Finite Group Databasebeta

← #27428252

Subgroups — #27428252

Order 13568.

1150 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×#16810723C211yesmaximal, characteristic, complemented
3#20278240C211yesmaximal, characteristic, complemented
4#20276243C211yesmaximal, characteristic, complemented
5#20276146C211yesmaximal, characteristic, complemented
6#20276032C211yesmaximal, characteristic, complemented
7#20275918C211yesmaximal, characteristic, complemented
8#20275415C211yesmaximal, characteristic, complemented
9#20275330C211yesmaximal, characteristic, complemented
10#20275073C211yesmaximal, characteristic, complemented
11#20275049C211yesmaximal, characteristic, complemented
12#20274962C211yesmaximal, 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—
21#16810723—24no—
22C2×#13133150C2211yescharacteristic, complemented
23C2×#13133150C2211yescharacteristic, 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×#13133128C2211yescharacteristic, 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#13133150—22no—
88#13133150—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—
100#13133128—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—22no—
203C22⋊C4×C53—22no—
204C22⋊C4×C53—42no—
205C22⋊C4×C53—42no—
206C22⋊C4×C53—42no—
207C22⋊C4×C53—42no—
208C22⋊C4×C53—42no—
209C22⋊C4×C53—81no—
210C22⋊C4×C53—81no—
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×C53#13712yes—
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—21no—
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—41no—
305C2×C4×C53—84no—
306C2×C4×C53—84no—
307C2×C4×C53AGL(1,ℤ/8)12yes—
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#24921—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—42no—
344C22×C53—42no—
345C22×C53—41no—
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×C53C2×AGL(1,ℤ/8)11yescharacteristic
361C22×C53C2×#13711yescharacteristic
362C22×C53#57611yescharacteristic
363C22×C53#57711yescharacteristic
364C4×C53—22no—
365C4×C53—41no—
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×#440—531no—
381#2423—531no—
382D4×C22⋊C4D5311yescharacteristic
383#2093—531no—
384#2076—531no—
385#2055—531no—
386#2036—531no—
387#1936—531no—
388#1924—531no—
389#1880—531no—
390#1877—531no—
391#1862—531no—
392#1802—531no—
393#1786—531no—
394C2×C53—42no—
395C2×C53—44no—
396C2×C53—82no—
397C2×C53#241811yescharacteristic
398C2×C53#311011yescharacteristic
399C2×C53#311811yescharacteristic
400C2×C53#326611yescharacteristic
401C2×C53#327411yescharacteristic
402C2×C53#331011yescharacteristic
403C2×C53#331411yescharacteristic
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—
413#440—1064no—
414C2×#107—531no—
415C2×#107—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×#97—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#2492111yescharacteristic, 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#107—1062no—
508#107—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—
520#97—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—22no—
617C22⋊C4—22no—
618C22⋊C4—42no—
619C22⋊C4—42no—
620C22⋊C4—42no—
621C22⋊C4—42no—
622C22⋊C4—42no—
623C22⋊C4—81no—
624C22⋊C4—81no—
625C22⋊C4—4241no—
626C22⋊C4—2122no—
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—
659C23#1313324712yes—
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—21no—
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—41no—
698C2×C4—84no—
699C2×C4—84no—
700C2×C4—1062no—
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×C4—2121no—
712C2×C4#1313324312yes—
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—22no—
726C22—24no—
727C22—42no—
728C22—42no—
729C22—41no—
730C22—42no—
731C22—42no—
732C22—41no—
733C22—42no—
734C22—41no—
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
748C22C2×#1313324311yescharacteristic
749C22C2×#1313324711yescharacteristic
750C22#1681142611yescharacteristic
751C22#1681143411yescharacteristic
752C4—22no—
753C4—41no—
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#2028481411yescharacteristic
772C2#2028489911yescharacteristic
773C2#2028622111yescharacteristic
774C2#2028633111yescharacteristic
775C2#2028673611yescharacteristic
776C2#2028679611yescharacteristic
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#24921
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×#16810723C2semidirect
3. #20278240C2semidirect
4. #20276243C2semidirect
5. #20276146C2semidirect
6. #20276032C2semidirect
7. #20275918C2semidirect
8. #20275415C2semidirect
9. #20275330C2semidirect
10. #20275073C2semidirect
11. #20275049C2semidirect
12. #20274962C2semidirect
13. #20274715C2semidirect
19. C2×C4×Dic106C22semidirect
22. C2×#13133150C22semidirect
23. C2×#13133150C22semidirect
24. C2×C4⋊#88322C22semidirect
25. C2×#13133140C22semidirect
26. C2×#13133140C22semidirect
35. C2×#13133128C22semidirect
38. #16810529C22semidirect
39. #16810521C22semidirect
42. #16810493C22semidirect
44. #16810385C22semidirect
45. #16810385C22semidirect
46. #16810385C22semidirect
47. #16810385C22semidirect
48. #16810378C22semidirect
49. #16810378C22semidirect
449. C53#24921semidirect

Maximal subgroups

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

subgroupindex
C2×#168107742
C2×#168107232
#202782402
#202762432
#202761462
#202760322
#202759182
#202754152
#202753302
#202750732
#202750492
#202749622
#202747152
#202746462
D4×C22⋊C4×C532
#2492153