Finite Group Databasebeta

← #27401127

Subgroups — #27401127

Order 13568.

990 conjugacy classes of subgroups.

The subgroup lattice has 764 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16810681C211yesmaximal, characteristic, complemented
2C2×#16810588C211yesmaximal, characteristic
3#20277205C211yesmaximal, characteristic
4#20275327C211yesmaximal, characteristic, complemented
5#20275326C211yesmaximal, characteristic, complemented
6#20275326C211yesmaximal, characteristic, complemented
7#20275320C211yesmaximal, characteristic, complemented
8#20274896C211yesmaximal, characteristic, complemented
9#20274891C211yesmaximal, characteristic, complemented
10#20274784C211yesmaximal, characteristic, complemented
11#20274626C211yesmaximal, characteristic
12#20274497C211yesmaximal, characteristic, complemented
13#20274490C211yesmaximal, characteristic, complemented
14#20274477C211yesmaximal, characteristic, complemented
15C53×#1797C211yesmaximal, characteristic, complemented
16C22×#11719945C2211yescharacteristic
17C22×#11719912C2211yescharacteristic
18C22×C8×D53C2211yescharacteristic
19C2×#13133176C2211yescharacteristic
20#16810681—24no—
21C2×#13133146C2211yescharacteristic
22C2×#13133146C2211yescharacteristic
23#16810588—24no—
24C2×C22⋊#88322C2211yescharacteristic
25C2×C22⋊#88322C2211yescharacteristic
26C2×#13133129C2211yescharacteristic
27C2×#13133129C2211yescharacteristic
28C2×#13133129C2211yescharacteristic
29C2×#13133129C2211yescharacteristic
30C2×#13133129C2211yescharacteristic
31C2×#13133129C2211yescharacteristic
32C2×#13133128C2211yescharacteristic
33C2×#13133128C2211yescharacteristic
34C2×#13133127C2211yescharacteristic
35C2×C8×Dic53C2211yescharacteristic
36#16810529C411yescharacteristic
37#16810529C411yescharacteristic
38#16810525C411yescharacteristic
39#16810525C411yescharacteristic
40#16810502C411yescharacteristic
41#16810502C411yescharacteristic
42#16810502C411yescharacteristic
43#16810502C411yescharacteristic
44C4×#11719921C2211yescharacteristic
45C4×#11719921C2211yescharacteristic
46C4×#11719921C2211yescharacteristic
47C4×#11719921C2211yescharacteristic
48#16810378C2211yescharacteristic
49#16810378C2211yescharacteristic
50#16810377C2211yescharacteristic
51#16810377C2211yescharacteristic
52#16810377C2211yescharacteristic
53#16810377C2211yescharacteristic
54C22×C42×C53C2211yescharacteristic
55C2×C4⋊C8×C53C2211yescharacteristic
56C2×C4⋊C8×C53C2211yescharacteristic
57C2×C22⋊C8×C53C2211yescharacteristic
58C2×C22⋊C8×C53C2211yescharacteristic
59C53×#336C2211yescharacteristic
60C53×#336C2211yescharacteristic
61C2×#11719945—22no—
62C2×#11719945—22no—
63C2×#11719945—22no—
64C2×#11719945—22no—
65C2×#11719945—41no—
66C2×#11719945—41no—
67C22×Dic106C2×C411yescharacteristic
68C22×D212C2×C411yescharacteristic
69C22×C22⋊D53C2×C411yescharacteristic
70C22×C22⋊D53C2×C411yescharacteristic
71C22×C4×D53C2311yescharacteristic
72C22×C4×D53C2311yescharacteristic
73C2×#11719912—22no—
74C2×#11719912—22no—
75C2×#11719912—41no—
76C22×#88322C2311yescharacteristic
77C22×#88322C2311yescharacteristic
78C22×#88322C2311yescharacteristic
79C22×#88322C2311yescharacteristic
80C2×C8×D53—22no—
81C2×C8×D53—22no—
82C2×C8×D53—41no—
83#13133176—22no—
84#13133176—22no—
85C2×C4⋊Dic53C2×C411yescharacteristic
86C2×C4⋊Dic53C2×C411yescharacteristic
87C2×C22⋊Dic53C2×C411yescharacteristic
88C2×C22⋊Dic53C2×C411yescharacteristic
89C2×#11719921C2×C411yescharacteristic
90C2×#11719921C2×C411yescharacteristic
91C2×#11719921C2×C411yescharacteristic
92C2×#11719921C2×C411yescharacteristic
93C2×#11719921C2×C411yescharacteristic
94C2×#11719921C2×C411yescharacteristic
95C2×#11719921C2×C411yescharacteristic
96C2×#11719921C2×C411yescharacteristic
97C2×C4×Dic53C2311yescharacteristic
98C2×C4×Dic53C2311yescharacteristic
99#13133146—22no—
100#13133146—22no—
101C22⋊#88322—22no—
102C22⋊#88322D414yes—
103#13133129—22no—
104#13133129—22no—
105#13133129—22no—
106#13133129—22no—
107#13133129—41no—
108#13133129—41no—
109#13133128—41no—
110#13133128—41no—
111#13133127—22no—
112C8×Dic53—22no—
113#13133124C2×C411yescharacteristic
114#13133124C2×C411yescharacteristic
115#13133124C2×C411yescharacteristic
116#13133124C2×C411yescharacteristic
117#13133124C2×C411yescharacteristic
118#13133124C2×C411yescharacteristic
119#13133124C2×C411yescharacteristic
120#13133124C2×C411yescharacteristic
121C23×C4×C53C2×C411yescharacteristic
122C23×C4×C53C2×C411yescharacteristic
123C23×C4×C53C2311yescharacteristic
124C22×C8×C53C2311yescharacteristic
125C22×C8×C53C2311yescharacteristic
126C22×C8×C53C2311yescharacteristic
127C22×C8×C53C2311yescharacteristic
128C2×C42×C53—41no—
129C2×C42×C53—41no—
130C2×C42×C53C2×C411yescharacteristic
131C2×C42×C53C2×C411yescharacteristic
132C2×C42×C53C2311yescharacteristic
133C2×C42×C53C2311yescharacteristic
134C4⋊C8×C53—41no—
135C4⋊C8×C53—41no—
136C22⋊C8×C53—22no—
137C22⋊C8×C53—22no—
138C24×C53C22×C411yescharacteristic
139C23×D53C22×C411yescharacteristic
140C23×D53C22×C411yescharacteristic
141C22×C4×C53—21no—
142C22×C4×C53—21no—
143C22×C4×C53—21no—
144C22×C4×C53—21no—
145C22×C4×C53—22no—
146C22×C4×C53—41no—
147C22×C4×C53—41no—
148C22×C4×C53—41no—
149C22×C4×C53—41no—
150C22×C4×C53—41no—
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
171#11719945—44no—
172#11719945—44no—
173#11719945—44no—
174#11719945—44no—
175C2×D212—22no—
176C2×D212—22no—
177C2×D212—41no—
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—
186C2×C4×D53—21no—
187C2×C4×D53—21no—
188C2×C4×D53#4112yes—
189C2×C4×D53#4112yes—
190C2×Dic106—22no—
191C2×Dic106—22no—
192C2×Dic106—41no—
193C2×C8×C53—21no—
194C2×C8×C53—21no—
195C2×C8×C53—21no—
196C2×C8×C53—21no—
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—
205C42×C53—21no—
206C42×C53—21no—
207C42×C53—21no—
208C42×C53—21no—
209C42×C53—41no—
210C42×C53—41no—
211C22⋊Dic53—22no—
212C22⋊Dic53—22no—
213#11719921—22no—
214#11719921—22no—
215#11719921—41no—
216#11719921—41no—
217#11719921—41no—
218#11719921—41no—
219#11719921—41no—
220#11719921—41no—
221C4⋊Dic53—22no—
222C4⋊Dic53—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×#88322C2×D412yes—
238C2×#88322C2×D412yes—
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#11712yes—
263C2×C4×C53—21no—
264C2×C4×C53—21no—
265C2×C4×C53—21no—
266C2×C4×C53—21no—
267C2×C4×C53—22no—
268C2×C4×C53—22no—
269C2×C4×C53—22no—
270C2×C4×C53—22no—
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—21no—
278C2×C4×C53—21no—
279C2×C4×C53—21no—
280C2×C4×C53—44no—
281C2×C4×C53—44no—
282C2×C4×C53C4×D412yes—
283C2×C4×C53#13112yes—
284C2×C4×C53C22×D411yescharacteristic
285C2×C4×C53C2×#4111yescharacteristic
286C2×C4×C53C2×#4111yescharacteristic
287C2×C4×C53C2×#4111yescharacteristic
288C2×C4×C53H(5,𝔽2)11yescharacteristic
289C2×C4×C53H(5,𝔽2)11yescharacteristic
290C22⋊D53—44no—
291C22⋊D53—44no—
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—21no—
308C2×Dic53—21no—
309C2×Dic53#11712yes—
310D212—44no—
311C4×D53—22no—
312C4×D53—22no—
313C4×D53—22no—
314C4×D53—22no—
315C4×D53—41no—
316C4×D53—41no—
317C4×D53—41no—
318C4×D53—41no—
319Dic106—44no—
320C8×C53—41no—
321C8×C53—41no—
322C8×C53—41no—
323C8×C53—41no—
324#88322—22no—
325#88322—22no—
326#88322—41no—
327#88322—41no—
328#22561—531nomaximal, Sylow
329C22×C53—22no—
330C22×C53—22no—
331C22×C53—22no—
332C22×C53—41no—
333C22×C53—41no—
334C22×C53—41no—
335C22×C53—41no—
336C22×C53C2×#11711yescharacteristic
337C22×C53C2×C4×D411yescharacteristic
338C22×C53#51811yescharacteristic
339C22×C53C2×#13111yescharacteristic
340C22×C53#56811yescharacteristic
341C22×C53#56811yescharacteristic
342C22×C53#56811yescharacteristic
343C2×D53—22no—
344C2×D53—22no—
345C2×D53—22no—
346C2×D53—41no—
347C2×D53—41no—
348C2×D53—41no—
349C2×D53—41no—
350C2×D53—41no—
351C2×D53—41no—
352C2×D53—41no—
353C2×D53—41no—
354C2×D53—41no—
355C2×D53—41no—
356C2×D53—41no—
357C4×C53—22no—
358C4×C53—22no—
359C4×C53—41no—
360C4×C53—41no—
361C4×C53—41no—
362C4×C53#54611yescharacteristic
363C4×C53#54611yescharacteristic
364C4×C53#55111yescharacteristic
365C4×C53#55111yescharacteristic
366Dic53—22no—
367Dic53—41no—
368Dic53—41no—
369Dic53—41no—
370Dic53—41no—
371Dic53—41no—
372C2×#433—531no—
373C2×#408—531no—
374#2297—531no—
375#1924—531no—
376#1924—531no—
377#1924—531no—
378#1923—531no—
379#1851—531no—
380#1850—531no—
381#1818—531no—
382#1797D5311yescharacteristic, complemented
383#1780—531no—
384#1753—531no—
385#1752—531no—
386#1749—531no—
387C2×C53—42no—
388C2×C53#234211yescharacteristic
389C2×C53#292311yescharacteristic
390C2×C53#292511yescharacteristic
391C2×C53#293211yescharacteristic
392C2×C53#293511yescharacteristic
393C2×C53#297611yescharacteristic
394C2×C53#297811yescharacteristic
395D53—42no—
396D53—81no—
397C22×#41—531no—
398C22×M16—531no—
399C23×C8—531no—
400C2×#117—531no—
401C22×C42C2×D5311yescharacteristic
402#433—1064no—
403C2×C4⋊C8—531no—
404C2×C4⋊C8—531no—
405C2×C4⋊C8C2×D5311yescharacteristic
406C2×C4⋊C8C2×D5311yescharacteristic
407#408—1064no—
408C2×C22⋊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⋊C8C2×D5311yescharacteristic
417C2×C22⋊C8C2×D5311yescharacteristic
418C2×#97—531no—
419C2×#97—531no—
420C2×#97—531no—
421C2×C4×C8—531no—
422#391—531no—
423#391—531no—
424#390—531no—
425#390—531no—
426#386—531no—
427#386—531no—
428#386—531no—
429#386—531no—
430C4×C22⋊C4—531no—
431C4×C22⋊C4—531no—
432C4×C22⋊C4—531no—
433C4×C22⋊C4—531no—
434#336—531no—
435#336—531no—
436#336—531no—
437#336—531no—
438#336—531no—
439#336—531no—
440#336C2×D5311yescharacteristic
441#336C2×D5311yescharacteristic
442C53#2256111yescharacteristic, complemented, Sylow
443C2×#41—1062no—
444C2×#41—1062no—
445C2×#41—1062no—
446C2×#41—1062no—
447C2×#41—2121no—
448C2×#41—2121no—
449C22×Q8—531no—
450C22×D4—531no—
451C22×D4—531no—
452C22×D4—531no—
453C23×C4—531no—
454C23×C4—531no—
455C23×C4C4×D5311yescharacteristic
456C23×C4C4×D5311yescharacteristic
457C23×C4C22×D5311yescharacteristic
458C2×M16—1062no—
459C2×M16—1062no—
460C2×M16—2121no—
461C22×C8—531no—
462C22×C8—531no—
463C22×C8—531no—
464C22×C8—531no—
465C22×C8—1062no—
466C22×C8—1062no—
467C22×C8—2121no—
468C22×C8C22×D5311yescharacteristic
469C22×C8C22×D5311yescharacteristic
470C22×C8C22×D5311yescharacteristic
471C22×C8C22×D5311yescharacteristic
472#117—1062no—
473#117—1062no—
474C2×C4⋊C4—531no—
475C2×C4⋊C4—531no—
476C2×C22⋊C4—531no—
477C2×C22⋊C4—531no—
478C2×C22⋊C4—531no—
479C2×C22⋊C4—531no—
480C2×C22⋊C4—531no—
481C2×C22⋊C4—531no—
482C2×C22⋊C4—531no—
483C2×C22⋊C4—531no—
484C2×C22⋊C4—531no—
485C2×C22⋊C4—531no—
486C2×C42—41no—
487C2×C42—41no—
488C2×C42—531no—
489C2×C42—531no—
490C2×C42C4×D5311yescharacteristic
491C2×C42C4×D5311yescharacteristic
492C2×C42C22×D5311yescharacteristic
493C2×C42C22×D5311yescharacteristic
494C4⋊C8—41no—
495C4⋊C8—41no—
496C4⋊C8—1062no—
497C4⋊C8—1062no—
498C22⋊C8—22no—
499C22⋊C8—22no—
500C22⋊C8—534no—
501C22⋊C8—1062no—
502C22⋊C8—1062no—
503C22⋊C8—1062no—
504C22⋊C8—1062no—
505C22⋊C8—1062no—
506C22⋊C8—2121no—
507C22⋊C8—2121no—
508#97—1062no—
509#97—2121no—
510#97—2121no—
511C4×C8—1062no—
512#95—531no—
513#95—531no—
514#95—531no—
515#95—531no—
516#95—531no—
517#95—531no—
518#95—531no—
519#95—531no—
520C24—531no—
521C24—531no—
522C24C2×C4×D5311yescharacteristic
523#41—2124no—
524#41—2124no—
525#41—2124no—
526#41—2124no—
527C2×Q8—1062no—
528C2×Q8—1062no—
529C2×Q8—2121no—
530C2×D4—1062no—
531C2×D4—1062no—
532C2×D4—1062no—
533C2×D4—1062no—
534C2×D4—1062no—
535C2×D4—1062no—
536C2×D4—2121no—
537C2×D4—2121no—
538C2×D4—2121no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—22no—
544C22×C4—41no—
545C22×C4—41no—
546C22×C4—41no—
547C22×C4—41no—
548C22×C4—41no—
549C22×C4—531no—
550C22×C4—532no—
551C22×C4—532no—
552C22×C4—531no—
553C22×C4—531no—
554C22×C4—531no—
555C22×C4—531no—
556C22×C4—531no—
557C22×C4—1061no—
558C22×C4—1061no—
559C22×C4—1061no—
560C22×C4—1061no—
561C22×C4—1061no—
562C22×C4—1061no—
563C22×C4—1061no—
564C22×C4—1061no—
565C22×C4—1061no—
566C22×C4—1061no—
567C22×C4C2×C4×D5311yescharacteristic
568C22×C4C2×C4×D5311yescharacteristic
569C22×C4C2×C4×D5311yescharacteristic
570C22×C4C2×C4×D5311yescharacteristic
571C22×C4C2×C4×D5311yescharacteristic
572C22×C4D4×D5312yes—
573C22×C4#1171994912yes—
574C22×C4C23×D5311yescharacteristic
575M16—2124no—
576C2×C8—21no—
577C2×C8—21no—
578C2×C8—21no—
579C2×C8—21no—
580C2×C8—21no—
581C2×C8—21no—
582C2×C8—21no—
583C2×C8—21no—
584C2×C8—21no—
585C2×C8—21no—
586C2×C8—21no—
587C2×C8—21no—
588C2×C8—532no—
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—2124no—
601C4⋊C4—1062no—
602C4⋊C4—1062no—
603C22⋊C4—1062no—
604C22⋊C4—1062no—
605C22⋊C4—1062no—
606C22⋊C4—1062no—
607C22⋊C4—2121no—
608C22⋊C4—2121no—
609C22⋊C4—2121no—
610C22⋊C4—2121no—
611C22⋊C4—2121no—
612C22⋊C4—2121no—
613C42—21no—
614C42—21no—
615C42—21no—
616C42—21no—
617C42—41no—
618C42—41no—
619C42—1061no—
620C42—1061no—
621C42—1061no—
622C42—1061no—
623C23—21no—
624C23—21no—
625C23—21no—
626C23—21no—
627C23—21no—
628C23—21no—
629C23—532no—
630C23—1061no—
631C23—1061no—
632C23—1061no—
633C23—1061no—
634C23—1061no—
635C23—1061no—
636C23—1061no—
637C23—1061no—
638C23—1061no—
639C23—1061no—
640C23—1061no—
641C23—1061no—
642C23—1061no—
643C23#1313317912yes—
644C23C22×C4×D5311yescharacteristic
645Q8—2124no—
646D4—2124no—
647D4—2124no—
648D4—2124no—
649C2×C4—21no—
650C2×C4—21no—
651C2×C4—21no—
652C2×C4—21no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—21no—
666C2×C4—44no—
667C2×C4—44no—
668C2×C4—532no—
669C2×C4—1061no—
670C2×C4—1061no—
671C2×C4—1062no—
672C2×C4—1062no—
673C2×C4—1062no—
674C2×C4—1062no—
675C2×C4—1061no—
676C2×C4—1061no—
677C2×C4—1061no—
678C2×C4—1061no—
679C2×C4—1061no—
680C2×C4—1061no—
681C2×C4—1061no—
682C2×C4—1061no—
683C2×C4—1061no—
684C2×C4—1061no—
685C2×C4—1061no—
686C2×C4—1061no—
687C2×C4—1061no—
688C2×C4—1061no—
689C2×C4—1061no—
690C2×C4—2121no—
691C2×C4—2121no—
692C2×C4—2121no—
693C2×C4—2121no—
694C2×C4#1313317912yes—
695C2×C4#1313322312yes—
696C2×C4C2×D4×D5311yescharacteristic
697C2×C4#41×D5311yescharacteristic
698C2×C4#41×D5311yescharacteristic
699C2×C4C2×#1171994911yescharacteristic
700C2×C4#1313326211yescharacteristic
701C2×C4#1313326211yescharacteristic
702C8—41no—
703C8—41no—
704C8—41no—
705C8—41no—
706C8—1062no—
707C8—1062no—
708C8—2121no—
709C8—2121no—
710C22—22no—
711C22—22no—
712C22—22no—
713C22—41no—
714C22—41no—
715C22—41no—
716C22—41no—
717C22—1062no—
718C22—1062no—
719C22—1062no—
720C22—2121no—
721C22—2121no—
722C22—2121no—
723C22—2121no—
724C22—2121no—
725C22—2121no—
726C22—2121no—
727C22—2121no—
728C22—2121no—
729C22—2121no—
730C22—2121no—
731C22#117×D5311yescharacteristic
732C22C2×#1313317911yescharacteristic
733C22#1681109611yescharacteristic
734C22C2×#1313322311yescharacteristic
735C22#1681138911yescharacteristic
736C22#1681138911yescharacteristic
737C22#1681138911yescharacteristic
738C4—22no—
739C4—22no—
740C4—41no—
741C4—41no—
742C4—41no—
743C4—1062no—
744C4—2121no—
745C4—2121no—
746C4—2121no—
747C4—2121no—
748C4—2121no—
749C4#1681126211yescharacteristic
750C4#1681126211yescharacteristic
751C4#1681130011yescharacteristic
752C4#1681130011yescharacteristic
753C2—42no—
754C2—4241no—
755C2—2122no—
756C2#2027756111yescharacteristic
757C2#2028336111yescharacteristic
758C2#2028337611yescharacteristic
759C2#2028343211yescharacteristic
760C2#2028345811yescharacteristic
761C2#2028376011yescharacteristic
762C2#2028377511yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D53
commutator, socleC23×C53C23×C4
FittingC53×#1797C2
prime radicalC22×#11719945C22
cosocleC22×C4×C53C24
hypercenter#1797D53
hypocenterC53#22561
LCSG ▷ C23×C53 ▷ C53
UCSC1 ◁ C22×C4 ◁ #1797

Complements

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

NH ≅ G/Ntype
1. C2×#16810681C2semidirect
4. #20275327C2semidirect
5. #20275326C2semidirect
6. #20275326C2semidirect
7. #20275320C2semidirect
8. #20274896C2semidirect
9. #20274891C2semidirect
10. #20274784C2semidirect
12. #20274497C2semidirect
13. #20274490C2semidirect
14. #20274477C2semidirect
15. C53×#1797C2semidirect
382. #1797D53semidirect
442. C53#22561semidirect

Maximal subgroups

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

subgroupindex
C2×#168106812
C2×#168105882
#202772052
#202753272
#202753262
#202753202
#202748962
#202748912
#202747842
#202746262
#202744972
#202744902
#202744772
C53×#17972
#2256153