Finite Group Databasebeta

← #27307303

Subgroups — #27307303

Order 13568.

2106 conjugacy classes of subgroups.

The subgroup lattice has 1070 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16810522C211yesmaximal, characteristic, complemented
2C2×#16810498C211yesmaximal, characteristic
3C2×#16810498C211yesmaximal, characteristic
4C2×#16810483C211yesmaximal, characteristic
5C2×C22⋊C4×Dic53C211yesmaximal, characteristic
6C22×#13133124C211yesmaximal, characteristic
7#20272980C211yesmaximal, characteristic, complemented
8#20272972C211yesmaximal, characteristic, complemented
9#20272968C211yesmaximal, characteristic, complemented
10#20272968C211yesmaximal, characteristic, complemented
11#20272949C211yesmaximal, characteristic, complemented
12#20272949C211yesmaximal, characteristic, complemented
13#20272944C211yesmaximal, characteristic, complemented
14#20272937C211yesmaximal, characteristic
15C2×C53×#385C211yesmaximal, characteristic
16C24×Dic53C2211yescharacteristic
17C24×Dic53C2211yescharacteristic
18C22×C4⋊Dic53C2211yescharacteristic
19C22×C4⋊Dic53C2211yescharacteristic
20C22×C4⋊Dic53C2211yescharacteristic
21C22×C4⋊Dic53C2211yescharacteristic
22C22×C4⋊Dic53C2211yescharacteristic
23C22×C4⋊Dic53C2211yescharacteristic
24C22×C22⋊Dic53C2211yescharacteristic
25C22×C22⋊Dic53C2211yescharacteristic
26C22×C4×Dic53C2211yescharacteristic
27C22×C4×Dic53C2211yescharacteristic
28#16810522—24no—
29#16810498—24no—
30#16810498—24no—
31#16810483—24no—
32C22⋊C4×Dic53—24no—
33C2×#13133124—24no—
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
48C2×#13133124C2211yescharacteristic
49C2×#13133124C2211yescharacteristic
50C24×C4×C53C2211yescharacteristic
51C22×C4⋊C4×C53C2211yescharacteristic
52C22×C4⋊C4×C53C2211yescharacteristic
53C22×C22⋊C4×C53C2211yescharacteristic
54C22×C22⋊C4×C53C2211yescharacteristic
55C53×#385C418yescomplemented
56C2×#95×C53C2211yescharacteristic
57C2×#95×C53C2211yescharacteristic
58C23×Dic53—22no—
59C23×Dic53—22no—
60C23×Dic53—22no—
61C23×Dic53—22no—
62C23×Dic53—22no—
63C23×Dic53—22no—
64C23×Dic53—22no—
65C23×Dic53—22no—
66C23×Dic53—22no—
67C23×Dic53—41no—
68C23×Dic53—41no—
69C23×Dic53—41no—
70C23×Dic53—41no—
71C23×Dic53Q814yes—
72C23×Dic53C2311yescharacteristic
73C23×Dic53C2311yescharacteristic
74C23×Dic53C2311yescharacteristic
75C23×Dic53C2311yescharacteristic
76C23×Dic53C2311yescharacteristic
77C23×Dic53C2311yescharacteristic
78C23×Dic53C2311yescharacteristic
79C23×Dic53C2311yescharacteristic
80C2×C4⋊Dic53—22no—
81C2×C4⋊Dic53—22no—
82C2×C4⋊Dic53—22no—
83C2×C4⋊Dic53—22no—
84C2×C4⋊Dic53—22no—
85C2×C4⋊Dic53—22no—
86C2×C4⋊Dic53—22no—
87C2×C4⋊Dic53—22no—
88C2×C4⋊Dic53—22no—
89C2×C4⋊Dic53—22no—
90C2×C4⋊Dic53—22no—
91C2×C4⋊Dic53—22no—
92C2×C4⋊Dic53—41no—
93C2×C4⋊Dic53—41no—
94C2×C4⋊Dic53—41no—
95C2×C4⋊Dic53—41no—
96C2×C4⋊Dic53—41no—
97C2×C4⋊Dic53—41no—
98C2×C22⋊Dic53—22no—
99C2×C22⋊Dic53—22no—
100C2×C22⋊Dic53—22no—
101C2×C22⋊Dic53—22no—
102C2×C22⋊Dic53—22no—
103C2×C22⋊Dic53D414yes—
104C2×C4×Dic53—22no—
105C2×C4×Dic53—22no—
106C2×C4×Dic53—22no—
107C2×C4×Dic53—22no—
108C2×C4×Dic53—41no—
109C2×C4×Dic53—41no—
110#13133124—22no—
111#13133124—22no—
112#13133124—22no—
113#13133124—22no—
114#13133124—22no—
115#13133124—22no—
116#13133124—22no—
117#13133124—22no—
118#13133124—22no—
119#13133124—22no—
120#13133124—22no—
121#13133124—22no—
122#13133124—22no—
123#13133124—41no—
124#13133124—41no—
125#13133124D414yes—
126C25×C53C2311yescharacteristic
127C23×C4×C53—22no—
128C23×C4×C53—22no—
129C23×C4×C53—22no—
130C23×C4×C53—22no—
131C23×C4×C53—41no—
132C23×C4×C53—41no—
133C23×C4×C53C2×C414yes—
134C23×C4×C53C2311yescharacteristic
135C23×C4×C53C2311yescharacteristic
136C23×C4×C53C2311yescharacteristic
137C23×C4×C53C2311yescharacteristic
138C23×C4×C53C2311yescharacteristic
139C23×C4×C53C2311yescharacteristic
140C2×C4⋊C4×C53—22no—
141C2×C4⋊C4×C53—22no—
142C2×C4⋊C4×C53—41no—
143C2×C4⋊C4×C53—41no—
144C2×C4⋊C4×C53C2×C414yescomplemented
145C2×C4⋊C4×C53C2×C414yescomplemented
146C2×C22⋊C4×C53—22no—
147C2×C22⋊C4×C53—22no—
148C2×C22⋊C4×C53C2×C414yes—
149C2×C22⋊C4×C53C2×C414yes—
150C2×C22⋊C4×C53D414yes—
151C2×C22⋊C4×C53Q814yes—
152#95×C53C2×C414yescomplemented
153#95×C53C2×C414yescomplemented
154C24×C53—21no—
155C24×C53—21no—
156C24×C53—21no—
157C24×C53—21no—
158C24×C53—21no—
159C24×C53—21no—
160C24×C53—21no—
161C24×C53—21no—
162C24×C53C22×C412yes—
163C24×C53C2×D412yes—
164C24×C53C2×D412yes—
165C24×C53C2×Q812yes—
166C24×C53C2×Q812yes—
167C24×C53#4112yes—
168C24×C53#4112yes—
169C24×C53C2411yescharacteristic
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—28no—
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×C53—21no—
195C22×C4×C53—21no—
196C22×C4×C53—21no—
197C22×C4×C53—21no—
198C22×C4×C53—21no—
199C22×C4×C53—21no—
200C22×C4×C53—21no—
201C22×C4×C53—28no—
202C22×C4×C53—44no—
203C22×C4×C53—44no—
204C22×C4×C53—44no—
205C22×C4×C53—44no—
206C22×C4×C53—44no—
207C22×C4×C53C22×C412yes—
208C22×C4×C53C22×C412yes—
209C22×C4×C53C22×C412yes—
210C22×C4×C53C22×C412yes—
211C22×C4×C53C22×C412yes—
212C22×C4×C53C22×C412yes—
213C22×C4×C53C2×D412yes—
214C22×C4×C53C2×D412yes—
215C22×C4×C53C2×D412yes—
216C22×C4×C53C2×Q812yes—
217C22×C4×C53C2×Q812yes—
218C22×C4×C53#4112yes—
219C22×Dic53—21no—
220C22×Dic53—21no—
221C22×Dic53—21no—
222C22×Dic53—21no—
223C22×Dic53—28no—
224C22×Dic53—28no—
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—21no—
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—21no—
252C22×Dic53—21no—
253C22×Dic53—21no—
254C22×Dic53—21no—
255C22×Dic53—28no—
256C22×Dic53—21no—
257C22×Dic53—21no—
258C22×Dic53—21no—
259C22×Dic53—21no—
260C22×Dic53—21no—
261C22×Dic53—21no—
262C22×Dic53—21no—
263C22×Dic53—21no—
264C22×Dic53—21no—
265C22×Dic53—21no—
266C22×Dic53—21no—
267C22×Dic53—21no—
268C22×Dic53—21no—
269C22×Dic53—21no—
270C22×Dic53—44no—
271C22×Dic53—44no—
272C22×Dic53—44no—
273C22×Dic53—44no—
274C22×Dic53—44no—
275C22×Dic53—44no—
276C22×Dic53—44no—
277C22×Dic53—44no—
278C22×Dic53—44no—
279C22×Dic53—44no—
280C22×Dic53—44no—
281C22×Dic53C2×D412yes—
282C22×Dic53C2×D412yes—
283C22×Dic53C2×D412yes—
284C22×Dic53C2×D412yes—
285C22×Dic53C2×Q812yes—
286C22×Dic53C2×Q812yes—
287C22×Dic53#4112yes—
288C22×Dic53#4112yes—
289C4⋊C4×C53—28no—
290C4⋊C4×C53—44no—
291C22⋊C4×C53—28no—
292C22⋊C4×C53C4⋊C4116yescomplemented
293C22⋊Dic53—28no—
294C22⋊Dic53—44no—
295C4⋊Dic53—44no—
296C4⋊Dic53—44no—
297C4⋊Dic53—44no—
298C4⋊Dic53—44no—
299C4⋊Dic53—44no—
300C4⋊Dic53—44no—
301C4×Dic53—44no—
302C4×Dic53—44no—
303C23×C53—22no—
304C23×C53—22no—
305C23×C53—22no—
306C23×C53—22no—
307C23×C53—22no—
308C23×C53—22no—
309C23×C53—22no—
310C23×C53—22no—
311C23×C53—22no—
312C23×C53—22no—
313C23×C53—22no—
314C23×C53—22no—
315C23×C53—22no—
316C23×C53—22no—
317C23×C53—22no—
318C23×C53—22no—
319C23×C53—22no—
320C23×C53—22no—
321C23×C53—22no—
322C23×C53—22no—
323C23×C53—22no—
324C23×C53—22no—
325C23×C53—22no—
326C23×C53—22no—
327C23×C53—22no—
328C23×C53—22no—
329C23×C53—22no—
330C23×C53—22no—
331C23×C53C2×C4⋊C414yes—
332C23×C53C4×D414yes—
333C23×C53C4×Q814yes—
334C23×C53#12114yes—
335C23×C53C22⋊Q814yes—
336C23×C53#12514yes—
337C23×C53C4⋊Q814yes—
338C23×C53C23×C411yescharacteristic
339C23×C53C22×D411yescharacteristic
340C23×C53C22×D411yescharacteristic
341C23×C53C22×D411yescharacteristic
342C23×C53C22×Q811yescharacteristic
343C23×C53C22×Q811yescharacteristic
344C23×C53C2×#4111yescharacteristic
345C23×C53C2×#4111yescharacteristic
346C23×C53C2×#4111yescharacteristic
347C23×C53C2×#4111yescharacteristic
348C23×C53C2×#4111yescharacteristic
349C23×C53H(5,𝔽2)11yescharacteristic
350C23×C53H(5,𝔽2)11yescharacteristic
351C23×C53H(5,𝔽2)11yescharacteristic
352C23×C532−1+411yescharacteristic
353C2×C4×C53—22no—
354C2×C4×C53—22no—
355C2×C4×C53—22no—
356C2×C4×C53—22no—
357C2×C4×C53—22no—
358C2×C4×C53—22no—
359C2×C4×C53—22no—
360C2×C4×C53—22no—
361C2×C4×C53—22no—
362C2×C4×C53—22no—
363C2×C4×C53—22no—
364C2×C4×C53—22no—
365C2×C4×C53—22no—
366C2×C4×C53—22no—
367C2×C4×C53—22no—
368C2×C4×C53—22no—
369C2×C4×C53—22no—
370C2×C4×C53—22no—
371C2×C4×C53—22no—
372C2×C4×C53—22no—
373C2×C4×C53—22no—
374C2×C4×C53—22no—
375C2×C4×C53—22no—
376C2×C4×C53—22no—
377C2×C4×C53—22no—
378C2×C4×C53—22no—
379C2×C4×C53—22no—
380C2×C4×C53—416no—
381C2×C4×C53—41no—
382C2×C4×C53—41no—
383C2×C4×C53—41no—
384C2×C4×C53—41no—
385C2×C4×C53—41no—
386C2×C4×C53—41no—
387C2×C4×C53—41no—
388C2×C4×C53—41no—
389C2×C4×C53—41no—
390C2×C4×C53—41no—
391C2×C4×C53—41no—
392C2×C4×C53—41no—
393C2×C4×C53C2×C4⋊C414yes—
394C2×C4×C53C2×C4⋊C414yes—
395C2×C4×C53C4×D414yes—
396C2×Dic53—22no—
397C2×Dic53—22no—
398C2×Dic53—22no—
399C2×Dic53—22no—
400C2×Dic53—22no—
401C2×Dic53—22no—
402C2×Dic53—22no—
403C2×Dic53—22no—
404C2×Dic53—22no—
405C2×Dic53—22no—
406C2×Dic53—22no—
407C2×Dic53—22no—
408C2×Dic53—22no—
409C2×Dic53—22no—
410C2×Dic53—22no—
411C2×Dic53—22no—
412C2×Dic53—22no—
413C2×Dic53—22no—
414C2×Dic53—22no—
415C2×Dic53—22no—
416C2×Dic53—22no—
417C2×Dic53—416no—
418C2×Dic53—416no—
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×Dic53—41no—
430C2×Dic53—41no—
431C2×Dic53—41no—
432C2×Dic53—41no—
433C2×Dic53—41no—
434C2×Dic53—41no—
435C2×Dic53—41no—
436C2×Dic53—41no—
437C2×Dic53—41no—
438C2×Dic53—41no—
439C2×Dic53—41no—
440C2×Dic53—41no—
441C2×Dic53—41no—
442C2×Dic53—41no—
443C2×Dic53—41no—
444C2×Dic53—41no—
445C2×Dic53—41no—
446C2×Dic53—41no—
447C2×Dic53—41no—
448C2×Dic53—41no—
449C2×Dic53—41no—
450C2×Dic53—41no—
451C2×Dic53—41no—
452C2×Dic53—41no—
453C2×Dic53C22⋊Q814yes—
454#14004—531nomaximal, Sylow
455C22×C53—24no—
456C22×C53—24no—
457C22×C53—24no—
458C22×C53—24no—
459C22×C53—24no—
460C22×C53—24no—
461C22×C53—24no—
462C22×C53—24no—
463C22×C53—24no—
464C22×C53—24no—
465C22×C53—24no—
466C22×C53—24no—
467C22×C53—24no—
468C22×C53—24no—
469C22×C53#38918yescomplemented
470C22×C53C22×C4⋊C411yescharacteristic
471C22×C53C2×C4×D411yescharacteristic
472C22×C53C2×C4×D411yescharacteristic
473C22×C53C2×C4×Q811yescharacteristic
474C22×C53C4×#4111yescharacteristic
475C22×C53#51811yescharacteristic
476C22×C53#52011yescharacteristic
477C22×C53C2×#12111yescharacteristic
478C22×C53C2×C22⋊Q811yescharacteristic
479C22×C53C2×C22⋊Q811yescharacteristic
480C22×C53#52511yescharacteristic
481C22×C53C2×#12511yescharacteristic
482C22×C53#52911yescharacteristic
483C22×C53C2×C4⋊Q811yescharacteristic
484C22×C53#53311yescharacteristic
485C22×C53#53811yescharacteristic
486C22×C53#53911yescharacteristic
487C22×C53#54311yescharacteristic
488C22×C53#54411yescharacteristic
489C22×C53D4211yescharacteristic
490C22×C53D4211yescharacteristic
491C22×C53#54611yescharacteristic
492C22×C53#54611yescharacteristic
493C22×C53#54611yescharacteristic
494C22×C53#54611yescharacteristic
495C22×C53#54611yescharacteristic
496C22×C53#54711yescharacteristic
497C22×C53#54711yescharacteristic
498C22×C53D4×Q811yescharacteristic
499C22×C53#55111yescharacteristic
500C22×C53#55111yescharacteristic
501C22×C53#55211yescharacteristic
502C22×C53#55411yescharacteristic
503C22×C53#55411yescharacteristic
504C22×C53#55411yescharacteristic
505C4×C53—24no—
506C4×C53—24no—
507C4×C53—24no—
508C4×C53—42no—
509C4×C53—42no—
510C4×C53—42no—
511Dic53—24no—
512Dic53—42no—
513Dic53—42no—
514Dic53—42no—
515Dic53—42no—
516Dic53—42no—
517Dic53—81no—
518Dic53—81no—
519C2×#389—531no—
520C2×#385—531no—
521C2×#385—531no—
522C2×#385D5311yescharacteristic
523C2×#380—531no—
524C2×C4×C22⋊C4—531no—
525C22×#95—531no—
526#1444—531no—
527#1442—531no—
528#1441—531no—
529#1441—531no—
530#1436—531no—
531#1436—531no—
532C4⋊#95—531no—
533C22⋊#95—531no—
534C2×C53—28no—
535C2×C53C2×#38911yescharacteristic
536C2×C53C4×C22⋊Q811yescharacteristic
537C2×C53#232911yescharacteristic
538C2×C53D4×C4⋊C411yescharacteristic
539C2×C53#234911yescharacteristic
540C2×C53#235811yescharacteristic
541C2×C53#235911yescharacteristic
542C2×C53#242411yescharacteristic
543C2×C53#242511yescharacteristic
544C2×C53#243711yescharacteristic
545C2×C53#243811yescharacteristic
546C2×C53#244011yescharacteristic
547C2×C53#247311yescharacteristic
548C2×C53#250511yescharacteristic
549C2×C53#254911yescharacteristic
550C24×C4—531no—
551C24×C4—531no—
552C24×C4C2×D5311yescharacteristic
553C22×C4⋊C4—531no—
554C22×C4⋊C4—531no—
555C22×C4⋊C4—531no—
556C22×C4⋊C4—531no—
557C22×C4⋊C4—531no—
558C22×C4⋊C4—531no—
559C22×C4⋊C4C2×D5311yescharacteristic
560C22×C4⋊C4C2×D5311yescharacteristic
561C22×C22⋊C4—531no—
562C22×C22⋊C4—531no—
563C22×C22⋊C4C2×D5311yescharacteristic
564C22×C22⋊C4C2×D5311yescharacteristic
565C22×C42—531no—
566C22×C42—531no—
567#389—1064no—
568#385—1064no—
569#385—1064no—
570#385Dic5318yescomplemented
571#380—1064no—
572C4×C22⋊C4—1064no—
573C2×#95—531no—
574C2×#95—531no—
575C2×#95—531no—
576C2×#95—531no—
577C2×#95—531no—
578C2×#95—531no—
579C2×#95—531no—
580C2×#95—531no—
581C2×#95—531no—
582C2×#95—531no—
583C2×#95—531no—
584C2×#95—531no—
585C2×#95—531no—
586C2×#95—531no—
587C2×#95—531no—
588C2×#95—531no—
589C2×#95—1064no—
590C2×#95C2×D5311yescharacteristic
591C2×#95C2×D5311yescharacteristic
592C53#1400411yescharacteristic, complemented, Sylow
593C25C22×D5311yescharacteristic
594C23×C4—22no—
595C23×C4—22no—
596C23×C4—22no—
597C23×C4—22no—
598C23×C4—41no—
599C23×C4—41no—
600C23×C4—531no—
601C23×C4—531no—
602C23×C4—531no—
603C23×C4—531no—
604C23×C4—531no—
605C23×C4—531no—
606C23×C4—534no—
607C23×C4—531no—
608C23×C4—531no—
609C23×C4—1062no—
610C23×C4—1062no—
611C23×C4—1062no—
612C23×C4—1062no—
613C23×C4—1062no—
614C23×C4—1062no—
615C23×C4—1062no—
616C23×C4—1062no—
617C23×C4—1062no—
618C23×C4—2121no—
619C23×C4—2121no—
620C23×C4—2121no—
621C23×C4—2121no—
622C23×C4C2×Dic5314yes—
623C23×C4C22×D5311yescharacteristic
624C23×C4C22×D5311yescharacteristic
625C23×C4C22×D5311yescharacteristic
626C23×C4C22×D5311yescharacteristic
627C23×C4C22×D5311yescharacteristic
628C23×C4C22×D5311yescharacteristic
629C2×C4⋊C4—22no—
630C2×C4⋊C4—22no—
631C2×C4⋊C4—41no—
632C2×C4⋊C4—41no—
633C2×C4⋊C4—1062no—
634C2×C4⋊C4—1062no—
635C2×C4⋊C4—1062no—
636C2×C4⋊C4—1062no—
637C2×C4⋊C4—1062no—
638C2×C4⋊C4—1062no—
639C2×C4⋊C4—1062no—
640C2×C4⋊C4—1062no—
641C2×C4⋊C4—1062no—
642C2×C4⋊C4—1062no—
643C2×C4⋊C4—1062no—
644C2×C4⋊C4—1062no—
645C2×C4⋊C4—2121no—
646C2×C4⋊C4—2121no—
647C2×C4⋊C4—2121no—
648C2×C4⋊C4—2121no—
649C2×C4⋊C4—2121no—
650C2×C4⋊C4—2121no—
651C2×C4⋊C4C2×Dic5314yescomplemented
652C2×C4⋊C4C2×Dic5314yescomplemented
653C2×C22⋊C4—22no—
654C2×C22⋊C4—22no—
655C2×C22⋊C4—534no—
656C2×C22⋊C4—1062no—
657C2×C22⋊C4—1062no—
658C2×C22⋊C4—1062no—
659C2×C22⋊C4—1062no—
660C2×C22⋊C4—1062no—
661C2×C22⋊C4Dic10614yes—
662C2×C22⋊C4D21214yes—
663C2×C22⋊C4C2×Dic5314yes—
664C2×C22⋊C4C2×Dic5314yes—
665C2×C42—1062no—
666C2×C42—1062no—
667C2×C42—1062no—
668C2×C42—1062no—
669C2×C42—2121no—
670C2×C42—2121no—
671#95—534no—
672#95—1062no—
673#95—1062no—
674#95—1062no—
675#95—1062no—
676#95—1062no—
677#95—1062no—
678#95—1062no—
679#95—1062no—
680#95—1062no—
681#95—1062no—
682#95—1062no—
683#95—1062no—
684#95—1062no—
685#95—2121no—
686#95—2121no—
687#95C2×Dic5314yescomplemented
688#95C2×Dic5314yescomplemented
689C24—21no—
690C24—21no—
691C24—21no—
692C24—21no—
693C24—21no—
694C24—21no—
695C24—21no—
696C24—21no—
697C24C2×Dic10612yes—
698C24C2×D21212yes—
699C24D4×D5312yes—
700C24#1171994712yes—
701C24Q8×D5312yes—
702C24#1171994912yes—
703C24C22×Dic5312yes—
704C24C23×D5311yescharacteristic
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—28no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—21no—
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—21no—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—21no—
733C22×C4—21no—
734C22×C4—21no—
735C22×C4—21no—
736C22×C4—28no—
737C22×C4—44no—
738C22×C4—44no—
739C22×C4—44no—
740C22×C4—44no—
741C22×C4—44no—
742C22×C4—532no—
743C22×C4—532no—
744C22×C4—532no—
745C22×C4—532no—
746C22×C4—532no—
747C22×C4—532no—
748C22×C4—532no—
749C22×C4—532no—
750C22×C4—1068no—
751C22×C4—1061no—
752C22×C4—1061no—
753C22×C4—1061no—
754C22×C4—1061no—
755C22×C4—1068no—
756C22×C4—1068no—
757C22×C4—1061no—
758C22×C4—1061no—
759C22×C4—1061no—
760C22×C4—1061no—
761C22×C4—1061no—
762C22×C4—1061no—
763C22×C4—1061no—
764C22×C4—1061no—
765C22×C4—1061no—
766C22×C4—1061no—
767C22×C4—1061no—
768C22×C4—1061no—
769C22×C4—1061no—
770C22×C4—1061no—
771C22×C4—1061no—
772C22×C4—1061no—
773C22×C4—1061no—
774C22×C4—1061no—
775C22×C4—1061no—
776C22×C4—1061no—
777C22×C4—1061no—
778C22×C4—1061no—
779C22×C4—1061no—
780C22×C4—1061no—
781C22×C4—1061no—
782C22×C4—1061no—
783C22×C4—1061no—
784C22×C4—1061no—
785C22×C4—1061no—
786C22×C4—1061no—
787C22×C4—1061no—
788C22×C4—1061no—
789C22×C4—1061no—
790C22×C4—1061no—
791C22×C4—1061no—
792C22×C4—1061no—
793C22×C4—1061no—
794C22×C4—1061no—
795C22×C4—1061no—
796C22×C4—1061no—
797C22×C4—1061no—
798C22×C4—1061no—
799C22×C4—1061no—
800C22×C4—1061no—
801C22×C4—2124no—
802C22×C4—2124no—
803C22×C4—2124no—
804C22×C4—2124no—
805C22×C4—2124no—
806C22×C4—2124no—
807C22×C4—2124no—
808C22×C4—2124no—
809C22×C4—2124no—
810C22×C4—2124no—
811C22×C4—2124no—
812C22×C4C2×Dic10612yes—
813C22×C4C2×Dic10612yes—
814C22×C4C2×D21212yes—
815C22×C4C2×D21212yes—
816C22×C4D4×D5312yes—
817C22×C4#1171994712yes—
818C22×C4C22×Dic5312yes—
819C22×C4C22×Dic5312yes—
820C22×C4C22×Dic5312yes—
821C22×C4C22×Dic5312yes—
822C22×C4C22×Dic5312yes—
823C22×C4C22×Dic5312yes—
824C4⋊C4—28no—
825C4⋊C4—44no—
826C4⋊C4—2124no—
827C4⋊C4—2124no—
828C4⋊C4—2124no—
829C4⋊C4—2124no—
830C4⋊C4—2124no—
831C4⋊C4—2124no—
832C22⋊C4—28no—
833C22⋊C4—1068no—
834C22⋊C4—2124no—
835C22⋊C4C4⋊Dic53116yescomplemented
836C42—2124no—
837C42—2124no—
838C23—22no—
839C23—22no—
840C23—22no—
841C23—22no—
842C23—22no—
843C23—22no—
844C23—22no—
845C23—22no—
846C23—22no—
847C23—22no—
848C23—22no—
849C23—22no—
850C23—22no—
851C23—22no—
852C23—22no—
853C23—22no—
854C23—22no—
855C23—22no—
856C23—22no—
857C23—22no—
858C23—22no—
859C23—22no—
860C23—22no—
861C23—22no—
862C23—22no—
863C23—22no—
864C23—22no—
865C23—22no—
866C23C2×C4⋊Dic5314yes—
867C23D4×Dic5314yes—
868C23Q8×Dic5314yes—
869C23#1313319214yes—
870C23#1313319714yes—
871C23#1313320814yes—
872C23#1313321614yes—
873C23C23×Dic5311yescharacteristic
874C23C2×D4×D5311yescharacteristic
875C23C2×D4×D5311yescharacteristic
876C23C22×D21211yescharacteristic
877C23C2×Q8×D5311yescharacteristic
878C23C22×Dic10611yescharacteristic
879C23#41×D5311yescharacteristic
880C23#41×D5311yescharacteristic
881C23C2×#1171994711yescharacteristic
882C23C2×#1171994711yescharacteristic
883C23C2×#1171994911yescharacteristic
884C23#1313326211yescharacteristic
885C23#1313326211yescharacteristic
886C23#1313326311yescharacteristic
887C23#1313326411yescharacteristic
888C2×C4—22no—
889C2×C4—22no—
890C2×C4—22no—
891C2×C4—22no—
892C2×C4—22no—
893C2×C4—22no—
894C2×C4—22no—
895C2×C4—22no—
896C2×C4—22no—
897C2×C4—22no—
898C2×C4—22no—
899C2×C4—22no—
900C2×C4—22no—
901C2×C4—22no—
902C2×C4—22no—
903C2×C4—22no—
904C2×C4—22no—
905C2×C4—22no—
906C2×C4—22no—
907C2×C4—22no—
908C2×C4—22no—
909C2×C4—22no—
910C2×C4—22no—
911C2×C4—22no—
912C2×C4—22no—
913C2×C4—22no—
914C2×C4—22no—
915C2×C4—416no—
916C2×C4—41no—
917C2×C4—41no—
918C2×C4—41no—
919C2×C4—41no—
920C2×C4—41no—
921C2×C4—41no—
922C2×C4—41no—
923C2×C4—41no—
924C2×C4—41no—
925C2×C4—41no—
926C2×C4—41no—
927C2×C4—41no—
928C2×C4—534no—
929C2×C4—1062no—
930C2×C4—1062no—
931C2×C4—1062no—
932C2×C4—1062no—
933C2×C4—1062no—
934C2×C4—1062no—
935C2×C4—1062no—
936C2×C4—1062no—
937C2×C4—1062no—
938C2×C4—1062no—
939C2×C4—1062no—
940C2×C4—1062no—
941C2×C4—1062no—
942C2×C4—1062no—
943C2×C4—1062no—
944C2×C4—1062no—
945C2×C4—1062no—
946C2×C4—1062no—
947C2×C4—1062no—
948C2×C4—1062no—
949C2×C4—1062no—
950C2×C4—21216no—
951C2×C4—2121no—
952C2×C4—2121no—
953C2×C4—2121no—
954C2×C4—2121no—
955C2×C4—2121no—
956C2×C4—2121no—
957C2×C4—2121no—
958C2×C4—2121no—
959C2×C4—2121no—
960C2×C4—2121no—
961C2×C4—2121no—
962C2×C4—2121no—
963C2×C4—2121no—
964C2×C4—2121no—
965C2×C4—21216no—
966C2×C4—2121no—
967C2×C4—2121no—
968C2×C4—2121no—
969C2×C4—2121no—
970C2×C4—2121no—
971C2×C4—2121no—
972C2×C4—2121no—
973C2×C4—2121no—
974C2×C4—2121no—
975C2×C4—2121no—
976C2×C4—2121no—
977C2×C4—2121no—
978C2×C4—2121no—
979C2×C4—2121no—
980C2×C4—2121no—
981C2×C4—2121no—
982C2×C4—2121no—
983C2×C4—2121no—
984C2×C4—2121no—
985C2×C4—2121no—
986C2×C4C2×C4⋊Dic5314yes—
987C2×C4C2×C4⋊Dic5314yes—
988C2×C4D4×Dic5314yes—
989C22—24no—
990C22—24no—
991C22—24no—
992C22—24no—
993C22—24no—
994C22—24no—
995C22—24no—
996C22—24no—
997C22—24no—
998C22—24no—
999C22—24no—
1000C22—24no—
1001C22—24no—
1002C22—24no—
1003C22#1681052218yescomplemented
1004C22C22×C4⋊Dic5311yescharacteristic
1005C22C2×D4×Dic5311yescharacteristic
1006C22C2×D4×Dic5311yescharacteristic
1007C22C2×Q8×Dic5311yescharacteristic
1008C22#41×Dic5311yescharacteristic
1009C22#1681109811yescharacteristic
1010C22#1681110611yescharacteristic
1011C22C2×#1313319211yescharacteristic
1012C22C22⋊Q8×D5311yescharacteristic
1013C22C2×#1313319711yescharacteristic
1014C22#1681113611yescharacteristic
1015C22C2×#1313320811yescharacteristic
1016C22#1681115911yescharacteristic
1017C22C2×#1313321611yescharacteristic
1018C22#1681117511yescharacteristic
1019C22#1681121311yescharacteristic
1020C22#1681122211yescharacteristic
1021C22#1681124811yescharacteristic
1022C22#1681125211yescharacteristic
1023C22#1681125511yescharacteristic
1024C22D4×D21211yescharacteristic
1025C22#1681126011yescharacteristic
1026C22#1681126011yescharacteristic
1027C22#1681126511yescharacteristic
1028C22#1681126811yescharacteristic
1029C22#1681126811yescharacteristic
1030C22#1681127111yescharacteristic
1031C22#1681127711yescharacteristic
1032C22D4×Dic10611yescharacteristic
1033C22#1681129611yescharacteristic
1034C22#1681130411yescharacteristic
1035C22#1681131011yescharacteristic
1036C22#1681133011yescharacteristic
1037C22#1681133211yescharacteristic
1038C22#1681133211yescharacteristic
1039C4—24no—
1040C4—24no—
1041C4—24no—
1042C4—42no—
1043C4—42no—
1044C4—42no—
1045C4—1064no—
1046C4—4241no—
1047C4—4241no—
1048C4—2122no—
1049C4—2122no—
1050C4—2122no—
1051C4—2122no—
1052C4—2122no—
1053C2—28no—
1054C2C2×#1681052211yescharacteristic
1055C2C22⋊Q8×Dic5311yescharacteristic
1056C2#2027745011yescharacteristic
1057C2D4×C4⋊Dic5311yescharacteristic
1058C2#2027762511yescharacteristic
1059C2#2027769911yescharacteristic
1060C2#2027771111yescharacteristic
1061C2#2027824911yescharacteristic
1062C2#2027826411yescharacteristic
1063C2#2027837911yescharacteristic
1064C2#2027838911yescharacteristic
1065C2#2027841611yescharacteristic
1066C2#2027886311yescharacteristic
1067C2#2027922011yescharacteristic
1068C2#2027972811yescharacteristic
subgroupG/H
center, FrattiniC24C23×D53
commutatorC23×C53C23×C4
FittingC2×C53×#385C2
socle, cosocleC24×C53C24
prime radicalC25×C53C23
hypercenterC2×#385D53
hypocenterC53#14004
LCSG ▷ C23×C53 ▷ C53
UCSC1 ◁ C24 ◁ C2×#385

Complements

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

NH ≅ G/Ntype
1. C2×#16810522C2semidirect
7. #20272980C2semidirect
8. #20272972C2semidirect
9. #20272968C2semidirect
10. #20272968C2semidirect
11. #20272949C2semidirect
12. #20272949C2semidirect
13. #20272944C2semidirect
55. C53×#385C4semidirect
144. C2×C4⋊C4×C53C2×C4semidirect
145. C2×C4⋊C4×C53C2×C4semidirect
152. #95×C53C2×C4semidirect
153. #95×C53C2×C4semidirect
292. C22⋊C4×C53C4⋊C4semidirect
469. C22×C53#389semidirect
570. #385Dic53semidirect
592. C53#14004semidirect
651. C2×C4⋊C4C2×Dic53semidirect
652. C2×C4⋊C4C2×Dic53semidirect
687. #95C2×Dic53semidirect
688. #95C2×Dic53semidirect
835. C22⋊C4C4⋊Dic53semidirect
1003. C22#16810522semidirect

Maximal subgroups

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

subgroupindex
C2×#168105222
C2×#168104982
C2×#168104832
C2×C22⋊C4×Dic532
C22×#131331242
#202729802
#202729722
#202729682
#202729492
#202729442
#202729372
C2×C53×#3852
#1400453