Finite Group Databasebeta

← #27306328

Subgroups — #27306328

Order 13568.

2430 conjugacy classes of subgroups.

The subgroup lattice has 988 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×C22⋊D53C211yesmaximal, characteristic
2C2×#16810488C211yesmaximal, characteristic, complemented
3C2×#16810483C211yesmaximal, characteristic, complemented
4C2×#16810480C211yesmaximal, characteristic, complemented
5C2×#16810480C211yesmaximal, characteristic, complemented
6C2×C4⋊C4×Dic53C211yesmaximal, characteristic, complemented
7#20272981C212yesmaximal, complemented
8#20272954C212yesmaximal
9#20272952C212yesmaximal, complemented
10#20272951C212yesmaximal, complemented
11C2×C53×#380C211yesmaximal, characteristic, complemented
12C23×C22⋊D53C2211yescharacteristic
13C23×C4×D53C2211yescharacteristic
14C2×C4×C22⋊D53—24no—
15C2×C4×C22⋊D53—24no—
16C2×C4×C22⋊D53C418yescomplemented
17C22×C4⋊Dic53C2211yescharacteristic
18C22×C4⋊Dic53C2211yescharacteristic
19C22×#11719919C2211yescharacteristic
20C22×C22⋊Dic53C2212yes—
21C22×C22⋊Dic53C2211yescharacteristic
22C22×#11719921C2212yes—
23C22×#11719921C2212yes—
24C22×#11719921C2211yescharacteristic
25C22×C4×Dic53C2212yes—
26C22×C4×Dic53C2211yescharacteristic
27#16810488—24no—
28#16810483—24no—
29#16810480—24no—
30#16810480—24no—
31C4⋊C4×Dic53—24no—
32C2×#13133124C2212yes—
33C2×#13133124C2212yes—
34C2×#13133124C2212yes—
35C2×#13133124C2212yes—
36C2×#13133124C2212yes—
37C2×#13133124C2212yes—
38C24×C4×C53C2211yescharacteristic
39C22×C4⋊C4×C53C2211yescharacteristic
40C22×C4⋊C4×C53C2211yescharacteristic
41C22×C22⋊C4×C53C2212yes—
42C53×#380—24no—
43C2×#95×C53C2212yes—
44C24×D53C2311yescharacteristic
45C22×C22⋊D53—22no—
46C22×C22⋊D53—22no—
47C22×C22⋊D53—22no—
48C22×C22⋊D53—22no—
49C22×C22⋊D53—22no—
50C22×C22⋊D53—22no—
51C22×C22⋊D53C2×C414yes—
52C23×Dic53C2312yes—
53C23×Dic53C2311yescharacteristic
54C23×Dic53C2312yes—
55C23×Dic53C2311yescharacteristic
56C23×Dic53C2311yescharacteristic
57C22×C4×D53—22no—
58C22×C4×D53—22no—
59C22×C4×D53—22no—
60C22×C4×D53—22no—
61C22×C4×D53—22no—
62C22×C4×D53—22no—
63C22×C4×D53C2×C414yes—
64C4×C22⋊D53—232no—
65C2×C4⋊Dic53—22no—
66C2×C4⋊Dic53—22no—
67C2×C4⋊Dic53—22no—
68C2×C4⋊Dic53—22no—
69C2×C4⋊Dic53—22no—
70C2×C4⋊Dic53D414yescomplemented
71C2×#11719919—22no—
72C2×#11719919—22no—
73C2×#11719919C2×C414yes—
74C2×C22⋊Dic53—24no—
75C2×C22⋊Dic53—22no—
76C2×C22⋊Dic53—22no—
77C2×C22⋊Dic53—24no—
78C2×C22⋊Dic53—42no—
79C2×C22⋊Dic53C2×C414yes—
80C2×#11719921—24no—
81C2×#11719921—24no—
82C2×#11719921—24no—
83C2×#11719921—22no—
84C2×#11719921—22no—
85C2×#11719921—24no—
86C2×#11719921—42no—
87C2×#11719921—42no—
88C2×#11719921C2×C414yes—
89C2×C4×Dic53—24no—
90C2×C4×Dic53—42no—
91C2×C4×Dic53—42no—
92C2×C4×Dic53C2×C414yes—
93C2×C4×Dic53D414yes—
94C2×C4×Dic53D414yes—
95#13133124—24no—
96#13133124—24no—
97#13133124—24no—
98#13133124—24no—
99#13133124—24no—
100#13133124—24no—
101C25×C53C2311yescharacteristic
102C23×C4×C53—22no—
103C23×C4×C53—22no—
104C23×C4×C53—22no—
105C23×C4×C53—22no—
106C23×C4×C53—22no—
107C23×C4×C53—22no—
108C23×C4×C53C2×C414yes—
109C23×C4×C53C2312yes—
110C23×C4×C53C2311yescharacteristic
111C23×C4×C53C2312yes—
112C23×C4×C53C2311yescharacteristic
113C2×C4⋊C4×C53—22no—
114C2×C4⋊C4×C53—22no—
115C2×C4⋊C4×C53—22no—
116C2×C4⋊C4×C53—22no—
117C2×C4⋊C4×C53—22no—
118C2×C4⋊C4×C53D414yescomplemented
119C2×C22⋊C4×C53—24no—
120C2×C22⋊C4×C53—24no—
121C2×C22⋊C4×C53—42no—
122#95×C53—24no—
123C24×C53—21no—
124C24×C53—21no—
125C24×C53—21no—
126C24×C53—21no—
127C24×C53—21no—
128C24×C53—21no—
129C24×C53—21no—
130C24×C53—21no—
131C24×C53—21no—
132C24×C53—21no—
133C24×C53—21no—
134C24×C53—21no—
135C24×C53C22×C412yes—
136C24×C53#4112yes—
137C24×C53#4112yes—
138C24×C53C2411yescharacteristic
139C23×D53—21no—
140C23×D53—21no—
141C23×D53—21no—
142C23×D53—21no—
143C23×D53—21no—
144C23×D53—21no—
145C23×D53—21no—
146C23×D53—21no—
147C23×D53—21no—
148C23×D53—21no—
149C23×D53—21no—
150C23×D53—21no—
151C23×D53C22×C412yes—
152C23×D53#4112yes—
153C23×D53#4112yes—
154C22×C4×C53—21no—
155C22×C4×C53—22no—
156C22×C4×C53—21no—
157C22×C4×C53—21no—
158C22×C4×C53—21no—
159C22×C4×C53—22no—
160C22×C4×C53—22no—
161C22×C4×C53—21no—
162C22×C4×C53—21no—
163C22×C4×C53—22no—
164C22×C4×C53—22no—
165C22×C4×C53—22no—
166C22×C4×C53—28no—
167C22×C4×C53—28no—
168C22×C4×C53—28no—
169C22×C4×C53—22no—
170C22×C4×C53—22no—
171C22×C4×C53—22no—
172C22×C4×C53—22no—
173C22×C4×C53—22no—
174C22×C4×C53—22no—
175C22×C4×C53—22no—
176C22×C4×C53—44no—
177C22×C4×C53—44no—
178C22×C4×C53—44no—
179C22×C4×C53—44no—
180C22×C4×C53C22×C412yes—
181C22×C4×C53C22×C412yes—
182C22×C4×C53C2×D414yes—
183C22×C4×C53C2×D412yes—
184C22×C4×C53C2×D412yes—
185C22×C4×C53C2×D412yes—
186C22×C4×C53C2×D412yes—
187C22×C4×C53#4112yes—
188C22×C4×C53#4112yes—
189C2×C22⋊D53—28no—
190C2×C22⋊D53—28no—
191C2×C22⋊D53—28no—
192C2×C22⋊D53—28no—
193C2×C22⋊D53—28no—
194C2×C22⋊D53—28no—
195C2×C22⋊D53—28no—
196C22×Dic53—21no—
197C22×Dic53—21no—
198C22×Dic53—21no—
199C22×Dic53—21no—
200C22×Dic53—21no—
201C22×Dic53—21no—
202C22×Dic53—21no—
203C22×Dic53—21no—
204C22×Dic53—21no—
205C22×Dic53—21no—
206C22×Dic53—22no—
207C22×Dic53—21no—
208C22×Dic53—21no—
209C22×Dic53—22no—
210C22×Dic53—22no—
211C22×Dic53—22no—
212C22×Dic53—21no—
213C22×Dic53—21no—
214C22×Dic53—22no—
215C22×Dic53—22no—
216C22×Dic53—22no—
217C22×Dic53—22no—
218C22×Dic53—22no—
219C22×Dic53—22no—
220C22×Dic53—22no—
221C22×Dic53—22no—
222C22×Dic53—22no—
223C22×Dic53C22×C412yes—
224C22×Dic53C22×C412yes—
225C22×Dic53C22×C412yes—
226C22×Dic53C2×D414yes—
227C22×Dic53C2×D412yes—
228C22×Dic53C2×D412yes—
229C22×Dic53C2×D412yes—
230C22×Dic53C2×D412yes—
231C2×C4×D53—28no—
232C2×C4×D53—28no—
233C2×C4×D53—28no—
234C2×C4×D53—44no—
235C2×C4×D53—44no—
236C2×C4×D53—44no—
237C2×C4×D53—44no—
238C4⋊C4×C53—28no—
239C4⋊C4×C53—44no—
240C22⋊C4×C53—48no—
241C22⋊Dic53—28no—
242C22⋊Dic53—48no—
243#11719921—28no—
244#11719921—48no—
245#11719921—48no—
246C4⋊Dic53—28no—
247C4⋊Dic53—44no—
248#11719919—28no—
249C4×Dic53—48no—
250C4×Dic53C22⋊C4116yescomplemented
251C23×C53—22no—
252C23×C53—22no—
253C23×C53—22no—
254C23×C53—22no—
255C23×C53—22no—
256C23×C53—22no—
257C23×C53—22no—
258C23×C53—22no—
259C23×C53—22no—
260C23×C53—22no—
261C23×C53—22no—
262C23×C53—22no—
263C23×C53—22no—
264C23×C53—22no—
265C23×C53—22no—
266C23×C53—22no—
267C23×C53—22no—
268C23×C53—22no—
269C23×C53—41no—
270C23×C53—41no—
271C23×C53—41no—
272C23×C53—41no—
273C23×C53—41no—
274C23×C53—41no—
275C23×C53—41no—
276C23×C53—41no—
277C23×C53—41no—
278C23×C53—41no—
279C23×C53—41no—
280C23×C53—41no—
281C23×C53—41no—
282C23×C53—41no—
283C23×C53—41no—
284C23×C53—41no—
285C23×C53#11714yes—
286C23×C53C23×C411yescharacteristic
287C23×C53C22×D411yescharacteristic
288C23×C53C22×D411yescharacteristic
289C23×C53C22×D411yescharacteristic
290C23×C53C22×D411yescharacteristic
291C23×C53C2×#4111yescharacteristic
292C23×C53C2×#4111yescharacteristic
293C23×C53C2×#4111yescharacteristic
294C23×C53C2×#4111yescharacteristic
295C23×C53C2×#4111yescharacteristic
296C23×C53C2×#4111yescharacteristic
297C23×C53H(5,𝔽2)11yescharacteristic
298C23×C53H(5,𝔽2)11yescharacteristic
299C23×C532−1+411yescharacteristic
300C23×C532−1+411yescharacteristic
301C22×D53—22no—
302C22×D53—22no—
303C22×D53—22no—
304C22×D53—22no—
305C22×D53—22no—
306C22×D53—22no—
307C22×D53—22no—
308C22×D53—22no—
309C22×D53—22no—
310C22×D53—22no—
311C22×D53—22no—
312C22×D53—22no—
313C22×D53—22no—
314C22×D53—22no—
315C22×D53—22no—
316C22×D53—22no—
317C22×D53—22no—
318C22×D53—22no—
319C22×D53—41no—
320C22×D53—41no—
321C22×D53—41no—
322C22×D53—41no—
323C22×D53—41no—
324C22×D53—41no—
325C22×D53—41no—
326C22×D53—41no—
327C22×D53—41no—
328C22×D53—41no—
329C22×D53—41no—
330C22×D53—41no—
331C22×D53—41no—
332C22×D53—41no—
333C22×D53—41no—
334C22×D53—41no—
335C22×D53#11714yes—
336C2×C4×C53—22no—
337C2×C4×C53—22no—
338C2×C4×C53—22no—
339C2×C4×C53—24no—
340C2×C4×C53—24no—
341C2×C4×C53—24no—
342C2×C4×C53—41no—
343C2×C4×C53—41no—
344C2×C4×C53—42no—
345C2×C4×C53—41no—
346C2×C4×C53—41no—
347C2×C4×C53—42no—
348C2×C4×C53—42no—
349C2×C4×C53—42no—
350C2×C4×C53—416no—
351C2×C4×C53—42no—
352C2×C4×C53—42no—
353C2×C4×C53—42no—
354C2×C4×C53—42no—
355C2×C4×C53—42no—
356C2×C4×C53—42no—
357C2×C4×C53—42no—
358C2×C4×C53C2×C22⋊C414yes—
359C2×C4×C53C4×D414yes—
360C2×C4×C53C4×D414yes—
361C2×C4×C53#12114yes—
362C2×C4×C53#12114yes—
363C2×C4×C53#12414yes—
364C2×C4×C53#12714yes—
365C22⋊D53—232no—
366C2×Dic53—22no—
367C2×Dic53—22no—
368C2×Dic53—22no—
369C2×Dic53—22no—
370C2×Dic53—22no—
371C2×Dic53—22no—
372C2×Dic53—22no—
373C2×Dic53—22no—
374C2×Dic53—22no—
375C2×Dic53—22no—
376C2×Dic53—22no—
377C2×Dic53—22no—
378C2×Dic53—22no—
379C2×Dic53—22no—
380C2×Dic53—22no—
381C2×Dic53—24no—
382C2×Dic53—24no—
383C2×Dic53—24no—
384C2×Dic53—41no—
385C2×Dic53—41no—
386C2×Dic53—42no—
387C2×Dic53—41no—
388C2×Dic53—41no—
389C2×Dic53—42no—
390C2×Dic53—42no—
391C2×Dic53—42no—
392C2×Dic53—42no—
393C2×Dic53—42no—
394C2×Dic53—42no—
395C2×Dic53—42no—
396C2×Dic53—42no—
397C2×Dic53—42no—
398C2×Dic53—42no—
399C2×Dic53C2×C22⋊C414yes—
400C2×Dic53C2×C22⋊C414yes—
401C4×D53—416no—
402#13905—531nomaximal, Sylow
403C22×C53—24no—
404C22×C53—24no—
405C22×C53—24no—
406C22×C53—42no—
407C22×C53—42no—
408C22×C53—42no—
409C22×C53—42no—
410C22×C53—42no—
411C22×C53—42no—
412C22×C53—42no—
413C22×C53—42no—
414C22×C53—42no—
415C22×C53—42no—
416C22×C53—42no—
417C22×C53—42no—
418C22×C53C22×C22⋊C411yescharacteristic
419C22×C53C2×#11711yescharacteristic
420C22×C53C2×#11711yescharacteristic
421C22×C53C2×C4×D411yescharacteristic
422C22×C53C2×C4×D411yescharacteristic
423C22×C53#52011yescharacteristic
424C22×C53#52011yescharacteristic
425C22×C53C2×#12111yescharacteristic
426C22×C53C2×#12111yescharacteristic
427C22×C53#52511yescharacteristic
428C22×C53#52511yescharacteristic
429C22×C53#52511yescharacteristic
430C22×C53#52511yescharacteristic
431C22×C53C2×#12411yescharacteristic
432C22×C53C2×#12711yescharacteristic
433C22×C53#53511yescharacteristic
434C22×C53#53611yescharacteristic
435C22×C53#53711yescharacteristic
436C22×C53#53711yescharacteristic
437C22×C53#54611yescharacteristic
438C22×C53#54611yescharacteristic
439C22×C53#54611yescharacteristic
440C22×C53#54611yescharacteristic
441C22×C53#54811yescharacteristic
442C22×C53#54811yescharacteristic
443C22×C53#54811yescharacteristic
444C22×C53#54811yescharacteristic
445C22×C53#55211yescharacteristic
446C22×C53#55211yescharacteristic
447C22×C53#55211yescharacteristic
448C22×C53#55211yescharacteristic
449C22×C53#55311yescharacteristic
450C22×C53#55311yescharacteristic
451C22×C53#55311yescharacteristic
452C22×C53#55311yescharacteristic
453C2×D53—24no—
454C2×D53—24no—
455C2×D53—24no—
456C2×D53—42no—
457C2×D53—42no—
458C2×D53—42no—
459C2×D53—42no—
460C2×D53—42no—
461C2×D53—42no—
462C2×D53—42no—
463C2×D53—42no—
464C2×D53—42no—
465C2×D53—42no—
466C2×D53—42no—
467C2×D53—42no—
468C4×C53—44no—
469C4×C53—42no—
470C4×C53—82no—
471C4×C53#39018yes—
472Dic53—24no—
473Dic53—24no—
474Dic53—44no—
475Dic53—42no—
476Dic53—82no—
477C22×C4×D4—531no—
478C2×#382—531no—
479C2×#380—531no—
480C2×#380—531no—
481C2×#380—531no—
482C2×#380D5311yescharacteristic, complemented
483C2×C4×C4⋊C4—531no—
484#1445—532no—
485#1438—532no—
486#1437—532no—
487#1437—532no—
488C2×C53—44no—
489C2×C53#228011yescharacteristic
490C2×C53C2×#39011yescharacteristic
491C2×C53#231111yescharacteristic
492C2×C53#235211yescharacteristic
493C2×C53#235211yescharacteristic
494C2×C53#235211yescharacteristic
495C2×C53#235211yescharacteristic
496C2×C53#253511yescharacteristic
497C2×C53#253511yescharacteristic
498C2×C53#253611yescharacteristic
499C2×C53#253611yescharacteristic
500C2×C53#254011yescharacteristic
501C2×C53#254011yescharacteristic
502C2×C53#256211yescharacteristic
503C2×C53#256211yescharacteristic
504D53—44no—
505C23×D4—531no—
506C24×C4—531no—
507C24×C4C2×D5311yescharacteristic
508C2×C4×D4—538no—
509C2×C4×D4—1064no—
510C2×C4×D4—1064no—
511C22×C4⋊C4—531no—
512C22×C4⋊C4—531no—
513C22×C4⋊C4—531no—
514C22×C4⋊C4C2×D5311yescharacteristic
515C22×C4⋊C4C2×D5311yescharacteristic
516C22×C22⋊C4—531no—
517C22×C22⋊C4—531no—
518C22×C22⋊C4—532no—
519C22×C22⋊C4—532no—
520C22×C22⋊C4—532no—
521C22×C22⋊C4C2×D5312yes—
522C22×C42—531no—
523C22×C42—532no—
524#382—1064no—
525#380—24no—
526#380—1064no—
527#380—1064no—
528#380—1064no—
529C4×C4⋊C4—1064no—
530C2×#95—532no—
531C2×#95—532no—
532C2×#95—532no—
533C2×#95—532no—
534C2×#95—532no—
535C2×#95—532no—
536C2×#95C2×D5312yes—
537C53#1390511yescharacteristic, complemented, Sylow
538C25—531no—
539C25C22×D5311yescharacteristic
540C22×D4—534no—
541C22×D4—1062no—
542C22×D4—1062no—
543C22×D4—1062no—
544C22×D4—1062no—
545C22×D4—1062no—
546C22×D4—1062no—
547C23×C4—22no—
548C23×C4—22no—
549C23×C4—22no—
550C23×C4—22no—
551C23×C4—22no—
552C23×C4—22no—
553C23×C4—531no—
554C23×C4—531no—
555C23×C4—532no—
556C23×C4—531no—
557C23×C4—534no—
558C23×C4—532no—
559C23×C4—1062no—
560C23×C4—1062no—
561C23×C4—1062no—
562C23×C4—1062no—
563C23×C4—1062no—
564C23×C4—1062no—
565C23×C4C4×D5314yes—
566C23×C4C22×D5312yes—
567C23×C4C22×D5311yescharacteristic
568C23×C4C22×D5312yes—
569C23×C4C22×D5311yescharacteristic
570C4×D4—10632no—
571C2×C4⋊C4—22no—
572C2×C4⋊C4—22no—
573C2×C4⋊C4—22no—
574C2×C4⋊C4—22no—
575C2×C4⋊C4—22no—
576C2×C4⋊C4—534no—
577C2×C4⋊C4—534no—
578C2×C4⋊C4—1062no—
579C2×C4⋊C4—1062no—
580C2×C4⋊C4—1062no—
581C2×C4⋊C4—1062no—
582C2×C4⋊C4—1062no—
583C2×C4⋊C4—1062no—
584C2×C4⋊C4—1062no—
585C2×C4⋊C4C22⋊D5314yescomplemented
586C2×C22⋊C4—24no—
587C2×C22⋊C4—24no—
588C2×C22⋊C4—42no—
589C2×C22⋊C4—534no—
590C2×C22⋊C4—534no—
591C2×C22⋊C4—1062no—
592C2×C22⋊C4—1062no—
593C2×C22⋊C4—1062no—
594C2×C22⋊C4—1062no—
595C2×C22⋊C4—1064no—
596C2×C22⋊C4—1064no—
597C2×C22⋊C4—1064no—
598C2×C22⋊C4—1064no—
599C2×C22⋊C4—1064no—
600C2×C22⋊C4—1064no—
601C2×C22⋊C4—2122no—
602C2×C22⋊C4—2122no—
603C2×C22⋊C4—2122no—
604C2×C42—534no—
605C2×C42—534no—
606C2×C42—534no—
607C2×C42—1064no—
608C2×C42—2122no—
609C2×C42—2122no—
610#95—24no—
611#95—1064no—
612#95—1064no—
613#95—1064no—
614#95—1064no—
615#95—1064no—
616#95—1064no—
617C24—21no—
618C24—21no—
619C24—21no—
620C24—21no—
621C24—21no—
622C24—21no—
623C24—21no—
624C24—21no—
625C24—21no—
626C24—21no—
627C24—21no—
628C24—21no—
629C24—532no—
630C24—532no—
631C24—532no—
632C24—1061no—
633C24—1061no—
634C24—1061no—
635C24—1061no—
636C24—1061no—
637C24—1061no—
638C24—1061no—
639C24—1061no—
640C24—1061no—
641C24—1061no—
642C24—1061no—
643C24—1061no—
644C24C2×C4×D5312yes—
645C24#1171994712yes—
646C24#1171994912yes—
647C24C23×D5311yescharacteristic
648C2×D4—1068no—
649C2×D4—1068no—
650C2×D4—1068no—
651C2×D4—1068no—
652C2×D4—1068no—
653C2×D4—1068no—
654C2×D4—1068no—
655C22×C4—21no—
656C22×C4—22no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—22no—
661C22×C4—22no—
662C22×C4—22no—
663C22×C4—21no—
664C22×C4—21no—
665C22×C4—22no—
666C22×C4—22no—
667C22×C4—28no—
668C22×C4—28no—
669C22×C4—28no—
670C22×C4—22no—
671C22×C4—22no—
672C22×C4—22no—
673C22×C4—22no—
674C22×C4—22no—
675C22×C4—22no—
676C22×C4—22no—
677C22×C4—44no—
678C22×C4—44no—
679C22×C4—44no—
680C22×C4—44no—
681C22×C4—532no—
682C22×C4—532no—
683C22×C4—532no—
684C22×C4—532no—
685C22×C4—532no—
686C22×C4—532no—
687C22×C4—532no—
688C22×C4—534no—
689C22×C4—1061no—
690C22×C4—1061no—
691C22×C4—1061no—
692C22×C4—1061no—
693C22×C4—1061no—
694C22×C4—1061no—
695C22×C4—1061no—
696C22×C4—1061no—
697C22×C4—1061no—
698C22×C4—1062no—
699C22×C4—1061no—
700C22×C4—1061no—
701C22×C4—1061no—
702C22×C4—1062no—
703C22×C4—1061no—
704C22×C4—1062no—
705C22×C4—1061no—
706C22×C4—1062no—
707C22×C4—1062no—
708C22×C4—1062no—
709C22×C4—1068no—
710C22×C4—1068no—
711C22×C4—1068no—
712C22×C4—1062no—
713C22×C4—1062no—
714C22×C4—1062no—
715C22×C4—1062no—
716C22×C4—1062no—
717C22×C4—1062no—
718C22×C4—1062no—
719C22×C4—2124no—
720C22×C4—2124no—
721C22×C4—2124no—
722C22×C4—2124no—
723C22×C4C2×C4×D5312yes—
724C22×C4C2×C4×D5312yes—
725C22×C4#1171994512yes—
726C22×C4D4×D5312yes—
727C22×C4D4×D5312yes—
728C22×C4D4×D5312yes—
729C22×C4#1171994712yes—
730C22×C4C2×C22⋊D5314yes—
731C22×C4C2×C22⋊D5312yes—
732C4⋊C4—28no—
733C4⋊C4—44no—
734C4⋊C4—1068no—
735C4⋊C4—1068no—
736C4⋊C4—2124no—
737C22⋊C4—48no—
738C22⋊C4—1068no—
739C22⋊C4—1068no—
740C22⋊C4—2128no—
741C22⋊C4—2128no—
742C22⋊C4—2128no—
743C42—5316no—
744C42—2128no—
745C23—22no—
746C23—22no—
747C23—22no—
748C23—22no—
749C23—22no—
750C23—22no—
751C23—22no—
752C23—22no—
753C23—22no—
754C23—22no—
755C23—22no—
756C23—22no—
757C23—22no—
758C23—22no—
759C23—22no—
760C23—22no—
761C23—22no—
762C23—22no—
763C23—41no—
764C23—41no—
765C23—41no—
766C23—41no—
767C23—41no—
768C23—41no—
769C23—41no—
770C23—41no—
771C23—41no—
772C23—41no—
773C23—41no—
774C23—41no—
775C23—41no—
776C23—41no—
777C23—41no—
778C23—41no—
779C23—534no—
780C23—1062no—
781C23—1062no—
782C23—1062no—
783C23—1062no—
784C23—1062no—
785C23—1062no—
786C23—1062no—
787C23—1062no—
788C23—1062no—
789C23—1062no—
790C23—1062no—
791C23—1062no—
792C23—1062no—
793C23—1062no—
794C23—1062no—
795C23—1062no—
796C23—1062no—
797C23—1062no—
798C23—2121no—
799C23—2121no—
800C23—2121no—
801C23—2121no—
802C23—2121no—
803C23—2121no—
804C23—2121no—
805C23—2121no—
806C23—2121no—
807C23—2121no—
808C23—2121no—
809C23—2121no—
810C23—2121no—
811C23—2121no—
812C23—2121no—
813C23—2121no—
814C23#1313317514yes—
815C23C22×C4×D5311yescharacteristic
816C23C2×D4×D5311yescharacteristic
817C23C2×D4×D5311yescharacteristic
818C23C2×D4×D5311yescharacteristic
819C23C22×C22⋊D5311yescharacteristic
820C23#41×D5311yescharacteristic
821C23#41×D5311yescharacteristic
822C23C2×#1171994711yescharacteristic
823C23C2×#1171994711yescharacteristic
824C23C2×#1171994511yescharacteristic
825C23C2×#1171994911yescharacteristic
826C23#1313326211yescharacteristic
827C23#1313326311yescharacteristic
828C23#1313326411yescharacteristic
829C23#1313326511yescharacteristic
830D4—10632no—
831C2×C4—24no—
832C2×C4—22no—
833C2×C4—22no—
834C2×C4—22no—
835C2×C4—24no—
836C2×C4—24no—
837C2×C4—42no—
838C2×C4—42no—
839C2×C4—41no—
840C2×C4—41no—
841C2×C4—42no—
842C2×C4—41no—
843C2×C4—41no—
844C2×C4—42no—
845C2×C4—416no—
846C2×C4—42no—
847C2×C4—42no—
848C2×C4—42no—
849C2×C4—42no—
850C2×C4—42no—
851C2×C4—42no—
852C2×C4—42no—
853C2×C4—534no—
854C2×C4—534no—
855C2×C4—1062no—
856C2×C4—1062no—
857C2×C4—1062no—
858C2×C4—1062no—
859C2×C4—1062no—
860C2×C4—1062no—
861C2×C4—1062no—
862C2×C4—1062no—
863C2×C4—1062no—
864C2×C4—1062no—
865C2×C4—1062no—
866C2×C4—1062no—
867C2×C4—1064no—
868C2×C4—1064no—
869C2×C4—1062no—
870C2×C4—1062no—
871C2×C4—1062no—
872C2×C4—1064no—
873C2×C4—2122no—
874C2×C4—2122no—
875C2×C4—2122no—
876C2×C4—2122no—
877C2×C4—2122no—
878C2×C4—2122no—
879C2×C4—2122no—
880C2×C4—2122no—
881C2×C4—2122no—
882C2×C4—2121no—
883C2×C4—2121no—
884C2×C4—2122no—
885C2×C4—2121no—
886C2×C4—2121no—
887C2×C4—2122no—
888C2×C4—21216no—
889C2×C4C22⋊C4×D5314yes—
890C2×C4#1313317714yes—
891C2×C4C4×C22⋊D5314yes—
892C2×C4#1313318914yes—
893C2×C4#1313319014yes—
894C2×C4#1313320314yes—
895C2×C4#1313321314yes—
896C22—24no—
897C22—24no—
898C22—24no—
899C22—42no—
900C22—42no—
901C22—42no—
902C22—42no—
903C22—42no—
904C22—42no—
905C22—42no—
906C22—42no—
907C22—42no—
908C22—42no—
909C22—42no—
910C22—42no—
911C22—1064no—
912C22—1064no—
913C22—1064no—
914C22—2122no—
915C22—2122no—
916C22—2122no—
917C22—2122no—
918C22—2122no—
919C22—2122no—
920C22—2122no—
921C22—2122no—
922C22—2122no—
923C22—2122no—
924C22—2122no—
925C22—2122no—
926C22C2×C22⋊C4×D5311yescharacteristic
927C22#117×D5311yescharacteristic
928C22C2×#1313317511yescharacteristic
929C22C2×#1313317711yescharacteristic
930C22C2×C4×C22⋊D5311yescharacteristic
931C22#1681110311yescharacteristic
932C22#1681110411yescharacteristic
933C22C2×#1313318911yescharacteristic
934C22C2×#1313319011yescharacteristic
935C22#1681113311yescharacteristic
936C22#1681113311yescharacteristic
937C22#1681113611yescharacteristic
938C22#1681113611yescharacteristic
939C22C2×#1313320311yescharacteristic
940C22C2×#1313321311yescharacteristic
941C22#1681118911yescharacteristic
942C22#1681119611yescharacteristic
943C22#1681120211yescharacteristic
944C22#1681120311yescharacteristic
945C22#1681126111yescharacteristic
946C22#1681126411yescharacteristic
947C22#1681126711yescharacteristic
948C22#1681127011yescharacteristic
949C22#1681127911yescharacteristic
950C22#1681128011yescharacteristic
951C22#1681128311yescharacteristic
952C22#1681128411yescharacteristic
953C22#1681130711yescharacteristic
954C22#1681130811yescharacteristic
955C22#1681131211yescharacteristic
956C22#1681131511yescharacteristic
957C22#1681131711yescharacteristic
958C22#1681132011yescharacteristic
959C22#1681132111yescharacteristic
960C22#1681132511yescharacteristic
961C4—44no—
962C4—42no—
963C4—82no—
964C4—1064no—
965C4—1064no—
966C4—4242no—
967C4—2124no—
968C4—2122no—
969C4#1681052318yes—
970C2—44no—
971C2—2124no—
972C2#2027709711yescharacteristic
973C2C2×#1681052311yescharacteristic
974C2#2027730411yescharacteristic
975C2#2027763711yescharacteristic
976C2#2027764011yescharacteristic
977C2#2027764511yescharacteristic
978C2#2027764611yescharacteristic
979C2#2027961411yescharacteristic
980C2#2027961811yescharacteristic
981C2#2027962211yescharacteristic
982C2#2027962611yescharacteristic
983C2#2027965111yescharacteristic
984C2#2027965311yescharacteristic
985C2#2027987811yescharacteristic
986C2#2027988011yescharacteristic
subgroupG/H
center, FrattiniC24C23×D53
commutatorC23×C53C23×C4
FittingC2×C53×#380C2
socle, cosocleC24×C53C24
prime radicalC23×C22⋊D53C22
hypercenterC2×#380D53
hypocenterC53#13905
LCSG ▷ C23×C53 ▷ C53
UCSC1 ◁ C24 ◁ C2×#380

Complements

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

NH ≅ G/Ntype
2. C2×#16810488C2semidirect
3. C2×#16810483C2semidirect
4. C2×#16810480C2semidirect
5. C2×#16810480C2semidirect
6. C2×C4⋊C4×Dic53C2semidirect
7. #20272981C2semidirect
9. #20272952C2semidirect
10. #20272951C2semidirect
11. C2×C53×#380C2semidirect
16. C2×C4×C22⋊D53C4semidirect
70. C2×C4⋊Dic53D4semidirect
118. C2×C4⋊C4×C53D4semidirect
250. C4×Dic53C22⋊C4semidirect
482. C2×#380D53semidirect
537. C53#13905semidirect
585. C2×C4⋊C4C22⋊D53semidirect

Maximal subgroups

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

subgroupindex
C22×C4×C22⋊D532
C2×#168104882
C2×#168104832
C2×#168104802
C2×C4⋊C4×Dic532
#202729812
#202729542
#202729522
#202729512
C2×C53×#3802
#1390553