Finite Group Databasebeta

← #27404833

Subgroups — #27404833

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
1C2×#16810745C211yesmaximal, characteristic, complemented
2#20283442C211yesmaximal, characteristic, complemented
3C22×#13133144C211yesmaximal, characteristic, complemented
4#20283164C211yesmaximal, characteristic, complemented
5#20275609C211yesmaximal, characteristic, complemented
6#20275428C211yesmaximal, characteristic, complemented
7#20275365C211yesmaximal, characteristic, complemented
8#20275159C211yesmaximal, characteristic, complemented
9#20275044C211yesmaximal, characteristic, complemented
10#20275044C211yesmaximal, characteristic, complemented
11#20274992C211yesmaximal, characteristic, complemented
12#20274922C211yesmaximal, characteristic, complemented
13#20274562C211yesmaximal, characteristic, complemented
14#20274479C211yesmaximal, characteristic, complemented
15C53×#3002C211yesmaximal, characteristic
16C2×#13133224C2211yescharacteristic
17C2×#13133224C2211yescharacteristic
18C2×#13133224C2211yescharacteristic, complemented
19C22×#11719917C2211yescharacteristic
20C22×C4×Dic53C2211yescharacteristic
21#16810745—24no—
22#16810701—21no—
23#16810695—21no—
24#16810695—21no—
25D4×#88322—21no—
26C2×#13133153C2211yescharacteristic, complemented
27C2×#13133153C2211yescharacteristic, complemented
28#16810650C2211yescharacteristic, complemented
29C2×#13133144—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×#13133127C2211yescharacteristic, 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
69C23×Dic53—21no—
70#13133224—22no—
71#13133224—22no—
72#13133224—22no—
73#13133224—41no—
74#13133224—41no—
75#13133224—41no—
76C2×#11719917—21no—
77C2×#11719917—21no—
78C2×#11719917—21no—
79C2×#11719917—22no—
80C2×#11719917—21no—
81C2×#11719917—41no—
82C2×#11719917C2311yescharacteristic
83C2×#11719917C2311yescharacteristic
84C2×#11719917C2311yescharacteristic
85C2×#11719917C2311yescharacteristic
86C22×#88322—21no—
87C22×#88322—21no—
88C22×#88322—21no—
89C22×#88322—21no—
90C22×#88322C2311yescharacteristic
91C22×#88322C2311yescharacteristic
92C2×C4×Dic53—21no—
93C2×C4×Dic53—22no—
94C2×C4×Dic53—41no—
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—
121#13133127—41no—
122C4×#88322—21no—
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, complemented
144C2×Q16×C53C2×C411yescharacteristic, complemented
145C2×SD16×C53C2×C411yescharacteristic, complemented
146C2×SD16×C53C2×C411yescharacteristic, complemented
147C2×SD16×C53C2×C411yescharacteristic, complemented
148C2×SD16×C53C2×C411yescharacteristic, complemented
149C2×D8×C53C2×C411yescharacteristic, complemented
150C2×D8×C53C2×C411yescharacteristic, complemented
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, complemented
163#103×C53C2×C411yescharacteristic, complemented
164#103×C53C2×C411yescharacteristic, complemented
165#103×C53C2×C411yescharacteristic, complemented
166#102×C53C2×C411yescharacteristic, complemented
167#102×C53C2×C411yescharacteristic, complemented
168#102×C53C2×C411yescharacteristic, complemented
169#102×C53C2×C411yescharacteristic, complemented
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—
237C22×Dic53—42no—
238C22×Dic53—42no—
239C22×Dic53—42no—
240Q16×C53—22no—
241Q16×C53—41no—
242SD16×C53—22no—
243SD16×C53—22no—
244SD16×C53—41no—
245SD16×C53—41no—
246D8×C53—22no—
247D8×C53—41no—
248C2×C8×C53—21no—
249C2×C8×C53—21no—
250C2×C8×C53—21no—
251C2×C8×C53—21no—
252C2×C8×C53C22×C411yescharacteristic
253C2×C8×C53C22×C411yescharacteristic
254C2×C8×C53C22×C411yescharacteristic
255C2×C8×C53C22×C411yescharacteristic
256C4⋊C4×C53—21no—
257C4⋊C4×C53—21no—
258C4⋊C4×C53C22×C411yescharacteristic
259C4⋊C4×C53C22×C411yescharacteristic
260C22⋊C4×C53—21no—
261C22⋊C4×C53—21no—
262C22⋊C4×C53—21no—
263C22⋊C4×C53—21no—
264C22⋊C4×C53—21no—
265C42×C53—21no—
266C4×Dic53—21no—
267C4×Dic53—21no—
268C4×Dic53—21no—
269C4×Dic53—42no—
270C4×Dic53C2×D412yes—
271#11719917—21no—
272#11719917—21no—
273#11719917—21no—
274#11719917—21no—
275#11719917—21no—
276#11719917—21no—
277#11719917—21no—
278#11719917—42no—
279#11719917—42no—
280#11719917—42no—
281#11719917—42no—
282#11719917C2×D412yes—
283C2×#88322—21no—
284C2×#88322—21no—
285C2×#88322—21no—
286C2×#88322—21no—
287C2×#88322—21no—
288C2×#88322—21no—
289C2×#88322—21no—
290C2×#88322—21no—
291C2×#88322—42no—
292C2×#88322—42no—
293C2×#88322—42no—
294C2×#88322—42no—
295C2×#88322C2×D411yescharacteristic
296C2×#88322C2×D411yescharacteristic
297C2×#88322C2×D411yescharacteristic
298C2×#88322C2×D411yescharacteristic
299C23×C53—21no—
300C23×C53—21no—
301C23×C53—21no—
302C23×C53—22no—
303C23×C53—21no—
304C23×C53—21no—
305C23×C53—41no—
306C23×C53—42no—
307C23×C53—42no—
308C23×C53—81no—
309C23×C53C4×D411yescharacteristic
310C23×C53C4×D411yescharacteristic
311C23×C53C2×#4111yescharacteristic
312Q8×C53—21no—
313Q8×C53—21no—
314Q8×C53—21no—
315Q8×C53—21no—
316Q8×C53—21no—
317Q8×C53—42no—
318Q8×C53C4×D412yes—
319D4×C53—22no—
320D4×C53—22no—
321D4×C53—21no—
322D4×C53—21no—
323D4×C53—21no—
324D4×C53—21no—
325D4×C53—21no—
326D4×C53—42no—
327D4×C53—42no—
328D4×C53—42no—
329D4×C53—41no—
330D4×C53—41no—
331D4×C53—41no—
332D4×C53—41no—
333D4×C53—42no—
334D4×C53—81no—
335D4×C53C4×D412yes—
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—21no—
344C2×C4×C53—21no—
345C2×C4×C53—22no—
346C2×C4×C53—21no—
347C2×C4×C53—21no—
348C2×C4×C53—22no—
349C2×C4×C53—21no—
350C2×C4×C53—21no—
351C2×C4×C53—21no—
352C2×C4×C53—21no—
353C2×C4×C53—42no—
354C2×C4×C53—42no—
355C2×C4×C53—42no—
356C2×C4×C53—41no—
357C2×C4×C53—41no—
358C2×C4×C53—41no—
359C2×C4×C53—41no—
360C2×C4×C53C4×D411yescharacteristic
361C2×C4×C53C4×D411yescharacteristic
362C2×C4×C53C23×C411yescharacteristic
363C2×C4×C53C22×D411yescharacteristic
364C2×C4×C53C22×D411yescharacteristic
365C2×C4×C53C2×#4111yescharacteristic
366C2×C4×C53H(5,𝔽2)11yescharacteristic
367C2×C4×C53H(5,𝔽2)11yescharacteristic
368C2×Dic53—22no—
369C2×Dic53—22no—
370C2×Dic53—41no—
371C2×Dic53—41no—
372C2×Dic53—41no—
373C2×Dic53—48no—
374C2×Dic53—41no—
375C8×C53—21no—
376C8×C53—21no—
377C8×C53—21no—
378C8×C53—21no—
379#88322—21no—
380#88322—21no—
381#88322—22no—
382#88322—21no—
383#88322—21no—
384#88322—41no—
385#88322—41no—
386#88322—41no—
387#22886—531nomaximal, Sylow
388C22×C53—21no—
389C22×C53—21no—
390C22×C53—21no—
391C22×C53—21no—
392C22×C53—21no—
393C22×C53—22no—
394C22×C53—21no—
395C22×C53—21no—
396C22×C53—42no—
397C22×C53—42no—
398C22×C53—41no—
399C22×C53—41no—
400C22×C53—41no—
401C22×C53—41no—
402C22×C53—41no—
403C22×C53—41no—
404C22×C53—41no—
405C22×C53—41no—
406C22×C53—84no—
407C22×C53#44412yescomplemented
408C22×C53C2×C4×D411yescharacteristic
409C22×C53#54611yescharacteristic
410C22×C53#55111yescharacteristic
411C4×C53—21no—
412C4×C53—21no—
413C4×C53—22no—
414C4×C53—41no—
415C4×C53—41no—
416C4×C53—41no—
417C4×C53—41no—
418C4×C53C2×C4×D411yescharacteristic
419C4×C53#51811yescharacteristic
420C4×C53D4211yescharacteristic
421C4×C53#54611yescharacteristic
422Dic53—42no—
423Dic53—42no—
424#3002D5311yescharacteristic
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#1765—531no—
438#1749—531no—
439C2×C53—21no—
440C2×C53—22no—
441C2×C53—21no—
442C2×C53—41no—
443C2×C53—42no—
444C2×C53—81no—
445C2×C53—81no—
446C2×C53#235811yescharacteristic
447C2×C53C2×#44411yescharacteristic
448C2×C53#295611yescharacteristic
449C22×#41C2×D5311yescharacteristic
450C2×#135C2×D5311yescharacteristic
451C2×#135C2×D5311yescharacteristic
452C2×#131—531no—
453C2×#131—531no—
454C2×#131—531no—
455C22×M16—531no—
456#525C2×D5311yescharacteristic
457C22×C42—531no—
458#452Dic5311yescharacteristic, complemented
459#452Dic5311yescharacteristic, complemented
460#451Dic5311yescharacteristic, complemented
461#450Dic5311yescharacteristic, complemented
462#449Dic5311yescharacteristic, complemented
463#449Dic5311yescharacteristic, complemented
464#448Dic5311yescharacteristic, complemented
465#447Dic5311yescharacteristic, complemented
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—531no—
480C2×#104—1064no—
481#416C2×D5311yescharacteristic
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—1061no—
492C2×C22⋊C8C2×D5311yescharacteristic
493#405—531no—
494C2×#97—531no—
495C2×#97—531no—
496#341—531no—
497#341—531no—
498#339—531no—
499#339—531no—
500#336—531no—
501#336—531no—
502C53#2288611yescharacteristic, complemented, Sylow
503C2×#41—21no—
504C2×#41—21no—
505C2×#41—22no—
506C2×#41—22no—
507C2×#41—41no—
508C2×#41—41no—
509C2×#41C2×Dic5311yescharacteristic
510C2×#41C2×Dic5311yescharacteristic
511C2×#41C22×D5311yescharacteristic
512C2×#41C22×D5311yescharacteristic
513C2×#41C22×D5311yescharacteristic
514C22×Q8C2×Dic5311yescharacteristic
515C22×D4—21no—
516C22×D4C2×Dic5311yescharacteristic
517C23×C4—21no—
518C23×C4—1061no—
519C23×C4C22×D5311yescharacteristic
520#135—22no—
521#135—22no—
522#135—41no—
523#135—41no—
524C2×Q16C2×Dic5311yescharacteristic, complemented
525C2×Q16C2×Dic5311yescharacteristic, complemented
526C2×SD16C2×Dic5311yescharacteristic, complemented
527C2×SD16C2×Dic5311yescharacteristic, complemented
528C2×SD16C2×Dic5311yescharacteristic, complemented
529C2×SD16C2×Dic5311yescharacteristic, complemented
530C2×D8C2×Dic5311yescharacteristic, complemented
531C2×D8C2×Dic5311yescharacteristic, complemented
532#131—1062no—
533#131—1062no—
534#131—1062no—
535#131—2121no—
536#131—2121no—
537#131—2121no—
538C2×M16—531no—
539C2×M16—531no—
540C2×M16—531no—
541C2×M16—531no—
542C2×M16—1061no—
543C2×M16—1061no—
544C2×M16—1061no—
545C2×M16—1061no—
546C2×M16—1062no—
547C2×M16—2121no—
548C22×C8—531no—
549C22×C8—531no—
550C22×C8—1061no—
551C22×C8—1061no—
552C22×C8—1061no—
553C22×C8—1061no—
554C22×C8C22×D5311yescharacteristic
555C22×C8C22×D5311yescharacteristic
556#123—21no—
557C22⋊Q8C2×Dic5311yescharacteristic
558C22⋊Q8C2×Dic5311yescharacteristic
559#121C2×Dic5311yescharacteristic
560#121C2×Dic5311yescharacteristic
561#120—21no—
562C4×D4—21no—
563C4×D4—21no—
564#117C22×D5311yescharacteristic
565C2×C42—531no—
566C2×C42—531no—
567C2×C42—1062no—
568C2×C42—1061no—
569C2×C42—2121no—
570#108—1062no—
571#108—2121no—
572C4⋊C8—1061no—
573C4⋊C8—1061no—
574#104—534no—
575#104—1062no—
576#104—1062no—
577#104—1062no—
578#104—1062no—
579#104—2121no—
580#103C2×Dic5311yescharacteristic, complemented
581#103C2×Dic5311yescharacteristic, complemented
582#103C2×Dic5311yescharacteristic, complemented
583#103C2×Dic5311yescharacteristic, complemented
584#102C2×Dic5311yescharacteristic, complemented
585#102C2×Dic5311yescharacteristic, complemented
586#102C2×Dic5311yescharacteristic, complemented
587#102C2×Dic5311yescharacteristic, complemented
588C22⋊C8—531no—
589C22⋊C8—531no—
590C22⋊C8—531no—
591C22⋊C8—531no—
592C22⋊C8—1061no—
593C22⋊C8—1061no—
594C22⋊C8—1061no—
595C22⋊C8—1061no—
596C22⋊C8—1061no—
597C22⋊C8—1061no—
598C22⋊C8—1061no—
599C22⋊C8—1061no—
600C22⋊C8C2×Dic5311yescharacteristic
601C22⋊C8C2×Dic5311yescharacteristic
602C22⋊C8C2×Dic5311yescharacteristic
603C22⋊C8C2×Dic5311yescharacteristic
604#97—1061no—
605#97—1062no—
606#97—2121no—
607C4×C8—1061no—
608C24—21no—
609C24#1171994711yescharacteristic
610#41—21no—
611#41—21no—
612#41—22no—
613#41—22no—
614#41—21no—
615#41—21no—
616#41—21no—
617#41—21no—
618#41—21no—
619#41—21no—
620#41—21no—
621#41—21no—
622#41—42no—
623#41—42no—
624#41—41no—
625#41—41no—
626#41—42no—
627#41—42no—
628#41D4×D5312yes—
629#41#1171994712yes—
630C2×Q8—21no—
631C2×Q8—22no—
632C2×Q8—41no—
633C2×Q8C22×Dic5311yescharacteristic
634C2×Q8C22×Dic5311yescharacteristic
635C2×Q8C22×Dic5311yescharacteristic
636C2×D4—21no—
637C2×D4—22no—
638C2×D4—21no—
639C2×D4—21no—
640C2×D4—21no—
641C2×D4—21no—
642C2×D4—21no—
643C2×D4—21no—
644C2×D4—21no—
645C2×D4—41no—
646C2×D4—42no—
647C2×D4—42no—
648C2×D4C22×Dic5311yescharacteristic
649C2×D4C22×Dic5311yescharacteristic
650C2×D4C22×Dic5311yescharacteristic
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—42no—
662C22×C4—42no—
663C22×C4—1061no—
664C22×C4—1061no—
665C22×C4—2122no—
666C22×C4—2122no—
667C22×C4—2122no—
668C22×C4D4×D5311yescharacteristic
669C22×C4D4×D5311yescharacteristic
670C22×C4#1171994711yescharacteristic
671C22×C4C22×Dic5311yescharacteristic
672C22×C4C22×Dic5311yescharacteristic
673C22×C4C23×D5311yescharacteristic
674Q16—22no—
675Q16—41no—
676SD16—22no—
677SD16—22no—
678SD16—41no—
679SD16—41no—
680D8—22no—
681D8—41no—
682M16—532no—
683M16—1061no—
684M16—1061no—
685M16—1061no—
686M16—1061no—
687M16—1061no—
688M16—1061no—
689M16—1061no—
690M16—2122no—
691M16—2122no—
692M16—2122no—
693M16—2122no—
694C2×C8—21no—
695C2×C8—21no—
696C2×C8—21no—
697C2×C8—21no—
698C2×C8—531no—
699C2×C8—531no—
700C2×C8—531no—
701C2×C8—531no—
702C2×C8—1061no—
703C2×C8—1061no—
704C2×C8—1061no—
705C2×C8—1061no—
706C2×C8—1061no—
707C2×C8—1061no—
708C2×C8—1061no—
709C2×C8—1061no—
710C2×C8—2122no—
711C2×C8—2122no—
712C2×C8—2122no—
713C2×C8—2122no—
714C2×C8C22×Dic5311yescharacteristic
715C2×C8C22×Dic5311yescharacteristic
716C2×C8C22×Dic5311yescharacteristic
717C2×C8C22×Dic5311yescharacteristic
718C4⋊C4—21no—
719C4⋊C4—21no—
720C4⋊C4C22×Dic5311yescharacteristic
721C4⋊C4C22×Dic5311yescharacteristic
722C22⋊C4—21no—
723C22⋊C4—21no—
724C22⋊C4—21no—
725C22⋊C4—21no—
726C22⋊C4—21no—
727C42—21no—
728C42—532no—
729C42—1061no—
730C42—1061no—
731C42—1061no—
732C42—2122no—
733C23—21no—
734C23—21no—
735C23—22no—
736C23—21no—
737C23—21no—
738C23—21no—
739C23—41no—
740C23—42no—
741C23—42no—
742C23—81no—
743C23D4×Dic5311yescharacteristic
744C23D4×Dic5311yescharacteristic
745C23C2×#1171994711yescharacteristic
746Q8—21no—
747Q8—21no—
748Q8—21no—
749Q8—21no—
750Q8—21no—
751Q8—42no—
752Q8D4×Dic5312yes—
753D4—22no—
754D4—22no—
755D4—21no—
756D4—21no—
757D4—21no—
758D4—21no—
759D4—21no—
760D4—42no—
761D4—42no—
762D4—42no—
763D4—41no—
764D4—41no—
765D4—42no—
766D4—41no—
767D4—41no—
768D4—81no—
769D4D4×Dic5312yes—
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—21no—
780C2×C4—22no—
781C2×C4—21no—
782C2×C4—21no—
783C2×C4—21no—
784C2×C4—21no—
785C2×C4—21no—
786C2×C4—21no—
787C2×C4—42no—
788C2×C4—42no—
789C2×C4—42no—
790C2×C4—41no—
791C2×C4—41no—
792C2×C4—41no—
793C2×C4—41no—
794C2×C4—1062no—
795C2×C4—1062no—
796C2×C4—2121no—
797C2×C4—2121no—
798C2×C4—2121no—
799C2×C4—2128no—
800C2×C4—2121no—
801C2×C4D4×Dic5311yescharacteristic
802C2×C4D4×Dic5311yescharacteristic
803C2×C4C23×Dic5311yescharacteristic
804C2×C4C2×D4×D5311yescharacteristic
805C2×C4C2×D4×D5311yescharacteristic
806C2×C4C2×#1171994711yescharacteristic
807C2×C4#1313326211yescharacteristic
808C2×C4#1313326211yescharacteristic
809C8—21no—
810C8—21no—
811C8—21no—
812C8—21no—
813C8—1061no—
814C8—1061no—
815C8—1062no—
816C8—1061no—
817C8—1061no—
818C8—2121no—
819C8—2121no—
820C8—2121no—
821C22—21no—
822C22—21no—
823C22—21no—
824C22—21no—
825C22—21no—
826C22—22no—
827C22—21no—
828C22—21no—
829C22—42no—
830C22—42no—
831C22—41no—
832C22—41no—
833C22—41no—
834C22—41no—
835C22—41no—
836C22—41no—
837C22—41no—
838C22—41no—
839C22—84no—
840C22#1681074512yescomplemented
841C22C2×D4×Dic5311yescharacteristic
842C22#1681126011yescharacteristic
843C22#1681130411yescharacteristic
844C4—21no—
845C4—21no—
846C4—22no—
847C4—41no—
848C4—41no—
849C4—41no—
850C4—41no—
851C4—2122no—
852C4—2122no—
853C4C2×D4×Dic5311yescharacteristic
854C4#1681109811yescharacteristic
855C4#1681125511yescharacteristic
856C4#1681126011yescharacteristic
857C2—21no—
858C2—22no—
859C2—21no—
860C2—41no—
861C2—42no—
862C2—81no—
863C2—81no—
864C2#2027769911yescharacteristic
865C2C2×#1681074511yescharacteristic
866C2#2028362511yescharacteristic
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#22886
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. C22×#13133144C2semidirect
4. #20283164C2semidirect
5. #20275609C2semidirect
6. #20275428C2semidirect
7. #20275365C2semidirect
8. #20275159C2semidirect
9. #20275044C2semidirect
10. #20275044C2semidirect
11. #20274992C2semidirect
12. #20274922C2semidirect
13. #20274562C2semidirect
14. #20274479C2semidirect
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×#13133127C22semidirect
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
143. C2×Q16×C53C2×C4semidirect
144. C2×Q16×C53C2×C4semidirect
145. C2×SD16×C53C2×C4semidirect
146. C2×SD16×C53C2×C4semidirect
147. C2×SD16×C53C2×C4semidirect
148. C2×SD16×C53C2×C4semidirect
149. C2×D8×C53C2×C4semidirect
150. C2×D8×C53C2×C4semidirect
162. #103×C53C2×C4semidirect
163. #103×C53C2×C4semidirect
164. #103×C53C2×C4semidirect
165. #103×C53C2×C4semidirect
166. #102×C53C2×C4semidirect
167. #102×C53C2×C4semidirect
168. #102×C53C2×C4semidirect
169. #102×C53C2×C4semidirect
407. C22×C53#444semidirect
458. #452Dic53semidirect
459. #452Dic53semidirect
460. #451Dic53semidirect
461. #450Dic53semidirect
462. #449Dic53semidirect
463. #449Dic53semidirect
464. #448Dic53semidirect
465. #447Dic53semidirect
502. C53#22886semidirect
524. C2×Q16C2×Dic53semidirect
525. C2×Q16C2×Dic53semidirect
526. C2×SD16C2×Dic53semidirect
527. C2×SD16C2×Dic53semidirect
528. C2×SD16C2×Dic53semidirect
529. C2×SD16C2×Dic53semidirect
530. C2×D8C2×Dic53semidirect
531. C2×D8C2×Dic53semidirect
580. #103C2×Dic53semidirect
581. #103C2×Dic53semidirect
582. #103C2×Dic53semidirect
583. #103C2×Dic53semidirect
584. #102C2×Dic53semidirect
585. #102C2×Dic53semidirect
586. #102C2×Dic53semidirect
587. #102C2×Dic53semidirect
840. C22#16810745semidirect

Maximal subgroups

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

subgroupindex
C2×#168107452
#202834422
C22×#131331442
#202831642
#202756092
#202754282
#202753652
#202751592
#202750442
#202749922
#202749222
#202745622
#202744792
C53×#30022
#2288653