Finite Group Databasebeta

← #27427952

Subgroups — #27427952

Order 13568.

1156 conjugacy classes of subgroups.

The subgroup lattice has 778 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16810774C211yesmaximal, characteristic
2C2×C4×#11719923C211yesmaximal, characteristic, complemented
3#20278240C211yesmaximal, characteristic, complemented
4#20276248C211yesmaximal, characteristic, complemented
5#20276151C211yesmaximal, characteristic, complemented
6#20276032C211yesmaximal, characteristic, complemented
7#20275911C211yesmaximal, characteristic, complemented
8#20275401C211yesmaximal, characteristic, complemented
9#20275323C211yesmaximal, characteristic, complemented
10#20275073C211yesmaximal, characteristic, complemented
11#20275049C211yesmaximal, characteristic, complemented
12#20274976C211yesmaximal, characteristic, complemented
13#20274715C211yesmaximal, characteristic, complemented
14#20274646C211yesmaximal, characteristic
15D4×C22⋊C4×C53C211yesmaximal, characteristic
16C22×#11719923C2211yescharacteristic
17C22×#11719923C2211yescharacteristic
18C2×#13133196C2211yescharacteristic
19C2×C4×Dic106C2211yescharacteristic, complemented
20#16810774—24no—
21C4×#11719923—24no—
22C2×#13133148C2211yescharacteristic, complemented
23C2×#13133148C2211yescharacteristic, complemented
24C2×C4⋊#88322C2211yescharacteristic, complemented
25C2×#13133140C2211yescharacteristic, complemented
26C2×#13133140C2211yescharacteristic, complemented
27C2×#13133138C2211yescharacteristic
28C2×#13133138C2211yescharacteristic
29C2×#13133138C2211yescharacteristic
30C2×#13133138C2211yescharacteristic
31C2×#13133138C2211yescharacteristic
32C2×#13133138C2211yescharacteristic
33C2×C22⋊#88322C2211yescharacteristic
34C2×C22⋊#88322C2211yescharacteristic
35C2×C4×#88322C2211yescharacteristic, complemented
36#16810559—21no—
37#16810557—21no—
38#16810529C2211yescharacteristic, complemented
39#16810521C2211yescharacteristic, complemented
40#16810516—21no—
41#16810506—21no—
42#16810493C2211yescharacteristic, complemented
43#16810483C2211yescharacteristic
44#16810385C2211yescharacteristic, complemented
45#16810385C2211yescharacteristic, complemented
46#16810385C2211yescharacteristic, complemented
47#16810385C2211yescharacteristic, complemented
48#16810378C2211yescharacteristic, complemented
49#16810378C2211yescharacteristic, complemented
50C23×D4×C53C2211yescharacteristic
51C2×C4×D4×C53C2211yescharacteristic
52C2×C4×D4×C53C2211yescharacteristic
53C22×C22⋊C4×C53—21no—
54C53×#390C2211yescharacteristic
55C53×#390C2211yescharacteristic
56C53×#386—21no—
57C53×#386—21no—
58C53×#380C2211yescharacteristic
59C53×#379—21no—
60C4×C22⋊C4×C53C2211yescharacteristic
61C22×Dic106C2311yescharacteristic
62C2×#11719923—22no—
63C2×#11719923—22no—
64C2×#11719923—22no—
65C2×#11719923—22no—
66C2×#11719923—41no—
67C2×#11719923D414yes—
68C22×#88322C2311yescharacteristic
69C22×#88322C2311yescharacteristic
70C22×#88322C2311yescharacteristic
71C22×#88322C2311yescharacteristic
72#13133196—22no—
73#13133196—41no—
74C4×Dic106—22no—
75C4×Dic106—41no—
76C2×C4⋊Dic53—21no—
77C2×C4⋊Dic53—21no—
78C2×C4⋊Dic53C2311yescharacteristic
79C2×C4⋊Dic53C2311yescharacteristic
80C2×C4⋊Dic53C2311yescharacteristic
81C2×#11719919—21no—
82C2×#11719919—21no—
83C2×#11719919—21no—
84C2×C22⋊Dic53—21no—
85C2×C22⋊Dic53—21no—
86C2×C4×Dic53—21no—
87#13133148—22no—
88#13133148—41no—
89C4⋊#88322—41no—
90#13133140—22no—
91#13133140—41no—
92#13133138—22no—
93#13133138—22no—
94#13133138—22no—
95#13133138—22no—
96#13133138—22no—
97#13133138—41no—
98C22⋊#88322—22no—
99C22⋊#88322—41no—
100C4×#88322—22no—
101#13133124—21no—
102#13133124—21no—
103#13133124—21no—
104#13133124—21no—
105C25×C53—21no—
106C22×D4×C53—22no—
107C22×D4×C53—22no—
108C22×D4×C53—22no—
109C22×D4×C53—22no—
110C22×D4×C53—21no—
111C22×D4×C53—41no—
112C22×D4×C53—41no—
113C22×D4×C53C2311yescharacteristic
114C22×D4×C53C2311yescharacteristic
115C23×C4×C53—21no—
116C23×C4×C53—21no—
117C23×C4×C53C2311yescharacteristic
118C4×D4×C53—22no—
119C4×D4×C53—22no—
120C4×D4×C53—41no—
121C4×D4×C53—41no—
122C2×C4⋊C4×C53C2311yescharacteristic
123C2×C4⋊C4×C53C2311yescharacteristic
124C2×C22⋊C4×C53—21no—
125C2×C22⋊C4×C53—21no—
126C2×C22⋊C4×C53—21no—
127C2×C22⋊C4×C53—21no—
128C2×C22⋊C4×C53—21no—
129C2×C22⋊C4×C53—21no—
130C2×C22⋊C4×C53—21no—
131C2×C22⋊C4×C53—44no—
132C2×C22⋊C4×C53D411yescharacteristic
133C2×C22⋊C4×C53D411yescharacteristic
134C2×C42×C53C2311yescharacteristic
135C2×C42×C53C2311yescharacteristic
136#95×C53—21no—
137#95×C53D411yescharacteristic
138#95×C53D411yescharacteristic
139C24×C53—21no—
140C24×C53—24no—
141C24×C53—21no—
142C24×C53—42no—
143C24×C53—42no—
144C24×C53—42no—
145C24×C53—42no—
146C24×C53—81no—
147C24×C53—81no—
148C24×C53C2×D411yescharacteristic
149C2×D4×C53—24no—
150C2×D4×C53—21no—
151C2×D4×C53—21no—
152C2×D4×C53—21no—
153C2×D4×C53—21no—
154C2×D4×C53—21no—
155C2×D4×C53—21no—
156C2×D4×C53—21no—
157C2×D4×C53—21no—
158C2×D4×C53—42no—
159C2×D4×C53—42no—
160C2×D4×C53—44no—
161C2×D4×C53—44no—
162C2×D4×C53—44no—
163C2×D4×C53—44no—
164C2×D4×C53C2×D412yes—
165C2×D4×C53#4112yes—
166C2×D4×C53#4112yes—
167C2×D4×C53#4112yes—
168C22×C4×C53—21no—
169C22×C4×C53—21no—
170C22×C4×C53—21no—
171C22×C4×C53—21no—
172C22×C4×C53—21no—
173C22×C4×C53—21no—
174C22×C4×C53—21no—
175C22×C4×C53—21no—
176C22×C4×C53—42no—
177C22×C4×C53—42no—
178C22×C4×C53—42no—
179C22×C4×C53—42no—
180C22×C4×C53—81no—
181C22×C4×C53—81no—
182C22×C4×C53C2×D411yescharacteristic
183C22×C4×C53C2×D411yescharacteristic
184C22×C4×C53C2×D411yescharacteristic
185C22×C4×C53C2×D411yescharacteristic
186C22×C4×C53C2×D411yescharacteristic
187C22×C4×C53C2411yescharacteristic
188C22×Dic53—21no—
189C22×Dic53—21no—
190C22×Dic53—21no—
191C22×Dic53—21no—
192C2×Dic106—21no—
193C2×Dic106—21no—
194C2×Dic106—21no—
195C2×Dic106—21no—
196C2×Dic106—21no—
197C2×Dic106C2×D412yes—
198C4⋊C4×C53—21no—
199C4⋊C4×C53—21no—
200C4⋊C4×C53—21no—
201C4⋊C4×C53—21no—
202C22⋊C4×C53—41no—
203C22⋊C4×C53—42no—
204C22⋊C4×C53—42no—
205C22⋊C4×C53—42no—
206C22⋊C4×C53—42no—
207C22⋊C4×C53—42no—
208C22⋊C4×C53—81no—
209C22⋊C4×C53—81no—
210C22⋊C4×C53SD1614yescomplemented
211C42×C53—21no—
212C42×C53—21no—
213C42×C53—21no—
214C42×C53—21no—
215C22⋊Dic53—42no—
216C22⋊Dic53—81no—
217#11719923—28no—
218#11719923—44no—
219C4⋊Dic53—21no—
220C4⋊Dic53—21no—
221C4⋊Dic53—21no—
222C4⋊Dic53—21no—
223C4⋊Dic53—21no—
224C4⋊Dic53—21no—
225C4⋊Dic53—42no—
226C4⋊Dic53—81no—
227#11719919—42no—
228#11719919—42no—
229#11719919—81no—
230C4×Dic53—42no—
231C2×#88322—21no—
232C2×#88322—21no—
233C2×#88322—21no—
234C2×#88322—21no—
235C2×#88322—21no—
236C2×#88322—21no—
237C2×#88322—21no—
238C2×#88322—21no—
239C2×#88322—21no—
240C2×#88322—21no—
241C2×#88322—21no—
242C2×#88322C2×D412yes—
243C23×C53—21no—
244C23×C53—22no—
245C23×C53—21no—
246C23×C53—22no—
247C23×C53—21no—
248C23×C53—22no—
249C23×C53—21no—
250C23×C53—21no—
251C23×C53—21no—
252C23×C53—22no—
253C23×C53—48no—
254C23×C53—48no—
255C23×C53—41no—
256C23×C53—41no—
257C23×C53—41no—
258C23×C53—41no—
259C23×C53—41no—
260C23×C53—41no—
261C23×C53—41no—
262C23×C53—41no—
263C23×C53—41no—
264C23×C53—41no—
265C23×C53—84no—
266C23×C53—84no—
267C23×C53—84no—
268C23×C53—84no—
269C23×C53—84no—
270C23×C53C2×SD1612yes—
271C23×C53C22×D411yescharacteristic
272D4×C53—22no—
273D4×C53—22no—
274D4×C53—22no—
275D4×C53—22no—
276D4×C53—22no—
277D4×C53—48no—
278D4×C53—41no—
279D4×C53—41no—
280D4×C53#12314yes—
281C2×C4×C53—21no—
282C2×C4×C53—21no—
283C2×C4×C53—21no—
284C2×C4×C53—21no—
285C2×C4×C53—21no—
286C2×C4×C53—21no—
287C2×C4×C53—21no—
288C2×C4×C53—21no—
289C2×C4×C53—21no—
290C2×C4×C53—21no—
291C2×C4×C53—21no—
292C2×C4×C53—21no—
293C2×C4×C53—21no—
294C2×C4×C53—41no—
295C2×C4×C53—41no—
296C2×C4×C53—41no—
297C2×C4×C53—41no—
298C2×C4×C53—41no—
299C2×C4×C53—41no—
300C2×C4×C53—41no—
301C2×C4×C53—41no—
302C2×C4×C53—41no—
303C2×C4×C53—41no—
304C2×C4×C53—84no—
305C2×C4×C53—84no—
306C2×C4×C53C2×SD1612yes—
307C2×C4×C53C2×SD1612yes—
308C2×C4×C53C22×D411yescharacteristic
309C2×C4×C53C2×#4111yescharacteristic
310C2×C4×C53C2×#4111yescharacteristic
311C2×C4×C53C2×#4111yescharacteristic
312C2×C4×C53H(5,𝔽2)11yescharacteristic
313C2×C4×C53H(5,𝔽2)11yescharacteristic
314C2×Dic53—22no—
315C2×Dic53—41no—
316C2×Dic53—41no—
317C2×Dic53—41no—
318C2×Dic53—41no—
319C2×Dic53—41no—
320C2×Dic53—41no—
321C2×Dic53—41no—
322C2×Dic53—41no—
323C2×Dic53—41no—
324C2×Dic53—41no—
325C2×Dic53—41no—
326Dic106—22no—
327Dic106—22no—
328Dic106—41no—
329Dic106—41no—
330#88322—22no—
331#88322—41no—
332#88322—41no—
333#88322—41no—
334#24901—531nomaximal, Sylow
335C22×C53—22no—
336C22×C53—24no—
337C22×C53—22no—
338C22×C53—22no—
339C22×C53—42no—
340C22×C53—41no—
341C22×C53—42no—
342C22×C53—41no—
343C22×C53—41no—
344C22×C53—42no—
345C22×C53—42no—
346C22×C53—42no—
347C22×C53—41no—
348C22×C53—42no—
349C22×C53—42no—
350C22×C53—42no—
351C22×C53—42no—
352C22×C53—816no—
353C22×C53—81no—
354C22×C53—81no—
355C22×C53—81no—
356C22×C53—81no—
357C22×C53#52511yescharacteristic
358C22×C53D4211yescharacteristic
359C22×C53#54611yescharacteristic
360C22×C53C22×SD1611yescharacteristic
361C22×C53#57511yescharacteristic
362C22×C53#57611yescharacteristic
363C22×C53#57711yescharacteristic
364C4×C53—22no—
365C4×C53—22no—
366C4×C53—41no—
367C4×C53—41no—
368C4×C53—41no—
369C4×C53—81no—
370C4×C53—81no—
371C4×C53C2×#12311yescharacteristic
372C4×C53#53811yescharacteristic
373C4×C53#54611yescharacteristic
374C4×C53#55111yescharacteristic
375Dic53—42no—
376Dic53—81no—
377Dic53—81no—
378Dic53—81no—
379C2×#450—531no—
380C2×C4×SD16—531no—
381#2423—531no—
382D4×C22⋊C4D5311yescharacteristic
383#2094—531no—
384#2077—531no—
385#2055—531no—
386#2035—531no—
387#1934—531no—
388#1923—531no—
389#1880—531no—
390#1877—531no—
391#1864—531no—
392#1802—531no—
393#1786—531no—
394C2×C53—42no—
395C2×C53—44no—
396C2×C53—82no—
397C2×C53#241811yescharacteristic
398C2×C53#310111yescharacteristic
399C2×C53#311811yescharacteristic
400C2×C53#326811yescharacteristic
401C2×C53D4×SD1611yescharacteristic
402C2×C53#329511yescharacteristic
403C2×C53#332311yescharacteristic
404C23×D4C2×D5311yescharacteristic
405C22×SD16—531no—
406C22×SD16—531no—
407C2×C22⋊Q8—531no—
408C2×C4×Q8—531no—
409C2×C4×D4C2×D5311yescharacteristic
410C2×C4×D4C2×D5311yescharacteristic
411C22×C22⋊C4—21no—
412#450—1064no—
413C4×SD16—1064no—
414C2×#106—531no—
415C2×#106—531no—
416C2×C4⋊C8—531no—
417C2×#103—531no—
418C2×#103—531no—
419C2×#102—531no—
420C2×#102—531no—
421C2×#102—531no—
422C2×#102—531no—
423C2×#102—531no—
424C2×#102—531no—
425C2×C22⋊C8—531no—
426C2×C22⋊C8—531no—
427C2×C4×C8—531no—
428#399—1061no—
429#398—1061no—
430#391—531no—
431#390C2×D5311yescharacteristic
432#390C2×D5311yescharacteristic
433#389—531no—
434#388—1061no—
435#387—1061no—
436#386—21no—
437#386—21no—
438#384—531no—
439#380—531no—
440#380C2×D5311yescharacteristic
441#379—21no—
442C4×C22⋊C4C2×D5311yescharacteristic
443#340—531no—
444#340—531no—
445#340—531no—
446#340—531no—
447#336—531no—
448#336—531no—
449C53#2490111yescharacteristic, complemented, Sylow
450C25—21no—
451C22×Q8—531no—
452C22×D4—22no—
453C22×D4—22no—
454C22×D4—22no—
455C22×D4—22no—
456C22×D4—21no—
457C22×D4—41no—
458C22×D4—41no—
459C22×D4C22×D5311yescharacteristic
460C22×D4C22×D5311yescharacteristic
461C23×C4—21no—
462C23×C4—21no—
463C23×C4C22×D5311yescharacteristic
464C2×SD16—534no—
465C2×SD16—1062no—
466C2×SD16—1062no—
467C2×SD16—1062no—
468C2×SD16—1062no—
469C2×SD16—2121no—
470C22×C8—531no—
471C22×C8—531no—
472C22×C8—531no—
473C22×C8—531no—
474C22⋊Q8—1062no—
475C22⋊Q8—2121no—
476C4×Q8—1062no—
477C4×Q8—2121no—
478C4×D4—22no—
479C4×D4—22no—
480C4×D4—41no—
481C4×D4—41no—
482C2×C4⋊C4—531no—
483C2×C4⋊C4—531no—
484C2×C4⋊C4—531no—
485C2×C4⋊C4—1061no—
486C2×C4⋊C4—1061no—
487C2×C4⋊C4—1061no—
488C2×C4⋊C4—1061no—
489C2×C4⋊C4—1061no—
490C2×C4⋊C4C22×D5311yescharacteristic
491C2×C4⋊C4C22×D5311yescharacteristic
492C2×C22⋊C4—21no—
493C2×C22⋊C4—21no—
494C2×C22⋊C4—21no—
495C2×C22⋊C4—21no—
496C2×C22⋊C4—21no—
497C2×C22⋊C4—21no—
498C2×C22⋊C4—21no—
499C2×C22⋊C4—44no—
500C2×C22⋊C4—1061no—
501C2×C22⋊C4—1061no—
502C2×C22⋊C4C22⋊D5311yescharacteristic
503C2×C22⋊C4C22⋊D5311yescharacteristic
504C2×C42—1061no—
505C2×C42C22×D5311yescharacteristic
506C2×C42C22×D5311yescharacteristic
507#106—1062no—
508#106—2121no—
509C4⋊C8—2121no—
510#103—1062no—
511#103—2121no—
512#102—1062no—
513#102—1062no—
514#102—1062no—
515#102—1062no—
516#102—1062no—
517#102—2121no—
518C22⋊C8—1062no—
519C22⋊C8—2121no—
520C4×C8—1062no—
521#95—21no—
522#95—1061no—
523#95—1061no—
524#95—1061no—
525#95—1061no—
526#95C22⋊D5311yescharacteristic
527#95C22⋊D5311yescharacteristic
528C24—21no—
529C24—24no—
530C24—21no—
531C24—42no—
532C24—42no—
533C24—42no—
534C24—42no—
535C24—81no—
536C24—81no—
537C24C2×C22⋊D5311yescharacteristic
538C2×Q8—532no—
539C2×Q8—1061no—
540C2×Q8—1061no—
541C2×Q8—1061no—
542C2×Q8—1061no—
543C2×Q8—1061no—
544C2×D4—24no—
545C2×D4—21no—
546C2×D4—21no—
547C2×D4—21no—
548C2×D4—21no—
549C2×D4—21no—
550C2×D4—21no—
551C2×D4—21no—
552C2×D4—21no—
553C2×D4—42no—
554C2×D4—42no—
555C2×D4—44no—
556C2×D4—44no—
557C2×D4—44no—
558C2×D4—44no—
559C2×D4#1171994512yes—
560C2×D4#1171994512yes—
561C2×D4D4×D5312yes—
562C2×D4#1171994712yes—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—42no—
572C22×C4—42no—
573C22×C4—42no—
574C22×C4—42no—
575C22×C4—81no—
576C22×C4—81no—
577C22×C4—1061no—
578C22×C4—1061no—
579C22×C4—1061no—
580C22×C4—1061no—
581C22×C4C2×C22⋊D5311yescharacteristic
582C22×C4C2×C22⋊D5311yescharacteristic
583C22×C4C2×C22⋊D5311yescharacteristic
584C22×C4C2×C22⋊D5311yescharacteristic
585C22×C4C2×C22⋊D5311yescharacteristic
586C22×C4C23×D5311yescharacteristic
587SD16—1068no—
588SD16—2124no—
589C2×C8—532no—
590C2×C8—1061no—
591C2×C8—1061no—
592C2×C8—1061no—
593C2×C8—1061no—
594C2×C8—1061no—
595C2×C8—1061no—
596C2×C8—1061no—
597C2×C8—1061no—
598C2×C8—1061no—
599C2×C8—1061no—
600C2×C8—1061no—
601C4⋊C4—21no—
602C4⋊C4—21no—
603C4⋊C4—21no—
604C4⋊C4—21no—
605C4⋊C4—1061no—
606C4⋊C4—1061no—
607C4⋊C4—1061no—
608C4⋊C4—1061no—
609C4⋊C4—1061no—
610C4⋊C4—1061no—
611C4⋊C4—4241no—
612C4⋊C4—4241no—
613C4⋊C4—2122no—
614C4⋊C4—2122no—
615C4⋊C4—2122no—
616C22⋊C4—41no—
617C22⋊C4—42no—
618C22⋊C4—42no—
619C22⋊C4—42no—
620C22⋊C4—42no—
621C22⋊C4—42no—
622C22⋊C4—81no—
623C22⋊C4—81no—
624C22⋊C4—4241no—
625C22⋊C4—2122no—
626C22⋊C4#1171992314yescomplemented
627C42—21no—
628C42—21no—
629C42—21no—
630C42—21no—
631C42—2122no—
632C23—22no—
633C23—21no—
634C23—21no—
635C23—22no—
636C23—21no—
637C23—21no—
638C23—21no—
639C23—22no—
640C23—21no—
641C23—22no—
642C23—48no—
643C23—48no—
644C23—41no—
645C23—41no—
646C23—41no—
647C23—41no—
648C23—41no—
649C23—41no—
650C23—41no—
651C23—41no—
652C23—41no—
653C23—41no—
654C23—84no—
655C23—84no—
656C23—84no—
657C23—84no—
658C23—84no—
659C23C2×#1171992312yes—
660C23C22×C22⋊D5311yescharacteristic
661Q8—1062no—
662Q8—1062no—
663Q8—2121no—
664Q8—2121no—
665D4—22no—
666D4—22no—
667D4—22no—
668D4—22no—
669D4—22no—
670D4—48no—
671D4—41no—
672D4—41no—
673D4#1313319914yes—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—21no—
685C2×C4—21no—
686C2×C4—21no—
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—84no—
698C2×C4—84no—
699C2×C4—1062no—
700C2×C4—2121no—
701C2×C4—2121no—
702C2×C4—2121no—
703C2×C4—2121no—
704C2×C4—2121no—
705C2×C4—2121no—
706C2×C4—2121no—
707C2×C4—2121no—
708C2×C4—2121no—
709C2×C4—2121no—
710C2×C4—2121no—
711C2×C4C2×#1171992312yes—
712C2×C4C2×#1171992312yes—
713C2×C4C2×D4×D5311yescharacteristic
714C2×C4C2×#1171994711yescharacteristic
715C2×C4C2×#1171994511yescharacteristic
716C2×C4C2×#1171994511yescharacteristic
717C2×C4#1313326211yescharacteristic
718C2×C4#1313326211yescharacteristic
719C8—1062no—
720C8—2121no—
721C8—2121no—
722C8—2121no—
723C22—22no—
724C22—22no—
725C22—24no—
726C22—22no—
727C22—41no—
728C22—42no—
729C22—42no—
730C22—42no—
731C22—41no—
732C22—42no—
733C22—41no—
734C22—42no—
735C22—41no—
736C22—42no—
737C22—42no—
738C22—42no—
739C22—42no—
740C22—816no—
741C22—81no—
742C22—81no—
743C22—81no—
744C22—81no—
745C22#1681113411yescharacteristic
746C22D4×C22⋊D5311yescharacteristic
747C22#1681126711yescharacteristic
748C22C22×#1171992311yescharacteristic
749C22#1681142111yescharacteristic
750C22#1681142611yescharacteristic
751C22#1681143411yescharacteristic
752C4—22no—
753C4—22no—
754C4—41no—
755C4—41no—
756C4—41no—
757C4—81no—
758C4—81no—
759C4—4241no—
760C4—4241no—
761C4—4241no—
762C4—2122no—
763C4C2×#1313319911yescharacteristic
764C4#1681121111yescharacteristic
765C4#1681126311yescharacteristic
766C4#1681129911yescharacteristic
767C2—42no—
768C2—44no—
769C2—82no—
770C2#2027817711yescharacteristic
771C2#2028472311yescharacteristic
772C2#2028489911yescharacteristic
773C2#2028625111yescharacteristic
774C2D4×#1171992311yescharacteristic
775C2#2028653911yescharacteristic
776C2#2028693111yescharacteristic
subgroupG/H
centerC23C22×C22⋊D53
commutator, cosocleC22×C4×C53C24
FrattiniC22×C4C23×D53
FittingD4×C22⋊C4×C53C2
socleC23×C53C22×D4
prime radicalC23×D4×C53C22
hypercenterD4×C22⋊C4D53
hypocenterC53#24901
LCSG ▷ C22×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ D4×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×C4×#11719923C2semidirect
3. #20278240C2semidirect
4. #20276248C2semidirect
5. #20276151C2semidirect
6. #20276032C2semidirect
7. #20275911C2semidirect
8. #20275401C2semidirect
9. #20275323C2semidirect
10. #20275073C2semidirect
11. #20275049C2semidirect
12. #20274976C2semidirect
13. #20274715C2semidirect
19. C2×C4×Dic106C22semidirect
22. C2×#13133148C22semidirect
23. C2×#13133148C22semidirect
24. C2×C4⋊#88322C22semidirect
25. C2×#13133140C22semidirect
26. C2×#13133140C22semidirect
35. C2×C4×#88322C22semidirect
38. #16810529C22semidirect
39. #16810521C22semidirect
42. #16810493C22semidirect
44. #16810385C22semidirect
45. #16810385C22semidirect
46. #16810385C22semidirect
47. #16810385C22semidirect
48. #16810378C22semidirect
49. #16810378C22semidirect
210. C22⋊C4×C53SD16semidirect
449. C53#24901semidirect
626. C22⋊C4#11719923semidirect

Maximal subgroups

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

subgroupindex
C2×#168107742
C2×C4×#117199232
#202782402
#202762482
#202761512
#202760322
#202759112
#202754012
#202753232
#202750732
#202750492
#202749762
#202747152
#202746462
D4×C22⋊C4×C532
#2490153