Finite Group Databasebeta

← #27350363

Subgroups — #27350363

Order 13568.

1060 conjugacy classes of subgroups.

The subgroup lattice has 980 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811302C211yesmaximal, characteristic
2#20283750C211yesmaximal, characteristic, complemented
3#20273085C211yesmaximal, characteristic, complemented
4#20273082C211yesmaximal, characteristic, complemented
5#20273080C211yesmaximal, characteristic, complemented
6#20273078C211yesmaximal, characteristic, complemented
7#20273064C211yesmaximal, characteristic, complemented
8#20273061C211yesmaximal, characteristic, complemented
9#20273051C211yesmaximal, characteristic, complemented
10#20273047C211yesmaximal, characteristic, complemented
11#20273041C211yesmaximal, characteristic, complemented
12#20273031C211yesmaximal, characteristic, complemented
13#20273027C211yesmaximal, characteristic, complemented
14C2×#16810346C211yesmaximal, characteristic, complemented
15C53×#2974C211yesmaximal, characteristic, complemented
16#16811302—21no—
17#16811302—21no—
18#16811302—21no—
19#16811302—21no—
20#16811302—21no—
21#16811302—21no—
22#16811302—21no—
23#16811302—21no—
24C2×#13133212C411yescharacteristic
25C2×#13133211C2211yescharacteristic
26C2×#13133203C411yescharacteristic
27C2×#13133200C2211yescharacteristic
28C2×#13133199C411yescharacteristic
29C2×#13133198C411yescharacteristic
30C2×#13133196C2211yescharacteristic
31C2×#13133195C411yescharacteristic
32C2×#13133185C411yescharacteristic
33C2×C4×C22⋊D53C2211yescharacteristic
34C2×#13133174C2211yescharacteristic
35C2×#13133173C411yescharacteristic
36C22×#11719921C2211yescharacteristic
37C2×C22⋊C4×D53C411yescharacteristic
38#16810701—21no—
39#16810695—21no—
40#16810695—21no—
41D4×#88322—21no—
42#16810680C2211yescharacteristic, complemented
43#16810676C2211yescharacteristic, complemented
44#16810587C2211yescharacteristic
45#16810587C2211yescharacteristic, complemented
46C2×C22⋊#88322C2211yescharacteristic
47C2×C22⋊#88322C2211yescharacteristic, complemented
48#16810348C2211yescharacteristic, complemented
49#16810348C2211yescharacteristic, complemented
50#16810348C2211yescharacteristic, complemented
51#16810348C2211yescharacteristic, complemented
52#16810348C2211yescharacteristic, complemented
53#16810348C2211yescharacteristic, complemented
54#16810348C2211yescharacteristic, complemented
55#16810348C2211yescharacteristic, complemented
56#16810346C2211yescharacteristic
57#16810346C2211yescharacteristic
58#16810346C2211yescharacteristic
59#16810346C2211yescharacteristic
60#16810346C2211yescharacteristic
61#16810346C2211yescharacteristic
62#16810346C2211yescharacteristic
63#16810346C2211yescharacteristic
64C2×C4×D4×C53C2211yescharacteristic
65C53×#436—21no—
66C53×#435—21no—
67C53×#435—21no—
68C8×D4×C53—21no—
69C53×#432C2211yescharacteristic, complemented
70C53×#431C2211yescharacteristic, complemented
71C53×#407C2211yescharacteristic
72C53×#407C2211yescharacteristic, complemented
73C2×C22⋊C8×C53C2211yescharacteristic
74C2×C22⋊C8×C53C2211yescharacteristic, complemented
75C24×D53C2×C411yescharacteristic
76C22×Dic106C2×C411yescharacteristic
77C22×C22⋊D53C2×C411yescharacteristic
78C22×C22⋊D53C2×C411yescharacteristic
79C23×Dic53C2×C411yescharacteristic
80C22×C4×D53C2×C411yescharacteristic
81C22×C4×D53C2×C411yescharacteristic
82C2×#11719917—21no—
83C2×#11719917—21no—
84C22×#88322—21no—
85C22×#88322—21no—
86#13133212—21no—
87#13133212—21no—
88#13133212—21no—
89#13133212—21no—
90#13133211—21no—
91#13133211—21no—
92#13133211—21no—
93#13133211—21no—
94#13133203—21no—
95#13133203—21no—
96#13133203—21no—
97#13133203—21no—
98#13133200—21no—
99#13133200—21no—
100#13133200—21no—
101#13133200—21no—
102#13133199—21no—
103#13133199—21no—
104#13133199—21no—
105#13133199—21no—
106#13133198—21no—
107#13133198—21no—
108#13133198—21no—
109#13133198—21no—
110#13133196—21no—
111#13133196—21no—
112#13133196—21no—
113#13133196—21no—
114#13133195—21no—
115#13133195—21no—
116#13133195—21no—
117#13133195—21no—
118#13133185—21no—
119#13133185—21no—
120#13133185—21no—
121#13133185—21no—
122C4×C22⋊D53—21no—
123C4×C22⋊D53—21no—
124C4×C22⋊D53—21no—
125C4×C22⋊D53—21no—
126#13133174—21no—
127#13133174—21no—
128#13133174—21no—
129#13133174—21no—
130#13133173—21no—
131#13133173—21no—
132#13133173—21no—
133#13133173—21no—
134C2×C4⋊Dic53C2×C411yescharacteristic
135C2×#11719919C2×C411yescharacteristic
136C2×#11719919C2×C411yescharacteristic
137C2×#11719919C2×C411yescharacteristic
138C2×#11719919C2×C411yescharacteristic
139C2×#11719919C2311yescharacteristic
140C2×#11719919C2311yescharacteristic
141C2×C22⋊Dic53C2×C411yescharacteristic
142C2×C22⋊Dic53C2×C411yescharacteristic
143C2×C22⋊Dic53C2×C411yescharacteristic
144C2×C22⋊Dic53C2×C411yescharacteristic
145C2×#11719921—21no—
146C2×#11719921—21no—
147C2×#11719921—21no—
148C2×#11719921—21no—
149C2×#11719921C2×C411yescharacteristic
150C2×#11719921C2×C411yescharacteristic
151C2×#11719921C2×C411yescharacteristic
152C2×#11719921C2×C411yescharacteristic
153C2×#11719921C2×C411yescharacteristic
154C2×#11719921C2×C411yescharacteristic
155C2×#11719921C2311yescharacteristic
156C2×#11719921C2311yescharacteristic
157C22⋊C4×D53—21no—
158C22⋊C4×D53—21no—
159C22⋊C4×D53—21no—
160C22⋊C4×D53—21no—
161C2×C4×Dic53C2×C411yescharacteristic
162C2×C4×Dic53C2×C411yescharacteristic
163C4⋊#88322—21no—
164C4⋊#88322—21no—
165C22⋊#88322—21no—
166C22⋊#88322—21no—
167C22⋊#88322—21no—
168C22⋊#88322—21no—
169C22⋊#88322C2311yescharacteristic
170C22⋊#88322C2311yescharacteristic
171C22⋊#88322C2311yescharacteristic
172C22⋊#88322C2311yescharacteristic
173#13133128—21no—
174C4×#88322—21no—
175C22×D4×C53C2×C411yescharacteristic
176C23×C4×C53C2311yescharacteristic
177C23×C4×C53C2311yescharacteristic
178C2×M16×C53—21no—
179C2×M16×C53—21no—
180C22×C8×C53—21no—
181C22×C8×C53—21no—
182C4×D4×C53D411yescharacteristic
183C4×D4×C53D411yescharacteristic
184C4×D4×C53D411yescharacteristic
185C4×D4×C53D411yescharacteristic
186C4×D4×C53D411yescharacteristic
187C4×D4×C53D411yescharacteristic
188C4×D4×C53D411yescharacteristic
189C4×D4×C53D411yescharacteristic
190C2×C4⋊C4×C53C2×C411yescharacteristic
191C2×C22⋊C4×C53C2×C411yescharacteristic
192C2×C22⋊C4×C53C2×C411yescharacteristic
193C2×C42×C53C2311yescharacteristic
194C4⋊C8×C53—21no—
195C4⋊C8×C53—21no—
196C22⋊C8×C53—21no—
197C22⋊C8×C53—21no—
198C22⋊C8×C53—21no—
199C22⋊C8×C53—21no—
200C22⋊C8×C53C2311yescharacteristic
201C22⋊C8×C53C2311yescharacteristic
202C22⋊C8×C53C2311yescharacteristic
203C22⋊C8×C53C2311yescharacteristic
204#97×C53—21no—
205C4×C8×C53—21no—
206C24×C53C22×C411yescharacteristic
207C24×C53C22×C411yescharacteristic
208C23×D53—21no—
209C23×D53—21no—
210C23×D53—22no—
211C23×D53—41no—
212C23×D53—42no—
213C23×D53—81no—
214C23×D53C22×C411yescharacteristic
215C23×D53C22×C411yescharacteristic
216C2×D4×C53—42no—
217C2×D4×C53C22⋊C411yescharacteristic
218C2×D4×C53C22⋊C411yescharacteristic
219C2×D4×C53C22⋊C411yescharacteristic
220C2×D4×C53C22⋊C411yescharacteristic
221C22×C4×C53—81no—
222C22×C4×C53—81no—
223C22×C4×C53C22×C411yescharacteristic
224C22×C4×C53C22×C411yescharacteristic
225C22×C4×C53C22×C411yescharacteristic
226C22×C4×C53C22×C411yescharacteristic
227C22×C4×C53C2×D411yescharacteristic
228C22×C4×C53C2×D411yescharacteristic
229C22×C4×C53C2×D411yescharacteristic
230C22×C4×C53C2×D411yescharacteristic
231C22×C4×C53C2×D411yescharacteristic
232C22×C4×C53C2×D411yescharacteristic
233C22×C4×C53C2×D411yescharacteristic
234C22×C4×C53C2×D411yescharacteristic
235C22×C4×C53C2411yescharacteristic
236C2×C22⋊D53—21no—
237C2×C22⋊D53—21no—
238C2×C22⋊D53—22no—
239C2×C22⋊D53—21no—
240C2×C22⋊D53—21no—
241C2×C22⋊D53—41no—
242C2×C22⋊D53—81no—
243C22×Dic53—21no—
244C22×Dic53—21no—
245C22×Dic53—42no—
246C22×Dic53C22×C411yescharacteristic
247C22×Dic53C22×C411yescharacteristic
248C22×Dic53C22×C411yescharacteristic
249C22×Dic53C22×C411yescharacteristic
250C22×Dic53C22×C411yescharacteristic
251C22×Dic53C22×C411yescharacteristic
252C2×C4×D53—22no—
253C2×C4×D53—21no—
254C2×C4×D53—21no—
255C2×C4×D53—21no—
256C2×C4×D53—21no—
257C2×C4×D53—41no—
258C2×C4×D53—81no—
259C2×Dic106—21no—
260C2×Dic106—21no—
261C2×Dic106—81no—
262M16×C53—81no—
263M16×C53—81no—
264C2×C8×C53—21no—
265C2×C8×C53—21no—
266C2×C8×C53—21no—
267C2×C8×C53—21no—
268C2×C8×C53—81no—
269C2×C8×C53—81no—
270C4⋊C4×C53C22⋊C411yescharacteristic
271C4⋊C4×C53C22⋊C411yescharacteristic
272C4⋊C4×C53C22⋊C411yescharacteristic
273C4⋊C4×C53C22⋊C411yescharacteristic
274C22⋊C4×C53C22⋊C411yescharacteristic
275C22⋊C4×C53C22⋊C411yescharacteristic
276C22⋊C4×C53C22⋊C411yescharacteristic
277C22⋊C4×C53C22⋊C411yescharacteristic
278C22⋊C4×C53C22⋊C411yescharacteristic
279C22⋊C4×C53C22⋊C411yescharacteristic
280C22⋊C4×C53C22⋊C411yescharacteristic
281C22⋊C4×C53C22⋊C411yescharacteristic
282C42×C53C2×D411yescharacteristic
283C42×C53C2×D411yescharacteristic
284C42×C53C2×D411yescharacteristic
285C42×C53C2×D411yescharacteristic
286C22⋊Dic53—21no—
287C22⋊Dic53—21no—
288C22⋊Dic53—21no—
289C22⋊Dic53—21no—
290C22⋊Dic53—21no—
291C22⋊Dic53—21no—
292C22⋊Dic53—21no—
293C22⋊Dic53—21no—
294#11719921—21no—
295#11719921—21no—
296#11719921—21no—
297#11719921—21no—
298#11719921—21no—
299#11719921—21no—
300#11719921—21no—
301#11719921—21no—
302#11719921—21no—
303#11719921—21no—
304#11719921—21no—
305#11719921—21no—
306#11719921—21no—
307#11719921—21no—
308#11719921—21no—
309#11719921—21no—
310C4⋊Dic53—21no—
311C4⋊Dic53—21no—
312#11719919—21no—
313#11719919—21no—
314#11719919—21no—
315#11719919—21no—
316#11719919—21no—
317#11719919—21no—
318#11719919—21no—
319#11719919—21no—
320#11719919—21no—
321#11719919—21no—
322#11719919—21no—
323#11719919—21no—
324C4×Dic53—21no—
325C4×Dic53—21no—
326C4×Dic53—21no—
327C4×Dic53—21no—
328#11719917—81no—
329#11719917—81no—
330C2×#88322—21no—
331C2×#88322—21no—
332C2×#88322—21no—
333C2×#88322—21no—
334C2×#88322—81no—
335C2×#88322—81no—
336C23×C53—21no—
337C23×C53—21no—
338C23×C53—22no—
339C23×C53—21no—
340C23×C53—21no—
341C23×C53—41no—
342C23×C53—41no—
343C23×C53—41no—
344C23×C53C2×C22⋊C411yescharacteristic
345C23×C53C2×C22⋊C411yescharacteristic
346C23×C53C2×C22⋊C411yescharacteristic
347C23×C53C2×C22⋊C411yescharacteristic
348C23×C53C23×C411yescharacteristic
349C22×D53—21no—
350C22×D53—21no—
351C22×D53—21no—
352C22×D53—21no—
353C22×D53—21no—
354C22×D53—42no—
355C22×D53—42no—
356C22×D53—41no—
357C22×D53—41no—
358C22×D53—42no—
359C22×D53—42no—
360C22×D53—41no—
361C22×D53—41no—
362C22×D53—81no—
363C22×D53—81no—
364C22×D53—84no—
365C22×D53—84no—
366C22×D53#13112yes—
367D4×C53—22no—
368D4×C53—22no—
369D4×C53—41no—
370D4×C53—41no—
371C2×C4×C53—21no—
372C2×C4×C53—21no—
373C2×C4×C53—41no—
374C2×C4×C53—41no—
375C2×C4×C53—41no—
376C2×C4×C53—41no—
377C2×C4×C53—41no—
378C2×C4×C53—41no—
379C2×C4×C53—41no—
380C2×C4×C53—41no—
381C2×C4×C53—41no—
382C2×C4×C53—41no—
383C2×C4×C53—41no—
384C2×C4×C53—41no—
385C2×C4×C53C2×C22⋊C411yescharacteristic
386C2×C4×C53C2×C22⋊C411yescharacteristic
387C2×C4×C53C2×C22⋊C411yescharacteristic
388C2×C4×C53C2×C22⋊C411yescharacteristic
389C2×C4×C53C2×C22⋊C411yescharacteristic
390C2×C4×C53C2×C22⋊C411yescharacteristic
391C2×C4×C53C2×C22⋊C411yescharacteristic
392C2×C4×C53C2×C22⋊C411yescharacteristic
393C2×C4×C53C22×D411yescharacteristic
394C2×C4×C53C22×D411yescharacteristic
395C22⋊D53—42no—
396C22⋊D53—42no—
397C22⋊D53—81no—
398C22⋊D53—81no—
399C2×Dic53—21no—
400C2×Dic53—21no—
401C2×Dic53—21no—
402C2×Dic53—21no—
403C2×Dic53—21no—
404C2×Dic53—21no—
405C2×Dic53—21no—
406C2×Dic53—21no—
407C2×Dic53—21no—
408C2×Dic53—21no—
409C2×Dic53—42no—
410C2×Dic53—42no—
411C2×Dic53—41no—
412C2×Dic53—41no—
413C2×Dic53—41no—
414C2×Dic53—41no—
415C4×D53—42no—
416C4×D53—42no—
417C4×D53—81no—
418C4×D53—81no—
419Dic106—81no—
420Dic106—81no—
421C8×C53—41no—
422C8×C53—41no—
423C8×C53—41no—
424C8×C53—41no—
425#88322—41no—
426#88322—41no—
427#88322—41no—
428#88322—41no—
429#17422—531nomaximal, Sylow
430C22×C53—21no—
431C22×C53—21no—
432C22×C53—21no—
433C22×C53—21no—
434C22×C53—21no—
435C22×C53—21no—
436C22×C53—21no—
437C22×C53—21no—
438C22×C53—21no—
439C22×C53—21no—
440C22×C53—21no—
441C22×C53—21no—
442C22×C53—21no—
443C22×C53—42no—
444C22×C53—42no—
445C22×C53—81no—
446C22×C53—81no—
447C22×C53#41312yes—
448C22×C53C22×C22⋊C411yescharacteristic
449C22×C53C2×#13111yescharacteristic
450C22×C53#56811yescharacteristic
451C2×D53—22no—
452C2×D53—42no—
453C2×D53—41no—
454C2×D53—41no—
455C2×D53—42no—
456C2×D53—41no—
457C2×D53—41no—
458C2×D53—41no—
459C2×D53—84no—
460C2×D53—84no—
461C2×D53—81no—
462C2×D53—81no—
463C4×C53—21no—
464C4×C53—21no—
465C4×C53—21no—
466C4×C53—21no—
467C4×C53—21no—
468C4×C53—21no—
469C4×C53—21no—
470C4×C53—21no—
471C4×C53—21no—
472C4×C53—21no—
473Dic53—41no—
474Dic53—41no—
475Dic53—41no—
476Dic53—41no—
477Dic53—41no—
478Dic53—41no—
479C2×#551—531no—
480#2974—531no—
481#2974D5311yescharacteristic, complemented
482#1473—531no—
483#1473—531no—
484#1472—531no—
485#1472—531no—
486#1468—531no—
487#1468—531no—
488#1465—531no—
489#1464—531no—
490#1462—531no—
491#1459—531no—
492#1458—531no—
493C2×#323—531no—
494C2×C53—21no—
495C2×C53—21no—
496C2×C53—22no—
497C2×C53—41no—
498C2×C53—41no—
499C2×C53—41no—
500C2×C53#288011yescharacteristic
501C2×C53#288311yescharacteristic
502C2×C53C2×#41311yescharacteristic
503D53—42no—
504D53—81no—
505#551—1061no—
506#551—1061no—
507#551—1061no—
508#551—1061no—
509#551—1061no—
510#551—1061no—
511#551—1061no—
512#551—1061no—
513C2×#126—531no—
514C2×#126—531no—
515C2×#124—531no—
516C2×#123—531no—
517C2×#123—531no—
518C2×#123—531no—
519C2×C22⋊Q8—531no—
520C2×C22⋊Q8—531no—
521C2×#120—531no—
522C2×C4×D4—531no—
523C2×C4×D4C2×D5311yescharacteristic
524C2×#117—531no—
525C2×#117—531no—
526C22×C22⋊C4—531no—
527C22×C22⋊C4—531no—
528#436—21no—
529#436—1061no—
530#435—21no—
531#435—21no—
532#435—1061no—
533#435—1061no—
534C8×D4—21no—
535C8×D4—1061no—
536#432—531no—
537#432C2×D5311yescharacteristic, complemented
538#431—531no—
539#431C2×D5311yescharacteristic, complemented
540#407—531no—
541#407—531no—
542#407C2×D5311yescharacteristic
543#407C2×D5311yescharacteristic, complemented
544C2×C22⋊C8—531no—
545C2×C22⋊C8—531no—
546C2×C22⋊C8C2×D5311yescharacteristic
547C2×C22⋊C8C2×D5311yescharacteristic, complemented
548#324—531no—
549#324—531no—
550#324—531no—
551#324—531no—
552#324—531no—
553#324—531no—
554#324—531no—
555#324—531no—
556#323—531no—
557#323—531no—
558#323—531no—
559#323—531no—
560#323—531no—
561#323—531no—
562#323—531no—
563#323—531no—
564C53#1742211yescharacteristic, complemented, Sylow
565C25—531no—
566C22×Q8—531no—
567C22×D4—531no—
568C22×D4—531no—
569C22×D4C4×D5311yescharacteristic
570C23×C4—531no—
571C23×C4—531no—
572C23×C4—531no—
573C23×C4C22×D5311yescharacteristic
574C23×C4C22×D5311yescharacteristic
575C2×M16—21no—
576C2×M16—21no—
577C2×M16—1061no—
578C2×M16—1061no—
579C22×C8—21no—
580C22×C8—21no—
581C22×C8—1061no—
582C22×C8—1061no—
583#126—1061no—
584#126—1061no—
585#126—1061no—
586#126—1061no—
587#126—1061no—
588#126—1061no—
589#126—1061no—
590#126—1061no—
591#124—1061no—
592#124—1061no—
593#124—1061no—
594#124—1061no—
595#123—1061no—
596#123—1061no—
597#123—1061no—
598#123—1061no—
599#123—1061no—
600#123—1061no—
601#123—1061no—
602#123—1061no—
603#123—1061no—
604#123—1061no—
605#123—1061no—
606#123—1061no—
607C22⋊Q8—1061no—
608C22⋊Q8—1061no—
609C22⋊Q8—1061no—
610C22⋊Q8—1061no—
611C22⋊Q8—1061no—
612C22⋊Q8—1061no—
613C22⋊Q8—1061no—
614C22⋊Q8—1061no—
615#120—1061no—
616#120—1061no—
617#120—1061no—
618#120—1061no—
619C4×D4—1061no—
620C4×D4—1061no—
621C4×D4—1061no—
622C4×D4—1061no—
623C4×D4D21211yescharacteristic
624C4×D4D21211yescharacteristic
625C4×D4D21211yescharacteristic
626C4×D4D21211yescharacteristic
627C4×D4C22⋊D5311yescharacteristic
628C4×D4C22⋊D5311yescharacteristic
629C4×D4C22⋊D5311yescharacteristic
630C4×D4C22⋊D5311yescharacteristic
631#117—1061no—
632#117—1061no—
633#117—1061no—
634#117—1061no—
635#117—1061no—
636#117—1061no—
637#117—1061no—
638#117—1061no—
639C2×C4⋊C4—531no—
640C2×C4⋊C4—531no—
641C2×C4⋊C4—531no—
642C2×C4⋊C4—531no—
643C2×C4⋊C4—531no—
644C2×C4⋊C4—531no—
645C2×C4⋊C4—531no—
646C2×C4⋊C4C4×D5311yescharacteristic
647C2×C22⋊C4—531no—
648C2×C22⋊C4—531no—
649C2×C22⋊C4—531no—
650C2×C22⋊C4—531no—
651C2×C22⋊C4—531no—
652C2×C22⋊C4—531no—
653C2×C22⋊C4—531no—
654C2×C22⋊C4—531no—
655C2×C22⋊C4—531no—
656C2×C22⋊C4—531no—
657C2×C22⋊C4—531no—
658C2×C22⋊C4—531no—
659C2×C22⋊C4—1061no—
660C2×C22⋊C4—1061no—
661C2×C22⋊C4—1061no—
662C2×C22⋊C4—1061no—
663C2×C22⋊C4—1061no—
664C2×C22⋊C4—1061no—
665C2×C22⋊C4—1061no—
666C2×C22⋊C4—1061no—
667C2×C22⋊C4C4×D5311yescharacteristic
668C2×C22⋊C4C4×D5311yescharacteristic
669C2×C42—531no—
670C2×C42—531no—
671C2×C42C22×D5311yescharacteristic
672C4⋊C8—21no—
673C4⋊C8—21no—
674C4⋊C8—1061no—
675C4⋊C8—1061no—
676C22⋊C8—21no—
677C22⋊C8—21no—
678C22⋊C8—21no—
679C22⋊C8—21no—
680C22⋊C8—531no—
681C22⋊C8—531no—
682C22⋊C8—531no—
683C22⋊C8—531no—
684C22⋊C8—1061no—
685C22⋊C8—1061no—
686C22⋊C8—1061no—
687C22⋊C8—1061no—
688C22⋊C8C22×D5311yescharacteristic
689C22⋊C8C22×D5311yescharacteristic
690C22⋊C8C22×D5311yescharacteristic
691C22⋊C8C22×D5311yescharacteristic
692#97—21no—
693#97—1061no—
694C4×C8—21no—
695C4×C8—1061no—
696C24—531no—
697C24—531no—
698C24—1062no—
699C24—1061no—
700C24—1061no—
701C24—4241no—
702C24—2121no—
703C24—2122no—
704C24C2×C4×D5311yescharacteristic
705C24C2×C4×D5311yescharacteristic
706C2×Q8—1061no—
707C2×Q8—1061no—
708C2×Q8—4241no—
709C2×D4—42no—
710C2×D4—1061no—
711C2×D4—1061no—
712C2×D4—1062no—
713C2×D4—1061no—
714C2×D4—1061no—
715C2×D4—4241no—
716C2×D4—2121no—
717C2×D4#1171992111yescharacteristic
718C2×D4#1171992111yescharacteristic
719C2×D4#1171992111yescharacteristic
720C2×D4#1171992111yescharacteristic
721C22×C4—81no—
722C22×C4—81no—
723C22×C4—531no—
724C22×C4—531no—
725C22×C4—531no—
726C22×C4—531no—
727C22×C4—531no—
728C22×C4—531no—
729C22×C4—1062no—
730C22×C4—1061no—
731C22×C4—1061no—
732C22×C4—1061no—
733C22×C4—1061no—
734C22×C4—1061no—
735C22×C4—1061no—
736C22×C4—4241no—
737C22×C4—2121no—
738C22×C4—2122no—
739C22×C4C2×C4×D5311yescharacteristic
740C22×C4C2×C4×D5311yescharacteristic
741C22×C4C2×C4×D5311yescharacteristic
742C22×C4C2×C4×D5311yescharacteristic
743C22×C4C2×D21211yescharacteristic
744C22×C4C2×D21211yescharacteristic
745C22×C4C2×D21211yescharacteristic
746C22×C4C2×D21211yescharacteristic
747C22×C4C2×C22⋊D5311yescharacteristic
748C22×C4C2×C22⋊D5311yescharacteristic
749C22×C4C2×C22⋊D5311yescharacteristic
750C22×C4C2×C22⋊D5311yescharacteristic
751C22×C4C23×D5311yescharacteristic
752M16—81no—
753M16—81no—
754M16—4241no—
755M16—4241no—
756C2×C8—21no—
757C2×C8—21no—
758C2×C8—21no—
759C2×C8—21no—
760C2×C8—81no—
761C2×C8—81no—
762C2×C8—1061no—
763C2×C8—1061no—
764C2×C8—1061no—
765C2×C8—1061no—
766C2×C8—4241no—
767C2×C8—4241no—
768C4⋊C4—1061no—
769C4⋊C4—1061no—
770C4⋊C4—1061no—
771C4⋊C4—1061no—
772C4⋊C4—1061no—
773C4⋊C4—1061no—
774C4⋊C4—1061no—
775C4⋊C4—1061no—
776C4⋊C4—1061no—
777C4⋊C4—1061no—
778C4⋊C4—1061no—
779C4⋊C4—1061no—
780C4⋊C4—1061no—
781C4⋊C4—1061no—
782C4⋊C4#1171992111yescharacteristic
783C4⋊C4#1171992111yescharacteristic
784C4⋊C4#1171992111yescharacteristic
785C4⋊C4#1171992111yescharacteristic
786C22⋊C4—1061no—
787C22⋊C4—1061no—
788C22⋊C4—1061no—
789C22⋊C4—1061no—
790C22⋊C4—1061no—
791C22⋊C4—1061no—
792C22⋊C4—1061no—
793C22⋊C4—1061no—
794C22⋊C4—1061no—
795C22⋊C4—1061no—
796C22⋊C4—1061no—
797C22⋊C4—1061no—
798C22⋊C4—1061no—
799C22⋊C4—1061no—
800C22⋊C4—1061no—
801C22⋊C4—1061no—
802C22⋊C4—1061no—
803C22⋊C4—1061no—
804C22⋊C4—1061no—
805C22⋊C4—1061no—
806C22⋊C4—1061no—
807C22⋊C4—1061no—
808C22⋊C4—1061no—
809C22⋊C4—1061no—
810C22⋊C4#1171992111yescharacteristic
811C22⋊C4#1171992111yescharacteristic
812C22⋊C4#1171992111yescharacteristic
813C22⋊C4#1171992111yescharacteristic
814C22⋊C4#1171992111yescharacteristic
815C22⋊C4#1171992111yescharacteristic
816C22⋊C4#1171992111yescharacteristic
817C22⋊C4#1171992111yescharacteristic
818C42—1061no—
819C42—1061no—
820C42—1061no—
821C42—1061no—
822C42C2×D21211yescharacteristic
823C42C2×D21211yescharacteristic
824C42C2×C22⋊D5311yescharacteristic
825C42C2×C22⋊D5311yescharacteristic
826C23—22no—
827C23—21no—
828C23—21no—
829C23—21no—
830C23—21no—
831C23—41no—
832C23—41no—
833C23—41no—
834C23—532no—
835C23—1061no—
836C23—1061no—
837C23—1061no—
838C23—1061no—
839C23—1061no—
840C23—4241no—
841C23—4241no—
842C23—4244no—
843C23—4244no—
844C23—2122no—
845C23—2122no—
846C23—2121no—
847C23—2121no—
848C23—2122no—
849C23—2121no—
850C23—2121no—
851C23—2122no—
852C23C2×#1171992111yescharacteristic
853C23C2×#1171992111yescharacteristic
854C23C2×#1171992111yescharacteristic
855C23C2×#1171992111yescharacteristic
856C23C22×C4×D5311yescharacteristic
857Q8—4241no—
858Q8—4241no—
859D4—22no—
860D4—22no—
861D4—41no—
862D4—41no—
863D4—4241no—
864D4—4241no—
865D4—2122no—
866D4—2122no—
867C2×C4—21no—
868C2×C4—21no—
869C2×C4—41no—
870C2×C4—41no—
871C2×C4—41no—
872C2×C4—41no—
873C2×C4—41no—
874C2×C4—41no—
875C2×C4—41no—
876C2×C4—41no—
877C2×C4—41no—
878C2×C4—41no—
879C2×C4—41no—
880C2×C4—41no—
881C2×C4—1061no—
882C2×C4—1061no—
883C2×C4—1061no—
884C2×C4—1061no—
885C2×C4—1061no—
886C2×C4—1061no—
887C2×C4—1061no—
888C2×C4—1061no—
889C2×C4—1061no—
890C2×C4—1061no—
891C2×C4—4241no—
892C2×C4—4241no—
893C2×C4—2122no—
894C2×C4—2122no—
895C2×C4—2122no—
896C2×C4—2122no—
897C2×C4—2121no—
898C2×C4—2121no—
899C2×C4—2121no—
900C2×C4—2121no—
901C2×C4C2×#1171992111yescharacteristic
902C2×C4C2×#1171992111yescharacteristic
903C2×C4C2×#1171992111yescharacteristic
904C2×C4C2×#1171992111yescharacteristic
905C2×C4C2×#1171992111yescharacteristic
906C2×C4C2×#1171992111yescharacteristic
907C2×C4C2×#1171992111yescharacteristic
908C2×C4C2×#1171992111yescharacteristic
909C2×C4C22×C22⋊D5311yescharacteristic
910C2×C4C22×D21211yescharacteristic
911C8—41no—
912C8—41no—
913C8—41no—
914C8—41no—
915C8—2121no—
916C8—2121no—
917C8—2121no—
918C8—2121no—
919C22—21no—
920C22—21no—
921C22—21no—
922C22—21no—
923C22—21no—
924C22—21no—
925C22—21no—
926C22—21no—
927C22—21no—
928C22—21no—
929C22—21no—
930C22—21no—
931C22—21no—
932C22—42no—
933C22—42no—
934C22—81no—
935C22—81no—
936C22—1062no—
937C22—4241no—
938C22—4241no—
939C22—4244no—
940C22—4244no—
941C22—2122no—
942C22—2122no—
943C22—2121no—
944C22—2121no—
945C22—2121no—
946C22—2121no—
947C22—2121no—
948C22#1681060512yes—
949C22C22×#1171992111yescharacteristic
950C22#131×D5311yescharacteristic
951C22#1681138811yescharacteristic
952C4—21no—
953C4—21no—
954C4—21no—
955C4—21no—
956C4—21no—
957C4—21no—
958C4—21no—
959C4—21no—
960C4—21no—
961C4—21no—
962C4—2121no—
963C4—2121no—
964C4—2121no—
965C4—2121no—
966C4—2121no—
967C4—2121no—
968C2—21no—
969C2—21no—
970C2—22no—
971C2—41no—
972C2—41no—
973C2—41no—
974C2—4241no—
975C2—2122no—
976C2#2028316211yescharacteristic
977C2#2028317511yescharacteristic
978C2C2×#1681060511yescharacteristic
subgroupG/H
centerC22C22×#11719921
commutatorC23×C53C23×C4
FrattiniC22×C4C23×D53
FittingC53×#2974C2
socleC22×C53C22×C22⋊C4
prime radicalC2×#13133185C4
cosocleC22×C4×C53C24
hypercenter#2974D53
hypocenterC53#17422
LCSG ▷ C23×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C22 ◁ C2×C4×D4 ◁ #2974

Complements

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

NH ≅ G/Ntype
2. #20283750C2semidirect
3. #20273085C2semidirect
4. #20273082C2semidirect
5. #20273080C2semidirect
6. #20273078C2semidirect
7. #20273064C2semidirect
8. #20273061C2semidirect
9. #20273051C2semidirect
10. #20273047C2semidirect
11. #20273041C2semidirect
12. #20273031C2semidirect
13. #20273027C2semidirect
14. C2×#16810346C2semidirect
15. C53×#2974C2semidirect
42. #16810680C22semidirect
43. #16810676C22semidirect
45. #16810587C22semidirect
47. C2×C22⋊#88322C22semidirect
48. #16810348C22semidirect
49. #16810348C22semidirect
50. #16810348C22semidirect
51. #16810348C22semidirect
52. #16810348C22semidirect
53. #16810348C22semidirect
54. #16810348C22semidirect
55. #16810348C22semidirect
69. C53×#432C22semidirect
70. C53×#431C22semidirect
72. C53×#407C22semidirect
74. C2×C22⋊C8×C53C22semidirect
481. #2974D53semidirect
537. #432C2×D53semidirect
539. #431C2×D53semidirect
543. #407C2×D53semidirect
547. C2×C22⋊C8C2×D53semidirect
564. C53#17422semidirect

Maximal subgroups

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

subgroupindex
C2×#168113022
#202837502
#202730852
#202730822
#202730802
#202730782
#202730642
#202730612
#202730512
#202730472
#202730412
#202730312
#202730272
C2×#168103462
C53×#29742
#1742253