Finite Group Databasebeta

← D61×#3213 #30551254

Subgroups — D61×#3213 #30551254

Order 15616.

2522 conjugacy classes of subgroups.

The subgroup lattice has 1124 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#532×D61C211yesmaximal, characteristic, complemented
2C2×#124×D61C211yesmaximal, characteristic, complemented
3#21456808C211yesmaximal, characteristic, complemented
4#21456807C212yesmaximal, complemented
5#21456806C211yesmaximal, characteristic, complemented
6#21456805C212yesmaximal, complemented
7#21456804C214yesmaximal, complemented
8#21456803C212yesmaximal, complemented
9#21456802C211yesmaximal, characteristic, complemented
10#21456801C212yesmaximal, complemented
11#496×D61C212yesmaximal, complemented
12#489×D61C212yesmaximal, complemented
13#463×D61C214yesmaximal, complemented
14#448×D61C212yesmaximal, complemented
15#447×D61C212yesmaximal, complemented
16#432×D61C211yesmaximal, characteristic, complemented
17C61×#3213C211yesmaximal, characteristic, complemented
18C2×#41×D61—21no—
19C22×Q8×D61C2211yescharacteristic
20C22×D4×D61C2211yescharacteristic
21C2×SD16×D61C2214yescomplemented
22C2×D8×D61C2214yes—
23#16840313C2211yescharacteristic, complemented
24#16840312C2211yescharacteristic, complemented
25#16840311—21no—
26#16840310C2211yescharacteristic, complemented
27#16840309—21no—
28#16840309C2212yescomplemented
29#16840308—21no—
30#16840307—21no—
31#16840307C2212yescomplemented
32C4⋊Q8×D61C2211yescharacteristic, complemented
33#127×D61C2211yescharacteristic, complemented
34C2×#14519766C2211yescharacteristic, complemented
35C2×#14519765C2211yescharacteristic, complemented
36C2×#14519764C2211yescharacteristic, complemented
37C2×#14519763—21no—
38C2×#14519763—21no—
39#124×D61—21no—
40#124×D61—21no—
41#124×D61—21no—
42#124×D61—21no—
43#124×D61—21no—
44#124×D61C2212yes—
45#124×D61C2212yes—
46#124×D61C2212yescomplemented
47#124×D61C2212yescomplemented
48#121×D61—21no—
49#121×D61C2212yes—
50C4×D4×D61—21no—
51C4×D4×D61C2212yescomplemented
52C2×C22⋊C4×D61—21no—
53C2×C22⋊C4×D61—21no—
54C2×C42×D61C2211yescharacteristic
55#16840152C2212yescomplemented
56#16840151C2212yescomplemented
57#16840150C2214yescomplemented
58#16840149C2212yescomplemented
59#16840148C2214yescomplemented
60#16840124C2212yescomplemented
61#16840123C2214yescomplemented
62#16840122C2212yescomplemented
63#16840121C2212yescomplemented
64#16840120C2214yescomplemented
65#16839980C2214yescomplemented
66#16839979C2214yescomplemented
67#16839978C2214yescomplemented
68#16839977C2214yescomplemented
69#16839976C2214yescomplemented
70#16839975C2214yescomplemented
71#16839974C2214yescomplemented
72#16839903C2212yescomplemented
73#16839902C2214yescomplemented
74#16839901C2212yescomplemented
75#16839900C2212yescomplemented
76#16839899C2214yescomplemented
77#16839898C2212yescomplemented
78#16839897C2214yescomplemented
79#16839896C2212yescomplemented
80#16839895C2212yescomplemented
81#16839894C2214yescomplemented
82#16839819C2211yescharacteristic, complemented
83#16839818C2212yescomplemented
84#16839817C2212yescomplemented
85#16839816C2212yescomplemented
86C4⋊C8×D61C2212yescomplemented
87#103×D61C2214yescomplemented
88#102×D61C2214yes—
89C22⋊C8×D61C2212yes—
90#97×D61C2212yescomplemented
91C61×#532C2211yescharacteristic, complemented
92C2×#124×C61C2211yescharacteristic, complemented
93C61×#496C2212yescomplemented
94C61×#489C2212yescomplemented
95C61×#463C2214yescomplemented
96C61×#448C2212yescomplemented
97C61×#447C2212yescomplemented
98C61×#432C2211yescharacteristic, complemented
99C24×D61—21no—
100C2×#11758226—21no—
101C2×#11758222—21no—
102C2×#11758222—22no—
103C2×#11758224—22no—
104C2×#11758224—21no—
105#41×D61—48no—
106C22×Dic122—21no—
107C22×Dic122C2311yescharacteristic
108C2×Q8×D61—21no—
109C2×Q8×D61—21no—
110C2×Q8×D61—21no—
111C2×Q8×D61—44no—
112C2×Q8×D61C2312yes—
113C2×Q8×D61C2312yes—
114C22×D244C2311yescharacteristic
115C22×C22⋊D61—21no—
116C2×D4×D61—22no—
117C2×D4×D61—21no—
118C2×D4×D61—21no—
119C2×D4×D61—21no—
120C2×D4×D61—21no—
121C2×D4×D61—44no—
122C2×D4×D61C2312yes—
123C2×D4×D61C2312yes—
124C2×D4×D61C2312yes—
125C22×C4×D61—21no—
126C22×C4×D61—22no—
127C22×C4×D61D411yescharacteristic
128C22×C4×D61D411yescharacteristic
129C22×C4×D61C2311yescharacteristic
130C2×#11758190C2314yescomplemented
131C2×#11758200C2314yescomplemented
132C2×#11758201C2314yescomplemented
133SD16×D61—48no—
134C2×D488C2314yes—
135C2×#11758199C2314yes—
136C2×#11758199C2314yes—
137D8×D61—48no—
138C2×C8×D61C2314yes—
139#14519777C2311yescharacteristic, complemented
140#14519776—21no—
141#14519776C2312yescomplemented
142#14519775—21no—
143#14519774C2311yescharacteristic, complemented
144#14519773—21no—
145#14519773—21no—
146#14519773C2312yescomplemented
147#14519766—21no—
148#14519766—21no—
149#14519766—21no—
150#14519766C2312yes—
151#14519766C2312yes—
152#14519765—21no—
153#14519765—21no—
154#14519765—21no—
155#14519765C2312yes—
156#14519765C2312yes—
157#14519764—21no—
158#14519764—21no—
159#14519764—21no—
160#14519764C2312yes—
161#14519764C2312yes—
162#14519763—22no—
163#14519763—22no—
164#14519763—22no—
165#14519763—22no—
166#14519763—22no—
167#14519763—22no—
168#14519763—22no—
169#14519763—22no—
170#14519763—22no—
171#14519763—22no—
172#14519752—21no—
173#14519752C2312yes—
174#14519751—21no—
175#14519751C2312yes—
176#14519750—22no—
177#14519750—22no—
178#14519749—22no—
179#14519749—22no—
180#14519748—21no—
181#14519748C2312yes—
182C4×D244—21no—
183C4×D244C2312yescomplemented
184D4×Dic61—21no—
185D4×Dic61C2312yescomplemented
186#14519739—21no—
187#14519739C2312yescomplemented
188C4×C22⋊D61—22no—
189C4×C22⋊D61—22no—
190#14519737—22no—
191#14519737—22no—
192C4⋊C4×D61—21no—
193C4⋊C4×D61C2312yes—
194C2×C22⋊Dic61—21no—
195C2×C22⋊Dic61—21no—
196C2×#11758198—21no—
197C2×#11758198—21no—
198C2×#11758198—21no—
199C2×#11758198—21no—
200C22⋊C4×D61—22no—
201C22⋊C4×D61—22no—
202C22⋊C4×D61—22no—
203C22⋊C4×D61—22no—
204C22⋊C4×D61—22no—
205C22⋊C4×D61—22no—
206C22⋊C4×D61—22no—
207C22⋊C4×D61—22no—
208C22⋊C4×D61—22no—
209C22⋊C4×D61—22no—
210C2×C4×Dic61D411yescharacteristic
211C2×C4×Dic61D411yescharacteristic
212C2×C4×Dic61C2311yescharacteristic
213C42×D61D411yescharacteristic
214C42×D61D411yescharacteristic
215C42×D61D411yescharacteristic
216C42×D61D411yescharacteristic
217C42×D61C2311yescharacteristic
218C42×D61C2311yescharacteristic
219C42×D61C2311yescharacteristic
220C42×D61C2311yescharacteristic
221C4⋊#92418C2312yescomplemented
222#14519706C2314yescomplemented
223#14519702C2314yescomplemented
224#14519701C2314yescomplemented
225#14519700C2314yescomplemented
226#14519699C2314yes—
227#14519698C2314yes—
228#14519697C2314yes—
229C22⋊#92418C2312yes—
230#14519689C2314yes—
231#14519688C2312yescomplemented
232#14519687C2314yescomplemented
233C2×#41×C61—21no—
234C22×Q8×C61C2311yescharacteristic
235C22×D4×C61C2311yescharacteristic
236C2×SD16×C61C2314yescomplemented
237C2×D8×C61C2314yes—
238C4⋊Q8×C61C2311yescharacteristic, complemented
239#127×C61C2311yescharacteristic, complemented
240#124×C61—21no—
241#124×C61—21no—
242#124×C61—21no—
243#124×C61C2312yes—
244#124×C61C2312yes—
245#121×C61—21no—
246#121×C61C2312yes—
247C4×D4×C61—21no—
248C4×D4×C61C2312yescomplemented
249C2×C22⋊C4×C61—21no—
250C2×C22⋊C4×C61—21no—
251C2×C42×C61C2311yescharacteristic
252C4⋊C8×C61C2312yescomplemented
253#103×C61C2314yescomplemented
254#102×C61C2314yes—
255C22⋊C8×C61C2312yes—
256#97×C61C2312yescomplemented
257C24×C61—21no—
258C23×D61—21no—
259C23×D61—22no—
260C23×D61—22no—
261C23×D61—22no—
262C23×D61—44no—
263C23×D61—44no—
264C23×D61—44no—
265C23×D61C2×D411yescharacteristic
266#41×C61—44no—
267C2×Q8×C61—21no—
268C2×Q8×C61—21no—
269C2×Q8×C61—42no—
270C2×Q8×C61C2412yes—
271C2×D4×C61—22no—
272C2×D4×C61—21no—
273C2×D4×C61—21no—
274C2×D4×C61—21no—
275C2×D4×C61—42no—
276C2×D4×C61C2412yes—
277C2×D4×C61C2412yes—
278C22×C4×C61—21no—
279C22×C4×C61—22no—
280C22×C4×C61C2×D411yescharacteristic
281C22×C4×C61C2×D411yescharacteristic
282C22×C4×C61C2411yescharacteristic
283C2×C22⋊D61—22no—
284C2×C22⋊D61—22no—
285C2×C22⋊D61—22no—
286C2×C22⋊D61—22no—
287C2×C22⋊D61—22no—
288C2×C22⋊D61—22no—
289C2×C22⋊D61—22no—
290C2×C22⋊D61—44no—
291C22×Dic61—21no—
292C22×Dic61—22no—
293C22×Dic61C2×D411yescharacteristic
294C22×Dic61C2×D411yescharacteristic
295C22×Dic61C2×D411yescharacteristic
296#11758226—44no—
297Q8×D61—28no—
298Q8×D61—44no—
299Q8×D61—44no—
300Q8×D61—44no—
301Q8×D61—44no—
302#11758224—44no—
303#11758224—48no—
304D4×D61—28no—
305D4×D61—28no—
306D4×D61—44no—
307D4×D61—44no—
308D4×D61—44no—
309D4×D61—44no—
310D4×D61—44no—
311D4×D61—48no—
312#11758222—48no—
313#11758222—44no—
314C2×D244—22no—
315C2×D244—21no—
316C2×D244—21no—
317C2×D244—21no—
318C2×D244—42no—
319C2×D244C2412yes—
320C2×D244C2412yes—
321C2×C4×D61—24no—
322C2×C4×D61—24no—
323C2×C4×D61—22no—
324C2×C4×D61—22no—
325C2×C4×D61—22no—
326C2×C4×D61—22no—
327C2×C4×D61—22no—
328C2×C4×D61—42no—
329C2×C4×D61—48no—
330C2×C4×D61—44no—
331C2×C4×D61C2×D411yescharacteristic
332C2×C4×D61C2×D411yescharacteristic
333C2×C4×D61C2×D411yescharacteristic
334C2×C4×D61C2×D411yescharacteristic
335C2×C4×D61C2×D411yescharacteristic
336C2×C4×D61C2×D411yescharacteristic
337C2×C4×D61C2×D411yescharacteristic
338C2×C4×D61C2×D411yescharacteristic
339C2×C4×D61C2×D411yescharacteristic
340C2×C4×D61C2×D411yescharacteristic
341C2×C4×D61C2411yescharacteristic
342C2×C4×D61C2411yescharacteristic
343C2×Dic122—21no—
344C2×Dic122—21no—
345C2×Dic122—22no—
346C2×Dic122—22no—
347C2×Dic122—22no—
348C2×Dic122—42no—
349C2×Dic122—44no—
350C2×Dic122C2412yes—
351SD16×C61—44no—
352D8×C61—44no—
353C2×C8×C61C2414yes—
354C4⋊C4×C61—21no—
355C4⋊C4×C61C2412yes—
356C22⋊C4×C61—22no—
357C22⋊C4×C61—22no—
358C22⋊C4×C61—22no—
359C22⋊C4×C61—22no—
360C22⋊C4×C61—22no—
361C22⋊C4×C61—22no—
362C42×C61C2×D411yescharacteristic
363C42×C61C2×D411yescharacteristic
364C42×C61C2411yescharacteristic
365C42×C61C2411yescharacteristic
366C22⋊Dic61—22no—
367C22⋊Dic61—22no—
368C22⋊Dic61—22no—
369C22⋊Dic61—22no—
370C22⋊Dic61—22no—
371C22⋊Dic61—22no—
372#11758201—44no—
373#11758200—44no—
374#11758199—44no—
375#11758199—44no—
376#11758198—22no—
377#11758198—22no—
378#11758198—22no—
379#11758198—22no—
380#11758198—22no—
381#11758198—22no—
382#11758198—22no—
383#11758198—22no—
384#11758198—22no—
385#11758198—22no—
386#11758198—22no—
387#11758198—22no—
388C4⋊Dic61—21no—
389C4⋊Dic61C2412yes—
390#11758196—22no—
391#11758196—22no—
392C4×Dic61C2×D411yescharacteristic
393C4×Dic61C2×D411yescharacteristic
394C4×Dic61C2×D411yescharacteristic
395C4×Dic61C2×D411yescharacteristic
396C4×Dic61C2×D411yescharacteristic
397C4×Dic61C2×D411yescharacteristic
398C4×Dic61C2×D411yescharacteristic
399C4×Dic61C2×D411yescharacteristic
400C4×Dic61C2×D411yescharacteristic
401C4×Dic61C2×D411yescharacteristic
402C4×Dic61C2411yescharacteristic
403C4×Dic61C2411yescharacteristic
404C2×#92418C2414yes—
405D488—44no—
406#11758190—44no—
407C8×D61—28no—
408C23×C61—22no—
409C23×C61—22no—
410C23×C61—42no—
411C23×C61—42no—
412C23×C61—42no—
413C23×C61C22×D411yescharacteristic
414C22×D61—22no—
415C22×D61—22no—
416C22×D61—22no—
417C22×D61—22no—
418C22×D61—44no—
419C22×D61—44no—
420C22×D61—42no—
421C22×D61—42no—
422C22×D61—42no—
423C22×D61—44no—
424C22×D61—44no—
425C22×D61—44no—
426C22×D61—44no—
427C22×D61—44no—
428C22×D61—44no—
429C22×D61—44no—
430C22×D61—816no—
431C22×D61AGL(1,ℤ/8)14yes—
432C22×D61C22×D411yescharacteristic
433C22×D61C22×D411yescharacteristic
434Q8×C61—24no—
435Q8×C61—42no—
436Q8×C61—42no—
437D4×C61—24no—
438D4×C61—24no—
439D4×C61—42no—
440D4×C61—42no—
441D4×C61—42no—
442D4×C61—44no—
443C2×C4×C61—22no—
444C2×C4×C61—22no—
445C2×C4×C61—22no—
446C2×C4×C61—22no—
447C2×C4×C61—41no—
448C2×C4×C61—44no—
449C2×C4×C61—42no—
450C2×C4×C61C22×D411yescharacteristic
451C2×C4×C61C22×D411yescharacteristic
452C2×C4×C61C22×D411yescharacteristic
453C2×C4×C61C22×D411yescharacteristic
454C2×C4×C61C22×D411yescharacteristic
455C2×C4×C61C2511yescharacteristic
456C22⋊D61—44no—
457C22⋊D61—44no—
458C22⋊D61—44no—
459C22⋊D61—44no—
460C22⋊D61—44no—
461C22⋊D61—44no—
462C22⋊D61—44no—
463C2×Dic61—22no—
464C2×Dic61—22no—
465C2×Dic61—22no—
466C2×Dic61—22no—
467C2×Dic61—41no—
468C2×Dic61—44no—
469C2×Dic61—42no—
470C2×Dic61C22×D411yescharacteristic
471C2×Dic61C22×D411yescharacteristic
472C2×Dic61C22×D411yescharacteristic
473C2×Dic61C22×D411yescharacteristic
474C2×Dic61C22×D411yescharacteristic
475C2×Dic61C22×D411yescharacteristic
476D244—24no—
477D244—24no—
478D244—42no—
479D244—42no—
480D244—42no—
481D244—44no—
482C4×D61—22no—
483C4×D61—22no—
484C4×D61—22no—
485C4×D61—22no—
486C4×D61—22no—
487C4×D61—22no—
488C4×D61—22no—
489C4×D61—22no—
490C4×D61—22no—
491C4×D61—41no—
492C4×D61—41no—
493C4×D61—44no—
494C4×D61—44no—
495C4×D61—44no—
496C4×D61—44no—
497C4×D61—44no—
498C4×D61H(5,𝔽2)14yes—
499Dic122—24no—
500Dic122—44no—
501Dic122—44no—
502Dic122—42no—
503Dic122—42no—
504Dic122—44no—
505C8×C61—24no—
506#92418—24no—
507C2×#3213—611nomaximal, Sylow
508C22×C61—21no—
509C22×C61—21no—
510C22×C61—42no—
511C22×C61—42no—
512C22×C61—42no—
513C22×C61—42no—
514C22×C61—42no—
515C22×C61—42no—
516C22×C61—84no—
517C22×C61C2×AGL(1,ℤ/8)12yes—
518C22×C61C23×D411yescharacteristic
519C2×D61—21no—
520C2×D61—21no—
521C2×D61—28no—
522C2×D61—42no—
523C2×D61—42no—
524C2×D61—42no—
525C2×D61—42no—
526C2×D61—42no—
527C2×D61—42no—
528C2×D61—88no—
529C2×D61—84no—
530C2×D61—88no—
531C2×D61—88no—
532C2×D61#53512yes—
533C2×D61C2×AGL(1,ℤ/8)12yes—
534C2×D61C2×AGL(1,ℤ/8)12yes—
535C2×D61#57512yes—
536C4×C61—21no—
537C4×C61—21no—
538C4×C61—21no—
539C4×C61—21no—
540C4×C61—21no—
541C4×C61—42no—
542C4×C61—42no—
543C4×C61C2×H(5,𝔽2)12yes—
544Dic61—21no—
545Dic61—21no—
546Dic61—21no—
547Dic61—21no—
548Dic61—21no—
549Dic61—42no—
550Dic61—42no—
551Dic61#53512yes—
552C2×#532—611no—
553C22×#124—611no—
554#3213—612no—
555#3213—612no—
556#3213—614no—
557#3213—612no—
558#3213—612no—
559#3213—611no—
560#3213—611no—
561#3213—611no—
562#3213D6111yescharacteristic, direct product factor
563C2×#496—612no—
564C2×#489—612no—
565C2×#463—614no—
566C2×#448—612no—
567C2×#447—612no—
568C2×#432—611no—
569C2×C61—22no—
570C2×C61—82no—
571C2×C61—82no—
572C2×C61C2×#53511yescharacteristic
573C2×C61C22×AGL(1,ℤ/8)11yescharacteristic
574C2×C61C2×#57511yescharacteristic
575D61—22no—
576D61—82no—
577D61—82no—
578D61#321314yesdirect product factor
579C22×#41—1221no—
580C23×Q8—611no—
581C23×D4—611no—
582C22×SD16—614no—
583C22×D8—614no—
584#532—611no—
585#532—611no—
586#532—612no—
587#532—612no—
588#532—611no—
589#532—1221no—
590#532—1221no—
591#532—1221no—
592#532—1221no—
593#532C2×D6111yescharacteristic, complemented
594C2×C4⋊Q8—611no—
595C2×#127—611no—
596C2×#124—611no—
597C2×#124—611no—
598C2×#124—612no—
599C2×#124—612no—
600C2×#124—612no—
601C2×#124—612no—
602C2×#124—611no—
603C2×#124—1221no—
604C2×#124—1221no—
605C2×#124—1221no—
606C2×#124—1221no—
607C2×#124—1221no—
608C2×#124—1221no—
609C2×#124—1221no—
610C2×#124C2×D6111yescharacteristic, complemented
611C2×#121—612no—
612C2×#121—1221no—
613C2×C4×D4—612no—
614C2×C4×D4—1221no—
615C22×C22⋊C4—1221no—
616C22×C22⋊C4—1221no—
617C22×C42—611no—
618#496—614no—
619#496—614no—
620#496—612no—
621#496—612no—
622#496—612no—
623#496C2×D6112yescomplemented
624#489—612no—
625#489—612no—
626#489—614no—
627#489—614no—
628#489—612no—
629#489C2×D6112yescomplemented
630#463—614no—
631#463—614no—
632#463—614no—
633#463—614no—
634#463—614no—
635#463—614no—
636#463—614no—
637#463C2×D6114yescomplemented
638#448—612no—
639#448—614no—
640#448—612no—
641#448—614no—
642#448—612no—
643#448C2×D6112yescomplemented
644#447—612no—
645#447—614no—
646#447—612no—
647#447—614no—
648#447—612no—
649#447C2×D6112yescomplemented
650#432—611no—
651#432—612no—
652#432—612no—
653#432—612no—
654#432C2×D6111yescharacteristic, complemented
655C2×C4⋊C8—612no—
656C2×#103—614no—
657C2×#102—614no—
658C2×C22⋊C8—612no—
659C2×#97—612no—
660C61C2×#321311yescharacteristic, complemented, Sylow
661C25—1221no—
662C2×#41—21no—
663C2×#41—1222no—
664C2×#41—1222no—
665C2×#41—1221no—
666C2×#41—1221no—
667C2×#41—1221no—
668C2×#41—2448no—
669C22×Q8—612no—
670C22×Q8—612no—
671C22×Q8—611no—
672C22×Q8—1221no—
673C22×Q8—1221no—
674C22×Q8—1221no—
675C22×Q8—1221no—
676C22×Q8—2444no—
677C22×Q8C22×D6111yescharacteristic
678C22×D4—612no—
679C22×D4—612no—
680C22×D4—612no—
681C22×D4—611no—
682C22×D4—1221no—
683C22×D4—1221no—
684C22×D4—1221no—
685C22×D4—1221no—
686C22×D4—1221no—
687C22×D4—1222no—
688C22×D4—2444no—
689C22×D4C22×D6111yescharacteristic
690C23×C4—611no—
691C23×C4—611no—
692C23×C4—611no—
693C23×C4—1222no—
694C23×C4—1221no—
695C2×SD16—614no—
696C2×SD16—614no—
697C2×SD16—614no—
698C2×SD16—2448no—
699C2×SD16C22×D6114yescomplemented
700C2×D8—614no—
701C2×D8—614no—
702C2×D8—614no—
703C2×D8—2448no—
704C2×D8C22×D6114yes—
705C22×C8—614no—
706C4⋊Q8—612no—
707C4⋊Q8—611no—
708C4⋊Q8—1221no—
709C4⋊Q8—1221no—
710C4⋊Q8C22×D6111yescharacteristic, complemented
711#127—612no—
712#127—611no—
713#127—1221no—
714#127—1221no—
715#127C22×D6111yescharacteristic, complemented
716#124—21no—
717#124—21no—
718#124—21no—
719#124—612no—
720#124—612no—
721#124—612no—
722#124—612no—
723#124—612no—
724#124—612no—
725#124—1222no—
726#124—1222no—
727#124—1222no—
728#124—1222no—
729#124—1222no—
730#124—1222no—
731#124—1222no—
732#124—1222no—
733#124—1222no—
734#124—1222no—
735#124—1221no—
736#124—1221no—
737#124—1221no—
738#124—1221no—
739#124—1221no—
740#124—1221no—
741#124—1221no—
742#124—1221no—
743#124—1221no—
744#124C22×D6112yes—
745#124C22×D6112yes—
746#121—21no—
747#121—612no—
748#121—612no—
749#121—612no—
750#121—1222no—
751#121—1222no—
752#121—1221no—
753#121—1222no—
754#121—1221no—
755#121—1222no—
756#121—1221no—
757#121C22×D6112yes—
758C4×D4—21no—
759C4×D4—612no—
760C4×D4—612no—
761C4×D4—612no—
762C4×D4—1222no—
763C4×D4—1222no—
764C4×D4—1221no—
765C4×D4—1222no—
766C4×D4—1222no—
767C4×D4—1221no—
768C4×D4—1221no—
769C4×D4C22×D6112yescomplemented
770C2×C4⋊C4—612no—
771C2×C4⋊C4—1221no—
772C2×C22⋊C4—21no—
773C2×C22⋊C4—21no—
774C2×C22⋊C4—1222no—
775C2×C22⋊C4—1222no—
776C2×C22⋊C4—1222no—
777C2×C22⋊C4—1222no—
778C2×C22⋊C4—1222no—
779C2×C22⋊C4—1222no—
780C2×C22⋊C4—1222no—
781C2×C22⋊C4—1222no—
782C2×C22⋊C4—1222no—
783C2×C22⋊C4—1222no—
784C2×C22⋊C4—1221no—
785C2×C22⋊C4—1221no—
786C2×C22⋊C4—1221no—
787C2×C22⋊C4—1221no—
788C2×C22⋊C4—1221no—
789C2×C22⋊C4—1221no—
790C2×C42—611no—
791C2×C42—611no—
792C2×C42—611no—
793C2×C42—611no—
794C2×C42—611no—
795C2×C42—611no—
796C2×C42—611no—
797C2×C42—611no—
798C2×C42—611no—
799C2×C42—611no—
800C2×C42—611no—
801C2×C42C22×D6111yescharacteristic
802C4⋊C8—614no—
803C4⋊C8—612no—
804C4⋊C8C22×D6112yescomplemented
805#103—614no—
806#103—614no—
807#103—614no—
808#103C22×D6114yescomplemented
809#102—614no—
810#102—614no—
811#102—614no—
812#102C22×D6114yes—
813C22⋊C8—612no—
814C22⋊C8—614no—
815C22⋊C8C22×D6112yes—
816#97—614no—
817#97—612no—
818#97C22×D6112yescomplemented
819C24—21no—
820C24—611no—
821C24—1222no—
822C24—1222no—
823C24—1222no—
824C24—1221no—
825C24—2444no—
826C24—2444no—
827C24—2444no—
828#41—44no—
829#41—2444no—
830#41—2448no—
831#41—2444no—
832#41—2448no—
833#41—2444no—
834C2×Q8—21no—
835C2×Q8—21no—
836C2×Q8—42no—
837C2×Q8—612no—
838C2×Q8—1222no—
839C2×Q8—1222no—
840C2×Q8—1222no—
841C2×Q8—1228no—
842C2×Q8—1221no—
843C2×Q8—1221no—
844C2×Q8—2442no—
845C2×Q8—2444no—
846C2×Q8—2444no—
847C2×Q8—2444no—
848C2×Q8—2444no—
849C2×Q8—2444no—
850C2×Q8C23×D6112yes—
851C2×D4—22no—
852C2×D4—21no—
853C2×D4—21no—
854C2×D4—21no—
855C2×D4—42no—
856C2×D4—612no—
857C2×D4—612no—
858C2×D4—1222no—
859C2×D4—1228no—
860C2×D4—1228no—
861C2×D4—1222no—
862C2×D4—1222no—
863C2×D4—1222no—
864C2×D4—1222no—
865C2×D4—1222no—
866C2×D4—1222no—
867C2×D4—1222no—
868C2×D4—1221no—
869C2×D4—1221no—
870C2×D4—1221no—
871C2×D4—2442no—
872C2×D4—2444no—
873C2×D4—2444no—
874C2×D4—2444no—
875C2×D4—2444no—
876C2×D4—2444no—
877C2×D4—2444no—
878C2×D4—2448no—
879C2×D4C23×D6112yes—
880C2×D4C23×D6112yes—
881C22×C4—21no—
882C22×C4—22no—
883C22×C4—611no—
884C22×C4—611no—
885C22×C4—611no—
886C22×C4—611no—
887C22×C4—611no—
888C22×C4—611no—
889C22×C4—611no—
890C22×C4—611no—
891C22×C4—611no—
892C22×C4—611no—
893C22×C4—611no—
894C22×C4—611no—
895C22×C4—611no—
896C22×C4—611no—
897C22×C4—611no—
898C22×C4—1224no—
899C22×C4—1222no—
900C22×C4—1224no—
901C22×C4—1222no—
902C22×C4—1222no—
903C22×C4—1222no—
904C22×C4—1222no—
905C22×C4—1221no—
906C22×C4—1222no—
907C22×C4—2442no—
908C22×C4—2448no—
909C22×C4—2444no—
910C22×C4D4×D6111yescharacteristic
911C22×C4D4×D6111yescharacteristic
912C22×C4C23×D6111yescharacteristic
913SD16—44no—
914SD16—2444no—
915SD16—2444no—
916SD16—2444no—
917D8—44no—
918D8—2444no—
919D8—2444no—
920D8—2444no—
921C2×C8—614no—
922C2×C8—1228no—
923C2×C8C23×D6114yes—
924C4⋊C4—21no—
925C4⋊C4—612no—
926C4⋊C4—1222no—
927C4⋊C4—1222no—
928C4⋊C4—1221no—
929C4⋊C4C23×D6112yes—
930C22⋊C4—22no—
931C22⋊C4—22no—
932C22⋊C4—22no—
933C22⋊C4—22no—
934C22⋊C4—22no—
935C22⋊C4—22no—
936C22⋊C4—1222no—
937C22⋊C4—1222no—
938C22⋊C4—1222no—
939C22⋊C4—1222no—
940C22⋊C4—1222no—
941C22⋊C4—1222no—
942C22⋊C4—1222no—
943C22⋊C4—1222no—
944C22⋊C4—1222no—
945C22⋊C4—1222no—
946C22⋊C4—1222no—
947C22⋊C4—1222no—
948C22⋊C4—1222no—
949C22⋊C4—1222no—
950C22⋊C4—1222no—
951C22⋊C4—1222no—
952C22⋊C4—1222no—
953C22⋊C4—1222no—
954C42—611no—
955C42—611no—
956C42—611no—
957C42—611no—
958C42—611no—
959C42—611no—
960C42—611no—
961C42—611no—
962C42—611no—
963C42—611no—
964C42—611no—
965C42—611no—
966C42D4×D6111yescharacteristic
967C42D4×D6111yescharacteristic
968C42C23×D6111yescharacteristic
969C42C23×D6111yescharacteristic
970C23—22no—
971C23—22no—
972C23—42no—
973C23—42no—
974C23—42no—
975C23—611no—
976C23—614no—
977C23—611no—
978C23—1222no—
979C23—1222no—
980C23—1222no—
981C23—1222no—
982C23—48816no—
983C23—2442no—
984C23—2442no—
985C23—2444no—
986C23—2444no—
987C23—2444no—
988C23—2444no—
989C23—2444no—
990C23—2444no—
991C23—2444no—
992C23—2444no—
993C23—2444no—
994C23—2442no—
995C23C2×D4×D6111yescharacteristic
996Q8—24no—
997Q8—42no—
998Q8—42no—
999Q8—1224no—
1000Q8—2442no—
1001Q8—2442no—
1002Q8—2444no—
1003Q8—2444no—
1004Q8—2444no—
1005D4—24no—
1006D4—24no—
1007D4—42no—
1008D4—42no—
1009D4—42no—
1010D4—44no—
1011D4—1224no—
1012D4—1224no—
1013D4—2442no—
1014D4—2442no—
1015D4—2442no—
1016D4—2444no—
1017D4—2444no—
1018D4—2444no—
1019D4—2444no—
1020D4—2444no—
1021D4—2444no—
1022D4—2444no—
1023D4—2444no—
1024C2×C4—22no—
1025C2×C4—22no—
1026C2×C4—22no—
1027C2×C4—22no—
1028C2×C4—41no—
1029C2×C4—44no—
1030C2×C4—42no—
1031C2×C4—611no—
1032C2×C4—614no—
1033C2×C4—611no—
1034C2×C4—611no—
1035C2×C4—611no—
1036C2×C4—611no—
1037C2×C4—611no—
1038C2×C4—1222no—
1039C2×C4—1222no—
1040C2×C4—1222no—
1041C2×C4—1222no—
1042C2×C4—1222no—
1043C2×C4—1222no—
1044C2×C4—1222no—
1045C2×C4—1222no—
1046C2×C4—1222no—
1047C2×C4—1222no—
1048C2×C4—1222no—
1049C2×C4—1222no—
1050C2×C4—1222no—
1051C2×C4—2441no—
1052C2×C4—2441no—
1053C2×C4—2444no—
1054C2×C4—2444no—
1055C2×C4—2444no—
1056C2×C4—2444no—
1057C2×C4—2444no—
1058C2×C4—2441no—
1059C2×C4—2444no—
1060C2×C4—2442no—
1061C2×C4C2×D4×D6111yescharacteristic
1062C2×C4C2×D4×D6111yescharacteristic
1063C2×C4C2×D4×D6111yescharacteristic
1064C2×C4C2×D4×D6111yescharacteristic
1065C2×C4C2×D4×D6111yescharacteristic
1066C2×C4C24×D6111yescharacteristic
1067C8—24no—
1068C8—1224no—
1069C22—21no—
1070C22—21no—
1071C22—42no—
1072C22—42no—
1073C22—42no—
1074C22—42no—
1075C22—42no—
1076C22—42no—
1077C22—84no—
1078C22—612no—
1079C22—612no—
1080C22—612no—
1081C22—612no—
1082C22—1228no—
1083C22—1221no—
1084C22—1221no—
1085C22—4884no—
1086C22—4888no—
1087C22—4888no—
1088C22—4888no—
1089C22—2442no—
1090C22—2442no—
1091C22—2442no—
1092C22—2442no—
1093C22—2442no—
1094C22—2442no—
1095C22AGL(1,ℤ/8)×D6112yes—
1096C22C22×D4×D6111yescharacteristic
1097C4—21no—
1098C4—21no—
1099C4—21no—
1100C4—21no—
1101C4—21no—
1102C4—42no—
1103C4—42no—
1104C4—612no—
1105C4—1221no—
1106C4—1221no—
1107C4—1221no—
1108C4—1221no—
1109C4—1221no—
1110C4—2442no—
1111C4—2442no—
1112C4H(5,𝔽2)×D6112yes—
1113C2—22no—
1114C2—82no—
1115C2—82no—
1116C2—614no—
1117C2—1222no—
1118C2—4882no—
1119C2—4882no—
1120C2#535×D6111yescharacteristic
1121C2C2×AGL(1,ℤ/8)×D6111yescharacteristic
1122C2#575×D6111yescharacteristic
subgroupG/H
centerC22C22×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC61×#3213C2
socleC22×C61C23×D4
hypercenter#3213D61
hypocenterC61C2×#3213
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3213

Complements

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

NH ≅ G/Ntype
1. #532×D61C2semidirect
2. C2×#124×D61C2semidirect
3. #21456808C2semidirect
4. #21456807C2semidirect
5. #21456806C2semidirect
6. #21456805C2semidirect
7. #21456804C2semidirect
8. #21456803C2semidirect
9. #21456802C2semidirect
10. #21456801C2semidirect
11. #496×D61C2semidirect
12. #489×D61C2semidirect
13. #463×D61C2semidirect
14. #448×D61C2semidirect
15. #447×D61C2semidirect
16. #432×D61C2semidirect
17. C61×#3213C2semidirect
21. C2×SD16×D61C22semidirect
23. #16840313C22semidirect
24. #16840312C22semidirect
26. #16840310C22semidirect
28. #16840309C22semidirect
31. #16840307C22semidirect
32. C4⋊Q8×D61C22semidirect
33. #127×D61C22semidirect
34. C2×#14519766C22semidirect
35. C2×#14519765C22semidirect
36. C2×#14519764C22semidirect
46. #124×D61C22semidirect
47. #124×D61C22semidirect
51. C4×D4×D61C22semidirect
55. #16840152C22semidirect
56. #16840151C22semidirect
57. #16840150C22semidirect
58. #16840149C22semidirect
59. #16840148C22semidirect
60. #16840124C22semidirect
61. #16840123C22semidirect
62. #16840122C22semidirect
63. #16840121C22semidirect
64. #16840120C22semidirect
65. #16839980C22semidirect
66. #16839979C22semidirect
67. #16839978C22semidirect
68. #16839977C22semidirect
69. #16839976C22semidirect
70. #16839975C22semidirect
71. #16839974C22semidirect
72. #16839903C22semidirect
73. #16839902C22semidirect
74. #16839901C22semidirect
75. #16839900C22semidirect
76. #16839899C22semidirect
77. #16839898C22semidirect
78. #16839897C22semidirect
79. #16839896C22semidirect
80. #16839895C22semidirect
81. #16839894C22semidirect
82. #16839819C22semidirect
83. #16839818C22semidirect
84. #16839817C22semidirect
85. #16839816C22semidirect
86. C4⋊C8×D61C22semidirect
87. #103×D61C22semidirect
90. #97×D61C22semidirect
91. C61×#532C22semidirect
92. C2×#124×C61C22semidirect
93. C61×#496C22semidirect
94. C61×#489C22semidirect
95. C61×#463C22semidirect
96. C61×#448C22semidirect
97. C61×#447C22semidirect
98. C61×#432C22semidirect
130. C2×#11758190C23semidirect
131. C2×#11758200C23semidirect
132. C2×#11758201C23semidirect
139. #14519777C23semidirect
141. #14519776C23semidirect
143. #14519774C23semidirect
146. #14519773C23semidirect
183. C4×D244C23semidirect
185. D4×Dic61C23semidirect
187. #14519739C23semidirect
221. C4⋊#92418C23semidirect
222. #14519706C23semidirect
223. #14519702C23semidirect
224. #14519701C23semidirect
225. #14519700C23semidirect
231. #14519688C23semidirect
232. #14519687C23semidirect
236. C2×SD16×C61C23semidirect
238. C4⋊Q8×C61C23semidirect
239. #127×C61C23semidirect
248. C4×D4×C61C23semidirect
252. C4⋊C8×C61C23semidirect
253. #103×C61C23semidirect
256. #97×C61C23semidirect
562. #3213D61direct (N × H)
578. D61#3213direct (N × H)
593. #532C2×D61semidirect
610. C2×#124C2×D61semidirect
623. #496C2×D61semidirect
629. #489C2×D61semidirect
637. #463C2×D61semidirect
643. #448C2×D61semidirect
649. #447C2×D61semidirect
654. #432C2×D61semidirect
660. C61C2×#3213semidirect
699. C2×SD16C22×D61semidirect
710. C4⋊Q8C22×D61semidirect
715. #127C22×D61semidirect
769. C4×D4C22×D61semidirect
804. C4⋊C8C22×D61semidirect
808. #103C22×D61semidirect
818. #97C22×D61semidirect

Maximal subgroups

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

subgroupindex
#532×D612
C2×#124×D612
#214568082
#214568072
#214568062
#214568052
#214568042
#214568032
#214568022
#214568012
#496×D612
#489×D612
#463×D612
#448×D612
#447×D612
#432×D612
C61×#32132
C2×#321361