Finite Group Databasebeta

← #30548463

Subgroups — #30548463

Order 15616.

2148 conjugacy classes of subgroups.

The subgroup lattice has 1140 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840317C211yesmaximal, characteristic, complemented
2C4×#41×D61C211yesmaximal, characteristic
3#21455984C212yesmaximal, complemented
4#21455983C212yesmaximal, complemented
5#21455951C212yesmaximal, complemented
6#21455920C212yesmaximal, complemented
7#21455893C212yesmaximal, complemented
8#21455892C212yesmaximal, complemented
9#21455860C212yesmaximal, complemented
10#21455829C212yesmaximal, complemented
11#21455769C212yesmaximal, complemented
12#21455628C211yesmaximal, characteristic, complemented
13#21455307C211yesmaximal, characteristic, complemented
14#21455306C211yesmaximal, characteristic, complemented
15#21455080C212yesmaximal
16#21454643C212yesmaximal, complemented
17#21454637C212yesmaximal, complemented
18#21454451C211yesmaximal, characteristic, complemented
19C61×#3079C211yesmaximal, characteristic, complemented
20C2×#41×D61C2211yescharacteristic
21C2×#14519810C2212yes—
22C2×#14519807C2212yes—
23#16840317—21no—
24#16840317—21no—
25#16840317—21no—
26#16840317—21no—
27#16840317C2212yes—
28#16840317C2212yes—
29#16840317C2212yescomplemented
30#16840317C2212yescomplemented
31C2×#14519777C2211yescharacteristic, complemented
32C2×#14519768—21no—
33C2×#14519757C2212yes—
34C2×#14519753—21no—
35#41×Dic61C2211yescharacteristic
36C4×#11758226C2211yescharacteristic
37C4×#11758226C2211yescharacteristic
38C4×#11758222—21no—
39C4×#11758222C2211yescharacteristic
40#16840230—21no—
41#16840230C2211yescharacteristic
42C4×#11758224—21no—
43C4×#11758224—21no—
44C4×#11758224C2211yescharacteristic
45C4×#11758224C2211yescharacteristic
46C2×Q8×Dic61—21no—
47C2×#14519742C2212yescomplemented
48C4×Q8×D61C2211yescharacteristic
49C4×Q8×D61C2211yescharacteristic
50C4×D4×D61—21no—
51C4×D4×D61—21no—
52C4×D4×D61C2211yescharacteristic
53C4×D4×D61C2211yescharacteristic
54C2×#14519735—21no—
55#117×D61—21no—
56#117×D61C2211yescharacteristic
57C2×C42×D61—21no—
58C2×C42×D61C2211yescharacteristic
59#16840106C2214yescomplemented
60#16840105C2214yescomplemented
61#16840099C2214yes—
62#16840094C2214yes—
63#16840054C2212yescomplemented
64#16840049C2212yescomplemented
65#16840044C2212yescomplemented
66#16840039C2212yescomplemented
67#16839973C2212yescomplemented
68#16839973C2212yescomplemented
69#16839972C2212yescomplemented
70#16839972C2212yescomplemented
71#16839968C2212yescomplemented
72#16839968C2212yescomplemented
73#16839967C2212yescomplemented
74#16839967C2212yescomplemented
75#16839927C2214yes—
76#16839925C2214yes—
77#16839919C2214yes—
78#16839914C2214yes—
79#16839868C2214yescomplemented
80#16839866C2214yescomplemented
81#16839861C2214yescomplemented
82#16839859C2214yescomplemented
83#16839856C2214yescomplemented
84#16839854C2214yescomplemented
85#16839853C2214yescomplemented
86#16839849C2214yescomplemented
87#16839818C2212yes—
88#16839818C2212yescomplemented
89#16839814C2212yes—
90#16839814C2212yescomplemented
91#16839802C2212yescomplemented
92#16839786C2211yescharacteristic, complemented
93#16839772C2212yescomplemented
94#16839770C2212yescomplemented
95#16839761C2212yes—
96#16839725C2212yes—
97M16×Dic61C2212yescomplemented
98C2×C4⋊Q8×C61C2211yescharacteristic, complemented
99C4×#41×C61C2211yescharacteristic
100C61×#477C2212yescomplemented
101C61×#476C2212yescomplemented
102C61×#475C2212yescomplemented
103C61×#474C2212yescomplemented
104C61×#428C2212yescomplemented
105C61×#423C2211yescharacteristic, complemented
106C61×#417C2212yes—
107C2×#11758226C2311yescharacteristic
108C2×#11758222—21no—
109C2×#11758222C2311yescharacteristic
110C2×#11758224—21no—
111C2×#11758224C2311yescharacteristic
112#41×D61—24no—
113#41×D61—24no—
114C22×Dic122C2312yes—
115C2×Q8×D61C2311yescharacteristic
116C2×D4×D61—21no—
117C2×D4×D61C2311yescharacteristic
118C22×C4×D61—21no—
119C22×C4×D61—21no—
120C22×C4×D61—21no—
121C22×C4×D61D411yescharacteristic
122C22×C4×D61D411yescharacteristic
123C22×C4×D61C2311yescharacteristic
124#14519810—28no—
125#14519807—28no—
126C2×Dic244C2314yes—
127C2×#11758202C2314yes—
128C2×#11758190C2314yes—
129C2×#11758200C2314yes—
130C2×#11758194C2312yes—
131#14519777—21no—
132#14519777—21no—
133#14519777C2312yes—
134#14519777C2312yes—
135#14519768—22no—
136#14519768—22no—
137#14519768—22no—
138#14519768—22no—
139#14519757—22no—
140#14519757—22no—
141#14519757C2314yes—
142#14519757C2314yes—
143#14519753—22no—
144#14519753—22no—
145#14519753—22no—
146#14519753—22no—
147Q8×Dic61—22no—
148Q8×Dic61—22no—
149Q8×Dic61—22no—
150Q8×Dic61—22no—
151Q8×Dic61C2311yescharacteristic
152Q8×Dic61C2311yescharacteristic
153C4×Dic122—21no—
154C4×Dic122—21no—
155C4×Dic122C2311yescharacteristic
156C4×Dic122C2311yescharacteristic
157#14519742—21no—
158#14519742—21no—
159#14519742—22no—
160#14519742—22no—
161#14519742C2311yescharacteristic
162#14519742C2311yescharacteristic
163#14519742C2314yes—
164#14519742C2314yes—
165C4×D244—21no—
166C4×D244—21no—
167C4×D244C2311yescharacteristic
168C4×D244C2311yescharacteristic
169D4×Dic61—21no—
170D4×Dic61—21no—
171D4×Dic61C2311yescharacteristic
172D4×Dic61C2311yescharacteristic
173#14519739—21no—
174#14519739—21no—
175#14519739C2311yescharacteristic
176#14519739C2311yescharacteristic
177C4×C22⋊D61—21no—
178C4×C22⋊D61—21no—
179C4×C22⋊D61—21no—
180C4×C22⋊D61—21no—
181C4×C22⋊D61—21no—
182C4×C22⋊D61—21no—
183#14519737—21no—
184#14519737—21no—
185#14519737—21no—
186#14519737—21no—
187#14519737—21no—
188#14519737—21no—
189#14519736—21no—
190#14519736C2311yescharacteristic
191#14519735—22no—
192#14519735—22no—
193#14519735—22no—
194#14519735—22no—
195#14519735—21no—
196#14519735—21no—
197#14519735C2311yescharacteristic
198#14519735C2311yescharacteristic
199#14519734—21no—
200#14519734—21no—
201#14519734—21no—
202#14519733—21no—
203#14519733—21no—
204#14519733—21no—
205C2×C4⋊Dic61—21no—
206C2×C4⋊Dic61—21no—
207C2×C4⋊Dic61—22no—
208C2×#11758196—22no—
209C4⋊C4×D61—21no—
210C4⋊C4×D61—21no—
211C4⋊C4×D61C2311yescharacteristic
212C4⋊C4×D61C2311yescharacteristic
213C2×#11758198—22no—
214C22⋊C4×D61—21no—
215C22⋊C4×D61—21no—
216C22⋊C4×D61—21no—
217C2×C4×Dic61—22no—
218C2×C4×Dic61—21no—
219C2×C4×Dic61—21no—
220C2×C4×Dic61—21no—
221C2×C4×Dic61D411yescharacteristic
222C2×C4×Dic61D411yescharacteristic
223C2×C4×Dic61C2311yescharacteristic
224C42×D61—21no—
225C42×D61—21no—
226C42×D61—21no—
227C42×D61—21no—
228C42×D61—21no—
229C42×D61—21no—
230C42×D61—21no—
231C42×D61D411yescharacteristic
232C42×D61D411yescharacteristic
233C42×D61D411yescharacteristic
234C42×D61D411yescharacteristic
235C42×D61C2311yescharacteristic
236C42×D61C2311yescharacteristic
237C42×D61C2311yescharacteristic
238C42×D61C2311yescharacteristic
239#14519710C2314yes—
240#14519708C2314yes—
241C4⋊#92418C2312yes—
242C4⋊#92418C2312yes—
243#14519702C2314yes—
244#14519702C2314yes—
245#14519700C2314yes—
246#14519700C2314yes—
247#14519700C2314yes—
248#14519697C2314yes—
249#14519689C2314yes—
250#14519689C2314yes—
251#14519687C2314yes—
252C8×Dic61C2314yes—
253C2×#41×C61C2311yescharacteristic
254C22×Q8×C61—21no—
255C2×M16×C61C2312yes—
256C4⋊Q8×C61—21no—
257C4⋊Q8×C61—21no—
258C4⋊Q8×C61C2312yes—
259C4⋊Q8×C61C2312yes—
260C4×Q8×C61C2311yescharacteristic
261C4×Q8×C61C2311yescharacteristic
262C4×D4×C61—21no—
263C4×D4×C61—21no—
264C4×D4×C61C2311yescharacteristic
265C4×D4×C61C2311yescharacteristic
266#117×C61—21no—
267#117×C61C2311yescharacteristic
268C2×C4⋊C4×C61—21no—
269C2×C4⋊C4×C61C2312yes—
270C2×C42×C61—21no—
271C2×C42×C61C2311yescharacteristic
272#107×C61C2314yes—
273#106×C61C2314yes—
274C4⋊C8×C61C2312yes—
275C4⋊C8×C61C2312yes—
276#103×C61C2314yes—
277#102×C61C2314yes—
278C23×D61—21no—
279C23×D61C2×D411yescharacteristic
280#41×C61—22no—
281#41×C61#4114yes—
282C2×Q8×C61—22no—
283C2×Q8×C61—22no—
284C2×Q8×C61—44no—
285C2×Q8×C61C2411yescharacteristic
286C2×D4×C61—21no—
287C2×D4×C61C2411yescharacteristic
288C22×C4×C61—21no—
289C22×C4×C61—22no—
290C22×C4×C61—21no—
291C22×C4×C61—21no—
292C22×C4×C61C2×D411yescharacteristic
293C22×C4×C61C2×D411yescharacteristic
294C22×C4×C61C2411yescharacteristic
295C2×C22⋊D61—21no—
296C2×C22⋊D61—21no—
297C2×C22⋊D61—21no—
298C22×Dic61—21no—
299C22×Dic61—22no—
300C22×Dic61—21no—
301C22×Dic61—21no—
302C22×Dic61C2×D411yescharacteristic
303C22×Dic61C2×D411yescharacteristic
304C22×Dic61C2×D411yescharacteristic
305#11758226—22no—
306#11758226—22no—
307Q8×D61—22no—
308Q8×D61—22no—
309#11758224—28no—
310#11758224—22no—
311#11758224—22no—
312D4×D61—28no—
313D4×D61—22no—
314D4×D61—22no—
315#11758222—28no—
316#11758222—22no—
317#11758222#4114yes—
318C2×D244—21no—
319C2×D244C2411yescharacteristic
320C2×C4×D61—28no—
321C2×C4×D61—21no—
322C2×C4×D61—21no—
323C2×C4×D61—22no—
324C2×C4×D61—22no—
325C2×C4×D61—21no—
326C2×C4×D61—24no—
327C2×C4×D61—21no—
328C2×C4×D61—21no—
329C2×C4×D61—21no—
330C2×C4×D61—21no—
331C2×C4×D61—21no—
332C2×C4×D61—21no—
333C2×C4×D61—42no—
334C2×C4×D61—44no—
335C2×C4×D61—44no—
336C2×C4×D61C2×D411yescharacteristic
337C2×C4×D61C2×D411yescharacteristic
338C2×C4×D61C2×D411yescharacteristic
339C2×C4×D61C2×D411yescharacteristic
340C2×C4×D61C2×D411yescharacteristic
341C2×C4×D61C2×D411yescharacteristic
342C2×C4×D61C2×D411yescharacteristic
343C2×C4×D61C2×D411yescharacteristic
344C2×C4×D61C2×D411yescharacteristic
345C2×C4×D61C2×D411yescharacteristic
346C2×C4×D61C2411yescharacteristic
347C2×C4×D61C2411yescharacteristic
348C2×Dic122—21no—
349C2×Dic122—24no—
350C2×Dic122—24no—
351C2×Dic122—22no—
352C2×Dic122C2414yes—
353C2×Dic122C2411yescharacteristic
354M16×C61—24no—
355C2×C8×C61C2414yes—
356C4⋊C4×C61—22no—
357C4⋊C4×C61—22no—
358C4⋊C4×C61—22no—
359C4⋊C4×C61—21no—
360C4⋊C4×C61—21no—
361C4⋊C4×C61C2414yes—
362C4⋊C4×C61C2411yescharacteristic
363C4⋊C4×C61C2411yescharacteristic
364C22⋊C4×C61—21no—
365C22⋊C4×C61—21no—
366C22⋊C4×C61—21no—
367C42×C61—21no—
368C42×C61—21no—
369C42×C61—21no—
370C42×C61C2×D411yescharacteristic
371C42×C61C2×D411yescharacteristic
372C42×C61C2411yescharacteristic
373C42×C61C2411yescharacteristic
374C22⋊Dic61—21no—
375C22⋊Dic61—21no—
376C22⋊Dic61—21no—
377#11758202—28no—
378#11758200—28no—
379#11758198—21no—
380#11758198—21no—
381#11758198—24no—
382#11758198—24no—
383#11758198—21no—
384#11758198—21no—
385#11758198—21no—
386#11758198—21no—
387C4⋊Dic61—22no—
388C4⋊Dic61—22no—
389C4⋊Dic61—22no—
390C4⋊Dic61—22no—
391C4⋊Dic61—21no—
392C4⋊Dic61—21no—
393C4⋊Dic61—24no—
394C4⋊Dic61—24no—
395C4⋊Dic61C2411yescharacteristic
396C4⋊Dic61C2411yescharacteristic
397#11758196—21no—
398#11758196—21no—
399#11758196—21no—
400#11758196—21no—
401#11758196—21no—
402#11758196—21no—
403#11758196—24no—
404#11758196—24no—
405C4×Dic61—21no—
406C4×Dic61—21no—
407C4×Dic61—21no—
408C4×Dic61—21no—
409C4×Dic61—21no—
410C4×Dic61—21no—
411C4×Dic61—21no—
412C4×Dic61—21no—
413C4×Dic61—21no—
414C4×Dic61—24no—
415C4×Dic61—24no—
416C4×Dic61C2×D411yescharacteristic
417C4×Dic61C2×D411yescharacteristic
418C4×Dic61C2×D411yescharacteristic
419C4×Dic61C2×D411yescharacteristic
420C4×Dic61C2×D411yescharacteristic
421C4×Dic61C2×D411yescharacteristic
422C4×Dic61C2×D411yescharacteristic
423C4×Dic61C2×D411yescharacteristic
424C4×Dic61C2×D411yescharacteristic
425C4×Dic61C2×D411yescharacteristic
426C4×Dic61C2411yescharacteristic
427C4×Dic61C2411yescharacteristic
428#11758194—24no—
429C2×#92418C2414yes—
430Dic244—28no—
431#11758190—28no—
432C23×C61—21no—
433C23×C61C22×D411yescharacteristic
434C22×D61—24no—
435C22×D61—22no—
436C22×D61—21no—
437C22×D61—22no—
438C22×D61—41no—
439C22×D61—42no—
440C22×D61—42no—
441C22×D61C22×D411yescharacteristic
442C22×D61C22×D411yescharacteristic
443Q8×C61—21no—
444Q8×C61—44no—
445Q8×C61—44no—
446Q8×C61C2×#4112yes—
447D4×C61—24no—
448D4×C61—21no—
449D4×C61C2×#4112yes—
450C2×C4×C61—21no—
451C2×C4×C61—24no—
452C2×C4×C61—22no—
453C2×C4×C61—22no—
454C2×C4×C61—24no—
455C2×C4×C61—21no—
456C2×C4×C61—21no—
457C2×C4×C61—44no—
458C2×C4×C61—42no—
459C2×C4×C61—42no—
460C2×C4×C61C22×D411yescharacteristic
461C2×C4×C61C22×D411yescharacteristic
462C2×C4×C61C22×D411yescharacteristic
463C2×C4×C61C22×D411yescharacteristic
464C2×C4×C61C22×D411yescharacteristic
465C2×C4×C61C2×#4112yes—
466C2×C4×C61C2×#4112yes—
467C2×C4×C61C2511yescharacteristic
468C22⋊D61—24no—
469C22⋊D61—24no—
470C22⋊D61—24no—
471C2×Dic61—24no—
472C2×Dic61—22no—
473C2×Dic61—21no—
474C2×Dic61—22no—
475C2×Dic61—21no—
476C2×Dic61—21no—
477C2×Dic61—24no—
478C2×Dic61—41no—
479C2×Dic61—42no—
480C2×Dic61—44no—
481C2×Dic61—42no—
482C2×Dic61C22×D411yescharacteristic
483C2×Dic61C22×D411yescharacteristic
484C2×Dic61C22×D411yescharacteristic
485C2×Dic61C22×D411yescharacteristic
486C2×Dic61C22×D411yescharacteristic
487C2×Dic61C22×D411yescharacteristic
488D244—24no—
489D244—21no—
490D244C2×#4112yes—
491C4×D61—24no—
492C4×D61—24no—
493C4×D61—22no—
494C4×D61—22no—
495C4×D61—24no—
496C4×D61—22no—
497C4×D61—22no—
498C4×D61—22no—
499C4×D61—22no—
500C4×D61—21no—
501C4×D61—21no—
502C4×D61—21no—
503C4×D61—21no—
504C4×D61—22no—
505C4×D61—41no—
506C4×D61—41no—
507C4×D61—42no—
508C4×D61—42no—
509C4×D61—42no—
510C4×D61—42no—
511C4×D61—42no—
512C4×D61—42no—
513C4×D61#13714yescomplemented
514Dic122—24no—
515Dic122—21no—
516Dic122—24no—
517Dic122—24no—
518Dic122—44no—
519Dic122C2×#4112yes—
520C8×C61—24no—
521#92418—24no—
522#60562—611nomaximal, Sylow
523C22×C61—21no—
524C22×C61—21no—
525C22×C61—22no—
526C22×C61—41no—
527C22×C61—41no—
528C22×C61#52512yes—
529C22×C61C23×D411yescharacteristic
530C2×D61—21no—
531C2×D61—21no—
532C2×D61—21no—
533C2×D61—22no—
534C2×D61—21no—
535C2×D61—21no—
536C2×D61—44no—
537C2×D61—48no—
538C2×D61—41no—
539C2×D61—41no—
540C2×D61C2×#13712yes—
541C4×C61—22no—
542C4×C61—21no—
543C4×C61—21no—
544C4×C61—41no—
545C4×C61—41no—
546C4×C61—44no—
547C4×C61#52512yes—
548C4×C61C2×#13712yes—
549C4×C61#57512yes—
550C4×C61C22×#4111yescharacteristic
551C4×C61C22×#4111yescharacteristic
552Dic61—21no—
553Dic61—22no—
554Dic61—21no—
555Dic61—21no—
556Dic61—21no—
557Dic61—21no—
558Dic61—44no—
559Dic61—41no—
560Dic61—41no—
561Dic61C2×#13712yes—
562C2×#533—611no—
563C2×C4×#41—611no—
564#3116—612no—
565#3116—612no—
566#3113—612no—
567#3110—612no—
568#3107—612no—
569#3107—612no—
570#3104—612no—
571#3101—612no—
572#3095—612no—
573#3079—611no—
574#3079D6111yescharacteristic, complemented
575#3039—611no—
576#3039—611no—
577#3007—612no—
578C4×#137—612no—
579C4×#137—612no—
580#2920—611no—
581C2×C61—22no—
582C2×C61—42no—
583C2×C61C2×#52511yescharacteristic
584C2×C61C22×#13711yescharacteristic
585C2×C61C2×#57511yescharacteristic
586D61—22no—
587D61—41no—
588D61—42no—
589C22×#41—611no—
590C2×#137—612no—
591C2×#137—612no—
592#533—612no—
593#533—612no—
594#533—612no—
595#533—612no—
596#533—1221no—
597#533—1221no—
598#533—1221no—
599#533—1221no—
600C2×C4⋊Q8—611no—
601C2×C4⋊Q8C2×D6111yescharacteristic, complemented
602C2×#125—1221no—
603C2×C22⋊Q8—612no—
604C2×C22⋊Q8—1221no—
605C4×#41—611no—
606C4×#41—611no—
607C4×#41—611no—
608C4×#41—611no—
609C4×#41—611no—
610C4×#41—611no—
611C4×#41—611no—
612C4×#41—1221no—
613C4×#41—1221no—
614C4×#41—1221no—
615C4×#41—1221no—
616C4×#41C2×D6111yescharacteristic
617C2×C4×Q8—611no—
618C2×C4×Q8—611no—
619C2×C4×Q8—612no—
620C2×C4×Q8—1221no—
621C2×C4×D4—611no—
622C2×C4×D4—611no—
623C2×C4×D4—1221no—
624C2×C4×D4—1221no—
625C2×#117—611no—
626C2×#117—1221no—
627C2×#117—1221no—
628C22×C42—611no—
629C22×C42—1221no—
630#485—614no—
631#485—614no—
632#484—614no—
633#483—614no—
634#477—612no—
635#477C2×D6112yescomplemented
636#476—612no—
637#476C2×D6112yescomplemented
638#475—612no—
639#475C2×D6112yescomplemented
640#474—612no—
641#474C2×D6112yescomplemented
642#462—612no—
643#462—612no—
644#462—612no—
645#462—612no—
646#461—612no—
647#461—612no—
648#461—612no—
649#461—612no—
650#452—614no—
651#452—614no—
652#451—614no—
653#450—614no—
654#441—614no—
655#441—614no—
656#440—614no—
657#440—614no—
658C4×Q16—614no—
659C4×Q16—614no—
660C4×SD16—614no—
661C4×SD16—614no—
662#432—612no—
663#432—612no—
664#431—612no—
665#431—612no—
666#428—612no—
667#428C2×D6112yescomplemented
668#423—611no—
669#423C2×D6111yescharacteristic, complemented
670#419—612no—
671#419—612no—
672#417—612no—
673#417C2×D6112yes—
674#407—612no—
675C4×M16—612no—
676C61#6056211yescharacteristic, complemented, Sylow
677C2×#41—611no—
678C2×#41—611no—
679C2×#41—611no—
680C2×#41—1221no—
681C2×#41—1221no—
682C2×#41—1224no—
683C2×#41—1224no—
684C2×#41C22×D6111yescharacteristic
685C22×Q8—21no—
686C22×Q8—611no—
687C22×Q8—612no—
688C22×D4—611no—
689C22×D4—1221no—
690C23×C4—611no—
691C23×C4—611no—
692C23×C4—611no—
693C23×C4—1221no—
694C23×C4—1221no—
695C23×C4—1221no—
696#137—1228no—
697#137—1228no—
698C2×Q16—614no—
699C2×Q16—614no—
700C2×SD16—614no—
701C2×SD16—614no—
702C2×M16—612no—
703C2×M16C22×D6112yes—
704C4⋊Q8—21no—
705C4⋊Q8—21no—
706C4⋊Q8—612no—
707C4⋊Q8—612no—
708C4⋊Q8—1221no—
709C4⋊Q8—1221no—
710C4⋊Q8C22×D6112yes—
711C4⋊Q8C22×D6112yes—
712#125—1222no—
713#125—1222no—
714#125—1222no—
715#125—1222no—
716C22⋊Q8—614no—
717C22⋊Q8—614no—
718C22⋊Q8—1222no—
719C22⋊Q8—1222no—
720C22⋊Q8—1222no—
721C22⋊Q8—1222no—
722C22⋊Q8—1222no—
723C22⋊Q8—1222no—
724C4×Q8—611no—
725C4×Q8—611no—
726C4×Q8—611no—
727C4×Q8—611no—
728C4×Q8—614no—
729C4×Q8—614no—
730C4×Q8—611no—
731C4×Q8—611no—
732C4×Q8—1221no—
733C4×Q8—1221no—
734C4×Q8—1221no—
735C4×Q8—1221no—
736C4×Q8—1222no—
737C4×Q8—1222no—
738C4×Q8—1222no—
739C4×Q8—1222no—
740C4×Q8—1222no—
741C4×Q8—1222no—
742C4×Q8C22×D6111yescharacteristic
743C4×Q8C22×D6111yescharacteristic
744C4×D4—21no—
745C4×D4—21no—
746C4×D4—611no—
747C4×D4—611no—
748C4×D4—611no—
749C4×D4—611no—
750C4×D4—611no—
751C4×D4—611no—
752C4×D4—1221no—
753C4×D4—1221no—
754C4×D4—1221no—
755C4×D4—1221no—
756C4×D4—1221no—
757C4×D4—1221no—
758C4×D4—1221no—
759C4×D4—1221no—
760C4×D4—1221no—
761C4×D4—1221no—
762C4×D4—1221no—
763C4×D4—1221no—
764C4×D4—1221no—
765C4×D4—1221no—
766C4×D4—1221no—
767C4×D4—1221no—
768C4×D4—1221no—
769C4×D4—1221no—
770C4×D4C22×D6111yescharacteristic
771C4×D4C22×D6111yescharacteristic
772#117—21no—
773#117—611no—
774#117—611no—
775#117—611no—
776#117—1221no—
777#117—1221no—
778#117—1221no—
779#117—1221no—
780#117—1221no—
781#117—1221no—
782#117—1221no—
783#117—1221no—
784#117—1222no—
785#117—1222no—
786#117—1222no—
787#117—1222no—
788#117—1221no—
789#117C22×D6111yescharacteristic
790C2×C4⋊C4—21no—
791C2×C4⋊C4—611no—
792C2×C4⋊C4—611no—
793C2×C4⋊C4—1221no—
794C2×C4⋊C4—1221no—
795C2×C4⋊C4—1222no—
796C2×C4⋊C4—1222no—
797C2×C4⋊C4—1221no—
798C2×C4⋊C4—1221no—
799C2×C4⋊C4C22×D6112yes—
800C2×C22⋊C4—1221no—
801C2×C22⋊C4—1221no—
802C2×C22⋊C4—1221no—
803C2×C22⋊C4—1222no—
804C2×C42—21no—
805C2×C42—611no—
806C2×C42—611no—
807C2×C42—611no—
808C2×C42—611no—
809C2×C42—611no—
810C2×C42—611no—
811C2×C42—611no—
812C2×C42—611no—
813C2×C42—611no—
814C2×C42—611no—
815C2×C42—611no—
816C2×C42—1221no—
817C2×C42—1221no—
818C2×C42—1221no—
819C2×C42—1221no—
820C2×C42—1221no—
821C2×C42—1221no—
822C2×C42—1221no—
823C2×C42—1221no—
824C2×C42—1221no—
825C2×C42—1222no—
826C2×C42—1221no—
827C2×C42C22×D6111yescharacteristic
828#107—614no—
829#107C22×D6114yes—
830#106—614no—
831#106C22×D6114yes—
832C4⋊C8—612no—
833C4⋊C8—612no—
834C4⋊C8C22×D6112yes—
835C4⋊C8C22×D6112yes—
836#103—614no—
837#103—614no—
838#103—614no—
839#103—614no—
840#103—614no—
841#103C22×D6114yes—
842#102—614no—
843#102C22×D6114yes—
844C22⋊C8—614no—
845C22⋊C8—614no—
846#97—614no—
847C4×C8—614no—
848C24—611no—
849C24—1221no—
850#41—22no—
851#41—614no—
852#41—1228no—
853#41—1222no—
854#41—1228no—
855#41—1222no—
856#41—1222no—
857#41—1222no—
858#41—1222no—
859#41#1175822614yes—
860C2×Q8—22no—
861C2×Q8—22no—
862C2×Q8—44no—
863C2×Q8—611no—
864C2×Q8—614no—
865C2×Q8—1221no—
866C2×Q8—1222no—
867C2×Q8—1222no—
868C2×Q8—1222no—
869C2×Q8—1224no—
870C2×Q8—1224no—
871C2×Q8C23×D6111yescharacteristic
872C2×D4—21no—
873C2×D4—611no—
874C2×D4—1221no—
875C2×D4—1221no—
876C2×D4—1222no—
877C2×D4—1228no—
878C2×D4—1221no—
879C2×D4—1221no—
880C2×D4—1222no—
881C2×D4C23×D6111yescharacteristic
882C22×C4—21no—
883C22×C4—22no—
884C22×C4—21no—
885C22×C4—21no—
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—611no—
899C22×C4—611no—
900C22×C4—611no—
901C22×C4—1221no—
902C22×C4—1224no—
903C22×C4—1221no—
904C22×C4—1221no—
905C22×C4—1221no—
906C22×C4—1228no—
907C22×C4—1221no—
908C22×C4—1221no—
909C22×C4—1221no—
910C22×C4—1221no—
911C22×C4—1221no—
912C22×C4—1221no—
913C22×C4—1222no—
914C22×C4—1222no—
915C22×C4—1222no—
916C22×C4—1221no—
917C22×C4—1221no—
918C22×C4—2442no—
919C22×C4—2444no—
920C22×C4—2444no—
921C22×C4D4×D6111yescharacteristic
922C22×C4D4×D6111yescharacteristic
923C22×C4C23×D6111yescharacteristic
924Q16—1228no—
925Q16—1228no—
926SD16—1228no—
927SD16—1228no—
928M16—24no—
929M16—1224no—
930C2×C8—614no—
931C2×C8C23×D6114yes—
932C4⋊C4—22no—
933C4⋊C4—22no—
934C4⋊C4—21no—
935C4⋊C4—21no—
936C4⋊C4—22no—
937C4⋊C4—611no—
938C4⋊C4—611no—
939C4⋊C4—1221no—
940C4⋊C4—1221no—
941C4⋊C4—1221no—
942C4⋊C4—1221no—
943C4⋊C4—1224no—
944C4⋊C4—1224no—
945C4⋊C4—1221no—
946C4⋊C4—1221no—
947C4⋊C4—1224no—
948C4⋊C4—1224no—
949C4⋊C4—1221no—
950C4⋊C4—1221no—
951C4⋊C4—1222no—
952C4⋊C4—1222no—
953C4⋊C4—1222no—
954C4⋊C4—1222no—
955C4⋊C4C23×D6114yes—
956C4⋊C4C23×D6111yescharacteristic
957C4⋊C4C23×D6111yescharacteristic
958C22⋊C4—21no—
959C22⋊C4—21no—
960C22⋊C4—21no—
961C22⋊C4—1221no—
962C22⋊C4—1221no—
963C22⋊C4—1221no—
964C22⋊C4—1221no—
965C22⋊C4—1224no—
966C22⋊C4—1224no—
967C22⋊C4—1221no—
968C22⋊C4—1221no—
969C22⋊C4—1221no—
970C22⋊C4—1221no—
971C22⋊C4—1221no—
972C42—21no—
973C42—21no—
974C42—21no—
975C42—611no—
976C42—611no—
977C42—611no—
978C42—611no—
979C42—611no—
980C42—611no—
981C42—611no—
982C42—611no—
983C42—611no—
984C42—611no—
985C42—611no—
986C42—611no—
987C42—1221no—
988C42—1221no—
989C42—1221no—
990C42—1221no—
991C42—1221no—
992C42—1221no—
993C42—1224no—
994C42—1224no—
995C42—1221no—
996C42—1221no—
997C42—1221no—
998C42D4×D6111yescharacteristic
999C42D4×D6111yescharacteristic
1000C42C23×D6111yescharacteristic
1001C42C23×D6111yescharacteristic
1002C23—21no—
1003C23—611no—
1004C23—611no—
1005C23—1222no—
1006C23—1224no—
1007C23—1222no—
1008C23—1221no—
1009C23—2441no—
1010C23—2442no—
1011C23—2442no—
1012C23C2×D4×D6111yescharacteristic
1013Q8—21no—
1014Q8—44no—
1015Q8—44no—
1016Q8—612no—
1017Q8—1224no—
1018Q8—1221no—
1019Q8—1224no—
1020Q8—1224no—
1021Q8—2444no—
1022Q8C2×#1175822612yes—
1023D4—24no—
1024D4—21no—
1025D4—612no—
1026D4—1224no—
1027D4—1224no—
1028D4—1224no—
1029D4—1224no—
1030D4—1221no—
1031D4C2×#1175822612yes—
1032C2×C4—21no—
1033C2×C4—24no—
1034C2×C4—22no—
1035C2×C4—22no—
1036C2×C4—21no—
1037C2×C4—21no—
1038C2×C4—24no—
1039C2×C4—44no—
1040C2×C4—42no—
1041C2×C4—42no—
1042C2×C4—611no—
1043C2×C4—614no—
1044C2×C4—611no—
1045C2×C4—611no—
1046C2×C4—611no—
1047C2×C4—611no—
1048C2×C4—611no—
1049C2×C4—1222no—
1050C2×C4—1222no—
1051C2×C4—1224no—
1052C2×C4—1224no—
1053C2×C4—1222no—
1054C2×C4—1224no—
1055C2×C4—1222no—
1056C2×C4—1221no—
1057C2×C4—1222no—
1058C2×C4—1222no—
1059C2×C4—1224no—
1060C2×C4—1222no—
1061C2×C4—1222no—
1062C2×C4—1222no—
1063C2×C4—1221no—
1064C2×C4—1221no—
1065C2×C4—1221no—
1066C2×C4—1221no—
1067C2×C4—1221no—
1068C2×C4—1221no—
1069C2×C4—1224no—
1070C2×C4—2441no—
1071C2×C4—2441no—
1072C2×C4—2442no—
1073C2×C4—2442no—
1074C2×C4—2442no—
1075C2×C4—2442no—
1076C2×C4—2442no—
1077C2×C4—2441no—
1078C2×C4—2442no—
1079C2×C4—2444no—
1080C2×C4—2442no—
1081C2×C4—2442no—
1082C2×C4C2×D4×D6111yescharacteristic
1083C2×C4C2×D4×D6111yescharacteristic
1084C2×C4C2×D4×D6111yescharacteristic
1085C2×C4C2×D4×D6111yescharacteristic
1086C2×C4C2×D4×D6111yescharacteristic
1087C2×C4#41×D6112yes—
1088C2×C4C2×#1175822612yes—
1089C2×C4C24×D6111yescharacteristic
1090C8—24no—
1091C8—1224no—
1092C22—21no—
1093C22—21no—
1094C22—22no—
1095C22—41no—
1096C22—41no—
1097C22—612no—
1098C22—1221no—
1099C22—1221no—
1100C22—1221no—
1101C22—1221no—
1102C22—1222no—
1103C22—1221no—
1104C22—2444no—
1105C22—2448no—
1106C22—2441no—
1107C22—2441no—
1108C22#1684027512yes—
1109C22C22×D4×D6111yescharacteristic
1110C4—21no—
1111C4—21no—
1112C4—22no—
1113C4—41no—
1114C4—41no—
1115C4—44no—
1116C4—612no—
1117C4—1221no—
1118C4—1221no—
1119C4—1221no—
1120C4—1221no—
1121C4—1221no—
1122C4—1222no—
1123C4—2441no—
1124C4—2441no—
1125C4—2444no—
1126C4#1684027512yes—
1127C4#137×D6112yes—
1128C4#1684055812yes—
1129C4C2×#41×D6111yescharacteristic
1130C4C22×#1175822611yescharacteristic
1131C2—22no—
1132C2—42no—
1133C2—1222no—
1134C2—2441no—
1135C2—2442no—
1136C2C2×#1684027511yescharacteristic
1137C2C2×#137×D6111yescharacteristic
1138C2C2×#1684055811yescharacteristic
subgroupG/H
centerC22C22×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC61×#3079C2
socleC22×C61C23×D4
prime radicalC2×#41×D61C22
hypercenter#3079D61
hypocenterC61#60562
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3079

Complements

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

NH ≅ G/Ntype
1. C2×#16840317C2semidirect
3. #21455984C2semidirect
4. #21455983C2semidirect
5. #21455951C2semidirect
6. #21455920C2semidirect
7. #21455893C2semidirect
8. #21455892C2semidirect
9. #21455860C2semidirect
10. #21455829C2semidirect
11. #21455769C2semidirect
12. #21455628C2semidirect
13. #21455307C2semidirect
14. #21455306C2semidirect
16. #21454643C2semidirect
17. #21454637C2semidirect
18. #21454451C2semidirect
19. C61×#3079C2semidirect
29. #16840317C22semidirect
30. #16840317C22semidirect
31. C2×#14519777C22semidirect
47. C2×#14519742C22semidirect
59. #16840106C22semidirect
60. #16840105C22semidirect
63. #16840054C22semidirect
64. #16840049C22semidirect
65. #16840044C22semidirect
66. #16840039C22semidirect
67. #16839973C22semidirect
68. #16839973C22semidirect
69. #16839972C22semidirect
70. #16839972C22semidirect
71. #16839968C22semidirect
72. #16839968C22semidirect
73. #16839967C22semidirect
74. #16839967C22semidirect
79. #16839868C22semidirect
80. #16839866C22semidirect
81. #16839861C22semidirect
82. #16839859C22semidirect
83. #16839856C22semidirect
84. #16839854C22semidirect
85. #16839853C22semidirect
86. #16839849C22semidirect
88. #16839818C22semidirect
90. #16839814C22semidirect
91. #16839802C22semidirect
92. #16839786C22semidirect
93. #16839772C22semidirect
94. #16839770C22semidirect
97. M16×Dic61C22semidirect
98. C2×C4⋊Q8×C61C22semidirect
100. C61×#477C22semidirect
101. C61×#476C22semidirect
102. C61×#475C22semidirect
103. C61×#474C22semidirect
104. C61×#428C22semidirect
105. C61×#423C22semidirect
513. C4×D61#137semidirect
574. #3079D61semidirect
601. C2×C4⋊Q8C2×D61semidirect
635. #477C2×D61semidirect
637. #476C2×D61semidirect
639. #475C2×D61semidirect
641. #474C2×D61semidirect
667. #428C2×D61semidirect
669. #423C2×D61semidirect
676. C61#60562semidirect

Maximal subgroups

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

subgroupindex
C2×#168403172
C4×#41×D612
#214559842
#214559832
#214559512
#214559202
#214558932
#214558922
#214558602
#214558292
#214557692
#214556282
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