Finite Group Databasebeta

← #27307152

Subgroups — #27307152

Order 13568.

1586 conjugacy classes of subgroups.

The subgroup lattice has 994 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16810517C211yesmaximal, characteristic
2C2×#16810490C211yesmaximal, characteristic, complemented
3C2×C4×C22⋊Dic53C211yesmaximal, characteristic
4#20272981C211yesmaximal, characteristic, complemented
5#20272971C211yesmaximal, characteristic, complemented
6#20272962C211yesmaximal, characteristic
7#20272960C211yesmaximal, characteristic
8#20272952C211yesmaximal, characteristic
9#20272949C211yesmaximal, characteristic, complemented
10#20272946C211yesmaximal, characteristic, complemented
11#20272941C211yesmaximal, characteristic, complemented
12#20272939C211yesmaximal, characteristic, complemented
13#20272938C211yesmaximal, characteristic
14#95×Dic53C211yesmaximal, characteristic, complemented
15C53×C22⋊#95C211yesmaximal, characteristic
16C22×C4⋊Dic53C2211yescharacteristic
17C22×#11719919C2211yescharacteristic
18C22×C22⋊Dic53C2211yescharacteristic
19C22×C22⋊Dic53C2211yescharacteristic
20C22×C22⋊Dic53C2211yescharacteristic
21C22×C22⋊Dic53C2211yescharacteristic
22C22×C4×Dic53C2211yescharacteristic
23C22×C4×Dic53C2211yescharacteristic
24C22×C4×Dic53C2211yescharacteristic
25C22×C4×Dic53C2211yescharacteristic
26#16810517C418yescomplemented
27#16810490—24no—
28C4×C22⋊Dic53—24no—
29C2×#13133124C2211yescharacteristic
30C2×#13133124C2211yescharacteristic
31C2×#13133124C2211yescharacteristic
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
47C24×C4×C53C2211yescharacteristic
48C22×C22⋊C4×C53C2211yescharacteristic
49C22×C22⋊C4×C53C2211yescharacteristic
50C2×#95×C53C2211yescharacteristic
51C2×#95×C53C2211yescharacteristic
52C2×#95×C53C2211yescharacteristic
53C2×#95×C53C2211yescharacteristic
54C23×Dic53C2311yescharacteristic
55C23×Dic53C2311yescharacteristic
56C23×Dic53C2311yescharacteristic
57C23×Dic53C2311yescharacteristic
58C23×Dic53C2311yescharacteristic
59C23×Dic53C2311yescharacteristic
60C23×Dic53C2311yescharacteristic
61C23×Dic53C2311yescharacteristic
62C2×C4⋊Dic53—22no—
63C2×C4⋊Dic53—41no—
64C2×C4⋊Dic53—41no—
65C2×#11719919—41no—
66C2×#11719919—41no—
67C2×#11719919C2×C414yescomplemented
68C2×C22⋊Dic53—22no—
69C2×C22⋊Dic53—22no—
70C2×C22⋊Dic53—22no—
71C2×C22⋊Dic53—22no—
72C2×C22⋊Dic53—22no—
73C2×C22⋊Dic53—22no—
74C2×C22⋊Dic53—22no—
75C2×C22⋊Dic53—22no—
76C2×C22⋊Dic53—22no—
77C2×C22⋊Dic53—41no—
78C2×C22⋊Dic53C2×C414yes—
79C2×C22⋊Dic53C2×C414yes—
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—41no—
89C2×C4×Dic53—41no—
90C2×C4×Dic53—41no—
91C2×C4×Dic53C2×C414yescomplemented
92#13133124—22no—
93#13133124—22no—
94#13133124—22no—
95#13133124—22no—
96#13133124—22no—
97#13133124—22no—
98#13133124—22no—
99#13133124—22no—
100#13133124—22no—
101#13133124—22no—
102#13133124—22no—
103#13133124—41no—
104#13133124—41no—
105#13133124—41no—
106#13133124—41no—
107#13133124C2×C414yescomplemented
108#13133124C2×C414yescomplemented
109#13133124D414yes—
110C25×C53C2311yescharacteristic
111C23×C4×C53—22no—
112C23×C4×C53—22no—
113C23×C4×C53—22no—
114C23×C4×C53—22no—
115C23×C4×C53—22no—
116C23×C4×C53—41no—
117C23×C4×C53—41no—
118C23×C4×C53C2311yescharacteristic
119C23×C4×C53C2311yescharacteristic
120C23×C4×C53C2311yescharacteristic
121C23×C4×C53C2311yescharacteristic
122C23×C4×C53C2311yescharacteristic
123C23×C4×C53C2311yescharacteristic
124C2×C22⋊C4×C53—22no—
125C2×C22⋊C4×C53—22no—
126C2×C22⋊C4×C53—41no—
127C2×C22⋊C4×C53—41no—
128C2×C22⋊C4×C53—41no—
129C2×C22⋊C4×C53C2×C414yes—
130#95×C53—22no—
131#95×C53—22no—
132#95×C53—22no—
133#95×C53—41no—
134C24×C53—21no—
135C24×C53—21no—
136C24×C53—21no—
137C24×C53—21no—
138C24×C53—21no—
139C24×C53—21no—
140C24×C53—21no—
141C24×C53—21no—
142C24×C53—21no—
143C24×C53—21no—
144C24×C53—21no—
145C24×C53—21no—
146C24×C53C22×C412yes—
147C24×C53#4112yes—
148C24×C53#4112yes—
149C24×C53C2411yescharacteristic
150C22×C4×C53—21no—
151C22×C4×C53—21no—
152C22×C4×C53—21no—
153C22×C4×C53—21no—
154C22×C4×C53—28no—
155C22×C4×C53—21no—
156C22×C4×C53—21no—
157C22×C4×C53—21no—
158C22×C4×C53—21no—
159C22×C4×C53—21no—
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—44no—
187C22×C4×C53—44no—
188C22×C4×C53—44no—
189C22×C4×C53—44no—
190C22×C4×C53—44no—
191C22×C4×C53—44no—
192C22×C4×C53C22×C412yes—
193C22×C4×C53C22×C412yes—
194C22×C4×C53C2×D412yes—
195C22×C4×C53#4112yes—
196C22×C4×C53#4112yes—
197C22×C4×C53#4112yes—
198C22×C4×C53#4112yes—
199C22×Dic53—21no—
200C22×Dic53—21no—
201C22×Dic53—21no—
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—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×Dic53C22×C412yes—
247C22×Dic53C22×C412yes—
248C22×Dic53C22×C412yes—
249C22×Dic53C22×C412yes—
250C22×Dic53C2×D412yes—
251C22×Dic53C2×D412yes—
252C22×Dic53#4112yes—
253C22×Dic53#4112yes—
254C22×Dic53#4112yes—
255C22⋊C4×C53—44no—
256C22⋊C4×C53—44no—
257C22⋊Dic53—28no—
258C22⋊Dic53—28no—
259C22⋊Dic53—28no—
260C22⋊Dic53—44no—
261C4⋊Dic53—44no—
262#11719919—44no—
263C4×Dic53—28no—
264C4×Dic53—44no—
265C4×Dic53—44no—
266C4×Dic53—44no—
267C23×C53—22no—
268C23×C53—22no—
269C23×C53—22no—
270C23×C53—22no—
271C23×C53—22no—
272C23×C53—22no—
273C23×C53—22no—
274C23×C53—22no—
275C23×C53—22no—
276C23×C53—22no—
277C23×C53—22no—
278C23×C53—22no—
279C23×C53—22no—
280C23×C53—22no—
281C23×C53—22no—
282C23×C53—22no—
283C23×C53—22no—
284C23×C53—22no—
285C23×C53—41no—
286C23×C53—41no—
287C23×C53—41no—
288C23×C53—41no—
289C23×C53—41no—
290C23×C53—41no—
291C23×C53—41no—
292C23×C53—41no—
293C23×C53—41no—
294C23×C53—41no—
295C23×C53—41no—
296C23×C53—41no—
297C23×C53—41no—
298C23×C53—41no—
299C23×C53—41no—
300C23×C53—41no—
301C23×C53#11714yes—
302C23×C53C23×C411yescharacteristic
303C23×C53C22×D411yescharacteristic
304C23×C53C2×#4111yescharacteristic
305C23×C53C2×#4111yescharacteristic
306C23×C53C2×#4111yescharacteristic
307C23×C53C2×#4111yescharacteristic
308C23×C53C2×#4111yescharacteristic
309C23×C53C2×#4111yescharacteristic
310C23×C53C2×#4111yescharacteristic
311C23×C53C2×#4111yescharacteristic
312C23×C53C2×#4111yescharacteristic
313C23×C53H(5,𝔽2)11yescharacteristic
314C23×C53H(5,𝔽2)11yescharacteristic
315C23×C53H(5,𝔽2)11yescharacteristic
316C23×C532−1+411yescharacteristic
317C2×C4×C53—22no—
318C2×C4×C53—22no—
319C2×C4×C53—22no—
320C2×C4×C53—22no—
321C2×C4×C53—22no—
322C2×C4×C53—22no—
323C2×C4×C53—22no—
324C2×C4×C53—22no—
325C2×C4×C53—22no—
326C2×C4×C53—22no—
327C2×C4×C53—22no—
328C2×C4×C53—22no—
329C2×C4×C53—22no—
330C2×C4×C53—22no—
331C2×C4×C53—22no—
332C2×C4×C53—22no—
333C2×C4×C53—22no—
334C2×C4×C53—22no—
335C2×C4×C53—416no—
336C2×C4×C53—41no—
337C2×C4×C53—41no—
338C2×C4×C53—41no—
339C2×C4×C53—41no—
340C2×C4×C53—41no—
341C2×C4×C53—41no—
342C2×C4×C53—41no—
343C2×C4×C53—41no—
344C2×C4×C53—41no—
345C2×C4×C53—41no—
346C2×C4×C53—41no—
347C2×C4×C53—41no—
348C2×C4×C53—41no—
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#12614yes—
360C2×Dic53—22no—
361C2×Dic53—22no—
362C2×Dic53—22no—
363C2×Dic53—22no—
364C2×Dic53—22no—
365C2×Dic53—22no—
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—22no—
382C2×Dic53—22no—
383C2×Dic53—22no—
384C2×Dic53—41no—
385C2×Dic53—41no—
386C2×Dic53—41no—
387C2×Dic53—41no—
388C2×Dic53—41no—
389C2×Dic53—41no—
390C2×Dic53—41no—
391C2×Dic53—41no—
392C2×Dic53—41no—
393C2×Dic53—41no—
394C2×Dic53—41no—
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×Dic53C4×D414yes—
416#13990—531nomaximal, Sylow
417C22×C53—24no—
418C22×C53—24no—
419C22×C53—24no—
420C22×C53—42no—
421C22×C53—42no—
422C22×C53—42no—
423C22×C53—42no—
424C22×C53—42no—
425C22×C53—42no—
426C22×C53—42no—
427C22×C53—42no—
428C22×C53—42no—
429C22×C53—42no—
430C22×C53—42no—
431C22×C53—42no—
432C22×C53C2×#11711yescharacteristic
433C22×C53C2×C4×D411yescharacteristic
434C22×C53C4×#4111yescharacteristic
435C22×C53C4×#4111yescharacteristic
436C22×C53C4×#4111yescharacteristic
437C22×C53#51811yescharacteristic
438C22×C53#52011yescharacteristic
439C22×C53#52511yescharacteristic
440C22×C53#52511yescharacteristic
441C22×C53C2×#12611yescharacteristic
442C22×C53#52911yescharacteristic
443C22×C53#52911yescharacteristic
444C22×C53#52911yescharacteristic
445C22×C53#52911yescharacteristic
446C22×C53#52911yescharacteristic
447C22×C53#53811yescharacteristic
448C22×C53#53811yescharacteristic
449C22×C53#54211yescharacteristic
450C22×C53#54211yescharacteristic
451C22×C53#54611yescharacteristic
452C22×C53#54611yescharacteristic
453C22×C53#54711yescharacteristic
454C22×C53#55011yescharacteristic
455C22×C53#55111yescharacteristic
456C22×C53#55111yescharacteristic
457C22×C53#55111yescharacteristic
458C22×C53#55111yescharacteristic
459C22×C53#55111yescharacteristic
460C22×C53#55211yescharacteristic
461C22×C53#55211yescharacteristic
462C22×C53#55211yescharacteristic
463C22×C53#55311yescharacteristic
464C22×C53#55311yescharacteristic
465C22×C53#55311yescharacteristic
466C22×C53#55511yescharacteristic
467C4×C53—24no—
468C4×C53—42no—
469C4×C53—42no—
470C4×C53—42no—
471C4×C53—42no—
472C4×C53—81no—
473Dic53—24no—
474Dic53—42no—
475Dic53—42no—
476Dic53—42no—
477Dic53—42no—
478Dic53—42no—
479Dic53—42no—
480Dic53—81no—
481C2×#388—531no—
482C2×#383—531no—
483C2×C4×C22⋊C4—531no—
484#1445—531no—
485#1442—531no—
486#1440—531no—
487#1439—531no—
488#1437—531no—
489#1436—531no—
490#1436—531no—
491#1434—531no—
492#1434—531no—
493C22⋊#95—531no—
494C22⋊#95D5311yescharacteristic
495C4×#95—531no—
496C2×C53—44no—
497C2×C53#229011yescharacteristic
498C2×C53C4×#12611yescharacteristic
499C2×C53#233711yescharacteristic
500C2×C53#234311yescharacteristic
501C2×C53#235311yescharacteristic
502C2×C53#235911yescharacteristic
503C2×C53#236311yescharacteristic
504C2×C53#246711yescharacteristic
505C2×C53#246811yescharacteristic
506C2×C53#247911yescharacteristic
507C2×C53#248011yescharacteristic
508C2×C53#249511yescharacteristic
509C2×C53#251511yescharacteristic
510C2×C53#257211yescharacteristic
511C2×C53#257811yescharacteristic
512C24×C4C2×D5311yescharacteristic
513C22×C4⋊C4—531no—
514C22×C4⋊C4—531no—
515C22×C22⋊C4—531no—
516C22×C22⋊C4—531no—
517C22×C22⋊C4—531no—
518C22×C22⋊C4—531no—
519C22×C22⋊C4C2×D5311yescharacteristic
520C22×C22⋊C4C2×D5311yescharacteristic
521C22×C42—531no—
522C22×C42—531no—
523C22×C42—531no—
524C22×C42—531no—
525#388—538no—
526#383—1064no—
527C4×C22⋊C4—1064no—
528C2×#95—531no—
529C2×#95—531no—
530C2×#95—531no—
531C2×#95—531no—
532C2×#95—531no—
533C2×#95—531no—
534C2×#95—531no—
535C2×#95—531no—
536C2×#95—531no—
537C2×#95—531no—
538C2×#95—531no—
539C2×#95—531no—
540C2×#95—531no—
541C2×#95—531no—
542C2×#95—531no—
543C2×#95—531no—
544C2×#95—531no—
545C2×#95—531no—
546C2×#95C2×D5311yescharacteristic
547C2×#95C2×D5311yescharacteristic
548C2×#95C2×D5311yescharacteristic
549C2×#95C2×D5311yescharacteristic
550C53#1399011yescharacteristic, complemented, Sylow
551C25C22×D5311yescharacteristic
552C23×C4—22no—
553C23×C4—22no—
554C23×C4—22no—
555C23×C4—22no—
556C23×C4—22no—
557C23×C4—41no—
558C23×C4—41no—
559C23×C4—531no—
560C23×C4—531no—
561C23×C4—531no—
562C23×C4—531no—
563C23×C4—531no—
564C23×C4—531no—
565C23×C4—531no—
566C23×C4—531no—
567C23×C4C22×D5311yescharacteristic
568C23×C4C22×D5311yescharacteristic
569C23×C4C22×D5311yescharacteristic
570C23×C4C22×D5311yescharacteristic
571C23×C4C22×D5311yescharacteristic
572C23×C4C22×D5311yescharacteristic
573C2×C4⋊C4—534no—
574C2×C4⋊C4—1062no—
575C2×C4⋊C4—2121no—
576C2×C4⋊C4—2121no—
577C2×C4⋊C4—2121no—
578C2×C4⋊C4—2121no—
579C2×C22⋊C4—22no—
580C2×C22⋊C4—22no—
581C2×C22⋊C4—41no—
582C2×C22⋊C4—41no—
583C2×C22⋊C4—41no—
584C2×C22⋊C4—534no—
585C2×C22⋊C4—534no—
586C2×C22⋊C4—1062no—
587C2×C22⋊C4—1062no—
588C2×C22⋊C4—1062no—
589C2×C22⋊C4—1062no—
590C2×C22⋊C4—1062no—
591C2×C22⋊C4—1062no—
592C2×C22⋊C4—1062no—
593C2×C22⋊C4—1062no—
594C2×C22⋊C4—1062no—
595C2×C22⋊C4—2121no—
596C2×C22⋊C4C4×D5314yes—
597C2×C42—534no—
598C2×C42—1062no—
599C2×C42—1062no—
600C2×C42—1062no—
601C2×C42—1062no—
602C2×C42—1062no—
603C2×C42—1062no—
604C2×C42—1062no—
605C2×C42—1062no—
606C2×C42—2121no—
607C2×C42—2121no—
608C2×C42—2121no—
609#95—22no—
610#95—22no—
611#95—22no—
612#95—41no—
613#95—534no—
614#95—534no—
615#95—534no—
616#95—1062no—
617#95—1062no—
618#95—1062no—
619#95—1062no—
620#95—1062no—
621#95—1062no—
622#95—1062no—
623#95—1062no—
624#95—1062no—
625#95—1062no—
626#95—1062no—
627#95—2121no—
628#95—2121no—
629#95—2121no—
630#95—2121no—
631C24—21no—
632C24—21no—
633C24—21no—
634C24—21no—
635C24—21no—
636C24—21no—
637C24—21no—
638C24—21no—
639C24—21no—
640C24—21no—
641C24—21no—
642C24—21no—
643C24C2×C4×D5312yes—
644C24#1171994712yes—
645C24#1171994912yes—
646C24C23×D5311yescharacteristic
647C22×C4—21no—
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—28no—
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—21no—
662C22×C4—21no—
663C22×C4—21no—
664C22×C4—21no—
665C22×C4—21no—
666C22×C4—21no—
667C22×C4—21no—
668C22×C4—21no—
669C22×C4—21no—
670C22×C4—21no—
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—44no—
684C22×C4—44no—
685C22×C4—44no—
686C22×C4—44no—
687C22×C4—44no—
688C22×C4—44no—
689C22×C4—532no—
690C22×C4—532no—
691C22×C4—532no—
692C22×C4—532no—
693C22×C4—532no—
694C22×C4—532no—
695C22×C4—532no—
696C22×C4—532no—
697C22×C4—532no—
698C22×C4—1061no—
699C22×C4—1061no—
700C22×C4—1061no—
701C22×C4—1061no—
702C22×C4—1061no—
703C22×C4—1061no—
704C22×C4—1061no—
705C22×C4—1061no—
706C22×C4—1061no—
707C22×C4—1061no—
708C22×C4—1061no—
709C22×C4—1061no—
710C22×C4—1061no—
711C22×C4—1061no—
712C22×C4—1061no—
713C22×C4—1061no—
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×C4C2×C4×D5312yes—
746C22×C4C2×C4×D5312yes—
747C22×C4#1171994512yes—
748C22×C4#1171994512yes—
749C22×C4D4×D5312yes—
750C22×C4#1171994712yes—
751C22×C4#1171994712yes—
752C4⋊C4—2124no—
753C4⋊C4—2124no—
754C22⋊C4—44no—
755C22⋊C4—44no—
756C22⋊C4—1068no—
757C22⋊C4—1068no—
758C22⋊C4—1068no—
759C22⋊C4—2124no—
760C42—1068no—
761C42—2124no—
762C42—2124no—
763C42—2124no—
764C23—22no—
765C23—22no—
766C23—22no—
767C23—22no—
768C23—22no—
769C23—22no—
770C23—22no—
771C23—22no—
772C23—22no—
773C23—22no—
774C23—22no—
775C23—22no—
776C23—22no—
777C23—22no—
778C23—22no—
779C23—22no—
780C23—22no—
781C23—22no—
782C23—41no—
783C23—41no—
784C23—41no—
785C23—41no—
786C23—41no—
787C23—41no—
788C23—41no—
789C23—41no—
790C23—41no—
791C23—41no—
792C23—41no—
793C23—41no—
794C23—41no—
795C23—41no—
796C23—41no—
797C23—41no—
798C23#1313317514yes—
799C23C22×C4×D5311yescharacteristic
800C23C2×D4×D5311yescharacteristic
801C23#41×D5311yescharacteristic
802C23#41×D5311yescharacteristic
803C23#41×D5311yescharacteristic
804C23C2×#1171994711yescharacteristic
805C23C2×#1171994711yescharacteristic
806C23C2×#1171994711yescharacteristic
807C23C2×#1171994511yescharacteristic
808C23C2×#1171994511yescharacteristic
809C23C2×#1171994911yescharacteristic
810C23#1313326211yescharacteristic
811C23#1313326211yescharacteristic
812C23#1313326211yescharacteristic
813C23#1313326411yescharacteristic
814C2×C4—22no—
815C2×C4—22no—
816C2×C4—22no—
817C2×C4—22no—
818C2×C4—22no—
819C2×C4—22no—
820C2×C4—22no—
821C2×C4—22no—
822C2×C4—22no—
823C2×C4—22no—
824C2×C4—22no—
825C2×C4—22no—
826C2×C4—22no—
827C2×C4—22no—
828C2×C4—22no—
829C2×C4—22no—
830C2×C4—22no—
831C2×C4—22no—
832C2×C4—416no—
833C2×C4—41no—
834C2×C4—41no—
835C2×C4—41no—
836C2×C4—41no—
837C2×C4—41no—
838C2×C4—41no—
839C2×C4—41no—
840C2×C4—41no—
841C2×C4—41no—
842C2×C4—41no—
843C2×C4—41no—
844C2×C4—41no—
845C2×C4—41no—
846C2×C4—41no—
847C2×C4—41no—
848C2×C4—41no—
849C2×C4—41no—
850C2×C4—41no—
851C2×C4—41no—
852C2×C4—41no—
853C2×C4—41no—
854C2×C4—41no—
855C2×C4—41no—
856C2×C4—534no—
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—1062no—
868C2×C4—1062no—
869C2×C4—1062no—
870C2×C4—1062no—
871C2×C4—1062no—
872C2×C4—1062no—
873C2×C4—1062no—
874C2×C4—1062no—
875C2×C4—1062no—
876C2×C4—1062no—
877C2×C4—1062no—
878C2×C4—1062no—
879C2×C4—1062no—
880C2×C4—1062no—
881C2×C4—2121no—
882C2×C4—2121no—
883C2×C4—2121no—
884C2×C4—2121no—
885C2×C4—2121no—
886C2×C4—2121no—
887C2×C4—2121no—
888C2×C4—2121no—
889C2×C4—2121no—
890C2×C4—2121no—
891C2×C4—2121no—
892C2×C4—2121no—
893C2×C4—2121no—
894C2×C4—2121no—
895C2×C4—2121no—
896C2×C4—2121no—
897C2×C4—2121no—
898C2×C4—2121no—
899C2×C4—2121no—
900C2×C4—2121no—
901C2×C4—2121no—
902C2×C4—2121no—
903C2×C4—2121no—
904C2×C4—2121no—
905C2×C4—2121no—
906C2×C4—2121no—
907C2×C4—2121no—
908C2×C4—2121no—
909C2×C4—2121no—
910C2×C4—2121no—
911C2×C4—2121no—
912C2×C4#1313321014yes—
913C22—24no—
914C22—24no—
915C22—24no—
916C22—42no—
917C22—42no—
918C22—42no—
919C22—42no—
920C22—42no—
921C22—42no—
922C22—42no—
923C22—42no—
924C22—42no—
925C22—42no—
926C22—42no—
927C22—42no—
928C22C2×#1313317511yescharacteristic
929C22C4×D4×D5311yescharacteristic
930C22C4×#1171994711yescharacteristic
931C22C4×#1171994711yescharacteristic
932C22C4×#1171994511yescharacteristic
933C22#1681109611yescharacteristic
934C22#1681110211yescharacteristic
935C22#1681112911yescharacteristic
936C22#1681113611yescharacteristic
937C22C2×#1313321011yescharacteristic
938C22#1681115011yescharacteristic
939C22#1681115111yescharacteristic
940C22#1681115311yescharacteristic
941C22#1681115511yescharacteristic
942C22#1681115911yescharacteristic
943C22#1681120511yescharacteristic
944C22#1681120811yescharacteristic
945C22#1681124011yescharacteristic
946C22#1681124111yescharacteristic
947C22#1681126011yescharacteristic
948C22#1681126311yescharacteristic
949C22#1681127811yescharacteristic
950C22#1681129111yescharacteristic
951C22#1681129911yescharacteristic
952C22#1681129911yescharacteristic
953C22#1681130011yescharacteristic
954C22#1681130211yescharacteristic
955C22#1681130411yescharacteristic
956C22#1681131011yescharacteristic
957C22#1681131211yescharacteristic
958C22#1681131511yescharacteristic
959C22#1681131811yescharacteristic
960C22#1681132111yescharacteristic
961C22#1681132111yescharacteristic
962C22#1681133711yescharacteristic
963C4—24no—
964C4—42no—
965C4—42no—
966C4—42no—
967C4—42no—
968C4—81no—
969C4—1064no—
970C4—4241no—
971C4—2122no—
972C4—2122no—
973C4—2122no—
974C4—2122no—
975C4—2122no—
976C4—2122no—
977C2—44no—
978C2#2027715111yescharacteristic
979C2C4×#1313321011yescharacteristic
980C2#2027752411yescharacteristic
981C2#2027757311yescharacteristic
982C2#2027765111yescharacteristic
983C2#2027770811yescharacteristic
984C2#2027775611yescharacteristic
985C2#2027877311yescharacteristic
986C2#2027878811yescharacteristic
987C2#2027894511yescharacteristic
988C2#2027896011yescharacteristic
989C2#2027912211yescharacteristic
990C2#2027933011yescharacteristic
991C2#2027996611yescharacteristic
992C2#2028004811yescharacteristic
subgroupG/H
center, FrattiniC24C23×D53
commutatorC23×C53C23×C4
FittingC53×C22⋊#95C2
socle, cosocleC24×C53C24
prime radicalC25×C53C23
hypercenterC22⋊#95D53
hypocenterC53#13990
LCSG ▷ C23×C53 ▷ C53
UCSC1 ◁ C24 ◁ C22⋊#95

Complements

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

NH ≅ G/Ntype
2. C2×#16810490C2semidirect
4. #20272981C2semidirect
5. #20272971C2semidirect
9. #20272949C2semidirect
10. #20272946C2semidirect
11. #20272941C2semidirect
12. #20272939C2semidirect
14. #95×Dic53C2semidirect
26. #16810517C4semidirect
67. C2×#11719919C2×C4semidirect
91. C2×C4×Dic53C2×C4semidirect
107. #13133124C2×C4semidirect
108. #13133124C2×C4semidirect
550. C53#13990semidirect

Maximal subgroups

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

subgroupindex
C2×#168105172
C2×#168104902
C2×C4×C22⋊Dic532
#202729812
#202729712
#202729622
#202729602
#202729522
#202729492
#202729462
#202729412
#202729392
#202729382
#95×Dic532
C53×C22⋊#952
#1399053