Finite Group Databasebeta

← #27404365

Subgroups — #27404365

Order 13568.

1170 conjugacy classes of subgroups.

The subgroup lattice has 748 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16810761C211yesmaximal, characteristic
2C2×#16810723C211yesmaximal, characteristic, complemented
3C22×#13133140C211yesmaximal, characteristic, complemented
4C22⋊C4×Dic106C211yesmaximal, characteristic, complemented
5#20275595C211yesmaximal, characteristic, complemented
6#20275404C211yesmaximal, characteristic, complemented
7#20275356C211yesmaximal, characteristic, complemented
8#20275144C211yesmaximal, characteristic
9#20275073C211yesmaximal, characteristic, complemented
10#20275049C211yesmaximal, characteristic, complemented
11#20274968C211yesmaximal, characteristic, complemented
12#20274903C211yesmaximal, characteristic, complemented
13#20274548C211yesmaximal, characteristic, complemented
14#20274493C211yesmaximal, characteristic, complemented
15C53×#2361C211yesmaximal, characteristic
16C23×Dic106C2211yescharacteristic
17C22×#11719923C2211yescharacteristic
18C22×#11719923C2211yescharacteristic
19C23×#88322C2211yescharacteristic
20C2×C4×Dic106C2211yescharacteristic
21C2×C4×Dic106C2211yescharacteristic
22#16810761C418yescomplemented
23#16810723—24no—
24C2×#13133150C2211yescharacteristic
25C2×#13133150C2211yescharacteristic
26C2×#13133140—24no—
27C2×#13133140C2211yescharacteristic
28C2×#13133140C2211yescharacteristic
29C2×#13133140C2211yescharacteristic
30C2×#13133140C2211yescharacteristic
31C2×#13133140C2211yescharacteristic
32C2×#13133140C2211yescharacteristic
33C2×#13133138C2211yescharacteristic
34C2×#13133138C2211yescharacteristic
35C2×C22⋊#88322C2211yescharacteristic
36C2×#13133128C2211yescharacteristic
37C2×#13133128C2211yescharacteristic
38#16810529C2211yescharacteristic
39#16810529C2211yescharacteristic
40#16810527—21no—
41#16810527—21no—
42#16810483C2211yescharacteristic
43#16810481—21no—
44C22⋊C4×Dic53—21no—
45#16810385C2211yescharacteristic
46#16810385C2211yescharacteristic
47#16810385C2211yescharacteristic
48#16810385C2211yescharacteristic
49#16810378C2211yescharacteristic
50#16810378C2211yescharacteristic
51C2×#121×C53C2211yescharacteristic
52C2×C4×D4×C53—21no—
53C2×C4×D4×C53C2211yescharacteristic
54C22×C4⋊C4×C53C2211yescharacteristic
55C53×#390C2211yescharacteristic
56C53×#389C2211yescharacteristic
57C53×#388—21no—
58C53×#386—21no—
59C53×#385—21no—
60C4×C4⋊C4×C53C2211yescharacteristic
61C4×C22⋊C4×C53C2211yescharacteristic
62C22×Dic106—22no—
63C22×Dic106—22no—
64C22×Dic106—21no—
65C22×Dic106—22no—
66C22×Dic106—41no—
67C22×Dic106—41no—
68C22×Dic106C2×C414yescomplemented
69C22×Dic106C2311yescharacteristic
70C22×Dic106C2311yescharacteristic
71C23×Dic53—21no—
72C2×#11719923—22no—
73C2×#11719923—22no—
74C2×#11719923—41no—
75C2×#11719923—41no—
76C2×#11719923C2×C414yescomplemented
77C2×#11719923C2×C414yescomplemented
78C22×#88322—22no—
79C22×#88322—22no—
80C22×#88322—41no—
81C22×#88322C2311yescharacteristic
82C22×#88322C2311yescharacteristic
83C22×#88322C2311yescharacteristic
84C22×#88322C2311yescharacteristic
85C4×Dic106—22no—
86C4×Dic106—22no—
87C4×Dic106—41no—
88C4×Dic106—41no—
89C2×C4⋊Dic53C2311yescharacteristic
90C2×C4⋊Dic53C2311yescharacteristic
91C2×#11719919—21no—
92C2×#11719919—21no—
93C2×C22⋊Dic53—21no—
94C2×C4×Dic53—21no—
95C2×C4×Dic53—21no—
96#13133150—22no—
97#13133150—41no—
98#13133140—22no—
99#13133140—22no—
100#13133140—22no—
101#13133140C2×C414yescomplemented
102#13133140C2×C414yescomplemented
103#13133140D414yescomplemented
104#13133138—22no—
105#13133138—41no—
106C22⋊#88322C2×C414yescomplemented
107#13133128—22no—
108#13133128—41no—
109#13133124—21no—
110#13133124—21no—
111#13133124—21no—
112#13133124—21no—
113#13133124—21no—
114C22×D4×C53—21no—
115C22×D4×C53C2311yescharacteristic
116C23×C4×C53—21no—
117C23×C4×C53—21no—
118C23×C4×C53C2311yescharacteristic
119#121×C53—22no—
120#121×C53C2×C414yes—
121C4×D4×C53—22no—
122C4×D4×C53—41no—
123C4×D4×C53—44no—
124C2×C4⋊C4×C53—21no—
125C2×C4⋊C4×C53—21no—
126C2×C4⋊C4×C53—22no—
127C2×C4⋊C4×C53—41no—
128C2×C4⋊C4×C53C2311yescharacteristic
129C2×C4⋊C4×C53C2311yescharacteristic
130C2×C4⋊C4×C53C2311yescharacteristic
131C2×C22⋊C4×C53—21no—
132C2×C22⋊C4×C53—21no—
133C2×C22⋊C4×C53—21no—
134C2×C22⋊C4×C53—21no—
135C2×C22⋊C4×C53D411yescharacteristic
136C2×C22⋊C4×C53D411yescharacteristic
137C2×C42×C53—21no—
138C2×C42×C53C2311yescharacteristic
139C2×C42×C53C2311yescharacteristic
140#95×C53—21no—
141#95×C53—21no—
142#95×C53D411yescharacteristic
143#95×C53D411yescharacteristic
144C24×C53—21no—
145C24×C53C2×D411yescharacteristic
146C2×D4×C53—24no—
147C2×D4×C53—21no—
148C2×D4×C53—21no—
149C2×D4×C53—21no—
150C2×D4×C53—21no—
151C2×D4×C53—21no—
152C2×D4×C53—42no—
153C2×D4×C53—42no—
154C2×D4×C53C22×C412yes—
155C22×C4×C53—21no—
156C22×C4×C53—21no—
157C22×C4×C53—21no—
158C22×C4×C53—21no—
159C22×C4×C53—21no—
160C22×C4×C53—21no—
161C22×C4×C53—21no—
162C22×C4×C53—42no—
163C22×C4×C53—42no—
164C22×C4×C53—42no—
165C22×C4×C53—42no—
166C22×C4×C53—81no—
167C22×C4×C53—81no—
168C22×C4×C53C22×C412yes—
169C22×C4×C53C2×D411yescharacteristic
170C22×C4×C53C2×D411yescharacteristic
171C22×C4×C53C2×D411yescharacteristic
172C22×C4×C53C2×D411yescharacteristic
173C22×C4×C53C2×D411yescharacteristic
174C22×C4×C53#4112yes—
175C22×C4×C53C2411yescharacteristic
176C22×Dic53—21no—
177C22×Dic53—24no—
178C22×Dic53—21no—
179C22×Dic53—21no—
180C22×Dic53—21no—
181C22×Dic53—42no—
182C22×Dic53—42no—
183C2×Dic106—21no—
184C2×Dic106—21no—
185C2×Dic106—21no—
186C2×Dic106—21no—
187C2×Dic106—21no—
188C2×Dic106—21no—
189C2×Dic106—21no—
190C2×Dic106—28no—
191C2×Dic106—24no—
192C2×Dic106—21no—
193C2×Dic106—44no—
194C2×Dic106—44no—
195C2×Dic106—44no—
196C2×Dic106—42no—
197C2×Dic106—42no—
198C2×Dic106C22×C412yes—
199C2×Dic106C22×C412yes—
200C2×Dic106C2×D412yes—
201C2×Dic106#4112yes—
202C4⋊C4×C53—21no—
203C4⋊C4×C53—21no—
204C4⋊C4×C53—21no—
205C4⋊C4×C53—21no—
206C4⋊C4×C53—42no—
207C4⋊C4×C53—42no—
208C4⋊C4×C53C22×C412yes—
209C4⋊C4×C53C2×D412yes—
210C22⋊C4×C53—22no—
211C22⋊C4×C53—22no—
212C22⋊C4×C53—24no—
213C22⋊C4×C53—42no—
214C22⋊C4×C53—42no—
215C22⋊C4×C53—81no—
216C42×C53—21no—
217C42×C53—21no—
218C42×C53—21no—
219C42×C53—21no—
220C42×C53—42no—
221C22⋊Dic53—42no—
222#11719923—28no—
223#11719923—44no—
224C4⋊Dic53—21no—
225C4⋊Dic53—21no—
226C4⋊Dic53—21no—
227C4⋊Dic53—21no—
228#11719919—42no—
229#11719919—42no—
230C4×Dic53—42no—
231C4×Dic53—42no—
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—44no—
242C2×#88322C22×C412yes—
243C2×#88322C22×C412yes—
244C2×#88322C2×D412yes—
245C23×C53—21no—
246C23×C53—21no—
247C23×C53—21no—
248C23×C53—21no—
249C23×C53—22no—
250C23×C53—41no—
251C23×C53—41no—
252C23×C53—41no—
253C23×C53—41no—
254C23×C53—41no—
255C23×C53—41no—
256C23×C53C4×D412yes—
257C23×C53AGL(1,ℤ/8)12yes—
258C23×C53#13712yes—
259C23×C53C22×D411yescharacteristic
260D4×C53—22no—
261D4×C53—22no—
262D4×C53—48no—
263D4×C53—41no—
264D4×C53—41no—
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—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×C53—21no—
280C2×C4×C53—21no—
281C2×C4×C53—21no—
282C2×C4×C53—21no—
283C2×C4×C53—21no—
284C2×C4×C53—21no—
285C2×C4×C53—41no—
286C2×C4×C53—41no—
287C2×C4×C53—41no—
288C2×C4×C53—41no—
289C2×C4×C53—41no—
290C2×C4×C53—41no—
291C2×C4×C53—41no—
292C2×C4×C53—84no—
293C2×C4×C53—84no—
294C2×C4×C53C4×D412yes—
295C2×C4×C53C23×C411yescharacteristic
296C2×C4×C53C22×D411yescharacteristic
297C2×C4×C53C2×#4111yescharacteristic
298C2×C4×C53C2×#4111yescharacteristic
299C2×C4×C53H(5,𝔽2)11yescharacteristic
300C2×C4×C53H(5,𝔽2)11yescharacteristic
301C2×Dic53—22no—
302C2×Dic53—22no—
303C2×Dic53—22no—
304C2×Dic53—22no—
305C2×Dic53—48no—
306C2×Dic53—41no—
307C2×Dic53—41no—
308C2×Dic53—41no—
309C2×Dic53—41no—
310C2×Dic53—41no—
311C2×Dic53—41no—
312C2×Dic53—41no—
313C2×Dic53—41no—
314Dic106—22no—
315Dic106—22no—
316Dic106—22no—
317Dic106—22no—
318Dic106—22no—
319Dic106—48no—
320Dic106—41no—
321Dic106—41no—
322Dic106C4×D414yescomplemented
323#88322—22no—
324#88322—22no—
325#88322—22no—
326#88322—41no—
327#22855—531nomaximal, Sylow
328C22×C53—22no—
329C22×C53—22no—
330C22×C53—22no—
331C22×C53—22no—
332C22×C53—22no—
333C22×C53—22no—
334C22×C53—42no—
335C22×C53—42no—
336C22×C53—42no—
337C22×C53—81no—
338C22×C53—81no—
339C22×C53—81no—
340C22×C53—81no—
341C22×C53#44014yescomplemented
342C22×C53C2×C4×D411yescharacteristic
343C22×C53D4211yescharacteristic
344C22×C53#54611yescharacteristic
345C22×C53C2×AGL(1,ℤ/8)11yescharacteristic
346C22×C53C2×#13711yescharacteristic
347C22×C53#57711yescharacteristic
348C22×C53#57811yescharacteristic
349C4×C53—22no—
350C4×C53—42no—
351C4×C53—41no—
352C4×C53—42no—
353C4×C53—41no—
354C4×C53—41no—
355C4×C53—41no—
356C4×C53—81no—
357C4×C53C2×C4×D411yescharacteristic
358C4×C53#51811yescharacteristic
359C4×C53#54611yescharacteristic
360C4×C53#55111yescharacteristic
361Dic53—24no—
362Dic53—42no—
363Dic53—81no—
364Dic53—81no—
365C2×#448—531no—
366C2×#440—531no—
367C22×#103—531no—
368#2361D5311yescharacteristic
369Q8×C22⋊C4—531no—
370#1973—531no—
371#1935—531no—
372#1928—531no—
373#1893—531no—
374#1880—531no—
375#1877—531no—
376#1863—531no—
377#1852—531no—
378#1763—531no—
379#1752—531no—
380C2×C53—24no—
381C2×C53—82no—
382C2×C53#235811yescharacteristic
383C2×C53C2×#44011yescharacteristic
384C2×C53#294711yescharacteristic
385C2×C53#326511yescharacteristic
386C2×C53#327011yescharacteristic
387C2×C53#330811yescharacteristic
388C2×C53#332011yescharacteristic
389C23×Q8—531no—
390C22×SD16—531no—
391C22×SD16—531no—
392C23×C8—531no—
393C2×#121C2×D5311yescharacteristic
394C2×C4×Q8—531no—
395C2×C4×Q8—531no—
396C2×C4×D4—21no—
397C2×C4×D4C2×D5311yescharacteristic
398C22×C4⋊C4C2×D5311yescharacteristic
399#448—538no—
400#440—1064no—
401C2×#107—531no—
402C2×#107—531no—
403C2×#103—531no—
404C2×#103—531no—
405C2×#103—531no—
406C2×#103—531no—
407C2×#103—531no—
408C2×#103—531no—
409C2×#103—1064no—
410C2×#102—531no—
411C2×#102—531no—
412C2×C22⋊C8—531no—
413C2×#97—531no—
414C2×#97—531no—
415#391—531no—
416#391—531no—
417#391—1061no—
418#391—1061no—
419#390C2×D5311yescharacteristic
420#389C2×D5311yescharacteristic
421#388—21no—
422#386—21no—
423#385—21no—
424#380—531no—
425#380—1061no—
426C4×C4⋊C4C2×D5311yescharacteristic
427C4×C22⋊C4—1061no—
428C4×C22⋊C4C2×D5311yescharacteristic
429#340—531no—
430#340—531no—
431#340—531no—
432#340—531no—
433#336—531no—
434#336—531no—
435C53#2285511yescharacteristic, complemented, Sylow
436C22×Q8—534no—
437C22×Q8—531no—
438C22×Q8—531no—
439C22×Q8—1062no—
440C22×Q8—1062no—
441C22×Q8—1062no—
442C22×Q8—1061no—
443C22×Q8—2121no—
444C22×Q8—2121no—
445C22×D4—21no—
446C22×D4C22×D5311yescharacteristic
447C23×C4—21no—
448C23×C4—21no—
449C23×C4—1061no—
450C23×C4C22×D5311yescharacteristic
451C2×SD16—534no—
452C2×SD16—534no—
453C2×SD16—1062no—
454C2×SD16—1062no—
455C2×SD16—2121no—
456C2×SD16—2121no—
457C22×C8—531no—
458C22×C8—531no—
459C22×C8—531no—
460C22×C8—531no—
461C22×C8—1062no—
462C22×C8—1062no—
463C22×C8—2121no—
464#121—22no—
465#121C4×D5314yes—
466C4×Q8—1062no—
467C4×Q8—1062no—
468C4×Q8—2121no—
469C4×Q8—2121no—
470C4×D4—22no—
471C4×D4—41no—
472C4×D4—44no—
473C2×C4⋊C4—22no—
474C2×C4⋊C4—21no—
475C2×C4⋊C4—21no—
476C2×C4⋊C4—41no—
477C2×C4⋊C4—531no—
478C2×C4⋊C4—531no—
479C2×C4⋊C4—1061no—
480C2×C4⋊C4—1061no—
481C2×C4⋊C4C22×D5311yescharacteristic
482C2×C4⋊C4C22×D5311yescharacteristic
483C2×C4⋊C4C22×D5311yescharacteristic
484C2×C22⋊C4—21no—
485C2×C22⋊C4—21no—
486C2×C22⋊C4—21no—
487C2×C22⋊C4—21no—
488C2×C22⋊C4—1061no—
489C2×C22⋊C4C22⋊D5311yescharacteristic
490C2×C22⋊C4C22⋊D5311yescharacteristic
491C2×C42—21no—
492C2×C42—1061no—
493C2×C42—1061no—
494C2×C42C22×D5311yescharacteristic
495C2×C42C22×D5311yescharacteristic
496#107—1062no—
497#107—2121no—
498#103—534no—
499#103—534no—
500#103—534no—
501#103—1062no—
502#103—1062no—
503#103—1062no—
504#102—1062no—
505#102—2121no—
506C22⋊C8—534no—
507#97—1062no—
508#97—2121no—
509#95—21no—
510#95—21no—
511#95—1061no—
512#95—1061no—
513#95—1061no—
514#95—1061no—
515#95—1061no—
516#95C22⋊D5311yescharacteristic
517#95C22⋊D5311yescharacteristic
518C24—21no—
519C24C2×C22⋊D5311yescharacteristic
520C2×Q8—532no—
521C2×Q8—532no—
522C2×Q8—532no—
523C2×Q8—532no—
524C2×Q8—1068no—
525C2×Q8—1064no—
526C2×Q8—1061no—
527C2×Q8—1061no—
528C2×Q8—1061no—
529C2×Q8—1061no—
530C2×Q8—1061no—
531C2×Q8—1061no—
532C2×Q8—1061no—
533C2×Q8—1061no—
534C2×Q8—2122no—
535C2×Q8—2122no—
536C2×Q8—2124no—
537C2×Q8—2124no—
538C2×Q8—2124no—
539C2×D4—24no—
540C2×D4—21no—
541C2×D4—21no—
542C2×D4—21no—
543C2×D4—21no—
544C2×D4—21no—
545C2×D4—42no—
546C2×D4—42no—
547C2×D4C2×C4×D5312yes—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—42no—
556C22×C4—42no—
557C22×C4—42no—
558C22×C4—42no—
559C22×C4—81no—
560C22×C4—81no—
561C22×C4—1061no—
562C22×C4—1064no—
563C22×C4—1061no—
564C22×C4—1061no—
565C22×C4—1061no—
566C22×C4—2122no—
567C22×C4—2122no—
568C22×C4C2×C4×D5312yes—
569C22×C4#1171994512yes—
570C22×C4C2×C22⋊D5311yescharacteristic
571C22×C4C2×C22⋊D5311yescharacteristic
572C22×C4C2×C22⋊D5311yescharacteristic
573C22×C4C2×C22⋊D5311yescharacteristic
574C22×C4C2×C22⋊D5311yescharacteristic
575C22×C4C23×D5311yescharacteristic
576SD16—1068no—
577SD16—2124no—
578C2×C8—532no—
579C2×C8—532no—
580C2×C8—532no—
581C2×C8—1061no—
582C2×C8—1061no—
583C2×C8—1061no—
584C2×C8—1061no—
585C2×C8—1061no—
586C2×C8—1061no—
587C2×C8—1061no—
588C2×C8—1061no—
589C2×C8—1061no—
590C2×C8—2124no—
591C4⋊C4—21no—
592C4⋊C4—21no—
593C4⋊C4—21no—
594C4⋊C4—21no—
595C4⋊C4—42no—
596C4⋊C4—42no—
597C4⋊C4—1061no—
598C4⋊C4—1061no—
599C4⋊C4—1061no—
600C4⋊C4—1061no—
601C4⋊C4—2122no—
602C4⋊C4—2122no—
603C4⋊C4C2×C4×D5312yes—
604C4⋊C4D4×D5312yes—
605C22⋊C4—22no—
606C22⋊C4—22no—
607C22⋊C4—24no—
608C22⋊C4—42no—
609C22⋊C4—42no—
610C22⋊C4—81no—
611C22⋊C4—2122no—
612C42—21no—
613C42—21no—
614C42—21no—
615C42—21no—
616C42—42no—
617C42—2122no—
618C42—2122no—
619C23—21no—
620C23—21no—
621C23—21no—
622C23—21no—
623C23—22no—
624C23—41no—
625C23—41no—
626C23—41no—
627C23—41no—
628C23—41no—
629C23—41no—
630C23C4×C22⋊D5312yes—
631C23#1313324312yes—
632C23#1313324712yes—
633C23C22×C22⋊D5311yescharacteristic
634Q8—534no—
635Q8—1062no—
636Q8—1062no—
637Q8—1062no—
638Q8—1062no—
639Q8—1062no—
640Q8—2128no—
641Q8—2121no—
642Q8—2121no—
643D4—22no—
644D4—22no—
645D4—48no—
646D4—41no—
647D4—41no—
648C2×C4—21no—
649C2×C4—21no—
650C2×C4—22no—
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—21no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—22no—
666C2×C4—21no—
667C2×C4—21no—
668C2×C4—41no—
669C2×C4—41no—
670C2×C4—41no—
671C2×C4—41no—
672C2×C4—41no—
673C2×C4—41no—
674C2×C4—41no—
675C2×C4—84no—
676C2×C4—84no—
677C2×C4—1062no—
678C2×C4—1062no—
679C2×C4—1062no—
680C2×C4—1062no—
681C2×C4—2128no—
682C2×C4—2121no—
683C2×C4—2121no—
684C2×C4—2121no—
685C2×C4—2121no—
686C2×C4—2121no—
687C2×C4—2121no—
688C2×C4—2121no—
689C2×C4—2121no—
690C2×C4C4×C22⋊D5312yes—
691C2×C4C22×C4×D5311yescharacteristic
692C2×C4C2×D4×D5311yescharacteristic
693C2×C4#41×D5311yescharacteristic
694C2×C4C2×#1171994511yescharacteristic
695C2×C4#1313326211yescharacteristic
696C2×C4#1313326311yescharacteristic
697C8—1062no—
698C8—1062no—
699C8—1062no—
700C8—2121no—
701C22—22no—
702C22—22no—
703C22—22no—
704C22—22no—
705C22—22no—
706C22—22no—
707C22—42no—
708C22—42no—
709C22—42no—
710C22—81no—
711C22—81no—
712C22—81no—
713C22—81no—
714C22#1681072314yescomplemented
715C22C2×C4×C22⋊D5311yescharacteristic
716C22D4×C22⋊D5311yescharacteristic
717C22#1681126111yescharacteristic
718C22C2×#1313324311yescharacteristic
719C22C2×#1313324711yescharacteristic
720C22#1681143411yescharacteristic
721C22#1681143811yescharacteristic
722C4—22no—
723C4—41no—
724C4—42no—
725C4—41no—
726C4—41no—
727C4—41no—
728C4—42no—
729C4—81no—
730C4—1064no—
731C4—4241no—
732C4—4241no—
733C4—2122no—
734C4C4×D4×D5311yescharacteristic
735C4#1681109511yescharacteristic
736C4#1681126911yescharacteristic
737C4#1681130211yescharacteristic
738C2—24no—
739C2—82no—
740C2#2027769211yescharacteristic
741C2C2×#1681072311yescharacteristic
742C2#2028355411yescharacteristic
743C2#2028620611yescharacteristic
744C2#2028628111yescharacteristic
745C2#2028670011yescharacteristic
746C2#2028688011yescharacteristic
subgroupG/H
centerC23C22×C22⋊D53
commutatorC2×C4×C53C23×C4
FrattiniC22×C4C23×D53
FittingC53×#2361C2
socleC23×C53C22×D4
prime radicalC2×#121×C53C22
cosocleC22×C4×C53C24
hypercenter#2361D53
hypocenterC53#22855
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2361

Complements

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

NH ≅ G/Ntype
2. C2×#16810723C2semidirect
3. C22×#13133140C2semidirect
4. C22⋊C4×Dic106C2semidirect
5. #20275595C2semidirect
6. #20275404C2semidirect
7. #20275356C2semidirect
9. #20275073C2semidirect
10. #20275049C2semidirect
11. #20274968C2semidirect
12. #20274903C2semidirect
13. #20274548C2semidirect
14. #20274493C2semidirect
22. #16810761C4semidirect
68. C22×Dic106C2×C4semidirect
76. C2×#11719923C2×C4semidirect
77. C2×#11719923C2×C4semidirect
101. #13133140C2×C4semidirect
102. #13133140C2×C4semidirect
103. #13133140D4semidirect
106. C22⋊#88322C2×C4semidirect
322. Dic106C4×D4semidirect
341. C22×C53#440semidirect
435. C53#22855semidirect
714. C22#16810723semidirect

Maximal subgroups

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

subgroupindex
C2×#168107612
C2×#168107232
C22×#131331402
C22⋊C4×Dic1062
#202755952
#202754042
#202753562
#202751442
#202750732
#202750492
#202749682
#202749032
#202745482
#202744932
C53×#23612
#2285553