Finite Group Databasebeta

← #30550788

Subgroups — #30550788

Order 15616.

2362 conjugacy classes of subgroups.

The subgroup lattice has 1182 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840273C211yesmaximal, characteristic, complemented
2C2×#16840273C211yesmaximal, characteristic, complemented
3#21456661C214yesmaximal, complemented
4#21456651C212yesmaximal, complemented
5#21456635C212yesmaximal, complemented
6#21456612C214yesmaximal, complemented
7#21456602C212yesmaximal, complemented
8#21456586C212yesmaximal, complemented
9#21455768C211yesmaximal, characteristic, complemented
10#21455760C211yesmaximal, characteristic, complemented
11#21455752C212yesmaximal, complemented
12#21455449C212yesmaximal, complemented
13#21455438C212yesmaximal, complemented
14#21455081C211yesmaximal, characteristic, complemented
15#21455073C211yesmaximal, characteristic, complemented
16#21455064C212yesmaximal, complemented
17C2×C61×#407C211yesmaximal, characteristic, complemented
18C22×#11758222C2211yescharacteristic
19C22×#11758222C2211yescharacteristic, complemented
20C2×#14519810C2212yescomplemented
21C2×#14519805C2212yescomplemented
22#16840273—21no—
23#16840273—21no—
24#16840273—21no—
25#16840273—21no—
26#16840273—21no—
27#16840273—21no—
28#16840273—21no—
29#16840273—21no—
30#16840273C2212yes—
31#16840273C2212yes—
32#16840273C2212yes—
33#16840273C2212yes—
34#16840273C2212yescomplemented
35#16840273C2212yescomplemented
36#16840273C2212yescomplemented
37#16840273C2212yescomplemented
38C2×#14519760—21no—
39C2×#14519760—21no—
40C2×#14519756C2211yescharacteristic
41C2×#14519756C2211yescharacteristic, complemented
42C2×#14519756C2211yescharacteristic, complemented
43C2×#14519756C2211yescharacteristic, complemented
44C2×#14519751C2211yescharacteristic
45C2×#14519751C2211yescharacteristic, complemented
46C2×#14519751C2211yescharacteristic, complemented
47C2×#14519751C2211yescharacteristic, complemented
48C2×#14519746—21no—
49C2×#14519746—21no—
50C2×C4×C22⋊D61—21no—
51C2×C4×C22⋊D61—21no—
52C2×C4×C22⋊D61—21no—
53C2×C4×C22⋊D61—21no—
54C2×#14519736C2211yescharacteristic
55C2×#14519736C2211yescharacteristic, complemented
56#16840104C2214yescomplemented
57#16840104C2214yescomplemented
58#16840104C2214yescomplemented
59#16840098C2212yescomplemented
60#16840093C2212yescomplemented
61#16840087C2214yescomplemented
62#16840087C2214yescomplemented
63#16840087C2214yescomplemented
64#16840081C2212yescomplemented
65#16840076C2212yescomplemented
66#16840020C2214yescomplemented
67#16840015C2214yescomplemented
68#16840008C2214yescomplemented
69#16840008C2214yescomplemented
70#16840003C2214yescomplemented
71#16839998C2214yescomplemented
72#16839991C2214yescomplemented
73#16839991C2214yescomplemented
74#16839926C2214yescomplemented
75#16839926C2214yescomplemented
76#16839926C2214yescomplemented
77#16839920C2212yescomplemented
78#16839915C2212yescomplemented
79#16839909C2214yescomplemented
80#16839909C2214yescomplemented
81#16839909C2214yescomplemented
82#16839903C2212yescomplemented
83#16839898C2212yescomplemented
84#16839804C2212yescomplemented
85#16839804C2212yescomplemented
86#16839772C2212yescomplemented
87#16839768C2212yescomplemented
88#16839764C2212yescomplemented
89#16839764C2212yescomplemented
90C24×C4×C61C2211yescharacteristic
91C22×M16×C61C2212yescomplemented
92C61×#407C2211yescharacteristic
93C61×#407C2211yescharacteristic
94C61×#407C2212yescomplemented
95C61×#407C2212yescomplemented
96C61×#407C2212yescomplemented
97C2×C22⋊C8×C61C2212yescomplemented
98C2×C22⋊C8×C61C2212yescomplemented
99C2×#11758222—21no—
100C2×#11758222—21no—
101C2×#11758222—21no—
102C2×#11758222—21no—
103C2×#11758222—44no—
104C2×#11758222—44no—
105C2×#11758222C2312yes—
106C2×#11758222C2312yes—
107C2×#11758222C2312yes—
108C2×#11758222C2312yes—
109C22×Dic122C2311yescharacteristic
110C22×Dic122C2311yescharacteristic
111C22×D244C2311yescharacteristic
112C22×D244C2311yescharacteristic
113C22×C22⋊D61—21no—
114C22×C22⋊D61—21no—
115C22×C22⋊D61—21no—
116C22×C22⋊D61—21no—
117C22×C22⋊D61—21no—
118C22×C22⋊D61—21no—
119C22×C4×D61—21no—
120C22×C4×D61—21no—
121#14519810—44no—
122#14519805—44no—
123C2×Dic244C2314yescomplemented
124C2×#11758190C2314yescomplemented
125C2×#11758190C2314yescomplemented
126C2×D488C2314yescomplemented
127#14519760—22no—
128#14519760—22no—
129#14519760—22no—
130#14519760—22no—
131#14519760—22no—
132#14519760—22no—
133#14519760—22no—
134#14519760—22no—
135#14519756—21no—
136#14519756—21no—
137#14519756—21no—
138#14519756—21no—
139#14519756—21no—
140#14519756—21no—
141#14519756—21no—
142#14519756—21no—
143#14519756C2312yes—
144#14519756C2312yes—
145#14519756C2312yes—
146#14519756C2312yes—
147#14519756C2312yes—
148#14519756C2312yes—
149#14519756C2312yes—
150#14519756C2312yes—
151#14519751—21no—
152#14519751—21no—
153#14519751—21no—
154#14519751—21no—
155#14519751—21no—
156#14519751—21no—
157#14519751—21no—
158#14519751—21no—
159#14519751C2312yes—
160#14519751C2312yes—
161#14519751C2312yes—
162#14519751C2312yes—
163#14519751C2312yes—
164#14519751C2312yes—
165#14519751C2312yes—
166#14519751C2312yes—
167#14519746—22no—
168#14519746—22no—
169#14519746—22no—
170#14519746—22no—
171#14519746—22no—
172#14519746—22no—
173#14519746—22no—
174#14519746—22no—
175C4×C22⋊D61—22no—
176C4×C22⋊D61—22no—
177C4×C22⋊D61—22no—
178C4×C22⋊D61—22no—
179C4×C22⋊D61—22no—
180C4×C22⋊D61—22no—
181C4×C22⋊D61—22no—
182C4×C22⋊D61—22no—
183C4×C22⋊D61—22no—
184C4×C22⋊D61—22no—
185C4×C22⋊D61—22no—
186C4×C22⋊D61—22no—
187C4×C22⋊D61—22no—
188C4×C22⋊D61—22no—
189C4×C22⋊D61—22no—
190C4×C22⋊D61—22no—
191#14519736—21no—
192#14519736—21no—
193#14519736—21no—
194#14519736—21no—
195#14519736C2312yes—
196#14519736C2312yes—
197#14519736C2312yes—
198#14519736C2312yes—
199C2×C4⋊Dic61C2311yescharacteristic
200C2×C4⋊Dic61C2311yescharacteristic
201C2×C4⋊Dic61C2311yescharacteristic
202C2×C4⋊Dic61C2311yescharacteristic
203C2×#11758196—21no—
204C2×#11758196—21no—
205C2×#11758196—21no—
206C2×#11758196—21no—
207C2×C22⋊Dic61—21no—
208C2×C22⋊Dic61—21no—
209C2×C22⋊Dic61—21no—
210C2×C22⋊Dic61—21no—
211C2×C22⋊Dic61—21no—
212C2×C22⋊Dic61—21no—
213C2×#11758198—21no—
214C2×#11758198—21no—
215C2×#11758198—21no—
216C2×#11758198—21no—
217C2×C4×Dic61—21no—
218C2×C4×Dic61—21no—
219#14519711C2314yescomplemented
220#14519711C2314yescomplemented
221#14519709C2314yescomplemented
222#14519709C2314yescomplemented
223#14519702C2314yescomplemented
224#14519702C2314yescomplemented
225#14519702C2314yescomplemented
226#14519702C2314yescomplemented
227#14519699C2314yescomplemented
228#14519699C2314yescomplemented
229#14519699C2314yescomplemented
230#14519699C2314yescomplemented
231C25×C61D411yescharacteristic
232C23×C4×C61—44no—
233C23×C4×C61D411yescharacteristic
234C23×C4×C61D411yescharacteristic
235C23×C4×C61D411yescharacteristic
236C23×C4×C61D411yescharacteristic
237C23×C4×C61D411yescharacteristic
238C23×C4×C61D411yescharacteristic
239C23×C4×C61D411yescharacteristic
240C23×C4×C61C2311yescharacteristic
241C23×C4×C61C2311yescharacteristic
242C23×C4×C61C2311yescharacteristic
243C23×C4×C61C2311yescharacteristic
244C23×C4×C61C2311yescharacteristic
245C23×C4×C61C2311yescharacteristic
246C23×C4×C61C2311yescharacteristic
247C2×M16×C61—44no—
248C2×M16×C61C2312yes—
249C2×M16×C61C2312yes—
250C2×M16×C61C2314yes—
251C22×C8×C61C2314yes—
252C22⋊C8×C61C2312yes—
253C22⋊C8×C61C2312yes—
254C22⋊C8×C61C2312yes—
255C22⋊C8×C61C2312yes—
256C22⋊C8×C61C2314yes—
257C22⋊C8×C61C2314yes—
258C24×C61—42no—
259C24×C61—42no—
260C24×C61—42no—
261C24×C61C2×D411yescharacteristic
262C24×C61C2×D411yescharacteristic
263C24×C61C2×D411yescharacteristic
264C24×C61C2×D411yescharacteristic
265C24×C61C2×D411yescharacteristic
266C24×C61C2×D411yescharacteristic
267C24×C61C2×D411yescharacteristic
268C23×D61—21no—
269C23×D61—21no—
270C22×C4×C61—24no—
271C22×C4×C61—24no—
272C22×C4×C61—24no—
273C22×C4×C61—42no—
274C22×C4×C61—42no—
275C22×C4×C61—42no—
276C22×C4×C61—42no—
277C22×C4×C61—42no—
278C22×C4×C61—42no—
279C22×C4×C61—42no—
280C22×C4×C61—42no—
281C22×C4×C61—42no—
282C22×C4×C61—42no—
283C22×C4×C61—42no—
284C22×C4×C61C2×D411yescharacteristic
285C22×C4×C61C2×D411yescharacteristic
286C22×C4×C61C2×D411yescharacteristic
287C22×C4×C61C2×D411yescharacteristic
288C22×C4×C61C2×D411yescharacteristic
289C22×C4×C61C2×D411yescharacteristic
290C22×C4×C61C2×D411yescharacteristic
291C22×C4×C61C2×D411yescharacteristic
292C22×C4×C61C2×D411yescharacteristic
293C22×C4×C61C2×D411yescharacteristic
294C22×C4×C61C2×D411yescharacteristic
295C22×C4×C61C2×D411yescharacteristic
296C22×C4×C61C2×D411yescharacteristic
297C22×C4×C61C2×D411yescharacteristic
298C22×C4×C61C2×D411yescharacteristic
299C22×C4×C61C2×D411yescharacteristic
300C22×C4×C61C2×D411yescharacteristic
301C22×C4×C61C2×D411yescharacteristic
302C22×C4×C61C2×D411yescharacteristic
303C22×C4×C61C2×D411yescharacteristic
304C22×C4×C61C2×D411yescharacteristic
305C22×C4×C61C2411yescharacteristic
306C22×C4×C61C2411yescharacteristic
307C22×C4×C61C2411yescharacteristic
308C22×C4×C61C2411yescharacteristic
309C22×C4×C61C2411yescharacteristic
310C22×C4×C61C2411yescharacteristic
311C22×C4×C61C2411yescharacteristic
312C2×C22⋊D61—22no—
313C2×C22⋊D61—22no—
314C2×C22⋊D61—22no—
315C2×C22⋊D61—22no—
316C2×C22⋊D61—22no—
317C2×C22⋊D61—22no—
318C2×C22⋊D61—22no—
319C2×C22⋊D61—22no—
320C2×C22⋊D61—22no—
321C2×C22⋊D61—22no—
322C2×C22⋊D61—22no—
323C2×C22⋊D61—22no—
324C2×C22⋊D61—44no—
325C2×C22⋊D61—44no—
326C2×C22⋊D61—44no—
327C2×C22⋊D61—44no—
328C2×C22⋊D61—44no—
329C2×C22⋊D61—44no—
330C22×Dic61—21no—
331C22×Dic61—21no—
332C22×Dic61—21no—
333C22×Dic61—21no—
334C22×Dic61—21no—
335C22×Dic61—21no—
336#11758222—24no—
337#11758222—24no—
338#11758222—42no—
339#11758222—44no—
340#11758222—44no—
341#11758222—42no—
342#11758222—44no—
343#11758222—44no—
344#11758222—44no—
345#11758222—44no—
346C2×D244—24no—
347C2×D244—21no—
348C2×D244—21no—
349C2×D244—42no—
350C2×D244C2412yes—
351C2×D244C2412yes—
352C2×C4×D61—22no—
353C2×C4×D61—22no—
354C2×C4×D61—22no—
355C2×C4×D61—22no—
356C2×C4×D61—44no—
357C2×C4×D61—44no—
358C2×Dic122—24no—
359C2×Dic122—21no—
360C2×Dic122—21no—
361C2×Dic122—42no—
362C2×Dic122C2412yes—
363C2×Dic122C2412yes—
364M16×C61—24no—
365M16×C61—24no—
366M16×C61—44no—
367C2×C8×C61—44no—
368C2×C8×C61C2414yes—
369C2×C8×C61C2414yes—
370C22⋊Dic61—22no—
371C22⋊Dic61—22no—
372C22⋊Dic61—22no—
373C22⋊Dic61—22no—
374C22⋊Dic61—22no—
375C22⋊Dic61—22no—
376C22⋊Dic61—22no—
377C22⋊Dic61—22no—
378C22⋊Dic61—22no—
379C22⋊Dic61—22no—
380C22⋊Dic61—22no—
381C22⋊Dic61—22no—
382#11758198—22no—
383#11758198—22no—
384#11758198—22no—
385#11758198—22no—
386#11758198—22no—
387#11758198—22no—
388#11758198—22no—
389#11758198—22no—
390C4⋊Dic61—21no—
391C4⋊Dic61—21no—
392C4⋊Dic61—21no—
393C4⋊Dic61—21no—
394C4⋊Dic61C2412yes—
395C4⋊Dic61C2412yes—
396C4⋊Dic61C2412yes—
397C4⋊Dic61C2412yes—
398#11758196—22no—
399#11758196—22no—
400#11758196—22no—
401#11758196—22no—
402#11758196—22no—
403#11758196—22no—
404#11758196—22no—
405#11758196—22no—
406C4×Dic61—22no—
407C4×Dic61—22no—
408C4×Dic61—22no—
409C4×Dic61—22no—
410Dic244—44no—
411D488—44no—
412#11758190—44no—
413#11758190—44no—
414C23×C61—22no—
415C23×C61—22no—
416C23×C61—22no—
417C23×C61—22no—
418C23×C61—22no—
419C23×C61—22no—
420C23×C61—22no—
421C23×C61—22no—
422C23×C61—22no—
423C23×C61—41no—
424C23×C61—41no—
425C23×C61—41no—
426C23×C61—41no—
427C23×C61—41no—
428C23×C61—41no—
429C23×C61—41no—
430C23×C61—41no—
431C23×C61—41no—
432C23×C61—41no—
433C23×C61—41no—
434C23×C61—41no—
435C23×C61—416no—
436C23×C61C22×D411yescharacteristic
437C23×C61C22×D411yescharacteristic
438C23×C61C22×D411yescharacteristic
439C23×C61C22×D411yescharacteristic
440C23×C61C22×D411yescharacteristic
441C23×C61C22×D411yescharacteristic
442C23×C61C22×D411yescharacteristic
443C22×D61—22no—
444C22×D61—22no—
445C22×D61—42no—
446C22×D61—42no—
447C22×D61—42no—
448C22×D61—42no—
449C22×D61—42no—
450C22×D61—42no—
451C2×C4×C61—22no—
452C2×C4×C61—22no—
453C2×C4×C61—22no—
454C2×C4×C61—22no—
455C2×C4×C61—22no—
456C2×C4×C61—22no—
457C2×C4×C61—22no—
458C2×C4×C61—22no—
459C2×C4×C61—22no—
460C2×C4×C61—22no—
461C2×C4×C61—22no—
462C2×C4×C61—22no—
463C2×C4×C61—22no—
464C2×C4×C61—22no—
465C2×C4×C61—22no—
466C2×C4×C61—41no—
467C2×C4×C61—41no—
468C2×C4×C61—41no—
469C2×C4×C61—41no—
470C2×C4×C61—41no—
471C2×C4×C61—41no—
472C2×C4×C61—41no—
473C2×C4×C61—41no—
474C2×C4×C61—41no—
475C2×C4×C61—41no—
476C2×C4×C61—41no—
477C2×C4×C61—41no—
478C2×C4×C61C22×D411yescharacteristic
479C2×C4×C61C22×D411yescharacteristic
480C2×C4×C61C22×D411yescharacteristic
481C2×C4×C61C22×D411yescharacteristic
482C2×C4×C61C22×D411yescharacteristic
483C2×C4×C61C22×D411yescharacteristic
484C2×C4×C61C22×D411yescharacteristic
485C2×C4×C61H(5,𝔽2)14yes—
486C2×C4×C61C2511yescharacteristic
487C22⋊D61—44no—
488C22⋊D61—44no—
489C22⋊D61—44no—
490C22⋊D61—44no—
491C22⋊D61—44no—
492C22⋊D61—44no—
493C22⋊D61—44no—
494C22⋊D61—44no—
495C22⋊D61—44no—
496C22⋊D61—44no—
497C22⋊D61—44no—
498C22⋊D61—44no—
499C2×Dic61—22no—
500C2×Dic61—22no—
501C2×Dic61—22no—
502C2×Dic61—22no—
503C2×Dic61—22no—
504C2×Dic61—22no—
505C2×Dic61—42no—
506C2×Dic61—42no—
507C2×Dic61—42no—
508C2×Dic61—42no—
509C2×Dic61—42no—
510C2×Dic61—42no—
511D244—22no—
512D244—24no—
513D244—22no—
514D244—42no—
515D244—42no—
516C4×D61—44no—
517C4×D61—44no—
518C4×D61—44no—
519C4×D61—44no—
520Dic122—22no—
521Dic122—24no—
522Dic122—22no—
523Dic122—42no—
524Dic122—42no—
525C8×C61—24no—
526C8×C61—24no—
527#60752—611nomaximal, Sylow
528C22×C61—21no—
529C22×C61—21no—
530C22×C61—21no—
531C22×C61—21no—
532C22×C61—21no—
533C22×C61—21no—
534C22×C61—21no—
535C22×C61—21no—
536C22×C61—21no—
537C22×C61—21no—
538C22×C61—21no—
539C22×C61—21no—
540C22×C61—21no—
541C22×C61—21no—
542C22×C61—21no—
543C22×C61—21no—
544C22×C61—21no—
545C22×C61—21no—
546C22×C61—44no—
547C22×C61—44no—
548C22×C61—44no—
549C22×C61—44no—
550C22×C61—44no—
551C22×C61—44no—
552C22×C61—44no—
553C22×C61#53412yes—
554C22×C61#57512yes—
555C22×C61#57512yes—
556C22×C61C23×D411yescharacteristic
557C2×D61—42no—
558C2×D61—42no—
559C2×D61—42no—
560C2×D61—42no—
561C2×D61—42no—
562C2×D61—42no—
563C2×D61—84no—
564C2×D61—84no—
565C4×C61—21no—
566C4×C61—21no—
567C4×C61—21no—
568C4×C61—21no—
569C4×C61—21no—
570C4×C61—21no—
571C4×C61#53412yes—
572C4×C61C2×H(5,𝔽2)12yes—
573Dic61—42no—
574Dic61—42no—
575Dic61—42no—
576Dic61—42no—
577Dic61—42no—
578Dic61—42no—
579C2×#525—611no—
580C2×#525—611no—
581#3197—614no—
582#3196—612no—
583#3194—612no—
584#3191—614no—
585#3190—612no—
586#3188—612no—
587#3095—611no—
588#3094—611no—
589#3093—612no—
590#3056—612no—
591#3055—612no—
592#3007—611no—
593#3006—611no—
594#3005—612no—
595C2×#407D6111yescharacteristic, complemented
596C2×C61—22no—
597C2×C61—22no—
598C2×C61—22no—
599C2×C61—41no—
600C2×C61—41no—
601C2×C61—41no—
602C2×C61—41no—
603C2×C61C2×#53411yescharacteristic
604C2×C61C2×#57511yescharacteristic
605C2×C61C2×#57511yescharacteristic
606D61—82no—
607D61—82no—
608C22×#41—611no—
609C22×#41—611no—
610C24×C4C2×D6111yescharacteristic
611C2×#137—612no—
612C2×AGL(1,ℤ/8)—612no—
613C22×M16C2×D6112yescomplemented
614#525—612no—
615#525—612no—
616#525—612no—
617#525—612no—
618#525—612no—
619#525—612no—
620#525—612no—
621#525—612no—
622#525—1221no—
623#525—1221no—
624#525—1221no—
625#525—1221no—
626#525—1221no—
627#525—1221no—
628#525—1221no—
629#525—1221no—
630C2×#123—1221no—
631C2×#123—1221no—
632C2×C22⋊Q8—611no—
633C2×C22⋊Q8—611no—
634C2×C22⋊Q8—611no—
635C2×C22⋊Q8—611no—
636C2×#121—611no—
637C2×#121—611no—
638C2×#121—611no—
639C2×#121—611no—
640C2×#120—1221no—
641C2×#120—1221no—
642C2×C4×D4—1221no—
643C2×C4×D4—1221no—
644C2×C4×D4—1221no—
645C2×C4×D4—1221no—
646C2×#117—611no—
647C2×#117—611no—
648#485—614no—
649#485—614no—
650#485—614no—
651#484—612no—
652#483—612no—
653#482—614no—
654#482—614no—
655#482—614no—
656#481—612no—
657#480—612no—
658#470—614no—
659#469—614no—
660#468—614no—
661#468—614no—
662#467—614no—
663#466—614no—
664#465—614no—
665#465—614no—
666#452—614no—
667#452—614no—
668#452—614no—
669#451—612no—
670#450—612no—
671#449—614no—
672#449—614no—
673#449—614no—
674#448—612no—
675#447—612no—
676#428—612no—
677#428—612no—
678#419—612no—
679#418—612no—
680#417—612no—
681#417—612no—
682#407C2×D6111yescharacteristic
683#407C2×D6111yescharacteristic
684#407C2×D6112yescomplemented
685#407C2×D6112yescomplemented
686#407C2×D6112yescomplemented
687C2×C22⋊C8C2×D6112yescomplemented
688C2×C22⋊C8C2×D6112yescomplemented
689C61#6075211yescharacteristic, complemented, Sylow
690C25D24411yescharacteristic
691C2×#41—612no—
692C2×#41—612no—
693C2×#41—612no—
694C2×#41—612no—
695C2×#41—1221no—
696C2×#41—1221no—
697C2×#41—1221no—
698C2×#41—1221no—
699C2×#41—2444no—
700C2×#41—2444no—
701C22×Q8—611no—
702C22×Q8—611no—
703C22×D4—611no—
704C22×D4—611no—
705C22×D4—1221no—
706C22×D4—1221no—
707C22×D4—1221no—
708C22×D4—1221no—
709C22×D4—1221no—
710C22×D4—1221no—
711C23×C4—44no—
712C23×C4—1221no—
713C23×C4—1221no—
714C23×C4D24411yescharacteristic
715C23×C4D24411yescharacteristic
716C23×C4D24411yescharacteristic
717C23×C4D24411yescharacteristic
718C23×C4D24411yescharacteristic
719C23×C4D24411yescharacteristic
720C23×C4D24411yescharacteristic
721C23×C4C22×D6111yescharacteristic
722C23×C4C22×D6111yescharacteristic
723C23×C4C22×D6111yescharacteristic
724C23×C4C22×D6111yescharacteristic
725C23×C4C22×D6111yescharacteristic
726C23×C4C22×D6111yescharacteristic
727C23×C4C22×D6111yescharacteristic
728#137—2444no—
729AGL(1,ℤ/8)—2444no—
730C2×Q16—614no—
731C2×SD16—614no—
732C2×SD16—614no—
733C2×D8—614no—
734C2×M16—44no—
735C2×M16C22×D6112yes—
736C2×M16C22×D6112yes—
737C2×M16C22×D6114yes—
738C22×C8C22×D6114yes—
739#123—1222no—
740#123—1222no—
741#123—1222no—
742#123—1222no—
743#123—1222no—
744#123—1222no—
745#123—1222no—
746#123—1222no—
747C22⋊Q8—612no—
748C22⋊Q8—612no—
749C22⋊Q8—612no—
750C22⋊Q8—612no—
751C22⋊Q8—612no—
752C22⋊Q8—612no—
753C22⋊Q8—612no—
754C22⋊Q8—612no—
755C22⋊Q8—1221no—
756C22⋊Q8—1221no—
757C22⋊Q8—1221no—
758C22⋊Q8—1221no—
759C22⋊Q8—1221no—
760C22⋊Q8—1221no—
761C22⋊Q8—1221no—
762C22⋊Q8—1221no—
763#121—612no—
764#121—612no—
765#121—612no—
766#121—612no—
767#121—612no—
768#121—612no—
769#121—612no—
770#121—612no—
771#121—1221no—
772#121—1221no—
773#121—1221no—
774#121—1221no—
775#121—1221no—
776#121—1221no—
777#121—1221no—
778#121—1221no—
779#120—1222no—
780#120—1222no—
781#120—1222no—
782#120—1222no—
783#120—1222no—
784#120—1222no—
785#120—1222no—
786#120—1222no—
787C4×D4—1222no—
788C4×D4—1222no—
789C4×D4—1222no—
790C4×D4—1222no—
791C4×D4—1222no—
792C4×D4—1222no—
793C4×D4—1222no—
794C4×D4—1222no—
795C4×D4—1222no—
796C4×D4—1222no—
797C4×D4—1222no—
798C4×D4—1222no—
799C4×D4—1222no—
800C4×D4—1222no—
801C4×D4—1222no—
802C4×D4—1222no—
803#117—612no—
804#117—612no—
805#117—612no—
806#117—612no—
807#117—1221no—
808#117—1221no—
809#117—1221no—
810#117—1221no—
811C2×C4⋊C4—611no—
812C2×C4⋊C4—611no—
813C2×C4⋊C4—611no—
814C2×C4⋊C4—611no—
815C2×C4⋊C4—1221no—
816C2×C4⋊C4—1221no—
817C2×C4⋊C4—1221no—
818C2×C4⋊C4—1221no—
819C2×C22⋊C4—1221no—
820C2×C22⋊C4—1221no—
821C2×C22⋊C4—1221no—
822C2×C22⋊C4—1221no—
823C2×C22⋊C4—1221no—
824C2×C22⋊C4—1221no—
825C2×C22⋊C4—1221no—
826C2×C22⋊C4—1221no—
827C2×C22⋊C4—1221no—
828C2×C22⋊C4—1221no—
829C2×C42—1221no—
830C2×C42—1221no—
831#107—614no—
832#107—614no—
833#106—614no—
834#106—614no—
835#103—614no—
836#103—614no—
837#103—614no—
838#103—614no—
839#102—614no—
840#102—614no—
841#102—614no—
842#102—614no—
843C22⋊C8C22×D6112yes—
844C22⋊C8C22×D6112yes—
845C22⋊C8C22×D6112yes—
846C22⋊C8C22×D6112yes—
847C22⋊C8C22×D6114yes—
848C22⋊C8C22×D6114yes—
849C24—42no—
850C24—42no—
851C24—42no—
852C24—1221no—
853C24—1221no—
854C24C2×D24411yescharacteristic
855C24C2×D24411yescharacteristic
856C24C2×D24411yescharacteristic
857C24C2×D24411yescharacteristic
858C24C2×D24411yescharacteristic
859C24C2×D24411yescharacteristic
860C24C2×D24411yescharacteristic
861#41—1224no—
862#41—1224no—
863#41—2442no—
864#41—2444no—
865#41—2444no—
866#41—2442no—
867#41—2444no—
868#41—2444no—
869#41—2444no—
870#41—2444no—
871C2×Q8—612no—
872C2×Q8—612no—
873C2×Q8—1221no—
874C2×Q8—1221no—
875C2×Q8—1224no—
876C2×Q8—2442no—
877C2×D4—612no—
878C2×D4—612no—
879C2×D4—1222no—
880C2×D4—1222no—
881C2×D4—1222no—
882C2×D4—1222no—
883C2×D4—1222no—
884C2×D4—1222no—
885C2×D4—1222no—
886C2×D4—1222no—
887C2×D4—1222no—
888C2×D4—1222no—
889C2×D4—1222no—
890C2×D4—1222no—
891C2×D4—1221no—
892C2×D4—1221no—
893C2×D4—1224no—
894C2×D4—2442no—
895C2×D4—2444no—
896C2×D4—2444no—
897C2×D4—2444no—
898C2×D4—2444no—
899C2×D4—2444no—
900C2×D4—2444no—
901C22×C4—24no—
902C22×C4—24no—
903C22×C4—24no—
904C22×C4—42no—
905C22×C4—42no—
906C22×C4—42no—
907C22×C4—42no—
908C22×C4—42no—
909C22×C4—42no—
910C22×C4—42no—
911C22×C4—42no—
912C22×C4—42no—
913C22×C4—42no—
914C22×C4—42no—
915C22×C4—1221no—
916C22×C4—1221no—
917C22×C4—1221no—
918C22×C4—1221no—
919C22×C4—1221no—
920C22×C4—1221no—
921C22×C4—1222no—
922C22×C4—1222no—
923C22×C4—1222no—
924C22×C4—1222no—
925C22×C4—2444no—
926C22×C4—2444no—
927C22×C4C2×D24411yescharacteristic
928C22×C4C2×D24411yescharacteristic
929C22×C4C2×D24411yescharacteristic
930C22×C4C2×D24411yescharacteristic
931C22×C4C2×D24411yescharacteristic
932C22×C4C2×D24411yescharacteristic
933C22×C4C2×D24411yescharacteristic
934C22×C4C2×D24411yescharacteristic
935C22×C4C2×D24411yescharacteristic
936C22×C4C2×D24411yescharacteristic
937C22×C4C2×D24411yescharacteristic
938C22×C4C2×D24411yescharacteristic
939C22×C4C2×D24411yescharacteristic
940C22×C4C2×D24411yescharacteristic
941C22×C4C2×D24411yescharacteristic
942C22×C4C2×D24411yescharacteristic
943C22×C4C2×D24411yescharacteristic
944C22×C4C2×D24411yescharacteristic
945C22×C4C2×D24411yescharacteristic
946C22×C4C2×D24411yescharacteristic
947C22×C4C2×D24411yescharacteristic
948C22×C4C23×D6111yescharacteristic
949C22×C4C23×D6111yescharacteristic
950C22×C4C23×D6111yescharacteristic
951C22×C4C23×D6111yescharacteristic
952C22×C4C23×D6111yescharacteristic
953C22×C4C23×D6111yescharacteristic
954C22×C4C23×D6111yescharacteristic
955Q16—2444no—
956SD16—2444no—
957SD16—2444no—
958D8—2444no—
959M16—24no—
960M16—24no—
961M16—44no—
962C2×C8—44no—
963C2×C8C23×D6114yes—
964C2×C8C23×D6114yes—
965C4⋊C4—612no—
966C4⋊C4—612no—
967C4⋊C4—612no—
968C4⋊C4—612no—
969C4⋊C4—1221no—
970C4⋊C4—1221no—
971C4⋊C4—1221no—
972C4⋊C4—1221no—
973C4⋊C4—1222no—
974C4⋊C4—1222no—
975C4⋊C4—1222no—
976C4⋊C4—1222no—
977C4⋊C4—1222no—
978C4⋊C4—1222no—
979C4⋊C4—1222no—
980C4⋊C4—1222no—
981C22⋊C4—1222no—
982C22⋊C4—1222no—
983C22⋊C4—1222no—
984C22⋊C4—1222no—
985C22⋊C4—1222no—
986C22⋊C4—1222no—
987C22⋊C4—1222no—
988C22⋊C4—1222no—
989C22⋊C4—1222no—
990C22⋊C4—1222no—
991C22⋊C4—1222no—
992C22⋊C4—1222no—
993C22⋊C4—1222no—
994C22⋊C4—1222no—
995C22⋊C4—1222no—
996C22⋊C4—1222no—
997C22⋊C4—1222no—
998C22⋊C4—1222no—
999C22⋊C4—1222no—
1000C22⋊C4—1222no—
1001C42—1222no—
1002C42—1222no—
1003C42—1222no—
1004C42—1222no—
1005C23—22no—
1006C23—22no—
1007C23—22no—
1008C23—22no—
1009C23—22no—
1010C23—22no—
1011C23—22no—
1012C23—22no—
1013C23—22no—
1014C23—41no—
1015C23—41no—
1016C23—41no—
1017C23—41no—
1018C23—41no—
1019C23—41no—
1020C23—41no—
1021C23—41no—
1022C23—41no—
1023C23—41no—
1024C23—41no—
1025C23—41no—
1026C23—416no—
1027C23—1222no—
1028C23—1222no—
1029C23—2442no—
1030C23—2442no—
1031C23—2442no—
1032C23—2442no—
1033C23—2442no—
1034C23—2442no—
1035C23C22×D24411yescharacteristic
1036C23C22×D24411yescharacteristic
1037C23C22×D24411yescharacteristic
1038C23C22×D24411yescharacteristic
1039C23C22×D24411yescharacteristic
1040C23C22×D24411yescharacteristic
1041C23C22×D24411yescharacteristic
1042Q8—1222no—
1043Q8—1224no—
1044Q8—1222no—
1045Q8—2442no—
1046Q8—2442no—
1047D4—1222no—
1048D4—1224no—
1049D4—1222no—
1050D4—2442no—
1051D4—2444no—
1052D4—2444no—
1053D4—2444no—
1054D4—2444no—
1055D4—2444no—
1056D4—2444no—
1057D4—2444no—
1058D4—2444no—
1059D4—2444no—
1060D4—2444no—
1061D4—2444no—
1062D4—2444no—
1063D4—2442no—
1064C2×C4—22no—
1065C2×C4—22no—
1066C2×C4—22no—
1067C2×C4—22no—
1068C2×C4—22no—
1069C2×C4—22no—
1070C2×C4—22no—
1071C2×C4—22no—
1072C2×C4—22no—
1073C2×C4—22no—
1074C2×C4—22no—
1075C2×C4—22no—
1076C2×C4—22no—
1077C2×C4—22no—
1078C2×C4—22no—
1079C2×C4—41no—
1080C2×C4—41no—
1081C2×C4—41no—
1082C2×C4—41no—
1083C2×C4—41no—
1084C2×C4—41no—
1085C2×C4—41no—
1086C2×C4—41no—
1087C2×C4—41no—
1088C2×C4—41no—
1089C2×C4—41no—
1090C2×C4—41no—
1091C2×C4—1222no—
1092C2×C4—1222no—
1093C2×C4—1222no—
1094C2×C4—1222no—
1095C2×C4—1222no—
1096C2×C4—1222no—
1097C2×C4—2444no—
1098C2×C4—2444no—
1099C2×C4—2444no—
1100C2×C4—2442no—
1101C2×C4—2442no—
1102C2×C4—2442no—
1103C2×C4—2442no—
1104C2×C4—2442no—
1105C2×C4—2442no—
1106C2×C4—2444no—
1107C2×C4C22×D24411yescharacteristic
1108C2×C4C22×D24411yescharacteristic
1109C2×C4C22×D24411yescharacteristic
1110C2×C4C22×D24411yescharacteristic
1111C2×C4C22×D24411yescharacteristic
1112C2×C4C22×D24411yescharacteristic
1113C2×C4C22×D24411yescharacteristic
1114C2×C4#1451982214yes—
1115C2×C4C24×D6111yescharacteristic
1116C8—24no—
1117C8—24no—
1118C22—21no—
1119C22—21no—
1120C22—21no—
1121C22—21no—
1122C22—21no—
1123C22—21no—
1124C22—21no—
1125C22—21no—
1126C22—21no—
1127C22—21no—
1128C22—21no—
1129C22—21no—
1130C22—21no—
1131C22—21no—
1132C22—21no—
1133C22—21no—
1134C22—21no—
1135C22—21no—
1136C22—44no—
1137C22—44no—
1138C22—44no—
1139C22—44no—
1140C22—44no—
1141C22—44no—
1142C22—44no—
1143C22—4884no—
1144C22—4884no—
1145C22—2442no—
1146C22—2442no—
1147C22—2442no—
1148C22—2442no—
1149C22—2442no—
1150C22—2442no—
1151C22#1684032412yes—
1152C22#1684056212yes—
1153C22#1684056212yes—
1154C22C23×D24411yescharacteristic
1155C4—21no—
1156C4—21no—
1157C4—21no—
1158C4—21no—
1159C4—21no—
1160C4—21no—
1161C4—2442no—
1162C4—2442no—
1163C4—2442no—
1164C4—2442no—
1165C4—2442no—
1166C4—2442no—
1167C4#1684032412yes—
1168C4C2×#1451982212yes—
1169C2—22no—
1170C2—22no—
1171C2—22no—
1172C2—41no—
1173C2—41no—
1174C2—41no—
1175C2—41no—
1176C2—4882no—
1177C2—4882no—
1178C2C2×#1684032411yescharacteristic
1179C2C2×#1684056211yescharacteristic
1180C2C2×#1684056211yescharacteristic
subgroupG/H
centerC22C23×D244
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#407C2
socleC22×C61C23×D4
hypercenterC2×#407D61
hypocenterC61#60752
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C24×C4 ◁ C2×#407

Complements

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

NH ≅ G/Ntype
1. C2×#16840273C2semidirect
2. C2×#16840273C2semidirect
3. #21456661C2semidirect
4. #21456651C2semidirect
5. #21456635C2semidirect
6. #21456612C2semidirect
7. #21456602C2semidirect
8. #21456586C2semidirect
9. #21455768C2semidirect
10. #21455760C2semidirect
11. #21455752C2semidirect
12. #21455449C2semidirect
13. #21455438C2semidirect
14. #21455081C2semidirect
15. #21455073C2semidirect
16. #21455064C2semidirect
17. C2×C61×#407C2semidirect
19. C22×#11758222C22semidirect
20. C2×#14519810C22semidirect
21. C2×#14519805C22semidirect
34. #16840273C22semidirect
35. #16840273C22semidirect
36. #16840273C22semidirect
37. #16840273C22semidirect
41. C2×#14519756C22semidirect
42. C2×#14519756C22semidirect
43. C2×#14519756C22semidirect
45. C2×#14519751C22semidirect
46. C2×#14519751C22semidirect
47. C2×#14519751C22semidirect
55. C2×#14519736C22semidirect
56. #16840104C22semidirect
57. #16840104C22semidirect
58. #16840104C22semidirect
59. #16840098C22semidirect
60. #16840093C22semidirect
61. #16840087C22semidirect
62. #16840087C22semidirect
63. #16840087C22semidirect
64. #16840081C22semidirect
65. #16840076C22semidirect
66. #16840020C22semidirect
67. #16840015C22semidirect
68. #16840008C22semidirect
69. #16840008C22semidirect
70. #16840003C22semidirect
71. #16839998C22semidirect
72. #16839991C22semidirect
73. #16839991C22semidirect
74. #16839926C22semidirect
75. #16839926C22semidirect
76. #16839926C22semidirect
77. #16839920C22semidirect
78. #16839915C22semidirect
79. #16839909C22semidirect
80. #16839909C22semidirect
81. #16839909C22semidirect
82. #16839903C22semidirect
83. #16839898C22semidirect
84. #16839804C22semidirect
85. #16839804C22semidirect
86. #16839772C22semidirect
87. #16839768C22semidirect
88. #16839764C22semidirect
89. #16839764C22semidirect
91. C22×M16×C61C22semidirect
94. C61×#407C22semidirect
95. C61×#407C22semidirect
96. C61×#407C22semidirect
97. C2×C22⋊C8×C61C22semidirect
98. C2×C22⋊C8×C61C22semidirect
123. C2×Dic244C23semidirect
124. C2×#11758190C23semidirect
125. C2×#11758190C23semidirect
126. C2×D488C23semidirect
219. #14519711C23semidirect
220. #14519711C23semidirect
221. #14519709C23semidirect
222. #14519709C23semidirect
223. #14519702C23semidirect
224. #14519702C23semidirect
225. #14519702C23semidirect
226. #14519702C23semidirect
227. #14519699C23semidirect
228. #14519699C23semidirect
229. #14519699C23semidirect
230. #14519699C23semidirect
595. C2×#407D61semidirect
613. C22×M16C2×D61semidirect
684. #407C2×D61semidirect
685. #407C2×D61semidirect
686. #407C2×D61semidirect
687. C2×C22⋊C8C2×D61semidirect
688. C2×C22⋊C8C2×D61semidirect
689. C61#60752semidirect

Maximal subgroups

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

subgroupindex
C2×#168402732
#214566612
#214566512
#214566352
#214566122
#214566022
#214565862
#214557682
#214557602
#214557522
#214554492
#214554382
#214550812
#214550732
#214550642
C2×C61×#4072
#6075261