Finite Group Databasebeta

← #27305990

Subgroups — #27305990

Order 13568.

2590 conjugacy classes of subgroups.

The subgroup lattice has 990 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×D212C211yesmaximal, characteristic
2C22×#13133175C211yesmaximal, characteristic, complemented
3C2×#16810480C211yesmaximal, characteristic, complemented
4C2×#16810480C211yesmaximal, characteristic, complemented
5C2×#16810480C211yesmaximal, characteristic, complemented
6#20272963C212yesmaximal, complemented
7#20272955C212yesmaximal
8#20272951C212yesmaximal, complemented
9#20272949C212yesmaximal, complemented
10#20272945C211yesmaximal, characteristic, complemented
11C53×C4⋊#95C211yesmaximal, characteristic, complemented
12C23×D212C2211yescharacteristic
13C23×C4×D53C2211yescharacteristic
14C23×C4×D53C2211yescharacteristic
15C2×C4×D212—24no—
16C2×C4×D212—24no—
17C2×C4×D212C418yescomplemented
18C2×#13133175—24no—
19C2×#13133175—24no—
20C2×#13133175—24no—
21C22×C4⋊Dic53C2211yescharacteristic
22C22×C4⋊Dic53C2211yescharacteristic
23C22×C4⋊Dic53C2211yescharacteristic
24C22×#11719921C2212yes—
25C22×#11719921C2212yes—
26C22×#11719921C2212yes—
27C22×#11719921C2211yescharacteristic
28C22×#11719921C2211yescharacteristic
29C22×#11719921C2212yes—
30C22×C4×Dic53C2212yes—
31#16810480—24no—
32#16810480—24no—
33#16810480—24no—
34C2×#13133124C2212yes—
35C2×#13133124C2212yes—
36C2×#13133124C2212yes—
37C2×#13133124C2212yes—
38C2×#13133124C2212yes—
39C22×C4⋊C4×C53C2211yescharacteristic
40C22×C4⋊C4×C53C2211yescharacteristic
41C22×C42×C53C2211yescharacteristic
42C2×#95×C53C2212yes—
43C2×#95×C53C2212yes—
44C24×D53C2311yescharacteristic
45C24×D53C2311yescharacteristic
46C22×D212—22no—
47C22×D212—22no—
48C22×D212—22no—
49C22×D212—22no—
50C22×D212—22no—
51C22×D212—22no—
52C22×D212C2×C414yes—
53C23×Dic53C2312yes—
54C23×Dic53C2311yescharacteristic
55C23×Dic53C2312yes—
56C23×Dic53C2311yescharacteristic
57C22×C4×D53—22no—
58C22×C4×D53—22no—
59C22×C4×D53—22no—
60C22×C4×D53—22no—
61C22×C4×D53—22no—
62C22×C4×D53—22no—
63C22×C4×D53—22no—
64C22×C4×D53—22no—
65C22×C4×D53—22no—
66C22×C4×D53—22no—
67C22×C4×D53C2×C414yes—
68C22×C4×D53C2×C414yes—
69C22×C4×D53D414yes—
70C22×C4×D53D414yes—
71C4×D212—232no—
72#13133175—232no—
73C2×C4⋊Dic53—22no—
74C2×C4⋊Dic53—22no—
75C2×C4⋊Dic53—22no—
76C2×C4⋊Dic53—22no—
77C2×C4⋊Dic53—22no—
78C2×C4⋊Dic53—22no—
79C2×C4⋊Dic53—22no—
80C2×C4⋊Dic53C2×C414yes—
81C2×C4⋊Dic53D414yescomplemented
82C2×#11719921—24no—
83C2×#11719921—22no—
84C2×#11719921—22no—
85C2×#11719921—24no—
86C2×#11719921—24no—
87C2×#11719921—24no—
88C2×#11719921—24no—
89C2×#11719921—24no—
90C2×#11719921—24no—
91C2×#11719921—22no—
92C2×#11719921—22no—
93C2×#11719921—24no—
94C2×#11719921—42no—
95C2×#11719921—42no—
96C2×#11719921—42no—
97C2×#11719921—42no—
98C2×#11719921C2×C414yes—
99C2×#11719921C2×C414yes—
100C2×C4×Dic53—24no—
101C2×C4×Dic53—24no—
102C2×C4×Dic53—24no—
103#13133124—24no—
104#13133124—24no—
105#13133124—24no—
106#13133124—24no—
107#13133124—42no—
108C23×C4×C53C2312yes—
109C23×C4×C53C2311yescharacteristic
110C23×C4×C53C2312yes—
111C23×C4×C53C2311yescharacteristic
112C23×C4×C53C2311yescharacteristic
113C2×C4⋊C4×C53—22no—
114C2×C4⋊C4×C53—22no—
115C2×C4⋊C4×C53—22no—
116C2×C4⋊C4×C53—22no—
117C2×C4⋊C4×C53—22no—
118C2×C4⋊C4×C53D414yescomplemented
119C2×C42×C53—22no—
120C2×C42×C53—22no—
121C2×C42×C53C2×C414yes—
122#95×C53—24no—
123#95×C53—42no—
124C24×C53C2411yescharacteristic
125C23×D53—21no—
126C23×D53—21no—
127C23×D53—21no—
128C23×D53—21no—
129C23×D53—21no—
130C23×D53—21no—
131C23×D53—21no—
132C23×D53—21no—
133C23×D53—21no—
134C23×D53—21no—
135C23×D53—21no—
136C23×D53—21no—
137C23×D53—21no—
138C23×D53—21no—
139C23×D53—21no—
140C23×D53—21no—
141C23×D53—21no—
142C23×D53—21no—
143C23×D53—21no—
144C23×D53—21no—
145C23×D53—21no—
146C23×D53—21no—
147C23×D53—21no—
148C23×D53—21no—
149C23×D53C22×C412yes—
150C23×D53C22×C412yes—
151C23×D53C2×D412yes—
152C23×D53C2×D412yes—
153C23×D53#4112yes—
154C23×D53#4112yes—
155C22×C4×C53—21no—
156C22×C4×C53—21no—
157C22×C4×C53—21no—
158C22×C4×C53—21no—
159C22×C4×C53—21no—
160C22×C4×C53—21no—
161C22×C4×C53—22no—
162C22×C4×C53—22no—
163C22×C4×C53—22no—
164C22×C4×C53—22no—
165C22×C4×C53—21no—
166C22×C4×C53—22no—
167C22×C4×C53—21no—
168C22×C4×C53—21no—
169C22×C4×C53—21no—
170C22×C4×C53—22no—
171C22×C4×C53—22no—
172C22×C4×C53—22no—
173C22×C4×C53—22no—
174C22×C4×C53—22no—
175C22×C4×C53—22no—
176C22×C4×C53—22no—
177C22×C4×C53—22no—
178C22×C4×C53C22×C412yes—
179C22×C4×C53C22×C412yes—
180C22×C4×C53C22×C412yes—
181C22×C4×C53C2×D414yes—
182C22×C4×C53C2×D412yes—
183C22×C4×C53C2×D412yes—
184C22×C4×C53C2×D412yes—
185C22×C4×C53C2×D412yes—
186C22×C4×C53#4112yes—
187C22×C4×C53#4112yes—
188C22×C4×C53#4112yes—
189C22×C4×C53#4112yes—
190C22×Dic53—21no—
191C22×Dic53—21no—
192C22×Dic53—21no—
193C22×Dic53—21no—
194C22×Dic53—21no—
195C22×Dic53—21no—
196C22×Dic53—22no—
197C22×Dic53—22no—
198C22×Dic53—21no—
199C22×Dic53—21no—
200C22×Dic53—22no—
201C22×Dic53—22no—
202C22×Dic53—21no—
203C22×Dic53—21no—
204C22×Dic53—22no—
205C22×Dic53—22no—
206C22×Dic53—22no—
207C22×Dic53—22no—
208C22×Dic53—22no—
209C22×Dic53—22no—
210C22×Dic53—22no—
211C22×Dic53—22no—
212C22×Dic53—22no—
213C22×Dic53C22×C412yes—
214C22×Dic53C22×C412yes—
215C22×Dic53C2×D414yes—
216C22×Dic53C2×D412yes—
217C22×Dic53C2×D412yes—
218C2×D212—28no—
219C2×D212—28no—
220C2×D212—28no—
221C2×D212—28no—
222C2×D212—28no—
223C2×D212—28no—
224C2×D212—28no—
225C2×C4×D53—28no—
226C2×C4×D53—28no—
227C2×C4×D53—28no—
228C2×C4×D53—28no—
229C2×C4×D53—28no—
230C2×C4×D53—28no—
231C2×C4×D53—28no—
232C2×C4×D53—28no—
233C2×C4×D53—28no—
234C2×C4×D53—44no—
235C2×C4×D53—44no—
236C2×C4×D53—44no—
237C2×C4×D53—44no—
238C2×C4×D53C22⋊C4116yescomplemented
239C4⋊C4×C53—28no—
240C4⋊C4×C53—44no—
241C42×C53—28no—
242#11719921—216no—
243#11719921—28no—
244#11719921—28no—
245#11719921—48no—
246#11719921—48no—
247#11719921—48no—
248C4⋊Dic53—28no—
249C4⋊Dic53—28no—
250C4⋊Dic53—44no—
251C4×Dic53—216no—
252C23×C53C23×C411yescharacteristic
253C23×C53C22×D411yescharacteristic
254C23×C53C22×D411yescharacteristic
255C23×C53C22×D411yescharacteristic
256C23×C53C22×D411yescharacteristic
257C23×C53C2×#4111yescharacteristic
258C23×C53C2×#4111yescharacteristic
259C23×C53C2×#4111yescharacteristic
260C23×C53C2×#4111yescharacteristic
261C23×C53C2×#4111yescharacteristic
262C23×C53C2×#4111yescharacteristic
263C23×C53H(5,𝔽2)11yescharacteristic
264C23×C53H(5,𝔽2)11yescharacteristic
265C23×C532−1+411yescharacteristic
266C23×C532−1+411yescharacteristic
267C22×D53—22no—
268C22×D53—22no—
269C22×D53—22no—
270C22×D53—22no—
271C22×D53—22no—
272C22×D53—22no—
273C22×D53—22no—
274C22×D53—22no—
275C22×D53—22no—
276C22×D53—22no—
277C22×D53—22no—
278C22×D53—22no—
279C22×D53—22no—
280C22×D53—22no—
281C22×D53—22no—
282C22×D53—22no—
283C22×D53—22no—
284C22×D53—22no—
285C22×D53—22no—
286C22×D53—22no—
287C22×D53—22no—
288C22×D53—22no—
289C22×D53—22no—
290C22×D53—22no—
291C22×D53—22no—
292C22×D53—22no—
293C22×D53—22no—
294C22×D53—22no—
295C22×D53—22no—
296C22×D53—22no—
297C22×D53—22no—
298C22×D53—22no—
299C22×D53—22no—
300C22×D53—22no—
301C22×D53—22no—
302C22×D53—22no—
303C22×D53—41no—
304C22×D53—41no—
305C22×D53—41no—
306C22×D53—41no—
307C22×D53—41no—
308C22×D53—41no—
309C22×D53—41no—
310C22×D53—41no—
311C22×D53—41no—
312C22×D53—41no—
313C22×D53—41no—
314C22×D53—41no—
315C22×D53—41no—
316C22×D53—41no—
317C22×D53—41no—
318C22×D53—41no—
319C22×D53—41no—
320C22×D53—41no—
321C22×D53—41no—
322C22×D53—41no—
323C22×D53—41no—
324C22×D53—41no—
325C22×D53—41no—
326C22×D53—41no—
327C22×D53—41no—
328C22×D53—41no—
329C22×D53—41no—
330C22×D53—41no—
331C22×D53—41no—
332C22×D53—41no—
333C22×D53—41no—
334C22×D53—41no—
335C22×D53C2×C22⋊C414yes—
336C22×D53#11714yescomplemented
337C2×C4×C53—22no—
338C2×C4×C53—22no—
339C2×C4×C53—22no—
340C2×C4×C53—22no—
341C2×C4×C53—22no—
342C2×C4×C53—22no—
343C2×C4×C53—22no—
344C2×C4×C53—22no—
345C2×C4×C53—22no—
346C2×C4×C53—24no—
347C2×C4×C53—24no—
348C2×C4×C53—24no—
349C2×C4×C53—42no—
350C2×C4×C53—41no—
351C2×C4×C53—41no—
352C2×C4×C53—41no—
353C2×C4×C53—42no—
354C2×C4×C53—41no—
355C2×C4×C53—42no—
356C2×C4×C53—42no—
357C2×C4×C53—42no—
358C2×C4×C53—42no—
359C2×C4×C53—42no—
360C2×C4×C53—42no—
361C2×C4×C53—42no—
362C2×C4×C53—42no—
363C2×C4×C53—42no—
364C2×C4×C53C2×C22⋊C414yes—
365C2×C4×C53#11714yescomplemented
366C2×C4×C53C4×D414yes—
367C2×C4×C53C4×D414yes—
368C2×C4×C53#12014yes—
369C2×C4×C53#12114yes—
370C2×C4×C53#12114yes—
371C2×C4×C53#12314yes—
372C2×Dic53—22no—
373C2×Dic53—22no—
374C2×Dic53—22no—
375C2×Dic53—22no—
376C2×Dic53—22no—
377C2×Dic53—22no—
378C2×Dic53—22no—
379C2×Dic53—22no—
380C2×Dic53—22no—
381C2×Dic53—24no—
382C2×Dic53—24no—
383C2×Dic53—24no—
384C2×Dic53—41no—
385C2×Dic53—41no—
386C2×Dic53—41no—
387C2×Dic53—41no—
388C2×Dic53—42no—
389C2×Dic53—42no—
390C2×Dic53—42no—
391C2×Dic53—42no—
392C2×Dic53—42no—
393C2×Dic53—42no—
394C2×Dic53—42no—
395C2×Dic53—42no—
396C2×Dic53—42no—
397C2×Dic53—42no—
398C2×Dic53—42no—
399C2×Dic53C2×C22⋊C414yes—
400D212—232no—
401C4×D53—232no—
402C4×D53—416no—
403#13871—531nomaximal, Sylow
404C22×C53C22×C22⋊C411yescharacteristic
405C22×C53C2×#11711yescharacteristic
406C22×C53C2×#11711yescharacteristic
407C22×C53C2×C4×D411yescharacteristic
408C22×C53C2×C4×D411yescharacteristic
409C22×C53#52011yescharacteristic
410C22×C53#52011yescharacteristic
411C22×C53C2×#12011yescharacteristic
412C22×C53C2×#12111yescharacteristic
413C22×C53C2×#12111yescharacteristic
414C22×C53C2×#12311yescharacteristic
415C22×C53#52511yescharacteristic
416C22×C53#52511yescharacteristic
417C22×C53#52511yescharacteristic
418C22×C53#52511yescharacteristic
419C22×C53#53511yescharacteristic
420C22×C53#53611yescharacteristic
421C22×C53#53711yescharacteristic
422C22×C53#53711yescharacteristic
423C22×C53#54611yescharacteristic
424C22×C53#54611yescharacteristic
425C22×C53#54711yescharacteristic
426C22×C53#54711yescharacteristic
427C22×C53#54811yescharacteristic
428C22×C53#54811yescharacteristic
429C22×C53#55011yescharacteristic
430C22×C53#55011yescharacteristic
431C22×C53#55211yescharacteristic
432C22×C53#55211yescharacteristic
433C22×C53#55311yescharacteristic
434C22×C53#55311yescharacteristic
435C22×C53#55511yescharacteristic
436C22×C53#55511yescharacteristic
437C22×C53#55611yescharacteristic
438C22×C53#55611yescharacteristic
439C2×D53—24no—
440C2×D53—24no—
441C2×D53—24no—
442C2×D53—24no—
443C2×D53—24no—
444C2×D53—24no—
445C2×D53—42no—
446C2×D53—42no—
447C2×D53—42no—
448C2×D53—42no—
449C2×D53—42no—
450C2×D53—42no—
451C2×D53—42no—
452C2×D53—42no—
453C2×D53—42no—
454C2×D53—42no—
455C2×D53—42no—
456C2×D53—42no—
457C2×D53—42no—
458C2×D53—42no—
459C2×D53—42no—
460C2×D53—42no—
461C2×D53—42no—
462C2×D53—42no—
463C2×D53—42no—
464C2×D53—42no—
465C2×D53—42no—
466C2×D53—42no—
467C2×D53—42no—
468C2×D53—42no—
469C4×C53—24no—
470C4×C53—42no—
471C4×C53—44no—
472C4×C53—82no—
473C4×C53#38618yes—
474Dic53—24no—
475Dic53—44no—
476Dic53—42no—
477Dic53—82no—
478C22×C4×D4—531no—
479C22×#117—531no—
480C2×#380—531no—
481C2×#380—531no—
482C2×#380—531no—
483#1440—532no—
484#1438—532no—
485#1437—532no—
486#1436—532no—
487C4⋊#95—531no—
488C4⋊#95D5311yescharacteristic, complemented
489C2×C53#228011yescharacteristic
490C2×C53C2×#38611yescharacteristic
491C2×C53#231111yescharacteristic
492C2×C53#235211yescharacteristic
493C2×C53#235211yescharacteristic
494C2×C53#235411yescharacteristic
495C2×C53#235411yescharacteristic
496C2×C53#240711yescharacteristic
497C2×C53#240711yescharacteristic
498C2×C53#241411yescharacteristic
499C2×C53#241411yescharacteristic
500C2×C53#241511yescharacteristic
501C2×C53#241511yescharacteristic
502C2×C53#248511yescharacteristic
503C2×C53#248511yescharacteristic
504D53—44no—
505D53—44no—
506C23×D4—531no—
507C24×C4—531no—
508C24×C4—531no—
509C2×C4×D4—538no—
510C2×C4×D4—1064no—
511C2×C4×D4—1064no—
512C2×#117—1064no—
513C2×#117—1064no—
514C2×#117—1064no—
515C22×C4⋊C4—531no—
516C22×C4⋊C4—531no—
517C22×C4⋊C4—531no—
518C22×C4⋊C4C2×D5311yescharacteristic
519C22×C4⋊C4C2×D5311yescharacteristic
520C22×C22⋊C4—531no—
521C22×C22⋊C4—531no—
522C22×C22⋊C4—532no—
523C22×C22⋊C4—532no—
524C22×C22⋊C4—532no—
525C22×C22⋊C4—532no—
526C22×C42—532no—
527C22×C42C2×D5311yescharacteristic
528#380—1064no—
529#380—1064no—
530#380—1064no—
531C2×#95—532no—
532C2×#95—532no—
533C2×#95—532no—
534C2×#95—532no—
535C2×#95—532no—
536C2×#95C2×D5312yes—
537C2×#95C2×D5312yes—
538C53#1387111yescharacteristic, complemented, Sylow
539C25—531no—
540C25—531no—
541C22×D4—534no—
542C22×D4—1062no—
543C22×D4—1062no—
544C22×D4—1062no—
545C22×D4—1062no—
546C22×D4—1062no—
547C22×D4—1062no—
548C23×C4—531no—
549C23×C4—534no—
550C23×C4—534no—
551C23×C4—534no—
552C23×C4—532no—
553C23×C4—531no—
554C23×C4—534no—
555C23×C4—532no—
556C23×C4—1062no—
557C23×C4—1062no—
558C23×C4—1062no—
559C23×C4—1062no—
560C23×C4—1062no—
561C23×C4—1062no—
562C23×C4—1062no—
563C23×C4—1062no—
564C23×C4—1062no—
565C23×C4—1062no—
566C23×C4C22×D5312yes—
567C23×C4C22×D5311yescharacteristic
568C23×C4C22×D5312yes—
569C23×C4C22×D5311yescharacteristic
570C23×C4C22×D5311yescharacteristic
571C4×D4—10632no—
572#117—10632no—
573C2×C4⋊C4—22no—
574C2×C4⋊C4—22no—
575C2×C4⋊C4—22no—
576C2×C4⋊C4—22no—
577C2×C4⋊C4—22no—
578C2×C4⋊C4—534no—
579C2×C4⋊C4—534no—
580C2×C4⋊C4—1062no—
581C2×C4⋊C4—1062no—
582C2×C4⋊C4—1062no—
583C2×C4⋊C4—1062no—
584C2×C4⋊C4—1062no—
585C2×C4⋊C4—1062no—
586C2×C4⋊C4—1062no—
587C2×C4⋊C4D21214yescomplemented
588C2×C22⋊C4—534no—
589C2×C22⋊C4—534no—
590C2×C22⋊C4—1064no—
591C2×C22⋊C4—1062no—
592C2×C22⋊C4—1062no—
593C2×C22⋊C4—1064no—
594C2×C22⋊C4—1062no—
595C2×C22⋊C4—1062no—
596C2×C22⋊C4—1064no—
597C2×C22⋊C4—1064no—
598C2×C22⋊C4—1064no—
599C2×C22⋊C4—1064no—
600C2×C22⋊C4—1064no—
601C2×C22⋊C4—1064no—
602C2×C22⋊C4—2122no—
603C2×C22⋊C4—2122no—
604C2×C22⋊C4—2122no—
605C2×C22⋊C4—2122no—
606C2×C42—22no—
607C2×C42—22no—
608C2×C42—1064no—
609C2×C42—1064no—
610C2×C42—1064no—
611C2×C42C4×D5314yes—
612#95—24no—
613#95—42no—
614#95—1064no—
615#95—1064no—
616#95—1064no—
617#95—1064no—
618#95—2122no—
619C24—532no—
620C24—532no—
621C24—532no—
622C24—532no—
623C24—532no—
624C24—532no—
625C24—1061no—
626C24—1061no—
627C24—1061no—
628C24—1061no—
629C24—1061no—
630C24—1061no—
631C24—1061no—
632C24—1061no—
633C24—1061no—
634C24—1061no—
635C24—1061no—
636C24—1061no—
637C24—1061no—
638C24—1061no—
639C24—1061no—
640C24—1061no—
641C24—1061no—
642C24—1061no—
643C24—1061no—
644C24—1061no—
645C24—1061no—
646C24—1061no—
647C24—1061no—
648C24—1061no—
649C24C23×D5311yescharacteristic
650C2×D4—1068no—
651C2×D4—1068no—
652C2×D4—1068no—
653C2×D4—1068no—
654C2×D4—1068no—
655C2×D4—1068no—
656C2×D4—1068no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—22no—
664C22×C4—22no—
665C22×C4—22no—
666C22×C4—22no—
667C22×C4—21no—
668C22×C4—22no—
669C22×C4—21no—
670C22×C4—22no—
671C22×C4—21no—
672C22×C4—21no—
673C22×C4—22no—
674C22×C4—22no—
675C22×C4—22no—
676C22×C4—22no—
677C22×C4—22no—
678C22×C4—22no—
679C22×C4—22no—
680C22×C4—532no—
681C22×C4—532no—
682C22×C4—532no—
683C22×C4—5316no—
684C22×C4—532no—
685C22×C4—534no—
686C22×C4—1061no—
687C22×C4—1061no—
688C22×C4—1061no—
689C22×C4—1061no—
690C22×C4—1068no—
691C22×C4—1068no—
692C22×C4—1068no—
693C22×C4—1068no—
694C22×C4—1068no—
695C22×C4—1068no—
696C22×C4—1061no—
697C22×C4—1062no—
698C22×C4—1061no—
699C22×C4—1061no—
700C22×C4—1061no—
701C22×C4—1062no—
702C22×C4—1062no—
703C22×C4—1061no—
704C22×C4—1062no—
705C22×C4—1061no—
706C22×C4—1062no—
707C22×C4—1062no—
708C22×C4—1068no—
709C22×C4—1068no—
710C22×C4—1068no—
711C22×C4—1062no—
712C22×C4—1062no—
713C22×C4—1062no—
714C22×C4—1062no—
715C22×C4—1062no—
716C22×C4—1062no—
717C22×C4—1062no—
718C22×C4—2124no—
719C22×C4—2124no—
720C22×C4—2124no—
721C22×C4—2124no—
722C22×C4C2×C4×D5312yes—
723C22×C4C2×C4×D5312yes—
724C22×C4C2×C4×D5312yes—
725C22×C4C2×D21214yes—
726C22×C4C2×D21212yes—
727C22×C4#1171994512yes—
728C22×C4D4×D5312yes—
729C22×C4D4×D5312yes—
730C22×C4D4×D5312yes—
731C22×C4#1171994712yes—
732C22×C4#1171994912yes—
733C22×C4#1171994912yes—
734C4⋊C4—28no—
735C4⋊C4—44no—
736C4⋊C4—1068no—
737C4⋊C4—1068no—
738C4⋊C4—2124no—
739C22⋊C4—1068no—
740C22⋊C4—1068no—
741C22⋊C4—10616no—
742C22⋊C4—2128no—
743C22⋊C4—2128no—
744C22⋊C4—2128no—
745C42—28no—
746C42—10616no—
747C23—534no—
748C23—534no—
749C23—1062no—
750C23—1062no—
751C23—1062no—
752C23—1062no—
753C23—1062no—
754C23—1062no—
755C23—1062no—
756C23—1062no—
757C23—1062no—
758C23—1062no—
759C23—1062no—
760C23—1062no—
761C23—1062no—
762C23—1062no—
763C23—1062no—
764C23—1062no—
765C23—1062no—
766C23—1062no—
767C23—1062no—
768C23—1062no—
769C23—1062no—
770C23—1062no—
771C23—1062no—
772C23—1062no—
773C23—1062no—
774C23—1062no—
775C23—1062no—
776C23—1062no—
777C23—1062no—
778C23—1062no—
779C23—1062no—
780C23—1062no—
781C23—1062no—
782C23—1062no—
783C23—1062no—
784C23—1062no—
785C23—2121no—
786C23—2121no—
787C23—2121no—
788C23—2121no—
789C23—2121no—
790C23—2121no—
791C23—2121no—
792C23—2121no—
793C23—2121no—
794C23—2121no—
795C23—2121no—
796C23—2121no—
797C23—2121no—
798C23—2121no—
799C23—2121no—
800C23—2121no—
801C23—2121no—
802C23—2121no—
803C23—2121no—
804C23—2121no—
805C23—2121no—
806C23—2121no—
807C23—2121no—
808C23—2121no—
809C23—2121no—
810C23—2121no—
811C23—2121no—
812C23—2121no—
813C23—2121no—
814C23—2121no—
815C23—2121no—
816C23—2121no—
817C23C22×C4×D5311yescharacteristic
818C23C2×D4×D5311yescharacteristic
819C23C2×D4×D5311yescharacteristic
820C23C2×D4×D5311yescharacteristic
821C23C22×D21211yescharacteristic
822C23#41×D5311yescharacteristic
823C23#41×D5311yescharacteristic
824C23C2×#1171994711yescharacteristic
825C23C2×#1171994511yescharacteristic
826C23C2×#1171994911yescharacteristic
827C23C2×#1171994911yescharacteristic
828C23#1313326211yescharacteristic
829C23#1313326311yescharacteristic
830C23#1313326411yescharacteristic
831C23#1313326511yescharacteristic
832D4—10632no—
833C2×C4—22no—
834C2×C4—22no—
835C2×C4—22no—
836C2×C4—22no—
837C2×C4—22no—
838C2×C4—22no—
839C2×C4—24no—
840C2×C4—24no—
841C2×C4—22no—
842C2×C4—22no—
843C2×C4—22no—
844C2×C4—24no—
845C2×C4—42no—
846C2×C4—42no—
847C2×C4—42no—
848C2×C4—41no—
849C2×C4—41no—
850C2×C4—42no—
851C2×C4—41no—
852C2×C4—41no—
853C2×C4—42no—
854C2×C4—42no—
855C2×C4—42no—
856C2×C4—42no—
857C2×C4—42no—
858C2×C4—42no—
859C2×C4—42no—
860C2×C4—534no—
861C2×C4—1062no—
862C2×C4—1062no—
863C2×C4—1062no—
864C2×C4—1062no—
865C2×C4—1062no—
866C2×C4—1062no—
867C2×C4—10632no—
868C2×C4—1064no—
869C2×C4—1064no—
870C2×C4—1062no—
871C2×C4—1062no—
872C2×C4—1062no—
873C2×C4—1064no—
874C2×C4—2122no—
875C2×C4—2122no—
876C2×C4—2122no—
877C2×C4—2122no—
878C2×C4—2122no—
879C2×C4—2122no—
880C2×C4—2122no—
881C2×C4—2122no—
882C2×C4—2122no—
883C2×C4—2121no—
884C2×C4—2121no—
885C2×C4—2121no—
886C2×C4—2121no—
887C2×C4—2122no—
888C2×C4—2122no—
889C2×C4—21216no—
890C2×C4C22⋊C4×D5314yes—
891C2×C4#1313317514yescomplemented
892C2×C4#1313317914yes—
893C2×C4C4×D21214yes—
894C2×C4#1313318714yes—
895C2×C4#1313319014yes—
896C2×C4#1313319214yes—
897C2×C4#1313320214yes—
898C22—1064no—
899C22—1064no—
900C22—1064no—
901C22—1064no—
902C22—1064no—
903C22—1064no—
904C22—2122no—
905C22—2122no—
906C22—2122no—
907C22—2122no—
908C22—2122no—
909C22—2122no—
910C22—2122no—
911C22—2122no—
912C22—2122no—
913C22—2122no—
914C22—2122no—
915C22—2122no—
916C22—2122no—
917C22—2122no—
918C22—2122no—
919C22—2122no—
920C22—2122no—
921C22—2122no—
922C22—2122no—
923C22—2122no—
924C22—2122no—
925C22—2122no—
926C22—2122no—
927C22—2122no—
928C22C2×C22⋊C4×D5311yescharacteristic
929C22#117×D5311yescharacteristic
930C22C2×#1313317511yescharacteristic
931C22C2×#1313317911yescharacteristic
932C22C2×C4×D21211yescharacteristic
933C22#1681110311yescharacteristic
934C22#1681110411yescharacteristic
935C22C2×#1313318711yescharacteristic
936C22C2×#1313319011yescharacteristic
937C22C2×#1313319211yescharacteristic
938C22C2×#1313320211yescharacteristic
939C22#1681113311yescharacteristic
940C22#1681113311yescharacteristic
941C22#1681113611yescharacteristic
942C22#1681113611yescharacteristic
943C22#1681118911yescharacteristic
944C22#1681119611yescharacteristic
945C22#1681120211yescharacteristic
946C22#1681120311yescharacteristic
947C22#1681126611yescharacteristic
948C22#1681126811yescharacteristic
949C22#1681127611yescharacteristic
950C22#1681127711yescharacteristic
951C22#1681128111yescharacteristic
952C22#1681128511yescharacteristic
953C22#1681129311yescharacteristic
954C22#1681129511yescharacteristic
955C22#1681131111yescharacteristic
956C22#1681131411yescharacteristic
957C22#1681132311yescharacteristic
958C22#1681132611yescharacteristic
959C22#1681133811yescharacteristic
960C22#1681133911yescharacteristic
961C22#1681134611yescharacteristic
962C22#1681134711yescharacteristic
963C4—24no—
964C4—44no—
965C4—42no—
966C4—82no—
967C4—1064no—
968C4—4242no—
969C4—2124no—
970C4—2122no—
971C4#1681050118yes—
972C2—2124no—
973C2—2124no—
974C2#2027709711yescharacteristic
975C2C2×#1681050111yescharacteristic
976C2#2027730411yescharacteristic
977C2#2027764111yescharacteristic
978C2#2027764711yescharacteristic
979C2#2027766211yescharacteristic
980C2#2027766611yescharacteristic
981C2#2027805811yescharacteristic
982C2#2027806311yescharacteristic
983C2#2027813111yescharacteristic
984C2#2027813611yescharacteristic
985C2#2027814211yescharacteristic
986C2#2027814711yescharacteristic
987C2#2027901011yescharacteristic
988C2#2027901511yescharacteristic
subgroupG/H
center, FrattiniC24C23×D53
commutatorC23×C53C23×C4
FittingC53×C4⋊#95C2
socle, cosocleC24×C53C24
prime radicalC23×D212C22
hypercenterC4⋊#95D53
hypocenterC53#13871
LCSG ▷ C23×C53 ▷ C53
UCSC1 ◁ C24 ◁ C4⋊#95

Complements

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

NH ≅ G/Ntype
2. C22×#13133175C2semidirect
3. C2×#16810480C2semidirect
4. C2×#16810480C2semidirect
5. C2×#16810480C2semidirect
6. #20272963C2semidirect
8. #20272951C2semidirect
9. #20272949C2semidirect
10. #20272945C2semidirect
11. C53×C4⋊#95C2semidirect
17. C2×C4×D212C4semidirect
81. C2×C4⋊Dic53D4semidirect
118. C2×C4⋊C4×C53D4semidirect
238. C2×C4×D53C22⋊C4semidirect
336. C22×D53#117semidirect
365. C2×C4×C53#117semidirect
488. C4⋊#95D53semidirect
538. C53#13871semidirect
587. C2×C4⋊C4D212semidirect
891. C2×C4#13133175semidirect

Maximal subgroups

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

subgroupindex
C22×C4×D2122
C22×#131331752
C2×#168104802
#202729632
#202729552
#202729512
#202729492
#202729452
C53×C4⋊#952
#1387153