Finite Group Databasebeta

← #27404349

Subgroups — #27404349

Order 13568.

1302 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16810774C211yesmaximal, characteristic
2C2×#16810720C211yesmaximal, characteristic, complemented
3#20277720C211yesmaximal, characteristic, complemented
4D4×C22⋊Dic53C211yesmaximal, characteristic
5#20275597C211yesmaximal, characteristic, complemented
6#20275409C211yesmaximal, characteristic, complemented
7#20275338C211yesmaximal, characteristic, complemented
8#20275138C211yesmaximal, characteristic, complemented
9#20275067C211yesmaximal, characteristic, complemented
10#20275047C211yesmaximal, characteristic, complemented
11#20274960C211yesmaximal, characteristic, complemented
12#20274903C211yesmaximal, characteristic, complemented
13#20274542C211yesmaximal, characteristic, complemented
14#20274491C211yesmaximal, characteristic, complemented
15C22×#102×C53C211yesmaximal, characteristic
16C22×#11719923C2211yescharacteristic
17C22×#11719923C2211yescharacteristic
18C2×#13133196C2211yescharacteristic
19C2×#13133182C2211yescharacteristic, complemented
20C2×D4×Dic53C2211yescharacteristic
21C2×D4×Dic53C2211yescharacteristic
22C22×C22⋊Dic53—21no—
23#16810774C418yescomplemented
24#16810720—24no—
25C2×#13133150C2211yescharacteristic, complemented
26C2×#13133150C2211yescharacteristic, complemented
27C2×#13133142C2211yescharacteristic, complemented
28C2×#13133142C2211yescharacteristic, complemented
29C2×#13133138C2211yescharacteristic
30C2×#13133138C2211yescharacteristic
31C2×C22⋊#88322C2211yescharacteristic
32C2×#13133127C2211yescharacteristic, complemented
33C2×#13133127C2211yescharacteristic, complemented
34#16810528C2211yescharacteristic, complemented
35#16810526C2211yescharacteristic
36#16810526C2211yescharacteristic
37#16810519C2211yescharacteristic, complemented
38#16810518—21no—
39#16810504—21no—
40#16810503—21no—
41#16810503—21no—
42#16810496—21no—
43#16810483C2211yescharacteristic
44#16810479—21no—
45C4⋊C4×Dic53C2211yescharacteristic, complemented
46C4×C22⋊Dic53—21no—
47C4×C22⋊Dic53C2211yescharacteristic
48#16810386C2211yescharacteristic, complemented
49#16810386C2211yescharacteristic, complemented
50#16810385C2211yescharacteristic, complemented
51#16810385C2211yescharacteristic, complemented
52#16810377C2211yescharacteristic, complemented
53#16810377C2211yescharacteristic, complemented
54C23×D4×C53C2211yescharacteristic
55C23×C8×C53C2211yescharacteristic
56C22×C4⋊C4×C53C2211yescharacteristic
57C2×#102×C53—24no—
58C2×#102×C53C2211yescharacteristic
59C2×#102×C53C2211yescharacteristic
60C2×#102×C53C2211yescharacteristic
61C2×#102×C53C2211yescharacteristic
62C22×Dic106C2311yescharacteristic
63C23×Dic53—21no—
64C23×Dic53—21no—
65C2×#11719923—22no—
66C2×#11719923—22no—
67C2×#11719923—41no—
68C2×#11719923—41no—
69C2×#11719923C2×C414yescomplemented
70C2×#11719923C2×C414yescomplemented
71C22×#88322C2311yescharacteristic
72C22×#88322C2311yescharacteristic
73#13133196—22no—
74#13133196C2×C414yescomplemented
75#13133182—22no—
76#13133182—41no—
77D4×Dic53—22no—
78D4×Dic53—22no—
79D4×Dic53—41no—
80D4×Dic53—41no—
81C2×C4⋊Dic53C2311yescharacteristic
82C2×C4⋊Dic53C2311yescharacteristic
83C2×C4⋊Dic53C2311yescharacteristic
84C2×#11719919—21no—
85C2×#11719919—21no—
86C2×#11719919—21no—
87C2×C22⋊Dic53—21no—
88C2×C22⋊Dic53—21no—
89C2×C22⋊Dic53—21no—
90C2×C22⋊Dic53—21no—
91C2×C22⋊Dic53—21no—
92C2×C22⋊Dic53—21no—
93C2×C22⋊Dic53—21no—
94C2×C22⋊Dic53—21no—
95C2×C22⋊Dic53—44no—
96C2×C22⋊Dic53D411yescharacteristic
97C2×C22⋊Dic53D411yescharacteristic
98C2×C4×Dic53—21no—
99C2×C4×Dic53—21no—
100C2×C4×Dic53C2311yescharacteristic
101C2×C4×Dic53C2311yescharacteristic
102#13133150—22no—
103#13133150—41no—
104#13133142—22no—
105#13133142—41no—
106#13133138C2×C414yescomplemented
107#13133138C2×C414yescomplemented
108C22⋊#88322C2×C414yescomplemented
109#13133127—22no—
110#13133127—41no—
111#13133124—21no—
112#13133124—21no—
113#13133124—21no—
114#13133124—21no—
115#13133124—21no—
116#13133124D411yescharacteristic
117#13133124D411yescharacteristic
118C25×C53—21no—
119C22×D4×C53—22no—
120C22×D4×C53—22no—
121C22×D4×C53—21no—
122C22×D4×C53—22no—
123C22×D4×C53—41no—
124C22×D4×C53—41no—
125C22×D4×C53C2×C414yes—
126C22×D4×C53C2311yescharacteristic
127C22×D4×C53C2311yescharacteristic
128C23×C4×C53—21no—
129C23×C4×C53C2311yescharacteristic
130C22×C8×C53—22no—
131C22×C8×C53—22no—
132C22×C8×C53—41no—
133C22×C8×C53C2311yescharacteristic
134C22×C8×C53C2311yescharacteristic
135C2×C4⋊C4×C53—21no—
136C2×C4⋊C4×C53—22no—
137C2×C4⋊C4×C53—41no—
138C2×C4⋊C4×C53C2311yescharacteristic
139C2×C4⋊C4×C53C2311yescharacteristic
140#102×C53—22no—
141#102×C53—22no—
142#102×C53—22no—
143#102×C53D414yes—
144C24×C53—21no—
145C24×C53—21no—
146C24×C53—24no—
147C24×C53—42no—
148C24×C53—42no—
149C24×C53—42no—
150C24×C53—42no—
151C24×C53—81no—
152C24×C53—81no—
153C24×C53C2×D411yescharacteristic
154C2×D4×C53—28no—
155C2×D4×C53—24no—
156C2×D4×C53—21no—
157C2×D4×C53—21no—
158C2×D4×C53—21no—
159C2×D4×C53—21no—
160C2×D4×C53—21no—
161C2×D4×C53—21no—
162C2×D4×C53—21no—
163C2×D4×C53—21no—
164C2×D4×C53—44no—
165C2×D4×C53—44no—
166C2×D4×C53—44no—
167C2×D4×C53—42no—
168C2×D4×C53—42no—
169C2×D4×C53C22×C412yes—
170C2×D4×C53C22×C412yes—
171C2×D4×C53C2×D412yes—
172C2×D4×C53#4112yes—
173C22×C4×C53—21no—
174C22×C4×C53—21no—
175C22×C4×C53—21no—
176C22×C4×C53—21no—
177C22×C4×C53—21no—
178C22×C4×C53—21no—
179C22×C4×C53—42no—
180C22×C4×C53—42no—
181C22×C4×C53—81no—
182C22×C4×C53C22×C412yes—
183C22×C4×C53C2×D411yescharacteristic
184C22×C4×C53#4112yes—
185C22×C4×C53C2411yescharacteristic
186C22×Dic53—21no—
187C22×Dic53—21no—
188C22×Dic53—21no—
189C22×Dic53—21no—
190C22×Dic53—42no—
191C22×Dic53—42no—
192C22×Dic53—42no—
193C22×Dic53—42no—
194C22×Dic53—81no—
195C22×Dic53—81no—
196C22×Dic53C2×D411yescharacteristic
197C22×Dic53C2×D411yescharacteristic
198C22×Dic53C2×D411yescharacteristic
199C22×Dic53C2×D411yescharacteristic
200C2×Dic106—21no—
201C2×Dic106—21no—
202C2×Dic106—21no—
203C2×Dic106—21no—
204C2×Dic106—21no—
205C2×Dic106C22×C412yes—
206C2×C8×C53—21no—
207C2×C8×C53—21no—
208C2×C8×C53—21no—
209C2×C8×C53—21no—
210C2×C8×C53—21no—
211C2×C8×C53—44no—
212C2×C8×C53C2×D412yes—
213C4⋊C4×C53—21no—
214C4⋊C4×C53—21no—
215C4⋊C4×C53—21no—
216C4⋊C4×C53—42no—
217C4⋊C4×C53C2×D412yes—
218C22⋊Dic53—24no—
219C22⋊Dic53—22no—
220C22⋊Dic53—22no—
221C22⋊Dic53—42no—
222C22⋊Dic53—42no—
223C22⋊Dic53—42no—
224C22⋊Dic53—42no—
225C22⋊Dic53—42no—
226C22⋊Dic53—81no—
227C22⋊Dic53—81no—
228#11719923—28no—
229#11719923—44no—
230C4⋊Dic53—21no—
231C4⋊Dic53—21no—
232C4⋊Dic53—21no—
233C4⋊Dic53—21no—
234C4⋊Dic53—21no—
235C4⋊Dic53C22×C412yes—
236#11719919—24no—
237#11719919—42no—
238#11719919—81no—
239C4×Dic53—21no—
240C4×Dic53—21no—
241C4×Dic53—21no—
242C4×Dic53—21no—
243C4×Dic53—42no—
244C4×Dic53—81no—
245C2×#88322—21no—
246C2×#88322—21no—
247C2×#88322—21no—
248C2×#88322—21no—
249C2×#88322C22×C412yes—
250C2×#88322C22×C412yes—
251C23×C53—21no—
252C23×C53—21no—
253C23×C53—21no—
254C23×C53—21no—
255C23×C53—22no—
256C23×C53—22no—
257C23×C53—22no—
258C23×C53—22no—
259C23×C53—48no—
260C23×C53—41no—
261C23×C53—41no—
262C23×C53—41no—
263C23×C53—41no—
264C23×C53—41no—
265C23×C53—41no—
266C23×C53—41no—
267C23×C53—41no—
268C23×C53—41no—
269C23×C53—41no—
270C23×C53—48no—
271C23×C53—84no—
272C23×C53—84no—
273C23×C53—84no—
274C23×C53—84no—
275C23×C53—84no—
276C23×C53C4×D412yes—
277C23×C53AGL(1,ℤ/8)12yes—
278C23×C53#13712yes—
279C23×C53C22×D411yescharacteristic
280D4×C53—22no—
281D4×C53—22no—
282D4×C53—22no—
283D4×C53—22no—
284D4×C53—22no—
285D4×C53—48no—
286D4×C53—41no—
287D4×C53—41no—
288D4×C53C4×D414yes—
289C2×C4×C53—21no—
290C2×C4×C53—21no—
291C2×C4×C53—22no—
292C2×C4×C53—22no—
293C2×C4×C53—22no—
294C2×C4×C53—22no—
295C2×C4×C53—22no—
296C2×C4×C53—41no—
297C2×C4×C53—41no—
298C2×C4×C53—41no—
299C2×C4×C53—41no—
300C2×C4×C53—41no—
301C2×C4×C53—84no—
302C2×C4×C53C4×D412yes—
303C2×C4×C53C23×C411yescharacteristic
304C2×C4×C53C22×D411yescharacteristic
305C2×C4×C53C2×#4111yescharacteristic
306C2×C4×C53C2×#4111yescharacteristic
307C2×C4×C53H(5,𝔽2)11yescharacteristic
308C2×C4×C53H(5,𝔽2)11yescharacteristic
309C2×Dic53—22no—
310C2×Dic53—22no—
311C2×Dic53—21no—
312C2×Dic53—21no—
313C2×Dic53—21no—
314C2×Dic53—21no—
315C2×Dic53—21no—
316C2×Dic53—21no—
317C2×Dic53—21no—
318C2×Dic53—21no—
319C2×Dic53—21no—
320C2×Dic53—21no—
321C2×Dic53—21no—
322C2×Dic53—21no—
323C2×Dic53—41no—
324C2×Dic53—41no—
325C2×Dic53—41no—
326C2×Dic53—41no—
327C2×Dic53—41no—
328C2×Dic53—41no—
329C2×Dic53—41no—
330C2×Dic53—41no—
331C2×Dic53—41no—
332C2×Dic53—41no—
333C2×Dic53—84no—
334C2×Dic53—84no—
335Dic106—22no—
336Dic106—22no—
337Dic106—41no—
338Dic106—41no—
339C8×C53—22no—
340C8×C53—41no—
341#88322—22no—
342#88322—22no—
343#22854—531nomaximal, Sylow
344C22×C53—22no—
345C22×C53—22no—
346C22×C53—22no—
347C22×C53—22no—
348C22×C53—22no—
349C22×C53—22no—
350C22×C53—24no—
351C22×C53—42no—
352C22×C53—42no—
353C22×C53—42no—
354C22×C53—42no—
355C22×C53—42no—
356C22×C53—42no—
357C22×C53—42no—
358C22×C53—42no—
359C22×C53—42no—
360C22×C53—816no—
361C22×C53—81no—
362C22×C53—81no—
363C22×C53—81no—
364C22×C53—81no—
365C22×C53#44014yescomplemented
366C22×C53C2×C4×D411yescharacteristic
367C22×C53D4211yescharacteristic
368C22×C53#54611yescharacteristic
369C22×C53C2×AGL(1,ℤ/8)11yescharacteristic
370C22×C53C2×#13711yescharacteristic
371C22×C53#57611yescharacteristic
372C22×C53#57711yescharacteristic
373C4×C53—22no—
374C4×C53—42no—
375C4×C53—81no—
376C4×C53C2×C4×D411yescharacteristic
377C4×C53#51811yescharacteristic
378C4×C53#54611yescharacteristic
379C4×C53#55111yescharacteristic
380Dic53—42no—
381Dic53—42no—
382Dic53—41no—
383Dic53—41no—
384Dic53—41no—
385Dic53—41no—
386Dic53—81no—
387Dic53—81no—
388C2×#450—531no—
389C2×#440—531no—
390C22×#102D5311yescharacteristic
391#2360—531no—
392D4×C22⋊C4—531no—
393#1973—531no—
394#1936—531no—
395#1925—531no—
396#1892—531no—
397#1880—531no—
398#1877—531no—
399#1862—531no—
400#1852—531no—
401#1762—531no—
402#1752—531no—
403C2×C53—24no—
404C2×C53—44no—
405C2×C53—82no—
406C2×C53#235811yescharacteristic
407C2×C53C2×#44011yescharacteristic
408C2×C53#294611yescharacteristic
409C2×C53#326411yescharacteristic
410C2×C53#326611yescharacteristic
411C2×C53#331011yescharacteristic
412C2×C53#331411yescharacteristic
413C23×D4C2×D5311yescharacteristic
414C22×SD16—531no—
415C22×SD16—531no—
416C23×C8C2×D5311yescharacteristic
417C2×C22⋊Q8—531no—
418C2×C4×Q8—531no—
419C2×C4×D4—531no—
420C2×C4×D4—531no—
421C22×C4⋊C4C2×D5311yescharacteristic
422C22×C22⋊C4—1061no—
423#450—538no—
424#440—1064no—
425C2×#107—531no—
426C2×#107—531no—
427C2×#103—531no—
428C2×#103—531no—
429C2×#102—24no—
430C2×#102—531no—
431C2×#102—531no—
432C2×#102C2×D5311yescharacteristic
433C2×#102C2×D5311yescharacteristic
434C2×#102C2×D5311yescharacteristic
435C2×#102C2×D5311yescharacteristic
436C2×C22⋊C8—531no—
437C2×#97—531no—
438C2×#97—531no—
439#391—531no—
440#390—531no—
441#390—531no—
442#389—531no—
443#389—1061no—
444#387—1061no—
445#386—1061no—
446#386—1061no—
447#385—1061no—
448#380—531no—
449#379—1061no—
450C4×C4⋊C4—531no—
451C4×C22⋊C4—531no—
452C4×C22⋊C4—1061no—
453#340—531no—
454#340—531no—
455#340—531no—
456#340—531no—
457#336—531no—
458#336—531no—
459C53#2285411yescharacteristic, complemented, Sylow
460C25—21no—
461C22×Q8—531no—
462C22×D4—22no—
463C22×D4—22no—
464C22×D4—21no—
465C22×D4—22no—
466C22×D4—41no—
467C22×D4—41no—
468C22×D4C4×D5314yes—
469C22×D4C22×D5311yescharacteristic
470C22×D4C22×D5311yescharacteristic
471C23×C4—21no—
472C23×C4—1061no—
473C23×C4—1061no—
474C23×C4C22×D5311yescharacteristic
475C2×SD16—534no—
476C2×SD16—534no—
477C2×SD16—1062no—
478C2×SD16—1062no—
479C2×SD16—2121no—
480C2×SD16—2121no—
481C22×C8—22no—
482C22×C8—22no—
483C22×C8—41no—
484C22×C8—531no—
485C22×C8—531no—
486C22×C8C22×D5311yescharacteristic
487C22×C8C22×D5311yescharacteristic
488C22⋊Q8—534no—
489C22⋊Q8—1062no—
490C4×Q8—1062no—
491C4×Q8—2121no—
492C4×D4—1062no—
493C4×D4—1062no—
494C4×D4—2121no—
495C4×D4—2121no—
496C2×C4⋊C4—22no—
497C2×C4⋊C4—21no—
498C2×C4⋊C4—41no—
499C2×C4⋊C4—531no—
500C2×C4⋊C4—531no—
501C2×C4⋊C4—531no—
502C2×C4⋊C4—1061no—
503C2×C4⋊C4—1061no—
504C2×C4⋊C4—1061no—
505C2×C4⋊C4C22×D5311yescharacteristic
506C2×C4⋊C4C22×D5311yescharacteristic
507C2×C22⋊C4—531no—
508C2×C22⋊C4—531no—
509C2×C22⋊C4—1061no—
510C2×C22⋊C4—1061no—
511C2×C22⋊C4—1061no—
512C2×C22⋊C4—1061no—
513C2×C22⋊C4—1061no—
514C2×C22⋊C4—1061no—
515C2×C22⋊C4—1061no—
516C2×C22⋊C4—1061no—
517C2×C22⋊C4—2124no—
518C2×C42—531no—
519C2×C42—531no—
520C2×C42—1061no—
521C2×C42—1061no—
522#107—1062no—
523#107—2121no—
524#103—1062no—
525#103—2121no—
526#102—22no—
527#102—22no—
528#102—22no—
529#102—534no—
530#102—534no—
531#102C22⋊D5314yes—
532C22⋊C8—534no—
533#97—1062no—
534#97—2121no—
535#95—531no—
536#95—531no—
537#95—1061no—
538#95—1061no—
539#95—1061no—
540#95—1061no—
541#95—1061no—
542C24—21no—
543C24—21no—
544C24—24no—
545C24—42no—
546C24—42no—
547C24—42no—
548C24—42no—
549C24—81no—
550C24—81no—
551C24D4×D5311yescharacteristic
552C2×Q8—532no—
553C2×Q8—1061no—
554C2×Q8—1061no—
555C2×Q8—1061no—
556C2×Q8—1061no—
557C2×Q8—1061no—
558C2×D4—28no—
559C2×D4—24no—
560C2×D4—21no—
561C2×D4—21no—
562C2×D4—21no—
563C2×D4—21no—
564C2×D4—21no—
565C2×D4—21no—
566C2×D4—21no—
567C2×D4—21no—
568C2×D4—44no—
569C2×D4—44no—
570C2×D4—44no—
571C2×D4—42no—
572C2×D4—42no—
573C2×D4C2×C4×D5312yes—
574C2×D4C2×C4×D5312yes—
575C2×D4#1171994512yes—
576C2×D4C2×C22⋊D5312yes—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—42no—
584C22×C4—42no—
585C22×C4—81no—
586C22×C4—531no—
587C22×C4—531no—
588C22×C4—531no—
589C22×C4—531no—
590C22×C4—1061no—
591C22×C4—1061no—
592C22×C4—1061no—
593C22×C4—1061no—
594C22×C4—4241no—
595C22×C4—4241no—
596C22×C4—2122no—
597C22×C4—2122no—
598C22×C4—2122no—
599C22×C4—2122no—
600C22×C4C2×C4×D5312yes—
601C22×C4D4×D5311yescharacteristic
602C22×C4#1171994712yes—
603C22×C4C23×D5311yescharacteristic
604SD16—1068no—
605SD16—2124no—
606C2×C8—21no—
607C2×C8—21no—
608C2×C8—21no—
609C2×C8—21no—
610C2×C8—21no—
611C2×C8—44no—
612C2×C8—532no—
613C2×C8—532no—
614C2×C8—1061no—
615C2×C8—1061no—
616C2×C8—1061no—
617C2×C8—1061no—
618C2×C8C2×C22⋊D5312yes—
619C4⋊C4—21no—
620C4⋊C4—21no—
621C4⋊C4—21no—
622C4⋊C4—42no—
623C4⋊C4—532no—
624C4⋊C4—1064no—
625C4⋊C4—1061no—
626C4⋊C4—1061no—
627C4⋊C4—1061no—
628C4⋊C4—1061no—
629C4⋊C4—1061no—
630C4⋊C4—4241no—
631C4⋊C4—2122no—
632C4⋊C4C2×C22⋊D5312yes—
633C22⋊C4—1064no—
634C22⋊C4—1062no—
635C22⋊C4—1062no—
636C22⋊C4—4241no—
637C22⋊C4—4241no—
638C22⋊C4—2122no—
639C22⋊C4—2122no—
640C22⋊C4—2122no—
641C22⋊C4—2122no—
642C22⋊C4—2122no—
643C42—1061no—
644C42—1061no—
645C42—1061no—
646C42—1061no—
647C42—4241no—
648C42—2122no—
649C23—21no—
650C23—21no—
651C23—21no—
652C23—21no—
653C23—22no—
654C23—22no—
655C23—22no—
656C23—22no—
657C23—48no—
658C23—41no—
659C23—41no—
660C23—41no—
661C23—41no—
662C23—41no—
663C23—41no—
664C23—41no—
665C23—41no—
666C23—48no—
667C23—41no—
668C23—41no—
669C23—84no—
670C23—84no—
671C23—84no—
672C23—84no—
673C23—84no—
674C23#1313317712yes—
675C23#1313324112yes—
676C23#1313324612yes—
677C23C2×D4×D5311yescharacteristic
678Q8—1062no—
679Q8—1062no—
680Q8—2121no—
681Q8—2121no—
682D4—22no—
683D4—22no—
684D4—22no—
685D4—22no—
686D4—22no—
687D4—48no—
688D4—41no—
689D4—41no—
690D4C4×C22⋊D5314yes—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—84no—
704C2×C4—1062no—
705C2×C4—1062no—
706C2×C4—1061no—
707C2×C4—1061no—
708C2×C4—1061no—
709C2×C4—1061no—
710C2×C4—1061no—
711C2×C4—1061no—
712C2×C4—1061no—
713C2×C4—1061no—
714C2×C4—1061no—
715C2×C4—1061no—
716C2×C4—1061no—
717C2×C4—1061no—
718C2×C4—4244no—
719C2×C4—4244no—
720C2×C4—2121no—
721C2×C4—2121no—
722C2×C4—2121no—
723C2×C4—2121no—
724C2×C4—2121no—
725C2×C4—2121no—
726C2×C4—2121no—
727C2×C4—2121no—
728C2×C4—2121no—
729C2×C4—2121no—
730C2×C4#1313317712yes—
731C2×C4C22×C4×D5311yescharacteristic
732C2×C4C22×C22⋊D5311yescharacteristic
733C2×C4C2×#1171994711yescharacteristic
734C2×C4C2×#1171994511yescharacteristic
735C2×C4#1313326211yescharacteristic
736C2×C4#1313326211yescharacteristic
737C8—22no—
738C8—41no—
739C8—1062no—
740C8—1062no—
741C22—22no—
742C22—22no—
743C22—22no—
744C22—22no—
745C22—22no—
746C22—22no—
747C22—24no—
748C22—42no—
749C22—42no—
750C22—42no—
751C22—42no—
752C22—42no—
753C22—42no—
754C22—42no—
755C22—42no—
756C22—42no—
757C22—816no—
758C22—81no—
759C22—81no—
760C22—81no—
761C22—81no—
762C22#1681072014yescomplemented
763C22C2×#1313317711yescharacteristic
764C22D4×C22⋊D5311yescharacteristic
765C22#1681126311yescharacteristic
766C22C2×#1313324111yescharacteristic
767C22C2×#1313324611yescharacteristic
768C22#1681142411yescharacteristic
769C22#1681142911yescharacteristic
770C4—22no—
771C4—42no—
772C4—81no—
773C4—4241no—
774C4—4241no—
775C4—2121no—
776C4—2121no—
777C4—2121no—
778C4—2122no—
779C4—2122no—
780C4—2121no—
781C4C2×C4×C22⋊D5311yescharacteristic
782C4#1681109611yescharacteristic
783C4#1681126711yescharacteristic
784C4#1681129911yescharacteristic
785C2—24no—
786C2—44no—
787C2—82no—
788C2#2027769411yescharacteristic
789C2C2×#1681072011yescharacteristic
790C2#2028354111yescharacteristic
791C2#2028619511yescharacteristic
792C2#2028622511yescharacteristic
793C2#2028673211yescharacteristic
794C2#2028679211yescharacteristic
subgroupG/H
centerC23C2×D4×D53
commutatorC2×C4×C53C23×C4
FrattiniC22×C4C23×D53
FittingC22×#102×C53C2
socleC23×C53C22×D4
prime radicalC23×D4×C53C22
cosocleC22×C4×C53C24
hypercenterC22×#102D53
hypocenterC53#22854
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×#102

Complements

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

NH ≅ G/Ntype
2. C2×#16810720C2semidirect
3. #20277720C2semidirect
5. #20275597C2semidirect
6. #20275409C2semidirect
7. #20275338C2semidirect
8. #20275138C2semidirect
9. #20275067C2semidirect
10. #20275047C2semidirect
11. #20274960C2semidirect
12. #20274903C2semidirect
13. #20274542C2semidirect
14. #20274491C2semidirect
19. C2×#13133182C22semidirect
23. #16810774C4semidirect
25. C2×#13133150C22semidirect
26. C2×#13133150C22semidirect
27. C2×#13133142C22semidirect
28. C2×#13133142C22semidirect
32. C2×#13133127C22semidirect
33. C2×#13133127C22semidirect
34. #16810528C22semidirect
37. #16810519C22semidirect
45. C4⋊C4×Dic53C22semidirect
48. #16810386C22semidirect
49. #16810386C22semidirect
50. #16810385C22semidirect
51. #16810385C22semidirect
52. #16810377C22semidirect
53. #16810377C22semidirect
69. C2×#11719923C2×C4semidirect
70. C2×#11719923C2×C4semidirect
74. #13133196C2×C4semidirect
106. #13133138C2×C4semidirect
107. #13133138C2×C4semidirect
108. C22⋊#88322C2×C4semidirect
365. C22×C53#440semidirect
459. C53#22854semidirect
762. C22#16810720semidirect

Maximal subgroups

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

subgroupindex
C2×#168107742
C2×#168107202
#202777202
D4×C22⋊Dic532
#202755972
#202754092
#202753382
#202751382
#202750672
#202750472
#202749602
#202749032
#202745422
#202744912
C22×#102×C532
#2285453