Finite Group Databasebeta

← #27350403

Subgroups — #27350403

Order 13568.

1022 conjugacy classes of subgroups.

The subgroup lattice has 972 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811322C211yesmaximal, characteristic
2#20283750C211yesmaximal, characteristic, complemented
3#20273085C211yesmaximal, characteristic, complemented
4#20273082C211yesmaximal, characteristic, complemented
5#20273076C211yesmaximal, characteristic, complemented
6#20273074C211yesmaximal, characteristic, complemented
7#20273064C211yesmaximal, characteristic, complemented
8#20273061C211yesmaximal, characteristic, complemented
9#20273051C211yesmaximal, characteristic, complemented
10#20273047C211yesmaximal, characteristic, complemented
11#20273044C211yesmaximal, characteristic, complemented
12#20273031C211yesmaximal, characteristic, complemented
13#20273027C211yesmaximal, characteristic, complemented
14C2×#16810348C211yesmaximal, characteristic, complemented
15C53×#2974C211yesmaximal, characteristic, complemented
16#16811322—21no—
17#16811322—21no—
18#16811322—21no—
19#16811322—21no—
20#16811322—21no—
21#16811322—21no—
22#16811322—21no—
23#16811322—21no—
24C2×#13133211C2211yescharacteristic
25C2×#13133210C411yescharacteristic
26C2×#13133207C411yescharacteristic
27C2×#13133202C411yescharacteristic
28C2×#13133200C2211yescharacteristic
29C2×#13133191C2211yescharacteristic
30C2×#13133190C411yescharacteristic
31C2×#13133189C411yescharacteristic
32C2×#13133189C411yescharacteristic
33C2×C4×C22⋊D53C2211yescharacteristic
34C2×#13133177C411yescharacteristic
35C2×#13133177C411yescharacteristic
36C2×#13133174C2211yescharacteristic
37C22×#11719919C2211yescharacteristic
38#16810701—21no—
39#16810695—21no—
40#16810695—21no—
41D4×#88322—21no—
42#16810680C2211yescharacteristic
43#16810676C2211yescharacteristic
44#16810587C2211yescharacteristic
45#16810587C2211yescharacteristic
46C2×C22⋊#88322C2211yescharacteristic
47C2×C22⋊#88322C2211yescharacteristic
48#16810348C2211yescharacteristic
49#16810348C2211yescharacteristic
50#16810348C2211yescharacteristic
51#16810348C2211yescharacteristic
52#16810348C2211yescharacteristic
53#16810348C2211yescharacteristic
54#16810348C2211yescharacteristic
55#16810348C2211yescharacteristic
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
70C53×#431C2211yescharacteristic
71C53×#407C2211yescharacteristic
72C53×#407C2211yescharacteristic
73C2×C22⋊C8×C53C2211yescharacteristic
74C2×C22⋊C8×C53C2211yescharacteristic
75C22×D212C2×C411yescharacteristic
76C22×C22⋊D53C2×C411yescharacteristic
77C22×C22⋊D53C2×C411yescharacteristic
78C22×C22⋊D53C2×C411yescharacteristic
79C22×C22⋊D53C2×C411yescharacteristic
80C23×Dic53C2×C411yescharacteristic
81C23×Dic53C2×C411yescharacteristic
82C22×C4×D53C2×C411yescharacteristic
83C22×C4×D53C2×C411yescharacteristic
84C2×#11719917—21no—
85C2×#11719917—21no—
86C22×#88322—21no—
87C22×#88322—21no—
88#13133211—21no—
89#13133211—21no—
90#13133211—21no—
91#13133211—21no—
92#13133210—21no—
93#13133210—21no—
94#13133210—21no—
95#13133210—21no—
96#13133207—21no—
97#13133207—21no—
98#13133207—21no—
99#13133207—21no—
100#13133202—21no—
101#13133202—21no—
102#13133202—21no—
103#13133202—21no—
104#13133200—21no—
105#13133200—21no—
106#13133200—21no—
107#13133200—21no—
108#13133191—21no—
109#13133191—21no—
110#13133191—21no—
111#13133191—21no—
112#13133190—21no—
113#13133190—21no—
114#13133190—21no—
115#13133190—21no—
116#13133189—21no—
117#13133189—21no—
118#13133189—21no—
119#13133189—21no—
120#13133189—21no—
121#13133189—21no—
122#13133189—21no—
123#13133189—21no—
124C4×C22⋊D53—21no—
125C4×C22⋊D53—21no—
126C4×C22⋊D53—21no—
127C4×C22⋊D53—21no—
128#13133177—21no—
129#13133177—21no—
130#13133177—21no—
131#13133177—21no—
132#13133177—21no—
133#13133177—21no—
134#13133177—21no—
135#13133177—21no—
136#13133174—21no—
137#13133174—21no—
138#13133174—21no—
139#13133174—21no—
140C2×C4⋊Dic53C2×C411yescharacteristic
141C2×#11719919—21no—
142C2×#11719919—21no—
143C2×#11719919—21no—
144C2×#11719919—21no—
145C2×#11719919C2×C411yescharacteristic
146C2×#11719919C2×C411yescharacteristic
147C2×#11719919C2×C411yescharacteristic
148C2×#11719919C2×C411yescharacteristic
149C2×#11719919C2×C411yescharacteristic
150C2×#11719919C2×C411yescharacteristic
151C2×#11719919C2311yescharacteristic
152C2×#11719919C2311yescharacteristic
153C2×C22⋊Dic53C2×C411yescharacteristic
154C2×C22⋊Dic53C2×C411yescharacteristic
155C2×#11719921C2×C411yescharacteristic
156C2×#11719921C2×C411yescharacteristic
157C2×#11719921C2×C411yescharacteristic
158C2×#11719921C2×C411yescharacteristic
159C2×#11719921C2311yescharacteristic
160C2×#11719921C2311yescharacteristic
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×D53C22×C411yescharacteristic
209C23×D53C22×C411yescharacteristic
210C2×D4×C53—42no—
211C2×D4×C53C22⋊C411yescharacteristic
212C2×D4×C53C22⋊C411yescharacteristic
213C2×D4×C53C22⋊C411yescharacteristic
214C2×D4×C53C22⋊C411yescharacteristic
215C22×C4×C53—81no—
216C22×C4×C53—81no—
217C22×C4×C53C22×C411yescharacteristic
218C22×C4×C53C22×C411yescharacteristic
219C22×C4×C53C22×C411yescharacteristic
220C22×C4×C53C22×C411yescharacteristic
221C22×C4×C53C2×D411yescharacteristic
222C22×C4×C53C2×D411yescharacteristic
223C22×C4×C53C2×D411yescharacteristic
224C22×C4×C53C2×D411yescharacteristic
225C22×C4×C53C2×D411yescharacteristic
226C22×C4×C53C2×D411yescharacteristic
227C22×C4×C53C2×D411yescharacteristic
228C22×C4×C53C2×D411yescharacteristic
229C22×C4×C53C2411yescharacteristic
230C2×C22⋊D53—21no—
231C2×C22⋊D53—21no—
232C2×C22⋊D53—21no—
233C2×C22⋊D53—21no—
234C2×C22⋊D53—21no—
235C2×C22⋊D53—21no—
236C2×C22⋊D53—21no—
237C2×C22⋊D53—21no—
238C2×C22⋊D53—22no—
239C2×C22⋊D53—41no—
240C2×C22⋊D53—42no—
241C2×C22⋊D53—42no—
242C2×C22⋊D53—81no—
243C22×Dic53—21no—
244C22×Dic53—21no—
245C22×Dic53—21no—
246C22×Dic53—21no—
247C22×Dic53—22no—
248C22×Dic53—41no—
249C22×Dic53—81no—
250C22×Dic53C22×C411yescharacteristic
251C22×Dic53C22×C411yescharacteristic
252C22×Dic53C22×C411yescharacteristic
253C22×Dic53C22×C411yescharacteristic
254C22×Dic53C22×C411yescharacteristic
255C22×Dic53C22×C411yescharacteristic
256C2×D212—21no—
257C2×D212—21no—
258C2×D212—81no—
259C2×C4×D53—21no—
260C2×C4×D53—21no—
261C2×C4×D53—22no—
262C2×C4×D53—21no—
263C2×C4×D53—21no—
264C2×C4×D53—41no—
265C2×C4×D53—81no—
266M16×C53—81no—
267M16×C53—81no—
268C2×C8×C53—21no—
269C2×C8×C53—21no—
270C2×C8×C53—21no—
271C2×C8×C53—21no—
272C2×C8×C53—81no—
273C2×C8×C53—81no—
274C4⋊C4×C53C22⋊C411yescharacteristic
275C4⋊C4×C53C22⋊C411yescharacteristic
276C4⋊C4×C53C22⋊C411yescharacteristic
277C4⋊C4×C53C22⋊C411yescharacteristic
278C22⋊C4×C53C22⋊C411yescharacteristic
279C22⋊C4×C53C22⋊C411yescharacteristic
280C22⋊C4×C53C22⋊C411yescharacteristic
281C22⋊C4×C53C22⋊C411yescharacteristic
282C22⋊C4×C53C22⋊C411yescharacteristic
283C22⋊C4×C53C22⋊C411yescharacteristic
284C22⋊C4×C53C22⋊C411yescharacteristic
285C22⋊C4×C53C22⋊C411yescharacteristic
286C42×C53C2×D411yescharacteristic
287C42×C53C2×D411yescharacteristic
288C42×C53C2×D411yescharacteristic
289C42×C53C2×D411yescharacteristic
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—
306C4⋊Dic53—21no—
307C4⋊Dic53—21no—
308#11719919—21no—
309#11719919—21no—
310#11719919—21no—
311#11719919—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—21no—
355C22×D53—41no—
356C22×D53—41no—
357C22×D53—41no—
358C22×D53—41no—
359D4×C53—22no—
360D4×C53—22no—
361D4×C53—41no—
362D4×C53—41no—
363C2×C4×C53—21no—
364C2×C4×C53—21no—
365C2×C4×C53—41no—
366C2×C4×C53—41no—
367C2×C4×C53—41no—
368C2×C4×C53—41no—
369C2×C4×C53—41no—
370C2×C4×C53—41no—
371C2×C4×C53—41no—
372C2×C4×C53—41no—
373C2×C4×C53—41no—
374C2×C4×C53—41no—
375C2×C4×C53—41no—
376C2×C4×C53—41no—
377C2×C4×C53C2×C22⋊C411yescharacteristic
378C2×C4×C53C2×C22⋊C411yescharacteristic
379C2×C4×C53C2×C22⋊C411yescharacteristic
380C2×C4×C53C2×C22⋊C411yescharacteristic
381C2×C4×C53C2×C22⋊C411yescharacteristic
382C2×C4×C53C2×C22⋊C411yescharacteristic
383C2×C4×C53C2×C22⋊C411yescharacteristic
384C2×C4×C53C2×C22⋊C411yescharacteristic
385C2×C4×C53C22×D411yescharacteristic
386C2×C4×C53C22×D411yescharacteristic
387C22⋊D53—42no—
388C22⋊D53—42no—
389C22⋊D53—42no—
390C22⋊D53—42no—
391C22⋊D53—42no—
392C22⋊D53—42no—
393C22⋊D53—81no—
394C22⋊D53—81no—
395C2×Dic53—21no—
396C2×Dic53—21no—
397C2×Dic53—21no—
398C2×Dic53—21no—
399C2×Dic53—21no—
400C2×Dic53—21no—
401C2×Dic53—21no—
402C2×Dic53—21no—
403C2×Dic53—21no—
404C2×Dic53—42no—
405C2×Dic53—42no—
406C2×Dic53—41no—
407C2×Dic53—41no—
408C2×Dic53—41no—
409C2×Dic53—41no—
410C2×Dic53—81no—
411C2×Dic53—81no—
412C2×Dic53#13112yes—
413D212—81no—
414D212—81no—
415C4×D53—42no—
416C4×D53—42no—
417C4×D53—81no—
418C4×D53—81no—
419C8×C53—41no—
420C8×C53—41no—
421C8×C53—41no—
422C8×C53—41no—
423#88322—41no—
424#88322—41no—
425#88322—41no—
426#88322—41no—
427#17427—531nomaximal, Sylow
428C22×C53—21no—
429C22×C53—21no—
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—42no—
442C22×C53—42no—
443C22×C53—81no—
444C22×C53—81no—
445C22×C53#41312yes—
446C22×C53C22×C22⋊C411yescharacteristic
447C22×C53C2×#13111yescharacteristic
448C22×C53#56811yescharacteristic
449C2×D53—41no—
450C2×D53—41no—
451C2×D53—41no—
452C2×D53—41no—
453C2×D53—41no—
454C2×D53—41no—
455C2×D53—81no—
456C2×D53—81no—
457C2×D53—81no—
458C2×D53—81no—
459C4×C53—21no—
460C4×C53—21no—
461C4×C53—21no—
462C4×C53—21no—
463C4×C53—21no—
464C4×C53—21no—
465C4×C53—21no—
466C4×C53—21no—
467C4×C53—21no—
468C4×C53—21no—
469Dic53—22no—
470Dic53—41no—
471Dic53—41no—
472Dic53—41no—
473Dic53—41no—
474Dic53—41no—
475C2×#553—531no—
476#2974—531no—
477#2974D5311yescharacteristic, complemented
478#1473—531no—
479#1473—531no—
480#1471—531no—
481#1471—531no—
482#1468—531no—
483#1468—531no—
484#1465—531no—
485#1464—531no—
486#1463—531no—
487#1459—531no—
488#1458—531no—
489C2×#324—531no—
490C2×C53—21no—
491C2×C53—21no—
492C2×C53—22no—
493C2×C53—41no—
494C2×C53—41no—
495C2×C53—41no—
496C2×C53#288011yescharacteristic
497C2×C53#288311yescharacteristic
498C2×C53C2×#41311yescharacteristic
499D53—81no—
500D53—81no—
501#553—1061no—
502#553—1061no—
503#553—1061no—
504#553—1061no—
505#553—1061no—
506#553—1061no—
507#553—1061no—
508#553—1061no—
509C2×#126—531no—
510C2×#126—531no—
511C2×#125—531no—
512C2×#123—531no—
513C2×#123—531no—
514C2×#121—531no—
515C2×#121—531no—
516C2×#121—531no—
517C2×#121—531no—
518C2×C4×D4—531no—
519C2×C4×D4—531no—
520C2×C4×D4—531no—
521C2×C4×D4C2×D5311yescharacteristic
522C2×#117—531no—
523C22×C4⋊C4—531no—
524#436—21no—
525#436—1061no—
526#435—21no—
527#435—21no—
528#435—1061no—
529#435—1061no—
530C8×D4—21no—
531C8×D4—1061no—
532#432—531no—
533#432C2×D5311yescharacteristic
534#431—531no—
535#431C2×D5311yescharacteristic
536#407—531no—
537#407—531no—
538#407C2×D5311yescharacteristic
539#407C2×D5311yescharacteristic
540C2×C22⋊C8—531no—
541C2×C22⋊C8—531no—
542C2×C22⋊C8C2×D5311yescharacteristic
543C2×C22⋊C8C2×D5311yescharacteristic
544#324—531no—
545#324—531no—
546#324—531no—
547#324—531no—
548#324—531no—
549#324—531no—
550#324—531no—
551#324—531no—
552#323—531no—
553#323—531no—
554#323—531no—
555#323—531no—
556#323—531no—
557#323—531no—
558#323—531no—
559#323—531no—
560C53#1742711yescharacteristic, complemented, Sylow
561C22×D4—531no—
562C22×D4—531no—
563C22×D4—531no—
564C22×D4—531no—
565C22×D4—531no—
566C22×D4C4×D5311yescharacteristic
567C23×C4—531no—
568C23×C4—531no—
569C23×C4—531no—
570C23×C4—531no—
571C23×C4C22×D5311yescharacteristic
572C23×C4C22×D5311yescharacteristic
573C2×M16—21no—
574C2×M16—21no—
575C2×M16—1061no—
576C2×M16—1061no—
577C22×C8—21no—
578C22×C8—21no—
579C22×C8—1061no—
580C22×C8—1061no—
581#126—1061no—
582#126—1061no—
583#126—1061no—
584#126—1061no—
585#126—1061no—
586#126—1061no—
587#126—1061no—
588#126—1061no—
589#125—1061no—
590#125—1061no—
591#125—1061no—
592#125—1061no—
593#123—1061no—
594#123—1061no—
595#123—1061no—
596#123—1061no—
597#123—1061no—
598#123—1061no—
599#123—1061no—
600#123—1061no—
601#121—1061no—
602#121—1061no—
603#121—1061no—
604#121—1061no—
605#121—1061no—
606#121—1061no—
607#121—1061no—
608#121—1061no—
609#121—1061no—
610#121—1061no—
611#121—1061no—
612#121—1061no—
613#121—1061no—
614#121—1061no—
615#121—1061no—
616#121—1061no—
617C4×D4—1061no—
618C4×D4—1061no—
619C4×D4—1061no—
620C4×D4—1061no—
621C4×D4—1061no—
622C4×D4—1061no—
623C4×D4—1061no—
624C4×D4—1061no—
625C4×D4—1061no—
626C4×D4—1061no—
627C4×D4—1061no—
628C4×D4—1061no—
629C4×D4D21211yescharacteristic
630C4×D4D21211yescharacteristic
631C4×D4D21211yescharacteristic
632C4×D4D21211yescharacteristic
633C4×D4C22⋊D5311yescharacteristic
634C4×D4C22⋊D5311yescharacteristic
635C4×D4C22⋊D5311yescharacteristic
636C4×D4C22⋊D5311yescharacteristic
637#117—1061no—
638#117—1061no—
639#117—1061no—
640#117—1061no—
641C2×C4⋊C4—531no—
642C2×C4⋊C4—531no—
643C2×C4⋊C4—531no—
644C2×C4⋊C4—531no—
645C2×C4⋊C4—531no—
646C2×C4⋊C4—531no—
647C2×C4⋊C4—531no—
648C2×C4⋊C4—531no—
649C2×C4⋊C4—531no—
650C2×C4⋊C4—1061no—
651C2×C4⋊C4—1061no—
652C2×C4⋊C4—1061no—
653C2×C4⋊C4—1061no—
654C2×C4⋊C4C4×D5311yescharacteristic
655C2×C22⋊C4—531no—
656C2×C22⋊C4—531no—
657C2×C22⋊C4—531no—
658C2×C22⋊C4—531no—
659C2×C22⋊C4—531no—
660C2×C22⋊C4—531no—
661C2×C22⋊C4—531no—
662C2×C22⋊C4—531no—
663C2×C22⋊C4C4×D5311yescharacteristic
664C2×C22⋊C4C4×D5311yescharacteristic
665C2×C42—531no—
666C2×C42—531no—
667C2×C42C22×D5311yescharacteristic
668C4⋊C8—21no—
669C4⋊C8—21no—
670C4⋊C8—1061no—
671C4⋊C8—1061no—
672C22⋊C8—21no—
673C22⋊C8—21no—
674C22⋊C8—21no—
675C22⋊C8—21no—
676C22⋊C8—531no—
677C22⋊C8—531no—
678C22⋊C8—531no—
679C22⋊C8—531no—
680C22⋊C8—1061no—
681C22⋊C8—1061no—
682C22⋊C8—1061no—
683C22⋊C8—1061no—
684C22⋊C8C22×D5311yescharacteristic
685C22⋊C8C22×D5311yescharacteristic
686C22⋊C8C22×D5311yescharacteristic
687C22⋊C8C22×D5311yescharacteristic
688#97—21no—
689#97—1061no—
690C4×C8—21no—
691C4×C8—1061no—
692C24—531no—
693C24—531no—
694C24C2×C4×D5311yescharacteristic
695C24C2×C4×D5311yescharacteristic
696C2×D4—42no—
697C2×D4—1062no—
698C2×D4—1061no—
699C2×D4—1061no—
700C2×D4—1061no—
701C2×D4—1061no—
702C2×D4—1061no—
703C2×D4—1061no—
704C2×D4—1061no—
705C2×D4—1061no—
706C2×D4—1061no—
707C2×D4—1061no—
708C2×D4—4241no—
709C2×D4—4241no—
710C2×D4—2121no—
711C2×D4—2122no—
712C2×D4—2122no—
713C2×D4#1171992111yescharacteristic
714C2×D4#1171992111yescharacteristic
715C2×D4#1171992111yescharacteristic
716C2×D4#1171992111yescharacteristic
717C22×C4—81no—
718C22×C4—81no—
719C22×C4—531no—
720C22×C4—531no—
721C22×C4—531no—
722C22×C4—531no—
723C22×C4—531no—
724C22×C4—531no—
725C22×C4—1062no—
726C22×C4—1062no—
727C22×C4—1061no—
728C22×C4—1061no—
729C22×C4—1061no—
730C22×C4—1061no—
731C22×C4—1061no—
732C22×C4—1061no—
733C22×C4—1061no—
734C22×C4—1061no—
735C22×C4—4241no—
736C22×C4—4241no—
737C22×C4—2121no—
738C22×C4—2121no—
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—1061no—
783C4⋊C4—1061no—
784C4⋊C4—1061no—
785C4⋊C4—1061no—
786C4⋊C4#1171992111yescharacteristic
787C4⋊C4#1171992111yescharacteristic
788C4⋊C4#1171992111yescharacteristic
789C4⋊C4#1171992111yescharacteristic
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#1171992111yescharacteristic
807C22⋊C4#1171992111yescharacteristic
808C22⋊C4#1171992111yescharacteristic
809C22⋊C4#1171992111yescharacteristic
810C22⋊C4#1171992111yescharacteristic
811C22⋊C4#1171992111yescharacteristic
812C22⋊C4#1171992111yescharacteristic
813C22⋊C4#1171992111yescharacteristic
814C42—1061no—
815C42—1061no—
816C42—1061no—
817C42—1061no—
818C42C2×D21211yescharacteristic
819C42C2×D21211yescharacteristic
820C42C2×C22⋊D5311yescharacteristic
821C42C2×C22⋊D5311yescharacteristic
822C23—22no—
823C23—21no—
824C23—21no—
825C23—21no—
826C23—21no—
827C23—41no—
828C23—41no—
829C23—41no—
830C23—1061no—
831C23—1061no—
832C23—1061no—
833C23—1061no—
834C23—1061no—
835C23—1061no—
836C23—2121no—
837C23—2121no—
838C23—2121no—
839C23—2121no—
840C23C2×#1171992111yescharacteristic
841C23C2×#1171992111yescharacteristic
842C23C2×#1171992111yescharacteristic
843C23C2×#1171992111yescharacteristic
844C23C22×C4×D5311yescharacteristic
845D4—22no—
846D4—22no—
847D4—41no—
848D4—41no—
849D4—4241no—
850D4—4241no—
851D4—4241no—
852D4—4241no—
853D4—2122no—
854D4—2122no—
855D4—2122no—
856D4—2122no—
857D4—2122no—
858D4—2122no—
859C2×C4—21no—
860C2×C4—21no—
861C2×C4—41no—
862C2×C4—41no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—41no—
869C2×C4—41no—
870C2×C4—41no—
871C2×C4—41no—
872C2×C4—41no—
873C2×C4—532no—
874C2×C4—1061no—
875C2×C4—1061no—
876C2×C4—1061no—
877C2×C4—1061no—
878C2×C4—1061no—
879C2×C4—1061no—
880C2×C4—1061no—
881C2×C4—1061no—
882C2×C4—1061no—
883C2×C4—4241no—
884C2×C4—4241no—
885C2×C4—4241no—
886C2×C4—4241no—
887C2×C4—2122no—
888C2×C4—2122no—
889C2×C4—2122no—
890C2×C4—2122no—
891C2×C4—2121no—
892C2×C4—2121no—
893C2×C4—2121no—
894C2×C4—2121no—
895C2×C4C2×#1171992111yescharacteristic
896C2×C4C2×#1171992111yescharacteristic
897C2×C4C2×#1171992111yescharacteristic
898C2×C4C2×#1171992111yescharacteristic
899C2×C4C2×#1171992111yescharacteristic
900C2×C4C2×#1171992111yescharacteristic
901C2×C4C2×#1171992111yescharacteristic
902C2×C4C2×#1171992111yescharacteristic
903C2×C4C22×C22⋊D5311yescharacteristic
904C2×C4C22×D21211yescharacteristic
905C8—41no—
906C8—41no—
907C8—41no—
908C8—41no—
909C8—2121no—
910C8—2121no—
911C8—2121no—
912C8—2121no—
913C22—21no—
914C22—21no—
915C22—21no—
916C22—21no—
917C22—21no—
918C22—21no—
919C22—21no—
920C22—21no—
921C22—21no—
922C22—21no—
923C22—21no—
924C22—21no—
925C22—21no—
926C22—42no—
927C22—42no—
928C22—81no—
929C22—81no—
930C22—4241no—
931C22—4241no—
932C22—4241no—
933C22—4241no—
934C22—2121no—
935C22—2121no—
936C22—2121no—
937C22—2121no—
938C22—2121no—
939C22—2121no—
940C22#1681060512yes—
941C22C22×#1171992111yescharacteristic
942C22#131×D5311yescharacteristic
943C22#1681138811yescharacteristic
944C4—21no—
945C4—21no—
946C4—21no—
947C4—21no—
948C4—21no—
949C4—21no—
950C4—21no—
951C4—21no—
952C4—21no—
953C4—21no—
954C4—1062no—
955C4—2121no—
956C4—2121no—
957C4—2121no—
958C4—2121no—
959C4—2121no—
960C2—21no—
961C2—21no—
962C2—22no—
963C2—41no—
964C2—41no—
965C2—41no—
966C2—4241no—
967C2—4241no—
968C2#2028316211yescharacteristic
969C2#2028317511yescharacteristic
970C2C2×#1681060511yescharacteristic
subgroupG/H
centerC22C22×#11719921
commutatorC23×C53C23×C4
FrattiniC22×C4C23×D53
FittingC53×#2974C2
socleC22×C53C22×C22⋊C4
prime radicalC2×#16811322C2
cosocleC22×C4×C53C24
hypercenter#2974D53
hypocenterC53#17427
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. #20273076C2semidirect
6. #20273074C2semidirect
7. #20273064C2semidirect
8. #20273061C2semidirect
9. #20273051C2semidirect
10. #20273047C2semidirect
11. #20273044C2semidirect
12. #20273031C2semidirect
13. #20273027C2semidirect
14. C2×#16810348C2semidirect
15. C53×#2974C2semidirect
477. #2974D53semidirect
560. C53#17427semidirect

Maximal subgroups

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

subgroupindex
C2×#168113222
#202837502
#202730852
#202730822
#202730762
#202730742
#202730642
#202730612
#202730512
#202730472
#202730442
#202730312
#202730272
C2×#168103482
C53×#29742
#1742753