Finite Group Databasebeta

← #30564934

Subgroups — #30564934

Order 15616.

2254 conjugacy classes of subgroups.

The subgroup lattice has 920 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21459673C211yesmaximal, characteristic, complemented
2C2×#16840405C211yesmaximal, characteristic, complemented
3#21457974C214yesmaximal, complemented
4#21457862C214yesmaximal, complemented
5#21457354C214yesmaximal, complemented
6#21457343C214yesmaximal, complemented
7#21456806C211yesmaximal, characteristic, complemented
8#21456652C212yesmaximal, complemented
9#21456587C212yesmaximal, complemented
10#21455914C211yesmaximal, characteristic, complemented
11#21455911C211yesmaximal, characteristic, complemented
12#21455047C212yesmaximal, complemented
13#21455042C212yesmaximal, complemented
14#21454847C211yesmaximal, characteristic, complemented
15C61×#3215C211yesmaximal, characteristic, complemented
16C22×#11758226C2211yescharacteristic
17C22×D4×D61C2211yescharacteristic
18C2×#14519804C2214yescomplemented
19C2×#14519800C2214yescomplemented
20#16840497—22no—
21#16840485C2212yescomplemented
22#16840478C2212yescomplemented
23#16840465—22no—
24#16840434C2212yescomplemented
25#16840415C2212yescomplemented
26#16840405—22no—
27#16840405—22no—
28#16840405C2214yes—
29#16840405C2214yes—
30#16840352—21no—
31#16840352—21no—
32#16840331—21no—
33#16840312C2211yescharacteristic, complemented
34#16840275C2212yes—
35#16840275C2212yescomplemented
36C2×#14519759—21no—
37C2×#14519753C2211yescharacteristic
38C2×#14519750—21no—
39C2×#14519748C2211yescharacteristic
40C2×#14519747—21no—
41#16840242—21no—
42C2×C4×D244C2211yescharacteristic
43C2×C4×D244C2211yescharacteristic
44C2×C22⋊C4×D61—21no—
45#16840152C2212yescomplemented
46#16840121C2212yescomplemented
47#16840101C2214yescomplemented
48#16840095C2212yescomplemented
49#16840085C2214yescomplemented
50#16840081C2212yescomplemented
51#16840053C2212yescomplemented
52#16840039C2212yescomplemented
53#16840017C2214yescomplemented
54#16840011C2214yescomplemented
55#16839997C2214yescomplemented
56#16839988C2214yescomplemented
57#16839974C2214yescomplemented
58#16839964C2212yescomplemented
59#16839958C2212yescomplemented
60#16839923C2214yescomplemented
61#16839923C2214yescomplemented
62#16839912C2212yes—
63#16839911C2214yescomplemented
64#16839910C2214yescomplemented
65#16839906C2214yescomplemented
66#16839901C2212yescomplemented
67#16839898C2212yes—
68#16839897C2214yescomplemented
69#16839896C2212yes—
70#16839875C2214yescomplemented
71#16839860C2214yescomplemented
72#16839835C2214yescomplemented
73#16839832C2214yescomplemented
74#16839819C2211yescharacteristic, complemented
75#16839765C2214yescomplemented
76#16839757C2214yescomplemented
77#16839724C2212yes—
78C22⋊C8×D61C2212yescomplemented
79C61×#533C2211yescharacteristic, complemented
80C2×#124×C61C2211yescharacteristic
81C61×#497C2212yescomplemented
82C61×#489C2212yescomplemented
83C61×#464C2214yescomplemented
84C61×#451C2212yescomplemented
85C61×#450C2212yes—
86C61×#432C2211yescharacteristic, complemented
87C24×D61—21no—
88C2×#11758226—22no—
89C2×#11758226—44no—
90C2×#11758226C2314yes—
91C2×#11758226C2312yes—
92C2×#11758226C2312yescomplemented
93C2×#11758222—21no—
94C22×D244—21no—
95C22×D244D411yescharacteristic
96C22×D244C2311yescharacteristic
97C22×C22⋊D61—21no—
98C22×C22⋊D61—21no—
99C2×D4×D61—22no—
100C2×D4×D61—44no—
101C2×D4×D61C2314yes—
102C22×C4×D61—21no—
103C22×C4×D61—21no—
104C22×C4×D61C2311yescharacteristic
105C22×C4×D61C2311yescharacteristic
106#14519804—48no—
107#14519800—48no—
108C2×#11758201C2314yes—
109C2×#11758201C2314yescomplemented
110C2×D488C2314yes—
111C2×#11758199C2314yes—
112C2×#11758189C2314yes—
113C2×C8×D61C2314yescomplemented
114#14519777C2311yescharacteristic, complemented
115#14519774—22no—
116#14519774C2311yescharacteristic, complemented
117#14519772—22no—
118#14519772—22no—
119#14519766—22no—
120#14519766—22no—
121#14519765—22no—
122#14519765—21no—
123#14519762—22no—
124#14519762—22no—
125#14519762—22no—
126#14519762—22no—
127#14519759—24no—
128#14519759—24no—
129#14519753—22no—
130#14519753C2312yes—
131#14519753C2314yes—
132#14519753C2312yescomplemented
133#14519752—22no—
134#14519752—22no—
135#14519752—22no—
136#14519752—22no—
137#14519752C2312yes—
138#14519752C2312yescomplemented
139#14519751—21no—
140#14519751C2312yes—
141#14519750—24no—
142#14519750—24no—
143#14519748—22no—
144#14519748C2314yes—
145#14519747—22no—
146#14519747—22no—
147#14519747—24no—
148#14519747—24no—
149C4×Dic122—22no—
150C4×D244—21no—
151C4×D244—21no—
152C4×D244—21no—
153C4×D244—22no—
154C4×D244D412yes—
155C4×D244D412yes—
156C4×D244C2312yes—
157C4×D244C2312yes—
158C4×D244C2312yes—
159C4×D244C2312yes—
160C4×D244C2312yescomplemented
161#14519739—22no—
162#14519739—22no—
163#14519737—22no—
164#14519737—22no—
165#14519735—22no—
166#14519735C2312yes—
167#14519735C2312yescomplemented
168C2×C4⋊Dic61D411yescharacteristic
169C2×C4⋊Dic61C2311yescharacteristic
170C2×#11758196—21no—
171C4⋊C4×D61—22no—
172C2×C22⋊Dic61—21no—
173C2×#11758198—21no—
174C2×#11758198—21no—
175C2×#11758198D411yescharacteristic
176C2×#11758198D411yescharacteristic
177C22⋊C4×D61—24no—
178C22⋊C4×D61—24no—
179#14519710C2314yescomplemented
180#14519709C2314yescomplemented
181C4⋊#92418C2312yescomplemented
182#14519701C2314yescomplemented
183#14519701C2314yescomplemented
184#14519699C2314yes—
185#14519699C2314yescomplemented
186#14519698C2314yes—
187#14519697C2314yes—
188C22⋊#92418C2312yes—
189#14519689C2314yes—
190#14519689C2314yescomplemented
191#14519688C2312yescomplemented
192C22×Q8×C61C2311yescharacteristic
193C22×D4×C61C2311yescharacteristic
194C2×Q16×C61C2314yescomplemented
195C2×SD16×C61C2314yes—
196C4⋊Q8×C61C2311yescharacteristic, complemented
197C4⋊Q8×C61C2311yescharacteristic, complemented
198#125×C61—21no—
199#124×C61—21no—
200#124×C61—21no—
201#124×C61C2312yes—
202#124×C61C2312yes—
203C22⋊Q8×C61—21no—
204C22⋊Q8×C61C2312yes—
205C4×Q8×C61—21no—
206C4×Q8×C61C2312yescomplemented
207#117×C61—21no—
208C2×C22⋊C4×C61—21no—
209C2×C22⋊C4×C61—21no—
210C2×C42×C61C2311yescharacteristic
211C4⋊C8×C61C2312yescomplemented
212#103×C61C2314yescomplemented
213#102×C61C2314yes—
214C22⋊C8×C61C2312yes—
215#97×C61C2312yescomplemented
216C24×C61—21no—
217C23×D61—21no—
218C23×D61—24no—
219C23×D61—44no—
220C23×D61—44no—
221C23×D61—82no—
222C23×D61C2×D411yescharacteristic
223C23×D61C2×D411yescharacteristic
224C2×Q8×C61—21no—
225C2×Q8×C61—21no—
226C2×Q8×C61—42no—
227C2×Q8×C61C2412yes—
228C2×Q8×C61C2412yes—
229C2×D4×C61—21no—
230C2×D4×C61—42no—
231C2×D4×C61C2412yes—
232C22×C4×C61—21no—
233C22×C4×C61C2×D411yescharacteristic
234C22×C4×C61C2×D411yescharacteristic
235C22×C4×C61C2411yescharacteristic
236C2×C22⋊D61—22no—
237C2×C22⋊D61—24no—
238C2×C22⋊D61—24no—
239C2×C22⋊D61—44no—
240C2×C22⋊D61—82no—
241C22×Dic61—21no—
242C22×Dic61C2×D411yescharacteristic
243C22×Dic61C2×D411yescharacteristic
244#11758226—28no—
245#11758226—44no—
246#11758226—44no—
247#11758226—44no—
248#11758226—48no—
249D4×D61—28no—
250D4×D61—44no—
251D4×D61—48no—
252#11758222—44no—
253C2×D244—21no—
254C2×D244—24no—
255C2×D244—24no—
256C2×D244—21no—
257C2×D244—22no—
258C2×D244—22no—
259C2×D244—22no—
260C2×D244—22no—
261C2×D244—21no—
262C2×D244—42no—
263C2×D244—44no—
264C2×D244C2×D412yes—
265C2×D244C2×D412yes—
266C2×D244C2412yes—
267C2×D244C2412yes—
268C2×C4×D61—22no—
269C2×C4×D61—24no—
270C2×C4×D61—22no—
271C2×C4×D61—22no—
272C2×C4×D61—22no—
273C2×C4×D61—22no—
274C2×C4×D61—42no—
275C2×C4×D61—42no—
276C2×C4×D61—44no—
277C2×C4×D61—82no—
278C2×C4×D61C2×D412yes—
279C2×C4×D61C2×D412yes—
280C2×C4×D61C2412yes—
281C2×C4×D61C2412yes—
282C2×Dic122—21no—
283Q16×C61—44no—
284SD16×C61—44no—
285C2×C8×C61C2414yes—
286C4⋊C4×C61—21no—
287C4⋊C4×C61—21no—
288C4⋊C4×C61—21no—
289C4⋊C4×C61—22no—
290C4⋊C4×C61—22no—
291C4⋊C4×C61C2412yes—
292C22⋊C4×C61—22no—
293C22⋊C4×C61—22no—
294C22⋊C4×C61—22no—
295C22⋊C4×C61—22no—
296C22⋊C4×C61—22no—
297C42×C61—22no—
298C42×C61C2×D411yescharacteristic
299C42×C61C2×D411yescharacteristic
300C42×C61C2411yescharacteristic
301C42×C61C2411yescharacteristic
302C22⋊Dic61—24no—
303#11758201—28no—
304#11758201—44no—
305#11758199—44no—
306#11758198—24no—
307#11758198—22no—
308#11758198—22no—
309#11758198—22no—
310#11758198—22no—
311#11758198—22no—
312#11758198—22no—
313#11758198—22no—
314#11758198—22no—
315#11758198—22no—
316#11758198—22no—
317#11758198C2×D412yes—
318#11758198C2×D412yes—
319#11758198C2×D412yes—
320#11758198C2×D412yes—
321C4⋊Dic61—21no—
322C4⋊Dic61—21no—
323C4⋊Dic61C2×D412yes—
324C4⋊Dic61C2×D412yes—
325C4⋊Dic61C2412yes—
326C4⋊Dic61C2412yes—
327#11758196—22no—
328#11758196—22no—
329#11758196—24no—
330C4×Dic61—22no—
331C4×Dic61—22no—
332C2×#92418C2414yes—
333D488—28no—
334#11758189—44no—
335C8×D61—44no—
336C23×C61—22no—
337C23×C61—42no—
338C23×C61—42no—
339C23×C61—42no—
340C23×C61C22×D411yescharacteristic
341C22×D61—24no—
342C22×D61—22no—
343C22×D61—22no—
344C22×D61—22no—
345C22×D61—22no—
346C22×D61—41no—
347C22×D61—41no—
348C22×D61—41no—
349C22×D61—41no—
350C22×D61—48no—
351C22×D61—48no—
352C22×D61—42no—
353C22×D61—42no—
354C22×D61—84no—
355C22×D61—816no—
356C22×D61C22×D412yes—
357C22×D61C22×D412yes—
358Q8×C61—24no—
359Q8×C61—24no—
360Q8×C61—42no—
361Q8×C61—81no—
362D4×C61—24no—
363D4×C61—42no—
364C2×C4×C61—22no—
365C2×C4×C61—22no—
366C2×C4×C61—22no—
367C2×C4×C61—22no—
368C2×C4×C61—22no—
369C2×C4×C61—41no—
370C2×C4×C61—42no—
371C2×C4×C61C22×D411yescharacteristic
372C2×C4×C61C22×D411yescharacteristic
373C2×C4×C61C22×D411yescharacteristic
374C2×C4×C61C22×D411yescharacteristic
375C2×C4×C61C22×D411yescharacteristic
376C2×C4×C61C2511yescharacteristic
377C22⋊D61—48no—
378C22⋊D61—44no—
379C22⋊D61—84no—
380C2×Dic61—22no—
381C2×Dic61—22no—
382C2×Dic61—41no—
383C2×Dic61—41no—
384C2×Dic61—42no—
385C2×Dic61C22×D412yes—
386C2×Dic61C22×D412yes—
387D244—24no—
388D244—22no—
389D244—24no—
390D244—42no—
391D244—42no—
392D244—42no—
393D244—48no—
394D244—81no—
395D244—82no—
396D244—82no—
397D244—82no—
398D244—82no—
399D244H(5,𝔽2)14yes—
400C4×D61—24no—
401C4×D61—24no—
402C4×D61—42no—
403C4×D61—42no—
404C4×D61—48no—
405C4×D61—44no—
406C4×D61—82no—
407C4×D61—82no—
408C4×D61—82no—
409C4×D61—82no—
410Dic122—42no—
411C8×C61—24no—
412#92418—24no—
413#61576—611nomaximal, Sylow
414C22×C61—21no—
415C22×C61—21no—
416C22×C61—42no—
417C22×C61—42no—
418C22×C61—42no—
419C22×C61—84no—
420C22×C61#57512yes—
421C22×C61C23×D411yescharacteristic
422C2×D61—22no—
423C2×D61—22no—
424C2×D61—22no—
425C2×D61—22no—
426C2×D61—24no—
427C2×D61—22no—
428C2×D61—22no—
429C2×D61—48no—
430C2×D61—44no—
431C2×D61—42no—
432C2×D61—42no—
433C2×D61—42no—
434C2×D61—42no—
435C2×D61—42no—
436C2×D61—82no—
437C2×D61—816no—
438C4×C61—21no—
439C4×C61—21no—
440C4×C61—21no—
441C4×C61—21no—
442C4×C61—21no—
443C4×C61—42no—
444C4×C61—42no—
445C4×C61—42no—
446C4×C61C2×H(5,𝔽2)12yes—
447Dic61—22no—
448Dic61—22no—
449Dic61—42no—
450Dic61—42no—
451#3506—611no—
452C2×#546—611no—
453#3319—614no—
454#3311—614no—
455#3268—614no—
456#3267—614no—
457#3215D6111yescharacteristic, complemented
458#3213—611no—
459#3196—612no—
460#3188—612no—
461#3110—611no—
462#3109—611no—
463#3003—612no—
464#3002—612no—
465#2973—611no—
466C2×C61—22no—
467C2×C61—82no—
468C2×C61#348411yescharacteristic
469C2×C61C2×#57511yescharacteristic
470C2×C61#358511yescharacteristic
471D61—42no—
472D61—42no—
473D61—44no—
474D61—82no—
475C22×#41—611no—
476C23×D4—611no—
477C2×AGL(1,ℤ/8)—614no—
478C2×#135—614no—
479#559—1222no—
480#556—612no—
481#555—612no—
482#553—1222no—
483#550—612no—
484#547—612no—
485#546—614no—
486#546—614no—
487#546—1222no—
488#546—1222no—
489#538—1221no—
490#538—1221no—
491#535—1221no—
492#533C2×D6111yescharacteristic, complemented
493#532—611no—
494C2×#124C2×D6111yescharacteristic
495#525—612no—
496#525—612no—
497C2×#123—1221no—
498C2×C22⋊Q8—611no—
499C2×#121—611no—
500C2×#121—1221no—
501C2×#120—1221no—
502#520—1221no—
503C2×C4×D4—611no—
504C2×C4×D4—611no—
505C22×C22⋊C4—1221no—
506#497C2×D6112yescomplemented
507#496—612no—
508#489—612no—
509#489C2×D6112yescomplemented
510#485—614no—
511#484—612no—
512#482—614no—
513#481—612no—
514#476—612no—
515#474—612no—
516#470—614no—
517#468—614no—
518#466—614no—
519#465—614no—
520#464C2×D6114yescomplemented
521#463—614no—
522#461—612no—
523#459—612no—
524#452—614no—
525#452—614no—
526#451C2×D6112yescomplemented
527#450—614no—
528#450—612no—
529#450C2×D6112yes—
530#449—614no—
531#449—614no—
532#448—612no—
533#447—612no—
534#447—614no—
535#447—612no—
536#442—614no—
537#440—614no—
538#435—614no—
539#435—614no—
540#432—611no—
541#432C2×D6111yescharacteristic, complemented
542#418—614no—
543#416—614no—
544#407—612no—
545C2×C22⋊C8—612no—
546C61#6157611yescharacteristic, complemented, Sylow
547C25—1221no—
548C2×#41—614no—
549C2×#41—612no—
550C2×#41—612no—
551C2×#41—1222no—
552C2×#41—1221no—
553C2×#41—2444no—
554C22×Q8C22×D6111yescharacteristic
555C22×D4—614no—
556C22×D4—611no—
557C22×D4—611no—
558C22×D4—1221no—
559C22×D4—1222no—
560C22×D4—1221no—
561C22×D4—1221no—
562C22×D4—2444no—
563C22×D4C22×D6111yescharacteristic
564C23×C4—611no—
565C23×C4—611no—
566C23×C4—1221no—
567C23×C4—1221no—
568AGL(1,ℤ/8)—2448no—
569#135—2448no—
570C2×Q16C22×D6114yescomplemented
571C2×SD16—614no—
572C2×SD16—614no—
573C2×SD16C22×D6114yes—
574C2×D8—614no—
575C2×D8—614no—
576C2×M16—614no—
577C22×C8—614no—
578C4⋊Q8—611no—
579C4⋊Q8C22×D6111yescharacteristic, complemented
580C4⋊Q8C22×D6111yescharacteristic, complemented
581#127—611no—
582#127—1222no—
583#126—1222no—
584#126—1222no—
585#125—21no—
586#124—21no—
587#124—21no—
588#124—1222no—
589#124—1222no—
590#124—1222no—
591#124—1221no—
592#124C22×D6112yes—
593#124C22×D6112yes—
594#123—1224no—
595#123—1224no—
596#123—1222no—
597#123—1222no—
598#123—1222no—
599#123—1222no—
600C22⋊Q8—21no—
601C22⋊Q8—614no—
602C22⋊Q8—612no—
603C22⋊Q8—612no—
604C22⋊Q8—1222no—
605C22⋊Q8C22×D6112yes—
606#121—614no—
607#121—612no—
608#121—612no—
609#121—612no—
610#121—1224no—
611#121—1224no—
612#121—1222no—
613#121—1222no—
614#121—1222no—
615#121—1222no—
616#121—1222no—
617#121—1221no—
618#120—1224no—
619#120—1224no—
620#120—1222no—
621#120—1222no—
622C4×Q8—21no—
623C4×Q8—1222no—
624C4×Q8C22×D6112yescomplemented
625C4×D4—612no—
626C4×D4—612no—
627C4×D4—612no—
628C4×D4—612no—
629C4×D4—612no—
630C4×D4—612no—
631C4×D4—612no—
632C4×D4—1222no—
633C4×D4—1222no—
634C4×D4—1222no—
635C4×D4—1222no—
636C4×D4—1222no—
637C4×D4—1221no—
638C4×D4—1221no—
639C4×D4—1221no—
640#117—21no—
641#117—612no—
642#117—612no—
643#117—1222no—
644C2×C4⋊C4—611no—
645C2×C4⋊C4—611no—
646C2×C4⋊C4—1222no—
647C2×C4⋊C4—1221no—
648C2×C22⋊C4—21no—
649C2×C22⋊C4—21no—
650C2×C22⋊C4—611no—
651C2×C22⋊C4—611no—
652C2×C22⋊C4—1224no—
653C2×C22⋊C4—1224no—
654C2×C22⋊C4—1221no—
655C2×C22⋊C4—1221no—
656C2×C22⋊C4—1221no—
657C2×C42C22×D6111yescharacteristic
658#107—614no—
659#106—614no—
660C4⋊C8—612no—
661C4⋊C8C22×D6112yescomplemented
662#103—614no—
663#103—614no—
664#103C22×D6114yescomplemented
665#102—614no—
666#102—614no—
667#102—614no—
668#102—614no—
669#102C22×D6114yes—
670C22⋊C8—612no—
671C22⋊C8—614no—
672C22⋊C8—614no—
673C22⋊C8C22×D6112yes—
674#97—612no—
675#97C22×D6112yescomplemented
676C24—21no—
677C24—611no—
678C24—611no—
679C24—1224no—
680C24—1221no—
681C24—4882no—
682C24—2444no—
683C24—2444no—
684#41—1228no—
685#41—2444no—
686#41—2444no—
687#41—2444no—
688#41—2444no—
689#41—2448no—
690C2×Q8—21no—
691C2×Q8—21no—
692C2×Q8—42no—
693C2×Q8—1221no—
694C2×Q8C23×D6112yes—
695C2×Q8C23×D6112yes—
696C2×D4—21no—
697C2×D4—42no—
698C2×D4—612no—
699C2×D4—612no—
700C2×D4—612no—
701C2×D4—612no—
702C2×D4—1224no—
703C2×D4—1222no—
704C2×D4—1222no—
705C2×D4—1222no—
706C2×D4—1222no—
707C2×D4—1224no—
708C2×D4—1224no—
709C2×D4—1228no—
710C2×D4—1224no—
711C2×D4—1222no—
712C2×D4—1221no—
713C2×D4—1221no—
714C2×D4—1221no—
715C2×D4—4882no—
716C2×D4—2442no—
717C2×D4—2444no—
718C2×D4—2444no—
719C2×D4—2448no—
720C2×D4—2444no—
721C2×D4C23×D6112yes—
722C22×C4—21no—
723C22×C4—611no—
724C22×C4—611no—
725C22×C4—612no—
726C22×C4—612no—
727C22×C4—612no—
728C22×C4—612no—
729C22×C4—1222no—
730C22×C4—1222no—
731C22×C4—1224no—
732C22×C4—1221no—
733C22×C4—1222no—
734C22×C4—1222no—
735C22×C4—1222no—
736C22×C4—4882no—
737C22×C4—2442no—
738C22×C4—2442no—
739C22×C4—2444no—
740C22×C4D4×D6111yescharacteristic
741C22×C4D4×D6111yescharacteristic
742C22×C4C23×D6111yescharacteristic
743Q16—44no—
744SD16—44no—
745SD16—1228no—
746SD16—2444no—
747D8—1228no—
748D8—2444no—
749M16—2444no—
750C2×C8—614no—
751C2×C8—2444no—
752C2×C8C23×D6114yes—
753C4⋊C4—21no—
754C4⋊C4—21no—
755C4⋊C4—22no—
756C4⋊C4—21no—
757C4⋊C4—22no—
758C4⋊C4—612no—
759C4⋊C4—612no—
760C4⋊C4—612no—
761C4⋊C4—612no—
762C4⋊C4—1222no—
763C4⋊C4—1222no—
764C4⋊C4—1224no—
765C4⋊C4—1221no—
766C4⋊C4—1221no—
767C4⋊C4C23×D6112yes—
768C22⋊C4—22no—
769C22⋊C4—22no—
770C22⋊C4—22no—
771C22⋊C4—22no—
772C22⋊C4—22no—
773C22⋊C4—612no—
774C22⋊C4—612no—
775C22⋊C4—612no—
776C22⋊C4—612no—
777C22⋊C4—1222no—
778C22⋊C4—1222no—
779C22⋊C4—1224no—
780C22⋊C4—1222no—
781C22⋊C4—1222no—
782C22⋊C4—1222no—
783C22⋊C4—1222no—
784C22⋊C4—1224no—
785C22⋊C4—1222no—
786C22⋊C4—1222no—
787C22⋊C4—1222no—
788C22⋊C4—1222no—
789C42—22no—
790C42—1222no—
791C42—1222no—
792C42D4×D6111yescharacteristic
793C42D4×D6111yescharacteristic
794C42C23×D6111yescharacteristic
795C42C23×D6111yescharacteristic
796C23—22no—
797C23—42no—
798C23—42no—
799C23—42no—
800C23—612no—
801C23—612no—
802C23—1224no—
803C23—1222no—
804C23—1222no—
805C23—1222no—
806C23—1222no—
807C23—4884no—
808C23—48816no—
809C23—2441no—
810C23—2441no—
811C23—2441no—
812C23—2441no—
813C23—2442no—
814C23—2448no—
815C23—2448no—
816C23—2442no—
817C23C2×D4×D6111yescharacteristic
818Q8—24no—
819Q8—24no—
820Q8—42no—
821Q8—81no—
822Q8—2442no—
823D4—24no—
824D4—42no—
825D4—614no—
826D4—1224no—
827D4—1222no—
828D4—1224no—
829D4—4881no—
830D4—4882no—
831D4—4882no—
832D4—4882no—
833D4—4882no—
834D4—4884no—
835D4—2442no—
836D4—2442no—
837D4—2442no—
838D4—2448no—
839D4—2448no—
840D4—2444no—
841C2×C4—22no—
842C2×C4—22no—
843C2×C4—22no—
844C2×C4—22no—
845C2×C4—22no—
846C2×C4—41no—
847C2×C4—42no—
848C2×C4—612no—
849C2×C4—612no—
850C2×C4—1224no—
851C2×C4—1224no—
852C2×C4—1222no—
853C2×C4—1222no—
854C2×C4—4882no—
855C2×C4—4882no—
856C2×C4—4882no—
857C2×C4—4882no—
858C2×C4—2442no—
859C2×C4—2442no—
860C2×C4—2444no—
861C2×C4—2448no—
862C2×C4—2441no—
863C2×C4—2441no—
864C2×C4—2442no—
865C2×C4C2×D4×D6111yescharacteristic
866C2×C4C2×D4×D6111yescharacteristic
867C2×C4C2×D4×D6111yescharacteristic
868C2×C4C2×D4×D6111yescharacteristic
869C2×C4C2×D4×D6111yescharacteristic
870C2×C4C24×D6111yescharacteristic
871C8—24no—
872C8—1224no—
873C22—21no—
874C22—21no—
875C22—42no—
876C22—42no—
877C22—42no—
878C22—84no—
879C22—1222no—
880C22—1222no—
881C22—1222no—
882C22—1222no—
883C22—1222no—
884C22—1222no—
885C22—1224no—
886C22—4882no—
887C22—48816no—
888C22—2444no—
889C22—2448no—
890C22—2442no—
891C22—2442no—
892C22—2442no—
893C22—2442no—
894C22—2442no—
895C22#1684056112yes—
896C22C22×D4×D6111yescharacteristic
897C4—21no—
898C4—21no—
899C4—21no—
900C4—21no—
901C4—21no—
902C4—42no—
903C4—42no—
904C4—42no—
905C4—1222no—
906C4—1222no—
907C4—2442no—
908C4—2442no—
909C4H(5,𝔽2)×D6112yes—
910C2—22no—
911C2—82no—
912C2—4882no—
913C2—2442no—
914C2—2442no—
915C2—2444no—
916C2#2145945311yescharacteristic
917C2C2×#1684056111yescharacteristic
918C2#2146059611yescharacteristic
subgroupG/H
centerC22C22×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC61×#3215C2
socleC22×C61C23×D4
hypercenter#3215D61
hypocenterC61#61576
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3215

Complements

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

NH ≅ G/Ntype
1. #21459673C2semidirect
2. C2×#16840405C2semidirect
3. #21457974C2semidirect
4. #21457862C2semidirect
5. #21457354C2semidirect
6. #21457343C2semidirect
7. #21456806C2semidirect
8. #21456652C2semidirect
9. #21456587C2semidirect
10. #21455914C2semidirect
11. #21455911C2semidirect
12. #21455047C2semidirect
13. #21455042C2semidirect
14. #21454847C2semidirect
15. C61×#3215C2semidirect
18. C2×#14519804C22semidirect
19. C2×#14519800C22semidirect
21. #16840485C22semidirect
22. #16840478C22semidirect
24. #16840434C22semidirect
25. #16840415C22semidirect
33. #16840312C22semidirect
35. #16840275C22semidirect
45. #16840152C22semidirect
46. #16840121C22semidirect
47. #16840101C22semidirect
48. #16840095C22semidirect
49. #16840085C22semidirect
50. #16840081C22semidirect
51. #16840053C22semidirect
52. #16840039C22semidirect
53. #16840017C22semidirect
54. #16840011C22semidirect
55. #16839997C22semidirect
56. #16839988C22semidirect
57. #16839974C22semidirect
58. #16839964C22semidirect
59. #16839958C22semidirect
60. #16839923C22semidirect
61. #16839923C22semidirect
63. #16839911C22semidirect
64. #16839910C22semidirect
65. #16839906C22semidirect
66. #16839901C22semidirect
68. #16839897C22semidirect
70. #16839875C22semidirect
71. #16839860C22semidirect
72. #16839835C22semidirect
73. #16839832C22semidirect
74. #16839819C22semidirect
75. #16839765C22semidirect
76. #16839757C22semidirect
78. C22⋊C8×D61C22semidirect
79. C61×#533C22semidirect
81. C61×#497C22semidirect
82. C61×#489C22semidirect
83. C61×#464C22semidirect
84. C61×#451C22semidirect
86. C61×#432C22semidirect
92. C2×#11758226C23semidirect
109. C2×#11758201C23semidirect
113. C2×C8×D61C23semidirect
114. #14519777C23semidirect
116. #14519774C23semidirect
132. #14519753C23semidirect
138. #14519752C23semidirect
160. C4×D244C23semidirect
167. #14519735C23semidirect
179. #14519710C23semidirect
180. #14519709C23semidirect
181. C4⋊#92418C23semidirect
182. #14519701C23semidirect
183. #14519701C23semidirect
185. #14519699C23semidirect
190. #14519689C23semidirect
191. #14519688C23semidirect
194. C2×Q16×C61C23semidirect
196. C4⋊Q8×C61C23semidirect
197. C4⋊Q8×C61C23semidirect
206. C4×Q8×C61C23semidirect
211. C4⋊C8×C61C23semidirect
212. #103×C61C23semidirect
215. #97×C61C23semidirect
457. #3215D61semidirect
492. #533C2×D61semidirect
506. #497C2×D61semidirect
509. #489C2×D61semidirect
520. #464C2×D61semidirect
526. #451C2×D61semidirect
541. #432C2×D61semidirect
546. C61#61576semidirect
570. C2×Q16C22×D61semidirect
579. C4⋊Q8C22×D61semidirect
580. C4⋊Q8C22×D61semidirect
624. C4×Q8C22×D61semidirect
661. C4⋊C8C22×D61semidirect
664. #103C22×D61semidirect
675. #97C22×D61semidirect

Maximal subgroups

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

subgroupindex
#214596732
C2×#168404052
#214579742
#214578622
#214573542
#214573432
#214568062
#214566522
#214565872
#214559142
#214559112
#214550472
#214550422
#214548472
C61×#32152
#6157661