Finite Group Databasebeta

← #27441274

Subgroups — #27441274

Order 13568.

1206 conjugacy classes of subgroups.

The subgroup lattice has 772 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16810914C211yesmaximal, characteristic, complemented
2C22×#13133139C211yesmaximal, characteristic
3#20278417C211yesmaximal, characteristic, complemented
4C22⋊C4×D212C211yesmaximal, characteristic
5#20276247C211yesmaximal, characteristic, complemented
6#20276088C211yesmaximal, characteristic, complemented
7#20276088C211yesmaximal, characteristic, complemented
8#20275852C211yesmaximal, characteristic, complemented
9#20274979C211yesmaximal, characteristic, complemented
10#20274979C211yesmaximal, characteristic, complemented
11#20274910C211yesmaximal, characteristic, complemented
12#20274740C211yesmaximal, characteristic, complemented
13#20274716C211yesmaximal, characteristic, complemented
14#20274647C211yesmaximal, characteristic
15C53×#1850C211yesmaximal, characteristic, complemented
16C23×D212C2211yescharacteristic
17C2×#13133217C2211yescharacteristic, complemented
18C2×#13133194—21no—
19C2×C4×D212C2211yescharacteristic
20C2×C4×D212C2211yescharacteristic
21C22×C4⋊Dic53C2211yescharacteristic
22C2×C22⋊C4×D53—21no—
23#16810914—24no—
24C2×#13133149C2211yescharacteristic, complemented
25C2×#13133149C2211yescharacteristic, complemented
26C2×#13133149C2211yescharacteristic, complemented
27C2×#13133149C2211yescharacteristic, complemented
28C2×#13133139—24no—
29C2×#13133139C2211yescharacteristic
30C2×#13133139C2211yescharacteristic
31C2×#13133139C2211yescharacteristic
32C2×#13133139C2211yescharacteristic
33C2×#13133139C2211yescharacteristic
34C2×#13133139C2211yescharacteristic
35C2×#13133139C2211yescharacteristic
36C2×#13133139C2211yescharacteristic
37#16810555—21no—
38#16810544—21no—
39#16810525C2211yescharacteristic
40#16810525C2211yescharacteristic
41#16810521C2211yescharacteristic, complemented
42#16810521C2211yescharacteristic, complemented
43#16810501—21no—
44#16810501—21no—
45#16810498—21no—
46#16810493C2211yescharacteristic, complemented
47#16810483C2211yescharacteristic
48#16810483C2211yescharacteristic
49#16810478—21no—
50#16810386C2211yescharacteristic, complemented
51#16810386C2211yescharacteristic, complemented
52#16810386C2211yescharacteristic, complemented
53#16810386C2211yescharacteristic, complemented
54C23×C8×C53C2211yescharacteristic
55C2×C4⋊C8×C53C2211yescharacteristic, complemented
56C2×C4⋊C8×C53C2211yescharacteristic, complemented
57C2×C22⋊C8×C53C2211yescharacteristic
58C4×C22⋊C4×C53C2211yescharacteristic
59C53×#336C2211yescharacteristic, complemented
60C53×#336C2211yescharacteristic, complemented
61C24×D53—21no—
62C22×Dic106—21no—
63C22×D212—22no—
64C22×D212—22no—
65C22×D212—21no—
66C22×D212—22no—
67C22×D212—41no—
68C22×D212—41no—
69C22×D212Q814yescomplemented
70C22×D212C2311yescharacteristic
71C22×D212C2311yescharacteristic
72C23×Dic53—21no—
73C22×C4×D53—21no—
74C22×C4×D53—21no—
75#13133217—22no—
76#13133217—41no—
77#13133194—44no—
78C4×D212—22no—
79C4×D212—22no—
80C4×D212—41no—
81C4×D212—41no—
82C2×C4⋊Dic53—21no—
83C2×C4⋊Dic53—21no—
84C2×C4⋊Dic53—21no—
85C2×C4⋊Dic53—21no—
86C2×C4⋊Dic53—22no—
87C2×C4⋊Dic53—41no—
88C2×C4⋊Dic53C2311yescharacteristic
89C2×C4⋊Dic53C2311yescharacteristic
90C2×C4⋊Dic53C2311yescharacteristic
91C2×C4⋊Dic53C2311yescharacteristic
92C2×C4⋊Dic53C2311yescharacteristic
93C2×C4⋊Dic53C2311yescharacteristic
94C2×#11719919—21no—
95C2×#11719919—21no—
96C2×C22⋊Dic53—21no—
97C2×C22⋊Dic53—21no—
98C2×#11719921—21no—
99C2×#11719921—21no—
100C2×#11719921—21no—
101C2×#11719921—21no—
102C2×#11719921—21no—
103C2×#11719921—21no—
104C22⋊C4×D53—44no—
105#13133149—22no—
106#13133149—22no—
107#13133149—41no—
108#13133149—41no—
109#13133139—22no—
110#13133139—22no—
111#13133139—22no—
112#13133139—22no—
113#13133139—22no—
114#13133139—41no—
115#13133139—41no—
116#13133139D414yes—
117#13133124—21no—
118#13133124—21no—
119#13133124—21no—
120#13133124—21no—
121C23×C4×C53C2311yescharacteristic
122C22×C8×C53—22no—
123C22×C8×C53—22no—
124C22×C8×C53—41no—
125C22×C8×C53C2311yescharacteristic
126C22×C8×C53C2311yescharacteristic
127C22×C8×C53C2311yescharacteristic
128C22×C8×C53C2311yescharacteristic
129C2×C22⋊C4×C53D411yescharacteristic
130C2×C22⋊C4×C53D411yescharacteristic
131C2×C42×C53C2311yescharacteristic
132C2×C42×C53C2311yescharacteristic
133C4⋊C8×C53—22no—
134C4⋊C8×C53—41no—
135C22⋊C8×C53—22no—
136#95×C53D411yescharacteristic
137#95×C53D411yescharacteristic
138C24×C53C2×D411yescharacteristic
139C23×D53—21no—
140C23×D53—21no—
141C23×D53—24no—
142C23×D53—42no—
143C23×D53—42no—
144C23×D53—42no—
145C23×D53—42no—
146C23×D53—81no—
147C23×D53—81no—
148C22×C4×C53—21no—
149C22×C4×C53—21no—
150C22×C4×C53—21no—
151C22×C4×C53—21no—
152C22×C4×C53C2×D411yescharacteristic
153C22×C4×C53C2×D411yescharacteristic
154C22×C4×C53C2×D411yescharacteristic
155C22×C4×C53C2×D411yescharacteristic
156C22×C4×C53C2×D411yescharacteristic
157C22×C4×C53C2×Q812yes—
158C22×C4×C53#4112yes—
159C22×C4×C53C2411yescharacteristic
160C22×Dic53—21no—
161C22×Dic53—21no—
162C22×Dic53—21no—
163C22×Dic53—21no—
164C22×Dic53—21no—
165C22×Dic53—21no—
166C22×Dic53—42no—
167C22×Dic53—42no—
168C22×Dic53—81no—
169C2×D212—21no—
170C2×D212—21no—
171C2×D212—21no—
172C2×D212—21no—
173C2×D212—21no—
174C2×D212—21no—
175C2×D212—21no—
176C2×D212—28no—
177C2×D212—24no—
178C2×D212—21no—
179C2×D212—44no—
180C2×D212—44no—
181C2×D212—44no—
182C2×D212—42no—
183C2×D212—42no—
184C2×D212C2×D412yes—
185C2×D212C2×Q812yes—
186C2×D212C2×Q812yes—
187C2×D212#4112yes—
188C2×C4×D53—42no—
189C2×C4×D53—42no—
190C2×C4×D53—42no—
191C2×C4×D53—42no—
192C2×C4×D53—81no—
193C2×C4×D53—81no—
194C2×Dic106—42no—
195C2×Dic106—42no—
196C2×Dic106—81no—
197C2×C8×C53—21no—
198C2×C8×C53—21no—
199C2×C8×C53—21no—
200C2×C8×C53—21no—
201C2×C8×C53—21no—
202C2×C8×C53—21no—
203C2×C8×C53—21no—
204C2×C8×C53—21no—
205C2×C8×C53—21no—
206C2×C8×C53—21no—
207C2×C8×C53—21no—
208C2×C8×C53—44no—
209C2×C8×C53C2×D412yes—
210C22⋊C4×C53—22no—
211C22⋊C4×C53SD1614yes—
212C42×C53—21no—
213C42×C53—21no—
214C42×C53—21no—
215C42×C53—21no—
216C22⋊Dic53—42no—
217C22⋊Dic53—42no—
218#11719921—42no—
219#11719921—42no—
220#11719921—42no—
221#11719921—42no—
222#11719921—81no—
223#11719921—81no—
224C4⋊Dic53—21no—
225C4⋊Dic53—21no—
226C4⋊Dic53—21no—
227C4⋊Dic53—21no—
228C4⋊Dic53—21no—
229C4⋊Dic53—21no—
230C4⋊Dic53—21no—
231C4⋊Dic53—21no—
232C4⋊Dic53—21no—
233C4⋊Dic53—21no—
234C4⋊Dic53—21no—
235C4⋊Dic53—42no—
236C4⋊Dic53—42no—
237C4⋊Dic53—42no—
238C4⋊Dic53—81no—
239C4⋊Dic53C2×D412yes—
240#11719919—42no—
241#11719919—42no—
242C23×C53—21no—
243C23×C53—21no—
244C23×C53—21no—
245C23×C53—21no—
246C23×C53C22⋊Q812yes—
247C23×C53C2×SD1612yes—
248C23×C53AGL(1,ℤ/8)12yes—
249C23×C53C22×D411yescharacteristic
250C22×D53—22no—
251C22×D53—22no—
252C22×D53—22no—
253C22×D53—22no—
254C22×D53—48no—
255C22×D53—41no—
256C22×D53—41no—
257C22×D53—41no—
258C22×D53—41no—
259C22×D53—41no—
260C22×D53—41no—
261C22×D53—41no—
262C22×D53—41no—
263C22×D53—41no—
264C22×D53—41no—
265C22×D53—48no—
266C22×D53—84no—
267C22×D53—84no—
268C22×D53—84no—
269C22×D53—84no—
270C22×D53—84no—
271C2×C4×C53—21no—
272C2×C4×C53—21no—
273C2×C4×C53—21no—
274C2×C4×C53—21no—
275C2×C4×C53—21no—
276C2×C4×C53—21no—
277C2×C4×C53—22no—
278C2×C4×C53—22no—
279C2×C4×C53—22no—
280C2×C4×C53—22no—
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×C53C22⋊Q812yes—
288C2×C4×C53C2×SD1612yes—
289C2×C4×C53C2×SD1612yes—
290C2×C4×C53C22×D411yescharacteristic
291C2×C4×C53C22×Q811yescharacteristic
292C2×C4×C53C2×#4111yescharacteristic
293C2×C4×C53C2×#4111yescharacteristic
294C2×C4×C53H(5,𝔽2)11yescharacteristic
295C2×C4×C53H(5,𝔽2)11yescharacteristic
296C2×Dic53—22no—
297C2×Dic53—41no—
298C2×Dic53—41no—
299C2×Dic53—41no—
300C2×Dic53—41no—
301C2×Dic53—41no—
302C2×Dic53—41no—
303C2×Dic53—41no—
304C2×Dic53—41no—
305C2×Dic53—41no—
306C2×Dic53—41no—
307C2×Dic53—41no—
308C2×Dic53—41no—
309C2×Dic53—41no—
310C2×Dic53—41no—
311C2×Dic53—41no—
312C2×Dic53—41no—
313C2×Dic53—41no—
314C2×Dic53—84no—
315D212—22no—
316D212—22no—
317D212—22no—
318D212—22no—
319D212—22no—
320D212—48no—
321D212—41no—
322D212—41no—
323D212C22⋊Q814yescomplemented
324C4×D53—84no—
325C4×D53—84no—
326Dic106—84no—
327C8×C53—22no—
328C8×C53—41no—
329C8×C53—41no—
330C8×C53—41no—
331#25958—531nomaximal, Sylow
332C22×C53—22no—
333C22×C53—22no—
334C22×C53—22no—
335C22×C53—22no—
336C22×C53—22no—
337C22×C53—22no—
338C22×C53#47614yescomplemented
339C22×C53C2×C22⋊Q811yescharacteristic
340C22×C53D4211yescharacteristic
341C22×C53#54611yescharacteristic
342C22×C53C22×SD1611yescharacteristic
343C22×C53C2×AGL(1,ℤ/8)11yescharacteristic
344C22×C53#57611yescharacteristic
345C22×C53#57711yescharacteristic
346C2×D53—24no—
347C2×D53—42no—
348C2×D53—42no—
349C2×D53—42no—
350C2×D53—42no—
351C2×D53—42no—
352C2×D53—42no—
353C2×D53—42no—
354C2×D53—42no—
355C2×D53—42no—
356C2×D53—816no—
357C2×D53—81no—
358C2×D53—81no—
359C2×D53—81no—
360C2×D53—81no—
361C4×C53—22no—
362C4×C53—22no—
363C4×C53—22no—
364C4×C53—41no—
365C4×C53—41no—
366C4×C53C2×C22⋊Q811yescharacteristic
367C4×C53#54311yescharacteristic
368C4×C53#54611yescharacteristic
369C4×C53#55111yescharacteristic
370Dic53—42no—
371Dic53—81no—
372Dic53—81no—
373Dic53—81no—
374Dic53—81no—
375Dic53—81no—
376C2×#476—531no—
377C22×#102—531no—
378#2440—531no—
379D4×C22⋊C4—531no—
380#2094—531no—
381#2065—531no—
382#2065—531no—
383#2023—531no—
384#1864—531no—
385#1864—531no—
386#1853—531no—
387#1850D5311yescharacteristic, complemented
388#1807—531no—
389#1802—531no—
390#1786—531no—
391C2×C53—24no—
392C2×C53#243711yescharacteristic
393C2×C53C2×#47611yescharacteristic
394C2×C53#308111yescharacteristic
395C2×C53#326411yescharacteristic
396C2×C53D4×SD1611yescharacteristic
397C2×C53#329511yescharacteristic
398C2×C53#330611yescharacteristic
399D53—44no—
400D53—82no—
401C23×D4—531no—
402C23×C8C2×D5311yescharacteristic
403C2×C4⋊Q8—531no—
404C2×C22⋊Q8—1061no—
405C2×C4×D4—531no—
406C2×C4×D4—531no—
407C22×C4⋊C4—531no—
408C22×C22⋊C4—1061no—
409#476—1064no—
410C2×#106—531no—
411C2×#106—531no—
412C2×#106—531no—
413C2×#106—531no—
414C2×C4⋊C8C2×D5311yescharacteristic, complemented
415C2×C4⋊C8C2×D5311yescharacteristic, complemented
416C2×#102—531no—
417C2×#102—531no—
418C2×#102—531no—
419C2×#102—531no—
420C2×#102—531no—
421C2×#102—531no—
422C2×#102—531no—
423C2×#102—531no—
424C2×#102—1064no—
425C2×C22⋊C8C2×D5311yescharacteristic
426#398—1061no—
427#395—1061no—
428#390—531no—
429#390—531no—
430#389—531no—
431#389—531no—
432#386—1061no—
433#386—1061no—
434#385—1061no—
435#384—531no—
436#380—531no—
437#380—531no—
438#379—1061no—
439C4×C22⋊C4C2×D5311yescharacteristic
440#340—531no—
441#340—531no—
442#340—531no—
443#340—531no—
444#336C2×D5311yescharacteristic, complemented
445#336C2×D5311yescharacteristic, complemented
446C53#2595811yescharacteristic, complemented, Sylow
447C25—1061no—
448C22×Q8—1061no—
449C22×D4—534no—
450C22×D4—531no—
451C22×D4—531no—
452C22×D4—1062no—
453C22×D4—1062no—
454C22×D4—1061no—
455C22×D4—1062no—
456C22×D4—2121no—
457C22×D4—2121no—
458C23×C4—1061no—
459C23×C4—1061no—
460C23×C4—1061no—
461C23×C4C22×D5311yescharacteristic
462C22×C8—22no—
463C22×C8—22no—
464C22×C8—41no—
465C22×C8C22×D5311yescharacteristic
466C22×C8C22×D5311yescharacteristic
467C22×C8C22×D5311yescharacteristic
468C22×C8C22×D5311yescharacteristic
469C4⋊Q8—1062no—
470C4⋊Q8—2121no—
471C22⋊Q8—2124no—
472C4×D4—1062no—
473C4×D4—1062no—
474C4×D4—2121no—
475C4×D4—2121no—
476C2×C4⋊C4—531no—
477C2×C4⋊C4—531no—
478C2×C4⋊C4—531no—
479C2×C4⋊C4—531no—
480C2×C4⋊C4—531no—
481C2×C4⋊C4—531no—
482C2×C4⋊C4—1062no—
483C2×C4⋊C4—1061no—
484C2×C4⋊C4—1061no—
485C2×C4⋊C4—1061no—
486C2×C4⋊C4—1061no—
487C2×C4⋊C4—1061no—
488C2×C4⋊C4—1061no—
489C2×C4⋊C4—2121no—
490C2×C22⋊C4—1061no—
491C2×C22⋊C4—1061no—
492C2×C22⋊C4—1061no—
493C2×C22⋊C4—1061no—
494C2×C22⋊C4—1061no—
495C2×C22⋊C4—1061no—
496C2×C22⋊C4—1061no—
497C2×C22⋊C4—1061no—
498C2×C22⋊C4—2124no—
499C2×C22⋊C4D21211yescharacteristic
500C2×C22⋊C4D21211yescharacteristic
501C2×C42C22×D5311yescharacteristic
502C2×C42C22×D5311yescharacteristic
503#106—1062no—
504#106—1062no—
505#106—2121no—
506#106—2121no—
507C4⋊C8—22no—
508C4⋊C8—41no—
509#102—534no—
510#102—1062no—
511#102—1062no—
512#102—1062no—
513#102—1062no—
514#102—1062no—
515#102—2121no—
516#102—2121no—
517C22⋊C8—22no—
518#95—1061no—
519#95—1061no—
520#95—1061no—
521#95—1061no—
522#95D21211yescharacteristic
523#95D21211yescharacteristic
524C24—1061no—
525C24—1064no—
526C24—1061no—
527C24—4241no—
528C24—4241no—
529C24—2122no—
530C24—2122no—
531C24—2122no—
532C24—2122no—
533C24C2×D21211yescharacteristic
534C2×Q8—4241no—
535C2×Q8—2122no—
536C2×Q8—2122no—
537C2×D4—532no—
538C2×D4—532no—
539C2×D4—532no—
540C2×D4—532no—
541C2×D4—1068no—
542C2×D4—1064no—
543C2×D4—1061no—
544C2×D4—1061no—
545C2×D4—1061no—
546C2×D4—1061no—
547C2×D4—1061no—
548C2×D4—1061no—
549C2×D4—1061no—
550C2×D4—1061no—
551C2×D4—2124no—
552C2×D4—2124no—
553C2×D4—2124no—
554C2×D4—2122no—
555C2×D4—2122no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—1061no—
561C22×C4—1061no—
562C22×C4—1061no—
563C22×C4—1061no—
564C22×C4—1061no—
565C22×C4—1061no—
566C22×C4—4241no—
567C22×C4—4241no—
568C22×C4—4241no—
569C22×C4—2122no—
570C22×C4—2122no—
571C22×C4—2122no—
572C22×C4—2122no—
573C22×C4—2122no—
574C22×C4—2122no—
575C22×C4C2×D21211yescharacteristic
576C22×C4C2×D21211yescharacteristic
577C22×C4C2×D21211yescharacteristic
578C22×C4C2×D21211yescharacteristic
579C22×C4C2×D21211yescharacteristic
580C22×C4#1171994712yes—
581C22×C4Q8×D5312yes—
582C22×C4C23×D5311yescharacteristic
583C2×C8—21no—
584C2×C8—21no—
585C2×C8—21no—
586C2×C8—21no—
587C2×C8—21no—
588C2×C8—21no—
589C2×C8—21no—
590C2×C8—21no—
591C2×C8—21no—
592C2×C8—21no—
593C2×C8—21no—
594C2×C8—44no—
595C2×C8D4×D5312yes—
596C4⋊C4—532no—
597C4⋊C4—1061no—
598C4⋊C4—1061no—
599C4⋊C4—1061no—
600C4⋊C4—1061no—
601C4⋊C4—1061no—
602C4⋊C4—1061no—
603C4⋊C4—1061no—
604C4⋊C4—1061no—
605C4⋊C4—1061no—
606C4⋊C4—1061no—
607C4⋊C4—1061no—
608C4⋊C4—4241no—
609C4⋊C4—2122no—
610C4⋊C4—2122no—
611C4⋊C4—2122no—
612C4⋊C4—2122no—
613C4⋊C4—2122no—
614C22⋊C4—22no—
615C22⋊C4—4241no—
616C22⋊C4—4241no—
617C22⋊C4—2122no—
618C22⋊C4—2122no—
619C22⋊C4—2122no—
620C22⋊C4—2122no—
621C22⋊C4—2122no—
622C22⋊C4—2122no—
623C22⋊C4#1171991314yes—
624C42—21no—
625C42—21no—
626C42—21no—
627C42—21no—
628C23—21no—
629C23—21no—
630C23—21no—
631C23—21no—
632C23—1062no—
633C23—1062no—
634C23—1062no—
635C23—1062no—
636C23—4244no—
637C23—4244no—
638C23—4244no—
639C23—4244no—
640C23—4244no—
641C23—2128no—
642C23—2121no—
643C23—2121no—
644C23—2121no—
645C23—2128no—
646C23—2121no—
647C23—2121no—
648C23—2121no—
649C23—2121no—
650C23—2121no—
651C23—2121no—
652C23—2121no—
653C23#1313319712yes—
654C23C2×#1171991312yes—
655C23#1313324512yes—
656C23C22×D21211yescharacteristic
657Q8—4244no—
658D4—534no—
659D4—1062no—
660D4—1062no—
661D4—1062no—
662D4—1062no—
663D4—1062no—
664D4—2128no—
665D4—2121no—
666D4—2121no—
667C2×C4—21no—
668C2×C4—21no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—21no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—1062no—
684C2×C4—4244no—
685C2×C4—4244no—
686C2×C4—4244no—
687C2×C4—2121no—
688C2×C4—2121no—
689C2×C4—2121no—
690C2×C4—2121no—
691C2×C4—2121no—
692C2×C4—2121no—
693C2×C4—2121no—
694C2×C4—2121no—
695C2×C4—2121no—
696C2×C4—2121no—
697C2×C4—2121no—
698C2×C4—2121no—
699C2×C4—2121no—
700C2×C4—2121no—
701C2×C4—2121no—
702C2×C4—2121no—
703C2×C4—2121no—
704C2×C4#1313319712yes—
705C2×C4C2×#1171991312yes—
706C2×C4C2×#1171991312yes—
707C2×C4C2×D4×D5311yescharacteristic
708C2×C4C2×Q8×D5311yescharacteristic
709C2×C4#41×D5311yescharacteristic
710C2×C4C2×#1171994711yescharacteristic
711C2×C4#1313326211yescharacteristic
712C2×C4#1313326311yescharacteristic
713C8—22no—
714C8—41no—
715C8—41no—
716C8—41no—
717C22—22no—
718C22—22no—
719C22—22no—
720C22—22no—
721C22—22no—
722C22—22no—
723C22—1064no—
724C22—42416no—
725C22—4241no—
726C22—4241no—
727C22—4241no—
728C22—4241no—
729C22—2122no—
730C22—2122no—
731C22—2122no—
732C22—2122no—
733C22—2122no—
734C22—2122no—
735C22—2122no—
736C22—2122no—
737C22—2122no—
738C22#1681091414yescomplemented
739C22C2×#1313319711yescharacteristic
740C22D4×D21211yescharacteristic
741C22#1681126811yescharacteristic
742C22C22×#1171991311yescharacteristic
743C22C2×#1313324511yescharacteristic
744C22#1681142811yescharacteristic
745C22#1681143511yescharacteristic
746C4—22no—
747C4—22no—
748C4—22no—
749C4—41no—
750C4—41no—
751C4—4241no—
752C4—4241no—
753C4—4241no—
754C4—4241no—
755C4—4241no—
756C4—2122no—
757C4C22⋊Q8×D5311yescharacteristic
758C4#1681124811yescharacteristic
759C4#1681126011yescharacteristic
760C4#1681129611yescharacteristic
761C2—24no—
762C2—4242no—
763C2—2124no—
764C2#2027837911yescharacteristic
765C2C2×#1681091411yescharacteristic
766C2#2028454711yescharacteristic
767C2#2028620011yescharacteristic
768C2D4×#1171991311yescharacteristic
769C2#2028654011yescharacteristic
770C2#2028667811yescharacteristic
subgroupG/H
centerC23C22×D212
commutator, cosocleC22×C4×C53C24
FrattiniC22×C4C23×D53
FittingC53×#1850C2
socleC23×C53C22×D4
prime radicalC23×D212C22
hypercenter#1850D53
hypocenterC53#25958
LCSG ▷ C22×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #1850

Complements

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

NH ≅ G/Ntype
1. C2×#16810914C2semidirect
3. #20278417C2semidirect
5. #20276247C2semidirect
6. #20276088C2semidirect
7. #20276088C2semidirect
8. #20275852C2semidirect
9. #20274979C2semidirect
10. #20274979C2semidirect
11. #20274910C2semidirect
12. #20274740C2semidirect
13. #20274716C2semidirect
15. C53×#1850C2semidirect
17. C2×#13133217C22semidirect
24. C2×#13133149C22semidirect
25. C2×#13133149C22semidirect
26. C2×#13133149C22semidirect
27. C2×#13133149C22semidirect
41. #16810521C22semidirect
42. #16810521C22semidirect
46. #16810493C22semidirect
50. #16810386C22semidirect
51. #16810386C22semidirect
52. #16810386C22semidirect
53. #16810386C22semidirect
55. C2×C4⋊C8×C53C22semidirect
56. C2×C4⋊C8×C53C22semidirect
59. C53×#336C22semidirect
60. C53×#336C22semidirect
69. C22×D212Q8semidirect
323. D212C22⋊Q8semidirect
338. C22×C53#476semidirect
387. #1850D53semidirect
414. C2×C4⋊C8C2×D53semidirect
415. C2×C4⋊C8C2×D53semidirect
444. #336C2×D53semidirect
445. #336C2×D53semidirect
446. C53#25958semidirect
738. C22#16810914semidirect

Maximal subgroups

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

subgroupindex
C2×#168109142
C22×#131331392
#202784172
C22⋊C4×D2122
#202762472
#202760882
#202758522
#202749792
#202749102
#202747402
#202747162
#202746472
C53×#18502
#2595853