C2×C4×Q8C2×D6111yescharacteristic
475C2×C4×D4—1221no—
476C2×C4×D4—1221no—
477C22×C4⋊C4—611no—
478C22×C4⋊C4—1221no—
479C22×C42—611no—
480C22×C42—1221no—
481#464—618no—
482#464—618no—
483#464—618no—
484#464C2×D6118yescomplemented
485#462—618no—
486#462—618no—
487#460—618no—
488#460—618no—
489#423—618no—
490C2×C4⋊C8—611no—
491C2×C4⋊C8—611no—
492C2×C4⋊C8—611no—
493C2×C4⋊C8C2×D6111yescharacteristic
494#417—618no—
495#417—618no—
496C2×#103—611no—
497C2×#103—611no—
498C2×#103—611no—
499C2×#103C2×D6111yescharacteristic
500C2×#102—611no—
501C2×#102—611no—
502C2×#102—611no—
503C2×#102C2×D6111yescharacteristic
504C61C2×#303711yescharacteristic, complemented, Sylow
505C2×#41—614no—
506C2×#41—614no—
507C2×#41—1222no—
508C2×#41—1222no—
509C2×#41—1224no—
510C2×#41—1224no—
511C2×#41—1224no—
512C2×#41—1224no—
513C22×Q8—618no—
514C22×Q8—614no—
515C22×Q8—611no—
516C22×Q8—611no—
517C22×Q8—1221no—
518C22×Q8—1222no—
519C22×Q8—1224no—
520C22×Q8C22×D6111yescharacteristic
521C22×Q8C22×D6111yescharacteristic
522C22×D4—611no—
523C22×D4—1221no—
524C22×D4—1221no—
525C22×D4—1221no—
526C22×D4—1221no—
527C22×D4C22×D6111yescharacteristic
528C23×C4—611no—
529C23×C4—611no—
530C23×C4—611no—
531C23×C4—1221no—
532C23×C4—1221no—
533C23×C4—1221no—
534C23×C4—1221no—
535#137—12232no—
536#137—12232no—
537C2×Q16—24no—
538C2×Q16—614no—
539C2×Q16—614no—
540C2×Q16—614no—
541C2×Q16—1224no—
542C2×Q16—1224no—
543C2×Q16—1224no—
544C2×Q16C22×D6114yes—
545C2×SD16—24no—
546C2×SD16—614no—
547C2×SD16—614no—
548C2×SD16—614no—
549C2×SD16—1224no—
550C2×SD16—1224no—
551C2×SD16—1224no—
552C2×SD16C22×D6114yes—
553C2×M16—614no—
554C2×M16—614no—
555C2×M16—1224no—
556C2×M16—1224no—
557C22×C8—611no—
558C22×C8—611no—
559C22×C8C22×D6111yescharacteristic
560C22×C8C22×D6111yescharacteristic
561C4⋊Q8—614no—
562C4⋊Q8—1222no—
563#127—614no—
564#127—1222no—
565#124—22no—
566#124—614no—
567#124—1222no—
568#124C22×D6114yes—
569#121—1228no—
570#121—1228no—
571C4×Q8—22no—
572C4×Q8—614no—
573C4×Q8—614no—
574C4×Q8—614no—
575C4×Q8—1228no—
576C4×Q8—1228no—
577C4×Q8—1222no—
578C4×Q8—1222no—
579C4×Q8—1222no—
580C4×Q8C22×D6114yes—
581C4×D4—1228no—
582C4×D4—1228no—
583C2×C4⋊C4—21no—
584C2×C4⋊C4—611no—
585C2×C4⋊C4—614no—
586C2×C4⋊C4—1222no—
587C2×C4⋊C4—1228no—
588C2×C4⋊C4—1221no—
589C2×C4⋊C4—1221no—
590C2×C4⋊C4—1221no—
591C2×C4⋊C4—1221no—
592C2×C4⋊C4—1221no—
593C2×C4⋊C4—1221no—
594C2×C4⋊C4C22×D6111yescharacteristic
595C2×C22⋊C4—21no—
596C2×C22⋊C4—21no—
597C2×C22⋊C4—1221no—
598C2×C22⋊C4—1221no—
599C2×C42—21no—
600C2×C42—611no—
601C2×C42—611no—
602C2×C42—611no—
603C2×C42—614no—
604C2×C42—614no—
605C2×C42—1228no—
606C2×C42—1221no—
607C2×C42—1221no—
608C2×C42—1221no—
609C2×C42C22×D6111yescharacteristic
610C4⋊C8—614no—
611C4⋊C8—614no—
612C4⋊C8—614no—
613C4⋊C8C22×D6114yes—
614#103—614no—
615#103—614no—
616#103—614no—
617#103C22×D6114yes—
618#102—614no—
619#102—614no—
620#102—614no—
621#102C22×D6114yes—
622C24—21no—
623C24—611no—
624C24—1221no—
625#41—1228no—
626#41—1228no—
627#41—1228no—
628#41—1228no—
629#41—2448no—
630#41—2448no—
631C2×Q8—21no—
632C2×Q8—21no—
633C2×Q8—22no—
634C2×Q8—22no—
635C2×Q8—22no—
636C2×Q8—6116no—
637C2×Q8—614no—
638C2×Q8—612no—
639C2×Q8—612no—
640C2×Q8—1224no—
641C2×Q8—1228no—
642C2×Q8—12216no—
643C2×Q8—1228no—
644C2×Q8—1221no—
645C2×Q8—1221no—
646C2×Q8—1222no—
647C2×Q8—1222no—
648C2×Q8—1222no—
649C2×Q8D4×D6114yes—
650C2×Q8C23×D6112yes—
651C2×Q8C23×D6112yes—
652C2×D4—22no—
653C2×D4—21no—
654C2×D4—22no—
655C2×D4—612no—
656C2×D4—1224no—
657C2×D4—1224no—
658C2×D4—1224no—
659C2×D4—1224no—
660C2×D4—1222no—
661C2×D4—1221no—
662C2×D4—1222no—
663C2×D4—2444no—
664C2×D4—2444no—
665C2×D4—2444no—
666C2×D4—2444no—
667C2×D4C23×D6112yes—
668C22×C4—21no—
669C22×C4—21no—
670C22×C4—21no—
671C22×C4—611no—
672C22×C4—611no—
673C22×C4—612no—
674C22×C4—614no—
675C22×C4—614no—
676C22×C4—612no—
677C22×C4—611no—
678C22×C4—614no—
679C22×C4—614no—
680C22×C4—1224no—
681C22×C4—1224no—
682C22×C4—1224no—
683C22×C4—1228no—
684C22×C4—1224no—
685C22×C4—1224no—
686C22×C4—1221no—
687C22×C4—1221no—
688C22×C4—1221no—
689C22×C4—2442no—
690C22×C4—2444no—
691C22×C4—2444no—
692C22×C4—2444no—
693C22×C4D4×D6111yescharacteristic
694C22×C4D4×D6111yescharacteristic
695C22×C4C23×D6111yescharacteristic
696Q16—28no—
697Q16—1228no—
698Q16—1228no—
699Q16—1228no—
700SD16—28no—
701SD16—1228no—
702SD16—1228no—
703SD16—1228no—
704M16—1228no—
705M16—1228no—
706C2×C8—22no—
707C2×C8—22no—
708C2×C8—612no—
709C2×C8—612no—
710C2×C8—1222no—
711C2×C8—1222no—
712C2×C8C23×D6112yes—
713C2×C8C23×D6112yes—
714C4⋊C4—24no—
715C4⋊C4—21no—
716C4⋊C4—612no—
717C4⋊C4—1224no—
718C4⋊C4—1224no—
719C4⋊C4—1224no—
720C4⋊C4—1224no—
721C4⋊C4—1224no—
722C4⋊C4—1221no—
723C4⋊C4—1224no—
724C4⋊C4C23×D6112yes—
725C22⋊C4—24no—
726C22⋊C4—24no—
727C22⋊C4—1224no—
728C22⋊C4—1224no—
729C42—24no—
730C42—614no—
731C42—614no—
732C42—612no—
733C42—612no—
734C42—1224no—
735C42—1224no—
736C42—1224no—
737C42D4×D6112yes—
738C42C23×D6112yes—
739C23—22no—
740C23—42no—
741C23—42no—
742C23—42no—
743C23—614no—
744C23—612no—
745C23—1222no—
746C23—1222no—
747C23—1222no—
748C23—2442no—
749C23—2442no—
750C23—2442no—
751C23C2×D4×D6111yescharacteristic
752Q8—24no—
753Q8—22no—
754Q8—22no—
755Q8—22no—
756Q8—42no—
757Q8—614no—
758Q8—12216no—
759Q8—1224no—
760Q8—1222no—
761Q8—1222no—
762Q8—1222no—
763Q8—2442no—
764Q8C2×D4×D6114yes—
765D4—22no—
766D4—22no—
767D4—42no—
768D4—1222no—
769D4—1222no—
770D4—2448no—
771D4—2448no—
772D4—2448no—
773D4—2448no—
774D4—2442no—
775C2×C4—24no—
776C2×C4—22no—
777C2×C4—22no—
778C2×C4—22no—
779C2×C4—22no—
780C2×C4—22no—
781C2×C4—42no—
782C2×C4—42no—
783C2×C4—614no—
784C2×C4—614no—
785C2×C4—612no—
786C2×C4—612no—
787C2×C4—618no—
788C2×C4—614no—
789C2×C4—614no—
790C2×C4—612no—
791C2×C4—1228no—
792C2×C4—12216no—
793C2×C4—1224no—
794C2×C4—1222no—
795C2×C4—1222no—
796C2×C4—1222no—
797C2×C4—1222no—
798C2×C4—2444no—
799C2×C4—2448no—
800C2×C4—2448no—
801C2×C4—2448no—
802C2×C4—2442no—
803C2×C4—2442no—
804C2×C4C2×D4×D6112yes—
805C2×C4C2×D4×D6112yes—
806C2×C4C2×D4×D6111yescharacteristic
807C2×C4C2×D4×D6112yes—
808C2×C4#41×D6112yes—
809C2×C4C24×D6111yescharacteristic
810C8—22no—
811C8—22no—
812C8—1222no—
813C8—1222no—
814C22—42no—
815C22—42no—
816C22—42no—
817C22—84no—
818C22—614no—
819C22—1222no—
820C22—1222no—
821C22—1228no—
822C22—4884no—
823C22—2442no—
824C22—2442no—
825C22—2442no—
826C22#121×D6112yes—
827C22#137×D6112yes—
828C22#1684055912yes—
829C22C22×D4×D6111yescharacteristic
830C4—22no—
831C4—22no—
832C4—24no—
833C4—42no—
834C4—42no—
835C4—614no—
836C4—614no—
837C4—1222no—
838C4—1224no—
839C4—2442no—
840C4—2442no—
841C4#121×D6112yes—
842C4C22×D4×D6111yescharacteristic
843C4C2×#41×D6111yescharacteristic
844C2—82no—
845C2—1224no—
846C2—4882no—
847C2#2145528914yesdirect product factor
848C2C2×#121×D6111yescharacteristic
849C2C2×#137×D6111yescharacteristic
850C2C2×#1684055911yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#464C2
socleC23×C61C22×D4
prime radicalC2×#16840311C2
hypercenterC2×#464D61
hypocenterC61C2×#3037
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#464

Complements

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

NH ≅ G/Ntype
1. C22×#14519809C2semidirect
2. C22×#14519806C2semidirect
4. C2×C4×Q8×D61C2semidirect
5. #21455289C2direct (N × H)
6. C2×#16839985C2semidirect
7. C2×#16839984C2semidirect
8. C2×#16839981C2semidirect
9. C2×#16839971C2semidirect
10. C2×#16839970C2semidirect
11. C2×#16839961C2semidirect
12. C2×#16839960C2semidirect
13. C2×#16839784C2semidirect
14. C2×#16839762C2semidirect
15. C2×#16839760C2semidirect
16. C2×C61×#464C2semidirect
21. C2×#14519809C22semidirect
23. C2×#14519806C22semidirect
45. C4×Q8×D61C22semidirect
52. #16839985C22semidirect
53. #16839984C22semidirect
54. #16839981C22semidirect
55. #16839971C22semidirect
56. #16839970C22semidirect
57. #16839961C22semidirect
58. #16839960C22semidirect
59. #16839784C22semidirect
63. #16839762C22semidirect
64. #16839760C22semidirect
75. C61×#464C22semidirect
92. C2×Q8×D61D4semidirect
236. Q8×D61C2×D4semidirect
361. C2×Dic61#137semidirect
418. Dic61C2×#137semidirect
427. C2×#464D61semidirect
436. C2×C61#3037semidirect
484. #464C2×D61semidirect
504. C61C2×#3037semidirect
847. C2#21455289direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145198092
C22×#145198062
C2×#168403112
C2×C4×Q8×D612
#214552892
C2×#168399852
C2×#168399842
C2×#168399812
C2×#168399712
C2×#168399702
C2×#168399612
C2×#168399602
C2×#168397842
C2×#168397622
C2×#168397602
C2×C61×#4642
C2×#303761