Finite Group Databasebeta

← #27401463

Subgroups — #27401463

Order 13568.

888 conjugacy classes of subgroups.

The subgroup lattice has 790 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20283373C211yesmaximal, characteristic, complemented
2#20283164C211yesmaximal, characteristic
3#20275428C211yesmaximal, characteristic, complemented
4#20275421C211yesmaximal, characteristic, complemented
5#20275365C211yesmaximal, characteristic, complemented
6#20275365C211yesmaximal, characteristic, complemented
7#20274992C211yesmaximal, characteristic, complemented
8#20274992C211yesmaximal, characteristic, complemented
9#20274814C211yesmaximal, characteristic, complemented
10#20274757C211yesmaximal, characteristic, complemented
11#20274659C211yesmaximal, characteristic
12#20274562C211yesmaximal, characteristic, complemented
13#20274555C211yesmaximal, characteristic, complemented
14#20274496C211yesmaximal, characteristic, complemented
15C53×#2896C211yesmaximal, characteristic
16C2×#13133224C2211yescharacteristic
17C2×#13133224C2211yescharacteristic
18#16810684—21no—
19#16810684—21no—
20#16810680—21no—
21#16810676—21no—
22C2×#13133153C2211yescharacteristic, complemented
23C2×#13133153C2211yescharacteristic, complemented
24#16810650C2211yescharacteristic, complemented
25#16810650C2211yescharacteristic, complemented
26C2×#13133144C2211yescharacteristic
27C2×#13133144C2211yescharacteristic
28C2×#13133144C2211yescharacteristic
29C2×#13133144C2211yescharacteristic
30#16810590—21no—
31#16810590—21no—
32#16810590C2211yescharacteristic
33#16810590C2211yescharacteristic
34#16810587—21no—
35#16810587C2211yescharacteristic
36#16810587C2211yescharacteristic
37C2×C22⋊#88322—21no—
38C2×C22⋊#88322C2211yescharacteristic
39#16810579C2211yescharacteristic, complemented
40#16810579C2211yescharacteristic, complemented
41C2×#13133127C2211yescharacteristic, complemented
42C2×C8×Dic53C2211yescharacteristic, complemented
43C4×C22⋊Dic53C2211yescharacteristic
44#16810388C2211yescharacteristic, complemented
45#16810388C2211yescharacteristic, complemented
46#16810382C2211yescharacteristic, complemented
47#16810382C2211yescharacteristic, complemented
48#16810382C2211yescharacteristic, complemented
49#16810382C2211yescharacteristic, complemented
50#16810377C2211yescharacteristic, complemented
51#16810377C2211yescharacteristic, complemented
52C22×#41×C53C2211yescharacteristic
53C22×M16×C53C2211yescharacteristic
54C2×#117×C53C2211yescharacteristic
55C53×#419C411yescharacteristic, complemented
56C53×#419C411yescharacteristic, complemented
57C53×#418C411yescharacteristic, complemented
58C53×#418C411yescharacteristic, complemented
59C53×#417C411yescharacteristic, complemented
60C53×#417C411yescharacteristic, complemented
61C53×#417C411yescharacteristic, complemented
62C53×#417C411yescharacteristic, complemented
63C53×#416C2211yescharacteristic
64C53×#416C2211yescharacteristic
65C53×#416C2211yescharacteristic
66C53×#416C2211yescharacteristic
67#13133224—22no—
68#13133224—22no—
69#13133224—41no—
70#13133224—41no—
71C2×#11719917—21no—
72C2×#11719917—21no—
73C2×#11719917C2311yescharacteristic
74C2×#11719917C2311yescharacteristic
75C2×#11719917C2311yescharacteristic
76C2×#11719917C2311yescharacteristic
77C22×#88322—21no—
78C22×#88322—21no—
79C22×#88322C2311yescharacteristic
80C22×#88322C2311yescharacteristic
81C2×C22⋊Dic53—21no—
82C2×C4×Dic53C2311yescharacteristic
83C2×C4×Dic53C2311yescharacteristic
84#13133153—41no—
85#13133153—41no—
86C4⋊#88322—21no—
87C4⋊#88322—21no—
88C4⋊#88322—21no—
89C4⋊#88322—21no—
90#13133144—22no—
91#13133144—22no—
92#13133144—41no—
93#13133144—41no—
94C22⋊#88322—21no—
95C22⋊#88322—21no—
96C22⋊#88322—21no—
97C22⋊#88322—21no—
98C22⋊#88322—21no—
99C22⋊#88322—21no—
100C22⋊#88322—21no—
101C22⋊#88322—21no—
102C22⋊#88322D411yescharacteristic
103C22⋊#88322D411yescharacteristic
104C22⋊#88322D411yescharacteristic
105C22⋊#88322D411yescharacteristic
106#13133128—21no—
107#13133128—21no—
108#13133127—41no—
109C4×#88322—21no—
110C4×#88322—21no—
111C8×Dic53—41no—
112#13133124—21no—
113C2×#41×C53—21no—
114C2×#41×C53—21no—
115C2×#41×C53—22no—
116C2×#41×C53—22no—
117C2×#41×C53—41no—
118C2×#41×C53—41no—
119C2×#41×C53C2×C411yescharacteristic
120C2×#41×C53C2×C411yescharacteristic
121C2×#41×C53C2311yescharacteristic
122C2×#41×C53C2311yescharacteristic
123C22×Q8×C53C2×C411yescharacteristic
124C22×D4×C53—21no—
125C22×D4×C53C2×C411yescharacteristic
126C23×C4×C53—21no—
127C23×C4×C53C2311yescharacteristic
128C2×M16×C53—41no—
129C2×M16×C53—41no—
130C2×M16×C53C2×C411yescharacteristic
131C2×M16×C53C2×C411yescharacteristic
132C2×M16×C53C2×C411yescharacteristic
133C2×M16×C53C2×C411yescharacteristic
134C22×C8×C53C2311yescharacteristic
135C22×C8×C53C2311yescharacteristic
136#117×C53—21no—
137#117×C53—21no—
138#117×C53C2×C411yescharacteristic
139#117×C53C2×C411yescharacteristic
140#117×C53C2311yescharacteristic
141#117×C53C2311yescharacteristic
142C2×C4⋊C4×C53C2×C411yescharacteristic
143C2×C4⋊C4×C53C2×C411yescharacteristic
144C2×C22⋊C4×C53—21no—
145C2×C42×C53—21no—
146#103×C53C2×C411yescharacteristic
147#103×C53C2×C411yescharacteristic
148#103×C53C2×C411yescharacteristic
149#103×C53C2×C411yescharacteristic
150#103×C53C2×C411yescharacteristic
151#103×C53C2×C411yescharacteristic
152#103×C53C2×C411yescharacteristic
153#103×C53C2×C411yescharacteristic
154#102×C53C2×C411yescharacteristic
155#102×C53C2×C411yescharacteristic
156#102×C53C2×C411yescharacteristic
157#102×C53C2×C411yescharacteristic
158#102×C53C2×C411yescharacteristic
159#102×C53C2×C411yescharacteristic
160#102×C53C2×C411yescharacteristic
161#102×C53C2×C411yescharacteristic
162C24×C53—21no—
163C24×C53#4111yescharacteristic
164#41×C53—21no—
165#41×C53—21no—
166#41×C53—22no—
167#41×C53—22no—
168#41×C53—21no—
169#41×C53—21no—
170#41×C53—21no—
171#41×C53—21no—
172#41×C53—42no—
173#41×C53—42no—
174#41×C53—41no—
175#41×C53—41no—
176#41×C53—42no—
177#41×C53—42no—
178#41×C53#4112yes—
179#41×C53#4112yes—
180C2×Q8×C53—21no—
181C2×Q8×C53—22no—
182C2×Q8×C53—41no—
183C2×Q8×C53C22×C411yescharacteristic
184C2×Q8×C53C22×C411yescharacteristic
185C2×D4×C53—21no—
186C2×D4×C53—22no—
187C2×D4×C53—21no—
188C2×D4×C53—21no—
189C2×D4×C53—21no—
190C2×D4×C53—21no—
191C2×D4×C53—41no—
192C2×D4×C53—42no—
193C2×D4×C53—42no—
194C2×D4×C53C22×C411yescharacteristic
195C2×D4×C53C22×C411yescharacteristic
196C22×C4×C53—21no—
197C22×C4×C53—21no—
198C22×C4×C53—21no—
199C22×C4×C53—21no—
200C22×C4×C53—21no—
201C22×C4×C53—21no—
202C22×C4×C53—21no—
203C22×C4×C53—21no—
204C22×C4×C53—21no—
205C22×C4×C53—21no—
206C22×C4×C53—21no—
207C22×C4×C53—42no—
208C22×C4×C53—42no—
209C22×C4×C53C22×C411yescharacteristic
210C22×C4×C53C22×C411yescharacteristic
211C22×C4×C53C2×D411yescharacteristic
212C22×C4×C53C2×D411yescharacteristic
213C22×C4×C53#4111yescharacteristic
214C22×C4×C53C2411yescharacteristic
215C22×Dic53—21no—
216C22×Dic53—21no—
217M16×C53—41no—
218M16×C53—41no—
219M16×C53—41no—
220M16×C53—41no—
221C2×C8×C53—21no—
222C2×C8×C53—21no—
223C2×C8×C53—21no—
224C2×C8×C53—21no—
225C2×C8×C53C22×C411yescharacteristic
226C2×C8×C53C22×C411yescharacteristic
227C2×C8×C53C22×C411yescharacteristic
228C2×C8×C53C22×C411yescharacteristic
229C4⋊C4×C53—21no—
230C4⋊C4×C53—21no—
231C4⋊C4×C53C22×C411yescharacteristic
232C4⋊C4×C53C22×C411yescharacteristic
233C4⋊C4×C53C22×C411yescharacteristic
234C4⋊C4×C53C22×C411yescharacteristic
235C22⋊C4×C53—21no—
236C22⋊C4×C53—21no—
237C22⋊C4×C53—21no—
238C22⋊C4×C53—21no—
239C42×C53—21no—
240C42×C53—21no—
241C42×C53—21no—
242C42×C53—21no—
243C22⋊Dic53—42no—
244C4×Dic53—21no—
245C4×Dic53—21no—
246C4×Dic53—21no—
247C4×Dic53—21no—
248#11719917—21no—
249#11719917—21no—
250#11719917—21no—
251#11719917—21no—
252#11719917—21no—
253#11719917—21no—
254#11719917—21no—
255#11719917—21no—
256#11719917—42no—
257#11719917—42no—
258C2×#88322—21no—
259C2×#88322—21no—
260C2×#88322—21no—
261C2×#88322—21no—
262C2×#88322—21no—
263C2×#88322—21no—
264C2×#88322—21no—
265C2×#88322—21no—
266C2×#88322—42no—
267C2×#88322—42no—
268C2×#88322C2×D411yescharacteristic
269C2×#88322C2×D411yescharacteristic
270C2×#88322C2×D411yescharacteristic
271C2×#88322C2×D411yescharacteristic
272C23×C53—21no—
273C23×C53—21no—
274C23×C53—21no—
275C23×C53—21no—
276C23×C53—41no—
277C23×C53—41no—
278C23×C53—42no—
279C23×C53—42no—
280C23×C53—81no—
281C23×C53C4×D411yescharacteristic
282C23×C53C4×D411yescharacteristic
283C23×C53C2×#4111yescharacteristic
284Q8×C53—21no—
285Q8×C53—21no—
286Q8×C53—21no—
287Q8×C53—42no—
288Q8×C53#11712yes—
289D4×C53—22no—
290D4×C53—22no—
291D4×C53—21no—
292D4×C53—21no—
293D4×C53—21no—
294D4×C53—42no—
295D4×C53—42no—
296D4×C53—42no—
297D4×C53—41no—
298D4×C53—41no—
299D4×C53#11712yes—
300C2×C4×C53—21no—
301C2×C4×C53—21no—
302C2×C4×C53—21no—
303C2×C4×C53—21no—
304C2×C4×C53—21no—
305C2×C4×C53—21no—
306C2×C4×C53—21no—
307C2×C4×C53—21no—
308C2×C4×C53—21no—
309C2×C4×C53—21no—
310C2×C4×C53—21no—
311C2×C4×C53—22no—
312C2×C4×C53—22no—
313C2×C4×C53—21no—
314C2×C4×C53—21no—
315C2×C4×C53—21no—
316C2×C4×C53—21no—
317C2×C4×C53—21no—
318C2×C4×C53—42no—
319C2×C4×C53—42no—
320C2×C4×C53—42no—
321C2×C4×C53—42no—
322C2×C4×C53—41no—
323C2×C4×C53—41no—
324C2×C4×C53—81no—
325C2×C4×C53C4×D411yescharacteristic
326C2×C4×C53C4×D411yescharacteristic
327C2×C4×C53C23×C411yescharacteristic
328C2×C4×C53C22×D411yescharacteristic
329C2×C4×C53C2×#4111yescharacteristic
330C2×C4×C53C2×#4111yescharacteristic
331C2×C4×C53H(5,𝔽2)11yescharacteristic
332C2×C4×C53H(5,𝔽2)11yescharacteristic
333C2×Dic53—22no—
334C2×Dic53—41no—
335C2×Dic53—41no—
336C2×Dic53—41no—
337C2×Dic53—41no—
338C2×Dic53—41no—
339C8×C53—21no—
340C8×C53—21no—
341C8×C53—21no—
342C8×C53—21no—
343#88322—21no—
344#88322—21no—
345#88322—21no—
346#88322—21no—
347#88322—41no—
348#88322—41no—
349#88322—41no—
350#88322—41no—
351#22588—531nomaximal, Sylow
352C22×C53—21no—
353C22×C53—21no—
354C22×C53—21no—
355C22×C53—21no—
356C22×C53—22no—
357C22×C53—21no—
358C22×C53—21no—
359C22×C53—21no—
360C22×C53—21no—
361C22×C53—41no—
362C22×C53—41no—
363C22×C53—41no—
364C22×C53—41no—
365C22×C53—41no—
366C22×C53—81no—
367C22×C53—81no—
368C22×C53—84no—
369C22×C53C2×C4×D411yescharacteristic
370C22×C53#55111yescharacteristic
371C22×C53#55111yescharacteristic
372C4×C53—21no—
373C4×C53—21no—
374C4×C53—22no—
375C4×C53—41no—
376C4×C53—41no—
377C4×C53—41no—
378C4×C53—41no—
379C4×C53—41no—
380C4×C53C2×#11711yescharacteristic
381C4×C53#51811yescharacteristic
382C4×C53#54611yescharacteristic
383C4×C53#54611yescharacteristic
384Dic53—42no—
385Dic53—81no—
386#2924—531no—
387#2896D5311yescharacteristic
388#2880—531no—
389#1938—531no—
390#1937—531no—
391#1929—531no—
392#1929—531no—
393#1866—531no—
394#1866—531no—
395#1826—531no—
396#1811—531no—
397#1789—531no—
398#1765—531no—
399#1764—531no—
400#1753—531no—
401C2×C53—21no—
402C2×C53—21no—
403C2×C53—41no—
404C2×C53—41no—
405C2×C53—42no—
406C2×C53—81no—
407C2×C53#234211yescharacteristic
408C2×C53#295511yescharacteristic
409C2×C53#295611yescharacteristic
410C22×#41C2×D5311yescharacteristic
411C2×#131—531no—
412C2×#131—531no—
413C22×M16C2×D5311yescharacteristic
414C2×#117C2×D5311yescharacteristic
415#433—1061no—
416#433—1061no—
417#432—1061no—
418#431—1061no—
419C2×#108—531no—
420C2×#108—531no—
421#424—531no—
422#424—531no—
423C2×#104—531no—
424C2×#104—531no—
425C2×#104—531no—
426C2×#104—531no—
427#419Dic5311yescharacteristic, complemented
428#419Dic5311yescharacteristic, complemented
429#418Dic5311yescharacteristic, complemented
430#418Dic5311yescharacteristic, complemented
431#417Dic5311yescharacteristic, complemented
432#417Dic5311yescharacteristic, complemented
433#417Dic5311yescharacteristic, complemented
434#417Dic5311yescharacteristic, complemented
435#416C2×D5311yescharacteristic
436#416C2×D5311yescharacteristic
437#416C2×D5311yescharacteristic
438#416C2×D5311yescharacteristic
439#408—531no—
440#408—531no—
441#408—1061no—
442#408—1061no—
443#407—531no—
444#407—531no—
445#407—1061no—
446C2×C22⋊C8—531no—
447C2×C22⋊C8—1061no—
448#405—531no—
449#405—531no—
450C2×#97—531no—
451C2×C4×C8—531no—
452C4×C22⋊C4—531no—
453#341—531no—
454#341—531no—
455#339—531no—
456#339—531no—
457#339—531no—
458#339—531no—
459#336—531no—
460#336—531no—
461C53#2258811yescharacteristic, complemented, Sylow
462C2×#41—21no—
463C2×#41—21no—
464C2×#41—22no—
465C2×#41—22no—
466C2×#41—41no—
467C2×#41—41no—
468C2×#41C2×Dic5311yescharacteristic
469C2×#41C2×Dic5311yescharacteristic
470C2×#41C22×D5311yescharacteristic
471C2×#41C22×D5311yescharacteristic
472C22×Q8C2×Dic5311yescharacteristic
473C22×D4—21no—
474C22×D4C2×Dic5311yescharacteristic
475C23×C4—21no—
476C23×C4C22×D5311yescharacteristic
477#131—1062no—
478#131—1062no—
479#131—2121no—
480#131—2121no—
481C2×M16—41no—
482C2×M16—41no—
483C2×M16—531no—
484C2×M16—531no—
485C2×M16—531no—
486C2×M16—531no—
487C2×M16—1061no—
488C2×M16—1061no—
489C2×M16C2×Dic5311yescharacteristic
490C2×M16C2×Dic5311yescharacteristic
491C2×M16C2×Dic5311yescharacteristic
492C2×M16C2×Dic5311yescharacteristic
493C22×C8—531no—
494C22×C8—531no—
495C22×C8—1061no—
496C22×C8—1061no—
497C22×C8C22×D5311yescharacteristic
498C22×C8C22×D5311yescharacteristic
499#117—21no—
500#117—21no—
501#117C2×Dic5311yescharacteristic
502#117C2×Dic5311yescharacteristic
503#117C22×D5311yescharacteristic
504#117C22×D5311yescharacteristic
505C2×C4⋊C4C2×Dic5311yescharacteristic
506C2×C4⋊C4C2×Dic5311yescharacteristic
507C2×C22⋊C4—21no—
508C2×C22⋊C4—1061no—
509C2×C42—21no—
510C2×C42—531no—
511C2×C42—531no—
512#108—2121no—
513#108—2121no—
514C4⋊C8—1061no—
515C4⋊C8—1061no—
516C4⋊C8—1061no—
517C4⋊C8—1061no—
518#104—1062no—
519#104—1062no—
520#104—2121no—
521#104—2121no—
522#103C2×Dic5311yescharacteristic
523#103C2×Dic5311yescharacteristic
524#103C2×Dic5311yescharacteristic
525#103C2×Dic5311yescharacteristic
526#103C2×Dic5311yescharacteristic
527#103C2×Dic5311yescharacteristic
528#103C2×Dic5311yescharacteristic
529#103C2×Dic5311yescharacteristic
530#102C2×Dic5311yescharacteristic
531#102C2×Dic5311yescharacteristic
532#102C2×Dic5311yescharacteristic
533#102C2×Dic5311yescharacteristic
534#102C2×Dic5311yescharacteristic
535#102C2×Dic5311yescharacteristic
536#102C2×Dic5311yescharacteristic
537#102C2×Dic5311yescharacteristic
538C22⋊C8—531no—
539C22⋊C8—531no—
540C22⋊C8—531no—
541C22⋊C8—531no—
542C22⋊C8—1061no—
543C22⋊C8—1061no—
544C22⋊C8—1061no—
545C22⋊C8—1061no—
546C22⋊C8—1061no—
547C22⋊C8—1061no—
548C22⋊C8—1061no—
549C22⋊C8—1061no—
550#97—1061no—
551#97—1061no—
552#97—2121no—
553C4×C8—1061no—
554C4×C8—1061no—
555C4×C8—2121no—
556#95—1061no—
557C24—21no—
558C24#1171994711yescharacteristic
559#41—21no—
560#41—21no—
561#41—22no—
562#41—22no—
563#41—21no—
564#41—21no—
565#41—21no—
566#41—21no—
567#41—42no—
568#41—42no—
569#41—41no—
570#41—41no—
571#41—42no—
572#41—42no—
573#41#1171994512yes—
574#41#1171994512yes—
575C2×Q8—21no—
576C2×Q8—22no—
577C2×Q8—41no—
578C2×Q8C22×Dic5311yescharacteristic
579C2×Q8C22×Dic5311yescharacteristic
580C2×D4—21no—
581C2×D4—22no—
582C2×D4—21no—
583C2×D4—21no—
584C2×D4—21no—
585C2×D4—21no—
586C2×D4—41no—
587C2×D4—42no—
588C2×D4—42no—
589C2×D4C22×Dic5311yescharacteristic
590C2×D4C22×Dic5311yescharacteristic
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—42no—
603C22×C4—42no—
604C22×C4—1061no—
605C22×C4—1061no—
606C22×C4D4×D5311yescharacteristic
607C22×C4D4×D5311yescharacteristic
608C22×C4#1171994711yescharacteristic
609C22×C4C22×Dic5311yescharacteristic
610C22×C4C22×Dic5311yescharacteristic
611C22×C4C23×D5311yescharacteristic
612M16—41no—
613M16—41no—
614M16—41no—
615M16—41no—
616M16—1061no—
617M16—1061no—
618M16—1061no—
619M16—1061no—
620M16—1061no—
621M16—1061no—
622M16—1061no—
623M16—1061no—
624M16—2122no—
625M16—2122no—
626C2×C8—21no—
627C2×C8—21no—
628C2×C8—21no—
629C2×C8—21no—
630C2×C8—531no—
631C2×C8—531no—
632C2×C8—531no—
633C2×C8—531no—
634C2×C8—1061no—
635C2×C8—1061no—
636C2×C8—1061no—
637C2×C8—1061no—
638C2×C8—1061no—
639C2×C8—1061no—
640C2×C8—1061no—
641C2×C8—1061no—
642C2×C8—2122no—
643C2×C8—2122no—
644C2×C8C22×Dic5311yescharacteristic
645C2×C8C22×Dic5311yescharacteristic
646C2×C8C22×Dic5311yescharacteristic
647C2×C8C22×Dic5311yescharacteristic
648C4⋊C4—21no—
649C4⋊C4—21no—
650C4⋊C4C22×Dic5311yescharacteristic
651C4⋊C4C22×Dic5311yescharacteristic
652C4⋊C4C22×Dic5311yescharacteristic
653C4⋊C4C22×Dic5311yescharacteristic
654C22⋊C4—21no—
655C22⋊C4—21no—
656C22⋊C4—21no—
657C22⋊C4—21no—
658C22⋊C4—2122no—
659C42—21no—
660C42—21no—
661C42—21no—
662C42—21no—
663C42—1061no—
664C42—1061no—
665C42—1061no—
666C42—1061no—
667C23—21no—
668C23—21no—
669C23—21no—
670C23—21no—
671C23—41no—
672C23—41no—
673C23—42no—
674C23—42no—
675C23—81no—
676C23D4×Dic5311yescharacteristic
677C23D4×Dic5311yescharacteristic
678C23C2×#1171994711yescharacteristic
679Q8—21no—
680Q8—21no—
681Q8—21no—
682Q8—42no—
683Q8#1313317612yes—
684D4—22no—
685D4—22no—
686D4—21no—
687D4—21no—
688D4—21no—
689D4—42no—
690D4—42no—
691D4—42no—
692D4—41no—
693D4—41no—
694D4#1313317612yes—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—42no—
714C2×C4—42no—
715C2×C4—42no—
716C2×C4—42no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—81no—
720C2×C4—1062no—
721C2×C4—2121no—
722C2×C4—2121no—
723C2×C4—2121no—
724C2×C4—2121no—
725C2×C4—2121no—
726C2×C4D4×Dic5311yescharacteristic
727C2×C4D4×Dic5311yescharacteristic
728C2×C4C23×Dic5311yescharacteristic
729C2×C4C2×D4×D5311yescharacteristic
730C2×C4C2×#1171994511yescharacteristic
731C2×C4C2×#1171994511yescharacteristic
732C2×C4#1313326211yescharacteristic
733C2×C4#1313326211yescharacteristic
734C8—21no—
735C8—21no—
736C8—21no—
737C8—21no—
738C8—1061no—
739C8—1061no—
740C8—1061no—
741C8—1061no—
742C8—2121no—
743C8—2121no—
744C8—2121no—
745C8—2121no—
746C22—21no—
747C22—21no—
748C22—21no—
749C22—21no—
750C22—22no—
751C22—21no—
752C22—21no—
753C22—21no—
754C22—21no—
755C22—41no—
756C22—41no—
757C22—41no—
758C22—41no—
759C22—41no—
760C22—81no—
761C22—81no—
762C22—84no—
763C22C2×D4×Dic5311yescharacteristic
764C22#1681129911yescharacteristic
765C22#1681129911yescharacteristic
766C4—21no—
767C4—21no—
768C4—22no—
769C4—41no—
770C4—41no—
771C4—41no—
772C4—41no—
773C4—41no—
774C4—4241no—
775C4—2122no—
776C4C2×#1313317611yescharacteristic
777C4#1681109811yescharacteristic
778C4#1681126311yescharacteristic
779C4#1681126311yescharacteristic
780C2—21no—
781C2—21no—
782C2—41no—
783C2—41no—
784C2—42no—
785C2—81no—
786C2#2027756411yescharacteristic
787C2#2028361811yescharacteristic
788C2#2028362511yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D53
commutatorC2×C4×C53C23×C4
FrattiniC22×C4C23×D53
FittingC53×#2896C2
socleC22×C53C2×C4×D4
prime radicalC22×#41×C53C22
cosocleC22×C4×C53C24
hypercenter#2896D53
hypocenterC53#22588
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #2896

Complements

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

NH ≅ G/Ntype
1. #20283373C2semidirect
3. #20275428C2semidirect
4. #20275421C2semidirect
5. #20275365C2semidirect
6. #20275365C2semidirect
7. #20274992C2semidirect
8. #20274992C2semidirect
9. #20274814C2semidirect
10. #20274757C2semidirect
12. #20274562C2semidirect
13. #20274555C2semidirect
14. #20274496C2semidirect
22. C2×#13133153C22semidirect
23. C2×#13133153C22semidirect
24. #16810650C22semidirect
25. #16810650C22semidirect
39. #16810579C22semidirect
40. #16810579C22semidirect
41. C2×#13133127C22semidirect
42. C2×C8×Dic53C22semidirect
44. #16810388C22semidirect
45. #16810388C22semidirect
46. #16810382C22semidirect
47. #16810382C22semidirect
48. #16810382C22semidirect
49. #16810382C22semidirect
50. #16810377C22semidirect
51. #16810377C22semidirect
55. C53×#419C4semidirect
56. C53×#419C4semidirect
57. C53×#418C4semidirect
58. C53×#418C4semidirect
59. C53×#417C4semidirect
60. C53×#417C4semidirect
61. C53×#417C4semidirect
62. C53×#417C4semidirect
427. #419Dic53semidirect
428. #419Dic53semidirect
429. #418Dic53semidirect
430. #418Dic53semidirect
431. #417Dic53semidirect
432. #417Dic53semidirect
433. #417Dic53semidirect
434. #417Dic53semidirect
461. C53#22588semidirect

Maximal subgroups

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

subgroupindex
#202833732
#202831642
#202754282
#202754212
#202753652
#202749922
#202748142
#202747572
#202746592
#202745622
#202745552
#202744962
C53×#28962
#2258853