Finite Group Databasebeta

← #27307193

Subgroups — #27307193

Order 13568.

1802 conjugacy classes of subgroups.

The subgroup lattice has 816 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16810521C211yesmaximal, characteristic, complemented
2C2×#16810511C212yesmaximal
3C2×#16810483C211yesmaximal, characteristic
4C2×#16810483C211yesmaximal, characteristic
5C2×C4×C4⋊Dic53C211yesmaximal, characteristic, complemented
6#20272970C212yesmaximal, complemented
7#20272962C212yesmaximal
8#20272945C211yesmaximal, characteristic, complemented
9#20272945C211yesmaximal, characteristic, complemented
10#20272939C212yesmaximal, complemented
11C2×C4×C22⋊C4×C53C211yesmaximal, characteristic
12C22×C4⋊Dic53C2211yescharacteristic
13C22×C4⋊Dic53C2211yescharacteristic
14C22×C4⋊Dic53C2211yescharacteristic
15C22×C4⋊Dic53C2211yescharacteristic
16C22×#11719919C2212yes—
17C22×C22⋊Dic53C2212yes—
18C22×C22⋊Dic53C2212yes—
19C22×C4×Dic53C2212yes—
20#16810521—24no—
21#16810511—28no—
22#16810483—24no—
23#16810483C418yescomplemented
24C4×C4⋊Dic53—24no—
25C2×#13133124C2212yes—
26C2×#13133124C2212yes—
27C2×#13133124C2212yes—
28C2×#13133124C2212yes—
29C2×#13133124C2212yes—
30C2×#13133124C2212yes—
31C2×#13133124C2212yes—
32C2×#13133124C2212yes—
33C24×C4×C53C2211yescharacteristic
34C22×C22⋊C4×C53C2211yescharacteristic
35C22×C22⋊C4×C53C2211yescharacteristic
36C22×C42×C53C2211yescharacteristic
37C22×C42×C53C2211yescharacteristic
38C4×C22⋊C4×C53—24no—
39C2×#95×C53C2211yescharacteristic
40C2×#95×C53C2211yescharacteristic
41C23×Dic53C2312yes—
42C23×Dic53C2312yes—
43C23×Dic53C2312yes—
44C23×Dic53C2312yes—
45C2×C4⋊Dic53—22no—
46C2×C4⋊Dic53—22no—
47C2×C4⋊Dic53—22no—
48C2×C4⋊Dic53—22no—
49C2×C4⋊Dic53—22no—
50C2×C4⋊Dic53—22no—
51C2×C4⋊Dic53—22no—
52C2×C4⋊Dic53—22no—
53C2×C4⋊Dic53—22no—
54C2×C4⋊Dic53C2×C414yes—
55C2×C4⋊Dic53C2×C414yes—
56C2×C4⋊Dic53D414yes—
57C2×#11719919—24no—
58C2×#11719919—24no—
59C2×#11719919—42no—
60C2×C22⋊Dic53—24no—
61C2×C22⋊Dic53—24no—
62C2×C22⋊Dic53—24no—
63C2×C22⋊Dic53—24no—
64C2×C22⋊Dic53—42no—
65C2×C22⋊Dic53C2×C418yes—
66C2×C4×Dic53—24no—
67C2×C4×Dic53—24no—
68C2×C4×Dic53—24no—
69#13133124—24no—
70#13133124—24no—
71#13133124—24no—
72#13133124—24no—
73#13133124—24no—
74#13133124—24no—
75#13133124—42no—
76#13133124C2×C418yes—
77C25×C53C2311yescharacteristic
78C23×C4×C53—22no—
79C23×C4×C53—22no—
80C23×C4×C53—22no—
81C23×C4×C53—22no—
82C23×C4×C53—22no—
83C23×C4×C53—22no—
84C23×C4×C53C2×C414yes—
85C23×C4×C53C2311yescharacteristic
86C23×C4×C53C2311yescharacteristic
87C23×C4×C53C2311yescharacteristic
88C23×C4×C53C2311yescharacteristic
89C23×C4×C53C2311yescharacteristic
90C23×C4×C53C2311yescharacteristic
91C2×C22⋊C4×C53—22no—
92C2×C22⋊C4×C53—22no—
93C2×C22⋊C4×C53—22no—
94C2×C22⋊C4×C53—22no—
95C2×C22⋊C4×C53—22no—
96C2×C22⋊C4×C53D414yes—
97C2×C42×C53—22no—
98C2×C42×C53—22no—
99C2×C42×C53—22no—
100C2×C42×C53—22no—
101C2×C42×C53—22no—
102C2×C42×C53D414yes—
103#95×C53—22no—
104#95×C53—22no—
105C24×C53—21no—
106C24×C53—21no—
107C24×C53—21no—
108C24×C53—21no—
109C24×C53—21no—
110C24×C53—21no—
111C24×C53—21no—
112C24×C53—21no—
113C24×C53—21no—
114C24×C53—21no—
115C24×C53—21no—
116C24×C53—21no—
117C24×C53C22×C412yes—
118C24×C53C2×D412yes—
119C24×C53#4112yes—
120C24×C53C2411yescharacteristic
121C22×C4×C53—21no—
122C22×C4×C53—21no—
123C22×C4×C53—21no—
124C22×C4×C53—21no—
125C22×C4×C53—21no—
126C22×C4×C53—21no—
127C22×C4×C53—21no—
128C22×C4×C53—21no—
129C22×C4×C53—21no—
130C22×C4×C53—21no—
131C22×C4×C53—21no—
132C22×C4×C53—21no—
133C22×C4×C53—21no—
134C22×C4×C53—21no—
135C22×C4×C53—21no—
136C22×C4×C53—21no—
137C22×C4×C53—21no—
138C22×C4×C53—21no—
139C22×C4×C53—21no—
140C22×C4×C53—21no—
141C22×C4×C53—21no—
142C22×C4×C53—21no—
143C22×C4×C53—21no—
144C22×C4×C53—21no—
145C22×C4×C53—21no—
146C22×C4×C53—21no—
147C22×C4×C53—21no—
148C22×C4×C53—21no—
149C22×C4×C53—28no—
150C22×C4×C53—28no—
151C22×C4×C53—28no—
152C22×C4×C53—44no—
153C22×C4×C53—44no—
154C22×C4×C53—44no—
155C22×C4×C53—44no—
156C22×C4×C53C22×C412yes—
157C22×C4×C53C22×C412yes—
158C22×C4×C53C2×D412yes—
159C22×C4×C53C2×D412yes—
160C22×C4×C53C2×D412yes—
161C22×C4×C53C2×D412yes—
162C22×C4×C53C2×D412yes—
163C22×C4×C53C2×D412yes—
164C22×C4×C53#4112yes—
165C22×C4×C53#4112yes—
166C22×C4×C53#4112yes—
167C22×C4×C53#4112yes—
168C22×C4×C53#4112yes—
169C22×C4×C53#4112yes—
170C22×Dic53—22no—
171C22×Dic53—22no—
172C22×Dic53—22no—
173C22×Dic53—22no—
174C22×Dic53—22no—
175C22×Dic53—22no—
176C22×Dic53—22no—
177C22×Dic53—22no—
178C22×Dic53—22no—
179C22×Dic53—22no—
180C22×Dic53—22no—
181C22×Dic53—22no—
182C22×Dic53—22no—
183C22×Dic53—22no—
184C22×Dic53—22no—
185C22×Dic53—22no—
186C22×Dic53—22no—
187C22×Dic53—22no—
188C22×Dic53—22no—
189C22×Dic53—22no—
190C22×Dic53—22no—
191C22×Dic53—22no—
192C22×Dic53—22no—
193C22×Dic53—22no—
194C22×Dic53—22no—
195C22×Dic53C22×C414yes—
196C22×Dic53C22×C414yes—
197C22×Dic53C2×D414yes—
198C22⋊C4×C53—28no—
199C22⋊C4×C53—28no—
200C42×C53—28no—
201C42×C53—44no—
202C22⋊Dic53—216no—
203C22⋊Dic53—48no—
204C4⋊Dic53—28no—
205C4⋊Dic53—28no—
206C4⋊Dic53—28no—
207C4⋊Dic53—44no—
208#11719919—48no—
209C4×Dic53—48no—
210C23×C53—22no—
211C23×C53—22no—
212C23×C53—22no—
213C23×C53—22no—
214C23×C53—22no—
215C23×C53—22no—
216C23×C53—22no—
217C23×C53—22no—
218C23×C53—22no—
219C23×C53—22no—
220C23×C53—22no—
221C23×C53—22no—
222C23×C53—22no—
223C23×C53—22no—
224C23×C53—22no—
225C23×C53—22no—
226C23×C53—22no—
227C23×C53—22no—
228C23×C53—41no—
229C23×C53—41no—
230C23×C53—41no—
231C23×C53—41no—
232C23×C53—41no—
233C23×C53—41no—
234C23×C53—41no—
235C23×C53—41no—
236C23×C53—41no—
237C23×C53—41no—
238C23×C53—41no—
239C23×C53—41no—
240C23×C53—41no—
241C23×C53—41no—
242C23×C53—41no—
243C23×C53—41no—
244C23×C53C4×D414yes—
245C23×C53C23×C411yescharacteristic
246C23×C53C22×D411yescharacteristic
247C23×C53C22×D411yescharacteristic
248C23×C53C22×D411yescharacteristic
249C23×C53C2×#4111yescharacteristic
250C23×C53C2×#4111yescharacteristic
251C23×C53C2×#4111yescharacteristic
252C23×C53C2×#4111yescharacteristic
253C23×C53C2×#4111yescharacteristic
254C23×C53C2×#4111yescharacteristic
255C23×C53C2×#4111yescharacteristic
256C23×C53H(5,𝔽2)11yescharacteristic
257C23×C532−1+411yescharacteristic
258C23×C532−1+411yescharacteristic
259C23×C532−1+411yescharacteristic
260C2×C4×C53—22no—
261C2×C4×C53—22no—
262C2×C4×C53—22no—
263C2×C4×C53—22no—
264C2×C4×C53—22no—
265C2×C4×C53—22no—
266C2×C4×C53—22no—
267C2×C4×C53—22no—
268C2×C4×C53—22no—
269C2×C4×C53—22no—
270C2×C4×C53—22no—
271C2×C4×C53—22no—
272C2×C4×C53—22no—
273C2×C4×C53—22no—
274C2×C4×C53—22no—
275C2×C4×C53—22no—
276C2×C4×C53—22no—
277C2×C4×C53—22no—
278C2×C4×C53—41no—
279C2×C4×C53—41no—
280C2×C4×C53—41no—
281C2×C4×C53—41no—
282C2×C4×C53—41no—
283C2×C4×C53—41no—
284C2×C4×C53—41no—
285C2×C4×C53—41no—
286C2×C4×C53—41no—
287C2×C4×C53—41no—
288C2×C4×C53—41no—
289C2×C4×C53—41no—
290C2×C4×C53—41no—
291C2×C4×C53—41no—
292C2×C4×C53—41no—
293C2×C4×C53—41no—
294C2×C4×C53—416no—
295C2×C4×C53#11714yes—
296C2×C4×C53C4×D414yes—
297C2×C4×C53C4×D414yes—
298C2×C4×C53#12114yes—
299C2×C4×C53#12114yes—
300C2×C4×C53#12314yes—
301C2×C4×C53#12414yes—
302C2×C4×C53#12614yes—
303C2×Dic53—24no—
304C2×Dic53—24no—
305C2×Dic53—24no—
306C2×Dic53—24no—
307C2×Dic53—24no—
308C2×Dic53—24no—
309C2×Dic53—24no—
310C2×Dic53—24no—
311C2×Dic53—24no—
312C2×Dic53—42no—
313C2×Dic53—42no—
314C2×Dic53—42no—
315C2×Dic53—42no—
316C2×Dic53—42no—
317C2×Dic53—42no—
318C2×Dic53—42no—
319C2×Dic53—42no—
320C2×Dic53—42no—
321C2×Dic53—42no—
322C2×Dic53—42no—
323C2×Dic53—42no—
324C2×Dic53—42no—
325C2×Dic53—42no—
326C2×Dic53—42no—
327C2×Dic53—42no—
328C2×Dic53—42no—
329C2×Dic53—42no—
330C2×Dic53—42no—
331#13994—531nomaximal, Sylow
332C22×C53—24no—
333C22×C53—24no—
334C22×C53—24no—
335C22×C53—42no—
336C22×C53—42no—
337C22×C53—42no—
338C22×C53—42no—
339C22×C53—42no—
340C22×C53—42no—
341C22×C53—42no—
342C22×C53—42no—
343C22×C53—42no—
344C22×C53—42no—
345C22×C53—42no—
346C22×C53—42no—
347C22×C53C2×#11711yescharacteristic
348C22×C53C2×C4×D411yescharacteristic
349C22×C53C2×C4×D411yescharacteristic
350C22×C53C2×C4×D411yescharacteristic
351C22×C53C4×#4111yescharacteristic
352C22×C53#51911yescharacteristic
353C22×C53#52011yescharacteristic
354C22×C53C2×#12111yescharacteristic
355C22×C53C2×#12111yescharacteristic
356C22×C53C2×#12311yescharacteristic
357C22×C53#52511yescharacteristic
358C22×C53C2×#12411yescharacteristic
359C22×C53C2×#12611yescharacteristic
360C22×C53#52911yescharacteristic
361C22×C53#53211yescharacteristic
362C22×C53#53611yescharacteristic
363C22×C53#53711yescharacteristic
364C22×C53#54111yescharacteristic
365C22×C53#54211yescharacteristic
366C22×C53D4211yescharacteristic
367C22×C53#54711yescharacteristic
368C22×C53#54711yescharacteristic
369C22×C53#54711yescharacteristic
370C22×C53#54711yescharacteristic
371C22×C53#54811yescharacteristic
372C22×C53#54811yescharacteristic
373C22×C53#55211yescharacteristic
374C22×C53#55211yescharacteristic
375C22×C53#55211yescharacteristic
376C22×C53#55211yescharacteristic
377C22×C53#55211yescharacteristic
378C22×C53#55311yescharacteristic
379C22×C53#55511yescharacteristic
380C22×C53#55511yescharacteristic
381C22×C53#55611yescharacteristic
382C4×C53—24no—
383C4×C53—42no—
384C4×C53—42no—
385C4×C53—42no—
386C4×C53—42no—
387C4×C53#38818yescomplemented
388Dic53—44no—
389Dic53—44no—
390Dic53—44no—
391Dic53—82no—
392C2×#389—531no—
393C2×#388—532no—
394C2×#380—531no—
395C2×#380—531no—
396C2×C4×C4⋊C4—531no—
397C2×C4×C22⋊C4D5311yescharacteristic
398#1442—532no—
399#1440—532no—
400C4⋊#95—531no—
401C4⋊#95—531no—
402#1434—532no—
403C2×C53—44no—
404C2×C53C2×#38811yescharacteristic
405C2×C53C4×#12111yescharacteristic
406C2×C53#232311yescharacteristic
407C2×C53#234411yescharacteristic
408C2×C53#234611yescharacteristic
409C2×C53#236111yescharacteristic
410C2×C53#236211yescharacteristic
411C2×C53#248511yescharacteristic
412C2×C53#248611yescharacteristic
413C2×C53#248911yescharacteristic
414C2×C53#249111yescharacteristic
415C2×C53#249511yescharacteristic
416C2×C53#249611yescharacteristic
417C2×C53#253611yescharacteristic
418C2×C53#253711yescharacteristic
419C24×C4C2×D5311yescharacteristic
420C22×C4⋊C4—531no—
421C22×C4⋊C4—531no—
422C22×C4⋊C4—531no—
423C22×C4⋊C4—531no—
424C22×C4⋊C4—532no—
425C22×C22⋊C4—532no—
426C22×C22⋊C4—532no—
427C22×C22⋊C4C2×D5311yescharacteristic
428C22×C22⋊C4C2×D5311yescharacteristic
429C22×C42—532no—
430C22×C42C2×D5311yescharacteristic
431C22×C42C2×D5311yescharacteristic
432#389—1064no—
433#388—1068no—
434#380—538no—
435#380—1064no—
436C4×C4⋊C4—1064no—
437C4×C22⋊C4—24no—
438C2×#95—532no—
439C2×#95—532no—
440C2×#95—532no—
441C2×#95—532no—
442C2×#95—532no—
443C2×#95—532no—
444C2×#95—532no—
445C2×#95—532no—
446C2×#95C2×D5311yescharacteristic
447C2×#95C2×D5311yescharacteristic
448C53#1399411yescharacteristic, complemented, Sylow
449C25C22×D5311yescharacteristic
450C23×C4—22no—
451C23×C4—22no—
452C23×C4—22no—
453C23×C4—22no—
454C23×C4—22no—
455C23×C4—22no—
456C23×C4—532no—
457C23×C4—532no—
458C23×C4—532no—
459C23×C4—532no—
460C23×C4C4×D5314yes—
461C23×C4C22×D5311yescharacteristic
462C23×C4C22×D5311yescharacteristic
463C23×C4C22×D5311yescharacteristic
464C23×C4C22×D5311yescharacteristic
465C23×C4C22×D5311yescharacteristic
466C23×C4C22×D5311yescharacteristic
467C2×C4⋊C4—534no—
468C2×C4⋊C4—534no—
469C2×C4⋊C4—534no—
470C2×C4⋊C4—1062no—
471C2×C4⋊C4—1062no—
472C2×C4⋊C4—1062no—
473C2×C4⋊C4—1062no—
474C2×C4⋊C4—1062no—
475C2×C4⋊C4—1062no—
476C2×C4⋊C4—1064no—
477C2×C4⋊C4—1064no—
478C2×C4⋊C4—1062no—
479C2×C4⋊C4—1062no—
480C2×C4⋊C4—1062no—
481C2×C4⋊C4—2122no—
482C2×C22⋊C4—22no—
483C2×C22⋊C4—22no—
484C2×C22⋊C4—22no—
485C2×C22⋊C4—22no—
486C2×C22⋊C4—22no—
487C2×C22⋊C4—538no—
488C2×C22⋊C4—1064no—
489C2×C22⋊C4—1064no—
490C2×C22⋊C4—1064no—
491C2×C22⋊C4—1064no—
492C2×C22⋊C4—2122no—
493C2×C22⋊C4D21214yes—
494C2×C42—22no—
495C2×C42—22no—
496C2×C42—22no—
497C2×C42—22no—
498C2×C42—22no—
499C2×C42—1064no—
500C2×C42—1064no—
501C2×C42—1064no—
502C2×C42C22⋊D5314yes—
503#95—22no—
504#95—22no—
505#95—538no—
506#95—1064no—
507#95—1064no—
508#95—1064no—
509#95—1064no—
510#95—1064no—
511#95—1064no—
512#95—2122no—
513C24—21no—
514C24—21no—
515C24—21no—
516C24—21no—
517C24—21no—
518C24—21no—
519C24—21no—
520C24—21no—
521C24—21no—
522C24—21no—
523C24—21no—
524C24—21no—
525C24C2×C4×D5312yes—
526C24C2×D21212yes—
527C24#1171994512yes—
528C24C23×D5311yescharacteristic
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—28no—
558C22×C4—28no—
559C22×C4—28no—
560C22×C4—44no—
561C22×C4—44no—
562C22×C4—44no—
563C22×C4—44no—
564C22×C4—534no—
565C22×C4—534no—
566C22×C4—534no—
567C22×C4—1062no—
568C22×C4—1062no—
569C22×C4—1062no—
570C22×C4—1062no—
571C22×C4—1062no—
572C22×C4—1062no—
573C22×C4—1062no—
574C22×C4—1062no—
575C22×C4—1062no—
576C22×C4—1062no—
577C22×C4—1062no—
578C22×C4—1062no—
579C22×C4—1062no—
580C22×C4—1062no—
581C22×C4—1062no—
582C22×C4—1062no—
583C22×C4—1062no—
584C22×C4—1062no—
585C22×C4—1062no—
586C22×C4—1062no—
587C22×C4—1062no—
588C22×C4—1062no—
589C22×C4—1062no—
590C22×C4—1062no—
591C22×C4—1062no—
592C22×C4C2×C4×D5312yes—
593C22×C4C2×C4×D5312yes—
594C22×C4C2×D21212yes—
595C22×C4C2×D21212yes—
596C22×C4#1171994512yes—
597C22×C4#1171994512yes—
598C22×C4#1171994512yes—
599C22×C4D4×D5312yes—
600C22×C4#1171994712yes—
601C22×C4#1171994712yes—
602C22×C4#1171994712yes—
603C22×C4C2×C22⋊D5312yes—
604C22×C4C2×C22⋊D5312yes—
605C22×C4C2×C22⋊D5312yes—
606C4⋊C4—1068no—
607C4⋊C4—1068no—
608C4⋊C4—1068no—
609C4⋊C4—2128no—
610C4⋊C4—2124no—
611C22⋊C4—28no—
612C22⋊C4—28no—
613C22⋊C4—10616no—
614C22⋊C4—2128no—
615C42—28no—
616C42—44no—
617C42—2128no—
618C23—22no—
619C23—22no—
620C23—22no—
621C23—22no—
622C23—22no—
623C23—22no—
624C23—22no—
625C23—22no—
626C23—22no—
627C23—22no—
628C23—22no—
629C23—22no—
630C23—22no—
631C23—22no—
632C23—22no—
633C23—22no—
634C23—22no—
635C23—22no—
636C23—41no—
637C23—41no—
638C23—41no—
639C23—41no—
640C23—41no—
641C23—41no—
642C23—41no—
643C23—41no—
644C23—41no—
645C23—41no—
646C23—41no—
647C23—41no—
648C23—41no—
649C23—41no—
650C23—41no—
651C23—41no—
652C23C4×D21214yes—
653C23C22×C4×D5311yescharacteristic
654C23C2×D4×D5311yescharacteristic
655C23C22×C22⋊D5311yescharacteristic
656C23C22×D21211yescharacteristic
657C23C2×#1171994711yescharacteristic
658C23C2×#1171994711yescharacteristic
659C23C2×#1171994711yescharacteristic
660C23C2×#1171994511yescharacteristic
661C23C2×#1171994511yescharacteristic
662C23C2×#1171994511yescharacteristic
663C23C2×#1171994511yescharacteristic
664C23#1313326311yescharacteristic
665C23#1313326411yescharacteristic
666C23#1313326411yescharacteristic
667C23#1313326411yescharacteristic
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—41no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—416no—
703C2×C4—1064no—
704C2×C4—1064no—
705C2×C4—1064no—
706C2×C4—1064no—
707C2×C4—1064no—
708C2×C4—1064no—
709C2×C4—1064no—
710C2×C4—1064no—
711C2×C4—1064no—
712C2×C4—2122no—
713C2×C4—2122no—
714C2×C4—2122no—
715C2×C4—2122no—
716C2×C4—2122no—
717C2×C4—2122no—
718C2×C4—2122no—
719C2×C4—2122no—
720C2×C4—2122no—
721C2×C4—2122no—
722C2×C4—2122no—
723C2×C4—2122no—
724C2×C4—2122no—
725C2×C4—2122no—
726C2×C4—2122no—
727C2×C4—2122no—
728C2×C4—2122no—
729C2×C4—2122no—
730C2×C4—2122no—
731C2×C4#1313317314yes—
732C2×C4#1313317714yes—
733C2×C4C4×C22⋊D5314yes—
734C2×C4#1313318814yes—
735C2×C4#1313319114yes—
736C2×C4#1313319814yes—
737C2×C4#1313320314yes—
738C2×C4#1313321014yes—
739C22—24no—
740C22—24no—
741C22—24no—
742C22—42no—
743C22—42no—
744C22—42no—
745C22—42no—
746C22—42no—
747C22—42no—
748C22—42no—
749C22—42no—
750C22—42no—
751C22—42no—
752C22—42no—
753C22—42no—
754C22C2×#1313317311yescharacteristic
755C22C2×#1313317711yescharacteristic
756C22C2×C4×C22⋊D5311yescharacteristic
757C22C2×C4×D21211yescharacteristic
758C22C4×#1171994511yescharacteristic
759C22#1681110011yescharacteristic
760C22#1681110311yescharacteristic
761C22C2×#1313318811yescharacteristic
762C22C2×#1313319111yescharacteristic
763C22C2×#1313319811yescharacteristic
764C22#1681113411yescharacteristic
765C22C2×#1313320311yescharacteristic
766C22C2×#1313321011yescharacteristic
767C22#1681115711yescharacteristic
768C22#1681117311yescharacteristic
769C22#1681119411yescharacteristic
770C22#1681120111yescharacteristic
771C22#1681123511yescharacteristic
772C22#1681124411yescharacteristic
773C22D4×D21211yescharacteristic
774C22#1681127711yescharacteristic
775C22#1681127711yescharacteristic
776C22#1681127711yescharacteristic
777C22#1681127811yescharacteristic
778C22#1681128211yescharacteristic
779C22#1681128211yescharacteristic
780C22#1681131311yescharacteristic
781C22#1681131311yescharacteristic
782C22#1681131311yescharacteristic
783C22#1681131311yescharacteristic
784C22#1681131311yescharacteristic
785C22#1681131911yescharacteristic
786C22#1681133811yescharacteristic
787C22#1681133811yescharacteristic
788C22#1681134311yescharacteristic
789C4—24no—
790C4—42no—
791C4—42no—
792C4—42no—
793C4—42no—
794C4—4242no—
795C4—2124no—
796C4—2124no—
797C4—2124no—
798C4#1681051118yescomplemented
799C2—44no—
800C2C2×#1681051111yescharacteristic
801C2C4×#1313319111yescharacteristic
802C2#2027739711yescharacteristic
803C2#2027758211yescharacteristic
804C2#2027759811yescharacteristic
805C2#2027772911yescharacteristic
806C2#2027774011yescharacteristic
807C2#2027901211yescharacteristic
808C2#2027902311yescharacteristic
809C2#2027905611yescharacteristic
810C2#2027907811yescharacteristic
811C2#2027912611yescharacteristic
812C2#2027913711yescharacteristic
813C2#2027962411yescharacteristic
814C2#2027962811yescharacteristic
subgroupG/H
center, FrattiniC24C23×D53
commutatorC23×C53C23×C4
FittingC2×C4×C22⋊C4×C53C2
socle, cosocleC24×C53C24
prime radicalC25×C53C23
hypercenterC2×C4×C22⋊C4D53
hypocenterC53#13994
LCSG ▷ C23×C53 ▷ C53
UCSC1 ◁ C24 ◁ C2×C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#16810521C2semidirect
5. C2×C4×C4⋊Dic53C2semidirect
6. #20272970C2semidirect
8. #20272945C2semidirect
9. #20272945C2semidirect
10. #20272939C2semidirect
23. #16810483C4semidirect
387. C4×C53#388semidirect
448. C53#13994semidirect
798. C4#16810511semidirect

Maximal subgroups

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

subgroupindex
C2×#168105212
C2×#168105112
C2×#168104832
C2×C4×C4⋊Dic532
#202729702
#202729622
#202729452
#202729392
C2×C4×C22⋊C4×C532
#1399453