Finite Group Databasebeta

← #27312104

Subgroups — #27312104

Order 13568.

1650 conjugacy classes of subgroups.

The subgroup lattice has 1022 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16810519C211yesmaximal, characteristic, complemented
2C2×#16810516C211yesmaximal, characteristic
3C2×#16810498C211yesmaximal, characteristic
4C2×#16810481C211yesmaximal, characteristic
5#20272979C211yesmaximal, characteristic, complemented
6#20272974C211yesmaximal, characteristic, complemented
7#20272967C211yesmaximal, characteristic, complemented
8#20272967C211yesmaximal, characteristic, complemented
9#20272958C211yesmaximal, characteristic
10#20272958C211yesmaximal, characteristic
11#20272948C211yesmaximal, characteristic, complemented
12#20272946C211yesmaximal, characteristic, complemented
13#20272945C211yesmaximal, characteristic, complemented
14#20272937C211yesmaximal, characteristic
15C2×C53×#388C211yesmaximal, characteristic
16C24×Dic53C2211yescharacteristic
17C22×C4⋊Dic53C2211yescharacteristic
18C22×C4⋊Dic53C2211yescharacteristic
19C22×C4⋊Dic53C2211yescharacteristic
20C22×#11719919C2211yescharacteristic
21C22×#11719919C2211yescharacteristic
22C22×#11719919C2211yescharacteristic
23C22×#11719919C2211yescharacteristic
24C22×C22⋊Dic53C2211yescharacteristic
25C22×C22⋊Dic53C2211yescharacteristic
26C22×C22⋊Dic53C2211yescharacteristic
27C22×C4×Dic53C2211yescharacteristic
28#16810519—24no—
29#16810516—24no—
30#16810498C418yescomplemented
31#16810481—24no—
32C2×#13133124C2211yescharacteristic
33C2×#13133124C2211yescharacteristic
34C2×#13133124C2211yescharacteristic
35C2×#13133124C2211yescharacteristic
36C2×#13133124C2211yescharacteristic
37C2×#13133124C2211yescharacteristic
38C2×#13133124C2211yescharacteristic
39C2×#13133124C2211yescharacteristic
40C2×#13133124C2211yescharacteristic
41C2×#13133124C2211yescharacteristic
42C2×#13133124C2211yescharacteristic
43C2×#13133124C2211yescharacteristic
44C2×#13133124C2211yescharacteristic
45C2×#13133124C2211yescharacteristic
46C2×#13133124C2211yescharacteristic
47C2×#13133124C2211yescharacteristic
48C22×C4⋊C4×C53C2211yescharacteristic
49C22×C22⋊C4×C53C2211yescharacteristic
50C22×C22⋊C4×C53C2211yescharacteristic
51C22×C22⋊C4×C53C2211yescharacteristic
52C22×C42×C53C2211yescharacteristic
53C53×#388—24no—
54C2×#95×C53C2211yescharacteristic
55C2×#95×C53C2211yescharacteristic
56C23×Dic53—22no—
57C23×Dic53—22no—
58C23×Dic53—41no—
59C23×Dic53—41no—
60C23×Dic53—41no—
61C23×Dic53—41no—
62C23×Dic53C2×C414yes—
63C23×Dic53C2311yescharacteristic
64C23×Dic53C2311yescharacteristic
65C23×Dic53C2311yescharacteristic
66C23×Dic53C2311yescharacteristic
67C23×Dic53C2311yescharacteristic
68C23×Dic53C2311yescharacteristic
69C23×Dic53C2311yescharacteristic
70C23×Dic53C2311yescharacteristic
71C2×C4⋊Dic53—22no—
72C2×C4⋊Dic53—22no—
73C2×C4⋊Dic53—22no—
74C2×C4⋊Dic53—22no—
75C2×C4⋊Dic53—41no—
76C2×C4⋊Dic53—41no—
77C2×C4⋊Dic53—41no—
78C2×C4⋊Dic53C2×C414yes—
79C2×C4⋊Dic53C2×C414yes—
80C2×#11719919—22no—
81C2×#11719919—22no—
82C2×#11719919—22no—
83C2×#11719919—41no—
84C2×#11719919—41no—
85C2×#11719919—41no—
86C2×#11719919—41no—
87C2×#11719919—41no—
88C2×#11719919—41no—
89C2×#11719919—41no—
90C2×#11719919—41no—
91C2×#11719919D414yes—
92C2×C22⋊Dic53—22no—
93C2×C22⋊Dic53—22no—
94C2×C22⋊Dic53—22no—
95C2×C22⋊Dic53—22no—
96C2×C22⋊Dic53—41no—
97C2×C22⋊Dic53—41no—
98C2×C22⋊Dic53—41no—
99C2×C22⋊Dic53—41no—
100C2×C22⋊Dic53C2×C414yes—
101C2×C4×Dic53—22no—
102C2×C4×Dic53—22no—
103C2×C4×Dic53—41no—
104#13133124—22no—
105#13133124—22no—
106#13133124—22no—
107#13133124—22no—
108#13133124—22no—
109#13133124—22no—
110#13133124—22no—
111#13133124—22no—
112#13133124—41no—
113#13133124—41no—
114#13133124—41no—
115#13133124—41no—
116#13133124—41no—
117#13133124—41no—
118#13133124C2×C414yes—
119#13133124C2×C414yes—
120C25×C53C2311yescharacteristic
121C23×C4×C53C2311yescharacteristic
122C23×C4×C53C2311yescharacteristic
123C23×C4×C53C2311yescharacteristic
124C23×C4×C53C2311yescharacteristic
125C23×C4×C53C2311yescharacteristic
126C23×C4×C53C2311yescharacteristic
127C2×C4⋊C4×C53—22no—
128C2×C4⋊C4×C53—22no—
129C2×C4⋊C4×C53—41no—
130C2×C22⋊C4×C53—22no—
131C2×C22⋊C4×C53—22no—
132C2×C22⋊C4×C53—22no—
133C2×C22⋊C4×C53—22no—
134C2×C22⋊C4×C53—41no—
135C2×C22⋊C4×C53—41no—
136C2×C22⋊C4×C53C2×C414yes—
137C2×C22⋊C4×C53D414yes—
138C2×C22⋊C4×C53Q814yes—
139C2×C42×C53—22no—
140C2×C42×C53—22no—
141C2×C42×C53—41no—
142#95×C53—22no—
143#95×C53—22no—
144C24×C53—21no—
145C24×C53—21no—
146C24×C53—21no—
147C24×C53—21no—
148C24×C53—21no—
149C24×C53—21no—
150C24×C53—21no—
151C24×C53—21no—
152C24×C53—21no—
153C24×C53—21no—
154C24×C53—21no—
155C24×C53—21no—
156C24×C53C22×C412yes—
157C24×C53C2×D412yes—
158C24×C53C2×Q812yes—
159C24×C53C2411yescharacteristic
160C22×C4×C53—21no—
161C22×C4×C53—21no—
162C22×C4×C53—21no—
163C22×C4×C53—21no—
164C22×C4×C53—21no—
165C22×C4×C53—21no—
166C22×C4×C53—21no—
167C22×C4×C53—21no—
168C22×C4×C53—21no—
169C22×C4×C53—21no—
170C22×C4×C53—21no—
171C22×C4×C53—21no—
172C22×C4×C53—21no—
173C22×C4×C53—21no—
174C22×C4×C53—21no—
175C22×C4×C53—21no—
176C22×C4×C53—21no—
177C22×C4×C53—21no—
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×C53—21no—
186C22×C4×C53—21no—
187C22×C4×C53—21no—
188C22×C4×C53—21no—
189C22×C4×C53—21no—
190C22×C4×C53—21no—
191C22×C4×C53—21no—
192C22×C4×C53—21no—
193C22×C4×C53—21no—
194C22×C4×C53C22×C412yes—
195C22×C4×C53C22×C412yes—
196C22×C4×C53C2×D412yes—
197C22×C4×C53C2×D412yes—
198C22×C4×C53C2×D412yes—
199C22×C4×C53C2×Q812yes—
200C22×C4×C53C2×Q812yes—
201C22×C4×C53#4112yes—
202C22×Dic53—21no—
203C22×Dic53—21no—
204C22×Dic53—21no—
205C22×Dic53—21no—
206C22×Dic53—21no—
207C22×Dic53—21no—
208C22×Dic53—21no—
209C22×Dic53—21no—
210C22×Dic53—21no—
211C22×Dic53—21no—
212C22×Dic53—21no—
213C22×Dic53—21no—
214C22×Dic53—21no—
215C22×Dic53—21no—
216C22×Dic53—21no—
217C22×Dic53—21no—
218C22×Dic53—21no—
219C22×Dic53—21no—
220C22×Dic53—21no—
221C22×Dic53—21no—
222C22×Dic53—21no—
223C22×Dic53—21no—
224C22×Dic53—21no—
225C22×Dic53—21no—
226C22×Dic53—21no—
227C22×Dic53—21no—
228C22×Dic53—21no—
229C22×Dic53—21no—
230C22×Dic53—21no—
231C22×Dic53—21no—
232C22×Dic53—21no—
233C22×Dic53—21no—
234C22×Dic53—21no—
235C22×Dic53—21no—
236C22×Dic53—28no—
237C22×Dic53—21no—
238C22×Dic53—21no—
239C22×Dic53—21no—
240C22×Dic53—21no—
241C22×Dic53—21no—
242C22×Dic53—21no—
243C22×Dic53—21no—
244C22×Dic53—21no—
245C22×Dic53—21no—
246C22×Dic53—21no—
247C22×Dic53—21no—
248C22×Dic53—21no—
249C22×Dic53—21no—
250C22×Dic53—21no—
251C22×Dic53—44no—
252C22×Dic53—44no—
253C22×Dic53—44no—
254C22×Dic53—44no—
255C22×Dic53—44no—
256C22×Dic53—44no—
257C22×Dic53C22×C412yes—
258C22×Dic53C22×C412yes—
259C22×Dic53C22×C412yes—
260C22×Dic53C22×C412yes—
261C22×Dic53C2×D412yes—
262C22×Dic53C2×D412yes—
263C22×Dic53#4112yes—
264C22×Dic53#4112yes—
265C4⋊C4×C53—44no—
266C22⋊C4×C53—44no—
267C22⋊C4×C53—44no—
268C22⋊C4×C53C4⋊C4116yescomplemented
269C42×C53—44no—
270C22⋊Dic53—44no—
271C22⋊Dic53—44no—
272C22⋊Dic53—44no—
273C4⋊Dic53—28no—
274C4⋊Dic53—44no—
275C4⋊Dic53—44no—
276#11719919—44no—
277#11719919—44no—
278#11719919—44no—
279#11719919—44no—
280C4×Dic53—44no—
281C23×C53—22no—
282C23×C53—22no—
283C23×C53—22no—
284C23×C53—22no—
285C23×C53—22no—
286C23×C53—22no—
287C23×C53—22no—
288C23×C53—22no—
289C23×C53—22no—
290C23×C53—22no—
291C23×C53—22no—
292C23×C53—22no—
293C23×C53—22no—
294C23×C53—22no—
295C23×C53—22no—
296C23×C53—22no—
297C23×C53—22no—
298C23×C53—22no—
299C23×C53—41no—
300C23×C53—41no—
301C23×C53—41no—
302C23×C53—41no—
303C23×C53—41no—
304C23×C53—41no—
305C23×C53—41no—
306C23×C53—41no—
307C23×C53—41no—
308C23×C53—41no—
309C23×C53—41no—
310C23×C53—41no—
311C23×C53—41no—
312C23×C53—41no—
313C23×C53—41no—
314C23×C53—41no—
315C23×C53C2×C4⋊C414yes—
316C23×C53C23×C411yescharacteristic
317C23×C53C22×D411yescharacteristic
318C23×C53C22×D411yescharacteristic
319C23×C53C22×Q811yescharacteristic
320C23×C53C2×#4111yescharacteristic
321C23×C53C2×#4111yescharacteristic
322C23×C53C2×#4111yescharacteristic
323C23×C53H(5,𝔽2)11yescharacteristic
324C23×C53H(5,𝔽2)11yescharacteristic
325C23×C53H(5,𝔽2)11yescharacteristic
326C23×C53H(5,𝔽2)11yescharacteristic
327C23×C53H(5,𝔽2)11yescharacteristic
328C23×C532−1+411yescharacteristic
329C23×C532−1+411yescharacteristic
330C23×C532−1+411yescharacteristic
331C2×C4×C53—22no—
332C2×C4×C53—22no—
333C2×C4×C53—22no—
334C2×C4×C53—22no—
335C2×C4×C53—22no—
336C2×C4×C53—22no—
337C2×C4×C53—22no—
338C2×C4×C53—22no—
339C2×C4×C53—22no—
340C2×C4×C53—22no—
341C2×C4×C53—22no—
342C2×C4×C53—22no—
343C2×C4×C53—22no—
344C2×C4×C53—22no—
345C2×C4×C53—22no—
346C2×C4×C53—22no—
347C2×C4×C53—22no—
348C2×C4×C53—22no—
349C2×C4×C53—41no—
350C2×C4×C53—41no—
351C2×C4×C53—41no—
352C2×C4×C53—41no—
353C2×C4×C53—41no—
354C2×C4×C53—41no—
355C2×C4×C53—41no—
356C2×C4×C53—41no—
357C2×C4×C53—41no—
358C2×C4×C53—41no—
359C2×C4×C53—41no—
360C2×C4×C53—41no—
361C2×C4×C53—41no—
362C2×C4×C53—41no—
363C2×C4×C53—41no—
364C2×C4×C53—41no—
365C2×C4×C53—41no—
366C2×C4×C53—41no—
367C2×C4×C53—41no—
368C2×C4×C53—41no—
369C2×C4×C53—41no—
370C2×C4×C53—41no—
371C2×C4×C53C2×C4⋊C414yes—
372C2×C4×C53C2×C4⋊C414yes—
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—22no—
382C2×Dic53—22no—
383C2×Dic53—22no—
384C2×Dic53—22no—
385C2×Dic53—22no—
386C2×Dic53—22no—
387C2×Dic53—22no—
388C2×Dic53—22no—
389C2×Dic53—22no—
390C2×Dic53—22no—
391C2×Dic53—22no—
392C2×Dic53—22no—
393C2×Dic53—22no—
394C2×Dic53—416no—
395C2×Dic53—41no—
396C2×Dic53—41no—
397C2×Dic53—41no—
398C2×Dic53—41no—
399C2×Dic53—41no—
400C2×Dic53—41no—
401C2×Dic53—41no—
402C2×Dic53—41no—
403C2×Dic53—41no—
404C2×Dic53—41no—
405C2×Dic53—41no—
406C2×Dic53—41no—
407C2×Dic53—41no—
408C2×Dic53—41no—
409C2×Dic53—41no—
410C2×Dic53—41no—
411C2×Dic53—41no—
412C2×Dic53—41no—
413C2×Dic53—41no—
414C2×Dic53—41no—
415C2×Dic53—41no—
416C2×Dic53—41no—
417C2×Dic53—41no—
418C2×Dic53—41no—
419C2×Dic53—41no—
420C2×Dic53—41no—
421C2×Dic53—41no—
422C2×Dic53—41no—
423C2×Dic53—41no—
424C2×Dic53—41no—
425C2×Dic53—41no—
426C2×Dic53—41no—
427C2×Dic53—41no—
428C2×Dic53—41no—
429C2×Dic53C4×D414yes—
430#14408—531nomaximal, Sylow
431C22×C53—24no—
432C22×C53—24no—
433C22×C53—24no—
434C22×C53—42no—
435C22×C53—42no—
436C22×C53—42no—
437C22×C53—42no—
438C22×C53—42no—
439C22×C53—42no—
440C22×C53—42no—
441C22×C53—42no—
442C22×C53—42no—
443C22×C53—42no—
444C22×C53—42no—
445C22×C53—42no—
446C22×C53C22×C4⋊C411yescharacteristic
447C22×C53C2×C4×D411yescharacteristic
448C22×C53C4×#4111yescharacteristic
449C22×C53#51811yescharacteristic
450C22×C53#51811yescharacteristic
451C22×C53#51911yescharacteristic
452C22×C53#52011yescharacteristic
453C22×C53#53411yescharacteristic
454C22×C53#53511yescharacteristic
455C22×C53#53711yescharacteristic
456C22×C53#53711yescharacteristic
457C22×C53#53811yescharacteristic
458C22×C53#53811yescharacteristic
459C22×C53#53811yescharacteristic
460C22×C53#53911yescharacteristic
461C22×C53#54011yescharacteristic
462C22×C53#54211yescharacteristic
463C22×C53#54411yescharacteristic
464C22×C53#54411yescharacteristic
465C22×C53D4211yescharacteristic
466C22×C53#54611yescharacteristic
467C22×C53#54611yescharacteristic
468C22×C53#54711yescharacteristic
469C22×C53#54711yescharacteristic
470C22×C53#54811yescharacteristic
471C22×C53D4×Q811yescharacteristic
472C22×C53#55211yescharacteristic
473C22×C53#55411yescharacteristic
474C22×C53#55411yescharacteristic
475C22×C53#55411yescharacteristic
476C22×C53#55611yescharacteristic
477C22×C53#56211yescharacteristic
478C22×C53#56211yescharacteristic
479C22×C53#56311yescharacteristic
480C22×C53#56311yescharacteristic
481C4×C53—24no—
482C4×C53—24no—
483C4×C53—42no—
484C4×C53—42no—
485C4×C53—81no—
486C4×C53—81no—
487Dic53—24no—
488Dic53—42no—
489Dic53—42no—
490Dic53—42no—
491Dic53—42no—
492Dic53—42no—
493Dic53—81no—
494Dic53—81no—
495C2×#389—531no—
496C2×#388—531no—
497C2×#388D5311yescharacteristic
498C2×#385—531no—
499C2×#380—531no—
500#1444—531no—
501#1442—531no—
502#1441—531no—
503#1441—531no—
504#1439—531no—
505#1439—531no—
506#1436—531no—
507#1436—531no—
508C4⋊#95—531no—
509C22⋊#95—531no—
510C2×C53—44no—
511C2×C53#231611yescharacteristic
512C2×C53#232111yescharacteristic
513C2×C53#233511yescharacteristic
514C2×C53D4×C4⋊C411yescharacteristic
515C2×C53#234911yescharacteristic
516C2×C53#236211yescharacteristic
517C2×C53#237811yescharacteristic
518C2×C53#267111yescharacteristic
519C2×C53#267611yescharacteristic
520C2×C53#269511yescharacteristic
521C2×C53#271511yescharacteristic
522C2×C53#272011yescharacteristic
523C2×C53#272911yescharacteristic
524C2×C53#276811yescharacteristic
525C2×C53#278811yescharacteristic
526C24×C4—531no—
527C22×C4⋊C4—531no—
528C22×C4⋊C4—531no—
529C22×C4⋊C4—531no—
530C22×C4⋊C4—531no—
531C22×C4⋊C4—531no—
532C22×C4⋊C4—531no—
533C22×C4⋊C4—531no—
534C22×C4⋊C4C2×D5311yescharacteristic
535C22×C22⋊C4—531no—
536C22×C22⋊C4—531no—
537C22×C22⋊C4—531no—
538C22×C22⋊C4C2×D5311yescharacteristic
539C22×C22⋊C4C2×D5311yescharacteristic
540C22×C22⋊C4C2×D5311yescharacteristic
541C22×C42—531no—
542C22×C42C2×D5311yescharacteristic
543#389—1064no—
544#388—24no—
545#388—1064no—
546#385—538no—
547#380—1064no—
548C2×#95—531no—
549C2×#95—531no—
550C2×#95—531no—
551C2×#95—531no—
552C2×#95—531no—
553C2×#95—531no—
554C2×#95—531no—
555C2×#95—531no—
556C2×#95—531no—
557C2×#95—531no—
558C2×#95—531no—
559C2×#95—531no—
560C2×#95—531no—
561C2×#95—531no—
562C2×#95—531no—
563C2×#95—531no—
564C2×#95C2×D5311yescharacteristic
565C2×#95C2×D5311yescharacteristic
566C53#1440811yescharacteristic, complemented, Sylow
567C25C22×D5311yescharacteristic
568C23×C4—531no—
569C23×C4—531no—
570C23×C4—531no—
571C23×C4—531no—
572C23×C4—531no—
573C23×C4—531no—
574C23×C4—534no—
575C23×C4—531no—
576C23×C4—531no—
577C23×C4—1062no—
578C23×C4—1062no—
579C23×C4—2121no—
580C23×C4—2121no—
581C23×C4—2121no—
582C23×C4—2121no—
583C23×C4C22×D5311yescharacteristic
584C23×C4C22×D5311yescharacteristic
585C23×C4C22×D5311yescharacteristic
586C23×C4C22×D5311yescharacteristic
587C23×C4C22×D5311yescharacteristic
588C23×C4C22×D5311yescharacteristic
589C2×C4⋊C4—22no—
590C2×C4⋊C4—22no—
591C2×C4⋊C4—41no—
592C2×C4⋊C4—534no—
593C2×C4⋊C4—534no—
594C2×C4⋊C4—534no—
595C2×C4⋊C4—1062no—
596C2×C4⋊C4—1062no—
597C2×C4⋊C4—1062no—
598C2×C4⋊C4—1062no—
599C2×C4⋊C4—1062no—
600C2×C4⋊C4—1062no—
601C2×C4⋊C4—1062no—
602C2×C4⋊C4—2121no—
603C2×C4⋊C4—2121no—
604C2×C4⋊C4—2121no—
605C2×C4⋊C4—2121no—
606C2×C4⋊C4—2121no—
607C2×C4⋊C4—2121no—
608C2×C4⋊C4—2121no—
609C2×C4⋊C4—2121no—
610C2×C4⋊C4—2121no—
611C2×C4⋊C4—2121no—
612C2×C4⋊C4—2121no—
613C2×C22⋊C4—22no—
614C2×C22⋊C4—22no—
615C2×C22⋊C4—22no—
616C2×C22⋊C4—22no—
617C2×C22⋊C4—41no—
618C2×C22⋊C4—41no—
619C2×C22⋊C4—534no—
620C2×C22⋊C4—1062no—
621C2×C22⋊C4—1062no—
622C2×C22⋊C4—1062no—
623C2×C22⋊C4—1062no—
624C2×C22⋊C4—2121no—
625C2×C22⋊C4—2121no—
626C2×C22⋊C4—2121no—
627C2×C22⋊C4—2121no—
628C2×C22⋊C4Dic10614yes—
629C2×C22⋊C4C4×D5314yes—
630C2×C22⋊C4C22⋊D5314yes—
631C2×C42—22no—
632C2×C42—22no—
633C2×C42—41no—
634C2×C42—1062no—
635C2×C42—1062no—
636C2×C42—2121no—
637#95—22no—
638#95—22no—
639#95—534no—
640#95—534no—
641#95—1062no—
642#95—1062no—
643#95—1062no—
644#95—1062no—
645#95—1062no—
646#95—1062no—
647#95—1062no—
648#95—1062no—
649#95—2121no—
650#95—2121no—
651#95—2121no—
652#95—2121no—
653#95—2121no—
654#95—2121no—
655C24—21no—
656C24—21no—
657C24—21no—
658C24—21no—
659C24—21no—
660C24—21no—
661C24—21no—
662C24—21no—
663C24—21no—
664C24—21no—
665C24—21no—
666C24—21no—
667C24C2×Dic10612yes—
668C24C2×C4×D5312yes—
669C24C2×C22⋊D5312yes—
670C24C23×D5311yescharacteristic
671C22×C4—21no—
672C22×C4—21no—
673C22×C4—21no—
674C22×C4—21no—
675C22×C4—21no—
676C22×C4—21no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—21no—
681C22×C4—21no—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—21no—
702C22×C4—21no—
703C22×C4—21no—
704C22×C4—21no—
705C22×C4—532no—
706C22×C4—532no—
707C22×C4—532no—
708C22×C4—532no—
709C22×C4—532no—
710C22×C4—532no—
711C22×C4—532no—
712C22×C4—532no—
713C22×C4—1068no—
714C22×C4—1061no—
715C22×C4—1061no—
716C22×C4—1061no—
717C22×C4—1061no—
718C22×C4—1061no—
719C22×C4—1061no—
720C22×C4—1061no—
721C22×C4—1061no—
722C22×C4—1061no—
723C22×C4—1061no—
724C22×C4—1061no—
725C22×C4—1061no—
726C22×C4—1061no—
727C22×C4—1061no—
728C22×C4—1061no—
729C22×C4—1061no—
730C22×C4—1061no—
731C22×C4—1061no—
732C22×C4—1061no—
733C22×C4—1061no—
734C22×C4—1061no—
735C22×C4—1061no—
736C22×C4—1061no—
737C22×C4—1061no—
738C22×C4—1061no—
739C22×C4—1061no—
740C22×C4—1061no—
741C22×C4—1061no—
742C22×C4—1061no—
743C22×C4—1061no—
744C22×C4—1061no—
745C22×C4—1061no—
746C22×C4—1061no—
747C22×C4—1061no—
748C22×C4—1061no—
749C22×C4—1061no—
750C22×C4—1061no—
751C22×C4—1061no—
752C22×C4—1061no—
753C22×C4—1061no—
754C22×C4—1061no—
755C22×C4—1061no—
756C22×C4—1061no—
757C22×C4—1061no—
758C22×C4—1061no—
759C22×C4—1061no—
760C22×C4—1061no—
761C22×C4—1061no—
762C22×C4—2124no—
763C22×C4—2124no—
764C22×C4—2124no—
765C22×C4—2124no—
766C22×C4—2124no—
767C22×C4—2124no—
768C22×C4C2×Dic10612yes—
769C22×C4C2×Dic10612yes—
770C22×C4C2×C4×D5312yes—
771C22×C4C2×C4×D5312yes—
772C22×C4D4×D5312yes—
773C22×C4#1171994712yes—
774C22×C4C2×C22⋊D5312yes—
775C22×C4C2×C22⋊D5312yes—
776C4⋊C4—44no—
777C4⋊C4—1068no—
778C4⋊C4—2124no—
779C4⋊C4—2124no—
780C4⋊C4—2124no—
781C4⋊C4—2124no—
782C4⋊C4—2124no—
783C4⋊C4—2124no—
784C22⋊C4—44no—
785C22⋊C4—44no—
786C22⋊C4—2124no—
787C22⋊C4—2124no—
788C22⋊C4—2124no—
789C22⋊C4#11719919116yescomplemented
790C42—44no—
791C42—2124no—
792C23—22no—
793C23—22no—
794C23—22no—
795C23—22no—
796C23—22no—
797C23—22no—
798C23—22no—
799C23—22no—
800C23—22no—
801C23—22no—
802C23—22no—
803C23—22no—
804C23—22no—
805C23—22no—
806C23—22no—
807C23—22no—
808C23—22no—
809C23—22no—
810C23—41no—
811C23—41no—
812C23—41no—
813C23—41no—
814C23—41no—
815C23—41no—
816C23—41no—
817C23—41no—
818C23—41no—
819C23—41no—
820C23—41no—
821C23—41no—
822C23—41no—
823C23—41no—
824C23—41no—
825C23—41no—
826C23C2×#1171991914yes—
827C23C22×C4×D5311yescharacteristic
828C23C2×D4×D5311yescharacteristic
829C23C22×C22⋊D5311yescharacteristic
830C23C22×Dic10611yescharacteristic
831C23#41×D5311yescharacteristic
832C23#41×D5311yescharacteristic
833C23C2×#1171994711yescharacteristic
834C23#1313326211yescharacteristic
835C23#1313326211yescharacteristic
836C23#1313326311yescharacteristic
837C23#1313326311yescharacteristic
838C23#1313326311yescharacteristic
839C23#1313326411yescharacteristic
840C23#1313326411yescharacteristic
841C23#1313326411yescharacteristic
842C2×C4—22no—
843C2×C4—22no—
844C2×C4—22no—
845C2×C4—22no—
846C2×C4—22no—
847C2×C4—22no—
848C2×C4—22no—
849C2×C4—22no—
850C2×C4—22no—
851C2×C4—22no—
852C2×C4—22no—
853C2×C4—22no—
854C2×C4—22no—
855C2×C4—22no—
856C2×C4—22no—
857C2×C4—22no—
858C2×C4—22no—
859C2×C4—22no—
860C2×C4—41no—
861C2×C4—41no—
862C2×C4—41no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—41no—
869C2×C4—41no—
870C2×C4—41no—
871C2×C4—41no—
872C2×C4—41no—
873C2×C4—41no—
874C2×C4—41no—
875C2×C4—41no—
876C2×C4—41no—
877C2×C4—41no—
878C2×C4—41no—
879C2×C4—41no—
880C2×C4—41no—
881C2×C4—41no—
882C2×C4—534no—
883C2×C4—1062no—
884C2×C4—1062no—
885C2×C4—1062no—
886C2×C4—1062no—
887C2×C4—1062no—
888C2×C4—1062no—
889C2×C4—1062no—
890C2×C4—1062no—
891C2×C4—1062no—
892C2×C4—1062no—
893C2×C4—1062no—
894C2×C4—1062no—
895C2×C4—1062no—
896C2×C4—1062no—
897C2×C4—1062no—
898C2×C4—1062no—
899C2×C4—1062no—
900C2×C4—1062no—
901C2×C4—1062no—
902C2×C4—1062no—
903C2×C4—1062no—
904C2×C4—21216no—
905C2×C4—2121no—
906C2×C4—2121no—
907C2×C4—2121no—
908C2×C4—2121no—
909C2×C4—2121no—
910C2×C4—2121no—
911C2×C4—2121no—
912C2×C4—2121no—
913C2×C4—2121no—
914C2×C4—2121no—
915C2×C4—2121no—
916C2×C4—2121no—
917C2×C4—2121no—
918C2×C4—2121no—
919C2×C4—2121no—
920C2×C4—2121no—
921C2×C4—2121no—
922C2×C4—2121no—
923C2×C4—2121no—
924C2×C4—2121no—
925C2×C4—2121no—
926C2×C4—2121no—
927C2×C4—2121no—
928C2×C4—2121no—
929C2×C4—2121no—
930C2×C4—2121no—
931C2×C4—2121no—
932C2×C4—2121no—
933C2×C4—2121no—
934C2×C4—2121no—
935C2×C4—2121no—
936C2×C4—2121no—
937C2×C4—2121no—
938C2×C4—2121no—
939C2×C4C2×#1171991914yes—
940C2×C4C2×#1171991914yes—
941C22—24no—
942C22—24no—
943C22—24no—
944C22—42no—
945C22—42no—
946C22—42no—
947C22—42no—
948C22—42no—
949C22—42no—
950C22—42no—
951C22—42no—
952C22—42no—
953C22—42no—
954C22—42no—
955C22—42no—
956C22C22×#1171991911yescharacteristic
957C22C4×D4×D5311yescharacteristic
958C22C4×#1171994711yescharacteristic
959C22#1681109511yescharacteristic
960C22#1681109711yescharacteristic
961C22#1681110011yescharacteristic
962C22#1681110211yescharacteristic
963C22#1681118111yescharacteristic
964C22#1681119111yescharacteristic
965C22#1681120111yescharacteristic
966C22#1681120111yescharacteristic
967C22#1681120711yescharacteristic
968C22#1681120911yescharacteristic
969C22#1681121211yescharacteristic
970C22#1681121711yescharacteristic
971C22#1681122611yescharacteristic
972C22#1681123911yescharacteristic
973C22#1681125111yescharacteristic
974C22#1681125111yescharacteristic
975C22D4×C22⋊D5311yescharacteristic
976C22#1681126111yescharacteristic
977C22#1681126711yescharacteristic
978C22#1681127211yescharacteristic
979C22#1681127311yescharacteristic
980C22#1681128111yescharacteristic
981C22D4×Dic10611yescharacteristic
982C22#1681131011yescharacteristic
983C22#1681133011yescharacteristic
984C22#1681133211yescharacteristic
985C22#1681133211yescharacteristic
986C22#1681134011yescharacteristic
987C22#1681136711yescharacteristic
988C22#1681136811yescharacteristic
989C22#1681137511yescharacteristic
990C22#1681137611yescharacteristic
991C4—24no—
992C4—24no—
993C4—42no—
994C4—42no—
995C4—81no—
996C4—81no—
997C4—1064no—
998C4—4241no—
999C4—4241no—
1000C4—2122no—
1001C4—2122no—
1002C4—2122no—
1003C4—2122no—
1004C4—2122no—
1005C2—44no—
1006C2#2027733111yescharacteristic
1007C2#2027736811yescharacteristic
1008C2#2027751011yescharacteristic
1009C2D4×#1171991911yescharacteristic
1010C2#2027762011yescharacteristic
1011C2#2027773911yescharacteristic
1012C2#2027788211yescharacteristic
1013C2#2028094611yescharacteristic
1014C2#2028101111yescharacteristic
1015C2#2028124611yescharacteristic
1016C2#2028152211yescharacteristic
1017C2#2028159211yescharacteristic
1018C2#2028169411yescharacteristic
1019C2#2028219911yescharacteristic
1020C2#2028246211yescharacteristic
subgroupG/H
center, FrattiniC24C23×D53
commutatorC23×C53C23×C4
FittingC2×C53×#388C2
socle, cosocleC24×C53C24
prime radicalC25×C53C23
hypercenterC2×#388D53
hypocenterC53#14408
LCSG ▷ C23×C53 ▷ C53
UCSC1 ◁ C24 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
1. C2×#16810519C2semidirect
5. #20272979C2semidirect
6. #20272974C2semidirect
7. #20272967C2semidirect
8. #20272967C2semidirect
11. #20272948C2semidirect
12. #20272946C2semidirect
13. #20272945C2semidirect
30. #16810498C4semidirect
268. C22⋊C4×C53C4⋊C4semidirect
566. C53#14408semidirect
789. C22⋊C4#11719919semidirect

Maximal subgroups

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

subgroupindex
C2×#168105192
C2×#168105162
C2×#168104982
C2×#168104812
#202729792
#202729742
#202729672
#202729582
#202729482
#202729462
#202729452
#202729372
C2×C53×#3882
#1440853