Finite Group Databasebeta

← #27404831

Subgroups — #27404831

Order 13568.

1058 conjugacy classes of subgroups.

The subgroup lattice has 868 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20283935C211yesmaximal, characteristic
2C2×#16810742C211yesmaximal, characteristic, complemented
3#20283443C211yesmaximal, characteristic, complemented
4C2×#104×D53C211yesmaximal, characteristic, complemented
5#20283162C211yesmaximal, characteristic, complemented
6#20275608C211yesmaximal, characteristic, complemented
7#20275427C211yesmaximal, characteristic, complemented
8#20275363C211yesmaximal, characteristic, complemented
9#20275157C211yesmaximal, characteristic, complemented
10#20275043C211yesmaximal, characteristic, complemented
11#20275042C211yesmaximal, characteristic, complemented
12#20274992C211yesmaximal, characteristic, complemented
13#20274921C211yesmaximal, characteristic, complemented
14#20274478C211yesmaximal, characteristic, complemented
15C53×#1765C211yesmaximal, characteristic, complemented
16C2×#41×D53C2211yescharacteristic
17C2×#13133239C2211yescharacteristic
18C2×#13133237C2211yescharacteristic
19C2×#13133225C2211yescharacteristic, complemented
20C2×#13133224C2211yescharacteristic
21C2×M16×D53C2211yescharacteristic
22#16811135C2211yescharacteristic
23C2×C42×D53C2211yescharacteristic
24#16810788C411yescharacteristic, complemented
25#16810786C411yescharacteristic, complemented
26#16810780C411yescharacteristic, complemented
27#16810775C411yescharacteristic, complemented
28#16810771C411yescharacteristic, complemented
29#16810769C411yescharacteristic, complemented
30#16810763C411yescharacteristic, complemented
31#16810758C411yescharacteristic, complemented
32#16810742—24no—
33#16810702—21no—
34#16810696—21no—
35#16810696—21no—
36C8×D212—21no—
37C2×#13133153C2211yescharacteristic, complemented
38C2×#13133152C2211yescharacteristic, complemented
39#16810650C2211yescharacteristic, complemented
40C2×#13133145C2211yescharacteristic
41C2×#13133145C2211yescharacteristic, complemented
42C2×#13133144C2211yescharacteristic
43C2×#13133143C2211yescharacteristic
44C2×#13133143C2211yescharacteristic, complemented
45#104×D53—24no—
46#16810617C2211yescharacteristic
47#16810591—21no—
48#16810591C2211yescharacteristic
49#16810589—21no—
50#16810589C2211yescharacteristic
51#16810589C2211yescharacteristic, complemented
52#16810586—21no—
53#16810586C2211yescharacteristic
54C2×#13133129—21no—
55C2×#13133129C2211yescharacteristic
56C2×#13133129C2211yescharacteristic
57C2×#13133128C2211yescharacteristic, complemented
58#16810387C2211yescharacteristic, complemented
59#16810382C2211yescharacteristic, complemented
60#16810377C2211yescharacteristic, complemented
61#16810377C2211yescharacteristic, complemented
62C2×#131×C53C2211yescharacteristic
63C2×#104×C53C2211yescharacteristic
64C53×#416C2211yescharacteristic
65C53×#405C2211yescharacteristic, complemented
66C2×#97×C53C2211yescharacteristic, complemented
67C53×#341C2211yescharacteristic, complemented
68C53×#339C2211yescharacteristic, complemented
69C2×#11719949C2×C411yescharacteristic
70C2×#11719945—21no—
71C2×#11719945C2311yescharacteristic
72C2×#11719945C2311yescharacteristic
73C2×#11719947—21no—
74C2×#11719947C2×C411yescharacteristic
75#41×D53—22no—
76#41×D53—22no—
77#41×D53—41no—
78#41×D53—41no—
79C2×Q8×D53C2×C411yescharacteristic
80C2×D4×D53—21no—
81C2×D4×D53C2×C411yescharacteristic
82C22×C4×D53—21no—
83C22×C4×D53—21no—
84C22×C4×D53C2311yescharacteristic
85#13133239—41no—
86#13133239—41no—
87#13133237—22no—
88#13133237—22no—
89C2×Dic212C2×C411yescharacteristic, complemented
90C2×#11719925C2×C411yescharacteristic, complemented
91C2×#11719913C2×C411yescharacteristic, complemented
92C2×#11719913C2×C411yescharacteristic, complemented
93C2×#11719923C2×C411yescharacteristic, complemented
94C2×#11719924C2×C411yescharacteristic, complemented
95C2×D424C2×C411yescharacteristic, complemented
96C2×#11719922C2×C411yescharacteristic, complemented
97#13133225—22no—
98#13133225—41no—
99#13133224—22no—
100#13133224—41no—
101C2×#11719917—21no—
102C2×#11719917C2311yescharacteristic
103C2×#11719917C2311yescharacteristic
104C2×#11719912—21no—
105C2×#11719912—21no—
106M16×D53—22no—
107M16×D53—41no—
108C22×#88322—21no—
109C22×#88322C2311yescharacteristic
110C22×#88322C2311yescharacteristic
111C2×C8×D53—21no—
112C2×C8×D53—21no—
113#13133201—21no—
114#13133197C2×C411yescharacteristic
115#13133197C2×C411yescharacteristic
116#13133192C2×C411yescharacteristic
117#13133192C2×C411yescharacteristic
118#13133187—21no—
119C4×D212—21no—
120C4×D212—21no—
121C2×C4×Dic53—21no—
122C2×C4×Dic53C2311yescharacteristic
123C42×D53—22no—
124C42×D53—41no—
125#13133153—41no—
126#13133152—22no—
127C4⋊#88322—21no—
128C4⋊#88322—21no—
129#13133145—22no—
130#13133145—22no—
131#13133144—22no—
132#13133143—22no—
133#13133143—41no—
134#13133140C2×C411yescharacteristic, complemented
135#13133140C2×C411yescharacteristic, complemented
136#13133137C2×C411yescharacteristic, complemented
137#13133137C2×C411yescharacteristic, complemented
138#13133129—21no—
139#13133129—21no—
140#13133129—21no—
141#13133129—21no—
142#13133129—21no—
143#13133129—21no—
144#13133129—21no—
145#13133129—21no—
146#13133129C2×C411yescharacteristic
147#13133129C2×C411yescharacteristic
148#13133129C2×C411yescharacteristic
149#13133129C2×C411yescharacteristic
150#13133129D411yescharacteristic
151#13133129D411yescharacteristic
152#13133129D411yescharacteristic
153#13133129D411yescharacteristic
154#13133128—22no—
155C2×#41×C53C2311yescharacteristic
156#131×C53—22no—
157#131×C53—41no—
158C2×M16×C53—21no—
159C2×M16×C53C2311yescharacteristic
160C2×M16×C53C2311yescharacteristic
161C22×C8×C53—21no—
162C22×C8×C53C2311yescharacteristic
163C22×C8×C53C2311yescharacteristic
164#117×C53C2311yescharacteristic
165C2×C42×C53C2311yescharacteristic
166#104×C53D414yescomplemented
167#103×C53C2×C411yescharacteristic, complemented
168#103×C53C2×C411yescharacteristic, complemented
169#102×C53C2×C411yescharacteristic, complemented
170#102×C53C2×C411yescharacteristic, complemented
171#97×C53—21no—
172#97×C53—41no—
173C4×C8×C53—21no—
174C23×D53—21no—
175C23×D53#4111yescharacteristic
176#41×C53—21no—
177#41×C53—21no—
178#41×C53C2×D412yes—
179#41×C53#4112yes—
180C2×Q8×C53C22×C411yescharacteristic
181C2×D4×C53—21no—
182C2×D4×C53C22×C411yescharacteristic
183C22×C4×C53—21no—
184C22×C4×C53—21no—
185C22×C4×C53C2411yescharacteristic
186C2×C22⋊D53—21no—
187C2×C22⋊D53—21no—
188C2×C22⋊D53—21no—
189C2×C22⋊D53—21no—
190C22×Dic53—21no—
191C22×Dic53—21no—
192C22×Dic53#4111yescharacteristic
193#11719949—22no—
194#11719949—41no—
195Q8×D53—22no—
196Q8×D53—41no—
197#11719947—22no—
198#11719947—41no—
199#11719947—42no—
200#11719947—42no—
201D4×D53—22no—
202D4×D53—41no—
203D4×D53—42no—
204D4×D53—42no—
205#11719945—21no—
206#11719945—21no—
207#11719945—21no—
208#11719945—21no—
209#11719945—21no—
210#11719945—21no—
211#11719945—21no—
212#11719945—21no—
213#11719945—42no—
214#11719945—42no—
215C2×D212—21no—
216C2×D212—21no—
217C2×D212—21no—
218C2×D212C22×C411yescharacteristic
219C2×D212C22×C411yescharacteristic
220C2×C4×D53—21no—
221C2×C4×D53—21no—
222C2×C4×D53—21no—
223C2×C4×D53—21no—
224C2×C4×D53—21no—
225C2×C4×D53—21no—
226C2×C4×D53—21no—
227C2×C4×D53—21no—
228C2×C4×D53—42no—
229C2×C4×D53—42no—
230C2×C4×D53—42no—
231C2×C4×D53—42no—
232C2×C4×D53—42no—
233C2×C4×D53C22×C411yescharacteristic
234C2×C4×D53C22×C411yescharacteristic
235C2×C4×D53C2×D411yescharacteristic
236C2×C4×D53C2×D411yescharacteristic
237C2×Dic106—21no—
238C2×Dic106C22×C411yescharacteristic
239C2×Dic106C22×C411yescharacteristic
240M16×C53—21no—
241M16×C53—21no—
242M16×C53—21no—
243M16×C53—42no—
244M16×C53C2×D412yes—
245C2×C8×C53—21no—
246C2×C8×C53—21no—
247C2×C8×C53—21no—
248C2×C8×C53—21no—
249C2×C8×C53—21no—
250C2×C8×C53—21no—
251C2×C8×C53—42no—
252C2×C8×C53C22×C411yescharacteristic
253C2×C8×C53C22×C411yescharacteristic
254C2×C8×C53C2×D411yescharacteristic
255C2×C8×C53C2×D411yescharacteristic
256C4⋊C4×C53C22×C411yescharacteristic
257C4⋊C4×C53C22×C411yescharacteristic
258C22⋊C4×C53—21no—
259C42×C53—21no—
260C42×C53—21no—
261C42×C53C2×D412yes—
262#11719925—22no—
263#11719924—22no—
264#11719923—22no—
265#11719922—22no—
266#11719921—21no—
267#11719921—21no—
268#11719921—21no—
269#11719921—21no—
270C4⋊Dic53—21no—
271C4⋊Dic53—21no—
272C4×Dic53—21no—
273C4×Dic53—21no—
274C4×Dic53—42no—
275#11719917—21no—
276#11719917—21no—
277#11719917—21no—
278#11719917—21no—
279#11719917—42no—
280C2×#88322—21no—
281C2×#88322—21no—
282C2×#88322—21no—
283C2×#88322—21no—
284C2×#88322—21no—
285C2×#88322—21no—
286C2×#88322—42no—
287C2×#88322C22×C411yescharacteristic
288C2×#88322C22×C411yescharacteristic
289C2×#88322C2×D411yescharacteristic
290C2×#88322C2×D411yescharacteristic
291Dic212—41no—
292D424—41no—
293#11719913—41no—
294#11719913—41no—
295#11719912—42no—
296#11719912—42no—
297C8×D53—42no—
298C8×D53—42no—
299C23×C53—21no—
300C23×C53C2×#4111yescharacteristic
301C22×D53—21no—
302C22×D53—21no—
303C22×D53—22no—
304C22×D53—21no—
305C22×D53—21no—
306C22×D53—41no—
307C22×D53—42no—
308C22×D53—42no—
309C22×D53—81no—
310C22×D53C4×D411yescharacteristic
311C22×D53C4×D411yescharacteristic
312Q8×C53—21no—
313Q8×C53C4×D412yes—
314D4×C53—22no—
315D4×C53—22no—
316D4×C53—21no—
317D4×C53C4×D412yes—
318C2×C4×C53—21no—
319C2×C4×C53—22no—
320C2×C4×C53—22no—
321C2×C4×C53—21no—
322C2×C4×C53—21no—
323C2×C4×C53—22no—
324C2×C4×C53—41no—
325C2×C4×C53—41no—
326C2×C4×C53C23×C411yescharacteristic
327C2×C4×C53C22×D411yescharacteristic
328C2×C4×C53C22×D411yescharacteristic
329C2×C4×C53C2×#4111yescharacteristic
330C2×C4×C53H(5,𝔽2)11yescharacteristic
331C2×C4×C53H(5,𝔽2)11yescharacteristic
332C22⋊D53—42no—
333C22⋊D53—42no—
334C22⋊D53—41no—
335C22⋊D53—41no—
336C22⋊D53—41no—
337C22⋊D53—41no—
338C2×Dic53—21no—
339C2×Dic53—21no—
340C2×Dic53—22no—
341C2×Dic53—21no—
342C2×Dic53—21no—
343C2×Dic53—42no—
344C2×Dic53—41no—
345C2×Dic53—41no—
346C2×Dic53C4×D411yescharacteristic
347C2×Dic53C4×D411yescharacteristic
348D212—21no—
349D212—21no—
350D212—21no—
351D212—21no—
352D212—42no—
353D212—42no—
354D212—81no—
355C4×D53—21no—
356C4×D53—21no—
357C4×D53—21no—
358C4×D53—21no—
359C4×D53—21no—
360C4×D53—21no—
361C4×D53—21no—
362C4×D53—21no—
363C4×D53—42no—
364C4×D53—42no—
365C4×D53—48no—
366C4×D53—41no—
367C4×D53—41no—
368C4×D53—41no—
369C4×D53—41no—
370Dic106—21no—
371Dic106—21no—
372Dic106—21no—
373Dic106—21no—
374Dic106—42no—
375C8×C53—21no—
376C8×C53—21no—
377C8×C53—22no—
378C8×C53—21no—
379C8×C53—21no—
380C8×C53—41no—
381#88322—21no—
382#88322—21no—
383#88322—21no—
384#88322—21no—
385#88322—41no—
386#88322—41no—
387#22886—531nomaximal, Sylow
388C22×C53—21no—
389C22×C53—21no—
390C22×C53—22no—
391C22×C53—41no—
392C22×C53—41no—
393C22×C53C2×C4×D411yescharacteristic
394C22×C53#54611yescharacteristic
395C22×C53#55111yescharacteristic
396C2×D53—21no—
397C2×D53—21no—
398C2×D53—21no—
399C2×D53—21no—
400C2×D53—21no—
401C2×D53—42no—
402C2×D53—42no—
403C2×D53—41no—
404C2×D53—41no—
405C2×D53—41no—
406C2×D53—41no—
407C2×D53—41no—
408C2×D53—41no—
409C2×D53—84no—
410C2×D53#44412yescomplemented
411C4×C53—22no—
412C4×C53—42no—
413C4×C53—41no—
414C4×C53—41no—
415C4×C53C2×C4×D411yescharacteristic
416C4×C53#51811yescharacteristic
417C4×C53D4211yescharacteristic
418C4×C53#54611yescharacteristic
419Dic53—21no—
420Dic53—21no—
421Dic53—42no—
422Dic53—41no—
423Dic53—41no—
424#3002—531no—
425C2×#444—531no—
426#2933—531no—
427C22×#104—531no—
428#2880—531no—
429#1975—531no—
430#1938—531no—
431#1929—531no—
432#1896—531no—
433#1876—531no—
434#1876—531no—
435#1866—531no—
436#1855—531no—
437#1765D5311yescharacteristic, complemented
438#1749—531no—
439C2×C53—21no—
440C2×C53—21no—
441C2×C53—42no—
442C2×C53#235811yescharacteristic
443C2×C53C2×#44411yescharacteristic
444C2×C53#295611yescharacteristic
445D53—22no—
446D53—41no—
447D53—81no—
448D53—81no—
449C22×#41—531no—
450C2×#135—531no—
451C2×#135—531no—
452C2×#131—531no—
453C2×#131—531no—
454C2×#131C2×D5311yescharacteristic
455C22×M16—531no—
456#525—531no—
457C22×C42—531no—
458#452—531no—
459#452—531no—
460#451—531no—
461#450—531no—
462#449—531no—
463#449—531no—
464#448—531no—
465#447—531no—
466#444—1064no—
467#436—1061no—
468#435—1061no—
469#435—1061no—
470C8×D4—1061no—
471C2×#108—531no—
472C2×#108—531no—
473#424—531no—
474C2×#104—531no—
475C2×#104—531no—
476C2×#104—531no—
477C2×#104—531no—
478C2×#104—531no—
479C2×#104—1064no—
480C2×#104C2×D5311yescharacteristic
481#416—531no—
482#416C2×D5311yescharacteristic
483#408—531no—
484#408—531no—
485#408—531no—
486#408—1061no—
487#408—1061no—
488#407—531no—
489#407—1061no—
490C2×C22⋊C8—531no—
491C2×C22⋊C8—531no—
492C2×C22⋊C8—1061no—
493#405C2×D5311yescharacteristic, complemented
494C2×#97—531no—
495C2×#97C2×D5311yescharacteristic, complemented
496#341—531no—
497#341C2×D5311yescharacteristic, complemented
498#339—531no—
499#339C2×D5311yescharacteristic, complemented
500#336—531no—
501#336—531no—
502C53#2288611yescharacteristic, complemented, Sylow
503C2×#41—531no—
504C2×#41—531no—
505C2×#41—531no—
506C2×#41—531no—
507C2×#41—1061no—
508C2×#41—1061no—
509C2×#41—1062no—
510C2×#41—1062no—
511C2×#41—2121no—
512C2×#41—2121no—
513C2×#41C22×D5311yescharacteristic
514C22×Q8—531no—
515C22×D4—531no—
516C22×D4—1061no—
517C23×C4—531no—
518C23×C4—1061no—
519C23×C4—1061no—
520#135—1062no—
521#135—1062no—
522#135—2121no—
523#135—2121no—
524C2×Q16—531no—
525C2×Q16—531no—
526C2×SD16—531no—
527C2×SD16—531no—
528C2×SD16—531no—
529C2×SD16—531no—
530C2×D8—531no—
531C2×D8—531no—
532#131—22no—
533#131—41no—
534#131—1062no—
535#131—1062no—
536#131—2121no—
537#131—2121no—
538C2×M16—21no—
539C2×M16—531no—
540C2×M16—531no—
541C2×M16—1061no—
542C2×M16—1061no—
543C2×M16—1061no—
544C2×M16—1062no—
545C2×M16—2121no—
546C2×M16C22×D5311yescharacteristic
547C2×M16C22×D5311yescharacteristic
548C22×C8—21no—
549C22×C8—531no—
550C22×C8—531no—
551C22×C8—1061no—
552C22×C8—1061no—
553C22×C8—1061no—
554C22×C8C22×D5311yescharacteristic
555C22×C8C22×D5311yescharacteristic
556#123—1061no—
557C22⋊Q8—531no—
558C22⋊Q8—531no—
559#121—531no—
560#121—531no—
561#120—1061no—
562C4×D4—1061no—
563C4×D4—1061no—
564#117C22×D5311yescharacteristic
565C2×C42—531no—
566C2×C42—1062no—
567C2×C42—1061no—
568C2×C42—2121no—
569C2×C42C22×D5311yescharacteristic
570#108—1062no—
571#108—2121no—
572C4⋊C8—1061no—
573C4⋊C8—1061no—
574#104—1062no—
575#104—1062no—
576#104—1062no—
577#104—1062no—
578#104—2121no—
579#104D21214yescomplemented
580#103—531no—
581#103—531no—
582#103C4×D5311yescharacteristic, complemented
583#103C4×D5311yescharacteristic, complemented
584#102—531no—
585#102—531no—
586#102C4×D5311yescharacteristic, complemented
587#102C4×D5311yescharacteristic, complemented
588C22⋊C8—531no—
589C22⋊C8—531no—
590C22⋊C8—531no—
591C22⋊C8—531no—
592C22⋊C8—531no—
593C22⋊C8—531no—
594C22⋊C8—531no—
595C22⋊C8—531no—
596C22⋊C8—1061no—
597C22⋊C8—1061no—
598C22⋊C8—1061no—
599C22⋊C8—1061no—
600C22⋊C8—1061no—
601C22⋊C8—1061no—
602C22⋊C8—1061no—
603C22⋊C8—1061no—
604#97—21no—
605#97—41no—
606#97—1062no—
607C4×C8—21no—
608C24—531no—
609C24—1061no—
610#41—21no—
611#41—21no—
612#41—1062no—
613#41—1062no—
614#41—1061no—
615#41—1061no—
616#41—1061no—
617#41—1061no—
618#41—1061no—
619#41—1061no—
620#41—1061no—
621#41—1061no—
622#41—2122no—
623#41—2122no—
624#41—2121no—
625#41—2122no—
626#41—2122no—
627#41—2121no—
628#41C2×D21212yes—
629#41#1171994512yes—
630C2×Q8—531no—
631C2×Q8—531no—
632C2×Q8—1061no—
633C2×Q8—1062no—
634C2×Q8—2121no—
635C2×Q8C2×C4×D5311yescharacteristic
636C2×D4—21no—
637C2×D4—531no—
638C2×D4—531no—
639C2×D4—1061no—
640C2×D4—1061no—
641C2×D4—1061no—
642C2×D4—1061no—
643C2×D4—1062no—
644C2×D4—1061no—
645C2×D4—1061no—
646C2×D4—1061no—
647C2×D4—2121no—
648C2×D4—2122no—
649C2×D4—2122no—
650C2×D4C2×C4×D5311yescharacteristic
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—531no—
654C22×C4—531no—
655C22×C4—531no—
656C22×C4—531no—
657C22×C4—531no—
658C22×C4—1061no—
659C22×C4—1061no—
660C22×C4—1061no—
661C22×C4—1061no—
662C22×C4—1061no—
663C22×C4—1061no—
664C22×C4—1061no—
665C22×C4—1061no—
666C22×C4—1061no—
667C22×C4—1061no—
668C22×C4—2122no—
669C22×C4—2122no—
670C22×C4—2122no—
671C22×C4—2122no—
672C22×C4—2122no—
673C22×C4C23×D5311yescharacteristic
674Q16—1062no—
675Q16—2121no—
676SD16—1062no—
677SD16—1062no—
678SD16—2121no—
679SD16—2121no—
680D8—1062no—
681D8—2121no—
682M16—21no—
683M16—21no—
684M16—21no—
685M16—42no—
686M16—1061no—
687M16—1061no—
688M16—1061no—
689M16—1061no—
690M16—2122no—
691M16—2122no—
692M16—2122no—
693M16C2×D21212yes—
694C2×C8—21no—
695C2×C8—21no—
696C2×C8—21no—
697C2×C8—21no—
698C2×C8—21no—
699C2×C8—21no—
700C2×C8—42no—
701C2×C8—531no—
702C2×C8—531no—
703C2×C8—531no—
704C2×C8—531no—
705C2×C8—1061no—
706C2×C8—1061no—
707C2×C8—1061no—
708C2×C8—1061no—
709C2×C8—1061no—
710C2×C8—1061no—
711C2×C8—2122no—
712C2×C8—2122no—
713C2×C8—2122no—
714C2×C8C2×C4×D5311yescharacteristic
715C2×C8C2×C4×D5311yescharacteristic
716C2×C8D4×D5311yescharacteristic
717C2×C8D4×D5311yescharacteristic
718C4⋊C4—1061no—
719C4⋊C4—1061no—
720C4⋊C4C2×C4×D5311yescharacteristic
721C4⋊C4C2×C4×D5311yescharacteristic
722C22⋊C4—21no—
723C22⋊C4—1061no—
724C22⋊C4—1061no—
725C22⋊C4—1061no—
726C22⋊C4—1061no—
727C42—21no—
728C42—21no—
729C42—1061no—
730C42—1061no—
731C42—2122no—
732C42C2×D21212yes—
733C23—21no—
734C23—531no—
735C23—531no—
736C23—1062no—
737C23—1061no—
738C23—1061no—
739C23—1061no—
740C23—1061no—
741C23—4241no—
742C23—2121no—
743C23—2122no—
744C23—2122no—
745C23#41×D5311yescharacteristic
746Q8—21no—
747Q8—1061no—
748Q8—1061no—
749Q8—1061no—
750Q8—1061no—
751Q8—2122no—
752Q8C4×D21212yes—
753D4—22no—
754D4—22no—
755D4—21no—
756D4—1061no—
757D4—1061no—
758D4—1061no—
759D4—1061no—
760D4—4241no—
761D4—2122no—
762D4—2122no—
763D4—2122no—
764D4—2122no—
765D4—2121no—
766D4—2121no—
767D4—2121no—
768D4—2121no—
769D4C4×D21212yes—
770C2×C4—21no—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—21no—
775C2×C4—21no—
776C2×C4—41no—
777C2×C4—41no—
778C2×C4—531no—
779C2×C4—531no—
780C2×C4—1061no—
781C2×C4—1061no—
782C2×C4—1061no—
783C2×C4—1061no—
784C2×C4—1061no—
785C2×C4—1061no—
786C2×C4—1061no—
787C2×C4—1061no—
788C2×C4—1061no—
789C2×C4—1061no—
790C2×C4—1062no—
791C2×C4—1061no—
792C2×C4—1061no—
793C2×C4—2122no—
794C2×C4—2122no—
795C2×C4—2128no—
796C2×C4—2122no—
797C2×C4—2121no—
798C2×C4—2121no—
799C2×C4—2121no—
800C2×C4—2121no—
801C2×C4—2121no—
802C2×C4—2121no—
803C2×C4C22×C4×D5311yescharacteristic
804C2×C4C2×D4×D5311yescharacteristic
805C2×C4C22×D21211yescharacteristic
806C2×C4C2×#1171994511yescharacteristic
807C2×C4#1313326211yescharacteristic
808C2×C4#1313326311yescharacteristic
809C8—21no—
810C8—21no—
811C8—22no—
812C8—21no—
813C8—21no—
814C8—41no—
815C8—1061no—
816C8—1061no—
817C8—1061no—
818C8—1061no—
819C8—2121no—
820C8—2121no—
821C22—21no—
822C22—21no—
823C22—22no—
824C22—41no—
825C22—41no—
826C22—532no—
827C22—1061no—
828C22—1061no—
829C22—1061no—
830C22—1061no—
831C22—1061no—
832C22—4244no—
833C22—2122no—
834C22—2122no—
835C22—2121no—
836C22—2121no—
837C22—2121no—
838C22—2121no—
839C22—2121no—
840C22—2121no—
841C22C4×D4×D5311yescharacteristic
842C22#1681126811yescharacteristic
843C22#1681129711yescharacteristic
844C4—22no—
845C4—42no—
846C4—41no—
847C4—41no—
848C4—1061no—
849C4—1061no—
850C4—2122no—
851C4—2121no—
852C4—2121no—
853C4C2×C4×D21211yescharacteristic
854C4#1681109511yescharacteristic
855C4D4×D21211yescharacteristic
856C4#1681126311yescharacteristic
857C2—21no—
858C2—21no—
859C2—42no—
860C2—1062no—
861C2—4241no—
862C2—4241no—
863C2—2121no—
864C2#2027769711yescharacteristic
865C2#444×D5311yescharacteristic
866C2#2028362311yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D53
commutatorC2×C4×C53C23×C4
FrattiniC22×C4C23×D53
FittingC53×#1765C2
socleC22×C53C2×C4×D4
prime radical#20283935C2
cosocleC22×C4×C53C24
hypercenter#1765D53
hypocenterC53#22886
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ #1765

Complements

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

NH ≅ G/Ntype
2. C2×#16810742C2semidirect
3. #20283443C2semidirect
4. C2×#104×D53C2semidirect
5. #20283162C2semidirect
6. #20275608C2semidirect
7. #20275427C2semidirect
8. #20275363C2semidirect
9. #20275157C2semidirect
10. #20275043C2semidirect
11. #20275042C2semidirect
12. #20274992C2semidirect
13. #20274921C2semidirect
14. #20274478C2semidirect
15. C53×#1765C2semidirect
19. C2×#13133225C22semidirect
24. #16810788C4semidirect
25. #16810786C4semidirect
26. #16810780C4semidirect
27. #16810775C4semidirect
28. #16810771C4semidirect
29. #16810769C4semidirect
30. #16810763C4semidirect
31. #16810758C4semidirect
37. C2×#13133153C22semidirect
38. C2×#13133152C22semidirect
39. #16810650C22semidirect
41. C2×#13133145C22semidirect
44. C2×#13133143C22semidirect
51. #16810589C22semidirect
57. C2×#13133128C22semidirect
58. #16810387C22semidirect
59. #16810382C22semidirect
60. #16810377C22semidirect
61. #16810377C22semidirect
65. C53×#405C22semidirect
66. C2×#97×C53C22semidirect
67. C53×#341C22semidirect
68. C53×#339C22semidirect
89. C2×Dic212C2×C4semidirect
90. C2×#11719925C2×C4semidirect
91. C2×#11719913C2×C4semidirect
92. C2×#11719913C2×C4semidirect
93. C2×#11719923C2×C4semidirect
94. C2×#11719924C2×C4semidirect
95. C2×D424C2×C4semidirect
96. C2×#11719922C2×C4semidirect
134. #13133140C2×C4semidirect
135. #13133140C2×C4semidirect
136. #13133137C2×C4semidirect
137. #13133137C2×C4semidirect
166. #104×C53D4semidirect
167. #103×C53C2×C4semidirect
168. #103×C53C2×C4semidirect
169. #102×C53C2×C4semidirect
170. #102×C53C2×C4semidirect
410. C2×D53#444semidirect
437. #1765D53semidirect
493. #405C2×D53semidirect
495. C2×#97C2×D53semidirect
497. #341C2×D53semidirect
499. #339C2×D53semidirect
502. C53#22886semidirect
579. #104D212semidirect
582. #103C4×D53semidirect
583. #103C4×D53semidirect
586. #102C4×D53semidirect
587. #102C4×D53semidirect

Maximal subgroups

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

subgroupindex
#202839352
C2×#168107422
#202834432
C2×#104×D532
#202831622
#202756082
#202754272
#202753632
#202751572
#202750432
#202750422
#202749922
#202749212
#202744782
C53×#17652
#2288653