Finite Group Databasebeta

← #30547925

Subgroups — #30547925

Order 15616.

2170 conjugacy classes of subgroups.

The subgroup lattice has 906 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840342C211yesmaximal, characteristic
2#21459020C211yesmaximal, characteristic, complemented
3#21455805C214yesmaximal, complemented
4#21455803C214yesmaximal, complemented
5#21455800C214yesmaximal, complemented
6#21455798C214yesmaximal, complemented
7#21455765C212yesmaximal, complemented
8#21455763C211yesmaximal, characteristic, complemented
9#21455761C212yesmaximal, complemented
10#21455760C211yesmaximal, characteristic, complemented
11#21455759C211yesmaximal, characteristic, complemented
12#428×D61C212yesmaximal, complemented
13#21454337C212yesmaximal, complemented
14#21454262C211yesmaximal, characteristic, complemented
15C61×#3095C211yesmaximal, characteristic, complemented
16C22×#11758226C2211yescharacteristic
17C22×#11758222C2211yescharacteristic
18C2×M16×D61C2212yes—
19#16840342—22no—
20#16840342—22no—
21#16840342C2214yes—
22#16840342C2214yes—
23C2×#14519755—21no—
24C2×#14519753C2211yescharacteristic
25C2×#14519752—21no—
26C2×#14519752C2211yescharacteristic
27C2×#14519751C2211yescharacteristic
28C2×#14519750—21no—
29C2×#14519750—21no—
30#16840243C2212yescomplemented
31#16840243C2212yescomplemented
32#16840242C2212yescomplemented
33#16840242C2212yescomplemented
34#16840239—21no—
35#16840236—21no—
36#16840235—21no—
37#16840235—21no—
38C4×#11758222—22no—
39#16840230—22no—
40C2×#14519736C2211yescharacteristic
41#117×D61C2212yes—
42#117×D61C2212yes—
43C2×C4⋊C4×D61C2211yescharacteristic
44#16840102C2214yescomplemented
45#16840101C2214yescomplemented
46#16840100C2214yescomplemented
47#16840096C2214yescomplemented
48#16840095C2212yescomplemented
49#16840091C2214yescomplemented
50#16840090C2212yescomplemented
51#16840089C2214yescomplemented
52#16840088C2214yescomplemented
53#16840087C2214yescomplemented
54#16840086C2214yescomplemented
55#16840082C2214yescomplemented
56#16840081C2212yescomplemented
57#16840080C2212yescomplemented
58#16840077C2214yescomplemented
59#16840076C2212yescomplemented
60#16840075C2212yescomplemented
61#16839805C2212yes—
62#16839804C2212yes—
63#16839803C2214yescomplemented
64#16839802C2212yes—
65#16839801C2214yescomplemented
66#107×D61C2214yescomplemented
67#106×D61C2214yescomplemented
68#16839771C2212yes—
69#16839768C2212yes—
70#16839766C2212yes—
71#16839762C2214yescomplemented
72#16839762C2214yescomplemented
73#16839757C2214yescomplemented
74#16839757C2214yescomplemented
75#16839727C2214yescomplemented
76#16839727C2214yescomplemented
77#16839726C2211yescharacteristic
78#16839725C2212yes—
79C2×C22⋊Q8×C61C2211yescharacteristic
80C2×#117×C61C2211yescharacteristic
81C61×#485C2214yescomplemented
82C61×#484C2212yescomplemented
83C61×#483C2212yescomplemented
84C61×#428C2212yes—
85C61×#419C2212yes—
86C61×#407C2211yescharacteristic
87C2×#11758226—22no—
88C2×#11758226—28no—
89C2×#11758226C2314yes—
90C2×#11758222—28no—
91C2×#11758222D412yes—
92C2×#11758222D412yes—
93C2×#11758222C2312yes—
94C2×#11758222C2312yes—
95C22×Dic122D411yescharacteristic
96C22×D244—21no—
97C22×D244—21no—
98C22×D244D411yescharacteristic
99C22×D244C2311yescharacteristic
100C22×C22⋊D61—21no—
101C22×C22⋊D61D411yescharacteristic
102C22×C22⋊D61D411yescharacteristic
103C22×C4×D61—21no—
104C22×C4×D61—21no—
105C22×C4×D61C2311yescharacteristic
106C22×C4×D61C2311yescharacteristic
107C2×#11758194C2312yes—
108C2×#11758189C2314yes—
109M16×D61—28no—
110C2×C8×D61C2314yes—
111#14519755—24no—
112#14519755—24no—
113#14519753—22no—
114#14519753C2314yes—
115#14519752—24no—
116#14519752—24no—
117#14519752—22no—
118#14519752C2314yes—
119#14519751—21no—
120#14519751—21no—
121#14519751C2312yes—
122#14519751C2312yes—
123#14519750—24no—
124#14519750—24no—
125#14519750—24no—
126#14519750—24no—
127C4×Dic122—22no—
128C4×Dic122—22no—
129#14519742—22no—
130#14519742—22no—
131C4×D244—22no—
132C4×D244—22no—
133#14519739—22no—
134#14519739—22no—
135C4×C22⋊D61—22no—
136C4×C22⋊D61—22no—
137C4×C22⋊D61—22no—
138C4×C22⋊D61—22no—
139#14519737—22no—
140#14519737—22no—
141#14519737—22no—
142#14519737—22no—
143#14519736—21no—
144#14519736—21no—
145#14519736C2312yes—
146#14519736C2312yes—
147#14519735C2312yes—
148#14519735C2312yes—
149#14519735C2312yes—
150#14519735C2312yes—
151#14519734—22no—
152#14519734—22no—
153#14519733—22no—
154#14519733—22no—
155C2×C4⋊Dic61C2311yescharacteristic
156C2×C4⋊Dic61C2311yescharacteristic
157C2×C4⋊Dic61C2311yescharacteristic
158C2×#11758196—21no—
159C2×#11758196—21no—
160C4⋊C4×D61—22no—
161C4⋊C4×D61C2314yes—
162C4⋊C4×D61C2312yes—
163C4⋊C4×D61C2312yes—
164C4⋊C4×D61C2312yes—
165C4⋊C4×D61C2312yes—
166C2×C22⋊Dic61—21no—
167C2×#11758198—21no—
168C2×#11758198—21no—
169C2×#11758198—21no—
170C22⋊C4×D61—22no—
171C22⋊C4×D61—22no—
172C2×C4×Dic61—21no—
173C42×D61—22no—
174C42×D61—22no—
175#14519711C2314yes—
176#14519710C2314yes—
177#14519710C2314yes—
178#14519709C2314yes—
179#14519708C2314yes—
180#14519708C2314yes—
181#14519701C2314yes—
182#14519701C2314yes—
183#14519699C2314yes—
184#14519699C2314yes—
185#14519697C2314yes—
186#14519697C2314yes—
187C22⋊#92418C2312yes—
188C22⋊#92418C2312yes—
189#14519689C2314yes—
190#14519689C2314yes—
191C22×Q8×C61C2311yescharacteristic
192C23×C4×C61C2311yescharacteristic
193C2×M16×C61C2312yes—
194C22⋊Q8×C61—21no—
195C22⋊Q8×C61—21no—
196C22⋊Q8×C61C2312yes—
197C22⋊Q8×C61C2312yes—
198#117×C61—21no—
199#117×C61—21no—
200#117×C61C2312yes—
201#117×C61C2312yes—
202C2×C4⋊C4×C61—21no—
203C2×C4⋊C4×C61C2311yescharacteristic
204C2×C4⋊C4×C61C2311yescharacteristic
205C2×C4⋊C4×C61C2311yescharacteristic
206C2×C22⋊C4×C61—21no—
207C2×C22⋊C4×C61—21no—
208C2×C42×C61—21no—
209#107×C61C2314yes—
210#106×C61C2314yes—
211#103×C61C2314yes—
212#103×C61C2314yes—
213C22⋊C8×C61C2312yes—
214C22⋊C8×C61C2312yes—
215C24×C61C2×D411yescharacteristic
216C23×D61—21no—
217C23×D61C2×D411yescharacteristic
218C23×D61C2×D411yescharacteristic
219C2×Q8×C61—21no—
220C2×Q8×C61—24no—
221C2×Q8×C61C2412yes—
222C22×C4×C61—24no—
223C22×C4×C61—21no—
224C22×C4×C61—21no—
225C22×C4×C61—21no—
226C22×C4×C61—21no—
227C22×C4×C61C2×D411yescharacteristic
228C22×C4×C61C2×D411yescharacteristic
229C22×C4×C61C2×D411yescharacteristic
230C22×C4×C61C2411yescharacteristic
231C22×C4×C61C2411yescharacteristic
232C22×C4×C61C2411yescharacteristic
233C2×C22⋊D61—24no—
234C2×C22⋊D61—22no—
235C2×C22⋊D61—22no—
236C2×C22⋊D61—24no—
237C2×C22⋊D61—82no—
238C2×C22⋊D61C2×D412yes—
239C2×C22⋊D61C2×D412yes—
240C2×C22⋊D61C2×D412yes—
241C2×C22⋊D61C2×D412yes—
242C22×Dic61—21no—
243C22×Dic61—21no—
244C22×Dic61—21no—
245C22×Dic61C2×D411yescharacteristic
246C22×Dic61C2×D411yescharacteristic
247#11758226—28no—
248#11758226—28no—
249#11758226—48no—
250#11758222—28no—
251#11758222—28no—
252#11758222—24no—
253#11758222—24no—
254#11758222—24no—
255#11758222—24no—
256C2×D244—24no—
257C2×D244—24no—
258C2×D244—24no—
259C2×D244—21no—
260C2×D244—24no—
261C2×D244—44no—
262C2×D244—82no—
263C2×D244C2×D412yes—
264C2×D244C2×D412yes—
265C2×D244C2412yes—
266C2×C4×D61—24no—
267C2×C4×D61—24no—
268C2×C4×D61—24no—
269C2×C4×D61—22no—
270C2×C4×D61—22no—
271C2×C4×D61—22no—
272C2×C4×D61—22no—
273C2×C4×D61—44no—
274C2×C4×D61—82no—
275C2×C4×D61C2×D412yes—
276C2×C4×D61C2×D412yes—
277C2×C4×D61#4118yes—
278C2×C4×D61C2412yes—
279C2×C4×D61C2412yes—
280C2×Dic122—24no—
281C2×Dic122C2×D412yes—
282C2×Dic122C2×D412yes—
283M16×C61—24no—
284C2×C8×C61C2414yes—
285C4⋊C4×C61—22no—
286C4⋊C4×C61—22no—
287C4⋊C4×C61—21no—
288C4⋊C4×C61—21no—
289C4⋊C4×C61—21no—
290C4⋊C4×C61C2412yes—
291C4⋊C4×C61C2412yes—
292C4⋊C4×C61C2412yes—
293C22⋊C4×C61—22no—
294C22⋊C4×C61—22no—
295C22⋊C4×C61—22no—
296C22⋊C4×C61—22no—
297C42×C61—22no—
298C42×C61—22no—
299C22⋊Dic61—22no—
300C22⋊Dic61—22no—
301#11758198—22no—
302#11758198—22no—
303#11758198—22no—
304#11758198—22no—
305#11758198—24no—
306#11758198—22no—
307#11758198—22no—
308#11758198—24no—
309C4⋊Dic61—21no—
310C4⋊Dic61—21no—
311C4⋊Dic61—21no—
312C4⋊Dic61C2412yes—
313C4⋊Dic61C2412yes—
314C4⋊Dic61C2412yes—
315#11758196—24no—
316#11758196—22no—
317#11758196—22no—
318#11758196—22no—
319#11758196—22no—
320#11758196—24no—
321C4×Dic61—22no—
322C4×Dic61—22no—
323C4×Dic61—22no—
324C4×Dic61—22no—
325C4×Dic61—22no—
326C4×Dic61—22no—
327#11758194—24no—
328C2×#92418C2414yes—
329#11758189—28no—
330C8×D61—28no—
331C23×C61—22no—
332C23×C61—41no—
333C23×C61—41no—
334C23×C61C22×D411yescharacteristic
335C23×C61C22×D411yescharacteristic
336C23×C61C22×D411yescharacteristic
337C22×D61—22no—
338C22×D61—22no—
339C22×D61—41no—
340C22×D61—41no—
341C22×D61—41no—
342C22×D61—41no—
343C22×D61—42no—
344C22×D61—42no—
345C22×D61—42no—
346C22×D61#12314yes—
347C22×D61C22×D412yes—
348C22×D61C22×D412yes—
349Q8×C61—24no—
350Q8×C61—42no—
351C2×C4×C61—22no—
352C2×C4×C61—22no—
353C2×C4×C61—22no—
354C2×C4×C61—22no—
355C2×C4×C61—22no—
356C2×C4×C61—22no—
357C2×C4×C61—22no—
358C2×C4×C61—22no—
359C2×C4×C61—22no—
360C2×C4×C61—42no—
361C2×C4×C61—42no—
362C2×C4×C61—81no—
363C2×C4×C61—81no—
364C2×C4×C61C22×D411yescharacteristic
365C2×C4×C61C22×D411yescharacteristic
366C2×C4×C61C22×D411yescharacteristic
367C2×C4×C61C2×#4114yes—
368C2×C4×C61C2511yescharacteristic
369C22⋊D61—24no—
370C22⋊D61—24no—
371C22⋊D61—24no—
372C22⋊D61—24no—
373C22⋊D61—82no—
374C22⋊D61—82no—
375C2×Dic61—22no—
376C2×Dic61—22no—
377C2×Dic61—22no—
378C2×Dic61—22no—
379C2×Dic61—42no—
380C2×Dic61—81no—
381C2×Dic61—81no—
382C2×Dic61#12314yes—
383C2×Dic61C22×D412yes—
384C2×Dic61C22×D412yes—
385D244—24no—
386D244—24no—
387D244—24no—
388D244—48no—
389D244—42no—
390D244—84no—
391C4×D61—24no—
392C4×D61—22no—
393C4×D61—22no—
394C4×D61—48no—
395C4×D61—82no—
396C4×D61—82no—
397C4×D61—82no—
398C4×D61—82no—
399C4×D61—84no—
400C4×D61#12318yes—
401C4×D61C2×#4114yes—
402C4×D61C2×#4114yes—
403Dic122—24no—
404Dic122—24no—
405C8×C61—24no—
406#92418—24no—
407#60520—611nomaximal, Sylow
408C22×C61—21no—
409C22×C61—21no—
410C22×C61—21no—
411C22×C61—21no—
412C22×C61—21no—
413C22×C61—21no—
414C22×C61—21no—
415C22×C61—21no—
416C22×C61—82no—
417C22×C61C2×#12312yes—
418C22×C61C23×D411yescharacteristic
419C2×D61—22no—
420C2×D61—22no—
421C2×D61—22no—
422C2×D61—22no—
423C2×D61—22no—
424C2×D61—44no—
425C2×D61—42no—
426C2×D61—42no—
427C2×D61—42no—
428C2×D61—82no—
429C2×D61—84no—
430C2×D61C2×#12314yes—
431C4×C61—21no—
432C4×C61—21no—
433C4×C61—42no—
434C4×C61—42no—
435C4×C61—42no—
436C4×C61—42no—
437C4×C61C2×#12312yes—
438C4×C61C22×#4112yes—
439Dic61—22no—
440Dic61—42no—
441Dic61—42no—
442Dic61—42no—
443Dic61C2×#12314yes—
444C2×#537—611no—
445#3428—611no—
446#3099—614no—
447#3099—614no—
448#3098—614no—
449#3098—614no—
450#3095—612no—
451#3095—611no—
452#3095D6111yescharacteristic, complemented
453#3094—612no—
454#3094—611no—
455#3094—611no—
456C2×#428—612no—
457#2896—612no—
458#2879—611no—
459C2×C61—22no—
460C2×C61—41no—
461C2×C61—41no—
462C2×C61C22×#12311yescharacteristic
463C2×C61#358511yescharacteristic
464C2×C61#358611yescharacteristic
465D61—24no—
466D61—42no—
467D61—82no—
468C22×#41—611no—
469C22×#41—611no—
470C22×M16—612no—
471#537—614no—
472#537—614no—
473#537—1222no—
474#537—1222no—
475C2×C22⋊Q8—611no—
476C2×C22⋊Q8—1221no—
477C2×C22⋊Q8C2×D6111yescharacteristic
478C2×#121—611no—
479C2×#121—611no—
480C2×#121—1221no—
481C2×#121—1221no—
482C2×#121—1221no—
483#520—612no—
484#520—612no—
485#520—612no—
486#520—612no—
487#519—1221no—
488#518—1221no—
489#518—1221no—
490#518—1221no—
491C4×#41—1222no—
492C4×#41—1222no—
493C2×#117—611no—
494C2×#117—612no—
495C2×#117—612no—
496C2×#117C2×D6111yescharacteristic
497C22×C4⋊C4—611no—
498#485—614no—
499#485—614no—
500#485—614no—
501#485C2×D6114yescomplemented
502#484—612no—
503#484—614no—
504#484C2×D6112yescomplemented
505#483—612no—
506#483—614no—
507#483C2×D6112yescomplemented
508#482—614no—
509#482—614no—
510#482—614no—
511#482—614no—
512#481—612no—
513#481—614no—
514#481—612no—
515#480—612no—
516#480—614no—
517#480—612no—
518#428—612no—
519#428—612no—
520#428—612no—
521#428—614no—
522#428—614no—
523#428C2×D6112yes—
524C2×#107—614no—
525C2×#106—614no—
526#419—612no—
527#419C2×D6112yes—
528#418—612no—
529#418—612no—
530#417—614no—
531#417—614no—
532#416—614no—
533#416—614no—
534#408—614no—
535#408—614no—
536#407—611no—
537#407—612no—
538#407C2×D6111yescharacteristic
539C61#6052011yescharacteristic, complemented, Sylow
540C2×#41—612no—
541C2×#41—612no—
542C2×#41—612no—
543C2×#41—612no—
544C2×#41—614no—
545C2×#41—1228no—
546C2×#41—1222no—
547C2×#41—1228no—
548C22×Q8—611no—
549C22×Q8C22×D6111yescharacteristic
550C22×D4—611no—
551C22×D4—611no—
552C22×D4—611no—
553C22×D4—611no—
554C22×D4—1221no—
555C22×D4—1221no—
556C22×D4—1221no—
557C23×C4—611no—
558C23×C4—611no—
559C23×C4—1221no—
560C23×C4—1221no—
561C23×C4C22×D6111yescharacteristic
562C2×M16—612no—
563C2×M16—614no—
564C2×M16—1228no—
565C2×M16C22×D6112yes—
566C22×C8—614no—
567C22⋊Q8—21no—
568C22⋊Q8—21no—
569C22⋊Q8—614no—
570C22⋊Q8—1224no—
571C22⋊Q8—1224no—
572C22⋊Q8—1222no—
573C22⋊Q8C22×D6112yes—
574C22⋊Q8C22×D6112yes—
575#121—612no—
576#121—612no—
577#121—614no—
578#121—1224no—
579#121—1224no—
580#121—1224no—
581#121—1224no—
582#121—1222no—
583#121—1224no—
584#121—1224no—
585#121—1221no—
586#121—1221no—
587C4×Q8—1222no—
588C4×Q8—1222no—
589C4×Q8—1222no—
590C4×Q8—1222no—
591C4×D4—1222no—
592C4×D4—1222no—
593C4×D4—1222no—
594C4×D4—1222no—
595C4×D4—1222no—
596C4×D4—1222no—
597C4×D4—1222no—
598C4×D4—1222no—
599C4×D4—1222no—
600C4×D4—1222no—
601C4×D4—1222no—
602C4×D4—1222no—
603#117—21no—
604#117—21no—
605#117—612no—
606#117—612no—
607#117—612no—
608#117—612no—
609#117—612no—
610#117—612no—
611#117—1222no—
612#117—1222no—
613#117—1222no—
614#117—1222no—
615#117—1221no—
616#117—1221no—
617#117C22×D6112yes—
618#117C22×D6112yes—
619C2×C4⋊C4—21no—
620C2×C4⋊C4—611no—
621C2×C4⋊C4—611no—
622C2×C4⋊C4—611no—
623C2×C4⋊C4—614no—
624C2×C4⋊C4—612no—
625C2×C4⋊C4—612no—
626C2×C4⋊C4—612no—
627C2×C4⋊C4—612no—
628C2×C4⋊C4—1222no—
629C2×C4⋊C4—1221no—
630C2×C4⋊C4—1221no—
631C2×C4⋊C4C22×D6111yescharacteristic
632C2×C4⋊C4C22×D6111yescharacteristic
633C2×C4⋊C4C22×D6111yescharacteristic
634C2×C22⋊C4—21no—
635C2×C22⋊C4—21no—
636C2×C22⋊C4—1222no—
637C2×C22⋊C4—1222no—
638C2×C22⋊C4—1221no—
639C2×C22⋊C4—1221no—
640C2×C22⋊C4—1221no—
641C2×C22⋊C4—1221no—
642C2×C42—21no—
643C2×C42—1222no—
644C2×C42—1222no—
645C2×C42—1221no—
646#107—614no—
647#107—614no—
648#107—614no—
649#107C22×D6114yes—
650#106—614no—
651#106—614no—
652#106—614no—
653#106C22×D6114yes—
654#103—614no—
655#103—614no—
656#103C22×D6114yes—
657#103C22×D6114yes—
658#102—614no—
659#102—614no—
660#102—614no—
661#102—614no—
662C22⋊C8—612no—
663C22⋊C8—612no—
664C22⋊C8—614no—
665C22⋊C8—614no—
666C22⋊C8C22×D6112yes—
667C22⋊C8C22×D6112yes—
668C24—611no—
669C24—611no—
670C24—1221no—
671C24D4×D6111yescharacteristic
672#41—1228no—
673#41—1228no—
674#41—1224no—
675#41—1224no—
676#41—1224no—
677#41—1224no—
678#41—1228no—
679#41—1228no—
680#41—2448no—
681C2×Q8—21no—
682C2×Q8—24no—
683C2×Q8—612no—
684C2×Q8—612no—
685C2×Q8—1224no—
686C2×Q8C23×D6112yes—
687C2×D4—612no—
688C2×D4—612no—
689C2×D4—612no—
690C2×D4—612no—
691C2×D4—612no—
692C2×D4—612no—
693C2×D4—612no—
694C2×D4—1224no—
695C2×D4—1224no—
696C2×D4—1224no—
697C2×D4—1224no—
698C2×D4—1224no—
699C2×D4—1222no—
700C2×D4—1222no—
701C2×D4—1221no—
702C2×D4—1224no—
703C2×D4—4882no—
704C2×D4—4882no—
705C2×D4—2444no—
706C22×C4—24no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—611no—
712C22×C4—612no—
713C22×C4—618no—
714C22×C4—612no—
715C22×C4—611no—
716C22×C4—612no—
717C22×C4—612no—
718C22×C4—1224no—
719C22×C4—1222no—
720C22×C4—1222no—
721C22×C4—1222no—
722C22×C4—1222no—
723C22×C4—1224no—
724C22×C4—1224no—
725C22×C4—1221no—
726C22×C4—1221no—
727C22×C4—1221no—
728C22×C4—4882no—
729C22×C4—2444no—
730C22×C4D4×D6111yescharacteristic
731C22×C4D4×D6111yescharacteristic
732C22×C4D4×D6111yescharacteristic
733C22×C4C23×D6111yescharacteristic
734C22×C4C23×D6111yescharacteristic
735C22×C4C23×D6111yescharacteristic
736M16—24no—
737M16—1228no—
738M16—1224no—
739C2×C8—614no—
740C2×C8—1228no—
741C2×C8C23×D6114yes—
742C4⋊C4—22no—
743C4⋊C4—22no—
744C4⋊C4—21no—
745C4⋊C4—21no—
746C4⋊C4—21no—
747C4⋊C4—612no—
748C4⋊C4—612no—
749C4⋊C4—612no—
750C4⋊C4—1224no—
751C4⋊C4—1222no—
752C4⋊C4—1222no—
753C4⋊C4—1222no—
754C4⋊C4—1222no—
755C4⋊C4—1224no—
756C4⋊C4—1221no—
757C4⋊C4—1221no—
758C4⋊C4—1221no—
759C4⋊C4C23×D6112yes—
760C4⋊C4C23×D6112yes—
761C4⋊C4C23×D6112yes—
762C22⋊C4—22no—
763C22⋊C4—22no—
764C22⋊C4—22no—
765C22⋊C4—22no—
766C22⋊C4—1224no—
767C22⋊C4—1222no—
768C22⋊C4—1222no—
769C22⋊C4—1222no—
770C22⋊C4—1222no—
771C22⋊C4—1224no—
772C22⋊C4—1222no—
773C22⋊C4—1222no—
774C22⋊C4—1222no—
775C22⋊C4—1222no—
776C42—22no—
777C42—22no—
778C42—1222no—
779C42—1222no—
780C42—1222no—
781C42—1222no—
782C42—1222no—
783C42—1222no—
784C23—22no—
785C23—41no—
786C23—41no—
787C23—612no—
788C23—614no—
789C23—612no—
790C23—1222no—
791C23—1222no—
792C23—2441no—
793C23—2441no—
794C23—2441no—
795C23—2441no—
796C23—2442no—
797C23—2442no—
798C23—2442no—
799C23C2×D4×D6111yescharacteristic
800C23C2×D4×D6111yescharacteristic
801C23C2×D4×D6111yescharacteristic
802Q8—24no—
803Q8—42no—
804Q8—1224no—
805Q8—1224no—
806D4—1224no—
807D4—1224no—
808D4—1224no—
809D4—1224no—
810D4—1224no—
811D4—1224no—
812D4—1224no—
813D4—4884no—
814D4—4882no—
815D4—4882no—
816D4—2448no—
817D4—2442no—
818C2×C4—22no—
819C2×C4—22no—
820C2×C4—22no—
821C2×C4—22no—
822C2×C4—22no—
823C2×C4—22no—
824C2×C4—22no—
825C2×C4—22no—
826C2×C4—22no—
827C2×C4—42no—
828C2×C4—42no—
829C2×C4—81no—
830C2×C4—81no—
831C2×C4—614no—
832C2×C4—612no—
833C2×C4—618no—
834C2×C4—614no—
835C2×C4—614no—
836C2×C4—612no—
837C2×C4—1222no—
838C2×C4—1224no—
839C2×C4—1222no—
840C2×C4—1222no—
841C2×C4—1222no—
842C2×C4—1222no—
843C2×C4—1222no—
844C2×C4—4882no—
845C2×C4—4882no—
846C2×C4—4882no—
847C2×C4—4882no—
848C2×C4—4884no—
849C2×C4—4881no—
850C2×C4—4881no—
851C2×C4—2448no—
852C2×C4—2442no—
853C2×C4C2×D4×D6111yescharacteristic
854C2×C4C2×D4×D6111yescharacteristic
855C2×C4C2×D4×D6111yescharacteristic
856C2×C4#41×D6114yes—
857C2×C4C24×D6111yescharacteristic
858C8—24no—
859C8—1224no—
860C22—21no—
861C22—21no—
862C22—21no—
863C22—21no—
864C22—21no—
865C22—21no—
866C22—21no—
867C22—21no—
868C22—82no—
869C22—614no—
870C22—1222no—
871C22—1222no—
872C22—1222no—
873C22—1222no—
874C22—1222no—
875C22—4884no—
876C22—4882no—
877C22—2444no—
878C22—2442no—
879C22—2442no—
880C22—2442no—
881C22#123×D6112yes—
882C22C22×D4×D6111yescharacteristic
883C4—21no—
884C4—21no—
885C4—42no—
886C4—42no—
887C4—42no—
888C4—42no—
889C4—614no—
890C4—1222no—
891C4—2442no—
892C4—2442no—
893C4—2442no—
894C4#123×D6112yes—
895C4C2×#41×D6112yes—
896C2—22no—
897C2—41no—
898C2—41no—
899C2—1224no—
900C2—4882no—
901C2—2442no—
902C2C2×#123×D6111yescharacteristic
903C2#2146059611yescharacteristic
904C2#2146060211yescharacteristic
subgroupG/H
centerC22C22×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC61×#3095C2
socleC22×C61C23×D4
prime radicalC2×#16840342C2
hypercenter#3095D61
hypocenterC61#60520
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #3095

Complements

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

NH ≅ G/Ntype
2. #21459020C2semidirect
3. #21455805C2semidirect
4. #21455803C2semidirect
5. #21455800C2semidirect
6. #21455798C2semidirect
7. #21455765C2semidirect
8. #21455763C2semidirect
9. #21455761C2semidirect
10. #21455760C2semidirect
11. #21455759C2semidirect
12. #428×D61C2semidirect
13. #21454337C2semidirect
14. #21454262C2semidirect
15. C61×#3095C2semidirect
30. #16840243C22semidirect
31. #16840243C22semidirect
32. #16840242C22semidirect
33. #16840242C22semidirect
44. #16840102C22semidirect
45. #16840101C22semidirect
46. #16840100C22semidirect
47. #16840096C22semidirect
48. #16840095C22semidirect
49. #16840091C22semidirect
50. #16840090C22semidirect
51. #16840089C22semidirect
52. #16840088C22semidirect
53. #16840087C22semidirect
54. #16840086C22semidirect
55. #16840082C22semidirect
56. #16840081C22semidirect
57. #16840080C22semidirect
58. #16840077C22semidirect
59. #16840076C22semidirect
60. #16840075C22semidirect
63. #16839803C22semidirect
65. #16839801C22semidirect
66. #107×D61C22semidirect
67. #106×D61C22semidirect
71. #16839762C22semidirect
72. #16839762C22semidirect
73. #16839757C22semidirect
74. #16839757C22semidirect
75. #16839727C22semidirect
76. #16839727C22semidirect
81. C61×#485C22semidirect
82. C61×#484C22semidirect
83. C61×#483C22semidirect
452. #3095D61semidirect
501. #485C2×D61semidirect
504. #484C2×D61semidirect
507. #483C2×D61semidirect
539. C61#60520semidirect

Maximal subgroups

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

subgroupindex
C2×#168403422
#214590202
#214558052
#214558032
#214558002
#214557982
#214557652
#214557632
#214557612
#214557602
#214557592
#428×D612
#214543372
#214542622
C61×#30952
#6052061