Finite Group Databasebeta

← #29647143

Subgroups — #29647143

Order 15616.

1116 conjugacy classes of subgroups.

The subgroup lattice has 830 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#529×D61C211yesmaximal, characteristic
2#21454447C211yesmaximal, characteristic, complemented
3#21448158C211yesmaximal, characteristic, complemented
4#21444343C212yesmaximal, complemented
5#21444341C212yesmaximal, complemented
6#21444337C212yesmaximal, complemented
7#21444333C212yesmaximal
8#21444306C211yesmaximal, characteristic, complemented
9#21444305C211yesmaximal, characteristic, complemented
10#21444303C211yesmaximal, characteristic, complemented
11C61×#1500C211yesmaximal, characteristic, complemented
12#16840299C411yescharacteristic, complemented
13#16840298C2211yescharacteristic
14#16840297C411yescharacteristic, complemented
15#16840296C2211yescharacteristic
16#16840295—21no—
17#16840294C411yescharacteristic, complemented
18#16840293C2211yescharacteristic
19#16840292—21no—
20#16840291C411yescharacteristic, complemented
21#16840290—21no—
22#16840289—21no—
23#126×D61—21no—
24#125×D61C411yescharacteristic, complemented
25#124×D61C411yescharacteristic, complemented
26#123×D61—21no—
27C22⋊Q8×D61C2211yescharacteristic
28#121×D61C2211yescharacteristic
29C4×Q8×D61C411yescharacteristic, complemented
30C4×D4×D61—21no—
31C4×D4×D61C411yescharacteristic, complemented
32C2×#14519734—21no—
33#117×D61—21no—
34C2×C42×D61C2211yescharacteristic
35#16839818—21no—
36#16839816C2212yescomplemented
37#16839815C2211yescharacteristic, complemented
38#16839813—21no—
39#16839784—21no—
40#16839724C2212yes—
41C4×#11758189—21no—
42#16839613—21no—
43#16839613C2212yescomplemented
44#16839609—21no—
45#16839609C2212yes—
46#16839608C2211yescharacteristic, complemented
47C42×Dic61—21no—
48#16839500C2212yescomplemented
49#16839499C2212yescomplemented
50#16839498C2212yescomplemented
51#16839497C2212yes—
52#16839496C2212yes—
53#16839495C2212yes—
54C61×#529C2211yescharacteristic
55C61×#431C2211yescharacteristic, complemented
56C61×#376C2211yescharacteristic, complemented
57C61×#328C2212yescomplemented
58C61×#327C2212yes—
59C2×Q8×D61C2×C411yescharacteristic
60C2×D4×D61—21no—
61C2×D4×D61C2×C411yescharacteristic
62C22×C4×D61—21no—
63C22×C4×D61D411yescharacteristic
64C22×C4×D61D411yescharacteristic
65C22×C4×D61C2311yescharacteristic
66C2×#11758189—22no—
67#14519772—21no—
68#14519772—21no—
69#14519772—21no—
70#14519771—21no—
71#14519770—21no—
72#14519770—21no—
73#14519770—21no—
74#14519769C2×C411yescharacteristic
75#14519768C2×C411yescharacteristic
76#14519768C2×C411yescharacteristic
77#14519767—21no—
78#14519767—21no—
79#14519766C2×C411yescharacteristic
80#14519765C2×C411yescharacteristic
81#14519764C2×C411yescharacteristic
82#14519763—21no—
83#14519763—21no—
84#14519762—21no—
85#14519762—21no—
86#14519761—21no—
87#14519760—21no—
88#14519759—21no—
89#14519759—21no—
90#14519758—21no—
91#14519757C2×C411yescharacteristic
92#14519756C2311yescharacteristic
93#14519755—21no—
94#14519754—21no—
95#14519753C2×C411yescharacteristic
96#14519752C2×C411yescharacteristic
97#14519751C2311yescharacteristic
98#14519750—21no—
99#14519749—21no—
100#14519748C2×C411yescharacteristic
101Q8×Dic61C2×C411yescharacteristic
102C4×Dic122—21no—
103C4×Dic122C2×C411yescharacteristic
104#14519742—21no—
105#14519742C2×C411yescharacteristic
106C4×D244—21no—
107C4×D244C2×C411yescharacteristic
108D4×Dic61—21no—
109D4×Dic61C2×C411yescharacteristic
110#14519739—21no—
111#14519739C2×C411yescharacteristic
112C4×C22⋊D61—21no—
113C4×C22⋊D61—21no—
114C4×C22⋊D61—21no—
115#14519737—21no—
116#14519737—21no—
117#14519737—21no—
118#14519736—21no—
119#14519735—21no—
120#14519735—21no—
121#14519734—28no—
122#14519734—21no—
123#14519734—21no—
124#14519733—21no—
125#14519733—21no—
126C2×#11758196—22no—
127C4⋊C4×D61—21no—
128C4⋊C4×D61—21no—
129C4⋊C4×D61—21no—
130C4⋊C4×D61—21no—
131C4⋊C4×D61C2×C411yescharacteristic
132C4⋊C4×D61C2×C411yescharacteristic
133C2×#11758198—22no—
134C22⋊C4×D61—21no—
135C22⋊C4×D61—21no—
136C22⋊C4×D61—21no—
137C22⋊C4×D61—21no—
138C22⋊C4×D61—21no—
139C2×C4×Dic61—21no—
140C2×C4×Dic61—22no—
141C2×C4×Dic61—22no—
142C2×C4×Dic61D411yescharacteristic
143C2×C4×Dic61D411yescharacteristic
144C2×C4×Dic61C2311yescharacteristic
145C42×D61—21no—
146C42×D61C2×C411yescharacteristic
147C42×D61C2×C411yescharacteristic
148C42×D61C2×C411yescharacteristic
149C42×D61C2×C411yescharacteristic
150C42×D61D411yescharacteristic
151C42×D61D411yescharacteristic
152C42×D61D411yescharacteristic
153C42×D61D411yescharacteristic
154C4⋊#92418—21no—
155#14519706—22no—
156C22⋊#92418C2312yes—
157#14519689—22no—
158#14519687—22no—
159C4×#92418—21no—
160#14519684—21no—
161#14519684C2312yes—
162#126×C61—21no—
163#125×C61C2×C411yescharacteristic
164#124×C61C2×C411yescharacteristic
165#123×C61—21no—
166C22⋊Q8×C61C2311yescharacteristic
167#121×C61C2311yescharacteristic
168C4×Q8×C61C2×C411yescharacteristic
169C4×D4×C61—21no—
170C4×D4×C61C2×C411yescharacteristic
171#117×C61—21no—
172C2×C42×C61—21no—
173C2×C42×C61C2311yescharacteristic
174C4⋊C8×C61—21no—
175C22⋊C8×C61C2312yes—
176C4×C8×C61—21no—
177#95×C61—21no—
178#95×C61C2312yes—
179C23×D61—21no—
180C23×D61C2×D411yescharacteristic
181C2×Q8×C61C22×C411yescharacteristic
182C2×D4×C61—21no—
183C2×D4×C61C22×C411yescharacteristic
184C22×C4×C61—22no—
185C22×C4×C61—21no—
186C22×C4×C61C2×D411yescharacteristic
187C22×C4×C61C2×D411yescharacteristic
188C22×C4×C61C2411yescharacteristic
189C2×C22⋊D61—21no—
190C2×C22⋊D61—21no—
191C2×C22⋊D61—21no—
192C22×Dic61—22no—
193C22×Dic61—21no—
194C22×Dic61C2×D411yescharacteristic
195C22×Dic61C2×D411yescharacteristic
196C22×Dic61C2×D411yescharacteristic
197Q8×D61—42no—
198D4×D61—42no—
199D4×D61—44no—
200C2×D244—21no—
201C2×D244C22×C411yescharacteristic
202C2×C4×D61—24no—
203C2×C4×D61—21no—
204C2×C4×D61—21no—
205C2×C4×D61—21no—
206C2×C4×D61—21no—
207C2×C4×D61—21no—
208C2×C4×D61—42no—
209C2×C4×D61—42no—
210C2×C4×D61—44no—
211C2×C4×D61C22⋊C411yescharacteristic
212C2×C4×D61C22⋊C411yescharacteristic
213C2×C4×D61C22⋊C411yescharacteristic
214C2×C4×D61C22⋊C411yescharacteristic
215C2×C4×D61C22⋊C411yescharacteristic
216C2×C4×D61C22⋊C411yescharacteristic
217C2×C4×D61C22⋊C411yescharacteristic
218C2×C4×D61C22⋊C411yescharacteristic
219C2×C4×D61C22×C411yescharacteristic
220C2×C4×D61C22×C411yescharacteristic
221C2×C4×D61C2×D411yescharacteristic
222C2×C4×D61C2×D411yescharacteristic
223C2×Dic122—21no—
224C2×Dic122C22×C411yescharacteristic
225C2×C8×C61—22no—
226C4⋊C4×C61—21no—
227C4⋊C4×C61—21no—
228C4⋊C4×C61—21no—
229C4⋊C4×C61—21no—
230C4⋊C4×C61C22×C411yescharacteristic
231C4⋊C4×C61C22×C411yescharacteristic
232C22⋊C4×C61—21no—
233C22⋊C4×C61—21no—
234C22⋊C4×C61—21no—
235C22⋊C4×C61—21no—
236C22⋊C4×C61—21no—
237C42×C61—24no—
238C42×C61—21no—
239C42×C61C22×C411yescharacteristic
240C42×C61C22×C411yescharacteristic
241C42×C61C2×D411yescharacteristic
242C42×C61C2×D411yescharacteristic
243C22⋊Dic61—21no—
244C22⋊Dic61—21no—
245C22⋊Dic61—21no—
246C22⋊Dic61—21no—
247C22⋊Dic61—21no—
248#11758198—28no—
249#11758198—21no—
250#11758198—21no—
251#11758198—21no—
252#11758198—21no—
253#11758198—21no—
254#11758198—21no—
255#11758198—21no—
256#11758198—21no—
257#11758198—21no—
258#11758198—21no—
259C4⋊Dic61—21no—
260C4⋊Dic61—21no—
261C4⋊Dic61—21no—
262C4⋊Dic61—21no—
263C4⋊Dic61C22×C411yescharacteristic
264C4⋊Dic61C22×C411yescharacteristic
265#11758196—28no—
266#11758196—21no—
267#11758196—21no—
268#11758196—21no—
269#11758196—21no—
270#11758196—21no—
271#11758196—21no—
272#11758196—21no—
273#11758196—21no—
274#11758196—21no—
275#11758196—21no—
276C4×Dic61—24no—
277C4×Dic61—21no—
278C4×Dic61—21no—
279C4×Dic61—21no—
280C4×Dic61—44no—
281C4×Dic61—44no—
282C4×Dic61C22⋊C411yescharacteristic
283C4×Dic61C22⋊C411yescharacteristic
284C4×Dic61C22⋊C411yescharacteristic
285C4×Dic61C22⋊C411yescharacteristic
286C4×Dic61C22⋊C411yescharacteristic
287C4×Dic61C22⋊C411yescharacteristic
288C4×Dic61C22⋊C411yescharacteristic
289C4×Dic61C22⋊C411yescharacteristic
290C4×Dic61C22×C411yescharacteristic
291C4×Dic61C22×C411yescharacteristic
292C4×Dic61C2×D411yescharacteristic
293C4×Dic61C2×D411yescharacteristic
294C2×#92418—22no—
295#11758189—44no—
296C23×C61—21no—
297C23×C61C22×D411yescharacteristic
298C22×D61—22no—
299C22×D61—22no—
300C22×D61—21no—
301C22×D61—41no—
302C22×D61—42no—
303C22×D61—42no—
304C22×D61—42no—
305C22×D61C2×C22⋊C411yescharacteristic
306C22×D61C2×C22⋊C411yescharacteristic
307Q8×C61—41no—
308D4×C61—41no—
309D4×C61—42no—
310C2×C4×C61—22no—
311C2×C4×C61—22no—
312C2×C4×C61—24no—
313C2×C4×C61—21no—
314C2×C4×C61—21no—
315C2×C4×C61—21no—
316C2×C4×C61—41no—
317C2×C4×C61—42no—
318C2×C4×C61—42no—
319C2×C4×C61—42no—
320C2×C4×C61C2×C22⋊C411yescharacteristic
321C2×C4×C61C2×C22⋊C411yescharacteristic
322C2×C4×C61C2×C22⋊C411yescharacteristic
323C2×C4×C61C2×C22⋊C411yescharacteristic
324C2×C4×C61C23×C411yescharacteristic
325C2×C4×C61C22×D411yescharacteristic
326C22⋊D61—42no—
327C22⋊D61—42no—
328C22⋊D61—42no—
329C2×Dic61—22no—
330C2×Dic61—22no—
331C2×Dic61—22no—
332C2×Dic61—24no—
333C2×Dic61—21no—
334C2×Dic61—21no—
335C2×Dic61—21no—
336C2×Dic61—42no—
337C2×Dic61—42no—
338C2×Dic61—42no—
339C2×Dic61C2×C22⋊C411yescharacteristic
340C2×Dic61C2×C22⋊C411yescharacteristic
341C2×Dic61C2×C22⋊C411yescharacteristic
342C2×Dic61C2×C22⋊C411yescharacteristic
343C2×Dic61C2×C22⋊C411yescharacteristic
344C2×Dic61C2×C22⋊C411yescharacteristic
345D244—41no—
346D244—42no—
347C4×D61—22no—
348C4×D61—22no—
349C4×D61—22no—
350C4×D61—22no—
351C4×D61—22no—
352C4×D61—41no—
353C4×D61—41no—
354C4×D61—41no—
355C4×D61—41no—
356C4×D61—41no—
357C4×D61—41no—
358C4×D61—42no—
359C4×D61—42no—
360C4×D61—42no—
361C4×D61—42no—
362C4×D61—42no—
363C4×D61#10414yes—
364Dic122—42no—
365Dic122—41no—
366C8×C61—42no—
367#92418—42no—
368#17537—611nomaximal, Sylow
369C22×C61—21no—
370C22×C61—21no—
371C22×C61—41no—
372C22×C61—41no—
373C22×C61—41no—
374C22×C61C22×C22⋊C411yescharacteristic
375C22×C61#57512yes—
376C2×D61—21no—
377C2×D61—21no—
378C2×D61—21no—
379C2×D61—21no—
380C2×D61—21no—
381C2×D61—44no—
382C2×D61—41no—
383C2×D61—41no—
384C2×D61—41no—
385C2×D61—84no—
386C2×D61C2×#10412yes—
387C4×C61—21no—
388C4×C61—21no—
389C4×C61—21no—
390C4×C61—21no—
391C4×C61—21no—
392C4×C61—44no—
393C4×C61—41no—
394C4×C61—41no—
395C4×C61—41no—
396C4×C61C2×#10412yes—
397Dic61—21no—
398Dic61—21no—
399Dic61—21no—
400Dic61—21no—
401Dic61—44no—
402Dic61—41no—
403Dic61—41no—
404Dic61—41no—
405Dic61#41012yes—
406Dic61C2×#10412yes—
407C2×#529—611no—
408#2920—611no—
409C4×#117—611no—
410#1509—612no—
411#1509—612no—
412#1508—612no—
413#1507—612no—
414#1500—611no—
415#1500—611no—
416#1500—611no—
417#1500D6111yescharacteristic, complemented
418C2×C61—22no—
419C2×C61—81no—
420C2×C61C2×#41011yescharacteristic
421C2×C61#289611yescharacteristic
422C2×C61C22×#10411yescharacteristic
423D61—22no—
424D61—41no—
425D61—81no—
426#529—611no—
427#529—611no—
428#529—611no—
429#529—611no—
430#529—611no—
431#529—611no—
432#529—611no—
433#529—1221no—
434#529—1221no—
435#529—1221no—
436#529—1221no—
437#529C2×D6111yescharacteristic
438C2×#126—1221no—
439C2×#125—611no—
440C2×#124—611no—
441C2×#123—1221no—
442C2×C22⋊Q8—611no—
443C2×#121—611no—
444C2×C4×Q8—611no—
445C2×C4×D4—611no—
446C2×C4×D4—1221no—
447C2×#117—1221no—
448C2×#117—1221no—
449C22×C42—611no—
450#432—612no—
451#432—1221no—
452#431—611no—
453#431—1221no—
454#431C2×D6111yescharacteristic, complemented
455#423—1221no—
456#407—612no—
457C4×M16—1221no—
458C4×C4⋊C4—612no—
459C4×C4⋊C4—1221no—
460C4×C22⋊C4—612no—
461C4×C22⋊C4—1221no—
462#376—611no—
463#376C2×D6111yescharacteristic, complemented
464C43—1221no—
465#328—612no—
466#328—612no—
467#328—612no—
468#328C2×D6112yescomplemented
469#327—612no—
470#327—612no—
471#327—612no—
472#327C2×D6112yes—
473C61#1753711yescharacteristic, complemented, Sylow
474C22×Q8—611no—
475C22×D4—611no—
476C22×D4—1221no—
477C23×C4—611no—
478C23×C4—611no—
479C23×C4—611no—
480C23×C4—1221no—
481C2×M16—1222no—
482#126—21no—
483#126—1221no—
484#126—1221no—
485#126—1221no—
486#126—1221no—
487#126—1221no—
488#126—1221no—
489#126—1221no—
490#125—611no—
491#125—611no—
492#125—611no—
493#125—1221no—
494#125—1221no—
495#125C4×D6111yescharacteristic
496#124—611no—
497#124—611no—
498#124—611no—
499#124—1221no—
500#124—1221no—
501#124C4×D6111yescharacteristic
502#123—21no—
503#123—1221no—
504#123—1221no—
505#123—1221no—
506#123—1221no—
507#123—1221no—
508#123—1221no—
509#123—1221no—
510C22⋊Q8—611no—
511C22⋊Q8—611no—
512C22⋊Q8—611no—
513C22⋊Q8—1221no—
514C22⋊Q8—1221no—
515C22⋊Q8C22×D6111yescharacteristic
516#121—611no—
517#121—611no—
518#121—611no—
519#121—1221no—
520#121—1221no—
521#121C22×D6111yescharacteristic
522C4×Q8—611no—
523C4×Q8—611no—
524C4×Q8—611no—
525C4×Q8—1221no—
526C4×Q8—1221no—
527C4×Q8C4×D6111yescharacteristic
528C4×D4—21no—
529C4×D4—611no—
530C4×D4—611no—
531C4×D4—611no—
532C4×D4—1221no—
533C4×D4—1221no—
534C4×D4—1221no—
535C4×D4—1221no—
536C4×D4—1221no—
537C4×D4—1221no—
538C4×D4—1221no—
539C4×D4—1221no—
540C4×D4—1221no—
541C4×D4C4×D6111yescharacteristic
542#117—21no—
543#117—1221no—
544#117—1228no—
545#117—1221no—
546#117—1221no—
547#117—1221no—
548#117—1221no—
549#117—1221no—
550#117—1221no—
551C2×C4⋊C4—611no—
552C2×C4⋊C4—611no—
553C2×C4⋊C4—1221no—
554C2×C4⋊C4—1221no—
555C2×C4⋊C4—1221no—
556C2×C4⋊C4—1221no—
557C2×C4⋊C4—1222no—
558C2×C22⋊C4—1221no—
559C2×C22⋊C4—1221no—
560C2×C22⋊C4—1221no—
561C2×C22⋊C4—1221no—
562C2×C22⋊C4—1221no—
563C2×C22⋊C4—1222no—
564C2×C42—21no—
565C2×C42—611no—
566C2×C42—611no—
567C2×C42—611no—
568C2×C42—611no—
569C2×C42—611no—
570C2×C42—611no—
571C2×C42—611no—
572C2×C42—611no—
573C2×C42—611no—
574C2×C42—611no—
575C2×C42—611no—
576C2×C42—1221no—
577C2×C42—1221no—
578C2×C42—1222no—
579C2×C42—1222no—
580C2×C42C22×D6111yescharacteristic
581C4⋊C8—21no—
582C4⋊C8—1222no—
583C4⋊C8—1221no—
584C22⋊C8—612no—
585C22⋊C8—1222no—
586C22⋊C8C22×D6112yes—
587#97—1222no—
588C4×C8—21no—
589C4×C8—1221no—
590#95—21no—
591#95—612no—
592#95—1221no—
593#95C22×D6112yes—
594C24—611no—
595C24—1221no—
596C2×Q8—611no—
597C2×Q8—1221no—
598C2×Q8—2442no—
599C2×Q8C2×C4×D6111yescharacteristic
600C2×D4—21no—
601C2×D4—611no—
602C2×D4—1221no—
603C2×D4—1221no—
604C2×D4—1221no—
605C2×D4—1221no—
606C2×D4—2442no—
607C2×D4—2444no—
608C2×D4C2×C4×D6111yescharacteristic
609C22×C4—22no—
610C22×C4—21no—
611C22×C4—611no—
612C22×C4—611no—
613C22×C4—611no—
614C22×C4—611no—
615C22×C4—611no—
616C22×C4—611no—
617C22×C4—611no—
618C22×C4—611no—
619C22×C4—611no—
620C22×C4—611no—
621C22×C4—611no—
622C22×C4—611no—
623C22×C4—611no—
624C22×C4—611no—
625C22×C4—611no—
626C22×C4—1224no—
627C22×C4—1221no—
628C22×C4—1221no—
629C22×C4—1221no—
630C22×C4—1221no—
631C22×C4—1221no—
632C22×C4—1222no—
633C22×C4—1221no—
634C22×C4—2442no—
635C22×C4—2444no—
636C22×C4—2442no—
637C22×C4D4×D6111yescharacteristic
638C22×C4D4×D6111yescharacteristic
639C22×C4C23×D6111yescharacteristic
640M16—2444no—
641C2×C8—22no—
642C2×C8—1222no—
643C4⋊C4—21no—
644C4⋊C4—21no—
645C4⋊C4—21no—
646C4⋊C4—21no—
647C4⋊C4—611no—
648C4⋊C4—611no—
649C4⋊C4—1221no—
650C4⋊C4—1221no—
651C4⋊C4—1221no—
652C4⋊C4—1221no—
653C4⋊C4—1221no—
654C4⋊C4—1221no—
655C4⋊C4—1221no—
656C4⋊C4—1221no—
657C4⋊C4—1221no—
658C4⋊C4—1221no—
659C4⋊C4—1228no—
660C4⋊C4—1221no—
661C4⋊C4—1221no—
662C4⋊C4—1221no—
663C4⋊C4—1221no—
664C4⋊C4C2×C4×D6111yescharacteristic
665C4⋊C4C2×C4×D6111yescharacteristic
666C22⋊C4—21no—
667C22⋊C4—21no—
668C22⋊C4—21no—
669C22⋊C4—21no—
670C22⋊C4—21no—
671C22⋊C4—1221no—
672C22⋊C4—1221no—
673C22⋊C4—1221no—
674C22⋊C4—1221no—
675C22⋊C4—1221no—
676C22⋊C4—1221no—
677C22⋊C4—1228no—
678C22⋊C4—1221no—
679C22⋊C4—1221no—
680C22⋊C4—1221no—
681C22⋊C4—1221no—
682C22⋊C4—1221no—
683C22⋊C4—1221no—
684C22⋊C4—1221no—
685C22⋊C4—1221no—
686C22⋊C4—1221no—
687C42—24no—
688C42—21no—
689C42—611no—
690C42—611no—
691C42—611no—
692C42—611no—
693C42—611no—
694C42—611no—
695C42—611no—
696C42—611no—
697C42—611no—
698C42—611no—
699C42—611no—
700C42—611no—
701C42—1221no—
702C42—1221no—
703C42—1224no—
704C42—1221no—
705C42—2444no—
706C42—2444no—
707C42C2×C4×D6111yescharacteristic
708C42C2×C4×D6111yescharacteristic
709C42D4×D6111yescharacteristic
710C42D4×D6111yescharacteristic
711C23—21no—
712C23—611no—
713C23—611no—
714C23—1222no—
715C23—1222no—
716C23—1221no—
717C23—2441no—
718C23—2442no—
719C23—2442no—
720C23—2442no—
721C23C2×D4×D6111yescharacteristic
722Q8—41no—
723Q8—2441no—
724Q8—2442no—
725D4—41no—
726D4—42no—
727D4—2441no—
728D4—2442no—
729D4—2442no—
730D4—2442no—
731D4—2442no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—24no—
735C2×C4—21no—
736C2×C4—21no—
737C2×C4—21no—
738C2×C4—41no—
739C2×C4—42no—
740C2×C4—42no—
741C2×C4—42no—
742C2×C4—611no—
743C2×C4—611no—
744C2×C4—614no—
745C2×C4—611no—
746C2×C4—611no—
747C2×C4—611no—
748C2×C4—611no—
749C2×C4—1222no—
750C2×C4—1222no—
751C2×C4—1222no—
752C2×C4—1222no—
753C2×C4—1222no—
754C2×C4—1222no—
755C2×C4—1222no—
756C2×C4—1222no—
757C2×C4—1224no—
758C2×C4—1221no—
759C2×C4—1221no—
760C2×C4—1221no—
761C2×C4—2441no—
762C2×C4—2441no—
763C2×C4—2441no—
764C2×C4—2441no—
765C2×C4—2441no—
766C2×C4—2441no—
767C2×C4—2442no—
768C2×C4—2442no—
769C2×C4—2442no—
770C2×C4—2442no—
771C2×C4—2442no—
772C2×C4—2442no—
773C2×C4—2442no—
774C2×C4—2442no—
775C2×C4C22⋊C4×D6111yescharacteristic
776C2×C4C22⋊C4×D6111yescharacteristic
777C2×C4C22⋊C4×D6111yescharacteristic
778C2×C4C22⋊C4×D6111yescharacteristic
779C2×C4C22×C4×D6111yescharacteristic
780C2×C4C2×D4×D6111yescharacteristic
781C8—42no—
782C8—2442no—
783C22—21no—
784C22—21no—
785C22—41no—
786C22—41no—
787C22—41no—
788C22—612no—
789C22—1221no—
790C22—1221no—
791C22—1221no—
792C22—1221no—
793C22—1221no—
794C22—4884no—
795C22—2444no—
796C22—2441no—
797C22—2441no—
798C22—2441no—
799C22C2×C22⋊C4×D6111yescharacteristic
800C22#1684055912yes—
801C4—21no—
802C4—21no—
803C4—21no—
804C4—21no—
805C4—21no—
806C4—44no—
807C4—41no—
808C4—41no—
809C4—41no—
810C4—612no—
811C4—612no—
812C4—1221no—
813C4—1221no—
814C4—1221no—
815C4—1221no—
816C4—2444no—
817C4—2441no—
818C4—2441no—
819C4—2441no—
820C4#104×D6112yes—
821C2—22no—
822C2—81no—
823C2—1222no—
824C2—4881no—
825C2—2441no—
826C2#410×D6111yescharacteristic
827C2#2145433411yescharacteristic
828C2C2×#104×D6111yescharacteristic
subgroupG/H
centerC2×C4C22⋊C4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1500C2
socleC22×C61C22×C22⋊C4
prime radical#121×D61C22
cosocleC22×C4×C61C24
hypercenter#1500D61
hypocenterC61#17537
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1500

Complements

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

NH ≅ G/Ntype
2. #21454447C2semidirect
3. #21448158C2semidirect
4. #21444343C2semidirect
5. #21444341C2semidirect
6. #21444337C2semidirect
8. #21444306C2semidirect
9. #21444305C2semidirect
10. #21444303C2semidirect
11. C61×#1500C2semidirect
12. #16840299C4semidirect
14. #16840297C4semidirect
17. #16840294C4semidirect
20. #16840291C4semidirect
24. #125×D61C4semidirect
25. #124×D61C4semidirect
29. C4×Q8×D61C4semidirect
31. C4×D4×D61C4semidirect
36. #16839816C22semidirect
37. #16839815C22semidirect
43. #16839613C22semidirect
46. #16839608C22semidirect
48. #16839500C22semidirect
49. #16839499C22semidirect
50. #16839498C22semidirect
55. C61×#431C22semidirect
56. C61×#376C22semidirect
57. C61×#328C22semidirect
417. #1500D61semidirect
454. #431C2×D61semidirect
463. #376C2×D61semidirect
468. #328C2×D61semidirect
473. C61#17537semidirect

Maximal subgroups

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

subgroupindex
#529×D612
#214544472
#214481582
#214443432
#214443412
#214443372
#214443332
#214443062
#214443052
#214443032
C61×#15002
#1753761