Finite Group Databasebeta

← #30552185

Subgroups — #30552185

Order 15616.

1780 conjugacy classes of subgroups.

The subgroup lattice has 1054 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21459113C211yesmaximal, characteristic
2C2×#16840317C211yesmaximal, characteristic, complemented
3#21457060C212yesmaximal, complemented
4#21457054C212yesmaximal, complemented
5#21457051C211yesmaximal, characteristic, complemented
6#21457046C211yesmaximal, characteristic, complemented
7#21457040C211yesmaximal, characteristic, complemented
8#21457031C212yesmaximal, complemented
9#21457022C212yesmaximal, complemented
10#21457015C212yesmaximal, complemented
11#21457006C212yesmaximal, complemented
12#21456340C212yesmaximal, complemented
13#21456161C212yesmaximal, complemented
14#21455733C212yesmaximal, complemented
15#21455727C212yesmaximal, complemented
16#21455610C212yesmaximal, complemented
17#21455608C212yesmaximal, complemented
18#432×D61C211yesmaximal, characteristic, complemented
19C61×#3238C211yesmaximal, characteristic, complemented
20#16840318C2211yescharacteristic
21#16840317—21no—
22#16840317—21no—
23#16840317—21no—
24#16840317—21no—
25#16840317C2212yes—
26#16840317C2212yes—
27#16840317C2212yes—
28#16840317C2212yes—
29#16840316C2211yescharacteristic
30#16840314C2211yescharacteristic
31#16840311C2211yescharacteristic
32#16840309C2211yescharacteristic
33#16840307C2211yescharacteristic
34C2×#14519777C2211yescharacteristic
35#16840297C2211yescharacteristic
36#16840296C2211yescharacteristic
37#16840295—21no—
38#16840295—21no—
39#16840291C2211yescharacteristic
40#16840290—21no—
41#16840289—21no—
42C2×#14519768C2212yes—
43#16840275C2211yescharacteristic
44#16840272C2211yescharacteristic
45#16840271—21no—
46#16840270—21no—
47C2×#14519757—21no—
48C2×#14519753—21no—
49C4×#11758226C2211yescharacteristic
50#16840230—21no—
51C4×#11758224—21no—
52C4×#11758224C2211yescharacteristic
53C2×Q8×Dic61—21no—
54C2×#14519742—21no—
55C2×#14519735C2212yes—
56C2×C42×D61C2211yescharacteristic
57#16840172C2212yescomplemented
58#16840171C2212yescomplemented
59#16840170C2214yescomplemented
60#16840169C2214yescomplemented
61#16840168C2212yescomplemented
62#16840129C2214yescomplemented
63#16840125C2214yescomplemented
64#16840124C2212yescomplemented
65#16840122C2212yescomplemented
66#16840121C2212yescomplemented
67#16840105C2214yes—
68#16840101C2214yes—
69#16840098C2212yes—
70#16840095C2212yes—
71#16840092C2212yes—
72#16840088C2214yes—
73#16840084C2214yes—
74#16840081C2212yes—
75#16840078C2212yes—
76#16840075C2212yes—
77#16840072C2214yescomplemented
78#16840071C2214yescomplemented
79#16840065C2214yescomplemented
80#16840064C2214yescomplemented
81#16840054C2212yescomplemented
82#16840049C2212yescomplemented
83#16840048C2212yescomplemented
84#16840047C2212yescomplemented
85#16840043C2212yescomplemented
86#16840042C2212yescomplemented
87#16839819C2211yescharacteristic
88#16839818C2212yes—
89#16839817C2212yes—
90#16839816C2212yes—
91#16839799C2214yes—
92#16839797C2214yes—
93C4⋊C8×D61C2212yes—
94#16839757C2214yes—
95#16839755C2214yes—
96C22⋊C8×D61C2212yes—
97#97×D61C2212yes—
98C2×C4⋊Q8×C61C2211yescharacteristic
99C61×#529C2211yescharacteristic
100C61×#501C2212yescomplemented
101C61×#489C2212yescomplemented
102C61×#483C2212yes—
103C61×#480C2212yes—
104C61×#477C2212yescomplemented
105C61×#476C2212yescomplemented
106C61×#432C2211yescharacteristic
107C2×#11758226C2311yescharacteristic
108C2×#11758222—21no—
109C2×#11758224—21no—
110C2×#11758224C2311yescharacteristic
111C22×Dic122—21no—
112C22×C4×D61D411yescharacteristic
113C22×C4×D61D411yescharacteristic
114C22×C4×D61C2311yescharacteristic
115C2×C8×D61C2314yes—
116#14519777—21no—
117#14519777—21no—
118#14519777C2312yes—
119#14519777C2312yes—
120#14519776C2311yescharacteristic
121#14519776C2311yescharacteristic
122#14519775C2311yescharacteristic
123#14519773C2311yescharacteristic
124#14519772—21no—
125#14519771—21no—
126#14519770—21no—
127#14519769C2311yescharacteristic
128#14519768—22no—
129#14519768—22no—
130#14519768C2314yes—
131#14519768C2314yes—
132#14519767—21no—
133#14519767—21no—
134#14519765C2311yescharacteristic
135#14519763—21no—
136#14519763—21no—
137#14519762—21no—
138#14519762—21no—
139#14519760—21no—
140#14519759—21no—
141#14519759—21no—
142#14519757—22no—
143#14519757—22no—
144#14519757—22no—
145#14519757—22no—
146#14519757C2311yescharacteristic
147#14519756C2311yescharacteristic
148#14519755—21no—
149#14519755—21no—
150#14519755—21no—
151#14519754—21no—
152#14519753—22no—
153#14519753—22no—
154#14519753—22no—
155#14519753—22no—
156#14519753C2311yescharacteristic
157#14519752C2311yescharacteristic
158#14519751C2311yescharacteristic
159#14519750—21no—
160#14519750—21no—
161#14519750—21no—
162#14519749—21no—
163#14519748C2311yescharacteristic
164#14519747—21no—
165#14519745—21no—
166Q8×Dic61—22no—
167Q8×Dic61—22no—
168Q8×Dic61—22no—
169Q8×Dic61—22no—
170Q8×Dic61C2311yescharacteristic
171C4×Dic122—21no—
172C4×Dic122C2311yescharacteristic
173#14519742—22no—
174#14519742—22no—
175#14519742—22no—
176#14519742—22no—
177#14519742—21no—
178#14519742—21no—
179#14519742—21no—
180#14519742C2311yescharacteristic
181C4×D244—21no—
182C4×D244C2311yescharacteristic
183D4×Dic61—21no—
184D4×Dic61C2311yescharacteristic
185#14519739—21no—
186#14519739—21no—
187#14519739—21no—
188#14519739C2311yescharacteristic
189C4×C22⋊D61—21no—
190C4×C22⋊D61—21no—
191C4×C22⋊D61—21no—
192#14519737—21no—
193#14519737—21no—
194#14519737—21no—
195#14519737—21no—
196#14519737—21no—
197#14519737—21no—
198#14519737—21no—
199#14519735—22no—
200#14519735—22no—
201#14519735—21no—
202#14519735—21no—
203#14519735C2314yes—
204#14519735C2314yes—
205#14519735C2311yescharacteristic
206#14519735C2311yescharacteristic
207#14519734—21no—
208#14519734—21no—
209#14519733—21no—
210#14519733—21no—
211#14519733—21no—
212C2×C4⋊Dic61—21no—
213C2×C4⋊Dic61—22no—
214C2×C4⋊Dic61C2312yes—
215C2×#11758196—22no—
216C2×#11758198—22no—
217C2×C4×Dic61—22no—
218C2×C4×Dic61—21no—
219C2×C4×Dic61D411yescharacteristic
220C2×C4×Dic61D411yescharacteristic
221C2×C4×Dic61C2311yescharacteristic
222C42×D61—21no—
223C42×D61D411yescharacteristic
224C42×D61D411yescharacteristic
225C42×D61D411yescharacteristic
226C42×D61D411yescharacteristic
227C42×D61C2311yescharacteristic
228C42×D61C2311yescharacteristic
229C42×D61C2311yescharacteristic
230C42×D61C2311yescharacteristic
231#14519711C2314yes—
232#14519710C2314yes—
233#14519710C2314yes—
234#14519709C2314yes—
235#14519708C2314yes—
236#14519708C2314yes—
237C4⋊#92418C2312yes—
238#14519706C2314yes—
239#14519702C2314yes—
240#14519701C2314yes—
241#14519700C2314yes—
242#14519699C2314yes—
243#14519698C2314yes—
244#14519697C2314yes—
245C22⋊#92418C2312yes—
246#14519689C2314yes—
247#14519688C2312yes—
248#14519687C2314yes—
249C22×Q8×C61—21no—
250C4⋊Q8×C61—21no—
251C4⋊Q8×C61—21no—
252C4⋊Q8×C61C2312yes—
253C4⋊Q8×C61C2312yes—
254#126×C61—21no—
255#125×C61C2311yescharacteristic
256#124×C61C2311yescharacteristic
257#123×C61—21no—
258C22⋊Q8×C61C2311yescharacteristic
259#121×C61C2311yescharacteristic
260C4×Q8×C61C2311yescharacteristic
261C4×D4×C61—21no—
262C4×D4×C61C2311yescharacteristic
263#117×C61—21no—
264C2×C4⋊C4×C61—21no—
265C2×C4⋊C4×C61C2312yes—
266C2×C42×C61C2311yescharacteristic
267#107×C61C2314yes—
268#106×C61C2314yes—
269C4⋊C8×C61C2312yes—
270#103×C61C2314yes—
271#102×C61C2314yes—
272C22⋊C8×C61C2312yes—
273#97×C61C2312yes—
274C23×D61C2×D411yescharacteristic
275C2×Q8×C61—22no—
276C2×Q8×C61—22no—
277C2×Q8×C61—44no—
278C2×Q8×C61C2411yescharacteristic
279C2×D4×C61—21no—
280C2×D4×C61C2411yescharacteristic
281C22×C4×C61—22no—
282C22×C4×C61—21no—
283C22×C4×C61C2×D411yescharacteristic
284C22×C4×C61C2×D411yescharacteristic
285C22×C4×C61C2411yescharacteristic
286C2×C22⋊D61—21no—
287C2×C22⋊D61—21no—
288C2×C22⋊D61—21no—
289C2×C22⋊D61—21no—
290C2×C22⋊D61—21no—
291C22×Dic61—22no—
292C22×Dic61—21no—
293C22×Dic61—21no—
294C22×Dic61C2×D411yescharacteristic
295C22×Dic61C2×D411yescharacteristic
296C22×Dic61C2×D411yescharacteristic
297#11758226—24no—
298#11758224—24no—
299#11758224—44no—
300#11758222—44no—
301C2×D244—21no—
302C2×D244—21no—
303C2×D244C2411yescharacteristic
304C2×C4×D61—24no—
305C2×C4×D61—21no—
306C2×C4×D61—21no—
307C2×C4×D61—21no—
308C2×C4×D61—42no—
309C2×C4×D61—42no—
310C2×C4×D61C2×D411yescharacteristic
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×D61C2411yescharacteristic
321C2×C4×D61C2411yescharacteristic
322C2×Dic122—22no—
323C2×Dic122—22no—
324C2×Dic122—21no—
325C2×Dic122—21no—
326C2×Dic122—44no—
327C2×Dic122C2411yescharacteristic
328C2×C8×C61C2414yes—
329C4⋊C4×C61—22no—
330C4⋊C4×C61—22no—
331C4⋊C4×C61—22no—
332C4⋊C4×C61—21no—
333C4⋊C4×C61—21no—
334C4⋊C4×C61—21no—
335C4⋊C4×C61—21no—
336C4⋊C4×C61C2414yes—
337C4⋊C4×C61C2411yescharacteristic
338C4⋊C4×C61C2411yescharacteristic
339C22⋊C4×C61—21no—
340C22⋊C4×C61—21no—
341C22⋊C4×C61—21no—
342C22⋊C4×C61—21no—
343C22⋊C4×C61—21no—
344C42×C61—21no—
345C42×C61C2×D411yescharacteristic
346C42×C61C2×D411yescharacteristic
347C42×C61C2411yescharacteristic
348C42×C61C2411yescharacteristic
349C22⋊Dic61—21no—
350C22⋊Dic61—21no—
351C22⋊Dic61—21no—
352#11758198—24no—
353#11758198—24no—
354#11758198—21no—
355#11758198—21no—
356#11758198—21no—
357#11758198—21no—
358#11758198—21no—
359#11758198—21no—
360#11758198—21no—
361#11758198—21no—
362#11758198—21no—
363#11758198—21no—
364C4⋊Dic61—22no—
365C4⋊Dic61—22no—
366C4⋊Dic61—22no—
367C4⋊Dic61—24no—
368C4⋊Dic61—24no—
369C4⋊Dic61—21no—
370C4⋊Dic61—21no—
371C4⋊Dic61C2414yes—
372C4⋊Dic61C2411yescharacteristic
373C4⋊Dic61C2411yescharacteristic
374#11758196—21no—
375#11758196—21no—
376#11758196—21no—
377#11758196—21no—
378#11758196—24no—
379#11758196—24no—
380#11758196—21no—
381#11758196—21no—
382#11758196—21no—
383#11758196—21no—
384#11758196—21no—
385#11758196—21no—
386C4×Dic61—21no—
387C4×Dic61—21no—
388C4×Dic61—21no—
389C4×Dic61—21no—
390C4×Dic61—21no—
391C4×Dic61—24no—
392C4×Dic61—24no—
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×Dic61C2×D411yescharacteristic
403C4×Dic61C2411yescharacteristic
404C4×Dic61C2411yescharacteristic
405C2×#92418C2414yes—
406C8×D61—28no—
407C23×C61—21no—
408C23×C61C22×D411yescharacteristic
409C22×D61—22no—
410C22×D61—22no—
411C22×D61—21no—
412C22×D61—41no—
413C22×D61C22×D411yescharacteristic
414C22×D61C22×D411yescharacteristic
415Q8×C61—22no—
416Q8×C61—44no—
417Q8×C61—44no—
418D4×C61—22no—
419D4×C61—42no—
420C2×C4×C61—22no—
421C2×C4×C61—22no—
422C2×C4×C61—22no—
423C2×C4×C61—24no—
424C2×C4×C61—21no—
425C2×C4×C61—21no—
426C2×C4×C61—21no—
427C2×C4×C61—44no—
428C2×C4×C61—42no—
429C2×C4×C61C22×D411yescharacteristic
430C2×C4×C61C22×D411yescharacteristic
431C2×C4×C61C22×D411yescharacteristic
432C2×C4×C61C22×D411yescharacteristic
433C2×C4×C61C22×D411yescharacteristic
434C2×C4×C61C2511yescharacteristic
435C22⋊D61—42no—
436C22⋊D61—42no—
437C22⋊D61—42no—
438C22⋊D61—42no—
439C22⋊D61—42no—
440C2×Dic61—22no—
441C2×Dic61—22no—
442C2×Dic61—21no—
443C2×Dic61—21no—
444C2×Dic61—21no—
445C2×Dic61—24no—
446C2×Dic61—41no—
447C2×Dic61—42no—
448C2×Dic61—44no—
449C2×Dic61—42no—
450C2×Dic61C22×D411yescharacteristic
451C2×Dic61C22×D411yescharacteristic
452C2×Dic61C22×D411yescharacteristic
453C2×Dic61C22×D411yescharacteristic
454C2×Dic61C22×D411yescharacteristic
455C2×Dic61C22×D411yescharacteristic
456D244—22no—
457D244—42no—
458D244—42no—
459C4×D61—22no—
460C4×D61—22no—
461C4×D61—22no—
462C4×D61—22no—
463C4×D61—22no—
464C4×D61—41no—
465C4×D61—41no—
466C4×D61—41no—
467C4×D61—41no—
468C4×D61—41no—
469C4×D61—41no—
470C4×D61—42no—
471C4×D61—42no—
472C4×D61—42no—
473C4×D612−1+414yes—
474Dic122—22no—
475Dic122—42no—
476Dic122—42no—
477Dic122—44no—
478Dic122—44no—
479C8×C61—24no—
480#92418—24no—
481#60854—611nomaximal, Sylow
482C22×C61—21no—
483C22×C61—21no—
484C22×C61—41no—
485C22×C61—41no—
486C22×C61—41no—
487C22×C61#57512yes—
488C22×C61C23×D411yescharacteristic
489C2×D61—21no—
490C2×D61—21no—
491C2×D61—21no—
492C2×D61—21no—
493C2×D61—21no—
494C2×D61—44no—
495C2×D61—41no—
496C2×D61—41no—
497C2×D61—41no—
498C2×D61#53612yes—
499C4×C61—21no—
500C4×C61—21no—
501C4×C61—21no—
502C4×C61—21no—
503C4×C61—41no—
504C4×C61—41no—
505C4×C61—41no—
506C4×C61—44no—
507C4×C61#57512yes—
508C4×C61C2×2−1+412yes—
509Dic61—21no—
510Dic61—21no—
511Dic61—21no—
512Dic61—21no—
513Dic61—21no—
514Dic61—41no—
515Dic61—44no—
516Dic61—41no—
517Dic61—41no—
518Dic61#53612yes—
519#3444—611no—
520C2×#533—611no—
521#3240—612no—
522#3240—612no—
523#3239—611no—
524#3239—611no—
525#3238—611no—
526#3238D6111yescharacteristic, complemented
527#3237—612no—
528#3236—612no—
529#3235—612no—
530#3234—612no—
531#3162—612no—
532#3135—612no—
533#3091—612no—
534#3091—612no—
535#3076—612no—
536#3076—612no—
537C2×#432—611no—
538C2×C61—22no—
539C2×C61—81no—
540C2×C61C2×#53611yescharacteristic
541C2×C61C2×#57511yescharacteristic
542C2×C61C2×#57511yescharacteristic
543D61—22no—
544D61—41no—
545D61—81no—
546#533—612no—
547#533—612no—
548#533—612no—
549#533—612no—
550#533—611no—
551#533—611no—
552#533—611no—
553#533—1221no—
554#533—1221no—
555#533—1221no—
556#533—1221no—
557#532—611no—
558#532—611no—
559#532—611no—
560C2×C4⋊Q8—611no—
561C2×C4⋊Q8C2×D6111yescharacteristic
562#529—611no—
563#529—611no—
564#529—611no—
565#529—1221no—
566#529—1221no—
567#529—1221no—
568#529—1221no—
569#529C2×D6111yescharacteristic
570C2×#125—612no—
571#525—611no—
572#525—611no—
573#525—1221no—
574#525—1221no—
575C2×C22⋊Q8—1221no—
576C2×C22⋊Q8—1221no—
577C4×#41—611no—
578C4×#41—611no—
579C4×#41—1221no—
580C4×#41—1221no—
581C2×C4×Q8—1221no—
582C2×C4×Q8—1221no—
583C2×#117—612no—
584C22×C42—611no—
585#501—612no—
586#501—612no—
587#501—614no—
588#501—614no—
589#501—612no—
590#501C2×D6112yescomplemented
591#491—614no—
592#490—614no—
593#489—612no—
594#489—612no—
595#489—612no—
596#489C2×D6112yescomplemented
597#485—614no—
598#485—614no—
599#484—612no—
600#484—612no—
601#483—612no—
602#483C2×D6112yes—
603#482—614no—
604#482—614no—
605#481—612no—
606#481—612no—
607#480—612no—
608#480C2×D6112yes—
609#479—614no—
610#479—614no—
611#478—614no—
612#478—614no—
613#477—612no—
614#477C2×D6112yescomplemented
615#476—612no—
616#476C2×D6112yescomplemented
617#475—612no—
618#475—612no—
619#474—612no—
620#474—612no—
621#432—611no—
622#432—612no—
623#432—612no—
624#432—612no—
625#432C2×D6111yescharacteristic
626#427—614no—
627#427—614no—
628C2×C4⋊C8—612no—
629#416—614no—
630#416—614no—
631C2×C22⋊C8—612no—
632C2×#97—612no—
633C61#6085411yescharacteristic, complemented, Sylow
634C2×#41—611no—
635C2×#41—611no—
636C2×#41—1221no—
637C2×#41—1221no—
638C22×Q8—21no—
639C22×Q8—1221no—
640C23×C4—611no—
641C23×C4—611no—
642C23×C4—611no—
643C22×C8—614no—
644C4⋊Q8—21no—
645C4⋊Q8—21no—
646C4⋊Q8—611no—
647C4⋊Q8—611no—
648C4⋊Q8—611no—
649C4⋊Q8—612no—
650C4⋊Q8—612no—
651C4⋊Q8—1221no—
652C4⋊Q8—1221no—
653C4⋊Q8C22×D6112yes—
654C4⋊Q8C22×D6112yes—
655#127—611no—
656#126—21no—
657#126—1221no—
658#126—1221no—
659#126—1221no—
660#125—614no—
661#125—614no—
662#125—611no—
663#125—1222no—
664#125—1222no—
665#125—1221no—
666#125—1221no—
667#125C22×D6111yescharacteristic
668#124—611no—
669#124—1221no—
670#124—1221no—
671#124C22×D6111yescharacteristic
672#123—21no—
673#123—1221no—
674#123—1221no—
675#123—1221no—
676#123—1221no—
677#123—1221no—
678C22⋊Q8—611no—
679C22⋊Q8—611no—
680C22⋊Q8—611no—
681C22⋊Q8—1221no—
682C22⋊Q8—1222no—
683C22⋊Q8—1222no—
684C22⋊Q8—1222no—
685C22⋊Q8—1222no—
686C22⋊Q8—1221no—
687C22⋊Q8—1221no—
688C22⋊Q8—1221no—
689C22⋊Q8—1222no—
690C22⋊Q8—1222no—
691C22⋊Q8—1222no—
692C22⋊Q8—1222no—
693C22⋊Q8C22×D6111yescharacteristic
694#121—611no—
695#121—611no—
696#121—611no—
697#121—1221no—
698#121—1221no—
699#121—1221no—
700#121—1221no—
701#121C22×D6111yescharacteristic
702#120—1221no—
703#120—1221no—
704C4×Q8—611no—
705C4×Q8—611no—
706C4×Q8—611no—
707C4×Q8—1221no—
708C4×Q8—1222no—
709C4×Q8—1222no—
710C4×Q8—1222no—
711C4×Q8—1222no—
712C4×Q8—1221no—
713C4×Q8—1221no—
714C4×Q8—1221no—
715C4×Q8—1222no—
716C4×Q8—1222no—
717C4×Q8—1222no—
718C4×Q8—1222no—
719C4×Q8C22×D6111yescharacteristic
720C4×D4—21no—
721C4×D4—611no—
722C4×D4—611no—
723C4×D4—611no—
724C4×D4—1221no—
725C4×D4—1221no—
726C4×D4—1221no—
727C4×D4—1221no—
728C4×D4—1221no—
729C4×D4—1221no—
730C4×D4—1221no—
731C4×D4—1221no—
732C4×D4—1221no—
733C4×D4—1221no—
734C4×D4—1221no—
735C4×D4—1221no—
736C4×D4—1221no—
737C4×D4—1221no—
738C4×D4—1221no—
739C4×D4C22×D6111yescharacteristic
740#117—21no—
741#117—614no—
742#117—614no—
743#117—611no—
744#117—611no—
745#117—1221no—
746#117—1221no—
747#117—1221no—
748#117—1221no—
749#117—1221no—
750#117—1221no—
751#117—1222no—
752#117—1222no—
753#117—1221no—
754C2×C4⋊C4—21no—
755C2×C4⋊C4—612no—
756C2×C4⋊C4—1222no—
757C2×C4⋊C4—1222no—
758C2×C4⋊C4—1221no—
759C2×C4⋊C4C22×D6112yes—
760C2×C22⋊C4—1222no—
761C2×C42—611no—
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—1221no—
773C2×C42—1221no—
774C2×C42—1222no—
775C2×C42C22×D6111yescharacteristic
776#107—614no—
777#107—614no—
778#107—614no—
779#107C22×D6114yes—
780#106—614no—
781#106—614no—
782#106—614no—
783#106C22×D6114yes—
784C4⋊C8—614no—
785C4⋊C8—612no—
786C4⋊C8C22×D6112yes—
787#103—614no—
788#103—614no—
789#103—614no—
790#103C22×D6114yes—
791#102—614no—
792#102—614no—
793#102—614no—
794#102C22×D6114yes—
795C22⋊C8—612no—
796C22⋊C8—614no—
797C22⋊C8C22×D6112yes—
798#97—614no—
799#97—612no—
800#97C22×D6112yes—
801C24—611no—
802#41—1224no—
803#41—1224no—
804#41—2444no—
805#41—2444no—
806C2×Q8—22no—
807C2×Q8—22no—
808C2×Q8—44no—
809C2×Q8—611no—
810C2×Q8—1221no—
811C2×Q8—1221no—
812C2×Q8—1222no—
813C2×Q8—1222no—
814C2×Q8—2444no—
815C2×Q8C23×D6111yescharacteristic
816C2×D4—21no—
817C2×D4—611no—
818C2×D4—1221no—
819C2×D4—1221no—
820C2×D4—1221no—
821C2×D4—1221no—
822C2×D4—1221no—
823C2×D4—1221no—
824C2×D4—1221no—
825C2×D4C23×D6111yescharacteristic
826C22×C4—22no—
827C22×C4—21no—
828C22×C4—611no—
829C22×C4—611no—
830C22×C4—611no—
831C22×C4—611no—
832C22×C4—611no—
833C22×C4—611no—
834C22×C4—611no—
835C22×C4—611no—
836C22×C4—611no—
837C22×C4—611no—
838C22×C4—611no—
839C22×C4—611no—
840C22×C4—611no—
841C22×C4—611no—
842C22×C4—611no—
843C22×C4—1224no—
844C22×C4—1221no—
845C22×C4—1221no—
846C22×C4—1221no—
847C22×C4—1221no—
848C22×C4—1222no—
849C22×C4—1221no—
850C22×C4—2442no—
851C22×C4—2442no—
852C22×C4D4×D6111yescharacteristic
853C22×C4D4×D6111yescharacteristic
854C22×C4C23×D6111yescharacteristic
855C2×C8—614no—
856C2×C8—1228no—
857C2×C8C23×D6114yes—
858C4⋊C4—22no—
859C4⋊C4—22no—
860C4⋊C4—22no—
861C4⋊C4—21no—
862C4⋊C4—21no—
863C4⋊C4—21no—
864C4⋊C4—21no—
865C4⋊C4—614no—
866C4⋊C4—611no—
867C4⋊C4—611no—
868C4⋊C4—1224no—
869C4⋊C4—1224no—
870C4⋊C4—1224no—
871C4⋊C4—1224no—
872C4⋊C4—1221no—
873C4⋊C4—1221no—
874C4⋊C4—1221no—
875C4⋊C4—1221no—
876C4⋊C4—1221no—
877C4⋊C4—1221no—
878C4⋊C4—1221no—
879C4⋊C4—1221no—
880C4⋊C4—1222no—
881C4⋊C4—1222no—
882C4⋊C4—1222no—
883C4⋊C4—1221no—
884C4⋊C4—1221no—
885C4⋊C4—1221no—
886C4⋊C4—1221no—
887C4⋊C4C23×D6114yes—
888C4⋊C4C23×D6111yescharacteristic
889C4⋊C4C23×D6111yescharacteristic
890C22⋊C4—21no—
891C22⋊C4—21no—
892C22⋊C4—21no—
893C22⋊C4—21no—
894C22⋊C4—21no—
895C22⋊C4—1221no—
896C22⋊C4—1221no—
897C22⋊C4—1224no—
898C22⋊C4—1224no—
899C22⋊C4—1221no—
900C22⋊C4—1221no—
901C22⋊C4—1221no—
902C22⋊C4—1221no—
903C22⋊C4—1221no—
904C22⋊C4—1221no—
905C22⋊C4—1221no—
906C22⋊C4—1221no—
907C22⋊C4—1221no—
908C22⋊C4—1221no—
909C22⋊C4—1221no—
910C42—21no—
911C42—611no—
912C42—611no—
913C42—611no—
914C42—611no—
915C42—611no—
916C42—611no—
917C42—611no—
918C42—611no—
919C42—611no—
920C42—611no—
921C42—611no—
922C42—611no—
923C42—1221no—
924C42—1221no—
925C42—1224no—
926C42—1224no—
927C42—1221no—
928C42—1221no—
929C42—1221no—
930C42D4×D6111yescharacteristic
931C42D4×D6111yescharacteristic
932C42C23×D6111yescharacteristic
933C42C23×D6111yescharacteristic
934C23—21no—
935C23—611no—
936C23—611no—
937C23—1222no—
938C23—1222no—
939C23—1221no—
940C23—2441no—
941C23C2×D4×D6111yescharacteristic
942Q8—22no—
943Q8—44no—
944Q8—44no—
945Q8—1222no—
946Q8—2444no—
947Q8—2442no—
948Q8—2442no—
949Q8—2444no—
950D4—22no—
951D4—42no—
952D4—1222no—
953D4—2442no—
954D4—2442no—
955D4—2442no—
956D4—2442no—
957D4—2442no—
958D4—2442no—
959D4—2442no—
960C2×C4—22no—
961C2×C4—22no—
962C2×C4—22no—
963C2×C4—21no—
964C2×C4—21no—
965C2×C4—21no—
966C2×C4—24no—
967C2×C4—44no—
968C2×C4—42no—
969C2×C4—611no—
970C2×C4—614no—
971C2×C4—611no—
972C2×C4—611no—
973C2×C4—611no—
974C2×C4—611no—
975C2×C4—611no—
976C2×C4—1222no—
977C2×C4—1222no—
978C2×C4—1222no—
979C2×C4—1222no—
980C2×C4—1222no—
981C2×C4—1222no—
982C2×C4—1222no—
983C2×C4—1221no—
984C2×C4—1221no—
985C2×C4—1221no—
986C2×C4—1224no—
987C2×C4—2441no—
988C2×C4—2441no—
989C2×C4—2441no—
990C2×C4—2441no—
991C2×C4—2441no—
992C2×C4—2441no—
993C2×C4—2442no—
994C2×C4—2442no—
995C2×C4—2442no—
996C2×C4—2441no—
997C2×C4—2442no—
998C2×C4—2444no—
999C2×C4—2442no—
1000C2×C4C2×D4×D6111yescharacteristic
1001C2×C4C2×D4×D6111yescharacteristic
1002C2×C4C2×D4×D6111yescharacteristic
1003C2×C4C2×D4×D6111yescharacteristic
1004C2×C4C2×D4×D6111yescharacteristic
1005C2×C4C24×D6111yescharacteristic
1006C8—24no—
1007C8—1224no—
1008C22—21no—
1009C22—21no—
1010C22—41no—
1011C22—41no—
1012C22—41no—
1013C22—612no—
1014C22—1221no—
1015C22—1221no—
1016C22—1221no—
1017C22—1221no—
1018C22—1221no—
1019C22—2444no—
1020C22—2441no—
1021C22—2441no—
1022C22—2441no—
1023C22#1684055812yes—
1024C22C22×D4×D6111yescharacteristic
1025C4—21no—
1026C4—21no—
1027C4—21no—
1028C4—21no—
1029C4—44no—
1030C4—41no—
1031C4—41no—
1032C4—41no—
1033C4—612no—
1034C4—1221no—
1035C4—1221no—
1036C4—1221no—
1037C4—1221no—
1038C4—1221no—
1039C4—2441no—
1040C4—2441no—
1041C4—2444no—
1042C4—2441no—
1043C4#1684056112yes—
1044C42−1+4×D6112yes—
1045C2—22no—
1046C2—81no—
1047C2—1222no—
1048C2—4881no—
1049C2—2441no—
1050C2#536×D6111yescharacteristic
1051C2C2×#1684055811yescharacteristic
1052C2C2×#1684056111yescharacteristic
subgroupG/H
centerC22C22×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC61×#3238C2
socleC22×C61C23×D4
prime radical#21459113C2
hypercenter#3238D61
hypocenterC61#60854
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3238

Complements

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

NH ≅ G/Ntype
2. C2×#16840317C2semidirect
3. #21457060C2semidirect
4. #21457054C2semidirect
5. #21457051C2semidirect
6. #21457046C2semidirect
7. #21457040C2semidirect
8. #21457031C2semidirect
9. #21457022C2semidirect
10. #21457015C2semidirect
11. #21457006C2semidirect
12. #21456340C2semidirect
13. #21456161C2semidirect
14. #21455733C2semidirect
15. #21455727C2semidirect
16. #21455610C2semidirect
17. #21455608C2semidirect
18. #432×D61C2semidirect
19. C61×#3238C2semidirect
57. #16840172C22semidirect
58. #16840171C22semidirect
59. #16840170C22semidirect
60. #16840169C22semidirect
61. #16840168C22semidirect
62. #16840129C22semidirect
63. #16840125C22semidirect
64. #16840124C22semidirect
65. #16840122C22semidirect
66. #16840121C22semidirect
77. #16840072C22semidirect
78. #16840071C22semidirect
79. #16840065C22semidirect
80. #16840064C22semidirect
81. #16840054C22semidirect
82. #16840049C22semidirect
83. #16840048C22semidirect
84. #16840047C22semidirect
85. #16840043C22semidirect
86. #16840042C22semidirect
100. C61×#501C22semidirect
101. C61×#489C22semidirect
104. C61×#477C22semidirect
105. C61×#476C22semidirect
526. #3238D61semidirect
590. #501C2×D61semidirect
596. #489C2×D61semidirect
614. #477C2×D61semidirect
616. #476C2×D61semidirect
633. C61#60854semidirect

Maximal subgroups

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

subgroupindex
#214591132
C2×#168403172
#214570602
#214570542
#214570512
#214570462
#214570402
#214570312
#214570222
#214570152
#214570062
#214563402
#214561612
#214557332
#214557272
#214556102
#214556082
#432×D612
C61×#32382
#6085461