Finite Group Databasebeta

← #27404337

Subgroups — #27404337

Order 13568.

1164 conjugacy classes of subgroups.

The subgroup lattice has 842 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16810701C211yesmaximal, characteristic, complemented
2C2×#16810698C211yesmaximal, characteristic, complemented
3C2×#16810589C211yesmaximal, characteristic, complemented
4C2×#16810588C211yesmaximal, characteristic, complemented
5#20277930C211yesmaximal, characteristic
6#20275507C211yesmaximal, characteristic, complemented
7#20275322C211yesmaximal, characteristic, complemented
8#20275319C211yesmaximal, characteristic, complemented
9#20275010C211yesmaximal, characteristic, complemented
10#20275004C211yesmaximal, characteristic, complemented
11#20274899C211yesmaximal, characteristic, complemented
12#20274897C211yesmaximal, characteristic, complemented
13C8×C22⋊Dic53C211yesmaximal, characteristic, complemented
14#20274485C211yesmaximal, characteristic, complemented
15C53×#1869C211yesmaximal, characteristic, complemented
16C22×#11719945C2211yescharacteristic
17C22×#11719917C2211yescharacteristic
18C22×#11719917C2211yescharacteristic
19C22×#11719912C2211yescharacteristic
20C22×C8×D53C2211yescharacteristic
21C2×C4×C22⋊D53C2211yescharacteristic
22C2×C4×C22⋊D53C2211yescharacteristic
23#16810701—24no—
24#16810698—24no—
25C2×C4⋊#88322C2211yescharacteristic
26C2×#13133146C2211yescharacteristic
27C2×#13133146C2211yescharacteristic
28#16810589—24no—
29#16810588—24no—
30C2×C22⋊#88322C2211yescharacteristic
31C2×C22⋊#88322C2211yescharacteristic
32C2×#13133129C2211yescharacteristic
33C2×#13133129C2211yescharacteristic
34C2×#13133129C2211yescharacteristic
35C2×#13133129C2211yescharacteristic
36C2×#13133129C2211yescharacteristic
37C2×#13133129C2211yescharacteristic
38C2×C4×#88322C2211yescharacteristic
39C2×C8×Dic53C2211yescharacteristic
40C2×C8×Dic53C2211yescharacteristic
41#16810543C411yescharacteristic
42#16810540C411yescharacteristic
43#16810538C411yescharacteristic
44#16810538C411yescharacteristic
45#16810535C411yescharacteristic
46#16810532C411yescharacteristic
47#16810531C411yescharacteristic
48#16810531C411yescharacteristic
49C4×#11719921C2211yescharacteristic
50C4×#11719921C2211yescharacteristic
51C4×C22⋊Dic53C2211yescharacteristic
52#16810377C2211yescharacteristic
53#16810377C2211yescharacteristic
54#16810377C2211yescharacteristic
55#16810377C2211yescharacteristic
56C23×C8×C53C2211yescharacteristic
57C2×C4×D4×C53C2211yescharacteristic
58C2×C22⋊C8×C53C2211yescharacteristic
59C2×C22⋊C8×C53C2211yescharacteristic
60C2×C22⋊C8×C53C2211yescharacteristic
61C53×#336C2211yescharacteristic
62C53×#336C2211yescharacteristic
63C2×#11719945—22no—
64C2×#11719945—22no—
65C2×#11719945—22no—
66C2×#11719945—22no—
67C2×#11719945—41no—
68C2×#11719945—41no—
69C22×Dic106C2×C411yescharacteristic
70C22×D212C2×C411yescharacteristic
71C22×C22⋊D53C2×C411yescharacteristic
72C22×C22⋊D53C2×C411yescharacteristic
73C22×C22⋊D53C2×C411yescharacteristic
74C22×C22⋊D53C2×C411yescharacteristic
75C22×C4×D53C2311yescharacteristic
76C22×C4×D53C2311yescharacteristic
77C2×#11719917—22no—
78C2×#11719917—22no—
79C2×#11719917—22no—
80C2×#11719917—22no—
81C2×#11719917—41no—
82C2×#11719917—41no—
83C2×#11719912—22no—
84C2×#11719912—22no—
85C2×#11719912—41no—
86C22×#88322C2311yescharacteristic
87C22×#88322C2311yescharacteristic
88C22×#88322C2311yescharacteristic
89C22×#88322C2311yescharacteristic
90C2×C8×D53—22no—
91C2×C8×D53—22no—
92C2×C8×D53—41no—
93C4×C22⋊D53—22no—
94C4×C22⋊D53—22no—
95C4×C22⋊D53—41no—
96C4×C22⋊D53—41no—
97C2×#11719919C2×C411yescharacteristic
98C2×#11719919C2×C411yescharacteristic
99C2×C22⋊Dic53C2×C411yescharacteristic
100C2×C22⋊Dic53C2×C411yescharacteristic
101C2×C22⋊Dic53C2×C411yescharacteristic
102C2×C22⋊Dic53C2×C411yescharacteristic
103C2×#11719921C2×C411yescharacteristic
104C2×#11719921C2×C411yescharacteristic
105C2×#11719921C2×C411yescharacteristic
106C2×#11719921C2×C411yescharacteristic
107C2×#11719921C2×C411yescharacteristic
108C2×#11719921C2×C411yescharacteristic
109C2×C4×Dic53C2311yescharacteristic
110C2×C4×Dic53C2311yescharacteristic
111C4⋊#88322—22no—
112#13133146—22no—
113#13133146—41no—
114C22⋊#88322—22no—
115C22⋊#88322D414yescomplemented
116#13133129—22no—
117#13133129—22no—
118#13133129—22no—
119#13133129—22no—
120#13133129—22no—
121#13133129D414yescomplemented
122C4×#88322—22no—
123C8×Dic53—22no—
124C8×Dic53—41no—
125#13133124C2×C411yescharacteristic
126#13133124C2×C411yescharacteristic
127#13133124C2×C411yescharacteristic
128#13133124C2×C411yescharacteristic
129#13133124C2×C411yescharacteristic
130#13133124C2×C411yescharacteristic
131C22×D4×C53C2×C411yescharacteristic
132C23×C4×C53C2311yescharacteristic
133C23×C4×C53C2311yescharacteristic
134C22×C8×C53—22no—
135C22×C8×C53—22no—
136C22×C8×C53—41no—
137C22×C8×C53C2311yescharacteristic
138C22×C8×C53C2311yescharacteristic
139C22×C8×C53C2311yescharacteristic
140C22×C8×C53C2311yescharacteristic
141C4×D4×C53—22no—
142C4×D4×C53—22no—
143C2×C4⋊C4×C53C2×C411yescharacteristic
144C2×C22⋊C4×C53C2×C411yescharacteristic
145C2×C22⋊C4×C53C2×C411yescharacteristic
146C2×C42×C53C2311yescharacteristic
147C22⋊C8×C53—22no—
148C22⋊C8×C53—22no—
149C22⋊C8×C53—41no—
150C24×C53C22×C411yescharacteristic
151C24×C53C22×C411yescharacteristic
152C23×D53C22×C411yescharacteristic
153C23×D53C22×C411yescharacteristic
154C2×D4×C53—22no—
155C2×D4×C53—22no—
156C2×D4×C53—41no—
157C22×C4×C53—21no—
158C22×C4×C53—21no—
159C22×C4×C53—21no—
160C22×C4×C53—21no—
161C22×C4×C53—21no—
162C22×C4×C53—21no—
163C22×C4×C53—21no—
164C22×C4×C53—21no—
165C22×C4×C53—21no—
166C22×C4×C53—21no—
167C22×C4×C53C22×C411yescharacteristic
168C22×C4×C53C22×C411yescharacteristic
169C22×C4×C53C22×C411yescharacteristic
170C22×C4×C53C22×C411yescharacteristic
171C22×C4×C53C2×D412yes—
172C22×C4×C53#4112yes—
173C22×C4×C53C2411yescharacteristic
174C2×C22⋊D53—22no—
175C2×C22⋊D53—22no—
176C2×C22⋊D53—22no—
177C2×C22⋊D53—22no—
178C2×C22⋊D53—22no—
179C2×C22⋊D53—22no—
180C2×C22⋊D53—22no—
181C2×C22⋊D53—41no—
182C2×C22⋊D53—41no—
183C2×C22⋊D53—41no—
184C2×C22⋊D53—41no—
185C2×C22⋊D53—41no—
186C22×Dic53C22×C411yescharacteristic
187C22×Dic53C22×C411yescharacteristic
188C22×Dic53C22×C411yescharacteristic
189C22×Dic53C22×C411yescharacteristic
190C22×Dic53C22×C411yescharacteristic
191C22×Dic53C22×C411yescharacteristic
192#11719945—44no—
193#11719945—44no—
194#11719945—44no—
195#11719945—44no—
196C2×D212—22no—
197C2×D212—22no—
198C2×D212—41no—
199C2×C4×D53—21no—
200C2×C4×D53—21no—
201C2×C4×D53—21no—
202C2×C4×D53—21no—
203C2×C4×D53—21no—
204C2×C4×D53—21no—
205C2×C4×D53—21no—
206C2×C4×D53—21no—
207C2×C4×D53—21no—
208C2×C4×D53—21no—
209C2×C4×D53C2×D412yes—
210C2×C4×D53#4112yes—
211C2×Dic106—22no—
212C2×Dic106—22no—
213C2×Dic106—41no—
214C2×C8×C53—21no—
215C2×C8×C53—21no—
216C2×C8×C53—21no—
217C2×C8×C53—21no—
218C2×C8×C53—21no—
219C2×C8×C53—21no—
220C2×C8×C53—21no—
221C2×C8×C53—21no—
222C2×C8×C53—21no—
223C2×C8×C53—21no—
224C2×C8×C53—21no—
225C2×C8×C53—44no—
226C2×C8×C53C2×D412yes—
227C4⋊C4×C53—22no—
228C22⋊C4×C53—22no—
229C22⋊C4×C53—22no—
230C42×C53—21no—
231C42×C53—21no—
232C22⋊Dic53—22no—
233C22⋊Dic53—22no—
234C22⋊Dic53—22no—
235C22⋊Dic53—41no—
236#11719921—22no—
237#11719921—22no—
238#11719921—22no—
239#11719921—22no—
240#11719921—22no—
241#11719921—41no—
242#11719919—22no—
243#11719919—41no—
244C4×Dic53—21no—
245C4×Dic53—21no—
246C4×Dic53—21no—
247C4×Dic53—21no—
248#11719917—44no—
249#11719917—44no—
250C2×#88322—21no—
251C2×#88322—21no—
252C2×#88322—21no—
253C2×#88322—21no—
254C2×#88322—21no—
255C2×#88322—21no—
256C2×#88322—21no—
257C2×#88322—21no—
258C2×#88322—21no—
259C2×#88322C2×D412yes—
260C2×#88322C2×D412yes—
261C2×#88322C2×D412yes—
262#11719912—44no—
263C8×D53—44no—
264C23×C53—21no—
265C23×C53—21no—
266C23×C53—21no—
267C23×C53—21no—
268C23×C53—21no—
269C23×C53—21no—
270C23×C53—21no—
271C23×C53—21no—
272C23×C53—21no—
273C23×C53—21no—
274C23×C53—21no—
275C23×C53—21no—
276C23×C53—21no—
277C23×C53C4×D412yes—
278C23×C53C23×C411yescharacteristic
279C22×D53—21no—
280C22×D53—21no—
281C22×D53—21no—
282C22×D53—21no—
283C22×D53—21no—
284C22×D53—21no—
285C22×D53—21no—
286C22×D53—21no—
287C22×D53—21no—
288C22×D53—21no—
289C22×D53—21no—
290C22×D53—21no—
291C22×D53—21no—
292C22×D53C4×D412yes—
293D4×C53—44no—
294C2×C4×C53—21no—
295C2×C4×C53—21no—
296C2×C4×C53—21no—
297C2×C4×C53—21no—
298C2×C4×C53—22no—
299C2×C4×C53—22no—
300C2×C4×C53—22no—
301C2×C4×C53—22no—
302C2×C4×C53—21no—
303C2×C4×C53—21no—
304C2×C4×C53—21no—
305C2×C4×C53—21no—
306C2×C4×C53—21no—
307C2×C4×C53—21no—
308C2×C4×C53—41no—
309C2×C4×C53—41no—
310C2×C4×C53—41no—
311C2×C4×C53—41no—
312C2×C4×C53C4×D412yes—
313C2×C4×C53#13112yes—
314C2×C4×C53C22×D411yescharacteristic
315C2×C4×C53C22×D411yescharacteristic
316C2×C4×C53C2×#4111yescharacteristic
317C2×C4×C53C2×#4111yescharacteristic
318C2×C4×C53H(5,𝔽2)11yescharacteristic
319C2×C4×C53H(5,𝔽2)11yescharacteristic
320C22⋊D53—44no—
321C22⋊D53—44no—
322C22⋊D53—44no—
323C22⋊D53—44no—
324C2×Dic53—21no—
325C2×Dic53—21no—
326C2×Dic53—21no—
327C2×Dic53—21no—
328C2×Dic53—21no—
329C2×Dic53—21no—
330C2×Dic53—21no—
331C2×Dic53—21no—
332C2×Dic53—21no—
333C2×Dic53—21no—
334C2×Dic53—21no—
335C2×Dic53—21no—
336C2×Dic53—21no—
337C2×Dic53—21no—
338C2×Dic53—21no—
339C2×Dic53C4×D412yes—
340C2×Dic53#13112yes—
341C2×Dic53#13112yes—
342D212—44no—
343C4×D53—22no—
344C4×D53—22no—
345C4×D53—22no—
346C4×D53—22no—
347C4×D53—41no—
348C4×D53—41no—
349C4×D53—41no—
350C4×D53—41no—
351Dic106—44no—
352C8×C53—22no—
353C8×C53—41no—
354C8×C53—41no—
355C8×C53—41no—
356#88322—22no—
357#88322—22no—
358#88322—22no—
359#88322—41no—
360#22853—531nomaximal, Sylow
361C22×C53—22no—
362C22×C53—22no—
363C22×C53—22no—
364C22×C53—41no—
365C22×C53—41no—
366C22×C53—41no—
367C22×C53—41no—
368C22×C53—41no—
369C22×C53—41no—
370C22×C53—41no—
371C22×C53—41no—
372C22×C53—41no—
373C22×C53—41no—
374C22×C53—41no—
375C22×C53C2×C4×D411yescharacteristic
376C22×C53C2×C4×D411yescharacteristic
377C22×C53#51811yescharacteristic
378C22×C53C2×#13111yescharacteristic
379C22×C53C2×#13111yescharacteristic
380C22×C53C2×#13111yescharacteristic
381C22×C53#56811yescharacteristic
382C2×D53—22no—
383C2×D53—22no—
384C2×D53—22no—
385C2×D53—41no—
386C2×D53—41no—
387C2×D53—41no—
388C2×D53—41no—
389C2×D53—41no—
390C2×D53—41no—
391C2×D53—41no—
392C2×D53—41no—
393C2×D53—41no—
394C2×D53—41no—
395C2×D53—41no—
396C4×C53—22no—
397C4×C53—22no—
398C4×C53—41no—
399C4×C53—41no—
400C4×C53D4211yescharacteristic
401C4×C53#54611yescharacteristic
402C4×C53#54611yescharacteristic
403C4×C53#55111yescharacteristic
404Dic53—22no—
405Dic53—22no—
406Dic53—22no—
407Dic53—41no—
408Dic53—41no—
409Dic53—41no—
410C2×#436—531no—
411C2×#436—531no—
412C2×#408—531no—
413C2×#408—531no—
414#2388—531no—
415#1954—531no—
416#1923—531no—
417#1923—531no—
418#1870—531no—
419#1869—531no—
420#1869D5311yescharacteristic, complemented
421#1851—531no—
422#1851—531no—
423C8×C22⋊C4—531no—
424C8×C22⋊C4—531no—
425C2×C53—42no—
426C2×C53—81no—
427C2×C53#235811yescharacteristic
428C2×C53#293111yescharacteristic
429C2×C53#293111yescharacteristic
430C2×C53#293311yescharacteristic
431C2×C53#293311yescharacteristic
432C2×C53#297611yescharacteristic
433C2×C53#297911yescharacteristic
434D53—42no—
435D53—81no—
436C22×#41—531no—
437C22×M16—531no—
438C22×M16—531no—
439C22×M16—531no—
440C23×C8—531no—
441C23×C8C2×D5311yescharacteristic
442C2×C4×D4—531no—
443C2×C4×D4—531no—
444C2×C4×D4C2×D5311yescharacteristic
445#436—1064no—
446#436—1064no—
447C2×C4⋊C8—531no—
448C2×C4⋊C8—531no—
449C2×C4⋊C8—531no—
450#408—1064no—
451#408—1064no—
452C2×C22⋊C8—531no—
453C2×C22⋊C8—531no—
454C2×C22⋊C8—531no—
455C2×C22⋊C8—531no—
456C2×C22⋊C8—531no—
457C2×C22⋊C8—531no—
458C2×C22⋊C8—531no—
459C2×C22⋊C8—531no—
460C2×C22⋊C8C2×D5311yescharacteristic
461C2×C22⋊C8C2×D5311yescharacteristic
462C2×C22⋊C8C2×D5311yescharacteristic
463C2×C4×C8—531no—
464C2×C4×C8—531no—
465C2×C4×C8—531no—
466#395—531no—
467#394—531no—
468#394—531no—
469#394—531no—
470#393—531no—
471#392—531no—
472#392—531no—
473#392—531no—
474C4×C22⋊C4—531no—
475C4×C22⋊C4—531no—
476C4×C22⋊C4—531no—
477#336—531no—
478#336—531no—
479#336—531no—
480#336—531no—
481#336C2×D5311yescharacteristic
482#336C2×D5311yescharacteristic
483C53#2285311yescharacteristic, complemented, Sylow
484C2×#41—1062no—
485C2×#41—1062no—
486C2×#41—1062no—
487C2×#41—1062no—
488C2×#41—2121no—
489C2×#41—2121no—
490C22×Q8—531no—
491C22×D4—531no—
492C22×D4—531no—
493C22×D4—531no—
494C22×D4—531no—
495C22×D4—531no—
496C22×D4C4×D5311yescharacteristic
497C23×C4—531no—
498C23×C4—531no—
499C23×C4C22×D5311yescharacteristic
500C23×C4C22×D5311yescharacteristic
501C2×M16—1062no—
502C2×M16—1062no—
503C2×M16—1062no—
504C2×M16—1062no—
505C2×M16—1062no—
506C2×M16—1062no—
507C2×M16—2121no—
508C2×M16—2121no—
509C2×M16—2121no—
510C22×C8—22no—
511C22×C8—22no—
512C22×C8—41no—
513C22×C8—531no—
514C22×C8—531no—
515C22×C8—531no—
516C22×C8—531no—
517C22×C8—1062no—
518C22×C8—1062no—
519C22×C8—2121no—
520C22×C8C22×D5311yescharacteristic
521C22×C8C22×D5311yescharacteristic
522C22×C8C22×D5311yescharacteristic
523C22×C8C22×D5311yescharacteristic
524C4×D4—22no—
525C4×D4—22no—
526C4×D4—1062no—
527C4×D4—1062no—
528C4×D4—2121no—
529C4×D4—2121no—
530C2×C4⋊C4—531no—
531C2×C4⋊C4—531no—
532C2×C4⋊C4C4×D5311yescharacteristic
533C2×C22⋊C4—531no—
534C2×C22⋊C4—531no—
535C2×C22⋊C4—531no—
536C2×C22⋊C4—531no—
537C2×C22⋊C4—531no—
538C2×C22⋊C4—531no—
539C2×C22⋊C4—531no—
540C2×C22⋊C4—531no—
541C2×C22⋊C4—531no—
542C2×C22⋊C4—531no—
543C2×C22⋊C4C4×D5311yescharacteristic
544C2×C22⋊C4C4×D5311yescharacteristic
545C2×C42—531no—
546C2×C42—531no—
547C2×C42C22×D5311yescharacteristic
548C4⋊C8—1062no—
549C4⋊C8—1062no—
550C4⋊C8—2121no—
551C22⋊C8—22no—
552C22⋊C8—22no—
553C22⋊C8—41no—
554C22⋊C8—534no—
555C22⋊C8—534no—
556C22⋊C8—1062no—
557C22⋊C8—1062no—
558C22⋊C8—1062no—
559C22⋊C8—1062no—
560C22⋊C8—1062no—
561C22⋊C8—1062no—
562C4×C8—1062no—
563C4×C8—1062no—
564C4×C8—2121no—
565#95—531no—
566#95—531no—
567#95—531no—
568#95—531no—
569#95—531no—
570#95—531no—
571C24—531no—
572C24—531no—
573C24C2×C4×D5311yescharacteristic
574C24C2×C4×D5311yescharacteristic
575#41—2124no—
576#41—2124no—
577#41—2124no—
578#41—2124no—
579C2×Q8—1062no—
580C2×Q8—1062no—
581C2×Q8—2121no—
582C2×D4—22no—
583C2×D4—22no—
584C2×D4—41no—
585C2×D4—1062no—
586C2×D4—1062no—
587C2×D4—1062no—
588C2×D4—1062no—
589C2×D4—1062no—
590C2×D4—1062no—
591C2×D4—1062no—
592C2×D4—1062no—
593C2×D4—1062no—
594C2×D4—2121no—
595C2×D4—2121no—
596C2×D4—2121no—
597C2×D4—2121no—
598C2×D4—2121no—
599C2×D4—2121no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—21no—
608C22×C4—21no—
609C22×C4—21no—
610C22×C4—531no—
611C22×C4—531no—
612C22×C4—531no—
613C22×C4—532no—
614C22×C4—532no—
615C22×C4—531no—
616C22×C4—531no—
617C22×C4—531no—
618C22×C4—1061no—
619C22×C4—1061no—
620C22×C4—1061no—
621C22×C4—1061no—
622C22×C4—1061no—
623C22×C4—1061no—
624C22×C4—1061no—
625C22×C4—1061no—
626C22×C4—1061no—
627C22×C4—1061no—
628C22×C4C2×C4×D5311yescharacteristic
629C22×C4C2×C4×D5311yescharacteristic
630C22×C4C2×C4×D5311yescharacteristic
631C22×C4C2×C4×D5311yescharacteristic
632C22×C4D4×D5312yes—
633C22×C4#1171994712yes—
634C22×C4C23×D5311yescharacteristic
635M16—2124no—
636M16—2124no—
637M16—2124no—
638C2×C8—21no—
639C2×C8—21no—
640C2×C8—21no—
641C2×C8—21no—
642C2×C8—21no—
643C2×C8—21no—
644C2×C8—21no—
645C2×C8—21no—
646C2×C8—21no—
647C2×C8—21no—
648C2×C8—21no—
649C2×C8—44no—
650C2×C8—532no—
651C2×C8—532no—
652C2×C8—532no—
653C2×C8—1061no—
654C2×C8—1061no—
655C2×C8—1061no—
656C2×C8—1061no—
657C2×C8—1061no—
658C2×C8—1061no—
659C2×C8—1061no—
660C2×C8—1061no—
661C2×C8—1061no—
662C2×C8—2124no—
663C2×C8D4×D5312yes—
664C4⋊C4—22no—
665C4⋊C4—1062no—
666C4⋊C4—2121no—
667C22⋊C4—22no—
668C22⋊C4—22no—
669C22⋊C4—1062no—
670C22⋊C4—1062no—
671C22⋊C4—1062no—
672C22⋊C4—1062no—
673C22⋊C4—1062no—
674C22⋊C4—1062no—
675C22⋊C4—1062no—
676C22⋊C4—1062no—
677C22⋊C4—2121no—
678C22⋊C4—2121no—
679C42—21no—
680C42—21no—
681C42—1061no—
682C42—1061no—
683C42—1061no—
684C42—1061no—
685C23—21no—
686C23—21no—
687C23—21no—
688C23—21no—
689C23—21no—
690C23—21no—
691C23—21no—
692C23—21no—
693C23—21no—
694C23—21no—
695C23—21no—
696C23—21no—
697C23—21no—
698C23—532no—
699C23—1061no—
700C23—1061no—
701C23—1061no—
702C23—1061no—
703C23—1061no—
704C23—1061no—
705C23—1061no—
706C23—1061no—
707C23—1061no—
708C23—1061no—
709C23—1061no—
710C23—1061no—
711C23—1061no—
712C23#1313317712yes—
713C23C22×C4×D5311yescharacteristic
714Q8—2124no—
715D4—44no—
716D4—2124no—
717D4—2124no—
718D4—2124no—
719D4—2124no—
720D4—2124no—
721C2×C4—21no—
722C2×C4—21no—
723C2×C4—21no—
724C2×C4—21no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—21no—
730C2×C4—21no—
731C2×C4—21no—
732C2×C4—21no—
733C2×C4—21no—
734C2×C4—21no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—41no—
739C2×C4—532no—
740C2×C4—532no—
741C2×C4—532no—
742C2×C4—1061no—
743C2×C4—1061no—
744C2×C4—1061no—
745C2×C4—1061no—
746C2×C4—1061no—
747C2×C4—1061no—
748C2×C4—1062no—
749C2×C4—1062no—
750C2×C4—1062no—
751C2×C4—1062no—
752C2×C4—1061no—
753C2×C4—1061no—
754C2×C4—1061no—
755C2×C4—1061no—
756C2×C4—1061no—
757C2×C4—1061no—
758C2×C4—1061no—
759C2×C4—1061no—
760C2×C4—1061no—
761C2×C4—2121no—
762C2×C4—2121no—
763C2×C4—2121no—
764C2×C4—2121no—
765C2×C4#1313317712yes—
766C2×C4#1313322312yes—
767C2×C4C2×D4×D5311yescharacteristic
768C2×C4C2×D4×D5311yescharacteristic
769C2×C4#41×D5311yescharacteristic
770C2×C4C2×#1171994711yescharacteristic
771C2×C4#1313326211yescharacteristic
772C2×C4#1313326311yescharacteristic
773C8—22no—
774C8—41no—
775C8—41no—
776C8—41no—
777C8—1062no—
778C8—1062no—
779C8—1062no—
780C8—2121no—
781C22—22no—
782C22—22no—
783C22—22no—
784C22—41no—
785C22—41no—
786C22—41no—
787C22—41no—
788C22—41no—
789C22—41no—
790C22—41no—
791C22—41no—
792C22—41no—
793C22—41no—
794C22—41no—
795C22—1062no—
796C22—1062no—
797C22—1062no—
798C22—2121no—
799C22—2121no—
800C22—2121no—
801C22—2121no—
802C22—2121no—
803C22—2121no—
804C22—2121no—
805C22—2121no—
806C22—2121no—
807C22—2121no—
808C22—2121no—
809C22C4×D4×D5311yescharacteristic
810C22C2×#1313317711yescharacteristic
811C22#1681109511yescharacteristic
812C22#131×D5311yescharacteristic
813C22#131×D5311yescharacteristic
814C22C2×#1313322311yescharacteristic
815C22#1681138911yescharacteristic
816C4—22no—
817C4—22no—
818C4—41no—
819C4—41no—
820C4—1062no—
821C4—1062no—
822C4—1062no—
823C4—2121no—
824C4—2121no—
825C4—2121no—
826C4#1681125711yescharacteristic
827C4#1681126011yescharacteristic
828C4#1681126211yescharacteristic
829C4#1681129611yescharacteristic
830C2—42no—
831C2—81no—
832C2—4241no—
833C2—2122no—
834C2#2027769511yescharacteristic
835C2#2028342211yescharacteristic
836C2#2028342311yescharacteristic
837C2#2028343611yescharacteristic
838C2#2028343811yescharacteristic
839C2#2028376211yescharacteristic
840C2#2028377811yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D53
commutator, socleC23×C53C23×C4
FittingC53×#1869C2
prime radical#20277930C2
cosocleC22×C4×C53C24
hypercenter#1869D53
hypocenterC53#22853
LCSG ▷ C23×C53 ▷ C53
UCSC1 ◁ C22×C4 ◁ #1869

Complements

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

NH ≅ G/Ntype
1. C2×#16810701C2semidirect
2. C2×#16810698C2semidirect
3. C2×#16810589C2semidirect
4. C2×#16810588C2semidirect
6. #20275507C2semidirect
7. #20275322C2semidirect
8. #20275319C2semidirect
9. #20275010C2semidirect
10. #20275004C2semidirect
11. #20274899C2semidirect
12. #20274897C2semidirect
13. C8×C22⋊Dic53C2semidirect
14. #20274485C2semidirect
15. C53×#1869C2semidirect
115. C22⋊#88322D4semidirect
121. #13133129D4semidirect
420. #1869D53semidirect
483. C53#22853semidirect

Maximal subgroups

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

subgroupindex
C2×#168107012
C2×#168106982
C2×#168105892
C2×#168105882
#202779302
#202755072
#202753222
#202753192
#202750102
#202750042
#202748992
#202748972
C8×C22⋊Dic532
#202744852
C53×#18692
#2285353