Finite Group Databasebeta

← #27390253

Subgroups — #27390253

Order 13568.

1044 conjugacy classes of subgroups.

The subgroup lattice has 758 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16810699C211yesmaximal, characteristic, complemented
2C2×#16810696C211yesmaximal, characteristic, complemented
3C2×#16810692C211yesmaximal, characteristic, complemented
4#20277951C211yesmaximal, characteristic
5#20275509C211yesmaximal, characteristic, complemented
6#20275433C211yesmaximal, characteristic, complemented
7#20275328C211yesmaximal, characteristic, complemented
8#20275328C211yesmaximal, characteristic, complemented
9#20275007C211yesmaximal, characteristic, complemented
10#20275007C211yesmaximal, characteristic, complemented
11#20274699C211yesmaximal, characteristic, complemented
12#20274587C211yesmaximal, characteristic, complemented
13#20274498C211yesmaximal, characteristic, complemented
14C8×#11719921C211yesmaximal, characteristic, complemented
15C2×C53×#405C211yesmaximal, characteristic, complemented
16C22×#11719912C2211yescharacteristic
17C22×C8×D53C2211yescharacteristic
18C2×C4×D212C2211yescharacteristic
19C2×C4×C22⋊D53C2211yescharacteristic
20C2×C4×C22⋊D53C2211yescharacteristic
21#16810699—24no—
22#16810696—24no—
23#16810692—24no—
24C2×C4⋊#88322C2211yescharacteristic
25C2×C4⋊#88322C2211yescharacteristic
26C2×#13133146C2211yescharacteristic
27C2×#13133146C2211yescharacteristic
28C2×C22⋊#88322C2211yescharacteristic
29C2×C22⋊#88322C2211yescharacteristic
30C2×#13133129C2211yescharacteristic
31C2×#13133129C2211yescharacteristic
32C2×#13133129C2211yescharacteristic
33C2×#13133129C2211yescharacteristic
34C2×#13133129C2211yescharacteristic
35C2×#13133129C2211yescharacteristic
36C2×#13133127C2211yescharacteristic
37C2×C8×Dic53C2211yescharacteristic
38#16810553C411yescharacteristic
39#16810548C411yescharacteristic
40#16810545C411yescharacteristic
41#16810545C411yescharacteristic
42#16810540C411yescharacteristic
43#16810539C411yescharacteristic
44#16810539C411yescharacteristic
45#16810532C411yescharacteristic
46C4×C4⋊Dic53C2211yescharacteristic
47C4×#11719921C2211yescharacteristic
48C4×#11719921C2211yescharacteristic
49#16810378C2211yescharacteristic
50#16810378C2211yescharacteristic
51#16810377C2211yescharacteristic
52#16810377C2211yescharacteristic
53#16810377C2211yescharacteristic
54#16810377C2211yescharacteristic
55C22×M16×C53C2211yescharacteristic
56C23×C8×C53C2211yescharacteristic
57C2×#117×C53C2211yescharacteristic
58C53×#405—24no—
59C2×#97×C53C2211yescharacteristic
60C2×#97×C53C2211yescharacteristic
61C2×C4×C8×C53C2211yescharacteristic
62C2×C4×C8×C53C2211yescharacteristic
63C22×D212C2×C411yescharacteristic
64C22×C22⋊D53C2×C411yescharacteristic
65C22×C22⋊D53C2×C411yescharacteristic
66C22×C4×D53C2311yescharacteristic
67C22×C4×D53C2311yescharacteristic
68C2×#11719912—22no—
69C2×#11719912—22no—
70C2×#11719912—22no—
71C22×#88322C2311yescharacteristic
72C22×#88322C2311yescharacteristic
73C22×#88322C2311yescharacteristic
74C22×#88322C2311yescharacteristic
75C2×C8×D53—22no—
76C2×C8×D53—22no—
77C2×C8×D53—22no—
78C4×D212—22no—
79C4×D212—22no—
80C4×C22⋊D53—22no—
81C4×C22⋊D53—22no—
82C4×C22⋊D53—22no—
83C4×C22⋊D53—22no—
84C2×C4⋊Dic53C2×C411yescharacteristic
85C2×C4⋊Dic53C2×C411yescharacteristic
86C2×C4⋊Dic53C2×C411yescharacteristic
87C2×#11719919C2×C411yescharacteristic
88C2×#11719919C2×C411yescharacteristic
89C2×C22⋊Dic53C2×C411yescharacteristic
90C2×C22⋊Dic53C2×C411yescharacteristic
91C2×#11719921C2×C411yescharacteristic
92C2×#11719921C2×C411yescharacteristic
93C2×#11719921C2×C411yescharacteristic
94C2×#11719921C2×C411yescharacteristic
95C2×#11719921C2×C411yescharacteristic
96C2×#11719921C2×C411yescharacteristic
97C2×#11719921C2×C411yescharacteristic
98C2×#11719921C2×C411yescharacteristic
99C2×C4×Dic53C2311yescharacteristic
100C2×C4×Dic53C2311yescharacteristic
101C4⋊#88322—22no—
102C4⋊#88322—22no—
103#13133146—22no—
104#13133146—22no—
105C22⋊#88322—22no—
106C22⋊#88322—22no—
107#13133129—22no—
108#13133129—22no—
109#13133129—22no—
110#13133129—22no—
111#13133129—22no—
112#13133129—22no—
113#13133127—22no—
114C8×Dic53—22no—
115#13133124C2×C411yescharacteristic
116#13133124C2×C411yescharacteristic
117#13133124C2×C411yescharacteristic
118#13133124C2×C411yescharacteristic
119#13133124C2×C411yescharacteristic
120#13133124C2×C411yescharacteristic
121C23×C4×C53C2311yescharacteristic
122C2×M16×C53—22no—
123C2×M16×C53—22no—
124C2×M16×C53D414yescomplemented
125C22×C8×C53—22no—
126C22×C8×C53—22no—
127C22×C8×C53—22no—
128C22×C8×C53C2311yescharacteristic
129C22×C8×C53C2311yescharacteristic
130C22×C8×C53C2311yescharacteristic
131C22×C8×C53C2311yescharacteristic
132#117×C53—22no—
133#117×C53—22no—
134C2×C4⋊C4×C53C2×C411yescharacteristic
135C2×C4⋊C4×C53C2×C411yescharacteristic
136C2×C22⋊C4×C53C2×C411yescharacteristic
137C2×C22⋊C4×C53C2×C411yescharacteristic
138C2×C42×C53C2311yescharacteristic
139C2×C42×C53C2311yescharacteristic
140#97×C53—22no—
141#97×C53D414yescomplemented
142C4×C8×C53—22no—
143C4×C8×C53—22no—
144C24×C53C22×C411yescharacteristic
145C23×D53C22×C411yescharacteristic
146C23×D53C22×C411yescharacteristic
147C22×C4×C53—21no—
148C22×C4×C53—21no—
149C22×C4×C53—21no—
150C22×C4×C53—21no—
151C22×C4×C53C22×C411yescharacteristic
152C22×C4×C53C22×C411yescharacteristic
153C22×C4×C53C22×C411yescharacteristic
154C22×C4×C53C22×C411yescharacteristic
155C22×C4×C53C22×C411yescharacteristic
156C22×C4×C53C2×D412yes—
157C22×C4×C53#4112yes—
158C22×C4×C53C2411yescharacteristic
159C2×C22⋊D53—22no—
160C2×C22⋊D53—22no—
161C2×C22⋊D53—22no—
162C2×C22⋊D53—22no—
163C2×C22⋊D53—41no—
164C2×C22⋊D53—41no—
165C22×Dic53C22×C411yescharacteristic
166C22×Dic53C22×C411yescharacteristic
167C22×Dic53C22×C411yescharacteristic
168C22×Dic53C22×C411yescharacteristic
169C22×Dic53C22×C411yescharacteristic
170C22×Dic53C22×C411yescharacteristic
171C2×D212—22no—
172C2×D212—22no—
173C2×D212—41no—
174C2×C4×D53—21no—
175C2×C4×D53—21no—
176C2×C4×D53—21no—
177C2×C4×D53—21no—
178C2×C4×D53—21no—
179C2×C4×D53—21no—
180C2×C4×D53—21no—
181C2×C4×D53—21no—
182C2×C4×D53—21no—
183C2×C4×D53—21no—
184C2×C4×D53—21no—
185C2×C4×D53—21no—
186M16×C53—28no—
187C2×C8×C53—28no—
188C2×C8×C53—21no—
189C2×C8×C53—21no—
190C2×C8×C53—21no—
191C2×C8×C53—21no—
192C2×C8×C53—21no—
193C2×C8×C53—21no—
194C2×C8×C53C2×D412yes—
195C2×C8×C53C2×D412yes—
196C2×C8×C53C2×D412yes—
197C2×C8×C53C2×D412yes—
198C2×C8×C53#4112yes—
199C2×C8×C53#4112yes—
200C4⋊C4×C53—22no—
201C4⋊C4×C53—22no—
202C22⋊C4×C53—22no—
203C22⋊C4×C53—22no—
204C42×C53—21no—
205C42×C53—21no—
206C42×C53C2×D412yes—
207C42×C53#4112yes—
208C22⋊Dic53—22no—
209C22⋊Dic53—22no—
210#11719921—22no—
211#11719921—22no—
212#11719921—22no—
213#11719921—22no—
214#11719921—22no—
215#11719921—22no—
216#11719921—41no—
217#11719921—41no—
218C4⋊Dic53—22no—
219C4⋊Dic53—22no—
220C4⋊Dic53—41no—
221#11719919—22no—
222#11719919—22no—
223C4×Dic53—21no—
224C4×Dic53—21no—
225C4×Dic53—21no—
226C4×Dic53—21no—
227C2×#88322—21no—
228C2×#88322—21no—
229C2×#88322—21no—
230C2×#88322—21no—
231C2×#88322—21no—
232C2×#88322—21no—
233C2×#88322—21no—
234C2×#88322—21no—
235C2×#88322—21no—
236C2×#88322—21no—
237C2×#88322—21no—
238C2×#88322—21no—
239#11719912—44no—
240C8×D53—44no—
241C23×C53—21no—
242C23×C53—21no—
243C23×C53—21no—
244C23×C53—21no—
245C23×C53—21no—
246C23×C53—21no—
247C23×C53C4×D412yes—
248C23×C53C23×C411yescharacteristic
249C22×D53—21no—
250C22×D53—21no—
251C22×D53—21no—
252C22×D53—21no—
253C22×D53—21no—
254C22×D53—21no—
255C22×D53—21no—
256C22×D53—21no—
257C22×D53—21no—
258C22×D53—21no—
259C22×D53—21no—
260C22×D53—21no—
261C22×D53—21no—
262C22×D53#13112yes—
263C2×C4×C53—21no—
264C2×C4×C53—21no—
265C2×C4×C53—21no—
266C2×C4×C53—21no—
267C2×C4×C53—21no—
268C2×C4×C53—21no—
269C2×C4×C53—22no—
270C2×C4×C53—22no—
271C2×C4×C53—22no—
272C2×C4×C53—22no—
273C2×C4×C53—21no—
274C2×C4×C53—21no—
275C2×C4×C53—21no—
276C2×C4×C53—21no—
277C2×C4×C53—21no—
278C2×C4×C53—21no—
279C2×C4×C53C4×D412yes—
280C2×C4×C53C4×D412yes—
281C2×C4×C53C4×D412yes—
282C2×C4×C53C22×D411yescharacteristic
283C2×C4×C53C22×D411yescharacteristic
284C2×C4×C53C2×#4111yescharacteristic
285C2×C4×C53C2×#4111yescharacteristic
286C2×C4×C53C2×#4111yescharacteristic
287C2×C4×C53C2×#4111yescharacteristic
288C22⋊D53—44no—
289C22⋊D53—44no—
290C2×Dic53—21no—
291C2×Dic53—21no—
292C2×Dic53—21no—
293C2×Dic53—21no—
294C2×Dic53—21no—
295C2×Dic53—21no—
296C2×Dic53—21no—
297C2×Dic53—21no—
298C2×Dic53—21no—
299C2×Dic53—21no—
300C2×Dic53—21no—
301C2×Dic53—21no—
302C2×Dic53—21no—
303C2×Dic53—21no—
304C2×Dic53—21no—
305C2×Dic53—21no—
306C2×Dic53—21no—
307C2×Dic53#13112yes—
308D212—44no—
309C4×D53—41no—
310C4×D53—41no—
311C4×D53—41no—
312C4×D53—41no—
313C4×D53—41no—
314C4×D53—41no—
315C4×D53—41no—
316C4×D53—41no—
317C8×C53—22no—
318C8×C53—22no—
319C8×C53—22no—
320C8×C53#12114yes—
321#88322—41no—
322#88322—41no—
323#88322—41no—
324#88322—41no—
325#21496—531nomaximal, Sylow
326C22×C53—22no—
327C22×C53—22no—
328C22×C53—22no—
329C22×C53—41no—
330C22×C53—41no—
331C22×C53—41no—
332C22×C53—41no—
333C22×C53C2×C4×D411yescharacteristic
334C22×C53C2×C4×D411yescharacteristic
335C22×C53C4×#4111yescharacteristic
336C22×C53C2×#13111yescharacteristic
337C22×C53C2×#13111yescharacteristic
338C22×C53#56811yescharacteristic
339C22×C53#56811yescharacteristic
340C2×D53—22no—
341C2×D53—22no—
342C2×D53—22no—
343C2×D53—41no—
344C2×D53—41no—
345C2×D53—41no—
346C2×D53—41no—
347C2×D53—41no—
348C2×D53—41no—
349C2×D53—41no—
350C2×D53—41no—
351C2×D53—41no—
352C2×D53—41no—
353C2×D53—41no—
354C4×C53—22no—
355C4×C53—22no—
356C4×C53—22no—
357C4×C53—41no—
358C4×C53—41no—
359C4×C53C2×#12111yescharacteristic
360C4×C53#52511yescharacteristic
361C4×C53#52911yescharacteristic
362C4×C53#53211yescharacteristic
363Dic53—22no—
364Dic53—41no—
365Dic53—41no—
366Dic53—41no—
367Dic53—41no—
368Dic53—41no—
369C2×#436—531no—
370C2×#435—531no—
371C2×#435—531no—
372C2×#405D5311yescharacteristic, complemented
373#2392—531no—
374#1954—531no—
375#1939—531no—
376#1924—531no—
377#1924—531no—
378#1869—531no—
379#1869—531no—
380#1798—531no—
381#1771—531no—
382#1753—531no—
383C8×C22⋊C4—531no—
384C2×C53—42no—
385C2×C53C4×#12111yescharacteristic
386C2×C53#293311yescharacteristic
387C2×C53#293311yescharacteristic
388C2×C53#293311yescharacteristic
389C2×C53#293511yescharacteristic
390C2×C53#296611yescharacteristic
391C2×C53#296711yescharacteristic
392D53—42no—
393D53—81no—
394C22×M16—531no—
395C22×M16C2×D5311yescharacteristic
396C23×C8—531no—
397C23×C8C2×D5311yescharacteristic
398C2×C4×D4—531no—
399C2×C4×D4—531no—
400C2×C4×D4—531no—
401C2×#117C2×D5311yescharacteristic
402#436—1064no—
403#435—1064no—
404#435—1064no—
405C2×C4⋊C8—531no—
406C2×C4⋊C8—531no—
407C2×C4⋊C8—531no—
408C2×C4⋊C8—531no—
409C2×C22⋊C8—531no—
410C2×C22⋊C8—531no—
411C2×C22⋊C8—531no—
412C2×C22⋊C8—531no—
413C2×C22⋊C8—531no—
414C2×C22⋊C8—531no—
415C2×C22⋊C8—531no—
416C2×C22⋊C8—531no—
417#405—24no—
418C2×#97—531no—
419C2×#97C2×D5311yescharacteristic
420C2×#97C2×D5311yescharacteristic
421C2×C4×C8—531no—
422C2×C4×C8C2×D5311yescharacteristic
423C2×C4×C8C2×D5311yescharacteristic
424#398—531no—
425#397—531no—
426#396—531no—
427#396—531no—
428#394—531no—
429#394—531no—
430#394—531no—
431#392—531no—
432C4×C4⋊C4—531no—
433C4×C22⋊C4—531no—
434C4×C22⋊C4—531no—
435#336—531no—
436#336—531no—
437#336—531no—
438#336—531no—
439#336—531no—
440#336—531no—
441C53#2149611yescharacteristic, complemented, Sylow
442C22×D4—531no—
443C22×D4—531no—
444C22×D4—531no—
445C23×C4—531no—
446C23×C4—531no—
447C23×C4C22×D5311yescharacteristic
448C2×M16—22no—
449C2×M16—22no—
450C2×M16—1062no—
451C2×M16—1062no—
452C2×M16—1062no—
453C2×M16D21214yescomplemented
454C22×C8—22no—
455C22×C8—22no—
456C22×C8—22no—
457C22×C8—531no—
458C22×C8—531no—
459C22×C8—531no—
460C22×C8—531no—
461C22×C8—1062no—
462C22×C8—1062no—
463C22×C8—1062no—
464C22×C8C22×D5311yescharacteristic
465C22×C8C22×D5311yescharacteristic
466C22×C8C22×D5311yescharacteristic
467C22×C8C22×D5311yescharacteristic
468C4×D4—1062no—
469C4×D4—1062no—
470C4×D4—1062no—
471C4×D4—1062no—
472C4×D4—1062no—
473C4×D4—1062no—
474#117—22no—
475#117—22no—
476C2×C4⋊C4—531no—
477C2×C4⋊C4—531no—
478C2×C4⋊C4—531no—
479C2×C4⋊C4—531no—
480C2×C4⋊C4—531no—
481C2×C4⋊C4C4×D5311yescharacteristic
482C2×C4⋊C4C4×D5311yescharacteristic
483C2×C22⋊C4—531no—
484C2×C22⋊C4—531no—
485C2×C22⋊C4—531no—
486C2×C22⋊C4—531no—
487C2×C22⋊C4—531no—
488C2×C22⋊C4—531no—
489C2×C22⋊C4—531no—
490C2×C22⋊C4—531no—
491C2×C22⋊C4—531no—
492C2×C22⋊C4—531no—
493C2×C22⋊C4C4×D5311yescharacteristic
494C2×C22⋊C4C4×D5311yescharacteristic
495C2×C42—531no—
496C2×C42—531no—
497C2×C42C22×D5311yescharacteristic
498C2×C42C22×D5311yescharacteristic
499C4⋊C8—1062no—
500C4⋊C8—1062no—
501C4⋊C8—1062no—
502C4⋊C8—1062no—
503C22⋊C8—1062no—
504C22⋊C8—1062no—
505C22⋊C8—1062no—
506C22⋊C8—1062no—
507C22⋊C8—1062no—
508C22⋊C8—1062no—
509C22⋊C8—1062no—
510C22⋊C8—1062no—
511#97—22no—
512#97—1062no—
513#97C22⋊D5314yescomplemented
514C4×C8—22no—
515C4×C8—22no—
516C4×C8—1062no—
517#95—531no—
518#95—531no—
519#95—531no—
520#95—531no—
521#95—531no—
522#95—531no—
523C24—531no—
524C24—531no—
525C24C2×C4×D5311yescharacteristic
526C2×D4—1062no—
527C2×D4—1062no—
528C2×D4—1062no—
529C2×D4—1062no—
530C2×D4—1062no—
531C2×D4—1062no—
532C2×D4—2121no—
533C2×D4—2121no—
534C2×D4—2121no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—531no—
540C22×C4—531no—
541C22×C4—531no—
542C22×C4—531no—
543C22×C4—531no—
544C22×C4—531no—
545C22×C4—1061no—
546C22×C4—1061no—
547C22×C4—1061no—
548C22×C4—1061no—
549C22×C4—1061no—
550C22×C4—1061no—
551C22×C4—1061no—
552C22×C4—1061no—
553C22×C4—1061no—
554C22×C4—1061no—
555C22×C4—1061no—
556C22×C4—1061no—
557C22×C4C2×C4×D5311yescharacteristic
558C22×C4C2×C4×D5311yescharacteristic
559C22×C4C2×C4×D5311yescharacteristic
560C22×C4C2×C4×D5311yescharacteristic
561C22×C4C2×C4×D5311yescharacteristic
562C22×C4C2×D21212yes—
563C22×C4#1171994512yes—
564C22×C4C23×D5311yescharacteristic
565M16—28no—
566M16—2124no—
567C2×C8—28no—
568C2×C8—21no—
569C2×C8—21no—
570C2×C8—21no—
571C2×C8—21no—
572C2×C8—21no—
573C2×C8—21no—
574C2×C8—1061no—
575C2×C8—1061no—
576C2×C8—1061no—
577C2×C8—1061no—
578C2×C8—1061no—
579C2×C8—1061no—
580C2×C8—1061no—
581C2×C8—1061no—
582C2×C8—1061no—
583C2×C8—1061no—
584C2×C8—1061no—
585C2×C8—1061no—
586C2×C8—2124no—
587C2×C8C2×D21212yes—
588C2×C8C2×D21212yes—
589C2×C8#1171994512yes—
590C2×C8#1171994512yes—
591C2×C8C2×C22⋊D5312yes—
592C2×C8C2×C22⋊D5312yes—
593C4⋊C4—22no—
594C4⋊C4—22no—
595C4⋊C4—1062no—
596C4⋊C4—1062no—
597C4⋊C4—1062no—
598C4⋊C4—1062no—
599C4⋊C4—2121no—
600C22⋊C4—22no—
601C22⋊C4—22no—
602C22⋊C4—1062no—
603C22⋊C4—1062no—
604C22⋊C4—1062no—
605C22⋊C4—1062no—
606C22⋊C4—1062no—
607C22⋊C4—1062no—
608C22⋊C4—1062no—
609C22⋊C4—1062no—
610C22⋊C4—2121no—
611C22⋊C4—2121no—
612C42—21no—
613C42—21no—
614C42—1061no—
615C42—1061no—
616C42—1061no—
617C42—1061no—
618C42#1171994512yes—
619C42C2×C22⋊D5312yes—
620C23—21no—
621C23—21no—
622C23—21no—
623C23—21no—
624C23—21no—
625C23—21no—
626C23—532no—
627C23—1061no—
628C23—1061no—
629C23—1061no—
630C23—1061no—
631C23—1061no—
632C23—1061no—
633C23—1061no—
634C23—1061no—
635C23—1061no—
636C23—1061no—
637C23—1061no—
638C23—1061no—
639C23—1061no—
640C23C4×D21212yes—
641C23C22×C4×D5311yescharacteristic
642D4—2124no—
643D4—2124no—
644D4—2124no—
645C2×C4—21no—
646C2×C4—21no—
647C2×C4—21no—
648C2×C4—21no—
649C2×C4—21no—
650C2×C4—21no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—21no—
656C2×C4—21no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—532no—
662C2×C4—1061no—
663C2×C4—1061no—
664C2×C4—1061no—
665C2×C4—1061no—
666C2×C4—1061no—
667C2×C4—1061no—
668C2×C4—1061no—
669C2×C4—1061no—
670C2×C4—1061no—
671C2×C4—1061no—
672C2×C4—1061no—
673C2×C4—1061no—
674C2×C4—1061no—
675C2×C4—1061no—
676C2×C4—1061no—
677C2×C4—1061no—
678C2×C4—1061no—
679C2×C4—2121no—
680C2×C4—2121no—
681C2×C4—2121no—
682C2×C4—2121no—
683C2×C4—2121no—
684C2×C4—2121no—
685C2×C4—2121no—
686C2×C4—2121no—
687C2×C4C4×C22⋊D5312yes—
688C2×C4C4×C22⋊D5312yes—
689C2×C4C4×D21212yes—
690C2×C4C22×C22⋊D5311yescharacteristic
691C2×C4C22×D21211yescharacteristic
692C2×C4C2×#1171994511yescharacteristic
693C2×C4C2×#1171994511yescharacteristic
694C2×C4C2×#1171994511yescharacteristic
695C2×C4C2×#1171994511yescharacteristic
696C8—22no—
697C8—22no—
698C8—22no—
699C8—2121no—
700C8—2121no—
701C8—2121no—
702C8—2121no—
703C8#1313319114yes—
704C22—22no—
705C22—22no—
706C22—22no—
707C22—41no—
708C22—41no—
709C22—41no—
710C22—41no—
711C22—1062no—
712C22—1062no—
713C22—1062no—
714C22—2121no—
715C22—2121no—
716C22—2121no—
717C22—2121no—
718C22—2121no—
719C22—2121no—
720C22—2121no—
721C22—2121no—
722C22—2121no—
723C22—2121no—
724C22—2121no—
725C22C2×C4×C22⋊D5311yescharacteristic
726C22C2×C4×D21211yescharacteristic
727C22C4×#1171994511yescharacteristic
728C22#131×D5311yescharacteristic
729C22#131×D5311yescharacteristic
730C22#1681138811yescharacteristic
731C22#1681138811yescharacteristic
732C4—22no—
733C4—22no—
734C4—22no—
735C4—41no—
736C4—41no—
737C4—1062no—
738C4—2121no—
739C4—2121no—
740C4—2121no—
741C4—2121no—
742C4—2121no—
743C4C2×#1313319111yescharacteristic
744C4#1681113411yescharacteristic
745C4#1681115711yescharacteristic
746C4#1681117311yescharacteristic
747C2—42no—
748C2—4241no—
749C2—2122no—
750C2C4×#1313319111yescharacteristic
751C2#2028343711yescharacteristic
752C2#2028344311yescharacteristic
753C2#2028344311yescharacteristic
754C2#2028345711yescharacteristic
755C2#2028368611yescharacteristic
756C2#2028369611yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D53
commutator, socleC23×C53C23×C4
FittingC2×C53×#405C2
prime radical#16810532C4
cosocleC22×C4×C53C24
hypercenterC2×#405D53
hypocenterC53#21496
LCSG ▷ C23×C53 ▷ C53
UCSC1 ◁ C22×C4 ◁ C2×#405

Complements

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

NH ≅ G/Ntype
1. C2×#16810699C2semidirect
2. C2×#16810696C2semidirect
3. C2×#16810692C2semidirect
5. #20275509C2semidirect
6. #20275433C2semidirect
7. #20275328C2semidirect
8. #20275328C2semidirect
9. #20275007C2semidirect
10. #20275007C2semidirect
11. #20274699C2semidirect
12. #20274587C2semidirect
13. #20274498C2semidirect
14. C8×#11719921C2semidirect
15. C2×C53×#405C2semidirect
124. C2×M16×C53D4semidirect
141. #97×C53D4semidirect
372. C2×#405D53semidirect
441. C53#21496semidirect
453. C2×M16D212semidirect
513. #97C22⋊D53semidirect

Maximal subgroups

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

subgroupindex
C2×#168106992
C2×#168106962
C2×#168106922
#202779512
#202755092
#202754332
#202753282
#202750072
#202746992
#202745872
#202744982
C8×#117199212
C2×C53×#4052
#2149653