Finite Group Databasebeta

← #27399446

Subgroups — #27399446

Order 13568.

1544 conjugacy classes of subgroups.

The subgroup lattice has 1042 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811269C211yesmaximal, characteristic
2D4×#11719917C211yesmaximal, characteristic, complemented
3C2×#16810605C211yesmaximal, characteristic, complemented
4C22×#13133133C211yesmaximal, characteristic, complemented
5#20275564C211yesmaximal, characteristic, complemented
6#20275562C211yesmaximal, characteristic, complemented
7#20275183C211yesmaximal, characteristic, complemented
8#20275181C211yesmaximal, characteristic, complemented
9#20275178C211yesmaximal, characteristic, complemented
10#20275176C211yesmaximal, characteristic, complemented
11#20274704C211yesmaximal, characteristic, complemented
12#20274641C211yesmaximal, characteristic, complemented
13#20274635C211yesmaximal, characteristic, complemented
14C4×#13133133C211yesmaximal, characteristic, complemented
15D4×M16×C53C211yesmaximal, characteristic, complemented
16C22×#11719945C2211yescharacteristic
17C23×D212C2211yescharacteristic
18C22×#11719917C2211yescharacteristic
19C22×#11719917C2211yescharacteristic, complemented
20#16811269—21no—
21#16811269—21no—
22#16811269—21no—
23#16811269—21no—
24#16811269—21no—
25#16811269—21no—
26#16811269—21no—
27#16811269—21no—
28C2×#13133205C2211yescharacteristic
29C2×#13133202C412yes—
30C2×#13133196C2211yescharacteristic
31C2×#13133191C2211yescharacteristic
32C2×#13133190C412yes—
33C2×#13133185C412yes—
34C2×C4×D212C2211yescharacteristic
35C2×C22⋊C4×D53C412yes—
36#16810701—21no—
37#16810695—21no—
38#16810695—21no—
39D4×#88322—21no—
40#16810647C2211yescharacteristic, complemented
41#16810605—24no—
42C2×#13133135C2211yescharacteristic, complemented
43C2×#13133135C2211yescharacteristic, complemented
44C2×#13133135C2211yescharacteristic, complemented
45C2×#13133135C2211yescharacteristic, complemented
46C2×#13133133—24no—
47C2×#13133133C2211yescharacteristic
48C2×#13133133C2211yescharacteristic
49C2×#13133133C2211yescharacteristic
50C2×#13133133C2211yescharacteristic
51C2×#13133133C2211yescharacteristic
52C2×#13133133C2211yescharacteristic
53C2×#13133133C2211yescharacteristic
54C2×#13133133C2211yescharacteristic
55#16810587C2211yescharacteristic
56#16810587C2211yescharacteristic, complemented
57C4×#11719917C2211yescharacteristic, complemented
58#16810391C2211yescharacteristic, complemented
59#16810391C2211yescharacteristic, complemented
60#16810391C2211yescharacteristic, complemented
61#16810391C2211yescharacteristic, complemented
62C22×M16×C53C2211yescharacteristic
63C22×M16×C53C2211yescharacteristic, complemented
64C2×C4×D4×C53C2211yescharacteristic
65C53×#436—21no—
66C53×#435—21no—
67C53×#435—21no—
68C8×D4×C53—21no—
69C53×#423C2211yescharacteristic, complemented
70C53×#407C2211yescharacteristic
71C53×#407C2211yescharacteristic, complemented
72C4×M16×C53C2211yescharacteristic, complemented
73C24×D53C2×C412yes—
74C2×#11719945—21no—
75C2×#11719945—21no—
76C2×#11719945—21no—
77C2×#11719945—21no—
78C2×#11719945—22no—
79C2×#11719945—22no—
80C2×#11719945—41no—
81C2×#11719945—41no—
82C22×Dic106C2311yescharacteristic
83C22×D212—21no—
84C22×D212—21no—
85C22×D212—21no—
86C22×D212—21no—
87C22×D212—22no—
88C22×D212—22no—
89C22×D212—41no—
90C22×D212—41no—
91C22×D212C2×C412yes—
92C22×D212C2311yescharacteristic
93C22×D212C2311yescharacteristic
94C22×C22⋊D53C2×C412yes—
95C22×C22⋊D53C2×C412yes—
96C22×C4×D53C2×C412yes—
97C22×C4×D53C2×C412yes—
98C2×#11719917—22no—
99C2×#11719917—22no—
100C2×#11719917—21no—
101C2×#11719917—21no—
102C2×#11719917—41no—
103C2×#11719917—41no—
104C2×#11719917C2311yescharacteristic
105C2×#11719917C2311yescharacteristic
106C2×#11719917C2311yescharacteristic
107C2×#11719917C2311yescharacteristic
108C22×#88322—21no—
109C22×#88322—21no—
110#13133205—21no—
111#13133205—21no—
112#13133205—21no—
113#13133205—21no—
114#13133202—22no—
115#13133202—22no—
116#13133202—22no—
117#13133202—22no—
118#13133196—21no—
119#13133196—21no—
120#13133196—21no—
121#13133196—21no—
122#13133191—21no—
123#13133191—21no—
124#13133191—21no—
125#13133191—21no—
126#13133190—22no—
127#13133190—22no—
128#13133190—22no—
129#13133190—22no—
130#13133185—22no—
131#13133185—22no—
132#13133185—22no—
133#13133185—22no—
134C4×D212—21no—
135C4×D212—21no—
136C4×D212—21no—
137C4×D212—21no—
138C2×C4⋊Dic53C2311yescharacteristic
139C2×#11719919C2×C412yes—
140C2×C22⋊Dic53C2×C412yes—
141C2×#11719921C2×C412yes—
142C2×#11719921C2×C412yes—
143C2×#11719921C2×C412yes—
144C2×#11719921C2×C412yes—
145C22⋊C4×D53—22no—
146C22⋊C4×D53—22no—
147C22⋊C4×D53—22no—
148C22⋊C4×D53—22no—
149C4⋊#88322—21no—
150C4⋊#88322—21no—
151#13133135—22no—
152#13133135—22no—
153#13133135—41no—
154#13133135—41no—
155#13133133—22no—
156#13133133—22no—
157#13133133—22no—
158#13133133—22no—
159#13133133—22no—
160#13133133—41no—
161#13133133—41no—
162#13133133D414yescomplemented
163C22⋊#88322—21no—
164C22⋊#88322—21no—
165C22⋊#88322—21no—
166C22⋊#88322—21no—
167#13133128—21no—
168C4×#88322—21no—
169C22×D4×C53C2×C411yescharacteristic
170C23×C4×C53C2311yescharacteristic
171C23×C4×C53C2311yescharacteristic
172C2×M16×C53—22no—
173C2×M16×C53—22no—
174C2×M16×C53—21no—
175C2×M16×C53—21no—
176C2×M16×C53—41no—
177C2×M16×C53—41no—
178C2×M16×C53C2311yescharacteristic
179C2×M16×C53C2311yescharacteristic
180C2×M16×C53C2311yescharacteristic
181C2×M16×C53C2311yescharacteristic
182C22×C8×C53—21no—
183C22×C8×C53—21no—
184C4×D4×C53D411yescharacteristic
185C4×D4×C53D411yescharacteristic
186C4×D4×C53D411yescharacteristic
187C4×D4×C53D411yescharacteristic
188C4×D4×C53D411yescharacteristic
189C4×D4×C53D411yescharacteristic
190C4×D4×C53D411yescharacteristic
191C4×D4×C53D411yescharacteristic
192C2×C4⋊C4×C53C2×C411yescharacteristic
193C2×C22⋊C4×C53C2×C411yescharacteristic
194C2×C22⋊C4×C53C2×C411yescharacteristic
195C2×C42×C53C2311yescharacteristic
196C4⋊C8×C53—21no—
197C4⋊C8×C53—21no—
198C22⋊C8×C53—21no—
199C22⋊C8×C53—21no—
200C22⋊C8×C53—21no—
201C22⋊C8×C53—21no—
202#97×C53—21no—
203C4×C8×C53—21no—
204C24×C53C22×C411yescharacteristic
205C24×C53C22×C411yescharacteristic
206C23×D53—22no—
207C23×D53—22no—
208C23×D53—24no—
209C23×D53—42no—
210C23×D53—44no—
211C23×D53—82no—
212C23×D53C22×C412yes—
213C23×D53C22×C412yes—
214C2×D4×C53—42no—
215C2×D4×C53C22⋊C411yescharacteristic
216C2×D4×C53C22⋊C411yescharacteristic
217C2×D4×C53C22⋊C411yescharacteristic
218C2×D4×C53C22⋊C411yescharacteristic
219C22×C4×C53—21no—
220C22×C4×C53—21no—
221C22×C4×C53—21no—
222C22×C4×C53—21no—
223C22×C4×C53—21no—
224C22×C4×C53—21no—
225C22×C4×C53—21no—
226C22×C4×C53—21no—
227C22×C4×C53C22×C411yescharacteristic
228C22×C4×C53C22×C411yescharacteristic
229C22×C4×C53C22×C411yescharacteristic
230C22×C4×C53C22×C411yescharacteristic
231C22×C4×C53C2×D411yescharacteristic
232C22×C4×C53C2×D411yescharacteristic
233C22×C4×C53C2×D411yescharacteristic
234C22×C4×C53C2×D411yescharacteristic
235C22×C4×C53C2×D411yescharacteristic
236C22×C4×C53C2×D411yescharacteristic
237C22×C4×C53C2×D411yescharacteristic
238C22×C4×C53C2×D411yescharacteristic
239C22×C4×C53C2411yescharacteristic
240C2×C22⋊D53—22no—
241C2×C22⋊D53—22no—
242C2×C22⋊D53—24no—
243C2×C22⋊D53—22no—
244C2×C22⋊D53—22no—
245C2×C22⋊D53—42no—
246C2×C22⋊D53—82no—
247C22×Dic53C22×C412yes—
248C22×Dic53C22×C412yes—
249#11719945—42no—
250#11719945—42no—
251#11719945—42no—
252#11719945—42no—
253#11719945—42no—
254#11719945—42no—
255#11719945—42no—
256#11719945—42no—
257C2×D212—21no—
258C2×D212—21no—
259C2×D212—21no—
260C2×D212—21no—
261C2×D212—24no—
262C2×D212—22no—
263C2×D212—22no—
264C2×D212—21no—
265C2×D212—21no—
266C2×D212—21no—
267C2×D212—21no—
268C2×D212—21no—
269C2×D212—21no—
270C2×D212—42no—
271C2×D212—42no—
272C2×D212—42no—
273C2×D212—42no—
274C2×D212—42no—
275C2×D212—42no—
276C2×D212—42no—
277C2×D212—42no—
278C2×D212—42no—
279C2×D212C2×D412yes—
280C2×D212#4112yes—
281C2×C4×D53—24no—
282C2×C4×D53—22no—
283C2×C4×D53—22no—
284C2×C4×D53—22no—
285C2×C4×D53—22no—
286C2×C4×D53—42no—
287C2×C4×D53—82no—
288C2×Dic106—21no—
289C2×Dic106—21no—
290C2×Dic106—21no—
291C2×Dic106—21no—
292C2×Dic106—21no—
293C2×Dic106—21no—
294M16×C53—21no—
295M16×C53—21no—
296M16×C53—21no—
297M16×C53—21no—
298M16×C53—21no—
299M16×C53—21no—
300M16×C53—21no—
301M16×C53—42no—
302M16×C53—42no—
303M16×C53C2×D412yes—
304C2×C8×C53—21no—
305C2×C8×C53—21no—
306C2×C8×C53—21no—
307C2×C8×C53—21no—
308C2×C8×C53—42no—
309C2×C8×C53—42no—
310C4⋊C4×C53C22⋊C411yescharacteristic
311C4⋊C4×C53C22⋊C411yescharacteristic
312C4⋊C4×C53C22⋊C411yescharacteristic
313C4⋊C4×C53C22⋊C411yescharacteristic
314C22⋊C4×C53C22⋊C411yescharacteristic
315C22⋊C4×C53C22⋊C411yescharacteristic
316C22⋊C4×C53C22⋊C411yescharacteristic
317C22⋊C4×C53C22⋊C411yescharacteristic
318C22⋊C4×C53C22⋊C411yescharacteristic
319C22⋊C4×C53C22⋊C411yescharacteristic
320C22⋊C4×C53C22⋊C411yescharacteristic
321C22⋊C4×C53C22⋊C411yescharacteristic
322C42×C53C2×D411yescharacteristic
323C42×C53C2×D411yescharacteristic
324C42×C53C2×D411yescharacteristic
325C42×C53C2×D411yescharacteristic
326C22⋊Dic53—22no—
327C22⋊Dic53—22no—
328#11719921—22no—
329#11719921—22no—
330#11719921—22no—
331#11719921—22no—
332#11719921—22no—
333#11719921—22no—
334#11719921—22no—
335#11719921—22no—
336C4⋊Dic53—21no—
337C4⋊Dic53—21no—
338#11719919—22no—
339#11719919—22no—
340#11719917—21no—
341#11719917—21no—
342#11719917—21no—
343#11719917—21no—
344#11719917—21no—
345#11719917—21no—
346#11719917—21no—
347#11719917—42no—
348#11719917—42no—
349#11719917C2×D412yes—
350C2×#88322—21no—
351C2×#88322—21no—
352C2×#88322—21no—
353C2×#88322—21no—
354C2×#88322—42no—
355C2×#88322—42no—
356C23×C53—21no—
357C23×C53—21no—
358C23×C53—22no—
359C23×C53—21no—
360C23×C53—21no—
361C23×C53—41no—
362C23×C53—41no—
363C23×C53—41no—
364C23×C53C2×C22⋊C411yescharacteristic
365C23×C53C2×C22⋊C411yescharacteristic
366C23×C53C2×C22⋊C411yescharacteristic
367C23×C53C2×C22⋊C411yescharacteristic
368C23×C53C23×C411yescharacteristic
369C22×D53—22no—
370C22×D53—22no—
371C22×D53—22no—
372C22×D53—22no—
373C22×D53—22no—
374C22×D53—44no—
375C22×D53—44no—
376C22×D53—42no—
377C22×D53—42no—
378C22×D53—44no—
379C22×D53—44no—
380C22×D53—42no—
381C22×D53—42no—
382C22×D53—82no—
383C22×D53—82no—
384C22×D53—88no—
385C22×D53—88no—
386C22×D53C4×D414yes—
387D4×C53—22no—
388D4×C53—22no—
389D4×C53—41no—
390D4×C53—41no—
391C2×C4×C53—21no—
392C2×C4×C53—21no—
393C2×C4×C53—21no—
394C2×C4×C53—21no—
395C2×C4×C53—21no—
396C2×C4×C53—21no—
397C2×C4×C53—21no—
398C2×C4×C53—21no—
399C2×C4×C53—21no—
400C2×C4×C53—21no—
401C2×C4×C53—21no—
402C2×C4×C53—21no—
403C2×C4×C53—21no—
404C2×C4×C53—21no—
405C2×C4×C53—21no—
406C2×C4×C53—21no—
407C2×C4×C53—21no—
408C2×C4×C53—21no—
409C2×C4×C53—21no—
410C2×C4×C53—21no—
411C2×C4×C53—41no—
412C2×C4×C53—41no—
413C2×C4×C53C2×C22⋊C411yescharacteristic
414C2×C4×C53C2×C22⋊C411yescharacteristic
415C2×C4×C53C2×C22⋊C411yescharacteristic
416C2×C4×C53C2×C22⋊C411yescharacteristic
417C2×C4×C53C2×C22⋊C411yescharacteristic
418C2×C4×C53C2×C22⋊C411yescharacteristic
419C2×C4×C53C2×C22⋊C411yescharacteristic
420C2×C4×C53C2×C22⋊C411yescharacteristic
421C2×C4×C53C22×D411yescharacteristic
422C2×C4×C53C22×D411yescharacteristic
423C2×C4×C53C22×D411yescharacteristic
424C2×C4×C53C2×#4111yescharacteristic
425C2×C4×C53H(5,𝔽2)11yescharacteristic
426C2×C4×C53H(5,𝔽2)11yescharacteristic
427C22⋊D53—44no—
428C22⋊D53—44no—
429C22⋊D53—82no—
430C22⋊D53—82no—
431C2×Dic53—22no—
432C2×Dic53—22no—
433C2×Dic53—22no—
434C2×Dic53—22no—
435C2×Dic53—42no—
436D212—22no—
437D212—22no—
438D212—22no—
439D212—22no—
440D212—44no—
441D212—44no—
442D212—41no—
443D212—41no—
444D212—41no—
445D212—41no—
446C4×D53—44no—
447C4×D53—44no—
448C4×D53—82no—
449C4×D53—82no—
450Dic106—41no—
451Dic106—41no—
452Dic106—41no—
453Dic106—41no—
454C8×C53—22no—
455C8×C53—41no—
456C8×C53—41no—
457C8×C53—41no—
458#88322—22no—
459#88322—41no—
460#88322—41no—
461#88322—41no—
462#22408—531nomaximal, Sylow
463C22×C53—21no—
464C22×C53—21no—
465C22×C53—21no—
466C22×C53—21no—
467C22×C53—21no—
468C22×C53—21no—
469C22×C53—21no—
470C22×C53—21no—
471C22×C53—21no—
472C22×C53—21no—
473C22×C53—21no—
474C22×C53—21no—
475C22×C53—21no—
476C22×C53—42no—
477C22×C53—42no—
478C22×C53—81no—
479C22×C53—81no—
480C22×C53#41312yescomplemented
481C22×C53C22×C22⋊C411yescharacteristic
482C22×C53C2×C4×D411yescharacteristic
483C22×C53#51811yescharacteristic
484C2×D53—24no—
485C2×D53—44no—
486C2×D53—42no—
487C2×D53—42no—
488C2×D53—44no—
489C2×D53—42no—
490C2×D53—42no—
491C2×D53—42no—
492C2×D53—88no—
493C2×D53—88no—
494C2×D53—82no—
495C2×D53—82no—
496C4×C53—21no—
497C4×C53—21no—
498C4×C53—21no—
499C4×C53—21no—
500C4×C53—21no—
501C4×C53—21no—
502C4×C53—21no—
503C4×C53—21no—
504C4×C53D4211yescharacteristic
505C4×C53D4211yescharacteristic
506C4×C53#54611yescharacteristic
507C4×C53#54611yescharacteristic
508Dic53—42no—
509Dic53—42no—
510C2×#546—531no—
511D4×M16—531no—
512D4×M16D5311yescharacteristic, complemented
513C2×#413—531no—
514C22×#100—531no—
515#1967—531no—
516#1967—531no—
517#1901—531no—
518#1901—531no—
519#1900—531no—
520#1900—531no—
521#1800—531no—
522#1785—531no—
523#1783—531no—
524C4×#100—531no—
525C2×C53—21no—
526C2×C53—21no—
527C2×C53—22no—
528C2×C53—41no—
529C2×C53—41no—
530C2×C53—41no—
531C2×C53D4×C22⋊C411yescharacteristic
532C2×C53C2×#41311yescharacteristic
533C2×C53#288811yescharacteristic
534D53—44no—
535D53—82no—
536C22×#41—531no—
537C23×D4—531no—
538C22×M16—531no—
539C22×M16—531no—
540C22×M16C2×D5311yescharacteristic
541C22×M16C2×D5311yescharacteristic, complemented
542#546—1061no—
543#546—1061no—
544#546—1061no—
545#546—1061no—
546#546—1061no—
547#546—1061no—
548#546—1061no—
549#546—1061no—
550C2×#124—531no—
551C2×#123—532no—
552C2×C22⋊Q8—531no—
553C2×#121—531no—
554C2×#121—532no—
555C2×#120—532no—
556C2×C4×D4—531no—
557C2×C4×D4C2×D5311yescharacteristic
558C22×C22⋊C4—532no—
559#436—21no—
560#436—1061no—
561#435—21no—
562#435—21no—
563#435—1061no—
564#435—1061no—
565C8×D4—21no—
566C8×D4—1061no—
567#423—531no—
568#423C2×D5311yescharacteristic, complemented
569#413—1064no—
570C2×#101—531no—
571C2×#101—531no—
572C2×#101—531no—
573C2×#101—531no—
574C2×#100—531no—
575C2×#100—531no—
576C2×#100—531no—
577C2×#100—531no—
578C2×#100—531no—
579C2×#100—531no—
580C2×#100—531no—
581C2×#100—531no—
582C2×#100—1064no—
583#407—531no—
584#407—531no—
585#407C2×D5311yescharacteristic
586#407C2×D5311yescharacteristic, complemented
587C4×M16—531no—
588C4×M16C2×D5311yescharacteristic, complemented
589#343—531no—
590#343—531no—
591#343—531no—
592#343—531no—
593C53#2240811yescharacteristic, complemented, Sylow
594C25—532no—
595C2×#41—1062no—
596C2×#41—1062no—
597C2×#41—1061no—
598C2×#41—1061no—
599C2×#41—1061no—
600C2×#41—1061no—
601C2×#41—2121no—
602C2×#41—2121no—
603C22×Q8—531no—
604C22×D4—532no—
605C22×D4—532no—
606C22×D4—532no—
607C22×D4—531no—
608C22×D4—531no—
609C22×D4—1062no—
610C22×D4—1062no—
611C22×D4—1061no—
612C22×D4—1061no—
613C22×D4—1061no—
614C22×D4—1061no—
615C22×D4—2121no—
616C22×D4—2121no—
617C22×D4C4×D5311yescharacteristic
618C23×C4—532no—
619C23×C4—532no—
620C23×C4C22×D5311yescharacteristic
621C23×C4C22×D5311yescharacteristic
622C2×M16—21no—
623C2×M16—21no—
624C2×M16—22no—
625C2×M16—22no—
626C2×M16—41no—
627C2×M16—41no—
628C2×M16—531no—
629C2×M16—531no—
630C2×M16—531no—
631C2×M16—531no—
632C2×M16—1061no—
633C2×M16—1061no—
634C2×M16—1062no—
635C2×M16—1062no—
636C2×M16—2121no—
637C2×M16—2121no—
638C2×M16C22×D5311yescharacteristic
639C2×M16C22×D5311yescharacteristic
640C2×M16C22×D5311yescharacteristic
641C2×M16C22×D5311yescharacteristic
642C22×C8—21no—
643C22×C8—21no—
644C22×C8—1061no—
645C22×C8—1061no—
646#124—1061no—
647#124—1061no—
648#124—1061no—
649#124—1061no—
650#123—1062no—
651#123—1062no—
652#123—1062no—
653#123—1062no—
654C22⋊Q8—1061no—
655C22⋊Q8—1061no—
656C22⋊Q8—1061no—
657C22⋊Q8—1061no—
658#121—1061no—
659#121—1061no—
660#121—1061no—
661#121—1061no—
662#121—1062no—
663#121—1062no—
664#121—1062no—
665#121—1062no—
666#120—1062no—
667#120—1062no—
668#120—1062no—
669#120—1062no—
670C4×D4—1061no—
671C4×D4—1061no—
672C4×D4—1061no—
673C4×D4—1061no—
674C4×D4D21211yescharacteristic
675C4×D4D21211yescharacteristic
676C4×D4D21211yescharacteristic
677C4×D4D21211yescharacteristic
678C4×D4C22⋊D5311yescharacteristic
679C4×D4C22⋊D5311yescharacteristic
680C4×D4C22⋊D5311yescharacteristic
681C4×D4C22⋊D5311yescharacteristic
682C2×C4⋊C4—532no—
683C2×C4⋊C4—531no—
684C2×C4⋊C4C4×D5311yescharacteristic
685C2×C22⋊C4—532no—
686C2×C22⋊C4—532no—
687C2×C22⋊C4—532no—
688C2×C22⋊C4—532no—
689C2×C22⋊C4—532no—
690C2×C22⋊C4—1062no—
691C2×C22⋊C4—1062no—
692C2×C22⋊C4—1062no—
693C2×C22⋊C4—1062no—
694C2×C22⋊C4C4×D5311yescharacteristic
695C2×C22⋊C4C4×D5311yescharacteristic
696C2×C42C22×D5311yescharacteristic
697C4⋊C8—21no—
698C4⋊C8—21no—
699C4⋊C8—1061no—
700C4⋊C8—1061no—
701#101—1062no—
702#101—1062no—
703#101—2121no—
704#101—2121no—
705#100—534no—
706#100—1062no—
707#100—1062no—
708#100—1062no—
709#100—1062no—
710#100—1062no—
711#100—2121no—
712#100—2121no—
713C22⋊C8—21no—
714C22⋊C8—21no—
715C22⋊C8—21no—
716C22⋊C8—21no—
717C22⋊C8—1061no—
718C22⋊C8—1061no—
719C22⋊C8—1061no—
720C22⋊C8—1061no—
721#97—21no—
722#97—1061no—
723C4×C8—21no—
724C4×C8—1061no—
725C24—532no—
726C24—532no—
727C24—1064no—
728C24—1062no—
729C24—1062no—
730C24—4242no—
731C24—2122no—
732C24—2124no—
733C24C2×C4×D5311yescharacteristic
734C24C2×C4×D5311yescharacteristic
735#41—2122no—
736#41—2122no—
737#41—2122no—
738#41—2122no—
739#41—2122no—
740#41—2122no—
741#41—2122no—
742#41—2122no—
743C2×Q8—1061no—
744C2×Q8—1061no—
745C2×Q8—1061no—
746C2×Q8—1061no—
747C2×Q8—1061no—
748C2×Q8—1061no—
749C2×D4—42no—
750C2×D4—532no—
751C2×D4—532no—
752C2×D4—1064no—
753C2×D4—1062no—
754C2×D4—1062no—
755C2×D4—1064no—
756C2×D4—1062no—
757C2×D4—1062no—
758C2×D4—1062no—
759C2×D4—1062no—
760C2×D4—1061no—
761C2×D4—1061no—
762C2×D4—1061no—
763C2×D4—1061no—
764C2×D4—1061no—
765C2×D4—1061no—
766C2×D4—1061no—
767C2×D4—1061no—
768C2×D4—1061no—
769C2×D4—1061no—
770C2×D4—4242no—
771C2×D4—2122no—
772C2×D4—2122no—
773C2×D4—2122no—
774C2×D4—2122no—
775C2×D4—2122no—
776C2×D4—2122no—
777C2×D4—2122no—
778C2×D4—2122no—
779C2×D4—2122no—
780C2×D4—2122no—
781C2×D4#1171992111yescharacteristic
782C2×D4#1171992111yescharacteristic
783C2×D4#1171992111yescharacteristic
784C2×D4#1171992111yescharacteristic
785C22×C4—21no—
786C22×C4—21no—
787C22×C4—21no—
788C22×C4—21no—
789C22×C4—21no—
790C22×C4—21no—
791C22×C4—21no—
792C22×C4—21no—
793C22×C4—532no—
794C22×C4—532no—
795C22×C4—1064no—
796C22×C4—1062no—
797C22×C4—1062no—
798C22×C4—1062no—
799C22×C4—1062no—
800C22×C4—4242no—
801C22×C4—2122no—
802C22×C4C2×C4×D5311yescharacteristic
803C22×C4C2×C4×D5311yescharacteristic
804C22×C4C2×C4×D5311yescharacteristic
805C22×C4C2×C4×D5311yescharacteristic
806C22×C4C2×D21211yescharacteristic
807C22×C4C2×D21211yescharacteristic
808C22×C4C2×D21211yescharacteristic
809C22×C4C2×D21211yescharacteristic
810C22×C4C2×C22⋊D5311yescharacteristic
811C22×C4C2×C22⋊D5311yescharacteristic
812C22×C4C2×C22⋊D5311yescharacteristic
813C22×C4C2×C22⋊D5311yescharacteristic
814C22×C4C23×D5311yescharacteristic
815M16—21no—
816M16—21no—
817M16—21no—
818M16—21no—
819M16—21no—
820M16—21no—
821M16—21no—
822M16—42no—
823M16—42no—
824M16—532no—
825M16—1061no—
826M16—1061no—
827M16—1061no—
828M16—1061no—
829M16—1061no—
830M16—1061no—
831M16—1061no—
832M16—2122no—
833M16—2122no—
834M16D4×D5312yes—
835C2×C8—21no—
836C2×C8—21no—
837C2×C8—21no—
838C2×C8—21no—
839C2×C8—42no—
840C2×C8—42no—
841C2×C8—1061no—
842C2×C8—1061no—
843C2×C8—1061no—
844C2×C8—1061no—
845C2×C8—2122no—
846C2×C8—2122no—
847C4⋊C4—1062no—
848C4⋊C4—1062no—
849C4⋊C4—1061no—
850C4⋊C4—1061no—
851C4⋊C4#1171992111yescharacteristic
852C4⋊C4#1171992111yescharacteristic
853C4⋊C4#1171992111yescharacteristic
854C4⋊C4#1171992111yescharacteristic
855C22⋊C4—1062no—
856C22⋊C4—1062no—
857C22⋊C4—1062no—
858C22⋊C4—1062no—
859C22⋊C4—1062no—
860C22⋊C4—1062no—
861C22⋊C4—1062no—
862C22⋊C4—1062no—
863C22⋊C4—1062no—
864C22⋊C4—1062no—
865C22⋊C4#1171992111yescharacteristic
866C22⋊C4#1171992111yescharacteristic
867C22⋊C4#1171992111yescharacteristic
868C22⋊C4#1171992111yescharacteristic
869C22⋊C4#1171992111yescharacteristic
870C22⋊C4#1171992111yescharacteristic
871C22⋊C4#1171992111yescharacteristic
872C22⋊C4#1171992111yescharacteristic
873C42C2×D21211yescharacteristic
874C42C2×D21211yescharacteristic
875C42C2×C22⋊D5311yescharacteristic
876C42C2×C22⋊D5311yescharacteristic
877C23—21no—
878C23—21no—
879C23—22no—
880C23—21no—
881C23—21no—
882C23—41no—
883C23—41no—
884C23—41no—
885C23—534no—
886C23—1062no—
887C23—1062no—
888C23—1062no—
889C23—1062no—
890C23—1062no—
891C23—4242no—
892C23—4242no—
893C23—4248no—
894C23—4248no—
895C23—2124no—
896C23—2124no—
897C23—2122no—
898C23—2122no—
899C23—2124no—
900C23—2122no—
901C23—2122no—
902C23—2124no—
903C23C2×#1171992111yescharacteristic
904C23C2×#1171992111yescharacteristic
905C23C2×#1171992111yescharacteristic
906C23C2×#1171992111yescharacteristic
907C23C22×C4×D5311yescharacteristic
908Q8—2121no—
909Q8—2121no—
910Q8—2121no—
911Q8—2121no—
912D4—22no—
913D4—22no—
914D4—41no—
915D4—41no—
916D4—1062no—
917D4—1062no—
918D4—1062no—
919D4—1062no—
920D4—4242no—
921D4—4242no—
922D4—2124no—
923D4—2124no—
924D4—2124no—
925D4—2124no—
926D4—2121no—
927D4—2121no—
928D4—2121no—
929D4—2121no—
930C2×C4—21no—
931C2×C4—21no—
932C2×C4—21no—
933C2×C4—21no—
934C2×C4—21no—
935C2×C4—21no—
936C2×C4—21no—
937C2×C4—21no—
938C2×C4—21no—
939C2×C4—21no—
940C2×C4—21no—
941C2×C4—21no—
942C2×C4—21no—
943C2×C4—21no—
944C2×C4—21no—
945C2×C4—21no—
946C2×C4—21no—
947C2×C4—21no—
948C2×C4—21no—
949C2×C4—21no—
950C2×C4—41no—
951C2×C4—41no—
952C2×C4—1062no—
953C2×C4—1062no—
954C2×C4—1062no—
955C2×C4—1062no—
956C2×C4—4242no—
957C2×C4—4242no—
958C2×C4—2124no—
959C2×C4—2124no—
960C2×C4—2122no—
961C2×C4C2×#1171992111yescharacteristic
962C2×C4C2×#1171992111yescharacteristic
963C2×C4C2×#1171992111yescharacteristic
964C2×C4C2×#1171992111yescharacteristic
965C2×C4C2×#1171992111yescharacteristic
966C2×C4C2×#1171992111yescharacteristic
967C2×C4C2×#1171992111yescharacteristic
968C2×C4C2×#1171992111yescharacteristic
969C2×C4C2×D4×D5311yescharacteristic
970C2×C4C22×C22⋊D5311yescharacteristic
971C2×C4C22×D21211yescharacteristic
972C2×C4#41×D5311yescharacteristic
973C2×C4#1313326211yescharacteristic
974C2×C4#1313326311yescharacteristic
975C8—22no—
976C8—41no—
977C8—41no—
978C8—41no—
979C8—1062no—
980C8—2121no—
981C8—2121no—
982C8—2121no—
983C22—21no—
984C22—21no—
985C22—21no—
986C22—21no—
987C22—21no—
988C22—21no—
989C22—21no—
990C22—21no—
991C22—21no—
992C22—21no—
993C22—21no—
994C22—21no—
995C22—21no—
996C22—42no—
997C22—42no—
998C22—81no—
999C22—81no—
1000C22—1064no—
1001C22—4242no—
1002C22—4242no—
1003C22—4248no—
1004C22—4248no—
1005C22—2124no—
1006C22—2124no—
1007C22—2122no—
1008C22—2122no—
1009C22—2122no—
1010C22—2122no—
1011C22—2122no—
1012C22#1681060512yescomplemented
1013C22C22×#1171992111yescharacteristic
1014C22C4×D4×D5311yescharacteristic
1015C22#1681109511yescharacteristic
1016C4—21no—
1017C4—21no—
1018C4—21no—
1019C4—21no—
1020C4—21no—
1021C4—21no—
1022C4—21no—
1023C4—21no—
1024C4—2122no—
1025C4—2122no—
1026C4D4×C22⋊D5311yescharacteristic
1027C4D4×D21211yescharacteristic
1028C4#1681126111yescharacteristic
1029C4#1681126811yescharacteristic
1030C2—21no—
1031C2—21no—
1032C2—22no—
1033C2—41no—
1034C2—41no—
1035C2—41no—
1036C2—4242no—
1037C2—2124no—
1038C2D4×#1171992111yescharacteristic
1039C2C2×#1681060511yescharacteristic
1040C2#2028319311yescharacteristic
subgroupG/H
centerC22C22×#11719921
commutatorC23×C53C23×C4
FrattiniC22×C4C23×D53
FittingD4×M16×C53C2
socleC22×C53C22×C22⋊C4
prime radicalC2×#16811269C2
cosocleC22×C4×C53C24
hypercenterD4×M16D53
hypocenterC53#22408
LCSG ▷ C23×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C22 ◁ C2×C4×D4 ◁ D4×M16

Complements

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

NH ≅ G/Ntype
2. D4×#11719917C2semidirect
3. C2×#16810605C2semidirect
4. C22×#13133133C2semidirect
5. #20275564C2semidirect
6. #20275562C2semidirect
7. #20275183C2semidirect
8. #20275181C2semidirect
9. #20275178C2semidirect
10. #20275176C2semidirect
11. #20274704C2semidirect
12. #20274641C2semidirect
13. #20274635C2semidirect
14. C4×#13133133C2semidirect
15. D4×M16×C53C2semidirect
19. C22×#11719917C22semidirect
40. #16810647C22semidirect
42. C2×#13133135C22semidirect
43. C2×#13133135C22semidirect
44. C2×#13133135C22semidirect
45. C2×#13133135C22semidirect
56. #16810587C22semidirect
57. C4×#11719917C22semidirect
58. #16810391C22semidirect
59. #16810391C22semidirect
60. #16810391C22semidirect
61. #16810391C22semidirect
63. C22×M16×C53C22semidirect
69. C53×#423C22semidirect
71. C53×#407C22semidirect
72. C4×M16×C53C22semidirect
162. #13133133D4semidirect
480. C22×C53#413semidirect
512. D4×M16D53semidirect
541. C22×M16C2×D53semidirect
568. #423C2×D53semidirect
586. #407C2×D53semidirect
588. C4×M16C2×D53semidirect
593. C53#22408semidirect
1012. C22#16810605semidirect

Maximal subgroups

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

subgroupindex
C2×#168112692
D4×#117199172
C2×#168106052
C22×#131331332
#202755642
#202755622
#202751832
#202751812
#202751782
#202751762
#202747042
#202746412
#202746352
C4×#131331332
D4×M16×C532
#2240853