Finite Group Databasebeta

← #27307490

Subgroups — #27307490

Order 13568.

2474 conjugacy classes of subgroups.

The subgroup lattice has 862 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×D212C211yesmaximal, characteristic
2C2×#16810524C211yesmaximal, characteristic
3C2×#16810524C211yesmaximal, characteristic
4C2×#16810522C211yesmaximal, characteristic, complemented
5C2×#16810497C212yesmaximal, complemented
6C2×C4×#11719919C211yesmaximal, characteristic, complemented
7#20272961C212yesmaximal, complemented
8#20272959C212yesmaximal, complemented
9#20272944C211yesmaximal, characteristic, complemented
10#20272936C212yesmaximal, complemented
11C53×C4⋊#95C211yesmaximal, characteristic, complemented
12C23×D212C2211yescharacteristic
13C23×C4×D53C2212yes—
14C2×C4×D212—24no—
15C2×C4×D212—24no—
16C2×C4×D212—24no—
17C22×C4⋊Dic53C2212yes—
18C22×C4⋊Dic53C2211yescharacteristic
19C22×#11719919C2211yescharacteristic
20C22×#11719919C2211yescharacteristic
21C22×#11719921C2212yes—
22C22×#11719921C2212yes—
23C22×#11719921C2212yes—
24C22×#11719921C2212yes—
25C22×#11719921C2212yes—
26C22×C4×Dic53C2211yescharacteristic
27C22×C4×Dic53C2211yescharacteristic
28#16810524—24no—
29#16810524C418yescomplemented
30#16810522—24no—
31#16810497—28no—
32C4×#11719919—24no—
33C2×#13133124C2211yescharacteristic
34C2×#13133124C2212yes—
35C2×#13133124C2212yes—
36C2×#13133124C2211yescharacteristic
37C2×#13133124C2212yes—
38C22×C4⋊C4×C53C2211yescharacteristic
39C22×C4⋊C4×C53C2211yescharacteristic
40C22×C42×C53C2211yescharacteristic
41C2×#95×C53C2212yes—
42C2×#95×C53C2212yes—
43C24×D53C2312yes—
44C22×D212—22no—
45C22×D212—22no—
46C22×D212—22no—
47C22×D212—22no—
48C22×D212C2×C414yes—
49C22×D212D414yes—
50C22×D212Q814yes—
51C23×Dic53C2311yescharacteristic
52C23×Dic53C2311yescharacteristic
53C23×Dic53C2312yes—
54C23×Dic53C2311yescharacteristic
55C23×Dic53C2311yescharacteristic
56C22×C4×D53—24no—
57C22×C4×D53—24no—
58C22×C4×D53—24no—
59C22×C4×D53—24no—
60C22×C4×D53—24no—
61C22×C4×D53—42no—
62C22×C4×D53—42no—
63C4×D212—232no—
64C2×C4⋊Dic53—22no—
65C2×C4⋊Dic53—22no—
66C2×C4⋊Dic53—24no—
67C2×C4⋊Dic53—24no—
68C2×C4⋊Dic53—42no—
69C2×C4⋊Dic53D414yes—
70C2×#11719919—22no—
71C2×#11719919—22no—
72C2×#11719919—22no—
73C2×#11719919—22no—
74C2×#11719919—22no—
75C2×#11719919D414yescomplemented
76C2×#11719921—24no—
77C2×#11719921—24no—
78C2×#11719921—24no—
79C2×#11719921—24no—
80C2×#11719921—24no—
81C2×#11719921—24no—
82C2×#11719921—24no—
83C2×#11719921—24no—
84C2×#11719921—24no—
85C2×#11719921—42no—
86C2×#11719921—42no—
87C2×#11719921—42no—
88C2×#11719921—42no—
89C2×#11719921C2×C418yescomplemented
90C2×#11719921C2×C418yescomplemented
91C2×C4×Dic53—22no—
92C2×C4×Dic53—22no—
93C2×C4×Dic53—22no—
94C2×C4×Dic53—22no—
95C2×C4×Dic53—22no—
96C2×C4×Dic53C2×C414yescomplemented
97#13133124—22no—
98#13133124—22no—
99#13133124—24no—
100#13133124—24no—
101#13133124—42no—
102C23×C4×C53C2312yes—
103C23×C4×C53C2312yes—
104C23×C4×C53C2311yescharacteristic
105C23×C4×C53C2311yescharacteristic
106C23×C4×C53C2311yescharacteristic
107C2×C4⋊C4×C53—22no—
108C2×C4⋊C4×C53—22no—
109C2×C4⋊C4×C53—22no—
110C2×C4⋊C4×C53—22no—
111C2×C4⋊C4×C53—22no—
112C2×C4⋊C4×C53C2×C414yescomplemented
113C2×C42×C53—22no—
114C2×C42×C53—22no—
115C2×C42×C53D414yes—
116#95×C53—24no—
117#95×C53—42no—
118C24×C53C2411yescharacteristic
119C23×D53—22no—
120C23×D53—22no—
121C23×D53—22no—
122C23×D53—22no—
123C23×D53—22no—
124C23×D53—22no—
125C23×D53—22no—
126C23×D53—22no—
127C23×D53—22no—
128C23×D53—22no—
129C23×D53—22no—
130C23×D53—22no—
131C23×D53C22×C414yes—
132C23×D53C2×D414yes—
133C23×D53C2×Q814yes—
134C22×C4×C53—21no—
135C22×C4×C53—21no—
136C22×C4×C53—21no—
137C22×C4×C53—21no—
138C22×C4×C53—22no—
139C22×C4×C53—21no—
140C22×C4×C53—21no—
141C22×C4×C53—22no—
142C22×C4×C53—22no—
143C22×C4×C53—22no—
144C22×C4×C53—21no—
145C22×C4×C53—21no—
146C22×C4×C53—21no—
147C22×C4×C53—22no—
148C22×C4×C53—22no—
149C22×C4×C53—21no—
150C22×C4×C53—22no—
151C22×C4×C53—22no—
152C22×C4×C53—22no—
153C22×C4×C53—22no—
154C22×C4×C53—22no—
155C22×C4×C53—22no—
156C22×C4×C53—22no—
157C22×C4×C53C22×C414yes—
158C22×C4×C53C22×C412yes—
159C22×C4×C53C2×D412yes—
160C22×C4×C53C2×D412yes—
161C22×C4×C53C2×D412yes—
162C22×C4×C53C2×D412yes—
163C22×C4×C53C2×D412yes—
164C22×C4×C53C2×D412yes—
165C22×C4×C53C2×Q812yes—
166C22×C4×C53#4112yes—
167C22×C4×C53#4112yes—
168C22×C4×C53#4112yes—
169C22×Dic53—21no—
170C22×Dic53—21no—
171C22×Dic53—21no—
172C22×Dic53—21no—
173C22×Dic53—21no—
174C22×Dic53—21no—
175C22×Dic53—21no—
176C22×Dic53—21no—
177C22×Dic53—22no—
178C22×Dic53—21no—
179C22×Dic53—21no—
180C22×Dic53—21no—
181C22×Dic53—22no—
182C22×Dic53—22no—
183C22×Dic53—21no—
184C22×Dic53—21no—
185C22×Dic53—21no—
186C22×Dic53—22no—
187C22×Dic53—21no—
188C22×Dic53—22no—
189C22×Dic53—21no—
190C22×Dic53—21no—
191C22×Dic53—21no—
192C22×Dic53—21no—
193C22×Dic53—21no—
194C22×Dic53—22no—
195C22×Dic53—21no—
196C22×Dic53—21no—
197C22×Dic53C22×C412yes—
198C22×Dic53C22×C412yes—
199C22×Dic53C2×D414yes—
200C22×Dic53C2×D412yes—
201C22×Dic53C2×D412yes—
202C22×Dic53#4112yes—
203C22×Dic53#4112yes—
204C2×D212—28no—
205C2×D212—28no—
206C2×D212—28no—
207C2×D212—28no—
208C2×D212—28no—
209C2×D212—28no—
210C2×D212C4⋊C4116yescomplemented
211C2×C4×D53—216no—
212C2×C4×D53—48no—
213C2×C4×D53—48no—
214C2×C4×D53—48no—
215C2×C4×D53—48no—
216C2×C4×D53—48no—
217C2×C4×D53—48no—
218C4⋊C4×C53—28no—
219C4⋊C4×C53—44no—
220C42×C53—28no—
221#11719921—216no—
222#11719921—216no—
223#11719921—48no—
224#11719921—48no—
225#11719921—48no—
226C4⋊Dic53—28no—
227C4⋊Dic53—48no—
228#11719919—28no—
229#11719919—28no—
230C4×Dic53—28no—
231C4×Dic53—44no—
232C23×C53C23×C411yescharacteristic
233C23×C53C22×D411yescharacteristic
234C23×C53C22×D411yescharacteristic
235C23×C53C22×D411yescharacteristic
236C23×C53C22×D411yescharacteristic
237C23×C53C22×Q811yescharacteristic
238C23×C53C2×#4111yescharacteristic
239C23×C53C2×#4111yescharacteristic
240C23×C53C2×#4111yescharacteristic
241C23×C53C2×#4111yescharacteristic
242C23×C53C2×#4111yescharacteristic
243C23×C53H(5,𝔽2)11yescharacteristic
244C23×C53H(5,𝔽2)11yescharacteristic
245C23×C53H(5,𝔽2)11yescharacteristic
246C23×C532−1+411yescharacteristic
247C22×D53—24no—
248C22×D53—24no—
249C22×D53—24no—
250C22×D53—24no—
251C22×D53—24no—
252C22×D53—24no—
253C22×D53—24no—
254C22×D53—24no—
255C22×D53—24no—
256C22×D53—24no—
257C22×D53—24no—
258C22×D53—24no—
259C22×D53—24no—
260C22×D53—24no—
261C22×D53—24no—
262C22×D53—24no—
263C22×D53—24no—
264C22×D53—24no—
265C22×D53—42no—
266C22×D53—42no—
267C22×D53—42no—
268C22×D53—42no—
269C22×D53—42no—
270C22×D53—42no—
271C22×D53—42no—
272C22×D53—42no—
273C22×D53—42no—
274C22×D53—42no—
275C22×D53—42no—
276C22×D53—42no—
277C22×D53—42no—
278C22×D53—42no—
279C22×D53—42no—
280C22×D53—42no—
281C22×D53C2×C4⋊C418yes—
282C2×C4×C53—22no—
283C2×C4×C53—22no—
284C2×C4×C53—22no—
285C2×C4×C53—22no—
286C2×C4×C53—22no—
287C2×C4×C53—22no—
288C2×C4×C53—24no—
289C2×C4×C53—24no—
290C2×C4×C53—24no—
291C2×C4×C53—22no—
292C2×C4×C53—22no—
293C2×C4×C53—22no—
294C2×C4×C53—42no—
295C2×C4×C53—41no—
296C2×C4×C53—41no—
297C2×C4×C53—41no—
298C2×C4×C53—42no—
299C2×C4×C53—41no—
300C2×C4×C53—42no—
301C2×C4×C53—42no—
302C2×C4×C53—42no—
303C2×C4×C53—42no—
304C2×C4×C53—42no—
305C2×C4×C53—42no—
306C2×C4×C53—42no—
307C2×C4×C53—42no—
308C2×C4×C53—42no—
309C2×C4×C53C2×C4⋊C414yes—
310C2×C4×C53C4×D414yes—
311C2×C4×C53C4×D414yes—
312C2×C4×C53#12014yes—
313C2×C4×C53#12114yes—
314C2×C4×C53C22⋊Q814yes—
315C2×C4×C53C22⋊Q814yes—
316C2×C4×C53#12314yes—
317C2×Dic53—22no—
318C2×Dic53—22no—
319C2×Dic53—22no—
320C2×Dic53—22no—
321C2×Dic53—22no—
322C2×Dic53—22no—
323C2×Dic53—22no—
324C2×Dic53—22no—
325C2×Dic53—22no—
326C2×Dic53—24no—
327C2×Dic53—22no—
328C2×Dic53—22no—
329C2×Dic53—24no—
330C2×Dic53—22no—
331C2×Dic53—22no—
332C2×Dic53—24no—
333C2×Dic53—22no—
334C2×Dic53—22no—
335C2×Dic53—41no—
336C2×Dic53—41no—
337C2×Dic53—42no—
338C2×Dic53—42no—
339C2×Dic53—41no—
340C2×Dic53—41no—
341C2×Dic53—41no—
342C2×Dic53—41no—
343C2×Dic53—41no—
344C2×Dic53—41no—
345C2×Dic53—42no—
346C2×Dic53—42no—
347C2×Dic53—41no—
348C2×Dic53—41no—
349C2×Dic53—41no—
350C2×Dic53—41no—
351C2×Dic53C4×D414yescomplemented
352D212—232no—
353C4×D53—432no—
354#14018—531nomaximal, Sylow
355C22×C53C22×C4⋊C411yescharacteristic
356C22×C53C2×C4×D411yescharacteristic
357C22×C53C2×C4×D411yescharacteristic
358C22×C53C2×C4×D411yescharacteristic
359C22×C53C4×#4111yescharacteristic
360C22×C53#51811yescharacteristic
361C22×C53#52011yescharacteristic
362C22×C53C2×#12011yescharacteristic
363C22×C53C2×#12111yescharacteristic
364C22×C53C2×C22⋊Q811yescharacteristic
365C22×C53C2×C22⋊Q811yescharacteristic
366C22×C53C2×#12311yescharacteristic
367C22×C53#52511yescharacteristic
368C22×C53#52911yescharacteristic
369C22×C53#53211yescharacteristic
370C22×C53#53511yescharacteristic
371C22×C53#53711yescharacteristic
372C22×C53#54011yescharacteristic
373C22×C53#54211yescharacteristic
374C22×C53D4211yescharacteristic
375C22×C53D4211yescharacteristic
376C22×C53#54611yescharacteristic
377C22×C53#54611yescharacteristic
378C22×C53#54611yescharacteristic
379C22×C53#54711yescharacteristic
380C22×C53#54811yescharacteristic
381C22×C53D4×Q811yescharacteristic
382C22×C53#55011yescharacteristic
383C22×C53#55011yescharacteristic
384C22×C53#55411yescharacteristic
385C22×C53#55411yescharacteristic
386C22×C53#55411yescharacteristic
387C22×C53#55611yescharacteristic
388C22×C53#55911yescharacteristic
389C22×C53#55911yescharacteristic
390C2×D53—28no—
391C2×D53—28no—
392C2×D53—28no—
393C2×D53—44no—
394C2×D53—44no—
395C2×D53—44no—
396C2×D53—44no—
397C2×D53—44no—
398C2×D53—44no—
399C2×D53—44no—
400C2×D53—44no—
401C2×D53—44no—
402C2×D53—44no—
403C2×D53—44no—
404C2×D53—44no—
405C4×C53—24no—
406C4×C53—44no—
407C4×C53—42no—
408C4×C53—82no—
409C4×C53#38518yescomplemented
410Dic53—24no—
411Dic53—42no—
412Dic53—42no—
413Dic53—44no—
414Dic53—42no—
415C22×C4×D4—531no—
416C2×#390—531no—
417C2×#390—531no—
418C2×#389—531no—
419C2×#385—532no—
420C2×C4×C4⋊C4—531no—
421#1439—532no—
422#1439—532no—
423C4⋊#95—531no—
424C4⋊#95D5311yescharacteristic, complemented
425C22⋊#95—532no—
426C2×C53C2×#38511yescharacteristic
427C2×C53C4×#12111yescharacteristic
428C2×C53#232411yescharacteristic
429C2×C53D4×C4⋊C411yescharacteristic
430C2×C53#234911yescharacteristic
431C2×C53#236611yescharacteristic
432C2×C53#236711yescharacteristic
433C2×C53#240711yescharacteristic
434C2×C53#240811yescharacteristic
435C2×C53#244511yescharacteristic
436C2×C53#244711yescharacteristic
437C2×C53#245211yescharacteristic
438C2×C53#245411yescharacteristic
439C2×C53#253811yescharacteristic
440C2×C53#258011yescharacteristic
441D53—48no—
442C23×D4—531no—
443C24×C4—532no—
444C2×C4×D4—1064no—
445C2×C4×D4—1064no—
446C2×C4×D4—1064no—
447C22×C4⋊C4—531no—
448C22×C4⋊C4—531no—
449C22×C4⋊C4—531no—
450C22×C4⋊C4—532no—
451C22×C4⋊C4C2×D5311yescharacteristic
452C22×C4⋊C4C2×D5311yescharacteristic
453C22×C22⋊C4—532no—
454C22×C22⋊C4—532no—
455C22×C22⋊C4—532no—
456C22×C22⋊C4—532no—
457C22×C22⋊C4—532no—
458C22×C42—531no—
459C22×C42—531no—
460C22×C42C2×D5311yescharacteristic
461#390—538no—
462#390—1064no—
463#389—1064no—
464#385—1068no—
465C4×C4⋊C4—1064no—
466C2×#95—531no—
467C2×#95—532no—
468C2×#95—532no—
469C2×#95—531no—
470C2×#95—532no—
471C2×#95C2×D5312yes—
472C2×#95C2×D5312yes—
473C53#1401811yescharacteristic, complemented, Sylow
474C25—532no—
475C22×D4—534no—
476C22×D4—534no—
477C22×D4—534no—
478C22×D4—1062no—
479C22×D4—1062no—
480C22×D4—1062no—
481C22×D4—1062no—
482C23×C4—531no—
483C23×C4—531no—
484C23×C4—531no—
485C23×C4—531no—
486C23×C4—532no—
487C23×C4—1064no—
488C23×C4—1064no—
489C23×C4—1064no—
490C23×C4—1064no—
491C23×C4—1064no—
492C23×C4—2122no—
493C23×C4—2122no—
494C23×C4C22×D5312yes—
495C23×C4C22×D5312yes—
496C23×C4C22×D5311yescharacteristic
497C23×C4C22×D5311yescharacteristic
498C23×C4C22×D5311yescharacteristic
499C4×D4—10632no—
500C2×C4⋊C4—22no—
501C2×C4⋊C4—22no—
502C2×C4⋊C4—22no—
503C2×C4⋊C4—22no—
504C2×C4⋊C4—22no—
505C2×C4⋊C4—534no—
506C2×C4⋊C4—534no—
507C2×C4⋊C4—1062no—
508C2×C4⋊C4—1062no—
509C2×C4⋊C4—1062no—
510C2×C4⋊C4—1062no—
511C2×C4⋊C4—1062no—
512C2×C4⋊C4—1062no—
513C2×C4⋊C4—1062no—
514C2×C4⋊C4—1064no—
515C2×C4⋊C4—1064no—
516C2×C4⋊C4—2122no—
517C2×C4⋊C4C4×D5314yescomplemented
518C2×C22⋊C4—538no—
519C2×C22⋊C4—538no—
520C2×C22⋊C4—1064no—
521C2×C22⋊C4—1064no—
522C2×C22⋊C4—1064no—
523C2×C22⋊C4—1064no—
524C2×C22⋊C4—1064no—
525C2×C22⋊C4—1064no—
526C2×C22⋊C4—1064no—
527C2×C22⋊C4—1064no—
528C2×C22⋊C4—1064no—
529C2×C22⋊C4—2122no—
530C2×C22⋊C4—2122no—
531C2×C22⋊C4—2122no—
532C2×C22⋊C4—2122no—
533C2×C42—22no—
534C2×C42—22no—
535C2×C42—534no—
536C2×C42—1062no—
537C2×C42—1062no—
538C2×C42—1062no—
539C2×C42—1062no—
540C2×C42—1062no—
541C2×C42D21214yes—
542#95—24no—
543#95—42no—
544#95—1064no—
545#95—1064no—
546#95—1062no—
547#95—1062no—
548#95—2122no—
549C24—534no—
550C24—534no—
551C24—534no—
552C24—1062no—
553C24—1062no—
554C24—1062no—
555C24—1062no—
556C24—1062no—
557C24—1062no—
558C24—1062no—
559C24—1062no—
560C24—1062no—
561C24—1062no—
562C24—1062no—
563C24—1062no—
564C24C23×D5311yescharacteristic
565C2×D4—5316no—
566C2×D4—1068no—
567C2×D4—1068no—
568C2×D4—1068no—
569C2×D4—1068no—
570C2×D4—1068no—
571C2×D4—1068no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—22no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—22no—
584C22×C4—21no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—21no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—22no—
591C22×C4—22no—
592C22×C4—22no—
593C22×C4—22no—
594C22×C4—22no—
595C22×C4—532no—
596C22×C4—532no—
597C22×C4—532no—
598C22×C4—532no—
599C22×C4—534no—
600C22×C4—532no—
601C22×C4—532no—
602C22×C4—10616no—
603C22×C4—1061no—
604C22×C4—1061no—
605C22×C4—1061no—
606C22×C4—1061no—
607C22×C4—1061no—
608C22×C4—1062no—
609C22×C4—1061no—
610C22×C4—1061no—
611C22×C4—1061no—
612C22×C4—1062no—
613C22×C4—1061no—
614C22×C4—1061no—
615C22×C4—1061no—
616C22×C4—1062no—
617C22×C4—1061no—
618C22×C4—1061no—
619C22×C4—1061no—
620C22×C4—1062no—
621C22×C4—1061no—
622C22×C4—1061no—
623C22×C4—1061no—
624C22×C4—1062no—
625C22×C4—1061no—
626C22×C4—1061no—
627C22×C4—1061no—
628C22×C4—1062no—
629C22×C4—1061no—
630C22×C4—1061no—
631C22×C4—2128no—
632C22×C4—2128no—
633C22×C4—2128no—
634C22×C4—2128no—
635C22×C4—2128no—
636C22×C4—2128no—
637C22×C4C2×C4×D5314yes—
638C22×C4C2×C4×D5312yes—
639C22×C4C2×D21212yes—
640C22×C4C2×D21212yes—
641C22×C4C2×D21212yes—
642C22×C4#1171994512yes—
643C22×C4D4×D5312yes—
644C22×C4D4×D5312yes—
645C22×C4D4×D5312yes—
646C22×C4#1171994712yes—
647C22×C4Q8×D5312yes—
648C22×C4#1171994912yes—
649C4⋊C4—28no—
650C4⋊C4—44no—
651C4⋊C4—1068no—
652C4⋊C4—1068no—
653C4⋊C4—1068no—
654C4⋊C4—2128no—
655C22⋊C4—10616no—
656C22⋊C4—10616no—
657C22⋊C4—2128no—
658C22⋊C4—2128no—
659C22⋊C4—2128no—
660C42—28no—
661C42—1068no—
662C42—2124no—
663C23—538no—
664C23—1064no—
665C23—1064no—
666C23—1064no—
667C23—1064no—
668C23—1064no—
669C23—1064no—
670C23—1064no—
671C23—1064no—
672C23—1064no—
673C23—1064no—
674C23—1064no—
675C23—1064no—
676C23—1064no—
677C23—1064no—
678C23—1064no—
679C23—1064no—
680C23—1064no—
681C23—1064no—
682C23—2122no—
683C23—2122no—
684C23—2122no—
685C23—2122no—
686C23—2122no—
687C23—2122no—
688C23—2122no—
689C23—2122no—
690C23—2122no—
691C23—2122no—
692C23—2122no—
693C23—2122no—
694C23—2122no—
695C23—2122no—
696C23—2122no—
697C23—2122no—
698C23C22×C4×D5311yescharacteristic
699C23C2×D4×D5311yescharacteristic
700C23C2×D4×D5311yescharacteristic
701C23C2×D4×D5311yescharacteristic
702C23C22×D21211yescharacteristic
703C23C2×Q8×D5311yescharacteristic
704C23#41×D5311yescharacteristic
705C23#41×D5311yescharacteristic
706C23C2×#1171994711yescharacteristic
707C23C2×#1171994511yescharacteristic
708C23C2×#1171994911yescharacteristic
709C23#1313326211yescharacteristic
710C23#1313326311yescharacteristic
711C23#1313326311yescharacteristic
712C23#1313326511yescharacteristic
713D4—10632no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—24no—
721C2×C4—24no—
722C2×C4—24no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—42no—
730C2×C4—41no—
731C2×C4—42no—
732C2×C4—42no—
733C2×C4—42no—
734C2×C4—42no—
735C2×C4—42no—
736C2×C4—42no—
737C2×C4—42no—
738C2×C4—42no—
739C2×C4—42no—
740C2×C4—42no—
741C2×C4—534no—
742C2×C4—1062no—
743C2×C4—1062no—
744C2×C4—1062no—
745C2×C4—1062no—
746C2×C4—1062no—
747C2×C4—1062no—
748C2×C4—1064no—
749C2×C4—1062no—
750C2×C4—1062no—
751C2×C4—1062no—
752C2×C4—1062no—
753C2×C4—1062no—
754C2×C4—1064no—
755C2×C4—1062no—
756C2×C4—1062no—
757C2×C4—1062no—
758C2×C4—1062no—
759C2×C4—1064no—
760C2×C4—21232no—
761C2×C4—2121no—
762C2×C4—2121no—
763C2×C4—2122no—
764C2×C4—2121no—
765C2×C4—2121no—
766C2×C4—2121no—
767C2×C4—2121no—
768C2×C4—2122no—
769C2×C4—2121no—
770C2×C4—2121no—
771C2×C4—2122no—
772C2×C4—2121no—
773C2×C4—2121no—
774C2×C4—2121no—
775C2×C4—2121no—
776C2×C4—2122no—
777C2×C4C4⋊C4×D5314yes—
778C2×C4#1313317714yes—
779C2×C4C4×D21214yes—
780C2×C4#1313318714yes—
781C2×C4#1313319214yes—
782C2×C4#1313319514yes—
783C2×C4#1313319714yes—
784C2×C4#1313319914yes—
785C22—1068no—
786C22—1068no—
787C22—1068no—
788C22—2124no—
789C22—2124no—
790C22—2124no—
791C22—2124no—
792C22—2124no—
793C22—2124no—
794C22—2124no—
795C22—2124no—
796C22—2124no—
797C22—2124no—
798C22—2124no—
799C22—2124no—
800C22C2×C4⋊C4×D5311yescharacteristic
801C22C4×D4×D5311yescharacteristic
802C22C2×#1313317711yescharacteristic
803C22C2×C4×D21211yescharacteristic
804C22C4×#1171994911yescharacteristic
805C22#1681109511yescharacteristic
806C22#1681110511yescharacteristic
807C22C2×#1313318711yescharacteristic
808C22C2×#1313319211yescharacteristic
809C22C2×#1313319511yescharacteristic
810C22C2×#1313319711yescharacteristic
811C22C2×#1313319911yescharacteristic
812C22#1681113511yescharacteristic
813C22#1681116011yescharacteristic
814C22#1681117011yescharacteristic
815C22#1681119211yescharacteristic
816C22#1681120411yescharacteristic
817C22#1681122411yescharacteristic
818C22#1681124511yescharacteristic
819C22#1681125711yescharacteristic
820C22#1681125711yescharacteristic
821C22#1681126411yescharacteristic
822C22#1681126411yescharacteristic
823C22#1681127011yescharacteristic
824C22#1681127511yescharacteristic
825C22#1681128311yescharacteristic
826C22#1681128811yescharacteristic
827C22#1681129111yescharacteristic
828C22#1681129311yescharacteristic
829C22#1681132911yescharacteristic
830C22#1681132911yescharacteristic
831C22#1681133411yescharacteristic
832C22#1681134711yescharacteristic
833C22#1681135511yescharacteristic
834C22#1681135511yescharacteristic
835C4—24no—
836C4—44no—
837C4—42no—
838C4—82no—
839C4—1064no—
840C4—2122no—
841C4—2124no—
842C4—2122no—
843C4—2122no—
844C4#1681049718yescomplemented
845C2—2128no—
846C2C2×#1681049711yescharacteristic
847C2C4×#1313319211yescharacteristic
848C2#2027740911yescharacteristic
849C2#2027761611yescharacteristic
850C2#2027762411yescharacteristic
851C2#2027777611yescharacteristic
852C2#2027779111yescharacteristic
853C2#2027806111yescharacteristic
854C2#2027807211yescharacteristic
855C2#2027848111yescharacteristic
856C2#2027850311yescharacteristic
857C2#2027856611yescharacteristic
858C2#2027858811yescharacteristic
859C2#2027963811yescharacteristic
860C2#2028007411yescharacteristic
subgroupG/H
center, FrattiniC24C23×D53
commutatorC23×C53C23×C4
FittingC53×C4⋊#95C2
socle, cosocleC24×C53C24
prime radicalC23×D212C22
hypercenterC4⋊#95D53
hypocenterC53#14018
LCSG ▷ C23×C53 ▷ C53
UCSC1 ◁ C24 ◁ C4⋊#95

Complements

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

NH ≅ G/Ntype
4. C2×#16810522C2semidirect
5. C2×#16810497C2semidirect
6. C2×C4×#11719919C2semidirect
7. #20272961C2semidirect
8. #20272959C2semidirect
9. #20272944C2semidirect
10. #20272936C2semidirect
11. C53×C4⋊#95C2semidirect
29. #16810524C4semidirect
75. C2×#11719919D4semidirect
89. C2×#11719921C2×C4semidirect
90. C2×#11719921C2×C4semidirect
96. C2×C4×Dic53C2×C4semidirect
112. C2×C4⋊C4×C53C2×C4semidirect
210. C2×D212C4⋊C4semidirect
351. C2×Dic53C4×D4semidirect
409. C4×C53#385semidirect
424. C4⋊#95D53semidirect
473. C53#14018semidirect
517. C2×C4⋊C4C4×D53semidirect
844. C4#16810497semidirect

Maximal subgroups

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

subgroupindex
C22×C4×D2122
C2×#168105242
C2×#168105222
C2×#168104972
C2×C4×#117199192
#202729612
#202729592
#202729442
#202729362
C53×C4⋊#952
#1401853