Finite Group Databasebeta

← #30551445

Subgroups — #30551445

Order 15616.

2262 conjugacy classes of subgroups.

The subgroup lattice has 1072 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21459114C211yesmaximal, characteristic, complemented
2C2×#124×D61C211yesmaximal, characteristic, complemented
3#21456824C211yesmaximal, characteristic, complemented
4#21456823C212yesmaximal, complemented
5#21456822C211yesmaximal, characteristic, complemented
6#21456802C211yesmaximal, characteristic, complemented
7#21456801C212yesmaximal, complemented
8#21456783C212yesmaximal, complemented
9#21456782C214yesmaximal, complemented
10#21456781C212yesmaximal, complemented
11#21456284C212yesmaximal, complemented
12#21456204C212yesmaximal, complemented
13#21455308C214yesmaximal, complemented
14#21455050C212yesmaximal, complemented
15#21455043C212yesmaximal, complemented
16#21454449C211yesmaximal, characteristic, complemented
17C61×#3213C211yesmaximal, characteristic, complemented
18C22×Q8×D61C2211yescharacteristic
19C22×D4×D61C2211yescharacteristic
20C2×#14519806C2214yescomplemented
21C2×#14519801C2214yes—
22#16840319C2211yescharacteristic, complemented
23#16840317C2211yescharacteristic, complemented
24#16840317C2211yescharacteristic, complemented
25#16840310C2211yescharacteristic, complemented
26#16840310C2211yescharacteristic, complemented
27#16840294—21no—
28#16840294C2212yescomplemented
29#16840293—21no—
30#16840293C2212yescomplemented
31#16840291—21no—
32#16840291—21no—
33C2×#14519766C2211yescharacteristic
34C2×#14519765C2211yescharacteristic
35C2×#14519764C2211yescharacteristic
36C2×#14519763—21no—
37C2×#14519763—21no—
38#124×D61—21no—
39#124×D61—21no—
40#124×D61—21no—
41#124×D61—21no—
42#124×D61C2212yes—
43#124×D61C2212yes—
44#124×D61C2212yes—
45#124×D61C2212yes—
46#16840272—21no—
47#16840272C2212yes—
48#16840269—21no—
49#41×Dic61—21no—
50C4×#11758224—21no—
51C4×#11758224C2212yescomplemented
52C2×C22⋊C4×D61—21no—
53C2×C22⋊C4×D61—21no—
54C2×C42×D61C2211yescharacteristic
55#16840157C2212yescomplemented
56#16840156C2212yescomplemented
57#16840149C2212yescomplemented
58#16840145C2214yescomplemented
59#16840143C2214yescomplemented
60#16840124C2212yescomplemented
61#16840122C2212yescomplemented
62#16840121C2212yescomplemented
63#16840118C2214yescomplemented
64#16840115C2214yescomplemented
65#16839987C2214yescomplemented
66#16839985C2214yescomplemented
67#16839983C2214yescomplemented
68#16839981C2214yescomplemented
69#16839979C2214yescomplemented
70#16839977C2214yescomplemented
71#16839975C2214yescomplemented
72#16839920C2212yescomplemented
73#16839919C2214yescomplemented
74#16839918C2212yescomplemented
75#16839915C2212yes—
76#16839914C2214yes—
77#16839913C2212yes—
78#16839900C2212yescomplemented
79#16839899C2214yescomplemented
80#16839895C2212yes—
81#16839894C2214yes—
82#16839819C2211yescharacteristic, complemented
83#16839817C2212yescomplemented
84#16839814C2212yescomplemented
85#16839812C2212yescomplemented
86#16839784C2212yescomplemented
87#16839769C2214yescomplemented
88#16839765C2214yes—
89#16839724C2212yes—
90#16839714C2212yescomplemented
91C61×#532C2211yescharacteristic, complemented
92C2×#124×C61C2211yescharacteristic
93C61×#496C2212yescomplemented
94C61×#489C2212yescomplemented
95C61×#463C2214yescomplemented
96C61×#448C2212yescomplemented
97C61×#447C2212yes—
98C61×#432C2211yescharacteristic, complemented
99C24×D61—21no—
100C2×#11758224—21no—
101C2×#11758224C2312yes—
102C22×Dic122—21no—
103C22×Dic122C2311yescharacteristic
104C2×Q8×D61—21no—
105C2×Q8×D61—21no—
106C2×Q8×D61—44no—
107C2×Q8×D61C2312yes—
108C2×Q8×D61C2312yes—
109C22×D244C2311yescharacteristic
110C22×C22⋊D61—21no—
111C2×D4×D61—21no—
112C2×D4×D61—21no—
113C2×D4×D61—44no—
114C2×D4×D61C2312yes—
115C2×D4×D61C2312yes—
116C22×C4×D61—21no—
117C22×C4×D61D411yescharacteristic
118C22×C4×D61D411yescharacteristic
119C22×C4×D61C2311yescharacteristic
120#14519806—48no—
121#14519801—48no—
122C2×Dic244C2314yescomplemented
123C2×#11758202C2314yescomplemented
124C2×#11758190C2314yes—
125C2×#11758200C2314yes—
126C2×#11758200C2314yescomplemented
127C2×#11758199C2314yes—
128C2×#11758189C2314yes—
129#14519777C2311yescharacteristic, complemented
130#14519777C2311yescharacteristic, complemented
131#14519770—22no—
132#14519770—22no—
133#14519769—21no—
134#14519768—21no—
135#14519768C2312yescomplemented
136#14519766—21no—
137#14519766—21no—
138#14519766C2312yes—
139#14519766C2312yes—
140#14519765—21no—
141#14519765—21no—
142#14519765C2312yes—
143#14519765C2312yes—
144#14519764—21no—
145#14519764—21no—
146#14519764—21no—
147#14519764C2312yes—
148#14519764C2312yes—
149#14519764C2312yescomplemented
150#14519763—22no—
151#14519763—22no—
152#14519763—22no—
153#14519763—22no—
154#14519763—22no—
155#14519763—22no—
156#14519763—22no—
157#14519763—22no—
158#14519759—22no—
159#14519759—22no—
160#14519758—22no—
161#14519757—21no—
162#14519757C2312yes—
163#14519756—21no—
164#14519756C2312yes—
165#14519753—21no—
166#14519753—21no—
167#14519748—21no—
168#14519748—21no—
169#14519748—21no—
170#14519748C2312yes—
171#14519745—22no—
172Q8×Dic61—21no—
173Q8×Dic61—21no—
174C4×Dic122—21no—
175C4×Dic122C2312yescomplemented
176#14519742—21no—
177#14519742C2312yescomplemented
178D4×Dic61—22no—
179D4×Dic61—22no—
180D4×Dic61—21no—
181D4×Dic61—21no—
182D4×Dic61—21no—
183D4×Dic61C2312yescomplemented
184C4×C22⋊D61—22no—
185C4×C22⋊D61—22no—
186#14519737—22no—
187#14519737—22no—
188#14519736—21no—
189#14519736—22no—
190#14519735—21no—
191#14519735C2312yes—
192#14519733—22no—
193#14519733—22no—
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—
208C2×C4×Dic61—22no—
209C2×C4×Dic61D411yescharacteristic
210C2×C4×Dic61D411yescharacteristic
211C2×C4×Dic61C2311yescharacteristic
212C42×D61D411yescharacteristic
213C42×D61D411yescharacteristic
214C42×D61D411yescharacteristic
215C42×D61D411yescharacteristic
216C42×D61C2311yescharacteristic
217C42×D61C2311yescharacteristic
218C42×D61C2311yescharacteristic
219C42×D61C2311yescharacteristic
220C4⋊#92418C2312yescomplemented
221#14519706C2314yescomplemented
222#14519702C2314yescomplemented
223#14519701C2314yescomplemented
224#14519700C2314yescomplemented
225#14519699C2314yes—
226#14519698C2314yes—
227#14519697C2314yes—
228C22⋊#92418C2312yes—
229#14519689C2314yes—
230#14519688C2312yescomplemented
231C8×Dic61C2314yescomplemented
232C2×#41×C61—21no—
233C22×Q8×C61C2311yescharacteristic
234C22×D4×C61C2311yescharacteristic
235C2×SD16×C61C2314yescomplemented
236C2×D8×C61C2314yes—
237C4⋊Q8×C61C2311yescharacteristic, complemented
238#127×C61C2311yescharacteristic, complemented
239#124×C61—21no—
240#124×C61—21no—
241#124×C61—21no—
242#124×C61C2312yes—
243#124×C61C2312yes—
244#121×C61—21no—
245#121×C61C2312yes—
246C4×D4×C61—21no—
247C4×D4×C61C2312yescomplemented
248C2×C22⋊C4×C61—21no—
249C2×C22⋊C4×C61—21no—
250C2×C42×C61C2311yescharacteristic
251C4⋊C8×C61C2312yescomplemented
252#103×C61C2314yescomplemented
253#102×C61C2314yes—
254C22⋊C8×C61C2312yes—
255#97×C61C2312yescomplemented
256C24×C61—21no—
257C23×D61—21no—
258C23×D61—22no—
259C23×D61—22no—
260C23×D61—44no—
261C23×D61—44no—
262C23×D61—44no—
263C23×D61C2×D411yescharacteristic
264#41×C61—44no—
265C2×Q8×C61—21no—
266C2×Q8×C61—21no—
267C2×Q8×C61—42no—
268C2×Q8×C61C2412yes—
269C2×D4×C61—22no—
270C2×D4×C61—21no—
271C2×D4×C61—21no—
272C2×D4×C61—21no—
273C2×D4×C61—42no—
274C2×D4×C61C2412yes—
275C2×D4×C61C2412yes—
276C22×C4×C61—21no—
277C22×C4×C61—22no—
278C22×C4×C61C2×D411yescharacteristic
279C22×C4×C61C2×D411yescharacteristic
280C22×C4×C61C2411yescharacteristic
281C2×C22⋊D61—22no—
282C2×C22⋊D61—22no—
283C2×C22⋊D61—22no—
284C2×C22⋊D61—22no—
285C2×C22⋊D61—44no—
286C22×Dic61—21no—
287C22×Dic61—22no—
288C22×Dic61—22no—
289C22×Dic61C2×D411yescharacteristic
290C22×Dic61C2×D411yescharacteristic
291C22×Dic61C2×D411yescharacteristic
292Q8×D61—28no—
293Q8×D61—44no—
294Q8×D61—44no—
295Q8×D61—44no—
296#11758224—28no—
297#11758224—44no—
298D4×D61—28no—
299D4×D61—44no—
300D4×D61—44no—
301D4×D61—44no—
302C2×D244—21no—
303C2×D244—42no—
304C2×D244C2412yes—
305C2×C4×D61—24no—
306C2×C4×D61—22no—
307C2×C4×D61—22no—
308C2×C4×D61—42no—
309C2×C4×D61—42no—
310C2×C4×D61—44no—
311C2×C4×D61C2×D411yescharacteristic
312C2×C4×D61C2×D411yescharacteristic
313C2×C4×D61C2×D411yescharacteristic
314C2×C4×D61C2×D411yescharacteristic
315C2×C4×D61C2×D411yescharacteristic
316C2×C4×D61C2×D411yescharacteristic
317C2×C4×D61C2×D411yescharacteristic
318C2×C4×D61C2×D411yescharacteristic
319C2×C4×D61C2×D411yescharacteristic
320C2×C4×D61C2×D411yescharacteristic
321C2×C4×D61C2411yescharacteristic
322C2×C4×D61C2411yescharacteristic
323C2×Dic122—21no—
324C2×Dic122—21no—
325C2×Dic122—22no—
326C2×Dic122—22no—
327C2×Dic122—42no—
328C2×Dic122—44no—
329C2×Dic122C2412yes—
330C2×Dic122C2412yes—
331SD16×C61—44no—
332D8×C61—44no—
333C2×C8×C61C2414yes—
334C4⋊C4×C61—21no—
335C4⋊C4×C61C2412yes—
336C22⋊C4×C61—22no—
337C22⋊C4×C61—22no—
338C22⋊C4×C61—22no—
339C22⋊C4×C61—22no—
340C22⋊C4×C61—22no—
341C22⋊C4×C61—22no—
342C42×C61C2×D411yescharacteristic
343C42×C61C2×D411yescharacteristic
344C42×C61C2411yescharacteristic
345C42×C61C2411yescharacteristic
346C22⋊Dic61—22no—
347C22⋊Dic61—22no—
348C22⋊Dic61—22no—
349C22⋊Dic61—22no—
350C22⋊Dic61—22no—
351C22⋊Dic61—22no—
352C22⋊Dic61—22no—
353C22⋊Dic61—22no—
354C22⋊Dic61—22no—
355#11758202—44no—
356#11758200—44no—
357#11758200—44no—
358#11758199—44no—
359#11758198—22no—
360#11758198—22no—
361#11758198—22no—
362#11758198—22no—
363#11758198—22no—
364#11758198—22no—
365#11758198—22no—
366#11758198—22no—
367#11758198—22no—
368#11758198—22no—
369C4⋊Dic61—21no—
370C4⋊Dic61—21no—
371C4⋊Dic61—21no—
372C4⋊Dic61—22no—
373C4⋊Dic61—22no—
374C4⋊Dic61C2412yes—
375#11758196—22no—
376#11758196—22no—
377#11758196—22no—
378#11758196—22no—
379C4×Dic61—22no—
380C4×Dic61—22no—
381C4×Dic61—22no—
382C4×Dic61C2×D411yescharacteristic
383C4×Dic61C2×D411yescharacteristic
384C4×Dic61C2×D411yescharacteristic
385C4×Dic61C2×D411yescharacteristic
386C4×Dic61C2×D411yescharacteristic
387C4×Dic61C2×D411yescharacteristic
388C4×Dic61C2×D411yescharacteristic
389C4×Dic61C2×D411yescharacteristic
390C4×Dic61C2×D411yescharacteristic
391C4×Dic61C2×D411yescharacteristic
392C4×Dic61C2411yescharacteristic
393C4×Dic61C2411yescharacteristic
394C2×#92418C2414yes—
395Dic244—44no—
396#11758190—44no—
397#11758189—28no—
398C23×C61—22no—
399C23×C61—22no—
400C23×C61—42no—
401C23×C61—42no—
402C23×C61—42no—
403C23×C61C22×D411yescharacteristic
404C22×D61—22no—
405C22×D61—22no—
406C22×D61—22no—
407C22×D61—22no—
408C22×D61—44no—
409C22×D61—44no—
410C22×D61—44no—
411C22×D61—44no—
412C22×D61—42no—
413C22×D61—42no—
414C22×D61—42no—
415C22×D61—44no—
416C22×D61—44no—
417C22×D61—816no—
418C22×D61C22×D411yescharacteristic
419C22×D61C22×D411yescharacteristic
420Q8×C61—24no—
421Q8×C61—42no—
422Q8×C61—42no—
423D4×C61—24no—
424D4×C61—24no—
425D4×C61—42no—
426D4×C61—42no—
427D4×C61—42no—
428D4×C61—44no—
429C2×C4×C61—22no—
430C2×C4×C61—22no—
431C2×C4×C61—22no—
432C2×C4×C61—22no—
433C2×C4×C61—41no—
434C2×C4×C61—44no—
435C2×C4×C61—42no—
436C2×C4×C61C22×D411yescharacteristic
437C2×C4×C61C22×D411yescharacteristic
438C2×C4×C61C22×D411yescharacteristic
439C2×C4×C61C22×D411yescharacteristic
440C2×C4×C61C22×D411yescharacteristic
441C2×C4×C61C2511yescharacteristic
442C22⋊D61—44no—
443C22⋊D61—44no—
444C22⋊D61—44no—
445C22⋊D61—44no—
446C2×Dic61—22no—
447C2×Dic61—22no—
448C2×Dic61—22no—
449C2×Dic61—22no—
450C2×Dic61—22no—
451C2×Dic61—41no—
452C2×Dic61—44no—
453C2×Dic61—42no—
454C2×Dic61—44no—
455C2×Dic61C22×D411yescharacteristic
456C2×Dic61C22×D411yescharacteristic
457C2×Dic61C22×D411yescharacteristic
458C2×Dic61C22×D411yescharacteristic
459C2×Dic61C22×D411yescharacteristic
460C2×Dic61C22×D411yescharacteristic
461D244—24no—
462D244—42no—
463C4×D61—22no—
464C4×D61—22no—
465C4×D61—22no—
466C4×D61—22no—
467C4×D61—22no—
468C4×D61—41no—
469C4×D61—41no—
470C4×D61—41no—
471C4×D61—41no—
472C4×D61—41no—
473C4×D61—41no—
474C4×D61—44no—
475C4×D61—44no—
476C4×D61H(5,𝔽2)14yes—
477Dic122—24no—
478Dic122—24no—
479Dic122—44no—
480Dic122—42no—
481Dic122—42no—
482Dic122—44no—
483C8×C61—24no—
484#92418—24no—
485#60799—611nomaximal, Sylow
486C22×C61—21no—
487C22×C61—21no—
488C22×C61—42no—
489C22×C61—42no—
490C22×C61—42no—
491C22×C61—42no—
492C22×C61—42no—
493C22×C61—42no—
494C22×C61—84no—
495C22×C61#57512yes—
496C22×C61C23×D411yescharacteristic
497C2×D61—28no—
498C2×D61—21no—
499C2×D61—21no—
500C2×D61—21no—
501C2×D61—21no—
502C2×D61—42no—
503C2×D61—42no—
504C2×D61—42no—
505C2×D61—88no—
506C2×D61—88no—
507C2×D61—84no—
508C2×D61#53512yes—
509C2×D61#57512yes—
510C4×C61—21no—
511C4×C61—21no—
512C4×C61—21no—
513C4×C61—21no—
514C4×C61—21no—
515C4×C61—42no—
516C4×C61—42no—
517C4×C61C2×H(5,𝔽2)12yes—
518Dic61—21no—
519Dic61—21no—
520Dic61—21no—
521Dic61—21no—
522Dic61—21no—
523Dic61—42no—
524Dic61—42no—
525Dic61—42no—
526Dic61#53512yes—
527#3444—611no—
528C22×#124—611no—
529#3215—612no—
530#3215—611no—
531#3215—611no—
532#3213—612no—
533#3213—611no—
534#3213D6111yescharacteristic, complemented
535#3211—614no—
536#3211—612no—
537#3211—612no—
538#3153—612no—
539#3140—612no—
540#3040—614no—
541#3004—612no—
542#3003—612no—
543#2920—611no—
544C2×C61—22no—
545C2×C61—82no—
546C2×C61—82no—
547C2×C61C2×#53511yescharacteristic
548C2×C61C2×#57511yescharacteristic
549C2×C61C2×#57511yescharacteristic
550D61—22no—
551D61—22no—
552D61—82no—
553C23×Q8—611no—
554C23×D4—611no—
555C2×#137—614no—
556C2×AGL(1,ℤ/8)—614no—
557#533—611no—
558#533—611no—
559#533—611no—
560#532—611no—
561#532—611no—
562#532C2×D6111yescharacteristic, complemented
563#529—612no—
564#529—612no—
565#529—1221no—
566#529—1221no—
567#529—1221no—
568#529—1221no—
569C2×#124—611no—
570C2×#124—611no—
571C2×#124—612no—
572C2×#124—612no—
573C2×#124—612no—
574C2×#124—612no—
575C2×#124—611no—
576C2×#124—1221no—
577C2×#124—1221no—
578C2×#124—1221no—
579C2×#124—1221no—
580C2×#124—1221no—
581C2×#124—1221no—
582C2×#124C2×D6111yescharacteristic
583#525—612no—
584#525—1221no—
585#525—1221no—
586C4×#41—612no—
587C4×#41—1221no—
588C4×#41—1221no—
589C22×C22⋊C4—1221no—
590C22×C22⋊C4—1221no—
591C22×C42—611no—
592#497—612no—
593#497—612no—
594#496—612no—
595#496C2×D6112yescomplemented
596#495—614no—
597#495—614no—
598#489—612no—
599#489—612no—
600#489—612no—
601#489C2×D6112yescomplemented
602#488—614no—
603#488—614no—
604#464—614no—
605#464—614no—
606#464—614no—
607#464—614no—
608#463—614no—
609#463—614no—
610#463—614no—
611#463C2×D6114yescomplemented
612#451—612no—
613#451—614no—
614#451—612no—
615#450—612no—
616#450—614no—
617#450—612no—
618#448—614no—
619#448—612no—
620#448C2×D6112yescomplemented
621#447—614no—
622#447—612no—
623#447C2×D6112yes—
624#432—611no—
625#432—612no—
626#432C2×D6111yescharacteristic, complemented
627#431—612no—
628#431—612no—
629#423—612no—
630#419—614no—
631#418—614no—
632#407—612no—
633C4×M16—612no—
634C61#6079911yescharacteristic, complemented, Sylow
635C25—1221no—
636C2×#41—21no—
637C2×#41—612no—
638C2×#41—1221no—
639C22×Q8—612no—
640C22×Q8—612no—
641C22×Q8—611no—
642C22×Q8—1221no—
643C22×Q8—1221no—
644C22×Q8—1221no—
645C22×Q8—2444no—
646C22×Q8C22×D6111yescharacteristic
647C22×D4—612no—
648C22×D4—612no—
649C22×D4—611no—
650C22×D4—1221no—
651C22×D4—1221no—
652C22×D4—1221no—
653C22×D4—2444no—
654C22×D4C22×D6111yescharacteristic
655C23×C4—611no—
656C23×C4—611no—
657C23×C4—611no—
658C23×C4—1221no—
659#137—2448no—
660AGL(1,ℤ/8)—2448no—
661C2×Q16—614no—
662C2×Q16—614no—
663C2×SD16—614no—
664C2×SD16—614no—
665C2×SD16—614no—
666C2×SD16C22×D6114yescomplemented
667C2×D8—614no—
668C2×D8C22×D6114yes—
669C2×M16—614no—
670C4⋊Q8—611no—
671C4⋊Q8—611no—
672C4⋊Q8C22×D6111yescharacteristic, complemented
673#127C22×D6111yescharacteristic, complemented
674#126—1222no—
675#126—1222no—
676#125—612no—
677#125—1221no—
678#125—1221no—
679#124—21no—
680#124—21no—
681#124—21no—
682#124—612no—
683#124—612no—
684#124—612no—
685#124—612no—
686#124—612no—
687#124—612no—
688#124—612no—
689#124—1222no—
690#124—1222no—
691#124—1222no—
692#124—1222no—
693#124—1222no—
694#124—1222no—
695#124—1222no—
696#124—1222no—
697#124—1221no—
698#124—1221no—
699#124—1221no—
700#124—1221no—
701#124—1221no—
702#124—1221no—
703#124—1221no—
704#124C22×D6112yes—
705#124C22×D6112yes—
706#123—1222no—
707#123—1222no—
708#123—1222no—
709C22⋊Q8—612no—
710C22⋊Q8—612no—
711C22⋊Q8—1221no—
712C22⋊Q8—1221no—
713C22⋊Q8—1221no—
714C22⋊Q8—1221no—
715#121—21no—
716#121—612no—
717#121—1221no—
718#121—1221no—
719#121—1221no—
720#121C22×D6112yes—
721#120—1222no—
722C4×Q8—612no—
723C4×Q8—612no—
724C4×Q8—1221no—
725C4×Q8—1221no—
726C4×Q8—1221no—
727C4×Q8—1221no—
728C4×D4—21no—
729C4×D4—612no—
730C4×D4—1221no—
731C4×D4—1221no—
732C4×D4—1221no—
733C4×D4—1222no—
734C4×D4—1222no—
735C4×D4—1222no—
736C4×D4—1222no—
737C4×D4—1222no—
738C4×D4—1222no—
739C4×D4C22×D6112yescomplemented
740#117—612no—
741#117—1222no—
742#117—1222no—
743#117—1222no—
744#117—1221no—
745#117—1221no—
746C2×C22⋊C4—21no—
747C2×C22⋊C4—21no—
748C2×C22⋊C4—1222no—
749C2×C22⋊C4—1222no—
750C2×C22⋊C4—1222no—
751C2×C22⋊C4—1222no—
752C2×C22⋊C4—1222no—
753C2×C22⋊C4—1222no—
754C2×C22⋊C4—1222no—
755C2×C22⋊C4—1222no—
756C2×C22⋊C4—1221no—
757C2×C22⋊C4—1221no—
758C2×C22⋊C4—1221no—
759C2×C22⋊C4—1221no—
760C2×C22⋊C4—1221no—
761C2×C22⋊C4—1221no—
762C2×C42—611no—
763C2×C42—611no—
764C2×C42—611no—
765C2×C42—611no—
766C2×C42—611no—
767C2×C42—611no—
768C2×C42—611no—
769C2×C42—611no—
770C2×C42—611no—
771C2×C42—611no—
772C2×C42—611no—
773C2×C42—1222no—
774C2×C42C22×D6111yescharacteristic
775C4⋊C8—614no—
776C4⋊C8—612no—
777C4⋊C8C22×D6112yescomplemented
778#103—614no—
779#103—614no—
780#103—614no—
781#103C22×D6114yescomplemented
782#102—614no—
783#102—614no—
784#102—614no—
785#102C22×D6114yes—
786C22⋊C8—612no—
787C22⋊C8—614no—
788C22⋊C8C22×D6112yes—
789#97—612no—
790#97C22×D6112yescomplemented
791C4×C8—614no—
792C24—21no—
793C24—611no—
794C24—1222no—
795C24—1222no—
796C24—1221no—
797C24—2444no—
798C24—2444no—
799C24—2444no—
800#41—44no—
801#41—1228no—
802#41—2444no—
803C2×Q8—21no—
804C2×Q8—21no—
805C2×Q8—42no—
806C2×Q8—612no—
807C2×Q8—612no—
808C2×Q8—1222no—
809C2×Q8—1222no—
810C2×Q8—1228no—
811C2×Q8—1221no—
812C2×Q8—1221no—
813C2×Q8—2442no—
814C2×Q8—2444no—
815C2×Q8—2444no—
816C2×Q8—2444no—
817C2×Q8—2444no—
818C2×Q8C23×D6112yes—
819C2×D4—22no—
820C2×D4—21no—
821C2×D4—21no—
822C2×D4—21no—
823C2×D4—42no—
824C2×D4—612no—
825C2×D4—1228no—
826C2×D4—1222no—
827C2×D4—1222no—
828C2×D4—1222no—
829C2×D4—1222no—
830C2×D4—1221no—
831C2×D4—2442no—
832C2×D4—2444no—
833C2×D4—2444no—
834C2×D4—2444no—
835C2×D4—2444no—
836C2×D4C23×D6112yes—
837C2×D4C23×D6112yes—
838C22×C4—21no—
839C22×C4—22no—
840C22×C4—611no—
841C22×C4—611no—
842C22×C4—611no—
843C22×C4—611no—
844C22×C4—611no—
845C22×C4—611no—
846C22×C4—611no—
847C22×C4—611no—
848C22×C4—611no—
849C22×C4—611no—
850C22×C4—611no—
851C22×C4—611no—
852C22×C4—611no—
853C22×C4—611no—
854C22×C4—611no—
855C22×C4—1224no—
856C22×C4—1222no—
857C22×C4—1222no—
858C22×C4—1222no—
859C22×C4—1222no—
860C22×C4—1221no—
861C22×C4—2442no—
862C22×C4—2442no—
863C22×C4—2444no—
864C22×C4D4×D6111yescharacteristic
865C22×C4D4×D6111yescharacteristic
866C22×C4C23×D6111yescharacteristic
867Q16—2444no—
868Q16—2444no—
869SD16—44no—
870SD16—2444no—
871SD16—2444no—
872SD16—2444no—
873D8—44no—
874D8—2444no—
875M16—1228no—
876C2×C8—614no—
877C2×C8C23×D6114yes—
878C4⋊C4—21no—
879C4⋊C4—612no—
880C4⋊C4—1222no—
881C4⋊C4—1222no—
882C4⋊C4—1222no—
883C4⋊C4—1222no—
884C4⋊C4—1222no—
885C4⋊C4—1222no—
886C4⋊C4—1221no—
887C4⋊C4—1221no—
888C4⋊C4—1221no—
889C4⋊C4C23×D6112yes—
890C22⋊C4—22no—
891C22⋊C4—22no—
892C22⋊C4—22no—
893C22⋊C4—22no—
894C22⋊C4—22no—
895C22⋊C4—22no—
896C22⋊C4—1222no—
897C22⋊C4—1222no—
898C22⋊C4—1222no—
899C22⋊C4—1222no—
900C22⋊C4—1222no—
901C22⋊C4—1222no—
902C22⋊C4—1222no—
903C22⋊C4—1222no—
904C22⋊C4—1222no—
905C22⋊C4—1222no—
906C22⋊C4—1222no—
907C22⋊C4—1222no—
908C22⋊C4—1222no—
909C22⋊C4—1222no—
910C22⋊C4—1222no—
911C22⋊C4—1222no—
912C22⋊C4—1222no—
913C22⋊C4—1222no—
914C22⋊C4—1222no—
915C42—611no—
916C42—611no—
917C42—611no—
918C42—611no—
919C42—611no—
920C42—611no—
921C42—611no—
922C42—611no—
923C42—611no—
924C42—611no—
925C42—611no—
926C42—611no—
927C42—1222no—
928C42—1222no—
929C42—1222no—
930C42D4×D6111yescharacteristic
931C42D4×D6111yescharacteristic
932C42C23×D6111yescharacteristic
933C42C23×D6111yescharacteristic
934C23—22no—
935C23—22no—
936C23—42no—
937C23—42no—
938C23—42no—
939C23—611no—
940C23—611no—
941C23—1222no—
942C23—1222no—
943C23—1222no—
944C23—1222no—
945C23—48816no—
946C23—2442no—
947C23—2442no—
948C23—2444no—
949C23—2444no—
950C23—2444no—
951C23—2444no—
952C23—2444no—
953C23—2444no—
954C23—2442no—
955C23C2×D4×D6111yescharacteristic
956Q8—24no—
957Q8—42no—
958Q8—42no—
959Q8—1224no—
960Q8—1224no—
961Q8—2442no—
962Q8—2442no—
963Q8—2444no—
964Q8—2444no—
965D4—24no—
966D4—24no—
967D4—42no—
968D4—42no—
969D4—42no—
970D4—44no—
971D4—1224no—
972D4—2442no—
973D4—2444no—
974D4—2444no—
975D4—2444no—
976D4—2444no—
977C2×C4—22no—
978C2×C4—22no—
979C2×C4—22no—
980C2×C4—22no—
981C2×C4—41no—
982C2×C4—44no—
983C2×C4—42no—
984C2×C4—611no—
985C2×C4—614no—
986C2×C4—611no—
987C2×C4—611no—
988C2×C4—611no—
989C2×C4—611no—
990C2×C4—611no—
991C2×C4—1222no—
992C2×C4—1222no—
993C2×C4—1222no—
994C2×C4—1222no—
995C2×C4—1222no—
996C2×C4—1222no—
997C2×C4—1222no—
998C2×C4—1222no—
999C2×C4—1222no—
1000C2×C4—1222no—
1001C2×C4—2441no—
1002C2×C4—2441no—
1003C2×C4—2441no—
1004C2×C4—2441no—
1005C2×C4—2441no—
1006C2×C4—2441no—
1007C2×C4—2444no—
1008C2×C4—2444no—
1009C2×C4—2444no—
1010C2×C4—2441no—
1011C2×C4—2444no—
1012C2×C4—2442no—
1013C2×C4C2×D4×D6111yescharacteristic
1014C2×C4C2×D4×D6111yescharacteristic
1015C2×C4C2×D4×D6111yescharacteristic
1016C2×C4C2×D4×D6111yescharacteristic
1017C2×C4C2×D4×D6111yescharacteristic
1018C2×C4C24×D6111yescharacteristic
1019C8—24no—
1020C8—1224no—
1021C22—21no—
1022C22—21no—
1023C22—42no—
1024C22—42no—
1025C22—42no—
1026C22—42no—
1027C22—42no—
1028C22—42no—
1029C22—84no—
1030C22—612no—
1031C22—612no—
1032C22—1228no—
1033C22—1221no—
1034C22—1221no—
1035C22—1221no—
1036C22—1221no—
1037C22—4884no—
1038C22—4888no—
1039C22—4888no—
1040C22—2442no—
1041C22—2442no—
1042C22—2442no—
1043C22#1684055812yes—
1044C22C22×D4×D6111yescharacteristic
1045C4—21no—
1046C4—21no—
1047C4—21no—
1048C4—21no—
1049C4—21no—
1050C4—42no—
1051C4—42no—
1052C4—612no—
1053C4—1221no—
1054C4—1221no—
1055C4—1221no—
1056C4—1221no—
1057C4—1221no—
1058C4—2442no—
1059C4—2442no—
1060C4—2442no—
1061C4H(5,𝔽2)×D6112yes—
1062C2—22no—
1063C2—82no—
1064C2—82no—
1065C2—1222no—
1066C2—1222no—
1067C2—4882no—
1068C2#535×D6111yescharacteristic
1069C2#575×D6111yescharacteristic
1070C2C2×#1684055811yescharacteristic
subgroupG/H
centerC22C22×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC61×#3213C2
socleC22×C61C23×D4
hypercenter#3213D61
hypocenterC61#60799
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. #21459114C2semidirect
2. C2×#124×D61C2semidirect
3. #21456824C2semidirect
4. #21456823C2semidirect
5. #21456822C2semidirect
6. #21456802C2semidirect
7. #21456801C2semidirect
8. #21456783C2semidirect
9. #21456782C2semidirect
10. #21456781C2semidirect
11. #21456284C2semidirect
12. #21456204C2semidirect
13. #21455308C2semidirect
14. #21455050C2semidirect
15. #21455043C2semidirect
16. #21454449C2semidirect
17. C61×#3213C2semidirect
20. C2×#14519806C22semidirect
22. #16840319C22semidirect
23. #16840317C22semidirect
24. #16840317C22semidirect
25. #16840310C22semidirect
26. #16840310C22semidirect
28. #16840294C22semidirect
30. #16840293C22semidirect
51. C4×#11758224C22semidirect
55. #16840157C22semidirect
56. #16840156C22semidirect
57. #16840149C22semidirect
58. #16840145C22semidirect
59. #16840143C22semidirect
60. #16840124C22semidirect
61. #16840122C22semidirect
62. #16840121C22semidirect
63. #16840118C22semidirect
64. #16840115C22semidirect
65. #16839987C22semidirect
66. #16839985C22semidirect
67. #16839983C22semidirect
68. #16839981C22semidirect
69. #16839979C22semidirect
70. #16839977C22semidirect
71. #16839975C22semidirect
72. #16839920C22semidirect
73. #16839919C22semidirect
74. #16839918C22semidirect
78. #16839900C22semidirect
79. #16839899C22semidirect
82. #16839819C22semidirect
83. #16839817C22semidirect
84. #16839814C22semidirect
85. #16839812C22semidirect
86. #16839784C22semidirect
87. #16839769C22semidirect
90. #16839714C22semidirect
91. C61×#532C22semidirect
93. C61×#496C22semidirect
94. C61×#489C22semidirect
95. C61×#463C22semidirect
96. C61×#448C22semidirect
98. C61×#432C22semidirect
122. C2×Dic244C23semidirect
123. C2×#11758202C23semidirect
126. C2×#11758200C23semidirect
129. #14519777C23semidirect
130. #14519777C23semidirect
135. #14519768C23semidirect
149. #14519764C23semidirect
175. C4×Dic122C23semidirect
177. #14519742C23semidirect
183. D4×Dic61C23semidirect
220. C4⋊#92418C23semidirect
221. #14519706C23semidirect
222. #14519702C23semidirect
223. #14519701C23semidirect
224. #14519700C23semidirect
230. #14519688C23semidirect
231. C8×Dic61C23semidirect
235. C2×SD16×C61C23semidirect
237. C4⋊Q8×C61C23semidirect
238. #127×C61C23semidirect
247. C4×D4×C61C23semidirect
251. C4⋊C8×C61C23semidirect
252. #103×C61C23semidirect
255. #97×C61C23semidirect
534. #3213D61semidirect
562. #532C2×D61semidirect
595. #496C2×D61semidirect
601. #489C2×D61semidirect
611. #463C2×D61semidirect
620. #448C2×D61semidirect
626. #432C2×D61semidirect
634. C61#60799semidirect
666. C2×SD16C22×D61semidirect
672. C4⋊Q8C22×D61semidirect
673. #127C22×D61semidirect
739. C4×D4C22×D61semidirect
777. C4⋊C8C22×D61semidirect
781. #103C22×D61semidirect
790. #97C22×D61semidirect

Maximal subgroups

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

subgroupindex
#214591142
C2×#124×D612
#214568242
#214568232
#214568222
#214568022
#214568012
#214567832
#214567822
#214567812
#214562842
#214562042
#214553082
#214550502
#214550432
#214544492
C61×#32132
#6079961