Finite Group Databasebeta

← #27320792

Subgroups — #27320792

Order 13568.

1906 conjugacy classes of subgroups.

The subgroup lattice has 836 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16810545C212yesmaximal, complemented
2C2×#16810525C211yesmaximal, characteristic
3C2×#16810524C211yesmaximal, characteristic
4C2×#16810524C211yesmaximal, characteristic
5C2×#16810522C211yesmaximal, characteristic, complemented
6C2×#16810519C211yesmaximal, characteristic, complemented
7#20272961C212yesmaximal, complemented
8#20272959C212yesmaximal, complemented
9#20272957C212yesmaximal, complemented
10C4×#13133124C211yesmaximal, characteristic, complemented
11C2×C53×#389C211yesmaximal, characteristic, complemented
12C23×D212C2211yescharacteristic
13C22×C4⋊Dic53C2212yes—
14C22×C4⋊Dic53C2211yescharacteristic
15C22×#11719919C2212yes—
16C22×#11719921C2212yes—
17C22×#11719921C2212yes—
18C22×#11719921C2212yes—
19C22×#11719921C2212yes—
20C22×#11719921C2212yes—
21C22×#11719921C2212yes—
22C22×C4×Dic53C2211yescharacteristic
23C22×C4×Dic53C2211yescharacteristic
24#16810545—28no—
25#16810525—24no—
26#16810524—24no—
27#16810524—24no—
28#16810522—24no—
29#16810519—24no—
30C2×#13133124C2211yescharacteristic
31C2×#13133124C2211yescharacteristic
32C2×#13133124C2211yescharacteristic
33C2×#13133124C2212yes—
34C2×#13133124C2212yes—
35C2×#13133124C2211yescharacteristic
36C22×C4⋊C4×C53C2212yes—
37C22×C4⋊C4×C53C2211yescharacteristic
38C22×C4⋊C4×C53C2211yescharacteristic
39C22×C42×C53C2211yescharacteristic
40C53×#389—24no—
41C2×#95×C53C2212yes—
42C24×D53C2312yes—
43C22×D212—22no—
44C22×D212—22no—
45C22×D212—22no—
46C22×D212—22no—
47C22×D212—22no—
48C22×D212—22no—
49C22×D212Q814yes—
50C23×Dic53C2311yescharacteristic
51C23×Dic53C2311yescharacteristic
52C23×Dic53C2312yes—
53C23×Dic53C2311yescharacteristic
54C23×Dic53C2311yescharacteristic
55C2×C4⋊Dic53—22no—
56C2×C4⋊Dic53—22no—
57C2×C4⋊Dic53—24no—
58C2×C4⋊Dic53—24no—
59C2×C4⋊Dic53—42no—
60C2×C4⋊Dic53D414yes—
61C2×#11719919—24no—
62C2×#11719919—24no—
63C2×#11719919—42no—
64C2×#11719921—24no—
65C2×#11719921—24no—
66C2×#11719921—24no—
67C2×#11719921—24no—
68C2×#11719921—24no—
69C2×#11719921—24no—
70C2×#11719921—24no—
71C2×#11719921—24no—
72C2×#11719921—24no—
73C2×#11719921—24no—
74C2×#11719921—24no—
75C2×#11719921—24no—
76C2×#11719921—42no—
77C2×#11719921—42no—
78C2×#11719921—42no—
79C2×#11719921—42no—
80C2×#11719921—42no—
81C2×#11719921—42no—
82C2×C4×Dic53—22no—
83C2×C4×Dic53—22no—
84C2×C4×Dic53—22no—
85C2×C4×Dic53—22no—
86C2×C4×Dic53—22no—
87C2×C4×Dic53—22no—
88#13133124—24no—
89#13133124—22no—
90#13133124—24no—
91#13133124—22no—
92#13133124—22no—
93#13133124D414yescomplemented
94C23×C4×C53C2311yescharacteristic
95C23×C4×C53C2312yes—
96C23×C4×C53C2312yes—
97C23×C4×C53C2311yescharacteristic
98C23×C4×C53C2311yescharacteristic
99C2×C4⋊C4×C53—22no—
100C2×C4⋊C4×C53—22no—
101C2×C4⋊C4×C53—24no—
102C2×C4⋊C4×C53—24no—
103C2×C4⋊C4×C53—22no—
104C2×C4⋊C4×C53—22no—
105C2×C4⋊C4×C53—42no—
106C2×C4⋊C4×C53D414yes—
107C2×C4⋊C4×C53D414yes—
108C2×C42×C53—22no—
109C2×C42×C53—22no—
110C2×C42×C53—22no—
111#95×C53—24no—
112C24×C53C2411yescharacteristic
113C23×D53—22no—
114C23×D53—22no—
115C23×D53—22no—
116C23×D53—22no—
117C23×D53—22no—
118C23×D53—22no—
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×D53C2×Q814yes—
128C22×C4×C53—21no—
129C22×C4×C53—22no—
130C22×C4×C53—21no—
131C22×C4×C53—21no—
132C22×C4×C53—21no—
133C22×C4×C53—22no—
134C22×C4×C53—22no—
135C22×C4×C53—22no—
136C22×C4×C53—21no—
137C22×C4×C53—21no—
138C22×C4×C53—22no—
139C22×C4×C53—22no—
140C22×C4×C53—21no—
141C22×C4×C53—21no—
142C22×C4×C53—22no—
143C22×C4×C53—22no—
144C22×C4×C53—21no—
145C22×C4×C53—22no—
146C22×C4×C53—22no—
147C22×C4×C53—21no—
148C22×C4×C53—21no—
149C22×C4×C53—22no—
150C22×C4×C53—22no—
151C22×C4×C53—21no—
152C22×C4×C53C2×D414yes—
153C22×C4×C53C2×D412yes—
154C22×C4×C53C2×D414yes—
155C22×C4×C53C2×D412yes—
156C22×C4×C53C2×D412yes—
157C22×C4×C53C2×D412yes—
158C22×C4×C53C2×Q812yes—
159C22×C4×C53#4112yes—
160C22×C4×C53#4112yes—
161C22×C4×C53#4112yes—
162C22×C4×C53#4112yes—
163C22×Dic53—21no—
164C22×Dic53—21no—
165C22×Dic53—22no—
166C22×Dic53—21no—
167C22×Dic53—21no—
168C22×Dic53—21no—
169C22×Dic53—21no—
170C22×Dic53—21no—
171C22×Dic53—21no—
172C22×Dic53—22no—
173C22×Dic53—21no—
174C22×Dic53—21no—
175C22×Dic53—21no—
176C22×Dic53—21no—
177C22×Dic53—21no—
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—21no—
187C22×Dic53—22no—
188C22×Dic53—22no—
189C22×Dic53—21no—
190C22×Dic53—21no—
191C22×Dic53—21no—
192C22×Dic53—21no—
193C22×Dic53C2×D414yes—
194C22×Dic53C2×D412yes—
195C22×Dic53C2×D412yes—
196C22×Dic53#4112yes—
197C22×Dic53#4112yes—
198C2×D212—28no—
199C2×D212—28no—
200C2×D212—28no—
201C2×D212—44no—
202C2×D212—44no—
203C2×D212—44no—
204C2×D212—44no—
205C4⋊C4×C53—28no—
206C4⋊C4×C53—28no—
207C4⋊C4×C53—48no—
208C42×C53—44no—
209#11719921—48no—
210#11719921—48no—
211#11719921—48no—
212#11719921—48no—
213#11719921—48no—
214#11719921—48no—
215C4⋊Dic53—28no—
216C4⋊Dic53—48no—
217#11719919—48no—
218C4×Dic53—44no—
219C4×Dic53—44no—
220C23×C53C22×D411yescharacteristic
221C23×C53C22×D411yescharacteristic
222C23×C53C22×D411yescharacteristic
223C23×C53C22×D411yescharacteristic
224C23×C53C22×Q811yescharacteristic
225C23×C53C2×#4111yescharacteristic
226C23×C53C2×#4111yescharacteristic
227C23×C53C2×#4111yescharacteristic
228C23×C53C2×#4111yescharacteristic
229C23×C53C2×#4111yescharacteristic
230C23×C53C2×#4111yescharacteristic
231C23×C53H(5,𝔽2)11yescharacteristic
232C23×C53H(5,𝔽2)11yescharacteristic
233C23×C53H(5,𝔽2)11yescharacteristic
234C23×C532−1+411yescharacteristic
235C22×D53—24no—
236C22×D53—24no—
237C22×D53—24no—
238C22×D53—24no—
239C22×D53—24no—
240C22×D53—24no—
241C22×D53—24no—
242C22×D53—42no—
243C22×D53—42no—
244C22×D53—42no—
245C22×D53—42no—
246C22×D53—42no—
247C22×D53—42no—
248C22×D53—42no—
249C22×D53—42no—
250C22×D53—42no—
251C22×D53—42no—
252C22×D53—42no—
253C22×D53—42no—
254C22×D53—42no—
255C22×D53—42no—
256C22×D53—42no—
257C22×D53—42no—
258C22×D53—42no—
259C22×D53—42no—
260C22×D53—42no—
261C22×D53—42no—
262C22×D53—42no—
263C22×D53—42no—
264C22×D53—42no—
265C22×D53—42no—
266C22×D53—42no—
267C22×D53—42no—
268C22×D53—42no—
269C22×D53—42no—
270C2×C4×C53—24no—
271C2×C4×C53—24no—
272C2×C4×C53—22no—
273C2×C4×C53—22no—
274C2×C4×C53—24no—
275C2×C4×C53—22no—
276C2×C4×C53—24no—
277C2×C4×C53—22no—
278C2×C4×C53—24no—
279C2×C4×C53—24no—
280C2×C4×C53—22no—
281C2×C4×C53—22no—
282C2×C4×C53—41no—
283C2×C4×C53—41no—
284C2×C4×C53—42no—
285C2×C4×C53—42no—
286C2×C4×C53—42no—
287C2×C4×C53—41no—
288C2×C4×C53—42no—
289C2×C4×C53—41no—
290C2×C4×C53—42no—
291C2×C4×C53—42no—
292C2×C4×C53—41no—
293C2×C4×C53—41no—
294C2×C4×C53—41no—
295C2×C4×C53—42no—
296C2×C4×C53—41no—
297C2×C4×C53—42no—
298C2×C4×C53#12114yes—
299C2×C4×C53#12114yes—
300C2×C4×C53#12114yes—
301C2×C4×C53C22⋊Q814yes—
302C2×C4×C53C22⋊Q814yes—
303C2×C4×C53C22⋊Q814yes—
304C2×C4×C53#12614yes—
305C2×Dic53—24no—
306C2×Dic53—22no—
307C2×Dic53—22no—
308C2×Dic53—22no—
309C2×Dic53—22no—
310C2×Dic53—22no—
311C2×Dic53—22no—
312C2×Dic53—24no—
313C2×Dic53—22no—
314C2×Dic53—22no—
315C2×Dic53—24no—
316C2×Dic53—22no—
317C2×Dic53—22no—
318C2×Dic53—22no—
319C2×Dic53—22no—
320C2×Dic53—41no—
321C2×Dic53—41no—
322C2×Dic53—41no—
323C2×Dic53—41no—
324C2×Dic53—42no—
325C2×Dic53—41no—
326C2×Dic53—41no—
327C2×Dic53—42no—
328C2×Dic53—41no—
329C2×Dic53—41no—
330C2×Dic53—42no—
331C2×Dic53—41no—
332C2×Dic53—41no—
333C2×Dic53—41no—
334C2×Dic53—41no—
335C2×Dic53—41no—
336C2×Dic53—41no—
337C2×Dic53—41no—
338C2×Dic53—42no—
339C2×Dic53—41no—
340D212—416no—
341#15141—531nomaximal, Sylow
342C22×C53C2×#12111yescharacteristic
343C22×C53C2×#12111yescharacteristic
344C22×C53C2×#12111yescharacteristic
345C22×C53C2×C22⋊Q811yescharacteristic
346C22×C53C2×C22⋊Q811yescharacteristic
347C22×C53C2×C22⋊Q811yescharacteristic
348C22×C53C2×#12611yescharacteristic
349C22×C53#52911yescharacteristic
350C22×C53#52911yescharacteristic
351C22×C53#52911yescharacteristic
352C22×C53#53211yescharacteristic
353C22×C53#53211yescharacteristic
354C22×C53#53211yescharacteristic
355C22×C53#54011yescharacteristic
356C22×C53#54011yescharacteristic
357C22×C53#54011yescharacteristic
358C22×C53#54211yescharacteristic
359C22×C53#54211yescharacteristic
360C22×C53#54211yescharacteristic
361C22×C53D4211yescharacteristic
362C22×C53D4211yescharacteristic
363C22×C53D4211yescharacteristic
364C22×C53#54611yescharacteristic
365C22×C53#54611yescharacteristic
366C22×C53#54611yescharacteristic
367C22×C53#54811yescharacteristic
368C22×C53#54811yescharacteristic
369C22×C53#54811yescharacteristic
370C22×C53D4×Q811yescharacteristic
371C22×C53#55011yescharacteristic
372C22×C53#55011yescharacteristic
373C22×C53#55011yescharacteristic
374C22×C53#55411yescharacteristic
375C22×C53#55411yescharacteristic
376C22×C53#55411yescharacteristic
377C2×D53—44no—
378C2×D53—44no—
379C2×D53—44no—
380C2×D53—44no—
381C2×D53—44no—
382C2×D53—44no—
383C2×D53—44no—
384C2×D53—82no—
385C2×D53—82no—
386C2×D53—82no—
387C2×D53—82no—
388C2×D53—82no—
389C2×D53—82no—
390C2×D53—82no—
391C2×D53—82no—
392C4×C53—42no—
393C4×C53—44no—
394C4×C53—44no—
395C4×C53—42no—
396C4×C53#39618yescomplemented
397Dic53—42no—
398Dic53—42no—
399Dic53—42no—
400Dic53—44no—
401Dic53—42no—
402C2×#396—532no—
403C2×#390—531no—
404C2×#390—531no—
405C2×#390—531no—
406C2×#389—531no—
407C2×#389—531no—
408C2×#389D5311yescharacteristic, complemented
409#1439—532no—
410#1439—532no—
411#1439—532no—
412C4×#95—531no—
413C2×C53C2×#39611yescharacteristic
414C2×C53#242611yescharacteristic
415C2×C53#242611yescharacteristic
416C2×C53#242611yescharacteristic
417C2×C53#242811yescharacteristic
418C2×C53#242811yescharacteristic
419C2×C53#242811yescharacteristic
420C2×C53#245211yescharacteristic
421C2×C53#245211yescharacteristic
422C2×C53#245211yescharacteristic
423C2×C53#245411yescharacteristic
424C2×C53#245411yescharacteristic
425C2×C53#245411yescharacteristic
426C2×C53#264411yescharacteristic
427C2×C53#286011yescharacteristic
428D53—84no—
429C23×D4—531no—
430C22×C4⋊C4—531no—
431C22×C4⋊C4—532no—
432C22×C4⋊C4—532no—
433C22×C4⋊C4C2×D5312yes—
434C22×C4⋊C4C2×D5311yescharacteristic
435C22×C4⋊C4C2×D5311yescharacteristic
436C22×C22⋊C4—532no—
437C22×C22⋊C4—532no—
438C22×C22⋊C4—532no—
439C22×C22⋊C4—532no—
440C22×C22⋊C4—532no—
441C22×C22⋊C4—532no—
442C22×C42—531no—
443C22×C42—531no—
444C22×C42C2×D5311yescharacteristic
445#396—1068no—
446#390—1064no—
447#390—1064no—
448#390—1064no—
449#389—24no—
450#389—1064no—
451#389—1064no—
452C2×#95—531no—
453C2×#95—531no—
454C2×#95—531no—
455C2×#95—531no—
456C2×#95—532no—
457C2×#95—532no—
458C2×#95C2×D5312yes—
459C53#1514111yescharacteristic, complemented, Sylow
460C25—532no—
461C22×D4—534no—
462C22×D4—1062no—
463C22×D4—1062no—
464C22×D4—1062no—
465C22×D4—1062no—
466C22×D4—1062no—
467C22×D4—1062no—
468C23×C4—532no—
469C23×C4—531no—
470C23×C4—531no—
471C23×C4—531no—
472C23×C4—531no—
473C23×C4C22×D5312yes—
474C23×C4C22×D5311yescharacteristic
475C23×C4C22×D5311yescharacteristic
476C23×C4C22×D5312yes—
477C23×C4C22×D5311yescharacteristic
478C2×C4⋊C4—22no—
479C2×C4⋊C4—22no—
480C2×C4⋊C4—22no—
481C2×C4⋊C4—22no—
482C2×C4⋊C4—24no—
483C2×C4⋊C4—24no—
484C2×C4⋊C4—42no—
485C2×C4⋊C4—534no—
486C2×C4⋊C4—1062no—
487C2×C4⋊C4—1062no—
488C2×C4⋊C4—1064no—
489C2×C4⋊C4—1064no—
490C2×C4⋊C4—1064no—
491C2×C4⋊C4—1064no—
492C2×C4⋊C4—2122no—
493C2×C4⋊C4—2122no—
494C2×C4⋊C4D21214yes—
495C2×C4⋊C4C22⋊D5314yes—
496C2×C22⋊C4—1064no—
497C2×C22⋊C4—1064no—
498C2×C22⋊C4—1064no—
499C2×C22⋊C4—1064no—
500C2×C22⋊C4—1064no—
501C2×C22⋊C4—1064no—
502C2×C22⋊C4—1064no—
503C2×C22⋊C4—1064no—
504C2×C22⋊C4—1064no—
505C2×C22⋊C4—1064no—
506C2×C22⋊C4—1064no—
507C2×C22⋊C4—1064no—
508C2×C22⋊C4—2122no—
509C2×C22⋊C4—2122no—
510C2×C22⋊C4—2122no—
511C2×C22⋊C4—2122no—
512C2×C22⋊C4—2122no—
513C2×C22⋊C4—2122no—
514C2×C42—22no—
515C2×C42—22no—
516C2×C42—22no—
517C2×C42—1062no—
518C2×C42—1062no—
519C2×C42—1062no—
520C2×C42—1062no—
521C2×C42—1062no—
522C2×C42—1062no—
523#95—24no—
524#95—534no—
525#95—1062no—
526#95—1062no—
527#95—1064no—
528#95—1064no—
529#95—1062no—
530C24—534no—
531C24—1062no—
532C24—1062no—
533C24—1062no—
534C24—1062no—
535C24—1062no—
536C24—1062no—
537C24—1062no—
538C24—1062no—
539C24—1062no—
540C24—1062no—
541C24—1062no—
542C24—1062no—
543C24—1062no—
544C24—1062no—
545C24C23×D5311yescharacteristic
546C2×D4—1068no—
547C2×D4—1068no—
548C2×D4—1068no—
549C2×D4—2124no—
550C2×D4—2124no—
551C2×D4—2124no—
552C2×D4—2124no—
553C22×C4—22no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—21no—
559C22×C4—22no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—21no—
577C22×C4—532no—
578C22×C4—532no—
579C22×C4—534no—
580C22×C4—532no—
581C22×C4—532no—
582C22×C4—1061no—
583C22×C4—1061no—
584C22×C4—1062no—
585C22×C4—1061no—
586C22×C4—1061no—
587C22×C4—1061no—
588C22×C4—1062no—
589C22×C4—1061no—
590C22×C4—1061no—
591C22×C4—1061no—
592C22×C4—1061no—
593C22×C4—1061no—
594C22×C4—1061no—
595C22×C4—1061no—
596C22×C4—1061no—
597C22×C4—1061no—
598C22×C4—1061no—
599C22×C4—1061no—
600C22×C4—1062no—
601C22×C4—1062no—
602C22×C4—1061no—
603C22×C4—1061no—
604C22×C4—1061no—
605C22×C4—1061no—
606C22×C4—1062no—
607C22×C4—1062no—
608C22×C4—1061no—
609C22×C4—1061no—
610C22×C4—1061no—
611C22×C4—1061no—
612C22×C4C2×D21214yes—
613C22×C4C2×D21212yes—
614C22×C4#1171994512yes—
615C22×C4D4×D5312yes—
616C22×C4D4×D5312yes—
617C22×C4#1171994712yes—
618C22×C4Q8×D5312yes—
619C22×C4#1171994912yes—
620C22×C4#1171994912yes—
621C22×C4C2×C22⋊D5314yes—
622C22×C4C2×C22⋊D5312yes—
623C4⋊C4—28no—
624C4⋊C4—28no—
625C4⋊C4—48no—
626C4⋊C4—1068no—
627C4⋊C4—2128no—
628C4⋊C4—2128no—
629C22⋊C4—2128no—
630C22⋊C4—2128no—
631C22⋊C4—2128no—
632C22⋊C4—2128no—
633C22⋊C4—2128no—
634C22⋊C4—2128no—
635C42—44no—
636C42—2124no—
637C42—2124no—
638C23—1064no—
639C23—1064no—
640C23—1064no—
641C23—1064no—
642C23—1064no—
643C23—1064no—
644C23—1064no—
645C23—2122no—
646C23—2122no—
647C23—2122no—
648C23—2122no—
649C23—2122no—
650C23—2122no—
651C23—2122no—
652C23—2122no—
653C23—2122no—
654C23—2122no—
655C23—2122no—
656C23—2122no—
657C23—2122no—
658C23—2122no—
659C23—2122no—
660C23—2122no—
661C23—2122no—
662C23—2122no—
663C23—2122no—
664C23—2122no—
665C23—2122no—
666C23—2122no—
667C23—2122no—
668C23—2122no—
669C23—2122no—
670C23—2122no—
671C23—2122no—
672C23—2122no—
673C23C2×D4×D5311yescharacteristic
674C23C2×D4×D5311yescharacteristic
675C23C22×C22⋊D5311yescharacteristic
676C23C22×D21211yescharacteristic
677C23C2×Q8×D5311yescharacteristic
678C23#41×D5311yescharacteristic
679C23#41×D5311yescharacteristic
680C23C2×#1171994711yescharacteristic
681C23C2×#1171994511yescharacteristic
682C23C2×#1171994911yescharacteristic
683C23C2×#1171994911yescharacteristic
684C23#1313326211yescharacteristic
685C23#1313326311yescharacteristic
686C23#1313326311yescharacteristic
687C23#1313326511yescharacteristic
688D4—21216no—
689C2×C4—22no—
690C2×C4—24no—
691C2×C4—22no—
692C2×C4—24no—
693C2×C4—24no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—24no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—24no—
700C2×C4—24no—
701C2×C4—41no—
702C2×C4—42no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—42no—
706C2×C4—41no—
707C2×C4—41no—
708C2×C4—42no—
709C2×C4—42no—
710C2×C4—42no—
711C2×C4—41no—
712C2×C4—42no—
713C2×C4—41no—
714C2×C4—42no—
715C2×C4—42no—
716C2×C4—41no—
717C2×C4—1064no—
718C2×C4—1062no—
719C2×C4—1062no—
720C2×C4—1062no—
721C2×C4—1064no—
722C2×C4—1062no—
723C2×C4—1062no—
724C2×C4—1062no—
725C2×C4—1062no—
726C2×C4—1062no—
727C2×C4—1064no—
728C2×C4—1062no—
729C2×C4—1062no—
730C2×C4—1062no—
731C2×C4—1062no—
732C2×C4—2121no—
733C2×C4—2121no—
734C2×C4—2121no—
735C2×C4—2121no—
736C2×C4—2121no—
737C2×C4—2121no—
738C2×C4—2121no—
739C2×C4—2122no—
740C2×C4—2121no—
741C2×C4—2121no—
742C2×C4—2121no—
743C2×C4—2121no—
744C2×C4—2121no—
745C2×C4—2122no—
746C2×C4—2121no—
747C2×C4—2121no—
748C2×C4—2122no—
749C2×C4—2121no—
750C2×C4—2121no—
751C2×C4—2122no—
752C2×C4#1313318914yes—
753C2×C4#1313319114yes—
754C2×C4#1313319214yes—
755C2×C4#1313319314yes—
756C2×C4#1313319514yes—
757C2×C4#1313319714yes—
758C2×C4#1313321214yes—
759C22—4242no—
760C22—4242no—
761C22—4242no—
762C22—4242no—
763C22—4242no—
764C22—4242no—
765C22—4242no—
766C22—4242no—
767C22—2124no—
768C22—2124no—
769C22—2124no—
770C22—2124no—
771C22—2124no—
772C22—2124no—
773C22—2124no—
774C22C2×#1313318911yescharacteristic
775C22C2×#1313319111yescharacteristic
776C22C2×#1313319211yescharacteristic
777C22C2×#1313319311yescharacteristic
778C22C2×#1313319511yescharacteristic
779C22C2×#1313319711yescharacteristic
780C22C2×#1313321211yescharacteristic
781C22#1681115811yescharacteristic
782C22#1681115911yescharacteristic
783C22#1681116011yescharacteristic
784C22#1681116811yescharacteristic
785C22#1681117011yescharacteristic
786C22#1681117411yescharacteristic
787C22#1681122411yescharacteristic
788C22#1681122611yescharacteristic
789C22#1681122911yescharacteristic
790C22#1681124511yescharacteristic
791C22#1681124611yescharacteristic
792C22#1681124711yescharacteristic
793C22D4×C22⋊D5311yescharacteristic
794C22#1681125711yescharacteristic
795C22D4×D21211yescharacteristic
796C22#1681126111yescharacteristic
797C22#1681126411yescharacteristic
798C22#1681126811yescharacteristic
799C22#1681128311yescharacteristic
800C22#1681128411yescharacteristic
801C22#1681128511yescharacteristic
802C22#1681128811yescharacteristic
803C22#1681129111yescharacteristic
804C22#1681129211yescharacteristic
805C22#1681129511yescharacteristic
806C22#1681132911yescharacteristic
807C22#1681132911yescharacteristic
808C22#1681133411yescharacteristic
809C4—42no—
810C4—44no—
811C4—44no—
812C4—42no—
813C4—2122no—
814C4—2122no—
815C4—2122no—
816C4—2124no—
817C4—2122no—
818C4#1681054518yescomplemented
819C2—4244no—
820C2C2×#1681054511yescharacteristic
821C2#2027827511yescharacteristic
822C2#2027827911yescharacteristic
823C2#2027828311yescharacteristic
824C2#2027829711yescharacteristic
825C2#2027830111yescharacteristic
826C2#2027830511yescharacteristic
827C2#2027856111yescharacteristic
828C2#2027856311yescharacteristic
829C2#2027856611yescharacteristic
830C2#2027858311yescharacteristic
831C2#2027858511yescharacteristic
832C2#2027858811yescharacteristic
833C2#2028067811yescharacteristic
834C2#2028308311yescharacteristic
subgroupG/H
center, FrattiniC24C23×D53
commutator, socle, cosocleC24×C53C24
FittingC2×C53×#389C2
prime radicalC23×D212C22
hypercenterC2×#389D53
hypocenterC53#15141
LCSG ▷ C24×C53 ▷ C53
UCSC1 ◁ C24 ◁ C2×#389

Complements

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

NH ≅ G/Ntype
1. C2×#16810545C2semidirect
5. C2×#16810522C2semidirect
6. C2×#16810519C2semidirect
7. #20272961C2semidirect
8. #20272959C2semidirect
9. #20272957C2semidirect
10. C4×#13133124C2semidirect
11. C2×C53×#389C2semidirect
93. #13133124D4semidirect
396. C4×C53#396semidirect
408. C2×#389D53semidirect
459. C53#15141semidirect
818. C4#16810545semidirect

Maximal subgroups

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

subgroupindex
C2×#168105452
C2×#168105252
C2×#168105242
C2×#168105222
C2×#168105192
#202729612
#202729592
#202729572
C4×#131331242
C2×C53×#3892
#1514153