Finite Group Databasebeta

← #27404848

Subgroups — #27404848

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
1C2×#16810745C211yesmaximal, characteristic, complemented
2#20283442C211yesmaximal, characteristic, complemented
3C2×#16810640C211yesmaximal, characteristic, complemented
4#20283164C211yesmaximal, characteristic, complemented
5#20275604C211yesmaximal, characteristic, complemented
6#20275428C211yesmaximal, characteristic, complemented
7#20275365C211yesmaximal, characteristic, complemented
8#20275164C211yesmaximal, characteristic, complemented
9#20275044C211yesmaximal, characteristic, complemented
10#20275044C211yesmaximal, characteristic, complemented
11#20274992C211yesmaximal, characteristic, complemented
12#20274922C211yesmaximal, characteristic, complemented
13#20274555C211yesmaximal, characteristic, complemented
14#20274483C211yesmaximal, characteristic, complemented
15C53×#3002C211yesmaximal, characteristic
16C2×#13133224C2211yescharacteristic
17C2×#13133224C2211yescharacteristic
18C2×#13133224C2211yescharacteristic, complemented
19C22×#11719917C2211yescharacteristic
20C2×#13133176C2211yescharacteristic
21#16810745—24no—
22#16810701—21no—
23#16810695—21no—
24#16810695—21no—
25D4×#88322—21no—
26C2×#13133153C2211yescharacteristic, complemented
27C2×#13133153C2211yescharacteristic, complemented
28#16810650C2211yescharacteristic, complemented
29#16810640—24no—
30C2×#13133144C2211yescharacteristic
31C2×#13133144C2211yescharacteristic
32C2×#13133144C2211yescharacteristic
33C2×#13133144C2211yescharacteristic
34C2×#13133144C2211yescharacteristic, complemented
35C2×#13133144C2211yescharacteristic, complemented
36#16810590—21no—
37#16810590—21no—
38#16810590C2211yescharacteristic
39#16810590C2211yescharacteristic
40#16810590C2211yescharacteristic, complemented
41#16810587—21no—
42#16810587C2211yescharacteristic
43C2×C22⋊#88322—21no—
44C2×C22⋊#88322C2211yescharacteristic
45#16810579C2211yescharacteristic, complemented
46C2×#13133127C2211yescharacteristic, complemented
47C2×C8×Dic53C2211yescharacteristic, complemented
48#16810388C2211yescharacteristic, complemented
49#16810388C2211yescharacteristic, complemented
50#16810382C2211yescharacteristic, complemented
51#16810382C2211yescharacteristic, complemented
52#16810377C2211yescharacteristic, complemented
53#16810377C2211yescharacteristic, complemented
54C22×#41×C53C2211yescharacteristic
55C2×#135×C53C2211yescharacteristic
56C2×#135×C53C2211yescharacteristic
57C53×#525C2211yescharacteristic
58C53×#452C411yescharacteristic, complemented
59C53×#452C411yescharacteristic, complemented
60C53×#451C411yescharacteristic, complemented
61C53×#450C411yescharacteristic, complemented
62C53×#449C411yescharacteristic, complemented
63C53×#449C411yescharacteristic, complemented
64C53×#448C411yescharacteristic, complemented
65C53×#447C411yescharacteristic, complemented
66C53×#416C2211yescharacteristic
67C53×#416C2211yescharacteristic
68C2×C22⋊C8×C53C2211yescharacteristic
69#13133224—22no—
70#13133224—22no—
71#13133224—22no—
72#13133224—41no—
73#13133224—41no—
74#13133224—41no—
75C2×#11719917—21no—
76C2×#11719917—21no—
77C2×#11719917—21no—
78C2×#11719917—22no—
79C2×#11719917—21no—
80C2×#11719917—41no—
81C2×#11719917C2311yescharacteristic
82C2×#11719917C2311yescharacteristic
83C2×#11719917C2311yescharacteristic
84C2×#11719917C2311yescharacteristic
85C22×#88322—21no—
86C22×#88322—21no—
87C22×#88322—21no—
88C22×#88322—21no—
89C22×#88322C2311yescharacteristic
90C22×#88322C2311yescharacteristic
91#13133176—22no—
92#13133176—41no—
93C2×C4⋊Dic53—21no—
94C2×C22⋊Dic53—21no—
95C2×C4×Dic53C2311yescharacteristic
96C2×C4×Dic53C2311yescharacteristic
97#13133153—22no—
98#13133153—41no—
99C4⋊#88322—21no—
100C4⋊#88322—21no—
101#13133144—22no—
102#13133144—22no—
103#13133144—22no—
104#13133144—22no—
105#13133144—41no—
106#13133144D414yescomplemented
107C22⋊#88322—21no—
108C22⋊#88322—21no—
109C22⋊#88322—21no—
110C22⋊#88322—21no—
111C22⋊#88322—21no—
112C22⋊#88322—21no—
113C22⋊#88322—21no—
114C22⋊#88322—21no—
115C22⋊#88322D411yescharacteristic
116C22⋊#88322D411yescharacteristic
117C22⋊#88322D411yescharacteristic
118C22⋊#88322D411yescharacteristic
119#13133128—21no—
120#13133127—22no—
121C4×#88322—21no—
122C8×Dic53—41no—
123C2×#41×C53—21no—
124C2×#41×C53—21no—
125C2×#41×C53—22no—
126C2×#41×C53—22no—
127C2×#41×C53—41no—
128C2×#41×C53—41no—
129C2×#41×C53C2×C411yescharacteristic
130C2×#41×C53C2×C411yescharacteristic
131C2×#41×C53C2311yescharacteristic
132C2×#41×C53C2311yescharacteristic
133C2×#41×C53C2311yescharacteristic
134C22×Q8×C53C2×C411yescharacteristic
135C22×D4×C53—21no—
136C22×D4×C53C2×C411yescharacteristic
137C23×C4×C53—21no—
138C23×C4×C53C2311yescharacteristic
139#135×C53—22no—
140#135×C53—22no—
141#135×C53—41no—
142#135×C53—41no—
143C2×Q16×C53C2×C411yescharacteristic
144C2×Q16×C53C2×C411yescharacteristic
145C2×SD16×C53C2×C411yescharacteristic
146C2×SD16×C53C2×C411yescharacteristic
147C2×SD16×C53C2×C411yescharacteristic
148C2×SD16×C53C2×C411yescharacteristic
149C2×D8×C53C2×C411yescharacteristic
150C2×D8×C53C2×C411yescharacteristic
151C22×C8×C53C2311yescharacteristic
152C22×C8×C53C2311yescharacteristic
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
162#103×C53C2×C411yescharacteristic
163#103×C53C2×C411yescharacteristic
164#103×C53C2×C411yescharacteristic
165#103×C53C2×C411yescharacteristic
166#102×C53C2×C411yescharacteristic
167#102×C53C2×C411yescharacteristic
168#102×C53C2×C411yescharacteristic
169#102×C53C2×C411yescharacteristic
170C22⋊C8×C53C2×C411yescharacteristic
171C22⋊C8×C53C2×C411yescharacteristic
172C22⋊C8×C53C2×C411yescharacteristic
173C22⋊C8×C53C2×C411yescharacteristic
174C24×C53—21no—
175C24×C53#4111yescharacteristic
176#41×C53—21no—
177#41×C53—21no—
178#41×C53—22no—
179#41×C53—22no—
180#41×C53—21no—
181#41×C53—21no—
182#41×C53—21no—
183#41×C53—21no—
184#41×C53—21no—
185#41×C53—21no—
186#41×C53—21no—
187#41×C53—21no—
188#41×C53—42no—
189#41×C53—42no—
190#41×C53—41no—
191#41×C53—41no—
192#41×C53—42no—
193#41×C53—42no—
194#41×C53C2×D412yes—
195#41×C53#4112yes—
196C2×Q8×C53—21no—
197C2×Q8×C53—22no—
198C2×Q8×C53—41no—
199C2×Q8×C53C22×C411yescharacteristic
200C2×Q8×C53C22×C411yescharacteristic
201C2×Q8×C53C22×C411yescharacteristic
202C2×D4×C53—21no—
203C2×D4×C53—22no—
204C2×D4×C53—21no—
205C2×D4×C53—21no—
206C2×D4×C53—21no—
207C2×D4×C53—21no—
208C2×D4×C53—21no—
209C2×D4×C53—21no—
210C2×D4×C53—21no—
211C2×D4×C53—41no—
212C2×D4×C53—42no—
213C2×D4×C53—42no—
214C2×D4×C53C22×C411yescharacteristic
215C2×D4×C53C22×C411yescharacteristic
216C2×D4×C53C22×C411yescharacteristic
217C22×C4×C53—21no—
218C22×C4×C53—21no—
219C22×C4×C53—21no—
220C22×C4×C53—21no—
221C22×C4×C53—21no—
222C22×C4×C53—21no—
223C22×C4×C53—21no—
224C22×C4×C53—21no—
225C22×C4×C53—21no—
226C22×C4×C53—21no—
227C22×C4×C53—42no—
228C22×C4×C53—42no—
229C22×C4×C53C22×C411yescharacteristic
230C22×C4×C53C22×C411yescharacteristic
231C22×C4×C53C2×D411yescharacteristic
232C22×C4×C53C2×D411yescharacteristic
233C22×C4×C53#4111yescharacteristic
234C22×C4×C53C2411yescharacteristic
235C22×Dic53—21no—
236C22×Dic53—21no—
237Q16×C53—22no—
238Q16×C53—41no—
239SD16×C53—22no—
240SD16×C53—22no—
241SD16×C53—41no—
242SD16×C53—41no—
243D8×C53—22no—
244D8×C53—41no—
245C2×C8×C53—21no—
246C2×C8×C53—21no—
247C2×C8×C53—21no—
248C2×C8×C53—21no—
249C2×C8×C53C22×C411yescharacteristic
250C2×C8×C53C22×C411yescharacteristic
251C2×C8×C53C22×C411yescharacteristic
252C2×C8×C53C22×C411yescharacteristic
253C4⋊C4×C53—21no—
254C4⋊C4×C53—21no—
255C4⋊C4×C53C22×C411yescharacteristic
256C4⋊C4×C53C22×C411yescharacteristic
257C22⋊C4×C53—21no—
258C22⋊C4×C53—21no—
259C22⋊C4×C53—21no—
260C22⋊C4×C53—21no—
261C22⋊C4×C53—21no—
262C42×C53—21no—
263C22⋊Dic53—42no—
264C4⋊Dic53—42no—
265C4×Dic53—21no—
266C4×Dic53—21no—
267C4×Dic53—21no—
268C4×Dic53C2×D412yes—
269#11719917—21no—
270#11719917—21no—
271#11719917—21no—
272#11719917—21no—
273#11719917—21no—
274#11719917—21no—
275#11719917—21no—
276#11719917—42no—
277#11719917—42no—
278#11719917—42no—
279#11719917—42no—
280#11719917C2×D412yes—
281C2×#88322—21no—
282C2×#88322—21no—
283C2×#88322—21no—
284C2×#88322—21no—
285C2×#88322—21no—
286C2×#88322—21no—
287C2×#88322—21no—
288C2×#88322—21no—
289C2×#88322—42no—
290C2×#88322—42no—
291C2×#88322—42no—
292C2×#88322—42no—
293C2×#88322C2×D411yescharacteristic
294C2×#88322C2×D411yescharacteristic
295C2×#88322C2×D411yescharacteristic
296C2×#88322C2×D411yescharacteristic
297C23×C53—21no—
298C23×C53—21no—
299C23×C53—21no—
300C23×C53—21no—
301C23×C53—21no—
302C23×C53—41no—
303C23×C53—41no—
304C23×C53—42no—
305C23×C53—42no—
306C23×C53—81no—
307C23×C53C4×D411yescharacteristic
308C23×C53C4×D411yescharacteristic
309C23×C53C2×#4111yescharacteristic
310Q8×C53—21no—
311Q8×C53—21no—
312Q8×C53—21no—
313Q8×C53—21no—
314Q8×C53—21no—
315Q8×C53—42no—
316Q8×C53C4×D412yes—
317D4×C53—22no—
318D4×C53—22no—
319D4×C53—21no—
320D4×C53—21no—
321D4×C53—21no—
322D4×C53—21no—
323D4×C53—21no—
324D4×C53—42no—
325D4×C53—42no—
326D4×C53—42no—
327D4×C53—42no—
328D4×C53—41no—
329D4×C53—41no—
330D4×C53—41no—
331D4×C53—41no—
332D4×C53—81no—
333D4×C53C4×D412yes—
334C2×C4×C53—21no—
335C2×C4×C53—21no—
336C2×C4×C53—21no—
337C2×C4×C53—21no—
338C2×C4×C53—21no—
339C2×C4×C53—21no—
340C2×C4×C53—21no—
341C2×C4×C53—21no—
342C2×C4×C53—21no—
343C2×C4×C53—22no—
344C2×C4×C53—21no—
345C2×C4×C53—21no—
346C2×C4×C53—22no—
347C2×C4×C53—21no—
348C2×C4×C53—21no—
349C2×C4×C53—21no—
350C2×C4×C53—21no—
351C2×C4×C53—42no—
352C2×C4×C53—42no—
353C2×C4×C53—42no—
354C2×C4×C53—41no—
355C2×C4×C53—41no—
356C2×C4×C53—41no—
357C2×C4×C53—41no—
358C2×C4×C53C4×D411yescharacteristic
359C2×C4×C53C4×D411yescharacteristic
360C2×C4×C53C23×C411yescharacteristic
361C2×C4×C53C22×D411yescharacteristic
362C2×C4×C53C22×D411yescharacteristic
363C2×C4×C53C2×#4111yescharacteristic
364C2×C4×C53H(5,𝔽2)11yescharacteristic
365C2×C4×C53H(5,𝔽2)11yescharacteristic
366C2×Dic53—22no—
367C2×Dic53—41no—
368C2×Dic53—41no—
369C2×Dic53—41no—
370C2×Dic53—41no—
371C2×Dic53—41no—
372C8×C53—21no—
373C8×C53—21no—
374C8×C53—21no—
375C8×C53—21no—
376#88322—21no—
377#88322—21no—
378#88322—22no—
379#88322—21no—
380#88322—21no—
381#88322—41no—
382#88322—41no—
383#88322—41no—
384#22887—531nomaximal, Sylow
385C22×C53—21no—
386C22×C53—21no—
387C22×C53—21no—
388C22×C53—21no—
389C22×C53—22no—
390C22×C53—21no—
391C22×C53—21no—
392C22×C53—21no—
393C22×C53—21no—
394C22×C53—41no—
395C22×C53—41no—
396C22×C53—41no—
397C22×C53—41no—
398C22×C53—41no—
399C22×C53—41no—
400C22×C53—41no—
401C22×C53—41no—
402C22×C53—81no—
403C22×C53—81no—
404C22×C53—84no—
405C22×C53C2×C4×D411yescharacteristic
406C22×C53#54611yescharacteristic
407C22×C53#55111yescharacteristic
408C4×C53—21no—
409C4×C53—21no—
410C4×C53—22no—
411C4×C53—41no—
412C4×C53—41no—
413C4×C53—41no—
414C4×C53—41no—
415C4×C53C2×C4×D411yescharacteristic
416C4×C53#51811yescharacteristic
417C4×C53D4211yescharacteristic
418C4×C53#54611yescharacteristic
419Dic53—42no—
420Dic53—81no—
421#3002D5311yescharacteristic
422C2×#444—531no—
423#2933—531no—
424C2×#421—531no—
425#2880—531no—
426#1974—531no—
427#1938—531no—
428#1929—531no—
429#1897—531no—
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—42no—
441C2×C53—81no—
442C2×C53—81no—
443C2×C53#235811yescharacteristic
444C2×C53#295511yescharacteristic
445C2×C53#295711yescharacteristic
446C22×#41C2×D5311yescharacteristic
447C2×#135C2×D5311yescharacteristic
448C2×#135C2×D5311yescharacteristic
449C2×#131—531no—
450C2×#131—531no—
451C2×#131—531no—
452C22×M16—531no—
453#525C2×D5311yescharacteristic
454C2×#117—531no—
455#452Dic5311yescharacteristic, complemented
456#452Dic5311yescharacteristic, complemented
457#451Dic5311yescharacteristic, complemented
458#450Dic5311yescharacteristic, complemented
459#449Dic5311yescharacteristic, complemented
460#449Dic5311yescharacteristic, complemented
461#448Dic5311yescharacteristic, complemented
462#447Dic5311yescharacteristic, complemented
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×#104—531no—
477C2×#104—531no—
478#416C2×D5311yescharacteristic
479#416C2×D5311yescharacteristic
480#408—531no—
481#408—531no—
482#408—531no—
483#408—1061no—
484#408—1061no—
485#407—531no—
486#407—1061no—
487C2×C22⋊C8—531no—
488C2×C22⋊C8—1061no—
489C2×C22⋊C8C2×D5311yescharacteristic
490#405—531no—
491C2×#97—531no—
492C2×C4×C8—531no—
493#341—531no—
494#341—531no—
495#339—531no—
496#339—531no—
497#336—531no—
498#336—531no—
499C53#2288711yescharacteristic, complemented, Sylow
500C2×#41—21no—
501C2×#41—21no—
502C2×#41—22no—
503C2×#41—22no—
504C2×#41—41no—
505C2×#41—41no—
506C2×#41C2×Dic5311yescharacteristic
507C2×#41C2×Dic5311yescharacteristic
508C2×#41C22×D5311yescharacteristic
509C2×#41C22×D5311yescharacteristic
510C2×#41C22×D5311yescharacteristic
511C22×Q8C2×Dic5311yescharacteristic
512C22×D4—21no—
513C22×D4C2×Dic5311yescharacteristic
514C23×C4—21no—
515C23×C4C22×D5311yescharacteristic
516#135—22no—
517#135—22no—
518#135—41no—
519#135—41no—
520C2×Q16C2×Dic5311yescharacteristic
521C2×Q16C2×Dic5311yescharacteristic
522C2×SD16C2×Dic5311yescharacteristic
523C2×SD16C2×Dic5311yescharacteristic
524C2×SD16C2×Dic5311yescharacteristic
525C2×SD16C2×Dic5311yescharacteristic
526C2×D8C2×Dic5311yescharacteristic
527C2×D8C2×Dic5311yescharacteristic
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—531no—
537C2×M16—531no—
538C2×M16—1061no—
539C2×M16—1061no—
540C2×M16—1061no—
541C2×M16—1061no—
542C2×M16—1062no—
543C2×M16—2121no—
544C22×C8—531no—
545C22×C8—531no—
546C22×C8—1061no—
547C22×C8—1061no—
548C22×C8—1061no—
549C22×C8—1061no—
550C22×C8C22×D5311yescharacteristic
551C22×C8C22×D5311yescharacteristic
552#123—21no—
553C22⋊Q8C2×Dic5311yescharacteristic
554C22⋊Q8C2×Dic5311yescharacteristic
555#121C2×Dic5311yescharacteristic
556#121C2×Dic5311yescharacteristic
557#120—21no—
558C4×D4—21no—
559C4×D4—21no—
560#117—1062no—
561#117—2121no—
562#117C22×D5311yescharacteristic
563C2×C4⋊C4—1061no—
564C2×C22⋊C4—1061no—
565C2×C42—531no—
566C2×C42—531no—
567#108—1062no—
568#108—2121no—
569C4⋊C8—1061no—
570C4⋊C8—1061no—
571#104—534no—
572#104—1062no—
573#104—1062no—
574#104—1062no—
575#104—1062no—
576#104—2121no—
577#103C2×Dic5311yescharacteristic
578#103C2×Dic5311yescharacteristic
579#103C2×Dic5311yescharacteristic
580#103C2×Dic5311yescharacteristic
581#102C2×Dic5311yescharacteristic
582#102C2×Dic5311yescharacteristic
583#102C2×Dic5311yescharacteristic
584#102C2×Dic5311yescharacteristic
585C22⋊C8—531no—
586C22⋊C8—531no—
587C22⋊C8—531no—
588C22⋊C8—531no—
589C22⋊C8—1061no—
590C22⋊C8—1061no—
591C22⋊C8—1061no—
592C22⋊C8—1061no—
593C22⋊C8—1061no—
594C22⋊C8—1061no—
595C22⋊C8—1061no—
596C22⋊C8—1061no—
597C22⋊C8C2×Dic5311yescharacteristic
598C22⋊C8C2×Dic5311yescharacteristic
599C22⋊C8C2×Dic5311yescharacteristic
600C22⋊C8C2×Dic5311yescharacteristic
601#97—1061no—
602#97—1062no—
603C4×C8—1061no—
604C4×C8—2121no—
605C24—21no—
606C24#1171994711yescharacteristic
607#41—21no—
608#41—21no—
609#41—22no—
610#41—22no—
611#41—21no—
612#41—21no—
613#41—21no—
614#41—21no—
615#41—21no—
616#41—21no—
617#41—21no—
618#41—21no—
619#41—42no—
620#41—42no—
621#41—41no—
622#41—41no—
623#41—42no—
624#41—42no—
625#41D4×D5312yes—
626#41#1171994712yes—
627C2×Q8—21no—
628C2×Q8—22no—
629C2×Q8—41no—
630C2×Q8C22×Dic5311yescharacteristic
631C2×Q8C22×Dic5311yescharacteristic
632C2×Q8C22×Dic5311yescharacteristic
633C2×D4—21no—
634C2×D4—22no—
635C2×D4—21no—
636C2×D4—21no—
637C2×D4—21no—
638C2×D4—21no—
639C2×D4—21no—
640C2×D4—21no—
641C2×D4—21no—
642C2×D4—41no—
643C2×D4—42no—
644C2×D4—42no—
645C2×D4C22×Dic5311yescharacteristic
646C2×D4C22×Dic5311yescharacteristic
647C2×D4C22×Dic5311yescharacteristic
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—42no—
659C22×C4—42no—
660C22×C4—1061no—
661C22×C4—1061no—
662C22×C4D4×D5311yescharacteristic
663C22×C4D4×D5311yescharacteristic
664C22×C4#1171994711yescharacteristic
665C22×C4C22×Dic5311yescharacteristic
666C22×C4C22×Dic5311yescharacteristic
667C22×C4C23×D5311yescharacteristic
668Q16—22no—
669Q16—41no—
670SD16—22no—
671SD16—22no—
672SD16—41no—
673SD16—41no—
674D8—22no—
675D8—41no—
676M16—532no—
677M16—1061no—
678M16—1061no—
679M16—1061no—
680M16—1061no—
681M16—1061no—
682M16—1061no—
683M16—1061no—
684M16—2122no—
685M16—2122no—
686M16—2122no—
687M16—2122no—
688C2×C8—21no—
689C2×C8—21no—
690C2×C8—21no—
691C2×C8—21no—
692C2×C8—531no—
693C2×C8—531no—
694C2×C8—531no—
695C2×C8—531no—
696C2×C8—1061no—
697C2×C8—1061no—
698C2×C8—1061no—
699C2×C8—1061no—
700C2×C8—1061no—
701C2×C8—1061no—
702C2×C8—1061no—
703C2×C8—1061no—
704C2×C8—2122no—
705C2×C8—2122no—
706C2×C8—2122no—
707C2×C8—2122no—
708C2×C8C22×Dic5311yescharacteristic
709C2×C8C22×Dic5311yescharacteristic
710C2×C8C22×Dic5311yescharacteristic
711C2×C8C22×Dic5311yescharacteristic
712C4⋊C4—21no—
713C4⋊C4—21no—
714C4⋊C4—2122no—
715C4⋊C4C22×Dic5311yescharacteristic
716C4⋊C4C22×Dic5311yescharacteristic
717C22⋊C4—21no—
718C22⋊C4—21no—
719C22⋊C4—21no—
720C22⋊C4—21no—
721C22⋊C4—21no—
722C22⋊C4—2122no—
723C42—21no—
724C42—532no—
725C42—1061no—
726C42—1061no—
727C42—1061no—
728C23—21no—
729C23—21no—
730C23—21no—
731C23—21no—
732C23—21no—
733C23—41no—
734C23—41no—
735C23—42no—
736C23—42no—
737C23—81no—
738C23D4×Dic5311yescharacteristic
739C23D4×Dic5311yescharacteristic
740C23C2×#1171994711yescharacteristic
741Q8—21no—
742Q8—21no—
743Q8—21no—
744Q8—21no—
745Q8—21no—
746Q8—42no—
747Q8D4×Dic5312yes—
748D4—22no—
749D4—22no—
750D4—21no—
751D4—21no—
752D4—21no—
753D4—21no—
754D4—21no—
755D4—42no—
756D4—42no—
757D4—42no—
758D4—42no—
759D4—41no—
760D4—41no—
761D4—41no—
762D4—41no—
763D4—81no—
764D4D4×Dic5312yes—
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—22no—
774C2×C4—21no—
775C2×C4—22no—
776C2×C4—21no—
777C2×C4—21no—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—21no—
782C2×C4—42no—
783C2×C4—42no—
784C2×C4—42no—
785C2×C4—41no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—1062no—
790C2×C4—2121no—
791C2×C4—2121no—
792C2×C4—2121no—
793C2×C4—2121no—
794C2×C4—2121no—
795C2×C4D4×Dic5311yescharacteristic
796C2×C4D4×Dic5311yescharacteristic
797C2×C4C23×Dic5311yescharacteristic
798C2×C4C2×D4×D5311yescharacteristic
799C2×C4C2×D4×D5311yescharacteristic
800C2×C4C2×#1171994711yescharacteristic
801C2×C4#1313326211yescharacteristic
802C2×C4#1313326211yescharacteristic
803C8—21no—
804C8—21no—
805C8—21no—
806C8—21no—
807C8—1061no—
808C8—1061no—
809C8—1062no—
810C8—1061no—
811C8—1061no—
812C8—2121no—
813C8—2121no—
814C8—2121no—
815C22—21no—
816C22—21no—
817C22—21no—
818C22—21no—
819C22—22no—
820C22—21no—
821C22—21no—
822C22—21no—
823C22—21no—
824C22—41no—
825C22—41no—
826C22—41no—
827C22—41no—
828C22—41no—
829C22—41no—
830C22—41no—
831C22—41no—
832C22—81no—
833C22—81no—
834C22—84no—
835C22C2×D4×Dic5311yescharacteristic
836C22#1681126011yescharacteristic
837C22#1681130411yescharacteristic
838C4—21no—
839C4—21no—
840C4—22no—
841C4—41no—
842C4—41no—
843C4—41no—
844C4—41no—
845C4—4241no—
846C4—2122no—
847C4C2×D4×Dic5311yescharacteristic
848C4#1681109811yescharacteristic
849C4#1681125511yescharacteristic
850C4#1681126011yescharacteristic
851C2—21no—
852C2—21no—
853C2—41no—
854C2—41no—
855C2—42no—
856C2—81no—
857C2—81no—
858C2#2027769911yescharacteristic
859C2#2028361811yescharacteristic
860C2#2028363211yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D53
commutatorC2×C4×C53C23×C4
FrattiniC22×C4C23×D53
Fitting, prime radicalC53×#3002C2
socleC22×C53C2×C4×D4
cosocleC22×C4×C53C24
hypercenter#3002D53
hypocenterC53#22887
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #3002

Complements

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

NH ≅ G/Ntype
1. C2×#16810745C2semidirect
2. #20283442C2semidirect
3. C2×#16810640C2semidirect
4. #20283164C2semidirect
5. #20275604C2semidirect
6. #20275428C2semidirect
7. #20275365C2semidirect
8. #20275164C2semidirect
9. #20275044C2semidirect
10. #20275044C2semidirect
11. #20274992C2semidirect
12. #20274922C2semidirect
13. #20274555C2semidirect
14. #20274483C2semidirect
18. C2×#13133224C22semidirect
26. C2×#13133153C22semidirect
27. C2×#13133153C22semidirect
28. #16810650C22semidirect
34. C2×#13133144C22semidirect
35. C2×#13133144C22semidirect
40. #16810590C22semidirect
45. #16810579C22semidirect
46. C2×#13133127C22semidirect
47. C2×C8×Dic53C22semidirect
48. #16810388C22semidirect
49. #16810388C22semidirect
50. #16810382C22semidirect
51. #16810382C22semidirect
52. #16810377C22semidirect
53. #16810377C22semidirect
58. C53×#452C4semidirect
59. C53×#452C4semidirect
60. C53×#451C4semidirect
61. C53×#450C4semidirect
62. C53×#449C4semidirect
63. C53×#449C4semidirect
64. C53×#448C4semidirect
65. C53×#447C4semidirect
106. #13133144D4semidirect
455. #452Dic53semidirect
456. #452Dic53semidirect
457. #451Dic53semidirect
458. #450Dic53semidirect
459. #449Dic53semidirect
460. #449Dic53semidirect
461. #448Dic53semidirect
462. #447Dic53semidirect
499. C53#22887semidirect

Maximal subgroups

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

subgroupindex
C2×#168107452
#202834422
C2×#168106402
#202831642
#202756042
#202754282
#202753652
#202751642
#202750442
#202749922
#202749222
#202745552
#202744832
C53×#30022
#2288753