Finite Group Databasebeta

← #27406630

Subgroups — #27406630

Order 13568.

892 conjugacy classes of subgroups.

The subgroup lattice has 768 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20284293C211yesmaximal, characteristic
2C2×#16810737C211yesmaximal, characteristic, complemented
3#20283442C211yesmaximal, characteristic, complemented
4#20283440C211yesmaximal, characteristic, complemented
5C22×#13133152C211yesmaximal, characteristic, complemented
6#20275600C211yesmaximal, characteristic, complemented
7#20275462C211yesmaximal, characteristic, complemented
8#20275366C211yesmaximal, characteristic, complemented
9#20275361C211yesmaximal, characteristic, complemented
10#20275015C211yesmaximal, characteristic, complemented
11#20274991C211yesmaximal, characteristic, complemented
12#20274988C211yesmaximal, characteristic, complemented
13#20274593C211yesmaximal, characteristic, complemented
14C22⋊C4×#88322C211yesmaximal, characteristic, complemented
15C53×#1871C211yesmaximal, characteristic, complemented
16C2×#13133237C2211yescharacteristic
17C2×#13133225C2211yescharacteristic
18C2×#13133224C2211yescharacteristic
19C22×#11719917C2211yescharacteristic
20C23×#88322C2211yescharacteristic
21#16811134C2211yescharacteristic
22#16810862C411yescharacteristic, complemented
23#16810862C411yescharacteristic, complemented
24#16810857C411yescharacteristic, complemented
25#16810857C411yescharacteristic, complemented
26#16810854C411yescharacteristic, complemented
27#16810854C411yescharacteristic, complemented
28#16810850C411yescharacteristic, complemented
29#16810850C411yescharacteristic, complemented
30#16810737—24no—
31#16810701—21no—
32#16810699—21no—
33#16810695—21no—
34#16810695—21no—
35#16810694—21no—
36#16810692—21no—
37D4×#88322—21no—
38C8×C22⋊D53—21no—
39C2×#13133152—24no—
40C2×#13133152C2211yescharacteristic
41C2×#13133152C2211yescharacteristic
42C2×#13133152C2211yescharacteristic
43C2×#13133152C2211yescharacteristic
44#16810659C2211yescharacteristic
45#16810651C2211yescharacteristic
46#16810650C2211yescharacteristic
47C2×#13133145C2211yescharacteristic
48C2×#13133145C2211yescharacteristic
49#16810619C2211yescharacteristic
50#16810617C2211yescharacteristic
51#16810591C2211yescharacteristic
52#16810590C2211yescharacteristic
53C2×C22⋊#88322C2211yescharacteristic
54#16810581C2211yescharacteristic
55#16810579C2211yescharacteristic
56C2×C4×#88322C2211yescharacteristic
57C2×C4×#88322C2211yescharacteristic
58#16810383C2211yescharacteristic
59#16810383C2211yescharacteristic
60#16810378C2211yescharacteristic
61#16810378C2211yescharacteristic
62C22×M16×C53C2211yescharacteristic
63C53×#525C2211yescharacteristic
64C2×#104×C53C2211yescharacteristic
65C2×#104×C53C2211yescharacteristic
66C4×C22⋊C4×C53C2211yescharacteristic
67C53×#339C2211yescharacteristic
68C53×#339C2211yescharacteristic
69C2×#11719945C2311yescharacteristic
70#13133237—22no—
71#13133237—22no—
72C2×#11719925C2×C411yescharacteristic
73C2×#11719923C2×C411yescharacteristic
74C2×#11719924C2×C411yescharacteristic
75C2×#11719922C2×C411yescharacteristic
76#13133225—22no—
77#13133225—41no—
78#13133224—22no—
79#13133224—41no—
80C2×#11719917—21no—
81C2×#11719917—22no—
82C2×#11719917—21no—
83C2×#11719917—41no—
84C2×#11719917C2311yescharacteristic
85C2×#11719917C2311yescharacteristic
86C2×#11719912—21no—
87C22×#88322—22no—
88C22×#88322—22no—
89C22×#88322—21no—
90C22×#88322—21no—
91C22×#88322C2×C411yescharacteristic
92C22×#88322C2×C411yescharacteristic
93C22×#88322C2×C411yescharacteristic
94C22×#88322C2×C411yescharacteristic
95C22×#88322C2311yescharacteristic
96C22×#88322C2311yescharacteristic
97C22×#88322C2311yescharacteristic
98C22×#88322C2311yescharacteristic
99C2×C8×D53—21no—
100#13133200—21no—
101#13133196C2×C411yescharacteristic
102#13133196C2×C411yescharacteristic
103#13133191C2×C411yescharacteristic
104#13133191C2×C411yescharacteristic
105#13133186—21no—
106C4×C22⋊D53—21no—
107C4×C22⋊D53—21no—
108#13133176C2311yescharacteristic
109#13133152—22no—
110#13133152—22no—
111#13133152—22no—
112#13133152D414yescomplemented
113#13133150C2×C411yescharacteristic
114#13133150C2×C411yescharacteristic
115#13133148C2×C411yescharacteristic
116#13133148C2×C411yescharacteristic
117C4⋊#88322—21no—
118C4⋊#88322—21no—
119#13133146—21no—
120#13133146—21no—
121#13133145—22no—
122#13133145—41no—
123#13133141C2×C411yescharacteristic
124#13133141C2×C411yescharacteristic
125#13133140C2×C411yescharacteristic
126#13133140C2×C411yescharacteristic
127#13133138C2×C411yescharacteristic
128#13133138C2×C411yescharacteristic
129#13133137C2×C411yescharacteristic
130#13133137C2×C411yescharacteristic
131C22⋊#88322—21no—
132C22⋊#88322—21no—
133C22⋊#88322D411yescharacteristic
134C22⋊#88322D411yescharacteristic
135C22⋊#88322D411yescharacteristic
136C22⋊#88322D411yescharacteristic
137#13133129—21no—
138#13133129—21no—
139#13133128—21no—
140#13133127—21no—
141C4×#88322—22no—
142C4×#88322—21no—
143C4×#88322—22no—
144C8×Dic53—21no—
145C2×#41×C53C2311yescharacteristic
146C23×C4×C53C2311yescharacteristic
147C2×M16×C53—22no—
148C2×M16×C53—21no—
149C2×M16×C53—41no—
150C2×M16×C53C2311yescharacteristic
151C2×M16×C53C2311yescharacteristic
152C22×C8×C53—21no—
153#123×C53—21no—
154C22⋊Q8×C53C2×C411yescharacteristic
155C22⋊Q8×C53C2×C411yescharacteristic
156#121×C53C2×C411yescharacteristic
157#121×C53C2×C411yescharacteristic
158#120×C53—21no—
159C4×D4×C53—21no—
160C4×D4×C53—21no—
161#117×C53C2311yescharacteristic
162C2×C22⋊C4×C53—21no—
163C2×C42×C53C2311yescharacteristic
164C2×C42×C53C2311yescharacteristic
165#104×C53—22no—
166#104×C53—41no—
167#95×C53—21no—
168C24×C53#4111yescharacteristic
169#41×C53—21no—
170#41×C53—21no—
171#41×C53—21no—
172#41×C53—21no—
173C2×Q8×C53C22×C411yescharacteristic
174C2×D4×C53—21no—
175C2×D4×C53—21no—
176C2×D4×C53—21no—
177C2×D4×C53C22×C411yescharacteristic
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×C53C22×C411yescharacteristic
186C22×C4×C53C22×C411yescharacteristic
187C22×C4×C53C2×D411yescharacteristic
188C22×C4×C53C2×D411yescharacteristic
189C22×C4×C53#4111yescharacteristic
190C22×C4×C53C2411yescharacteristic
191C2×C22⋊D53—21no—
192C2×C22⋊D53—21no—
193C2×C22⋊D53—21no—
194#11719945—21no—
195#11719945—21no—
196#11719945—21no—
197#11719945—21no—
198C2×D212C22×C411yescharacteristic
199C2×C4×D53—21no—
200C2×Dic106C22×C411yescharacteristic
201M16×C53—21no—
202M16×C53—21no—
203M16×C53—21no—
204M16×C53—42no—
205M16×C53C2×D412yes—
206C2×C8×C53—21no—
207C2×C8×C53—21no—
208C2×C8×C53—42no—
209C4⋊C4×C53—21no—
210C4⋊C4×C53—21no—
211C4⋊C4×C53C22×C411yescharacteristic
212C4⋊C4×C53C22×C411yescharacteristic
213C22⋊C4×C53—24no—
214C22⋊C4×C53—21no—
215C22⋊C4×C53—21no—
216C22⋊C4×C53—21no—
217C22⋊C4×C53—21no—
218C22⋊C4×C53—21no—
219C42×C53—21no—
220C42×C53—21no—
221C42×C53—21no—
222C42×C53—21no—
223C42×C53—21no—
224C22⋊Dic53—21no—
225C22⋊Dic53—21no—
226C22⋊Dic53—21no—
227#11719925—22no—
228#11719924—22no—
229#11719923—22no—
230#11719922—22no—
231#11719921—21no—
232#11719921—21no—
233C4⋊Dic53C22×C411yescharacteristic
234C4⋊Dic53C22×C411yescharacteristic
235#11719919—21no—
236#11719919—21no—
237C4×Dic53—21no—
238#11719917—21no—
239#11719917—21no—
240#11719917—21no—
241#11719917—42no—
242#11719917—42no—
243#11719917C2×D412yes—
244C2×#88322—21no—
245C2×#88322—21no—
246C2×#88322—21no—
247C2×#88322—21no—
248C2×#88322—21no—
249C2×#88322—21no—
250C2×#88322—21no—
251C2×#88322—22no—
252C2×#88322—22no—
253C2×#88322—22no—
254C2×#88322—22no—
255C2×#88322—21no—
256C2×#88322—42no—
257C2×#88322—42no—
258C2×#88322C22×C411yescharacteristic
259C2×#88322C22×C411yescharacteristic
260C2×#88322C22×C411yescharacteristic
261C2×#88322C22×C411yescharacteristic
262C2×#88322C2×D411yescharacteristic
263C2×#88322C2×D411yescharacteristic
264C2×#88322C2×D411yescharacteristic
265C2×#88322C2×D411yescharacteristic
266C2×#88322C2×D412yes—
267C2×#88322#4112yes—
268#11719912—42no—
269C8×D53—42no—
270C23×C53—21no—
271C23×C53—21no—
272C23×C53—22no—
273C23×C53—21no—
274C23×C53—41no—
275C23×C53C4×D411yescharacteristic
276C23×C53C4×D411yescharacteristic
277C23×C53C2×#4111yescharacteristic
278C22×D53—21no—
279Q8×C53—21no—
280Q8×C53—21no—
281D4×C53—21no—
282D4×C53—21no—
283D4×C53—41no—
284D4×C53—41no—
285D4×C53—42no—
286D4×C53—81no—
287C2×C4×C53—21no—
288C2×C4×C53—21no—
289C2×C4×C53—21no—
290C2×C4×C53—21no—
291C2×C4×C53—21no—
292C2×C4×C53—21no—
293C2×C4×C53—21no—
294C2×C4×C53—21no—
295C2×C4×C53—21no—
296C2×C4×C53—21no—
297C2×C4×C53—22no—
298C2×C4×C53—22no—
299C2×C4×C53—21no—
300C2×C4×C53—21no—
301C2×C4×C53—21no—
302C2×C4×C53—41no—
303C2×C4×C53—41no—
304C2×C4×C53—41no—
305C2×C4×C53—41no—
306C2×C4×C53—41no—
307C2×C4×C53—41no—
308C2×C4×C53C4×D411yescharacteristic
309C2×C4×C53C4×D411yescharacteristic
310C2×C4×C53C23×C411yescharacteristic
311C2×C4×C53C22×D411yescharacteristic
312C2×C4×C53C22×D411yescharacteristic
313C2×C4×C53C2×#4111yescharacteristic
314C2×C4×C53H(5,𝔽2)11yescharacteristic
315C2×C4×C532−1+411yescharacteristic
316C22⋊D53—41no—
317C22⋊D53—41no—
318C22⋊D53—42no—
319C22⋊D53—81no—
320C2×Dic53—21no—
321C2×Dic53—21no—
322C2×Dic53—21no—
323D212—21no—
324D212—21no—
325C4×D53—41no—
326C4×D53—41no—
327Dic106—21no—
328Dic106—21no—
329C8×C53—22no—
330C8×C53—41no—
331#88322—21no—
332#88322—21no—
333#88322—21no—
334#88322—21no—
335#88322—22no—
336#88322—21no—
337#88322—21no—
338#88322—41no—
339#88322C4×D412yes—
340#88322C4×D412yes—
341#23018—531nomaximal, Sylow
342C22×C53—21no—
343C22×C53—21no—
344C22×C53—21no—
345C22×C53—21no—
346C22×C53—21no—
347C22×C53—21no—
348C22×C53—21no—
349C22×C53—42no—
350C22×C53—42no—
351C22×C53—41no—
352C22×C53—41no—
353C22×C53—41no—
354C22×C53#44312yescomplemented
355C22×C53C2×C4×D411yescharacteristic
356C22×C53#54811yescharacteristic
357C22×C53#55311yescharacteristic
358C2×D53—41no—
359C2×D53—41no—
360C2×D53—41no—
361C4×C53—21no—
362C4×C53—21no—
363C4×C53—42no—
364C4×C53—42no—
365C4×C53—41no—
366C4×C53—41no—
367C4×C53—41no—
368C4×C53C2×C4×D411yescharacteristic
369C4×C53#52011yescharacteristic
370C4×C53D4211yescharacteristic
371C4×C53#54711yescharacteristic
372Dic53—41no—
373Dic53—41no—
374Dic53—41no—
375#3050—531no—
376C2×#443—531no—
377#2933—531no—
378#2933—531no—
379C22×#108—531no—
380#1974—531no—
381#1945—531no—
382#1929—531no—
383#1929—531no—
384#1871—531no—
385#1871D5311yescharacteristic, complemented
386#1866—531no—
387#1866—531no—
388#1772—531no—
389C8×C22⋊C4—531no—
390C2×C53—21no—
391C2×C53—21no—
392C2×C53—22no—
393C2×C53—41no—
394C2×C53—81no—
395C2×C53#236111yescharacteristic
396C2×C53C2×#44311yescharacteristic
397C2×C53#295711yescharacteristic
398D53—81no—
399C2×#135—531no—
400C2×#131—531no—
401C2×#131—531no—
402C22×M16—531no—
403C22×M16C2×D5311yescharacteristic
404C23×C8—531no—
405#525—531no—
406#525C2×D5311yescharacteristic
407#467—531no—
408#467—531no—
409#466—531no—
410#466—531no—
411#465—531no—
412#465—531no—
413#465—531no—
414#465—531no—
415#443—1064no—
416#436—1061no—
417#436—1061no—
418#435—1061no—
419#435—1061no—
420#435—1061no—
421#435—1061no—
422C8×D4—1061no—
423C8×D4—1061no—
424C2×#108—531no—
425C2×#108—531no—
426C2×#108—531no—
427C2×#108—531no—
428C2×#108—1064no—
429#427—531no—
430#424—531no—
431#424—531no—
432C2×#104—531no—
433C2×#104—531no—
434C2×#104C2×D5311yescharacteristic
435C2×#104C2×D5311yescharacteristic
436#416—531no—
437#416—531no—
438#408—531no—
439#408—531no—
440C2×C22⋊C8—531no—
441#405—531no—
442#405—531no—
443C2×C4×C8—531no—
444C2×C4×C8—531no—
445C4×C22⋊C4C2×D5311yescharacteristic
446#339—531no—
447#339—531no—
448#339C2×D5311yescharacteristic
449#339C2×D5311yescharacteristic
450#336—531no—
451#336—531no—
452C53#2301811yescharacteristic, complemented, Sylow
453C2×#41—531no—
454C2×#41C22×D5311yescharacteristic
455C23×C4C22×D5311yescharacteristic
456#135—1062no—
457#135—1062no—
458C2×Q16—531no—
459C2×SD16—531no—
460C2×SD16—531no—
461C2×D8—531no—
462#131—1062no—
463#131—1062no—
464#131—2121no—
465#131—2121no—
466C2×M16—21no—
467C2×M16—22no—
468C2×M16—41no—
469C2×M16—531no—
470C2×M16—531no—
471C2×M16—1061no—
472C2×M16—1061no—
473C2×M16—1061no—
474C2×M16—1062no—
475C2×M16—2121no—
476C2×M16C22×D5311yescharacteristic
477C2×M16C22×D5311yescharacteristic
478C22×C8—21no—
479C22×C8—531no—
480C22×C8—531no—
481C22×C8—531no—
482C22×C8—531no—
483C22×C8—531no—
484C22×C8—531no—
485C22×C8—531no—
486C22×C8—531no—
487C22×C8—1061no—
488C22×C8—1062no—
489C22×C8—1062no—
490C22×C8—1061no—
491C22×C8—1061no—
492#123—21no—
493#123—1061no—
494C22⋊Q8—531no—
495C22⋊Q8—531no—
496C22⋊Q8C4×D5311yescharacteristic
497C22⋊Q8C4×D5311yescharacteristic
498#121—531no—
499#121—531no—
500#121C4×D5311yescharacteristic
501#121C4×D5311yescharacteristic
502#120—21no—
503#120—1061no—
504C4×D4—21no—
505C4×D4—21no—
506C4×D4—1061no—
507C4×D4—1061no—
508#117—531no—
509#117C22×D5311yescharacteristic
510C2×C22⋊C4—21no—
511C2×C42C22×D5311yescharacteristic
512C2×C42C22×D5311yescharacteristic
513#108—534no—
514#108—1062no—
515#108—1062no—
516#108—1062no—
517#107—531no—
518#107—531no—
519#106—531no—
520#106—531no—
521C4⋊C8—1061no—
522C4⋊C8—1061no—
523C4⋊C8—1061no—
524C4⋊C8—1061no—
525#104—22no—
526#104—41no—
527#104—1062no—
528#104—2121no—
529#103—531no—
530#103—531no—
531#103—531no—
532#103—531no—
533#102—531no—
534#102—531no—
535#102—531no—
536#102—531no—
537C22⋊C8—531no—
538C22⋊C8—531no—
539C22⋊C8—531no—
540C22⋊C8—531no—
541C22⋊C8—1061no—
542C22⋊C8—1061no—
543C22⋊C8—1061no—
544C22⋊C8—1061no—
545#97—1061no—
546#97—1061no—
547C4×C8—1062no—
548C4×C8—1062no—
549C4×C8—1061no—
550C4×C8—1061no—
551#95—21no—
552C24#1171994711yescharacteristic
553#41—21no—
554#41—21no—
555#41—21no—
556#41—21no—
557#41—1061no—
558#41—1061no—
559#41—1061no—
560#41—1061no—
561C2×Q8—531no—
562C2×Q8C2×C4×D5311yescharacteristic
563C2×D4—21no—
564C2×D4—21no—
565C2×D4—21no—
566C2×D4—531no—
567C2×D4—1061no—
568C2×D4—1061no—
569C2×D4—1061no—
570C2×D4C2×C4×D5311yescharacteristic
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—1061no—
579C22×C4C2×C4×D5311yescharacteristic
580C22×C4C2×C4×D5311yescharacteristic
581C22×C4D4×D5311yescharacteristic
582C22×C4D4×D5311yescharacteristic
583C22×C4#1171994711yescharacteristic
584C22×C4C23×D5311yescharacteristic
585Q16—1062no—
586SD16—1062no—
587SD16—1062no—
588D8—1062no—
589M16—21no—
590M16—21no—
591M16—21no—
592M16—42no—
593M16—532no—
594M16—1061no—
595M16—1061no—
596M16—1061no—
597M16—2122no—
598M16—2122no—
599M16—2122no—
600M16D4×D5312yes—
601C2×C8—21no—
602C2×C8—21no—
603C2×C8—42no—
604C2×C8—531no—
605C2×C8—531no—
606C2×C8—532no—
607C2×C8—532no—
608C2×C8—531no—
609C2×C8—531no—
610C2×C8—531no—
611C2×C8—531no—
612C2×C8—531no—
613C2×C8—531no—
614C2×C8—1062no—
615C2×C8—1062no—
616C2×C8—1062no—
617C2×C8—1062no—
618C2×C8—1061no—
619C2×C8—1061no—
620C2×C8—1061no—
621C2×C8—1061no—
622C2×C8—1061no—
623C2×C8—1061no—
624C2×C8—1061no—
625C2×C8—1061no—
626C2×C8—2122no—
627C2×C8—2122no—
628C2×C8—2122no—
629C4⋊C4—21no—
630C4⋊C4—21no—
631C4⋊C4—531no—
632C4⋊C4—531no—
633C4⋊C4—1061no—
634C4⋊C4—1061no—
635C4⋊C4C2×C4×D5311yescharacteristic
636C4⋊C4C2×C4×D5311yescharacteristic
637C22⋊C4—24no—
638C22⋊C4—21no—
639C22⋊C4—21no—
640C22⋊C4—21no—
641C22⋊C4—21no—
642C22⋊C4—21no—
643C22⋊C4—1061no—
644C22⋊C4—1061no—
645C22⋊C4—1061no—
646C22⋊C4—1061no—
647C22⋊C4—1061no—
648C42—21no—
649C42—21no—
650C42—21no—
651C42—21no—
652C42—21no—
653C42—1061no—
654C23—21no—
655C23—21no—
656C23—22no—
657C23—21no—
658C23—41no—
659C23—1061no—
660C23#1313317711yescharacteristic
661C23#1313317711yescharacteristic
662C23C2×#1171994711yescharacteristic
663Q8—21no—
664Q8—21no—
665Q8—1061no—
666Q8—1061no—
667D4—21no—
668D4—21no—
669D4—41no—
670D4—41no—
671D4—42no—
672D4—81no—
673D4—1061no—
674D4—1061no—
675D4—4241no—
676D4—2121no—
677D4—2121no—
678D4—2122no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—21no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—21no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—21no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—1061no—
701C2×C4—1061no—
702C2×C4—1061no—
703C2×C4—2121no—
704C2×C4—2121no—
705C2×C4#1313317711yescharacteristic
706C2×C4#1313317711yescharacteristic
707C2×C4C22×C4×D5311yescharacteristic
708C2×C4C2×D4×D5311yescharacteristic
709C2×C4C2×D4×D5311yescharacteristic
710C2×C4#41×D5311yescharacteristic
711C2×C4#1313326211yescharacteristic
712C2×C4#1313326411yescharacteristic
713C8—22no—
714C8—41no—
715C8—532no—
716C8—532no—
717C8—1061no—
718C8—1061no—
719C8—1061no—
720C8—1061no—
721C8—1061no—
722C8—1061no—
723C8—1062no—
724C8—2121no—
725C22—21no—
726C22—21no—
727C22—21no—
728C22—21no—
729C22—21no—
730C22—21no—
731C22—21no—
732C22—42no—
733C22—42no—
734C22—41no—
735C22—41no—
736C22—41no—
737C22—2121no—
738C22—2121no—
739C22—2121no—
740C22#1681073712yescomplemented
741C22C2×#1313317711yescharacteristic
742C22#1681127911yescharacteristic
743C22#1681131611yescharacteristic
744C4—21no—
745C4—21no—
746C4—42no—
747C4—42no—
748C4—41no—
749C4—41no—
750C4—41no—
751C4—2121no—
752C4—2121no—
753C4—2121no—
754C4C4×D4×D5311yescharacteristic
755C4#1681110211yescharacteristic
756C4#1681125511yescharacteristic
757C4#1681127111yescharacteristic
758C2—21no—
759C2—21no—
760C2—22no—
761C2—41no—
762C2—81no—
763C2—4241no—
764C2#2027772611yescharacteristic
765C2C2×#1681073711yescharacteristic
766C2#2028362811yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D53
commutatorC2×C4×C53C23×C4
FrattiniC22×C4C23×D53
FittingC53×#1871C2
socleC22×C53C2×C4×D4
prime radical#20284293C2
cosocleC22×C4×C53C24
hypercenter#1871D53
hypocenterC53#23018
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #1871

Complements

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

NH ≅ G/Ntype
2. C2×#16810737C2semidirect
3. #20283442C2semidirect
4. #20283440C2semidirect
5. C22×#13133152C2semidirect
6. #20275600C2semidirect
7. #20275462C2semidirect
8. #20275366C2semidirect
9. #20275361C2semidirect
10. #20275015C2semidirect
11. #20274991C2semidirect
12. #20274988C2semidirect
13. #20274593C2semidirect
14. C22⋊C4×#88322C2semidirect
15. C53×#1871C2semidirect
22. #16810862C4semidirect
23. #16810862C4semidirect
24. #16810857C4semidirect
25. #16810857C4semidirect
26. #16810854C4semidirect
27. #16810854C4semidirect
28. #16810850C4semidirect
29. #16810850C4semidirect
112. #13133152D4semidirect
354. C22×C53#443semidirect
385. #1871D53semidirect
452. C53#23018semidirect
740. C22#16810737semidirect

Maximal subgroups

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

subgroupindex
#202842932
C2×#168107372
#202834422
#202834402
C22×#131331522
#202756002
#202754622
#202753662
#202753612
#202750152
#202749912
#202749882
#202745932
C22⋊C4×#883222
C53×#18712
#2301853