Finite Group Databasebeta

← #27393203

Subgroups — #27393203

Order 13568.

1390 conjugacy classes of subgroups.

The subgroup lattice has 872 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811201C211yesmaximal, characteristic
2C2×#16810590C211yesmaximal, characteristic, complemented
3#20275151C211yesmaximal, characteristic, complemented
4#20275146C211yesmaximal, characteristic, complemented
5#20275141C211yesmaximal, characteristic, complemented
6#20275136C211yesmaximal, characteristic, complemented
7#20275037C211yesmaximal, characteristic, complemented
8#20275032C211yesmaximal, characteristic, complemented
9#20275027C211yesmaximal, characteristic, complemented
10#20275022C211yesmaximal, characteristic, complemented
11#20274803C211yesmaximal, characteristic, complemented
12#20274799C211yesmaximal, characteristic, complemented
13#20274653C211yesmaximal, characteristic, complemented
14#20274653C211yesmaximal, characteristic, complemented
15C53×#2311C211yesmaximal, characteristic, complemented
16C22×#11719945C2211yescharacteristic
17C22×#11719917C2211yescharacteristic
18C23×#88322C2211yescharacteristic
19#16811201—24no—
20#16811201C418yescomplemented
21C2×#13133196C2211yescharacteristic
22C2×#13133196C2211yescharacteristic
23C2×#13133193—21no—
24C2×#13133191C2211yescharacteristic
25C2×#13133191C2211yescharacteristic
26C2×#13133189—21no—
27C2×#13133189—21no—
28C2×#13133188—21no—
29C22×C4⋊Dic53C2211yescharacteristic
30C2×#13133140C2211yescharacteristic
31C2×#13133140C2211yescharacteristic
32C2×#13133140C2211yescharacteristic
33C2×#13133140C2211yescharacteristic
34C2×#13133137C2211yescharacteristic
35C2×#13133137C2211yescharacteristic
36C2×#13133137C2211yescharacteristic
37C2×#13133137C2211yescharacteristic
38#16810590—24no—
39C2×C22⋊#88322C2211yescharacteristic
40C2×C22⋊#88322C2211yescharacteristic
41C2×C22⋊#88322C2211yescharacteristic
42C2×C22⋊#88322C2211yescharacteristic
43#16810385C2211yescharacteristic
44#16810385C2211yescharacteristic
45#16810385C2211yescharacteristic
46#16810385C2211yescharacteristic
47#16810385C2211yescharacteristic
48#16810385C2211yescharacteristic
49#16810385C2211yescharacteristic
50#16810385C2211yescharacteristic
51C22×#41×C53C2211yescharacteristic
52C2×#117×C53C2211yescharacteristic
53C22×C4⋊C4×C53C2211yescharacteristic
54C53×#391—21no—
55C53×#390—21no—
56C53×#386—21no—
57C53×#386—21no—
58C53×#380C2211yescharacteristic
59C53×#380C2211yescharacteristic
60C53×#380C2211yescharacteristic
61C53×#380C2211yescharacteristic
62C2×#11719945—22no—
63C2×#11719945—41no—
64C2×#11719945—41no—
65C2×#11719945—41no—
66C2×#11719945—41no—
67C2×#11719945C2×C414yescomplemented
68C22×Dic106C2311yescharacteristic
69C22×D212C2311yescharacteristic
70C22×C22⋊D53—21no—
71C22×C22⋊D53—21no—
72C22×C22⋊D53—21no—
73C23×Dic53—21no—
74C22×C4×D53—21no—
75C2×#11719917—22no—
76C2×#11719917—41no—
77C2×#11719917—41no—
78C22×#88322—22no—
79C22×#88322—41no—
80C22×#88322—41no—
81C22×#88322C2311yescharacteristic
82C22×#88322C2311yescharacteristic
83C22×#88322C2311yescharacteristic
84C22×#88322C2311yescharacteristic
85#13133196—22no—
86#13133196—22no—
87#13133196C2×C414yes—
88#13133196C2×C414yescomplemented
89#13133193—28no—
90#13133191—22no—
91#13133191—22no—
92#13133191C2×C414yes—
93#13133191C2×C414yescomplemented
94#13133189—28no—
95#13133189—28no—
96#13133188—28no—
97C2×C4⋊Dic53—21no—
98C2×C4⋊Dic53—22no—
99C2×C4⋊Dic53C2×C414yescomplemented
100C2×C4⋊Dic53C2311yescharacteristic
101C2×C4⋊Dic53C2311yescharacteristic
102C2×#11719919—21no—
103C2×#11719919—21no—
104C2×C22⋊Dic53—21no—
105C2×C22⋊Dic53—21no—
106C2×#11719921—21no—
107C2×#11719921—21no—
108#13133140—41no—
109#13133140—41no—
110#13133140—41no—
111#13133140—41no—
112#13133137—41no—
113#13133137—41no—
114#13133137—41no—
115#13133137—41no—
116C22⋊#88322—22no—
117C22⋊#88322—22no—
118C22⋊#88322—22no—
119C22⋊#88322—22no—
120C2×#41×C53—41no—
121C2×#41×C53—41no—
122C2×#41×C53—41no—
123C2×#41×C53—41no—
124C2×#41×C53C2×C414yes—
125C2×#41×C53D414yes—
126C22×Q8×C53D411yescharacteristic
127C22×D4×C53D411yescharacteristic
128C22×D4×C53D411yescharacteristic
129C22×D4×C53D411yescharacteristic
130C23×C4×C53—21no—
131C23×C4×C53C2311yescharacteristic
132C23×C4×C53C2311yescharacteristic
133C23×C4×C53C2311yescharacteristic
134#117×C53—41no—
135#117×C53—41no—
136C2×C4⋊C4×C53—21no—
137C2×C4⋊C4×C53—41no—
138C2×C4⋊C4×C53—41no—
139C2×C4⋊C4×C53C2311yescharacteristic
140C2×C4⋊C4×C53C2311yescharacteristic
141C2×C4⋊C4×C53C2311yescharacteristic
142C2×C4⋊C4×C53C2311yescharacteristic
143C2×C22⋊C4×C53—21no—
144C2×C22⋊C4×C53—21no—
145C2×C22⋊C4×C53—21no—
146C2×C22⋊C4×C53—21no—
147C2×C22⋊C4×C53—21no—
148C2×C42×C53—21no—
149#95×C53—21no—
150#95×C53—21no—
151#95×C53—21no—
152#95×C53—21no—
153C24×C53C2×D411yescharacteristic
154C24×C53C2×D411yescharacteristic
155C24×C53C2×D411yescharacteristic
156C23×D53—21no—
157#41×C53—44no—
158#41×C53—44no—
159#41×C53—44no—
160#41×C53—44no—
161C2×Q8×C53—41no—
162C2×Q8×C53—41no—
163C2×Q8×C53C22⋊C414yes—
164C2×D4×C53—41no—
165C2×D4×C53—41no—
166C2×D4×C53—41no—
167C2×D4×C53—41no—
168C2×D4×C53—41no—
169C2×D4×C53—41no—
170C2×D4×C53C22⋊C414yes—
171C2×D4×C53C22⋊C414yes—
172C2×D4×C53C22⋊C414yes—
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—21no—
180C22×C4×C53—21no—
181C22×C4×C53—21no—
182C22×C4×C53—21no—
183C22×C4×C53—21no—
184C22×C4×C53—21no—
185C22×C4×C53—21no—
186C22×C4×C53—21no—
187C22×C4×C53—21no—
188C22×C4×C53—21no—
189C22×C4×C53—42no—
190C22×C4×C53—81no—
191C22×C4×C53—81no—
192C22×C4×C53C22×C412yes—
193C22×C4×C53C22×C412yes—
194C22×C4×C53C22×C412yes—
195C22×C4×C53C2×D411yescharacteristic
196C22×C4×C53C2×D411yescharacteristic
197C22×C4×C53C2×D411yescharacteristic
198C22×C4×C53C2×D412yes—
199C22×C4×C53C2×D412yes—
200C22×C4×C53C2×D412yes—
201C22×C4×C53C2411yescharacteristic
202C2×C22⋊D53—24no—
203C2×C22⋊D53—24no—
204C2×C22⋊D53—24no—
205C2×C22⋊D53—42no—
206C2×C22⋊D53—42no—
207C2×C22⋊D53—81no—
208C2×C22⋊D53—81no—
209C2×C22⋊D53—81no—
210C2×C22⋊D53—81no—
211C22×Dic53—21no—
212C22×Dic53—21no—
213C22×Dic53—21no—
214C22×Dic53—24no—
215C22×Dic53—81no—
216C22×Dic53—81no—
217#11719945—44no—
218#11719945—44no—
219#11719945—44no—
220#11719945—44no—
221C2×D212—21no—
222C2×D212—21no—
223C2×D212—21no—
224C2×D212—21no—
225C2×D212—21no—
226C2×D212C22×C412yes—
227C2×C4×D53—24no—
228C2×C4×D53—42no—
229C2×C4×D53—42no—
230C2×Dic106—21no—
231C2×Dic106—21no—
232C2×Dic106—21no—
233C2×Dic106—21no—
234C2×Dic106—21no—
235C2×Dic106C22×C412yes—
236C4⋊C4×C53—21no—
237C4⋊C4×C53—21no—
238C4⋊C4×C53—21no—
239C4⋊C4×C53—21no—
240C4⋊C4×C53—21no—
241C4⋊C4×C53—21no—
242C4⋊C4×C53—21no—
243C4⋊C4×C53—21no—
244C4⋊C4×C53—42no—
245C22⋊C4×C53—42no—
246C22⋊C4×C53—81no—
247C22⋊C4×C53—81no—
248C22⋊C4×C53—81no—
249C22⋊C4×C53—81no—
250C42×C53—42no—
251C22⋊Dic53—24no—
252C22⋊Dic53—24no—
253#11719921—24no—
254#11719921—24no—
255C4⋊Dic53—24no—
256C4⋊Dic53—21no—
257C4⋊Dic53—21no—
258C4⋊Dic53C22×C412yes—
259C4⋊Dic53C22×C412yes—
260#11719919—24no—
261#11719919—24no—
262#11719917—44no—
263C2×#88322—21no—
264C2×#88322—21no—
265C2×#88322—21no—
266C2×#88322—21no—
267C2×#88322—21no—
268C2×#88322—21no—
269C2×#88322—21no—
270C2×#88322—21no—
271C2×#88322—21no—
272C2×#88322—21no—
273C2×#88322—21no—
274C2×#88322—21no—
275C2×#88322—44no—
276C23×C53—21no—
277C23×C53—21no—
278C23×C53—21no—
279C23×C53—21no—
280C23×C53—21no—
281C23×C53—21no—
282C23×C53—21no—
283C23×C53—21no—
284C23×C53—21no—
285C23×C53—21no—
286C23×C53—21no—
287C23×C53—21no—
288C23×C53—21no—
289C23×C53—21no—
290C23×C53—21no—
291C23×C53—21no—
292C23×C53—21no—
293C23×C53—21no—
294C23×C53C2×C22⋊C412yes—
295C23×C53C2×C22⋊C412yes—
296C23×C53C2×C22⋊C412yes—
297C23×C53C22×D411yescharacteristic
298C22×D53—22no—
299C22×D53—41no—
300C22×D53—41no—
301C22×D53—41no—
302C22×D53—41no—
303C22×D53—41no—
304C22×D53—41no—
305Q8×C53—44no—
306D4×C53—44no—
307D4×C53—44no—
308D4×C53—44no—
309C2×C4×C53—21no—
310C2×C4×C53—21no—
311C2×C4×C53—21no—
312C2×C4×C53—21no—
313C2×C4×C53—21no—
314C2×C4×C53—21no—
315C2×C4×C53—22no—
316C2×C4×C53—22no—
317C2×C4×C53—22no—
318C2×C4×C53—22no—
319C2×C4×C53—22no—
320C2×C4×C53—22no—
321C2×C4×C53—22no—
322C2×C4×C53—22no—
323C2×C4×C53—22no—
324C2×C4×C53—22no—
325C2×C4×C53—22no—
326C2×C4×C53—22no—
327C2×C4×C53—41no—
328C2×C4×C53—41no—
329C2×C4×C53—41no—
330C2×C4×C53—41no—
331C2×C4×C53—41no—
332C2×C4×C53—41no—
333C2×C4×C53—41no—
334C2×C4×C53—41no—
335C2×C4×C53—41no—
336C2×C4×C53—41no—
337C2×C4×C53—41no—
338C2×C4×C53—41no—
339C2×C4×C53—84no—
340C2×C4×C53C2×C22⋊C412yes—
341C2×C4×C53C2×C22⋊C412yes—
342C2×C4×C53C2×C22⋊C412yes—
343C2×C4×C53C23×C411yescharacteristic
344C2×C4×C53C22×D411yescharacteristic
345C2×C4×C53H(5,𝔽2)11yescharacteristic
346C2×C4×C53H(5,𝔽2)11yescharacteristic
347C2×C4×C53H(5,𝔽2)11yescharacteristic
348C2×C4×C53H(5,𝔽2)11yescharacteristic
349C22⋊D53—48no—
350C22⋊D53—84no—
351C22⋊D53—84no—
352C2×Dic53—22no—
353C2×Dic53—22no—
354C2×Dic53—22no—
355C2×Dic53—41no—
356C2×Dic53—41no—
357C2×Dic53—41no—
358C2×Dic53—41no—
359C2×Dic53—41no—
360C2×Dic53—41no—
361C2×Dic53—84no—
362D212—22no—
363D212—22no—
364D212—41no—
365D212—41no—
366C4×D53—48no—
367Dic106—22no—
368Dic106—22no—
369Dic106—41no—
370Dic106—41no—
371#88322—41no—
372#88322—41no—
373#88322—41no—
374#88322—41no—
375#21772—531nomaximal, Sylow
376C22×C53—22no—
377C22×C53—22no—
378C22×C53—22no—
379C22×C53—22no—
380C22×C53—22no—
381C22×C53—22no—
382C22×C53—22no—
383C22×C53—22no—
384C22×C53—22no—
385C22×C53—41no—
386C22×C53—41no—
387C22×C53—41no—
388C22×C53—41no—
389C22×C53—41no—
390C22×C53—41no—
391C22×C53—41no—
392C22×C53—41no—
393C22×C53—41no—
394C22×C53—41no—
395C22×C53—41no—
396C22×C53—41no—
397C22×C53C22×C22⋊C411yescharacteristic
398C22×C53#53411yescharacteristic
399C22×C53#53411yescharacteristic
400C22×C53#57611yescharacteristic
401C22×C53#57711yescharacteristic
402C22×C53#57711yescharacteristic
403C22×C53#57811yescharacteristic
404C2×D53—42no—
405C2×D53—42no—
406C2×D53—42no—
407C2×D53—81no—
408C2×D53—81no—
409C2×D53—81no—
410C2×D53—81no—
411C4×C53—22no—
412C4×C53—22no—
413C4×C53—22no—
414C4×C53—81no—
415C4×C53—81no—
416C4×C53—81no—
417C4×C53—81no—
418C4×C53#51811yescharacteristic
419C4×C53#51811yescharacteristic
420C4×C53#53411yescharacteristic
421C4×C53#53411yescharacteristic
422Dic53—42no—
423Dic53—42no—
424Dic53—42no—
425C2×#537—531no—
426C2×#408—531no—
427#2311D5311yescharacteristic, complemented
428#1895—531no—
429#1894—531no—
430#1893—531no—
431#1892—531no—
432#1875—531no—
433#1874—531no—
434#1873—531no—
435#1872—531no—
436#1824—531no—
437#1823—531no—
438#1788—531no—
439#1788—531no—
440C2×C53—42no—
441C2×C53—42no—
442C2×C53—42no—
443C2×C53#230811yescharacteristic
444C2×C53#289711yescharacteristic
445C2×C53#289811yescharacteristic
446C2×C53#319811yescharacteristic
447C2×C53#320111yescharacteristic
448C2×C53#320311yescharacteristic
449C2×C53#320411yescharacteristic
450D53—82no—
451C22×#41—531no—
452C22×#41C2×D5311yescharacteristic
453C22×M16—531no—
454C23×C8—531no—
455#537—538no—
456#537—1064no—
457C2×C22⋊Q8—531no—
458C2×C22⋊Q8—531no—
459C2×C22⋊Q8—1061no—
460C2×#121—531no—
461C2×#121—531no—
462C2×#121—1061no—
463C2×#121—1061no—
464C2×#121—1061no—
465C2×#117C2×D5311yescharacteristic
466C22×C4⋊C4—531no—
467C22×C4⋊C4C2×D5311yescharacteristic
468C2×#103—531no—
469C2×#103—531no—
470C2×#103—531no—
471C2×#103—531no—
472C2×#102—531no—
473C2×#102—531no—
474C2×#102—531no—
475C2×#102—531no—
476#408—1064no—
477C2×C22⋊C8—531no—
478C2×C22⋊C8—531no—
479C2×C22⋊C8—531no—
480C2×C22⋊C8—531no—
481#391—21no—
482#390—21no—
483#386—21no—
484#386—21no—
485#380C2×D5311yescharacteristic
486#380C2×D5311yescharacteristic
487#380C2×D5311yescharacteristic
488#380C2×D5311yescharacteristic
489#340—531no—
490#340—531no—
491#340—531no—
492#340—531no—
493#340—531no—
494#340—531no—
495#340—531no—
496#340—531no—
497C53#2177211yescharacteristic, complemented, Sylow
498C2×#41—41no—
499C2×#41—41no—
500C2×#41—41no—
501C2×#41—41no—
502C2×#41—534no—
503C2×#41—1062no—
504C2×#41—2121no—
505C2×#41—2121no—
506C2×#41—2121no—
507C2×#41—2121no—
508C2×#41C4×D5314yes—
509C2×#41D21214yes—
510C22×Q8—531no—
511C22×Q8C22⋊D5311yescharacteristic
512C22×D4—531no—
513C22×D4—1061no—
514C22×D4—1061no—
515C22×D4—1061no—
516C22×D4C22⋊D5311yescharacteristic
517C22×D4C22⋊D5311yescharacteristic
518C22×D4C22⋊D5311yescharacteristic
519C23×C4—21no—
520C23×C4—1061no—
521C23×C4—1061no—
522C23×C4C22×D5311yescharacteristic
523C23×C4C22×D5311yescharacteristic
524C23×C4C22×D5311yescharacteristic
525C2×M16—1062no—
526C2×M16—2121no—
527C2×M16—2121no—
528C22×C8—531no—
529C22×C8—531no—
530C22×C8—531no—
531C22×C8—531no—
532C22×C8—1062no—
533C22×C8—2121no—
534C22×C8—2121no—
535C22⋊Q8—534no—
536C22⋊Q8—534no—
537C22⋊Q8—1068no—
538C22⋊Q8—1062no—
539C22⋊Q8—1062no—
540#121—534no—
541#121—534no—
542#121—1068no—
543#121—1068no—
544#121—1068no—
545#121—1062no—
546#121—1062no—
547#117—41no—
548#117—41no—
549C2×C4⋊C4—21no—
550C2×C4⋊C4—41no—
551C2×C4⋊C4—41no—
552C2×C4⋊C4—534no—
553C2×C4⋊C4—531no—
554C2×C4⋊C4—531no—
555C2×C4⋊C4—1062no—
556C2×C4⋊C4—1061no—
557C2×C4⋊C4—1061no—
558C2×C4⋊C4—1061no—
559C2×C4⋊C4C22×D5311yescharacteristic
560C2×C4⋊C4C22×D5311yescharacteristic
561C2×C4⋊C4C22×D5311yescharacteristic
562C2×C4⋊C4C22×D5311yescharacteristic
563C2×C22⋊C4—21no—
564C2×C22⋊C4—21no—
565C2×C22⋊C4—21no—
566C2×C22⋊C4—21no—
567C2×C22⋊C4—21no—
568C2×C22⋊C4—1061no—
569C2×C22⋊C4—1061no—
570C2×C22⋊C4—1061no—
571C2×C22⋊C4—1061no—
572C2×C42—21no—
573#103—2121no—
574#103—2121no—
575#103—2121no—
576#103—2121no—
577#102—2121no—
578#102—2121no—
579#102—2121no—
580#102—2121no—
581C22⋊C8—1062no—
582C22⋊C8—1062no—
583C22⋊C8—1062no—
584C22⋊C8—1062no—
585#95—21no—
586#95—21no—
587#95—21no—
588#95—21no—
589C24—1061no—
590C24C2×C22⋊D5311yescharacteristic
591C24C2×C22⋊D5311yescharacteristic
592C24C2×C22⋊D5311yescharacteristic
593#41—44no—
594#41—44no—
595#41—44no—
596#41—44no—
597#41—2124no—
598#41—2124no—
599#41—2124no—
600#41—2124no—
601C2×Q8—41no—
602C2×Q8—41no—
603C2×Q8—532no—
604C2×Q8—1061no—
605C2×Q8—1061no—
606C2×Q8—1061no—
607C2×Q8—1061no—
608C2×Q8—1061no—
609C2×Q8#1171992114yes—
610C2×D4—41no—
611C2×D4—41no—
612C2×D4—41no—
613C2×D4—41no—
614C2×D4—41no—
615C2×D4—41no—
616C2×D4—532no—
617C2×D4—1064no—
618C2×D4—1064no—
619C2×D4—1064no—
620C2×D4—1061no—
621C2×D4—1061no—
622C2×D4—1061no—
623C2×D4—1061no—
624C2×D4—1061no—
625C2×D4—4241no—
626C2×D4—4241no—
627C2×D4—4241no—
628C2×D4—4241no—
629C2×D4—2122no—
630C2×D4—2122no—
631C2×D4#1171992114yes—
632C2×D4#1171992114yes—
633C2×D4#1171992114yes—
634C22×C4—21no—
635C22×C4—21no—
636C22×C4—21no—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—21no—
643C22×C4—21no—
644C22×C4—21no—
645C22×C4—21no—
646C22×C4—21no—
647C22×C4—21no—
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—42no—
651C22×C4—81no—
652C22×C4—81no—
653C22×C4—1064no—
654C22×C4—1061no—
655C22×C4—1061no—
656C22×C4—1061no—
657C22×C4—1064no—
658C22×C4—4241no—
659C22×C4—4241no—
660C22×C4—2122no—
661C22×C4—2122no—
662C22×C4C2×C4×D5312yes—
663C22×C4C2×C4×D5312yes—
664C22×C4C2×C4×D5312yes—
665C22×C4C2×D21212yes—
666C22×C4C2×D21212yes—
667C22×C4C2×D21212yes—
668C22×C4C2×C22⋊D5311yescharacteristic
669C22×C4C2×C22⋊D5311yescharacteristic
670C22×C4C2×C22⋊D5311yescharacteristic
671C22×C4C23×D5311yescharacteristic
672M16—2124no—
673C2×C8—1061no—
674C2×C8—1061no—
675C2×C8—1061no—
676C2×C8—1061no—
677C2×C8—1061no—
678C2×C8—1061no—
679C2×C8—1061no—
680C2×C8—1061no—
681C2×C8—1061no—
682C2×C8—1061no—
683C2×C8—1061no—
684C2×C8—1061no—
685C2×C8—2124no—
686C4⋊C4—21no—
687C4⋊C4—21no—
688C4⋊C4—21no—
689C4⋊C4—21no—
690C4⋊C4—21no—
691C4⋊C4—21no—
692C4⋊C4—21no—
693C4⋊C4—21no—
694C4⋊C4—42no—
695C4⋊C4—532no—
696C4⋊C4—532no—
697C4⋊C4—1064no—
698C4⋊C4—1064no—
699C4⋊C4—1064no—
700C4⋊C4—1061no—
701C4⋊C4—1061no—
702C22⋊C4—42no—
703C22⋊C4—81no—
704C22⋊C4—81no—
705C22⋊C4—81no—
706C22⋊C4—81no—
707C22⋊C4—1064no—
708C22⋊C4—1064no—
709C22⋊C4—1064no—
710C22⋊C4—1064no—
711C42—42no—
712C23—21no—
713C23—21no—
714C23—21no—
715C23—21no—
716C23—21no—
717C23—21no—
718C23—21no—
719C23—21no—
720C23—21no—
721C23—21no—
722C23—21no—
723C23—21no—
724C23—21no—
725C23—21no—
726C23—21no—
727C23—21no—
728C23—21no—
729C23—21no—
730C23—1062no—
731C23—2121no—
732C23—2121no—
733C23—2121no—
734C23—2121no—
735C23—2121no—
736C23—2121no—
737C23C2×#1171992112yes—
738C23C2×#1171992112yes—
739C23C2×#1171992112yes—
740C23C22×C22⋊D5311yescharacteristic
741Q8—44no—
742Q8—1062no—
743Q8—1062no—
744Q8—2121no—
745Q8—2121no—
746D4—44no—
747D4—44no—
748D4—44no—
749D4—1062no—
750D4—1062no—
751D4—4244no—
752D4—4244no—
753D4—2128no—
754D4—2121no—
755D4—2121no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—21no—
759C2×C4—21no—
760C2×C4—21no—
761C2×C4—21no—
762C2×C4—22no—
763C2×C4—22no—
764C2×C4—22no—
765C2×C4—22no—
766C2×C4—22no—
767C2×C4—22no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—41no—
775C2×C4—41no—
776C2×C4—41no—
777C2×C4—41no—
778C2×C4—41no—
779C2×C4—41no—
780C2×C4—41no—
781C2×C4—41no—
782C2×C4—41no—
783C2×C4—41no—
784C2×C4—41no—
785C2×C4—41no—
786C2×C4—84no—
787C2×C4—1062no—
788C2×C4—1062no—
789C2×C4—1062no—
790C2×C4—4244no—
791C2×C4—2128no—
792C2×C4—2121no—
793C2×C4—2121no—
794C2×C4—2121no—
795C2×C4—2121no—
796C2×C4—2121no—
797C2×C4—2121no—
798C2×C4C2×#1171992112yes—
799C2×C4C2×#1171992112yes—
800C2×C4C2×#1171992112yes—
801C2×C4C22×C4×D5311yescharacteristic
802C2×C4C22×D21211yescharacteristic
803C2×C4#1313326211yescharacteristic
804C2×C4#1313326211yescharacteristic
805C2×C4#1313326211yescharacteristic
806C2×C4#1313326211yescharacteristic
807C8—2121no—
808C8—2121no—
809C8—2121no—
810C8—2121no—
811C22—22no—
812C22—22no—
813C22—22no—
814C22—22no—
815C22—22no—
816C22—22no—
817C22—22no—
818C22—22no—
819C22—22no—
820C22—41no—
821C22—41no—
822C22—41no—
823C22—41no—
824C22—41no—
825C22—41no—
826C22—41no—
827C22—41no—
828C22—41no—
829C22—41no—
830C22—41no—
831C22—41no—
832C22—4241no—
833C22—4241no—
834C22—4241no—
835C22—4241no—
836C22—2122no—
837C22—2122no—
838C22—2122no—
839C22C22×#1171992111yescharacteristic
840C22#1681118211yescharacteristic
841C22#1681118211yescharacteristic
842C22#1681142611yescharacteristic
843C22#1681143111yescharacteristic
844C22#1681143411yescharacteristic
845C22#1681143811yescharacteristic
846C4—22no—
847C4—22no—
848C4—22no—
849C4—81no—
850C4—81no—
851C4—81no—
852C4—81no—
853C4—2122no—
854C4—2122no—
855C4—2122no—
856C4#1681109611yescharacteristic
857C4#1681109611yescharacteristic
858C4#1681118511yescharacteristic
859C4#1681118511yescharacteristic
860C2—42no—
861C2—42no—
862C2—42no—
863C2—4242no—
864C2#2027729011yescharacteristic
865C2#2028323811yescharacteristic
866C2#2028324511yescharacteristic
867C2#2028556711yescharacteristic
868C2#2028559711yescharacteristic
869C2#2028561211yescharacteristic
870C2#2028562111yescharacteristic
subgroupG/H
centerC23C22×C22⋊D53
commutatorC2×C4×C53C23×C4
FrattiniC22×C4C23×D53
FittingC53×#2311C2
socleC23×C53C22×D4
prime radicalC2×#16811201C2
cosocleC22×C4×C53C24
hypercenter#2311D53
hypocenterC53#21772
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C22×#41 ◁ #2311

Complements

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

NH ≅ G/Ntype
2. C2×#16810590C2semidirect
3. #20275151C2semidirect
4. #20275146C2semidirect
5. #20275141C2semidirect
6. #20275136C2semidirect
7. #20275037C2semidirect
8. #20275032C2semidirect
9. #20275027C2semidirect
10. #20275022C2semidirect
11. #20274803C2semidirect
12. #20274799C2semidirect
13. #20274653C2semidirect
14. #20274653C2semidirect
15. C53×#2311C2semidirect
20. #16811201C4semidirect
67. C2×#11719945C2×C4semidirect
88. #13133196C2×C4semidirect
93. #13133191C2×C4semidirect
99. C2×C4⋊Dic53C2×C4semidirect
427. #2311D53semidirect
497. C53#21772semidirect

Maximal subgroups

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

subgroupindex
C2×#168112012
C2×#168105902
#202751512
#202751462
#202751412
#202751362
#202750372
#202750322
#202750272
#202750222
#202748032
#202747992
#202746532
C53×#23112
#2177253