Finite Group Databasebeta

← #27404841

Subgroups — #27404841

Order 13568.

1020 conjugacy classes of subgroups.

The subgroup lattice has 862 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20283931C211yesmaximal, characteristic
2C2×#16810742C211yesmaximal, characteristic, complemented
3#20283442C211yesmaximal, characteristic, complemented
4C2×#16810641C211yesmaximal, characteristic, complemented
5#20283165C211yesmaximal, characteristic, complemented
6#20275600C211yesmaximal, characteristic, complemented
7#20275427C211yesmaximal, characteristic, complemented
8#20275361C211yesmaximal, characteristic, complemented
9#20275040C211yesmaximal, characteristic, complemented
10#20275039C211yesmaximal, characteristic, complemented
11#20274991C211yesmaximal, characteristic, complemented
12#20274919C211yesmaximal, characteristic, complemented
13#20274549C211yesmaximal, characteristic, complemented
14#20274481C211yesmaximal, characteristic, complemented
15C53×#1897C211yesmaximal, characteristic, complemented
16C22×#11719945C2211yescharacteristic
17C2×#13133237C2211yescharacteristic
18C2×#13133237C2211yescharacteristic
19C2×#13133225C2211yescharacteristic
20C2×#13133225C2211yescharacteristic
21C2×#13133224C2211yescharacteristic, complemented
22C22×#11719917C2211yescharacteristic
23#16810783C411yescharacteristic, complemented
24#16810783C411yescharacteristic, complemented
25#16810778C411yescharacteristic, complemented
26#16810773C411yescharacteristic, complemented
27#16810766C411yescharacteristic, complemented
28#16810766C411yescharacteristic, complemented
29#16810761C411yescharacteristic, complemented
30#16810756C411yescharacteristic, complemented
31#16810742—24no—
32#16810701—21no—
33#16810695—21no—
34#16810695—21no—
35D4×#88322—21no—
36C2×#13133152C2211yescharacteristic, complemented
37C2×#13133152C2211yescharacteristic, complemented
38#16810650C2211yescharacteristic, complemented
39#16810641—24no—
40C2×#13133145C2211yescharacteristic
41C2×#13133145C2211yescharacteristic
42C2×#13133145C2211yescharacteristic
43C2×#13133145C2211yescharacteristic
44#16810617C2211yescharacteristic
45#16810617C2211yescharacteristic
46#16810591C2211yescharacteristic
47#16810591C2211yescharacteristic
48#16810590C2211yescharacteristic, complemented
49#16810588—21no—
50#16810588—21no—
51#16810585—21no—
52C2×C22⋊#88322C2211yescharacteristic
53C2×C22⋊#88322C2211yescharacteristic
54C22⋊C8×D53—21no—
55#16810579C2211yescharacteristic, complemented
56C2×#13133128C2211yescharacteristic, complemented
57C2×C4×#88322C2211yescharacteristic, complemented
58#16810387C2211yescharacteristic, complemented
59#16810387C2211yescharacteristic, complemented
60#16810378C2211yescharacteristic, complemented
61#16810378C2211yescharacteristic, complemented
62C53×#525C2211yescharacteristic
63C2×#117×C53C2211yescharacteristic
64C2×#104×C53C2211yescharacteristic, complemented
65C2×#104×C53C2211yescharacteristic, complemented
66C53×#407C2211yescharacteristic
67C53×#339C2211yescharacteristic, complemented
68C53×#339C2211yescharacteristic, complemented
69C2×#11719945—21no—
70C2×#11719945—21no—
71C2×#11719945—22no—
72C2×#11719945—22no—
73C2×#11719945—41no—
74C2×#11719945—41no—
75C2×#11719945C2×C411yescharacteristic
76C2×#11719945C2×C411yescharacteristic
77C2×#11719945C2311yescharacteristic
78C2×#11719945C2311yescharacteristic
79C22×Dic106C2×C411yescharacteristic
80C22×D212C2×C411yescharacteristic
81C22×C22⋊D53—21no—
82C22×C4×D53—21no—
83#13133237—22no—
84#13133237—22no—
85#13133237—41no—
86#13133237—41no—
87C2×#11719925C2×C411yescharacteristic
88C2×#11719925C2×C411yescharacteristic
89C2×#11719923C2×C411yescharacteristic
90C2×#11719923C2×C411yescharacteristic
91C2×#11719924C2×C411yescharacteristic
92C2×#11719924C2×C411yescharacteristic
93C2×#11719922C2×C411yescharacteristic
94C2×#11719922C2×C411yescharacteristic
95#13133225—22no—
96#13133225—22no—
97#13133225—41no—
98#13133225—41no—
99#13133224—22no—
100#13133224—41no—
101C2×#11719917—21no—
102C2×#11719917—22no—
103C2×#11719917—21no—
104C2×#11719917—41no—
105C2×#11719917C2311yescharacteristic
106C2×#11719917C2311yescharacteristic
107C2×#11719912—21no—
108C2×#11719912—21no—
109C22×#88322—21no—
110C22×#88322—21no—
111C22×#88322C2311yescharacteristic
112C22×#88322C2311yescharacteristic
113C22×#88322C2311yescharacteristic
114C22×#88322C2311yescharacteristic
115C2×C8×D53—21no—
116C2×C8×D53—21no—
117#13133152—22no—
118#13133152—41no—
119C4⋊#88322—21no—
120C4⋊#88322—21no—
121#13133145—22no—
122#13133145—22no—
123#13133145—22no—
124#13133145D414yescomplemented
125#13133140C2×C411yescharacteristic
126#13133140C2×C411yescharacteristic
127#13133140C2×C411yescharacteristic
128#13133140C2×C411yescharacteristic
129#13133137C2×C411yescharacteristic
130#13133137C2×C411yescharacteristic
131#13133137C2×C411yescharacteristic
132#13133137C2×C411yescharacteristic
133C22⋊#88322—21no—
134C22⋊#88322—21no—
135C22⋊#88322C2×C411yescharacteristic
136C22⋊#88322C2×C411yescharacteristic
137C22⋊#88322C2×C411yescharacteristic
138C22⋊#88322C2×C411yescharacteristic
139C22⋊#88322D411yescharacteristic
140C22⋊#88322D411yescharacteristic
141C22⋊#88322D411yescharacteristic
142C22⋊#88322D411yescharacteristic
143#13133129—21no—
144#13133129—21no—
145#13133129—21no—
146#13133129—21no—
147#13133128—22no—
148#13133128—21no—
149C4×#88322—21no—
150C4×#88322—41no—
151C2×#41×C53C2311yescharacteristic
152C23×C4×C53C2311yescharacteristic
153C2×M16×C53C2311yescharacteristic
154C2×M16×C53C2311yescharacteristic
155#123×C53—21no—
156C22⋊Q8×C53C2×C411yescharacteristic
157C22⋊Q8×C53C2×C411yescharacteristic
158#121×C53C2×C411yescharacteristic
159#121×C53C2×C411yescharacteristic
160#120×C53—21no—
161C4×D4×C53—21no—
162C4×D4×C53—21no—
163#117×C53—22no—
164#117×C53—41no—
165#117×C53C2311yescharacteristic
166C2×C4⋊C4×C53—21no—
167C2×C22⋊C4×C53—21no—
168C2×C42×C53C2311yescharacteristic
169C2×C42×C53C2311yescharacteristic
170#104×C53—22no—
171#104×C53—41no—
172C22⋊C8×C53—21no—
173C22⋊C8×C53—21no—
174C24×C53#4111yescharacteristic
175C23×D53—21no—
176#41×C53—21no—
177#41×C53—21no—
178#41×C53—21no—
179#41×C53—21no—
180C2×Q8×C53C22×C411yescharacteristic
181C2×D4×C53—21no—
182C2×D4×C53—21no—
183C2×D4×C53—21no—
184C2×D4×C53C22×C411yescharacteristic
185C22×C4×C53—21no—
186C22×C4×C53—21no—
187C22×C4×C53—21no—
188C22×C4×C53—21no—
189C22×C4×C53—21no—
190C22×C4×C53—21no—
191C22×C4×C53—21no—
192C22×C4×C53C22×C411yescharacteristic
193C22×C4×C53C22×C411yescharacteristic
194C22×C4×C53C2×D411yescharacteristic
195C22×C4×C53C2×D411yescharacteristic
196C22×C4×C53#4111yescharacteristic
197C22×C4×C53C2411yescharacteristic
198C2×C22⋊D53—21no—
199C2×C22⋊D53—21no—
200C2×C22⋊D53—21no—
201C2×C22⋊D53—21no—
202C2×C22⋊D53—42no—
203C2×C22⋊D53—42no—
204C22×Dic53—21no—
205#11719945—21no—
206#11719945—21no—
207#11719945—21no—
208#11719945—21no—
209#11719945—21no—
210#11719945—21no—
211#11719945—22no—
212#11719945—22no—
213#11719945—41no—
214#11719945—41no—
215#11719945—42no—
216#11719945—42no—
217#11719945—42no—
218#11719945—42no—
219#11719945C2×D412yes—
220#11719945#4112yes—
221C2×D212—22no—
222C2×D212—21no—
223C2×D212—41no—
224C2×D212C22×C411yescharacteristic
225C2×D212C22×C411yescharacteristic
226C2×C4×D53—21no—
227C2×C4×D53—21no—
228C2×C4×D53—21no—
229C2×C4×D53—21no—
230C2×C4×D53—42no—
231C2×C4×D53—42no—
232C2×Dic106—22no—
233C2×Dic106—21no—
234C2×Dic106—41no—
235C2×Dic106C22×C411yescharacteristic
236C2×Dic106C22×C411yescharacteristic
237M16×C53—21no—
238M16×C53—21no—
239M16×C53—21no—
240M16×C53—21no—
241C2×C8×C53—21no—
242C2×C8×C53—21no—
243C4⋊C4×C53—21no—
244C4⋊C4×C53—21no—
245C4⋊C4×C53—42no—
246C4⋊C4×C53C22×C411yescharacteristic
247C4⋊C4×C53C22×C411yescharacteristic
248C22⋊C4×C53—21no—
249C22⋊C4×C53—21no—
250C22⋊C4×C53—21no—
251C22⋊C4×C53—21no—
252C22⋊C4×C53—21no—
253C22⋊C4×C53—42no—
254C42×C53—21no—
255C42×C53—21no—
256C42×C53—21no—
257C42×C53—21no—
258C42×C53C2×D412yes—
259#11719925—22no—
260#11719925—41no—
261#11719924—22no—
262#11719924—41no—
263#11719923—22no—
264#11719923—41no—
265#11719922—22no—
266#11719922—41no—
267#11719917—21no—
268#11719917—21no—
269#11719917—21no—
270#11719917—42no—
271#11719917—42no—
272#11719917C2×D412yes—
273C2×#88322—21no—
274C2×#88322—21no—
275C2×#88322—21no—
276C2×#88322—21no—
277C2×#88322—21no—
278C2×#88322—21no—
279C2×#88322—21no—
280C2×#88322—21no—
281C2×#88322—21no—
282C2×#88322—21no—
283C2×#88322—42no—
284C2×#88322—42no—
285C2×#88322C22×C411yescharacteristic
286C2×#88322C22×C411yescharacteristic
287C2×#88322C22×C411yescharacteristic
288C2×#88322C22×C411yescharacteristic
289C2×#88322C2×D411yescharacteristic
290C2×#88322C2×D411yescharacteristic
291C2×#88322C2×D411yescharacteristic
292C2×#88322C2×D411yescharacteristic
293#11719912—42no—
294#11719912—42no—
295C8×D53—42no—
296C8×D53—42no—
297C23×C53—21no—
298C23×C53—21no—
299C23×C53—21no—
300C23×C53—41no—
301C23×C53—41no—
302C23×C53C4×D411yescharacteristic
303C23×C53C4×D411yescharacteristic
304C23×C53C2×#4111yescharacteristic
305C22×D53—21no—
306C22×D53—21no—
307C22×D53—42no—
308C22×D53—42no—
309C22×D53—81no—
310Q8×C53—21no—
311Q8×C53—21no—
312D4×C53—21no—
313D4×C53—21no—
314D4×C53—42no—
315D4×C53—41no—
316D4×C53—41no—
317D4×C53—81no—
318C2×C4×C53—21no—
319C2×C4×C53—21no—
320C2×C4×C53—21no—
321C2×C4×C53—21no—
322C2×C4×C53—21no—
323C2×C4×C53—21no—
324C2×C4×C53—21no—
325C2×C4×C53—21no—
326C2×C4×C53—21no—
327C2×C4×C53—21no—
328C2×C4×C53—21no—
329C2×C4×C53—21no—
330C2×C4×C53—21no—
331C2×C4×C53—22no—
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×C53C4×D411yescharacteristic
340C2×C4×C53C4×D411yescharacteristic
341C2×C4×C53C23×C411yescharacteristic
342C2×C4×C53C22×D411yescharacteristic
343C2×C4×C53C22×D411yescharacteristic
344C2×C4×C53C2×#4111yescharacteristic
345C2×C4×C53H(5,𝔽2)11yescharacteristic
346C2×C4×C53H(5,𝔽2)11yescharacteristic
347C22⋊D53—22no—
348C22⋊D53—22no—
349C22⋊D53—42no—
350C22⋊D53—42no—
351C22⋊D53—41no—
352C22⋊D53—41no—
353C2×Dic53—21no—
354C2×Dic53—21no—
355C2×Dic53—42no—
356D212—21no—
357D212—21no—
358D212—21no—
359D212—42no—
360D212C4×D412yes—
361C4×D53—22no—
362C4×D53—22no—
363C4×D53—42no—
364C4×D53—42no—
365C4×D53—41no—
366C4×D53—41no—
367Dic106—21no—
368Dic106—21no—
369Dic106—21no—
370Dic106—42no—
371Dic106C4×D412yes—
372C8×C53—41no—
373C8×C53—41no—
374#88322—21no—
375#88322—21no—
376#88322—21no—
377#88322—21no—
378#88322—21no—
379#88322—21no—
380#88322—22no—
381#88322—21no—
382#88322—21no—
383#88322—41no—
384#22887—531nomaximal, Sylow
385C22×C53—21no—
386C22×C53—21no—
387C22×C53—21no—
388C22×C53—21no—
389C22×C53—21no—
390C22×C53—21no—
391C22×C53—21no—
392C22×C53—21no—
393C22×C53—41no—
394C22×C53—41no—
395C22×C53—41no—
396C22×C53—81no—
397C22×C53—81no—
398C22×C53C2×C4×D411yescharacteristic
399C22×C53#54611yescharacteristic
400C22×C53#55111yescharacteristic
401C2×D53—22no—
402C2×D53—41no—
403C2×D53—41no—
404C2×D53—41no—
405C2×D53—41no—
406C2×D53—41no—
407C2×D53—84no—
408C4×C53—21no—
409C4×C53—21no—
410C4×C53—42no—
411C4×C53—41no—
412C4×C53—41no—
413C4×C53—41no—
414C4×C53—81no—
415C4×C53C2×C4×D411yescharacteristic
416C4×C53#51811yescharacteristic
417C4×C53D4211yescharacteristic
418C4×C53#54611yescharacteristic
419Dic53—22no—
420Dic53—41no—
421#3002—531no—
422C2×#444—531no—
423#2933—531no—
424C2×#421—531no—
425#2880—531no—
426#1974—531no—
427#1938—531no—
428#1929—531no—
429#1897D5311yescharacteristic, complemented
430#1876—531no—
431#1876—531no—
432#1866—531no—
433#1855—531no—
434#1764—531no—
435#1750—531no—
436C2×C53—21no—
437C2×C53—21no—
438C2×C53—41no—
439C2×C53—41no—
440C2×C53—81no—
441C2×C53#235811yescharacteristic
442C2×C53#295511yescharacteristic
443C2×C53#295711yescharacteristic
444D53—42no—
445D53—81no—
446C22×#41—531no—
447C2×#135—531no—
448C2×#135—531no—
449C2×#131—531no—
450C2×#131—531no—
451C2×#131—531no—
452C22×M16—531no—
453#525C2×D5311yescharacteristic
454C2×#117C2×D5311yescharacteristic
455#452—531no—
456#452—531no—
457#451—531no—
458#450—531no—
459#449—531no—
460#449—531no—
461#448—531no—
462#447—531no—
463#444—1064no—
464#436—1061no—
465#435—1061no—
466#435—1061no—
467C8×D4—1061no—
468C2×#108—531no—
469C2×#108—531no—
470#424—531no—
471#421—1064no—
472C2×#104—531no—
473C2×#104—531no—
474C2×#104—531no—
475C2×#104—531no—
476C2×#104C2×D5311yescharacteristic, complemented
477C2×#104C2×D5311yescharacteristic, complemented
478#416—531no—
479#416—531no—
480#408—531no—
481#408—531no—
482#408—531no—
483#408—1061no—
484#408—1061no—
485#407—1061no—
486#407C2×D5311yescharacteristic
487C2×C22⋊C8—531no—
488C2×C22⋊C8—531no—
489C2×C22⋊C8—1061no—
490#405—531no—
491C2×#97—531no—
492C2×C4×C8—531no—
493#341—531no—
494#341—531no—
495#339C2×D5311yescharacteristic, complemented
496#339C2×D5311yescharacteristic, complemented
497#336—531no—
498#336—531no—
499C53#2288711yescharacteristic, complemented, Sylow
500C2×#41—531no—
501C2×#41—531no—
502C2×#41—531no—
503C2×#41—531no—
504C2×#41—1062no—
505C2×#41—1062no—
506C2×#41—1061no—
507C2×#41—1061no—
508C2×#41—2121no—
509C2×#41—2121no—
510C2×#41C22×D5311yescharacteristic
511C22×Q8—531no—
512C22×D4—531no—
513C22×D4—1061no—
514C23×C4—1061no—
515C23×C4C22×D5311yescharacteristic
516#135—1062no—
517#135—1062no—
518#135—2121no—
519#135—2121no—
520C2×Q16—531no—
521C2×Q16—531no—
522C2×SD16—531no—
523C2×SD16—531no—
524C2×SD16—531no—
525C2×SD16—531no—
526C2×D8—531no—
527C2×D8—531no—
528#131—1062no—
529#131—1062no—
530#131—1062no—
531#131—2121no—
532#131—2121no—
533#131—2121no—
534C2×M16—531no—
535C2×M16—531no—
536C2×M16—1061no—
537C2×M16—1061no—
538C2×M16—1061no—
539C2×M16—1061no—
540C2×M16—1062no—
541C2×M16—2121no—
542C2×M16C22×D5311yescharacteristic
543C2×M16C22×D5311yescharacteristic
544C22×C8—531no—
545C22×C8—531no—
546C22×C8—531no—
547C22×C8—531no—
548C22×C8—1061no—
549C22×C8—1061no—
550C22×C8—1061no—
551C22×C8—1061no—
552#123—21no—
553C22⋊Q8C4×D5311yescharacteristic
554C22⋊Q8C4×D5311yescharacteristic
555#121C4×D5311yescharacteristic
556#121C4×D5311yescharacteristic
557#120—21no—
558C4×D4—21no—
559C4×D4—21no—
560#117—22no—
561#117—41no—
562#117C22×D5311yescharacteristic
563C2×C4⋊C4—21no—
564C2×C22⋊C4—21no—
565C2×C42C22×D5311yescharacteristic
566C2×C42C22×D5311yescharacteristic
567#108—1062no—
568#108—2121no—
569C4⋊C8—1061no—
570C4⋊C8—1061no—
571#104—22no—
572#104—41no—
573#104—534no—
574#104—1062no—
575#104—1062no—
576#104—1062no—
577#103—531no—
578#103—531no—
579#103—531no—
580#103—531no—
581#102—531no—
582#102—531no—
583#102—531no—
584#102—531no—
585C22⋊C8—21no—
586C22⋊C8—21no—
587C22⋊C8—531no—
588C22⋊C8—531no—
589C22⋊C8—531no—
590C22⋊C8—531no—
591C22⋊C8—531no—
592C22⋊C8—531no—
593C22⋊C8—531no—
594C22⋊C8—531no—
595C22⋊C8—1061no—
596C22⋊C8—1061no—
597C22⋊C8—1061no—
598C22⋊C8—1061no—
599C22⋊C8—1061no—
600C22⋊C8—1061no—
601#97—1061no—
602#97—1062no—
603C4×C8—1061no—
604C4×C8—2121no—
605C24—1061no—
606C24#1171994711yescharacteristic
607#41—21no—
608#41—21no—
609#41—21no—
610#41—21no—
611#41—532no—
612#41—532no—
613#41—1062no—
614#41—1062no—
615#41—1061no—
616#41—1061no—
617#41—1061no—
618#41—1061no—
619#41—1061no—
620#41—1061no—
621#41—2122no—
622#41—2122no—
623#41—2121no—
624#41—2121no—
625#41—2122no—
626#41—2122no—
627C2×Q8—531no—
628C2×Q8—531no—
629C2×Q8—1062no—
630C2×Q8—1061no—
631C2×Q8—2121no—
632C2×Q8C2×C4×D5311yescharacteristic
633C2×D4—21no—
634C2×D4—21no—
635C2×D4—21no—
636C2×D4—531no—
637C2×D4—531no—
638C2×D4—1062no—
639C2×D4—1061no—
640C2×D4—1061no—
641C2×D4—1061no—
642C2×D4—1061no—
643C2×D4—1061no—
644C2×D4—2121no—
645C2×D4—2122no—
646C2×D4—2122no—
647C2×D4C2×C4×D5311yescharacteristic
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—1061no—
656C22×C4—1061no—
657C22×C4—1061no—
658C22×C4—1061no—
659C22×C4—1061no—
660C22×C4—2122no—
661C22×C4—2122no—
662C22×C4C2×C4×D5311yescharacteristic
663C22×C4C2×C4×D5311yescharacteristic
664C22×C4D4×D5311yescharacteristic
665C22×C4D4×D5311yescharacteristic
666C22×C4#1171994711yescharacteristic
667C22×C4C23×D5311yescharacteristic
668Q16—1062no—
669Q16—2121no—
670SD16—1062no—
671SD16—1062no—
672SD16—2121no—
673SD16—2121no—
674D8—1062no—
675D8—2121no—
676M16—21no—
677M16—21no—
678M16—21no—
679M16—21no—
680M16—532no—
681M16—1061no—
682M16—1061no—
683M16—1061no—
684M16—2122no—
685M16—2122no—
686M16—2122no—
687M16—2122no—
688C2×C8—21no—
689C2×C8—21no—
690C2×C8—531no—
691C2×C8—531no—
692C2×C8—531no—
693C2×C8—531no—
694C2×C8—531no—
695C2×C8—531no—
696C2×C8—531no—
697C2×C8—531no—
698C2×C8—1061no—
699C2×C8—1061no—
700C2×C8—1061no—
701C2×C8—1061no—
702C2×C8—1061no—
703C2×C8—1061no—
704C2×C8—1061no—
705C2×C8—1061no—
706C2×C8—1061no—
707C2×C8—1061no—
708C2×C8—2122no—
709C2×C8—2122no—
710C2×C8—2122no—
711C2×C8—2122no—
712C4⋊C4—21no—
713C4⋊C4—21no—
714C4⋊C4—42no—
715C4⋊C4C2×C4×D5311yescharacteristic
716C4⋊C4C2×C4×D5311yescharacteristic
717C22⋊C4—21no—
718C22⋊C4—21no—
719C22⋊C4—21no—
720C22⋊C4—21no—
721C22⋊C4—21no—
722C22⋊C4—42no—
723C42—21no—
724C42—21no—
725C42—21no—
726C42—21no—
727C42D4×D5312yes—
728C23—21no—
729C23—21no—
730C23—21no—
731C23—41no—
732C23—41no—
733C23—1061no—
734C23—1061no—
735C23—4241no—
736C23—2122no—
737C23—2122no—
738C23#1313317711yescharacteristic
739C23#1313317711yescharacteristic
740C23C2×#1171994711yescharacteristic
741Q8—21no—
742Q8—21no—
743Q8—532no—
744Q8—1061no—
745Q8—1061no—
746Q8—1061no—
747Q8—2122no—
748D4—21no—
749D4—21no—
750D4—42no—
751D4—41no—
752D4—41no—
753D4—81no—
754D4—532no—
755D4—1062no—
756D4—1062no—
757D4—1061no—
758D4—1061no—
759D4—1061no—
760D4—2122no—
761D4—2122no—
762D4—2122no—
763D4—2121no—
764D4—2121no—
765C2×C4—21no—
766C2×C4—21no—
767C2×C4—21no—
768C2×C4—21no—
769C2×C4—21no—
770C2×C4—21no—
771C2×C4—21no—
772C2×C4—21no—
773C2×C4—21no—
774C2×C4—21no—
775C2×C4—21no—
776C2×C4—21no—
777C2×C4—21no—
778C2×C4—22no—
779C2×C4—41no—
780C2×C4—41no—
781C2×C4—41no—
782C2×C4—41no—
783C2×C4—41no—
784C2×C4—41no—
785C2×C4—41no—
786C2×C4—1061no—
787C2×C4—1062no—
788C2×C4—1062no—
789C2×C4—1061no—
790C2×C4—2122no—
791C2×C4—2122no—
792C2×C4—2122no—
793C2×C4—2121no—
794C2×C4—2121no—
795C2×C4#1313317711yescharacteristic
796C2×C4#1313317711yescharacteristic
797C2×C4C22×C4×D5311yescharacteristic
798C2×C4C2×D4×D5311yescharacteristic
799C2×C4C2×D4×D5311yescharacteristic
800C2×C4#41×D5311yescharacteristic
801C2×C4#1313326211yescharacteristic
802C2×C4#1313326311yescharacteristic
803C8—41no—
804C8—41no—
805C8—1061no—
806C8—1061no—
807C8—1061no—
808C8—1061no—
809C8—1061no—
810C8—1061no—
811C8—1062no—
812C8—1061no—
813C8—1061no—
814C8—2121no—
815C22—21no—
816C22—21no—
817C22—21no—
818C22—21no—
819C22—21no—
820C22—21no—
821C22—21no—
822C22—21no—
823C22—41no—
824C22—41no—
825C22—41no—
826C22—81no—
827C22—81no—
828C22—1062no—
829C22—4244no—
830C22—2121no—
831C22—2121no—
832C22—2121no—
833C22—2121no—
834C22—2121no—
835C22C2×#1313317711yescharacteristic
836C22#1681126011yescharacteristic
837C22#1681129611yescharacteristic
838C4—21no—
839C4—21no—
840C4—42no—
841C4—41no—
842C4—41no—
843C4—41no—
844C4—81no—
845C4—1062no—
846C4—2121no—
847C4C4×D4×D5311yescharacteristic
848C4#1681109511yescharacteristic
849C4#1681125711yescharacteristic
850C4#1681126211yescharacteristic
851C2—21no—
852C2—21no—
853C2—41no—
854C2—41no—
855C2—81no—
856C2—4241no—
857C2—2122no—
858C2#2027769511yescharacteristic
859C2#2028361411yescharacteristic
860C2#2028362811yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D53
commutatorC2×C4×C53C23×C4
FrattiniC22×C4C23×D53
FittingC53×#1897C2
socleC22×C53C2×C4×D4
prime radical#20283931C2
cosocleC22×C4×C53C24
hypercenter#1897D53
hypocenterC53#22887
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #1897

Complements

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

NH ≅ G/Ntype
2. C2×#16810742C2semidirect
3. #20283442C2semidirect
4. C2×#16810641C2semidirect
5. #20283165C2semidirect
6. #20275600C2semidirect
7. #20275427C2semidirect
8. #20275361C2semidirect
9. #20275040C2semidirect
10. #20275039C2semidirect
11. #20274991C2semidirect
12. #20274919C2semidirect
13. #20274549C2semidirect
14. #20274481C2semidirect
15. C53×#1897C2semidirect
21. C2×#13133224C22semidirect
23. #16810783C4semidirect
24. #16810783C4semidirect
25. #16810778C4semidirect
26. #16810773C4semidirect
27. #16810766C4semidirect
28. #16810766C4semidirect
29. #16810761C4semidirect
30. #16810756C4semidirect
36. C2×#13133152C22semidirect
37. C2×#13133152C22semidirect
38. #16810650C22semidirect
48. #16810590C22semidirect
55. #16810579C22semidirect
56. C2×#13133128C22semidirect
57. C2×C4×#88322C22semidirect
58. #16810387C22semidirect
59. #16810387C22semidirect
60. #16810378C22semidirect
61. #16810378C22semidirect
64. C2×#104×C53C22semidirect
65. C2×#104×C53C22semidirect
67. C53×#339C22semidirect
68. C53×#339C22semidirect
124. #13133145D4semidirect
429. #1897D53semidirect
476. C2×#104C2×D53semidirect
477. C2×#104C2×D53semidirect
495. #339C2×D53semidirect
496. #339C2×D53semidirect
499. C53#22887semidirect

Maximal subgroups

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

subgroupindex
#202839312
C2×#168107422
#202834422
C2×#168106412
#202831652
#202756002
#202754272
#202753612
#202750402
#202750392
#202749912
#202749192
#202745492
#202744812
C53×#18972
#2288753